diff --git "a/count_connected_components_in_lcm_graph/haskell_tests/Main.hs" "b/count_connected_components_in_lcm_graph/haskell_tests/Main.hs"
new file mode 100644--- /dev/null
+++ "b/count_connected_components_in_lcm_graph/haskell_tests/Main.hs"
@@ -0,0 +1,45 @@
+
+module Main where
+import Test.HUnit
+
+--Program start
+
+--Program end
+
+-- Test cases
+
+test1 :: Test
+test1 = TestCase (assertEqual "for (countComponents [2,4,8,3,9] 5)," 4 (countComponents [2,4,8,3,9] 5))
+
+test2 :: Test
+test2 = TestCase (assertEqual "for (countComponents [2,4,8,3,9,12] 10)," 2 (countComponents [2,4,8,3,9,12] 10))
+
+test3 :: Test
+test3 = TestCase (assertEqual "for (countComponents [773604687, 448579925, 155329471, 166712019, 877239210, 640614879, 942187959, 818280523, 129006545, 42262948, 383727634, 875226296, 488371161, 241322020, 519276178, 182269857, 726520434, 244473548, 258063898, 95327682, 775036569, 825443776, 660547888, 674057596, 418287540, 405066638, 147656258, 568234166, 311609699, 169498577, 902811954, 488476536, 675199834, 502438623, 542036980, 501393325, 362601295, 298877382, 512669830, 576152062, 5889482, 911861847, 98589765, 587916672, 407486359, 784243743, 801823803, 766835773, 673130479, 483113307, 93711712, 43137115, 963290463, 616464972, 388063463, 984378851, 507879689, 233525507, 352619303, 878686700, 791592736, 545426418, 222626124, 43556266, 187040614, 478669698, 8842001, 34097926, 181039479, 436148881, 631848400, 129736657, 695822296, 56784397, 924199429, 720942719, 282723465, 524331341, 904533819, 199948794, 948975326, 486866916, 814342033, 453779685, 892261089, 553410022, 802379393, 37459506, 162547141, 886429196, 800668761, 823087541, 517508755, 586457195, 700751401, 526231407, 930906156, 42413483, 759974106, 959174247, 628280633, 883400179, 848597977, 713091589, 573928634, 193807580, 518178390, 616444239, 692165593, 793825519, 923443312, 40759333, 730921043, 790142583, 906750807, 960643287, 579273493, 148846275, 260289571, 736249220, 943821111, 58046655, 484077424, 217045020, 879265583, 702912508, 745212016, 355103877, 985768754, 767685310, 481128063, 849741391, 143571111, 524745859, 583472765, 81471039, 115432688, 875174724, 206275860, 328843273, 555056164, 850221471, 314700060, 340441111, 674030339, 486420864, 488945836, 865414119, 368077169, 160583496, 345448871, 491228646, 820580279, 620991973, 160007992, 914083696, 421636526, 927786712, 885864438, 568398916, 932606415, 40028145, 469965174, 268863382, 685417581, 70458814, 888604916, 80941018, 554578613, 332254016, 699033834, 844348355, 775057494, 681957049, 172571232, 798986844, 799626273, 55554262, 148480998, 217802062, 459510606, 620541077, 620147353, 880511503, 8116855, 119512023, 767020371, 140557548, 929410273, 710388446, 770542739, 536240060, 380113140, 847136193, 859860887, 244849540, 988646263, 624041025, 164602898, 281301760, 964313787, 154573834, 469169760, 227861414, 736071615, 462723569, 452758777, 710828679, 285048849, 499871148, 220975111, 283508887, 281296853, 106183731, 253511032, 866952914, 196282153, 644805232, 137768226, 422364749, 809275619, 744017797, 172723217, 894172628, 688446131, 813770717, 305246302, 715639350, 702276798, 270794557, 456391106, 942275155, 546214308, 927174429, 722693221, 115776766, 259102240, 823289481, 584282930, 202013072, 500827653, 722084392, 977223900, 727998651, 759027854, 29007143, 504814228, 81520099, 25967593, 552092986, 638032810, 631727722, 650848859, 112887424, 106590303, 552465710, 389816978, 59574042, 39133476, 6172, 370928674, 810862973, 306224386, 835072794, 319947812, 929532721, 305072567, 343186287, 526103667, 443130428, 176197843, 521462776, 72053424, 816193432, 220895537, 236517864, 587191456, 917178326, 490176926, 306166693, 695559100, 458290207, 590571490, 844653837, 94254309, 776023377, 341897473, 267790655, 173541246, 332921652, 139075995, 733955828, 503442749, 560754699, 997760425, 462969029, 126113842, 496962389, 243968776, 867583231, 336153547, 764379694, 80521931, 207891599, 377837429, 438539637, 736650053, 190990461, 255170252, 499805501, 413843765, 117511011, 587797157, 931388709, 279336277, 17879267, 882845701, 418520273, 80050265, 672036721, 716757221, 662893430, 351104220, 193028252, 577836236, 401702828, 500253873, 879701108, 155471203, 743207152, 124239399, 248437090, 19520845, 59896032, 98966899, 89313000, 294961371, 658485604, 822777375, 14434420, 640208699, 817930614, 113261430, 894116867, 780402100, 334069256, 536607559, 90957693, 74839496, 116868374, 209753537, 863362615, 285767119, 498258948, 219971265, 655176127, 547621851, 714142993, 793207133, 776821301, 422145802, 580670119, 150056389, 407508312, 886607090, 580609259, 48387318, 581880395, 964007430, 220378458, 454658335, 972687788, 638305374, 684577244, 567367686, 597143019, 568077938, 84352922, 715512919, 161694276, 768147220, 305367940, 744761684, 578918625, 853873937, 909027380, 482256054, 801571916, 111416762, 109759025, 457968994, 164120951, 430778918, 874450690, 647091010, 269527817, 477979440, 869845561, 634224695, 70139682, 769037716, 362820926, 689149391, 613746238, 481617296, 636561161, 936239060, 648112364, 855751266, 121342811, 865314688, 35320879, 601367176, 496980862, 870607137, 771648518, 665038409, 238923941, 179667691, 707854453, 657183816, 646810025, 203154841, 25556896, 204069956, 980906388, 357977014, 933590696, 66784668, 678540215, 915360269, 648008694, 186526693, 405668436, 962371411, 941480193, 347933444, 914634483, 744153499, 453976024, 877577286, 558722256, 140002953, 626730291, 429832431, 352938703, 350832020, 378209921, 207408841, 203074860, 575495997, 437124533, 210049417, 860749652, 733503144, 616974421, 914658505, 837889212, 5968079, 866006440, 696431023, 314253275, 624636351, 395377498, 869455269, 652002471, 350382675, 150264968, 876522943, 277112050, 659394845, 335605020, 616874831, 750036836, 291664833, 558906539, 946681803, 641887095, 259100230, 291860811, 360422023, 478226867, 330990748, 714320485, 916591723, 952419225, 184157427, 691572298, 189283975, 543735036, 879913487, 492394488, 142673970, 680623593, 298920936, 732803640, 466499939, 195512899, 296106083, 151380369, 923103280, 492145450, 302920203, 185116018, 256525286, 702615319, 506206570, 284187541, 416353419, 703642154, 76151369, 293889415, 614653505, 397721632, 901215671, 775490679, 207596110, 833045661, 749467318, 517597785, 410658746, 429026661, 154355136, 153408748, 656517391, 72954851, 426904130, 627269973, 639513070, 696621038, 176989085, 630040758, 452088333, 663001369, 1966407, 678838043, 632054137, 954810431, 314989523, 992471798, 348084260, 774515448, 323867568, 156761531, 377649788, 101629164, 30999278, 333470963, 595589999, 60184760, 28798490, 392106562, 574536954, 74426895, 227810765, 776730635, 594762226, 726118092, 207500221, 136672087, 747777283, 743125190, 205434604, 71355751, 408214938, 901756282, 514786537, 994223794, 276024092, 491480970, 75446216, 474283357, 625636529, 150484597, 850132639, 534424813, 485163328, 318449709, 699839148, 876726168, 756097682, 468930153, 797978137, 548801254, 475863971, 671272701, 918828737, 503087821, 122612653, 62903650, 741391066, 118563397, 893344700, 502236591, 840253426, 616131169, 700980808, 194111348, 465277416, 890626233, 941926922, 785579192, 821848882, 755171147, 889929749, 559003156, 279031614, 271425854, 430873691, 473565657, 566863498, 457866596, 551301361, 153460790, 943923017, 768845024, 261915432, 508716076, 560038892, 21777776, 111511175, 509694852, 944404588, 486647986, 492462030, 646491245, 23148300, 589669160, 214375656, 500255811, 791081146, 343890411, 750135318, 663328907, 783682926, 924535585, 834987045, 839549757, 921053876, 380171719, 407672559, 539239433, 474526435, 891474670, 364368619, 800982166, 70240254, 496085435, 628156217, 23776407, 717035095, 660345110, 992371142, 916368060, 378275662, 408852276, 479021976, 978631016, 567074251, 979715337, 858095177, 525281502, 919782049, 751956856, 209821921, 111751135, 696076870, 536156703, 909116169, 265928857, 803347946, 508392290, 983843135, 399441802, 695315633, 44808764, 877340491, 709068152, 655742641, 5630224, 764627924, 831075358, 276239792, 839133045, 410599036, 638382203, 248125135, 272021874, 260187978, 996793479, 894797656, 476067215, 749436721, 720121562, 227290470, 249424878, 331163510, 40865476, 221512095, 432028039, 349224210, 481961170, 789509124, 473129686, 504025591, 138083097, 445961628, 753034830, 402187719, 992573706, 717171675, 322296968, 994995604, 593249155, 540914644, 545726810, 423564254, 790646902, 358132956, 742959568, 215826681, 202128743, 750720962, 814039796, 522470818, 54220024, 824743943, 119547885, 585903926, 894937314, 374168756, 378852797, 414311847, 76853074, 866336749, 317034381, 383509646, 825835458, 144406240, 46860641, 519153280, 186131415, 228380161, 22493673, 655161357, 962521041, 318852792, 800188231, 198438951, 448269513, 737155526, 517533303, 30526031, 498818261, 871350377, 485909232, 699850222, 661778137, 394969395, 498740915, 945579654, 806727996, 158734784, 243036552, 34170359, 171350421, 255607588, 391511344, 761734859, 382313770, 217953493, 37585769, 655935719, 181219254, 342696516, 741275661, 368003854, 63138434, 12381289, 719578961, 530274639, 221543559, 15969411, 45400759, 976923500, 588977897, 599435638, 160736357, 678100684, 578819213, 903829549, 403291616, 465822836, 24862112, 688493130, 822375065, 517665628, 981969475, 903394108, 810705094, 97850052, 484836551, 928134239, 642510053, 298388076, 815189144, 178377620, 620608594, 663900006, 318508001, 814903827, 42500741, 821593970, 286965921, 108856048, 482009884, 130125974, 933946088, 73044829, 550254241, 997726594, 617161159, 646228353, 115202603, 305021256, 590988543, 749574644, 113199304, 331868580, 482800732, 702107532, 286415756, 449190403, 144011843, 939633937, 43983303, 827906971, 739973206, 796428788, 956632859, 952087983, 467312566, 788782355, 614997495, 477284499, 369813301, 727158238, 658537165, 452149826, 360572324, 949812277, 91583051, 910759604, 340742832, 854944369, 330315100, 691298153, 585337424, 359080713, 470677869, 785773559, 317897911, 122496984, 98257702, 171547537, 607334271, 811349659, 20635516, 524102634, 289700055, 20984224, 556724161, 585959037, 496002930, 497433249, 936326790, 465687538, 40474859, 220214383, 101808639, 149298125, 361798190, 167190642, 705918685, 981706219, 425914301, 187417646, 388527679, 66795259, 960684875, 509425903, 995863193, 725533101, 771965810, 527313977, 367815466, 343790259, 594523073, 394882068, 31594598, 199761526, 271443225, 389344304, 172933376, 481477332, 521908257, 115138545, 638290914, 606476572, 60923560, 849871603, 144534974, 590260673, 163035114, 555280035, 711855826, 885116213, 281920792, 285774744, 167153085, 173221535, 938805237, 606593608, 558996297, 128762756, 381527397, 779969599, 120634893, 425523949, 871529842, 411795145, 237304681, 24664886, 876622930, 620199964, 746029758, 782538862, 229615132, 452343251, 853233092, 319931094, 722932234, 132251956, 522911188, 338033450, 785727960, 292992292, 404529741, 119568300, 237411465, 715630843, 973059619, 245115091, 867621998, 411837661, 322715089, 991056877, 318334803, 809637171, 675556076, 746282607, 792866937, 946217806, 192147744, 609128736, 744343478, 729615938, 269355894, 194648505, 533294046, 584264799, 360713118, 791693030, 876115203, 520219254, 613494501, 774787192, 861917726, 686252649, 321980984, 247060088, 521216350, 673737428, 28765460, 605307425, 870744862, 842830227, 540419874, 805484299, 700835062, 406384115, 468811710, 413357928, 641791990, 361092864, 345684870, 303814436, 571064465, 845795818, 182478386, 806458591, 893744975, 791198014, 624788154, 519845404, 825197123, 900191054, 746763709, 600202746, 904406630, 111972096, 878913185, 358149613, 312232897, 175314256, 459095696, 629226392, 941360153, 399377561, 861740323, 237987276, 596560230, 903232096, 790920862, 704314235, 750457901, 418492838, 822597602, 165939385, 643945523, 740094791, 434533538, 541516275, 597359565, 799169412, 944068406, 710466244, 699768851, 745647447, 911083665, 667946353, 995737165, 683483563, 926358352, 664194113, 428971504, 620342692, 969805453, 785089147, 107646287, 537671299, 614467172, 579031944, 188178900, 217348020, 187096216, 933533229, 627201339, 52152888, 123743207, 879960680, 976160874, 98548580, 970410504, 101902543, 931619725, 21966401, 700270631, 359065499, 56179219, 815747625, 97678562, 116878632, 938152838, 730971136, 523736866, 80644605, 584283372, 864306760, 653969898, 793865533, 730001130, 261917816, 694878051, 483611649, 87516016, 649003918, 310416526, 13801089, 429799532, 577223214, 147392164, 647614261, 412548549, 170260834, 964986053, 49735693, 20607071, 686495968, 615677127, 733562844, 19428142, 643362954, 408956432, 66466799, 760486696, 527755474, 31064772, 875988388, 774649561, 931209499, 805011522, 79462194, 372291292, 713241798, 848563751, 498384559, 929252000, 851568478, 64208290, 329241293, 788999189, 280817407, 427041923, 301430553, 71176643, 512488716, 238863183, 584371254, 862650790, 120856450, 694195015, 430519251, 725885603, 726590787, 184605129, 763116438, 607353319, 420291716, 886283626, 587315879, 906366274, 774688902, 746801731, 410251456, 7018046, 194807992, 315712517, 921075936, 756832583, 453604140, 196057043, 899260337, 8797000, 543384783, 59125478, 298497050, 115841187, 516355555, 414423874, 323578116, 782161055, 325686822, 128725245, 311984098, 454534557, 774236052, 93072678, 222072880, 894389487, 284925707, 806788765, 532952780, 679043365, 624153501, 558552303, 987046580, 598073264, 285968922, 413529650, 499145979, 908215511, 160355726, 278228267, 922581864, 864358146, 387182409, 996479054, 134699685, 335874057, 714779940, 834776737, 349831759, 782437455, 46177410, 205446024, 350985493, 531825368, 26284301, 909477142, 987658732, 320582690, 866653846, 491681478, 506742734, 151004965, 979882504, 967089164, 46297658, 786661513, 294863224, 596350282, 756186916, 724643768, 955195995, 858453617, 390988723, 213516522, 292989727, 829422978, 498083091, 147773529, 236372202, 854800558, 606392382, 240163751, 429941645, 981824926, 167571770, 667465757, 362590806, 789965965, 147547810, 121223091, 96676294, 436768063, 419382027, 822000810, 688343916, 618564614, 583925664, 712217736, 184135173, 147812132, 488000248, 485801448, 366743309, 175106014, 415595264, 808987687, 164197847, 912379461, 82493477, 618724520, 606892427, 47021923, 158421184, 749987843, 7123770, 317485811, 635099853, 628346201, 203480279, 266381437, 11029653, 254085754, 342720051, 267117381, 804875338, 172270580, 430533681, 473262327, 196606359, 275858032, 736666759, 38596846, 624701444, 517757704, 271458175, 940264288, 491146285, 247287288, 549158407, 412944807, 673072485, 73964207, 280558971, 414487806, 920115644, 130796886, 654905655, 343769062, 546720368, 619968372, 165807708, 789403008, 926955677, 663163918, 662796414, 719881580, 760316535, 711215050, 939208848, 630115201, 561948377, 687917817, 141247207, 560110532, 409357005, 116386746, 380859101, 39802854, 694228327, 132195166, 536947234, 241280297, 669194954, 506340363, 422021421, 738857367, 924863683, 54800315, 632410148, 282412357, 750716930, 982712442, 167858222, 143785681, 408758857, 860855960, 351478803, 229863833, 943677692, 680310370, 859523791, 147894723, 513187766, 256735377, 918925570, 617065692, 38424341, 264167360, 729883106, 183781854, 597455825, 342233260, 537045320, 733025194, 24229327, 896509, 6849050, 291307346, 942664416, 46887603, 631794086, 560686038, 623303619, 817860686, 827398096, 387039782, 619271090, 355605553, 54361502, 238776258, 318536870, 388595063, 477175831, 13296172, 429309119, 449671833, 858217693, 486435029, 419887126, 816935615, 215613638, 882375701, 253059423, 408960689, 850752853, 163276133, 443146579, 941445479, 704018466, 967873414, 524018586, 286595771, 356557585, 50174477, 980350903, 638074538, 911459898, 709334156, 195879146, 72408439, 455930797, 912029757, 816104838, 304183017, 302031544, 821708984, 744084684, 757629722, 113565478, 758322158, 969108462, 360563472, 493010167, 96132494, 964756571, 100352417, 848909637, 473461251, 501885168, 523557410, 971280828, 589834475, 615250492, 308411471, 458501907, 231633434, 498776970, 574334205, 878414897, 289234686, 60525226, 536098003, 674628476, 689988821, 763005814, 346986720, 63066835, 356398145, 706745558, 350028400, 480331084, 899617979, 167310297, 746309183, 152934408, 526628992, 735935287, 219872909, 179567257, 534487517, 404409148, 346415270, 921756386, 376830732, 24875804, 745260287, 93367563, 201087748, 238504879, 620384912, 489513243, 908819206, 851712564, 944051249, 471895848, 647814172, 735191036, 465943573, 277484649, 66780299, 60216161, 306667100, 862540036, 478463790, 269581140, 900014920, 427599110, 556464638, 153838441, 336334974, 274669093, 799579769, 502677642, 538878248, 553972680, 670208939, 81857580, 498503697, 194683945, 743418299, 357411743, 92606305, 426606949, 58299843, 484386340, 521413914, 505984379, 775740528, 52581507, 107662460, 642021919, 405019065, 516228534, 378192644, 949723727, 823824018, 767416093, 317828542, 925793081, 171514585, 446204087, 2245277, 475028500, 421493701, 134561728, 382456846, 868098394, 635354809, 771159512, 947437671, 573378231, 221101593, 171853555, 33832552, 297441147, 951771374, 42955194, 127824331, 884298343, 225862201, 419317451, 829400820, 928724353, 654983508, 336824387, 994043490, 837850400, 572268040, 819870128, 315222802, 865162206, 573939767, 883762272, 459422102, 224104634, 156409575, 21409659, 860619833, 572569611, 281007299, 955418600, 273341535, 601808388, 110183471, 188114425, 346500958, 343698800, 620640465, 290274051, 832644100, 695918092, 325887920, 485069893, 163178736, 601020179, 467735606, 32145618, 805324561, 6480508, 495977825, 260207849, 237982947, 463645667, 710618555, 630584005, 416744454, 190106111, 845710250, 719626475, 65472542, 282670459, 506938027, 220267399, 603688556, 376098696, 350429128, 267579703, 820907564, 941362710, 531039207, 742290438, 746578912, 425621311, 7327612, 4283529, 258744051, 329199006, 121079811, 153665028, 344356733, 764498365, 38487973, 464241990, 775032464, 11084150, 235508401, 196106539, 232606467, 776111143, 770288238, 756267908, 53938454, 86368063, 693756797, 336569772, 425632388, 714982111, 693164585, 862886181, 486390876, 488914843, 107771298, 670701213, 275441067, 365428819, 209384066, 192297031, 477426558, 739554866, 536008517, 465921915, 489826094, 728030442, 604819726, 236409492, 531258643, 8828772, 671860269, 317036418, 670933888, 182887045, 665904919, 631216513, 886286438, 182039531, 45977639, 960640419, 862125749, 498390395, 325622174, 820769495, 444070228, 187214663, 462321115, 73987536, 179687773, 439757846, 31386051, 317689836, 499386475, 36422134, 824080623, 395484452, 505658370, 332777456, 338022605, 520821617, 738504809, 741297899, 812181579, 910399001, 757510463, 777593791, 794062201, 763028619, 21562375, 304950854, 143428072, 630330686, 86248218, 67116272, 326385524, 801832724, 612627047, 989497259, 45929049, 706167648, 501405011, 777273209, 187586514, 530705873, 177682223, 903675071, 421432933, 783515528, 575016377, 103164289, 707178581, 866314369, 82141891, 422470832, 964673576, 154408784, 205443278, 985412000, 870192417, 750555404, 754783649, 891897450, 283400563, 770038947, 272492409, 300222799, 873937874, 63654989, 396328873, 571275394, 519508980, 710221251, 75221896, 332983186, 912941546, 474212082, 512216601, 62965564, 526305152, 752782642, 79247142, 41669184, 717692684, 963443106, 149052191, 688315788, 505408697, 470441191, 31847558, 632618949, 434613869, 921001068, 937463219, 370292133, 230152578, 309310129, 906459427, 111437311, 516279177, 267716701, 329794926, 146730042, 464315393, 402974958, 207445532, 556859066, 524895253, 789938745, 968089059, 546556941, 979463547, 259810573, 178680835, 527499221, 466639126, 175597706, 901047981, 149138853, 906568039, 826405975, 672551619, 69038091, 155032300, 768667123, 361112036, 42639684, 321537979, 868614883, 559111351, 403150571, 693142945, 795182715, 553499138, 813962184, 721467961, 429521648, 462760834, 12099068, 1035573, 431160569, 778704414, 984323016, 979654546, 90550535, 783457539, 701511275, 635122772, 551925405, 323445682, 678423071, 306448964, 632018900, 460720828, 671432628, 331985928, 65114380, 772042725, 498460726, 572145363, 373643063, 681036893, 969144234, 520484014, 105442888, 37930901, 735825919, 863216803, 935944703, 419867717, 476201507, 434274820, 561596365, 401697957, 254631520, 711996336, 956457474, 358283912, 673093727, 5948789, 419652086, 288356830, 139310176, 238576591, 661292610, 769535348, 642434415, 53783723, 657941032, 720676072, 346871697, 891144920, 213998353, 548524644, 254386208, 39680777, 644277833, 348147869, 161250307, 19975096, 985132263, 336846527, 285192497, 468589095, 156795942, 288625060, 791102522, 9411962, 300247337, 544675965, 256357014, 227932933, 688631519, 881405319, 82040010, 580807591, 963512876, 476789714, 524764782, 597894599, 361444334, 45308679, 831225839, 92222959, 846365388, 41899031, 989367348, 112752759, 882102883, 231006010, 843066146, 704746026, 706875344, 147774573, 346581165, 34642826, 390090523, 57692204, 373694876, 446945411, 1054215, 287303569, 907370800, 791095286, 23458846, 668254895, 895070788, 753800237, 523718197, 820638351, 712204076, 199640383, 463810243, 626864518, 620102432, 788924374, 527030252, 604297497, 150901421, 889155187, 295632638, 112452142, 484424213, 936054368, 796808265, 716634567, 719742344, 398949905, 455508726, 602874490, 296558459, 186172443, 71039680, 973222624, 904835888, 697966483, 671386197, 935840453, 736141068, 92722932, 159030103, 579233981, 772130657, 359516524, 85713148, 698155680, 602792905, 292226004, 347716181, 799501418, 242554823, 555869627, 46044668, 848017520, 868639772, 605555894, 92378832, 584844826, 244350337, 2811672, 997277781, 45504441, 712580621, 520592950, 27372353, 439804364, 236060734, 458712579, 997058027, 198963222, 55244538, 851271021, 174627230, 15934973, 747194672, 296275428, 235956576, 220934777, 814021005, 13301575, 485367337, 439427916, 325255788, 821274158, 270991014, 673950479, 788862028, 929144227, 622851159, 164879573, 163912588, 15042598, 326060767, 599695101, 311985272, 850144451, 791506413, 265973691, 229901236, 503608625, 135350721, 14514235, 83084299, 763806321, 111511361, 830864342, 922591109, 944757334, 797636452, 405396295, 777741288, 166283463, 9078150, 457013547, 337021419, 729423199, 728672163, 368529873, 139773301, 398987105, 183100890, 20862020, 113125379, 125211312, 750936344, 151804053, 270891955, 753653968, 92044470, 660051924, 698408607, 74553653, 814895020, 885816526, 735066471, 603668893, 676209200, 585667477, 162463538, 2573170, 380280501, 360668530, 499156564, 244326793, 924714554, 37058092, 422571832, 759550534, 811867215, 875297923, 742888744, 451950444, 755785508, 646898740, 291793826, 810829097, 927023412, 168857813, 605264692, 609430488, 803001927, 175239515, 114594741, 980307318, 557151000, 433608122, 617271048, 294361554, 819853266, 533507557, 625094354, 118350047, 441084972, 857656295, 19464671, 916015393, 465894309, 862193549, 525122210, 862078604, 306228468, 668396752, 230902556, 234625875, 938691270, 579663636, 19661958, 844659595, 438903922, 938476970, 333949476, 531685201, 633290329, 365020659, 926025975, 768524499, 87474106, 759246850, 7228404, 488415621, 382030287, 538125615, 971693047, 512495273, 181941813, 257577672, 161536537, 386653358, 609622345, 423056551, 472768841, 287659308, 192311499, 583922209, 680521558, 875878362, 650970022, 933593100, 634182756, 989453770, 131808697, 574442824, 192370572, 319911050, 332351881, 503969131, 307977427, 241993722, 892724545, 461105305, 154263133, 262679144, 645238830, 686412808, 754114769, 964957756, 161990292, 327344204, 345078180, 903040549, 269323436, 998707888, 494945306, 988565126, 784643761, 293849936, 108609816, 342783465, 29004837, 237526248, 945032783, 645794626, 663482611, 83813156, 963400854, 922214628, 604681964, 844062474, 16892507, 51194774, 32007638, 834226268, 932218935, 660963477, 847551490, 398124251, 260080696, 512299431, 557008287, 204652523, 176530935, 490018294, 729203766, 614071309, 113124552, 367069532, 454063368, 269445358, 438227380, 283751967, 87615064, 856834036, 660352501, 828091205, 375263925, 67273838, 248112117, 530863119, 754478077, 886115175, 158661905, 467461407, 171497413, 393902139, 325825672, 40134227, 94121735, 960242391, 975964865, 459215533, 228101976, 838137905, 285137492, 641173682, 437752642, 626303062, 39759681, 772643283, 200991951, 299754597, 276744015, 359463925, 790540966, 151017688, 211960724, 912946354, 339854620, 38291877, 627327566, 764439763, 290978780, 413837371, 888793023, 734430655, 575951116, 748712240, 138431087, 775887007, 842097616, 745235991, 691665508, 917765847, 801689326, 382905403, 558941105, 658513741, 402604125, 760797351, 455658237, 966519449, 100446217, 508113681, 389490376, 650855411, 88572469, 347730533, 322442293, 941298310, 585619739, 274197696, 380047491, 941382380, 117506066, 840625963, 323555257, 861972769, 816389285, 355249124, 585585143, 370081571, 566454253, 457074912, 279369493, 138951707, 885518071, 785889440, 991893383, 891288790, 606338186, 691495685, 307778732, 215988047, 152925044, 30868110, 309613419, 755883731, 1644167, 18680499, 867609582, 239638934, 924105373, 432823349, 304912321, 435820521, 784435178, 389942284, 175431275, 627820500, 684278738, 851670460, 173363864, 362468077, 95978044, 907919799, 667085025, 929434567, 430634174, 513978708, 151879590, 332767958, 179215555, 808266302, 280138765, 843173902, 512924790, 887363872, 265834416, 393636865, 702171341, 586235607, 432565174, 896174090, 553558497, 277690514, 108723834, 47455328, 650734007, 113290820, 170049189, 568630979, 753619590, 926319901, 133686938, 275909339, 283913582, 516971698, 664015140, 271903162, 974397292, 884450236, 828174839, 495454546, 54171065, 623965503, 436926663, 804679961, 17080611, 387858533, 299795837, 377620653, 510764727, 814821368, 106107947, 878827390, 929220063, 842628007, 353817668, 137553110, 263330573, 87082574, 22121417, 276448097, 355382837, 450182278, 601840080, 501983829, 118703331, 631310772, 31444829, 922525841, 738194332, 853179342, 970679126, 770974501, 699099934, 803687199, 292541147, 548144489, 262993130, 297362396, 696894540, 807250778, 954949072, 146282528, 194823974, 495119493, 216431599, 128078196, 800684876, 796135256, 264496777, 836061246, 370719640, 406705779, 207908842, 664533986, 958354522, 612686543, 777102446, 306140101, 153926187, 302288596, 71322708, 524700988, 916898235, 380751829, 890626438, 400486253, 90297549, 498506340, 925176094, 354643195, 544176798, 525465375, 279674702, 910974833, 455557740, 426595477, 394237939, 228363234, 117301934, 306637765, 793828431, 241588102, 378591204, 658243815, 971596248, 585726604, 963232161, 712017278, 905034574, 259687407, 350389391, 557263674, 937318231, 165091874, 509309670, 278570888, 117068546, 38854896, 705322677, 117794835, 608458842, 59822070, 910751387, 285662665, 740684548, 647596064, 629406014, 764996535, 717802134, 155956343, 571666035, 37561044, 777382471, 446955576, 616518780, 523608314, 533379624, 381798084, 76166145, 108169210, 311221579, 351047501, 171419089, 86982261, 467981775, 700051608, 81755095, 435752452, 782376961, 862245527, 62299619, 445477358, 764834086, 84708188, 179432381, 234999491, 61661618, 169530340, 997099562, 776680346, 843631643, 613113997, 783198225, 645000783, 365608541, 133283703, 895507337, 345878407, 76072706, 179147781, 302121354, 423004128, 134785705, 838508512, 80723263, 232236521, 430010951, 571508043, 295417607, 200766975, 20947302, 349153241, 279282511, 296469158, 196905404, 923524308, 650823894, 114143651, 694066214, 802520271, 772080507, 569053923, 527292820, 328329316, 369877568, 335322367, 699438178, 944231906, 649095439, 68720346, 950432844, 195753189, 799209488, 292625234, 547738587, 744124502, 73499557, 786575347, 850768431, 578259038, 856567803, 322392563, 139422398, 801747154, 118677647, 420199162, 815709714, 16459944, 261351046, 879297717, 604108656, 352762400, 966984599, 951323293, 633463983, 278137619, 32779102, 117523022, 914306181, 187750589, 736099159, 580926186, 949782482, 967122683, 191923516, 747548046, 460121628, 241645332, 887442058, 882088797, 122085341, 623862102, 178510791, 929722855, 6815903, 685959445, 287129577, 651656301, 328654906, 486988531, 730761201, 127112621, 149896530, 771762632, 108819516, 316217462, 350484507, 212814610, 520914939, 540636976, 307387734, 919502398, 679766543, 27407040, 888966085, 479134223, 557552857, 650183900, 224240846, 950094056, 943799936, 65268655, 915347591, 259986859, 694663864, 441515474, 283822745, 667348038, 298212462, 360445422, 870274516, 367280729, 836259705, 119572355, 357468427, 228567000, 809190517, 620040113, 918522133, 470389888, 471380511, 157186927, 984259842, 839655437, 119065528, 858014539, 835947850, 568401946, 259563317, 61721589, 365871114, 259340692, 624587345, 405433145, 619233603, 102140355, 240619460, 267617061, 975168383, 547570425, 81083129, 932354190, 86192483, 828996474, 449400338, 960313333, 71161250, 594812888, 354406419, 145917350, 570614270, 503959219, 991983586, 706709475, 490281999, 427608009, 535360559, 561728298, 297643937, 163290728, 285378692, 138299912, 25612806, 393491371, 734345785, 476337285, 248473258, 975214783, 909471010, 499434560, 343895531, 550759933, 484705735, 973328940, 946709033, 254671209, 285302686, 892259250, 830891554, 947743577, 413089328, 872091580, 355627791, 783697543, 94756194, 526704306, 132458221, 846167877, 310095514, 288699100, 50316588, 388631796, 37176270, 809632954, 593594383, 221541801, 146476104, 506835505, 859427521, 847879497, 600610979, 115568334, 329236299, 500218090, 830597657, 30874573, 241530093, 379562782, 143482364, 524544625, 274465107, 8468963, 509738592, 608311663, 544461157, 874402397, 119122677, 534626890, 977661905, 699613020, 863751160, 236371509, 880467456, 384500622, 903466600, 752209344, 229413655, 590013634, 315874443, 199881625, 530333894, 310794778, 288077078, 846357539, 467731166, 55571125, 337570760, 602095949, 239761292, 924141407, 146921176, 349989890, 816650647, 138884818, 604562736, 746653095, 361102827, 746020614, 693159259, 973868311, 95902063, 496389139, 610091630, 685966910, 388773067, 430633167, 238879110, 665189003, 862401100, 524434324, 64540986, 84793003, 877267862, 841006904, 344918262, 487765847, 400751939, 544801145, 27859043, 593444036, 359843806, 305933917, 157970168, 183554709, 643422186, 664064664, 608739124, 233879956, 452257541, 804038177, 197539952, 770411410, 675353244, 555940667, 692380609, 570174484, 389847839, 328409465, 235982440, 80030617, 467643027, 9660523, 420214423, 737868652, 776967644, 482865004, 797433958, 908232668, 749883727, 384225137, 905190858, 404578556, 132092483, 373096176, 929217705, 796667746, 381803605, 770556470, 973019850, 864315681, 64556433, 221688456, 249181177, 91790458, 764110649, 151048988, 361242779, 20134590, 801103189, 341643460, 61577145, 687872929, 354152754, 82259355, 73766986, 823785250, 151293732, 372779721, 450536574, 569578159, 877694581, 286635143, 334817158, 342459669, 184357665, 966188263, 648492950, 248947725, 56648551, 292733458, 616102790, 615334756, 62244658, 517958920, 433442544, 477981801, 687837668, 222532853, 93337645, 423421758, 433936003, 574977746, 985915246, 163045371, 93383983, 411137130, 893111989, 32989590, 836392918, 93643172, 383224648, 907396063, 566914020, 213746292, 552816088, 33995662, 607887448, 694597261, 527237119, 421761314, 164004787, 540741677, 741673706, 16669333, 662876764, 37559959, 564155077, 80349888, 188574817, 405272298, 117383746, 475959833, 372452894, 485828823, 24062034, 386946835, 436689972, 728414403, 671176753, 712428198, 857537419, 700860114, 442485166, 158149985, 190171876, 707164515, 372150244, 764704270, 146029348, 781072461, 532546791, 395881177, 969064680, 214069878, 938594405, 432510981, 723898385, 555251623, 172558642, 837275626, 968979825, 555745992, 379961080, 808796976, 609109760, 10532523, 224707394, 927632244, 20854823, 208661341, 602468534, 961326322, 90131964, 145488724, 799725411, 723843405, 445664541, 130635517, 256278627, 753553562, 752105431, 723192881, 790143559, 828293129, 726491755, 765869528, 901877960, 24807810, 832864892, 977679627, 311587134, 388624774, 436487914, 866131102, 623335631, 25537616, 30801263, 795670814, 550151876, 836207469, 739817368, 783684611, 235949964, 3528237, 487383616, 401323089, 537450372, 83360858, 264311184, 928162665, 799519153, 611591689, 320577125, 359005455, 173247351, 90038081, 880834334, 675037943, 746319612, 741844534, 352120683, 170753229, 403056338, 690031599, 559893875, 5431649, 979780266, 620263197, 244022667, 543364532, 598070849, 258212646, 429670035, 577703226, 190524945, 686413862, 129106856, 749399019, 855438440, 698729746, 934765083, 461915466, 195065402, 396203909, 994750125, 676884417, 545306362, 43721767, 401392579, 446366183, 565173479, 110718501, 892491219, 350200629, 773444570, 314473649, 881175341, 700789739, 795588797, 774396852, 206829010, 291886626, 966737938, 899118868, 451052111, 585029435, 992391267, 234403493, 503067524, 365474031, 751838372, 558009671, 913737300, 649385973, 452892799, 188907399, 431126526, 649519731, 789803159, 218091099, 270203962, 826312362, 212113181, 950178133, 392723286, 610548647, 888845582, 68134999, 220042541, 405745508, 478016560, 759398697, 712877016, 954850257, 56474559, 961097138, 702115228, 3113975, 981263033, 645357183, 969138727, 610363356, 9372482, 79279359, 590896866, 554377624, 454766105, 677051066, 800994439, 257051092, 886204559, 776528553, 9783661, 436550164, 76420817, 603143813, 634567589, 509964566, 338007820, 430622748, 102322409, 571364448, 999302538, 521813659, 425099611, 780358630, 932290267, 453586762, 442658727, 102494013, 151536700, 51057726, 229248517, 54219725, 337648578, 283838519, 802377334, 564195927, 334231266, 405511825, 263880342, 225115809, 817071379, 372650009, 832282301, 535233076, 799015940, 885715572, 756846502, 917476349, 789433658, 301558128, 907861785, 33297003, 962201382, 920897871, 883588388, 895295187, 562807813, 487192784, 755371412, 66569566, 984223734, 701219530, 923112008, 811271738, 379569766, 304141663, 769432074, 16625652, 422956056, 84357376, 357873921, 308545913, 992684024, 795159991, 349582353, 169205946, 501307850, 444868083, 284977749, 965617176, 736358373, 552554610, 519617828, 1728435, 77232063, 300330496, 62629554, 923986183, 17653803, 402119922, 171872577, 899613491, 63965786, 174358002, 383181324, 39731797, 156827695, 906165611, 394826168, 315197448, 365078864, 373491727, 250210239, 260390457, 364521704, 487180094, 79217939, 153243360, 110032015, 730902555, 64533351, 589775025, 953299463, 295382711, 735836890, 989032538, 298021791, 758547182, 188183156, 48837703, 642235168, 594050295, 70312477, 170857872, 647145958, 971995854, 307835423, 950932065, 860816221, 298500258, 98350765, 959907008, 625354402, 750468033, 938335772, 96060622, 779364875, 589244651, 179377242, 519482074, 11884348, 873634747, 698454037, 971490371, 837551971, 776501181, 901829786, 176761372, 936826416, 222854646, 905683335, 686318137, 5849724, 678435193, 630428321, 162259492, 961950506, 533650280, 476783666, 250458423, 485298258, 276923388, 978157159, 686562240, 2461319, 456666786, 208103695, 632430626, 482623360, 110321603, 44795322, 849174755, 940407168, 390929229, 481954717, 439541950, 66209922, 509265748, 289957704, 761110655, 91832229, 892061447, 205895274, 131689191, 136261723, 159782526, 321701683, 503728538, 351035894, 651822922, 213992623, 245502867, 646908904, 252631208, 748822594, 954758386, 867082399, 887907668, 235641780, 255490207, 466843901, 525473240, 718956139, 995479176, 525066613, 616696926, 560943065, 689469789, 768105008, 233871821, 226742512, 367984622, 919810306, 580667730, 652528764, 465277980, 909518119, 814364761, 340233816, 821569333, 362107146, 306876147, 831712996, 63166539, 823453117, 15859888, 60137116, 579392175, 197125415, 617431509, 661314500, 122472198, 438585353, 911058066, 749979568, 470926586, 6587014, 544861479, 221454056, 206019344, 740666341, 465914621, 918690984, 301210744, 50683205, 520445902, 860939864, 402827706, 348174100, 151823295, 142952046, 607096712, 743816200, 592220447, 754509562, 648397454, 258840901, 618562180, 542862670, 130232544, 781560760, 648273313, 185791463, 15465197, 762075938, 3863788, 623076549, 748849386, 39609705, 823211169, 54658502, 778575485, 636237363, 221852574, 794584101, 110414246, 401867582, 930059488, 799179825, 81185687, 453020256, 591518926, 950780233, 773207339, 285886859, 365466883, 157507493, 747892615, 22228860, 634070385, 64801961, 123395606, 634529790, 380224261, 800169033, 41678798, 923633806, 680586062, 277597023, 60116107, 393343729, 950367938, 324966558, 942393728, 435556127, 72750641, 990252148, 182751118, 160379202, 275112081, 22958772, 13910780, 800916918, 628705391, 302099855, 480591823, 27404497, 731378981, 718045718, 483620970, 713303570, 858494543, 736147139, 68320196, 728656660, 515877487, 127273276, 110459885, 602579712, 395647665, 94138508, 728098142, 47050033, 359652488, 411429268, 826750305, 129547505, 770866104, 84823060, 434852934, 380463581, 705678392, 446898413, 854815231, 258397860, 881023435, 981616722, 417074066, 685861593, 459495417, 93869580, 881273580, 997983117, 102902159, 33434117, 923540391, 821127812, 761560814, 976276553, 177267732, 731974958, 54656684, 118679438, 262501506, 523614734, 492858880, 802483885, 553277992, 82788339, 196109156, 207350064, 657859269, 450583350, 859375081, 249411469, 719655460, 838256565, 11978978, 817686887, 905023510, 934601637, 492333084, 500987933, 86032871, 256522669, 721463853, 618574999, 462967633, 573984853, 911209107, 453928920, 960283889, 84678022, 705107687, 937671542, 34910974, 639135976, 729594666, 44117489, 51235591, 724018578, 121496311, 696982526, 250396946, 368452698, 764425476, 214406209, 352961768, 31111001, 666363246, 148794398, 560001969, 190885370, 236422597, 895176637, 69550585, 631069496, 70917116, 15392036, 163013425, 799830054, 220117287, 754713027, 133295185, 754412207, 274878656, 174582360, 274431416, 894270293, 693711409, 893775109, 958715021, 783852766, 485509878, 681634285, 102123749, 134674998, 848055809, 229044272, 810581276, 953161813, 828199421, 330287044, 72264357, 144163242, 382833088, 869978781, 513474411, 608987738, 821246233, 238482661, 567656832, 53041884, 707001280, 49648170, 671295077, 874511031, 289342995, 349857972, 323228274, 647276856, 211557613, 767863145, 989979287, 656893057, 395204324, 811275207, 719790934, 523995108, 193511877, 312779574, 72041866, 106504309, 636605454, 380593722, 491947354, 933701430, 807056262, 254728843, 999334297, 658304831, 796459396, 318171931, 463673170, 998043534, 642152292, 498421256, 72977843, 313990373, 448805421, 894201862, 161475735, 769466260, 884625371, 116070037, 135923979, 729691842, 936805009, 106873242, 575807711, 225883044, 389558752, 529589059, 189475448, 649907177, 437367310, 617295886, 154327647, 63442312, 217942961, 489950645, 761506826, 614405456, 949889348, 195655088, 358717685, 481890021, 337947107, 691996020, 899927271, 912545303, 860534982, 834379752, 10147191, 117923381, 282257379, 16726792, 151224002, 789824453, 815048669, 493196840, 632919682, 733995829, 18719756, 880586070, 632825878, 975686917, 144126226, 649241734, 15785222, 220386133, 211920782, 704623249, 459164191, 390063765, 687399155, 487351229, 886661796, 783301869, 277127095, 601351079, 832896799, 326232548, 229640855, 25589653, 449215475, 513366825, 645823506, 842229589, 573413956, 428545447, 502895705, 682994040, 364180665, 368253015, 735149096, 230699540, 488265468, 296063719, 886033875, 134562916, 526925308, 187242236, 98742863, 9397181, 951645946, 272810610, 970123001, 457047580, 234619606, 939484285, 838654706, 751785589, 474572405, 670568929, 224620158, 970161105, 309945092, 842184137, 9161593, 126059395, 212617692, 644356030, 720131581, 107302565, 995266412, 272660597, 84218395, 394230867, 330328831, 70277740, 561416954, 303601873, 77301015, 184729732, 318057302, 394246042, 858871233, 585280746, 223083242, 938920794, 878214308, 456258088, 399055633, 561249708, 57939671, 674146772, 511322072, 734606849, 226907131, 243059620, 40391163, 396857905, 470397201, 917256657, 694492841, 489236565, 210141947, 46207288, 683506647, 552338099, 31649255, 806508060, 311307613, 258044536, 445805842, 533360405, 165148780, 174273765, 565051074, 110407577, 733820170, 413226931, 850921283, 281963467, 892425406, 653221170, 247214868, 64504890, 723774071, 773843237, 786685217, 643366401, 225401998, 969602066, 548132865, 640167919, 26828008, 193251622, 93120916, 137864942, 885208241, 418501178, 406883770, 513607271, 739835744, 230020142, 940334282, 849109322, 153773129, 8952886, 987801434, 85891679, 364697611, 93854906, 234460677, 825982626, 33188023, 134525949, 136143170, 74100068, 902152655, 947918606, 817397441, 531057967, 586697752, 326569397, 512065720, 389238394, 13749902, 11852853, 920903038, 485664199, 596799209, 856818745, 631201097, 585828596, 163455227, 706475380, 861987310, 893654169, 732801457, 298294918, 506729123, 998238661, 123867733, 963295336, 787387782, 373161313, 619461974, 91719364, 398290435, 159395293, 431349880, 689404934, 386598861, 69540756, 57259587, 208010628, 681359455, 227705172, 539495475, 920589892, 55500715, 8621601, 948040427, 779642036, 738385452, 773497799, 713133833, 748031532, 894785662, 966328554, 641006158, 787718489, 783569135, 932679674, 740245161, 524634189, 2222621, 750502244, 545559542, 432570630, 384357913, 555865825, 976708360, 966272221, 752604370, 500086058, 54330635, 357598951, 153470567, 702222392, 143041639, 831199247, 963226472, 574642906, 238898152, 349162127, 378049164, 185457090, 184178666, 637064648, 690345153, 501312676, 363680133, 778260980, 819904592, 607042057, 648466927, 882472159, 815163765, 308784262, 819481391, 550470879, 323721766, 324987196, 128731564, 33412656, 736449157, 86498310, 994921508, 899814774, 288707724, 720758338, 59945847, 929897056, 539665625, 757833975, 62009687, 52144658, 982176963, 506511309, 535302786, 484585262, 252605621, 29221006, 718617678, 161581812, 526276254, 850316349, 301606427, 171025310, 817584633, 272248531, 207531357, 538318778, 136075196, 437321838, 100448790, 325730506, 252734814, 649952564, 345366046, 764733030, 56280647, 64322710, 580745732, 17378552, 909879159, 652100602, 342101129, 326831269, 106183370, 377254765, 280335919, 371253150, 309860420, 180521472, 817989331, 114738282, 743812539, 653811520, 159804971, 110459838, 741888539, 507463800, 391677987, 448434460, 56144755, 554126666, 391586328, 449498549, 192009928, 289645327, 61328760, 523665592, 502041279, 746221325, 522194214, 1587502, 982784451, 981530300, 732230325, 864633519, 580762088, 687849410, 699403549, 624401647, 747037509, 722596944, 985091609, 1437584, 253397676, 716557998, 830453440, 847305528, 538792672, 794045363, 912774848, 653292497, 954317234, 960976356, 936341427, 983506780, 108777022, 930869316, 544760763, 868265760, 20343292, 542919663, 669446481, 94011242, 794840291, 65135367, 449669076, 442378931, 579485152, 652443849, 925904586, 342700499, 936228351, 894702983, 694024225, 202011126, 473045874, 869035306, 414087412, 804858091, 977104558, 926909542, 239120285, 977574892, 424406645, 254075633, 764047195, 9943087, 225677778, 233248916, 146129231, 614797461, 931366506, 493450434, 933377059, 477915853, 794527732, 396052198, 627083766, 123266545, 576280187, 43835697, 275820546, 371716890, 554657463, 482986164, 641560120, 835254263, 856293061, 53503002, 604441751, 334355480, 879079665, 625476544, 885438299, 996840576, 31944734, 854149300, 876958668, 596326501, 569189069, 546834843, 182578652, 922835134, 969664412, 663070114, 266142863, 884068676, 814041890, 583925918, 36496265, 357454191, 274017259, 238155087, 209117074, 986092291, 449003536, 86690039, 110191334, 541362025, 122980, 543441249, 764998211, 570412325, 270984209, 165067923, 596549644, 457507600, 576884586, 288403243, 857121117, 493598848, 417547418, 802295584, 511754747, 154006568, 8575246, 599672192, 856991228, 155491765, 175565743, 456230665, 53637205, 723747141, 236978429, 377564946, 56254505, 962524462, 384265302, 55898900, 301186910, 537614715, 792195095, 205542115, 663874710, 846457457, 650178554, 216624268, 954925536, 815580447, 372721776, 980043165, 511521780, 640341555, 794783528, 130166681, 139033113, 236663702, 914419740, 195651330, 410140714, 203376094, 959818171, 284186051, 56311001, 128300493, 728736313, 275519361, 784683807, 108079845, 827307686, 174973718, 99583100, 630247067, 276190655, 690283843, 757660607, 914277109, 394135629, 630866276, 342546834, 867969653, 565035007, 389854945, 188162872, 231042874, 596861529, 735872144, 675649622, 63225235, 970111261, 392699176, 169681787, 901429271, 325989123, 71841601, 156967203, 839154898, 535240994, 324297611, 332402706, 954014857, 491626495, 844739593, 297980192, 52965430, 841913275, 561558729, 419908634, 533325884, 776954971, 150122086, 578713027, 874024763, 521702454, 840771098, 726719709, 570323525, 923786849, 281840942, 590885459, 696798476, 528003765, 87592792, 302493651, 613791893, 620610438, 451284428, 594961514, 885800617, 675776001, 500322049, 487303813, 191726947, 899465483, 33732432, 920647989, 855018261, 650065276, 523484431, 652069162, 530858448, 529077544, 738943132, 152783501, 928587408, 478321622, 647531074, 926039911, 78012250, 98232104, 176063512, 605438839, 15971960, 520281376, 119967754, 651919911, 699799231, 430867543, 93165837, 475402335, 638591285, 5248655, 757461114, 688013992, 26113016, 70642250, 301659190, 43063891, 984192077, 732251869, 903218977, 326588246, 808989753, 528262033, 459267830, 496072260, 722183740, 650061187, 972218514, 61185723, 848780555, 817205647, 438593596, 488642463, 4721609, 219104011, 968483415, 310936320, 4309055, 598297025, 389714631, 348282695, 257617826, 675947483, 380058204, 204521470, 132671040, 150146963, 860826792, 627021346, 881571442, 624115416, 257229537, 127190740, 969691706, 2242197, 224393564, 321677477, 693728840, 563816539, 611722327, 613190054, 493661018, 355938263, 35630502, 289071088, 9910765, 542056694, 280063385, 29885690, 380542968, 373483347, 314698859, 255326679, 814694075, 736207747, 778042337, 42607015, 667333888, 619710483, 548275999, 404492999, 49775754, 221596254, 947741195, 527774587, 15860235, 987517509, 166997191, 535755107, 372746089, 705409195, 185617689, 834025671, 945389695, 352692016, 770850860, 334197952, 396533309, 899920884, 234743590, 442112705, 282715677, 274276131, 19220033, 781101698, 753832877, 704127188, 178286217, 852488270, 559649264, 700530391, 905826779, 786108750, 774969379, 733307522, 824582331, 705414040, 447392762, 761185156, 878200651, 235672696, 829836430, 906082289, 657618459, 709221379, 584764901, 117556369, 555055279, 553037374, 873024823, 750962010, 208747675, 405582120, 54506567, 454257113, 683390184, 502750452, 307784829, 930036828, 44810881, 64875908, 716357985, 754821047, 371587005, 70276148, 463677059, 52497641, 520005460, 432073131, 797746006, 60497175, 551448005, 620141098, 689334553, 624453253, 244510896, 436127632, 151143069, 589160740, 934859108, 909377514, 638321916, 311477080, 132783308, 170608583, 768521090, 566774452, 63990887, 584066338, 355668894, 590529510, 532250676, 34163934, 618130424, 375252259, 357213763, 30496442, 732587029, 157894001, 437536434, 452202444, 924435772, 101214668, 990766652, 293478301, 781294342, 224032917, 784279121, 490709986, 878570717, 251707422, 733288942, 249057724, 915477996, 978596008, 419293533, 917023084, 253038593, 536310334, 494807925, 668493228, 133631548, 92924917, 358856110, 532560207, 694980401, 379895635, 837872635, 598986571, 446471775, 239691262, 568096356, 946004539, 128322558, 511800815, 744133859, 384893574, 772265732, 683948902, 601030120, 350536519, 92342067, 822798057, 80319215, 38586303, 570596143, 639419449, 946883567, 696660480, 53702269, 684716309, 916590457, 74895009, 402250407, 759447432, 313036864, 384721950, 443842521, 693555646, 104182919, 62225391, 284432069, 829785209, 22511927, 734751368, 723239883, 884269262, 333501267, 758692886, 846738857, 254212179, 122002343, 432425179, 833402394, 796780324, 302915039, 121966193, 656337681, 567756248, 573071007, 388838525, 756026038, 731844076, 916069027, 798519628, 795993549, 518671199, 944606611, 643143331, 149260527, 840276703, 10136624, 758720936, 143398516, 612404845, 828152247, 155812760, 67630501, 478011917, 235810487, 687196141, 127641743, 142948260, 35699271, 391947966, 32687478, 790069096, 747166860, 62765129, 800014459, 140759044, 448764855, 296063154, 195698858, 792445502, 550916285, 904502696, 474188702, 154598154, 408748719, 730234563, 686431856, 795878205, 156935689, 155400703, 85782243, 322666084, 854044925, 322332252, 377491124, 42839435, 546688323, 545871612, 241502383, 936743042, 136394195, 422795479, 988486026, 53023213, 706579429, 154671957, 274856710, 741328699, 472022220, 953519040, 726156911, 634857294, 248013058, 368553538, 528428595, 266533803, 134998374, 105144579, 539865331, 314112340, 791154637, 774311530, 904545581, 804534902, 721624202, 607450829, 697937171, 895540184, 476257762, 362521690, 224113385, 929260497, 864698354, 875985289, 298845948, 258859099, 385518619, 147344169, 784043236, 840192706, 583199143, 972907643, 17849421, 930131432, 888839860, 834477440, 515139388, 148398951, 324701829, 591529443, 842385572, 374011040, 804965598, 462918908, 812162033, 481506903, 640657661, 560798902, 586443954, 234632180, 705769683, 989196677, 700169733, 932189342, 473580580, 58386475, 182020649, 505911339, 930744344, 242568882, 672964773, 947244009, 535650343, 499148152, 368119931, 934872125, 295848055, 463774018, 395616062, 832551757, 414447691, 557190708, 475193124, 461599926, 662968420, 121775678, 655795381, 577268589, 264496201, 844962422, 467822722, 403732485, 114411639, 194234375, 785599590, 824290198, 647028576, 108748668, 959134722, 644637663, 365907150, 724512205, 127855946, 87272925, 672678667, 11323924, 481511425, 653146161, 923413254, 418156191, 735008073, 842774835, 990946267, 563833699, 44309961, 266861627, 735138646, 206631291, 955855293, 70180134, 184902781, 261693339, 638810708, 972664916, 820775049, 750213719, 487753877, 629737497, 331118804, 997480091, 418552488, 788410635, 547994323, 933305781, 677409093, 884926578, 309496626, 312501042, 997340705, 681236893, 797842451, 503734030, 365422798, 428089504, 728067784, 707056752, 890656172, 473936424, 73225061, 824663447, 987710862, 438040345, 933880554, 222650123, 506487204, 837131207, 156145075, 429304567, 951933929, 142573228, 342903947, 948444430, 914475341, 805304811, 689962616, 668256052, 632029162, 838368218, 583071652, 831487, 170174685, 997893043, 707582290, 666463842, 863711349, 87498648, 406658246, 98739421, 848236731, 110919549, 328250696, 495352339, 320948358, 995674196, 559989220, 119986374, 557478474, 696207428, 345028527, 313710851, 64220264, 540158258, 736272193, 736210554, 756383722, 724520764, 873425527, 406624495, 935364533, 949822275, 637784794, 870642966, 577132165, 771088138, 307704315, 873540358, 505535306, 304056863, 141940920, 871187317, 978426692, 241872446, 757584554, 258535686, 242765697, 743322006, 832785280, 279690602, 419977580, 667158453, 512635013, 116294278, 877524265, 917579296, 514652486, 39915424, 327244515, 704167696, 647444442, 286163920, 453211165, 350311622, 122750789, 757549000, 989452206, 844954157, 792174636, 675386257, 328854396, 140197889, 779562374, 344840790, 670595838, 950808860, 481701643, 150776368, 510976820, 983991822, 530042265, 46157104, 947744949, 861537254, 29172731, 490471719, 137762904, 731706291, 392369918, 137031938, 764622353, 323422412, 688461127, 324724699, 174142364, 122883055, 71561478, 972294411, 400605649, 829709158, 333971857, 57343485, 377474042, 414656013, 926468237, 328494432, 323469157, 662511344, 605398767, 767486173, 972810528, 602511811, 890570737, 534481793, 82687635, 218331595, 527739654, 934583832, 696599433, 785194509, 320524596, 52590127, 261318805, 389680678, 772499369, 328202768, 984909613, 224221164, 702713806, 950186768, 582234260, 478286795, 407102967, 609954726, 347419683, 356768770, 360447108, 924039556, 278504412, 996720834, 429647072, 633259370, 41138647, 442640618, 606845192, 508011008, 913925471, 259167491, 993781696, 165475601, 932289874, 14753833, 437080064, 71685657, 757675484, 716262936, 85574935, 113893897, 819204843, 349305608, 597734750, 308562203, 619065423, 620221952, 981252170, 134120251, 757856313, 697992587, 551684940, 838091976, 648470713, 923743936, 632946031, 224173318, 482557, 25917386, 535598439, 761855734, 325525146, 561192473, 47819002, 115237059, 745999308, 955860457, 292523452, 151858296, 765861019, 378730335, 764171826, 707559683, 601015469, 577921328, 559897905, 349851352, 714043250, 728123832, 704100256, 277913960, 740717809, 185263436, 767639136, 759589000, 542291122, 158734356, 902599671, 138385365, 503722474, 209554260, 616011666, 444420838, 190512130, 652776713, 6861969, 362599179, 671085574, 69675725, 855304616, 992417649, 965003414, 34022412, 546591731, 274299269, 9587064, 626837959, 89794346, 340660961, 69689478, 690001322, 274324560, 733805559, 237886414, 305455331, 685817411, 906607210, 395201244, 145661543, 613895389, 272353001, 524926512, 292030358, 751548748, 958165360, 187554576, 485489670, 682688272, 511339252, 389551616, 535885257, 265533499, 947672522, 358825848, 282220620, 614137165, 487648844, 260454821, 842523172, 336665098, 924148974, 710940765, 514674705, 306776697, 88271316, 444774756, 407845338, 600355222, 698188703, 848109958, 533982645, 341116448, 201342052, 540213352, 8199866, 141819287, 492970138, 873166155, 644210546, 119777696, 940207120, 611411074, 552778997, 729435904, 565929956, 182128644, 797841671, 361037347, 275438989, 424060856, 250636392, 864112691, 670890582, 341747623, 696952437, 341602154, 606111938, 387744899, 129717385, 85855711, 117734830, 112566179, 251949445, 97053846, 215580572, 662924442, 420799234, 286482757, 653543811, 51400624, 760293653, 525524460, 414851523, 841084917, 967628811, 426467947, 614252130, 30707002, 61909892, 202486743, 302848070, 706561627, 662479391, 317927633, 511908138, 717714227, 436553945, 804469373, 100020778, 190788243, 159639031, 332014416, 308279266, 961911441, 964076645, 873167673, 489421718, 532314498, 481332285, 877165505, 256831195, 692931077, 106056091, 171340789, 318046738, 142750312, 184197156, 304791917, 969505347, 201238276, 573578445, 824431145, 743832060, 452720356, 43625969, 250770948, 245760375, 334562970, 41579905, 513618976, 92397234, 479973055, 852277975, 649265936, 738791702, 23649869, 381600410, 884600134, 288043852, 484854122, 372057251, 973344021, 966062509, 987739009, 668030732, 106981872, 339805439, 948622389, 716820012, 364464326, 346891376, 696038293, 293915382, 566022825, 408967912, 444609752, 821275786, 720077810, 748893073, 660719508, 185686365, 882535508, 310341478, 802900878, 529347335, 399177374, 765925856, 53300404, 239561767, 137532773, 799799843, 959618399, 607972374, 895223415, 486503451, 463205163, 385861244, 638460835, 201668050, 520082574, 88497657, 635470854, 263318629, 598736022, 803586606, 825584248, 74628523, 261656342, 64486489, 144114793, 293646278, 158347576, 881144828, 777037806, 768611789, 936431937, 660484927, 596250819, 276778793, 55571700, 918142032, 894928692, 807470516, 157466920, 833875300, 60630460, 773295767, 931356008, 15953996, 314549443, 141199519, 308960062, 937499062, 270590208, 267703099, 922860305, 319390062, 298184237, 124688873, 374981886, 49038406, 383000151, 439774227, 438062378, 738516112, 579803017, 68582575, 718690789, 753437862, 364300994, 720663936, 143840468, 204285786, 889433243, 173857361, 868104381, 952186598, 354947941, 679287675, 766836056, 413095114, 9640369, 38264751, 152552752, 413589537, 356364159, 860641820, 567392354, 526097773, 380514271, 839343448, 332716369, 638096850, 822913435, 890959230, 173637092, 16700898, 542723040, 248899867, 987472546, 270140678, 2929139, 830720979, 882044120, 850426755, 386807306, 328325938, 771224806, 360693085, 224134800, 111162424, 320678773, 127321903, 296574463, 465216551, 539786873, 759631226, 660206928, 56315602, 57181874, 198750576, 350845158, 411364720, 392930076, 710249922, 119516272, 534312988, 972018966, 552403214, 819738555, 850138696, 313145015, 447020722, 333974578, 218288049, 575645600, 985221654, 605546550, 582248864, 771891258, 537505235, 627312332, 661943504, 953371667, 473272580, 80629315, 348055566, 538661411, 847861194, 763783671, 778247784, 54600227, 78130413, 887719206, 857655904, 634110031, 528791282, 427807966, 729768806, 979270789, 21810296, 371170101, 918671714, 102963814, 817431353, 877665666, 113688571, 606187244, 649834352, 460533559, 923978862, 682566890, 731940708, 400721820, 531404097, 55995190, 360576746, 3641227, 593427016, 537885627, 4620882, 109984910, 384172756, 307264688, 724942985, 944521843, 892133099, 395395123, 928887823, 49689458, 209010535, 782126839, 254930103, 693898756, 67088814, 120468579, 993974379, 531304597, 392717196, 536211951, 826170269, 629430706, 827696626, 56966873, 523038147, 201786842, 90165248, 981057427, 45524306, 211277071, 435756108, 217341875, 120609654, 933513875, 627118691, 760153471, 650448204, 48554591, 107054292, 207724310, 291330774, 391315975, 896856435, 448925433, 759872365, 654428857, 117547279, 203098404, 768604009, 661931598, 178936133, 118062119, 733028834, 291676336, 635221747, 845137830, 713387326, 746448150, 976248014, 739044329, 807140976, 298265439, 410060335, 471408256, 2152472, 776368872, 932226372, 22933523, 885136165, 382356100, 43522705, 218636447, 241084455, 298751288, 665847415, 643190041, 302431060, 496555458, 945763015, 188357068, 683571031, 593046845, 121245991, 201930647, 753380450, 248025970, 632773249, 762887352, 980260144, 600839619, 723378501, 39574818, 280717927, 192683381, 555655739, 939044123, 120046929, 259251191, 314755048, 849350656, 611578549, 20019465, 650291332, 516942195, 482816860, 262950878, 851833695, 94645359, 623734897, 163436966, 156333584, 545332093, 609321597, 943345542, 112794196, 467479483, 584200945, 470599368, 983455340, 850699533, 811460482, 824638171, 429526803, 427825220, 622631571, 414727919, 950218743, 784099768, 376726897, 810044283, 844806364, 616679039, 701447547, 187299260, 173258746, 361750306, 845048441, 152740119, 566519139, 62195671, 621231896, 722850631, 942175368, 136842305, 985394866, 547747642, 665312984, 413517768, 263856131, 794478547, 995621141, 174958368, 900943567, 715958479, 802831297, 278234817, 122297111, 95925981, 229541655, 868979173, 186797797, 74455492, 199891464, 196923495, 851584140, 722756819, 458441589, 175217220, 136610378, 258171514, 760181774, 638903109, 592512474, 516724890, 445797089, 507873069, 468333090, 421698963, 479387362, 144842896, 858146988, 487512393, 807680846, 274711944, 304132858, 792673932, 348582141, 390142207, 401575771, 244042345, 627107344, 667566541, 520598589, 553278595, 164246416, 220154100, 953035334, 254904190, 428889571, 283676528, 681023593, 905784610, 26831566, 899854482, 886276399, 549401579, 60884619, 838750316, 939522153, 118487834, 310928891, 870421145, 881960250, 397987261, 657768655, 616263751, 539399832, 855083048, 253763624, 393058502, 396059481, 7710221, 704661287, 347421612, 928243155, 713442620, 343852777, 969968905, 275092074, 62386840, 349851500, 835603748, 766663396, 505446068, 620618599, 57072908, 728002481, 568169316, 418490693, 595662764, 482924112, 401545187, 914367431, 847978626, 406226434, 336798617, 325587835, 348546591, 177722576, 134492484, 334500991, 199730328, 683664617, 520290749, 728302858, 672302048, 891642881, 962833607, 808884061, 713419144, 848366583, 514265410, 182945037, 753961428, 650235435, 304728467, 832520763, 139721563, 778585125, 732661889, 398840113, 339792025, 712103213, 604569734, 213671332, 118987689, 851251753, 88235824, 123313840, 253304450, 222309897, 754625011, 288864046, 734812868, 905907612, 567044439, 609952250, 214929063, 872068961, 832873598, 224155075, 571745289, 539443912, 980431306, 634842369, 260281556, 230097438, 540158707, 13494598, 729514877, 425118558, 958327299, 409265309, 853961539, 288460244, 61997681, 908028506, 156265148, 756055206, 444662453, 459602289, 322318259, 762200476, 457842998, 754367450, 293563310, 429509245, 7631211, 281091029, 357564048, 909111125, 405867657, 12854260, 406756345, 933839089, 881247179, 503678689, 847924266, 588137492, 544364758, 85885317, 438938065, 530771029, 675354042, 439232415, 511421596, 751860166, 276131825, 540177455, 862362449, 880717920, 571763790, 216997795, 696846367, 11880674, 29865540, 274554509, 741248435, 917993907, 582069270, 216971627, 239127628, 771822698, 969762585, 969714506, 225514113, 337849289, 280843212, 480327049, 10795566, 347655899, 428876818, 207351248, 363937885, 940064515, 234373279, 105566075, 559757367, 993914817, 782338851, 917266493, 440440327, 788059753, 707275178, 538682314, 363446716, 923219556, 893040788, 108600299, 878142920, 289243269, 351748014, 894512617, 71318602, 989236488, 974809618, 135715819, 338313562, 73840429, 783923971, 89495948, 435235654, 53782510, 967184607, 214976249, 732831789, 75120431, 783051424, 104649193, 24720272, 476256400, 856883019, 138940324, 528250259, 120463987, 939534226, 110073129, 326624143, 430087522, 32463462, 844052102, 866681985, 280338433, 666471240, 622028693, 399373637, 909507341, 675866740, 239907064, 441823302, 969029231, 244739757, 402266172, 347382768, 558507472, 213768138, 23640508, 700355498, 459599819, 790578189, 406227710, 433776751, 176638368, 983584647, 510462993, 792360434, 363090123, 223840503, 522922419, 494597073, 939175210, 616561193, 450118805, 752565833, 576797294, 477776996, 957683039, 184729594, 179805669, 937629277, 958657844, 158830750, 891967975, 119693139, 312911444, 383806616, 886584244, 571658667, 628023587, 768020810, 45667712, 348638422, 859140299, 380033630, 708529067, 686127408, 929846045, 3638660, 77158068, 330573130, 354997028, 945039781, 908585295, 441571973, 960711328, 545474296, 209745650, 946427905, 205085589, 788449949, 206984174, 684713310, 462284377, 121988443, 615958945, 940584446, 250759172, 860090203, 443785191, 935919132, 768851997, 301122727, 794884111, 832167696, 764019031, 619067414, 14871767, 176893874, 972770954, 656330560, 458983505, 688120574, 43872673, 311118529, 630129740, 39744331, 699076643, 322822265, 371183539, 417513406, 850874473, 796422579, 922333040, 682738385, 705342947, 360440177, 416746245, 465014785, 944052932, 310525682, 1850210, 325829183, 662889567, 181616250, 682804747, 908945203, 446353410, 233305599, 245059633, 138307510, 404556343, 382137726, 908272398, 734493794, 670638829, 298683160, 25237091, 217395951, 532092833, 62515900, 804134443, 711340095, 539628256, 896062106, 387373457, 718976180, 241112212, 367844138, 426507476, 75984109, 559221792, 213165884, 202530598, 211410089, 636924552, 734140286, 872826348, 743830867, 210343490, 831670862, 424696589, 377159785, 147362626, 705605847, 605220862, 741947346, 225759468, 107960809, 989755490, 888395160, 909762627, 338387261, 840452428, 313685761, 199907481, 868084136, 985942178, 515356761, 912221412, 115359044, 408866706, 584289705, 283051945, 578043273, 682105622, 917711772, 919219868, 571397361, 48226357, 924265409, 852959486, 714302094, 30253442, 253652485, 718352336, 271089986, 369600418, 502575299, 613460445, 291998040, 772837291, 559012214, 810514070, 849798442, 19398638, 566672613, 424564513, 234822113, 129635425, 383894562, 326654371, 583202920, 646277411, 471042978, 32768695, 489669411, 858016935, 293793302, 898303903, 561080712, 322368850, 606274904, 411819410, 735744611, 558177818, 238398935, 510601187, 715472482, 914227793, 795560556, 479665434, 712952170, 563740994, 78450691, 702037593, 337891618, 531687179, 653203221, 948010264, 309552814, 119204520, 471337115, 805213491, 452423949, 410637599, 267105269, 104687601, 23613287, 251108821, 440804991, 10363600, 623062417, 555789430, 442237857, 840880547, 265797170, 912574851, 317905435, 380682099, 815909260, 264931650, 275848678, 208477600, 13595266, 756560869, 75134172, 755129241, 205743645, 788477402, 706617513, 141916487, 455105126, 533566306, 550307114, 311518267, 677533294, 939096451, 914780702, 662470713, 224646102, 789220676, 310856875, 501600931, 33515658, 989495706, 165004274, 878794021, 964955787, 352314786, 773794939, 768629587, 728340096, 81133988, 467956681, 262832104, 259364126, 322553086, 342814171, 185884890, 687180524, 72755813, 505646776, 957927951, 487636577, 943872701, 485390577, 96945818, 144640202, 179245200, 743352466, 589411782, 244831826, 894846468, 97774359, 4899483, 227609134, 429218261, 252961944, 161254712, 471365306, 496162864, 960417470, 729116573, 747194693, 376414588, 392389080, 837024192, 360309347, 189411704, 229769406, 9957248, 392955719, 963011360, 519492462, 230646822, 841503333, 516305523, 224872316, 943419841, 323937910, 182689232, 808391587, 361053120, 739700097, 768487926, 230914371, 552669508, 87541609, 186184712, 790483755, 998473437, 189062100, 470230429, 300792221, 854035064, 955750905, 501747790, 808914452, 486499464, 151643142, 405855455, 682758604, 765575892, 500100529, 577650941, 470118635, 409497514, 863827489, 808289745, 205801100, 256897078, 269779033, 493677801, 158175415, 562026625, 706740847, 169646196, 8458415, 666554062, 446670900, 587633914, 569995496, 408451044, 255109149, 80197981, 364575139, 267803735, 641987844, 643291537, 511252249, 196637058, 457574597, 172060886, 800819346, 580719493, 302195092, 244292805, 396332967, 807096873, 53874486, 11569066, 424467406, 392893121, 132323910, 612542599, 960601070, 925862403, 160039163, 675123464, 932376261, 76944727, 424124596, 831010178, 574170875, 579907397, 139254847, 841499301, 723352979, 541093916, 521179198, 707320947, 721194407, 424715795, 487094806, 136982642, 366206954, 133692970, 537928141, 898859548, 592788644, 888878020, 281536978, 158065169, 86969797, 319077836, 479987702, 98924722, 740771545, 418074559, 238404881, 726310184, 673210734, 830326816, 883883485, 480630188, 217577955, 357530432, 164387745, 883747773, 270664570, 988235180, 768558699, 879348061, 148943041, 705478432, 509152478, 903015536, 149820569, 349299775, 900237330, 886239562, 625829734, 616837171, 277609186, 700381541, 512402228, 14337864, 925079886, 396126570, 240830642, 318877978, 994582372, 270810494, 658697183, 128178802, 614137558, 341556199, 186338820, 947911800, 328573721, 167403660, 586721857, 562471970, 167994643, 220304149, 97712467, 570240568, 257743740, 243642954, 664943559, 629800996, 191906601, 543809644, 942144108, 930763544, 223718631, 357807615, 990351224, 877895612, 494779269, 620808760, 652723834, 228117466, 940606580, 333080223, 657460139, 256922087, 709846356, 172313460, 171508919, 470432450, 160384145, 55047657, 263078085, 975599784, 292233955, 42297180, 772602037, 582613183, 590783008, 501419091, 438808423, 112933235, 148689574, 328784054, 309503032, 804156066, 87764331, 706904112, 481437780, 844471804, 763558691, 557503403, 467357683, 124039542, 227831322, 537275162, 114565478, 770288394, 924781599, 567177052, 251161332, 304954581, 372537756, 939454560, 280588013, 606180237, 719381270, 91483111, 837855954, 20374270, 414098543, 428778046, 308803619, 102339753, 119109164, 584843647, 820235415, 358627513, 993807879, 971849254, 629571970, 98943090, 463506445, 680897547, 338526843, 706391594, 95020473, 650892988, 201993883, 199720925, 656367049, 962371194, 641841243, 86914233, 372776811, 560085608, 570856263, 5092804, 327505061, 899634220, 273988800, 440391710, 10026965, 296404704, 617470229, 947737927, 328193206, 628832038, 588708549, 196139665, 433258975, 677178656, 716348680, 332259073, 979781675, 498827923, 335278848, 95516097, 162245149, 741694599, 435699170, 69729983, 107417495, 143348430, 936045, 749162767, 344242135, 421156560, 394763698, 770281968, 231640241, 651077848, 372366916, 729720739, 950406514, 331690474, 670073234, 532572632, 11008984, 518364747, 134369813, 8462624, 443428677, 504872186, 574454861, 242544430, 457484592, 837663150, 957010000, 503408098, 342637175, 709280001, 152401379, 833503006, 464544116, 773411441, 105423451, 400625649, 445026521, 570033864, 645394185, 923994143, 979690702, 588992941, 551762647, 895779039, 311939672, 244713387, 372684439, 9768816, 564647956, 4162568, 50283083, 437848557, 631246166, 248417383, 848394673, 350740229, 833388713, 556601517, 643284376, 487773956, 920137385, 374182153, 830693968, 725870005, 491329192, 29590773, 607106158, 953803371, 51979873, 307782499, 756911344, 877441465, 919639844, 318337212, 25325653, 110182863, 990449462, 723184444, 986285305, 289974803, 927754948, 35197263, 961659501, 850351525, 114387204, 929247579, 329353855, 762478001, 409292651, 689056961, 954109060, 986365777, 641361005, 729401831, 255263650, 308880623, 965533726, 195999607, 341665311, 163561943, 714363736, 226396198, 303942912, 31299585, 72753708, 246212286, 742664683, 530952886, 895621546, 613228508, 369685703, 491526427, 98699353, 365053312, 335940656, 806202678, 766078497, 771323192, 321777370, 295238670, 766512453, 168881202, 457809194, 68638679, 680435008, 684937571, 879729715, 279924908, 657299965, 628248728, 377239970, 211726861, 437757549, 911769470, 847885954, 427439985, 288470780, 668821590, 27345416, 232363192, 960050415, 13796559, 426103917, 42889495, 964341021, 196640537, 961802140, 651692915, 654894289, 459643321, 697880421, 57195400, 115266591, 196266450, 845514928, 203805454, 619699181, 551679044, 358923674, 745446334, 757725504, 454077562, 334809932, 768192839, 714814769, 246662893, 726947192, 543288865, 581628514, 810289578, 134046660, 53675065, 759810381, 450344411, 559202508, 368096147, 634208380, 723302182, 19381934, 82076382, 784617074, 915727200, 531226356, 218560720, 569285977, 424028359, 445333630, 244650995, 161633777, 367929816, 582425551, 756977212, 438056362, 783737876, 136765294, 898226442, 249889003, 431322385, 21729582, 29906476, 504691444, 188057274, 436185683, 371569395, 934450487, 64727534, 205689592, 239553833, 1780503, 698949008, 234661117, 504019751, 545710744, 907834805, 378845562, 528046820, 431344127, 893523587, 938535056, 699573625, 14145569, 298427083, 397102463, 460853942, 299654157, 743233161, 641397779, 46663003, 693515791, 356356822, 654848507, 980876819, 938871138, 86368621, 240751027, 716828212, 530749892, 222042224, 455335545, 351260702, 245804007, 895413406, 177693513, 572365163, 395620957, 222653132, 33663126, 126926556, 693000922, 15413449, 737502443, 734687427, 978950582, 254037225, 187772981, 775530039, 68705622, 597161571, 917246591, 660027743, 58404849, 733822537, 895792618, 640036616, 742783175, 619199190, 735128890, 807880396, 355906419, 270438639, 496946343, 513955575, 593596697, 809951637, 714840197, 861226561, 175319618, 8649996, 654050040, 481676137, 190448586, 698593026, 618928858, 176631290, 945986550, 949783656, 209997553, 226278982, 208109347, 325810539, 138535354, 454803682, 134227277, 620917754, 780470463, 303028265, 256896250, 572017212, 893193277, 581632383, 834841552, 629457694, 480212134, 209887110, 775381815, 680100739, 942408624, 9911284, 162409242, 35475699, 276176230, 785196090, 685399436, 791906978, 854777451, 31164109, 839254873, 483341012, 12901018, 322806633, 290367573, 328471107, 350897789, 765493619, 494060040, 101871415, 696638576, 63895464, 877584240, 313876379, 882683396, 261218353, 143267419, 316896357, 356292835, 84306694, 577869459, 735359122, 541002709, 546664496, 352754675, 685184560, 880400565, 537402237, 234068062, 254074514, 739029775, 597240234, 484694985, 101605011, 911942639, 437638002, 611174301, 314491898, 729785121, 490549067, 252056080, 352827918, 792484674, 949245530, 887135528, 707242514, 697970836, 172272859, 319974776, 613129838, 916946477, 33521686, 302820295, 361928516, 713129886, 264297130, 925095052, 409180072, 159700583, 343877758, 195529775, 153253309, 154306376, 129929465, 714763560, 826886713, 459904264, 439076106, 768878398, 214091745, 215415036, 302306459, 706627012, 659996971, 504563990, 67543931, 956770321, 884880738, 657537178, 946631162, 399021699, 676642818, 87107039, 547987078, 489425480, 6558701, 742556537, 595132309, 544099321, 560137728, 614766554, 542368563, 112336860, 191122378, 820702131, 136026422, 694772593, 253282976, 823047296, 615050712, 122721989, 486476743, 843727898, 531112620, 897398752, 859839592, 58554134, 338221280, 816001492, 151757606, 775213049, 431036457, 774329531, 839764106, 98840786, 260394010, 852633507, 552244381, 84939839, 891663270, 223045077, 694825874, 865527221, 629288439, 799477130, 554812192, 3481381, 270840322, 461968471, 237130822, 20781386, 380165185, 353747664, 717397277, 92902747, 503253688, 652420746, 407211491, 394573537, 156724363, 932041087, 831364118, 541907552, 138303803, 587439622, 900957917, 587834479, 24256303, 868238038, 659212183, 627269214, 926601892, 346056842, 419249747, 27713239, 540220456, 848878746, 746444800, 14879583, 195351106, 420491770, 688586919, 401085346, 992996918, 453232630, 47069784, 99910042, 361547563, 209479291, 811175979, 673451853, 630604213, 593459058, 281246263, 183900985, 689901107, 690251877, 927171906, 647669276, 959706983, 328297454, 267158219, 462171187, 374081088, 257786888, 818594105, 738917250, 201005592, 302675693, 877072758, 457980495, 674570386, 986575651, 112220297, 770050787, 359144411, 246012884, 987665564, 257388139, 960634817, 317828803, 44976602, 390442164, 47466530, 162882582, 456600719, 813663138, 176342944, 833874205, 228658142, 886352084, 488560102, 638920305, 400747729, 615537381, 470292733, 579375982, 450399076, 655371369, 207975196, 397760703, 260347623, 492346884, 8947560, 271955823, 975827623, 861142234, 494923667, 696623660, 581141994, 496201633, 766644062, 676740247, 779547663, 469224601, 904573186, 274801869, 5885597, 486484905, 570327891, 818035701, 860453913, 903346952, 222342023, 234302371, 900036578, 316373665, 204285065, 269233636, 507570139, 709083452, 330019728, 743927184, 511937540, 917411408, 867776099, 5393995, 124363823, 382941799, 579112591, 56829369, 335559568, 448851407, 119281359, 417662793, 986000011, 95424323, 667982962, 179563532, 411991161, 255323014, 396106849, 31093622, 925487265, 524611736, 853147029, 207968276, 23329913, 999497180, 406502992, 42642904, 281720470, 547697446, 208573418, 585206464, 129650897, 650443795, 230282549, 596832742, 967056089, 116761013, 183001275, 152716244, 447536811, 338985586, 923316350, 503237724, 940751665, 636695250, 707785942, 127161446, 476557597, 932843696, 255649686, 80141327, 909990716, 31778764, 219848993, 378240370, 733850276, 624989246, 988655266, 675392830, 117745944, 163394778, 604574905, 974683601, 684523286, 461797837, 574800173, 28226863, 616675726, 976278181, 135793145, 257663313, 699410945, 36998273, 594115105, 603087502, 307573241, 284904326, 226859890, 922163193, 628078442, 152104480, 222393617, 828220663, 490702090, 788872538, 434959268, 755752501, 49609492, 824961471, 422692539, 447247427, 460893485, 260065895, 300032253, 745635816, 547842199, 247447236, 493728363, 798176760, 619804196, 69976985, 815101188, 891799143, 987083557, 767855842, 687650720, 473402055, 791209087, 899042860, 673040471, 754009305, 420435367, 489146302, 689197204, 97194640, 568250048, 974880775, 267377753, 17014341, 906809005, 271820383, 27639881, 188962720, 903975671, 774897353, 905975272, 565827133, 765935615, 656852038, 881680537, 867920451, 613037228, 872961925, 219808020, 446235516, 956987940, 26210451, 682885356, 985712669, 323686650, 322014581, 702899885, 877471755, 77149122, 845668402, 916607219, 864336095, 398672699, 644692104, 810020065, 864482523, 586100059, 412719183, 515645048, 843298120, 676099748, 294640821, 900092876, 929943081, 818132927, 548699587, 742101201, 915733666, 167202625, 960318107, 157582070, 390101263, 283591862, 829897730, 61525283, 855052144, 383753614, 411311630, 772653776, 768408507, 410879143, 212503208, 911763180, 980679076, 966523181, 904451431, 314953113, 846682645, 100904861, 312994482, 326328057, 311925394, 914531166, 19448514, 969880114, 56108383, 501723396, 674325293, 767783707, 767414404, 249138083, 662082254, 214404588, 662198784, 87130442, 348811681, 18476440, 550599987, 970712915, 124788072, 52060895, 220823740, 79041981, 2817132, 121141639, 949333544, 489120815, 490397329, 578619783, 216473655, 854535130, 602848392, 79532334, 834673151, 784429459, 6604494, 456089775, 726573511, 207550952, 578918232, 426590310, 69386344, 388440971, 44647718, 556673854, 589277169, 110321902, 26859978, 508767553, 220196772, 401626815, 12776893, 821784351, 42418747, 651592700, 21767650, 290601806, 91367510, 967150377, 835990088, 265821605, 798309468, 433549986, 879746841, 681685736, 856439123, 406902696, 606119810, 702649642, 252884001, 285766693, 505039073, 220945088, 52817839, 425081588, 279664175, 152272232, 843397431, 786873689, 121940530, 103386611, 517390993, 121816320, 278562705, 332436440, 511544526, 142598039, 649389717, 331881635, 447335464, 207947881, 551263442, 569930276, 999398350, 875783929, 934110292, 710383165, 539750114, 771177400, 815278473, 634864031, 180477180, 803956501, 318310270, 199397545, 918721380, 401564033, 406455121, 923876948, 702101090, 131674841, 729900957, 261151242, 234122784, 356764633, 560120074, 849727012, 324161973, 699530042, 6889930, 762427698, 507357091, 538054615, 17657983, 479576809, 738741127, 832126410, 868465067, 886278670, 389762325, 939823479, 78712368, 689395912, 376003646, 799914085, 169481231, 233970197, 374599966, 915547278, 535192409, 748413925, 325263952, 830080109, 252435266, 54006230, 775247578, 468469837, 713858642, 51227331, 172625440, 848250745, 950605694, 552885306, 173437731, 114200573, 322213419, 915189714, 97955603, 402108742, 498483789, 561074755, 902253761, 248167238, 665886203, 847681679, 317259473, 977882351, 350108209, 970037873, 154713393, 240614526, 353932203, 616708353, 495447337, 225716280, 352441899, 171108922, 424427420, 134586418, 340425423, 781407300, 836560831, 414406594, 268702111, 647039941, 726184506, 17368507, 894757822, 213808453, 417105794, 3446566, 635780669, 542561383, 387386427, 415319601, 976421949, 153914881, 494635812, 415975466, 387739161, 781722012, 111244935, 850755002, 122525967, 287848227, 168616824, 470602540, 244628677, 806504745, 642151555, 131638319, 658642813, 131720601, 538043408, 799807277, 566152660, 506266450, 172850601, 893319581, 907824222, 581660041, 387628306, 902983297, 948939042, 510853530, 772120869, 585722096, 481301357, 939114332, 846280417, 999922589, 223153128, 665340795, 899839854, 183952040, 230667466, 312720255, 510770328, 851830662, 618582067, 421641729, 974296645, 995010512, 137379432, 166740981, 520156380, 579464997, 913938930, 627046395, 632581415, 178748764, 884518039, 520027917, 635716340, 795433705, 17655652, 628595770, 600562269, 235493706, 629536304, 313918017, 750439792, 95341623, 227651953, 40614682, 748057086, 843295890, 525056877, 892975297, 856601623, 830406242, 536053115, 464019267, 241805194, 529423600, 803296845, 479048976, 394400802, 543547556, 447141995, 879774560, 617710712, 611581713, 662678752, 132155603, 759313403, 439666750, 433917373, 373839079, 765131874, 37764632, 807711309, 58231820, 917243509, 470398542, 896419954, 678815822, 385715484, 233736428, 437512115, 304088496, 742324293, 681392713, 680470498, 915383065, 626844801, 717040033, 414394482, 973606533, 902518935, 149368881, 30892997, 445581451, 830726848, 61672851, 170983136, 524194168, 162169218, 416154862, 333091315, 126807327, 418776972, 733796801, 929214964, 379630410, 264595224, 814984196, 565092459, 266607462, 26895109, 797863509, 937976040, 488057540, 896212945, 885549645, 515297267, 562369057, 87242203, 957512325, 933414094, 45154118, 755370568, 658602028, 122720577, 888416874, 479712283, 534964472, 987926419, 849456382, 649208653, 120902241, 847866374, 761403057, 765157606, 858070733, 654793448, 965399389, 115710293, 802142342, 864662787, 163771623, 433348735, 11182569, 759633447, 336406889, 593945870, 520466116, 35045989, 943706677, 854566172, 467925136, 551407249, 651362224, 511753778, 970919178, 801199815, 293967876, 800098735, 218571897, 524084212, 734468148, 535616501, 200146882, 798214704, 733494712, 194737054, 116596939, 530441916, 861487761, 785238951, 923229577, 303640203, 564846930, 854377816, 793040450, 295565013, 634755119, 91875235, 678321405, 7975360, 894990924, 634983946, 404009953, 594476510, 642968277, 901413321, 917122737, 38557846, 311161243, 632404360, 833900946, 6566972, 97141816, 269339645, 63342597, 133653894, 756164606, 434367072, 219513028, 802759135, 898825419, 152354428, 931601994, 171877566, 252087679, 25359001, 483047249, 545972693, 186195336, 587779036, 400885712, 642632113, 116519693, 387151156, 815672965, 441202593, 642254813, 743341364, 260100428, 358921844, 528450313, 119161373, 310896771, 38706745, 48756221, 251996582, 328313189, 995024225, 228946445, 514038242, 246583857, 12392174, 673664732, 494611562, 588593642, 9466715, 319652294, 187924640, 838087905, 485001049, 712594814, 313098815, 352865904, 40562519, 612302375, 808192943, 678331242, 347028414, 886870449, 659697108, 817604123, 312761998, 379744255, 88199157, 893610800, 595815234, 286313122, 333507979, 510628548, 206104115, 956981765, 161555964, 510143842, 476729094, 446709211, 960637553, 293977694, 371263858, 909546884, 748662773, 737086909, 453155846, 737178284, 888515668, 800652819, 419751063, 865605524, 931342378, 235007221, 602187165, 349755610, 161618810, 579437980, 22766693, 689417008, 752471846, 187037712, 848599670, 417331128, 653741379, 719271819, 908341559, 707086252, 610816770, 798086655, 14777037, 513629332, 671928792, 438088671, 128228210, 483741689, 292351978, 497557729, 614622115, 732299053, 779010010, 775440983, 457010465, 828829514, 979579784, 4873640, 739820720, 828791769, 350496540, 642381527, 749685759, 841980255, 226674044, 837322071, 561482019, 769618426, 668674466, 279515469, 568109425, 140583434, 354321961, 571326886, 712811414, 679393336, 471420103, 979639634, 436183970, 595026149, 928580972, 809349427, 758703049, 588446602, 166836733, 349020997, 826398007, 108608160, 920565303, 531025823, 1619431, 783287927, 387271759, 987375119, 404515727, 887505650, 80789403, 937531004, 817646305, 652023477, 370765584, 218741457, 396023842, 62800706, 847708372, 622358754, 935822434, 856393962, 302415674, 26021798, 67786662, 168920738, 77671671, 248880365, 719725999, 742098852, 777488627, 263197033, 572202040, 583986812, 358866994, 668674309, 324348083, 636768419, 481765900, 371794851, 317351091, 703480547, 377687185, 425337048, 673277328, 263512674, 635460967, 680432876, 120485550, 376821809, 436202861, 153617959, 371013579, 731388732, 35866762, 132219061, 211722691, 208945749, 318547116, 196738626, 657899234, 122546698, 43482388, 931855357, 686915181, 274917445, 913306376, 372656514, 604050370, 23814637, 822058823, 867922878, 102987239, 259641573, 153782684, 833993408, 831943372, 313770487, 148748123, 522453391, 745562573, 849350729, 586928388, 336551659, 703412802, 246301247, 641226872, 714838970, 932490126, 211816899, 439659168, 505595015, 762092819, 389994387, 372505740, 25726018, 68707014, 252910120, 256398321, 642437650, 319664972, 415283349, 341519729, 207181597, 723126981, 695111984, 475284493, 594639753, 767794962, 514942368, 215701076, 23069159, 23027304, 578313001, 607193113, 789576995, 942080068, 611724062, 371392330, 646643271, 186637257, 94478936, 95951632, 599728470, 988411670, 6676010, 457393556, 14692469, 499830786, 303391150, 926066299, 702964220, 937342245, 75252096, 364416534, 73057913, 837871325, 731702034, 837163283, 804992378, 412360088, 829672050, 364596916, 707346032, 607902995, 14232298, 760266378, 49297382, 436847087, 948221039, 118956924, 314431043, 234699220, 656092008, 437102117, 890151225, 52906511, 553359548, 874171610, 499009493, 397345249, 875269783, 479256550, 777953996, 677389747, 871348481, 209167818, 231455827, 626026331, 968632944, 92153932, 820984735, 264443377, 516265233, 844567836, 763583342, 800978371, 71421090, 363580620, 740835808, 858800494, 818691727, 251370414, 367374535, 212822243, 322020741, 359514350, 946343083, 663561540, 150991938, 908944766, 564495479, 203633019, 810664484, 939161733, 279471316, 441705920, 384447326, 334928811, 788209219, 343807104, 109637059, 925523593, 686190254, 122459551, 462803087, 911826070, 341902178, 320464100, 173427438, 193367856, 519379866, 610229463, 587068465, 453234311, 405484303, 152186154, 181493266, 40075416, 998283753, 340613828, 670080428, 121758237, 845734224, 129266506, 165486757, 350195244, 791510672, 632659924, 816173063, 129451336, 342366962, 620882620, 762504967, 829612925, 758913236, 931164293, 493681048, 382900725, 564063787, 521026722, 363776242, 651482578, 316769953, 414088118, 421227570, 708129952, 51453644, 681798029, 655380769, 110199623, 743626200, 115596945, 677076670, 221179698, 108688924, 623386539, 118784327, 720573727, 935122898, 451882821, 469275601, 95527554, 202804946, 671124443, 344392118, 500203588, 11235846, 451284928, 396733161, 341337021, 61231653, 66803645, 537113730, 148507830, 693537341, 603441736, 922998012, 397656471, 697382159, 617830199, 208416480, 337789695, 717321476, 653773602, 392715674, 34186425, 650261814, 481238291, 61019541, 441517041, 970229136, 96614138, 128240210, 75303023, 486307311, 862272051, 107866351, 708470671, 221488862, 361849429, 66600145, 554422108, 696750780, 734082900, 424379962, 543467935, 180060547, 645651789, 101324355, 721376377, 712874694, 309920254, 789561475, 316856787, 401139377, 635648236, 179320442, 199901321, 929633498, 803453158, 496116008, 863295755, 470119475, 385598243, 748865391, 650103765, 162008314, 387750759, 128101807, 276090349, 88235679, 346112585, 996753185, 61373336, 658305348, 35938002, 17730824, 378129964, 188448759, 63243008, 780779111, 90273238, 277324496, 9756194, 848089757, 903690913, 554911748, 601619814, 754278437, 888578739, 917417912, 409445575, 645909367, 47548491, 551376228, 389005785, 736535124, 979187693, 994283421, 334793469, 262149945, 537515059, 218083049, 596248596, 693400179, 724568852, 458666228, 685732896, 544824644, 750194381, 321803483, 290218054, 954472611, 611868317, 885506249, 982516439, 282771750, 919372316, 414799792, 400331220, 863728498, 667550806, 516119206, 776794176, 851231521, 119224845, 224082835, 707198432, 98105231, 132381186, 139289390, 73325535, 176423861, 988291053, 347773400, 312412797, 954784360, 944449260, 658275230, 884266131, 420322974, 629580315, 173192013, 636963529, 73822814, 132659522, 935372469, 555900672, 958017483, 844514377, 523834276, 654144109, 881230569, 548695822, 376562180, 664554633, 320883639, 344170217, 888397496, 749851754, 509111444, 186256108, 785405232, 263108011, 30464853, 670124146, 743625685, 195794513, 269819991, 941718496, 134097955, 361794159, 214769679, 998132326, 182612806, 627071960, 443920506, 711941948, 333859405, 965978144, 213406096, 155322089, 146279614, 494217556, 111541426, 256816601, 209948689, 722348960, 626215322, 591931497, 75312704, 892758786, 757830970, 123691697, 597193500, 7238813, 503607856, 831778804, 992437051, 507021010, 592023533, 864387779, 940167143, 152464595, 446311912, 474474980, 657190983, 636519739, 442402618, 626180078, 392114880, 26778334, 820440469, 886744108, 128509994, 266788730, 846154642, 572047441, 27919015, 649780272, 980483144, 716183484, 212701943, 680495128, 351923158, 259954477, 387786967, 594521257, 78220032, 855631362, 274390968, 974690628, 812695138, 406139144, 747087514, 374053754, 289449743, 784428670, 396668926, 702919219, 577855061, 479416961, 304966760, 580614055, 97580796, 584695691, 710366956, 731625714, 848981007, 979698290, 406955947, 990266686, 152815168, 589683389, 57150659, 621927937, 162768422, 446669537, 21584094, 573457697, 76593100, 291071750, 441921355, 338270913, 394665762, 649011061, 730523150, 877599107, 153530634, 767491315, 162631317, 559754679, 991865773, 239919507, 559586128, 563388672, 702938519, 343909832, 137477302, 992326170, 599856955, 599791355, 840952796, 623378899, 98843519, 27265152, 844622441, 143195541, 666199527, 997780668, 458422493, 208092814, 217728017, 256397548, 540977475, 765353593, 358934628, 598034367, 383906143, 824750026, 940862706, 670380099, 600133312, 464545, 568529473, 913487180, 979265876, 621578128, 457247340, 447943701, 530037114, 301864882, 895215387, 530695844, 781263912, 217341699, 793097133, 140038605, 232216266, 763712321, 168631683, 814116220, 860084085, 224129139, 963032943, 145544591, 830504103, 802983539, 228634054, 210509551, 620586473, 133752560, 331429055, 889031423, 853177353, 586835415, 592486712, 934788601, 612367264, 387928902, 927368719, 782254990, 651309423, 518229504, 260075068, 893875495, 415379315, 321495268, 683200343, 19135065, 906455168, 59690315, 15713636, 844945144, 956133525, 525088730, 638442986, 174483690, 112063563, 515874544, 903166415, 663988449, 464624946, 409234664, 716830666, 295937679, 77614623, 47626492, 190702095, 439842875, 573538056, 675507872, 309103681, 54031082, 563860430, 520192507, 844204277, 554668361, 906673824, 566415956, 844767641, 691021026, 653542767, 854229834, 818903615, 487832487, 312386196, 979571885, 796192886, 439738309, 940720820, 984082364, 483726482, 783152015, 2461517, 666938993, 824322820, 71177837, 284980270, 3768207, 304281224, 747776135, 682472058, 166419431, 818604418, 372508926, 635295218, 812216169, 711136033, 526034766, 766782992, 689212764, 338010842, 726031567, 843027865, 94912010, 707398396, 869044849, 553996761, 633048378, 959685179, 749230720, 27721169, 307195158, 258758933, 826532477, 457699674, 188848637, 622520261, 131548314, 235741824, 249443938, 305175094, 16401788, 923369198, 531702320, 113686142, 76873536, 200816301, 726107970, 567324910, 851200151, 575370500, 712696529, 232869241, 373234433, 215377634, 590702508, 354603917, 233333141, 130439933, 174568280, 816328790, 839924878, 917187754, 211189092, 726244777, 219753911, 382368904, 743928770, 418624922, 450977791, 2131513, 638797834, 321003168, 6352251, 765621170, 712290493, 591790431, 70787269, 742670578, 86827882, 710648444, 835824674, 632586483, 841658012, 780588611, 513306063, 468846218, 101552732, 344487796, 792664740, 906950067, 191414332, 414107553, 671875519, 7658065, 186996503, 442402306, 336181313, 788377910, 863891164, 27237166, 247721898, 662536594, 705851863, 192049053, 869378668, 920979480, 798590421, 131094339, 692313108, 929825516, 498790429, 233690924, 146270767, 88445200, 762127971, 157104827, 721331917, 622064361, 221782698, 663910394, 432406909, 298298391, 918162507, 766036342, 303743542, 363990707, 8420028, 610338662, 276280078, 946572098, 813545156, 2193997, 617075229, 445362478, 338599557, 980790787, 988557435, 81124083, 290179236, 829567179, 167507884, 373801604, 824056407, 965193758, 390567728, 680276795, 36881322, 333631598, 871191458, 313428778, 814210305, 921647435, 361587740, 328120, 138058445, 152821628, 765294393, 886716064, 767075940, 957728072, 249247870, 150067726, 40259881, 381631498, 458901983, 200783858, 789534675, 148984505, 999828982, 118012666, 771683174, 908560372, 273956645, 621002435, 796325674, 734077757, 844443871, 393398298, 623338584, 525636769, 392146689, 394741047, 204951917, 67690295, 478266691, 683966268, 872231851, 480172338, 988068671, 933932138, 489512730, 75939780, 781350240, 362701750, 76600329, 974671790, 695856093, 193219726, 710796092, 97561234, 397172881, 652661190, 549093919, 395293829, 850494874, 955117200, 469255054, 287593468, 459648438, 911886826, 777764263, 757835505, 892561608, 468971370, 740524584, 682099128, 570618944, 194947630, 732587265, 852541327, 754349080, 604992164, 671927592, 120794774, 883352380, 246998700, 134148262, 121587123, 471318557, 543475590, 585023797, 574697547, 356685207, 349293687, 868812614, 37100252, 75961630, 982045699, 250454217, 757715733, 132345371, 206337005, 136500535, 573133907, 987713080, 559829075, 506874781, 847258094, 965660273, 682760636, 960922782, 634832473, 657989472, 178060361, 508696110, 432014359, 386748021, 228749119, 958609583, 191838408, 792944323, 974819811, 367967038, 907358506, 72684397, 153894538, 65139806, 760054168, 787666259, 731823586, 320426559, 559578819, 467192272, 524491347, 983766790, 913774620, 938034504, 846169726, 32523162, 183800574, 299298453, 853624317, 180822655, 863812493, 31195241, 323419135, 329503934, 666733216, 354321092, 328950964, 958725476, 222859652, 236441470, 313042000, 418557928, 406515476, 42059204, 414225350, 76523979, 889234222, 221891864, 880404439, 913820989, 327235596, 208384996, 490238926, 461593193, 185604710, 705459763, 883481050, 841754309, 596752825, 91344282, 257990866, 346235194, 751483286, 212386225, 376765505, 143113517, 324732292, 51205748, 136826613, 747119653, 609620241, 920481500, 308216589, 606150472, 118082783, 70802294, 806614551, 377802302, 904283721, 597339651, 687704429, 169658975, 31752266, 574654918, 615656733, 393753348, 852312816, 531242489, 665275787, 542056407, 19111806, 271049511, 189416014, 766806227, 769198777, 341968764, 200397359, 116689105, 862625494, 208137457, 52636231, 31040932, 651110595, 458789147, 91049852, 644207558, 564299056, 341342276, 125727097, 620516761, 126008789, 290784364, 934980596, 479164719, 263932140, 611099214, 716670232, 754008434, 460406063, 271346711, 424723700, 761685342, 247931383, 639853176, 845634406, 284778405, 445992922, 572675756, 538099416, 831521153, 880098648, 201192508, 714169106, 648378355, 928072460, 266734692, 439463654, 816714339, 322673920, 226046021, 174809893, 301439042, 618161666, 192009233, 670849339, 159744839, 36181455, 96876449, 374189547, 909413261, 130631406, 75726324, 719464313, 860507609, 332314359, 400053476, 766193014, 364198686, 866324684, 257337731, 232863540, 997579487, 384497860, 130965689, 645701443, 328595164, 213714532, 326382530, 144945780, 596234371, 454843166, 217605571, 917415616, 468317100, 924736755, 760706032, 577118875, 738420717, 792407011, 675289817, 984864449, 928795096, 100303808, 838500266, 112788899, 799523016, 357029193, 127340594, 302943263, 677906075, 350655956, 568149718, 877622195, 601135569, 858060787, 334776219, 538059633, 343688651, 686183207, 663343499, 328252361, 275341726, 473927939, 392136791, 925015084, 624562466, 778306486, 245219002, 11519956, 561031070, 661240235, 748262740, 502685543, 615358282, 703834199, 398251848, 95554651, 240172562, 843836290, 464569711, 2934306, 137199523, 663325888, 708192279, 292744795, 756358010, 856530496, 171833586, 118559648, 743998990, 126403761, 609944650, 575406403, 968801703, 984312084, 206825103, 40236283, 441981700, 59507144, 202613676, 521618617, 794526527, 870107567, 134190449, 134154347, 650414831, 632289775, 946008163, 606764043, 492194169, 949590369, 730790551, 832327275, 783807847, 813767095, 289437481, 190728119, 300342332, 669378289, 674715630, 138958089, 228703877, 868436440, 896506610, 816738097, 399746237, 894414768, 394004232, 788888822, 570031514, 386186200, 890919559, 887590309, 811440126, 47592264, 400673571, 380315858, 246743530, 182221344, 360419162, 709358794, 970426495, 113921393, 514904494, 983739448, 776608201, 258194534, 980002877, 225837162, 802628716, 343900265, 716645057, 11629535, 209067027, 774214089, 941542824, 575297152, 560641473, 889178300, 345221753, 470281510, 159857548, 154685695, 34571658, 274602354, 451020600, 680750087, 107178997, 450283258, 696162847, 596009120, 562207055, 355317206, 910450774, 964810399, 70155783, 516069217, 838968788, 929298949, 510782359, 833080184, 810647717, 412647682, 468308207, 338910826, 845180980, 383911180, 163103236, 192436449, 234817273, 154743896, 197747246, 752973022, 121860359, 768340710, 413096304, 46625231, 388803708, 827037936, 223603386, 855583041, 710581405, 808587570, 19318343, 115428154, 964420099, 995014678, 696575653, 714888478, 580375108, 284562754, 483752952, 261003879, 501488255, 698438054, 568774245, 445032991, 470499370, 619648840, 897535954, 71996639, 895594073, 698050514, 866894411, 779008660, 78969995, 855199883, 174127175, 415809077, 853481815, 996102725, 916506946, 598661455, 119818070, 914550353, 361915303, 102231751, 667394745, 301141840, 490404186, 128447518, 537271662, 429734261, 952744495, 511156432, 656932866, 143693244, 558305825, 577012302, 439716966, 908488864, 136546355, 135533741, 952195000, 305368757, 478254050, 126734436, 277339946, 580408516, 768308885, 527732972, 487313402, 342927692, 409420034, 712086774, 861288888, 516274755, 790569957, 19130792, 522843886, 827633866, 43496534, 920479346, 583971192, 413085037, 277762354, 338538937, 500441022, 874580150, 285387981, 279441669, 46020169, 209566569, 584210245, 622898253, 736845461, 343044056, 193571, 549238016, 709487566, 619075014, 598480040, 857267876, 452621723, 668578209, 823890018, 404000002, 437737818, 746353182, 596598381, 86325246, 809015982, 349900930, 434288688, 878148820, 139002531, 894991942, 449610451, 661595850, 22116383, 431081644, 974408280, 270852149, 777059036, 653057241, 609127765, 569396292, 238133745, 999495635, 379773678, 906378214, 133247088, 485118248, 21043139, 991906159, 669766547, 440641541, 987475279, 983360021, 832135949, 590515666, 926470055, 877570734, 915640518, 989532424, 654328666, 473704303, 309781506, 380762540, 46799569, 61990154, 629820577, 196848907, 766535126, 769655109, 374327652, 989978457, 326148345, 254592341, 183959853, 68362344, 773484820, 22942052, 394319565, 603110757, 157206553, 880486242, 105475617, 898178747, 767025676, 93584274, 936425538, 835668748, 169121172, 827636548, 31682036, 943870868, 228794465, 651950100, 123347446, 417302305, 815665569, 170788223, 955617825, 66063594, 347757633, 863432369, 570574891, 82201842, 798100158, 347255564, 661226964, 242119253, 988554964, 989176211, 82609275, 508292392, 468863414, 991917146, 192861020, 200911130, 779778241, 356937973, 728479435, 820396418, 617347733, 753772952, 515156387, 719451529, 900723529, 912057470, 37651766, 378769912, 659506340, 586584014, 533188254, 600869863, 765238930, 859706985, 706360271, 866073224, 213083701, 182428014, 267913492, 522551307, 859652118, 96152451, 333042830, 688235742, 999812891, 400620674, 739735599, 277522892, 640827796, 948670066, 867687892, 351830035, 923674179, 24764018, 311862756, 134824805, 384420182, 421407719, 752060198, 674304353, 359915021, 433996661, 215907147, 311414677, 781086164, 576567729, 168268059, 491483037, 138751169, 744669133, 937221779, 412665598, 121240756, 969144051, 50582898, 427179610, 192832094, 229656909, 316093928, 653130696, 594867198, 31262874, 55685259, 936848073, 275603707, 22271535, 204733032, 639321685, 204011394, 111932430, 825947385, 364085909, 779760174, 187140908, 321153604, 29581905, 534509050, 730080642, 196248873, 290578839, 292553581, 757349835, 43584069, 155538137, 859821914, 418740939, 551420237, 77708439, 310557422, 836542734, 791019757, 912182027, 303704787, 22689972, 577997498, 881115882, 443702178, 496249509, 237308618, 290825125, 937435908, 171143621, 286688925, 653515735, 838232670, 89409733, 424701204, 750708761, 495496492, 500993540, 483422856, 541959056, 917014605, 178599880, 426193672, 647530524, 782443836, 689291287, 950798516, 84930714, 640719301, 937162284, 212666642, 256413744, 937506385, 158316628, 488473836, 384738735, 697021346, 252701845, 690810469, 991842269, 605303106, 793355918, 428257416, 914941982, 903085702, 522628152, 420075249, 873167910, 855732059, 941826106, 26793111, 580826250, 663381767, 152977594, 248341948, 386577779, 418080109, 583683350, 190824976, 496738222, 496805979, 425128203, 345414361, 461869299, 764898753, 505337877, 714359315, 802438727, 910657715, 720065061, 861907258, 488585924, 79105802, 208294944, 582334550, 387386431, 475903521, 335309250, 40828947, 542795512, 81068775, 491596185, 5076637, 757150590, 370387487, 647500835, 753348998, 857232493, 906487265, 748148338, 845317258, 417974183, 342469504, 236816030, 28618267, 552313116, 301850950, 455979580, 558150540, 137927263, 260809533, 819620704, 946814884, 708721639, 64013272, 649758196, 235729061, 294975211, 551072773, 185744872, 631152777, 330849865, 476348605, 684221371, 819585603, 586318953, 10559470, 24849363, 186991793, 922691338, 387673209, 190524844, 591451252, 713998425, 25453568, 207364119, 517109755, 754196216, 407981586, 361613341, 561426297, 661498740, 863933978, 792144999, 537828611, 980201851, 65232869, 708519563, 833643297, 99977400, 257320315, 751263866, 563107131, 841002867, 585610838, 442628875, 856652007, 821675062, 436243400, 104639015, 892149554, 605836152, 177251467, 11109621, 254712760, 246009893, 718023552, 766523185, 660451064, 3593097, 318526505, 580139913, 136131652, 831279798, 119253317, 85107077, 562571113, 312920249, 158971282, 230084503, 876943627, 613133797, 842414103, 477768918, 331446759, 597845621, 249728110, 339604426, 482404385, 962126879, 498258896, 580291015, 371809278, 75877624, 860205594, 710108251, 209658271, 309509540, 506205995, 789386623, 206405238, 452552857, 256185167, 3046984, 10738692, 142885722, 910976169, 825619274, 703928684, 274111177, 106781146, 403216315, 536838586, 677284225, 905951581, 395688171, 777707265, 556571005, 15948446, 966498787, 213449425, 906187473, 946103458, 745871645, 56990920, 770181221, 578170749, 247901362, 551072557, 133458346, 963826900, 970749431, 31460312, 141845583, 330454356, 176738203, 351176062, 292822148, 351546724, 974076562, 259424661, 93178264, 468710852, 296275535, 154012529, 960955999, 404965948, 18024630, 475109036, 491593621, 903594823, 287794158, 329582901, 504734125, 667329583, 216164992, 125633856, 291712847, 529472219, 418161918, 807166503, 432915712, 162826651, 782382197, 329372003, 210610699, 702665693, 731164399, 846077907, 152046634, 907074121, 400448385, 935973310, 219503929, 829868222, 942963809, 992759354, 416432125, 744587267, 346778616, 107402251, 258054417, 96934698, 140796318, 929147762, 427928952, 437118198, 549324673, 92380113, 901299779, 324044348, 598851485, 747694110, 273603854, 138140614, 693518120, 4592929, 789747539, 354806014, 417917135, 513617217, 507561958, 28817744, 154184780, 775153585, 892734383, 627796864, 50582626, 256280018, 470616765, 912492746, 492122912, 325865146, 899750805, 920677174, 240606448, 785243890, 78149162, 180141223, 182303718, 658636972, 206180535, 45019466, 150631513, 218474095, 461356985, 231905714, 351662308, 242196037, 477109449, 832108981, 639303186, 84952320, 692989368, 845040334, 868744703, 993742685, 469078240, 775091425, 174123168, 567984810, 144308217, 444504994, 192126903, 901676512, 681739901, 893532120, 494129562, 929940800, 135269769, 484023533, 916137485, 525661222, 15487818, 126041939, 159871663, 533899647, 632291539, 866622194, 779040639, 159591969, 148958385, 390428381, 7657332, 15855944, 349276178, 199983303, 570232971, 269915175, 477516616, 855217230, 169082480, 925746410, 25302423, 88793528, 830737424, 173984810, 693097065, 80147196, 872806868, 546235430, 433745078, 705144017, 556958424, 878777368, 811366892, 802489738, 351198205, 73501370, 232157716, 967789108, 216101027, 891340734, 100161261, 856500113, 923364215, 765595001, 863071052, 562822491, 104041430, 276232071, 233715617, 265302507, 869981165, 553019834, 790861931, 969523592, 221878202, 650119216, 552756273, 233388459, 738660623, 995536016, 602524072, 642133962, 137272178, 672952767, 327331738, 998925990, 80351929, 416609305, 838258092, 770077982, 224390449, 822313593, 930831598, 826827118, 790523648, 292409694, 727304023, 456807204, 795094371, 981064132, 319006087, 9671432, 194679420, 425310412, 408019580, 343023251, 127794914, 452658915, 714263553, 961485508, 928755639, 853751681, 716413804, 329345645, 696740369, 572105190, 24263606, 344963407, 519244298, 864592456, 484681304, 969966325, 686971391, 388467095, 158638915, 132324314, 474657227, 137005056, 2719448, 105702415, 84460273, 86289001, 349763797, 815999059, 554291014, 232482012, 418995792, 906093371, 859376593, 967628413, 931222996, 573951030, 875669356, 417959635, 741771902, 25761196, 885656980, 140862154, 331614694, 121834172, 511168907, 721982464, 824474646, 439516311, 839071378, 861708150, 368995934, 75522181, 581713677, 352510902, 582833358, 823398422, 359754841, 537548644, 788934913, 24134738, 118403577, 38295428, 425478958, 14746140, 295468932, 877426399, 431400788, 630125613, 165577631, 830993854, 859944534, 761903451, 880865302, 168125281, 459220269, 957652266, 742434389, 728440053, 223003421, 604715823, 193659840, 774879340, 815711542, 218330839, 329873590, 959111085, 578163906, 66639837, 453944653, 572568840, 67227445, 994979349, 751711431, 629677551, 440168382, 995431521, 803019627, 372494056, 233776024, 482722005, 567187278, 647130086, 307719487, 137916271, 678437080, 788987922, 660198605, 673007460, 476141054, 508625830, 122049448, 652631450, 798005210, 373148464, 973892386, 375409920, 779184474, 825336691, 545064818, 144309194, 471526292, 917285558, 622376981, 970214859, 549248534, 254567371, 409717476, 541533611, 310462783, 685929397, 185580787, 601707098, 664356142, 195039733, 560396207, 971277093, 535785271, 177184223, 497924380, 416397902, 758940923, 659298940, 634121185, 381248079, 96997824, 404318949, 536037967, 305576386, 419709611, 199458303, 636650225, 962450991, 5453255, 730005125, 967738260, 635800821, 24560759, 647002442, 306607846, 691260718, 373820820, 742124258, 456570, 414989067, 849260267, 785946520, 9757533, 697717537, 289946461, 715884386, 846737880, 940922269, 609744778, 225148973, 591187689, 164457333, 92346994, 267710214, 865759626, 40082810, 551177006, 989460863, 204470682, 77147171, 513297086, 111337143, 49118819, 236597397, 754377605, 376853728, 334995140, 542314159, 474681771, 668564021, 170261583, 267433334, 934359906, 210156165, 930106853, 995662347, 88234902, 677938277, 193873018, 201589724, 64948387, 517040643, 201583978, 92471597, 357675849, 930844922, 727345034, 282525664, 125185935, 276214240, 771061024, 43845051, 735896382, 634561186, 409289745, 669111356, 707351195, 407199811, 938285703, 897878547, 307942009, 931042738, 984848791, 330264428, 728363476, 494811992, 765057647, 504707501, 313123776, 919892721, 426416060, 837938744, 45039959, 983711393, 571760303, 343728722, 169072079, 825427959, 874571983, 567228801, 876900917, 658640658, 813557539, 983143753, 817391053, 385783286, 384143864, 39264010, 657826739, 94020327, 431343453, 52292080, 552907686, 153326395, 780451974, 487216542, 35157292, 222336291, 294506818, 454254305, 94439489, 157169802, 861835393, 227872277, 404956951, 455740114, 30945264, 749999235, 686258303, 53242600, 456825461, 166780427, 538287735, 369899675, 209728577, 686701000, 60598013, 499182817, 95394949, 409817889, 123908510, 621592978, 828428756, 148241607, 491683855, 721140294, 877243668, 145082098, 88338594, 471598997, 796439480, 134264396, 147730500, 584700790, 634938091, 416563288, 210367746, 213544229, 519402518, 953640662, 344616283, 427508815, 816918560, 449516321, 153237723, 629687832, 878868639, 841751815, 32254646, 379817333, 710849691, 923196051, 277868606, 518567377, 45972887, 390403880, 458808835, 574323948, 959087756, 277671246, 276579603, 433245881, 708233613, 17721287, 197711381, 561292458, 864936224, 172121702, 906173261, 975119759, 345854123, 526452177, 145026328, 35123658, 350742790, 539104628, 780772525, 92756946, 27817094, 249503535, 590890959, 82431431, 131848377, 252034756, 184322478, 650933657, 292505635, 89858923, 893517917, 712891483, 331227792, 553023266, 549025415, 787970192, 967181766, 178981861, 330462283, 832766100, 748241707, 473956570, 522327286, 99998756, 420600058, 766229779, 342219546, 924968953, 654070545, 774749000, 54008307, 639759856, 62366658, 676674333, 524589049, 974415290, 921474635, 288141756, 439589400, 218530184, 120954132, 224272291, 624710178, 170738452, 391072950, 837126435, 206776413, 740973194, 207196052, 725633093, 695362846, 703502332, 762658531, 546409972, 308876248, 673285010, 505709274, 225366760, 296782838, 257191658, 351732486, 684629191, 507652740, 251829326, 593177432, 259605182, 554873368, 520826458, 794110303, 435024470, 9579784, 759947727, 1129497, 922852321, 181905218, 114911685, 262628927, 259639726, 347831118, 875122227, 435302684, 855268582, 503715321, 550226345, 126178322, 174814154, 3653848, 145289962, 234394644, 516160617, 68480929, 945120837, 850291778, 902976738, 637440832, 997554789, 324745315, 222438016, 725264543, 626803664, 982497, 599062457, 782610034, 236454288, 455923187, 889950758, 657054896, 981216604, 602857423, 61033880, 453972124, 892730974, 297544468, 628475401, 128616273, 185584018, 42503287, 24288218, 489237743, 896582752, 947329648, 778040093, 11453221, 517305517, 497092190, 906374131, 461940372, 824827077, 478343840, 142299601, 278908260, 851101577, 859114305, 374253314, 571283689, 911098431, 576167603, 727375265, 351921354, 515807971, 159245585, 53960762, 770837615, 832651153, 916344445, 52969397, 494255546, 932201806, 558830406, 89678440, 634892427, 991584876, 838019174, 306335556, 129916871, 413103604, 288602737, 522281673, 931778256, 624244925, 868552077, 38056061, 339815046, 799493, 644349358, 761745526, 645742117, 480163139, 607488034, 290321385, 691757444, 848200639, 684551178, 770867368, 721231969, 690015765, 931495035, 58154279, 714669923, 748341227, 688254132, 268654675, 785736479, 649572942, 269758557, 497851549, 105985497, 197316033, 587270885, 904970586, 824787959, 239716825, 760405192, 781083973, 680955571, 472994077, 406496783, 14055110, 532510522, 265446565, 801455840, 615737682, 473857767, 708891711, 64841411, 382884016, 690622411, 840427592, 731158211, 602868297, 376556835, 312256843, 508222738, 413123409, 184935101, 937182223, 176349700, 662176304, 224292312, 385365409, 109563935, 637963815, 712585338, 744927525, 714368279, 207467646, 502377571, 302620832, 841467488, 514359352, 420849643, 625851296, 472403602, 988605384, 899582174, 766140864, 285595016, 614695049, 844707743, 861030746, 856106720, 443456823, 833266205, 556700127, 215742363, 38243819, 846308125, 355379848, 930637801, 714951299, 627524780, 624798166, 455759316, 515143100, 845670108, 829590347, 362867192, 822262399, 119712719, 206470295, 671011159, 785447199, 872612070, 860166342, 781598483, 66251118, 321368147, 777888748, 82644549, 553939183, 843837890, 462984107, 406745553, 482338920, 604558444, 7754493, 87252245, 8683457, 538975306, 992949972, 744913129, 487841221, 484937791, 849083834, 504993872, 959750986, 425928914, 816232769, 500110629, 755592175, 871070563, 612181763, 859715681, 383673357, 423211501, 333778723, 253953358, 313493092, 616646706, 549356231, 110052972, 415184813, 618382175, 240175878, 393479813, 254994042, 760479596, 480729062, 914498620, 476712720, 672980817, 745891863, 33033367, 714501965, 681531916, 177465804, 303829635, 597164397, 91044025, 58471271, 603246616, 142471359, 202761013, 798107672, 498639709, 271014753, 622577873, 355683023, 45398539, 74150309, 333540110, 541476803, 179347271, 892370281, 515001342, 837390193, 873482735, 297531578, 966030395, 569061879, 238120406, 522674343, 94380300, 813579889, 102133655, 549444938, 103074137, 856479933, 527865985, 163566882, 653959818, 913227191, 685129183, 352953958, 397809137, 612966422, 623648999, 540989568, 547082720, 357561775, 412010789, 471936900, 110606207, 433936714, 546396191, 532951434, 725685748, 85486409, 820767689, 433024587, 702587916, 968694576, 659847893, 335655033, 530236448, 944787652, 585107819, 482789380, 457672986, 321142092, 510497436, 433038841, 262707363, 578818728, 301781481, 523953023, 244190093, 356888502, 341778410, 114808427, 994967612, 199008393, 17527931, 931030635, 765107430, 198159519, 156300939, 725071982, 144546790, 579381417, 805474179, 169089944, 794830675, 490432799, 301195312, 940169704, 697161730, 914219120, 316358923, 339269967, 347736797, 12033136, 181169460, 903538108, 588375483, 168080873, 15278844, 636338831, 456948514, 644955362, 597708394, 486239963, 714912943, 431990414, 447820789, 464961421, 803350883, 714133351, 539134588, 955412407, 784014755, 288492497, 215503844, 241898844, 367899214, 644708724, 287590012, 161125836, 677145055, 110660780, 420093749, 620563559, 643030753, 379366439, 773521240, 639545884, 884055177, 497897291, 962502017, 246500706, 259549668, 755281814, 139176477, 732385835, 568670054, 341097367, 310545835, 504064702, 11089293, 917718619, 978335719, 675801504, 754131991, 360007549, 198968246, 650770231, 622840382, 628949486, 677818508, 693638970, 35175995, 28525367, 282883954, 732019188, 499451683, 938033107, 781370811, 613140057, 119487479, 298973495, 163238990, 72304805, 670007001, 242894081, 552869859, 352738988, 483724745, 476345620, 59335451, 456657154, 373709856, 699751266, 390740586, 720878038, 132128298, 273538453, 971145993, 151807165, 778851516, 236882707, 438323337, 589962158, 962657577, 691946567, 646973529, 631776310, 780376168, 759249101, 212111128, 761165715, 525444382, 237297728, 782532788, 66654799, 133008517, 334730608, 197630217, 563472482, 343670746, 314055140, 717222179, 125348125, 207626093, 417662467, 886054310, 788746561, 907313183, 562698750, 583134534, 906793991, 733571998, 532952889, 94963401, 227548196, 141458393, 984292333, 987895305, 371605950, 842037297, 391869864, 236136826, 172816236, 695146796, 313802286, 602845823, 312526422, 241389192, 721750898, 727069335, 341602979, 623014333, 129802474, 9346180, 493955571, 223611522, 551723214, 549100686, 258515477, 223981468, 853339543, 354183129, 425604010, 902306329, 729441664, 147112229, 462920384, 768751426, 733553430, 41434762, 545488827, 117554756, 660627204, 779388752, 311086231, 329341713, 381123673, 262306552, 672449345, 993641280, 533547164, 713297280, 625598141, 181726145, 442394981, 396950765, 130914533, 826145490, 581418013, 717006261, 866332118, 726358737, 969304585, 667919947, 464318607, 233444042, 347649582, 705851369, 149141438, 174356163, 187833710, 860233255, 572228808, 817737076, 376819125, 679374585, 605386809, 377155561, 475183202, 13642942, 812389095, 894937810, 375570293, 735447983, 815258638, 147753744, 714279887, 12104163, 754100496, 136806730, 19652686, 993131003, 973250748, 743960404, 200075301, 894469043, 515477929, 405153350, 141919755, 807514015, 940360726, 16517104, 265558400, 263966841, 182618467, 359064885, 692573751, 385864250, 831433478, 426924966, 468529321, 948404450, 624190737, 139561271, 515419393, 155058493, 706628702, 190935691, 663620150, 467224224, 300276898, 359926140, 163218593, 516581458, 694354634, 418503161, 123429205, 818567372, 955326874, 246096739, 830941726, 685793948, 800202045, 507833913, 509663340, 608182302, 59272141, 572721344, 402635416, 277935892, 790277457, 311707519, 744188639, 648293237, 541807989, 910741074, 977973967, 492294997, 325820379, 972510138, 179650912, 402805995, 474822682, 685954367, 639330975, 976652792, 141352729, 514151486, 591200910, 106926472, 559617264, 514496370, 56149019, 996547487, 361764430, 673224347, 613545081, 134846888, 905172597, 534490098, 236813601, 27162244, 971516473, 373188170, 36827755, 931579665, 244797247, 221424396, 793929525, 633488255, 49034433, 631949961, 895554798, 266104701, 23672513, 489391643, 987100772, 665334417, 615907865, 516355297, 811514575, 902132069, 624250664, 306161600, 681484551, 97531108, 445081417, 382173977, 927113099, 633193072, 887879881, 757911916, 158773835, 368542748, 70823441, 189379955, 611816919, 106672270, 199710947, 750982343, 385742554, 832806308, 754332309, 918121907, 618872, 159784515, 379889512, 584623442, 942973051, 179334036, 926601671, 547199966, 723875188, 476458451, 445447342, 355070683, 491074200, 130836223, 29635223, 298257723, 186025766, 239253550, 573014504, 562390694, 814589902, 225130177, 614529425, 356624314, 589207961, 538199386, 731874056, 444907822, 901719014, 875933621, 251994031, 207219071, 454068797, 448230863, 881034248, 871550035, 582929878, 968930382, 605467910, 28954368, 873651971, 152511654, 541582413, 662952713, 691935877, 935667372, 727492103, 188723786, 398072464, 691640103, 341460828, 294824265, 710559551, 24919521, 399906450, 869716862, 304016285, 999778087, 118206256, 467988726, 535753453, 299065302, 877236308, 464789693, 43680758, 173753236, 903810012, 357833178, 454767857, 33106194, 813880986, 1931960, 7886363, 416630350, 412691229, 99731501, 413158201, 635298095, 638262859, 686268954, 43441534, 481604457, 407721012, 91141032, 550252779, 188206434, 821441207, 641687924, 417639883, 321658991, 957678305, 610686210, 304551385, 380265042, 455279186, 302961010, 433412113, 835646141, 626706492, 450492592, 359560322, 457336822, 353046823, 305528725, 352136115, 282673102, 239412918, 957999117, 135944843, 245829271, 472212073, 979589541, 115229802, 462369346, 998570725, 352385126, 755802423, 731258644, 514078876, 413090317, 196897292, 4527846, 876401026, 724851816, 329729877, 781955853, 874083679, 484785793, 500356961, 755761823, 979476284, 518328295, 217499983, 27216772, 263447202, 264538234, 914855915, 217538000, 76829021, 344987194, 968459205, 137857071, 831327243, 935337341, 318184499, 510363315, 840975380, 982018609, 446633462, 482095414, 257687504, 101928297, 863671267, 630063789, 982968106, 928276595, 677865784, 410276607, 179894978, 178039906, 893862546, 541300613, 141085823, 21153645, 407937520, 736181636, 852809044, 639689552, 614190427, 868669007, 146414736, 210110579, 714566873, 520601505, 396286287, 427123556, 783366853, 901190948, 321625504, 27217803, 720270710, 424607879, 733236514, 453738503, 373533933, 161095449, 672373254, 293178659, 976635386, 349028712, 704426670, 932216577, 279351082, 5545547, 256913468, 695748431, 645400063, 475372283, 555527899, 880616335, 452529526, 844109416, 82905345, 77781205, 107873416, 624245417, 923463529, 18655464, 574775207, 619724390, 513585055, 733143930, 999059644, 858708721, 639112971, 272748742, 409322509, 91335594, 897013133, 294480423, 445374359, 564752570, 954715514, 258010894, 489214768, 581785669, 207563334, 955502788, 578204781, 365926774, 759673679, 580904314, 536994986, 963540916, 234034378, 871133184, 248967901, 517721222, 685653980, 784974295, 502619957, 541481917, 559313254, 745846806, 95702591, 192567311, 193864836, 98891109, 384090235, 59331577, 647075501, 434084862, 94983836, 596577895, 766735483, 142763228, 767358469, 754194493, 795841612, 243791200, 341383563, 579993276, 561537195, 665230581, 201757073, 23779062, 978825500, 124200628, 36049077, 27956314, 95876821, 114089346, 72875120, 740485839, 633373222, 136330882, 126979889, 489660069, 454788590, 789478468, 296613502, 161396680, 221007558, 377023825, 339097240, 699399811, 725498656, 94801606, 714844098, 228967828, 632862768, 477591695, 35317104, 733202535, 485982782, 801227329, 128753290, 840036847, 415602593, 576657760, 41295250, 261755643, 370101332, 8341196, 881952154, 750632432, 141128795, 458513173, 780583474, 525547165, 504473687, 744859074, 677826060, 86634233, 606158617, 317633561, 379755136, 177491977, 710456492, 777432556, 454787597, 913691699, 400614506, 560128118, 168640884, 325299156, 139075201, 861702527, 371734938, 591534118, 471261337, 129737213, 185470454, 94763617, 594287087, 975808382, 301325206, 265106257, 303332258, 170075845, 318803386, 749397522, 704651888, 714080400, 76804315, 795842190, 624873996, 549663185, 673686583, 70643436, 240076197, 276200981, 129031927, 923626648, 312645181, 414468807, 986334756, 401718843, 441191952, 221793861, 397465349, 318012874, 13054162, 224351106, 658850055, 654988701, 320556645, 993983202, 659011282, 512324848, 436634306, 391825724, 614428736, 531341651, 840322785, 27539943, 733660964, 704838563, 689621476, 926044484, 575695621, 581506658, 9567034, 164348903, 126483168, 880235310, 600326193, 88044879, 48832733, 247797474, 436953094, 577557413, 897956023, 652171805, 825660244, 990095031, 52224715, 668785202, 915010699, 270931272, 573966700, 315948685, 631664865, 575309422, 62394117, 430817797, 787343954, 587453630, 832454545, 491154290, 345603862, 798169023, 558963449, 645745676, 380907854, 322950833, 335977541, 371386407, 621413264, 803914335, 240936888, 150120701, 431148701, 612538222, 106980925, 93410493, 74621250, 67582522, 903118601, 660294125, 424385120, 585209065, 995733131, 408827315, 170966714, 553684060, 863126383, 59748978, 816021338, 912606629, 591277697, 346957644, 953502921, 76944383, 923341004, 793998778, 62490160, 907831267, 662704497, 551260337, 626588005, 745902138, 588973315, 927081813, 213706604, 283527795, 109407378, 904031338, 835362593, 925836161, 763565348, 641436966, 775796590, 213257999, 801711002, 111299699, 668854429, 473320712, 946609725, 745675736, 734748086, 122226744, 983897211, 319618358, 810632569, 953878206, 501221006, 796795889, 480516019, 748984011, 123530388, 964442239, 715363440, 295476725, 932830138, 589774023, 285132646, 42897444, 838001426, 367021555, 423192014, 317491332, 937470528, 551425457, 771587832, 80924443, 710968953, 361861511, 351182178, 112228130, 486030033, 234595598, 280400229, 698729765, 105380255, 361663811, 186784046, 447006606, 872426915, 810253951, 51919118, 371249737, 153728546, 481313739, 892856890, 849754061, 351479721, 684501181, 763929584, 924257564, 262596430, 998687693, 86310202, 392906324, 239987976, 115924416, 364208242, 360153963, 622272213, 593182461, 357489409, 495095450, 868569915, 337032424, 122930848, 775091762, 465482916, 110334563, 678173671, 584066241, 76729375, 689137910, 507783291, 377231180, 721440191, 63384746, 523756454, 912398322, 475132271, 904722394, 896820155, 235222962, 409710773, 623029332, 727542706, 377274703, 274739407, 819365252, 137416283, 22398362, 408857918, 282934272, 205807978, 824789863, 417519056, 550970792, 515994803, 946722870, 758071393, 166660110, 121921170, 506898957, 20164338, 697883466, 876375529, 886840597, 819112490, 921052692, 579466779, 134009305, 441951248, 619181126, 71868342, 573063114, 998700346, 288853925, 194127416, 386612345, 948523930, 732521897, 828584390, 596048180, 65820418, 783639528, 203029904, 773453636, 897196199, 219768049, 313903108, 315713172, 22128486, 903373768, 201267765, 627628370, 519677367, 171993254, 520438800, 397690222, 12192261, 298270202, 462824075, 674475733, 593206063, 394200312, 369040790, 381324188, 623665019, 830293704, 394132139, 889269207, 849716320, 526520000, 723942007, 60990547, 298759870, 498147262, 934150261, 826522820, 223306824, 768392012, 45819544, 471246214, 170080056, 552978206, 868166108, 136785290, 606568989, 931178861, 209277814, 202311633, 196287762, 450732914, 625708545, 129239082, 221940655, 12558390, 7681775, 32022629, 183191927, 888806611, 959740150, 528163824, 29619826, 778351980, 344138395, 195469279, 730247783, 143527647, 750821726, 725679310, 68142530, 925806194, 865788926, 385958589, 73794490, 106769461, 322534007, 576428042, 47243456, 385047293, 172733422, 417087532, 553187998, 920847141, 427312858, 65355665, 836928348, 152538682, 892086287, 393124991, 242065213, 10057358, 839757355, 805124567, 528076654, 253711002, 544170608, 533755422, 423587810, 698703679, 702678306, 5188646, 796161247, 946259908, 893781680, 393216379, 963751054, 832379065, 976928706, 893303598, 413041021, 931287166, 643843946, 416783448, 236831000, 826980497, 723316735, 682894546, 992428200, 664209864, 646238689, 508907417, 623477013, 779562910, 214959610, 492917890, 562712472, 253756648, 124889697, 408205976, 56297643, 29610706, 865507209, 861356918, 275700027, 373817618, 740379538, 703816665, 77613391, 441817959, 434197121, 477202982, 927319118, 774608565, 437938855, 504865844, 583276704, 200599731, 301684829, 12659873, 335416614, 298621179, 651918974, 874102388, 572275913, 390101541, 162761251, 858358360, 507394139, 896790638, 20362128, 527571403, 474064871, 114604798, 801094921, 355966032, 319396439, 683971610, 55143544, 347956180, 121277585, 385914643, 936460254, 814448485, 378835662, 274727537, 286325518, 765438384, 535483061, 362525121, 531015844, 273692403, 981014704, 425946257, 921805397, 682939727, 108096687, 434914787, 710464916, 660295849, 221122174, 322503561, 890731218, 195909851, 533863646, 848463923, 358785180, 550545471, 577040942, 604817206, 683220722, 23700762, 992141676, 204799657, 751914983, 553865906, 611369119, 83087256, 690123203, 767155931, 686849821, 583303428, 264683641, 958291280, 987887189, 974882745, 719315459, 16934351, 809956063, 778833810, 471408882, 669799361, 713645284, 742613930, 362841525, 365383310, 393824199, 551340488, 723586005, 272490290, 712943474, 125392592, 273642346, 520216359, 70958523, 478776269, 109299555, 413386264, 949163741, 603449914, 667404160, 640178075, 855046392, 438208201, 920811159, 254171329, 713974596, 732838695, 904369180, 956225707, 217392294, 196056932, 988809269, 38437892, 659697634, 689451872, 271506537, 785405367, 422625044, 423195579, 719696545, 361766552, 839016669, 294989284, 256176514, 987699371, 442745924, 924599791, 966152476, 906563362, 2460555, 187116654, 34693215, 527544916, 598936087, 957670309, 153810734, 159147237, 600013529, 557192140, 697951122, 797103368, 382670619, 409352909, 57595790, 384060256, 958839394, 796034762, 68013052, 796413290, 537428449, 763051145, 160784947, 996866227, 864532123, 807437194, 776909563, 857869195, 860893593, 104661123, 417009516, 553511264, 690660593, 409939101, 190219004, 659644445, 533724391, 699577630, 943429946, 317067747, 569266800, 304989856, 801359187, 326736888, 628227381, 726381045, 482261466, 417670762, 992858712, 249621164, 604231375, 230049079, 27702529, 444692693, 278418171, 465134173, 550610511, 147504307, 75474235, 97429233, 154093499, 86401615, 454084429, 506089199, 87777363, 140119911, 361205423, 698631369, 272490063, 486579206, 352835015, 842869620, 512787022, 651768878, 976695842, 605290666, 168229735, 124952418, 691630628, 635732583, 867099886, 110892250, 129423543, 176663903, 669628294, 355915310, 891128167, 960320457, 969321818, 221380690, 48899442, 881558338, 537628402, 545314795, 972256849, 94818388, 97911607, 255294272, 443803807, 151749634, 724639699, 912334504, 292123922, 218137323, 226247923, 173834492, 71757699, 298210707, 585301168, 565616097, 659645466, 163460490, 864850531, 168781196, 924081196, 162817335, 957752689, 116763841, 750657380, 72928132, 231978129, 589340896, 361373168, 262002620, 475665234, 712628509, 37123283, 547517915, 387633864, 736850271, 318807885, 367442098, 84684143, 422379166, 587195870, 514149579, 295753670, 267991131, 985607895, 966887680, 725700008, 608958749, 763715279, 205244682, 835660736, 319302537, 697556948, 164276195, 896967286, 268780174, 398204613, 690440732, 128057356, 756800724, 307315771, 851512551, 524098127, 49988820, 604189629, 902406602, 435839386, 727511915, 109014818, 196825107, 505196694, 489946798, 444592783, 905159260, 25797974, 339097362, 264323460, 200457757, 45648546, 411135055, 760333065, 251376822, 235967000, 436358795, 272489127, 938647882, 62890, 303601466, 699290869, 319234956, 900252262, 827131216, 738979156, 667151776, 172242857, 103695256, 271802721, 298213357, 607823695, 159589573, 6788452, 437640288, 857491061, 381321421, 596682665, 792101859, 880768012, 824102612, 72325827, 90464448, 499929574, 334312612, 312981460, 710017682, 994695968, 974567128, 674417690, 618020597, 949565629, 419520927, 454271858, 713236296, 428340946, 458398309, 211524793, 45394784, 419807355, 562910485, 222217337, 971218923, 577960482, 964718726, 656324121, 650938678, 243339659, 549979733, 441749483, 523463572, 952851982, 875437558, 125427257, 157570366, 427988676, 149842487, 215994395, 937020501, 771381153, 655526297, 101981654, 218378436, 577947274, 436830341, 964657376, 33161917, 969102785, 510647869, 175992816, 33082259, 120780270, 837459287, 974559895, 383162689, 490916223, 574195344, 840276128, 734284328, 887969944, 848932391, 717989086, 551512619, 74247937, 560336968, 326997277, 688063016, 456987995, 890682766, 391444104, 212170945, 306800863, 856982679, 642071535, 409247444, 955656587, 693530909, 266542888, 758446523, 905699267, 23218695, 939989069, 63388586, 240904587, 509682233, 374705802, 864216735, 605887917, 131447968, 608429325, 912797353, 949915416, 91881909, 133181911, 423375887, 358744294, 750342975, 768474332, 744602877, 222135874, 259450344, 70413492, 973578099, 308471386, 704525289, 450636646, 46768591, 451770675, 318191364, 940573471, 823413774, 72043870, 291840706, 208034510, 652558425, 691690967, 934293299, 944020374, 242753062, 185489567, 62840720, 424101084, 656326499, 396660831, 778765996, 205698530, 385423602, 248261713, 848827456, 795004343, 334619542, 650577475, 123707184, 816795852, 433376954, 309087221, 637914915, 940896404, 921279700, 166404735, 763352962, 867600737, 384042853, 288065287, 121054861, 201007904, 528869397, 584930064, 808629251, 452289021, 397675472, 43557345, 252068193, 806184999, 650427263, 25386091, 102868595, 244310768, 421099813, 216537794, 250836209, 724979694, 138932554, 376741133, 693263991, 68807450, 669240208, 89012339, 640551212, 831205135, 737420333, 315358949, 388358123, 568831786, 599551385, 279327425, 38500218, 714419464, 73118147, 624512062, 682341013, 15504259, 700832629, 724376357, 38370190, 937282379, 412044060, 911189312, 46352164, 291764482, 984809607, 627347605, 863579592, 987600331, 959262000, 324523297, 54189574, 724637618, 983508080, 816925729, 452365255, 236585890, 615233058, 249094190, 642419477, 168716422, 217643429, 293543256, 535778897, 184877308, 349373286, 505619092, 660550058, 562436061, 964143715, 750028299, 412178254, 978006708, 871783438, 960104232, 887981494, 60335187, 743129969, 107260384, 885276919, 265155041, 577361352, 716259643, 199055647, 115855744, 116729883, 524936567, 507950413, 268174930, 189335751, 38197711, 694401914, 488861579, 530944529, 949105798, 94475658, 433674660, 244047866, 208643166, 882389453, 898612295, 19370617, 909910369, 989042403, 78414701, 177239236, 943675670, 823896105, 692494607, 789999970, 676806131, 680136154, 643093179, 420443450, 163392273, 229818750, 565897198, 845640594, 942624159, 186841987, 83953649, 324821402, 965341799, 955992296, 685724411, 876221239, 435593890, 460716598, 152274503, 993943141, 392234837, 223768208, 342642874, 454331589, 277267138, 819869558, 773343485, 376681709, 19682393, 522573323, 239175986, 692185631, 855785877, 774179304, 847662845, 376127613, 543167274, 483989440, 770023109, 788094884, 935346407, 382817396, 244274060, 872963253, 55847252, 129218673, 811047467, 447378304, 374340975, 487140612, 51109105, 860213836, 952525401, 820009901, 616298943, 16833540, 297148790, 376351301, 577144247, 821623670, 343748635, 422298008, 777902624, 58666588, 983822056, 99332661, 373066656, 141368970, 116811481, 594431582, 185028601, 424446023, 797289808, 577510966, 323921883, 214298167, 963571350, 388857326, 241687553, 397171051, 613855096, 425901945, 617175105, 92621990, 140254911, 30060348, 591733453, 923977710, 530145350, 224999851, 809011096, 63670356, 948867257, 883471952, 76718216, 298410663, 328441549, 239458928, 857835792, 580961261, 972733479, 591952506, 306858362, 180607336, 970363360, 298949744, 639093143, 502269150, 867264140, 63037851, 59934686, 537649989, 606504647, 932694820, 336844901, 580956484, 802571513, 851504292, 308831442, 477033123, 981396525, 342171844, 745834667, 674604265, 992766694, 951164358, 2064621, 925373831, 39638422, 809655666, 975794759, 140790697, 66006567, 121752594, 586981879, 110475092, 191279813, 344084168, 457603414, 618127554, 936718787, 132190291, 323709344, 851769116, 267462190, 426957985, 836853383, 348375128, 429182276, 743160024, 481104986, 312609401, 837218057, 781225504, 763090041, 355215564, 207729695, 806082400, 800442603, 94274231, 652903009, 709778487, 907076916, 379570582, 291030003, 405985434, 16505934, 254782152, 178465627, 373481460, 838140045, 594956866, 338984271, 974631981, 630491009, 375075771, 764901093, 911981804, 53384508, 538743485, 503483074, 496920232, 723739640, 243843702, 546220139, 999087819, 14835980, 60246212, 487125148, 48283221, 979104867, 731792753, 858884252, 93013304, 868289744, 308765786, 473502625, 655781637, 719412324, 202863953, 481000932, 337248166, 885001508, 125826826, 738513813, 425875434, 492691020, 961188521, 885978935, 681104478, 976635443, 268201869, 720951132, 649737542, 322914397, 855479582, 925007860, 754172359, 757357079, 377524586, 513345552, 486147010, 649485290, 971871041, 659838298, 199357190, 9981123, 205583762, 938614970, 475208919, 759159266, 702091072, 51165941, 864722760, 692328480, 739353389, 545835967, 51099079, 656008666, 57731449, 599885964, 254097459, 553485861, 298078677, 99738144, 322200571, 246060134, 221563178, 604884924, 223267631, 564821628, 889261823, 799028938, 644486650, 296173891, 946140937, 227280024, 128598375, 762243384, 673689218, 928848571, 519966739, 465306740, 837426417, 149592649, 67895692, 391352133, 95574480, 791696248, 27421801, 408392181, 296657310, 517492701, 73152477, 660790231, 75420645, 831776718, 768019787, 137311920, 899719740, 190196245, 843970586, 723935399, 946304414, 707082006, 363009319, 307141647, 779636928, 316431219, 66457112, 972017143, 250262882, 444536561, 863910337, 159783405, 339626993, 904119878, 439651701, 789857623, 890794813, 612620421, 355035408, 273943780, 702192014, 178606343, 193769433, 971906029, 616825260, 484713137, 64306648, 153514176, 78995878, 495065538, 913780965, 971534951, 323097812, 936940171, 917870943, 845969909, 635460641, 957379026, 831430126, 12947896, 341166836, 869415607, 775642311, 95738521, 836454703, 91891496, 605343776, 130410228, 894148339, 949971004, 989761502, 89073511, 285421294, 967950628, 130632574, 364474585, 131118047, 686304427, 16946689, 812621477, 461030293, 305459304, 285707511, 315096979, 843924982, 836277888, 448386124, 384788670, 223354709, 583349614, 317695393, 693488777, 288893264, 773345564, 395914868, 412689759, 178691263, 387016116, 859066181, 276630524, 92597317, 722472745, 850763020, 220384836, 15928255, 135891140, 771964680, 859936862, 42650501, 41088044, 607823923, 277658200, 415031240, 85094155, 449893161, 86081394, 233774375, 826041086, 976176554, 305124545, 550306415, 124726883, 25185328, 859811931, 280134885, 223184362, 9019974, 68388226, 933400596, 446411417, 488418991, 815320288, 49188909, 608131156, 367315831, 680813394, 975673816, 571068438, 711040207, 400266012, 183585185, 916389127, 849831288, 677063160, 260922297, 378109212, 608852964, 348274069, 716732349, 742617028, 686707904, 597140240, 102863544, 820690322, 850884909, 344545072, 91636917, 847346025, 78751, 947499777, 25574850, 326105523, 112033599, 268985357, 663811869, 485769611, 899219812, 536158083, 560085107, 44935139, 984869385, 228041908, 50172042, 803607408, 971417924, 910305805, 844550394, 391357135, 661066336, 687922909, 117473732, 874485416, 871891949, 680945286, 228602997, 467919699, 763075661, 886460946, 548784332, 432157368, 525104745, 847286035, 327777700, 606641397, 499470935, 275204454, 82973300, 437124110, 114673883, 556666529, 156714416, 17162565, 634172257, 257129335, 799034098, 354496888, 84959144, 175403639, 81885910, 838934603, 511108713, 353801378, 983051603, 108253595, 802056467, 615646074, 813883043, 449815713, 324635579, 171467049, 269457566, 394441775, 488678771, 243854474, 467221619, 877321525, 739348417, 277495864, 707362306, 881763397, 625155147, 529907834, 139984149, 198419632, 321146772, 364603621, 778713356, 684496255, 919881325, 563933181, 352128619, 574328411, 578264658, 255625035, 834660430, 3437257, 308078107, 555338244, 670368401, 800189065, 355209184, 663232692, 623440114, 449066468, 520782022, 167837254, 619407863, 888187053, 932184822, 392974069, 643288204, 75326118, 220384696, 423263903, 672492327, 705640213, 293081442, 249712786, 745169075, 40486761, 297980780, 153655971, 645737001, 787475295, 934682188, 409993750, 250305589, 673974189, 28880107, 824363137, 178605371, 633342734, 561420938, 610422545, 731239130, 647154014, 698916518, 209305523, 504109879, 49007009, 701639883, 68592984, 367545074, 849923386, 751188553, 141565987, 208115671, 448455428, 979294324, 161566624, 418553645, 571454306, 728588150, 761578943, 779533611, 209538345, 210928670, 955838118, 798537108, 311165879, 404269724, 147192310, 263538331, 523965437, 930677984, 942214847, 327080047, 434641007, 77819804, 787846746, 779743191, 842010302, 795768244, 189129422, 157349520, 846661833, 515258983, 45486031, 969045898, 621335060, 883513749, 540323402, 893332216, 929123925, 442695392, 499121156, 439989732, 258160420, 548373176, 311298870, 324004843, 410557326, 371020366, 218048631, 396994134, 184543932, 671395960, 23341352, 14234986, 997714441, 956486642, 410118002, 596774330, 612181876, 877573758, 185012584, 62216890, 480756670, 850024398, 825607960, 193031340, 191821932, 374176125, 738871866, 674529901, 461084977, 132323928, 634367068, 492811756, 502890387, 861926369, 935077773, 968543157, 520692504, 23395418, 982177785, 538340926, 731667309, 700022242, 258760117, 108273308, 21836570, 745603005, 263696984, 625896121, 381815045, 718320204, 321129326, 115275877, 769776122, 18406361, 401987021, 216712805, 231180301, 950776991, 715430774, 76968077, 673117970, 862319056, 152192984, 594279008, 77695768, 251308482, 811288571, 103271920, 40237621, 398814615, 104254656, 78825503, 236897201, 8578409, 316274350, 429321342, 989621874, 499539899, 935475366, 862024926, 409444093, 547540720, 147873237, 302755641, 251064515, 439273820, 454047463, 257979076, 326152222, 305519475, 429626167, 850874545, 14675463, 295349120, 348272331, 291519018, 522196203, 644166284, 12095654, 649728647, 192410321, 799286961, 721825113, 921871445, 70181030, 728880287, 240183260, 861673237, 44598610, 614779020, 706075214, 568215383, 98168589, 946013634, 162785002, 129455506, 342166051, 802505125, 991247599, 140497957, 399988531, 39351765, 284762588, 203462852, 709947208, 591039437, 673603191, 184887647, 596013702, 881560715, 555553517, 987623457, 695013207, 689680351, 813283931, 624652388, 536781534, 489545890, 929684910, 534876765, 788175324, 584144267, 799572300, 116757500, 461364317, 577275411, 519439584, 110747884, 446680781, 331296772, 161217828, 351879665, 606584698, 114559752, 680077352, 681947904, 519017568, 89446390, 273474601, 912716814, 351905363, 235285774, 39733137, 498216970, 912836442, 627110759, 207566707, 334183952, 627382893, 745254157, 77355328, 533785604, 616870372, 335902543, 748239478, 781899552, 457488512, 374233006, 509411805, 723076719, 455567723, 321820463, 173197335, 757041430, 392118014, 515314621, 387219209, 491878755, 465454484, 810077925, 617817753, 9054686, 981878534, 990800704, 624720965, 621912913, 568197067, 607967958, 838276964, 532279271, 781798494, 225962335, 107185667, 342304802, 684766579, 885135960, 992464887, 513506443, 554965404, 770450931, 447215910, 390534290, 824429438, 241519558, 793769805, 87020820, 745281187, 975493612, 461427803, 939457910, 531746997, 988629672, 843542843, 970852526, 745433840, 105222577, 332811353, 355432404, 149119319, 617388687, 276083963, 784770504, 697148332, 699818565, 648689065, 149921774, 774418395, 678386053, 94724130, 353664183, 817830581, 942518948, 19297542, 885856780, 410667799, 912361892, 900517904, 581292011, 76495840, 538078650, 987130855, 644566976, 745449058, 623427076, 262091684, 74423300, 742710547, 642767087, 811681686, 72124174, 878781359, 34641779, 950943022, 396409663, 718539556, 944033670, 360912751, 447373145, 328639800, 714283775, 194661951, 260403741, 456590714, 420769335, 340814386, 873957376, 463905476, 985599086, 194036720, 848961944, 478413193, 607921973, 748263036, 58971256, 811404862, 304934860, 324366689, 393134822, 645147686, 652395349, 987075646, 543777596, 399046325, 955320518, 439151112, 41759985, 499452030, 845874615, 212256562, 878797144, 426029790, 158924490, 777087750, 218765274, 35330331, 531890359, 270748827, 603469138, 941704058, 25187342, 121528112, 491539395, 399240680, 971787136, 709698953, 477258494, 813601678, 889642273, 399328898, 622406732, 294951870, 84119487, 854947676, 360351028, 453986212, 810471154, 608741925, 995527066, 806025285, 275912680, 995902570, 741719404, 192925972, 143488870, 189153107, 720478238, 39869972, 867983008, 431193661, 188359230, 787172235, 372160132, 70918965, 453306478, 280734150, 650187928, 998864477, 143492438, 403066563, 166367846, 677613746, 930029746, 20006971, 492271206, 129136696, 671331781, 464807181, 897139740, 121262668, 67134236, 137115251, 697453014, 604634674, 512896482, 507352901, 434200962, 945160476, 396739302, 848407307, 237399976, 347982327, 942619348, 751073616, 441291728, 775229432, 292526793, 5026310, 637356107, 452209042, 296736265, 963065001, 263912006, 325393096, 706012784, 419895119, 678006833, 425247434, 882797638, 681797639, 513122850, 152564240, 145648579, 582956822, 343644687, 472713298, 184754974, 155961060, 718622519, 945542758, 214097421, 533679195, 737518793, 817052989, 575445808, 807588296, 770263764, 851307213, 102432418, 590482707, 124242299, 70965259, 164588678, 933575609, 468355981, 908315057, 234725711, 835555353, 695079538, 266414914, 847623623, 277926016, 740571158, 892508302, 679647012, 495737680, 529314454, 517395461, 968339898, 197070695, 765684883, 646041110, 84427450, 376728252, 731801237, 526574040, 595295864, 164440639, 262955013, 890482243, 410903891, 413133584, 288330236, 890105850, 39941016, 762898531, 274496129, 458735477, 623906685, 371090390, 444541816, 494604983, 523720774, 476962144, 95694236, 758153474, 490041921, 515428723, 198901707, 179595647, 303595529, 240415413, 962828344, 815743021, 195143929, 591106415, 837951912, 6527619, 873700936, 62944807, 57579582, 554856089, 139213731, 279253957, 780786453, 665920692, 744194753, 747468828, 795119563, 271594255, 685197367, 955888502, 534117415, 475010708, 222318969, 323363460, 849122795, 807610924, 735972110, 217826568, 527422947, 823989713, 610821566, 75383292, 467287663, 302218773, 732293279, 898122296, 83300711, 994462419, 331721140, 731164583, 891691534, 534175086, 662181424, 101350790, 534230657, 868859366, 418390305, 260561902, 93326186, 577416915, 259190452, 215113952, 107996420, 86444389, 928589464, 197262168, 383344825, 970616742, 940598941, 875743966, 23064450, 26262429, 901868863, 560204925, 973315619, 624013781, 318267543, 73623629, 396047753, 636623907, 899847660, 945001344, 330605678, 330081217, 161639878, 162095657, 530900097, 289579221, 916037298, 219241168, 616977833, 610939347, 197323560, 246615704, 78036249, 519099979, 158281914, 231958270, 572786070, 587566809, 804814750, 62455446, 1854525, 845706623, 109639129, 556631176, 297090547, 598195451, 254386876, 444709089, 793816200, 720004758, 820528616, 292888840, 383585771, 733929138, 866303185, 571510885, 943814885, 904657626, 860332798, 349206750, 773385642, 349233614, 498867128, 980717864, 764694693, 6599552, 923722954, 761233598, 914535247, 387968589, 124479808, 885270912, 213518264, 293021467, 961944691, 948945618, 803904464, 616182410, 458918695, 112576090, 794048015, 195647582, 583571214, 142172883, 973399236, 495491902, 846719900, 310553358, 513774734, 451147894, 747432287, 620606286, 393207099, 128378320, 935358039, 650452055, 904657276, 274857330, 545127503, 586958503, 932541957, 974285702, 429424303, 509233671, 928372431, 232214036, 957686551, 122887396, 181090135, 963834235, 947642810, 323767672, 255171789, 808233537, 112289041, 216206130, 54273151, 637781340, 723853064, 113264483, 454064122, 518834908, 821727087, 557618239, 894346368, 26637197, 251304870, 72544041, 512430991, 494660401, 264879632, 212651526, 845871247, 940914937, 203279634, 812941714, 337531545, 319678520, 234071623, 58482821, 874658902, 177978152, 484270408, 273229106, 2010358, 963533106, 990021386, 298308480, 173761929, 871037561, 247125859, 9320691, 430890352, 575505870, 524227214, 254145846, 419517304, 520604252, 751415452, 59087701, 441473450, 70561048, 285877079, 203756799, 585623614, 306049083, 663914485, 14042451, 295537525, 796152494, 334371873, 596493016, 131018460, 481939205, 252025111, 765495637, 152630523, 588367080, 932949361, 776970479, 268331612, 818489555, 353631430, 739681433, 159495127, 913831752, 511858069, 459520179, 536399692, 368081439, 427027817, 445780221, 452120144, 939993920, 838697709, 673659885, 189205713, 690662845, 353237650, 410500591, 517955685, 417714699, 120871469, 744106989, 577842588, 57752796, 751733071, 298643807, 919653070, 455789634, 239980744, 380808181, 500102099, 222338013, 190129211, 788620469, 854635044, 900327694, 241065735, 642751662, 907129473, 426093444, 364293645, 13336768, 826046502, 16576938, 523149555, 525685886, 74700154, 605604696, 816654182, 893834697, 399057154, 662501221, 265386914, 827866675, 380054915, 687835906, 91009649, 211907479, 316343123, 102000649, 699154016, 1545796, 428778066, 915376477, 613688419, 281585636, 527258173, 377016300, 195088190, 157387361, 315813386, 53080637, 999928819, 287596025, 594748423, 62630381, 421892799, 888964483, 377707293, 739001007, 148088338, 694152888, 549024947, 788766214, 378363953, 710470954, 21652122, 154680642, 507032223, 253944725, 157191214, 800719602, 652118651, 72300147, 64859938, 390979077, 794186075, 956106904, 598086259, 590832763, 223373330, 124727635, 30418398, 6581392, 944965786, 79390220, 207117713, 230971771, 45083898, 563641767, 957985391, 755140432, 259151961, 169575203, 982114119, 636753461, 954010195, 367234141, 572644747, 934701310, 405257139, 573952583, 216307446, 125289726, 97853726, 375071113, 18410848, 239131430, 600344757, 775388445, 709394299, 377248658, 898304830, 915733280, 294775709, 344786975, 924363340, 217199147, 24451297, 727861725, 497053729, 234123184, 927716105, 473519346, 285361547, 915045191, 651521414, 40922496, 42982248, 864614641, 867412154, 371861544, 352462195, 653412768, 231398655, 819558095, 83031349, 328640106, 222748344, 382324141, 191758533, 653601678, 491241931, 932244194, 940832605, 292954373, 151607332, 712731524, 102986340, 953633145, 861399770, 837978039, 811040180, 967095517, 107699530, 166769536, 279837456, 113199378, 571551359, 900197874, 638163757, 379755354, 584588780, 476679374, 767506271, 276885887, 958961256, 44086412, 879432332, 941626136, 94450201, 713334016, 512067280, 670874296, 443118029, 629525344, 169626038, 359431590, 695050749, 248021775, 61979947, 874572800, 10398274, 421618819, 127127038, 606450184, 307323978, 875830948, 94240509, 998314717, 334763936, 696288548, 116303516, 458013775, 783376144, 153840996, 550049312, 343794240, 25631553, 100657457, 498462030, 919104030, 730664436, 349477733, 879173716, 826782936, 945229660, 26238405, 434324761, 66306761, 130735899, 237870691, 963162464, 952856040, 425338516, 698840519, 51780971, 374226328, 177961220, 385863170, 435643071, 500053937, 468585571, 699613472, 69855994, 144167949, 469939105, 944591539, 784784338, 174836913, 447082511, 108492627, 644530707, 757785374, 490468834, 966884683, 281495298, 880390304, 999686312, 94268178, 637134707, 621531341, 134385903, 37692656, 842669904, 514057285, 143746124, 181937631, 830762776, 255351778, 485410699, 757315896, 336581379, 55467186, 984287462, 201703135, 255196609, 931706799, 781477007, 973512607, 709766616, 166083129, 898403953, 717395923, 568416869, 880396333, 390152401, 793221488, 179811391, 973699282, 736189543, 496638588, 331501699, 505734086, 371309111, 190232290, 38262677, 753017454, 147582028, 902802504, 100054734, 890547387, 265765874, 343461929, 224283221, 361778966, 685953320, 817885539, 720810344, 34741944, 214489351, 676319271, 617113063, 317087994, 762646767, 955198741, 598859451, 635988816, 425334720, 597973859, 259676557, 14700373, 272849474, 512365352, 593713907, 219167808, 276678675, 256394937, 921746575, 806437663, 256450334, 609931408, 51835198, 368769586, 767255150, 321545855, 426920309, 453869004, 88866526, 904335700, 491193479, 606339470, 894459253, 181980888, 105957572, 318811452, 732018900, 6797158, 30569556, 867092731, 879574385, 374354176, 844531688, 433119824, 576034910, 471921503, 13899708, 470924301, 452968433, 543298434, 62156849, 84970082, 879730664, 647200076, 850743493, 469325494, 815472682, 180862694, 933423726, 168886260, 362182745, 482695894, 575933566, 222593069, 364319041, 581200990, 318552066, 10157247, 170214087, 618335006, 998781041, 716733709, 657981818, 228981993, 914445105, 315753605, 177359790, 2640154, 149487873, 679185390, 492790695, 691466299, 103439907, 844498999, 335487253, 106003005, 847203569, 796929622, 763777951, 48664139, 627517073, 765912767, 299593761, 27344373, 683911910, 411270045, 405151891, 499576757, 589194893, 28149903, 955500502, 374696582, 593218487, 568280922, 764257779, 788310119, 242420471, 108246785, 159343666, 917770310, 337108209, 21432690, 49657548, 733722841, 248382615, 570204604, 365252429, 643183197, 148974759, 914948006, 740594899, 984574038, 413727151, 718267393, 710269716, 603045127, 846819202, 63506814, 967910770, 879361585, 370013256, 778520405, 415536277, 289537848, 300762837, 655161956, 647672215, 300945761, 894704523, 843323887, 364398480, 806682901, 110593685, 314922018, 596954515, 947613210, 976612540, 762965382, 550521429, 626508320, 437834529, 79988028, 450354961, 297239307, 640646894, 107014905, 428118099, 606120729, 568955192, 504864843, 54580986, 400694132, 486685688, 599480653, 298310393, 456474330, 203506471, 608309306, 209896787, 829376855, 415797149, 957773814, 316548079, 537452915, 562966114, 996090857, 333426163, 691173309, 789491777, 568008041, 689741044, 210100346, 365464547, 121731130, 264574979, 206033438, 375031391, 301445828, 808645503, 506472730, 782404240, 259369685, 291000002, 416030855, 52870538, 620044669, 577883229, 13988322, 699336911, 735512479, 763185071, 988399211, 576660466, 252264014, 663574847, 964942792, 158553757, 548912347, 518441836, 508616701, 126000443, 307041432, 643564146, 407851473, 302823251, 634513674, 15144894, 660166488, 629785281, 464353606, 569012899, 735266327, 129922474, 110064802, 128285440, 897447638, 325549933, 740760054, 362238185, 561794254, 284156581, 21361800, 448640405, 804247139, 640423646, 181670610, 717551191, 924902602, 184350660, 34433470, 44804614, 178751382, 669707611, 802074800, 815160463, 970474524, 901468143, 693320151, 323222594, 424028749, 588806566, 452122944, 424931255, 203750035, 700668962, 903972716, 765989376, 910403213, 268278750, 845759912, 101834638, 221846232, 335263872, 749890196, 148817123, 962041968, 948885285, 731124277, 470100724, 932830329, 138372745, 713690681, 645500218, 999843826, 159956039, 948815275, 221213322, 563786016, 518361494, 63638457, 128334033, 331175925, 374649117, 531162235, 716989742, 99166322, 68967473, 942948759, 161215196, 359827464, 89974193, 389265703, 66588632, 334193001, 950174000, 345173659, 553070939, 139847962, 12185630, 256311493, 470399604, 151888153, 66295390, 919618539, 210436991, 277893170, 762400649, 748256021, 34736001, 798403524, 543916528, 899956553, 33099728, 686780494, 600808730, 232430387, 601169600, 542467708, 239262578, 267128451, 814474408, 888920941, 480751485, 554276043, 260070585, 328097200, 424152231, 381299844, 447771825, 964849549, 28539743, 322151936, 98584508, 314854360, 948543078, 306602578, 171604792, 648373400, 490414100, 380054217, 994526754, 974771616, 284375334, 197273168, 198646534, 950860296, 338130646, 841552319, 477901173, 201194646, 329882317, 765546722, 732818165, 937951097, 514939689, 33465424, 942965141, 417279928, 268780343, 987311145, 807720450, 301820570, 255512553, 399062552, 469265128, 645017014, 751558208, 701009755, 377683071, 864342440, 72621939, 425165796, 714484746, 408129481, 959132123, 643853332, 861578089, 18356688, 766548094, 504045124, 213873363, 348381558, 9991392, 799651134, 303887172, 537302722, 890073951, 435537708, 806996882, 388064507, 703114255, 542711995, 838121108, 272181360, 187062381, 375831294, 781200797, 890300302, 342889974, 189147973, 216861575, 996961846, 607701016, 129951966, 235004401, 989488550, 610515929, 899215202, 399078310, 620722782, 637024152, 670930090, 773731561, 481055446, 369865098, 208272850, 463479357, 984926345, 252947460, 211221356, 96000728, 693965365, 108875987, 871669853, 988339056, 764033119, 605388919, 947969318, 420199911, 577847030, 524286781, 87824498, 681114958, 789913207, 564885553, 962594337, 865140750, 160451758, 181178219, 821666296, 194479614, 770056594, 705870278, 154473315, 404776812, 470969234, 838644660, 745240306, 611187355, 126284418, 996820349, 878771258, 181235222, 938053161, 376417859, 502802555, 229744268, 462079285, 594353758, 167483124, 453126610, 599253764, 909103828, 488490481, 990469894, 743712348, 466482009, 781672399, 441608552, 490859295, 664787324, 410470374, 77151822, 612883165, 12811997, 611077977, 319078684, 96624996, 554328852, 776758194, 466319388, 729212473, 360315252, 825984882, 152367163, 109233732, 370217839, 747757938, 142172406, 824794805, 782801289, 246140904, 333336699, 180783762, 500565070, 183017410, 416452685, 873357243, 358642694, 22352548, 363531197, 336261610, 525976516, 4843788, 678646241, 467024206, 308692960, 420281902, 242518927, 260665827, 214578477, 756256596, 960258395, 401817512, 202401441, 864970128, 989599104, 241856222, 88736128, 608105725, 546756068, 742512375, 504695426, 481670694, 792656222, 793673183, 762045617, 152532544, 156683993, 697031248, 758218028, 737323126, 192939504, 109063170, 562971951, 816596324, 137290495, 653203883, 201377819, 310044732, 528003464, 610630691, 828036976, 50277375, 78627902, 897271143, 667260989, 729050457, 843845508, 882003505, 383553830, 548692070, 560322105, 200915551, 701558286, 641447259, 46734066, 771072553, 903501457, 769383294, 301836807, 232911673, 449975253, 830518809, 906343859, 327529151, 706317032, 229867985, 35215600, 344915759, 290903947, 536103871, 220136453, 571540204, 724354635, 943304036, 23585381, 642851797, 264685257, 508679978, 133969078, 945941565, 488131471, 576477422, 248648152, 66735513, 975447016, 799481377, 96843856, 62122659, 229778786, 871321333, 473736214, 269572142, 675297960, 654880262, 287993343, 244784368, 725029177, 788030893, 773404904, 729051231, 613672592, 198324750, 439872523, 209964837, 565024619, 766058605, 411579319, 519821605, 456890318, 269437265, 114522386, 492001509, 391815689, 175197604, 848502140, 673252664, 804371541, 268963449, 665438688, 860296129, 479534889, 458087588, 402742708, 149555202, 608826015, 527444440, 603070018, 624851800, 730026922, 950371064, 58879110, 23022989, 109673329, 746879299, 561609140, 395055865, 716160678, 390693657, 317576382, 759811954, 128697185, 222375106, 846548557, 371203016, 547689382, 611324848, 284023853, 345189117, 326960779, 325857497, 658112850, 850609329, 428339989, 605612105, 97482304, 663813756, 24458106, 155552260, 907932877, 439598355, 282613277, 645152814, 293204752, 755716601, 495614383, 261857097, 10474830, 67678774, 699367212, 896789441, 634430391, 669672133, 512954274, 688896214, 649071701, 86069286, 474169754, 983208817, 57352734, 947355631, 455937159, 947759819, 876773392, 607569816, 433597255, 454327049, 379990446, 767217725, 376056528, 853839908, 730640304, 167248463, 958429480, 719210542, 395304701, 927925730, 989682802, 50774493, 69357282, 601627882, 118932522, 958886791, 958116331, 533728445, 606544334, 624451676, 719822950, 102298855, 56962202, 334698129, 329892736, 167087712, 41360055, 955163765, 905480801, 567868357, 518714911, 99842851, 369280407, 581858053, 19544378, 765425363, 93551475, 279231308, 253877898, 534752168, 299135049, 494973190, 800840587, 959201617, 643193084, 595129291, 459106686, 950309057, 468677320, 228965733, 563955856, 783551082, 411401141, 876141994, 763896451, 954562014, 534556716, 494573135, 836092895, 640936316, 576024994, 589678190, 126139025, 497464269, 912134349, 845863531, 611380704, 463634914, 433694216, 464530299, 347989783, 316898180, 452312288, 486417888, 771389255, 888590024, 437382930, 910767242, 593523322, 242260956, 665277758, 661158924, 20440583, 203805439, 884138581, 881215250, 209436591, 329150240, 153845864, 282930441, 249620898, 348620134, 971395726, 778318287, 305814433, 787515602, 312040677, 569693163, 390837716, 19520922, 705804765, 195154056, 936662976, 578320906, 17665431, 571087852, 885406818, 989856838, 878037606, 343927088, 424055104, 315845924, 448768490, 804220806, 710883331, 297185578, 24117761, 685278501, 770308785, 142953102, 607224376, 590824042, 981564077, 387676903, 1973318, 316558037, 525241799, 622791612, 25404427, 976346272, 741780673, 365797720, 579141516, 760957596, 210527335, 792750052, 849767918, 270328768, 737213549, 689887436, 791472134, 470649383, 894995767, 367575710, 615254309, 858934754, 124434712, 871509379, 119683159, 153973949, 554122629, 813669570, 720132912, 410953353, 567855650, 547454115, 879743486, 822272717, 681615373, 923372580, 615678561, 55447957, 937162883, 625971914, 66179990, 565258229, 220297760, 866856088, 427633508, 473041272, 471851348, 665101468, 523301981, 110527563, 982094415, 641064043, 535918980, 947416370, 904529259, 992034394, 456785746, 208275051, 496790486, 144487109, 275859759, 824575600, 908776809, 918533793, 883749243, 451079214, 514659084, 711134223, 667131555, 876874304, 209188096, 852341533, 143407436, 86741960, 542648394, 912192683, 672800292, 111698693, 144989886, 948272171, 55297028, 67046045, 512585491, 577173894, 782111720, 805338855, 889310852, 339460801, 39388513, 308613734, 930803936, 838357508, 513128743, 415492157, 732029731, 673275626, 131918994, 936984875, 805956735, 949512740, 175097434, 990208833, 553969015, 441138555, 995631937, 869225184, 681662235, 663694675, 250155544, 642292583, 898274894, 630057460, 904585515, 665629914, 13451273, 92538965, 478151091, 601958768, 89746435, 604889317, 42216379, 224305133, 472311164, 167710970, 670315354, 856795442, 497556799, 204568492, 773056337, 148627623, 975554384, 311167621, 909675887, 323929564, 487186016, 606093375, 370155717, 576876381, 560872370, 940678692, 302759601, 580519354, 457766840, 715471254, 618540244, 26399621, 667392731, 504749967, 408039828, 854194355, 24785730, 373843243, 808848418, 751818835, 513848141, 851387948, 947537768, 27310410, 885201751, 236358131, 394386944, 759554824, 922190742, 680587103, 739202141, 4376820, 986821237, 636871559, 162960518, 154017744, 648819068, 707360729, 43972850, 397138677, 569928888, 358708528, 101013399, 942926087, 142675499, 110629272, 649792385, 170861831, 38115493, 99329430, 575859919, 973733903, 726725472, 730538628, 738698545, 296148174, 831866580, 29755276, 326098941, 39616238, 741593022, 548780414, 748864646, 500783477, 200605271, 726099156, 646918337, 744000976, 646612915, 465857258, 146333014, 672648856, 212515225, 785184408, 799903364, 648511409, 449974285, 654492957, 925059137, 195727728, 414439069, 375150343, 457563510, 564711189, 586554293, 178490691, 238006267, 476591517, 97950895, 180076441, 426468205, 611260765, 30033837, 483167894, 778659504, 456252404, 860605208, 219969506, 391484663, 963426002, 105926031, 944387882, 102686568, 599559598, 965060642, 870209330, 228149407, 523893360, 813094577, 275002956, 396645977, 971845730, 725227847, 63284873, 256145770, 497580248, 672200968, 603765025, 542095962, 634775578, 769063813, 998087921, 533112198, 347394738, 731950922, 305432515, 836355024, 888136169, 503450506, 618237185, 145284958, 491349468, 255452838, 490617181, 823846132, 967444027, 902783376, 765375343, 405912331, 82110668, 946003051, 612399659, 763817565, 849980934, 601868498, 830979222, 846108278, 26841160, 83099126, 139650696, 399558762, 491474559, 251195734, 769585762, 626331749, 519637222, 903432571, 778313501, 667265269, 964366969, 296551101, 892601436, 380019254, 736729663, 950422188, 651558099, 834409450, 67575096, 221439297, 584661472, 927774740, 67993747, 202596453, 730144711, 351337010, 110777411, 949901331, 719864059, 575348484, 113928824, 263108596, 413938275, 697868585, 882710780, 536076409, 542212713, 748436206, 424742586, 180235579, 131939089, 975851494, 555243734, 784525718, 822168888, 816386142, 232855387, 868347484, 260044483, 321186130, 251048183, 647835185, 586161307, 183524143, 995850144, 841864976, 953596643, 929050425, 943047930, 851342796, 817445453, 725207030, 79395245, 50717958, 73039670, 206153185, 307633978, 922201000, 150757709, 101305965, 121243727, 656672020, 812256281, 217380369, 106170844, 590806499, 784575267, 100458425, 513747520, 940083951, 381900984, 953657990, 496467722, 256765763, 575013530, 784946229, 951089531, 371910673, 934060930, 53757829, 348692704, 719586927, 436982188, 895015164, 929667763, 638750920, 598023486, 582543061, 18629785, 108894503, 627245562, 243585782, 934093945, 939848711, 749642316, 235062982, 706235249, 679942073, 409473622, 905983413, 228249860, 297173334, 317728851, 758116101, 41282787, 122609709, 6607024, 485488765, 331351021, 487364713, 625245036, 317303583, 801504452, 855668360, 395795834, 646221441, 455237801, 289936541, 253045552, 56616102, 60487305, 714897693, 767337027, 696028924, 278537814, 585329512, 617308878, 802879524, 428327833, 771522415, 275446082, 337949979, 794094654, 204493257, 19753538, 868053144, 869938448, 611332659, 972821733, 614188854, 687525860, 868902117, 168929376, 827603061, 427284118, 334387174, 362273604, 342236471, 568133479, 773589395, 553612342, 235729407, 554446245, 499327607, 166470258, 850009503, 580386944, 947270605, 247742861, 819560907, 698919358, 298206008, 898050914, 667802317, 634415515, 629616100, 312119259, 260865425, 256947860, 605336172, 808583480, 941378840, 527825701, 510434736, 854646419, 551321774, 283846216, 547350013, 806011058, 645878155, 554274355, 711834869, 913378537, 346707430, 887299723, 300047438, 905571184, 441825127, 609880697, 996171854, 232657154, 9289512, 734690539, 590114671, 730653053, 38309458, 63216687, 909015146, 448766851, 54740628, 76426823, 489068945, 148257718, 122372566, 875693825, 875428584, 804773115, 277971858, 635211602, 325706333, 761118826, 898150885, 294266147, 777962213, 947409493, 259386399, 847594146, 868896767, 760716666, 166894256, 11537642, 660419204, 514271796, 797725750, 961092255, 796005160, 569653335, 715917210, 529821273, 70588513, 734458507, 465807294, 624847167, 780047835, 519118180, 697850088, 827461458, 422749140, 116234782, 43025603, 810741921, 129172367, 501902360, 936644766, 433631754, 592540910, 236775519, 475756250, 582308916, 602914315, 740437070, 756725841, 265206511, 267714486, 736057584, 182619681, 814134081, 657977201, 383000006, 677624383, 174685312, 444174775, 240607263, 627203076, 698075246, 838884267, 972112393, 558564247, 473343573, 431668579, 716407467, 800620033, 866295378, 676071920, 958106925, 601752440, 457386792, 237236829, 457422208, 198202069, 418642565, 455960317, 147211605, 37374511, 627963856, 34860678, 425963150, 561954998, 899040499, 718768771, 166356923, 269041989, 256345246, 844899207, 776236, 611571434, 728444007, 410024871, 718347517, 855587018, 125167402, 967395520, 571832955, 658293106, 20790253, 532720034, 538811710, 386182003, 922764049, 716904585, 661039797, 779480857, 589978254, 16974181, 662565004, 571625791, 461245718, 356111565, 509093060, 876386964, 816203141, 387437439, 670384580, 793426070, 886387856, 197353865, 592879161, 20811717, 391959160, 99987756, 873015810, 541151549, 95170682, 828004500, 861573574, 964693016, 230740797, 653527598, 126452888, 991675579, 943359862, 984887295, 48321744, 447659910, 775379967, 623937608, 413601517, 232035043, 163801531, 559469421, 338708339, 163376589, 249478647, 370839801, 458718439, 759419098, 265860626, 534842177, 825572638, 859497265, 646513836, 511536424, 216983714, 130785257, 82553466, 315434785, 553535164, 85063026, 720294439, 81503747, 450015707, 691237486, 249713260, 153056922, 622235029, 266292345, 96743856, 901770440, 233546308, 478251679, 873724018, 723233686, 272336098, 246776383, 238824354, 669389747, 936548056, 385355596, 884228024, 851281405, 891637159, 848124825, 470945614, 991851205, 808796342, 561091302, 920236638, 479580210, 213718544, 868423597, 769862455, 927718434, 386526351, 359998227, 390619413, 260220363, 43436707, 193581732, 712209517, 286540348, 875155319, 965515482, 754560733, 901038833, 696544534, 949483417, 85146938, 231509493, 236574901, 542750433, 635085005, 510333139, 911412576, 912995132, 26539774, 667968995, 362100565, 170725535, 670968655, 133241736, 848484607, 458377520, 869715598, 753845013, 698145179, 498275640, 622444782, 229960003, 174749354, 83630309, 598143925, 881963221, 30633561, 909723963, 254729546, 767353781, 990282411, 831231779, 36921313, 519381480, 492924233, 712421345, 314514903, 571568388, 100191206, 70304236, 12329897, 201836816, 921314710, 388877684, 967079429, 271118121, 131559977, 439295007, 669541934, 671257432, 381082007, 998899988, 327833662, 89171648, 434419001, 305696585, 956052568, 300968004, 9923455, 670731349, 975430092, 725174011, 472892487, 987094827, 892356434, 461557524, 471931741, 108881224, 158497484, 926445027, 8602998, 129069793, 126970636, 389374636, 253064528, 80803834, 950112616, 496103992, 258717409, 8802477, 46099857, 692254209, 298008812, 165769373, 192829599, 293582492, 544357950, 560793754, 217527407, 99733112, 957318891, 4808264, 75319619, 885053190, 566008941, 556730747, 220175974, 244127337, 660393242, 82949503, 23758581, 142194616, 307623030, 278494317, 308132484, 418767401, 374945185, 629624055, 578577256, 461171158, 202565668, 469727580, 426811409, 570918856, 934914077, 208642855, 137447247, 691669622, 466800625, 290726799, 393374189, 64172297, 40944073, 35878931, 970762946, 57397501, 566730088, 45097011, 760222687, 227242420, 571106673, 336000194, 347710648, 706268056, 727322546, 195054907, 344874821, 3963483, 64057993, 429824167, 932144299, 784754641, 28333222, 378699558, 676416272, 728815688, 399584216, 671035089, 491675208, 130579904, 659702736, 561838308, 729562985, 660644213, 13362591, 457592458, 323728743, 185876027, 728273116, 3759853, 935851904, 799378830, 265806952, 142950485, 703939331, 827117879, 406974278, 107769890, 937328891, 665211452, 9759834, 565070613, 926115696, 29010964, 826229542, 571193144, 902747595, 97105473, 397119747, 126080284, 742555226, 107694878, 489852685, 967261439, 868538799, 467596095, 947255814, 212024496, 417563122, 749656165, 783369698, 941995749, 971939417, 789540247, 207709664, 919482443, 547270931, 988584537, 285219048, 71105548, 808903371, 490039057, 165773540, 763516560, 875886649, 604182998, 766819599, 347978620, 362828646, 833982785, 796097330, 521254578, 716775556, 401046846, 733575458, 277745285, 978380478, 561615191, 438007805, 675722193, 406250718, 666211252, 608435917, 347383338, 910773554, 595787701, 183750522, 559541755, 829050735, 162457913, 714375660, 213693773, 865010261, 267649832, 974395767, 271688688, 313700224, 817985658, 631673451, 674707433, 445840120, 601588056, 743823666, 703298974, 767657662, 2982866, 257161563, 558812822, 742148034, 204113306, 81552640, 352472967, 743945357, 630544501, 116040438, 650711830, 568928850, 479624175, 290535578, 781898567, 671499272, 336276058, 386610003, 490109555, 16597843, 529967888, 452853780, 24713825, 281892153, 363398919, 591333788, 269175211, 751632936, 959224224, 803511035, 734782807, 942652128, 862831702, 562764868, 580892647, 574964376, 758090135, 587365304, 226078221, 264730030, 894146577, 963389771, 487970324, 862667356, 298672452, 386134065, 285433242, 602010669, 350233550, 148224646, 446503933, 834294900, 253102670, 605731254, 786493894, 170987447, 88975862, 330576481, 90826787, 515503420, 27507147, 656058845, 945230873, 696602486, 735482337, 288094028, 660689781, 875330852, 204262611, 253019179, 348058406, 865899207, 632775427, 151368160, 999181737, 185291850, 761021460, 715428955, 477386378, 808609977, 435128009, 145270300, 359805680, 310020976, 661449402, 179320090, 852105389, 555012555, 104622266, 773560205, 55395634, 630802424, 115579844, 641192678, 569539870, 512671811, 272919289, 204616167, 416413572, 894185841, 205717229, 56501840, 953836314, 226820336, 351997384, 228323907, 885220098, 371520964, 142408967, 186527769, 726655626, 269537648, 427321477, 878431829, 790591539, 450945796, 530921124, 575523776, 129783815, 254952147, 805938848, 580949601, 435367635, 988178605, 785697923, 102671592, 316087141, 549287345, 945875700, 644593166, 681019106, 909305053, 822198933, 749360513, 788278309, 205069271, 621723595, 248230141, 178211155, 954790997, 903802548, 536816818, 435874807, 837191350, 791586830, 721733230, 183124357, 722924660, 133892660, 778054984, 33035901, 166708071, 696631817, 224932043, 150396264, 696174918, 171603857, 36088166, 913280557, 88903409, 299866798, 322357577, 634121866, 318344841, 149365416, 457484233, 30829112, 653422330, 698269517, 378763683, 931062565, 393383040, 652339196, 963115127, 960350890, 353003362, 962887215, 459779896, 244656513, 488151438, 92539425, 158199868, 556999055, 983177258, 266686699, 467370765, 361727912, 108422875, 173682038, 51070506, 541689265, 23904452, 582884234, 632126464, 610335253, 673514064, 205017742, 820752197, 271916803, 774015184, 49509864, 171177706, 847271033, 841651298, 255512118, 387093864, 952883594, 900987411, 899220125, 818954697, 952905155, 208696525, 448552931, 783951880, 321844747, 200463454, 423030871, 786670385, 735316830, 63124525, 302568725, 685100314, 2293479, 142350796, 556913102, 746521522, 522041725, 350293253, 622538271, 283394076, 861993746, 284173846, 63590063, 710682624, 542559828, 631011986, 431451815, 949088130, 607440088, 676792070, 203571781, 406602421, 37136317, 711733511, 793455766, 706263112, 594502087, 205467895, 698458508, 380891952, 526545778, 139613720, 634968826, 825663128, 884731483, 36270227, 230477181, 383093616, 505595619, 985791226, 973277178, 342122286, 235382989, 841528579, 428668652, 489938805, 850978965, 211206630, 622390557, 771881328, 543432579, 737501907, 37809530, 44819159, 534284237, 448198208, 232511895, 250743209, 961480610, 842129145, 280230470, 884028681, 712413700, 598746015, 459616120, 519104078, 859805160, 175688392, 59335860, 58429467, 826863721, 680523312, 433926141, 494342506, 697384439, 593947662, 897995099, 931276148, 368868107, 330177607, 1768026, 763510650, 818044343, 185618379, 980572214, 484859697, 643453243, 754339942, 140027942, 33161101, 57478263, 377805387, 49045106, 322611526, 237976507, 657652749, 14746949, 553031572, 911597877, 306636390, 654603776, 95842906, 67236799, 929274069, 796148033, 186496265, 747802984, 957233333, 763115727, 839218343, 124042476, 669214767, 257520988, 773980604, 691354144, 983389359, 283607938, 584000481, 861390436, 608848487, 511202202, 289694196, 613817658, 381087811, 812912608, 493577372, 599079008, 305320848, 542495380, 725845124, 586149965, 449764465, 885582581, 613225548, 372235311, 834989377, 171201199, 571651375, 916498525, 98941061, 867223179, 776407157, 885787679, 495325968, 279278634, 147531386, 555374406, 272772419, 894693673, 920276966, 897484754, 566383345, 43597248, 275282848, 789737133, 165575951, 476765191, 455552393, 419564280, 279438061, 376498957, 272203987, 273838543, 903251143, 429580675, 12548010, 927236900, 932114627, 422748104, 400043963, 142154060, 137311609, 245937759, 428884171, 695802606, 385463019, 238380203, 600179932, 438680055, 429298434, 893757772, 702032591, 366174303, 715515501, 903471945, 558287990, 788171912, 174022236, 168598077, 77694333, 51023043, 521261398, 518823462, 775635664, 4409802, 415225889, 350115460, 410944067, 471679207, 938625305, 324289078, 604221683, 997819284, 540643235, 6451649, 320550439, 949190601, 418104136, 685690196, 23222039, 859623359, 567891395, 136066555, 69634728, 586029743, 357937850, 633253150, 390234258, 108793308, 653504976, 552274088, 656118031, 28015452, 206053688, 253671394, 801149114, 931935049, 502583680, 252772525, 879916903, 123418168, 441968265, 607140916, 38922610, 914585943, 411766745, 641275439, 877520385, 382112550, 490231065, 304369501, 600851846, 229995964, 530180451, 272046981, 621158667, 769100965, 714934974, 47374760, 714702493, 699153927, 313875426, 777936926, 978869241, 147935786, 806749923, 624663010, 741521432, 58144279, 4669845, 522815302, 621938774, 692452662, 139175196, 385447291, 431957352, 585633229, 422648663, 442574108, 234519142, 370271529, 47442374, 572997076, 441008723, 719738079, 248144230, 104991562, 641780780, 221925414, 322111555, 577945262, 690843516, 707365091, 677920310, 187667263, 601727217, 80157736, 201036628, 398903827, 478438562, 222984147, 215748439, 567227935, 764690304, 125240674, 165539927, 837707462, 96394794, 311165297, 906921180, 121194161, 929951718, 676838145, 250905658, 324793514, 592381030, 647721559, 816293490, 578446683, 809264443, 658959216, 953606828, 343515342, 876045618, 76565077, 787935893, 552751188, 558472533, 210758069, 489176046, 539091534, 654752838, 343965797, 893857729, 689514235, 700477732, 741742547, 936736190, 32795183, 598570371, 565898641, 200601369, 343581074, 582424064, 276101063, 343579977, 706379044, 201807693, 142315914, 369276638, 973305229, 836134719, 629434270, 928583641, 923893517, 157013761, 972641642, 268844150, 138403152, 724864250, 773115163, 117754517, 352302101, 597542966, 222412709, 784545020, 43638891, 660821098, 887222293, 726420880, 521818264, 9355938, 908364816, 692359633, 660392357, 214408255, 521500626, 590519597, 600058627, 512073058, 394605428, 760298296, 231694802, 198711990, 987895318, 701002828, 856971799, 747240675, 202668731, 444338524, 273185518, 956348855, 648328729, 245020032, 223174782, 883277317, 456747184, 463635349, 453082083, 843959034, 274117803, 443793388, 694530142, 412081722, 569537776, 832907830, 985558547, 233556616, 343050973, 820920296, 982113752, 341208970, 964461970, 758107123, 182015251, 26371136, 874484740, 301054222, 467838715, 226595589, 689554715, 760506289, 903900893, 99002182, 674973228, 38689791, 612574950, 11741961, 583448645, 422735022, 66886436, 221518601, 353074405, 328075547, 995507400, 484287910, 245779777, 193735154, 924698399, 96195281, 202115537, 755374775, 773691246, 810016538, 2423260, 114564299, 877870364, 220499561, 976482223, 765546179, 284273356, 987929972, 609673311, 334428101, 682413442, 944308213, 139317890, 179291325, 533163268, 848428316, 947428010, 77334530, 832706797, 624996274, 701484136, 952971293, 670677308, 820393690, 95534508, 731912278, 364345505, 967483501, 899888598, 215099169, 414189476, 817438191, 650352547, 210496457, 788027047, 349038758, 46241559, 67581917, 645716435, 69973289, 166687886, 890100959, 152346749, 25573720, 309930463, 418150709, 98557103, 430692763, 220899703, 868138551, 186213924, 319796286, 870417385, 343324825, 133545501, 972552292, 576180663, 319806925, 15796603, 10862839, 730837797, 852198931, 341396980, 350428842, 565896504, 348263558, 850509990, 2030500, 538128218, 213085160, 798625442, 638420543, 406010660, 939180175, 846240920, 181498434, 973427505, 907836587, 5554264, 703886393, 646982458, 556298467, 967518037, 406203648, 140441158, 671399645, 342409066, 196839238, 759363348, 770265983, 162879156, 432389159, 120077181, 505418909, 785395226, 673428938, 546209521, 289710835, 10517960, 35293939, 983547625, 535295282, 200966264, 268229511, 11270774, 728423933, 941872019, 385729634, 772836857, 116343673, 875285132, 763403491, 630844353, 173749835, 223346410, 981864509, 455575936, 745326262, 742313520, 610821624, 143200908, 931813061, 556329186, 52448870, 966826386, 4325908, 445119759, 297632592, 381216272, 79869461, 709780932, 716084465, 295259386, 521971053, 676653802, 569910039, 295285901, 627138537, 9548459, 684189309, 227932227, 494674812, 491721777, 586080326, 796641229, 912564510, 74285783, 683589556, 273953243, 543639707, 217789846, 292209246, 580759427, 292331236, 563905532, 119913159, 742155912, 900530960, 768478915, 310448213, 170361379, 879431527, 983545354, 947578101, 842012793, 507313604, 100741624, 111719683, 774201694, 350587226, 892464468, 917037737, 869186859, 904300983, 380182734, 306440194, 626279369, 312397848, 452996680, 992452382, 907269608, 254620311, 625361562, 185081770, 928948996, 933759802, 968531397, 786043920, 821863938, 980079585, 864979196, 849602257, 351894446, 1241799, 757388707, 354558357, 492693747, 73753629, 926151777, 597923321, 591575979, 75723669, 842913653, 881672474, 939947348, 98716777, 269610203, 634116871, 613018587, 773506988, 590527885, 522090433, 21184456, 170308684, 945177194, 16446624, 284850299, 928273282, 773137990, 587380225, 283999943, 626093678, 65225674, 31251552, 278755765, 234447933, 196594782, 80666909, 40938148, 366301364, 831292215, 986121988, 366152541, 577154333, 827684868, 922826313, 66450568, 354328388, 803661357, 585900117, 861875792, 307980098, 261974556, 908329522, 955819427, 276435561, 298544633, 214529478, 790154430, 753237872, 572127466, 501853700, 883311319, 433416476, 881061606, 397773308, 93542569, 661770628, 64171548, 540166336, 932729723, 566062865, 14523970, 594448999, 449661795, 885342280, 124739103, 328439532, 920855935, 773757567, 314054659, 639936298, 65210227, 308997900, 733567556, 398831254, 571564958, 887868487, 625653438, 173198265, 769040056, 794483825, 83658772, 936232199, 424371909, 329399465, 115830814, 646719744, 357560733, 995707831, 280200162, 26675229, 157753496, 774820259, 166863833, 797879185, 131918517, 979353381, 346103336, 116032021, 638009535, 158615391, 527441239, 752041214, 18154982, 841399250, 857585913, 657369043, 795175644, 666677082, 468431471, 342275012, 726695451, 702688602, 12165007, 57231374, 372994768, 623308201, 935101116, 116000840, 550915796, 281723757, 859911587, 597869346, 170236535, 215327984, 296182567, 781912446, 667376160, 386578541, 990304091, 485498043, 800819171, 312451629, 252600935, 756165169, 161086614, 759693073, 271995401, 623622980, 400076717, 181422900, 43716672, 206474685, 819847359, 222484008, 756039865, 288289896, 905807970, 708398115, 385791847, 260787500, 570089209, 525228390, 782871519, 74290098, 35560912, 30494063, 781875777, 122387676, 969801962, 346514818, 870459568, 602264296, 761899919, 936422751, 643875696, 253982519, 971973904, 262296907, 608676228, 619066779, 75066037, 885580201, 748820652, 410147349, 995866247, 63464827, 267503204, 973860174, 232969636, 777813045, 837760192, 685583017, 93743727, 643993645, 175874157, 318690095, 7025332, 38158996, 599883746, 115692942, 973990194, 777454834, 378516662, 840896593, 594230819, 426496562, 509429025, 199872488, 844450225, 362388088, 263549449, 942382138, 162612259, 970389509, 666946984, 273093500, 322925367, 249049170, 150808859, 708533963, 730490012, 149495025, 615593210, 88132652, 921469115, 714133731, 224987040, 246287076, 30656034, 899365519, 320848307, 156364092, 212105045, 579790198, 588570781, 648669342, 815978968, 936184963, 995086363, 273186148, 472810868, 444284796, 131764204, 441664859, 872731759, 303846017, 480368897, 202908574, 58736094, 940736020, 999670745, 754794698, 806326517, 130774756, 627328984, 3693478, 587199201, 718557656, 868189157, 730570082, 880927227, 589568076, 191538469, 294804283, 40436027, 356185333, 198135487, 742880112, 951505425, 611583685, 258310254, 227217798, 479129908, 208208167, 973067127, 999626028, 955288854, 255052907, 202027387, 883358444, 504542817, 768142542, 304948775, 106772658, 806695304, 95385783, 6788609, 374283580, 8167989, 655067319, 390145430, 474525819, 376699877, 540809630, 822561821, 88525525, 935471031, 53473425, 342602647, 898933712, 271108287, 683083053, 491438956, 377700909, 505897761, 427694535, 59212581, 753769277, 387493239, 840772804, 7261730, 766547562, 492708501, 236901566, 293431198, 923535691, 916568374, 941506609, 662115763, 628906758, 443097348, 249564417, 538485910, 57214439, 649809102, 730965687, 362350517, 172370651, 798107027, 633429910, 753121582, 995146350, 313256773, 507087021, 474636934, 53117804, 341237712, 703380744, 977259551, 547431724, 754470646, 773482784, 894488026, 606412430, 2840237, 567209281, 188108507, 732249740, 770874481, 749229168, 437201376, 251183295, 28781, 536068182, 744685711, 943677892, 446351896, 355389879, 958458977, 658933708, 872779861, 551807398, 6007088, 147065721, 448832031, 610529921, 221497569, 974607805, 444512287, 939573477, 410418952, 755041061, 308074141, 434255615, 250008459, 664677705, 812085575, 755276867, 59331431, 441076759, 859901181, 774474816, 720143193, 74465121, 522337084, 307042469, 971868595, 621841554, 719081896, 132659371, 940587018, 979377484, 770804555, 891781013, 155625009, 898670980, 370870734, 526774923, 961668529, 423546074, 813279549, 672540296, 498808041, 663462510, 46531969, 393491805, 249552150, 858713273, 364685488, 383971632, 476536272, 555352135, 428706917, 263766545, 554886521, 781250854, 839090344, 119786312, 706533947, 547619261, 890420281, 737314067, 838660135, 825580873, 371044816, 510530317, 86464663, 834166614, 796063840, 902820923, 444873940, 65051458, 828757672, 418951770, 83455387, 679930456, 104520358, 980267448, 46436720, 189459688, 657360723, 859715673, 706560321, 440244842, 660687185, 771366899, 149903587, 392011120, 258661060, 704375578, 524522392, 863144567, 514018132, 276476809, 741681447, 837536936, 132543157, 39921685, 499215753, 261448036, 734538734, 671101636, 570237609, 171655464, 343899835, 652176775, 544706750, 119276997, 489763524, 656803756, 97317066, 439123969, 137663213, 149186381, 62228819, 833748497, 741392340, 192941636, 797712670, 6641855, 43603690, 452952058, 332722444, 773756490, 58372177, 866644438, 216707049, 603715956, 167739194, 933963062, 437016053, 614163042, 429071909, 24972223, 576697827, 882370134, 142493042, 56157869, 405511133, 63353629, 263948086, 569513286, 70712511, 957180095, 431915024, 588370174, 299632087, 772572503, 390711213, 227910846, 480231764, 569855944, 824773420, 725095763, 579450404, 8121304, 720955051, 425922287, 721683238, 497620907, 66256806, 220474462, 71011071, 573902770, 21730352, 738971140, 583199955, 788806316, 101725112, 713715045, 339237771, 783740859, 207881665, 50857799, 194667753, 300029860, 376023187, 30563406, 268965489, 340608738, 752208540, 5904370, 443104828, 365129570, 406497834, 891028021, 192682737, 59239884, 208790671, 674327250, 532154980, 249779074, 329067631, 727790752, 47826698, 342757551, 834653644, 495906491, 646442594, 576501615, 406266697, 622239945, 636740626, 39268518, 27239744, 581365673, 393430874, 838249600, 847085531, 625441804, 818401586, 631115453, 19457520, 521630386, 134228089, 871001200, 548940144, 773108786, 408331942, 921006654, 678952140, 372847431, 190492685, 281740023, 523510321, 987030618, 963503053, 92620724, 856097255, 784504031, 196416775, 912593610, 262284773, 940549449, 810932503, 385633623, 806126091, 768582125, 319831748, 354037510, 301454323, 906838760, 695378674, 604563980, 223748419, 122894254, 521310378, 687445015, 793881787, 934137086, 190359078, 921280567, 64984970, 361727538, 313021977, 848131627, 870636691, 270534874, 771572268, 599369686, 456418941, 274735580, 434775909, 550162714, 60241576, 144105415, 332090759, 620743934, 476246629, 911793764, 153497638, 914034848, 613099060, 494623559, 65735533, 99257693, 861887524, 937129556, 222472556, 438278340, 434963809, 874998975, 614814677, 524266798, 498298649, 551023391, 514983722, 267565286, 204597627, 775775540, 351416712, 807075590, 568093290, 526559749, 925175827, 911196727, 965678865, 353809169, 502560097, 644545754, 777822838, 158362822, 471040868, 308675609, 649079251, 357848077, 635765825, 372874211, 501858866, 572947887, 462121036, 522030607, 32662179, 900942105, 665718467, 419181143, 743711958, 891258210, 810695443, 261873050, 860595653, 19982373, 230194415, 995346071, 800718529, 691541865, 855852330, 452491415, 219737099, 804408276, 500014418, 796924644, 601740393, 850873654, 593007926, 63371554, 668278874, 758419691, 435884785, 966642533, 38546127, 29282188, 244111992, 918341755, 76264712, 791462178, 780227568, 196021726, 114628219, 952811990, 419258322, 20873418, 251210621, 152583731, 221882833, 226798122, 788344155, 452391946, 203525739, 286767813, 989650405, 235132411, 537117679, 929995819, 720676765, 48559464, 607560921, 681500546, 653686137, 617560796, 364740095, 487085781, 998868, 871731496, 738982901, 243058973, 98481485, 581681126, 2253853, 285024853, 154964520, 842903140, 155574979, 874233254, 143174759, 420880403, 266443027, 322069289, 130671581, 582032577, 53499350, 299771291, 8914151, 172379908, 98992580, 155698448, 662392866, 46509204, 737658524, 62043080, 591337568, 315110893, 466795490, 814026525, 75741541, 130726291, 87144807, 720772333, 444519483, 813147043, 509066928, 288248111, 930577232, 271720101, 283187532, 339853694, 699220675, 434629291, 826475876, 84215293, 343465807, 345266847, 932176377, 760230747, 287989608, 371815883, 377396533, 993104014, 586068116, 94560849, 102280975, 153816200, 375711050, 962215898, 292474226, 978229554, 19735077, 244497138, 408548343, 363273329, 350654211, 548723805, 655153981, 107356534, 652369617, 246416814, 195779752, 240434135, 714516991, 559975814, 81982207, 525795697, 965056759, 231997064, 726743878, 764745252, 160899458, 76520574, 474880225, 295105452, 341791562, 29373077, 964160822, 740158925, 698378306, 561033044, 89230859, 37197055, 811845341, 323821640, 313625898, 550168729, 607981528, 613374777, 644643249, 911883065, 346481735, 66216127, 234246093, 780839513, 752865701, 253236984, 205465050, 934651972, 794057031, 854462218, 905959189, 614237680, 117593740, 855512861, 975191454, 29553780, 874275503, 732493028, 145798698, 798104887, 184967788, 187897837, 221676075, 350876160, 755311664, 449245648, 599284890, 985793632, 458342588, 916326033, 510472193, 552902443, 362422359, 85144902, 689463825, 21822117, 794790730, 528944461, 107253078, 632869893, 979152324, 690340980, 939195936, 135656101, 360169034, 850995601, 750676760, 590204071, 825092616, 441041026, 963637885, 609852171, 380249509, 345945038, 694400818, 711596131, 526070504, 987900760, 441307741, 740273000, 247256905, 662607293, 834156150, 426312731, 66438980, 589131227, 657444718, 711537615, 934844319, 605276048, 38485112, 308271446, 933469038, 862239689, 259155810, 165035029, 663530225, 751527942, 82005509, 524404488, 847429734, 10783, 891145322, 967483561, 515091517, 687480847, 432281687, 385566362, 316028947, 567290654, 650123922, 853608703, 960203699, 480814442, 206046734, 5437419, 375768717, 735789732, 109414073, 753876650, 473977298, 446372382, 116261282, 313175209, 679884925, 22844930, 980861441, 346127201, 189705879, 509738157, 578998426, 877506535, 996423992, 588667976, 45514723, 445544900, 199193075, 262347456, 516673934, 257348033, 177607361, 363446519, 209859794, 534771329, 470465036, 7116952, 602492476, 532561829, 395311495, 468969870, 770853196, 19401797, 514563802, 668344189, 763964105, 589347079, 463305624, 807386340, 435065629, 928600503, 736699185, 794002565, 847050629, 627694243, 858994053, 750780129, 351940224, 690432526, 160459396, 141985556, 825306433, 391994241, 89898724, 876687258, 919925252, 349294506, 838297412, 191195686, 908947410, 994951211, 963885819, 651292554, 369810369, 147361788, 292864122, 896511502, 244857168, 679644608, 438034863, 886913119, 355944790, 658669769, 417664703, 250658792, 912992170, 463541491, 541712331, 691250829, 967379354, 240327550, 579155759, 147855690, 267274765, 623004846, 808853138, 884463947, 579276219, 225803222, 971961000, 748880329, 973722932, 926263792, 528965300, 678259283, 380801148, 807876838, 939043808, 618629658, 197381745, 688353308, 901030159, 469022534, 224351500, 501331630, 23712731, 245030066, 508471640, 680260194, 642533552, 770736915, 810076051, 201763312, 663649645, 373757915, 120807464, 540727873, 440092157, 204166625, 857559122, 135133632, 895442252, 312224482, 948378688, 353970054, 171287580, 754176139, 396702244, 731435348, 667064942, 912307740, 673057777, 967670333, 387669828, 447397179, 636738539, 250982948, 495493317, 677458323, 811628742, 241391960, 233728241, 721049889, 452439661, 797233086, 807808001, 299208580, 284647994, 618258235, 867982045, 245222688, 720815570, 755675549, 35301666, 730288104, 630523818, 970674182, 813324758, 42207272, 471693026, 924827524, 851127434, 220050272, 38426531, 706205870, 284225753, 511111245, 132479837, 382248587, 577573631, 682132153, 589397842, 352106432, 615908965, 293336877, 448605440, 828307061, 147933362, 958119984, 791383399, 198373245, 91874587, 622551959, 731041620, 463852643, 450463718, 363558872, 548602181, 542470699, 362574409, 967317299, 832097680, 304468285, 823583999, 318113835, 711828236, 292677883, 596338206, 518638419, 377248715, 427813754, 103083603, 795045798, 216417851, 920044708, 486066661, 490993067, 809678194, 403588386, 633206858, 948270863, 383688982, 901905774, 869812010, 15138104, 565550387, 253964280, 182218512, 176566078, 997455351, 507979045, 706506477, 922861836, 868827311, 11263679, 784735739, 88465611, 964414426, 702169174, 324855302, 851556376, 363690345, 347299673, 197829214, 116046606, 342031189, 372249953, 203766941, 503314233, 253295142, 562745384, 847698111, 981695918, 276338163, 471052698, 338695666, 204734590, 98005565, 411067139, 108506160, 147391198, 180909762, 84749131, 501911627, 726169185, 672697045, 61872525, 996432257, 970943635, 381450984, 885808027, 907401963, 226257850, 793049261, 934620162, 658436587, 299213671, 714416244, 966138350, 135567109, 639376670, 660858687, 765816651, 546295251, 765244354, 424264476, 110204974, 380816879, 102306566, 270908957, 267122626, 884201741, 535710821, 44777760, 157623759, 640925399, 866112498, 484738243, 294785382, 257733132, 662220220, 872540675, 609893626, 335964510, 626311931, 512252086, 551472425, 391929860, 752091745, 197255468, 290437296, 346947797, 19281933, 839969468, 180482502, 239266326, 256057698, 573445591, 427552896, 525833559, 694152751, 46418508, 891059442, 16121256, 411211393, 112100770, 217175366, 157192487, 356211655, 660010685, 454511237, 172757944, 607514654, 354661828, 522684469, 137413195, 909908582, 608730163, 235659577, 628794215, 454480558, 275216233, 982982250, 215793167, 552845569, 162686503, 552448245, 583549779, 576480384, 678746668, 65385372, 786689976, 342887908, 240666465, 251265133, 699888802, 425853820, 931424385, 991819307, 190567492, 525320738, 55922221, 763626434, 562308431, 188149268, 429779417, 561926160, 922522204, 60752751, 816376252, 79743893, 627196348, 262364670, 497868391, 452511756, 820005579, 278923199, 791250193, 488757324, 218048007, 540906627, 655433378, 939902746, 780158478, 13787151, 976985572, 953460934, 300436624, 918995931, 317009325, 447367252, 10149257, 884350320, 703619658, 412979409, 823374977, 491373315, 731787088, 586938645, 158092784, 515674111, 487603406, 439164413, 507972551, 617647275, 659268196, 501385637, 323150593, 564773354, 259347277, 231553117, 494979086, 566552986, 952788954, 729665510, 612855448, 515729813, 882951093, 463068529, 137077489, 915508553, 750935161, 599258290, 88353951, 846014031, 597321970, 597861479, 498695734, 421257100, 967632678, 431614574, 88687686, 471864333, 358997777, 845764517, 30989850, 14084829, 455201729, 238537413, 328011146, 717488994, 944999806, 437085807, 964484386, 381695428, 481580260, 774643700, 295410033, 716561743, 549878698, 164345462, 149377376, 783003528, 956681905, 642682020, 828452004, 14518017, 612387165, 684389000, 801371048, 234467628, 628498227, 271868922, 744689532, 518653521, 454753283, 617902014, 799103818, 875707364, 28013364, 702666064, 646894215, 926379770, 232112995, 942908207, 977932795, 163096920, 117899708, 845987094, 62787387, 778386532, 415873382, 309066817, 184416977, 71774910, 236325488, 518699568, 967939850, 511860866, 11915522, 298050972, 843259950, 689719400, 999198461, 766145347, 226180456, 948464958, 931507142, 489599867, 152696781, 223890982, 496896039, 524673271, 489354602, 339418918, 651149209, 254638610, 484129106, 405980459, 780790425, 897262526, 464675223, 954874106, 253059488, 480274660, 858364137, 524623897, 311925174, 955912684, 305933563, 846976738, 505236329, 903062555, 987308563, 648152577, 43822461, 746604529, 566700741, 344744490, 674858542, 922319854, 233132919, 334473809, 725481650, 849816463, 557222409, 695454381, 258829110, 373340778, 431766823, 225541705, 762405364, 135360938, 342416936, 312722261, 68532627, 78776481, 528465265, 856162229, 72941040, 314267522, 872942571, 107728750, 871815178, 908006566, 752709428, 191784651, 196809622, 843098073, 108473300, 800152494, 805756533, 700826094, 390093627, 388871495, 493237667, 103559289, 303794705, 40304595, 682159834, 430314175, 746181208, 560964204, 803490917, 772273507, 962797667, 841765689, 655170123, 128962952, 237713745, 550422321, 369415329, 857331438, 478406759, 915290507, 583779887, 622087259, 829108709, 664813071, 359341131, 726603777, 171493191, 980418549, 933891267, 725810102, 342211745, 940383781, 792644164, 973445216, 821092863, 619138427, 444216287, 966923967, 638576058, 100808977, 857479405, 449404605, 817969372, 671584170, 929424267, 170020163, 617422238, 715678411, 44810445, 536359405, 413330536, 923244917, 712512442, 389509803, 622404114, 209654682, 70438799, 129106552, 492779154, 925841650, 809698170, 561359000, 641201114, 325943258, 646088574, 440024803, 358766452, 548068726, 519006782, 373629871, 660542252, 576266186, 71495094, 353006497, 931636923, 373268569, 299619481, 330698886, 156734000, 360413063, 98658931, 232825256, 138262398, 725232237, 579046611, 148958937, 137841579, 626527778, 554566997, 999675101, 455031674, 601326064, 358314304, 699831689, 257490082, 465623426, 847341917, 934760464, 635991686, 883107997, 172684314, 370578401, 789074673, 962030272, 491554143, 281455733, 885411553, 818184032, 628314899, 397421488, 997255199, 492030934, 339340852, 232425974, 29783292, 764879869, 851666335, 542148752, 6494736, 797783239, 487403178, 186335339, 750551423, 398221133, 452309635, 940369057, 496616141, 698932062, 512472979, 390408490, 16817195, 217319637, 994861315, 46019948, 518469543, 310640983, 142266325, 896340518, 93041067, 954202215, 188408508, 836526489, 715997623, 963513588, 11659095, 776405891, 644381323, 882262836, 292370747, 85044575, 633430476, 341069833, 578589848, 872300970, 122340460, 723951909, 128064582, 199850482, 805507207, 99656239, 787925279, 567965077, 448003757, 670629872, 212454177, 701495542, 278120879, 454132168, 939341576, 3823318, 741443912, 948335828, 541863301, 795701412, 432961187, 171886605, 97107796, 445769140, 329628560, 707409968, 999224698, 658117109, 771582444, 757295132, 572814338, 115590441, 156453257, 242851499, 290268631, 829608852, 21605037, 807141639, 258842366, 891346684, 32074373, 725229546, 863275963, 393862138, 940837241, 539905675, 123203844, 323611060, 341526407, 425085667, 484473835, 427594065, 742932338, 656535258, 176128342, 195354006, 392143659, 750839266, 18357775, 384984608, 272701024, 881031448, 203326467, 966243109, 254169407, 758558419, 282475777, 320767352, 37335691, 290574499, 632450906, 634658342, 441530053, 891767062, 481743873, 73554107, 710293909, 752040508, 831200643, 908732473, 790668174, 81038557, 388153728, 557809796, 682607396, 299234511, 68620168, 258924596, 361802286, 198259160, 487189564, 731607804, 700736032, 110915316, 831772073, 232692071, 237745067, 710433364, 868134114, 989784000, 874994585, 222669519, 702459852, 589884596, 851115362, 490637927, 337749417, 420238897, 709485567, 803170447, 220742749, 198187243, 787495360, 635434982, 276335225, 853828425, 32365108, 470611654, 152640020, 161054714, 198249643, 78780981, 662578660, 180361702, 528394518, 502425591, 201781734, 127057766, 643087522, 704033432, 544679353, 736460627, 7883926, 593232536, 477783471, 996975539, 69710310, 738676624, 222278707, 658223862, 555945066, 463485037, 20441312, 763599068, 812900536, 86556938, 252204241, 973470725, 419080338, 505708945, 459588665, 339945304, 225455198, 826378450, 528327840, 299444396, 991839072, 773338487, 338771947, 623383935, 538475466, 106363775, 547365232, 628548092, 47134837, 605738347, 648987992, 106291560, 221980256, 523200507, 965884214, 759768951, 76709675, 679456297, 931526625, 933216338, 301815324, 832823058, 606117601, 221420167, 10548972, 530617791, 414497279, 647564830, 944119427, 546691527, 316065823, 937521332, 845613013, 991565766, 519280202, 607116, 954802639, 374037903, 703570552, 384702657, 275403084, 352635802, 779476996, 133906863, 416519939, 104268837, 404951765, 213897688, 896387122, 527524538, 574172884, 955838585, 412537002, 457463173, 31026317, 629493478, 578270546, 603691598, 847509043, 497403161, 919832736, 630213917, 643054114, 293709087, 925920424, 907631341, 548250862, 465666740, 183004228, 239365294, 292955572, 800050667, 469765198, 679791100, 657132279, 711335152, 834242899, 332590223, 165917787, 310138863, 289435702, 506957605, 548272653, 786219249, 679107298, 858154666, 786119787, 181264058, 702806540, 940676074, 512792268, 90291699, 312516636, 21395487, 498814781, 779394649, 65101442, 724778716, 375498767, 186776123, 866414492, 834122705, 651679498, 175972123, 372543927, 199340165, 728062054, 772977157, 642930141, 204836055, 419938520, 947502744, 940938648, 115474753, 327217895, 443693831, 613767859, 256017546, 946223435, 344821315, 532901678, 294400793, 585018509, 713232001, 294718236, 6604611, 871453549, 725588609, 671906751, 508535337, 436042213, 533138575, 427394779, 244517888, 265546691, 492251145, 168528713, 548950248, 37421263, 488740127, 541883155, 673257506, 706116237, 286735764, 907267316, 73461589, 242969308, 726594637, 759509243, 19596228, 894406542, 92326761, 861090808, 107631283, 847962342, 766597292, 111064665, 177903041, 543725064, 446736464, 333475413, 269924800, 924269604, 468116131, 15159968, 913401615, 325819403, 517114607, 339517032, 640615986, 275754841, 297651573, 717619897, 254009548, 268973500, 475914602, 581753749, 906017539, 553176307, 551681859, 466202545, 907841782, 12263599, 751312917, 753709204, 665724840, 342273595, 552807861, 247175554, 348280801, 513777765, 703272162, 511351141, 543728051, 570595700, 235289496, 195425456, 961560427, 849529968, 776968083, 530426585, 516213521, 659649439, 419474259, 13753376, 317080555, 165822040, 432462214, 8520475, 803241849, 79555172, 461899626, 324760900, 404082933, 545342364, 520341263, 443948246, 290905024, 345746050, 707095170, 181723275, 6231717, 588973474, 889315921, 656596240, 94745510, 205188822, 230843919, 34998164, 114361270, 293024810, 607016839, 689083698, 602973023, 391425837, 100149918, 235287044, 429560791, 715387229, 539441598, 378428006, 886364144, 720245379, 373699332, 216546382, 519825327, 451916479, 520887414, 570909662, 293022635, 420188451, 720053908, 850161418, 528292946, 338741321, 755107047, 418359735, 664275126, 446867928, 113644725, 432529794, 551642148, 816414323, 517829021, 34926449, 623573096, 119428120, 607285072, 457342328, 986211441, 449717684, 924910102, 616201860, 148232542, 48169620, 678272581, 609469509, 493820714, 74781518, 823667718, 529447434, 518985610, 89487991, 293815276, 493643004, 581798398, 442491172, 725952351, 239887529, 337796851, 298372419, 703980271, 27967295, 927193681, 817399102, 259552796, 478359851, 391409152, 677786631, 768457344, 260120677, 841232466, 628570582, 542297667, 926281487, 617845452, 84155835, 389073684, 208927989, 587564057, 186242919, 383603017, 146643755, 82898550, 861585748, 866617796, 786991105, 896881859, 529996092, 534310445, 68633647, 999792316, 596615897, 717363693, 920516352, 817898685, 816209962, 364468093, 144394701, 198130246, 43885586, 764792400, 98784108, 581869545, 17369108, 354651810, 458603898, 807911342, 983710643, 495168771, 703229427, 343560619, 888155979, 560036119, 907375313, 340068683, 108917417, 962759707, 198158288, 120832460, 49367121, 289392648, 504056945, 89923825, 963254565, 553876751, 650932264, 207279617, 116315197, 482415666, 251461193, 468098971, 651390637, 492620510, 916502087, 119151804, 784131325, 256582214, 884903632, 949209676, 961795279, 13441405, 249122745, 237427578, 998808689, 209558294, 530655270, 922489005, 948838299, 655487478, 982709586, 462130155, 369983721, 450284232, 59632455, 756983805, 180429521, 57734662, 983327228, 15167911, 561937978, 749920853, 580123101, 852114546, 698501492, 426638753, 939472389, 324895296, 742453937, 652799644, 26211285, 480152099, 746847748, 85443670, 386749180, 464422008, 85575487, 711766811, 685305040, 922351333, 99872500, 569882887, 86268501, 18549819, 211498716, 433317717, 138087816, 429483297, 604497272, 957720976, 922049603, 763531896, 559365621, 489548290, 992844991, 918745673, 263416433, 832085547, 665309596, 899801636, 637808152, 137185532, 352576291, 389049924, 609488584, 433851786, 475927067, 269373942, 127135031, 627836194, 318310129, 177152435, 15728592, 97400048, 482774832, 731656565, 703887870, 792866051, 304850386, 649284010, 359916795, 211822254, 559635026, 135301767, 805043307, 860498064, 425863621, 923502400, 701512995, 9164794, 35100752, 550709987, 479354824, 752910315, 522145307, 254499736, 899896016, 258006880, 546147843, 678042908, 43122087, 965320552, 307621993, 459880088, 884048360, 753709100, 992501540, 318904500, 21148898, 887639145, 933294362, 941728405, 448580565, 792268848, 20028176, 290851234, 687276561, 143531382, 987592482, 326354727, 153611044, 974398249, 246854504, 256269690, 297499664, 941442231, 267773318, 600314140, 401720944, 571286384, 128505625, 984663546, 16976206, 101533742, 86622801, 635233447, 434939292, 361367692, 517100018, 402418653, 80210662, 27580638, 470167433, 679427800, 775778795, 515913989, 877793576, 941641282, 116092308, 572497173, 870467496, 86787013, 787632674, 660931827, 145444305, 826592002, 281427337, 636829499, 586999470, 808810674, 8934393, 97581069, 715297997, 703211678, 236207457, 393225673, 878480663, 63307391, 68191933, 452797370, 175120534, 137434787, 410758774, 705635045, 402578529, 537298557, 387653648, 875840386, 255950700, 508908644, 185968896, 926485845, 215015308, 377917064, 950595092, 971629616, 907758040, 137309440, 765145880, 282319444, 691871496, 3813766, 621304420, 618923826, 882036869, 516432655, 308341050, 86848883, 760117757, 901268797, 990861349, 205420876, 42627082, 882626616, 706533551, 580906896, 707767061, 713895151, 659685568, 298316188, 793060865, 249679592, 576930737, 894436506, 618681994, 559670635, 283073173, 809697305, 11371227, 281797092, 400216302, 470233917, 461118710, 435733105, 224284767, 376324828, 791164846, 257376288, 598725348, 495374903, 325108954, 164005347, 306645892, 584835611, 152081708, 803646608, 951430654, 202171827, 182938760, 783447761, 396632827, 304790555, 908701750, 713662101, 627291001, 800268793, 590377220, 870766059, 943067063, 633678397, 642034912, 510191153, 974420168, 661918066, 284101549, 193168560, 657205311, 874538101, 308264238, 325069193, 552211099, 817312396, 351210768, 107566170, 434918734, 104719818, 469350112, 795834511, 157946862, 535989918, 434657008, 762635668, 725203375, 42066713, 670922586, 193524070, 937623849, 731267726, 734935226, 736274460, 156621147, 38615979, 156310199, 858235952, 864984524, 30214648, 959844199, 30550336, 738469275, 905024698, 618842130, 675193334, 700569198, 803713862, 535681611, 543802429, 342371462, 626218912, 352755544, 536304533, 152548748, 907379194, 576409150, 187035685, 711353016, 290828161, 254145386, 706314680, 497766590, 402397022, 865298714, 678037477, 304928562, 479601025, 680788639, 182183980, 443131224, 167649980, 537362954, 744885639, 764722668, 999154566, 709546042, 155477947, 214548395, 127223043, 269522037, 677997659, 671871120, 792406193, 825887234, 818647349, 902665280, 189194320, 576125305, 738246562, 138059110, 203101297, 166745812, 672497605, 948959705, 793184939, 995761128, 591728878, 722397215, 884320238, 864936532, 59861237, 788737661, 418278639, 604085604, 901995224, 651422433, 678196325, 424895005, 330100024, 434248194, 587041540, 650740057, 96715302, 924183893, 68401380, 942754587, 206263127, 752758615, 413346116, 169213565, 887673874, 459494552, 840567628, 535999331, 402124071, 532613588, 919199126, 211574886, 755830940, 570207147, 560183635, 345209413, 246177416, 448944656, 506866845, 388907156, 12071752, 501481436, 314219589, 578860527, 213099165, 390049353, 71138536, 335383357, 940226903, 36529734, 15114052, 180145835, 381575873, 202097676, 565897134, 936298873, 124995412, 966390905, 180288248, 316161602, 478548244, 852729765, 863597885, 272903421, 617274829, 962580958, 377950292, 119425751, 423861680, 402146582, 190204220, 170066681, 274271825, 627749461, 107135715, 197077922, 860354778, 910474898, 557377020, 681684026, 935205958, 709089644, 606080292, 532666654, 914515856, 670307710, 730836847, 686792618, 150821474, 286655078, 961188651, 887040005, 429007367, 784791835, 545235719, 983304968, 95970143, 110677843, 277124780, 642506547, 146711347, 467561206, 140730108, 326963234, 588711124, 578497749, 466810968, 863893924, 297793993, 323026636, 140874016, 490760664, 560628241, 360503882, 333992763, 929960183, 938249998, 196566412, 96666256, 8541039, 495557200, 452554941, 793899104, 475177219, 118400297, 938058926, 924862593, 314689343, 115034711, 390898295, 826754375, 686939856, 46782012, 281088100, 624230281, 388999199, 530229945, 549070338, 595586238, 536288785, 608820061, 332547298, 124765627, 278116046, 471242937, 950591641, 383740832, 890138659, 488609489, 477446183, 658591137, 324997701, 473216805, 377121249, 817416484, 361978105, 49662419, 557882784, 166399513, 477914118, 922826210, 897042712, 691555528, 896030937, 6375167, 869917462, 270828922, 450039123, 756771086, 580317320, 19089774, 180356912, 749995503, 686176042, 542724109, 922956418, 144126465, 705311849, 194273444, 653129362, 598901117, 335331877, 67428598, 481717815, 945574558, 281468792, 955659606, 468588280, 320144648, 262299692, 247485089, 338817030, 180292189, 984355645, 497345137, 900100338, 689462524, 709266235, 441135022, 258824370, 211137889, 790555012, 188741455, 512866162, 215763486, 573168419, 593633648, 771012416, 158508311, 852815647, 124687043, 257247637, 893383105, 311396537, 817275473, 736442140, 510773934, 591623381, 570447719, 846418265, 241072927, 390977924, 287864039, 60573069, 944756488, 255157106, 866859473, 152409889, 474479441, 222074375, 799193511, 650180925, 989749074, 904286553, 8886072, 110411870, 644341302, 894237461, 11428390, 309280394, 424130582, 653619473, 850111309, 630226748, 904647863, 992688606, 430658112, 458619621, 702078665, 169274879, 275161231, 868881134, 101830992, 341268359, 704088145, 545581068, 436787053, 402388734, 166054682, 378740800, 568514440, 277068722, 322637210, 404659433, 365223259, 696117757, 186356566, 507431793, 867192197, 952993576, 447973889, 984346199, 116986256, 645191826, 343106161, 302929421, 126225019, 385617740, 498826741, 641840856, 533386515, 100003775, 591898502, 618736575, 146509983, 854467222, 742080552, 505756300, 908052528, 800465696, 538069813, 314928044, 37628123, 899222979, 213020674, 844337030, 652504734, 163283176, 699580286, 875108622, 824193451, 487145612, 476593815, 559331794, 991723798, 10043685, 152563469, 169261055, 959154417, 767894563, 103035098, 36094540, 120244265, 823350508, 390428430, 282551570, 413113657, 894951960, 524973311, 507429630, 114872507, 280759001, 568046874, 235574972, 898335013, 762753785, 53311529, 60036793, 663308517, 527054405, 829002835, 122092972, 105274186, 709594046, 212620323, 612286049, 431459023, 552675189, 791288107, 830409497, 890938611, 596692127, 871350665, 701901875, 182066841, 223074786, 78263523, 753971913, 243501561, 962023892, 275241063, 447195077, 340399166, 511568225, 480537345, 550900223, 375839580, 150947323, 129092351, 218442728, 781988201, 672359661, 852480977, 400038970, 969161790, 742086218, 451024916, 173122961, 277473101, 512250818, 878095709, 386519346, 437850494, 432484961, 996622618, 536052018, 675474402, 876671368, 161465315, 907771933, 412548131, 79910240, 438222584, 741393686, 18944079, 108295236, 218539853, 340941155, 714949554, 773667999, 183452970, 543829658, 294367915, 755865451, 821467619, 255221333, 706529744, 327582837, 654842135, 886479207, 255841658, 678586324, 771743357, 24068389, 766735260, 434990094, 506385710, 122791607, 43784868, 894690474, 100193623, 460341184, 100776752, 398560387, 723393135, 807356487, 447496210, 991820591, 402760814, 196069605, 485272079, 143075493, 499239046, 105384409, 700250427, 15929019, 230939092, 986851752, 129988316, 550832446, 397297528, 810729422, 65939474, 100636627, 383878491, 559125300, 38033233, 248577368, 776743402, 300087107, 495750800, 971885440, 133645363, 17731395, 276268650, 274897059, 804875270, 890263014, 680207074, 322496229, 228707363, 360257530, 663558081, 951693678, 548194272, 278678256, 897654931, 418677483, 891133154, 710088042, 757224035, 267298193, 217671729, 495891241, 844740761, 167785297, 934577912, 778506524, 180985022, 997709940, 454441217, 773072686, 364592272, 771545003, 130079342, 761511312, 112502249, 636266299, 45590313, 52325679, 531960421, 127465577, 776752125, 297679744, 5283070, 761591335, 886038873, 301477499, 618580145, 664083072, 66922803, 233116042, 554098257, 555786483, 414955333, 669517634, 125989419, 157108009, 227207074, 732548390, 95813025, 493613937, 124713276, 379093962, 558298822, 904317318, 193875773, 126459522, 899294552, 269799758, 207487403, 990776764, 86123288, 200505722, 304117246, 556013751, 514406390, 831823813, 401470890, 247773803, 678045366, 32253788, 915009245, 416447889, 934405177, 885714219, 923087082, 816470281, 169576439, 830668035, 511269666, 846429125, 362388245, 211289536, 136718694, 172859761, 73373944, 658670386, 118959903, 415722145, 726800935, 101888337, 489800179, 2563440, 438378239, 364413508, 770424396, 798855983, 636818753, 800840797, 526641469, 72236827, 748260080, 820179846, 259902725, 627120631, 870285598, 313610715, 341479877, 742117855, 775518853, 998953039, 737950631, 68775443, 474758479, 787589644, 838511866, 738352632, 442813911, 190870499, 466289007, 258198747, 616572055, 395985351, 564499218, 132834464, 691114718, 518687833, 890326112, 228937212, 808548709, 897932763, 962813062, 276940111, 297606191, 369606649, 988865567, 785365748, 73549608, 122170701, 822156204, 911243952, 837397327, 173197278, 863732496, 184367615, 99621762, 708665346, 307857929, 149939117, 608673864, 254842430, 98454493, 91290981, 799745597, 589492630, 97265768, 811156193, 886114657, 749423460, 549696541, 873291991, 840285629, 611690640, 232296596, 275051791, 323171075, 428883419, 431356724, 369592352, 964346885, 641534741, 517641583, 796196374, 46645670, 40135563, 559872806, 739206254, 866400406, 799613797, 787073521, 386840004, 295422832, 870257468, 523874881, 322354286, 252728385, 426881727, 996824149, 898320277, 927116868, 522806602, 300001069, 353936417, 779068455, 987574014, 865854831, 650020588, 391808129, 46989806, 179261957, 303887068, 899979882, 42356662, 252828057, 409092355, 16139748, 143539537, 479093742, 734401074, 674727140, 803342940, 5092866, 497719022, 595873391, 713175592, 651162703, 792053938, 354847599, 76752299, 516233029, 835884588, 37763306, 504984439, 428765564, 25215962, 198172353, 834620359, 705104303, 82431823, 379258841, 346369174, 846962583, 700414902, 360433333, 824429108, 359169065, 289613495, 760287229, 669668743, 49618553, 694127820, 486457858, 974313677, 85285687, 266714532, 230962075, 42447574, 635963856, 684736727, 497026929, 421762731, 484040949, 647774548, 824412264, 615114854, 211121702, 968243608, 468719744, 308046252, 264187488, 476569298, 93338324, 971316690, 483161249, 858557143, 142010665, 798705427, 295291807, 692790470, 308211225, 233429360, 225910377, 255949205, 914123563, 869398355, 109825072, 701182991, 71171815, 214112881, 745386349, 869703708, 343999277, 70071300, 77745484, 563913175, 245717296, 12456431, 984085208, 918873915, 393526015, 204417163, 652279022, 608397964, 794752705, 186740833, 267308406, 308223898, 478628321, 245868515, 953927432, 936001085, 6990459, 118120549, 611576085, 628125634, 556884160, 862338778, 559470766, 94036819, 983119567, 417932572, 223109684, 758005349, 649522648, 532615652, 252436914, 548558101, 790388277, 983699542, 638670073, 593947334, 209362459, 449043098, 844688897, 131376183, 562402312, 884977865, 149415551, 497884316, 615459468, 811839222, 886477888, 891317924, 700604872, 261719620, 115266601, 496933021, 146822522, 655164013, 713701014, 597600370, 483401277, 434909556, 513728976, 463201226, 615825016, 407771417, 883724273, 781568266, 580914081, 95547953, 814754773, 17318509, 559723005, 436101521, 999386088, 582765539, 98055857, 339155455, 760051370, 756444997, 673644626, 728226647, 691360206, 968537634, 60501608, 283490693, 258033746, 653182979, 102762260, 528644112, 501762981, 19229630, 966459443, 638189833, 514594656, 612349792, 732713009, 56869987, 850689717, 309261027, 862584642, 818347163, 257095350, 979235486, 606023658, 328603982, 966113521, 530927857, 939980169, 630589421, 824260818, 385479593, 596323739, 219122214, 866354269, 498382760, 475363216, 382779887, 957520215, 895988128, 754885122, 234212610, 85624353, 301764752, 394666873, 612766202, 604855333, 837237496, 265414588, 424418197, 64853983, 565311657, 974708500, 710133087, 148811799, 841477376, 788787309, 292706200, 406591218, 139811681, 72293404, 504300805, 381461862, 487104741, 703721233, 314254320, 643671449, 789257080, 786419812, 803636132, 623648068, 604513091, 63802930, 497320564, 556500484, 860767978, 443465982, 463968861, 479871226, 921711718, 359686933, 413734618, 626124379, 60829547, 621217927, 904536913, 310782537, 970046169, 396428063, 659240476, 723004890, 187114875, 508286266, 503614142, 405840809, 216400434, 734491842, 464317783, 782690886, 194569130, 859727165, 955007852, 30402639, 479103810, 166274458, 482186318, 289695440, 673196192, 400419365, 961280646, 933639018, 113668247, 640422632, 132601568, 948121839, 65544346, 280225671, 427447333, 277362291, 443646628, 633170631, 651199797, 947315834, 114832863, 122349438, 931135018, 796933698, 916527108, 717620029, 186865653, 775305331, 483671893, 816391000, 917242167, 627508263, 346102730, 723268740, 422389421, 940107990, 339655227, 186992814, 823528488, 526416458, 628879092, 713757364, 516046980, 245381335, 606744435, 402371193, 85103708, 209601681, 103445368, 296907949, 221261118, 186134659, 623066200, 400328675, 39709063, 607492227, 24145453, 372430138, 544521643, 440862542, 633393148, 492103206, 788594635, 282212200, 610939231, 379474519, 682494253, 459196400, 672312116, 300239313, 208272916, 578409806, 792254245, 509040789, 634272965, 958038369, 719465669, 293314022, 268190324, 459330403, 583058338, 47301306, 280945577, 4424813, 48883134, 266495159, 70651425, 696020224, 127212717, 287521045, 534079335, 582341743, 530707174, 691444702, 95881527, 687069353, 122852252, 512271051, 79507486, 12205336, 973585707, 211822901, 293700580, 694682840, 160848923, 882311150, 293074048, 278311532, 47457403, 11308932, 812762083, 999716300, 792117431, 221969106, 780851782, 963106673, 722535177, 285653424, 418288679, 570645569, 252285324, 510882755, 395556202, 847333439, 827716202, 653317475, 201262645, 86458063, 729903796, 904801989, 554766780, 787621901, 165911492, 944089401, 563747516, 715065293, 674549506, 874154689, 719747207, 845640254, 168673404, 654612124, 595090803, 109729317, 79874594, 592026188, 422135348, 474866894, 937361390, 657835523, 448870312, 29946161, 264282461, 148492267, 424809599, 332374319, 474604207, 754679284, 831679618, 101878899, 444519095, 836391952, 256093637, 136498614, 718771734, 333267340, 274473770, 531431436, 188302777, 742103853, 808612287, 170359912, 29938293, 694305511, 90225800, 81855939, 220143015, 640868828, 170331041, 966977056, 937646925, 316656258, 512608826, 272693705, 795826232, 498598424, 451764022, 215064152, 484833129, 643115227, 62200391, 727574001, 612898528, 898584927, 736414201, 331570493, 987679586, 866471117, 939426280, 299891604, 378839316, 820837574, 56807948, 398133579, 853100768, 813762903, 392668730, 926072273, 651921464, 587715585, 532989545, 39049112, 736832506, 879825478, 705323065, 553565677, 158520365, 430799821, 998151157, 299912253, 61493738, 723433852, 977806314, 358738063, 58194883, 778493406, 607521919, 536231249, 94689336, 145026363, 930253920, 703079718, 562922789, 441192701, 197517637, 730872253, 358339769, 210332173, 402200276, 316928630, 16782443, 688244225, 539286661, 210844423, 980606374, 649510878, 76982253, 137128698, 599593435, 268743499, 91281782, 119456125, 182157425, 731309525, 707281819, 500882961, 460892422, 280182596, 546527895, 326011002, 561693409, 298073939, 189682649, 98317846, 281712763, 366063920, 123114543, 384733504, 787394372, 694971366, 906774484, 895515314, 672798385, 401138821, 555145953, 69919813, 835184299, 932766229, 911291137, 273114228, 496042764, 146647560, 832531896, 779802563, 227984263, 278758791, 281391753, 722424255, 514968527, 646960796, 631664385, 402432086, 605664543, 265843369, 633874715, 60605905, 933698861, 648195180, 105943118, 210079114, 30722450, 932818218, 6806061, 485108560, 339047735, 473335724, 694965290, 397043307, 930267568, 289327128, 664313552, 937673181, 75001781, 252811390, 906808175, 167288349, 958989077, 802107908, 545911814, 688742061, 437523174, 988682091, 9185235, 385807300, 687092218, 775939519, 9701255, 486283452, 726155603, 81997954, 321483390, 849897958, 99185707, 885526396, 280195968, 155883301, 103038704, 86190311, 921117210, 409805786, 751879756, 223211940, 805683, 813978255, 784427529, 707341533, 551144808, 499537042, 347425336, 375401311, 386731936, 948851846, 486558995, 424115424, 932264704, 635773051, 230361739, 995844314, 430964823, 880322385, 18286088, 800702343, 592755527, 831367935, 380472951, 899708426, 420373622, 125948131, 673372304, 728595464, 975926981, 447185283, 177734633, 846991380, 190254625, 568788385, 325540146, 937840048, 384610643, 166851689, 286243544, 365836590, 97886250, 552146630, 454738710, 644211126, 181330995, 111885033, 108440002, 872053254, 63019879, 519991297, 181840415, 808075722, 621751062, 659644507, 569993199, 870215689, 535442108, 361851037, 443435351, 563750096, 559921214, 674746772, 87508191, 774169461, 562169520, 772684120, 519139212, 898795140, 77530584, 357548764, 506682846, 449878817, 305957786, 529271774, 888875211, 836835575, 476947995, 617974836, 632537446, 538755481, 439418103, 278657276, 758604462, 280183787, 814675245, 993797762, 580046804, 98644024, 281429373, 572501592, 568550600, 699090176, 956674011, 722933097, 356590657, 579778088, 642852335, 200400476, 521495397, 929868264, 86526715, 408538953, 863824741, 521972422, 335251532, 292776903, 409108511, 274003485, 253316349, 963958747, 581959961, 29772770, 452091097, 71673087, 321627320, 463456830, 799865432, 925717467, 326201804, 608835477, 62568450, 512972143, 514779244, 181065212, 403936102, 926769124, 529925405, 368381114, 334450966, 107376087, 689357146, 954798191, 275946131, 25036765, 890499872, 155383167, 642347076, 303123075, 523597006, 76854076, 596607091, 280197367, 687927253, 785176656, 865005338, 730641284, 525001451, 173984413, 160176549, 901419018, 262581049, 500555859, 116809533, 225960356, 456613724, 296092730, 992365924, 244844204, 142172453, 917870491, 142707768, 977233867, 565842459, 139683896, 385077792, 714693345, 638182261, 569462466, 380924763, 539856931, 63906819, 483266220, 59016568, 137897888, 488019501, 579448255, 189167580, 435667312, 255424552, 844281394, 634226982, 238558435, 453349495, 140283082, 257611234, 205072866, 456137721, 859300895, 222958718, 807827549, 506778487, 276145765, 936269025, 13094580, 913665693, 461659668, 559829887, 264939621, 939223609, 850624553, 261418401, 614828247, 949597074, 712029187, 374461380, 817084466, 326586141, 994679150, 436751250, 50328831, 280056935, 880398265, 151361575, 337331667, 871115000, 395119161, 589206064, 517061126, 578460341, 898867625, 22979896, 122717693, 284476462, 225662850, 65535824, 44979262, 669831158, 552347673, 412046873, 206103278, 859132687, 876682412, 422866463, 468806533, 220657598, 993268289, 942010858, 559152341, 974651478, 882452149, 650723120, 33557292, 665177230, 321224158, 200309272, 756582490, 689497245, 104024116, 817938258, 348510063, 580546137, 386620604, 751068013, 616410956, 146690834, 790472121, 226261268, 434012133, 572664132, 218240757, 805027139, 576516934, 812721752, 146247377, 734339050, 511310520, 770607483, 982400692, 318265418, 708969267, 210713394, 747009855, 96758460, 813505632, 850191044, 400085277, 450514458, 662534224, 282271348, 842977941, 822542529, 944200806, 701172381, 689566738, 730676237, 387000792, 808429723, 898780076, 952929389, 595343852, 555576486, 947426559, 361563077, 835522989, 808692727, 443570544, 420194199, 855946200, 402691341, 504258546, 120199612, 291323576, 623560466, 439830188, 460841327, 146419861, 197569559, 403239284, 282791035, 415889045, 533893985, 991856761, 473183641, 239148370, 449243795, 219621224, 288468785, 488518146, 970860683, 522444597, 670780186, 200011917, 214506895, 582059137, 576032728, 500410309, 168924222, 989392234, 139944546, 132394384, 978193542, 476972557, 308589741, 288725694, 22847054, 106101507, 962793883, 290938089, 385917353, 900829000, 248762421, 11791982, 169917357, 872660469, 26556823, 946032235, 41753920, 619242989, 953224336, 152767626, 501662180, 841415274, 665276193, 979899081, 401274923, 424624359, 941765157, 853341231, 649373594, 305468564, 482757190, 655203211, 165298607, 141324533, 304861319, 611447351, 782004574, 299115955, 338350677, 405066184, 807953454, 313808299, 859438470, 440156982, 361709250, 539377052, 757279914, 777266793, 148350016, 859998426, 959625213, 743153679, 498595782, 787155040, 877133176, 186846300, 464824019, 79914424, 56242351, 892988437, 765487844, 673164505, 403977119, 664626209, 346238401, 470525425, 833097299, 615997794, 957401413, 283285558, 440848461, 8399075, 505290976, 484099279, 484187256, 545682286, 493405309, 76689302, 162316136, 192589506, 864501480, 659291493, 388806197, 838354463, 294991402, 578572921, 537909152, 307083785, 318275820, 540687888, 275375855, 629970610, 249011147, 102780953, 52236087, 981655854, 483734502, 909294233, 151100412, 458691221, 608969984, 698885184, 206915352, 648558813, 935240478, 72092342, 141096853, 391941027, 828634978, 507258277, 853272672, 199178206, 591810747, 532137411, 584781853, 47401537, 41962248, 450110140, 566635298, 666336180, 427521789, 403114804, 851561375, 38108005, 958227972, 103985448, 665329527, 711998089, 624804277, 123144328, 861494365, 923555838, 316561575, 73112318, 553513726, 637189926, 901459400, 491842964, 272671487, 806862487, 54259391, 395310176, 524758784, 241092550, 468448190, 540317122, 597787319, 150288741, 556711944, 791524086, 117069820, 197568241, 700447093, 168605705, 28374871, 927673852, 673790500, 671668435, 853694856, 352425522, 899192471, 281204898, 734617120, 948506100, 473197055, 163828106, 820428627, 260886750, 737249041, 753983710, 3884753, 78594674, 849172311, 285753317, 895455150, 859699408, 357396011, 535166102, 182612001, 265967872, 851276658, 706372903, 283465384, 733635062, 396950739, 43984984, 836173778, 885948132, 690824723, 194394286, 651804245, 210353612, 265803880, 743936709, 927415504, 864954372, 642465704, 898676552, 886186709, 436763594, 362780573, 391041051, 470607578, 262233470, 903041845, 133735376, 489191982, 998547523, 27652947, 783737071, 401345016, 119127545, 508890526, 61015277, 321082093, 852614390, 206127189, 733359959, 897330687, 788781871, 968452968, 558797781, 220470247, 214630945, 790097153, 439440307, 659734895, 514676779, 641917220, 115534930, 390835960, 862193148, 658379522, 111359714, 143245618, 360107307, 264278541, 318448268, 225565524, 218730490, 777852170, 633290867, 866992697, 540023948, 965074536, 993680498, 207133535, 467228851, 180349999, 900775931, 610306280, 159233872, 473480652, 342314649, 614887730, 431783792, 496696393, 29908671, 173457058, 202122074, 163346497, 366867335, 66902517, 158087753, 685074338, 527859820, 198564518, 526866460, 556979800, 730388489, 414014199, 891997055, 578625819, 619609667, 874627121, 153139360, 989676781, 522934404, 797591505, 338399344, 407737324, 307218938, 188690268, 594211993, 458811617, 799255629, 775471245, 324359247, 882041427, 768650821, 252903005, 787787573, 617972820, 995514339, 633654332, 701765313, 713039822, 87446268, 193900402, 999323167, 965139224, 36607231, 333802067, 727854417, 268523815, 329135209, 239582147, 381534141, 890517570, 198841525, 881743534, 702519157, 833637200, 107243190, 804397429, 620758752, 429418348, 386751777, 585896569, 116163531, 232038343, 803614108, 818952210, 491597217, 493072755, 589594082, 188579563, 640543833, 783221787, 521260747, 792818941, 451467285, 484525434, 941539729, 822264954, 146263828, 383821340, 918736606, 658416986, 270743634, 149405098, 676739394, 907622199, 663173137, 787080784, 51573478, 928063813, 23577438, 952857803, 840834129, 333843068, 399449785, 746840974, 389378643, 629716298, 474645550, 474327825, 506939329, 287540342, 384494716, 6724757, 678168805, 374595830, 965575102, 869911634, 796588508, 410483115, 156057859, 472464795, 215765312, 229594686, 425028369, 195609848, 639246418, 654724477, 991893318, 406547473, 658449026, 249836042, 624258042, 962450580, 345276507, 114977698, 397189875, 39210639, 261961702, 19922704, 462006134, 253775662, 716020669, 676370356, 291245504, 960084667, 491598862, 212657510, 806579056, 105036221, 636546316, 196571414, 419816858, 448517063, 606217672, 785031508, 911900146, 512677765, 296288986, 489237442, 325990582, 409185420, 138458587, 277277397, 408680543, 258125428, 267634801, 403816745, 77744183, 157651254, 679226105, 504509112, 818013600, 877610709, 93971425, 554621386, 592209523, 155760027, 190400046, 927205397, 903126226, 161285447, 183971491, 789922636, 931012327, 248629429, 176878907, 257808082, 249527415, 371956403, 241037468, 152924225, 722972608, 482649258, 43460375, 689455938, 729609068, 454676862, 842302877, 768659955, 389714771, 829236888, 329728402, 44096246, 278892856, 493815342, 980767242, 549726119, 990616399, 580189582, 878159607, 156691724, 190162314, 501252274, 370175027, 461008470, 542213141, 707042594, 579976572, 692183334, 959909283, 854370156, 22014570, 981895971, 440586600, 93075295, 656437670, 594323810, 572789999, 400083985, 563373806, 553169844, 452408531, 204625031, 955467420, 885156137, 4148912, 349626492, 312827482, 423992682, 11766159, 461029332, 400777966, 950449571, 976546146, 34463069, 39309823, 378406109, 672800035, 59679717, 67965546, 243852790, 148970896, 134800315, 265325214, 379936862, 870113415, 367778957, 562312447, 175975630, 373734152, 552489772, 906559782, 252693955, 533540576, 810456105, 701933657, 632680742, 471843882, 183013602, 386462463, 709626567, 398828143, 830766766, 372771733, 652993954, 549605009, 508898474, 824402992, 355984656, 157024012, 606187677, 278042694, 293653566, 193616381, 964162028, 133409744, 141453454, 800167118, 154434188, 342037647, 904755435, 374627744, 261093415, 355894787, 406911200, 254706803, 323842032, 564346777, 855459930, 325598257, 67678944, 75542870, 814492770, 95719053, 505802825, 607430783, 210145986, 795176609, 260802953, 450174908, 485288373, 695421347, 690795291, 137332113, 639135334, 174731275, 408526225, 549383441, 76267145, 10513997, 215404587, 172191756, 875239315, 868414794, 500083475, 329244043, 231027355, 332428508, 19882077, 126017819, 335591927, 419301485, 878281751, 10316622, 174443791, 65670063, 104659980, 53729298, 918465235, 711355706, 301858414, 114970119, 438475400, 983176543, 683944511, 767973292, 466515125, 840427575, 280893391, 155630691, 51632683, 753457153, 627760393, 858438060, 207174694, 280291183, 827263736, 301771431, 294631358, 607258852, 650851805, 239971772, 82762889, 625743684, 232618702, 831443410, 14651014, 899694609, 486237416, 428899689, 874505863, 453092262, 132429360, 827329945, 943929531, 288920475, 497848537, 558775524, 600300099, 611869888, 775550483, 344393147, 280957587, 286273169, 432896782, 793955994, 814012815, 67834181, 323323729, 43586184, 696008712, 769104606, 644975254, 165565500, 136846454, 209943615, 254872920, 19508611, 75199602, 319882877, 14112144, 765947072, 940472402, 308681695, 12372686, 135836747, 466319866, 516577454, 343745985, 859210910, 704032806, 500075576, 741552382, 127920204, 620481562, 510506122, 162294227, 230173828, 11915207, 644944304, 235911912, 729852993, 729488812, 55022742, 44136831, 970720020, 585741149, 937255067, 40483747, 121356566, 364068987, 85840922, 210537536, 478423125, 601537188, 385019704, 869394656, 77797683, 958014334, 497076998, 912954075, 390665010, 675422128, 161122690, 881148829, 490925029, 21763250, 126393392, 234444354, 733926071, 634977018, 648224211, 916120796, 791249833, 250670908, 537286097, 886604619, 615354208, 826315318, 341511576, 658324204, 67068859, 68369736, 149076397, 338006346, 789187903, 184291585, 129119252, 568237836, 13007766, 607543034, 964929741, 928877897, 643457335, 990300097, 706097610, 921676398, 366595341, 55248152, 577069242, 448707539, 600450475, 797508494, 307770245, 781029846, 831052721, 891106871, 324683315, 672496770, 671775791, 439960983, 394317602, 197248500, 466387312, 394328959, 571232056, 561432695, 766384733, 328067744, 859004915, 706214966, 104911706, 329652750, 14645417, 739902065, 923689145, 239475499, 97039748, 730161821, 746435983, 961377058, 327658035, 305836934, 129613515, 321045040, 672023221, 177240701, 400144154, 252806724, 873274100, 325461001, 51470506, 640400783, 542118631, 408452566, 959177382, 164960210, 365044065, 403965535, 452063481, 292213926, 33250847, 452032557, 123264103, 542071128, 50051980, 261234333, 526353023, 696881676, 992039601, 185095880, 632291615, 360526737, 477301076, 647280355, 423340967, 71464984, 4370333, 809508931, 16805168, 854014939, 897483449, 222448786, 964013900, 37582995, 16237059, 858430630, 789455844, 484682559, 419087361, 357972393, 748531263, 331802866, 500998673, 710740220, 510956632, 12968869, 2457460, 419490069, 826560014, 972822578, 702945890, 300863900, 259329619, 334762324, 846734270, 30582268, 947029436, 312943772, 17413051, 122223946, 37184755, 586453854, 648747796, 270996118, 162228000, 735696328, 863590173, 970001909, 171757419, 443601773, 549887144, 336993982, 526913247, 75510985, 316850159, 496550228, 420476641, 827206944, 289245175, 974159342, 486292619, 318294379, 75857075, 849122025, 620979737, 384025548, 367961180, 344405454, 242270512, 169773341, 804309014, 122125272, 544559192, 456934312, 321420288, 748119561, 223813601, 641353842, 111131546, 979280112, 473914070, 697944513, 274639152, 209073430, 804645554, 245509193, 413503764, 495141224, 367256067, 945013390, 320106519, 750625974, 634019662, 208581772, 386658226, 554641035, 787019973, 392658766, 16326572, 872982162, 177718001, 244288784, 530954950, 835482687, 539782142, 900616050, 539669196, 199666457, 322980485, 926273302, 544771120, 135325030, 761024576, 795503016, 76207964, 381402907, 662034853, 977760805, 976587707, 131859667, 351208985, 199024610, 938772774, 624875619, 694279100, 332921105, 970882748, 950484158, 965786009, 181953644, 274663967, 213404115, 82100629, 945530731, 57215758, 533194157, 354358923, 953898475, 254885148, 532330037, 648936573, 266685066, 850610757, 407248787, 598677582, 132820345, 886734627, 385841906, 559646192, 652895589, 762120497, 36412546, 362395874, 338356932, 85901763, 970207862, 613968713, 635606351, 937240619, 450654391, 425406360, 181014859, 928461547, 841212649, 891603617, 256179008, 932564034, 262707359, 288348393, 238582801, 218670156, 923942309, 195523425, 429388855, 987116249, 875273481, 138364270, 477770270, 944112045, 88959932, 64355289, 817106114, 427338074, 573787617, 135621123, 55365606, 471798345, 368090032, 860968156, 8611789, 782663323, 602187597, 752384715, 86184312, 5625155, 567920262, 121779467, 346373604, 899082373, 934202753, 269403534, 647262677, 444563769, 147573781, 335647320, 144917533, 39832632, 275487905, 320555817, 866435188, 510866511, 896591492, 444214793, 472154715, 638397491, 656642081, 794277569, 312664094, 804280430, 637473297, 45301314, 481587645, 271239182, 231057532, 671314506, 329438083, 471075543, 768672762, 840051739, 461130091, 188240403, 558532722, 355411895, 914856419, 742563753, 113368097, 648348861, 226314786, 768546615, 19402443, 699181587, 621255635, 712239465, 766113586, 397795586, 232652975, 710825720, 509319916, 73178947, 344533111, 571063612, 852746581, 412409160, 198553421, 111078100, 700702763, 638976725, 756799488, 334282557, 924291743, 639014212, 508955525, 25382928, 645023891, 281229743, 809714406, 248756804, 722631243, 135800540, 432621689, 969418309, 290269274, 829665455, 712934511, 714653713, 983614561, 97943165, 12259124, 24526340, 602587246, 885853320, 687426901, 784626757, 960319007, 66752709, 975094137, 264742528, 797560185, 278191102, 790058806, 61216474, 911162640, 716585991, 139505978, 709073456, 465835025, 264389397, 202506751, 889354281, 392054264, 932802992, 657004412, 65890320, 183530855, 435060069, 636711035, 477674715, 470871791, 351806579, 264433379, 655614303, 286408114, 313860845, 197318084, 118124628, 824756117, 318940936, 347282876, 350891511, 546174491, 303721743, 257135980, 781322631, 902316906, 755840387, 58134383, 566928535, 673518717, 95429157, 261127211, 407234842, 810914875, 146212220, 200876402, 206658710, 989114328, 290388605, 261466239, 558571125, 515515030, 669005425, 528841015, 803731628, 822320269, 996343329, 612725472, 338963152, 88078993, 849245609, 633506911, 643644314, 536220550, 33483783, 3707466, 706220892, 104832956, 836197767, 697864204, 492862885, 554465937, 342136420, 940377394, 827828971, 459516604, 214586509, 42979321, 787801528, 641962309, 169460096, 356084645, 318546208, 70622076, 240676096, 437995361, 709078373, 693562599, 357933382, 893983219, 62397358, 721271633, 144524863, 816642342, 160385968, 735232174, 1411968, 105931636, 794793619, 933047340, 669160159, 767607267, 788885264, 835921384, 167107987, 176581751, 145698346, 116237131, 886315836, 603966762, 810991570, 9453367, 795564456, 195303756, 432204538, 882013923, 677842768, 769942813, 304833313, 936596621, 106264103, 310185210, 994210272, 379225642, 202165780, 455297818, 356383817, 464778100, 504198753, 720609472, 773186734, 582413005, 27808237, 296611305, 264982193, 186216845, 573451394, 359089672, 693068749, 500425621, 724835960, 996760337, 615266652, 257111077, 629869931, 975649237, 417741257, 652708849, 245069868, 773350635, 254288677, 293257487, 31089094, 791903744, 352760939, 82541336, 763195422, 983151647, 284084985, 641880430, 806868964, 370915770, 798958311, 346456895, 271866274, 569200374, 557727545, 572993784, 971159884, 903304066, 590005031, 470863081, 614195183, 503609023, 374481076, 380986807, 671860549, 222448259, 635642986, 259361774, 716985273, 479255725, 212495884, 421606481, 483260648, 300830121, 407272147, 584515570, 181518348, 864158227, 63883273, 723771742, 162602813, 35647301, 61947601, 833500889, 928563821, 627944334, 6680889, 929097159, 867619416, 43986416, 421672353, 790154541, 311274987, 790782715, 871343059, 520889943, 745744729, 492108413, 303106931, 232783072, 23953434, 463927910, 571268073, 632740483, 769761525, 734972137, 96369487, 989124168, 326701227, 876577665, 169032531, 549756440, 762167042, 146850073, 176765494, 130686026, 93119186, 506971002, 481940117, 735645563, 538209170, 396075944, 55755549, 878708122, 118184394, 448581731, 259355329, 105308267, 101826729, 169626156, 580835251, 430198011, 887446695, 360008236, 240544259, 230260928, 700633969, 830116103, 769075448, 198955490, 671037678, 240604719, 309091131, 462752695, 921904198, 952521431, 740432608, 911067082, 772406257, 526665884, 415206791, 684156200, 554943623, 102145053, 964158984, 355680010, 181401971, 580327389, 650111114, 269128180, 180512007, 733381768, 952958413, 398532647, 41856430, 394329998, 667959442, 657230176, 17789943, 482479783, 126412096, 882598387, 761518773, 781193151, 83150947, 514235959, 663199467, 182335474, 6196109, 45315495, 609895036, 991034955, 389027937, 168103640, 443387018, 382333234, 629802900, 512791223, 54290444, 338353603, 638042616, 334770827, 593136433, 182251658, 121122327, 818165984, 684241025, 669063341, 25137251, 686064061, 848774852, 385498912, 273341963, 54766557, 617356286, 660089783, 727792244, 219854453, 901898411, 266835156, 495202515, 637675213, 486733785, 190339202, 211574615, 998207390, 659346864, 370311928, 583784966, 393408203, 796010857, 747899916, 648991936, 538667380, 317219637, 973944497, 159942068, 654975769, 192111846, 140786622, 771228260, 77408799, 712204880, 461461161, 273556252, 747300612, 725529100, 539522825, 669454309, 936417968, 138812480, 737736097, 297689767, 565452246, 723142381, 770967711, 148810030, 223012958, 335198671, 706545240, 550249279, 211609390, 899249604, 519486499, 213454096, 825477628, 508677005, 911127336, 233682524, 619723274, 731081826, 969255465, 295821945, 619912276, 228116687, 939470267, 431817568, 413738179, 180084304, 707968259, 114881305, 986790420, 389915551, 728536138, 694831050, 311548181, 380421364, 778551194, 318932147, 531912131, 82370836, 12533752, 774190694, 421371384, 499131912, 873915036, 486386003, 109976080, 688393940, 696777094, 456556105, 128481365, 22988533, 37967010, 550763323, 50639718, 476557457, 557874515, 475711120, 141509243, 396160196, 785298276, 432765431, 901317585, 811169847, 42368747, 680364949, 156792076, 986287801, 778147102, 346800274, 143170319, 380645763, 476821407, 142957576, 744088810, 650383717, 57964268, 923563380, 392519719, 272909567, 354654106, 141405649, 675687222, 286761736, 932771102, 941114478, 169110612, 274421958, 991902865, 30912864, 242942770, 314578529, 187187250, 351488658, 407047886, 866586197, 514104775, 45792785, 985430507, 10254456, 26204501, 198673655, 499337543, 990578579, 844246259, 369699044, 533665320, 318059600, 553040062, 433944215, 48862753, 140269469, 854829466, 33807833, 613115278, 952395702, 293021228, 379281520, 661991698, 914081747, 362783163, 790125111, 305328821, 796960591, 403127414, 569762886, 171454787, 367230840, 352357029, 673691660, 14288910, 445695159, 578451691, 39108570, 167872621, 933116102, 215612841, 545998558, 224558209, 128809851, 987119035, 747088083, 170282465, 567831573, 126957403, 848234094, 316966218, 112322451, 497852355, 330774625, 516340543, 559220817, 547600172, 20865527, 302851721, 392429171, 969000058, 987292021, 313074037, 785670918, 687471211, 846199107, 921085393, 892873383, 161696080, 624771715, 12607292, 428961757, 796042001, 140971975, 336060249, 642903207, 45713442, 745969780, 592850901, 772504955, 174085342, 963951480, 265730839, 494153342, 140769178, 356662254, 644152710, 675447333, 559087335, 579224705, 277694315, 848986265, 63855760, 250910752, 346240717, 700778530, 105198782, 662854383, 971023620, 182351124, 579671916, 722152076, 657416336, 332826110, 804115475, 618228642, 746549441, 509759645, 569671092, 511886719, 622410541, 182170498, 494160991, 936594169, 543229758, 518492545, 607628702, 306347843, 737173645, 380640071, 511202257, 48032543, 648344664, 201882304, 892377232, 597222526, 334052662, 684209270, 348554469, 140499531, 350146543, 542301418, 888001305, 475627113, 194851824, 516052377, 866526604, 217116117, 672906441, 932474766, 501997029, 727046663, 461512428, 972606661, 414128952, 73192219, 703562707, 725224176, 886810627, 134147929, 148200333, 594778717, 414924522, 353272920, 577514762, 344755171, 225228415, 270509542, 603824400, 639670936, 843106619, 142210717, 708985706, 102415247, 450197479, 922897903, 165525066, 760481339, 854120097, 754693218, 322926540, 627618300, 258030559, 575535364, 323055072, 336484667, 905254622, 656031033, 498782189, 902534337, 732399857, 4654347, 523240988, 225907032, 989778008, 810561259, 54960070, 688281305, 667688830, 754129205, 667682972, 972258249, 381502235, 134222654, 471528443, 3715808, 510376297, 236326520, 671681006, 344183407, 656474335, 152700090, 654979131, 948918217, 602112971, 923130999, 219362934, 258653425, 365108317, 71904893, 216178349, 630024616, 190381002, 686563378, 500573206, 584209144, 878903139, 379459031, 118017976, 610560199, 84410463, 971706742, 192550040, 609385092, 238063393, 361298709, 676683480, 911453423, 564386270, 130127802, 390825205, 890200085, 842648676, 450665453, 207178760, 531436585, 617418624, 714348098, 379388288, 290246371, 271631730, 449210465, 577442312, 45934659, 791400603, 805882698, 143328036, 160301619, 984552556, 249510190, 594094511, 842128400, 179857671, 799312005, 47989413, 994417347, 194055418, 144109353, 78602629, 895903096, 637965825, 51596067, 501322719, 329777635, 559568753, 104058921, 89900658, 362937024, 919634459, 741938567, 706093204, 863115563, 279933560, 231354527, 154856676, 612296383, 290173371, 971559596, 85715238, 532533323, 848436127, 83078452, 178375228, 635578330, 237449175, 166223478, 383578831, 409300932, 412208639, 431155359, 138620710, 466677085, 400540227, 567544687, 726893054, 826690701, 425361869, 914675196, 755110480, 526348225, 766598230, 890499402, 641742430, 911250194, 888834512, 62472753, 699631934, 956578959, 970714289, 416190504, 524512415, 942142215, 602668751, 331268265, 668167131, 696381106, 298102083, 928288464, 737020577, 58687338, 950437197, 458393062, 906849920, 582464485, 597101185, 656478718, 848977904, 478120431, 801924706, 828929931, 636676969, 445014568, 850338178, 512069821, 521925571, 647572022, 432656942, 178548185, 241570419, 188622784, 601553847, 128386514, 494958848, 487592432, 706676346, 910877561, 103299196, 543292747, 954507892, 198826191, 6426256, 959707365, 344264200, 897003804, 812190849, 780971184, 781844989, 419223121, 973198761, 301843099, 912687660, 904892812, 531536430, 108458461, 979346890, 264146099, 451314547, 468717923, 644917911, 932490502, 434383894, 323804339, 109559580, 466076167, 3383739, 234971728, 54435993, 527053124, 364931975, 307815212, 902517071, 344840854, 34810830, 533551395, 60826611, 766594376, 81284854, 507108968, 300753497, 442596968, 122091827, 799843798, 603721049, 1447566, 753096017, 824440625, 248414030, 720562399, 142075761, 203503976, 815508434, 940244094, 676719452, 833397606, 544564467, 46057189, 914040131, 539516382, 612292854, 809592475, 691943591, 825832516, 624513847, 402394465, 763136521, 427268670, 100123307, 868958352, 953291471, 670779610, 503524976, 620113563, 516428884, 156319889, 654249672, 703027070, 843799193, 579810451, 549139967, 737200101, 447932064, 437130932, 883885393, 749716862, 972978431, 497487587, 414516788, 137049374, 458060372, 615888394, 219050275, 699666036, 839184838, 289125149, 208103440, 957772788, 902557042, 531259905, 155213928, 852593111, 940447727, 586842973, 560818812, 992720570, 72746320, 293026556, 597552612, 671310973, 954750446, 676944790, 261033859, 852356673, 334120821, 370778939, 35840815, 666003970, 539296197, 925382488, 572976814, 92522984, 615240610, 859570200, 123971610, 765789694, 398746046, 193285403, 521136634, 401426835, 57754605, 955259205, 494179510, 88663621, 496026388, 240868134, 952140556, 458508163, 912451893, 494042535, 642686472, 854962470, 144554300, 14659381, 898200925, 193086102, 287096087, 264692859, 66122974, 338233598, 906747598, 827752257, 506642319, 906474893, 833738383, 685921528, 990047773, 38505558, 457384015, 107702261, 574247093, 197244968, 134199391, 482361474, 17490876, 417591089, 687853905, 288976779, 36997422, 53393023, 885766979, 735443233, 236291553, 643519482, 944739723, 233441107, 233503284, 214339218, 438008204, 897774303, 387159048, 306550350, 650193292, 252536738, 537041375, 502259778, 107259757, 258501694, 56842662, 197039931, 886637138, 257582674, 961746294, 276209038, 632443405, 886868971, 128822414, 357401761, 810591382, 64960247, 931801188, 713525010, 282772277, 113025697, 184863717, 725842604, 979510954, 383507524, 768921763, 890132642, 254593568, 52534534, 51063852, 507248490, 503723513, 620075098, 237541940, 436066232, 553972975, 479637065, 988364200, 398149952, 190281581, 916009354, 786321057, 22857803, 816126592, 533715099, 83866294, 664357596, 255082181, 197416420, 290887231, 202754530, 646447940, 101687811, 226098764, 924402992, 692600986, 521340404, 277035101, 382344551, 812984279, 761781649, 486984511, 235324011, 487670561, 559228659, 891968479, 585687841, 301513501, 501767536, 114843402, 198225844, 24119552, 292762918, 590894026, 201587628, 19350439, 972115983, 521075142, 749820350, 816012401, 613570123, 169456086, 156544358, 391764625, 285506511, 600651307, 40550275, 9453786, 653532446, 513028943, 124164909, 959855919, 177074329, 104637572, 16961821, 158024418, 488843727, 825106253, 392259902, 613558132, 70777589, 156216145, 830180666, 222319880, 380010631, 291041824, 969841986, 574202560, 473725950, 757483649, 9450774, 414920195, 171030602, 523708779, 81855826, 885704483, 180672466, 332969228, 392399976, 563107748, 610470208, 343282722, 721964387, 539848779, 394240241, 472217140, 227577789, 829192721, 697445768, 997824271, 275221470, 329271581, 403741374, 619607997, 757975532, 953550268, 7676696, 497434708, 236370838, 733980405, 284906317, 414093342, 94940506, 885467460, 270556373, 746233562, 899632420, 755842643, 956362589, 494203184, 191865715, 642275488, 468154097, 21704353, 270841990, 727431923, 644831892, 569474313, 133303414, 144469359, 416930871, 671546521, 649369633, 357435570, 69931823, 380810623, 525515866, 300917585, 376938990, 907385188, 727593033, 820192385, 533882293, 358033907, 26193739, 612212226, 56801122, 301826650, 5024969, 58647053, 815773243, 574010999, 128457434, 147347063, 61793845, 228644020, 275211987, 513441361, 787567059, 146537173, 774491947, 132806915, 494732143, 33624546, 4519044, 146496739, 996359558, 335238480, 60122521, 324098255, 24446121, 265560913, 489132312, 573831034, 222072143, 500190314, 38432125, 384549062, 248284105, 602028388, 465816100, 702873895, 702736595, 268700111, 831197808, 496482272, 708501265, 963481281, 283724706, 514864554, 169081255, 151444593, 822496068, 990736060, 871941754, 544836860, 399343252, 680366618, 789161798, 568728459, 173777457, 925004807, 694800011, 69095264, 462144254, 920569034, 669946286, 40567670, 133300073, 234471775, 701663084, 963073432, 725723177, 103277991, 68893897, 402174240, 143169525, 223317051, 646082546, 969895389, 313805530, 871944789, 788854535, 60644392, 703744233, 477252043, 470913997, 832122881, 922033613, 94026979, 803825569, 338286226, 906312474, 347626210, 350855689, 928028722, 630201499, 320104284, 24280081, 859200045, 8718944, 102707728, 284283873, 779206872, 709822632, 505618860, 766425734, 202787161, 112177294, 129263563, 764526774, 454262459, 544904511, 265432219, 264173357, 222432868, 592863520, 890286456, 543112310, 593094856, 403697238, 972948393, 709703434, 764060918, 121785176, 608416633, 962652530, 365979865, 325464200, 169067096, 430184359, 659897237, 447035373, 964124235, 990116556, 422693106, 199304428, 319623416, 692660981, 423130884, 826672717, 692011902, 165742965, 225829330, 444241350, 121882592, 243882375, 61492169, 110243074, 314918976, 557238310, 531196223, 716763999, 459054040, 835817501, 372970021, 265884256, 255571056, 523614562, 204533213, 741677154, 351425163, 69600499, 206028592, 690641636, 606126540, 892741242, 841082714, 360557279, 413675177, 382866588, 703604366, 903586862, 960042401, 945486498, 977997911, 814647532, 656074464, 102437777, 537236944, 523491211, 145628047, 882796794, 252942161, 374286573, 927672674, 12298277, 716357201, 416344991, 522234844, 40055741, 492579967, 378524401, 370140698, 989097220, 650918110, 6534668, 892669225, 722996110, 129907380, 770088545, 64571270, 702194136, 732792842, 80944314, 916565373, 706055914, 699824634, 374525389, 81815850, 194685482, 245888924, 721136241, 441829359, 670315118, 149836435, 257929848, 30923001, 206173270, 173681788, 571414840, 988415890, 5447119, 589186535, 373189314, 527058813, 665152283, 140040241, 720478547, 312140848, 627328188, 42723408, 876183815, 427200525, 486392964, 352931879, 434080, 941464305, 753777729, 526801628, 62251652, 642133637, 920441301, 455624737, 42162412, 771471230, 63930424, 12826519, 937138027, 721311735, 496339252, 761663620, 663709607, 395762608, 577068773, 775042337, 385945949, 582086717, 841948696, 715779918, 676799518, 409572389, 576405496, 646220491, 879943094, 915329662, 315500111, 471561771, 595080288, 628062839, 429880324, 137107203, 269342290, 287841400, 187482081, 477737505, 948798610, 538115889, 678552736, 522354335, 827784907, 956678914, 147906300, 353887537, 459810842, 558922997, 825674820, 527004289, 108817951, 156709353, 211279724, 795010686, 680114124, 462603117, 324202392, 801916257, 61395629, 316837723, 290323965, 380040576, 454234677, 303121168, 503566258, 718842841, 539815100, 484979346, 239563935, 31505332, 298614802, 420094159, 832041678, 152354838, 49715479, 649734832, 830541130, 437831891, 129069522, 646749935, 360571266, 989917640, 752446775, 856810768, 735092234, 869356431, 69777018, 697876557, 975379662, 682378822, 416522423, 278698301, 999697166, 518267255, 739396561, 385607044, 515724356, 154627866, 870050073, 83815087, 750834986, 243870658, 360569840, 313791379, 284222210, 726715179, 404310484, 896142696, 57602217, 891106411, 260732146, 523689869, 449907001, 866794617, 4035621, 420649003, 984380347, 697410681, 801743864, 196196731, 754718516, 429321327, 249719517, 751980471, 354389858, 842808225, 262294259, 444206626, 679861163, 244379858, 576299696, 374046099, 501626724, 354681840, 732617014, 203430712, 787777350, 462751640, 911856, 57695509, 913710155, 293707628, 247383536, 521935020, 477091811, 71797805, 40533698, 665971012, 649981171, 450650063, 721727687, 972289765, 555124142, 550064114, 713832645, 900722734, 786680160, 466117708, 300547759, 347817847, 324065210, 126121075, 523811550, 964387672, 407554339, 902265998, 440289703, 398806333, 106430936, 477156818, 423921328, 491197389, 127552265, 876661603, 499045332, 270782441, 35061523, 473494408, 904130775, 810604446, 495752381, 727009475, 680120672, 785480270, 14452254, 99347540, 734146399, 60023465, 909703216, 55438213, 463892292, 323413625, 522487495, 748102972, 688266666, 389450481, 780443169, 966364998, 937106713, 520235468, 118973257, 646538704, 498046473, 215933167, 308251807, 885897342, 139997525, 101578786, 338394303, 152922648, 469852420, 19625845, 876192409, 684375683, 510404565, 901064083, 675704047, 859388799, 353393069, 945985894, 460287303, 977105344, 366658576, 898288520, 916728426, 702778056, 188618953, 892203860, 299781051, 911637890, 418517495, 99364745, 550521262, 846859634, 762608296, 825894040, 962070564, 199183762, 520873455, 708290597, 90540165, 260605798, 730924199, 511614453, 44636753, 586913534, 130277138, 421877634, 408685869, 616691990, 3460145, 192812674, 105073956, 608401656, 664852719, 291452843, 196170413, 776571782, 325679243, 464953900, 472586134, 529505209, 454788636, 388467876, 741800409, 977289480, 509332426, 262458049, 532583007, 517693223, 454026541, 668321323, 607008344, 179252356, 798054951, 751477062, 221814690, 515590235, 796875807, 765677586, 114154668, 375238120, 137208336, 206804670, 626098485, 18361418, 10168171, 802128147, 478378774, 997681581, 876762898, 245624318, 177749388, 574113527, 528396421, 486713980, 890792038, 195332600, 207649542, 684423437, 516679604, 441557836, 714018472, 524104762, 832937054, 646134111, 907917470, 126289245, 209678582, 494171486, 677523407, 615255759, 902714111, 544027497, 319887943, 310740127, 264284716, 27111337, 91102397, 205637475, 362000905, 364262138, 578644624, 151927850, 633559090, 262573666, 517076298, 7277148, 117110871, 115246781, 496725397, 933143239, 681737567, 205294908, 475344364, 376116465, 415766946, 682699307, 684361575, 981132499, 159870874, 740817544, 635630034, 904904133, 218071566, 877064089, 521784042, 399538644, 489208641, 745671846, 165600124, 646280520, 570871140, 857020844, 186531538, 529063065, 739396963, 166353438, 34787921, 477512846, 389441421, 222318463, 183878558, 309886406, 904891259, 340258682, 202498370, 118812913, 793434642, 253023597, 221735319, 671473737, 490919917, 605069438, 549523381, 838292114, 385914951, 619828030, 590551623, 358160928, 69697136, 736425339, 971922727, 201489051, 196698777, 842059902, 924749257, 633041344, 874067305, 957606528, 511425172, 295087471, 981843941, 4487740, 28962938, 663302878, 769076306, 314107092, 734670647, 51840792, 497323295, 904806405, 708969126, 115542108, 689275578, 79374104, 178757277, 797320554, 529526394, 737253808, 654292366, 99969475, 41002953, 517714722, 655114860, 452563536, 15746896, 163458943, 204614971, 663819322, 514876233, 967944497, 546829443, 646170064, 862217735, 106399619, 197754258, 732339700, 940495849, 659747520, 34330070, 715602071, 412321578, 107100137, 278674231, 15336739, 57845869, 720804912, 977102220, 854081818, 400373847, 854178801, 940536054, 754648839, 69208189, 797345870, 520177364, 59840960, 641661336, 449348616, 58107934, 694830834, 12565934, 560217404, 594738462, 7856430, 994356891, 518384170, 46340035, 82422405, 555637944, 679900489, 987297532, 300151486, 860911132, 242510672, 662829738, 586066071, 457689022, 224385507, 823321059, 765776437, 286118102, 939775837, 966349784, 799678652, 670921761, 80093864, 449620251, 410253322, 985478056, 406736938, 104820069, 13520898, 408546432, 392889548, 83312910, 614461405, 947022771, 698400788, 488564685, 681356211, 973696019, 601825716, 88683384, 70107556, 860948285, 857133706, 69622130, 251530987, 877574680, 879457254, 337112819, 523132468, 772787237, 748751626, 448864631, 383483475, 513572224, 151035693, 496447293, 806302644, 540154213, 350649634, 64381751, 804132629, 683578987, 14384459, 744509184, 42281444, 688832314, 776400809, 152687499, 202276858, 638747943, 834713237, 477826038, 219573931, 740264059, 364420441, 850695158, 530627332, 317531255, 287883049, 22439147, 275915442, 826306679, 620203050, 701589719, 525379438, 139836875, 740820692, 671989666, 174814382, 708050565, 564047796, 335079362, 482207414, 533729768, 569230993, 125669178, 198885375, 814655482, 298590464, 103224721, 307455484, 429068802, 456794178, 851668451, 875857608, 796518149, 263966997, 140943624, 704715648, 774299435, 868065797, 931072990, 601941316, 312796618, 613457240, 981384770, 807610711, 619565305, 650344452, 929277602, 527334270, 866867465, 861764059, 861719819, 488717679, 326341929, 787668531, 738391436, 499153737, 711456262, 723586049, 998851369, 843841653, 42570460, 838056163, 366642381, 339142498, 336305062, 883544890, 755043130, 193565389, 795420791, 145330846, 457472161, 892904086, 522296016, 275290884, 17634968, 859877417, 945112932, 366263223, 706517739, 593543336, 90804537, 628606689, 730744448, 710319144, 64120151, 482982685, 2094927, 717600077, 912720396, 11739703, 954521106, 262480391, 722416843, 779388413, 222904857, 660881093, 211464547, 118351379, 50373235, 518943379, 951177002, 274904384, 324138275, 471408410, 58049552, 251072950, 130481618, 878096732, 320381608, 28533743, 218318616, 151004811, 68700034, 828721600, 82073089, 805945735, 456659035, 975507723, 718039987, 986051061, 130222037, 874801610, 194473015, 615186155, 813114951, 1597100, 546938766, 130060478, 795688428, 382426902, 292970830, 660485204, 158642221, 594192461, 621482341, 982461573, 860120920, 925178662, 90487221, 59659029, 825955165, 174339229, 762757844, 549471017, 715812583, 878028594, 579477209, 998856587, 845392443, 781913668, 689873298, 991226201, 442170605, 706781346, 178924456, 827747023, 192711085, 299118070, 379029606, 100192538, 89967196, 671844243, 118116574, 421094978, 509731362, 24306578, 511397153, 718222041, 230808912, 405881114, 679192251, 546084667, 79665584, 842112429, 493675166, 290233214, 748375380, 802189713, 26999968, 191834037, 724380777, 332493755, 991166677, 734291995, 260233284, 368256336, 973240891, 693177279, 165581859, 123191180, 859570617, 906743470, 835075855, 503867794, 69661822, 222858355, 927274179, 707090555, 540780155, 477388229, 748214453, 670099519, 771509652, 733411214, 677869660, 786915168, 57250175, 248211281, 738033216, 39638877, 682109426, 599357741, 145142530, 840090294, 492673741, 940914305, 828060444, 211727446, 144210643, 52605143, 693223758, 517655456, 831621905, 964780771, 408366691, 388581898, 285914875, 175681106, 281276239, 779892574, 146953627, 71740993, 459988689, 281113966, 141367302, 976789497, 207477614, 93596299, 200774824, 370067754, 137667721, 9156302, 537302755, 860659366, 753576845, 106838249, 823383548, 263021507, 415094312, 302625242, 310247157, 464507085, 355698647, 543097933, 944075771, 794377459, 964740256, 983098977, 912231318, 314128879, 367627023, 138374956, 550539044, 469760936, 738772434, 501462980, 71003933, 662899517, 864705054, 541478856, 576963577, 332662566, 472347359, 20612376, 242370709, 285716454, 368647444, 983037496, 411117911, 518147566, 406543544, 286688010, 251118229, 577986439, 39222985, 527357704, 324501338, 168963827, 241608151, 285211698, 29023834, 888351083, 388555270, 422263612, 476302290, 388083911, 60067105, 66862735, 736700477, 348560953, 32943735, 618235764, 6681747, 74938835, 398029306, 758722320, 899032828, 752614925, 430510445, 866563215, 570812101, 284042941, 696809181, 126197948, 845408107, 89266160, 122525502, 48002299, 275629888, 345955489, 698929697, 694342869, 445363407, 928477089, 841438170, 532693559, 200727225, 20702777, 597556415, 275551369, 495372363, 765705576, 244589509, 717633751, 197531471, 490678791, 305056780, 559926660, 301913799, 637644172, 887115810, 431661283, 669072555, 413871006, 291110746, 95569806, 390555415, 773892811, 831353057, 315578028, 343104416, 209223439, 782031792, 483482675, 358164497, 78654125, 467837833, 474318634, 640182413, 243339435, 620411462, 373190880, 595270918, 675693593, 996215604, 328105113, 89936506, 254284832, 846457085, 986692111, 245907592, 15169637, 28398566, 61277558, 564837895, 220825377, 667145049, 764735802, 84535116, 304832063, 713286370, 881360774, 542883092, 184909544, 218269815, 670671837, 981539844, 289425413, 548311862, 523944891, 188665457, 373135696, 576575620, 128500009, 462327509, 639924932, 537872827, 868565505, 250705294, 677427282, 79609849, 687353759, 742815878, 418160088, 245222174, 101387882, 7687084, 383852055, 699456964, 782345528, 827656605, 910503816, 452892614, 760523446, 651710106, 866688800, 457064582, 979337636, 41797901, 919853148, 959541545, 926666113, 878398401, 628539138, 659725471, 115357499, 674574671, 330826084, 958339060, 835217940, 381287539, 488051930, 363745572, 102372389, 452998242, 471798628, 436262557, 235401753, 946994830, 440059321, 487701991, 741945568, 19496483, 235050892, 475667529, 730506407, 71923546, 42601426, 81997691, 679248112, 975230139, 114677539, 37814440, 166934827, 396738178, 356371940, 519494279, 744146819, 706705651, 983543899, 468974172, 114810183, 664787753, 148975155, 770867377, 612057334, 627270188, 678403528, 378298120, 443966058, 610436911, 840514368, 555461410, 176634640, 889690449, 918899875, 318214597, 228237175, 650774645, 746511411, 117941706, 611962738, 909908839, 846852088, 36825623, 169172767, 856874435, 967740129, 898290653, 407722369, 254667685, 459458395, 248397385, 475372131, 860839809, 412866164, 984735725, 703022137, 176870235, 10307823, 6678172, 28191887, 315777954, 951235556, 374259822, 458968274, 651911449, 554440794, 688813236, 75886120, 892203610, 216461558, 230304042, 78107506, 870592897, 140232099, 970463911, 783435287, 688091706, 259907662, 1723434, 730974675, 991984831, 239789220, 856277252, 799275433, 379412328, 107295579, 477552656, 253516580, 426224123, 530597354, 274627645, 210769869, 828925885, 941429931, 263879774, 661463367, 402792859, 106358232, 114126636, 533956844, 171282841, 844545847, 901364087, 161353018, 443103183, 862568295, 17174911, 909055927, 204214864, 197909076, 695828639, 572386129, 977508670, 25530280, 234670690, 826830698, 264281253, 437572330, 411387633, 112705922, 559295315, 718042704, 468883020, 514774952, 275260645, 101109702, 372101682, 483952294, 560644531, 528638344, 680087940, 19678995, 650196786, 580531971, 179664807, 142127438, 78226671, 556479091, 562265692, 636410707, 691959833, 792164500, 845070453, 140470702, 707725630, 612935928, 433939286, 643771515, 413817562, 225132806, 227644393, 946692531, 815770526, 270868467, 870323973, 438460976, 302197464, 322630786, 172704609, 161309004, 776061640, 535150189, 662533418, 378562440, 445806981, 298212706, 48159807, 995585167, 631793726, 939608509, 288393909, 665840428, 876004343, 114615982, 3831068, 263420073, 647265595, 239798849, 786532106, 789656385, 486568710, 769253789, 691580128, 210362537, 728248044, 976955765, 44223350, 152746211, 250943765, 755812039, 667341900, 637568974, 639612338, 139039912, 956136201, 306660261, 14557413, 293959019, 170642149, 293071569, 772460688, 796809984, 963706406, 151463807, 614529320, 559923353, 347297250, 870668589, 363299533, 478531936, 265023967, 566887632, 660429227, 631516417, 997050934, 133422674, 627184251, 572912289, 958701595, 201239323, 547695293, 297687773, 112928845, 569972251, 38154877, 851675268, 994758160, 715371289, 381246014, 865005550, 887215706, 512323946, 13293699, 670467776, 502905401, 346943382, 38544435, 376998101, 666362143, 860916034, 925952100, 140124583, 27872108, 276673319, 167108684, 135108164, 526758550, 811320317, 971703126, 434900809, 615414465, 883060268, 467750344, 701257246, 886120887, 872570558, 475917971, 482416947, 848759295, 759576728, 872596545, 94901665, 246281016, 203157895, 854193270, 902167555, 321552809, 322625427, 841195159, 309979749, 786904714, 421194345, 117452602, 655925863, 78142369, 305456175, 910781780, 956649956, 724244658, 460584235, 269493703, 853790248, 717862895, 432926429, 876885114, 245927377, 725172699, 862491877, 670389196, 784194331, 638805493, 229202199, 260762173, 389136622, 144618329, 28166938, 469605520, 280646927, 685430002, 763091091, 810028948, 865988347, 418955219, 325170788, 810504019, 312434135, 139543470, 614490099, 481654596, 276824029, 469491469, 421156020, 586620248, 194966235, 160496105, 879289082, 147315419, 941226382, 501305246, 637635192, 164899515, 438457971, 368123304, 97970495, 904753013, 862629174, 527291559, 893121707, 318763459, 912913929, 962460380, 898789697, 961097149, 743813769, 625175846, 403149547, 491051575, 970854287, 932186180, 486242115, 723047776, 826783847, 266358224, 993728938, 960988834, 252451897, 99901943, 550797835, 958771990, 713682812, 938405143, 346929772, 168776314, 746083160, 441812383, 418552813, 706386480, 801548691, 517287353, 212858191, 164584640, 539878030, 923234129, 10922280, 768242893, 472019861, 588672118, 916015523, 834298121, 675717081, 412823650, 549290664, 26516143, 120991201, 324624216, 21360747, 5786993, 650007805, 311224221, 779423594, 682790044, 149749689, 740300258, 165847994, 649216456, 1031458, 886385816, 683672717, 84240380, 395785986, 849124217, 967094770, 373760844, 266109870, 684630849, 152445959, 186873003, 89470862, 853106928, 119774635, 499952639, 289620492, 683348190, 976692047, 430342110, 809191523, 559609328, 755478257, 356706450, 209777469, 105932180, 724286955, 710007520, 852941988, 544395628, 218495342, 314865320, 289831750, 326526086, 291675774, 908520537, 876326511, 334577081, 233899955, 979163455, 317044150, 103863073, 335504248, 111786175, 391625417, 751145585, 990890124, 785981661, 220080527, 522988731, 936963084, 67805249, 569904271, 762874146, 751812636, 112930702, 824146484, 246130989, 462670971, 871383453, 292115434, 947400736, 931070776, 381182746, 158406207, 155771787, 686965108, 563338793, 422702573, 73716050, 70028966, 269394469, 128446423, 802410244, 508222934, 66314082, 649415891, 860694385, 107827010, 179340648, 40450197, 86650705, 462551638, 834963668, 850754148, 993254386, 540718434, 483663359, 10473619, 182399375, 395838567, 799303256, 984465242, 225605664, 317457818, 173866889, 80731602, 454264015, 249990564, 890040956, 562590127, 554294652, 103183595, 988829812, 880273750, 683591803, 310388440, 512297564, 915554070, 702071906, 628858167, 61986033, 833728498, 67755290, 997900550, 774932257, 534789502, 151253791, 285428105, 321128026, 913154879, 633192637, 815815109, 286049706, 135041814, 40111740, 992154780, 562130102, 458262125, 618423957, 267707645, 139111249, 679860331, 842524021, 236698484, 32616095, 116627808, 656053596, 950150176, 492885452, 708169309, 79282622, 582979430, 332674556, 514819352, 928941710, 711248091, 837671676, 848980588, 295017320, 554004671, 302125494, 114555262, 868949868, 228582795, 583998913, 899064925, 74538452, 532799404, 58977465, 761236096, 575191440, 346801239, 610837277, 113226171, 773757757, 395621285, 542772485, 309594113, 505657463, 413268486, 938434294, 929776628, 401503476, 338791800, 319962842, 252427697, 707296411, 860168417, 73079822, 221314272, 347165042, 734491872, 682977545, 144021603, 371314743, 812460911, 185239371, 952708974, 519445164, 564401750, 982896953, 746834807, 678970528, 44997850, 764813621, 716412673, 12115537, 297694181, 559377209, 799305364, 545857237, 504710374, 361915629, 478174217, 997496869, 120222538, 120149352, 485161027, 794690797, 558821045, 532323672, 44846486, 262590393, 39322579, 849537007, 802851167, 651254775, 507536601, 682593415, 833218963, 319475612, 761615067, 775874975, 793998176, 442318567, 941487911, 865011668, 650408439, 342643178, 72321115, 682218486, 228295988, 832606917, 925491210, 584310312, 376755700, 690502180, 429651052, 367107278, 191092618, 487921809, 57988459, 92916887, 71396023, 966509504, 85835091, 617579822, 392695015, 169498430, 765379752, 907664477, 842207350, 149814318, 703939499, 309457212, 120197159, 32744024, 814769500, 189670968, 742948442, 576742669, 386362088, 780290101, 760889626, 169851386, 548320288, 418160055, 153677719, 701871788, 582293389, 562450960, 297608726, 187322813, 790246441, 941663635, 992762292, 596320926, 150492622, 868669011, 864701309, 90850703, 663942090, 772621380, 621462386, 616725087, 212207729, 791094914, 325865399, 239207281, 463397300, 759060817, 659693235, 953711389, 563681900, 596969957, 703997886, 453542058, 926059641, 330807890, 981895136, 213131008, 921576345, 739847856, 910487609, 13205346, 372838778, 556718220, 289082517, 907619512, 975400352, 429181764, 694278933, 734941383, 426790702, 434900174, 818363857, 763726574, 313788539, 447471120, 791469747, 105854972, 848649133, 172199555, 436890392, 824745621, 381901587, 912588797, 187288525, 604811388, 195007722, 775431227, 186508973, 570140105, 705692159, 215304528, 282644343, 384618663, 10988738, 888104418, 132963543, 453166109, 747756442, 274227108, 42540266, 298132906, 594064854, 66434832, 895977362, 493510310, 947489786, 460371655, 661442057, 874430112, 33262035, 388237261, 832163198, 100431268, 136292499, 195351177, 1324969, 780044832, 611419335, 564818160, 187724302, 990593676, 288381242, 157120244, 473491177, 965625256, 950831280, 949958256, 28901437, 891042095, 874224967, 525901164, 197618165, 21309579, 540114154, 466405913, 779924406, 239671472, 250475246, 244142642, 788116001, 589133033, 154025422, 187562851, 785295414, 181071621, 161992728, 618228149, 322886421, 788469965, 501286398, 850652699, 135438833, 351931597, 953755720, 17652747, 398382119, 881184704, 161987385, 102230505, 986732276, 250018342, 250022241, 992937667, 238068994, 751098544, 24042352, 467145601, 830366872, 592724538, 315927805, 870849730, 593579507, 757441253, 113248313, 780965219, 945760680, 79979908, 154410526, 535865494, 11545608, 439752428, 757243175, 511261562, 438256573, 122934444, 737557398, 39200720, 198594357, 321273161, 951686009, 433156526, 573628598, 876947629, 275767046, 455574673, 506897867, 119643325, 691735425, 323426538, 193214784, 183992229, 861398406, 675803648, 234547403, 713180352, 569564844, 536458532, 316827487, 52425738, 151805960, 63414727, 94906778, 523940696, 574888868, 890973586, 43342649, 886267716, 971391885, 889621297, 924290789, 119767300, 311239909, 602848867, 411933722, 447215839, 740742238, 834407697, 843148104, 984981093, 80970454, 510391938, 984101607, 677027616, 912878733, 191649526, 956465480, 263944685, 23591192, 753268498, 563108036, 546481825, 635399, 356479501, 471753640, 763377209, 471370339, 650393777, 206572323, 32055351, 197195053, 110233448, 123879247, 277808978, 755607734, 962577539, 226206105, 723590375, 501771250, 447104254, 104787269, 967073180, 671638662, 754866362, 629180236, 450862009, 419493868, 851423653, 199958854, 654232075, 450090313, 617869683, 215935238, 452508870, 902838343, 949247588, 676682462, 393516989, 767117107, 114703143, 506479999, 113032401, 500028936, 388262549, 951269714, 840607568, 792951546, 194622903, 721628050, 494335958, 363570259, 723995556, 639557965, 931320078, 923350570, 520763791, 992088861, 206383310, 668989448, 289561290, 289663722, 672107088, 621625565, 167562795, 488013283, 792176886, 384526098, 930548242, 884652741, 254566485, 256313402, 259698449, 385277523, 528658767, 390283108, 680552002, 97877111, 293113333, 460072706, 257979829, 794651607, 266402210, 814779572, 122508608, 926926368, 248916526, 573413965, 490636636, 4109859, 228664903, 98004972, 583163174, 406511570, 42011506, 227653667, 914008140, 641746266, 136651018, 618487377, 106330275, 136429971, 64570958, 507721627, 306223182, 571936851, 441935595, 685978587, 178969305, 576102610, 859175526, 485167640, 192409961, 559796643, 113338300, 839254715, 54227336, 699400115, 785075800, 667906594, 237844102, 995345891, 913923469, 756018673, 942178052, 215244658, 675844303, 267636882, 319827045, 347096456, 77698532, 397047744, 476467843, 356443002, 632884446, 754479621, 374482180, 69223646, 87494174, 491313195, 103881810, 928527388, 103449552, 374394085, 721106546, 333221218, 989946254, 245049128, 945297421, 323977091, 222251591, 727545645, 617134318, 170718448, 914930674, 659125748, 975930289, 52327151, 300241350, 353852956, 173958543, 393659879, 488258888, 634863997, 980015318, 685557074, 536223696, 393938920, 230068561, 553574742, 484263515, 747745571, 846205409, 371666063, 122082772, 999354148, 359031575, 294993954, 777479489, 512528523, 465662532, 948689153, 416834298, 742524655, 593970041, 391948710, 660631116, 371948441, 489519073, 429928495, 299939858, 541403853, 246593009, 704469162, 649703823, 504252758, 593244354, 550519337, 578061481, 585628251, 18094641, 385971385, 64220150, 655593323, 444642230, 881239694, 162087472, 938323569, 99478820, 348162150, 839963530, 536359880, 365960630, 588658647, 378579861, 888727230, 862133540, 200332166, 240458990, 282661195, 519990720, 987116343, 130824988, 45153118, 214134578, 958437733, 142766921, 591810204, 515124483, 912372967, 140329078, 24244446, 507597629, 913780593, 592807234, 833239710, 698293624, 364818880, 702888861, 824162552, 234558455, 851653453, 21168692, 53990333, 513746306, 1636639, 940356495, 65631760, 97840038, 240935593, 206835837, 971069155, 854266070, 171405348, 125465023, 36474507, 859339058, 983648898, 187793265, 102474585, 8222709, 717669388, 161464477, 918404834, 926306953, 847094092, 209058165, 306266172, 957193071, 168211191, 722343582, 446732344, 881227261, 383262366, 481076027, 309773096, 202086056, 620842921, 685196822, 667209113, 716456990, 201117990, 692352154, 785965462, 490210109, 606540222, 977732588, 636229652, 254337705, 3847484, 434848182, 466403195, 906262732, 203919586, 735199379, 209561321, 78299766, 483798016, 755215700, 335143756, 322295131, 635281272, 422572445, 419746475, 713225794, 801796920, 727946160, 384689809, 504998884, 551998226, 784769592, 68789450, 799197557, 854104625, 189190646, 473019097, 122971842, 236190885, 799868821, 24769563, 231776336, 316474453, 760510644, 53256346, 76616513, 756721080, 198385121, 564683992, 215051849, 41471742, 961006569, 441780151, 827528761, 9602795, 512420501, 148934081, 150133819, 249295285, 390591331, 881261738, 186997962, 70570781, 341497263, 203429698, 136160014, 282330901, 561733009, 853125864, 836359828, 612545552, 733287992, 87997015, 945002652, 888612230, 378400420, 757604346, 965083998, 26004971, 944995371, 700749826, 175635783, 536289612, 590701763, 368265497, 918738211, 789138945, 137095162, 57772865, 758312989, 612325684, 996414263, 644367840, 460047986, 353115019, 163095424, 885055123, 229818536, 169953549, 382364453, 571774517, 618564655, 585528815, 764147443, 921647800, 993807227, 350843710, 162334220, 826528703, 783251128, 570786679, 76888895, 691005569, 684543428, 190677281, 767195854, 276325281, 958185125, 716938398, 449824411, 202244007, 224631449, 321294537, 514957085, 858134614, 285638654, 203351841, 16609646, 843190070, 332623322, 263161712, 597829064, 687478898, 329661606, 257292193, 434082732, 425640187, 495225698, 317278343, 745836432, 255612577, 556981017, 818070543, 687578232, 665084990, 776159634, 736766606, 823857862, 737985201, 386398460, 901590424, 637125303, 931299754, 141621448, 460937487, 457581815, 211528784, 633693871, 870853841, 518128983, 395485638, 288789132, 277708075, 17388258, 945649012, 840719948, 236485357, 41167384, 65676230, 652198595, 201355421, 391425155, 603412413, 39084062, 371817575, 663876266, 405563095, 884788132, 517904533, 256526228, 19062665, 3592176, 875641660, 376746096, 547672389, 558587673, 82917805, 848537371, 440660784, 965924672, 316108848, 60477923, 294699230, 329146093, 253722063, 355434774, 3398014, 839303215, 341459530, 253585983, 869143505, 776992601, 860066079, 597185653, 111720149, 69338196, 826078777, 744552765, 88835095, 885159199, 451940864, 460806612, 888264240, 450616422, 626738661, 455228308, 728191615, 546649055, 519132179, 898192634, 977427991, 812479755, 730128228, 842664024, 946143527, 925480546, 154372466, 790827230, 67770915, 465293932, 762000496, 880430777, 893354091, 297512457, 499451709, 328194129, 796374831, 997919316, 641917888, 889205587, 328215348, 176828740, 213226511, 862215390, 984679021, 799324710, 294999622, 302828319, 373990738, 374129840, 431568511, 340409940, 568466218, 1432654, 519424425, 38883187, 776847024, 632256570, 321707127, 780035916, 570948337, 799852357, 374080643, 477057084, 809167522, 630304323, 233839876, 230712382, 175071232, 422677968, 798665310, 711592005, 319822576, 710188491, 320362319, 784452765, 686887004, 477826760, 947055691, 835098465, 918146476, 761130256, 792094702, 698721147, 847683131, 830873827, 628349132, 751556277, 155477914, 107378449, 45419634, 613198830, 697088287, 544928305, 679103387, 212215220, 395791282, 548555665, 46651019, 36866570, 907111163, 713732734, 941076078, 917750016, 402868765, 517471868, 565386371, 975740561, 749442875, 814008807, 425182465, 762143916, 906359300, 484419887, 374024408, 777690600, 390460880, 837828966, 23241147, 666165049, 681773425, 918527941, 880613736, 773159702, 300393331, 480081194, 43498607, 759544742, 639101844, 325748140, 33476848, 622516286, 193893812, 148583014, 679177910, 820711188, 533275699, 883627504, 332908915, 421398462, 331875291, 72430699, 483215729, 309323352, 317021493, 78935541, 458232757, 122751381, 288531606, 985974513, 338373589, 515503401, 84378293, 83369989, 932527395, 528045814, 168227653, 596994011, 507384935, 85456812, 667206158, 431782019, 98482224, 875505108, 255309087, 906329601, 804065998, 498543560, 68634284, 954617066, 387551810, 87306185, 546954451, 535129212, 98933329, 892499932, 952028489, 732196117, 120495220, 960304494, 433117588, 897766684, 925127280, 118811956, 176789894, 138992617, 735245484, 969856258, 153129677, 802518048, 418506968, 221208023, 214289635, 702153151, 536368366, 713347991, 698818058, 958319590, 532476323, 610535038, 930526434, 202560966, 988089896, 153565088, 800306615, 978704392, 149623791, 690493020, 186401204, 405942000, 369262181, 758749325, 491224786, 492165002, 238298748, 371295827, 918434943, 476794104, 16741933, 952386089, 330720118, 890677933, 240069379, 350551604, 567318639, 497319735, 960605891, 861532265, 544607488, 685301311, 659790368, 750023864, 362331092, 554221969, 967729320, 950035537, 867652413, 796201232, 386787582, 451489378, 665064116, 270493194, 890597035, 952543370, 101503057, 321429456, 464969487, 695170639, 109564892, 421228976, 547988449, 341030724, 605622162, 560431694, 899255468, 999022295, 788482602, 873717575, 574041877, 977226879, 218347592, 969523203, 485883122, 355069280, 629769639, 10926628, 405364746, 150908430, 394474250, 854717709, 94358994, 804998564, 186878675, 329275417, 670348996, 381849122, 21437618, 12201546, 865450060, 826558720, 117538980, 897063894, 870145077, 744444617, 1505988, 620204055, 898193520, 509189725, 972488002, 559684391, 885019942, 923413542, 198886570, 401925415, 307024413, 374665538, 517265447, 117663315, 915186514, 187323965, 799958214, 221061424, 221411127, 37844453, 778538352, 55575344, 506240781, 779158354, 815041185, 45646120, 355466591, 580470979, 457254156, 871296034, 373008445, 541804781, 716128633, 638797501, 914916391, 227075435, 105609167, 564159061, 197780650, 963278223, 970973745, 903522691, 459817186, 480374316, 580157058, 797140001, 905500706, 168535557, 957950752, 521800108, 278186352, 956007534, 954789885, 71254802, 138631997, 16561583, 295894979, 739550537, 184456498, 899966060, 422731356, 534526263, 567622551, 448565653, 735791691, 137537938, 127852918, 956337142, 554965918, 972208662, 531993802, 739389134, 232291020, 955582679, 220033977, 509341619, 813374778, 697399593, 593152162, 977613905, 264059655, 657768608, 722937984, 600241101, 455216766, 485509969, 644837785, 477694213, 845299234, 618077048, 658607222, 374653437, 896673355, 609247634, 552380909, 744772866, 556100033, 236095300, 355564213, 378329240, 372012864, 220777160, 712825816, 996245369, 732550186, 788951988, 930020871, 666281830, 551449967, 484112944, 528550681, 745581677, 137346314, 406382436, 403412634, 694847229, 513646441, 103178299, 362518680, 747449857, 414646378, 260933425, 179711999, 169241012, 725614726, 541946194, 976465832, 515799772, 689604933, 736591507, 202496141, 475432313, 781008260, 573121479, 594173700, 438516317, 310377780, 975603358, 56290528, 914021598, 134769590, 239256359, 416155330, 851591116, 664784455, 525391994, 591590281, 686672144, 233795654, 227624938, 53999644, 792888146, 164383638, 459968679, 86718352, 833261359, 986381739, 658323309, 11737579, 817504074, 696501404, 169602177, 144777139, 559864172, 627884294, 309595021, 540760717, 962291135, 65748031, 299324757, 163785247, 338206938, 600316358, 941642172, 208437597, 400186505, 319749892, 347935210, 724473181, 98100842, 237727301, 333526924, 40377408, 454063298, 285698805, 442726261, 856144820, 290413988, 15209755, 315805971, 14187957, 315258179, 351154131, 144378377, 125983744, 585189712, 211171264, 347136685, 858709771, 559536171, 750391126, 85821300, 402091352, 952407402, 158525041, 33727501, 495194029, 339038596, 255318183, 58553457, 49058610, 851722198, 214503938, 665670951, 590900137, 111546181, 752358460, 40272664, 292697067, 944145478, 877153670, 317847313, 915622423, 15434329, 787727493, 805101446, 246008614, 622775163, 360311855, 898627845, 61675524, 794923830, 266655783, 966647314, 777425000, 154512823, 824756277, 562608957, 118079623, 288366550, 549886462, 215293851, 199090055, 77222131, 862794452, 186941884, 927811169, 965005838, 927792769, 635514649, 515879437, 175122696, 73677261, 464523032, 141940616, 567314855, 794367713, 557435414, 511276395, 396957531, 932402404, 138677507, 962208410, 552294531, 351650778, 30766725, 580915870, 113923456, 731939032, 597215132, 663212093, 159192350, 857833149, 474696322, 42667889, 366651797, 801432304, 290279512, 588891575, 626208464, 194684829, 920576556, 656349423, 546102696, 941748024, 945119542, 302983164, 565119348, 314090111, 573786685, 367175528, 190124266, 349910318, 538293342, 808739308, 266894790, 758148794, 353995346, 348152880, 876960088, 533285597, 716135144, 817515264, 713851021, 115318272, 869560536, 231751456, 117259155, 506269422, 773509433, 74426906, 777642317, 81812832, 107759005, 715474703, 625553410, 391234085, 622086939, 546191105, 39595251, 938416871, 725209629, 53104254, 359959128, 305955027, 913784921, 545482311, 733810563, 538983861, 845760811, 948282572, 487318521, 328407683, 797056655, 981293536, 243892687, 865099115, 499103804, 664116205, 178329319, 939852730, 24095270, 960222373, 680041600, 76710317, 789623872, 710089755, 562033731, 81639211, 458659651, 959010938, 867082417, 310165130, 79334447, 408634090, 544374176, 247707967, 68945894, 238492679, 42096765, 368071498, 193611059, 477115302, 473805163, 438547690, 899828285, 243697238, 192024723, 522691133, 38603943, 436166512, 28440406, 871497237, 478685544, 775607029, 273725542, 257125457, 64907869, 555308209, 212220489, 878101728, 544219136, 431340680, 60842998, 273788952, 995833515, 413543931, 208653288, 222809323, 560386879, 68086685, 47964063, 178975586, 316793502, 485602071, 687493175, 152461150, 503178080, 684681869, 731960440, 246035806, 133002214, 428056569, 738892704, 303347852, 506079552, 624487219, 704189963, 707666249, 598960752, 123055675, 374703154, 589842605, 870010536, 676941317, 757333078, 131274129, 450105773, 175347017, 964580868, 764032754, 595900512, 901091391, 845893595, 978254907, 143318901, 985869688, 863606053, 146188858, 414965873, 543303923, 229881445, 649933407, 39777995, 651556270, 868061447, 746484267, 509395670, 359655805, 539734722, 51465675, 725568715, 189824484, 326554139, 161697442, 41009282, 562760844, 575205092, 929415629, 33353302, 808497257, 946896646, 843646105, 260390076, 365643116, 717038682, 754412904, 199573692, 441567516, 118371818, 784627364, 475060200, 169332439, 358544640, 481390810, 900428320, 719281095, 714052780, 258889594, 755413400, 167226229, 916344045, 60826389, 945690874, 424601279, 856468250, 706813331, 945348528, 681504664, 235036345, 965072187, 133614174, 572885831, 912830844, 328413969, 738432495, 361587899, 620440364, 862032366, 127640705, 569462740, 546230373, 404991328, 100719147, 633497114, 49863589, 854068921, 309912238, 271391788, 948318658, 838070266, 316877287, 820113876, 27322263, 651828144, 180606532, 254721980, 765511651, 206603121, 493008413, 966050424, 492613437, 258749326, 556520789, 633511233, 713655289, 694053125, 91606328, 404513143, 231411202, 653846150, 617202272, 732375796, 231720198, 755823581, 83176894, 759694967, 664224229, 461737498, 549326242, 32083751, 973276505, 17674416, 101693197, 118089180, 607882758, 574439797, 215543800, 764389348, 982087185, 824767535, 95684245, 240802593, 340300334, 397217742, 752595754, 233162550, 762383058, 299671924, 548590295, 159472740, 15855778, 89320537, 9165492, 759297472, 146278340, 911604403, 821561237, 560757836, 78337944, 510036230, 691744686, 563206609, 552920608, 328697434, 62413177, 45783880, 336948805, 630185966, 310291539, 637358520, 361694192, 312039250, 421639205, 573462281, 247293724, 538922144, 311080634, 360762087, 795032102, 992656927, 842129908, 884331530, 13086637, 52999352, 487727179, 250995999, 380793509, 17387694, 749674582, 347843721, 465466406, 650223484, 495489236, 928036084, 964760705, 551054795, 798747354, 705317208, 900959355, 807771881, 185697702, 264808965, 629687681, 23826705, 966761794, 811135667, 575650971, 736815242, 486468865, 443909610, 53484201, 483668779, 404866670, 658736511, 534806134, 709417642, 134686879, 248090733, 545713674, 774358997, 361244809, 875286170, 392540957, 560716577, 582616747, 174541769, 87602150, 252235907, 508537872, 154843115, 662294507, 471043058, 615107223, 990477310, 518447009, 937415555, 213724125, 465212420, 57942766, 254222242, 912372753, 286288162, 375530969, 280391529, 390932992, 709611833, 496611390, 418365935, 524858027, 86509099, 244965214, 416387831, 727600830, 848301321, 908337893, 75325383, 655494984, 155684652, 557272940, 20741718, 671419355, 589061392, 616188594, 490653361, 216692193, 47231380, 616701940, 860885389, 622554432, 587461231, 987420606, 860316933, 298074414, 892395373, 591235043, 666205827, 523415446, 673086571, 815130705, 34106549, 372501174, 906468185, 887151198, 716786509, 778692350, 751733197, 303969924, 257792555, 579892288, 590111182, 633027629, 435536775, 618242808, 339493536, 294365996, 722134898, 82969150, 702442871, 503848633, 948226560, 576954562, 705779647, 948749396, 409733545, 273232691, 371675415, 624173823, 373709659, 399398164, 364732563, 802722247, 619394925, 94213886, 508701115, 284847542, 661499443, 324858684, 830531268, 212279297, 703021314, 346163696, 129582278, 632913604, 973022, 636512324, 935347703, 866776380, 205512021, 106594677, 561019449, 26936779, 544118518, 828516194, 213190896, 551183221, 317671020, 540590617, 560210750, 104709314, 340938882, 879382961, 382307875, 228190275, 548456129, 910978260, 43602649, 807762856, 57250325, 24218756, 155340565, 193025649, 160395378, 733615543, 621376295, 622263607, 384704892, 432336273, 793789857, 233112427, 938008349, 897861734, 820228719, 908352161, 53338711, 779654351, 427381470, 546374453, 375485990, 747510306, 783341964, 573062930, 162879529, 679405606, 923791886, 987425796, 265061380, 510467573, 252741381, 64376777, 381114662, 395978912, 839766337, 337575958, 938662920, 348589216, 805283640, 152236229, 549881241, 950164959, 728346044, 817809414, 156467685, 908116555, 701458000, 80941342, 278841357, 800973648, 272720251, 944042246, 430012579, 403362386, 48617459, 883687837, 914423926, 315419320, 32907210, 375310436, 428336235, 709490923, 61394518, 993037558, 157557705, 234068421, 775399496, 590520472, 381604208, 923068805, 124802118, 345831268, 347113452, 965561013, 599579270, 308491573, 460073318, 769251104, 312285564, 234829117, 993717420, 264664628, 930163828, 990245613, 808729001, 278561106, 546078549, 785163466, 809926353, 17665533, 715819509, 360946594, 157624612, 931480495, 480016731, 992639148, 278649854, 155930351, 628560747, 550300947, 370040755, 317807475, 759092239, 602106885, 216856977, 198402565, 255298594, 567463600, 2958624, 819352503, 70058594, 23731236, 10435947, 187425344, 362984440, 524080825, 251942392, 523053124, 132264852, 907036294, 909109285, 215854865, 439778273, 541114209, 866414216, 945876574, 84145112, 80379846, 846951040, 297801535, 893154953, 821964737, 898425898, 885693128, 479012124, 712922519, 452683010, 851429253, 319750070, 998622618, 476959601, 480743826, 468003709, 873425988, 267208542, 108917671, 888719383, 893681964, 736986820, 995627387, 552954579, 804684304, 518528782, 611639187, 819317011, 260086464, 771893660, 91160870, 500386986, 29260920, 119092612, 415688125, 372425830, 481186149, 771802450, 149484822, 770554502, 263939413, 13309946, 875576390, 455240671, 515797192, 323249609, 606624902, 773440066, 55842983, 387466486, 278657665, 137193042, 99949594, 497177989, 757692337, 3861841, 189020717, 395444865, 448850812, 114342983, 626451652, 260187698, 584207587, 313066013, 362480041, 587028760, 695280044, 341069085, 480813739, 325336265, 321313919, 300428707, 985995358, 855755957, 617947938, 696841429, 35258300, 116734579, 404420479, 972432916, 54301658, 547509381, 963955238, 462373502, 94269980, 883363338, 711551434, 678457787, 937382657, 336249964, 292520890, 432812248, 542868113, 508272168, 359675165, 501069822, 73896796, 421898964, 786987622, 82923374, 44865377, 825598844, 698702888, 326360274, 783823530, 369875318, 724845347, 409418349, 658016656, 947971174, 941511473, 338292062, 684566657, 638332174, 997441332, 936041810, 822180589, 706116180, 992585690, 279131865, 420603565, 163533808, 346150044, 274550273, 652950875, 879864162, 445357787, 88982257, 135923622, 911152655, 123925987, 800392828, 416345077, 917369576, 417384845, 33497929, 570793476, 44780072, 497489008, 890323301, 515047344, 43475240, 960689797, 174828118, 184981082, 555620709, 157691964, 381123732, 315050709, 994609336, 297286382, 37088099, 458774174, 766132851, 15019459, 559459466, 730788430, 934329167, 917181221, 107933218, 463405224, 744414189, 170093370, 746354190, 638805537, 654388762, 451976648, 222128240, 123318673, 874766820, 596446443, 869890912, 811726297, 397525233, 723093456, 99638735, 209490192, 762555224, 780964065, 114963565, 807472674, 468052782, 141820773, 476128729, 896534056, 174413478, 793787838, 71526556, 838758682, 387480818, 4952578, 528407844, 725093427, 929616366, 118184897, 569441627, 244137494, 655405459, 991755984, 372643647, 708119797, 30859937, 406888944, 629052667, 28160519, 683672889, 309217122, 405207346, 552094154, 738106432, 662948580, 674815786, 88294521, 569936812, 47970706, 285914980, 789144642, 930667165, 243911843, 632631116, 607575476, 480088694, 292536918, 326943395, 667344559, 729918451, 354441417, 586075849, 645843258, 870000933, 638711437, 295271854, 929805674, 504827973, 431605404, 648461160, 842168400, 687806188, 441454871, 265995372, 570367797, 176853515, 954239488, 517595479, 194084638, 129935867, 21153829, 26746733, 530595005, 629043457, 84731025, 631916045, 266264364, 144329811, 756990134, 229488350, 657025264, 114890948, 854876609, 158753031, 505668759, 277525373, 621543280, 715945210, 769150485, 654822897, 264435145, 941851756, 404246345, 889786237, 868577555, 593176152, 942484134, 615764359, 320596903, 978342491, 536429951, 871529648, 641777092, 438873117, 710444276, 971431577, 913922254, 259282696, 178772015, 779051928, 10561623, 92028842, 459039732, 578892362, 487702139, 379266051, 297684384, 772728921, 37695663, 553439977, 335457750, 762451943, 437114727, 920529415, 64417962, 497251917, 202103633, 645590169, 162860345, 613849792, 174628602, 784493440, 375432524, 682220555, 490446362, 176649001, 73428213, 301056826, 784732774, 152596799, 521809488, 141986105, 169670574, 96622694, 491085990, 519265461, 522887669, 531694689, 98512357, 51455726, 31339483, 200992706, 339161913, 837861678, 546809590, 258778614, 158348076, 347815013, 593049487, 276655608, 181902313, 422858781, 130710598, 880775990, 130224608, 501928539, 782433911, 553917966, 52890702, 787491196, 526806127, 292145593, 405788860, 598216076, 630557734, 874864860, 864370362, 530882205, 159371429, 591760222, 122560032, 681702513, 500892097, 474049300, 750562801, 382631232, 131294763, 865412295, 943941492, 641314318, 435961673, 855718485, 142619733, 344186192, 864711350, 946010865, 977962358, 896961026, 461913490, 725532882, 500441013, 834162282, 808903056, 178395445, 933198155, 340708357, 726051423, 276124425, 383022769, 635933690, 611596320, 737075291, 208457453, 163591565, 644591636, 119926053, 389343607, 91562768, 923837360, 780595605, 509474735, 467973904, 876470512, 413687916, 931008132, 446987639, 23260903, 140482559, 375075153, 165327022, 217780170, 366908721, 168760472, 438804558, 283910135, 578517994, 302687875, 978898968, 142363059, 367935330, 946622964, 664679838, 908290049, 142332690, 265944727, 318376272, 339959512, 793519108, 70225310, 124056902, 875920425, 693619549, 734324518, 765310503, 208816093, 536343938, 774570513, 260611468, 290520264, 288528224, 140490278, 913572187, 719597166, 909155525, 965481330, 502518456, 984152417, 652101073, 789675198, 69857074, 822361297, 382791117, 9215554, 635757067, 268315292, 592029838, 70636734, 47480651, 240218571, 965513717, 233281544, 150114871, 496206307, 688187494, 965038184, 433200262, 908914526, 756756087, 377223617, 956170661, 542355604, 323599160, 375093327, 645801722, 284900489, 34973833, 542375826, 596574224, 776554066, 977379201, 930992953, 147654993, 789034371, 508861503, 214551260, 190051246, 853771012, 808350644, 837958224, 197092179, 549525866, 912452429, 790285868, 31459979, 672273434, 274227092, 245997474, 403829477, 837226701, 51293425, 414013014, 218066244, 702321866, 408011178, 728180562, 902464171, 852383394, 405934225, 639283595, 599493104, 532078167, 911678709, 833952026, 866117722, 216642127, 485616958, 567294503, 783669561, 475617040, 273059736, 555631127, 597538730, 766556952, 963017475, 841796506, 708751403, 329699849, 866259645, 877580655, 508882067, 138301637, 728366793, 55717812, 461909777, 688121024, 343444836, 653048821, 535226690, 848842233, 358600093, 49556521, 398344239, 465830030, 85731371, 567345683, 493132823, 862359973, 669584989, 796056339, 762217340, 197486013, 731336156, 65817954, 727313668, 111684067, 381196954, 181594015, 605964923, 213672107, 3102375, 612578917, 244754052, 646779650, 218682508, 786217172, 804352312, 731960939, 32873606, 94210866, 591414751, 947642807, 256541058, 854382645, 916442303, 594092024, 369286725, 336950165, 913783677, 991558890, 558043955, 128102079, 256228781, 122238396, 808794828, 80282395, 132518657, 496419890, 867338798, 470157838, 373697661, 716230166, 360722829, 802508368, 140284027, 359130439, 230071086, 224515536, 775017798, 482972735, 731737862, 563217758, 529726210, 676526152, 306607556, 649981053, 24083855, 178793582, 386546722, 570164754, 789542037, 353854974, 424472964, 471347818, 834633704, 810947532, 996308084, 102243205, 738941201, 117987849, 4303370, 270546582, 724895458, 352744596, 402274772, 528884770, 205236440, 465930370, 582746416, 445400080, 767443427, 286860535, 667734057, 774543396, 309996077, 562214367, 790691087, 265508604, 246358402, 317095507, 45089243, 371909380, 125138144, 325611017, 888189596, 181661983, 591154849, 697880063, 359031656, 480030694, 383616584, 764452172, 290914237, 852260713, 526321299, 434345622, 898485437, 580537853, 165847210, 440541589, 909881068, 122191215, 275595547, 955388355, 940231584, 577828639, 289232931, 831576754, 154238075, 351243232, 665884858, 410836134, 515427830, 382447017, 573501658, 405634358, 471560522, 186851773, 467003265, 803186970, 921251216, 347174267, 534453652, 154758264, 170859792, 336537390, 663673483, 948874700, 233532337, 365111385, 414255293, 973647954, 449304214, 946901601, 179412333, 404948629, 871972945, 890009225, 189429457, 282097314, 783982197, 302638793, 743869864, 548744674, 709458013, 418947493, 674055654, 944876053, 209552016, 78897793, 174468385, 82684730, 266292226, 765931656, 898112298, 930056456, 887016335, 634686712, 844098367, 39529589, 657069628, 178147042, 637581243, 173755598, 593924282, 801241164, 618192653, 243312380, 69654562, 772912374, 219423297, 149660472, 356739703, 785983485, 513687487, 424922934, 217570116, 670197415, 955467322, 753636116, 7727892, 323152634, 863809478, 797689575, 176925053, 489473647, 47128445, 969019432, 848082504, 953645019, 124429023, 575590945, 241304466, 122818865, 52420868, 172016809, 123186303, 664792898, 810253028, 792717061, 31139210, 438967117, 787159536, 842026832, 297926621, 515900304, 152990964, 790978765, 927188566, 474092578, 984571523, 537252843, 567149330, 824091303, 236110808, 898733404, 897458862, 227428970, 503649383, 249039166, 947331010, 14331762, 963300774, 177880237, 812210116, 900463673, 689079533, 730191995, 81836871, 566100145, 638053880, 131988790, 873149846, 816493320, 670117367, 349388349, 770960348, 81471348, 319397189, 269129789, 382520600, 960052290, 630644238, 734366368, 245791628, 677004528, 614709129, 762601947, 17377202, 493336083, 709773036, 847699589, 369838249, 822350945, 251499992, 21561348, 703513098, 866668643, 715011265, 111400990, 478619618, 380907531, 597693785, 238699649, 946668084, 923246700, 321261336, 355132696, 359116120, 307926681, 322922692, 555232530, 571365994, 693879349, 403637751, 564625748, 508156708, 712088571, 223583608, 957392578, 330179945, 862762827, 915012828, 141865764, 774164984, 732901967, 429262422, 570264309, 458053699, 274185448, 670481165, 674249717, 569590472, 405596369, 6781410, 200291898, 161707958, 708441421, 525997378, 122850509, 462861612, 655206095, 482102209, 135224008, 794181863, 268585106, 370722621, 606179189, 935205460, 462653064, 694084465, 440601107, 996284658, 615250912, 180421356, 441844251, 632970988, 739077104, 983755279, 231944861, 483146492, 448081741, 700755055, 374431579, 532892198, 536823166, 302996339, 302030104, 77298814, 129881717, 564064235, 63920495, 240484887, 166817402, 764444814, 460015830, 149620868, 274146453, 315275280, 159212712, 655537091, 502805761, 731722628, 428840369, 507827191, 763026603, 136513822, 802614971, 636322556, 217164661, 308933521, 238567811, 226196953, 878070841, 690993070, 238556880, 657268196, 58681949, 667842503, 192835428, 534612648, 104098273, 961288208, 353574274, 249080222, 71913459, 643631349, 897480707, 169990930, 905512372, 595618670, 798153036, 713402884, 765057518, 322885831, 251366714, 650473997, 251623753, 891774804, 708415513, 261247984, 15571910, 846897266, 20686900, 462425299, 879204715, 286368524, 126752231, 536005915, 698512644, 763343617, 712289260, 756293977, 752784099, 648624107, 325189980, 586138620, 289686098, 464048750, 848616889, 589499140, 555312941, 185225003, 687379050, 835451006, 548607474, 70187102, 550763416, 460687105, 672399452, 416480710, 201463136, 767668864, 844188076, 823583647, 302666148, 288469596, 541286405, 307504918, 247820533, 680389115, 382497693, 327471414, 188038830, 419865628, 980126708, 591535122, 380421947, 91208854, 211060046, 877247510, 948179779, 270949074, 856503644, 228722534, 537169584, 276143436, 250363614, 838696160, 280501835, 625303482, 16066998, 277714398, 121262478, 535068458, 346326878, 560582397, 740117107, 773965371, 893256042, 774397167, 873233568, 795466029, 975363834, 121029888, 659118374, 366201777, 115398837, 350689864, 311769349, 750401653, 337719570, 790629588, 978621524, 985290896, 768050596, 668807608, 86466299, 255482758, 76059204, 489572084, 217329168, 488644884, 107149482, 515684544, 600508272, 245720220, 821801824, 374103870, 219546385, 334722026, 763803542, 281179417, 902494161, 351645746, 306940809, 595248002, 834194643, 193165533, 170433443, 89148315, 500268503, 126925751, 633579554, 474124423, 227741845, 580465668, 870165443, 995248773, 863302062, 623934965, 840220560, 144473231, 846641118, 782120381, 32659779, 761720082, 288802284, 599111312, 413759436, 420387444, 314234565, 895257001, 860020619, 971310808, 44911555, 319423183, 739948716, 775745585, 93463137, 35623519, 315777670, 636564036, 402007501, 424538352, 861003895, 186036566, 911821261, 684648453, 602213515, 16174299, 497656028, 859999376, 665681450, 956030151, 425479817, 275924383, 557728902, 737160208, 621567756, 341092280, 865672427, 752907751, 718337932, 324690200, 753856439, 100201571, 181756427, 984201192, 695403396, 723071820, 801656157, 223857741, 764846981, 764871791, 107881994, 828783085, 641009598, 900890839, 241552405, 464055361, 100499596, 286928352, 55876320, 223131120, 124243817, 25472099, 887327909, 996064666, 913855335, 509129155, 144864287, 922096250, 862101332, 482732347, 335455029, 626468772, 86440955, 47197819, 94249166, 157732961, 985328098, 840791484, 682738896, 554371766, 218337091, 322523789, 693765168, 744427996, 413549845, 907164111, 247272275, 976133318, 451728765, 145169463, 505185894, 728406175, 504876018, 357734206, 947449147, 957927349, 822715446, 589375686, 930601921, 125084974, 683042711, 367186006, 780067970, 529987171, 946682227, 354396420, 653067671, 694318990, 844495796, 279758759, 459156268, 687018056, 655107115, 9784788, 583261520, 371158993, 660589979, 427929873, 662145958, 138290330, 86837067, 591921362, 796189290, 418548688, 292549793, 54929671, 517863892, 132725369, 717933417, 320391791, 181343632, 507586813, 545742052, 863875518, 625972323, 765184604, 714084657, 880638662, 205658178, 288661452, 218070887, 545624343, 718360059, 539675258, 942218190, 818007178, 609736193, 102207731, 470350642, 144002747, 885113922, 38152731, 19487567, 215083588, 752271733, 68954635, 849595259, 680905395, 395373583, 205460791, 875311335, 254641366, 922134762, 526028803, 331322561, 818895314, 369453859, 618518423, 5548510, 415027095, 755184918, 850556043, 343750324, 48475109, 468335674, 594584090, 470739100, 641017063, 574656066, 663586786, 72954552, 289532751, 759170862, 121053504, 234877223, 308512148, 435623100, 38344674, 325824429, 631789992, 576503976, 512791385, 806606872, 445340961, 561761343, 259815254, 35335309, 347507496, 336808367, 668415673, 409196659, 621506729, 388775041, 107918475, 767675897, 214872674, 334119508, 655228644, 348863018, 300899069, 579719155, 3438078, 537531064, 695607234, 375749041, 481840546, 640585633, 119550574, 90046821, 176740903, 989423005, 927092108, 513333238, 167462867, 61902776, 349916769, 793828986, 60283818, 422828941, 76222982, 889471389, 268996378, 621247664, 821952994, 372659494, 508775931, 471616854, 323650946, 602813593, 983199473, 821407715, 980504108, 971211500, 156831214, 759194376, 136656479, 432104721, 533847143, 377552021, 193563085, 940622772, 299427747, 855927713, 439813539, 752993132, 409823478, 452042516, 53638679, 598617373, 474728817, 550378126, 147641618, 462610975, 770694693, 355297362, 1796530, 519179480, 242109678, 400786292, 391606821, 371517354, 384015507, 741943744, 716668083, 695338154, 495760545, 885311053, 151356417, 184823538, 417398370, 962521687, 776358271, 229321573, 384956072, 452513507, 586771337, 609700719, 272379901, 251088403, 823060579, 636261180, 2992582, 583067650, 459657781, 384627008, 384929974, 332729909, 243406368, 461398777, 463372591, 201470882, 310107230, 803550375, 855418584, 953088746, 759638548, 259221683, 203397261, 591986023, 955439484, 978994677, 593395462, 250501725, 114117379, 82810886, 102918294, 937859497, 13509800, 423474689, 944950269, 485773728, 106483580, 845516441, 57159895, 993296215, 574007516, 815610794, 176067106, 800134666, 680098126, 424517613, 164690697, 435183627, 453020125, 581209801, 585150027, 548872309, 146703669, 577853665, 647584056, 744479989, 938323111, 716012613, 224673281, 158866008, 749664659, 65262591, 42614159, 388743047, 775242681, 758859638, 145049629, 596215449, 67205224, 217338071, 966505838, 865770433, 461122518, 831969051, 193471476, 140623870, 796671210, 712000304, 728222102, 944252733, 778613170, 20435167, 763834442, 154702308, 283274820, 174172225, 666104412, 91074102, 596067317, 508172089, 409109240, 220558035, 895362435, 492295349, 207470910, 976757118, 391230996, 463629870, 562150108, 678827785, 471266361, 482486830, 568754402, 833264314, 399284547, 240192230, 34843995, 249676974, 658755828, 883276820, 441681129, 210673926, 859180851, 897532133, 18445214, 321138142, 183150373, 539264232, 485507575, 593991055, 267339207, 835839418, 611922001, 658099787, 933759826, 941047968, 663993306, 878723023, 343546152, 10441051, 215752082, 855753831, 61968157, 116140826, 672371331, 75417063, 731105965, 355322700, 414473794, 535016902, 32914248, 714303799, 303358286, 929335866, 297409535, 701947980, 786166156, 850146045, 63298149, 161226136, 725159351, 53969375, 164767734, 258187444, 13361818, 850753975, 559340200, 323688783, 384916442, 325304878, 167561263, 158788847, 94399741, 517709825, 500984100, 995510333, 334172050, 846839266, 201517692, 799959522, 58912260, 728557285, 312287708, 630810947, 550196688, 542972176, 780309193, 91372741, 416230086, 572138258, 259565953, 695968578, 721313437, 522977499, 634554551, 41194361, 118704143, 805637054, 708795877, 808770805, 289908194, 206554862, 545601501, 961868804, 790213760, 99426038, 559284978, 846195515, 969809148, 529076820, 94280643, 250906834, 292033120, 186254294, 103574904, 6104469, 382387978, 744235949, 449393419, 530578243, 226391711, 548671486, 264734084, 394717254, 604466666, 505425195, 427952312, 353090602, 206309022, 710329789, 356933579, 35182815, 990070463, 463791490, 893458627, 636850016, 92631585, 554026376, 418967308, 558452678, 250889818, 510741722, 569406059, 457904791, 763727210, 289629050, 782295752, 886852675, 592003226, 605505475, 710916705, 989473216, 706195031, 672626299, 835538175, 294960465, 37400608, 868336192, 924269091, 940472666, 814159776, 625313393, 58867492, 717218304, 187554490, 695040442, 661560479, 573185993, 849610630, 829417860, 255710025, 355090818, 824290720, 634340247, 319133998, 830152216, 654216745, 459094151, 329437848, 791093033, 112138974, 169913125, 997032104, 703482302, 922616316, 434342316, 879670354, 841258763, 727371026, 112998246, 155024095, 967077821, 276827374, 25222212, 868359324, 365029957, 310616410, 31685447, 144233915, 48128853, 833280493, 760858049, 309624301, 983319023, 958202164, 791527042, 637899676, 812658407, 805206605, 482911540, 128874675, 437300373, 775339371, 127296925, 379735078, 570331543, 154024773, 979975287, 795062977, 149540643, 443036487, 941461893, 348552763, 9128700, 315438725, 428473714, 592737835, 986254826, 168626385, 379363051, 669342151, 245976258, 865578516, 637922009, 784681336, 364143582, 338474146, 888522484, 430486684, 536923365, 59565708, 62637474, 11958886, 269146021, 203494894, 254117477, 318696059, 496924172, 162233579, 819156083, 589571575, 258595452, 195158898, 15867850, 345828221, 73685344, 630688689, 454737805, 671335146, 892040614, 196587127, 310510407, 493991530, 90214398, 834125324, 409345157, 115422857, 736483206, 479698274, 637668114, 372715814, 625805391, 954912396, 135072690, 77947633, 752737006, 485209690, 758835678, 894675809, 595433154, 992841896, 143642501, 237451978, 262493533, 778301844, 985020133, 705402442, 428371157, 893079652, 94480064, 537129902, 935845920, 589668607, 964715656, 239277726, 780142034, 235622315, 352795429, 817447250, 323443362, 981246720, 470747271, 206096038, 934051143, 956963075, 675612702, 145608498, 239031201, 657433368, 16942107, 821528909, 743566382, 801215961, 654347516, 194034159, 570322277, 455667256, 651706095, 102197677, 503117016, 411901878, 427384149, 770847974, 361473147, 596813796, 604683279, 225117431, 781042908, 414821106, 205039700, 347799450, 233738475, 446528832, 351316288, 813555293, 850371426, 725074918, 569205162, 618293208, 387998660, 827355291, 139340848, 691341325, 117309400, 618739558, 641511725, 7796089, 127357304, 175204112, 290928358, 13444097, 994207887, 359202769, 699201291, 235337255, 643483235, 264495724, 201539745, 851762319, 539859747, 490841085, 531128056, 149273825, 560810192, 223868737, 907842347, 858968620, 141085973, 917928694, 898120231, 429143927, 542901565, 99087572, 139264123, 423160586, 994153476, 735642554, 552380773, 640812255, 567458279, 366989771, 607759531, 131068734, 58143078, 409249392, 785947719, 182738790, 259534978, 775711350, 204770100, 904726672, 339722564, 126195286, 499503529, 103061390, 873363546, 853720438, 810750018, 453840636, 660594540, 163489304, 803837794, 183853839, 52365880, 781999163, 97959106, 825344493, 963005043, 642490533, 441563195, 26845624, 406405246, 965140810, 246441436, 518491471, 596553462, 743794973, 870444761, 516917857, 943119076, 242317037, 894607350, 834705229, 959433399, 115606558, 244019474, 668810456, 926955489, 515471787, 645208970, 489523198, 469748643, 349613528, 334953433, 494051315, 220482998, 226607213, 168943061, 158659867, 691653483, 402154317, 211935717, 743790495, 775634643, 420723999, 444101753, 65397702, 750479711, 898017593, 161483787, 302433391, 5383978, 83111071, 536347516, 670003193, 608586046, 528765533, 276633482, 664901483, 73283938, 269909703, 517394228, 783168604, 964560327, 739190157, 516364381, 57627350, 52863606, 796854776, 963543218, 587179626, 804840246, 631075370, 298489760, 739935255, 840475784, 504586089, 121465250, 497463823, 759122800, 347726433, 566334401, 999418879, 672749292, 607900919, 77063591, 679924196, 345189974, 560722620, 487721380, 820639941, 878306082, 229820722, 287715092, 489870870, 482387398, 257519662, 731449444, 708535967, 422824048, 864789242, 43245030, 882008102, 534191773, 200859244, 346587954, 539996358, 697963197, 105537402, 510427955, 649503423, 478609177, 277841884, 495218809, 795722885, 989126463, 534041494, 674480159, 876413513, 267564146, 572287573, 213308356, 811061234, 493598190, 577633829, 909576639, 654089276, 68736824, 82254504, 844619694, 105615516, 556926710, 697846660, 282397490, 260338480, 324268432, 367699666, 553288871, 15162744, 845647209, 236660495, 483643815, 148301957, 926577911, 15988651, 384192170, 929874577, 810550518, 643076745, 864181103, 769397636, 345560405, 606053911, 467931829, 872871520, 466811241, 66217517, 834319642, 722462756, 30837045, 61659356, 321317899, 488303745, 765757345, 166012375, 140099608, 845080221, 874827359, 904921983, 687594000, 866199537, 670127818, 916612985, 659500088, 526916466, 55297944, 197931864, 978335674, 168449426, 913347519, 462864692, 938591376, 103332193, 868323542, 152469118, 562822329, 61783094, 892440605, 680001360, 601147530, 973702487, 74714046, 392097171, 713474866, 102028051, 377399449, 782655784, 826616533, 501146844, 119941336, 188609472, 247034526, 148501718, 338549563, 936508101, 547889957, 607281538, 83131561, 761341157, 219512285, 894980180, 391990382, 618943559, 69691089, 901264094, 597732848, 788790054, 207670590, 707299278, 959527732, 934117377, 955835092, 810431359, 763773276, 826919878, 403589869, 434595603, 657387543, 567044040, 895288812, 154533174, 729338064, 686638775, 815473405, 658707377, 951080666, 841055369, 751981637, 91566353, 891087459, 405743885, 514661130, 386104391, 637155487, 722861306, 531970240, 415197634, 128531637, 378552403, 354734174, 856021570, 679716824, 334286379, 855200026, 674990072, 101165528, 3983419, 458410243, 236785444, 83483705, 981737724, 537730932, 174669587, 288290323, 166752440, 714735368, 273038792, 580983753, 324649734, 636845582, 134567873, 407254947, 352914556, 206115649, 424659482, 602098903, 716219092, 255606173, 125535100, 950234780, 242063981, 401085476, 783248038, 793134730, 938152789, 760555118, 343419289, 431057053, 652167252, 364529095, 978187120, 833487663, 341451004, 932910829, 327392854, 724427460, 824290076, 601479668, 239481447, 218318374, 134353645, 48134547, 342455101, 760334352, 913688949, 893283675, 848988765, 470141259, 451953184, 462767830, 567721808, 30763708, 740283990, 483056048, 245127253, 780508198, 373352533, 776627376, 874632625, 244627614, 16129880, 119898420, 494758061, 925754771, 204978679, 694511311, 368692394, 63710449, 271906538, 214763425, 635661793, 332481415, 341479495, 311332839, 201453943, 629479333, 833987110, 399746488, 996008069, 810386271, 724524855, 868237284, 164116512, 243248700, 601052387, 994537724, 763397813, 857716710, 921454748, 812196514, 194065607, 664376927, 349560714, 737399390, 694242214, 213783105, 335801913, 12177932, 808872140, 944176872, 77919581, 238719305, 2404416, 394900292, 59523410, 507436504, 823262752, 65396351, 486963758, 561489200, 122882115, 378695575, 230582886, 826637524, 649041800, 792839678, 313093891, 337215316, 9241979, 150862382, 667215098, 838774040, 552196973, 173134974, 589420750, 108024659, 107399556, 217645191, 965360753, 494958352, 142011479, 804664537, 478185974, 579977444, 881390657, 956132608, 196350874, 520420181, 473653715, 781091937, 893637205, 720206506, 342102108, 77690532, 196118767, 210178671, 83632791, 733860550, 784609770, 939538463, 172224714, 892362312, 237128483, 191658076, 952813501, 105658446, 390053227, 316019547, 180237853, 883707194, 22227863, 568968441, 568473771, 688660217, 689626306, 32236009, 67526369, 72101862, 8038951, 681152522, 349440345, 550354879, 211935922, 837454963, 36794889, 365840468, 325523925, 516804725, 892064608, 112775000, 119261500, 443420844, 322725162, 472318179, 278644220, 966095195, 316488692, 902370763, 957341474, 576704719, 914278467, 867363297, 769446834, 338688468, 903768896, 836962695, 861947711, 419841685, 954871252, 633624369, 62397229, 791285110, 470055102, 97913029, 986129644, 801779493, 350595863, 614993132, 653245994, 239747730, 57151263, 762692909, 490383325, 905845474, 593499675, 376299884, 305329341, 692044408, 368391296, 376919266, 660403775, 203602276, 504217165, 44550707, 758071654, 19160899, 99164903, 213220605, 742507468, 493355126, 603073738, 544038372, 751691324, 226665881, 431828891, 172139450, 844717294, 151408544, 290338170, 856807234, 453117289, 889521315, 179833210, 281856604, 215745077, 522504816, 994115557, 44452966, 758667658, 413380274, 1328528, 930531927, 95712832, 934569436, 566212549, 971859501, 313131987, 81561612, 868975220, 81123909, 983161520, 829338030, 791355587, 468180728, 407822410, 590279268, 205874048, 923089456, 839283841, 545244833, 99881505, 543521389, 852951653, 422187374, 323686832, 653548262, 356166781, 307815240, 927988936, 894154072, 290791312, 842366378, 814284051, 931977271, 238161115, 982075629, 966574880, 964546339, 14712393, 867281931, 908480343, 66492526, 805164109, 980306292, 480000478, 564990608, 42274345, 2170057, 665575421, 881098579, 109029125, 354050518, 511958702, 261823963, 613783512, 13939100, 761965477, 989538640, 49608876, 839183823, 192114829, 247972194, 246198790, 593930463, 387683317, 170527973, 507383376, 625982461, 18843093, 948570235, 888114876, 89524963, 192808513, 212792213, 71892595, 727070380, 664383791, 894932788, 424424211, 116628789, 52851308, 934964604, 645689766, 762450285, 958932955, 842180826, 963932110, 696852770, 450766934, 968606607, 984317726, 903132684, 288194276, 229069958, 467217764, 947950602, 701237931, 551538319, 888719004, 531527379, 784464833, 5668986, 591776359, 211184084, 111233793, 443194627, 349422646, 443198779, 323012975, 890981564, 780704776, 946571089, 387802682, 46231508, 564746341, 579413996, 162957513, 527884858, 808063394, 766185301, 715397998, 428131986, 744696973, 966645742, 913772707, 716433774, 447374971, 592494344, 251014022, 379647, 89504349, 95621496, 2496666, 630315980, 586108803, 36840258, 594252935, 802701188, 988664269, 705768442, 167303439, 790337972, 178273434, 409654010, 371328713, 187469402, 763430227, 568930652, 515627556, 944096889, 190222983, 491579755, 794587814, 913184115, 43358501, 227031555, 426186308, 841688241, 575163996, 814637817, 304758941, 130323014, 45443898, 305938153, 219475846, 827268383, 211185209, 606127146, 763623655, 572494810, 86611537, 675010340, 347345179, 994651251, 560290773, 986711078, 780198770, 225060649, 638130604, 451532344, 618998915, 542964171, 292808956, 663553174, 801919491, 306225258, 596403774, 274488822, 666776476, 872168035, 502092172, 130146400, 264225489, 688074928, 988792847, 370477316, 334643624, 504637185, 264188128, 893655680, 960449584, 613503042, 941339966, 429673834, 354082810, 133460078, 254727751, 117746912, 986211251, 352813910, 329824335, 106735068, 697393957, 262742128, 654448494, 925800431, 847263714, 326277038, 874956719, 75511047, 606285665, 889393820, 259564626, 17327463, 157025678, 475214576, 340620607, 668227229, 626292276, 216065210, 185569564, 938431038, 517908182, 835397135, 112720823, 4205267, 386624661, 664126177, 207397136, 122809944, 961552456, 567233531, 788652393, 331273761, 477710559, 853672733, 207797774, 529459397, 188814437, 832577009, 998974564, 709425581, 473658104, 264693421, 264638316, 679026125, 195318831, 271872953, 600293518, 199516424, 588940811, 636943951, 744390077, 525008620, 814580840, 416608275, 938897855, 464122962, 349700090, 978593505, 521998653, 703205294, 976193539, 150738605, 626492371, 709354252, 140743362, 985299033, 77376519, 210491203, 995451897, 874311364, 751439101, 206120445, 744527160, 137209132, 290881433, 208318363, 643995548, 459239953, 815285284, 665874366, 680952175, 781992377, 216468044, 772187088, 280307626, 609646331, 928152153, 114121654, 896839260, 77344835, 673321221, 94270340, 267977846, 99996318, 963267528, 958552266, 760465588, 675537188, 187778904, 73105734, 834206176, 625068716, 554411714, 36697061, 264862855, 65628925, 457166092, 208442123, 730912170, 38138581, 492329633, 136913032, 183206906, 815335144, 663737126, 302477588, 585710955, 146009199, 151495103, 528355537, 197684554, 844436091, 518561604, 588963759, 549080637, 917509685, 523976944, 650445142, 901063248, 372161428, 957205130, 660206753, 916087910, 225831399, 515982250, 987700949, 476676685, 884035467, 74344803, 186685371, 113431961, 353496945, 267381387, 801127595, 938688693, 860901689, 216022030, 81838235, 461344850, 64668169, 203417607, 801496883, 422330181, 86928566, 986527179, 350565432, 199692304, 905882034, 716188980, 604222098, 693333962, 535277941, 964215131, 533930444, 426168317, 665231800, 325252018, 737808946, 794293480, 365543706, 559622941, 117970657, 91223162, 298855735, 938427755, 719802707, 644792710, 584780420, 394598964, 838827213, 806628726, 747521359, 785087894, 172886650, 731071516, 838759211, 64491216, 314930813, 242460452, 771214986, 964899793, 960801675, 25843799, 540173873, 485414295, 772344639, 910079334, 13791943, 503935392, 858676844, 162885977, 249643905, 801967288, 137289012, 508310778, 415788662, 663342988, 967171451, 207899470, 310381663, 775611672, 64909884, 463653108, 617039731, 759948317, 663096655, 930956864, 869889647, 968881826, 795813233, 57060501, 544292702, 293389333, 362491429, 77043713, 982221168, 98455329, 789209428, 875829181, 365318238, 69272427, 108674091, 600331134, 87613602, 409713328, 899241964, 310081247, 105081420, 953569521, 64992936, 337845907, 993754507, 865146761, 704460009, 914365544, 754834879, 983879088, 677107107, 33736359, 765113141, 602259832, 109631394, 815222418, 356406259, 432688863, 17762772, 148184984, 400995754, 670208868, 871939690, 543802422, 24655835, 317169765, 528859536, 12023402, 118901058, 190000364, 512627676, 48575701, 294851969, 794819428, 139670959, 532733001, 25359315, 748932696, 434751081, 132815877, 217541073, 824899522, 300766435, 811142730, 916145785, 400898846, 346763951, 871420756, 935065074, 24554697, 877596629, 617133362, 796621915, 67181776, 575290515, 128023717, 700691942, 120721573, 165239314, 212682580, 470831905, 360333541, 336564236, 321963078, 140816534, 439384619, 998268961, 379127409, 654717112, 605833, 707414878, 212249474, 437060051, 85254192, 781902522, 720194802, 76749272, 806077430, 733265659, 756841185, 7894950, 463567329, 61445993, 607515058, 440640232, 470855012, 677349894, 63466483, 732439126, 3349679, 1165051, 921541346, 829436279, 677890487, 455873153, 880980649, 438025804, 6604058, 453215629, 466844653, 927512843, 1673247, 265503766, 678575249, 971477453, 291622163, 372650704, 233713038, 123145164, 46859427, 389326251, 571072832, 139290696, 48494348, 708288085, 354829064, 323774110, 786679592, 351859189, 260602970, 212655668, 111229055, 769167050, 245365876, 646482524, 177724712, 846527778, 473796781, 612122013, 242099224, 120901548, 228780968, 301209288, 327751718, 503179422, 114748843, 844844267, 364199445, 318985276, 508540000, 720415447, 70185604, 417108822, 114045604, 750980731, 77324830, 752988046, 309912015, 899169487, 770474574, 136248384, 642880995, 547601637, 213303289, 740132354, 245063319, 325687259, 953506751, 257724934, 290186472, 271767516, 885538098, 732498831, 171139281, 184172519, 171951989, 551963617, 575154815, 663529415, 736769517, 212216169, 876824566, 358282902, 352184418, 537253901, 244222665, 838338632, 935620596, 602926459, 674487232, 96685685, 830600291, 491033072, 347042028, 835070470, 419706396, 636307956, 736623387, 952835740, 114436348, 934517166, 334879148, 17306821, 838343808, 584127006, 866679920, 90016018, 702101457, 516347346, 260142498, 415495157, 532439677, 596149274, 837528787, 665380568, 960221801, 354421121, 287924681, 873358738, 537436069, 239298116, 924575670, 289397946, 84627513, 84101907, 203510904, 875384455, 517986608, 2728642, 372954689, 291252732, 370606650, 993639748, 260757108, 242201060, 996976110, 185154599, 505508166, 423528170, 807811967, 206714584, 838146287, 435131774, 293937939, 43068099, 691087167, 274292874, 178942365, 367117111, 168648405, 853241194, 457362149, 497511281, 771369242, 825349417, 958300678, 352840698, 941943029, 117378771, 394606922, 616645134, 911202601, 165975703, 65272546, 641315430, 869261304, 538485698, 296035518, 240414464, 35643043, 617395894, 829407924, 649566552, 936367938, 39594868, 702106662, 48712199, 546779979, 773865012, 7177958, 835748191, 210174402, 285385620, 870252227, 239449560, 772978205, 761384942, 710956861, 628979101, 589813049, 941658379, 112259207, 134726378, 598099041, 943193604, 610924787, 90737332, 88056903, 446688437, 791084767, 645032772, 897321356, 533962751, 868321997, 57835076, 726166144, 416521402, 248795109, 737939376, 500473676, 185212863, 72738493, 104438602, 746687795, 115952966, 964949652, 62628212, 98019044, 436905681, 799914299, 869486249, 918610264, 598939536, 49330328, 902596169, 910840858, 497527926, 804583566, 998285968, 827365571, 495019736, 68441774, 645128036, 526099544, 742785947, 388941947, 295800513, 25241587, 713141094, 59088232, 321020350, 632583727, 318105809, 260238659, 266667928, 101533051, 676447859, 367879830, 557835866, 928095421, 517553657, 569522835, 312428435, 476523871, 634103979, 472364117, 595197143, 253989922, 201062358, 2525842, 857483488, 228051072, 853452660, 174774220, 574883024, 746144987, 535180268, 138191900, 683965101, 177343220, 959349114, 632818355, 364704282, 582872995, 952659428, 623400598, 396729217, 394937174, 379710796, 163210803, 877895345, 734128946, 600263152, 949720899, 837027971, 8914849, 327931600, 341963187, 734939360, 98862056, 291139696, 39277034, 352497808, 580553028, 632084531, 79083591, 615668414, 744222102, 819607688, 679015209, 406748133, 293906438, 820129721, 876429764, 267401140, 185893457, 111229386, 367024541, 954391303, 768354625, 914687800, 419000055, 329797451, 695893127, 122151618, 272487913, 750594903, 573933815, 277723757, 627922412, 29540190, 774142639, 308360850, 993050563, 49948119, 153741663, 25534451, 656165294, 701136313, 600366212, 280726706, 278477365, 912821167, 84263048, 441639959, 36506092, 250000958, 933906075, 568010916, 243054224, 291842592, 589664599, 843662330, 616024839, 85682543, 470014414, 867226799, 100070147, 66694844, 569840200, 661855790, 548768262, 461159578, 256679208, 827848420, 36106738, 762086290, 673338101, 795146527, 515654027, 102806480, 955138550, 632202263, 787703554, 734955364, 505353756, 983265463, 174646140, 55163723, 882024331, 105991539, 646858370, 273798475, 596258725, 704490262, 211877359, 352701514, 47886232, 609765595, 613048153, 778106993, 782516431, 808709819, 33775680, 676344638, 141473837, 3311665, 828792809, 247535053, 75898452, 559159922, 743090746, 332385061, 658929293, 356520927, 648639790, 139052886, 133006489, 222391043, 732416908, 523958286, 729330580, 390152821, 908145957, 238897255, 806495593, 341343379, 14177436, 810115747, 415920279, 854475033, 60928304, 774206955, 982137954, 830966383, 735721847, 183473707, 258455781, 825926562, 744175998, 661033583, 865688363, 734827442, 808252619, 359183109, 277089570, 926921017, 141791995, 969723151, 309989224, 460499516, 118416480, 297605045, 877245486, 215680829, 19258235, 543550658, 75993409, 624689135, 641468518, 111236281, 103963619, 211559047, 393640035, 278712796, 283026636, 653836068, 75238804, 705356635, 191874783, 115933748, 502050905, 6419465, 436790097, 565825283, 787391135, 94807730, 71055267, 374429877, 73520476, 481589678, 985524221, 263290293, 324871965, 32366482, 458247834, 270818147, 864666278, 391276604, 752652121, 968637810, 640633538, 914791441, 605867661, 642973772, 676970497, 640015472, 686007078, 245205507, 443890337, 207837423, 340124351, 840099849, 357041385, 305351915, 704302764, 836698491, 966433972, 215908426, 564490102, 780326669, 786507474, 479479271, 470398661, 160490844, 713730634, 890013390, 867816261, 389787506, 90630414, 905220952, 869392628, 425765171, 987746626, 811533415, 382053783, 266106657, 599757799, 479807493, 101310736, 882213759, 484318134, 370871462, 324572761, 981411316, 771406400, 647629895, 786401124, 471368280, 917950161, 611805376, 696986995, 923104034, 900264888, 774322579, 533647988, 710885156, 256596405, 131154191, 372687450, 531981701, 196058064, 229170483, 961940178, 828490287, 126075827, 433808733, 57512298, 29002765, 293650940, 621881624, 925101292, 550112723, 522232623, 554521120, 136928239, 984537902, 660736229, 616954152, 173324248, 302743088, 371724536, 451101061, 703274631, 973964500, 275505839, 942516678, 152629356, 378837662, 566549534, 503112386, 894077383, 503226997, 868626993, 576115895, 158944892, 786413784, 824360590, 20419699, 364304454, 385873848, 765816767, 860583524, 214437646, 315054771, 331354693, 598050972, 480750342, 990782429, 601526789, 683197946, 951670398, 390094918, 237008882, 563087253, 865299937, 350795873, 405045150, 435361908, 11570173, 903402959, 706109740, 854345063, 6792186, 398594647, 792342761, 83542116, 308250105, 68411676, 378875215, 605502373, 869312200, 770900033, 439129394, 876745241, 488971545, 996861876, 109333806, 760053486, 582027829, 558220471, 573135724, 780173056, 67115736, 993403702, 453307927, 273392713, 933015566, 221777190, 257753959, 801034288, 931839090, 752228977, 83523043, 272829162, 859099270, 857305579, 397772987, 756795261, 319044056, 81410677, 714565428, 889599767, 850964065, 150491943, 59293733, 671457771, 934058931, 881284330, 864765002, 677753473, 432257232, 556594397, 58002099, 897660843, 880845566, 697621769, 61387146, 685765273, 252844570, 509141476, 267480550, 426554737, 917184833, 363878096, 8416555, 864060093, 654394700, 372383294, 918147988, 186119437, 446476364, 10629712, 729248017, 541227151, 933933266, 320853056, 365012151, 176405197, 240624181, 556039590, 491588304, 79857787, 316709415, 415213327, 115076297, 465425072, 869626112, 696777252, 269691363, 225084311, 101179758, 488477193, 547255542, 450717500, 549774189, 410371737, 223327769, 779803264, 206141184, 991591996, 71308822, 633883464, 282698106, 996546927, 721018210, 879962228, 704249309, 381048763, 131673126, 660622167, 502552740, 484656822, 306149465, 39583793, 458742472, 890106126, 374246765, 989487133, 832161308, 342104730, 994302544, 706914195, 16517344, 485793242, 668152308, 459427415, 725547954, 475547772, 516323118, 272267657, 71849391, 161920908, 331176669, 258936714, 136337056, 317288262, 184482824, 598930542, 308911201, 905953752, 168969389, 208968149, 918438815, 8471611, 112161382, 100123266, 676646333, 327447059, 734641017, 212661588, 419587079, 948911398, 420576006, 158708417, 559077802, 993105817, 534138113, 785712485, 734063793, 295846958, 683234637, 617552508, 750496620, 489385410, 629437730, 984424551, 900807984, 402975809, 5862496, 413752138, 524532564, 254431899, 521605044, 968009596, 520880016, 626446447, 319759118, 296764883, 251825133, 261089982, 14211269, 979639621, 350580561, 220427705, 554447887, 258395696, 696663207, 177220696, 907926354, 908358472, 558605223, 397788041, 265116788, 763166576, 854099281, 500604838, 11208672, 961279065, 963527086, 364149501, 961140640, 999499232, 221055135, 519290543, 49687058, 282034502, 351642341, 690729865, 941671590, 755261577, 24821890, 514777567, 141247111, 779618632, 976275362, 718645376, 562879773, 524746820, 387954110, 129423172, 667667945, 371539680, 48359503, 445607012, 181474897, 252846310, 380758427, 770695054, 720579345, 149815209, 637149179, 918775164, 515930558, 100462186, 469232549, 225268394, 726275017, 402593639, 729949514, 230015310, 875552635, 567043854, 112917665, 841057887, 99270225, 743902136, 89904896, 626031447, 546830025, 599668850, 233255875, 918571964, 579590309, 834622165, 389825931, 226732597, 235341599, 100159454, 258382178, 723899431, 633571828, 886301764, 305723744, 707824063, 637019914, 311011797, 903594280, 201201771, 998556853, 343457720, 175097488, 409595451, 302895379, 799385493, 62932486, 589315133, 709389324, 822178984, 342023499, 687621444, 429289597, 372892468, 943990462, 639983243, 458669025, 416296386, 907364485, 315264956, 120017243, 217185740, 648368621, 888093103, 479773203, 141872562, 978413467, 845295124, 624121910, 545051748, 995288535, 499848952, 398906793, 354803095, 925810070, 814943599, 317709561, 744532131, 439083972, 814886596, 965405290, 60255780, 668198360, 596181881, 221045035, 275863100, 250664969, 954857229, 633669005, 632810687, 323851727, 975415365, 557952150, 236875554, 695289681, 85815700, 755015496, 104495933, 213236634, 419316699, 13485388, 845596888, 567516284, 310923403, 648051350, 270906078, 483699176, 182105059, 926870319, 977929421, 687820416, 326314985, 778684507, 612934969, 669094285, 713526376, 628802776, 412628634, 206163534, 879103948, 241521449, 999059229, 864134234, 410009302, 527144020, 978731631, 584257290, 253839782, 878054376, 160162681, 110672071, 67501441, 729963668, 324548810, 931178128, 73009238, 185177916, 566735301, 469388393, 216170891, 499898984, 16659737, 302864383, 241213450, 586019827, 695345969, 352871813, 270872550, 830529628, 883594652, 8071336, 620623713, 454222133, 924961942, 899138695, 746539179, 816104327, 910705756, 272268341, 807217696, 789225456, 535614629, 118543606, 560220488, 97751466, 223126285, 245437752, 372463421, 195149546, 958279427, 554374693, 852693837, 38301053, 362974270, 762937518, 755048450, 506533217, 297703183, 478458553, 610310592, 707488254, 189429489, 567126074, 413728863, 746808523, 933911305, 851821249, 627305676, 81659804, 459389684, 515220725, 297190359, 287449015, 48332474, 828949730, 505890823, 137925807, 29768021, 58154392, 29017674, 938974335, 753678842, 600287690, 524139164, 395446950, 236570575, 116618804, 311859588, 509103731, 857188781, 470176628, 612779663, 717913467, 578317572, 789297877, 128211559, 590153674, 336615357, 320308821, 74827317, 614074075, 743832609, 473878210, 663729103, 822396086, 344593106, 741531617, 288198760, 813692555, 747337692, 504709005, 31847412, 428855454, 849950874, 64783974, 942385937, 636838180, 1574872, 807020811, 536406514, 265394772, 734209664, 719930418, 899606214, 413650070, 435855865, 283046233, 90409798, 900674533, 21162368, 357661192, 517684994, 971219203, 662357463, 759550247, 536771351, 909514354, 586416494, 316427570, 187760105, 786856264, 676485899, 115645665, 279635747, 875808711, 635101718, 761582564, 504773027, 16057153, 916799284, 299086528, 959807011, 566769707, 47379116, 125069163, 664431081, 192387380, 257184114, 57417609, 397190304, 238126319, 691845357, 245118952, 923568333, 486318442, 182004698, 417242419, 998178336, 24715744, 186475968, 690742390, 424500999, 725461857, 511540979, 130663369, 657400018, 912211962, 813796962, 232090602, 331335092, 702614264, 141713449, 542253619, 605994186, 231734120, 558638710, 458504546, 648622320, 330313489, 688662654, 909714270, 619343379, 846085928, 21566813, 162437841, 18005936, 380045006, 759688650, 428163526, 639771952, 809774702, 545691155, 207680708, 830138355, 353098286, 807189016, 463459941, 827407676, 53560098, 312635435, 812534474, 587205109, 171652060, 938202034, 108082352, 246050765, 432778045, 426800165, 649746772, 567704867, 583816070, 216104402, 145491677, 700784685, 444088375, 841555637, 447844796, 198067434, 308647404, 325393749, 207172120, 391769571, 513813238, 652559070, 258138574, 816692069, 48967198, 355075597, 981361724, 196056071, 466497303, 279747703, 223304666, 347912567, 605698106, 201971459, 758904529, 828915828, 360617646, 433312896, 539042217, 566055309, 419113712, 636728409, 384847966, 467153251, 893295059, 297665018, 77133095, 727197131, 559486765, 818970674, 987420210, 69054379, 656377561, 52992849, 618191383, 770739877, 384073030, 45873422, 537465748, 790875592, 703899633, 826571792, 357779237, 529919460, 561683375, 567670745, 293093635, 784968520, 766640302, 678894696, 112448649, 734214269, 573125370, 424817896, 26779144, 230387775, 853344002, 351757681, 463870821, 777738180, 369238270, 553344204, 345521891, 547219732, 163605657, 490820607, 521837327, 254840578, 481139520, 309687812, 619581558, 612783060, 164497024, 166479122, 843334651, 7786205, 889679294, 443277818, 110053979, 94616302, 841525426, 506842502, 26693980, 593929738, 176801029, 795387965, 609039871, 598938388, 819615912, 395923803, 122891590, 773692366, 68510379, 934372555, 124187341, 290090077, 410761153, 675870737, 969422356, 462566129, 456876343, 777562569, 895098231, 392593352, 708274061, 860040407, 413143766, 297160577, 113517020, 337320086, 454941647, 835978850, 899250221, 125395415, 294405493, 403012937, 481488662, 856619003, 320032630, 431923793, 950819806, 979781886, 448933096, 546594205, 496880805, 51603804, 132456702, 541460555, 527697504, 9287358, 465714624, 794846434, 838033483, 547210310, 327441637, 750702649, 478378682, 907959016, 652298423, 198384800, 62244703, 995422688, 785485425, 738524553, 216022717, 290401964, 997402683, 80587212, 362518552, 904670772, 989229945, 474100743, 483465766, 966276182, 215937906, 371973132, 596082029, 362098465, 627367186, 939480456, 326956147, 4680871, 653781108, 429414613, 876495132, 664367063, 142445251, 447828969, 137940093, 791063694, 732110269, 3983974, 613466443, 705619617, 831721918, 53065615, 540733668, 107486228, 249587740, 469145576, 851726147, 41351388, 261083319, 388530651, 942811028, 163782199, 24627239, 833979900, 565093394, 61866946, 47469512, 785630781, 94262967, 225469042, 136413914, 20130708, 583884374, 67121597, 170983869, 275174583, 220170473, 776594206, 778229957, 321312347, 787512472, 116867288, 693014419, 361004133, 209109336, 724584782, 168172015, 695127482, 696490267, 625051175, 883143896, 359586866, 166371345, 223542764, 404517035, 223233159, 385305601, 949178616, 165953868, 352807848, 460550153, 760221936, 107103398, 202022714, 415530183, 403521785, 850793670, 688532543, 739965199, 458650595, 597271313, 438327856, 231583355, 438139507, 196965801, 286052013, 930417034, 499906130, 112793091, 140747010, 260928069, 974583392, 270517041, 964846236, 452400973, 900763038, 262265300, 439551405, 964838637, 378517122, 456814762, 767844695, 590623431, 23190862, 373851464, 624192468, 660880594, 828202264, 750447459, 267684140, 272784390, 797367897, 734945427, 485107585, 642680330, 440965318, 271783660, 422684422, 178665398, 389949748, 423464198, 781719519, 785165368, 683914395, 661195650, 161046580, 673977291, 141380942, 723581271, 19146798, 325587390, 307038933, 156854039, 843235954, 682604030, 638222716, 291416937, 20445502, 724508734, 413919862, 585454138, 809512605, 775668940, 996907517, 873901558, 541210816, 145764319, 76932986, 766459950, 493176095, 583456640, 909491031, 387210253, 901236104, 136541142, 73909087, 113778609, 726630583, 899324930, 169473227, 638487715, 173174019, 384078132, 989088188, 796250111, 177370405, 505259248, 794875003, 381782126, 120607713, 165642557, 116062259, 449823093, 430470350, 39019753, 316047100, 367565742, 101625377, 261427306, 101022159, 613705449, 232261774, 933011802, 94056364, 794194559, 855220340, 176188725, 970297900, 191447384, 134938740, 241491553, 512338940, 937998808, 562579897, 252711220, 789571542, 493241828, 26581874, 819433225, 138846074, 955058380, 758475406, 363737889, 43160463, 436623617, 83590851, 39662076, 262689560, 414112382, 867738485, 871658789, 275160674, 876520384, 129191139, 575189095, 932050829, 824931805, 929804141, 312721737, 31359972, 244009154, 662313669, 741970949, 4107562, 411990619, 225602885, 671373505, 825258312, 264317515, 493842881, 797276192, 812063660, 377356943, 890827850, 658185554, 750763380, 271541234, 90419554, 129255963, 181327487, 822742538, 566059624, 179153876, 616383379, 155277285, 171695303, 626170159, 257526380, 804381786, 786966677, 525867349, 22416038, 72591391, 232933382, 538746188, 116163839, 919476524, 775405076, 478485097, 704428575, 168498200, 746862088, 852400441, 569788261, 170012013, 653253167, 437045691, 3858538, 165138434, 652731406, 160304866, 886456048, 550096532, 97852106, 830777593, 203808113, 893325642, 447167405, 304502951, 386680427, 944046112, 488662090, 104478507, 787064376, 646772278, 88250936, 310543439, 229786365, 312894892, 352104728, 657664665, 460324863, 116893741, 680472860, 345807401, 203805144, 366514840, 780537261, 250667913, 205878836, 169068516, 262876237, 400576206, 502160843, 565149223, 956448875, 592493159, 594115618, 206420426, 435391083, 361681615, 952373985, 156329727, 143233202, 993013231, 499533196, 943389567, 870999752, 969529675, 117491613, 352204689, 878271350, 771204213, 8353434, 911356899, 85715802, 663683360, 887894950, 394727512, 800019140, 141893275, 408086859, 139232390, 487802235, 415983626, 131316479, 886402177, 728713224, 20354535, 895804940, 688904596, 431135021, 394286153, 462588397, 348033870, 267638376, 528896348, 725611327, 128269411, 37836481, 65033054, 272745818, 907991437, 260180489, 346396164, 880178672, 654491944, 914095665, 863914513, 434352820, 64005561, 618792954, 435766583, 885833461, 477004812, 453292587, 894975528, 147620795, 4852050, 943358001, 945983534, 141154194, 949862436, 737436686, 938070149, 746698905, 787026143, 877979424, 874866942, 74580415, 853387266, 809886845, 276386019, 754847486, 107675987, 241767027, 931486396, 55710472, 772018346, 131136865, 145957688, 331821711, 896777933, 647715552, 371850821, 485877432, 656403331, 577892013, 797631213, 627669516, 176625310, 531840103, 873079137, 664704856, 830043302, 6637168, 492160628, 777884502, 666487525, 153245438, 974568109, 138502002, 920322138, 405737162, 946821293, 525858708, 729763584, 967309017, 12242636, 598986387, 779330324, 428623271, 731570798, 882060259, 24988430, 537754214, 390841451, 924176288, 381866496, 354867108, 390519748, 993156736, 815649552, 929622906, 595433601, 59019708, 689727411, 290671751, 501445851, 916849187, 341110277, 614392887, 487584466, 656704593, 133029290, 3185942, 165415952, 67549420, 958689989, 401110306, 296553932, 50572423, 733302700, 890689412, 709641334, 145787900, 555126443, 794704932, 776420538, 369485487, 343067666, 913389903, 262617584, 869947863, 701601694, 561247682, 295855685, 187179384, 169129667, 918257202, 173938485, 582328900, 558232327, 886890705, 518064364, 237137352, 846840130, 152005860, 696587284, 251804075, 41152631, 905124130, 868950514, 808277444, 335793952, 901231487, 348952374, 147413050, 397201373, 252127316, 886598578, 184245201, 977202879, 19453719, 416643776, 89848148, 76193238, 872870732, 993140359, 123734398, 462780703, 767314703, 921379568, 442856409, 312911219, 555522556, 726851442, 631550318, 654808586, 979876454, 770200372, 257425756, 954949422, 113155473, 822725720, 344273196, 966197350, 43891639, 749331995, 644552985, 823187917, 919308348, 222102946, 190872400, 414977550, 525359148, 504131085, 517127406, 653053363, 490350245, 39300538, 459453160, 162306282, 942695450, 300972269, 241060926, 897753173, 163174872, 832917708, 805048708, 598431628, 812884111, 103612596, 549036513, 597480390, 294298697, 543168726, 975457532, 584171930, 762073603, 473816153, 157659055, 581228973, 371362821, 770880757, 160996625, 165827250, 730335516, 115103741, 423199064, 311062703, 480258410, 478306659, 636313, 639549538, 165554193, 869987365, 117379611, 753569722, 838141573, 91698922, 410615338, 790310685, 860214992, 601245982, 147092720, 638085938, 65242550, 46675853, 692523299, 195232441, 838298821, 649550264, 349380070, 265342665, 84466785, 275363595, 550019824, 454239778, 520591760, 421390430, 532782075, 618655739, 800072610, 834419354, 444446874, 950859077, 945064365, 716618191, 934405483, 542445123, 934644085, 787078438, 457549546, 445884845, 368866163, 771670612, 670618650, 59013959, 708319593, 653500847, 135910089, 963089490, 530924152, 390251886, 784614193, 928316276, 248484324, 158199193, 294450252, 521307959, 360844996, 779286716, 561448531, 540581521, 779012451, 195423634, 874077252, 963929687, 245028454, 27765436, 798469973, 543280948, 906978567, 420448440, 947104284, 127770961, 603034459, 396090171, 332248854, 515053866, 655425144, 249850970, 739864592, 88879753, 816590707, 490986475, 541252129, 563661596, 839836917, 285528159, 348223539, 998538629, 233198022, 491063969, 637799609, 589558411, 680674128, 335362809, 340475087, 963434301, 548979341, 619254000, 823100247, 697578892, 515442208, 857816167, 456750833, 912283976, 313988946, 240571164, 995329484, 719547284, 549889689, 706033945, 344142237, 443633289, 557474315, 880472278, 159769475, 692589796, 245668976, 974728445, 498466059, 161947225, 53248796, 842138202, 10832984, 313500541, 846416091, 673723402, 779645365, 267496916, 494187244, 820772391, 72371917, 8111964, 664300052, 389475906, 814228287, 422322467, 641445881, 56347636, 593054093, 757966009, 669838897, 856417239, 551004365, 9099887, 921414077, 627625878, 907106233, 655138550, 397989503, 891297778, 544496302, 467310097, 241834645, 524890929, 98646144, 389840954, 41567707, 165084586, 311349553, 710255951, 743543504, 176887200, 426961552, 18937801, 21172231, 664041, 795098967, 414466045, 508269737, 422419522, 977935737, 566863615, 440208772, 803720171, 937336769, 240608061, 281794531, 397652545, 812827348, 916093060, 943272861, 649900028, 344135230, 490228263, 234359794, 873597204, 50702697, 171028300, 574142263, 609099807, 663852332, 849317134, 413548761, 34089269, 597901640, 238013406, 789020660, 893140415, 491177622, 106965272, 320814594, 473976977, 862556303, 555752985, 941539347, 386581301, 665545466, 20897595, 111757515, 347079190, 285779698, 553713394, 949988294, 283049958, 494351676, 79900758, 242273563, 15823756, 708096232, 877946145, 43792736, 651159962, 494175828, 476899271, 681095175, 184788913, 377186737, 86904466, 889731046, 866661627, 500019146, 656226898, 993868649, 436953140, 825670709, 870179667, 125038300, 797115724, 414390295, 902740499, 808868652, 364959006, 592571804, 135740789, 121003554, 431876085, 854814249, 660945310, 498213866, 38253722, 882539455, 877002025, 5429267, 456378668, 226931729, 7881145, 953023861, 56320033, 119018959, 346480433, 456171758, 195557412, 626832283, 947469594, 400623811, 790946476, 223348149, 989666335, 239224385, 705281004, 267503647, 225704902, 904354202, 960696227, 886056623, 933668817, 385139960, 415833113, 2577315, 331762985, 807839877, 676423217, 904756922, 132767936, 943841898, 474844528, 461425868, 913749127, 165432140, 674178916, 103620961, 934389537, 402997332, 207113878, 443144330, 940340048, 549781835, 147241707, 614886356, 751129063, 184987682, 105424496, 55157423, 14412902, 198592560, 55419784, 230242217, 121101715, 831972655, 944038684, 900389132, 300715502, 688256401, 170617884, 572475556, 827182575, 540212398, 18511565, 420924035, 670683212, 4308702, 883396050, 991225915, 378830505, 157326563, 242590218, 575319276, 484763803, 669438698, 707919382, 694537548, 91999849, 332073072, 776656788, 877713515, 938010425, 252967637, 282813426, 106142883, 270833553, 961053972, 257673498, 257686222, 346556192, 717181036, 761628620, 398718516, 176907676, 383120282, 179650588, 192171378, 500834526, 608571385, 693868873, 849297735, 812083113, 130148617, 38947478, 841119932, 659905846, 530077387, 405703041, 524375153, 352513890, 600925881, 356793591, 168775364, 996786875, 905734762, 656095453, 356733041, 136682761, 259988712, 228205150, 709165784, 195315295, 758966955, 471813265, 387410420, 731316928, 179750542, 290395779, 41965476, 857397352, 173959078, 990300547, 486043594, 427856556, 87212694, 651893889, 771615775, 381788871, 842964839, 514640160, 703643777, 254376000, 373677916, 788798294, 551171361, 529577309, 222651724, 311973933, 346016157, 620591412, 158535582, 212567179, 95274443, 713852611, 117916666, 269670121, 764021248, 650393072, 278927358, 350211185, 717489294, 933923171, 236331143, 435437132, 382450455, 111758015, 676799855, 209918025, 350948794, 221597173, 396586493, 590207239, 113587720, 432141379, 972210842, 222454892, 681149664, 938754857, 30005568, 276597511, 207420850, 180369159, 959042418, 440316485, 3559576, 480010683, 274122550, 840992584, 891029778, 583967672, 567669895, 437071517, 516560477, 595655590, 960501506, 978797675, 589378465, 840331120, 669871345, 383457659, 35402087, 696423034, 164210662, 800620570, 756994978, 651165323, 324311466, 674913507, 322119678, 222458805, 323327972, 567795506, 827318940, 381196288, 607962886, 685846305, 24105793, 413762740, 340152160, 283435278, 501616683, 412611749, 751737440, 237438153, 261163433, 598270932, 637432333, 519396791, 147768799, 174257866, 558115457, 60771452, 752708307, 104103351, 675802395, 598167219, 385996504, 406181638, 251260600, 887713643, 19636393, 129612498, 477782148, 641198205, 392537834, 432408885, 406957531, 6407805, 751133801, 710917037, 675994469, 366338750, 524228579, 688241215, 292724878, 392998519, 342200628, 947981589, 264433540, 390426557, 535893069, 747107971, 741286744, 194588187, 971674861, 568353258, 231516158, 137528207, 906094269, 310462660, 119485816, 777107785, 422675322, 434793057, 8646882, 68036754, 741575421, 360950733, 262812128, 395394810, 969359290, 280245110, 313001095, 148854286, 289049574, 546486821, 440867168, 510776609, 338964970, 38927087, 358095998, 73224208, 338998317, 742231001, 683351733, 509359827, 388932027, 967961010, 763649119, 659029904, 529084841, 212409051, 778279409, 194642597, 749828066, 121915448, 896048710, 337402972, 773486722, 420298851, 17366964, 907246888, 297636749, 84380442, 346235879, 591475543, 635235162, 525849984, 871393236, 28917836, 371445750, 796087116, 954186444, 842498521, 948621857, 600281458, 303764844, 292195395, 97283773, 361011476, 800771249, 869835845, 853278121, 721177283, 188090751, 260055543, 595819452, 888270838, 760108715, 617651931, 832345375, 624632363, 371621788, 88613008, 913393187, 815445460, 543698381, 18906198, 610962839, 319699397, 256383588, 257430675, 498893465, 24962987, 252454508, 686416429, 664471479, 838414207, 767484592, 780786326, 812331694, 345025704, 429812432, 936256706, 853208095, 505947049, 372271580, 828948489, 847479489, 550297291, 424954712, 91027176, 465264632, 711222345, 951845719, 353026823, 866615471, 652212196, 193066214, 686682905, 593908408, 532331578, 568429392, 659153115, 740649109, 887005134, 422071187, 933195086, 961743360, 195629212, 354995240, 366262674, 279950620, 943012038, 577812152, 796140915, 970376019, 986600690, 155528510, 412405594, 134875935, 679554297, 389857372, 170149993, 958666216, 752553377, 254909849, 893756220, 293916316, 31618937, 159165834, 541242445, 465571494, 100244552, 141340684, 592439214, 224079569, 418796915, 246406936, 26206893, 38868085, 702575107, 715803010, 972072382, 786573421, 393457458, 947379039, 688018388, 524099303, 647670211, 686023063, 397466627, 557110990, 95331735, 94171549, 352473686, 362706888, 770398051, 271291681, 957914903, 921050801, 16680653, 325074478, 776018591, 708281201, 450263233, 82111309, 827312832, 134530193, 127039289, 343308152, 396845354, 815076492, 265508219, 786063939, 295428734, 915580785, 981184460, 459348543, 919236948, 712746318, 775644290, 690128563, 153867336, 271696682, 739354613, 484253933, 571102078, 495271957, 530762977, 264593840, 682645606, 552738768, 755750301, 250777233, 7308977, 362330377, 126163424, 454989147, 206526392, 542007578, 545181299, 998747938, 981046424, 332018589, 619026985, 779651034, 17912617, 407765283, 836705236, 855398933, 2012012, 559014436, 685539814, 919300035, 955709891, 163561005, 957371882, 473138257, 267242573, 106918439, 921414691, 424761420, 634968692, 19734718, 936384880, 364269141, 366382235, 200907157, 46415995, 58792999, 240964580, 831525153, 373029418, 947134268, 316208901, 485741648, 188536544, 810348939, 216607529, 545902744, 906864646, 306799257, 893476594, 548939857, 339966070, 976406851, 212106501, 333733990, 996596441, 418469503, 480316869, 409341929, 717938682, 13691844, 407541917, 687816549, 941092097, 650567554, 777935488, 531528797, 439500838, 606425860, 915016226, 907706899, 723549328, 956384427, 238704627, 261559451, 238422576, 660396111, 672549006, 297299453, 390420361, 490688912, 964675672, 135572625, 204878656, 521712859, 942642024, 809860513, 664970603, 574250594, 250947271, 256237784, 522715923, 167800349, 167610386, 782268481, 92488216, 418440469, 896582827, 270775734, 193431736, 943635544, 103210956, 202292640, 405378202, 691344155, 339508664, 63665291, 800833676, 977639759, 342057169, 704222532, 978965264, 531973742, 760329956, 923830106, 231084609, 859954536, 800303729, 525542703, 280278975, 90728540, 668987182, 343074332, 932288594, 95660872, 972291101, 9363814, 260248502, 492730588, 418406802, 827787733, 614850876, 651071936, 2161542, 203724255, 279626733, 474081433, 610604048, 768044019, 941214284, 407892798, 293480057, 63184473, 652581649, 447868689, 981829362, 173583396, 450033097, 247563713, 346346967, 34348881, 557522049, 531516779, 718012203, 787085339, 291516414, 842754307, 250267466, 111958210, 244624089, 235062965, 911632170, 48942079, 695821645, 840263677, 523916, 787280327, 373974049, 840761911, 248852038, 773720777, 938937147, 170659418, 124169349, 228735081, 927906952, 668783259, 565579682, 320313603, 814790802, 478675496, 141172445, 699780075, 117509835, 772165267, 795227351, 259594952, 668576594, 963089990, 970625244, 590593822, 91099166, 418629077, 761070511, 270644219, 797595969, 543562138, 851316563, 97450574, 314635750, 38781146, 305188954, 267931321, 55572539, 57833759, 904320272, 882563370, 717064409, 892712771, 100873648, 350431852, 655534295, 998280522, 480441297, 515604087, 458653346, 943898386, 933249621, 884401585, 467552984, 913732387, 770422935, 754257886, 453285456, 600023737, 594161874, 314111355, 494725017, 907490995, 104859868, 828060618, 404901587, 115958193, 856593060, 534180006, 986482265, 978605179, 821585110, 420231487, 518060826, 130872856, 895618899, 343204416, 54210936, 947579734, 200857749, 924491269, 730945259, 77218234, 551226504, 654392589, 607118437, 176124610, 263201836, 688410200, 692973101, 207806996, 773423137, 541576635, 890640665, 350632610, 124986504, 72665482, 87109267, 988620334, 250703641, 433025453, 737711446, 946658091, 788370827, 161048123, 385803, 544650212, 432899911, 772798479, 24679177, 665066620, 325461997, 490290749, 344548281, 319794612, 425292390, 660046904, 131086844, 934023653, 233138029, 148519036, 798023895, 640366765, 375569647, 816172363, 820041727, 574812189, 400410907, 311244084, 396767581, 748582059, 731682632, 924554307, 310546511, 975896415, 40014514, 842492282, 329896754, 791138109, 461553675, 792000806, 191300200, 914265437, 90184537, 493297442, 121555117, 793639361, 967528, 968147765, 13640345, 670822757, 494524929, 392923640, 131249796, 78147267, 940475375, 60302118, 232654487, 733632071, 461282967, 720742489, 742388973, 63092760, 412257714, 937252826, 447296984, 32512331, 245068223, 483875249, 470465533, 369505893, 126404120, 507260888, 491419874, 182158201, 80809926, 629417672, 138634556, 660626554, 306424574, 65429535, 870457335, 18284113, 749140516, 328269169, 596375806, 132563068, 324204588, 618763293, 812099143, 452522115, 165861586, 50738151, 867477873, 675621074, 138819083, 988441591, 494391399, 49630456, 963672758, 995253169, 582552674, 332842841, 309099101, 301232441, 302980265, 637137185, 899910926, 192176198, 407378729, 794800254, 87321978, 360940302, 15392262, 525574731, 300873446, 178647593, 571166336, 846875397, 968381304, 605426952, 812433696, 711964135, 821689529, 578540988, 868560788, 167609894, 492361693, 551639799, 741436324, 219803813, 154619570, 957895289, 371021958, 223618095, 766595750, 463638925, 99622848, 197504963, 462599349, 332891010, 545613906, 314899578, 446476505, 354136328, 611499715, 850781025, 270337910, 121198500, 393927343, 536454091, 350472080, 637073479, 285557764, 664595456, 7621385, 42801229, 778656380, 481492752, 953764544, 765118627, 463274143, 326923226, 612337497, 428881242, 849445566, 777683539, 608510701, 279206323, 868272049, 763570694, 527598991, 459122750, 324169861, 184923292, 907923376, 584698121, 503089721, 956589730, 708051730, 145964486, 696073252, 860288338, 886315197, 269691462, 146950204, 634240171, 231984387, 320482981, 50785729, 571433305, 27085455, 188104481, 791495130, 114083689, 653286249, 453359397, 499203484, 974985240, 561801110, 326664907, 92864088, 929990735, 303494541, 322031107, 580182067, 758619990, 481896894, 21253361, 647416880, 447760887, 824660894, 174842485, 51145207, 916210028, 420733548, 828475967, 761503960, 732842900, 62826814, 75343140, 62130133, 387174794, 873542702, 362926445, 488099424, 393061389, 992746337, 150866000, 37688879, 930930261, 673886157, 42988109, 47288025, 681328469, 721778997, 648646832, 445609568, 298167402, 162706846, 937210603, 817588774, 87332767, 657328699, 769100139, 652969842, 840695194, 177062977, 293614308, 832509216, 511687468, 652906706, 574621035, 963275788, 669682538, 688859097, 203100858, 494246536, 149083594, 372733628, 676554999, 156472999, 884061656, 178687583, 954313673, 908530868, 36719719, 273439449, 869857069, 615272733, 676094198, 337817305, 543764578, 704647691, 693058071, 869033108, 998352284, 754151440, 476505832, 600159382, 735771058, 224816267, 500044696, 209303538, 288886703, 389233703, 301111458, 11376371, 152273178, 285631629, 675424703, 338784745, 764146114, 966442454, 425158298, 90271584, 832889173, 878543227, 293049449, 368179168, 331778467, 451978959, 971182799, 80880236, 27861765, 540710220, 343886797, 869875980, 251873738, 726399856, 29096587, 433415456, 570425363, 111329536, 489045559, 646203514, 938605746, 345428097, 220773865, 619207702, 720584783, 774616654, 352086212, 431922115, 975155414, 869171959, 251284012, 227202976, 746633978, 866503060, 546012490, 882206229, 821593438, 435899314, 512314616, 235515708, 809740857, 568524743, 311171894, 603393134, 183826842, 480001415, 295252298, 749699297, 277679331, 386484056, 659976492, 889398925, 181860305, 332829263, 649023081, 147551140, 75856517, 534616687, 765647632, 397571172, 51259157, 554281667, 744816155, 439408190, 836935267, 863063935, 457265306, 732224255, 460585570, 75805974, 485871692, 166945546, 670540068, 830848661, 866801956, 810053727, 626092604, 523909283, 321538676, 313222540, 180721293, 73668590, 417806558, 841596493, 42690659, 523695720, 988256436, 741212802, 473741865, 754478473, 869453393, 578937366, 806630433, 899108388, 147173396, 952123936, 980264036, 981660883, 475874840, 192822654, 845841750, 312439100, 815303100, 616443613, 598421448, 519697235, 360461817, 618229419, 202752478, 322849636, 659093699, 114413144, 306763270, 595159877, 724635725, 39033228, 394489772, 501652280, 782108971, 360392083, 611792665, 296862962, 435186208, 28507941, 561613794, 588684322, 955746536, 318132215, 696404555, 324887853, 181595877, 43863161, 760865738, 609214995, 151840005, 789715542, 489262085, 774329787, 414118254, 477581050, 884949223, 431404837, 229935063, 999220110, 406743389, 692393829, 768838040, 820200307, 548171912, 281982809, 779777365, 610531036, 946834888, 845798042, 322606661, 421520780, 9642447, 389824514, 481355543, 811073478, 757870595, 89820025, 872861984, 914813717, 593116482, 867886593, 498132459, 904699014, 470085923, 780080554, 279337586, 742816018, 834764500, 824350196, 744762637, 890261642, 568327107, 719425049, 696890168, 649097516, 728803324, 346102063, 523905246, 179859650, 255022810, 577803469, 770531406, 877958477, 524329222, 429528933, 67484630, 622022312, 506026788, 234622967, 381468551, 620750713, 656206026, 139432269, 862351568, 150076282, 497660493, 196848579, 869795737, 472965136, 793979132, 867315746, 88923173, 602800784, 309996711, 166704737, 303933533, 738855807, 850966192, 357884965, 284623957, 378782479, 964925317, 138902893, 344821927, 652841416, 479928526, 889613687, 161957640, 382811762, 664875518, 579317476, 548923974, 418834162, 44488850, 498624450, 424993620, 452634809, 647103815, 27527249, 563937778, 493763424, 986505017, 742930769, 134659767, 758337693, 752037360, 757086423, 532192554, 218485458, 315029439, 597731969, 78276550, 727068843, 320727167, 605655193, 899396023, 274198600, 950140646, 671130930, 947838631, 782909566, 957142846, 448602475, 563243241, 850983529, 202637325, 165091258, 542318468, 409148343, 43403686, 520397037, 200781040, 361719776, 292034747, 183203787, 272494049, 794042388, 290477233, 75921072, 630367392, 995612544, 274134804, 233824650, 528924608, 537730227, 106623264, 734162644, 958999204, 576364787, 230026859, 45203679, 974491292, 238540010, 786045521, 468599149, 908529944, 491088330, 331845091, 503686543, 731546565, 408527531, 143927879, 769575161, 429537176, 757470520, 1010224, 152831808, 239172893, 703142690, 272787652, 130213835, 913107461, 277542009, 36123585, 23728183, 457428719, 327145472, 982821805, 21607659, 175550195, 131453163, 925679298, 982467618, 523177435, 58100494, 267448559, 365650405, 562904711, 270883808, 93202984, 290587375, 352358048, 686837982, 453628341, 88294622, 698635727, 813784243, 7129643, 329286280, 854237347, 433984236, 19118431, 782088755, 260302686, 675255799, 824971299, 242613925, 161163495, 425477827, 853853247, 872770906, 744335429, 258352733, 423804918, 890737164, 800974619, 64925163, 616266298, 15392005, 959640844, 476004972, 225906349, 754614249, 91615334, 296049731, 681283374, 961347433, 911829710, 806844122, 794924088, 556876247, 235094637, 740946143, 325871499, 92643126, 153348995, 852433161, 298226916, 812823193, 560624427, 54275586, 402388875, 427274796, 766077993, 95042708, 15712285, 909660186, 291831437, 855554762, 624981637, 445782705, 8229232, 680119894, 531878291, 53404224, 409622556, 982205735, 29881448, 183166292, 322200500, 276147948, 859528382, 871660619, 396420943, 404981908, 150214753, 549685691, 288754812, 981408876, 522168155, 129182686, 513814431, 671034534, 402238865, 909874374, 984163778, 357922495, 720799274, 279356165, 932258409, 359111996, 68448958, 131255478, 835138378, 459805522, 890441004, 496590349, 340063241, 885650238, 106066987, 934686950, 76225360, 964174787, 244755631, 593617531, 106903910, 960646331, 948956872, 844207844, 270212531, 363528436, 434677731, 175012223, 261169919, 546581509, 125775689, 940406400, 364128717, 892887811, 277730427, 823375194, 266596358, 154165735, 437405697, 210271257, 13439872, 122967316, 246413586, 229107079, 673768725, 713064946, 157407552, 985986465, 227945336, 517958565, 549809985, 110306889, 175040107, 587770060, 871301626, 565736197, 997993940, 505960600, 8322877, 660720287, 76473241, 473399335, 327034429, 970436352, 781121394, 370826276, 822351749, 793868438, 20736964, 388219037, 589651963, 751115566, 918391023, 677040608, 738162366, 355123089, 189261562, 256141040, 86714791, 580445176, 198986197, 654403696, 147522133, 135841294, 988447726, 13004289, 783307437, 38524867, 265672919, 230533665, 37001741, 381927559, 76641101, 371312362, 447816143, 213992725, 339901541, 293833495, 197123714, 856072765, 61816229, 622906624, 759999377, 383679473, 339441815, 450681854, 882774273, 180723030, 466133516, 947210789, 189878014, 410944461, 250629162, 602388900, 388729476, 997486311, 725990407, 178952712, 951735941, 385476714, 950237780, 115792389, 265759865, 278134734, 742108527, 653911240, 910681677, 924423241, 36145496, 108647218, 662997449, 706256835, 225468464, 175605759, 639152229, 23261771, 352784050, 983547550, 211433416, 512367118, 972726705, 260257889, 503164518, 874018616, 552721191, 90061946, 743809434, 2206983, 909207307, 530841063, 436555165, 791083498, 590233654, 230260477, 321301962, 588451882, 381708201, 897425218, 530593879, 802172334, 209307413, 758313375, 746198625, 509922609, 64337542, 782240050, 787597149, 524190305, 34149630, 91369013, 391703948, 174117120, 238300247, 651359936, 152575168, 176792592, 829277795, 710288904, 680211359, 482624926, 744630188, 662978749, 898326508, 761233412, 123810696, 334847455, 739263159, 45049902, 379227416, 40852929, 20138905, 222887123, 415949169, 139820528, 215690760, 765438467, 471754698, 923981604, 627678699, 405579027, 172674582, 439721696, 38366911, 187928743, 79633320, 881557798, 470215622, 318941313, 432005221, 806135915, 588715986, 129692921, 196146786, 197834026, 875511873, 482507874, 439178243, 834184598, 301659459, 75622670, 10941795, 181063194, 546177604, 32761076, 886448606, 234975353, 942695584, 905880855, 698758086, 869376049, 962982989, 390273311, 177771742, 489540470, 520185345, 557843764, 391261631, 430273183, 451732070, 966857210, 956549041, 525361291, 958538583, 926392117, 480717746, 951605764, 504807241, 559713052, 251302415, 538197868, 885347040, 372310247, 314939492, 483173159, 954582889, 669910968, 581133397, 824484770, 315198716, 232222891, 327894960, 244977875, 703699560, 294970160, 424639412, 47648262, 50425911, 226988404, 976624257, 172320018, 103634048, 858101462, 335640352, 450850117, 124220661, 857118216, 285645427, 78098820, 485196259, 513904880, 688978903, 932370335, 254315065, 292869978, 894947601, 851622285, 666099410, 306610174, 57864078, 371268174, 232245340, 672369352, 710077251, 350654846, 892043865, 791649496, 997248683, 131779293, 828202903, 34337618, 685991091, 438731550, 356856326, 600338625, 471106180, 538609403, 332580194, 779429951, 719613255, 342639016, 169816715, 252734927, 526383261, 782976626, 388010105, 285704980, 788387429, 927772249, 595009267, 616200176, 327684596, 52453541, 518983998, 134165484, 201059014, 688881505, 48330726, 694021170, 711897038, 689061349, 109751409, 779656755, 932378564, 156851409, 709981413, 846554653, 848129885, 404982993, 557559634, 97824185, 166682963, 566472021, 61819734, 256923794, 655752448, 232229315, 758116025, 132493636, 53243856, 860902093, 704293461, 677797832, 952010415, 503324990, 458724705, 904372743, 513507647, 121428853, 920741584, 571238420, 94662740, 777962302, 819076390, 466884455, 392787437, 521579862, 863789793, 70409835, 448000931, 64040048, 587581497, 225606101, 510699215, 605809129, 545289298, 173293602, 442083273, 361929406, 819728750, 504977534, 591151833, 316781130, 216762883, 57668125, 51662817, 955349686, 840010036, 313859784, 857493208, 596415959, 652050892, 182032721, 41074490, 589613, 306432096, 764144449, 683519807, 533785339, 612620019, 158687375, 336170680, 983374093, 62980539, 189087913, 923963864, 124026729, 490535719, 435928335, 342388007, 202781856, 130416735, 139839865, 386981570, 337145132, 336077203, 498640914, 160927075, 746249259, 959654490, 428717407, 228522308, 693729158, 139396682, 822062512, 939288901, 308002411, 356929085, 201152662, 732158970, 790074515, 418748241, 756036426, 750209497, 337550768, 376036418, 833574935, 578666948, 736594106, 884487529, 499985370, 304541974, 898175314, 844824095, 215021840, 730683079, 472853989, 741029156, 123218874, 719777190, 648540766, 976890485, 44782090, 971405435, 354852399, 750523469, 321917430, 691063366, 695815563, 799262505, 5457735, 398136472, 14209102, 333846407, 123413665, 437863054, 897301457, 556921789, 448301928, 694457355, 445819181, 262451390, 56671432, 918003904, 222551927, 612112949, 7875771, 958167651, 36095340, 561887354, 438922619, 739222732, 305984398, 954727772, 570079293, 173899264, 555023102, 398251838, 797292676, 67569042, 27416441, 997549076, 284451128, 711700916, 643672932, 160509604, 652072196, 875417229, 876821388, 613389565, 60145344, 99877434, 843877122, 385843235, 274710825, 976931313, 110006068, 417897001, 897742487, 303579656, 690132098, 752074240, 878564302, 440520771, 595628229, 257083020, 765422360, 172366253, 26575655, 879506765, 346333674, 681887937, 707610719, 518876603, 86462177, 989758004, 454215737, 934749844, 864344418, 510517718, 64895377, 528169751, 68541125, 290765778, 46515829, 671081243, 67434462, 187566310, 421014114, 737658889, 706784972, 948418672, 579843039, 825471341, 414429904, 199803038, 966262169, 457322664, 158176496, 496771062, 487444901, 707589007, 418393626, 631902040, 196956838, 883864822, 708819216, 226146531, 155052861, 961466967, 378977282, 217959848, 197541503, 732186861, 201895477, 369765039, 445023736, 966383673, 984114978, 892269577, 513460798, 535918831, 753778757, 817878532, 908640122, 677598418, 251497609, 474007369, 328755722, 923146232, 400803115, 796280730, 229226198, 445083813, 307304274, 862291891, 558645081, 123919291, 370847775, 899632832, 84059127, 368878519, 822634718, 177060034, 822253619, 683001874, 556551763, 775431604, 684032157, 463231853, 34983190, 434661704, 674884863, 620652815, 906111177, 836544335, 883241882, 856918847, 962397209, 42652550, 306097740, 86222756, 149421526, 941348742, 995795093, 498603825, 597017484, 424777161, 829862847, 824661211, 619776486, 806541261, 812872621, 878571192, 725707268, 405806858, 10988068, 283547617, 974311693, 647427709, 199105439, 414698439, 390392060, 995790647, 931770406, 984754714, 886473087, 16415837, 903877807, 129974024, 978737533, 912306100, 571944909, 221028868, 998054110, 298311766, 37751022, 453781114, 259987093, 496011654, 585753711, 326844853, 441628813, 458756110, 530804732, 59769732, 69661954, 96789233, 494499523, 623315328, 906614730, 875963133, 357729413, 907970710, 877509234, 65665021, 768883780, 129238816, 62310143, 310418087, 832878354, 13986471, 508205341, 27199986, 679937108, 42237977, 507531262, 754788256, 390028527, 871970165, 291790567, 189807007, 750418647, 5094485, 119080746, 84143913, 333037616, 891862046, 878850075, 533310487, 760877097, 815984221, 755128570, 208624292, 630241410, 798235084, 348476599, 54933500, 451759777, 223147432, 352618855, 956848565, 310166316, 445376782, 539002233, 699328976, 435329481, 610893988, 396618962, 39783610, 349606217, 205520718, 297938195, 305079603, 189096614, 318350867, 490553921, 473118028, 813931337, 59067119, 7259296, 182737080, 322656920, 833549679, 38521704, 125715907, 124685417, 277302421, 941939734, 149224600, 572595320, 35506625, 418943378, 804289485, 532147451, 548386077, 747240344, 764818565, 988851710, 789046772, 278673843, 251261404, 683156183, 453053926, 25367742, 593736815, 493236468, 48139918, 212804220, 75603317, 569838342, 71624150, 4681588, 59403229, 165063888, 526933620, 395484377, 219093852, 323714933, 690123080, 678840358, 781172844, 457761823, 307921224, 383781126, 875213217, 779963718, 454304319, 687874454, 600660679, 629272118, 605864657, 830044030, 46044033, 342734184, 375606299, 746341816, 1452416, 423360452, 161995549, 497337203, 939044308, 758195136, 610921650, 410731791, 822649529, 671980011, 967566229, 935705241, 454523832, 945144694, 167804993, 820706856, 522625625, 415781390, 687548324, 401947290, 790430236, 146638973, 558452093, 52356955, 808454338, 651368558, 996194511, 478196911, 790021523, 15026293, 696007557, 792874512, 583446859, 831074797, 398764143, 584418952, 534856137, 862584436, 77432820, 938419847, 923486673, 210347424, 441696983, 126158373, 219842989, 792153929, 433951894, 835630247, 803906223, 7848678, 769751437, 617484841, 835553096, 746731109, 548962570, 633735409, 205286390, 810377052, 316930174, 623948040, 685936805, 577768706, 696731173, 382107839, 582353923, 857267845, 945507836, 565674420, 173422214, 255064938, 497656183, 723416594, 119480434, 838062804, 493317985, 756140136, 958572076, 915325577, 428828626, 174421878, 129253523, 171355974, 495845696, 202117645, 250207452, 107323923, 144030321, 549116539, 710200175, 857374784, 217914079, 334041458, 473437709, 881247005, 56603472, 445729930, 164634178, 51167057, 967472422, 818338859, 72508483, 480616218, 451036382, 223915606, 850590541, 338068843, 752533129, 632455334, 878935606, 911781066, 19640771, 830781701, 960971459, 828867426, 124822483, 904533296, 438334787, 324570133, 676327037, 273873515, 148630483, 436118823, 886580560, 38367424, 631824933, 221795015, 834799235, 812140123, 687487611, 343807820, 817262804, 985015780, 257488062, 437545286, 192170327, 658676510, 912249404, 126261325, 924489756, 142936799, 642785502, 731549175, 453228762, 824184951, 365160788, 907778231, 625368757, 696011841, 683348629, 707129448, 851551012, 467017185, 405776738, 905752178, 358774062, 969490479, 453049261, 99049227, 48076372, 150947179, 704815957, 382591199, 526687612, 308595211, 583839429, 483347380, 383570046, 475886489, 10936687, 383613632, 298349919, 894506055, 830230224, 591616766, 305445075, 217862743, 795327751, 130689906, 263026604, 269556379, 408795761, 479535070, 409342698, 980479558, 441010111, 603274154, 155035456, 987263300, 126417353, 519044424, 514386726, 726106592, 985977426, 110671834, 198733474, 386472057, 116979964, 865666220, 907926009, 340051071, 886253756, 863206046, 348695536, 600366476, 122894705, 319577193, 738203583, 30133221, 441688887, 702176898, 615645985, 426193287, 937432730, 941603061, 237664632, 443736664, 90153215, 286180311, 396118743, 531786574, 55573973, 511411227, 981939126, 807449038, 601839139, 251216295, 165397952, 477789654, 872856334, 492978811, 454377115, 758045205, 143921218, 605353412, 243517637, 940823085, 911229346, 195784767, 461718623, 754217117, 522577340, 626812968, 790823920, 385786435, 741493696, 208349139, 905009919, 897406319, 243070732, 303294464, 697799566, 547686513, 434355919, 191073480, 843666311, 29296765, 935810204, 172503029, 329734403, 79213554, 907252149, 834119914, 791934909, 858080022, 876650447, 807574758, 13327925, 910102910, 676422027, 476811349, 718125560, 751198198, 613059518, 29515154, 205820400, 27762768, 116226176, 183712076, 67200343, 348054275, 813869408, 740624188, 883110375, 554380165, 133429613, 477549560, 742411868, 896394296, 699958564, 972078664, 503491690, 598335849, 391761050, 436991192, 495458754, 321352372, 42627100, 133505032, 380462001, 879713347, 371964873, 837119552, 15176775, 687583819, 944870187, 850540095, 785223186, 302187685, 436255343, 785405704, 638461737, 680297740, 741302080, 116901800, 640482223, 127803239, 826477900, 167496195, 84567485, 829597700, 430789605, 911918624, 863910277, 661137918, 491899789, 882496984, 572328259, 77037140, 360228320, 302737969, 613302043, 19525730, 741894934, 678349286, 52180962, 816420194, 471206783, 16869714, 916613330, 585172548, 521287965, 53720496, 123964618, 495458281, 284054296, 597083427, 712036030, 685379543, 115068389, 36230227, 173650951, 548382934, 978784666, 920138764, 848450824, 903460797, 301491961, 81820704, 530767890, 578473583, 964381317, 61491195, 647886579, 976235008, 722816889, 278129627, 521602752, 646352387, 225714495, 989726800, 229663186, 628134373, 661084289, 118433937, 92655855, 332229065, 936405216, 938784099, 546523733, 123194735, 691984015, 366442942, 503646972, 785833818, 175205532, 172533167, 875698382, 683822576, 116093419, 715792434, 541893525, 188874462, 172307914, 124385453, 795495724, 235368800, 637794632, 763664932, 381232223, 737537248, 40112748, 936120306, 246904073, 657919833, 424663576, 556257433, 555251562, 735821764, 889561668, 854959140, 629292121, 286047062, 191792102, 541569492, 667572079, 548793788, 243223033, 28986767, 504182884, 312750300, 644650994, 851847591, 884678218, 944603517, 460111822, 772680397, 281383689, 29707575, 116095675, 172898568, 196163262, 957710724, 789850682, 236462792, 236951668, 875128598, 914205455, 897763278, 480085065, 729819034, 822804301, 246451381, 18501222, 968112243, 5418026, 432749603, 671626706, 126626254, 421552854, 623272211, 329274964, 711804176, 78096972, 966300689, 918607217, 46579561, 376934170, 44700898, 410418702, 696783706, 152626309, 798802388, 423455430, 130808820, 149263658, 336612649, 40606739, 707694324, 516135566, 740181344, 954083174, 50615366, 15309351, 775759152, 607819341, 8780105, 656967259, 804248153, 167320514, 658296455, 676014369, 527888602, 901471589, 210286343, 420335160, 258105315, 321358982, 275056009, 116985358, 861798776, 685195679, 827276117, 427004444, 276968072, 25535313, 861537391, 89380291, 506936892, 867523133, 999384313, 280117829, 407554766, 857683033, 368534545, 573911418, 789252911, 149358812, 854425567, 424194331, 286965382, 782286659, 462698385, 503648498, 234457846, 367294345, 506909628, 355936164, 964502334, 987528010, 412610658, 852976964, 988803132, 628913675, 793904699, 337897768, 744090408, 579348161, 626822470, 162862964, 288930339, 326756721, 229725280, 798593888, 445696194, 724830522, 664785536, 352175478, 105620689, 922078395, 188005909, 251156903, 921178987, 571139312, 601287176, 573019432, 29665390, 977137503, 767876769, 978508419, 958978156, 956738786, 14712311, 96398589, 919539994, 659071864, 791905817, 699106695, 284908235, 252476643, 599088837, 42288612, 464208004, 106672708, 762401389, 504439853, 696198538, 383036799, 531959563, 251104312, 618697240, 583860507, 557620972, 26190421, 794724879, 578029050, 521714490, 175405406, 620585280, 124771788, 181761954, 363389375, 902549741, 226313181, 753239994, 597599330, 917577945, 736942063, 888726555, 765490291, 213920377, 803836939, 388365, 96993819, 980971581, 258795003, 319412452, 292984871, 556039704, 941223022, 803122893, 863956252, 306435744, 353472835, 713963349, 58849828, 205597070, 475549692, 246163671, 901543563, 937227241, 150978135, 426287782, 935570669, 698381489, 32203628, 181816754, 812713167, 552831622, 696068408, 277668437, 488792, 10161551, 172411936, 605720227, 113387484, 227015935, 651540150, 212742457, 509906474, 101009653, 107091772, 321239181, 556761458, 877497146, 386045044, 265773967, 610711772, 761855302, 206655696, 155743474, 364393821, 309919422, 646628250, 786069163, 442639608, 95880833, 124196174, 312928128, 998024407, 530503919, 206669083, 358237276, 508956748, 52668565, 338727594, 844072842, 56639387, 296267482, 328543373, 301014305, 420512611, 644462926, 744161217, 192109383, 435963277, 302114186, 373593866, 185977253, 249647707, 717825647, 166140265, 278947427, 447493582, 144350786, 135714416, 438733520, 734025812, 512000189, 87665500, 858111568, 590384829, 106114519, 161162560, 503873038, 900937039, 492860730, 567217091, 3401256, 74739068, 878685795, 456340254, 867250934, 426260372, 82493442, 897704421, 881902392, 192475025, 586279053, 108330209, 160997224, 75270497, 548687858, 145142501, 414506910, 904897190, 831387820, 69945783, 76473513, 250906919, 676714948, 750859966, 869296623, 13606765, 947811734, 761766076, 587949289, 411763527, 55797296, 800101098, 589234611, 598640332, 739169865, 704244036, 539506657, 411152970, 89008120, 487223325, 879799696, 119294707, 232886398, 607729537, 808724591, 87567690, 96998222, 898680311, 750221255, 937598641, 8030589, 691530799, 130496876, 830555643, 33785600, 900815477, 757622976, 814153075, 858003944, 445039794, 840707761, 291249930, 850201094, 752955108, 398105796, 78455495, 235493606, 886840029, 912092749, 79501953, 217956067, 718145712, 475206601, 913553077, 773178317, 729974365, 120332994, 249160368, 102117078, 107168152, 773060694, 14553320, 743727303, 745913758, 619909507, 989382911, 435237145, 519757585, 401331240, 381944812, 998830295, 41510774, 507404770, 266794719, 254847124, 357954843, 988194002, 760127419, 716447271, 422470923, 165001158, 89648909, 847738309, 784929962, 920916123, 345349515, 81681586, 269272142, 712772726, 890173641, 691459382, 412764521, 711744000, 234250636, 21452022, 193796914, 73194176, 932440095, 569098844, 572966664, 569926812, 538328595, 355176975, 83300874, 611098791, 496641651, 151882898, 615459395, 986989753, 762378282, 742504216, 963645612, 433437393, 405116893, 714125989, 707883404, 389584585, 827825285, 373397839, 9194607, 51826113, 754105813, 435946882, 610712748, 194203867, 986156156, 740905789, 69385591, 872282588, 491272271, 728795800, 767304798, 565113823, 619130905, 276560487, 530855623, 225316371, 754033821, 307188413, 432461135, 412586366, 545495581, 50045096, 800519526, 17149848, 412293652, 94746565, 404001791, 386465853, 284604398, 790224284, 110766759, 344104860, 401879147, 310084091, 288902792, 273093995, 253764775, 928438832, 552829705, 647575807, 20342647, 462883399, 284652575, 130278255, 963258214, 818751797, 829018355, 194950168, 72106757, 177826319, 297432055, 766386511, 124919354, 227027882, 345709335, 900710855, 853008724, 275046040, 677769531, 114494834, 96607286, 786535062, 144108635, 525436995, 319795977, 301138244, 648863233, 129870412, 79076638, 934484216, 722094275, 117456799, 297161540, 638257005, 130282271, 379073287, 926607975, 333946154, 293454395, 776768099, 645983340, 216504075, 363990203, 700710683, 406739092, 594951602, 803677594, 666143470, 876971700, 683731188, 159269499, 314983600, 574744351, 851061309, 324825816, 10141630, 213009970, 795558801, 768733907, 252828124, 54158000, 290331139, 267265818, 848388138, 596940076, 921983848, 782425577, 566840327, 310937912, 739238421, 571706132, 899935228, 255659938, 444773944, 574047617, 926164504, 947127174, 485969761, 546259401, 981525447, 602770829, 263766033, 685101958, 590119432, 479845615, 868632805, 700314854, 562278694, 116086632, 472949537, 36232951, 335003569, 748449831, 501707241, 703430052, 534799300, 885645917, 394197645, 850655290, 464055711, 625425377, 31768780, 371345297, 930815167, 886748736, 529155059, 410785132, 900475125, 54101512, 194510527, 683627750, 445160777, 344809857, 426768082, 413679465, 361007662, 642830528, 978630129, 555330800, 936192185, 368395130, 818580403, 324739915, 477948912, 158815252, 516508357, 871496617, 612933491, 695441367, 318724367, 316820379, 140648235, 462006931, 718454535, 149781250, 842462691, 517112894, 540281660, 535758228, 95585000, 106373956, 467627690, 522138579, 58435303, 511608030, 231382232, 816419057, 937260022, 930448997, 152397751, 920510256, 945339785, 315488745, 152147433, 727832012, 503018377, 906214536, 644308956, 125528584, 230498502, 768377050, 245600627, 942130686, 971552822, 446830460, 198844341, 15127533, 29324363, 812901042, 737068128, 849722839, 37986067, 420093764, 249329660, 289388244, 560732859, 500585835, 460318126, 632445880, 737917490, 148598705, 796590174, 170072294, 931708888, 696103584, 633699742, 791935784, 746770431, 871453977, 78776725, 663511421, 569402422, 148787847, 658809574, 105934542, 358625575, 93908418, 400258540, 173839461, 26942941, 246983823, 887848506, 603019791, 999252429, 396408898, 344554858, 888870234, 131103512, 763883773, 838703880, 308841150, 75999829, 136189231, 33189363, 249070698, 416502424, 911402215, 469164548, 951239739, 262185175, 113172479, 823678159, 179262719, 116689099, 972949860, 781165275, 953618479, 9475737, 704320228, 34236075, 1940908, 844061593, 945303198, 206455390, 385055034, 982626009, 793965997, 123948534, 729400376, 306267240, 294286132, 821163675, 911054071, 517493625, 870052474, 789619984, 219676383, 660302797, 12251700, 217501732, 1845292, 453446438, 79712951, 660866921, 988553632, 430249315, 521606690, 722852804, 851685468, 590362477, 976855519, 813982496, 184646981, 110151052, 949119889, 342820095, 123847182, 168680411, 196661757, 659885117, 709240287, 136237260, 365956021, 586384167, 552641263, 898661415, 720143846, 641209295, 418883068, 731469043, 549814219, 59739059, 947352625, 777840114, 426880210, 603078665, 710260562, 441997068, 339314563, 281559684, 143705179, 622670898, 321392497, 30405669, 599087190, 169153599, 622032450, 255798394, 94321371, 15153128, 784238329, 671142723, 313141270, 340823213, 577222090, 507557144, 30426465, 805711598, 811374041, 730335466, 764979394, 475693799, 956864317, 874613260, 636244357, 615904482, 622122387, 799443109, 61641952, 660657781, 511367514, 788589368, 327085412, 738579578, 78241268, 528191124, 62903198, 70886878, 122675543, 461686644, 992858607, 114265489, 217483034, 462123624, 854740968, 452254760, 108944861, 805779896, 80651093, 90853678, 228129814, 325736705, 720611909, 928548376, 683163119, 854673994, 600786412, 404649030, 325719284, 363672256, 260467687, 230830038, 149062462, 286401428, 852683440, 138741037, 152744091, 63809604, 672037583, 903814888, 94475154, 740497398, 731856787, 433267583, 670132329, 543775897, 352604401, 974900400, 914933367, 444975579, 359112917, 362998578, 315941348, 307682813, 632180629, 714942194, 28855843, 742319045, 113090013, 47992461, 532929694, 612532038, 41059312, 63369335, 848115765, 846096460, 467376268, 685557919, 126764034, 663701392, 964402325, 473217279, 127066457, 219694219, 485457900, 828789721, 6435049, 714595095, 53843282, 408599398, 983464017, 616301950, 535581887, 690372429, 927328903, 485128098, 738471640, 846869185, 79934397, 859565063, 66040995, 566957540, 147237858, 620616798, 951076738, 195372107, 300896151, 766837812, 845175407, 200287421, 692001175, 639843775, 30916344, 435082082, 677551289, 827833440, 292470586, 651163478, 156308561, 27679145, 233919368, 942561184, 902417250, 47700759, 702188293, 219585025, 276875441, 725277441, 575824810, 116526419, 426097244, 508460419, 823942047, 388547653, 534780944, 421722593, 481394718, 939320418, 486129174, 929094999, 588506395, 136516291, 185410876, 912991557, 797961499, 654867847, 773619289, 935758005, 446099854, 504674581, 646455379, 944835556, 793334595, 243033525, 599101798, 500390828, 781566701, 325534928, 897164229, 444563974, 723259331, 359627246, 606090515, 700534232, 187728928, 107729046, 53291557, 781110802, 717805310, 165796375, 475295395, 937507277, 792183137, 127303680, 596829728, 824489519, 559050036, 20634774, 861329530, 287665155, 365120812, 540990185, 99045961, 596227806, 15375927, 609654206, 676247117, 639617751, 694419978, 905006102, 632361930, 216827621, 217802253, 215902987, 466306369, 47545215, 583047093, 789797434, 977298190, 646339541, 366844583, 409809829, 636684436, 684167709, 965663778, 767846334, 116790844, 610281311, 954759482, 843715332, 33093793, 212349037, 590444501, 226371767, 888261281, 68298436, 808237741, 870510462, 712849370, 833990403, 89331505, 49973524, 637090222, 650290095, 220597505, 99893621, 71845008, 75430694, 877249433, 243374408, 303534058, 749456903, 544964489, 240589549, 733762530, 571194580, 113962348, 762828445, 838022440, 857712724, 504023326, 134346105, 328189037, 111268309, 240478714, 531298916, 997007614, 579369703, 462904344, 911440133, 427810016, 107890068, 979714645, 596176442, 149195969, 574393488, 253238244, 319780834, 508723326, 407057936, 722014518, 104240584, 199568815, 22520804, 441020298, 270361591, 149792764, 77873214, 585765891, 17609961, 252388084, 617782625, 603405776, 237858644, 466306084, 516951979, 831577122, 664610759, 566125808, 767892866, 97452054, 802205751, 650102833, 750995040, 218402847, 651328441, 352207927, 608030342, 137206136, 714239527, 455977510, 534854372, 983782095, 644456023, 336914611, 275907817, 73037818, 387121122, 525988874, 694396709, 669671176, 457563191, 389390983, 299020689, 284445841, 933224965, 654903653, 103737382, 968070880, 797452724, 938050153, 610216873, 686344389, 31035070, 865480729, 753696548, 811443407, 425940642, 506997169, 136929658, 934844332, 109094593, 37367089, 492301907, 522298144, 651824315, 424862382, 305746329, 659938341, 125253510, 831574786, 644005793, 135234075, 871572732, 609001590, 609248688, 860597724, 403870148, 183042420, 646163432, 723897692, 834658590, 722703088, 41685094, 901443454, 633623237, 928105247, 309892819, 850574922, 127821594, 387252482, 483130258, 651700392, 214628711, 491960068, 43570359, 833126022, 427566252, 922427748, 357364398, 798344423, 661774906, 474233803, 245800921, 100476193, 387883211, 434227476, 329903491, 572494407, 663546336, 545329390, 138518136, 105413489, 195590192, 545591004, 591932799, 534419165, 346388255, 412560699, 392374357, 701894286, 121091054, 983517972, 786389263, 612022242, 869940590, 421885951, 809992411, 135481798, 286856624, 431480287, 747245278, 515660553, 528823901, 19633772, 114918052, 732258820, 81909034, 531628395, 753453867, 116721607, 796584520, 864235958, 50795615, 536329888, 313536696, 921618505, 128392589, 373443553, 477344786, 571496654, 33865124, 279898473, 398748306, 149486374, 750406149, 654024787, 431180915, 56225036, 844283583, 999488106, 195511939, 909158639, 503156775, 505946462, 465530271, 562027900, 725888148, 684725393, 138084118, 558858527, 374517340, 598755803, 429898305, 644033005, 135579050, 55502026, 888723845, 419967818, 935377554, 567922845, 833938140, 307598263, 798321144, 562984122, 590743374, 412000677, 935804634, 387551566, 487224620, 40312763, 925415636, 647614623, 514259873, 73480095, 615782822, 546961279, 220685150, 386616518, 467432714, 85978529, 159607579, 370140105, 887908514, 419454849, 838728296, 408352290, 277570307, 516984667, 98818792, 243399077, 472087098, 689206046, 40326615, 9307438, 464505229, 506161674, 573300215, 961509965, 695550626, 641618390, 713350563, 776496835, 655553826, 670140076, 821476862, 257099568, 711973300, 995403979, 314297879, 77796453, 652385701, 409095732, 963082742, 472971504, 111216786, 312662450, 520263665, 620019800, 404641273, 565430137, 741529288, 36621650, 234903491, 282954138, 784679482, 275057671, 219851308, 283407374, 875061693, 362296167, 630448746, 520892916, 192426053, 510710440, 282845815, 245558851, 188016299, 199896468, 773638662, 55771545, 890376917, 611612530, 643243423, 206529146, 456807907, 81948225, 22130829, 621879263, 837543692, 78047568, 303227179, 140358974, 116743477, 510112061, 797282332, 359362411, 67958992, 366442807, 374681901, 883430294, 414202137, 881067859, 480314783, 195128400, 786754531, 510660251, 725135904, 598663531, 437729406, 178013924, 547805598, 139056667, 467903556, 601916159, 446146257, 574733916, 92558266, 661633481, 778179082, 501881557, 186379023, 191616076, 966822157, 774227218, 444196241, 346624658, 229823396, 991061969, 320494228, 341738920, 544819295, 853018942, 39552547, 178852332, 885122678, 403949743, 540912262, 688603281, 921095416, 392050180, 328491701, 366782035, 81516451, 700903811, 705872431, 200514800, 621785531, 708381226, 381742917, 177144105, 918003391, 160058747, 945195559, 892652599, 960625351, 181770937, 394637852, 827378612, 401379185, 282674553, 846465884, 976593693, 496156255, 63606143, 706011179, 349631100, 839633140, 626567067, 432425753, 818416699, 650292004, 231961593, 325884166, 381791854, 939818174, 912143929, 942445206, 512223714, 116405318, 737458100, 153973494, 352998906, 958565975, 659855315, 892980068, 886849728, 701952011, 681229417, 222675191, 601609233, 781990623, 573899308, 734850537, 440763877, 241891518, 717015008, 248392509, 615467713, 89087389, 65198641, 206380604, 835817493, 496300625, 697793499, 425466370, 464929845, 846313572, 404869848, 60848303, 109642656, 170517327, 490669658, 275542918, 958854370, 185108886, 68190892, 303718842, 305786100, 981147945, 305516608, 768074594, 446131319, 779462708, 458465413, 152289638, 718051990, 342440778, 387152372, 516791567, 680015465, 582472776, 526253095, 647687345, 470800003, 188847403, 443081457, 562622858, 414213357, 295516247, 369692313, 875095039, 993728808, 503893225, 502009273, 782986446, 915103943, 177864427, 684843355, 779047124, 980583410, 17416970, 281146283, 557994896, 418814117, 929552834, 342788747, 116306551, 513481672, 206664753, 339550119, 144226532, 786471938, 161341160, 67044861, 864546201, 500853451, 281311800, 784347505, 241247450, 399427397, 483416610, 410162279, 931703124, 39515086, 603632663, 615704909, 960790724, 474882754, 209073474, 277236275, 826152870, 925287131, 917206986, 646038566, 829148099, 207294716, 134298447, 921471760, 320750763, 640543548, 504391064, 735761215, 699985156, 277894296, 122646528, 989662847, 391193904, 577519226, 105177490, 21288381, 468055875, 500782034, 587258954, 58192962, 80092620, 392119161, 357232903, 504878771, 22365837, 600491897, 56924564, 178192785, 434812172, 474059299, 153246973, 827267008, 372605815, 719792934, 790640482, 509417354, 352942954, 658021460, 290480118, 916497829, 573240508, 223801898, 159621496, 502371819, 766975695, 858396201, 646446314, 321589339, 152069202, 78128576, 676886699, 571110939, 774393998, 943996022, 599653462, 773892219, 156736472, 56596708, 553596261, 255569423, 102448402, 476524571, 108067167, 464646845, 33357699, 173957906, 216811453, 268156382, 981908731, 888892585, 993766454, 105444322, 563469291, 921839947, 199380128, 249833174, 954331046, 54475418, 800223054, 409323667, 185117149, 312671621, 573353407, 971347427, 284854660, 80099106, 772878521, 893704258, 335925368, 43684267, 980993519, 504435849, 686159168, 989563436, 706329581, 657225573, 409299440, 560319678, 139941083, 118007090, 203476333, 246562322, 825484751, 815797924, 423084834, 833773241, 48912148, 550594482, 629908359, 308404964, 103590001, 242652577, 760508136, 289014120, 384006218, 651905060, 247061764, 888419684, 524040038, 357096837, 739720210, 509540490, 414928819, 184780026, 804521851, 845224946, 91000723, 210509311, 804446580, 668362506, 157078289, 929455635, 939822201, 627950166, 482358823, 766713405, 566024023, 732452, 988432016, 568898293, 574396722, 699442681, 289370262, 876101632, 551615329, 556701089, 882257437, 159503175, 816323799, 828394628, 700488082, 802227118, 357029983, 973584035, 323777426, 855705507, 491655659, 809460449, 660114791, 354986707, 87985094, 938954953, 297986458, 95880098, 611548715, 536689866, 933064827, 139762527, 939848523, 363502603, 220231838, 239518876, 97929129, 827578049, 672044948, 79075287, 128712679, 149719195, 206227283, 456614990, 492537324, 630523216, 450478445, 737937628, 842997322, 267628795, 642881077, 818301855, 652635223, 113654184, 556768469, 63062312, 774162392, 615136005, 471925116, 940189267, 690569751, 756406933, 898099333, 577729450, 715573113, 690910018, 108582905, 71715450, 868249891, 423810583, 34863871, 814333792, 931538076, 535960264, 894450236, 711949305, 925002871, 255296241, 168960132, 674664091, 544460021, 516047070, 90515141, 470410086, 526642701, 619878047, 511148568, 382872103, 133759458, 610520372, 533940665, 88744367, 874739213, 86941012, 353564833, 544216980, 628731827, 566577961, 508545382, 409837325, 476144634, 650077184, 326222382, 934721290, 580207953, 947403900, 25833045, 405661319, 143041786, 477705677, 778538043, 852083209, 191302259, 476786038, 662475239, 987060167, 956470252, 107866314, 878591382, 186767941, 768747622, 764783217, 212995661, 851222898, 212269311, 775275018, 858625528, 957471318, 336696452, 505489554, 363328618, 670914257, 737101081, 141947025, 926122532, 458684302, 807703221, 666642107, 313341731, 252710387, 695772599, 794600545, 15773618, 241614987, 302912835, 750474129, 712400236, 772109596, 883081123, 477323271, 271193032, 981401648, 235362731, 209988973, 693622119, 532060829, 341237789, 576419662, 420575635, 396608892, 825294652, 157286155, 584997378, 259131460, 506995241, 363828819, 237117435, 965922049, 940728001, 26909814, 683132004, 816811245, 45073980, 260489697, 64098574, 991287297, 586835631, 931614660, 702693752, 843792237, 287045064, 423111916, 467213418, 701143815, 108443826, 19827472, 826151715, 856920991, 740961472, 879129710, 920604070, 590484977, 861975285, 19740922, 170209807, 146629000, 428596717, 38037815, 524494597, 832072531, 102914816, 342965912, 46387243, 147688365, 818867192, 710445638, 837058385, 982265012, 856488249, 637331663, 946409235, 540915193, 371923755, 570258754, 87386761, 859581786, 422110794, 770708201, 839857276, 708610561, 434985523, 739377749, 129977113, 648268238, 436717812, 807749971, 679093575, 80168720, 153710746, 153118319, 953393131, 413724791, 20346267, 510629712, 646157522, 750832122, 930448718, 153129160, 635534849, 215022757, 388087750, 883120923, 238138055, 814925598, 584867059, 90635570, 561679587, 978531092, 582576686, 357428498, 194252274, 322129523, 358046624, 160514668, 901032940, 393607660, 58608372, 917428911, 92439882, 139217251, 448928230, 754337122, 876520976, 535475324, 807186361, 631921815, 293435621, 133472886, 745605970, 138768742, 702560612, 807517448, 715000436, 549442586, 429835329, 162741716, 745625567, 332212187, 834265467, 523215659, 65663854, 860471126, 549773806, 860425443, 648612814, 73362720, 493465495, 678921851, 748345080, 939344020, 550825038, 11933244, 5606454, 465847934, 9516738, 308790381, 387215681, 554201759, 117621434, 397480818, 844048457, 582713312, 14683425, 652694254, 518558098, 4011436, 904266663, 782751642, 519462427, 261333269, 116766080, 702404286, 324087797, 828249201, 968461931, 742317675, 634528636, 315712589, 860645156, 504647984, 341947942, 631730354, 328738112, 470611013, 899562684, 732471129, 994809836, 210517944, 680231232, 709860743, 406608164, 702866525, 477326238, 369931457, 16770487, 850609244, 193785137, 879597762, 273123995, 850402292, 572849375, 919096708, 645893322, 913623513, 347107985, 454574901, 833206332, 190018587, 210653063, 62620298, 411179218, 708377107, 777994919, 672805249, 771711704, 123852166, 317478412, 566406604, 705447189, 68994775, 608200277, 137273923, 736782172, 908675085, 894112310, 311275106, 637526121, 795780146, 555426249, 716635468, 962950028, 6880615, 307955360, 114977372, 862916646, 654119580, 633711600, 351792821, 822785456, 695601680, 383624622, 6843644, 607314851, 883536090, 444936744, 183663128, 254660564, 306113067, 783035434, 313025422, 985438280, 205666181, 431660337, 559960391, 593495754, 303693959, 987477354, 617892410, 150773316, 808274627, 850095206, 632759142, 523722443, 491728307, 403128830, 768036972, 212072826, 557855, 509090448, 352401238, 244322638, 436383561, 687782041, 579603077, 31561833, 710761525, 315313434, 387737812, 589073533, 838101105, 32774728, 729120922, 10008651, 597985353, 853829215, 245472154, 218082362, 502146530, 945283012, 463336379, 901290133, 880158227, 532126481, 261428308, 734668730, 359457147, 548948186, 88997775, 6786919, 454453730, 57031391, 18200693, 360642648, 383600890, 981354614, 488224796, 995164089, 106135103, 774980841, 192815674, 271668847, 416256771, 250847827, 618399696, 79568320, 583970188, 65219679, 808734989, 6548544, 301030643, 402774383, 121613919, 799094022, 478544989, 970819438, 809479159, 373911889, 472332970, 568867730, 122474512, 950854190, 370194547, 260613487, 648429017, 782106398, 853740159, 994310190, 363294802, 399085179, 145170929, 944433212, 741508478, 220698946, 144719784, 344034125, 914635532, 806448950, 834008224, 539626968, 213195491, 868047710, 646232270, 657387360, 296675442, 193420881, 534821669, 87221519, 53185693, 932369412, 408411860, 600004588, 772728253, 84946745, 671098784, 836606319, 913719500, 428663519, 406464373, 444295741, 9200706, 608598350, 642079923, 910851138, 794071686, 938509667, 628080668, 662166983, 153821694, 208822414, 162634652, 46660487, 118794242, 392890936, 547982260, 832184005, 939063839, 319831271, 72240518, 678242089, 229640144, 943109153, 492085692, 54015248, 323839753, 456702753, 190206970, 93886277, 800365576, 12628516, 581287103, 755759470, 705357027, 85765835, 721584288, 59446530, 983418756, 244520959, 82282859, 888093126, 349540254, 286940938, 136351896, 113430054, 400169565, 600686528, 486003597, 180228717, 655754161, 148484975, 802313953, 18247378, 496397131, 432838954, 909254549, 718288610, 291119527, 583996503, 539453016, 239422153, 43451324, 953111117, 223627494, 365191491, 818572396, 485584121, 692608214, 866130276, 445198815, 781283819, 571112556, 740514333, 27880302, 348281950, 865559032, 290681420, 821692248, 498232692, 789310237, 788059804, 370843426, 822578743, 186843765, 27211750, 873138060, 400519089, 14121881, 599681424, 20867706, 856311483, 824274508, 24740920, 43405807, 515751800, 818324989, 704031100, 20959151, 193025820, 204784252, 98080526, 856684060, 197935423, 170135886, 855738033, 667188355, 981568320, 191652901, 940190459, 675821560, 154465018, 798494704, 909360891, 148270953, 589286746, 872551898, 966457278, 816738374, 432126348, 290602131, 55946605, 288825643, 345545901, 467999860, 179311189, 857526991, 875780994, 445728070, 725721333, 385249056, 115137026, 161390033, 760170053, 414560826, 898559188, 404607119, 40074987, 82835624, 330942792, 238569028, 219266307, 323079177, 395624314, 301876425, 79557502, 634212767, 948798021, 400345111, 4234226, 642885246, 201860819, 540205431, 451555561, 962884148, 352687661, 792841726, 450857455, 640115663, 718895896, 778936287, 853940915, 306877901, 51759271, 673683465, 406947796, 168161729, 639490776, 169503015, 474212091, 207354520, 316676391, 279647127, 140151521, 90816656, 75004716, 511951621, 154334370, 414756911, 140214782, 611456684, 974056320, 923490559, 361198607, 65443659, 667891962, 244280647, 745745864, 317098191, 240164167, 562195817, 572178942, 975749067, 947800586, 575714005, 778924378, 960908958, 95719815, 362348556, 819808364, 246576716, 102829838, 221519311, 370553991, 877802644, 922051485, 166588727, 127266449, 582103876, 775108843, 505372946, 400875880, 54854555, 700188618, 297916886, 600180083, 77517740, 98576068, 615166154, 94889503, 750746258, 495124112, 84681117, 379124769, 86922475, 571660379, 368557666, 478713686, 238860515, 400196540, 669449666, 244928624, 148841185, 785683050, 858582039, 952109972, 680903048, 357369389, 147349365, 186717601, 425497036, 221563288, 158799266, 709633631, 423049242, 487507284, 290833668, 986610625, 942928978, 493619149, 652910825, 562692093, 308623387, 201359293, 454640939, 252008193, 574480536, 723199106, 211782817, 444253563, 844153504, 764002527, 861742035, 332133379, 549574262, 580098373, 238733142, 707449557, 606743671, 959279070, 288933010, 247726727, 798340160, 549635859, 438773932, 183496107, 832438852, 319200376, 55525206, 714746144, 561627254, 499737650, 169225730, 283118431, 682146837, 300932308, 860079893, 6491481, 499156461, 77041657, 552066078, 497933084, 530577284, 502354790, 806580117, 402547854, 610731330, 309659234, 739892276, 38283924, 763569567, 794519269, 218476877, 237262861, 948041097, 800643821, 593983388, 237182719, 144286676, 620930020, 302426640, 147819720, 434477705, 151940687, 317596211, 194138837, 928700116, 52220143, 561629137, 924936532, 688688599, 363593534, 543190575, 423070937, 536476684, 127335432, 910879508, 543809105, 638301358, 196135320, 326835300, 524417682, 474674598, 856956130, 938069138, 973651275, 206743377, 927721318, 765511765, 936441322, 606307934, 122316973, 377238653, 883099301, 476609463, 395842592, 377859843, 198079181, 682200309, 346356764, 214215438, 468264497, 839826706, 224349565, 176322612, 613062978, 984638682, 118345073, 572609592, 580787534, 76898525, 525152536, 746563656, 390512168, 249084821, 883675967, 972563152, 907970469, 945833293, 668856603, 68848970, 554544285, 856385279, 738166518, 617541826, 777184939, 724767375, 391092, 354992610, 375447520, 234979523, 486956731, 358626764, 401069816, 349947118, 719727636, 506106598, 567223906, 153169233, 958312229, 803926887, 874911073, 473214009, 181591397, 919365527, 369400045, 358298279, 877449041, 249994033, 999521412, 690658394, 179446387, 502254202, 659559182, 696630549, 212903170, 428381352, 661192732, 649080345, 140738677, 248565419, 705600105, 451026941, 188719369, 240352759, 233186061, 234972906, 893640264, 932208388, 196532880, 872458643, 114842344, 18670639, 366097003, 545869644, 432874381, 374328017, 286506419, 263763793, 886773474, 22691884, 699689097, 705894288, 853878867, 449282376, 821698240, 628638529, 160844361, 919882096, 92694910, 218251393, 613628676, 447070862, 522328239, 67797594, 170299044, 390568265, 265700263, 380678228, 748831205, 437145283, 341563977, 179926491, 90309079, 863235684, 406055439, 284113118, 835700643, 159413364, 57554676, 496313572, 113247344, 322934212, 641859093, 354902, 995721219, 274527971, 9114946, 411945853, 959504325, 867179544, 34483422, 589404266, 123708485, 1901374, 12048958, 812668129, 819404410, 368021393, 469105814, 359054649, 439612027, 817677524, 16159927, 505954683, 250391312, 442538642, 854681355, 464123119, 409119643, 332896691, 764975484, 180909526, 950404744, 230467861, 312383648, 868723522, 237774047, 418010377, 208282105, 54616392, 188940769, 869620708, 21624801, 911004293, 372451998, 592459926, 368219276, 935379960, 380759383, 403752008, 794714580, 27682088, 981759045, 933527822, 603562129, 216378233, 922622848, 159781524, 943214412, 321177888, 888140810, 221716299, 764066581, 623392074, 533658098, 116331653, 465944358, 194165400, 525561927, 958251185, 362951944, 277839645, 412534164, 590095604, 449619983, 835720554, 860877140, 473716503, 676071350, 361963269, 801460065, 476170138, 956770468, 824080819, 359751931, 220562066, 786770611, 988103322, 751340479, 841887395, 511811937, 975727388, 627000159, 553867711, 815756205, 977861876, 919210693, 59002323, 457732184, 564946355, 919983289, 720828316, 791221363, 404918855, 93643261, 816188462, 302833638, 732381506, 683079931, 231357529, 127368991, 517926030, 553703183, 395758838, 727162563, 711187836, 957846922, 172439462, 747843969, 878889550, 342332830, 975876758, 332902365, 979944156, 162833095, 376631073, 655356397, 125976272, 108388509, 844053692, 74767725, 628553837, 733789817, 300798797, 323063964, 70137530, 751506598, 784999176, 74380236, 680887617, 160715214, 550762013, 607652666, 578813996, 934870258, 900931655, 154851849, 518173343, 715147156, 151111751, 169470390, 703484700, 245044, 869194589, 663005604, 207682406, 835812346, 326167633, 404657543, 539099574, 681213720, 532706057, 693934011, 393527855, 790721535, 596006913, 791895166, 187469555, 581484421, 726047825, 716414067, 305580552, 514372892, 983987913, 385217571, 555433478, 981228497, 890375629, 515029643, 103856854, 897787525, 728131639, 386875479, 276797950, 930924928, 259067612, 465678576, 92713854, 713840660, 948778788, 264357061, 854891249, 285053106, 368123412, 993346436, 157710824, 612107365, 23643369, 24218802, 195530567, 268431872, 447654104, 882662485, 776233050, 884272525, 234275674, 918355681, 53449266, 444960253, 608059079, 299975939, 119293957, 993545306, 768614011, 47233966, 977199531, 964964765, 513388870, 313600082, 495656556, 689464789, 987776493, 191802323, 411213659, 500909822, 872262811, 588626997, 736013006, 867219219, 664585383, 690294033, 19659728, 872457471, 467985538, 489919005, 706316344, 56069438, 486058434, 980519369, 663051196, 71509343, 443562978, 415899188, 934559967, 311796192, 512787356, 55113930, 858829733, 80978239, 222916004, 974957186, 676339997, 591945474, 972528800, 21994083, 387611116, 24779590, 838610861, 780805371, 823801476, 76480102, 345411957, 386639045, 711130745, 392594109, 543914266, 224107929, 592105492, 602430711, 955995392, 456245200, 173434851, 415935795, 261508601, 215907323, 316837629, 20502780, 154895109, 422513872, 429239027, 706081294, 674579477, 547532169, 662713795, 741581147, 450301120, 343980911, 164026923, 640124905, 250480091, 672051598, 496424982, 730477090, 689292870, 554661355, 97691908, 489453472, 529195999, 729242222, 381058009, 180984673, 314421409, 786404039, 24026831, 547202256, 59745999, 256226234, 376941929, 199536384, 846751169, 233582117, 855965037, 369809620, 112875246, 535860506, 308765216, 837710875, 195354501, 659434468, 651564015, 309473835, 565128131, 364454454, 29322934, 96014379, 881736267, 677420551, 62317962, 274352286, 473484552, 119577798, 841267784, 564651074, 159000868, 303493780, 668842786, 688602549, 620474547, 386391718, 489892216, 99801765, 966343016, 905425870, 376984456, 116560254, 400190800, 519522878, 204976796, 28725687, 810313493, 328502771, 467985194, 330999695, 457358494, 160076719, 448788103, 429612486, 137759379, 784980315, 237534395, 688403044, 495984596, 399197842, 576826513, 548907486, 780449662, 304445746, 749435326, 449614864, 244847069, 456867449, 978627401, 531788607, 109163595, 642183788, 652314212, 668321632, 101001944, 267151096, 803955521, 929342762, 747342451, 287971269, 204915418, 66244712, 672591776, 578510252, 963992519, 776110131, 518374516, 483388199, 124474298, 722963762, 715486337, 923201780, 84923216, 450393468, 46512151, 864503072, 29814276, 228390065, 466579228, 883942595, 272189963, 937419180, 610181898, 248682366, 716493834, 565822477, 709366087, 664680566, 980073433, 912409174, 367907341, 357877264, 515092102, 593583063, 131746244, 774490001, 862469558, 444347339, 82117692, 580315051, 744196092, 907291874, 997309783, 579141, 517183621, 458241900, 75279796, 447537952, 320841354, 124394697, 975203235, 461895056, 588344150, 656542570, 195913641, 51336612, 223346029, 328407368, 778032030, 231544671, 824808479, 578766984, 208501204, 906090229, 818855934, 282201787, 183532174, 827738498, 462114286, 332974977, 601689095, 638328446, 222998594, 31147360, 930315782, 58981262, 416269365, 803163378, 24869889, 138572831, 95911731, 920562787, 501029150, 19367491, 788419393, 434545416, 471930425, 655256932, 982780086, 654893142, 602470387, 63485614, 234901852, 165393023, 454415925, 921879405, 433309871, 990492403, 271525969, 436600048, 772726255, 792375757, 868470374, 702060968, 788512496, 891098005, 840607330, 981098158, 634015295, 136825474, 74164279, 98095793, 885599874, 70749789, 300081854, 213366636, 824678187, 628933339, 103438476, 866842171, 15161972, 240674946, 619066922, 758989299, 542952655, 136294503, 137367818, 765246296, 739628195, 955396122, 116184908, 749810458, 518437810, 220311203, 270553373, 983179955, 398248053, 828843118, 86864499, 847927457, 283244625, 886728252, 467486758, 672853705, 424501129, 212899860, 705701939, 841025008, 446962106, 927623760, 791792940, 662913072, 956287220, 103164833, 78816633, 330542486, 512442720, 719147007, 344000042, 774687212, 879940773, 708323258, 840324695, 428632461, 336243576, 21474504, 202482242, 845928330, 888967775, 40150671, 500146419, 366089112, 732856031, 425485451, 666882033, 489783264, 735604087, 722181247, 973830408, 705465423, 64336205, 592893518, 538794649, 622887151, 456012480, 346689160, 54294805, 347119395, 855995225, 286685149, 118138454, 112296461, 164649672, 323776608, 772508836, 281612621, 994028489, 518705929, 884396555, 836990542, 65529349, 811487384, 796263298, 17029762, 381366838, 806783446, 602128360, 960708007, 946604183, 144232392, 446915595, 597873305, 542295284, 166831952, 296231403, 798364034, 509821688, 528372217, 166371790, 985855164, 658548449, 370791249, 743900537, 552308777, 2796548, 102756703, 659439838, 626709223, 990406260, 807381561, 602509107, 16665908, 772387495, 174703204, 249201593, 444149968, 337461861, 372831929, 576581969, 591065538, 204242368, 355309549, 542994552, 599929508, 554556868, 89205952, 520126680, 902511550, 426227501, 726390210, 563815904, 579872834, 532613475, 100283886, 376632225, 132020618, 549409645, 977868461, 822163322, 871740601, 237839031, 268512532, 308023419, 630675773, 937790052, 323692484, 635177001, 942293259, 616906057, 754977591, 214912706, 751343172, 873436317, 684877973, 167491421, 652143843, 576866426, 465794408, 949967227, 317241185, 93819801, 409216948, 536306350, 591174936, 257851378, 15524397, 190380270, 247056455, 126775238, 926390152, 828142247, 534897173, 188165169, 661722722, 367591729, 447480185, 950637867, 873105787, 396002777, 184385571, 375936018, 654965119, 923499360, 254471405, 383079517, 845051168, 531962229, 947701469, 557235997, 733976336, 220550167, 461384818, 625152228, 287911576, 447794593, 242022106, 958390161, 735226791, 812643300, 316652977, 362250017, 505082642, 266238398, 475022471, 118726620, 215958592, 839950604, 617434413, 124608756, 955264294, 311229053, 63218294, 693195277, 198942710, 171777421, 610635470, 188498480, 661024973, 613053505, 397451459, 669241003, 666124620, 590685523, 190886221, 210636016, 142993490, 496280986, 965341120, 667483159, 892986650, 479113035, 127422026, 590304318, 279393471, 795268162, 872799494, 266304845, 92144967, 297706697, 675265706, 83747361, 998589408, 849151373, 978436372, 931916144, 822974156, 153792225, 97211047, 23986792, 872039353, 90489921, 695797375, 209217412, 65123795, 91377546, 910369262, 491414608, 758009642, 135350585, 437547282, 426358586, 609311111, 382618298, 149255079, 852279081, 527120147, 969104280, 749530079, 587574807, 538918175, 135710776, 506344378, 413527918, 651893827, 397458209, 475409776, 111085258, 890260701, 10075594, 276650852, 903027712, 625960903, 74124363, 743366607, 228933893, 428718956, 399558971, 867342402, 780253167, 433312626, 176405290, 548157887, 819724584, 86264151, 869638594, 873600860, 620967387, 562775181, 191003396, 423986799, 41567212, 193472441, 379422043, 890820215, 391894262, 561206919, 672091739, 355301290, 749051549, 970788223, 870137645, 555869336, 337591502, 950982399, 583252238, 370977959, 222834528, 294899014, 659653871, 700033153, 93641536, 843106951, 901575010, 337630971, 939983430, 863863183, 830668063, 317951580, 786227159, 668886603, 904417797, 276762702, 883594615, 827862392, 583873465, 858804601, 994776503, 105365070, 99828590, 733312923, 956615332, 32521150, 52700833, 715139269, 392078919, 513644044, 41254915, 209126458, 200924035, 890161191, 815643084, 250430804, 768983561, 146689915, 362813575, 260478109, 935907488, 331126712, 746513876, 204599915, 876272584, 187329008, 587384291, 955098425, 571429056, 922269497, 712056273, 216381314, 883967266, 147942047, 948483947, 73541209, 710925989, 972833169, 616725582, 32886529, 331123675, 500852967, 126399464, 651205904, 135316068, 225657237, 324368083, 772567218, 277270407, 222920709, 441206992, 728235680, 851780718, 480804989, 646399377, 823114779, 784843180, 663787647, 290186745, 123282749, 990882401, 7339394, 106597765, 517572799, 15764604, 282548332, 42989170, 917944420, 386416825, 958858386, 905122798, 611936421, 62835248, 808804995, 170073292, 520326402, 149916790, 531512357, 617523329, 148391544, 167236292, 475311202, 631177865, 895827445, 691288617, 309189743, 863240047, 797242022, 564206623, 984036769, 217451537, 514756720, 779537444, 784830209, 300560094, 236672638, 132453444, 869875804, 331238873, 296344909, 634700402, 102356757, 266217342, 558150276, 523928089, 333519597, 578998821, 543093761, 348063162, 622167468, 425566239, 181489046, 528698040, 955782774, 942918802, 876729652, 39309991, 94397531, 930558631, 750335129, 581185745, 234723923, 516470684, 617213906, 863643358, 20851710, 611449951, 701992969, 675849836, 891287388, 349835095, 531568684, 986361131, 380217868, 891832942, 804241742, 449701196, 318818266, 677826607, 187513191, 725597677, 449931198, 844320440, 259620361, 167701030, 752538903, 978753359, 841507615, 572635659, 683948488, 797155697, 985724646, 960764204, 429151454, 608745359, 276052906, 155040197, 171549639, 446196168, 977782873, 945171782, 278452384, 332359183, 730026519, 361001410, 809984941, 918735835, 409959948, 22837472, 410440469, 4891829, 385202502, 421972193, 182191602, 8990311, 393029073, 381471859, 5216813, 182418553, 8277254, 19577326, 949838992, 72591277, 307573174, 365059545, 370065468, 131126331, 639249472, 386574287, 595391587, 169599078, 531663258, 826453414, 451866640, 116507546, 685822964, 709713364, 360512660, 197038135, 618276961, 495331424, 982947900, 649892173, 872158146, 810339781, 662374896, 422003157, 971804262, 871729090, 387304829, 139877775, 362171906, 263385287, 193233805, 303910573, 363925862, 288006447, 875667223, 111188179, 757731211, 458623887, 550501946, 395355108, 481741923, 255146511, 589272584, 854325481, 275567132, 797048578, 756656948, 951345943, 915358715, 397068061, 62614561, 915202193, 962739797, 697863125, 417836899, 503245225, 92192552, 495818530, 271117190, 526652347, 445209928, 970968272, 644510658, 906706708, 252736342, 728948919, 326260522, 467879057, 754043337, 77012393, 709822222, 656636596, 878661215, 588207291, 435982849, 61182401, 166440512, 647005679, 767356113, 92593684, 744455405, 341892853, 378718987, 627741975, 379362378, 623923094, 289128225, 39774874, 930552415, 751582118, 796490725, 50886584, 30611502, 423779516, 918683438, 153985708, 225363851, 535184817, 955631204, 225629905, 688348139, 902096440, 316977768, 648831667, 525643553, 198741062, 882924341, 588718099, 293747653, 378357928, 522766802, 687671755, 403888577, 652992207, 525751771, 345527931, 229949481, 188077853, 685149244, 236526785, 215417188, 557437225, 165183895, 643432342, 487175636, 933245934, 89689300, 239524300, 622161832, 400582662, 869583100, 731058881, 378028950, 412381722, 752795738, 979274128, 494434996, 793865683, 821858354, 160840630, 372015766, 179583308, 963367537, 532386462, 945167829, 14615335, 142330676, 607298669, 535192848, 338008358, 177197928, 705664886, 495485504, 93987928, 183439850, 404998129, 192150828, 970016382, 59513380, 803401926, 712005379, 506271701, 951674296, 620142985, 306020846, 936434719, 933880810, 77463259, 140572037, 192374745, 420543445, 226414875, 789349352, 193009976, 664839403, 202192636, 145069928, 702339260, 361244095, 820497755, 896385543, 335940131, 146197936, 278944875, 317281810, 361095824, 551034649, 716513948, 915284497, 579197590, 495144036, 427886282, 562236518, 168962412, 844959848, 731043104, 305925897, 526994265, 855132792, 988217573, 139340136, 997678727, 18838320, 827235585, 304113238, 957181435, 474249923, 973445252, 281005251, 406281789, 189204896, 521386376, 681317955, 821697479, 848882488, 152204599, 104033200, 498226767, 519251005, 362823209, 929952055, 659592517, 552929137, 290629149, 703282937, 680453372, 411495707, 90588153, 911927436, 25861896, 332958128, 268205642, 95385711, 550873672, 165312110, 94212436, 922441422, 682135290, 258945433, 12094781, 911495884, 811276517, 191616062, 990201461, 700885810, 673740502, 617392501, 543549610, 449481712, 663304906, 364866530, 43809973, 791918338, 812960230, 146804933, 889539715, 154092306, 369944944, 109113382, 309994103, 701323686, 509566019, 175980714, 5805556, 980715361, 883521720, 981131409, 86663112, 31394456, 688041096, 260731562, 471885232, 432429371, 996249206, 416280660, 903281945, 108100485, 881750556, 844902281, 203172332, 483933159, 750356295, 844676117, 283918825, 727369480, 274144294, 671558641, 747278013, 943714133, 752911566, 138819514, 408629185, 410551862, 190211472, 524065377, 164780052, 24482655, 771599811, 91498713, 540204824, 951890648, 428523413, 204696145, 227202941, 220393453, 844795700, 763567437, 621016517, 631877563, 779742359, 356829948, 725077826, 386733029, 900886998, 978444077, 240092390, 407963069, 608454538, 351664392, 485238369, 167157298, 58285900, 510456302, 209321432, 24822263, 83444595, 76345356, 729396826, 366222547, 461495519, 168777120, 317199249, 805001765, 912255659, 330526028, 141384557, 341818197, 328906782, 112192107, 57154553, 407009562, 918883794, 414061613, 659641085, 345120319, 479010582, 322043526, 435536368, 171026715, 627275425, 381759500, 632033299, 213884436, 551819951, 689930251, 660082192, 357093724, 57850806, 523755543, 384594989, 632673716, 663080179, 956452999, 975234454, 678895496, 625137568, 781646231, 369460269, 436377974, 282405993, 399958766, 901108803, 113596047, 400151264, 370763254, 267064821, 776485874, 37048782, 535305475, 503743182, 450070752, 255134564, 682426750, 258408886, 496390002, 403682355, 263847652, 152764554, 879267686, 42979065, 472889398, 376718695, 949483692, 143432910, 964976941, 653049576, 878355951, 123244157, 171428649, 158670245, 172528725, 399986567, 128595162, 426165733, 357056794, 308345180, 211028128, 475751600, 436423037, 613768257, 570698977, 356283118, 112296625, 32303447, 727490836, 490007919, 336506501, 327990626, 430748706, 500385222, 47471225, 145788440, 764604677, 644556933, 231053289, 355437197, 639072650, 739097240, 234846985, 976503207, 866051750, 602055117, 904731429, 539833677, 16286505, 29875077, 214156156, 770661775, 134541429, 243032499, 720270129, 921415823, 728538062, 520943354, 597371212, 681049542, 458761181, 678142358, 912381145, 505607319, 37060937, 150145477, 589409538, 149743015, 555330748, 900563826, 778314668, 180685254, 354226319, 965654821, 265778555, 753911353, 902157025, 587263689, 487717471, 723060434, 475467422, 6027168, 120980233, 136518565, 400719129, 126520634, 56341331, 359473597, 987557333, 537156436, 65073752, 126612978, 396070399, 77278627, 524406674, 325917590, 817577704, 472210400, 640390534, 375400200, 326212140, 92665938, 484163171, 986306865, 501260634, 133812281, 71034014, 931311012, 13514863, 240200392, 549289815, 455491438, 63344066, 721868674, 305736131, 454478902, 510380607, 163492128, 924641255, 430488529, 670412733, 432681648, 932575527, 873243960, 63471363, 338364766, 816979094, 553542115, 647015188, 468163371, 563741516, 983484239, 312830002, 466870293, 899317222, 4993627, 970334569, 906136143, 873635782, 591893349, 861396226, 879620196, 391605792, 170960551, 340777880, 800966759, 953058799, 14759927, 923753719, 91381904, 752870032, 611705845, 42370342, 623145133, 843428338, 186563324, 134413014, 111209129, 198210913, 387816260, 80490989, 698514038, 145351155, 283699288, 200577819, 848810272, 280262792, 440751527, 10663350, 273277843, 205072414, 974335303, 374719442, 895387198, 805128414, 849473883, 264823987, 961874196, 942962539, 237538842, 138137666, 528959308, 87179449, 10925915, 311841547, 579121994, 126503388, 890845433, 8735273, 628873184, 387338644, 861571024, 432074959, 393581442, 177138473, 522166457, 340716397, 206327777, 476728236, 58485619, 876513469, 52195469, 761729069, 878031110, 402226393, 165296032, 211919923, 741945781, 93371022, 500582381, 263351445, 798994877, 898567055, 991062358, 759919212, 607760143, 244735563, 382285416, 51527966, 193947641, 62453984, 285539191, 206611141, 938048042, 327712609, 929959462, 672441371, 262381445, 257052791, 568139858, 792268433, 329750038, 116510818, 714402674, 945717156, 594907429, 211932791, 958429288, 238946699, 609207164, 687382189, 372560372, 573870521, 104911498, 535139463, 776446224, 65923437, 102269222, 351231117, 628498250, 576256803, 813148469, 662772913, 237326130, 3657248, 23669304, 449889203, 716725147, 521255071, 107142325, 442824644, 141049494, 806728712, 599087665, 595128546, 147445001, 139531230, 738490277, 979196831, 98691017, 263293175, 18251936, 260253746, 255015053, 160026807, 121771658, 1450373, 40215029, 930487541, 892608509, 660726659, 748195418, 882470550, 349040207, 354526877, 217624546, 875173939, 947687334, 279379765, 580053528, 20196656, 604500526, 726072826, 199191178, 366221434, 929817485, 268099118, 897224291, 295010725, 638400815, 392001645, 375009231, 974572326, 155567558, 222451843, 947826343, 337602019, 68565637, 22844, 360349182, 45372442, 821296883, 540795768, 829312559, 251890661, 670442388, 803554511, 106283973, 73903478, 435288815, 964405198, 4835464, 10087371, 403612307, 308167892, 685514923, 112084168, 130034200, 642063412, 456894889, 211352738, 305394380, 726523947, 339664170, 640543760, 333592232, 747511625, 796205897, 704422477, 681390415, 783280045, 347261383, 667300505, 740148815, 817645119, 806683210, 737204710, 609932197, 23407245, 278397361, 624292799, 625287195, 381613445, 359409517, 383731174, 99419503, 163427092, 793199168, 520624291, 778397422, 416960916, 155193724, 588732736, 982505037, 585108426, 338963793, 68038216, 565494916, 854158626, 92865490, 930996626, 252429496, 195910100, 660605845, 197891343, 783275123, 425101614, 40895695, 644111493, 197794306, 758418005, 786523581, 739472893, 513653800, 212475791, 373620920, 74822035, 346695955, 90683461, 290924439, 628205692, 61437420, 441242463, 268084298, 942586109, 968582207, 139875566, 510149450, 342075117, 590987786, 670389995, 382136812, 694851248, 445214180, 917955973, 14401264, 430718201, 468344590, 651291343, 576295164, 471131276, 792571598, 435120113, 704484539, 605296660, 888354371, 412129866, 945973799, 231908272, 916103794, 973080743, 684690524, 758935945, 782474168, 23822934, 290960374, 27483051, 977267468, 978039370, 49215093, 436388851, 281938450, 431313821, 969258802, 883734694, 290250831, 567077338, 560315531, 545527704, 88993741, 819954358, 153666950, 695260339, 109847469, 409597709, 981449095, 312984763, 640894672, 372598705, 519154211, 580145857, 901971530, 472543732, 609593958, 97228836, 682715360, 958402426, 521672158, 197222872, 348492813, 777933406, 122402454, 7409047, 248712623, 174150583, 754190138, 605054340, 994104707, 853823910, 542746614, 968878440, 164210324, 130563503, 37076658, 13885932, 867274691, 942730574, 901252434, 693106405, 574219811, 513235575, 319357371, 149319491, 909818925, 861204822, 428375272, 984047800, 756195034, 871826241, 539271252, 246917270, 695586513, 564191637, 7541645, 979872696, 602372358, 15251190, 933102591, 210169731, 800415902, 330469694, 131158359, 745409892, 237636577, 694393747, 719784251, 547733871, 531089063, 182605364, 961957605, 859728619, 244479816, 672608548, 630233807, 749297032, 214099301, 610713993, 787390388, 805556667, 849577430, 368645930, 51480719, 421496656, 855569980, 821006988, 843225724, 563656385, 908716666, 535705932, 784624527, 339135818, 864150438, 627842394, 140487112, 643910082, 181853519, 174108053, 924719009, 205249822, 275612058, 310340491, 387917959, 937397632, 93610680, 305093323, 679590442, 365792671, 487506716, 330162878, 726351735, 715031997, 880515538, 14484008, 456131024, 922610108, 132640663, 63980154, 298675152, 230584457, 254336239, 892891446, 767847062, 623253869, 370456068, 722166659, 107384663, 522668551, 336931680, 343887236, 153002374, 129313037, 522492578, 296815128, 846372030, 665458191, 538618782, 731526403, 35550381, 735240579, 11642631, 716213379, 327560695, 685207961, 794107997, 392757679, 954148914, 512289133, 547333423, 828635322, 387769156, 54942153, 582328579, 942790767, 692950950, 584670681, 659519076, 791497936, 746912510, 849291429, 808690873, 863115422, 767554821, 972503916, 526878610, 831454873, 535625694, 663474427, 872533116, 907321962, 927443196, 586681902, 712577708, 106073598, 512987672, 573752663, 886056065, 987443668, 606289545, 158061573, 249823150, 626504937, 47690819, 685671329, 64951447, 323809190, 666323151, 480282069, 706018935, 204939281, 316879902, 760560405, 315190155, 804691396, 600456815, 960349985, 266465864, 535940860, 655653261, 863946203, 975277793, 694985301, 925618077, 602154401, 215896264, 109963863, 299807348, 738478129, 33587278, 161297937, 197232275, 744858747, 716441874, 43552373, 704693352, 834849672, 179643184, 77777313, 200492352, 563560226, 57852929, 295930447, 751523106, 81002483, 220737231, 893955464, 702039494, 535595309, 510213124, 623840094, 441531730, 577919619, 346095714, 677054665, 491072564, 295912744, 271128112, 798418692, 337141472, 264390641, 556240223, 455663660, 561579652, 411625928, 449359839, 270532960, 978493295, 968635084, 661950713, 891677667, 739196901, 779643291, 664568186, 368764701, 353835886, 825362806, 337388339, 218927920, 430808143, 243019562, 134485087, 893765770, 941952447, 390706985, 440376702, 507153154, 202551862, 277932471, 120329354, 9819081, 661512623, 985214655, 331853423, 745159768, 843297440, 778107458, 252030389, 788764853, 986007016, 468938199, 414208284, 77419450, 806892587, 933685539, 227744509, 421383117, 432817785, 820289479, 862023126, 576055573, 777862475, 20918417, 537866418, 838229619, 233073381, 405902708, 80255176, 411990222, 198352539, 194751913, 149874618, 750604076, 448758071, 842620095, 682925474, 950462761, 155812393, 702470505, 404717933, 818781209, 892701682, 289109915, 281258169, 908538512, 182019246, 703034598, 458737001, 435681296, 288045719, 410900478, 29815548, 336703860, 362379943, 935635572, 735537545, 323366761, 6718365, 589087401, 662092930, 538166221, 133743479, 290686095, 195628618, 67969507, 57739230, 511318830, 530839533, 448901267, 799544449, 582239131, 87641414, 3769614, 809803005, 785895528, 443204671, 774522841, 958614801, 561882405, 791624508, 349185046, 29284544, 264592546, 354876240, 960637690, 238221316, 590318978, 532152649, 336693320, 72118323, 571770017, 950460237, 243050922, 30233571, 234454434, 718478918, 727951882, 605791475, 704147180, 277897374, 251146195, 132461359, 697548838, 169204607, 773976750, 319161749, 30856724, 264659114, 284994743, 203412786, 680873825, 890869947, 129814362, 182012179, 591907176, 901164981, 101408971, 249788992, 323266560, 218105685, 975215330, 133196795, 827929406, 850695382, 880577301, 632957508, 438890103, 445171800, 367015455, 95145996, 459926664, 152018008, 538566645, 124737802, 106966452, 878877387, 759999251, 797660431, 555891288, 728085909, 112505950, 323027875, 390884532, 511961283, 737060903, 377074586, 435067782, 335774972, 487158887, 8608886, 375610008, 425183886, 829921969, 959851379, 283932060, 645666492, 359842795, 789746926, 832201226, 52345738, 646177962, 177762303, 277887186, 482980160, 543785819, 234603828, 674539502, 735084519, 121745573, 827362000, 43145350, 875681255, 23182359, 121502937, 822187239, 672328392, 769436149, 331645589, 611213622, 878949859, 355666073, 813956476, 847115274, 962077407, 504733222, 821683141, 418802064, 697032360, 135169954, 854951486, 651882652, 447369843, 14072471, 349828841, 395193187, 23064983, 841653464, 825024783, 356337192, 199937651, 171127474, 959729189, 546067868, 411586058, 781315031, 181544251, 961199114, 794513091, 765065854, 897073582, 681136344, 681747563, 909213742, 994606756, 335160562, 128457793, 687258126, 432865146, 150883772, 939756524, 128911496, 24408244, 135632615, 953736405, 409620839, 209353747, 555552223, 498024927, 136671776, 371069942, 493867341, 401727871, 516662841, 836848717, 42300468, 179603530, 26802132, 889392943, 417129440, 682292232, 574765126, 763000842, 497465939, 199415050, 762518326, 141805349, 465045941, 593822163, 381539723, 965754141, 212273472, 829666045, 763558884, 66592132, 548549020, 987320717, 562841521, 203664547, 961662245, 661161209, 25755792, 308859813, 318282433, 967955567, 978215264, 775670401, 1433500, 542751357, 182421169, 311293771, 859320122, 420787925, 136191174, 873975282, 794784094, 133208544, 886301877, 510629652, 200766052, 62516161, 296032258, 418542727, 627605884, 236412820, 122253472, 121224569, 460170403, 585280946, 533471638, 588429692, 861764382, 604712345, 387110812, 741753100, 257214685, 164920146, 344061756, 970108069, 112434607, 631961381, 217413678, 462975266, 25010105, 405778025, 207680971, 959203280, 36962588, 101276367, 617962563, 277529631, 82122812, 870403307, 137149218, 619687802, 795759192, 826192396, 295059654, 573328583, 634691862, 204420532, 309650866, 943909902, 286540256, 554474041, 750925541, 600738984, 693685020, 223819956, 253308454, 956583066, 222425943, 741349094, 314765336, 147134410, 879159063, 319142788, 166251860, 546599620, 78977313, 192099457, 411920783, 515470915, 627450985, 772285173, 14111581, 615148181, 434241048, 536742863, 148706503, 315029852, 157674252, 415386174, 329081474, 53145536, 244431449, 773849819, 976897111, 201249750, 698938077, 178039489, 81566566, 426883143, 765324108, 641081997, 796889520, 932655050, 428887349, 680636253, 840852229, 928598419, 85933477, 441215886, 993288092, 521203827, 244702307, 319158970, 286413807, 252760850, 264506977, 858383589, 253666455, 632583884, 775382933, 461377390, 274549448, 253169189, 679902105, 75649506, 416146024, 372404482, 335309086, 755831843, 837735654, 87595169, 688490062, 893481285, 164442539, 705041488, 412328146, 722356984, 769265210, 823195667, 143391706, 719557938, 23457948, 453912058, 858583725, 515793096, 554776127, 304525272, 842610502, 282505745, 117053642, 821323203, 184631026, 497748910, 568097006, 587153218, 132760436, 356548246, 878440975, 531095292, 690938061, 813045289, 426553115, 336819862, 859167358, 915441666, 467851340, 243106653, 515362049, 819231404, 880915893, 332450131, 649109028, 636545624, 728968213, 918574695, 787715306, 475413333, 1761067, 696175265, 611564688, 728138277, 737138180, 415051900, 584273051, 109663105, 610593981, 981672983, 16275726, 639472890, 900278490, 70492850, 154613252, 444353378, 331183293, 140025643, 147304115, 947589835, 341411008, 560307151, 20268336, 30263528, 853794013, 41167189, 618271150, 983511571, 480233841, 441058909, 730331986, 820381897, 673210170, 933853403, 768914591, 542727844, 651559984, 755884919, 947849850, 866589111, 707411604, 910437080, 704912081, 101728614, 413442579, 743767778, 952100189, 967572300, 937755248, 503228568, 804874933, 538904924, 321527509, 562292916, 837499532, 883370092, 602449001, 494962434, 166551657, 559634583, 796526097, 110134550, 890412641, 832964401, 857006768, 933315970, 574451435, 550561906, 751162879, 307669579, 139781684, 872437526, 255243117, 541280855, 52655940, 29624634, 892750962, 894105451, 236684009, 208802266, 281291222, 482610454, 903228757, 760383592, 941335866, 143443948, 477663448, 508522212, 448987397, 438422396, 854434086, 987733019, 823583963, 773904321, 803689845, 615608907, 823896978, 578167665, 492452251, 644647696, 969587115, 849878479, 496237434, 999776175, 276717240, 74725700, 797636483, 475023494, 699020933, 152778963, 143357309, 430689211, 30388381, 622104389, 52918706, 760548301, 961337098, 620977063, 213735908, 498203566, 936900046, 674244362, 435256369, 981851899, 757547732, 623201512, 325556332, 856375928, 699552927, 173167556, 870344382, 743383028, 545925198, 660894237, 283656830, 646661473, 263853749, 152657028, 410517596, 370411438, 3460452, 638510091, 83566128, 871111575, 698250050, 991177001, 40655281, 405744605, 97740901, 348083399, 530284972, 102421869, 130469342, 437017238, 883039957, 400147337, 781705590, 482686543, 268813907, 955950276, 765234288, 388090484, 225449055, 902652658, 3905747, 545539033, 211164214, 236138866, 533834122, 88870348, 964472575, 464698637, 443139069, 372481383, 405810791, 149343167, 368323299, 631868334, 540431635, 442459383, 993132809, 225567405, 341505084, 582689480, 557913060, 146852083, 961331530, 10193047, 812807296, 810813318, 40907243, 235700089, 345733084, 452329693, 696281752, 10567026, 365669414, 410084796, 942152443, 579385406, 992502996, 36171886, 19999791, 862200846, 284156753, 653491302, 243845060, 387038938, 174813595, 123685414, 1557520, 115587215, 865643590, 192955735, 476767359, 244596847, 125169642, 270610701, 324334406, 403684285, 297217811, 958017442, 701039462, 756733406, 720644964, 53106456, 312869094, 921219701, 695254672, 275035245, 660110606, 526930028, 952169132, 258917010, 455542184, 263410129, 153638848, 662757648, 403014606, 937883375, 586857198, 146338374, 83998804, 716180056, 73298791, 544806986, 809023950, 696620179, 335550152, 313206865, 267585963, 768416681, 976547131, 49651928, 290174632, 645706974, 337869733, 393480802, 499795569, 246201499, 935136602, 524688029, 571437524, 847821505, 644976497, 313689950, 765774099, 872330365, 286840366, 251153276, 194204675, 70086446, 870043324, 84818295, 572111196, 264708973, 113180244, 140769400, 594659763, 660366320, 283162893, 984541158, 99415527, 655943873, 802238991, 117655285, 674927842, 869194096, 43915101, 339751155, 34101082, 750130157, 422644702, 77959970, 651153963, 78488321, 531002472, 74426061, 618350373, 56747416, 665118542, 268469980, 72279667, 455712509, 83815698, 542709868, 596722972, 693919787, 753706492, 463166587, 332296243, 382041967, 1024669, 665598102, 214140713, 581485348, 240803065, 712950265, 301235428, 826758696, 259299237, 807176707, 431846001, 226858124, 696074168, 347486742, 60407805, 906269116, 258907050, 282042322, 80584082, 963077613, 503843062, 520429664, 699959820, 647693150, 863187213, 675704013, 214163385, 253539690, 369963363, 391876267, 14563110, 533424835, 488833161, 802330698, 857880971, 619487114, 732296824, 639224716, 687114703, 434987252, 736733867, 396102443, 382770681, 345852815, 615662184, 200372235, 181839239, 470241216, 175428494, 51094895, 484784331, 582340234, 303779654, 539041566, 89696018, 934466981, 120055825, 12472278, 95974203, 538305399, 301133130, 342058310, 215505180, 100097868, 452011061, 589988288, 235762051, 148255284, 913780375, 235748436, 108972995, 694875884, 146683492, 724605667, 511994387, 151947308, 679572546, 559252888, 554738802, 397773886, 213673910, 90484235, 608198699, 800538916, 25494605, 987689372, 582018820, 622897459, 93359731, 803086006, 388932238, 778775610, 266409933, 385007911, 725387262, 677661019, 45021562, 886590748, 107543933, 425521150, 165179599, 538549005, 782239645, 997386459, 353802959, 860003613, 986585613, 190219452, 485611272, 162964090, 918166240, 99858231, 502418042, 694274014, 722533920, 226551552, 498816915, 63660816, 914420531, 789346814, 156402808, 108593969, 298848832, 20234759, 971500272, 524871562, 239040652, 497244473, 800564540, 53850358, 532714579, 534677703, 252703396, 947739479, 429117151, 494100442, 383006575, 585526520, 871705913, 538357144, 122684885, 698013164, 660700874, 769055901, 170337689, 150889263, 686093291, 62092802, 470773619, 493327870, 512678987, 406879477, 527110886, 580687486, 616436115, 809793480, 769489177, 898667400, 563688929, 875499064, 319864725, 783245226, 919743451, 579779224, 982632868, 694413891, 262268221, 22098326, 147439307, 866614901, 969166303, 255911400, 689600392, 177125040, 652485788, 122809412, 491338610, 59471286, 828347945, 27188576, 770455086, 913140292, 245780833, 50258931, 170836554, 734622777, 727649907, 974304312, 943616255, 720390702, 682246254, 577916763, 565803454, 339208673, 397080188, 384569181, 639256830, 982208535, 970596943, 306584969, 496521148, 994132839, 406223249, 193671029, 472890228, 190806505, 641480797, 432529222, 966435282, 220641714, 773331794, 389729234, 837096805, 247100018, 379962803, 362910880, 996925717, 69535456, 937707744, 494475997, 232688307, 310036248, 331289800, 559772519, 529069723, 303265489, 805657133, 466764423, 882422839, 442841695, 842985591, 924698283, 985030797, 864349144, 170346441, 974989490, 823568187, 784154451, 123425015, 503420046, 339161257, 998350916, 696242425, 820072598, 356274006, 935731313, 484745978, 111983662, 786174908, 328298431, 239589675, 48102001, 494248942, 547915278, 121965464, 541700172, 410775149, 300543678, 51422762, 243328447, 738944949, 683263384, 89043977, 641379708, 786489524, 79970183, 106424729, 100203079, 805242369, 561637482, 526503541, 410374396, 565039369, 571577501, 738990109, 648277688, 971825996, 319621788, 425362484, 356106170, 656106429, 881487097, 393340006, 613417413, 1365018, 451825106, 784999621, 335475759, 374705313, 520301550, 283567379, 307490882, 100960473, 918021708, 379743507, 498113269, 896733690, 165467187, 411591317, 590954153, 792258438, 362223107, 593231493, 304014714, 667722298, 541188018, 139086780, 424417979, 707035708, 271576905, 246586625, 528899870, 804070075, 200575435, 233524187, 209712342, 630747972, 135828651, 23870199, 906417545, 971347279, 811737122, 19278995, 48684313, 852297903, 452766613, 112866662, 844099230, 798154748, 911807600, 376434607, 996058715, 200454806, 427044018, 376894776, 257639433, 685201355, 903080704, 711661560, 394942602, 713243143, 341925250, 457729703, 996282096, 213991545, 53298000, 887126098, 463070418, 78551199, 655087389, 696312848, 588220517, 28783957, 189393551, 697988084, 352658747, 277930614, 343197792, 901183483, 606976517, 969050570, 424561930, 349134676, 902786821, 799170322, 360656567, 561254046, 530282192, 279989048, 46800517, 84754770, 396232365, 736273668, 887363464, 903173857, 968066919, 106843615, 930260220, 489355675, 529666326, 80816320, 63281335, 385910166, 240396948, 779285790, 576394807, 690558007, 369201819, 109252081, 275886704, 987549595, 547805808, 274373585, 414655556, 515614669, 929839491, 492493650, 871716094, 731374413, 322305814, 410240195, 473262031, 459173979, 213767905, 631194868, 176680149, 645640887, 333245443, 460636987, 768568393, 323380013, 830718675, 314336922, 246687591, 283578092, 711106898, 632425773, 590343196, 996331435, 414744446, 273819401, 801013803, 133229142, 49650759, 693287451, 292155564, 842713196, 347051044, 333004307, 622427385, 236790653, 133298038, 527956115, 316719184, 107213097, 688077228, 354748342, 479963800, 578697768, 495252092, 546894996, 87306067, 144417224, 472575742, 10972800, 41080318, 637831038, 779948688, 114357036, 623018583, 506382409, 613857283, 327961045, 352420335, 37263146, 599724501, 503135970, 456938229, 779082736, 192011533, 833540940, 321678148, 414043286, 882462818, 492070937, 205878149, 178613009, 598962155, 975784782, 386400658, 289641371, 31401613, 508706047, 637643808, 364919533, 46540761, 302654350, 32251120, 569624946, 453957438, 74309089, 992149926, 933507546, 835468945, 209262469, 634678030, 776117867, 399610532, 606204177, 207805876, 16621583, 273304711, 923242457, 438558060, 338344703, 540789533, 924924399, 648444904, 227811875, 15187646, 947058080, 562882157, 12274713, 381903282, 669940695, 323439110, 628095002, 208254539, 710579927, 758725245, 350710659, 495499426, 187122796, 626915024, 967591252, 180744228, 319070595, 905602641, 178876784, 945255847, 787835702, 304629129, 819903952, 991445728, 764953910, 500755575, 653589162, 394395691, 421635851, 26374522, 628970899, 663611690, 453535993, 288916231, 164409404, 310425686, 505782542, 63505333, 532802078, 75356627, 436764496, 858431026, 121880370, 287088309, 312643278, 991570893, 620792525, 64854837, 671922489, 170256170, 187882414, 773504676, 592014869, 561376888, 34074822, 641453727, 374375958, 483285562, 484623747, 341776599, 893591798, 870849404, 376479994, 321120823, 302310724, 29818060, 286821701, 875512298, 266605607, 148374047, 15990550, 116858430, 545027049, 526343363, 971356414, 9830688, 160795912, 342217087, 27801844, 723283393, 162397065, 461438468, 559323085, 362995381, 795802390, 157556638, 882622634, 528097557, 475216580, 537653062, 579438501, 561170634, 569274537, 959417725, 925415290, 763352169, 701128236, 872345470, 364246852, 396579415, 54609358, 40151259, 459784328, 990707951, 111130375, 842284213, 861976765, 504713819, 937743123, 780296117, 454187924, 161192782, 887818332, 963694867, 876840926, 626778927, 267872210, 591235314, 915337489, 931281134, 214606024, 613159864, 317141402, 423244652, 602921942, 75225830, 410697715, 223899038, 370458489, 491233270, 132061955, 971748541, 977818802, 542285861, 59178521, 781045357, 107656082, 736432296, 942839397, 617782424, 471522995, 416741990, 546191923, 271376745, 331558466, 518266977, 104394715, 530861067, 912259861, 122561113, 111165178, 794182959, 772203221, 635284353, 58349437, 93642969, 965411864, 821595764, 522093798, 433990170, 457075690, 225604253, 277678816, 809094067, 880702086, 44584706, 679649700, 145090485, 235179673, 419424588, 159781023, 366790679, 476872393, 136454121, 713249058, 240707883, 23238373, 257943274, 12976863, 450891486, 448839905, 623030872, 27909158, 597044533, 165754452, 237906834, 14050416, 217868666, 915445655, 419072731, 813567757, 260552908, 248008817, 369987779, 548198300, 14002841, 508472583, 552064992, 64876199, 931828879, 816202287, 165765011, 328902321, 773285655, 725564340, 343484855, 61833003, 880273507, 53676137, 73744464, 689280012, 916284736, 129645501, 27824368, 829117871, 991663767, 974037666, 222679829, 134053984, 981915334, 354575775, 281877873, 110036933, 848029883, 129925776, 815951770, 683306457, 818104604, 634642283, 807875899, 800511021, 216945471, 458399388, 414910891, 554834405, 908274077, 968784463, 607350220, 991561107, 800574123, 997197216, 603650501, 643531074, 448013185, 800448617, 945222424, 913946405, 728731070, 500747678, 427407152, 552172867, 192149937, 222928231, 412703945, 207781385, 33793039, 466092544, 404457417, 881981617, 239680184, 726152427, 507001402, 777001448, 404019052, 748780453, 213546111, 870645165, 891323898, 747924542, 840106491, 64104893, 410037862, 834207225, 68719897, 68123487, 793443633, 505523335, 749629934, 100718124, 399002877, 622555185, 913603289, 294269221, 531717366, 217092418, 369389658, 744054552, 949673066, 700454394, 311273192, 67027350, 644976791, 586899945, 420579079, 707117794, 549837661, 568162891, 414534996, 397557397, 554472977, 574591135, 909245283, 715348468, 506828736, 93999898, 720244868, 295665870, 950566120, 200645000, 149044421, 195246915, 163095185, 320291362, 237328651, 714811282, 171282032, 564233910, 341022142, 423735523, 796815601, 482526923, 110574500, 746762692, 552501444, 64024905, 160193683, 819450812, 597879941, 815034761, 317165663, 875813246, 99794486, 700959749, 433130719, 211435, 924213844, 92276983, 663768463, 87419416, 557956493, 798289428, 226657322, 104874048, 656722665, 104437625, 783741009, 495781786, 935596729, 64087071, 644927058, 816972515, 400125792, 323172190, 456307032, 238669616, 804393186, 735616859, 434187125, 279143518, 983807016, 180004228, 440768574, 395870986, 118366938, 48744737, 899298775, 441475030, 594530722, 500024468, 706085729, 213958144, 602600727, 928265584, 950892236, 609855671, 21350810, 696311707, 842829011, 635406614, 748030386, 206241956, 256056456, 288995561, 609939357, 319831788, 273047244, 956551217, 333004732, 263293763, 988769420, 736352291, 722589612, 325445999, 721873117, 863933757, 542978622, 963789852, 277294393, 663051585, 38619418, 299362002, 731974806, 162780892, 582334612, 642385055, 543451053, 358396149, 663693588, 713531349, 913316840, 155744443, 546415698, 573072956, 516836229, 170282801, 825080193, 66611314, 417544976, 701056926, 891456233, 665272888, 977859501, 103084787, 332439036, 513748493, 592445881, 292434013, 989930534, 470253536, 563755822, 495454779, 557312807, 465975274, 301865497, 92822857, 239200835, 697721794, 970032689, 84138317, 670475898, 466670279, 103765756, 815297202, 869023827, 661760814, 639135781, 945259403, 562347497, 16578543, 568980967, 434499107, 702068805, 286091179, 648465221, 468775520, 500810475, 603585890, 684795935, 758944291, 338304784, 234609920, 996620110, 471358187, 453849562, 72522282, 377286382, 289005512, 579387461, 196898967, 837910087, 397079285, 891334408, 861720960, 177827866, 922943927, 541296423, 751168696, 726352372, 363673138, 859827474, 289309558, 972046480, 243436682, 542244911, 472752117, 259653758, 669855606, 799161649, 626416147, 178114551, 100231781, 448772734, 312739023, 241434989, 63161027, 244241151, 802554248, 561793367, 639466931, 293255498, 498331408, 540298945, 125392018, 276744997, 799836567, 461425793, 485140509, 640828011, 603795864, 435988824, 80791255, 446463655, 467007980, 997933353, 731207870, 385224508, 433187833, 196775043, 620330795, 885362066, 133438012, 799406316, 416693290, 321713264, 720656034, 812870516, 134909913, 110632514, 444313409, 399444887, 621029320, 885296255, 966384264, 121668346, 81499569, 757127379, 371131269, 662351599, 653561026, 789254342, 84888915, 63827446, 517901764, 319628108, 635161611, 141056899, 387903320, 218733845, 183750506, 464435659, 670351431, 576900596, 352767785, 685887142, 794865402, 890923450, 284828750, 548371748, 512013407, 257596047, 316132575, 304560554, 685542950, 377863511, 609766058, 734905564, 764728317, 563711088, 171931007, 804374138, 825073258, 57989380, 245813700, 135062291, 776157994, 737917867, 411387679, 570735955, 743676329, 6868685, 230357068, 203235020, 393705907, 373520569, 592602647, 174332700, 268853549, 331125079, 556790735, 810925519, 284200229, 824573441, 694147693, 265570560, 859200530, 420235009, 54133997, 615714560, 335204442, 561549122, 122271034, 36948340, 981538730, 886930686, 103466625, 837725059, 266108813, 138827645, 855889231, 769281171, 518968544, 72541250, 194190452, 972731881, 637006807, 613534208, 391718076, 267034926, 662855502, 138893705, 32254657, 296686537, 667329486, 676822324, 411753784, 7441395, 69717145, 188946335, 858666884, 732652396, 461165538, 62598248, 668948940, 269330043, 41492521, 818686788, 191990527, 859147938, 911547932, 830351414, 571138185, 473971452, 931095324, 278219969, 487717959, 88774386, 552988103, 866308434, 108578359, 890796927, 994299738, 838295681, 434101761, 41796569, 469036180, 294725377, 14838445, 239374213, 779595672, 393753256, 994086387, 823595792, 453139507, 158341349, 260122219, 510564777, 827516434, 25440339, 833262511, 433004880, 2139491, 71786269, 713838678, 785947301, 306900351, 19084686, 568800153, 6858436, 863603672, 500829015, 391793727, 138968297, 16643425, 814949032, 641945106, 672453613, 334427962, 866759049, 104502681, 324908302, 198968053, 119958981, 197556733, 94778414, 852982358, 377479014, 439378645, 268312171, 852604021, 648903432, 132488610, 253692382, 233432315, 60539181, 444701800, 702129684, 584034359, 818931428, 165193307, 516097226, 766933817, 37990650, 287802038, 548099797, 424015461, 117215995, 810106825, 227367543, 912361678, 540060856, 558782601, 827807536, 560787201, 872012795, 826186811, 921831165, 584634285, 124005522, 191665120, 338136749, 20268687, 536668930, 419234490, 45939781, 757677608, 66672842, 712194897, 149401726, 971224200, 13092556, 642464565, 314320703, 463255612, 671679314, 848926674, 243069944, 690003326, 558359496, 255247407, 827276450, 915073836, 258002946, 573886167, 244233992, 415166920, 419452632, 660950658, 902791764, 82284644, 395899152, 523519316, 973741359, 815504432, 59782550, 533418385, 1251395, 508380780, 380057560, 549039226, 643898981, 812149991, 345499204, 491909982, 279781898, 932941211, 284758037, 549025752, 459555969, 781488407, 694578063, 547970454, 179824253, 791867771, 293434610, 746322207, 504133310, 62818515, 87246601, 921289398, 876282823, 750018008, 544892387, 23540960, 959328069, 482399119, 261385741, 895836503, 843325635, 4685646, 714839560, 258161522, 188917401, 212440850, 760514736, 877273293, 177293925, 416703006, 626708886, 361407905, 653710421, 636396167, 394244591, 576494306, 376110167, 625022134, 247405677, 317776296, 839902457, 565032756, 376186806, 661173133, 372523492, 858547853, 463736336, 527924399, 856034981, 660547262, 51295878, 653282473, 211027303, 653486996, 118762734, 278366354, 434588490, 663094769, 354036611, 319189467, 777647032, 546985556, 923866098, 133289912, 16843169, 194230787, 927797276, 34863099, 542069400, 912712959, 691604089, 193677773, 3070899, 453204454, 909405621, 56729589, 296402603, 616490093, 685204698, 26737933, 465412057, 897311482, 735028691, 754740988, 687255532, 193959819, 657233654, 430690021, 989165408, 450552439, 926085155, 362360226, 668705635, 554233788, 106970109, 598618845, 198116848, 839749812, 83862547, 535983033, 468390971, 507681504, 521921754, 749584834, 569260720, 350043747, 121655713, 546810934, 337875694, 332058996, 665501798, 329009420, 915802547, 384329418, 128978291, 303316074, 469032571, 973750783, 863379370, 627767295, 948541691, 295278841, 148933274, 407288554, 656810449, 470639665, 283931986, 471610570, 456109300, 967664068, 986645332, 52970024, 629565980, 900736012, 110838623, 86877155, 394081228, 794399078, 423966136, 451635675, 463641944, 222227837, 590519035, 576016989, 826400142, 511564669, 143760636, 250605103, 375244503, 427421180, 863105805, 102779337, 489936009, 568049159, 581289199, 375417946, 277214404, 129473512, 526253548, 310302247, 785368072, 879671220, 345332048, 949599530, 538223291, 347293296, 692120834, 75081099, 485318061, 333554257, 627098412, 817701385, 56567247, 183960887, 594567679, 791800307, 330331640, 237844218, 609966598, 434378386, 957307303, 384808882, 274805106, 544625277, 708514979, 281053525, 775864265, 453994000, 927500475, 955692170, 477894701, 364789276, 154572810, 937966656, 130474746, 649350816, 57672337, 914055384, 56131220, 98153226, 755544501, 70176208, 910863771, 199073996, 963708438, 720099016, 723691354, 4849957, 422705611, 321859930, 401388830, 814417116, 47354924, 54381608, 552397649, 589006850, 448024282, 762851039, 582901932, 823356980, 535118040, 402758620, 564030780, 626631862, 589127092, 427950439, 417302641, 530391785, 164712630, 397750015, 437755615, 530249905, 859445055, 782261212, 160773396, 273650314, 252702982, 357669085, 961557717, 316116301, 165416305, 628643489, 714250739, 229707096, 23877176, 805653257, 711131965, 606319714, 824765522, 938572564, 213558620, 956151786, 869887554, 872405985, 944707258, 211714109, 338040121, 995260480, 795910222, 865381912, 840243746, 696673419, 850125536, 818729824, 503103204, 303166903, 267941084, 613409439, 185018420, 582760067, 126969797, 437285541, 593308487, 753318968, 203603624, 677799966, 926712419, 596031294, 490288864, 407807260, 616176353, 168589355, 620895606, 11304227, 786118087, 198076634, 26373692, 552924395, 428890733, 423244956, 665866174, 393059691, 126375166, 780870509, 749049581, 271217816, 46372211, 495322490, 503305276, 643122082, 368567782, 843600264, 746904051, 422173472, 539889259, 568475802, 973176755, 809475321, 494604408, 638177118, 874676230, 841859510, 608820637, 268522000, 409906128, 395816333, 998012431, 214781277, 939200208, 497490279, 642740935, 199474970, 685543364, 635872235, 885396423, 292312088, 768768437, 610235426, 307128181, 933570580, 845482624, 82581981, 214314445, 31351475, 207193329, 180437619, 143321669, 704650200, 175502344, 495824784, 992468116, 478259870, 664620379, 926559541, 858945435, 777353034, 437616481, 609001048, 390500514, 940081576, 495747001, 339426314, 392220801, 862157421, 210868296, 37697811, 206004304, 655621237, 125736699, 623132746, 211100440, 329283838, 6009824, 802167687, 467364360, 754693574, 593687250, 926841101, 319941531, 816403255, 905062660, 196713265, 777480824, 489308630, 184198140, 687785476, 249795212, 705549579, 538565008, 701317777, 321264655, 998628076, 576619929, 461138398, 800514801, 506194968, 381106746, 622395493, 49555410, 680783620, 871410777, 805412973, 648870192, 898347914, 851621214, 270772152, 859233042, 485749128, 317913672, 830780092, 443341037, 104718845, 819321115, 501280254, 909719131, 360467645, 311564122, 789198206, 910260892, 829171696, 702462711, 697231244, 1617448, 55000551, 960637161, 165943446, 191795463, 490625645, 768353728, 596525069, 361599021, 985121812, 281412368, 220490810, 237149756, 282290901, 517379325, 351625997, 861229787, 414597895, 486516466, 398713349, 55757801, 50186060, 464112154, 793742146, 23300062, 81281415, 516983106, 900148251, 65736881, 480579819, 128831471, 741916603, 98393060, 643681207, 589490264, 633883220, 293060504, 360071086, 545390907, 350254285, 120098657, 981456203, 37402407, 768471415, 689134599, 188525531, 794798038, 899659274, 584641771, 278374071, 488872000, 794693656, 31251883, 101155825, 921464732, 13221702, 655842202, 53223964, 180388163, 801200102, 456006422, 109010219, 700882245, 943565111, 710728909, 773946100, 703631415, 349382847, 63307555, 816533329, 819475384, 122446190, 373115519, 364034875, 60364384, 987429681, 798195776, 586197091, 876047035, 908298863, 389560058, 608659319, 77413762, 735318985, 491416664, 451190791, 187896098, 244329857, 354576597, 200569340, 420686313, 768511595, 301476035, 675527439, 701991559, 306272323, 93912839, 798160724, 497187098, 882448714, 248130284, 307271287, 103304477, 937766097, 785578527, 271212895, 193477148, 972367283, 17107655, 445610099, 623078945, 582480724, 948832409, 1282331, 553469560, 967259272, 964421919, 303275072, 404068160, 525012359, 387420994, 834041945, 962918562, 354482995, 232021445, 202869996, 514106897, 879388331, 860380568, 298061207, 318820690, 960613466, 579170485, 470644403, 992804601, 136486104, 997911893, 753726469, 612427456, 105306659, 23760455, 312554010, 174928031, 614627329, 278039071, 651493342, 356056078, 254792264, 619175783, 831699830, 670046659, 167299465, 453728711, 324649818, 653560134, 444300958, 864058944, 201657143, 317913227, 669781762, 337183685, 916354518, 130565391, 342437041, 488283848, 647768280, 990336532, 104239745, 668639765, 4213105, 884430084, 672251132, 932895974, 759570594, 794422038, 163385338, 304864318, 375994259, 233778160, 99454126, 611941671, 998039227, 50201175, 992056068, 938746561, 625522843, 258481999, 521990310, 6655441, 146202545, 211811834, 882821116, 755507937, 400469582, 538958519, 298317559, 685833945, 837998168, 555269192, 339679519, 250606629, 743887955, 561068599, 756153061, 473660044, 684943373, 348021292, 962884545, 198224977, 535389167, 828650373, 792111876, 61044528, 518043592, 315280266, 303098902, 364588491, 401521131, 228125843, 267291886, 700690178, 207406991, 815009891, 574830268, 329439692, 279050466, 749701414, 242171430, 58759662, 556137984, 462111765, 513484465, 296674834, 596839910, 893848798, 367695884, 555666546, 409179876, 210971649, 183859561, 448585219, 971596683, 773821484, 888958586, 211516435, 495318895, 107529339, 995648207, 532482731, 683471453, 508008499, 725523507, 719960491, 310702353, 617535502, 189049307, 359645760, 651273875, 84229711, 773669050, 407577677, 285870533, 33001139, 235318186, 47261206, 24473876, 576273207, 533478356, 486887231, 661334683, 880972965, 863299917, 533948266, 117167592, 902657431, 173896301, 712702819, 314815872, 467611301, 547473500, 912356043, 336471522, 752669176, 301203353, 681530479, 631814567, 913028154, 740064368, 231701595, 510847048, 508410458, 599338012, 983749520, 772368266, 304540154, 243457915, 484968922, 929756510, 400899628, 414207471, 582064480, 219351966, 388183527, 960599944, 20221691, 958866576, 590437262, 787352013, 527518469, 970272800, 188161236, 353258771, 304996404, 630143483, 757388197, 242672389, 324468224, 814451191, 827938206, 263864367, 978967714, 447896310, 387988229, 790347118, 338528449, 348968143, 117115949, 451947063, 863847220, 579042844, 818335831, 814725711, 75873670, 220871505, 638913608, 615800660, 712130449, 298170237, 201900998, 140793747, 661406661, 158285267, 691872466, 654700787, 211276152, 613617534, 697809927, 97155624, 581858126, 127202891, 599879912, 549226715, 868505123, 113679422, 348346346, 37734937, 860348874, 943977925, 388992888, 404977192, 767151830, 345938956, 282661282, 902705822, 427744848, 263550088, 256140430, 206858150, 863500470, 244639549, 894421384, 292787126, 351171184, 49444425, 761883046, 189706281, 17224848, 92568621, 639268508, 510649436, 438803814, 770371187, 914797250, 543467015, 335596202, 182364244, 932503286, 116064358, 677005214, 304784691, 553822500, 214431154, 207563285, 544494825, 191745589, 846165479, 26110445, 542174802, 203307466, 665686763, 413014728, 746138249, 875300061, 613840355, 114700804, 555935108, 431046990, 298041616, 468848780, 731406858, 531831873, 941340004, 487361893, 782667472, 908579248, 371221170, 708459755, 164123741, 737875068, 228164034, 207026526, 882082566, 179760829, 405433832, 707909701, 116471384, 659772522, 315407673, 62677321, 473570055, 414263593, 800026663, 349037471, 409294186, 462000276, 97843197, 639647848, 781983, 650430774, 729723719, 712634709, 601224598, 568834191, 746464542, 156076263, 334253148, 798320058, 425158058, 927596186, 940002779, 932810139, 421519723, 649837922, 995225083, 542890935, 798885209, 287067240, 714480977, 429652747, 175513334, 242178861, 513902074, 236012421, 122204323, 322500600, 899653343, 657924984, 879549775, 672243495, 418275352, 68573530, 625090259, 324621962, 306257713, 485884974, 390023960, 350668489, 916187464, 758441430, 193521921, 862889007, 901979143, 339851174, 421036781, 993329064, 341041644, 985462770, 238141866, 436582020, 640131928, 535710759, 456720452, 323477821, 745640149, 455136075, 849606456, 802343976, 197425233, 180826444, 445269420, 23379204, 109909922, 582272275, 549439304, 357994414, 362341736, 368008388, 991368357, 576319203, 160792252, 260256293, 471926711, 961389342, 151296238, 175877359, 480448015, 841794545, 307476135, 744142219, 351931303, 421682477, 33729417, 881824209, 721896514, 774560324, 489592911, 741131162, 314993968, 488389182, 29469937, 821800858, 661119685, 989258671, 622880421, 611427481, 919602243, 657278096, 828427725, 182918348, 800452634, 376547051, 728986609, 97000894, 926886686, 436011344, 316865868, 291704994, 835238326, 744467965, 786920567, 850589430, 676278752, 298105727, 325217016, 283825783, 728333465, 597581680, 550995507, 305202844, 71366970, 596939568, 592475376, 887789447, 497602218, 342850025, 795678236, 631673542, 792355280, 290476790, 243757293, 131069919, 170727184, 469036549, 856272919, 224125821, 851529386, 957376369, 809467585, 521754029, 907477472, 953546040, 843968547, 79885340, 205334580, 571949895, 926748818, 233294349, 207542163, 379654532, 944550560, 185319579, 696757566, 673082165, 467409045, 651442220, 750681115, 630753629, 592714565, 67462188, 752088871, 43841727, 701774313, 277868872, 706370622, 745404562, 744571823, 674315030, 89573566, 796855050, 911487822, 54302169, 67206484, 166501307, 430982081, 288812249, 580797316, 15279707, 556901740, 620443189, 156536163, 281261367, 261594970, 616482363, 35492391, 150013980, 976933026, 517893140, 507766198, 622321035, 420551083, 396323837, 187148939, 4024634, 893493355, 553211823, 248086665, 599684586, 276387584, 501187166, 186156529, 301941876, 64315555, 167295361, 706927831, 155195957, 114256412, 486438231, 426583403, 104838416, 912512460, 443496709, 190147971, 103474598, 897059074, 193715817, 324033986, 824500188, 198148716, 470788664, 104674287, 423375960, 282213139, 41443411, 200417486, 634822685, 358679751, 236093074, 969601282, 67889172, 899382409, 764346355, 511405482, 838714106, 921829959, 374738063, 982370508, 27320958, 400228407, 515939223, 712052487, 612509222, 115470575, 255976451, 885967514, 697406324, 776173998, 680743263, 938539503, 445448333, 425835266, 68978369, 346805697, 6226378, 994704521, 162362871, 921333539, 375240064, 653847776, 64128698, 558895490, 995373223, 940782375, 130098044, 240766488, 362758600, 477472313, 722995887, 802460334, 693097400, 984038794, 852754575, 713081644, 33435678, 202933907, 315701316, 830288175, 230563297, 552420545, 772053026, 489848835, 663412839, 893735836, 902205940, 894605876, 604745383, 533656300, 552436123, 19856519, 141816939, 875185469, 518666090, 74741358, 480674858, 71506003, 586907982, 132803862, 995783708, 610673731, 404564369, 333039584, 315279881, 718618407, 971445799, 451555195, 161178016, 363886073, 284743942, 866771801, 262182813, 618447906, 822433493, 80772587, 393738677, 941644865, 57263169, 533096533, 510307234, 460129501, 76348903, 297024370, 489200883, 955274048, 562403028, 386094784, 636176118, 540514478, 264988939, 532285943, 930158788, 904717478, 432816621, 839542081, 568569141, 82163926, 675450076, 498907476, 883584006, 291505597, 631829501, 504942662, 34948118, 755341917, 282480263, 530782003, 638334003, 705266390, 931583576, 965936136, 926119079, 622415733, 422162861, 377188165, 942156378, 276765508, 706424769, 466530231, 864535085, 128911977, 236877201, 247793400, 299179268, 665936294, 175567029, 469808561, 561411061, 893329112, 594511624, 240259757, 546499285, 838349142, 880645600, 25567620, 890385105, 7001416, 235086894, 719487018, 323673644, 52969847, 864086125, 320484122, 981648248, 817547279, 459962845, 986275137, 738210501, 425269259, 280524508, 846524045, 604864902, 439430053, 308818173, 777714188, 203817798, 804232746, 58808640, 806019895, 874958617, 111492162, 475799718, 592908537, 688222334, 704967879, 779406570, 501221846, 79906625, 201876347, 995120550, 816563427, 447562312, 432195635, 694353449, 760707939, 501589977, 833404396, 479106273, 940527761, 579260066, 798296942, 283685116, 97179908, 34778812, 361633649, 433301822, 860514639, 510824401, 656876841, 330790611, 466045581, 942117222, 142679939, 327237600, 351361171, 430652057, 303638943, 245390952, 872141397, 931926380, 791542125, 275836305, 302326223, 834569020, 725557193, 42896220, 711909656, 847737235, 381833109, 271133386, 346600526, 932330444, 92072774, 635337952, 504730286, 4925159, 692001389, 962018398, 107614683, 19581604, 473944731, 880825175, 759832661, 218664549, 910684154, 960964494, 988171187, 47340168, 365487548, 158123208, 614332102, 986033673, 411716575, 936327153, 629827, 829387294, 958558551, 596826419, 185086624, 83438908, 811122015, 508228388, 476063402, 903915958, 148871450, 689215688, 477817824, 509974404, 109283686, 426212007, 691198523, 965885673, 86602206, 950184294, 164457441, 170955583, 167550002, 864753205, 751686591, 760850752, 468635656, 930585760, 680265557, 642651364, 436390210, 245953471, 311584052, 425190142, 887619313, 557686572, 325142151, 809939833, 809766104, 911549181, 960810229, 314249341, 72504849, 620322767, 681035641, 78028366, 16692181, 766988842, 387669198, 339602917, 114528275, 559410255, 31417532, 145589910, 597290814, 224380982, 468135148, 95748264, 80272745, 64493726, 586486819, 735506092, 624827877, 914523875, 574908558, 756306871, 745635517, 666027849, 926815212, 698744283, 890504725, 442683752, 630358746, 573854877, 831030647, 534596893, 838878921, 633962010, 75969391, 548521955, 866509855, 753917031, 896417452, 919323131, 673051605, 949231325, 888677066, 958734054, 559294914, 659014825, 188770383, 268584185, 162922861, 277450567, 664941375, 543583959, 914762996, 775702795, 197896874, 114282341, 691423683, 699996273, 592554151, 719852885, 978224325, 544351885, 158704263, 799285158, 612630892, 924512884, 550794095, 523898983, 817358885, 523157254, 136312938, 323885203, 104835920, 27708248, 851385317, 774241614, 260287391, 380317143, 721248175, 957400825, 680321911, 406728271, 991551219, 531450178, 32468206, 30102183, 275985480, 781575737, 651465343, 263197583, 685358816, 380384986, 425594997, 517594469, 898833123, 37665365, 912288465, 199723434, 283383696, 202280966, 870556625, 509203162, 274589932, 100469364, 345943633, 826814791, 258076153, 274475079, 672845101, 986141839, 430045135, 692992055, 613615700, 987800154, 479119479, 405996869, 309996000, 864049217, 372113679, 733876330, 348939199, 265658887, 214063702, 534207461, 892827969, 864958820, 86490314, 389916089, 370213912, 747914072, 882989630, 430808580, 83892637, 623029131, 662142714, 469347310, 41518523, 692953132, 993093606, 894841376, 940653117, 32302946, 973609670, 769539267, 593964143, 148048268, 326790154, 825429197, 458952225, 926702356, 724416094, 736027279, 557529443, 474476262, 167293425, 261120186, 472419753, 948855669, 909050485, 534839501, 980812922, 497665728, 340262971, 82015307, 737647406, 591804786, 803334981, 548196847, 939488229, 196786096, 960214506, 832134025, 875545902, 200586564, 713855138, 435475963, 147075324, 556753385, 218125961, 588455255, 681853419, 229137715, 215655198, 840760950, 295649362, 177426369, 505286071, 991451523, 209444968, 29045700, 394511712, 378084939, 631995003, 929854989, 267704795, 476242977, 165303754, 450223634, 914443370, 488810903, 487772800, 588549290, 650744138, 423842969, 545550477, 485408756, 76668728, 478754899, 895820894, 558604818, 97784475, 611549533, 339398516, 714906993, 690870132, 155150288, 739003853, 160207107, 51583478, 584872075, 666374935, 202657545, 227529783, 736179596, 616954800, 672009928, 610201985, 509361027, 671716020, 74936913, 904136206, 790255674, 625647163, 458815167, 193651707, 789790170, 953658495, 580658450, 227459067, 231167738, 581001030, 970581403, 570492465, 360696131, 932572211, 83849060, 793547845, 404963337, 875773982, 220452482, 775984497, 174198484, 300984808, 400535982, 986439064, 498671642, 776707521, 690898680, 59620405, 327305015, 254127508, 808578038, 19573745, 921767666, 656135945, 284003676, 59369156, 47136898, 287889715, 113548769, 705853488, 109072616, 55158118, 21651567, 649085841, 368227018, 224786040, 699674140, 940502263, 729427378, 595234007, 324956659, 510169760, 572053013, 691471015, 650934229, 792401435, 557969394, 237916488, 322591331, 388287840, 956447844, 512857627, 354326916, 401081649, 492013308, 588532110, 966902678, 187723943, 266702603, 332828965, 688680027, 866281666, 93320337, 638610764, 76518223, 568542523, 716726120, 719573930, 398497993, 563309653, 73622998, 401036524, 810636190, 498115266, 488349486, 768093511, 711415257, 34319662, 628069266, 421831376, 900638805, 201424308, 664799835, 317165127, 74678889, 930974725, 237768103, 34251782, 33836289, 614003306, 984118136, 60136385, 346249261, 948681994, 669604496, 819501113, 230775233, 549580252, 240750610, 79199046, 210989032, 298930648, 905981817, 785471465, 970162048, 503687547, 957767401, 944164086, 769826546, 820873754, 655932953, 943643098, 331423759, 287221274, 556219420, 141983788, 875182614, 224385595, 645563617, 375118493, 128886995, 790501249, 399787373, 15950820, 551374492, 188899463, 530045887, 748356867, 594980485, 44748219, 319561419, 406997600, 510938597, 482297340, 939933982, 877653617, 822843485, 535305827, 111881698, 224507671, 897024053, 385734639, 440141673, 898175505, 941294163, 540342846, 865855254, 501782902, 403972434, 962302047, 641303258, 151089599, 414484453, 688792777, 266213404, 163934709, 904081320, 986394307, 473869720, 213523360, 958228073, 276850419, 515010915, 900366760, 405434966, 52859262, 77839012, 620827138, 581305688, 936920020, 614495249, 396306207, 915255890, 383174052, 611398467, 375065293, 723579978, 616288180, 622443942, 488167107, 502256931, 289989537, 267850524, 364110798, 5987281, 647655462, 399613643, 625981868, 240241977, 550672788, 71035538, 368957663, 959115085, 130001035, 758477276, 424789157, 539008287, 682610276, 284530732, 224028630, 859693093, 78168444, 309012481, 486696051, 42081229, 433601202, 547039224, 660755926, 318443591, 700209854, 899862623, 161982175, 190757750, 770959834, 822033661, 109410010, 576851244, 820639642, 129371775, 312297841, 312041663, 728779557, 998550191, 744357725, 312554232, 717383768, 217452821, 664284266, 708123791, 53782920, 834168543, 692536660, 752307306, 598977937, 693019547, 427191065, 672193748, 980359132, 779203966, 797517604, 132006645, 692093012, 930023814, 249199390, 58365076, 57881861, 867062989, 172142635, 33390407, 770416963, 90694416, 144925681, 985716882, 894492107, 962593512, 343728040, 742049439, 694854628, 735471553, 552138393, 557349120, 478407878, 408642762, 490677782, 689765973, 937286782, 61672570, 219788359, 683568401, 2634711, 564478147, 148695792, 908676336, 414602089, 918447597, 739529280, 818083356, 108265072, 514308356, 687460838, 946945004, 738789690, 833828981, 348088032, 258214040, 978850827, 376700119, 50509980, 749505509, 618500407, 515453089, 353375837, 586570875, 508987795, 723810027, 234301737, 579656159, 505802201, 90249818, 472000139, 768622174, 919817611, 717718402, 370958115, 250764128, 255327658, 84586446, 974216077, 473783564, 598397895, 211453055, 124476164, 904749127, 732391880, 946458091, 63614999, 199670340, 951090865, 510436802, 283933709, 471628110, 590693, 327146676, 624221719, 708560050, 250345476, 626366146, 985717841, 77203053, 572263706, 868353726, 336002978, 902507279, 584477055, 791096966, 873743447, 608176812, 334374869, 142949374, 105907077, 586726491, 63854350, 263341337, 71875837, 749966668, 183444516, 551814506, 208084341, 239240204, 665871230, 128674411, 203853359, 590253518, 793483046, 640585464, 228095544, 272636197, 817405515, 717870789, 649077233, 922006248, 877097595, 214596448, 341224548, 14177478, 838031044, 27933258, 177471971, 428100243, 917198829, 501285849, 652972089, 113140618, 663405232, 396630306, 107158195, 73542592, 55395715, 676199317, 44262713, 393341004, 377281654, 281575401, 803054923, 183095151, 321952875, 934134792, 31454734, 987301963, 547380193, 710510895, 589749026, 186863585, 807558205, 90776018, 267383195, 859366465, 130290120, 64160690, 539896732, 737457935, 193432161, 34209883, 983001487, 780008471, 324917525, 26264199, 480856937, 487085816, 126995123, 85622895, 439913830, 309380249, 934772247, 813298179, 636462832, 715951970, 981790447, 866535613, 212899715, 781552449, 80506735, 658741534, 964522401, 31827489, 395466689, 61250243, 401456545, 659984161, 676560221, 93289112, 93527062, 516796907, 888497754, 35106892, 522410552, 824134360, 942065717, 967599580, 242757469, 687987953, 46270765, 371711727, 412000352, 394901883, 819800481, 739591729, 652943874, 325443207, 935687919, 320226248, 327149645, 194023112, 836743924, 23107094, 71949232, 992809332, 915139558, 304858898, 441876923, 539307657, 128607005, 119177831, 783536538, 371733175, 719757369, 513276911, 393122908, 377818703, 935341399, 421517714, 12887343, 74300057, 117359453, 544108496, 233042207, 44025665, 143586350, 886401782, 461117023, 265983532, 27235943, 13548618, 884450820, 312018797, 179539063, 251277239, 180460707, 681293018, 790523431, 998310438, 221095211, 283777706, 717297966, 42825952, 660525001, 265714307, 451915867, 74311893, 508286844, 815217584, 477608589, 844919243, 30567410, 335835919, 177648828, 114578062, 281553630, 191760748, 292693915, 264190509, 540941452, 171904276, 698566218, 887095901, 995459801, 936341699, 680538570, 19884899, 641279774, 46609671, 419958841, 721565436, 353604152, 59377763, 97136320, 343058267, 480411259, 23489076, 249212791, 860609419, 570691029, 288385968, 653442829, 371648117, 635454018, 985827563, 845954361, 329838239, 138420821, 258574251, 95603886, 195112057, 758360315, 564283772, 595024483, 314680249, 557776119, 465221236, 827327507, 552652603, 401330595, 379986943, 386023736, 311063738, 215770258, 940571874, 226229969, 565459772, 19249130, 205854730, 475025440, 573841095, 755113555, 356200570, 253478925, 721067192, 758942282, 949871467, 159742280, 222284128, 290647196, 704460453, 729510271, 503938913, 527813721, 699259707, 623800103, 731318984, 646593925, 420592316, 443402912, 282389448, 944940139, 442288118, 431731739, 269976378, 312122524, 181039535, 822591396, 216072878, 576437911, 891288013, 259963820, 949661542, 83155950, 586689856, 680473921, 863595338, 397053965, 349508141, 391710469, 747722729, 374529560, 122343981, 580634131, 702521264, 312795367, 522615472, 183190637, 873659463, 630169137, 765680494, 600809527, 551597620, 395656865, 573983733, 551225564, 614268917, 822330749, 887401920, 837632720, 857180575, 795927500, 886669782, 494573958, 275507187, 824257238, 645866763, 314905025, 158468828, 185625857, 394020786, 814982741, 653319284, 483236913, 900091177, 749869745, 736331800, 148817935, 535701205, 972683510, 397718411, 950277386, 697303390, 694355021, 468812523, 676354173, 770936793, 361340674, 72329016, 307733954, 306866748, 364044395, 323003405, 302739679, 159965106, 649026749, 202948816, 81295871, 163779161, 202778464, 139368817, 638451615, 150348810, 490007211, 230981844, 490361737, 803445178, 766904920, 630874902, 285011689, 373716069, 992679561, 425955305, 424846725, 988336168, 930220256, 62058355, 565952501, 287966645, 223098188, 23538287, 581943220, 489181945, 730606258, 616227239, 234601797, 779894446, 199818698, 593817966, 360780018, 480221791, 549255095, 223802431, 322412111, 714083048, 439861181, 321302879, 802444471, 39888868, 630678374, 703276304, 819026255, 100059834, 118295997, 943503236, 518197721, 659510306, 25207860, 528943664, 304480088, 817619908, 17454568, 857830958, 715128800, 411263884, 183090622, 141812191, 823490189, 299571957, 165204592, 454045679, 969084565, 438426412, 348875545, 659064314, 824400576, 133718793, 414457157, 828323793, 19073, 551509906, 238505459, 922834623, 727505734, 851705449, 854707551, 751370995, 316592414, 405668416, 527613908, 800824155, 95165059, 543310755, 67526463, 909843450, 834826298, 96295890, 737109929, 712081995, 57775428, 598007305, 658956976, 770502594, 50594348, 779695163, 146059019, 114549921, 661779252, 731765710, 930432310, 913513656, 113843641, 909465868, 58183421, 307196143, 253983282, 391610748, 125273058, 945808526, 84253064, 533903803, 292134609, 901289359, 680113313, 322838576, 832142693, 511169706, 996413423, 557093643, 959894219, 267473417, 768421929, 976231867, 415271591, 709584170, 10095374, 847472061, 649589937, 859823004, 844724852, 915499028, 923718196, 950363239, 357782606, 62752555, 142588873, 651258419, 461059261, 505514679, 93181889, 153966112, 185684330, 682779085, 344893043, 411813040, 400300375, 140327732, 139268264, 746217639, 69012248, 507834655, 929454771, 831689501, 977936144, 359491708, 488446179, 454081670, 812068262, 3470812, 245397394, 982620889, 540089608, 449066611, 36511230, 558753439, 144228899, 366901968, 85509762, 72769901, 895082359, 291594012, 666345773, 661347068, 859574277, 832328926, 513611079, 809765833, 280490773, 823105676, 937794090, 518451413, 708492663, 860264254, 521419036, 268268461, 428423944, 648280185, 189100533, 998465805, 533328526, 49125338, 766078881, 784291497, 62377316, 128574616, 595620060, 53992188, 443956993, 331462845, 103556119, 106090744, 174822942, 275495496, 199240325, 300796706, 741044981, 164195611, 754102296, 811044679, 421410290, 957489762, 304418480, 786077168, 707745265, 280697935, 32330266, 35022588, 955130193, 469412901, 926671291, 3703439, 570402004, 852440254, 829827110, 42793749, 558297336, 34043586, 389877164, 149437918, 672369008, 772727732, 255574131, 489620648, 403072024, 19828716, 845794157, 292623613, 235156484, 82320875, 11044696, 877277063, 130190774, 141472545, 250106285, 514844333, 583526967, 874720669, 885707493, 437502548, 11063364, 19598364, 995744513, 905819416, 323057800, 713119884, 784634094, 728740442, 834282961, 61518840, 739390853, 341730925, 693988028, 667052800, 726259404, 64507467, 165236088, 481910410, 912976027, 960906513, 996774914, 578809712, 901463220, 779893030, 542173117, 542002955, 244508552, 923755292, 352892772, 615241041, 433340493, 224045598, 746104547, 386699594, 719378557, 834425374, 591743010, 493420735, 699737867, 930657892, 697790105, 84688631, 226131662, 384168041, 115444249, 630841811, 522428196, 286178946, 195370327, 460294668, 175563684, 737501207, 257993488, 397584921, 493498554, 366142176, 717955353, 799536587, 396178310, 368690098, 189995585, 934934755, 812670614, 31474772, 188961841, 820490555, 862334472, 858132537, 331292823, 479036235, 389924344, 930601839, 15194760, 594571659, 208197444, 899421234, 258835295, 258895202, 547453889, 860472186, 164125727, 941088023, 178060955, 627656208, 613472781, 858404733, 393264176, 384396736, 79295973, 11904133, 303624907, 16345985, 917807795, 323638882, 826311081, 762022490, 528601802, 152069740, 371574722, 740157125, 139063881, 213963165, 680539404, 820473779, 840554451, 626976251, 443247500, 312916664, 887811457, 299790680, 985989587, 254568875, 591159216, 640500996, 558103102, 814605234, 29664112, 923722236, 469784652, 681455948, 32255673, 420843158, 426020762, 225134971, 28073749, 665445541, 884721073, 861893513, 840220201, 478585445, 213227777, 711016946, 379036945, 20070149, 593631916, 75568694, 270444865, 671632675, 191481074, 640322196, 766864525, 728790838, 264160337, 387170383, 981252108, 794248397, 631808197, 546140395, 734399229, 193761126, 967945308, 102273020, 633439888, 463742211, 101407989, 773310679, 629831443, 315667931, 863353267, 523470129, 222457051, 658382054, 706711983, 173510372, 876444471, 70703591, 55705506, 789980760, 432651650, 861647378, 888816978, 959715435, 580813124, 714679573, 80914472, 576783884, 585816251, 353404168, 513830652, 437044233, 63268142, 31326867, 480095487, 277942610, 960003394, 129157151, 338746221, 742038268, 762137963, 560048039, 331430929, 207371342, 672174660, 723222295, 102199408, 241910666, 829825374, 501756098, 637837923, 964187616, 484078005, 879950655, 433204118, 573106884, 904807421, 928528826, 861756384, 215079100, 460738632, 626424138, 367572898, 709426860, 871690613, 750423162, 813817232, 895316350, 857865466, 380861975, 146577507, 215350433, 850929506, 928350398, 708210895, 769122186, 53706373, 582317985, 225468734, 86437450, 421642942, 963887699, 197454262, 329220279, 751875491, 260958450, 217991806, 386480036, 125570226, 796659123, 755349943, 933113986, 383280584, 917869846, 29651099, 3748307, 937172050, 813699515, 7929175, 913195830, 669546656, 1211788, 252970726, 142322108, 773848833, 58325738, 390564187, 811318163, 22780805, 946833336, 992577581, 466487622, 22578743, 170362663, 251094164, 474473145, 161263444, 258396383, 220550531, 984607396, 599425951, 517134584, 430292553, 693731435, 661953091, 620270834, 940699384, 544118102, 550589005, 183418841, 782436345, 519241071, 305180060, 91264428, 120640999, 538196283, 30989689, 286375057, 869162044, 39848133, 796508234, 550352622, 227478889, 835529403, 844421116, 241124850, 360335556, 791327572, 60028345, 82311804, 32580903, 861411589, 363969138, 596926675, 66231599, 494637666, 384890640, 599116839, 115667575, 939763073, 247815259, 600951354, 993231842, 324490621, 315671898, 97965609, 718489052, 463249393, 454543239, 267173968, 920332620, 159383650, 903841669, 993830723, 654988473, 306281058, 967132961, 371176865, 270794476, 658960606, 811085237, 490887246, 380257622, 578248977, 525148686, 803554771, 968600454, 350426274, 525192426, 338397963, 496705595, 647652832, 346879055, 808424884, 894133271, 969801483, 931328898, 440486559, 751352218, 799829452, 639559445, 799338538, 210387778, 575600551, 347831031, 435980549, 557822839, 736864639, 378139106, 678467705, 92891442, 553583351, 978365953, 190679330, 534075979, 983693234, 810034331, 818725307, 46647318, 835881682, 479597862, 583082965, 221495172, 544251413, 629693130, 471852748, 636525997, 675818809, 334924568, 173349384, 817495336, 193656315, 425769686, 371966691, 501234683, 298380011, 139004649, 658000906, 292153063, 578795561, 14811354, 793120123, 511048498, 96606796, 895243788, 821763825, 185031030, 346351925, 595390692, 40144858, 863381229, 266142345, 298056904, 926141330, 442034379, 752166893, 171069921, 426991968, 596383971, 634654391, 599281467, 729706210, 269862432, 18886242, 710284973, 479750971, 949410582, 28281729, 976546242, 627875972, 108178685, 25283769, 896754687, 585716305, 549916952, 423629367, 696603842, 951126159, 144743660, 447623106, 555650599, 780911401, 129659165, 291277721, 282812631, 543857314, 514884214, 531300468, 233202375, 244390755, 581249535, 169160529, 979630716, 598914470, 287090551, 530601009, 164200198, 638156238, 9077604, 770321687, 375555595, 433749094, 36582539, 980443452, 850495023, 311910953, 434561262, 960930651, 667772276, 616894850, 871506932, 372354745, 153340478, 876104660, 872295410, 840743756, 60457805, 464629953, 107149553, 325791447, 710409620, 565254603, 864156878, 313880886, 596188761, 794630742, 991817937, 342080143, 231845003, 624267816, 90509587, 112244274, 40110003, 701295338, 374263471, 182513646, 36011901, 879209435, 757268183, 930894846, 387905022, 90917824, 285826209, 462054719, 264296618, 995388512, 389318451, 961867405, 792215855, 616770398, 915939619, 779157759, 524291182, 170224204, 655311333, 556025747, 745499034, 508628500, 760686773, 12112280, 734164768, 953186631, 763212472, 791132013, 951423854, 835992931, 60205111, 472043710, 400922315, 794273199, 871918227, 495947391, 80473094, 774319422, 229654948, 4800530, 116502660, 118553200, 796977473, 839042599, 443063039, 455365562, 688923688, 201505663, 158114186, 761684340, 946722679, 741437352, 663028022, 305248239, 942001252, 765609588, 683733982, 964129711, 544964402, 278375464, 222850586, 590937767, 965099095, 111672113, 622427532, 797823030, 167050625, 364858210, 506747622, 263476872, 631022415, 447159499, 49037243, 186133678, 274089921, 366515879, 581947484, 484039272, 221985481, 701130352, 99091308, 448407100, 417447787, 412569182, 744743123, 596139376, 974211355, 83105302, 689845985, 950715662, 797613843, 588942564, 780093548, 350126686, 352705759, 808252062, 412789355, 587101247, 606331486, 821845756, 233295673, 684661743, 267728020, 525086113, 768454170, 305643569, 285840311, 471199273, 640177279, 950933185, 856132030, 889824549, 894206545, 110233502, 522315866, 829197803, 72916437, 746941097, 202381645, 167162934, 580640459, 517221304, 639888091, 698341468, 7332873, 439536892, 536006485, 997217309, 756045113, 64444927, 515141997, 16866663, 94612134, 262979837, 388118026, 903802513, 739930303, 888261384, 958206034, 526437704, 251434733, 439973772, 773147182, 607595641, 788493757, 118035632, 890137708, 870890494, 445876115, 28107571, 967147084, 656739335, 754124759, 673049070, 340618536, 366880317, 443746593, 750272710, 248179795, 11386760, 817815813, 912389662, 938382399, 466638210, 487088221, 8700240, 408979738, 156778405, 897031412, 268241905, 330907379, 606735539, 968532042, 424949043, 57730167, 194993183, 957414941, 461403788, 30555557, 486425, 121058262, 414107722, 683682404, 604339476, 757054631, 662873688, 966860877, 33934127, 433870844, 144026653, 659585157, 665996218, 666430093, 722428016, 683777382, 85424827, 727217461, 296507742, 962413827, 141583387, 190679003, 525378680, 352785017, 345923102, 951688214, 65064924, 994637645, 501078606, 250423483, 140192825, 572885880, 520323637, 553093256, 599376529, 827852638, 34181880, 300457569, 136180964, 6938488, 387793103, 265540049, 503654856, 887060866, 148728307, 265362385, 847604894, 359992445, 462252947, 780773782, 37680986, 511354010, 993783236, 484043155, 681121634, 663387224, 808721971, 756864936, 411174007, 314064160, 758392411, 642850159, 483620148, 970713704, 896992696, 527690462, 144246273, 682655719, 64483249, 588886235, 876253980, 371366241, 777333253, 314747960, 613471682, 450176279, 620261880, 292426526, 197071094, 297683503, 71308062, 381138807, 979747537, 312724391, 749000267, 189176662, 681789330, 34462644, 921277395, 862437105, 154071955, 968610231, 447439950, 144372913, 631310428, 599691548, 330670947, 456316478, 952486305, 847446874, 852909293, 830111038, 386882219, 29701996, 547539937, 95209762, 840403939, 787555757, 104669475, 377321235, 689888716, 646751400, 951625663, 4478101, 300606096, 58462229, 74783233, 193802384, 594780530, 847862494, 962409418, 915762128, 783853665, 391382766, 114066282, 521974810, 592100037, 961633126, 354819377, 396965986, 990322171, 289574940, 494905403, 778635528, 161484717, 189011037, 771081805, 819579685, 469674890, 405860278, 870115270, 855442643, 667397046, 368465919, 143223402, 883406016, 12967012, 680107051, 375670268, 651088930, 727026602, 232141882, 344438643, 422849233, 538817856, 948121359, 503988986, 707291464, 84265670, 66502809, 516277384, 539106410, 540736006, 954287763, 295119098, 681604698, 656359524, 750186130, 998600223, 129844958, 531787472, 52840358, 918860240, 336238923, 561486993, 144041721, 801382182, 580957289, 348451902, 796887155, 208657868, 966893413, 419886054, 874975360, 446192276, 154860772, 193592474, 293648082, 883738075, 126477544, 90308614, 331078926, 965772088, 479988831, 947652058, 64882566, 9542581, 251932826, 621748907, 788859209, 837094510, 747880034, 389723340, 672890894, 931433284, 693300552, 820001947, 590816007, 339030603, 555785630, 562512975, 215647413, 430706198, 389566094, 511993433, 786781016, 921188804, 32575369, 702089079, 414156958, 278808416, 860788563, 451897287, 924126242, 368204032, 157165506, 595844771, 30753678, 636264438, 176897231, 268757747, 832945574, 400545674, 138979595, 248205264, 317999990, 286650793, 785737763, 918159856, 905065660, 628384177, 814680427, 624992406, 556875444, 164816051, 419958770, 642158226, 365559816, 857058255, 194018361, 294626809, 604046790, 944414288, 131809362, 732646865, 591917592, 302467002, 673432656, 930235991, 763703664, 942805563, 88000794, 939442624, 539903182, 939319476, 740356280, 971337183, 669932293, 486350374, 94177461, 432439876, 298406152, 712895277, 652788965, 771284809, 740283207, 307150329, 109159620, 873464219, 271039204, 497916296, 159500674, 196125425, 579463640, 370076970, 504616934, 510798381, 712892957, 121257147, 163146772, 137642804, 714047757, 855480124, 275420751, 817033538, 938068334, 638396138, 385765254, 212353075, 845843328, 244861474, 872593696, 691072920, 896215625, 711349763, 892856003, 577937198, 727793588, 686509286, 968428683, 213795750, 1641840, 440851941, 961011257, 621573393, 211529147, 786165237, 75432556, 293021596, 540800283, 197214002, 430024444, 317549687, 129392004, 932277411, 543594531, 374393610, 422671072, 559656672, 387895633, 296191119, 730192475, 471970626, 679943827, 145447354, 569230762, 13479003, 335974843, 713652604, 961845980, 784500848, 997369295, 24605272, 79575554, 222527050, 339179300, 532902319, 919955182, 949725619, 806736046, 803881431, 520364334, 420223980, 380856057, 547654411, 137678764, 780296799, 14940315, 11779649, 381320320, 282423196, 69239565, 87447463, 938919019, 854987826, 645314248, 469792939, 358076546, 715591828, 134817998, 18874451, 433842400, 168376189, 750772112, 273189927, 51158251, 560583637, 592056531, 426613678, 209685313, 736744410, 759637548, 175284615, 828632623, 672461025, 421289790, 228669656, 273357226, 644078450, 758556207, 855236694, 663109605, 548919676, 215310441, 565130135, 377966313, 977376887, 511807518, 807000230, 859167736, 424783718, 475056613, 328898600, 876787727, 604683877, 667204090, 982188674, 833046036, 299195408, 645742676, 655547476, 822367317, 414908058, 208685496, 771834339, 796089482, 198786091, 977840695, 160268462, 637609963, 566499040, 638255186, 730524827, 186414113, 335426934, 557124958, 25877692, 969507978, 162405100, 61399825, 945702715, 453153796, 920189690, 153350984, 372364895, 822686103, 629678377, 618171220, 309266971, 903262392, 582371207, 957258439, 308395537, 627281608, 763390479, 430517076, 823953289, 109733266, 695439872, 258928788, 169611212, 923467835, 96793517, 852773238, 733853056, 23844856, 888882755, 451589569, 965003733, 351692876, 180251788, 904898568, 962805427, 323662929, 360429714, 98158262, 542453991, 709324594, 195785029, 375665289, 713414255, 935111055, 525001836, 614078907, 752777662, 352580882, 814101740, 702007188, 456849500, 282732556, 41600947, 109831685, 602677756, 249386847, 966279934, 634316347, 448969148, 335960777, 923421969, 472841032, 121004300, 297216139, 972925105, 224031313, 695518497, 987457118, 622944101, 247322161, 174638808, 504856874, 576706397, 398220569, 488946829, 948959104, 371079241, 654225624, 620129933, 453187993, 370537939, 347071289, 59471648, 947723612, 819453195, 855112429, 520718360, 682783961, 290252387, 883172299, 872373685, 994886227, 798287402, 522319753, 23125975, 220120875, 525109515, 603114937, 253444949, 644750279, 808970683, 989550776, 163213167, 110731041, 967071217, 25462159, 439926603, 263549080, 716126477, 112812642, 59118149, 223402813, 144808020, 979470287, 474988923, 42333560, 431048067, 714390158, 758789967, 923339648, 232413240, 937013388, 678449493, 478834143, 665661483, 279987968, 261396248, 523648920, 522626113, 573891239, 93910170, 644751142, 675539008, 63457841, 584243710, 12100028, 17002887, 328070545, 319379855, 69329961, 528247497, 302775060, 982713555, 171218834, 145684906, 629470882, 66829129, 215816093, 75111466, 634033792, 787195164, 637562791, 483230688, 844535578, 469577190, 563179581, 728039788, 257767960, 825486206, 702951077, 166933547, 22205176, 706854250, 504776688, 700267501, 888787982, 761676624, 889393736, 577903632, 841925282, 791058653, 837697822, 553574327, 107585651, 178224145, 720355120, 545276728, 111605956, 615114073, 537595455, 939564896, 490757231, 633181485, 904009493, 672879388, 500652407, 16176041, 539621644, 357573632, 222394902, 140519502, 116552440, 34356237, 505571392, 654145475, 259677195, 529938187, 112595571, 214505501, 964778075, 740024266, 690018327, 386920185, 188348622, 391862782, 933414781, 578051941, 394680554, 442508844, 838160508, 319738901, 455554920, 167591271, 873308568, 665083675, 461931887, 193743295, 203243411, 909019162, 701798243, 753165009, 642298700, 641254415, 729754727, 324486210, 850605239, 870075721, 545650103, 995651374, 35979147, 562492122, 487901869, 742440128, 307032614, 383949934, 350824146, 115640679, 409794724, 649909205, 98176409, 876858179, 514216581, 240246121, 685872183, 536923172, 737008683, 362805630, 111228371, 674862182, 736556211, 200412362, 742642807, 983020673, 407018899, 951262328, 85886147, 161469011, 736388533, 256001362, 75173931, 496747826, 529589949, 50946049, 907463780, 800065672, 284692574, 308406476, 332002413, 624231250, 256377067, 610989643, 321543283, 517741101, 175959240, 773676266, 585245787, 376377178, 544800735, 948526262, 691876701, 891490260, 965188001, 743311946, 57220258, 571618186, 745275696, 345409557, 348202813, 799058982, 993103735, 646133191, 96676009, 918212699, 242603993, 997602393, 893673359, 930911567, 158525803, 946920183, 472443448, 327615780, 641102795, 516313242, 951570234, 911858258, 647896192, 131715812, 665939837, 333444757, 342737571, 561929230, 27594519, 280312456, 567416790, 479334467, 217505308, 191863983, 584390277, 289796572, 585435675, 454892848, 128790572, 829128287, 144135862, 647224211, 213192896, 39956475, 851738322, 670534053, 723421254, 125505696, 795240022, 955088084, 87604784, 574411224, 945816787, 863860194, 29638839, 824392317, 140983, 341813657, 610003321, 900032658, 153509154, 239975880, 937137743, 500493972, 745236871, 744412407, 465325833, 251828495, 707566076, 813861103, 507893705, 922481948, 479557571, 776775890, 990631499, 51190244, 602539719, 483090711, 116927594, 473286993, 332185419, 610004170, 628242464, 76126905, 925928085, 654456012, 398115326, 381554623, 196894285, 265333773, 955741611, 628655679, 273470947, 203693680, 983331854, 917183093, 675262450, 562700431, 838045517, 612514841, 309208686, 639875697, 600360282, 863304100, 151586605, 84924596, 224228878, 411996155, 691136289, 490465281, 162804636, 390482204, 682891861, 127849003, 630207189, 340140887, 926964369, 68242735, 640203666, 198090371, 270396336, 558652656, 386450660, 86700182, 209764825, 836951326, 122973848, 557936930, 460892594, 229232566, 26441840, 172174843, 541679176, 310612951, 751043424, 894470467, 389887722, 803571834, 243982010, 344196969, 994700370, 124416498, 360631492, 64107839, 365938101, 320352454, 162245490, 633334953, 680485482, 370693499, 788989512, 210641378, 550303134, 346960644, 41639974, 850182030, 294581752, 904808036, 82961806, 76246554, 731470684, 67201059, 769118581, 303406542, 949372048, 655877415, 531098919, 865101575, 136003074, 420933703, 851510135, 588885214, 530445995, 622752769, 206035564, 455258871, 565586675, 817514630, 135884219, 776604660, 162205380, 718751905, 565842825, 520764960, 565549698, 514241171, 593714823, 481231190, 809591910, 753862174, 813712688, 787184073, 124058767, 464900425, 691447641, 162891804, 343380877, 486829160, 153686139, 182031817, 937580220, 915258304, 811569083, 220444160, 894419324, 808379538, 902182096, 857135100, 778227780, 85080703, 556399860, 383250748, 420165345, 8588659, 583294101, 134265239, 240510910, 154161553, 388956885, 519933186, 353661866, 216538230, 292346903, 53544298, 683170259, 363712674, 347566573, 637741470, 964727651, 619800962, 305348266, 721174730, 575389329, 312194994, 34803002, 108026306, 937631354, 649607234, 685748493, 856998708, 417765510, 324282067, 730896703, 15906807, 653855460, 945542096, 305731823, 558503218, 556337982, 445857136, 526166175, 40756440, 26128095, 831579007, 549673722, 929188678, 288981574, 153589869, 806490273, 430262405, 332276984, 207386639, 810065741, 587707020, 581674414, 896175382, 76345353, 195176103, 302987165, 986914093, 773760326, 419214419, 765399554, 105880206, 428331502, 334925556, 565999530, 203891741, 667540526, 244042581, 713488803, 100589781, 999810650, 714678110, 563986335, 24386022, 631319189, 240250336, 735118053, 638656494, 634625209, 914780790, 678658183, 834731224, 469868773, 200720422, 761643677, 727334406, 596589816, 716562860, 716560946, 954132533, 581734099, 151976516, 955115215, 830951185, 245027220, 184222037, 571038607, 93805571, 811377174, 844418666, 517765326, 717755754, 397496802, 717739380, 365809859, 303668203, 726241474, 562778972, 839391970, 808828409, 688878662, 130339623, 126354090, 110591358, 155558748, 844690772, 67755134, 749111406, 753891134, 267833779, 306886548, 66009120, 110193573, 304859009, 687833162, 218482324, 474794366, 843199444, 54097627, 823114417, 892592330, 770031939, 921892295, 751494938, 814182290, 177203637, 888854772, 712032735, 460556666, 656256478, 680784362, 601308473, 841612767, 283803030, 811710069, 404045495, 177038138, 166125661, 920355108, 166522481, 840100014, 749055716, 414256001, 618273328, 171671916, 992541229, 740973906, 721097637, 668939831, 215301539, 466707223, 789905631, 913397999, 455001968, 130777230, 198057111, 924306739, 9033552, 583722338, 1756191, 865116496, 11003555, 662230090, 894769532, 15880551, 610259905, 7994801, 743537047, 215680124, 832360649, 665214831, 215822407, 903225050, 973265458, 323911441, 736415614, 48918300, 532247442, 693826419, 74256980, 545649518, 38052571, 391857961, 431249610, 793072358, 503201390, 212600620, 919656149, 610816764, 853823388, 166853998, 869205441, 678334736, 480518964, 204419839, 611276293, 955446680, 593147167, 174200, 419624742, 284141278, 997716723, 897235445, 512672250, 811326573, 756920279, 742362914, 626123594, 396861702, 248685257, 232554420, 224479005, 245733389, 325583865, 361383258, 904156695, 119983794, 550227581, 945833903, 240557330, 966943034, 433161319, 585552440, 279899977, 825395453, 349986299, 983244686, 585960672, 86450311, 854316434, 384011324, 133805263, 922839832, 469067444, 68229431, 525747391, 822470161, 531159295, 622563917, 485892188, 305334428, 280534424, 655703314, 437949674, 278555052, 20764217, 256165174, 811289169, 414681011, 533442612, 575443288, 592372174, 514570674, 258614821, 475483238, 389824998, 754320545, 307627497, 514386953, 131142708, 532698811, 886342787, 963720974, 818267067, 633628522, 864435682, 250877917, 507788416, 421917581, 437017887, 71686457, 827917686, 400263536, 714352491, 663148780, 154725485, 157939662, 850373470, 952830957, 244514337, 172758919, 812185055, 625743842, 731755629, 485549194, 150617961, 677799053, 317934394, 247219498, 366987258, 243827524, 492911914, 546329887, 765663883, 621839945, 618440390, 197826475, 772650448, 518108344, 251434209, 307135482, 270838980, 468021096, 209940056, 95544754, 87338871, 99128301, 729196021, 885621812, 764284211, 822285305, 298109117, 389602402, 754528032, 298721396, 206994609, 890452382, 730738899, 37679162, 363530744, 764520210, 438072144, 241812385, 117385103, 124666614, 322740276, 127226821, 652020193, 791659493, 889439705, 904453941, 574235051, 336125247, 388284209, 595937983, 275373142, 750733004, 19025603, 655613754, 678343778, 673718127, 453332896, 707993615, 323629277, 347797590, 401719101, 262745898, 309759518, 866402403, 952014509, 463504420, 160809430, 321005871, 325029550, 889444826, 224539013, 566048390, 403569081, 527824218, 35547715, 637104555, 286187745, 542413287, 464947200, 588025958, 747397241, 47661275, 75673872, 992683289, 14800674, 8569233, 191362346, 509012348, 702957498, 693333365, 299516891, 879751626, 322264026, 981603575, 296450523, 270395833, 466694010, 274291497, 966115956, 209815409, 768175593, 208719947, 953565192, 584848616, 155789519, 387850511, 747928286, 745847561, 416217054, 827941710, 267590169, 841204550, 82487462, 54352030, 887928166, 704303455, 64717494, 328084227, 952553383, 496549639, 258954564, 706786468, 209206839, 737066894, 711706194, 185646250, 392771944, 660957378, 827567756, 169762866, 4130049, 753395551, 372294553, 874729916, 471544700, 461019613, 170671246, 997340972, 995811236, 261953853, 706340537, 193010338, 92898923, 855780286, 415988600, 54624710, 94958235, 971874698, 367995209, 520341708, 685023221, 597527121, 535670305, 838176770, 336182551, 535179494, 50421853, 861812454, 659441605, 606940468, 590597057, 228618827, 556930709, 915280737, 78705099, 808008854, 306610122, 595492365, 817723358, 515024895, 13184066, 463894760, 562975370, 825687244, 874789976, 133886404, 633386034, 179598159, 933634646, 731916989, 820241366, 753574111, 597289710, 755209177, 704649660, 939643585, 84936307, 787363979, 5135849, 769324013, 330750310, 220291872, 637105953, 473750508, 802258019, 287320594, 107803901, 810997941, 971284896, 402393024, 658257987, 418059185, 447459916, 295639353, 363996798, 688866257, 586219056, 565776623, 552499912, 132532721, 508521848, 618397093, 445942187, 697205016, 176486839, 582785959, 106502253, 38975813, 287553823, 288083949, 630331476, 695585073, 127231165, 261145530, 722192716, 5380190, 893744227, 653350975, 513074378, 243139665, 715207511, 377319263, 449136184, 99116304, 824505517, 627320312, 843458312, 105672461, 413054168, 419739097, 171449954, 979500258, 888658187, 188872070, 513727972, 411597329, 286910980, 365908032, 749558019, 443822170, 352422406, 814584119, 297661554, 268249285, 648256955, 758778128, 885049700, 65294815, 74491942, 938644541, 292457052, 163432095, 162255450, 315920280, 532692707, 490454289, 174084155, 407808560, 309320999, 976012213, 903507908, 869534934, 589942939, 171776333, 197191708, 688248041, 727792876, 463188536, 305119368, 291671553, 91920113, 67621668, 948858625, 425473771, 196001561, 730542056, 690448450, 647521229, 641076849, 941780001, 346861400, 131793801, 921030118, 677143495, 507382264, 462869540, 368959027, 69273412, 135057485, 739186337, 920878518, 717439598, 403390635, 1153332, 799963800, 299744010, 191256683, 577247557, 965273412, 190369775, 2208858, 355388217, 618626265, 862547648, 379821364, 306075370, 928624095, 60907543, 679017210, 224852391, 659107048, 454353523, 789862205, 554381418, 361028327, 17171241, 620187841, 251917503, 599842763, 624565946, 714852991, 7044230, 94871375, 641646161, 713410554, 284807019, 406471115, 159334516, 180370379, 628931420, 126176383, 854500341, 186206090, 812694428, 823727343, 927139304, 308876019, 707988256, 162095071, 332883544, 305194437, 339817691, 232643050, 597576738, 407592567, 317294707, 349952881, 93029825, 392196389, 871682593, 222874289, 422409782, 987804124, 728014751, 660612088, 200598570, 360947540, 47477485, 92034843, 58814241, 207330888, 33112601, 313835576, 416738802, 836034745, 735416515, 455539943, 808766144, 181381619, 350506629, 371304990, 837223299, 468085303, 911816808, 523880323, 474196514, 345122627, 694341641, 800565860, 380820054, 872406613, 427838675, 623030155, 367385772, 684360652, 657771264, 156415397, 640377107, 447270393, 685102989, 175938360, 510715901, 419701603, 2569187, 274108645, 929150587, 836448023, 647494279, 602384320, 730438997, 115986702, 29125614, 381161520, 993238365, 496941993, 320526639, 746137897, 479808115, 639705363, 144095138, 902511665, 495574187, 212503470, 982710592, 601005692, 704754155, 659144575, 264028164, 552774308, 585243042, 760263719, 898722832, 266331864, 596845864, 3134351, 311747354, 763464972, 303109941, 843655026, 473576851, 751633105, 11642481, 525825603, 865008699, 247484678, 883789161, 84974018, 736892124, 258095309, 581897592, 531152166, 208220735, 476621112, 113518597, 403467420, 4373663, 306033696, 543719710, 956782916, 224133374, 200514882, 309924084, 521870846, 976457517, 530789282, 60028199, 697311042, 906180989, 288949589, 342598091, 765814388, 479120934, 793354438, 811390872, 567383440, 592573555, 285020934, 454318379, 30322366, 35798123, 387137548, 618628437, 588026680, 904453557, 536264215, 551256696, 893660124, 743423427, 657010791, 935300934, 933613205, 725636729, 918094060, 934716436, 668590426, 32702442, 521190175, 748627386, 709102632, 841333250, 11461125, 223589470, 146444840, 52324714, 379191458, 468994596, 225373252, 313536650, 532419783, 13849098, 883271445, 623964852, 591509385, 28803404, 589373434, 528855851, 354133578, 80319898, 23316627, 272103990, 455058477, 823491166, 401666315, 574542002, 951603746, 857086391, 66231858, 417908770, 816412749, 399234296, 378818188, 736314745, 381101072, 346790168, 547690875, 953534958, 734947252, 962556640, 650667607, 759432146, 77638699, 629834963, 728386295, 249086275, 281779494, 208763811, 249216052, 595987414, 183846602, 116268630, 624803545, 265527438, 795952045, 73375697, 796433383, 202439098, 225908327, 158983944, 213571723, 291449019, 155448757, 24132694, 61829323, 560583621, 260045336, 245456947, 432505715, 90724961, 411430914, 652784866, 343125509, 297611289, 258355552, 720520103, 366331605, 715572605, 854786151, 60947715, 42098014, 433434476, 35321688, 793315249, 853428216, 504028393, 284007122, 622178586, 65888162, 338211280, 785024281, 321340157, 624357219, 904166413, 263482379, 444617882, 463885759, 216716930, 950988501, 9974265, 17562546, 893086778, 234744925, 249199620, 630796252, 544565893, 487568952, 550241547, 733419176, 541703711, 734636559, 150737849, 990485296, 466000426, 221410727, 541060016, 116792769, 730928438, 429595311, 660274238, 351148568, 916162750, 116624943, 631670193, 691368177, 931581173, 881022432, 753267146, 291988942, 763726989, 394970553, 189578673, 999868077, 582997542, 917094389, 683627259, 890947557, 413250308, 30758807, 395607987, 618748245, 725449357, 227690969, 789054429, 721392913, 469161877, 741528944, 855185760, 195933516, 60300842, 928443850, 188910027, 85667143, 770534123, 816490950, 661312699, 259949136, 827011157, 835135143, 291214648, 994472535, 723854275, 924525000, 496095660, 640793996, 750910653, 598856214, 345919582, 266383566, 473881090, 257707156, 43525438, 442970020, 289937360, 219131943, 552440040, 123129022, 879817529, 154652575, 78793204, 921466939, 477274024, 412026704, 287405855, 679522950, 986763724, 871985634, 727126347, 67083470, 181274817, 305090011, 603604266, 78370679, 409738660, 626781739, 290317304, 666195390, 927149881, 65779877, 325287112, 844600700, 169528527, 191953271, 807435948, 348023334, 464180471, 935340939, 893547636, 927286405, 137393101, 239764267, 258807193, 538114902, 588943966, 540771071, 731484224, 91014937, 310966374, 542860147, 984821260, 310560881, 210048479, 515175422, 387851914, 5450498, 570124449, 134857551, 618312531, 372935819, 806278686, 515759525, 690559271, 68381072, 424284588, 320822451, 853224383, 866385989, 677260599, 638609159, 653440660, 752550242, 98398382, 802950197, 863154172, 116178737, 132206092, 430107708, 672393981, 733057478, 605824611, 416523216, 760365977, 790759442, 639705211, 522822717, 272122654, 138928809, 643843090, 933125050, 28360454, 562211866, 986645127, 322700371, 722544581, 666682917, 411776439, 131796334, 269126251, 178262951, 490065996, 804572473, 19549457, 35369688, 952872891, 127219040, 798151828, 518202653, 32364766, 243225788, 771107138, 908768333, 356124435, 882986753, 499508881, 881870482, 971177002, 104117017, 436562342, 852808055, 989565398, 152541901, 144726590, 502359661, 229654482, 239581011, 459938033, 827533349, 957869637, 826732166, 994780061, 102608203, 17536775, 871263210, 509553285, 184948973, 839684360, 749148651, 75644418, 292427789, 915094064, 951615219, 342717094, 7746708, 858083785, 146096523, 85086823, 11961741, 918785664, 407315645, 734415616, 917757653, 170338814, 399446570, 952730674, 37689457, 665584245, 179669010, 461558286, 381495760, 170992445, 799867715, 550486923, 844146523, 431472813, 665410011, 890704584, 699454199, 546164716, 509327002, 35814609, 587073511, 434465404, 389349309, 600868215, 772498489, 240609314, 957995157, 524594543, 212528421, 463806734, 77862873, 787018147, 591172896, 317561296, 1519469, 274859647, 981353251, 970131610, 301934789, 850362475, 220363364, 896946162, 742983239, 883281704, 520324351, 339411772, 93930495, 358418429, 691063823, 845263400, 652362890, 734652129, 883163803, 91892694, 79801857, 617877032, 938238465, 949434466, 229070371, 483616874, 243865824, 631622058, 412203120, 172122343, 880166633, 6466850, 254512698, 912820706, 970591752, 378662591, 366597899, 861475080, 92576593, 72226837, 147261193, 817291675, 292139762, 341880683, 45726862, 910360790, 124882649, 959134472, 690197837, 280010494, 827983436, 267498706, 478998578, 301226660, 35568612, 622699612, 183659231, 39391773, 290325958, 690017194, 534483127, 179639654, 478004125, 9653559, 733122232, 814191306, 125032268, 970184216, 78278840, 563387969, 70461442, 534949134, 935426366, 328875290, 374291444, 617436912, 47783033, 307310568, 22772547, 215021650, 864055279, 358280975, 336323791, 355358043, 848873742, 311921666, 946476143, 610075486, 800407653, 628502500, 280094568, 201777773, 433414493, 708693384, 76093355, 823403680, 744843646, 729445043, 24016152, 817947972, 813979056, 159307392, 821913326, 100075496, 393721045, 739725293, 229466985, 157190047, 19189907, 881719896, 119458369, 271020455, 205996983, 806402443, 226610684, 639523772, 519261536, 432664888, 206394401, 386457485, 611216347, 137819407, 131886817, 669669820, 536820013, 7255341, 748269132, 847164649, 916066802, 932433579, 918990598, 498570352, 980120879, 200418323, 503623898, 283999234, 844685317, 895203897, 298390072, 853192766, 218343955, 732316604, 889014059, 777895976, 742061833, 765993622, 319648780, 43833200, 583783084, 959375093, 401906841, 874952739, 465085991, 935482659, 494554114, 574899745, 143562005, 881765084, 841721157, 810539929, 28212408, 780381845, 727165488, 800602975, 318956742, 217274193, 414886392, 322176396, 469015765, 871793140, 699435710, 213731589, 18855763, 521286873, 344308195, 756638348, 133262281, 109567823, 540422620, 64197520, 492238600, 303307113, 827657298, 53145637, 963267086, 410216149, 928032676, 57755021, 165637067, 312381208, 94501645, 359495911, 818035369, 516718092, 291766132, 241441872, 115134016, 101441454, 227924297, 180432914, 835537302, 944471580, 962418156, 810297362, 769991488, 583951033, 119640057, 907153958, 131566760, 469797259, 896952155, 546625444, 308804185, 381894128, 571195961, 178790513, 194153201, 879880807, 859092389, 243828234, 89517891, 254138405, 604454818, 614241387, 579177895, 137199401, 219498033, 745917292, 297784367, 642017510, 447343568, 902869197, 607310406, 808135257, 525911230, 729525237, 312532397, 754890497, 128688394, 625865752, 536768252, 140670552, 723639746, 785675172, 353185828, 485929060, 650063681, 454107025, 378680397, 488460363, 847589936, 40386200, 143252760, 110868099, 877626425, 42765475, 203355685, 451346998, 647042355, 315603189, 689983559, 965880071, 671019229, 85081960, 577261233, 935090077, 802553285, 715651195, 815633026, 841684193, 853226569, 609201097, 21092271, 507633570, 973600689, 935955941, 255629669, 992452913, 313695138, 158573211, 594078739, 592569020, 353808417, 130776523, 318780042, 496760898, 530197370, 246268040, 715854479, 757584698, 388453824, 85810877, 97468608, 446363371, 251129390, 405550313, 780887840, 59011078, 319717643, 698017529, 992574111, 682077815, 9027505, 981919739, 462828643, 876328265, 919200276, 790696931, 49919238, 503948045, 214617317, 71266306, 634601822, 511792973, 138064708, 509157567, 984154052, 143693235, 189846089, 74903451, 394804810, 656429784, 505207924, 506165623, 701024487, 495539809, 703784712, 21955389, 516948463, 60028456, 553452832, 982703785, 594058577, 826179798, 242602134, 824729111, 545434278, 842129654, 781819296, 594609721, 673892671, 509429296, 300850757, 728704038, 296363069, 133609833, 440745342, 531185906, 557257261, 973878182, 82405598, 219527531, 456243492, 400243750, 488763629, 617547348, 822422904, 645693529, 46125411, 776709648, 186504227, 432331091, 551665713, 569322416, 855777451, 388214377, 169627177, 43692715, 260957980, 61333117, 128168988, 362254036, 720632991, 551442852, 19139977, 438677077, 341887542, 631561381, 863445695, 115775382, 44578244, 993348922, 465677277, 512275084, 110007436, 568058241, 111055761, 12540857, 940666535, 963144853, 642768723, 291035019, 837193036, 636553094, 344580004, 789018046, 206069299, 942599204, 913207051, 320942742, 670390328, 642797764, 292946663, 58049638, 544884321, 795070547, 727067385, 177839953, 340610222, 505886928, 498829369, 235306119, 940100161, 44724510, 285468481, 132527911, 527952260, 62637876, 645183565, 827400987, 778014446, 622114919, 267864732, 321143486, 302641792, 390292763, 966841157, 103049052, 778861022, 202735780, 315047282, 174838034, 162018926, 480013148, 52141052, 373305531, 873640372, 48111901, 636859836, 68638543, 263515397, 988384469, 612981063, 640648148, 572575984, 249095312, 438963696, 678653892, 452427598, 607028776, 572647326, 220681960, 133864098, 772088235, 935933559, 778014122, 999646649, 916846275, 94102186, 546328000, 395494752, 353758933, 335468499, 176071744, 991216361, 383998586, 908964492, 702967490, 299585714, 934528124, 592198279, 83284220, 853360367, 113007957, 311645407, 728619685, 554451342, 786667274, 671641775, 864665928, 205233038, 202082886, 986925991, 318793011, 567429508, 467616714, 946275276, 519988283, 580609078, 312093144, 345425458, 270903303, 957214935, 807447813, 56923518, 463496472, 922287680, 805837135, 3803803, 854575249, 258598635, 782979605, 929230230, 44521767, 719530951, 400220989, 750953934, 96186387, 279482613, 464259053, 760497035, 338524490, 940364266, 648338314, 852505319, 146635143, 931506548, 27452622, 715643205, 677447757, 33885595, 760068038, 3656102, 215276148, 40727842, 826491521, 312691144, 739909069, 457680821, 219900381, 261614067, 882699959, 141429139, 962196221, 936134641, 967368074, 63946514, 224497313, 418075031, 822541770, 285730838, 653960139, 513864836, 950802800, 153650795, 172147782, 283367148, 911138549, 582321238, 301081275, 675070096, 601290656, 600422510, 242506866, 836793991, 705971781, 762110787, 518056365, 913185031, 847788176, 311514801, 447644630, 58606638, 728756460, 267196471, 235508996, 877331709, 725463963, 682607061, 697099998, 138037725, 992042851, 198762178, 6031373, 846149552, 376474099, 303432726, 656964065, 379989911, 62754186, 390433635, 813276339, 402777813, 726889542, 830560261, 823669563, 453075255, 39446261, 753173119, 33223392, 452673026, 322120840, 713084105, 474458553, 34157061, 197543378, 383886956, 734906691, 250296184, 188534097, 215443894, 322805477, 730743183, 279345258, 978747336, 46596878, 263026002, 64254818, 969622463, 479300763, 340946706, 138748023, 220387668, 290810348, 208632219, 117803163, 64064071, 920513959, 864042457, 821125374, 843811894, 970565474, 586853705, 355599725, 812599193, 93028049, 472322805, 745351766, 705354234, 916132962, 868512580, 113082783, 358454006, 250478789, 285636381, 266516273, 811301361, 442426914, 525723853, 500813230, 62424836, 37018334, 281444920, 725904524, 439745294, 736856717, 116780846, 182827098, 696038359, 617919526, 591224159, 936538081, 443760681, 893490824, 451575879, 69353422, 338390501, 16899001, 988638284, 129824953, 98555219, 907580098, 648703711, 14003237, 990103873, 681602967, 60033953, 474531679, 126967269, 786897353, 26523072, 488103913, 677484596, 549334033, 526859093, 175093417, 824895314, 979073266, 590190371, 653476580, 250464303, 758390482, 970376240, 792152320, 470338896, 275949703, 999835177, 873194353, 802740705, 905758768, 264076679, 789633537, 901324164, 356403604, 415834492, 282184038, 64832472, 875440902, 364640593, 499317910, 448164219, 958211192, 182329424, 451263950, 377938600, 636071661, 834629373, 798565181, 703122318, 15386342, 321644753, 357423083, 513853882, 561644014, 471899966, 274883929, 539078443, 25541931, 719251198, 65933127, 222859333, 162038720, 838075820, 839618832, 162676097, 800732164, 49645650, 529280040, 377952400, 29968597, 584366550, 99876960, 191991093, 99355811, 670691294, 983643366, 613813618, 511318304, 285846832, 211510425, 211969168, 43374611, 982236096, 363945653, 436510947, 875130680, 307197822, 155190757, 303426858, 691251607, 659824171, 91796827, 726800491, 333482849, 51651729, 700509104, 879154998, 823180404, 498285825, 527747780, 302887902, 176629390, 574380570, 820726932, 201370461, 241290799, 245964733, 997815005, 179205091, 975234161, 720317309, 220308026, 600874351, 266226719, 677370943, 526587949, 974201330, 550782850, 706728014, 736376337, 785383683, 298202571, 227795658, 370418856, 390648188, 637589377, 432126002, 791215999, 683629817, 461931180, 224074141, 737194424, 590277926, 530782266, 167750546, 347661169, 709492640, 680761673, 310941891, 276161275, 724021702, 49428938, 659152736, 466369391, 465917626, 517917420, 149964134, 668736085, 107931521, 847078131, 86798572, 407616000, 168372901, 275157260, 210303915, 714887473, 347281885, 511371328, 568000238, 235904918, 529173215, 260493982, 196239008, 123943775, 217966269, 77236577, 952403655, 582537380, 700403611, 411523359, 831521460, 519382159, 919997398, 656889125, 805673115, 116584486, 407066161, 804282395, 250881883, 57017194, 272672612, 96477197, 715074990, 931380516, 285560528, 240401273, 23372068, 265443115, 916456481, 452169325, 141536405, 261631369, 380754719, 309476376, 75166512, 141760595, 13317685, 206102119, 702970288, 16409049, 676394157, 792374288, 761351718, 538153661, 642780141, 413707699, 345022461, 965982075, 169848592, 486407712, 145221311, 616784913, 689257708, 301418626, 580981610, 592006276, 340325945, 9410334, 557058702, 682328447, 66669915, 762902371, 589310935, 258161103, 674688321, 530005402, 76123551, 297347089, 434593297, 955285232, 9442927, 701130196, 610965, 434824948, 162438489, 850452095, 562647092, 690877099, 786070536, 435497355, 947993916, 166270752, 765172391, 813382256, 632328703, 828611272, 676755149, 190879402, 181677844, 404160355, 458666674, 548249429, 154078209, 800684591, 209437530, 148450298, 806633872, 965109707, 563659734, 144242783, 354886464, 406287019, 316561019, 842618532, 450748832, 142764864, 330278595, 574989537, 860756750, 771447204, 587957336, 468492272, 844553985, 871796504, 360631159, 483260488, 870648710, 49755370, 965117637, 348781223, 581474343, 863285095, 355020116, 701439181, 739369470, 323209211, 951277449, 369658743, 71140062, 392281352, 903063049, 20575673, 247574561, 438033381, 642207351, 160611229, 679806852, 631087622, 208720695, 449503754, 201140341, 742062031, 205595973, 390111885, 851823939, 171551734, 482096345, 985780143, 319335272, 464825761, 817036866, 832405375, 42638439, 787527425, 541323603, 692129347, 839377960, 272185351, 811770873, 591758497, 204058029, 505833946, 694888339, 273490316, 637502396, 876268058, 123186703, 985810449, 726393683, 309988784, 365664853, 565967114, 223059233, 408955510, 378458739, 176411697, 877175825, 791653468, 338263893, 233347010, 418421032, 679558688, 723830848, 362407498, 848109684, 488287453, 802706348, 920604959, 173576007, 117655004, 983001965, 532596377, 136658555, 941970768, 321637989, 202695816, 140604085, 463711825, 787829020, 168372794, 682205963, 960805382, 538760238, 162665829, 966056674, 423682987, 506686443, 978829500, 684077753, 692729619, 720369128, 533900534, 442848826, 734769571, 465708525, 180158723, 997177387, 253775842, 229554753, 4580624, 665997733, 855520172, 464432171, 265873341, 633078334, 683574033, 75887865, 711731791, 778303648, 824172488, 737517343, 543780787, 404643366, 658283958, 995748258, 849713729, 225603794, 162589249, 190553286, 21631136, 10238701, 373487945, 746947783, 461231665, 193240715, 9184843, 286028648, 876502747, 423720286, 149968189, 301988783, 579933618, 545420511, 767729409, 132205036, 267960145, 583653932, 264917903, 877969827, 308148075, 742568169, 13507234, 721284743, 888843101, 559165298, 978743530, 320177763, 223760183, 939745020, 924083033, 566523645, 49000160, 322645874, 182025034, 740503134, 980831119, 15851635, 805602293, 300570817, 370797050, 853878197, 987634092, 235811784, 658795576, 885677001, 318241796, 987949545, 495588444, 670969709, 5609348, 22665670, 340341757, 600420971, 365141808, 803272536, 500570920, 449349442, 439647280, 505796811, 715738362, 446408652, 130936647, 985448484, 302661072, 705163379, 817498596, 111325314, 534525264, 721092577, 735548362, 395406705, 861215328, 674696104, 737547750, 348861348, 6100734, 977002630, 316210373, 557945193, 512515281, 588361142, 549721133, 116051460, 543486506, 687388883, 463569868, 536050245, 526492533, 540242889, 889126583, 100664617, 952387027, 742802765, 530988417, 334595101, 257989855, 15402560, 215397596, 578763408, 138392768, 243247788, 8233245, 154120590, 656907426, 919739689, 348598508, 999581862, 725982707, 804952096, 129974797, 964388693, 604376278, 349584982, 742277475, 846751454, 187016716, 819457817, 837485667, 339276719, 291407210, 102866681, 146641044, 940650142, 17627086, 959459062, 157803806, 456812147, 868695822, 826889911, 410180958, 75199178, 113336502, 71368389, 505041533, 130543428, 399569197, 823130960, 348971571, 929492671, 123442217, 651417662, 308617413, 226343200, 152495917, 823556330, 363148681, 303413488, 790878825, 906119302, 610566191, 331400291, 442905078, 702813382, 902237118, 909431102, 819507243, 890206838, 383850220, 126570548, 535445444, 820223342, 211248279, 331194729, 986147195, 709892639, 434195019, 124290748, 720717062, 977793934, 799863180, 5307110, 338555060, 613952239, 873741159, 577746282, 178657145, 453391396, 837775148, 180773647, 754054118, 481264605, 838651926, 392514838, 664781544, 74867503, 394577837, 320202397, 497989422, 582216028, 731812582, 567762084, 215136770, 870524911, 791245553, 328626038, 892828979, 399002889, 843912993, 604123767, 720244982, 152809527, 739727066, 921004751, 235585917, 426103685, 817178590, 725343638, 757661249, 85065123, 886458727, 243962431, 516090126, 705844822, 575020099, 290270351, 335714706, 16406203, 398297086, 583075425, 159968859, 28111125, 532675678, 933372993, 281025288, 58677774, 439951854, 776598159, 398374736, 341474399, 877564408, 742190892, 223182092, 71127246, 99898168, 189637950, 437356372, 168496506, 909450846, 138150329, 572026274, 430067981, 285381126, 383169068, 744205616, 723000952, 532832472, 367552999, 385612463, 646443097, 726902300, 534960903, 566656870, 469612902, 172728089, 663951721, 9050821, 943250205, 728735237, 222555247, 203592528, 433777883, 174278374, 698677770, 578763095, 701558390, 916848172, 43107140, 378992623, 97819100, 137192886, 940506237, 83583461, 36308955, 765295985, 614257756, 918754090, 912807083, 796931967, 235168259, 43589736, 647098423, 567063219, 704200414, 935981295, 339840494, 427320191, 860733427, 110490329, 935672903, 334973649, 840641659, 327143088, 610435709, 475072673, 947492279, 163838087, 514506852, 811806217, 554226572, 248390974, 963840146, 257535699, 327833489, 604166502, 715122089, 161650939, 469336820, 308071795, 316014888, 236417121, 97822881, 417104998, 237710701, 712517118, 83150830, 657009636, 798041940, 174054674, 988322646, 369897923, 268454017, 344264789, 731963227, 730914837, 336705621, 209448544, 173244051, 527709199, 653355890, 541873764, 55995564, 231630571, 210701400, 46551744, 521783378, 695735817, 331842469, 548489136, 333625749, 616720871, 522170701, 864660009, 214105712, 221718056, 595179588, 111534386, 837935683, 845881012, 469611871, 418913936, 309515463, 359653507, 903836590, 626684021, 250038663, 835327038, 786621522, 407543540, 258874195, 554603249, 7325927, 831534651, 893441788, 540697586, 295948722, 548302544, 780726548, 145047649, 814802162, 117868617, 906089677, 589160664, 763558617, 966215971, 702017497, 876311779, 558757801, 666896506, 515641743, 483143359, 249692309, 985102301, 853930382, 11364496, 306665661, 811898710, 152620252, 164961899, 857650020, 418958532, 995950589, 82235304, 461148536, 949593040, 681084219, 992229707, 159585165, 287378900, 14323140, 132956484, 215418196, 785367961, 678353603, 497344749, 586556743, 171294012, 905107362, 989348278, 254530948, 341426672, 89430419, 913053309, 436935738, 452678646, 944186404, 252310499, 876650645, 710822927, 92417846, 469320445, 956986420, 851981780, 416652483, 957951949, 546023420, 741760402, 922774777, 189787795, 987940724, 236276907, 353561130, 149124806, 205188157, 612061721, 689872675, 896861932, 997948454, 106566336, 592668659, 263810164, 364122747, 860124654, 77448130, 700066209, 276049247, 921868064, 946503372, 774926818, 542783001, 282190432, 165074492, 133309298, 763891799, 211318491, 419452478, 602833811, 146766263, 15275775, 312476633, 68083511, 445747485, 466413131, 520263509, 592849955, 626098590, 727609807, 891899677, 836828787, 497216434, 271564541, 890039114, 70472781, 997150784, 419210152, 541773643, 926716798, 837632072, 4801813, 205003022, 283137530, 437859902, 713712592, 163867826, 751058334, 987221004, 932685575, 699999519, 932728380, 24224369, 571871907, 142898629, 483492203, 724725522, 384297287, 768669923, 306115996, 890925464, 587856532, 982363517, 203812406, 608469718, 738215317, 504240172, 277700598, 996462329, 662893244, 625076954, 640606044, 968465792, 651192714, 630173278, 506922227, 597553856, 113108294, 164644908, 225461649, 598225091, 96749147, 795050969, 503334825, 68278746, 891847381, 528194765, 401864837, 94174317, 188130195, 424879249, 244501343, 987249029, 777560963, 714667151, 208832110, 738030046, 380886718, 787831340, 355372921, 365574784, 72854579, 80197501, 570021750, 120077232, 687346343, 288686759, 553557701, 375060652, 267015433, 364165758, 564209217, 169493414, 733927230, 326241449, 308353620, 181855720, 761239029, 912473032, 872665617, 48354402, 51707545, 484041158, 399648038, 40354635, 308835391, 213795581, 14675506, 972282891, 311229215, 681688732, 806554691, 935390507, 966427801, 437438418, 891668146, 632210840, 966864907, 276205467, 387659710, 345865984, 895040578, 140542614, 89741519, 657241215, 507943716, 419700482, 421590807, 254736220, 186008089, 561487586, 574954540, 891915813, 939835397, 69384991, 652747373, 566241253, 461576771, 245579999, 991559800, 220971531, 524527833, 100455110, 897576986, 486840465, 494979604, 307017270, 559117554, 682039396, 179659013, 362308599, 342677156, 243757745, 986985563, 342374508, 165732485, 936160134, 118788814, 187958688, 672767964, 221895953, 580960138, 440153094, 46649926, 416283663, 517946760, 718953702, 240367872, 23567920, 924895021, 844725194, 451140228, 827276420, 431365614, 924209005, 20229527, 419845873, 295824592, 595735755, 553688395, 527947640, 166401026, 790354791, 966578958, 29580115, 66350828, 536562760, 461662457, 604010847, 444545031, 934127219, 460370993, 220628374, 234776546, 416226780, 164891656, 699614742, 790647926, 121968114, 909825333, 590209523, 765407961, 40197017, 651271687, 831724344, 534829668, 458318436, 396476617, 484473698, 294379264, 488156512, 184070143, 364511867, 641832769, 366599776, 547595687, 905562358, 807577454, 471307459, 816623976, 971991147, 231420037, 47820277, 625721716, 177135080, 753970630, 239898232, 311778624, 202451570, 291004431, 346507973, 172678677, 356369189, 663465333, 365109459, 360623594, 750487756, 868881105, 484647144, 621583492, 828445135, 254657051, 399365892, 503113273, 660489480, 109168706, 170215921, 961750504, 391052273, 563851969, 956569635, 330445986, 971877211, 817440771, 757776397, 197254574, 319035370, 544558164, 873465019, 262569642, 170948636, 86202957, 226547396, 803552886, 112889358, 490514085, 361517548, 172793179, 562923906, 122851040, 939048106, 668884062, 555896374, 82574914, 848523595, 253002739, 124863928, 138461135, 913712243, 667350961, 536372502, 306925583, 896117055, 174463491, 519310103, 963192676, 571785889, 831647683, 311359184, 296255045, 27629513, 968173801, 463395251, 454511160, 670437049, 259377348, 116104578, 632333846, 141651624, 135178367, 753967445, 204240778, 870408926, 320755513, 722066938, 535270421, 982985431, 242461805, 481200706, 306525506, 941456016, 287335735, 335699017, 919427385, 618818215, 422962126, 245335386, 679300033, 593597948, 41688183, 825851956, 443382942, 210815088, 104935940, 357940739, 402830033, 459971687, 947716359, 625094141, 891119136, 167137385, 801193039, 355553178, 31407274, 653715687, 104086185, 981337155, 955297814, 511939194, 231821676, 809386462, 141262582, 593575681, 659977783, 598450479, 180815948, 37567839, 353914470, 658728713, 996336393, 629945250, 508010607, 957935701, 871419540, 587301508, 317395882, 516689266, 24999265, 521520277, 484591937, 2539885, 125943241, 434574380, 911359104, 800616075, 406936020, 552760877, 166170356, 373950989, 593592853, 350867010, 847057312, 600681255, 50654278, 6373677, 221820516, 396971112, 978212391, 368066030, 148121639, 315884272, 796261964, 950119298, 738357488, 687283345, 600548509, 232451882, 775581852, 84044734, 391774419, 329311779, 658056, 505265237, 683449949, 203902258, 337550285, 672286770, 582486883, 479244684, 427104602, 977033319, 137023498, 992511330, 112611297, 438844485, 240060035, 124678599, 32787455, 231986208, 983516552, 246552118, 189616928, 844180726, 582823382, 490025411, 653478743, 881492627, 636498007, 197121253, 519562743, 221669223, 898238897, 695797075, 891033591, 747402912, 668098845, 677817360, 496935840, 413460068, 39768481, 217030498, 882184140, 897385076, 395448192, 110700709, 479002605, 30079669, 874517674, 142198517, 379482026, 99232880, 610836524, 973471393, 310526330, 7502606, 388912680, 114551163, 487808091, 680856731, 331147817, 48174784, 114973173, 991378317, 605593895, 171527242, 978351490, 787130426, 699159934, 639626600, 220584360, 532065109, 787306436, 192621520, 615290735, 116070375, 204294626, 685740982, 416011882, 752843321, 846720287, 139236796, 400584161, 352282217, 584004960, 164643295, 398054651, 31036254, 704251984, 155200386, 38602915, 348684756, 893155388, 623521364, 378169147, 803540605, 174188631, 787574282, 346258816, 363639769, 492546093, 247440656, 270997961, 95587914, 935373673, 423200960, 989640590, 373679159, 776947250, 493601459, 186998281, 81293366, 153245580, 88035368, 809504158, 149791335, 196794869, 296373960, 19905728, 526947487, 967459186, 314106304, 990866205, 836464106, 93346760, 713338833, 849453050, 481361605, 406471898, 701667948, 342660044, 968533169, 397239137, 248265163, 565350987, 399709872, 53639751, 523982738, 267575274, 616697732, 421494434, 706656175, 613167708, 415281445, 528380620, 867094446, 855856109, 273921447, 326224259, 864669232, 578014720, 847871870, 5802551, 86368991, 508962849, 137639792, 851067292, 344454635, 436361056, 289567135, 173208491, 42470202, 227945082, 430982486, 956521997, 458695392, 579242700, 21153434, 498386548, 160502360, 534493132, 769101502, 267802252, 241460073, 41633274, 405007655, 712803567, 291088946, 888116349, 13339431, 276157145, 575992288, 389707980, 152715662, 730635304, 135938416, 917099285, 925768010, 613419269, 243224751, 447609651, 607504276, 218252421, 291355618, 934163807, 413487975, 137304486, 865899274, 570288813, 146513525, 207533602, 383451939, 64066418, 104720, 38294539, 428212300, 268979051, 486399220, 957097968, 659960728, 710929191, 742239331, 849475076, 433612094, 596373258, 855111891, 999441306, 914634391, 723749044, 381584533, 120122035, 662293986, 387374837, 295061293, 567828247, 611794542, 532612253, 192992248, 93593332, 140773816, 344949905, 154244414, 624396607, 105041733, 188032944, 331707742, 859500466, 543893339, 315572213, 663499896, 420651205, 826987822, 304196589, 29703696, 683534154, 106943995, 131603233, 244835709, 638866974, 767283385, 502699255, 800918298, 66774301, 931896936, 56916504, 415177116, 367627594, 852059331, 464096145, 515244615, 41818596, 931670499, 904598448, 858886304, 655759345, 675607507, 977782066, 631270357, 309967956, 299396779, 211555544, 309523398, 105159172, 51454624, 26303608, 863033828, 528104046, 136692598, 88448573, 656998943, 49264645, 920577623, 116154953, 295029573, 51282333, 3193153, 742370314, 214642844, 51946718, 183828849, 809541843, 709561791, 836866513, 284762921, 246745343, 963985222, 351731720, 934928974, 358450758, 774265892, 562304871, 827061265, 167465583, 405257240, 370846380, 62545156, 244898556, 458701812, 492181851, 607037837, 493321837, 956294278, 448017173, 150220604, 943449281, 750413761, 324653413, 492633007, 374220049, 577084659, 230582836, 582239013, 957332585, 972314205, 154144433, 84078369, 417939957, 393850943, 741445163, 118067240, 690231661, 829638968, 336203365, 533008779, 595338059, 800604956, 217824466, 560775927, 62893159, 313698251, 968076891, 62012860, 943783206, 236371090, 554697107, 887126117, 158993583, 492738581, 447233750, 352846299, 810711832, 324332520, 301187959, 897592282, 665193976, 302167909, 415414809, 50611341, 484995285, 23517472, 443680898, 974991713, 373174067, 499089265, 81799529, 1849736, 397332658, 326110100, 875105777, 179832, 64918947, 286970887, 994877352, 721551075, 756348709, 536739897, 308605526, 155025953, 1560419, 150435341, 564775318, 213287832, 869265477, 878561771, 222918429, 818091744, 857711662, 402933684, 347369834, 443952569, 450755128, 66681427, 257052005, 41145608, 299974728, 945692969, 972875845, 64548776, 161008705, 301982165, 381968744, 832494920, 502677352, 425310353, 985763081, 620602849, 901431669, 265048839, 991168533, 755921364, 413520742, 83334455, 50101939, 226561992, 654291699, 210526267, 176688884, 947114787, 837914299, 392625165, 419149076, 110188399, 916867977, 632531927, 5522101, 617381610, 918818762, 385751245, 145517542, 917811168, 997699424, 292592947, 61203759, 93547143, 331827487, 296334441, 394828216, 372343454, 737527555, 460003431, 83430125, 709944881, 454057941, 935645619, 965812461, 309188550, 27716370, 48855113, 616859137, 361050677, 982281632, 804859383, 807629670, 752144896, 803314139, 670119987, 122968471, 675160053, 204302556, 447427980, 921739486, 382982038, 901219897, 996856749, 677629138, 230337918, 337481809, 747489051, 835859558, 547265428, 891753096, 527815543, 456851993, 726738849, 934960422, 448387300, 30949507, 217786883, 726565560, 393981040, 994495360, 913090737, 619788458, 582562562, 319136403, 16686404, 164238829, 957481413, 832048033, 572720746, 984068585, 552460567, 311811494, 720790970, 607774216, 247389595, 160292774, 328293337, 593282641, 652968514, 413121937, 70130536, 618228368, 893969544, 47427866, 782373184, 854466175, 610250450, 255126795, 600052723, 869342420, 717858868, 866041095, 79734508, 284360623, 824496206, 788485812, 236895479, 110364918, 319018838, 48316446, 477360826, 934475710, 144856553, 962363974, 739870332, 379957855, 199772185, 848217534, 60557465, 153530286, 806258202, 883387887, 579292539, 856437180, 200144993, 491001698, 200256030, 226297356, 436144630, 927019651, 570790337, 807343742, 76255479, 750065469, 285136991, 59004815, 164279412, 724128773, 606702890, 745221970, 843582923, 774408142, 449130437, 398296524, 951609261, 465227103, 371807346, 444735466, 992667233, 297104716, 519479634, 295556163, 663550126, 841701232, 638469609, 534904383, 574597069, 495263095, 391669582, 768232233, 298973242, 375178494, 742131433, 757394969, 184617385, 8279326, 814634309, 930665528, 681367322, 775246941, 622437633, 549027936, 945461043, 558039318, 210104748, 286438357, 108584516, 714376143, 52054519, 478328314, 344046514, 726429673, 393952751, 338237718, 696269459, 914575852, 658897945, 130774387, 250542915, 606304811, 526202193, 533364729, 375113401, 460953319, 458164874, 822243181, 486277958, 716685358, 772989627, 697248613, 414466820, 635933702, 139221037, 773820571, 822106102, 412290927, 380230648, 652828138, 176044546, 401415865, 697102345, 438925011, 877773564, 273734734, 469714408, 826988877, 971264451, 509987440, 600170223, 238377206, 49264923, 314389696, 195040331, 420897446, 286398082, 272753715, 73050793, 686390411, 523128232, 694135134, 748904569, 813643741, 16670081, 765191264, 336210831, 340619291, 558517621, 221776481, 213656870, 135875324, 571992757, 646440993, 865603922, 759753365, 526797555, 882016952, 661127565, 564405406, 19895793, 970779928, 747189480, 414850221, 916222152, 752869410, 102597689, 271036047, 339693600, 458598082, 47141449, 294600490, 594733555, 758618039, 790404687, 201290349, 730784821, 463530704, 190305423, 428000590, 622156395, 611154703, 205006690, 132430311, 958364225, 472231327, 668735211, 466132366, 184919713, 461394140, 760361245, 304891814, 730828451, 951508765, 237336180, 836783357, 445892783, 433991068, 150446759, 675250154, 674265959, 722357478, 435961905, 942928856, 944122603, 342918513, 711432834, 848489371, 329341614, 993346412, 597202165, 459966463, 657524819, 198627616, 747691462, 154333591, 239287520, 372202481, 741727043, 34532054, 265781414, 668724043, 320876282, 344052319, 647392095, 546164523, 7336920, 112498128, 159329175, 524835270, 413962796, 515605909, 107098229, 200691332, 972921028, 50121639, 539089577, 691300089, 718895805, 343973763, 183790369, 135405409, 822823220, 68455976, 76485831, 336543467, 17400943, 276858713, 515715755, 311342096, 927188283, 642218023, 983196771, 698925635, 148660264, 907702761, 546054978, 549607248, 141154804, 125366434, 756234220, 607367243, 866994692, 602136181, 147424948, 566729319, 769334306, 102533144, 701382246, 719762825, 66620113, 12287624, 160457446, 673146022, 643834193, 633590341, 343695327, 855838910, 971941030, 418674514, 506890046, 42012066, 126276486, 365170879, 871271727, 348454146, 330212573, 77114291, 594791104, 146124356, 996886817, 834283873, 388969736, 98237432, 297225576, 741323572, 577602224, 370170983, 299353999, 784152482, 427572328, 802917480, 570380629, 992954859, 278339275, 75190841, 981517340, 618004093, 657841603, 342824633, 270777008, 24940004, 502884924, 176626731, 137782111, 307555130, 817944054, 628129014, 276903498, 392940402, 934226349, 874367556, 395768874, 949574778, 242865930, 405262900, 794334049, 414331009, 565729267, 933195266, 816589991, 119835563, 611722527, 951970842, 61371377, 83534137, 972135296, 584133017, 203483747, 431581523, 321031555, 91239731, 385931005, 295722598, 984857098, 806310965, 545089453, 849411388, 651859273, 333675593, 174989731, 530529334, 773855417, 283707067, 421208352, 720840587, 700483721, 153001700, 129574501, 121444190, 627827020, 633699806, 219753988, 51312318, 373339552, 514269565, 777401411, 170094995, 921460436, 264703121, 446995797, 267499012, 266398335, 319527523, 936593144, 348046682, 387998206, 422295390, 490318976, 479350564, 406500253, 295795267, 233369749, 938954810, 438956999, 916405471, 253327583, 10378096, 16156111, 24610805, 984665448, 738655123, 904555017, 400018227, 343473696, 909998561, 538405330, 214734809, 96734697, 133572116, 697508737, 361632105, 184281638, 535173498, 110973778, 152592542, 766660331, 802017705, 155926315, 665382955, 62996006, 990369602, 628503786, 788286498, 801795067, 403354491, 819477312, 17103090, 819150809, 780793492, 306480402, 332916359, 480760426, 769514674, 118339546, 431905819, 349540340, 849974332, 307818213, 460117986, 848352093, 353556933, 532892052, 768384826, 996881380, 97050283, 116291911, 488637702, 699987822, 865064888, 718878457, 4535910, 667433163, 464903494, 806542437, 263736990, 571164947, 681095481, 768341601, 839125284, 119583983, 663714324, 805111510, 551338403, 737420916, 669878230, 333158490, 8975025, 979192888, 779335892, 451538305, 688341458, 698253402, 392499422, 656537088, 356616007, 933291163, 260969186, 200085233, 890519019, 771192283, 277887025, 16561508, 312775461, 712762271, 702468415, 595854578, 126302578, 354247945, 250196737, 863236638, 735624544, 709023051, 962863702, 118119044, 694964639, 583717837, 245324510, 316634950, 316855873, 177335867, 277528090, 132421373, 363193628, 30386177, 623935698, 586237325, 937167796, 689549339, 358869134, 796603027, 172070818, 561278433, 914495060, 858952468, 481736051, 886031571, 913566677, 696148423, 936423301, 387426634, 857158306, 847228343, 405728403, 910083947, 357179057, 179550030, 891159699, 249221911, 357716950, 697830408, 827230891, 223758582, 376021339, 771697879, 652518890, 763707075, 930094244, 492685948, 14913443, 761179368, 502641737, 870339788, 776963119, 341706425, 554970945, 669185155, 387150075, 485116478, 360248786, 790774269, 196728228, 313951669, 244264320, 148609178, 135410666, 214092645, 278936586, 522744316, 625274360, 858823038, 525866447, 756622430, 194187218, 439677319, 349792257, 353653436, 319197655, 719322133, 948333429, 34385632, 626939796, 3975929, 767773083, 482412888, 369459322, 737535742, 500147655, 810443118, 694399559, 431629424, 686672, 374272333, 632712335, 663319671, 862852169, 164616270, 614921795, 91027600, 368146335, 189767205, 418667996, 465920829, 891013256, 781219893, 914289145, 499746582, 854016093, 735367484, 468994642, 664654680, 361619200, 593465667, 842868706, 718543396, 916382983, 447782039, 83170438, 493016706, 650625195, 743145379, 743743259, 459840114, 57500984, 783033500, 75815510, 636311182, 395241594, 42217089, 920672224, 933286339, 170121469, 702813065, 685102992, 585654894, 956710376, 321348568, 412342978, 185668897, 280576694, 598463486, 445260425, 89783772, 854793743, 580663463, 259249939, 631069977, 683771692, 666336497, 58597755, 851451394, 234035200, 89327305, 613140707, 13802815, 754903684, 266303516, 149118048, 813984373, 700180543, 724180355, 146067134, 695732553, 819404196, 228915643, 179972408, 679581092, 126211855, 593784984, 813482050, 682315175, 429491726, 734418117, 144695997, 432527844, 9807539, 813497224, 883121452, 685680627, 355181899, 481368192, 647552142, 941427238, 845832775, 779191804, 374481565, 109744614, 250488362, 839645675, 505863461, 397517038, 372369145, 335309180, 358419329, 706747887, 661257656, 883477533, 180648081, 945693033, 902441048, 824783675, 244835093, 860348126, 178881414, 666615636, 607653234, 939481137, 95090993, 663839900, 523483607, 300365016, 217266731, 714993948, 249486238, 374537071, 957124264, 2162147, 792506138, 809991001, 966883412, 348188798, 163409198, 217126749, 341867503, 220142907, 297388618, 926674906, 663459719, 315708768, 121011520, 717829882, 23726743, 416128018, 681650477, 733658610, 962382896, 925695646, 453717478, 817052181, 116313747, 94089643, 821300898, 32221221, 788746678, 387298516, 3785579, 250524480, 951667233, 44344359, 423835893, 754970162, 360210079, 689695419, 134906508, 665301149, 860725193, 453980546, 568421085, 775360222, 964733354, 985180421, 606366150, 712955649, 933766316, 563913449, 596002957, 70101026, 553329224, 373144814, 101722274, 772527384, 77245533, 545256177, 955186641, 400283853, 444817565, 34538518, 324592890, 538634281, 501988143, 688943917, 816644386, 767512313, 572098982, 640494278, 858687914, 204983807, 669978262, 948527929, 447248835, 553560065, 916105765, 404921858, 545897615, 379782138, 729267849, 264596790, 1777368, 548042525, 70382050, 226787089, 287704206, 963813511, 618973421, 928073601, 20681142, 439787357, 799196581, 411858612, 797429496, 666065742, 50655915, 873992979, 846818721, 721623655, 237718301, 858310590, 104010053, 946740169, 491550696, 678294743, 620181587, 293469380, 196618226, 272986848, 56506542, 866070533, 177629150, 973321927, 770687200, 377298216, 756361275, 38981775, 416306338, 426057989, 634520595, 414827411, 953694678, 725677836, 145754753, 153757938, 141890847, 887205363, 260000700, 5315399, 764747688, 852062262, 916821560, 777785542, 568931190, 316424551, 575556853, 524784244, 650025205, 41604235, 455470215, 203300029, 550876455, 102723016, 286776832, 894775530, 838856486, 139620789, 939042961, 151513043, 906002248, 749986564, 819300778, 771279008, 987015122, 771059611, 232967912, 844344519, 659519050, 750968827, 568083586, 371033028, 154917340, 354351601, 382972918, 659068436, 660276856, 641514431, 555214734, 984479774, 990464074, 516904183, 783987347, 899693107, 896544386, 828969932, 229998151, 254566958, 180776871, 7069687, 705349183, 300316288, 768091629, 505272856, 540144937, 410141615, 584756257, 601810859, 964662115, 956281565, 969757081, 259521311, 245097786, 442958030, 475019506, 512055506, 6231464, 462430351, 80114268, 26646932, 734733234, 529968811, 742771598, 646656219, 672773829, 22975924, 311908591, 325959972, 870748603, 165728530, 326670322, 467553604, 927885564, 572863601, 288155855, 868881438, 407497022, 950718720, 687809268, 794020595, 273648899, 245816941, 401964136, 540652331, 343074028, 317509351, 516169191, 153482223, 328816784, 940927059, 559599085, 876174440, 793094138, 237377941, 609660154, 435853321, 473179952, 132685902, 188956265, 376526522, 352514459, 174384997, 350251713, 446498300, 981681801, 135869420, 783310539, 150740476, 96052776, 13994961, 660112273, 736222144, 893198802, 160797286, 371864733, 394220175, 684745792, 820414411, 453428147, 987614054, 243737131, 887463283, 101696987, 999379116, 991080665, 708097568, 945920389, 153770523, 317329880, 200637301, 748045572, 61933894, 357203913, 498613473, 732436858, 213665565, 206753009, 651302612, 936322825, 553664445, 627538539, 801312908, 383763832, 453090512, 498932255, 314826392, 654555799, 882245136, 930538570, 711376723, 277147268, 359464167, 671839889, 68233075, 136097587, 68809771, 189562825, 45971399, 776954161, 281197543, 592978224, 514974948, 68746372, 598770416, 674879917, 664101438, 303190921, 103483869, 287435351, 859896303, 459008422, 583336679, 785978403, 269049937, 793704040, 237204181, 331614038, 861066632, 800233337, 913153563, 169788116, 804718797, 937772457, 613745514, 541430040, 763583624, 439848669, 328779617, 699015974, 797402269, 738292669, 657086889, 984792424, 8419942, 305848416, 796017854, 484896081, 16404984, 177335636, 837506301, 167180112, 520746553, 650895517, 715511431, 387043052, 583671279, 424001760, 498843573, 986769476, 753263355, 937462544, 639327110, 441996860, 130189434, 925700841, 165356423, 748657964, 908420718, 377452793, 536394220, 939875318, 215950711, 51589682, 989842408, 379712078, 485005743, 673638572, 28846599, 187034489, 874886107, 60724951, 825625618, 649907087, 968232872, 358434786, 649775511, 673919461, 810606440, 406300090, 946202485, 580919898, 102764303, 660942561, 210928161, 684702812, 925430021, 290892312, 769001309, 775721831, 37041715, 910630280, 358583055, 371824250, 502454148, 962041015, 848374066, 142994109, 590255212, 813065821, 20546712, 827464261, 828542010, 330014769, 307113540, 288802351, 740527174, 706500360, 48929795, 611617502, 142752515, 407705713, 445310106, 413544952, 78725108, 587190894, 702010163, 758292817, 19870765, 468665546, 375459272, 345668685, 836852811, 189691742, 867756912, 589959954, 764371552, 220508831, 299620208, 323722137, 449088591, 698479323, 881025184, 146445364, 848486828, 785224629, 389375267, 328315665, 690997436, 746845894, 706927440, 936504512, 887536660, 753740163, 762966388, 759107693, 808503922, 980643425, 781750462, 601472813, 64709921, 32418229, 622045482, 21520853, 616315825, 108153057, 248106334, 571311049, 773416470, 838904778, 597991326, 574228436, 517575510, 158743751, 527319218, 754719688, 148994953, 535045038, 270485504, 766368979, 914178034, 52147355, 83444556, 698699202, 265827023, 330075675, 92800020, 517689112, 195818363, 307094324, 839729271, 909725631, 614390107, 250471782, 153187269, 515433693, 112515602, 482413608, 917578300, 29141148, 646079549, 89588739, 421047904, 881472301, 668491543, 949353007, 197276980, 675795532, 726195408, 159232435, 716127103, 414638833, 523782077, 736999332, 888765805, 760795438, 796290380, 858176291, 145315453, 277934040, 364028252, 104575960, 802298472, 748591476, 386293584, 631260588, 440953393, 76097465, 367107193, 527113910, 453869886, 677183474, 800234497, 413958229, 654937323, 499287731, 312566480, 103813840, 540688794, 755440798, 509407030, 461741958, 584950429, 400994697, 660934213, 179454817, 785679179, 492645553, 863644164, 368753156, 445588951, 531466783, 143902397, 32035426, 820488376, 910741032, 975025146, 432667379, 782782374, 952810130, 24002416, 669934882, 300037631, 126429821, 602504125, 363438517, 389694647, 904441440, 624605575, 804007364, 311541382, 133596339, 48263592, 438687204, 478900168, 518800840, 976740075, 496436775, 927314125, 310603099, 564129632, 7458480, 197113110, 578306214, 736668056, 641954833, 931965797, 674170137, 298166665, 83970813, 705063696, 224094466, 658064701, 876044804, 490511617, 319890286, 431714484, 802463232, 483118698, 272107623, 325020423, 497323281, 319657570, 66000592, 238306618, 718699678, 753576744, 780908781, 676178927, 447324248, 330123609, 773576896, 587313004, 682748294, 80806993, 256972024, 259555948, 535804692, 43486467, 794195911, 846950897, 547986040, 675107252, 910906315, 820628937, 408336651, 37864361, 702931512, 152719460, 83188389, 642300234, 928711074, 253322384, 874132048, 719242056, 278949278, 408512031, 769280949, 440422878, 615971499, 195717820, 434953669, 253583926, 469084661, 40843034, 47388840, 400572741, 278006367, 150541592, 721425133, 223371933, 433996988, 946389123, 566141762, 640584850, 829355585, 505144637, 306517725, 876963198, 34177058, 859402682, 298856742, 153722688, 715512015, 836842582, 38499367, 7327409, 428561007, 847580725, 107356955, 914546226, 41890375, 155563347, 444173447, 200684023, 499712935, 87410735, 407385781, 135508711, 173481782, 509646921, 367265675, 403077584, 462430718, 47520140, 445669707, 55907484, 320728153, 550549218, 865476349, 541541139, 321159342, 415993957, 38076905, 304075479, 876766356, 476106574, 540496929, 22424222, 965124220, 597791852, 964299346, 931303827, 792863524, 31133222, 87423055, 964757417, 950912266, 18681659, 602792064, 810517861, 95316784, 512488179, 411570599, 179348780, 24445003, 567050147, 161332134, 426502532, 214318772, 356527334, 743576759, 898948472, 6657134, 643585587, 392595209, 763411880, 911405518, 85058024, 835174824, 229305527, 236170413, 630020838, 50421611, 721153871, 707196875, 53927104, 175558453, 767708830, 391065032, 852197650, 966811550, 612389816, 962967659, 2389994, 273025157, 377835843, 467873638, 479561856, 658897313, 279568084, 465247300, 470710338, 569406077, 490942838, 748016696, 931985312, 519124553, 790798634, 797173596, 197692220, 404795663, 67337862, 406711140, 322837417, 72310142, 701444801, 462763128, 650265394, 357445851, 259390263, 50715693, 348417870, 283277017, 881821871, 371898695, 328262921, 152070520, 574465596, 48894261, 105765092, 189396862, 817934317, 809118531, 202141437, 113966709, 101389971, 207584169, 740138245, 31727203, 502272039, 595603666, 335541762, 604186583, 922478784, 505307045, 575740433, 935235771, 783295020, 936535523, 236071420, 557534878, 331995330, 415837475, 187858146, 541916379, 12483303, 166770205, 631723560, 238195490, 156702429, 617937748, 958231954, 913157637, 574791761, 347029212, 662058523, 163017829, 564945219, 633486334, 939514069, 213035339, 121493295, 639350308, 694830216, 825410589, 497939093, 157984065, 53196659, 268971643, 968652415, 972346720, 429686110, 335335876, 893403903, 320889189, 20628047, 481857599, 975420905, 685766460, 622875192, 858485111, 689890040, 633188714, 153620690, 91344298, 801908473, 74201993, 972255170, 477015158, 171170040, 592888599, 226064911, 936567579, 565491527, 835516641, 748207139, 243015691, 909518345, 139918621, 885550082, 45927824, 300736365, 732396664, 114092641, 518243233, 227870104, 507792155, 181859824, 369943488, 402764189, 784826898, 585798356, 449382644, 395075502, 612060714, 849101680, 660923768, 56479476, 601703670, 646688168, 390174463, 497700655, 74715111, 748384715, 301923790, 174212094, 233533055, 733766905, 934142419, 269116332, 270434270, 188367344, 263313121, 911804518, 980150196, 635935753, 722844963, 129003828, 579183845, 756889514, 279091956, 856301489, 949457523, 201162351, 290351976, 96246401, 208392082, 529984747, 417291323, 407739288, 337936101, 949991128, 209464143, 475932076, 523165050, 95761237, 491456103, 379794160, 471629496, 705875620, 719767334, 42140098, 992862135, 285605360, 188622016, 922671106, 361467995, 955827138, 741771449, 822396692, 82225429, 586617630, 136809524, 793184723, 705990863, 627665635, 782399492, 39717233, 634707422, 442874464, 816358172, 219442601, 982798370, 699129594, 926217781, 114062667, 938839553, 791199094, 10463997, 282636500, 450815888, 347683560, 279013514, 238217413, 647724426, 904305684, 586094219, 233132981, 782364455, 17861890, 81655384, 570727507, 22236246, 564750181, 414395175, 87357827, 881285762, 368710160, 726548759, 473399692, 458736155, 630129218, 883690882, 110375993, 181924643, 423821033, 699988610, 320143550, 289256687, 285021622, 47481476, 75303985, 548505102, 809125597, 473685360, 716137929, 345444788, 934525628, 198851243, 387702508, 733915886, 343722848, 6437232, 138207722, 112370234, 507005187, 690460480, 711736360, 471395500, 188489153, 391546022, 396359631, 625288742, 510243047, 626068318, 233824928, 619908877, 357698425, 744548741, 910244244, 868992491, 128060487, 418861650, 252951993, 533966648, 703409842, 425027279, 856811974, 122588782, 831167708, 240123512, 440279660, 770824657, 964547086, 418454621, 927493241, 47085041, 257489826, 606388418, 205211268, 829861874, 357129002, 771685254, 189972794, 823260405, 378853403, 923251009, 475690043, 376384678, 658496374, 812205363, 570941888, 58860851, 387023676, 226039445, 281287653, 837454881, 31286919, 308946156, 258517846, 327188228, 930883135, 198746020, 216161217, 691229225, 746981649, 514915090, 300028248, 102716560, 729394495, 962260298, 747375007, 545093922, 520243479, 664470945, 50386412, 300218552, 214960121, 321668494, 558695583, 850353317, 598193500, 478611134, 574438501, 350148763, 750938643, 781576000, 230196251, 855790909, 390674701, 131305306, 501234936, 140050724, 795473825, 218957699, 497873671, 940732844, 639386785, 348137742, 340638528, 61005941, 618314577, 29027934, 476479428, 914309427, 216719717, 746208781, 838430655, 808566934, 412407730, 782843930, 323669841, 490865125, 693324873, 328788581, 873942809, 65413546, 8551921, 869560345, 703347888, 563062079, 287031143, 232272337, 342348032, 673280003, 529547223, 421089311, 52696009, 824181472, 534141141, 107065481, 152877459, 333136964, 439732978, 725110271, 489995456, 469454793, 535740965, 794444799, 781851091, 300358831, 713808505, 288447856, 97320314, 617875288, 573664382, 774596066, 548760736, 608186881, 962773522, 265794022, 702478936, 531748095, 444526031, 783901808, 929569327, 78994594, 668474228, 631982588, 707447215, 220044704, 759518480, 280755019, 619889021, 920966608, 11871048, 563415883, 49072294, 327937331, 56017972, 57311939, 10233544, 363546742, 142399384, 685945357, 102136934, 591046234, 398140980, 350008632, 864942879, 667722699, 82277133, 235325892, 753094992, 152872884, 444593504, 732742970, 780696397, 793013855, 740271536, 10109125, 648305983, 207166905, 547395128, 652285402, 821761782, 300711609, 812841036, 755128504, 962668972, 971058588, 580835306, 869347614, 456711980, 518390720, 771856152, 397531858, 562496399, 228955264, 553583330, 305760850, 971002518, 913796340, 403977387, 901252501, 734570760, 952902394, 590316030, 99286335, 434050408, 79960616, 767875288, 172605466, 960850263, 679151894, 707636918, 419403898, 998544692, 642075818, 241511237, 325102105, 907026315, 658297157, 747089169, 718179790, 291368942, 92047071, 98389708, 344003657, 195038510, 57694582, 595293917, 7578598, 336915476, 204579783, 995873079, 251474129, 692201581, 707327284, 346878475, 543406943, 747579028, 829530127, 48848246, 504856930, 62958543, 127333003, 360807690, 239941569, 736738228, 379707175, 430456460, 904222263, 174493827, 145009725, 197423739, 213714010, 605602706, 668745743, 180074092, 621005251, 466445426, 189387340, 482219975, 450219525, 758815313, 478212542, 586179130, 459999673, 195820981, 870866312, 83968397, 935383761, 570151795, 970357994, 957895231, 346163754, 1763280, 172248966, 489599240, 165419248, 463067364, 19898754, 860235, 620389436, 895133065, 857187084, 675972110, 601803388, 725321574, 471473217, 499906377, 549977121, 38568499, 504711128, 738519254, 157943128, 909256164, 404527147, 93355790, 512500511, 988565779, 686770582, 996854330, 974402473, 117610068, 162048308, 875548382, 80491164, 942913531, 364120806, 278111887, 695771146, 911722191, 92875516, 464224885, 655448226, 727336837, 498402939, 51991515, 15478108, 675875624, 837256294, 943427533, 815299027, 919692627, 386084249, 674126225, 465351306, 328176185, 132546365, 750248962, 540127860, 257581142, 854293543, 106117044, 595580024, 312172568, 353239991, 540763252, 829084877, 290216970, 833701533, 436189342, 294212746, 189589239, 223913985, 359115340, 308917799, 591119235, 731115473, 151234528, 585725176, 257449879, 904836033, 669131435, 782011104, 812454352, 188901596, 633041849, 91740280, 524429241, 330074788, 157787196, 255838036, 16814310, 354200891, 537681391, 640715155, 381634699, 393277207, 931345096, 842638029, 729918072, 743555949, 463334186, 410720208, 376995814, 702087328, 419647542, 787579433, 638934368, 273747888, 986090669, 559245319, 687701776, 248680503, 180266094, 280349372, 465624132, 612019322, 682527834, 690429412, 55394762, 649040644, 692527081, 819708514, 801026514, 226934178, 31666766, 403615288, 300068754, 587180599, 36795267, 629607347, 240490179, 558606314, 52458679, 979796718, 810194369, 812752688, 563622792, 485375012, 857431160, 134889279, 737895642, 494263010, 358164994, 186720718, 277873476, 52042494, 502748112, 485205630, 425705549, 900286465, 486159040, 654532989, 259634625, 122158405, 977827706, 861442950, 155571413, 91372087, 932031677, 429503359, 64580958, 270650533, 409532250, 836206279, 867748663, 761893898, 915203251, 640228272, 413720192, 16295523, 267501178, 527003282, 313540115, 735120976, 694436914, 460596356, 588040083, 491425011, 195115410, 926092386, 97423090, 77994861, 151597411, 963835117, 671876062, 834666879, 769153288, 858844919, 448573954, 2190918, 250068462, 516913795, 52414366, 504597834, 586217192, 679323003, 174443827, 197799263, 394931440, 52184706, 808572960, 454260333, 488648557, 638855335, 502599651, 365612627, 25770639, 803164545, 985381374, 897193786, 843136754, 790956979, 957751477, 29010630, 585648998, 287355775, 156177759, 819491736, 974130632, 790326491, 233289540, 123122385, 660438594, 426041567, 496238617, 142978424, 405501842, 175456142, 178949955, 678111709, 251289494, 775734746, 287457738, 748018830, 113318070, 948180376, 403968855, 545240650, 961131590, 823861922, 837450186, 921686806, 930593062, 386150910, 270399502, 222051889, 232790624, 769104364, 472881025, 175885940, 454961595, 713330555, 962208962, 23984787, 574237169, 477368453, 717142148, 278899029, 623407013, 70609974, 78154245, 123928231, 14170183, 739775448, 639642291, 559922281, 217204238, 537969787, 378222624, 637672843, 157922337, 569734157, 220403829, 654761134, 345126877, 791916169, 378588018, 90115294, 388630282, 168130828, 118309812, 712054837, 627157257, 653283898, 737912746, 851110829, 670752484, 41069938, 630642327, 441866736, 480036700, 128176674, 11490511, 760172033, 836557941, 682780520, 512045405, 980752310, 199405572, 349696325, 669146132, 216545787, 757249324, 86896936, 832030077, 963121789, 514672936, 903624524, 945677669, 997176613, 249700767, 876167483, 405000704, 701463187, 317568943, 8972370, 91580684, 107237964, 654342944, 539658540, 519683501, 190485684, 713956696, 78150385, 730160228, 925357450, 42629326, 339978347, 997620347, 81692960, 309258035, 389657718, 580331441, 929601324, 769378911, 386104145, 462488367, 936240791, 431002443, 112361876, 836503893, 870966996, 471477331, 573085316, 10020635, 286499197, 149153840, 665626489, 235537129, 597259263, 776481321, 279454151, 33912590, 952403994, 258929810, 763516722, 356194229, 995065659, 477988327, 204828883, 530019452, 193654158, 354895599, 158332541, 869752575, 203364831, 751729055, 92796826, 969921848, 19531513, 140654515, 534798132, 227914964, 254966521, 231999495, 687727562, 983530974, 305222255, 288180908, 253935257, 400539994, 462524537, 644146725, 533450173, 820859154, 733940313, 696968057, 401670232, 311861491, 749775042, 37498565, 419306078, 251908119, 570490330, 562260670, 211352924, 622084652, 912732988, 596264950, 550425880, 228235104, 918527369, 247933653, 349529092, 684101765, 20818795, 109497151, 678276106, 795358438, 536256651, 297166374, 15130122, 154724843, 971693973, 727253278, 708576114, 419132858, 869776218, 538153483, 481608986, 210411505, 669313150, 507183033, 78582090, 356620366, 326440607, 109878354, 190689001, 61095875, 580927056, 572130000, 251859196, 469670142, 984816927, 979077401, 84812301, 217108501, 646372779, 238341524, 215985032, 338193428, 54567506, 924370637, 708958141, 685974253, 837458122, 236484218, 780477524, 9175980, 76269407, 261173473, 994321454, 138154013, 739612116, 370167249, 140373596, 730598304, 585572375, 216776244, 933539689, 379893109, 926066425, 588156574, 662215885, 276471257, 50708856, 193041257, 142573328, 956506228, 338876559, 808847928, 681814007, 457016692, 435139545, 182777984, 704436319, 495072780, 213332579, 922795365, 683233791, 592128555, 589591044, 227659358, 516709915, 512662910, 957443636, 79429859, 208305381, 738874251, 371969944, 300000026, 968047520, 965111899, 349919051, 372120104, 766466203, 478162107, 175871622, 379711466, 887509313, 822655576, 415694103, 1242933, 503055544, 207667573, 65831134, 885248740, 738750221, 693900060, 752493889, 22666666, 656489234, 840038574, 623444441, 606108205, 441947779, 719302370, 123163369, 941706952, 941795007, 318364509, 678527355, 126654681, 554335477, 915165690, 153544851, 161110051, 600321126, 661413170, 805071077, 453156112, 915870871, 313912363, 122211243, 696718942, 514081824, 801812991, 776511845, 439547635, 803034523, 375386720, 384192918, 117834292, 934056302, 573503395, 24023744, 612303111, 930020233, 955419916, 59943439, 749455251, 964545757, 956800377, 667369434, 72391836, 172568026, 176713260, 766760044, 932370771, 34412387, 874829371, 999925891, 756854170, 476252532, 18658297, 86365232, 490447409, 294973453, 21321013, 49726827, 897418951, 160099330, 113405012, 826737107, 811933615, 858368126, 49921870, 317994981, 382840715, 216988662, 600231510, 886848998, 154854597, 956066132, 625573025, 359923417, 354924584, 280908925, 289276457, 121484652, 431831385, 724052794, 185350209, 37737754, 228432041, 265778595, 779720607, 477906987, 611781854, 765475672, 844687255, 659629696, 538130026, 272190819, 808270442, 851503189, 809059333, 491113230, 500738112, 307073702, 949500875, 154136617, 773056804, 651027824, 852511592, 709646109, 183492777, 649530512, 244402513, 545743005, 579965286, 285369977, 809788106, 381426757, 829893123, 508394615, 660853248, 886571593, 598158132, 809008745, 956520257, 203233763, 180861338, 950583200, 484539651, 397996562, 710748668, 625085967, 889687012, 517681907, 523648458, 587415686, 686768964, 750350681, 235606859, 815966463, 539144812, 491066422, 4522534, 569840335, 6175056, 346906481, 921080530, 21400324, 427599216, 695704599, 966848057, 556583680, 570671227, 293449341, 709709165, 397832590, 438103841, 288494665, 959858067, 740317324, 451733748, 959238692, 970808645, 750662557, 483832607, 447631895, 681397204, 506318577, 324002041, 445542160, 326792842, 114897890, 458390786, 753405882, 263599620, 677782357, 659634594, 426387867, 409609256, 920123248, 200139927, 950158415, 16187844, 320257455, 375937478, 590665216, 520847382, 14514547, 258827817, 827271875, 911985533, 721842484, 882259614, 923834739, 97732558, 631654234, 640130601, 987816905, 653890766, 994275194, 278932250, 39771520, 863699063, 233466413, 993428749, 930090557, 602077989, 8447296, 850809346, 301401063, 232075360, 687646350, 303734235, 298959370, 77065771, 839775250, 708666899, 94952985, 822608767, 738398167, 626239047, 215250695, 298626905, 842715487, 96008073, 770479318, 852749623, 779884548, 732579536, 137756094, 814439047, 881992602, 432630599, 712158286, 571487768, 104234375, 819008039, 52269991, 594607989, 912795832, 459567506, 410395468, 445991580, 612769896, 988172913, 766953111, 232013591, 892595766, 994935415, 241159574, 877604620, 589961914, 456810429, 723464270, 729688319, 96308506, 162874454, 368455822, 983245449, 227895482, 14038552, 656926976, 592699702, 538249467, 432694798, 956280613, 39213917, 333384671, 303277209, 792537138, 314321863, 332954421, 789963227, 630171154, 428663123, 182833773, 160574575, 287191344, 717851330, 177211762, 986146158, 112079600, 126581015, 209191136, 737996780, 691351948, 798533382, 554449773, 327890164, 675818889, 626032197, 91827004, 632520877, 710441899, 872059484, 667714493, 69239853, 562692158, 142643035, 914873337, 130872807, 876228510, 595255005, 820709012, 622943192, 797799494, 752530817, 401676906, 962203200, 900816610, 383099047, 28866420, 147336881, 996058774, 506964821, 64474025, 431293575, 501817268, 948897808, 526456757, 267497345, 321353389, 13891543, 878421350, 968146047, 777667195, 744758606, 738844882, 809783441, 654990109, 169063919, 750157953, 751123594, 208180398, 111147998, 152585269, 956764815, 678817723, 547076337, 856985543, 235363502, 122760203, 537753723, 861092907, 638910942, 342744642, 943252881, 668906066, 797781843, 881501452, 48159359, 793494669, 744854859, 391738941, 630526478, 43025718, 434375048, 309043048, 643256909, 929085981, 261921361, 208945795, 631404164, 471937949, 85229783, 753337593, 962668078, 194811601, 848727000, 48376623, 706955786, 784778666, 811578253, 891348545, 795291844, 121625624, 18391846, 567162401, 190455376, 639095182, 71551748, 453162943, 738234480, 797053628, 988428774, 381228749, 667668471, 137632787, 868700239, 42301913, 690270194, 143647013, 775947740, 504306064, 23004600, 748670096, 545660085, 65513022, 860862779, 858436322, 360713710, 418902938, 255930151, 805954109, 880212882, 260124804, 769476669, 461163746, 323077699, 204796559, 30824965, 812691726, 771033789, 394477128, 784519644, 32693883, 691172834, 795528287, 488802821, 146234953, 219718465, 293274807, 502151464, 880445965, 802957346, 411630620, 411578915, 761228626, 963274399, 616178960, 669764424, 22748181, 707788978, 834272624, 899461645, 449175398, 77909814, 792420986, 529664589, 572969987, 234106640, 647327323, 161796139, 630962317, 943436602, 354681759, 321644943, 64989589, 81794480, 456613135, 632145351, 429680117, 827465332, 753821859, 413826108, 967124544, 996057569, 842647032, 337996201, 87516139, 596502465, 110453116, 568236465, 497758908, 609724851, 716915614, 70364264, 470173227, 704968482, 383320149, 981438676, 675818358, 284495641, 33620891, 951020041, 305852987, 457882255, 419242159, 524411258, 524742833, 150306555, 992611391, 959646216, 891795761, 630605072, 534975532, 805150926, 761237435, 49206127, 14983301, 968240059, 695095210, 645170764, 210594319, 174323405, 637827932, 20413785, 787436195, 644388480, 69269283, 464933376, 518659869, 245898082, 633099354, 10644913, 81377942, 511477257, 768887790, 665085802, 103752082, 976839676, 247328973, 483568495, 799300535, 31968413, 144119913, 934814554, 352613583, 171672921, 166546007, 393318814, 892367132, 854869939, 389163682, 579083723, 801171996, 981598700, 430478250, 672541807, 57284032, 90181188, 796777205, 535333747, 895301660, 677922108, 884798916, 783512438, 387142808, 971700977, 726661453, 489629277, 69332786, 812447967, 751511500, 142930372, 243879075, 536895097, 7307897, 128909656, 175470994, 867962140, 817154030, 387907573, 215368674, 892472067, 186324689, 219577421, 62907113, 555264895, 458236338, 594689758, 210318497, 641078528, 45497955, 289403865, 379245760, 572783630, 513119690, 866861327, 215719081, 803077119, 388534762, 82190010, 120158052, 41157609, 121560372, 14560596, 631786016, 422385447, 644794138, 285852883, 989082342, 286122100, 607226510, 477626952, 310215241, 948240990, 315526584, 134714403, 570916460, 811958038, 593291127, 982466157, 180688223, 33165987, 818313265, 584301895, 348381390, 9137347, 57793455, 575273635, 185907899, 990607179, 650029971, 778627223, 467049639, 564520872, 675713587, 930763723, 285798710, 730045923, 59024313, 182555786, 562744034, 114791017, 28824252, 351943186, 118710414, 490219151, 485313399, 767076884, 394348217, 435951661, 621116693, 558012502, 867350520, 963560928, 768101390, 682530364, 619848624, 252304447, 589158066, 167497061, 942062986, 666851107, 552716910, 798568954, 659859408, 667326037, 237386716, 132769380, 399794172, 653431866, 22023170, 788804255, 829739719, 713948753, 784081612, 714442716, 638332204, 276044649, 240093493, 416177188, 20290255, 269299268, 284367553, 322948222, 797789094, 237413716, 136166218, 195037209, 378816584, 357367740, 477523785, 607150603, 640725337, 121195869, 940454453, 91568144, 58605160, 882511108, 703742641, 270610101, 649262597, 256399912, 771229336, 955970609, 894026715, 49135851, 616430606, 95749177, 163704304, 214974767, 794137912, 406957544, 864919268, 107960411, 715671477, 555465513, 7776608, 413602260, 412379192, 431740822, 582326744, 237386177, 584350271, 806394465, 669299343, 895029364, 16915104, 957569529, 726320499, 799716819, 903503733, 311325718, 322563485, 827597540, 718025739, 992156277, 639087873, 357487850, 813560360, 342639907, 358348905, 156145992, 769618685, 528265100, 910045178, 284256983, 356458173, 689869679, 472912783, 44439099, 262524420, 322410721, 463125677, 189026646, 377740257, 485827113, 110148651, 293652405, 113706957, 669686899, 500294827, 781496275, 352034385, 129944350, 256439246, 869194058, 660138288, 338363789, 873038899, 11351607, 459510524, 785410375, 753043979, 465725296, 78029866, 654048070, 698465580, 598130774, 846632779, 190323256, 615995770, 462120405, 805838511, 802470103, 295890412, 449342095, 212255615, 690921599, 173032282, 357892693, 954483157, 310287382, 967200807, 539367128, 54522449, 47846315, 917450139, 264859123, 202965448, 745514743, 533432938, 642085328, 194669140, 839186567, 267051814, 425477528, 498250683, 128586273, 533736245, 199294490, 638879718, 690068032, 102936407, 707010265, 292255803, 445841501, 899873475, 205875881, 280336164, 654769302, 88068505, 934972261, 750384970, 671317871, 349995510, 256646589, 989090556, 145613394, 811077091, 271133265, 42735565, 990644591, 563993336, 822843316, 733869008, 115531461, 45157210, 264523275, 754789899, 543149425, 95687178, 722447001, 866518918, 702481798, 255961714, 141007489, 792789399, 760767911, 594523741, 166897981, 411931301, 626201016, 231531801, 991153647, 748822629, 169886092, 53308297, 370726415, 224892172, 982430341, 692284017, 514648324, 942755724, 944239189, 161425045, 53502562, 135058621, 471308782, 305358868, 456835631, 434295785, 902343089, 30303258, 749300524, 608400519, 672084613, 706303560, 490694693, 439470507, 26372627, 272678559, 193296677, 452158766, 417097698, 196291389, 238098624, 854671648, 105788207, 620909660, 677457369, 85381103, 617746327, 226729797, 493294674, 282740884, 588029993, 160066012, 974792029, 504179423, 891832363, 452646892, 152941970, 126500401, 39746152, 459959086, 480401281, 867339295, 637148329, 188033101, 614015068, 600839039, 932296927, 376107801, 40453408, 377346690, 479027029, 963712563, 94041379, 724877954, 775919620, 550586261, 149619478, 781745205, 334526527, 91552539, 411553760, 567176792, 256264461, 561633961, 322434534, 842751239, 535691372, 354633355, 934401681, 660133448, 919632916, 969575702, 100573440, 836211589, 150341827, 516501109, 693080700, 429364431, 796741189, 174814793, 923154713, 173633968, 414488778, 231177385, 265656889, 711884411, 864975260, 188224425, 246766567, 237893502, 317418741, 556491693, 106509462, 858530819, 262215691, 301036376, 830671151, 76819007, 474204682, 338622106, 466920672, 970800730, 380148489, 953513026, 962554728, 983906212, 947017236, 162196131, 86030043, 329705642, 385722316, 717864843, 230281035, 128040737, 799994307, 647140821, 855013725, 744863637, 797247119, 637227235, 207229076, 941319438, 223831832, 692623712, 176576905, 71530865, 208455085, 682817185, 747205719, 82323430, 102192133, 447012736, 97467415, 785351218, 99257241, 515595311, 990250083, 604778255, 11063971, 467407358, 509394295, 127923010, 198004505, 486829444, 596496617, 100407730, 211903758, 101092272, 212493993, 839563013, 933153493, 29088626, 315459427, 370402488, 694612627, 528784218, 269550380, 393062144, 322279087, 670961380, 602936709, 642173165, 612798496, 712883551, 715518304, 817117156, 247795575, 963262949, 914753999, 697328674, 816854135, 924491286, 891075903, 144546990, 687330503, 786727410, 487557583, 398322557, 424218309, 435999306, 354259236, 530710619, 45841780, 445282531, 550036701, 141693513, 136107528, 759838446, 92798639, 300720873, 105136299, 8346152, 424512604, 113325211, 242768082, 866356601, 14367081, 540358517, 103012863, 857831764, 421632376, 595209117, 804489562, 903761464, 422844060, 611637010, 872390275, 23227472, 605298344, 163304695, 260875677, 267899868, 418171985, 785862424, 830433867, 198788199, 519566477, 993794493, 133593637, 337106492, 316591054, 952044430, 77962308, 131199148, 777319664, 302185911, 706446711, 651502802, 676899786, 215051467, 794227218, 120989369, 391627238, 102901522, 379549408, 470588571, 880808444, 218605879, 308771595, 719075079, 504395515, 233913279, 175634792, 927615971, 120149404, 148808351, 312496455, 731388860, 484092863, 676192624, 619089640, 638876131, 657909730, 79837545, 264620503, 604213080, 720443424, 358479008, 388222594, 986801074, 774690642, 799696602, 796505722, 872239161, 612430946, 316325960, 327158362, 319575972, 30219916, 658915120, 69908018, 269179514, 574513940, 994030774, 877026206, 885963233, 54643236, 470299256, 747486364, 332211013, 582243432, 30674604, 270601848, 959370373, 631851978, 408752094, 64032365, 194085199, 818814452, 197917196, 594180736, 880133740, 839696302, 866612447, 957884893, 400235611, 175299256, 720835744, 971910634, 237278391, 320880793, 752804307, 534480269, 862152026, 55902228, 897115161, 535107452, 36164874, 639725240, 343646668, 476132375, 461415234, 116651223, 597666448, 348079680, 338703819, 959975737, 686941759, 967376471, 923910374, 741270274, 88994352, 517004230, 635709585, 210742375, 367249091, 252525543, 663615106, 589629576, 51487909, 60611028, 664644564, 464575288, 307093051, 567339771, 44134653, 435574766, 394129752, 13966981, 40565563, 29716757, 502794112, 729767493, 734249616, 519311138, 337452192, 80246111, 942778989, 104151271, 541187517, 791897370, 787651715, 234846760, 781937278, 904058948, 338548599, 613018717, 661846368, 541336516, 708419029, 133224443, 139514351, 23401844, 960533892, 991674959, 798799549, 466397830, 333771506, 234841524, 68976898, 712718682, 549372983, 790916915, 88663625, 692609926, 607794618, 771889912, 249390995, 288867314, 200023180, 356816490, 716304555, 686985233, 92270832, 602306342, 789070954, 448201531, 749471745, 642444627, 511624851, 82434336, 212612231, 210549098, 480583028, 543087145, 109513700, 830331039, 764242913, 133922108, 43843614, 771148544, 352634422, 931549504, 495079293, 825969320, 594329622, 787665948, 568338495, 548942358, 654616207, 384362793, 242144287, 264153487, 597643814, 956706536, 716749848, 727950973, 104128068, 661174825, 570748196, 132096433, 212498715, 813904392, 659299494, 218129884, 958288857, 781608153, 664098279, 882789873, 730866680, 813538232, 201466569, 287311579, 783603270, 567122487, 328222867, 51095039, 71615233, 127930440, 597693812, 870576289, 245715461, 370789898, 352978002, 793114172, 725374103, 661176600, 400876539, 578325876, 773839141, 188573566, 774735034, 87304056, 937085906, 604048282, 864879613, 682150253, 370997439, 695260641, 62901833, 460984697, 966448615, 381128047, 391040947, 82077916, 92816333, 562359212, 723990829, 327900709, 209370470, 445359706, 259478277, 369430843, 298921873, 149576211, 217087527, 51086519, 812977662, 752237281, 778845877, 993424718, 607397534, 337441327, 882323170, 351338429, 291869453, 445062188, 145871453, 651889287, 91785161, 290253806, 233126572, 150697815, 514606461, 549497983, 829393751, 56859747, 432557509, 771933782, 931855781, 335166517, 17840848, 158736889, 989973006, 189281403, 753070979, 429291411, 766547609, 967708770, 402210004, 420516887, 603827925, 453432998, 126591065, 229279545, 801081318, 848737863, 67513222, 100042803, 459809606, 699498885, 885179408, 202985470, 906153852, 936486844, 786347131, 286274757, 581043138, 459274101, 804540059, 710193779, 899672436, 631515955, 262739612, 965294119, 744606388, 218121531, 253113979, 723008772, 426841069, 6802096, 528259004, 479154074, 375600058, 69293997, 834281772, 356348431, 991887530, 995675873, 360854406, 960641569, 661751420, 383354258, 449077745, 868455231, 310996290, 707449886, 420818796, 9087991, 306383644, 6835381, 786553274, 78975286, 461601338, 852492773, 562824416, 719615063, 696705931, 895584104, 864187265, 86913336, 620256353, 284423306, 926096682, 865765495, 903894076, 368830753, 389601617, 947470922, 659829249, 967755455, 899430191, 807128761, 777601694, 258586706, 748914221, 232229754, 62132728, 800355409, 161149041, 574843247, 782774729, 439745369, 670877463, 871557759, 105271069, 899230409, 614538810, 329531539, 445949496, 813592856, 845424476, 443300161, 817383036, 302080118, 662772242, 562639009, 427825690, 483382298, 853747638, 724151778, 532582984, 717313806, 148599981, 538239267, 688347988, 301898162, 99161348, 490558895, 491973107, 226275065, 373614385, 549110124, 734279006, 469063703, 3347285, 593644365, 286772715, 41425855, 979700726, 959808315, 157787505, 620597034, 973874611, 499607191, 105717864, 594515251, 517667138, 675267873, 432346772, 126414053, 777683447, 90036515, 15374940, 911504848, 179926562, 834760556, 400958759, 490665529, 587921893, 124497546, 84664706, 343387785, 397572884, 804571483, 246044397, 619206326, 347459491, 881615936, 295187625, 115839615, 766350929, 426342918, 933960317, 768563152, 952022993, 296149990, 85244871, 783940640, 511562794, 940608567, 504511707, 556868119, 221543103, 265675335, 834280648, 133024451, 841196815, 775707233, 922897723, 258770791, 175876702, 957382170, 529784736, 620040367, 399799523, 329580385, 490433023, 66982594, 148052403, 565744809, 362668374, 48458540, 282239268, 538486877, 357737543, 586749419, 908315584, 194950775, 829445145, 120446244, 181486040, 965908257, 820615760, 191236524, 311380073, 743729650, 132519868, 35084043, 213762789, 494173337, 915819623, 983834633, 349274518, 61912327, 671724969, 580444071, 271356150, 988683285, 623447156, 786951200, 470865722, 794295644, 680374721, 13107731, 48330518, 671251480, 535469585, 681691034, 133720155, 894145241, 725651470, 738890521, 934338231, 824499256, 146262649, 987815136, 904424890, 477164383, 678908768, 238158662, 140340782, 749846669, 429298916, 25444052, 580369879, 25881165, 178697243, 515528724, 328737368, 881574788, 551822501, 232855259, 675023366, 20923588, 945097534, 134665711, 5118282, 765401747, 546988404, 230625388, 207600172, 786768662, 424600372, 82604897, 841674073, 142931089, 769166415, 991755805, 359779540, 941267491, 605410019, 84321072, 443475004, 833001885, 302386105, 298172023, 264344807, 696240525, 96818657, 36244899, 632776012, 358121957, 209589919, 138858444, 506156468, 373050674, 832287249, 443577399, 432100545, 389595323, 497638867, 835240802, 84008576, 204950509, 661212080, 177745786, 337499338, 130257547, 899855284, 84719674, 608030283, 808720414, 649685469, 324970417, 388349043, 875182978, 181997543, 629966519, 677227869, 702711496, 518187887, 365603517, 601796895, 225034822, 444448226, 824685920, 121232064, 421613427, 319782231, 442664461, 502262753, 221104250, 729886209, 206967931, 206325782, 723798351, 710801761, 719352771, 607811703, 680364530, 723173925, 72060617, 913636861, 216397007, 38874064, 209509034, 803277829, 55965168, 717481592, 972149375, 842273480, 826121524, 914464229, 462522962, 684428761, 134163702, 381910510, 910660075, 606981352, 884383318, 530071026, 191743839, 800092491, 62826416, 65499085, 675851930, 27542617, 917714366, 990917081, 559330026, 976901629, 45507407, 678338990, 755155188, 1203944, 815105392, 249335594, 414357692, 299832486, 291416768, 796779779, 390712484, 881341228, 66437413, 640793647, 510759063, 956382524, 587920238, 202378835, 205491576, 161557655, 705553139, 304508978, 331260518, 645190937, 978957722, 869740753, 622854019, 531710171, 533829740, 827995321, 900244664, 302583260, 3861506, 583116255, 548912508, 711335193, 470451631, 586024253, 262046366, 752919985, 394147443, 958083859, 548820170, 319628150, 935158490, 593147269, 195958179, 757637812, 728218553, 237925436, 105692960, 63557437, 161296638, 700689836, 922384960, 530680318, 805460292, 559836839, 603744356, 736758880, 752304772, 138827758, 92160486, 433345705, 930404744, 618980807, 83330226, 144239709, 832621356, 428597856, 121114674, 451829244, 691882535, 840921315, 719517497, 250281720, 851896193, 875219547, 23367459, 294149306, 941971398, 295254646, 99589128, 860243675, 905946378, 633612767, 259161534, 333333328, 961959115, 839730254, 844802341, 928298209, 693705837, 924996678, 405423222, 163012597, 628798531, 911301899, 566636216, 761397131, 572920250, 394137633, 476701197, 596957803, 395343474, 884191950, 42288038, 734552921, 639362624, 921450002, 813677139, 578050944, 508166435, 889089302, 663438610, 665013787, 632555771, 328459885, 710183894, 980000063, 174186539, 762533797, 972862812, 901430392, 5263153, 891275106, 214198517, 971693996, 127126736, 391471944, 210278132, 300380599, 552740444, 776521678, 958162118, 525021432, 37815412, 24258498, 377904967, 974860664, 58424510, 155137942, 116333336, 942380884, 295436724, 580097210, 205856019, 594624434, 384455153, 346618229, 425802405, 407647836, 834921617, 219156273, 824693455, 926964161, 881345223, 460894259, 87717022, 20152164, 224238528, 411042969, 619368884, 428774461, 390005249, 997221207, 656025780, 693752225, 886729879, 195001449, 701705062, 95625257, 499220969, 3427563, 916690255, 602514865, 761464196, 437361213, 616409182, 793869895, 426356034, 280976922, 171631599, 829463256, 719906656, 627607532, 243371478, 369829471, 998954531, 988726200, 639608903, 775255165, 116853002, 424686106, 278603594, 386623563, 514855292, 933156155, 214711168, 748709137, 129552482, 248331298, 613582747, 89042220, 845583164, 230145956, 66997606, 581801732, 899107779, 598938298, 975594941, 570075343, 538250057, 294999488, 269587472, 144449293, 46692124, 566014155, 586922954, 706696754, 991546425, 964205295, 174215953, 836410568, 118601835, 462185624, 107919067, 144515098, 688223631, 390341417, 25745460, 415950074, 844207271, 752426687, 246594290, 128480675, 982130444, 901578454, 606932067, 708875081, 65620433, 439988524, 178615457, 964183094, 182578085, 152818701, 746930510, 842716275, 805326949, 763558296, 756295835, 412066288, 42534648, 464388037, 41532211, 350892422, 807041667, 216059492, 937041559, 637977081, 886773376, 113518163, 911840100, 673175985, 815386071, 916672915, 848957239, 975137603, 127008881, 386566067, 575326742, 718565094, 83722356, 61020290, 87396259, 133976986, 173603624, 800745881, 768992322, 776153285, 304793107, 643100504, 920390694, 541017961, 353481213, 994818859, 959062550, 759148039, 775900541, 671453480, 391727135, 816951181, 217149241, 611255843, 367875940, 924048611, 625299411, 976995575, 437576719, 242135757, 778418175, 466607259, 783500975, 454795838, 911601166, 985424071, 753929290, 697983330, 528486944, 102281914, 388479330, 582991303, 433921793, 960998876, 686706231, 646058746, 453838310, 614430556, 101364429, 837774551, 297654480, 907416371, 61072356, 420081839, 249863135, 817649558, 869720979, 390290392, 561034366, 881557397, 875745994, 906644596, 937414585, 392056785, 903450051, 902640182, 655602653, 614029746, 726366661, 998523822, 358752835, 110273124, 530668082, 482080376, 852045594, 189035488, 615846760, 695147758, 285081332, 896972346, 283193183, 290498338, 548527717, 283699302, 570526286, 159706300, 768878099, 410611760, 563158325, 764302173, 407469538, 950148028, 322508314, 574849030, 894248272, 922438506, 424690383, 592752415, 537472299, 595320111, 604025039, 387679452, 884681106, 1447521, 112750053, 916383674, 964705081, 184427249, 56805399, 210925600, 963097194, 715201946, 773096044, 798287055, 800695690, 403346691, 534718423, 430114893, 602374744, 627681548, 764227246, 90467619, 455598760, 89319053, 601521936, 127614219, 295415556, 844523146, 446959684, 495862849, 995863382, 112758751, 224025778, 271109759, 512073750, 404732479, 158110876, 10052820, 439223916, 636816332, 395956495, 421019817, 715346949, 400499981, 976173530, 274420673, 734125780, 543712152, 97458901, 223513105, 979897641, 722604258, 878764792, 430690916, 445073851, 213608792, 778058981, 410588717, 55793700, 659027275, 171419977, 264148652, 830566387, 653870637, 767008836, 149294401, 460270396, 178420095, 410011232, 858433835, 814505055, 124988096, 903426836, 877993556, 538154404, 572636939, 31765828, 687666119, 623452786, 187825339, 236704506, 334564297, 147723610, 967758455, 676941574, 206516933, 83331328, 416504102, 199452471, 951531551, 42037349, 5362740, 676313871, 310570499, 311868124, 258179596, 932811946, 622686194, 614304908, 654964037, 436990382, 33939172, 773562451, 253369653, 482253662, 139492815, 91055143, 565722407, 964555831, 320060396, 382981646, 95725429, 952286301, 124478698, 489224938, 767850158, 531356769, 274346802, 487095812, 598353604, 739078277, 582272148, 157716790, 75360784, 939526756, 616281114, 177749892, 857552218, 379601652, 535084970, 205777518, 642384015, 441959151, 985930456, 313813064, 738070801, 430562642, 43528703, 204018477, 982573733, 965972987, 718972733, 827333389, 367155755, 378829083, 482327968, 182787050, 960600037, 56834560, 30952884, 827642561, 43023398, 214088595, 594184738, 422791504, 929500736, 502623387, 819014499, 310492633, 66759003, 706009249, 266690325, 430374751, 675484030, 238882692, 929109720, 580102212, 42820856, 58617348, 483706502, 550395925, 235278445, 84307127, 926385797, 749600093, 279461213, 250931823, 82027797, 215933414, 925078654, 736507304, 383665297, 629207495, 320626061, 439168485, 88997963, 711033132, 968482431, 934029122, 972489052, 664501018, 362509741, 454988295, 632980156, 487054098, 149156084, 372812789, 862983651, 308280420, 341930376, 700469918, 666453023, 683931396, 607957512, 483600292, 231273244, 680322871, 957116512, 59596794, 159043128, 901877800, 826703918, 611189862, 32047132, 884765994, 835418431, 741290959, 292460505, 615818023, 306227487, 488650770, 728236841, 554537757, 396985732, 53752486, 797986832, 879790688, 64895967, 888097617, 286640682, 930230766, 58098410, 385524570, 768958173, 13046404, 903033873, 625838662, 975803341, 865627636, 74579037, 41950710, 169811266, 156548337, 584171107, 267500976, 778602689, 882165124, 675987458, 328691873, 577115277, 802749146, 556242641, 973491225, 293576302, 350449236, 449115645, 2351534, 892605883, 216837588, 265901736, 352038268, 284754963, 236829295, 649386860, 128900960, 988664132, 808433761, 451139695, 39616331, 759081614, 475004400, 812708014, 458472478, 657448576, 316630386, 993996909, 97743921, 740024964, 950216626, 139830702, 168641231, 446700609, 643242629, 309732587, 530367402, 928696314, 656111357, 42969602, 808711175, 865695000, 90549862, 239764771, 515690677, 142324120, 933402730, 614551710, 246968408, 878328206, 73932028, 604551614, 662660710, 100962375, 838549336, 388074158, 944219603, 390531843, 259455827, 789772356, 18999536, 497458450, 402558201, 213817116, 118793945, 384312389, 684830757, 501107314, 905780318, 834398157, 537105809, 445659887, 567593109, 27770169, 512755490, 81291969, 995222866, 82669191, 14387390, 368777947, 281570159, 752324688, 869362720, 67413285, 591134774, 485288672, 284328459, 73338206, 965313182, 68392900, 175078238, 467852742, 229053341, 17653814, 71433359, 650008170, 862338008, 334066515, 335153735, 907602949, 614014656, 843148232, 20911616, 432551341, 173871556, 484844837, 554409687, 899366281, 806724559, 148440135, 746765536, 777510734, 833319788, 167920242, 887904340, 157378631, 523093363, 325810971, 178429939, 271495367, 659515382, 470407678, 560075992, 836856689, 280393747, 488368801, 805950177, 914469668, 832616717, 885578331, 80922813, 551861839, 429068625, 365248416, 438924392, 582810242, 687048220, 847314, 504554043, 775371985, 541857678, 847665973, 738769372, 948866585, 730077623, 703311801, 328317093, 628257347, 415526665, 950322004, 508775775, 695554037, 466561224, 358003649, 993295939, 132818162, 823186742, 820583583, 305677708, 653773819, 640697639, 712310748, 906235514, 515661749, 809078180, 12821184, 74950552, 251986635, 542357196, 582723073, 280371253, 986292015, 509728254, 59341812, 341622381, 93016993, 260993720, 965140852, 483313097, 609934736, 610120375, 108616273, 245155658, 307052275, 72626528, 353024113, 337164219, 812667946, 196783530, 94329546, 126685301, 199285249, 674785907, 24133980, 321707381, 938600492, 816741209, 702747482, 67467005, 120460193, 702494040, 327998891, 679666349, 131211563, 766811877, 546994264, 496452590, 626494657, 836882204, 543318563, 909412639, 409233420, 42668174, 936483400, 531276233, 807376137, 619117149, 136487227, 85030000, 727250883, 706552980, 262511861, 921876194, 132918625, 266193253, 725454935, 161252825, 186970877, 658250864, 535959597, 108640143, 770419214, 293883034, 48172987, 538786829, 108683472, 350641066, 246210721, 4456939, 584598431, 535842281, 525181021, 714954460, 54267130, 187636589, 409727996, 272568320, 866686115, 520433601, 641118186, 83477884, 236949025, 411076960, 333414032, 535853489, 208498625, 167136231, 370719688, 198953157, 765337445, 39317175, 702910213, 29227854, 261041697, 520997778, 202840229, 75681009, 929669072, 859460338, 941125549, 869092732, 357343777, 243558449, 556211919, 658408445, 420611797, 648305953, 98533118, 452612022, 918258361, 211622564, 577393493, 6099044, 643448072, 800561984, 414502993, 433362082, 438415016, 979474723, 15575879, 634485006, 807663616, 426250239, 966902555, 244068325, 586247776, 842869932, 810913733, 397043984, 239557980, 221087698, 104038150, 81973571, 253205809, 868218670, 178629881, 238119806, 644333728, 183038945, 544958846, 230576425, 518760230, 850972692, 480683071, 557141673, 878414532, 645387141, 505665771, 752106484, 929612534, 51869169, 901233970, 210637006, 574519331, 841566050, 760303192, 643538959, 307966840, 739076741, 47209442, 827790165, 113481899, 878316952, 667166105, 596049308, 23892799, 208463744, 333017168, 318108217, 307399200, 698358625, 509907391, 585956808, 512291539, 314160774, 990761034, 812146542, 837422254, 863363282, 14547602, 136801634, 333675560, 742365709, 778200443, 177908663, 915886859, 287543954, 298239360, 80324552, 883328176, 22959369, 890725460, 939575185, 706294299, 80245588, 431479837, 688849300, 957985872, 949090000, 373345212, 893649738, 489919225, 12394751, 838589197, 462464709, 702060468, 141322356, 829032344, 31408845, 88407364, 284655338, 498673864, 490797489, 585564138, 24505692, 801409476, 761874773, 883321554, 891962738, 12582910, 686963373, 671684567, 239329942, 209349137, 478946941, 103194268, 889798777, 305987276, 795488380, 121558914, 356226669, 295902840, 316677949, 369467670, 994834731, 848055224, 71447273, 95442309, 204203746, 925922959, 52606550, 493577283, 422042599, 969430005, 590877045, 476763206, 438913079, 996828898, 330678055, 441496273, 396903219, 677473543, 998821612, 574276505, 912370259, 89474954, 594837537, 400632523, 708887842, 760432296, 401659097, 189729367, 287937881, 760459559, 316779210, 221276655, 571048540, 934704302, 642791027, 379897611, 286524040, 172781761, 66329379, 786294285, 623642043, 156267141, 856382188, 458219013, 799325185, 479324292, 979457888, 597175990, 62594478, 430107680, 112184885, 996530030, 979360737, 797225045, 996334888, 549398377, 565989241, 206877232, 347089893, 260184407, 396812133, 8064846, 394670163, 189101435, 936175425, 325414729, 624668710, 76812075, 714821768, 286701244, 729111565, 720046569, 503862164, 827889865, 311332881, 198327981, 858318081, 157374510, 746824729, 325173866, 120922187, 929594655, 351595042, 524686483, 979313104, 566852879, 877536159, 243777860, 956848473, 453935606, 706446128, 440553342, 36141452, 2588864, 331530031, 664517265, 832440567, 124422129, 485071376, 341591027, 847156078, 234216977, 308358438, 50377571, 640392847, 180132611, 3664537, 172434192, 789248224, 219116358, 363927793, 431622634, 563570663, 334404713, 337033603, 817156350, 39574664, 821474144, 560013345, 784085745, 616124768, 789646535, 264244149, 119078793, 294946359, 11396283, 528509764, 620356217, 379789166, 748593898, 844364166, 517905181, 961572178, 736385855, 7612348, 364219658, 598292854, 673983140, 229905190, 119575432, 259122298, 165936668, 3305293, 339637074, 880633948, 189443840, 27956598, 316939259, 871650972, 743979629, 41291659, 416373406, 37946655, 141465288, 754456205, 474420941, 50591880, 458001443, 747946832, 894614184, 625527264, 438754876, 6502174, 408518495, 349174038, 179729804, 587691898, 627921546, 459773476, 227858473, 686363573, 358151799, 212112440, 390686992, 916320747, 766945549, 625265356, 264150498, 186536455, 147480151, 594292336, 565799256, 328439536, 592765251, 439535786, 727090145, 801570333, 88655478, 371307450, 502257766, 692291399, 526857361, 827516461, 875342858, 427985731, 353552925, 652754994, 557814312, 78989893, 746287024, 168165170, 534859142, 562791690, 231953562, 699641921, 683796354, 220772901, 761691736, 136879136, 236106123, 64941981, 975069486, 960216820, 74718976, 728943143, 156549334, 875430396, 5711939, 222180562, 667950221, 157215571, 588550190, 541124803, 565278302, 806154841, 284240740, 83884089, 638633055, 225276438, 23085420, 639686750, 152483065, 231284243, 599115184, 946689516, 758443492, 67039534, 703570778, 509594224, 647828391, 696008021, 134790234, 627521627, 11513464, 542843337, 35032195, 348458381, 646839910, 717790404, 1128315, 345223615, 609920253, 269815073, 291106931, 287407496, 255181701, 292044310, 639344209, 674087934, 57921831, 927860902, 964407413, 115925612, 411680890, 321178883, 190553297, 569915912, 80459077, 403665611, 91861555, 281556202, 383296662, 97765596, 199414386, 752143468, 474345946, 92097623, 225719581, 380413735, 69498284, 170975192, 227758653, 376679217, 333977535, 975453650, 241695780, 968468593, 698355593, 30937551, 277756353, 867903237, 834374569, 903810214, 430136930, 868389856, 723161772, 37408443, 870762614, 828181787, 536771999, 142730359, 604388781, 967511725, 963799077, 883362719, 646914911, 986492653, 999429675, 410591357, 394331621, 763712300, 18904539, 84749545, 485298489, 554668668, 288813379, 720113939, 127657813, 737810833, 13425369, 688912985, 62636756, 137159883, 550765623, 364868842, 821230746, 720530054, 51782007, 95401712, 260154785, 799609633, 968982439, 301853519, 510154196, 943174618, 643438667, 230570892, 586778139, 541839865, 20589306, 652291277, 728271173, 835297673, 506049608, 119122873, 512647771, 714824605, 956489502, 5709403, 51866107, 178727125, 976229983, 319857167, 389869482, 12197612, 249932113, 723209341, 599208557, 380080741, 262649278, 493823859, 230569526, 723751557, 673668447, 992706000, 232952059, 198562728, 711295673, 966534486, 145200985, 375748359, 209942358, 533304693, 847076874, 320657578, 199002499, 988539612, 185637563, 548132729, 972686143, 79856687, 535501400, 199515405, 723767246, 295738624, 857294409, 847284825, 666110815, 937497564, 915775037, 513352958, 147672158, 806300234, 590340893, 798766212, 13158541, 253282000, 732171815, 698579723, 4711760, 594976548, 441467491, 148099115, 882093116, 361691397, 681531868, 355103774, 982520381, 993223405, 538114651, 101969258, 106087696, 469704379, 583886458, 44820788, 934137085, 866364765, 774601766, 496124022, 725547950, 28090662, 852512900, 807077211, 416127914, 357699396, 230856898, 240611178, 913846036, 93546250, 646619736, 268216725, 631646800, 672073478, 384342218, 208452524, 120065465, 801477709, 94778796, 820876571, 785908296, 937759565, 52453093, 773473444, 103457692, 813711404, 500280767, 710968371, 333301985, 63227687, 551782220, 588420888, 963212005, 944560177, 811621343, 852726877, 113282302, 687965493, 727206640, 137697646, 623688010, 359597314, 653425042, 222390355, 992754808, 482830059, 354572812, 849985423, 658531224, 150659812, 959437707, 404849199, 845151300, 528287295, 935794759, 964332399, 813091899, 577571875, 85678015, 24723376, 890731356, 508243243, 295999602, 463687144, 62216828, 724404983, 656318930, 989087396, 927774689, 524460306, 258547416, 314954158, 338988479, 640382983, 880432863, 686857933, 488933115, 531122053, 415073825, 338998401, 159500633, 691551337, 722764261, 194454991, 152468842, 794969579, 289893272, 94622006, 265849255, 643849468, 917725554, 904467514, 877508246, 259334860, 467007810, 468829592, 419527096, 312676223, 22505579, 316945254, 601537085, 399551507, 109555975, 640471808, 18381858, 298023283, 353673250, 7456409, 81881737, 691683080, 521923254, 596733103, 326039341, 780766904, 688450165, 703501684, 490766327, 742224042, 732918177, 266229164, 15393475, 342223279, 176643057, 28624229, 195013128, 332069318, 486821789, 861695544, 186344684, 450873514, 519340242, 675862519, 992954759, 773315890, 198739798, 629404291, 124655627, 959849693, 32270015, 718047291, 706822473, 781526380, 294246165, 994554044, 814839528, 710839659, 76558694, 890852723, 299665594, 938648316, 11954194, 253100689, 187106964, 943405423, 403239836, 146092595, 467741272, 891623522, 629866134, 456703845, 594755889, 534109229, 285059314, 147216983, 768661839, 460790019, 455359748, 1449622, 878717931, 542688149, 793153907, 782147401, 561065315, 281192374, 414028970, 36228870, 880384857, 81075967, 577571940, 343582838, 511668054, 420322643, 888817241, 734535872, 295793038, 29309070, 672264147, 269166004, 478882943, 144569082, 772407105, 776649527, 477461768, 944159872, 149290076, 841465800, 164377861, 421429291, 832257561, 628749913, 309744168, 338508548, 782425519, 694770346, 127095843, 434258776, 946199998, 812162900, 593288006, 583131701, 754253745, 314091229, 506140888, 44866610, 135653559, 474226118, 131526211, 135645475, 249786762, 96069607, 693626011, 36192160, 535788512, 661104077, 652994069, 374396488, 918181184, 41366719, 714737656, 98667238, 111513490, 247954648, 101639173, 787184168, 628450072, 755695598, 187205625, 27841375, 592372489, 406096645, 421818036, 895054749, 725780887, 976615335, 301273724, 110153372, 586262479, 451343587, 122333892, 832638898, 68814007, 577112420, 11281219, 7631553, 701843109, 379242194, 979020930, 193218294, 462249113, 659924117, 135894922, 31466156, 976928960, 551962927, 142825432, 905690905, 470417782, 222616463, 544335778, 944722865, 303150788, 478586254, 65242667, 585874795, 988895385, 656794193, 916606607, 173494033, 359008895, 911280091, 587799352, 646235028, 425328539, 4609673, 268908926, 45390204, 12707030, 962928340, 255925316, 969504926, 591342595, 575545837, 53937142, 492931067, 790545591, 214205873, 202612975, 127799659, 301230656, 664713647, 792010351, 357055066, 24713306, 283862012, 426165478, 890851048, 183429233, 381121132, 155445379, 854736763, 20993333, 459623503, 101225059, 687669867, 955799777, 291321812, 134532644, 865957824, 956104150, 58031879, 994281849, 812554911, 731514125, 898385472, 731277376, 514309512, 270557909, 76688290, 519979294, 361792226, 307378388, 874494707, 568901025, 789371107, 870858241, 121300570, 762756338, 88559634, 573124867, 30954728, 462625996, 610850236, 168577513, 89631906, 348618079, 391622746, 495728584, 845644384, 282510957, 641682271, 229646376, 547076648, 224155231, 484274085, 639963198, 85020470, 93000096, 732247018, 478790488, 462774837, 828346870, 514857242, 671386114, 971455162, 28625432, 918977281, 33359744, 41824374, 18406701, 360436909, 114861389, 823613549, 910902941, 179944116, 677904726, 140146700, 60432347, 26750675, 281115411, 646938205, 17401988, 136403778, 6331832, 364430077, 642109564, 56775425, 169740936, 501441646, 932170006, 678470107, 260445102, 947894091, 70130100, 581318720, 510578573, 311539555, 769676023, 875263581, 14033528, 100984392, 938910541, 865769698, 223224625, 697909791, 489500722, 282688266, 374094562, 127489178, 563260331, 685994105, 203820607, 602693678, 743846050, 67130675, 824228323, 112483794, 834891914, 798555999, 867308219, 481650519, 616772870, 683629280, 637060839, 441645582, 936619911, 410218576, 502091152, 358396476, 524757114, 349570518, 700003965, 194194209, 254074704, 222308644, 567142988, 553401103, 666716663, 915797075, 510897059, 830298377, 30481556, 981814909, 304999880, 219367012, 81209614, 593678330, 585026522, 127834297, 971115735, 969560570, 400181089, 275553267, 507537847, 687458072, 701337329, 548036257, 93227965, 896700550, 871086705, 170374488, 53908433, 312570960, 815325856, 916380841, 112735599, 215209390, 471063191, 426055448, 251914907, 340727127, 274247225, 295861235, 431159679, 265197683, 688763400, 324559480, 483333498, 773626546, 632257721, 864560198, 623962236, 663025223, 132715762, 930822089, 360495285, 822870325, 26475539, 378521333, 539786266, 541476734, 16423135, 679888320, 111621176, 301812347, 139136135, 249795673, 337715768, 31000355, 931993379, 339593441, 110569168, 744689423, 834106782, 608287248, 897187713, 803966958, 156049141, 418942814, 312724568, 722171912, 89441698, 145707091, 990020635, 991862514, 718341213, 472755952, 563604868, 631578563, 766836300, 219634021, 549658761, 302571156, 905928509, 992731753, 331660809, 95483781, 891077151, 749699178, 381221637, 884448272, 166149915, 922910801, 346095446, 449399814, 855069456, 759701625, 486579491, 762568679, 669425853, 16314444, 44310063, 594919060, 108497476, 796832684, 261491750, 817742319, 252145976, 711257362, 172088759, 48457259, 743551634, 459280804, 30259562, 675236853, 198567849, 340785206, 729437835, 361066309, 296973857, 309191546, 470640576, 678853220, 101726622, 751273818, 34045556, 911321964, 803646629, 186912707, 223076570, 936063939, 505057165, 285811336, 731110588, 728830503, 75566174, 88367664, 531564251, 538211461, 247252341, 842027866, 555734604, 19208934, 92577977, 839433232, 196614929, 544098924, 950270516, 235681619, 359591310, 236213590, 338593170, 299741873, 187038064, 18563860, 965101126, 514304823, 8733833, 289966670, 798757266, 968667706, 822910189, 650708269, 794683311, 394741744, 617672507, 449200279, 683104237, 83518203, 239287533, 673868177, 882138757, 882024920, 566614678, 222682912, 863994207, 26903406, 676576317, 827206826, 892531154, 640817436, 84292023, 754165382, 65677247, 97421641, 936524469, 78158719, 991628720, 440879190, 630883695, 565241382, 140306536, 499190764, 956569475, 528515169, 125295285, 675401626, 706384996, 496077159, 39195250, 642760602, 517798633, 27275985, 652155759, 27681335, 779113450, 794901706, 481316402, 788459520, 419265661, 737922801, 968713467, 989234087, 303693095, 684112462, 572496730, 42695236, 673095474, 298280166, 618579453, 28562609, 39496949, 806418514, 534508500, 547929506, 577183902, 58125042, 103882827, 387888878, 6480914, 655556981, 658008317, 415952847, 78092497, 717866409, 351305123, 600770508, 298235674, 415490893, 164805982, 301431518, 944366596, 413821871, 479124484, 266606919, 583331369, 809639963, 274059544, 123551813, 47439227, 718664567, 257893795, 365379713, 63584722, 388748419, 420238445, 954492776, 724618686, 875550722, 671347096, 587547867, 512889999, 161247804, 146509557, 884632215, 515986177, 830765109, 807684794, 782244272, 676069567, 597753682, 516980483, 212769919, 188242986, 771762357, 131133970, 909503695, 366154626, 220733597, 641886102, 57313491, 333183940, 758743183, 165003849, 497449931, 873123609, 736618960, 405256419, 200986257, 326871556, 7159581, 786966529, 849702307, 330147881, 586387488, 942860466, 868125140, 519684954, 398183122, 845521321, 779129393, 382284071, 32949628, 712098024, 982246084, 161599495, 561738773, 290367138, 684836727, 582671445, 972859949, 453933409, 947543990, 89219006, 81475053, 150235867, 177364339, 299245197, 445458973, 373481570, 300457943, 815214053, 745738287, 613720035, 475574227, 862299069, 623745634, 895198934, 652909802, 867049067, 582865938, 179193059, 916661895, 227139502, 121396775, 425192569, 743017727, 944774627, 273394915, 420420537, 294002910, 723539949, 162007026, 91674428, 296959121, 252938886, 458462147, 748175837, 669675987, 811045533, 400329569, 600934646, 113593383, 863236685, 986101497, 857309717, 336025537, 777872934, 820587726, 435334410, 959354299, 953407255, 16152609, 920555831, 903878162, 116239118, 23386110, 923739058, 261948137, 819005275, 33070017, 606115853, 313651036, 98614945, 433710070, 865506206, 582399250, 562499804, 192767183, 156063418, 901072763, 207752188, 279908571, 268232966, 876057606, 115641472, 936201191, 637108440, 486416929, 912327045, 626978631, 886018805, 270937846, 477290638, 615914972, 23014998, 888674861, 463527308, 281159564, 902650579, 42898189, 543811881, 27715905, 704543397, 309638399, 980320545, 571472820, 271427722, 280600760, 855839205, 930678172, 892435753, 852981655, 910243905, 752411206, 549927815, 969348844, 926979271, 473670544, 530516580, 278692810, 713423079, 929840398, 528585883, 311417402, 240028731, 862031238, 216829528, 549307794, 605816034, 81603291, 725874482, 665710933, 585523945, 836478905, 462041847, 244168973, 965725627, 314544685, 19442001, 266369118, 750899403, 69083425, 85435653, 386038511, 5802740, 267145252, 336211948, 559623566, 764006772, 654612797, 533495323, 321122098, 858076969, 783303185, 979724791, 409401639, 797799994, 530840845, 524076107, 246098837, 896492580, 414220448, 512618169, 594504051, 297212820, 551262785, 709200582, 488538443, 109169568, 924868233, 354922372, 625101047, 457953895, 858583392, 382552620, 720043420, 321700825, 929346216, 521606840, 392097607, 502913717, 383804056, 651245826, 701771481, 110752905, 361674256, 855343599, 777746918, 272842343, 178737790, 19813957, 677145067, 661318090, 688029768, 81062346, 413729063, 566856182, 680136681, 545854820, 731284216, 390133149, 127957459, 15533664, 928637708, 510742458, 647682354, 465258438, 426416564, 829513641, 328657860, 85275975, 202103508, 122699708, 542199664, 211431583, 735558208, 877504577, 826005407, 834124445, 72409496, 195572793, 497338766, 23451941, 992194577, 740521741, 691671420, 400185104, 901469224, 180087794, 251570947, 458610928, 819674000, 470000458, 168682936, 913182641, 886896173, 73485271, 630764940, 51743710, 186324629, 120587485, 646298454, 865225183, 72007992, 196187103, 402530768, 81943559, 190672248, 535626671, 796374162, 338875422, 983597897, 805989961, 308044769, 52395145, 717658081, 95090982, 138895913, 510870146, 442792836, 761673184, 939987297, 881556951, 735683178, 155596329, 518674052, 4273151, 735049620, 562959585, 593507665, 865444944, 649126366, 241584219, 467240280, 495406171, 616628670, 388757001, 837100332, 917756619, 949312512, 797312314, 875962173, 143218070, 21348275, 155097587, 585222431, 196346089, 438538050, 581540925, 56707022, 499894067, 413406750, 48385345, 34833065, 756034656, 284435760, 2894072, 989330716, 803552859, 729700247, 791980292, 971884418, 234445327, 857014038, 842617911, 893582824, 566589668, 533013377, 890176501, 72829200, 107998379, 13400711, 822805448, 668219807, 598963811, 651406046, 852373913, 674923391, 91329958, 176155804, 357309956, 633617583, 834495624, 133536845, 229103554, 261454756, 831791481, 106323140, 458381500, 552022914, 761120538, 151162401, 21415804, 679117114, 631367277, 424444262, 791984539, 46754962, 988878321, 286882460, 200295083, 757527124, 643228880, 460451977, 801188156, 32451034, 845722987, 178628172, 389722150, 364458151, 90689558, 558926062, 52994806, 636036870, 219568757, 889018471, 604643266, 80462846, 253566621, 710329878, 629987500, 47642510, 227899583, 681926343, 476517024, 116253400, 600899979, 809242508, 17634276, 969047098, 572161290, 397831315, 940899651, 517854080, 228240431, 454450164, 492638843, 402829033, 757690490, 194490673, 957907534, 758261593, 232905655, 775782215, 62898154, 234133122, 860426229, 111052598, 301355133, 780668786, 506178767, 184097131, 844786731, 36988445, 671260864, 250180151, 905275288, 321235871, 201352726, 448455748, 681393489, 768797315, 496195799, 37822596, 324785966, 246558497, 926928104, 518251413, 982254441, 897420464, 656684089, 840764417, 174155642, 809660401, 361886528, 667331192, 133184792, 9616640, 756612014, 798598152, 121066857, 700330953, 759881038, 548585633, 219957348, 694596621, 952026657, 16643733, 159408013, 266630149, 200959020, 105671557, 166714857, 993876096, 636923169, 713663659, 595159089, 24173580, 390187070, 167972892, 863582617, 816248412, 635418387, 221223244, 560705659, 228213392, 564761697, 232946455, 261002554, 980912321, 743835735, 395971365, 101904081, 229656297, 485655943, 615870880, 901849946, 571136141, 501835936, 529887331, 70893766, 185366453, 760709369, 68792081, 587475630, 987447251, 744165084, 590579572, 862273287, 366061653, 954295131, 783362720, 525583959, 735771248, 874043512, 758421857, 710459717, 582669964, 697395723, 131516992, 272193085, 766715312, 631348975, 962751724, 240299867, 354040106, 849434615, 952044558, 981112539, 796226557, 634260113, 953426422, 928350750, 984923906, 902672443, 365491080, 977548597, 634555770, 809248536, 828235643, 953809994, 826339366, 119209838, 797135829, 370971087, 366755009, 215425166, 986941828, 827253366, 737503185, 332583713, 931399137, 959145783, 388576464, 258195473, 884896770, 951851093, 687415971, 680712278, 862433911, 23512445, 459920130, 984323884, 11518874, 757644295, 726062444, 747794126, 944424729, 527075962, 220747886, 418403089, 507909932, 116877444, 659332000, 98272211, 429715809, 508966234, 791006802, 483964593, 231160889, 718320791, 900995455, 774688582, 754606717, 783675361, 350140458, 284089910, 349197322, 206405491, 293330402, 291122754, 180350633, 828486190, 591564819, 384482593, 49587067, 353797319, 757445034, 394467941, 174099866, 181309117, 863663409, 131411475, 514841526, 863580383, 270785761, 840850636, 356094969, 788411421, 157305297, 733239697, 482234974, 363724245, 22544591, 550970762, 320841040, 361936650, 87809896, 107006310, 255060234, 488372425, 192364438, 55152409, 797060062, 19134796, 173671046, 914482717, 557788341, 974170134, 202339044, 363656293, 81242461, 324841771, 871613151, 117990857, 338903552, 954980087, 655679232, 884751407, 811178821, 877935699, 349810387, 81620826, 989220066, 317352960, 105993997, 382880701, 277059682, 621355171, 974303000, 4301319, 872081354, 415403294, 830460474, 725199440, 707014350, 287714414, 605839612, 424601709, 10516853, 849873741, 14293996, 932057010, 446248807, 649323558, 655559436, 648201271, 142899899, 593082879, 626050006, 153519936, 964709055, 336005535, 271745585, 42448135, 897739380, 861123978, 547877353, 850881641, 147276465, 510558324, 988068572, 479483140, 208067707, 950580870, 128494540, 383225921, 116059357, 614193730, 77099956, 975228949, 10874771, 38923708, 754858262, 268502308, 889790766, 590790014, 463118005, 445529655, 250839731, 229689437, 917401215, 842454147, 9654850, 141465632, 920422788, 173145934, 746093950, 916221868, 715167269, 501425896, 172845165, 974069017, 964990303, 869073404, 124611141, 891404130, 305176393, 149419013, 694390931, 393128066, 270731683] 11263)," 55191 (countComponents [773604687, 448579925, 155329471, 166712019, 877239210, 640614879, 942187959, 818280523, 129006545, 42262948, 383727634, 875226296, 488371161, 241322020, 519276178, 182269857, 726520434, 244473548, 258063898, 95327682, 775036569, 825443776, 660547888, 674057596, 418287540, 405066638, 147656258, 568234166, 311609699, 169498577, 902811954, 488476536, 675199834, 502438623, 542036980, 501393325, 362601295, 298877382, 512669830, 576152062, 5889482, 911861847, 98589765, 587916672, 407486359, 784243743, 801823803, 766835773, 673130479, 483113307, 93711712, 43137115, 963290463, 616464972, 388063463, 984378851, 507879689, 233525507, 352619303, 878686700, 791592736, 545426418, 222626124, 43556266, 187040614, 478669698, 8842001, 34097926, 181039479, 436148881, 631848400, 129736657, 695822296, 56784397, 924199429, 720942719, 282723465, 524331341, 904533819, 199948794, 948975326, 486866916, 814342033, 453779685, 892261089, 553410022, 802379393, 37459506, 162547141, 886429196, 800668761, 823087541, 517508755, 586457195, 700751401, 526231407, 930906156, 42413483, 759974106, 959174247, 628280633, 883400179, 848597977, 713091589, 573928634, 193807580, 518178390, 616444239, 692165593, 793825519, 923443312, 40759333, 730921043, 790142583, 906750807, 960643287, 579273493, 148846275, 260289571, 736249220, 943821111, 58046655, 484077424, 217045020, 879265583, 702912508, 745212016, 355103877, 985768754, 767685310, 481128063, 849741391, 143571111, 524745859, 583472765, 81471039, 115432688, 875174724, 206275860, 328843273, 555056164, 850221471, 314700060, 340441111, 674030339, 486420864, 488945836, 865414119, 368077169, 160583496, 345448871, 491228646, 820580279, 620991973, 160007992, 914083696, 421636526, 927786712, 885864438, 568398916, 932606415, 40028145, 469965174, 268863382, 685417581, 70458814, 888604916, 80941018, 554578613, 332254016, 699033834, 844348355, 775057494, 681957049, 172571232, 798986844, 799626273, 55554262, 148480998, 217802062, 459510606, 620541077, 620147353, 880511503, 8116855, 119512023, 767020371, 140557548, 929410273, 710388446, 770542739, 536240060, 380113140, 847136193, 859860887, 244849540, 988646263, 624041025, 164602898, 281301760, 964313787, 154573834, 469169760, 227861414, 736071615, 462723569, 452758777, 710828679, 285048849, 499871148, 220975111, 283508887, 281296853, 106183731, 253511032, 866952914, 196282153, 644805232, 137768226, 422364749, 809275619, 744017797, 172723217, 894172628, 688446131, 813770717, 305246302, 715639350, 702276798, 270794557, 456391106, 942275155, 546214308, 927174429, 722693221, 115776766, 259102240, 823289481, 584282930, 202013072, 500827653, 722084392, 977223900, 727998651, 759027854, 29007143, 504814228, 81520099, 25967593, 552092986, 638032810, 631727722, 650848859, 112887424, 106590303, 552465710, 389816978, 59574042, 39133476, 6172, 370928674, 810862973, 306224386, 835072794, 319947812, 929532721, 305072567, 343186287, 526103667, 443130428, 176197843, 521462776, 72053424, 816193432, 220895537, 236517864, 587191456, 917178326, 490176926, 306166693, 695559100, 458290207, 590571490, 844653837, 94254309, 776023377, 341897473, 267790655, 173541246, 332921652, 139075995, 733955828, 503442749, 560754699, 997760425, 462969029, 126113842, 496962389, 243968776, 867583231, 336153547, 764379694, 80521931, 207891599, 377837429, 438539637, 736650053, 190990461, 255170252, 499805501, 413843765, 117511011, 587797157, 931388709, 279336277, 17879267, 882845701, 418520273, 80050265, 672036721, 716757221, 662893430, 351104220, 193028252, 577836236, 401702828, 500253873, 879701108, 155471203, 743207152, 124239399, 248437090, 19520845, 59896032, 98966899, 89313000, 294961371, 658485604, 822777375, 14434420, 640208699, 817930614, 113261430, 894116867, 780402100, 334069256, 536607559, 90957693, 74839496, 116868374, 209753537, 863362615, 285767119, 498258948, 219971265, 655176127, 547621851, 714142993, 793207133, 776821301, 422145802, 580670119, 150056389, 407508312, 886607090, 580609259, 48387318, 581880395, 964007430, 220378458, 454658335, 972687788, 638305374, 684577244, 567367686, 597143019, 568077938, 84352922, 715512919, 161694276, 768147220, 305367940, 744761684, 578918625, 853873937, 909027380, 482256054, 801571916, 111416762, 109759025, 457968994, 164120951, 430778918, 874450690, 647091010, 269527817, 477979440, 869845561, 634224695, 70139682, 769037716, 362820926, 689149391, 613746238, 481617296, 636561161, 936239060, 648112364, 855751266, 121342811, 865314688, 35320879, 601367176, 496980862, 870607137, 771648518, 665038409, 238923941, 179667691, 707854453, 657183816, 646810025, 203154841, 25556896, 204069956, 980906388, 357977014, 933590696, 66784668, 678540215, 915360269, 648008694, 186526693, 405668436, 962371411, 941480193, 347933444, 914634483, 744153499, 453976024, 877577286, 558722256, 140002953, 626730291, 429832431, 352938703, 350832020, 378209921, 207408841, 203074860, 575495997, 437124533, 210049417, 860749652, 733503144, 616974421, 914658505, 837889212, 5968079, 866006440, 696431023, 314253275, 624636351, 395377498, 869455269, 652002471, 350382675, 150264968, 876522943, 277112050, 659394845, 335605020, 616874831, 750036836, 291664833, 558906539, 946681803, 641887095, 259100230, 291860811, 360422023, 478226867, 330990748, 714320485, 916591723, 952419225, 184157427, 691572298, 189283975, 543735036, 879913487, 492394488, 142673970, 680623593, 298920936, 732803640, 466499939, 195512899, 296106083, 151380369, 923103280, 492145450, 302920203, 185116018, 256525286, 702615319, 506206570, 284187541, 416353419, 703642154, 76151369, 293889415, 614653505, 397721632, 901215671, 775490679, 207596110, 833045661, 749467318, 517597785, 410658746, 429026661, 154355136, 153408748, 656517391, 72954851, 426904130, 627269973, 639513070, 696621038, 176989085, 630040758, 452088333, 663001369, 1966407, 678838043, 632054137, 954810431, 314989523, 992471798, 348084260, 774515448, 323867568, 156761531, 377649788, 101629164, 30999278, 333470963, 595589999, 60184760, 28798490, 392106562, 574536954, 74426895, 227810765, 776730635, 594762226, 726118092, 207500221, 136672087, 747777283, 743125190, 205434604, 71355751, 408214938, 901756282, 514786537, 994223794, 276024092, 491480970, 75446216, 474283357, 625636529, 150484597, 850132639, 534424813, 485163328, 318449709, 699839148, 876726168, 756097682, 468930153, 797978137, 548801254, 475863971, 671272701, 918828737, 503087821, 122612653, 62903650, 741391066, 118563397, 893344700, 502236591, 840253426, 616131169, 700980808, 194111348, 465277416, 890626233, 941926922, 785579192, 821848882, 755171147, 889929749, 559003156, 279031614, 271425854, 430873691, 473565657, 566863498, 457866596, 551301361, 153460790, 943923017, 768845024, 261915432, 508716076, 560038892, 21777776, 111511175, 509694852, 944404588, 486647986, 492462030, 646491245, 23148300, 589669160, 214375656, 500255811, 791081146, 343890411, 750135318, 663328907, 783682926, 924535585, 834987045, 839549757, 921053876, 380171719, 407672559, 539239433, 474526435, 891474670, 364368619, 800982166, 70240254, 496085435, 628156217, 23776407, 717035095, 660345110, 992371142, 916368060, 378275662, 408852276, 479021976, 978631016, 567074251, 979715337, 858095177, 525281502, 919782049, 751956856, 209821921, 111751135, 696076870, 536156703, 909116169, 265928857, 803347946, 508392290, 983843135, 399441802, 695315633, 44808764, 877340491, 709068152, 655742641, 5630224, 764627924, 831075358, 276239792, 839133045, 410599036, 638382203, 248125135, 272021874, 260187978, 996793479, 894797656, 476067215, 749436721, 720121562, 227290470, 249424878, 331163510, 40865476, 221512095, 432028039, 349224210, 481961170, 789509124, 473129686, 504025591, 138083097, 445961628, 753034830, 402187719, 992573706, 717171675, 322296968, 994995604, 593249155, 540914644, 545726810, 423564254, 790646902, 358132956, 742959568, 215826681, 202128743, 750720962, 814039796, 522470818, 54220024, 824743943, 119547885, 585903926, 894937314, 374168756, 378852797, 414311847, 76853074, 866336749, 317034381, 383509646, 825835458, 144406240, 46860641, 519153280, 186131415, 228380161, 22493673, 655161357, 962521041, 318852792, 800188231, 198438951, 448269513, 737155526, 517533303, 30526031, 498818261, 871350377, 485909232, 699850222, 661778137, 394969395, 498740915, 945579654, 806727996, 158734784, 243036552, 34170359, 171350421, 255607588, 391511344, 761734859, 382313770, 217953493, 37585769, 655935719, 181219254, 342696516, 741275661, 368003854, 63138434, 12381289, 719578961, 530274639, 221543559, 15969411, 45400759, 976923500, 588977897, 599435638, 160736357, 678100684, 578819213, 903829549, 403291616, 465822836, 24862112, 688493130, 822375065, 517665628, 981969475, 903394108, 810705094, 97850052, 484836551, 928134239, 642510053, 298388076, 815189144, 178377620, 620608594, 663900006, 318508001, 814903827, 42500741, 821593970, 286965921, 108856048, 482009884, 130125974, 933946088, 73044829, 550254241, 997726594, 617161159, 646228353, 115202603, 305021256, 590988543, 749574644, 113199304, 331868580, 482800732, 702107532, 286415756, 449190403, 144011843, 939633937, 43983303, 827906971, 739973206, 796428788, 956632859, 952087983, 467312566, 788782355, 614997495, 477284499, 369813301, 727158238, 658537165, 452149826, 360572324, 949812277, 91583051, 910759604, 340742832, 854944369, 330315100, 691298153, 585337424, 359080713, 470677869, 785773559, 317897911, 122496984, 98257702, 171547537, 607334271, 811349659, 20635516, 524102634, 289700055, 20984224, 556724161, 585959037, 496002930, 497433249, 936326790, 465687538, 40474859, 220214383, 101808639, 149298125, 361798190, 167190642, 705918685, 981706219, 425914301, 187417646, 388527679, 66795259, 960684875, 509425903, 995863193, 725533101, 771965810, 527313977, 367815466, 343790259, 594523073, 394882068, 31594598, 199761526, 271443225, 389344304, 172933376, 481477332, 521908257, 115138545, 638290914, 606476572, 60923560, 849871603, 144534974, 590260673, 163035114, 555280035, 711855826, 885116213, 281920792, 285774744, 167153085, 173221535, 938805237, 606593608, 558996297, 128762756, 381527397, 779969599, 120634893, 425523949, 871529842, 411795145, 237304681, 24664886, 876622930, 620199964, 746029758, 782538862, 229615132, 452343251, 853233092, 319931094, 722932234, 132251956, 522911188, 338033450, 785727960, 292992292, 404529741, 119568300, 237411465, 715630843, 973059619, 245115091, 867621998, 411837661, 322715089, 991056877, 318334803, 809637171, 675556076, 746282607, 792866937, 946217806, 192147744, 609128736, 744343478, 729615938, 269355894, 194648505, 533294046, 584264799, 360713118, 791693030, 876115203, 520219254, 613494501, 774787192, 861917726, 686252649, 321980984, 247060088, 521216350, 673737428, 28765460, 605307425, 870744862, 842830227, 540419874, 805484299, 700835062, 406384115, 468811710, 413357928, 641791990, 361092864, 345684870, 303814436, 571064465, 845795818, 182478386, 806458591, 893744975, 791198014, 624788154, 519845404, 825197123, 900191054, 746763709, 600202746, 904406630, 111972096, 878913185, 358149613, 312232897, 175314256, 459095696, 629226392, 941360153, 399377561, 861740323, 237987276, 596560230, 903232096, 790920862, 704314235, 750457901, 418492838, 822597602, 165939385, 643945523, 740094791, 434533538, 541516275, 597359565, 799169412, 944068406, 710466244, 699768851, 745647447, 911083665, 667946353, 995737165, 683483563, 926358352, 664194113, 428971504, 620342692, 969805453, 785089147, 107646287, 537671299, 614467172, 579031944, 188178900, 217348020, 187096216, 933533229, 627201339, 52152888, 123743207, 879960680, 976160874, 98548580, 970410504, 101902543, 931619725, 21966401, 700270631, 359065499, 56179219, 815747625, 97678562, 116878632, 938152838, 730971136, 523736866, 80644605, 584283372, 864306760, 653969898, 793865533, 730001130, 261917816, 694878051, 483611649, 87516016, 649003918, 310416526, 13801089, 429799532, 577223214, 147392164, 647614261, 412548549, 170260834, 964986053, 49735693, 20607071, 686495968, 615677127, 733562844, 19428142, 643362954, 408956432, 66466799, 760486696, 527755474, 31064772, 875988388, 774649561, 931209499, 805011522, 79462194, 372291292, 713241798, 848563751, 498384559, 929252000, 851568478, 64208290, 329241293, 788999189, 280817407, 427041923, 301430553, 71176643, 512488716, 238863183, 584371254, 862650790, 120856450, 694195015, 430519251, 725885603, 726590787, 184605129, 763116438, 607353319, 420291716, 886283626, 587315879, 906366274, 774688902, 746801731, 410251456, 7018046, 194807992, 315712517, 921075936, 756832583, 453604140, 196057043, 899260337, 8797000, 543384783, 59125478, 298497050, 115841187, 516355555, 414423874, 323578116, 782161055, 325686822, 128725245, 311984098, 454534557, 774236052, 93072678, 222072880, 894389487, 284925707, 806788765, 532952780, 679043365, 624153501, 558552303, 987046580, 598073264, 285968922, 413529650, 499145979, 908215511, 160355726, 278228267, 922581864, 864358146, 387182409, 996479054, 134699685, 335874057, 714779940, 834776737, 349831759, 782437455, 46177410, 205446024, 350985493, 531825368, 26284301, 909477142, 987658732, 320582690, 866653846, 491681478, 506742734, 151004965, 979882504, 967089164, 46297658, 786661513, 294863224, 596350282, 756186916, 724643768, 955195995, 858453617, 390988723, 213516522, 292989727, 829422978, 498083091, 147773529, 236372202, 854800558, 606392382, 240163751, 429941645, 981824926, 167571770, 667465757, 362590806, 789965965, 147547810, 121223091, 96676294, 436768063, 419382027, 822000810, 688343916, 618564614, 583925664, 712217736, 184135173, 147812132, 488000248, 485801448, 366743309, 175106014, 415595264, 808987687, 164197847, 912379461, 82493477, 618724520, 606892427, 47021923, 158421184, 749987843, 7123770, 317485811, 635099853, 628346201, 203480279, 266381437, 11029653, 254085754, 342720051, 267117381, 804875338, 172270580, 430533681, 473262327, 196606359, 275858032, 736666759, 38596846, 624701444, 517757704, 271458175, 940264288, 491146285, 247287288, 549158407, 412944807, 673072485, 73964207, 280558971, 414487806, 920115644, 130796886, 654905655, 343769062, 546720368, 619968372, 165807708, 789403008, 926955677, 663163918, 662796414, 719881580, 760316535, 711215050, 939208848, 630115201, 561948377, 687917817, 141247207, 560110532, 409357005, 116386746, 380859101, 39802854, 694228327, 132195166, 536947234, 241280297, 669194954, 506340363, 422021421, 738857367, 924863683, 54800315, 632410148, 282412357, 750716930, 982712442, 167858222, 143785681, 408758857, 860855960, 351478803, 229863833, 943677692, 680310370, 859523791, 147894723, 513187766, 256735377, 918925570, 617065692, 38424341, 264167360, 729883106, 183781854, 597455825, 342233260, 537045320, 733025194, 24229327, 896509, 6849050, 291307346, 942664416, 46887603, 631794086, 560686038, 623303619, 817860686, 827398096, 387039782, 619271090, 355605553, 54361502, 238776258, 318536870, 388595063, 477175831, 13296172, 429309119, 449671833, 858217693, 486435029, 419887126, 816935615, 215613638, 882375701, 253059423, 408960689, 850752853, 163276133, 443146579, 941445479, 704018466, 967873414, 524018586, 286595771, 356557585, 50174477, 980350903, 638074538, 911459898, 709334156, 195879146, 72408439, 455930797, 912029757, 816104838, 304183017, 302031544, 821708984, 744084684, 757629722, 113565478, 758322158, 969108462, 360563472, 493010167, 96132494, 964756571, 100352417, 848909637, 473461251, 501885168, 523557410, 971280828, 589834475, 615250492, 308411471, 458501907, 231633434, 498776970, 574334205, 878414897, 289234686, 60525226, 536098003, 674628476, 689988821, 763005814, 346986720, 63066835, 356398145, 706745558, 350028400, 480331084, 899617979, 167310297, 746309183, 152934408, 526628992, 735935287, 219872909, 179567257, 534487517, 404409148, 346415270, 921756386, 376830732, 24875804, 745260287, 93367563, 201087748, 238504879, 620384912, 489513243, 908819206, 851712564, 944051249, 471895848, 647814172, 735191036, 465943573, 277484649, 66780299, 60216161, 306667100, 862540036, 478463790, 269581140, 900014920, 427599110, 556464638, 153838441, 336334974, 274669093, 799579769, 502677642, 538878248, 553972680, 670208939, 81857580, 498503697, 194683945, 743418299, 357411743, 92606305, 426606949, 58299843, 484386340, 521413914, 505984379, 775740528, 52581507, 107662460, 642021919, 405019065, 516228534, 378192644, 949723727, 823824018, 767416093, 317828542, 925793081, 171514585, 446204087, 2245277, 475028500, 421493701, 134561728, 382456846, 868098394, 635354809, 771159512, 947437671, 573378231, 221101593, 171853555, 33832552, 297441147, 951771374, 42955194, 127824331, 884298343, 225862201, 419317451, 829400820, 928724353, 654983508, 336824387, 994043490, 837850400, 572268040, 819870128, 315222802, 865162206, 573939767, 883762272, 459422102, 224104634, 156409575, 21409659, 860619833, 572569611, 281007299, 955418600, 273341535, 601808388, 110183471, 188114425, 346500958, 343698800, 620640465, 290274051, 832644100, 695918092, 325887920, 485069893, 163178736, 601020179, 467735606, 32145618, 805324561, 6480508, 495977825, 260207849, 237982947, 463645667, 710618555, 630584005, 416744454, 190106111, 845710250, 719626475, 65472542, 282670459, 506938027, 220267399, 603688556, 376098696, 350429128, 267579703, 820907564, 941362710, 531039207, 742290438, 746578912, 425621311, 7327612, 4283529, 258744051, 329199006, 121079811, 153665028, 344356733, 764498365, 38487973, 464241990, 775032464, 11084150, 235508401, 196106539, 232606467, 776111143, 770288238, 756267908, 53938454, 86368063, 693756797, 336569772, 425632388, 714982111, 693164585, 862886181, 486390876, 488914843, 107771298, 670701213, 275441067, 365428819, 209384066, 192297031, 477426558, 739554866, 536008517, 465921915, 489826094, 728030442, 604819726, 236409492, 531258643, 8828772, 671860269, 317036418, 670933888, 182887045, 665904919, 631216513, 886286438, 182039531, 45977639, 960640419, 862125749, 498390395, 325622174, 820769495, 444070228, 187214663, 462321115, 73987536, 179687773, 439757846, 31386051, 317689836, 499386475, 36422134, 824080623, 395484452, 505658370, 332777456, 338022605, 520821617, 738504809, 741297899, 812181579, 910399001, 757510463, 777593791, 794062201, 763028619, 21562375, 304950854, 143428072, 630330686, 86248218, 67116272, 326385524, 801832724, 612627047, 989497259, 45929049, 706167648, 501405011, 777273209, 187586514, 530705873, 177682223, 903675071, 421432933, 783515528, 575016377, 103164289, 707178581, 866314369, 82141891, 422470832, 964673576, 154408784, 205443278, 985412000, 870192417, 750555404, 754783649, 891897450, 283400563, 770038947, 272492409, 300222799, 873937874, 63654989, 396328873, 571275394, 519508980, 710221251, 75221896, 332983186, 912941546, 474212082, 512216601, 62965564, 526305152, 752782642, 79247142, 41669184, 717692684, 963443106, 149052191, 688315788, 505408697, 470441191, 31847558, 632618949, 434613869, 921001068, 937463219, 370292133, 230152578, 309310129, 906459427, 111437311, 516279177, 267716701, 329794926, 146730042, 464315393, 402974958, 207445532, 556859066, 524895253, 789938745, 968089059, 546556941, 979463547, 259810573, 178680835, 527499221, 466639126, 175597706, 901047981, 149138853, 906568039, 826405975, 672551619, 69038091, 155032300, 768667123, 361112036, 42639684, 321537979, 868614883, 559111351, 403150571, 693142945, 795182715, 553499138, 813962184, 721467961, 429521648, 462760834, 12099068, 1035573, 431160569, 778704414, 984323016, 979654546, 90550535, 783457539, 701511275, 635122772, 551925405, 323445682, 678423071, 306448964, 632018900, 460720828, 671432628, 331985928, 65114380, 772042725, 498460726, 572145363, 373643063, 681036893, 969144234, 520484014, 105442888, 37930901, 735825919, 863216803, 935944703, 419867717, 476201507, 434274820, 561596365, 401697957, 254631520, 711996336, 956457474, 358283912, 673093727, 5948789, 419652086, 288356830, 139310176, 238576591, 661292610, 769535348, 642434415, 53783723, 657941032, 720676072, 346871697, 891144920, 213998353, 548524644, 254386208, 39680777, 644277833, 348147869, 161250307, 19975096, 985132263, 336846527, 285192497, 468589095, 156795942, 288625060, 791102522, 9411962, 300247337, 544675965, 256357014, 227932933, 688631519, 881405319, 82040010, 580807591, 963512876, 476789714, 524764782, 597894599, 361444334, 45308679, 831225839, 92222959, 846365388, 41899031, 989367348, 112752759, 882102883, 231006010, 843066146, 704746026, 706875344, 147774573, 346581165, 34642826, 390090523, 57692204, 373694876, 446945411, 1054215, 287303569, 907370800, 791095286, 23458846, 668254895, 895070788, 753800237, 523718197, 820638351, 712204076, 199640383, 463810243, 626864518, 620102432, 788924374, 527030252, 604297497, 150901421, 889155187, 295632638, 112452142, 484424213, 936054368, 796808265, 716634567, 719742344, 398949905, 455508726, 602874490, 296558459, 186172443, 71039680, 973222624, 904835888, 697966483, 671386197, 935840453, 736141068, 92722932, 159030103, 579233981, 772130657, 359516524, 85713148, 698155680, 602792905, 292226004, 347716181, 799501418, 242554823, 555869627, 46044668, 848017520, 868639772, 605555894, 92378832, 584844826, 244350337, 2811672, 997277781, 45504441, 712580621, 520592950, 27372353, 439804364, 236060734, 458712579, 997058027, 198963222, 55244538, 851271021, 174627230, 15934973, 747194672, 296275428, 235956576, 220934777, 814021005, 13301575, 485367337, 439427916, 325255788, 821274158, 270991014, 673950479, 788862028, 929144227, 622851159, 164879573, 163912588, 15042598, 326060767, 599695101, 311985272, 850144451, 791506413, 265973691, 229901236, 503608625, 135350721, 14514235, 83084299, 763806321, 111511361, 830864342, 922591109, 944757334, 797636452, 405396295, 777741288, 166283463, 9078150, 457013547, 337021419, 729423199, 728672163, 368529873, 139773301, 398987105, 183100890, 20862020, 113125379, 125211312, 750936344, 151804053, 270891955, 753653968, 92044470, 660051924, 698408607, 74553653, 814895020, 885816526, 735066471, 603668893, 676209200, 585667477, 162463538, 2573170, 380280501, 360668530, 499156564, 244326793, 924714554, 37058092, 422571832, 759550534, 811867215, 875297923, 742888744, 451950444, 755785508, 646898740, 291793826, 810829097, 927023412, 168857813, 605264692, 609430488, 803001927, 175239515, 114594741, 980307318, 557151000, 433608122, 617271048, 294361554, 819853266, 533507557, 625094354, 118350047, 441084972, 857656295, 19464671, 916015393, 465894309, 862193549, 525122210, 862078604, 306228468, 668396752, 230902556, 234625875, 938691270, 579663636, 19661958, 844659595, 438903922, 938476970, 333949476, 531685201, 633290329, 365020659, 926025975, 768524499, 87474106, 759246850, 7228404, 488415621, 382030287, 538125615, 971693047, 512495273, 181941813, 257577672, 161536537, 386653358, 609622345, 423056551, 472768841, 287659308, 192311499, 583922209, 680521558, 875878362, 650970022, 933593100, 634182756, 989453770, 131808697, 574442824, 192370572, 319911050, 332351881, 503969131, 307977427, 241993722, 892724545, 461105305, 154263133, 262679144, 645238830, 686412808, 754114769, 964957756, 161990292, 327344204, 345078180, 903040549, 269323436, 998707888, 494945306, 988565126, 784643761, 293849936, 108609816, 342783465, 29004837, 237526248, 945032783, 645794626, 663482611, 83813156, 963400854, 922214628, 604681964, 844062474, 16892507, 51194774, 32007638, 834226268, 932218935, 660963477, 847551490, 398124251, 260080696, 512299431, 557008287, 204652523, 176530935, 490018294, 729203766, 614071309, 113124552, 367069532, 454063368, 269445358, 438227380, 283751967, 87615064, 856834036, 660352501, 828091205, 375263925, 67273838, 248112117, 530863119, 754478077, 886115175, 158661905, 467461407, 171497413, 393902139, 325825672, 40134227, 94121735, 960242391, 975964865, 459215533, 228101976, 838137905, 285137492, 641173682, 437752642, 626303062, 39759681, 772643283, 200991951, 299754597, 276744015, 359463925, 790540966, 151017688, 211960724, 912946354, 339854620, 38291877, 627327566, 764439763, 290978780, 413837371, 888793023, 734430655, 575951116, 748712240, 138431087, 775887007, 842097616, 745235991, 691665508, 917765847, 801689326, 382905403, 558941105, 658513741, 402604125, 760797351, 455658237, 966519449, 100446217, 508113681, 389490376, 650855411, 88572469, 347730533, 322442293, 941298310, 585619739, 274197696, 380047491, 941382380, 117506066, 840625963, 323555257, 861972769, 816389285, 355249124, 585585143, 370081571, 566454253, 457074912, 279369493, 138951707, 885518071, 785889440, 991893383, 891288790, 606338186, 691495685, 307778732, 215988047, 152925044, 30868110, 309613419, 755883731, 1644167, 18680499, 867609582, 239638934, 924105373, 432823349, 304912321, 435820521, 784435178, 389942284, 175431275, 627820500, 684278738, 851670460, 173363864, 362468077, 95978044, 907919799, 667085025, 929434567, 430634174, 513978708, 151879590, 332767958, 179215555, 808266302, 280138765, 843173902, 512924790, 887363872, 265834416, 393636865, 702171341, 586235607, 432565174, 896174090, 553558497, 277690514, 108723834, 47455328, 650734007, 113290820, 170049189, 568630979, 753619590, 926319901, 133686938, 275909339, 283913582, 516971698, 664015140, 271903162, 974397292, 884450236, 828174839, 495454546, 54171065, 623965503, 436926663, 804679961, 17080611, 387858533, 299795837, 377620653, 510764727, 814821368, 106107947, 878827390, 929220063, 842628007, 353817668, 137553110, 263330573, 87082574, 22121417, 276448097, 355382837, 450182278, 601840080, 501983829, 118703331, 631310772, 31444829, 922525841, 738194332, 853179342, 970679126, 770974501, 699099934, 803687199, 292541147, 548144489, 262993130, 297362396, 696894540, 807250778, 954949072, 146282528, 194823974, 495119493, 216431599, 128078196, 800684876, 796135256, 264496777, 836061246, 370719640, 406705779, 207908842, 664533986, 958354522, 612686543, 777102446, 306140101, 153926187, 302288596, 71322708, 524700988, 916898235, 380751829, 890626438, 400486253, 90297549, 498506340, 925176094, 354643195, 544176798, 525465375, 279674702, 910974833, 455557740, 426595477, 394237939, 228363234, 117301934, 306637765, 793828431, 241588102, 378591204, 658243815, 971596248, 585726604, 963232161, 712017278, 905034574, 259687407, 350389391, 557263674, 937318231, 165091874, 509309670, 278570888, 117068546, 38854896, 705322677, 117794835, 608458842, 59822070, 910751387, 285662665, 740684548, 647596064, 629406014, 764996535, 717802134, 155956343, 571666035, 37561044, 777382471, 446955576, 616518780, 523608314, 533379624, 381798084, 76166145, 108169210, 311221579, 351047501, 171419089, 86982261, 467981775, 700051608, 81755095, 435752452, 782376961, 862245527, 62299619, 445477358, 764834086, 84708188, 179432381, 234999491, 61661618, 169530340, 997099562, 776680346, 843631643, 613113997, 783198225, 645000783, 365608541, 133283703, 895507337, 345878407, 76072706, 179147781, 302121354, 423004128, 134785705, 838508512, 80723263, 232236521, 430010951, 571508043, 295417607, 200766975, 20947302, 349153241, 279282511, 296469158, 196905404, 923524308, 650823894, 114143651, 694066214, 802520271, 772080507, 569053923, 527292820, 328329316, 369877568, 335322367, 699438178, 944231906, 649095439, 68720346, 950432844, 195753189, 799209488, 292625234, 547738587, 744124502, 73499557, 786575347, 850768431, 578259038, 856567803, 322392563, 139422398, 801747154, 118677647, 420199162, 815709714, 16459944, 261351046, 879297717, 604108656, 352762400, 966984599, 951323293, 633463983, 278137619, 32779102, 117523022, 914306181, 187750589, 736099159, 580926186, 949782482, 967122683, 191923516, 747548046, 460121628, 241645332, 887442058, 882088797, 122085341, 623862102, 178510791, 929722855, 6815903, 685959445, 287129577, 651656301, 328654906, 486988531, 730761201, 127112621, 149896530, 771762632, 108819516, 316217462, 350484507, 212814610, 520914939, 540636976, 307387734, 919502398, 679766543, 27407040, 888966085, 479134223, 557552857, 650183900, 224240846, 950094056, 943799936, 65268655, 915347591, 259986859, 694663864, 441515474, 283822745, 667348038, 298212462, 360445422, 870274516, 367280729, 836259705, 119572355, 357468427, 228567000, 809190517, 620040113, 918522133, 470389888, 471380511, 157186927, 984259842, 839655437, 119065528, 858014539, 835947850, 568401946, 259563317, 61721589, 365871114, 259340692, 624587345, 405433145, 619233603, 102140355, 240619460, 267617061, 975168383, 547570425, 81083129, 932354190, 86192483, 828996474, 449400338, 960313333, 71161250, 594812888, 354406419, 145917350, 570614270, 503959219, 991983586, 706709475, 490281999, 427608009, 535360559, 561728298, 297643937, 163290728, 285378692, 138299912, 25612806, 393491371, 734345785, 476337285, 248473258, 975214783, 909471010, 499434560, 343895531, 550759933, 484705735, 973328940, 946709033, 254671209, 285302686, 892259250, 830891554, 947743577, 413089328, 872091580, 355627791, 783697543, 94756194, 526704306, 132458221, 846167877, 310095514, 288699100, 50316588, 388631796, 37176270, 809632954, 593594383, 221541801, 146476104, 506835505, 859427521, 847879497, 600610979, 115568334, 329236299, 500218090, 830597657, 30874573, 241530093, 379562782, 143482364, 524544625, 274465107, 8468963, 509738592, 608311663, 544461157, 874402397, 119122677, 534626890, 977661905, 699613020, 863751160, 236371509, 880467456, 384500622, 903466600, 752209344, 229413655, 590013634, 315874443, 199881625, 530333894, 310794778, 288077078, 846357539, 467731166, 55571125, 337570760, 602095949, 239761292, 924141407, 146921176, 349989890, 816650647, 138884818, 604562736, 746653095, 361102827, 746020614, 693159259, 973868311, 95902063, 496389139, 610091630, 685966910, 388773067, 430633167, 238879110, 665189003, 862401100, 524434324, 64540986, 84793003, 877267862, 841006904, 344918262, 487765847, 400751939, 544801145, 27859043, 593444036, 359843806, 305933917, 157970168, 183554709, 643422186, 664064664, 608739124, 233879956, 452257541, 804038177, 197539952, 770411410, 675353244, 555940667, 692380609, 570174484, 389847839, 328409465, 235982440, 80030617, 467643027, 9660523, 420214423, 737868652, 776967644, 482865004, 797433958, 908232668, 749883727, 384225137, 905190858, 404578556, 132092483, 373096176, 929217705, 796667746, 381803605, 770556470, 973019850, 864315681, 64556433, 221688456, 249181177, 91790458, 764110649, 151048988, 361242779, 20134590, 801103189, 341643460, 61577145, 687872929, 354152754, 82259355, 73766986, 823785250, 151293732, 372779721, 450536574, 569578159, 877694581, 286635143, 334817158, 342459669, 184357665, 966188263, 648492950, 248947725, 56648551, 292733458, 616102790, 615334756, 62244658, 517958920, 433442544, 477981801, 687837668, 222532853, 93337645, 423421758, 433936003, 574977746, 985915246, 163045371, 93383983, 411137130, 893111989, 32989590, 836392918, 93643172, 383224648, 907396063, 566914020, 213746292, 552816088, 33995662, 607887448, 694597261, 527237119, 421761314, 164004787, 540741677, 741673706, 16669333, 662876764, 37559959, 564155077, 80349888, 188574817, 405272298, 117383746, 475959833, 372452894, 485828823, 24062034, 386946835, 436689972, 728414403, 671176753, 712428198, 857537419, 700860114, 442485166, 158149985, 190171876, 707164515, 372150244, 764704270, 146029348, 781072461, 532546791, 395881177, 969064680, 214069878, 938594405, 432510981, 723898385, 555251623, 172558642, 837275626, 968979825, 555745992, 379961080, 808796976, 609109760, 10532523, 224707394, 927632244, 20854823, 208661341, 602468534, 961326322, 90131964, 145488724, 799725411, 723843405, 445664541, 130635517, 256278627, 753553562, 752105431, 723192881, 790143559, 828293129, 726491755, 765869528, 901877960, 24807810, 832864892, 977679627, 311587134, 388624774, 436487914, 866131102, 623335631, 25537616, 30801263, 795670814, 550151876, 836207469, 739817368, 783684611, 235949964, 3528237, 487383616, 401323089, 537450372, 83360858, 264311184, 928162665, 799519153, 611591689, 320577125, 359005455, 173247351, 90038081, 880834334, 675037943, 746319612, 741844534, 352120683, 170753229, 403056338, 690031599, 559893875, 5431649, 979780266, 620263197, 244022667, 543364532, 598070849, 258212646, 429670035, 577703226, 190524945, 686413862, 129106856, 749399019, 855438440, 698729746, 934765083, 461915466, 195065402, 396203909, 994750125, 676884417, 545306362, 43721767, 401392579, 446366183, 565173479, 110718501, 892491219, 350200629, 773444570, 314473649, 881175341, 700789739, 795588797, 774396852, 206829010, 291886626, 966737938, 899118868, 451052111, 585029435, 992391267, 234403493, 503067524, 365474031, 751838372, 558009671, 913737300, 649385973, 452892799, 188907399, 431126526, 649519731, 789803159, 218091099, 270203962, 826312362, 212113181, 950178133, 392723286, 610548647, 888845582, 68134999, 220042541, 405745508, 478016560, 759398697, 712877016, 954850257, 56474559, 961097138, 702115228, 3113975, 981263033, 645357183, 969138727, 610363356, 9372482, 79279359, 590896866, 554377624, 454766105, 677051066, 800994439, 257051092, 886204559, 776528553, 9783661, 436550164, 76420817, 603143813, 634567589, 509964566, 338007820, 430622748, 102322409, 571364448, 999302538, 521813659, 425099611, 780358630, 932290267, 453586762, 442658727, 102494013, 151536700, 51057726, 229248517, 54219725, 337648578, 283838519, 802377334, 564195927, 334231266, 405511825, 263880342, 225115809, 817071379, 372650009, 832282301, 535233076, 799015940, 885715572, 756846502, 917476349, 789433658, 301558128, 907861785, 33297003, 962201382, 920897871, 883588388, 895295187, 562807813, 487192784, 755371412, 66569566, 984223734, 701219530, 923112008, 811271738, 379569766, 304141663, 769432074, 16625652, 422956056, 84357376, 357873921, 308545913, 992684024, 795159991, 349582353, 169205946, 501307850, 444868083, 284977749, 965617176, 736358373, 552554610, 519617828, 1728435, 77232063, 300330496, 62629554, 923986183, 17653803, 402119922, 171872577, 899613491, 63965786, 174358002, 383181324, 39731797, 156827695, 906165611, 394826168, 315197448, 365078864, 373491727, 250210239, 260390457, 364521704, 487180094, 79217939, 153243360, 110032015, 730902555, 64533351, 589775025, 953299463, 295382711, 735836890, 989032538, 298021791, 758547182, 188183156, 48837703, 642235168, 594050295, 70312477, 170857872, 647145958, 971995854, 307835423, 950932065, 860816221, 298500258, 98350765, 959907008, 625354402, 750468033, 938335772, 96060622, 779364875, 589244651, 179377242, 519482074, 11884348, 873634747, 698454037, 971490371, 837551971, 776501181, 901829786, 176761372, 936826416, 222854646, 905683335, 686318137, 5849724, 678435193, 630428321, 162259492, 961950506, 533650280, 476783666, 250458423, 485298258, 276923388, 978157159, 686562240, 2461319, 456666786, 208103695, 632430626, 482623360, 110321603, 44795322, 849174755, 940407168, 390929229, 481954717, 439541950, 66209922, 509265748, 289957704, 761110655, 91832229, 892061447, 205895274, 131689191, 136261723, 159782526, 321701683, 503728538, 351035894, 651822922, 213992623, 245502867, 646908904, 252631208, 748822594, 954758386, 867082399, 887907668, 235641780, 255490207, 466843901, 525473240, 718956139, 995479176, 525066613, 616696926, 560943065, 689469789, 768105008, 233871821, 226742512, 367984622, 919810306, 580667730, 652528764, 465277980, 909518119, 814364761, 340233816, 821569333, 362107146, 306876147, 831712996, 63166539, 823453117, 15859888, 60137116, 579392175, 197125415, 617431509, 661314500, 122472198, 438585353, 911058066, 749979568, 470926586, 6587014, 544861479, 221454056, 206019344, 740666341, 465914621, 918690984, 301210744, 50683205, 520445902, 860939864, 402827706, 348174100, 151823295, 142952046, 607096712, 743816200, 592220447, 754509562, 648397454, 258840901, 618562180, 542862670, 130232544, 781560760, 648273313, 185791463, 15465197, 762075938, 3863788, 623076549, 748849386, 39609705, 823211169, 54658502, 778575485, 636237363, 221852574, 794584101, 110414246, 401867582, 930059488, 799179825, 81185687, 453020256, 591518926, 950780233, 773207339, 285886859, 365466883, 157507493, 747892615, 22228860, 634070385, 64801961, 123395606, 634529790, 380224261, 800169033, 41678798, 923633806, 680586062, 277597023, 60116107, 393343729, 950367938, 324966558, 942393728, 435556127, 72750641, 990252148, 182751118, 160379202, 275112081, 22958772, 13910780, 800916918, 628705391, 302099855, 480591823, 27404497, 731378981, 718045718, 483620970, 713303570, 858494543, 736147139, 68320196, 728656660, 515877487, 127273276, 110459885, 602579712, 395647665, 94138508, 728098142, 47050033, 359652488, 411429268, 826750305, 129547505, 770866104, 84823060, 434852934, 380463581, 705678392, 446898413, 854815231, 258397860, 881023435, 981616722, 417074066, 685861593, 459495417, 93869580, 881273580, 997983117, 102902159, 33434117, 923540391, 821127812, 761560814, 976276553, 177267732, 731974958, 54656684, 118679438, 262501506, 523614734, 492858880, 802483885, 553277992, 82788339, 196109156, 207350064, 657859269, 450583350, 859375081, 249411469, 719655460, 838256565, 11978978, 817686887, 905023510, 934601637, 492333084, 500987933, 86032871, 256522669, 721463853, 618574999, 462967633, 573984853, 911209107, 453928920, 960283889, 84678022, 705107687, 937671542, 34910974, 639135976, 729594666, 44117489, 51235591, 724018578, 121496311, 696982526, 250396946, 368452698, 764425476, 214406209, 352961768, 31111001, 666363246, 148794398, 560001969, 190885370, 236422597, 895176637, 69550585, 631069496, 70917116, 15392036, 163013425, 799830054, 220117287, 754713027, 133295185, 754412207, 274878656, 174582360, 274431416, 894270293, 693711409, 893775109, 958715021, 783852766, 485509878, 681634285, 102123749, 134674998, 848055809, 229044272, 810581276, 953161813, 828199421, 330287044, 72264357, 144163242, 382833088, 869978781, 513474411, 608987738, 821246233, 238482661, 567656832, 53041884, 707001280, 49648170, 671295077, 874511031, 289342995, 349857972, 323228274, 647276856, 211557613, 767863145, 989979287, 656893057, 395204324, 811275207, 719790934, 523995108, 193511877, 312779574, 72041866, 106504309, 636605454, 380593722, 491947354, 933701430, 807056262, 254728843, 999334297, 658304831, 796459396, 318171931, 463673170, 998043534, 642152292, 498421256, 72977843, 313990373, 448805421, 894201862, 161475735, 769466260, 884625371, 116070037, 135923979, 729691842, 936805009, 106873242, 575807711, 225883044, 389558752, 529589059, 189475448, 649907177, 437367310, 617295886, 154327647, 63442312, 217942961, 489950645, 761506826, 614405456, 949889348, 195655088, 358717685, 481890021, 337947107, 691996020, 899927271, 912545303, 860534982, 834379752, 10147191, 117923381, 282257379, 16726792, 151224002, 789824453, 815048669, 493196840, 632919682, 733995829, 18719756, 880586070, 632825878, 975686917, 144126226, 649241734, 15785222, 220386133, 211920782, 704623249, 459164191, 390063765, 687399155, 487351229, 886661796, 783301869, 277127095, 601351079, 832896799, 326232548, 229640855, 25589653, 449215475, 513366825, 645823506, 842229589, 573413956, 428545447, 502895705, 682994040, 364180665, 368253015, 735149096, 230699540, 488265468, 296063719, 886033875, 134562916, 526925308, 187242236, 98742863, 9397181, 951645946, 272810610, 970123001, 457047580, 234619606, 939484285, 838654706, 751785589, 474572405, 670568929, 224620158, 970161105, 309945092, 842184137, 9161593, 126059395, 212617692, 644356030, 720131581, 107302565, 995266412, 272660597, 84218395, 394230867, 330328831, 70277740, 561416954, 303601873, 77301015, 184729732, 318057302, 394246042, 858871233, 585280746, 223083242, 938920794, 878214308, 456258088, 399055633, 561249708, 57939671, 674146772, 511322072, 734606849, 226907131, 243059620, 40391163, 396857905, 470397201, 917256657, 694492841, 489236565, 210141947, 46207288, 683506647, 552338099, 31649255, 806508060, 311307613, 258044536, 445805842, 533360405, 165148780, 174273765, 565051074, 110407577, 733820170, 413226931, 850921283, 281963467, 892425406, 653221170, 247214868, 64504890, 723774071, 773843237, 786685217, 643366401, 225401998, 969602066, 548132865, 640167919, 26828008, 193251622, 93120916, 137864942, 885208241, 418501178, 406883770, 513607271, 739835744, 230020142, 940334282, 849109322, 153773129, 8952886, 987801434, 85891679, 364697611, 93854906, 234460677, 825982626, 33188023, 134525949, 136143170, 74100068, 902152655, 947918606, 817397441, 531057967, 586697752, 326569397, 512065720, 389238394, 13749902, 11852853, 920903038, 485664199, 596799209, 856818745, 631201097, 585828596, 163455227, 706475380, 861987310, 893654169, 732801457, 298294918, 506729123, 998238661, 123867733, 963295336, 787387782, 373161313, 619461974, 91719364, 398290435, 159395293, 431349880, 689404934, 386598861, 69540756, 57259587, 208010628, 681359455, 227705172, 539495475, 920589892, 55500715, 8621601, 948040427, 779642036, 738385452, 773497799, 713133833, 748031532, 894785662, 966328554, 641006158, 787718489, 783569135, 932679674, 740245161, 524634189, 2222621, 750502244, 545559542, 432570630, 384357913, 555865825, 976708360, 966272221, 752604370, 500086058, 54330635, 357598951, 153470567, 702222392, 143041639, 831199247, 963226472, 574642906, 238898152, 349162127, 378049164, 185457090, 184178666, 637064648, 690345153, 501312676, 363680133, 778260980, 819904592, 607042057, 648466927, 882472159, 815163765, 308784262, 819481391, 550470879, 323721766, 324987196, 128731564, 33412656, 736449157, 86498310, 994921508, 899814774, 288707724, 720758338, 59945847, 929897056, 539665625, 757833975, 62009687, 52144658, 982176963, 506511309, 535302786, 484585262, 252605621, 29221006, 718617678, 161581812, 526276254, 850316349, 301606427, 171025310, 817584633, 272248531, 207531357, 538318778, 136075196, 437321838, 100448790, 325730506, 252734814, 649952564, 345366046, 764733030, 56280647, 64322710, 580745732, 17378552, 909879159, 652100602, 342101129, 326831269, 106183370, 377254765, 280335919, 371253150, 309860420, 180521472, 817989331, 114738282, 743812539, 653811520, 159804971, 110459838, 741888539, 507463800, 391677987, 448434460, 56144755, 554126666, 391586328, 449498549, 192009928, 289645327, 61328760, 523665592, 502041279, 746221325, 522194214, 1587502, 982784451, 981530300, 732230325, 864633519, 580762088, 687849410, 699403549, 624401647, 747037509, 722596944, 985091609, 1437584, 253397676, 716557998, 830453440, 847305528, 538792672, 794045363, 912774848, 653292497, 954317234, 960976356, 936341427, 983506780, 108777022, 930869316, 544760763, 868265760, 20343292, 542919663, 669446481, 94011242, 794840291, 65135367, 449669076, 442378931, 579485152, 652443849, 925904586, 342700499, 936228351, 894702983, 694024225, 202011126, 473045874, 869035306, 414087412, 804858091, 977104558, 926909542, 239120285, 977574892, 424406645, 254075633, 764047195, 9943087, 225677778, 233248916, 146129231, 614797461, 931366506, 493450434, 933377059, 477915853, 794527732, 396052198, 627083766, 123266545, 576280187, 43835697, 275820546, 371716890, 554657463, 482986164, 641560120, 835254263, 856293061, 53503002, 604441751, 334355480, 879079665, 625476544, 885438299, 996840576, 31944734, 854149300, 876958668, 596326501, 569189069, 546834843, 182578652, 922835134, 969664412, 663070114, 266142863, 884068676, 814041890, 583925918, 36496265, 357454191, 274017259, 238155087, 209117074, 986092291, 449003536, 86690039, 110191334, 541362025, 122980, 543441249, 764998211, 570412325, 270984209, 165067923, 596549644, 457507600, 576884586, 288403243, 857121117, 493598848, 417547418, 802295584, 511754747, 154006568, 8575246, 599672192, 856991228, 155491765, 175565743, 456230665, 53637205, 723747141, 236978429, 377564946, 56254505, 962524462, 384265302, 55898900, 301186910, 537614715, 792195095, 205542115, 663874710, 846457457, 650178554, 216624268, 954925536, 815580447, 372721776, 980043165, 511521780, 640341555, 794783528, 130166681, 139033113, 236663702, 914419740, 195651330, 410140714, 203376094, 959818171, 284186051, 56311001, 128300493, 728736313, 275519361, 784683807, 108079845, 827307686, 174973718, 99583100, 630247067, 276190655, 690283843, 757660607, 914277109, 394135629, 630866276, 342546834, 867969653, 565035007, 389854945, 188162872, 231042874, 596861529, 735872144, 675649622, 63225235, 970111261, 392699176, 169681787, 901429271, 325989123, 71841601, 156967203, 839154898, 535240994, 324297611, 332402706, 954014857, 491626495, 844739593, 297980192, 52965430, 841913275, 561558729, 419908634, 533325884, 776954971, 150122086, 578713027, 874024763, 521702454, 840771098, 726719709, 570323525, 923786849, 281840942, 590885459, 696798476, 528003765, 87592792, 302493651, 613791893, 620610438, 451284428, 594961514, 885800617, 675776001, 500322049, 487303813, 191726947, 899465483, 33732432, 920647989, 855018261, 650065276, 523484431, 652069162, 530858448, 529077544, 738943132, 152783501, 928587408, 478321622, 647531074, 926039911, 78012250, 98232104, 176063512, 605438839, 15971960, 520281376, 119967754, 651919911, 699799231, 430867543, 93165837, 475402335, 638591285, 5248655, 757461114, 688013992, 26113016, 70642250, 301659190, 43063891, 984192077, 732251869, 903218977, 326588246, 808989753, 528262033, 459267830, 496072260, 722183740, 650061187, 972218514, 61185723, 848780555, 817205647, 438593596, 488642463, 4721609, 219104011, 968483415, 310936320, 4309055, 598297025, 389714631, 348282695, 257617826, 675947483, 380058204, 204521470, 132671040, 150146963, 860826792, 627021346, 881571442, 624115416, 257229537, 127190740, 969691706, 2242197, 224393564, 321677477, 693728840, 563816539, 611722327, 613190054, 493661018, 355938263, 35630502, 289071088, 9910765, 542056694, 280063385, 29885690, 380542968, 373483347, 314698859, 255326679, 814694075, 736207747, 778042337, 42607015, 667333888, 619710483, 548275999, 404492999, 49775754, 221596254, 947741195, 527774587, 15860235, 987517509, 166997191, 535755107, 372746089, 705409195, 185617689, 834025671, 945389695, 352692016, 770850860, 334197952, 396533309, 899920884, 234743590, 442112705, 282715677, 274276131, 19220033, 781101698, 753832877, 704127188, 178286217, 852488270, 559649264, 700530391, 905826779, 786108750, 774969379, 733307522, 824582331, 705414040, 447392762, 761185156, 878200651, 235672696, 829836430, 906082289, 657618459, 709221379, 584764901, 117556369, 555055279, 553037374, 873024823, 750962010, 208747675, 405582120, 54506567, 454257113, 683390184, 502750452, 307784829, 930036828, 44810881, 64875908, 716357985, 754821047, 371587005, 70276148, 463677059, 52497641, 520005460, 432073131, 797746006, 60497175, 551448005, 620141098, 689334553, 624453253, 244510896, 436127632, 151143069, 589160740, 934859108, 909377514, 638321916, 311477080, 132783308, 170608583, 768521090, 566774452, 63990887, 584066338, 355668894, 590529510, 532250676, 34163934, 618130424, 375252259, 357213763, 30496442, 732587029, 157894001, 437536434, 452202444, 924435772, 101214668, 990766652, 293478301, 781294342, 224032917, 784279121, 490709986, 878570717, 251707422, 733288942, 249057724, 915477996, 978596008, 419293533, 917023084, 253038593, 536310334, 494807925, 668493228, 133631548, 92924917, 358856110, 532560207, 694980401, 379895635, 837872635, 598986571, 446471775, 239691262, 568096356, 946004539, 128322558, 511800815, 744133859, 384893574, 772265732, 683948902, 601030120, 350536519, 92342067, 822798057, 80319215, 38586303, 570596143, 639419449, 946883567, 696660480, 53702269, 684716309, 916590457, 74895009, 402250407, 759447432, 313036864, 384721950, 443842521, 693555646, 104182919, 62225391, 284432069, 829785209, 22511927, 734751368, 723239883, 884269262, 333501267, 758692886, 846738857, 254212179, 122002343, 432425179, 833402394, 796780324, 302915039, 121966193, 656337681, 567756248, 573071007, 388838525, 756026038, 731844076, 916069027, 798519628, 795993549, 518671199, 944606611, 643143331, 149260527, 840276703, 10136624, 758720936, 143398516, 612404845, 828152247, 155812760, 67630501, 478011917, 235810487, 687196141, 127641743, 142948260, 35699271, 391947966, 32687478, 790069096, 747166860, 62765129, 800014459, 140759044, 448764855, 296063154, 195698858, 792445502, 550916285, 904502696, 474188702, 154598154, 408748719, 730234563, 686431856, 795878205, 156935689, 155400703, 85782243, 322666084, 854044925, 322332252, 377491124, 42839435, 546688323, 545871612, 241502383, 936743042, 136394195, 422795479, 988486026, 53023213, 706579429, 154671957, 274856710, 741328699, 472022220, 953519040, 726156911, 634857294, 248013058, 368553538, 528428595, 266533803, 134998374, 105144579, 539865331, 314112340, 791154637, 774311530, 904545581, 804534902, 721624202, 607450829, 697937171, 895540184, 476257762, 362521690, 224113385, 929260497, 864698354, 875985289, 298845948, 258859099, 385518619, 147344169, 784043236, 840192706, 583199143, 972907643, 17849421, 930131432, 888839860, 834477440, 515139388, 148398951, 324701829, 591529443, 842385572, 374011040, 804965598, 462918908, 812162033, 481506903, 640657661, 560798902, 586443954, 234632180, 705769683, 989196677, 700169733, 932189342, 473580580, 58386475, 182020649, 505911339, 930744344, 242568882, 672964773, 947244009, 535650343, 499148152, 368119931, 934872125, 295848055, 463774018, 395616062, 832551757, 414447691, 557190708, 475193124, 461599926, 662968420, 121775678, 655795381, 577268589, 264496201, 844962422, 467822722, 403732485, 114411639, 194234375, 785599590, 824290198, 647028576, 108748668, 959134722, 644637663, 365907150, 724512205, 127855946, 87272925, 672678667, 11323924, 481511425, 653146161, 923413254, 418156191, 735008073, 842774835, 990946267, 563833699, 44309961, 266861627, 735138646, 206631291, 955855293, 70180134, 184902781, 261693339, 638810708, 972664916, 820775049, 750213719, 487753877, 629737497, 331118804, 997480091, 418552488, 788410635, 547994323, 933305781, 677409093, 884926578, 309496626, 312501042, 997340705, 681236893, 797842451, 503734030, 365422798, 428089504, 728067784, 707056752, 890656172, 473936424, 73225061, 824663447, 987710862, 438040345, 933880554, 222650123, 506487204, 837131207, 156145075, 429304567, 951933929, 142573228, 342903947, 948444430, 914475341, 805304811, 689962616, 668256052, 632029162, 838368218, 583071652, 831487, 170174685, 997893043, 707582290, 666463842, 863711349, 87498648, 406658246, 98739421, 848236731, 110919549, 328250696, 495352339, 320948358, 995674196, 559989220, 119986374, 557478474, 696207428, 345028527, 313710851, 64220264, 540158258, 736272193, 736210554, 756383722, 724520764, 873425527, 406624495, 935364533, 949822275, 637784794, 870642966, 577132165, 771088138, 307704315, 873540358, 505535306, 304056863, 141940920, 871187317, 978426692, 241872446, 757584554, 258535686, 242765697, 743322006, 832785280, 279690602, 419977580, 667158453, 512635013, 116294278, 877524265, 917579296, 514652486, 39915424, 327244515, 704167696, 647444442, 286163920, 453211165, 350311622, 122750789, 757549000, 989452206, 844954157, 792174636, 675386257, 328854396, 140197889, 779562374, 344840790, 670595838, 950808860, 481701643, 150776368, 510976820, 983991822, 530042265, 46157104, 947744949, 861537254, 29172731, 490471719, 137762904, 731706291, 392369918, 137031938, 764622353, 323422412, 688461127, 324724699, 174142364, 122883055, 71561478, 972294411, 400605649, 829709158, 333971857, 57343485, 377474042, 414656013, 926468237, 328494432, 323469157, 662511344, 605398767, 767486173, 972810528, 602511811, 890570737, 534481793, 82687635, 218331595, 527739654, 934583832, 696599433, 785194509, 320524596, 52590127, 261318805, 389680678, 772499369, 328202768, 984909613, 224221164, 702713806, 950186768, 582234260, 478286795, 407102967, 609954726, 347419683, 356768770, 360447108, 924039556, 278504412, 996720834, 429647072, 633259370, 41138647, 442640618, 606845192, 508011008, 913925471, 259167491, 993781696, 165475601, 932289874, 14753833, 437080064, 71685657, 757675484, 716262936, 85574935, 113893897, 819204843, 349305608, 597734750, 308562203, 619065423, 620221952, 981252170, 134120251, 757856313, 697992587, 551684940, 838091976, 648470713, 923743936, 632946031, 224173318, 482557, 25917386, 535598439, 761855734, 325525146, 561192473, 47819002, 115237059, 745999308, 955860457, 292523452, 151858296, 765861019, 378730335, 764171826, 707559683, 601015469, 577921328, 559897905, 349851352, 714043250, 728123832, 704100256, 277913960, 740717809, 185263436, 767639136, 759589000, 542291122, 158734356, 902599671, 138385365, 503722474, 209554260, 616011666, 444420838, 190512130, 652776713, 6861969, 362599179, 671085574, 69675725, 855304616, 992417649, 965003414, 34022412, 546591731, 274299269, 9587064, 626837959, 89794346, 340660961, 69689478, 690001322, 274324560, 733805559, 237886414, 305455331, 685817411, 906607210, 395201244, 145661543, 613895389, 272353001, 524926512, 292030358, 751548748, 958165360, 187554576, 485489670, 682688272, 511339252, 389551616, 535885257, 265533499, 947672522, 358825848, 282220620, 614137165, 487648844, 260454821, 842523172, 336665098, 924148974, 710940765, 514674705, 306776697, 88271316, 444774756, 407845338, 600355222, 698188703, 848109958, 533982645, 341116448, 201342052, 540213352, 8199866, 141819287, 492970138, 873166155, 644210546, 119777696, 940207120, 611411074, 552778997, 729435904, 565929956, 182128644, 797841671, 361037347, 275438989, 424060856, 250636392, 864112691, 670890582, 341747623, 696952437, 341602154, 606111938, 387744899, 129717385, 85855711, 117734830, 112566179, 251949445, 97053846, 215580572, 662924442, 420799234, 286482757, 653543811, 51400624, 760293653, 525524460, 414851523, 841084917, 967628811, 426467947, 614252130, 30707002, 61909892, 202486743, 302848070, 706561627, 662479391, 317927633, 511908138, 717714227, 436553945, 804469373, 100020778, 190788243, 159639031, 332014416, 308279266, 961911441, 964076645, 873167673, 489421718, 532314498, 481332285, 877165505, 256831195, 692931077, 106056091, 171340789, 318046738, 142750312, 184197156, 304791917, 969505347, 201238276, 573578445, 824431145, 743832060, 452720356, 43625969, 250770948, 245760375, 334562970, 41579905, 513618976, 92397234, 479973055, 852277975, 649265936, 738791702, 23649869, 381600410, 884600134, 288043852, 484854122, 372057251, 973344021, 966062509, 987739009, 668030732, 106981872, 339805439, 948622389, 716820012, 364464326, 346891376, 696038293, 293915382, 566022825, 408967912, 444609752, 821275786, 720077810, 748893073, 660719508, 185686365, 882535508, 310341478, 802900878, 529347335, 399177374, 765925856, 53300404, 239561767, 137532773, 799799843, 959618399, 607972374, 895223415, 486503451, 463205163, 385861244, 638460835, 201668050, 520082574, 88497657, 635470854, 263318629, 598736022, 803586606, 825584248, 74628523, 261656342, 64486489, 144114793, 293646278, 158347576, 881144828, 777037806, 768611789, 936431937, 660484927, 596250819, 276778793, 55571700, 918142032, 894928692, 807470516, 157466920, 833875300, 60630460, 773295767, 931356008, 15953996, 314549443, 141199519, 308960062, 937499062, 270590208, 267703099, 922860305, 319390062, 298184237, 124688873, 374981886, 49038406, 383000151, 439774227, 438062378, 738516112, 579803017, 68582575, 718690789, 753437862, 364300994, 720663936, 143840468, 204285786, 889433243, 173857361, 868104381, 952186598, 354947941, 679287675, 766836056, 413095114, 9640369, 38264751, 152552752, 413589537, 356364159, 860641820, 567392354, 526097773, 380514271, 839343448, 332716369, 638096850, 822913435, 890959230, 173637092, 16700898, 542723040, 248899867, 987472546, 270140678, 2929139, 830720979, 882044120, 850426755, 386807306, 328325938, 771224806, 360693085, 224134800, 111162424, 320678773, 127321903, 296574463, 465216551, 539786873, 759631226, 660206928, 56315602, 57181874, 198750576, 350845158, 411364720, 392930076, 710249922, 119516272, 534312988, 972018966, 552403214, 819738555, 850138696, 313145015, 447020722, 333974578, 218288049, 575645600, 985221654, 605546550, 582248864, 771891258, 537505235, 627312332, 661943504, 953371667, 473272580, 80629315, 348055566, 538661411, 847861194, 763783671, 778247784, 54600227, 78130413, 887719206, 857655904, 634110031, 528791282, 427807966, 729768806, 979270789, 21810296, 371170101, 918671714, 102963814, 817431353, 877665666, 113688571, 606187244, 649834352, 460533559, 923978862, 682566890, 731940708, 400721820, 531404097, 55995190, 360576746, 3641227, 593427016, 537885627, 4620882, 109984910, 384172756, 307264688, 724942985, 944521843, 892133099, 395395123, 928887823, 49689458, 209010535, 782126839, 254930103, 693898756, 67088814, 120468579, 993974379, 531304597, 392717196, 536211951, 826170269, 629430706, 827696626, 56966873, 523038147, 201786842, 90165248, 981057427, 45524306, 211277071, 435756108, 217341875, 120609654, 933513875, 627118691, 760153471, 650448204, 48554591, 107054292, 207724310, 291330774, 391315975, 896856435, 448925433, 759872365, 654428857, 117547279, 203098404, 768604009, 661931598, 178936133, 118062119, 733028834, 291676336, 635221747, 845137830, 713387326, 746448150, 976248014, 739044329, 807140976, 298265439, 410060335, 471408256, 2152472, 776368872, 932226372, 22933523, 885136165, 382356100, 43522705, 218636447, 241084455, 298751288, 665847415, 643190041, 302431060, 496555458, 945763015, 188357068, 683571031, 593046845, 121245991, 201930647, 753380450, 248025970, 632773249, 762887352, 980260144, 600839619, 723378501, 39574818, 280717927, 192683381, 555655739, 939044123, 120046929, 259251191, 314755048, 849350656, 611578549, 20019465, 650291332, 516942195, 482816860, 262950878, 851833695, 94645359, 623734897, 163436966, 156333584, 545332093, 609321597, 943345542, 112794196, 467479483, 584200945, 470599368, 983455340, 850699533, 811460482, 824638171, 429526803, 427825220, 622631571, 414727919, 950218743, 784099768, 376726897, 810044283, 844806364, 616679039, 701447547, 187299260, 173258746, 361750306, 845048441, 152740119, 566519139, 62195671, 621231896, 722850631, 942175368, 136842305, 985394866, 547747642, 665312984, 413517768, 263856131, 794478547, 995621141, 174958368, 900943567, 715958479, 802831297, 278234817, 122297111, 95925981, 229541655, 868979173, 186797797, 74455492, 199891464, 196923495, 851584140, 722756819, 458441589, 175217220, 136610378, 258171514, 760181774, 638903109, 592512474, 516724890, 445797089, 507873069, 468333090, 421698963, 479387362, 144842896, 858146988, 487512393, 807680846, 274711944, 304132858, 792673932, 348582141, 390142207, 401575771, 244042345, 627107344, 667566541, 520598589, 553278595, 164246416, 220154100, 953035334, 254904190, 428889571, 283676528, 681023593, 905784610, 26831566, 899854482, 886276399, 549401579, 60884619, 838750316, 939522153, 118487834, 310928891, 870421145, 881960250, 397987261, 657768655, 616263751, 539399832, 855083048, 253763624, 393058502, 396059481, 7710221, 704661287, 347421612, 928243155, 713442620, 343852777, 969968905, 275092074, 62386840, 349851500, 835603748, 766663396, 505446068, 620618599, 57072908, 728002481, 568169316, 418490693, 595662764, 482924112, 401545187, 914367431, 847978626, 406226434, 336798617, 325587835, 348546591, 177722576, 134492484, 334500991, 199730328, 683664617, 520290749, 728302858, 672302048, 891642881, 962833607, 808884061, 713419144, 848366583, 514265410, 182945037, 753961428, 650235435, 304728467, 832520763, 139721563, 778585125, 732661889, 398840113, 339792025, 712103213, 604569734, 213671332, 118987689, 851251753, 88235824, 123313840, 253304450, 222309897, 754625011, 288864046, 734812868, 905907612, 567044439, 609952250, 214929063, 872068961, 832873598, 224155075, 571745289, 539443912, 980431306, 634842369, 260281556, 230097438, 540158707, 13494598, 729514877, 425118558, 958327299, 409265309, 853961539, 288460244, 61997681, 908028506, 156265148, 756055206, 444662453, 459602289, 322318259, 762200476, 457842998, 754367450, 293563310, 429509245, 7631211, 281091029, 357564048, 909111125, 405867657, 12854260, 406756345, 933839089, 881247179, 503678689, 847924266, 588137492, 544364758, 85885317, 438938065, 530771029, 675354042, 439232415, 511421596, 751860166, 276131825, 540177455, 862362449, 880717920, 571763790, 216997795, 696846367, 11880674, 29865540, 274554509, 741248435, 917993907, 582069270, 216971627, 239127628, 771822698, 969762585, 969714506, 225514113, 337849289, 280843212, 480327049, 10795566, 347655899, 428876818, 207351248, 363937885, 940064515, 234373279, 105566075, 559757367, 993914817, 782338851, 917266493, 440440327, 788059753, 707275178, 538682314, 363446716, 923219556, 893040788, 108600299, 878142920, 289243269, 351748014, 894512617, 71318602, 989236488, 974809618, 135715819, 338313562, 73840429, 783923971, 89495948, 435235654, 53782510, 967184607, 214976249, 732831789, 75120431, 783051424, 104649193, 24720272, 476256400, 856883019, 138940324, 528250259, 120463987, 939534226, 110073129, 326624143, 430087522, 32463462, 844052102, 866681985, 280338433, 666471240, 622028693, 399373637, 909507341, 675866740, 239907064, 441823302, 969029231, 244739757, 402266172, 347382768, 558507472, 213768138, 23640508, 700355498, 459599819, 790578189, 406227710, 433776751, 176638368, 983584647, 510462993, 792360434, 363090123, 223840503, 522922419, 494597073, 939175210, 616561193, 450118805, 752565833, 576797294, 477776996, 957683039, 184729594, 179805669, 937629277, 958657844, 158830750, 891967975, 119693139, 312911444, 383806616, 886584244, 571658667, 628023587, 768020810, 45667712, 348638422, 859140299, 380033630, 708529067, 686127408, 929846045, 3638660, 77158068, 330573130, 354997028, 945039781, 908585295, 441571973, 960711328, 545474296, 209745650, 946427905, 205085589, 788449949, 206984174, 684713310, 462284377, 121988443, 615958945, 940584446, 250759172, 860090203, 443785191, 935919132, 768851997, 301122727, 794884111, 832167696, 764019031, 619067414, 14871767, 176893874, 972770954, 656330560, 458983505, 688120574, 43872673, 311118529, 630129740, 39744331, 699076643, 322822265, 371183539, 417513406, 850874473, 796422579, 922333040, 682738385, 705342947, 360440177, 416746245, 465014785, 944052932, 310525682, 1850210, 325829183, 662889567, 181616250, 682804747, 908945203, 446353410, 233305599, 245059633, 138307510, 404556343, 382137726, 908272398, 734493794, 670638829, 298683160, 25237091, 217395951, 532092833, 62515900, 804134443, 711340095, 539628256, 896062106, 387373457, 718976180, 241112212, 367844138, 426507476, 75984109, 559221792, 213165884, 202530598, 211410089, 636924552, 734140286, 872826348, 743830867, 210343490, 831670862, 424696589, 377159785, 147362626, 705605847, 605220862, 741947346, 225759468, 107960809, 989755490, 888395160, 909762627, 338387261, 840452428, 313685761, 199907481, 868084136, 985942178, 515356761, 912221412, 115359044, 408866706, 584289705, 283051945, 578043273, 682105622, 917711772, 919219868, 571397361, 48226357, 924265409, 852959486, 714302094, 30253442, 253652485, 718352336, 271089986, 369600418, 502575299, 613460445, 291998040, 772837291, 559012214, 810514070, 849798442, 19398638, 566672613, 424564513, 234822113, 129635425, 383894562, 326654371, 583202920, 646277411, 471042978, 32768695, 489669411, 858016935, 293793302, 898303903, 561080712, 322368850, 606274904, 411819410, 735744611, 558177818, 238398935, 510601187, 715472482, 914227793, 795560556, 479665434, 712952170, 563740994, 78450691, 702037593, 337891618, 531687179, 653203221, 948010264, 309552814, 119204520, 471337115, 805213491, 452423949, 410637599, 267105269, 104687601, 23613287, 251108821, 440804991, 10363600, 623062417, 555789430, 442237857, 840880547, 265797170, 912574851, 317905435, 380682099, 815909260, 264931650, 275848678, 208477600, 13595266, 756560869, 75134172, 755129241, 205743645, 788477402, 706617513, 141916487, 455105126, 533566306, 550307114, 311518267, 677533294, 939096451, 914780702, 662470713, 224646102, 789220676, 310856875, 501600931, 33515658, 989495706, 165004274, 878794021, 964955787, 352314786, 773794939, 768629587, 728340096, 81133988, 467956681, 262832104, 259364126, 322553086, 342814171, 185884890, 687180524, 72755813, 505646776, 957927951, 487636577, 943872701, 485390577, 96945818, 144640202, 179245200, 743352466, 589411782, 244831826, 894846468, 97774359, 4899483, 227609134, 429218261, 252961944, 161254712, 471365306, 496162864, 960417470, 729116573, 747194693, 376414588, 392389080, 837024192, 360309347, 189411704, 229769406, 9957248, 392955719, 963011360, 519492462, 230646822, 841503333, 516305523, 224872316, 943419841, 323937910, 182689232, 808391587, 361053120, 739700097, 768487926, 230914371, 552669508, 87541609, 186184712, 790483755, 998473437, 189062100, 470230429, 300792221, 854035064, 955750905, 501747790, 808914452, 486499464, 151643142, 405855455, 682758604, 765575892, 500100529, 577650941, 470118635, 409497514, 863827489, 808289745, 205801100, 256897078, 269779033, 493677801, 158175415, 562026625, 706740847, 169646196, 8458415, 666554062, 446670900, 587633914, 569995496, 408451044, 255109149, 80197981, 364575139, 267803735, 641987844, 643291537, 511252249, 196637058, 457574597, 172060886, 800819346, 580719493, 302195092, 244292805, 396332967, 807096873, 53874486, 11569066, 424467406, 392893121, 132323910, 612542599, 960601070, 925862403, 160039163, 675123464, 932376261, 76944727, 424124596, 831010178, 574170875, 579907397, 139254847, 841499301, 723352979, 541093916, 521179198, 707320947, 721194407, 424715795, 487094806, 136982642, 366206954, 133692970, 537928141, 898859548, 592788644, 888878020, 281536978, 158065169, 86969797, 319077836, 479987702, 98924722, 740771545, 418074559, 238404881, 726310184, 673210734, 830326816, 883883485, 480630188, 217577955, 357530432, 164387745, 883747773, 270664570, 988235180, 768558699, 879348061, 148943041, 705478432, 509152478, 903015536, 149820569, 349299775, 900237330, 886239562, 625829734, 616837171, 277609186, 700381541, 512402228, 14337864, 925079886, 396126570, 240830642, 318877978, 994582372, 270810494, 658697183, 128178802, 614137558, 341556199, 186338820, 947911800, 328573721, 167403660, 586721857, 562471970, 167994643, 220304149, 97712467, 570240568, 257743740, 243642954, 664943559, 629800996, 191906601, 543809644, 942144108, 930763544, 223718631, 357807615, 990351224, 877895612, 494779269, 620808760, 652723834, 228117466, 940606580, 333080223, 657460139, 256922087, 709846356, 172313460, 171508919, 470432450, 160384145, 55047657, 263078085, 975599784, 292233955, 42297180, 772602037, 582613183, 590783008, 501419091, 438808423, 112933235, 148689574, 328784054, 309503032, 804156066, 87764331, 706904112, 481437780, 844471804, 763558691, 557503403, 467357683, 124039542, 227831322, 537275162, 114565478, 770288394, 924781599, 567177052, 251161332, 304954581, 372537756, 939454560, 280588013, 606180237, 719381270, 91483111, 837855954, 20374270, 414098543, 428778046, 308803619, 102339753, 119109164, 584843647, 820235415, 358627513, 993807879, 971849254, 629571970, 98943090, 463506445, 680897547, 338526843, 706391594, 95020473, 650892988, 201993883, 199720925, 656367049, 962371194, 641841243, 86914233, 372776811, 560085608, 570856263, 5092804, 327505061, 899634220, 273988800, 440391710, 10026965, 296404704, 617470229, 947737927, 328193206, 628832038, 588708549, 196139665, 433258975, 677178656, 716348680, 332259073, 979781675, 498827923, 335278848, 95516097, 162245149, 741694599, 435699170, 69729983, 107417495, 143348430, 936045, 749162767, 344242135, 421156560, 394763698, 770281968, 231640241, 651077848, 372366916, 729720739, 950406514, 331690474, 670073234, 532572632, 11008984, 518364747, 134369813, 8462624, 443428677, 504872186, 574454861, 242544430, 457484592, 837663150, 957010000, 503408098, 342637175, 709280001, 152401379, 833503006, 464544116, 773411441, 105423451, 400625649, 445026521, 570033864, 645394185, 923994143, 979690702, 588992941, 551762647, 895779039, 311939672, 244713387, 372684439, 9768816, 564647956, 4162568, 50283083, 437848557, 631246166, 248417383, 848394673, 350740229, 833388713, 556601517, 643284376, 487773956, 920137385, 374182153, 830693968, 725870005, 491329192, 29590773, 607106158, 953803371, 51979873, 307782499, 756911344, 877441465, 919639844, 318337212, 25325653, 110182863, 990449462, 723184444, 986285305, 289974803, 927754948, 35197263, 961659501, 850351525, 114387204, 929247579, 329353855, 762478001, 409292651, 689056961, 954109060, 986365777, 641361005, 729401831, 255263650, 308880623, 965533726, 195999607, 341665311, 163561943, 714363736, 226396198, 303942912, 31299585, 72753708, 246212286, 742664683, 530952886, 895621546, 613228508, 369685703, 491526427, 98699353, 365053312, 335940656, 806202678, 766078497, 771323192, 321777370, 295238670, 766512453, 168881202, 457809194, 68638679, 680435008, 684937571, 879729715, 279924908, 657299965, 628248728, 377239970, 211726861, 437757549, 911769470, 847885954, 427439985, 288470780, 668821590, 27345416, 232363192, 960050415, 13796559, 426103917, 42889495, 964341021, 196640537, 961802140, 651692915, 654894289, 459643321, 697880421, 57195400, 115266591, 196266450, 845514928, 203805454, 619699181, 551679044, 358923674, 745446334, 757725504, 454077562, 334809932, 768192839, 714814769, 246662893, 726947192, 543288865, 581628514, 810289578, 134046660, 53675065, 759810381, 450344411, 559202508, 368096147, 634208380, 723302182, 19381934, 82076382, 784617074, 915727200, 531226356, 218560720, 569285977, 424028359, 445333630, 244650995, 161633777, 367929816, 582425551, 756977212, 438056362, 783737876, 136765294, 898226442, 249889003, 431322385, 21729582, 29906476, 504691444, 188057274, 436185683, 371569395, 934450487, 64727534, 205689592, 239553833, 1780503, 698949008, 234661117, 504019751, 545710744, 907834805, 378845562, 528046820, 431344127, 893523587, 938535056, 699573625, 14145569, 298427083, 397102463, 460853942, 299654157, 743233161, 641397779, 46663003, 693515791, 356356822, 654848507, 980876819, 938871138, 86368621, 240751027, 716828212, 530749892, 222042224, 455335545, 351260702, 245804007, 895413406, 177693513, 572365163, 395620957, 222653132, 33663126, 126926556, 693000922, 15413449, 737502443, 734687427, 978950582, 254037225, 187772981, 775530039, 68705622, 597161571, 917246591, 660027743, 58404849, 733822537, 895792618, 640036616, 742783175, 619199190, 735128890, 807880396, 355906419, 270438639, 496946343, 513955575, 593596697, 809951637, 714840197, 861226561, 175319618, 8649996, 654050040, 481676137, 190448586, 698593026, 618928858, 176631290, 945986550, 949783656, 209997553, 226278982, 208109347, 325810539, 138535354, 454803682, 134227277, 620917754, 780470463, 303028265, 256896250, 572017212, 893193277, 581632383, 834841552, 629457694, 480212134, 209887110, 775381815, 680100739, 942408624, 9911284, 162409242, 35475699, 276176230, 785196090, 685399436, 791906978, 854777451, 31164109, 839254873, 483341012, 12901018, 322806633, 290367573, 328471107, 350897789, 765493619, 494060040, 101871415, 696638576, 63895464, 877584240, 313876379, 882683396, 261218353, 143267419, 316896357, 356292835, 84306694, 577869459, 735359122, 541002709, 546664496, 352754675, 685184560, 880400565, 537402237, 234068062, 254074514, 739029775, 597240234, 484694985, 101605011, 911942639, 437638002, 611174301, 314491898, 729785121, 490549067, 252056080, 352827918, 792484674, 949245530, 887135528, 707242514, 697970836, 172272859, 319974776, 613129838, 916946477, 33521686, 302820295, 361928516, 713129886, 264297130, 925095052, 409180072, 159700583, 343877758, 195529775, 153253309, 154306376, 129929465, 714763560, 826886713, 459904264, 439076106, 768878398, 214091745, 215415036, 302306459, 706627012, 659996971, 504563990, 67543931, 956770321, 884880738, 657537178, 946631162, 399021699, 676642818, 87107039, 547987078, 489425480, 6558701, 742556537, 595132309, 544099321, 560137728, 614766554, 542368563, 112336860, 191122378, 820702131, 136026422, 694772593, 253282976, 823047296, 615050712, 122721989, 486476743, 843727898, 531112620, 897398752, 859839592, 58554134, 338221280, 816001492, 151757606, 775213049, 431036457, 774329531, 839764106, 98840786, 260394010, 852633507, 552244381, 84939839, 891663270, 223045077, 694825874, 865527221, 629288439, 799477130, 554812192, 3481381, 270840322, 461968471, 237130822, 20781386, 380165185, 353747664, 717397277, 92902747, 503253688, 652420746, 407211491, 394573537, 156724363, 932041087, 831364118, 541907552, 138303803, 587439622, 900957917, 587834479, 24256303, 868238038, 659212183, 627269214, 926601892, 346056842, 419249747, 27713239, 540220456, 848878746, 746444800, 14879583, 195351106, 420491770, 688586919, 401085346, 992996918, 453232630, 47069784, 99910042, 361547563, 209479291, 811175979, 673451853, 630604213, 593459058, 281246263, 183900985, 689901107, 690251877, 927171906, 647669276, 959706983, 328297454, 267158219, 462171187, 374081088, 257786888, 818594105, 738917250, 201005592, 302675693, 877072758, 457980495, 674570386, 986575651, 112220297, 770050787, 359144411, 246012884, 987665564, 257388139, 960634817, 317828803, 44976602, 390442164, 47466530, 162882582, 456600719, 813663138, 176342944, 833874205, 228658142, 886352084, 488560102, 638920305, 400747729, 615537381, 470292733, 579375982, 450399076, 655371369, 207975196, 397760703, 260347623, 492346884, 8947560, 271955823, 975827623, 861142234, 494923667, 696623660, 581141994, 496201633, 766644062, 676740247, 779547663, 469224601, 904573186, 274801869, 5885597, 486484905, 570327891, 818035701, 860453913, 903346952, 222342023, 234302371, 900036578, 316373665, 204285065, 269233636, 507570139, 709083452, 330019728, 743927184, 511937540, 917411408, 867776099, 5393995, 124363823, 382941799, 579112591, 56829369, 335559568, 448851407, 119281359, 417662793, 986000011, 95424323, 667982962, 179563532, 411991161, 255323014, 396106849, 31093622, 925487265, 524611736, 853147029, 207968276, 23329913, 999497180, 406502992, 42642904, 281720470, 547697446, 208573418, 585206464, 129650897, 650443795, 230282549, 596832742, 967056089, 116761013, 183001275, 152716244, 447536811, 338985586, 923316350, 503237724, 940751665, 636695250, 707785942, 127161446, 476557597, 932843696, 255649686, 80141327, 909990716, 31778764, 219848993, 378240370, 733850276, 624989246, 988655266, 675392830, 117745944, 163394778, 604574905, 974683601, 684523286, 461797837, 574800173, 28226863, 616675726, 976278181, 135793145, 257663313, 699410945, 36998273, 594115105, 603087502, 307573241, 284904326, 226859890, 922163193, 628078442, 152104480, 222393617, 828220663, 490702090, 788872538, 434959268, 755752501, 49609492, 824961471, 422692539, 447247427, 460893485, 260065895, 300032253, 745635816, 547842199, 247447236, 493728363, 798176760, 619804196, 69976985, 815101188, 891799143, 987083557, 767855842, 687650720, 473402055, 791209087, 899042860, 673040471, 754009305, 420435367, 489146302, 689197204, 97194640, 568250048, 974880775, 267377753, 17014341, 906809005, 271820383, 27639881, 188962720, 903975671, 774897353, 905975272, 565827133, 765935615, 656852038, 881680537, 867920451, 613037228, 872961925, 219808020, 446235516, 956987940, 26210451, 682885356, 985712669, 323686650, 322014581, 702899885, 877471755, 77149122, 845668402, 916607219, 864336095, 398672699, 644692104, 810020065, 864482523, 586100059, 412719183, 515645048, 843298120, 676099748, 294640821, 900092876, 929943081, 818132927, 548699587, 742101201, 915733666, 167202625, 960318107, 157582070, 390101263, 283591862, 829897730, 61525283, 855052144, 383753614, 411311630, 772653776, 768408507, 410879143, 212503208, 911763180, 980679076, 966523181, 904451431, 314953113, 846682645, 100904861, 312994482, 326328057, 311925394, 914531166, 19448514, 969880114, 56108383, 501723396, 674325293, 767783707, 767414404, 249138083, 662082254, 214404588, 662198784, 87130442, 348811681, 18476440, 550599987, 970712915, 124788072, 52060895, 220823740, 79041981, 2817132, 121141639, 949333544, 489120815, 490397329, 578619783, 216473655, 854535130, 602848392, 79532334, 834673151, 784429459, 6604494, 456089775, 726573511, 207550952, 578918232, 426590310, 69386344, 388440971, 44647718, 556673854, 589277169, 110321902, 26859978, 508767553, 220196772, 401626815, 12776893, 821784351, 42418747, 651592700, 21767650, 290601806, 91367510, 967150377, 835990088, 265821605, 798309468, 433549986, 879746841, 681685736, 856439123, 406902696, 606119810, 702649642, 252884001, 285766693, 505039073, 220945088, 52817839, 425081588, 279664175, 152272232, 843397431, 786873689, 121940530, 103386611, 517390993, 121816320, 278562705, 332436440, 511544526, 142598039, 649389717, 331881635, 447335464, 207947881, 551263442, 569930276, 999398350, 875783929, 934110292, 710383165, 539750114, 771177400, 815278473, 634864031, 180477180, 803956501, 318310270, 199397545, 918721380, 401564033, 406455121, 923876948, 702101090, 131674841, 729900957, 261151242, 234122784, 356764633, 560120074, 849727012, 324161973, 699530042, 6889930, 762427698, 507357091, 538054615, 17657983, 479576809, 738741127, 832126410, 868465067, 886278670, 389762325, 939823479, 78712368, 689395912, 376003646, 799914085, 169481231, 233970197, 374599966, 915547278, 535192409, 748413925, 325263952, 830080109, 252435266, 54006230, 775247578, 468469837, 713858642, 51227331, 172625440, 848250745, 950605694, 552885306, 173437731, 114200573, 322213419, 915189714, 97955603, 402108742, 498483789, 561074755, 902253761, 248167238, 665886203, 847681679, 317259473, 977882351, 350108209, 970037873, 154713393, 240614526, 353932203, 616708353, 495447337, 225716280, 352441899, 171108922, 424427420, 134586418, 340425423, 781407300, 836560831, 414406594, 268702111, 647039941, 726184506, 17368507, 894757822, 213808453, 417105794, 3446566, 635780669, 542561383, 387386427, 415319601, 976421949, 153914881, 494635812, 415975466, 387739161, 781722012, 111244935, 850755002, 122525967, 287848227, 168616824, 470602540, 244628677, 806504745, 642151555, 131638319, 658642813, 131720601, 538043408, 799807277, 566152660, 506266450, 172850601, 893319581, 907824222, 581660041, 387628306, 902983297, 948939042, 510853530, 772120869, 585722096, 481301357, 939114332, 846280417, 999922589, 223153128, 665340795, 899839854, 183952040, 230667466, 312720255, 510770328, 851830662, 618582067, 421641729, 974296645, 995010512, 137379432, 166740981, 520156380, 579464997, 913938930, 627046395, 632581415, 178748764, 884518039, 520027917, 635716340, 795433705, 17655652, 628595770, 600562269, 235493706, 629536304, 313918017, 750439792, 95341623, 227651953, 40614682, 748057086, 843295890, 525056877, 892975297, 856601623, 830406242, 536053115, 464019267, 241805194, 529423600, 803296845, 479048976, 394400802, 543547556, 447141995, 879774560, 617710712, 611581713, 662678752, 132155603, 759313403, 439666750, 433917373, 373839079, 765131874, 37764632, 807711309, 58231820, 917243509, 470398542, 896419954, 678815822, 385715484, 233736428, 437512115, 304088496, 742324293, 681392713, 680470498, 915383065, 626844801, 717040033, 414394482, 973606533, 902518935, 149368881, 30892997, 445581451, 830726848, 61672851, 170983136, 524194168, 162169218, 416154862, 333091315, 126807327, 418776972, 733796801, 929214964, 379630410, 264595224, 814984196, 565092459, 266607462, 26895109, 797863509, 937976040, 488057540, 896212945, 885549645, 515297267, 562369057, 87242203, 957512325, 933414094, 45154118, 755370568, 658602028, 122720577, 888416874, 479712283, 534964472, 987926419, 849456382, 649208653, 120902241, 847866374, 761403057, 765157606, 858070733, 654793448, 965399389, 115710293, 802142342, 864662787, 163771623, 433348735, 11182569, 759633447, 336406889, 593945870, 520466116, 35045989, 943706677, 854566172, 467925136, 551407249, 651362224, 511753778, 970919178, 801199815, 293967876, 800098735, 218571897, 524084212, 734468148, 535616501, 200146882, 798214704, 733494712, 194737054, 116596939, 530441916, 861487761, 785238951, 923229577, 303640203, 564846930, 854377816, 793040450, 295565013, 634755119, 91875235, 678321405, 7975360, 894990924, 634983946, 404009953, 594476510, 642968277, 901413321, 917122737, 38557846, 311161243, 632404360, 833900946, 6566972, 97141816, 269339645, 63342597, 133653894, 756164606, 434367072, 219513028, 802759135, 898825419, 152354428, 931601994, 171877566, 252087679, 25359001, 483047249, 545972693, 186195336, 587779036, 400885712, 642632113, 116519693, 387151156, 815672965, 441202593, 642254813, 743341364, 260100428, 358921844, 528450313, 119161373, 310896771, 38706745, 48756221, 251996582, 328313189, 995024225, 228946445, 514038242, 246583857, 12392174, 673664732, 494611562, 588593642, 9466715, 319652294, 187924640, 838087905, 485001049, 712594814, 313098815, 352865904, 40562519, 612302375, 808192943, 678331242, 347028414, 886870449, 659697108, 817604123, 312761998, 379744255, 88199157, 893610800, 595815234, 286313122, 333507979, 510628548, 206104115, 956981765, 161555964, 510143842, 476729094, 446709211, 960637553, 293977694, 371263858, 909546884, 748662773, 737086909, 453155846, 737178284, 888515668, 800652819, 419751063, 865605524, 931342378, 235007221, 602187165, 349755610, 161618810, 579437980, 22766693, 689417008, 752471846, 187037712, 848599670, 417331128, 653741379, 719271819, 908341559, 707086252, 610816770, 798086655, 14777037, 513629332, 671928792, 438088671, 128228210, 483741689, 292351978, 497557729, 614622115, 732299053, 779010010, 775440983, 457010465, 828829514, 979579784, 4873640, 739820720, 828791769, 350496540, 642381527, 749685759, 841980255, 226674044, 837322071, 561482019, 769618426, 668674466, 279515469, 568109425, 140583434, 354321961, 571326886, 712811414, 679393336, 471420103, 979639634, 436183970, 595026149, 928580972, 809349427, 758703049, 588446602, 166836733, 349020997, 826398007, 108608160, 920565303, 531025823, 1619431, 783287927, 387271759, 987375119, 404515727, 887505650, 80789403, 937531004, 817646305, 652023477, 370765584, 218741457, 396023842, 62800706, 847708372, 622358754, 935822434, 856393962, 302415674, 26021798, 67786662, 168920738, 77671671, 248880365, 719725999, 742098852, 777488627, 263197033, 572202040, 583986812, 358866994, 668674309, 324348083, 636768419, 481765900, 371794851, 317351091, 703480547, 377687185, 425337048, 673277328, 263512674, 635460967, 680432876, 120485550, 376821809, 436202861, 153617959, 371013579, 731388732, 35866762, 132219061, 211722691, 208945749, 318547116, 196738626, 657899234, 122546698, 43482388, 931855357, 686915181, 274917445, 913306376, 372656514, 604050370, 23814637, 822058823, 867922878, 102987239, 259641573, 153782684, 833993408, 831943372, 313770487, 148748123, 522453391, 745562573, 849350729, 586928388, 336551659, 703412802, 246301247, 641226872, 714838970, 932490126, 211816899, 439659168, 505595015, 762092819, 389994387, 372505740, 25726018, 68707014, 252910120, 256398321, 642437650, 319664972, 415283349, 341519729, 207181597, 723126981, 695111984, 475284493, 594639753, 767794962, 514942368, 215701076, 23069159, 23027304, 578313001, 607193113, 789576995, 942080068, 611724062, 371392330, 646643271, 186637257, 94478936, 95951632, 599728470, 988411670, 6676010, 457393556, 14692469, 499830786, 303391150, 926066299, 702964220, 937342245, 75252096, 364416534, 73057913, 837871325, 731702034, 837163283, 804992378, 412360088, 829672050, 364596916, 707346032, 607902995, 14232298, 760266378, 49297382, 436847087, 948221039, 118956924, 314431043, 234699220, 656092008, 437102117, 890151225, 52906511, 553359548, 874171610, 499009493, 397345249, 875269783, 479256550, 777953996, 677389747, 871348481, 209167818, 231455827, 626026331, 968632944, 92153932, 820984735, 264443377, 516265233, 844567836, 763583342, 800978371, 71421090, 363580620, 740835808, 858800494, 818691727, 251370414, 367374535, 212822243, 322020741, 359514350, 946343083, 663561540, 150991938, 908944766, 564495479, 203633019, 810664484, 939161733, 279471316, 441705920, 384447326, 334928811, 788209219, 343807104, 109637059, 925523593, 686190254, 122459551, 462803087, 911826070, 341902178, 320464100, 173427438, 193367856, 519379866, 610229463, 587068465, 453234311, 405484303, 152186154, 181493266, 40075416, 998283753, 340613828, 670080428, 121758237, 845734224, 129266506, 165486757, 350195244, 791510672, 632659924, 816173063, 129451336, 342366962, 620882620, 762504967, 829612925, 758913236, 931164293, 493681048, 382900725, 564063787, 521026722, 363776242, 651482578, 316769953, 414088118, 421227570, 708129952, 51453644, 681798029, 655380769, 110199623, 743626200, 115596945, 677076670, 221179698, 108688924, 623386539, 118784327, 720573727, 935122898, 451882821, 469275601, 95527554, 202804946, 671124443, 344392118, 500203588, 11235846, 451284928, 396733161, 341337021, 61231653, 66803645, 537113730, 148507830, 693537341, 603441736, 922998012, 397656471, 697382159, 617830199, 208416480, 337789695, 717321476, 653773602, 392715674, 34186425, 650261814, 481238291, 61019541, 441517041, 970229136, 96614138, 128240210, 75303023, 486307311, 862272051, 107866351, 708470671, 221488862, 361849429, 66600145, 554422108, 696750780, 734082900, 424379962, 543467935, 180060547, 645651789, 101324355, 721376377, 712874694, 309920254, 789561475, 316856787, 401139377, 635648236, 179320442, 199901321, 929633498, 803453158, 496116008, 863295755, 470119475, 385598243, 748865391, 650103765, 162008314, 387750759, 128101807, 276090349, 88235679, 346112585, 996753185, 61373336, 658305348, 35938002, 17730824, 378129964, 188448759, 63243008, 780779111, 90273238, 277324496, 9756194, 848089757, 903690913, 554911748, 601619814, 754278437, 888578739, 917417912, 409445575, 645909367, 47548491, 551376228, 389005785, 736535124, 979187693, 994283421, 334793469, 262149945, 537515059, 218083049, 596248596, 693400179, 724568852, 458666228, 685732896, 544824644, 750194381, 321803483, 290218054, 954472611, 611868317, 885506249, 982516439, 282771750, 919372316, 414799792, 400331220, 863728498, 667550806, 516119206, 776794176, 851231521, 119224845, 224082835, 707198432, 98105231, 132381186, 139289390, 73325535, 176423861, 988291053, 347773400, 312412797, 954784360, 944449260, 658275230, 884266131, 420322974, 629580315, 173192013, 636963529, 73822814, 132659522, 935372469, 555900672, 958017483, 844514377, 523834276, 654144109, 881230569, 548695822, 376562180, 664554633, 320883639, 344170217, 888397496, 749851754, 509111444, 186256108, 785405232, 263108011, 30464853, 670124146, 743625685, 195794513, 269819991, 941718496, 134097955, 361794159, 214769679, 998132326, 182612806, 627071960, 443920506, 711941948, 333859405, 965978144, 213406096, 155322089, 146279614, 494217556, 111541426, 256816601, 209948689, 722348960, 626215322, 591931497, 75312704, 892758786, 757830970, 123691697, 597193500, 7238813, 503607856, 831778804, 992437051, 507021010, 592023533, 864387779, 940167143, 152464595, 446311912, 474474980, 657190983, 636519739, 442402618, 626180078, 392114880, 26778334, 820440469, 886744108, 128509994, 266788730, 846154642, 572047441, 27919015, 649780272, 980483144, 716183484, 212701943, 680495128, 351923158, 259954477, 387786967, 594521257, 78220032, 855631362, 274390968, 974690628, 812695138, 406139144, 747087514, 374053754, 289449743, 784428670, 396668926, 702919219, 577855061, 479416961, 304966760, 580614055, 97580796, 584695691, 710366956, 731625714, 848981007, 979698290, 406955947, 990266686, 152815168, 589683389, 57150659, 621927937, 162768422, 446669537, 21584094, 573457697, 76593100, 291071750, 441921355, 338270913, 394665762, 649011061, 730523150, 877599107, 153530634, 767491315, 162631317, 559754679, 991865773, 239919507, 559586128, 563388672, 702938519, 343909832, 137477302, 992326170, 599856955, 599791355, 840952796, 623378899, 98843519, 27265152, 844622441, 143195541, 666199527, 997780668, 458422493, 208092814, 217728017, 256397548, 540977475, 765353593, 358934628, 598034367, 383906143, 824750026, 940862706, 670380099, 600133312, 464545, 568529473, 913487180, 979265876, 621578128, 457247340, 447943701, 530037114, 301864882, 895215387, 530695844, 781263912, 217341699, 793097133, 140038605, 232216266, 763712321, 168631683, 814116220, 860084085, 224129139, 963032943, 145544591, 830504103, 802983539, 228634054, 210509551, 620586473, 133752560, 331429055, 889031423, 853177353, 586835415, 592486712, 934788601, 612367264, 387928902, 927368719, 782254990, 651309423, 518229504, 260075068, 893875495, 415379315, 321495268, 683200343, 19135065, 906455168, 59690315, 15713636, 844945144, 956133525, 525088730, 638442986, 174483690, 112063563, 515874544, 903166415, 663988449, 464624946, 409234664, 716830666, 295937679, 77614623, 47626492, 190702095, 439842875, 573538056, 675507872, 309103681, 54031082, 563860430, 520192507, 844204277, 554668361, 906673824, 566415956, 844767641, 691021026, 653542767, 854229834, 818903615, 487832487, 312386196, 979571885, 796192886, 439738309, 940720820, 984082364, 483726482, 783152015, 2461517, 666938993, 824322820, 71177837, 284980270, 3768207, 304281224, 747776135, 682472058, 166419431, 818604418, 372508926, 635295218, 812216169, 711136033, 526034766, 766782992, 689212764, 338010842, 726031567, 843027865, 94912010, 707398396, 869044849, 553996761, 633048378, 959685179, 749230720, 27721169, 307195158, 258758933, 826532477, 457699674, 188848637, 622520261, 131548314, 235741824, 249443938, 305175094, 16401788, 923369198, 531702320, 113686142, 76873536, 200816301, 726107970, 567324910, 851200151, 575370500, 712696529, 232869241, 373234433, 215377634, 590702508, 354603917, 233333141, 130439933, 174568280, 816328790, 839924878, 917187754, 211189092, 726244777, 219753911, 382368904, 743928770, 418624922, 450977791, 2131513, 638797834, 321003168, 6352251, 765621170, 712290493, 591790431, 70787269, 742670578, 86827882, 710648444, 835824674, 632586483, 841658012, 780588611, 513306063, 468846218, 101552732, 344487796, 792664740, 906950067, 191414332, 414107553, 671875519, 7658065, 186996503, 442402306, 336181313, 788377910, 863891164, 27237166, 247721898, 662536594, 705851863, 192049053, 869378668, 920979480, 798590421, 131094339, 692313108, 929825516, 498790429, 233690924, 146270767, 88445200, 762127971, 157104827, 721331917, 622064361, 221782698, 663910394, 432406909, 298298391, 918162507, 766036342, 303743542, 363990707, 8420028, 610338662, 276280078, 946572098, 813545156, 2193997, 617075229, 445362478, 338599557, 980790787, 988557435, 81124083, 290179236, 829567179, 167507884, 373801604, 824056407, 965193758, 390567728, 680276795, 36881322, 333631598, 871191458, 313428778, 814210305, 921647435, 361587740, 328120, 138058445, 152821628, 765294393, 886716064, 767075940, 957728072, 249247870, 150067726, 40259881, 381631498, 458901983, 200783858, 789534675, 148984505, 999828982, 118012666, 771683174, 908560372, 273956645, 621002435, 796325674, 734077757, 844443871, 393398298, 623338584, 525636769, 392146689, 394741047, 204951917, 67690295, 478266691, 683966268, 872231851, 480172338, 988068671, 933932138, 489512730, 75939780, 781350240, 362701750, 76600329, 974671790, 695856093, 193219726, 710796092, 97561234, 397172881, 652661190, 549093919, 395293829, 850494874, 955117200, 469255054, 287593468, 459648438, 911886826, 777764263, 757835505, 892561608, 468971370, 740524584, 682099128, 570618944, 194947630, 732587265, 852541327, 754349080, 604992164, 671927592, 120794774, 883352380, 246998700, 134148262, 121587123, 471318557, 543475590, 585023797, 574697547, 356685207, 349293687, 868812614, 37100252, 75961630, 982045699, 250454217, 757715733, 132345371, 206337005, 136500535, 573133907, 987713080, 559829075, 506874781, 847258094, 965660273, 682760636, 960922782, 634832473, 657989472, 178060361, 508696110, 432014359, 386748021, 228749119, 958609583, 191838408, 792944323, 974819811, 367967038, 907358506, 72684397, 153894538, 65139806, 760054168, 787666259, 731823586, 320426559, 559578819, 467192272, 524491347, 983766790, 913774620, 938034504, 846169726, 32523162, 183800574, 299298453, 853624317, 180822655, 863812493, 31195241, 323419135, 329503934, 666733216, 354321092, 328950964, 958725476, 222859652, 236441470, 313042000, 418557928, 406515476, 42059204, 414225350, 76523979, 889234222, 221891864, 880404439, 913820989, 327235596, 208384996, 490238926, 461593193, 185604710, 705459763, 883481050, 841754309, 596752825, 91344282, 257990866, 346235194, 751483286, 212386225, 376765505, 143113517, 324732292, 51205748, 136826613, 747119653, 609620241, 920481500, 308216589, 606150472, 118082783, 70802294, 806614551, 377802302, 904283721, 597339651, 687704429, 169658975, 31752266, 574654918, 615656733, 393753348, 852312816, 531242489, 665275787, 542056407, 19111806, 271049511, 189416014, 766806227, 769198777, 341968764, 200397359, 116689105, 862625494, 208137457, 52636231, 31040932, 651110595, 458789147, 91049852, 644207558, 564299056, 341342276, 125727097, 620516761, 126008789, 290784364, 934980596, 479164719, 263932140, 611099214, 716670232, 754008434, 460406063, 271346711, 424723700, 761685342, 247931383, 639853176, 845634406, 284778405, 445992922, 572675756, 538099416, 831521153, 880098648, 201192508, 714169106, 648378355, 928072460, 266734692, 439463654, 816714339, 322673920, 226046021, 174809893, 301439042, 618161666, 192009233, 670849339, 159744839, 36181455, 96876449, 374189547, 909413261, 130631406, 75726324, 719464313, 860507609, 332314359, 400053476, 766193014, 364198686, 866324684, 257337731, 232863540, 997579487, 384497860, 130965689, 645701443, 328595164, 213714532, 326382530, 144945780, 596234371, 454843166, 217605571, 917415616, 468317100, 924736755, 760706032, 577118875, 738420717, 792407011, 675289817, 984864449, 928795096, 100303808, 838500266, 112788899, 799523016, 357029193, 127340594, 302943263, 677906075, 350655956, 568149718, 877622195, 601135569, 858060787, 334776219, 538059633, 343688651, 686183207, 663343499, 328252361, 275341726, 473927939, 392136791, 925015084, 624562466, 778306486, 245219002, 11519956, 561031070, 661240235, 748262740, 502685543, 615358282, 703834199, 398251848, 95554651, 240172562, 843836290, 464569711, 2934306, 137199523, 663325888, 708192279, 292744795, 756358010, 856530496, 171833586, 118559648, 743998990, 126403761, 609944650, 575406403, 968801703, 984312084, 206825103, 40236283, 441981700, 59507144, 202613676, 521618617, 794526527, 870107567, 134190449, 134154347, 650414831, 632289775, 946008163, 606764043, 492194169, 949590369, 730790551, 832327275, 783807847, 813767095, 289437481, 190728119, 300342332, 669378289, 674715630, 138958089, 228703877, 868436440, 896506610, 816738097, 399746237, 894414768, 394004232, 788888822, 570031514, 386186200, 890919559, 887590309, 811440126, 47592264, 400673571, 380315858, 246743530, 182221344, 360419162, 709358794, 970426495, 113921393, 514904494, 983739448, 776608201, 258194534, 980002877, 225837162, 802628716, 343900265, 716645057, 11629535, 209067027, 774214089, 941542824, 575297152, 560641473, 889178300, 345221753, 470281510, 159857548, 154685695, 34571658, 274602354, 451020600, 680750087, 107178997, 450283258, 696162847, 596009120, 562207055, 355317206, 910450774, 964810399, 70155783, 516069217, 838968788, 929298949, 510782359, 833080184, 810647717, 412647682, 468308207, 338910826, 845180980, 383911180, 163103236, 192436449, 234817273, 154743896, 197747246, 752973022, 121860359, 768340710, 413096304, 46625231, 388803708, 827037936, 223603386, 855583041, 710581405, 808587570, 19318343, 115428154, 964420099, 995014678, 696575653, 714888478, 580375108, 284562754, 483752952, 261003879, 501488255, 698438054, 568774245, 445032991, 470499370, 619648840, 897535954, 71996639, 895594073, 698050514, 866894411, 779008660, 78969995, 855199883, 174127175, 415809077, 853481815, 996102725, 916506946, 598661455, 119818070, 914550353, 361915303, 102231751, 667394745, 301141840, 490404186, 128447518, 537271662, 429734261, 952744495, 511156432, 656932866, 143693244, 558305825, 577012302, 439716966, 908488864, 136546355, 135533741, 952195000, 305368757, 478254050, 126734436, 277339946, 580408516, 768308885, 527732972, 487313402, 342927692, 409420034, 712086774, 861288888, 516274755, 790569957, 19130792, 522843886, 827633866, 43496534, 920479346, 583971192, 413085037, 277762354, 338538937, 500441022, 874580150, 285387981, 279441669, 46020169, 209566569, 584210245, 622898253, 736845461, 343044056, 193571, 549238016, 709487566, 619075014, 598480040, 857267876, 452621723, 668578209, 823890018, 404000002, 437737818, 746353182, 596598381, 86325246, 809015982, 349900930, 434288688, 878148820, 139002531, 894991942, 449610451, 661595850, 22116383, 431081644, 974408280, 270852149, 777059036, 653057241, 609127765, 569396292, 238133745, 999495635, 379773678, 906378214, 133247088, 485118248, 21043139, 991906159, 669766547, 440641541, 987475279, 983360021, 832135949, 590515666, 926470055, 877570734, 915640518, 989532424, 654328666, 473704303, 309781506, 380762540, 46799569, 61990154, 629820577, 196848907, 766535126, 769655109, 374327652, 989978457, 326148345, 254592341, 183959853, 68362344, 773484820, 22942052, 394319565, 603110757, 157206553, 880486242, 105475617, 898178747, 767025676, 93584274, 936425538, 835668748, 169121172, 827636548, 31682036, 943870868, 228794465, 651950100, 123347446, 417302305, 815665569, 170788223, 955617825, 66063594, 347757633, 863432369, 570574891, 82201842, 798100158, 347255564, 661226964, 242119253, 988554964, 989176211, 82609275, 508292392, 468863414, 991917146, 192861020, 200911130, 779778241, 356937973, 728479435, 820396418, 617347733, 753772952, 515156387, 719451529, 900723529, 912057470, 37651766, 378769912, 659506340, 586584014, 533188254, 600869863, 765238930, 859706985, 706360271, 866073224, 213083701, 182428014, 267913492, 522551307, 859652118, 96152451, 333042830, 688235742, 999812891, 400620674, 739735599, 277522892, 640827796, 948670066, 867687892, 351830035, 923674179, 24764018, 311862756, 134824805, 384420182, 421407719, 752060198, 674304353, 359915021, 433996661, 215907147, 311414677, 781086164, 576567729, 168268059, 491483037, 138751169, 744669133, 937221779, 412665598, 121240756, 969144051, 50582898, 427179610, 192832094, 229656909, 316093928, 653130696, 594867198, 31262874, 55685259, 936848073, 275603707, 22271535, 204733032, 639321685, 204011394, 111932430, 825947385, 364085909, 779760174, 187140908, 321153604, 29581905, 534509050, 730080642, 196248873, 290578839, 292553581, 757349835, 43584069, 155538137, 859821914, 418740939, 551420237, 77708439, 310557422, 836542734, 791019757, 912182027, 303704787, 22689972, 577997498, 881115882, 443702178, 496249509, 237308618, 290825125, 937435908, 171143621, 286688925, 653515735, 838232670, 89409733, 424701204, 750708761, 495496492, 500993540, 483422856, 541959056, 917014605, 178599880, 426193672, 647530524, 782443836, 689291287, 950798516, 84930714, 640719301, 937162284, 212666642, 256413744, 937506385, 158316628, 488473836, 384738735, 697021346, 252701845, 690810469, 991842269, 605303106, 793355918, 428257416, 914941982, 903085702, 522628152, 420075249, 873167910, 855732059, 941826106, 26793111, 580826250, 663381767, 152977594, 248341948, 386577779, 418080109, 583683350, 190824976, 496738222, 496805979, 425128203, 345414361, 461869299, 764898753, 505337877, 714359315, 802438727, 910657715, 720065061, 861907258, 488585924, 79105802, 208294944, 582334550, 387386431, 475903521, 335309250, 40828947, 542795512, 81068775, 491596185, 5076637, 757150590, 370387487, 647500835, 753348998, 857232493, 906487265, 748148338, 845317258, 417974183, 342469504, 236816030, 28618267, 552313116, 301850950, 455979580, 558150540, 137927263, 260809533, 819620704, 946814884, 708721639, 64013272, 649758196, 235729061, 294975211, 551072773, 185744872, 631152777, 330849865, 476348605, 684221371, 819585603, 586318953, 10559470, 24849363, 186991793, 922691338, 387673209, 190524844, 591451252, 713998425, 25453568, 207364119, 517109755, 754196216, 407981586, 361613341, 561426297, 661498740, 863933978, 792144999, 537828611, 980201851, 65232869, 708519563, 833643297, 99977400, 257320315, 751263866, 563107131, 841002867, 585610838, 442628875, 856652007, 821675062, 436243400, 104639015, 892149554, 605836152, 177251467, 11109621, 254712760, 246009893, 718023552, 766523185, 660451064, 3593097, 318526505, 580139913, 136131652, 831279798, 119253317, 85107077, 562571113, 312920249, 158971282, 230084503, 876943627, 613133797, 842414103, 477768918, 331446759, 597845621, 249728110, 339604426, 482404385, 962126879, 498258896, 580291015, 371809278, 75877624, 860205594, 710108251, 209658271, 309509540, 506205995, 789386623, 206405238, 452552857, 256185167, 3046984, 10738692, 142885722, 910976169, 825619274, 703928684, 274111177, 106781146, 403216315, 536838586, 677284225, 905951581, 395688171, 777707265, 556571005, 15948446, 966498787, 213449425, 906187473, 946103458, 745871645, 56990920, 770181221, 578170749, 247901362, 551072557, 133458346, 963826900, 970749431, 31460312, 141845583, 330454356, 176738203, 351176062, 292822148, 351546724, 974076562, 259424661, 93178264, 468710852, 296275535, 154012529, 960955999, 404965948, 18024630, 475109036, 491593621, 903594823, 287794158, 329582901, 504734125, 667329583, 216164992, 125633856, 291712847, 529472219, 418161918, 807166503, 432915712, 162826651, 782382197, 329372003, 210610699, 702665693, 731164399, 846077907, 152046634, 907074121, 400448385, 935973310, 219503929, 829868222, 942963809, 992759354, 416432125, 744587267, 346778616, 107402251, 258054417, 96934698, 140796318, 929147762, 427928952, 437118198, 549324673, 92380113, 901299779, 324044348, 598851485, 747694110, 273603854, 138140614, 693518120, 4592929, 789747539, 354806014, 417917135, 513617217, 507561958, 28817744, 154184780, 775153585, 892734383, 627796864, 50582626, 256280018, 470616765, 912492746, 492122912, 325865146, 899750805, 920677174, 240606448, 785243890, 78149162, 180141223, 182303718, 658636972, 206180535, 45019466, 150631513, 218474095, 461356985, 231905714, 351662308, 242196037, 477109449, 832108981, 639303186, 84952320, 692989368, 845040334, 868744703, 993742685, 469078240, 775091425, 174123168, 567984810, 144308217, 444504994, 192126903, 901676512, 681739901, 893532120, 494129562, 929940800, 135269769, 484023533, 916137485, 525661222, 15487818, 126041939, 159871663, 533899647, 632291539, 866622194, 779040639, 159591969, 148958385, 390428381, 7657332, 15855944, 349276178, 199983303, 570232971, 269915175, 477516616, 855217230, 169082480, 925746410, 25302423, 88793528, 830737424, 173984810, 693097065, 80147196, 872806868, 546235430, 433745078, 705144017, 556958424, 878777368, 811366892, 802489738, 351198205, 73501370, 232157716, 967789108, 216101027, 891340734, 100161261, 856500113, 923364215, 765595001, 863071052, 562822491, 104041430, 276232071, 233715617, 265302507, 869981165, 553019834, 790861931, 969523592, 221878202, 650119216, 552756273, 233388459, 738660623, 995536016, 602524072, 642133962, 137272178, 672952767, 327331738, 998925990, 80351929, 416609305, 838258092, 770077982, 224390449, 822313593, 930831598, 826827118, 790523648, 292409694, 727304023, 456807204, 795094371, 981064132, 319006087, 9671432, 194679420, 425310412, 408019580, 343023251, 127794914, 452658915, 714263553, 961485508, 928755639, 853751681, 716413804, 329345645, 696740369, 572105190, 24263606, 344963407, 519244298, 864592456, 484681304, 969966325, 686971391, 388467095, 158638915, 132324314, 474657227, 137005056, 2719448, 105702415, 84460273, 86289001, 349763797, 815999059, 554291014, 232482012, 418995792, 906093371, 859376593, 967628413, 931222996, 573951030, 875669356, 417959635, 741771902, 25761196, 885656980, 140862154, 331614694, 121834172, 511168907, 721982464, 824474646, 439516311, 839071378, 861708150, 368995934, 75522181, 581713677, 352510902, 582833358, 823398422, 359754841, 537548644, 788934913, 24134738, 118403577, 38295428, 425478958, 14746140, 295468932, 877426399, 431400788, 630125613, 165577631, 830993854, 859944534, 761903451, 880865302, 168125281, 459220269, 957652266, 742434389, 728440053, 223003421, 604715823, 193659840, 774879340, 815711542, 218330839, 329873590, 959111085, 578163906, 66639837, 453944653, 572568840, 67227445, 994979349, 751711431, 629677551, 440168382, 995431521, 803019627, 372494056, 233776024, 482722005, 567187278, 647130086, 307719487, 137916271, 678437080, 788987922, 660198605, 673007460, 476141054, 508625830, 122049448, 652631450, 798005210, 373148464, 973892386, 375409920, 779184474, 825336691, 545064818, 144309194, 471526292, 917285558, 622376981, 970214859, 549248534, 254567371, 409717476, 541533611, 310462783, 685929397, 185580787, 601707098, 664356142, 195039733, 560396207, 971277093, 535785271, 177184223, 497924380, 416397902, 758940923, 659298940, 634121185, 381248079, 96997824, 404318949, 536037967, 305576386, 419709611, 199458303, 636650225, 962450991, 5453255, 730005125, 967738260, 635800821, 24560759, 647002442, 306607846, 691260718, 373820820, 742124258, 456570, 414989067, 849260267, 785946520, 9757533, 697717537, 289946461, 715884386, 846737880, 940922269, 609744778, 225148973, 591187689, 164457333, 92346994, 267710214, 865759626, 40082810, 551177006, 989460863, 204470682, 77147171, 513297086, 111337143, 49118819, 236597397, 754377605, 376853728, 334995140, 542314159, 474681771, 668564021, 170261583, 267433334, 934359906, 210156165, 930106853, 995662347, 88234902, 677938277, 193873018, 201589724, 64948387, 517040643, 201583978, 92471597, 357675849, 930844922, 727345034, 282525664, 125185935, 276214240, 771061024, 43845051, 735896382, 634561186, 409289745, 669111356, 707351195, 407199811, 938285703, 897878547, 307942009, 931042738, 984848791, 330264428, 728363476, 494811992, 765057647, 504707501, 313123776, 919892721, 426416060, 837938744, 45039959, 983711393, 571760303, 343728722, 169072079, 825427959, 874571983, 567228801, 876900917, 658640658, 813557539, 983143753, 817391053, 385783286, 384143864, 39264010, 657826739, 94020327, 431343453, 52292080, 552907686, 153326395, 780451974, 487216542, 35157292, 222336291, 294506818, 454254305, 94439489, 157169802, 861835393, 227872277, 404956951, 455740114, 30945264, 749999235, 686258303, 53242600, 456825461, 166780427, 538287735, 369899675, 209728577, 686701000, 60598013, 499182817, 95394949, 409817889, 123908510, 621592978, 828428756, 148241607, 491683855, 721140294, 877243668, 145082098, 88338594, 471598997, 796439480, 134264396, 147730500, 584700790, 634938091, 416563288, 210367746, 213544229, 519402518, 953640662, 344616283, 427508815, 816918560, 449516321, 153237723, 629687832, 878868639, 841751815, 32254646, 379817333, 710849691, 923196051, 277868606, 518567377, 45972887, 390403880, 458808835, 574323948, 959087756, 277671246, 276579603, 433245881, 708233613, 17721287, 197711381, 561292458, 864936224, 172121702, 906173261, 975119759, 345854123, 526452177, 145026328, 35123658, 350742790, 539104628, 780772525, 92756946, 27817094, 249503535, 590890959, 82431431, 131848377, 252034756, 184322478, 650933657, 292505635, 89858923, 893517917, 712891483, 331227792, 553023266, 549025415, 787970192, 967181766, 178981861, 330462283, 832766100, 748241707, 473956570, 522327286, 99998756, 420600058, 766229779, 342219546, 924968953, 654070545, 774749000, 54008307, 639759856, 62366658, 676674333, 524589049, 974415290, 921474635, 288141756, 439589400, 218530184, 120954132, 224272291, 624710178, 170738452, 391072950, 837126435, 206776413, 740973194, 207196052, 725633093, 695362846, 703502332, 762658531, 546409972, 308876248, 673285010, 505709274, 225366760, 296782838, 257191658, 351732486, 684629191, 507652740, 251829326, 593177432, 259605182, 554873368, 520826458, 794110303, 435024470, 9579784, 759947727, 1129497, 922852321, 181905218, 114911685, 262628927, 259639726, 347831118, 875122227, 435302684, 855268582, 503715321, 550226345, 126178322, 174814154, 3653848, 145289962, 234394644, 516160617, 68480929, 945120837, 850291778, 902976738, 637440832, 997554789, 324745315, 222438016, 725264543, 626803664, 982497, 599062457, 782610034, 236454288, 455923187, 889950758, 657054896, 981216604, 602857423, 61033880, 453972124, 892730974, 297544468, 628475401, 128616273, 185584018, 42503287, 24288218, 489237743, 896582752, 947329648, 778040093, 11453221, 517305517, 497092190, 906374131, 461940372, 824827077, 478343840, 142299601, 278908260, 851101577, 859114305, 374253314, 571283689, 911098431, 576167603, 727375265, 351921354, 515807971, 159245585, 53960762, 770837615, 832651153, 916344445, 52969397, 494255546, 932201806, 558830406, 89678440, 634892427, 991584876, 838019174, 306335556, 129916871, 413103604, 288602737, 522281673, 931778256, 624244925, 868552077, 38056061, 339815046, 799493, 644349358, 761745526, 645742117, 480163139, 607488034, 290321385, 691757444, 848200639, 684551178, 770867368, 721231969, 690015765, 931495035, 58154279, 714669923, 748341227, 688254132, 268654675, 785736479, 649572942, 269758557, 497851549, 105985497, 197316033, 587270885, 904970586, 824787959, 239716825, 760405192, 781083973, 680955571, 472994077, 406496783, 14055110, 532510522, 265446565, 801455840, 615737682, 473857767, 708891711, 64841411, 382884016, 690622411, 840427592, 731158211, 602868297, 376556835, 312256843, 508222738, 413123409, 184935101, 937182223, 176349700, 662176304, 224292312, 385365409, 109563935, 637963815, 712585338, 744927525, 714368279, 207467646, 502377571, 302620832, 841467488, 514359352, 420849643, 625851296, 472403602, 988605384, 899582174, 766140864, 285595016, 614695049, 844707743, 861030746, 856106720, 443456823, 833266205, 556700127, 215742363, 38243819, 846308125, 355379848, 930637801, 714951299, 627524780, 624798166, 455759316, 515143100, 845670108, 829590347, 362867192, 822262399, 119712719, 206470295, 671011159, 785447199, 872612070, 860166342, 781598483, 66251118, 321368147, 777888748, 82644549, 553939183, 843837890, 462984107, 406745553, 482338920, 604558444, 7754493, 87252245, 8683457, 538975306, 992949972, 744913129, 487841221, 484937791, 849083834, 504993872, 959750986, 425928914, 816232769, 500110629, 755592175, 871070563, 612181763, 859715681, 383673357, 423211501, 333778723, 253953358, 313493092, 616646706, 549356231, 110052972, 415184813, 618382175, 240175878, 393479813, 254994042, 760479596, 480729062, 914498620, 476712720, 672980817, 745891863, 33033367, 714501965, 681531916, 177465804, 303829635, 597164397, 91044025, 58471271, 603246616, 142471359, 202761013, 798107672, 498639709, 271014753, 622577873, 355683023, 45398539, 74150309, 333540110, 541476803, 179347271, 892370281, 515001342, 837390193, 873482735, 297531578, 966030395, 569061879, 238120406, 522674343, 94380300, 813579889, 102133655, 549444938, 103074137, 856479933, 527865985, 163566882, 653959818, 913227191, 685129183, 352953958, 397809137, 612966422, 623648999, 540989568, 547082720, 357561775, 412010789, 471936900, 110606207, 433936714, 546396191, 532951434, 725685748, 85486409, 820767689, 433024587, 702587916, 968694576, 659847893, 335655033, 530236448, 944787652, 585107819, 482789380, 457672986, 321142092, 510497436, 433038841, 262707363, 578818728, 301781481, 523953023, 244190093, 356888502, 341778410, 114808427, 994967612, 199008393, 17527931, 931030635, 765107430, 198159519, 156300939, 725071982, 144546790, 579381417, 805474179, 169089944, 794830675, 490432799, 301195312, 940169704, 697161730, 914219120, 316358923, 339269967, 347736797, 12033136, 181169460, 903538108, 588375483, 168080873, 15278844, 636338831, 456948514, 644955362, 597708394, 486239963, 714912943, 431990414, 447820789, 464961421, 803350883, 714133351, 539134588, 955412407, 784014755, 288492497, 215503844, 241898844, 367899214, 644708724, 287590012, 161125836, 677145055, 110660780, 420093749, 620563559, 643030753, 379366439, 773521240, 639545884, 884055177, 497897291, 962502017, 246500706, 259549668, 755281814, 139176477, 732385835, 568670054, 341097367, 310545835, 504064702, 11089293, 917718619, 978335719, 675801504, 754131991, 360007549, 198968246, 650770231, 622840382, 628949486, 677818508, 693638970, 35175995, 28525367, 282883954, 732019188, 499451683, 938033107, 781370811, 613140057, 119487479, 298973495, 163238990, 72304805, 670007001, 242894081, 552869859, 352738988, 483724745, 476345620, 59335451, 456657154, 373709856, 699751266, 390740586, 720878038, 132128298, 273538453, 971145993, 151807165, 778851516, 236882707, 438323337, 589962158, 962657577, 691946567, 646973529, 631776310, 780376168, 759249101, 212111128, 761165715, 525444382, 237297728, 782532788, 66654799, 133008517, 334730608, 197630217, 563472482, 343670746, 314055140, 717222179, 125348125, 207626093, 417662467, 886054310, 788746561, 907313183, 562698750, 583134534, 906793991, 733571998, 532952889, 94963401, 227548196, 141458393, 984292333, 987895305, 371605950, 842037297, 391869864, 236136826, 172816236, 695146796, 313802286, 602845823, 312526422, 241389192, 721750898, 727069335, 341602979, 623014333, 129802474, 9346180, 493955571, 223611522, 551723214, 549100686, 258515477, 223981468, 853339543, 354183129, 425604010, 902306329, 729441664, 147112229, 462920384, 768751426, 733553430, 41434762, 545488827, 117554756, 660627204, 779388752, 311086231, 329341713, 381123673, 262306552, 672449345, 993641280, 533547164, 713297280, 625598141, 181726145, 442394981, 396950765, 130914533, 826145490, 581418013, 717006261, 866332118, 726358737, 969304585, 667919947, 464318607, 233444042, 347649582, 705851369, 149141438, 174356163, 187833710, 860233255, 572228808, 817737076, 376819125, 679374585, 605386809, 377155561, 475183202, 13642942, 812389095, 894937810, 375570293, 735447983, 815258638, 147753744, 714279887, 12104163, 754100496, 136806730, 19652686, 993131003, 973250748, 743960404, 200075301, 894469043, 515477929, 405153350, 141919755, 807514015, 940360726, 16517104, 265558400, 263966841, 182618467, 359064885, 692573751, 385864250, 831433478, 426924966, 468529321, 948404450, 624190737, 139561271, 515419393, 155058493, 706628702, 190935691, 663620150, 467224224, 300276898, 359926140, 163218593, 516581458, 694354634, 418503161, 123429205, 818567372, 955326874, 246096739, 830941726, 685793948, 800202045, 507833913, 509663340, 608182302, 59272141, 572721344, 402635416, 277935892, 790277457, 311707519, 744188639, 648293237, 541807989, 910741074, 977973967, 492294997, 325820379, 972510138, 179650912, 402805995, 474822682, 685954367, 639330975, 976652792, 141352729, 514151486, 591200910, 106926472, 559617264, 514496370, 56149019, 996547487, 361764430, 673224347, 613545081, 134846888, 905172597, 534490098, 236813601, 27162244, 971516473, 373188170, 36827755, 931579665, 244797247, 221424396, 793929525, 633488255, 49034433, 631949961, 895554798, 266104701, 23672513, 489391643, 987100772, 665334417, 615907865, 516355297, 811514575, 902132069, 624250664, 306161600, 681484551, 97531108, 445081417, 382173977, 927113099, 633193072, 887879881, 757911916, 158773835, 368542748, 70823441, 189379955, 611816919, 106672270, 199710947, 750982343, 385742554, 832806308, 754332309, 918121907, 618872, 159784515, 379889512, 584623442, 942973051, 179334036, 926601671, 547199966, 723875188, 476458451, 445447342, 355070683, 491074200, 130836223, 29635223, 298257723, 186025766, 239253550, 573014504, 562390694, 814589902, 225130177, 614529425, 356624314, 589207961, 538199386, 731874056, 444907822, 901719014, 875933621, 251994031, 207219071, 454068797, 448230863, 881034248, 871550035, 582929878, 968930382, 605467910, 28954368, 873651971, 152511654, 541582413, 662952713, 691935877, 935667372, 727492103, 188723786, 398072464, 691640103, 341460828, 294824265, 710559551, 24919521, 399906450, 869716862, 304016285, 999778087, 118206256, 467988726, 535753453, 299065302, 877236308, 464789693, 43680758, 173753236, 903810012, 357833178, 454767857, 33106194, 813880986, 1931960, 7886363, 416630350, 412691229, 99731501, 413158201, 635298095, 638262859, 686268954, 43441534, 481604457, 407721012, 91141032, 550252779, 188206434, 821441207, 641687924, 417639883, 321658991, 957678305, 610686210, 304551385, 380265042, 455279186, 302961010, 433412113, 835646141, 626706492, 450492592, 359560322, 457336822, 353046823, 305528725, 352136115, 282673102, 239412918, 957999117, 135944843, 245829271, 472212073, 979589541, 115229802, 462369346, 998570725, 352385126, 755802423, 731258644, 514078876, 413090317, 196897292, 4527846, 876401026, 724851816, 329729877, 781955853, 874083679, 484785793, 500356961, 755761823, 979476284, 518328295, 217499983, 27216772, 263447202, 264538234, 914855915, 217538000, 76829021, 344987194, 968459205, 137857071, 831327243, 935337341, 318184499, 510363315, 840975380, 982018609, 446633462, 482095414, 257687504, 101928297, 863671267, 630063789, 982968106, 928276595, 677865784, 410276607, 179894978, 178039906, 893862546, 541300613, 141085823, 21153645, 407937520, 736181636, 852809044, 639689552, 614190427, 868669007, 146414736, 210110579, 714566873, 520601505, 396286287, 427123556, 783366853, 901190948, 321625504, 27217803, 720270710, 424607879, 733236514, 453738503, 373533933, 161095449, 672373254, 293178659, 976635386, 349028712, 704426670, 932216577, 279351082, 5545547, 256913468, 695748431, 645400063, 475372283, 555527899, 880616335, 452529526, 844109416, 82905345, 77781205, 107873416, 624245417, 923463529, 18655464, 574775207, 619724390, 513585055, 733143930, 999059644, 858708721, 639112971, 272748742, 409322509, 91335594, 897013133, 294480423, 445374359, 564752570, 954715514, 258010894, 489214768, 581785669, 207563334, 955502788, 578204781, 365926774, 759673679, 580904314, 536994986, 963540916, 234034378, 871133184, 248967901, 517721222, 685653980, 784974295, 502619957, 541481917, 559313254, 745846806, 95702591, 192567311, 193864836, 98891109, 384090235, 59331577, 647075501, 434084862, 94983836, 596577895, 766735483, 142763228, 767358469, 754194493, 795841612, 243791200, 341383563, 579993276, 561537195, 665230581, 201757073, 23779062, 978825500, 124200628, 36049077, 27956314, 95876821, 114089346, 72875120, 740485839, 633373222, 136330882, 126979889, 489660069, 454788590, 789478468, 296613502, 161396680, 221007558, 377023825, 339097240, 699399811, 725498656, 94801606, 714844098, 228967828, 632862768, 477591695, 35317104, 733202535, 485982782, 801227329, 128753290, 840036847, 415602593, 576657760, 41295250, 261755643, 370101332, 8341196, 881952154, 750632432, 141128795, 458513173, 780583474, 525547165, 504473687, 744859074, 677826060, 86634233, 606158617, 317633561, 379755136, 177491977, 710456492, 777432556, 454787597, 913691699, 400614506, 560128118, 168640884, 325299156, 139075201, 861702527, 371734938, 591534118, 471261337, 129737213, 185470454, 94763617, 594287087, 975808382, 301325206, 265106257, 303332258, 170075845, 318803386, 749397522, 704651888, 714080400, 76804315, 795842190, 624873996, 549663185, 673686583, 70643436, 240076197, 276200981, 129031927, 923626648, 312645181, 414468807, 986334756, 401718843, 441191952, 221793861, 397465349, 318012874, 13054162, 224351106, 658850055, 654988701, 320556645, 993983202, 659011282, 512324848, 436634306, 391825724, 614428736, 531341651, 840322785, 27539943, 733660964, 704838563, 689621476, 926044484, 575695621, 581506658, 9567034, 164348903, 126483168, 880235310, 600326193, 88044879, 48832733, 247797474, 436953094, 577557413, 897956023, 652171805, 825660244, 990095031, 52224715, 668785202, 915010699, 270931272, 573966700, 315948685, 631664865, 575309422, 62394117, 430817797, 787343954, 587453630, 832454545, 491154290, 345603862, 798169023, 558963449, 645745676, 380907854, 322950833, 335977541, 371386407, 621413264, 803914335, 240936888, 150120701, 431148701, 612538222, 106980925, 93410493, 74621250, 67582522, 903118601, 660294125, 424385120, 585209065, 995733131, 408827315, 170966714, 553684060, 863126383, 59748978, 816021338, 912606629, 591277697, 346957644, 953502921, 76944383, 923341004, 793998778, 62490160, 907831267, 662704497, 551260337, 626588005, 745902138, 588973315, 927081813, 213706604, 283527795, 109407378, 904031338, 835362593, 925836161, 763565348, 641436966, 775796590, 213257999, 801711002, 111299699, 668854429, 473320712, 946609725, 745675736, 734748086, 122226744, 983897211, 319618358, 810632569, 953878206, 501221006, 796795889, 480516019, 748984011, 123530388, 964442239, 715363440, 295476725, 932830138, 589774023, 285132646, 42897444, 838001426, 367021555, 423192014, 317491332, 937470528, 551425457, 771587832, 80924443, 710968953, 361861511, 351182178, 112228130, 486030033, 234595598, 280400229, 698729765, 105380255, 361663811, 186784046, 447006606, 872426915, 810253951, 51919118, 371249737, 153728546, 481313739, 892856890, 849754061, 351479721, 684501181, 763929584, 924257564, 262596430, 998687693, 86310202, 392906324, 239987976, 115924416, 364208242, 360153963, 622272213, 593182461, 357489409, 495095450, 868569915, 337032424, 122930848, 775091762, 465482916, 110334563, 678173671, 584066241, 76729375, 689137910, 507783291, 377231180, 721440191, 63384746, 523756454, 912398322, 475132271, 904722394, 896820155, 235222962, 409710773, 623029332, 727542706, 377274703, 274739407, 819365252, 137416283, 22398362, 408857918, 282934272, 205807978, 824789863, 417519056, 550970792, 515994803, 946722870, 758071393, 166660110, 121921170, 506898957, 20164338, 697883466, 876375529, 886840597, 819112490, 921052692, 579466779, 134009305, 441951248, 619181126, 71868342, 573063114, 998700346, 288853925, 194127416, 386612345, 948523930, 732521897, 828584390, 596048180, 65820418, 783639528, 203029904, 773453636, 897196199, 219768049, 313903108, 315713172, 22128486, 903373768, 201267765, 627628370, 519677367, 171993254, 520438800, 397690222, 12192261, 298270202, 462824075, 674475733, 593206063, 394200312, 369040790, 381324188, 623665019, 830293704, 394132139, 889269207, 849716320, 526520000, 723942007, 60990547, 298759870, 498147262, 934150261, 826522820, 223306824, 768392012, 45819544, 471246214, 170080056, 552978206, 868166108, 136785290, 606568989, 931178861, 209277814, 202311633, 196287762, 450732914, 625708545, 129239082, 221940655, 12558390, 7681775, 32022629, 183191927, 888806611, 959740150, 528163824, 29619826, 778351980, 344138395, 195469279, 730247783, 143527647, 750821726, 725679310, 68142530, 925806194, 865788926, 385958589, 73794490, 106769461, 322534007, 576428042, 47243456, 385047293, 172733422, 417087532, 553187998, 920847141, 427312858, 65355665, 836928348, 152538682, 892086287, 393124991, 242065213, 10057358, 839757355, 805124567, 528076654, 253711002, 544170608, 533755422, 423587810, 698703679, 702678306, 5188646, 796161247, 946259908, 893781680, 393216379, 963751054, 832379065, 976928706, 893303598, 413041021, 931287166, 643843946, 416783448, 236831000, 826980497, 723316735, 682894546, 992428200, 664209864, 646238689, 508907417, 623477013, 779562910, 214959610, 492917890, 562712472, 253756648, 124889697, 408205976, 56297643, 29610706, 865507209, 861356918, 275700027, 373817618, 740379538, 703816665, 77613391, 441817959, 434197121, 477202982, 927319118, 774608565, 437938855, 504865844, 583276704, 200599731, 301684829, 12659873, 335416614, 298621179, 651918974, 874102388, 572275913, 390101541, 162761251, 858358360, 507394139, 896790638, 20362128, 527571403, 474064871, 114604798, 801094921, 355966032, 319396439, 683971610, 55143544, 347956180, 121277585, 385914643, 936460254, 814448485, 378835662, 274727537, 286325518, 765438384, 535483061, 362525121, 531015844, 273692403, 981014704, 425946257, 921805397, 682939727, 108096687, 434914787, 710464916, 660295849, 221122174, 322503561, 890731218, 195909851, 533863646, 848463923, 358785180, 550545471, 577040942, 604817206, 683220722, 23700762, 992141676, 204799657, 751914983, 553865906, 611369119, 83087256, 690123203, 767155931, 686849821, 583303428, 264683641, 958291280, 987887189, 974882745, 719315459, 16934351, 809956063, 778833810, 471408882, 669799361, 713645284, 742613930, 362841525, 365383310, 393824199, 551340488, 723586005, 272490290, 712943474, 125392592, 273642346, 520216359, 70958523, 478776269, 109299555, 413386264, 949163741, 603449914, 667404160, 640178075, 855046392, 438208201, 920811159, 254171329, 713974596, 732838695, 904369180, 956225707, 217392294, 196056932, 988809269, 38437892, 659697634, 689451872, 271506537, 785405367, 422625044, 423195579, 719696545, 361766552, 839016669, 294989284, 256176514, 987699371, 442745924, 924599791, 966152476, 906563362, 2460555, 187116654, 34693215, 527544916, 598936087, 957670309, 153810734, 159147237, 600013529, 557192140, 697951122, 797103368, 382670619, 409352909, 57595790, 384060256, 958839394, 796034762, 68013052, 796413290, 537428449, 763051145, 160784947, 996866227, 864532123, 807437194, 776909563, 857869195, 860893593, 104661123, 417009516, 553511264, 690660593, 409939101, 190219004, 659644445, 533724391, 699577630, 943429946, 317067747, 569266800, 304989856, 801359187, 326736888, 628227381, 726381045, 482261466, 417670762, 992858712, 249621164, 604231375, 230049079, 27702529, 444692693, 278418171, 465134173, 550610511, 147504307, 75474235, 97429233, 154093499, 86401615, 454084429, 506089199, 87777363, 140119911, 361205423, 698631369, 272490063, 486579206, 352835015, 842869620, 512787022, 651768878, 976695842, 605290666, 168229735, 124952418, 691630628, 635732583, 867099886, 110892250, 129423543, 176663903, 669628294, 355915310, 891128167, 960320457, 969321818, 221380690, 48899442, 881558338, 537628402, 545314795, 972256849, 94818388, 97911607, 255294272, 443803807, 151749634, 724639699, 912334504, 292123922, 218137323, 226247923, 173834492, 71757699, 298210707, 585301168, 565616097, 659645466, 163460490, 864850531, 168781196, 924081196, 162817335, 957752689, 116763841, 750657380, 72928132, 231978129, 589340896, 361373168, 262002620, 475665234, 712628509, 37123283, 547517915, 387633864, 736850271, 318807885, 367442098, 84684143, 422379166, 587195870, 514149579, 295753670, 267991131, 985607895, 966887680, 725700008, 608958749, 763715279, 205244682, 835660736, 319302537, 697556948, 164276195, 896967286, 268780174, 398204613, 690440732, 128057356, 756800724, 307315771, 851512551, 524098127, 49988820, 604189629, 902406602, 435839386, 727511915, 109014818, 196825107, 505196694, 489946798, 444592783, 905159260, 25797974, 339097362, 264323460, 200457757, 45648546, 411135055, 760333065, 251376822, 235967000, 436358795, 272489127, 938647882, 62890, 303601466, 699290869, 319234956, 900252262, 827131216, 738979156, 667151776, 172242857, 103695256, 271802721, 298213357, 607823695, 159589573, 6788452, 437640288, 857491061, 381321421, 596682665, 792101859, 880768012, 824102612, 72325827, 90464448, 499929574, 334312612, 312981460, 710017682, 994695968, 974567128, 674417690, 618020597, 949565629, 419520927, 454271858, 713236296, 428340946, 458398309, 211524793, 45394784, 419807355, 562910485, 222217337, 971218923, 577960482, 964718726, 656324121, 650938678, 243339659, 549979733, 441749483, 523463572, 952851982, 875437558, 125427257, 157570366, 427988676, 149842487, 215994395, 937020501, 771381153, 655526297, 101981654, 218378436, 577947274, 436830341, 964657376, 33161917, 969102785, 510647869, 175992816, 33082259, 120780270, 837459287, 974559895, 383162689, 490916223, 574195344, 840276128, 734284328, 887969944, 848932391, 717989086, 551512619, 74247937, 560336968, 326997277, 688063016, 456987995, 890682766, 391444104, 212170945, 306800863, 856982679, 642071535, 409247444, 955656587, 693530909, 266542888, 758446523, 905699267, 23218695, 939989069, 63388586, 240904587, 509682233, 374705802, 864216735, 605887917, 131447968, 608429325, 912797353, 949915416, 91881909, 133181911, 423375887, 358744294, 750342975, 768474332, 744602877, 222135874, 259450344, 70413492, 973578099, 308471386, 704525289, 450636646, 46768591, 451770675, 318191364, 940573471, 823413774, 72043870, 291840706, 208034510, 652558425, 691690967, 934293299, 944020374, 242753062, 185489567, 62840720, 424101084, 656326499, 396660831, 778765996, 205698530, 385423602, 248261713, 848827456, 795004343, 334619542, 650577475, 123707184, 816795852, 433376954, 309087221, 637914915, 940896404, 921279700, 166404735, 763352962, 867600737, 384042853, 288065287, 121054861, 201007904, 528869397, 584930064, 808629251, 452289021, 397675472, 43557345, 252068193, 806184999, 650427263, 25386091, 102868595, 244310768, 421099813, 216537794, 250836209, 724979694, 138932554, 376741133, 693263991, 68807450, 669240208, 89012339, 640551212, 831205135, 737420333, 315358949, 388358123, 568831786, 599551385, 279327425, 38500218, 714419464, 73118147, 624512062, 682341013, 15504259, 700832629, 724376357, 38370190, 937282379, 412044060, 911189312, 46352164, 291764482, 984809607, 627347605, 863579592, 987600331, 959262000, 324523297, 54189574, 724637618, 983508080, 816925729, 452365255, 236585890, 615233058, 249094190, 642419477, 168716422, 217643429, 293543256, 535778897, 184877308, 349373286, 505619092, 660550058, 562436061, 964143715, 750028299, 412178254, 978006708, 871783438, 960104232, 887981494, 60335187, 743129969, 107260384, 885276919, 265155041, 577361352, 716259643, 199055647, 115855744, 116729883, 524936567, 507950413, 268174930, 189335751, 38197711, 694401914, 488861579, 530944529, 949105798, 94475658, 433674660, 244047866, 208643166, 882389453, 898612295, 19370617, 909910369, 989042403, 78414701, 177239236, 943675670, 823896105, 692494607, 789999970, 676806131, 680136154, 643093179, 420443450, 163392273, 229818750, 565897198, 845640594, 942624159, 186841987, 83953649, 324821402, 965341799, 955992296, 685724411, 876221239, 435593890, 460716598, 152274503, 993943141, 392234837, 223768208, 342642874, 454331589, 277267138, 819869558, 773343485, 376681709, 19682393, 522573323, 239175986, 692185631, 855785877, 774179304, 847662845, 376127613, 543167274, 483989440, 770023109, 788094884, 935346407, 382817396, 244274060, 872963253, 55847252, 129218673, 811047467, 447378304, 374340975, 487140612, 51109105, 860213836, 952525401, 820009901, 616298943, 16833540, 297148790, 376351301, 577144247, 821623670, 343748635, 422298008, 777902624, 58666588, 983822056, 99332661, 373066656, 141368970, 116811481, 594431582, 185028601, 424446023, 797289808, 577510966, 323921883, 214298167, 963571350, 388857326, 241687553, 397171051, 613855096, 425901945, 617175105, 92621990, 140254911, 30060348, 591733453, 923977710, 530145350, 224999851, 809011096, 63670356, 948867257, 883471952, 76718216, 298410663, 328441549, 239458928, 857835792, 580961261, 972733479, 591952506, 306858362, 180607336, 970363360, 298949744, 639093143, 502269150, 867264140, 63037851, 59934686, 537649989, 606504647, 932694820, 336844901, 580956484, 802571513, 851504292, 308831442, 477033123, 981396525, 342171844, 745834667, 674604265, 992766694, 951164358, 2064621, 925373831, 39638422, 809655666, 975794759, 140790697, 66006567, 121752594, 586981879, 110475092, 191279813, 344084168, 457603414, 618127554, 936718787, 132190291, 323709344, 851769116, 267462190, 426957985, 836853383, 348375128, 429182276, 743160024, 481104986, 312609401, 837218057, 781225504, 763090041, 355215564, 207729695, 806082400, 800442603, 94274231, 652903009, 709778487, 907076916, 379570582, 291030003, 405985434, 16505934, 254782152, 178465627, 373481460, 838140045, 594956866, 338984271, 974631981, 630491009, 375075771, 764901093, 911981804, 53384508, 538743485, 503483074, 496920232, 723739640, 243843702, 546220139, 999087819, 14835980, 60246212, 487125148, 48283221, 979104867, 731792753, 858884252, 93013304, 868289744, 308765786, 473502625, 655781637, 719412324, 202863953, 481000932, 337248166, 885001508, 125826826, 738513813, 425875434, 492691020, 961188521, 885978935, 681104478, 976635443, 268201869, 720951132, 649737542, 322914397, 855479582, 925007860, 754172359, 757357079, 377524586, 513345552, 486147010, 649485290, 971871041, 659838298, 199357190, 9981123, 205583762, 938614970, 475208919, 759159266, 702091072, 51165941, 864722760, 692328480, 739353389, 545835967, 51099079, 656008666, 57731449, 599885964, 254097459, 553485861, 298078677, 99738144, 322200571, 246060134, 221563178, 604884924, 223267631, 564821628, 889261823, 799028938, 644486650, 296173891, 946140937, 227280024, 128598375, 762243384, 673689218, 928848571, 519966739, 465306740, 837426417, 149592649, 67895692, 391352133, 95574480, 791696248, 27421801, 408392181, 296657310, 517492701, 73152477, 660790231, 75420645, 831776718, 768019787, 137311920, 899719740, 190196245, 843970586, 723935399, 946304414, 707082006, 363009319, 307141647, 779636928, 316431219, 66457112, 972017143, 250262882, 444536561, 863910337, 159783405, 339626993, 904119878, 439651701, 789857623, 890794813, 612620421, 355035408, 273943780, 702192014, 178606343, 193769433, 971906029, 616825260, 484713137, 64306648, 153514176, 78995878, 495065538, 913780965, 971534951, 323097812, 936940171, 917870943, 845969909, 635460641, 957379026, 831430126, 12947896, 341166836, 869415607, 775642311, 95738521, 836454703, 91891496, 605343776, 130410228, 894148339, 949971004, 989761502, 89073511, 285421294, 967950628, 130632574, 364474585, 131118047, 686304427, 16946689, 812621477, 461030293, 305459304, 285707511, 315096979, 843924982, 836277888, 448386124, 384788670, 223354709, 583349614, 317695393, 693488777, 288893264, 773345564, 395914868, 412689759, 178691263, 387016116, 859066181, 276630524, 92597317, 722472745, 850763020, 220384836, 15928255, 135891140, 771964680, 859936862, 42650501, 41088044, 607823923, 277658200, 415031240, 85094155, 449893161, 86081394, 233774375, 826041086, 976176554, 305124545, 550306415, 124726883, 25185328, 859811931, 280134885, 223184362, 9019974, 68388226, 933400596, 446411417, 488418991, 815320288, 49188909, 608131156, 367315831, 680813394, 975673816, 571068438, 711040207, 400266012, 183585185, 916389127, 849831288, 677063160, 260922297, 378109212, 608852964, 348274069, 716732349, 742617028, 686707904, 597140240, 102863544, 820690322, 850884909, 344545072, 91636917, 847346025, 78751, 947499777, 25574850, 326105523, 112033599, 268985357, 663811869, 485769611, 899219812, 536158083, 560085107, 44935139, 984869385, 228041908, 50172042, 803607408, 971417924, 910305805, 844550394, 391357135, 661066336, 687922909, 117473732, 874485416, 871891949, 680945286, 228602997, 467919699, 763075661, 886460946, 548784332, 432157368, 525104745, 847286035, 327777700, 606641397, 499470935, 275204454, 82973300, 437124110, 114673883, 556666529, 156714416, 17162565, 634172257, 257129335, 799034098, 354496888, 84959144, 175403639, 81885910, 838934603, 511108713, 353801378, 983051603, 108253595, 802056467, 615646074, 813883043, 449815713, 324635579, 171467049, 269457566, 394441775, 488678771, 243854474, 467221619, 877321525, 739348417, 277495864, 707362306, 881763397, 625155147, 529907834, 139984149, 198419632, 321146772, 364603621, 778713356, 684496255, 919881325, 563933181, 352128619, 574328411, 578264658, 255625035, 834660430, 3437257, 308078107, 555338244, 670368401, 800189065, 355209184, 663232692, 623440114, 449066468, 520782022, 167837254, 619407863, 888187053, 932184822, 392974069, 643288204, 75326118, 220384696, 423263903, 672492327, 705640213, 293081442, 249712786, 745169075, 40486761, 297980780, 153655971, 645737001, 787475295, 934682188, 409993750, 250305589, 673974189, 28880107, 824363137, 178605371, 633342734, 561420938, 610422545, 731239130, 647154014, 698916518, 209305523, 504109879, 49007009, 701639883, 68592984, 367545074, 849923386, 751188553, 141565987, 208115671, 448455428, 979294324, 161566624, 418553645, 571454306, 728588150, 761578943, 779533611, 209538345, 210928670, 955838118, 798537108, 311165879, 404269724, 147192310, 263538331, 523965437, 930677984, 942214847, 327080047, 434641007, 77819804, 787846746, 779743191, 842010302, 795768244, 189129422, 157349520, 846661833, 515258983, 45486031, 969045898, 621335060, 883513749, 540323402, 893332216, 929123925, 442695392, 499121156, 439989732, 258160420, 548373176, 311298870, 324004843, 410557326, 371020366, 218048631, 396994134, 184543932, 671395960, 23341352, 14234986, 997714441, 956486642, 410118002, 596774330, 612181876, 877573758, 185012584, 62216890, 480756670, 850024398, 825607960, 193031340, 191821932, 374176125, 738871866, 674529901, 461084977, 132323928, 634367068, 492811756, 502890387, 861926369, 935077773, 968543157, 520692504, 23395418, 982177785, 538340926, 731667309, 700022242, 258760117, 108273308, 21836570, 745603005, 263696984, 625896121, 381815045, 718320204, 321129326, 115275877, 769776122, 18406361, 401987021, 216712805, 231180301, 950776991, 715430774, 76968077, 673117970, 862319056, 152192984, 594279008, 77695768, 251308482, 811288571, 103271920, 40237621, 398814615, 104254656, 78825503, 236897201, 8578409, 316274350, 429321342, 989621874, 499539899, 935475366, 862024926, 409444093, 547540720, 147873237, 302755641, 251064515, 439273820, 454047463, 257979076, 326152222, 305519475, 429626167, 850874545, 14675463, 295349120, 348272331, 291519018, 522196203, 644166284, 12095654, 649728647, 192410321, 799286961, 721825113, 921871445, 70181030, 728880287, 240183260, 861673237, 44598610, 614779020, 706075214, 568215383, 98168589, 946013634, 162785002, 129455506, 342166051, 802505125, 991247599, 140497957, 399988531, 39351765, 284762588, 203462852, 709947208, 591039437, 673603191, 184887647, 596013702, 881560715, 555553517, 987623457, 695013207, 689680351, 813283931, 624652388, 536781534, 489545890, 929684910, 534876765, 788175324, 584144267, 799572300, 116757500, 461364317, 577275411, 519439584, 110747884, 446680781, 331296772, 161217828, 351879665, 606584698, 114559752, 680077352, 681947904, 519017568, 89446390, 273474601, 912716814, 351905363, 235285774, 39733137, 498216970, 912836442, 627110759, 207566707, 334183952, 627382893, 745254157, 77355328, 533785604, 616870372, 335902543, 748239478, 781899552, 457488512, 374233006, 509411805, 723076719, 455567723, 321820463, 173197335, 757041430, 392118014, 515314621, 387219209, 491878755, 465454484, 810077925, 617817753, 9054686, 981878534, 990800704, 624720965, 621912913, 568197067, 607967958, 838276964, 532279271, 781798494, 225962335, 107185667, 342304802, 684766579, 885135960, 992464887, 513506443, 554965404, 770450931, 447215910, 390534290, 824429438, 241519558, 793769805, 87020820, 745281187, 975493612, 461427803, 939457910, 531746997, 988629672, 843542843, 970852526, 745433840, 105222577, 332811353, 355432404, 149119319, 617388687, 276083963, 784770504, 697148332, 699818565, 648689065, 149921774, 774418395, 678386053, 94724130, 353664183, 817830581, 942518948, 19297542, 885856780, 410667799, 912361892, 900517904, 581292011, 76495840, 538078650, 987130855, 644566976, 745449058, 623427076, 262091684, 74423300, 742710547, 642767087, 811681686, 72124174, 878781359, 34641779, 950943022, 396409663, 718539556, 944033670, 360912751, 447373145, 328639800, 714283775, 194661951, 260403741, 456590714, 420769335, 340814386, 873957376, 463905476, 985599086, 194036720, 848961944, 478413193, 607921973, 748263036, 58971256, 811404862, 304934860, 324366689, 393134822, 645147686, 652395349, 987075646, 543777596, 399046325, 955320518, 439151112, 41759985, 499452030, 845874615, 212256562, 878797144, 426029790, 158924490, 777087750, 218765274, 35330331, 531890359, 270748827, 603469138, 941704058, 25187342, 121528112, 491539395, 399240680, 971787136, 709698953, 477258494, 813601678, 889642273, 399328898, 622406732, 294951870, 84119487, 854947676, 360351028, 453986212, 810471154, 608741925, 995527066, 806025285, 275912680, 995902570, 741719404, 192925972, 143488870, 189153107, 720478238, 39869972, 867983008, 431193661, 188359230, 787172235, 372160132, 70918965, 453306478, 280734150, 650187928, 998864477, 143492438, 403066563, 166367846, 677613746, 930029746, 20006971, 492271206, 129136696, 671331781, 464807181, 897139740, 121262668, 67134236, 137115251, 697453014, 604634674, 512896482, 507352901, 434200962, 945160476, 396739302, 848407307, 237399976, 347982327, 942619348, 751073616, 441291728, 775229432, 292526793, 5026310, 637356107, 452209042, 296736265, 963065001, 263912006, 325393096, 706012784, 419895119, 678006833, 425247434, 882797638, 681797639, 513122850, 152564240, 145648579, 582956822, 343644687, 472713298, 184754974, 155961060, 718622519, 945542758, 214097421, 533679195, 737518793, 817052989, 575445808, 807588296, 770263764, 851307213, 102432418, 590482707, 124242299, 70965259, 164588678, 933575609, 468355981, 908315057, 234725711, 835555353, 695079538, 266414914, 847623623, 277926016, 740571158, 892508302, 679647012, 495737680, 529314454, 517395461, 968339898, 197070695, 765684883, 646041110, 84427450, 376728252, 731801237, 526574040, 595295864, 164440639, 262955013, 890482243, 410903891, 413133584, 288330236, 890105850, 39941016, 762898531, 274496129, 458735477, 623906685, 371090390, 444541816, 494604983, 523720774, 476962144, 95694236, 758153474, 490041921, 515428723, 198901707, 179595647, 303595529, 240415413, 962828344, 815743021, 195143929, 591106415, 837951912, 6527619, 873700936, 62944807, 57579582, 554856089, 139213731, 279253957, 780786453, 665920692, 744194753, 747468828, 795119563, 271594255, 685197367, 955888502, 534117415, 475010708, 222318969, 323363460, 849122795, 807610924, 735972110, 217826568, 527422947, 823989713, 610821566, 75383292, 467287663, 302218773, 732293279, 898122296, 83300711, 994462419, 331721140, 731164583, 891691534, 534175086, 662181424, 101350790, 534230657, 868859366, 418390305, 260561902, 93326186, 577416915, 259190452, 215113952, 107996420, 86444389, 928589464, 197262168, 383344825, 970616742, 940598941, 875743966, 23064450, 26262429, 901868863, 560204925, 973315619, 624013781, 318267543, 73623629, 396047753, 636623907, 899847660, 945001344, 330605678, 330081217, 161639878, 162095657, 530900097, 289579221, 916037298, 219241168, 616977833, 610939347, 197323560, 246615704, 78036249, 519099979, 158281914, 231958270, 572786070, 587566809, 804814750, 62455446, 1854525, 845706623, 109639129, 556631176, 297090547, 598195451, 254386876, 444709089, 793816200, 720004758, 820528616, 292888840, 383585771, 733929138, 866303185, 571510885, 943814885, 904657626, 860332798, 349206750, 773385642, 349233614, 498867128, 980717864, 764694693, 6599552, 923722954, 761233598, 914535247, 387968589, 124479808, 885270912, 213518264, 293021467, 961944691, 948945618, 803904464, 616182410, 458918695, 112576090, 794048015, 195647582, 583571214, 142172883, 973399236, 495491902, 846719900, 310553358, 513774734, 451147894, 747432287, 620606286, 393207099, 128378320, 935358039, 650452055, 904657276, 274857330, 545127503, 586958503, 932541957, 974285702, 429424303, 509233671, 928372431, 232214036, 957686551, 122887396, 181090135, 963834235, 947642810, 323767672, 255171789, 808233537, 112289041, 216206130, 54273151, 637781340, 723853064, 113264483, 454064122, 518834908, 821727087, 557618239, 894346368, 26637197, 251304870, 72544041, 512430991, 494660401, 264879632, 212651526, 845871247, 940914937, 203279634, 812941714, 337531545, 319678520, 234071623, 58482821, 874658902, 177978152, 484270408, 273229106, 2010358, 963533106, 990021386, 298308480, 173761929, 871037561, 247125859, 9320691, 430890352, 575505870, 524227214, 254145846, 419517304, 520604252, 751415452, 59087701, 441473450, 70561048, 285877079, 203756799, 585623614, 306049083, 663914485, 14042451, 295537525, 796152494, 334371873, 596493016, 131018460, 481939205, 252025111, 765495637, 152630523, 588367080, 932949361, 776970479, 268331612, 818489555, 353631430, 739681433, 159495127, 913831752, 511858069, 459520179, 536399692, 368081439, 427027817, 445780221, 452120144, 939993920, 838697709, 673659885, 189205713, 690662845, 353237650, 410500591, 517955685, 417714699, 120871469, 744106989, 577842588, 57752796, 751733071, 298643807, 919653070, 455789634, 239980744, 380808181, 500102099, 222338013, 190129211, 788620469, 854635044, 900327694, 241065735, 642751662, 907129473, 426093444, 364293645, 13336768, 826046502, 16576938, 523149555, 525685886, 74700154, 605604696, 816654182, 893834697, 399057154, 662501221, 265386914, 827866675, 380054915, 687835906, 91009649, 211907479, 316343123, 102000649, 699154016, 1545796, 428778066, 915376477, 613688419, 281585636, 527258173, 377016300, 195088190, 157387361, 315813386, 53080637, 999928819, 287596025, 594748423, 62630381, 421892799, 888964483, 377707293, 739001007, 148088338, 694152888, 549024947, 788766214, 378363953, 710470954, 21652122, 154680642, 507032223, 253944725, 157191214, 800719602, 652118651, 72300147, 64859938, 390979077, 794186075, 956106904, 598086259, 590832763, 223373330, 124727635, 30418398, 6581392, 944965786, 79390220, 207117713, 230971771, 45083898, 563641767, 957985391, 755140432, 259151961, 169575203, 982114119, 636753461, 954010195, 367234141, 572644747, 934701310, 405257139, 573952583, 216307446, 125289726, 97853726, 375071113, 18410848, 239131430, 600344757, 775388445, 709394299, 377248658, 898304830, 915733280, 294775709, 344786975, 924363340, 217199147, 24451297, 727861725, 497053729, 234123184, 927716105, 473519346, 285361547, 915045191, 651521414, 40922496, 42982248, 864614641, 867412154, 371861544, 352462195, 653412768, 231398655, 819558095, 83031349, 328640106, 222748344, 382324141, 191758533, 653601678, 491241931, 932244194, 940832605, 292954373, 151607332, 712731524, 102986340, 953633145, 861399770, 837978039, 811040180, 967095517, 107699530, 166769536, 279837456, 113199378, 571551359, 900197874, 638163757, 379755354, 584588780, 476679374, 767506271, 276885887, 958961256, 44086412, 879432332, 941626136, 94450201, 713334016, 512067280, 670874296, 443118029, 629525344, 169626038, 359431590, 695050749, 248021775, 61979947, 874572800, 10398274, 421618819, 127127038, 606450184, 307323978, 875830948, 94240509, 998314717, 334763936, 696288548, 116303516, 458013775, 783376144, 153840996, 550049312, 343794240, 25631553, 100657457, 498462030, 919104030, 730664436, 349477733, 879173716, 826782936, 945229660, 26238405, 434324761, 66306761, 130735899, 237870691, 963162464, 952856040, 425338516, 698840519, 51780971, 374226328, 177961220, 385863170, 435643071, 500053937, 468585571, 699613472, 69855994, 144167949, 469939105, 944591539, 784784338, 174836913, 447082511, 108492627, 644530707, 757785374, 490468834, 966884683, 281495298, 880390304, 999686312, 94268178, 637134707, 621531341, 134385903, 37692656, 842669904, 514057285, 143746124, 181937631, 830762776, 255351778, 485410699, 757315896, 336581379, 55467186, 984287462, 201703135, 255196609, 931706799, 781477007, 973512607, 709766616, 166083129, 898403953, 717395923, 568416869, 880396333, 390152401, 793221488, 179811391, 973699282, 736189543, 496638588, 331501699, 505734086, 371309111, 190232290, 38262677, 753017454, 147582028, 902802504, 100054734, 890547387, 265765874, 343461929, 224283221, 361778966, 685953320, 817885539, 720810344, 34741944, 214489351, 676319271, 617113063, 317087994, 762646767, 955198741, 598859451, 635988816, 425334720, 597973859, 259676557, 14700373, 272849474, 512365352, 593713907, 219167808, 276678675, 256394937, 921746575, 806437663, 256450334, 609931408, 51835198, 368769586, 767255150, 321545855, 426920309, 453869004, 88866526, 904335700, 491193479, 606339470, 894459253, 181980888, 105957572, 318811452, 732018900, 6797158, 30569556, 867092731, 879574385, 374354176, 844531688, 433119824, 576034910, 471921503, 13899708, 470924301, 452968433, 543298434, 62156849, 84970082, 879730664, 647200076, 850743493, 469325494, 815472682, 180862694, 933423726, 168886260, 362182745, 482695894, 575933566, 222593069, 364319041, 581200990, 318552066, 10157247, 170214087, 618335006, 998781041, 716733709, 657981818, 228981993, 914445105, 315753605, 177359790, 2640154, 149487873, 679185390, 492790695, 691466299, 103439907, 844498999, 335487253, 106003005, 847203569, 796929622, 763777951, 48664139, 627517073, 765912767, 299593761, 27344373, 683911910, 411270045, 405151891, 499576757, 589194893, 28149903, 955500502, 374696582, 593218487, 568280922, 764257779, 788310119, 242420471, 108246785, 159343666, 917770310, 337108209, 21432690, 49657548, 733722841, 248382615, 570204604, 365252429, 643183197, 148974759, 914948006, 740594899, 984574038, 413727151, 718267393, 710269716, 603045127, 846819202, 63506814, 967910770, 879361585, 370013256, 778520405, 415536277, 289537848, 300762837, 655161956, 647672215, 300945761, 894704523, 843323887, 364398480, 806682901, 110593685, 314922018, 596954515, 947613210, 976612540, 762965382, 550521429, 626508320, 437834529, 79988028, 450354961, 297239307, 640646894, 107014905, 428118099, 606120729, 568955192, 504864843, 54580986, 400694132, 486685688, 599480653, 298310393, 456474330, 203506471, 608309306, 209896787, 829376855, 415797149, 957773814, 316548079, 537452915, 562966114, 996090857, 333426163, 691173309, 789491777, 568008041, 689741044, 210100346, 365464547, 121731130, 264574979, 206033438, 375031391, 301445828, 808645503, 506472730, 782404240, 259369685, 291000002, 416030855, 52870538, 620044669, 577883229, 13988322, 699336911, 735512479, 763185071, 988399211, 576660466, 252264014, 663574847, 964942792, 158553757, 548912347, 518441836, 508616701, 126000443, 307041432, 643564146, 407851473, 302823251, 634513674, 15144894, 660166488, 629785281, 464353606, 569012899, 735266327, 129922474, 110064802, 128285440, 897447638, 325549933, 740760054, 362238185, 561794254, 284156581, 21361800, 448640405, 804247139, 640423646, 181670610, 717551191, 924902602, 184350660, 34433470, 44804614, 178751382, 669707611, 802074800, 815160463, 970474524, 901468143, 693320151, 323222594, 424028749, 588806566, 452122944, 424931255, 203750035, 700668962, 903972716, 765989376, 910403213, 268278750, 845759912, 101834638, 221846232, 335263872, 749890196, 148817123, 962041968, 948885285, 731124277, 470100724, 932830329, 138372745, 713690681, 645500218, 999843826, 159956039, 948815275, 221213322, 563786016, 518361494, 63638457, 128334033, 331175925, 374649117, 531162235, 716989742, 99166322, 68967473, 942948759, 161215196, 359827464, 89974193, 389265703, 66588632, 334193001, 950174000, 345173659, 553070939, 139847962, 12185630, 256311493, 470399604, 151888153, 66295390, 919618539, 210436991, 277893170, 762400649, 748256021, 34736001, 798403524, 543916528, 899956553, 33099728, 686780494, 600808730, 232430387, 601169600, 542467708, 239262578, 267128451, 814474408, 888920941, 480751485, 554276043, 260070585, 328097200, 424152231, 381299844, 447771825, 964849549, 28539743, 322151936, 98584508, 314854360, 948543078, 306602578, 171604792, 648373400, 490414100, 380054217, 994526754, 974771616, 284375334, 197273168, 198646534, 950860296, 338130646, 841552319, 477901173, 201194646, 329882317, 765546722, 732818165, 937951097, 514939689, 33465424, 942965141, 417279928, 268780343, 987311145, 807720450, 301820570, 255512553, 399062552, 469265128, 645017014, 751558208, 701009755, 377683071, 864342440, 72621939, 425165796, 714484746, 408129481, 959132123, 643853332, 861578089, 18356688, 766548094, 504045124, 213873363, 348381558, 9991392, 799651134, 303887172, 537302722, 890073951, 435537708, 806996882, 388064507, 703114255, 542711995, 838121108, 272181360, 187062381, 375831294, 781200797, 890300302, 342889974, 189147973, 216861575, 996961846, 607701016, 129951966, 235004401, 989488550, 610515929, 899215202, 399078310, 620722782, 637024152, 670930090, 773731561, 481055446, 369865098, 208272850, 463479357, 984926345, 252947460, 211221356, 96000728, 693965365, 108875987, 871669853, 988339056, 764033119, 605388919, 947969318, 420199911, 577847030, 524286781, 87824498, 681114958, 789913207, 564885553, 962594337, 865140750, 160451758, 181178219, 821666296, 194479614, 770056594, 705870278, 154473315, 404776812, 470969234, 838644660, 745240306, 611187355, 126284418, 996820349, 878771258, 181235222, 938053161, 376417859, 502802555, 229744268, 462079285, 594353758, 167483124, 453126610, 599253764, 909103828, 488490481, 990469894, 743712348, 466482009, 781672399, 441608552, 490859295, 664787324, 410470374, 77151822, 612883165, 12811997, 611077977, 319078684, 96624996, 554328852, 776758194, 466319388, 729212473, 360315252, 825984882, 152367163, 109233732, 370217839, 747757938, 142172406, 824794805, 782801289, 246140904, 333336699, 180783762, 500565070, 183017410, 416452685, 873357243, 358642694, 22352548, 363531197, 336261610, 525976516, 4843788, 678646241, 467024206, 308692960, 420281902, 242518927, 260665827, 214578477, 756256596, 960258395, 401817512, 202401441, 864970128, 989599104, 241856222, 88736128, 608105725, 546756068, 742512375, 504695426, 481670694, 792656222, 793673183, 762045617, 152532544, 156683993, 697031248, 758218028, 737323126, 192939504, 109063170, 562971951, 816596324, 137290495, 653203883, 201377819, 310044732, 528003464, 610630691, 828036976, 50277375, 78627902, 897271143, 667260989, 729050457, 843845508, 882003505, 383553830, 548692070, 560322105, 200915551, 701558286, 641447259, 46734066, 771072553, 903501457, 769383294, 301836807, 232911673, 449975253, 830518809, 906343859, 327529151, 706317032, 229867985, 35215600, 344915759, 290903947, 536103871, 220136453, 571540204, 724354635, 943304036, 23585381, 642851797, 264685257, 508679978, 133969078, 945941565, 488131471, 576477422, 248648152, 66735513, 975447016, 799481377, 96843856, 62122659, 229778786, 871321333, 473736214, 269572142, 675297960, 654880262, 287993343, 244784368, 725029177, 788030893, 773404904, 729051231, 613672592, 198324750, 439872523, 209964837, 565024619, 766058605, 411579319, 519821605, 456890318, 269437265, 114522386, 492001509, 391815689, 175197604, 848502140, 673252664, 804371541, 268963449, 665438688, 860296129, 479534889, 458087588, 402742708, 149555202, 608826015, 527444440, 603070018, 624851800, 730026922, 950371064, 58879110, 23022989, 109673329, 746879299, 561609140, 395055865, 716160678, 390693657, 317576382, 759811954, 128697185, 222375106, 846548557, 371203016, 547689382, 611324848, 284023853, 345189117, 326960779, 325857497, 658112850, 850609329, 428339989, 605612105, 97482304, 663813756, 24458106, 155552260, 907932877, 439598355, 282613277, 645152814, 293204752, 755716601, 495614383, 261857097, 10474830, 67678774, 699367212, 896789441, 634430391, 669672133, 512954274, 688896214, 649071701, 86069286, 474169754, 983208817, 57352734, 947355631, 455937159, 947759819, 876773392, 607569816, 433597255, 454327049, 379990446, 767217725, 376056528, 853839908, 730640304, 167248463, 958429480, 719210542, 395304701, 927925730, 989682802, 50774493, 69357282, 601627882, 118932522, 958886791, 958116331, 533728445, 606544334, 624451676, 719822950, 102298855, 56962202, 334698129, 329892736, 167087712, 41360055, 955163765, 905480801, 567868357, 518714911, 99842851, 369280407, 581858053, 19544378, 765425363, 93551475, 279231308, 253877898, 534752168, 299135049, 494973190, 800840587, 959201617, 643193084, 595129291, 459106686, 950309057, 468677320, 228965733, 563955856, 783551082, 411401141, 876141994, 763896451, 954562014, 534556716, 494573135, 836092895, 640936316, 576024994, 589678190, 126139025, 497464269, 912134349, 845863531, 611380704, 463634914, 433694216, 464530299, 347989783, 316898180, 452312288, 486417888, 771389255, 888590024, 437382930, 910767242, 593523322, 242260956, 665277758, 661158924, 20440583, 203805439, 884138581, 881215250, 209436591, 329150240, 153845864, 282930441, 249620898, 348620134, 971395726, 778318287, 305814433, 787515602, 312040677, 569693163, 390837716, 19520922, 705804765, 195154056, 936662976, 578320906, 17665431, 571087852, 885406818, 989856838, 878037606, 343927088, 424055104, 315845924, 448768490, 804220806, 710883331, 297185578, 24117761, 685278501, 770308785, 142953102, 607224376, 590824042, 981564077, 387676903, 1973318, 316558037, 525241799, 622791612, 25404427, 976346272, 741780673, 365797720, 579141516, 760957596, 210527335, 792750052, 849767918, 270328768, 737213549, 689887436, 791472134, 470649383, 894995767, 367575710, 615254309, 858934754, 124434712, 871509379, 119683159, 153973949, 554122629, 813669570, 720132912, 410953353, 567855650, 547454115, 879743486, 822272717, 681615373, 923372580, 615678561, 55447957, 937162883, 625971914, 66179990, 565258229, 220297760, 866856088, 427633508, 473041272, 471851348, 665101468, 523301981, 110527563, 982094415, 641064043, 535918980, 947416370, 904529259, 992034394, 456785746, 208275051, 496790486, 144487109, 275859759, 824575600, 908776809, 918533793, 883749243, 451079214, 514659084, 711134223, 667131555, 876874304, 209188096, 852341533, 143407436, 86741960, 542648394, 912192683, 672800292, 111698693, 144989886, 948272171, 55297028, 67046045, 512585491, 577173894, 782111720, 805338855, 889310852, 339460801, 39388513, 308613734, 930803936, 838357508, 513128743, 415492157, 732029731, 673275626, 131918994, 936984875, 805956735, 949512740, 175097434, 990208833, 553969015, 441138555, 995631937, 869225184, 681662235, 663694675, 250155544, 642292583, 898274894, 630057460, 904585515, 665629914, 13451273, 92538965, 478151091, 601958768, 89746435, 604889317, 42216379, 224305133, 472311164, 167710970, 670315354, 856795442, 497556799, 204568492, 773056337, 148627623, 975554384, 311167621, 909675887, 323929564, 487186016, 606093375, 370155717, 576876381, 560872370, 940678692, 302759601, 580519354, 457766840, 715471254, 618540244, 26399621, 667392731, 504749967, 408039828, 854194355, 24785730, 373843243, 808848418, 751818835, 513848141, 851387948, 947537768, 27310410, 885201751, 236358131, 394386944, 759554824, 922190742, 680587103, 739202141, 4376820, 986821237, 636871559, 162960518, 154017744, 648819068, 707360729, 43972850, 397138677, 569928888, 358708528, 101013399, 942926087, 142675499, 110629272, 649792385, 170861831, 38115493, 99329430, 575859919, 973733903, 726725472, 730538628, 738698545, 296148174, 831866580, 29755276, 326098941, 39616238, 741593022, 548780414, 748864646, 500783477, 200605271, 726099156, 646918337, 744000976, 646612915, 465857258, 146333014, 672648856, 212515225, 785184408, 799903364, 648511409, 449974285, 654492957, 925059137, 195727728, 414439069, 375150343, 457563510, 564711189, 586554293, 178490691, 238006267, 476591517, 97950895, 180076441, 426468205, 611260765, 30033837, 483167894, 778659504, 456252404, 860605208, 219969506, 391484663, 963426002, 105926031, 944387882, 102686568, 599559598, 965060642, 870209330, 228149407, 523893360, 813094577, 275002956, 396645977, 971845730, 725227847, 63284873, 256145770, 497580248, 672200968, 603765025, 542095962, 634775578, 769063813, 998087921, 533112198, 347394738, 731950922, 305432515, 836355024, 888136169, 503450506, 618237185, 145284958, 491349468, 255452838, 490617181, 823846132, 967444027, 902783376, 765375343, 405912331, 82110668, 946003051, 612399659, 763817565, 849980934, 601868498, 830979222, 846108278, 26841160, 83099126, 139650696, 399558762, 491474559, 251195734, 769585762, 626331749, 519637222, 903432571, 778313501, 667265269, 964366969, 296551101, 892601436, 380019254, 736729663, 950422188, 651558099, 834409450, 67575096, 221439297, 584661472, 927774740, 67993747, 202596453, 730144711, 351337010, 110777411, 949901331, 719864059, 575348484, 113928824, 263108596, 413938275, 697868585, 882710780, 536076409, 542212713, 748436206, 424742586, 180235579, 131939089, 975851494, 555243734, 784525718, 822168888, 816386142, 232855387, 868347484, 260044483, 321186130, 251048183, 647835185, 586161307, 183524143, 995850144, 841864976, 953596643, 929050425, 943047930, 851342796, 817445453, 725207030, 79395245, 50717958, 73039670, 206153185, 307633978, 922201000, 150757709, 101305965, 121243727, 656672020, 812256281, 217380369, 106170844, 590806499, 784575267, 100458425, 513747520, 940083951, 381900984, 953657990, 496467722, 256765763, 575013530, 784946229, 951089531, 371910673, 934060930, 53757829, 348692704, 719586927, 436982188, 895015164, 929667763, 638750920, 598023486, 582543061, 18629785, 108894503, 627245562, 243585782, 934093945, 939848711, 749642316, 235062982, 706235249, 679942073, 409473622, 905983413, 228249860, 297173334, 317728851, 758116101, 41282787, 122609709, 6607024, 485488765, 331351021, 487364713, 625245036, 317303583, 801504452, 855668360, 395795834, 646221441, 455237801, 289936541, 253045552, 56616102, 60487305, 714897693, 767337027, 696028924, 278537814, 585329512, 617308878, 802879524, 428327833, 771522415, 275446082, 337949979, 794094654, 204493257, 19753538, 868053144, 869938448, 611332659, 972821733, 614188854, 687525860, 868902117, 168929376, 827603061, 427284118, 334387174, 362273604, 342236471, 568133479, 773589395, 553612342, 235729407, 554446245, 499327607, 166470258, 850009503, 580386944, 947270605, 247742861, 819560907, 698919358, 298206008, 898050914, 667802317, 634415515, 629616100, 312119259, 260865425, 256947860, 605336172, 808583480, 941378840, 527825701, 510434736, 854646419, 551321774, 283846216, 547350013, 806011058, 645878155, 554274355, 711834869, 913378537, 346707430, 887299723, 300047438, 905571184, 441825127, 609880697, 996171854, 232657154, 9289512, 734690539, 590114671, 730653053, 38309458, 63216687, 909015146, 448766851, 54740628, 76426823, 489068945, 148257718, 122372566, 875693825, 875428584, 804773115, 277971858, 635211602, 325706333, 761118826, 898150885, 294266147, 777962213, 947409493, 259386399, 847594146, 868896767, 760716666, 166894256, 11537642, 660419204, 514271796, 797725750, 961092255, 796005160, 569653335, 715917210, 529821273, 70588513, 734458507, 465807294, 624847167, 780047835, 519118180, 697850088, 827461458, 422749140, 116234782, 43025603, 810741921, 129172367, 501902360, 936644766, 433631754, 592540910, 236775519, 475756250, 582308916, 602914315, 740437070, 756725841, 265206511, 267714486, 736057584, 182619681, 814134081, 657977201, 383000006, 677624383, 174685312, 444174775, 240607263, 627203076, 698075246, 838884267, 972112393, 558564247, 473343573, 431668579, 716407467, 800620033, 866295378, 676071920, 958106925, 601752440, 457386792, 237236829, 457422208, 198202069, 418642565, 455960317, 147211605, 37374511, 627963856, 34860678, 425963150, 561954998, 899040499, 718768771, 166356923, 269041989, 256345246, 844899207, 776236, 611571434, 728444007, 410024871, 718347517, 855587018, 125167402, 967395520, 571832955, 658293106, 20790253, 532720034, 538811710, 386182003, 922764049, 716904585, 661039797, 779480857, 589978254, 16974181, 662565004, 571625791, 461245718, 356111565, 509093060, 876386964, 816203141, 387437439, 670384580, 793426070, 886387856, 197353865, 592879161, 20811717, 391959160, 99987756, 873015810, 541151549, 95170682, 828004500, 861573574, 964693016, 230740797, 653527598, 126452888, 991675579, 943359862, 984887295, 48321744, 447659910, 775379967, 623937608, 413601517, 232035043, 163801531, 559469421, 338708339, 163376589, 249478647, 370839801, 458718439, 759419098, 265860626, 534842177, 825572638, 859497265, 646513836, 511536424, 216983714, 130785257, 82553466, 315434785, 553535164, 85063026, 720294439, 81503747, 450015707, 691237486, 249713260, 153056922, 622235029, 266292345, 96743856, 901770440, 233546308, 478251679, 873724018, 723233686, 272336098, 246776383, 238824354, 669389747, 936548056, 385355596, 884228024, 851281405, 891637159, 848124825, 470945614, 991851205, 808796342, 561091302, 920236638, 479580210, 213718544, 868423597, 769862455, 927718434, 386526351, 359998227, 390619413, 260220363, 43436707, 193581732, 712209517, 286540348, 875155319, 965515482, 754560733, 901038833, 696544534, 949483417, 85146938, 231509493, 236574901, 542750433, 635085005, 510333139, 911412576, 912995132, 26539774, 667968995, 362100565, 170725535, 670968655, 133241736, 848484607, 458377520, 869715598, 753845013, 698145179, 498275640, 622444782, 229960003, 174749354, 83630309, 598143925, 881963221, 30633561, 909723963, 254729546, 767353781, 990282411, 831231779, 36921313, 519381480, 492924233, 712421345, 314514903, 571568388, 100191206, 70304236, 12329897, 201836816, 921314710, 388877684, 967079429, 271118121, 131559977, 439295007, 669541934, 671257432, 381082007, 998899988, 327833662, 89171648, 434419001, 305696585, 956052568, 300968004, 9923455, 670731349, 975430092, 725174011, 472892487, 987094827, 892356434, 461557524, 471931741, 108881224, 158497484, 926445027, 8602998, 129069793, 126970636, 389374636, 253064528, 80803834, 950112616, 496103992, 258717409, 8802477, 46099857, 692254209, 298008812, 165769373, 192829599, 293582492, 544357950, 560793754, 217527407, 99733112, 957318891, 4808264, 75319619, 885053190, 566008941, 556730747, 220175974, 244127337, 660393242, 82949503, 23758581, 142194616, 307623030, 278494317, 308132484, 418767401, 374945185, 629624055, 578577256, 461171158, 202565668, 469727580, 426811409, 570918856, 934914077, 208642855, 137447247, 691669622, 466800625, 290726799, 393374189, 64172297, 40944073, 35878931, 970762946, 57397501, 566730088, 45097011, 760222687, 227242420, 571106673, 336000194, 347710648, 706268056, 727322546, 195054907, 344874821, 3963483, 64057993, 429824167, 932144299, 784754641, 28333222, 378699558, 676416272, 728815688, 399584216, 671035089, 491675208, 130579904, 659702736, 561838308, 729562985, 660644213, 13362591, 457592458, 323728743, 185876027, 728273116, 3759853, 935851904, 799378830, 265806952, 142950485, 703939331, 827117879, 406974278, 107769890, 937328891, 665211452, 9759834, 565070613, 926115696, 29010964, 826229542, 571193144, 902747595, 97105473, 397119747, 126080284, 742555226, 107694878, 489852685, 967261439, 868538799, 467596095, 947255814, 212024496, 417563122, 749656165, 783369698, 941995749, 971939417, 789540247, 207709664, 919482443, 547270931, 988584537, 285219048, 71105548, 808903371, 490039057, 165773540, 763516560, 875886649, 604182998, 766819599, 347978620, 362828646, 833982785, 796097330, 521254578, 716775556, 401046846, 733575458, 277745285, 978380478, 561615191, 438007805, 675722193, 406250718, 666211252, 608435917, 347383338, 910773554, 595787701, 183750522, 559541755, 829050735, 162457913, 714375660, 213693773, 865010261, 267649832, 974395767, 271688688, 313700224, 817985658, 631673451, 674707433, 445840120, 601588056, 743823666, 703298974, 767657662, 2982866, 257161563, 558812822, 742148034, 204113306, 81552640, 352472967, 743945357, 630544501, 116040438, 650711830, 568928850, 479624175, 290535578, 781898567, 671499272, 336276058, 386610003, 490109555, 16597843, 529967888, 452853780, 24713825, 281892153, 363398919, 591333788, 269175211, 751632936, 959224224, 803511035, 734782807, 942652128, 862831702, 562764868, 580892647, 574964376, 758090135, 587365304, 226078221, 264730030, 894146577, 963389771, 487970324, 862667356, 298672452, 386134065, 285433242, 602010669, 350233550, 148224646, 446503933, 834294900, 253102670, 605731254, 786493894, 170987447, 88975862, 330576481, 90826787, 515503420, 27507147, 656058845, 945230873, 696602486, 735482337, 288094028, 660689781, 875330852, 204262611, 253019179, 348058406, 865899207, 632775427, 151368160, 999181737, 185291850, 761021460, 715428955, 477386378, 808609977, 435128009, 145270300, 359805680, 310020976, 661449402, 179320090, 852105389, 555012555, 104622266, 773560205, 55395634, 630802424, 115579844, 641192678, 569539870, 512671811, 272919289, 204616167, 416413572, 894185841, 205717229, 56501840, 953836314, 226820336, 351997384, 228323907, 885220098, 371520964, 142408967, 186527769, 726655626, 269537648, 427321477, 878431829, 790591539, 450945796, 530921124, 575523776, 129783815, 254952147, 805938848, 580949601, 435367635, 988178605, 785697923, 102671592, 316087141, 549287345, 945875700, 644593166, 681019106, 909305053, 822198933, 749360513, 788278309, 205069271, 621723595, 248230141, 178211155, 954790997, 903802548, 536816818, 435874807, 837191350, 791586830, 721733230, 183124357, 722924660, 133892660, 778054984, 33035901, 166708071, 696631817, 224932043, 150396264, 696174918, 171603857, 36088166, 913280557, 88903409, 299866798, 322357577, 634121866, 318344841, 149365416, 457484233, 30829112, 653422330, 698269517, 378763683, 931062565, 393383040, 652339196, 963115127, 960350890, 353003362, 962887215, 459779896, 244656513, 488151438, 92539425, 158199868, 556999055, 983177258, 266686699, 467370765, 361727912, 108422875, 173682038, 51070506, 541689265, 23904452, 582884234, 632126464, 610335253, 673514064, 205017742, 820752197, 271916803, 774015184, 49509864, 171177706, 847271033, 841651298, 255512118, 387093864, 952883594, 900987411, 899220125, 818954697, 952905155, 208696525, 448552931, 783951880, 321844747, 200463454, 423030871, 786670385, 735316830, 63124525, 302568725, 685100314, 2293479, 142350796, 556913102, 746521522, 522041725, 350293253, 622538271, 283394076, 861993746, 284173846, 63590063, 710682624, 542559828, 631011986, 431451815, 949088130, 607440088, 676792070, 203571781, 406602421, 37136317, 711733511, 793455766, 706263112, 594502087, 205467895, 698458508, 380891952, 526545778, 139613720, 634968826, 825663128, 884731483, 36270227, 230477181, 383093616, 505595619, 985791226, 973277178, 342122286, 235382989, 841528579, 428668652, 489938805, 850978965, 211206630, 622390557, 771881328, 543432579, 737501907, 37809530, 44819159, 534284237, 448198208, 232511895, 250743209, 961480610, 842129145, 280230470, 884028681, 712413700, 598746015, 459616120, 519104078, 859805160, 175688392, 59335860, 58429467, 826863721, 680523312, 433926141, 494342506, 697384439, 593947662, 897995099, 931276148, 368868107, 330177607, 1768026, 763510650, 818044343, 185618379, 980572214, 484859697, 643453243, 754339942, 140027942, 33161101, 57478263, 377805387, 49045106, 322611526, 237976507, 657652749, 14746949, 553031572, 911597877, 306636390, 654603776, 95842906, 67236799, 929274069, 796148033, 186496265, 747802984, 957233333, 763115727, 839218343, 124042476, 669214767, 257520988, 773980604, 691354144, 983389359, 283607938, 584000481, 861390436, 608848487, 511202202, 289694196, 613817658, 381087811, 812912608, 493577372, 599079008, 305320848, 542495380, 725845124, 586149965, 449764465, 885582581, 613225548, 372235311, 834989377, 171201199, 571651375, 916498525, 98941061, 867223179, 776407157, 885787679, 495325968, 279278634, 147531386, 555374406, 272772419, 894693673, 920276966, 897484754, 566383345, 43597248, 275282848, 789737133, 165575951, 476765191, 455552393, 419564280, 279438061, 376498957, 272203987, 273838543, 903251143, 429580675, 12548010, 927236900, 932114627, 422748104, 400043963, 142154060, 137311609, 245937759, 428884171, 695802606, 385463019, 238380203, 600179932, 438680055, 429298434, 893757772, 702032591, 366174303, 715515501, 903471945, 558287990, 788171912, 174022236, 168598077, 77694333, 51023043, 521261398, 518823462, 775635664, 4409802, 415225889, 350115460, 410944067, 471679207, 938625305, 324289078, 604221683, 997819284, 540643235, 6451649, 320550439, 949190601, 418104136, 685690196, 23222039, 859623359, 567891395, 136066555, 69634728, 586029743, 357937850, 633253150, 390234258, 108793308, 653504976, 552274088, 656118031, 28015452, 206053688, 253671394, 801149114, 931935049, 502583680, 252772525, 879916903, 123418168, 441968265, 607140916, 38922610, 914585943, 411766745, 641275439, 877520385, 382112550, 490231065, 304369501, 600851846, 229995964, 530180451, 272046981, 621158667, 769100965, 714934974, 47374760, 714702493, 699153927, 313875426, 777936926, 978869241, 147935786, 806749923, 624663010, 741521432, 58144279, 4669845, 522815302, 621938774, 692452662, 139175196, 385447291, 431957352, 585633229, 422648663, 442574108, 234519142, 370271529, 47442374, 572997076, 441008723, 719738079, 248144230, 104991562, 641780780, 221925414, 322111555, 577945262, 690843516, 707365091, 677920310, 187667263, 601727217, 80157736, 201036628, 398903827, 478438562, 222984147, 215748439, 567227935, 764690304, 125240674, 165539927, 837707462, 96394794, 311165297, 906921180, 121194161, 929951718, 676838145, 250905658, 324793514, 592381030, 647721559, 816293490, 578446683, 809264443, 658959216, 953606828, 343515342, 876045618, 76565077, 787935893, 552751188, 558472533, 210758069, 489176046, 539091534, 654752838, 343965797, 893857729, 689514235, 700477732, 741742547, 936736190, 32795183, 598570371, 565898641, 200601369, 343581074, 582424064, 276101063, 343579977, 706379044, 201807693, 142315914, 369276638, 973305229, 836134719, 629434270, 928583641, 923893517, 157013761, 972641642, 268844150, 138403152, 724864250, 773115163, 117754517, 352302101, 597542966, 222412709, 784545020, 43638891, 660821098, 887222293, 726420880, 521818264, 9355938, 908364816, 692359633, 660392357, 214408255, 521500626, 590519597, 600058627, 512073058, 394605428, 760298296, 231694802, 198711990, 987895318, 701002828, 856971799, 747240675, 202668731, 444338524, 273185518, 956348855, 648328729, 245020032, 223174782, 883277317, 456747184, 463635349, 453082083, 843959034, 274117803, 443793388, 694530142, 412081722, 569537776, 832907830, 985558547, 233556616, 343050973, 820920296, 982113752, 341208970, 964461970, 758107123, 182015251, 26371136, 874484740, 301054222, 467838715, 226595589, 689554715, 760506289, 903900893, 99002182, 674973228, 38689791, 612574950, 11741961, 583448645, 422735022, 66886436, 221518601, 353074405, 328075547, 995507400, 484287910, 245779777, 193735154, 924698399, 96195281, 202115537, 755374775, 773691246, 810016538, 2423260, 114564299, 877870364, 220499561, 976482223, 765546179, 284273356, 987929972, 609673311, 334428101, 682413442, 944308213, 139317890, 179291325, 533163268, 848428316, 947428010, 77334530, 832706797, 624996274, 701484136, 952971293, 670677308, 820393690, 95534508, 731912278, 364345505, 967483501, 899888598, 215099169, 414189476, 817438191, 650352547, 210496457, 788027047, 349038758, 46241559, 67581917, 645716435, 69973289, 166687886, 890100959, 152346749, 25573720, 309930463, 418150709, 98557103, 430692763, 220899703, 868138551, 186213924, 319796286, 870417385, 343324825, 133545501, 972552292, 576180663, 319806925, 15796603, 10862839, 730837797, 852198931, 341396980, 350428842, 565896504, 348263558, 850509990, 2030500, 538128218, 213085160, 798625442, 638420543, 406010660, 939180175, 846240920, 181498434, 973427505, 907836587, 5554264, 703886393, 646982458, 556298467, 967518037, 406203648, 140441158, 671399645, 342409066, 196839238, 759363348, 770265983, 162879156, 432389159, 120077181, 505418909, 785395226, 673428938, 546209521, 289710835, 10517960, 35293939, 983547625, 535295282, 200966264, 268229511, 11270774, 728423933, 941872019, 385729634, 772836857, 116343673, 875285132, 763403491, 630844353, 173749835, 223346410, 981864509, 455575936, 745326262, 742313520, 610821624, 143200908, 931813061, 556329186, 52448870, 966826386, 4325908, 445119759, 297632592, 381216272, 79869461, 709780932, 716084465, 295259386, 521971053, 676653802, 569910039, 295285901, 627138537, 9548459, 684189309, 227932227, 494674812, 491721777, 586080326, 796641229, 912564510, 74285783, 683589556, 273953243, 543639707, 217789846, 292209246, 580759427, 292331236, 563905532, 119913159, 742155912, 900530960, 768478915, 310448213, 170361379, 879431527, 983545354, 947578101, 842012793, 507313604, 100741624, 111719683, 774201694, 350587226, 892464468, 917037737, 869186859, 904300983, 380182734, 306440194, 626279369, 312397848, 452996680, 992452382, 907269608, 254620311, 625361562, 185081770, 928948996, 933759802, 968531397, 786043920, 821863938, 980079585, 864979196, 849602257, 351894446, 1241799, 757388707, 354558357, 492693747, 73753629, 926151777, 597923321, 591575979, 75723669, 842913653, 881672474, 939947348, 98716777, 269610203, 634116871, 613018587, 773506988, 590527885, 522090433, 21184456, 170308684, 945177194, 16446624, 284850299, 928273282, 773137990, 587380225, 283999943, 626093678, 65225674, 31251552, 278755765, 234447933, 196594782, 80666909, 40938148, 366301364, 831292215, 986121988, 366152541, 577154333, 827684868, 922826313, 66450568, 354328388, 803661357, 585900117, 861875792, 307980098, 261974556, 908329522, 955819427, 276435561, 298544633, 214529478, 790154430, 753237872, 572127466, 501853700, 883311319, 433416476, 881061606, 397773308, 93542569, 661770628, 64171548, 540166336, 932729723, 566062865, 14523970, 594448999, 449661795, 885342280, 124739103, 328439532, 920855935, 773757567, 314054659, 639936298, 65210227, 308997900, 733567556, 398831254, 571564958, 887868487, 625653438, 173198265, 769040056, 794483825, 83658772, 936232199, 424371909, 329399465, 115830814, 646719744, 357560733, 995707831, 280200162, 26675229, 157753496, 774820259, 166863833, 797879185, 131918517, 979353381, 346103336, 116032021, 638009535, 158615391, 527441239, 752041214, 18154982, 841399250, 857585913, 657369043, 795175644, 666677082, 468431471, 342275012, 726695451, 702688602, 12165007, 57231374, 372994768, 623308201, 935101116, 116000840, 550915796, 281723757, 859911587, 597869346, 170236535, 215327984, 296182567, 781912446, 667376160, 386578541, 990304091, 485498043, 800819171, 312451629, 252600935, 756165169, 161086614, 759693073, 271995401, 623622980, 400076717, 181422900, 43716672, 206474685, 819847359, 222484008, 756039865, 288289896, 905807970, 708398115, 385791847, 260787500, 570089209, 525228390, 782871519, 74290098, 35560912, 30494063, 781875777, 122387676, 969801962, 346514818, 870459568, 602264296, 761899919, 936422751, 643875696, 253982519, 971973904, 262296907, 608676228, 619066779, 75066037, 885580201, 748820652, 410147349, 995866247, 63464827, 267503204, 973860174, 232969636, 777813045, 837760192, 685583017, 93743727, 643993645, 175874157, 318690095, 7025332, 38158996, 599883746, 115692942, 973990194, 777454834, 378516662, 840896593, 594230819, 426496562, 509429025, 199872488, 844450225, 362388088, 263549449, 942382138, 162612259, 970389509, 666946984, 273093500, 322925367, 249049170, 150808859, 708533963, 730490012, 149495025, 615593210, 88132652, 921469115, 714133731, 224987040, 246287076, 30656034, 899365519, 320848307, 156364092, 212105045, 579790198, 588570781, 648669342, 815978968, 936184963, 995086363, 273186148, 472810868, 444284796, 131764204, 441664859, 872731759, 303846017, 480368897, 202908574, 58736094, 940736020, 999670745, 754794698, 806326517, 130774756, 627328984, 3693478, 587199201, 718557656, 868189157, 730570082, 880927227, 589568076, 191538469, 294804283, 40436027, 356185333, 198135487, 742880112, 951505425, 611583685, 258310254, 227217798, 479129908, 208208167, 973067127, 999626028, 955288854, 255052907, 202027387, 883358444, 504542817, 768142542, 304948775, 106772658, 806695304, 95385783, 6788609, 374283580, 8167989, 655067319, 390145430, 474525819, 376699877, 540809630, 822561821, 88525525, 935471031, 53473425, 342602647, 898933712, 271108287, 683083053, 491438956, 377700909, 505897761, 427694535, 59212581, 753769277, 387493239, 840772804, 7261730, 766547562, 492708501, 236901566, 293431198, 923535691, 916568374, 941506609, 662115763, 628906758, 443097348, 249564417, 538485910, 57214439, 649809102, 730965687, 362350517, 172370651, 798107027, 633429910, 753121582, 995146350, 313256773, 507087021, 474636934, 53117804, 341237712, 703380744, 977259551, 547431724, 754470646, 773482784, 894488026, 606412430, 2840237, 567209281, 188108507, 732249740, 770874481, 749229168, 437201376, 251183295, 28781, 536068182, 744685711, 943677892, 446351896, 355389879, 958458977, 658933708, 872779861, 551807398, 6007088, 147065721, 448832031, 610529921, 221497569, 974607805, 444512287, 939573477, 410418952, 755041061, 308074141, 434255615, 250008459, 664677705, 812085575, 755276867, 59331431, 441076759, 859901181, 774474816, 720143193, 74465121, 522337084, 307042469, 971868595, 621841554, 719081896, 132659371, 940587018, 979377484, 770804555, 891781013, 155625009, 898670980, 370870734, 526774923, 961668529, 423546074, 813279549, 672540296, 498808041, 663462510, 46531969, 393491805, 249552150, 858713273, 364685488, 383971632, 476536272, 555352135, 428706917, 263766545, 554886521, 781250854, 839090344, 119786312, 706533947, 547619261, 890420281, 737314067, 838660135, 825580873, 371044816, 510530317, 86464663, 834166614, 796063840, 902820923, 444873940, 65051458, 828757672, 418951770, 83455387, 679930456, 104520358, 980267448, 46436720, 189459688, 657360723, 859715673, 706560321, 440244842, 660687185, 771366899, 149903587, 392011120, 258661060, 704375578, 524522392, 863144567, 514018132, 276476809, 741681447, 837536936, 132543157, 39921685, 499215753, 261448036, 734538734, 671101636, 570237609, 171655464, 343899835, 652176775, 544706750, 119276997, 489763524, 656803756, 97317066, 439123969, 137663213, 149186381, 62228819, 833748497, 741392340, 192941636, 797712670, 6641855, 43603690, 452952058, 332722444, 773756490, 58372177, 866644438, 216707049, 603715956, 167739194, 933963062, 437016053, 614163042, 429071909, 24972223, 576697827, 882370134, 142493042, 56157869, 405511133, 63353629, 263948086, 569513286, 70712511, 957180095, 431915024, 588370174, 299632087, 772572503, 390711213, 227910846, 480231764, 569855944, 824773420, 725095763, 579450404, 8121304, 720955051, 425922287, 721683238, 497620907, 66256806, 220474462, 71011071, 573902770, 21730352, 738971140, 583199955, 788806316, 101725112, 713715045, 339237771, 783740859, 207881665, 50857799, 194667753, 300029860, 376023187, 30563406, 268965489, 340608738, 752208540, 5904370, 443104828, 365129570, 406497834, 891028021, 192682737, 59239884, 208790671, 674327250, 532154980, 249779074, 329067631, 727790752, 47826698, 342757551, 834653644, 495906491, 646442594, 576501615, 406266697, 622239945, 636740626, 39268518, 27239744, 581365673, 393430874, 838249600, 847085531, 625441804, 818401586, 631115453, 19457520, 521630386, 134228089, 871001200, 548940144, 773108786, 408331942, 921006654, 678952140, 372847431, 190492685, 281740023, 523510321, 987030618, 963503053, 92620724, 856097255, 784504031, 196416775, 912593610, 262284773, 940549449, 810932503, 385633623, 806126091, 768582125, 319831748, 354037510, 301454323, 906838760, 695378674, 604563980, 223748419, 122894254, 521310378, 687445015, 793881787, 934137086, 190359078, 921280567, 64984970, 361727538, 313021977, 848131627, 870636691, 270534874, 771572268, 599369686, 456418941, 274735580, 434775909, 550162714, 60241576, 144105415, 332090759, 620743934, 476246629, 911793764, 153497638, 914034848, 613099060, 494623559, 65735533, 99257693, 861887524, 937129556, 222472556, 438278340, 434963809, 874998975, 614814677, 524266798, 498298649, 551023391, 514983722, 267565286, 204597627, 775775540, 351416712, 807075590, 568093290, 526559749, 925175827, 911196727, 965678865, 353809169, 502560097, 644545754, 777822838, 158362822, 471040868, 308675609, 649079251, 357848077, 635765825, 372874211, 501858866, 572947887, 462121036, 522030607, 32662179, 900942105, 665718467, 419181143, 743711958, 891258210, 810695443, 261873050, 860595653, 19982373, 230194415, 995346071, 800718529, 691541865, 855852330, 452491415, 219737099, 804408276, 500014418, 796924644, 601740393, 850873654, 593007926, 63371554, 668278874, 758419691, 435884785, 966642533, 38546127, 29282188, 244111992, 918341755, 76264712, 791462178, 780227568, 196021726, 114628219, 952811990, 419258322, 20873418, 251210621, 152583731, 221882833, 226798122, 788344155, 452391946, 203525739, 286767813, 989650405, 235132411, 537117679, 929995819, 720676765, 48559464, 607560921, 681500546, 653686137, 617560796, 364740095, 487085781, 998868, 871731496, 738982901, 243058973, 98481485, 581681126, 2253853, 285024853, 154964520, 842903140, 155574979, 874233254, 143174759, 420880403, 266443027, 322069289, 130671581, 582032577, 53499350, 299771291, 8914151, 172379908, 98992580, 155698448, 662392866, 46509204, 737658524, 62043080, 591337568, 315110893, 466795490, 814026525, 75741541, 130726291, 87144807, 720772333, 444519483, 813147043, 509066928, 288248111, 930577232, 271720101, 283187532, 339853694, 699220675, 434629291, 826475876, 84215293, 343465807, 345266847, 932176377, 760230747, 287989608, 371815883, 377396533, 993104014, 586068116, 94560849, 102280975, 153816200, 375711050, 962215898, 292474226, 978229554, 19735077, 244497138, 408548343, 363273329, 350654211, 548723805, 655153981, 107356534, 652369617, 246416814, 195779752, 240434135, 714516991, 559975814, 81982207, 525795697, 965056759, 231997064, 726743878, 764745252, 160899458, 76520574, 474880225, 295105452, 341791562, 29373077, 964160822, 740158925, 698378306, 561033044, 89230859, 37197055, 811845341, 323821640, 313625898, 550168729, 607981528, 613374777, 644643249, 911883065, 346481735, 66216127, 234246093, 780839513, 752865701, 253236984, 205465050, 934651972, 794057031, 854462218, 905959189, 614237680, 117593740, 855512861, 975191454, 29553780, 874275503, 732493028, 145798698, 798104887, 184967788, 187897837, 221676075, 350876160, 755311664, 449245648, 599284890, 985793632, 458342588, 916326033, 510472193, 552902443, 362422359, 85144902, 689463825, 21822117, 794790730, 528944461, 107253078, 632869893, 979152324, 690340980, 939195936, 135656101, 360169034, 850995601, 750676760, 590204071, 825092616, 441041026, 963637885, 609852171, 380249509, 345945038, 694400818, 711596131, 526070504, 987900760, 441307741, 740273000, 247256905, 662607293, 834156150, 426312731, 66438980, 589131227, 657444718, 711537615, 934844319, 605276048, 38485112, 308271446, 933469038, 862239689, 259155810, 165035029, 663530225, 751527942, 82005509, 524404488, 847429734, 10783, 891145322, 967483561, 515091517, 687480847, 432281687, 385566362, 316028947, 567290654, 650123922, 853608703, 960203699, 480814442, 206046734, 5437419, 375768717, 735789732, 109414073, 753876650, 473977298, 446372382, 116261282, 313175209, 679884925, 22844930, 980861441, 346127201, 189705879, 509738157, 578998426, 877506535, 996423992, 588667976, 45514723, 445544900, 199193075, 262347456, 516673934, 257348033, 177607361, 363446519, 209859794, 534771329, 470465036, 7116952, 602492476, 532561829, 395311495, 468969870, 770853196, 19401797, 514563802, 668344189, 763964105, 589347079, 463305624, 807386340, 435065629, 928600503, 736699185, 794002565, 847050629, 627694243, 858994053, 750780129, 351940224, 690432526, 160459396, 141985556, 825306433, 391994241, 89898724, 876687258, 919925252, 349294506, 838297412, 191195686, 908947410, 994951211, 963885819, 651292554, 369810369, 147361788, 292864122, 896511502, 244857168, 679644608, 438034863, 886913119, 355944790, 658669769, 417664703, 250658792, 912992170, 463541491, 541712331, 691250829, 967379354, 240327550, 579155759, 147855690, 267274765, 623004846, 808853138, 884463947, 579276219, 225803222, 971961000, 748880329, 973722932, 926263792, 528965300, 678259283, 380801148, 807876838, 939043808, 618629658, 197381745, 688353308, 901030159, 469022534, 224351500, 501331630, 23712731, 245030066, 508471640, 680260194, 642533552, 770736915, 810076051, 201763312, 663649645, 373757915, 120807464, 540727873, 440092157, 204166625, 857559122, 135133632, 895442252, 312224482, 948378688, 353970054, 171287580, 754176139, 396702244, 731435348, 667064942, 912307740, 673057777, 967670333, 387669828, 447397179, 636738539, 250982948, 495493317, 677458323, 811628742, 241391960, 233728241, 721049889, 452439661, 797233086, 807808001, 299208580, 284647994, 618258235, 867982045, 245222688, 720815570, 755675549, 35301666, 730288104, 630523818, 970674182, 813324758, 42207272, 471693026, 924827524, 851127434, 220050272, 38426531, 706205870, 284225753, 511111245, 132479837, 382248587, 577573631, 682132153, 589397842, 352106432, 615908965, 293336877, 448605440, 828307061, 147933362, 958119984, 791383399, 198373245, 91874587, 622551959, 731041620, 463852643, 450463718, 363558872, 548602181, 542470699, 362574409, 967317299, 832097680, 304468285, 823583999, 318113835, 711828236, 292677883, 596338206, 518638419, 377248715, 427813754, 103083603, 795045798, 216417851, 920044708, 486066661, 490993067, 809678194, 403588386, 633206858, 948270863, 383688982, 901905774, 869812010, 15138104, 565550387, 253964280, 182218512, 176566078, 997455351, 507979045, 706506477, 922861836, 868827311, 11263679, 784735739, 88465611, 964414426, 702169174, 324855302, 851556376, 363690345, 347299673, 197829214, 116046606, 342031189, 372249953, 203766941, 503314233, 253295142, 562745384, 847698111, 981695918, 276338163, 471052698, 338695666, 204734590, 98005565, 411067139, 108506160, 147391198, 180909762, 84749131, 501911627, 726169185, 672697045, 61872525, 996432257, 970943635, 381450984, 885808027, 907401963, 226257850, 793049261, 934620162, 658436587, 299213671, 714416244, 966138350, 135567109, 639376670, 660858687, 765816651, 546295251, 765244354, 424264476, 110204974, 380816879, 102306566, 270908957, 267122626, 884201741, 535710821, 44777760, 157623759, 640925399, 866112498, 484738243, 294785382, 257733132, 662220220, 872540675, 609893626, 335964510, 626311931, 512252086, 551472425, 391929860, 752091745, 197255468, 290437296, 346947797, 19281933, 839969468, 180482502, 239266326, 256057698, 573445591, 427552896, 525833559, 694152751, 46418508, 891059442, 16121256, 411211393, 112100770, 217175366, 157192487, 356211655, 660010685, 454511237, 172757944, 607514654, 354661828, 522684469, 137413195, 909908582, 608730163, 235659577, 628794215, 454480558, 275216233, 982982250, 215793167, 552845569, 162686503, 552448245, 583549779, 576480384, 678746668, 65385372, 786689976, 342887908, 240666465, 251265133, 699888802, 425853820, 931424385, 991819307, 190567492, 525320738, 55922221, 763626434, 562308431, 188149268, 429779417, 561926160, 922522204, 60752751, 816376252, 79743893, 627196348, 262364670, 497868391, 452511756, 820005579, 278923199, 791250193, 488757324, 218048007, 540906627, 655433378, 939902746, 780158478, 13787151, 976985572, 953460934, 300436624, 918995931, 317009325, 447367252, 10149257, 884350320, 703619658, 412979409, 823374977, 491373315, 731787088, 586938645, 158092784, 515674111, 487603406, 439164413, 507972551, 617647275, 659268196, 501385637, 323150593, 564773354, 259347277, 231553117, 494979086, 566552986, 952788954, 729665510, 612855448, 515729813, 882951093, 463068529, 137077489, 915508553, 750935161, 599258290, 88353951, 846014031, 597321970, 597861479, 498695734, 421257100, 967632678, 431614574, 88687686, 471864333, 358997777, 845764517, 30989850, 14084829, 455201729, 238537413, 328011146, 717488994, 944999806, 437085807, 964484386, 381695428, 481580260, 774643700, 295410033, 716561743, 549878698, 164345462, 149377376, 783003528, 956681905, 642682020, 828452004, 14518017, 612387165, 684389000, 801371048, 234467628, 628498227, 271868922, 744689532, 518653521, 454753283, 617902014, 799103818, 875707364, 28013364, 702666064, 646894215, 926379770, 232112995, 942908207, 977932795, 163096920, 117899708, 845987094, 62787387, 778386532, 415873382, 309066817, 184416977, 71774910, 236325488, 518699568, 967939850, 511860866, 11915522, 298050972, 843259950, 689719400, 999198461, 766145347, 226180456, 948464958, 931507142, 489599867, 152696781, 223890982, 496896039, 524673271, 489354602, 339418918, 651149209, 254638610, 484129106, 405980459, 780790425, 897262526, 464675223, 954874106, 253059488, 480274660, 858364137, 524623897, 311925174, 955912684, 305933563, 846976738, 505236329, 903062555, 987308563, 648152577, 43822461, 746604529, 566700741, 344744490, 674858542, 922319854, 233132919, 334473809, 725481650, 849816463, 557222409, 695454381, 258829110, 373340778, 431766823, 225541705, 762405364, 135360938, 342416936, 312722261, 68532627, 78776481, 528465265, 856162229, 72941040, 314267522, 872942571, 107728750, 871815178, 908006566, 752709428, 191784651, 196809622, 843098073, 108473300, 800152494, 805756533, 700826094, 390093627, 388871495, 493237667, 103559289, 303794705, 40304595, 682159834, 430314175, 746181208, 560964204, 803490917, 772273507, 962797667, 841765689, 655170123, 128962952, 237713745, 550422321, 369415329, 857331438, 478406759, 915290507, 583779887, 622087259, 829108709, 664813071, 359341131, 726603777, 171493191, 980418549, 933891267, 725810102, 342211745, 940383781, 792644164, 973445216, 821092863, 619138427, 444216287, 966923967, 638576058, 100808977, 857479405, 449404605, 817969372, 671584170, 929424267, 170020163, 617422238, 715678411, 44810445, 536359405, 413330536, 923244917, 712512442, 389509803, 622404114, 209654682, 70438799, 129106552, 492779154, 925841650, 809698170, 561359000, 641201114, 325943258, 646088574, 440024803, 358766452, 548068726, 519006782, 373629871, 660542252, 576266186, 71495094, 353006497, 931636923, 373268569, 299619481, 330698886, 156734000, 360413063, 98658931, 232825256, 138262398, 725232237, 579046611, 148958937, 137841579, 626527778, 554566997, 999675101, 455031674, 601326064, 358314304, 699831689, 257490082, 465623426, 847341917, 934760464, 635991686, 883107997, 172684314, 370578401, 789074673, 962030272, 491554143, 281455733, 885411553, 818184032, 628314899, 397421488, 997255199, 492030934, 339340852, 232425974, 29783292, 764879869, 851666335, 542148752, 6494736, 797783239, 487403178, 186335339, 750551423, 398221133, 452309635, 940369057, 496616141, 698932062, 512472979, 390408490, 16817195, 217319637, 994861315, 46019948, 518469543, 310640983, 142266325, 896340518, 93041067, 954202215, 188408508, 836526489, 715997623, 963513588, 11659095, 776405891, 644381323, 882262836, 292370747, 85044575, 633430476, 341069833, 578589848, 872300970, 122340460, 723951909, 128064582, 199850482, 805507207, 99656239, 787925279, 567965077, 448003757, 670629872, 212454177, 701495542, 278120879, 454132168, 939341576, 3823318, 741443912, 948335828, 541863301, 795701412, 432961187, 171886605, 97107796, 445769140, 329628560, 707409968, 999224698, 658117109, 771582444, 757295132, 572814338, 115590441, 156453257, 242851499, 290268631, 829608852, 21605037, 807141639, 258842366, 891346684, 32074373, 725229546, 863275963, 393862138, 940837241, 539905675, 123203844, 323611060, 341526407, 425085667, 484473835, 427594065, 742932338, 656535258, 176128342, 195354006, 392143659, 750839266, 18357775, 384984608, 272701024, 881031448, 203326467, 966243109, 254169407, 758558419, 282475777, 320767352, 37335691, 290574499, 632450906, 634658342, 441530053, 891767062, 481743873, 73554107, 710293909, 752040508, 831200643, 908732473, 790668174, 81038557, 388153728, 557809796, 682607396, 299234511, 68620168, 258924596, 361802286, 198259160, 487189564, 731607804, 700736032, 110915316, 831772073, 232692071, 237745067, 710433364, 868134114, 989784000, 874994585, 222669519, 702459852, 589884596, 851115362, 490637927, 337749417, 420238897, 709485567, 803170447, 220742749, 198187243, 787495360, 635434982, 276335225, 853828425, 32365108, 470611654, 152640020, 161054714, 198249643, 78780981, 662578660, 180361702, 528394518, 502425591, 201781734, 127057766, 643087522, 704033432, 544679353, 736460627, 7883926, 593232536, 477783471, 996975539, 69710310, 738676624, 222278707, 658223862, 555945066, 463485037, 20441312, 763599068, 812900536, 86556938, 252204241, 973470725, 419080338, 505708945, 459588665, 339945304, 225455198, 826378450, 528327840, 299444396, 991839072, 773338487, 338771947, 623383935, 538475466, 106363775, 547365232, 628548092, 47134837, 605738347, 648987992, 106291560, 221980256, 523200507, 965884214, 759768951, 76709675, 679456297, 931526625, 933216338, 301815324, 832823058, 606117601, 221420167, 10548972, 530617791, 414497279, 647564830, 944119427, 546691527, 316065823, 937521332, 845613013, 991565766, 519280202, 607116, 954802639, 374037903, 703570552, 384702657, 275403084, 352635802, 779476996, 133906863, 416519939, 104268837, 404951765, 213897688, 896387122, 527524538, 574172884, 955838585, 412537002, 457463173, 31026317, 629493478, 578270546, 603691598, 847509043, 497403161, 919832736, 630213917, 643054114, 293709087, 925920424, 907631341, 548250862, 465666740, 183004228, 239365294, 292955572, 800050667, 469765198, 679791100, 657132279, 711335152, 834242899, 332590223, 165917787, 310138863, 289435702, 506957605, 548272653, 786219249, 679107298, 858154666, 786119787, 181264058, 702806540, 940676074, 512792268, 90291699, 312516636, 21395487, 498814781, 779394649, 65101442, 724778716, 375498767, 186776123, 866414492, 834122705, 651679498, 175972123, 372543927, 199340165, 728062054, 772977157, 642930141, 204836055, 419938520, 947502744, 940938648, 115474753, 327217895, 443693831, 613767859, 256017546, 946223435, 344821315, 532901678, 294400793, 585018509, 713232001, 294718236, 6604611, 871453549, 725588609, 671906751, 508535337, 436042213, 533138575, 427394779, 244517888, 265546691, 492251145, 168528713, 548950248, 37421263, 488740127, 541883155, 673257506, 706116237, 286735764, 907267316, 73461589, 242969308, 726594637, 759509243, 19596228, 894406542, 92326761, 861090808, 107631283, 847962342, 766597292, 111064665, 177903041, 543725064, 446736464, 333475413, 269924800, 924269604, 468116131, 15159968, 913401615, 325819403, 517114607, 339517032, 640615986, 275754841, 297651573, 717619897, 254009548, 268973500, 475914602, 581753749, 906017539, 553176307, 551681859, 466202545, 907841782, 12263599, 751312917, 753709204, 665724840, 342273595, 552807861, 247175554, 348280801, 513777765, 703272162, 511351141, 543728051, 570595700, 235289496, 195425456, 961560427, 849529968, 776968083, 530426585, 516213521, 659649439, 419474259, 13753376, 317080555, 165822040, 432462214, 8520475, 803241849, 79555172, 461899626, 324760900, 404082933, 545342364, 520341263, 443948246, 290905024, 345746050, 707095170, 181723275, 6231717, 588973474, 889315921, 656596240, 94745510, 205188822, 230843919, 34998164, 114361270, 293024810, 607016839, 689083698, 602973023, 391425837, 100149918, 235287044, 429560791, 715387229, 539441598, 378428006, 886364144, 720245379, 373699332, 216546382, 519825327, 451916479, 520887414, 570909662, 293022635, 420188451, 720053908, 850161418, 528292946, 338741321, 755107047, 418359735, 664275126, 446867928, 113644725, 432529794, 551642148, 816414323, 517829021, 34926449, 623573096, 119428120, 607285072, 457342328, 986211441, 449717684, 924910102, 616201860, 148232542, 48169620, 678272581, 609469509, 493820714, 74781518, 823667718, 529447434, 518985610, 89487991, 293815276, 493643004, 581798398, 442491172, 725952351, 239887529, 337796851, 298372419, 703980271, 27967295, 927193681, 817399102, 259552796, 478359851, 391409152, 677786631, 768457344, 260120677, 841232466, 628570582, 542297667, 926281487, 617845452, 84155835, 389073684, 208927989, 587564057, 186242919, 383603017, 146643755, 82898550, 861585748, 866617796, 786991105, 896881859, 529996092, 534310445, 68633647, 999792316, 596615897, 717363693, 920516352, 817898685, 816209962, 364468093, 144394701, 198130246, 43885586, 764792400, 98784108, 581869545, 17369108, 354651810, 458603898, 807911342, 983710643, 495168771, 703229427, 343560619, 888155979, 560036119, 907375313, 340068683, 108917417, 962759707, 198158288, 120832460, 49367121, 289392648, 504056945, 89923825, 963254565, 553876751, 650932264, 207279617, 116315197, 482415666, 251461193, 468098971, 651390637, 492620510, 916502087, 119151804, 784131325, 256582214, 884903632, 949209676, 961795279, 13441405, 249122745, 237427578, 998808689, 209558294, 530655270, 922489005, 948838299, 655487478, 982709586, 462130155, 369983721, 450284232, 59632455, 756983805, 180429521, 57734662, 983327228, 15167911, 561937978, 749920853, 580123101, 852114546, 698501492, 426638753, 939472389, 324895296, 742453937, 652799644, 26211285, 480152099, 746847748, 85443670, 386749180, 464422008, 85575487, 711766811, 685305040, 922351333, 99872500, 569882887, 86268501, 18549819, 211498716, 433317717, 138087816, 429483297, 604497272, 957720976, 922049603, 763531896, 559365621, 489548290, 992844991, 918745673, 263416433, 832085547, 665309596, 899801636, 637808152, 137185532, 352576291, 389049924, 609488584, 433851786, 475927067, 269373942, 127135031, 627836194, 318310129, 177152435, 15728592, 97400048, 482774832, 731656565, 703887870, 792866051, 304850386, 649284010, 359916795, 211822254, 559635026, 135301767, 805043307, 860498064, 425863621, 923502400, 701512995, 9164794, 35100752, 550709987, 479354824, 752910315, 522145307, 254499736, 899896016, 258006880, 546147843, 678042908, 43122087, 965320552, 307621993, 459880088, 884048360, 753709100, 992501540, 318904500, 21148898, 887639145, 933294362, 941728405, 448580565, 792268848, 20028176, 290851234, 687276561, 143531382, 987592482, 326354727, 153611044, 974398249, 246854504, 256269690, 297499664, 941442231, 267773318, 600314140, 401720944, 571286384, 128505625, 984663546, 16976206, 101533742, 86622801, 635233447, 434939292, 361367692, 517100018, 402418653, 80210662, 27580638, 470167433, 679427800, 775778795, 515913989, 877793576, 941641282, 116092308, 572497173, 870467496, 86787013, 787632674, 660931827, 145444305, 826592002, 281427337, 636829499, 586999470, 808810674, 8934393, 97581069, 715297997, 703211678, 236207457, 393225673, 878480663, 63307391, 68191933, 452797370, 175120534, 137434787, 410758774, 705635045, 402578529, 537298557, 387653648, 875840386, 255950700, 508908644, 185968896, 926485845, 215015308, 377917064, 950595092, 971629616, 907758040, 137309440, 765145880, 282319444, 691871496, 3813766, 621304420, 618923826, 882036869, 516432655, 308341050, 86848883, 760117757, 901268797, 990861349, 205420876, 42627082, 882626616, 706533551, 580906896, 707767061, 713895151, 659685568, 298316188, 793060865, 249679592, 576930737, 894436506, 618681994, 559670635, 283073173, 809697305, 11371227, 281797092, 400216302, 470233917, 461118710, 435733105, 224284767, 376324828, 791164846, 257376288, 598725348, 495374903, 325108954, 164005347, 306645892, 584835611, 152081708, 803646608, 951430654, 202171827, 182938760, 783447761, 396632827, 304790555, 908701750, 713662101, 627291001, 800268793, 590377220, 870766059, 943067063, 633678397, 642034912, 510191153, 974420168, 661918066, 284101549, 193168560, 657205311, 874538101, 308264238, 325069193, 552211099, 817312396, 351210768, 107566170, 434918734, 104719818, 469350112, 795834511, 157946862, 535989918, 434657008, 762635668, 725203375, 42066713, 670922586, 193524070, 937623849, 731267726, 734935226, 736274460, 156621147, 38615979, 156310199, 858235952, 864984524, 30214648, 959844199, 30550336, 738469275, 905024698, 618842130, 675193334, 700569198, 803713862, 535681611, 543802429, 342371462, 626218912, 352755544, 536304533, 152548748, 907379194, 576409150, 187035685, 711353016, 290828161, 254145386, 706314680, 497766590, 402397022, 865298714, 678037477, 304928562, 479601025, 680788639, 182183980, 443131224, 167649980, 537362954, 744885639, 764722668, 999154566, 709546042, 155477947, 214548395, 127223043, 269522037, 677997659, 671871120, 792406193, 825887234, 818647349, 902665280, 189194320, 576125305, 738246562, 138059110, 203101297, 166745812, 672497605, 948959705, 793184939, 995761128, 591728878, 722397215, 884320238, 864936532, 59861237, 788737661, 418278639, 604085604, 901995224, 651422433, 678196325, 424895005, 330100024, 434248194, 587041540, 650740057, 96715302, 924183893, 68401380, 942754587, 206263127, 752758615, 413346116, 169213565, 887673874, 459494552, 840567628, 535999331, 402124071, 532613588, 919199126, 211574886, 755830940, 570207147, 560183635, 345209413, 246177416, 448944656, 506866845, 388907156, 12071752, 501481436, 314219589, 578860527, 213099165, 390049353, 71138536, 335383357, 940226903, 36529734, 15114052, 180145835, 381575873, 202097676, 565897134, 936298873, 124995412, 966390905, 180288248, 316161602, 478548244, 852729765, 863597885, 272903421, 617274829, 962580958, 377950292, 119425751, 423861680, 402146582, 190204220, 170066681, 274271825, 627749461, 107135715, 197077922, 860354778, 910474898, 557377020, 681684026, 935205958, 709089644, 606080292, 532666654, 914515856, 670307710, 730836847, 686792618, 150821474, 286655078, 961188651, 887040005, 429007367, 784791835, 545235719, 983304968, 95970143, 110677843, 277124780, 642506547, 146711347, 467561206, 140730108, 326963234, 588711124, 578497749, 466810968, 863893924, 297793993, 323026636, 140874016, 490760664, 560628241, 360503882, 333992763, 929960183, 938249998, 196566412, 96666256, 8541039, 495557200, 452554941, 793899104, 475177219, 118400297, 938058926, 924862593, 314689343, 115034711, 390898295, 826754375, 686939856, 46782012, 281088100, 624230281, 388999199, 530229945, 549070338, 595586238, 536288785, 608820061, 332547298, 124765627, 278116046, 471242937, 950591641, 383740832, 890138659, 488609489, 477446183, 658591137, 324997701, 473216805, 377121249, 817416484, 361978105, 49662419, 557882784, 166399513, 477914118, 922826210, 897042712, 691555528, 896030937, 6375167, 869917462, 270828922, 450039123, 756771086, 580317320, 19089774, 180356912, 749995503, 686176042, 542724109, 922956418, 144126465, 705311849, 194273444, 653129362, 598901117, 335331877, 67428598, 481717815, 945574558, 281468792, 955659606, 468588280, 320144648, 262299692, 247485089, 338817030, 180292189, 984355645, 497345137, 900100338, 689462524, 709266235, 441135022, 258824370, 211137889, 790555012, 188741455, 512866162, 215763486, 573168419, 593633648, 771012416, 158508311, 852815647, 124687043, 257247637, 893383105, 311396537, 817275473, 736442140, 510773934, 591623381, 570447719, 846418265, 241072927, 390977924, 287864039, 60573069, 944756488, 255157106, 866859473, 152409889, 474479441, 222074375, 799193511, 650180925, 989749074, 904286553, 8886072, 110411870, 644341302, 894237461, 11428390, 309280394, 424130582, 653619473, 850111309, 630226748, 904647863, 992688606, 430658112, 458619621, 702078665, 169274879, 275161231, 868881134, 101830992, 341268359, 704088145, 545581068, 436787053, 402388734, 166054682, 378740800, 568514440, 277068722, 322637210, 404659433, 365223259, 696117757, 186356566, 507431793, 867192197, 952993576, 447973889, 984346199, 116986256, 645191826, 343106161, 302929421, 126225019, 385617740, 498826741, 641840856, 533386515, 100003775, 591898502, 618736575, 146509983, 854467222, 742080552, 505756300, 908052528, 800465696, 538069813, 314928044, 37628123, 899222979, 213020674, 844337030, 652504734, 163283176, 699580286, 875108622, 824193451, 487145612, 476593815, 559331794, 991723798, 10043685, 152563469, 169261055, 959154417, 767894563, 103035098, 36094540, 120244265, 823350508, 390428430, 282551570, 413113657, 894951960, 524973311, 507429630, 114872507, 280759001, 568046874, 235574972, 898335013, 762753785, 53311529, 60036793, 663308517, 527054405, 829002835, 122092972, 105274186, 709594046, 212620323, 612286049, 431459023, 552675189, 791288107, 830409497, 890938611, 596692127, 871350665, 701901875, 182066841, 223074786, 78263523, 753971913, 243501561, 962023892, 275241063, 447195077, 340399166, 511568225, 480537345, 550900223, 375839580, 150947323, 129092351, 218442728, 781988201, 672359661, 852480977, 400038970, 969161790, 742086218, 451024916, 173122961, 277473101, 512250818, 878095709, 386519346, 437850494, 432484961, 996622618, 536052018, 675474402, 876671368, 161465315, 907771933, 412548131, 79910240, 438222584, 741393686, 18944079, 108295236, 218539853, 340941155, 714949554, 773667999, 183452970, 543829658, 294367915, 755865451, 821467619, 255221333, 706529744, 327582837, 654842135, 886479207, 255841658, 678586324, 771743357, 24068389, 766735260, 434990094, 506385710, 122791607, 43784868, 894690474, 100193623, 460341184, 100776752, 398560387, 723393135, 807356487, 447496210, 991820591, 402760814, 196069605, 485272079, 143075493, 499239046, 105384409, 700250427, 15929019, 230939092, 986851752, 129988316, 550832446, 397297528, 810729422, 65939474, 100636627, 383878491, 559125300, 38033233, 248577368, 776743402, 300087107, 495750800, 971885440, 133645363, 17731395, 276268650, 274897059, 804875270, 890263014, 680207074, 322496229, 228707363, 360257530, 663558081, 951693678, 548194272, 278678256, 897654931, 418677483, 891133154, 710088042, 757224035, 267298193, 217671729, 495891241, 844740761, 167785297, 934577912, 778506524, 180985022, 997709940, 454441217, 773072686, 364592272, 771545003, 130079342, 761511312, 112502249, 636266299, 45590313, 52325679, 531960421, 127465577, 776752125, 297679744, 5283070, 761591335, 886038873, 301477499, 618580145, 664083072, 66922803, 233116042, 554098257, 555786483, 414955333, 669517634, 125989419, 157108009, 227207074, 732548390, 95813025, 493613937, 124713276, 379093962, 558298822, 904317318, 193875773, 126459522, 899294552, 269799758, 207487403, 990776764, 86123288, 200505722, 304117246, 556013751, 514406390, 831823813, 401470890, 247773803, 678045366, 32253788, 915009245, 416447889, 934405177, 885714219, 923087082, 816470281, 169576439, 830668035, 511269666, 846429125, 362388245, 211289536, 136718694, 172859761, 73373944, 658670386, 118959903, 415722145, 726800935, 101888337, 489800179, 2563440, 438378239, 364413508, 770424396, 798855983, 636818753, 800840797, 526641469, 72236827, 748260080, 820179846, 259902725, 627120631, 870285598, 313610715, 341479877, 742117855, 775518853, 998953039, 737950631, 68775443, 474758479, 787589644, 838511866, 738352632, 442813911, 190870499, 466289007, 258198747, 616572055, 395985351, 564499218, 132834464, 691114718, 518687833, 890326112, 228937212, 808548709, 897932763, 962813062, 276940111, 297606191, 369606649, 988865567, 785365748, 73549608, 122170701, 822156204, 911243952, 837397327, 173197278, 863732496, 184367615, 99621762, 708665346, 307857929, 149939117, 608673864, 254842430, 98454493, 91290981, 799745597, 589492630, 97265768, 811156193, 886114657, 749423460, 549696541, 873291991, 840285629, 611690640, 232296596, 275051791, 323171075, 428883419, 431356724, 369592352, 964346885, 641534741, 517641583, 796196374, 46645670, 40135563, 559872806, 739206254, 866400406, 799613797, 787073521, 386840004, 295422832, 870257468, 523874881, 322354286, 252728385, 426881727, 996824149, 898320277, 927116868, 522806602, 300001069, 353936417, 779068455, 987574014, 865854831, 650020588, 391808129, 46989806, 179261957, 303887068, 899979882, 42356662, 252828057, 409092355, 16139748, 143539537, 479093742, 734401074, 674727140, 803342940, 5092866, 497719022, 595873391, 713175592, 651162703, 792053938, 354847599, 76752299, 516233029, 835884588, 37763306, 504984439, 428765564, 25215962, 198172353, 834620359, 705104303, 82431823, 379258841, 346369174, 846962583, 700414902, 360433333, 824429108, 359169065, 289613495, 760287229, 669668743, 49618553, 694127820, 486457858, 974313677, 85285687, 266714532, 230962075, 42447574, 635963856, 684736727, 497026929, 421762731, 484040949, 647774548, 824412264, 615114854, 211121702, 968243608, 468719744, 308046252, 264187488, 476569298, 93338324, 971316690, 483161249, 858557143, 142010665, 798705427, 295291807, 692790470, 308211225, 233429360, 225910377, 255949205, 914123563, 869398355, 109825072, 701182991, 71171815, 214112881, 745386349, 869703708, 343999277, 70071300, 77745484, 563913175, 245717296, 12456431, 984085208, 918873915, 393526015, 204417163, 652279022, 608397964, 794752705, 186740833, 267308406, 308223898, 478628321, 245868515, 953927432, 936001085, 6990459, 118120549, 611576085, 628125634, 556884160, 862338778, 559470766, 94036819, 983119567, 417932572, 223109684, 758005349, 649522648, 532615652, 252436914, 548558101, 790388277, 983699542, 638670073, 593947334, 209362459, 449043098, 844688897, 131376183, 562402312, 884977865, 149415551, 497884316, 615459468, 811839222, 886477888, 891317924, 700604872, 261719620, 115266601, 496933021, 146822522, 655164013, 713701014, 597600370, 483401277, 434909556, 513728976, 463201226, 615825016, 407771417, 883724273, 781568266, 580914081, 95547953, 814754773, 17318509, 559723005, 436101521, 999386088, 582765539, 98055857, 339155455, 760051370, 756444997, 673644626, 728226647, 691360206, 968537634, 60501608, 283490693, 258033746, 653182979, 102762260, 528644112, 501762981, 19229630, 966459443, 638189833, 514594656, 612349792, 732713009, 56869987, 850689717, 309261027, 862584642, 818347163, 257095350, 979235486, 606023658, 328603982, 966113521, 530927857, 939980169, 630589421, 824260818, 385479593, 596323739, 219122214, 866354269, 498382760, 475363216, 382779887, 957520215, 895988128, 754885122, 234212610, 85624353, 301764752, 394666873, 612766202, 604855333, 837237496, 265414588, 424418197, 64853983, 565311657, 974708500, 710133087, 148811799, 841477376, 788787309, 292706200, 406591218, 139811681, 72293404, 504300805, 381461862, 487104741, 703721233, 314254320, 643671449, 789257080, 786419812, 803636132, 623648068, 604513091, 63802930, 497320564, 556500484, 860767978, 443465982, 463968861, 479871226, 921711718, 359686933, 413734618, 626124379, 60829547, 621217927, 904536913, 310782537, 970046169, 396428063, 659240476, 723004890, 187114875, 508286266, 503614142, 405840809, 216400434, 734491842, 464317783, 782690886, 194569130, 859727165, 955007852, 30402639, 479103810, 166274458, 482186318, 289695440, 673196192, 400419365, 961280646, 933639018, 113668247, 640422632, 132601568, 948121839, 65544346, 280225671, 427447333, 277362291, 443646628, 633170631, 651199797, 947315834, 114832863, 122349438, 931135018, 796933698, 916527108, 717620029, 186865653, 775305331, 483671893, 816391000, 917242167, 627508263, 346102730, 723268740, 422389421, 940107990, 339655227, 186992814, 823528488, 526416458, 628879092, 713757364, 516046980, 245381335, 606744435, 402371193, 85103708, 209601681, 103445368, 296907949, 221261118, 186134659, 623066200, 400328675, 39709063, 607492227, 24145453, 372430138, 544521643, 440862542, 633393148, 492103206, 788594635, 282212200, 610939231, 379474519, 682494253, 459196400, 672312116, 300239313, 208272916, 578409806, 792254245, 509040789, 634272965, 958038369, 719465669, 293314022, 268190324, 459330403, 583058338, 47301306, 280945577, 4424813, 48883134, 266495159, 70651425, 696020224, 127212717, 287521045, 534079335, 582341743, 530707174, 691444702, 95881527, 687069353, 122852252, 512271051, 79507486, 12205336, 973585707, 211822901, 293700580, 694682840, 160848923, 882311150, 293074048, 278311532, 47457403, 11308932, 812762083, 999716300, 792117431, 221969106, 780851782, 963106673, 722535177, 285653424, 418288679, 570645569, 252285324, 510882755, 395556202, 847333439, 827716202, 653317475, 201262645, 86458063, 729903796, 904801989, 554766780, 787621901, 165911492, 944089401, 563747516, 715065293, 674549506, 874154689, 719747207, 845640254, 168673404, 654612124, 595090803, 109729317, 79874594, 592026188, 422135348, 474866894, 937361390, 657835523, 448870312, 29946161, 264282461, 148492267, 424809599, 332374319, 474604207, 754679284, 831679618, 101878899, 444519095, 836391952, 256093637, 136498614, 718771734, 333267340, 274473770, 531431436, 188302777, 742103853, 808612287, 170359912, 29938293, 694305511, 90225800, 81855939, 220143015, 640868828, 170331041, 966977056, 937646925, 316656258, 512608826, 272693705, 795826232, 498598424, 451764022, 215064152, 484833129, 643115227, 62200391, 727574001, 612898528, 898584927, 736414201, 331570493, 987679586, 866471117, 939426280, 299891604, 378839316, 820837574, 56807948, 398133579, 853100768, 813762903, 392668730, 926072273, 651921464, 587715585, 532989545, 39049112, 736832506, 879825478, 705323065, 553565677, 158520365, 430799821, 998151157, 299912253, 61493738, 723433852, 977806314, 358738063, 58194883, 778493406, 607521919, 536231249, 94689336, 145026363, 930253920, 703079718, 562922789, 441192701, 197517637, 730872253, 358339769, 210332173, 402200276, 316928630, 16782443, 688244225, 539286661, 210844423, 980606374, 649510878, 76982253, 137128698, 599593435, 268743499, 91281782, 119456125, 182157425, 731309525, 707281819, 500882961, 460892422, 280182596, 546527895, 326011002, 561693409, 298073939, 189682649, 98317846, 281712763, 366063920, 123114543, 384733504, 787394372, 694971366, 906774484, 895515314, 672798385, 401138821, 555145953, 69919813, 835184299, 932766229, 911291137, 273114228, 496042764, 146647560, 832531896, 779802563, 227984263, 278758791, 281391753, 722424255, 514968527, 646960796, 631664385, 402432086, 605664543, 265843369, 633874715, 60605905, 933698861, 648195180, 105943118, 210079114, 30722450, 932818218, 6806061, 485108560, 339047735, 473335724, 694965290, 397043307, 930267568, 289327128, 664313552, 937673181, 75001781, 252811390, 906808175, 167288349, 958989077, 802107908, 545911814, 688742061, 437523174, 988682091, 9185235, 385807300, 687092218, 775939519, 9701255, 486283452, 726155603, 81997954, 321483390, 849897958, 99185707, 885526396, 280195968, 155883301, 103038704, 86190311, 921117210, 409805786, 751879756, 223211940, 805683, 813978255, 784427529, 707341533, 551144808, 499537042, 347425336, 375401311, 386731936, 948851846, 486558995, 424115424, 932264704, 635773051, 230361739, 995844314, 430964823, 880322385, 18286088, 800702343, 592755527, 831367935, 380472951, 899708426, 420373622, 125948131, 673372304, 728595464, 975926981, 447185283, 177734633, 846991380, 190254625, 568788385, 325540146, 937840048, 384610643, 166851689, 286243544, 365836590, 97886250, 552146630, 454738710, 644211126, 181330995, 111885033, 108440002, 872053254, 63019879, 519991297, 181840415, 808075722, 621751062, 659644507, 569993199, 870215689, 535442108, 361851037, 443435351, 563750096, 559921214, 674746772, 87508191, 774169461, 562169520, 772684120, 519139212, 898795140, 77530584, 357548764, 506682846, 449878817, 305957786, 529271774, 888875211, 836835575, 476947995, 617974836, 632537446, 538755481, 439418103, 278657276, 758604462, 280183787, 814675245, 993797762, 580046804, 98644024, 281429373, 572501592, 568550600, 699090176, 956674011, 722933097, 356590657, 579778088, 642852335, 200400476, 521495397, 929868264, 86526715, 408538953, 863824741, 521972422, 335251532, 292776903, 409108511, 274003485, 253316349, 963958747, 581959961, 29772770, 452091097, 71673087, 321627320, 463456830, 799865432, 925717467, 326201804, 608835477, 62568450, 512972143, 514779244, 181065212, 403936102, 926769124, 529925405, 368381114, 334450966, 107376087, 689357146, 954798191, 275946131, 25036765, 890499872, 155383167, 642347076, 303123075, 523597006, 76854076, 596607091, 280197367, 687927253, 785176656, 865005338, 730641284, 525001451, 173984413, 160176549, 901419018, 262581049, 500555859, 116809533, 225960356, 456613724, 296092730, 992365924, 244844204, 142172453, 917870491, 142707768, 977233867, 565842459, 139683896, 385077792, 714693345, 638182261, 569462466, 380924763, 539856931, 63906819, 483266220, 59016568, 137897888, 488019501, 579448255, 189167580, 435667312, 255424552, 844281394, 634226982, 238558435, 453349495, 140283082, 257611234, 205072866, 456137721, 859300895, 222958718, 807827549, 506778487, 276145765, 936269025, 13094580, 913665693, 461659668, 559829887, 264939621, 939223609, 850624553, 261418401, 614828247, 949597074, 712029187, 374461380, 817084466, 326586141, 994679150, 436751250, 50328831, 280056935, 880398265, 151361575, 337331667, 871115000, 395119161, 589206064, 517061126, 578460341, 898867625, 22979896, 122717693, 284476462, 225662850, 65535824, 44979262, 669831158, 552347673, 412046873, 206103278, 859132687, 876682412, 422866463, 468806533, 220657598, 993268289, 942010858, 559152341, 974651478, 882452149, 650723120, 33557292, 665177230, 321224158, 200309272, 756582490, 689497245, 104024116, 817938258, 348510063, 580546137, 386620604, 751068013, 616410956, 146690834, 790472121, 226261268, 434012133, 572664132, 218240757, 805027139, 576516934, 812721752, 146247377, 734339050, 511310520, 770607483, 982400692, 318265418, 708969267, 210713394, 747009855, 96758460, 813505632, 850191044, 400085277, 450514458, 662534224, 282271348, 842977941, 822542529, 944200806, 701172381, 689566738, 730676237, 387000792, 808429723, 898780076, 952929389, 595343852, 555576486, 947426559, 361563077, 835522989, 808692727, 443570544, 420194199, 855946200, 402691341, 504258546, 120199612, 291323576, 623560466, 439830188, 460841327, 146419861, 197569559, 403239284, 282791035, 415889045, 533893985, 991856761, 473183641, 239148370, 449243795, 219621224, 288468785, 488518146, 970860683, 522444597, 670780186, 200011917, 214506895, 582059137, 576032728, 500410309, 168924222, 989392234, 139944546, 132394384, 978193542, 476972557, 308589741, 288725694, 22847054, 106101507, 962793883, 290938089, 385917353, 900829000, 248762421, 11791982, 169917357, 872660469, 26556823, 946032235, 41753920, 619242989, 953224336, 152767626, 501662180, 841415274, 665276193, 979899081, 401274923, 424624359, 941765157, 853341231, 649373594, 305468564, 482757190, 655203211, 165298607, 141324533, 304861319, 611447351, 782004574, 299115955, 338350677, 405066184, 807953454, 313808299, 859438470, 440156982, 361709250, 539377052, 757279914, 777266793, 148350016, 859998426, 959625213, 743153679, 498595782, 787155040, 877133176, 186846300, 464824019, 79914424, 56242351, 892988437, 765487844, 673164505, 403977119, 664626209, 346238401, 470525425, 833097299, 615997794, 957401413, 283285558, 440848461, 8399075, 505290976, 484099279, 484187256, 545682286, 493405309, 76689302, 162316136, 192589506, 864501480, 659291493, 388806197, 838354463, 294991402, 578572921, 537909152, 307083785, 318275820, 540687888, 275375855, 629970610, 249011147, 102780953, 52236087, 981655854, 483734502, 909294233, 151100412, 458691221, 608969984, 698885184, 206915352, 648558813, 935240478, 72092342, 141096853, 391941027, 828634978, 507258277, 853272672, 199178206, 591810747, 532137411, 584781853, 47401537, 41962248, 450110140, 566635298, 666336180, 427521789, 403114804, 851561375, 38108005, 958227972, 103985448, 665329527, 711998089, 624804277, 123144328, 861494365, 923555838, 316561575, 73112318, 553513726, 637189926, 901459400, 491842964, 272671487, 806862487, 54259391, 395310176, 524758784, 241092550, 468448190, 540317122, 597787319, 150288741, 556711944, 791524086, 117069820, 197568241, 700447093, 168605705, 28374871, 927673852, 673790500, 671668435, 853694856, 352425522, 899192471, 281204898, 734617120, 948506100, 473197055, 163828106, 820428627, 260886750, 737249041, 753983710, 3884753, 78594674, 849172311, 285753317, 895455150, 859699408, 357396011, 535166102, 182612001, 265967872, 851276658, 706372903, 283465384, 733635062, 396950739, 43984984, 836173778, 885948132, 690824723, 194394286, 651804245, 210353612, 265803880, 743936709, 927415504, 864954372, 642465704, 898676552, 886186709, 436763594, 362780573, 391041051, 470607578, 262233470, 903041845, 133735376, 489191982, 998547523, 27652947, 783737071, 401345016, 119127545, 508890526, 61015277, 321082093, 852614390, 206127189, 733359959, 897330687, 788781871, 968452968, 558797781, 220470247, 214630945, 790097153, 439440307, 659734895, 514676779, 641917220, 115534930, 390835960, 862193148, 658379522, 111359714, 143245618, 360107307, 264278541, 318448268, 225565524, 218730490, 777852170, 633290867, 866992697, 540023948, 965074536, 993680498, 207133535, 467228851, 180349999, 900775931, 610306280, 159233872, 473480652, 342314649, 614887730, 431783792, 496696393, 29908671, 173457058, 202122074, 163346497, 366867335, 66902517, 158087753, 685074338, 527859820, 198564518, 526866460, 556979800, 730388489, 414014199, 891997055, 578625819, 619609667, 874627121, 153139360, 989676781, 522934404, 797591505, 338399344, 407737324, 307218938, 188690268, 594211993, 458811617, 799255629, 775471245, 324359247, 882041427, 768650821, 252903005, 787787573, 617972820, 995514339, 633654332, 701765313, 713039822, 87446268, 193900402, 999323167, 965139224, 36607231, 333802067, 727854417, 268523815, 329135209, 239582147, 381534141, 890517570, 198841525, 881743534, 702519157, 833637200, 107243190, 804397429, 620758752, 429418348, 386751777, 585896569, 116163531, 232038343, 803614108, 818952210, 491597217, 493072755, 589594082, 188579563, 640543833, 783221787, 521260747, 792818941, 451467285, 484525434, 941539729, 822264954, 146263828, 383821340, 918736606, 658416986, 270743634, 149405098, 676739394, 907622199, 663173137, 787080784, 51573478, 928063813, 23577438, 952857803, 840834129, 333843068, 399449785, 746840974, 389378643, 629716298, 474645550, 474327825, 506939329, 287540342, 384494716, 6724757, 678168805, 374595830, 965575102, 869911634, 796588508, 410483115, 156057859, 472464795, 215765312, 229594686, 425028369, 195609848, 639246418, 654724477, 991893318, 406547473, 658449026, 249836042, 624258042, 962450580, 345276507, 114977698, 397189875, 39210639, 261961702, 19922704, 462006134, 253775662, 716020669, 676370356, 291245504, 960084667, 491598862, 212657510, 806579056, 105036221, 636546316, 196571414, 419816858, 448517063, 606217672, 785031508, 911900146, 512677765, 296288986, 489237442, 325990582, 409185420, 138458587, 277277397, 408680543, 258125428, 267634801, 403816745, 77744183, 157651254, 679226105, 504509112, 818013600, 877610709, 93971425, 554621386, 592209523, 155760027, 190400046, 927205397, 903126226, 161285447, 183971491, 789922636, 931012327, 248629429, 176878907, 257808082, 249527415, 371956403, 241037468, 152924225, 722972608, 482649258, 43460375, 689455938, 729609068, 454676862, 842302877, 768659955, 389714771, 829236888, 329728402, 44096246, 278892856, 493815342, 980767242, 549726119, 990616399, 580189582, 878159607, 156691724, 190162314, 501252274, 370175027, 461008470, 542213141, 707042594, 579976572, 692183334, 959909283, 854370156, 22014570, 981895971, 440586600, 93075295, 656437670, 594323810, 572789999, 400083985, 563373806, 553169844, 452408531, 204625031, 955467420, 885156137, 4148912, 349626492, 312827482, 423992682, 11766159, 461029332, 400777966, 950449571, 976546146, 34463069, 39309823, 378406109, 672800035, 59679717, 67965546, 243852790, 148970896, 134800315, 265325214, 379936862, 870113415, 367778957, 562312447, 175975630, 373734152, 552489772, 906559782, 252693955, 533540576, 810456105, 701933657, 632680742, 471843882, 183013602, 386462463, 709626567, 398828143, 830766766, 372771733, 652993954, 549605009, 508898474, 824402992, 355984656, 157024012, 606187677, 278042694, 293653566, 193616381, 964162028, 133409744, 141453454, 800167118, 154434188, 342037647, 904755435, 374627744, 261093415, 355894787, 406911200, 254706803, 323842032, 564346777, 855459930, 325598257, 67678944, 75542870, 814492770, 95719053, 505802825, 607430783, 210145986, 795176609, 260802953, 450174908, 485288373, 695421347, 690795291, 137332113, 639135334, 174731275, 408526225, 549383441, 76267145, 10513997, 215404587, 172191756, 875239315, 868414794, 500083475, 329244043, 231027355, 332428508, 19882077, 126017819, 335591927, 419301485, 878281751, 10316622, 174443791, 65670063, 104659980, 53729298, 918465235, 711355706, 301858414, 114970119, 438475400, 983176543, 683944511, 767973292, 466515125, 840427575, 280893391, 155630691, 51632683, 753457153, 627760393, 858438060, 207174694, 280291183, 827263736, 301771431, 294631358, 607258852, 650851805, 239971772, 82762889, 625743684, 232618702, 831443410, 14651014, 899694609, 486237416, 428899689, 874505863, 453092262, 132429360, 827329945, 943929531, 288920475, 497848537, 558775524, 600300099, 611869888, 775550483, 344393147, 280957587, 286273169, 432896782, 793955994, 814012815, 67834181, 323323729, 43586184, 696008712, 769104606, 644975254, 165565500, 136846454, 209943615, 254872920, 19508611, 75199602, 319882877, 14112144, 765947072, 940472402, 308681695, 12372686, 135836747, 466319866, 516577454, 343745985, 859210910, 704032806, 500075576, 741552382, 127920204, 620481562, 510506122, 162294227, 230173828, 11915207, 644944304, 235911912, 729852993, 729488812, 55022742, 44136831, 970720020, 585741149, 937255067, 40483747, 121356566, 364068987, 85840922, 210537536, 478423125, 601537188, 385019704, 869394656, 77797683, 958014334, 497076998, 912954075, 390665010, 675422128, 161122690, 881148829, 490925029, 21763250, 126393392, 234444354, 733926071, 634977018, 648224211, 916120796, 791249833, 250670908, 537286097, 886604619, 615354208, 826315318, 341511576, 658324204, 67068859, 68369736, 149076397, 338006346, 789187903, 184291585, 129119252, 568237836, 13007766, 607543034, 964929741, 928877897, 643457335, 990300097, 706097610, 921676398, 366595341, 55248152, 577069242, 448707539, 600450475, 797508494, 307770245, 781029846, 831052721, 891106871, 324683315, 672496770, 671775791, 439960983, 394317602, 197248500, 466387312, 394328959, 571232056, 561432695, 766384733, 328067744, 859004915, 706214966, 104911706, 329652750, 14645417, 739902065, 923689145, 239475499, 97039748, 730161821, 746435983, 961377058, 327658035, 305836934, 129613515, 321045040, 672023221, 177240701, 400144154, 252806724, 873274100, 325461001, 51470506, 640400783, 542118631, 408452566, 959177382, 164960210, 365044065, 403965535, 452063481, 292213926, 33250847, 452032557, 123264103, 542071128, 50051980, 261234333, 526353023, 696881676, 992039601, 185095880, 632291615, 360526737, 477301076, 647280355, 423340967, 71464984, 4370333, 809508931, 16805168, 854014939, 897483449, 222448786, 964013900, 37582995, 16237059, 858430630, 789455844, 484682559, 419087361, 357972393, 748531263, 331802866, 500998673, 710740220, 510956632, 12968869, 2457460, 419490069, 826560014, 972822578, 702945890, 300863900, 259329619, 334762324, 846734270, 30582268, 947029436, 312943772, 17413051, 122223946, 37184755, 586453854, 648747796, 270996118, 162228000, 735696328, 863590173, 970001909, 171757419, 443601773, 549887144, 336993982, 526913247, 75510985, 316850159, 496550228, 420476641, 827206944, 289245175, 974159342, 486292619, 318294379, 75857075, 849122025, 620979737, 384025548, 367961180, 344405454, 242270512, 169773341, 804309014, 122125272, 544559192, 456934312, 321420288, 748119561, 223813601, 641353842, 111131546, 979280112, 473914070, 697944513, 274639152, 209073430, 804645554, 245509193, 413503764, 495141224, 367256067, 945013390, 320106519, 750625974, 634019662, 208581772, 386658226, 554641035, 787019973, 392658766, 16326572, 872982162, 177718001, 244288784, 530954950, 835482687, 539782142, 900616050, 539669196, 199666457, 322980485, 926273302, 544771120, 135325030, 761024576, 795503016, 76207964, 381402907, 662034853, 977760805, 976587707, 131859667, 351208985, 199024610, 938772774, 624875619, 694279100, 332921105, 970882748, 950484158, 965786009, 181953644, 274663967, 213404115, 82100629, 945530731, 57215758, 533194157, 354358923, 953898475, 254885148, 532330037, 648936573, 266685066, 850610757, 407248787, 598677582, 132820345, 886734627, 385841906, 559646192, 652895589, 762120497, 36412546, 362395874, 338356932, 85901763, 970207862, 613968713, 635606351, 937240619, 450654391, 425406360, 181014859, 928461547, 841212649, 891603617, 256179008, 932564034, 262707359, 288348393, 238582801, 218670156, 923942309, 195523425, 429388855, 987116249, 875273481, 138364270, 477770270, 944112045, 88959932, 64355289, 817106114, 427338074, 573787617, 135621123, 55365606, 471798345, 368090032, 860968156, 8611789, 782663323, 602187597, 752384715, 86184312, 5625155, 567920262, 121779467, 346373604, 899082373, 934202753, 269403534, 647262677, 444563769, 147573781, 335647320, 144917533, 39832632, 275487905, 320555817, 866435188, 510866511, 896591492, 444214793, 472154715, 638397491, 656642081, 794277569, 312664094, 804280430, 637473297, 45301314, 481587645, 271239182, 231057532, 671314506, 329438083, 471075543, 768672762, 840051739, 461130091, 188240403, 558532722, 355411895, 914856419, 742563753, 113368097, 648348861, 226314786, 768546615, 19402443, 699181587, 621255635, 712239465, 766113586, 397795586, 232652975, 710825720, 509319916, 73178947, 344533111, 571063612, 852746581, 412409160, 198553421, 111078100, 700702763, 638976725, 756799488, 334282557, 924291743, 639014212, 508955525, 25382928, 645023891, 281229743, 809714406, 248756804, 722631243, 135800540, 432621689, 969418309, 290269274, 829665455, 712934511, 714653713, 983614561, 97943165, 12259124, 24526340, 602587246, 885853320, 687426901, 784626757, 960319007, 66752709, 975094137, 264742528, 797560185, 278191102, 790058806, 61216474, 911162640, 716585991, 139505978, 709073456, 465835025, 264389397, 202506751, 889354281, 392054264, 932802992, 657004412, 65890320, 183530855, 435060069, 636711035, 477674715, 470871791, 351806579, 264433379, 655614303, 286408114, 313860845, 197318084, 118124628, 824756117, 318940936, 347282876, 350891511, 546174491, 303721743, 257135980, 781322631, 902316906, 755840387, 58134383, 566928535, 673518717, 95429157, 261127211, 407234842, 810914875, 146212220, 200876402, 206658710, 989114328, 290388605, 261466239, 558571125, 515515030, 669005425, 528841015, 803731628, 822320269, 996343329, 612725472, 338963152, 88078993, 849245609, 633506911, 643644314, 536220550, 33483783, 3707466, 706220892, 104832956, 836197767, 697864204, 492862885, 554465937, 342136420, 940377394, 827828971, 459516604, 214586509, 42979321, 787801528, 641962309, 169460096, 356084645, 318546208, 70622076, 240676096, 437995361, 709078373, 693562599, 357933382, 893983219, 62397358, 721271633, 144524863, 816642342, 160385968, 735232174, 1411968, 105931636, 794793619, 933047340, 669160159, 767607267, 788885264, 835921384, 167107987, 176581751, 145698346, 116237131, 886315836, 603966762, 810991570, 9453367, 795564456, 195303756, 432204538, 882013923, 677842768, 769942813, 304833313, 936596621, 106264103, 310185210, 994210272, 379225642, 202165780, 455297818, 356383817, 464778100, 504198753, 720609472, 773186734, 582413005, 27808237, 296611305, 264982193, 186216845, 573451394, 359089672, 693068749, 500425621, 724835960, 996760337, 615266652, 257111077, 629869931, 975649237, 417741257, 652708849, 245069868, 773350635, 254288677, 293257487, 31089094, 791903744, 352760939, 82541336, 763195422, 983151647, 284084985, 641880430, 806868964, 370915770, 798958311, 346456895, 271866274, 569200374, 557727545, 572993784, 971159884, 903304066, 590005031, 470863081, 614195183, 503609023, 374481076, 380986807, 671860549, 222448259, 635642986, 259361774, 716985273, 479255725, 212495884, 421606481, 483260648, 300830121, 407272147, 584515570, 181518348, 864158227, 63883273, 723771742, 162602813, 35647301, 61947601, 833500889, 928563821, 627944334, 6680889, 929097159, 867619416, 43986416, 421672353, 790154541, 311274987, 790782715, 871343059, 520889943, 745744729, 492108413, 303106931, 232783072, 23953434, 463927910, 571268073, 632740483, 769761525, 734972137, 96369487, 989124168, 326701227, 876577665, 169032531, 549756440, 762167042, 146850073, 176765494, 130686026, 93119186, 506971002, 481940117, 735645563, 538209170, 396075944, 55755549, 878708122, 118184394, 448581731, 259355329, 105308267, 101826729, 169626156, 580835251, 430198011, 887446695, 360008236, 240544259, 230260928, 700633969, 830116103, 769075448, 198955490, 671037678, 240604719, 309091131, 462752695, 921904198, 952521431, 740432608, 911067082, 772406257, 526665884, 415206791, 684156200, 554943623, 102145053, 964158984, 355680010, 181401971, 580327389, 650111114, 269128180, 180512007, 733381768, 952958413, 398532647, 41856430, 394329998, 667959442, 657230176, 17789943, 482479783, 126412096, 882598387, 761518773, 781193151, 83150947, 514235959, 663199467, 182335474, 6196109, 45315495, 609895036, 991034955, 389027937, 168103640, 443387018, 382333234, 629802900, 512791223, 54290444, 338353603, 638042616, 334770827, 593136433, 182251658, 121122327, 818165984, 684241025, 669063341, 25137251, 686064061, 848774852, 385498912, 273341963, 54766557, 617356286, 660089783, 727792244, 219854453, 901898411, 266835156, 495202515, 637675213, 486733785, 190339202, 211574615, 998207390, 659346864, 370311928, 583784966, 393408203, 796010857, 747899916, 648991936, 538667380, 317219637, 973944497, 159942068, 654975769, 192111846, 140786622, 771228260, 77408799, 712204880, 461461161, 273556252, 747300612, 725529100, 539522825, 669454309, 936417968, 138812480, 737736097, 297689767, 565452246, 723142381, 770967711, 148810030, 223012958, 335198671, 706545240, 550249279, 211609390, 899249604, 519486499, 213454096, 825477628, 508677005, 911127336, 233682524, 619723274, 731081826, 969255465, 295821945, 619912276, 228116687, 939470267, 431817568, 413738179, 180084304, 707968259, 114881305, 986790420, 389915551, 728536138, 694831050, 311548181, 380421364, 778551194, 318932147, 531912131, 82370836, 12533752, 774190694, 421371384, 499131912, 873915036, 486386003, 109976080, 688393940, 696777094, 456556105, 128481365, 22988533, 37967010, 550763323, 50639718, 476557457, 557874515, 475711120, 141509243, 396160196, 785298276, 432765431, 901317585, 811169847, 42368747, 680364949, 156792076, 986287801, 778147102, 346800274, 143170319, 380645763, 476821407, 142957576, 744088810, 650383717, 57964268, 923563380, 392519719, 272909567, 354654106, 141405649, 675687222, 286761736, 932771102, 941114478, 169110612, 274421958, 991902865, 30912864, 242942770, 314578529, 187187250, 351488658, 407047886, 866586197, 514104775, 45792785, 985430507, 10254456, 26204501, 198673655, 499337543, 990578579, 844246259, 369699044, 533665320, 318059600, 553040062, 433944215, 48862753, 140269469, 854829466, 33807833, 613115278, 952395702, 293021228, 379281520, 661991698, 914081747, 362783163, 790125111, 305328821, 796960591, 403127414, 569762886, 171454787, 367230840, 352357029, 673691660, 14288910, 445695159, 578451691, 39108570, 167872621, 933116102, 215612841, 545998558, 224558209, 128809851, 987119035, 747088083, 170282465, 567831573, 126957403, 848234094, 316966218, 112322451, 497852355, 330774625, 516340543, 559220817, 547600172, 20865527, 302851721, 392429171, 969000058, 987292021, 313074037, 785670918, 687471211, 846199107, 921085393, 892873383, 161696080, 624771715, 12607292, 428961757, 796042001, 140971975, 336060249, 642903207, 45713442, 745969780, 592850901, 772504955, 174085342, 963951480, 265730839, 494153342, 140769178, 356662254, 644152710, 675447333, 559087335, 579224705, 277694315, 848986265, 63855760, 250910752, 346240717, 700778530, 105198782, 662854383, 971023620, 182351124, 579671916, 722152076, 657416336, 332826110, 804115475, 618228642, 746549441, 509759645, 569671092, 511886719, 622410541, 182170498, 494160991, 936594169, 543229758, 518492545, 607628702, 306347843, 737173645, 380640071, 511202257, 48032543, 648344664, 201882304, 892377232, 597222526, 334052662, 684209270, 348554469, 140499531, 350146543, 542301418, 888001305, 475627113, 194851824, 516052377, 866526604, 217116117, 672906441, 932474766, 501997029, 727046663, 461512428, 972606661, 414128952, 73192219, 703562707, 725224176, 886810627, 134147929, 148200333, 594778717, 414924522, 353272920, 577514762, 344755171, 225228415, 270509542, 603824400, 639670936, 843106619, 142210717, 708985706, 102415247, 450197479, 922897903, 165525066, 760481339, 854120097, 754693218, 322926540, 627618300, 258030559, 575535364, 323055072, 336484667, 905254622, 656031033, 498782189, 902534337, 732399857, 4654347, 523240988, 225907032, 989778008, 810561259, 54960070, 688281305, 667688830, 754129205, 667682972, 972258249, 381502235, 134222654, 471528443, 3715808, 510376297, 236326520, 671681006, 344183407, 656474335, 152700090, 654979131, 948918217, 602112971, 923130999, 219362934, 258653425, 365108317, 71904893, 216178349, 630024616, 190381002, 686563378, 500573206, 584209144, 878903139, 379459031, 118017976, 610560199, 84410463, 971706742, 192550040, 609385092, 238063393, 361298709, 676683480, 911453423, 564386270, 130127802, 390825205, 890200085, 842648676, 450665453, 207178760, 531436585, 617418624, 714348098, 379388288, 290246371, 271631730, 449210465, 577442312, 45934659, 791400603, 805882698, 143328036, 160301619, 984552556, 249510190, 594094511, 842128400, 179857671, 799312005, 47989413, 994417347, 194055418, 144109353, 78602629, 895903096, 637965825, 51596067, 501322719, 329777635, 559568753, 104058921, 89900658, 362937024, 919634459, 741938567, 706093204, 863115563, 279933560, 231354527, 154856676, 612296383, 290173371, 971559596, 85715238, 532533323, 848436127, 83078452, 178375228, 635578330, 237449175, 166223478, 383578831, 409300932, 412208639, 431155359, 138620710, 466677085, 400540227, 567544687, 726893054, 826690701, 425361869, 914675196, 755110480, 526348225, 766598230, 890499402, 641742430, 911250194, 888834512, 62472753, 699631934, 956578959, 970714289, 416190504, 524512415, 942142215, 602668751, 331268265, 668167131, 696381106, 298102083, 928288464, 737020577, 58687338, 950437197, 458393062, 906849920, 582464485, 597101185, 656478718, 848977904, 478120431, 801924706, 828929931, 636676969, 445014568, 850338178, 512069821, 521925571, 647572022, 432656942, 178548185, 241570419, 188622784, 601553847, 128386514, 494958848, 487592432, 706676346, 910877561, 103299196, 543292747, 954507892, 198826191, 6426256, 959707365, 344264200, 897003804, 812190849, 780971184, 781844989, 419223121, 973198761, 301843099, 912687660, 904892812, 531536430, 108458461, 979346890, 264146099, 451314547, 468717923, 644917911, 932490502, 434383894, 323804339, 109559580, 466076167, 3383739, 234971728, 54435993, 527053124, 364931975, 307815212, 902517071, 344840854, 34810830, 533551395, 60826611, 766594376, 81284854, 507108968, 300753497, 442596968, 122091827, 799843798, 603721049, 1447566, 753096017, 824440625, 248414030, 720562399, 142075761, 203503976, 815508434, 940244094, 676719452, 833397606, 544564467, 46057189, 914040131, 539516382, 612292854, 809592475, 691943591, 825832516, 624513847, 402394465, 763136521, 427268670, 100123307, 868958352, 953291471, 670779610, 503524976, 620113563, 516428884, 156319889, 654249672, 703027070, 843799193, 579810451, 549139967, 737200101, 447932064, 437130932, 883885393, 749716862, 972978431, 497487587, 414516788, 137049374, 458060372, 615888394, 219050275, 699666036, 839184838, 289125149, 208103440, 957772788, 902557042, 531259905, 155213928, 852593111, 940447727, 586842973, 560818812, 992720570, 72746320, 293026556, 597552612, 671310973, 954750446, 676944790, 261033859, 852356673, 334120821, 370778939, 35840815, 666003970, 539296197, 925382488, 572976814, 92522984, 615240610, 859570200, 123971610, 765789694, 398746046, 193285403, 521136634, 401426835, 57754605, 955259205, 494179510, 88663621, 496026388, 240868134, 952140556, 458508163, 912451893, 494042535, 642686472, 854962470, 144554300, 14659381, 898200925, 193086102, 287096087, 264692859, 66122974, 338233598, 906747598, 827752257, 506642319, 906474893, 833738383, 685921528, 990047773, 38505558, 457384015, 107702261, 574247093, 197244968, 134199391, 482361474, 17490876, 417591089, 687853905, 288976779, 36997422, 53393023, 885766979, 735443233, 236291553, 643519482, 944739723, 233441107, 233503284, 214339218, 438008204, 897774303, 387159048, 306550350, 650193292, 252536738, 537041375, 502259778, 107259757, 258501694, 56842662, 197039931, 886637138, 257582674, 961746294, 276209038, 632443405, 886868971, 128822414, 357401761, 810591382, 64960247, 931801188, 713525010, 282772277, 113025697, 184863717, 725842604, 979510954, 383507524, 768921763, 890132642, 254593568, 52534534, 51063852, 507248490, 503723513, 620075098, 237541940, 436066232, 553972975, 479637065, 988364200, 398149952, 190281581, 916009354, 786321057, 22857803, 816126592, 533715099, 83866294, 664357596, 255082181, 197416420, 290887231, 202754530, 646447940, 101687811, 226098764, 924402992, 692600986, 521340404, 277035101, 382344551, 812984279, 761781649, 486984511, 235324011, 487670561, 559228659, 891968479, 585687841, 301513501, 501767536, 114843402, 198225844, 24119552, 292762918, 590894026, 201587628, 19350439, 972115983, 521075142, 749820350, 816012401, 613570123, 169456086, 156544358, 391764625, 285506511, 600651307, 40550275, 9453786, 653532446, 513028943, 124164909, 959855919, 177074329, 104637572, 16961821, 158024418, 488843727, 825106253, 392259902, 613558132, 70777589, 156216145, 830180666, 222319880, 380010631, 291041824, 969841986, 574202560, 473725950, 757483649, 9450774, 414920195, 171030602, 523708779, 81855826, 885704483, 180672466, 332969228, 392399976, 563107748, 610470208, 343282722, 721964387, 539848779, 394240241, 472217140, 227577789, 829192721, 697445768, 997824271, 275221470, 329271581, 403741374, 619607997, 757975532, 953550268, 7676696, 497434708, 236370838, 733980405, 284906317, 414093342, 94940506, 885467460, 270556373, 746233562, 899632420, 755842643, 956362589, 494203184, 191865715, 642275488, 468154097, 21704353, 270841990, 727431923, 644831892, 569474313, 133303414, 144469359, 416930871, 671546521, 649369633, 357435570, 69931823, 380810623, 525515866, 300917585, 376938990, 907385188, 727593033, 820192385, 533882293, 358033907, 26193739, 612212226, 56801122, 301826650, 5024969, 58647053, 815773243, 574010999, 128457434, 147347063, 61793845, 228644020, 275211987, 513441361, 787567059, 146537173, 774491947, 132806915, 494732143, 33624546, 4519044, 146496739, 996359558, 335238480, 60122521, 324098255, 24446121, 265560913, 489132312, 573831034, 222072143, 500190314, 38432125, 384549062, 248284105, 602028388, 465816100, 702873895, 702736595, 268700111, 831197808, 496482272, 708501265, 963481281, 283724706, 514864554, 169081255, 151444593, 822496068, 990736060, 871941754, 544836860, 399343252, 680366618, 789161798, 568728459, 173777457, 925004807, 694800011, 69095264, 462144254, 920569034, 669946286, 40567670, 133300073, 234471775, 701663084, 963073432, 725723177, 103277991, 68893897, 402174240, 143169525, 223317051, 646082546, 969895389, 313805530, 871944789, 788854535, 60644392, 703744233, 477252043, 470913997, 832122881, 922033613, 94026979, 803825569, 338286226, 906312474, 347626210, 350855689, 928028722, 630201499, 320104284, 24280081, 859200045, 8718944, 102707728, 284283873, 779206872, 709822632, 505618860, 766425734, 202787161, 112177294, 129263563, 764526774, 454262459, 544904511, 265432219, 264173357, 222432868, 592863520, 890286456, 543112310, 593094856, 403697238, 972948393, 709703434, 764060918, 121785176, 608416633, 962652530, 365979865, 325464200, 169067096, 430184359, 659897237, 447035373, 964124235, 990116556, 422693106, 199304428, 319623416, 692660981, 423130884, 826672717, 692011902, 165742965, 225829330, 444241350, 121882592, 243882375, 61492169, 110243074, 314918976, 557238310, 531196223, 716763999, 459054040, 835817501, 372970021, 265884256, 255571056, 523614562, 204533213, 741677154, 351425163, 69600499, 206028592, 690641636, 606126540, 892741242, 841082714, 360557279, 413675177, 382866588, 703604366, 903586862, 960042401, 945486498, 977997911, 814647532, 656074464, 102437777, 537236944, 523491211, 145628047, 882796794, 252942161, 374286573, 927672674, 12298277, 716357201, 416344991, 522234844, 40055741, 492579967, 378524401, 370140698, 989097220, 650918110, 6534668, 892669225, 722996110, 129907380, 770088545, 64571270, 702194136, 732792842, 80944314, 916565373, 706055914, 699824634, 374525389, 81815850, 194685482, 245888924, 721136241, 441829359, 670315118, 149836435, 257929848, 30923001, 206173270, 173681788, 571414840, 988415890, 5447119, 589186535, 373189314, 527058813, 665152283, 140040241, 720478547, 312140848, 627328188, 42723408, 876183815, 427200525, 486392964, 352931879, 434080, 941464305, 753777729, 526801628, 62251652, 642133637, 920441301, 455624737, 42162412, 771471230, 63930424, 12826519, 937138027, 721311735, 496339252, 761663620, 663709607, 395762608, 577068773, 775042337, 385945949, 582086717, 841948696, 715779918, 676799518, 409572389, 576405496, 646220491, 879943094, 915329662, 315500111, 471561771, 595080288, 628062839, 429880324, 137107203, 269342290, 287841400, 187482081, 477737505, 948798610, 538115889, 678552736, 522354335, 827784907, 956678914, 147906300, 353887537, 459810842, 558922997, 825674820, 527004289, 108817951, 156709353, 211279724, 795010686, 680114124, 462603117, 324202392, 801916257, 61395629, 316837723, 290323965, 380040576, 454234677, 303121168, 503566258, 718842841, 539815100, 484979346, 239563935, 31505332, 298614802, 420094159, 832041678, 152354838, 49715479, 649734832, 830541130, 437831891, 129069522, 646749935, 360571266, 989917640, 752446775, 856810768, 735092234, 869356431, 69777018, 697876557, 975379662, 682378822, 416522423, 278698301, 999697166, 518267255, 739396561, 385607044, 515724356, 154627866, 870050073, 83815087, 750834986, 243870658, 360569840, 313791379, 284222210, 726715179, 404310484, 896142696, 57602217, 891106411, 260732146, 523689869, 449907001, 866794617, 4035621, 420649003, 984380347, 697410681, 801743864, 196196731, 754718516, 429321327, 249719517, 751980471, 354389858, 842808225, 262294259, 444206626, 679861163, 244379858, 576299696, 374046099, 501626724, 354681840, 732617014, 203430712, 787777350, 462751640, 911856, 57695509, 913710155, 293707628, 247383536, 521935020, 477091811, 71797805, 40533698, 665971012, 649981171, 450650063, 721727687, 972289765, 555124142, 550064114, 713832645, 900722734, 786680160, 466117708, 300547759, 347817847, 324065210, 126121075, 523811550, 964387672, 407554339, 902265998, 440289703, 398806333, 106430936, 477156818, 423921328, 491197389, 127552265, 876661603, 499045332, 270782441, 35061523, 473494408, 904130775, 810604446, 495752381, 727009475, 680120672, 785480270, 14452254, 99347540, 734146399, 60023465, 909703216, 55438213, 463892292, 323413625, 522487495, 748102972, 688266666, 389450481, 780443169, 966364998, 937106713, 520235468, 118973257, 646538704, 498046473, 215933167, 308251807, 885897342, 139997525, 101578786, 338394303, 152922648, 469852420, 19625845, 876192409, 684375683, 510404565, 901064083, 675704047, 859388799, 353393069, 945985894, 460287303, 977105344, 366658576, 898288520, 916728426, 702778056, 188618953, 892203860, 299781051, 911637890, 418517495, 99364745, 550521262, 846859634, 762608296, 825894040, 962070564, 199183762, 520873455, 708290597, 90540165, 260605798, 730924199, 511614453, 44636753, 586913534, 130277138, 421877634, 408685869, 616691990, 3460145, 192812674, 105073956, 608401656, 664852719, 291452843, 196170413, 776571782, 325679243, 464953900, 472586134, 529505209, 454788636, 388467876, 741800409, 977289480, 509332426, 262458049, 532583007, 517693223, 454026541, 668321323, 607008344, 179252356, 798054951, 751477062, 221814690, 515590235, 796875807, 765677586, 114154668, 375238120, 137208336, 206804670, 626098485, 18361418, 10168171, 802128147, 478378774, 997681581, 876762898, 245624318, 177749388, 574113527, 528396421, 486713980, 890792038, 195332600, 207649542, 684423437, 516679604, 441557836, 714018472, 524104762, 832937054, 646134111, 907917470, 126289245, 209678582, 494171486, 677523407, 615255759, 902714111, 544027497, 319887943, 310740127, 264284716, 27111337, 91102397, 205637475, 362000905, 364262138, 578644624, 151927850, 633559090, 262573666, 517076298, 7277148, 117110871, 115246781, 496725397, 933143239, 681737567, 205294908, 475344364, 376116465, 415766946, 682699307, 684361575, 981132499, 159870874, 740817544, 635630034, 904904133, 218071566, 877064089, 521784042, 399538644, 489208641, 745671846, 165600124, 646280520, 570871140, 857020844, 186531538, 529063065, 739396963, 166353438, 34787921, 477512846, 389441421, 222318463, 183878558, 309886406, 904891259, 340258682, 202498370, 118812913, 793434642, 253023597, 221735319, 671473737, 490919917, 605069438, 549523381, 838292114, 385914951, 619828030, 590551623, 358160928, 69697136, 736425339, 971922727, 201489051, 196698777, 842059902, 924749257, 633041344, 874067305, 957606528, 511425172, 295087471, 981843941, 4487740, 28962938, 663302878, 769076306, 314107092, 734670647, 51840792, 497323295, 904806405, 708969126, 115542108, 689275578, 79374104, 178757277, 797320554, 529526394, 737253808, 654292366, 99969475, 41002953, 517714722, 655114860, 452563536, 15746896, 163458943, 204614971, 663819322, 514876233, 967944497, 546829443, 646170064, 862217735, 106399619, 197754258, 732339700, 940495849, 659747520, 34330070, 715602071, 412321578, 107100137, 278674231, 15336739, 57845869, 720804912, 977102220, 854081818, 400373847, 854178801, 940536054, 754648839, 69208189, 797345870, 520177364, 59840960, 641661336, 449348616, 58107934, 694830834, 12565934, 560217404, 594738462, 7856430, 994356891, 518384170, 46340035, 82422405, 555637944, 679900489, 987297532, 300151486, 860911132, 242510672, 662829738, 586066071, 457689022, 224385507, 823321059, 765776437, 286118102, 939775837, 966349784, 799678652, 670921761, 80093864, 449620251, 410253322, 985478056, 406736938, 104820069, 13520898, 408546432, 392889548, 83312910, 614461405, 947022771, 698400788, 488564685, 681356211, 973696019, 601825716, 88683384, 70107556, 860948285, 857133706, 69622130, 251530987, 877574680, 879457254, 337112819, 523132468, 772787237, 748751626, 448864631, 383483475, 513572224, 151035693, 496447293, 806302644, 540154213, 350649634, 64381751, 804132629, 683578987, 14384459, 744509184, 42281444, 688832314, 776400809, 152687499, 202276858, 638747943, 834713237, 477826038, 219573931, 740264059, 364420441, 850695158, 530627332, 317531255, 287883049, 22439147, 275915442, 826306679, 620203050, 701589719, 525379438, 139836875, 740820692, 671989666, 174814382, 708050565, 564047796, 335079362, 482207414, 533729768, 569230993, 125669178, 198885375, 814655482, 298590464, 103224721, 307455484, 429068802, 456794178, 851668451, 875857608, 796518149, 263966997, 140943624, 704715648, 774299435, 868065797, 931072990, 601941316, 312796618, 613457240, 981384770, 807610711, 619565305, 650344452, 929277602, 527334270, 866867465, 861764059, 861719819, 488717679, 326341929, 787668531, 738391436, 499153737, 711456262, 723586049, 998851369, 843841653, 42570460, 838056163, 366642381, 339142498, 336305062, 883544890, 755043130, 193565389, 795420791, 145330846, 457472161, 892904086, 522296016, 275290884, 17634968, 859877417, 945112932, 366263223, 706517739, 593543336, 90804537, 628606689, 730744448, 710319144, 64120151, 482982685, 2094927, 717600077, 912720396, 11739703, 954521106, 262480391, 722416843, 779388413, 222904857, 660881093, 211464547, 118351379, 50373235, 518943379, 951177002, 274904384, 324138275, 471408410, 58049552, 251072950, 130481618, 878096732, 320381608, 28533743, 218318616, 151004811, 68700034, 828721600, 82073089, 805945735, 456659035, 975507723, 718039987, 986051061, 130222037, 874801610, 194473015, 615186155, 813114951, 1597100, 546938766, 130060478, 795688428, 382426902, 292970830, 660485204, 158642221, 594192461, 621482341, 982461573, 860120920, 925178662, 90487221, 59659029, 825955165, 174339229, 762757844, 549471017, 715812583, 878028594, 579477209, 998856587, 845392443, 781913668, 689873298, 991226201, 442170605, 706781346, 178924456, 827747023, 192711085, 299118070, 379029606, 100192538, 89967196, 671844243, 118116574, 421094978, 509731362, 24306578, 511397153, 718222041, 230808912, 405881114, 679192251, 546084667, 79665584, 842112429, 493675166, 290233214, 748375380, 802189713, 26999968, 191834037, 724380777, 332493755, 991166677, 734291995, 260233284, 368256336, 973240891, 693177279, 165581859, 123191180, 859570617, 906743470, 835075855, 503867794, 69661822, 222858355, 927274179, 707090555, 540780155, 477388229, 748214453, 670099519, 771509652, 733411214, 677869660, 786915168, 57250175, 248211281, 738033216, 39638877, 682109426, 599357741, 145142530, 840090294, 492673741, 940914305, 828060444, 211727446, 144210643, 52605143, 693223758, 517655456, 831621905, 964780771, 408366691, 388581898, 285914875, 175681106, 281276239, 779892574, 146953627, 71740993, 459988689, 281113966, 141367302, 976789497, 207477614, 93596299, 200774824, 370067754, 137667721, 9156302, 537302755, 860659366, 753576845, 106838249, 823383548, 263021507, 415094312, 302625242, 310247157, 464507085, 355698647, 543097933, 944075771, 794377459, 964740256, 983098977, 912231318, 314128879, 367627023, 138374956, 550539044, 469760936, 738772434, 501462980, 71003933, 662899517, 864705054, 541478856, 576963577, 332662566, 472347359, 20612376, 242370709, 285716454, 368647444, 983037496, 411117911, 518147566, 406543544, 286688010, 251118229, 577986439, 39222985, 527357704, 324501338, 168963827, 241608151, 285211698, 29023834, 888351083, 388555270, 422263612, 476302290, 388083911, 60067105, 66862735, 736700477, 348560953, 32943735, 618235764, 6681747, 74938835, 398029306, 758722320, 899032828, 752614925, 430510445, 866563215, 570812101, 284042941, 696809181, 126197948, 845408107, 89266160, 122525502, 48002299, 275629888, 345955489, 698929697, 694342869, 445363407, 928477089, 841438170, 532693559, 200727225, 20702777, 597556415, 275551369, 495372363, 765705576, 244589509, 717633751, 197531471, 490678791, 305056780, 559926660, 301913799, 637644172, 887115810, 431661283, 669072555, 413871006, 291110746, 95569806, 390555415, 773892811, 831353057, 315578028, 343104416, 209223439, 782031792, 483482675, 358164497, 78654125, 467837833, 474318634, 640182413, 243339435, 620411462, 373190880, 595270918, 675693593, 996215604, 328105113, 89936506, 254284832, 846457085, 986692111, 245907592, 15169637, 28398566, 61277558, 564837895, 220825377, 667145049, 764735802, 84535116, 304832063, 713286370, 881360774, 542883092, 184909544, 218269815, 670671837, 981539844, 289425413, 548311862, 523944891, 188665457, 373135696, 576575620, 128500009, 462327509, 639924932, 537872827, 868565505, 250705294, 677427282, 79609849, 687353759, 742815878, 418160088, 245222174, 101387882, 7687084, 383852055, 699456964, 782345528, 827656605, 910503816, 452892614, 760523446, 651710106, 866688800, 457064582, 979337636, 41797901, 919853148, 959541545, 926666113, 878398401, 628539138, 659725471, 115357499, 674574671, 330826084, 958339060, 835217940, 381287539, 488051930, 363745572, 102372389, 452998242, 471798628, 436262557, 235401753, 946994830, 440059321, 487701991, 741945568, 19496483, 235050892, 475667529, 730506407, 71923546, 42601426, 81997691, 679248112, 975230139, 114677539, 37814440, 166934827, 396738178, 356371940, 519494279, 744146819, 706705651, 983543899, 468974172, 114810183, 664787753, 148975155, 770867377, 612057334, 627270188, 678403528, 378298120, 443966058, 610436911, 840514368, 555461410, 176634640, 889690449, 918899875, 318214597, 228237175, 650774645, 746511411, 117941706, 611962738, 909908839, 846852088, 36825623, 169172767, 856874435, 967740129, 898290653, 407722369, 254667685, 459458395, 248397385, 475372131, 860839809, 412866164, 984735725, 703022137, 176870235, 10307823, 6678172, 28191887, 315777954, 951235556, 374259822, 458968274, 651911449, 554440794, 688813236, 75886120, 892203610, 216461558, 230304042, 78107506, 870592897, 140232099, 970463911, 783435287, 688091706, 259907662, 1723434, 730974675, 991984831, 239789220, 856277252, 799275433, 379412328, 107295579, 477552656, 253516580, 426224123, 530597354, 274627645, 210769869, 828925885, 941429931, 263879774, 661463367, 402792859, 106358232, 114126636, 533956844, 171282841, 844545847, 901364087, 161353018, 443103183, 862568295, 17174911, 909055927, 204214864, 197909076, 695828639, 572386129, 977508670, 25530280, 234670690, 826830698, 264281253, 437572330, 411387633, 112705922, 559295315, 718042704, 468883020, 514774952, 275260645, 101109702, 372101682, 483952294, 560644531, 528638344, 680087940, 19678995, 650196786, 580531971, 179664807, 142127438, 78226671, 556479091, 562265692, 636410707, 691959833, 792164500, 845070453, 140470702, 707725630, 612935928, 433939286, 643771515, 413817562, 225132806, 227644393, 946692531, 815770526, 270868467, 870323973, 438460976, 302197464, 322630786, 172704609, 161309004, 776061640, 535150189, 662533418, 378562440, 445806981, 298212706, 48159807, 995585167, 631793726, 939608509, 288393909, 665840428, 876004343, 114615982, 3831068, 263420073, 647265595, 239798849, 786532106, 789656385, 486568710, 769253789, 691580128, 210362537, 728248044, 976955765, 44223350, 152746211, 250943765, 755812039, 667341900, 637568974, 639612338, 139039912, 956136201, 306660261, 14557413, 293959019, 170642149, 293071569, 772460688, 796809984, 963706406, 151463807, 614529320, 559923353, 347297250, 870668589, 363299533, 478531936, 265023967, 566887632, 660429227, 631516417, 997050934, 133422674, 627184251, 572912289, 958701595, 201239323, 547695293, 297687773, 112928845, 569972251, 38154877, 851675268, 994758160, 715371289, 381246014, 865005550, 887215706, 512323946, 13293699, 670467776, 502905401, 346943382, 38544435, 376998101, 666362143, 860916034, 925952100, 140124583, 27872108, 276673319, 167108684, 135108164, 526758550, 811320317, 971703126, 434900809, 615414465, 883060268, 467750344, 701257246, 886120887, 872570558, 475917971, 482416947, 848759295, 759576728, 872596545, 94901665, 246281016, 203157895, 854193270, 902167555, 321552809, 322625427, 841195159, 309979749, 786904714, 421194345, 117452602, 655925863, 78142369, 305456175, 910781780, 956649956, 724244658, 460584235, 269493703, 853790248, 717862895, 432926429, 876885114, 245927377, 725172699, 862491877, 670389196, 784194331, 638805493, 229202199, 260762173, 389136622, 144618329, 28166938, 469605520, 280646927, 685430002, 763091091, 810028948, 865988347, 418955219, 325170788, 810504019, 312434135, 139543470, 614490099, 481654596, 276824029, 469491469, 421156020, 586620248, 194966235, 160496105, 879289082, 147315419, 941226382, 501305246, 637635192, 164899515, 438457971, 368123304, 97970495, 904753013, 862629174, 527291559, 893121707, 318763459, 912913929, 962460380, 898789697, 961097149, 743813769, 625175846, 403149547, 491051575, 970854287, 932186180, 486242115, 723047776, 826783847, 266358224, 993728938, 960988834, 252451897, 99901943, 550797835, 958771990, 713682812, 938405143, 346929772, 168776314, 746083160, 441812383, 418552813, 706386480, 801548691, 517287353, 212858191, 164584640, 539878030, 923234129, 10922280, 768242893, 472019861, 588672118, 916015523, 834298121, 675717081, 412823650, 549290664, 26516143, 120991201, 324624216, 21360747, 5786993, 650007805, 311224221, 779423594, 682790044, 149749689, 740300258, 165847994, 649216456, 1031458, 886385816, 683672717, 84240380, 395785986, 849124217, 967094770, 373760844, 266109870, 684630849, 152445959, 186873003, 89470862, 853106928, 119774635, 499952639, 289620492, 683348190, 976692047, 430342110, 809191523, 559609328, 755478257, 356706450, 209777469, 105932180, 724286955, 710007520, 852941988, 544395628, 218495342, 314865320, 289831750, 326526086, 291675774, 908520537, 876326511, 334577081, 233899955, 979163455, 317044150, 103863073, 335504248, 111786175, 391625417, 751145585, 990890124, 785981661, 220080527, 522988731, 936963084, 67805249, 569904271, 762874146, 751812636, 112930702, 824146484, 246130989, 462670971, 871383453, 292115434, 947400736, 931070776, 381182746, 158406207, 155771787, 686965108, 563338793, 422702573, 73716050, 70028966, 269394469, 128446423, 802410244, 508222934, 66314082, 649415891, 860694385, 107827010, 179340648, 40450197, 86650705, 462551638, 834963668, 850754148, 993254386, 540718434, 483663359, 10473619, 182399375, 395838567, 799303256, 984465242, 225605664, 317457818, 173866889, 80731602, 454264015, 249990564, 890040956, 562590127, 554294652, 103183595, 988829812, 880273750, 683591803, 310388440, 512297564, 915554070, 702071906, 628858167, 61986033, 833728498, 67755290, 997900550, 774932257, 534789502, 151253791, 285428105, 321128026, 913154879, 633192637, 815815109, 286049706, 135041814, 40111740, 992154780, 562130102, 458262125, 618423957, 267707645, 139111249, 679860331, 842524021, 236698484, 32616095, 116627808, 656053596, 950150176, 492885452, 708169309, 79282622, 582979430, 332674556, 514819352, 928941710, 711248091, 837671676, 848980588, 295017320, 554004671, 302125494, 114555262, 868949868, 228582795, 583998913, 899064925, 74538452, 532799404, 58977465, 761236096, 575191440, 346801239, 610837277, 113226171, 773757757, 395621285, 542772485, 309594113, 505657463, 413268486, 938434294, 929776628, 401503476, 338791800, 319962842, 252427697, 707296411, 860168417, 73079822, 221314272, 347165042, 734491872, 682977545, 144021603, 371314743, 812460911, 185239371, 952708974, 519445164, 564401750, 982896953, 746834807, 678970528, 44997850, 764813621, 716412673, 12115537, 297694181, 559377209, 799305364, 545857237, 504710374, 361915629, 478174217, 997496869, 120222538, 120149352, 485161027, 794690797, 558821045, 532323672, 44846486, 262590393, 39322579, 849537007, 802851167, 651254775, 507536601, 682593415, 833218963, 319475612, 761615067, 775874975, 793998176, 442318567, 941487911, 865011668, 650408439, 342643178, 72321115, 682218486, 228295988, 832606917, 925491210, 584310312, 376755700, 690502180, 429651052, 367107278, 191092618, 487921809, 57988459, 92916887, 71396023, 966509504, 85835091, 617579822, 392695015, 169498430, 765379752, 907664477, 842207350, 149814318, 703939499, 309457212, 120197159, 32744024, 814769500, 189670968, 742948442, 576742669, 386362088, 780290101, 760889626, 169851386, 548320288, 418160055, 153677719, 701871788, 582293389, 562450960, 297608726, 187322813, 790246441, 941663635, 992762292, 596320926, 150492622, 868669011, 864701309, 90850703, 663942090, 772621380, 621462386, 616725087, 212207729, 791094914, 325865399, 239207281, 463397300, 759060817, 659693235, 953711389, 563681900, 596969957, 703997886, 453542058, 926059641, 330807890, 981895136, 213131008, 921576345, 739847856, 910487609, 13205346, 372838778, 556718220, 289082517, 907619512, 975400352, 429181764, 694278933, 734941383, 426790702, 434900174, 818363857, 763726574, 313788539, 447471120, 791469747, 105854972, 848649133, 172199555, 436890392, 824745621, 381901587, 912588797, 187288525, 604811388, 195007722, 775431227, 186508973, 570140105, 705692159, 215304528, 282644343, 384618663, 10988738, 888104418, 132963543, 453166109, 747756442, 274227108, 42540266, 298132906, 594064854, 66434832, 895977362, 493510310, 947489786, 460371655, 661442057, 874430112, 33262035, 388237261, 832163198, 100431268, 136292499, 195351177, 1324969, 780044832, 611419335, 564818160, 187724302, 990593676, 288381242, 157120244, 473491177, 965625256, 950831280, 949958256, 28901437, 891042095, 874224967, 525901164, 197618165, 21309579, 540114154, 466405913, 779924406, 239671472, 250475246, 244142642, 788116001, 589133033, 154025422, 187562851, 785295414, 181071621, 161992728, 618228149, 322886421, 788469965, 501286398, 850652699, 135438833, 351931597, 953755720, 17652747, 398382119, 881184704, 161987385, 102230505, 986732276, 250018342, 250022241, 992937667, 238068994, 751098544, 24042352, 467145601, 830366872, 592724538, 315927805, 870849730, 593579507, 757441253, 113248313, 780965219, 945760680, 79979908, 154410526, 535865494, 11545608, 439752428, 757243175, 511261562, 438256573, 122934444, 737557398, 39200720, 198594357, 321273161, 951686009, 433156526, 573628598, 876947629, 275767046, 455574673, 506897867, 119643325, 691735425, 323426538, 193214784, 183992229, 861398406, 675803648, 234547403, 713180352, 569564844, 536458532, 316827487, 52425738, 151805960, 63414727, 94906778, 523940696, 574888868, 890973586, 43342649, 886267716, 971391885, 889621297, 924290789, 119767300, 311239909, 602848867, 411933722, 447215839, 740742238, 834407697, 843148104, 984981093, 80970454, 510391938, 984101607, 677027616, 912878733, 191649526, 956465480, 263944685, 23591192, 753268498, 563108036, 546481825, 635399, 356479501, 471753640, 763377209, 471370339, 650393777, 206572323, 32055351, 197195053, 110233448, 123879247, 277808978, 755607734, 962577539, 226206105, 723590375, 501771250, 447104254, 104787269, 967073180, 671638662, 754866362, 629180236, 450862009, 419493868, 851423653, 199958854, 654232075, 450090313, 617869683, 215935238, 452508870, 902838343, 949247588, 676682462, 393516989, 767117107, 114703143, 506479999, 113032401, 500028936, 388262549, 951269714, 840607568, 792951546, 194622903, 721628050, 494335958, 363570259, 723995556, 639557965, 931320078, 923350570, 520763791, 992088861, 206383310, 668989448, 289561290, 289663722, 672107088, 621625565, 167562795, 488013283, 792176886, 384526098, 930548242, 884652741, 254566485, 256313402, 259698449, 385277523, 528658767, 390283108, 680552002, 97877111, 293113333, 460072706, 257979829, 794651607, 266402210, 814779572, 122508608, 926926368, 248916526, 573413965, 490636636, 4109859, 228664903, 98004972, 583163174, 406511570, 42011506, 227653667, 914008140, 641746266, 136651018, 618487377, 106330275, 136429971, 64570958, 507721627, 306223182, 571936851, 441935595, 685978587, 178969305, 576102610, 859175526, 485167640, 192409961, 559796643, 113338300, 839254715, 54227336, 699400115, 785075800, 667906594, 237844102, 995345891, 913923469, 756018673, 942178052, 215244658, 675844303, 267636882, 319827045, 347096456, 77698532, 397047744, 476467843, 356443002, 632884446, 754479621, 374482180, 69223646, 87494174, 491313195, 103881810, 928527388, 103449552, 374394085, 721106546, 333221218, 989946254, 245049128, 945297421, 323977091, 222251591, 727545645, 617134318, 170718448, 914930674, 659125748, 975930289, 52327151, 300241350, 353852956, 173958543, 393659879, 488258888, 634863997, 980015318, 685557074, 536223696, 393938920, 230068561, 553574742, 484263515, 747745571, 846205409, 371666063, 122082772, 999354148, 359031575, 294993954, 777479489, 512528523, 465662532, 948689153, 416834298, 742524655, 593970041, 391948710, 660631116, 371948441, 489519073, 429928495, 299939858, 541403853, 246593009, 704469162, 649703823, 504252758, 593244354, 550519337, 578061481, 585628251, 18094641, 385971385, 64220150, 655593323, 444642230, 881239694, 162087472, 938323569, 99478820, 348162150, 839963530, 536359880, 365960630, 588658647, 378579861, 888727230, 862133540, 200332166, 240458990, 282661195, 519990720, 987116343, 130824988, 45153118, 214134578, 958437733, 142766921, 591810204, 515124483, 912372967, 140329078, 24244446, 507597629, 913780593, 592807234, 833239710, 698293624, 364818880, 702888861, 824162552, 234558455, 851653453, 21168692, 53990333, 513746306, 1636639, 940356495, 65631760, 97840038, 240935593, 206835837, 971069155, 854266070, 171405348, 125465023, 36474507, 859339058, 983648898, 187793265, 102474585, 8222709, 717669388, 161464477, 918404834, 926306953, 847094092, 209058165, 306266172, 957193071, 168211191, 722343582, 446732344, 881227261, 383262366, 481076027, 309773096, 202086056, 620842921, 685196822, 667209113, 716456990, 201117990, 692352154, 785965462, 490210109, 606540222, 977732588, 636229652, 254337705, 3847484, 434848182, 466403195, 906262732, 203919586, 735199379, 209561321, 78299766, 483798016, 755215700, 335143756, 322295131, 635281272, 422572445, 419746475, 713225794, 801796920, 727946160, 384689809, 504998884, 551998226, 784769592, 68789450, 799197557, 854104625, 189190646, 473019097, 122971842, 236190885, 799868821, 24769563, 231776336, 316474453, 760510644, 53256346, 76616513, 756721080, 198385121, 564683992, 215051849, 41471742, 961006569, 441780151, 827528761, 9602795, 512420501, 148934081, 150133819, 249295285, 390591331, 881261738, 186997962, 70570781, 341497263, 203429698, 136160014, 282330901, 561733009, 853125864, 836359828, 612545552, 733287992, 87997015, 945002652, 888612230, 378400420, 757604346, 965083998, 26004971, 944995371, 700749826, 175635783, 536289612, 590701763, 368265497, 918738211, 789138945, 137095162, 57772865, 758312989, 612325684, 996414263, 644367840, 460047986, 353115019, 163095424, 885055123, 229818536, 169953549, 382364453, 571774517, 618564655, 585528815, 764147443, 921647800, 993807227, 350843710, 162334220, 826528703, 783251128, 570786679, 76888895, 691005569, 684543428, 190677281, 767195854, 276325281, 958185125, 716938398, 449824411, 202244007, 224631449, 321294537, 514957085, 858134614, 285638654, 203351841, 16609646, 843190070, 332623322, 263161712, 597829064, 687478898, 329661606, 257292193, 434082732, 425640187, 495225698, 317278343, 745836432, 255612577, 556981017, 818070543, 687578232, 665084990, 776159634, 736766606, 823857862, 737985201, 386398460, 901590424, 637125303, 931299754, 141621448, 460937487, 457581815, 211528784, 633693871, 870853841, 518128983, 395485638, 288789132, 277708075, 17388258, 945649012, 840719948, 236485357, 41167384, 65676230, 652198595, 201355421, 391425155, 603412413, 39084062, 371817575, 663876266, 405563095, 884788132, 517904533, 256526228, 19062665, 3592176, 875641660, 376746096, 547672389, 558587673, 82917805, 848537371, 440660784, 965924672, 316108848, 60477923, 294699230, 329146093, 253722063, 355434774, 3398014, 839303215, 341459530, 253585983, 869143505, 776992601, 860066079, 597185653, 111720149, 69338196, 826078777, 744552765, 88835095, 885159199, 451940864, 460806612, 888264240, 450616422, 626738661, 455228308, 728191615, 546649055, 519132179, 898192634, 977427991, 812479755, 730128228, 842664024, 946143527, 925480546, 154372466, 790827230, 67770915, 465293932, 762000496, 880430777, 893354091, 297512457, 499451709, 328194129, 796374831, 997919316, 641917888, 889205587, 328215348, 176828740, 213226511, 862215390, 984679021, 799324710, 294999622, 302828319, 373990738, 374129840, 431568511, 340409940, 568466218, 1432654, 519424425, 38883187, 776847024, 632256570, 321707127, 780035916, 570948337, 799852357, 374080643, 477057084, 809167522, 630304323, 233839876, 230712382, 175071232, 422677968, 798665310, 711592005, 319822576, 710188491, 320362319, 784452765, 686887004, 477826760, 947055691, 835098465, 918146476, 761130256, 792094702, 698721147, 847683131, 830873827, 628349132, 751556277, 155477914, 107378449, 45419634, 613198830, 697088287, 544928305, 679103387, 212215220, 395791282, 548555665, 46651019, 36866570, 907111163, 713732734, 941076078, 917750016, 402868765, 517471868, 565386371, 975740561, 749442875, 814008807, 425182465, 762143916, 906359300, 484419887, 374024408, 777690600, 390460880, 837828966, 23241147, 666165049, 681773425, 918527941, 880613736, 773159702, 300393331, 480081194, 43498607, 759544742, 639101844, 325748140, 33476848, 622516286, 193893812, 148583014, 679177910, 820711188, 533275699, 883627504, 332908915, 421398462, 331875291, 72430699, 483215729, 309323352, 317021493, 78935541, 458232757, 122751381, 288531606, 985974513, 338373589, 515503401, 84378293, 83369989, 932527395, 528045814, 168227653, 596994011, 507384935, 85456812, 667206158, 431782019, 98482224, 875505108, 255309087, 906329601, 804065998, 498543560, 68634284, 954617066, 387551810, 87306185, 546954451, 535129212, 98933329, 892499932, 952028489, 732196117, 120495220, 960304494, 433117588, 897766684, 925127280, 118811956, 176789894, 138992617, 735245484, 969856258, 153129677, 802518048, 418506968, 221208023, 214289635, 702153151, 536368366, 713347991, 698818058, 958319590, 532476323, 610535038, 930526434, 202560966, 988089896, 153565088, 800306615, 978704392, 149623791, 690493020, 186401204, 405942000, 369262181, 758749325, 491224786, 492165002, 238298748, 371295827, 918434943, 476794104, 16741933, 952386089, 330720118, 890677933, 240069379, 350551604, 567318639, 497319735, 960605891, 861532265, 544607488, 685301311, 659790368, 750023864, 362331092, 554221969, 967729320, 950035537, 867652413, 796201232, 386787582, 451489378, 665064116, 270493194, 890597035, 952543370, 101503057, 321429456, 464969487, 695170639, 109564892, 421228976, 547988449, 341030724, 605622162, 560431694, 899255468, 999022295, 788482602, 873717575, 574041877, 977226879, 218347592, 969523203, 485883122, 355069280, 629769639, 10926628, 405364746, 150908430, 394474250, 854717709, 94358994, 804998564, 186878675, 329275417, 670348996, 381849122, 21437618, 12201546, 865450060, 826558720, 117538980, 897063894, 870145077, 744444617, 1505988, 620204055, 898193520, 509189725, 972488002, 559684391, 885019942, 923413542, 198886570, 401925415, 307024413, 374665538, 517265447, 117663315, 915186514, 187323965, 799958214, 221061424, 221411127, 37844453, 778538352, 55575344, 506240781, 779158354, 815041185, 45646120, 355466591, 580470979, 457254156, 871296034, 373008445, 541804781, 716128633, 638797501, 914916391, 227075435, 105609167, 564159061, 197780650, 963278223, 970973745, 903522691, 459817186, 480374316, 580157058, 797140001, 905500706, 168535557, 957950752, 521800108, 278186352, 956007534, 954789885, 71254802, 138631997, 16561583, 295894979, 739550537, 184456498, 899966060, 422731356, 534526263, 567622551, 448565653, 735791691, 137537938, 127852918, 956337142, 554965918, 972208662, 531993802, 739389134, 232291020, 955582679, 220033977, 509341619, 813374778, 697399593, 593152162, 977613905, 264059655, 657768608, 722937984, 600241101, 455216766, 485509969, 644837785, 477694213, 845299234, 618077048, 658607222, 374653437, 896673355, 609247634, 552380909, 744772866, 556100033, 236095300, 355564213, 378329240, 372012864, 220777160, 712825816, 996245369, 732550186, 788951988, 930020871, 666281830, 551449967, 484112944, 528550681, 745581677, 137346314, 406382436, 403412634, 694847229, 513646441, 103178299, 362518680, 747449857, 414646378, 260933425, 179711999, 169241012, 725614726, 541946194, 976465832, 515799772, 689604933, 736591507, 202496141, 475432313, 781008260, 573121479, 594173700, 438516317, 310377780, 975603358, 56290528, 914021598, 134769590, 239256359, 416155330, 851591116, 664784455, 525391994, 591590281, 686672144, 233795654, 227624938, 53999644, 792888146, 164383638, 459968679, 86718352, 833261359, 986381739, 658323309, 11737579, 817504074, 696501404, 169602177, 144777139, 559864172, 627884294, 309595021, 540760717, 962291135, 65748031, 299324757, 163785247, 338206938, 600316358, 941642172, 208437597, 400186505, 319749892, 347935210, 724473181, 98100842, 237727301, 333526924, 40377408, 454063298, 285698805, 442726261, 856144820, 290413988, 15209755, 315805971, 14187957, 315258179, 351154131, 144378377, 125983744, 585189712, 211171264, 347136685, 858709771, 559536171, 750391126, 85821300, 402091352, 952407402, 158525041, 33727501, 495194029, 339038596, 255318183, 58553457, 49058610, 851722198, 214503938, 665670951, 590900137, 111546181, 752358460, 40272664, 292697067, 944145478, 877153670, 317847313, 915622423, 15434329, 787727493, 805101446, 246008614, 622775163, 360311855, 898627845, 61675524, 794923830, 266655783, 966647314, 777425000, 154512823, 824756277, 562608957, 118079623, 288366550, 549886462, 215293851, 199090055, 77222131, 862794452, 186941884, 927811169, 965005838, 927792769, 635514649, 515879437, 175122696, 73677261, 464523032, 141940616, 567314855, 794367713, 557435414, 511276395, 396957531, 932402404, 138677507, 962208410, 552294531, 351650778, 30766725, 580915870, 113923456, 731939032, 597215132, 663212093, 159192350, 857833149, 474696322, 42667889, 366651797, 801432304, 290279512, 588891575, 626208464, 194684829, 920576556, 656349423, 546102696, 941748024, 945119542, 302983164, 565119348, 314090111, 573786685, 367175528, 190124266, 349910318, 538293342, 808739308, 266894790, 758148794, 353995346, 348152880, 876960088, 533285597, 716135144, 817515264, 713851021, 115318272, 869560536, 231751456, 117259155, 506269422, 773509433, 74426906, 777642317, 81812832, 107759005, 715474703, 625553410, 391234085, 622086939, 546191105, 39595251, 938416871, 725209629, 53104254, 359959128, 305955027, 913784921, 545482311, 733810563, 538983861, 845760811, 948282572, 487318521, 328407683, 797056655, 981293536, 243892687, 865099115, 499103804, 664116205, 178329319, 939852730, 24095270, 960222373, 680041600, 76710317, 789623872, 710089755, 562033731, 81639211, 458659651, 959010938, 867082417, 310165130, 79334447, 408634090, 544374176, 247707967, 68945894, 238492679, 42096765, 368071498, 193611059, 477115302, 473805163, 438547690, 899828285, 243697238, 192024723, 522691133, 38603943, 436166512, 28440406, 871497237, 478685544, 775607029, 273725542, 257125457, 64907869, 555308209, 212220489, 878101728, 544219136, 431340680, 60842998, 273788952, 995833515, 413543931, 208653288, 222809323, 560386879, 68086685, 47964063, 178975586, 316793502, 485602071, 687493175, 152461150, 503178080, 684681869, 731960440, 246035806, 133002214, 428056569, 738892704, 303347852, 506079552, 624487219, 704189963, 707666249, 598960752, 123055675, 374703154, 589842605, 870010536, 676941317, 757333078, 131274129, 450105773, 175347017, 964580868, 764032754, 595900512, 901091391, 845893595, 978254907, 143318901, 985869688, 863606053, 146188858, 414965873, 543303923, 229881445, 649933407, 39777995, 651556270, 868061447, 746484267, 509395670, 359655805, 539734722, 51465675, 725568715, 189824484, 326554139, 161697442, 41009282, 562760844, 575205092, 929415629, 33353302, 808497257, 946896646, 843646105, 260390076, 365643116, 717038682, 754412904, 199573692, 441567516, 118371818, 784627364, 475060200, 169332439, 358544640, 481390810, 900428320, 719281095, 714052780, 258889594, 755413400, 167226229, 916344045, 60826389, 945690874, 424601279, 856468250, 706813331, 945348528, 681504664, 235036345, 965072187, 133614174, 572885831, 912830844, 328413969, 738432495, 361587899, 620440364, 862032366, 127640705, 569462740, 546230373, 404991328, 100719147, 633497114, 49863589, 854068921, 309912238, 271391788, 948318658, 838070266, 316877287, 820113876, 27322263, 651828144, 180606532, 254721980, 765511651, 206603121, 493008413, 966050424, 492613437, 258749326, 556520789, 633511233, 713655289, 694053125, 91606328, 404513143, 231411202, 653846150, 617202272, 732375796, 231720198, 755823581, 83176894, 759694967, 664224229, 461737498, 549326242, 32083751, 973276505, 17674416, 101693197, 118089180, 607882758, 574439797, 215543800, 764389348, 982087185, 824767535, 95684245, 240802593, 340300334, 397217742, 752595754, 233162550, 762383058, 299671924, 548590295, 159472740, 15855778, 89320537, 9165492, 759297472, 146278340, 911604403, 821561237, 560757836, 78337944, 510036230, 691744686, 563206609, 552920608, 328697434, 62413177, 45783880, 336948805, 630185966, 310291539, 637358520, 361694192, 312039250, 421639205, 573462281, 247293724, 538922144, 311080634, 360762087, 795032102, 992656927, 842129908, 884331530, 13086637, 52999352, 487727179, 250995999, 380793509, 17387694, 749674582, 347843721, 465466406, 650223484, 495489236, 928036084, 964760705, 551054795, 798747354, 705317208, 900959355, 807771881, 185697702, 264808965, 629687681, 23826705, 966761794, 811135667, 575650971, 736815242, 486468865, 443909610, 53484201, 483668779, 404866670, 658736511, 534806134, 709417642, 134686879, 248090733, 545713674, 774358997, 361244809, 875286170, 392540957, 560716577, 582616747, 174541769, 87602150, 252235907, 508537872, 154843115, 662294507, 471043058, 615107223, 990477310, 518447009, 937415555, 213724125, 465212420, 57942766, 254222242, 912372753, 286288162, 375530969, 280391529, 390932992, 709611833, 496611390, 418365935, 524858027, 86509099, 244965214, 416387831, 727600830, 848301321, 908337893, 75325383, 655494984, 155684652, 557272940, 20741718, 671419355, 589061392, 616188594, 490653361, 216692193, 47231380, 616701940, 860885389, 622554432, 587461231, 987420606, 860316933, 298074414, 892395373, 591235043, 666205827, 523415446, 673086571, 815130705, 34106549, 372501174, 906468185, 887151198, 716786509, 778692350, 751733197, 303969924, 257792555, 579892288, 590111182, 633027629, 435536775, 618242808, 339493536, 294365996, 722134898, 82969150, 702442871, 503848633, 948226560, 576954562, 705779647, 948749396, 409733545, 273232691, 371675415, 624173823, 373709659, 399398164, 364732563, 802722247, 619394925, 94213886, 508701115, 284847542, 661499443, 324858684, 830531268, 212279297, 703021314, 346163696, 129582278, 632913604, 973022, 636512324, 935347703, 866776380, 205512021, 106594677, 561019449, 26936779, 544118518, 828516194, 213190896, 551183221, 317671020, 540590617, 560210750, 104709314, 340938882, 879382961, 382307875, 228190275, 548456129, 910978260, 43602649, 807762856, 57250325, 24218756, 155340565, 193025649, 160395378, 733615543, 621376295, 622263607, 384704892, 432336273, 793789857, 233112427, 938008349, 897861734, 820228719, 908352161, 53338711, 779654351, 427381470, 546374453, 375485990, 747510306, 783341964, 573062930, 162879529, 679405606, 923791886, 987425796, 265061380, 510467573, 252741381, 64376777, 381114662, 395978912, 839766337, 337575958, 938662920, 348589216, 805283640, 152236229, 549881241, 950164959, 728346044, 817809414, 156467685, 908116555, 701458000, 80941342, 278841357, 800973648, 272720251, 944042246, 430012579, 403362386, 48617459, 883687837, 914423926, 315419320, 32907210, 375310436, 428336235, 709490923, 61394518, 993037558, 157557705, 234068421, 775399496, 590520472, 381604208, 923068805, 124802118, 345831268, 347113452, 965561013, 599579270, 308491573, 460073318, 769251104, 312285564, 234829117, 993717420, 264664628, 930163828, 990245613, 808729001, 278561106, 546078549, 785163466, 809926353, 17665533, 715819509, 360946594, 157624612, 931480495, 480016731, 992639148, 278649854, 155930351, 628560747, 550300947, 370040755, 317807475, 759092239, 602106885, 216856977, 198402565, 255298594, 567463600, 2958624, 819352503, 70058594, 23731236, 10435947, 187425344, 362984440, 524080825, 251942392, 523053124, 132264852, 907036294, 909109285, 215854865, 439778273, 541114209, 866414216, 945876574, 84145112, 80379846, 846951040, 297801535, 893154953, 821964737, 898425898, 885693128, 479012124, 712922519, 452683010, 851429253, 319750070, 998622618, 476959601, 480743826, 468003709, 873425988, 267208542, 108917671, 888719383, 893681964, 736986820, 995627387, 552954579, 804684304, 518528782, 611639187, 819317011, 260086464, 771893660, 91160870, 500386986, 29260920, 119092612, 415688125, 372425830, 481186149, 771802450, 149484822, 770554502, 263939413, 13309946, 875576390, 455240671, 515797192, 323249609, 606624902, 773440066, 55842983, 387466486, 278657665, 137193042, 99949594, 497177989, 757692337, 3861841, 189020717, 395444865, 448850812, 114342983, 626451652, 260187698, 584207587, 313066013, 362480041, 587028760, 695280044, 341069085, 480813739, 325336265, 321313919, 300428707, 985995358, 855755957, 617947938, 696841429, 35258300, 116734579, 404420479, 972432916, 54301658, 547509381, 963955238, 462373502, 94269980, 883363338, 711551434, 678457787, 937382657, 336249964, 292520890, 432812248, 542868113, 508272168, 359675165, 501069822, 73896796, 421898964, 786987622, 82923374, 44865377, 825598844, 698702888, 326360274, 783823530, 369875318, 724845347, 409418349, 658016656, 947971174, 941511473, 338292062, 684566657, 638332174, 997441332, 936041810, 822180589, 706116180, 992585690, 279131865, 420603565, 163533808, 346150044, 274550273, 652950875, 879864162, 445357787, 88982257, 135923622, 911152655, 123925987, 800392828, 416345077, 917369576, 417384845, 33497929, 570793476, 44780072, 497489008, 890323301, 515047344, 43475240, 960689797, 174828118, 184981082, 555620709, 157691964, 381123732, 315050709, 994609336, 297286382, 37088099, 458774174, 766132851, 15019459, 559459466, 730788430, 934329167, 917181221, 107933218, 463405224, 744414189, 170093370, 746354190, 638805537, 654388762, 451976648, 222128240, 123318673, 874766820, 596446443, 869890912, 811726297, 397525233, 723093456, 99638735, 209490192, 762555224, 780964065, 114963565, 807472674, 468052782, 141820773, 476128729, 896534056, 174413478, 793787838, 71526556, 838758682, 387480818, 4952578, 528407844, 725093427, 929616366, 118184897, 569441627, 244137494, 655405459, 991755984, 372643647, 708119797, 30859937, 406888944, 629052667, 28160519, 683672889, 309217122, 405207346, 552094154, 738106432, 662948580, 674815786, 88294521, 569936812, 47970706, 285914980, 789144642, 930667165, 243911843, 632631116, 607575476, 480088694, 292536918, 326943395, 667344559, 729918451, 354441417, 586075849, 645843258, 870000933, 638711437, 295271854, 929805674, 504827973, 431605404, 648461160, 842168400, 687806188, 441454871, 265995372, 570367797, 176853515, 954239488, 517595479, 194084638, 129935867, 21153829, 26746733, 530595005, 629043457, 84731025, 631916045, 266264364, 144329811, 756990134, 229488350, 657025264, 114890948, 854876609, 158753031, 505668759, 277525373, 621543280, 715945210, 769150485, 654822897, 264435145, 941851756, 404246345, 889786237, 868577555, 593176152, 942484134, 615764359, 320596903, 978342491, 536429951, 871529648, 641777092, 438873117, 710444276, 971431577, 913922254, 259282696, 178772015, 779051928, 10561623, 92028842, 459039732, 578892362, 487702139, 379266051, 297684384, 772728921, 37695663, 553439977, 335457750, 762451943, 437114727, 920529415, 64417962, 497251917, 202103633, 645590169, 162860345, 613849792, 174628602, 784493440, 375432524, 682220555, 490446362, 176649001, 73428213, 301056826, 784732774, 152596799, 521809488, 141986105, 169670574, 96622694, 491085990, 519265461, 522887669, 531694689, 98512357, 51455726, 31339483, 200992706, 339161913, 837861678, 546809590, 258778614, 158348076, 347815013, 593049487, 276655608, 181902313, 422858781, 130710598, 880775990, 130224608, 501928539, 782433911, 553917966, 52890702, 787491196, 526806127, 292145593, 405788860, 598216076, 630557734, 874864860, 864370362, 530882205, 159371429, 591760222, 122560032, 681702513, 500892097, 474049300, 750562801, 382631232, 131294763, 865412295, 943941492, 641314318, 435961673, 855718485, 142619733, 344186192, 864711350, 946010865, 977962358, 896961026, 461913490, 725532882, 500441013, 834162282, 808903056, 178395445, 933198155, 340708357, 726051423, 276124425, 383022769, 635933690, 611596320, 737075291, 208457453, 163591565, 644591636, 119926053, 389343607, 91562768, 923837360, 780595605, 509474735, 467973904, 876470512, 413687916, 931008132, 446987639, 23260903, 140482559, 375075153, 165327022, 217780170, 366908721, 168760472, 438804558, 283910135, 578517994, 302687875, 978898968, 142363059, 367935330, 946622964, 664679838, 908290049, 142332690, 265944727, 318376272, 339959512, 793519108, 70225310, 124056902, 875920425, 693619549, 734324518, 765310503, 208816093, 536343938, 774570513, 260611468, 290520264, 288528224, 140490278, 913572187, 719597166, 909155525, 965481330, 502518456, 984152417, 652101073, 789675198, 69857074, 822361297, 382791117, 9215554, 635757067, 268315292, 592029838, 70636734, 47480651, 240218571, 965513717, 233281544, 150114871, 496206307, 688187494, 965038184, 433200262, 908914526, 756756087, 377223617, 956170661, 542355604, 323599160, 375093327, 645801722, 284900489, 34973833, 542375826, 596574224, 776554066, 977379201, 930992953, 147654993, 789034371, 508861503, 214551260, 190051246, 853771012, 808350644, 837958224, 197092179, 549525866, 912452429, 790285868, 31459979, 672273434, 274227092, 245997474, 403829477, 837226701, 51293425, 414013014, 218066244, 702321866, 408011178, 728180562, 902464171, 852383394, 405934225, 639283595, 599493104, 532078167, 911678709, 833952026, 866117722, 216642127, 485616958, 567294503, 783669561, 475617040, 273059736, 555631127, 597538730, 766556952, 963017475, 841796506, 708751403, 329699849, 866259645, 877580655, 508882067, 138301637, 728366793, 55717812, 461909777, 688121024, 343444836, 653048821, 535226690, 848842233, 358600093, 49556521, 398344239, 465830030, 85731371, 567345683, 493132823, 862359973, 669584989, 796056339, 762217340, 197486013, 731336156, 65817954, 727313668, 111684067, 381196954, 181594015, 605964923, 213672107, 3102375, 612578917, 244754052, 646779650, 218682508, 786217172, 804352312, 731960939, 32873606, 94210866, 591414751, 947642807, 256541058, 854382645, 916442303, 594092024, 369286725, 336950165, 913783677, 991558890, 558043955, 128102079, 256228781, 122238396, 808794828, 80282395, 132518657, 496419890, 867338798, 470157838, 373697661, 716230166, 360722829, 802508368, 140284027, 359130439, 230071086, 224515536, 775017798, 482972735, 731737862, 563217758, 529726210, 676526152, 306607556, 649981053, 24083855, 178793582, 386546722, 570164754, 789542037, 353854974, 424472964, 471347818, 834633704, 810947532, 996308084, 102243205, 738941201, 117987849, 4303370, 270546582, 724895458, 352744596, 402274772, 528884770, 205236440, 465930370, 582746416, 445400080, 767443427, 286860535, 667734057, 774543396, 309996077, 562214367, 790691087, 265508604, 246358402, 317095507, 45089243, 371909380, 125138144, 325611017, 888189596, 181661983, 591154849, 697880063, 359031656, 480030694, 383616584, 764452172, 290914237, 852260713, 526321299, 434345622, 898485437, 580537853, 165847210, 440541589, 909881068, 122191215, 275595547, 955388355, 940231584, 577828639, 289232931, 831576754, 154238075, 351243232, 665884858, 410836134, 515427830, 382447017, 573501658, 405634358, 471560522, 186851773, 467003265, 803186970, 921251216, 347174267, 534453652, 154758264, 170859792, 336537390, 663673483, 948874700, 233532337, 365111385, 414255293, 973647954, 449304214, 946901601, 179412333, 404948629, 871972945, 890009225, 189429457, 282097314, 783982197, 302638793, 743869864, 548744674, 709458013, 418947493, 674055654, 944876053, 209552016, 78897793, 174468385, 82684730, 266292226, 765931656, 898112298, 930056456, 887016335, 634686712, 844098367, 39529589, 657069628, 178147042, 637581243, 173755598, 593924282, 801241164, 618192653, 243312380, 69654562, 772912374, 219423297, 149660472, 356739703, 785983485, 513687487, 424922934, 217570116, 670197415, 955467322, 753636116, 7727892, 323152634, 863809478, 797689575, 176925053, 489473647, 47128445, 969019432, 848082504, 953645019, 124429023, 575590945, 241304466, 122818865, 52420868, 172016809, 123186303, 664792898, 810253028, 792717061, 31139210, 438967117, 787159536, 842026832, 297926621, 515900304, 152990964, 790978765, 927188566, 474092578, 984571523, 537252843, 567149330, 824091303, 236110808, 898733404, 897458862, 227428970, 503649383, 249039166, 947331010, 14331762, 963300774, 177880237, 812210116, 900463673, 689079533, 730191995, 81836871, 566100145, 638053880, 131988790, 873149846, 816493320, 670117367, 349388349, 770960348, 81471348, 319397189, 269129789, 382520600, 960052290, 630644238, 734366368, 245791628, 677004528, 614709129, 762601947, 17377202, 493336083, 709773036, 847699589, 369838249, 822350945, 251499992, 21561348, 703513098, 866668643, 715011265, 111400990, 478619618, 380907531, 597693785, 238699649, 946668084, 923246700, 321261336, 355132696, 359116120, 307926681, 322922692, 555232530, 571365994, 693879349, 403637751, 564625748, 508156708, 712088571, 223583608, 957392578, 330179945, 862762827, 915012828, 141865764, 774164984, 732901967, 429262422, 570264309, 458053699, 274185448, 670481165, 674249717, 569590472, 405596369, 6781410, 200291898, 161707958, 708441421, 525997378, 122850509, 462861612, 655206095, 482102209, 135224008, 794181863, 268585106, 370722621, 606179189, 935205460, 462653064, 694084465, 440601107, 996284658, 615250912, 180421356, 441844251, 632970988, 739077104, 983755279, 231944861, 483146492, 448081741, 700755055, 374431579, 532892198, 536823166, 302996339, 302030104, 77298814, 129881717, 564064235, 63920495, 240484887, 166817402, 764444814, 460015830, 149620868, 274146453, 315275280, 159212712, 655537091, 502805761, 731722628, 428840369, 507827191, 763026603, 136513822, 802614971, 636322556, 217164661, 308933521, 238567811, 226196953, 878070841, 690993070, 238556880, 657268196, 58681949, 667842503, 192835428, 534612648, 104098273, 961288208, 353574274, 249080222, 71913459, 643631349, 897480707, 169990930, 905512372, 595618670, 798153036, 713402884, 765057518, 322885831, 251366714, 650473997, 251623753, 891774804, 708415513, 261247984, 15571910, 846897266, 20686900, 462425299, 879204715, 286368524, 126752231, 536005915, 698512644, 763343617, 712289260, 756293977, 752784099, 648624107, 325189980, 586138620, 289686098, 464048750, 848616889, 589499140, 555312941, 185225003, 687379050, 835451006, 548607474, 70187102, 550763416, 460687105, 672399452, 416480710, 201463136, 767668864, 844188076, 823583647, 302666148, 288469596, 541286405, 307504918, 247820533, 680389115, 382497693, 327471414, 188038830, 419865628, 980126708, 591535122, 380421947, 91208854, 211060046, 877247510, 948179779, 270949074, 856503644, 228722534, 537169584, 276143436, 250363614, 838696160, 280501835, 625303482, 16066998, 277714398, 121262478, 535068458, 346326878, 560582397, 740117107, 773965371, 893256042, 774397167, 873233568, 795466029, 975363834, 121029888, 659118374, 366201777, 115398837, 350689864, 311769349, 750401653, 337719570, 790629588, 978621524, 985290896, 768050596, 668807608, 86466299, 255482758, 76059204, 489572084, 217329168, 488644884, 107149482, 515684544, 600508272, 245720220, 821801824, 374103870, 219546385, 334722026, 763803542, 281179417, 902494161, 351645746, 306940809, 595248002, 834194643, 193165533, 170433443, 89148315, 500268503, 126925751, 633579554, 474124423, 227741845, 580465668, 870165443, 995248773, 863302062, 623934965, 840220560, 144473231, 846641118, 782120381, 32659779, 761720082, 288802284, 599111312, 413759436, 420387444, 314234565, 895257001, 860020619, 971310808, 44911555, 319423183, 739948716, 775745585, 93463137, 35623519, 315777670, 636564036, 402007501, 424538352, 861003895, 186036566, 911821261, 684648453, 602213515, 16174299, 497656028, 859999376, 665681450, 956030151, 425479817, 275924383, 557728902, 737160208, 621567756, 341092280, 865672427, 752907751, 718337932, 324690200, 753856439, 100201571, 181756427, 984201192, 695403396, 723071820, 801656157, 223857741, 764846981, 764871791, 107881994, 828783085, 641009598, 900890839, 241552405, 464055361, 100499596, 286928352, 55876320, 223131120, 124243817, 25472099, 887327909, 996064666, 913855335, 509129155, 144864287, 922096250, 862101332, 482732347, 335455029, 626468772, 86440955, 47197819, 94249166, 157732961, 985328098, 840791484, 682738896, 554371766, 218337091, 322523789, 693765168, 744427996, 413549845, 907164111, 247272275, 976133318, 451728765, 145169463, 505185894, 728406175, 504876018, 357734206, 947449147, 957927349, 822715446, 589375686, 930601921, 125084974, 683042711, 367186006, 780067970, 529987171, 946682227, 354396420, 653067671, 694318990, 844495796, 279758759, 459156268, 687018056, 655107115, 9784788, 583261520, 371158993, 660589979, 427929873, 662145958, 138290330, 86837067, 591921362, 796189290, 418548688, 292549793, 54929671, 517863892, 132725369, 717933417, 320391791, 181343632, 507586813, 545742052, 863875518, 625972323, 765184604, 714084657, 880638662, 205658178, 288661452, 218070887, 545624343, 718360059, 539675258, 942218190, 818007178, 609736193, 102207731, 470350642, 144002747, 885113922, 38152731, 19487567, 215083588, 752271733, 68954635, 849595259, 680905395, 395373583, 205460791, 875311335, 254641366, 922134762, 526028803, 331322561, 818895314, 369453859, 618518423, 5548510, 415027095, 755184918, 850556043, 343750324, 48475109, 468335674, 594584090, 470739100, 641017063, 574656066, 663586786, 72954552, 289532751, 759170862, 121053504, 234877223, 308512148, 435623100, 38344674, 325824429, 631789992, 576503976, 512791385, 806606872, 445340961, 561761343, 259815254, 35335309, 347507496, 336808367, 668415673, 409196659, 621506729, 388775041, 107918475, 767675897, 214872674, 334119508, 655228644, 348863018, 300899069, 579719155, 3438078, 537531064, 695607234, 375749041, 481840546, 640585633, 119550574, 90046821, 176740903, 989423005, 927092108, 513333238, 167462867, 61902776, 349916769, 793828986, 60283818, 422828941, 76222982, 889471389, 268996378, 621247664, 821952994, 372659494, 508775931, 471616854, 323650946, 602813593, 983199473, 821407715, 980504108, 971211500, 156831214, 759194376, 136656479, 432104721, 533847143, 377552021, 193563085, 940622772, 299427747, 855927713, 439813539, 752993132, 409823478, 452042516, 53638679, 598617373, 474728817, 550378126, 147641618, 462610975, 770694693, 355297362, 1796530, 519179480, 242109678, 400786292, 391606821, 371517354, 384015507, 741943744, 716668083, 695338154, 495760545, 885311053, 151356417, 184823538, 417398370, 962521687, 776358271, 229321573, 384956072, 452513507, 586771337, 609700719, 272379901, 251088403, 823060579, 636261180, 2992582, 583067650, 459657781, 384627008, 384929974, 332729909, 243406368, 461398777, 463372591, 201470882, 310107230, 803550375, 855418584, 953088746, 759638548, 259221683, 203397261, 591986023, 955439484, 978994677, 593395462, 250501725, 114117379, 82810886, 102918294, 937859497, 13509800, 423474689, 944950269, 485773728, 106483580, 845516441, 57159895, 993296215, 574007516, 815610794, 176067106, 800134666, 680098126, 424517613, 164690697, 435183627, 453020125, 581209801, 585150027, 548872309, 146703669, 577853665, 647584056, 744479989, 938323111, 716012613, 224673281, 158866008, 749664659, 65262591, 42614159, 388743047, 775242681, 758859638, 145049629, 596215449, 67205224, 217338071, 966505838, 865770433, 461122518, 831969051, 193471476, 140623870, 796671210, 712000304, 728222102, 944252733, 778613170, 20435167, 763834442, 154702308, 283274820, 174172225, 666104412, 91074102, 596067317, 508172089, 409109240, 220558035, 895362435, 492295349, 207470910, 976757118, 391230996, 463629870, 562150108, 678827785, 471266361, 482486830, 568754402, 833264314, 399284547, 240192230, 34843995, 249676974, 658755828, 883276820, 441681129, 210673926, 859180851, 897532133, 18445214, 321138142, 183150373, 539264232, 485507575, 593991055, 267339207, 835839418, 611922001, 658099787, 933759826, 941047968, 663993306, 878723023, 343546152, 10441051, 215752082, 855753831, 61968157, 116140826, 672371331, 75417063, 731105965, 355322700, 414473794, 535016902, 32914248, 714303799, 303358286, 929335866, 297409535, 701947980, 786166156, 850146045, 63298149, 161226136, 725159351, 53969375, 164767734, 258187444, 13361818, 850753975, 559340200, 323688783, 384916442, 325304878, 167561263, 158788847, 94399741, 517709825, 500984100, 995510333, 334172050, 846839266, 201517692, 799959522, 58912260, 728557285, 312287708, 630810947, 550196688, 542972176, 780309193, 91372741, 416230086, 572138258, 259565953, 695968578, 721313437, 522977499, 634554551, 41194361, 118704143, 805637054, 708795877, 808770805, 289908194, 206554862, 545601501, 961868804, 790213760, 99426038, 559284978, 846195515, 969809148, 529076820, 94280643, 250906834, 292033120, 186254294, 103574904, 6104469, 382387978, 744235949, 449393419, 530578243, 226391711, 548671486, 264734084, 394717254, 604466666, 505425195, 427952312, 353090602, 206309022, 710329789, 356933579, 35182815, 990070463, 463791490, 893458627, 636850016, 92631585, 554026376, 418967308, 558452678, 250889818, 510741722, 569406059, 457904791, 763727210, 289629050, 782295752, 886852675, 592003226, 605505475, 710916705, 989473216, 706195031, 672626299, 835538175, 294960465, 37400608, 868336192, 924269091, 940472666, 814159776, 625313393, 58867492, 717218304, 187554490, 695040442, 661560479, 573185993, 849610630, 829417860, 255710025, 355090818, 824290720, 634340247, 319133998, 830152216, 654216745, 459094151, 329437848, 791093033, 112138974, 169913125, 997032104, 703482302, 922616316, 434342316, 879670354, 841258763, 727371026, 112998246, 155024095, 967077821, 276827374, 25222212, 868359324, 365029957, 310616410, 31685447, 144233915, 48128853, 833280493, 760858049, 309624301, 983319023, 958202164, 791527042, 637899676, 812658407, 805206605, 482911540, 128874675, 437300373, 775339371, 127296925, 379735078, 570331543, 154024773, 979975287, 795062977, 149540643, 443036487, 941461893, 348552763, 9128700, 315438725, 428473714, 592737835, 986254826, 168626385, 379363051, 669342151, 245976258, 865578516, 637922009, 784681336, 364143582, 338474146, 888522484, 430486684, 536923365, 59565708, 62637474, 11958886, 269146021, 203494894, 254117477, 318696059, 496924172, 162233579, 819156083, 589571575, 258595452, 195158898, 15867850, 345828221, 73685344, 630688689, 454737805, 671335146, 892040614, 196587127, 310510407, 493991530, 90214398, 834125324, 409345157, 115422857, 736483206, 479698274, 637668114, 372715814, 625805391, 954912396, 135072690, 77947633, 752737006, 485209690, 758835678, 894675809, 595433154, 992841896, 143642501, 237451978, 262493533, 778301844, 985020133, 705402442, 428371157, 893079652, 94480064, 537129902, 935845920, 589668607, 964715656, 239277726, 780142034, 235622315, 352795429, 817447250, 323443362, 981246720, 470747271, 206096038, 934051143, 956963075, 675612702, 145608498, 239031201, 657433368, 16942107, 821528909, 743566382, 801215961, 654347516, 194034159, 570322277, 455667256, 651706095, 102197677, 503117016, 411901878, 427384149, 770847974, 361473147, 596813796, 604683279, 225117431, 781042908, 414821106, 205039700, 347799450, 233738475, 446528832, 351316288, 813555293, 850371426, 725074918, 569205162, 618293208, 387998660, 827355291, 139340848, 691341325, 117309400, 618739558, 641511725, 7796089, 127357304, 175204112, 290928358, 13444097, 994207887, 359202769, 699201291, 235337255, 643483235, 264495724, 201539745, 851762319, 539859747, 490841085, 531128056, 149273825, 560810192, 223868737, 907842347, 858968620, 141085973, 917928694, 898120231, 429143927, 542901565, 99087572, 139264123, 423160586, 994153476, 735642554, 552380773, 640812255, 567458279, 366989771, 607759531, 131068734, 58143078, 409249392, 785947719, 182738790, 259534978, 775711350, 204770100, 904726672, 339722564, 126195286, 499503529, 103061390, 873363546, 853720438, 810750018, 453840636, 660594540, 163489304, 803837794, 183853839, 52365880, 781999163, 97959106, 825344493, 963005043, 642490533, 441563195, 26845624, 406405246, 965140810, 246441436, 518491471, 596553462, 743794973, 870444761, 516917857, 943119076, 242317037, 894607350, 834705229, 959433399, 115606558, 244019474, 668810456, 926955489, 515471787, 645208970, 489523198, 469748643, 349613528, 334953433, 494051315, 220482998, 226607213, 168943061, 158659867, 691653483, 402154317, 211935717, 743790495, 775634643, 420723999, 444101753, 65397702, 750479711, 898017593, 161483787, 302433391, 5383978, 83111071, 536347516, 670003193, 608586046, 528765533, 276633482, 664901483, 73283938, 269909703, 517394228, 783168604, 964560327, 739190157, 516364381, 57627350, 52863606, 796854776, 963543218, 587179626, 804840246, 631075370, 298489760, 739935255, 840475784, 504586089, 121465250, 497463823, 759122800, 347726433, 566334401, 999418879, 672749292, 607900919, 77063591, 679924196, 345189974, 560722620, 487721380, 820639941, 878306082, 229820722, 287715092, 489870870, 482387398, 257519662, 731449444, 708535967, 422824048, 864789242, 43245030, 882008102, 534191773, 200859244, 346587954, 539996358, 697963197, 105537402, 510427955, 649503423, 478609177, 277841884, 495218809, 795722885, 989126463, 534041494, 674480159, 876413513, 267564146, 572287573, 213308356, 811061234, 493598190, 577633829, 909576639, 654089276, 68736824, 82254504, 844619694, 105615516, 556926710, 697846660, 282397490, 260338480, 324268432, 367699666, 553288871, 15162744, 845647209, 236660495, 483643815, 148301957, 926577911, 15988651, 384192170, 929874577, 810550518, 643076745, 864181103, 769397636, 345560405, 606053911, 467931829, 872871520, 466811241, 66217517, 834319642, 722462756, 30837045, 61659356, 321317899, 488303745, 765757345, 166012375, 140099608, 845080221, 874827359, 904921983, 687594000, 866199537, 670127818, 916612985, 659500088, 526916466, 55297944, 197931864, 978335674, 168449426, 913347519, 462864692, 938591376, 103332193, 868323542, 152469118, 562822329, 61783094, 892440605, 680001360, 601147530, 973702487, 74714046, 392097171, 713474866, 102028051, 377399449, 782655784, 826616533, 501146844, 119941336, 188609472, 247034526, 148501718, 338549563, 936508101, 547889957, 607281538, 83131561, 761341157, 219512285, 894980180, 391990382, 618943559, 69691089, 901264094, 597732848, 788790054, 207670590, 707299278, 959527732, 934117377, 955835092, 810431359, 763773276, 826919878, 403589869, 434595603, 657387543, 567044040, 895288812, 154533174, 729338064, 686638775, 815473405, 658707377, 951080666, 841055369, 751981637, 91566353, 891087459, 405743885, 514661130, 386104391, 637155487, 722861306, 531970240, 415197634, 128531637, 378552403, 354734174, 856021570, 679716824, 334286379, 855200026, 674990072, 101165528, 3983419, 458410243, 236785444, 83483705, 981737724, 537730932, 174669587, 288290323, 166752440, 714735368, 273038792, 580983753, 324649734, 636845582, 134567873, 407254947, 352914556, 206115649, 424659482, 602098903, 716219092, 255606173, 125535100, 950234780, 242063981, 401085476, 783248038, 793134730, 938152789, 760555118, 343419289, 431057053, 652167252, 364529095, 978187120, 833487663, 341451004, 932910829, 327392854, 724427460, 824290076, 601479668, 239481447, 218318374, 134353645, 48134547, 342455101, 760334352, 913688949, 893283675, 848988765, 470141259, 451953184, 462767830, 567721808, 30763708, 740283990, 483056048, 245127253, 780508198, 373352533, 776627376, 874632625, 244627614, 16129880, 119898420, 494758061, 925754771, 204978679, 694511311, 368692394, 63710449, 271906538, 214763425, 635661793, 332481415, 341479495, 311332839, 201453943, 629479333, 833987110, 399746488, 996008069, 810386271, 724524855, 868237284, 164116512, 243248700, 601052387, 994537724, 763397813, 857716710, 921454748, 812196514, 194065607, 664376927, 349560714, 737399390, 694242214, 213783105, 335801913, 12177932, 808872140, 944176872, 77919581, 238719305, 2404416, 394900292, 59523410, 507436504, 823262752, 65396351, 486963758, 561489200, 122882115, 378695575, 230582886, 826637524, 649041800, 792839678, 313093891, 337215316, 9241979, 150862382, 667215098, 838774040, 552196973, 173134974, 589420750, 108024659, 107399556, 217645191, 965360753, 494958352, 142011479, 804664537, 478185974, 579977444, 881390657, 956132608, 196350874, 520420181, 473653715, 781091937, 893637205, 720206506, 342102108, 77690532, 196118767, 210178671, 83632791, 733860550, 784609770, 939538463, 172224714, 892362312, 237128483, 191658076, 952813501, 105658446, 390053227, 316019547, 180237853, 883707194, 22227863, 568968441, 568473771, 688660217, 689626306, 32236009, 67526369, 72101862, 8038951, 681152522, 349440345, 550354879, 211935922, 837454963, 36794889, 365840468, 325523925, 516804725, 892064608, 112775000, 119261500, 443420844, 322725162, 472318179, 278644220, 966095195, 316488692, 902370763, 957341474, 576704719, 914278467, 867363297, 769446834, 338688468, 903768896, 836962695, 861947711, 419841685, 954871252, 633624369, 62397229, 791285110, 470055102, 97913029, 986129644, 801779493, 350595863, 614993132, 653245994, 239747730, 57151263, 762692909, 490383325, 905845474, 593499675, 376299884, 305329341, 692044408, 368391296, 376919266, 660403775, 203602276, 504217165, 44550707, 758071654, 19160899, 99164903, 213220605, 742507468, 493355126, 603073738, 544038372, 751691324, 226665881, 431828891, 172139450, 844717294, 151408544, 290338170, 856807234, 453117289, 889521315, 179833210, 281856604, 215745077, 522504816, 994115557, 44452966, 758667658, 413380274, 1328528, 930531927, 95712832, 934569436, 566212549, 971859501, 313131987, 81561612, 868975220, 81123909, 983161520, 829338030, 791355587, 468180728, 407822410, 590279268, 205874048, 923089456, 839283841, 545244833, 99881505, 543521389, 852951653, 422187374, 323686832, 653548262, 356166781, 307815240, 927988936, 894154072, 290791312, 842366378, 814284051, 931977271, 238161115, 982075629, 966574880, 964546339, 14712393, 867281931, 908480343, 66492526, 805164109, 980306292, 480000478, 564990608, 42274345, 2170057, 665575421, 881098579, 109029125, 354050518, 511958702, 261823963, 613783512, 13939100, 761965477, 989538640, 49608876, 839183823, 192114829, 247972194, 246198790, 593930463, 387683317, 170527973, 507383376, 625982461, 18843093, 948570235, 888114876, 89524963, 192808513, 212792213, 71892595, 727070380, 664383791, 894932788, 424424211, 116628789, 52851308, 934964604, 645689766, 762450285, 958932955, 842180826, 963932110, 696852770, 450766934, 968606607, 984317726, 903132684, 288194276, 229069958, 467217764, 947950602, 701237931, 551538319, 888719004, 531527379, 784464833, 5668986, 591776359, 211184084, 111233793, 443194627, 349422646, 443198779, 323012975, 890981564, 780704776, 946571089, 387802682, 46231508, 564746341, 579413996, 162957513, 527884858, 808063394, 766185301, 715397998, 428131986, 744696973, 966645742, 913772707, 716433774, 447374971, 592494344, 251014022, 379647, 89504349, 95621496, 2496666, 630315980, 586108803, 36840258, 594252935, 802701188, 988664269, 705768442, 167303439, 790337972, 178273434, 409654010, 371328713, 187469402, 763430227, 568930652, 515627556, 944096889, 190222983, 491579755, 794587814, 913184115, 43358501, 227031555, 426186308, 841688241, 575163996, 814637817, 304758941, 130323014, 45443898, 305938153, 219475846, 827268383, 211185209, 606127146, 763623655, 572494810, 86611537, 675010340, 347345179, 994651251, 560290773, 986711078, 780198770, 225060649, 638130604, 451532344, 618998915, 542964171, 292808956, 663553174, 801919491, 306225258, 596403774, 274488822, 666776476, 872168035, 502092172, 130146400, 264225489, 688074928, 988792847, 370477316, 334643624, 504637185, 264188128, 893655680, 960449584, 613503042, 941339966, 429673834, 354082810, 133460078, 254727751, 117746912, 986211251, 352813910, 329824335, 106735068, 697393957, 262742128, 654448494, 925800431, 847263714, 326277038, 874956719, 75511047, 606285665, 889393820, 259564626, 17327463, 157025678, 475214576, 340620607, 668227229, 626292276, 216065210, 185569564, 938431038, 517908182, 835397135, 112720823, 4205267, 386624661, 664126177, 207397136, 122809944, 961552456, 567233531, 788652393, 331273761, 477710559, 853672733, 207797774, 529459397, 188814437, 832577009, 998974564, 709425581, 473658104, 264693421, 264638316, 679026125, 195318831, 271872953, 600293518, 199516424, 588940811, 636943951, 744390077, 525008620, 814580840, 416608275, 938897855, 464122962, 349700090, 978593505, 521998653, 703205294, 976193539, 150738605, 626492371, 709354252, 140743362, 985299033, 77376519, 210491203, 995451897, 874311364, 751439101, 206120445, 744527160, 137209132, 290881433, 208318363, 643995548, 459239953, 815285284, 665874366, 680952175, 781992377, 216468044, 772187088, 280307626, 609646331, 928152153, 114121654, 896839260, 77344835, 673321221, 94270340, 267977846, 99996318, 963267528, 958552266, 760465588, 675537188, 187778904, 73105734, 834206176, 625068716, 554411714, 36697061, 264862855, 65628925, 457166092, 208442123, 730912170, 38138581, 492329633, 136913032, 183206906, 815335144, 663737126, 302477588, 585710955, 146009199, 151495103, 528355537, 197684554, 844436091, 518561604, 588963759, 549080637, 917509685, 523976944, 650445142, 901063248, 372161428, 957205130, 660206753, 916087910, 225831399, 515982250, 987700949, 476676685, 884035467, 74344803, 186685371, 113431961, 353496945, 267381387, 801127595, 938688693, 860901689, 216022030, 81838235, 461344850, 64668169, 203417607, 801496883, 422330181, 86928566, 986527179, 350565432, 199692304, 905882034, 716188980, 604222098, 693333962, 535277941, 964215131, 533930444, 426168317, 665231800, 325252018, 737808946, 794293480, 365543706, 559622941, 117970657, 91223162, 298855735, 938427755, 719802707, 644792710, 584780420, 394598964, 838827213, 806628726, 747521359, 785087894, 172886650, 731071516, 838759211, 64491216, 314930813, 242460452, 771214986, 964899793, 960801675, 25843799, 540173873, 485414295, 772344639, 910079334, 13791943, 503935392, 858676844, 162885977, 249643905, 801967288, 137289012, 508310778, 415788662, 663342988, 967171451, 207899470, 310381663, 775611672, 64909884, 463653108, 617039731, 759948317, 663096655, 930956864, 869889647, 968881826, 795813233, 57060501, 544292702, 293389333, 362491429, 77043713, 982221168, 98455329, 789209428, 875829181, 365318238, 69272427, 108674091, 600331134, 87613602, 409713328, 899241964, 310081247, 105081420, 953569521, 64992936, 337845907, 993754507, 865146761, 704460009, 914365544, 754834879, 983879088, 677107107, 33736359, 765113141, 602259832, 109631394, 815222418, 356406259, 432688863, 17762772, 148184984, 400995754, 670208868, 871939690, 543802422, 24655835, 317169765, 528859536, 12023402, 118901058, 190000364, 512627676, 48575701, 294851969, 794819428, 139670959, 532733001, 25359315, 748932696, 434751081, 132815877, 217541073, 824899522, 300766435, 811142730, 916145785, 400898846, 346763951, 871420756, 935065074, 24554697, 877596629, 617133362, 796621915, 67181776, 575290515, 128023717, 700691942, 120721573, 165239314, 212682580, 470831905, 360333541, 336564236, 321963078, 140816534, 439384619, 998268961, 379127409, 654717112, 605833, 707414878, 212249474, 437060051, 85254192, 781902522, 720194802, 76749272, 806077430, 733265659, 756841185, 7894950, 463567329, 61445993, 607515058, 440640232, 470855012, 677349894, 63466483, 732439126, 3349679, 1165051, 921541346, 829436279, 677890487, 455873153, 880980649, 438025804, 6604058, 453215629, 466844653, 927512843, 1673247, 265503766, 678575249, 971477453, 291622163, 372650704, 233713038, 123145164, 46859427, 389326251, 571072832, 139290696, 48494348, 708288085, 354829064, 323774110, 786679592, 351859189, 260602970, 212655668, 111229055, 769167050, 245365876, 646482524, 177724712, 846527778, 473796781, 612122013, 242099224, 120901548, 228780968, 301209288, 327751718, 503179422, 114748843, 844844267, 364199445, 318985276, 508540000, 720415447, 70185604, 417108822, 114045604, 750980731, 77324830, 752988046, 309912015, 899169487, 770474574, 136248384, 642880995, 547601637, 213303289, 740132354, 245063319, 325687259, 953506751, 257724934, 290186472, 271767516, 885538098, 732498831, 171139281, 184172519, 171951989, 551963617, 575154815, 663529415, 736769517, 212216169, 876824566, 358282902, 352184418, 537253901, 244222665, 838338632, 935620596, 602926459, 674487232, 96685685, 830600291, 491033072, 347042028, 835070470, 419706396, 636307956, 736623387, 952835740, 114436348, 934517166, 334879148, 17306821, 838343808, 584127006, 866679920, 90016018, 702101457, 516347346, 260142498, 415495157, 532439677, 596149274, 837528787, 665380568, 960221801, 354421121, 287924681, 873358738, 537436069, 239298116, 924575670, 289397946, 84627513, 84101907, 203510904, 875384455, 517986608, 2728642, 372954689, 291252732, 370606650, 993639748, 260757108, 242201060, 996976110, 185154599, 505508166, 423528170, 807811967, 206714584, 838146287, 435131774, 293937939, 43068099, 691087167, 274292874, 178942365, 367117111, 168648405, 853241194, 457362149, 497511281, 771369242, 825349417, 958300678, 352840698, 941943029, 117378771, 394606922, 616645134, 911202601, 165975703, 65272546, 641315430, 869261304, 538485698, 296035518, 240414464, 35643043, 617395894, 829407924, 649566552, 936367938, 39594868, 702106662, 48712199, 546779979, 773865012, 7177958, 835748191, 210174402, 285385620, 870252227, 239449560, 772978205, 761384942, 710956861, 628979101, 589813049, 941658379, 112259207, 134726378, 598099041, 943193604, 610924787, 90737332, 88056903, 446688437, 791084767, 645032772, 897321356, 533962751, 868321997, 57835076, 726166144, 416521402, 248795109, 737939376, 500473676, 185212863, 72738493, 104438602, 746687795, 115952966, 964949652, 62628212, 98019044, 436905681, 799914299, 869486249, 918610264, 598939536, 49330328, 902596169, 910840858, 497527926, 804583566, 998285968, 827365571, 495019736, 68441774, 645128036, 526099544, 742785947, 388941947, 295800513, 25241587, 713141094, 59088232, 321020350, 632583727, 318105809, 260238659, 266667928, 101533051, 676447859, 367879830, 557835866, 928095421, 517553657, 569522835, 312428435, 476523871, 634103979, 472364117, 595197143, 253989922, 201062358, 2525842, 857483488, 228051072, 853452660, 174774220, 574883024, 746144987, 535180268, 138191900, 683965101, 177343220, 959349114, 632818355, 364704282, 582872995, 952659428, 623400598, 396729217, 394937174, 379710796, 163210803, 877895345, 734128946, 600263152, 949720899, 837027971, 8914849, 327931600, 341963187, 734939360, 98862056, 291139696, 39277034, 352497808, 580553028, 632084531, 79083591, 615668414, 744222102, 819607688, 679015209, 406748133, 293906438, 820129721, 876429764, 267401140, 185893457, 111229386, 367024541, 954391303, 768354625, 914687800, 419000055, 329797451, 695893127, 122151618, 272487913, 750594903, 573933815, 277723757, 627922412, 29540190, 774142639, 308360850, 993050563, 49948119, 153741663, 25534451, 656165294, 701136313, 600366212, 280726706, 278477365, 912821167, 84263048, 441639959, 36506092, 250000958, 933906075, 568010916, 243054224, 291842592, 589664599, 843662330, 616024839, 85682543, 470014414, 867226799, 100070147, 66694844, 569840200, 661855790, 548768262, 461159578, 256679208, 827848420, 36106738, 762086290, 673338101, 795146527, 515654027, 102806480, 955138550, 632202263, 787703554, 734955364, 505353756, 983265463, 174646140, 55163723, 882024331, 105991539, 646858370, 273798475, 596258725, 704490262, 211877359, 352701514, 47886232, 609765595, 613048153, 778106993, 782516431, 808709819, 33775680, 676344638, 141473837, 3311665, 828792809, 247535053, 75898452, 559159922, 743090746, 332385061, 658929293, 356520927, 648639790, 139052886, 133006489, 222391043, 732416908, 523958286, 729330580, 390152821, 908145957, 238897255, 806495593, 341343379, 14177436, 810115747, 415920279, 854475033, 60928304, 774206955, 982137954, 830966383, 735721847, 183473707, 258455781, 825926562, 744175998, 661033583, 865688363, 734827442, 808252619, 359183109, 277089570, 926921017, 141791995, 969723151, 309989224, 460499516, 118416480, 297605045, 877245486, 215680829, 19258235, 543550658, 75993409, 624689135, 641468518, 111236281, 103963619, 211559047, 393640035, 278712796, 283026636, 653836068, 75238804, 705356635, 191874783, 115933748, 502050905, 6419465, 436790097, 565825283, 787391135, 94807730, 71055267, 374429877, 73520476, 481589678, 985524221, 263290293, 324871965, 32366482, 458247834, 270818147, 864666278, 391276604, 752652121, 968637810, 640633538, 914791441, 605867661, 642973772, 676970497, 640015472, 686007078, 245205507, 443890337, 207837423, 340124351, 840099849, 357041385, 305351915, 704302764, 836698491, 966433972, 215908426, 564490102, 780326669, 786507474, 479479271, 470398661, 160490844, 713730634, 890013390, 867816261, 389787506, 90630414, 905220952, 869392628, 425765171, 987746626, 811533415, 382053783, 266106657, 599757799, 479807493, 101310736, 882213759, 484318134, 370871462, 324572761, 981411316, 771406400, 647629895, 786401124, 471368280, 917950161, 611805376, 696986995, 923104034, 900264888, 774322579, 533647988, 710885156, 256596405, 131154191, 372687450, 531981701, 196058064, 229170483, 961940178, 828490287, 126075827, 433808733, 57512298, 29002765, 293650940, 621881624, 925101292, 550112723, 522232623, 554521120, 136928239, 984537902, 660736229, 616954152, 173324248, 302743088, 371724536, 451101061, 703274631, 973964500, 275505839, 942516678, 152629356, 378837662, 566549534, 503112386, 894077383, 503226997, 868626993, 576115895, 158944892, 786413784, 824360590, 20419699, 364304454, 385873848, 765816767, 860583524, 214437646, 315054771, 331354693, 598050972, 480750342, 990782429, 601526789, 683197946, 951670398, 390094918, 237008882, 563087253, 865299937, 350795873, 405045150, 435361908, 11570173, 903402959, 706109740, 854345063, 6792186, 398594647, 792342761, 83542116, 308250105, 68411676, 378875215, 605502373, 869312200, 770900033, 439129394, 876745241, 488971545, 996861876, 109333806, 760053486, 582027829, 558220471, 573135724, 780173056, 67115736, 993403702, 453307927, 273392713, 933015566, 221777190, 257753959, 801034288, 931839090, 752228977, 83523043, 272829162, 859099270, 857305579, 397772987, 756795261, 319044056, 81410677, 714565428, 889599767, 850964065, 150491943, 59293733, 671457771, 934058931, 881284330, 864765002, 677753473, 432257232, 556594397, 58002099, 897660843, 880845566, 697621769, 61387146, 685765273, 252844570, 509141476, 267480550, 426554737, 917184833, 363878096, 8416555, 864060093, 654394700, 372383294, 918147988, 186119437, 446476364, 10629712, 729248017, 541227151, 933933266, 320853056, 365012151, 176405197, 240624181, 556039590, 491588304, 79857787, 316709415, 415213327, 115076297, 465425072, 869626112, 696777252, 269691363, 225084311, 101179758, 488477193, 547255542, 450717500, 549774189, 410371737, 223327769, 779803264, 206141184, 991591996, 71308822, 633883464, 282698106, 996546927, 721018210, 879962228, 704249309, 381048763, 131673126, 660622167, 502552740, 484656822, 306149465, 39583793, 458742472, 890106126, 374246765, 989487133, 832161308, 342104730, 994302544, 706914195, 16517344, 485793242, 668152308, 459427415, 725547954, 475547772, 516323118, 272267657, 71849391, 161920908, 331176669, 258936714, 136337056, 317288262, 184482824, 598930542, 308911201, 905953752, 168969389, 208968149, 918438815, 8471611, 112161382, 100123266, 676646333, 327447059, 734641017, 212661588, 419587079, 948911398, 420576006, 158708417, 559077802, 993105817, 534138113, 785712485, 734063793, 295846958, 683234637, 617552508, 750496620, 489385410, 629437730, 984424551, 900807984, 402975809, 5862496, 413752138, 524532564, 254431899, 521605044, 968009596, 520880016, 626446447, 319759118, 296764883, 251825133, 261089982, 14211269, 979639621, 350580561, 220427705, 554447887, 258395696, 696663207, 177220696, 907926354, 908358472, 558605223, 397788041, 265116788, 763166576, 854099281, 500604838, 11208672, 961279065, 963527086, 364149501, 961140640, 999499232, 221055135, 519290543, 49687058, 282034502, 351642341, 690729865, 941671590, 755261577, 24821890, 514777567, 141247111, 779618632, 976275362, 718645376, 562879773, 524746820, 387954110, 129423172, 667667945, 371539680, 48359503, 445607012, 181474897, 252846310, 380758427, 770695054, 720579345, 149815209, 637149179, 918775164, 515930558, 100462186, 469232549, 225268394, 726275017, 402593639, 729949514, 230015310, 875552635, 567043854, 112917665, 841057887, 99270225, 743902136, 89904896, 626031447, 546830025, 599668850, 233255875, 918571964, 579590309, 834622165, 389825931, 226732597, 235341599, 100159454, 258382178, 723899431, 633571828, 886301764, 305723744, 707824063, 637019914, 311011797, 903594280, 201201771, 998556853, 343457720, 175097488, 409595451, 302895379, 799385493, 62932486, 589315133, 709389324, 822178984, 342023499, 687621444, 429289597, 372892468, 943990462, 639983243, 458669025, 416296386, 907364485, 315264956, 120017243, 217185740, 648368621, 888093103, 479773203, 141872562, 978413467, 845295124, 624121910, 545051748, 995288535, 499848952, 398906793, 354803095, 925810070, 814943599, 317709561, 744532131, 439083972, 814886596, 965405290, 60255780, 668198360, 596181881, 221045035, 275863100, 250664969, 954857229, 633669005, 632810687, 323851727, 975415365, 557952150, 236875554, 695289681, 85815700, 755015496, 104495933, 213236634, 419316699, 13485388, 845596888, 567516284, 310923403, 648051350, 270906078, 483699176, 182105059, 926870319, 977929421, 687820416, 326314985, 778684507, 612934969, 669094285, 713526376, 628802776, 412628634, 206163534, 879103948, 241521449, 999059229, 864134234, 410009302, 527144020, 978731631, 584257290, 253839782, 878054376, 160162681, 110672071, 67501441, 729963668, 324548810, 931178128, 73009238, 185177916, 566735301, 469388393, 216170891, 499898984, 16659737, 302864383, 241213450, 586019827, 695345969, 352871813, 270872550, 830529628, 883594652, 8071336, 620623713, 454222133, 924961942, 899138695, 746539179, 816104327, 910705756, 272268341, 807217696, 789225456, 535614629, 118543606, 560220488, 97751466, 223126285, 245437752, 372463421, 195149546, 958279427, 554374693, 852693837, 38301053, 362974270, 762937518, 755048450, 506533217, 297703183, 478458553, 610310592, 707488254, 189429489, 567126074, 413728863, 746808523, 933911305, 851821249, 627305676, 81659804, 459389684, 515220725, 297190359, 287449015, 48332474, 828949730, 505890823, 137925807, 29768021, 58154392, 29017674, 938974335, 753678842, 600287690, 524139164, 395446950, 236570575, 116618804, 311859588, 509103731, 857188781, 470176628, 612779663, 717913467, 578317572, 789297877, 128211559, 590153674, 336615357, 320308821, 74827317, 614074075, 743832609, 473878210, 663729103, 822396086, 344593106, 741531617, 288198760, 813692555, 747337692, 504709005, 31847412, 428855454, 849950874, 64783974, 942385937, 636838180, 1574872, 807020811, 536406514, 265394772, 734209664, 719930418, 899606214, 413650070, 435855865, 283046233, 90409798, 900674533, 21162368, 357661192, 517684994, 971219203, 662357463, 759550247, 536771351, 909514354, 586416494, 316427570, 187760105, 786856264, 676485899, 115645665, 279635747, 875808711, 635101718, 761582564, 504773027, 16057153, 916799284, 299086528, 959807011, 566769707, 47379116, 125069163, 664431081, 192387380, 257184114, 57417609, 397190304, 238126319, 691845357, 245118952, 923568333, 486318442, 182004698, 417242419, 998178336, 24715744, 186475968, 690742390, 424500999, 725461857, 511540979, 130663369, 657400018, 912211962, 813796962, 232090602, 331335092, 702614264, 141713449, 542253619, 605994186, 231734120, 558638710, 458504546, 648622320, 330313489, 688662654, 909714270, 619343379, 846085928, 21566813, 162437841, 18005936, 380045006, 759688650, 428163526, 639771952, 809774702, 545691155, 207680708, 830138355, 353098286, 807189016, 463459941, 827407676, 53560098, 312635435, 812534474, 587205109, 171652060, 938202034, 108082352, 246050765, 432778045, 426800165, 649746772, 567704867, 583816070, 216104402, 145491677, 700784685, 444088375, 841555637, 447844796, 198067434, 308647404, 325393749, 207172120, 391769571, 513813238, 652559070, 258138574, 816692069, 48967198, 355075597, 981361724, 196056071, 466497303, 279747703, 223304666, 347912567, 605698106, 201971459, 758904529, 828915828, 360617646, 433312896, 539042217, 566055309, 419113712, 636728409, 384847966, 467153251, 893295059, 297665018, 77133095, 727197131, 559486765, 818970674, 987420210, 69054379, 656377561, 52992849, 618191383, 770739877, 384073030, 45873422, 537465748, 790875592, 703899633, 826571792, 357779237, 529919460, 561683375, 567670745, 293093635, 784968520, 766640302, 678894696, 112448649, 734214269, 573125370, 424817896, 26779144, 230387775, 853344002, 351757681, 463870821, 777738180, 369238270, 553344204, 345521891, 547219732, 163605657, 490820607, 521837327, 254840578, 481139520, 309687812, 619581558, 612783060, 164497024, 166479122, 843334651, 7786205, 889679294, 443277818, 110053979, 94616302, 841525426, 506842502, 26693980, 593929738, 176801029, 795387965, 609039871, 598938388, 819615912, 395923803, 122891590, 773692366, 68510379, 934372555, 124187341, 290090077, 410761153, 675870737, 969422356, 462566129, 456876343, 777562569, 895098231, 392593352, 708274061, 860040407, 413143766, 297160577, 113517020, 337320086, 454941647, 835978850, 899250221, 125395415, 294405493, 403012937, 481488662, 856619003, 320032630, 431923793, 950819806, 979781886, 448933096, 546594205, 496880805, 51603804, 132456702, 541460555, 527697504, 9287358, 465714624, 794846434, 838033483, 547210310, 327441637, 750702649, 478378682, 907959016, 652298423, 198384800, 62244703, 995422688, 785485425, 738524553, 216022717, 290401964, 997402683, 80587212, 362518552, 904670772, 989229945, 474100743, 483465766, 966276182, 215937906, 371973132, 596082029, 362098465, 627367186, 939480456, 326956147, 4680871, 653781108, 429414613, 876495132, 664367063, 142445251, 447828969, 137940093, 791063694, 732110269, 3983974, 613466443, 705619617, 831721918, 53065615, 540733668, 107486228, 249587740, 469145576, 851726147, 41351388, 261083319, 388530651, 942811028, 163782199, 24627239, 833979900, 565093394, 61866946, 47469512, 785630781, 94262967, 225469042, 136413914, 20130708, 583884374, 67121597, 170983869, 275174583, 220170473, 776594206, 778229957, 321312347, 787512472, 116867288, 693014419, 361004133, 209109336, 724584782, 168172015, 695127482, 696490267, 625051175, 883143896, 359586866, 166371345, 223542764, 404517035, 223233159, 385305601, 949178616, 165953868, 352807848, 460550153, 760221936, 107103398, 202022714, 415530183, 403521785, 850793670, 688532543, 739965199, 458650595, 597271313, 438327856, 231583355, 438139507, 196965801, 286052013, 930417034, 499906130, 112793091, 140747010, 260928069, 974583392, 270517041, 964846236, 452400973, 900763038, 262265300, 439551405, 964838637, 378517122, 456814762, 767844695, 590623431, 23190862, 373851464, 624192468, 660880594, 828202264, 750447459, 267684140, 272784390, 797367897, 734945427, 485107585, 642680330, 440965318, 271783660, 422684422, 178665398, 389949748, 423464198, 781719519, 785165368, 683914395, 661195650, 161046580, 673977291, 141380942, 723581271, 19146798, 325587390, 307038933, 156854039, 843235954, 682604030, 638222716, 291416937, 20445502, 724508734, 413919862, 585454138, 809512605, 775668940, 996907517, 873901558, 541210816, 145764319, 76932986, 766459950, 493176095, 583456640, 909491031, 387210253, 901236104, 136541142, 73909087, 113778609, 726630583, 899324930, 169473227, 638487715, 173174019, 384078132, 989088188, 796250111, 177370405, 505259248, 794875003, 381782126, 120607713, 165642557, 116062259, 449823093, 430470350, 39019753, 316047100, 367565742, 101625377, 261427306, 101022159, 613705449, 232261774, 933011802, 94056364, 794194559, 855220340, 176188725, 970297900, 191447384, 134938740, 241491553, 512338940, 937998808, 562579897, 252711220, 789571542, 493241828, 26581874, 819433225, 138846074, 955058380, 758475406, 363737889, 43160463, 436623617, 83590851, 39662076, 262689560, 414112382, 867738485, 871658789, 275160674, 876520384, 129191139, 575189095, 932050829, 824931805, 929804141, 312721737, 31359972, 244009154, 662313669, 741970949, 4107562, 411990619, 225602885, 671373505, 825258312, 264317515, 493842881, 797276192, 812063660, 377356943, 890827850, 658185554, 750763380, 271541234, 90419554, 129255963, 181327487, 822742538, 566059624, 179153876, 616383379, 155277285, 171695303, 626170159, 257526380, 804381786, 786966677, 525867349, 22416038, 72591391, 232933382, 538746188, 116163839, 919476524, 775405076, 478485097, 704428575, 168498200, 746862088, 852400441, 569788261, 170012013, 653253167, 437045691, 3858538, 165138434, 652731406, 160304866, 886456048, 550096532, 97852106, 830777593, 203808113, 893325642, 447167405, 304502951, 386680427, 944046112, 488662090, 104478507, 787064376, 646772278, 88250936, 310543439, 229786365, 312894892, 352104728, 657664665, 460324863, 116893741, 680472860, 345807401, 203805144, 366514840, 780537261, 250667913, 205878836, 169068516, 262876237, 400576206, 502160843, 565149223, 956448875, 592493159, 594115618, 206420426, 435391083, 361681615, 952373985, 156329727, 143233202, 993013231, 499533196, 943389567, 870999752, 969529675, 117491613, 352204689, 878271350, 771204213, 8353434, 911356899, 85715802, 663683360, 887894950, 394727512, 800019140, 141893275, 408086859, 139232390, 487802235, 415983626, 131316479, 886402177, 728713224, 20354535, 895804940, 688904596, 431135021, 394286153, 462588397, 348033870, 267638376, 528896348, 725611327, 128269411, 37836481, 65033054, 272745818, 907991437, 260180489, 346396164, 880178672, 654491944, 914095665, 863914513, 434352820, 64005561, 618792954, 435766583, 885833461, 477004812, 453292587, 894975528, 147620795, 4852050, 943358001, 945983534, 141154194, 949862436, 737436686, 938070149, 746698905, 787026143, 877979424, 874866942, 74580415, 853387266, 809886845, 276386019, 754847486, 107675987, 241767027, 931486396, 55710472, 772018346, 131136865, 145957688, 331821711, 896777933, 647715552, 371850821, 485877432, 656403331, 577892013, 797631213, 627669516, 176625310, 531840103, 873079137, 664704856, 830043302, 6637168, 492160628, 777884502, 666487525, 153245438, 974568109, 138502002, 920322138, 405737162, 946821293, 525858708, 729763584, 967309017, 12242636, 598986387, 779330324, 428623271, 731570798, 882060259, 24988430, 537754214, 390841451, 924176288, 381866496, 354867108, 390519748, 993156736, 815649552, 929622906, 595433601, 59019708, 689727411, 290671751, 501445851, 916849187, 341110277, 614392887, 487584466, 656704593, 133029290, 3185942, 165415952, 67549420, 958689989, 401110306, 296553932, 50572423, 733302700, 890689412, 709641334, 145787900, 555126443, 794704932, 776420538, 369485487, 343067666, 913389903, 262617584, 869947863, 701601694, 561247682, 295855685, 187179384, 169129667, 918257202, 173938485, 582328900, 558232327, 886890705, 518064364, 237137352, 846840130, 152005860, 696587284, 251804075, 41152631, 905124130, 868950514, 808277444, 335793952, 901231487, 348952374, 147413050, 397201373, 252127316, 886598578, 184245201, 977202879, 19453719, 416643776, 89848148, 76193238, 872870732, 993140359, 123734398, 462780703, 767314703, 921379568, 442856409, 312911219, 555522556, 726851442, 631550318, 654808586, 979876454, 770200372, 257425756, 954949422, 113155473, 822725720, 344273196, 966197350, 43891639, 749331995, 644552985, 823187917, 919308348, 222102946, 190872400, 414977550, 525359148, 504131085, 517127406, 653053363, 490350245, 39300538, 459453160, 162306282, 942695450, 300972269, 241060926, 897753173, 163174872, 832917708, 805048708, 598431628, 812884111, 103612596, 549036513, 597480390, 294298697, 543168726, 975457532, 584171930, 762073603, 473816153, 157659055, 581228973, 371362821, 770880757, 160996625, 165827250, 730335516, 115103741, 423199064, 311062703, 480258410, 478306659, 636313, 639549538, 165554193, 869987365, 117379611, 753569722, 838141573, 91698922, 410615338, 790310685, 860214992, 601245982, 147092720, 638085938, 65242550, 46675853, 692523299, 195232441, 838298821, 649550264, 349380070, 265342665, 84466785, 275363595, 550019824, 454239778, 520591760, 421390430, 532782075, 618655739, 800072610, 834419354, 444446874, 950859077, 945064365, 716618191, 934405483, 542445123, 934644085, 787078438, 457549546, 445884845, 368866163, 771670612, 670618650, 59013959, 708319593, 653500847, 135910089, 963089490, 530924152, 390251886, 784614193, 928316276, 248484324, 158199193, 294450252, 521307959, 360844996, 779286716, 561448531, 540581521, 779012451, 195423634, 874077252, 963929687, 245028454, 27765436, 798469973, 543280948, 906978567, 420448440, 947104284, 127770961, 603034459, 396090171, 332248854, 515053866, 655425144, 249850970, 739864592, 88879753, 816590707, 490986475, 541252129, 563661596, 839836917, 285528159, 348223539, 998538629, 233198022, 491063969, 637799609, 589558411, 680674128, 335362809, 340475087, 963434301, 548979341, 619254000, 823100247, 697578892, 515442208, 857816167, 456750833, 912283976, 313988946, 240571164, 995329484, 719547284, 549889689, 706033945, 344142237, 443633289, 557474315, 880472278, 159769475, 692589796, 245668976, 974728445, 498466059, 161947225, 53248796, 842138202, 10832984, 313500541, 846416091, 673723402, 779645365, 267496916, 494187244, 820772391, 72371917, 8111964, 664300052, 389475906, 814228287, 422322467, 641445881, 56347636, 593054093, 757966009, 669838897, 856417239, 551004365, 9099887, 921414077, 627625878, 907106233, 655138550, 397989503, 891297778, 544496302, 467310097, 241834645, 524890929, 98646144, 389840954, 41567707, 165084586, 311349553, 710255951, 743543504, 176887200, 426961552, 18937801, 21172231, 664041, 795098967, 414466045, 508269737, 422419522, 977935737, 566863615, 440208772, 803720171, 937336769, 240608061, 281794531, 397652545, 812827348, 916093060, 943272861, 649900028, 344135230, 490228263, 234359794, 873597204, 50702697, 171028300, 574142263, 609099807, 663852332, 849317134, 413548761, 34089269, 597901640, 238013406, 789020660, 893140415, 491177622, 106965272, 320814594, 473976977, 862556303, 555752985, 941539347, 386581301, 665545466, 20897595, 111757515, 347079190, 285779698, 553713394, 949988294, 283049958, 494351676, 79900758, 242273563, 15823756, 708096232, 877946145, 43792736, 651159962, 494175828, 476899271, 681095175, 184788913, 377186737, 86904466, 889731046, 866661627, 500019146, 656226898, 993868649, 436953140, 825670709, 870179667, 125038300, 797115724, 414390295, 902740499, 808868652, 364959006, 592571804, 135740789, 121003554, 431876085, 854814249, 660945310, 498213866, 38253722, 882539455, 877002025, 5429267, 456378668, 226931729, 7881145, 953023861, 56320033, 119018959, 346480433, 456171758, 195557412, 626832283, 947469594, 400623811, 790946476, 223348149, 989666335, 239224385, 705281004, 267503647, 225704902, 904354202, 960696227, 886056623, 933668817, 385139960, 415833113, 2577315, 331762985, 807839877, 676423217, 904756922, 132767936, 943841898, 474844528, 461425868, 913749127, 165432140, 674178916, 103620961, 934389537, 402997332, 207113878, 443144330, 940340048, 549781835, 147241707, 614886356, 751129063, 184987682, 105424496, 55157423, 14412902, 198592560, 55419784, 230242217, 121101715, 831972655, 944038684, 900389132, 300715502, 688256401, 170617884, 572475556, 827182575, 540212398, 18511565, 420924035, 670683212, 4308702, 883396050, 991225915, 378830505, 157326563, 242590218, 575319276, 484763803, 669438698, 707919382, 694537548, 91999849, 332073072, 776656788, 877713515, 938010425, 252967637, 282813426, 106142883, 270833553, 961053972, 257673498, 257686222, 346556192, 717181036, 761628620, 398718516, 176907676, 383120282, 179650588, 192171378, 500834526, 608571385, 693868873, 849297735, 812083113, 130148617, 38947478, 841119932, 659905846, 530077387, 405703041, 524375153, 352513890, 600925881, 356793591, 168775364, 996786875, 905734762, 656095453, 356733041, 136682761, 259988712, 228205150, 709165784, 195315295, 758966955, 471813265, 387410420, 731316928, 179750542, 290395779, 41965476, 857397352, 173959078, 990300547, 486043594, 427856556, 87212694, 651893889, 771615775, 381788871, 842964839, 514640160, 703643777, 254376000, 373677916, 788798294, 551171361, 529577309, 222651724, 311973933, 346016157, 620591412, 158535582, 212567179, 95274443, 713852611, 117916666, 269670121, 764021248, 650393072, 278927358, 350211185, 717489294, 933923171, 236331143, 435437132, 382450455, 111758015, 676799855, 209918025, 350948794, 221597173, 396586493, 590207239, 113587720, 432141379, 972210842, 222454892, 681149664, 938754857, 30005568, 276597511, 207420850, 180369159, 959042418, 440316485, 3559576, 480010683, 274122550, 840992584, 891029778, 583967672, 567669895, 437071517, 516560477, 595655590, 960501506, 978797675, 589378465, 840331120, 669871345, 383457659, 35402087, 696423034, 164210662, 800620570, 756994978, 651165323, 324311466, 674913507, 322119678, 222458805, 323327972, 567795506, 827318940, 381196288, 607962886, 685846305, 24105793, 413762740, 340152160, 283435278, 501616683, 412611749, 751737440, 237438153, 261163433, 598270932, 637432333, 519396791, 147768799, 174257866, 558115457, 60771452, 752708307, 104103351, 675802395, 598167219, 385996504, 406181638, 251260600, 887713643, 19636393, 129612498, 477782148, 641198205, 392537834, 432408885, 406957531, 6407805, 751133801, 710917037, 675994469, 366338750, 524228579, 688241215, 292724878, 392998519, 342200628, 947981589, 264433540, 390426557, 535893069, 747107971, 741286744, 194588187, 971674861, 568353258, 231516158, 137528207, 906094269, 310462660, 119485816, 777107785, 422675322, 434793057, 8646882, 68036754, 741575421, 360950733, 262812128, 395394810, 969359290, 280245110, 313001095, 148854286, 289049574, 546486821, 440867168, 510776609, 338964970, 38927087, 358095998, 73224208, 338998317, 742231001, 683351733, 509359827, 388932027, 967961010, 763649119, 659029904, 529084841, 212409051, 778279409, 194642597, 749828066, 121915448, 896048710, 337402972, 773486722, 420298851, 17366964, 907246888, 297636749, 84380442, 346235879, 591475543, 635235162, 525849984, 871393236, 28917836, 371445750, 796087116, 954186444, 842498521, 948621857, 600281458, 303764844, 292195395, 97283773, 361011476, 800771249, 869835845, 853278121, 721177283, 188090751, 260055543, 595819452, 888270838, 760108715, 617651931, 832345375, 624632363, 371621788, 88613008, 913393187, 815445460, 543698381, 18906198, 610962839, 319699397, 256383588, 257430675, 498893465, 24962987, 252454508, 686416429, 664471479, 838414207, 767484592, 780786326, 812331694, 345025704, 429812432, 936256706, 853208095, 505947049, 372271580, 828948489, 847479489, 550297291, 424954712, 91027176, 465264632, 711222345, 951845719, 353026823, 866615471, 652212196, 193066214, 686682905, 593908408, 532331578, 568429392, 659153115, 740649109, 887005134, 422071187, 933195086, 961743360, 195629212, 354995240, 366262674, 279950620, 943012038, 577812152, 796140915, 970376019, 986600690, 155528510, 412405594, 134875935, 679554297, 389857372, 170149993, 958666216, 752553377, 254909849, 893756220, 293916316, 31618937, 159165834, 541242445, 465571494, 100244552, 141340684, 592439214, 224079569, 418796915, 246406936, 26206893, 38868085, 702575107, 715803010, 972072382, 786573421, 393457458, 947379039, 688018388, 524099303, 647670211, 686023063, 397466627, 557110990, 95331735, 94171549, 352473686, 362706888, 770398051, 271291681, 957914903, 921050801, 16680653, 325074478, 776018591, 708281201, 450263233, 82111309, 827312832, 134530193, 127039289, 343308152, 396845354, 815076492, 265508219, 786063939, 295428734, 915580785, 981184460, 459348543, 919236948, 712746318, 775644290, 690128563, 153867336, 271696682, 739354613, 484253933, 571102078, 495271957, 530762977, 264593840, 682645606, 552738768, 755750301, 250777233, 7308977, 362330377, 126163424, 454989147, 206526392, 542007578, 545181299, 998747938, 981046424, 332018589, 619026985, 779651034, 17912617, 407765283, 836705236, 855398933, 2012012, 559014436, 685539814, 919300035, 955709891, 163561005, 957371882, 473138257, 267242573, 106918439, 921414691, 424761420, 634968692, 19734718, 936384880, 364269141, 366382235, 200907157, 46415995, 58792999, 240964580, 831525153, 373029418, 947134268, 316208901, 485741648, 188536544, 810348939, 216607529, 545902744, 906864646, 306799257, 893476594, 548939857, 339966070, 976406851, 212106501, 333733990, 996596441, 418469503, 480316869, 409341929, 717938682, 13691844, 407541917, 687816549, 941092097, 650567554, 777935488, 531528797, 439500838, 606425860, 915016226, 907706899, 723549328, 956384427, 238704627, 261559451, 238422576, 660396111, 672549006, 297299453, 390420361, 490688912, 964675672, 135572625, 204878656, 521712859, 942642024, 809860513, 664970603, 574250594, 250947271, 256237784, 522715923, 167800349, 167610386, 782268481, 92488216, 418440469, 896582827, 270775734, 193431736, 943635544, 103210956, 202292640, 405378202, 691344155, 339508664, 63665291, 800833676, 977639759, 342057169, 704222532, 978965264, 531973742, 760329956, 923830106, 231084609, 859954536, 800303729, 525542703, 280278975, 90728540, 668987182, 343074332, 932288594, 95660872, 972291101, 9363814, 260248502, 492730588, 418406802, 827787733, 614850876, 651071936, 2161542, 203724255, 279626733, 474081433, 610604048, 768044019, 941214284, 407892798, 293480057, 63184473, 652581649, 447868689, 981829362, 173583396, 450033097, 247563713, 346346967, 34348881, 557522049, 531516779, 718012203, 787085339, 291516414, 842754307, 250267466, 111958210, 244624089, 235062965, 911632170, 48942079, 695821645, 840263677, 523916, 787280327, 373974049, 840761911, 248852038, 773720777, 938937147, 170659418, 124169349, 228735081, 927906952, 668783259, 565579682, 320313603, 814790802, 478675496, 141172445, 699780075, 117509835, 772165267, 795227351, 259594952, 668576594, 963089990, 970625244, 590593822, 91099166, 418629077, 761070511, 270644219, 797595969, 543562138, 851316563, 97450574, 314635750, 38781146, 305188954, 267931321, 55572539, 57833759, 904320272, 882563370, 717064409, 892712771, 100873648, 350431852, 655534295, 998280522, 480441297, 515604087, 458653346, 943898386, 933249621, 884401585, 467552984, 913732387, 770422935, 754257886, 453285456, 600023737, 594161874, 314111355, 494725017, 907490995, 104859868, 828060618, 404901587, 115958193, 856593060, 534180006, 986482265, 978605179, 821585110, 420231487, 518060826, 130872856, 895618899, 343204416, 54210936, 947579734, 200857749, 924491269, 730945259, 77218234, 551226504, 654392589, 607118437, 176124610, 263201836, 688410200, 692973101, 207806996, 773423137, 541576635, 890640665, 350632610, 124986504, 72665482, 87109267, 988620334, 250703641, 433025453, 737711446, 946658091, 788370827, 161048123, 385803, 544650212, 432899911, 772798479, 24679177, 665066620, 325461997, 490290749, 344548281, 319794612, 425292390, 660046904, 131086844, 934023653, 233138029, 148519036, 798023895, 640366765, 375569647, 816172363, 820041727, 574812189, 400410907, 311244084, 396767581, 748582059, 731682632, 924554307, 310546511, 975896415, 40014514, 842492282, 329896754, 791138109, 461553675, 792000806, 191300200, 914265437, 90184537, 493297442, 121555117, 793639361, 967528, 968147765, 13640345, 670822757, 494524929, 392923640, 131249796, 78147267, 940475375, 60302118, 232654487, 733632071, 461282967, 720742489, 742388973, 63092760, 412257714, 937252826, 447296984, 32512331, 245068223, 483875249, 470465533, 369505893, 126404120, 507260888, 491419874, 182158201, 80809926, 629417672, 138634556, 660626554, 306424574, 65429535, 870457335, 18284113, 749140516, 328269169, 596375806, 132563068, 324204588, 618763293, 812099143, 452522115, 165861586, 50738151, 867477873, 675621074, 138819083, 988441591, 494391399, 49630456, 963672758, 995253169, 582552674, 332842841, 309099101, 301232441, 302980265, 637137185, 899910926, 192176198, 407378729, 794800254, 87321978, 360940302, 15392262, 525574731, 300873446, 178647593, 571166336, 846875397, 968381304, 605426952, 812433696, 711964135, 821689529, 578540988, 868560788, 167609894, 492361693, 551639799, 741436324, 219803813, 154619570, 957895289, 371021958, 223618095, 766595750, 463638925, 99622848, 197504963, 462599349, 332891010, 545613906, 314899578, 446476505, 354136328, 611499715, 850781025, 270337910, 121198500, 393927343, 536454091, 350472080, 637073479, 285557764, 664595456, 7621385, 42801229, 778656380, 481492752, 953764544, 765118627, 463274143, 326923226, 612337497, 428881242, 849445566, 777683539, 608510701, 279206323, 868272049, 763570694, 527598991, 459122750, 324169861, 184923292, 907923376, 584698121, 503089721, 956589730, 708051730, 145964486, 696073252, 860288338, 886315197, 269691462, 146950204, 634240171, 231984387, 320482981, 50785729, 571433305, 27085455, 188104481, 791495130, 114083689, 653286249, 453359397, 499203484, 974985240, 561801110, 326664907, 92864088, 929990735, 303494541, 322031107, 580182067, 758619990, 481896894, 21253361, 647416880, 447760887, 824660894, 174842485, 51145207, 916210028, 420733548, 828475967, 761503960, 732842900, 62826814, 75343140, 62130133, 387174794, 873542702, 362926445, 488099424, 393061389, 992746337, 150866000, 37688879, 930930261, 673886157, 42988109, 47288025, 681328469, 721778997, 648646832, 445609568, 298167402, 162706846, 937210603, 817588774, 87332767, 657328699, 769100139, 652969842, 840695194, 177062977, 293614308, 832509216, 511687468, 652906706, 574621035, 963275788, 669682538, 688859097, 203100858, 494246536, 149083594, 372733628, 676554999, 156472999, 884061656, 178687583, 954313673, 908530868, 36719719, 273439449, 869857069, 615272733, 676094198, 337817305, 543764578, 704647691, 693058071, 869033108, 998352284, 754151440, 476505832, 600159382, 735771058, 224816267, 500044696, 209303538, 288886703, 389233703, 301111458, 11376371, 152273178, 285631629, 675424703, 338784745, 764146114, 966442454, 425158298, 90271584, 832889173, 878543227, 293049449, 368179168, 331778467, 451978959, 971182799, 80880236, 27861765, 540710220, 343886797, 869875980, 251873738, 726399856, 29096587, 433415456, 570425363, 111329536, 489045559, 646203514, 938605746, 345428097, 220773865, 619207702, 720584783, 774616654, 352086212, 431922115, 975155414, 869171959, 251284012, 227202976, 746633978, 866503060, 546012490, 882206229, 821593438, 435899314, 512314616, 235515708, 809740857, 568524743, 311171894, 603393134, 183826842, 480001415, 295252298, 749699297, 277679331, 386484056, 659976492, 889398925, 181860305, 332829263, 649023081, 147551140, 75856517, 534616687, 765647632, 397571172, 51259157, 554281667, 744816155, 439408190, 836935267, 863063935, 457265306, 732224255, 460585570, 75805974, 485871692, 166945546, 670540068, 830848661, 866801956, 810053727, 626092604, 523909283, 321538676, 313222540, 180721293, 73668590, 417806558, 841596493, 42690659, 523695720, 988256436, 741212802, 473741865, 754478473, 869453393, 578937366, 806630433, 899108388, 147173396, 952123936, 980264036, 981660883, 475874840, 192822654, 845841750, 312439100, 815303100, 616443613, 598421448, 519697235, 360461817, 618229419, 202752478, 322849636, 659093699, 114413144, 306763270, 595159877, 724635725, 39033228, 394489772, 501652280, 782108971, 360392083, 611792665, 296862962, 435186208, 28507941, 561613794, 588684322, 955746536, 318132215, 696404555, 324887853, 181595877, 43863161, 760865738, 609214995, 151840005, 789715542, 489262085, 774329787, 414118254, 477581050, 884949223, 431404837, 229935063, 999220110, 406743389, 692393829, 768838040, 820200307, 548171912, 281982809, 779777365, 610531036, 946834888, 845798042, 322606661, 421520780, 9642447, 389824514, 481355543, 811073478, 757870595, 89820025, 872861984, 914813717, 593116482, 867886593, 498132459, 904699014, 470085923, 780080554, 279337586, 742816018, 834764500, 824350196, 744762637, 890261642, 568327107, 719425049, 696890168, 649097516, 728803324, 346102063, 523905246, 179859650, 255022810, 577803469, 770531406, 877958477, 524329222, 429528933, 67484630, 622022312, 506026788, 234622967, 381468551, 620750713, 656206026, 139432269, 862351568, 150076282, 497660493, 196848579, 869795737, 472965136, 793979132, 867315746, 88923173, 602800784, 309996711, 166704737, 303933533, 738855807, 850966192, 357884965, 284623957, 378782479, 964925317, 138902893, 344821927, 652841416, 479928526, 889613687, 161957640, 382811762, 664875518, 579317476, 548923974, 418834162, 44488850, 498624450, 424993620, 452634809, 647103815, 27527249, 563937778, 493763424, 986505017, 742930769, 134659767, 758337693, 752037360, 757086423, 532192554, 218485458, 315029439, 597731969, 78276550, 727068843, 320727167, 605655193, 899396023, 274198600, 950140646, 671130930, 947838631, 782909566, 957142846, 448602475, 563243241, 850983529, 202637325, 165091258, 542318468, 409148343, 43403686, 520397037, 200781040, 361719776, 292034747, 183203787, 272494049, 794042388, 290477233, 75921072, 630367392, 995612544, 274134804, 233824650, 528924608, 537730227, 106623264, 734162644, 958999204, 576364787, 230026859, 45203679, 974491292, 238540010, 786045521, 468599149, 908529944, 491088330, 331845091, 503686543, 731546565, 408527531, 143927879, 769575161, 429537176, 757470520, 1010224, 152831808, 239172893, 703142690, 272787652, 130213835, 913107461, 277542009, 36123585, 23728183, 457428719, 327145472, 982821805, 21607659, 175550195, 131453163, 925679298, 982467618, 523177435, 58100494, 267448559, 365650405, 562904711, 270883808, 93202984, 290587375, 352358048, 686837982, 453628341, 88294622, 698635727, 813784243, 7129643, 329286280, 854237347, 433984236, 19118431, 782088755, 260302686, 675255799, 824971299, 242613925, 161163495, 425477827, 853853247, 872770906, 744335429, 258352733, 423804918, 890737164, 800974619, 64925163, 616266298, 15392005, 959640844, 476004972, 225906349, 754614249, 91615334, 296049731, 681283374, 961347433, 911829710, 806844122, 794924088, 556876247, 235094637, 740946143, 325871499, 92643126, 153348995, 852433161, 298226916, 812823193, 560624427, 54275586, 402388875, 427274796, 766077993, 95042708, 15712285, 909660186, 291831437, 855554762, 624981637, 445782705, 8229232, 680119894, 531878291, 53404224, 409622556, 982205735, 29881448, 183166292, 322200500, 276147948, 859528382, 871660619, 396420943, 404981908, 150214753, 549685691, 288754812, 981408876, 522168155, 129182686, 513814431, 671034534, 402238865, 909874374, 984163778, 357922495, 720799274, 279356165, 932258409, 359111996, 68448958, 131255478, 835138378, 459805522, 890441004, 496590349, 340063241, 885650238, 106066987, 934686950, 76225360, 964174787, 244755631, 593617531, 106903910, 960646331, 948956872, 844207844, 270212531, 363528436, 434677731, 175012223, 261169919, 546581509, 125775689, 940406400, 364128717, 892887811, 277730427, 823375194, 266596358, 154165735, 437405697, 210271257, 13439872, 122967316, 246413586, 229107079, 673768725, 713064946, 157407552, 985986465, 227945336, 517958565, 549809985, 110306889, 175040107, 587770060, 871301626, 565736197, 997993940, 505960600, 8322877, 660720287, 76473241, 473399335, 327034429, 970436352, 781121394, 370826276, 822351749, 793868438, 20736964, 388219037, 589651963, 751115566, 918391023, 677040608, 738162366, 355123089, 189261562, 256141040, 86714791, 580445176, 198986197, 654403696, 147522133, 135841294, 988447726, 13004289, 783307437, 38524867, 265672919, 230533665, 37001741, 381927559, 76641101, 371312362, 447816143, 213992725, 339901541, 293833495, 197123714, 856072765, 61816229, 622906624, 759999377, 383679473, 339441815, 450681854, 882774273, 180723030, 466133516, 947210789, 189878014, 410944461, 250629162, 602388900, 388729476, 997486311, 725990407, 178952712, 951735941, 385476714, 950237780, 115792389, 265759865, 278134734, 742108527, 653911240, 910681677, 924423241, 36145496, 108647218, 662997449, 706256835, 225468464, 175605759, 639152229, 23261771, 352784050, 983547550, 211433416, 512367118, 972726705, 260257889, 503164518, 874018616, 552721191, 90061946, 743809434, 2206983, 909207307, 530841063, 436555165, 791083498, 590233654, 230260477, 321301962, 588451882, 381708201, 897425218, 530593879, 802172334, 209307413, 758313375, 746198625, 509922609, 64337542, 782240050, 787597149, 524190305, 34149630, 91369013, 391703948, 174117120, 238300247, 651359936, 152575168, 176792592, 829277795, 710288904, 680211359, 482624926, 744630188, 662978749, 898326508, 761233412, 123810696, 334847455, 739263159, 45049902, 379227416, 40852929, 20138905, 222887123, 415949169, 139820528, 215690760, 765438467, 471754698, 923981604, 627678699, 405579027, 172674582, 439721696, 38366911, 187928743, 79633320, 881557798, 470215622, 318941313, 432005221, 806135915, 588715986, 129692921, 196146786, 197834026, 875511873, 482507874, 439178243, 834184598, 301659459, 75622670, 10941795, 181063194, 546177604, 32761076, 886448606, 234975353, 942695584, 905880855, 698758086, 869376049, 962982989, 390273311, 177771742, 489540470, 520185345, 557843764, 391261631, 430273183, 451732070, 966857210, 956549041, 525361291, 958538583, 926392117, 480717746, 951605764, 504807241, 559713052, 251302415, 538197868, 885347040, 372310247, 314939492, 483173159, 954582889, 669910968, 581133397, 824484770, 315198716, 232222891, 327894960, 244977875, 703699560, 294970160, 424639412, 47648262, 50425911, 226988404, 976624257, 172320018, 103634048, 858101462, 335640352, 450850117, 124220661, 857118216, 285645427, 78098820, 485196259, 513904880, 688978903, 932370335, 254315065, 292869978, 894947601, 851622285, 666099410, 306610174, 57864078, 371268174, 232245340, 672369352, 710077251, 350654846, 892043865, 791649496, 997248683, 131779293, 828202903, 34337618, 685991091, 438731550, 356856326, 600338625, 471106180, 538609403, 332580194, 779429951, 719613255, 342639016, 169816715, 252734927, 526383261, 782976626, 388010105, 285704980, 788387429, 927772249, 595009267, 616200176, 327684596, 52453541, 518983998, 134165484, 201059014, 688881505, 48330726, 694021170, 711897038, 689061349, 109751409, 779656755, 932378564, 156851409, 709981413, 846554653, 848129885, 404982993, 557559634, 97824185, 166682963, 566472021, 61819734, 256923794, 655752448, 232229315, 758116025, 132493636, 53243856, 860902093, 704293461, 677797832, 952010415, 503324990, 458724705, 904372743, 513507647, 121428853, 920741584, 571238420, 94662740, 777962302, 819076390, 466884455, 392787437, 521579862, 863789793, 70409835, 448000931, 64040048, 587581497, 225606101, 510699215, 605809129, 545289298, 173293602, 442083273, 361929406, 819728750, 504977534, 591151833, 316781130, 216762883, 57668125, 51662817, 955349686, 840010036, 313859784, 857493208, 596415959, 652050892, 182032721, 41074490, 589613, 306432096, 764144449, 683519807, 533785339, 612620019, 158687375, 336170680, 983374093, 62980539, 189087913, 923963864, 124026729, 490535719, 435928335, 342388007, 202781856, 130416735, 139839865, 386981570, 337145132, 336077203, 498640914, 160927075, 746249259, 959654490, 428717407, 228522308, 693729158, 139396682, 822062512, 939288901, 308002411, 356929085, 201152662, 732158970, 790074515, 418748241, 756036426, 750209497, 337550768, 376036418, 833574935, 578666948, 736594106, 884487529, 499985370, 304541974, 898175314, 844824095, 215021840, 730683079, 472853989, 741029156, 123218874, 719777190, 648540766, 976890485, 44782090, 971405435, 354852399, 750523469, 321917430, 691063366, 695815563, 799262505, 5457735, 398136472, 14209102, 333846407, 123413665, 437863054, 897301457, 556921789, 448301928, 694457355, 445819181, 262451390, 56671432, 918003904, 222551927, 612112949, 7875771, 958167651, 36095340, 561887354, 438922619, 739222732, 305984398, 954727772, 570079293, 173899264, 555023102, 398251838, 797292676, 67569042, 27416441, 997549076, 284451128, 711700916, 643672932, 160509604, 652072196, 875417229, 876821388, 613389565, 60145344, 99877434, 843877122, 385843235, 274710825, 976931313, 110006068, 417897001, 897742487, 303579656, 690132098, 752074240, 878564302, 440520771, 595628229, 257083020, 765422360, 172366253, 26575655, 879506765, 346333674, 681887937, 707610719, 518876603, 86462177, 989758004, 454215737, 934749844, 864344418, 510517718, 64895377, 528169751, 68541125, 290765778, 46515829, 671081243, 67434462, 187566310, 421014114, 737658889, 706784972, 948418672, 579843039, 825471341, 414429904, 199803038, 966262169, 457322664, 158176496, 496771062, 487444901, 707589007, 418393626, 631902040, 196956838, 883864822, 708819216, 226146531, 155052861, 961466967, 378977282, 217959848, 197541503, 732186861, 201895477, 369765039, 445023736, 966383673, 984114978, 892269577, 513460798, 535918831, 753778757, 817878532, 908640122, 677598418, 251497609, 474007369, 328755722, 923146232, 400803115, 796280730, 229226198, 445083813, 307304274, 862291891, 558645081, 123919291, 370847775, 899632832, 84059127, 368878519, 822634718, 177060034, 822253619, 683001874, 556551763, 775431604, 684032157, 463231853, 34983190, 434661704, 674884863, 620652815, 906111177, 836544335, 883241882, 856918847, 962397209, 42652550, 306097740, 86222756, 149421526, 941348742, 995795093, 498603825, 597017484, 424777161, 829862847, 824661211, 619776486, 806541261, 812872621, 878571192, 725707268, 405806858, 10988068, 283547617, 974311693, 647427709, 199105439, 414698439, 390392060, 995790647, 931770406, 984754714, 886473087, 16415837, 903877807, 129974024, 978737533, 912306100, 571944909, 221028868, 998054110, 298311766, 37751022, 453781114, 259987093, 496011654, 585753711, 326844853, 441628813, 458756110, 530804732, 59769732, 69661954, 96789233, 494499523, 623315328, 906614730, 875963133, 357729413, 907970710, 877509234, 65665021, 768883780, 129238816, 62310143, 310418087, 832878354, 13986471, 508205341, 27199986, 679937108, 42237977, 507531262, 754788256, 390028527, 871970165, 291790567, 189807007, 750418647, 5094485, 119080746, 84143913, 333037616, 891862046, 878850075, 533310487, 760877097, 815984221, 755128570, 208624292, 630241410, 798235084, 348476599, 54933500, 451759777, 223147432, 352618855, 956848565, 310166316, 445376782, 539002233, 699328976, 435329481, 610893988, 396618962, 39783610, 349606217, 205520718, 297938195, 305079603, 189096614, 318350867, 490553921, 473118028, 813931337, 59067119, 7259296, 182737080, 322656920, 833549679, 38521704, 125715907, 124685417, 277302421, 941939734, 149224600, 572595320, 35506625, 418943378, 804289485, 532147451, 548386077, 747240344, 764818565, 988851710, 789046772, 278673843, 251261404, 683156183, 453053926, 25367742, 593736815, 493236468, 48139918, 212804220, 75603317, 569838342, 71624150, 4681588, 59403229, 165063888, 526933620, 395484377, 219093852, 323714933, 690123080, 678840358, 781172844, 457761823, 307921224, 383781126, 875213217, 779963718, 454304319, 687874454, 600660679, 629272118, 605864657, 830044030, 46044033, 342734184, 375606299, 746341816, 1452416, 423360452, 161995549, 497337203, 939044308, 758195136, 610921650, 410731791, 822649529, 671980011, 967566229, 935705241, 454523832, 945144694, 167804993, 820706856, 522625625, 415781390, 687548324, 401947290, 790430236, 146638973, 558452093, 52356955, 808454338, 651368558, 996194511, 478196911, 790021523, 15026293, 696007557, 792874512, 583446859, 831074797, 398764143, 584418952, 534856137, 862584436, 77432820, 938419847, 923486673, 210347424, 441696983, 126158373, 219842989, 792153929, 433951894, 835630247, 803906223, 7848678, 769751437, 617484841, 835553096, 746731109, 548962570, 633735409, 205286390, 810377052, 316930174, 623948040, 685936805, 577768706, 696731173, 382107839, 582353923, 857267845, 945507836, 565674420, 173422214, 255064938, 497656183, 723416594, 119480434, 838062804, 493317985, 756140136, 958572076, 915325577, 428828626, 174421878, 129253523, 171355974, 495845696, 202117645, 250207452, 107323923, 144030321, 549116539, 710200175, 857374784, 217914079, 334041458, 473437709, 881247005, 56603472, 445729930, 164634178, 51167057, 967472422, 818338859, 72508483, 480616218, 451036382, 223915606, 850590541, 338068843, 752533129, 632455334, 878935606, 911781066, 19640771, 830781701, 960971459, 828867426, 124822483, 904533296, 438334787, 324570133, 676327037, 273873515, 148630483, 436118823, 886580560, 38367424, 631824933, 221795015, 834799235, 812140123, 687487611, 343807820, 817262804, 985015780, 257488062, 437545286, 192170327, 658676510, 912249404, 126261325, 924489756, 142936799, 642785502, 731549175, 453228762, 824184951, 365160788, 907778231, 625368757, 696011841, 683348629, 707129448, 851551012, 467017185, 405776738, 905752178, 358774062, 969490479, 453049261, 99049227, 48076372, 150947179, 704815957, 382591199, 526687612, 308595211, 583839429, 483347380, 383570046, 475886489, 10936687, 383613632, 298349919, 894506055, 830230224, 591616766, 305445075, 217862743, 795327751, 130689906, 263026604, 269556379, 408795761, 479535070, 409342698, 980479558, 441010111, 603274154, 155035456, 987263300, 126417353, 519044424, 514386726, 726106592, 985977426, 110671834, 198733474, 386472057, 116979964, 865666220, 907926009, 340051071, 886253756, 863206046, 348695536, 600366476, 122894705, 319577193, 738203583, 30133221, 441688887, 702176898, 615645985, 426193287, 937432730, 941603061, 237664632, 443736664, 90153215, 286180311, 396118743, 531786574, 55573973, 511411227, 981939126, 807449038, 601839139, 251216295, 165397952, 477789654, 872856334, 492978811, 454377115, 758045205, 143921218, 605353412, 243517637, 940823085, 911229346, 195784767, 461718623, 754217117, 522577340, 626812968, 790823920, 385786435, 741493696, 208349139, 905009919, 897406319, 243070732, 303294464, 697799566, 547686513, 434355919, 191073480, 843666311, 29296765, 935810204, 172503029, 329734403, 79213554, 907252149, 834119914, 791934909, 858080022, 876650447, 807574758, 13327925, 910102910, 676422027, 476811349, 718125560, 751198198, 613059518, 29515154, 205820400, 27762768, 116226176, 183712076, 67200343, 348054275, 813869408, 740624188, 883110375, 554380165, 133429613, 477549560, 742411868, 896394296, 699958564, 972078664, 503491690, 598335849, 391761050, 436991192, 495458754, 321352372, 42627100, 133505032, 380462001, 879713347, 371964873, 837119552, 15176775, 687583819, 944870187, 850540095, 785223186, 302187685, 436255343, 785405704, 638461737, 680297740, 741302080, 116901800, 640482223, 127803239, 826477900, 167496195, 84567485, 829597700, 430789605, 911918624, 863910277, 661137918, 491899789, 882496984, 572328259, 77037140, 360228320, 302737969, 613302043, 19525730, 741894934, 678349286, 52180962, 816420194, 471206783, 16869714, 916613330, 585172548, 521287965, 53720496, 123964618, 495458281, 284054296, 597083427, 712036030, 685379543, 115068389, 36230227, 173650951, 548382934, 978784666, 920138764, 848450824, 903460797, 301491961, 81820704, 530767890, 578473583, 964381317, 61491195, 647886579, 976235008, 722816889, 278129627, 521602752, 646352387, 225714495, 989726800, 229663186, 628134373, 661084289, 118433937, 92655855, 332229065, 936405216, 938784099, 546523733, 123194735, 691984015, 366442942, 503646972, 785833818, 175205532, 172533167, 875698382, 683822576, 116093419, 715792434, 541893525, 188874462, 172307914, 124385453, 795495724, 235368800, 637794632, 763664932, 381232223, 737537248, 40112748, 936120306, 246904073, 657919833, 424663576, 556257433, 555251562, 735821764, 889561668, 854959140, 629292121, 286047062, 191792102, 541569492, 667572079, 548793788, 243223033, 28986767, 504182884, 312750300, 644650994, 851847591, 884678218, 944603517, 460111822, 772680397, 281383689, 29707575, 116095675, 172898568, 196163262, 957710724, 789850682, 236462792, 236951668, 875128598, 914205455, 897763278, 480085065, 729819034, 822804301, 246451381, 18501222, 968112243, 5418026, 432749603, 671626706, 126626254, 421552854, 623272211, 329274964, 711804176, 78096972, 966300689, 918607217, 46579561, 376934170, 44700898, 410418702, 696783706, 152626309, 798802388, 423455430, 130808820, 149263658, 336612649, 40606739, 707694324, 516135566, 740181344, 954083174, 50615366, 15309351, 775759152, 607819341, 8780105, 656967259, 804248153, 167320514, 658296455, 676014369, 527888602, 901471589, 210286343, 420335160, 258105315, 321358982, 275056009, 116985358, 861798776, 685195679, 827276117, 427004444, 276968072, 25535313, 861537391, 89380291, 506936892, 867523133, 999384313, 280117829, 407554766, 857683033, 368534545, 573911418, 789252911, 149358812, 854425567, 424194331, 286965382, 782286659, 462698385, 503648498, 234457846, 367294345, 506909628, 355936164, 964502334, 987528010, 412610658, 852976964, 988803132, 628913675, 793904699, 337897768, 744090408, 579348161, 626822470, 162862964, 288930339, 326756721, 229725280, 798593888, 445696194, 724830522, 664785536, 352175478, 105620689, 922078395, 188005909, 251156903, 921178987, 571139312, 601287176, 573019432, 29665390, 977137503, 767876769, 978508419, 958978156, 956738786, 14712311, 96398589, 919539994, 659071864, 791905817, 699106695, 284908235, 252476643, 599088837, 42288612, 464208004, 106672708, 762401389, 504439853, 696198538, 383036799, 531959563, 251104312, 618697240, 583860507, 557620972, 26190421, 794724879, 578029050, 521714490, 175405406, 620585280, 124771788, 181761954, 363389375, 902549741, 226313181, 753239994, 597599330, 917577945, 736942063, 888726555, 765490291, 213920377, 803836939, 388365, 96993819, 980971581, 258795003, 319412452, 292984871, 556039704, 941223022, 803122893, 863956252, 306435744, 353472835, 713963349, 58849828, 205597070, 475549692, 246163671, 901543563, 937227241, 150978135, 426287782, 935570669, 698381489, 32203628, 181816754, 812713167, 552831622, 696068408, 277668437, 488792, 10161551, 172411936, 605720227, 113387484, 227015935, 651540150, 212742457, 509906474, 101009653, 107091772, 321239181, 556761458, 877497146, 386045044, 265773967, 610711772, 761855302, 206655696, 155743474, 364393821, 309919422, 646628250, 786069163, 442639608, 95880833, 124196174, 312928128, 998024407, 530503919, 206669083, 358237276, 508956748, 52668565, 338727594, 844072842, 56639387, 296267482, 328543373, 301014305, 420512611, 644462926, 744161217, 192109383, 435963277, 302114186, 373593866, 185977253, 249647707, 717825647, 166140265, 278947427, 447493582, 144350786, 135714416, 438733520, 734025812, 512000189, 87665500, 858111568, 590384829, 106114519, 161162560, 503873038, 900937039, 492860730, 567217091, 3401256, 74739068, 878685795, 456340254, 867250934, 426260372, 82493442, 897704421, 881902392, 192475025, 586279053, 108330209, 160997224, 75270497, 548687858, 145142501, 414506910, 904897190, 831387820, 69945783, 76473513, 250906919, 676714948, 750859966, 869296623, 13606765, 947811734, 761766076, 587949289, 411763527, 55797296, 800101098, 589234611, 598640332, 739169865, 704244036, 539506657, 411152970, 89008120, 487223325, 879799696, 119294707, 232886398, 607729537, 808724591, 87567690, 96998222, 898680311, 750221255, 937598641, 8030589, 691530799, 130496876, 830555643, 33785600, 900815477, 757622976, 814153075, 858003944, 445039794, 840707761, 291249930, 850201094, 752955108, 398105796, 78455495, 235493606, 886840029, 912092749, 79501953, 217956067, 718145712, 475206601, 913553077, 773178317, 729974365, 120332994, 249160368, 102117078, 107168152, 773060694, 14553320, 743727303, 745913758, 619909507, 989382911, 435237145, 519757585, 401331240, 381944812, 998830295, 41510774, 507404770, 266794719, 254847124, 357954843, 988194002, 760127419, 716447271, 422470923, 165001158, 89648909, 847738309, 784929962, 920916123, 345349515, 81681586, 269272142, 712772726, 890173641, 691459382, 412764521, 711744000, 234250636, 21452022, 193796914, 73194176, 932440095, 569098844, 572966664, 569926812, 538328595, 355176975, 83300874, 611098791, 496641651, 151882898, 615459395, 986989753, 762378282, 742504216, 963645612, 433437393, 405116893, 714125989, 707883404, 389584585, 827825285, 373397839, 9194607, 51826113, 754105813, 435946882, 610712748, 194203867, 986156156, 740905789, 69385591, 872282588, 491272271, 728795800, 767304798, 565113823, 619130905, 276560487, 530855623, 225316371, 754033821, 307188413, 432461135, 412586366, 545495581, 50045096, 800519526, 17149848, 412293652, 94746565, 404001791, 386465853, 284604398, 790224284, 110766759, 344104860, 401879147, 310084091, 288902792, 273093995, 253764775, 928438832, 552829705, 647575807, 20342647, 462883399, 284652575, 130278255, 963258214, 818751797, 829018355, 194950168, 72106757, 177826319, 297432055, 766386511, 124919354, 227027882, 345709335, 900710855, 853008724, 275046040, 677769531, 114494834, 96607286, 786535062, 144108635, 525436995, 319795977, 301138244, 648863233, 129870412, 79076638, 934484216, 722094275, 117456799, 297161540, 638257005, 130282271, 379073287, 926607975, 333946154, 293454395, 776768099, 645983340, 216504075, 363990203, 700710683, 406739092, 594951602, 803677594, 666143470, 876971700, 683731188, 159269499, 314983600, 574744351, 851061309, 324825816, 10141630, 213009970, 795558801, 768733907, 252828124, 54158000, 290331139, 267265818, 848388138, 596940076, 921983848, 782425577, 566840327, 310937912, 739238421, 571706132, 899935228, 255659938, 444773944, 574047617, 926164504, 947127174, 485969761, 546259401, 981525447, 602770829, 263766033, 685101958, 590119432, 479845615, 868632805, 700314854, 562278694, 116086632, 472949537, 36232951, 335003569, 748449831, 501707241, 703430052, 534799300, 885645917, 394197645, 850655290, 464055711, 625425377, 31768780, 371345297, 930815167, 886748736, 529155059, 410785132, 900475125, 54101512, 194510527, 683627750, 445160777, 344809857, 426768082, 413679465, 361007662, 642830528, 978630129, 555330800, 936192185, 368395130, 818580403, 324739915, 477948912, 158815252, 516508357, 871496617, 612933491, 695441367, 318724367, 316820379, 140648235, 462006931, 718454535, 149781250, 842462691, 517112894, 540281660, 535758228, 95585000, 106373956, 467627690, 522138579, 58435303, 511608030, 231382232, 816419057, 937260022, 930448997, 152397751, 920510256, 945339785, 315488745, 152147433, 727832012, 503018377, 906214536, 644308956, 125528584, 230498502, 768377050, 245600627, 942130686, 971552822, 446830460, 198844341, 15127533, 29324363, 812901042, 737068128, 849722839, 37986067, 420093764, 249329660, 289388244, 560732859, 500585835, 460318126, 632445880, 737917490, 148598705, 796590174, 170072294, 931708888, 696103584, 633699742, 791935784, 746770431, 871453977, 78776725, 663511421, 569402422, 148787847, 658809574, 105934542, 358625575, 93908418, 400258540, 173839461, 26942941, 246983823, 887848506, 603019791, 999252429, 396408898, 344554858, 888870234, 131103512, 763883773, 838703880, 308841150, 75999829, 136189231, 33189363, 249070698, 416502424, 911402215, 469164548, 951239739, 262185175, 113172479, 823678159, 179262719, 116689099, 972949860, 781165275, 953618479, 9475737, 704320228, 34236075, 1940908, 844061593, 945303198, 206455390, 385055034, 982626009, 793965997, 123948534, 729400376, 306267240, 294286132, 821163675, 911054071, 517493625, 870052474, 789619984, 219676383, 660302797, 12251700, 217501732, 1845292, 453446438, 79712951, 660866921, 988553632, 430249315, 521606690, 722852804, 851685468, 590362477, 976855519, 813982496, 184646981, 110151052, 949119889, 342820095, 123847182, 168680411, 196661757, 659885117, 709240287, 136237260, 365956021, 586384167, 552641263, 898661415, 720143846, 641209295, 418883068, 731469043, 549814219, 59739059, 947352625, 777840114, 426880210, 603078665, 710260562, 441997068, 339314563, 281559684, 143705179, 622670898, 321392497, 30405669, 599087190, 169153599, 622032450, 255798394, 94321371, 15153128, 784238329, 671142723, 313141270, 340823213, 577222090, 507557144, 30426465, 805711598, 811374041, 730335466, 764979394, 475693799, 956864317, 874613260, 636244357, 615904482, 622122387, 799443109, 61641952, 660657781, 511367514, 788589368, 327085412, 738579578, 78241268, 528191124, 62903198, 70886878, 122675543, 461686644, 992858607, 114265489, 217483034, 462123624, 854740968, 452254760, 108944861, 805779896, 80651093, 90853678, 228129814, 325736705, 720611909, 928548376, 683163119, 854673994, 600786412, 404649030, 325719284, 363672256, 260467687, 230830038, 149062462, 286401428, 852683440, 138741037, 152744091, 63809604, 672037583, 903814888, 94475154, 740497398, 731856787, 433267583, 670132329, 543775897, 352604401, 974900400, 914933367, 444975579, 359112917, 362998578, 315941348, 307682813, 632180629, 714942194, 28855843, 742319045, 113090013, 47992461, 532929694, 612532038, 41059312, 63369335, 848115765, 846096460, 467376268, 685557919, 126764034, 663701392, 964402325, 473217279, 127066457, 219694219, 485457900, 828789721, 6435049, 714595095, 53843282, 408599398, 983464017, 616301950, 535581887, 690372429, 927328903, 485128098, 738471640, 846869185, 79934397, 859565063, 66040995, 566957540, 147237858, 620616798, 951076738, 195372107, 300896151, 766837812, 845175407, 200287421, 692001175, 639843775, 30916344, 435082082, 677551289, 827833440, 292470586, 651163478, 156308561, 27679145, 233919368, 942561184, 902417250, 47700759, 702188293, 219585025, 276875441, 725277441, 575824810, 116526419, 426097244, 508460419, 823942047, 388547653, 534780944, 421722593, 481394718, 939320418, 486129174, 929094999, 588506395, 136516291, 185410876, 912991557, 797961499, 654867847, 773619289, 935758005, 446099854, 504674581, 646455379, 944835556, 793334595, 243033525, 599101798, 500390828, 781566701, 325534928, 897164229, 444563974, 723259331, 359627246, 606090515, 700534232, 187728928, 107729046, 53291557, 781110802, 717805310, 165796375, 475295395, 937507277, 792183137, 127303680, 596829728, 824489519, 559050036, 20634774, 861329530, 287665155, 365120812, 540990185, 99045961, 596227806, 15375927, 609654206, 676247117, 639617751, 694419978, 905006102, 632361930, 216827621, 217802253, 215902987, 466306369, 47545215, 583047093, 789797434, 977298190, 646339541, 366844583, 409809829, 636684436, 684167709, 965663778, 767846334, 116790844, 610281311, 954759482, 843715332, 33093793, 212349037, 590444501, 226371767, 888261281, 68298436, 808237741, 870510462, 712849370, 833990403, 89331505, 49973524, 637090222, 650290095, 220597505, 99893621, 71845008, 75430694, 877249433, 243374408, 303534058, 749456903, 544964489, 240589549, 733762530, 571194580, 113962348, 762828445, 838022440, 857712724, 504023326, 134346105, 328189037, 111268309, 240478714, 531298916, 997007614, 579369703, 462904344, 911440133, 427810016, 107890068, 979714645, 596176442, 149195969, 574393488, 253238244, 319780834, 508723326, 407057936, 722014518, 104240584, 199568815, 22520804, 441020298, 270361591, 149792764, 77873214, 585765891, 17609961, 252388084, 617782625, 603405776, 237858644, 466306084, 516951979, 831577122, 664610759, 566125808, 767892866, 97452054, 802205751, 650102833, 750995040, 218402847, 651328441, 352207927, 608030342, 137206136, 714239527, 455977510, 534854372, 983782095, 644456023, 336914611, 275907817, 73037818, 387121122, 525988874, 694396709, 669671176, 457563191, 389390983, 299020689, 284445841, 933224965, 654903653, 103737382, 968070880, 797452724, 938050153, 610216873, 686344389, 31035070, 865480729, 753696548, 811443407, 425940642, 506997169, 136929658, 934844332, 109094593, 37367089, 492301907, 522298144, 651824315, 424862382, 305746329, 659938341, 125253510, 831574786, 644005793, 135234075, 871572732, 609001590, 609248688, 860597724, 403870148, 183042420, 646163432, 723897692, 834658590, 722703088, 41685094, 901443454, 633623237, 928105247, 309892819, 850574922, 127821594, 387252482, 483130258, 651700392, 214628711, 491960068, 43570359, 833126022, 427566252, 922427748, 357364398, 798344423, 661774906, 474233803, 245800921, 100476193, 387883211, 434227476, 329903491, 572494407, 663546336, 545329390, 138518136, 105413489, 195590192, 545591004, 591932799, 534419165, 346388255, 412560699, 392374357, 701894286, 121091054, 983517972, 786389263, 612022242, 869940590, 421885951, 809992411, 135481798, 286856624, 431480287, 747245278, 515660553, 528823901, 19633772, 114918052, 732258820, 81909034, 531628395, 753453867, 116721607, 796584520, 864235958, 50795615, 536329888, 313536696, 921618505, 128392589, 373443553, 477344786, 571496654, 33865124, 279898473, 398748306, 149486374, 750406149, 654024787, 431180915, 56225036, 844283583, 999488106, 195511939, 909158639, 503156775, 505946462, 465530271, 562027900, 725888148, 684725393, 138084118, 558858527, 374517340, 598755803, 429898305, 644033005, 135579050, 55502026, 888723845, 419967818, 935377554, 567922845, 833938140, 307598263, 798321144, 562984122, 590743374, 412000677, 935804634, 387551566, 487224620, 40312763, 925415636, 647614623, 514259873, 73480095, 615782822, 546961279, 220685150, 386616518, 467432714, 85978529, 159607579, 370140105, 887908514, 419454849, 838728296, 408352290, 277570307, 516984667, 98818792, 243399077, 472087098, 689206046, 40326615, 9307438, 464505229, 506161674, 573300215, 961509965, 695550626, 641618390, 713350563, 776496835, 655553826, 670140076, 821476862, 257099568, 711973300, 995403979, 314297879, 77796453, 652385701, 409095732, 963082742, 472971504, 111216786, 312662450, 520263665, 620019800, 404641273, 565430137, 741529288, 36621650, 234903491, 282954138, 784679482, 275057671, 219851308, 283407374, 875061693, 362296167, 630448746, 520892916, 192426053, 510710440, 282845815, 245558851, 188016299, 199896468, 773638662, 55771545, 890376917, 611612530, 643243423, 206529146, 456807907, 81948225, 22130829, 621879263, 837543692, 78047568, 303227179, 140358974, 116743477, 510112061, 797282332, 359362411, 67958992, 366442807, 374681901, 883430294, 414202137, 881067859, 480314783, 195128400, 786754531, 510660251, 725135904, 598663531, 437729406, 178013924, 547805598, 139056667, 467903556, 601916159, 446146257, 574733916, 92558266, 661633481, 778179082, 501881557, 186379023, 191616076, 966822157, 774227218, 444196241, 346624658, 229823396, 991061969, 320494228, 341738920, 544819295, 853018942, 39552547, 178852332, 885122678, 403949743, 540912262, 688603281, 921095416, 392050180, 328491701, 366782035, 81516451, 700903811, 705872431, 200514800, 621785531, 708381226, 381742917, 177144105, 918003391, 160058747, 945195559, 892652599, 960625351, 181770937, 394637852, 827378612, 401379185, 282674553, 846465884, 976593693, 496156255, 63606143, 706011179, 349631100, 839633140, 626567067, 432425753, 818416699, 650292004, 231961593, 325884166, 381791854, 939818174, 912143929, 942445206, 512223714, 116405318, 737458100, 153973494, 352998906, 958565975, 659855315, 892980068, 886849728, 701952011, 681229417, 222675191, 601609233, 781990623, 573899308, 734850537, 440763877, 241891518, 717015008, 248392509, 615467713, 89087389, 65198641, 206380604, 835817493, 496300625, 697793499, 425466370, 464929845, 846313572, 404869848, 60848303, 109642656, 170517327, 490669658, 275542918, 958854370, 185108886, 68190892, 303718842, 305786100, 981147945, 305516608, 768074594, 446131319, 779462708, 458465413, 152289638, 718051990, 342440778, 387152372, 516791567, 680015465, 582472776, 526253095, 647687345, 470800003, 188847403, 443081457, 562622858, 414213357, 295516247, 369692313, 875095039, 993728808, 503893225, 502009273, 782986446, 915103943, 177864427, 684843355, 779047124, 980583410, 17416970, 281146283, 557994896, 418814117, 929552834, 342788747, 116306551, 513481672, 206664753, 339550119, 144226532, 786471938, 161341160, 67044861, 864546201, 500853451, 281311800, 784347505, 241247450, 399427397, 483416610, 410162279, 931703124, 39515086, 603632663, 615704909, 960790724, 474882754, 209073474, 277236275, 826152870, 925287131, 917206986, 646038566, 829148099, 207294716, 134298447, 921471760, 320750763, 640543548, 504391064, 735761215, 699985156, 277894296, 122646528, 989662847, 391193904, 577519226, 105177490, 21288381, 468055875, 500782034, 587258954, 58192962, 80092620, 392119161, 357232903, 504878771, 22365837, 600491897, 56924564, 178192785, 434812172, 474059299, 153246973, 827267008, 372605815, 719792934, 790640482, 509417354, 352942954, 658021460, 290480118, 916497829, 573240508, 223801898, 159621496, 502371819, 766975695, 858396201, 646446314, 321589339, 152069202, 78128576, 676886699, 571110939, 774393998, 943996022, 599653462, 773892219, 156736472, 56596708, 553596261, 255569423, 102448402, 476524571, 108067167, 464646845, 33357699, 173957906, 216811453, 268156382, 981908731, 888892585, 993766454, 105444322, 563469291, 921839947, 199380128, 249833174, 954331046, 54475418, 800223054, 409323667, 185117149, 312671621, 573353407, 971347427, 284854660, 80099106, 772878521, 893704258, 335925368, 43684267, 980993519, 504435849, 686159168, 989563436, 706329581, 657225573, 409299440, 560319678, 139941083, 118007090, 203476333, 246562322, 825484751, 815797924, 423084834, 833773241, 48912148, 550594482, 629908359, 308404964, 103590001, 242652577, 760508136, 289014120, 384006218, 651905060, 247061764, 888419684, 524040038, 357096837, 739720210, 509540490, 414928819, 184780026, 804521851, 845224946, 91000723, 210509311, 804446580, 668362506, 157078289, 929455635, 939822201, 627950166, 482358823, 766713405, 566024023, 732452, 988432016, 568898293, 574396722, 699442681, 289370262, 876101632, 551615329, 556701089, 882257437, 159503175, 816323799, 828394628, 700488082, 802227118, 357029983, 973584035, 323777426, 855705507, 491655659, 809460449, 660114791, 354986707, 87985094, 938954953, 297986458, 95880098, 611548715, 536689866, 933064827, 139762527, 939848523, 363502603, 220231838, 239518876, 97929129, 827578049, 672044948, 79075287, 128712679, 149719195, 206227283, 456614990, 492537324, 630523216, 450478445, 737937628, 842997322, 267628795, 642881077, 818301855, 652635223, 113654184, 556768469, 63062312, 774162392, 615136005, 471925116, 940189267, 690569751, 756406933, 898099333, 577729450, 715573113, 690910018, 108582905, 71715450, 868249891, 423810583, 34863871, 814333792, 931538076, 535960264, 894450236, 711949305, 925002871, 255296241, 168960132, 674664091, 544460021, 516047070, 90515141, 470410086, 526642701, 619878047, 511148568, 382872103, 133759458, 610520372, 533940665, 88744367, 874739213, 86941012, 353564833, 544216980, 628731827, 566577961, 508545382, 409837325, 476144634, 650077184, 326222382, 934721290, 580207953, 947403900, 25833045, 405661319, 143041786, 477705677, 778538043, 852083209, 191302259, 476786038, 662475239, 987060167, 956470252, 107866314, 878591382, 186767941, 768747622, 764783217, 212995661, 851222898, 212269311, 775275018, 858625528, 957471318, 336696452, 505489554, 363328618, 670914257, 737101081, 141947025, 926122532, 458684302, 807703221, 666642107, 313341731, 252710387, 695772599, 794600545, 15773618, 241614987, 302912835, 750474129, 712400236, 772109596, 883081123, 477323271, 271193032, 981401648, 235362731, 209988973, 693622119, 532060829, 341237789, 576419662, 420575635, 396608892, 825294652, 157286155, 584997378, 259131460, 506995241, 363828819, 237117435, 965922049, 940728001, 26909814, 683132004, 816811245, 45073980, 260489697, 64098574, 991287297, 586835631, 931614660, 702693752, 843792237, 287045064, 423111916, 467213418, 701143815, 108443826, 19827472, 826151715, 856920991, 740961472, 879129710, 920604070, 590484977, 861975285, 19740922, 170209807, 146629000, 428596717, 38037815, 524494597, 832072531, 102914816, 342965912, 46387243, 147688365, 818867192, 710445638, 837058385, 982265012, 856488249, 637331663, 946409235, 540915193, 371923755, 570258754, 87386761, 859581786, 422110794, 770708201, 839857276, 708610561, 434985523, 739377749, 129977113, 648268238, 436717812, 807749971, 679093575, 80168720, 153710746, 153118319, 953393131, 413724791, 20346267, 510629712, 646157522, 750832122, 930448718, 153129160, 635534849, 215022757, 388087750, 883120923, 238138055, 814925598, 584867059, 90635570, 561679587, 978531092, 582576686, 357428498, 194252274, 322129523, 358046624, 160514668, 901032940, 393607660, 58608372, 917428911, 92439882, 139217251, 448928230, 754337122, 876520976, 535475324, 807186361, 631921815, 293435621, 133472886, 745605970, 138768742, 702560612, 807517448, 715000436, 549442586, 429835329, 162741716, 745625567, 332212187, 834265467, 523215659, 65663854, 860471126, 549773806, 860425443, 648612814, 73362720, 493465495, 678921851, 748345080, 939344020, 550825038, 11933244, 5606454, 465847934, 9516738, 308790381, 387215681, 554201759, 117621434, 397480818, 844048457, 582713312, 14683425, 652694254, 518558098, 4011436, 904266663, 782751642, 519462427, 261333269, 116766080, 702404286, 324087797, 828249201, 968461931, 742317675, 634528636, 315712589, 860645156, 504647984, 341947942, 631730354, 328738112, 470611013, 899562684, 732471129, 994809836, 210517944, 680231232, 709860743, 406608164, 702866525, 477326238, 369931457, 16770487, 850609244, 193785137, 879597762, 273123995, 850402292, 572849375, 919096708, 645893322, 913623513, 347107985, 454574901, 833206332, 190018587, 210653063, 62620298, 411179218, 708377107, 777994919, 672805249, 771711704, 123852166, 317478412, 566406604, 705447189, 68994775, 608200277, 137273923, 736782172, 908675085, 894112310, 311275106, 637526121, 795780146, 555426249, 716635468, 962950028, 6880615, 307955360, 114977372, 862916646, 654119580, 633711600, 351792821, 822785456, 695601680, 383624622, 6843644, 607314851, 883536090, 444936744, 183663128, 254660564, 306113067, 783035434, 313025422, 985438280, 205666181, 431660337, 559960391, 593495754, 303693959, 987477354, 617892410, 150773316, 808274627, 850095206, 632759142, 523722443, 491728307, 403128830, 768036972, 212072826, 557855, 509090448, 352401238, 244322638, 436383561, 687782041, 579603077, 31561833, 710761525, 315313434, 387737812, 589073533, 838101105, 32774728, 729120922, 10008651, 597985353, 853829215, 245472154, 218082362, 502146530, 945283012, 463336379, 901290133, 880158227, 532126481, 261428308, 734668730, 359457147, 548948186, 88997775, 6786919, 454453730, 57031391, 18200693, 360642648, 383600890, 981354614, 488224796, 995164089, 106135103, 774980841, 192815674, 271668847, 416256771, 250847827, 618399696, 79568320, 583970188, 65219679, 808734989, 6548544, 301030643, 402774383, 121613919, 799094022, 478544989, 970819438, 809479159, 373911889, 472332970, 568867730, 122474512, 950854190, 370194547, 260613487, 648429017, 782106398, 853740159, 994310190, 363294802, 399085179, 145170929, 944433212, 741508478, 220698946, 144719784, 344034125, 914635532, 806448950, 834008224, 539626968, 213195491, 868047710, 646232270, 657387360, 296675442, 193420881, 534821669, 87221519, 53185693, 932369412, 408411860, 600004588, 772728253, 84946745, 671098784, 836606319, 913719500, 428663519, 406464373, 444295741, 9200706, 608598350, 642079923, 910851138, 794071686, 938509667, 628080668, 662166983, 153821694, 208822414, 162634652, 46660487, 118794242, 392890936, 547982260, 832184005, 939063839, 319831271, 72240518, 678242089, 229640144, 943109153, 492085692, 54015248, 323839753, 456702753, 190206970, 93886277, 800365576, 12628516, 581287103, 755759470, 705357027, 85765835, 721584288, 59446530, 983418756, 244520959, 82282859, 888093126, 349540254, 286940938, 136351896, 113430054, 400169565, 600686528, 486003597, 180228717, 655754161, 148484975, 802313953, 18247378, 496397131, 432838954, 909254549, 718288610, 291119527, 583996503, 539453016, 239422153, 43451324, 953111117, 223627494, 365191491, 818572396, 485584121, 692608214, 866130276, 445198815, 781283819, 571112556, 740514333, 27880302, 348281950, 865559032, 290681420, 821692248, 498232692, 789310237, 788059804, 370843426, 822578743, 186843765, 27211750, 873138060, 400519089, 14121881, 599681424, 20867706, 856311483, 824274508, 24740920, 43405807, 515751800, 818324989, 704031100, 20959151, 193025820, 204784252, 98080526, 856684060, 197935423, 170135886, 855738033, 667188355, 981568320, 191652901, 940190459, 675821560, 154465018, 798494704, 909360891, 148270953, 589286746, 872551898, 966457278, 816738374, 432126348, 290602131, 55946605, 288825643, 345545901, 467999860, 179311189, 857526991, 875780994, 445728070, 725721333, 385249056, 115137026, 161390033, 760170053, 414560826, 898559188, 404607119, 40074987, 82835624, 330942792, 238569028, 219266307, 323079177, 395624314, 301876425, 79557502, 634212767, 948798021, 400345111, 4234226, 642885246, 201860819, 540205431, 451555561, 962884148, 352687661, 792841726, 450857455, 640115663, 718895896, 778936287, 853940915, 306877901, 51759271, 673683465, 406947796, 168161729, 639490776, 169503015, 474212091, 207354520, 316676391, 279647127, 140151521, 90816656, 75004716, 511951621, 154334370, 414756911, 140214782, 611456684, 974056320, 923490559, 361198607, 65443659, 667891962, 244280647, 745745864, 317098191, 240164167, 562195817, 572178942, 975749067, 947800586, 575714005, 778924378, 960908958, 95719815, 362348556, 819808364, 246576716, 102829838, 221519311, 370553991, 877802644, 922051485, 166588727, 127266449, 582103876, 775108843, 505372946, 400875880, 54854555, 700188618, 297916886, 600180083, 77517740, 98576068, 615166154, 94889503, 750746258, 495124112, 84681117, 379124769, 86922475, 571660379, 368557666, 478713686, 238860515, 400196540, 669449666, 244928624, 148841185, 785683050, 858582039, 952109972, 680903048, 357369389, 147349365, 186717601, 425497036, 221563288, 158799266, 709633631, 423049242, 487507284, 290833668, 986610625, 942928978, 493619149, 652910825, 562692093, 308623387, 201359293, 454640939, 252008193, 574480536, 723199106, 211782817, 444253563, 844153504, 764002527, 861742035, 332133379, 549574262, 580098373, 238733142, 707449557, 606743671, 959279070, 288933010, 247726727, 798340160, 549635859, 438773932, 183496107, 832438852, 319200376, 55525206, 714746144, 561627254, 499737650, 169225730, 283118431, 682146837, 300932308, 860079893, 6491481, 499156461, 77041657, 552066078, 497933084, 530577284, 502354790, 806580117, 402547854, 610731330, 309659234, 739892276, 38283924, 763569567, 794519269, 218476877, 237262861, 948041097, 800643821, 593983388, 237182719, 144286676, 620930020, 302426640, 147819720, 434477705, 151940687, 317596211, 194138837, 928700116, 52220143, 561629137, 924936532, 688688599, 363593534, 543190575, 423070937, 536476684, 127335432, 910879508, 543809105, 638301358, 196135320, 326835300, 524417682, 474674598, 856956130, 938069138, 973651275, 206743377, 927721318, 765511765, 936441322, 606307934, 122316973, 377238653, 883099301, 476609463, 395842592, 377859843, 198079181, 682200309, 346356764, 214215438, 468264497, 839826706, 224349565, 176322612, 613062978, 984638682, 118345073, 572609592, 580787534, 76898525, 525152536, 746563656, 390512168, 249084821, 883675967, 972563152, 907970469, 945833293, 668856603, 68848970, 554544285, 856385279, 738166518, 617541826, 777184939, 724767375, 391092, 354992610, 375447520, 234979523, 486956731, 358626764, 401069816, 349947118, 719727636, 506106598, 567223906, 153169233, 958312229, 803926887, 874911073, 473214009, 181591397, 919365527, 369400045, 358298279, 877449041, 249994033, 999521412, 690658394, 179446387, 502254202, 659559182, 696630549, 212903170, 428381352, 661192732, 649080345, 140738677, 248565419, 705600105, 451026941, 188719369, 240352759, 233186061, 234972906, 893640264, 932208388, 196532880, 872458643, 114842344, 18670639, 366097003, 545869644, 432874381, 374328017, 286506419, 263763793, 886773474, 22691884, 699689097, 705894288, 853878867, 449282376, 821698240, 628638529, 160844361, 919882096, 92694910, 218251393, 613628676, 447070862, 522328239, 67797594, 170299044, 390568265, 265700263, 380678228, 748831205, 437145283, 341563977, 179926491, 90309079, 863235684, 406055439, 284113118, 835700643, 159413364, 57554676, 496313572, 113247344, 322934212, 641859093, 354902, 995721219, 274527971, 9114946, 411945853, 959504325, 867179544, 34483422, 589404266, 123708485, 1901374, 12048958, 812668129, 819404410, 368021393, 469105814, 359054649, 439612027, 817677524, 16159927, 505954683, 250391312, 442538642, 854681355, 464123119, 409119643, 332896691, 764975484, 180909526, 950404744, 230467861, 312383648, 868723522, 237774047, 418010377, 208282105, 54616392, 188940769, 869620708, 21624801, 911004293, 372451998, 592459926, 368219276, 935379960, 380759383, 403752008, 794714580, 27682088, 981759045, 933527822, 603562129, 216378233, 922622848, 159781524, 943214412, 321177888, 888140810, 221716299, 764066581, 623392074, 533658098, 116331653, 465944358, 194165400, 525561927, 958251185, 362951944, 277839645, 412534164, 590095604, 449619983, 835720554, 860877140, 473716503, 676071350, 361963269, 801460065, 476170138, 956770468, 824080819, 359751931, 220562066, 786770611, 988103322, 751340479, 841887395, 511811937, 975727388, 627000159, 553867711, 815756205, 977861876, 919210693, 59002323, 457732184, 564946355, 919983289, 720828316, 791221363, 404918855, 93643261, 816188462, 302833638, 732381506, 683079931, 231357529, 127368991, 517926030, 553703183, 395758838, 727162563, 711187836, 957846922, 172439462, 747843969, 878889550, 342332830, 975876758, 332902365, 979944156, 162833095, 376631073, 655356397, 125976272, 108388509, 844053692, 74767725, 628553837, 733789817, 300798797, 323063964, 70137530, 751506598, 784999176, 74380236, 680887617, 160715214, 550762013, 607652666, 578813996, 934870258, 900931655, 154851849, 518173343, 715147156, 151111751, 169470390, 703484700, 245044, 869194589, 663005604, 207682406, 835812346, 326167633, 404657543, 539099574, 681213720, 532706057, 693934011, 393527855, 790721535, 596006913, 791895166, 187469555, 581484421, 726047825, 716414067, 305580552, 514372892, 983987913, 385217571, 555433478, 981228497, 890375629, 515029643, 103856854, 897787525, 728131639, 386875479, 276797950, 930924928, 259067612, 465678576, 92713854, 713840660, 948778788, 264357061, 854891249, 285053106, 368123412, 993346436, 157710824, 612107365, 23643369, 24218802, 195530567, 268431872, 447654104, 882662485, 776233050, 884272525, 234275674, 918355681, 53449266, 444960253, 608059079, 299975939, 119293957, 993545306, 768614011, 47233966, 977199531, 964964765, 513388870, 313600082, 495656556, 689464789, 987776493, 191802323, 411213659, 500909822, 872262811, 588626997, 736013006, 867219219, 664585383, 690294033, 19659728, 872457471, 467985538, 489919005, 706316344, 56069438, 486058434, 980519369, 663051196, 71509343, 443562978, 415899188, 934559967, 311796192, 512787356, 55113930, 858829733, 80978239, 222916004, 974957186, 676339997, 591945474, 972528800, 21994083, 387611116, 24779590, 838610861, 780805371, 823801476, 76480102, 345411957, 386639045, 711130745, 392594109, 543914266, 224107929, 592105492, 602430711, 955995392, 456245200, 173434851, 415935795, 261508601, 215907323, 316837629, 20502780, 154895109, 422513872, 429239027, 706081294, 674579477, 547532169, 662713795, 741581147, 450301120, 343980911, 164026923, 640124905, 250480091, 672051598, 496424982, 730477090, 689292870, 554661355, 97691908, 489453472, 529195999, 729242222, 381058009, 180984673, 314421409, 786404039, 24026831, 547202256, 59745999, 256226234, 376941929, 199536384, 846751169, 233582117, 855965037, 369809620, 112875246, 535860506, 308765216, 837710875, 195354501, 659434468, 651564015, 309473835, 565128131, 364454454, 29322934, 96014379, 881736267, 677420551, 62317962, 274352286, 473484552, 119577798, 841267784, 564651074, 159000868, 303493780, 668842786, 688602549, 620474547, 386391718, 489892216, 99801765, 966343016, 905425870, 376984456, 116560254, 400190800, 519522878, 204976796, 28725687, 810313493, 328502771, 467985194, 330999695, 457358494, 160076719, 448788103, 429612486, 137759379, 784980315, 237534395, 688403044, 495984596, 399197842, 576826513, 548907486, 780449662, 304445746, 749435326, 449614864, 244847069, 456867449, 978627401, 531788607, 109163595, 642183788, 652314212, 668321632, 101001944, 267151096, 803955521, 929342762, 747342451, 287971269, 204915418, 66244712, 672591776, 578510252, 963992519, 776110131, 518374516, 483388199, 124474298, 722963762, 715486337, 923201780, 84923216, 450393468, 46512151, 864503072, 29814276, 228390065, 466579228, 883942595, 272189963, 937419180, 610181898, 248682366, 716493834, 565822477, 709366087, 664680566, 980073433, 912409174, 367907341, 357877264, 515092102, 593583063, 131746244, 774490001, 862469558, 444347339, 82117692, 580315051, 744196092, 907291874, 997309783, 579141, 517183621, 458241900, 75279796, 447537952, 320841354, 124394697, 975203235, 461895056, 588344150, 656542570, 195913641, 51336612, 223346029, 328407368, 778032030, 231544671, 824808479, 578766984, 208501204, 906090229, 818855934, 282201787, 183532174, 827738498, 462114286, 332974977, 601689095, 638328446, 222998594, 31147360, 930315782, 58981262, 416269365, 803163378, 24869889, 138572831, 95911731, 920562787, 501029150, 19367491, 788419393, 434545416, 471930425, 655256932, 982780086, 654893142, 602470387, 63485614, 234901852, 165393023, 454415925, 921879405, 433309871, 990492403, 271525969, 436600048, 772726255, 792375757, 868470374, 702060968, 788512496, 891098005, 840607330, 981098158, 634015295, 136825474, 74164279, 98095793, 885599874, 70749789, 300081854, 213366636, 824678187, 628933339, 103438476, 866842171, 15161972, 240674946, 619066922, 758989299, 542952655, 136294503, 137367818, 765246296, 739628195, 955396122, 116184908, 749810458, 518437810, 220311203, 270553373, 983179955, 398248053, 828843118, 86864499, 847927457, 283244625, 886728252, 467486758, 672853705, 424501129, 212899860, 705701939, 841025008, 446962106, 927623760, 791792940, 662913072, 956287220, 103164833, 78816633, 330542486, 512442720, 719147007, 344000042, 774687212, 879940773, 708323258, 840324695, 428632461, 336243576, 21474504, 202482242, 845928330, 888967775, 40150671, 500146419, 366089112, 732856031, 425485451, 666882033, 489783264, 735604087, 722181247, 973830408, 705465423, 64336205, 592893518, 538794649, 622887151, 456012480, 346689160, 54294805, 347119395, 855995225, 286685149, 118138454, 112296461, 164649672, 323776608, 772508836, 281612621, 994028489, 518705929, 884396555, 836990542, 65529349, 811487384, 796263298, 17029762, 381366838, 806783446, 602128360, 960708007, 946604183, 144232392, 446915595, 597873305, 542295284, 166831952, 296231403, 798364034, 509821688, 528372217, 166371790, 985855164, 658548449, 370791249, 743900537, 552308777, 2796548, 102756703, 659439838, 626709223, 990406260, 807381561, 602509107, 16665908, 772387495, 174703204, 249201593, 444149968, 337461861, 372831929, 576581969, 591065538, 204242368, 355309549, 542994552, 599929508, 554556868, 89205952, 520126680, 902511550, 426227501, 726390210, 563815904, 579872834, 532613475, 100283886, 376632225, 132020618, 549409645, 977868461, 822163322, 871740601, 237839031, 268512532, 308023419, 630675773, 937790052, 323692484, 635177001, 942293259, 616906057, 754977591, 214912706, 751343172, 873436317, 684877973, 167491421, 652143843, 576866426, 465794408, 949967227, 317241185, 93819801, 409216948, 536306350, 591174936, 257851378, 15524397, 190380270, 247056455, 126775238, 926390152, 828142247, 534897173, 188165169, 661722722, 367591729, 447480185, 950637867, 873105787, 396002777, 184385571, 375936018, 654965119, 923499360, 254471405, 383079517, 845051168, 531962229, 947701469, 557235997, 733976336, 220550167, 461384818, 625152228, 287911576, 447794593, 242022106, 958390161, 735226791, 812643300, 316652977, 362250017, 505082642, 266238398, 475022471, 118726620, 215958592, 839950604, 617434413, 124608756, 955264294, 311229053, 63218294, 693195277, 198942710, 171777421, 610635470, 188498480, 661024973, 613053505, 397451459, 669241003, 666124620, 590685523, 190886221, 210636016, 142993490, 496280986, 965341120, 667483159, 892986650, 479113035, 127422026, 590304318, 279393471, 795268162, 872799494, 266304845, 92144967, 297706697, 675265706, 83747361, 998589408, 849151373, 978436372, 931916144, 822974156, 153792225, 97211047, 23986792, 872039353, 90489921, 695797375, 209217412, 65123795, 91377546, 910369262, 491414608, 758009642, 135350585, 437547282, 426358586, 609311111, 382618298, 149255079, 852279081, 527120147, 969104280, 749530079, 587574807, 538918175, 135710776, 506344378, 413527918, 651893827, 397458209, 475409776, 111085258, 890260701, 10075594, 276650852, 903027712, 625960903, 74124363, 743366607, 228933893, 428718956, 399558971, 867342402, 780253167, 433312626, 176405290, 548157887, 819724584, 86264151, 869638594, 873600860, 620967387, 562775181, 191003396, 423986799, 41567212, 193472441, 379422043, 890820215, 391894262, 561206919, 672091739, 355301290, 749051549, 970788223, 870137645, 555869336, 337591502, 950982399, 583252238, 370977959, 222834528, 294899014, 659653871, 700033153, 93641536, 843106951, 901575010, 337630971, 939983430, 863863183, 830668063, 317951580, 786227159, 668886603, 904417797, 276762702, 883594615, 827862392, 583873465, 858804601, 994776503, 105365070, 99828590, 733312923, 956615332, 32521150, 52700833, 715139269, 392078919, 513644044, 41254915, 209126458, 200924035, 890161191, 815643084, 250430804, 768983561, 146689915, 362813575, 260478109, 935907488, 331126712, 746513876, 204599915, 876272584, 187329008, 587384291, 955098425, 571429056, 922269497, 712056273, 216381314, 883967266, 147942047, 948483947, 73541209, 710925989, 972833169, 616725582, 32886529, 331123675, 500852967, 126399464, 651205904, 135316068, 225657237, 324368083, 772567218, 277270407, 222920709, 441206992, 728235680, 851780718, 480804989, 646399377, 823114779, 784843180, 663787647, 290186745, 123282749, 990882401, 7339394, 106597765, 517572799, 15764604, 282548332, 42989170, 917944420, 386416825, 958858386, 905122798, 611936421, 62835248, 808804995, 170073292, 520326402, 149916790, 531512357, 617523329, 148391544, 167236292, 475311202, 631177865, 895827445, 691288617, 309189743, 863240047, 797242022, 564206623, 984036769, 217451537, 514756720, 779537444, 784830209, 300560094, 236672638, 132453444, 869875804, 331238873, 296344909, 634700402, 102356757, 266217342, 558150276, 523928089, 333519597, 578998821, 543093761, 348063162, 622167468, 425566239, 181489046, 528698040, 955782774, 942918802, 876729652, 39309991, 94397531, 930558631, 750335129, 581185745, 234723923, 516470684, 617213906, 863643358, 20851710, 611449951, 701992969, 675849836, 891287388, 349835095, 531568684, 986361131, 380217868, 891832942, 804241742, 449701196, 318818266, 677826607, 187513191, 725597677, 449931198, 844320440, 259620361, 167701030, 752538903, 978753359, 841507615, 572635659, 683948488, 797155697, 985724646, 960764204, 429151454, 608745359, 276052906, 155040197, 171549639, 446196168, 977782873, 945171782, 278452384, 332359183, 730026519, 361001410, 809984941, 918735835, 409959948, 22837472, 410440469, 4891829, 385202502, 421972193, 182191602, 8990311, 393029073, 381471859, 5216813, 182418553, 8277254, 19577326, 949838992, 72591277, 307573174, 365059545, 370065468, 131126331, 639249472, 386574287, 595391587, 169599078, 531663258, 826453414, 451866640, 116507546, 685822964, 709713364, 360512660, 197038135, 618276961, 495331424, 982947900, 649892173, 872158146, 810339781, 662374896, 422003157, 971804262, 871729090, 387304829, 139877775, 362171906, 263385287, 193233805, 303910573, 363925862, 288006447, 875667223, 111188179, 757731211, 458623887, 550501946, 395355108, 481741923, 255146511, 589272584, 854325481, 275567132, 797048578, 756656948, 951345943, 915358715, 397068061, 62614561, 915202193, 962739797, 697863125, 417836899, 503245225, 92192552, 495818530, 271117190, 526652347, 445209928, 970968272, 644510658, 906706708, 252736342, 728948919, 326260522, 467879057, 754043337, 77012393, 709822222, 656636596, 878661215, 588207291, 435982849, 61182401, 166440512, 647005679, 767356113, 92593684, 744455405, 341892853, 378718987, 627741975, 379362378, 623923094, 289128225, 39774874, 930552415, 751582118, 796490725, 50886584, 30611502, 423779516, 918683438, 153985708, 225363851, 535184817, 955631204, 225629905, 688348139, 902096440, 316977768, 648831667, 525643553, 198741062, 882924341, 588718099, 293747653, 378357928, 522766802, 687671755, 403888577, 652992207, 525751771, 345527931, 229949481, 188077853, 685149244, 236526785, 215417188, 557437225, 165183895, 643432342, 487175636, 933245934, 89689300, 239524300, 622161832, 400582662, 869583100, 731058881, 378028950, 412381722, 752795738, 979274128, 494434996, 793865683, 821858354, 160840630, 372015766, 179583308, 963367537, 532386462, 945167829, 14615335, 142330676, 607298669, 535192848, 338008358, 177197928, 705664886, 495485504, 93987928, 183439850, 404998129, 192150828, 970016382, 59513380, 803401926, 712005379, 506271701, 951674296, 620142985, 306020846, 936434719, 933880810, 77463259, 140572037, 192374745, 420543445, 226414875, 789349352, 193009976, 664839403, 202192636, 145069928, 702339260, 361244095, 820497755, 896385543, 335940131, 146197936, 278944875, 317281810, 361095824, 551034649, 716513948, 915284497, 579197590, 495144036, 427886282, 562236518, 168962412, 844959848, 731043104, 305925897, 526994265, 855132792, 988217573, 139340136, 997678727, 18838320, 827235585, 304113238, 957181435, 474249923, 973445252, 281005251, 406281789, 189204896, 521386376, 681317955, 821697479, 848882488, 152204599, 104033200, 498226767, 519251005, 362823209, 929952055, 659592517, 552929137, 290629149, 703282937, 680453372, 411495707, 90588153, 911927436, 25861896, 332958128, 268205642, 95385711, 550873672, 165312110, 94212436, 922441422, 682135290, 258945433, 12094781, 911495884, 811276517, 191616062, 990201461, 700885810, 673740502, 617392501, 543549610, 449481712, 663304906, 364866530, 43809973, 791918338, 812960230, 146804933, 889539715, 154092306, 369944944, 109113382, 309994103, 701323686, 509566019, 175980714, 5805556, 980715361, 883521720, 981131409, 86663112, 31394456, 688041096, 260731562, 471885232, 432429371, 996249206, 416280660, 903281945, 108100485, 881750556, 844902281, 203172332, 483933159, 750356295, 844676117, 283918825, 727369480, 274144294, 671558641, 747278013, 943714133, 752911566, 138819514, 408629185, 410551862, 190211472, 524065377, 164780052, 24482655, 771599811, 91498713, 540204824, 951890648, 428523413, 204696145, 227202941, 220393453, 844795700, 763567437, 621016517, 631877563, 779742359, 356829948, 725077826, 386733029, 900886998, 978444077, 240092390, 407963069, 608454538, 351664392, 485238369, 167157298, 58285900, 510456302, 209321432, 24822263, 83444595, 76345356, 729396826, 366222547, 461495519, 168777120, 317199249, 805001765, 912255659, 330526028, 141384557, 341818197, 328906782, 112192107, 57154553, 407009562, 918883794, 414061613, 659641085, 345120319, 479010582, 322043526, 435536368, 171026715, 627275425, 381759500, 632033299, 213884436, 551819951, 689930251, 660082192, 357093724, 57850806, 523755543, 384594989, 632673716, 663080179, 956452999, 975234454, 678895496, 625137568, 781646231, 369460269, 436377974, 282405993, 399958766, 901108803, 113596047, 400151264, 370763254, 267064821, 776485874, 37048782, 535305475, 503743182, 450070752, 255134564, 682426750, 258408886, 496390002, 403682355, 263847652, 152764554, 879267686, 42979065, 472889398, 376718695, 949483692, 143432910, 964976941, 653049576, 878355951, 123244157, 171428649, 158670245, 172528725, 399986567, 128595162, 426165733, 357056794, 308345180, 211028128, 475751600, 436423037, 613768257, 570698977, 356283118, 112296625, 32303447, 727490836, 490007919, 336506501, 327990626, 430748706, 500385222, 47471225, 145788440, 764604677, 644556933, 231053289, 355437197, 639072650, 739097240, 234846985, 976503207, 866051750, 602055117, 904731429, 539833677, 16286505, 29875077, 214156156, 770661775, 134541429, 243032499, 720270129, 921415823, 728538062, 520943354, 597371212, 681049542, 458761181, 678142358, 912381145, 505607319, 37060937, 150145477, 589409538, 149743015, 555330748, 900563826, 778314668, 180685254, 354226319, 965654821, 265778555, 753911353, 902157025, 587263689, 487717471, 723060434, 475467422, 6027168, 120980233, 136518565, 400719129, 126520634, 56341331, 359473597, 987557333, 537156436, 65073752, 126612978, 396070399, 77278627, 524406674, 325917590, 817577704, 472210400, 640390534, 375400200, 326212140, 92665938, 484163171, 986306865, 501260634, 133812281, 71034014, 931311012, 13514863, 240200392, 549289815, 455491438, 63344066, 721868674, 305736131, 454478902, 510380607, 163492128, 924641255, 430488529, 670412733, 432681648, 932575527, 873243960, 63471363, 338364766, 816979094, 553542115, 647015188, 468163371, 563741516, 983484239, 312830002, 466870293, 899317222, 4993627, 970334569, 906136143, 873635782, 591893349, 861396226, 879620196, 391605792, 170960551, 340777880, 800966759, 953058799, 14759927, 923753719, 91381904, 752870032, 611705845, 42370342, 623145133, 843428338, 186563324, 134413014, 111209129, 198210913, 387816260, 80490989, 698514038, 145351155, 283699288, 200577819, 848810272, 280262792, 440751527, 10663350, 273277843, 205072414, 974335303, 374719442, 895387198, 805128414, 849473883, 264823987, 961874196, 942962539, 237538842, 138137666, 528959308, 87179449, 10925915, 311841547, 579121994, 126503388, 890845433, 8735273, 628873184, 387338644, 861571024, 432074959, 393581442, 177138473, 522166457, 340716397, 206327777, 476728236, 58485619, 876513469, 52195469, 761729069, 878031110, 402226393, 165296032, 211919923, 741945781, 93371022, 500582381, 263351445, 798994877, 898567055, 991062358, 759919212, 607760143, 244735563, 382285416, 51527966, 193947641, 62453984, 285539191, 206611141, 938048042, 327712609, 929959462, 672441371, 262381445, 257052791, 568139858, 792268433, 329750038, 116510818, 714402674, 945717156, 594907429, 211932791, 958429288, 238946699, 609207164, 687382189, 372560372, 573870521, 104911498, 535139463, 776446224, 65923437, 102269222, 351231117, 628498250, 576256803, 813148469, 662772913, 237326130, 3657248, 23669304, 449889203, 716725147, 521255071, 107142325, 442824644, 141049494, 806728712, 599087665, 595128546, 147445001, 139531230, 738490277, 979196831, 98691017, 263293175, 18251936, 260253746, 255015053, 160026807, 121771658, 1450373, 40215029, 930487541, 892608509, 660726659, 748195418, 882470550, 349040207, 354526877, 217624546, 875173939, 947687334, 279379765, 580053528, 20196656, 604500526, 726072826, 199191178, 366221434, 929817485, 268099118, 897224291, 295010725, 638400815, 392001645, 375009231, 974572326, 155567558, 222451843, 947826343, 337602019, 68565637, 22844, 360349182, 45372442, 821296883, 540795768, 829312559, 251890661, 670442388, 803554511, 106283973, 73903478, 435288815, 964405198, 4835464, 10087371, 403612307, 308167892, 685514923, 112084168, 130034200, 642063412, 456894889, 211352738, 305394380, 726523947, 339664170, 640543760, 333592232, 747511625, 796205897, 704422477, 681390415, 783280045, 347261383, 667300505, 740148815, 817645119, 806683210, 737204710, 609932197, 23407245, 278397361, 624292799, 625287195, 381613445, 359409517, 383731174, 99419503, 163427092, 793199168, 520624291, 778397422, 416960916, 155193724, 588732736, 982505037, 585108426, 338963793, 68038216, 565494916, 854158626, 92865490, 930996626, 252429496, 195910100, 660605845, 197891343, 783275123, 425101614, 40895695, 644111493, 197794306, 758418005, 786523581, 739472893, 513653800, 212475791, 373620920, 74822035, 346695955, 90683461, 290924439, 628205692, 61437420, 441242463, 268084298, 942586109, 968582207, 139875566, 510149450, 342075117, 590987786, 670389995, 382136812, 694851248, 445214180, 917955973, 14401264, 430718201, 468344590, 651291343, 576295164, 471131276, 792571598, 435120113, 704484539, 605296660, 888354371, 412129866, 945973799, 231908272, 916103794, 973080743, 684690524, 758935945, 782474168, 23822934, 290960374, 27483051, 977267468, 978039370, 49215093, 436388851, 281938450, 431313821, 969258802, 883734694, 290250831, 567077338, 560315531, 545527704, 88993741, 819954358, 153666950, 695260339, 109847469, 409597709, 981449095, 312984763, 640894672, 372598705, 519154211, 580145857, 901971530, 472543732, 609593958, 97228836, 682715360, 958402426, 521672158, 197222872, 348492813, 777933406, 122402454, 7409047, 248712623, 174150583, 754190138, 605054340, 994104707, 853823910, 542746614, 968878440, 164210324, 130563503, 37076658, 13885932, 867274691, 942730574, 901252434, 693106405, 574219811, 513235575, 319357371, 149319491, 909818925, 861204822, 428375272, 984047800, 756195034, 871826241, 539271252, 246917270, 695586513, 564191637, 7541645, 979872696, 602372358, 15251190, 933102591, 210169731, 800415902, 330469694, 131158359, 745409892, 237636577, 694393747, 719784251, 547733871, 531089063, 182605364, 961957605, 859728619, 244479816, 672608548, 630233807, 749297032, 214099301, 610713993, 787390388, 805556667, 849577430, 368645930, 51480719, 421496656, 855569980, 821006988, 843225724, 563656385, 908716666, 535705932, 784624527, 339135818, 864150438, 627842394, 140487112, 643910082, 181853519, 174108053, 924719009, 205249822, 275612058, 310340491, 387917959, 937397632, 93610680, 305093323, 679590442, 365792671, 487506716, 330162878, 726351735, 715031997, 880515538, 14484008, 456131024, 922610108, 132640663, 63980154, 298675152, 230584457, 254336239, 892891446, 767847062, 623253869, 370456068, 722166659, 107384663, 522668551, 336931680, 343887236, 153002374, 129313037, 522492578, 296815128, 846372030, 665458191, 538618782, 731526403, 35550381, 735240579, 11642631, 716213379, 327560695, 685207961, 794107997, 392757679, 954148914, 512289133, 547333423, 828635322, 387769156, 54942153, 582328579, 942790767, 692950950, 584670681, 659519076, 791497936, 746912510, 849291429, 808690873, 863115422, 767554821, 972503916, 526878610, 831454873, 535625694, 663474427, 872533116, 907321962, 927443196, 586681902, 712577708, 106073598, 512987672, 573752663, 886056065, 987443668, 606289545, 158061573, 249823150, 626504937, 47690819, 685671329, 64951447, 323809190, 666323151, 480282069, 706018935, 204939281, 316879902, 760560405, 315190155, 804691396, 600456815, 960349985, 266465864, 535940860, 655653261, 863946203, 975277793, 694985301, 925618077, 602154401, 215896264, 109963863, 299807348, 738478129, 33587278, 161297937, 197232275, 744858747, 716441874, 43552373, 704693352, 834849672, 179643184, 77777313, 200492352, 563560226, 57852929, 295930447, 751523106, 81002483, 220737231, 893955464, 702039494, 535595309, 510213124, 623840094, 441531730, 577919619, 346095714, 677054665, 491072564, 295912744, 271128112, 798418692, 337141472, 264390641, 556240223, 455663660, 561579652, 411625928, 449359839, 270532960, 978493295, 968635084, 661950713, 891677667, 739196901, 779643291, 664568186, 368764701, 353835886, 825362806, 337388339, 218927920, 430808143, 243019562, 134485087, 893765770, 941952447, 390706985, 440376702, 507153154, 202551862, 277932471, 120329354, 9819081, 661512623, 985214655, 331853423, 745159768, 843297440, 778107458, 252030389, 788764853, 986007016, 468938199, 414208284, 77419450, 806892587, 933685539, 227744509, 421383117, 432817785, 820289479, 862023126, 576055573, 777862475, 20918417, 537866418, 838229619, 233073381, 405902708, 80255176, 411990222, 198352539, 194751913, 149874618, 750604076, 448758071, 842620095, 682925474, 950462761, 155812393, 702470505, 404717933, 818781209, 892701682, 289109915, 281258169, 908538512, 182019246, 703034598, 458737001, 435681296, 288045719, 410900478, 29815548, 336703860, 362379943, 935635572, 735537545, 323366761, 6718365, 589087401, 662092930, 538166221, 133743479, 290686095, 195628618, 67969507, 57739230, 511318830, 530839533, 448901267, 799544449, 582239131, 87641414, 3769614, 809803005, 785895528, 443204671, 774522841, 958614801, 561882405, 791624508, 349185046, 29284544, 264592546, 354876240, 960637690, 238221316, 590318978, 532152649, 336693320, 72118323, 571770017, 950460237, 243050922, 30233571, 234454434, 718478918, 727951882, 605791475, 704147180, 277897374, 251146195, 132461359, 697548838, 169204607, 773976750, 319161749, 30856724, 264659114, 284994743, 203412786, 680873825, 890869947, 129814362, 182012179, 591907176, 901164981, 101408971, 249788992, 323266560, 218105685, 975215330, 133196795, 827929406, 850695382, 880577301, 632957508, 438890103, 445171800, 367015455, 95145996, 459926664, 152018008, 538566645, 124737802, 106966452, 878877387, 759999251, 797660431, 555891288, 728085909, 112505950, 323027875, 390884532, 511961283, 737060903, 377074586, 435067782, 335774972, 487158887, 8608886, 375610008, 425183886, 829921969, 959851379, 283932060, 645666492, 359842795, 789746926, 832201226, 52345738, 646177962, 177762303, 277887186, 482980160, 543785819, 234603828, 674539502, 735084519, 121745573, 827362000, 43145350, 875681255, 23182359, 121502937, 822187239, 672328392, 769436149, 331645589, 611213622, 878949859, 355666073, 813956476, 847115274, 962077407, 504733222, 821683141, 418802064, 697032360, 135169954, 854951486, 651882652, 447369843, 14072471, 349828841, 395193187, 23064983, 841653464, 825024783, 356337192, 199937651, 171127474, 959729189, 546067868, 411586058, 781315031, 181544251, 961199114, 794513091, 765065854, 897073582, 681136344, 681747563, 909213742, 994606756, 335160562, 128457793, 687258126, 432865146, 150883772, 939756524, 128911496, 24408244, 135632615, 953736405, 409620839, 209353747, 555552223, 498024927, 136671776, 371069942, 493867341, 401727871, 516662841, 836848717, 42300468, 179603530, 26802132, 889392943, 417129440, 682292232, 574765126, 763000842, 497465939, 199415050, 762518326, 141805349, 465045941, 593822163, 381539723, 965754141, 212273472, 829666045, 763558884, 66592132, 548549020, 987320717, 562841521, 203664547, 961662245, 661161209, 25755792, 308859813, 318282433, 967955567, 978215264, 775670401, 1433500, 542751357, 182421169, 311293771, 859320122, 420787925, 136191174, 873975282, 794784094, 133208544, 886301877, 510629652, 200766052, 62516161, 296032258, 418542727, 627605884, 236412820, 122253472, 121224569, 460170403, 585280946, 533471638, 588429692, 861764382, 604712345, 387110812, 741753100, 257214685, 164920146, 344061756, 970108069, 112434607, 631961381, 217413678, 462975266, 25010105, 405778025, 207680971, 959203280, 36962588, 101276367, 617962563, 277529631, 82122812, 870403307, 137149218, 619687802, 795759192, 826192396, 295059654, 573328583, 634691862, 204420532, 309650866, 943909902, 286540256, 554474041, 750925541, 600738984, 693685020, 223819956, 253308454, 956583066, 222425943, 741349094, 314765336, 147134410, 879159063, 319142788, 166251860, 546599620, 78977313, 192099457, 411920783, 515470915, 627450985, 772285173, 14111581, 615148181, 434241048, 536742863, 148706503, 315029852, 157674252, 415386174, 329081474, 53145536, 244431449, 773849819, 976897111, 201249750, 698938077, 178039489, 81566566, 426883143, 765324108, 641081997, 796889520, 932655050, 428887349, 680636253, 840852229, 928598419, 85933477, 441215886, 993288092, 521203827, 244702307, 319158970, 286413807, 252760850, 264506977, 858383589, 253666455, 632583884, 775382933, 461377390, 274549448, 253169189, 679902105, 75649506, 416146024, 372404482, 335309086, 755831843, 837735654, 87595169, 688490062, 893481285, 164442539, 705041488, 412328146, 722356984, 769265210, 823195667, 143391706, 719557938, 23457948, 453912058, 858583725, 515793096, 554776127, 304525272, 842610502, 282505745, 117053642, 821323203, 184631026, 497748910, 568097006, 587153218, 132760436, 356548246, 878440975, 531095292, 690938061, 813045289, 426553115, 336819862, 859167358, 915441666, 467851340, 243106653, 515362049, 819231404, 880915893, 332450131, 649109028, 636545624, 728968213, 918574695, 787715306, 475413333, 1761067, 696175265, 611564688, 728138277, 737138180, 415051900, 584273051, 109663105, 610593981, 981672983, 16275726, 639472890, 900278490, 70492850, 154613252, 444353378, 331183293, 140025643, 147304115, 947589835, 341411008, 560307151, 20268336, 30263528, 853794013, 41167189, 618271150, 983511571, 480233841, 441058909, 730331986, 820381897, 673210170, 933853403, 768914591, 542727844, 651559984, 755884919, 947849850, 866589111, 707411604, 910437080, 704912081, 101728614, 413442579, 743767778, 952100189, 967572300, 937755248, 503228568, 804874933, 538904924, 321527509, 562292916, 837499532, 883370092, 602449001, 494962434, 166551657, 559634583, 796526097, 110134550, 890412641, 832964401, 857006768, 933315970, 574451435, 550561906, 751162879, 307669579, 139781684, 872437526, 255243117, 541280855, 52655940, 29624634, 892750962, 894105451, 236684009, 208802266, 281291222, 482610454, 903228757, 760383592, 941335866, 143443948, 477663448, 508522212, 448987397, 438422396, 854434086, 987733019, 823583963, 773904321, 803689845, 615608907, 823896978, 578167665, 492452251, 644647696, 969587115, 849878479, 496237434, 999776175, 276717240, 74725700, 797636483, 475023494, 699020933, 152778963, 143357309, 430689211, 30388381, 622104389, 52918706, 760548301, 961337098, 620977063, 213735908, 498203566, 936900046, 674244362, 435256369, 981851899, 757547732, 623201512, 325556332, 856375928, 699552927, 173167556, 870344382, 743383028, 545925198, 660894237, 283656830, 646661473, 263853749, 152657028, 410517596, 370411438, 3460452, 638510091, 83566128, 871111575, 698250050, 991177001, 40655281, 405744605, 97740901, 348083399, 530284972, 102421869, 130469342, 437017238, 883039957, 400147337, 781705590, 482686543, 268813907, 955950276, 765234288, 388090484, 225449055, 902652658, 3905747, 545539033, 211164214, 236138866, 533834122, 88870348, 964472575, 464698637, 443139069, 372481383, 405810791, 149343167, 368323299, 631868334, 540431635, 442459383, 993132809, 225567405, 341505084, 582689480, 557913060, 146852083, 961331530, 10193047, 812807296, 810813318, 40907243, 235700089, 345733084, 452329693, 696281752, 10567026, 365669414, 410084796, 942152443, 579385406, 992502996, 36171886, 19999791, 862200846, 284156753, 653491302, 243845060, 387038938, 174813595, 123685414, 1557520, 115587215, 865643590, 192955735, 476767359, 244596847, 125169642, 270610701, 324334406, 403684285, 297217811, 958017442, 701039462, 756733406, 720644964, 53106456, 312869094, 921219701, 695254672, 275035245, 660110606, 526930028, 952169132, 258917010, 455542184, 263410129, 153638848, 662757648, 403014606, 937883375, 586857198, 146338374, 83998804, 716180056, 73298791, 544806986, 809023950, 696620179, 335550152, 313206865, 267585963, 768416681, 976547131, 49651928, 290174632, 645706974, 337869733, 393480802, 499795569, 246201499, 935136602, 524688029, 571437524, 847821505, 644976497, 313689950, 765774099, 872330365, 286840366, 251153276, 194204675, 70086446, 870043324, 84818295, 572111196, 264708973, 113180244, 140769400, 594659763, 660366320, 283162893, 984541158, 99415527, 655943873, 802238991, 117655285, 674927842, 869194096, 43915101, 339751155, 34101082, 750130157, 422644702, 77959970, 651153963, 78488321, 531002472, 74426061, 618350373, 56747416, 665118542, 268469980, 72279667, 455712509, 83815698, 542709868, 596722972, 693919787, 753706492, 463166587, 332296243, 382041967, 1024669, 665598102, 214140713, 581485348, 240803065, 712950265, 301235428, 826758696, 259299237, 807176707, 431846001, 226858124, 696074168, 347486742, 60407805, 906269116, 258907050, 282042322, 80584082, 963077613, 503843062, 520429664, 699959820, 647693150, 863187213, 675704013, 214163385, 253539690, 369963363, 391876267, 14563110, 533424835, 488833161, 802330698, 857880971, 619487114, 732296824, 639224716, 687114703, 434987252, 736733867, 396102443, 382770681, 345852815, 615662184, 200372235, 181839239, 470241216, 175428494, 51094895, 484784331, 582340234, 303779654, 539041566, 89696018, 934466981, 120055825, 12472278, 95974203, 538305399, 301133130, 342058310, 215505180, 100097868, 452011061, 589988288, 235762051, 148255284, 913780375, 235748436, 108972995, 694875884, 146683492, 724605667, 511994387, 151947308, 679572546, 559252888, 554738802, 397773886, 213673910, 90484235, 608198699, 800538916, 25494605, 987689372, 582018820, 622897459, 93359731, 803086006, 388932238, 778775610, 266409933, 385007911, 725387262, 677661019, 45021562, 886590748, 107543933, 425521150, 165179599, 538549005, 782239645, 997386459, 353802959, 860003613, 986585613, 190219452, 485611272, 162964090, 918166240, 99858231, 502418042, 694274014, 722533920, 226551552, 498816915, 63660816, 914420531, 789346814, 156402808, 108593969, 298848832, 20234759, 971500272, 524871562, 239040652, 497244473, 800564540, 53850358, 532714579, 534677703, 252703396, 947739479, 429117151, 494100442, 383006575, 585526520, 871705913, 538357144, 122684885, 698013164, 660700874, 769055901, 170337689, 150889263, 686093291, 62092802, 470773619, 493327870, 512678987, 406879477, 527110886, 580687486, 616436115, 809793480, 769489177, 898667400, 563688929, 875499064, 319864725, 783245226, 919743451, 579779224, 982632868, 694413891, 262268221, 22098326, 147439307, 866614901, 969166303, 255911400, 689600392, 177125040, 652485788, 122809412, 491338610, 59471286, 828347945, 27188576, 770455086, 913140292, 245780833, 50258931, 170836554, 734622777, 727649907, 974304312, 943616255, 720390702, 682246254, 577916763, 565803454, 339208673, 397080188, 384569181, 639256830, 982208535, 970596943, 306584969, 496521148, 994132839, 406223249, 193671029, 472890228, 190806505, 641480797, 432529222, 966435282, 220641714, 773331794, 389729234, 837096805, 247100018, 379962803, 362910880, 996925717, 69535456, 937707744, 494475997, 232688307, 310036248, 331289800, 559772519, 529069723, 303265489, 805657133, 466764423, 882422839, 442841695, 842985591, 924698283, 985030797, 864349144, 170346441, 974989490, 823568187, 784154451, 123425015, 503420046, 339161257, 998350916, 696242425, 820072598, 356274006, 935731313, 484745978, 111983662, 786174908, 328298431, 239589675, 48102001, 494248942, 547915278, 121965464, 541700172, 410775149, 300543678, 51422762, 243328447, 738944949, 683263384, 89043977, 641379708, 786489524, 79970183, 106424729, 100203079, 805242369, 561637482, 526503541, 410374396, 565039369, 571577501, 738990109, 648277688, 971825996, 319621788, 425362484, 356106170, 656106429, 881487097, 393340006, 613417413, 1365018, 451825106, 784999621, 335475759, 374705313, 520301550, 283567379, 307490882, 100960473, 918021708, 379743507, 498113269, 896733690, 165467187, 411591317, 590954153, 792258438, 362223107, 593231493, 304014714, 667722298, 541188018, 139086780, 424417979, 707035708, 271576905, 246586625, 528899870, 804070075, 200575435, 233524187, 209712342, 630747972, 135828651, 23870199, 906417545, 971347279, 811737122, 19278995, 48684313, 852297903, 452766613, 112866662, 844099230, 798154748, 911807600, 376434607, 996058715, 200454806, 427044018, 376894776, 257639433, 685201355, 903080704, 711661560, 394942602, 713243143, 341925250, 457729703, 996282096, 213991545, 53298000, 887126098, 463070418, 78551199, 655087389, 696312848, 588220517, 28783957, 189393551, 697988084, 352658747, 277930614, 343197792, 901183483, 606976517, 969050570, 424561930, 349134676, 902786821, 799170322, 360656567, 561254046, 530282192, 279989048, 46800517, 84754770, 396232365, 736273668, 887363464, 903173857, 968066919, 106843615, 930260220, 489355675, 529666326, 80816320, 63281335, 385910166, 240396948, 779285790, 576394807, 690558007, 369201819, 109252081, 275886704, 987549595, 547805808, 274373585, 414655556, 515614669, 929839491, 492493650, 871716094, 731374413, 322305814, 410240195, 473262031, 459173979, 213767905, 631194868, 176680149, 645640887, 333245443, 460636987, 768568393, 323380013, 830718675, 314336922, 246687591, 283578092, 711106898, 632425773, 590343196, 996331435, 414744446, 273819401, 801013803, 133229142, 49650759, 693287451, 292155564, 842713196, 347051044, 333004307, 622427385, 236790653, 133298038, 527956115, 316719184, 107213097, 688077228, 354748342, 479963800, 578697768, 495252092, 546894996, 87306067, 144417224, 472575742, 10972800, 41080318, 637831038, 779948688, 114357036, 623018583, 506382409, 613857283, 327961045, 352420335, 37263146, 599724501, 503135970, 456938229, 779082736, 192011533, 833540940, 321678148, 414043286, 882462818, 492070937, 205878149, 178613009, 598962155, 975784782, 386400658, 289641371, 31401613, 508706047, 637643808, 364919533, 46540761, 302654350, 32251120, 569624946, 453957438, 74309089, 992149926, 933507546, 835468945, 209262469, 634678030, 776117867, 399610532, 606204177, 207805876, 16621583, 273304711, 923242457, 438558060, 338344703, 540789533, 924924399, 648444904, 227811875, 15187646, 947058080, 562882157, 12274713, 381903282, 669940695, 323439110, 628095002, 208254539, 710579927, 758725245, 350710659, 495499426, 187122796, 626915024, 967591252, 180744228, 319070595, 905602641, 178876784, 945255847, 787835702, 304629129, 819903952, 991445728, 764953910, 500755575, 653589162, 394395691, 421635851, 26374522, 628970899, 663611690, 453535993, 288916231, 164409404, 310425686, 505782542, 63505333, 532802078, 75356627, 436764496, 858431026, 121880370, 287088309, 312643278, 991570893, 620792525, 64854837, 671922489, 170256170, 187882414, 773504676, 592014869, 561376888, 34074822, 641453727, 374375958, 483285562, 484623747, 341776599, 893591798, 870849404, 376479994, 321120823, 302310724, 29818060, 286821701, 875512298, 266605607, 148374047, 15990550, 116858430, 545027049, 526343363, 971356414, 9830688, 160795912, 342217087, 27801844, 723283393, 162397065, 461438468, 559323085, 362995381, 795802390, 157556638, 882622634, 528097557, 475216580, 537653062, 579438501, 561170634, 569274537, 959417725, 925415290, 763352169, 701128236, 872345470, 364246852, 396579415, 54609358, 40151259, 459784328, 990707951, 111130375, 842284213, 861976765, 504713819, 937743123, 780296117, 454187924, 161192782, 887818332, 963694867, 876840926, 626778927, 267872210, 591235314, 915337489, 931281134, 214606024, 613159864, 317141402, 423244652, 602921942, 75225830, 410697715, 223899038, 370458489, 491233270, 132061955, 971748541, 977818802, 542285861, 59178521, 781045357, 107656082, 736432296, 942839397, 617782424, 471522995, 416741990, 546191923, 271376745, 331558466, 518266977, 104394715, 530861067, 912259861, 122561113, 111165178, 794182959, 772203221, 635284353, 58349437, 93642969, 965411864, 821595764, 522093798, 433990170, 457075690, 225604253, 277678816, 809094067, 880702086, 44584706, 679649700, 145090485, 235179673, 419424588, 159781023, 366790679, 476872393, 136454121, 713249058, 240707883, 23238373, 257943274, 12976863, 450891486, 448839905, 623030872, 27909158, 597044533, 165754452, 237906834, 14050416, 217868666, 915445655, 419072731, 813567757, 260552908, 248008817, 369987779, 548198300, 14002841, 508472583, 552064992, 64876199, 931828879, 816202287, 165765011, 328902321, 773285655, 725564340, 343484855, 61833003, 880273507, 53676137, 73744464, 689280012, 916284736, 129645501, 27824368, 829117871, 991663767, 974037666, 222679829, 134053984, 981915334, 354575775, 281877873, 110036933, 848029883, 129925776, 815951770, 683306457, 818104604, 634642283, 807875899, 800511021, 216945471, 458399388, 414910891, 554834405, 908274077, 968784463, 607350220, 991561107, 800574123, 997197216, 603650501, 643531074, 448013185, 800448617, 945222424, 913946405, 728731070, 500747678, 427407152, 552172867, 192149937, 222928231, 412703945, 207781385, 33793039, 466092544, 404457417, 881981617, 239680184, 726152427, 507001402, 777001448, 404019052, 748780453, 213546111, 870645165, 891323898, 747924542, 840106491, 64104893, 410037862, 834207225, 68719897, 68123487, 793443633, 505523335, 749629934, 100718124, 399002877, 622555185, 913603289, 294269221, 531717366, 217092418, 369389658, 744054552, 949673066, 700454394, 311273192, 67027350, 644976791, 586899945, 420579079, 707117794, 549837661, 568162891, 414534996, 397557397, 554472977, 574591135, 909245283, 715348468, 506828736, 93999898, 720244868, 295665870, 950566120, 200645000, 149044421, 195246915, 163095185, 320291362, 237328651, 714811282, 171282032, 564233910, 341022142, 423735523, 796815601, 482526923, 110574500, 746762692, 552501444, 64024905, 160193683, 819450812, 597879941, 815034761, 317165663, 875813246, 99794486, 700959749, 433130719, 211435, 924213844, 92276983, 663768463, 87419416, 557956493, 798289428, 226657322, 104874048, 656722665, 104437625, 783741009, 495781786, 935596729, 64087071, 644927058, 816972515, 400125792, 323172190, 456307032, 238669616, 804393186, 735616859, 434187125, 279143518, 983807016, 180004228, 440768574, 395870986, 118366938, 48744737, 899298775, 441475030, 594530722, 500024468, 706085729, 213958144, 602600727, 928265584, 950892236, 609855671, 21350810, 696311707, 842829011, 635406614, 748030386, 206241956, 256056456, 288995561, 609939357, 319831788, 273047244, 956551217, 333004732, 263293763, 988769420, 736352291, 722589612, 325445999, 721873117, 863933757, 542978622, 963789852, 277294393, 663051585, 38619418, 299362002, 731974806, 162780892, 582334612, 642385055, 543451053, 358396149, 663693588, 713531349, 913316840, 155744443, 546415698, 573072956, 516836229, 170282801, 825080193, 66611314, 417544976, 701056926, 891456233, 665272888, 977859501, 103084787, 332439036, 513748493, 592445881, 292434013, 989930534, 470253536, 563755822, 495454779, 557312807, 465975274, 301865497, 92822857, 239200835, 697721794, 970032689, 84138317, 670475898, 466670279, 103765756, 815297202, 869023827, 661760814, 639135781, 945259403, 562347497, 16578543, 568980967, 434499107, 702068805, 286091179, 648465221, 468775520, 500810475, 603585890, 684795935, 758944291, 338304784, 234609920, 996620110, 471358187, 453849562, 72522282, 377286382, 289005512, 579387461, 196898967, 837910087, 397079285, 891334408, 861720960, 177827866, 922943927, 541296423, 751168696, 726352372, 363673138, 859827474, 289309558, 972046480, 243436682, 542244911, 472752117, 259653758, 669855606, 799161649, 626416147, 178114551, 100231781, 448772734, 312739023, 241434989, 63161027, 244241151, 802554248, 561793367, 639466931, 293255498, 498331408, 540298945, 125392018, 276744997, 799836567, 461425793, 485140509, 640828011, 603795864, 435988824, 80791255, 446463655, 467007980, 997933353, 731207870, 385224508, 433187833, 196775043, 620330795, 885362066, 133438012, 799406316, 416693290, 321713264, 720656034, 812870516, 134909913, 110632514, 444313409, 399444887, 621029320, 885296255, 966384264, 121668346, 81499569, 757127379, 371131269, 662351599, 653561026, 789254342, 84888915, 63827446, 517901764, 319628108, 635161611, 141056899, 387903320, 218733845, 183750506, 464435659, 670351431, 576900596, 352767785, 685887142, 794865402, 890923450, 284828750, 548371748, 512013407, 257596047, 316132575, 304560554, 685542950, 377863511, 609766058, 734905564, 764728317, 563711088, 171931007, 804374138, 825073258, 57989380, 245813700, 135062291, 776157994, 737917867, 411387679, 570735955, 743676329, 6868685, 230357068, 203235020, 393705907, 373520569, 592602647, 174332700, 268853549, 331125079, 556790735, 810925519, 284200229, 824573441, 694147693, 265570560, 859200530, 420235009, 54133997, 615714560, 335204442, 561549122, 122271034, 36948340, 981538730, 886930686, 103466625, 837725059, 266108813, 138827645, 855889231, 769281171, 518968544, 72541250, 194190452, 972731881, 637006807, 613534208, 391718076, 267034926, 662855502, 138893705, 32254657, 296686537, 667329486, 676822324, 411753784, 7441395, 69717145, 188946335, 858666884, 732652396, 461165538, 62598248, 668948940, 269330043, 41492521, 818686788, 191990527, 859147938, 911547932, 830351414, 571138185, 473971452, 931095324, 278219969, 487717959, 88774386, 552988103, 866308434, 108578359, 890796927, 994299738, 838295681, 434101761, 41796569, 469036180, 294725377, 14838445, 239374213, 779595672, 393753256, 994086387, 823595792, 453139507, 158341349, 260122219, 510564777, 827516434, 25440339, 833262511, 433004880, 2139491, 71786269, 713838678, 785947301, 306900351, 19084686, 568800153, 6858436, 863603672, 500829015, 391793727, 138968297, 16643425, 814949032, 641945106, 672453613, 334427962, 866759049, 104502681, 324908302, 198968053, 119958981, 197556733, 94778414, 852982358, 377479014, 439378645, 268312171, 852604021, 648903432, 132488610, 253692382, 233432315, 60539181, 444701800, 702129684, 584034359, 818931428, 165193307, 516097226, 766933817, 37990650, 287802038, 548099797, 424015461, 117215995, 810106825, 227367543, 912361678, 540060856, 558782601, 827807536, 560787201, 872012795, 826186811, 921831165, 584634285, 124005522, 191665120, 338136749, 20268687, 536668930, 419234490, 45939781, 757677608, 66672842, 712194897, 149401726, 971224200, 13092556, 642464565, 314320703, 463255612, 671679314, 848926674, 243069944, 690003326, 558359496, 255247407, 827276450, 915073836, 258002946, 573886167, 244233992, 415166920, 419452632, 660950658, 902791764, 82284644, 395899152, 523519316, 973741359, 815504432, 59782550, 533418385, 1251395, 508380780, 380057560, 549039226, 643898981, 812149991, 345499204, 491909982, 279781898, 932941211, 284758037, 549025752, 459555969, 781488407, 694578063, 547970454, 179824253, 791867771, 293434610, 746322207, 504133310, 62818515, 87246601, 921289398, 876282823, 750018008, 544892387, 23540960, 959328069, 482399119, 261385741, 895836503, 843325635, 4685646, 714839560, 258161522, 188917401, 212440850, 760514736, 877273293, 177293925, 416703006, 626708886, 361407905, 653710421, 636396167, 394244591, 576494306, 376110167, 625022134, 247405677, 317776296, 839902457, 565032756, 376186806, 661173133, 372523492, 858547853, 463736336, 527924399, 856034981, 660547262, 51295878, 653282473, 211027303, 653486996, 118762734, 278366354, 434588490, 663094769, 354036611, 319189467, 777647032, 546985556, 923866098, 133289912, 16843169, 194230787, 927797276, 34863099, 542069400, 912712959, 691604089, 193677773, 3070899, 453204454, 909405621, 56729589, 296402603, 616490093, 685204698, 26737933, 465412057, 897311482, 735028691, 754740988, 687255532, 193959819, 657233654, 430690021, 989165408, 450552439, 926085155, 362360226, 668705635, 554233788, 106970109, 598618845, 198116848, 839749812, 83862547, 535983033, 468390971, 507681504, 521921754, 749584834, 569260720, 350043747, 121655713, 546810934, 337875694, 332058996, 665501798, 329009420, 915802547, 384329418, 128978291, 303316074, 469032571, 973750783, 863379370, 627767295, 948541691, 295278841, 148933274, 407288554, 656810449, 470639665, 283931986, 471610570, 456109300, 967664068, 986645332, 52970024, 629565980, 900736012, 110838623, 86877155, 394081228, 794399078, 423966136, 451635675, 463641944, 222227837, 590519035, 576016989, 826400142, 511564669, 143760636, 250605103, 375244503, 427421180, 863105805, 102779337, 489936009, 568049159, 581289199, 375417946, 277214404, 129473512, 526253548, 310302247, 785368072, 879671220, 345332048, 949599530, 538223291, 347293296, 692120834, 75081099, 485318061, 333554257, 627098412, 817701385, 56567247, 183960887, 594567679, 791800307, 330331640, 237844218, 609966598, 434378386, 957307303, 384808882, 274805106, 544625277, 708514979, 281053525, 775864265, 453994000, 927500475, 955692170, 477894701, 364789276, 154572810, 937966656, 130474746, 649350816, 57672337, 914055384, 56131220, 98153226, 755544501, 70176208, 910863771, 199073996, 963708438, 720099016, 723691354, 4849957, 422705611, 321859930, 401388830, 814417116, 47354924, 54381608, 552397649, 589006850, 448024282, 762851039, 582901932, 823356980, 535118040, 402758620, 564030780, 626631862, 589127092, 427950439, 417302641, 530391785, 164712630, 397750015, 437755615, 530249905, 859445055, 782261212, 160773396, 273650314, 252702982, 357669085, 961557717, 316116301, 165416305, 628643489, 714250739, 229707096, 23877176, 805653257, 711131965, 606319714, 824765522, 938572564, 213558620, 956151786, 869887554, 872405985, 944707258, 211714109, 338040121, 995260480, 795910222, 865381912, 840243746, 696673419, 850125536, 818729824, 503103204, 303166903, 267941084, 613409439, 185018420, 582760067, 126969797, 437285541, 593308487, 753318968, 203603624, 677799966, 926712419, 596031294, 490288864, 407807260, 616176353, 168589355, 620895606, 11304227, 786118087, 198076634, 26373692, 552924395, 428890733, 423244956, 665866174, 393059691, 126375166, 780870509, 749049581, 271217816, 46372211, 495322490, 503305276, 643122082, 368567782, 843600264, 746904051, 422173472, 539889259, 568475802, 973176755, 809475321, 494604408, 638177118, 874676230, 841859510, 608820637, 268522000, 409906128, 395816333, 998012431, 214781277, 939200208, 497490279, 642740935, 199474970, 685543364, 635872235, 885396423, 292312088, 768768437, 610235426, 307128181, 933570580, 845482624, 82581981, 214314445, 31351475, 207193329, 180437619, 143321669, 704650200, 175502344, 495824784, 992468116, 478259870, 664620379, 926559541, 858945435, 777353034, 437616481, 609001048, 390500514, 940081576, 495747001, 339426314, 392220801, 862157421, 210868296, 37697811, 206004304, 655621237, 125736699, 623132746, 211100440, 329283838, 6009824, 802167687, 467364360, 754693574, 593687250, 926841101, 319941531, 816403255, 905062660, 196713265, 777480824, 489308630, 184198140, 687785476, 249795212, 705549579, 538565008, 701317777, 321264655, 998628076, 576619929, 461138398, 800514801, 506194968, 381106746, 622395493, 49555410, 680783620, 871410777, 805412973, 648870192, 898347914, 851621214, 270772152, 859233042, 485749128, 317913672, 830780092, 443341037, 104718845, 819321115, 501280254, 909719131, 360467645, 311564122, 789198206, 910260892, 829171696, 702462711, 697231244, 1617448, 55000551, 960637161, 165943446, 191795463, 490625645, 768353728, 596525069, 361599021, 985121812, 281412368, 220490810, 237149756, 282290901, 517379325, 351625997, 861229787, 414597895, 486516466, 398713349, 55757801, 50186060, 464112154, 793742146, 23300062, 81281415, 516983106, 900148251, 65736881, 480579819, 128831471, 741916603, 98393060, 643681207, 589490264, 633883220, 293060504, 360071086, 545390907, 350254285, 120098657, 981456203, 37402407, 768471415, 689134599, 188525531, 794798038, 899659274, 584641771, 278374071, 488872000, 794693656, 31251883, 101155825, 921464732, 13221702, 655842202, 53223964, 180388163, 801200102, 456006422, 109010219, 700882245, 943565111, 710728909, 773946100, 703631415, 349382847, 63307555, 816533329, 819475384, 122446190, 373115519, 364034875, 60364384, 987429681, 798195776, 586197091, 876047035, 908298863, 389560058, 608659319, 77413762, 735318985, 491416664, 451190791, 187896098, 244329857, 354576597, 200569340, 420686313, 768511595, 301476035, 675527439, 701991559, 306272323, 93912839, 798160724, 497187098, 882448714, 248130284, 307271287, 103304477, 937766097, 785578527, 271212895, 193477148, 972367283, 17107655, 445610099, 623078945, 582480724, 948832409, 1282331, 553469560, 967259272, 964421919, 303275072, 404068160, 525012359, 387420994, 834041945, 962918562, 354482995, 232021445, 202869996, 514106897, 879388331, 860380568, 298061207, 318820690, 960613466, 579170485, 470644403, 992804601, 136486104, 997911893, 753726469, 612427456, 105306659, 23760455, 312554010, 174928031, 614627329, 278039071, 651493342, 356056078, 254792264, 619175783, 831699830, 670046659, 167299465, 453728711, 324649818, 653560134, 444300958, 864058944, 201657143, 317913227, 669781762, 337183685, 916354518, 130565391, 342437041, 488283848, 647768280, 990336532, 104239745, 668639765, 4213105, 884430084, 672251132, 932895974, 759570594, 794422038, 163385338, 304864318, 375994259, 233778160, 99454126, 611941671, 998039227, 50201175, 992056068, 938746561, 625522843, 258481999, 521990310, 6655441, 146202545, 211811834, 882821116, 755507937, 400469582, 538958519, 298317559, 685833945, 837998168, 555269192, 339679519, 250606629, 743887955, 561068599, 756153061, 473660044, 684943373, 348021292, 962884545, 198224977, 535389167, 828650373, 792111876, 61044528, 518043592, 315280266, 303098902, 364588491, 401521131, 228125843, 267291886, 700690178, 207406991, 815009891, 574830268, 329439692, 279050466, 749701414, 242171430, 58759662, 556137984, 462111765, 513484465, 296674834, 596839910, 893848798, 367695884, 555666546, 409179876, 210971649, 183859561, 448585219, 971596683, 773821484, 888958586, 211516435, 495318895, 107529339, 995648207, 532482731, 683471453, 508008499, 725523507, 719960491, 310702353, 617535502, 189049307, 359645760, 651273875, 84229711, 773669050, 407577677, 285870533, 33001139, 235318186, 47261206, 24473876, 576273207, 533478356, 486887231, 661334683, 880972965, 863299917, 533948266, 117167592, 902657431, 173896301, 712702819, 314815872, 467611301, 547473500, 912356043, 336471522, 752669176, 301203353, 681530479, 631814567, 913028154, 740064368, 231701595, 510847048, 508410458, 599338012, 983749520, 772368266, 304540154, 243457915, 484968922, 929756510, 400899628, 414207471, 582064480, 219351966, 388183527, 960599944, 20221691, 958866576, 590437262, 787352013, 527518469, 970272800, 188161236, 353258771, 304996404, 630143483, 757388197, 242672389, 324468224, 814451191, 827938206, 263864367, 978967714, 447896310, 387988229, 790347118, 338528449, 348968143, 117115949, 451947063, 863847220, 579042844, 818335831, 814725711, 75873670, 220871505, 638913608, 615800660, 712130449, 298170237, 201900998, 140793747, 661406661, 158285267, 691872466, 654700787, 211276152, 613617534, 697809927, 97155624, 581858126, 127202891, 599879912, 549226715, 868505123, 113679422, 348346346, 37734937, 860348874, 943977925, 388992888, 404977192, 767151830, 345938956, 282661282, 902705822, 427744848, 263550088, 256140430, 206858150, 863500470, 244639549, 894421384, 292787126, 351171184, 49444425, 761883046, 189706281, 17224848, 92568621, 639268508, 510649436, 438803814, 770371187, 914797250, 543467015, 335596202, 182364244, 932503286, 116064358, 677005214, 304784691, 553822500, 214431154, 207563285, 544494825, 191745589, 846165479, 26110445, 542174802, 203307466, 665686763, 413014728, 746138249, 875300061, 613840355, 114700804, 555935108, 431046990, 298041616, 468848780, 731406858, 531831873, 941340004, 487361893, 782667472, 908579248, 371221170, 708459755, 164123741, 737875068, 228164034, 207026526, 882082566, 179760829, 405433832, 707909701, 116471384, 659772522, 315407673, 62677321, 473570055, 414263593, 800026663, 349037471, 409294186, 462000276, 97843197, 639647848, 781983, 650430774, 729723719, 712634709, 601224598, 568834191, 746464542, 156076263, 334253148, 798320058, 425158058, 927596186, 940002779, 932810139, 421519723, 649837922, 995225083, 542890935, 798885209, 287067240, 714480977, 429652747, 175513334, 242178861, 513902074, 236012421, 122204323, 322500600, 899653343, 657924984, 879549775, 672243495, 418275352, 68573530, 625090259, 324621962, 306257713, 485884974, 390023960, 350668489, 916187464, 758441430, 193521921, 862889007, 901979143, 339851174, 421036781, 993329064, 341041644, 985462770, 238141866, 436582020, 640131928, 535710759, 456720452, 323477821, 745640149, 455136075, 849606456, 802343976, 197425233, 180826444, 445269420, 23379204, 109909922, 582272275, 549439304, 357994414, 362341736, 368008388, 991368357, 576319203, 160792252, 260256293, 471926711, 961389342, 151296238, 175877359, 480448015, 841794545, 307476135, 744142219, 351931303, 421682477, 33729417, 881824209, 721896514, 774560324, 489592911, 741131162, 314993968, 488389182, 29469937, 821800858, 661119685, 989258671, 622880421, 611427481, 919602243, 657278096, 828427725, 182918348, 800452634, 376547051, 728986609, 97000894, 926886686, 436011344, 316865868, 291704994, 835238326, 744467965, 786920567, 850589430, 676278752, 298105727, 325217016, 283825783, 728333465, 597581680, 550995507, 305202844, 71366970, 596939568, 592475376, 887789447, 497602218, 342850025, 795678236, 631673542, 792355280, 290476790, 243757293, 131069919, 170727184, 469036549, 856272919, 224125821, 851529386, 957376369, 809467585, 521754029, 907477472, 953546040, 843968547, 79885340, 205334580, 571949895, 926748818, 233294349, 207542163, 379654532, 944550560, 185319579, 696757566, 673082165, 467409045, 651442220, 750681115, 630753629, 592714565, 67462188, 752088871, 43841727, 701774313, 277868872, 706370622, 745404562, 744571823, 674315030, 89573566, 796855050, 911487822, 54302169, 67206484, 166501307, 430982081, 288812249, 580797316, 15279707, 556901740, 620443189, 156536163, 281261367, 261594970, 616482363, 35492391, 150013980, 976933026, 517893140, 507766198, 622321035, 420551083, 396323837, 187148939, 4024634, 893493355, 553211823, 248086665, 599684586, 276387584, 501187166, 186156529, 301941876, 64315555, 167295361, 706927831, 155195957, 114256412, 486438231, 426583403, 104838416, 912512460, 443496709, 190147971, 103474598, 897059074, 193715817, 324033986, 824500188, 198148716, 470788664, 104674287, 423375960, 282213139, 41443411, 200417486, 634822685, 358679751, 236093074, 969601282, 67889172, 899382409, 764346355, 511405482, 838714106, 921829959, 374738063, 982370508, 27320958, 400228407, 515939223, 712052487, 612509222, 115470575, 255976451, 885967514, 697406324, 776173998, 680743263, 938539503, 445448333, 425835266, 68978369, 346805697, 6226378, 994704521, 162362871, 921333539, 375240064, 653847776, 64128698, 558895490, 995373223, 940782375, 130098044, 240766488, 362758600, 477472313, 722995887, 802460334, 693097400, 984038794, 852754575, 713081644, 33435678, 202933907, 315701316, 830288175, 230563297, 552420545, 772053026, 489848835, 663412839, 893735836, 902205940, 894605876, 604745383, 533656300, 552436123, 19856519, 141816939, 875185469, 518666090, 74741358, 480674858, 71506003, 586907982, 132803862, 995783708, 610673731, 404564369, 333039584, 315279881, 718618407, 971445799, 451555195, 161178016, 363886073, 284743942, 866771801, 262182813, 618447906, 822433493, 80772587, 393738677, 941644865, 57263169, 533096533, 510307234, 460129501, 76348903, 297024370, 489200883, 955274048, 562403028, 386094784, 636176118, 540514478, 264988939, 532285943, 930158788, 904717478, 432816621, 839542081, 568569141, 82163926, 675450076, 498907476, 883584006, 291505597, 631829501, 504942662, 34948118, 755341917, 282480263, 530782003, 638334003, 705266390, 931583576, 965936136, 926119079, 622415733, 422162861, 377188165, 942156378, 276765508, 706424769, 466530231, 864535085, 128911977, 236877201, 247793400, 299179268, 665936294, 175567029, 469808561, 561411061, 893329112, 594511624, 240259757, 546499285, 838349142, 880645600, 25567620, 890385105, 7001416, 235086894, 719487018, 323673644, 52969847, 864086125, 320484122, 981648248, 817547279, 459962845, 986275137, 738210501, 425269259, 280524508, 846524045, 604864902, 439430053, 308818173, 777714188, 203817798, 804232746, 58808640, 806019895, 874958617, 111492162, 475799718, 592908537, 688222334, 704967879, 779406570, 501221846, 79906625, 201876347, 995120550, 816563427, 447562312, 432195635, 694353449, 760707939, 501589977, 833404396, 479106273, 940527761, 579260066, 798296942, 283685116, 97179908, 34778812, 361633649, 433301822, 860514639, 510824401, 656876841, 330790611, 466045581, 942117222, 142679939, 327237600, 351361171, 430652057, 303638943, 245390952, 872141397, 931926380, 791542125, 275836305, 302326223, 834569020, 725557193, 42896220, 711909656, 847737235, 381833109, 271133386, 346600526, 932330444, 92072774, 635337952, 504730286, 4925159, 692001389, 962018398, 107614683, 19581604, 473944731, 880825175, 759832661, 218664549, 910684154, 960964494, 988171187, 47340168, 365487548, 158123208, 614332102, 986033673, 411716575, 936327153, 629827, 829387294, 958558551, 596826419, 185086624, 83438908, 811122015, 508228388, 476063402, 903915958, 148871450, 689215688, 477817824, 509974404, 109283686, 426212007, 691198523, 965885673, 86602206, 950184294, 164457441, 170955583, 167550002, 864753205, 751686591, 760850752, 468635656, 930585760, 680265557, 642651364, 436390210, 245953471, 311584052, 425190142, 887619313, 557686572, 325142151, 809939833, 809766104, 911549181, 960810229, 314249341, 72504849, 620322767, 681035641, 78028366, 16692181, 766988842, 387669198, 339602917, 114528275, 559410255, 31417532, 145589910, 597290814, 224380982, 468135148, 95748264, 80272745, 64493726, 586486819, 735506092, 624827877, 914523875, 574908558, 756306871, 745635517, 666027849, 926815212, 698744283, 890504725, 442683752, 630358746, 573854877, 831030647, 534596893, 838878921, 633962010, 75969391, 548521955, 866509855, 753917031, 896417452, 919323131, 673051605, 949231325, 888677066, 958734054, 559294914, 659014825, 188770383, 268584185, 162922861, 277450567, 664941375, 543583959, 914762996, 775702795, 197896874, 114282341, 691423683, 699996273, 592554151, 719852885, 978224325, 544351885, 158704263, 799285158, 612630892, 924512884, 550794095, 523898983, 817358885, 523157254, 136312938, 323885203, 104835920, 27708248, 851385317, 774241614, 260287391, 380317143, 721248175, 957400825, 680321911, 406728271, 991551219, 531450178, 32468206, 30102183, 275985480, 781575737, 651465343, 263197583, 685358816, 380384986, 425594997, 517594469, 898833123, 37665365, 912288465, 199723434, 283383696, 202280966, 870556625, 509203162, 274589932, 100469364, 345943633, 826814791, 258076153, 274475079, 672845101, 986141839, 430045135, 692992055, 613615700, 987800154, 479119479, 405996869, 309996000, 864049217, 372113679, 733876330, 348939199, 265658887, 214063702, 534207461, 892827969, 864958820, 86490314, 389916089, 370213912, 747914072, 882989630, 430808580, 83892637, 623029131, 662142714, 469347310, 41518523, 692953132, 993093606, 894841376, 940653117, 32302946, 973609670, 769539267, 593964143, 148048268, 326790154, 825429197, 458952225, 926702356, 724416094, 736027279, 557529443, 474476262, 167293425, 261120186, 472419753, 948855669, 909050485, 534839501, 980812922, 497665728, 340262971, 82015307, 737647406, 591804786, 803334981, 548196847, 939488229, 196786096, 960214506, 832134025, 875545902, 200586564, 713855138, 435475963, 147075324, 556753385, 218125961, 588455255, 681853419, 229137715, 215655198, 840760950, 295649362, 177426369, 505286071, 991451523, 209444968, 29045700, 394511712, 378084939, 631995003, 929854989, 267704795, 476242977, 165303754, 450223634, 914443370, 488810903, 487772800, 588549290, 650744138, 423842969, 545550477, 485408756, 76668728, 478754899, 895820894, 558604818, 97784475, 611549533, 339398516, 714906993, 690870132, 155150288, 739003853, 160207107, 51583478, 584872075, 666374935, 202657545, 227529783, 736179596, 616954800, 672009928, 610201985, 509361027, 671716020, 74936913, 904136206, 790255674, 625647163, 458815167, 193651707, 789790170, 953658495, 580658450, 227459067, 231167738, 581001030, 970581403, 570492465, 360696131, 932572211, 83849060, 793547845, 404963337, 875773982, 220452482, 775984497, 174198484, 300984808, 400535982, 986439064, 498671642, 776707521, 690898680, 59620405, 327305015, 254127508, 808578038, 19573745, 921767666, 656135945, 284003676, 59369156, 47136898, 287889715, 113548769, 705853488, 109072616, 55158118, 21651567, 649085841, 368227018, 224786040, 699674140, 940502263, 729427378, 595234007, 324956659, 510169760, 572053013, 691471015, 650934229, 792401435, 557969394, 237916488, 322591331, 388287840, 956447844, 512857627, 354326916, 401081649, 492013308, 588532110, 966902678, 187723943, 266702603, 332828965, 688680027, 866281666, 93320337, 638610764, 76518223, 568542523, 716726120, 719573930, 398497993, 563309653, 73622998, 401036524, 810636190, 498115266, 488349486, 768093511, 711415257, 34319662, 628069266, 421831376, 900638805, 201424308, 664799835, 317165127, 74678889, 930974725, 237768103, 34251782, 33836289, 614003306, 984118136, 60136385, 346249261, 948681994, 669604496, 819501113, 230775233, 549580252, 240750610, 79199046, 210989032, 298930648, 905981817, 785471465, 970162048, 503687547, 957767401, 944164086, 769826546, 820873754, 655932953, 943643098, 331423759, 287221274, 556219420, 141983788, 875182614, 224385595, 645563617, 375118493, 128886995, 790501249, 399787373, 15950820, 551374492, 188899463, 530045887, 748356867, 594980485, 44748219, 319561419, 406997600, 510938597, 482297340, 939933982, 877653617, 822843485, 535305827, 111881698, 224507671, 897024053, 385734639, 440141673, 898175505, 941294163, 540342846, 865855254, 501782902, 403972434, 962302047, 641303258, 151089599, 414484453, 688792777, 266213404, 163934709, 904081320, 986394307, 473869720, 213523360, 958228073, 276850419, 515010915, 900366760, 405434966, 52859262, 77839012, 620827138, 581305688, 936920020, 614495249, 396306207, 915255890, 383174052, 611398467, 375065293, 723579978, 616288180, 622443942, 488167107, 502256931, 289989537, 267850524, 364110798, 5987281, 647655462, 399613643, 625981868, 240241977, 550672788, 71035538, 368957663, 959115085, 130001035, 758477276, 424789157, 539008287, 682610276, 284530732, 224028630, 859693093, 78168444, 309012481, 486696051, 42081229, 433601202, 547039224, 660755926, 318443591, 700209854, 899862623, 161982175, 190757750, 770959834, 822033661, 109410010, 576851244, 820639642, 129371775, 312297841, 312041663, 728779557, 998550191, 744357725, 312554232, 717383768, 217452821, 664284266, 708123791, 53782920, 834168543, 692536660, 752307306, 598977937, 693019547, 427191065, 672193748, 980359132, 779203966, 797517604, 132006645, 692093012, 930023814, 249199390, 58365076, 57881861, 867062989, 172142635, 33390407, 770416963, 90694416, 144925681, 985716882, 894492107, 962593512, 343728040, 742049439, 694854628, 735471553, 552138393, 557349120, 478407878, 408642762, 490677782, 689765973, 937286782, 61672570, 219788359, 683568401, 2634711, 564478147, 148695792, 908676336, 414602089, 918447597, 739529280, 818083356, 108265072, 514308356, 687460838, 946945004, 738789690, 833828981, 348088032, 258214040, 978850827, 376700119, 50509980, 749505509, 618500407, 515453089, 353375837, 586570875, 508987795, 723810027, 234301737, 579656159, 505802201, 90249818, 472000139, 768622174, 919817611, 717718402, 370958115, 250764128, 255327658, 84586446, 974216077, 473783564, 598397895, 211453055, 124476164, 904749127, 732391880, 946458091, 63614999, 199670340, 951090865, 510436802, 283933709, 471628110, 590693, 327146676, 624221719, 708560050, 250345476, 626366146, 985717841, 77203053, 572263706, 868353726, 336002978, 902507279, 584477055, 791096966, 873743447, 608176812, 334374869, 142949374, 105907077, 586726491, 63854350, 263341337, 71875837, 749966668, 183444516, 551814506, 208084341, 239240204, 665871230, 128674411, 203853359, 590253518, 793483046, 640585464, 228095544, 272636197, 817405515, 717870789, 649077233, 922006248, 877097595, 214596448, 341224548, 14177478, 838031044, 27933258, 177471971, 428100243, 917198829, 501285849, 652972089, 113140618, 663405232, 396630306, 107158195, 73542592, 55395715, 676199317, 44262713, 393341004, 377281654, 281575401, 803054923, 183095151, 321952875, 934134792, 31454734, 987301963, 547380193, 710510895, 589749026, 186863585, 807558205, 90776018, 267383195, 859366465, 130290120, 64160690, 539896732, 737457935, 193432161, 34209883, 983001487, 780008471, 324917525, 26264199, 480856937, 487085816, 126995123, 85622895, 439913830, 309380249, 934772247, 813298179, 636462832, 715951970, 981790447, 866535613, 212899715, 781552449, 80506735, 658741534, 964522401, 31827489, 395466689, 61250243, 401456545, 659984161, 676560221, 93289112, 93527062, 516796907, 888497754, 35106892, 522410552, 824134360, 942065717, 967599580, 242757469, 687987953, 46270765, 371711727, 412000352, 394901883, 819800481, 739591729, 652943874, 325443207, 935687919, 320226248, 327149645, 194023112, 836743924, 23107094, 71949232, 992809332, 915139558, 304858898, 441876923, 539307657, 128607005, 119177831, 783536538, 371733175, 719757369, 513276911, 393122908, 377818703, 935341399, 421517714, 12887343, 74300057, 117359453, 544108496, 233042207, 44025665, 143586350, 886401782, 461117023, 265983532, 27235943, 13548618, 884450820, 312018797, 179539063, 251277239, 180460707, 681293018, 790523431, 998310438, 221095211, 283777706, 717297966, 42825952, 660525001, 265714307, 451915867, 74311893, 508286844, 815217584, 477608589, 844919243, 30567410, 335835919, 177648828, 114578062, 281553630, 191760748, 292693915, 264190509, 540941452, 171904276, 698566218, 887095901, 995459801, 936341699, 680538570, 19884899, 641279774, 46609671, 419958841, 721565436, 353604152, 59377763, 97136320, 343058267, 480411259, 23489076, 249212791, 860609419, 570691029, 288385968, 653442829, 371648117, 635454018, 985827563, 845954361, 329838239, 138420821, 258574251, 95603886, 195112057, 758360315, 564283772, 595024483, 314680249, 557776119, 465221236, 827327507, 552652603, 401330595, 379986943, 386023736, 311063738, 215770258, 940571874, 226229969, 565459772, 19249130, 205854730, 475025440, 573841095, 755113555, 356200570, 253478925, 721067192, 758942282, 949871467, 159742280, 222284128, 290647196, 704460453, 729510271, 503938913, 527813721, 699259707, 623800103, 731318984, 646593925, 420592316, 443402912, 282389448, 944940139, 442288118, 431731739, 269976378, 312122524, 181039535, 822591396, 216072878, 576437911, 891288013, 259963820, 949661542, 83155950, 586689856, 680473921, 863595338, 397053965, 349508141, 391710469, 747722729, 374529560, 122343981, 580634131, 702521264, 312795367, 522615472, 183190637, 873659463, 630169137, 765680494, 600809527, 551597620, 395656865, 573983733, 551225564, 614268917, 822330749, 887401920, 837632720, 857180575, 795927500, 886669782, 494573958, 275507187, 824257238, 645866763, 314905025, 158468828, 185625857, 394020786, 814982741, 653319284, 483236913, 900091177, 749869745, 736331800, 148817935, 535701205, 972683510, 397718411, 950277386, 697303390, 694355021, 468812523, 676354173, 770936793, 361340674, 72329016, 307733954, 306866748, 364044395, 323003405, 302739679, 159965106, 649026749, 202948816, 81295871, 163779161, 202778464, 139368817, 638451615, 150348810, 490007211, 230981844, 490361737, 803445178, 766904920, 630874902, 285011689, 373716069, 992679561, 425955305, 424846725, 988336168, 930220256, 62058355, 565952501, 287966645, 223098188, 23538287, 581943220, 489181945, 730606258, 616227239, 234601797, 779894446, 199818698, 593817966, 360780018, 480221791, 549255095, 223802431, 322412111, 714083048, 439861181, 321302879, 802444471, 39888868, 630678374, 703276304, 819026255, 100059834, 118295997, 943503236, 518197721, 659510306, 25207860, 528943664, 304480088, 817619908, 17454568, 857830958, 715128800, 411263884, 183090622, 141812191, 823490189, 299571957, 165204592, 454045679, 969084565, 438426412, 348875545, 659064314, 824400576, 133718793, 414457157, 828323793, 19073, 551509906, 238505459, 922834623, 727505734, 851705449, 854707551, 751370995, 316592414, 405668416, 527613908, 800824155, 95165059, 543310755, 67526463, 909843450, 834826298, 96295890, 737109929, 712081995, 57775428, 598007305, 658956976, 770502594, 50594348, 779695163, 146059019, 114549921, 661779252, 731765710, 930432310, 913513656, 113843641, 909465868, 58183421, 307196143, 253983282, 391610748, 125273058, 945808526, 84253064, 533903803, 292134609, 901289359, 680113313, 322838576, 832142693, 511169706, 996413423, 557093643, 959894219, 267473417, 768421929, 976231867, 415271591, 709584170, 10095374, 847472061, 649589937, 859823004, 844724852, 915499028, 923718196, 950363239, 357782606, 62752555, 142588873, 651258419, 461059261, 505514679, 93181889, 153966112, 185684330, 682779085, 344893043, 411813040, 400300375, 140327732, 139268264, 746217639, 69012248, 507834655, 929454771, 831689501, 977936144, 359491708, 488446179, 454081670, 812068262, 3470812, 245397394, 982620889, 540089608, 449066611, 36511230, 558753439, 144228899, 366901968, 85509762, 72769901, 895082359, 291594012, 666345773, 661347068, 859574277, 832328926, 513611079, 809765833, 280490773, 823105676, 937794090, 518451413, 708492663, 860264254, 521419036, 268268461, 428423944, 648280185, 189100533, 998465805, 533328526, 49125338, 766078881, 784291497, 62377316, 128574616, 595620060, 53992188, 443956993, 331462845, 103556119, 106090744, 174822942, 275495496, 199240325, 300796706, 741044981, 164195611, 754102296, 811044679, 421410290, 957489762, 304418480, 786077168, 707745265, 280697935, 32330266, 35022588, 955130193, 469412901, 926671291, 3703439, 570402004, 852440254, 829827110, 42793749, 558297336, 34043586, 389877164, 149437918, 672369008, 772727732, 255574131, 489620648, 403072024, 19828716, 845794157, 292623613, 235156484, 82320875, 11044696, 877277063, 130190774, 141472545, 250106285, 514844333, 583526967, 874720669, 885707493, 437502548, 11063364, 19598364, 995744513, 905819416, 323057800, 713119884, 784634094, 728740442, 834282961, 61518840, 739390853, 341730925, 693988028, 667052800, 726259404, 64507467, 165236088, 481910410, 912976027, 960906513, 996774914, 578809712, 901463220, 779893030, 542173117, 542002955, 244508552, 923755292, 352892772, 615241041, 433340493, 224045598, 746104547, 386699594, 719378557, 834425374, 591743010, 493420735, 699737867, 930657892, 697790105, 84688631, 226131662, 384168041, 115444249, 630841811, 522428196, 286178946, 195370327, 460294668, 175563684, 737501207, 257993488, 397584921, 493498554, 366142176, 717955353, 799536587, 396178310, 368690098, 189995585, 934934755, 812670614, 31474772, 188961841, 820490555, 862334472, 858132537, 331292823, 479036235, 389924344, 930601839, 15194760, 594571659, 208197444, 899421234, 258835295, 258895202, 547453889, 860472186, 164125727, 941088023, 178060955, 627656208, 613472781, 858404733, 393264176, 384396736, 79295973, 11904133, 303624907, 16345985, 917807795, 323638882, 826311081, 762022490, 528601802, 152069740, 371574722, 740157125, 139063881, 213963165, 680539404, 820473779, 840554451, 626976251, 443247500, 312916664, 887811457, 299790680, 985989587, 254568875, 591159216, 640500996, 558103102, 814605234, 29664112, 923722236, 469784652, 681455948, 32255673, 420843158, 426020762, 225134971, 28073749, 665445541, 884721073, 861893513, 840220201, 478585445, 213227777, 711016946, 379036945, 20070149, 593631916, 75568694, 270444865, 671632675, 191481074, 640322196, 766864525, 728790838, 264160337, 387170383, 981252108, 794248397, 631808197, 546140395, 734399229, 193761126, 967945308, 102273020, 633439888, 463742211, 101407989, 773310679, 629831443, 315667931, 863353267, 523470129, 222457051, 658382054, 706711983, 173510372, 876444471, 70703591, 55705506, 789980760, 432651650, 861647378, 888816978, 959715435, 580813124, 714679573, 80914472, 576783884, 585816251, 353404168, 513830652, 437044233, 63268142, 31326867, 480095487, 277942610, 960003394, 129157151, 338746221, 742038268, 762137963, 560048039, 331430929, 207371342, 672174660, 723222295, 102199408, 241910666, 829825374, 501756098, 637837923, 964187616, 484078005, 879950655, 433204118, 573106884, 904807421, 928528826, 861756384, 215079100, 460738632, 626424138, 367572898, 709426860, 871690613, 750423162, 813817232, 895316350, 857865466, 380861975, 146577507, 215350433, 850929506, 928350398, 708210895, 769122186, 53706373, 582317985, 225468734, 86437450, 421642942, 963887699, 197454262, 329220279, 751875491, 260958450, 217991806, 386480036, 125570226, 796659123, 755349943, 933113986, 383280584, 917869846, 29651099, 3748307, 937172050, 813699515, 7929175, 913195830, 669546656, 1211788, 252970726, 142322108, 773848833, 58325738, 390564187, 811318163, 22780805, 946833336, 992577581, 466487622, 22578743, 170362663, 251094164, 474473145, 161263444, 258396383, 220550531, 984607396, 599425951, 517134584, 430292553, 693731435, 661953091, 620270834, 940699384, 544118102, 550589005, 183418841, 782436345, 519241071, 305180060, 91264428, 120640999, 538196283, 30989689, 286375057, 869162044, 39848133, 796508234, 550352622, 227478889, 835529403, 844421116, 241124850, 360335556, 791327572, 60028345, 82311804, 32580903, 861411589, 363969138, 596926675, 66231599, 494637666, 384890640, 599116839, 115667575, 939763073, 247815259, 600951354, 993231842, 324490621, 315671898, 97965609, 718489052, 463249393, 454543239, 267173968, 920332620, 159383650, 903841669, 993830723, 654988473, 306281058, 967132961, 371176865, 270794476, 658960606, 811085237, 490887246, 380257622, 578248977, 525148686, 803554771, 968600454, 350426274, 525192426, 338397963, 496705595, 647652832, 346879055, 808424884, 894133271, 969801483, 931328898, 440486559, 751352218, 799829452, 639559445, 799338538, 210387778, 575600551, 347831031, 435980549, 557822839, 736864639, 378139106, 678467705, 92891442, 553583351, 978365953, 190679330, 534075979, 983693234, 810034331, 818725307, 46647318, 835881682, 479597862, 583082965, 221495172, 544251413, 629693130, 471852748, 636525997, 675818809, 334924568, 173349384, 817495336, 193656315, 425769686, 371966691, 501234683, 298380011, 139004649, 658000906, 292153063, 578795561, 14811354, 793120123, 511048498, 96606796, 895243788, 821763825, 185031030, 346351925, 595390692, 40144858, 863381229, 266142345, 298056904, 926141330, 442034379, 752166893, 171069921, 426991968, 596383971, 634654391, 599281467, 729706210, 269862432, 18886242, 710284973, 479750971, 949410582, 28281729, 976546242, 627875972, 108178685, 25283769, 896754687, 585716305, 549916952, 423629367, 696603842, 951126159, 144743660, 447623106, 555650599, 780911401, 129659165, 291277721, 282812631, 543857314, 514884214, 531300468, 233202375, 244390755, 581249535, 169160529, 979630716, 598914470, 287090551, 530601009, 164200198, 638156238, 9077604, 770321687, 375555595, 433749094, 36582539, 980443452, 850495023, 311910953, 434561262, 960930651, 667772276, 616894850, 871506932, 372354745, 153340478, 876104660, 872295410, 840743756, 60457805, 464629953, 107149553, 325791447, 710409620, 565254603, 864156878, 313880886, 596188761, 794630742, 991817937, 342080143, 231845003, 624267816, 90509587, 112244274, 40110003, 701295338, 374263471, 182513646, 36011901, 879209435, 757268183, 930894846, 387905022, 90917824, 285826209, 462054719, 264296618, 995388512, 389318451, 961867405, 792215855, 616770398, 915939619, 779157759, 524291182, 170224204, 655311333, 556025747, 745499034, 508628500, 760686773, 12112280, 734164768, 953186631, 763212472, 791132013, 951423854, 835992931, 60205111, 472043710, 400922315, 794273199, 871918227, 495947391, 80473094, 774319422, 229654948, 4800530, 116502660, 118553200, 796977473, 839042599, 443063039, 455365562, 688923688, 201505663, 158114186, 761684340, 946722679, 741437352, 663028022, 305248239, 942001252, 765609588, 683733982, 964129711, 544964402, 278375464, 222850586, 590937767, 965099095, 111672113, 622427532, 797823030, 167050625, 364858210, 506747622, 263476872, 631022415, 447159499, 49037243, 186133678, 274089921, 366515879, 581947484, 484039272, 221985481, 701130352, 99091308, 448407100, 417447787, 412569182, 744743123, 596139376, 974211355, 83105302, 689845985, 950715662, 797613843, 588942564, 780093548, 350126686, 352705759, 808252062, 412789355, 587101247, 606331486, 821845756, 233295673, 684661743, 267728020, 525086113, 768454170, 305643569, 285840311, 471199273, 640177279, 950933185, 856132030, 889824549, 894206545, 110233502, 522315866, 829197803, 72916437, 746941097, 202381645, 167162934, 580640459, 517221304, 639888091, 698341468, 7332873, 439536892, 536006485, 997217309, 756045113, 64444927, 515141997, 16866663, 94612134, 262979837, 388118026, 903802513, 739930303, 888261384, 958206034, 526437704, 251434733, 439973772, 773147182, 607595641, 788493757, 118035632, 890137708, 870890494, 445876115, 28107571, 967147084, 656739335, 754124759, 673049070, 340618536, 366880317, 443746593, 750272710, 248179795, 11386760, 817815813, 912389662, 938382399, 466638210, 487088221, 8700240, 408979738, 156778405, 897031412, 268241905, 330907379, 606735539, 968532042, 424949043, 57730167, 194993183, 957414941, 461403788, 30555557, 486425, 121058262, 414107722, 683682404, 604339476, 757054631, 662873688, 966860877, 33934127, 433870844, 144026653, 659585157, 665996218, 666430093, 722428016, 683777382, 85424827, 727217461, 296507742, 962413827, 141583387, 190679003, 525378680, 352785017, 345923102, 951688214, 65064924, 994637645, 501078606, 250423483, 140192825, 572885880, 520323637, 553093256, 599376529, 827852638, 34181880, 300457569, 136180964, 6938488, 387793103, 265540049, 503654856, 887060866, 148728307, 265362385, 847604894, 359992445, 462252947, 780773782, 37680986, 511354010, 993783236, 484043155, 681121634, 663387224, 808721971, 756864936, 411174007, 314064160, 758392411, 642850159, 483620148, 970713704, 896992696, 527690462, 144246273, 682655719, 64483249, 588886235, 876253980, 371366241, 777333253, 314747960, 613471682, 450176279, 620261880, 292426526, 197071094, 297683503, 71308062, 381138807, 979747537, 312724391, 749000267, 189176662, 681789330, 34462644, 921277395, 862437105, 154071955, 968610231, 447439950, 144372913, 631310428, 599691548, 330670947, 456316478, 952486305, 847446874, 852909293, 830111038, 386882219, 29701996, 547539937, 95209762, 840403939, 787555757, 104669475, 377321235, 689888716, 646751400, 951625663, 4478101, 300606096, 58462229, 74783233, 193802384, 594780530, 847862494, 962409418, 915762128, 783853665, 391382766, 114066282, 521974810, 592100037, 961633126, 354819377, 396965986, 990322171, 289574940, 494905403, 778635528, 161484717, 189011037, 771081805, 819579685, 469674890, 405860278, 870115270, 855442643, 667397046, 368465919, 143223402, 883406016, 12967012, 680107051, 375670268, 651088930, 727026602, 232141882, 344438643, 422849233, 538817856, 948121359, 503988986, 707291464, 84265670, 66502809, 516277384, 539106410, 540736006, 954287763, 295119098, 681604698, 656359524, 750186130, 998600223, 129844958, 531787472, 52840358, 918860240, 336238923, 561486993, 144041721, 801382182, 580957289, 348451902, 796887155, 208657868, 966893413, 419886054, 874975360, 446192276, 154860772, 193592474, 293648082, 883738075, 126477544, 90308614, 331078926, 965772088, 479988831, 947652058, 64882566, 9542581, 251932826, 621748907, 788859209, 837094510, 747880034, 389723340, 672890894, 931433284, 693300552, 820001947, 590816007, 339030603, 555785630, 562512975, 215647413, 430706198, 389566094, 511993433, 786781016, 921188804, 32575369, 702089079, 414156958, 278808416, 860788563, 451897287, 924126242, 368204032, 157165506, 595844771, 30753678, 636264438, 176897231, 268757747, 832945574, 400545674, 138979595, 248205264, 317999990, 286650793, 785737763, 918159856, 905065660, 628384177, 814680427, 624992406, 556875444, 164816051, 419958770, 642158226, 365559816, 857058255, 194018361, 294626809, 604046790, 944414288, 131809362, 732646865, 591917592, 302467002, 673432656, 930235991, 763703664, 942805563, 88000794, 939442624, 539903182, 939319476, 740356280, 971337183, 669932293, 486350374, 94177461, 432439876, 298406152, 712895277, 652788965, 771284809, 740283207, 307150329, 109159620, 873464219, 271039204, 497916296, 159500674, 196125425, 579463640, 370076970, 504616934, 510798381, 712892957, 121257147, 163146772, 137642804, 714047757, 855480124, 275420751, 817033538, 938068334, 638396138, 385765254, 212353075, 845843328, 244861474, 872593696, 691072920, 896215625, 711349763, 892856003, 577937198, 727793588, 686509286, 968428683, 213795750, 1641840, 440851941, 961011257, 621573393, 211529147, 786165237, 75432556, 293021596, 540800283, 197214002, 430024444, 317549687, 129392004, 932277411, 543594531, 374393610, 422671072, 559656672, 387895633, 296191119, 730192475, 471970626, 679943827, 145447354, 569230762, 13479003, 335974843, 713652604, 961845980, 784500848, 997369295, 24605272, 79575554, 222527050, 339179300, 532902319, 919955182, 949725619, 806736046, 803881431, 520364334, 420223980, 380856057, 547654411, 137678764, 780296799, 14940315, 11779649, 381320320, 282423196, 69239565, 87447463, 938919019, 854987826, 645314248, 469792939, 358076546, 715591828, 134817998, 18874451, 433842400, 168376189, 750772112, 273189927, 51158251, 560583637, 592056531, 426613678, 209685313, 736744410, 759637548, 175284615, 828632623, 672461025, 421289790, 228669656, 273357226, 644078450, 758556207, 855236694, 663109605, 548919676, 215310441, 565130135, 377966313, 977376887, 511807518, 807000230, 859167736, 424783718, 475056613, 328898600, 876787727, 604683877, 667204090, 982188674, 833046036, 299195408, 645742676, 655547476, 822367317, 414908058, 208685496, 771834339, 796089482, 198786091, 977840695, 160268462, 637609963, 566499040, 638255186, 730524827, 186414113, 335426934, 557124958, 25877692, 969507978, 162405100, 61399825, 945702715, 453153796, 920189690, 153350984, 372364895, 822686103, 629678377, 618171220, 309266971, 903262392, 582371207, 957258439, 308395537, 627281608, 763390479, 430517076, 823953289, 109733266, 695439872, 258928788, 169611212, 923467835, 96793517, 852773238, 733853056, 23844856, 888882755, 451589569, 965003733, 351692876, 180251788, 904898568, 962805427, 323662929, 360429714, 98158262, 542453991, 709324594, 195785029, 375665289, 713414255, 935111055, 525001836, 614078907, 752777662, 352580882, 814101740, 702007188, 456849500, 282732556, 41600947, 109831685, 602677756, 249386847, 966279934, 634316347, 448969148, 335960777, 923421969, 472841032, 121004300, 297216139, 972925105, 224031313, 695518497, 987457118, 622944101, 247322161, 174638808, 504856874, 576706397, 398220569, 488946829, 948959104, 371079241, 654225624, 620129933, 453187993, 370537939, 347071289, 59471648, 947723612, 819453195, 855112429, 520718360, 682783961, 290252387, 883172299, 872373685, 994886227, 798287402, 522319753, 23125975, 220120875, 525109515, 603114937, 253444949, 644750279, 808970683, 989550776, 163213167, 110731041, 967071217, 25462159, 439926603, 263549080, 716126477, 112812642, 59118149, 223402813, 144808020, 979470287, 474988923, 42333560, 431048067, 714390158, 758789967, 923339648, 232413240, 937013388, 678449493, 478834143, 665661483, 279987968, 261396248, 523648920, 522626113, 573891239, 93910170, 644751142, 675539008, 63457841, 584243710, 12100028, 17002887, 328070545, 319379855, 69329961, 528247497, 302775060, 982713555, 171218834, 145684906, 629470882, 66829129, 215816093, 75111466, 634033792, 787195164, 637562791, 483230688, 844535578, 469577190, 563179581, 728039788, 257767960, 825486206, 702951077, 166933547, 22205176, 706854250, 504776688, 700267501, 888787982, 761676624, 889393736, 577903632, 841925282, 791058653, 837697822, 553574327, 107585651, 178224145, 720355120, 545276728, 111605956, 615114073, 537595455, 939564896, 490757231, 633181485, 904009493, 672879388, 500652407, 16176041, 539621644, 357573632, 222394902, 140519502, 116552440, 34356237, 505571392, 654145475, 259677195, 529938187, 112595571, 214505501, 964778075, 740024266, 690018327, 386920185, 188348622, 391862782, 933414781, 578051941, 394680554, 442508844, 838160508, 319738901, 455554920, 167591271, 873308568, 665083675, 461931887, 193743295, 203243411, 909019162, 701798243, 753165009, 642298700, 641254415, 729754727, 324486210, 850605239, 870075721, 545650103, 995651374, 35979147, 562492122, 487901869, 742440128, 307032614, 383949934, 350824146, 115640679, 409794724, 649909205, 98176409, 876858179, 514216581, 240246121, 685872183, 536923172, 737008683, 362805630, 111228371, 674862182, 736556211, 200412362, 742642807, 983020673, 407018899, 951262328, 85886147, 161469011, 736388533, 256001362, 75173931, 496747826, 529589949, 50946049, 907463780, 800065672, 284692574, 308406476, 332002413, 624231250, 256377067, 610989643, 321543283, 517741101, 175959240, 773676266, 585245787, 376377178, 544800735, 948526262, 691876701, 891490260, 965188001, 743311946, 57220258, 571618186, 745275696, 345409557, 348202813, 799058982, 993103735, 646133191, 96676009, 918212699, 242603993, 997602393, 893673359, 930911567, 158525803, 946920183, 472443448, 327615780, 641102795, 516313242, 951570234, 911858258, 647896192, 131715812, 665939837, 333444757, 342737571, 561929230, 27594519, 280312456, 567416790, 479334467, 217505308, 191863983, 584390277, 289796572, 585435675, 454892848, 128790572, 829128287, 144135862, 647224211, 213192896, 39956475, 851738322, 670534053, 723421254, 125505696, 795240022, 955088084, 87604784, 574411224, 945816787, 863860194, 29638839, 824392317, 140983, 341813657, 610003321, 900032658, 153509154, 239975880, 937137743, 500493972, 745236871, 744412407, 465325833, 251828495, 707566076, 813861103, 507893705, 922481948, 479557571, 776775890, 990631499, 51190244, 602539719, 483090711, 116927594, 473286993, 332185419, 610004170, 628242464, 76126905, 925928085, 654456012, 398115326, 381554623, 196894285, 265333773, 955741611, 628655679, 273470947, 203693680, 983331854, 917183093, 675262450, 562700431, 838045517, 612514841, 309208686, 639875697, 600360282, 863304100, 151586605, 84924596, 224228878, 411996155, 691136289, 490465281, 162804636, 390482204, 682891861, 127849003, 630207189, 340140887, 926964369, 68242735, 640203666, 198090371, 270396336, 558652656, 386450660, 86700182, 209764825, 836951326, 122973848, 557936930, 460892594, 229232566, 26441840, 172174843, 541679176, 310612951, 751043424, 894470467, 389887722, 803571834, 243982010, 344196969, 994700370, 124416498, 360631492, 64107839, 365938101, 320352454, 162245490, 633334953, 680485482, 370693499, 788989512, 210641378, 550303134, 346960644, 41639974, 850182030, 294581752, 904808036, 82961806, 76246554, 731470684, 67201059, 769118581, 303406542, 949372048, 655877415, 531098919, 865101575, 136003074, 420933703, 851510135, 588885214, 530445995, 622752769, 206035564, 455258871, 565586675, 817514630, 135884219, 776604660, 162205380, 718751905, 565842825, 520764960, 565549698, 514241171, 593714823, 481231190, 809591910, 753862174, 813712688, 787184073, 124058767, 464900425, 691447641, 162891804, 343380877, 486829160, 153686139, 182031817, 937580220, 915258304, 811569083, 220444160, 894419324, 808379538, 902182096, 857135100, 778227780, 85080703, 556399860, 383250748, 420165345, 8588659, 583294101, 134265239, 240510910, 154161553, 388956885, 519933186, 353661866, 216538230, 292346903, 53544298, 683170259, 363712674, 347566573, 637741470, 964727651, 619800962, 305348266, 721174730, 575389329, 312194994, 34803002, 108026306, 937631354, 649607234, 685748493, 856998708, 417765510, 324282067, 730896703, 15906807, 653855460, 945542096, 305731823, 558503218, 556337982, 445857136, 526166175, 40756440, 26128095, 831579007, 549673722, 929188678, 288981574, 153589869, 806490273, 430262405, 332276984, 207386639, 810065741, 587707020, 581674414, 896175382, 76345353, 195176103, 302987165, 986914093, 773760326, 419214419, 765399554, 105880206, 428331502, 334925556, 565999530, 203891741, 667540526, 244042581, 713488803, 100589781, 999810650, 714678110, 563986335, 24386022, 631319189, 240250336, 735118053, 638656494, 634625209, 914780790, 678658183, 834731224, 469868773, 200720422, 761643677, 727334406, 596589816, 716562860, 716560946, 954132533, 581734099, 151976516, 955115215, 830951185, 245027220, 184222037, 571038607, 93805571, 811377174, 844418666, 517765326, 717755754, 397496802, 717739380, 365809859, 303668203, 726241474, 562778972, 839391970, 808828409, 688878662, 130339623, 126354090, 110591358, 155558748, 844690772, 67755134, 749111406, 753891134, 267833779, 306886548, 66009120, 110193573, 304859009, 687833162, 218482324, 474794366, 843199444, 54097627, 823114417, 892592330, 770031939, 921892295, 751494938, 814182290, 177203637, 888854772, 712032735, 460556666, 656256478, 680784362, 601308473, 841612767, 283803030, 811710069, 404045495, 177038138, 166125661, 920355108, 166522481, 840100014, 749055716, 414256001, 618273328, 171671916, 992541229, 740973906, 721097637, 668939831, 215301539, 466707223, 789905631, 913397999, 455001968, 130777230, 198057111, 924306739, 9033552, 583722338, 1756191, 865116496, 11003555, 662230090, 894769532, 15880551, 610259905, 7994801, 743537047, 215680124, 832360649, 665214831, 215822407, 903225050, 973265458, 323911441, 736415614, 48918300, 532247442, 693826419, 74256980, 545649518, 38052571, 391857961, 431249610, 793072358, 503201390, 212600620, 919656149, 610816764, 853823388, 166853998, 869205441, 678334736, 480518964, 204419839, 611276293, 955446680, 593147167, 174200, 419624742, 284141278, 997716723, 897235445, 512672250, 811326573, 756920279, 742362914, 626123594, 396861702, 248685257, 232554420, 224479005, 245733389, 325583865, 361383258, 904156695, 119983794, 550227581, 945833903, 240557330, 966943034, 433161319, 585552440, 279899977, 825395453, 349986299, 983244686, 585960672, 86450311, 854316434, 384011324, 133805263, 922839832, 469067444, 68229431, 525747391, 822470161, 531159295, 622563917, 485892188, 305334428, 280534424, 655703314, 437949674, 278555052, 20764217, 256165174, 811289169, 414681011, 533442612, 575443288, 592372174, 514570674, 258614821, 475483238, 389824998, 754320545, 307627497, 514386953, 131142708, 532698811, 886342787, 963720974, 818267067, 633628522, 864435682, 250877917, 507788416, 421917581, 437017887, 71686457, 827917686, 400263536, 714352491, 663148780, 154725485, 157939662, 850373470, 952830957, 244514337, 172758919, 812185055, 625743842, 731755629, 485549194, 150617961, 677799053, 317934394, 247219498, 366987258, 243827524, 492911914, 546329887, 765663883, 621839945, 618440390, 197826475, 772650448, 518108344, 251434209, 307135482, 270838980, 468021096, 209940056, 95544754, 87338871, 99128301, 729196021, 885621812, 764284211, 822285305, 298109117, 389602402, 754528032, 298721396, 206994609, 890452382, 730738899, 37679162, 363530744, 764520210, 438072144, 241812385, 117385103, 124666614, 322740276, 127226821, 652020193, 791659493, 889439705, 904453941, 574235051, 336125247, 388284209, 595937983, 275373142, 750733004, 19025603, 655613754, 678343778, 673718127, 453332896, 707993615, 323629277, 347797590, 401719101, 262745898, 309759518, 866402403, 952014509, 463504420, 160809430, 321005871, 325029550, 889444826, 224539013, 566048390, 403569081, 527824218, 35547715, 637104555, 286187745, 542413287, 464947200, 588025958, 747397241, 47661275, 75673872, 992683289, 14800674, 8569233, 191362346, 509012348, 702957498, 693333365, 299516891, 879751626, 322264026, 981603575, 296450523, 270395833, 466694010, 274291497, 966115956, 209815409, 768175593, 208719947, 953565192, 584848616, 155789519, 387850511, 747928286, 745847561, 416217054, 827941710, 267590169, 841204550, 82487462, 54352030, 887928166, 704303455, 64717494, 328084227, 952553383, 496549639, 258954564, 706786468, 209206839, 737066894, 711706194, 185646250, 392771944, 660957378, 827567756, 169762866, 4130049, 753395551, 372294553, 874729916, 471544700, 461019613, 170671246, 997340972, 995811236, 261953853, 706340537, 193010338, 92898923, 855780286, 415988600, 54624710, 94958235, 971874698, 367995209, 520341708, 685023221, 597527121, 535670305, 838176770, 336182551, 535179494, 50421853, 861812454, 659441605, 606940468, 590597057, 228618827, 556930709, 915280737, 78705099, 808008854, 306610122, 595492365, 817723358, 515024895, 13184066, 463894760, 562975370, 825687244, 874789976, 133886404, 633386034, 179598159, 933634646, 731916989, 820241366, 753574111, 597289710, 755209177, 704649660, 939643585, 84936307, 787363979, 5135849, 769324013, 330750310, 220291872, 637105953, 473750508, 802258019, 287320594, 107803901, 810997941, 971284896, 402393024, 658257987, 418059185, 447459916, 295639353, 363996798, 688866257, 586219056, 565776623, 552499912, 132532721, 508521848, 618397093, 445942187, 697205016, 176486839, 582785959, 106502253, 38975813, 287553823, 288083949, 630331476, 695585073, 127231165, 261145530, 722192716, 5380190, 893744227, 653350975, 513074378, 243139665, 715207511, 377319263, 449136184, 99116304, 824505517, 627320312, 843458312, 105672461, 413054168, 419739097, 171449954, 979500258, 888658187, 188872070, 513727972, 411597329, 286910980, 365908032, 749558019, 443822170, 352422406, 814584119, 297661554, 268249285, 648256955, 758778128, 885049700, 65294815, 74491942, 938644541, 292457052, 163432095, 162255450, 315920280, 532692707, 490454289, 174084155, 407808560, 309320999, 976012213, 903507908, 869534934, 589942939, 171776333, 197191708, 688248041, 727792876, 463188536, 305119368, 291671553, 91920113, 67621668, 948858625, 425473771, 196001561, 730542056, 690448450, 647521229, 641076849, 941780001, 346861400, 131793801, 921030118, 677143495, 507382264, 462869540, 368959027, 69273412, 135057485, 739186337, 920878518, 717439598, 403390635, 1153332, 799963800, 299744010, 191256683, 577247557, 965273412, 190369775, 2208858, 355388217, 618626265, 862547648, 379821364, 306075370, 928624095, 60907543, 679017210, 224852391, 659107048, 454353523, 789862205, 554381418, 361028327, 17171241, 620187841, 251917503, 599842763, 624565946, 714852991, 7044230, 94871375, 641646161, 713410554, 284807019, 406471115, 159334516, 180370379, 628931420, 126176383, 854500341, 186206090, 812694428, 823727343, 927139304, 308876019, 707988256, 162095071, 332883544, 305194437, 339817691, 232643050, 597576738, 407592567, 317294707, 349952881, 93029825, 392196389, 871682593, 222874289, 422409782, 987804124, 728014751, 660612088, 200598570, 360947540, 47477485, 92034843, 58814241, 207330888, 33112601, 313835576, 416738802, 836034745, 735416515, 455539943, 808766144, 181381619, 350506629, 371304990, 837223299, 468085303, 911816808, 523880323, 474196514, 345122627, 694341641, 800565860, 380820054, 872406613, 427838675, 623030155, 367385772, 684360652, 657771264, 156415397, 640377107, 447270393, 685102989, 175938360, 510715901, 419701603, 2569187, 274108645, 929150587, 836448023, 647494279, 602384320, 730438997, 115986702, 29125614, 381161520, 993238365, 496941993, 320526639, 746137897, 479808115, 639705363, 144095138, 902511665, 495574187, 212503470, 982710592, 601005692, 704754155, 659144575, 264028164, 552774308, 585243042, 760263719, 898722832, 266331864, 596845864, 3134351, 311747354, 763464972, 303109941, 843655026, 473576851, 751633105, 11642481, 525825603, 865008699, 247484678, 883789161, 84974018, 736892124, 258095309, 581897592, 531152166, 208220735, 476621112, 113518597, 403467420, 4373663, 306033696, 543719710, 956782916, 224133374, 200514882, 309924084, 521870846, 976457517, 530789282, 60028199, 697311042, 906180989, 288949589, 342598091, 765814388, 479120934, 793354438, 811390872, 567383440, 592573555, 285020934, 454318379, 30322366, 35798123, 387137548, 618628437, 588026680, 904453557, 536264215, 551256696, 893660124, 743423427, 657010791, 935300934, 933613205, 725636729, 918094060, 934716436, 668590426, 32702442, 521190175, 748627386, 709102632, 841333250, 11461125, 223589470, 146444840, 52324714, 379191458, 468994596, 225373252, 313536650, 532419783, 13849098, 883271445, 623964852, 591509385, 28803404, 589373434, 528855851, 354133578, 80319898, 23316627, 272103990, 455058477, 823491166, 401666315, 574542002, 951603746, 857086391, 66231858, 417908770, 816412749, 399234296, 378818188, 736314745, 381101072, 346790168, 547690875, 953534958, 734947252, 962556640, 650667607, 759432146, 77638699, 629834963, 728386295, 249086275, 281779494, 208763811, 249216052, 595987414, 183846602, 116268630, 624803545, 265527438, 795952045, 73375697, 796433383, 202439098, 225908327, 158983944, 213571723, 291449019, 155448757, 24132694, 61829323, 560583621, 260045336, 245456947, 432505715, 90724961, 411430914, 652784866, 343125509, 297611289, 258355552, 720520103, 366331605, 715572605, 854786151, 60947715, 42098014, 433434476, 35321688, 793315249, 853428216, 504028393, 284007122, 622178586, 65888162, 338211280, 785024281, 321340157, 624357219, 904166413, 263482379, 444617882, 463885759, 216716930, 950988501, 9974265, 17562546, 893086778, 234744925, 249199620, 630796252, 544565893, 487568952, 550241547, 733419176, 541703711, 734636559, 150737849, 990485296, 466000426, 221410727, 541060016, 116792769, 730928438, 429595311, 660274238, 351148568, 916162750, 116624943, 631670193, 691368177, 931581173, 881022432, 753267146, 291988942, 763726989, 394970553, 189578673, 999868077, 582997542, 917094389, 683627259, 890947557, 413250308, 30758807, 395607987, 618748245, 725449357, 227690969, 789054429, 721392913, 469161877, 741528944, 855185760, 195933516, 60300842, 928443850, 188910027, 85667143, 770534123, 816490950, 661312699, 259949136, 827011157, 835135143, 291214648, 994472535, 723854275, 924525000, 496095660, 640793996, 750910653, 598856214, 345919582, 266383566, 473881090, 257707156, 43525438, 442970020, 289937360, 219131943, 552440040, 123129022, 879817529, 154652575, 78793204, 921466939, 477274024, 412026704, 287405855, 679522950, 986763724, 871985634, 727126347, 67083470, 181274817, 305090011, 603604266, 78370679, 409738660, 626781739, 290317304, 666195390, 927149881, 65779877, 325287112, 844600700, 169528527, 191953271, 807435948, 348023334, 464180471, 935340939, 893547636, 927286405, 137393101, 239764267, 258807193, 538114902, 588943966, 540771071, 731484224, 91014937, 310966374, 542860147, 984821260, 310560881, 210048479, 515175422, 387851914, 5450498, 570124449, 134857551, 618312531, 372935819, 806278686, 515759525, 690559271, 68381072, 424284588, 320822451, 853224383, 866385989, 677260599, 638609159, 653440660, 752550242, 98398382, 802950197, 863154172, 116178737, 132206092, 430107708, 672393981, 733057478, 605824611, 416523216, 760365977, 790759442, 639705211, 522822717, 272122654, 138928809, 643843090, 933125050, 28360454, 562211866, 986645127, 322700371, 722544581, 666682917, 411776439, 131796334, 269126251, 178262951, 490065996, 804572473, 19549457, 35369688, 952872891, 127219040, 798151828, 518202653, 32364766, 243225788, 771107138, 908768333, 356124435, 882986753, 499508881, 881870482, 971177002, 104117017, 436562342, 852808055, 989565398, 152541901, 144726590, 502359661, 229654482, 239581011, 459938033, 827533349, 957869637, 826732166, 994780061, 102608203, 17536775, 871263210, 509553285, 184948973, 839684360, 749148651, 75644418, 292427789, 915094064, 951615219, 342717094, 7746708, 858083785, 146096523, 85086823, 11961741, 918785664, 407315645, 734415616, 917757653, 170338814, 399446570, 952730674, 37689457, 665584245, 179669010, 461558286, 381495760, 170992445, 799867715, 550486923, 844146523, 431472813, 665410011, 890704584, 699454199, 546164716, 509327002, 35814609, 587073511, 434465404, 389349309, 600868215, 772498489, 240609314, 957995157, 524594543, 212528421, 463806734, 77862873, 787018147, 591172896, 317561296, 1519469, 274859647, 981353251, 970131610, 301934789, 850362475, 220363364, 896946162, 742983239, 883281704, 520324351, 339411772, 93930495, 358418429, 691063823, 845263400, 652362890, 734652129, 883163803, 91892694, 79801857, 617877032, 938238465, 949434466, 229070371, 483616874, 243865824, 631622058, 412203120, 172122343, 880166633, 6466850, 254512698, 912820706, 970591752, 378662591, 366597899, 861475080, 92576593, 72226837, 147261193, 817291675, 292139762, 341880683, 45726862, 910360790, 124882649, 959134472, 690197837, 280010494, 827983436, 267498706, 478998578, 301226660, 35568612, 622699612, 183659231, 39391773, 290325958, 690017194, 534483127, 179639654, 478004125, 9653559, 733122232, 814191306, 125032268, 970184216, 78278840, 563387969, 70461442, 534949134, 935426366, 328875290, 374291444, 617436912, 47783033, 307310568, 22772547, 215021650, 864055279, 358280975, 336323791, 355358043, 848873742, 311921666, 946476143, 610075486, 800407653, 628502500, 280094568, 201777773, 433414493, 708693384, 76093355, 823403680, 744843646, 729445043, 24016152, 817947972, 813979056, 159307392, 821913326, 100075496, 393721045, 739725293, 229466985, 157190047, 19189907, 881719896, 119458369, 271020455, 205996983, 806402443, 226610684, 639523772, 519261536, 432664888, 206394401, 386457485, 611216347, 137819407, 131886817, 669669820, 536820013, 7255341, 748269132, 847164649, 916066802, 932433579, 918990598, 498570352, 980120879, 200418323, 503623898, 283999234, 844685317, 895203897, 298390072, 853192766, 218343955, 732316604, 889014059, 777895976, 742061833, 765993622, 319648780, 43833200, 583783084, 959375093, 401906841, 874952739, 465085991, 935482659, 494554114, 574899745, 143562005, 881765084, 841721157, 810539929, 28212408, 780381845, 727165488, 800602975, 318956742, 217274193, 414886392, 322176396, 469015765, 871793140, 699435710, 213731589, 18855763, 521286873, 344308195, 756638348, 133262281, 109567823, 540422620, 64197520, 492238600, 303307113, 827657298, 53145637, 963267086, 410216149, 928032676, 57755021, 165637067, 312381208, 94501645, 359495911, 818035369, 516718092, 291766132, 241441872, 115134016, 101441454, 227924297, 180432914, 835537302, 944471580, 962418156, 810297362, 769991488, 583951033, 119640057, 907153958, 131566760, 469797259, 896952155, 546625444, 308804185, 381894128, 571195961, 178790513, 194153201, 879880807, 859092389, 243828234, 89517891, 254138405, 604454818, 614241387, 579177895, 137199401, 219498033, 745917292, 297784367, 642017510, 447343568, 902869197, 607310406, 808135257, 525911230, 729525237, 312532397, 754890497, 128688394, 625865752, 536768252, 140670552, 723639746, 785675172, 353185828, 485929060, 650063681, 454107025, 378680397, 488460363, 847589936, 40386200, 143252760, 110868099, 877626425, 42765475, 203355685, 451346998, 647042355, 315603189, 689983559, 965880071, 671019229, 85081960, 577261233, 935090077, 802553285, 715651195, 815633026, 841684193, 853226569, 609201097, 21092271, 507633570, 973600689, 935955941, 255629669, 992452913, 313695138, 158573211, 594078739, 592569020, 353808417, 130776523, 318780042, 496760898, 530197370, 246268040, 715854479, 757584698, 388453824, 85810877, 97468608, 446363371, 251129390, 405550313, 780887840, 59011078, 319717643, 698017529, 992574111, 682077815, 9027505, 981919739, 462828643, 876328265, 919200276, 790696931, 49919238, 503948045, 214617317, 71266306, 634601822, 511792973, 138064708, 509157567, 984154052, 143693235, 189846089, 74903451, 394804810, 656429784, 505207924, 506165623, 701024487, 495539809, 703784712, 21955389, 516948463, 60028456, 553452832, 982703785, 594058577, 826179798, 242602134, 824729111, 545434278, 842129654, 781819296, 594609721, 673892671, 509429296, 300850757, 728704038, 296363069, 133609833, 440745342, 531185906, 557257261, 973878182, 82405598, 219527531, 456243492, 400243750, 488763629, 617547348, 822422904, 645693529, 46125411, 776709648, 186504227, 432331091, 551665713, 569322416, 855777451, 388214377, 169627177, 43692715, 260957980, 61333117, 128168988, 362254036, 720632991, 551442852, 19139977, 438677077, 341887542, 631561381, 863445695, 115775382, 44578244, 993348922, 465677277, 512275084, 110007436, 568058241, 111055761, 12540857, 940666535, 963144853, 642768723, 291035019, 837193036, 636553094, 344580004, 789018046, 206069299, 942599204, 913207051, 320942742, 670390328, 642797764, 292946663, 58049638, 544884321, 795070547, 727067385, 177839953, 340610222, 505886928, 498829369, 235306119, 940100161, 44724510, 285468481, 132527911, 527952260, 62637876, 645183565, 827400987, 778014446, 622114919, 267864732, 321143486, 302641792, 390292763, 966841157, 103049052, 778861022, 202735780, 315047282, 174838034, 162018926, 480013148, 52141052, 373305531, 873640372, 48111901, 636859836, 68638543, 263515397, 988384469, 612981063, 640648148, 572575984, 249095312, 438963696, 678653892, 452427598, 607028776, 572647326, 220681960, 133864098, 772088235, 935933559, 778014122, 999646649, 916846275, 94102186, 546328000, 395494752, 353758933, 335468499, 176071744, 991216361, 383998586, 908964492, 702967490, 299585714, 934528124, 592198279, 83284220, 853360367, 113007957, 311645407, 728619685, 554451342, 786667274, 671641775, 864665928, 205233038, 202082886, 986925991, 318793011, 567429508, 467616714, 946275276, 519988283, 580609078, 312093144, 345425458, 270903303, 957214935, 807447813, 56923518, 463496472, 922287680, 805837135, 3803803, 854575249, 258598635, 782979605, 929230230, 44521767, 719530951, 400220989, 750953934, 96186387, 279482613, 464259053, 760497035, 338524490, 940364266, 648338314, 852505319, 146635143, 931506548, 27452622, 715643205, 677447757, 33885595, 760068038, 3656102, 215276148, 40727842, 826491521, 312691144, 739909069, 457680821, 219900381, 261614067, 882699959, 141429139, 962196221, 936134641, 967368074, 63946514, 224497313, 418075031, 822541770, 285730838, 653960139, 513864836, 950802800, 153650795, 172147782, 283367148, 911138549, 582321238, 301081275, 675070096, 601290656, 600422510, 242506866, 836793991, 705971781, 762110787, 518056365, 913185031, 847788176, 311514801, 447644630, 58606638, 728756460, 267196471, 235508996, 877331709, 725463963, 682607061, 697099998, 138037725, 992042851, 198762178, 6031373, 846149552, 376474099, 303432726, 656964065, 379989911, 62754186, 390433635, 813276339, 402777813, 726889542, 830560261, 823669563, 453075255, 39446261, 753173119, 33223392, 452673026, 322120840, 713084105, 474458553, 34157061, 197543378, 383886956, 734906691, 250296184, 188534097, 215443894, 322805477, 730743183, 279345258, 978747336, 46596878, 263026002, 64254818, 969622463, 479300763, 340946706, 138748023, 220387668, 290810348, 208632219, 117803163, 64064071, 920513959, 864042457, 821125374, 843811894, 970565474, 586853705, 355599725, 812599193, 93028049, 472322805, 745351766, 705354234, 916132962, 868512580, 113082783, 358454006, 250478789, 285636381, 266516273, 811301361, 442426914, 525723853, 500813230, 62424836, 37018334, 281444920, 725904524, 439745294, 736856717, 116780846, 182827098, 696038359, 617919526, 591224159, 936538081, 443760681, 893490824, 451575879, 69353422, 338390501, 16899001, 988638284, 129824953, 98555219, 907580098, 648703711, 14003237, 990103873, 681602967, 60033953, 474531679, 126967269, 786897353, 26523072, 488103913, 677484596, 549334033, 526859093, 175093417, 824895314, 979073266, 590190371, 653476580, 250464303, 758390482, 970376240, 792152320, 470338896, 275949703, 999835177, 873194353, 802740705, 905758768, 264076679, 789633537, 901324164, 356403604, 415834492, 282184038, 64832472, 875440902, 364640593, 499317910, 448164219, 958211192, 182329424, 451263950, 377938600, 636071661, 834629373, 798565181, 703122318, 15386342, 321644753, 357423083, 513853882, 561644014, 471899966, 274883929, 539078443, 25541931, 719251198, 65933127, 222859333, 162038720, 838075820, 839618832, 162676097, 800732164, 49645650, 529280040, 377952400, 29968597, 584366550, 99876960, 191991093, 99355811, 670691294, 983643366, 613813618, 511318304, 285846832, 211510425, 211969168, 43374611, 982236096, 363945653, 436510947, 875130680, 307197822, 155190757, 303426858, 691251607, 659824171, 91796827, 726800491, 333482849, 51651729, 700509104, 879154998, 823180404, 498285825, 527747780, 302887902, 176629390, 574380570, 820726932, 201370461, 241290799, 245964733, 997815005, 179205091, 975234161, 720317309, 220308026, 600874351, 266226719, 677370943, 526587949, 974201330, 550782850, 706728014, 736376337, 785383683, 298202571, 227795658, 370418856, 390648188, 637589377, 432126002, 791215999, 683629817, 461931180, 224074141, 737194424, 590277926, 530782266, 167750546, 347661169, 709492640, 680761673, 310941891, 276161275, 724021702, 49428938, 659152736, 466369391, 465917626, 517917420, 149964134, 668736085, 107931521, 847078131, 86798572, 407616000, 168372901, 275157260, 210303915, 714887473, 347281885, 511371328, 568000238, 235904918, 529173215, 260493982, 196239008, 123943775, 217966269, 77236577, 952403655, 582537380, 700403611, 411523359, 831521460, 519382159, 919997398, 656889125, 805673115, 116584486, 407066161, 804282395, 250881883, 57017194, 272672612, 96477197, 715074990, 931380516, 285560528, 240401273, 23372068, 265443115, 916456481, 452169325, 141536405, 261631369, 380754719, 309476376, 75166512, 141760595, 13317685, 206102119, 702970288, 16409049, 676394157, 792374288, 761351718, 538153661, 642780141, 413707699, 345022461, 965982075, 169848592, 486407712, 145221311, 616784913, 689257708, 301418626, 580981610, 592006276, 340325945, 9410334, 557058702, 682328447, 66669915, 762902371, 589310935, 258161103, 674688321, 530005402, 76123551, 297347089, 434593297, 955285232, 9442927, 701130196, 610965, 434824948, 162438489, 850452095, 562647092, 690877099, 786070536, 435497355, 947993916, 166270752, 765172391, 813382256, 632328703, 828611272, 676755149, 190879402, 181677844, 404160355, 458666674, 548249429, 154078209, 800684591, 209437530, 148450298, 806633872, 965109707, 563659734, 144242783, 354886464, 406287019, 316561019, 842618532, 450748832, 142764864, 330278595, 574989537, 860756750, 771447204, 587957336, 468492272, 844553985, 871796504, 360631159, 483260488, 870648710, 49755370, 965117637, 348781223, 581474343, 863285095, 355020116, 701439181, 739369470, 323209211, 951277449, 369658743, 71140062, 392281352, 903063049, 20575673, 247574561, 438033381, 642207351, 160611229, 679806852, 631087622, 208720695, 449503754, 201140341, 742062031, 205595973, 390111885, 851823939, 171551734, 482096345, 985780143, 319335272, 464825761, 817036866, 832405375, 42638439, 787527425, 541323603, 692129347, 839377960, 272185351, 811770873, 591758497, 204058029, 505833946, 694888339, 273490316, 637502396, 876268058, 123186703, 985810449, 726393683, 309988784, 365664853, 565967114, 223059233, 408955510, 378458739, 176411697, 877175825, 791653468, 338263893, 233347010, 418421032, 679558688, 723830848, 362407498, 848109684, 488287453, 802706348, 920604959, 173576007, 117655004, 983001965, 532596377, 136658555, 941970768, 321637989, 202695816, 140604085, 463711825, 787829020, 168372794, 682205963, 960805382, 538760238, 162665829, 966056674, 423682987, 506686443, 978829500, 684077753, 692729619, 720369128, 533900534, 442848826, 734769571, 465708525, 180158723, 997177387, 253775842, 229554753, 4580624, 665997733, 855520172, 464432171, 265873341, 633078334, 683574033, 75887865, 711731791, 778303648, 824172488, 737517343, 543780787, 404643366, 658283958, 995748258, 849713729, 225603794, 162589249, 190553286, 21631136, 10238701, 373487945, 746947783, 461231665, 193240715, 9184843, 286028648, 876502747, 423720286, 149968189, 301988783, 579933618, 545420511, 767729409, 132205036, 267960145, 583653932, 264917903, 877969827, 308148075, 742568169, 13507234, 721284743, 888843101, 559165298, 978743530, 320177763, 223760183, 939745020, 924083033, 566523645, 49000160, 322645874, 182025034, 740503134, 980831119, 15851635, 805602293, 300570817, 370797050, 853878197, 987634092, 235811784, 658795576, 885677001, 318241796, 987949545, 495588444, 670969709, 5609348, 22665670, 340341757, 600420971, 365141808, 803272536, 500570920, 449349442, 439647280, 505796811, 715738362, 446408652, 130936647, 985448484, 302661072, 705163379, 817498596, 111325314, 534525264, 721092577, 735548362, 395406705, 861215328, 674696104, 737547750, 348861348, 6100734, 977002630, 316210373, 557945193, 512515281, 588361142, 549721133, 116051460, 543486506, 687388883, 463569868, 536050245, 526492533, 540242889, 889126583, 100664617, 952387027, 742802765, 530988417, 334595101, 257989855, 15402560, 215397596, 578763408, 138392768, 243247788, 8233245, 154120590, 656907426, 919739689, 348598508, 999581862, 725982707, 804952096, 129974797, 964388693, 604376278, 349584982, 742277475, 846751454, 187016716, 819457817, 837485667, 339276719, 291407210, 102866681, 146641044, 940650142, 17627086, 959459062, 157803806, 456812147, 868695822, 826889911, 410180958, 75199178, 113336502, 71368389, 505041533, 130543428, 399569197, 823130960, 348971571, 929492671, 123442217, 651417662, 308617413, 226343200, 152495917, 823556330, 363148681, 303413488, 790878825, 906119302, 610566191, 331400291, 442905078, 702813382, 902237118, 909431102, 819507243, 890206838, 383850220, 126570548, 535445444, 820223342, 211248279, 331194729, 986147195, 709892639, 434195019, 124290748, 720717062, 977793934, 799863180, 5307110, 338555060, 613952239, 873741159, 577746282, 178657145, 453391396, 837775148, 180773647, 754054118, 481264605, 838651926, 392514838, 664781544, 74867503, 394577837, 320202397, 497989422, 582216028, 731812582, 567762084, 215136770, 870524911, 791245553, 328626038, 892828979, 399002889, 843912993, 604123767, 720244982, 152809527, 739727066, 921004751, 235585917, 426103685, 817178590, 725343638, 757661249, 85065123, 886458727, 243962431, 516090126, 705844822, 575020099, 290270351, 335714706, 16406203, 398297086, 583075425, 159968859, 28111125, 532675678, 933372993, 281025288, 58677774, 439951854, 776598159, 398374736, 341474399, 877564408, 742190892, 223182092, 71127246, 99898168, 189637950, 437356372, 168496506, 909450846, 138150329, 572026274, 430067981, 285381126, 383169068, 744205616, 723000952, 532832472, 367552999, 385612463, 646443097, 726902300, 534960903, 566656870, 469612902, 172728089, 663951721, 9050821, 943250205, 728735237, 222555247, 203592528, 433777883, 174278374, 698677770, 578763095, 701558390, 916848172, 43107140, 378992623, 97819100, 137192886, 940506237, 83583461, 36308955, 765295985, 614257756, 918754090, 912807083, 796931967, 235168259, 43589736, 647098423, 567063219, 704200414, 935981295, 339840494, 427320191, 860733427, 110490329, 935672903, 334973649, 840641659, 327143088, 610435709, 475072673, 947492279, 163838087, 514506852, 811806217, 554226572, 248390974, 963840146, 257535699, 327833489, 604166502, 715122089, 161650939, 469336820, 308071795, 316014888, 236417121, 97822881, 417104998, 237710701, 712517118, 83150830, 657009636, 798041940, 174054674, 988322646, 369897923, 268454017, 344264789, 731963227, 730914837, 336705621, 209448544, 173244051, 527709199, 653355890, 541873764, 55995564, 231630571, 210701400, 46551744, 521783378, 695735817, 331842469, 548489136, 333625749, 616720871, 522170701, 864660009, 214105712, 221718056, 595179588, 111534386, 837935683, 845881012, 469611871, 418913936, 309515463, 359653507, 903836590, 626684021, 250038663, 835327038, 786621522, 407543540, 258874195, 554603249, 7325927, 831534651, 893441788, 540697586, 295948722, 548302544, 780726548, 145047649, 814802162, 117868617, 906089677, 589160664, 763558617, 966215971, 702017497, 876311779, 558757801, 666896506, 515641743, 483143359, 249692309, 985102301, 853930382, 11364496, 306665661, 811898710, 152620252, 164961899, 857650020, 418958532, 995950589, 82235304, 461148536, 949593040, 681084219, 992229707, 159585165, 287378900, 14323140, 132956484, 215418196, 785367961, 678353603, 497344749, 586556743, 171294012, 905107362, 989348278, 254530948, 341426672, 89430419, 913053309, 436935738, 452678646, 944186404, 252310499, 876650645, 710822927, 92417846, 469320445, 956986420, 851981780, 416652483, 957951949, 546023420, 741760402, 922774777, 189787795, 987940724, 236276907, 353561130, 149124806, 205188157, 612061721, 689872675, 896861932, 997948454, 106566336, 592668659, 263810164, 364122747, 860124654, 77448130, 700066209, 276049247, 921868064, 946503372, 774926818, 542783001, 282190432, 165074492, 133309298, 763891799, 211318491, 419452478, 602833811, 146766263, 15275775, 312476633, 68083511, 445747485, 466413131, 520263509, 592849955, 626098590, 727609807, 891899677, 836828787, 497216434, 271564541, 890039114, 70472781, 997150784, 419210152, 541773643, 926716798, 837632072, 4801813, 205003022, 283137530, 437859902, 713712592, 163867826, 751058334, 987221004, 932685575, 699999519, 932728380, 24224369, 571871907, 142898629, 483492203, 724725522, 384297287, 768669923, 306115996, 890925464, 587856532, 982363517, 203812406, 608469718, 738215317, 504240172, 277700598, 996462329, 662893244, 625076954, 640606044, 968465792, 651192714, 630173278, 506922227, 597553856, 113108294, 164644908, 225461649, 598225091, 96749147, 795050969, 503334825, 68278746, 891847381, 528194765, 401864837, 94174317, 188130195, 424879249, 244501343, 987249029, 777560963, 714667151, 208832110, 738030046, 380886718, 787831340, 355372921, 365574784, 72854579, 80197501, 570021750, 120077232, 687346343, 288686759, 553557701, 375060652, 267015433, 364165758, 564209217, 169493414, 733927230, 326241449, 308353620, 181855720, 761239029, 912473032, 872665617, 48354402, 51707545, 484041158, 399648038, 40354635, 308835391, 213795581, 14675506, 972282891, 311229215, 681688732, 806554691, 935390507, 966427801, 437438418, 891668146, 632210840, 966864907, 276205467, 387659710, 345865984, 895040578, 140542614, 89741519, 657241215, 507943716, 419700482, 421590807, 254736220, 186008089, 561487586, 574954540, 891915813, 939835397, 69384991, 652747373, 566241253, 461576771, 245579999, 991559800, 220971531, 524527833, 100455110, 897576986, 486840465, 494979604, 307017270, 559117554, 682039396, 179659013, 362308599, 342677156, 243757745, 986985563, 342374508, 165732485, 936160134, 118788814, 187958688, 672767964, 221895953, 580960138, 440153094, 46649926, 416283663, 517946760, 718953702, 240367872, 23567920, 924895021, 844725194, 451140228, 827276420, 431365614, 924209005, 20229527, 419845873, 295824592, 595735755, 553688395, 527947640, 166401026, 790354791, 966578958, 29580115, 66350828, 536562760, 461662457, 604010847, 444545031, 934127219, 460370993, 220628374, 234776546, 416226780, 164891656, 699614742, 790647926, 121968114, 909825333, 590209523, 765407961, 40197017, 651271687, 831724344, 534829668, 458318436, 396476617, 484473698, 294379264, 488156512, 184070143, 364511867, 641832769, 366599776, 547595687, 905562358, 807577454, 471307459, 816623976, 971991147, 231420037, 47820277, 625721716, 177135080, 753970630, 239898232, 311778624, 202451570, 291004431, 346507973, 172678677, 356369189, 663465333, 365109459, 360623594, 750487756, 868881105, 484647144, 621583492, 828445135, 254657051, 399365892, 503113273, 660489480, 109168706, 170215921, 961750504, 391052273, 563851969, 956569635, 330445986, 971877211, 817440771, 757776397, 197254574, 319035370, 544558164, 873465019, 262569642, 170948636, 86202957, 226547396, 803552886, 112889358, 490514085, 361517548, 172793179, 562923906, 122851040, 939048106, 668884062, 555896374, 82574914, 848523595, 253002739, 124863928, 138461135, 913712243, 667350961, 536372502, 306925583, 896117055, 174463491, 519310103, 963192676, 571785889, 831647683, 311359184, 296255045, 27629513, 968173801, 463395251, 454511160, 670437049, 259377348, 116104578, 632333846, 141651624, 135178367, 753967445, 204240778, 870408926, 320755513, 722066938, 535270421, 982985431, 242461805, 481200706, 306525506, 941456016, 287335735, 335699017, 919427385, 618818215, 422962126, 245335386, 679300033, 593597948, 41688183, 825851956, 443382942, 210815088, 104935940, 357940739, 402830033, 459971687, 947716359, 625094141, 891119136, 167137385, 801193039, 355553178, 31407274, 653715687, 104086185, 981337155, 955297814, 511939194, 231821676, 809386462, 141262582, 593575681, 659977783, 598450479, 180815948, 37567839, 353914470, 658728713, 996336393, 629945250, 508010607, 957935701, 871419540, 587301508, 317395882, 516689266, 24999265, 521520277, 484591937, 2539885, 125943241, 434574380, 911359104, 800616075, 406936020, 552760877, 166170356, 373950989, 593592853, 350867010, 847057312, 600681255, 50654278, 6373677, 221820516, 396971112, 978212391, 368066030, 148121639, 315884272, 796261964, 950119298, 738357488, 687283345, 600548509, 232451882, 775581852, 84044734, 391774419, 329311779, 658056, 505265237, 683449949, 203902258, 337550285, 672286770, 582486883, 479244684, 427104602, 977033319, 137023498, 992511330, 112611297, 438844485, 240060035, 124678599, 32787455, 231986208, 983516552, 246552118, 189616928, 844180726, 582823382, 490025411, 653478743, 881492627, 636498007, 197121253, 519562743, 221669223, 898238897, 695797075, 891033591, 747402912, 668098845, 677817360, 496935840, 413460068, 39768481, 217030498, 882184140, 897385076, 395448192, 110700709, 479002605, 30079669, 874517674, 142198517, 379482026, 99232880, 610836524, 973471393, 310526330, 7502606, 388912680, 114551163, 487808091, 680856731, 331147817, 48174784, 114973173, 991378317, 605593895, 171527242, 978351490, 787130426, 699159934, 639626600, 220584360, 532065109, 787306436, 192621520, 615290735, 116070375, 204294626, 685740982, 416011882, 752843321, 846720287, 139236796, 400584161, 352282217, 584004960, 164643295, 398054651, 31036254, 704251984, 155200386, 38602915, 348684756, 893155388, 623521364, 378169147, 803540605, 174188631, 787574282, 346258816, 363639769, 492546093, 247440656, 270997961, 95587914, 935373673, 423200960, 989640590, 373679159, 776947250, 493601459, 186998281, 81293366, 153245580, 88035368, 809504158, 149791335, 196794869, 296373960, 19905728, 526947487, 967459186, 314106304, 990866205, 836464106, 93346760, 713338833, 849453050, 481361605, 406471898, 701667948, 342660044, 968533169, 397239137, 248265163, 565350987, 399709872, 53639751, 523982738, 267575274, 616697732, 421494434, 706656175, 613167708, 415281445, 528380620, 867094446, 855856109, 273921447, 326224259, 864669232, 578014720, 847871870, 5802551, 86368991, 508962849, 137639792, 851067292, 344454635, 436361056, 289567135, 173208491, 42470202, 227945082, 430982486, 956521997, 458695392, 579242700, 21153434, 498386548, 160502360, 534493132, 769101502, 267802252, 241460073, 41633274, 405007655, 712803567, 291088946, 888116349, 13339431, 276157145, 575992288, 389707980, 152715662, 730635304, 135938416, 917099285, 925768010, 613419269, 243224751, 447609651, 607504276, 218252421, 291355618, 934163807, 413487975, 137304486, 865899274, 570288813, 146513525, 207533602, 383451939, 64066418, 104720, 38294539, 428212300, 268979051, 486399220, 957097968, 659960728, 710929191, 742239331, 849475076, 433612094, 596373258, 855111891, 999441306, 914634391, 723749044, 381584533, 120122035, 662293986, 387374837, 295061293, 567828247, 611794542, 532612253, 192992248, 93593332, 140773816, 344949905, 154244414, 624396607, 105041733, 188032944, 331707742, 859500466, 543893339, 315572213, 663499896, 420651205, 826987822, 304196589, 29703696, 683534154, 106943995, 131603233, 244835709, 638866974, 767283385, 502699255, 800918298, 66774301, 931896936, 56916504, 415177116, 367627594, 852059331, 464096145, 515244615, 41818596, 931670499, 904598448, 858886304, 655759345, 675607507, 977782066, 631270357, 309967956, 299396779, 211555544, 309523398, 105159172, 51454624, 26303608, 863033828, 528104046, 136692598, 88448573, 656998943, 49264645, 920577623, 116154953, 295029573, 51282333, 3193153, 742370314, 214642844, 51946718, 183828849, 809541843, 709561791, 836866513, 284762921, 246745343, 963985222, 351731720, 934928974, 358450758, 774265892, 562304871, 827061265, 167465583, 405257240, 370846380, 62545156, 244898556, 458701812, 492181851, 607037837, 493321837, 956294278, 448017173, 150220604, 943449281, 750413761, 324653413, 492633007, 374220049, 577084659, 230582836, 582239013, 957332585, 972314205, 154144433, 84078369, 417939957, 393850943, 741445163, 118067240, 690231661, 829638968, 336203365, 533008779, 595338059, 800604956, 217824466, 560775927, 62893159, 313698251, 968076891, 62012860, 943783206, 236371090, 554697107, 887126117, 158993583, 492738581, 447233750, 352846299, 810711832, 324332520, 301187959, 897592282, 665193976, 302167909, 415414809, 50611341, 484995285, 23517472, 443680898, 974991713, 373174067, 499089265, 81799529, 1849736, 397332658, 326110100, 875105777, 179832, 64918947, 286970887, 994877352, 721551075, 756348709, 536739897, 308605526, 155025953, 1560419, 150435341, 564775318, 213287832, 869265477, 878561771, 222918429, 818091744, 857711662, 402933684, 347369834, 443952569, 450755128, 66681427, 257052005, 41145608, 299974728, 945692969, 972875845, 64548776, 161008705, 301982165, 381968744, 832494920, 502677352, 425310353, 985763081, 620602849, 901431669, 265048839, 991168533, 755921364, 413520742, 83334455, 50101939, 226561992, 654291699, 210526267, 176688884, 947114787, 837914299, 392625165, 419149076, 110188399, 916867977, 632531927, 5522101, 617381610, 918818762, 385751245, 145517542, 917811168, 997699424, 292592947, 61203759, 93547143, 331827487, 296334441, 394828216, 372343454, 737527555, 460003431, 83430125, 709944881, 454057941, 935645619, 965812461, 309188550, 27716370, 48855113, 616859137, 361050677, 982281632, 804859383, 807629670, 752144896, 803314139, 670119987, 122968471, 675160053, 204302556, 447427980, 921739486, 382982038, 901219897, 996856749, 677629138, 230337918, 337481809, 747489051, 835859558, 547265428, 891753096, 527815543, 456851993, 726738849, 934960422, 448387300, 30949507, 217786883, 726565560, 393981040, 994495360, 913090737, 619788458, 582562562, 319136403, 16686404, 164238829, 957481413, 832048033, 572720746, 984068585, 552460567, 311811494, 720790970, 607774216, 247389595, 160292774, 328293337, 593282641, 652968514, 413121937, 70130536, 618228368, 893969544, 47427866, 782373184, 854466175, 610250450, 255126795, 600052723, 869342420, 717858868, 866041095, 79734508, 284360623, 824496206, 788485812, 236895479, 110364918, 319018838, 48316446, 477360826, 934475710, 144856553, 962363974, 739870332, 379957855, 199772185, 848217534, 60557465, 153530286, 806258202, 883387887, 579292539, 856437180, 200144993, 491001698, 200256030, 226297356, 436144630, 927019651, 570790337, 807343742, 76255479, 750065469, 285136991, 59004815, 164279412, 724128773, 606702890, 745221970, 843582923, 774408142, 449130437, 398296524, 951609261, 465227103, 371807346, 444735466, 992667233, 297104716, 519479634, 295556163, 663550126, 841701232, 638469609, 534904383, 574597069, 495263095, 391669582, 768232233, 298973242, 375178494, 742131433, 757394969, 184617385, 8279326, 814634309, 930665528, 681367322, 775246941, 622437633, 549027936, 945461043, 558039318, 210104748, 286438357, 108584516, 714376143, 52054519, 478328314, 344046514, 726429673, 393952751, 338237718, 696269459, 914575852, 658897945, 130774387, 250542915, 606304811, 526202193, 533364729, 375113401, 460953319, 458164874, 822243181, 486277958, 716685358, 772989627, 697248613, 414466820, 635933702, 139221037, 773820571, 822106102, 412290927, 380230648, 652828138, 176044546, 401415865, 697102345, 438925011, 877773564, 273734734, 469714408, 826988877, 971264451, 509987440, 600170223, 238377206, 49264923, 314389696, 195040331, 420897446, 286398082, 272753715, 73050793, 686390411, 523128232, 694135134, 748904569, 813643741, 16670081, 765191264, 336210831, 340619291, 558517621, 221776481, 213656870, 135875324, 571992757, 646440993, 865603922, 759753365, 526797555, 882016952, 661127565, 564405406, 19895793, 970779928, 747189480, 414850221, 916222152, 752869410, 102597689, 271036047, 339693600, 458598082, 47141449, 294600490, 594733555, 758618039, 790404687, 201290349, 730784821, 463530704, 190305423, 428000590, 622156395, 611154703, 205006690, 132430311, 958364225, 472231327, 668735211, 466132366, 184919713, 461394140, 760361245, 304891814, 730828451, 951508765, 237336180, 836783357, 445892783, 433991068, 150446759, 675250154, 674265959, 722357478, 435961905, 942928856, 944122603, 342918513, 711432834, 848489371, 329341614, 993346412, 597202165, 459966463, 657524819, 198627616, 747691462, 154333591, 239287520, 372202481, 741727043, 34532054, 265781414, 668724043, 320876282, 344052319, 647392095, 546164523, 7336920, 112498128, 159329175, 524835270, 413962796, 515605909, 107098229, 200691332, 972921028, 50121639, 539089577, 691300089, 718895805, 343973763, 183790369, 135405409, 822823220, 68455976, 76485831, 336543467, 17400943, 276858713, 515715755, 311342096, 927188283, 642218023, 983196771, 698925635, 148660264, 907702761, 546054978, 549607248, 141154804, 125366434, 756234220, 607367243, 866994692, 602136181, 147424948, 566729319, 769334306, 102533144, 701382246, 719762825, 66620113, 12287624, 160457446, 673146022, 643834193, 633590341, 343695327, 855838910, 971941030, 418674514, 506890046, 42012066, 126276486, 365170879, 871271727, 348454146, 330212573, 77114291, 594791104, 146124356, 996886817, 834283873, 388969736, 98237432, 297225576, 741323572, 577602224, 370170983, 299353999, 784152482, 427572328, 802917480, 570380629, 992954859, 278339275, 75190841, 981517340, 618004093, 657841603, 342824633, 270777008, 24940004, 502884924, 176626731, 137782111, 307555130, 817944054, 628129014, 276903498, 392940402, 934226349, 874367556, 395768874, 949574778, 242865930, 405262900, 794334049, 414331009, 565729267, 933195266, 816589991, 119835563, 611722527, 951970842, 61371377, 83534137, 972135296, 584133017, 203483747, 431581523, 321031555, 91239731, 385931005, 295722598, 984857098, 806310965, 545089453, 849411388, 651859273, 333675593, 174989731, 530529334, 773855417, 283707067, 421208352, 720840587, 700483721, 153001700, 129574501, 121444190, 627827020, 633699806, 219753988, 51312318, 373339552, 514269565, 777401411, 170094995, 921460436, 264703121, 446995797, 267499012, 266398335, 319527523, 936593144, 348046682, 387998206, 422295390, 490318976, 479350564, 406500253, 295795267, 233369749, 938954810, 438956999, 916405471, 253327583, 10378096, 16156111, 24610805, 984665448, 738655123, 904555017, 400018227, 343473696, 909998561, 538405330, 214734809, 96734697, 133572116, 697508737, 361632105, 184281638, 535173498, 110973778, 152592542, 766660331, 802017705, 155926315, 665382955, 62996006, 990369602, 628503786, 788286498, 801795067, 403354491, 819477312, 17103090, 819150809, 780793492, 306480402, 332916359, 480760426, 769514674, 118339546, 431905819, 349540340, 849974332, 307818213, 460117986, 848352093, 353556933, 532892052, 768384826, 996881380, 97050283, 116291911, 488637702, 699987822, 865064888, 718878457, 4535910, 667433163, 464903494, 806542437, 263736990, 571164947, 681095481, 768341601, 839125284, 119583983, 663714324, 805111510, 551338403, 737420916, 669878230, 333158490, 8975025, 979192888, 779335892, 451538305, 688341458, 698253402, 392499422, 656537088, 356616007, 933291163, 260969186, 200085233, 890519019, 771192283, 277887025, 16561508, 312775461, 712762271, 702468415, 595854578, 126302578, 354247945, 250196737, 863236638, 735624544, 709023051, 962863702, 118119044, 694964639, 583717837, 245324510, 316634950, 316855873, 177335867, 277528090, 132421373, 363193628, 30386177, 623935698, 586237325, 937167796, 689549339, 358869134, 796603027, 172070818, 561278433, 914495060, 858952468, 481736051, 886031571, 913566677, 696148423, 936423301, 387426634, 857158306, 847228343, 405728403, 910083947, 357179057, 179550030, 891159699, 249221911, 357716950, 697830408, 827230891, 223758582, 376021339, 771697879, 652518890, 763707075, 930094244, 492685948, 14913443, 761179368, 502641737, 870339788, 776963119, 341706425, 554970945, 669185155, 387150075, 485116478, 360248786, 790774269, 196728228, 313951669, 244264320, 148609178, 135410666, 214092645, 278936586, 522744316, 625274360, 858823038, 525866447, 756622430, 194187218, 439677319, 349792257, 353653436, 319197655, 719322133, 948333429, 34385632, 626939796, 3975929, 767773083, 482412888, 369459322, 737535742, 500147655, 810443118, 694399559, 431629424, 686672, 374272333, 632712335, 663319671, 862852169, 164616270, 614921795, 91027600, 368146335, 189767205, 418667996, 465920829, 891013256, 781219893, 914289145, 499746582, 854016093, 735367484, 468994642, 664654680, 361619200, 593465667, 842868706, 718543396, 916382983, 447782039, 83170438, 493016706, 650625195, 743145379, 743743259, 459840114, 57500984, 783033500, 75815510, 636311182, 395241594, 42217089, 920672224, 933286339, 170121469, 702813065, 685102992, 585654894, 956710376, 321348568, 412342978, 185668897, 280576694, 598463486, 445260425, 89783772, 854793743, 580663463, 259249939, 631069977, 683771692, 666336497, 58597755, 851451394, 234035200, 89327305, 613140707, 13802815, 754903684, 266303516, 149118048, 813984373, 700180543, 724180355, 146067134, 695732553, 819404196, 228915643, 179972408, 679581092, 126211855, 593784984, 813482050, 682315175, 429491726, 734418117, 144695997, 432527844, 9807539, 813497224, 883121452, 685680627, 355181899, 481368192, 647552142, 941427238, 845832775, 779191804, 374481565, 109744614, 250488362, 839645675, 505863461, 397517038, 372369145, 335309180, 358419329, 706747887, 661257656, 883477533, 180648081, 945693033, 902441048, 824783675, 244835093, 860348126, 178881414, 666615636, 607653234, 939481137, 95090993, 663839900, 523483607, 300365016, 217266731, 714993948, 249486238, 374537071, 957124264, 2162147, 792506138, 809991001, 966883412, 348188798, 163409198, 217126749, 341867503, 220142907, 297388618, 926674906, 663459719, 315708768, 121011520, 717829882, 23726743, 416128018, 681650477, 733658610, 962382896, 925695646, 453717478, 817052181, 116313747, 94089643, 821300898, 32221221, 788746678, 387298516, 3785579, 250524480, 951667233, 44344359, 423835893, 754970162, 360210079, 689695419, 134906508, 665301149, 860725193, 453980546, 568421085, 775360222, 964733354, 985180421, 606366150, 712955649, 933766316, 563913449, 596002957, 70101026, 553329224, 373144814, 101722274, 772527384, 77245533, 545256177, 955186641, 400283853, 444817565, 34538518, 324592890, 538634281, 501988143, 688943917, 816644386, 767512313, 572098982, 640494278, 858687914, 204983807, 669978262, 948527929, 447248835, 553560065, 916105765, 404921858, 545897615, 379782138, 729267849, 264596790, 1777368, 548042525, 70382050, 226787089, 287704206, 963813511, 618973421, 928073601, 20681142, 439787357, 799196581, 411858612, 797429496, 666065742, 50655915, 873992979, 846818721, 721623655, 237718301, 858310590, 104010053, 946740169, 491550696, 678294743, 620181587, 293469380, 196618226, 272986848, 56506542, 866070533, 177629150, 973321927, 770687200, 377298216, 756361275, 38981775, 416306338, 426057989, 634520595, 414827411, 953694678, 725677836, 145754753, 153757938, 141890847, 887205363, 260000700, 5315399, 764747688, 852062262, 916821560, 777785542, 568931190, 316424551, 575556853, 524784244, 650025205, 41604235, 455470215, 203300029, 550876455, 102723016, 286776832, 894775530, 838856486, 139620789, 939042961, 151513043, 906002248, 749986564, 819300778, 771279008, 987015122, 771059611, 232967912, 844344519, 659519050, 750968827, 568083586, 371033028, 154917340, 354351601, 382972918, 659068436, 660276856, 641514431, 555214734, 984479774, 990464074, 516904183, 783987347, 899693107, 896544386, 828969932, 229998151, 254566958, 180776871, 7069687, 705349183, 300316288, 768091629, 505272856, 540144937, 410141615, 584756257, 601810859, 964662115, 956281565, 969757081, 259521311, 245097786, 442958030, 475019506, 512055506, 6231464, 462430351, 80114268, 26646932, 734733234, 529968811, 742771598, 646656219, 672773829, 22975924, 311908591, 325959972, 870748603, 165728530, 326670322, 467553604, 927885564, 572863601, 288155855, 868881438, 407497022, 950718720, 687809268, 794020595, 273648899, 245816941, 401964136, 540652331, 343074028, 317509351, 516169191, 153482223, 328816784, 940927059, 559599085, 876174440, 793094138, 237377941, 609660154, 435853321, 473179952, 132685902, 188956265, 376526522, 352514459, 174384997, 350251713, 446498300, 981681801, 135869420, 783310539, 150740476, 96052776, 13994961, 660112273, 736222144, 893198802, 160797286, 371864733, 394220175, 684745792, 820414411, 453428147, 987614054, 243737131, 887463283, 101696987, 999379116, 991080665, 708097568, 945920389, 153770523, 317329880, 200637301, 748045572, 61933894, 357203913, 498613473, 732436858, 213665565, 206753009, 651302612, 936322825, 553664445, 627538539, 801312908, 383763832, 453090512, 498932255, 314826392, 654555799, 882245136, 930538570, 711376723, 277147268, 359464167, 671839889, 68233075, 136097587, 68809771, 189562825, 45971399, 776954161, 281197543, 592978224, 514974948, 68746372, 598770416, 674879917, 664101438, 303190921, 103483869, 287435351, 859896303, 459008422, 583336679, 785978403, 269049937, 793704040, 237204181, 331614038, 861066632, 800233337, 913153563, 169788116, 804718797, 937772457, 613745514, 541430040, 763583624, 439848669, 328779617, 699015974, 797402269, 738292669, 657086889, 984792424, 8419942, 305848416, 796017854, 484896081, 16404984, 177335636, 837506301, 167180112, 520746553, 650895517, 715511431, 387043052, 583671279, 424001760, 498843573, 986769476, 753263355, 937462544, 639327110, 441996860, 130189434, 925700841, 165356423, 748657964, 908420718, 377452793, 536394220, 939875318, 215950711, 51589682, 989842408, 379712078, 485005743, 673638572, 28846599, 187034489, 874886107, 60724951, 825625618, 649907087, 968232872, 358434786, 649775511, 673919461, 810606440, 406300090, 946202485, 580919898, 102764303, 660942561, 210928161, 684702812, 925430021, 290892312, 769001309, 775721831, 37041715, 910630280, 358583055, 371824250, 502454148, 962041015, 848374066, 142994109, 590255212, 813065821, 20546712, 827464261, 828542010, 330014769, 307113540, 288802351, 740527174, 706500360, 48929795, 611617502, 142752515, 407705713, 445310106, 413544952, 78725108, 587190894, 702010163, 758292817, 19870765, 468665546, 375459272, 345668685, 836852811, 189691742, 867756912, 589959954, 764371552, 220508831, 299620208, 323722137, 449088591, 698479323, 881025184, 146445364, 848486828, 785224629, 389375267, 328315665, 690997436, 746845894, 706927440, 936504512, 887536660, 753740163, 762966388, 759107693, 808503922, 980643425, 781750462, 601472813, 64709921, 32418229, 622045482, 21520853, 616315825, 108153057, 248106334, 571311049, 773416470, 838904778, 597991326, 574228436, 517575510, 158743751, 527319218, 754719688, 148994953, 535045038, 270485504, 766368979, 914178034, 52147355, 83444556, 698699202, 265827023, 330075675, 92800020, 517689112, 195818363, 307094324, 839729271, 909725631, 614390107, 250471782, 153187269, 515433693, 112515602, 482413608, 917578300, 29141148, 646079549, 89588739, 421047904, 881472301, 668491543, 949353007, 197276980, 675795532, 726195408, 159232435, 716127103, 414638833, 523782077, 736999332, 888765805, 760795438, 796290380, 858176291, 145315453, 277934040, 364028252, 104575960, 802298472, 748591476, 386293584, 631260588, 440953393, 76097465, 367107193, 527113910, 453869886, 677183474, 800234497, 413958229, 654937323, 499287731, 312566480, 103813840, 540688794, 755440798, 509407030, 461741958, 584950429, 400994697, 660934213, 179454817, 785679179, 492645553, 863644164, 368753156, 445588951, 531466783, 143902397, 32035426, 820488376, 910741032, 975025146, 432667379, 782782374, 952810130, 24002416, 669934882, 300037631, 126429821, 602504125, 363438517, 389694647, 904441440, 624605575, 804007364, 311541382, 133596339, 48263592, 438687204, 478900168, 518800840, 976740075, 496436775, 927314125, 310603099, 564129632, 7458480, 197113110, 578306214, 736668056, 641954833, 931965797, 674170137, 298166665, 83970813, 705063696, 224094466, 658064701, 876044804, 490511617, 319890286, 431714484, 802463232, 483118698, 272107623, 325020423, 497323281, 319657570, 66000592, 238306618, 718699678, 753576744, 780908781, 676178927, 447324248, 330123609, 773576896, 587313004, 682748294, 80806993, 256972024, 259555948, 535804692, 43486467, 794195911, 846950897, 547986040, 675107252, 910906315, 820628937, 408336651, 37864361, 702931512, 152719460, 83188389, 642300234, 928711074, 253322384, 874132048, 719242056, 278949278, 408512031, 769280949, 440422878, 615971499, 195717820, 434953669, 253583926, 469084661, 40843034, 47388840, 400572741, 278006367, 150541592, 721425133, 223371933, 433996988, 946389123, 566141762, 640584850, 829355585, 505144637, 306517725, 876963198, 34177058, 859402682, 298856742, 153722688, 715512015, 836842582, 38499367, 7327409, 428561007, 847580725, 107356955, 914546226, 41890375, 155563347, 444173447, 200684023, 499712935, 87410735, 407385781, 135508711, 173481782, 509646921, 367265675, 403077584, 462430718, 47520140, 445669707, 55907484, 320728153, 550549218, 865476349, 541541139, 321159342, 415993957, 38076905, 304075479, 876766356, 476106574, 540496929, 22424222, 965124220, 597791852, 964299346, 931303827, 792863524, 31133222, 87423055, 964757417, 950912266, 18681659, 602792064, 810517861, 95316784, 512488179, 411570599, 179348780, 24445003, 567050147, 161332134, 426502532, 214318772, 356527334, 743576759, 898948472, 6657134, 643585587, 392595209, 763411880, 911405518, 85058024, 835174824, 229305527, 236170413, 630020838, 50421611, 721153871, 707196875, 53927104, 175558453, 767708830, 391065032, 852197650, 966811550, 612389816, 962967659, 2389994, 273025157, 377835843, 467873638, 479561856, 658897313, 279568084, 465247300, 470710338, 569406077, 490942838, 748016696, 931985312, 519124553, 790798634, 797173596, 197692220, 404795663, 67337862, 406711140, 322837417, 72310142, 701444801, 462763128, 650265394, 357445851, 259390263, 50715693, 348417870, 283277017, 881821871, 371898695, 328262921, 152070520, 574465596, 48894261, 105765092, 189396862, 817934317, 809118531, 202141437, 113966709, 101389971, 207584169, 740138245, 31727203, 502272039, 595603666, 335541762, 604186583, 922478784, 505307045, 575740433, 935235771, 783295020, 936535523, 236071420, 557534878, 331995330, 415837475, 187858146, 541916379, 12483303, 166770205, 631723560, 238195490, 156702429, 617937748, 958231954, 913157637, 574791761, 347029212, 662058523, 163017829, 564945219, 633486334, 939514069, 213035339, 121493295, 639350308, 694830216, 825410589, 497939093, 157984065, 53196659, 268971643, 968652415, 972346720, 429686110, 335335876, 893403903, 320889189, 20628047, 481857599, 975420905, 685766460, 622875192, 858485111, 689890040, 633188714, 153620690, 91344298, 801908473, 74201993, 972255170, 477015158, 171170040, 592888599, 226064911, 936567579, 565491527, 835516641, 748207139, 243015691, 909518345, 139918621, 885550082, 45927824, 300736365, 732396664, 114092641, 518243233, 227870104, 507792155, 181859824, 369943488, 402764189, 784826898, 585798356, 449382644, 395075502, 612060714, 849101680, 660923768, 56479476, 601703670, 646688168, 390174463, 497700655, 74715111, 748384715, 301923790, 174212094, 233533055, 733766905, 934142419, 269116332, 270434270, 188367344, 263313121, 911804518, 980150196, 635935753, 722844963, 129003828, 579183845, 756889514, 279091956, 856301489, 949457523, 201162351, 290351976, 96246401, 208392082, 529984747, 417291323, 407739288, 337936101, 949991128, 209464143, 475932076, 523165050, 95761237, 491456103, 379794160, 471629496, 705875620, 719767334, 42140098, 992862135, 285605360, 188622016, 922671106, 361467995, 955827138, 741771449, 822396692, 82225429, 586617630, 136809524, 793184723, 705990863, 627665635, 782399492, 39717233, 634707422, 442874464, 816358172, 219442601, 982798370, 699129594, 926217781, 114062667, 938839553, 791199094, 10463997, 282636500, 450815888, 347683560, 279013514, 238217413, 647724426, 904305684, 586094219, 233132981, 782364455, 17861890, 81655384, 570727507, 22236246, 564750181, 414395175, 87357827, 881285762, 368710160, 726548759, 473399692, 458736155, 630129218, 883690882, 110375993, 181924643, 423821033, 699988610, 320143550, 289256687, 285021622, 47481476, 75303985, 548505102, 809125597, 473685360, 716137929, 345444788, 934525628, 198851243, 387702508, 733915886, 343722848, 6437232, 138207722, 112370234, 507005187, 690460480, 711736360, 471395500, 188489153, 391546022, 396359631, 625288742, 510243047, 626068318, 233824928, 619908877, 357698425, 744548741, 910244244, 868992491, 128060487, 418861650, 252951993, 533966648, 703409842, 425027279, 856811974, 122588782, 831167708, 240123512, 440279660, 770824657, 964547086, 418454621, 927493241, 47085041, 257489826, 606388418, 205211268, 829861874, 357129002, 771685254, 189972794, 823260405, 378853403, 923251009, 475690043, 376384678, 658496374, 812205363, 570941888, 58860851, 387023676, 226039445, 281287653, 837454881, 31286919, 308946156, 258517846, 327188228, 930883135, 198746020, 216161217, 691229225, 746981649, 514915090, 300028248, 102716560, 729394495, 962260298, 747375007, 545093922, 520243479, 664470945, 50386412, 300218552, 214960121, 321668494, 558695583, 850353317, 598193500, 478611134, 574438501, 350148763, 750938643, 781576000, 230196251, 855790909, 390674701, 131305306, 501234936, 140050724, 795473825, 218957699, 497873671, 940732844, 639386785, 348137742, 340638528, 61005941, 618314577, 29027934, 476479428, 914309427, 216719717, 746208781, 838430655, 808566934, 412407730, 782843930, 323669841, 490865125, 693324873, 328788581, 873942809, 65413546, 8551921, 869560345, 703347888, 563062079, 287031143, 232272337, 342348032, 673280003, 529547223, 421089311, 52696009, 824181472, 534141141, 107065481, 152877459, 333136964, 439732978, 725110271, 489995456, 469454793, 535740965, 794444799, 781851091, 300358831, 713808505, 288447856, 97320314, 617875288, 573664382, 774596066, 548760736, 608186881, 962773522, 265794022, 702478936, 531748095, 444526031, 783901808, 929569327, 78994594, 668474228, 631982588, 707447215, 220044704, 759518480, 280755019, 619889021, 920966608, 11871048, 563415883, 49072294, 327937331, 56017972, 57311939, 10233544, 363546742, 142399384, 685945357, 102136934, 591046234, 398140980, 350008632, 864942879, 667722699, 82277133, 235325892, 753094992, 152872884, 444593504, 732742970, 780696397, 793013855, 740271536, 10109125, 648305983, 207166905, 547395128, 652285402, 821761782, 300711609, 812841036, 755128504, 962668972, 971058588, 580835306, 869347614, 456711980, 518390720, 771856152, 397531858, 562496399, 228955264, 553583330, 305760850, 971002518, 913796340, 403977387, 901252501, 734570760, 952902394, 590316030, 99286335, 434050408, 79960616, 767875288, 172605466, 960850263, 679151894, 707636918, 419403898, 998544692, 642075818, 241511237, 325102105, 907026315, 658297157, 747089169, 718179790, 291368942, 92047071, 98389708, 344003657, 195038510, 57694582, 595293917, 7578598, 336915476, 204579783, 995873079, 251474129, 692201581, 707327284, 346878475, 543406943, 747579028, 829530127, 48848246, 504856930, 62958543, 127333003, 360807690, 239941569, 736738228, 379707175, 430456460, 904222263, 174493827, 145009725, 197423739, 213714010, 605602706, 668745743, 180074092, 621005251, 466445426, 189387340, 482219975, 450219525, 758815313, 478212542, 586179130, 459999673, 195820981, 870866312, 83968397, 935383761, 570151795, 970357994, 957895231, 346163754, 1763280, 172248966, 489599240, 165419248, 463067364, 19898754, 860235, 620389436, 895133065, 857187084, 675972110, 601803388, 725321574, 471473217, 499906377, 549977121, 38568499, 504711128, 738519254, 157943128, 909256164, 404527147, 93355790, 512500511, 988565779, 686770582, 996854330, 974402473, 117610068, 162048308, 875548382, 80491164, 942913531, 364120806, 278111887, 695771146, 911722191, 92875516, 464224885, 655448226, 727336837, 498402939, 51991515, 15478108, 675875624, 837256294, 943427533, 815299027, 919692627, 386084249, 674126225, 465351306, 328176185, 132546365, 750248962, 540127860, 257581142, 854293543, 106117044, 595580024, 312172568, 353239991, 540763252, 829084877, 290216970, 833701533, 436189342, 294212746, 189589239, 223913985, 359115340, 308917799, 591119235, 731115473, 151234528, 585725176, 257449879, 904836033, 669131435, 782011104, 812454352, 188901596, 633041849, 91740280, 524429241, 330074788, 157787196, 255838036, 16814310, 354200891, 537681391, 640715155, 381634699, 393277207, 931345096, 842638029, 729918072, 743555949, 463334186, 410720208, 376995814, 702087328, 419647542, 787579433, 638934368, 273747888, 986090669, 559245319, 687701776, 248680503, 180266094, 280349372, 465624132, 612019322, 682527834, 690429412, 55394762, 649040644, 692527081, 819708514, 801026514, 226934178, 31666766, 403615288, 300068754, 587180599, 36795267, 629607347, 240490179, 558606314, 52458679, 979796718, 810194369, 812752688, 563622792, 485375012, 857431160, 134889279, 737895642, 494263010, 358164994, 186720718, 277873476, 52042494, 502748112, 485205630, 425705549, 900286465, 486159040, 654532989, 259634625, 122158405, 977827706, 861442950, 155571413, 91372087, 932031677, 429503359, 64580958, 270650533, 409532250, 836206279, 867748663, 761893898, 915203251, 640228272, 413720192, 16295523, 267501178, 527003282, 313540115, 735120976, 694436914, 460596356, 588040083, 491425011, 195115410, 926092386, 97423090, 77994861, 151597411, 963835117, 671876062, 834666879, 769153288, 858844919, 448573954, 2190918, 250068462, 516913795, 52414366, 504597834, 586217192, 679323003, 174443827, 197799263, 394931440, 52184706, 808572960, 454260333, 488648557, 638855335, 502599651, 365612627, 25770639, 803164545, 985381374, 897193786, 843136754, 790956979, 957751477, 29010630, 585648998, 287355775, 156177759, 819491736, 974130632, 790326491, 233289540, 123122385, 660438594, 426041567, 496238617, 142978424, 405501842, 175456142, 178949955, 678111709, 251289494, 775734746, 287457738, 748018830, 113318070, 948180376, 403968855, 545240650, 961131590, 823861922, 837450186, 921686806, 930593062, 386150910, 270399502, 222051889, 232790624, 769104364, 472881025, 175885940, 454961595, 713330555, 962208962, 23984787, 574237169, 477368453, 717142148, 278899029, 623407013, 70609974, 78154245, 123928231, 14170183, 739775448, 639642291, 559922281, 217204238, 537969787, 378222624, 637672843, 157922337, 569734157, 220403829, 654761134, 345126877, 791916169, 378588018, 90115294, 388630282, 168130828, 118309812, 712054837, 627157257, 653283898, 737912746, 851110829, 670752484, 41069938, 630642327, 441866736, 480036700, 128176674, 11490511, 760172033, 836557941, 682780520, 512045405, 980752310, 199405572, 349696325, 669146132, 216545787, 757249324, 86896936, 832030077, 963121789, 514672936, 903624524, 945677669, 997176613, 249700767, 876167483, 405000704, 701463187, 317568943, 8972370, 91580684, 107237964, 654342944, 539658540, 519683501, 190485684, 713956696, 78150385, 730160228, 925357450, 42629326, 339978347, 997620347, 81692960, 309258035, 389657718, 580331441, 929601324, 769378911, 386104145, 462488367, 936240791, 431002443, 112361876, 836503893, 870966996, 471477331, 573085316, 10020635, 286499197, 149153840, 665626489, 235537129, 597259263, 776481321, 279454151, 33912590, 952403994, 258929810, 763516722, 356194229, 995065659, 477988327, 204828883, 530019452, 193654158, 354895599, 158332541, 869752575, 203364831, 751729055, 92796826, 969921848, 19531513, 140654515, 534798132, 227914964, 254966521, 231999495, 687727562, 983530974, 305222255, 288180908, 253935257, 400539994, 462524537, 644146725, 533450173, 820859154, 733940313, 696968057, 401670232, 311861491, 749775042, 37498565, 419306078, 251908119, 570490330, 562260670, 211352924, 622084652, 912732988, 596264950, 550425880, 228235104, 918527369, 247933653, 349529092, 684101765, 20818795, 109497151, 678276106, 795358438, 536256651, 297166374, 15130122, 154724843, 971693973, 727253278, 708576114, 419132858, 869776218, 538153483, 481608986, 210411505, 669313150, 507183033, 78582090, 356620366, 326440607, 109878354, 190689001, 61095875, 580927056, 572130000, 251859196, 469670142, 984816927, 979077401, 84812301, 217108501, 646372779, 238341524, 215985032, 338193428, 54567506, 924370637, 708958141, 685974253, 837458122, 236484218, 780477524, 9175980, 76269407, 261173473, 994321454, 138154013, 739612116, 370167249, 140373596, 730598304, 585572375, 216776244, 933539689, 379893109, 926066425, 588156574, 662215885, 276471257, 50708856, 193041257, 142573328, 956506228, 338876559, 808847928, 681814007, 457016692, 435139545, 182777984, 704436319, 495072780, 213332579, 922795365, 683233791, 592128555, 589591044, 227659358, 516709915, 512662910, 957443636, 79429859, 208305381, 738874251, 371969944, 300000026, 968047520, 965111899, 349919051, 372120104, 766466203, 478162107, 175871622, 379711466, 887509313, 822655576, 415694103, 1242933, 503055544, 207667573, 65831134, 885248740, 738750221, 693900060, 752493889, 22666666, 656489234, 840038574, 623444441, 606108205, 441947779, 719302370, 123163369, 941706952, 941795007, 318364509, 678527355, 126654681, 554335477, 915165690, 153544851, 161110051, 600321126, 661413170, 805071077, 453156112, 915870871, 313912363, 122211243, 696718942, 514081824, 801812991, 776511845, 439547635, 803034523, 375386720, 384192918, 117834292, 934056302, 573503395, 24023744, 612303111, 930020233, 955419916, 59943439, 749455251, 964545757, 956800377, 667369434, 72391836, 172568026, 176713260, 766760044, 932370771, 34412387, 874829371, 999925891, 756854170, 476252532, 18658297, 86365232, 490447409, 294973453, 21321013, 49726827, 897418951, 160099330, 113405012, 826737107, 811933615, 858368126, 49921870, 317994981, 382840715, 216988662, 600231510, 886848998, 154854597, 956066132, 625573025, 359923417, 354924584, 280908925, 289276457, 121484652, 431831385, 724052794, 185350209, 37737754, 228432041, 265778595, 779720607, 477906987, 611781854, 765475672, 844687255, 659629696, 538130026, 272190819, 808270442, 851503189, 809059333, 491113230, 500738112, 307073702, 949500875, 154136617, 773056804, 651027824, 852511592, 709646109, 183492777, 649530512, 244402513, 545743005, 579965286, 285369977, 809788106, 381426757, 829893123, 508394615, 660853248, 886571593, 598158132, 809008745, 956520257, 203233763, 180861338, 950583200, 484539651, 397996562, 710748668, 625085967, 889687012, 517681907, 523648458, 587415686, 686768964, 750350681, 235606859, 815966463, 539144812, 491066422, 4522534, 569840335, 6175056, 346906481, 921080530, 21400324, 427599216, 695704599, 966848057, 556583680, 570671227, 293449341, 709709165, 397832590, 438103841, 288494665, 959858067, 740317324, 451733748, 959238692, 970808645, 750662557, 483832607, 447631895, 681397204, 506318577, 324002041, 445542160, 326792842, 114897890, 458390786, 753405882, 263599620, 677782357, 659634594, 426387867, 409609256, 920123248, 200139927, 950158415, 16187844, 320257455, 375937478, 590665216, 520847382, 14514547, 258827817, 827271875, 911985533, 721842484, 882259614, 923834739, 97732558, 631654234, 640130601, 987816905, 653890766, 994275194, 278932250, 39771520, 863699063, 233466413, 993428749, 930090557, 602077989, 8447296, 850809346, 301401063, 232075360, 687646350, 303734235, 298959370, 77065771, 839775250, 708666899, 94952985, 822608767, 738398167, 626239047, 215250695, 298626905, 842715487, 96008073, 770479318, 852749623, 779884548, 732579536, 137756094, 814439047, 881992602, 432630599, 712158286, 571487768, 104234375, 819008039, 52269991, 594607989, 912795832, 459567506, 410395468, 445991580, 612769896, 988172913, 766953111, 232013591, 892595766, 994935415, 241159574, 877604620, 589961914, 456810429, 723464270, 729688319, 96308506, 162874454, 368455822, 983245449, 227895482, 14038552, 656926976, 592699702, 538249467, 432694798, 956280613, 39213917, 333384671, 303277209, 792537138, 314321863, 332954421, 789963227, 630171154, 428663123, 182833773, 160574575, 287191344, 717851330, 177211762, 986146158, 112079600, 126581015, 209191136, 737996780, 691351948, 798533382, 554449773, 327890164, 675818889, 626032197, 91827004, 632520877, 710441899, 872059484, 667714493, 69239853, 562692158, 142643035, 914873337, 130872807, 876228510, 595255005, 820709012, 622943192, 797799494, 752530817, 401676906, 962203200, 900816610, 383099047, 28866420, 147336881, 996058774, 506964821, 64474025, 431293575, 501817268, 948897808, 526456757, 267497345, 321353389, 13891543, 878421350, 968146047, 777667195, 744758606, 738844882, 809783441, 654990109, 169063919, 750157953, 751123594, 208180398, 111147998, 152585269, 956764815, 678817723, 547076337, 856985543, 235363502, 122760203, 537753723, 861092907, 638910942, 342744642, 943252881, 668906066, 797781843, 881501452, 48159359, 793494669, 744854859, 391738941, 630526478, 43025718, 434375048, 309043048, 643256909, 929085981, 261921361, 208945795, 631404164, 471937949, 85229783, 753337593, 962668078, 194811601, 848727000, 48376623, 706955786, 784778666, 811578253, 891348545, 795291844, 121625624, 18391846, 567162401, 190455376, 639095182, 71551748, 453162943, 738234480, 797053628, 988428774, 381228749, 667668471, 137632787, 868700239, 42301913, 690270194, 143647013, 775947740, 504306064, 23004600, 748670096, 545660085, 65513022, 860862779, 858436322, 360713710, 418902938, 255930151, 805954109, 880212882, 260124804, 769476669, 461163746, 323077699, 204796559, 30824965, 812691726, 771033789, 394477128, 784519644, 32693883, 691172834, 795528287, 488802821, 146234953, 219718465, 293274807, 502151464, 880445965, 802957346, 411630620, 411578915, 761228626, 963274399, 616178960, 669764424, 22748181, 707788978, 834272624, 899461645, 449175398, 77909814, 792420986, 529664589, 572969987, 234106640, 647327323, 161796139, 630962317, 943436602, 354681759, 321644943, 64989589, 81794480, 456613135, 632145351, 429680117, 827465332, 753821859, 413826108, 967124544, 996057569, 842647032, 337996201, 87516139, 596502465, 110453116, 568236465, 497758908, 609724851, 716915614, 70364264, 470173227, 704968482, 383320149, 981438676, 675818358, 284495641, 33620891, 951020041, 305852987, 457882255, 419242159, 524411258, 524742833, 150306555, 992611391, 959646216, 891795761, 630605072, 534975532, 805150926, 761237435, 49206127, 14983301, 968240059, 695095210, 645170764, 210594319, 174323405, 637827932, 20413785, 787436195, 644388480, 69269283, 464933376, 518659869, 245898082, 633099354, 10644913, 81377942, 511477257, 768887790, 665085802, 103752082, 976839676, 247328973, 483568495, 799300535, 31968413, 144119913, 934814554, 352613583, 171672921, 166546007, 393318814, 892367132, 854869939, 389163682, 579083723, 801171996, 981598700, 430478250, 672541807, 57284032, 90181188, 796777205, 535333747, 895301660, 677922108, 884798916, 783512438, 387142808, 971700977, 726661453, 489629277, 69332786, 812447967, 751511500, 142930372, 243879075, 536895097, 7307897, 128909656, 175470994, 867962140, 817154030, 387907573, 215368674, 892472067, 186324689, 219577421, 62907113, 555264895, 458236338, 594689758, 210318497, 641078528, 45497955, 289403865, 379245760, 572783630, 513119690, 866861327, 215719081, 803077119, 388534762, 82190010, 120158052, 41157609, 121560372, 14560596, 631786016, 422385447, 644794138, 285852883, 989082342, 286122100, 607226510, 477626952, 310215241, 948240990, 315526584, 134714403, 570916460, 811958038, 593291127, 982466157, 180688223, 33165987, 818313265, 584301895, 348381390, 9137347, 57793455, 575273635, 185907899, 990607179, 650029971, 778627223, 467049639, 564520872, 675713587, 930763723, 285798710, 730045923, 59024313, 182555786, 562744034, 114791017, 28824252, 351943186, 118710414, 490219151, 485313399, 767076884, 394348217, 435951661, 621116693, 558012502, 867350520, 963560928, 768101390, 682530364, 619848624, 252304447, 589158066, 167497061, 942062986, 666851107, 552716910, 798568954, 659859408, 667326037, 237386716, 132769380, 399794172, 653431866, 22023170, 788804255, 829739719, 713948753, 784081612, 714442716, 638332204, 276044649, 240093493, 416177188, 20290255, 269299268, 284367553, 322948222, 797789094, 237413716, 136166218, 195037209, 378816584, 357367740, 477523785, 607150603, 640725337, 121195869, 940454453, 91568144, 58605160, 882511108, 703742641, 270610101, 649262597, 256399912, 771229336, 955970609, 894026715, 49135851, 616430606, 95749177, 163704304, 214974767, 794137912, 406957544, 864919268, 107960411, 715671477, 555465513, 7776608, 413602260, 412379192, 431740822, 582326744, 237386177, 584350271, 806394465, 669299343, 895029364, 16915104, 957569529, 726320499, 799716819, 903503733, 311325718, 322563485, 827597540, 718025739, 992156277, 639087873, 357487850, 813560360, 342639907, 358348905, 156145992, 769618685, 528265100, 910045178, 284256983, 356458173, 689869679, 472912783, 44439099, 262524420, 322410721, 463125677, 189026646, 377740257, 485827113, 110148651, 293652405, 113706957, 669686899, 500294827, 781496275, 352034385, 129944350, 256439246, 869194058, 660138288, 338363789, 873038899, 11351607, 459510524, 785410375, 753043979, 465725296, 78029866, 654048070, 698465580, 598130774, 846632779, 190323256, 615995770, 462120405, 805838511, 802470103, 295890412, 449342095, 212255615, 690921599, 173032282, 357892693, 954483157, 310287382, 967200807, 539367128, 54522449, 47846315, 917450139, 264859123, 202965448, 745514743, 533432938, 642085328, 194669140, 839186567, 267051814, 425477528, 498250683, 128586273, 533736245, 199294490, 638879718, 690068032, 102936407, 707010265, 292255803, 445841501, 899873475, 205875881, 280336164, 654769302, 88068505, 934972261, 750384970, 671317871, 349995510, 256646589, 989090556, 145613394, 811077091, 271133265, 42735565, 990644591, 563993336, 822843316, 733869008, 115531461, 45157210, 264523275, 754789899, 543149425, 95687178, 722447001, 866518918, 702481798, 255961714, 141007489, 792789399, 760767911, 594523741, 166897981, 411931301, 626201016, 231531801, 991153647, 748822629, 169886092, 53308297, 370726415, 224892172, 982430341, 692284017, 514648324, 942755724, 944239189, 161425045, 53502562, 135058621, 471308782, 305358868, 456835631, 434295785, 902343089, 30303258, 749300524, 608400519, 672084613, 706303560, 490694693, 439470507, 26372627, 272678559, 193296677, 452158766, 417097698, 196291389, 238098624, 854671648, 105788207, 620909660, 677457369, 85381103, 617746327, 226729797, 493294674, 282740884, 588029993, 160066012, 974792029, 504179423, 891832363, 452646892, 152941970, 126500401, 39746152, 459959086, 480401281, 867339295, 637148329, 188033101, 614015068, 600839039, 932296927, 376107801, 40453408, 377346690, 479027029, 963712563, 94041379, 724877954, 775919620, 550586261, 149619478, 781745205, 334526527, 91552539, 411553760, 567176792, 256264461, 561633961, 322434534, 842751239, 535691372, 354633355, 934401681, 660133448, 919632916, 969575702, 100573440, 836211589, 150341827, 516501109, 693080700, 429364431, 796741189, 174814793, 923154713, 173633968, 414488778, 231177385, 265656889, 711884411, 864975260, 188224425, 246766567, 237893502, 317418741, 556491693, 106509462, 858530819, 262215691, 301036376, 830671151, 76819007, 474204682, 338622106, 466920672, 970800730, 380148489, 953513026, 962554728, 983906212, 947017236, 162196131, 86030043, 329705642, 385722316, 717864843, 230281035, 128040737, 799994307, 647140821, 855013725, 744863637, 797247119, 637227235, 207229076, 941319438, 223831832, 692623712, 176576905, 71530865, 208455085, 682817185, 747205719, 82323430, 102192133, 447012736, 97467415, 785351218, 99257241, 515595311, 990250083, 604778255, 11063971, 467407358, 509394295, 127923010, 198004505, 486829444, 596496617, 100407730, 211903758, 101092272, 212493993, 839563013, 933153493, 29088626, 315459427, 370402488, 694612627, 528784218, 269550380, 393062144, 322279087, 670961380, 602936709, 642173165, 612798496, 712883551, 715518304, 817117156, 247795575, 963262949, 914753999, 697328674, 816854135, 924491286, 891075903, 144546990, 687330503, 786727410, 487557583, 398322557, 424218309, 435999306, 354259236, 530710619, 45841780, 445282531, 550036701, 141693513, 136107528, 759838446, 92798639, 300720873, 105136299, 8346152, 424512604, 113325211, 242768082, 866356601, 14367081, 540358517, 103012863, 857831764, 421632376, 595209117, 804489562, 903761464, 422844060, 611637010, 872390275, 23227472, 605298344, 163304695, 260875677, 267899868, 418171985, 785862424, 830433867, 198788199, 519566477, 993794493, 133593637, 337106492, 316591054, 952044430, 77962308, 131199148, 777319664, 302185911, 706446711, 651502802, 676899786, 215051467, 794227218, 120989369, 391627238, 102901522, 379549408, 470588571, 880808444, 218605879, 308771595, 719075079, 504395515, 233913279, 175634792, 927615971, 120149404, 148808351, 312496455, 731388860, 484092863, 676192624, 619089640, 638876131, 657909730, 79837545, 264620503, 604213080, 720443424, 358479008, 388222594, 986801074, 774690642, 799696602, 796505722, 872239161, 612430946, 316325960, 327158362, 319575972, 30219916, 658915120, 69908018, 269179514, 574513940, 994030774, 877026206, 885963233, 54643236, 470299256, 747486364, 332211013, 582243432, 30674604, 270601848, 959370373, 631851978, 408752094, 64032365, 194085199, 818814452, 197917196, 594180736, 880133740, 839696302, 866612447, 957884893, 400235611, 175299256, 720835744, 971910634, 237278391, 320880793, 752804307, 534480269, 862152026, 55902228, 897115161, 535107452, 36164874, 639725240, 343646668, 476132375, 461415234, 116651223, 597666448, 348079680, 338703819, 959975737, 686941759, 967376471, 923910374, 741270274, 88994352, 517004230, 635709585, 210742375, 367249091, 252525543, 663615106, 589629576, 51487909, 60611028, 664644564, 464575288, 307093051, 567339771, 44134653, 435574766, 394129752, 13966981, 40565563, 29716757, 502794112, 729767493, 734249616, 519311138, 337452192, 80246111, 942778989, 104151271, 541187517, 791897370, 787651715, 234846760, 781937278, 904058948, 338548599, 613018717, 661846368, 541336516, 708419029, 133224443, 139514351, 23401844, 960533892, 991674959, 798799549, 466397830, 333771506, 234841524, 68976898, 712718682, 549372983, 790916915, 88663625, 692609926, 607794618, 771889912, 249390995, 288867314, 200023180, 356816490, 716304555, 686985233, 92270832, 602306342, 789070954, 448201531, 749471745, 642444627, 511624851, 82434336, 212612231, 210549098, 480583028, 543087145, 109513700, 830331039, 764242913, 133922108, 43843614, 771148544, 352634422, 931549504, 495079293, 825969320, 594329622, 787665948, 568338495, 548942358, 654616207, 384362793, 242144287, 264153487, 597643814, 956706536, 716749848, 727950973, 104128068, 661174825, 570748196, 132096433, 212498715, 813904392, 659299494, 218129884, 958288857, 781608153, 664098279, 882789873, 730866680, 813538232, 201466569, 287311579, 783603270, 567122487, 328222867, 51095039, 71615233, 127930440, 597693812, 870576289, 245715461, 370789898, 352978002, 793114172, 725374103, 661176600, 400876539, 578325876, 773839141, 188573566, 774735034, 87304056, 937085906, 604048282, 864879613, 682150253, 370997439, 695260641, 62901833, 460984697, 966448615, 381128047, 391040947, 82077916, 92816333, 562359212, 723990829, 327900709, 209370470, 445359706, 259478277, 369430843, 298921873, 149576211, 217087527, 51086519, 812977662, 752237281, 778845877, 993424718, 607397534, 337441327, 882323170, 351338429, 291869453, 445062188, 145871453, 651889287, 91785161, 290253806, 233126572, 150697815, 514606461, 549497983, 829393751, 56859747, 432557509, 771933782, 931855781, 335166517, 17840848, 158736889, 989973006, 189281403, 753070979, 429291411, 766547609, 967708770, 402210004, 420516887, 603827925, 453432998, 126591065, 229279545, 801081318, 848737863, 67513222, 100042803, 459809606, 699498885, 885179408, 202985470, 906153852, 936486844, 786347131, 286274757, 581043138, 459274101, 804540059, 710193779, 899672436, 631515955, 262739612, 965294119, 744606388, 218121531, 253113979, 723008772, 426841069, 6802096, 528259004, 479154074, 375600058, 69293997, 834281772, 356348431, 991887530, 995675873, 360854406, 960641569, 661751420, 383354258, 449077745, 868455231, 310996290, 707449886, 420818796, 9087991, 306383644, 6835381, 786553274, 78975286, 461601338, 852492773, 562824416, 719615063, 696705931, 895584104, 864187265, 86913336, 620256353, 284423306, 926096682, 865765495, 903894076, 368830753, 389601617, 947470922, 659829249, 967755455, 899430191, 807128761, 777601694, 258586706, 748914221, 232229754, 62132728, 800355409, 161149041, 574843247, 782774729, 439745369, 670877463, 871557759, 105271069, 899230409, 614538810, 329531539, 445949496, 813592856, 845424476, 443300161, 817383036, 302080118, 662772242, 562639009, 427825690, 483382298, 853747638, 724151778, 532582984, 717313806, 148599981, 538239267, 688347988, 301898162, 99161348, 490558895, 491973107, 226275065, 373614385, 549110124, 734279006, 469063703, 3347285, 593644365, 286772715, 41425855, 979700726, 959808315, 157787505, 620597034, 973874611, 499607191, 105717864, 594515251, 517667138, 675267873, 432346772, 126414053, 777683447, 90036515, 15374940, 911504848, 179926562, 834760556, 400958759, 490665529, 587921893, 124497546, 84664706, 343387785, 397572884, 804571483, 246044397, 619206326, 347459491, 881615936, 295187625, 115839615, 766350929, 426342918, 933960317, 768563152, 952022993, 296149990, 85244871, 783940640, 511562794, 940608567, 504511707, 556868119, 221543103, 265675335, 834280648, 133024451, 841196815, 775707233, 922897723, 258770791, 175876702, 957382170, 529784736, 620040367, 399799523, 329580385, 490433023, 66982594, 148052403, 565744809, 362668374, 48458540, 282239268, 538486877, 357737543, 586749419, 908315584, 194950775, 829445145, 120446244, 181486040, 965908257, 820615760, 191236524, 311380073, 743729650, 132519868, 35084043, 213762789, 494173337, 915819623, 983834633, 349274518, 61912327, 671724969, 580444071, 271356150, 988683285, 623447156, 786951200, 470865722, 794295644, 680374721, 13107731, 48330518, 671251480, 535469585, 681691034, 133720155, 894145241, 725651470, 738890521, 934338231, 824499256, 146262649, 987815136, 904424890, 477164383, 678908768, 238158662, 140340782, 749846669, 429298916, 25444052, 580369879, 25881165, 178697243, 515528724, 328737368, 881574788, 551822501, 232855259, 675023366, 20923588, 945097534, 134665711, 5118282, 765401747, 546988404, 230625388, 207600172, 786768662, 424600372, 82604897, 841674073, 142931089, 769166415, 991755805, 359779540, 941267491, 605410019, 84321072, 443475004, 833001885, 302386105, 298172023, 264344807, 696240525, 96818657, 36244899, 632776012, 358121957, 209589919, 138858444, 506156468, 373050674, 832287249, 443577399, 432100545, 389595323, 497638867, 835240802, 84008576, 204950509, 661212080, 177745786, 337499338, 130257547, 899855284, 84719674, 608030283, 808720414, 649685469, 324970417, 388349043, 875182978, 181997543, 629966519, 677227869, 702711496, 518187887, 365603517, 601796895, 225034822, 444448226, 824685920, 121232064, 421613427, 319782231, 442664461, 502262753, 221104250, 729886209, 206967931, 206325782, 723798351, 710801761, 719352771, 607811703, 680364530, 723173925, 72060617, 913636861, 216397007, 38874064, 209509034, 803277829, 55965168, 717481592, 972149375, 842273480, 826121524, 914464229, 462522962, 684428761, 134163702, 381910510, 910660075, 606981352, 884383318, 530071026, 191743839, 800092491, 62826416, 65499085, 675851930, 27542617, 917714366, 990917081, 559330026, 976901629, 45507407, 678338990, 755155188, 1203944, 815105392, 249335594, 414357692, 299832486, 291416768, 796779779, 390712484, 881341228, 66437413, 640793647, 510759063, 956382524, 587920238, 202378835, 205491576, 161557655, 705553139, 304508978, 331260518, 645190937, 978957722, 869740753, 622854019, 531710171, 533829740, 827995321, 900244664, 302583260, 3861506, 583116255, 548912508, 711335193, 470451631, 586024253, 262046366, 752919985, 394147443, 958083859, 548820170, 319628150, 935158490, 593147269, 195958179, 757637812, 728218553, 237925436, 105692960, 63557437, 161296638, 700689836, 922384960, 530680318, 805460292, 559836839, 603744356, 736758880, 752304772, 138827758, 92160486, 433345705, 930404744, 618980807, 83330226, 144239709, 832621356, 428597856, 121114674, 451829244, 691882535, 840921315, 719517497, 250281720, 851896193, 875219547, 23367459, 294149306, 941971398, 295254646, 99589128, 860243675, 905946378, 633612767, 259161534, 333333328, 961959115, 839730254, 844802341, 928298209, 693705837, 924996678, 405423222, 163012597, 628798531, 911301899, 566636216, 761397131, 572920250, 394137633, 476701197, 596957803, 395343474, 884191950, 42288038, 734552921, 639362624, 921450002, 813677139, 578050944, 508166435, 889089302, 663438610, 665013787, 632555771, 328459885, 710183894, 980000063, 174186539, 762533797, 972862812, 901430392, 5263153, 891275106, 214198517, 971693996, 127126736, 391471944, 210278132, 300380599, 552740444, 776521678, 958162118, 525021432, 37815412, 24258498, 377904967, 974860664, 58424510, 155137942, 116333336, 942380884, 295436724, 580097210, 205856019, 594624434, 384455153, 346618229, 425802405, 407647836, 834921617, 219156273, 824693455, 926964161, 881345223, 460894259, 87717022, 20152164, 224238528, 411042969, 619368884, 428774461, 390005249, 997221207, 656025780, 693752225, 886729879, 195001449, 701705062, 95625257, 499220969, 3427563, 916690255, 602514865, 761464196, 437361213, 616409182, 793869895, 426356034, 280976922, 171631599, 829463256, 719906656, 627607532, 243371478, 369829471, 998954531, 988726200, 639608903, 775255165, 116853002, 424686106, 278603594, 386623563, 514855292, 933156155, 214711168, 748709137, 129552482, 248331298, 613582747, 89042220, 845583164, 230145956, 66997606, 581801732, 899107779, 598938298, 975594941, 570075343, 538250057, 294999488, 269587472, 144449293, 46692124, 566014155, 586922954, 706696754, 991546425, 964205295, 174215953, 836410568, 118601835, 462185624, 107919067, 144515098, 688223631, 390341417, 25745460, 415950074, 844207271, 752426687, 246594290, 128480675, 982130444, 901578454, 606932067, 708875081, 65620433, 439988524, 178615457, 964183094, 182578085, 152818701, 746930510, 842716275, 805326949, 763558296, 756295835, 412066288, 42534648, 464388037, 41532211, 350892422, 807041667, 216059492, 937041559, 637977081, 886773376, 113518163, 911840100, 673175985, 815386071, 916672915, 848957239, 975137603, 127008881, 386566067, 575326742, 718565094, 83722356, 61020290, 87396259, 133976986, 173603624, 800745881, 768992322, 776153285, 304793107, 643100504, 920390694, 541017961, 353481213, 994818859, 959062550, 759148039, 775900541, 671453480, 391727135, 816951181, 217149241, 611255843, 367875940, 924048611, 625299411, 976995575, 437576719, 242135757, 778418175, 466607259, 783500975, 454795838, 911601166, 985424071, 753929290, 697983330, 528486944, 102281914, 388479330, 582991303, 433921793, 960998876, 686706231, 646058746, 453838310, 614430556, 101364429, 837774551, 297654480, 907416371, 61072356, 420081839, 249863135, 817649558, 869720979, 390290392, 561034366, 881557397, 875745994, 906644596, 937414585, 392056785, 903450051, 902640182, 655602653, 614029746, 726366661, 998523822, 358752835, 110273124, 530668082, 482080376, 852045594, 189035488, 615846760, 695147758, 285081332, 896972346, 283193183, 290498338, 548527717, 283699302, 570526286, 159706300, 768878099, 410611760, 563158325, 764302173, 407469538, 950148028, 322508314, 574849030, 894248272, 922438506, 424690383, 592752415, 537472299, 595320111, 604025039, 387679452, 884681106, 1447521, 112750053, 916383674, 964705081, 184427249, 56805399, 210925600, 963097194, 715201946, 773096044, 798287055, 800695690, 403346691, 534718423, 430114893, 602374744, 627681548, 764227246, 90467619, 455598760, 89319053, 601521936, 127614219, 295415556, 844523146, 446959684, 495862849, 995863382, 112758751, 224025778, 271109759, 512073750, 404732479, 158110876, 10052820, 439223916, 636816332, 395956495, 421019817, 715346949, 400499981, 976173530, 274420673, 734125780, 543712152, 97458901, 223513105, 979897641, 722604258, 878764792, 430690916, 445073851, 213608792, 778058981, 410588717, 55793700, 659027275, 171419977, 264148652, 830566387, 653870637, 767008836, 149294401, 460270396, 178420095, 410011232, 858433835, 814505055, 124988096, 903426836, 877993556, 538154404, 572636939, 31765828, 687666119, 623452786, 187825339, 236704506, 334564297, 147723610, 967758455, 676941574, 206516933, 83331328, 416504102, 199452471, 951531551, 42037349, 5362740, 676313871, 310570499, 311868124, 258179596, 932811946, 622686194, 614304908, 654964037, 436990382, 33939172, 773562451, 253369653, 482253662, 139492815, 91055143, 565722407, 964555831, 320060396, 382981646, 95725429, 952286301, 124478698, 489224938, 767850158, 531356769, 274346802, 487095812, 598353604, 739078277, 582272148, 157716790, 75360784, 939526756, 616281114, 177749892, 857552218, 379601652, 535084970, 205777518, 642384015, 441959151, 985930456, 313813064, 738070801, 430562642, 43528703, 204018477, 982573733, 965972987, 718972733, 827333389, 367155755, 378829083, 482327968, 182787050, 960600037, 56834560, 30952884, 827642561, 43023398, 214088595, 594184738, 422791504, 929500736, 502623387, 819014499, 310492633, 66759003, 706009249, 266690325, 430374751, 675484030, 238882692, 929109720, 580102212, 42820856, 58617348, 483706502, 550395925, 235278445, 84307127, 926385797, 749600093, 279461213, 250931823, 82027797, 215933414, 925078654, 736507304, 383665297, 629207495, 320626061, 439168485, 88997963, 711033132, 968482431, 934029122, 972489052, 664501018, 362509741, 454988295, 632980156, 487054098, 149156084, 372812789, 862983651, 308280420, 341930376, 700469918, 666453023, 683931396, 607957512, 483600292, 231273244, 680322871, 957116512, 59596794, 159043128, 901877800, 826703918, 611189862, 32047132, 884765994, 835418431, 741290959, 292460505, 615818023, 306227487, 488650770, 728236841, 554537757, 396985732, 53752486, 797986832, 879790688, 64895967, 888097617, 286640682, 930230766, 58098410, 385524570, 768958173, 13046404, 903033873, 625838662, 975803341, 865627636, 74579037, 41950710, 169811266, 156548337, 584171107, 267500976, 778602689, 882165124, 675987458, 328691873, 577115277, 802749146, 556242641, 973491225, 293576302, 350449236, 449115645, 2351534, 892605883, 216837588, 265901736, 352038268, 284754963, 236829295, 649386860, 128900960, 988664132, 808433761, 451139695, 39616331, 759081614, 475004400, 812708014, 458472478, 657448576, 316630386, 993996909, 97743921, 740024964, 950216626, 139830702, 168641231, 446700609, 643242629, 309732587, 530367402, 928696314, 656111357, 42969602, 808711175, 865695000, 90549862, 239764771, 515690677, 142324120, 933402730, 614551710, 246968408, 878328206, 73932028, 604551614, 662660710, 100962375, 838549336, 388074158, 944219603, 390531843, 259455827, 789772356, 18999536, 497458450, 402558201, 213817116, 118793945, 384312389, 684830757, 501107314, 905780318, 834398157, 537105809, 445659887, 567593109, 27770169, 512755490, 81291969, 995222866, 82669191, 14387390, 368777947, 281570159, 752324688, 869362720, 67413285, 591134774, 485288672, 284328459, 73338206, 965313182, 68392900, 175078238, 467852742, 229053341, 17653814, 71433359, 650008170, 862338008, 334066515, 335153735, 907602949, 614014656, 843148232, 20911616, 432551341, 173871556, 484844837, 554409687, 899366281, 806724559, 148440135, 746765536, 777510734, 833319788, 167920242, 887904340, 157378631, 523093363, 325810971, 178429939, 271495367, 659515382, 470407678, 560075992, 836856689, 280393747, 488368801, 805950177, 914469668, 832616717, 885578331, 80922813, 551861839, 429068625, 365248416, 438924392, 582810242, 687048220, 847314, 504554043, 775371985, 541857678, 847665973, 738769372, 948866585, 730077623, 703311801, 328317093, 628257347, 415526665, 950322004, 508775775, 695554037, 466561224, 358003649, 993295939, 132818162, 823186742, 820583583, 305677708, 653773819, 640697639, 712310748, 906235514, 515661749, 809078180, 12821184, 74950552, 251986635, 542357196, 582723073, 280371253, 986292015, 509728254, 59341812, 341622381, 93016993, 260993720, 965140852, 483313097, 609934736, 610120375, 108616273, 245155658, 307052275, 72626528, 353024113, 337164219, 812667946, 196783530, 94329546, 126685301, 199285249, 674785907, 24133980, 321707381, 938600492, 816741209, 702747482, 67467005, 120460193, 702494040, 327998891, 679666349, 131211563, 766811877, 546994264, 496452590, 626494657, 836882204, 543318563, 909412639, 409233420, 42668174, 936483400, 531276233, 807376137, 619117149, 136487227, 85030000, 727250883, 706552980, 262511861, 921876194, 132918625, 266193253, 725454935, 161252825, 186970877, 658250864, 535959597, 108640143, 770419214, 293883034, 48172987, 538786829, 108683472, 350641066, 246210721, 4456939, 584598431, 535842281, 525181021, 714954460, 54267130, 187636589, 409727996, 272568320, 866686115, 520433601, 641118186, 83477884, 236949025, 411076960, 333414032, 535853489, 208498625, 167136231, 370719688, 198953157, 765337445, 39317175, 702910213, 29227854, 261041697, 520997778, 202840229, 75681009, 929669072, 859460338, 941125549, 869092732, 357343777, 243558449, 556211919, 658408445, 420611797, 648305953, 98533118, 452612022, 918258361, 211622564, 577393493, 6099044, 643448072, 800561984, 414502993, 433362082, 438415016, 979474723, 15575879, 634485006, 807663616, 426250239, 966902555, 244068325, 586247776, 842869932, 810913733, 397043984, 239557980, 221087698, 104038150, 81973571, 253205809, 868218670, 178629881, 238119806, 644333728, 183038945, 544958846, 230576425, 518760230, 850972692, 480683071, 557141673, 878414532, 645387141, 505665771, 752106484, 929612534, 51869169, 901233970, 210637006, 574519331, 841566050, 760303192, 643538959, 307966840, 739076741, 47209442, 827790165, 113481899, 878316952, 667166105, 596049308, 23892799, 208463744, 333017168, 318108217, 307399200, 698358625, 509907391, 585956808, 512291539, 314160774, 990761034, 812146542, 837422254, 863363282, 14547602, 136801634, 333675560, 742365709, 778200443, 177908663, 915886859, 287543954, 298239360, 80324552, 883328176, 22959369, 890725460, 939575185, 706294299, 80245588, 431479837, 688849300, 957985872, 949090000, 373345212, 893649738, 489919225, 12394751, 838589197, 462464709, 702060468, 141322356, 829032344, 31408845, 88407364, 284655338, 498673864, 490797489, 585564138, 24505692, 801409476, 761874773, 883321554, 891962738, 12582910, 686963373, 671684567, 239329942, 209349137, 478946941, 103194268, 889798777, 305987276, 795488380, 121558914, 356226669, 295902840, 316677949, 369467670, 994834731, 848055224, 71447273, 95442309, 204203746, 925922959, 52606550, 493577283, 422042599, 969430005, 590877045, 476763206, 438913079, 996828898, 330678055, 441496273, 396903219, 677473543, 998821612, 574276505, 912370259, 89474954, 594837537, 400632523, 708887842, 760432296, 401659097, 189729367, 287937881, 760459559, 316779210, 221276655, 571048540, 934704302, 642791027, 379897611, 286524040, 172781761, 66329379, 786294285, 623642043, 156267141, 856382188, 458219013, 799325185, 479324292, 979457888, 597175990, 62594478, 430107680, 112184885, 996530030, 979360737, 797225045, 996334888, 549398377, 565989241, 206877232, 347089893, 260184407, 396812133, 8064846, 394670163, 189101435, 936175425, 325414729, 624668710, 76812075, 714821768, 286701244, 729111565, 720046569, 503862164, 827889865, 311332881, 198327981, 858318081, 157374510, 746824729, 325173866, 120922187, 929594655, 351595042, 524686483, 979313104, 566852879, 877536159, 243777860, 956848473, 453935606, 706446128, 440553342, 36141452, 2588864, 331530031, 664517265, 832440567, 124422129, 485071376, 341591027, 847156078, 234216977, 308358438, 50377571, 640392847, 180132611, 3664537, 172434192, 789248224, 219116358, 363927793, 431622634, 563570663, 334404713, 337033603, 817156350, 39574664, 821474144, 560013345, 784085745, 616124768, 789646535, 264244149, 119078793, 294946359, 11396283, 528509764, 620356217, 379789166, 748593898, 844364166, 517905181, 961572178, 736385855, 7612348, 364219658, 598292854, 673983140, 229905190, 119575432, 259122298, 165936668, 3305293, 339637074, 880633948, 189443840, 27956598, 316939259, 871650972, 743979629, 41291659, 416373406, 37946655, 141465288, 754456205, 474420941, 50591880, 458001443, 747946832, 894614184, 625527264, 438754876, 6502174, 408518495, 349174038, 179729804, 587691898, 627921546, 459773476, 227858473, 686363573, 358151799, 212112440, 390686992, 916320747, 766945549, 625265356, 264150498, 186536455, 147480151, 594292336, 565799256, 328439536, 592765251, 439535786, 727090145, 801570333, 88655478, 371307450, 502257766, 692291399, 526857361, 827516461, 875342858, 427985731, 353552925, 652754994, 557814312, 78989893, 746287024, 168165170, 534859142, 562791690, 231953562, 699641921, 683796354, 220772901, 761691736, 136879136, 236106123, 64941981, 975069486, 960216820, 74718976, 728943143, 156549334, 875430396, 5711939, 222180562, 667950221, 157215571, 588550190, 541124803, 565278302, 806154841, 284240740, 83884089, 638633055, 225276438, 23085420, 639686750, 152483065, 231284243, 599115184, 946689516, 758443492, 67039534, 703570778, 509594224, 647828391, 696008021, 134790234, 627521627, 11513464, 542843337, 35032195, 348458381, 646839910, 717790404, 1128315, 345223615, 609920253, 269815073, 291106931, 287407496, 255181701, 292044310, 639344209, 674087934, 57921831, 927860902, 964407413, 115925612, 411680890, 321178883, 190553297, 569915912, 80459077, 403665611, 91861555, 281556202, 383296662, 97765596, 199414386, 752143468, 474345946, 92097623, 225719581, 380413735, 69498284, 170975192, 227758653, 376679217, 333977535, 975453650, 241695780, 968468593, 698355593, 30937551, 277756353, 867903237, 834374569, 903810214, 430136930, 868389856, 723161772, 37408443, 870762614, 828181787, 536771999, 142730359, 604388781, 967511725, 963799077, 883362719, 646914911, 986492653, 999429675, 410591357, 394331621, 763712300, 18904539, 84749545, 485298489, 554668668, 288813379, 720113939, 127657813, 737810833, 13425369, 688912985, 62636756, 137159883, 550765623, 364868842, 821230746, 720530054, 51782007, 95401712, 260154785, 799609633, 968982439, 301853519, 510154196, 943174618, 643438667, 230570892, 586778139, 541839865, 20589306, 652291277, 728271173, 835297673, 506049608, 119122873, 512647771, 714824605, 956489502, 5709403, 51866107, 178727125, 976229983, 319857167, 389869482, 12197612, 249932113, 723209341, 599208557, 380080741, 262649278, 493823859, 230569526, 723751557, 673668447, 992706000, 232952059, 198562728, 711295673, 966534486, 145200985, 375748359, 209942358, 533304693, 847076874, 320657578, 199002499, 988539612, 185637563, 548132729, 972686143, 79856687, 535501400, 199515405, 723767246, 295738624, 857294409, 847284825, 666110815, 937497564, 915775037, 513352958, 147672158, 806300234, 590340893, 798766212, 13158541, 253282000, 732171815, 698579723, 4711760, 594976548, 441467491, 148099115, 882093116, 361691397, 681531868, 355103774, 982520381, 993223405, 538114651, 101969258, 106087696, 469704379, 583886458, 44820788, 934137085, 866364765, 774601766, 496124022, 725547950, 28090662, 852512900, 807077211, 416127914, 357699396, 230856898, 240611178, 913846036, 93546250, 646619736, 268216725, 631646800, 672073478, 384342218, 208452524, 120065465, 801477709, 94778796, 820876571, 785908296, 937759565, 52453093, 773473444, 103457692, 813711404, 500280767, 710968371, 333301985, 63227687, 551782220, 588420888, 963212005, 944560177, 811621343, 852726877, 113282302, 687965493, 727206640, 137697646, 623688010, 359597314, 653425042, 222390355, 992754808, 482830059, 354572812, 849985423, 658531224, 150659812, 959437707, 404849199, 845151300, 528287295, 935794759, 964332399, 813091899, 577571875, 85678015, 24723376, 890731356, 508243243, 295999602, 463687144, 62216828, 724404983, 656318930, 989087396, 927774689, 524460306, 258547416, 314954158, 338988479, 640382983, 880432863, 686857933, 488933115, 531122053, 415073825, 338998401, 159500633, 691551337, 722764261, 194454991, 152468842, 794969579, 289893272, 94622006, 265849255, 643849468, 917725554, 904467514, 877508246, 259334860, 467007810, 468829592, 419527096, 312676223, 22505579, 316945254, 601537085, 399551507, 109555975, 640471808, 18381858, 298023283, 353673250, 7456409, 81881737, 691683080, 521923254, 596733103, 326039341, 780766904, 688450165, 703501684, 490766327, 742224042, 732918177, 266229164, 15393475, 342223279, 176643057, 28624229, 195013128, 332069318, 486821789, 861695544, 186344684, 450873514, 519340242, 675862519, 992954759, 773315890, 198739798, 629404291, 124655627, 959849693, 32270015, 718047291, 706822473, 781526380, 294246165, 994554044, 814839528, 710839659, 76558694, 890852723, 299665594, 938648316, 11954194, 253100689, 187106964, 943405423, 403239836, 146092595, 467741272, 891623522, 629866134, 456703845, 594755889, 534109229, 285059314, 147216983, 768661839, 460790019, 455359748, 1449622, 878717931, 542688149, 793153907, 782147401, 561065315, 281192374, 414028970, 36228870, 880384857, 81075967, 577571940, 343582838, 511668054, 420322643, 888817241, 734535872, 295793038, 29309070, 672264147, 269166004, 478882943, 144569082, 772407105, 776649527, 477461768, 944159872, 149290076, 841465800, 164377861, 421429291, 832257561, 628749913, 309744168, 338508548, 782425519, 694770346, 127095843, 434258776, 946199998, 812162900, 593288006, 583131701, 754253745, 314091229, 506140888, 44866610, 135653559, 474226118, 131526211, 135645475, 249786762, 96069607, 693626011, 36192160, 535788512, 661104077, 652994069, 374396488, 918181184, 41366719, 714737656, 98667238, 111513490, 247954648, 101639173, 787184168, 628450072, 755695598, 187205625, 27841375, 592372489, 406096645, 421818036, 895054749, 725780887, 976615335, 301273724, 110153372, 586262479, 451343587, 122333892, 832638898, 68814007, 577112420, 11281219, 7631553, 701843109, 379242194, 979020930, 193218294, 462249113, 659924117, 135894922, 31466156, 976928960, 551962927, 142825432, 905690905, 470417782, 222616463, 544335778, 944722865, 303150788, 478586254, 65242667, 585874795, 988895385, 656794193, 916606607, 173494033, 359008895, 911280091, 587799352, 646235028, 425328539, 4609673, 268908926, 45390204, 12707030, 962928340, 255925316, 969504926, 591342595, 575545837, 53937142, 492931067, 790545591, 214205873, 202612975, 127799659, 301230656, 664713647, 792010351, 357055066, 24713306, 283862012, 426165478, 890851048, 183429233, 381121132, 155445379, 854736763, 20993333, 459623503, 101225059, 687669867, 955799777, 291321812, 134532644, 865957824, 956104150, 58031879, 994281849, 812554911, 731514125, 898385472, 731277376, 514309512, 270557909, 76688290, 519979294, 361792226, 307378388, 874494707, 568901025, 789371107, 870858241, 121300570, 762756338, 88559634, 573124867, 30954728, 462625996, 610850236, 168577513, 89631906, 348618079, 391622746, 495728584, 845644384, 282510957, 641682271, 229646376, 547076648, 224155231, 484274085, 639963198, 85020470, 93000096, 732247018, 478790488, 462774837, 828346870, 514857242, 671386114, 971455162, 28625432, 918977281, 33359744, 41824374, 18406701, 360436909, 114861389, 823613549, 910902941, 179944116, 677904726, 140146700, 60432347, 26750675, 281115411, 646938205, 17401988, 136403778, 6331832, 364430077, 642109564, 56775425, 169740936, 501441646, 932170006, 678470107, 260445102, 947894091, 70130100, 581318720, 510578573, 311539555, 769676023, 875263581, 14033528, 100984392, 938910541, 865769698, 223224625, 697909791, 489500722, 282688266, 374094562, 127489178, 563260331, 685994105, 203820607, 602693678, 743846050, 67130675, 824228323, 112483794, 834891914, 798555999, 867308219, 481650519, 616772870, 683629280, 637060839, 441645582, 936619911, 410218576, 502091152, 358396476, 524757114, 349570518, 700003965, 194194209, 254074704, 222308644, 567142988, 553401103, 666716663, 915797075, 510897059, 830298377, 30481556, 981814909, 304999880, 219367012, 81209614, 593678330, 585026522, 127834297, 971115735, 969560570, 400181089, 275553267, 507537847, 687458072, 701337329, 548036257, 93227965, 896700550, 871086705, 170374488, 53908433, 312570960, 815325856, 916380841, 112735599, 215209390, 471063191, 426055448, 251914907, 340727127, 274247225, 295861235, 431159679, 265197683, 688763400, 324559480, 483333498, 773626546, 632257721, 864560198, 623962236, 663025223, 132715762, 930822089, 360495285, 822870325, 26475539, 378521333, 539786266, 541476734, 16423135, 679888320, 111621176, 301812347, 139136135, 249795673, 337715768, 31000355, 931993379, 339593441, 110569168, 744689423, 834106782, 608287248, 897187713, 803966958, 156049141, 418942814, 312724568, 722171912, 89441698, 145707091, 990020635, 991862514, 718341213, 472755952, 563604868, 631578563, 766836300, 219634021, 549658761, 302571156, 905928509, 992731753, 331660809, 95483781, 891077151, 749699178, 381221637, 884448272, 166149915, 922910801, 346095446, 449399814, 855069456, 759701625, 486579491, 762568679, 669425853, 16314444, 44310063, 594919060, 108497476, 796832684, 261491750, 817742319, 252145976, 711257362, 172088759, 48457259, 743551634, 459280804, 30259562, 675236853, 198567849, 340785206, 729437835, 361066309, 296973857, 309191546, 470640576, 678853220, 101726622, 751273818, 34045556, 911321964, 803646629, 186912707, 223076570, 936063939, 505057165, 285811336, 731110588, 728830503, 75566174, 88367664, 531564251, 538211461, 247252341, 842027866, 555734604, 19208934, 92577977, 839433232, 196614929, 544098924, 950270516, 235681619, 359591310, 236213590, 338593170, 299741873, 187038064, 18563860, 965101126, 514304823, 8733833, 289966670, 798757266, 968667706, 822910189, 650708269, 794683311, 394741744, 617672507, 449200279, 683104237, 83518203, 239287533, 673868177, 882138757, 882024920, 566614678, 222682912, 863994207, 26903406, 676576317, 827206826, 892531154, 640817436, 84292023, 754165382, 65677247, 97421641, 936524469, 78158719, 991628720, 440879190, 630883695, 565241382, 140306536, 499190764, 956569475, 528515169, 125295285, 675401626, 706384996, 496077159, 39195250, 642760602, 517798633, 27275985, 652155759, 27681335, 779113450, 794901706, 481316402, 788459520, 419265661, 737922801, 968713467, 989234087, 303693095, 684112462, 572496730, 42695236, 673095474, 298280166, 618579453, 28562609, 39496949, 806418514, 534508500, 547929506, 577183902, 58125042, 103882827, 387888878, 6480914, 655556981, 658008317, 415952847, 78092497, 717866409, 351305123, 600770508, 298235674, 415490893, 164805982, 301431518, 944366596, 413821871, 479124484, 266606919, 583331369, 809639963, 274059544, 123551813, 47439227, 718664567, 257893795, 365379713, 63584722, 388748419, 420238445, 954492776, 724618686, 875550722, 671347096, 587547867, 512889999, 161247804, 146509557, 884632215, 515986177, 830765109, 807684794, 782244272, 676069567, 597753682, 516980483, 212769919, 188242986, 771762357, 131133970, 909503695, 366154626, 220733597, 641886102, 57313491, 333183940, 758743183, 165003849, 497449931, 873123609, 736618960, 405256419, 200986257, 326871556, 7159581, 786966529, 849702307, 330147881, 586387488, 942860466, 868125140, 519684954, 398183122, 845521321, 779129393, 382284071, 32949628, 712098024, 982246084, 161599495, 561738773, 290367138, 684836727, 582671445, 972859949, 453933409, 947543990, 89219006, 81475053, 150235867, 177364339, 299245197, 445458973, 373481570, 300457943, 815214053, 745738287, 613720035, 475574227, 862299069, 623745634, 895198934, 652909802, 867049067, 582865938, 179193059, 916661895, 227139502, 121396775, 425192569, 743017727, 944774627, 273394915, 420420537, 294002910, 723539949, 162007026, 91674428, 296959121, 252938886, 458462147, 748175837, 669675987, 811045533, 400329569, 600934646, 113593383, 863236685, 986101497, 857309717, 336025537, 777872934, 820587726, 435334410, 959354299, 953407255, 16152609, 920555831, 903878162, 116239118, 23386110, 923739058, 261948137, 819005275, 33070017, 606115853, 313651036, 98614945, 433710070, 865506206, 582399250, 562499804, 192767183, 156063418, 901072763, 207752188, 279908571, 268232966, 876057606, 115641472, 936201191, 637108440, 486416929, 912327045, 626978631, 886018805, 270937846, 477290638, 615914972, 23014998, 888674861, 463527308, 281159564, 902650579, 42898189, 543811881, 27715905, 704543397, 309638399, 980320545, 571472820, 271427722, 280600760, 855839205, 930678172, 892435753, 852981655, 910243905, 752411206, 549927815, 969348844, 926979271, 473670544, 530516580, 278692810, 713423079, 929840398, 528585883, 311417402, 240028731, 862031238, 216829528, 549307794, 605816034, 81603291, 725874482, 665710933, 585523945, 836478905, 462041847, 244168973, 965725627, 314544685, 19442001, 266369118, 750899403, 69083425, 85435653, 386038511, 5802740, 267145252, 336211948, 559623566, 764006772, 654612797, 533495323, 321122098, 858076969, 783303185, 979724791, 409401639, 797799994, 530840845, 524076107, 246098837, 896492580, 414220448, 512618169, 594504051, 297212820, 551262785, 709200582, 488538443, 109169568, 924868233, 354922372, 625101047, 457953895, 858583392, 382552620, 720043420, 321700825, 929346216, 521606840, 392097607, 502913717, 383804056, 651245826, 701771481, 110752905, 361674256, 855343599, 777746918, 272842343, 178737790, 19813957, 677145067, 661318090, 688029768, 81062346, 413729063, 566856182, 680136681, 545854820, 731284216, 390133149, 127957459, 15533664, 928637708, 510742458, 647682354, 465258438, 426416564, 829513641, 328657860, 85275975, 202103508, 122699708, 542199664, 211431583, 735558208, 877504577, 826005407, 834124445, 72409496, 195572793, 497338766, 23451941, 992194577, 740521741, 691671420, 400185104, 901469224, 180087794, 251570947, 458610928, 819674000, 470000458, 168682936, 913182641, 886896173, 73485271, 630764940, 51743710, 186324629, 120587485, 646298454, 865225183, 72007992, 196187103, 402530768, 81943559, 190672248, 535626671, 796374162, 338875422, 983597897, 805989961, 308044769, 52395145, 717658081, 95090982, 138895913, 510870146, 442792836, 761673184, 939987297, 881556951, 735683178, 155596329, 518674052, 4273151, 735049620, 562959585, 593507665, 865444944, 649126366, 241584219, 467240280, 495406171, 616628670, 388757001, 837100332, 917756619, 949312512, 797312314, 875962173, 143218070, 21348275, 155097587, 585222431, 196346089, 438538050, 581540925, 56707022, 499894067, 413406750, 48385345, 34833065, 756034656, 284435760, 2894072, 989330716, 803552859, 729700247, 791980292, 971884418, 234445327, 857014038, 842617911, 893582824, 566589668, 533013377, 890176501, 72829200, 107998379, 13400711, 822805448, 668219807, 598963811, 651406046, 852373913, 674923391, 91329958, 176155804, 357309956, 633617583, 834495624, 133536845, 229103554, 261454756, 831791481, 106323140, 458381500, 552022914, 761120538, 151162401, 21415804, 679117114, 631367277, 424444262, 791984539, 46754962, 988878321, 286882460, 200295083, 757527124, 643228880, 460451977, 801188156, 32451034, 845722987, 178628172, 389722150, 364458151, 90689558, 558926062, 52994806, 636036870, 219568757, 889018471, 604643266, 80462846, 253566621, 710329878, 629987500, 47642510, 227899583, 681926343, 476517024, 116253400, 600899979, 809242508, 17634276, 969047098, 572161290, 397831315, 940899651, 517854080, 228240431, 454450164, 492638843, 402829033, 757690490, 194490673, 957907534, 758261593, 232905655, 775782215, 62898154, 234133122, 860426229, 111052598, 301355133, 780668786, 506178767, 184097131, 844786731, 36988445, 671260864, 250180151, 905275288, 321235871, 201352726, 448455748, 681393489, 768797315, 496195799, 37822596, 324785966, 246558497, 926928104, 518251413, 982254441, 897420464, 656684089, 840764417, 174155642, 809660401, 361886528, 667331192, 133184792, 9616640, 756612014, 798598152, 121066857, 700330953, 759881038, 548585633, 219957348, 694596621, 952026657, 16643733, 159408013, 266630149, 200959020, 105671557, 166714857, 993876096, 636923169, 713663659, 595159089, 24173580, 390187070, 167972892, 863582617, 816248412, 635418387, 221223244, 560705659, 228213392, 564761697, 232946455, 261002554, 980912321, 743835735, 395971365, 101904081, 229656297, 485655943, 615870880, 901849946, 571136141, 501835936, 529887331, 70893766, 185366453, 760709369, 68792081, 587475630, 987447251, 744165084, 590579572, 862273287, 366061653, 954295131, 783362720, 525583959, 735771248, 874043512, 758421857, 710459717, 582669964, 697395723, 131516992, 272193085, 766715312, 631348975, 962751724, 240299867, 354040106, 849434615, 952044558, 981112539, 796226557, 634260113, 953426422, 928350750, 984923906, 902672443, 365491080, 977548597, 634555770, 809248536, 828235643, 953809994, 826339366, 119209838, 797135829, 370971087, 366755009, 215425166, 986941828, 827253366, 737503185, 332583713, 931399137, 959145783, 388576464, 258195473, 884896770, 951851093, 687415971, 680712278, 862433911, 23512445, 459920130, 984323884, 11518874, 757644295, 726062444, 747794126, 944424729, 527075962, 220747886, 418403089, 507909932, 116877444, 659332000, 98272211, 429715809, 508966234, 791006802, 483964593, 231160889, 718320791, 900995455, 774688582, 754606717, 783675361, 350140458, 284089910, 349197322, 206405491, 293330402, 291122754, 180350633, 828486190, 591564819, 384482593, 49587067, 353797319, 757445034, 394467941, 174099866, 181309117, 863663409, 131411475, 514841526, 863580383, 270785761, 840850636, 356094969, 788411421, 157305297, 733239697, 482234974, 363724245, 22544591, 550970762, 320841040, 361936650, 87809896, 107006310, 255060234, 488372425, 192364438, 55152409, 797060062, 19134796, 173671046, 914482717, 557788341, 974170134, 202339044, 363656293, 81242461, 324841771, 871613151, 117990857, 338903552, 954980087, 655679232, 884751407, 811178821, 877935699, 349810387, 81620826, 989220066, 317352960, 105993997, 382880701, 277059682, 621355171, 974303000, 4301319, 872081354, 415403294, 830460474, 725199440, 707014350, 287714414, 605839612, 424601709, 10516853, 849873741, 14293996, 932057010, 446248807, 649323558, 655559436, 648201271, 142899899, 593082879, 626050006, 153519936, 964709055, 336005535, 271745585, 42448135, 897739380, 861123978, 547877353, 850881641, 147276465, 510558324, 988068572, 479483140, 208067707, 950580870, 128494540, 383225921, 116059357, 614193730, 77099956, 975228949, 10874771, 38923708, 754858262, 268502308, 889790766, 590790014, 463118005, 445529655, 250839731, 229689437, 917401215, 842454147, 9654850, 141465632, 920422788, 173145934, 746093950, 916221868, 715167269, 501425896, 172845165, 974069017, 964990303, 869073404, 124611141, 891404130, 305176393, 149419013, 694390931, 393128066, 270731683] 11263))
+
+test4 :: Test
+test4 = TestCase (assertEqual "for (countComponents [642098517, 592136333, 10316544, 270915225, 156082777, 230622305, 377603774, 295038140, 782504847, 259761538, 732552807, 796809407, 177162785, 695185260, 504820816, 217873219, 71373544, 885967978, 682483183, 61103833, 731028053, 668778591, 422745032, 370956633, 179375807, 537702512, 81479209, 858492597, 306119301, 108635884, 572032210, 559122068, 707647073, 75440080, 562595526, 398490308, 974028265, 491718480, 834435029, 992084533, 70142459, 855717664, 262338528, 590918581, 473300705, 838203235, 120713016, 623724806, 940235327, 460680611, 392899463, 240448852, 823958180, 506196035, 598102532, 880015372, 658948519, 412041542, 522650892, 286270559, 949259642, 248023424, 361850980, 849337477, 929679411, 550670838, 996942113, 556224194, 592054348, 821188986, 806503888, 280550326, 8094778, 153233216, 663101930, 215946965, 640362453, 495149788, 55572546, 929189449, 192636404, 999503992, 499938186, 940602578, 875101637, 273453179, 387286907, 513734716, 234195495, 666679810, 800693454, 385053787, 375056218, 899001280, 891913807, 830321625, 223580958, 148685608, 460378236, 963991895, 505248549, 442573382, 14830872, 580995323, 814318666, 13254122, 736735612, 750977137, 919396293, 701773318, 245856642, 909908034, 910258120, 612897678, 231984535, 18681413, 199991590, 606071400, 69850167, 25161787, 360309092, 10724803, 775042419, 242893242, 461765814, 998842974, 981605400, 316072036, 209058370, 486318686, 562233201, 461682238, 726929513, 945430062, 65650546, 97836419, 208101247, 56127349, 645891706, 289245055, 159412246, 853018591, 167076330, 825350544, 599385472, 5444315, 871826833, 664367645, 262777784, 671193015, 244229709, 917584252, 505600109, 131149007, 449913494, 822360693, 815769984, 836379615, 99570302, 546553201, 944138371, 147771540, 563361411, 617089031, 643350509, 684259162, 34602335, 595837851, 548477448, 806760276, 916787923, 590546026, 112029797, 991969630, 205736713, 538254048, 999289731, 60135316, 699729421, 896913787, 345711153, 168619996, 252492570, 52198673, 789855994, 536997493, 514728251, 601837717, 395342622, 351877133, 482827253, 347891100, 192917097, 719629948, 77119207, 679046394, 203086520, 643718486, 626414235, 864313118, 70364418, 781316787, 440681875, 681200897, 414762461, 728903002, 363844750, 50453206, 574583915, 526329157, 462612880, 74553937, 768785013, 435152113, 630299777, 404565709, 28229013, 725627961, 901752966, 911368511, 216295792, 86228641, 527014291, 155161286, 205266610, 332767047, 251668878, 377619816, 804113231, 987207513, 378262469, 609548413, 183495015, 322783757, 809145465, 986087186, 224849961, 628829716, 393942291, 908795219, 641778623, 111996763, 331353459, 555376015, 279065316, 622029867, 800957187, 509834250, 347423708, 858889869, 764898942, 635297486, 509523319, 933946968, 922165778, 25205773, 503349490, 714888621, 365567213, 194223499, 489935297, 484689577, 335053423, 632367838, 479239193, 793835890, 289309193, 242967245, 522727858, 903151, 556109055, 424572684, 410260844, 5639416, 429145304, 689651060, 304604682, 596991409, 712690242, 96345831, 279008715, 178350675, 581106402, 594230401, 7747701, 379640404, 967616610, 703113228, 614030073, 537559326, 576167389, 724564244, 72360361, 164466728, 867777604, 484785272, 342938499, 31204004, 91522137, 936457519, 779461098, 358702063, 571409863, 328220266, 232777354, 478420591, 163846191, 170682001, 219334654, 684381000, 663291989, 847548952, 755562663, 83532563, 605892658, 962597553, 22407620, 330526936, 842010406, 591598582, 194493029, 641378991, 554053177, 6300318, 209826312, 85148483, 912982088, 317878553, 745723311, 273756808, 182520502, 40364134, 131869003, 691222608, 796008007, 922250227, 414590656, 565400941, 566106067, 647883066, 461654503, 222550263, 306392262, 474213539, 41781760, 660265197, 357039379, 492269774, 778183575, 749385700, 671851314, 468308264, 879349826, 212699919, 944479714, 33882767, 761364392, 982865084, 746464150, 671444757, 853802934, 219405066, 622627339, 939588726, 295931570, 796761005, 196198707, 591378927, 740754791, 309868041, 797636383, 725379526, 4974186, 567021559, 16373549, 479113471, 905686896, 763759369, 178776839, 756116141, 131668603, 776187222, 369938981, 546091291, 691154248, 927834803, 480539736, 932384171, 529667016, 806236895, 997010444, 271587794, 98762920, 679727432, 796020760, 568444836, 831565337, 830064922, 447931005, 324019174, 154162512, 50656183, 699823043, 539713301, 792660328, 598440475, 456776120, 2725973, 55453140, 318714506, 704354613, 287984059, 5149074, 84092103, 22364627, 856086179, 848497304, 644950870, 301819382, 844848904, 227238292, 683713275, 328537552, 109160751, 912834243, 502978415, 449966463, 844152378, 920645292, 887694582, 272808266, 418396255, 295049073, 609156712, 527239528, 218432518, 466699299, 302226045, 903794424, 173691988, 881330617, 621482754, 315189109, 849416123, 997390539, 6400790, 49808428, 757487448, 191950604, 306986536, 233511162, 241833907, 751189194, 87709550, 509887122, 32964839, 195584917, 265765244, 45323392, 399622194, 472530066, 24442182, 808082987, 687953010, 534808101, 726412335, 817476904, 448908977, 705585359, 296318178, 305005992, 806952681, 107089293, 294870562, 496049971, 282222210, 640004487, 144784698, 85401522, 891400536, 946987892, 560365228, 695449613, 543097580, 689012289, 622096443, 361838134, 352118710, 480779653, 381320933, 35951226, 817538562, 989682152, 980833703, 770198700, 882118190, 409290669, 955843649, 471267135, 657914168, 611566017, 868660572, 77231255, 11014379, 365927336, 815772619, 729736584, 992541381, 76360548, 725659272, 684174094, 726455083, 910414402, 587396844, 134693600, 677231026, 784671874, 808364320, 661653836, 959204542, 705240586, 695760245, 758856025, 380494368, 804818065, 667216180, 324513631, 337885696, 17383115, 582150497, 420795139, 426801058, 924046023, 689475974, 814077523, 372259350, 430280436, 933032503, 353407901, 816832729, 516547748, 609549026, 870952782, 391691572, 540509433, 364893117, 588065677, 5933043, 699188804, 994800774, 38509104, 996726549, 745862755, 513835505, 971623791, 574902566, 25740357, 438435902, 369243558, 549834159, 175461238, 574206698, 917896145, 798348663, 249613073, 694411277, 519329398, 383939956, 319845424, 495291616, 543091201, 952584724, 510919167, 77552145, 61709722, 573424310, 654882640, 239348497, 135332613, 636552061, 323739395, 190380681, 39484128, 757974747, 670819775, 875906052, 710878058, 887308228, 180160601, 221244651, 974892049, 789676982, 979884428, 37865623, 332132550, 377692409, 795247077, 909747998, 776644770, 233745248, 152255092, 638988303, 242878561, 880430503, 866700486, 160028571, 461454051, 171359815, 331267045, 922227396, 333066890, 151967787, 678315666, 210912737, 508994220, 992757461, 282196545, 605019929, 370561405, 994153893, 72195023, 16287422, 551745501, 65544330, 331983800, 669730303, 250713743, 563389895, 852583831, 628985758, 153569757, 253704450, 354668211, 890158219, 538802247, 219087982, 439438800, 475234663, 426455377, 20840425, 854063085, 398046493, 113863731, 416667592, 635204945, 983349939, 833347329, 929224750, 125998890, 937977436, 703291940, 298139545, 211682649, 513248956, 589114207, 263825975, 148549888, 685055088, 866807002, 411216675, 325649892, 164313588, 898312787, 24916267, 892488319, 927942303, 963935465, 470490548, 169256013, 507417953, 374600977, 187879020, 53160834, 93101764, 670668858, 73401040, 643733865, 634982974, 268290956, 575390180, 948059502, 317545825, 363693139, 326397065, 458996748, 568531076, 966670599, 470952481, 237368204, 138273466, 959428828, 320625239, 979173520, 375317945, 512338642, 774191305, 348718798, 176765018, 688445449, 688574866, 742361586, 978105304, 319117516, 502100473, 855113626, 434871951, 169682821, 117529688, 379707645, 479054490, 268507463, 97889908, 543223310, 761603638, 192430411, 611731937, 673840575, 248893058, 769087110, 965546262, 746115671, 537130749, 794612442, 677490611, 138949309, 177414182, 76633417, 298620590, 853650468, 95216332, 866723306, 837577422, 347709313, 157737430, 94555387, 526768800, 742224674, 714415190, 324298734, 585430189, 684115479, 27066113, 373243816, 361721999, 95577100, 642354718, 80338033, 720824272, 954368799, 310088522, 289742984, 45168789, 504018395, 30358835, 969366231, 945718637, 181316862, 61477330, 74169517, 266366177, 942166363, 639691340, 569618588, 604841149, 105639076, 14982689, 179417952, 767082564, 586756946, 109966759, 462976163, 780295823, 208953432, 54305947, 739967325, 715202864, 408214882, 135978865, 868913127, 37194446, 672508503, 610626882, 694625620, 720598252, 262000145, 882789797, 457646281, 709998258, 343486472, 609642223, 10755425, 688353873, 439075294, 458284839, 567877044, 65728780, 587795102, 993020048, 93464050, 86751094, 594306258, 735350905, 788710243, 803792293, 422334519, 46941845, 398753411, 246849308, 208121671, 353482635, 308871639, 145853004, 580026666, 716363178, 63345856, 72416542, 227037223, 986451694, 527935943, 846838345, 798939603, 899029687, 665669444, 827776671, 117569163, 848461659, 81248906, 714785945, 218147225, 863423455, 795194452, 792612220, 799918790, 915873441, 479753687, 523419672, 806753663, 627187953, 884129979, 844649855, 871293211, 519833514, 866564289, 58610648, 363189796, 838897052, 853635871, 783069009, 856616146, 975849205, 503825756, 479906639, 803775237, 92231613, 637212139, 612931197, 78901013, 217045074, 675529951, 541360956, 279921115, 124328332, 399387644, 814430349, 650224373, 44534524, 834585382, 829922906, 39022714, 503039406, 819864707, 855263408, 206103874, 558577061, 912758335, 927454285, 7179860, 861017046, 605767844, 532717779, 692700379, 590255633, 156822586, 441502581, 550302566, 960512171, 259505703, 43957185, 250076777, 462715878, 97404416, 386801641, 733235860, 765924409, 805605747, 210601251, 371845173, 320896111, 287639811, 565203925, 873316610, 881064380, 700834777, 820869392, 488124589, 704069816, 516853487, 208043979, 891737733, 493790308, 97515117, 818265374, 669688470, 374406134, 182236019, 830923114, 632371173, 15434043, 499884891, 805587284, 639293542, 740904383, 519478616, 447799941, 755054014, 537121318, 984445535, 855540467, 184648972, 631332772, 969605060, 974770527, 882743982, 458756720, 111662212, 163854099, 169674392, 764514601, 387192714, 829496257, 715080424, 904635534, 512541616, 485706662, 349864430, 80057128, 96391222, 929663613, 522958121, 736024228, 902954459, 878774044, 425692334, 161254860, 85846546, 595024050, 551510909, 641302532, 904898730, 446714944, 366210419, 709275184, 672141149, 211296519, 783322339, 59939318, 543873981, 388850179, 559504801, 299690228, 593931981, 100679126, 260901683, 904300406, 608622559, 824668610, 669751033, 681641191, 239220701, 292189485, 101789405, 830350738, 55400677, 786280131, 635771128, 155463486, 52276572, 965872536, 644318539, 183722643, 114982394, 856212023, 395507021, 375009569, 134298688, 837953936, 665497923, 767878084, 376304129, 743099788, 969590133, 992835864, 439223597, 120036646, 508111710, 472407820, 92263812, 861367916, 694985998, 542438845, 683428520, 997101466, 267773733, 693487579, 459020424, 653560137, 141870658, 434284217, 744188184, 651569038, 634515317, 898550793, 334144814, 637486664, 3092898, 821894556, 78622536, 20054593, 564495460, 247848814, 3774099, 40877095, 552928464, 596551053, 230255581, 47926554, 446759463, 318309095, 223559453, 16460719, 801268201, 296286981, 276827969, 592715785, 723065119, 201156155, 182330437, 410771645, 855534609, 737552147, 394363455, 747293627, 833222469, 692883931, 84835137, 771917989, 811790547, 956088612, 56489045, 808772206, 284478769, 815828506, 826085292, 150419422, 791151571, 10758771, 292317244, 258395915, 491847971, 238025775, 792277994, 543651904, 785559343, 721043161, 305234995, 544931880, 906763254, 69358646, 259614104, 480868663, 369232731, 80590574, 164053986, 944797694, 12612136, 474291023, 956542940, 696253988, 110360430, 462355226, 161161350, 72035550, 656351263, 156851124, 32554170, 12345792, 182807943, 287116197, 479874724, 429322276, 916014104, 563300810, 577605613, 899515833, 483684242, 85269803, 727447048, 515632441, 148525181, 588065260, 898850144, 133195090, 65506827, 975400605, 362529790, 879700959, 144081112, 33161698, 488315269, 686886438, 727459716, 965875163, 208609068, 828031795, 269378903, 753947390, 177264054, 95556202, 335638262, 194842733, 365799470, 438965235, 759541476, 266420404, 353430460, 970103269, 636927163, 862246741, 511221611, 919628570, 114826933, 194443455, 710928315, 532472584, 836528613, 588569113, 801009720, 167628089, 487152718, 433606662, 120404204, 272748845, 347617604, 512476038, 252219225, 370222559, 571708296, 637688524, 698950887, 298071832, 332472970, 768964655, 31020210, 691785800, 62129713, 772369522, 515728601, 47457038, 125041571, 568845872, 164748963, 487198487, 872126294, 742060311, 371308816, 394247981, 987746682, 95064046, 587894942, 590733193, 262933275, 374683022, 4044468, 584971686, 332968964, 602876483, 73185053, 15407555, 342299341, 613581546, 790518391, 933938302, 387291621, 684911975, 308718539, 118107925, 186823976, 856665508, 609853140, 919440747, 230564845, 398172119, 99256484, 326238053, 113064991, 990712260, 928491820, 752231299, 179116299, 322155438, 458788574, 967681278, 151546322, 771562007, 855412304, 78789051, 631907543, 357383440, 84640576, 999580634, 482734388, 793266903, 780625245, 287452546, 692846653, 777606701, 907508019, 481269268, 454412694, 850308261, 479856420, 922740446, 816474033, 846943734, 195359636, 731006329, 205873167, 897396242, 304887252, 652075088, 476369243, 457785672, 416517445, 79208493, 282054377, 266015274, 519366564, 770838611, 981348768, 831807406, 774100283, 543660850, 391366726, 340528924, 594058366, 586717763, 425719958, 524102957, 817641725, 958865684, 450423946, 500044095, 875499785, 316544453, 275169398, 901673749, 63779648, 868074557, 834831230, 341818456, 180253007, 809357738, 497228607, 411169604, 96108848, 127237104, 605102921, 363655920, 555119001, 982797747, 185754717, 38981358, 692428957, 48072041, 276180911, 305618585, 290348302, 963388357, 182566300, 222013348, 293986609, 619075950, 202923834, 257287584, 468770571, 289340259, 607555829, 191629227, 13208433, 27558011, 144941037, 811167300, 579875783, 97857029, 124985382, 342950684, 200654088, 735961874, 585821534, 655707830, 558798782, 457953651, 998149435, 255942607, 574086739, 154502726, 277229124, 790040035, 756712250, 156217275, 587374304, 687515185, 811079396, 203334019, 707420598, 721914968, 637659257, 87520266, 707553856, 863692008, 161778203, 187829827, 943661241, 707561167, 407281857, 65308058, 283352593, 493192646, 300558259, 296467494, 618519823, 337337714, 383908881, 510379116, 734211838, 830413411, 731018643, 690078271, 714207674, 922452673, 521398114, 559267704, 522999652, 271942249, 825714170, 132513977, 160994478, 249899150, 355298549, 180343126, 827463639, 649851141, 376134804, 224405846, 409957079, 735851379, 393196104, 629819747, 698908433, 943004024, 796458170, 543671907, 868460704, 204512971, 218096952, 273150185, 712001480, 180408498, 185825785, 569980878, 490217981, 546557058, 556242663, 560727840, 123282731, 137938907, 472911446, 584048270, 993772928, 373604148, 361173817, 55358456, 300410008, 515587755, 341072379, 171257168, 783916563, 436919406, 758705776, 211671883, 596115541, 420021956, 866376986, 541459727, 646204126, 183017318, 982521122, 761497812, 43236886, 165790919, 754431818, 6632687, 446371028, 701472912, 313313550, 472335288, 127188261, 647887021, 119763576, 675475991, 383649623, 351395102, 160701791, 206125693, 157025755, 586226934, 839123652, 231666958, 635187886, 737644363, 78268132, 615928068, 957621154, 747669537, 798319953, 671029650, 775125714, 7887464, 540694214, 871006473, 817922172, 844624304, 571927017, 489497208, 596233040, 841763070, 219432305, 475445584, 712942241, 724322548, 648027661, 96570923, 535574988, 384023279, 509674761, 380718442, 586203107, 41701369, 996369280, 52837211, 517144563, 981626949, 356230341, 336666888, 718033083, 494771554, 39242573, 248087457, 474034219, 553813455, 857420591, 566452979, 755461294, 295264144, 495853729, 204544837, 220445255, 742918082, 707356527, 770843653, 102925782, 605520531, 565932304, 933058434, 708432083, 179701145, 696616656, 444810568, 513488974, 196873283, 246029956, 310042837, 902357957, 456004372, 779279251, 623044080, 442107680, 104968369, 130157736, 819340726, 75560735, 820472013, 51862015, 92560997, 766406407, 622969184, 697668091, 854548502, 256691140, 195363963, 473989162, 170384239, 139731735, 711563153, 404352818, 452231087, 246367910, 297379826, 918179617, 273457094, 933028678, 667155660, 396795766, 788901889, 635098145, 886072151, 242324847, 966275206, 750555931, 733256183, 380138801, 492976311, 294327705, 32446493, 909202134, 138302860, 969670587, 598497873, 896723778, 79736477, 346155756, 240643256, 330639902, 325544082, 133492833, 885951402, 3313878, 283758250, 689790849, 335404296, 471762276, 16040743, 320984340, 885756819, 182068628, 706646072, 265778701, 182717407, 113779932, 405876752, 393113930, 200895332, 335864428, 40139684, 256357760, 962482441, 246256104, 744548269, 610171599, 259858164, 175493486, 310998148, 709067580, 256851886, 372779164, 127141725, 143905209, 202316163, 372575029, 402183043, 85236533, 453351653, 849393943, 10241150, 351742855, 950740886, 265128880, 599832210, 853377750, 69399959, 279177250, 109703604, 777929263, 193634406, 276722110, 613362682, 791523110, 951880697, 616120169, 280277635, 35519046, 160536608, 508877024, 940990602, 151259521, 678014493, 323631542, 265852896, 378710933, 209201143, 836872692, 55557408, 136110859, 277179713, 476670913, 822056648, 756539252, 942622256, 726096249, 658183511, 861798173, 263321906, 393652869, 33390784, 824420810, 970611284, 910054597, 947275376, 884922106, 306874118, 717997363, 9729884, 948776972, 935744587, 300242830, 986748444, 693552715, 897662750, 338459944, 624564929, 578531732, 521983361, 788381939, 243145523, 185292258, 339030751, 364072321, 825205600, 338000196, 910796891, 72625376, 962457324, 568478477, 344541521, 992844753, 318069789, 569654582, 599828920, 873140767, 145298732, 706123105, 599401891, 474535047, 299420942, 15954459, 194408799, 134166329, 974592126, 475422642, 799784358, 565449112, 178613858, 854118412, 100882076, 25576675, 906321664, 220153191, 199911917, 550839495, 882792100, 267943580, 286300221, 137368303, 647244255, 631345469, 35640570, 824804690, 895421671, 744910211, 608599589, 539149592, 913076516, 105043794, 146194386, 728866996, 125145430, 584321251, 632403282, 895574543, 112409599, 397260207, 415736501, 903991441, 657536608, 907615030, 613259973, 218274461, 409658721, 210504286, 640581831, 656571634, 895404227, 911297711, 774458356, 739988287, 630082805, 92702894, 757721521, 655909343, 117986742, 971989319, 546268806, 377597740, 692617264, 466440342, 453013965, 865128795, 595781800, 599778539, 546124725, 620227023, 127538663, 466856898, 605030967, 619583697, 682663638, 225014857, 90899088, 830967575, 53751523, 182786647, 568785589, 823410635, 811652080, 310174044, 954194243, 338683711, 94358939, 103825203, 810892575, 273729975, 79731319, 485506985, 64844212, 666544220, 305658437, 191310440, 239661306, 296746208, 64289449, 267509845, 859447377, 662732147, 709878666, 167534665, 492099958, 741830134, 18948265, 753782424, 846601572, 762078643, 77177220, 107549073, 787267312, 935825802, 943035071, 485376493, 737987401, 99540628, 627681013, 125564905, 349757636, 600682637, 92576158, 624580290, 393514, 166464895, 618240020, 626602649, 665119140, 275672918, 698489642, 494733236, 879787610, 26108844, 129100961, 916503432, 771838472, 704225929, 302817591, 455134284, 328250631, 133771757, 368618143, 819293688, 748248266, 740435311, 852170933, 162638483, 65422998, 615864448, 707930351, 746015428, 599183503, 894242765, 488858986, 299378161, 425799656, 964817668, 412921097, 756470205, 438223878, 385049180, 653313961, 231794893, 485413998, 325994781, 934755358, 858963146, 91502825, 807942930, 993252323, 939225989, 485536338, 702059475, 684596157, 293851995, 858325255, 540726080, 670522262, 660971462, 137837050, 693076939, 902394802, 712080282, 879789298, 270226313, 166983700, 249096736, 297720960, 678181521, 995423525, 298889188, 956251109, 272009237, 295302874, 155586079, 70037980, 938860059, 572856622, 915623263, 894574492, 609152938, 820789504, 590010949, 32797070, 296151461, 958892622, 761242631, 735217784, 16959209, 910145547, 879838100, 3637783, 391699293, 521927927, 163370813, 339276674, 415396280, 663105601, 263898203, 552554566, 187138528, 107443875, 739312015, 590628872, 587364671, 364482278, 67886636, 95873019, 605985631, 165712384, 200612635, 432525244, 990363843, 528879635, 774719273, 528658543, 709684809, 914007329, 145466877, 705251522, 676640602, 419799671, 129866571, 61124559, 817219789, 947124549, 221623982, 565221434, 445824293, 35070377, 188866127, 323807815, 458266396, 194234787, 872037438, 458017110, 896840840, 67729638, 637461242, 176246297, 130502588, 889861940, 932836140, 422996609, 22700448, 289780785, 688802205, 478175905, 824613017, 92617090, 450147207, 563113014, 442943177, 305769504, 667871017, 330639476, 728009626, 456352675, 172910328, 641877078, 820282492, 214555998, 349432619, 767123620, 509467170, 516689815, 104727523, 602717975, 60974015, 499100747, 61483554, 544409140, 358953276, 62058381, 445489104, 665742697, 884247948, 116036268, 106455368, 821933855, 21336107, 558694240, 925407311, 164499037, 288846143, 223034454, 442397985, 451779015, 659064563, 596631270, 61971560, 155240908, 645492861, 776227173, 852663106, 418940917, 45673483, 474840510, 89185048, 475531109, 903523008, 413572504, 183613150, 845422041, 37254651, 637020591, 692442894, 776081084, 595579112, 349367101, 313303217, 839180704, 695631510, 402031611, 1223314, 165412050, 670416842, 140679101, 750862171, 221986481, 609246124, 793501614, 857873030, 346437643, 812492968, 722947344, 696244952, 287940468, 608126407, 615245661, 23216568, 434256984, 281000839, 30976833, 737587531, 900048919, 244051271, 447978947, 392614980, 114707068, 945891925, 962547663, 966293903, 704569832, 694550538, 808890429, 332082758, 516004789, 645187693, 37418596, 305887255, 369289049, 442021683, 643218321, 188086722, 48833288, 20935461, 810309261, 404665939, 991809344, 805381806, 601925404, 148951623, 239746149, 913164002, 27586625, 815785632, 199988165, 838543258, 188491616, 697862043, 609560445, 985514706, 671070442, 250913447, 927540697, 25939167, 51543930, 774107486, 394815297, 16866388, 810081132, 259972617, 911114530, 780410351, 318032308, 112473618, 139981601, 785703931, 828168341, 528372902, 119147674, 860346905, 339550719, 307810594, 205951824, 914129734, 333859485, 181869107, 104179405, 361852230, 845027979, 159235720, 476075008, 974492418, 476627489, 981363116, 892109842, 774114028, 649513838, 286285262, 638549101, 144824203, 448316762, 100740715, 278937446, 808323193, 238158508, 744414330, 465489738, 349944965, 255507503, 275743085, 59502181, 143685380, 516573478, 755908019, 630746383, 533064820, 434574333, 496529819, 308040213, 624991462, 419185959, 26988422, 187590100, 572462838, 726602578, 350123746, 391964568, 781880406, 434002635, 517313271, 24640888, 760297267, 252437933, 91894803, 254831178, 893126678, 302288229, 830709466, 234668481, 951929927, 208814825, 309259977, 249604091, 279128843, 152380637, 190356760, 166562029, 901352563, 445630386, 737243865, 144904473, 333095821, 73844661, 984527598, 210400245, 633143154, 197428059, 803107449, 274084718, 402452372, 276847372, 8457685, 114139669, 759038897, 884580004, 689799774, 411995458, 56496547, 764629085, 350240178, 841835345, 903003958, 603292600, 358387144, 228925140, 866699461, 464435793, 492029257, 3100184, 282825084, 709303707, 477846098, 306506875, 499401337, 651025184, 682092709, 950249789, 909200587, 492137016, 209538393, 253179707, 386100779, 496065789, 508388669, 995799463, 104062846, 120479122, 649277646, 796480988, 567999616, 39979167, 969909610, 735216964, 465368541, 468273845, 702208269, 348701402, 497713751, 261334755, 455163400, 334133166, 357001604, 905748968, 772611845, 410439643, 657816830, 481391684, 347706660, 131184934, 997874929, 731903224, 800995303, 428833444, 608578454, 481651242, 285492413, 47200487, 102591028, 915100928, 262098839, 962078764, 221489212, 915310537, 384271843, 735128527, 451936862, 624211663, 167598582, 95625570, 39529108, 141227375, 514822607, 65916336, 933928467, 538764044, 922903518, 124914483, 14876634, 691912315, 216808620, 950452847, 200085741, 574542421, 696599657, 46466518, 414244941, 466288670, 69373783, 744375158, 637935025, 969550851, 276651385, 506573379, 919844505, 124559408, 473336239, 922340045, 717429543, 403982897, 835228160, 187427549, 56064944, 266022926, 394618947, 845173483, 537946522, 230185345, 524478708, 137532556, 353782692, 825968475, 634344740, 608900118, 851637421, 911118845, 499531921, 963560734, 646248475, 530610123, 66459849, 808568077, 651131529, 569674461, 744724046, 978343704, 896767094, 212031373, 949569950, 877218033, 504410195, 505803123, 900860450, 890806203, 51251339, 480200964, 677153149, 525778412, 422812885, 553689081, 802797897, 790100482, 36743037, 159786866, 956477494, 164726146, 231906186, 923186756, 52831444, 545196226, 101927142, 602958280, 286752778, 453874155, 211257077, 769406131, 126536545, 831576207, 449415831, 233778065, 308016544, 119298694, 924604362, 115517470, 224146787, 521804482, 258760239, 144487075, 943966084, 4582418, 183710561, 89827190, 833930782, 322897342, 70442982, 947524130, 19848108, 695104967, 683732909, 429741679, 954715676, 994046041, 673835242, 711090666, 214880888, 781878745, 96171567, 986439312, 43807971, 386047209, 714671404, 251655929, 593910156, 381913548, 353726155, 599170219, 796427822, 960661708, 221313958, 50665980, 771975148, 468030233, 271184033, 813664699, 918913956, 448732408, 167471363, 443036034, 841033152, 757257893, 980299270, 382377431, 434599671, 859645251, 675578548, 215428066, 244048016, 896784609, 890270485, 332686137, 679589753, 434423446, 283682248, 737451538, 183342003, 893258078, 85973181, 666600143, 394503962, 736954135, 664021774, 769494378, 206213808, 938621444, 66420723, 964119644, 579923392, 747581050, 360312659, 169526823, 143351204, 369426648, 555123437, 871845699, 812305971, 48338666, 61100073, 542870335, 370767056, 149437220, 549404299, 190109923, 829700123, 872116446, 321165701, 415254565, 682769790, 234626971, 7097699, 246403882, 800166606, 726517513, 965373237, 203164005, 666585774, 998084053, 873375756, 407292643, 955646891, 554571714, 10396461, 915817636, 956816254, 132869289, 39478981, 234307360, 475164948, 626227524, 118167896, 932050922, 159066181, 723372754, 355109915, 597957672, 183585185, 208546582, 574003227, 658080290, 631185395, 121839234, 906535329, 72329588, 573956246, 67262275, 111435673, 918123871, 936857045, 535424620, 999052429, 515347068, 95875585, 239183449, 959011272, 57511777, 390876707, 341591261, 651398581, 115852372, 998285254, 371265702, 23480300, 513375710, 666059524, 985071803, 700424643, 294982580, 761041052, 59293368, 306242071, 68160145, 702241979, 161838010, 104321113, 120764369, 528255978, 440424703, 461014895, 629657521, 744941321, 780479957, 398240988, 47497073, 402672361, 10902242, 698363628, 16523987, 737630208, 404201215, 67286064, 792146528, 875175974, 170668620, 799129572, 16630821, 213182251, 591391506, 411310258, 761976421, 293359167, 747099206, 990652351, 458831988, 43920231, 847621574, 610779825, 176457300, 288773856, 346231327, 452806784, 745741997, 532929269, 663892808, 371441015, 769101907, 71704031, 628808908, 961704190, 105663352, 262961258, 705541955, 456734117, 37989969, 251483605, 509631827, 435076642, 311024185, 456011998, 924533986, 122726797, 458746693, 794222737, 968262522, 293197431, 460265041, 254550762, 800169758, 880977252, 567643443, 107212748, 870270488, 312706780, 958289206, 22748164, 653872022, 413573315, 70075162, 166410201, 503620930, 280071687, 341709425, 808722327, 967966465, 837069953, 274493833, 764500156, 339963171, 583990961, 218412772, 112308963, 173177804, 294160099, 979233632, 593077618, 387580191, 424832696, 515825141, 74305049, 258596314, 778008377, 451085027, 743544428, 371696287, 59262635, 863986950, 860163531, 734665658, 445219708, 570913426, 511347088, 338147246, 361591254, 752268473, 94437314, 490229067, 402578799, 859223181, 649804612, 423808028, 120127023, 545732847, 659856268, 336415588, 370871996, 175701184, 979892717, 816452365, 24216506, 484781843, 803730213, 89309058, 447615434, 977755095, 574701557, 217364708, 670017660, 506341037, 249013568, 310253746, 812732671, 660524710, 78290565, 996498855, 241098410, 156236972, 132466672, 564805975, 496805582, 69595909, 182299960, 98563715, 889444748, 815745341, 115733735, 904911269, 25784932, 876144653, 380470595, 714173313, 857190089, 165608, 154503822, 216065223, 238262217, 837016868, 24124509, 66348239, 960056232, 326432066, 515058023, 888151594, 582988252, 367053507, 147014491, 221066552, 825852651, 197594336, 729654325, 460344606, 323773409, 440455373, 184527482, 640187592, 327822016, 879598632, 590404496, 334485076, 855622451, 385552456, 618603339, 496981960, 289414274, 505792049, 363297081, 810030527, 146150223, 342712164, 934188352, 874566907, 783021291, 508346080, 409071564, 126478740, 644456037, 599651172, 354119193, 544029819, 24875071, 318402939, 226058630, 121336329, 239027574, 83221697, 214144855, 394764571, 643048913, 216549489, 187413070, 986834499, 179806972, 955378058, 950690589, 965098213, 593452248, 350150898, 926723242, 317536475, 399722214, 648463794, 172654013, 923746986, 753587688, 920530017, 87707880, 947032967, 657310988, 876283715, 556805744, 672763720, 628532766, 872500339, 759431381, 861080667, 783785988, 820963922, 815196629, 947982614, 50595032, 188268613, 327560582, 129226560, 740929614, 900240093, 81742643, 639332409, 209474893, 36785700, 95999725, 43198109, 145395084, 237782334, 452087722, 152830237, 900607431, 117842617, 303565575, 458940403, 874736072, 421648623, 770493909, 635414817, 70272251, 631237166, 639095125, 396618822, 510205949, 119484886, 882369852, 12457365, 324227247, 989888852, 695145868, 218787391, 352497619, 159430492, 683733589, 108424198, 259925123, 102467299, 462330267, 831922230, 14708719, 655859221, 230509418, 754153692, 974001044, 143146969, 702634857, 612583376, 129024066, 175412995, 969914380, 661024643, 122010387, 37357592, 889963194, 79669534, 988177019, 146889399, 468035279, 981208907, 698412096, 56685500, 823256141, 805567913, 994095226, 871405564, 598445323, 375098668, 448024146, 870497313, 321829806, 405533848, 172136247, 748025421, 18574479, 870027782, 396208300, 819533051, 797823540, 689083308, 119769199, 490776097, 980706794, 419899331, 851245387, 279513858, 372994446, 443556586, 236633336, 206796737, 429479264, 203372514, 712541912, 186700899, 90558010, 606418541, 819728329, 692637252, 390302923, 646650677, 750955933, 643622973, 732118110, 707334683, 52228436, 29173477, 562459116, 971148541, 588627979, 392782872, 776990351, 802964331, 292925819, 289612197, 495169008, 408987255, 420302589, 280637937, 959706337, 821443259, 895964535, 193797285, 560160363, 785472662, 14399982, 109772356, 947375361, 752788402, 185201107, 799126607, 57684950, 426211775, 487126110, 634111629, 346810293, 172546949, 988857438, 681113344, 998850926, 910042046, 789915785, 623285750, 826823558, 149096709, 198639098, 370938981, 746473603, 933952760, 555469572, 994888718, 205223098, 390970463, 567496632, 391443781, 738489494, 318088900, 222966123, 342525283, 26193798, 859043330, 872664547, 891326108, 755330995, 501125338, 769703079, 439792282, 793149410, 71630163, 86589773, 284854625, 892126887, 268048642, 442002647, 526411047, 817000448, 879950808, 709653680, 884845898, 907090713, 259202331, 165154441, 829359537, 856947676, 995599602, 224377033, 340579684, 431474208, 133832492, 719911125, 77504166, 917769796, 104829418, 942138930, 106576599, 198852831, 314015679, 54875450, 351662889, 419528525, 242386272, 345781680, 504253725, 258310877, 932238120, 242925165, 978162345, 307424284, 828918469, 508114705, 209883078, 71085266, 113182799, 574475438, 60345924, 379566368, 254380365, 156185110, 23462518, 684722232, 849020737, 530307470, 115647868, 75403230, 321012273, 574558647, 378921396, 297088420, 164374158, 342279509, 351750041, 367722745, 293601725, 293600409, 51189102, 58016984, 808037164, 705088238, 650970738, 746398692, 820357528, 220110489, 394913675, 684570201, 854355598, 314606615, 870663987, 683272593, 114159779, 117300944, 204335217, 777319099, 37158157, 274454211, 484631381, 973050956, 201958678, 96123755, 751554030, 385142321, 380995461, 907249582, 662968376, 487573113, 121770841, 601572157, 71812570, 489377757, 962606532, 426077270, 766705964, 926973162, 3294769, 940731524, 289913566, 668552518, 582275335, 341690976, 179083882, 671407974, 779259406, 804636924, 166537498, 374941974, 981871854, 346979588, 644372059, 563035873, 339803363, 585011526, 910120345, 683288235, 849584750, 955614464, 604532160, 818282636, 953188678, 158073207, 165879257, 46205601, 25010074, 612998720, 279701636, 772721638, 523717244, 333336753, 34506613, 685925674, 43879224, 821155439, 985235780, 161483395, 571598381, 581747359, 918206771, 780958084, 725118435, 43313332, 65680054, 84097765, 298135390, 540848121, 171734188, 108658166, 241643760, 769099046, 250873199, 409322778, 417030538, 974668205, 565133646, 367168045, 79396743, 184759624, 699909601, 518684157, 471599591, 273157560, 222713295, 9800218, 799271569, 701627099, 925385618, 276887590, 717721728, 323795386, 981145057, 427277303, 175982909, 618139521, 628853911, 296858868, 562260508, 601817105, 281060155, 716756797, 72890084, 934626076, 821177298, 758030264, 61130588, 286940774, 955501124, 426275159, 978137909, 248735333, 318583483, 397717922, 497824531, 524584339, 855063951, 421090887, 425718337, 390437505, 592671606, 862033023, 582277808, 534684744, 513910805, 491428896, 25619097, 76115951, 355175551, 906801393, 100136107, 989990175, 717567900, 441888345, 801891734, 544415958, 539566581, 385314666, 413961873, 655563076, 357052755, 209328609, 290044469, 419578119, 252164584, 853316379, 760714775, 129972415, 629567782, 834131323, 938190649, 455004058, 956582245, 300988963, 307289824, 660837816, 968484182, 507109192, 175656384, 166006965, 328053315, 802909860, 601767540, 726321297, 222888379, 691233927, 92730017, 758762901, 113532636, 37476494, 945425063, 500327238, 933707653, 755491775, 590943417, 720865425, 501947213, 947415190, 28738207, 1005835, 71724929, 363398119, 786648558, 681137760, 722136839, 306847453, 396980747, 900945640, 648985987, 300393031, 364095525, 382333179, 633633801, 51078798, 213295790, 92068314, 39779329, 577022580, 98630184, 645565778, 307664370, 310975202, 574961764, 996272569, 812110789, 514342491, 840119933, 201289836, 612475554, 167371420, 586113296, 58876513, 390799714, 447549985, 809181552, 437224853, 834683932, 405431404, 874045475, 472730247, 229966182, 1031538, 977408069, 436530677, 696436944, 937431600, 677921352, 816279044, 309260838, 787420398, 892999776, 508614046, 41477637, 982372950, 173081830, 751704261, 823407899, 293065451, 428514106, 427678546, 370149206, 878745286, 77486311, 371206770, 654832050, 74656688, 101294326, 276595844, 56284555, 1979362, 754793992, 519069653, 910180633, 834900594, 324061301, 689282958, 297529524, 976778368, 687672234, 345183193, 640693166, 809830260, 453724352, 150270104, 932837778, 185677304, 474129474, 854870611, 651181321, 467959004, 549200553, 536433883, 188611438, 142985171, 831001934, 327399583, 768226613, 32018566, 998726463, 751314610, 262825350, 972291413, 124580988, 260841542, 915797172, 790735083, 503456418, 263346820, 587941791, 538027947, 333153792, 885051065, 460694359, 299059901, 344098304, 302694738, 480678092, 708187954, 371236365, 265207622, 143928725, 546153392, 134142547, 222818925, 798360191, 969661293, 622645541, 925752103, 65843963, 287489046, 716638765, 77672169, 893937442, 867702396, 745397676, 12853731, 113220665, 420002688, 241085834, 420448283, 719216965, 902644348, 309450774, 499010568, 800358195, 783864820, 819773992, 215615485, 159810945, 190450925, 820271307, 469879951, 747113844, 981220260, 534470714, 562106451, 739622330, 495462255, 490943079, 971672954, 539380843, 174971018, 719026202, 92835352, 815032906, 147840543, 960243357, 19957881, 36339797, 861558066, 782392968, 431493139, 323705104, 667514647, 148080074, 22817289, 300014926, 62138425, 740978585, 225074441, 996550536, 313336877, 349917351, 740889558, 515614356, 162675445, 391571940, 980965281, 245595250, 934644288, 660044927, 233698219, 601822391, 790431514, 320201024, 274923731, 358337355, 493347210, 977731110, 450837180, 910739262, 811360054, 39443469, 161123761, 7147542, 532586585, 75406369, 292023701, 269116707, 739085841, 617555252, 241253046, 310320626, 749611297, 488812719, 85605615, 741977204, 278379589, 552513191, 618297799, 604535751, 21247390, 817156948, 297937288, 317426638, 389737886, 395669055, 476562544, 514573395, 880816858, 742718344, 240796100, 652209674, 373648078, 159290133, 214466358, 110459445, 389275213, 494177894, 193546793, 644365948, 465242052, 504598244, 402968233, 751974139, 810275130, 788228812, 11285416, 375518615, 482844914, 27592887, 168308086, 60206935, 756443364, 814593353, 891194459, 380537516, 386989782, 926536942, 602360053, 969032888, 634741593, 55436522, 640177510, 810143645, 249650844, 157551021, 722234661, 8490373, 101076613, 42105946, 291715146, 489168931, 169871434, 376972961, 569521790, 985003234, 570232999, 209223933, 279788024, 763405668, 421837401, 257826878, 922408913, 108203885, 287075059, 14728699, 977338412, 412576812, 403833845, 951775049, 58411460, 521933107, 801729479, 472434908, 345580685, 999453840, 742367752, 734282614, 468190961, 580871487, 871559600, 432408027, 305410683, 169275718, 498686574, 732561817, 659047187, 389927224, 522267240, 155687192, 892255002, 940188470, 243003481, 84870817, 809104064, 48784331, 480137071, 644452350, 425158885, 625795635, 249446015, 605351759, 40662966, 806150781, 733479326, 656422520, 782373424, 649131078, 860973475, 26176694, 172686466, 599198634, 314912556, 596017159, 599006, 306334750, 718129218, 130058593, 933478427, 807943898, 335847787, 811083459, 912627921, 601141214, 897531742, 100167856, 924579155, 496815330, 705588502, 698734999, 15592815, 142223532, 525519884, 60511616, 252769131, 936099609, 341361617, 858697117, 659947947, 264660142, 337802404, 298879220, 702762957, 23700032, 173548377, 845890325, 335408468, 340976954, 288487024, 578393984, 581463659, 122327280, 350992688, 746848789, 369793163, 632614749, 954165372, 185093521, 723398379, 191100151, 29517982, 808564794, 107955130, 294412286, 779345221, 597498869, 36046262, 752126578, 867151322, 696698567, 723244969, 946323958, 94809995, 226183488, 216100348, 577402977, 659300565, 270828332, 714678976, 810733527, 361578129, 986905033, 734170319, 158621591, 298808070, 122958513, 261868954, 148441049, 281961420, 672439192, 35615906, 590601241, 239956466, 301603226, 723574491, 378512753, 409700079, 702170455, 132768655, 218320117, 549267754, 283614336, 619986605, 520123842, 195143020, 188457836, 818012859, 738772618, 44299172, 776380556, 436173622, 567676194, 601406459, 28955049, 870007171, 652768799, 249274819, 708296520, 391688693, 140182185, 410291733, 376986492, 850385782, 189445558, 743146806, 984514739, 277318519, 76361684, 582395428, 242120589, 505011333, 405931642, 490733998, 29785453, 110544376, 518942389, 725018586, 287007060, 971796549, 483181323, 614005282, 281384781, 740892883, 978985656, 951027371, 738474605, 544812803, 245740747, 928438392, 490560054, 272268087, 478396648, 71663567, 481885603, 582234028, 531727139, 65927566, 448132258, 241486357, 426466552, 900847292, 319681016, 795185742, 876966553, 395782365, 597890707, 520853043, 677369086, 25279627, 386772068, 548506897, 221268337, 20638878, 830822141, 243782461, 342369802, 672938934, 177093186, 447943353, 205455607, 818385155, 433938779, 578905100, 172916284, 542902143, 114955125, 41158113, 832432568, 559181816, 938773329, 735234649, 237450111, 725476648, 158732758, 611484341, 500742467, 310937091, 864921962, 8973763, 736977528, 893555186, 952096941, 867836910, 944769721, 836223816, 588061913, 924225269, 955621391, 415945601, 907371236, 609792624, 77286002, 985239132, 500722882, 132850903, 340385682, 832336257, 133150046, 482251428, 518347202, 328724279, 513856531, 568791971, 139244494, 871821540, 797848791, 216871586, 959847622, 583953760, 658832368, 547120037, 424739427, 545889240, 763740202, 564630904, 117185761, 190703836, 604654636, 993789981, 197492929, 360714031, 293071706, 845738610, 120661086, 557532887, 499374537, 401625268, 557791321, 112302182, 726413953, 165092490, 541632577, 880300443, 546090248, 746461205, 361187193, 454809342, 674034658, 237637322, 331612902, 636341138, 956607670, 557516215, 913226363, 912557006, 458230740, 218175403, 194811171, 43579889, 313022076, 518649240, 65562823, 693277248, 528116909, 120991070, 928849834, 577017283, 162453980, 630084390, 772426852, 458497178, 93715155, 674039933, 91453390, 527476595, 861034007, 832215908, 167547238, 609340782, 331769838, 375243680, 390722132, 214951196, 771616645, 701855998, 3530299, 112393733, 994104818, 130637757, 274058916, 131602480, 47799468, 504691910, 309865857, 892549937, 10427027, 853447106, 973776357, 60331779, 597825036, 571676192, 713001904, 930743768, 957817991, 523999862, 92237064, 262507051, 447468532, 618823336, 745110100, 34909962, 508714331, 549473425, 246643712, 914331003, 7871936, 901843872, 93921525, 382033318, 613387756, 591290914, 80091175, 661459035, 341756317, 435401983, 760810404, 365112853, 580078567, 67730740, 880387934, 734822137, 921373169, 2801129, 777942510, 752409120, 283298641, 467372921, 396747321, 898280736, 453013594, 162349862, 76235176, 736763052, 619105144, 397455696, 467335349, 607948557, 47947392, 852274321, 888041368, 199387652, 256998841, 831234706, 151371095, 492664963, 942513998, 513118478, 655184576, 174808601, 212073767, 29123051, 826544103, 479369017, 752483898, 588274055, 338572740, 765249045, 685571915, 60963688, 439844963, 694333133, 643710225, 602309307, 829847053, 11633903, 948520153, 753698161, 276334988, 504250684, 264242954, 796573973, 475748178, 333582280, 152869057, 180598313, 119798804, 561705958, 902577479, 716338503, 618649471, 605555729, 675425809, 740551665, 296554398, 899284808, 763538813, 395452389, 563157488, 654973901, 228166586, 706980889, 702445055, 320260660, 94783673, 331775027, 1650138, 51469412, 20854351, 497652166, 903888527, 957764575, 132133341, 83224075, 98935883, 395254462, 85175116, 890091258, 244709640, 408299626, 311741518, 704510306, 844476256, 780636450, 100104370, 924017549, 776000426, 31809610, 996984897, 890903183, 165148946, 818566900, 15378093, 309910342, 203305305, 345888938, 910964759, 399094926, 544362202, 811482389, 967890076, 541909471, 545911049, 67990266, 954423897, 17487207, 162652413, 970980318, 216780587, 220340929, 698613383, 712093604, 743078551, 509401776, 905787824, 763691091, 291421918, 187325901, 863309326, 330074981, 753233300, 455212130, 112551138, 706766271, 361598579, 954258076, 229814205, 126348724, 919409928, 97723224, 724133771, 989128805, 32805358, 518593410, 46336671, 360247541, 679655437, 508138288, 929283691, 37578231, 805588125, 382244681, 981103857, 938839349, 913423026, 439265284, 470598068, 305511223, 444627470, 610972161, 814880401, 901538944, 938114093, 689916804, 949671677, 574626442, 606866523, 177404156, 282817523, 339889095, 340286835, 376707618, 187164743, 963042165, 617224182, 902342824, 660715465, 430199166, 557718493, 948000731, 84452469, 937777041, 926893640, 679006878, 659088030, 786685289, 543235720, 854299856, 644676960, 18651418, 872719571, 922534700, 462328784, 807880056, 111464552, 37371573, 547500361, 568700187, 551680785, 315606611, 201692843, 571868746, 433295234, 822477128, 686883522, 682622356, 987841015, 220286958, 433842314, 331161828, 470616737, 47499516, 828009809, 578330384, 762485736, 513779704, 486499101, 144935835, 783344054, 719060833, 440960282, 208752744, 455784676, 554217564, 80398585, 582548504, 840834585, 888450365, 153610137, 744821924, 898290618, 142151233, 735936340, 197881504, 273785218, 52706298, 800120834, 565199052, 130999638, 908013946, 812456358, 401979825, 158585013, 105135148, 839956198, 367358619, 585719025, 329770301, 5905581, 342678972, 219514892, 374187977, 533559502, 725642383, 890886413, 534262717, 869819893, 426611561, 680568992, 820459218, 703536757, 175174257, 270926955, 421622702, 22885777, 394213726, 112932420, 639575273, 614898387, 389395341, 295872978, 624819949, 212064223, 220775004, 728031792, 313941812, 663710880, 921616428, 867677589, 673571287, 259774134, 68507761, 674043010, 100013721, 139209938, 663684046, 865667531, 747358952, 675223895, 516257569, 151078375, 96709443, 995890210, 411144764, 778830652, 620260805, 945955261, 315405751, 905815971, 379878624, 216096215, 144893060, 339020288, 894736529, 415066836, 597587597, 58997104, 509474576, 359085229, 745427757, 214750089, 629908776, 68026553, 275515316, 87811767, 975565230, 740098166, 506146708, 183613070, 724317350, 870629919, 39035845, 476057281, 529680009, 60215069, 745011381, 294028923, 886367631, 212322274, 902749855, 925207767, 561782679, 38660602, 370655525, 154387399, 988533443, 136747977, 265451894, 133168531, 238590006, 330297661, 800103000, 940009322, 581637996, 382523155, 180973, 661719761, 154164966, 625313249, 473973257, 854790042, 260719890, 540481593, 540227347, 97362743, 927282998, 77901715, 454487254, 72246558, 784876938, 521029027, 51371553, 807533160, 461688882, 257181604, 998628349, 810877828, 55461097, 612358075, 329851904, 805980226, 65909044, 143788696, 174939705, 524293693, 601666945, 699529652, 450287539, 530350696, 830668660, 941463731, 223132087, 957249352, 761596763, 717734560, 615207891, 184675620, 845791834, 339121538, 647168446, 887185012, 922292381, 430057503, 295215442, 598962789, 488393662, 133604648, 374329769, 201091810, 176377924, 384046233, 530084199, 785018274, 859794057, 775327799, 117345321, 113258248, 169020669, 481004446, 206908786, 24115116, 468220742, 419095596, 957738287, 157751254, 121847324, 338122781, 313771061, 625923315, 596797748, 173531894, 84512799, 999683268, 92588929, 761021476, 362079616, 287302715, 915238102, 942293680, 233434860, 604487399, 591982239, 365152377, 661707394, 550445071, 488403574, 633821246, 954633223, 861788589, 92917278, 617434187, 275202628, 574649109, 406961183, 781482450, 261304739, 364920056, 932371337, 559685789, 680839953, 874831869, 835029573, 649892674, 419996197, 133935566, 467621785, 209668598, 770838620, 784300757, 194607587, 571793690, 663051877, 335986150, 639574425, 675463826, 14771968, 704361034, 729631814, 411504128, 626991241, 747704331, 650974946, 528582809, 48128457, 42645428, 472387398, 329752506, 361258540, 591133650, 463117037, 501046005, 817100347, 94272805, 806781061, 142351767, 486489598, 347345319, 987491136, 974070095, 299739106, 933085411, 283829253, 553660857, 563170308, 834933781, 283876363, 675195263, 577349531, 466337289, 627242964, 101399922, 933522338, 91614133, 490329557, 922532447, 259467355, 586759835, 11701347, 471308032, 65284159, 535174495, 165575035, 207778248, 223113633, 265971025, 952157876, 97643863, 785969017, 831470437, 730975446, 199486153, 821100865, 883651514, 1222074, 118905693, 874876058, 159176879, 969697109, 814504296, 216575194, 317614362, 530806565, 860545412, 921762050, 112272649, 892957330, 454970285, 506661394, 851329644, 602416668, 567541476, 104531301, 81208170, 482331308, 747560953, 583345209, 725885900, 366949774, 472431410, 650630710, 527425358, 276126896, 564241568, 455896074, 976571645, 689086805, 980630519, 2163863, 4028450, 381332051, 768028739, 621862568, 629607608, 981254569, 239151046, 523439731, 679923869, 15874998, 838950211, 767609356, 723179525, 235410860, 162139374, 93105162, 748852276, 890599634, 418316914, 742415816, 25977889, 562813526, 523374937, 940197834, 663323767, 388576303, 354638438, 130476234, 365177113, 625361191, 240067163, 601515120, 406172823, 886687638, 795994878, 247718277, 779070325, 924850851, 602024265, 743737851, 261912030, 255348098, 723250150, 437765585, 307050793, 597702005, 975101235, 544767393, 224207160, 722825217, 472006466, 373804340, 368982716, 737583923, 554614854, 772727856, 868219083, 436069492, 816078696, 231128319, 878817567, 173811384, 837565489, 643129536, 319902383, 574293983, 236959623, 714165276, 330783510, 467881960, 508501371, 712446244, 523107366, 162824731, 689082499, 560237546, 371322180, 872191521, 614863442, 348308704, 866655652, 745742751, 998956475, 463554193, 681972548, 945969189, 762765777, 371635011, 62590433, 748169891, 173393355, 611162694, 551305601, 387759769, 155252312, 392229620, 467932592, 328026508, 546777858, 659165425, 91326333, 963724826, 80020462, 162290733, 669123715, 294647785, 398050541, 608526144, 997879889, 664823336, 45819509, 207176391, 529940208, 103018891, 617163701, 890566211, 380094036, 993289405, 591862962, 726927876, 792691719, 316806240, 684506107, 838532388, 905963225, 75460168, 512836314, 362223162, 872795177, 473873392, 497204030, 723750465, 481553312, 503021823, 16684048, 225380548, 55331816, 830846958, 791521518, 59783803, 86587372, 921142481, 322585951, 899729248, 312734252, 222491678, 156776895, 928003006, 974391041, 201097854, 780618052, 766442424, 620114816, 872231517, 940060086, 105807199, 81868230, 641687945, 672148374, 167610766, 71973049, 679440288, 254612729, 756375182, 634170271, 834825014, 5101504, 772095832, 540828689, 10408654, 779255431, 150774523, 830574875, 539686295, 712668189, 267394789, 345789173, 156845122, 961438810, 882218547, 797303981, 956139987, 124753881, 937977990, 128689726, 291652481, 57179998, 777807436, 653358839, 725016254, 463340663, 609377795, 523597218, 930882862, 609195001, 590627434, 203918480, 851204035, 934266220, 984032134, 647102602, 493931891, 462717223, 402092717, 962587333, 269585940, 148761000, 666738976, 490800481, 389642574, 663352993, 768404396, 863500242, 934920951, 74080019, 958647779, 146942338, 442586288, 209266470, 643525298, 17675803, 989349645, 611928325, 727184042, 903238954, 243513088, 964271055, 451825478, 200390939, 892305307, 491385621, 639140497, 618929821, 926426095, 257571628, 859455578, 604130669, 591117998, 672081781, 500680298, 727418861, 736163207, 115881572, 505014087, 700764724, 604906074, 855711193, 400883427, 254294203, 569971249, 13880675, 732714269, 727314876, 650550625, 649093150, 839592102, 587713604, 314515657, 374837009, 401475564, 849376437, 448427562, 910698510, 484943168, 466502879, 39857859, 239619298, 140303540, 22628780, 608622827, 908608395, 869992182, 606719558, 825400931, 328479771, 817105800, 158918321, 466240889, 874200369, 508363514, 608957630, 223411772, 20481233, 900655052, 263868770, 317108434, 300753412, 33514466, 480086933, 669498764, 990650481, 760608127, 351969553, 61894792, 982157260, 447301336, 118301850, 678537131, 954305460, 816553206, 563748257, 220425258, 720004832, 626426431, 695375344, 562758807, 198456541, 979476345, 501661418, 162595998, 413143052, 10244401, 584186433, 928379955, 628992302, 790844614, 680448201, 118778276, 296513420, 768558621, 467315163, 363122589, 791615190, 98208282, 896412080, 266103725, 841810423, 650395783, 660582697, 952867192, 462236650, 670596827, 611290672, 903481074, 110163759, 542316147, 320264585, 806824390, 91414029, 846241052, 270675454, 862700148, 840533845, 75844601, 577414644, 369907995, 359420864, 278561712, 65930061, 640754608, 620646632, 650348939, 432007560, 195295139, 673063847, 18149788, 401047959, 781649346, 470895357, 173747634, 762701784, 671079780, 536503999, 353585093, 705604442, 123121723, 171208424, 888698192, 398119890, 274623641, 879911472, 537581144, 998105370, 689741174, 791014498, 589249369, 86301217, 230613313, 940283519, 924655410, 836820292, 442983125, 297784056, 648485101, 719321526, 607348109, 785970178, 998985752, 499182897, 410611447, 752819629, 337997257, 317389761, 705154031, 305585563, 657124777, 877879246, 305064774, 651862128, 443850655, 600925908, 945184721, 412028643, 257275607, 93986540, 170082116, 750845965, 844489896, 526341943, 165364687, 415789775, 611188363, 286091802, 546163571, 358695362, 701756997, 934408359, 205980988, 601144711, 235917391, 716762628, 349743980, 406437105, 77820442, 397454837, 869708284, 583022802, 809381989, 901101577, 256517081, 599096740, 491273570, 717781146, 720453615, 425768107, 804006938, 666582971, 418850767, 188153499, 201569622, 991481599, 110690294, 989435814, 41294472, 875038518, 734842517, 145506705, 864541709, 292186626, 791622565, 679741031, 346264944, 572554015, 194538460, 409303609, 343973256, 46032097, 312509444, 512773117, 465328190, 738521770, 146811957, 643369503, 672037308, 50842902, 702555408, 476897526, 93295034, 241481855, 43652177, 650987180, 519487455, 759287590, 582125127, 450491897, 199996855, 283937441, 149730671, 555353723, 788597574, 9092212, 378861436, 963444283, 109486076, 73348496, 66476245, 593687781, 660215268, 831138157, 536177519, 1246629, 174619695, 327719904, 315967995, 665343500, 478950594, 673632248, 842541502, 50529238, 986221234, 115366706, 126787974, 418410772, 944661158, 407166048, 811215238, 530853028, 684291233, 136340296, 984529135, 567670262, 110955116, 269935250, 888689306, 620529560, 284525080, 500770227, 111888521, 215906729, 74892311, 291312182, 680953530, 521528937, 450860877, 759233096, 466213360, 222065780, 617590597, 235902207, 725278935, 898288689, 903178047, 916639178, 932146577, 370568826, 338352871, 18169524, 31470869, 498934158, 753862416, 85360844, 541760724, 859293689, 459183307, 765510494, 450505009, 679346119, 358846252, 296449687, 125240150, 359868965, 584384685, 832351178, 786703821, 281306320, 650944920, 974677800, 560795785, 502322482, 671928149, 787721743, 594054474, 132182855, 375301990, 880072652, 699163732, 709839774, 687110741, 497633980, 665341103, 944709408, 425168841, 821479954, 698301058, 215004785, 829119608, 810604242, 137669520, 714583561, 377168085, 368749833, 946288294, 41032424, 829096840, 465856899, 339667473, 395946012, 797050324, 570917426, 597315945, 518714736, 185250560, 842721214, 895738603, 195463950, 706820396, 264980530, 311075758, 438656662, 322370866, 680324402, 238250002, 252387731, 423133393, 61170514, 468098019, 414966587, 511201508, 554211317, 480632376, 815472643, 361440602, 761072609, 733211398, 320203815, 851304024, 834521096, 182968241, 240141924, 211216983, 458345448, 177216957, 504048474, 753677543, 708898810, 857534367, 834604401, 4685390, 63786352, 592163154, 93964487, 735455537, 154686354, 198082807, 207082056, 460630433, 910089044, 454018805, 77246526, 206032320, 700855688, 316300767, 886523015, 846503878, 996149649, 648576077, 346103511, 944576769, 863721823, 90673597, 950434699, 596831601, 160960764, 634900499, 763998070, 763113859, 127499027, 167424531, 871738682, 614021837, 207169115, 213044923, 23547684, 121768198, 127882952, 897058615, 960097893, 202398111, 310828807, 717257269, 538680310, 817380010, 27087547, 349503450, 333952566, 819486278, 831619676, 718233818, 996297677, 820210226, 155272381, 276731005, 356691658, 189134210, 15433848, 542241673, 731442361, 782221126, 821065228, 282949520, 203363190, 781170687, 560360206, 915051402, 534672338, 559092636, 178997168, 136727697, 379610110, 327578084, 566541232, 728691589, 994113493, 415080387, 359263095, 596471742, 191170501, 655991985, 512183749, 588488520, 240988592, 248380477, 178074930, 91071701, 161170903, 957019664, 666103803, 86999117, 489532314, 767066786, 864785741, 415144135, 940912276, 497078625, 427478182, 393090672, 319641763, 839039237, 820102524, 468034698, 289134430, 525462372, 46273575, 404033085, 563740682, 895593419, 958188203, 881513951, 755370135, 94731648, 726693771, 612690786, 590738103, 597503986, 423368349, 405759620, 973440878, 963676592, 208853493, 108865494, 336113051, 529149573, 275730850, 722689552, 663585259, 141916407, 79405427, 915909429, 579834765, 834709587, 993327591, 702711163, 665711851, 137344603, 763149396, 343955240, 473626864, 335639929, 823895860, 547289356, 693574718, 490641813, 459088426, 313387011, 141981545, 148631966, 575455848, 408024880, 652411198, 724782803, 101102997, 236493209, 558439588, 845022977, 892498275, 813234515, 306518155, 253483975, 868667801, 121921525, 310780752, 88805925, 50997039, 945870451, 201145694, 227170230, 13381163, 953467379, 891900827, 918918159, 243756497, 546324226, 231966623, 909933035, 7039571, 698130889, 257415131, 786760019, 697921473, 422690305, 473500579, 969716906, 861909692, 971785295, 521988187, 26270368, 329863336, 955663920, 587648322, 804062073, 996106121, 340847426, 945776580, 420771406, 924311845, 499829738, 117709093, 831265223, 529819504, 112172952, 216620911, 22448771, 444639092, 636179115, 250342417, 138395878, 246992659, 593246725, 822195816, 130299868, 247870624, 602705896, 737987196, 833057671, 640568443, 228100207, 119932934, 317091051, 342449526, 795845182, 255217875, 692986919, 584630098, 958998244, 791214036, 883492369, 989463117, 657874689, 373606655, 539179730, 575827950, 84180742, 781776372, 427492225, 177792897, 819149663, 833115406, 93793502, 375142248, 279659577, 192047286, 443137866, 588797384, 359990979, 249079784, 283191991, 971151744, 282307114, 444627390, 818724144, 538857406, 125598584, 925165558, 884465746, 846078850, 572943691, 609899852, 677328821, 712500193, 626408075, 845022359, 912158558, 354569676, 733370328, 221331537, 393064371, 934572843, 573530433, 192358805, 439756709, 773706509, 834282862, 7753320, 408739810, 415229960, 325513422, 53936305, 336936786, 409308169, 43409819, 431364403, 195730873, 593915152, 878606093, 919239632, 464878693, 891736246, 708369385, 915000381, 880761133, 23286815, 789075158, 79250597, 352321864, 217434203, 276684859, 394293061, 947499845, 852398019, 405202172, 93066539, 544467967, 263517925, 73487374, 390542140, 49647809, 679351210, 595655029, 806582869, 383678400, 724039547, 105918094, 104552875, 429150038, 148804763, 656297714, 234166013, 923350423, 514136027, 83025993, 997188231, 713290525, 500875055, 88900529, 874404941, 959583449, 516379014, 226450271, 80335809, 289538157, 378846883, 343344729, 254969772, 279210198, 862328359, 348326459, 714980885, 822965830, 985626418, 142334500, 864621132, 72408554, 370780072, 386810604, 541547333, 478609022, 596092560, 878165680, 898777443, 333096984, 520015564, 729804897, 57513117, 605366539, 269786832, 587198779, 525082745, 684275632, 332217778, 401454618, 912698114, 765399749, 620604533, 315839989, 368363402, 74179779, 898091367, 679369537, 483866925, 380903407, 487728754, 47639114, 973986363, 253008626, 135641147, 99416278, 870595988, 400761834, 375355112, 902559529, 526425307, 916142876, 121273145, 605213469, 514094746, 833245688, 39006986, 450427219, 253982092, 663519201, 62326612, 302966240, 586463077, 562205107, 2682349, 345349994, 614290379, 54033993, 247915120, 972844326, 441565091, 507246362, 272514495, 315528109, 574372437, 714919, 54362464, 227515567, 457203091, 387063740, 726860678, 35439141, 753315440, 699159070, 320063011, 695978059, 465305319, 204582047, 899029057, 278887663, 542124130, 563914440, 761800593, 3046326, 786954531, 392911800, 478583049, 725099052, 42478771, 610412069, 34418631, 121197272, 361329576, 32304976, 809185109, 464135752, 936628070, 73803035, 479750342, 458227678, 126710672, 811509258, 621685997, 121424723, 715286785, 156051336, 810461447, 572889571, 764213994, 138778460, 15239821, 796135989, 113060517, 262494952, 279033150, 103839173, 801104971, 609403196, 935478306, 365720011, 732600487, 275701202, 890853908, 70046252, 980492934, 905792696, 119747158, 646161697, 817665259, 492608068, 997058188, 92006521, 584904766, 356137403, 116081303, 348893542, 819288965, 156686886, 162122464, 542760692, 249611274, 447233718, 590118117, 614452564, 683873095, 141453252, 134839494, 509308099, 13833966, 33907153, 281600719, 210882475, 73961478, 212247593, 97496964, 156365401, 187298374, 966770203, 224295487, 34752107, 925435970, 407439114, 379833385, 855921022, 524983752, 656138134, 697264452, 378352802, 362824508, 379238316, 95919858, 229316156, 520252535, 699262339, 51196991, 312380093, 166540334, 556968731, 822721646, 826255076, 754093261, 268578633, 542063042, 454583708, 311648828, 940966707, 742157065, 356428417, 335222277, 816117042, 948514163, 614213187, 830135065, 556820240, 854519511, 25412982, 91982611, 512038183, 967837061, 105679689, 576633580, 196794921, 828911987, 903849544, 35542585, 144886216, 595846933, 105234103, 792045933, 333977548, 201684211, 764426202, 240469575, 21884302, 66954225, 135971416, 901881059, 563168923, 36262022, 240191548, 735342427, 15164853, 515392901, 781523956, 230372145, 534818607, 163469993, 726488993, 352282917, 245908820, 138582284, 320791091, 231330085, 184605551, 256927234, 342919675, 220306227, 767947177, 424919955, 453090892, 550779050, 773116261, 150314450, 848166575, 838182249, 779906790, 756607345, 366733862, 445751919, 287981999, 831382499, 840938860, 579380470, 924435714, 72497118, 425064729, 925653559, 652184819, 945227693, 101167067, 99565514, 149647278, 754786382, 572416631, 684642552, 623848832, 453875531, 242143457, 562437437, 581554410, 323761796, 495097335, 837719691, 739559554, 339884355, 115698324, 837279136, 310207973, 81544442, 791335909, 750518901, 297447980, 92159638, 996562563, 59602849, 562344738, 60080284, 660032341, 257658224, 891744091, 433370439, 546036845, 656261379, 458342204, 482078909, 909283664, 84085585, 398948410, 479046987, 673257055, 205983376, 942107814, 550947127, 893061991, 407457955, 889601781, 352256110, 14651570, 122461354, 242965056, 554569045, 167606822, 211049943, 683902339, 846195931, 211223044, 682632282, 240600303, 488202201, 983556551, 977799808, 373139666, 548721020, 761019865, 737109185, 179852549, 372794284, 648764011, 759738622, 471758247, 744662014, 21612519, 324407876, 53748308, 847412392, 101118069, 969905361, 387225991, 825728303, 145525422, 271951847, 601597742, 122471313, 320975842, 788211437, 540314602, 414115397, 528941733, 951622631, 989573184, 212104480, 712250376, 652003802, 879360899, 331313435, 182734667, 542616573, 758031829, 9889336, 950769590, 218419849, 533555493, 981120171, 790534788, 240098922, 432953499, 148528152, 818396217, 969956146, 356624254, 728897799, 86866592, 789136264, 355094257, 965282575, 49509918, 564735126, 650239266, 58716868, 808306033, 397792085, 869327137, 245902221, 740960535, 28524319, 999499101, 698516898, 504059826, 696748098, 739097945, 460430742, 455952310, 372277133, 904168608, 510639491, 846851972, 835345463, 926721760, 408779227, 727268102, 231048453, 24651623, 721882273, 868581470, 507861701, 404081604, 400117978, 823835226, 521580138, 379450769, 612350696, 255648508, 86586446, 138816751, 559145470, 399926752, 871809023, 408119050, 678697524, 32612253, 370899453, 427254357, 187090453, 207617837, 628232054, 612919652, 115838379, 209846461, 357306828, 978486691, 145465500, 261401397, 349156602, 141759435, 234358762, 307313968, 362296252, 804277853, 649533094, 123492868, 649003905, 590290274, 579857231, 667272362, 762617518, 953280763, 282750149, 187349475, 235006534, 999326241, 646059124, 709950180, 67540494, 350351651, 442169168, 561687584, 831122534, 75283762, 157089267, 329648548, 382899233, 980583690, 75114835, 926127487, 971933027, 646473831, 537115420, 990840410, 645051701, 134571438, 857873090, 640181268, 148220497, 345296680, 333904400, 646017956, 314090353, 913217941, 71560199, 913762821, 749242502, 197443970, 722801638, 477278872, 460968134, 703669372, 366089522, 497978837, 94188094, 974876027, 450049330, 898589666, 406935331, 690009754, 905406120, 354762513, 121890988, 956891270, 713577382, 179622925, 254801116, 77685268, 565695376, 729784735, 446052714, 693084143, 881579577, 409722303, 950052309, 52569774, 136204996, 990901312, 393730439, 983427234, 121999679, 740003551, 103488525, 444602590, 649856942, 721332246, 379210221, 808571282, 958942582, 311772023, 184245521, 245047214, 380306165, 832296474, 808776205, 453509453, 815852376, 668642576, 93597834, 136179082, 158065894, 145564908, 571717436, 345762153, 453108330, 408585557, 360319633, 557904599, 542731011, 691887659, 260009996, 281462332, 470199840, 412565818, 22231531, 112616822, 104188676, 785897199, 305841790, 610353314, 968499268, 924675229, 881863638, 302127755, 81536743, 361133088, 93354319, 528065966, 286103608, 356785935, 978129114, 785975433, 395197764, 739431001, 133719643, 446760453, 117556105, 722793657, 810748952, 853231878, 757860510, 685347863, 925359239, 827566340, 90021340, 387811935, 957675647, 556536369, 618736637, 548577243, 273737190, 574360447, 151555735, 246342599, 789406476, 338653974, 743911741, 568829819, 720550812, 559015744, 549171538, 933685741, 406844115, 85444189, 364612841, 346132857, 933079852, 358007502, 390472236, 381512168, 22960746, 346245216, 3093192, 600857434, 511205107, 109240211, 791899536, 780821585, 764020619, 826052474, 350757721, 794417793, 678316131, 780057938, 144833324, 574357260, 819479192, 414020762, 609857644, 963661139, 814879916, 543733915, 392221859, 445397672, 48228030, 362770997, 261371435, 77887626, 603486717, 308537042, 207884698, 869910041, 517865316, 426744511, 306122785, 91302085, 49636547, 69290935, 907147413, 614066327, 856605662, 112924618, 793458430, 281851328, 560831547, 627918396, 358780886, 773153260, 300476326, 93010145, 760233894, 742734780, 711665726, 530178614, 386213762, 789047667, 962777430, 147872790, 945231959, 114107114, 128250966, 492903631, 292656929, 124175810, 659929955, 483124531, 235272138, 265829332, 90195673, 552399516, 207313613, 320577433, 687293386, 575230767, 613051873, 970235014, 802327496, 513374445, 334794470, 47011698, 32642315, 779233094, 827795442, 719778348, 661202466, 69179034, 719278994, 544966657, 243333835, 292366435, 567779932, 626986002, 258515116, 209156864, 352828036, 512693454, 614787226, 385620918, 198777086, 801404312, 360114984, 991934231, 71240165, 801906699, 748742908, 822964543, 816304188, 150964597, 278618397, 514018498, 185516189, 343546773, 489955952, 528611059, 456600463, 703017808, 724786354, 378669321, 655280414, 945215678, 704856863, 553598686, 871959812, 243917087, 945648804, 402730223, 11650230, 883843564, 91192457, 213997990, 85240553, 632768215, 25599184, 33123388, 367331407, 465075599, 537482331, 978833489, 205083671, 49096354, 700061442, 446848472, 13067459, 211774076, 933775963, 438342120, 245758773, 893913443, 181476928, 653042824, 98797292, 115639604, 600212196, 304038199, 313170700, 640088815, 433437996, 381119611, 425891882, 500788454, 698504655, 886737540, 338930353, 265573893, 923620162, 540212694, 842230764, 472261301, 954491576, 335160610, 709226073, 241703432, 856464950, 366938206, 348833149, 649944870, 813496724, 562326786, 540687202, 46452020, 674097212, 780454820, 942405725, 928945310, 667078188, 377332128, 275361510, 462608712, 959531794, 870959667, 659418106, 992079095, 211655989, 761942554, 228131058, 124841149, 920986006, 455545360, 249416456, 528293254, 902594832, 611941085, 52332182, 613812467, 411789468, 382707297, 586141534, 643149203, 728776189, 407447608, 308028936, 925478399, 43322460, 519535007, 752416281, 9330930, 633268409, 518593549, 933543404, 210671714, 69659386, 44637718, 991269727, 551693891, 350601140, 546939936, 458212772, 671514971, 994040001, 991068661, 668548070, 356719956, 789921000, 198181726, 581131759, 319381354, 331551587, 547872191, 960030930, 785198919, 360903550, 391354521, 340987346, 566634746, 687998072, 65158529, 453788719, 889080868, 869106415, 4690799, 152569425, 835923137, 579107843, 571493870, 281325834, 827170811, 319716627, 569519927, 440677616, 11574802, 557542095, 480267728, 683980326, 233770783, 682618332, 900763841, 257670652, 544516723, 543728385, 897010371, 195942551, 181226046, 291071254, 742582182, 804091130, 91343997, 216772844, 910540344, 22414860, 114139838, 217266194, 946392781, 929399217, 935291608, 643524411, 86668079, 255853770, 371960652, 874042777, 818899628, 296929728, 630528633, 550408786, 562725799, 33787076, 639287185, 648519968, 925770017, 290970199, 435017970, 578765389, 696193692, 159308267, 327080351, 524934623, 595993989, 777668119, 595055419, 721981244, 706567068, 630347615, 251533496, 871597424, 620427572, 106014862, 668689294, 321622162, 723519251, 1556720, 909149165, 648688053, 805185803, 726236503, 436984554, 162702740, 7162078, 574241669, 53738476, 680732917, 777745922, 380904348, 819007793, 330187329, 220048740, 139806335, 467666050, 404978828, 774800919, 301180190, 999813337, 588713503, 310795291, 769457459, 177172932, 472465640, 390726677, 36371235, 889197272, 460460446, 448012099, 817335758, 968087690, 486606536, 110255295, 670945696, 26544241, 808930018, 467152299, 812206155, 58535094, 352614992, 903780023, 684000649, 102371010, 376096881, 947545573, 211639272, 470300995, 633517279, 615811433, 78202307, 790819029, 470664822, 310217139, 870076811, 223503857, 708598931, 59950079, 516966253, 745510413, 179191453, 764286683, 354578287, 778447064, 998373053, 712602159, 774031017, 690139674, 930250557, 865478614, 938943379, 110518645, 445976544, 874685482, 225108983, 165576366, 22298115, 424005022, 393194574, 242272170, 246758435, 432904030, 65280604, 972099772, 214752109, 224957165, 404755769, 10313408, 922143921, 692037207, 91436397, 132875300, 928935649, 126732217, 560984488, 699188021, 553902813, 515191580, 829567212, 481621209, 962995481, 213409882, 560726035, 603150972, 157760348, 198909360, 246348347, 903148052, 35892158, 714058906, 67879385, 845376806, 835415107, 75777586, 188929428, 509232180, 247684816, 269521946, 754855485, 430481595, 156743658, 531262347, 947764210, 852076044, 870789194, 421852759, 621235130, 375263059, 957536020, 929923517, 849160690, 566381465, 186539876, 830395214, 524212032, 968619675, 321500692, 679524202, 581935765, 742327779, 261310319, 634346284, 756394006, 626237811, 465153126, 982807948, 361653957, 766568183, 433367726, 939531874, 248285265, 769379939, 682642079, 120659985, 737153318, 79751335, 190305059, 317349566, 956341769, 248462654, 191997300, 661532200, 44944027, 614117607, 96546061, 555798366, 493166899, 314159583, 142474830, 954195897, 468580419, 425947686, 490749818, 843824870, 602821869, 41148550, 857125133, 252883192, 649834282, 497174359, 328379348, 223130735, 986511960, 784065231, 790028278, 93051171, 858321564, 994431760, 257014271, 115169174, 886789435, 311944858, 445001274, 682796339, 774872409, 375640067, 533990521, 103331881, 653413678, 980622516, 63927897, 129989690, 752205339, 285625575, 119034266, 281176003, 86473071, 756152859, 501359583, 696758963, 694080852, 657017228, 690284082, 988725908, 975940279, 605448531, 119538936, 385874898, 668667215, 418949591, 349189688, 189129785, 720212763, 471085617, 133501132, 889462820, 378786929, 818312573, 5165823, 87274487, 110519108, 549929419, 900918833, 879331783, 358698541, 579161793, 402095656, 383566383, 876444, 231684622, 250277734, 837987862, 465566899, 972433169, 51667107, 335578727, 863686071, 596188812, 356813868, 603345789, 41237765, 801919257, 674238995, 45956181, 292335139, 501355037, 975394276, 915043849, 903777844, 698044965, 235542077, 721443796, 359058087, 558922350, 684212396, 332834950, 961002358, 960605740, 880986868, 423407538, 642273327, 761052242, 563208263, 777625293, 686640775, 880325199, 613688102, 965180940, 664536508, 187534205, 745366084, 204326617, 303538653, 527428802, 504767172, 323647190, 667759807, 286263028, 226211066, 130652374, 819863061, 863391585, 905516886, 90438273, 551162239, 409937157, 378894701, 568118363, 409972284, 399259655, 814565510, 451111148, 753446503, 899991803, 516250539, 603206644, 240761246, 274387549, 598317795, 506561702, 757972172, 316894480, 921026187, 626508184, 956657521, 448509775, 848363880, 785428896, 504781846, 557910090, 53850157, 718890135, 600617559, 178938466, 51452283, 175724663, 33086134, 463226804, 560471094, 942882410, 660997914, 976294081, 571436242, 390202084, 581171391, 23099505, 688642180, 564762034, 97179392, 470274608, 381438926, 711411155, 294186920, 958837661, 548684108, 820226916, 13539711, 123750530, 23009086, 547981087, 817509847, 265473633, 500592338, 409272069, 96939994, 352229777, 253301076, 633476017, 540202501, 929130953, 816721399, 278505057, 228512726, 447457078, 861318578, 48350549, 787491255, 372865505, 330020612, 895842105, 612893141, 984052217, 708629237, 133129531, 631616384, 181707205, 60566897, 598147374, 143900101, 690996054, 260706181, 297509519, 589831992, 516606361, 135972620, 479802990, 367303783, 2551368, 354948256, 33318991, 380744929, 255927285, 215533510, 793763140, 97228839, 61102509, 816265068, 96593818, 503425300, 923101236, 661418162, 224822710, 873673600, 833614667, 538080620, 476601084, 970417157, 267226692, 216104221, 316448963, 203609920, 350222985, 911153557, 79147956, 248238761, 48449357, 767033038, 703360608, 606107937, 565775004, 120672322, 947347509, 532764345, 37007764, 211628752, 30259131, 577389113, 508041875, 132234141, 717900104, 115893831, 828267222, 667141454, 429430082, 936730065, 645118245, 91601150, 683668299, 520398788, 620248837, 851378561, 834174472, 917756376, 169336858, 220970167, 472086840, 496198427, 647963881, 234483401, 553726790, 113238341, 90068209, 372806482, 480581161, 824366934, 884893186, 625592248, 207879360, 326598975, 70550679, 687281730, 603113535, 74962141, 899542332, 284949104, 368076970, 975080736, 860868255, 966587862, 16318443, 452359427, 715314524, 377918315, 796296676, 19074826, 632401594, 203793467, 452711856, 644559980, 63866082, 691200037, 125937862, 374864235, 990548248, 796133928, 6629407, 376818794, 357024114, 463287467, 398427609, 923539640, 455510608, 906502089, 505723893, 107924022, 543965963, 479335266, 246912842, 329872180, 577195216, 696657714, 426416293, 411780809, 943978915, 768398931, 108573563, 778133452, 94815540, 371575185, 406343135, 387462182, 117812886, 439751911, 164515468, 808154279, 8541990, 564899298, 508633519, 988958023, 874376065, 133638498, 132479969, 8122098, 419431287, 428358029, 132405551, 786529011, 630734264, 384418500, 59074148, 150102056, 826128092, 657273532, 566875095, 830350676, 966111066, 94968969, 235572153, 9513617, 635869507, 29242389, 354073753, 153770851, 342839629, 467617374, 365433964, 43553778, 89995664, 291391514, 225217739, 877616405, 98818534, 165366118, 317098726, 24742127, 814672861, 855204987, 436638518, 358861089, 560877342, 889871886, 349657123, 344958157, 858632311, 54197305, 951345083, 580002897, 717017571, 25411912, 632803917, 688359959, 376273966, 2542869, 170152371, 846715681, 301669113, 137088155, 783758398, 897003637, 293743620, 383114699, 426266711, 875800043, 702133310, 714395108, 314522362, 902058406, 855318623, 705025649, 311125587, 945759977, 179438994, 819602942, 587482702, 205131276, 860077672, 808504569, 671053102, 206424079, 613805623, 417447713, 494101136, 20539121, 783627954, 514645195, 509833373, 326588346, 144472051, 795891728, 294977759, 782224365, 688998917, 951693349, 308626423, 441608730, 574019346, 322269425, 651583597, 952456231, 553384523, 832846088, 936761560, 557541583, 996643237, 103898168, 931828990, 883381685, 936176075, 296437147, 691202425, 95825059, 240392243, 692054919, 723490385, 568152567, 373736476, 375109827, 689369773, 78751681, 968094914, 985489439, 655199708, 652819687, 101130160, 725973600, 7760638, 931432587, 135798554, 911924111, 586892309, 34524147, 521507435, 806163717, 378446532, 896492398, 467604322, 615724278, 396388721, 246243689, 630504722, 900196996, 738326405, 912208410, 93611752, 349557532, 649517436, 277335262, 403034414, 724936708, 967099115, 49950487, 100025120, 982903703, 582193686, 942661811, 488838784, 826926278, 636684674, 848744425, 110833528, 509902581, 953623509, 475108530, 758583379, 817900012, 347033530, 615187265, 767435264, 763085270, 134472285, 122270977, 606716439, 670661297, 569196198, 849314426, 292501832, 119005579, 381769464, 327755975, 805367129, 12070053, 872365848, 165110215, 212336157, 359092369, 383465187, 196824992, 610925839, 663826386, 898681139, 876610689, 715221210, 963259333, 43948610, 371516692, 607568577, 624533451, 169486144, 87857942, 551162894, 502902312, 131355212, 384740279, 560545191, 579198664, 623646398, 199648814, 72442911, 571185011, 865599303, 515862748, 462271566, 716140405, 982730896, 689465727, 948999047, 224058446, 154366227, 688447727, 288352927, 993122790, 332246582, 682799733, 746158589, 216236490, 124109957, 767410044, 286370440, 864593627, 335938902, 982159983, 308076342, 593980185, 55072370, 312160135, 825103987, 393048156, 292507008, 677052454, 687011566, 127800486, 672731001, 319324743, 214873772, 743512429, 743093365, 39322183, 772943647, 917706511, 998969427, 759734665, 288196013, 818530205, 798224070, 917552832, 839320987, 547282557, 969194963, 220701797, 550588091, 27671827, 367627075, 91061142, 367831653, 490968631, 395512261, 847784846, 174049742, 464037385, 967655543, 370985751, 228927013, 837082962, 972009010, 9254655, 598650536, 496226191, 498540609, 638918038, 953935183, 143668140, 263628889, 284123240, 377686872, 937382935, 34422553, 873267308, 86088627, 456296298, 726200256, 451067542, 739150867, 315934513, 4000514, 605828020, 903230631, 942504626, 316590855, 71156099, 285563722, 142680732, 806017397, 171531415, 484379691, 898836484, 525119830, 766455331, 428524871, 232494899, 447279954, 229571576, 191201338, 975789927, 659888793, 806946630, 666085686, 402980606, 318139979, 295527752, 460299102, 209316928, 584797066, 830971790, 436007035, 537773816, 357196239, 208006976, 392825063, 104980655, 807940813, 48977619, 969522308, 167083796, 336626823, 735763455, 871809819, 729016621, 978982369, 83485474, 149445452, 314851077, 194682818, 627778224, 39469967, 103737125, 760600891, 294251781, 542134014, 76279178, 740889731, 67399435, 700891514, 723424813, 221597963, 512194559, 677251645, 742947414, 717028449, 809988192, 910584249, 396250032, 330192262, 326813031, 461244333, 681976479, 471399611, 668424751, 251411014, 525315625, 113914575, 270930396, 516990749, 56308035, 6061374, 518772366, 854695166, 22538978, 107203833, 699448496, 778695993, 581967791, 196548312, 970944847, 120971702, 904864463, 344567809, 62278466, 359775363, 500912923, 884699687, 502475399, 422253867, 619424294, 66261453, 891787909, 120348233, 595026147, 968323464, 230094641, 631574873, 319163590, 682662674, 59129669, 149369699, 843587926, 643983766, 906848989, 254877268, 362272277, 538464910, 484895678, 321630806, 234234384, 731757936, 733055177, 667606345, 376598929, 369646725, 335521626, 727157445, 890968419, 513012017, 151902432, 549068638, 936336287, 533802919, 189716704, 436181320, 152311107, 196825445, 811763745, 353265339, 33007136, 173156842, 105196295, 599225579, 650619325, 53650868, 518731716, 177347343, 674710038, 765372011, 819695953, 235521238, 645774014, 917101770, 394178804, 354862121, 835933486, 596858009, 522263949, 165336946, 267069744, 932971383, 110597717, 148892166, 35297221, 511408975, 780690707, 389314616, 766255410, 688354166, 269269492, 278276593, 516385166, 943864023, 852466325, 997962699, 980152082, 664592276, 961864102, 654258841, 460779767, 135364133, 625304452, 585192094, 120017831, 866161595, 374849918, 709728596, 77236350, 492543438, 259835141, 526361020, 343597715, 125949979, 22006062, 168593664, 246749502, 748971699, 795902724, 898390605, 603929888, 546001111, 154594768, 762220273, 437419277, 14330542, 781335066, 246292592, 159636962, 161540819, 712887399, 262614908, 798260010, 194838580, 868974336, 80628900, 635173730, 174199447, 962649496, 865336173, 419781164, 474266760, 559341503, 398059624, 905604229, 802573622, 17575041, 343034632, 677333928, 268002434, 398494733, 343212772, 539018414, 528787327, 234796146, 686060179, 818693756, 305729521, 951442307, 584675840, 667721365, 569316501, 626181230, 914499560, 939465843, 988095153, 234705332, 464707961, 796907395, 349059196, 431055896, 395821679, 355676993, 410427771, 63487840, 899643882, 373031952, 81948777, 16892464, 199393470, 833121786, 984269034, 419824135, 748053356, 700353887, 938951259, 699661108, 734359617, 772576250, 236958077, 988494146, 354796062, 881266563, 645354984, 893564057, 789839987, 840844879, 400981650, 990421478, 172603144, 166370054, 611667795, 188687222, 677478373, 662765655, 919746323, 92059413, 128426545, 586020135, 430117166, 473826457, 147527941, 159490092, 140293512, 915105547, 998961064, 259035236, 495804551, 240455213, 724814227, 331229373, 432334087, 4370711, 836427578, 158805712, 91200122, 345231242, 114572465, 758658815, 369616335, 719777276, 5682049, 165686025, 833977707, 524511165, 279583475, 521478455, 233774361, 963872064, 233626432, 182942792, 377650687, 170093378, 684219041, 593427759, 940792596, 784776059, 139703093, 211255365, 268954659, 716117540, 78180453, 233933975, 21586318, 809261875, 251784899, 366330443, 42568682, 290768493, 11159641, 301818753, 208335975, 790268383, 601823764, 22082731, 215367397, 408438979, 591270316, 20694527, 429155544, 427143537, 676664661, 755077987, 546406376, 407350138, 83536801, 778645993, 64413560, 900675138, 533982612, 370718105, 335606827, 24082360, 8953845, 999877343, 975011191, 704858083, 2367760, 958627727, 394381369, 583603999, 433326959, 657058275, 712725571, 407063006, 92866495, 458739670, 70409519, 256859425, 489930615, 82795738, 536928212, 868465114, 711396637, 916103348, 683155777, 146904210, 411243923, 274711574, 364310891, 433530240, 102991077, 284008998, 488107310, 459536725, 434136492, 727915088, 282033728, 171984203, 420831174, 224207356, 242526372, 788104925, 33987242, 940362480, 576562126, 422483815, 886101250, 667159246, 145555853, 609557310, 793132202, 885598629, 534504488, 807910841, 959829197, 930055586, 550720760, 301615063, 763149536, 812436271, 687951352, 477207253, 233071624, 867193563, 598693517, 270588481, 465307504, 298561340, 84259122, 536135688, 309519075, 423038152, 318545790, 973988304, 799226275, 885213530, 941737768, 734869885, 904669663, 614562134, 599447058, 32923805, 754994982, 771880123, 135266352, 731801269, 819085719, 149538832, 691894210, 687966340, 424936382, 665006700, 442162811, 623216931, 556396088, 938312019, 994338790, 419605763, 107644975, 202571803, 608697068, 166903614, 473068262, 609880493, 58004202, 677159044, 318786589, 35147390, 684434865, 703724335, 467154123, 883626949, 76965386, 871391738, 368758006, 751566079, 431956341, 58641275, 425987765, 575049193, 908989511, 361648222, 741345242, 523300168, 299928046, 276654728, 50544983, 124554572, 965721057, 837553342, 526935328, 983778659, 555534419, 318886248, 824718354, 915809228, 846530330, 632067341, 313024744, 542912052, 284952307, 358546227, 991390535, 631440805, 481500959, 999392647, 97601582, 483043224, 271184591, 907711642, 343577025, 335754014, 141903109, 528886904, 304368397, 828106314, 997408664, 563568381, 995399052, 946123019, 657328621, 988021846, 37207296, 680730210, 960521466, 929505408, 890591590, 161021019, 513280007, 697006764, 136932569, 509334324, 983969677, 38453521, 344600897, 483228078, 758484966, 306275651, 453425197, 341703063, 673007337, 829950341, 712876435, 30178246, 315611507, 507565988, 772705656, 823743639, 320163708, 93786983, 613977749, 984797759, 38615902, 15879381, 416294080, 165667886, 714000678, 809335369, 475359505, 178584970, 467937319, 109907340, 253676021, 249472398, 361319231, 149818511, 14453872, 812947432, 137124894, 248293961, 748213859, 870109388, 675001820, 701478961, 406587108, 355477963, 171203444, 426145583, 856008514, 775363819, 539430292, 729862612, 618005096, 689605960, 854659009, 436890585, 893423670, 798687323, 507609777, 139074648, 105116209, 211592788, 490628474, 984643355, 574389524, 829961870, 15037688, 625959181, 294615738, 15390189, 926326111, 269535225, 963425931, 246627508, 740861566, 37709058, 480041102, 939524286, 235117207, 879487841, 308736359, 347605201, 922104388, 787578600, 773648976, 520293153, 530641166, 960456802, 903817647, 600177731, 531661369, 58922961, 623745957, 85233761, 346519823, 593956844, 412042249, 956228493, 712482164, 321110731, 729583752, 703633602, 24081079, 528279493, 905106882, 679520892, 349552289, 466463153, 886400857, 84670549, 549936686, 847270725, 361881260, 742233395, 911742258, 154939035, 838241011, 769879160, 206444320, 395361456, 517112128, 173531350, 790762826, 459831711, 644593458, 660232352, 833450446, 261197865, 206168371, 997082692, 547091223, 553085270, 127426139, 720656775, 758572853, 130863410, 206467639, 385161573, 471215499, 371925953, 630360883, 828736615, 790786562, 405680332, 795081261, 488865311, 990638795, 104657314, 955423810, 175971340, 808632571, 481803725, 789051902, 985631295, 174200392, 486220642, 124579045, 119939074, 907321957, 133893903, 302562290, 806703425, 631298254, 505304988, 301134358, 757217138, 86949714, 749985622, 834354879, 688133997, 781615034, 455657127, 433768381, 289615129, 254728950, 938633034, 451576706, 664619973, 960967876, 650921238, 345492714, 838969053, 531269142, 655062160, 726658544, 602984200, 382600134, 412367368, 679130455, 864509726, 301054792, 87658014, 229026797, 968792987, 560953459, 738542696, 941869073, 766391255, 296260300, 607064058, 985378399, 508937316, 337727835, 529305255, 148771733, 951540966, 370198439, 914584280, 883675847, 106324077, 703010155, 443710149, 64077123, 592882447, 704411343, 886655528, 600893732, 936331787, 245392632, 380772524, 199500505, 145267492, 518036836, 897269107, 191717942, 313511239, 44756377, 394112150, 397241341, 558706934, 78294539, 770209075, 24269751, 472023210, 475281921, 213149740, 804856006, 934197765, 931674340, 984513321, 660520928, 266835325, 771825114, 961603498, 870064470, 564391719, 617826553, 542495432, 500031488, 329240823, 755670121, 407522630, 535901960, 966548777, 543406455, 941826779, 394858038, 286585255, 871163286, 476954948, 569949933, 246536707, 710302304, 198381727, 546256564, 120318914, 646526098, 240730985, 439370610, 225017988, 776634037, 119665025, 208677381, 884432463, 324965831, 730080999, 28962128, 620720130, 198771578, 10615820, 368473212, 927001313, 423278683, 930152908, 453498588, 357991840, 538284692, 611894986, 340633509, 443715814, 925964938, 865810699, 257934181, 170904219, 906346476, 438573111, 927265483, 786285184, 383966987, 93942076, 951824532, 170766860, 545427812, 962492101, 194696316, 37379179, 360553026, 516746554, 932425164, 735444313, 357629555, 397322180, 279089111, 325073030, 223098866, 160901050, 635087582, 194304132, 226100920, 593043831, 462085475, 424582413, 112288873, 16174062, 115332415, 904668351, 819937881, 835899434, 524781089, 494503542, 208112900, 576708561, 142789837, 526047135, 929817280, 529827045, 525155149, 947190450, 627888574, 426505815, 870882123, 398136399, 193899535, 85450635, 659161054, 917415247, 703733723, 414235630, 452719771, 840863101, 741758499, 426714767, 726553489, 700956123, 693437010, 52507051, 23532020, 865023058, 786591231, 51293403, 383937177, 394621175, 354099602, 277800366, 72647644, 310458942, 866338066, 514191244, 373706038, 841907433, 930926746, 595186244, 430795131, 756876993, 775020168, 319493067, 15489494, 711599701, 501400508, 709445405, 779766130, 598639633, 763584841, 803509296, 117264945, 48116167, 7247153, 215705221, 370167120, 83371950, 446057410, 157450732, 406883357, 767489755, 94364178, 919557327, 301793365, 396686762, 866301893, 319837448, 720449703, 437930888, 413348192, 349419837, 724620138, 500965159, 779089795, 685618076, 572618959, 675487330, 841792495, 434929375, 143879056, 561437673, 658022526, 169491613, 659367720, 337160845, 228117137, 342936436, 936953293, 419939227, 991434020, 494784153, 184987698, 299852449, 23854400, 478829678, 680331077, 864841004, 536801020, 797290930, 773781289, 457627321, 998974773, 730010060, 416559531, 847255818, 72858893, 123721623, 628329113, 929116080, 191548279, 956891224, 715708935, 789622250, 269818153, 143132721, 319676013, 261544385, 50748080, 194931327, 203449884, 793439282, 231222603, 764996540, 110217476, 433084427, 19443640, 594887190, 204889188, 185839714, 316339472, 693042324, 133457835, 382540328, 871868804, 375908946, 795081963, 155037022, 808684506, 406131874, 697110607, 863403865, 268032038, 765717559, 676805718, 351330532, 511702693, 629137979, 223989050, 706850930, 382296301, 197193120, 349401896, 928744234, 732558973, 498713950, 865324942, 318418131, 873173986, 550895404, 89118638, 154178615, 560114414, 127651469, 278721159, 714547076, 16791021, 638005196, 918747693, 775750493, 710666528, 969091300, 861121320, 555668148, 456429450, 2374488, 769612282, 393694214, 638356203, 429132354, 106641719, 656737074, 716944608, 29315072, 966197205, 396084053, 127835630, 529576502, 226997937, 124071522, 260598745, 346781395, 777495903, 879365009, 480913041, 323539234, 931109786, 1902677, 533069665, 44330443, 96012078, 111772324, 994629606, 525924500, 566481604, 521520669, 585703083, 937848557, 141522406, 508844144, 127023041, 758972755, 575088215, 808181158, 18656950, 546617134, 860238259, 450767829, 115001241, 301360536, 263150389, 24664210, 230977086, 324860216, 829180157, 828416363, 199914505, 440509634, 171258599, 910065907, 334845839, 398312837, 650070658, 779828158, 591466473, 761609378, 236582255, 903571047, 593246062, 911882067, 744687616, 240710878, 305483963, 442953338, 549415551, 164695547, 905556609, 773043519, 605737308, 978923802, 883201209, 285659340, 563892504, 733832803, 925802478, 199693188, 489079941, 40675145, 133031606, 639895823, 890902496, 355861978, 128541163, 547605907, 493333177, 476841975, 389131767, 943391532, 429801578, 946729959, 846244997, 169390869, 219596066, 275877246, 489637209, 655461688, 739882108, 481523263, 471713361, 950913300, 803793131, 377786256, 72836215, 27021260, 444578617, 429185908, 127062732, 175302399, 711912917, 873114622, 885240812, 697360626, 36368554, 55915454, 48584642, 224654929, 995253286, 622837395, 172413882, 542460283, 168304981, 751496773, 177538723, 456904136, 13529156, 77089986, 760969858, 836966542, 464667331, 973561523, 840617976, 974826204, 615655869, 442979450, 854598516, 105976116, 140262785, 992460494, 364373042, 384457494, 576677666, 486631778, 246344131, 669906079, 577476305, 643631575, 52576857, 107582553, 442176828, 668466251, 658758871, 538167805, 462429021, 121140647, 18910346, 729515733, 266808930, 714533587, 526650045, 948318211, 833503516, 946388482, 310463158, 900726484, 823134304, 559872024, 181675961, 798134078, 84532509, 392903926, 678540213, 416729830, 949415688, 385913774, 166975063, 309950661, 579914086, 583381531, 634576055, 811284310, 383056512, 32101245, 654861963, 847053436, 61475265, 433746751, 623422074, 805765856, 230783448, 805498380, 827413821, 440108774, 158217126, 768683444, 171765642, 449082619, 598259577, 100768995, 725630518, 703583676, 236883576, 47867840, 737934418, 879788459, 476457371, 678275607, 230538111, 183616501, 696991113, 734553170, 990554958, 740347789, 915329279, 635671320, 17469054, 61918261, 930671248, 369376013, 458215077, 996691264, 920431364, 97430877, 992047777, 928857862, 582002388, 1253926, 179519499, 858971844, 631454824, 472329494, 678255594, 457799122, 346763796, 292466159, 81945428, 751934132, 353362163, 816115003, 82620108, 488584591, 782983383, 976105750, 733282660, 169062083, 296350077, 845686391, 699742123, 988498281, 865548504, 75361390, 630247313, 911111887, 900917960, 859477795, 376728227, 624802040, 803155647, 625644438, 497505053, 803271937, 403187761, 110794730, 617377914, 317268464, 215046463, 5912925, 154055801, 476937909, 940840737, 273436332, 148606984, 810812885, 306119718, 370967454, 309799070, 332857379, 585569565, 335767237, 13831091, 80394545, 191435826, 517215877, 624986860, 449884512, 846684755, 716971624, 83268232, 979797783, 211001592, 707084505, 427255050, 945064418, 336736382, 867771194, 260119961, 711569889, 935123718, 713692553, 483751411, 642765632, 830092217, 260053519, 632816350, 16639279, 433529981, 856363171, 929438461, 334940577, 873687319, 803493358, 260655874, 345938950, 81551012, 321952459, 242096921, 371802344, 306328239, 646889485, 616589454, 409629020, 406916219, 291868958, 886021497, 213278826, 80230482, 564387692, 479454533, 778359785, 288836457, 167340051, 88370178, 201188953, 110230262, 995691367, 269408673, 415152335, 560488035, 466256669, 718821796, 847014228, 309918280, 430901848, 430075411, 687909009, 334106892, 892131143, 500453989, 234417459, 676020671, 547669919, 716591436, 929806221, 338768244, 600069222, 918468504, 61142360, 714135327, 782116806, 277495269, 354178286, 139267265, 844092362, 394941103, 286436434, 872127148, 973791708, 583303634, 115629528, 356652848, 821606697, 217810417, 692567353, 175556370, 918712077, 740957478, 110416561, 211689831, 260165036, 419297180, 757094183, 686241788, 753330439, 696892947, 618474215, 666920166, 811567522, 461477985, 31501993, 851787802, 894431519, 235516462, 717275242, 742557085, 962704634, 179879817, 77455929, 553243918, 50794493, 332261022, 147347544, 555170893, 218037601, 876622468, 793341335, 291436395, 407479393, 695787874, 588628558, 590328843, 671097218, 694135178, 459257943, 626777444, 999949715, 234120153, 435307388, 71919945, 635525432, 869720954, 547687668, 720461358, 908574122, 998035761, 121319216, 533390465, 645938717, 527993633, 242276080, 90473044, 424269671, 73508389, 473497710, 846321946, 759188605, 990193800, 177856742, 545216988, 373778099, 273715538, 824310261, 252751639, 499296857, 191116986, 353955731, 227275389, 177893153, 158277420, 590476406, 710970557, 191627665, 835445648, 895977083, 647820355, 298908484, 167036983, 482409781, 386128681, 865948667, 82215307, 66179681, 675539764, 421022493, 958393484, 277458584, 886326957, 46718127, 86409513, 500292639, 809996058, 357641080, 382970633, 259297196, 757939379, 35071264, 815314189, 13809137, 469632868, 350213795, 107518450, 332473779, 314540221, 379402235, 141902849, 620017992, 547801391, 873124694, 18035705, 318560951, 825996616, 221136639, 729109688, 809091738, 858853288, 322555561, 409325832, 412297129, 73653670, 363404303, 289665564, 309921388, 890700560, 49008031, 809041750, 341289557, 381953136, 456104540, 22186363, 465495151, 103801780, 70957042, 719112237, 207009705, 799061581, 471684072, 144356824, 712473031, 973597891, 350669849, 556929814, 474561070, 699074165, 625319140, 345496295, 310683737, 250743516, 204814282, 89261381, 451868561, 839577913, 646360353, 560925586, 444311196, 57370550, 633917699, 472696523, 268965327, 244215871, 217066768, 974229885, 524625443, 57390091, 940123041, 897714256, 333345176, 614308853, 578712167, 339490060, 903438075, 594511561, 438939777, 396616842, 840138362, 569346574, 544305280, 712774049, 78442644, 92183658, 160850761, 581247818, 220576915, 856541929, 297699217, 377261166, 624795500, 17783679, 457983138, 379280004, 430178413, 199808652, 779135375, 360359589, 228760044, 729578593, 680700138, 867140860, 855228908, 328490516, 843869447, 956260248, 5130675, 688954066, 314033157, 761520274, 177143588, 28846650, 23454164, 620044513, 957159272, 108354239, 475613963, 925836751, 607695027, 344862296, 731559264, 831396880, 354504409, 217121708, 813537616, 150237482, 441192990, 625806559, 518326735, 59159868, 645327494, 529672256, 780884592, 21162375, 843176127, 222418939, 27343287, 973464209, 203937203, 256231252, 10138381, 177948275, 859937892, 874757298, 278588883, 460307708, 55066361, 510327240, 426642860, 422960457, 100372742, 182697730, 779160195, 338139533, 701611848, 84909141, 69346458, 809408079, 987596288, 127481151, 744197125, 960847014, 222399306, 383411529, 521496186, 468941830, 824808826, 248354802, 315252599, 62136451, 287648545, 157477349, 412621140, 879780266, 639306059, 437743558, 899247408, 639201155, 676056651, 153462240, 728768272, 710664593, 351516201, 420421864, 900744347, 867217281, 352863026, 452055940, 256595853, 268694648, 352431802, 238053780, 562476531, 421810587, 137836072, 485201216, 54103154, 36916525, 879763912, 447104750, 918807248, 692339199, 965733786, 178746149, 581639410, 962300067, 48308764, 375158175, 602441199, 572824890, 248020892, 56443894, 257957380, 161610609, 933897080, 114051666, 346829105, 514379297, 654230362, 852698664, 553321035, 553913521, 720508201, 341596656, 504405276, 692224112, 538433434, 279183151, 835613662, 399769721, 605083829, 235224583, 711159669, 934065499, 213591612, 986963735, 354690045, 2220541, 445984663, 981922695, 316013027, 524650958, 636010752, 642300682, 924633181, 590023122, 788823270, 457333199, 886394446, 912092933, 758153979, 756635638, 409778518, 757889509, 579298109, 253638118, 501247366, 408625212, 238639575, 552482040, 879900382, 107324729, 780868769, 156538433, 751986215, 592134429, 472913786, 961837364, 145186696, 692967039, 637567508, 747105141, 667178067, 256332391, 806036161, 593358372, 432954458, 308596542, 373505780, 720005882, 349498848, 651762790, 222641175, 542729390, 548174644, 426493243, 678356148, 718207767, 132511976, 640683875, 123979194, 370264916, 734983301, 896889269, 371189507, 409896036, 399244780, 626204800, 238225944, 147502026, 260954821, 477790827, 991321477, 726145685, 163734130, 711445650, 808436599, 530253334, 401592448, 60924042, 389368563, 70387088, 323240434, 948005835, 757604857, 301074771, 398290803, 71685072, 807814345, 164951632, 778243601, 964388442, 656263194, 160443081, 353812459, 176091735, 960734313, 837598386, 662192280, 201287250, 817598187, 744792154, 64722730, 801198629, 257415428, 759920091, 370977685, 804909288, 66636510, 555007579, 709339913, 415712160, 752702654, 155738521, 18854747, 215101216, 813292655, 374024012, 2282256, 878896880, 472496380, 882385668, 202892317, 628801658, 355364973, 651674429, 486120749, 971533863, 518823357, 715729803, 945347944, 105169138, 15634643, 861753270, 652233221, 952923201, 781505715, 505956681, 756808779, 648163037, 84812723, 428268312, 893924579, 81012694, 810865845, 830423404, 162528390, 142326938, 694009613, 53850413, 927358995, 702607616, 300648547, 482874505, 238290981, 240887162, 803149214, 927302809, 761595455, 939176332, 433550953, 656922296, 416901014, 257638214, 392587635, 911884121, 312500599, 495215930, 2558805, 868828097, 661516664, 487664447, 143053803, 672624436, 457061891, 941288155, 185927210, 340921814, 460007976, 181067114, 280696646, 526941761, 717642712, 608574919, 266398050, 907163833, 523453504, 49563755, 400308411, 918499720, 461801330, 727261059, 132212094, 704733398, 165419168, 608450746, 355251531, 393980762, 491541616, 94922851, 534675953, 432271985, 161715295, 11256274, 569405707, 336757433, 941002078, 359192981, 495278581, 652244689, 672886563, 532477626, 120282971, 908535368, 698337944, 120645819, 363934194, 241236941, 74747525, 118398044, 705954236, 98725505, 75116898, 557624209, 329395331, 411085182, 143542810, 995192828, 499291443, 399394154, 416952618, 786141656, 271739967, 131417353, 565444983, 865652171, 880262211, 983561581, 440311188, 558505094, 263442251, 573416058, 430959782, 389685318, 222294897, 553361709, 844843706, 939388649, 949859160, 89487304, 29744931, 400575842, 621134287, 194716389, 929692852, 712075050, 754829204, 428267858, 27469562, 754983658, 866285876, 918554042, 959305443, 413032518, 743166267, 966167313, 384065337, 322595690, 197599694, 794448658, 978036293, 808045756, 936647866, 354374683, 38072896, 761698838, 734249829, 283929914, 643709767, 657335293, 426847741, 73006926, 533351878, 356189423, 787844493, 972372455, 473707275, 454059489, 244235827, 808684748, 10168770, 45707857, 371668291, 804896946, 642323422, 660903797, 38103518, 684280208, 954800207, 760789484, 166039907, 430508460, 966203367, 562807897, 812516991, 176611737, 172840343, 195927807, 909831846, 254011668, 823646764, 505440566, 641619817, 984213883, 489613670, 338484567, 411924488, 957045950, 813511039, 123950990, 899460628, 189102253, 20366672, 81027961, 129258872, 597597550, 649195644, 472177321, 897971529, 234842772, 815508983, 973191202, 721595636, 468677711, 792869821, 944957504, 390365114, 42098542, 432800842, 213679185, 983576903, 54151156, 426628988, 240098934, 435805476, 170202763, 303688215, 101392619, 497115266, 683661329, 44636380, 80328173, 773164836, 819321945, 14610924, 304340544, 296856384, 237852020, 262143488, 364208784, 709889869, 399273002, 707982421, 787056118, 48912218, 990778416, 595034544, 996263191, 35947630, 19705991, 69401667, 135632576, 780020797, 445243314, 905708078, 948974110, 507684514, 685899914, 174114684, 588459824, 892243768, 8859895, 538150098, 130566433, 167051357, 887155467, 878800391, 780214997, 789398547, 875587040, 561311815, 168760146, 817322767, 434915554, 917478723, 878750803, 545229308, 891724001, 162433712, 764003450, 761741865, 831421500, 315192293, 851325391, 137919883, 931928094, 318024636, 465137067, 324824683, 655382869, 289367659, 120529508, 41702954, 831178486, 773704975, 834789395, 704167162, 691890888, 685958633, 550774960, 95437434, 947830350, 788283793, 230482272, 213820310, 493281378, 657077205, 483554115, 993061373, 117258101, 776909809, 757162616, 704551974, 877470708, 394756459, 345389495, 463596223, 815446317, 165355345, 653023752, 678778355, 154128087, 271236894, 364565340, 194669857, 427480606, 19794568, 734924374, 677234634, 838557395, 972191058, 349552823, 975978655, 818405164, 7451850, 840874005, 507426578, 527556166, 798534732, 68825362, 729354181, 991814397, 686176701, 773902937, 738744988, 802679161, 658183096, 972050623, 346016104, 365455169, 779753223, 403763145, 788045966, 678710902, 961270424, 56028422, 792787802, 554877083, 82357995, 968692375, 152944259, 119519963, 170454158, 39840138, 952813509, 184692585, 371330735, 333072344, 959801486, 160434814, 712808476, 480318267, 561131209, 789787861, 705517455, 144920092, 897621801, 495458786, 177102648, 326077467, 380812705, 595064150, 5712157, 237295199, 62634213, 493949241, 688395884, 305944990, 389549905, 970286824, 354675078, 784206169, 827865411, 955272897, 782443638, 76036320, 556631031, 702174333, 125327761, 667633541, 795333506, 659248438, 621004812, 498396916, 637936935, 531606865, 671962830, 422731957, 509907931, 948860749, 277256396, 49575366, 424316926, 191123892, 530420632, 979845228, 296720853, 262720136, 25954510, 989133649, 403900635, 694326225, 845515237, 974298760, 305484674, 313066021, 116750788, 310688998, 516539158, 128822184, 648130597, 800044882, 928937370, 320135837, 952500261, 549976333, 18593540, 122532557, 8890796, 75317921, 966521909, 327203788, 697188513, 749557784, 745942911, 77619358, 113993096, 463236827, 440412122, 283717340, 189147924, 483988885, 321326685, 590975028, 484545722, 920738122, 754833, 982211377, 995560017, 980390983, 778718830, 348961249, 750328423, 12007730, 533089901, 415835773, 726419849, 606466780, 228371956, 750899780, 134538395, 54607764, 935569944, 679888366, 782612640, 691543046, 408007018, 454441016, 346965505, 65495990, 403068254, 380063489, 851295683, 535206421, 881473202, 528032687, 684045345, 603082128, 113446569, 295939377, 333766066, 5970178, 296202880, 303072247, 486148766, 810228949, 898308878, 74426728, 641705233, 947442501, 959641285, 831571171, 338165466, 61752294, 305620847, 32473753, 318087924, 939239942, 728130817, 768507788, 831157904, 444443001, 965606369, 216060981, 595687880, 451120602, 148389065, 317712093, 442418526, 708547631, 623690453, 706644807, 452891664, 846006951, 337994988, 750129226, 156545307, 718513897, 133115136, 973504356, 385802269, 909370023, 329559751, 522957425, 564774229, 848746565, 654108467, 17074662, 231253945, 80964423, 480485533, 343332415, 674052381, 355945435, 641529708, 815097717, 835576171, 657857682, 314296121, 824167590, 633110108, 686648606, 634827667, 316787749, 416374561, 394098279, 251810021, 917179668, 974621436, 904360336, 313093781, 232889431, 169957884, 452990117, 448195227, 662504931, 197572305, 517912323, 712404348, 906592787, 508395675, 634066735, 934052578, 880732303, 882161855, 55646598, 614430567, 363419900, 508274464, 7668063, 887500260, 949074662, 969375005, 924240912, 211907878, 940734428, 720586854, 695833181, 23496588, 493209266, 543004438, 447905624, 786583412, 332763561, 855652617, 624428335, 642636122, 387184169, 285817722, 922239021, 628410172, 334685754, 816074368, 893150041, 308468179, 651790507, 555225321, 527582898, 814436071, 176506648, 250451928, 408858996, 555390085, 728700573, 448025963, 918713593, 950505447, 582282034, 792766719, 42577361, 255770817, 380429214, 736490440, 109412426, 463569522, 358106228, 107555804, 596034077, 548309469, 231278553, 802686712, 872575652, 400982920, 470422299, 707797789, 808126937, 973860763, 885328923, 474209574, 262160643, 244385947, 196809517, 757564092, 237621371, 213911250, 524272096, 167447916, 19056449, 302474251, 243610493, 690420167, 931425181, 652034213, 360336826, 702691711, 561947867, 295633127, 292115732, 215240751, 404679336, 30233537, 371443490, 190127273, 434101804, 571299473, 755079452, 934973079, 817770373, 455757685, 450656636, 720447131, 270480080, 309893600, 82441280, 739157134, 136269710, 158356684, 33528363, 90207960, 761385843, 403709303, 306966780, 959341550, 514437511, 808940210, 419544765, 503484372, 685087860, 461286099, 103523423, 979722293, 287756751, 752039131, 360871260, 440124185, 291508074, 941737330, 43691435, 690892617, 778605332, 543666081, 31183210, 504334853, 256495403, 466358817, 925747866, 524619133, 869420065, 837052616, 319676619, 499450338, 850207885, 395991059, 845825592, 115183063, 789782565, 832184368, 46350009, 266095955, 946807136, 23007553, 263987948, 561836651, 649168323, 137944923, 131459687, 781319219, 181525024, 151487336, 478284706, 606509757, 893984055, 153417928, 41584497, 56272536, 496414429, 945094231, 761384256, 157040644, 450610847, 179340145, 235901713, 495157460, 873770569, 769418554, 660064623, 816664872, 922314650, 365823358, 237173403, 213547903, 502282843, 506827713, 207466990, 526473139, 107009857, 627564612, 73309359, 758584185, 375518326, 765683135, 113996679, 188563657, 76618443, 89454314, 158700033, 358507432, 749683291, 24436332, 242619558, 277540396, 317684279, 517863358, 575961753, 307026325, 354505885, 803674415, 687995767, 496247436, 624758142, 89333872, 154654121, 958234854, 85942307, 875656385, 930715345, 768287922, 230858223, 616239674, 819416771, 732223508, 235334358, 921043069, 459715141, 905061436, 1319108, 500485962, 455546615, 812227855, 394279103, 17920504, 785962751, 429027680, 569458387, 963176884, 983928366, 601841273, 497059802, 934142231, 345012380, 307429794, 155233922, 634507711, 742802718, 702622138, 91637856, 929655897, 853119833, 605334112, 146367830, 587757027, 192697519, 94104672, 417853936, 595119137, 599971971, 183183537, 873367499, 300447234, 869504742, 94797755, 644628255, 669099037, 170838716, 26087392, 978861745, 555784020, 932583406, 282699924, 631981495, 663269739, 212667506, 870101130, 869594692, 767138221, 476464817, 533253408, 415395067, 235048331, 206260874, 317443211, 1482100, 13469314, 718394857, 744690066, 430081407, 882921918, 933433378, 285716711, 147883709, 302807528, 566554128, 80882524, 566911300, 911696095, 56083731, 834853313, 642583390, 964534982, 324498617, 874857810, 554614036, 393313570, 419106522, 778685884, 950487443, 896870014, 225221415, 463547658, 565240526, 641897162, 599185784, 966809598, 208880677, 623048360, 161290639, 349979869, 468820869, 619009887, 358584435, 164853030, 843712906, 73357450, 99292686, 5171960, 886166183, 456518890, 589311730, 488688272, 813853983, 209270973, 857748581, 871144362, 401458388, 904866452, 147574973, 12620255, 846217440, 166574415, 97022735, 288374362, 345424054, 20050575, 231777173, 282256669, 315334019, 508123227, 502518887, 732672828, 421866781, 348854462, 175551791, 100328170, 116278993, 303033789, 770232902, 774223336, 983607250, 360063697, 507049623, 3702860, 707944815, 504456356, 884766420, 362869764, 359551354, 990157604, 546211858, 597723104, 895172179, 409646793, 151171247, 338677762, 131959508, 705804470, 981799685, 741879585, 836591702, 312279967, 459320559, 854324588, 342087070, 911563309, 505477273, 217675110, 386010075, 953870681, 950713213, 878991313, 542911095, 196573905, 813613079, 616976066, 822470088, 171680555, 144576685, 878858579, 540881816, 327897104, 755794812, 856011206, 774021796, 50608894, 273581245, 657391070, 948865084, 211947122, 924485641, 5251805, 918259047, 298293154, 715419656, 272224483, 570126536, 717940217, 313526234, 77201804, 920532864, 731433633, 600112251, 953841580, 402246945, 810115594, 187552120, 267828202, 674105035, 530254555, 667338123, 915548023, 788345215, 570590348, 588324635, 507670595, 497344759, 704999433, 781316387, 578334697, 282635632, 634541812, 580418235, 618951821, 693388713, 211951575, 113248746, 839456566, 653980190, 692760802, 830542052, 465230534, 825996291, 315829781, 323221643, 70192854, 121135827, 883576921, 999206898, 961273276, 211903274, 68025861, 782923446, 914954115, 737750472, 73775496, 613158997, 271182014, 673050228, 892825858, 939809118, 625243904, 717457196, 24439541, 622179043, 946012269, 857961288, 412577520, 948087039, 466158479, 931292476, 85439748, 579957238, 657600796, 858710251, 174475184, 286723633, 740578195, 706087361, 218919952, 510567755, 702635151, 385830453, 458006698, 304778149, 459938603, 899060747, 144589003, 998769741, 605274949, 310707190, 484449012, 235939541, 188081668, 166992195, 583621957, 878632708, 239574470, 960432227, 757983174, 154948391, 116378206, 536983774, 615343401, 881469834, 48160195, 541832297, 330065961, 787313521, 88419890, 232655173, 514528413, 688197355, 323274257, 477934531, 117682512, 707574782, 331653321, 292580429, 442373295, 234802138, 251642357, 14019559, 813465218, 603481373, 348620261, 629787496, 821297478, 59463608, 459509738, 252313836, 835719494, 384619666, 709928185, 374306678, 890859529, 46344902, 692857306, 886668894, 900036191, 2821774, 565860142, 871707440, 699016642, 530706490, 424351801, 328600493, 739141161, 467303561, 504620263, 40050941, 725186887, 538600945, 889950843, 645850728, 607393864, 965131269, 31329842, 654403309, 61331377, 407498553, 329139157, 540599598, 467837655, 49069273, 394100180, 345554919, 25916562, 348552910, 155210145, 146753388, 479388403, 590705014, 576188984, 825072532, 978052541, 89549175, 378162244, 563961726, 850388314, 55522678, 693921701, 105626466, 353887018, 464664743, 32994739, 251852184, 398039755, 374223000, 889900542, 865770347, 964128995, 139043046, 528024547, 371739322, 233426456, 992831145, 56830233, 104924615, 574573591, 712927159, 159653349, 499805535, 924445991, 850734147, 337965360, 988782660, 92999631, 753169166, 332068689, 248097686, 122485067, 576739262, 62806421, 695074690, 215242014, 722552522, 914632698, 892100405, 740383346, 458467437, 587562731, 363673896, 420145778, 644215140, 361835120, 426555552, 503862133, 469548805, 977612881, 929312239, 738465822, 584632987, 187197154, 505346601, 19720430, 979544425, 703452678, 783683308, 313218490, 654071927, 407991146, 300643125, 809281136, 598574998, 308176260, 737419001, 780952245, 414070116, 170203038, 76168830, 942778438, 168431932, 543961647, 36809133, 585965383, 813802249, 618903747, 908700373, 821760461, 949024217, 510663406, 688985865, 386284843, 436367845, 293507065, 656304027, 566858797, 142316831, 948911822, 61142102, 310928018, 859814271, 435521692, 389879198, 112814899, 516905353, 138945373, 935922001, 99248505, 296292949, 889750139, 305692452, 657837017, 884563285, 863350408, 894369674, 63296757, 361756857, 131802778, 288104883, 944236912, 556337907, 255320253, 367179263, 612795335, 54798866, 794068952, 516112637, 745156208, 143680210, 958867204, 998854964, 804132001, 300196213, 630443265, 511818909, 97844321, 488069333, 379567066, 916736557, 144074372, 443817310, 756095337, 248862189, 527584504, 803738991, 117015989, 296352887, 541633468, 579602323, 142812012, 977035981, 128100487, 386633476, 231844763, 603793710, 258001937, 501747199, 66011513, 890302449, 773879757, 833240726, 537135662, 950970225, 764692346, 859286247, 232776594, 400120558, 20975298, 97854607, 884351013, 921148926, 270416189, 767041330, 180305985, 703375899, 224157665, 556595276, 601697501, 56001694, 919438240, 649519677, 559711610, 150600899, 6280171, 997100208, 604292208, 464344334, 23224479, 52815574, 601950838, 180547192, 873661138, 830430573, 370948768, 759448470, 745341221, 189744482, 787807083, 113212691, 495118645, 720211088, 963189592, 725873791, 60065219, 859854374, 215197737, 484455454, 6152804, 982995182, 34369122, 479805347, 489351602, 688750202, 63533818, 652421428, 664891156, 614782558, 870502244, 373222302, 23867478, 435649633, 204692456, 955197834, 340429997, 311761749, 507406133, 865481597, 163967819, 666625216, 540544527, 27758227, 579963227, 13081977, 699882023, 143653518, 571982262, 464623804, 731577776, 856970208, 82305025, 921365278, 68122836, 63521078, 18414939, 99950028, 752035338, 850595619, 92446010, 232567492, 821729284, 541708422, 22224494, 588798638, 558282697, 752262523, 967705022, 73875805, 955066944, 594706704, 340570477, 80949072, 619891738, 225531980, 206261297, 758020066, 244757101, 464627691, 494953358, 20649158, 203936405, 570083560, 984144802, 482397358, 844193936, 947798888, 948082289, 969174868, 883194474, 877324695, 834884648, 416001058, 638358918, 579972635, 818374308, 224826432, 325910627, 176570309, 3335413, 896967471, 675983155, 791724669, 481076088, 382473933, 688600666, 774495617, 880451356, 378167960, 461748351, 47065043, 831467028, 743093820, 936916284, 233315281, 588471036, 908420085, 145716329, 323513835, 700424602, 456638115, 887423385, 550734485, 907290118, 829470033, 555801436, 870307833, 351211587, 795505155, 213496157, 128928195, 614271129, 73115536, 786710214, 500373766, 29756367, 769597235, 39942947, 681837807, 904529050, 884993766, 402878164, 296906525, 374451100, 512966023, 366620782, 280482004, 170480304, 771857922, 446760628, 168175892, 568307136, 78172362, 933753386, 781812842, 493168346, 716768560, 961744200, 214310688, 224340946, 758161177, 469812669, 201444272, 785436511, 831290925, 40779217, 98816559, 570550343, 820984961, 141584739, 751517354, 769968700, 150684871, 644403461, 379116075, 26386795, 261296736, 497867032, 790882789, 805276326, 257317669, 876132154, 825837193, 942397569, 849220798, 341627001, 95875616, 280106013, 382221880, 144030861, 772056847, 340419869, 506461391, 537215507, 132856170, 873075436, 513766327, 96960314, 402543725, 851089019, 63370587, 302707000, 755668687, 43845540, 906987282, 357440369, 733059624, 368068938, 185391945, 448775646, 981961842, 461565840, 520773159, 970520857, 263862012, 703146949, 874813216, 500585598, 963709891, 555296532, 667837324, 760183639, 362671152, 186050990, 546993346, 580173277, 573636568, 440136806, 176194, 477630931, 877606410, 987267142, 954143163, 748850479, 739284123, 73463130, 895688886, 92754290, 987477055, 201533558, 564098152, 184081995, 760486264, 825834230, 330780585, 920571074, 786143949, 759709811, 644835817, 821835440, 443225869, 973570364, 934328480, 296639640, 76877758, 140880542, 612959897, 709406586, 228493729, 158239526, 57058580, 451455467, 863392916, 20750681, 376915196, 753256087, 269762892, 1674215, 453085086, 356791788, 95615689, 946608061, 502169386, 66699833, 937907625, 800519292, 247040091, 475249256, 361683325, 485528911, 953514044, 229198374, 859315097, 558644486, 1505370, 566351002, 516478076, 876873018, 859322924, 166557958, 622851016, 325136550, 241823951, 324962973, 365444636, 929258139, 861704083, 714592494, 690846113, 120091710, 489156783, 224718598, 596206950, 534834442, 828112054, 241055602, 975110712, 881586995, 249907040, 860726812, 328413108, 758663837, 251246969, 155824363, 694979081, 940321780, 270942328, 18641736, 728923789, 430415588, 165006384, 130739938, 442400317, 125047155, 94690529, 187502694, 947063316, 43425757, 160105716, 676363460, 476365718, 476978905, 853886824, 910630860, 880269378, 287128014, 664617930, 980173456, 731625524, 484570943, 134295136, 712897057, 259836786, 938554700, 204463712, 367565236, 114215436, 651592857, 289924282, 302813120, 491815661, 14787301, 778836836, 921600176, 833995066, 678870815, 775863273, 219678774, 497238061, 213158967, 585643045, 420291905, 156841946, 677839588, 609735181, 318458417, 634135481, 96067912, 788904911, 793063156, 708225798, 160518161, 614223683, 896154406, 359893274, 739146964, 943509579, 668483966, 328749992, 770601270, 111677867, 488517199, 685926556, 863540002, 117653885, 143601501, 650402988, 803030990, 344306650, 136964002, 532805871, 252744639, 764117474, 806644631, 578520750, 950384296, 390365551, 528209697, 831854828, 480760290, 708926729, 651799239, 694189833, 913118198, 235414135, 888769344, 469521680, 804892874, 756117545, 267461624, 246890970, 644900652, 650253414, 618222521, 303261930, 830909749, 550915976, 219540445, 66779344, 162735965, 457783055, 282827711, 946700608, 62179560, 916661668, 572062733, 132913061, 260675660, 842732715, 586772537, 219075080, 585339534, 504479777, 951588281, 129935171, 218014539, 754356942, 506556880, 965987219, 113499696, 403532028, 413732139, 904241295, 786699702, 926976187, 149645627, 868145254, 506462989, 233712177, 950643680, 882062219, 155517278, 459392413, 456717603, 203658784, 667179331, 321167325, 495129992, 856019856, 517289621, 410733701, 462023471, 782003938, 804835986, 187003814, 918477453, 477343847, 408849934, 730371575, 79594344, 537431261, 985791258, 956371603, 803380287, 115373914, 510923834, 897177387, 100706525, 371558809, 327733208, 925592991, 868232513, 275782629, 335173158, 155776162, 465588674, 116105420, 764648206, 279438626, 16244019, 579086518, 987682510, 469287624, 532258544, 589114092, 564419042, 717802490, 406140120, 819622277, 380928086, 557242024, 648383434, 690601492, 158373417, 828218461, 339309769, 578740825, 192624726, 970045572, 293897653, 989945600, 262901448, 399775841, 2054534, 910018011, 944341085, 192126485, 285265501, 664506258, 180893732, 655143684, 814408795, 892039531, 766658219, 405976343, 968884061, 347627999, 536627453, 188925613, 195334295, 692873344, 190999920, 760210350, 377941026, 588278302, 162376617, 634440993, 875686089, 542542655, 224200581, 589496859, 755485767, 69342149, 317740923, 983680568, 694469562, 345794106, 925699238, 943359014, 23447033, 103412423, 490482174, 137548718, 849356088, 871932103, 618507059, 881613555, 8518248, 437376862, 391330847, 600143596, 235134436, 958770390, 478770370, 518975449, 718936772, 602272937, 179943542, 826538946, 74311279, 476579115, 362974244, 77611297, 332120474, 644868420, 953898068, 303956032, 457444154, 747783398, 540040411, 984895330, 907516272, 736760530, 124217414, 434836767, 344155529, 979738311, 18381930, 895102529, 158342917, 275743487, 105100226, 149289421, 551318928, 682521960, 189907645, 771550809, 488083868, 212479506, 328530307, 380665238, 74593393, 492730958, 66936373, 629213940, 367513137, 988364000, 776690932, 678528861, 387460164, 516717936, 277164799, 609758117, 201483021, 858076193, 825075928, 496218949, 356547610, 236243735, 95134776, 546555885, 559755824, 869378030, 453633632, 17616857, 570227873, 431206526, 596864162, 124920040, 46405106, 501332314, 421584055, 37957767, 572557705, 664799140, 549190276, 849709931, 836046748, 488971615, 134880574, 914238906, 170554850, 591158346, 351602227, 377335390, 374858894, 9523045, 671083030, 659234520, 311486335, 970956634, 567073473, 917815645, 518773124, 956815816, 8632415, 649110699, 767260027, 360770537, 527117199, 252207381, 183947631, 945746923, 758318436, 514872837, 591959365, 548833412, 913742980, 905755128, 659021256, 507003143, 621482520, 282060706, 931627896, 609069886, 87099479, 333957755, 614699587, 897831887, 263930232, 413070420, 691229866, 891467604, 935915184, 82047175, 122751624, 271190216, 332617955, 503349532, 878827140, 556966301, 803349132, 250034665, 815851624, 624188492, 883729074, 568300655, 56268922, 552821126, 160019922, 153173500, 209384954, 898680247, 874266539, 811470293, 406785272, 871668111, 566679375, 4828143, 138135661, 760436595, 674205737, 721764495, 143283337, 29683015, 121741538, 471132158, 81031448, 337827175, 381250513, 804216176, 950131489, 314596499, 415349909, 743378111, 404151806, 898813248, 171704879, 500190426, 196964094, 4958125, 89636995, 788564443, 763445734, 513380336, 429010303, 712791110, 403378752, 648642765, 291996415, 434788888, 839745440, 495863329, 910803115, 644693143, 573826967, 150692820, 479858213, 210877964, 695948571, 316721400, 976894392, 924083488, 361395548, 791891466, 650991673, 314790862, 534407118, 780435190, 665910683, 99083007, 871179858, 456064667, 30160105, 358560142, 397764497, 725774694, 348666811, 401221525, 880800817, 458672456, 554544688, 926725942, 16527307, 958567506, 161133422, 65452044, 890378952, 3758371, 441073043, 257850937, 865637377, 540637540, 391728551, 213306319, 355376473, 610127369, 602051102, 484841029, 11773789, 14034266, 529765130, 319033345, 951726401, 858204943, 148530879, 820285329, 535927928, 343260283, 226659140, 575060005, 437730, 184465583, 252469361, 387170833, 130247970, 270838315, 327593313, 977416981, 464148700, 700960755, 599121117, 612540011, 375009399, 258863337, 102151207, 856770998, 42782490, 324806614, 636491657, 684752541, 128447158, 506900876, 220198729, 323564557, 936450548, 210387960, 317370277, 402703018, 481245120, 455919778, 636589904, 114937651, 674568278, 443046205, 844098732, 106014543, 966961433, 283833039, 387688988, 732553637, 153205209, 836935852, 864676391, 190954668, 614641361, 350709559, 766313601, 752384156, 900797010, 641238049, 691273727, 13510575, 83154496, 948602252, 344368788, 882631754, 96504063, 762963760, 7336492, 440559624, 445875364, 577628254, 991265117, 574355097, 938815004, 944094110, 419820019, 90433566, 163699356, 896781729, 720227282, 754116616, 285476791, 758997015, 424457036, 674120965, 365971192, 63467606, 688661046, 636325404, 121471342, 671621983, 782395568, 416449847, 985419227, 505875985, 719758572, 720310861, 313245788, 404900282, 529214776, 154439743, 109770261, 151625539, 619588509, 934451915, 899737312, 181148106, 599353822, 381341371, 414132297, 64785202, 242355012, 141224233, 57416907, 474991372, 240263482, 248271845, 262605527, 218652686, 309573609, 545739545, 852326696, 157825393, 153967149, 706063532, 241290155, 760820396, 824102186, 497114580, 108462116, 939519185, 993103483, 569457239, 621134993, 896619775, 231400569, 475881764, 835434335, 588640748, 928189570, 317075667, 723199693, 462714843, 323060552, 772046557, 478280016, 275911773, 909712890, 569896006, 136179769, 230125505, 361780816, 195554699, 485944954, 689719197, 335391441, 912338636, 565682128, 942944523, 217359688, 36246609, 814074876, 901884492, 733519995, 208946948, 584659520, 671849538, 768409800, 211008050, 862639359, 401204437, 701115793, 666517481, 605326371, 109313854, 989926253, 104007972, 969281134, 626772692, 21962268, 101905928, 938088111, 569516698, 842066010, 821214824, 538593877, 9687540, 337895324, 607280559, 979998927, 929480720, 63475895, 876908072, 46559768, 226279444, 782477793, 223658679, 721467961, 265776352, 105522078, 285405960, 629083427, 28206011, 525568375, 363761826, 94034746, 339378139, 820110612, 224941470, 580739572, 934835550, 118697302, 674043604, 303116927, 88335194, 178145017, 738204836, 4113716, 470534023, 916765379, 885997145, 549954693, 236350926, 120885074, 740652727, 196202427, 477747845, 847745005, 773693058, 468521497, 479688637, 242570761, 978455222, 84414279, 25328181, 900119134, 292135155, 150864013, 869568394, 517954424, 50890309, 873686204, 167907943, 92921548, 495578714, 80876270, 273763543, 862119291, 832580040, 917502348, 60798557, 942479423, 284944756, 828192794, 421952177, 273463859, 70713914, 240502862, 661176464, 282155384, 369894786, 569825798, 586420889, 646202853, 437503649, 587526804, 330772233, 994247942, 884706389, 886144920, 908418851, 274151731, 650159897, 52341940, 281881570, 702745472, 81263271, 738735726, 231830933, 466582115, 533049139, 828644292, 168431692, 158346431, 459527614, 583005887, 948663541, 219072450, 490166919, 869046946, 82150724, 711421511, 219979049, 822812058, 814490364, 149959395, 700384701, 196208915, 448321373, 390593012, 806296809, 4079385, 623791898, 7003170, 402043493, 871013756, 902482473, 644318420, 391879006, 407123560, 560134125, 920651496, 873436595, 931553373, 263588630, 590702424, 861566860, 423905765, 358634498, 364471675, 281047625, 557989212, 455672707, 361242348, 813701623, 476401740, 125834864, 545648825, 698957719, 771422640, 757240515, 100809586, 621493286, 503740195, 415850734, 594579519, 701797160, 712261701, 854719163, 938948068, 594199475, 21148848, 790497898, 940204274, 97272102, 854602999, 399499119, 802070197, 964154892, 656512412, 760454487, 672714820, 196000047, 283332664, 661582271, 865147181, 580926189, 863415376, 414843995, 22356721, 60620421, 28083521, 764129226, 283958276, 588785431, 932283556, 458462, 831852965, 687100047, 169947016, 514204272, 975417057, 782076887, 687553115, 142325146, 16728410, 297395008, 331636525, 918659731, 836063061, 171973638, 866497244, 587576705, 888047479, 530770816, 735903149, 387450800, 360065101, 478900905, 670152988, 49676893, 505248019, 819043567, 232663653, 737889305, 859452437, 148541871, 857636188, 930778244, 308185282, 73267437, 574903866, 798592341, 15074764, 889776270, 902161850, 196080698, 267287154, 19845356, 267381760, 54891982, 268931559, 512985765, 636304709, 417234542, 224033288, 480273305, 498906390, 540090381, 50784063, 549691836, 975140984, 375871180, 655125186, 939773205, 768453267, 119535587, 524025045, 700076711, 408781683, 89306562, 973408843, 904478537, 421669619, 509973387, 718424575, 400331003, 782232614, 585848778, 914356811, 750266753, 386127753, 126260029, 491717445, 308709784, 227136846, 728432744, 828868944, 757878208, 688172010, 953168724, 567992964, 465749962, 421595884, 17139414, 805259040, 883851067, 654482723, 826648754, 173044528, 642632653, 167101647, 161050749, 789945235, 306238760, 990246111, 720214485, 4545089, 638461639, 120302951, 199053355, 316827397, 503475663, 502781732, 124649255, 752062869, 644263448, 733670286, 299883959, 108793542, 889027541, 223115357, 82610437, 538004759, 85422044, 50067832, 993432076, 759659780, 87324175, 769923379, 762714966, 795069093, 193721905, 249891946, 663296778, 520819456, 665147741, 1937238, 160379612, 603462531, 385962621, 893282077, 100050719, 145227798, 136506598, 786350453, 112664473, 363185617, 627674225, 970521162, 789503585, 412764558, 656096947, 399767337, 788421648, 373018288, 319912747, 890998055, 249091221, 527546610, 563401012, 801252157, 461376757, 623619266, 454398078, 91539322, 826739855, 88802255, 643615029, 35186935, 701007684, 331964555, 617398128, 134804881, 174021591, 445799876, 203452334, 289138626, 568065694, 119131308, 552612668, 398892888, 133338885, 121220399, 811659539, 621822662, 437659325, 832172760, 76284770, 614129239, 523198241, 818072481, 216326853, 958394716, 20268877, 248340674, 791954567, 827821481, 912828399, 546394361, 721662423, 668587225, 602544910, 380372506, 507987202, 841621375, 499036311, 476882021, 248533767, 565508955, 44455217, 332848909, 986691621, 146890496, 718784567, 888512513, 576471482, 387739704, 902367379, 289976350, 868234097, 46688925, 404541626, 648533250, 883422698, 645120252, 175089719, 554958371, 612159762, 271261411, 692967975, 64598175, 2820640, 134980595, 272213846, 883638634, 190926031, 486430237, 955899363, 234541534, 385661103, 97807232, 851898505, 214453514, 194081879, 821145403, 644759553, 884526566, 527496365, 413485325, 135892696, 463241937, 917613339, 375349358, 688123865, 331605842, 518035241, 771849684, 549066247, 772266993, 469868606, 867605238, 776391869, 158739456, 326271687, 475728373, 300725625, 16256545, 800137712, 728619304, 59190181, 903182291, 314552748, 456802173, 328789450, 748840870, 264811840, 704750738, 559160698, 594057667, 698704646, 756082029, 889294982, 968058162, 797886699, 139801704, 996172271, 940971143, 542237633, 720504527, 285747909, 930538764, 836105668, 180049479, 207232963, 330410932, 255539422, 869877823, 13128480, 3620884, 169911027, 214900402, 53964675, 607923830, 530066594, 487417064, 150501246, 544527839, 666266945, 994377780, 439716476, 139029143, 730536661, 227544466, 901667981, 202019403, 980744436, 805705382, 310427110, 999020583, 722796705, 313581420, 716097429, 67288818, 151154542, 482037739, 927366960, 230087448, 675341761, 938357858, 838968173, 522405378, 243587638, 847232798, 619971109, 148720602, 595587140, 712660509, 858263525, 519799915, 767518761, 570358477, 947520057, 78623160, 625064159, 642695135, 324241880, 419701569, 298264760, 90347299, 859852950, 321986142, 412431732, 194652890, 5270362, 971277157, 255108736, 400311504, 366064212, 463197529, 210912144, 930297731, 205066523, 25974137, 577167078, 357706492, 872279015, 369044968, 175578671, 4028216, 82839381, 291179595, 681538150, 777264463, 169486182, 751129595, 494911920, 215923085, 371690395, 118123038, 679161507, 387335040, 202751979, 298240738, 478696368, 836710186, 847855456, 15076166, 64554607, 343775906, 262606149, 436994326, 374395959, 398513017, 692074910, 717456693, 67901797, 267166045, 82312147, 98123116, 925427651, 588444741, 158069171, 106697054, 720326501, 543133018, 812305136, 29167833, 663305862, 904959860, 730471834, 348950056, 549087283, 596940609, 456247750, 105127330, 471425451, 820253384, 614453142, 538871786, 653029522, 54356775, 584759746, 387219464, 47510862, 663029699, 340580490, 722057672, 989808836, 777100687, 525409643, 448678908, 907511932, 525523976, 606662391, 784174641, 509145123, 139445505, 567599636, 906908793, 482190161, 501040169, 883549445, 934014135, 398390902, 838096439, 255279212, 183413069, 491555543, 412519688, 904538267, 908248564, 987494904, 273229911, 60531080, 504376314, 631144216, 957525593, 80244481, 54787900, 854190689, 763904667, 617698774, 325381569, 282280737, 354418218, 996060262, 772936344, 64146104, 623019324, 691074092, 784031944, 883096194, 220260614, 167748481, 882007418, 130535836, 910886151, 436192278, 213367230, 622193177, 807852327, 768218349, 180772503, 431199706, 772104093, 703625037, 698304177, 231977285, 284609490, 804047141, 662586804, 792515836, 284383291, 76000920, 216952984, 211477367, 209349443, 578775936, 746099840, 419839618, 618168838, 456254971, 101175840, 744242623, 921835712, 82278784, 326364099, 860901458, 418105713, 957705653, 410086429, 125821986, 496901143, 185410247, 906458480, 832965891, 825539716, 355694240, 688671146, 351121800, 464998641, 252905582, 572172170, 474685867, 4823547, 630652917, 104084175, 193806260, 64956027, 726135407, 802430831, 661185401, 535375876, 935465300, 862740068, 740799833, 215364002, 817695046, 601378689, 504370547, 595690431, 620621138, 995248101, 288021052, 319597200, 585178219, 126780151, 982502347, 560272310, 757826987, 491508973, 318493791, 457127237, 157453144, 112162221, 33872931, 892474866, 879040176, 783460845, 67519419, 604544431, 150203244, 352473811, 478350315, 520355040, 378132203, 474311854, 68004041, 642330498, 588051654, 734238799, 966604573, 248769495, 570586883, 791929889, 6878267, 879456920, 479547230, 21178382, 689080051, 658958760, 950307722, 355897507, 978742252, 603796951, 902773980, 978224064, 182831019, 35423611, 838227435, 345706468, 290824700, 868634825, 491986843, 654803841, 878674737, 343725312, 566008162, 688283902, 471416519, 872299835, 511212210, 715035464, 694872308, 134248806, 454354509, 181742252, 534095736, 503765368, 585489937, 360300044, 635581710, 20161558, 201211447, 110826290, 217352463, 173649927, 90232948, 465874976, 648438066, 154910808, 269330804, 876899727, 314918187, 579629379, 792682206, 434016070, 122488893, 889019232, 787051430, 497028971, 248294481, 591678872, 906511479, 39726171, 24596150, 45890139, 241331402, 71929206, 693121013, 105223656, 178299148, 752592922, 975819303, 320929013, 409528236, 343434286, 274774004, 290949340, 101133950, 993296924, 414037385, 101484732, 467316179, 56165880, 295474737, 544650593, 336241662, 756169508, 868340959, 327113395, 453138566, 134164982, 632856048, 168132310, 846006136, 716250169, 760595328, 674298069, 156423928, 718230899, 561240395, 658691178, 814675652, 971384252, 117265765, 389565397, 630426641, 132615211, 497968837, 934399637, 459476725, 129557893, 659575011, 951970674, 805476150, 780442063, 802517901, 423405612, 704494646, 492923686, 910998911, 280050222, 507667134, 276119063, 989949516, 708398249, 679287777, 286579926, 869250423, 669762906, 642214445, 126684722, 153510613, 410387283, 935199744, 444828116, 306096430, 582302202, 727965797, 689991968, 415708936, 98497626, 459578787, 696141699, 238400318, 528105630, 737469897, 31847444, 26019367, 110431349, 419532347, 14210791, 515319752, 351714222, 978575347, 226747329, 487213812, 703388884, 518214356, 33118861, 734325295, 942662154, 744004203, 314780236, 281559197, 608449360, 360757429, 59925257, 639797858, 447240239, 513444569, 264190467, 427239918, 786698589, 876269470, 651384406, 931926921, 981009769, 548041286, 242927316, 26000343, 278961311, 267893285, 642070969, 601688646, 180644015, 22361258, 634499225, 971072793, 843481460, 544187010, 876706744, 496463878, 397462518, 108306376, 16965838, 932217374, 495759390, 390991554, 9559084, 171524185, 880104767, 684881030, 197862999, 396588674, 272663555, 490931009, 283478149, 644134528, 879910400, 250242677, 809593010, 676223285, 136079338, 266693232, 375435496, 258602949, 579804620, 731134055, 480814195, 303563658, 279876945, 43363248, 579782363, 541214667, 700408798, 267930448, 2549421, 383836328, 535148725, 539851463, 955850283, 911381736, 630626478, 51621565, 569208222, 45648983, 671743760, 965506210, 305017180, 201647576, 66872315, 679775039, 67220315, 873722217, 491649622, 538510423, 472187697, 39406995, 374471511, 347716185, 244443963, 770802682, 990758691, 255469233, 794753368, 138097167, 663162809, 727595992, 348041305, 23772522, 914035941, 265851667, 555017743, 258964051, 940631053, 122447123, 674116200, 669739987, 799611705, 23549277, 743957238, 83908842, 814076760, 69997368, 729296571, 158116936, 36185421, 109960708, 718047053, 428589450, 471896992, 348958081, 627475554, 18178358, 227102048, 54269131, 853831814, 295620004, 212375976, 372063273, 339429913, 35447202, 741214992, 848345206, 543017939, 65930120, 930297914, 337066391, 204417023, 78343685, 166720539, 752895078, 149910086, 404690442, 830311042, 797896558, 263299450, 965916475, 657689540, 922754980, 771516279, 713958985, 838353626, 460137604, 566488492, 902811995, 793041063, 274027838, 892687275, 952206605, 247109218, 975294234, 817400613, 440141799, 517186611, 948554299, 230802990, 437450633, 177346900, 318065521, 884616598, 973860604, 420112817, 899807056, 263045559, 628685838, 397925805, 523725719, 611872551, 687256920, 301415714, 24984511, 953139189, 90603543, 736263242, 814697123, 440383706, 465617858, 903178421, 187496695, 562016553, 289566505, 7024893, 240531270, 140460705, 222203173, 388312020, 898423790, 529631254, 255737856, 106945517, 604933973, 461725368, 637589801, 928796397, 91775572, 432158554, 886257329, 961397719, 774294566, 100145682, 684824419, 349778307, 199409037, 713210385, 753722851, 619150404, 41944147, 101793909, 33791723, 438036415, 761545929, 917538350, 963872383, 26500324, 303656326, 647062558, 736066498, 718526469, 394892389, 143465692, 403381124, 970039736, 732300771, 392754524, 918240287, 825559496, 195955284, 289661110, 134411508, 326604042, 929572005, 129623431, 496643203, 275191337, 799269573, 777315833, 12426244, 597925430, 363074599, 684937822, 673903768, 496698079, 952850070, 870282841, 534781193, 17690806, 439814839, 662746829, 625442434, 726508427, 631150513, 667833145, 270082640, 801922837, 477639161, 694894133, 5752651, 99159913, 141472416, 134720751, 593789968, 288982239, 65588080, 226945503, 920168676, 144434643, 650204568, 843381107, 811900477, 823206174, 51094670, 13462314, 806939314, 370632820, 97872634, 352424604, 329847015, 713691368, 241457895, 709589416, 365359740, 241064343, 220862739, 474405125, 715691534, 273435140, 804482853, 645690066, 986154502, 358655507, 67744008, 801171965, 47471660, 501939832, 901824636, 892837208, 672640666, 882123440, 361481075, 245184307, 901126888, 29809538, 778396644, 832591340, 813902214, 290194740, 80926431, 989625906, 216913487, 633446219, 101847378, 13802235, 196652527, 924935491, 9906858, 415464813, 966736534, 302385443, 876207792, 976599403, 477746229, 900370586, 282147013, 601635851, 852812853, 321758588, 431306091, 654747846, 406410, 13500093, 221291675, 980836459, 364722268, 10062676, 500704345, 431934552, 707843627, 440544674, 591578966, 279611040, 398178787, 690379657, 281386232, 283378827, 780150400, 612454979, 244433205, 591667134, 4034775, 922087116, 901569762, 388713121, 445736467, 310138835, 932491458, 426064054, 175074600, 728829222, 613006258, 929607351, 334362879, 523847094, 728228120, 302108289, 532901075, 6610420, 821629804, 801033904, 19581123, 113846461, 47999436, 929468106, 515420864, 195829015, 29860729, 172491647, 784632919, 243342788, 329189950, 905015279, 189568650, 771918175, 995981018, 407718036, 672728629, 596573610, 679425827, 711509620, 21585974, 137632765, 700460956, 371453517, 682781147, 740594766, 843444366, 847485943, 981614270, 13648020, 317490477, 109223349, 614231644, 58295018, 588259565, 340676645, 328470788, 913035384, 848567218, 250660387, 881865073, 25867019, 477661064, 664861651, 224056746, 657714016, 560586688, 425809419, 980470761, 678763846, 509829302, 989382915, 593822291, 785641686, 871608101, 446060676, 283025930, 197651600, 583015031, 606727529, 728250451, 221279052, 528764849, 32667369, 578846485, 240602213, 626021913, 512032121, 120474389, 49133020, 29443145, 769821558, 353847347, 929086814, 229930572, 285207096, 427787371, 971833517, 142483256, 250334115, 222684631, 628761467, 628269414, 124315867, 258505775, 356163837, 412577864, 154093042, 35181945, 828522410, 736639813, 207641274, 503782642, 560200443, 450696390, 571933738, 916430627, 547371204, 100217106, 199900259, 951515858, 500680176, 912191494, 53910343, 6207914, 256141498, 536304428, 101387440, 248871372, 150830203, 268349566, 212802479, 929175954, 901179871, 886188257, 267261495, 512109666, 397581735, 875052542, 915830446, 984917328, 337038307, 251957359, 470541380, 955417014, 776310247, 171304126, 676594217, 151604311, 703070622, 710261692, 481247756, 201782733, 352484383, 490330547, 592033103, 234307697, 450103949, 864561853, 553930681, 151816833, 436767411, 382859095, 872132262, 592889787, 285315545, 210815765, 169298909, 341909190, 298855004, 357063316, 451309517, 149506472, 496981619, 281002408, 571138849, 130580019, 199785065, 333877402, 715336488, 474296754, 896630853, 592012129, 663193799, 830373338, 104678510, 154989383, 272195466, 647552439, 695949047, 698923433, 110747305, 903772, 415088620, 789598719, 599731218, 368741683, 561354459, 168299598, 297086607, 12084869, 355906520, 997019020, 614602817, 504611351, 653226305, 41577402, 360560423, 659999792, 65273003, 432381907, 215535299, 530888832, 47112656, 743615950, 472683274, 445880226, 23044955, 485218467, 322137816, 947047919, 884041203, 139941753, 183019778, 785557864, 646684579, 685881260, 976052338, 569997552, 74666677, 466589196, 318858724, 698502655, 318842156, 606544083, 898656043, 88602982, 949303594, 386067694, 343794004, 317839790, 546506823, 414819429, 891091327, 670238410, 524409445, 488590777, 132319976, 443407588, 181548758, 493649450, 910870652, 686168621, 254486837, 596165531, 437878876, 26012020, 301496288, 804251267, 585584659, 532539659, 523492847, 724901628, 555783287, 268765429, 314903131, 971816343, 5600470, 614500512, 113395343, 717795739, 804418742, 198382184, 573781768, 855523677, 128707914, 626268738, 421187745, 866569825, 625004194, 72314495, 77913644, 106655187, 102473576, 764997125, 734114546, 909356529, 315592647, 409718469, 976653179, 728315483, 950832856, 11104841, 245175846, 552256210, 42159926, 390670590, 420364533, 897194273, 893263122, 807989749, 506209016, 89769700, 506094006, 903353245, 239896138, 312803798, 969131178, 774802039, 595663819, 464368633, 722809056, 541174684, 850294083, 445961064, 997968925, 888489785, 877207949, 393691736, 110400075, 248455838, 931114696, 6814915, 703043333, 148070337, 343912969, 854523540, 208627387, 893231847, 885706554, 313195589, 923982335, 981671907, 533082519, 548935707, 307123064, 485699406, 647655452, 688985042, 392406998, 886423628, 927539247, 56628771, 521509860, 820513279, 657235942, 48089352, 164669376, 369835481, 770729203, 224349441, 67714787, 120499402, 783086672, 848303861, 621279783, 898003928, 426864200, 710946422, 430366720, 915935920, 245144908, 844150600, 624339580, 253742657, 729187759, 933903189, 383673405, 774423558, 297530604, 24212343, 218582329, 624371091, 970382629, 596423621, 562776657, 377125560, 133306277, 907462213, 174318706, 244570044, 853262047, 835310455, 687263423, 439762541, 804746706, 701625595, 570911768, 829466803, 942077548, 830991069, 904570750, 520817375, 555357544, 344614901, 335579783, 925955901, 630078993, 761949163, 160249882, 236579199, 205804335, 285827756, 651452427, 423367957, 878266767, 467683003, 497264161, 3738691, 646800467, 340104798, 293472390, 256470702, 592402322, 711154184, 916329899, 957582035, 890842713, 848977003, 480238871, 636629471, 46715098, 109840257, 651735093, 736896914, 537693536, 636912359, 397762974, 426670866, 631538404, 664891881, 116018168, 803359738, 30394301, 685268143, 697690186, 779472177, 780305806, 320191702, 944170508, 468480174, 672431297, 815401663, 992336836, 942629308, 397101126, 82945595, 382785593, 127011223, 906093428, 596840232, 891666661, 919767844, 825901025, 964245836, 254819461, 640418041, 562859132, 977297579, 354976502, 324260940, 316370212, 186880013, 314062929, 381691692, 371796397, 296459960, 920340075, 684106991, 812691334, 36853363, 625995847, 789113340, 648909831, 373627732, 90798795, 930412677, 993175184, 97033463, 290305274, 229930580, 913488833, 75000495, 823703951, 676851634, 884856727, 976933714, 62692133, 25507558, 54378892, 368962408, 375046505, 611134918, 128366273, 768046492, 732716458, 944011695, 632684297, 498927470, 847906835, 985729454, 596852276, 496378783, 635426674, 354081329, 476053099, 969985647, 424191930, 213490409, 835779966, 73675880, 530338639, 552647513, 368623932, 317920630, 688773572, 338121649, 511242608, 758268165, 450458045, 847363816, 622849857, 396911814, 362784042, 496822747, 421468636, 892415538, 672904062, 261499768, 976313126, 259412286, 610577038, 108261473, 450917805, 549564328, 597229130, 268019787, 378005665, 200374409, 352409047, 179876989, 70517400, 220748080, 173612190, 524161847, 40343285, 582411435, 476117932, 692487182, 208833647, 997935929, 561609414, 850305582, 541173767, 12528738, 171560036, 276143152, 304664568, 830865453, 199382752, 971350534, 504200419, 217984022, 912314208, 572200047, 32734560, 752886152, 113299861, 167385886, 456678407, 483698235, 567341540, 475987977, 135486627, 943020051, 573232690, 603899454, 978495566, 201320712, 867476679, 472295030, 12716628, 37476725, 170281127, 733275023, 433421803, 940662105, 643334419, 954322516, 201826167, 384392655, 698986407, 324329358, 711876388, 329444459, 274579651, 769609590, 120106925, 754771235, 402868471, 892855612, 235583371, 834515798, 74154071, 677443439, 347595839, 857332173, 23277234, 446046763, 724273839, 476820921, 792888853, 631659447, 260099247, 490243760, 631547591, 467897861, 637190492, 255700340, 610607476, 706286446, 80770767, 54855922, 296718853, 605267923, 535561112, 684216540, 322363963, 994348557, 655832272, 980431260, 152882054, 479916949, 220435432, 210865070, 955655939, 924638966, 430522499, 47020151, 964059219, 284083551, 527713309, 832551832, 316393172, 349510375, 700734897, 885274055, 989157697, 391100294, 626153744, 151589998, 652229916, 701701224, 572142772, 40509172, 710152546, 507437847, 350797319, 528226621, 958305086, 870914504, 799234927, 884259638, 890262862, 765493028, 222851674, 336224809, 58888275, 995003680, 121202633, 864580354, 201230470, 7956512, 452850693, 845423887, 953794811, 371551932, 348118014, 269425804, 947145596, 421222828, 894721270, 944428142, 539423785, 610860160, 339924773, 854605339, 117118095, 6102426, 118013899, 818407080, 575767689, 537840089, 946877360, 798254067, 624177736, 789735543, 103744293, 504429942, 141063907, 409355421, 469778673, 434892617, 211371878, 383883012, 528583976, 808709429, 322462891, 219541136, 592345907, 384254567, 178504178, 644743890, 162481199, 849117964, 353277551, 471689206, 642512803, 575453872, 510215480, 5272942, 389159343, 373036992, 208649232, 67822488, 465724141, 287367677, 334153349, 587364833, 167361181, 499812135, 49967940, 947625369, 682696641, 273023817, 548219862, 440407747, 458447655, 768281741, 520136503, 211727482, 826232636, 195388415, 584351183, 334939151, 680157021, 576059840, 599511064, 825718156, 788672736, 133799408, 215396378, 708710235, 223380722, 916195236, 722633856, 351886501, 685933563, 709425836, 300079134, 646424086, 610165972, 170209932, 314847293, 945206164, 833627434, 523562509, 9702390, 710038160, 907972899, 514308611, 750476640, 701884796, 882705321, 472997167, 557371671, 51252972, 576946329, 862978023, 514457736, 238069544, 253637316, 980812846, 265360171, 755430853, 302362801, 379932300, 586024432, 920975497, 5513807, 905621865, 38121450, 497922676, 773489383, 875266429, 712320923, 651485897, 594282144, 616960405, 176928703, 836839340, 392667128, 838303594, 552013145, 792359613, 691098043, 307030384, 26943578, 769002075, 853738176, 61401857, 769623103, 140188217, 976071064, 198821648, 243831609, 968169179, 654175791, 453936703, 184691658, 548024130, 464913074, 158399434, 522970407, 636728869, 167480912, 216023781, 86916969, 647194647, 224217006, 130421189, 22881524, 728693046, 690033243, 298582738, 36730780, 705784560, 758445773, 479473259, 129252222, 419890239, 313932090, 100523810, 484771768, 870315763, 291179653, 451714107, 630633301, 168653964, 759501210, 604331493, 654698171, 74656742, 761079748, 593524566, 626506493, 199905514, 339969788, 141174017, 420446652, 486084650, 240861729, 260134769, 163305734, 978792804, 306378874, 973144943, 113361024, 324667435, 78866400, 635568236, 287091625, 334728519, 662270761, 23320254, 280143819, 71897565, 558462930, 831620890, 480284674, 494870726, 154120359, 949645488, 379444659, 990026260, 947518614, 508228940, 35609039, 614230411, 131623115, 294880381, 608149416, 28114648, 560524693, 118551457, 114276899, 262386728, 160875440, 282100609, 179199133, 11185037, 205948751, 295159117, 651087967, 572617114, 579443662, 801910723, 52536736, 566265370, 687309188, 741458739, 270724674, 467839551, 182065450, 906241534, 264297824, 138310589, 597782208, 294868109, 619557072, 664674440, 440920074, 140258888, 116626762, 874558313, 441898009, 285823559, 249417679, 274090349, 981633235, 479894687, 436661375, 926435130, 647181458, 958233893, 125275671, 115297141, 95029483, 745745665, 273365815, 545316456, 129491783, 634716184, 620807205, 267267985, 257378700, 258715993, 924085443, 774142631, 936480336, 864535885, 743017276, 352384068, 624430883, 71530978, 252307180, 871583195, 709397228, 73285081, 89054529, 151709353, 895123084, 356622153, 837243282, 420072164, 997596087, 458721341, 191614729, 464964307, 692344626, 621613501, 733008702, 42202482, 26091959, 526823219, 430156122, 819768221, 578133590, 32535954, 163677537, 267662430, 641268095, 473744132, 422550550, 5174157, 138213949, 162585261, 84933925, 595344810, 286820751, 758376964, 353821667, 746431747, 107614308, 420594917, 586204617, 740618346, 382376148, 533289256, 247904648, 560680999, 509492962, 257872592, 437599987, 349325665, 4174263, 99058247, 773713767, 283760919, 821905403, 229500062, 37114134, 879161921, 187797962, 612968254, 877974099, 587440011, 79540501, 615571205, 228125638, 494016682, 904613557, 622590392, 187890208, 755447728, 145432250, 930671654, 29513253, 670076647, 826627667, 548295234, 248048782, 402023195, 457957708, 251011299, 141905123, 100008381, 688621931, 644694337, 304760357, 614808130, 540791376, 17789278, 691894622, 337984354, 253144203, 926626054, 469654404, 434655016, 949034133, 874759620, 445511373, 220549883, 771618247, 886978818, 307064512, 508868964, 790112296, 458290612, 672319274, 475361018, 876286992, 942597408, 997275885, 854369851, 692662455, 190819766, 642513398, 507054568, 932942825, 249175083, 889833566, 841845818, 441507931, 761235244, 291722742, 544462597, 287465974, 833980613, 567751317, 667435026, 145611072, 852932719, 365638792, 977751884, 737221584, 597039218, 935974755, 677164662, 529152736, 403440664, 147405648, 664820902, 530753765, 546785326, 797316940, 109340516, 547373807, 264849075, 625899014, 667469990, 148342682, 922992590, 84236500, 429239807, 271706437, 467336503, 578998769, 570899862, 980522778, 122541759, 28313030, 536429912, 98092744, 340356438, 938049698, 899363293, 648718434, 204372614, 382710600, 972351849, 727208885, 628329662, 98249285, 238418492, 770024156, 661189599, 944381308, 404934125, 390986283, 208851321, 105038046, 425815191, 468946604, 66446542, 296040806, 462703092, 797748367, 374528433, 147111337, 587606390, 931328508, 45804416, 72938439, 885812614, 607855778, 234766681, 204359760, 788913523, 250551884, 966327734, 377841850, 235348015, 934006257, 237184828, 632231039, 655893373, 884196231, 343286595, 427199570, 748093532, 744449761, 676072872, 217250848, 527723519, 243832027, 380926477, 961558978, 750696022, 715953758, 374240408, 944160800, 429766942, 653543752, 391087406, 444264667, 451588802, 672511901, 386565535, 511951329, 155657223, 499731757, 784251242, 932970889, 205576429, 417606372, 540892734, 324614079, 334783680, 996804630, 536527368, 475288785, 854193938, 21373057, 687791999, 267029801, 244001137, 771789628, 115345489, 587268284, 437980469, 195362645, 381628476, 528060900, 448698045, 291212858, 801685939, 777032228, 337829064, 376654516, 410147876, 336219652, 383774559, 228417368, 446448047, 832832907, 727262142, 695463705, 480657423, 710189740, 585884402, 506065114, 602274131, 656879238, 394024815, 10001243, 625677608, 551745653, 907444621, 171418984, 703481589, 521441664, 844995023, 966860155, 389561151, 415124012, 720998693, 998628859, 694259064, 655870106, 88376876, 345905414, 885674815, 484010017, 270644642, 27581055, 415735108, 813607201, 399579380, 686477674, 338998877, 242736231, 115887029, 541236935, 179550317, 78631476, 77763165, 606215250, 697907445, 638270160, 908490745, 974448997, 915561652, 124317007, 753610812, 182776941, 753761638, 117239322, 594342283, 926044814, 768819405, 704395283, 153777916, 510166084, 982848370, 92696560, 719090908, 882829329, 289687715, 829398943, 984684036, 572536809, 749414495, 282461067, 429099495, 53745605, 661014980, 149542800, 21472247, 330105341, 525819285, 926411700, 449531534, 69980154, 481027515, 923518638, 29466109, 156250295, 146064641, 146634894, 373442239, 54286335, 316191876, 622961829, 654340582, 424175122, 121063, 426657071, 261171183, 136567417, 324155165, 503882699, 59837800, 751822260, 607065505, 131369607, 895853438, 614916675, 417779743, 702997674, 944685434, 712563528, 597468269, 935679248, 921049658, 355136087, 503122569, 419010847, 954223075, 368380543, 117958622, 741537150, 73140090, 978336835, 752184622, 832894935, 625157395, 770237287, 762957227, 185856413, 896214511, 116750232, 711877948, 926832776, 360998838, 937877541, 735710387, 240246967, 603149368, 331691152, 817636520, 627862555, 708336007, 526945176, 534435142, 697181908, 486638210, 313473207, 248342465, 805689722, 770181939, 694886933, 212469099, 698939731, 519911367, 673554557, 983729023, 354185604, 647754138, 541368483, 51498747, 624950279, 938633366, 775969545, 336227968, 100510656, 489375118, 67578594, 203015547, 258528092, 891896273, 936223297, 321067688, 991618573, 606667462, 246099054, 942444763, 617503062, 988956550, 978866180, 116187294, 148717142, 198753024, 330920335, 751927558, 339120736, 135828131, 897901284, 10922540, 931276873, 858728762, 862631004, 952328117, 707063008, 789149668, 311724821, 507960207, 339194859, 548449222, 501123480, 60773894, 72013787, 50422332, 734704273, 4167753, 496240279, 901667545, 90236828, 839153907, 142907001, 903181200, 745341678, 173018321, 833231210, 65435836, 927376284, 777954101, 219336160, 42944973, 423069902, 25359664, 877091062, 756242378, 851566635, 486946240, 813271462, 245307741, 969676229, 383336967, 961855516, 695917212, 367754192, 855704188, 250812397, 790487240, 129309613, 449040025, 667112856, 463073308, 930751342, 666390844, 811846384, 991594419, 748898776, 927664906, 835790216, 856220389, 703354466, 306747041, 356509919, 324255947, 571245230, 908708999, 993090824, 76179220, 974253674, 408314106, 298456502, 828051229, 517381248, 65985501, 717238667, 99852105, 530673390, 798498313, 2508879, 969615071, 865488189, 23853219, 792820567, 882444736, 452815369, 950108319, 517077734, 229331250, 228187117, 208434106, 11428584, 49696750, 972733695, 311176559, 505852747, 579858075, 891282820, 202447131, 245205010, 111381693, 966465979, 17114103, 14320389, 784033276, 292926238, 880496530, 504667729, 835739144, 745770510, 663005826, 903725271, 703981270, 167730615, 596243716, 784646465, 100024023, 791551773, 427103519, 723082318, 511780241, 328052759, 178406953, 857054993, 193605009, 219878888, 294312871, 305682215, 783641339, 915140904, 162712123, 510633484, 596156338, 25424085, 315904127, 355448037, 899261544, 698949946, 655669285, 329982889, 640652789, 365559081, 744179109, 556902298, 760752994, 729458614, 237830573, 965781297, 956803906, 505587655, 943092740, 765738373, 649586455, 952422587, 273597809, 254531296, 120644739, 821420293, 894684285, 502273951, 357917093, 596025089, 942096422, 210337013, 94835227, 879050618, 578862057, 406849290, 76023791, 607477662, 11477820, 945056314, 373548060, 252424407, 732614084, 876372756, 807432161, 136214250, 383561225, 859936414, 254744038, 523392795, 843931019, 410096441, 612270875, 414548968, 618168645, 373551427, 862785295, 544760992, 207072817, 471975447, 137711126, 878473638, 662839835, 550845416, 47593614, 550450202, 917520089, 317894288, 87415563, 711989628, 404808679, 532074246, 795606683, 314898849, 923636259, 294341622, 236966093, 408400223, 976088619, 174512753, 257915435, 162697695, 385213891, 478730995, 60745303, 954683569, 63071121, 764393839, 665195322, 375864852, 802025515, 300678877, 645428596, 833883579, 825959537, 923381564, 576975416, 407789216, 479462339, 581904026, 610610128, 870467862, 62921254, 824345241, 65880651, 587489490, 81510259, 952723356, 361533958, 747767532, 523336107, 962247733, 506242918, 429769605, 308509867, 652019599, 723264142, 722530902, 332825171, 927970164, 551556739, 591818717, 493650683, 205730211, 893094684, 120392663, 528362149, 244189413, 382090157, 626953202, 18762469, 152306309, 900165467, 984540667, 959062802, 147279091, 180763528, 801030356, 689803589, 769776597, 61350759, 663525319, 884959407, 523333063, 201035320, 372144839, 594486906, 373929415, 698576688, 74245039, 112147921, 65679713, 903287000, 873086362, 942369151, 457667082, 987574841, 380918116, 445569724, 504257939, 569144669, 975919759, 669654990, 690329180, 638066110, 189901136, 953940049, 903659729, 333374331, 744246780, 324760979, 326265984, 752550998, 767153252, 868728021, 591666940, 559089552, 397256827, 518642672, 919899452, 481467668, 84573614, 140099884, 199960638, 77943248, 751147415, 870423077, 562974605, 898017139, 412911426, 571271596, 613045371, 735206132, 826163821, 333239241, 236689750, 500551767, 286337279, 80917504, 168286671, 140652547, 791317109, 890988820, 506966903, 601832069, 501538006, 752379969, 685999084, 255788307, 560552311, 230422602, 97422672, 253352493, 978013272, 444032255, 389097231, 798326856, 807027217, 36074760, 122822099, 386692690, 460395806, 506513381, 545003564, 781691042, 390495527, 598865228, 644316776, 353951830, 178061711, 287801183, 32770755, 371233714, 850366122, 252957475, 577371197, 898508291, 174394339, 83409366, 639024102, 915577774, 455969209, 710090826, 543372927, 848676372, 416106404, 698447348, 325400708, 290405784, 104110837, 55649465, 299580935, 477713519, 439947788, 326968540, 633153367, 743082516, 879300971, 873895715, 668753971, 83125016, 91719118, 529833026, 934024816, 635739492, 987351158, 667953432, 651991275, 966954826, 687766795, 980716237, 813850968, 628759943, 700025664, 45709294, 25468454, 513300281, 745004617, 102308332, 372383887, 129576552, 93349490, 732492326, 686679029, 739763922, 783931776, 390540920, 104974586, 575288855, 751392191, 583332262, 255704892, 503971847, 675252470, 334544394, 804132453, 520888218, 580757093, 438742309, 59450848, 215467160, 558099518, 467302561, 801599105, 297472598, 747840352, 19946497, 874359752, 183755520, 451812020, 661724020, 293464606, 319255463, 596208100, 39081736, 205519719, 337876957, 109388785, 836254949, 152721453, 527047080, 975537811, 173538856, 901478654, 265800274, 341385784, 235896071, 306254025, 137526176, 107204603, 788093797, 414386840, 307032696, 918429903, 624031528, 517103802, 695132773, 958591486, 457946191, 720261742, 688192970, 701966454, 281655347, 121511983, 904708788, 316571658, 456372429, 816602659, 276506757, 599172533, 395104878, 549976117, 887548771, 143256698, 436999564, 25422439, 537840965, 893856560, 23892223, 228604049, 882607575, 144972333, 523335803, 329332915, 966817470, 29634209, 352304737, 520429714, 755740940, 272087697, 411855787, 22957447, 490405392, 305802015, 116520940, 97780089, 20686990, 269684937, 412361895, 307252825, 170282913, 545384050, 196059069, 389727849, 488088663, 369746862, 373325536, 921079338, 158230405, 386427689, 281870335, 886839653, 949814435, 133082443, 68139695, 596205858, 537253909, 294776786, 419393729, 832577293, 81584745, 476305028, 564767833, 313471107, 338033979, 228555240, 940536485, 733335124, 304277033, 939123587, 688109404, 399595367, 548521716, 596820333, 603384973, 115479420, 958005032, 818256706, 169701896, 941205227, 106671865, 106337891, 990252174, 333937550, 501802029, 522164960, 710240392, 176446408, 242087257, 669259753, 848804068, 854471824, 447805576, 938972146, 292269451, 975694401, 586698361, 162837142, 298052736, 987512108, 994439701, 248933278, 680831841, 657753657, 819485376, 867743054, 412784270, 119920307, 484477657, 699202984, 580837721, 133478771, 54340380, 301722637, 674064074, 159792442, 149928056, 225620331, 991747563, 157399949, 784720634, 247251019, 6153777, 443079160, 320662236, 348891170, 278525457, 117927971, 566811282, 232260799, 770263888, 785883648, 52054854, 619589606, 960388622, 910183155, 800953264, 837774250, 812819175, 178673534, 163254872, 215735283, 725794681, 178182874, 320576213, 758293236, 587956485, 375152476, 860804053, 586943422, 236722805, 842395471, 221338353, 731744948, 173343387, 300993737, 594576489, 693114531, 335668353, 541291946, 486600493, 496449269, 883148380, 969068938, 216700557, 966299524, 719998566, 497323892, 29174940, 627804480, 462878260, 554251893, 691804784, 7347115, 193153312, 41538441, 641153598, 530604134, 213980070, 377344703, 389627213, 917195198, 694169077, 692896055, 137332178, 195055619, 359598802, 7732582, 532844903, 309727155, 906243658, 124034972, 218508943, 569589519, 930884185, 863902580, 196963037, 818682132, 840476154, 450808459, 617499747, 421969621, 850302052, 576057102, 780673934, 930935093, 508512693, 776326141, 867934110, 806046998, 284762929, 239219647, 936011497, 673982107, 942280757, 630817006, 911802824, 446537049, 313082962, 806528533, 441306227, 424451104, 375846482, 26169113, 673744824, 278941113, 281587331, 338361576, 385020340, 825260855, 160810166, 734209156, 111165409, 960825901, 380197858, 567699189, 820172863, 151498874, 66760806, 469929557, 129714332, 635608734, 945571780, 780248052, 295312188, 331267876, 716920590, 853712795, 686799749, 100315733, 189230610, 905152170, 181560115, 722637730, 731875555, 235652745, 130138374, 953046713, 900813452, 88056566, 816185640, 932974237, 886645359, 999809019, 717369394, 486493253, 509542233, 954974182, 128613501, 544291384, 108851936, 145814504, 284804131, 27658935, 606358197, 413997504, 948002288, 947705626, 244307990, 779652479, 801115186, 157530291, 918945925, 587723176, 391911230, 376349695, 450103793, 3936988, 750898987, 295076028, 36611374, 268015075, 638284896, 750380538, 511151525, 263693563, 139030094, 517716059, 683665672, 556271849, 956714443, 563260410, 671753803, 66175494, 969554864, 293082412, 84149097, 680648187, 18453864, 612508654, 477595462, 863627202, 336028994, 897771135, 503230969, 89737514, 586424857, 165166693, 499352855, 761106970, 836933218, 759973366, 584195303, 134932657, 259829666, 216506658, 226490316, 95524773, 355618869, 863055795, 392544546, 322805384, 200434342, 856795704, 165889191, 56771723, 104784048, 968386601, 898248049, 738105843, 587489820, 958910706, 655061228, 794435943, 582971041, 674221402, 757304738, 742155220, 59418117, 990799441, 343564130, 364426084, 261207896, 108194414, 499756507, 718116669, 395644004, 283038333, 39213335, 820138872, 421020411, 772592493, 627735632, 42238719, 266396414, 405530442, 164646546, 286420761, 952386657, 959083330, 253907888, 912965907, 915876935, 753233604, 457001970, 9587917, 262773764, 53240510, 315616821, 214869315, 727486253, 964768913, 173270374, 707492911, 235456261, 265148821, 81296343, 533702875, 77253954, 760023212, 586845393, 934501410, 560101380, 627788396, 932869342, 731418150, 181331789, 783018825, 678012310, 76061662, 841979472, 67231811, 761520686, 872894575, 912975914, 165915474, 730889249, 309238106, 295132591, 668186528, 720936384, 36330019, 99104154, 872585556, 524155218, 127072648, 860379534, 610585950, 341699592, 119666411, 545745754, 479883683, 646916772, 938677822, 45228687, 611781676, 644799971, 941326357, 205076214, 480638315, 480211494, 956080729, 155900291, 807527665, 846142154, 711835850, 473980611, 706323251, 6021399, 778171596, 740389862, 980252440, 990975077, 882395341, 75594961, 164215605, 498833123, 342517570, 923841311, 908025663, 821126090, 561797694, 429747726, 271794402, 426455954, 972678732, 802864769, 272815669, 174134310, 450860836, 776203965, 8647512, 773132199, 357887044, 777568052, 647555599, 118683982, 587871365, 597839250, 700534959, 876101466, 435423682, 826930742, 514540068, 248311628, 252947793, 608063959, 890299399, 128918379, 437388267, 613880352, 272129110, 621401433, 878511171, 480923045, 565897426, 425032171, 850364432, 414365329, 284387406, 760988158, 325578536, 431187980, 354492253, 51849740, 156566901, 876138639, 242653034, 168123949, 867394770, 586402620, 220829005, 675643943, 245975352, 908270942, 941060774, 794851046, 252777466, 501846844, 280150833, 945248488, 839349074, 163211566, 152332959, 210601922, 787375226, 518381, 943512578, 169851669, 831912103, 747179674, 821543898, 30882849, 34753654, 545363084, 805481626, 759824387, 717633724, 395458476, 285569543, 203858783, 151950463, 702414908, 811344309, 867339513, 915765764, 164499146, 790332054, 279251877, 689919225, 61050283, 456203994, 757916281, 852295712, 630968399, 479474288, 256426011, 570442363, 882180977, 249133270, 971508464, 84201876, 138428149, 365442239, 201689572, 793198465, 368982935, 379396560, 543351383, 545328293, 204970377, 83799043, 825980014, 516296239, 623298935, 734385132, 699272447, 44145601, 254225203, 948099249, 440583948, 507039478, 589242261, 756840814, 496717407, 793305171, 152618442, 120137866, 410198833, 164696772, 698570670, 530100923, 192362585, 590560632, 333019204, 881035906, 128561025, 844731296, 240871709, 86820057, 107209706, 892524713, 723182634, 865560705, 949290163, 156174453, 488287445, 797802591, 544559989, 176835898, 809485572, 494824570, 96270618, 730356528, 461885849, 941129739, 24319866, 430382270, 251414909, 342169121, 3480852, 824494556, 271875761, 597788303, 831890081, 114435245, 90774411, 188632621, 694773154, 302791053, 912968075, 303479037, 190497686, 552542586, 134874496, 162446886, 272635097, 319460489, 542059169, 752365535, 416257183, 729220665, 914933869, 203695061, 65247929, 20187557, 497405632, 823791764, 255362976, 987887276, 808349446, 573902944, 186184973, 828209419, 660027173, 138273849, 602675918, 700782217, 257595171, 128446088, 281445805, 896162054, 983690214, 311651062, 722741921, 757947379, 465793788, 99025732, 782714795, 685860308, 561201033, 711389947, 185868323, 117808374, 12659934, 182979864, 303991751, 799579175, 621361150, 733815213, 430809815, 511648371, 888938556, 959826199, 974510563, 949575404, 574991167, 533640061, 860221536, 418913826, 96397779, 488588031, 600121113, 83898095, 116827868, 517852645, 614161728, 825637547, 78516437, 212867588, 123965757, 711097601, 599858194, 498755268, 757683956, 229499711, 11502516, 400153609, 353762624, 327086710, 266227440, 706320298, 438969535, 194541416, 177645588, 756057826, 175727045, 177277130, 13939263, 878440524, 771850554, 269529129, 443408312, 367257450, 110429800, 946365256, 941358813, 825030944, 25030817, 361542926, 101603182, 21446657, 276809149, 281270560, 645751651, 375437505, 882662747, 925445295, 167502818, 392125266, 837892240, 241022065, 59614092, 455783918, 176385645, 164860487, 38813666, 992572266, 851718645, 848386037, 906327189, 659919244, 973054859, 150564016, 159346486, 603851911, 447496709, 401866216, 749653509, 588046474, 808317048, 261443174, 967738960, 918667886, 716316664, 877132414, 34280644, 953775892, 590763545, 553430173, 73671292, 488617260, 461453534, 371306481, 107622128, 226510788, 615358482, 435014954, 632067902, 359952163, 151250428, 718711594, 553492136, 333838095, 208085206, 318125360, 638424383, 414380627, 508852665, 805801797, 143981429, 934429874, 625198385, 340059553, 869566563, 217778102, 320390713, 248401847, 816235271, 236091629, 811766786, 951452816, 887447827, 205302428, 383352362, 389040341, 432906030, 229939833, 928719694, 788284337, 117692471, 154643092, 256562778, 253064393, 289689432, 545992748, 447886502, 308797722, 241612501, 356437931, 70852734, 189876883, 757400652, 761895276, 854462052, 277865098, 662590351, 842029432, 819997342, 62666745, 443637247, 74933102, 235204182, 225819163, 202634598, 906271162, 984911307, 387638353, 798974363, 682274684, 189939081, 128810669, 631209296, 987230764, 503947648, 461151298, 362898028, 160745168, 155073730, 230512562, 586455190, 407452007, 281253331, 334428244, 827556721, 929538043, 911240978, 812700185, 450088687, 794865907, 209932866, 927717305, 603382877, 606939667, 803645303, 95314133, 737482394, 371592353, 67843178, 54202348, 967599368, 561617321, 650870318, 653846745, 195855861, 707053879, 65262751, 727553083, 422069779, 861019865, 53971078, 590180201, 479791590, 444606492, 768126575, 250770105, 55366090, 557461616, 959515460, 727251830, 36608258, 748978377, 356742922, 247618424, 869422411, 209536472, 134822944, 273015899, 174268380, 466685412, 102990610, 502957888, 220341732, 4974584, 759337174, 514805025, 298789889, 101171623, 612120628, 159481658, 336732667, 680640139, 986437498, 150470855, 898754594, 478716867, 223827838, 99671545, 596584008, 559436843, 416037224, 560110682, 112296447, 659380527, 738674586, 10114422, 647726650, 806427661, 586489004, 990449310, 917499801, 166152044, 998502264, 301634293, 912818938, 722724517, 618606549, 911182541, 995305492, 138822990, 367895005, 252229047, 658969923, 34267409, 769524831, 383325593, 366302369, 377724985, 991414673, 958542607, 531252965, 747077252, 112712976, 827138316, 578529491, 63819107, 229983019, 819474010, 139672396, 393862954, 415958629, 515963819, 169895917, 199048033, 915065038, 685876802, 659660951, 941034076, 211501338, 646809574, 249999335, 208570952, 929765614, 277339755, 321032424, 773073816, 977283000, 996625913, 139368932, 985536663, 121254152, 701288007, 155892817, 923458012, 589710977, 152501027, 56984121, 296354121, 25579211, 937494850, 286655508, 568419112, 1259577, 826754108, 12740259, 250428550, 847631218, 37516630, 219843911, 851280733, 441193945, 779193822, 2227921, 571738432, 509729281, 735725734, 191676575, 273010405, 207621090, 435438269, 406904429, 175494357, 249934750, 649342899, 155722506, 113961494, 338534515, 238448160, 669025611, 194643748, 123739064, 132130403, 687042956, 453464778, 407753794, 408137799, 554947854, 606902495, 776914053, 804456791, 654618274, 686639006, 172774709, 283683046, 240108797, 616216591, 221615296, 582837217, 14404079, 815159657, 939944040, 433311577, 891162046, 44455037, 606242558, 741428062, 489306511, 437201858, 61391895, 15990011, 421931051, 672503789, 134270203, 590261814, 319535772, 439451340, 219461259, 123966945, 983802622, 946682097, 662127520, 622620647, 587746938, 275048894, 884861771, 654927941, 308402647, 868946320, 715339293, 605631156, 337953435, 482657479, 264030905, 92423503, 503576915, 138646205, 562411478, 370612612, 50676286, 231807589, 418915451, 215768385, 714549493, 945806198, 307886152, 147982532, 393842458, 419781815, 995062506, 620512972, 156418339, 520875395, 361757258, 187265501, 412531784, 884629437, 982106497, 916756386, 430881479, 418563182, 425225654, 738489894, 660177118, 371607738, 987329962, 412596827, 674259944, 359699633, 263537825, 166398045, 778342456, 435215287, 750145506, 570235185, 336650486, 134177089, 546300642, 143934032, 258813355, 832878352, 88148753, 28660531, 979012583, 335324256, 895901747, 196059404, 957633693, 133642695, 974067434, 916533682, 137488337, 627560626, 55395961, 872970910, 438699494, 576883341, 829218911, 481795242, 394075832, 958244207, 237635886, 399573710, 514057719, 273133138, 547396918, 607913491, 826729861, 563810342, 327035649, 79911583, 819422298, 233202190, 883138409, 569451198, 621254625, 358406114, 155712449, 774141188, 15573377, 535177235, 955299867, 703347262, 216593517, 714505726, 811701086, 510616134, 362380872, 19655641, 692945442, 646477224, 970057678, 520568348, 296488162, 419448040, 363815579, 4626447, 49224277, 57610204, 682905680, 969705364, 842217798, 99235851, 160784673, 833907818, 771715050, 990424541, 662121267, 745790214, 912651229, 135174212, 528032449, 607385816, 951659960, 617821682, 37654401, 341824586, 182912597, 713330412, 937535703, 832293347, 532814680, 645562036, 115189129, 685040393, 186348807, 403719419, 532559258, 305306559, 760869167, 16631826, 423871789, 184658805, 526807060, 809389313, 996653205, 484781829, 447484898, 162885793, 588587872, 455997802, 902484503, 968639187, 895891432, 237575133, 53240534, 26099617, 253621323, 153183482, 356798857, 416246295, 302088554, 157632391, 201832481, 666788382, 246298481, 481510685, 241732013, 440584432, 354903651, 186376325, 253814770, 361745001, 320797921, 864761616, 213939765, 751217632, 582796581, 518386137, 96194298, 592479978, 777103835, 340421254, 387080631, 93990624, 605146271, 35809317, 698815079, 916860947, 70301374, 671889010, 798095799, 332481333, 388951204, 867475509, 598762351, 36702284, 567013981, 32261238, 525365539, 727074930, 665367154, 495416461, 19641625, 124963409, 82572646, 700820109, 583582495, 865398976, 557607773, 940561332, 387508074, 93136074, 268957080, 320692666, 57964992, 198307748, 645527661, 388964666, 163058711, 659381964, 724218791, 248902616, 990307343, 801164202, 818391812, 956171507, 608937158, 134963914, 33794216, 266610851, 713761650, 704931882, 213377618, 958701686, 90217961, 242776519, 837178185, 262589912, 230435345, 739231912, 960181114, 900466596, 335443674, 495478156, 76010677, 755314606, 756622425, 309643853, 215140406, 241691601, 371207164, 963418680, 556808466, 655480532, 850123748, 586839105, 706365970, 975132516, 306305531, 395754287, 380868958, 239696927, 462353770, 993824432, 300152817, 767108517, 27708445, 53527084, 314960950, 728297061, 390123720, 932101006, 271213955, 295336532, 445720007, 154427832, 237067261, 627109326, 637233393, 922029285, 949670365, 193090984, 396644842, 245850932, 203098489, 312689540, 128989877, 336159993, 197440367, 899119539, 41716413, 798054190, 379295385, 52917751, 643684987, 956040529, 939261594, 439783837, 34875409, 862960494, 432680647, 862584127, 497577488, 58675498, 706117312, 761517502, 878284394, 594285469, 935282850, 642424813, 230228393, 140523677, 931029802, 83003580, 203238091, 36990884, 114494172, 703982795, 680511010, 986072402, 151054305, 679165786, 712045336, 462150010, 584581720, 166210617, 701636338, 773736304, 502213492, 525541796, 397447068, 148877688, 122977358, 15695162, 503327602, 918504668, 470750362, 68045712, 511084203, 157185475, 56398151, 463486120, 706932477, 723442170, 369726044, 850150461, 683562592, 718100622, 471926063, 480321749, 868874218, 901572986, 177031012, 934977736, 261723186, 576342966, 708840977, 927299013, 626699863, 923495783, 250747389, 72256219, 36774048, 253580880, 478967575, 116234035, 796270929, 583427994, 472496522, 392239424, 311777005, 266524211, 807475341, 235506609, 36414040, 236848202, 1621700, 823695646, 147514867, 972831329, 460241614, 309960995, 217528234, 961649744, 385117374, 221570813, 122439384, 613391289, 175420173, 233328380, 818151481, 386528273, 858648363, 513806192, 569128923, 704773832, 548635063, 951990473, 731126853, 503459001, 136835003, 611418421, 786378016, 342825145, 322870520, 884751914, 834158, 893116051, 814769789, 180386681, 553325635, 54949946, 447564141, 376125603, 18891653, 921317913, 62009545, 803736146, 49591445, 688916890, 6449812, 446280884, 121261843, 549210344, 632888375, 132703681, 565142042, 475460521, 871759291, 525066009, 858089100, 550416261, 74825200, 356892938, 988457785, 96602396, 716449732, 165292419, 502288858, 667685155, 362008118, 77042241, 740478036, 791886174, 683646044, 250361963, 395791882, 316811565, 498566202, 367924045, 221236781, 586077933, 709905411, 31646383, 604967287, 106361363, 9815411, 793646625, 20449172, 172400664, 41696834, 689305334, 887906484, 79161381, 766839422, 131631736, 990639503, 648925393, 401176951, 169041291, 403194246, 307994454, 244516492, 121842841, 297582107, 165764575, 110689301, 707938344, 507585446, 131564823, 99031418, 566263319, 412397861, 246165934, 637617469, 34728402, 796630018, 242567121, 308801926, 77278406, 593938013, 647070826, 555162935, 466127099, 272245309, 362644166, 55983004, 146187625, 809408580, 381326636, 249662235, 969850768, 881895285, 977837013, 536002255, 557862195, 133879029, 722522029, 673985288, 83399362, 943186330, 271499309, 869215971, 696356104, 645107258, 926235621, 278237042, 27155985, 495028087, 502317871, 862226798, 64797760, 96709537, 985787190, 840923162, 669802952, 165745913, 170380926, 788508514, 359080226, 94054938, 126706091, 540841293, 568655193, 489140684, 524390910, 241898706, 549642931, 264993225, 261261360, 902640886, 160330874, 220493213, 565781831, 925422148, 514240734, 773198734, 960940978, 574245958, 974826429, 246914280, 394923358, 586075821, 98410036, 486626048, 158785771, 963420576, 187273676, 790507568, 604893785, 570680100, 425001297, 160809783, 612110845, 748935210, 26249989, 917309290, 30250364, 82455739, 986034454, 658715611, 79092922, 422150, 398005204, 124629286, 283689033, 704601261, 873099933, 660181210, 825024500, 392713988, 518397918, 136866645, 18740502, 140139137, 350177170, 270485620, 568082197, 554075640, 478672099, 857126308, 391053769, 946959617, 426941871, 852297892, 196112267, 178424918, 322412005, 573089882, 867110964, 435411215, 729174996, 604553895, 500169141, 149103995, 564477679, 991491276, 956622701, 957652842, 13326136, 675802353, 716041271, 401444328, 254241441, 503713555, 932627327, 258468212, 920537467, 349155074, 253763050, 642703689, 523173399, 874181774, 142892254, 601273595, 95514609, 159622906, 964672210, 380689302, 801456873, 29596914, 404104619, 84160792, 487526056, 399731745, 968790984, 778571363, 291742241, 367159536, 957087347, 265692492, 96908088, 175848357, 493240979, 556473718, 55315277, 874495945, 433907776, 714471612, 688241347, 760258452, 567712594, 733121291, 754200620, 358028371, 244178894, 330392084, 710474102, 389443991, 987309621, 661099649, 14551026, 969551263, 528108260, 411757136, 268810878, 131955197, 207666874, 32282129, 503857517, 468122360, 2096399, 822198379, 858398687, 533156753, 935999970, 434490254, 958066630, 737676683, 344781608, 122371285, 810632760, 922765592, 70336928, 897952283, 796500744, 854522270, 626417742, 480874631, 122011863, 686554425, 659876614, 88598444, 198652156, 488002308, 872035813, 18522576, 60209394, 882594474, 800172760, 470183441, 695288405, 383697648, 180506689, 93865794, 435173522, 402930679, 951414741, 273742431, 229725546, 244345455, 885225936, 650815246, 967063348, 812167658, 127142839, 861560726, 110964828, 937950576, 509329807, 992141428, 44456350, 168038655, 303555790, 503299515, 341968047, 415841205, 567584902, 309890371, 878297179, 625831112, 954176421, 317848207, 275278120, 929490219, 408885047, 362124902, 408558987, 424278545, 809946461, 337026675, 790386140, 59550813, 515149443, 71907408, 655971323, 320675378, 530600794, 851838825, 184184242, 242850548, 470535847, 332124302, 186223658, 116364933, 445725698, 630459095, 653222011, 141160536, 409559110, 214009636, 496541855, 501817755, 778211330, 924549291, 321179214, 167422737, 225796685, 498299249, 226682939, 229368737, 18140452, 473729732, 410484898, 239087562, 347342381, 504064050, 779221618, 292389508, 155406182, 222468064, 804275226, 809038119, 404652089, 562950581, 578482656, 993592713, 138944334, 78575999, 235193577, 761120874, 166524951, 107058457, 998490400, 862987481, 563865748, 803418349, 445110247, 688815393, 754612769, 347913883, 637916230, 510782515, 493113188, 699322111, 482817333, 444679564, 518131230, 930650484, 677264332, 739644283, 57580555, 452053739, 464544388, 810252122, 458358615, 57532318, 452809599, 670451973, 248036790, 898417731, 705026421, 770255139, 483525946, 926716025, 182478603, 663211721, 609230155, 260568595, 398234441, 347457649, 544974104, 684135245, 947393399, 531913556, 332412965, 269045873, 512977311, 877441353, 847570256, 118597822, 952177070, 542653608, 785272996, 631533228, 727715458, 9430451, 264117438, 343498628, 778780766, 712700669, 623330019, 889150486, 77948443, 479434158, 439659382, 290258434, 334082366, 671803316, 962025934, 793123416, 744385544, 967916616, 282148752, 350606331, 390853178, 731429273, 339048711, 218288996, 237928593, 867022674, 674765955, 961094633, 814241216, 108950867, 332172947, 466045129, 757440520, 813347781, 644942728, 223991302, 974316495, 586698951, 538360187, 202568965, 868496722, 121338898, 627166290, 892380459, 307778822, 497433093, 271376141, 539165967, 169739971, 716359102, 377527371, 844493220, 999108659, 395265904, 675103802, 36719103, 90579616, 946502853, 1870113, 29636895, 545818107, 849911264, 83691403, 386472006, 636560045, 816259553, 19156925, 82734310, 982172706, 229814071, 638995259, 629673147, 867456561, 981959160, 466948162, 87438948, 109040969, 968704443, 790394668, 430725449, 169604452, 349069203, 187135874, 266612434, 369038881, 558748393, 2167218, 325605863, 845295654, 499340891, 542126034, 741446959, 644099949, 767441494, 87929566, 796404698, 900602123, 510019814, 917151294, 521631264, 861431091, 662923645, 733898580, 997536439, 358561639, 773324823, 897572194, 811643995, 924900222, 867134997, 903715896, 551744590, 662123416, 704694604, 674211031, 146676134, 583006957, 671013566, 738955638, 221777844, 792889428, 540862294, 56443047, 353263933, 710750027, 386774640, 854825990, 860757106, 713488359, 949734562, 205650659, 358394600, 514313964, 686851240, 915286879, 19837892, 922449408, 131113693, 467856441, 542938797, 538336745, 384870933, 301359763, 159197785, 430284056, 437677070, 729744752, 398163064, 876188742, 302319293, 938448815, 513983646, 582326136, 862820588, 370944426, 369948661, 739142095, 679284280, 705449553, 65187039, 843652014, 5838032, 744333185, 681406568, 421560831, 826736006, 833134752, 374635804, 917056143, 34623613, 336297035, 123835320, 885835023, 161176944, 564406912, 845135137, 437410831, 972012565, 143950187, 641349353, 713530802, 246996485, 863004216, 217560090, 724770229, 111994522, 775022493, 201827834, 572532171, 96352135, 480958732, 444526518, 856378988, 777701076, 799712602, 219133589, 239289555, 654693230, 755189387, 260166475, 355347678, 75045694, 934751079, 69300598, 579641073, 653428482, 573976021, 797002509, 39670437, 219269192, 231487678, 959864461, 66454658, 450895327, 604479000, 825735685, 321073724, 164764304, 943768237, 898056682, 765503896, 823998491, 618699010, 368518391, 356496044, 905496346, 154451659, 321475137, 632282360, 790861491, 291340112, 342418090, 132153352, 909644081, 28747995, 804138703, 814245989, 454358399, 340982964, 516123055, 460402220, 542933237, 469429442, 148830708, 721604081, 222668860, 613131171, 691934788, 99091488, 848050498, 60094179, 71477799, 352541436, 82243852, 609386559, 245479521, 565060927, 47149771, 228735453, 6581690, 845825130, 208146500, 624839494, 15709241, 494070502, 831777088, 476386270, 580617461, 139684343, 555877770, 398089134, 488251706, 239719221, 808211235, 753876188, 901169485, 389386988, 757012817, 813267991, 390639218, 176096993, 423205366, 586045255, 318635332, 410660476, 784676579, 793880968, 794388805, 330478028, 254993845, 910240970, 573655964, 486869914, 31942728, 610204527, 260239947, 156985997, 840771323, 220461555, 969443174, 361644141, 616190109, 518482704, 122732765, 344178546, 496759504, 819024699, 838640527, 249102712, 948365092, 949841310, 116477840, 266347593, 2298691, 999282771, 901736044, 203059334, 486108963, 262651366, 226765553, 929351844, 38382603, 696520263, 765318683, 757784286, 696435484, 973428739, 491549637, 747822192, 935064248, 153790079, 634718974, 843279091, 302188555, 661792657, 366975577, 659421564, 155362576, 89960194, 550595268, 239015803, 612528645, 88785169, 685103314, 120704863, 166036874, 553239780, 563284244, 669126316, 722712147, 329807981, 618171665, 371370129, 636915973, 76837487, 316973886, 854944324, 344871088, 867851596, 59922136, 795643393, 432325097, 747235283, 788175184, 313722207, 773550865, 761904602, 730038692, 229128541, 849934376, 107553622, 220915838, 900828667, 579296294, 906041376, 707813323, 428112499, 711803545, 923459706, 793881674, 959213414, 21425202, 282951992, 79046466, 45902439, 598838860, 436851453, 279486292, 622216750, 462414212, 831612898, 450164185, 617105642, 203944207, 1648066, 722573131, 135171280, 585320280, 944782289, 34020102, 574935943, 261871342, 197636296, 642033071, 680867212, 229604059, 226152274, 911035892, 985434731, 211336455, 439937386, 399727084, 194624987, 440856193, 329235952, 792796909, 324920720, 335308412, 136435663, 175256847, 719135528, 67571197, 857962481, 170259372, 206211518, 428934409, 937626322, 732060613, 717812273, 275189376, 484692241, 466019874, 95997751, 879994813, 348788866, 942308568, 420757895, 6635507, 422376151, 793723481, 58778692, 821596714, 934079767, 490174259, 377623803, 954973405, 242527416, 642709539, 938753366, 328888245, 547216122, 792772352, 613350940, 653167233, 749495581, 872169733, 400214379, 447137053, 918888491, 670849849, 265472231, 556639947, 591248025, 233209301, 254167765, 983690647, 127298261, 248215309, 164418157, 414459993, 45469879, 729130992, 625867548, 491167947, 242639528, 328331477, 149097010, 606333430, 384760496, 568569566, 500743331, 766038112, 414266428, 663222285, 275127042, 113593486, 306642360, 187845127, 625850587, 103232750, 742855702, 597306114, 631816597, 843659989, 214946958, 644178036, 42024831, 39855762, 275974843, 372169792, 642987397, 96198426, 227851691, 17859300, 356420528, 766177787, 517348662, 462756787, 214739898, 167777550, 353686058, 523873171, 660284771, 697534105, 303192007, 382750052, 516765990, 267516377, 120202025, 971260014, 513538512, 802693193, 738417929, 749747101, 926322537, 533577925, 52865376, 748682465, 881111389, 477280, 492379048, 178302066, 764319921, 418528857, 492808642, 574711201, 944531575, 926781795, 508287088, 829533965, 224073059, 224490226, 965072871, 733956916, 532921644, 581467849, 916237902, 520574743, 6521137, 409442455, 428617303, 282128973, 260270592, 695313585, 606743726, 599839175, 998369446, 503071182, 711727791, 923079682, 376234982, 83508723, 39666946, 252497030, 857815927, 523162639, 654594219, 871933272, 838738739, 170462384, 774824464, 321323109, 673882768, 550550277, 149177753, 173910018, 540075905, 755592285, 109539670, 803580808, 116877202, 950542632, 195995748, 52241548, 657921216, 354671176, 244682556, 46174967, 49526080, 788226425, 528278361, 149668938, 398806938, 806738937, 939227850, 336483523, 535015107, 356434914, 995190185, 55842587, 812896981, 642917948, 583783892, 68034980, 917865087, 909813191, 955424164, 544481779, 143760853, 229365863, 776485111, 621914271, 348301490, 62197167, 469638880, 415574217, 819263356, 455900542, 362302032, 751136208, 173308239, 61795258, 976911004, 570155033, 324501790, 848349013, 289062671, 811242516, 968862867, 972571006, 421521930, 283500477, 42721340, 576874310, 359023122, 332776858, 680493313, 685388670, 714301453, 332994652, 667067869, 566306364, 873381686, 574456625, 469654252, 155410096, 25016091, 128099873, 817576623, 196191287, 647558464, 70407975, 418521706, 190216177, 304636583, 271018930, 830365370, 905248849, 534027951, 767118411, 919630722, 822904255, 543624677, 270148837, 15739290, 413847892, 707939197, 126995305, 371005453, 355874695, 656187001, 590726488, 580937327, 733476256, 489426963, 518222606, 939652707, 837520726, 829642043, 337095910, 87574898, 369719343, 327408418, 749217512, 632585809, 360279800, 265377621, 541589181, 826119430, 736539326, 429824035, 286871677, 732791595, 421855628, 832749438, 672795322, 627646964, 830864039, 812062053, 767602654, 69647918, 527365860, 226083954, 335639095, 781588385, 682430957, 324520460, 604530081, 737101935, 842425470, 642077473, 143911348, 872713353, 478776385, 921782995, 594617257, 121278691, 126836262, 438984868, 975689567, 708394629, 13046918, 746857095, 402139006, 559690061, 990036127, 267730780, 4924510, 439486085, 990545989, 696868817, 352014536, 926190404, 597502414, 750930651, 277123584, 32531865, 650104586, 871544921, 629970186, 253417647, 612827199, 626802869, 637379159, 90554676, 580870784, 840108061, 432024639, 597615808, 921819508, 850571743, 828302344, 275903218, 120121697, 294731973, 109650926, 592233220, 146760595, 255813433, 995158033, 366033574, 538561899, 818929437, 284671696, 669269635, 967913901, 799896894, 791088451, 112018883, 938438938, 978325519, 786014357, 294896492, 475302792, 226530837, 47822048, 219432695, 530342239, 415672056, 609107080, 512198772, 278350096, 776358226, 903967310, 227125355, 790738242, 989821838, 399646492, 501688106, 426912941, 53714056, 325926489, 603392369, 7956186, 513365468, 448817747, 356189116, 682755191, 785278994, 302930560, 4887645, 32495136, 420771325, 253557488, 150498276, 331929647, 229662115, 647151712, 211253215, 798943930, 107688214, 613344529, 949639545, 253399043, 91237755, 39764918, 106340123, 738576695, 251874521, 91617134, 902661074, 103435815, 420992693, 138996151, 727238082, 124060158, 761560072, 703720014, 787542549, 578564928, 530796477, 997880675, 852388324, 711655673, 801866248, 378425566, 151910180, 833275358, 180140184, 27665622, 601611700, 496425808, 322959666, 69762767, 207295020, 509128360, 864202187, 909533482, 167735924, 786882221, 848511718, 495581100, 882194427, 866622712, 945523744, 361338881, 886680048, 581548004, 355562426, 561238054, 935591228, 371791931, 158700258, 240630484, 988331346, 519866645, 335769380, 972864435, 88413753, 405940929, 922686190, 414951792, 72995797, 675687445, 318722720, 818678721, 122126149, 22559903, 849572990, 725502602, 805059845, 249596072, 118978433, 484370301, 174973556, 425165449, 568358061, 145649023, 906300620, 900266496, 832883587, 561522816, 416917852, 541203065, 187629512, 754463146, 356559754, 350434905, 427864503, 455247638, 105883613, 453809778, 546167750, 520292635, 772592913, 96531603, 768810868, 376268470, 926986227, 19195772, 877086506, 148445098, 378613876, 928206358, 58139468, 359885518, 121074146, 920402789, 485944931, 589299886, 301655780, 707094477, 292438097, 934386777, 201213970, 302482617, 845443583, 299243505, 365339985, 354429735, 467274881, 185254092, 941212596, 857868759, 278677370, 522804119, 204576323, 760282905, 372608801, 885662332, 64349328, 775452077, 406371629, 927111191, 501940897, 778455861, 90917601, 226602612, 526668808, 937147964, 80965348, 752257531, 774339413, 582233645, 937196562, 160747008, 806093001, 787775377, 225037055, 301852918, 595482702, 891790917, 461643635, 618006774, 450086405, 379600332, 828460204, 70264913, 555014408, 35327232, 771591231, 524436999, 75166704, 220154689, 398408658, 125723811, 930279628, 241245905, 432646563, 873622225, 439954122, 614544646, 68723745, 243882743, 388916921, 888959334, 403606451, 227769267, 787390332, 288331330, 935990516, 773428685, 866573175, 992451479, 807471575, 9630840, 818977831, 786835433, 889458372, 323987081, 572269927, 122399180, 197109812, 457892904, 794550984, 946648280, 338800747, 402109, 372674033, 237417690, 553444013, 788790919, 543372422, 715594293, 649334507, 695331910, 320474450, 647063193, 195875221, 294732771, 292278120, 412268070, 185569163, 23358477, 106305299, 936751091, 58577085, 173337605, 257723273, 741957898, 915388308, 871345814, 454760250, 878266335, 823525375, 475769769, 119318069, 205121151, 840624614, 826681570, 711177158, 618532778, 788365825, 230718286, 50067526, 762135413, 322691607, 805734674, 485324985, 919011950, 635605742, 43148077, 690481169, 127259432, 24141686, 184588493, 718586144, 790200303, 35297275, 658827629, 168759643, 302950434, 17984640, 240521752, 813568413, 468670956, 409809617, 572313525, 181650630, 464462276, 47027368, 713667032, 995976151, 262884129, 996611323, 970132270, 114069014, 125921261, 135507660, 951663487, 177495197, 374712150, 211678970, 952300344, 530295753, 126271459, 373277154, 778258194, 132458376, 101457785, 753378331, 647677507, 442736585, 519112814, 917178424, 148150892, 473279736, 853813014, 401914543, 387834387, 592932528, 858253879, 748345644, 411663133, 564808682, 725557251, 520959003, 175704925, 656831785, 394019522, 558085860, 561437676, 599596041, 104316987, 794808098, 260938874, 672085096, 948737337, 709954591, 335812289, 850083654, 219945515, 227797614, 345255454, 924304698, 481917706, 137831853, 472136179, 3906831, 108459911, 644253295, 455130133, 53305638, 889672366, 748572372, 495855437, 436806444, 204190161, 463459432, 24542956, 999754144, 427944850, 209605557, 26219687, 51379023, 184713512, 924613916, 289720717, 380785617, 942116830, 507057178, 323435703, 731974243, 484265032, 847082463, 900060031, 853655519, 134387895, 240825415, 297306275, 681141580, 567251326, 755267055, 915025151, 445899255, 947670732, 442190176, 733015426, 609745755, 565461526, 879504960, 736191441, 376640501, 912508120, 610463044, 604977494, 206885862, 1715149, 720632122, 184460621, 80372358, 720198923, 589960288, 817352042, 938331286, 340155319, 105913402, 637975947, 328665705, 618403389, 226787666, 597559520, 128199468, 47231306, 264163492, 485919102, 234904141, 942568019, 827540545, 905092303, 911317425, 840240904, 497644600, 494939415, 663343559, 918279072, 384570810, 586630523, 65985594, 170084352, 890542203, 59381112, 740821848, 268559242, 500157664, 254732374, 984705593, 372159649, 371642549, 755583692, 433477416, 368924644, 601239758, 670473318, 961630644, 155028377, 236033264, 99016381, 68759617, 590471092, 472573122, 126440634, 380431413, 940357931, 783455596, 235846233, 943517116, 982191222, 80766092, 633461530, 872816251, 176574802, 352875640, 399256339, 263715568, 832902545, 414752285, 841779340, 195713556, 78443801, 325158883, 177917222, 161269184, 142097928, 177223049, 580851494, 889440444, 352897578, 27266498, 908335008, 127602225, 292431051, 919024252, 427800126, 938335764, 564955411, 10476307, 541527624, 705165648, 808526134, 832695451, 175843264, 746701052, 511146, 625248271, 788594390, 653414038, 581722401, 212299953, 909796205, 405127185, 548799840, 475876390, 554050990, 347433827, 409274913, 605635433, 441401602, 79939981, 22311452, 67476254, 984803615, 8423383, 652237951, 7306549, 692263885, 220775034, 166029117, 145706597, 277948123, 457924232, 890893748, 596296250, 493135915, 52359655, 407675721, 870236379, 124708305, 267525123, 827538706, 568527938, 926521585, 879304852, 994684964, 945303813, 257107914, 198182002, 192109938, 146000239, 431576917, 757259720, 44917291, 959948146, 228022185, 699463125, 869841302, 295318798, 138057060, 521100918, 81409604, 628168317, 537329240, 742522972, 424909703, 21482618, 713468212, 88476623, 639271767, 601225161, 995012428, 808958790, 207926790, 967986682, 473124863, 746554706, 388344110, 925771202, 25399934, 559124622, 37412049, 942306407, 499614746, 594341873, 101170032, 875729191, 669391768, 47510460, 98611226, 152691145, 94955927, 957419216, 431643211, 663239629, 37293646, 548727501, 612650620, 52514238, 124382652, 326089653, 598990124, 508803046, 896444182, 714993175, 526377589, 450395952, 416753620, 238263106, 647799027, 746821957, 882738510, 611705653, 303626627, 205348039, 140994111, 348265196, 687038492, 622535202, 883050635, 90014530, 208981682, 940776351, 334740123, 157029250, 839564794, 299445314, 192198503, 482039339, 715977953, 626980648, 178628143, 512322651, 572182416, 124236312, 996422068, 665608666, 710103110, 733634540, 14679406, 911975454, 12850290, 348920, 220787217, 274450813, 430241, 517960577, 928621007, 739821169, 606819494, 923154202, 454306819, 877220310, 193243933, 850007471, 936668266, 657078809, 731384961, 920906473, 604261325, 118453075, 553506464, 826484465, 388720869, 155816885, 302063168, 360764504, 932486431, 601265047, 911781188, 274259394, 462132747, 326790901, 89797499, 308668208, 905594962, 488982636, 948896163, 385579913, 665246785, 838834952, 281768147, 964252780, 824638738, 948929820, 95609220, 840401152, 341263717, 65633847, 114562448, 965340085, 251386721, 872894789, 965247770, 854402734, 659495457, 697315318, 573609889, 627888422, 41268959, 511148575, 514441669, 510284970, 212140725, 969797648, 952857793, 208917240, 414373949, 195288766, 637284547, 502003415, 275091721, 116789432, 16268619, 234106550, 634823566, 600195552, 415019485, 521223749, 20503395, 732988482, 786701485, 780473204, 521918870, 859960745, 355201868, 731050004, 761376684, 270371230, 501660506, 31426368, 905645327, 724981854, 926225199, 520551587, 975597783, 455471675, 134711879, 587937241, 879083501, 532346064, 651929500, 653999017, 242875617, 633268313, 605326650, 913622372, 568424081, 945830236, 804863826, 184591923, 134272382, 313400572, 249696720, 387577701, 480809799, 90379593, 625096151, 907623960, 963116800, 283852841, 151487885, 652995246, 308495526, 667190813, 672457804, 854519824, 656493142, 598678353, 677742322, 866100767, 995299318, 5441336, 453386657, 530794739, 996438297, 405317869, 768083333, 94053451, 949767889, 284346687, 56910636, 626212228, 307254047, 313460148, 81845638, 702926330, 82921795, 788214251, 801754087, 175666172, 662055809, 444946448, 873291, 133908176, 145721947, 875783435, 490242130, 607644266, 954302047, 968722814, 594404712, 777988557, 565074695, 15756580, 740064545, 126799192, 394790768, 192870557, 94939267, 16159240, 320471373, 230118543, 660901678, 811120686, 146555500, 119299896, 331410887, 978171190, 377081306, 887050231, 850974501, 920864142, 99797674, 777227052, 393240077, 154838872, 697004024, 686680665, 348743475, 668178099, 916756140, 728839801, 440672671, 205184323, 751989559, 750918571, 930567482, 44610575, 262546703, 239066386, 39461743, 948532565, 436473144, 533334424, 926038615, 369734225, 687321319, 140375707, 233562565, 202775662, 413557845, 477907511, 977538846, 932700439, 994543297, 144363855, 41077759, 938382635, 450328719, 286843880, 259363220, 851690963, 219288483, 101053916, 145906278, 341626459, 385962357, 6714421, 617962845, 84696079, 630969124, 967235563, 799922085, 723615158, 519685527, 10718197, 13208133, 598313565, 649082218, 401593284, 207002530, 769402649, 207888241, 932189213, 945265418, 677398103, 134199381, 65823175, 945697642, 739475539, 866281538, 629397285, 178558513, 399078838, 91574856, 958679726, 28573789, 76782457, 362490425, 689006157, 534228665, 403881214, 393232767, 366901064, 21894306, 810318200, 141676310, 220541944, 127538699, 490639858, 570099338, 601087001, 158340453, 420264139, 574478657, 221742408, 790013401, 109342712, 10446304, 245097414, 479259504, 448917005, 715014646, 940249453, 261996878, 346967624, 85745964, 589927206, 747251040, 316502276, 850151804, 788355209, 231832611, 623911943, 508059149, 847712446, 915855913, 276585233, 583947638, 949275539, 834979726, 645668088, 796443919, 542503830, 208521861, 954189473, 712110660, 973082448, 296091585, 168851824, 389181249, 174666474, 518901764, 726989917, 318136596, 701799474, 341418912, 515971830, 455983266, 46395050, 264871800, 342701478, 355344961, 657059471, 827892016, 779055696, 22279918, 248539200, 536668314, 84509287, 76948671, 993771609, 626241566, 283639544, 141061412, 196966662, 193070139, 306952458, 715198105, 552301356, 660660812, 545276118, 677986683, 971912660, 299016581, 815364193, 481252447, 173803035, 522363709, 348288060, 604647236, 399456502, 995716331, 385613838, 823140621, 478581614, 929773671, 154526467, 427598931, 241290062, 476694180, 399683528, 652126863, 631411758, 851735582, 913718443, 416413042, 573929557, 253553541, 157172760, 56260036, 656645748, 121930001, 400200215, 951597618, 86484406, 779032273, 491112844, 49314393, 890080582, 860966307, 569629823, 552397335, 188657426, 364835770, 17239143, 457750836, 110970573, 205846746, 398922545, 137617103, 432265080, 957264541, 65050423, 251461280, 312185153, 647136771, 907075018, 821858743, 284928303, 688633487, 217481955, 491888410, 776098483, 207635796, 864834501, 464061678, 128302564, 70486774, 246564277, 856899198, 2050855, 689062054, 101731176, 917919223, 316205638, 400132221, 961559241, 325586271, 482758023, 943300703, 488610143, 187427415, 516354666, 26193857, 698294257, 629876325, 831860690, 571892050, 611553982, 843661894, 1182789, 881430494, 955982284, 719494103, 405241794, 601289748, 789601857, 887398869, 277691690, 217258262, 23216072, 922413047, 719433567, 409020255, 649450805, 163909418, 975909729, 766611252, 644366293, 153648842, 752925087, 326346668, 5188858, 685623909, 352089058, 641118373, 441795604, 572428529, 958221734, 280855149, 503777071, 690791281, 315481627, 534070105, 344212740, 808598172, 953584388, 691811153, 24706791, 923605569, 534659610, 958274210, 577190526, 138138656, 137717428, 717506530, 183960185, 625421620, 878746949, 209668786, 464536495, 61237058, 454336265, 57617916, 870179965, 441405371, 219075041, 291060840, 881938908, 109933709, 572084170, 436220987, 73987128, 759053835, 639333770, 944061782, 878774815, 186851177, 990566985, 487013443, 699612634, 222514554, 463078926, 956494867, 109266135, 754921553, 674911727, 872935517, 684147289, 625062747, 358189424, 531386549, 106751365, 481149362, 994008199, 42699368, 170879805, 43634397, 498743932, 337998452, 905408477, 386451773, 699304789, 25922102, 637006311, 884304512, 667254602, 588268529, 814507814, 881999137, 138304788, 671635863, 893760002, 990361081, 274901961, 209088730, 345696207, 983929652, 182294352, 176675658, 472257674, 553847394, 297418712, 565036123, 707937199, 245584258, 412108917, 98650995, 154654211, 400526203, 10890228, 347495463, 785899238, 775316076, 259193905, 534732550, 250568374, 883668454, 545778387, 212422406, 271985852, 935459793, 187961387, 82496432, 386031416, 283607997, 411531761, 861541950, 560479714, 229463852, 970652137, 515822223, 177700926, 439043014, 973672303, 984636667, 988980601, 912369282, 743203086, 866603292, 939869358, 494768150, 573412822, 912563141, 710904053, 913016717, 6515024, 404130631, 440381106, 704923174, 271073401, 628671003, 356049428, 693678517, 70259849, 345728275, 543556011, 637818098, 303137938, 547285197, 869158514, 92536957, 999784608, 747072333, 692763646, 773618211, 960975627, 500318951, 34612665, 541380411, 297916027, 372342690, 433976213, 105300526, 304583507, 334667869, 750022425, 973216652, 212638837, 128867026, 427510060, 837122243, 548250557, 972569213, 980183484, 593042800, 21396341, 40422421, 684027476, 986777196, 441330325, 452239514, 416822655, 160639182, 229706301, 699970831, 243901674, 552877891, 856929582, 773478426, 752192240, 581396474, 872867115, 323114628, 775309025, 659944452, 274788617, 129622636, 636871750, 624368398, 153342923, 349531907, 531827937, 916819914, 396034353, 934153520, 184510796, 831489295, 17082292, 710816369, 922644054, 971528559, 527816215, 926282172, 629047397, 520647739, 787047873, 628955041, 54468972, 895989416, 690433023, 139548081, 831362604, 97413460, 18649673, 409124904, 628352990, 963397789, 977528473, 363413722, 166109445, 814529530, 594475352, 989000117, 159310563, 43837844, 370144256, 512301061, 666933833, 838581428, 258350545, 788690143, 323761104, 41357671, 773090349, 751496547, 105042960, 462048564, 89726979, 118102612, 25428148, 541781741, 125728118, 846383032, 712818241, 377981031, 184890230, 981846015, 947010855, 418140804, 445841219, 420163411, 151034654, 271613448, 966665601, 56202849, 782855700, 221861879, 869450258, 395089608, 823126955, 175641533, 378475737, 605081560, 163062239, 595606364, 632571054, 521124462, 517792514, 175239021, 207155712, 884965761, 8586737, 447999066, 17977821, 260645690, 221477241, 770417626, 435759670, 574437152, 101838036, 589094863, 686797419, 63579588, 264463546, 961956550, 875216834, 398712495, 228219316, 667736271, 917595534, 578759047, 518400126, 410317599, 610335603, 916562072, 898839232, 455481361, 589143194, 431588890, 106519373, 568699843, 828336526, 983754866, 747392296, 308133340, 122836531, 845080956, 877407155, 615848834, 334828729, 177839767, 379178903, 103926398, 581133903, 567443869, 600063793, 227196810, 362743726, 986133151, 44396796, 899155391, 570950370, 899836696, 767388173, 385197429, 561753084, 949605647, 867512129, 778117587, 828016641, 905340293, 55960632, 993383297, 595664062, 512134181, 586457460, 412433211, 867666284, 71713066, 512968936, 809760134, 101085435, 923159461, 6819683, 438984595, 27826632, 39800580, 657754197, 58569416, 933249317, 2690275, 823073049, 931345312, 445113488, 863648490, 69953646, 151462367, 654577396, 429830514, 801535492, 735952463, 617511611, 132480503, 735343281, 497706613, 591878596, 276593348, 995747400, 416960307, 204007258, 318839615, 303431033, 41689177, 194919114, 795787007, 280921338, 440267514, 32545236, 381045797, 6770100, 609475973, 906381448, 48693314, 522800881, 591636986, 889662514, 6100235, 356398334, 843388302, 100086373, 714160096, 696521533, 521610585, 902485292, 259673504, 208339885, 190261163, 73102046, 823768584, 270485498, 935883778, 173193621, 688066401, 795359252, 836181013, 238656878, 819340310, 974433535, 989446140, 558692587, 393358511, 53011418, 425278858, 787718042, 585572963, 403173298, 317580240, 283266852, 144101223, 162787619, 309154980, 247040339, 3368455, 51965706, 449036048, 388539715, 528566181, 857636245, 724605956, 237349280, 991422141, 537759443, 546398519, 720731825, 478100643, 367083464, 479919895, 925377621, 297967490, 210256789, 106110223, 953688469, 592189651, 195582276, 658811166, 855578041, 719141271, 90449736, 402905433, 284447758, 326135067, 913673176, 400981662, 459211699, 498321658, 517431790, 108129349, 155014677, 404703569, 495928706, 728950782, 972585969, 495120035, 380963621, 587021389, 661159021, 145104168, 252718924, 45805087, 234731360, 325493200, 81077786, 832499336, 628068016, 617699844, 686755878, 796785178, 923815903, 245072478, 492135025, 107638678, 340116166, 382450333, 80050284, 894159766, 364991254, 604377731, 199186791, 323370717, 227802644, 94309775, 165220923, 848240331, 209869926, 257189571, 760036776, 382701550, 917476958, 367749629, 148600165, 702508123, 951424341, 152312078, 519583576, 772447421, 556820305, 91525046, 525915282, 677553844, 154787874, 537764504, 470594095, 461280919, 668688740, 851276577, 940633949, 156106315, 746856376, 958255973, 302352143, 770812793, 477043978, 226989267, 900636467, 651662362, 287172676, 441360273, 44320295, 184898870, 506369387, 200380804, 364745006, 926617135, 570464915, 403256599, 80279611, 88485626, 345478187, 554190755, 91135373, 161015977, 451458876, 462680139, 684213805, 788903312, 968733548, 613621186, 119572943, 786579169, 793701495, 590309264, 611502356, 624552399, 495344544, 999411182, 427835742, 933119862, 972951908, 35323387, 213475904, 982325262, 408866992, 304659319, 119455416, 293298056, 867887469, 561559231, 119176066, 360132905, 940942245, 151499284, 98044921, 684261055, 278708252, 393101886, 429349115, 640544834, 61703533, 965015924, 103424050, 846456717, 682626560, 79417367, 35499750, 967961172, 776539247, 803669700, 805645150, 268727392, 781363232, 331492689, 809461314, 63667041, 15113178, 647388287, 716614109, 608846626, 814649927, 216587766, 15895250, 849074986, 567311084, 809865402, 483115800, 85436865, 190227283, 403181128, 328762899, 64635761, 230699082, 384374359, 392198749, 654659380, 511492386, 8261837, 468545482, 370910023, 751189102, 202578643, 319859448, 166509376, 381402281, 399581777, 203050958, 390848273, 924149181, 572770190, 916831689, 881931010, 375570791, 297157452, 881246479, 838650969, 361957791, 995194093, 742801090, 947715406, 444775264, 367670303, 358679877, 129985934, 137645315, 147216470, 882879584, 274946167, 604446949, 957838378, 970088171, 710703794, 946547474, 808017761, 700260464, 688877634, 532679128, 870096788, 585335243, 594743934, 269399795, 813392753, 899156403, 459868641, 454475505, 530390940, 267176234, 140749580, 132625900, 60549984, 367804692, 920390939, 310680690, 623160203, 467704095, 737302971, 420829982, 948622892, 947415292, 687876561, 573626649, 774268741, 49572996, 431361956, 235649131, 779571079, 889413543, 204347610, 863302869, 846115575, 966032899, 890145595, 268929189, 70754622, 678896765, 814846791, 14548519, 304659666, 142246278, 273797157, 362313820, 577201316, 766301943, 106685373, 285394556, 376500765, 507439464, 617426872, 22879892, 394538838, 181417403, 876816753, 30387125, 992202546, 919991937, 902071518, 515318114, 1059852, 329111672, 770878140, 149547388, 826096947, 154691253, 249287527, 384101600, 261450697, 578049803, 960977432, 792148538, 937389608, 271733214, 796013121, 741657481, 694423696, 693914047, 858841962, 383657527, 268356418, 198761258, 700372242, 95966106, 107087605, 432065239, 585230335, 451614388, 877949392, 287419829, 871751834, 165172268, 402874766, 912850080, 533308948, 215791481, 138713861, 913497045, 339160856, 793008263, 129032920, 873820268, 745175841, 66150160, 963285932, 340010957, 40878725, 636504670, 897915569, 491238046, 617549166, 804061239, 486484576, 772452289, 815584815, 430287286, 548802968, 91530546, 686027891, 139003391, 999359957, 983948274, 663454730, 95871686, 566578711, 808754596, 587999581, 863865408, 783177955, 145424188, 480007288, 337450341, 37393905, 933680126, 880077856, 438097797, 472470798, 273897809, 844044585, 868773254, 42307163, 189569907, 648083160, 311634682, 468253462, 345103692, 314175262, 722707303, 662355038, 714658556, 975930319, 246977605, 767784076, 478279787, 258015557, 713775499, 825554060, 71470336, 278403446, 232375367, 575125219, 146575970, 13773578, 266369937, 301244673, 467172972, 171957986, 992768440, 641740481, 971633130, 783202585, 850858201, 11256748, 294552372, 750452727, 751428480, 133933360, 231394219, 809158607, 884024513, 11362210, 743953365, 342192148, 522939906, 699558908, 871851941, 808232446, 479754230, 772006260, 414662401, 569217425, 943617322, 660626488, 410132538, 143812972, 837931403, 838132811, 450263039, 955098207, 813787939, 755205740, 857541392, 335386297, 82739394, 953379170, 66020544, 736184959, 737656005, 545441064, 945162291, 873802150, 792943570, 399245394, 694400207, 487829117, 418220810, 81584365, 745110083, 471453484, 648133228, 639154197, 513241314, 404407984, 546722566, 276598157, 109151470, 769157756, 441158931, 236223649, 88129963, 724660420, 334416708, 861014211, 618753717, 958239184, 130282370, 693178295, 987113478, 279725303, 745774745, 892962575, 283340369, 813170030, 553963556, 552862036, 99724373, 406935123, 441461957, 435056097, 724400043, 50347933, 569017004, 464042317, 185585103, 373648331, 68306931, 759375084, 3841604, 182878240, 919332928, 400991142, 717812057, 853173155, 460620615, 656474422, 946831278, 909885643, 960609044, 366301162, 634466199, 791269108, 553306612, 494388421, 746868018, 71705120, 887536500, 183614337, 282851424, 197426410, 73721955, 137409710, 434486243, 490125152, 675048717, 931774365, 409127782, 181458242, 733932445, 755116229, 26062224, 677845260, 243888246, 245546205, 529056446, 313195284, 654623083, 495862987, 914880133, 698591935, 295863622, 266556133, 859909029, 669733615, 831772320, 274515078, 371930555, 724864355, 744840063, 277508600, 624309693, 418055288, 786763550, 287158800, 899903578, 708118608, 203758567, 574010417, 730236226, 220262487, 183733415, 943699337, 303780039, 306767957, 346308383, 736292226, 565940949, 309581765, 772468270, 7214876, 857473247, 688204424, 62410289, 327952533, 922707632, 756713112, 548404596, 421716831, 939887079, 342730404, 218071173, 726496369, 885298208, 658027083, 963776278, 563477038, 647769370, 486392528, 239277797, 515977528, 530141643, 171139250, 414162750, 908046510, 878100126, 291371724, 769171918, 288982303, 163697399, 685602824, 437250739, 714131477, 27909576, 116984877, 550862822, 932750208, 735521394, 434043715, 707565081, 107427190, 776749556, 820050095, 271022127, 303869068, 483021444, 138509457, 802323643, 685585641, 266934294, 812228309, 321127533, 62154538, 172060243, 994572538, 25709904, 575074174, 599332407, 438677803, 476834407, 167067390, 476799562, 589329167, 677629955, 975522432, 190589821, 527532598, 850472297, 349959010, 326546290, 377983412, 395594675, 21165271, 399299478, 898513340, 221868595, 230262559, 615767834, 713250791, 268702264, 13727810, 809316093, 250222828, 590261560, 330760508, 110188371, 777043603, 844572469, 73042559, 392085044, 838258845, 879194744, 372466821, 871812394, 510749461, 435528755, 594022863, 89279577, 591981386, 208915358, 985352102, 66178814, 863279776, 146661555, 461907096, 700590815, 189858459, 258087156, 590754543, 717515583, 697022445, 628153830, 714665099, 344218867, 801931435, 96495485, 269687502, 995442480, 78753365, 221487790, 446153923, 148283959, 309400976, 639948121, 864310306, 23424325, 398140994, 247748018, 289319778, 640329208, 201128997, 160651322, 482325540, 614068913, 807227290, 215449083, 393038817, 998764381, 175156728, 681824744, 846451946, 197523682, 814903615, 986219527, 51077386, 35905083, 413530752, 949152814, 432788568, 761925954, 419212736, 392769389, 988892025, 65339814, 806854514, 76753058, 963284530, 425508961, 546816711, 108440031, 236674492, 632622119, 915299919, 569185160, 525557985, 41461567, 885862532, 537287850, 370291171, 163942632, 50876788, 173264177, 133015792, 497170486, 214834194, 101210582, 477739835, 131865727, 129524064, 648831121, 539668436, 90593012, 919402568, 982951161, 653905965, 54615067, 952348534, 704951248, 538844261, 829586061, 541886848, 646948957, 218291737, 310074261, 254011648, 213832745, 812717983, 668566606, 285878433, 929537688, 832988703, 316088976, 705193296, 961808277, 644493953, 695787486, 387667054, 203663212, 204373503, 966691111, 653024446, 419082045, 875027331, 598042730, 244075887, 703662369, 71894421, 738489076, 365163701, 83525944, 366868352, 621829428, 937832281, 786104398, 907029830, 912418161, 764686537, 184720420, 315780738, 285468305, 851882451, 913053192, 644886513, 621587363, 661823266, 22945360, 543680065, 158115927, 281326590, 861050258, 306258994, 601534791, 967643244, 530871452, 960931421, 894643477, 144502065, 517346544, 446620504, 597314088, 812058974, 605365434, 471455382, 93499537, 220360112, 983177257, 969898986, 178699232, 519051754, 51031083, 308877234, 675737690, 546503614, 93999552, 179058000, 641432921, 628996169, 128832939, 557757370, 701309795, 190206105, 707366397, 805336835, 428616069, 751230835, 201007530, 742285783, 68687374, 11588900, 22814601, 203883159, 470399704, 28339016, 227423214, 645415317, 699204445, 921085599, 415045220, 248889411, 493034534, 855350235, 603258196, 776502608, 410191046, 931127039, 538463248, 168263989, 96650984, 119818006, 682142937, 300077199, 617132200, 193442148, 338953326, 312924207, 522159256, 381890710, 287917363, 563843254, 51497200, 416268136, 399213547, 433299193, 295128955, 332275834, 861020598, 811953023, 251593731, 287217734, 542230055, 911202702, 252536280, 364139096, 403925326, 627503363, 304837820, 151611439, 673661779, 472681756, 92604741, 239665886, 845613147, 5922688, 210789945, 569537699, 527697525, 620411758, 206237264, 724086414, 598512780, 40127745, 87925313, 535866858, 503995397, 99963941, 987451339, 887964559, 678542895, 977122363, 172143498, 723980675, 413419244, 83413487, 505347219, 78552349, 729022285, 12794246, 288642184, 592231440, 783863498, 701824430, 699115275, 650819526, 50816889, 877437255, 860772557, 517724710, 710677278, 420752911, 464973634, 737492783, 311118161, 168290582, 593886218, 704684522, 396591522, 451473043, 546941113, 107092913, 646128287, 110226340, 389675593, 117998775, 223766253, 355902106, 508689642, 813848824, 109714810, 42753381, 63954624, 672570454, 84534792, 402365662, 514782426, 378568138, 961754063, 170712689, 454746522, 623860784, 764154399, 197506730, 747537539, 769923023, 349598953, 727458796, 84360593, 89596604, 503514351, 882920737, 207264222, 523391721, 798846048, 850417842, 807880170, 828828228, 223165092, 161707346, 483348599, 631155933, 363514227, 458683892, 171334719, 64221051, 410238258, 392131616, 754767663, 258749276, 358396245, 293036754, 910918146, 299971556, 838954987, 359569404, 39253040, 843796175, 159210038, 532273357, 616408529, 792245146, 717295240, 951500280, 567334898, 382708481, 560435877, 367786696, 381962942, 308943066, 788597006, 349076435, 381361534, 609482523, 850896255, 350646136, 782217656, 72940292, 300422594, 985970971, 316039595, 129606542, 324457039, 843870914, 292190912, 604587014, 853920710, 172859488, 473109467, 850926147, 661222998, 465012564, 235796468, 550307145, 952248485, 140925651, 147970383, 225606943, 416718723, 588611569, 119479393, 254537601, 628796630, 285613523, 596645124, 635469536, 457786176, 762447246, 995010526, 459998899, 303572176, 864875606, 30468728, 516174273, 943368389, 727023167, 541509485, 642305806, 963109209, 997797842, 545498164, 624092152, 664682000, 909324904, 907422171, 988674161, 177403603, 40099347, 26934013, 223283197, 242208111, 615974757, 599285417, 623348057, 926784551, 217151987, 648235958, 422878269, 96657394, 685392133, 639166190, 483880898, 210898057, 832303106, 371301049, 550974951, 669555676, 915365181, 901540764, 207168708, 46090267, 341546914, 279456203, 734944639, 723894391, 415732806, 910310589, 912137729, 881350618, 888137511, 748195240, 927115890, 204066183, 633424468, 333023044, 978821038, 250857730, 203737689, 558445804, 905136105, 531356755, 78969217, 513862888, 151951979, 789741765, 895126691, 397231137, 859564064, 309272428, 353125528, 31685493, 34072998, 656575181, 385764873, 131837974, 154465129, 517394650, 930432894, 392494331, 376754227, 482780431, 932829354, 922870255, 180007934, 429742806, 408899558, 291832999, 825317842, 747687549, 296334780, 380342318, 708012142, 893629895, 696196434, 134509608, 999717276, 773301800, 959796830, 243199472, 57574752, 503686128, 851404921, 732630063, 325766470, 621159145, 392723494, 510659942, 592528705, 100339498, 591756442, 171853709, 652598034, 351342881, 129312887, 960819107, 768516871, 588101872, 866045733, 912829908, 54693228, 879945108, 571609699, 994493804, 813718507, 969428335, 84722531, 409837266, 806422071, 462159280, 828951470, 472810746, 577842375, 756705140, 715245821, 828509579, 778567957, 118518173, 963945212, 725552992, 785552687, 43680705, 530706053, 833108142, 151377616, 101538644, 305234831, 23665082, 998187760, 581644882, 892337367, 804173161, 462612304, 440160384, 339576732, 491100803, 134690174, 31243397, 362586530, 278835854, 579250815, 486275083, 639224200, 914018650, 715706285, 137219425, 885502048, 560205282, 185793390, 371048065, 134380076, 618912763, 970009536, 847099121, 38720002, 936165391, 828343507, 674098449, 362761478, 554193457, 905775023, 713706823, 893029655, 396617207, 117848732, 814350729, 152382617, 838624053, 676714790, 622257310, 14383278, 673313023, 401978132, 803059449, 661277968, 8042891, 698217368, 190070776, 196725433, 258255671, 922905851, 316133228, 736159396, 170278432, 257799441, 661651605, 132282928, 381917464, 843088373, 618845049, 301127487, 497129530, 904086460, 942866548, 412142648, 856432786, 241568596, 910406469, 157845484, 513729069, 416506746, 364337658, 989930375, 259229998, 182018816, 938514843, 899234858, 934036829, 806768267, 741750234, 922142296, 174529802, 165905913, 174143089, 635344475, 998332365, 509696239, 971505338, 766079920, 199440007, 679794752, 809951764, 924305885, 946671204, 83426162, 424775231, 949184293, 183222696, 544414020, 57979797, 403690591, 365215651, 107097932, 393145168, 683519033, 904329414, 258189685, 356763470, 594358707, 551933268, 440309210, 996581897, 502240956, 153822354, 354174021, 523946322, 508680343, 615844542, 32683502, 796533335, 273578382, 552190829, 712467425, 686006469, 206915379, 983709798, 223867577, 778957540, 759588672, 232742260, 174109129, 672209974, 946813457, 680888875, 340115107, 603349891, 334800646, 135421778, 193507160, 123254854, 568257356, 871795454, 699547098, 869843020, 252379213, 857817366, 340497749, 940040948, 728711806, 193860755, 855956032, 332851525, 909596063, 255943010, 515957560, 327562454, 728132480, 954841084, 772945331, 18263102, 521370819, 235783283, 668192779, 703064354, 559145097, 201501072, 499704188, 267483229, 496519146, 683720088, 101839192, 402466395, 882433733, 265367576, 778868580, 436039231, 755594353, 418319821, 337303586, 232520948, 718807521, 351643655, 979853297, 291580839, 723618984, 124415738, 601483173, 14462233, 133674746, 597079583, 230040139, 526353509, 348308792, 646526895, 371557652, 951024070, 215905802, 244634791, 936430060, 353352372, 231450690, 159886510, 208596308, 342004231, 924806393, 461205471, 690272011, 285666194, 643771651, 143968032, 301360764, 45824427, 707464700, 116662694, 164923975, 16546762, 217913943, 814969149, 415776296, 898705625, 180596603, 46897682, 768629511, 39133582, 991204995, 611672306, 75263188, 943520573, 373887023, 927251756, 364406100, 680361270, 22064558, 996078406, 298263292, 23517486, 898240428, 707489260, 375809543, 902844942, 271357998, 57947658, 75976555, 907870040, 953896609, 119400525, 502663930, 6996816, 41719862, 532839834, 438224881, 315406421, 908449871, 745449082, 870544952, 840820221, 346907742, 602187919, 360113991, 631725551, 764625993, 534134503, 360718340, 564006098, 802919317, 106158814, 648180442, 387359965, 625039402, 734435846, 674321416, 488522907, 957105092, 575232206, 145795220, 440358061, 421378656, 433280784, 101537795, 256049145, 117567052, 330811934, 6847838, 151633273, 550662792, 79709923, 723709884, 160575177, 812111291, 485178864, 126521568, 267357764, 37581622, 494606043, 256140304, 188878319, 4774073, 495255513, 455498805, 476584138, 390046444, 455283997, 665476020, 457537730, 613586503, 181575424, 562783445, 158793950, 310594420, 690766644, 336063589, 599199604, 872483111, 781075417, 922928097, 749650485, 595366532, 571411194, 793101024, 852350565, 252415350, 62158545, 762252064, 786384981, 655357537, 760938929, 213577556, 173280012, 603776701, 956392882, 896255246, 535227181, 521023106, 588563688, 193973971, 67443690, 862562836, 656234680, 458557671, 655226439, 717920980, 130628628, 776240506, 737881500, 59556924, 786015065, 964505349, 319107630, 905472645, 270819549, 290196844, 704023096, 863869189, 21088412, 563152184, 690265926, 255748124, 991297660, 441861075, 602003705, 735941688, 732807094, 894334525, 528981973, 383274066, 365490677, 25097615, 629401215, 329227277, 823245622, 330595453, 165365790, 756376642, 713308881, 143546162, 865837382, 663940040, 842670874, 997551040, 508907327, 158366562, 473604571, 850070490, 547886982, 597354176, 681732011, 416975176, 293033493, 250703000, 941881330, 688107425, 334201078, 521682954, 15885768, 146226820, 339814823, 734995533, 262002152, 74653982, 604930099, 853279783, 413149948, 248424850, 773809623, 924722280, 943044461, 206041673, 280867008, 643564807, 48249045, 100314220, 966924959, 7901570, 110422804, 213236024, 764137280, 8258574, 452171295, 7622833, 881947997, 42962038, 880015607, 358485997, 871829951, 657513728, 501148680, 555335814, 770137372, 514542256, 829859917, 989810548, 744149819, 663251374, 898928047, 872580228, 14324957, 192431019, 498845014, 32412271, 465365519, 463083322, 279127106, 224967479, 642202937, 123389093, 907936769, 595266967, 326834991, 295785213, 149962410, 636414122, 571242994, 422445419, 936162072, 436347124, 417985995, 14738890, 359780992, 59593988, 141575390, 191584218, 928278491, 684714814, 119480768, 279348935, 501027278, 820504070, 809753921, 277900423, 58740722, 145866059, 442926406, 168051327, 817975096, 665045850, 176634391, 517133440, 120729815, 324417881, 798538813, 160956680, 154033486, 287092462, 463461357, 868765160, 963126537, 133840376, 789497998, 293229304, 307002936, 11570748, 395088361, 1300803, 106574614, 743089727, 604193650, 601220219, 165186500, 95126329, 732082786, 987156637, 706234953, 169383532, 142901127, 719762136, 169600641, 856776395, 808903609, 816097649, 320614639, 109141690, 729533712, 433808343, 121742942, 457427442, 567097656, 664484708, 637705864, 734293762, 433047709, 446259993, 595043388, 745119428, 891258450, 340817908, 33892859, 507593750, 110531423, 923712939, 748252840, 413765182, 629646406, 243193243, 321972129, 7929182, 364657612, 339353010, 509283580, 856696566, 161009396, 988810979, 311107578, 991644138, 232682323, 486300847, 408398193, 35480116, 71269724, 365916299, 238088600, 133047673, 897903696, 739605032, 262153249, 569052888, 511626833, 524496949, 702836771, 100152665, 696203961, 584900587, 235241377, 245517800, 427527533, 557504709, 655364342, 127396906, 188910871, 674716548, 935482248, 476856966, 735255996, 690225821, 424171307, 696618115, 147345714, 272874390, 541660325, 214205802, 833151071, 10014428, 819327909, 129304772, 24066567, 973527028, 548035996, 458026122, 545594507, 93747696, 490220648, 684232716, 659027820, 992629713, 919872863, 918719788, 425938150, 234170230, 917105696, 63590566, 816777027, 794853478, 852387919, 413239459, 259294274, 914413842, 589120606, 420857566, 147095538, 269665463, 320739840, 464803875, 703979905, 891326809, 305381863, 193046044, 96733198, 60191906, 688770558, 967637750, 297332027, 284578298, 272222198, 647460240, 784242032, 97941211, 874054170, 124628244, 133795749, 773851240, 861764750, 498056246, 905935821, 924005346, 566652934, 243220114, 157102414, 221762843, 303936095, 147078518, 147721443, 848807112, 873547788, 909972210, 225061777, 586649724, 369840788, 632403932, 148320057, 101783184, 20523269, 522466069, 643961487, 14594846, 653926535, 270342839, 189508076, 300055328, 482832145, 402479170, 668333891, 325649057, 678296320, 718086501, 384678056, 186637540, 42943970, 495348437, 944120154, 200178303, 471300712, 297307511, 759584370, 40024218, 414376237, 732696059, 739300462, 863559440, 563246481, 515308897, 152075636, 137841113, 649463631, 509711905, 249221079, 572522641, 907249256, 951726451, 843053126, 551406299, 787760970, 484546978, 405758702, 49990940, 594586496, 389313517, 833039881, 119760776, 646029339, 900754990, 840419568, 950373416, 39950360, 908953461, 315234650, 276476741, 817253120, 309656017, 351273697, 432033780, 290511059, 611343162, 572847016, 818126751, 705706060, 685807438, 606652274, 827980234, 886587574, 747626041, 742969812, 199536700, 784454313, 197682784, 385804631, 926804216, 13187137, 658730842, 232046471, 374330456, 282715759, 733300074, 6183055, 185028803, 513174731, 189263949, 62908406, 613767051, 868363592, 93200185, 613426023, 705026655, 897563116, 849240922, 825108882, 59632573, 1220792, 83975626, 246887713, 949571329, 499734869, 225663610, 123189071, 601377659, 415351511, 256816179, 11690387, 155806305, 39607412, 636953664, 584506750, 762407674, 435819236, 118911696, 717694375, 388359794, 482830292, 626080804, 98572427, 123938826, 614112802, 222926000, 500764441, 691936724, 446657887, 614139310, 48041361, 620172996, 222541754, 939419192, 892411506, 130956228, 981681550, 636009626, 148518338, 872657688, 870353537, 116400056, 948275660, 879039151, 245457394, 261745358, 217327692, 167291357, 115632361, 471677543, 897424778, 18417987, 733014909, 919478417, 630125759, 250270814, 799845404, 227950276, 325743164, 420168253, 737035608, 877075713, 721597095, 661737474, 744640562, 422728809, 266993149, 791855678, 934190183, 735459602, 883623500, 559578379, 214282619, 724766370, 37365708, 979648113, 462372119, 350232953, 545288789, 780988526, 407918765, 668917316, 100770822, 842906599, 644158046, 353833242, 938444886, 573871060, 164405609, 935687518, 546905870, 30664762, 808147035, 423177950, 598652671, 560676469, 471361493, 584127000, 250030869, 695039381, 100450429, 887866683, 607838398, 681336103, 895560897, 772998876, 48785617, 38611162, 30785646, 405356437, 289855193, 688107686, 898040229, 331595598, 904572055, 552688140, 750803482, 670901090, 298475089, 290414414, 203797697, 999340422, 772709731, 988690148, 305549185, 97267704, 532361206, 110580694, 997969352, 882980032, 959480377, 401638133, 642989112, 376850623, 685544893, 720434766, 282078772, 695740827, 859476237, 509759655, 905542406, 885339569, 999612644, 139882040, 501229740, 294060557, 152647494, 538884736, 700286864, 342681295, 479516952, 455594109, 533222976, 653339102, 136178697, 357103525, 374884431, 303500095, 422309456, 588247768, 944656717, 14166441, 3982330, 957807825, 889525681, 317211858, 981640813, 501776854, 263587858, 395324788, 887356134, 15908467, 599984121, 10830672, 536792052, 448440880, 113372917, 346098460, 240826971, 92543970, 470391073, 394331281, 121790866, 618029732, 37786150, 911589337, 890274411, 806597465, 418092957, 917005714, 273115630, 954800027, 967009297, 866845139, 261186775, 220768333, 592555923, 105030749, 602262099, 884327001, 560387810, 255035958, 518607333, 180133851, 538023810, 309382151, 979361195, 872390655, 723998671, 194438297, 975828599, 506379167, 734507451, 244596245, 253311507, 445510116, 386288160, 504251089, 159352116, 985665360, 270492888, 711073104, 778149885, 265875922, 983806983, 458826496, 555553470, 762517164, 658243495, 631480486, 28437227, 946863682, 67206537, 664147175, 365334332, 93537429, 641443079, 625689445, 149883885, 442756933, 904225624, 851628422, 775803261, 450149577, 260182841, 454142456, 188574942, 346253696, 409671695, 276456740, 371588043, 579973983, 506274165, 768767283, 678433329, 248201960, 247507572, 587134974, 178609856, 64078413, 680921003, 140433240, 218624084, 435777867, 260969664, 159377767, 929471277, 732523876, 360034814, 428915586, 628437115, 992995203, 97350470, 928106443, 919205602, 853108643, 399532540, 632493135, 756952422, 938588853, 720819844, 381529824, 286790864, 530273473, 162849597, 679084531, 867039219, 410164415, 633014668, 506500547, 202883072, 14918023, 795205523, 431328887, 24481868, 896170148, 667220181, 117776057, 35747490, 720314362, 757084741, 258307641, 541670355, 911009329, 75245634, 19775428, 228956188, 81892116, 421401558, 911415914, 885490212, 983042836, 42621733, 755141765, 87613396, 798537668, 735931738, 911474832, 201828558, 124208053, 580090202, 335764913, 780169248, 159563633, 642060595, 153357735, 8594344, 239294915, 921348385, 90108617, 13373336, 6414141, 349434505, 6439810, 657310260, 917690035, 370155152, 226825875, 951044709, 546448856, 391412632, 361008820, 640910250, 254652133, 537424490, 985512451, 24457064, 261946801, 292409091, 852123912, 633786178, 924074646, 770189477, 926622648, 58047152, 838124692, 92122121, 281761248, 256817250, 570815218, 729919964, 547459210, 643814862, 763510947, 618540074, 598722060, 200529340, 339668179, 101617501, 464461555, 475804834, 243558360, 55178282, 380829753, 819455194, 455863137, 268455693, 506210088, 130884912, 294534607, 523049214, 805970520, 164576423, 455351230, 716311494, 205626654, 179839211, 633951912, 725956021, 785359944, 308435056, 564333547, 563836441, 57243744, 769394133, 299267356, 333757073, 722282383, 955578642, 678746716, 670027433, 472501894, 241303962, 863260161, 238357775, 551617303, 533291473, 880421351, 980606331, 558841148, 236585269, 49122266, 687348004, 923131657, 179630528, 982143497, 517199596, 684556999, 581180643, 345354096, 982089197, 772210758, 296783123, 467977529, 928997386, 164875054, 332596007, 941819079, 930578269, 601106716, 217638501, 120934937, 662402571, 861363288, 643971903, 727397951, 513473365, 359595236, 220340401, 289794499, 622913974, 210020632, 335869884, 770325299, 232336340, 492567582, 85173695, 566043307, 401358849, 422574585, 887311187, 604286654, 783800395, 568055327, 971478760, 411612470, 20323261, 531965472, 4900696, 45881115, 355662085, 274014509, 457989185, 644654414, 751313051, 519218877, 860060141, 937777879, 535041500, 565970958, 355659336, 546573178, 64024947, 330287248, 177870255, 956002621, 759796738, 218583565, 681916480, 966275333, 897640660, 488271582, 662298963, 777987809, 709677397, 237427771, 142530141, 937692477, 899326099, 970417154, 925678920, 862648993, 681267203, 131154267, 437428586, 270659484, 527308161, 459811234, 187882376, 755037997, 737409510, 716429497, 429547450, 905708805, 812530333, 299327277, 268047322, 774301521, 445792792, 741891787, 519602971, 764190779, 979267124, 425912947, 493248174, 410807991, 784900975, 162721368, 910026612, 111281109, 819399562, 457040688, 74225146, 758289163, 726658869, 996888226, 995871292, 455465220, 691778404, 426099607, 686370226, 687615758, 918641025, 788682513, 961745825, 716222999, 110406950, 931901678, 356777328, 399326146, 136595367, 475201669, 292185865, 23190019, 501656531, 4666190, 981606015, 179218638, 675391591, 226878614, 900240769, 891273899, 579324538, 220478902, 524823607, 629479118, 932211373, 955632762, 223928290, 612096863, 615628347, 115303156, 446899337, 257533319, 519649691, 184469609, 306139195, 967624169, 858156252, 628305493, 187176703, 201871616, 23767438, 941042145, 886014149, 771232964, 135310625, 504975733, 994203510, 183614059, 209591595, 83768923, 978774687, 600346080, 612635131, 733764433, 174239424, 208195014, 181078763, 22369909, 176259275, 395629179, 747920398, 257647155, 595990860, 650672685, 983751149, 503671477, 325809512, 337397130, 577121806, 92595913, 913536031, 197760340, 492317245, 254804537, 45824438, 92707509, 916539624, 689230593, 778235112, 176558491, 623655885, 407127281, 758067283, 631696287, 204617876, 967328030, 141436249, 198551313, 21033218, 739415200, 898536922, 97086930, 243460564, 613992604, 936633761, 550976161, 493889706, 864247143, 734639976, 545110171, 610522426, 672992954, 347095147, 939606022, 739784565, 852372300, 158141934, 857486876, 511458419, 493352451, 660042713, 377868939, 998877403, 624118472, 799556644, 797886893, 385946405, 226089134, 156567628, 875248229, 372666782, 547859522, 137754922, 359536384, 659017017, 837698999, 959508063, 111712465, 137261818, 704525428, 269615118, 746721217, 432065123, 260632406, 943400581, 797923546, 750203227, 245544349, 389635224, 936971647, 515910523, 680636052, 852454365, 200896797, 35341576, 124125628, 12793244, 916107624, 53082714, 433384053, 853651107, 53071409, 409746633, 110762151, 650893857, 69134748, 85564271, 145954712, 193842829, 217319257, 709327839, 196949296, 450325206, 429506677, 881999766, 122404269, 497071724, 372258099, 336601315, 180029745, 387474570, 650674840, 340182712, 431908376, 702831636, 745709143, 486242854, 364348842, 254705321, 788412840, 717964276, 172036366, 866843219, 895983557, 710794522, 39494214, 249791774, 78520434, 420065288, 803060862, 55312984, 440564699, 498846422, 6402697, 726098213, 964968829, 944962844, 777697764, 506352556, 229402866, 149899553, 833811785, 38012804, 379991054, 200443461, 988397943, 415815606, 450530126, 838974844, 852765901, 487193591, 614955143, 20468477, 171768627, 688735154, 602352556, 861724600, 639275199, 69045568, 337630961, 799625561, 283849880, 908578470, 372186334, 589957054, 173230736, 31342453, 430049293, 973261547, 884592408, 561548570, 638869134, 26202648, 723391171, 420443424, 807537089, 232554772, 558780050, 813876729, 376171258, 615734799, 450537502, 163729212, 673740660, 398378143, 339264443, 638206459, 397322088, 904946152, 180543496, 680427318, 931587537, 588322065, 519481352, 231769863, 606423552, 714025609, 91046269, 591769477, 80301195, 820924993, 899750678, 437667395, 817102513, 506705224, 961997528, 411541183, 732074620, 698439439, 21682791, 132447577, 776049377, 598299017, 182813220, 618549376, 902783632, 589564343, 850507037, 784728439, 753576768, 975719817, 740256914, 441577616, 7325827, 796634450, 676055076, 900577470, 919269752, 672417868, 710835681, 533118227, 245859260, 21826672, 303444562, 820969869, 649788029, 775659464, 435091754, 705339226, 888613071, 97541611, 663347403, 136135850, 928318429, 665512368, 812037107, 964110644, 643668812, 441652405, 591409870, 23604015, 148028436, 463343738, 590339875, 969695880, 414134782, 963130823, 921767781, 977845717, 41470882, 383141598, 243603295, 260896011, 863937314, 507522442, 648158642, 874472007, 468199263, 102077144, 500697298, 477874793, 712924121, 469126672, 998329691, 176728498, 199870977, 655889113, 312989487, 539609653, 680780893, 833170980, 201272404, 311209467, 314486128, 532931548, 715771647, 904995602, 323383431, 937847604, 563552582, 575162907, 783168542, 804259914, 338354883, 160093998, 18573070, 652560303, 542151658, 407516420, 745030949, 711778382, 394111303, 861616681, 139835406, 700338481, 851684105, 838933571, 91057011, 386590180, 995246777, 104252782, 20174872, 729127017, 84892207, 185616800, 483334539, 815322370, 527850509, 947163784, 991759670, 256353380, 529533312, 481856074, 714871468, 427914548, 54242299, 638818795, 995496789, 900557299, 175028962, 501444814, 248211296, 781172003, 697157152, 816390955, 867899982, 720062362, 80181770, 154014599, 215613630, 889599489, 302707033, 786544322, 945446119, 478436989, 411370020, 806780221, 693057110, 264665634, 317114751, 366404988, 647970943, 953884730, 900577237, 315834182, 717344140, 881785177, 520207652, 732564577, 407113309, 796455400, 301470139, 354517918, 509657552, 42524220, 488565252, 959020020, 171560400, 221125591, 258065069, 327980125, 794438009, 834220478, 690301144, 67801964, 642463048, 922082994, 919891533, 396693781, 263937415, 52992128, 421727355, 42288330, 189575793, 24657578, 622503636, 710906426, 450913687, 421166284, 840555524, 84312934, 58727316, 888538053, 947921205, 975476903, 811448795, 351471991, 926241480, 572132522, 899555291, 268080481, 94984639, 800157806, 213307438, 471591885, 535974022, 899744159, 547540376, 723814962, 591824409, 450260919, 487344657, 818316110, 813411773, 780183491, 137257374, 52947560, 99345860, 132659886, 171080580, 735053791, 471877449, 741863388, 653818454, 510345672, 704152776, 466533509, 819000751, 62959406, 617327004, 897949122, 994562975, 902892801, 940236148, 164699349, 427725374, 908050117, 386514886, 123934207, 441130736, 934267785, 608120306, 28751231, 279279995, 451895627, 712418635, 399587544, 585139981, 720539365, 441435865, 657807828, 202973355, 557622584, 985028219, 858089051, 610775313, 333633198, 78719984, 593912902, 431227733, 510979674, 835793775, 758334797, 602405857, 935102940, 29930707, 229906617, 534335909, 933709750, 680860291, 117950250, 891063637, 433215013, 383940244, 761548574, 131615051, 491385837, 304327036, 365161066, 330570590, 556017719, 767683235, 314611575, 281842725, 71363408, 747777222, 356537389, 958166025, 781650369, 614189887, 656731484, 659094737, 297890316, 182676583, 68157217, 524551447, 746561301, 486238689, 415571394, 727249704, 306078764, 759665765, 853837237, 332202506, 222084171, 911739487, 460834601, 472644666, 748196354, 508642287, 875575211, 111131346, 788946809, 555511930, 107755827, 333011740, 498777401, 180647238, 996632442, 647174930, 952630737, 728421037, 981677700, 951299451, 930871277, 445740, 357780741, 38072191, 881541040, 368272402, 120986608, 787276787, 383591513, 970760554, 990081841, 645771702, 87568826, 205674625, 192910040, 536736273, 192303639, 787605087, 545827650, 202808878, 523800681, 158315108, 912058226, 231494255, 861634046, 457998596, 324568242, 736908063, 505580432, 302982823, 562969149, 892668746, 117334499, 226690078, 473391243, 43344806, 745594287, 50395765, 943904755, 432238170, 665808410, 94501695, 679472760, 873208797, 481191362, 757947667, 358232462, 915291175, 222492321, 624430190, 341490343, 640301805, 547105675, 799723163, 821397818, 927184669, 764544890, 328461790, 997861006, 331845069, 991848170, 285902371, 51005004, 270203896, 885897664, 688221320, 541623812, 682478725, 654336422, 415834778, 488124195, 413539589, 978935415, 653890504, 108536028, 7985709, 843708648, 952861717, 542549009, 822502713, 408192388, 694002216, 749292342, 409372857, 319477506, 843142101, 889849420, 826150411, 619289448, 208738416, 381049023, 565284298, 331610661, 387326444, 41229746, 53758963, 498543447, 621426863, 164767606, 654199821, 556961258, 859171106, 494232459, 751651138, 780283051, 888931061, 846867870, 815344923, 652879208, 104753949, 640222287, 642260040, 324562356, 161664647, 761133868, 973310437, 492538289, 856406972, 695073429, 89351933, 951620971, 414736724, 15970072, 621342431, 923701010, 516701817, 902124472, 236010106, 702798599, 87351865, 801920204, 354388803, 94685133, 305950010, 980959770, 829073920, 990699902, 549823594, 961025204, 321640172, 938887149, 540339177, 740738371, 412484117, 723578844, 27620327, 813274226, 888979969, 426454313, 583843148, 391381407, 17706140, 614266674, 226943963, 844649112, 302133021, 131695603, 339116213, 139582164, 341249147, 620545885, 655893819, 678114593, 600847612, 532121397, 50724985, 178078868, 640815160, 898350275, 990398901, 543044846, 493845405, 776092308, 785524965, 429900838, 404439078, 188838733, 28900775, 593011002, 488542822, 116908303, 414819116, 656004654, 611801802, 251792569, 74625288, 56064364, 351209483, 784126168, 432116092, 21328417, 387345369, 331038403, 360974524, 769208653, 589761739, 169525861, 522374081, 263810446, 351431270, 563471980, 648164780, 866673001, 341408283, 193188168, 62099611, 858733953, 820376359, 142173466, 885033995, 260914998, 325553605, 509663289, 4927170, 362270931, 937937701, 634994132, 144074158, 773276045, 561000138, 284321913, 601991776, 291536203, 536543243, 659222810, 377724890, 37899396, 972873205, 97008432, 418607702, 801091935, 208461496, 326808060, 728835287, 128424715, 623542076, 539205523, 815932269, 28504999, 191183503, 434141476, 286287334, 599328652, 960333634, 71726554, 203207114, 461777470, 222891187, 54594736, 808909444, 313660293, 728045064, 927983134, 335132290, 520029325, 995764318, 942820460, 985711791, 467124712, 28851358, 253042102, 27512975, 141427796, 212163493, 721729871, 661876421, 282091179, 452804804, 931300290, 722728230, 736526808, 711420048, 189735562, 834983924, 190982168, 526883042, 575565883, 531408425, 628340591, 857570823, 534358759, 421223884, 433547896, 881412350, 991824702, 83215738, 436685152, 194864333, 699379072, 441385074, 19691638, 524033792, 99834721, 722244720, 366887693, 23015911, 223787149, 911816155, 589741828, 969318911, 506866626, 149211804, 929963830, 721815753, 319619404, 760564460, 31345484, 570087382, 209792233, 111164644, 288356179, 149484066, 127514048, 42719303, 90965231, 406576582, 998433325, 698268911, 280940264, 602754289, 899117988, 635757709, 785380488, 286527893, 346057025, 534157552, 313525782, 586917744, 673201865, 775267591, 840755113, 374393079, 732804672, 355173826, 143650946, 642700751, 134748985, 669988586, 967385472, 93846916, 602928729, 290225888, 932356274, 915802416, 908400350, 469171255, 166447888, 706874748, 673662601, 71373057, 949294032, 952088800, 416159387, 37787384, 658470524, 345761379, 479888658, 768896587, 552821685, 234955322, 323919497, 969519067, 950771921, 240656760, 77619888, 452067229, 908417921, 531558986, 305872882, 368583342, 217982838, 400394180, 137853525, 290690395, 795821999, 395109438, 786237852, 717002038, 935957634, 819411985, 672661868, 615319358, 214166977, 982093864, 828370021, 701423295, 703721494, 943315552, 497689717, 171642851, 720451136, 23148655, 69263281, 877449576, 28038136, 754050116, 75522063, 353850042, 617208494, 950645645, 680266040, 583140054, 894693306, 560449445, 915596885, 796015156, 590002495, 38644575, 71325682, 176195511, 10058295, 274889718, 427407872, 20691643, 589432011, 244139059, 571855113, 370524148, 587358909, 346846845, 280331246, 956599337, 398621972, 222833875, 392803283, 807438340, 727746755, 143130380, 116421657, 320049500, 911267188, 96411272, 301961671, 413535796, 836221649, 612230409, 491904381, 882345605, 916094045, 452064006, 249009244, 427074528, 725525954, 221298418, 706935808, 487449839, 857931927, 18062010, 893251016, 842804157, 85907171, 239833249, 227172084, 130464832, 478662367, 319849989, 402749984, 419284621, 720777353, 385196122, 974542067, 942163215, 301108172, 220689347, 980982088, 81643257, 881108459, 83810718, 120684509, 9244906, 988310554, 233061535, 209657986, 823498659, 71550637, 913416741, 646893343, 608680322, 477790438, 200485049, 252340468, 22627070, 426908388, 324403985, 15003760, 833075911, 707443774, 50653283, 233385910, 651616792, 493305744, 524062225, 108922185, 708454978, 279394881, 623834166, 962975382, 11351233, 448409581, 428523104, 901927983, 324731795, 704340758, 157874016, 951976205, 585144728, 582182910, 807112053, 587616383, 594886332, 965369683, 982230037, 196360077, 95320118, 992602205, 232414880, 999140310, 889330191, 905905246, 729271737, 664228406, 165458940, 244414424, 580666334, 407947074, 385613913, 34387382, 215621423, 145817288, 335159981, 829421001, 777872990, 485661598, 12534209, 396415492, 281003883, 140141064, 951952654, 375523767, 208050670, 427682243, 826909615, 201438538, 466185416, 29072876, 679575598, 375872933, 163317173, 337212837, 181591637, 405129802, 116515440, 967794972, 308785603, 636453845, 184974242, 66985775, 464290754, 921910888, 18006788, 226195937, 772315898, 585817243, 512563380, 855555498, 29749480, 419492744, 5369413, 860705326, 232541692, 634773185, 481007345, 544273223, 400813308, 571946770, 713101436, 804943676, 600905718, 487667312, 111610905, 175947456, 376271567, 272171630, 824463657, 665561854, 705115764, 296292656, 948315858, 32725435, 788224104, 895533301, 725910839, 617657393, 366356573, 695677599, 170377653, 552583445, 97728371, 345085139, 632401824, 843442071, 251101461, 668104334, 697050452, 580928558, 361865065, 516907326, 168434685, 186790844, 873433167, 888419600, 382196154, 97585769, 22585195, 107800255, 840599044, 370285897, 852911737, 685647801, 233116894, 595613298, 625416474, 925772264, 237793032, 560021901, 531394545, 822182904, 538392072, 891927705, 235872966, 550237258, 422370311, 560494449, 809085767, 854859817, 419874782, 229869581, 451862108, 845202019, 606687449, 865300862, 938453754, 89071399, 130478405, 56139336, 969975169, 138554710, 376748221, 310299831, 725080526, 127664061, 728208655, 308283461, 289122078, 22826752, 79269600, 89118824, 119641566, 74003123, 429652585, 798578670, 894131595, 321019626, 268386354, 219823935, 674359021, 804344835, 135571767, 909817544, 618249522, 498606259, 236473282, 901964823, 526739950, 584555799, 591883990, 954260025, 73944392, 568247015, 238076474, 549647287, 184960350, 937835001, 321618151, 20247828, 180630526, 639520746, 696835719, 950828707, 220976910, 396733174, 117470038, 336851340, 439682345, 803595856, 721656552, 846487044, 472850709, 505493819, 734594416, 870614983, 283362385, 397748022, 199543433, 573704580, 486503987, 756215703, 13027333, 592998894, 704802120, 60322763, 2647977, 739767247, 277006754, 813016551, 629145634, 738118785, 618373855, 199061353, 937215770, 550555827, 896413615, 830512509, 652508919, 759884580, 496066411, 265890221, 470971123, 193069802, 925504938, 99001646, 327498507, 536785454, 830652616, 749397804, 21201113, 644739952, 558035130, 7163687, 745218352, 216788468, 92749968, 657502334, 116941001, 308882729, 800614581, 298293658, 873937533, 627935522, 72445794, 799984397, 719498884, 289755299, 811693282, 350709817, 841734465, 998919048, 900449439, 624536685, 388436084, 692576081, 768651135, 135970632, 983862812, 851818849, 307826451, 387793482, 360201574, 450724501, 642560285, 544143977, 352100999, 221802382, 55227733, 901993959, 780576113, 653908849, 951905673, 408736378, 772213594, 928704024, 46399022, 743409631, 26220794, 927286051, 382803747, 281188661, 906652760, 814555162, 955953984, 913912333, 743576167, 748630322, 693533641, 369623093, 766593923, 894182940, 535504644, 652202646, 124887747, 905347639, 243571484, 579621921, 209510596, 90620473, 711601593, 495190273, 540074656, 294724105, 850526281, 12001506, 939216752, 946554616, 46082468, 678278973, 959955210, 155810837, 189139386, 638845738, 661901545, 473208690, 596650701, 687764212, 387746941, 31642453, 512649184, 135478796, 482744428, 324549431, 571498769, 9244934, 833080056, 497436617, 669402377, 747116512, 127396480, 536783433, 851077154, 724284296, 712571845, 343487853, 55717559, 604189860, 274307033, 892673075, 487216129, 736921019, 950842014, 862268678, 707869868, 112216474, 555874376, 582623990, 348817302, 391530919, 193750913, 255594642, 147536159, 51368026, 352917622, 411089383, 407168963, 980418437, 407175946, 568078336, 800808584, 458731848, 377368069, 155557546, 496751954, 109446814, 896439502, 510974819, 183106404, 546147745, 931934468, 619590296, 925854466, 919776937, 536122735, 633326471, 578704696, 53578079, 705593203, 834834961, 259919712, 543947850, 919839308, 781558276, 443916577, 358411173, 154966074, 595411711, 783404630, 698119095, 525514634, 152271659, 362526611, 319616841, 256236988, 212553419, 288521956, 862897596, 648251608, 929210758, 600280773, 406803219, 605306326, 340548794, 955554704, 9439602, 289013168, 915276215, 366705004, 66234393, 719223865, 952151868, 771552551, 673606291, 373880475, 525234608, 248967887, 395343443, 302943680, 792928807, 585332012, 825310965, 836537027, 654552034, 633140506, 226350523, 38919362, 127090499, 263802994, 476315572, 439141327, 261117172, 992557526, 393275439, 996416430, 669420988, 34956570, 758408608, 324398483, 633918144, 160701479, 329932021, 198146780, 419511701, 477324944, 173543152, 299816797, 63459367, 405905963, 239237302, 479442561, 555536506, 277426831, 649111906, 716923949, 973841271, 767128689, 557559767, 410750486, 489498632, 844518014, 76935111, 3249790, 690119644, 323647634, 810948552, 494332262, 444566971, 951368665, 361990686, 916378768, 645895476, 299813549, 86846546, 159671553, 129500982, 838600875, 265855307, 38534156, 504179220, 766985887, 21010417, 140468800, 579648217, 207079932, 476535372, 761229234, 354159370, 229776286, 457261701, 556233907, 774857681, 730467840, 609153769, 855865839, 851129885, 40401885, 864331866, 758291037, 329218980, 749362494, 222096643, 120956974, 443726678, 113057970, 817161470, 41474910, 248109067, 173387581, 786385617, 768119153, 678939506, 948424260, 461749244, 915895665, 936629083, 666706935, 179279612, 234690826, 530376858, 775138056, 522699290, 102469963, 736007166, 623310934, 710444719, 323811181, 368558786, 643657255, 854065093, 343027768, 367411022, 465304001, 998087881, 568247315, 647893121, 568066184, 541588484, 50630943, 794605156, 971328077, 277496805, 772745149, 588719296, 925753429, 192662297, 295993565, 258538769, 576407755, 379138672, 456973585, 623328169, 823090495, 636630557, 900419, 395143083, 563127824, 580443392, 640995634, 677430728, 140891212, 913326543, 141625256, 441837850, 274179348, 204009555, 416031053, 78053123, 494395237, 957769564, 996911748, 632207268, 46119560, 874885128, 361608711, 870275995, 883162946, 466917053, 257439726, 279066812, 4360997, 815611406, 96550410, 313767646, 545293893, 199056896, 150739017, 123931678, 76305759, 573111597, 368049643, 97138515, 447194518, 545789308, 497950774, 135168741, 489979706, 134691633, 692901443, 41001731, 933991006, 732407442, 912620526, 615559238, 46274077, 633459448, 499468540, 958716376, 699552560, 565247238, 380841653, 614218518, 510885205, 187294273, 918272890, 878948104, 396840258, 349434974, 170749821, 23667768, 943507265, 580865133, 558008412, 606217429, 955318018, 262646965, 117445848, 318419337, 139739501, 907721373, 762651374, 692824169, 48210484, 148809517, 677020881, 562424604, 935636399, 531490160, 344700666, 819423796, 23346940, 338155188, 375511435, 997928598, 267532868, 672533589, 809016529, 929848038, 879095016, 719356995, 973810570, 679008121, 74174449, 972246565, 227920302, 66047482, 796810304, 227523830, 38742919, 734440310, 789390769, 787556435, 667228243, 541331190, 868037458, 513788100, 253049411, 859786601, 52657128, 460875829, 507699958, 740346199, 962213258, 394864410, 451119203, 477601253, 926535124, 134033514, 614959100, 649699383, 409869025, 665443106, 759071567, 959098674, 723575628, 191775156, 781375759, 5573596, 121948711, 131279485, 887003659, 829941236, 307186188, 705759730, 173860778, 893164703, 583647588, 14188737, 250578326, 790567242, 890058814, 158710840, 488178887, 445127147, 931978519, 590544243, 47211093, 684528176, 821443376, 46763242, 658589978, 174755942, 34774797, 511652879, 402857599, 536227990, 810820379, 847920508, 828356507, 795758448, 317433157, 269297892, 439203275, 116880711, 29105088, 437067779, 895840695, 479702712, 995894282, 203755614, 805905915, 35122240, 540031356, 907818705, 325806082, 521910517, 986386215, 323662002, 551486723, 761129396, 556854891, 515661113, 567625510, 285437225, 118527356, 248248042, 65116696, 867757218, 838139100, 242177317, 987397725, 931918277, 511226488, 838243692, 358508549, 954523702, 778210335, 701946101, 939515260, 187513558, 430070653, 764656274, 654080506, 724310828, 410282933, 666899242, 284667426, 947016936, 786859231, 591737777, 837216599, 984750981, 418745051, 57486430, 575829629, 100046766, 78888598, 501058448, 293094846, 61735153, 334161116, 767386799, 936019045, 408929102, 314335992, 255435004, 224693722, 107212904, 892387031, 671445433, 642602863, 528251402, 971606499, 628259492, 176257153, 476129818, 451825182, 729017422, 552980341, 204596899, 121380710, 689245318, 968278562, 398998607, 733107778, 347463690, 595388406, 929827313, 621800054, 63307031, 847000415, 316464577, 6127117, 563504861, 845703953, 334134534, 762798057, 886414956, 574743549, 603062392, 423968474, 829079332, 274132616, 727584064, 408621553, 967513818, 817625072, 907760160, 966143587, 690370088, 574026679, 668893320, 37607216, 967735282, 592688366, 615629577, 310094426, 919242268, 506474488, 923759231, 398108188, 983120995, 680780702, 394878460, 915292460, 418158209, 914458717, 739382176, 542655604, 454307052, 876940753, 566092688, 684456377, 941907643, 104106423, 340176451, 351880903, 457723203, 776869657, 361511284, 532199723, 89078865, 178108326, 721648247, 261961863, 620031260, 960678682, 590491539, 296239665, 881048149, 100480198, 716293306, 14092734, 415730186, 250624970, 786589130, 289716708, 245562372, 671996744, 132263033, 506592420, 418294036, 374369032, 180804452, 117801967, 918074565, 436163574, 670359408, 124961256, 607856587, 932377859, 342176972, 998303006, 228878501, 336588759, 523975031, 129721230, 678720452, 879622563, 337341503, 699841215, 268553747, 352306461, 25131766, 624840127, 368386399, 512693603, 730170597, 539064711, 532634998, 971857155, 214993208, 325339471, 325746191, 525446415, 465627840, 158792857, 973257424, 560463989, 205114402, 974981000, 948824273, 980764528, 135578843, 247426593, 618000870, 26050572, 285007201, 215846397, 572798642, 487915963, 261098467, 889276309, 274033301, 390833257, 584117209, 807156507, 355927351, 713222292, 830350871, 393744385, 478577594, 739894130, 890035928, 283047256, 858528292, 791727111, 159434798, 196138214, 258198031, 839283439, 429508003, 175218908, 831293180, 582065156, 856586843, 203302839, 224296453, 967249609, 226413662, 970956651, 877157598, 172818761, 947590951, 677374540, 828974486, 884220350, 179109015, 362966199, 2634888, 494266043, 961249865, 494300555, 214613597, 84797206, 748489752, 367621530, 810281561, 51158026, 354360944, 794090368, 84701650, 448296321, 864045124, 624405361, 357170987, 297967828, 873875861, 645473558, 316637470, 696215875, 330544413, 870722358, 530283863, 357546048, 104826320, 255899734, 284524896, 35766710, 200686474, 560006959, 804162419, 40841975, 802710549, 231428741, 634293466, 711391219, 90002255, 258321962, 936780173, 213438754, 859921348, 420747664, 830659239, 129171470, 166754034, 467343866, 122458482, 890857968, 619587852, 941633569, 273557614, 588600122, 751295242, 55110469, 709230212, 180789000, 749278103, 775281782, 393468168, 489284703, 42060226, 72129006, 266226745, 116468398, 612564846, 869282854, 567261581, 906881791, 582352739, 390640990, 234195328, 717456247, 947821279, 903522535, 31855014, 413581656, 366003869, 83049478, 72028756, 726384230, 200878275, 303803434, 892038584, 251409749, 243756462, 527382320, 648223480, 557451629, 815707339, 510754485, 904509651, 401846263, 3492741, 942357430, 382470633, 265636208, 277982260, 190912159, 139004893, 66791571, 898783788, 590367175, 882415099, 427790296, 282360028, 741542408, 563068690, 79830859, 795314106, 954461872, 258004, 296889395, 370077959, 140601598, 17598809, 468936393, 39546358, 106718247, 377712547, 883158186, 198277998, 658587836, 515012586, 440912988, 625432656, 863859064, 777265773, 593428200, 808452247, 616948960, 852892653, 533546829, 333625045, 287642368, 498401187, 87523491, 299043159, 407738719, 884966588, 893226901, 4059790, 281773206, 619539700, 844818271, 353148457, 466206504, 302357695, 570305765, 607412275, 249517391, 703583743, 838685120, 709510326, 149221187, 744654444, 921612414, 865447420, 785776150, 189676483, 748885062, 899450390, 331870190, 94740530, 665039744, 335894600, 546485829, 129748496, 142487553, 572886753, 611839513, 459112159, 992741916, 744361400, 855275714, 542463825, 744959992, 926131146, 458741344, 894315438, 816200154, 930864793, 463303204, 318934579, 228327083, 903423371, 946769932, 128945644, 881652014, 513696494, 594119363, 304961255, 200820376, 73290408, 74379785, 975631319, 393708542, 71343137, 399912129, 117293889, 252355558, 70992091, 304387369, 128238664, 107220944, 383242283, 204188416, 891102289, 631620126, 868885691, 223659177, 453013837, 743236019, 661155174, 431738318, 836566181, 328496901, 420697684, 27855055, 643041399, 780780205, 886690492, 901673943, 325347753, 253354274, 842927175, 855631919, 766865065, 125794970, 984799763, 320766761, 680231877, 859068463, 872171668, 924935632, 515168229, 197085264, 463673950, 692228379, 145416915, 239165683, 513830591, 222555578, 734241113, 66756685, 568368536, 330444105, 257064098, 963984472, 702427742, 682442085, 407945285, 575520786, 744257517, 797748894, 127093662, 279751132, 391563808, 582619902, 929294663, 373398461, 827868475, 865846810, 165995110, 591996340, 307130676, 422789499, 18202383, 978087073, 508942217, 486127607, 902378533, 47059928, 645379711, 374121424, 721594949, 858677188, 290594664, 923490038, 379487415, 495769588, 420758518, 762060748, 535992051, 161208765, 112786903, 22807517, 928302806, 761238533, 71634063, 728483570, 934156392, 212960027, 497118115, 8274934, 441610415, 256012515, 460750646, 310229126, 52171022, 698032665, 296490255, 907670644, 826600338, 195433532, 787778792, 972564536, 664489109, 330545361, 608911977, 79287585, 262373338, 857529219, 230225218, 319016677, 809178604, 84243178, 203188562, 482443461, 866431881, 804221933, 334232669, 417582891, 166420040, 487841023, 139284381, 650790759, 220718398, 205896670, 514887379, 813108519, 37382147, 648318637, 821413896, 174520656, 516971110, 997522549, 341428964, 983308867, 256723955, 227329441, 616397664, 64720463, 508623918, 268380507, 181047103, 769528656, 800415260, 363910816, 585945320, 96903801, 290881702, 172357588, 82437998, 324881840, 370606113, 804261979, 805362904, 145456527, 400777381, 610360842, 743180228, 282089702, 227043180, 432739705, 798635676, 647619283, 525650436, 253364876, 675795532, 397700038, 284125968, 177867972, 701680423, 588623692, 80363117, 198999596, 507895147, 584406076, 283386302, 672742722, 31256114, 832037263, 540073726, 900027261, 629511894, 415774839, 685425637, 337273895, 651018598, 853323600, 175211359, 27321073, 578518158, 371397336, 48123662, 235734268, 386662990, 365897223, 884643181, 609253804, 552448300, 382063134, 143366784, 938760165, 279863663, 474652479, 205897392, 283040483, 493283115, 392788178, 210149104, 378731907, 306719608, 734052553, 552003708, 434190459, 356913024, 742443520, 649438592, 865184128, 221615024, 208710337, 349514076, 37857788, 498024147, 656440622, 990646499, 624571301, 588813492, 499618578, 341482793, 309105047, 638556639, 975166478, 791688155, 958872449, 180063146, 356185987, 366290508, 956103591, 691005518, 745986465, 503779291, 507888683, 951200338, 861064243, 99938028, 540214643, 721551740, 791955874, 160633300, 549450037, 740335646, 971650430, 589896766, 685495799, 281606809, 834729429, 900601855, 159007618, 958637866, 733985808, 448055937, 540501229, 9384772, 263152306, 499070866, 311191607, 716084316, 334435793, 971979740, 257337187, 797562927, 233098309, 127466494, 967434677, 499756701, 832488699, 684788665, 83569289, 881242171, 650750490, 717326103, 643304649, 790752963, 990710618, 263019542, 905092594, 341851902, 923293887, 279576753, 617754258, 34340550, 823244802, 554535751, 139261845, 899615264, 726110540, 326779672, 377035766, 675409410, 112124157, 549472038, 646777608, 531248687, 811825972, 480373436, 683548229, 367471607, 610484047, 902735255, 487806277, 340351286, 462210591, 428537541, 892053211, 841807144, 85184352, 813245400, 206222488, 459266717, 353381199, 871667130, 781387191, 427288030, 837835540, 149232030, 674492631, 200618920, 487128850, 760405853, 348490537, 488435491, 353279425, 917384283, 757787892, 299750702, 759873166, 230011498, 534081999, 806113057, 263153225, 76014776, 782695548, 283540184, 639810331, 220198581, 877850989, 747018716, 953850013, 161943812, 808295301, 801584475, 24149046, 326869649, 883428571, 456140021, 778029791, 632019586, 925266969, 752142410, 823814919, 313738635, 229483957, 805795199, 672864978, 931621031, 167764190, 839000119, 851337187, 681956453, 911902338, 633675967, 149692468, 629713423, 237054277, 85738807, 709882119, 841825190, 124881867, 37116474, 175121350, 280312745, 468635503, 324814814, 236484819, 57531195, 797751342, 204800999, 457790433, 393064438, 327896433, 171751319, 958533507, 626730292, 727994482, 260653974, 816705899, 724270294, 653657044, 461669813, 813646, 136466292, 401858342, 320236590, 32861942, 141238856, 582257687, 760386189, 638361286, 948521045, 794926627, 710199372, 363798524, 420667047, 596491275, 316549928, 875555957, 817518916, 805362541, 806119905, 389732473, 12915354, 833704261, 78269812, 927694616, 933121961, 959171060, 37926987, 670066036, 552966928, 989331695, 678129588, 754690029, 293617299, 62799842, 219518507, 44940016, 805380169, 285011142, 174206567, 940798064, 70491589, 23970287, 86471574, 291733781, 214320150, 983189061, 505947355, 868350508, 657975124, 370565057, 616295944, 472344361, 936654407, 820158394, 502187380, 287810982, 313617791, 612017183, 748190405, 994635174, 659057603, 498466909, 935957584, 238684408, 948899316, 854941183, 492528432, 899740461, 531726088, 414283771, 529525037, 589874368, 781522967, 630850451, 345705490, 125198979, 629291366, 363427339, 771001328, 698152653, 529540555, 337108301, 931062697, 649519637, 748381910, 466357956, 554138898, 813070279, 563628873, 486502004, 837031677, 77707657, 978679720, 258057744, 184226282, 417637171, 261450665, 436449979, 31642978, 562101633, 434122254, 391707015, 442610997, 862874181, 499517989, 881867396, 456593628, 585938440, 785850321, 195085074, 691905142, 782097174, 734183438, 348149005, 915766146, 91974002, 565400849, 866078328, 442235163, 503530795, 332583640, 379987408, 11690038, 249500886, 983879567, 211193410, 932902254, 36737707, 572939424, 723930142, 313435629, 749421779, 121411862, 91290147, 490333968, 7848785, 464208749, 763191065, 278164312, 621476907, 467562342, 266555968, 263587405, 765198274, 461886827, 598114386, 62496413, 840377405, 137028849, 184052015, 10070135, 115783683, 511226570, 639272720, 697866444, 897249329, 329501312, 271443899, 432740480, 101613970, 722658542, 58805691, 353520531, 751971596, 225052976, 725512122, 447495226, 690530328, 325914694, 397121854, 371920398, 329213935, 38527717, 910221663, 674240779, 178835496, 571716605, 186062941, 541608509, 726438919, 567768705, 745033292, 768740776, 878159476, 438278958, 74822276, 473974949, 188576704, 29758218, 364175398, 629237836, 443789685, 728374189, 511417840, 86339296, 324454158, 143733929, 703639397, 134270856, 328236401, 616357711, 576035911, 278140523, 679626897, 533512229, 758480901, 363405411, 286878081, 786715912, 44464375, 719696123, 381052899, 784888990, 235209051, 504931397, 191151045, 148025151, 209344048, 790344085, 190585686, 761971418, 216540418, 241239291, 769508414, 4739741, 247646040, 571561039, 56664766, 663637171, 645307470, 749303755, 106015730, 728900761, 536867853, 592613333, 11612891, 818019916, 947367424, 412032862, 440349566, 729169387, 120405759, 787465449, 71006527, 661171258, 416317053, 143580191, 117597421, 620255689, 442919725, 390277627, 585480575, 699125976, 432193321, 130567915, 483778327, 638052696, 381542688, 2916827, 734498277, 403416487, 990826705, 787819566, 233876497, 541102912, 827742526, 390504729, 346933037, 820466244, 768090554, 773663331, 830388414, 312893986, 215055921, 147085348, 354088384, 130458340, 173009510, 116803489, 670803097, 917782654, 687712044, 781194960, 974329994, 662037023, 52229017, 154937009, 402230717, 77914906, 152361998, 35777553, 260078499, 948061136, 171414439, 778149665, 653265258, 431756181, 615355670, 998317783, 963775154, 636057812, 904351941, 52833074, 302691063, 961998910, 778906452, 550858539, 838931294, 273112087, 659276115, 701198441, 609077194, 759104086, 71084930, 598681608, 506321557, 902134715, 240669519, 144774645, 412178312, 115752735, 837555131, 729507814, 931380244, 375246432, 67250557, 861172506, 923370376, 775733972, 511101429, 354938466, 292688617, 800797500, 444560902, 890428972, 225377320, 541491455, 891707801, 643555613, 298525197, 802171947, 436399053, 792422714, 55292907, 795487300, 827515962, 953002910, 969137133, 713770194, 544976274, 989928080, 472353523, 414718381, 978438415, 130910830, 735941006, 810100194, 767608267, 887536181, 838417175, 197002477, 743913585, 824182619, 695948345, 576547666, 115751708, 604824072, 21593608, 876876067, 461934028, 981583438, 340178840, 87600331, 646159880, 231038230, 552920855, 285547322, 92173262, 226981083, 424973171, 28627233, 80493195, 383275891, 694238520, 499362598, 395485787, 466849405, 169603844, 953363516, 818395539, 609000886, 516080016, 432407638, 589612132, 731987252, 816660977, 834734419, 766364137, 214240130, 344377256, 503582121, 893353464, 423650594, 763330327, 756630419, 53574986, 484166842, 351426550, 21557218, 587059174, 765589065, 809309488, 492241439, 244886268, 294188810, 661391300, 360549978, 907719214, 966492712, 350761020, 629290771, 345708009, 666401097, 429940847, 244804603, 77924915, 506196051, 430381503, 339096965, 710187383, 818268825, 52541100, 957161584, 891582442, 216592681, 170012570, 303217090, 73133023, 305428221, 214018162, 782344169, 248849595, 219691411, 811562763, 496936812, 46276668, 447433584, 206962610, 352135379, 601641555, 185014863, 51874823, 989527212, 740327296, 327550319, 945433035, 908318515, 947903226, 913486448, 875129054, 545643516, 949415909, 88382491, 563466929, 739976251, 230132571, 923867062, 860205541, 198402573, 36306683, 155688120, 646899170, 543666764, 86077108, 912855202, 281204454, 228420978, 371395268, 931799174, 4836107, 258638553, 562555871, 863422121, 228370878, 623596149, 821534578, 123213860, 436747326, 809313706, 71064871, 818739657, 913996527, 576982829, 621508690, 100149274, 747577132, 478095536, 943731594, 958724713, 741824645, 96041024, 352404043, 474451292, 191438782, 424561844, 975164359, 920343920, 928258475, 157908715, 50018102, 642970611, 513861840, 465294097, 251369213, 446886695, 271462699, 723982219, 534325202, 735228176, 818208394, 651383826, 752846330, 779557764, 816686056, 253897874, 604514830, 873941774, 843159986, 446984112, 990781355, 276238063, 962586480, 133143016, 598694053, 858895208, 640236638, 209813699, 899679842, 445776370, 862714528, 575737228, 240618232, 64761139, 605595100, 320323975, 541315317, 344639092, 842594778, 352825752, 398288447, 992729602, 663601866, 821688697, 483372102, 49509123, 796452663, 584917312, 856858577, 506942945, 713992493, 647140213, 465025961, 437711783, 863475646, 52197793, 698106064, 585510377, 858007292, 962158590, 415268121, 818968109, 260407694, 406318872, 586842542, 399451720, 780083034, 87031165, 911909329, 261576107, 189018806, 176795966, 576686327, 970920379, 778025396, 323092277, 157086103, 400136485, 208365209, 991193150, 275956935, 481155883, 242032094, 29784559, 207849626, 76946738, 939808585, 911759494, 595524053, 579253083, 473586638, 280537479, 306626991, 94890555, 88215268, 658607948, 722521868, 760414883, 412889696, 854532900, 550138808, 251597314, 630733227, 947305461, 582001734, 596839827, 605378274, 182959109, 231118336, 505210569, 397353609, 25431407, 764619246, 888310965, 772189516, 53052675, 598736809, 854669364, 478997662, 11447004, 957208177, 688751281, 940606053, 416905297, 696321369, 186315727, 888505203, 991224430, 104950910, 419993373, 395993911, 231777941, 611333337, 27547075, 339202565, 985054626, 366905575, 383209919, 368031007, 996548775, 167314173, 492084592, 33045618, 380198622, 35658739, 310284540, 184683611, 436846326, 752607794, 314412721, 180888058, 146394891, 371397019, 379170445, 607801771, 948633406, 789787878, 785619015, 886867872, 325860941, 105360558, 296238836, 58594956, 573594796, 561786768, 672369929, 642080208, 8703282, 439890350, 286650064, 951071630, 582985908, 53703484, 28285082, 484599297, 841334272, 99379370, 153411046, 725318103, 372303241, 422591330, 594678971, 664832216, 493047472, 937357814, 145621617, 183048913, 68204203, 991873576, 570435213, 171175723, 474379042, 806967307, 146872785, 690584618, 242225011, 882757771, 354428581, 196075259, 986182982, 843973629, 265892145, 461885001, 832142437, 284626834, 210845447, 719550011, 608973691, 87902119, 110015030, 805782332, 945967926, 123636101, 635608582, 363941811, 140996793, 714502086, 314731281, 673194229, 251449985, 667012046, 906564436, 553140927, 850239426, 326812578, 879280193, 719585419, 754323870, 174438644, 144214836, 71002455, 984605118, 780381952, 242727016, 848338390, 868374828, 290597157, 469455807, 262982434, 507457311, 614984462, 927688215, 500296410, 868982924, 502177036, 987396864, 744124445, 70360857, 442305265, 848360963, 37731380, 997341733, 405517961, 314742446, 447864808, 34428867, 647564223, 209835680, 789607737, 189294866, 821359626, 405848208, 597124559, 682974701, 567540149, 223100220, 1846015, 86337741, 804433804, 346860458, 637523074, 467199648, 178065329, 697516455, 244762604, 678823336, 113370105, 959515390, 217234083, 818105041, 715665700, 41312873, 63041107, 316087850, 948788833, 665192155, 630891931, 727493287, 770995506, 770832041, 160512010, 752393269, 295858426, 81798315, 93046472, 11969776, 422341402, 738747028, 741601331, 499147105, 383106442, 904734577, 923798519, 275223077, 947059179, 483986632, 990504613, 120272607, 988842758, 868471394, 501312730, 762265017, 267423668, 12397088, 664857226, 644387983, 508806081, 784084092, 784425386, 885191920, 14426594, 143037806, 289360319, 96368869, 7429589, 21193326, 633373119, 912351814, 5253158, 508715484, 244846469, 244128578, 581011486, 886690952, 486585812, 111246254, 620846233, 881978660, 972135209, 929640475, 513073534, 272041526, 455050455, 907522660, 403610523, 529729715, 65640434, 500871271, 758394991, 395238495, 520493878, 269239134, 387513075, 345351057, 215889750, 706242924, 365672609, 83065494, 651453081, 180885366, 764588474, 393289388, 569412810, 750520105, 285197883, 19581253, 722963780, 988944427, 468591395, 832287787, 656593873, 803013323, 341554808, 134929240, 875731243, 398144812, 984157615, 824908513, 14699809, 862846987, 414127957, 78010867, 851869899, 751018821, 609440764, 432560086, 8063612, 632906712, 756539408, 259300606, 471019509, 450440789, 79902253, 327094395, 581562450, 367027398, 203952219, 161098230, 888639857, 148505027, 983873968, 371822810, 940839757, 269967221, 284398261, 370845188, 184715805, 285108706, 815721967, 279684963, 542341026, 334246574, 492619090, 231417924, 89585287, 53957923, 939439573, 762613829, 854692852, 597497599, 667090920, 422049235, 334936078, 112898321, 936201808, 992585607, 660202938, 405317772, 710956853, 352680174, 688789832, 179862406, 312919423, 819846403, 797320523, 483039156, 527249531, 732851699, 13884065, 3968033, 876578607, 188913350, 513352060, 563155417, 315978268, 992001814, 512954736, 490730938, 996919179, 238719469, 407603369, 988480430, 618141794, 589847194, 71729118, 756336394, 687304241, 664937844, 431896733, 813507955, 212154872, 425227889, 935122972, 149136725, 302680738, 150003515, 380426159, 154503916, 495773707, 10712159, 986267749, 443588717, 641475524, 771174610, 321740327, 590480854, 506153772, 490927723, 120887896, 722261672, 959463791, 278586752, 479212955, 423920698, 293340782, 543717577, 956733381, 189907393, 155653311, 545932045, 258094666, 761041760, 949184211, 946484815, 967238490, 683411082, 860501349, 890521812, 776810228, 743741342, 958965693, 281122961, 735237549, 144563431, 950086100, 303506934, 225786054, 142770399, 734693040, 927028832, 344015362, 521943604, 605718192, 326637562, 654422160, 82650777, 56082144, 212880922, 800955830, 876903546, 985600580, 177952974, 545857992, 432990180, 820079343, 174907790, 14658399, 650267407, 754670123, 309508224, 147763736, 152310882, 537198933, 391492543, 822623327, 128281547, 843339115, 761782898, 786635461, 77724356, 461747118, 175634419, 382731839, 513771429, 923871426, 301446672, 989359782, 124992418, 927147796, 662809558, 992806554, 348932878, 107055229, 767352842, 301876572, 354907501, 485876292, 661960023, 241892978, 810481933, 391419550, 589712556, 301638219, 154242044, 303513496, 550840207, 351175686, 496456459, 150375317, 220856201, 556964503, 990277394, 929179214, 471788231, 262695408, 529475429, 185363918, 123167153, 192587963, 383577813, 843752, 798766633, 222142342, 910724491, 105083188, 369522759, 993153495, 949927818, 781698445, 282646107, 595072593, 429115936, 747831845, 782384345, 785265664, 446637922, 347145496, 838578786, 567687965, 639853120, 952816852, 420802417, 616229039, 984442210, 380312568, 383014865, 418645764, 177938136, 886443903, 779678855, 219813336, 939347110, 14133078, 201088558, 620359399, 160075462, 511558949, 354266256, 440744253, 850875728, 120483694, 276868542, 681439264, 614456803, 21105146, 589251391, 374907696, 546053551, 619216973, 575123329, 791643101, 459142252, 67431258, 792169492, 158313642, 240357163, 35309009, 120887209, 907530237, 751020037, 766758639, 866119910, 842645654, 15154524, 946836633, 729272852, 574992224, 424000414, 973346267, 5639356, 704495084, 114619663, 698267145, 472478947, 295002916, 423627000, 974935461, 908847168, 32068237, 148365010, 241367487, 248230661, 280194551, 642097800, 642276282, 479682142, 220360894, 865918454, 875572408, 85463236, 64382256, 925905484, 913964014, 905970967, 410216101, 411630608, 244480697, 341976149, 608747373, 15808639, 463222069, 598754434, 528881364, 486552921, 602787516, 485750753, 190114275, 428413732, 3420374, 635794779, 907242622, 607948808, 430483256, 413747927, 291349506, 116633681, 86487866, 151178703, 503248761, 439255888, 996097651, 89779996, 721897289, 346817769, 593421453, 55069752, 756778646, 33903462, 112634295, 473268551, 901615071, 119686753, 24294466, 428134250, 916482042, 538747613, 645126199, 422518151, 762868021, 896698705, 547329322, 956254700, 117137033, 258374750, 519995477, 190587447, 816014668, 783479441, 269362510, 599384451, 436622717, 97673898, 370202892, 276810355, 575741844, 114672431, 128402290, 217814429, 164637693, 539385223, 843108636, 661566726, 813894224, 405619405, 334661507, 824246404, 396059948, 136338157, 45244378, 764139621, 964054417, 936203201, 555708015, 829405734, 62531212, 716586266, 992348523, 861500209, 182197124, 590471667, 730474635, 328198087, 726134226, 769903437, 386262650, 128854866, 45399622, 414725222, 687564774, 327579179, 524822050, 952853151, 177057104, 686811822, 897723853, 162638275, 279119872, 489610359, 352172476, 710026269, 300317909, 76788936, 280477920, 314207621, 669772604, 121219283, 380589248, 5917941, 570196198, 289742165, 329527935, 288579640, 807603555, 876389872, 58785469, 867284097, 746528064, 924333619, 250066897, 865784919, 850363982, 466337491, 589497717, 4481151, 980152931, 744001304, 146547912, 108882698, 481692819, 630069609, 486620802, 356509948, 273788093, 635557264, 836059338, 650996631, 541185954, 557733556, 312541097, 344311844, 410976863, 118643842, 154508822, 106868785, 936684201, 343805101, 419625654, 512337378, 632110631, 247026968, 259371360, 409497847, 976035816, 442049421, 464115830, 54821076, 462703738, 998583950, 802487189, 115615558, 440539378, 447268685, 865514851, 483228150, 463115025, 353156965, 949055603, 802723806, 660026318, 874346649, 196976126, 234508625, 774217584, 487332028, 373783183, 910162765, 917694760, 92025403, 193753854, 718471244, 821807247, 956010331, 991020032, 340505556, 664233621, 853028075, 638504147, 515351987, 185005310, 137296920, 171369736, 316991231, 90462744, 236899516, 554836865, 923722172, 171686884, 46598150, 47366287, 339046437, 191989774, 728029644, 519413282, 407615749, 511688199, 71141098, 255712661, 382757112, 712648946, 408487556, 280426183, 666999736, 931179472, 318016280, 294857594, 394120623, 253268538, 38704109, 943605429, 910120205, 513667733, 181788577, 197862026, 768854377, 785298412, 591610739, 833177105, 234652211, 469631799, 136746343, 107540871, 114093759, 97858266, 829385309, 756280464, 14504148, 839927690, 942301152, 200886340, 778111472, 146427427, 383784805, 402765925, 836189904, 929600292, 628175572, 890948490, 527635642, 244318461, 728657850, 949457598, 402568329, 741462761, 680105956, 743009864, 786517206, 24312218, 484257516, 240781366, 754623701, 347096670, 933593935, 151449218, 760505952, 217001136, 212304028, 554557671, 457882556, 899805672, 554608357, 3941911, 549831167, 963020648, 776323880, 395874823, 206032105, 13121425, 617817695, 358036219, 846066519, 410964101, 106444334, 88060326, 666210371, 431702913, 304061062, 268601098, 70765262, 169440883, 503430641, 666070173, 301073862, 913915388, 970057664, 769081116, 920087740, 102417893, 284577072, 695006583, 613388324, 552018731, 651003882, 200827560, 144918260, 806525469, 924660109, 158982333, 937971775, 99338323, 435527481, 917048797, 387562190, 495591383, 838642432, 783871607, 30271948, 436969781, 176347140, 752455454, 918562187, 855773965, 926138247, 317976351, 719349476, 764846908, 48010882, 661820743, 18793362, 314063880, 523185492, 482948281, 570019555, 512635481, 872112960, 302855801, 961823991, 36215477, 907403068, 474308168, 552071700, 305348994, 681144968, 733383852, 837925303, 633617274, 238807637, 484731762, 370672060, 575343042, 537278802, 223663241, 543284471, 919916034, 13484286, 379203192, 152347553, 700343680, 16201801, 816318982, 437315152, 65581360, 591799224, 967659542, 895758435, 215853713, 397067267, 780690227, 674816270, 187783838, 920462682, 464667979, 590867370, 671868920, 72288991, 321936477, 271455477, 443977940, 21781348, 736060957, 184394096, 77162619, 167129115, 187891318, 288043847, 396468551, 229124173, 413533315, 821061470, 846147758, 595353899, 102507684, 169821336, 502514253, 979665482, 247823153, 177902716, 204479601, 67668431, 221051680, 102909210, 16394334, 620291693, 398951629, 43742292, 407544805, 21673865, 827559542, 213886733, 29144967, 115153054, 881880651, 241737358, 647058986, 131523377, 827794204, 82241505, 141526510, 243479444, 162616980, 430187690, 842832747, 808811904, 852907225, 961415116, 995803757, 62604013, 116857993, 301108956, 3859181, 382187773, 235549618, 744112981, 519498992, 42820985, 880990774, 272402012, 1163732, 477922976, 332955871, 567934293, 104352708, 514496867, 625741817, 92401496, 106888872, 174174334, 947535557, 185587062, 152067355, 565323675, 619446069, 65556239, 867529866, 642453443, 398362616, 242976412, 825212853, 814764124, 16837441, 610888116, 967451002, 887920058, 330168627, 912687921, 151249921, 964228953, 337810027, 661630628, 229489407, 951884315, 292005390, 675148261, 260225738, 917876835, 560045256, 735638020, 748818070, 960608581, 950384084, 712805869, 653861593, 728540199, 160064761, 821716542, 262711632, 143371404, 106740126, 560962424, 201524235, 389123393, 981933929, 314870508, 223269293, 482886748, 577258979, 580441513, 353876762, 732511067, 552519408, 720762595, 888926732, 568453453, 278202810, 276913819, 138413228, 740037201, 603902232, 430326908, 949249259, 928260951, 766277914, 1689579, 714590056, 767514668, 751013038, 699334906, 356698149, 164363967, 461055317, 920106895, 393584582, 74801868, 610292181, 119510105, 246961566, 207297988, 842214217, 403563627, 340566201, 553799347, 512674597, 366381294, 355330670, 797328081, 234499812, 125528366, 831706557, 830356961, 622975373, 236019912, 546363234, 599286198, 200713598, 525546031, 33841874, 47924081, 96007698, 533348384, 491836210, 140496048, 302483045, 673139311, 77414345, 254229544, 708193724, 803408296, 367326915, 975194461, 457850693, 670651904, 969943785, 939758797, 90870425, 473460525, 971227895, 611153385, 776392428, 976950120, 906314177, 470544669, 431968388, 583623034, 290180537, 845310667, 95804162, 349330434, 821527572, 632951900, 153795782, 254673390, 59195050, 964783551, 965157965, 668133847, 256735062, 222945730, 293139977, 489712763, 296561528, 827576341, 558068410, 487421855, 957435081, 624404826, 996426328, 628074870, 716806181, 447761345, 86322818, 235615756, 984433533, 143197528, 126524377, 171610579, 548477747, 549826370, 935944711, 896816640, 273878369, 387475377, 195175293, 667101412, 328619066, 462821977, 647728228, 36849105, 347609702, 988390957, 675851882, 312820272, 356880659, 753473900, 905428146, 576569603, 642804033, 515503388, 428089006, 115387591, 116303715, 479636697, 244485057, 136162163, 422790598, 402609781, 287152659, 594985507, 727395736, 821856598, 334663871, 194812932, 873243633, 359459438, 597811558, 279933520, 959030495, 896049361, 509491020, 366277498, 478030297, 958148515, 521223506, 743778210, 831423234, 701228232, 605436882, 792616129, 827874428, 410576201, 906266605, 480091720, 385508263, 995815174, 207658834, 980208955, 196900395, 766698491, 607991290, 692055561, 34789450, 213614008, 517638899, 442285150, 893849255, 565665433, 303422053, 140545832, 83251635, 46733735, 914257692, 352185626, 850223416, 659969631, 366083909, 741884861, 57565907, 646725856, 706143704, 413847058, 863321897, 789121897, 807936180, 584112572, 772414893, 371129962, 649671303, 319462087, 16096540, 839424340, 989431923, 515795522, 572643630, 90359331, 955354061, 182496142, 986051163, 59422459, 632921247, 60631899, 794194894, 612644953, 583750154, 279783195, 468970166, 242008396, 399005478, 964687953, 659983079, 638900475, 776455299, 387061020, 144623645, 147267071, 405799345, 845936004, 890759348, 526614566, 979305624, 254941947, 911570970, 729978559, 913645630, 870927167, 623977917, 757545329, 225820875, 589768459, 21055629, 55071088, 676388702, 535444678, 999115128, 936807016, 333938773, 298696712, 931567215, 761209986, 186487718, 810528241, 531711278, 734801664, 452165037, 726783493, 855842831, 339477830, 5271806, 10582389, 459059343, 506676761, 35196975, 863831034, 3318283, 477099298, 349016890, 361365211, 804192662, 430906995, 232959563, 826731729, 831614785, 922655957, 984684158, 579062316, 822270593, 19180654, 217763017, 882537324, 251738961, 715160360, 452375304, 873794226, 176100400, 917576532, 203157008, 644653150, 160359400, 546132774, 946127956, 17729020, 741345074, 447241629, 529808224, 632729735, 767731589, 870727141, 644684540, 205539476, 933241442, 889541683, 345385680, 971529878, 507693956, 281773121, 984085917, 842193866, 533712759, 793224065, 532230406, 389489503, 485638916, 844441799, 555359155, 812718300, 41329270, 340054923, 63065514, 569884599, 712507991, 279903184, 199359964, 779699071, 283606186, 209298844, 571602257, 8396013, 366870285, 319750522, 97357701, 240031074, 544606753, 879338556, 904486554, 889937285, 881786060, 837639436, 479085130, 21765387, 736692644, 732941273, 165041619, 705011403, 856471540, 504275451, 604959893, 12243066, 773302609, 885870762, 815311362, 146893063, 628888450, 834475700, 789847010, 661414553, 489901407, 712845501, 342071803, 136554159, 167902073, 74237085, 563193183, 942547191, 420252301, 880187855, 909082735, 1995438, 768620498, 247774302, 634602891, 670676313, 80806113, 821821968, 947019614, 838304457, 291007430, 538466378, 921770443, 713766180, 373630574, 253364979, 603189437, 105816872, 395588462, 780476736, 509883957, 3788413, 559820018, 318910630, 49806154, 537944363, 475547372, 102781904, 968457734, 383421350, 855115302, 944317986, 111241619, 372904298, 968800042, 981609711, 30547761, 883677383, 516509799, 367973182, 458396797, 106510335, 219291802, 106895727, 857879075, 469871055, 479843879, 58388688, 382389451, 730120568, 430766925, 586830662, 566649746, 925782107, 992529241, 44495205, 545770799, 359112028, 72118829, 512544695, 138977014, 417620012, 371922667, 631742526, 607013224, 724173234, 705099702, 829882741, 64801345, 494247498, 733086790, 305091876, 704962828, 807879871, 150610743, 514260164, 212653757, 77912027, 982631191, 989928938, 745294454, 466218884, 763495787, 348689874, 121534102, 460394454, 46218897, 355920187, 447765439, 334649493, 661181819, 227889919, 234818440, 862210136, 839242780, 223378545, 136698728, 282687448, 260253392, 817683807, 521086780, 72794340, 738126427, 946764463, 304227389, 518068233, 836928124, 473721255, 496130684, 403891487, 435055229, 486161878, 581269592, 41731005, 339483805, 230252012, 880197170, 397542349, 157440455, 993586154, 723092326, 735536530, 854573035, 719037813, 651250156, 359847442, 800201812, 710966721, 717499124, 584815302, 583463185, 629421443, 526521253, 312518808, 335259150, 655988833, 941063833, 117848194, 759327779, 162851711, 99291939, 518103558, 431119860, 953502083, 592741498, 390199164, 94959738, 51911315, 707419685, 943880319, 679805912, 859289720, 173419922, 624194631, 79588441, 502963863, 364094251, 698570396, 909794808, 397072502, 56989909, 971804104, 925131442, 311429799, 205389018, 841418934, 950055454, 57077943, 163575829, 459657292, 422200023, 485286489, 553858965, 855162779, 227182075, 788334934, 119117939, 499113644, 947514239, 517996950, 125116750, 422681781, 659450409, 333132816, 938099520, 965105401, 201371328, 805392974, 458584652, 838594318, 5985751, 671098331, 479230885, 563827317, 705821242, 47240510, 608794984, 129229554, 643273136, 517007012, 250716389, 464220925, 342874960, 654196498, 628692574, 259426969, 219108263, 732155227, 679450747, 436321258, 580984758, 510948119, 407250198, 65030975, 881454522, 169556409, 401604162, 889050529, 651057466, 215440634, 153510092, 998072582, 732377713, 574281404, 82146558, 328246724, 156109946, 718482581, 348569768, 388085809, 343355808, 72801272, 324737326, 900583948, 503881687, 169176997, 404091890, 700028503, 491804646, 214641092, 699446337, 399506676, 640749492, 371458245, 272412374, 961062158, 321113751, 431846646, 830174960, 134462455, 126557500, 677532948, 965731086, 282682297, 418963909, 448743909, 66080964, 276271688, 750767137, 345284643, 699006091, 926129518, 453650110, 740167408, 166516319, 698252720, 688280832, 342673316, 188589296, 9611, 784531740, 495027967, 630933091, 837331979, 658090402, 196268908, 42781914, 202255604, 732060300, 347924631, 399909515, 206461338, 32862381, 857131881, 664467724, 512982283, 138652390, 978345919, 526657158, 613021429, 921735581, 994959698, 87058938, 296836554, 637886410, 937263534, 801731540, 301913362, 951172918, 8534397, 16734935, 204635803, 300605820, 674176850, 639060810, 322595207, 28113732, 446453055, 300024881, 688518519, 196569425, 767761252, 733325053, 662166211, 900353057, 588072414, 244273204, 426071962, 549368753, 584425510, 557767224, 502766014, 896362576, 857021232, 147182015, 987294832, 74437864, 683422098, 942180434, 407162688, 541951486, 314589576, 905651311, 219022524, 728790040, 548106974, 230081771, 327765905, 934465451, 586886657, 905741473, 591312547, 794504756, 885076230, 855706530, 7602182, 537381556, 263289197, 603048570, 423607630, 838548775, 407972017, 102867085, 98503717, 729456688, 584407074, 129899718, 809476232, 927416575, 54509034, 220393433, 848840123, 315598378, 887904887, 363598026, 983944271, 438062904, 64439101, 859914350, 340472707, 624289354, 611671932, 786590871, 991218604, 225144943, 775727078, 784294742, 810208481, 328549207, 958399420, 654632575, 746393328, 115917075, 473169458, 94501836, 650093732, 262842251, 121371377, 811163691, 649954193, 697307320, 361307587, 579616032, 951415655, 565556094, 445543476, 640424781, 148954089, 836947197, 431594953, 790537259, 663316200, 183548489, 717668733, 897785723, 954155055, 845134203, 836269035, 249119065, 398755092, 618369449, 211323958, 969635422, 449504997, 346441861, 416660845, 175825398, 983476777, 697055389, 111537623, 392129584, 841254267, 220451960, 864074956, 675926767, 973779030, 338506765, 44757965, 673575167, 117506084, 995534485, 156637532, 680993362, 713809345, 901869517, 412520249, 694360714, 234445022, 862417911, 60401379, 678654037, 562580443, 567641580, 498320255, 297888196, 402337509, 907014735, 464404106, 382552917, 263394231, 87703109, 5377567, 81951987, 995796712, 553546738, 348305486, 60362656, 218297748, 744082989, 145791499, 634245441, 338339962, 739047768, 282932074, 386103420, 626035867, 810848458, 542904037, 956622870, 81882094, 786682250, 324990133, 303121415, 166504572, 230406866, 865643328, 280260083, 562404532, 408709989, 748118088, 408490815, 392552678, 429479873, 95315291, 732603561, 610675318, 312222876, 532721737, 180169036, 474101671, 183411642, 73543143, 318078917, 728695192, 813006106, 230993263, 669684009, 52344400, 589243197, 209227620, 407310917, 259139588, 597209693, 170521465, 721264432, 946995911, 94156246, 740319759, 86721298, 823101826, 895375787, 858465396, 957115790, 961022783, 799851394, 536312990, 665185816, 892313345, 60840015, 843789009, 49049551, 712342688, 499726037, 96188568, 326285484, 337987790, 648971750, 933190417, 760112476, 541601435, 433818659, 365366276, 638633806, 482528933, 348367172, 9688129, 398101223, 919461543, 42246127, 275671832, 968367187, 811245359, 417204590, 640403999, 275141657, 876478445, 624894479, 559092433, 230907392, 644854844, 741860993, 205747280, 137348347, 898238410, 395410255, 328574187, 160866687, 642114253, 210385002, 889461373, 476167515, 965509119, 797434138, 366833098, 322640033, 857763728, 795650060, 255426454, 68194037, 904843464, 720350304, 357510384, 787666319, 695013302, 203154892, 107548351, 781316411, 525058760, 392770341, 106358196, 269241568, 606697493, 588797734, 964730036, 450689367, 766927214, 648036550, 554955088, 574661021, 433920726, 582489213, 649423317, 219094782, 371920451, 435104849, 106160634, 893522632, 629068122, 12085009, 487441069, 390752175, 558615914, 952320720, 817443779, 469712096, 25655265, 390496455, 63368195, 176279182, 94607276, 623278630, 747647707, 222747152, 576754212, 524055099, 580489782, 493355250, 344454875, 58882168, 997213989, 327610100, 391028602, 644370007, 152626432, 607130676, 955589263, 354320582, 643860146, 122646442, 667712468, 710455120, 571570057, 494341195, 326653621, 612109743, 995488346, 135389170, 972837943, 412038343, 869105488, 501245917, 870508633, 879724337, 159244625, 69820239, 528960505, 2800192, 618942510, 819883858, 65715307, 219192986, 236622584, 423574729, 541402875, 577297344, 304603511, 607071246, 455777857, 221855199, 254449891, 151208694, 462336727, 899494108, 637690715, 965568311, 918587161, 943635608, 618322444, 425857759, 488728323, 318397401, 796020704, 426325029, 460646479, 858849600, 614815736, 190862311, 572832192, 237036635, 688419179, 214883414, 81848710, 838058760, 839320185, 953598407, 899830349, 478290467, 387492049, 261758299, 896995248, 394869698, 753839997, 230638667, 146848688, 745858881, 276237871, 880048602, 974748396, 737637901, 131319744, 349636724, 892257640, 687457056, 690137464, 840246943, 631564601, 949866691, 962453777, 469874663, 80929067, 860260622, 904838584, 732566614, 251732580, 332402208, 631169319, 178113421, 387483467, 507536263, 107061992, 33754894, 909902499, 367808239, 871653610, 349391046, 743850397, 64575696, 913790013, 260002177, 737445604, 514195002, 594871952, 727918706, 140174942, 443851891, 633293518, 9669218, 632691847, 615699670, 123074008, 199774024, 605703274, 659749236, 864805360, 816535742, 966059459, 837098095, 124277266, 739772353, 650654881, 68679204, 102477681, 201778384, 169969219, 308528021, 600659744, 826279710, 495984388, 489803474, 437458498, 605936725, 697596654, 278115911, 60557101, 898831167, 501727011, 338431807, 4414505, 597590498, 626843665, 431763653, 627695484, 544614895, 931291250, 183317064, 722330485, 907205256, 45929184, 694266174, 706078395, 430431778, 134494647, 525546607, 455352920, 938555780, 492648074, 925213310, 262947580, 846830183, 346320862, 441957787, 917995158, 648095194, 56781410, 351278014, 767274328, 13082199, 462679200, 544256975, 586399284, 413034501, 635656762, 622258630, 116438749, 981928833, 614392908, 963903684, 782854058, 453633062, 207647013, 41494500, 265695678, 84061943, 212516957, 611503938, 999454209, 241105907, 82414221, 164815987, 36533961, 646301914, 5750017, 530179769, 357567496, 328335992, 265182920, 850050560, 248242669, 643899333, 635469859, 667381999, 174714888, 442635446, 835398850, 73680848, 145736338, 158582911, 158000297, 380696536, 465097370, 424504456, 555907986, 418360660, 82037, 4216738, 169733839, 647849478, 733768236, 381884496, 552108950, 695530135, 652981744, 802070399, 522978841, 239297897, 799861706, 536463268, 80706352, 974787249, 594327057, 664184532, 292405207, 637991102, 695346070, 45841097, 998443797, 116973349, 39928314, 310647794, 414277194, 344883235, 843573553, 581082675, 228137349, 382854275, 427430600, 380969085, 100887043, 736319818, 899063202, 977415037, 401802693, 782634125, 614221080, 87080725, 421673127, 365522253, 399275627, 588965516, 903118737, 773592914, 253870839, 929210055, 558080183, 854913286, 424537832, 527991758, 265430045, 383334908, 127010690, 452004722, 44391826, 63189850, 205542254, 759071302, 994107507, 768994010, 892236068, 654174034, 721182771, 706697780, 11556082, 127160320, 989938913, 936267522, 739634266, 75842574, 886049631, 194554304, 629905497, 694900385, 836198433, 882247136, 568386373, 756423655, 686573250, 430427265, 281529459, 99522002, 96404864, 276526699, 993755506, 958120680, 146000018, 290311486, 796377052, 242466403, 266891403, 700721767, 420240546, 155812826, 940574563, 678235785, 129587077, 255590327, 469317424, 648009965, 416720026, 571304189, 268206342, 717614444, 982564692, 808371524, 28078495, 188399229, 146804029, 558042073, 553151155, 626427306, 389153967, 171816663, 515351994, 22985166, 665555470, 395821824, 716851824, 76880566, 22987034, 633031860, 912522738, 771671996, 667147699, 347995992, 281600182, 634418332, 723824642, 334530183, 426184612, 953188488, 814362313, 977651438, 718953800, 177131128, 601728300, 681134746, 315549845, 48007334, 731589717, 245553641, 713520595, 686515693, 113583807, 565947281, 839604927, 401170775, 908823250, 543348755, 327742244, 645265925, 317985332, 101943286, 542000665, 499276633, 469536426, 163336520, 216772705, 53939102, 810060305, 508381526, 412540975, 972015181, 559860385, 169009749, 190572866, 166845603, 252493662, 792932284, 338462183, 596931213, 368035385, 338610409, 191422267, 159846818, 388749724, 114401770, 51367961, 6218493, 226588582, 616985094, 781295752, 958534628, 683766196, 75821672, 345708026, 323186321, 574496664, 386139485, 726949291, 107346837, 710194553, 246024847, 552673161, 967765757, 529331590, 911444034, 309426285, 730291402, 618398672, 865707051, 55748693, 220710347, 874359408, 579992738, 613420334, 153422207, 168280023, 958957066, 82389944, 846889965, 500864746, 719229116, 491404072, 788746111, 151860353, 93686487, 850319525, 464361800, 746884561, 898777222, 609792245, 621711187, 266630180, 114725772, 654656772, 680263709, 290155826, 929266809, 584625045, 843860683, 426492351, 237265089, 637872413, 892006713, 47641792, 730834884, 225706467, 303094013, 282436604, 940001825, 240461115, 155271321, 543717956, 668735594, 468209563, 292082622, 413869798, 757019550, 828693665, 141933091, 209308403, 611704930, 910584013, 340516744, 272784622, 970923990, 196629554, 739687486, 860077038, 105828520, 628207070, 385522320, 188571433, 980368969, 807368682, 587217272, 902757235, 155443843, 955864749, 113215221, 774185169, 10280638, 541093412, 700983464, 76733085, 174794761, 683447166, 335374579, 858923408, 691935637, 429287040, 376094774, 815185553, 995182299, 681084358, 429839519, 607488707, 876345987, 513809822, 380172054, 972906721, 727994996, 436267625, 714699857, 106591097, 355946192, 171122869, 133157180, 643226687, 536321151, 520285311, 96769612, 937389058, 223552665, 755407743, 550037865, 535729456, 924789374, 822325679, 759264441, 965058031, 930613290, 353442724, 938293886, 809104905, 184824282, 731493560, 706777278, 209211989, 33282003, 404749630, 898874068, 153412023, 925482408, 661889881, 270734881, 664064300, 633630093, 813098923, 445445950, 854997607, 830646334, 148180486, 340673758, 104832568, 299660505, 711392429, 100788674, 807047564, 268421768, 715296570, 190305381, 443231568, 832225536, 269840080, 510701265, 282637166, 861348405, 381149131, 492248858, 936882449, 732564422, 439264705, 806532298, 492921658, 24422655, 310863419, 167176654, 175761472, 615795419, 124858677, 71064786, 843591469, 728806680, 390455938, 630633363, 716571758, 911415260, 83835412, 921676774, 440138509, 337637652, 383179451, 436930679, 748665777, 374991412, 87893374, 725950336, 791003097, 603640373, 722851513, 209598310, 418821309, 944742264, 162529191, 607091808, 600996285, 163693971, 476551688, 98537635, 609946838, 379674978, 194601055, 261535816, 150959352, 706255476, 311732951, 227779131, 276782136, 749996612, 637933579, 252685632, 826005972, 432190427, 898522653, 398586674, 659924352, 240606699, 605131435, 18360212, 101409664, 827201715, 86683296, 355004065, 946185208, 119851411, 692819801, 502233768, 233213801, 730659263, 342915550, 131929341, 255895929, 275765536, 213378664, 568522022, 126358582, 112644788, 641408612, 576018351, 52868212, 957095530, 349335350, 522962071, 981263746, 457367517, 628533501, 881644481, 506563343, 878269187, 881327422, 167498828, 304516088, 354705335, 735156465, 270348724, 286998709, 18124972, 403727661, 849482014, 365248580, 268669278, 475728279, 698899193, 924293464, 247976676, 637131790, 336571926, 326986566, 306634153, 272020552, 272653443, 112657518, 631836417, 896627493, 766676206, 625748599, 658574365, 270576139, 294906950, 616552184, 281359935, 33720847, 988285743, 249558277, 14860098, 804260711, 97216577, 513815014, 583222149, 819873397, 811343388, 144635492, 951042603, 112278366, 377158128, 774984685, 769022268, 374922556, 109942825, 682003020, 999540017, 402132093, 894685153, 508409259, 245449159, 990884046, 867994945, 786144719, 289540111, 400033045, 621867854, 537690587, 662493558, 837954632, 190455819, 856089658, 22366165, 545491834, 128052998, 576687592, 884025610, 350940500, 967340811, 191129310, 636671675, 251672598, 656404406, 256321489, 444848688, 51039353, 69651790, 286370919, 244038395, 360488413, 553502645, 686947078, 200459420, 729914270, 563316652, 547893883, 152735778, 503043220, 436647694, 621237481, 797983703, 585254950, 419923334, 817757317, 933561644, 441729310, 432165774, 891998462, 507075159, 267096343, 479350864, 386561792, 70695205, 728120989, 801691063, 693814568, 297364012, 940666776, 31447003, 294713896, 368847592, 162064922, 261033832, 394020574, 835691375, 484618667, 281235964, 918027300, 754111630, 835911400, 776790581, 794401896, 429786764, 402017919, 910602664, 697869572, 950284288, 765264238, 605437445, 616042383, 223380280, 865208167, 314018769, 820922569, 43891596, 67103114, 475120293, 839158025, 502393864, 732372832, 927034019, 170436225, 148527940, 703325329, 750470422, 438788063, 835250929, 606788296, 291309115, 157880234, 593990547, 919264683, 141917379, 812476307, 701420231, 713302795, 431070150, 66937139, 430294684, 852923237, 554855058, 979400022, 61284263, 347301885, 528129422, 161488366, 279051794, 859602756, 551993846, 380797151, 85694099, 398680997, 287463661, 258917882, 164750329, 491307001, 132407179, 422783144, 734864381, 692875759, 947496685, 308990082, 893671593, 411751534, 803014550, 356025412, 600245131, 205611994, 545159693, 319210335, 388949930, 461887222, 419495943, 683456510, 462758775, 970494550, 827475600, 673723351, 733379794, 683272554, 481937248, 95884559, 525779369, 680322556, 570026241, 103094296, 175642793, 943734347, 651593505, 462164404, 584556181, 512518242, 686962722, 621739082, 977007182, 815345094, 734222632, 599483890, 753884549, 960182092, 915437943, 455994541, 265267370, 386996778, 105786871, 511871962, 757013626, 138861006, 373012006, 849582509, 527173347, 681022417, 716907489, 188973052, 696703378, 639429089, 258897959, 212004240, 427879732, 25472837, 583436371, 580606791, 885892258, 128241369, 213116331, 822044426, 457591846, 362430284, 86857567, 433642503, 588357804, 715001928, 283513590, 732362454, 762294576, 392225892, 166749298, 657634612, 364888386, 21580881, 33099770, 746170843, 380390086, 292012551, 314592364, 43904488, 102662189, 461354381, 622029313, 401608188, 296334406, 349894971, 730705317, 949375375, 314481667, 284576318, 30821261, 915386926, 472520236, 751027135, 442551503, 837782564, 176387468, 991266243, 379462922, 401336480, 734093764, 416936778, 34718767, 728330587, 307665365, 362090188, 213851566, 911816903, 890355629, 932652180, 117865699, 559619881, 299531802, 96264037, 426812125, 446693696, 621938143, 11383760, 799580174, 796416567, 467854240, 531706617, 768732202, 214583689, 694637338, 387551456, 924731725, 429414192, 795508424, 875520708, 330935882, 400158540, 775038146, 693503935, 83093198, 266144664, 351300449, 311879168, 725055911, 874440522, 911485004, 968976784, 530921409, 346426572, 223169799, 528309515, 396633967, 416370212, 793299867, 833791036, 955514736, 698611768, 237171584, 473760587, 174888088, 484057627, 178507448, 737920691, 217955112, 800954789, 763537089, 888100756, 475315638, 297774054, 368534258, 1720268, 541957973, 638998806, 656435073, 963446243, 981042793, 313007957, 194205338, 561148725, 262482921, 730492185, 34159645, 167272210, 985835216, 728586816, 95238025, 514219583, 733383009, 285174185, 862611347, 473464708, 549416230, 948715887, 842572147, 793702048, 754760392, 162238097, 223759154, 200020829, 587603588, 907998172, 176729456, 887331714, 121551416, 67351609, 527871062, 528841854, 233486032, 418894727, 755445596, 651497938, 528896700, 345836829, 54827737, 636372394, 209727435, 330541304, 428315266, 759909366, 310684002, 341207016, 301352727, 445831062, 64486351, 935038276, 564413620, 811973069, 428120413, 806492043, 395622498, 836708325, 865442319, 877849738, 453663370, 869457411, 513239841, 299827825, 107965865, 752640701, 402360047, 788196590, 400546888, 919027457, 460290741, 562096011, 672395920, 555683420, 976875651, 373108972, 410425616, 107032971, 101585343, 265118413, 640209737, 595560018, 554952829, 940474560, 328293865, 416960300, 117164210, 856426131, 19065032, 822060131, 706802757, 191376123, 963938616, 633508904, 890566179, 342784911, 975317568, 386741310, 286230172, 138110470, 588951294, 967590386, 556709983, 427466447, 242978819, 17770074, 66015492, 429700332, 774573923, 761116382, 617921907, 840497380, 125112494, 126577286, 62620293, 516088437, 580549548, 409547954, 204624106, 496300122, 417182291, 701527603, 71177530, 178572700, 834732469, 787897824, 595062631, 344623008, 786816704, 134819850, 488929745, 322782283, 671725185, 464938354, 623431485, 875720955, 13314789, 263668336, 726236060, 594062863, 781584485, 817766359, 367678428, 993814043, 371421104, 187065170, 467588918, 471944493, 594442240, 600700890, 654852018, 223467843, 458540600, 535353808, 799582935, 166360684, 970447151, 284567766, 680417264, 257935388, 23788130, 731150132, 933983274, 341394442, 214025696, 53429401, 824379263, 603477484, 501091301, 433911646, 731793745, 771968207, 15749874, 891527351, 373608043, 868752248, 208622433, 93337472, 376471080, 728110243, 378904348, 196358113, 310823412, 173182789, 193662374, 487628501, 82486470, 550700386, 976135617, 322870233, 679632122, 449634613, 988093939, 167960867, 36525842, 88636333, 251624116, 264016494, 65590489, 319532464, 515764388, 277940838, 578644800, 330589390, 353656280, 570562647, 427426713, 499686928, 140939904, 233132789, 858756840, 978018257, 148392839, 120055241, 364926819, 272505105, 355648083, 966753184, 861210134, 32140945, 880971108, 127064732, 27472108, 83695903, 679503947, 884970346, 730591739, 969304544, 960031434, 547884844, 745677344, 503546732, 585315284, 865389915, 481120539, 361181309, 885686237, 8426229, 671728089, 665225170, 866864483, 423157632, 502853815, 949578511, 866095118, 314377091, 160053613, 847408130, 922097759, 304802348, 898751970, 700158164, 708770434, 783195008, 780778665, 370783117, 742960456, 545287500, 161359019, 787091049, 662347380, 12987165, 836718749, 169697688, 326890778, 661983668, 306858093, 357684376, 414512033, 222892586, 340237220, 911854777, 622804449, 419817385, 297471825, 629000351, 664896542, 226136320, 157944560, 94129555, 862286365, 706712502, 734687343, 267329386, 83485967, 305612072, 493808700, 861485712, 428820957, 865330469, 630359148, 995765845, 450457785, 487398972, 203904810, 717967195, 13241521, 414240845, 123196151, 574286375, 698300976, 577050137, 970178458, 655765315, 159049625, 996837163, 665423608, 232580514, 678433806, 823171871, 821611820, 738729067, 576976891, 369751090, 922959801, 406888679, 948401267, 561340100, 260720558, 425138105, 509368551, 439663019, 810620437, 979293753, 117336558, 431978653, 435610503, 417964244, 433587485, 115319505, 171412580, 679508607, 164686579, 532258357, 373225860, 66001073, 713491075, 123953225, 824750787, 533968550, 293521034, 545330664, 398116112, 400006521, 16210012, 444786994, 205481305, 981938833, 661106640, 337008705, 310524705, 614424640, 42000120, 289925693, 404922011, 595787976, 318014964, 469074467, 587491806, 438923108, 606140872, 398185822, 326394540, 145717030, 210980735, 727336149, 674220635, 62920728, 278956905, 371417190, 135618948, 664468271, 107157758, 17305839, 936713776, 905961938, 827510718, 688645544, 548215550, 713131299, 240760086, 237435764, 717431271, 87172114, 328839358, 195296194, 864543315, 901874621, 980124732, 654571850, 551797484, 725952062, 733121418, 403783522, 591402969, 59536165, 475732253, 274507430, 957540883, 683340213, 337249865, 868622334, 190887787, 314990005, 275109510, 559851969, 367564768, 737565449, 32388243, 357599551, 591407618, 16902936, 313774025, 504999649, 604721842, 664989337, 107639379, 13845142, 263475651, 590271413, 936284896, 905729821, 492800949, 926508730, 700083406, 686338517, 341183192, 842350717, 966954751, 206929085, 749049517, 302515916, 361122183, 457556049, 287683514, 774289294, 869591607, 320709805, 161394009, 311989403, 4808849, 637740063, 614208658, 205819006, 821420498, 478668784, 773955442, 427701236, 578521607, 930625514, 281380278, 482368798, 439347579, 712460028, 816445593, 134148033, 344653547, 649316219, 695813037, 680721754, 494774960, 533496814, 29227331, 112714115, 595567052, 712413245, 787013517, 682385388, 935554598, 870373229, 787948763, 349252587, 254738650, 911830024, 221421391, 752748532, 112204673, 16306974, 956106736, 380370407, 968936322, 101911457, 512258920, 864005316, 752795925, 176049202, 664836080, 772510359, 364876923, 205517288, 771088511, 774767135, 40942403, 233091708, 893990342, 882972225, 313219305, 542138973, 817385437, 198700570, 921653468, 949905067, 643586389, 272718512, 81701464, 688301529, 344617951, 750648465, 882046431, 541245211, 320810274, 104701876, 492094946, 880083868, 851077628, 125830015, 416907850, 565889912, 128522153, 823066256, 351725419, 892686240, 550209617, 848753004, 921794028, 890691725, 26915706, 394627828, 324015781, 857907590, 664982118, 611311114, 84765080, 356998515, 912607296, 579887733, 211298706, 27877958, 381508209, 540373409, 136768950, 238146557, 4619081, 969212173, 204203076, 146402041, 161638133, 882587275, 277847438, 189441891, 957060814, 591719778, 832274675, 804331967, 661382921, 475221117, 638929294, 669194435, 70155344, 442656394, 667639463, 424903695, 628025187, 537378798, 212537417, 497429894, 204168644, 824483748, 84481707, 464504742, 91307032, 843771366, 664249810, 90169370, 428634695, 805668845, 643024905, 776792911, 497129468, 155792179, 839002633, 203601809, 707952142, 484598038, 327713580, 481056414, 622497626, 273351494, 549503352, 851841009, 422216329, 395619021, 984737824, 447460198, 616121532, 63664154, 979231198, 739523099, 298703350, 65407579, 818779199, 505819174, 204270486, 97529214, 99912421, 61920555, 790268091, 509790537, 910974252, 323689857, 829052620, 426540057, 935538033, 195369513, 923675425, 33447410, 65426762, 54153529, 776904956, 284084202, 207246276, 52063948, 6006776, 274433568, 495724189, 334168391, 993488949, 155005479, 328193587, 923903263, 507498322, 794543223, 291129105, 789379942, 508456430, 529490737, 534451707, 500914921, 214041594, 423420291, 151059524, 263963822, 190039547, 61742905, 477437635, 754393308, 726263073, 12734914, 440707878, 76784962, 769546933, 757720945, 162864160, 363798047, 520321854, 840716339, 319979782, 483467146, 100292790, 595566425, 532088670, 391241113, 557032680, 717019583, 618444543, 413401142, 622092570, 943800254, 53691717, 327330149, 361175903, 928943329, 13148104, 898652331, 944446504, 907808507, 626319706, 221756546, 526986138, 337787080, 974374029, 626708361, 98475453, 109589058, 345422044, 720941418, 133107102, 693817928, 981612727, 357181537, 768614871, 100307145, 719412985, 854649650, 669130771, 133426106, 694034756, 932843646, 306552663, 965187258, 522486216, 990689478, 731790923, 228792295, 260990666, 612175662, 89764835, 557418046, 559822700, 682435678, 736018345, 114446761, 219906109, 185079061, 87398364, 382250549, 674297056, 830359811, 103032759, 878713628, 289659457, 777608708, 816227546, 677099604, 770189807, 298768309, 604405259, 835538774, 384282252, 483169347, 244405043, 195185268, 806214631, 857797315, 899272006, 68056353, 283453813, 142919673, 101858764, 811778290, 685422233, 999897749, 267578618, 798528860, 948657851, 379069403, 378198026, 439854062, 416054742, 686386547, 112820040, 244723191, 683500003, 99414092, 576638962, 951377941, 638656056, 458176416, 92270209, 984803659, 190760847, 966187018, 792887812, 952344635, 786872381, 874015671, 779839508, 62196257, 70455722, 227713800, 702667736, 617291483, 954360172, 371111099, 403741567, 337962612, 513737487, 231501376, 626831520, 768026277, 944684997, 744327035, 168558216, 105222950, 920427925, 616459507, 502991910, 933092195, 105608466, 639295865, 424843829, 702139544, 823185233, 203533591, 546543137, 823133293, 850567124, 9000803, 768618289, 207970299, 738303292, 56970624, 631381991, 720751095, 187681528, 471805501, 496434571, 797538264, 787377280, 184474952, 394904292, 135022931, 291981866, 414438017, 218170077, 222889650, 669971286, 276433697, 676938786, 816117981, 990129040, 642284167, 719281269, 427619331, 479587718, 127929455, 563041384, 448482090, 713685600, 808727446, 725218347, 218107668, 506444756, 191874882, 923821557, 446232516, 560354455, 42467479, 830381871, 861414854, 693707398, 842379769, 323078366, 325996991, 760363768, 914363208, 817994220, 306120918, 296604730, 276470972, 745503789, 246850028, 893673164, 900913862, 731222876, 575739468, 248014306, 664671472, 51072001, 239112958, 11276755, 86708599, 988084949, 22434890, 975077714, 802247792, 339810362, 969590040, 37782724, 761463894, 981667582, 899718677, 169056353, 218213144, 728056835, 897650681, 328739573, 489960980, 188917379, 832501786, 333499598, 939145312, 607254640, 176583050, 199824080, 989767746, 790342282, 130026743, 72194757, 881717436, 732834575, 628349666, 724686760, 936289446, 988998461, 688595419, 402633151, 265592644, 808812411, 854605419, 913919838, 851402594, 312033622, 321250516, 311834184, 847383232, 584290574, 740014048, 206021243, 335984636, 84319204, 876087174, 113429224, 132706352, 162369285, 293285399, 214616122, 469940437, 696671086, 982023718, 136335095, 550118706, 390257061, 640245930, 931000863, 728131047, 203107621, 183335551, 202820496, 37593042, 804531119, 791597020, 554831335, 936387493, 499588895, 958325169, 145937411, 849282675, 93419201, 209248250, 443465530, 904214035, 958972962, 542956340, 554846622, 458916097, 886230148, 800881740, 506403011, 4865360, 374099768, 102476894, 340407083, 444019349, 184419690, 647128146, 985244473, 320150555, 258342874, 454199013, 781197767, 922616093, 608333117, 398011729, 671472975, 854823821, 145939077, 512531904, 848762672, 618822228, 607435784, 327479511, 501750532, 99833177, 781710187, 361991934, 368264647, 317609255, 562730835, 562114360, 427496981, 206417460, 317207162, 56528319, 919883817, 421536636, 390368704, 767485443, 661512956, 30989696, 552837580, 43189917, 917112531, 670638812, 332983909, 200701835, 590125801, 5886770, 569831677, 671626238, 289890414, 17018978, 222105847, 11327690, 202570805, 118043150, 23295916, 494463161, 793854746, 359575816, 248732520, 326658812, 497700325, 589305969, 391814316, 729028940, 637928964, 447205693, 809982310, 201970047, 824035614, 723274776, 482420731, 528301204, 490860057, 611313260, 157158962, 260456288, 254394737, 391248362, 376302498, 612291622, 447041057, 143725749, 945158374, 16307228, 601995873, 658803534, 665360337, 945714670, 354570539, 631405761, 81261281, 909294123, 677817340, 667616384, 755786891, 129199823, 295777258, 948027410, 118580233, 307546377, 390800918, 618144090, 241331972, 418156853, 759516516, 774392882, 646998373, 82968443, 429717252, 483814650, 345752339, 331328511, 298539792, 988041391, 919307596, 240668677, 814370977, 616395329, 780649300, 977466491, 498552098, 823460416, 132892296, 543144699, 856209586, 943520334, 976985343, 767505393, 796720222, 990326908, 572088605, 759965686, 384910480, 100793896, 783071015, 924602960, 322425561, 966283574, 374251032, 589647524, 489663655, 629303642, 19271497, 822997909, 91383833, 453893093, 662697952, 661525785, 540604478, 144749113, 17274516, 530304763, 140042833, 757696101, 755705305, 707316277, 152739185, 595092650, 174711058, 389092128, 658382967, 554841401, 360583892, 48286341, 720914802, 289938676, 739194663, 872469459, 355232781, 644700390, 291482705, 918508013, 544858478, 215645637, 532544617, 222421603, 198914463, 427438002, 840341328, 334963469, 930886383, 585234300, 956016131, 352102341, 631812271, 552293835, 384939690, 234213847, 740674009, 720108586, 439371345, 319244395, 735692308, 904644528, 385956310, 25562107, 204739891, 93571276, 379729938, 483072022, 804155108, 859502361, 630086030, 422562316, 742041874, 535215821, 864569852, 980035049, 47871277, 626649719, 117051553, 347278214, 231555778, 610991335, 669751983, 871166786, 484615365, 460126362, 446073077, 26969642, 501857708, 171354483, 443716670, 392044487, 927757141, 184743451, 818173889, 55604910, 536862257, 807119425, 429265609, 559882399, 97575335, 65642656, 339331, 23804253, 627790515, 503795769, 214136282, 289566779, 499403756, 257364346, 798566747, 272476565, 291879651, 898135150, 517560716, 714002839, 824849205, 219547787, 660203669, 978574576, 17358427, 654057164, 950375092, 320126783, 857559375, 616274688, 424073530, 938572247, 25175076, 773346009, 148411536, 243481177, 305857503, 109060601, 74234239, 258265619, 19062809, 491484259, 913553319, 915906284, 659690196, 292668945, 837690426, 258957490, 615274669, 237866683, 953320443, 26481871, 660330326, 333455718, 867940495, 198685460, 828198347, 937846336, 720540467, 452617681, 695914565, 444096385, 483437160, 39590284, 482193061, 148511963, 588195137, 314236606, 445260262, 108639029, 772600875, 700791486, 719373539, 772487397, 138314729, 561976704, 237871161, 52584604, 510401948, 987756183, 364778135, 56187101, 971405597, 648958296, 601845484, 225218837, 66182370, 720135732, 408641812, 108327384, 805090597, 793767461, 600851479, 716965037, 721582051, 268896875, 914433939, 885830992, 532435797, 706803459, 58365371, 153506572, 127189805, 633796197, 760178210, 37987366, 49292266, 896128047, 694607640, 49674886, 636768625, 759412882, 555326417, 700743694, 691281095, 943539881, 128961912, 675383411, 354641078, 734089704, 474801586, 830746485, 480494626, 310914966, 615431829, 866218440, 599325339, 547290567, 442257840, 614241534, 451715120, 168220626, 859613149, 356344814, 59847954, 399671657, 675797429, 649267703, 888620399, 258410703, 313155985, 134957747, 857292221, 760618575, 761477397, 754788927, 511342487, 746201079, 647335536, 429985598, 293900870, 863809841, 188114276, 153644533, 716440379, 488301780, 513071431, 426474167, 75696817, 158383377, 929161281, 502603338, 187292778, 961841134, 554435356, 456889976, 175747660, 934033347, 850161475, 874791423, 892795707, 599742285, 681063253, 9164078, 714845353, 513059045, 572879221, 916776139, 173429271, 18691349, 282976994, 653369384, 73040846, 829736147, 494855500, 755891848, 277195803, 526875958, 10865451, 695287423, 46404343, 265057739, 446706707, 177525315, 152326694, 216931346, 38244568, 17396289, 530446602, 198102593, 507643436, 412655784, 334886810, 403944335, 52864117, 256549974, 368704997, 216230644, 642204721, 266175645, 919311843, 353863687, 833846960, 188932136, 674843967, 334916317, 997455029, 976610667, 987704926, 567299681, 624395116, 381265453, 839785104, 288382500, 31985075, 674377035, 517214971, 925531415, 719669426, 231662481, 627194120, 98469900, 169078183, 528505533, 152594486, 881089188, 559412326, 541398610, 890004882, 765889542, 667485755, 317419625, 777094394, 539885438, 453551912, 80345676, 925357538, 382708476, 366253055, 389789406, 635628030, 682635463, 257651747, 562039252, 135492170, 327518451, 888231952, 175895742, 556965564, 65116901, 877736186, 440533104, 754909484, 716450307, 331053517, 494143345, 740718247, 16066568, 853100021, 147000981, 251657090, 759880201, 1809734, 458906948, 804314224, 756617782, 385270893, 924455307, 608266367, 796139787, 104358867, 728340756, 395832875, 724300286, 676723997, 587989748, 819730069, 240864765, 394720596, 97241247, 8211692, 925916063, 363715316, 852401481, 999958825, 811477329, 195296365, 805592184, 227548878, 4230400, 415325139, 437646645, 997571434, 875797753, 138946283, 524892397, 773059611, 826507078, 584943172, 517815567, 271346352, 900253940, 803625369, 56813922, 467659189, 737829033, 101845701, 713102, 462293332, 256791261, 457100729, 113839967, 837564883, 606039665, 913790212, 823797315, 754421518, 682279692, 740204101, 245010298, 606060840, 991185291, 394500079, 956607329, 593438994, 60568657, 158096722, 378951035, 525985619, 564392473, 452845518, 203530079, 954409765, 366502965, 895339095, 219188263, 213571085, 366908646, 845210721, 349949596, 226090627, 604880097, 445838551, 472751816, 248488485, 831033981, 307146000, 126870744, 775565905, 315287762, 578775633, 684651682, 532594583, 161665205, 878897032, 848775940, 188272734, 469679650, 238793464, 393721992, 900868375, 760489204, 591250171, 501195257, 507467072, 479326142, 883686048, 172924814, 759655221, 499246587, 450273133, 70534712, 83660020, 443181803, 663065003, 603749729, 649057124, 908286883, 314724403, 448219679, 79198242, 298515258, 488314464, 338849412, 560924114, 674088175, 297391875, 208746871, 754492806, 325752813, 706696286, 686886039, 962881652, 132441272, 211518573, 629340770, 485491291, 983727599, 991073669, 294907703, 115950491, 364508287, 747369351, 483218360, 901209257, 967399592, 827233975, 21192208, 122943255, 114038323, 827611887, 39833087, 417099677, 655961550, 841517542, 529982085, 292738195, 710254465, 529285197, 185585, 542784773, 883122006, 56352603, 970500724, 22475583, 31883246, 937090549, 437466180, 876038129, 973344195, 120605070, 855265282, 432853873, 399930404, 524886748, 282668677, 730031527, 818685395, 138819956, 126863315, 334703175, 440803528, 16989218, 147537739, 130320043, 333260230, 991307720, 160221877, 516474618, 883554868, 127472660, 330661633, 451203802, 374479679, 789506435, 152887040, 626233189, 415458231, 82305033, 150020376, 888172662, 716766216, 194123031, 557137544, 641475335, 708181977, 235146726, 146808207, 233278250, 881825663, 264369334, 740106023, 661364512, 793738418, 842972132, 260170433, 233834282, 791439359, 60149634, 841015982, 807933599, 608418785, 442080234, 771189693, 106940467, 856237075, 245900297, 836125784, 293193815, 776613967, 112563274, 851135521, 746503573, 585325797, 176371376, 419249459, 944384047, 807329730, 619442983, 663747533, 557740934, 529804537, 635664967, 611374211, 987532921, 825339509, 379857345, 724062721, 286940437, 349813045, 833898568, 864705172, 980979778, 558560725, 392211393, 906109080, 937482696, 349431119, 453907392, 941858533, 462513021, 195879152, 530141952, 746959080, 161679477, 69182030, 112447987, 879193441, 842206019, 861664253, 703174944, 385022709, 899593552, 48396802, 659658358, 654138408, 133314890, 802181586, 756795142, 230038113, 326027316, 11208727, 124583564, 251113442, 632535825, 846253308, 947797797, 871185214, 86746218, 907748941, 220650919, 586250136, 812811255, 899747745, 310180555, 784641296, 549115548, 832127122, 559265452, 73905438, 527869579, 321588776, 612788146, 862844345, 497072760, 775086244, 838107442, 903716401, 775315667, 749902937, 586392151, 819857903, 321030007, 195277621, 288455044, 525904865, 684597091, 44596712, 454877548, 381609277, 579957399, 689316243, 181960884, 981882818, 402604958, 178250131, 797538580, 830056965, 689557378, 598782151, 634831824, 77080261, 983782792, 36953838, 229040817, 129774843, 633675542, 148991387, 981769796, 338436496, 329254890, 917910095, 774431111, 121089814, 25120099, 894768627, 353712279, 151161059, 803363710, 256145826, 255474817, 202121975, 469520521, 182028414, 443936114, 327476906, 201769575, 361726365, 812651687, 40015660, 526929481, 650016085, 94270255, 544181058, 475176551, 276247186, 317863191, 385763013, 964382133, 994540662, 386704036, 875477101, 842608728, 928053163, 793108301, 45453437, 137046777, 66123986, 539098959, 8963537, 86225618, 662712895, 637246923, 458332998, 66460530, 363947369, 668059037, 507373558, 407171901, 323791869, 427613465, 436268725, 883617698, 798706834, 736971193, 538460257, 481122202, 52352514, 802703929, 310514436, 426269702, 693374439, 26917092, 640676735, 365376358, 668572154, 475739592, 490768265, 243593602, 879222331, 205681313, 466252731, 137067203, 424506098, 653713164, 374089961, 639773167, 149453261, 55077789, 175303874, 180421663, 309370193, 715088546, 697965017, 568149095, 809682861, 541886009, 547863165, 717325992, 506050714, 312384973, 646352079, 297008533, 448263027, 297990724, 191617601, 623234869, 542452677, 338736797, 621221351, 592839404, 67035808, 304892796, 227966134, 499244569, 747634040, 342700146, 310975388, 355315564, 309004787, 744143387, 764161545, 469686041, 880724078, 296677321, 627905523, 945489729, 102675550, 804356945, 676506794, 541661016, 657904475, 634720468, 508604704, 434203522, 444699398, 324722012, 896545952, 534835573, 759655719, 739063205, 330429336, 44098070, 452590177, 933395799, 603700601, 741475026, 477030675, 130573838, 944715745, 787283638, 288776633, 697378146, 580821068, 513109039, 312821682, 704815193, 89358438, 277747956, 591232690, 556591507, 716049034, 60820407, 276576031, 393714098, 810433531, 32936779, 403638808, 945247050, 309334388, 585307733, 823020012, 554578493, 941614317, 325101190, 228649421, 611741148, 617364015, 740210271, 190891920, 280929408, 920021860, 835200648, 819083553, 906778136, 667043874, 793862354, 350904805, 442066893, 391982738, 70243920, 508030354, 73815445, 681424400, 164009228, 573651956, 281500716, 932848095, 172130761, 203963760, 445462117, 537513904, 734176525, 661837075, 474503328, 497283789, 847141409, 990612589, 284517453, 34968382, 285801644, 862176870, 313612021, 906553202, 468676784, 197378374, 360626094, 976039769, 107320028, 809549583, 308425595, 731481205, 702448995, 977768667, 776386689, 867660019, 512462945, 759109751, 52474684, 641003925, 208349136, 326209195, 37273425, 842616282, 549010842, 529410458, 817508986, 14236698, 278059981, 1987407, 57024863, 170669759, 105965395, 331809002, 808295205, 888426748, 977841872, 817440845, 61008923, 872259565, 797591007, 942883129, 453971972, 993084833, 282940101, 283075491, 257223232, 711456932, 150101845, 59698328, 696878646, 14862142, 477099981, 828393869, 166158604, 65578080, 351730056, 902487960, 810193390, 497334712, 798437339, 621810283, 74666207, 996276597, 946337712, 29458108, 734238029, 645820822, 422106305, 710383772, 131084114, 536960506, 135531781, 249103682, 24650598, 469680540, 932322203, 451890232, 718475581, 373951740, 562634011, 13188312, 238033372, 30357683, 901933519, 817831946, 501647742, 374819988, 593379452, 11882404, 622851564, 820712364, 848394617, 713331297, 933911652, 643738117, 843166622, 158344719, 320017157, 83363701, 880429952, 201325197, 946046637, 338025113, 409623645, 350129446, 633069426, 844224613, 677163037, 865694497, 81215657, 502698604, 350950658, 911568969, 799209924, 323851494, 929635044, 790097873, 447766101, 811192023, 922860149, 392704192, 764872759, 530953370, 31205327, 916404646, 972569493, 534422371, 19173348, 268339023, 486225729, 533710239, 814789860, 18310263, 616869790, 557262805, 890052375, 606239077, 621944459, 234545983, 400938145, 658184314, 225151905, 357081412, 8042026, 931618648, 826071791, 832867690, 286891324, 487670191, 73929385, 471393620, 824385131, 25130990, 776037761, 749103976, 562089886, 529165931, 503382358, 410129898, 342090348, 67361057, 930428083, 153220402, 644579021, 46989371, 877827643, 978323160, 546654340, 12696478, 764101501, 440219810, 982308833, 376837875, 11214426, 955493442, 914443335, 134124716, 898190954, 275894326, 421744163, 981058992, 802378737, 511623240, 614497707, 906352067, 335589126, 656192769, 890211044, 750041186, 668462555, 145139547, 593778760, 978050204, 198929405, 144751999, 944227400, 849412491, 816534452, 129482696, 899971031, 551142647, 104292314, 740836332, 784629181, 625824944, 722610372, 239477442, 336224022, 817512922, 361396978, 235328988, 46710416, 886381518, 638229379, 28681220, 958831774, 225398486, 799635289, 663658653, 644277404, 496961693, 883187685, 249174893, 301548749, 412766452, 63136860, 618928570, 925898561, 496941420, 603647776, 377658822, 55287374, 539544798, 940111959, 395384663, 299586838, 285568606, 728738630, 404566894, 894698906, 298716547, 170638656, 265795392, 938526321, 604165543, 648925700, 317411782, 987906381, 706638858, 443553595, 806490199, 990954126, 581748928, 762433417, 329647610, 608631856, 470471084, 133160565, 292585740, 541069883, 699595415, 754162243, 726343029, 360059692, 867504175, 194954734, 427647535, 426068924, 269228349, 791675967, 468609297, 274677636, 57575155, 786036431, 460538645, 816987315, 351991572, 800686151, 870793318, 335544140, 233821333, 598280367, 27092874, 372050713, 744955181, 800831555, 228566537, 876262144, 882634011, 776391647, 482908362, 945611496, 46240215, 667116364, 77863347, 143127636, 981771192, 862763081, 8481632, 795170202, 712939798, 851025647, 684260963, 708788338, 428023345, 424697111, 113606260, 618779229, 748467131, 698898659, 389766170, 526254278, 896394934, 680860241, 611188535, 476545070, 716737698, 512888057, 726307809, 45192577, 369858213, 821182258, 698747876, 926725986, 810297461, 76074900, 337270568, 310947272, 738609862, 85531331, 756531549, 732902061, 507925027, 20957759, 727324437, 828565822, 827713550, 848643401, 800591179, 188929944, 150941765, 722766339, 957641204, 568363530, 212260123, 272986710, 67015474, 716024740, 901636028, 43776957, 325803177, 984990716, 857357692, 294178314, 63319663, 41476972, 621894633, 550213662, 337643329, 346689688, 408828232, 333504510, 486914681, 463887360, 724726224, 173304840, 450353217, 42213763, 682800151, 580322222, 175122432, 915967115, 924045084, 215148173, 989433627, 881137412, 999035169, 373643345, 496132641, 785959341, 560778037, 543101751, 648052125, 170757094, 911296223, 448758928, 366987433, 351546884, 45866053, 627940118, 467063636, 917357734, 649739073, 66856893, 680017785, 341789239, 935743886, 187654208, 853284982, 569259858, 90129072, 950399859, 770794908, 675843585, 746895477, 378861509, 697993463, 857856870, 26650486, 198125331, 63240735, 736992230, 632584792, 207966037, 765079848, 845078004, 807769719, 225217447, 155819633, 890961301, 351621878, 204758018, 698293346, 919652435, 503725248, 540237828, 298799319, 115112145, 640573578, 606475760, 18079835, 252940359, 970304967, 765440882, 144521136, 23941531, 606894043, 830347462, 770737725, 577399218, 881561026, 460390691, 71983769, 265497243, 840704757, 941890489, 891259265, 40528045, 895909935, 142589115, 603137876, 393583426, 895261875, 880283990, 503501920, 258864170, 507364342, 245181083, 896219236, 887187308, 724430120, 359762388, 566508221, 241853854, 480858967, 906355375, 27775089, 36876645, 280956971, 128476952, 293647130, 942610434, 121365325, 168843609, 681038289, 623972177, 197004061, 271982401, 476740322, 249624259, 385021934, 749016105, 861901569, 504311242, 702983671, 847433860, 515092661, 184662680, 987803217, 617780096, 899856043, 100069214, 79613718, 599089593, 478872624, 195628971, 570488174, 541950669, 356946322, 698925937, 750339449, 788186764, 334371846, 265706856, 77964802, 463169665, 649170239, 407852703, 28804562, 592917028, 611306380, 282433886, 394357400, 187060052, 868739951, 650340344, 784390429, 897360714, 303626616, 402571693, 779407905, 219740039, 223672955, 205354462, 291551672, 721878805, 886894624, 541527513, 365542214, 741041943, 768964033, 432045895, 457457735, 798470815, 887618953, 533680931, 586008764, 455021326, 155283575, 424851806, 896525753, 405342114, 291035430, 879451927, 344781907, 91164255, 745482420, 257829273, 668796144, 776584420, 393075637, 111155500, 435252435, 391178369, 103182200, 826611015, 380148410, 799862994, 438311239, 817860367, 267658578, 721461036, 845249138, 388105055, 121483108, 444826344, 370112971, 425526445, 484388344, 829704328, 808762851, 935112323, 29728568, 321651372, 203795988, 667225139, 193104596, 191356718, 972021141, 143127667, 417990892, 455118414, 577642715, 477521355, 181627527, 887439300, 90019650, 713840866, 892553609, 653524922, 714514872, 80608449, 199249498, 527649937, 319394058, 435867045, 261607760, 412421231, 507210056, 795287082, 276602096, 646725343, 613613539, 880825152, 997464358, 868011278, 651391356, 54039497, 486682700, 248884937, 180225216, 190117682, 203196686, 933508517, 28456336, 570593339, 993273583, 877418735, 176307800, 391890745, 849824216, 133976166, 625198528, 971674954, 994664201, 750222657, 802452689, 230366835, 942297879, 706061654, 242719516, 829788299, 388947664, 821519099, 313446649, 365945522, 647490772, 205193244, 353761203, 55150366, 816288280, 290470003, 75138164, 928408258, 816801629, 59793186, 335399828, 592093519, 91665066, 792787287, 513447878, 641486546, 4556091, 870455630, 637064729, 244698502, 569670871, 751963915, 804271780, 169227087, 316635435, 347289116, 962828111, 698337781, 27307935, 400696295, 441544669, 675687007, 469825746, 465353085, 498526625, 188712917, 977705102, 68029052, 915710936, 182775756, 360275536, 126866241, 904935632, 326937803, 563474859, 462699519, 698287100, 937314634, 58305058, 730477732, 983068578, 283124904, 589002280, 117639927, 649803002, 442339727, 392692236, 694923631, 193020724, 809556691, 997570014, 574382008, 48739106, 394011792, 531761231, 96380076, 655095343, 865690180, 758099469, 52505047, 554206154, 207136971, 81424471, 325541873, 696612877, 547647321, 68179794, 224345897, 50085109, 223907829, 429134903, 257815006, 879743371, 101348912, 511334874, 501612300, 847532625, 872312910, 321890109, 558435026, 2031752, 115131957, 503027982, 800539055, 911882184, 651607975, 332807913, 893711612, 518009194, 921331002, 760974476, 720508603, 153541031, 358148658, 448130581, 123430145, 661935881, 221036260, 973170166, 201845477, 59975546, 674859118, 634267528, 276893607, 170372134, 62156160, 92276100, 495108381, 428307191, 659043603, 520189978, 798591227, 170779752, 420418110, 571815856, 360718595, 525842365, 569133845, 257791494, 406803354, 961309601, 319491399, 476029244, 924342640, 572020494, 709789966, 56344533, 590305796, 911722302, 533568824, 248031758, 868703568, 615925709, 634637387, 899282316, 399679289, 208990502, 516253288, 612626014, 501516217, 525415953, 586829945, 21068381, 726586390, 230823896, 748836874, 551842537, 161184406, 648439109, 327937728, 978433766, 407646274, 367562326, 632282609, 184464867, 821293639, 883084039, 236592764, 683636023, 509262694, 67081089, 393515101, 551448563, 661620820, 959328528, 131406706, 159071961, 144910121, 526409032, 839429304, 591063170, 452271070, 771825104, 105516880, 735056263, 260240956, 393984224, 366598946, 970365789, 850992788, 591432387, 731690630, 743779280, 963372751, 233553209, 989856347, 718309892, 622119615, 603644966, 481199586, 219653252, 278468640, 317106875, 815758299, 852077618, 98287481, 663446814, 150983397, 77175628, 114014387, 431825358, 600368639, 777057837, 347013131, 102963028, 246905170, 594606532, 602387872, 491537522, 456448700, 24256290, 482344213, 786536374, 124813252, 558709525, 235691064, 985530259, 659489177, 723947546, 195438293, 76558956, 985749123, 305676604, 725350097, 735766122, 482219264, 755115054, 865498191, 221848004, 524820948, 237523807, 295108055, 762526345, 843177949, 395148341, 206676719, 769910394, 757708638, 387330509, 409748897, 184688784, 912669778, 757043015, 308542298, 107307594, 553494769, 21779265, 877213410, 963260335, 174516390, 142730963, 752935888, 75394273, 144987946, 49849569, 520404288, 530382378, 216650130, 72316692, 303893455, 296702671, 687678354, 645207597, 166169878, 867274862, 114353081, 187895692, 397705997, 909159607, 134097978, 176622847, 37830029, 654280695, 217670723, 191922749, 779980441, 576567194, 489119861, 850404899, 425583773, 730622558, 730982146, 392792273, 848959159, 220281769, 386220694, 466336010, 218808556, 958802145, 543844513, 465689348, 385229497, 214035318, 227598686, 539346086, 415267083, 381241383, 231370450, 765440219, 648601716, 430394296, 959959129, 761740602, 106802270, 378302961, 871213517, 496571739, 694546527, 584592883, 498514642, 84833265, 229071302, 576132387, 882582977, 317938062, 794988064, 109156552, 730966334, 99302612, 450179482, 942867244, 293887332, 322697311, 292022487, 975046793, 896577308, 977610668, 611349098, 906085084, 266256322, 17969424, 38067721, 4424569, 307796332, 999280968, 789298425, 254490990, 262064353, 3900027, 751929560, 244882186, 203663313, 672291107, 577498309, 503741648, 699364602, 693776334, 839646898, 914199533, 867825086, 112120876, 320309235, 628520152, 755410863, 979283026, 469510452, 398937838, 488907413, 925182784, 763557164, 419896393, 33780361, 912203282, 660967823, 751389261, 98211276, 797031731, 382930177, 33018821, 529273621, 743847781, 157028330, 440221868, 108718501, 935088977, 784671438, 175795471, 529237957, 423097216, 208111056, 460000426, 714044332, 943927055, 230170008, 244620530, 230970517, 103560824, 735593327, 865971598, 16093832, 244862243, 359225011, 110653881, 747489688, 228068320, 219867296, 175117945, 24603431, 897636635, 145277815, 320577605, 532563857, 888081246, 532401909, 829826597, 590572705, 409925370, 682560455, 719446387, 110543620, 524378532, 641514459, 812391823, 111298630, 320545723, 606855178, 3854817, 475861338, 730204432, 14360383, 157292089, 769807164, 376561244, 12746343, 201386004, 54000252, 44541027, 243257565, 974091308, 914545147, 553386506, 562919777, 550624975, 49311461, 337548694, 921712079, 22137543, 994080618, 459552042, 373067999, 231413810, 585909031, 103386518, 968814188, 126195404, 184224714, 298042493, 124126983, 899531398, 154738845, 121504545, 447823559, 876329224, 224428834, 456879694, 522232921, 741173342, 295443096, 275359460, 94739037, 754329336, 584665599, 717711686, 861764699, 887007703, 638640838, 380944633, 343347467, 695021637, 297240078, 841764019, 589385620, 78910558, 217826283, 756561474, 861810760, 263518001, 70864686, 105526655, 859131601, 576058515, 63391453, 46124878, 602062017, 679905550, 943583844, 604288239, 532798555, 533286909, 173141365, 652512898, 26299511, 659290846, 56770376, 447744524, 734780561, 581193203, 611804930, 537884341, 626406, 365313138, 539811642, 359653959, 257238460, 934655795, 114233905, 358576545, 323927538, 690057583, 115929734, 972056736, 690450452, 22507905, 385914551, 773993172, 422295841, 593240956, 683021199, 415717073, 198217038, 652451353, 419548776, 48749797, 638316639, 608083864, 944303272, 89286586, 336860232, 126730805, 626371185, 460485773, 562586145, 414013192, 934857486, 876006539, 206041391, 722913726, 425266743, 448940687, 428860415, 166365137, 608644956, 590662506, 218423464, 222894877, 500089507, 26444448, 731061493, 782414900, 228064124, 894102884, 294102698, 434957798, 993714748, 51818231, 549990158, 111673304, 175083850, 539435990, 580245260, 171336203, 552204183, 390514327, 149634002, 450976413, 601054149, 291806122, 707236351, 44732601, 368180200, 704701386, 293349777, 82637470, 730093927, 366400803, 358441677, 929981248, 275056638, 390471767, 641513148, 400929618, 608146868, 648021242, 480780255, 382887734, 758946617, 717821739, 821575240, 456867796, 515161879, 374112793, 303218681, 458273084, 882843397, 971134083, 381456111, 915998348, 195646015, 771474736, 700411907, 391541653, 665886600, 7997522, 466054934, 290438237, 422161580, 579846209, 972177808, 672821117, 244438682, 357967009, 508829973, 923256975, 658088542, 18761019, 280951300, 993436924, 424872327, 225928781, 600915579, 908473379, 931122296, 835500756, 894928537, 730354798, 783529315, 70443676, 63215133, 95297755, 645402643, 52656722, 49777601, 280196018, 680530535, 477300460, 466005130, 636418637, 365331663, 725703020, 945447127, 977406354, 267212515, 863629610, 515225793, 569026405, 957290146, 626743667, 154330338, 904057169, 432414992, 685245919, 482883647, 794834582, 511055569, 973689024, 584904716, 860433178, 907157805, 981679639, 980946629, 90579129, 179183956, 698907009, 696787442, 533638606, 511212390, 670862379, 575803399, 349687071, 324760493, 99972804, 878174754, 379537414, 364480326, 938757076, 983838032, 581509226, 180351213, 708550357, 881514134, 890802762, 973720316, 519136984, 594333095, 453692701, 204364, 928107307, 231675776, 320026393, 610039675, 868905174, 268556808, 396184331, 491502917, 775292206, 206666209, 266200195, 426683055, 804784051, 12303846, 910818243, 834295879, 71790729, 835727271, 531754035, 503523634, 946677725, 421520073, 381467924, 762438437, 537209081, 673951930, 105539275, 153097382, 244413153, 925635436, 886668864, 495639055, 291089382, 158307140, 342385897, 720135278, 93207280, 410814806, 328738839, 258762029, 242714390, 259924511, 249511635, 169164697, 727291437, 720849690, 672164074, 412741181, 829927731, 429869407, 566805115, 85760801, 982267232, 232859023, 432683183, 56093702, 953846637, 689166045, 176998408, 966575340, 703652740, 70453597, 843245273, 518308813, 305278753, 690668819, 2831124, 105852071, 52499588, 272646744, 96626390, 359884012, 314979696, 116639975, 97791459, 846724622, 905207513, 287871066, 606157424, 804266878, 927661754, 216652173, 78210296, 960861178, 107934509, 30771710, 441182759, 496140342, 369158450, 584166011, 293208185, 466908349, 356907009, 986730859, 192411610, 277897909, 120328522, 834567691, 415942053, 907026330, 305895700, 158445177, 766926261, 765068432, 368020881, 90824711, 711923807, 350694885, 422762680, 659023383, 564698385, 916869315, 689334181, 18124455, 145920433, 277655475, 13692455, 699481640, 516480855, 344782801, 571216155, 306183838, 362320336, 399747888, 249186416, 165610020, 998520783, 279128662, 38163520, 717163035, 335716217, 259870407, 54575352, 508660550, 749530506, 778854893, 861817984, 849700081, 764497739, 695435001, 925975158, 596408360, 265084060, 260378758, 449194117, 452166605, 349815125, 285755613, 430280, 784980949, 460860622, 709312197, 602287690, 481171880, 332364457, 616517796, 981158834, 671929625, 550400612, 884698733, 852561927, 830692996, 794210173, 46494473, 267285202, 821422125, 503696031, 929170699, 943167287, 595239672, 61240892, 707311483, 390258216, 894454333, 642338631, 938940985, 137645687, 120442981, 32437627, 550476493, 133354517, 758194460, 507755339, 55297781, 642527206, 99321447, 761733018, 976620562, 775205247, 159676858, 572731757, 258198830, 687473705, 513538297, 420688729, 268795334, 258432746, 190215804, 961883541, 766957029, 443421564, 506810286, 779747995, 651633090, 921733604, 67894075, 657416718, 797662212, 349197265, 915967252, 491103114, 345072612, 540419288, 684187759, 607711067, 658141816, 585190385, 903606579, 951140999, 918771446, 278690479, 311141500, 75643138, 193807531, 986711192, 887025032, 6694499, 227368429, 342623521, 347721813, 200570150, 295030946, 141132639, 587401569, 411559241, 234674303, 846622938, 869171994, 415674374, 122808115, 846064563, 974763065, 735784928, 268341614, 190453545, 833468998, 273076748, 4797894, 554115679, 111843181, 192239391, 179073923, 785927807, 669489026, 973682394, 293409280, 58954635, 53002351, 366028702, 753593056, 762483730, 727553690, 58962134, 904823378, 252462804, 411531278, 767704664, 288508806, 774458413, 650866962, 657752208, 696625665, 577910896, 705484890, 501948289, 925977928, 324666791, 920778008, 957255542, 642941636, 823077853, 809860426, 998963296, 304164612, 378563253, 265476605, 490686486, 870023756, 607309926, 52999115, 331880241, 720395619, 777068431, 907165104, 608350082, 254462519, 850237022, 692670589, 886410869, 558993925, 147160252, 992092269, 829077685, 431881955, 464689812, 156129540, 869786865, 281480341, 390271009, 630340117, 361623581, 453961536, 102591587, 622281272, 754687536, 832017779, 990342336, 991418532, 876736476, 572938046, 857089332, 804185065, 57582962, 637671725, 740566215, 691609519, 947118581, 670754806, 583704787, 65839764, 501058879, 974692710, 454722964, 74854058, 680248748, 81051063, 132440334, 145870712, 987792906, 193557911, 544565839, 879333925, 507231455, 721939207, 141925047, 433555245, 670844965, 300567706, 291138788, 207744245, 503495240, 345670742, 57959714, 978373737, 478291778, 386496481, 119053575, 985956536, 968776179, 525850445, 904282407, 545472937, 25677068, 990318678, 683269829, 738738423, 387606008, 416988781, 311005030, 19568397, 225849341, 547996134, 742856908, 104536642, 618336254, 580956342, 285802122, 94235780, 974917223, 540866660, 597550264, 255095714, 857505034, 319582557, 854825720, 374579233, 672125777, 620844701, 89095646, 407787905, 428170481, 501862013, 31793639, 248781086, 891516722, 516954460, 479413290, 186146575, 255217966, 6730289, 845579139, 437857107, 903268522, 656523552, 683790526, 97957095, 549946843, 585689017, 793027328, 684014095, 691295561, 958879834, 84732929, 3121485, 397121338, 458476771, 324873834, 242440412, 25906115, 727934911, 614581165, 16730440, 65325847, 103172132, 535592710, 54697772, 112837219, 553179190, 19968452, 478714421, 775461738, 695067793, 118791693, 597092602, 511653548, 452894773, 507779108, 763196617, 77664764, 160282244, 598804480, 954316702, 478446535, 588725169, 23633867, 601907173, 866688516, 29737606, 114211470, 950216598, 955429454, 956594319, 298984422, 144990367, 772498720, 411894863, 973805645, 510838639, 580701588, 569732524, 758041995, 278458355, 152541458, 757900449, 461146299, 863948036, 851199191, 688228841, 176361345, 543750802, 518019706, 693291535, 663212440, 532248197, 86034246, 178902489, 831504762, 189173465, 815738024, 393520358, 211196506, 777231746, 38879262, 960197514, 846174404, 476278151, 595981653, 746152434, 751586822, 456024083, 672178564, 230435687, 990726486, 232801950, 314252542, 759773936, 245492662, 91400343, 9670254, 908656832, 492884065, 225641830, 389576955, 894961089, 312152665, 782463509, 844125228, 300164572, 518931619, 973817795, 763719090, 994081176, 338597252, 253073968, 955279570, 595032317, 68723327, 12135412, 1669022, 900353904, 681271960, 21125489, 173294586, 15300799, 882966434, 2387852, 561809975, 347828257, 454908293, 125744152, 537942576, 718527506, 20454104, 961276695, 895235423, 522994199, 817405751, 957419367, 924351729, 376824314, 414921082, 820084339, 177075860, 117838736, 993203684, 492403675, 955002184, 499760241, 252017869, 325905327, 97025179, 235386407, 269353647, 443758718, 686453790, 455935167, 23496772, 703591842, 955591509, 64228977, 715712645, 444689049, 901333639, 315336432, 299331755, 915105161, 345125840, 865607414, 146742914, 478349193, 568903434, 777091990, 863759055, 750879, 847352108, 723678858, 706428270, 208964143, 355713632, 2159431, 605419634, 450271942, 790997314, 922035874, 528128837, 867669563, 899260336, 696188729, 838509928, 171607847, 451726637, 100174076, 4215688, 449613022, 125909177, 857243139, 996632145, 129494642, 853397052, 358284306, 812559692, 44956109, 88916302, 473037800, 283777864, 706777620, 670460952, 11094493, 176001755, 263267950, 157700174, 870448301, 577735246, 558163593, 707265250, 569990767, 2930770, 258988166, 721559266, 816881015, 856544818, 653684810, 50037112, 925682383, 736674403, 893937474, 498459792, 839098473, 100430279, 294566800, 242573402, 297087416, 378809035, 158053352, 861542662, 434416946, 743198750, 264590462, 150505978, 794794793, 654789204, 579653555, 599516637, 651731053, 831684675, 613908357, 190003939, 165348776, 299436895, 277217086, 244829835, 322429636, 980428536, 307742637, 605775236, 60093830, 534201571, 998869757, 631846353, 26515467, 381383576, 140978286, 573476739, 554056095, 203421899, 961903609, 886370292, 19459005, 385628899, 701192516, 29239212, 797034330, 763237306, 516640905, 43977434, 769928425, 610059462, 723515190, 776550927, 108194811, 255622681, 485257616, 879512868, 306090503, 633464972, 137707241, 931975581, 557771366, 983051261, 203250316, 241086206, 309736514, 285638102, 214114922, 227810730, 391192034, 902478494, 978991437, 869150880, 151383125, 116195201, 360471630, 354327561, 683381705, 263158731, 250943527, 410388644, 138305675, 334379589, 587615537, 903003656, 389354353, 116501788, 243747130, 556517446, 773525411, 808066990, 325277840, 914792240, 7990674, 124144313, 161590467, 601534982, 135428052, 824639841, 523817537, 699050254, 118725019, 788365222, 827633891, 400186560, 928905736, 333371214, 208167951, 434203273, 390426843, 548963881, 150935714, 124788529, 255618394, 335516196, 439234363, 648214516, 859906497, 735620451, 103088933, 621438681, 474937566, 547943312, 747182301, 477788430, 377976242, 522974242, 94925387, 661690835, 381074501, 458709086, 211933984, 26663722, 973711586, 915910836, 151159715, 438866683, 272286928, 304841731, 893805040, 972243941, 154808568, 795438766, 621804150, 584285768, 521758253, 199143311, 32403352, 932931903, 264063449, 590817436, 408217384, 424410087, 503210293, 425143213, 847425771, 366438147, 635018998, 557362823, 54782803, 737179410, 455578569, 744072935, 996521953, 83021616, 768655742, 41267967, 593890281, 970570872, 755917543, 254391107, 434926233, 783746407, 397240837, 188637270, 615018185, 562623798, 635656874, 685835899, 390488266, 831053555, 866916411, 957492358, 494623880, 370624494, 984327718, 582525288, 657387610, 228068608, 338044635, 653607045, 281830962, 809946327, 487785944, 687313859, 39758138, 623671476, 681166556, 640940178, 195338022, 439619739, 284427716, 966250249, 841862695, 953137229, 218375606, 952638309, 157533460, 946612336, 962130819, 172670824, 338381395, 39436521, 411028269, 188328757, 979214239, 512003733, 921400262, 519750107, 596546267, 411309760, 259535045, 783045153, 288562238, 633813989, 657153074, 763157481, 848693031, 901280066, 214699774, 909285610, 288942086, 749001375, 96707900, 814637540, 785595311, 467378297, 247597532, 536092981, 992575993, 985302152, 173520996, 252761309, 235909727, 440998848, 659070605, 666419341, 257792079, 282083574, 672290564, 475323017, 268661696, 400495164, 975570864, 150401358, 564606819, 934327344, 94143987, 347754475, 828035576, 27698902, 83554314, 215561651, 367361282, 493941376, 684615265, 155620220, 900380412, 399963440, 665692274, 659448279, 173222151, 607995211, 307385120, 820757666, 406471044, 983911936, 206898343, 663315820, 624562560, 903004859, 327889475, 60292207, 860740915, 802802326, 742663933, 127526271, 199313061, 16437510, 681301758, 146949605, 331623204, 425352992, 102128610, 291446657, 988241314, 79697136, 455882215, 759864715, 99341544, 629922134, 458634598, 816316616, 681602008, 6629207, 841743384, 940159389, 146571356, 595981335, 263625798, 803603681, 956970914, 49791724, 771766219, 735000449, 995424244, 218683107, 647292831, 242229035, 373857138, 980516403, 545824493, 463608131, 595374920, 944603250, 549394493, 333687316, 979637009, 353651949, 442526236, 595927234, 44986759, 966073972, 708866183, 158065805, 163603725, 717083883, 922350699, 738977995, 143036394, 212483984, 319779627, 441189737, 64805080, 663606454, 673074293, 138789102, 811884716, 474826037, 72276378, 875482725, 131603078, 527247170, 771026714, 993986738, 24512030, 660996881, 673291868, 973544672, 830538677, 203945874, 35163156, 777567022, 669480115, 175850921, 763169332, 10583411, 744785286, 168247389, 413679251, 61596426, 675388153, 435980796, 50872359, 432229235, 241867509, 337116478, 267861202, 130132517, 525736618, 554443999, 247257085, 32410569, 203279699, 287738456, 775486221, 938259213, 762430019, 610232142, 608499706, 290035148, 213712877, 178244329, 791825509, 101927327, 929905881, 387044904, 527767321, 204507249, 825421655, 757326931, 898882650, 259296837, 435978168, 307005400, 407533204, 261207816, 432754812, 626227598, 803299735, 488936528, 164860289, 768373455, 600417062, 773425339, 8034558, 263475909, 942775368, 950817284, 918881940, 920701840, 28834849, 868200978, 471025993, 298275969, 940653977, 21510172, 808120999, 825061372, 927609489, 504301035, 791394475, 629828071, 975329610, 634387255, 208677753, 411230352, 393516860, 752443404, 535390815, 171353196, 714599000, 975368717, 786121932, 57147318, 775478376, 175558612, 322140678, 92345239, 754065117, 320159836, 515688769, 197636972, 433165476, 29688458, 237771340, 276085948, 742984273, 569261563, 512723022, 479134408, 224417625, 714229022, 86021400, 760173461, 392491207, 715437226, 179118309, 333008198, 851686124, 392098016, 587770063, 188107812, 376683313, 360231006, 390376192, 139320656, 371458538, 512779323, 38465022, 515239212, 21392184, 221610887, 502109998, 614933009, 264105845, 300584259, 580015844, 924672038, 640421565, 510076778, 890748678, 693372356, 694760722, 502744518, 231713069, 536941537, 644955709, 340063652, 285707564, 298666925, 881193814, 290274300, 979279078, 214149766, 960390164, 418253178, 873683671, 590567965, 667265728, 306321168, 441176529, 861179754, 829306227, 445609205, 470733681, 259713823, 72222857, 57954273, 884936900, 470634114, 550059204, 8866628, 520291932, 850376034, 768454421, 470386522, 689480216, 531459252, 379081442, 141490027, 47222435, 877706725, 657364232, 266490807, 811203632, 532295160, 354317598, 649400057, 772077503, 957495071, 919349282, 732848672, 75313789, 469699368, 162275424, 639777749, 71575889, 467580748, 85419926, 231720265, 884619533, 955933243, 225046271, 443851092, 585236583, 415902732, 227577985, 344618518, 148324289, 841585193, 579256362, 188788222, 789352211, 306418562, 755385944, 330757694, 799889633, 829126812, 173585365, 80633192, 432923482, 543076408, 162494436, 174237631, 427004041, 698384261, 641803657, 285523311, 939751793, 481575908, 695490914, 433438806, 398460142, 172524446, 733793439, 613161095, 702227302, 23814249, 563075947, 364316833, 487811140, 286387188, 986773467, 270409345, 556634986, 993749197, 397538688, 155281104, 895581057, 37978797, 490465549, 257284818, 629893098, 242704557, 226906760, 809864855, 634509572, 661508846, 198749306, 703786978, 57868055, 299718017, 308009344, 907451710, 711878379, 509522304, 775364341, 43333253, 997325050, 503297519, 167870188, 771573556, 840306658, 729170900, 259137327, 381781043, 336994613, 178488815, 775850410, 84122777, 738079137, 26642421, 319767753, 63397054, 475960158, 842040595, 220792827, 229726519, 633474461, 229728258, 290092649, 418192203, 209967373, 372112105, 644802248, 74820526, 763935006, 228949892, 188499931, 831826850, 220833846, 638612816, 529512605, 462629272, 547465546, 237716238, 460289629, 448215058, 885906167, 888309928, 877716108, 520298022, 644363924, 722135114, 825723903, 880495754, 746832754, 865739552, 258437719, 60830548, 192443586, 637403574, 512129646, 278817081, 614504625, 375665870, 248367312, 765279915, 374120276, 215567576, 266491390, 266935386, 818983769, 612550411, 467168226, 93483006, 871091785, 628902395, 536850791, 421794811, 393399575, 782261642, 72558103, 381589356, 263392129, 313949094, 843345429, 570577101, 445830991, 844128439, 132051073, 249261348, 45204498, 332032815, 724568537, 899552580, 421709820, 782641281, 651111803, 930552875, 2679461, 539807344, 109642029, 438262009, 368837655, 626409832, 636955189, 739129051, 13568393, 520690850, 367754991, 598888145, 74290255, 589948853, 758886213, 151973907, 696686498, 630340326, 348042292, 587356458, 228929153, 851522497, 105997465, 610954520, 905691959, 309070085, 989708609, 702988873, 647035304, 713100243, 564065405, 227312394, 630525227, 201230164, 549966016, 305213138, 876195925, 479535739, 44329804, 305181373, 425814450, 996475041, 382540000, 71063856, 477479692, 387498635, 166044312, 320238253, 339642578, 62791092, 517927561, 887575391, 906522419, 436245454, 972711997, 499924855, 365902069, 849509387, 656734334, 634466238, 53141443, 41232122, 995211050, 11924518, 233159478, 96997312, 550981630, 667703821, 301523965, 995441836, 703286088, 7011305, 424787194, 462902439, 754006025, 892383087, 75619318, 40176812, 892583619, 916829817, 73922813, 709819149, 991857967, 940304116, 827837423, 917142609, 16524909, 835120928, 445176549, 505833612, 200392786, 792241851, 958687719, 728517059, 964311885, 207014490, 710379152, 745706357, 974151056, 641021735, 75089153, 716826196, 33224905, 133247627, 726300932, 206880245, 35153419, 939109583, 847571558, 331215293, 356223081, 238329789, 858252425, 18652020, 908534225, 28193965, 163922160, 388503148, 401434099, 930108102, 744440779, 676264720, 835390557, 239387794, 293034370, 342688371, 846672623, 966206224, 734480197, 422509051, 774994519, 262739428, 60565170, 488272006, 332635300, 812840927, 226150734, 189218548, 152342778, 567923967, 158572506, 396430992, 6926143, 816665181, 340632637, 293024193, 88539527, 793121989, 361425852, 201555702, 612920359, 437477820, 934578770, 852950064, 113770354, 365677328, 897074522, 576760234, 967194609, 454642865, 637998388, 44623198, 689850370, 770727482, 204249025, 940665820, 767653025, 465115084, 986486093, 561715663, 330348980, 598651199, 952688228, 823709420, 95861150, 180027040, 2086471, 655488438, 228745927, 95579005, 696640845, 738981954, 669107370, 441908404, 572139563, 373935617, 949591797, 142003299, 883464946, 441827966, 119011839, 657704739, 368309264, 861659098, 60930145, 531277293, 488238720, 969192064, 562104463, 641047757, 319989817, 978940188, 699928275, 682122544, 21460893, 498893287, 432245586, 311572888, 408508673, 695791964, 872981557, 348566690, 495147524, 957816678, 402083928, 613183198, 386029879, 973712640, 272443677, 447936716, 459014341, 835730303, 124958676, 44592307, 997444082, 928000107, 91990713, 335522139, 658494047, 497865541, 724468515, 178253790, 194641246, 370580995, 616287472, 65325351, 948840147, 442767996, 190589105, 358921393, 168900734, 26456397, 80174750, 949299533, 538959864, 333394445, 819397848, 294964679, 866727431, 3112193, 864753649, 137722982, 232926335, 37318100, 973322952, 175028911, 885635874, 232870941, 47158652, 38628898, 577428373, 817631326, 803747309, 598657786, 434193850, 77331937, 866574461, 768715129, 234013590, 535458482, 703826796, 565633018, 710274450, 313850492, 719289487, 993077943, 328733046, 935434574, 344802090, 587578452, 257013553, 720128646, 394701694, 700791527, 397332729, 461015257, 907814818, 556983255, 572390202, 986463795, 381875526, 336304134, 389129082, 169947494, 915127523, 200302173, 315604138, 79666394, 770200891, 56823689, 194780539, 865578116, 716832878, 545278607, 850444314, 511604782, 256898495, 169451432, 679284824, 297305271, 195197361, 924807549, 106041372, 573690985, 608688032, 118552161, 510935711, 16170279, 501939907, 736285326, 246674047, 399292179, 610273782, 34980231, 862640145, 813151105, 980754676, 341160461, 492376095, 823357358, 79667564, 863240671, 719223342, 810948813, 656879575, 837569369, 344683535, 294869761, 998822023, 916851950, 647033040, 467506799, 593255156, 609459328, 627593114, 238168647, 473632791, 330538577, 22043009, 615306787, 852231414, 517012228, 614767014, 706728579, 217154244, 459110826, 883447787, 947505036, 212503011, 529561393, 52199771, 518061166, 197974447, 425033033, 920044350, 146330962, 662126683, 455598714, 933768053, 149045703, 98270001, 920817014, 654139827, 916706261, 419453027, 322303439, 812632321, 595033399, 114918017, 873342405, 984587384, 975321912, 980855746, 913520833, 89091936, 153069558, 891218029, 120536426, 271688464, 584690788, 770808401, 699363142, 776064698, 599729176, 5364316, 401284579, 41135880, 632061536, 933837366, 703225448, 76247991, 460776954, 963718425, 617311349, 673916635, 632183401, 164592766, 105699332, 340716335, 361304221, 285551667, 461953109, 431193109, 301571297, 928953453, 665292393, 319027477, 524990186, 827927568, 507344508, 940865676, 48074752, 644682634, 979663326, 184760031, 118066519, 111192005, 586839083, 35176670, 950309788, 764837087, 965903170, 98394249, 234786883, 150495783, 991562690, 887226104, 711653614, 247744403, 945691588, 747295490, 630827959, 703569015, 262580535, 8577608, 450455260, 918418917, 96673331, 112460973, 288389141, 581439288, 133979535, 344325172, 46952391, 71170542, 250904963, 643545823, 903503680, 57734459, 987485344, 395398630, 479198587, 86516541, 17811982, 375953995, 690325330, 38015799, 158489049, 9558264, 641548203, 810452537, 464397714, 427660253, 543349044, 142061719, 998587284, 647528657, 562544801, 496342702, 248301924, 630776070, 773007102, 850137748, 417311570, 892434876, 750186514, 307699846, 759009309, 807231041, 40211335, 248760572, 799113380, 652139811, 2681392, 250381405, 870437072, 185043862, 323606039, 677791691, 209007438, 637344120, 635191697, 428182573, 872956133, 62203732, 520760586, 155223769, 379153601, 996816567, 124564546, 906079050, 494257069, 510027594, 234165046, 721305105, 257517931, 271546967, 648015154, 227017563, 320299997, 291180985, 192923222, 480450135, 195033599, 820378006, 87581176, 656922824, 269736953, 741927462, 130874937, 986460849, 29160223, 535096358, 170315378, 828521350, 361298825, 385103418, 102671714, 990748099, 786878820, 869416196, 539709571, 303032102, 975505945, 179583907, 79823267, 940970958, 146762928, 29806147, 521502075, 563281924, 728042076, 25115466, 419597864, 228230250, 772197974, 654917147, 368835750, 25903805, 676545218, 449307362, 853726946, 272791345, 557575219, 508566723, 8234012, 145428351, 102626906, 376478134, 591691064, 398876072, 54975923, 485992892, 617817178, 713243907, 96755949, 348813689, 606379949, 165273080, 664942500, 47570263, 63839235, 214829281, 500942480, 474712502, 579841841, 280355868, 189506740, 813509496, 258066751, 14117707, 141786817, 260399396, 863102231, 547318034, 887942025, 898647821, 176288457, 481045549, 136785595, 463940361, 551425004, 734461784, 316934154, 499257357, 570456436, 502621690, 271703168, 587165459, 309951128, 775860470, 254398035, 155328970, 430237939, 355217567, 306835173, 355383630, 426173938, 970225664, 776158524, 995925960, 479144538, 818213036, 377320468, 754268536, 22146714, 347995279, 699492714, 585389677, 965746560, 472119539, 934823036, 241787974, 334165625, 697127254, 739482069, 610221236, 254840187, 912992329, 493581977, 874839863, 254066448, 217916299, 343639067, 729123164, 120745501, 24349134, 803108725, 814028545, 570327794, 354817751, 467496600, 139427222, 206724383, 789105936, 745446988, 630912478, 293029427, 255441773, 403647976, 438820483, 206770657, 515358626, 655304722, 519512556, 477438931, 401833845, 809062587, 614379670, 610237958, 904389168, 780277142, 800253715, 829715247, 456645855, 345776386, 131621643, 988587223, 200032177, 5391444, 455786982, 211091846, 653363984, 229083610, 272988426, 691486056, 172020421, 958987590, 910535090, 802465948, 739574202, 372464559, 654833542, 399714079, 327327061, 703461148, 796830980, 426263280, 597502471, 659187244, 880750720, 237151947, 514978658, 480955960, 242448727, 433311349, 304983335, 4479778, 419606983, 981758641, 660319473, 274720325, 638051599, 84064480, 307109205, 612209826, 566355589, 526869351, 801906074, 415182816, 499363109, 92582928, 183909021, 966719507, 762366173, 268146218, 26022108, 125201607, 615108093, 648406416, 939139957, 421582523, 146101911, 67303893, 592488802, 899860720, 388493082, 128125488, 406395370, 291198267, 435749395, 89854723, 521659741, 369805924, 874023176, 945505847, 536005789, 230121560, 651873045, 548431085, 427156196, 481332835, 315052824, 756872587, 396467011, 41678639, 201087349, 431230086, 207769569, 980496259, 233025900, 467040815, 874089403, 806952760, 807888211, 966794342, 904390922, 727866002, 118057239, 817827201, 645192373, 5834717, 210136693, 648771371, 953114166, 802240444, 245063535, 460390368, 198271398, 753233432, 409808431, 536053883, 352812506, 651277105, 268353035, 342778373, 970840948, 6265716, 162137517, 499289137, 439432891, 728566907, 911751834, 738470466, 250854728, 213286460, 833372456, 825475479, 559495828, 13325421, 23136649, 713633278, 871085014, 277742508, 334934567, 807300357, 391848952, 695958567, 755351230, 467126530, 832482762, 913839468, 201724300, 531126937, 362713655, 402575599, 78793153, 67769332, 224275755, 897262839, 187430224, 472299793, 428917964, 262945308, 934375484, 303220399, 140168440, 97523656, 422296534, 252454041, 218660442, 195325920, 291259646, 777815022, 554775112, 775800232, 73225534, 688194419, 999972533, 617084358, 641753643, 74543715, 118630050, 544538230, 184169229, 466149380, 565990789, 242377914, 98708216, 563906848, 184400092, 551981479, 215154634, 808582625, 202080355, 177931676, 440620618, 411574467, 6793899, 263016209, 985285710, 844147323, 724289974, 596729698, 909561242, 509629626, 151440661, 355263617, 861896159, 629724358, 433284572, 473481045, 664504285, 644718781, 304807583, 400950977, 782843442, 753392570, 662898397, 515390917, 340596394, 574232625, 873007675, 850320469, 653230936, 806810397, 343584569, 699440777, 557451616, 347262914, 344190304, 855406003, 645858150, 998497020, 70393960, 345856057, 940461541, 796220258, 487855385, 931203294, 711052740, 37403071, 80138979, 953442162, 698373924, 352429001, 469241154, 732635200, 230938742, 565318629, 3679972, 736577560, 158697187, 319422163, 427609936, 806544426, 416667007, 321555293, 288649873, 126104168, 933504539, 347085769, 659963641, 454375883, 488729633, 343665644, 339080736, 404806714, 971895097, 226188650, 672720513, 623711531, 919929639, 642725943, 491039542, 636961374, 56855559, 712299151, 265838945, 465373642, 146876610, 983506474, 859550378, 78211889, 191744604, 528390169, 411279151, 278112159, 352103482, 706265683, 55896226, 923969372, 216619715, 845719000, 773008449, 72020114, 343452421, 892372093, 888161596, 152350064, 191009326, 244130672, 198268676, 281310905, 323542954, 193817470, 22400121, 885152115, 309589263, 58682192, 732375774, 752528746, 326733411, 444449654, 608571449, 500185557, 166781141, 848753268, 388834487, 849608491, 726017960, 539432509, 868282899, 628120503, 125433796, 527373070, 99288257, 81999086, 84795307, 829033267, 684276103, 938868435, 424647101, 808140992, 225381156, 355299695, 208704216, 159261112, 581424602, 405189588, 348305342, 418946270, 952066790, 697338285, 352488833, 344532725, 337868199, 897258614, 352566591, 989633364, 139018679, 918000197, 348248076, 523823064, 307989169, 19265768, 28115445, 546348902, 205601852, 131470497, 743951971, 760064271, 504588919, 30648794, 213053418, 410889131, 776862154, 370066955, 307109002, 451636480, 948982059, 834394861, 963425498, 158844759, 525412245, 952774668, 54804711, 571829219, 722535638, 417301354, 941991514, 26205051, 61388039, 544254026, 462438464, 315965470, 166243688, 120094893, 589523775, 218036765, 634433539, 687413199, 279941262, 699188172, 494205934, 229592999, 886639712, 96577961, 870024558, 85256017, 808193182, 669571737, 886256555, 396645958, 915210481, 786721631, 880336275, 448067988, 48248149, 293293823, 615858635, 852057264, 796599392, 311155216, 584659029, 364419407, 991088902, 17664315, 519533755, 818186796, 875768365, 946340376, 737205390, 883455824, 155320163, 488296191, 51633363, 652208993, 51466141, 527667206, 58530884, 669140364, 656869318, 408655252, 485840124, 254570215, 88537697, 87318531, 471351734, 24188761, 739346760, 946630926, 292724713, 254103096, 612809836, 96680610, 307003899, 116566247, 61706729, 833086196, 441357514, 950874776, 495784712, 622525880, 229244195, 465243535, 64363735, 766618776, 456726902, 795686178, 827512441, 579848016, 67897218, 321732263, 112766009, 825592865, 508096728, 289884615, 238328479, 102182432, 211350645, 715323272, 275344687, 654186745, 263139406, 949199317, 616948393, 198757765, 973172997, 795402086, 993336054, 139018669, 594986356, 523489140, 637451858, 872483455, 757374889, 892502725, 738368686, 36768814, 907644547, 718985279, 414935137, 846551312, 847966146, 392912469, 485449111, 693116068, 209517691, 76278361, 728248185, 706539860, 962080262, 960658318, 805513088, 962266643, 419639959, 179968518, 752474159, 167875359, 858054718, 313170509, 840421043, 782196266, 670469479, 594858499, 224652248, 972005530, 100731359, 55453011, 342589568, 391013695, 800714699, 578499847, 114896505, 160286650, 752084926, 711011985, 93165626, 841700917, 239727225, 804041268, 365988491, 145869965, 558033604, 413564401, 183277132, 515950984, 750134135, 759297896, 495237429, 334726561, 445004592, 82936854, 722011149, 901559038, 355481809, 132277929, 811618758, 999898644, 17103993, 436038364, 82907271, 137386145, 406600288, 634018375, 419595509, 191978795, 347470204, 722589854, 736781379, 13434260, 746895171, 376933141, 458995674, 514557072, 596943260, 386980281, 338692439, 988003319, 319550044, 129255987, 933870920, 105588893, 625549649, 959356132, 27273779, 802490993, 4692897, 188943049, 385069188, 976822688, 522386221, 690295221, 403623623, 108719527, 855612612, 443701986, 646915803, 649318540, 953532757, 132022241, 194143108, 755072790, 351171314, 741804067, 757931370, 219645223, 358038962, 37549893, 415372539, 101608703, 583052706, 733382009, 799185253, 299273170, 654772682, 50640681, 476163751, 864265593, 47942661, 376154840, 854673861, 129354507, 552056560, 702536270, 963940306, 138857958, 955739317, 396101385, 746039678, 380503187, 511839791, 237093318, 854257910, 215596428, 941365387, 41081184, 394740005, 364151278, 466318159, 242047723, 259442694, 116731631, 294739187, 945030769, 232136203, 529568238, 207627916, 858693843, 664840223, 825567605, 865176858, 198981677, 235815318, 362187715, 44498219, 360452527, 151838470, 581734016, 260561023, 157410652, 499596845, 148744719, 309771926, 650838533, 27342326, 950377651, 449285852, 330199453, 755303857, 702102498, 409315885, 738023525, 558993544, 863206248, 523305718, 915555024, 666646613, 231312505, 102723992, 784383809, 870180807, 592577344, 26941216, 99283639, 319366716, 529855386, 857981722, 606162974, 445062688, 197722979, 680382236, 156338906, 411982164, 673580159, 840822292, 136222633, 195685053, 357174364, 239687356, 790399180, 680019776, 66573425, 526069421, 40704575, 115322733, 534466535, 545882156, 973182377, 593351054, 612835464, 168308973, 363178758, 989318718, 692142224, 26158011, 37930403, 216786423, 379100108, 518866430, 635234117, 688779470, 671264374, 249107709, 569447564, 176928123, 640333564, 521740707, 851556857, 667535966, 954268607, 489670611, 489172091, 781118750, 523136649, 453354008, 310106678, 625256141, 491547580, 374552319, 99770376, 891016140, 611419378, 105941560, 836852052, 899177736, 201036849, 904042070, 812413680, 193741933, 342371961, 75057053, 475183255, 877434298, 647245144, 828005379, 754851065, 145541535, 268616448, 242731102, 171096912, 184984276, 857196540, 685876040, 479026753, 668646497, 701594712, 623871315, 602137172, 958542630, 62128210, 247420543, 949071723, 650401983, 207477719, 330741036, 654739769, 323503237, 657309466, 419866702, 93824938, 44130737, 235134422, 693442025, 571422571, 545017854, 903982948, 671040344, 587886701, 500544164, 429149480, 848916848, 396497294, 477805773, 249412474, 425923188, 522260758, 928123037, 36551338, 520886997, 284258245, 574337435, 329580070, 954952165, 699574969, 107430435, 94480091, 37396683, 990122724, 894317586, 256007281, 77167797, 605605440, 265039657, 151863816, 294748397, 222717290, 18577840, 166049791, 239903625, 349743865, 448309677, 481586332, 672725153, 866012459, 294865060, 762909174, 699907090, 636342563, 990470298, 48422477, 749713716, 857997131, 392065538, 6403079, 378301042, 659430452, 192314756, 464352462, 39431274, 63625227, 631440436, 623715321, 374088591, 274322641, 420333785, 153505084, 820345901, 719462880, 850404728, 402450394, 514165144, 670130547, 209774160, 101215273, 996236131, 269218744, 265553829, 424812966, 820629038, 638004001, 692395156, 782856708, 824346497, 96652014, 770026610, 466180464, 74741968, 225220816, 889701605, 745811549, 308231276, 870648965, 783363059, 532299911, 823416702, 837586287, 796851868, 415640207, 571275738, 261273964, 371513970, 25449252, 275926258, 543870230, 473570710, 795017509, 309998764, 741083605, 582203496, 801570730, 208445567, 856213769, 554536396, 268392296, 482373448, 161611289, 595595760, 905203053, 946168430, 863021237, 68482262, 782411333, 286380145, 944478889, 796571628, 526725209, 495886535, 672746134, 881888691, 488006031, 442303627, 277859045, 490987211, 108822841, 135269700, 296171446, 293443169, 309076561, 945603270, 622278907, 847689313, 219041822, 103039336, 594556289, 77007245, 595309094, 103358977, 470753939, 369041575, 305868364, 514170852, 285646279, 202378672, 173309617, 504873868, 467554317, 781943126, 5881471, 533457565, 715092740, 328078539, 376630978, 777512330, 599676293, 576282906, 68818027, 340436400, 304639981, 701524270, 611627285, 847854002, 755484265, 153893751, 871477433, 748174760, 925798880, 954764682, 828321038, 854574599, 225344521, 403961395, 849153494, 662459742, 526129071, 420161326, 311367559, 324274813, 866713612, 823123217, 8123625, 323778746, 638041324, 624262762, 118846555, 919765551, 757931285, 301695224, 534873143, 175407206, 432365335, 256356256, 268181054, 977457931, 204981598, 951912340, 319600807, 370786960, 561603188, 731497068, 165959075, 814855591, 824175528, 721923471, 937652865, 990742674, 33204834, 680883027, 310959713, 584889853, 987572311, 558707837, 111781593, 608597075, 713116627, 44134059, 995003946, 159643980, 578558384, 160495551, 230608433, 250375254, 723798418, 442760793, 483620270, 291826209, 114067673, 699261704, 122430316, 488601918, 727095015, 364008078, 942412072, 998504081, 251215128, 14759237, 453010732, 420406642, 844370371, 62103623, 300679598, 761061957, 189678229, 435265157, 712912374, 687412453, 208258188, 427582061, 235447655, 513784961, 923862543, 470281236, 826775686, 722981210, 305817249, 655382107, 864503997, 755829015, 424463153, 882619882, 897481908, 770567976, 101864891, 178637667, 77450368, 498315525, 389339026, 513697848, 505821866, 928591212, 150981850, 863369146, 410479373, 993034671, 386497683, 7370332, 340336071, 568030258, 377733044, 965491060, 210914206, 862878426, 416164246, 769496925, 730539965, 759987218, 438942609, 9037457, 428136472, 118590949, 956425992, 38285370, 332338674, 297905295, 153213802, 325641190, 806422046, 662328405, 477272694, 799469922, 605010272, 759911171, 979869767, 848721034, 526962808, 57465923, 53542014, 107741530, 792799393, 841710, 796394734, 209798566, 298211787, 123319445, 541664716, 751333378, 551030789, 963729785, 589841038, 144867554, 202473936, 939769727, 559720595, 675209824, 333193927, 552854278, 235365727, 297666146, 667766310, 551420618, 107002878, 271801876, 3908461, 385724866, 335886756, 651100735, 875550108, 668997635, 315701228, 293943137, 367011763, 686072776, 309472187, 578276843, 663133020, 820734653, 102894679, 624565306, 899665876, 91022266, 882123688, 677752070, 355315254, 691548534, 369766993, 95674694, 522046551, 200296086, 252675550, 255644618, 40753517, 81640776, 834975944, 769373532, 526133437, 292881401, 939467917, 567648856, 292431825, 267346998, 427890185, 961297722, 138568069, 24979642, 770064173, 175559410, 871953715, 100863394, 366687088, 753021525, 859633312, 423891558, 524439530, 565443784, 891484423, 992753488, 843061250, 384260228, 621569621, 988956495, 606506324, 648771022, 830254379, 188663407, 43428331, 507799839, 981162121, 964966168, 451295298, 309843186, 554741823, 301733130, 47452302, 429889442, 228270156, 251992130, 934961140, 270338725, 941778312, 480287374, 195334239, 644705841, 849947748, 710944316, 542236820, 682295538, 871669189, 575812371, 167601196, 805599394, 820600013, 716569756, 883325680, 15144899, 702125163, 465354882, 726924394, 419893692, 582770027, 221843493, 691072031, 665374472, 161659296, 858105312, 492088009, 82517854, 822355990, 576440798, 824037241, 773968725, 882307988, 354092399, 387482772, 23417004, 236631993, 941815773, 351801418, 803862481, 536938305, 956518074, 338028413, 700669941, 598588033, 170170878, 93101897, 191474775, 650092320, 891116417, 936219242, 302799593, 921902203, 207849407, 925767039, 552966552, 128354274, 176964572, 895013050, 848848811, 923385321, 965849674, 574898248, 733084334, 39568389, 836354816, 103728208, 8777332, 43625857, 632389472, 862740020, 669677481, 987526230, 859108471, 819805772, 759599347, 943094834, 656559212, 945486697, 900866019, 454696411, 305656422, 444884544, 774350932, 718156335, 768068095, 510398391, 921155134, 173025774, 87363377, 463824238, 880942403, 421067684, 882932739, 608569773, 697627502, 11475703, 488541260, 632619786, 649701214, 636827146, 395280675, 500444573, 223778371, 625408861, 502691676, 498275675, 170522955, 509437996, 626627704, 914943351, 322197590, 931081039, 488170067, 462279995, 975017322, 711548589, 972489581, 372143849, 374174400, 963462358, 652714690, 539874581, 900428163, 379737010, 164942226, 280542447, 745626033, 189672244, 838922079, 949535251, 901185941, 979453525, 385368004, 936441502, 566136801, 506570912, 923301741, 626595351, 137092804, 273548556, 539474235, 528667215, 673713500, 523917394, 996094962, 321580186, 813601366, 710448755, 472062910, 496965780, 925841356, 668455789, 538611067, 880468411, 48535077, 851276193, 752199289, 596422237, 875164080, 752071922, 823981324, 294420088, 433525857, 839004586, 999784764, 110694686, 308437135, 226256410, 826396101, 388435270, 649146620, 3811072, 688874359, 233759384, 449582915, 534259863, 765961208, 283673746, 520062517, 830997441, 824197126, 447091583, 674535957, 979500606, 795424478, 628872496, 15917434, 126807517, 686118405, 552434293, 867842964, 959610799, 850888141, 802210517, 476572034, 358153179, 414021371, 578507411, 345938540, 824377581, 977306944, 338912091, 499750676, 318173352, 853747961, 739400547, 121796227, 602361110, 181997404, 40736322, 340402547, 939120315, 330865771, 6231157, 243295867, 562981071, 544011412, 128692606, 681512738, 717931343, 143799117, 762121739, 14286348, 473574424, 416229199, 709756809, 404229402, 662126944, 204042938, 843369383, 91098504, 886096385, 431821135, 515008143, 88118203, 891019948, 759736008, 289287066, 93482894, 688143114, 731939273, 198468991, 774231289, 810498271, 370529664, 939096983, 165769679, 393173736, 262513454, 211420449, 174653461, 586471434, 973464807, 475677110, 344994331, 312570358, 239701058, 427673036, 523948822, 557242590, 515357458, 331932316, 513414916, 161961629, 820423772, 528799114, 5377903, 261412035, 74854121, 256992327, 456508919, 766746432, 363347495, 884398293, 578413899, 416973929, 361647275, 626376611, 586162088, 64346876, 947852695, 703302308, 834206614, 693492580, 673184467, 256470327, 231756861, 190317459, 35637089, 428504455, 464391108, 821866001, 248327462, 332612003, 709209459, 830300521, 931478928, 2263362, 150005264, 302067623, 602570511, 70578878, 431896179, 543647934, 134504115, 749697310, 515710948, 354284599, 1931323, 483517386, 10460734, 675225238, 104014437, 531347060, 788049625, 78878347, 361069502, 661242625, 840082613, 368627299, 694545342, 557600539, 71164307, 524169040, 886885078, 435214834, 430954914, 874290492, 456542203, 14975533, 87794465, 769740673, 613875245, 429207757, 754030801, 393972172, 54233949, 387910902, 492339002, 320233681, 834804554, 174801643, 797037004, 472641662, 529565779, 855195338, 443244900, 742514711, 873159097, 249723530, 951631600, 690299676, 346152221, 428815551, 403578232, 921444859, 651333735, 449984413, 209693021, 179851777, 504783934, 957735954, 543220354, 446623093, 664042212, 591135816, 442899407, 220995495, 646647161, 176242800, 119762178, 430787231, 257776834, 791829700, 357837926, 319797441, 282157659, 31928713, 223082505, 623315295, 498787279, 997185581, 776387343, 715600993, 58564946, 205013782, 208182188, 442259692, 383433583, 206960425, 779792135, 785640987, 933412121, 684349842, 456832660, 645830591, 186488963, 648256046, 699985952, 855973187, 585043388, 660667840, 659340248, 83149654, 713460620, 98933794, 548630178, 498255063, 51981994, 809779099, 543268294, 485323592, 521352044, 467392840, 7465506, 130269600, 325709831, 94183989, 940149338, 421692164, 501928550, 270695516, 570255267, 216368545, 356278699, 274598219, 778442306, 959031297, 493889970, 651241324, 224013655, 679867399, 212891458, 261779640, 455215449, 275023240, 240217757, 866612044, 766068383, 730829678, 99892489, 140105529, 329432481, 545090718, 560690031, 603030837, 107330241, 362294203, 101662019, 259788622, 252699350, 73318833, 858533991, 778120970, 536239009, 91223073, 431076085, 190121658, 899210745, 799792701, 895018913, 131628423, 832834571, 290770248, 379042023, 828201826, 231727992, 639151314, 337511011, 536812173, 77099816, 96365228, 885564923, 252505948, 220213418, 891185636, 43972643, 223494654, 341507188, 383571857, 909347538, 783054861, 236566325, 90770266, 837270464, 534088699, 406703909, 292039967, 855709538, 527993355, 500890699, 132595619, 588712511, 237841287, 317405990, 357084601, 214145334, 957607403, 615587784, 636759849, 604380471, 808285239, 212089294, 446254600, 533617347, 183187074, 289250335, 227111367, 254630257, 505388070, 134177319, 234591814, 806453177, 968044939, 8364889, 897629663, 846110986, 740650791, 575958587, 71730656, 424012164, 516343857, 411777991, 534934698, 765223280, 527405997, 259133103, 923667748, 629181425, 841831383, 743959373, 642030419, 4916235, 386265821, 1182237, 28393389, 138133924, 564255288, 456978464, 867530161, 505403946, 156259279, 554144780, 663317728, 495223770, 942786135, 189526691, 198772750, 634324748, 897351674, 806485195, 612647725, 616272407, 414494414, 695361632, 105070053, 84846413, 844073398, 641898331, 43113792, 514040707, 334379123, 610685009, 835270057, 798058857, 277813659, 360710280, 76130623, 700414716, 46378438, 400810410, 284160807, 451907301, 184212942, 7190422, 807187951, 958524121, 667065992, 999939825, 615018519, 916873415, 917477873, 20103749, 370917692, 979135196, 664881151, 536021647, 703848614, 935220720, 48909794, 396116655, 923446001, 502323898, 958344675, 607540921, 41835164, 161091260, 265089221, 41098994, 999764167, 846510658, 160913136, 283852372, 413210258, 40099731, 255718593, 696136104, 173019175, 303329281, 679588155, 162268705, 216328431, 93799790, 786438377, 569549463, 366031823, 159868826, 4920083, 871868360, 687642785, 178464096, 9827097, 832010520, 376885788, 35355497, 184220881, 391136577, 917755111, 112782282, 852999779, 95641177, 198506623, 876630932, 250927127, 155762709, 166992956, 886203151, 815251831, 533756551, 364573731, 156652349, 374912392, 234629450, 769709417, 106445852, 638420532, 726327916, 113917309, 980427242, 953414182, 286871319, 604198529, 431893250, 258232373, 330812775, 839637605, 248672153, 351703149, 59166656, 622639168, 934414588, 788713999, 232521845, 628312339, 978064865, 857575177, 543412025, 299857514, 856956076, 255119451, 559339306, 649842844, 544220623, 864188268, 156192037, 367694189, 107035076, 856303924, 542216879, 162600181, 753784287, 99836788, 578484539, 470832506, 396936293, 745135177, 583741141, 240348851, 842516227, 975387862, 812012036, 291254503, 915147922, 426035897, 901655110, 28960219, 149613894, 166743417, 498323252, 884544290, 99406238, 512561088, 597325408, 870098046, 448482005, 30209127, 907780250, 627072177, 112775355, 862777125, 114300097, 680644936, 747049826, 453741277, 390315853, 889949681, 805284923, 555994693, 153834112, 893753564, 333871504, 821981015, 4369930, 830118259, 763476394, 39931221, 863948795, 979582558, 97250582, 989435752, 679933004, 544298664, 421403171, 385304260, 358351084, 797968478, 672690463, 35247906, 828385553, 955232519, 185600889, 57870900, 446735145, 919568978, 599180232, 103844761, 717751626, 551597618, 410033770, 866189488, 640897309, 393927850, 42909733, 39864737, 273327327, 709787785, 247348298, 956276453, 309451927, 412172697, 754106559, 257145915, 260569813, 267655876, 693608380, 69686111, 599024884, 175059265, 785121658, 412625657, 797991140, 357291311, 940931919, 112977253, 697063760, 634549816, 449273627, 787818218, 31636387, 902913740, 757510474, 154842704, 344559051, 676909726, 727144675, 537304560, 480028197, 116895024, 628560986, 356237799, 102155273, 863537160, 145351565, 753292708, 54691355, 768039463, 191304478, 453966067, 665517637, 402573891, 988189877, 414314744, 670935177, 306076687, 570104271, 769397570, 93878902, 188790333, 963044617, 81586365, 153874938, 160340052, 170921122, 313532171, 580386492, 701879423, 793707761, 508545278, 580796451, 905758981, 231542096, 630487723, 953260814, 795084491, 741293391, 486351114, 434406779, 440693116, 406545516, 627442397, 10221200, 196388327, 91408511, 159001299, 379076170, 846462085, 718302894, 252726052, 989770586, 396265721, 635364591, 579689716, 977573641, 884265036, 146393813, 634956042, 497676721, 456180303, 569809319, 239462242, 575214543, 279376542, 838750322, 76242497, 462784092, 258033610, 209350601, 777976596, 640281973, 320060563, 981084842, 448098721, 828431900, 531100990, 205014301, 827986844, 608241486, 643512828, 458506869, 375033508, 359149114, 58942307, 899466401, 963168616, 227741880, 640619391, 498787773, 277946334, 334114090, 622034727, 604049720, 698471264, 725175888, 723225601, 48507635, 726562654, 573258253, 533908703, 615130075, 63555120, 474189923, 954731021, 269960210, 49714668, 844440698, 713172505, 822597718, 728070354, 475448318, 487336030, 980690129, 189610759, 873982978, 654236733, 736822636, 376137182, 691709428, 389842796, 366230346, 426668386, 597843914, 704290367, 470928389, 163765319, 721484655, 837688040, 260340879, 500635330, 835726440, 165955961, 584673650, 753654707, 577660881, 656198577, 291263473, 699560476, 202453664, 562452471, 579904277, 502541308, 769536657, 872482975, 976851126, 309974893, 987198132, 785383237, 641586394, 865110402, 16408611, 855707506, 495806106, 909127156, 597368020, 395085007, 371981801, 991451026, 57034370, 781221065, 66948244, 600346111, 798744021, 699827365, 725148710, 629973676, 271884613, 194632810, 198340141, 788031731, 217361027, 166694200, 36817281, 970468503, 688337244, 407339907, 692217310, 814793398, 333806473, 569275090, 384165231, 944097613, 900538421, 314075643, 939529697, 464270495, 506917932, 729420379, 415373425, 854866657, 968343258, 884981369, 617899418, 225731757, 710495865, 733811699, 84483762, 260896989, 821777446, 149268670, 932359084, 968456365, 813826918, 639940560, 723230392, 492465978, 454478069, 908519366, 597847519, 870929113, 676454642, 716052122, 704548798, 687867742, 787322493, 779275810, 286525829, 212593230, 225989593, 252700597, 159041053, 654550821, 819716559, 273226506, 261280497, 526513043, 274026068, 610473214, 940292484, 370892092, 578050466, 412716099, 437379318, 187181158, 158145814, 150917307, 926528407, 140069761, 346813085, 314087022, 261727764, 23876482, 949996815, 431317732, 43414437, 291122323, 509478579, 64673333, 469723606, 700803519, 618113628, 187006380, 841232106, 713795399, 527770577, 559589126, 737392344, 545551594, 975473832, 884726258, 539278561, 415016853, 649616018, 694755103, 888998950, 671128705, 577204223, 933797816, 94270777, 116110724, 592648897, 234547852, 349693058, 739247599, 941581865, 709369677, 278861846, 563399872, 729807554, 993859651, 247193122, 286004509, 523298592, 226227190, 550626033, 31757392, 902084678, 474882397, 294315983, 785459280, 94254904, 446792647, 340516323, 263710723, 68966576, 684417400, 699974420, 681558276, 407688196, 912924146, 233755377, 846119761, 533357245, 245590348, 690879663, 844334223, 699674773, 801930545, 438231653, 307040749, 55814209, 720849253, 299512224, 99614243, 827653529, 357647925, 244761219, 220673475, 461804246, 292790060, 234521721, 252530355, 101005523, 924536532, 915771054, 405053630, 594717366, 885142911, 407788945, 491442072, 332972954, 894043294, 255029077, 800682002, 887722907, 93250857, 83991044, 701836244, 600406261, 248767085, 652167411, 711151540, 159086017, 730126677, 782955330, 818085774, 812137442, 982746150, 982427194, 638159679, 117001665, 227053230, 259816729, 599032825, 959935578, 544062700, 100952771, 96568870, 408676532, 280189694, 386966121, 14113992, 948815935, 940161071, 34829292, 825532527, 253187701, 706390293, 139063545, 573266673, 193645024, 991182013, 196873437, 985420451, 900723439, 371329424, 892342034, 473462153, 189195987, 873318341, 414461621, 422958796, 400457047, 577794189, 768895185, 20596293, 141495547, 278427289, 153694587, 586446199, 729460618, 996515887, 205204929, 273292089, 569572611, 249470463, 43052271, 104614221, 46258139, 781384892, 345805627, 945695451, 371606064, 270625085, 562056660, 464871386, 47777158, 299314231, 316444424, 490594352, 524479817, 306721615, 453332066, 908902272, 21058549, 400881111, 282540810, 733256737, 338711496, 60014355, 741552531, 705817797, 563120335, 535440955, 612092594, 398871667, 690631467, 837221453, 459428643, 919210873, 950258415, 494194380, 450967894, 246250482, 188643556, 693850373, 634923558, 668403861, 483005146, 286619712, 63153333, 882526274, 356185586, 150519809, 886973507, 822860650, 79804727, 787747315, 648081796, 178093503, 516248360, 459613274, 859861091, 469434483, 808831540, 151669300, 648174761, 530032266, 643982373, 861345898, 768299723, 483970763, 934868085, 826630478, 783458054, 188457185, 989402824, 503949594, 946389920, 609686296, 455755725, 813687262, 49379769, 727112383, 399543588, 617862973, 494656334, 906126935, 541007257, 572304365, 763558517, 90153446, 876943378, 218439085, 635011912, 355769731, 536549755, 560551518, 334113944, 875879999, 155864052, 783368583, 382090958, 533953951, 330554332, 424460244, 841660314, 944285842, 610146561, 611369541, 938749917, 530233920, 614559661, 576127376, 898699766, 848296885, 616068594, 579664928, 18372419, 620370434, 140525614, 834869683, 690538244, 31453294, 383287134, 421184773, 593996649, 657075606, 789701756, 943412762, 394718953, 950145883, 564458659, 102278367, 885550660, 447783162, 737190647, 850761064, 879841768, 691680965, 980183402, 666710041, 99528691, 319851539, 502729389, 529069900, 298542030, 733853418, 715194952, 716182655, 769747586, 245530187, 751059238, 429503208, 390545891, 672955786, 565372244, 318723483, 97009509, 105972664, 13710113, 554262738, 932329064, 126706756, 625157597, 200364530, 888585509, 21886408, 546863925, 402434768, 604113152, 343346003, 735672924, 853073163, 109110467, 702082477, 239162593, 166307739, 97893747, 797216670, 669669252, 110022779, 163791251, 248202725, 513725166, 455199422, 809487769, 988876946, 832776542, 314803147, 971530487, 570401022, 771756333, 543723081, 219233567, 91704329, 494287603, 272916621, 42305907, 420538827, 79936449, 559490958, 506071491, 114235310, 711948210, 114580237, 926786862, 551749218, 134764505, 586256253, 417319283, 386433030, 877786990, 347434400, 180008501, 140304293, 473958887, 965464378, 413943060, 850427132, 739741525, 150448083, 229104271, 168590187, 316105894, 582974526, 742433343, 182540592, 862279947, 521834954, 336748523, 337940151, 89504672, 731165639, 484733899, 380991609, 947179528, 960001003, 149347620, 664868812, 915188254, 720707664, 734547519, 547966286, 177164512, 978822403, 225572028, 872871499, 916969806, 178223487, 899445521, 745354801, 228590618, 825215546, 582514703, 852221202, 396042667, 553515876, 869630242, 130607772, 670647878, 475702298, 112991981, 753517085, 527567775, 956624604, 455373201, 446102147, 742578273, 765134126, 214126508, 565859966, 455902835, 512033782, 241808488, 836742676, 908533652, 201029179, 892531807, 657414724, 549620735, 127916214, 158860916, 270271435, 488783364, 632108492, 739000162, 697780915, 889173787, 751734899, 718143365, 407210782, 251138986, 113824476, 820255127, 356438891, 817369873, 445206225, 506344595, 549073849, 44528180, 853583379, 181779930, 931157187, 853430426, 6687315, 144401715, 447570865, 251876616, 354332349, 115317254, 835794831, 255332488, 761074127, 948781907, 319656251, 650673980, 457777584, 345903778, 577434011, 479757223, 471147577, 288553478, 930264526, 120766090, 759735723, 581748914, 635187756, 169205856, 816127143, 42099850, 827568154, 418276799, 551545842, 403205596, 690426657, 663623663, 945420203, 301475633, 451950722, 583653923, 507960098, 795831908, 832998073, 183903460, 300667915, 384985737, 963124285, 83343486, 580773487, 315948157, 123126273, 925309036, 188561970, 88872252, 753165386, 242064615, 219982935, 653844880, 867670210, 812496640, 116029932, 72335508, 379249975, 39561283, 420594812, 637494837, 573007339, 456995093, 667208335, 414015607, 50599492, 267802827, 223886184, 557794930, 24772349, 308227706, 746927332, 720087986, 564222085, 485995608, 779172711, 268763997, 174283702, 246675929, 853768412, 173590861, 693241809, 313254057, 989499523, 17377670, 881311161, 783433113, 439442106, 854906332, 565174807, 839495579, 402268307, 784017619, 489619602, 98984236, 602048702, 735622279, 32136763, 437122713, 100854593, 876540522, 491430923, 574787960, 410448975, 721637795, 674960384, 672602594, 67279181, 947181183, 426952075, 710736246, 462903900, 451521013, 42767304, 343118765, 183501254, 763642473, 237667986, 521190583, 546707457, 774601199, 196553806, 549854591, 456695901, 506915172, 376788013, 254427, 771337332, 289385936, 376775367, 789181456, 76711696, 527216121, 216678119, 484533131, 605909224, 483596971, 322479129, 96843513, 270903172, 387893469, 269430874, 363095377, 23317770, 658684610, 768651224, 726837862, 617749928, 917044949, 731211855, 806395120, 446404940, 507449797, 121418191, 999735111, 504775422, 882008386, 105744680, 687137004, 107679921, 798629518, 457745349, 328360604, 471871539, 46245097, 611768327, 623396098, 510069683, 153391699, 87987550, 944193016, 710696616, 336899875, 697657045, 638756716, 972210912, 906638765, 341155153, 7233795, 988514903, 495494024, 423050300, 161969240, 797076891, 303455882, 706690619, 30322434, 190355255, 986474214, 672469036, 769210173, 77636131, 741268226, 211870574, 881415250, 444700936, 149975557, 902978842, 504556769, 473735187, 871513159, 572261013, 624858639, 878332497, 617612176, 395870551, 934013539, 760388790, 546601555, 28465802, 81697431, 697476259, 241746233, 984018966, 54283723, 258688506, 947595008, 815835349, 476739866, 608503786, 836653724, 328905883, 359337238, 371656638, 772160121, 517340624, 696125481, 414620573, 105955670, 890421382, 296353460, 667636007, 241270097, 712179935, 825106199, 793675314, 153167152, 458101597, 807192322, 987431400, 856675930, 323686354, 185236059, 313352299, 363453968, 757776861, 927284749, 321332271, 742911876, 565727925, 872724608, 862242100, 463925644, 899675639, 229110333, 982887488, 824719211, 27485879, 487322539, 430851158, 946993551, 495513639, 34711916, 191829964, 764594266, 505717616, 432889213, 562990773, 506209767, 962997931, 451252762, 309042263, 481474075, 64266045, 412825347, 553935019, 748454855, 22075060, 596576812, 960894729, 254890721, 337525106, 353930960, 987133315, 57979631, 635421802, 575330606, 189676911, 721913557, 968787293, 797030531, 805516940, 456573140, 838441522, 890877341, 934912074, 125625418, 743688281, 201993562, 801913850, 382274791, 619366826, 26659563, 429694521, 607504814, 84906139, 537040861, 939037834, 545210324, 330259863, 962081559, 753542033, 241235780, 903267635, 851339787, 844866415, 142911149, 641939142, 769253829, 233538568, 613047922, 292277082, 94214753, 890894138, 688505132, 520191725, 316739090, 951435287, 209278605, 963802839, 569013837, 410871052, 762902999, 928563557, 719627743, 963183584, 23210867, 795399333, 434289344, 248480886, 230554598, 490427643, 84256267, 734971773, 132983253, 465306520, 598916906, 277621599, 173249957, 733091201, 359825956, 938959519, 725818281, 908507701, 393569923, 594712545, 199130100, 778494315, 206025593, 59659300, 673543802, 583267027, 196655425, 233156294, 102598744, 190115901, 11580447, 386224178, 160045851, 210272706, 864886274, 420482585, 419377329, 104752968, 42156510, 104814772, 60265062, 232334204, 758137191, 486535505, 502291421, 616169688, 833404797, 150867329, 704568562, 900302921, 899762963, 294519992, 929887214, 806365287, 891769447, 809720221, 201303687, 997854939, 455827435, 444834231, 376722969, 509648434, 795738695, 674176788, 432977664, 663225894, 643647176, 124434036, 269857856, 566551404, 828488207, 890084872, 289707188, 203167270, 695980470, 261339329, 995066270, 907222303, 143634813, 894802773, 122796690, 464005881, 884543445, 185484861, 746943101, 134128499, 551011875, 645964665, 757758461, 630322490, 540478229, 891065262, 435351361, 326460677, 683206026, 252763016, 462401492, 789369405, 219334370, 733502495, 652202588, 505499877, 304260962, 214950499, 860637954, 665538759, 980692911, 477774309, 463323100, 134989000, 625741435, 650787373, 692729201, 164212820, 1212944, 939273672, 855232449, 191355596, 18593517, 537305906, 511128788, 567510903, 52741132, 648126698, 37011370, 690026102, 849583273, 487747803, 62217845, 433097261, 375209705, 344509831, 371693833, 943110395, 290116039, 209758002, 56168111, 483841938, 789187370, 990225465, 43772030, 222218767, 702107422, 900101783, 951624047, 946177154, 906026476, 810347966, 631831630, 394346546, 420993269, 74412467, 633863311, 162041525, 670131135, 606724303, 642589146, 382078434, 33422759, 953210494, 397129054, 563325429, 110135375, 244414148, 619678970, 87679241, 126610127, 680112333, 646714739, 739302686, 620299787, 335432322, 946571494, 779875190, 464257546, 99359366, 372225979, 860049990, 440325758, 265766619, 384540277, 123174749, 497977502, 765405308, 473493849, 372647608, 689009297, 462401230, 697864175, 265719307, 73415986, 26024368, 211745118, 454621376, 201225426, 657945077, 750717048, 302304320, 615620792, 721422906, 661303041, 590839077, 136400721, 549561192, 261702042, 609361559, 929881225, 614951111, 49736433, 662918486, 100760150, 763750361, 647056922, 127907391, 64174595, 213507485, 645366695, 833662405, 521562955, 395574083, 379272315, 696297910, 363033992, 590043365, 718897644, 780043037, 981755891, 402328855, 245340525, 824354609, 279794643, 143384295, 636517127, 105333072, 587754437, 255492241, 933069684, 497009065, 251974135, 911934951, 419619189, 25834934, 964562262, 348656863, 798479253, 659763246, 319496696, 777116176, 515872833, 123521019, 434386303, 705901768, 640034019, 583590217, 709470131, 613970490, 131092840, 107224137, 30760600, 154722718, 128957775, 734666111, 354745977, 829624246, 986551524, 29422292, 211403935, 913487332, 937818896, 760765349, 763225394, 651648600, 559178597, 602356569, 290204325, 510578014, 558488693, 424748053, 369054475, 483722014, 715450505, 155268303, 585859363, 867746106, 516384887, 106157303, 812281867, 18219744, 671873821, 976493121, 832837666, 600007058, 197011929, 333336330, 918865262, 367947091, 657380867, 41798778, 305638369, 789778715, 766091180, 187289326, 312472265, 32213762, 815447943, 118798795, 24090217, 920220573, 983590575, 774349579, 418919061, 589804912, 94129847, 124610796, 653643661, 661119479, 538361784, 438424246, 242726398, 489266678, 301015570, 949496179, 885303417, 663101597, 587336347, 95908176, 754354794, 184324286, 799333166, 62249703, 887470877, 136983826, 712456719, 401223545, 919975037, 689334652, 986383678, 682729152, 11052967, 965657675, 366257258, 553680045, 381509241, 829444509, 918352361, 20294584, 84708278, 588131906, 33558896, 809398737, 22978482, 484721928, 911360228, 891891903, 733144229, 276798521, 392564164, 179005059, 377648475, 64116466, 36357013, 727720485, 877717775, 208137023, 32643473, 750955308, 432192744, 162243643, 738392805, 779033585, 618784988, 518642258, 505137328, 355209562, 605323967, 866804072, 10162190, 366804638, 652767141, 491758350, 713819503, 464584958, 806339353, 256435487, 195169968, 576633405, 369182669, 138883584, 338826979, 502580764, 104406869, 696301940, 299824852, 16578950, 357340328, 962686455, 825767270, 28154310, 889527861, 419390761, 182385742, 68119511, 951178178, 150454231, 507178373, 763500779, 30062467, 407432252, 459457771, 450178657, 378021565, 799450792, 386271699, 240021368, 622973358, 360224584, 227243842, 436129032, 502912154, 874172953, 988533807, 196032008, 303924587, 438211452, 666344740, 837704136, 749427149, 261532604, 571730397, 548305126, 105772831, 537593282, 242081139, 785675240, 683390857, 645452782, 546880829, 990901583, 232448203, 745375381, 209699746, 600831019, 883467121, 605925649, 58890296, 309415101, 525076308, 149233781, 652431202, 642902748, 313384853, 678535212, 533902942, 104387408, 571170677, 294817416, 381920308, 93735775, 801211671, 320425322, 968965176, 759619674, 165192267, 856758314, 177914887, 238825261, 119937606, 515305038, 656560468, 605395145, 319138098, 446814109, 837407418, 132124104, 726217393, 114261151, 323669141, 154431908, 762224958, 6197220, 454041306, 411139639, 157102062, 960327789, 803486557, 674134916, 940063499, 397822997, 94250089, 433967818, 580171216, 410325600, 145912840, 83120796, 216784244, 646001600, 301157194, 517337322, 317475265, 911681935, 50365982, 158080713, 201481837, 13744417, 291320795, 377920027, 485742521, 71279571, 212267967, 958785662, 953830554, 689743781, 490287637, 898377079, 64347012, 573461743, 94911338, 909946826, 658801495, 527539088, 951660045, 227597608, 942473503, 176543873, 89239099, 645290010, 446072917, 320334930, 386681524, 827658575, 966774978, 247293255, 299510148, 5349545, 103284470, 378082922, 660778681, 319807825, 432184125, 155373016, 725650439, 838856947, 280595769, 210245750, 773940602, 179753634, 541630236, 471080738, 925528597, 967379152, 748689779, 861097823, 703405602, 31263594, 733280188, 398950645, 780497107, 662212745, 296027375, 480241168, 792801146, 204400470, 510066365, 406467631, 989713586, 409251142, 779042685, 11601666, 880403912, 463258768, 960221215, 560125291, 745281398, 955999098, 494290083, 980145946, 755166342, 393599973, 79581752, 283905169, 864651078, 722039239, 773166186, 744603669, 68249917, 689518216, 26414906, 266190093, 75451017, 298328475, 583200608, 959138772, 343594575, 637843213, 376166102, 405810670, 392015003, 92172640, 899045566, 331906248, 49776227, 546137606, 967524129, 828951030, 143988366, 502858806, 583583319, 780565990, 974435190, 685581604, 442873013, 508333113, 509602886, 536409019, 352442052, 392496068, 452845460, 384136556, 654079624, 782216294, 526472504, 506667529, 421656762, 545207402, 411686181, 356850445, 613022870, 257525333, 455456229, 76162353, 662811953, 568471540, 323107665, 54018105, 104636787, 838423380, 343571956, 215538207, 335079184, 559286921, 498023610, 797747628, 241204905, 606706139, 70627856, 536699745, 502553301, 873017390, 63028952, 224864670, 726114901, 63373022, 721829863, 203222533, 747112756, 859181350, 967764339, 254820727, 872918306, 476993202, 365739963, 774755721, 504840827, 263676674, 314453346, 287987966, 415570674, 422744299, 483263307, 990120282, 952547590, 131679922, 315327626, 509569221, 844093902, 653291263, 897441729, 662909097, 914002889, 380037716, 164647109, 684792068, 934426240, 176007785, 206871077, 81947583, 923980147, 730732010, 495174116, 712150535, 234665658, 267160858, 277157605, 322618727, 756479524, 126758779, 440074666, 135257891, 477948642, 23854318, 26747678, 336592841, 822569571, 774439940, 740850541, 930027455, 344263261, 332794446, 782230897, 148153485, 36705772, 809394940, 558634639, 732456220, 537863719, 559948773, 169139715, 523405692, 397653051, 804322053, 573640262, 88493401, 100553834, 298331862, 388688480, 993960016, 807134846, 390333880, 711580476, 458640084, 795042052, 246412772, 508188779, 939751469, 105936570, 798736289, 304745599, 240453228, 556341989, 378482413, 8340371, 137454826, 923350527, 973417873, 30520474, 844467552, 414995380, 117637579, 963197069, 292086628, 690366219, 189568581, 722494615, 649029800, 252282830, 845671284, 743453392, 349095150, 357736562, 971841105, 909249728, 457757398, 185420450, 464116436, 442282774, 138518187, 634271954, 105825410, 234042788, 880117579, 5089785, 46572765, 412799188, 358741643, 229532740, 248425231, 300386428, 560950875, 841275643, 54544916, 307567094, 720926394, 437212127, 549050568, 77652180, 294755320, 620871794, 393858784, 835279334, 458441360, 246568006, 917944091, 846114638, 743443445, 539617477, 944404092, 970602029, 990135705, 154080273, 70140759, 514622573, 574267441, 90563018, 429338948, 572121977, 596824311, 444249817, 881742282, 366847561, 575579103, 671274286, 42278773, 208813785, 880320525, 12701983, 453445549, 626092161, 634747048, 126745619, 862023894, 949487270, 964536394, 334273464, 724535065, 799779530, 73707829, 15054143, 588030372, 47972005, 941770612, 698182349, 349235818, 893035767, 232545915, 533410053, 277183246, 924175478, 880306596, 950747663, 385231349, 876443727, 436785051, 14375572, 998082200, 563524356, 48617894, 908732767, 63133996, 897549459, 80754829, 785280864, 75663398, 303722845, 166385363, 100727115, 101464897, 521490095, 812879215, 535434275, 77776733, 6824088, 261328568, 108692483, 462829917, 325377197, 417163769, 736923353, 683589800, 119947455, 654307017, 488111694, 493891727, 821362987, 911662844, 295379849, 102298554, 70131804, 59686073, 32078554, 34053232, 79379196, 903433144, 44647178, 21307382, 941370686, 690334251, 68436284, 22036489, 819353158, 139968009, 812484175, 149615141, 908999210, 791533656, 205677382, 313941009, 536840839, 640464883, 839811443, 520470689, 724098377, 196388276, 107471670, 208829204, 568660991, 732368703, 985274771, 605402021, 199387520, 530912327, 374860418, 85064193, 747296797, 560220170, 576691872, 416461167, 792356387, 222724834, 279886591, 706828056, 282708568, 924613138, 257935102, 531287631, 329790613, 834009545, 379633041, 796652175, 535344387, 299043914, 500729997, 215283322, 895498085, 190900807, 60063262, 537312104, 560252451, 620327494, 32948409, 306110043, 948719165, 967501696, 991064736, 979987033, 536966414, 981058984, 608945755, 914408004, 939013355, 158735507, 583622022, 329203276, 197153178, 93975184, 489638608, 729935785, 231165676, 3168804, 283640314, 93747166, 700356867, 693625847, 205405001, 693837141, 169911002, 837734377, 525797480, 688217606, 636393411, 373220902, 735144432, 162258847, 103175567, 253387751, 551477232, 123056503, 517291122, 732394842, 390430487, 463638060, 560515348, 517234190, 978092886, 389592965, 205684291, 60566266, 692152774, 306867476, 282060699, 598367163, 394605508, 196880008, 69275484, 882771845, 185438448, 757828909, 288972798, 488182383, 260704919, 416807389, 429082164, 714609757, 748016284, 93529036, 574093273, 948338714, 753911531, 95180761, 909089631, 737272996, 693029103, 263202178, 507089747, 797609603, 775329320, 710265373, 349706402, 755718614, 295995591, 558141090, 790715567, 638162167, 828194840, 569833087, 348778049, 242604593, 29228048, 819339322, 376983174, 875930491, 806432361, 648570317, 233890858, 571807636, 691184604, 653126668, 895499515, 671392804, 158001455, 121420379, 759384148, 292631029, 65102502, 614419199, 854850075, 388920467, 452907818, 468638373, 307708884, 774176391, 527311315, 250366321, 631582172, 919555010, 801559525, 586365583, 603234467, 950610555, 537208058, 575919837, 760413952, 907721633, 751612175, 3328971, 513054565, 219913780, 49789054, 158339606, 6994861, 424931435, 433473536, 938112161, 191220304, 333176583, 171646413, 957648895, 868378313, 68161864, 517356070, 312271439, 476762128, 474011532, 46372651, 564145438, 117811726, 457762875, 532352217, 832068510, 561403379, 211050029, 224231387, 590063888, 127686756, 40022217, 616665610, 844201701, 714288911, 797717696, 707748549, 108239856, 139473435, 662114802, 184784814, 635534586, 227501896, 976767916, 183443074, 325342513, 541819388, 132939873, 454122776, 531317610, 13579540, 932737837, 299033244, 294605919, 419093656, 831028193, 42068373, 982799313, 650620788, 192205325, 123924252, 595181040, 591792798, 137408038, 94054858, 24822678, 454710665, 407424322, 394693338, 644503332, 742903169, 133910768, 180029639, 989975908, 198739239, 256454034, 893233580, 571182696, 948690404, 42075902, 200994199, 560244358, 494457112, 476116098, 328276990, 543054776, 683861786, 388927192, 426356650, 300838624, 241708024, 692701977, 715565850, 84639827, 366619377, 984294672, 474279794, 76562117, 571869795, 471405767, 467270164, 629424592, 413063134, 73404517, 70595989, 734344209, 316531770, 635677943, 320794212, 701890546, 511764371, 738711165, 604331653, 372426156, 285108378, 353097465, 69839760, 14197929, 960384616, 112894688, 538269017, 346777933, 640211134, 157058755, 244044818, 509835628, 283992935, 745848210, 994844691, 546615893, 358304859, 112411529, 464413272, 986319534, 113573545, 773618028, 107514879, 743923051, 787979837, 236967807, 129044732, 708776217, 906495600, 868965172, 479380642, 449255117, 342694496, 461835827, 877259367, 622599363, 771346653, 755239444, 600292243, 444021041, 735916163, 455446051, 718433698, 835255314, 579297479, 252948723, 428908903, 948367235, 112084414, 610969267, 906433160, 649233198, 993622156, 564564975, 760936712, 766675071, 630224457, 267271209, 633661446, 265855356, 473717626, 528806810, 559089531, 416366744, 105880721, 870397120, 166808763, 222543976, 92113194, 279546047, 750525537, 410904, 331369846, 882098525, 857702767, 341514119, 503197511, 985500692, 623877441, 598307650, 754251552, 344284721, 671721749, 118589471, 74058660, 343999645, 567101552, 695775288, 484659992, 843383979, 809388188, 428864439, 14683558, 935977992, 887369897, 346616460, 177200625, 634010950, 857540849, 9151935, 520957879, 425408838, 809042774, 396687629, 139434851, 755418991, 616451391, 381328771, 337551329, 426577448, 709381894, 244369358, 561811265, 80971685, 965190376, 40455523, 995008316, 138579867, 284632828, 337059797, 523499310, 507455013, 986438089, 307008377, 731925955, 405393121, 272688484, 334987508, 574175838, 747497821, 658212798, 16708711, 588232210, 348204459, 908753050, 487646105, 218272155, 968019734, 575660488, 964718799, 982195111, 614912591, 40217338, 760999571, 813648491, 694427887, 618746504, 889626679, 586103092, 939905362, 128669636, 763957858, 397351083, 928606918, 396868979, 521879743, 977580021, 273486787, 833936450, 804239332, 539718687, 714878471, 647329895, 338638003, 895333737, 171381310, 584323272, 429938959, 651657448, 493498841, 880463732, 283196145, 755403706, 420156719, 46534728, 161526233, 241256886, 536278697, 714055427, 410620008, 997279468, 494841600, 456148540, 679144108, 472568458, 709788816, 430275607, 865499935, 226718029, 948239655, 471268749, 420231357, 142866788, 577209171, 661832865, 352561373, 345528853, 270288604, 566696753, 785529236, 963896575, 318786103, 311779254, 496386519, 999989859, 453048008, 834312966, 245990274, 669018325, 725589070, 987592761, 918588092, 499158367, 383320300, 746235987, 156231073, 408335266, 268333063, 970772428, 641144549, 45712980, 142771890, 92510915, 454415232, 408635584, 29434966, 27366107, 677068690, 192601615, 201133908, 380779650, 452268269, 290937731, 614801690, 480515546, 410080793, 193289877, 116079036, 27507966, 224180621, 537902355, 288793925, 332208895, 34567110, 124529247, 873913265, 799672484, 46539068, 777129226, 126692631, 859757821, 773516760, 373380293, 864382886, 556292191, 614906249, 632721333, 690060344, 437435561, 72744380, 781671014, 485421998, 318564742, 414794758, 503832597, 488473309, 151807850, 305417910, 48839240, 54219992, 941153722, 855323422, 651689021, 407847032, 40248278, 175914609, 799976141, 619106221, 416212258, 706512677, 303300563, 899803214, 521606745, 289090488, 191023901, 902098487, 34688850, 569156580, 145668973, 344941224, 934668010, 638393500, 700396597, 618252607, 783411177, 565149389, 549329692, 743476635, 61248006, 313455447, 35225185, 80138795, 957647980, 119341537, 142531876, 626095366, 491130599, 51036641, 92424501, 732715633, 753882031, 132375409, 898130357, 272078879, 798816602, 838914928, 128956871, 54716154, 746794657, 952860706, 428527048, 303920886, 813916607, 241973846, 44185261, 56936727, 505797398, 936526283, 953055702, 594170477, 288859465, 9813528, 423031268, 528323364, 470721517, 371057824, 434410781, 376208292, 408123093, 509710910, 498915287, 648474107, 646420756, 435459281, 239570247, 745069712, 338639664, 334404881, 203409055, 976981381, 467216453, 218494036, 705264283, 887174041, 658737176, 7255966, 707415972, 377138573, 146962951, 43502199, 978419440, 719482362, 843075897, 582030792, 78673796, 428726585, 844489942, 256621058, 488824910, 843225726, 69918626, 214812903, 486768799, 207113429, 255833951, 1388851, 601170140, 83485439, 558225020, 958304069, 811748077, 520567813, 110630361, 573414694, 591197251, 71165965, 163778696, 831889138, 142304841, 708870135, 7798665, 888467322, 374291873, 884183874, 279254888, 96169424, 798951687, 749817033, 33209461, 791279617, 769301954, 518561928, 838630987, 795319538, 795284144, 436497018, 825744869, 699128068, 292486490, 185998834, 979717105, 990488423, 662161330, 747280188, 912795487, 424566970, 114947397, 476382592, 100137648, 809353140, 275576652, 523468707, 655182550, 727143303, 236409827, 565850486, 422717109, 73605070, 336667312, 204146641, 108068960, 143873989, 273847297, 218357401, 452847328, 330334264, 455497754, 486685225, 994759108, 699358554, 893771677, 83129869, 468577358, 756793935, 121465228, 778348040, 146569673, 450653058, 45864344, 127577816, 422410872, 669990437, 78944630, 212923629, 844407834, 275356858, 241285597, 895760922, 669264078, 568021595, 336199191, 45730611, 54462714, 625520337, 838896210, 45329440, 7856316, 28458047, 619081575, 919098728, 148970842, 926941229, 732667567, 658314841, 454274469, 50137840, 330142771, 50255517, 892682405, 370963868, 33951577, 787792858, 621604949, 968779848, 757280728, 241777929, 183658122, 197755025, 56225352, 817205605, 800262932, 336928249, 677949848, 169287943, 480140928, 199542539, 294860744, 243506291, 55500408, 631069993, 595388381, 951382463, 555525173, 23764706, 322720032, 25841650, 500149540, 32366794, 620267167, 288615381, 508898892, 454012425, 270552078, 272396174, 641312307, 826438819, 393932476, 584769545, 305848553, 604272512, 417080383, 219540525, 231640586, 381433710, 972551777, 861519407, 52651895, 920788573, 650781281, 645464950, 407606265, 320819105, 799891629, 620765074, 500904125, 107573305, 309102650, 191435789, 849206908, 59777870, 550367551, 214866118, 990366485, 9671137, 228440145, 292719583, 52570937, 829586725, 609314182, 29710350, 513793565, 865983296, 177358497, 741890879, 776839410, 932633672, 550624736, 754092589, 244941052, 585692177, 102709693, 740272831, 420804590, 583792132, 991813654, 908535778, 786034484, 369037267, 592038314, 749120717, 429623051, 716237303, 213694377, 233279163, 638747305, 916145763, 145664962, 964894140, 857993997, 653356842, 468152650, 356357584, 931845525, 522824818, 482721352, 601301617, 891497100, 13198821, 958644852, 661599345, 118722282, 84821546, 279771115, 999653629, 354260188, 118563850, 770595937, 810401836, 423010364, 357971689, 379754658, 632009740, 63418984, 599742936, 627456369, 954055997, 800932814, 355933199, 232120696, 381457522, 871311621, 811939426, 106492828, 362899445, 182223598, 423742728, 407273027, 728404768, 75873123, 996571414, 640211875, 773081744, 359252635, 159382157, 3687325, 589039077, 126611047, 183412657, 237529434, 945549778, 371099183, 680812319, 463743565, 223660039, 773481044, 79507372, 375371747, 199182163, 535747497, 982791297, 167330453, 178857109, 284589676, 137804402, 322911192, 633485595, 851906180, 507832659, 520719279, 267615971, 943181503, 956415466, 741677440, 589985757, 827135392, 624579237, 437658199, 700049216, 253405417, 80584766, 253556274, 269363495, 55107094, 774211520, 397907245, 878718541, 461601126, 787556808, 14806699, 807524245, 95939217, 82514374, 26077804, 136291200, 251602424, 958665867, 10605997, 332371464, 827080430, 68626133, 259786691, 431800005, 307578812, 205347281, 145538966, 563244128, 510666049, 838491630, 549353608, 812322847, 669603525, 803052775, 773777061, 478328156, 112346227, 529836634, 226951424, 633189210, 894723884, 172959217, 836492235, 947627568, 38804640, 215377012, 699290449, 758748885, 856581737, 576440887, 852828693, 902014570, 93570207, 202488049, 901380603, 971026432, 641250301, 535993116, 343538407, 172981247, 884540344, 831281918, 615363225, 123000792, 246733749, 388908119, 835493172, 398418390, 50672790, 828084724, 336700460, 43996308, 15165688, 81373240, 310496913, 4592279, 528337845, 310221605, 870960539, 7079634, 455412864, 767572759, 715937457, 333995281, 41697241, 393964725, 723184476, 852702906, 800069533, 366225531, 511292990, 931912378, 815488587, 219076241, 809013661, 655058479, 247447883, 737698439, 520103541, 424904799, 521776129, 769971610, 865547718, 907577169, 730560383, 987598908, 258961922, 662013050, 268652208, 15372299, 916869330, 143678317, 674544718, 511899139, 152622112, 815587520, 620825449, 162548579, 901452079, 229959951, 346737559, 266767154, 248242286, 962778393, 34778641, 444780170, 899567874, 448105691, 183982995, 994731404, 137432305, 705188748, 718366354, 307817795, 29593818, 323187597, 823286136, 772552531, 640621679, 325953595, 308457120, 953091115, 5511219, 363573832, 470311330, 248959411, 969076388, 411638925, 995879226, 233081673, 462761963, 588264599, 190701776, 608114499, 300082295, 345773845, 473680636, 297671790, 182645163, 54409362, 100808003, 145742338, 557679701, 3031836, 187787385, 910488591, 853391354, 232232721, 872552948, 766842368, 635754715, 697486084, 681004594, 368862127, 136390285, 431689651, 294562511, 890310315, 117062216, 526344253, 980002034, 40549376, 296280458, 703542081, 688184597, 1027745, 903003438, 155076229, 856138734, 350532299, 539415547, 929559103, 423976958, 528388870, 91169525, 25908062, 430236560, 944699641, 373387276, 609118278, 34901908, 774443143, 611797362, 556850082, 584136829, 388760105, 793563055, 382227192, 815555315, 796410187, 452174032, 323343346, 125729128, 296426631, 844383025, 96657907, 278823956, 55805219, 240365530, 564044496, 496999014, 783946249, 670040828, 620911318, 913944915, 765392845, 594479733, 10065982, 74689815, 87399729, 113636752, 722646202, 536542266, 960349701, 738810522, 754716081, 64650145, 796380789, 76956852, 576859601, 371493616, 815580568, 462312056, 575477757, 308082787, 684841439, 810910451, 383501775, 70898186, 671577539, 542847831, 301336437, 966389230, 793484872, 383654341, 189658057, 3483658, 824618195, 520828046, 461240445, 36632364, 334411948, 528548919, 738199859, 455515863, 55164712, 826134473, 8662399, 818558970, 143964413, 375721842, 536587865, 129969131, 552560920, 650752829, 345257621, 225119572, 80537844, 893958050, 900420030, 728645439, 16681465, 552793959, 592672704, 130355827, 778861698, 656047698, 270584295, 699429354, 7997461, 973668251, 420874269, 268062914, 493160314, 527729498, 248785190, 99866129, 895996731, 990889603, 347706795, 901691542, 383143706, 672520606, 82021874, 231694634, 264428121, 668274616, 500022099, 638619188, 22067187, 835521860, 349376494, 667337702, 183965239, 418290134, 417057935, 205340853, 744299569, 236188369, 305672874, 176346694, 520300645, 997993853, 453157096, 259395259, 125530573, 487031409, 324385946, 816512763, 704540741, 24912712, 923032541, 745397411, 350852946, 713326943, 606258845, 149932872, 264537320, 329312370, 975342143, 230146559, 585639918, 717506579, 636790240, 795978028, 400849577, 671505219, 352329482, 152217038, 650557122, 378375416, 117341409, 267046334, 354260900, 14146212, 786599795, 211038832, 490595322, 855306883, 352166213, 985279478, 489988532, 863141365, 177696058, 353095954, 460287141, 599199987, 573704017, 233306284, 847694475, 19126402, 611609558, 996664894, 483317566, 775034732, 434216462, 293233850, 970242779, 825824256, 817164971, 297112692, 631488457, 417338472, 232449903, 130881944, 573089066, 282539670, 311187089, 324021596, 519531952, 635494994, 50183096, 915959812, 741835540, 921014608, 421944044, 759914083, 453267964, 954757042, 369585003, 831272859, 664568101, 145229243, 504694511, 836390705, 583409999, 73888140, 648219356, 618920331, 44820803, 856037030, 736548123, 232136850, 991728968, 849351301, 446615681, 976037520, 929028464, 46526754, 345171667, 895589390, 9922045, 999708346, 308746157, 834730459, 260285403, 875729895, 877074889, 357629201, 153508195, 149325909, 324927517, 49047373, 804173737, 895820802, 131928443, 125226299, 110288576, 89011777, 86960382, 101685355, 494645297, 53790777, 985102221, 199464693, 923491647, 86718731, 11627963, 581722368, 632261557, 274081663, 970270095, 220680066, 371658244, 359165823, 524372236, 145147504, 968267996, 875479422, 780431917, 886987574, 18144310, 842947417, 984995303, 985653470, 470543195, 130353982, 195778977, 689066071, 297460495, 771727448, 781157887, 916552804, 445699519, 625756506, 358979002, 572124922, 472399772, 432073462, 457270012, 400243818, 394948306, 353263960, 857544779, 170690766, 277117944, 830712090, 568937839, 289017364, 984964558, 797591581, 446848659, 655823470, 188964279, 934882685, 584192623, 882317951, 953844665, 917601639, 728462037, 84528616, 408325630, 940391946, 611284706, 563863467, 870769934, 108838098, 11966125, 529941992, 446175445, 7695607, 676691626, 99384860, 758808979, 84694675, 19950171, 973645172, 931364105, 767077064, 368318738, 428908597, 507726227, 811944415, 300920595, 831339130, 766190942, 688562521, 371054465, 829534188, 192271346, 752671152, 812436411, 53697226, 144275962, 55081136, 968356367, 333845116, 850120874, 599630958, 299355449, 218689643, 375141097, 402620827, 322805138, 829987168, 653754394, 548315836, 618272707, 536946517, 902152573, 9427618, 535819541, 436119677, 531086987, 5141024, 231400505, 649391071, 520739784, 57372527, 951929624, 851458139, 577186997, 979708023, 872361964, 64434434, 351838948, 267090463, 365810608, 896769895, 380648793, 825865574, 844074162, 406536043, 760219042, 467154113, 204834944, 190945533, 925481669, 771501256, 901167715, 758342015, 311526952, 528178594, 94155758, 335883792, 474435919, 736575996, 666220320, 675910479, 254919697, 362150037, 821299042, 538600188, 261442198, 487169742, 292726538, 972066820, 12202514, 197071554, 633829648, 289034966, 274195893, 983247636, 128665221, 134373853, 445264749, 527989556, 440791861, 571763961, 967107514, 415443654, 60327259, 419241826, 645269012, 866880703, 547998979, 435768089, 557337225, 961774118, 141504341, 349866703, 936565486, 810798910, 563711752, 824617366, 779872488, 359778051, 916725083, 230002018, 680951855, 277833225, 921340759, 387698919, 628047365, 874250804, 741905328, 718799087, 6060132, 204532489, 827081120, 774003356, 978085920, 761710268, 476023442, 955571075, 713542688, 656581900, 395350047, 853464461, 375923505, 143916530, 525746467, 359519676, 139947779, 317505928, 715123940, 408932698, 10837757, 159659408, 920993769, 236773611, 472534362, 484830450, 923009055, 97975857, 525688852, 701636761, 181402884, 136327728, 386205305, 907345687, 884456004, 842461028, 392818986, 33016111, 110670340, 146178983, 333462474, 31104121, 109210700, 553521365, 43595379, 59481065, 334995613, 262170602, 526937256, 462094154, 936285954, 731374144, 654025112, 77212012, 778214635, 123577655, 735183064, 527934011, 658523737, 239880946, 208104801, 526268963, 561201712, 919021230, 697582256, 646742893, 673807057, 404357444, 119682119, 128894318, 609179959, 540696361, 571331969, 575514531, 906956684, 895245590, 638208433, 253457487, 509156412, 559719704, 833253760, 920673479, 324719912, 882705921, 720515369, 179273980, 436030051, 779545825, 402363064, 511198255, 875661027, 770097226, 394196000, 810067250, 782930946, 751182569, 215905056, 192372257, 328201034, 616818832, 488998342, 237138703, 551679845, 497621898, 192007577, 654781727, 212179647, 151109891, 671155921, 190657880, 690946120, 19254082, 776500286, 226589716, 132111283, 312444106, 507695576, 980793888, 250964653, 435144973, 315970132, 282476760, 178750535, 467080850, 184329995, 105729191, 603941481, 421626969, 448119028, 179708447, 196499949, 599824625, 339354955, 911263178, 170790791, 268400948, 793334390, 587162647, 434772101, 272753390, 696930534, 376723232, 132435811, 894018476, 731321913, 996577868, 218510875, 992722762, 464323995, 169185207, 634211397, 383981433, 632990982, 488591354, 626757656, 660349170, 325427660, 479735299, 337976591, 231961588, 593089743, 485993298, 529615720, 963662609, 346047176, 422010177, 5941042, 998255356, 279920227, 818206936, 901787845, 173755200, 376356859, 485894120, 846282402, 413175220, 826893137, 638304579, 72822914, 809677879, 206372926, 343965051, 594752084, 817206842, 122253544, 133507133, 436542930, 265078803, 215526034, 936321987, 909355672, 450938898, 203573166, 380726936, 522939162, 56004851, 990862784, 886170441, 594384094, 332473353, 929017737, 138185330, 561521627, 463567272, 895393434, 734140713, 59460074, 323047240, 908178026, 522688900, 618814369, 272223107, 392267487, 155376034, 351931658, 262440996, 551501175, 157187437, 251373311, 288938448, 973096886, 291397428, 320585930, 372770173, 877431231, 890283008, 407711735, 374091394, 287322695, 815542372, 77896937, 762548292, 53803145, 771655329, 761789944, 681944354, 169265733, 838235481, 497599906, 304722661, 470226442, 605324206, 358818773, 177821812, 150830020, 155151784, 240706642, 14901562, 82863301, 700420986, 956088010, 321719547, 822046556, 633198975, 247687560, 126628731, 901014309, 747519389, 853428805, 836292487, 419933908, 838066401, 805976065, 748520788, 205578867, 165927670, 255545235, 788679219, 96972230, 889623437, 365222406, 111001272, 215675978, 480601889, 353109674, 530945353, 938634564, 11533978, 335485720, 776393370, 90525105, 874363040, 55432624, 70107374, 959788465, 364877016, 623845181, 839493981, 954074712, 804773125, 240634123, 189377752, 508702284, 349536848, 227810379, 264895498, 924105986, 656312407, 531391368, 957392689, 227749209, 237562270, 286877188, 926465865, 799670670, 601460606, 658787088, 179165427, 14235844, 407590217, 731545385, 892116689, 764529961, 177488891, 971188455, 640772347, 10258033, 215263048, 811682510, 979555352, 454970716, 799498630, 935448666, 696151320, 138053597, 127749603, 904370569, 161999216, 203153608, 977472217, 294160880, 236677382, 462240787, 774681928, 610666770, 737228109, 949746887, 673532838, 430842215, 847601289, 578909239, 658254157, 697854350, 475827810, 917593433, 563704706, 230750287, 500862236, 898857675, 50900017, 910418055, 416207988, 918549399, 812899250, 454750741, 791224013, 638937204, 835575161, 20259761, 630352108, 577283043, 490527714, 844066627, 283918368, 738722667, 577030330, 116677184, 906410708, 542001186, 597858005, 930162384, 3068810, 596474389, 260414685, 375384982, 858488153, 671949230, 702670725, 257673907, 466454109, 949352009, 28290194, 640057456, 560833227, 410744612, 656409326, 562002535, 312669577, 447477556, 642789535, 361055988, 588259495, 895021571, 858789413, 55088588, 287460718, 934350667, 800978541, 467938050, 547328250, 387394343, 61657901, 617042915, 221536228, 972737043, 196260401, 270450144, 488473376, 873449307, 162746303, 636051044, 824068912, 714540367, 235592104, 176662094, 56812358, 105670214, 45174657, 791511841, 662197923, 457410652, 940629374, 369774275, 711316344, 61731863, 346961085, 384708751, 214965337, 238054718, 55163977, 327014056, 510852184, 940672989, 529634287, 691917270, 144436985, 497060240, 269482230, 923491468, 444275464, 638586388, 626149829, 863172450, 715383549, 571906145, 328812508, 434994117, 12230513, 54340017, 616490420, 913034973, 245326661, 537342627, 620996213, 957284051, 424552733, 551845896, 622870638, 476587990, 259562440, 778265689, 322006753, 20093732, 985648579, 913690766, 889685997, 629029625, 888698152, 709137337, 104465318, 792636094, 635230633, 764580744, 189125745, 244334938, 912844778, 713243395, 613803698, 223876885, 758897729, 57168861, 472225995, 884820667, 6748908, 768335549, 271442752, 902718016, 983780535, 802791262, 878964283, 498935941, 22407729, 998749281, 917994440, 542604839, 95216942, 578540968, 811539640, 147878367, 635990283, 714447113, 931933364, 611232922, 732080208, 744330249, 379159273, 764453916, 517817824, 692735242, 512481074, 494873489, 963567204, 370464954, 929952825, 916343606, 366901160, 702653559, 10455136, 59771811, 891589843, 634296665, 697576456, 396025762, 749687669, 362881273, 60407379, 836394503, 515520803, 94705041, 180074929, 788002289, 63002105, 769573922, 536016384, 246086959, 870574369, 286968866, 478319294, 792919910, 176114133, 949887189, 813671752, 345878450, 276987979, 792069209, 409565740, 991043605, 708965931, 199802341, 744151302, 764848304, 711644559, 261510940, 749942346, 299377997, 594854482, 783660430, 793059588, 366420693, 589537729, 617433956, 441996077, 885258429, 752320066, 560825312, 319616604, 678656396, 478778420, 445662144, 979634048, 774387730, 846763775, 543561343, 296973942, 976802807, 988551572, 451016262, 206661163, 588153052, 786432829, 696434794, 73331570, 966080695, 993681154, 38925179, 766593492, 366447842, 723894538, 190369290, 329781584, 887819327, 159036329, 817858178, 945231891, 505763362, 304866824, 41843992, 233758108, 80016739, 195432547, 906288763, 722659948, 775968350, 739027259, 347152070, 354303442, 122116684, 791564447, 295545938, 461123312, 655231074, 738175650, 200704301, 768617332, 772620417, 757215097, 591822009, 246028852, 30030230, 667786155, 569489099, 649721828, 322172807, 844477581, 440574397, 368677249, 843291298, 650058034, 694077294, 713830460, 805526954, 458602171, 659042733, 693913566, 785719833, 733292947, 23914404, 749545784, 962171939, 360545674, 568581684, 752877689, 899910676, 641980163, 518831049, 171203219, 650545125, 586509656, 617125067, 748878853, 756632892, 216148192, 382728569, 773327213, 5962518, 339226024, 62058798, 403540929, 924762348, 336047105, 447220530, 134034129, 629289014, 674435927, 418711447, 696933914, 640780943, 366385033, 741892950, 958169459, 701328180, 158003122, 117760584, 488736438, 37895260, 496797939, 698919416, 319912815, 847926312, 443469467, 370213944, 867793068, 750788239, 914416701, 274332780, 816773578, 733529044, 826531407, 946255377, 381841144, 26904141, 933772359, 102523071, 22953158, 909220795, 604819470, 968804576, 741017076, 313479661, 407681839, 925125230, 785622469, 36431987, 963378185, 898948021, 525308770, 908630100, 483366675, 207067897, 820960907, 317034794, 776196126, 547233862, 863212033, 35068583, 330460706, 277391884, 706861216, 7116349, 44925800, 990284402, 1734839, 787272384, 547451450, 784571590, 661488999, 38234430, 573754356, 298463966, 576183606, 144146169, 894703451, 762609397, 809789742, 664175833, 231098046, 515634360, 236881125, 602696331, 424200686, 181013270, 262632898, 917183959, 457939727, 899860428, 358715536, 790914959, 745126544, 687110221, 591141716, 169087129, 220112537, 132667196, 67307675, 224660623, 989709306, 815563863, 616648537, 367642620, 647693034, 332885157, 546273654, 449450033, 973679709, 842175715, 481373170, 920874065, 729535291, 314515760, 535240676, 329530327, 835587317, 915207390, 971297354, 835725860, 39720755, 112494793, 108117127, 14127780, 250658569, 792074115, 560445008, 698787283, 376563809, 313109621, 237679725, 647497002, 60201124, 306355037, 896688071, 396588833, 625107635, 599946929, 107209168, 650137160, 363711013, 828049946, 697710929, 745696243, 289010777, 756361405, 380039830, 925008651, 158840903, 416244312, 391179536, 719374276, 922613005, 824297878, 903366917, 872626275, 499159437, 594570751, 592155195, 298199767, 424470547, 983262850, 492538961, 277436209, 536207358, 787049856, 822694992, 656466198, 53281088, 489849504, 883799570, 554733207, 376858373, 681416782, 810492280, 936328995, 818606417, 155031658, 361214270, 335492759, 188389194, 66316185, 29303506, 451182158, 662942661, 980237904, 343382239, 844225608, 939275394, 565854431, 938430279, 442446790, 538326160, 923472419, 89203773, 647631048, 219198595, 570852031, 968860875, 355913905, 716161935, 83071939, 661417013, 754516033, 444908162, 215440268, 29155649, 34861762, 602737133, 910752928, 380795277, 646155811, 64686712, 648428704, 806232893, 578089383, 415030819, 357221222, 259922983, 997986620, 372364068, 170959349, 582893898, 899563107, 576034864, 356600098, 451033467, 136104545, 618517298, 352027055, 949739986, 198811920, 145073772, 745177127, 804731155, 280448017, 823579429, 550461699, 324689935, 995395928, 564206776, 524043163, 887683851, 440725135, 169484956, 810902038, 33141268, 643917037, 457774675, 601394463, 493118035, 100867434, 857917320, 840996815, 360957527, 897723622, 603755815, 302795436, 601548596, 226399722, 911508357, 65141238, 746993895, 835538249, 941932525, 933897010, 427918813, 213960920, 167983238, 154488951, 277161146, 628330767, 439337863, 436998418, 62466499, 646349989, 355634607, 273725579, 335082877, 213728931, 405075718, 727576748, 342440976, 774415422, 478714697, 125792180, 284393959, 834056793, 645985450, 463215393, 313026848, 989569077, 84045596, 296783794, 438781556, 873548637, 928120632, 69884229, 185636158, 51349959, 579037409, 167100416, 979904421, 493319626, 53719174, 725764374, 455996602, 131526235, 192076103, 190844462, 222258184, 936946894, 575529791, 823211773, 616648084, 752602961, 739029283, 51595366, 210010248, 129540100, 800582717, 969459207, 880020024, 76733560, 115013855, 964190254, 236264308, 457894547, 340439486, 435574295, 831721285, 215897970, 40300747, 934284011, 773352207, 313843421, 967314086, 474139992, 412591936, 339583851, 966798793, 193555291, 47576208, 806507315, 21347474, 192678711, 45979727, 708269315, 468072096, 707928509, 769624785, 317961352, 897313377, 674744462, 200681598, 348138817, 691012202, 488434752, 902950869, 178233463, 939509685, 97532440, 283352776, 249026767, 375826828, 505321768, 197077641, 3405445, 474334284, 873391239, 160890042, 675012167, 431293826, 507143402, 968816744, 236711956, 837896766, 311784695, 970797577, 361864196, 237755107, 949465501, 422176348, 145718248, 100315510, 855943342, 242987038, 478739064, 623352799, 760516234, 414956613, 719592722, 281863145, 628089052, 488184800, 959235941, 504138393, 308158547, 8371917, 32627652, 256863895, 897441071, 355541552, 407875421, 24184283, 516390665, 952761761, 543021436, 446131684, 58545054, 436710887, 974482231, 349455543, 990582395, 480217259, 12156138, 696224706, 717618863, 143804240, 198013598, 115580655, 904137836, 283039027, 690563300, 758972084, 645543969, 591623439, 222587012, 269851412, 479734759, 917625789, 556867899, 904664567, 713886164, 863833868, 43102017, 720415107, 104699948, 411073360, 191485505, 797227010, 447391593, 707903637, 52330871, 869124412, 284976958, 346974744, 615904125, 939707889, 432900923, 942758554, 8652164, 940665632, 787044968, 161561460, 807238109, 169451054, 17692206, 159147068, 960559645, 513491584, 34939719, 677230270, 337574595, 661739559, 171217361, 244879205, 252027345, 21973330, 857432172, 634179589, 769884231, 851191102, 113009220, 898593536, 954228072, 814344901, 246069895, 962274895, 270990358, 273501485, 339503463, 527789107, 166052688, 987306659, 216181473, 94342402, 417996095, 16497999, 868337154, 568424606, 227148197, 298102012, 863128523, 867547737, 260853230, 982131418, 438631456, 546489998, 321538914, 907533712, 441379382, 508727760, 146070503, 624927159, 497480571, 229539710, 667338267, 511833687, 321960306, 741676734, 790458937, 390330083, 149813130, 820382108, 668185062, 671764330, 745215957, 125224127, 888635182, 490721974, 561721617, 683144541, 615239342, 317838146, 132194457, 869220648, 921122008, 839660590, 740152631, 423281446, 815265165, 881583833, 868581699, 733838036, 668746119, 72690499, 997871932, 259180178, 745652179, 661524511, 9640554, 211723017, 111149287, 22869529, 633715775, 239936137, 666168216, 189980301, 752959494, 347341484, 461903997, 832294952, 448049507, 119921048, 422689914, 990767842, 999632446, 241907381, 577580149, 282465622, 667624188, 178430171, 253607819, 203601252, 513803749, 944211511, 568626626, 760282131, 396469282, 213656459, 206779780, 152103151, 850332829, 960273386, 698983159, 981798954, 738822501, 20353800, 783281806, 128642983, 900943406, 119588139, 684804245, 47821921, 32670649, 872232416, 22660921, 996065896, 483108164, 793901295, 852383506, 193519770, 231684774, 115806906, 305739025, 843717018, 729269911, 897749962, 609770279, 840361052, 120496098, 601936842, 4916380, 259201778, 664360271, 437872, 180617511, 950039794, 268249776, 352515362, 264173016, 239280727, 72673140, 60600943, 301694757, 562274243, 705514105, 876524517, 355633507, 702808072, 690457431, 990635412, 468819983, 326068019, 898700450, 609795908, 179860687, 22974936, 45556863, 848783204, 367037480, 128839083, 857547504, 232865496, 763286446, 626468125, 173819723, 887586224, 774179308, 258542402, 136162087, 407926197, 525687089, 789592269, 44855038, 400153451, 160123589, 24254679, 30488512, 528128234, 661809676, 536429773, 411095141, 99981146, 600770040, 280640431, 524881644, 620604040, 683986861, 74532098, 921309971, 404898472, 121393553, 187638388, 923504746, 110648018, 528373417, 433572526, 187405934, 901188683, 161049505, 364359165, 651948030, 451483222, 772687861, 438831744, 852437307, 395635000, 271405683, 318743648, 530361344, 477581957, 817692939, 276814311, 647743565, 167038011, 592120158, 376157292, 221082490, 795509031, 894696953, 854532663, 88017337, 333202724, 113322877, 90658435, 932672474, 883990526, 275596000, 819825326, 850014006, 809524098, 187630905, 587585099, 516662716, 985639234, 627050393, 637193670, 792070072, 25480330, 143792285, 542444778, 844387879, 384646318, 30148495, 419955563, 589257669, 973417119, 605603125, 272353277, 681836150, 313907337, 626056591, 825209374, 924723393, 853019680, 827506106, 695894756, 499959021, 544275964, 74943081, 720512717, 903483380, 145997797, 813987893, 450120779, 77330617, 524658672, 760808235, 755138920, 852205547, 726105009, 952355691, 693876605, 730711169, 460710322, 935221147, 827324521, 69585671, 694554697, 938819124, 769844794, 86833762, 536181876, 69448288, 678898834, 311399642, 230412665, 684989042, 791467009, 94972118, 665458724, 31247042, 560693290, 408763539, 160412143, 899218985, 895875228, 357213957, 33883541, 971362243, 541860566, 869852236, 43482126, 615480443, 129605068, 736577438, 30257078, 613813186, 768070156, 465401629, 71546248, 856962854, 554349991, 450784225, 345776202, 228730514, 968928855, 978547736, 892817832, 612624480, 488339228, 766810318, 861527052, 120527878, 850941187, 884599226, 747672508, 467678580, 156139828, 313253327, 85342106, 757559605, 649452221, 329406806, 801760563, 216682990, 991320922, 6281099, 727032612, 952934150, 434104737, 103242279, 748509702, 521820581, 501688467, 520700825, 29029426, 627223756, 791118476, 653537425, 767288454, 409420356, 849179757, 327387295, 826393915, 223229611, 593433483, 198901310, 272224885, 217181552, 696522204, 766129321, 659407771, 387710203, 195260830, 74991758, 367913199, 336150636, 540403592, 682155902, 374217874, 486246966, 826772621, 994432720, 910397445, 730691262, 510954302, 951234635, 527771919, 250389301, 189690068, 607503065, 413299307, 294779795, 946901258, 361490056, 844892094, 788907396, 105549397, 815472454, 486262159, 702976048, 607009721, 842548856, 648231017, 143038321, 481132795, 14224298, 332081171, 13162114, 173168404, 220885706, 792825805, 402594401, 234816345, 198123813, 652736719, 20244263, 233797938, 322948563, 802888999, 155275860, 187934341, 338845685, 220242422, 645525746, 245297577, 429757419, 534887541, 141970437, 738482378, 175794090, 859323688, 718798543, 34588019, 716713098, 698725857, 53865638, 416598266, 963657467, 262969928, 199415919, 326427252, 546618268, 411563819, 322988772, 7374986, 532819312, 865279689, 220467576, 513401616, 718608655, 562799573, 638675805, 185565974, 372464995, 306540260, 905739017, 132056275, 738225508, 409808802, 30713696, 225496576, 295915994, 627574693, 325217563, 174859626, 73184086, 325533991, 523327517, 875794772, 175383507, 770994072, 434284225, 752115571, 915338561, 821623779, 712929654, 344342622, 97792574, 278863930, 58975217, 78721977, 380058728, 894568157, 854094824, 916381974, 218738219, 466732445, 701731510, 885358251, 559618032, 156631115, 852419192, 853045333, 4472945, 313422868, 615240284, 493761984, 310768477, 845750876, 532714799, 124402519, 819203684, 807253548, 941911047, 686518214, 36101981, 607205867, 808676446, 745961804, 99933187, 427218857, 92279124, 252676990, 282901652, 555602343, 258866887, 236109693, 686813890, 370205748, 899256245, 206195035, 147234678, 829652481, 151826164, 283139327, 926069050, 568501350, 622435954, 833698369, 631886999, 300585659, 704285813, 680841763, 575202068, 183353366, 566870616, 165720712, 710800351, 433257799, 846074855, 282677028, 154094300, 941990514, 612999074, 575966452, 525488306, 40523623, 345969700, 950177736, 439694914, 174894666, 233040122, 607467896, 845203141, 132443822, 179188796, 512383277, 918902206, 669750635, 864125370, 441576635, 849339708, 879524370, 816522108, 429905658, 290515572, 525032899, 607354036, 248890647, 591708342, 443786844, 236454427, 72814655, 766402564, 761598427, 455698867, 494637190, 273466232, 650462700, 774602712, 914596966, 554717772, 833396485, 166466060, 278325701, 816025065, 747262838, 186331659, 871385691, 746946658, 282413883, 330548991, 862775962, 477695443, 613242027, 247134737, 689648168, 941070735, 436882030, 921385781, 165749406, 575017751, 388487671, 125973459, 909257453, 120318782, 731074499, 751850834, 571921440, 480588137, 901480337, 176404483, 524011942, 737165875, 675188618, 915826754, 363758806, 373601309, 241361855, 881279692, 855133932, 621893165, 957932427, 138792251, 354776775, 605614225, 820927437, 634341526, 934942870, 842932102, 334286967, 219202812, 407135040, 352277742, 148516948, 413820763, 117778045, 843236671, 880375103, 433605107, 173863603, 897022375, 36271762, 367874490, 169135275, 804851907, 578253476, 202136032, 22304807, 177950156, 741418431, 799233093, 35937071, 854868354, 212350646, 57692891, 845227246, 717194037, 86706194, 949285631, 126504205, 629838623, 624260119, 14186658, 421812094, 344707219, 260701741, 84150456, 2717715, 264098781, 495494752, 299017492, 89118651, 696757714, 702379928, 199299040, 935979784, 597431021, 81040381, 384164339, 979653602, 199359525, 744215440, 186520173, 398125773, 868383113, 248636834, 746101957, 206387837, 247718630, 579184577, 602375421, 235933017, 664851397, 25348662, 291416063, 769186123, 513339048, 605877696, 69812180, 50447749, 837275454, 745988944, 664978541, 342545172, 595704012, 157831287, 151749631, 452477397, 355296658, 180459322, 754776535, 841601745, 796071510, 686130599, 286040328, 496219447, 344203145, 753041082, 983880366, 954747424, 634373166, 590936400, 239338401, 341515141, 383089805, 756615379, 95099037, 861573234, 532845804, 593126304, 885715532, 569960922, 397294193, 935191835, 946067625, 935033996, 89783331, 928162607, 428478088, 800032143, 844605413, 544127902, 781062048, 542335339, 107943552, 256877508, 686948454, 633249758, 484164254, 89153913, 277942908, 507133572, 716159422, 201157197, 171906529, 769762205, 666110787, 467795687, 862754349, 874911066, 950142906, 833166557, 857901174, 919842914, 862468644, 887306888, 624832656, 408752796, 686651415, 617550370, 119664180, 19736714, 753944591, 599743052, 555769219, 940081443, 153604677, 407312545, 139310424, 589743365, 177723322, 235403842, 7182900, 377136934, 431032867, 38961680, 900481911, 917748787, 998292208, 382212835, 958748627, 521419036, 52178837, 244622841, 319573168, 478088771, 621001265, 407760601, 543736324, 153744016, 34701015, 246340362, 246758761, 965905694, 932564124, 572780851, 462150438, 371984873, 802668705, 449124806, 460820319, 383233556, 416292004, 936121309, 435738999, 641696659, 575212592, 165351226, 826939086, 992114073, 602813016, 681278593, 310121588, 714120220, 275567182, 464111395, 647559727, 314573129, 120296512, 163392106, 827928815, 958779767, 461364631, 851470025, 692109892, 577465088, 722918937, 845249554, 92279949, 356311577, 983103060, 120983922, 116317705, 12806449, 890194943, 884421969, 699881086, 386341867, 757054852, 246117576, 344802331, 208460116, 86316015, 59112106, 598215573, 46559873, 222236114, 705132913, 236031470, 350199672, 689196268, 396080785, 394420037, 914757386, 865169328, 367244624, 570661855, 527947790, 432362569, 984354056, 444742143, 988825258, 631931761, 149904432, 986965835, 175030240, 312252897, 116249241, 360098638, 25073709, 228197180, 12366815, 649999810, 521660858, 275934848, 513527209, 391196475, 376783994, 818868204, 216918552, 921181615, 418273777, 287613761, 311580728, 146990891, 596613466, 531621426, 514094283, 433299505, 689923795, 977568521, 108281625, 487160668, 478740586, 966032852, 970031246, 669779508, 36679575, 607693081, 686707021, 248260439, 521467396, 227117659, 374608518, 323920137, 574872967, 184246529, 271683505, 976319123, 218010693, 905455691, 357648455, 213647979, 882324344, 12733529, 431231678, 685530389, 494701835, 849517910, 317552985, 495425465, 340556046, 268905556, 362060579, 914159950, 954280095, 241953692, 742396251, 769008296, 244430723, 608938189, 337203166, 394263101, 151237291, 644583783, 281730742, 753053360, 267372106, 243121260, 222284020, 35302026, 911133168, 285783858, 882440252, 87582115, 556322346, 702641402, 623368190, 979337979, 965274570, 356353446, 427405348, 411384529, 502741217, 268203367, 380414885, 223521601, 378983118, 627636558, 624111022, 898902657, 234652091, 420317686, 439175565, 511875190, 79984530, 395982530, 111271157, 596494739, 706222910, 103291753, 481334215, 977313091, 853999849, 81606222, 432998383, 716907305, 137075327, 634011436, 351408096, 587161218, 538741587, 843018396, 64059428, 665670127, 684898090, 346157328, 609753649, 585523780, 456127455, 532971100, 41218749, 698250860, 356186915, 972458725, 563239908, 166596531, 222582548, 934131555, 586925078, 206678380, 890412611, 418757939, 123514343, 570868743, 829244119, 980064376, 224996881, 235664157, 916200780, 298937144, 945758062, 678284364, 51985440, 767149419, 223154399, 950061593, 437071600, 850788496, 476167090, 350010040, 351946587, 933384661, 50008732, 62405726, 117979192, 30049765, 217048062, 541008535, 563057765, 856348864, 304821855, 590401123, 299064786, 442432842, 510570090, 660821956, 4964557, 861033052, 541326123, 845386675, 232741772, 820163323, 631529520, 810058303, 421073534, 331106005, 312929973, 172229458, 294138938, 28171341, 130696248, 935440617, 793102260, 722902359, 806734344, 993652033, 517250005, 36672434, 833848814, 692505775, 773178197, 948802465, 387731614, 703062138, 224690648, 292871820, 610613008, 797629148, 730960335, 930023668, 858529568, 775736766, 708094534, 646958219, 775248726, 156777207, 107405023, 219416292, 868220260, 806993929, 149872840, 653693496, 777200365, 815566611, 197528182, 566236082, 939227235, 66955824, 987309226, 2091569, 105001442, 436533362, 56367467, 994800488, 561656351, 132006796, 284859349, 950884219, 217691010, 311431704, 561216675, 171436028, 612521042, 926914541, 702578780, 502247346, 892243583, 219288843, 341955396, 117669210, 101132717, 805439236, 306412372, 147309262, 302514912, 270343565, 967900348, 443361747, 41979896, 748397635, 116303998, 190018286, 865684982, 297993819, 996267007, 932550619, 286160066, 781676992, 365084957, 361411620, 479855663, 611464198, 193581443, 808767381, 75282101, 473368345, 95876631, 33828432, 336189331, 948194378, 646826075, 98721595, 147244066, 954126939, 129002378, 173069897, 715928578, 164957963, 523400660, 6015517, 587082552, 580982093, 31330620, 976661749, 409351992, 679088189, 565697598, 18888346, 968157302, 348648235, 533913024, 23762342, 138587218, 277110461, 639305374, 715038810, 505836156, 116924839, 409151937, 688893658, 323759422, 829592002, 599542341, 23013119, 822405893, 814138629, 148647764, 113791825, 868261475, 613113095, 255805643, 26469933, 785449305, 646970500, 651947977, 742686877, 837272312, 815910591, 277433234, 163947519, 777804401, 212777420, 118693197, 440581537, 77869834, 981067754, 362544164, 292500334, 74980662, 527002721, 859824749, 24334750, 582614925, 468308583, 456019310, 619491774, 5064649, 162805608, 226984084, 864509038, 643260220, 275597745, 996587791, 528332391, 233081109, 593143012, 312227587, 74642120, 400921331, 214734911, 20674390, 1717047, 809245312, 454464360, 490585615, 270882186, 121544412, 870943774, 432562777, 682265443, 305581124, 736372763, 877520151, 580085326, 359465190, 369961479, 701187328, 792267790, 394668511, 838698386, 541300941, 241737988, 161927693, 729929916, 795074507, 915712558, 964199864, 220537734, 646313732, 778465166, 625740645, 100974815, 733973768, 570425362, 748747250, 417121181, 767075700, 955012320, 992463626, 403498912, 986896518, 907446635, 903858339, 483180327, 475407905, 955068277, 480901271, 587500623, 915258069, 97729327, 88572781, 457025442, 732789615, 654478043, 65302740, 820282165, 442476894, 673975989, 106464854, 139838501, 140240680, 308855996, 411405252, 955883247, 755029497, 806505624, 547001383, 324529985, 413514569, 480923334, 496193440, 774391069, 772799790, 744112705, 82667574, 846119399, 692366682, 571126757, 630977263, 178224835, 274997746, 708318951, 623267636, 106044546, 186050700, 123553020, 207884516, 251912181, 246485012, 842750039, 89323672, 607939118, 884905823, 206464462, 963938513, 176616171, 490810870, 108693738, 676094558, 770625615, 995078169, 999794922, 345974597, 899005406, 974418235, 152880379, 178007185, 286010920, 721168599, 634083520, 473172153, 500803999, 755225792, 76436218, 962235276, 817682404, 375497486, 443157596, 536832860, 142782495, 83314244, 14586407, 771018356, 888613609, 710276957, 539981600, 687059081, 644644295, 901405402, 869714047, 970432802, 625195168, 584130877, 831095355, 970291313, 835450497, 826343357, 888670561, 565929183, 413297503, 994471111, 554491383, 836955395, 227858546, 781916028, 766262881, 139878195, 615027652, 467533766, 541794428, 699479186, 103268152, 614477050, 315067271, 140373883, 740407404, 6548450, 102432031, 409493280, 603261698, 961785326, 999658078, 800864442, 201992210, 267819472, 197560278, 306027910, 366654547, 995030813, 570739262, 467320968, 131424441, 685996041, 773390443, 947717790, 784451293, 848349808, 24267247, 893415066, 315710573, 510761228, 630511750, 232603050, 174629274, 280868970, 842541077, 138825793, 914715819, 105981293, 670433584, 242043375, 605732760, 220487849, 66241582, 45105139, 924132190, 6509145, 4922976, 33141619, 115927273, 640970852, 259722634, 636414838, 770124493, 575541753, 910590485, 114087077, 899684715, 750678761, 345336683, 712735610, 195793842, 846347189, 567517491, 414541528, 827344953, 515126198, 883784250, 210838402, 845690294, 581122058, 85954714, 23038872, 636880830, 178213255, 933438522, 159478328, 679304190, 671279797, 469868964, 662469075, 386743594, 289555206, 456153265, 825415900, 319793544, 446299444, 913175780, 384164560, 262710451, 725912447, 9886378, 820427377, 74896905, 257892113, 927620563, 946158514, 340323418, 322718475, 773844338, 307672526, 294031356, 119028605, 555496892, 486128257, 753240559, 462401817, 883353970, 271483705, 42861915, 507721629, 761357357, 457501488, 31365029, 340848977, 864826721, 815224486, 80010223, 31543667, 517667007, 873817147, 981745555, 666664852, 950784229, 813018102, 274998454, 988849548, 598600362, 99685913, 599459852, 45317599, 470058262, 741331190, 364564303, 239426108, 377163928, 707455204, 557771211, 715232970, 97245548, 914781902, 958863260, 812298071, 828252941, 122886904, 600570520, 636230700, 131898408, 401768102, 105172822, 250002422, 878431799, 662144459, 638096517, 186514201, 229806570, 893668594, 846524613, 895032708, 873194474, 541499277, 666834099, 892025406, 140394206, 423500683, 821930679, 529466460, 163190960, 825889159, 687285275, 811440083, 224635170, 410605019, 99238643, 638059331, 810323209, 440802645, 749496239, 686932608, 457377557, 641396788, 868219913, 530578182, 284536524, 702833567, 362618990, 808155091, 149745926, 537849013, 280941609, 806391315, 526958782, 146808553, 490930675, 749963514, 960643770, 472554826, 597286755, 700828532, 250169194, 38086407, 494160198, 541242382, 109424292, 727109049, 983105306, 105764869, 209721351, 906116029, 661439790, 504675360, 249710812, 605526061, 933841925, 602548068, 332090163, 986660516, 5088325, 849365861, 938610250, 64393556, 769791556, 710652792, 10578803, 279245960, 71393075, 236278130, 284138533, 52587481, 448529671, 671034983, 98338689, 181534741, 758821664, 646628783, 343025352, 572202175, 49246484, 769388680, 220507972, 614722882, 502596496, 809483147, 671147993, 618543324, 781685744, 293240842, 832354961, 298715423, 650984087, 47265215, 194502504, 695580748, 137862837, 761280558, 622936436, 380490722, 541045940, 914915909, 28422945, 158955702, 473012971, 389714176, 408043003, 791704791, 761304572, 918927801, 434042042, 340563850, 471923504, 384955718, 706181154, 211492771, 673375629, 38593328, 312485329, 203231423, 527171304, 725546652, 88521705, 91308756, 879734253, 664242009, 998705526, 463573536, 975520840, 364290146, 945926720, 458303508, 426130317, 51891742, 825701999, 802224851, 902454171, 263041305, 605996077, 838431432, 369438015, 157082761, 247363198, 706595497, 790899742, 130076678, 37572325, 984331931, 829637640, 475528160, 344541573, 125856359, 68441109, 282300608, 327820449, 847853613, 210585933, 569476344, 572754876, 832561089, 414634765, 441532801, 522782829, 524318319, 938317852, 822210071, 400438644, 689881704, 431079039, 688129858, 446037625, 137549685, 689108339, 133232504, 334402545, 926366559, 593018956, 910745454, 758874845, 89489782, 392378320, 845765894, 558381600, 358065198, 289743633, 206950975, 895581372, 712606287, 387515511, 289370672, 116737904, 816706094, 544441521, 58077167, 743524189, 809245754, 703575867, 370853375, 614180473, 495653696, 643549654, 605497169, 342093438, 459630328, 563609796, 981969960, 99732662, 950784356, 534620786, 778339626, 494303695, 266696634, 653640989, 377287325, 168023406, 782962798, 862868314, 325101249, 518204737, 117682779, 339737301, 412163107, 768620482, 307154426, 729412713, 474620106, 700561563, 86331798, 256945389, 991908617, 103111246, 771808556, 600271815, 60651990, 92390910, 721659166, 573807754, 896951129, 478365222, 735904476, 808789243, 86602953, 715515109, 490821357, 598244088, 614327838, 770313436, 439510688, 26867320, 385907648, 381852675, 188657094, 160472293, 637828165, 733970932, 811577064, 542984602, 238739998, 934852298, 314684020, 491726419, 160045412, 207035987, 593736087, 680898383, 32680287, 355869012, 307276531, 749259716, 783418467, 944375241, 327401372, 652709115, 882536696, 764095916, 670162198, 200379361, 129370702, 208640870, 632422481, 339059579, 935943424, 799059525, 490227881, 319664898, 423765576, 873773445, 493582900, 189433759, 638768848, 217732291, 4624015, 886491985, 646737680, 231968180, 727172809, 558887841, 547586858, 886313997, 806327891, 72433899, 10069160, 582697889, 882137781, 40663238, 84084187, 652733701, 404647208, 909568880, 999991734, 221764910, 785827085, 912498653, 151511199, 216427262, 66427795, 694589677, 111904324, 341316008, 67771941, 298234751, 599002964, 318177836, 393992072, 321068173, 679946809, 846910760, 646207854, 265967019, 320161206, 35464922, 857671815, 668768091, 377975736, 562778792, 208528852, 628945298, 945423081, 378891618, 802634035, 343712030, 514965605, 373510085, 723074842, 901114883, 983797142, 382921329, 25949337, 841498118, 746515717, 974885379, 431064605, 321887624, 871496249, 378510193, 811527147, 387000842, 101556979, 23026339, 882642703, 340777674, 743930550, 870263262, 440370633, 513837974, 648673097, 246722587, 615672071, 432461513, 651193919, 562790620, 136069159, 409528036, 587578181, 432520556, 328328748, 32291084, 546310012, 478143573, 103085872, 979880333, 216961800, 961100986, 873771314, 247821383, 354209043, 709221399, 280562658, 312824503, 525533549, 776022534, 236198198, 788891701, 953806248, 893330663, 382918699, 726263274, 311535508, 404160320, 262239818, 959761964, 711018014, 50391255, 751526247, 954913283, 400238457, 798049512, 329471888, 427301077, 889856559, 410730388, 671356749, 899383039, 147352189, 351813831, 556248580, 728068987, 381320104, 320688725, 506546379, 576355257, 505526438, 114326341, 953200154, 290696304, 238081480, 363159598, 153710768, 305296233, 925050772, 308684606, 206970381, 368632538, 881996646, 330206703, 582390783, 635759191, 227253780, 299795311, 165146296, 363366404, 814630473, 480741791, 721925033, 79863854, 153079781, 486513821, 703199835, 873189558, 217595200, 439499793, 519314140, 736520455, 231843782, 982372981, 757134060, 125072848, 341997911, 980946424, 74284260, 263984642, 621919768, 495459547, 930604849, 265985081, 540240295, 103364074, 516275848, 657398777, 211882512, 659769469, 633550247, 908804775, 260619738, 137851597, 892864460, 323179327, 374441018, 62835208, 768304336, 874293902, 44426854, 761822870, 458143378, 434093962, 467056352, 89645964, 792746326, 480127564, 525663814, 643596443, 931954609, 713243725, 849417161, 637255178, 349558901, 266540085, 944851953, 761084280, 885844543, 845608781, 8462391, 587569983, 670962886, 927158234, 541949318, 948097763, 403905670, 409953969, 183599367, 836206810, 131371949, 790455416, 934858454, 102381027, 373088918, 463635375, 888535495, 515437504, 568848097, 185927750, 701222473, 630745923, 789182183, 729145077, 793659368, 322997005, 784844137, 316691183, 171113934, 750621944, 675436433, 802298666, 416122226, 35654156, 211306035, 743425143, 245750922, 393343873, 602883048, 598359235, 346518522, 714517408, 231228466, 651599928, 729576055, 395259076, 492166071, 431436421, 102346592, 450984122, 264474807, 641900279, 921951628, 878574806, 249891198, 874862391, 469092213, 709464906, 434035167, 974450948, 9557851, 61816594, 333736661, 374690289, 450551269, 57959122, 473908083, 560178668, 922237321, 68194007, 78812739, 638448520, 476793658, 229699111, 52226256, 913243619, 935479815, 808243412, 182147673, 16726979, 475515729, 484445989, 224078834, 132105833, 170022389, 189460450, 519398382, 60758893, 465941498, 186389922, 507590300, 676831948, 89744684, 334878972, 620984443, 394139961, 789228136, 341068746, 189814933, 621374692, 984459553, 800902188, 746450381, 607483455, 836048694, 215270265, 769206563, 798303283, 58183350, 757754967, 730810667, 650601597, 880558174, 238008606, 885591277, 558099299, 385790389, 429110123, 619863037, 240625372, 454379221, 584373557, 492330565, 996630065, 794413620, 20037928, 399821508, 79170535, 152872836, 340874005, 693290951, 612878825, 280600542, 337723433, 40451232, 831451284, 82350276, 338646028, 714156629, 832289290, 151243030, 811702, 700034395, 980010365, 594438522, 181134977, 898123088, 242488226, 78339006, 264151129, 901373916, 514949128, 806944784, 594550288, 302457217, 6933693, 129250090, 956015417, 802993532, 468442940, 951691549, 799664153, 916305998, 893012967, 851813136, 662383348, 265661093, 387244355, 864786046, 864988868, 361560232, 333305284, 35345849, 447507463, 750308864, 84983100, 433466714, 334537465, 8988431, 861975319, 993030011, 92689578, 345629756, 836351922, 154653958, 628858977, 454183963, 789463954, 832018827, 852044580, 836601726, 425062043, 870340001, 351673616, 733510030, 450689370, 664603640, 362468116, 156445735, 674596494, 118017187, 640375952, 319225918, 689606034, 785521551, 325579041, 222774664, 89117734, 160785478, 533683126, 343421335, 765696332, 131438412, 21711604, 327474349, 915147432, 950846119, 337298242, 552555489, 490111683, 335952250, 871184966, 701070713, 755976242, 399648771, 321068727, 581877524, 35076580, 864804052, 366131312, 894224773, 763688814, 490501026, 325400256, 16443047, 975940201, 983805592, 164983621, 589900921, 474848999, 455322597, 730275005, 196991211, 93889698, 427178898, 514146962, 455948145, 714602089, 274667048, 517135663, 389187661, 442486611, 635546737, 716528756, 319942059, 901071381, 443379099, 288250246, 982194568, 250711079, 353526999, 109325652, 924661291, 520741942, 920324770, 965088811, 381821991, 476413151, 503990461, 563128778, 819386104, 593442171, 95014949, 370209850, 340898373, 460456228, 615230967, 204455824, 57922365, 383225023, 357787256, 55041494, 181251427, 993854680, 496179880, 734422709, 910148492, 106406704, 679032587, 205969630, 1473085, 213182477, 127123119, 945532222, 871435658, 202698572, 494859873, 777557915, 907747072, 162692375, 876536606, 615338581, 162643046, 163188892, 575957366, 241990447, 682599259, 59149989, 288129148, 331715868, 299176420, 228077100, 327821512, 415030130, 9109064, 727971255, 907451897, 977742441, 608991142, 589282381, 922122671, 264632660, 366262125, 870783701, 143628086, 466908875, 744930578, 393275900, 541758370, 686934962, 285975965, 123915191, 624388965, 440234127, 86223196, 835644185, 600016250, 204049532, 553643518, 7790886, 837618184, 837192102, 955016285, 474634939, 486487675, 896936472, 364419129, 166429610, 435157261, 106476745, 599052208, 643214569, 516096213, 885079687, 498074227, 806274815, 991964646, 987245081, 943485661, 844827833, 407049587, 368803501, 65120997, 896111051, 884171629, 203430059, 365058477, 824132663, 383420134, 993279910, 181841936, 786622851, 375651386, 710383766, 261191524, 125275645, 634760435, 396541716, 886763281, 156173482, 586401663, 382138048, 961491291, 182011887, 182060739, 432096757, 837774796, 81055543, 791229577, 184907735, 804750067, 963458749, 47994319, 656140759, 627299958, 243344913, 132594256, 264284863, 628166229, 423267347, 642403783, 615694146, 37971352, 791718304, 898866229, 608800699, 600232053, 494398240, 584242221, 519392954, 142625015, 260142606, 189427845, 686895283, 726450101, 147307668, 358202367, 804003455, 943053075, 844080898, 571165157, 872452957, 594707825, 369158948, 370504425, 968105866, 375460735, 184131532, 660026821, 320132134, 113942923, 146952466, 62316988, 410701966, 767367148, 585050232, 232819349, 481376207, 736686545, 452465019, 1594857, 752493095, 524731517, 248397858, 420218912, 790970232, 814373244, 568691525, 579452297, 550418862, 358082863, 840642052, 363864025, 472660475, 99598510, 557831020, 145334390, 609983554, 35316532, 797844676, 532803822, 646580426, 234900408, 85839940, 247931727, 219520002, 505862468, 949965984, 212399166, 610641789, 678310286, 174557548, 30205154, 912631779, 606988299, 42708209, 223760655, 293567395, 487867592, 203922433, 193005358, 178596632, 853861119, 370096905, 881689437, 27985052, 210114368, 722424563, 212716681, 803303147, 366753341, 93827864, 203347340, 232158874, 857889947, 511371339, 465294442, 678610637, 497702124, 214583922, 911078508, 625482359, 405187322, 713723784, 527514552, 698857263, 855990089, 666049934, 696543590, 799376011, 626119516, 159876381, 156072730, 426341106, 592636987, 837936318, 841501069, 512757904, 427097423, 646385216, 504905954, 882388125, 406554639, 6549926, 350162210, 618431281, 637347908, 705838577, 102472438, 141724060, 432216970, 732159160, 241994950, 59091009, 407749704, 586366053, 694220299, 780010409, 150150310, 339659611, 648728575, 991816096, 620033758, 299753640, 642236637, 89853455, 894736316, 966896574, 500140079, 798545437, 784316629, 459171531, 117636504, 810107677, 534487604, 301136322, 342363877, 463963274, 747043535, 568707998, 795887637, 561730452, 176017027, 724321930, 104575555, 44361019, 75564261, 691042961, 91613731, 458381012, 11047747, 69773607, 541783569, 112104450, 630490552, 281492866, 542048739, 744309783, 463931716, 226931452, 860166566, 33704112, 940433055, 546876688, 634981406, 138148050, 963738957, 668721793, 904125503, 715632749, 33973900, 108408964, 934237604, 871948336, 961199170, 548899580, 98407511, 870848156, 369324686, 470149639, 460797153, 744723267, 818246066, 419314951, 467972848, 551991705, 506257491, 592871740, 168693206, 498602104, 150714618, 263872903, 854697910, 992811863, 22121691, 599758693, 858166272, 948816246, 464554481, 341307748, 810763772, 330135761, 634667228, 881450323, 341569640, 346516408, 480491977, 571175093, 40999451, 82320595, 337826839, 402475003, 967449439, 838217512, 547475729, 766662025, 404798778, 228491050, 307912181, 291093875, 989601997, 382987653, 578954045, 177890679, 902263382, 468397471, 927920631, 472962753, 221303845, 289914143, 635290200, 291112065, 657831473, 938268744, 895622682, 397449355, 444530197, 451711155, 917415163, 586145278, 943013619, 347357813, 592202220, 547372376, 981031932, 554129171, 298163013, 75548863, 789934035, 264015884, 195176251, 760981046, 682513018, 638154964, 540353442, 926586424, 735801284, 495470516, 659863533, 544293670, 236384977, 172558051, 592257834, 153745099, 775009087, 217806336, 401200982, 834647561, 273022818, 497936631, 377617803, 477664292, 200274232, 578028211, 110047657, 921365630, 248060465, 485625801, 769978219, 935928475, 429880846, 99619147, 822510485, 960808888, 892616296, 378516413, 22806623, 504201113, 592272048, 535525551, 660994523, 66768340, 513210618, 596870759, 675326374, 506390044, 603697888, 128631891, 165719948, 773009208, 416238425, 797391405, 742433817, 146021504, 141645015, 442632883, 591467061, 686408276, 908353937, 794759910, 566880150, 176598852, 53509098, 752206419, 754926129, 35773446, 925126663, 241632301, 340551754, 96333231, 911338034, 302272424, 607383452, 804556631, 969683137, 481034119, 862558706, 736174245, 473022408, 851766599, 27730271, 531775089, 986776071, 506865631, 998230796, 200772179, 988108393, 861210273, 517825208, 379202496, 304054691, 763488990, 13297912, 167232794, 600750241, 317225040, 464021976, 997187776, 34789914, 647431773, 922256433, 823742194, 792839868, 385751937, 787308400, 55191033, 180633490, 889438819, 684134544, 394210397, 981592482, 11416387, 836575872, 744290171, 275323215, 544260185, 211177445, 624691353, 566865083, 594550828, 990505188, 958531627, 986135103, 183302762, 822676727, 479772269, 295249961, 573008031, 176317009, 73964140, 71560969, 487622264, 13974977, 258023868, 586587374, 351971683, 728793296, 568606739, 117859925, 186902706, 719265967, 574749648, 481413345, 158580295, 198420235, 540091171, 901661819, 153093862, 501351007, 351246179, 234953018, 913962910, 824969484, 740199420, 569554593, 861377489, 29085495, 69644599, 973214034, 345462304, 895805641, 295003440, 793350109, 573624736, 901223715, 363873081, 991154815, 492913492, 74138759, 891300893, 414232421, 873813730, 831404613, 41874274, 832509043, 296634459, 719503430, 766558247, 584307045, 138050480, 388000074, 903586988, 265622673, 465149462, 559823350, 998771006, 608259773, 245861409, 67683202, 726624681, 115463672, 27828916, 162777456, 956638820, 662024422, 880022110, 173515551, 299794751, 500968308, 122976199, 5984755, 182141407, 517812528, 464082195, 214345755, 833473359, 315228392, 886805446, 633406400, 701338116, 946935456, 278467058, 440820742, 534638906, 757376226, 940903395, 233185231, 420585888, 122247467, 466423017, 139483922, 134738791, 62466117, 682518284, 82572212, 140125132, 988660223, 125069369, 874351823, 173890975, 913727384, 953674904, 268086051, 850048855, 668210341, 181341143, 618617484, 828340387, 980454740, 947167104, 533575640, 606201896, 348932017, 820680242, 47013459, 831126264, 721962260, 378542126, 481328195, 795323453, 499181646, 859067676, 776519514, 624881100, 517104616, 265142817, 578841295, 706957782, 467233763, 614512075, 313134334, 216093761, 5059008, 204104029, 856110913, 481311654, 431686824, 637330184, 363211505, 780497764, 926947710, 891508882, 753959243, 288004955, 916609973, 609209132, 410728001, 889682248, 538683632, 95378204, 837732251, 753439757, 172199323, 73539544, 976822221, 912772349, 827709143, 228561940, 321163830, 700382117, 179629356, 802380242, 157655159, 136482184, 718874533, 806671533, 905900562, 339717994, 400140054, 710291052, 130665908, 510306894, 582245849, 872563333, 505035314, 559106029, 755303682, 36200439, 67869595, 416472564, 118303469, 662181529, 471509001, 64653851, 826676203, 825260021, 171809903, 610133622, 904443933, 185254754, 829920139, 435488261, 436861508, 149477454, 148627776, 226104369, 823542290, 164048053, 278609969, 283053480, 359633991, 716396555, 643628770, 426444930, 518681130, 910777684, 114109247, 857629106, 138524196, 384488753, 504296224, 204443765, 883426780, 181498807, 951089773, 871861342, 289450586, 450279027, 630685801, 849968837, 266515223, 96790234, 848948322, 404986180, 491087263, 463118944, 289978030, 295088777, 827051533, 575008555, 928865371, 847028869, 403812060, 901216218, 406909165, 525703608, 875900797, 854530619, 524404984, 871399420, 46459564, 730379582, 40980151, 101208218, 286718624, 638761333, 205359354, 970787378, 947803292, 222487976, 617265660, 476122369, 662498095, 380874073, 789663867, 604134982, 848519929, 393888403, 657297045, 444396223, 819845065, 857858182, 766166571, 343583032, 477445277, 625737509, 105337692, 48914282, 781823814, 621725392, 521440471, 954861703, 365039873, 194615952, 2052474, 3130336, 866216969, 34105122, 544476219, 91018503, 759274708, 753675807, 933910797, 766688615, 70905309, 47157904, 985876055, 214869461, 491508056, 526769371, 758879585, 396578462, 464665071, 758769341, 596116226, 438804878, 646503664, 970167676, 360954191, 844226975, 832939060, 828421952, 821051688, 730131563, 165578602, 913744245, 380897874, 775255951, 152749873, 417811936, 592034236, 710106698, 982276054, 754958391, 793041028, 40265288, 648465245, 729351484, 842750196, 203667496, 316560468, 207154958, 795526543, 100302813, 417159244, 575841088, 340962138, 75318612, 149557524, 532223403, 675459721, 333337843, 724895587, 47501697, 85836367, 294917341, 713606562, 221045417, 616004379, 950538947, 736688346, 993831065, 771816869, 132302179, 812509100, 423672716, 268261646, 447550677, 171096990, 17238268, 955666915, 624525773, 142810985, 68958305, 631192415, 670010969, 563595673, 721174124, 311796219, 612328942, 469466851, 156201517, 837355378, 107281925, 280748946, 732209823, 109434748, 729256729, 954053468, 646510406, 422010540, 815049772, 108276779, 508163910, 606973591, 634606769, 848207532, 829640735, 25922924, 668395669, 871850742, 538853395, 946670481, 31976777, 864725967, 231309575, 302319299, 612006145, 327357098, 262346963, 610465444, 813716458, 893630566, 108486846, 917130207, 802107597, 298126345, 167753165, 187395668, 369532762, 139472315, 186843682, 303465833, 209069354, 152654457, 531959281, 346790607, 150166255, 848992220, 884146482, 888885299, 104304865, 261786257, 776377519, 509602101, 808040746, 782535468, 654635420, 451948874, 127953552, 444950989, 778379282, 567429799, 538281016, 669083122, 503301231, 281053660, 849538819, 40759152, 601514138, 523863341, 198181387, 162490605, 604767779, 234583576, 457842429, 533956397, 157106526, 833153818, 607936068, 801415064, 62431424, 931143948, 814859806, 780043233, 858448928, 328526207, 754723733, 779977652, 23580008, 977038398, 750285211, 562714563, 234934664, 526004260, 641599632, 209009288, 608364233, 399417148, 72253006, 688883679, 160763134, 62393845, 736609556, 433112449, 668851313, 413511525, 917355683, 510898642, 412884387, 732314389, 394976635, 459433084, 83275404, 544674274, 777320052, 212980350, 120971239, 455982337, 606103265, 822005288, 632091111, 931550251, 568531252, 890530396, 416476095, 11548598, 45230662, 378220311, 119628133, 766602209, 27150365, 96559479, 879391755, 606579408, 836784294, 817960871, 211441281, 101727982, 73127355, 80476523, 817091416, 625784516, 566033612, 370634296, 284652231, 770497363, 7761295, 792104197, 635439549, 666875927, 911431373, 691298469, 545327568, 288934838, 349511085, 460725834, 670136182, 350027130, 634926857, 841092292, 560426148, 522997212, 943191733, 916185039, 889417351, 891193417, 767232458, 757969413, 194825567, 607540714, 352592382, 894179670, 248799343, 124765119, 944552686, 253404685, 713946632, 330809043, 957032512, 907911325, 21733118, 260329656, 558097167, 19966050, 187418053, 853351566, 181719469, 799485106, 52656556, 753448127, 763195487, 591826229, 679441821, 379794309, 68028530, 612264412, 400845548, 479402806, 300723689, 141752462, 952676832, 916939975, 900371764, 728095923, 633673503, 271822165, 390110161, 137984250, 663930043, 652894995, 638429662, 333908746, 3868692, 457360001, 617547344, 195912946, 903027050, 865896971, 934824262, 437706004, 989537600, 584213511, 107318246, 301914651, 160417246, 488993280, 944196935, 265324063, 882369388, 278822287, 58844907, 961704674, 658644176, 899567458, 595921961, 694313826, 146973430, 672439715, 569265871, 991436395, 150840903, 271520207, 178145651, 41565958, 681555026, 599093429, 43465770, 231694086, 330123499, 305209339, 915728358, 364414862, 696776574, 43228756, 121979769, 275670486, 527647971, 285238234, 427533658, 42110028, 938521145, 949912384, 440039175, 872041772, 279110898, 543178136, 251771478, 705471971, 703965107, 665401902, 333586435, 675382856, 910235522, 487759944, 786522662, 535281603, 710109016, 770499752, 520292123, 412312749, 736469748, 27007102, 138994829, 487742949, 276513858, 510517743, 271253521, 295235215, 47366166, 919430101, 432182650, 134694394, 929763420, 6660292, 827612185, 282252986, 408639877, 427370473, 410182710, 232741607, 462382277, 238339744, 193739106, 706051620, 436362394, 240348602, 682685255, 797965060, 63727529, 536121411, 468313704, 498431217, 676914327, 515171142, 795880893, 356297298, 155122623, 710829930, 811152648, 345362700, 879899206, 291430928, 312299502, 769964964, 823486234, 290056479, 411836626, 860962232, 358192746, 4705190, 970931519, 662386329, 128281560, 875167950, 171683378, 774011582, 314032456, 59184600, 574047311, 715903153, 246515552, 234854803, 366849093, 58201980, 70198622, 151927874, 212279751, 532345458, 16904294, 420403507, 116459530, 131424759, 83417322, 979596542, 706861640, 995654808, 457308567, 472842975, 429293048, 843856010, 406930432, 271306986, 476947008, 52016414, 308068350, 281324287, 718882398, 716784502, 167635880, 888134847, 708770419, 375558334, 140055066, 315613442, 436941691, 460084188, 981759090, 836682861, 622467841, 946071166, 795574240, 529707186, 250227913, 360434517, 450988743, 604973354, 514957988, 779444253, 697823540, 708523925, 925745183, 695678373, 612862473, 319816312, 382531564, 52081791, 203714515, 486384576, 229025383, 83384610, 252564805, 347130613, 944240316, 784112251, 513091594, 657184169, 234507575, 871813333, 461606654, 644703064, 85949410, 778712989, 55486482, 187542890, 169721757, 264797300, 796391159, 949740535, 515553215, 437680851, 559020067, 673466411, 888874804, 307562646, 773036429, 825961, 837654417, 311140473, 119534442, 53731277, 843166179, 371310634, 188047367, 637648371, 425009302, 806552048, 592068322, 764604594, 47305576, 886205002, 513241315, 964164056, 911400748, 903973495, 177718287, 340059559, 137770038, 685305756, 628350412, 405892683, 643743379, 832065789, 31583905, 334745495, 270016185, 986500111, 328373713, 764017310, 861330376, 207205379, 797069244, 921216749, 946668642, 580149293, 260695108, 754015947, 750150365, 543252530, 198165469, 368305579, 765443281, 139581147, 236926163, 153747176, 435561650, 166767943, 153444754, 311053991, 938494313, 33736877, 378724170, 111936915, 391368439, 366344893, 561186809, 543234338, 936230702, 622989122, 391500141, 670342298, 494920087, 977255380, 29072592, 967666292, 510457590, 382839583, 753359534, 229209135, 672153751, 604921009, 816626432, 941674791, 7914079, 950832140, 712106919, 31279010, 781174955, 226265953, 397960091, 701945927, 791136646, 625366074, 741821133, 152284250, 536463950, 389803819, 812487489, 92312999, 901707421, 856680802, 215656539, 130045840, 612572292, 751005934, 714371524, 215334057, 205235903, 241471002, 578441951, 41882332, 563849641, 840502731, 342283856, 25919611, 834523674, 830787727, 117950528, 659341706, 319954081, 481522004, 559454607, 511879386, 829357707, 24399770, 309346540, 313816725, 264489372, 725909751, 675409756, 379284700, 734963479, 567058011, 581433204, 713974397, 51851867, 752387517, 647801196, 870031783, 203290927, 448295487, 347741452, 94008111, 843827575, 586221914, 153591374, 783953576, 319365887, 812564933, 607580466, 197823193, 563564239, 398747377, 467012935, 297452161, 419303821, 433387452, 164941483, 919699252, 123097908, 653996073, 718285760, 97636441, 496529649, 311473499, 618936906, 899136404, 754433735, 716317643, 54977060, 151144135, 578254488, 143550916, 495925941, 262147351, 800700334, 998953166, 315550565, 911300957, 743864102, 21233998, 692355565, 40327130, 78544196, 511036881, 215162872, 526271639, 880471224, 239820376, 680628659, 247427326, 698375909, 986020035, 591643689, 668208471, 890558764, 750609808, 758726021, 72117490, 383225638, 805564978, 417709469, 976138923, 89003330, 14312876, 200660867, 684945398, 550062226, 929622203, 945140576, 384270949, 305563478, 910400821, 328505446, 842771516, 606169871, 223361040, 670190366, 156659834, 291481115, 438214388, 420066838, 364243327, 949277916, 589228926, 870020981, 594202351, 778635607, 869786779, 844048802, 722504589, 252304410, 269101127, 127269432, 868391499, 581980557, 72867042, 995701258, 93327298, 282281711, 497651364, 693110841, 390002819, 233896180, 248090065, 758532962, 133189820, 733218523, 465068585, 161278063, 149284729, 410188601, 578232119, 903296451, 135809465, 907344850, 924610036, 881235798, 876826991, 13121331, 659088958, 204662660, 578436246, 365548613, 271107601, 484255631, 533190509, 309599330, 192450768, 179105846, 365859656, 987101542, 482560398, 553010573, 447147978, 203369512, 922894201, 213146152, 710661195, 82019320, 300120583, 41407126, 711646376, 428715240, 490753918, 404981198, 710765410, 937948357, 27482372, 601039904, 79917589, 810835323, 832480659, 626822690, 285517308, 103026738, 743701095, 297327774, 701750766, 8344390, 380831617, 828453026, 541003035, 717502157, 128769655, 792577924, 955622397, 723508997, 751107343, 962659225, 473320402, 995365872, 100981630, 274771503, 697687133, 629570550, 61320656, 181742487, 743959944, 759757497, 119357020, 605759587, 521322546, 566254860, 613238893, 310289773, 71114940, 328077478, 747094657, 582297843, 824169743, 537909943, 859427259, 661327810, 382876479, 290206696, 980716678, 150794959, 759717594, 239204092, 37164844, 362169543, 103379705, 805330417, 516359252, 398477858, 893187058, 320198241, 73986009, 707291836, 506755546, 321435046, 332693336, 415072743, 151099409, 761958845, 23699271, 313471997, 332928291, 966636604, 965717374, 144034504, 963472398, 407417402, 16129991, 60321763, 760052878, 744270226, 80547170, 455027495, 532439913, 417025557, 743521190, 795450932, 587606704, 235465176, 575713169, 621315490, 50138100, 77735897, 913821780, 915196975, 967031099, 127697499, 208283439, 20916368, 792156902, 108936294, 733835608, 677346438, 783745500, 939466787, 718272764, 704756498, 110635577, 674060239, 626291540, 687241048, 468448292, 113852806, 442657614, 462127270, 791584150, 505195897, 262922256, 651280526, 98620063, 366253185, 443443711, 934905135, 927981297, 275680474, 607326878, 772731263, 626239739, 487772242, 246279959, 673986743, 631598091, 209730527, 702121681, 865699188, 384773658, 772604728, 720551862, 617412434, 338211747, 377077946, 803721125, 544217225, 699679204, 607517920, 660535016, 29657971, 586007808, 962825336, 925498566, 772174964, 264055488, 500924066, 955030313, 207826419, 88697010, 461692395, 890633843, 616527673, 947924389, 140346164, 245299817, 207767227, 690345829, 377175823, 272961726, 467983663, 691101301, 353464471, 356126580, 628934641, 661140537, 779155113, 591551044, 779940063, 946787464, 613675034, 348478589, 203982715, 146297355, 151255694, 525669086, 35919068, 523041579, 96684077, 75572896, 29138510, 136461305, 216498237, 702078857, 835146614, 246128864, 44096056, 733710085, 352457842, 992661946, 112058277, 363305741, 772253448, 408102553, 351875697, 239074289, 723116228, 543885579, 688885865, 589429200, 679404965, 671756211, 589445077, 101777200, 534935549, 206039647, 87739002, 600664306, 78063017, 233233708, 892765853, 284711954, 257535145, 520761449, 654962128, 974824518, 629132639, 694429209, 537486324, 935827341, 746895778, 574985536, 595235706, 131381916, 361532003, 327731310, 310590927, 220458319, 152939098, 567418547, 267206521, 29126018, 750113096, 6550830, 177209079, 705711136, 373122387, 438796062, 603365183, 237041058, 731682055, 543520733, 705962706, 93265229, 737799339, 648962808, 613336341, 368022360, 612058107, 168612607, 740098068, 473255762, 17753024, 126633214, 860713209, 206533640, 786616525, 575635555, 481538624, 732781021, 250175855, 918536692, 509839188, 64856786, 674243333, 850325349, 334882472, 961132927, 773632737, 814729463, 396284523, 16124388, 582402467, 534766829, 906730464, 90991423, 891360413, 199539387, 457338363, 299735117, 240263546, 504562327, 797422303, 773054717, 142021578, 72212492, 7445058, 338568852, 951304434, 776412321, 141045858, 904132283, 705991570, 19690327, 730721180, 143872495, 291533963, 767245588, 335460589, 35509458, 191683478, 783552540, 687609281, 192958864, 959935383, 382196175, 176928978, 965339308, 789928334, 15000586, 174724444, 447359195, 485667142, 824975282, 154891394, 664213084, 748644367, 228360072, 948257037, 276768827, 301670090, 141450706, 196617594, 587089176, 753277281, 482338517, 51322964, 10945942, 484073490, 722640025, 703154104, 396346638, 42310283, 217019345, 853282171, 401135313, 864539516, 835919284, 695053440, 692104504, 307730355, 487770413, 389339119, 659385662, 427454007, 294055709, 684372783, 676117148, 307826489, 790149543, 828684033, 973812442, 689673047, 562343108, 872423465, 147788661, 759389481, 482818873, 846576095, 659886983, 836302273, 274237026, 721441088, 436104907, 430791615, 105152135, 181838353, 404333656, 803532260, 274333249, 531871566, 455289070, 245266094, 686710820, 875284087, 609193680, 399098402, 305968904, 445769775, 271595487, 207042857, 241972519, 462586562, 386795680, 435387083, 114578882, 989015496, 93834446, 394019151, 132480282, 917221539, 391337857, 164887194, 775442799, 313058432, 136632184, 741495689, 290048478, 18592929, 881724033, 882822656, 985936355, 274967145, 293622706, 819031656, 635152377, 570297741, 704991901, 200729726, 273172856, 313736375, 445702669, 411437415, 324791537, 454172564, 94351576, 112702769, 395284802, 991331537, 163436372, 202219981, 435048310, 743543899, 828023606, 153889120, 863026958, 984505110, 798407996, 604074387, 423047908, 948463951, 396038529, 282712532, 758941356, 857889373, 774821247, 743775072, 453638239, 702924887, 362092796, 777333394, 986644090, 802357549, 18411561, 924193558, 9003312, 292589645, 808651178, 684748901, 400135533, 536169635, 952502120, 910148282, 540667885, 801360983, 962770904, 893078421, 869921911, 729669481, 428754887, 750535329, 282319956, 353556619, 34137808, 935631757, 318364232, 867047752, 286634982, 414389254, 741714763, 840097089, 209263799, 583045874, 107224985, 500324249, 984430620, 800981403, 518338947, 716369271, 71549375, 976535764, 944934751, 483693858, 871381482, 35918035, 420802618, 119242755, 770521228, 392084173, 63704560, 141093795, 644941485, 757272918, 179328182, 790748419, 602221355, 810480741, 412296007, 956823110, 902762314, 54387504, 298789347, 603980954, 490832177, 683739892, 866460626, 205809426, 738612865, 275278746, 770063822, 600805980, 632930959, 650355416, 849014368, 34868416, 881321912, 753407620, 809237182, 413915183, 106022455, 379593657, 405031864, 581620643, 408795750, 813043482, 674673308, 614445567, 349104607, 880529980, 864883686, 74234849, 324832206, 587430801, 793582743, 184840561, 157468333, 585710775, 686441194, 754556419, 691119763, 70762440, 336137893, 983333609, 939318498, 624052482, 466615419, 437740720, 420342747, 421150505, 60108146, 491686901, 244386895, 872140036, 995168768, 242676931, 919834595, 253004417, 869829540, 579846273, 344163271, 315014605, 399082996, 214913153, 483789690, 284412423, 693288607, 325320542, 630376545, 938273286, 567162941, 500369201, 518263689, 761066743, 109393255, 515227741, 845179678, 742938176, 665978439, 887247053, 87423133, 711822190, 920841806, 181631950, 886296531, 769284642, 871175389, 378813789, 548287798, 902819446, 121697943, 645984212, 553235351, 129255446, 2005898, 924084177, 44068255, 772256295, 358741801, 453249401, 221321222, 925374243, 199082821, 114842572, 953266800, 861875192, 772175453, 583002189, 186842903, 788711537, 588831714, 874821714, 545403384, 595675136, 177858888, 28907595, 7432490, 605684305, 417092244, 362709856, 608722773, 980736041, 349848040, 558112767, 172950333, 796900261, 474090327, 810302236, 922283126, 926180643, 373257931, 403606746, 345108411, 511463678, 908680911, 790542389, 109554804, 565040053, 178131332, 796870898, 556457545, 587929733, 874641383, 738458853, 692214405, 998955320, 276059054, 24084449, 437909344, 370793992, 602480052, 182699462, 951002343, 958250665, 449858068, 618946121, 59703091, 916419851, 502696059, 432956789, 5321711, 449169484, 986767381, 423219471, 405309625, 995337267, 601053182, 751197231, 550767424, 833858969, 913382736, 307126318, 225831692, 831770797, 593027839, 884592782, 215124319, 242690401, 977059862, 432122953, 390750219, 363250897, 999642429, 451530548, 831383177, 67978845, 280644709, 906878462, 959283417, 270314655, 359877090, 571302505, 273195987, 478339850, 495181961, 7342514, 520785324, 74380801, 780239217, 492850118, 376931010, 723069238, 922770547, 545938125, 138085572, 905125703, 502757137, 11612895, 20929424, 802936606, 346651230, 891477198, 146491859, 554276148, 457382138, 327845273, 250788577, 873798309, 593369578, 55127037, 654304037, 963113662, 637693028, 944925264, 864247595, 292771132, 394865986, 773539812, 751889554, 860099507, 165840459, 122459990, 373669637, 103057448, 277397970, 806750534, 571678650, 418353258, 721219722, 12540564, 913778547, 962751574, 924583624, 148944819, 323995819, 966737494, 574285330, 679292627, 507000047, 472582652, 804785842, 282380258, 585243756, 252023238, 591397975, 679728356, 517502347, 451610482, 650897008, 543401150, 410611287, 942997181, 853668624, 545620646, 464520981, 35216388, 988662339, 884980003, 302939009, 858733480, 914032411, 403232374, 964196795, 303948764, 200861382, 235262336, 779159037, 792619413, 903470827, 455868923, 609577312, 348675565, 256502428, 485252609, 607686329, 908963439, 298909343, 733436143, 353167543, 697162993, 235899951, 726133182, 584077781, 610641737, 783674301, 462768593, 683439255, 303017320, 394785946, 73934605, 891234004, 969458716, 115166, 808793960, 93864622, 174266953, 158329885, 823497632, 755852113, 174904068, 948684255, 798912043, 398100214, 610970927, 967785272, 106481026, 712143359, 223498207, 433867256, 261643175, 87827985, 637301057, 368355267, 956951492, 798553355, 638005967, 874436935, 945068190, 654544723, 414455320, 868975605, 979631491, 14239201, 819590801, 508485799, 959537834, 572635018, 978099362, 651370615, 236642041, 912573328, 569080725, 909849955, 186290806, 418653777, 310610196, 265573731, 230164408, 222234172, 330316175, 472005628, 140086200, 604818304, 819662145, 883357154, 514846981, 129386941, 975512387, 57506491, 59070894, 387107260, 821423433, 627142012, 114633913, 988152255, 203007718, 302664960, 918843443, 267061414, 441620121, 915904390, 495305525, 898140666, 586845494, 206441261, 675710009, 307755085, 213245461, 65794512, 696526925, 454192961, 982940760, 373568585, 599524433, 453229260, 274412031, 649348104, 435311071, 604800876, 753440617, 731359049, 25157803, 843782452, 676155885, 240623939, 515304660, 55122522, 515042358, 625827559, 656341970, 991949657, 997979498, 734832789, 872756851, 343212826, 680472501, 890757729, 18196517, 595341561, 598088328, 42201945, 318862527, 454892538, 183161821, 428823562, 891677430, 104481697, 676951926, 235762400, 637988379, 966167341, 564424345, 833293232, 374231671, 450027312, 96111248, 493729539, 183588558, 27943134, 212907866, 177044296, 243579684, 569241764, 93851338, 91562937, 567814391, 942740573, 756927288, 539875161, 436264093, 854800868, 586344914, 879616164, 90739381, 42682123, 138682071, 733044496, 884058973, 613691022, 318208344, 415170670, 644160752, 546484718, 329091041, 988034811, 877131942, 491520609, 601559481, 570233073, 184104926, 418478950, 267110260, 930263581, 240177623, 249198974, 925053325, 518641561, 111025709, 906635354, 837921442, 798579036, 943187593, 757915305, 643280584, 572177428, 190330366, 969003500, 548714671, 88569478, 414895960, 70107616, 827941820, 496927608, 24452616, 700232619, 985596379, 243540544, 962361302, 376436190, 386290540, 173970914, 253166726, 832519639, 569738332, 299402596, 102077152, 325320263, 733589976, 537396670, 438341199, 433174279, 568439668, 320991687, 634446740, 908107311, 751468446, 948136991, 683364983, 439012847, 453435747, 266923601, 984346047, 190475326, 415858679, 979338106, 908359163, 514413635, 918141913, 604463262, 288005446, 71011258, 538770873, 400981639, 421677478, 994467398, 556950278, 135644643, 139202320, 568589178, 458247503, 397683661, 797170372, 547439995, 567518170, 462177498, 702900342, 101471612, 38560130, 193627275, 387783675, 804922683, 700288556, 959071491, 598471191, 216472848, 948879298, 83455865, 112910844, 50573862, 357433874, 64558013, 922823149, 779069504, 128619802, 838564097, 795658450, 479823865, 763734851, 771255458, 660298486, 206087498, 241971126, 332063220, 95259955, 564965017, 521140826, 874678061, 45877451, 454422953, 328743204, 104658906, 396029010, 105964673, 438013953, 513777319, 980167852, 501978368, 884243015, 98183142, 674594560, 245257926, 842095420, 790786275, 131731976, 540064262, 789646672, 816348976, 63492267, 756813582, 867718841, 88769113, 503069986, 154078396, 676880540, 148102623, 765541837, 372501706, 294760059, 207023901, 171518157, 695134584, 532778844, 770557261, 630938969, 141140533, 788861976, 714317702, 811870814, 336051275, 490625025, 867529972, 537367003, 426733704, 442065264, 221442369, 747782246, 89532466, 830505491, 388577143, 584300168, 919262603, 248038224, 132310548, 836549546, 126095099, 901137218, 978963564, 184502151, 464271549, 927237329, 345124003, 438290752, 160700531, 299091292, 201380213, 854278620, 465693915, 881242077, 94313715, 380381478, 356687041, 951462625, 499040227, 78759796, 473477436, 94096698, 622549106, 536914977, 927077031, 833190509, 368680321, 34407326, 922802950, 329510561, 956825256, 983229904, 802458358, 849654007, 530545294, 565510792, 572272786, 135262411, 794229535, 179342424, 108042707, 71993563, 71811083, 544110719, 255702521, 965129321, 909204497, 206768507, 154226119, 190047038, 989653496, 112285905, 120002680, 176308944, 659995515, 411103495, 565878974, 159250160, 294190920, 924889478, 514721993, 357901646, 30821566, 387828455, 362093862, 6896451, 901156288, 606773506, 9746219, 998838241, 278455175, 672390697, 315107510, 672273397, 930727536, 676243916, 492044277, 506982084, 255656753, 817167628, 542721976, 484340125, 702479220, 609061011, 776578985, 476355379, 855725010, 689755171, 854843222, 161599834, 723640238, 619622469, 772348248, 109967449, 883400523, 120402821, 504235943, 695926997, 684600792, 440331575, 680792197, 677891183, 411182149, 693740568, 785145165, 186738852, 805855305, 407494192, 313442270, 679698359, 821491418, 131906940, 163255047, 82782892, 786180124, 26414774, 298825877, 26756887, 457714590, 210204449, 831444815, 879965185, 211778441, 759589772, 871699106, 429348409, 893917235, 652410518, 85375410, 856150652, 888412781, 518460398, 152031781, 321410325, 719845567, 31883788, 552694295, 887243302, 94834588, 821586353, 68703152, 625268110, 468803383, 953245563, 288008489, 396172431, 526973128, 793341622, 528272954, 516239836, 533970357, 566847940, 931350618, 202554862, 643777563, 399539341, 565196583, 272750745, 329255442, 874982652, 857462506, 749538552, 401784890, 37104601, 106320639, 459597180, 490020509, 947663949, 754224123, 107584986, 808503104, 467041635, 4864442, 579356489, 80501979, 582718740, 89847144, 431682305, 992394623, 126089716, 310582295, 223706443, 814096251, 221420429, 54790196, 988130237, 115717636, 862376693, 569514918, 517312787, 169347009, 846429666, 798679419, 511076827, 41411736, 829977461, 215555918, 678634502, 520540277, 998837265, 131063436, 158418201, 879867393, 13165882, 501319320, 693190244, 818582218, 443702280, 573552695, 357800559, 783268543, 794847764, 246420654, 221237617, 654140575, 333268141, 479403034, 435717525, 533726016, 848046783, 280862518, 416274981, 258685698, 98834056, 699968722, 928484282, 66452964, 831515058, 526791754, 403822428, 438086334, 334715696, 871810315, 368677829, 955562847, 690731618, 117752506, 411364174, 620948379, 300476092, 781683118, 936530461, 799504950, 615218766, 721967171, 377471943, 191431724, 70766285, 477064656, 681173253, 358563137, 965405293, 796420214, 50100517, 253384826, 876606737, 603132813, 611008827, 482214823, 298111892, 354142973, 95634060, 540909883, 990282962, 80332514, 573910743, 735872863, 502831703, 34764304, 214592871, 604220387, 339347780, 877337465, 91358992, 142794384, 964147993, 476910023, 423894235, 163404039, 928074242, 954578382, 287644745, 149247153, 233426647, 39775741, 698972182, 28736722, 668318540, 691492797, 98016621, 382742954, 967443227, 446441025, 416320839, 708147052, 768758344, 815061974, 499949333, 138012014, 509599692, 530755039, 408991124, 271711334, 25689868, 759246457, 516834351, 499516457, 973707668, 464068615, 936996624, 369596484, 42726009, 114513765, 835366193, 902331162, 443965288, 823203806, 772853332, 672331824, 600788068, 833294804, 847054714, 822941959, 23339901, 472016844, 958983477, 22669083, 410553230, 832846017, 805899642, 810874266, 692758820, 685279280, 714239879, 27760126, 768206901, 433744484, 592504452, 819786460, 155814801, 762743619, 188979599, 154763157, 430342193, 369728776, 328600782, 628963804, 74984063, 364196191, 83239371, 149165839, 270101988, 947465008, 365780420, 272759088, 429372586, 166133824, 731401631, 968679773, 640812873, 501359934, 14945672, 890581556, 636796978, 233747541, 305445500, 63405663, 666705030, 867870082, 905151936, 867388368, 959196697, 221431554, 501082518, 991646302, 77044942, 542877638, 35648335, 231303530, 916763538, 581792839, 544891190, 471198157, 415674773, 761245488, 298994950, 891816427, 840244642, 398740095, 712360312, 680943831, 891720041, 334811738, 979321028, 201390863, 951783674, 208299640, 917371475, 176508540, 153525022, 182468823, 869756992, 130069212, 795571901, 726167924, 95061399, 367827522, 677502758, 492092941, 838908174, 42819328, 523009853, 4283377, 427605523, 848674793, 686701136, 564076733, 761746374, 456763700, 794885729, 404841422, 819103866, 97111838, 36318716, 30432481, 190748200, 528014033, 723389800, 814712617, 440795455, 900330032, 313662331, 354826803, 607951532, 782996716, 478347149, 340505099, 444539617, 938993780, 330677399, 660277779, 946084198, 30636077, 676894384, 653015644, 609828713, 175988975, 610988077, 999706826, 668410877, 716926142, 110791990, 205223448, 484496509, 565418560, 787368328, 569323670, 110723386, 252024200, 288249049, 443070219, 943811559, 786703011, 404258895, 969433927, 462213926, 557977212, 298143317, 800379849, 377473551, 503155782, 38619994, 952662197, 835460009, 55917577, 466506970, 563849198, 653219534, 971682916, 619758726, 74796268, 847457008, 227885229, 137877848, 447598665, 252115312, 562361721, 213863388, 743598668, 33064582, 835317004, 836660888, 277195053, 835968160, 736223493, 898457533, 243199709, 652631320, 889534781, 894526636, 720668501, 600205753, 465720383, 675125944, 329662348, 959506811, 127195572, 90785345, 147426624, 449607010, 155204205, 34518525, 920077101, 503569867, 472609343, 784538816, 631119536, 182135814, 866418858, 556951473, 293240769, 402018275, 241374064, 88191295, 840717757, 378308836, 975770170, 18552440, 788770795, 122549168, 807473635, 88403694, 250843372, 692447385, 984359332, 60528874, 977228062, 318113619, 845613693, 255278096, 364189378, 253336231, 676301497, 366990474, 804343791, 207932515, 414276070, 241321716, 563161830, 39714668, 870483659, 175294393, 264982522, 653042841, 672588116, 874888894, 8735406, 554895268, 559701874, 797259169, 396187225, 846698528, 698084690, 203257753, 559263185, 4049148, 60190320, 443577445, 15121863, 581544509, 377090084, 512378303, 589966584, 572479874, 839910845, 63478105, 453832427, 994088980, 396689515, 95987733, 239307226, 350495475, 236576129, 68895894, 463450430, 880849826, 875049099, 159393002, 860748736, 131044676, 144847559, 44409983, 648706069, 963504767, 347633837, 186805059, 30203123, 854742562, 631417340, 16158731, 146396470, 198229772, 154143730, 499640253, 921610633, 336289251, 206745865, 547737651, 750581578, 268276934, 202241176, 441828413, 341949042, 26851474, 919260434, 256093114, 32089129, 72065935, 648177141, 34335978, 303114259, 839787482, 507920519, 700017649, 22133772, 592630159, 491278839, 674677542, 148119647, 358800012, 708663720, 805068822, 355573677, 481269618, 20932169, 528209038, 312727571, 399349519, 893557255, 592476611, 932656595, 648965451, 371822453, 815370084, 372772707, 263462870, 36315339, 18161503, 922356142, 563522394, 979522663, 390851478, 102198565, 242672615, 854341661, 207734559, 485388445, 547422943, 684782336, 316759710, 709892829, 115991649, 738574821, 791589190, 690612380, 702406191, 427534678, 718619493, 518595242, 763248907, 465655346, 133438718, 602921993, 449819139, 158887595, 82263507, 220643274, 454428769, 56566852, 329942306, 167206135, 895957150, 986623624, 362544147, 339591198, 549702184, 676796436, 153100736, 401312129, 531675194, 328998165, 580008827, 566190783, 485423642, 552844073, 728769452, 185886569, 591604433, 265011464, 889790768, 369003790, 956127200, 335562759, 155731951, 553731991, 930007667, 706355140, 515304610, 932531852, 225347644, 296668335, 672448281, 343133143, 904194338, 891192611, 847903075, 190337272, 309394176, 685317370, 810507783, 470806865, 432849215, 825813822, 793617464, 658939270, 377442203, 2305651, 755746644, 816706632, 617323918, 897434505, 449300299, 828528141, 785333122, 424938149, 100822890, 725303071, 651986594, 88887971, 45487762, 589285616, 163924927, 777345292, 820878606, 305384827, 975453383, 875679886, 423615061, 39058627, 750461539, 739419612, 131977333, 439889666, 883855800, 140850654, 927592295, 755259297, 855469397, 362751532, 607426629, 943377403, 937672320, 205286047, 375438347, 20923226, 771711033, 93270809, 210612783, 387960034, 279805686, 999050376, 74210189, 227465742, 1268255, 337972028, 714806794, 613383025, 114928757, 984651275, 563770358, 776385846, 453757794, 328018607, 303781, 498460409, 321905389, 18988968, 757501801, 705250713, 606266102, 672793007, 839791967, 1116682, 117883890, 811885780, 377321554, 357015549, 183493229, 241898554, 624800100, 104130858, 31744696, 76854606, 474593965, 811566652, 885226325, 456947796, 683942148, 796251361, 561026010, 381523480, 23206012, 565282053, 287272266, 101827915, 506255352, 784222874, 214513242, 919415388, 191918233, 729664682, 414463500, 289778162, 661040956, 790180898, 768986758, 526229016, 165775198, 36086608, 154960867, 557152203, 801531037, 443953478, 3999022, 858374861, 277947054, 87754115, 730967390, 441544123, 890707421, 124603906, 240697246, 578843352, 95632016, 821303074, 537357689, 257227001, 909110611, 241631495, 589042317, 881857350, 388771642, 221341165, 606454218, 555916017, 680028805, 102816783, 550453094, 589455187, 492505692, 780401834, 909852563, 756642246, 20182895, 123482676, 271589655, 65050646, 492075966, 647146919, 504485598, 848058673, 641159936, 161125472, 293517083, 506990829, 236865823, 159125742, 390400203, 795809980, 41531447, 611926498, 347719342, 981652528, 836956954, 733855488, 784618224, 784738230, 665119219, 424214617, 112032507, 33092102, 86392028, 85146431, 924386913, 835794725, 635835792, 147425836, 536667651, 407320457, 586656608, 492753212, 908420754, 63417852, 593540094, 754311972, 122719737, 915600487, 874375779, 299559448, 83708675, 649386352, 813712166, 701832616, 507636631, 262708252, 426679941, 215403940, 842774335, 842154790, 373808833, 238188924, 366698062, 747934728, 120379048, 890246339, 374446716, 216410524, 948246450, 941428366, 507030627, 40408970, 344630483, 462618273, 772916226, 476708634, 177503950, 125875816, 145983044, 339011681, 813655437, 434628067, 336101909, 888150495, 908405647, 927435721, 721818550, 952034495, 996227386, 447466930, 389036776, 996387048, 172055817, 430582111, 315734525, 343107562, 460811225, 151873705, 47429207, 641187872, 650034342, 668657404, 875706690, 510185099, 77454330, 403085339, 400389209, 116677637, 179653507, 186231011, 464157010, 743119452, 158251434, 770623968, 992572537, 636268936, 554775105, 472422327, 724728483, 463527483, 933721039, 188168466, 737336369, 130657553, 893128058, 232835901, 607893468, 644007978, 584638705, 57938395, 485310217, 818055794, 353190156, 416996189, 441561152, 160449046, 792226572, 679446618, 36716245, 630929358, 276169975, 947306760, 530529665, 874334135, 388051980, 275978536, 895392635, 561271796, 232460263, 924845579, 788881366, 256123854, 392371924, 598760829, 451357492, 116371404, 324055487, 28213892, 850411546, 944591518, 550970986, 745232739, 226552489, 719581837, 151641182, 27987218, 979510639, 301751686, 391640876, 415456653, 411139338, 632895581, 826197393, 515901019, 179437059, 117699395, 215995871, 55801105, 371093530, 721523026, 703974712, 95544390, 561787282, 139019092, 620273833, 23702472, 979581035, 697647190, 331933167, 452920056, 8753261, 366391787, 603998497, 900906987, 19434087, 828101844, 932729841, 898969648, 901928971, 325504806, 551341443, 481502988, 71130191, 799278450, 718734062, 469273172, 228450793, 654538570, 586974236, 59048397, 663386197, 98422426, 116225640, 913685051, 674498510, 888351355, 941553192, 364397042, 956044540, 990558399, 486791024, 124208034, 225958507, 394044363, 64182287, 8129514, 408343339, 128932941, 453128422, 279372209, 488862244, 625240843, 864655832, 582503560, 33887641, 17750255, 516033079, 278105169, 376376834, 591784987, 887077112, 472402267, 882548815, 64215752, 191617776, 170251269, 887554093, 942698504, 960352471, 500683236, 466443458, 735517470, 299695965, 34152143, 70907636, 724804219, 796830738, 525875647, 208895860, 194901215, 897065528, 83834078, 914234306, 44833898, 455755314, 14940457, 563070308, 842011108, 775899537, 631648070, 790818452, 965627219, 425333157, 580136, 437916879, 872931623, 773671356, 939689956, 505294945, 765675061, 195513907, 128351721, 473347135, 541544396, 471351080, 960719731, 340042954, 423818063, 27586641, 450253475, 188350198, 309735667, 343809525, 412060737, 488694667, 225823736, 176925126, 948447019, 120292959, 517180178, 648913753, 912612669, 19310051, 364928227, 525005611, 44664959, 415580729, 206342662, 774388242, 856698892, 636549594, 125307258, 939359771, 57797461, 955161776, 908108941, 640119532, 637472888, 821576251, 559481804, 871077925, 774069793, 515358118, 832995313, 976400514, 51087169, 349357299, 275234389, 400060815, 848308307, 642275910, 294512680, 996415410, 701247651, 839719903, 707829716, 423359442, 940895136, 625026859, 67621275, 463677184, 999341479, 12879248, 961113344, 909195655, 593510617, 5967819, 656039480, 616208122, 259406857, 283841963, 540718336, 168849928, 866866855, 594634693, 535749554, 290012321, 577242257, 161412914, 992113594, 466056839, 285982764, 572884844, 677864412, 498320369, 357285095, 548553493, 615584316, 361541010, 630755396, 466020089, 560491423, 288399517, 430638563, 380013079, 791226085, 209037035, 599829480, 29081649, 778040448, 692896957, 778990709, 839870318, 90786003, 550344664, 16916425, 275261673, 624902558, 440587684, 810573, 324238403, 84189107, 698338206, 281649777, 242197630, 368078664, 207900624, 910137206, 879597772, 773454403, 786947828, 768476585, 483421786, 408477948, 825299100, 381265108, 842967769, 352865611, 83880036, 836207215, 857783081, 21235091, 431113056, 571114055, 818000352, 565204715, 164167420, 853232598, 785939065, 198678345, 893899717, 754404785, 553507971, 771769152, 561685258, 652272569, 775571082, 647883511, 437888503, 206820085, 713932805, 501325400, 901373931, 768265774, 353451480, 471846233, 482195989, 383696593, 662289349, 815722130, 516586989, 168167170, 446015929, 30130835, 422759410, 685322951, 974706018, 247208109, 791247538, 500946663, 681869892, 216129977, 510328708, 296762846, 264088812, 808258034, 393751270, 297595712, 313668136, 457786149, 43461897, 740512172, 84338241, 382962713, 759364519, 907941563, 451650900, 450811145, 673470387, 255114717, 303754499, 218159363, 894315155, 842362679, 679728283, 978209959, 216099285, 40356556, 903649842, 269720453, 532211978, 142225627, 657062676, 698169251, 345886427, 311649318, 426893543, 371148292, 311382455, 428838081, 135024847, 219130112, 279213727, 454470531, 915357408, 401298167, 65583313, 587434510, 399384109, 176029607, 372742087, 525660936, 255304758, 782012157, 9011452, 773570878, 21028578, 907461049, 662789542, 578418026, 36902621, 248512162, 620245880, 297199865, 303610140, 763327956, 465962999, 121697087, 805959417, 951275565, 512183113, 625894058, 982171156, 418109299, 869844056, 563200479, 169661728, 910441741, 354440901, 671179465, 849997857, 669826292, 271707668, 805982046, 724499231, 683178455, 356676505, 74157933, 413495246, 799066031, 40046541, 662465596, 423929015, 389949861, 980105202, 408959224, 984160312, 480635174, 618597355, 695425287, 588760069, 583453534, 542508859, 419799256, 213932330, 8643687, 814861177, 396435353, 651203969, 868395098, 699532390, 720261718, 612491203, 647562544, 579208372, 220634313, 315311953, 824357709, 632258471, 426956052, 219687281, 34671055, 595375787, 382388442, 927180820, 660955077, 182959543, 672143748, 66595710, 953444978, 330006148, 27746340, 171239307, 32166187, 921637519, 63466762, 3339317, 441645427, 176590475, 222351055, 579518477, 10012232, 779897911, 464426285, 781127748, 616155205, 771682937, 820518741, 312645194, 628692996, 636034350, 873127189, 466499859, 409039714, 946900374, 849101288, 134356794, 724109984, 393463864, 636579569, 756591124, 563229328, 570807519, 597216967, 273542796, 721137608, 704536553, 420526937, 524234986, 715676190, 195687628, 203752367, 43358446, 412530558, 758751047, 48483053, 624751516, 33880733, 249511792, 96800096, 124321198, 585473444, 57701122, 726847955, 574943490, 263564354, 194385592, 86454658, 598753090, 132437080, 787035712, 30001713, 637141180, 790485856, 203251672, 760969709, 212945118, 254981126, 341441288, 34770413, 319758764, 974518210, 838749749, 810446463, 425621607, 548512440, 728930928, 743397904, 615089276, 572287466, 555686945, 52189051, 256500307, 413998665, 686778084, 890461428, 141992740, 540233362, 992417793, 288661757, 876827172, 243127279, 309984927, 632998535, 737081529, 824494921, 757494221, 496203689, 392568938, 565165534, 278516159, 294506339, 418976927, 426104948, 811960094, 343478195, 456844066, 611107040, 518449068, 785247200, 263219756, 952775763, 910379672, 90449435, 46081735, 611878562, 938340067, 961104739, 631945960, 243604018, 149705628, 195221447, 3061831, 340698516, 818262304, 808249262, 966753055, 841378219, 147418038, 14129621, 30162600, 825814824, 308098123, 228375914, 403620280, 684898930, 590465274, 188067642, 842423638, 110720409, 551645013, 549568145, 445864597, 307546937, 817916992, 251073534, 8032193, 253162275, 67436182, 169750472, 857566061, 607705019, 401446327, 465563113, 897202006, 417454251, 164643626, 245210896, 192955801, 583775874, 144718244, 96605261, 787970366, 336505643, 636137556, 556249495, 980900108, 413047423, 998525436, 931453139, 760303301, 521340177, 198848221, 384899893, 433043213, 148318336, 229614181, 2582189, 45469173, 459060383, 855161702, 585148922, 10791633, 922923134, 285923713, 298981758, 793736102, 370180102, 769429427, 440780396, 414469002, 252385909, 881729842, 933814081, 92056971, 666992735, 184096658, 450628014, 669916028, 139907838, 395010687, 540908001, 641065208, 151043087, 778492517, 821640574, 454379935, 464988014, 937644880, 999630292, 909292548, 2579849, 495086563, 470282896, 907146609, 133664693, 109246268, 570262410, 127918292, 359401932, 515271308, 477135596, 379570938, 501970867, 139096358, 341404891, 196752512, 585659897, 663238544, 788540220, 588197905, 586209281, 316341798, 941680086, 617253023, 898220576, 494661481, 825884352, 702997451, 555981148, 170131099, 578832515, 165904106, 317494353, 969231326, 690886721, 527396626, 724874334, 100235636, 906382809, 311892656, 221817800, 387216460, 34104408, 40878074, 202542971, 623875262, 909426109, 426183883, 616857314, 724440450, 740625086, 730480203, 403011752, 493810445, 769812165, 514481015, 813486836, 15802125, 409271363, 977960080, 218126077, 248189171, 491431231, 304376474, 815898346, 202152379, 403340541, 262170068, 254509753, 788656358, 917241557, 988846036, 717036079, 390717446, 749230941, 711202046, 544476347, 70509453, 976768724, 790349319, 735849018, 423040551, 14605140, 772180733, 375747488, 414925477, 186763583, 218095116, 702490742, 412473473, 418861913, 629103523, 838203252, 539195667, 787596674, 946598468, 240720339, 231505011, 361059534, 902609799, 37994510, 262976412, 649055226, 624879088, 663185921, 556285788, 662285347, 821681275, 12863540, 576441717, 329475529, 277062085, 79029091, 299299285, 395872566, 658574246, 953447348, 351006683, 89611814, 60206541, 103405859, 836432971, 469252974, 780666449, 814296382, 728948830, 853036333, 722392942, 561519600, 449253190, 41818700, 229136847, 850723433, 809319993, 124134781, 9002161, 65337125, 725079700, 28880621, 225114648, 379028788, 791897681, 340503195, 561045531, 257984834, 726536872, 148905877, 960592006, 469280412, 632652013, 431509516, 701477939, 606696499, 181610353, 488352809, 263110993, 891871645, 236459852, 683268319, 845732189, 710752307, 315371304, 900577660, 654038186, 766174482, 886546786, 345898414, 417351772, 33509268, 451077959, 862614106, 676367637, 563075939, 167421104, 643597829, 227257177, 411554272, 411916388, 169653106, 846262391, 674292159, 880781802, 113406469, 415923712, 67289826, 817534347, 752318002, 581784948, 774415495, 493480697, 2177000, 141255479, 647189745, 64498281, 172483460, 138502177, 155446097, 447662658, 410010960, 38422079, 870977683, 82462212, 360413815, 836784935, 293465002, 641089035, 94831316, 440059262, 582056935, 74046395, 319825133, 210539154, 862874597, 979751846, 30002100, 853604242, 754405787, 440428644, 814888379, 166345478, 623293527, 244233244, 216095932, 430045764, 940188185, 523606603, 116746322, 961055891, 30069652, 860443994, 515446500, 198988340, 248035553, 225977667, 685401464, 656924463, 694307082, 660963961, 207367595, 233423570, 360010384, 724378471, 550401873, 822120650, 660574860, 767611986, 663459719, 244573147, 234935120, 244354060, 760976468, 687115622, 433638413, 102880840, 886564706, 78519374, 539340908, 462211009, 29359473, 19170077, 392161306, 334437894, 834669520, 800400698, 920596460, 9025251, 723554118, 210867287, 88792086, 80721053, 818320994, 308080616, 305613239, 115972457, 312194839, 813861994, 411462860, 828212416, 496122786, 726368986, 494400428, 147720882, 179783223, 683623564, 551291573, 880767669, 187346003, 571152193, 491290678, 259663355, 771186384, 921004188, 269420726, 80458009, 398482115, 698229276, 329083188, 706201460, 764960730, 132301797, 462741103, 169906614, 214581362, 182859956, 842055992, 342894935, 539476110, 203599468, 767828667, 631004921, 844117678, 450717622, 400108890, 233308024, 622577868, 518623838, 100728699, 174987463, 724593353, 515921152, 18039214, 76051471, 814529731, 381636987, 676388061, 316579746, 525291974, 611771326, 274752293, 32717869, 988882110, 493624134, 800841954, 970510112, 461608312, 63414427, 853405355, 707535590, 822840512, 509000954, 126870985, 556054722, 141027506, 874842525, 83022421, 8200131, 165514777, 76990695, 782933060, 654143602, 775887814, 817471654, 111989377, 577163012, 321830285, 173277958, 629181721, 17790322, 933661029, 919530084, 96503730, 982017031, 768493892, 455240516, 948959330, 717594632, 252005177, 208381686, 843104002, 796861666, 962157933, 160732538, 132731859, 449094748, 429040118, 88634277, 500707624, 979801207, 759885599, 152493206, 488660341, 537924432, 140489734, 339072139, 149623819, 130283630, 354122973, 671711688, 301550686, 895399108, 558849034, 569808368, 824182801, 865523720, 788458455, 735703000, 10568571, 240683204, 276726133, 796220765, 559991828, 507166325, 790382572, 274536088, 387626008, 116583533, 296697509, 518749339, 807401367, 975473724, 561738008, 293144231, 202736168, 745235232, 176750577, 84204830, 588237475, 456791725, 293312151, 39694872, 259402509, 47182480, 384263456, 494233992, 77516173, 411234139, 101003865, 710884593, 817213643, 116204085, 810271281, 81415430, 721571408, 195271496, 787066300, 272761297, 581539111, 424703638, 107979782, 721703277, 854446800, 187608269, 631944532, 282492124, 254910542, 993681355, 187835099, 601590233, 627366792, 924916822, 447020738, 508487690, 345069753, 663005892, 499071883, 75399835, 364869780, 791809253, 797096619, 730806615, 978853795, 655740669, 391899124, 37975085, 506761701, 283411781, 203374710, 227978704, 122544730, 714281832, 197438581, 295443852, 758477991, 351581011, 137484285, 37161799, 649017324, 648804367, 846713234, 525154739, 124984989, 163087310, 404324589, 815081682, 555498329, 953725348, 223031923, 416473385, 528790477, 276846986, 953783144, 952628408, 556407986, 325752794, 344218503, 719227376, 959923210, 793274098, 983923790, 697108235, 265310693, 404720754, 44139422, 483736786, 292459936, 962752245, 544577401, 888928735, 862177486, 468895410, 886828110, 529949708, 96092881, 282916314, 530341716, 582066523, 114986439, 576192328, 733860319, 539929671, 473478458, 318837864, 505100290, 366452576, 784334530, 659178321, 260087396, 986685455, 457758940, 178844902, 738007407, 245869692, 658680650, 811774328, 810181000, 632374001, 320700726, 230826924, 462996142, 898464292, 546596011, 600771612, 755022215, 790754446, 266591909, 944863966, 577956231, 954640760, 454068861, 532174227, 169095822, 711892608, 114248890, 459315759, 808512630, 749886440, 94742275, 394207388, 992660922, 342985192, 572022877, 950556727, 923167011, 179616816, 231879435, 753387450, 238079908, 288243583, 985970301, 140637864, 9504250, 560881854, 581521400, 398458109, 912303414, 532173617, 352570509, 503313846, 722456985, 117494218, 162426200, 534014561, 899399455, 447129307, 593863173, 281841464, 715279813, 238422422, 172612409, 402245863, 401355235, 652782823, 404618737, 798751679, 429200568, 758911660, 44437031, 702730124, 516307547, 352339629, 672782362, 590148917, 999361859, 389602203, 434816927, 868211829, 675727185, 718987071, 405222641, 778402502, 450322078, 117512669, 244026588, 977487672, 500142249, 955574746, 10861916, 273413149, 193000533, 95772810, 179980337, 349674918, 703803790, 35598750, 788647964, 663698566, 527076483, 866139219, 808290781, 548544271, 638362472, 288824016, 758393689, 85282862, 278310644, 233623285, 208986608, 111120644, 789722816, 95981640, 201994558, 128732883, 406551882, 870118241, 672608057, 348562063, 231513793, 293576728, 503278418, 447888319, 270776247, 920720381, 352514479, 136414011, 532670740, 794223464, 211362627, 691754247, 724727059, 214293145, 956510411, 744625042, 571401990, 272095621, 597204452, 16828928, 83902937, 748299971, 465466756, 34634147, 84266669, 589527187, 227095065, 426742861, 183565500, 577735672, 723044908, 954716349, 188311505, 830346594, 276096704, 250518825, 881432564, 186792128, 678508875, 449661413, 74008136, 95423968, 438630292, 336557730, 660948072, 382147456, 560731262, 805430957, 266927074, 543319393, 624478606, 840534347, 294583758, 740022724, 206566618, 447741252, 299737949, 483142021, 726415450, 501879384, 903230244, 610597170, 695475385, 356759405, 663711067, 101841923, 931380993, 572742866, 908784891, 667344845, 455093150, 369581172, 633090755, 644599209, 863805416, 473881037, 106120135, 166098859, 690879040, 119494979, 967626036, 357488285, 835347323, 147378587, 789166911, 19235328, 777873214, 559228789, 897590686, 213470044, 108915499, 318275288, 599974987, 358763508, 112452660, 48104222, 736299058, 20489008, 559577273, 620085229, 952091718, 729314896, 581834304, 629813481, 574064684, 779864617, 354735048, 650629066, 30981779, 50727842, 583206444, 949221324, 177667594, 315946869, 701719977, 259663674, 928427555, 949102760, 541260356, 794329960, 579274067, 65518619, 537025668, 236893691, 995627310, 940273301, 3901838, 409022992, 138431263, 548317399, 994051029, 703165661, 134241488, 414793353, 767160354, 304919941, 897413320, 189753199, 484927317, 425726994, 618064931, 46876132, 203462417, 596731304, 371915057, 312466292, 279454686, 121653217, 93705838, 313179854, 651975682, 867210021, 829585057, 901623117, 235038108, 721238029, 567946228, 91194320, 302634956, 809056387, 786348745, 73008074, 277191255, 893014390, 596764934, 947420968, 232402695, 481061460, 90628629, 425736735, 61654078, 59962164, 58314976, 863580494, 580317282, 618292233, 834322330, 933461765, 317034256, 714945337, 145167922, 976234042, 31986512, 974270992, 605553118, 448823526, 705397578, 154899755, 504272328, 521364885, 773889368, 966916205, 341791784, 663342523, 229374478, 130460265, 234192731, 888793426, 194184564, 102807860, 33238818, 115680199, 569597755, 477818553, 376190193, 443762310, 735028629, 333536615, 855056969, 237741135, 377202321, 221749523, 513973620, 905017975, 137856677, 910109293, 676975962, 770015277, 62309629, 65953657, 797232774, 349895042, 717634834, 280183802, 359801146, 305491878, 439240201, 26230667, 963920483, 63712039, 13583747, 800348720, 732387598, 751173252, 38960386, 929846532, 888449209, 419380081, 95193949, 248183356, 454984523, 417296528, 80582932, 979535658, 479380823, 403987511, 118964322, 183801898, 744135384, 508318972, 666920368, 759485853, 880818251, 661424271, 782285987, 352723466, 270274594, 523036480, 487979865, 663310676, 96096692, 680285644, 794322777, 144578117, 486354083, 686417615, 151371347, 170116335, 209776545, 54339070, 659792876, 829702559, 919213529, 584340672, 516059771, 220638357, 798206523, 411520364, 690939630, 413847117, 808540988, 62979264, 576604770, 705566279, 886073465, 543557869, 461418464, 200632556, 652174546, 899391019, 123781323, 337587948, 68534660, 241615372, 280994538, 900679336, 272306999, 945373627, 699564586, 521844557, 904860895, 747937048, 470619494, 995787323, 700730228, 943351466, 963317606, 836364144, 404590236, 924140044, 702635514, 614058325, 832761297, 640360526, 992059929, 411450845, 859420335, 944852745, 124809907, 344640917, 750844222, 419586445, 778585715, 310076770, 428311714, 705061788, 174119278, 893056803, 522521728, 910838071, 883787428, 601919907, 680829881, 559011323, 352674462, 290767239, 710319241, 555354473, 379007892, 661168964, 911828803, 868899997, 103442888, 550138067, 467901154, 535854078, 260066394, 412704447, 370896649, 769632253, 673381724, 969147735, 839490289, 676249707, 828186090, 620306904, 102366314, 377814806, 558563673, 108897336, 919382641, 228147118, 673779203, 192730001, 989275344, 687837117, 157790344, 601791245, 15798837, 799752151, 77968997, 920059769, 173007398, 941786268, 491779409, 772869645, 538831595, 963055693, 448883987, 977508948, 923037516, 960849953, 668851966, 226222929, 146526469, 477015853, 376747863, 585124086, 531056056, 790461173, 966376655, 976441833, 208002088, 49672773, 4791451, 105930053, 190771975, 433072759, 361551152, 480072436, 223613749, 827270192, 411524188, 202758019, 18480584, 807789216, 200226609, 2860422, 251390858, 864996130, 679892369, 642199542, 978188339, 198562756, 245661466, 330499230, 479627841, 155860184, 303413071, 946411448, 413972042, 117899022, 310460470, 136827382, 785719471, 692849138, 784760658, 466852914, 486242496, 66242223, 682341831, 271783142, 458724435, 798706468, 89070881, 163553974, 693222016, 410399458, 228314531, 767042885, 807728695, 437385389, 306292555, 22566490, 429312854, 22011847, 71282920, 844006501, 87646040, 245919225, 180690359, 952116932, 388396480, 29030569, 510155380, 529560454, 645952058, 225416807, 775240211, 729305065, 576196984, 110138107, 628042443, 901352199, 256138823, 483111562, 126130692, 764337100, 973093967, 72797892, 944814347, 213586818, 103561025, 269445897, 759791575, 932676608, 44216165, 600944864, 486412735, 428754895, 101254884, 477912234, 764292074, 3516551, 22429168, 883204373, 605922335, 769750547, 344572666, 195191237, 438003284, 259030451, 612443299, 54819093, 968387423, 559601696, 185879608, 429187605, 276672112, 257979272, 308662830, 900767478, 635417982, 689671034, 11304027, 513413011, 521692634, 962340196, 255300023, 476478602, 307726630, 539416601, 43164275, 578969782, 244803069, 720181562, 636513054, 479244876, 280309924, 7115857, 378467143, 589828990, 252458810, 65267202, 364109519, 983602406, 495169667, 486992415, 578432068, 313500925, 439324451, 599186314, 212634131, 503929819, 845681449, 166747247, 846859321, 381319275, 850149526, 827638855, 538742074, 370276253, 130968778, 421137521, 573270541, 396758304, 41113427, 179772268, 463209814, 604749598, 136422838, 439724604, 498140360, 106806322, 627613073, 215377627, 594216010, 701739762, 319238864, 431966425, 988273868, 164245501, 285446455, 25034565, 228840130, 963646409, 271568193, 500825984, 384530117, 523337908, 774964526, 294576219, 950952973, 637312582, 112034915, 840398827, 36834684, 774536317, 175478396, 120174302, 528130161, 730702288, 978647342, 669099148, 920151462, 27930654, 509617895, 683175854, 601502711, 74571205, 903361251, 954067769, 983205403, 205095045, 580482117, 576583434, 234637551, 477554203, 838154481, 730542169, 182591158, 925433733, 511387584, 158903370, 989547091, 787919260, 850595911, 92034041, 781701220, 547384309, 469206482, 893595478, 464144977, 201516085, 857229361, 624792050, 626520800, 184824116, 546176386, 439744665, 573230524, 922517123, 737271886, 796252672, 936745320, 402027112, 434569920, 627211712, 555169493, 527561537, 946114175, 905653840, 143550703, 25266019, 969912466, 740396556, 973082032, 566138770, 566545061, 765480380, 250708753, 964886742, 185170595, 493396046, 854208341, 869612176, 387317831, 427431985, 444026373, 198508010, 700968270, 688083495, 117827530, 630047419, 178824650, 597076992, 869138931, 57844993, 991663014, 713011877, 504355248, 325397389, 243071463, 269726319, 133250924, 111708797, 838846004, 695168163, 52137310, 989468991, 816408474, 543667706, 285658311, 135092100, 332483021, 85362677, 689938277, 391940250, 533815822, 948661260, 419383803, 53690236, 101518099, 452164178, 820467747, 877903144, 564644962, 486028785, 76681602, 110808404, 440751928, 9924868, 509120360, 34545680, 545490737, 445799530, 80624805, 364188698, 168401080, 882057358, 903972610, 508477283, 266687740, 711100718, 622826673, 641945487, 187958779, 538931492, 625327000, 960507405, 76865169, 644466347, 391080510, 710872748, 528277301, 701091070, 902118677, 179453981, 334557079, 367166860, 601577544, 553211979, 608858958, 695873786, 951870982, 840747702, 662809648, 885829514, 540272316, 804759339, 71771433, 171507608, 856532923, 25692439, 873616803, 596735392, 213979840, 207099713, 700401249, 703538105, 941400269, 121028933, 401622057, 867600449, 461992973, 831448761, 619180490, 318408659, 810853951, 15699090, 93771994, 26445953, 513121188, 534173943, 515217038, 122291984, 798598673, 291354308, 381102164, 610351020, 754818442, 912894609, 34390003, 871517160, 465451759, 880782233, 29972461, 199623863, 646743877, 264494003, 794577212, 257719444, 570343137, 459080358, 25705581, 331884432, 861392687, 695141068, 492410070, 158967899, 559574745, 722078183, 899345702, 345357312, 354954507, 32777666, 670661412, 749752109, 611322541, 453890715, 685486984, 882949055, 48697640, 268933258, 394498650, 951988124, 622785898, 697430666, 117193516, 213829500, 295826137, 210624723, 387780650, 599453291, 94045955, 437894977, 768371716, 338378596, 731236624, 849227367, 115765446, 633339373, 981596187, 577442880, 226163036, 432943738, 84933605, 801790983, 545463793, 864218580, 185419017, 972151223, 641761148, 854050357, 532562527, 121911710, 5628947, 53289304, 710681464, 668932726, 881403224, 435331972, 348605021, 104938044, 928489927, 11997723, 321051807, 300999633, 201134388, 660254743, 892891857, 175905890, 10492044, 696907713, 997445259, 67482268, 964871519, 737459556, 57275605, 426144278, 865134106, 20074769, 803251610, 256856955, 581284472, 562769697, 623671977, 230847893, 81254851, 428265132, 637397588, 722488845, 178597562, 977860425, 819593020, 308528470, 903870553, 193615216, 473006289, 664003798, 329470986, 325648638, 519640764, 363477517, 392126363, 94607268, 683231627, 210128665, 782588749, 94838347, 805360134, 795410076, 474374934, 426128104, 425711706, 611089603, 266189389, 784971389, 225292746, 947594984, 48549135, 148970009, 598649718, 448086793, 25962779, 148464330, 652957239, 443639431, 263670363, 687064086, 600962701, 646768800, 637376096, 448035814, 855700045, 141673177, 422968144, 347677448, 364203717, 582815417, 863585784, 690623172, 470501374, 393836744, 487168594, 451695584, 871484213, 874666789, 638205836, 947955791, 399614869, 61533799, 908831315, 558850734, 511472831, 515851967, 840485484, 477941874, 132145915, 417716690, 869910028, 168422414, 249946142, 284421652, 297763502, 586902969, 210933381, 1156154, 669370136, 637736779, 844377470, 91468566, 718392768, 769425515, 132149276, 755032739, 612897386, 451533363, 883632889, 494532231, 900514892, 731622510, 599341147, 174707601, 523930199, 291027602, 243208906, 262632820, 527244695, 247515976, 302450497, 115666650, 358816039, 495070280, 962920736, 156240293, 868843717, 179245845, 983372886, 326134989, 313156130, 913680854, 586068735, 533851084, 207575159, 519417057, 602408244, 399776073, 428067493, 227881681, 252007211, 169960909, 494333046, 760115073, 351247376, 320571348, 846055574, 933048829, 299643878, 565407261, 246665464, 965784352, 697304678, 926488395, 928324757, 722883873, 253652711, 667993303, 449157704, 442628343, 597496595, 795988899, 600853882, 895493328, 20445204, 546289095, 742779853, 886310565, 730466232, 66279109, 479688354, 731309848, 986095224, 810917717, 305794872, 400695181, 400912494, 179054887, 528043912, 206679441, 739000794, 173001664, 428144302, 272853532, 414671965, 143475478, 31928757, 11503511, 362055813, 152789652, 407184299, 259729289, 43580292, 425059846, 547692511, 567297410, 710079880, 79988748, 462076167, 674543417, 961067691, 805993517, 972638913, 376350210, 237030673, 738594550, 171546872, 419737328, 694416054, 520533162, 572425147, 653952873, 649084687, 306030432, 462286474, 372047814, 252697273, 759309020, 144907194, 932538600, 995197368, 214236873, 801282093, 509210026, 31807390, 382640880, 45228587, 218686312, 608911654, 946799916, 413338860, 190233128, 153525804, 947562890, 892263407, 171564791, 710023747, 228818746, 47578663, 725003332, 699398466, 8683587, 35067507, 592947621, 790389772, 65439916, 754025463, 660880465, 371321023, 557242266, 714529571, 117343452, 450835423, 150481825, 857478412, 675809722, 580496654, 450858109, 48827831, 729998320, 234589661, 153343855, 867152837, 799049930, 451073759, 325596485, 242681192, 197336163, 917318280, 480969978, 702390961, 248216, 434232457, 394657670, 566962667, 121898952, 81432681, 881343385, 847921104, 479365949, 553909441, 879195426, 136440547, 47126634, 807514226, 278210706, 690273690, 629414226, 327731816, 54430737, 688124998, 53836437, 674075321, 964562130, 187714683, 466797662, 81706431, 126229159, 611608901, 665904314, 308391100, 18587676, 110784624, 223952928, 898887290, 925043241, 333585156, 942087983, 271114931, 507817341, 721481499, 545644316, 683419310, 917327226, 475788720, 759617293, 105879078, 819418995, 358329382, 722024308, 556380451, 274502323, 480570439, 495381628, 461771187, 91312962, 610618958, 436642496, 126705273, 593397154, 101026635, 721346792, 909001997, 344485431, 564919464, 783799194, 448036692, 143556156, 595271889, 989027286, 866154185, 691287366, 711594547, 961897644, 232501526, 227306168, 745180368, 430541743, 628387298, 802615751, 358797422, 748359697, 728569367, 224036801, 776664567, 772008978, 26322519, 605425600, 767883587, 944301683, 525662722, 591489777, 871268383, 130042778, 972315045, 812944702, 956480390, 39623081, 857646946, 249832656, 739812897, 954634519, 489002657, 153759972, 869045404, 954314654, 680591021, 747490561, 604825668, 753150976, 682525761, 774246809, 945319225, 574928092, 333120240, 720641613, 600033602, 366954723, 780523932, 220400116, 121654443, 922752345, 31803624, 578424649, 550668614, 856169871, 77274811, 892799375, 642358194, 364087927, 433473848, 894650990, 133703039, 939093040, 467740210, 566788767, 643626544, 916114396, 576813902, 470379452, 14211833, 462064472, 129580827, 650717434, 617244512, 414904135, 628058957, 700966571, 603654042, 174306158, 221009206, 712183828, 154151305, 610148481, 578575494, 768526856, 867335285, 381247701, 553841836, 910818295, 170182227, 457704718, 651902084, 189300056, 190826064, 176810672, 148411603, 439451943, 912578056, 709545490, 738723395, 662558191, 587953390, 498315437, 922289274, 484789630, 426192320, 396531559, 429340545, 625402045, 170814372, 729875822, 233969432, 27299324, 558652451, 326742562, 577841023, 855350606, 324401439, 997125464, 35386300, 294590501, 41804992, 476581710, 6637947, 589961075, 161781054, 832359117, 139329894, 831689460, 167636667, 815478285, 375714242, 74334883, 480715580, 670898743, 341505638, 19747055, 120321121, 679633909, 552611150, 964558544, 19940353, 204547131, 765521380, 193702710, 290171103, 868817717, 851446117, 421538681, 216957735, 943118447, 137536686, 909422977, 929484571, 788316903, 408034007, 83099214, 723262976, 516576027, 460357797, 667427624, 76524848, 560265057, 345749542, 162296878, 606051742, 973490837, 131406258, 472765379, 429486857, 95304176, 231162905, 931476799, 625873742, 900760060, 608751432, 826961667, 652738404, 702698447, 800761313, 378553597, 360017559, 456236644, 156665215, 84127665, 369861427, 101556795, 582068012, 504637092, 741070667, 45248480, 961900374, 759680249, 577030996, 535973801, 810727977, 3840583, 981347410, 144913142, 132028491, 218789800, 494683110, 264801289, 288913597, 854386384, 241616422, 548891665, 580719803, 740025423, 782026590, 657565741, 895164696, 612702795, 675791256, 367759968, 434879707, 279702856, 984969518, 532686206, 202075904, 368779738, 560494809, 450839372, 700905867, 444440025, 784467830, 87056622, 718320845, 512644339, 715296344, 442012785, 829882279, 376889777, 79496618, 193960064, 186544717, 225850156, 9074067, 859248463, 675177186, 908585829, 41237244, 334074562, 790990196, 633853973, 690465111, 197973191, 479958463, 782585481, 698950942, 441725401, 823556347, 215732978, 686335202, 68626046, 668262698, 770945634, 836950677, 864652040, 395640268, 787475114, 242500562, 228857704, 127213657, 445301684, 638524724, 613021823, 652695503, 237476145, 981645071, 880698749, 75421941, 5492010, 691884966, 210825114, 768166822, 335508746, 27478980, 379643026, 351775061, 235073325, 984074496, 326294251, 248889196, 536438566, 773859187, 415605045, 265939463, 864191664, 28623703, 328503581, 310953135, 95383606, 530797299, 964097034, 492359887, 659739020, 422577247, 854143284, 987301563, 321166843, 548230749, 314296791, 490772354, 205554116, 848288096, 755732017, 118568201, 477712273, 292178449, 962803867, 312977789, 171507524, 980901509, 894039075, 145571514, 31138781, 256751074, 165569646, 465616386, 231671399, 610807127, 671284491, 252489274, 156829556, 295395866, 92441513, 773300696, 158442953, 677075423, 797725661, 249122586, 309495206, 526557072, 544488885, 608286326, 589444790, 614130143, 899243535, 280781721, 603307230, 743372497, 254004058, 964700538, 304205022, 14714540, 98048161, 632679511, 347510911, 960130045, 33099891, 644436543, 588614402, 780664825, 406140662, 698186265, 70125663, 562258207, 368962405, 842669283, 559803610, 691189125, 337869920, 286049016, 414844772, 434987914, 985417858, 851404408, 858433519, 890557585, 968451462, 949364370, 166066017, 438539124, 803197041, 173182023, 255356774, 928055846, 677975733, 616185057, 323854785, 205780361, 689319816, 223091845, 131127622, 604669257, 924091873, 943808803, 465493416, 597995518, 92417245, 664151597, 781928005, 37945675, 866785777, 384896645, 37464132, 862111480, 107545301, 412432735, 900982060, 828405559, 747283962, 689491450, 813809007, 217352229, 534359782, 519313035, 273460208, 936159606, 415675590, 984448223, 259307925, 315550506, 5780658, 333750190, 213024605, 630829488, 662571179, 826324455, 780456462, 972475962, 150224944, 540685368, 247904879, 770825722, 992827476, 369837187, 297545077, 143042133, 380448478, 483433565, 657924235, 743244452, 806798554, 797257444, 771905401, 864571357, 856139432, 414695413, 365109261, 318410005, 351585402, 774920050, 67382692, 421764554, 634397436, 334690404, 939909143, 427462897, 116009658, 8401472, 409974400, 923291879, 694244901, 446092897, 230669785, 372725226, 69803875, 260009841, 985928763, 952700138, 746618692, 243649950, 224182497, 613354273, 904756432, 874595750, 744254487, 646464030, 392637008, 70092952, 625771497, 69306656, 830994441, 100248443, 238059633, 45562279, 654957596, 774880560, 456589885, 889085739, 839459664, 147964170, 578937096, 33639381, 527448395, 249585147, 414763777, 386473608, 859880947, 876477409, 721326082, 242907016, 556137561, 249444327, 852609167, 416370985, 335844313, 575322487, 146020582, 690559955, 314713618, 571013196, 324027556, 660868535, 758659363, 761295869, 230846772, 746089087, 771977973, 571654176, 635358778, 447081574, 766173475, 669435032, 491730110, 967770540, 388024560, 738844454, 112607810, 715799590, 273825282, 889760818, 535318681, 88548573, 150479395, 234286415, 334249582, 258567320, 525892756, 361845067, 6964407, 629921941, 42923491, 442869644, 537343507, 193355033, 411707383, 728419604, 978635933, 565265114, 122584855, 551076695, 630371872, 232017501, 980583050, 129054490, 590246190, 329319586, 451295541, 804224832, 146024936, 402626912, 246303328, 556368024, 426797618, 820458411, 430288917, 658826211, 694010163, 788979825, 990478302, 436477353, 187875219, 351642700, 17869924, 258790782, 595321821, 388330234, 319320729, 698589887, 266395266, 992732519, 386112942, 799413185, 399557112, 829164509, 900482804, 154000772, 367801340, 698691776, 241042800, 312632835, 293280755, 112907646, 937494170, 169968061, 940390841, 641092301, 200341701, 97430665, 154358170, 936321902, 415457786, 510371340, 104225857, 949789834, 617919909, 205132253, 597867006, 253590488, 674354035, 573935844, 689558384, 197938415, 436196167, 719163671, 224603971, 653863141, 530867042, 333649366, 922336222, 702668981, 686347446, 463661607, 733862690, 845121230, 461492165, 740809575, 745739848, 160492264, 129627767, 827271231, 410851551, 125208955, 848655168, 314528309, 339626697, 675042648, 251407587, 893634565, 477486336, 464407576, 688132364, 307773252, 526254792, 296458285, 572275700, 830166799, 448740975, 588223473, 932513160, 194666563, 100768906, 558494451, 950667989, 978270217, 408477181, 779657295, 158630823, 8829812, 275590709, 624513130, 269668546, 23161534, 275174735, 404332188, 424915566, 764253098, 950236758, 796376178, 169259031, 278374383, 995297944, 663152731, 64916629, 191249560, 994383740, 169632400, 473595379, 962927586, 255665471, 184500193, 892542634, 605828929, 690348886, 271484538, 308339834, 813065874, 511513403, 340738508, 649035121, 313247186, 567958995, 169563978, 537828918, 752124955, 215480394, 127079856, 748578632, 673200254, 674919863, 165790669, 162108838, 72894062, 395935275, 923032237, 331416390, 351417061, 234937162, 620783362, 519786681, 990740993, 867711578, 787576359, 275280376, 629140373, 613847385, 492450228, 761796489, 433658017, 997518560, 320573249, 125019308, 90343146, 950564624, 690006571, 572105172, 956631491, 280507366, 513516427, 144688095, 482327088, 924771918, 727549500, 558053371, 503322025, 816908658, 519493724, 103467081, 948615844, 307976882, 884526176, 78904274, 828375052, 949673729, 727154767, 732825379, 938331034, 114108315, 745740783, 783930688, 426480113, 946464150, 151550022, 386145853, 133705807, 573782449, 905431814, 646930369, 167175585, 929329401, 538128334, 781864218, 930909254, 785975823, 799204552, 965442393, 945480088, 8345764, 954601866, 156350573, 678596787, 787893862, 452785055, 144744441, 986631532, 348106278, 923308989, 918517842, 669996235, 550781033, 252512826, 790154251, 693347352, 649440325, 59826233, 377453722, 84574553, 97161012, 543924666, 971319894, 785416825, 331080949, 467697426, 177994561, 30815459, 97269807, 524434508, 313055189, 967726237, 520288657, 586613114, 191343287, 99880741, 882306362, 418219961, 267801145, 98942382, 536659539, 861657828, 67069392, 621072913, 2397588, 565320454, 957253473, 27887139, 706335418, 523475213, 71387226, 431226100, 276266845, 246183289, 995898632, 126508441, 837919589, 622590056, 3154665, 521727603, 617850311, 830596081, 320312701, 275533765, 712298181, 380977808, 325970795, 403084788, 288117096, 483641350, 727964603, 385385463, 555665323, 709075059, 224863005, 130186774, 772906619, 623353526, 953380508, 414311926, 455350224, 730828363, 143080146, 575823400, 349376896, 371966405, 992058283, 930295935, 593879624, 615520852, 624376070, 265094981, 995383878, 553212155, 678450915, 238889661, 552381485, 60813839, 499146335, 346613773, 536158330, 384240743, 120636582, 71918633, 291520161, 187918405, 490458348, 914456038, 979611111, 788477113, 299931132, 431042437, 703588870, 661912569, 512093129, 100659307, 656886712, 794643923, 360693874, 529929658, 175607243, 533437780, 780981743, 174793678, 110522940, 696726699, 563623924, 461178364, 620411851, 344911500, 233187715, 2323161, 811886165, 73112891, 415536279, 7940590, 622178830, 88653950, 530791915, 687995189, 639328111, 596458385, 766712121, 209568009, 849476493, 630458280, 843999743, 63555446, 881265831, 876660109, 832999831, 221072679, 278144305, 960690631, 116554453, 951761854, 28669337, 208100771, 430324550, 130232913, 814890068, 330742662, 656731293, 392069183, 707969302, 885982830, 588233051, 871831894, 291049289, 59975159, 519135276, 109297166, 570669387, 745559504, 360989548, 48242713, 596357397, 711852687, 353676433, 847991472, 560129780, 62708252, 495536821, 848126499, 866395252, 83618012, 989624657, 110242585, 919472468, 183447171, 635118640, 867185925, 527481619, 3083140, 42377151, 23459389, 592912724, 841197391, 12334554, 590497098, 263363643, 508941218, 539415310, 742461561, 494464151, 9982644, 106778074, 918212941, 686181490, 833385476, 790438558, 423963844, 476150909, 893416173, 623979796, 366335553, 369097972, 307403465, 606881222, 620818784, 226068376, 940756822, 34336993, 309717592, 239435285, 647927719, 579702822, 463396257, 670272700, 786315083, 525851384, 416978574, 220592292, 157311823, 842763419, 803512621, 174332919, 969628702, 942213308, 852333943, 101147602, 427050888, 381803288, 316252846, 952740585, 133705249, 818541735, 606337134, 955639861, 605867969, 885707709, 499662981, 680533127, 259872601, 746546685, 497087798, 132191538, 866467701, 633503729, 125185645, 6474702, 867339936, 958540236, 916983642, 623709831, 83917056, 479971129, 223288269, 931802130, 338326570, 937047066, 642208011, 703032869, 906588406, 853375656, 811071920, 551933852, 153109105, 679163929, 563289652, 787034030, 19486885, 371014170, 131299417, 340996993, 159635223, 668828752, 708155875, 788136697, 266990918, 20997460, 764740850, 455524179, 325450287, 277103721, 637265565, 472974141, 399584283, 886335153, 996083716, 411608202, 482733270, 647841266, 314796219, 211330709, 667406149, 142500224, 525323892, 942364020, 645984261, 57248352, 237497923, 592475480, 263026902, 505253505, 826074972, 257162337, 86606638, 913124541, 99564866, 806888118, 850400228, 716637976, 626508592, 526337948, 506887327, 571635641, 874949214, 995615596, 242435369, 846606026, 605373660, 376751249, 454437464, 300489107, 607967473, 202524951, 61537372, 573285775, 677889619, 896299426, 446809791, 825931285, 43956612, 967207274, 181324695, 908710812, 947423062, 586141368, 153677039, 140320997, 48411612, 156360998, 620428948, 106748152, 334973020, 662740287, 160232025, 699806711, 295377960, 764960927, 257295203, 266360550, 303512604, 306579112, 144699555, 491707957, 422148326, 483781305, 677516991, 180020848, 965614186, 307731304, 181092620, 534577383, 43607445, 354605448, 248268163, 908722923, 716467109, 257273315, 440925671, 681198596, 850957738, 919074663, 210506587, 516250711, 575676305, 893032858, 670974538, 552070885, 769950498, 682564189, 868924175, 2533289, 1409204, 845132236, 589395179, 174211220, 846453981, 479526365, 271384104, 68834659, 439898202, 257661865, 389874486, 251159510, 323503606, 262956850, 5428366, 692646952, 966233114, 316948455, 551996548, 470253318, 75157477, 199107733, 435265181, 684299089, 802631579, 709637179, 18209037, 965159500, 805486626, 543261364, 671875950, 420471802, 498345709, 955414687, 202525420, 272502457, 629404228, 212370327, 321986589, 244778402, 817994276, 231367576, 247560553, 259038150, 690546494, 197428194, 70015140, 872382937, 155413515, 16741470, 503062816, 302385650, 556193091, 320035641, 154448958, 958681198, 583079126, 763020628, 699011197, 919799515, 339284020, 50583000, 67684848, 779233670, 84820989, 116853612, 216439168, 55106664, 510753841, 149837882, 735190203, 954465390, 892704819, 355210786, 649555502, 121235486, 143617219, 326844153, 854827572, 424752801, 599872105, 421342488, 561165640, 825209010, 107471400, 585393840, 769100860, 749859437, 859834728, 818267072, 496799722, 668779780, 343371796, 844506720, 382633061, 942315656, 49728654, 829991148, 289608421, 661830158, 127715196, 285537374, 708591034, 833598459, 859338915, 989509608, 507551194, 836435541, 589860505, 540697388, 424580528, 228129534, 765348488, 631528405, 923293653, 116582298, 8385396, 285976034, 468164383, 222922791, 188729839, 137548469, 810136893, 523018197, 533467432, 230925143, 91574910, 15479772, 607175795, 301799161, 802926256, 257844461, 714084892, 253847175, 811475316, 168917598, 665277924, 953050023, 718768048, 480611699, 686230717, 51972892, 299191202, 312041423, 973543274, 392675129, 591698166, 173314622, 872798714, 80522902, 913624460, 410855714, 752140261, 620657710, 458273265, 377989034, 873352482, 452858310, 274394118, 716886554, 307915960, 574252220, 304001803, 862405552, 713730588, 789109758, 227245349, 983834320, 342207049, 430303056, 820857612, 875151784, 514267551, 562448032, 739758062, 34493495, 563105568, 488136356, 685671873, 172153170, 333676722, 850808693, 853035444, 460148054, 847129645, 495162410, 326651678, 877994679, 769928711, 534895681, 83900697, 585652271, 832878917, 7239948, 744990657, 350653542, 69885948, 790956702, 581226041, 318640005, 557890167, 333098977, 434585517, 348620469, 96710977, 493210713, 957332457, 378637790, 395864174, 983386604, 907398370, 521681559, 274543118, 106402327, 698780487, 966373238, 65843212, 626467479, 37628731, 862549163, 424596151, 443800732, 13914882, 643815834, 32001660, 775948622, 251472896, 119839134, 304969922, 544723830, 567504818, 101309317, 478822173, 408676121, 362338973, 81725688, 639224561, 538788389, 723446692, 685542309, 699007108, 656898430, 444309894, 681707381, 865092311, 881051306, 771871491, 564704111, 993591974, 915284514, 477989559, 197571345, 876069716, 168045196, 303637752, 270143460, 40326263, 574093466, 814809686, 824026861, 537161721, 43478803, 3176567, 101921703, 78756634, 290004791, 407649718, 723739602, 119304407, 400503624, 913549310, 368511676, 536608510, 592217714, 16634385, 895905544, 357658866, 675583647, 212934394, 694596044, 778469980, 740435304, 105605950, 437018375, 803018100, 612126451, 193297579, 700511050, 76227316, 416270495, 997938444, 154465676, 928336432, 594596625, 237520826, 522099910, 701556309, 98128119, 894867217, 606092687, 750963305, 46863058, 967429169, 226504091, 231008426, 207595265, 871902051, 458312402, 477694624, 557719658, 652225979, 351895450, 535032744, 869432629, 374162808, 725897735, 914394839, 969671800, 635621101, 229410446, 522195085, 627552776, 948842768, 129858932, 743521783, 264371186, 578507804, 829228762, 610823817, 546092200, 876607103, 258083972, 886755687, 352450265, 893728041, 688744602, 543813959, 272778996, 369426150, 858901791, 373354910, 915984626, 393340221, 488219928, 95700468, 161991761, 131361555, 99608815, 442989995, 21492834, 951263780, 336188836, 80146702, 888897625, 233465944, 733383468, 485825039, 240717881, 4311453, 372985575, 358674911, 952992588, 478479311, 854469858, 471225707, 999430023, 457389761, 527499506, 357923585, 492208384, 41114516, 173643743, 275212771, 217484831, 10650016, 472052138, 361182038, 655000838, 826893606, 341190376, 18333223, 818326703, 244561484, 628439966, 972892662, 549738724, 794179241, 793090927, 433768911, 959619578, 114099635, 512296165, 111675350, 652285479, 235075448, 423941982, 451877776, 621641794, 464818261, 97374473, 851659097, 711439140, 488052287, 281479288, 463481372, 124072077, 626815750, 212898757, 344787834, 591005050, 291601539, 345999405, 18328754, 566588724, 105429428, 965209041, 441705310, 479742328, 187928039, 946690242, 813256680, 478236163, 12429108, 126727582, 705921916, 723558885, 532141331, 600306720, 656654004, 823492481, 948202578, 399612572, 213821786, 286803203, 10116710, 255493580, 283370034, 597578798, 24313459, 107533616, 994310717, 886869428, 345738276, 916780161, 774251059, 44787241, 457971273, 710694199, 125964266, 530027564, 193512197, 763609664, 908109801, 31727032, 540283455, 421780329, 977409113, 774063186, 637575033, 171439682, 719497025, 700458193, 263808325, 511101499, 371429904, 907928939, 10959042, 642113606, 377769980, 352540295, 772321037, 376347183, 130159082, 43851794, 211785308, 654459092, 744332931, 377526332, 731091166, 775923243, 396673883, 717143635, 447854313, 667409415, 699619255, 62098946, 649486433, 336559117, 707979379, 703827626, 769971112, 514540441, 991347687, 227818427, 972141858, 345614011, 456957163, 664917990, 565448379, 360214035, 955574396, 787471562, 928445156, 470434131, 701855376, 194773866, 979825189, 535843429, 201321027, 7960565, 589698727, 447712211, 65006202, 168561338, 722556027, 838145337, 257902887, 750687505, 805764128, 980618143, 512434767, 23998517, 121892576, 221696315, 760555310, 794673576, 90572706, 733123241, 888305332, 720071260, 461969553, 168906821, 520071345, 681962928, 280346648, 267828462, 615865984, 703513591, 777569244, 848520305, 993089106, 981748962, 723404348, 227632004, 711704313, 870099790, 347193780, 772226390, 892556450, 85295172, 12516194, 558498424, 12654008, 938281250, 651109010, 551125480, 716121016, 17552593, 896427123, 196973614, 410341607, 546625731, 484348242, 703896002, 839733277, 854512192, 945711000, 791974626, 216653598, 702983017, 959817539, 316101239, 766965341, 646129881, 931538107, 632554914, 493207158, 390511437, 664569204, 345142316, 972369946, 978220118, 810594240, 341740414, 576132636, 614377509, 711452574, 593803426, 963441880, 976562182, 230694730, 420941207, 721059215, 207464697, 833722085, 173122348, 488113177, 325369205, 405923928, 409836988, 235548630, 619953327, 4877099, 702034825, 930024284, 497564804, 779689734, 516544001, 601433391, 421112235, 878998937, 99971189, 476729648, 689992981, 382326274, 702889078, 523065055, 954663570, 282383474, 891290276, 839686765, 949245205, 860734833, 255753374, 861837879, 849987131, 457783069, 640437876, 68497687, 816417624, 82803213, 939363318, 259392244, 840014587, 343725509, 608689989, 834024824, 788542161, 465074, 42580260, 642138576, 490792804, 117946571, 278112362, 148539495, 538073162, 952948445, 6945218, 305111009, 220896122, 861621661, 156198187, 96712280, 745098398, 665167132, 896879607, 585142108, 452984674, 959960215, 871375242, 10645293, 719051662, 838987985, 70279710, 273392699, 112392824, 179357311, 615076970, 346301992, 17441968, 284461964, 13769820, 289558744, 531461323, 936049918, 238134292, 856389950, 310777717, 340534240, 77127073, 928605807, 187444089, 149701190, 693357431, 709864642, 397282603, 892868917, 705177687, 778052271, 466699639, 557216740, 857514403, 698911886, 881080100, 497490063, 187477759, 690672469, 209661657, 769426971, 528777212, 522392124, 268202432, 875857100, 723738431, 619906337, 378388546, 569621697, 364869012, 551698362, 406546210, 648058043, 807163414, 425959365, 982906782, 873040664, 889814173, 325482327, 906771975, 310562571, 117658305, 689838729, 50675355, 683655508, 894377373, 543438546, 791198510, 76428109, 471002277, 793763131, 131871347, 581696547, 864894987, 322457867, 685318283, 824070738, 788001587, 176346615, 44240519, 116281780, 249017024, 44393366, 249471337, 942972621, 579154145, 4175503, 214004605, 932074352, 593370561, 451656025, 255690127, 496762188, 173059507, 611266631, 175416379, 92814563, 221635434, 669369328, 74717402, 298843424, 35720522, 225591443, 246796230, 726851773, 726637949, 918701962, 755663528, 938957937, 159075733, 272142104, 122876481, 110437830, 389587318, 493603555, 453056441, 964676372, 363290082, 949829622, 577155223, 14271531, 277042258, 320768108, 832306956, 642864349, 197226029, 217842481, 359827870, 733464102, 512016890, 794239364, 745260718, 331781809, 791074124, 685306426, 685105079, 107789538, 436125904, 165754615, 119018059, 353315536, 878351776, 631461380, 755103043, 795347746, 136294711, 385890043, 190201502, 105488917, 59537165, 478711281, 101873108, 582793478, 530330601, 720701797, 442646859, 975899426, 882265414, 92959722, 743326214, 384312569, 700236136, 718290900, 753193646, 601846551, 87700710, 890161437, 19579263, 251195930, 738286614, 633443353, 98860733, 805524044, 528501635, 385401470, 846057787, 900729157, 420436843, 491512831, 273047175, 341932010, 885178583, 579783947, 107225423, 381038847, 307855032, 222511534, 432498000, 856497362, 40513, 744169099, 228983269, 406094650, 239065685, 825377167, 27008440, 957373541, 77594822, 728777450, 247236760, 438402497, 4196247, 123247458, 106138119, 260180394, 284725875, 226669964, 861052008, 134406631, 987658246, 324523537, 273142363, 682131146, 286788895, 219955628, 666115669, 963194087, 278001930, 933988657, 805662515, 633364397, 875015846, 644649994, 109775058, 474274049, 950759607, 796216881, 381260156, 419365866, 160370272, 202144626, 530495175, 221910153, 212042772, 1193209, 476189967, 630292464, 104318846, 736545767, 640587909, 76511940, 70181175, 476340068, 623772037, 904970989, 271618393, 922750469, 175707852, 986609199, 45321214, 673912642, 584375019, 324167698, 545365790, 986023577, 19420931, 91166002, 675762618, 974347936, 963389846, 124290937, 637077201, 285762274, 642215810, 737032458, 273004243, 808873146, 942516832, 590569766, 716143464, 975303417, 91642336, 453874032, 439581122, 527678896, 443897592, 861585775, 427659301, 130697443, 977026226, 22462540, 378989746, 152082206, 406966828, 222224194, 346018149, 739194190, 475148479, 210205484, 94439314, 322002136, 583071547, 46758344, 143901156, 645883612, 432871070, 462809337, 14639918, 90898975, 592222154, 27785636, 76306192, 912756327, 504865217, 741190925, 851027319, 106664181, 163322282, 358273756, 875270140, 361475205, 280089538, 686593739, 48381613, 578027008, 22689842, 908770552, 436062911, 581969161, 121141517, 391687516, 250784853, 527478533, 559175976, 975999753, 924586011, 626756651, 679614372, 53335103, 176327736, 262709879, 105901889, 659015291, 388795251, 790199844, 618305858, 174129342, 807311767, 242894347, 659403243, 542913509, 268929276, 46119511, 886665056, 261544414, 635737480, 856659075, 274359584, 400974749, 2358338, 97481619, 524192656, 832300435, 447620780, 608851006, 185002234, 144691943, 249151870, 865758449, 615923397, 548841078, 711792264, 376665767, 856229451, 2081583, 982831652, 977354764, 406209993, 562855988, 934850561, 807856719, 830479294, 973798721, 161511252, 331581207, 964219675, 522202865, 121505525, 716781839, 967510039, 503081216, 728391664, 302920176, 541913225, 977000247, 623771927, 152514925, 223299493, 649069457, 901838444, 427396426, 206787395, 278429292, 290014884, 305017319, 610151155, 255735219, 800478186, 733555276, 509311905, 687403857, 692530707, 614503107, 601744471, 708592327, 169333922, 932040101, 489826847, 208338244, 360564094, 827626356, 745212309, 799549407, 161498817, 751804784, 246016, 479006176, 317013885, 527603185, 764830550, 449864645, 122327406, 455962331, 617355603, 618600918, 498448656, 867979029, 231074394, 397092279, 664250881, 461703583, 660712241, 172773424, 491759517, 448489103, 645255563, 97665890, 167624978, 469280408, 718860617, 729460291, 459352920, 945580825, 366170638, 727606832, 699790135, 730273350, 662893402, 416948838, 25448580, 834260072, 793285724, 593359044, 126632653, 526685226, 502348465, 156763444, 843215301, 123856298, 990577675, 921734592, 742390534, 998878139, 747365358, 221032288, 856214159, 481776870, 663681122, 861797762, 89196708, 879600438, 132156465, 53629474, 404844087, 533219233, 94288338, 253094639, 459269382, 915709783, 418956178, 358959990, 604716912, 500551584, 85410865, 924558562, 316624453, 80454826, 517651930, 180841101, 363180947, 141476354, 808514925, 332712035, 687799383, 183006280, 348684372, 374149357, 584123973, 363264017, 395736783, 871556152, 842951286, 549745458, 368431802, 921019845, 18833248, 345929952, 29911730, 811108839, 266009616, 990416841, 187855071, 336120395, 867714961, 494838297, 922005033, 273189316, 27365745, 757771186, 738643625, 115365731, 405274203, 31479675, 605730832, 9529061, 581459265, 20372725, 757831904, 767825818, 793342197, 91676519, 398344875, 165959908, 397877792, 862511006, 851443834, 646302194, 680976836, 705894849, 704207092, 507407391, 50911916, 711657107, 244146091, 482332031, 220668856, 479381049, 352514220, 817864313, 813914691, 550604966, 36208758, 528186622, 819325079, 608529523, 155309853, 424334410, 20501848, 59632882, 515572646, 132559514, 89986671, 240592425, 535384009, 891932829, 400221506, 408615279, 27315502, 944509235, 318277108, 188191902, 943009582, 287229500, 592961676, 865904527, 368534857, 598679743, 226431971, 338658038, 926016144, 603685921, 616489064, 760375732, 241322878, 977055520, 85100040, 671804180, 265362525, 855814190, 312129736, 585690239, 138694584, 549659745, 692058504, 139534387, 313763024, 142334056, 751922899, 400637783, 901973232, 271358182, 887998251, 446785912, 245902513, 311218196, 770199528, 994318036, 740605571, 212596502, 498135853, 969248877, 628408895, 417521079, 26762749, 468673157, 668638610, 435437363, 579166175, 271062715, 232252055, 703190746, 544471043, 703742266, 322841107, 51264627, 655555531, 375060797, 200101503, 360831288, 628278573, 45469154, 874633939, 760311658, 764548134, 881761118, 111338798, 704393416, 40422478, 347906176, 173452709, 927678483, 267666971, 406050806, 674717575, 672338600, 914707105, 835538746, 604513870, 892168337, 482394495, 661446848, 681558411, 988541516, 999185192, 411357039, 517319631, 119598003, 243722886, 733228555, 49812755, 470485951, 341603413, 822264342, 586755458, 565556945, 710574578, 149515, 707179476, 535959350, 202224696, 423062280, 21518805, 813229392, 791167196, 382737121, 577007669, 917223151, 681195435, 494498177, 117720548, 691677058, 665646387, 385676426, 742674243, 493063507, 407090217, 449894366, 941213308, 898326058, 537151975, 704095033, 800365460, 496485285, 454267412, 25484359, 981276436, 629144502, 927238599, 110490393, 213840140, 303341220, 559872720, 49174871, 177888986, 565457596, 224185923, 293260683, 325692850, 713577957, 528382477, 861324702, 736682777, 282649085, 455510217, 43432099, 297822634, 105512708, 74842719, 113293360, 243591766, 499900911, 721636272, 890883804, 803940598, 132936700, 949882633, 111258954, 680655738, 764107453, 317686002, 987595000, 84228499, 691596146, 551191801, 521900865, 743840733, 815470132, 279834461, 605026016, 716399819, 534826422, 322732062, 915276834, 281023855, 56295408, 744602834, 388502559, 71091467, 663801126, 238090351, 220611950, 448652886, 950607188, 969872436, 294216738, 655172340, 390321870, 169643219, 20968811, 538993008, 896612396, 383471576, 185687421, 166315023, 440672831, 503972916, 259181517, 582374952, 861745086, 694912074, 15984428, 220240312, 83642949, 386569824, 650376510, 936522795, 705294341, 978980096, 985546013, 379077802, 717871492, 151281514, 101082162, 84747929, 444806870, 127453849, 538034677, 449601113, 696181021, 244184836, 436820738, 472874631, 375097475, 510451508, 944966927, 563196592, 309426677, 996293879, 647253948, 405073987, 592717870, 323656925, 964588435, 94556934, 110958211, 27285486, 677422729, 87805868, 731705859, 807187279, 801619417, 208979631, 465030053, 436455905, 470089412, 738920287, 569709180, 15560370, 585386481, 557910388, 930765732, 765048716, 214916441, 549189167, 899756892, 382582087, 600640217, 763731696, 110075293, 181688167, 534968650, 918843608, 944999659, 19307862, 767586751, 926675200, 247089117, 56224627, 34592497, 17456976, 441035263, 657431015, 126737023, 916173512, 388024367, 806447469, 190742572, 631696413, 606193375, 268549212, 759647280, 758556039, 712378284, 643030520, 444522032, 48811573, 243778453, 189890624, 90513791, 457906836, 215559399, 131185088, 494119367, 909622896, 584210792, 496675471, 289139571, 610222868, 916195039, 485283370, 726398645, 714132442, 686448092, 99308617, 841735174, 662141549, 333333856, 732977749, 807399948, 797056195, 770275472, 333995807, 145755213, 606827910, 938884955, 231953733, 162320961, 481385491, 209517425, 925744882, 719213758, 590432892, 890547760, 688963074, 233195749, 168734538, 187377860, 402821264, 303173408, 117808158, 357997451, 556359768, 46352890, 204239170, 192766419, 557344412, 277913889, 895224501, 595536922, 660064212, 54819818, 415989639, 750970411, 14924531, 713572696, 844397219, 433635398, 305990323, 686102370, 61882231, 775306465, 942520898, 343089537, 891639874, 650746501, 402524776, 348727160, 910305734, 249220382, 669064852, 370731944, 398119319, 561274578, 791446724, 463206497, 24570615, 459257340, 132019381, 91058006, 489817096, 499021142, 593827459, 941102106, 90163495, 818855173, 977681131, 515324281, 904148077, 14547432, 118449948, 194137091, 472084997, 10583235, 519374910, 58105328, 340005006, 417636488, 986800934, 208911700, 603640646, 859137537, 246260654, 604682254, 967601312, 937667933, 587342075, 873384022, 570140284, 186434901, 635617694, 166242132, 296424464, 762406222, 29224141, 855027071, 140253628, 132587592, 60899340, 81665032, 801548740, 298970014, 775675712, 797496434, 171852997, 152145385, 444171111, 333633350, 617449861, 864304811, 968616599, 135429047, 438547390, 195394328, 885216866, 489722064, 844274619, 267035409, 317787648, 628804423, 978597252, 916582154, 518413849, 183506295, 170532453, 20905738, 346432231, 399867131, 149236401, 517695785, 277830662, 138200738, 290143337, 954965360, 574401244, 672036946, 828547910, 414411029, 288723824, 908100252, 907358790, 921755277, 471324250, 933303828, 922507144, 385889772, 477495817, 551976594, 479727437, 657157343, 491475149, 449896480, 445396000, 728571078, 772904976, 367865843, 993591036, 722119036, 601054927, 379455891, 35650105, 706811227, 878824855, 477093641, 234122982, 460522874, 859348892, 392724201, 442655496, 214410519, 88521476, 706509533, 98941863, 925984075, 10407681, 540424733, 722515712, 322462280, 600787400, 819446604, 654838812, 877134758, 467307117, 100221168, 279007038, 591706097, 174180959, 335384604, 646736161, 424675518, 728984887, 675297679, 628418734, 859726215, 729614966, 336046972, 405680775, 587521269, 827759116, 251529321, 264173792, 17771379, 69915343, 512834647, 578839161, 744942962, 567114460, 267627349, 938905094, 22812670, 975854415, 491624466, 69695820, 239982258, 438584506, 412397679, 687403584, 580567651, 754189811, 231911078, 967679347, 439621451, 348744680, 228586321, 61121040, 522395298, 307921696, 325586656, 761764344, 749316065, 651420623, 600619494, 444498551, 426704822, 455477242, 467678545, 646342599, 281012821, 49084226, 556964474, 726128057, 23175683, 897189459, 618429245, 761702823, 908317346, 497184566, 799800044, 74437495, 503230997, 108135763, 219022357, 161006958, 55898386, 323448166, 26165207, 413839211, 442187539, 636352068, 778084267, 811173025, 203763735, 22934533, 742593615, 136852146, 69859396, 111946835, 38925668, 671449426, 36670164, 96620124, 916264991, 38301182, 742438949, 551633236, 448287485, 156917187, 685531085, 633458449, 443627679, 960276651, 510023310, 768587593, 345466633, 172992616, 913358981, 133786307, 153371050, 82677510, 804976580, 671718307, 657406869, 511499884, 415497480, 159951887, 840937264, 546066865, 362260903, 794951024, 213492855, 316581357, 337311942, 986856776, 127746403, 591811643, 991153802, 241803528, 10828176, 375935113, 600244274, 648161205, 963542411, 465020785, 48711746, 30697833, 695315561, 719440440, 801634124, 161124609, 731929799, 802370950, 956290145, 41997852, 533978645, 511144905, 390133654, 887236238, 587721155, 353441564, 119701364, 788384393, 509483268, 441879516, 940512643, 114659245, 611765202, 791954695, 64757545, 232290390, 194953491, 108254003, 514170594, 502338457, 589774719, 331378401, 241645736, 747105600, 746019964, 166493694, 681453406, 745202381, 396954668, 595592231, 706576467, 362892907, 610577516, 141760476, 992996867, 429786228, 540781058, 453464937, 177217848, 83353022, 215494847, 531343452, 347482029, 326625081, 335637324, 698388102, 19655393, 609033207, 673889585, 99464791, 926977749, 671988086, 104424475, 274651310, 218082051, 204172499, 939097622, 290469916, 680217806, 280663749, 157154627, 729417252, 560155416, 243990561, 113415343, 710633672, 318221222, 562430572, 433669885, 292664930, 763277842, 233930329, 65557672, 917305314, 105954592, 717323979, 752365042, 928446069, 690629415, 745440638, 685567379, 305261277, 921107262, 521952804, 280596955, 643567686, 573068451, 819383935, 140881518, 972936392, 928996103, 383852540, 649824819, 361060235, 480227141, 349472885, 180680627, 988517991, 457773244, 339753008, 939721385, 500037865, 198195133, 198291087, 607083979, 937639448, 527882598, 341757699, 239334677, 815144238, 135291706, 904482792, 535895225, 353177691, 733364631, 858398899, 602658219, 24835513, 521939942, 631484735, 476205163, 262780436, 981792766, 812408140, 686911055, 453893299, 796362244, 423292149, 996809678, 74132164, 197214243, 860957867, 873576574, 468300935, 879589377, 457736403, 651448843, 431701074, 847488201, 552605035, 531487521, 160021815, 495192855, 714543018, 653011162, 75426838, 665077507, 582966259, 988391256, 666456165, 103819673, 792350922, 595612151, 489626545, 861588087, 314166061, 934563690, 369426138, 717221114, 284751259, 431875722, 115494253, 735155805, 658487269, 673880534, 268050787, 861372446, 291998252, 214786081, 738951392, 600180476, 762880599, 1024374, 453689156, 37690504, 827851588, 835861293, 868906030, 16563290, 439698186, 325228194, 368498813, 289772187, 308039509, 330933941, 429918546, 673294333, 544072654, 72959448, 72028651, 911167067, 562210796, 586419533, 37984326, 797386669, 871571624, 68972610, 43550197, 341127064, 972451225, 427801025, 640215926, 388584727, 819820955, 394650459, 751529448, 252919590, 716977543, 214529984, 878189587, 815794560, 206746704, 41315542, 461919126, 313263316, 390823021, 901933248, 572704297, 601050309, 58996725, 514312632, 402932609, 437830771, 68953280, 80280522, 373379824, 21975835, 989627454, 150358703, 26538070, 449613852, 666605452, 53821906, 155280344, 702142334, 246529528, 253515515, 160358415, 162183643, 355828183, 250748528, 629463965, 110578321, 299974079, 275002986, 350102530, 359422431, 843571022, 834895535, 320377224, 661737198, 342039328, 851026884, 972567772, 405161709, 278981741, 277544170, 92918076, 353714640, 356765746, 757253527, 830193245, 839841382, 859976845, 163114195, 528550649, 682239624, 436311088, 112404123, 463414547, 721067767, 94120043, 244167147, 495767534, 621546367, 452167060, 594756818, 190337319, 97050716, 895311832, 436878737, 550619627, 141117616, 817452678, 794080574, 943389572, 670049456, 399142356, 4583722, 462531539, 756296709, 748496083, 887357168, 698178924, 375371602, 107801275, 292824672, 936466477, 681948964, 254591002, 620839175, 737164441, 947033084, 172997302, 127953302, 86847796, 73903786, 886983815, 89897199, 789027757, 249037660, 768731350, 847530835, 662253921, 338913152, 179517885, 286758477, 193582299, 323019146, 626290913, 359017592, 378298496, 624977736, 549091650, 47366752, 989620136, 799125110, 69658453, 344792789, 323772038, 650075279, 490614286, 254731513, 314562940, 250120397, 423522612, 70087565, 188487930, 834651432, 768465459, 470537657, 663913016, 43045852, 582325905, 59076158, 961225737, 945194185, 713890089, 435241340, 537289437, 390607418, 208276625, 893617927, 586410318, 974115566, 97276794, 906387099, 478198809, 796732167, 996386676, 272969406, 536577583, 603672416, 808216851, 76923553, 255260878, 290857970, 520534604, 606567815, 216342667, 779769461, 453683860, 148579320, 190760870, 111718317, 601420510, 852670244, 703190639, 634823452, 370928769, 29910391, 139733591, 836924632, 28438397, 88155626, 277132394, 957302227, 841769546, 960801896, 378127311, 263473882, 150343388, 17457020, 66034634, 32454002, 50669562, 525829410, 885854764, 189508788, 880301324, 324192848, 711098835, 369007517, 169754616, 656052898, 447244001, 235415106, 175132999, 690932938, 598243673, 830071105, 614543562, 87820501, 139305607, 797462941, 895103535, 630238695, 131363737, 270268729, 792732460, 816689588, 607317081, 526832560, 147822532, 505279939, 515836858, 295003839, 75087770, 98698463, 572407874, 914925355, 917481480, 317847787, 583255761, 941104527, 184535345, 168711723, 754681378, 784286493, 307286110, 255745780, 218837630, 195479897, 869621067, 473482843, 940488548, 921390806, 8792033, 96711364, 405831716, 752251686, 962756822, 282790886, 891179633, 244486672, 500425952, 631642879, 564637390, 785868591, 222451684, 511123952, 352789503, 873990836, 817348963, 881078120, 68518902, 253533307, 920737052, 115452709, 948388443, 21833726, 772542396, 638985176, 142062061, 578629291, 801399777, 310014524, 167005107, 453388275, 435808033, 887201016, 541278491, 243256817, 457103356, 379536078, 400283541, 316733346, 273284400, 498911083, 245416273, 201799116, 61264423, 376804104, 610028324, 387172869, 697448288, 960992965, 177121655, 70816331, 138509624, 842564685, 979258009, 796772991, 337751988, 543618221, 619616357, 941734319, 426067338, 880940113, 434366953, 683773283, 616835560, 251918733, 195489427, 74281826, 846998252, 51184803, 8067733, 295194660, 448258130, 744409309, 238009993, 333070573, 269739822, 240803893, 347462047, 801955095, 313569148, 987709451, 942719662, 874348342, 475653444, 853984176, 835185562, 804520355, 864496714, 278925905, 690388797, 483820616, 820418763, 996023516, 698562518, 265361433, 937448220, 713515561, 854019688, 246061360, 660755858, 573222969, 835710442, 372906787, 614318159, 416720442, 644260288, 737354125, 793259894, 421767685, 158391391, 811163458, 175838279, 372672817, 936567075, 153479359, 832585299, 272387106, 936560609, 880393150, 957863842, 617591214, 234552544, 889619659, 294814695, 431914995, 615148363, 360169556, 241732440, 354367819, 227376313, 772096764, 282564545, 890205121, 360768691, 397772546, 384617623, 255793326, 500130742, 329166790, 968955153, 384187486, 681817988, 386870564, 929400975, 620229409, 479648094, 82764116, 444649851, 514242337, 738610225, 625113800, 901401146, 589472271, 839912224, 866873963, 911217328, 103140497, 385521505, 644606772, 397320505, 675449505, 254149819, 97594961, 396679478, 640510534, 666649222, 436723106, 549062798, 273252321, 556819221, 707539973, 720959772, 895831320, 588571834, 124328088, 749313648, 605754398, 450487059, 925806477, 52051771, 692933059, 411069946, 488729285, 892354248, 327771364, 632748861, 930771322, 324337387, 297528170, 657395518, 337164766, 360841138, 386471820, 411333073, 886510309, 587375411, 519026087, 925962455, 143360143, 226656857, 428790357, 384433990, 899246789, 780210278, 7050897, 296105175, 111758016, 360313543, 898768793, 950623262, 715116039, 786091276, 759037930, 562731931, 478500024, 60689187, 237764127, 517128148, 187034840, 662177050, 994748723, 283123138, 327586414, 266048361, 804022624, 611955051, 776691177, 845250088, 986413461, 558991943, 707393145, 398842434, 433671356, 251566913, 349249313, 426383146, 225749956, 435486132, 537484719, 792013633, 922892120, 229071607, 17463369, 574798898, 136717553, 974418251, 967410101, 783125419, 99059182, 235878123, 772098598, 634956507, 221013695, 165296802, 860906185, 186446184, 395963092, 293283616, 359243216, 203982711, 793908499, 944789147, 647024685, 536079623, 528891609, 280202562, 386829053, 148078511, 163996894, 51407996, 676193598, 733993688, 905815721, 254410723, 638272410, 167601242, 922061391, 806834247, 48039887, 812555951, 376107111, 227770024, 362289182, 789046064, 75379231, 153121635, 499253167, 512092035, 337683087, 890664230, 472180796, 70182053, 19951568, 42359488, 730338269, 973353089, 373002658, 994994593, 786818619, 301115874, 279989441, 144789429, 407659652, 478735016, 917757291, 69553243, 626558168, 687805424, 746140936, 762567192, 375634414, 486651775, 178762489, 922331914, 268774964, 56620855, 172591412, 979633325, 658482876, 489377589, 190722863, 579242012, 116642307, 753054395, 486918661, 153897800, 750922828, 630497738, 882975474, 384557157, 56990482, 4759156, 920286552, 799106834, 231689417, 864704165, 168264251, 834048766, 148336051, 491716402, 621405242, 973344434, 613875981, 907643008, 239060708, 603253771, 207417560, 447993627, 516351237, 871144060, 548543182, 392894385, 751137580, 133821604, 272476374, 370100377, 621070111, 222424786, 273309037, 507382691, 703279380, 568641636, 761099028, 137837070, 942651578, 866048902, 178146494, 211038560, 170962786, 960453718, 988585374, 113206094, 61427115, 458178441, 295498871, 206995807, 575326032, 974634332, 834476416, 76166577, 238786952, 494704004, 436740772, 613792715, 61780590, 500423413, 155712628, 304725442, 303300267, 567663283, 465429420, 864727112, 716812793, 949340086, 117500566, 728538718, 521305126, 13579541, 107875520, 407998811, 188432666, 601180837, 761245462, 272975581, 154574844, 599839976, 115663342, 996128050, 604833527, 248959274, 305246017, 464317193, 274929220, 681971498, 338692757, 245533195, 387359562, 764414542, 230701683, 995996567, 954558630, 997171809, 684845133, 899287100, 455167210, 164526436, 284847387, 332024904, 87161242, 109411999, 426984230, 405175629, 870389147, 445064463, 644223782, 864912535, 768250728, 814233879, 75628754, 40751368, 906174057, 397257125, 163268249, 128454706, 915757465, 482222017, 78130408, 118524061, 145994523, 803866131, 920993034, 571273601, 540623652, 259436680, 793557100, 884492321, 770980566, 826915121, 999693163, 573234435, 36804669, 76615130, 746370818, 113933311, 318544250, 836052815, 625035980, 934567584, 91886017, 909509509, 958123961, 14737057, 704332384, 727923600, 972861293, 760508982, 134868375, 116513256, 337180185, 396945670, 21767762, 754822925, 746909091, 790680141, 755413248, 151936747, 30810107, 144774189, 197067203, 114994520, 181801007, 684005564, 696154896, 68781487, 199237500, 724180192, 524915434, 308947107, 993959527, 699821128, 222636023, 988006838, 474908248, 259854204, 987726543, 649011728, 499275615, 28081832, 408713258, 227135682, 111973130, 331589567, 526803909, 816237485, 636254484, 82374774, 355029334, 488002891, 609854970, 675614846, 948411400, 559262569, 936195674, 771670016, 921198042, 525511190, 276311874, 246781344, 418646551, 645976674, 196685938, 439168551, 939521508, 165223573, 997024676, 692408387, 651458861, 762008721, 90864999, 112566773, 461702120, 894812730, 784552634, 819518940, 270344047, 633951748, 336068447, 161025708, 827636500, 629319960, 42707573, 957049053, 885284887, 364662058, 836710411, 201212288, 444112709, 36019187, 30537419, 241668625, 277113271, 823252064, 82392048, 299725198, 527296718, 404209471, 204228822, 803985672, 708905846, 750541612, 365348735, 468632771, 462715084, 296872683, 523269615, 112265037, 985433973, 950398004, 972056125, 178309246, 217124022, 295559664, 705169414, 634467997, 92424186, 807892662, 380318638, 28486113, 141163297, 918239299, 419289636, 130528383, 515275633, 736555816, 243240129, 417694135, 124752244, 989093402, 955707158, 116245797, 151105897, 101510875, 889002161, 613384043, 492018044, 631858215, 255312592, 697572606, 245254267, 118544559, 706032055, 287773020, 623413969, 358732970, 731361997, 931488916, 385448515, 319821404, 873063279, 96908903, 47038245, 838130872, 314430916, 495539895, 68596014, 644168771, 572307130, 538594158, 484600595, 830128619, 948671310, 785229024, 568959555, 138586135, 539183856, 874360213, 173735754, 477577703, 495836390, 257851262, 179219092, 623818308, 870825928, 685693319, 535633714, 897061364, 952183888, 722737746, 599195583, 422605845, 923633794, 613753359, 481584708, 390321108, 144571490, 723224454, 87075985, 319499956, 315658195, 542270055, 112348050, 616050177, 776051954, 276146162, 307307723, 455311856, 676001650, 512588921, 642281996, 150497167, 440110191, 380799186, 367488668, 654835904, 402094106, 395367077, 402560104, 695640448, 762691885, 510521927, 138568317, 661864642, 669121434, 254896025, 629516763, 823188326, 290509733, 525258188, 401836554, 237640663, 480174807, 972799590, 440104933, 963084966, 898021752, 565719489, 584886281, 19717183, 93110788, 683488174, 647585121, 216923122, 706962825, 154246700, 954681570, 937596224, 421303786, 478622391, 399921453, 693133599, 315487055, 595913420, 748459783, 461828738, 977746654, 285738756, 973374674, 793895665, 925768911, 839048953, 500365682, 899397019, 537532412, 914335551, 873285026, 592591986, 766530880, 839987726, 478372790, 20321861, 360103611, 993891066, 116086813, 542545388, 911069811, 764257681, 649155176, 538756021, 831353138, 260046372, 223588830, 985851866, 678331746, 929112007, 850340472, 276272444, 732012678, 465462868, 394910760, 438847111, 589089342, 182095027, 322500613, 769715217, 399231690, 288960620, 970271192, 30910874, 846257122, 755262746, 420729340, 721579078, 330702559, 488441320, 798257176, 901032602, 146282523, 406057990, 290124719, 672639645, 665677167, 422752082, 445789130, 658708727, 481403747, 914243257, 19349446, 908958684, 774595148, 440802032, 740533022, 427366192, 265461493, 675127533, 185896816, 11474515, 595764273, 531245600, 169481168, 753813990, 53604067, 594400209, 256702959, 259488070, 136995538, 281748483, 185332884, 82603977, 710429695, 426177168, 336653350, 346706578, 174294405, 399491398, 719639276, 123081315, 177607521, 884670950, 771459306, 782806631, 955798223, 295083028, 342298637, 528153379, 70696261, 373860590, 494449705, 476146842, 577919990, 505601195, 752889311, 665474035, 478182392, 578965138, 917142938, 247534482, 228794794, 345165840, 623590363, 317386694, 4661750, 283243248, 211695035, 850363871, 347175949, 10997663, 902719343, 379541129, 882364503, 315327511, 850317367, 844818500, 630944784, 602320765, 416604774, 330246739, 844906676, 568745911, 979520794, 955070616, 803718182, 485971536, 876225609, 32648287, 607968234, 238442019, 552171029, 159252625, 931907728, 210181116, 375915268, 324420915, 844287630, 740447418, 255717783, 967928314, 727005336, 289945298, 19536491, 936084893, 106660224, 624511279, 926366662, 924566802, 998846243, 570576817, 554047338, 823252976, 143900542, 333465762, 892372903, 309892072, 900656557, 493144214, 832997023, 696042863, 368752300, 745197843, 90889505, 191542357, 359350776, 816827251, 354362266, 932781683, 988852853, 451778520, 158699049, 297906652, 984512537, 61883583, 866776690, 467275989, 317093036, 59917717, 832535205, 524440513, 316908649, 314068263, 6646797, 574893793, 169351405, 535525129, 737221083, 744486041, 841193971, 500062083, 960998256, 218928449, 387167999, 980807296, 3527067, 940487001, 431075887, 584464530, 443742703, 778018433, 728018017, 789218818, 636250107, 77487044, 351630865, 239106660, 770109341, 262186543, 890373720, 32817659, 692352267, 973333055, 562008715, 641134855, 658237024, 434164752, 484801446, 902654826, 891296473, 139853894, 593071601, 19324281, 214229613, 701730584, 255107679, 386947267, 88933647, 531149775, 244804734, 20052556, 272787217, 446207517, 189168529, 383133965, 292226531, 537440297, 421544395, 121329772, 108621076, 844923828, 420662844, 12003039, 512673191, 160687695, 125324886, 309178427, 439564187, 477578639, 50169406, 537098199, 60189262, 942271996, 423816343, 773264804, 331420549, 190992562, 243002164, 962947045, 950372898, 320042686, 787298293, 728392124, 447571580, 590027133, 136986208, 388444032, 372264621, 877824039, 888913131, 907638449, 760791179, 979533460, 629396461, 970185913, 319576918, 956819705, 512456939, 713993415, 509451185, 119105630, 321239161, 472667792, 950476775, 549725522, 715585334, 524546396, 381746146, 472936415, 174532762, 177823636, 305148775, 886481836, 413881421, 265001050, 288824636, 554383339, 430848904, 118876670, 260271901, 259905104, 907410142, 442763880, 862520204, 634536377, 209761623, 504889345, 76987290, 556301839, 42751213, 672549692, 309491374, 960396627, 948278817, 343097549, 339037812, 843300881, 567785735, 59868732, 567073785, 528314845, 379869490, 158813971, 379533474, 199279294, 503446866, 138287096, 32840355, 510112892, 685284952, 551470282, 806038713, 251760254, 210320509, 846318927, 968290662, 929734591, 938036733, 678553920, 12888783, 95239588, 824639639, 820381274, 42264173, 134143645, 512062321, 275155074, 530340805, 518312881, 625235421, 114278173, 845075291, 437224248, 197153976, 342515320, 900618263, 841817450, 224872258, 328881230, 489581437, 564809303, 387554081, 564029934, 791640994, 356304147, 274799470, 136630698, 516738417, 348972330, 735892972, 661544886, 357933446, 458402954, 457297053, 724695403, 702742952, 126989414, 322229627, 472462882, 541870552, 375995506, 80438189, 871612165, 292945664, 612905957, 529593863, 462118677, 401310769, 446084283, 837289242, 587257951, 576728210, 534706795, 144088707, 28261086, 230091996, 861232675, 94242956, 180240844, 314750225, 120819132, 460868794, 131566611, 123966216, 235761066, 444573755, 164203832, 687300703, 893313484, 302221288, 413012870, 163159510, 428017955, 956724714, 855439035, 591849626, 212270001, 829008132, 319542067, 711754210, 816911126, 921685461, 136122915, 539667234, 609599999, 584626553, 696816561, 769498436, 657810994, 610760095, 731669099, 353490503, 393022432, 747908833, 847246360, 222318081, 763058796, 369472956, 214775057, 121818269, 705754989, 955060656, 968262316, 734992163, 17479005, 965251975, 65161240, 529520365, 625840140, 774157228, 240261084, 38379960, 794520797, 588399161, 313597850, 389123513, 553975624, 572753307, 506136794, 91809356, 778279114, 943456760, 941135361, 895064115, 665798567, 9474220, 743583488, 733930543, 852928890, 449771867, 794601266, 680310390, 637379685, 823362414, 209886594, 313407019, 119969430, 805901591, 382710127, 272788972, 609038603, 761442869, 337240803, 358926121, 198780579, 573804441, 310314146, 979191476, 140850920, 447401664, 953822093, 816935745, 876850469, 357652142, 418485353, 923788268, 998818097, 790694592, 827067516, 576634112, 537350238, 121254704, 801642252, 126833197, 767327655, 589652247, 338943467, 34471123, 407700279, 898963540, 656042238, 843246964, 443216371, 447037409, 644220109, 74868739, 73574092, 788427898, 617033313, 83465920, 303254583, 200152294, 716709480, 906739069, 607092278, 936274178, 218215672, 18316897, 678339165, 382882070, 332891232, 492720415, 931423845, 139790093, 140247474, 739573267, 350596566, 253450566, 905894747, 448784057, 669011213, 293899986, 983242507, 852894555, 103297766, 977638307, 181544008, 594201243, 965037366, 119123896, 810998089, 616856222, 405963614, 45799732, 559618721, 197057967, 706311546, 30968852, 660792745, 552710060, 746353934, 614685476, 705228267, 828882530, 939752075, 478293578, 514288005, 814486878, 227766435, 363079919, 670426000, 827562339, 568567430, 829056078, 983366359, 950077673, 719189868, 16906496, 292384770, 917969318, 701467664, 961815491, 668554007, 86515270, 585322234, 858197303, 962839939, 327300242, 265267474, 117588535, 805633759, 753869183, 136586747, 508500187, 740987619, 498175774, 526038998, 332468307, 295499793, 939027902, 378035605, 470556576, 775207929, 874624229, 642017101, 980431934, 360026225, 237072326, 936710911, 380120873, 282420109, 608731087, 438725169, 817174706, 670944964, 829858379, 704796134, 504419258, 329000126, 952966445, 612616743, 560540027, 763293927, 203433739, 511149779, 208505259, 614336895, 707381057, 17380255, 281881719, 655411885, 697485324, 647181278, 105943436, 448233965, 879225423, 59561095, 616186873, 625377840, 37107638, 604192286, 594193138, 194626538, 923916020, 396542613, 604013726, 9089045, 699207306, 460816657, 626509010, 456858475, 19863732, 505790343, 253668109, 599628723, 719928492, 21461030, 529432811, 555841803, 962594292, 211402718, 33911395, 421337751, 208242873, 323715418, 540855928, 434439509, 521362356, 449056644, 746067051, 573544964, 458855961, 344175578, 473900600, 977516335, 66054961, 910089269, 931801858, 622025316, 924712911, 554005299, 43564386, 344988429, 401352356, 104061615, 242042604, 933028275, 736140463, 10376582, 85425172, 672357168, 590612125, 301600569, 811632378, 872311386, 272230661, 344536569, 909471881, 127432507, 858380674, 292082738, 414333646, 155687166, 92153296, 525280322, 492335924, 801469238, 296115792, 622288534, 42371828, 754536310, 495972346, 707889267, 761485505, 264835680, 292490171, 425615379, 19001657, 520168099, 651978901, 311861560, 122634317, 151003281, 662052221, 770020239, 894467555, 414114818, 270857553, 928365400, 374649330, 788694470, 536785119, 110654461, 168559734, 958951631, 927515241, 437352819, 166754925, 943504265, 3456380, 73852676, 85285831, 241684747, 334440199, 975858453, 886202535, 872656792, 589652312, 422560097, 298918837, 115808176, 457436413, 32806884, 319769148, 893598249, 62774379, 970912321, 509933774, 16807833, 216806555, 214269155, 94663606, 608018555, 777301399, 884471408, 211274834, 508002722, 72743859, 397836886, 890703366, 706329009, 750455599, 317252298, 735893498, 799598821, 407257788, 76801055, 476383556, 286895440, 587160337, 281215669, 897567298, 574240908, 605952044, 223952342, 106465312, 643869545, 954236454, 989711612, 520499882, 841463917, 953632595, 876897156, 496494932, 589166944, 167341648, 629488775, 782920198, 150991196, 745728825, 280553544, 737669059, 19722636, 213999915, 594658881, 984703004, 919063622, 593364555, 276055561, 988408350, 767060826, 595487498, 129906809, 118840945, 49743896, 367702137, 523151041, 798424889, 556921243, 255752686, 304377195, 947008231, 379959755, 389676322, 658227442, 489570949, 961175330, 449473946, 635185090, 671370112, 117637025, 162083988, 680715876, 415165701, 993955494, 39776626, 440678953, 995759861, 654150041, 511317860, 417070550, 464659669, 16627766, 871452884, 767499349, 909125655, 300098418, 54784258, 487114695, 169844953, 456373928, 570541313, 96453647, 531173990, 677705676, 937505127, 735904743, 466716664, 613044791, 72012012, 500735372, 988011909, 26503495, 527290221, 725320435, 723890646, 505872496, 698283492, 167649691, 127235192, 262742761, 66234906, 433544311, 210973443, 646612414, 495099278, 326884014, 870385813, 725037754, 606001076, 209375299, 252986338, 748663927, 365802401, 752626084, 663903448, 367967872, 728425461, 837895258, 400920172, 832544346, 963505516, 357670240, 14069842, 694548792, 727863102, 283869855, 380740249, 739607262, 270766305, 834537292, 887571098, 673977118, 398658349, 770309042, 860905553, 833995115, 539724279, 387740670, 15009121, 382351535, 176234089, 620085220, 634199964, 189729327, 391202357, 635950347, 562579472, 394715882, 312526924, 953199651, 662691281, 748287884, 409548899, 646815218, 389735985, 791678874, 948180363, 847587670, 340938857, 42354647, 942470530, 684907726, 259396383, 323126562, 870785710, 499501250, 568936371, 159888018, 89919967, 302321427, 543897362, 397827937, 341223417, 580204459, 32191927, 694875825, 299873756, 444465547, 459790645, 975055249, 776311677, 894815433, 749756494, 265756612, 844566808, 233122092, 168694353, 661508734, 263592607, 670947755, 988289877, 293879949, 519747596, 50690273, 519271478, 814153649, 860134525, 88967048, 348463667, 634726172, 514426775, 949294054, 201770076, 176722050, 383902001, 864127616, 498420276, 440679845, 765996895, 775384622, 200187198, 731312688, 801828132, 481119151, 987499032, 716086548, 158830889, 208012948, 313229015, 789069749, 851779925, 810559556, 123209494, 307684693, 568298717, 744707090, 862527111, 983839741, 812040754, 793473796, 917921805, 491061501, 772184029, 476819839, 136769232, 952792296, 733934918, 472477164, 829525868, 996041839, 667928608, 52951158, 113102474, 65162229, 711834498, 719380551, 676962431, 209162771, 790480985, 56775836, 261907199, 364205075, 203515756, 184871732, 552183643, 223954064, 387463730, 701915798, 477312042, 522437510, 572125833, 492311510, 485567228, 985766284, 752892933, 415324510, 358102237, 424399613, 691834597, 292711342, 542667246, 699612423, 64032175, 798894363, 844859285, 556659731, 74993008, 25198003, 283348449, 105419381, 783184744, 912620368, 113896508, 152777657, 334825973, 186216599, 264163493, 744158051, 576324185, 110336049, 18974964, 207447704, 702575764, 195200199, 31844510, 278084465, 307337573, 616283203, 601701427, 936242429, 245231326, 58693595, 153266980, 549203128, 670997360, 453361687, 945905011, 440756522, 700836432, 431255832, 111737475, 760236799, 964085148, 951421095, 949029122, 845191306, 680605132, 157524109, 730728427, 709821462, 726335831, 492561223, 134807987, 428285660, 639238773, 875518155, 78967557, 939693877, 248442692, 51446926, 10998912, 641821046, 161671545, 467280024, 772049530, 575841616, 735933201, 566388801, 616327462, 532141466, 521257886, 177993979, 421758155, 17802888, 796610267, 187034529, 981258019, 821331196, 509154733, 597322524, 153919047, 884970387, 895497975, 832101019, 117581389, 976291067, 966534806, 299026495, 129356675, 5818909, 342765905, 339600184, 165395244, 688824342, 480830283, 520684446, 988880509, 89312132, 178893900, 641001770, 695173731, 412310043, 652830049, 323289097, 598061656, 675424529, 345461978, 20823439, 275926227, 951519769, 683793662, 97217058, 748061266, 386845504, 908942231, 181025529, 86876218, 413440800, 697344152, 886619665, 839196470, 840898144, 335129071, 628770823, 862749306, 295150407, 898615729, 749900075, 289559154, 198367798, 976250975, 354960738, 850867860, 488331872, 591569066, 22896690, 376876201, 128836410, 42136424, 657474327, 507912653, 81791438, 883648238, 394747124, 801897350, 665459910, 981289283, 294231312, 49031760, 77168514, 756871752, 927508627, 539553312, 66692381, 501295162, 762155907, 974348476, 21031084, 76183684, 452588937, 90636392, 313456596, 437934469, 665439972, 658612137, 309610586, 854234786, 917667022, 302398375, 354071821, 504521603, 543363965, 939486967, 775958910, 30703227, 447238924, 104330661, 905085644, 806946854, 970478783, 965833679, 307543502, 411745880, 353427383, 953357640, 189504129, 952247052, 999691273, 993276315, 591700806, 801413969, 329148210, 656089409, 919666413, 177126969, 427789775, 267620511, 959462209, 735522570, 540372697, 109587578, 862872237, 738154972, 326867338, 533495768, 838816978, 960316461, 238207155, 532093214, 88919516, 535670419, 753502208, 697249605, 324701783, 563691398, 951097853, 427380284, 615646693, 494167449, 149853606, 631940720, 53826251, 775466556, 399239360, 48541802, 549091645, 765313129, 61631504, 316507683, 811462309, 165780186, 464246213, 388506750, 975381897, 854423181, 3832316, 297603942, 576581324, 372810348, 806367912, 153808054, 771377633, 181312057, 532846232, 52800938, 886578992, 111567688, 233730802, 914282162, 198062828, 398597791, 32132391, 501164413, 295058888, 884315583, 856440689, 435916795, 961651325, 314816350, 255522728, 534444691, 199814546, 899779560, 549318404, 33201038, 76711720, 917523440, 908911063, 265420465, 341480311, 896114998, 671932549, 169661761, 989036940, 764970741, 212563717, 180281423, 681382287, 626497904, 274617382, 869322036, 308970361, 347471631, 105780051, 420023801, 449324919, 182977725, 948476640, 597370398, 50581747, 541572586, 510420901, 297810406, 463384078, 874543502, 657551718, 919549513, 257046369, 195660502, 115803531, 388485913, 988237150, 298750973, 45402467, 557009491, 887259326, 399539000, 887466576, 452607896, 815423193, 50416057, 503538481, 31489283, 243306490, 579484906, 920013508, 641244232, 407436955, 285619924, 421979579, 787009301, 339921633, 734946252, 470309029, 807465034, 757897450, 997561397, 799393666, 476813807, 336074591, 304030358, 764199890, 85488184, 881519675, 335957660, 74100036, 246738318, 430314301, 744498098, 706262217, 281184288, 440266348, 233245696, 225011729, 218463424, 245072491, 55156607, 325962466, 430268119, 247412279, 310078473, 115163566, 943566906, 850486489, 319383969, 435752985, 952041643, 831236324, 362929165, 178815701, 193715204, 608562716, 612144481, 843801521, 708703992, 648749127, 879557372, 727437662, 392863858, 330527862, 712276079, 561752202, 720741022, 849956928, 339104700, 202661144, 208243673, 524947696, 853848724, 764046427, 10451583, 213125396, 990776445, 78436484, 175708678, 208415856, 666613330, 657704138, 674367450, 993652323, 427093987, 76826584, 479651708, 200415452, 803638180, 594779928, 14013312, 491499439, 490419606, 511467463, 172157368, 537886784, 248237671, 128899613, 403052109, 48108103, 590322893, 555097030, 6982678, 564845428, 516073798, 733998867, 379919991, 664869936, 442882582, 637677187, 46772222, 813061764, 455906540, 930213246, 559262793, 186228559, 410530, 420276354, 986909077, 151483941, 3918323, 845017547, 677573426, 924826481, 195356761, 808727273, 765365060, 778706428, 952265263, 299929128, 409626500, 897385338, 114950722, 223696209, 813568703, 773327079, 314700851, 269940919, 398935294, 588553622, 972412570, 116158976, 279612612, 110284227, 335325164, 335251975, 898805729, 711925048, 553878034, 438267568, 922030264, 669048392, 640419337, 13087180, 237202447, 943993508, 331764904, 831691971, 565569418, 659925996, 624042387, 470940420, 708584800, 547325076, 848562825, 407222878, 970647451, 602019092, 772208154, 287991988, 428531152, 673226748, 582340100, 941000006, 135181148, 295686637, 118909667, 382497408, 670611281, 460557006, 667184502, 385216500, 546631044, 947411876, 995555829, 202243752, 572556772, 465949551, 809063938, 684194368, 411727905, 706506704, 888054021, 455546833, 888756068, 677011133, 904199963, 949535512, 301058532, 190812401, 578847929, 813249122, 12402735, 418465032, 883039223, 413941665, 883408459, 213217690, 345883260, 671514030, 992813289, 678698834, 132408081, 295700142, 64499671, 588794581, 502135396, 863144694, 730072597, 206592169, 282693915, 697094390, 214384265, 228077924, 298062847, 836102934, 623645989, 587780051, 404925604, 982223647, 438884234, 275260743, 431197651, 404908205, 134819485, 848182753, 886142478, 730422273, 571368671, 181092026, 173413661, 468196834, 902673714, 257168444, 136004693, 242210225, 982479605, 849032285, 956370012, 598127051, 954542171, 81608244, 687571178, 563009011, 116387902, 96395766, 345154254, 406176090, 813915760, 644422750, 140728378, 92189649, 345103929, 568622030, 311815213, 931958103, 140180290, 898642094, 455536612, 933737728, 835083550, 256764888, 263802264, 893051120, 31590884, 271046022, 808647107, 739608540, 676704071, 136562482, 120922724, 475656411, 378987843, 501016765, 571002473, 629942005, 904303191, 517243735, 62962148, 706906512, 481998149, 896616220, 465799441, 691534758, 342395904, 740619128, 882237675, 723933292, 491606319, 919855247, 958916657, 233841753, 30781325, 816046539, 956065566, 812773827, 803738485, 754723016, 358339386, 570321752, 209403986, 567178185, 898456465, 840969043, 653960783, 133080805, 421598208, 848144514, 458779491, 289761176, 69967895, 881910540, 414687916, 377841436, 891132650, 610386319, 303578580, 346147752, 918222155, 70297189, 563506478, 618243336, 211089380, 208452275, 891653927, 107146633, 72636391, 722732596, 367517688, 293504737, 757390286, 567429788, 63029707, 596276398, 722918089, 107691254, 362885634, 520990466, 377148566, 880409355, 104721762, 84337840, 299956637, 14092779, 14101165, 446075610, 137258784, 874571163, 987261751, 212417112, 977284308, 49105255, 767407021, 479615213, 406714707, 369880693, 888022377, 890550491, 54254083, 904867026, 973196385, 829105535, 811540190, 643086893, 204013914, 114490695, 212905301, 544359199, 732354624, 200870107, 182175375, 130118343, 417034757, 784421585, 650157368, 891138741, 303800177, 329359530, 194119030, 382036242, 894145575, 410601938, 434023843, 570363059, 291592184, 313876594, 45946079, 592888162, 564142667, 899398333, 497502058, 647633237, 733514723, 842514679, 518042238, 311261412, 119670341, 928180788, 252354424, 447600815, 716819779, 256909960, 412344450, 637518729, 430600721, 891141303, 565101836, 135332897, 126977049, 728613646, 751178370, 597304832, 468885014, 271820322, 301701380, 471185475, 286225438, 963301994, 871136876, 673481309, 815064331, 604139034, 964468134, 746692563, 119441016, 18691994, 285049147, 743925712, 28545379, 460216703, 62528231, 197424425, 775876770, 560475081, 771381290, 884804448, 250617066, 451967927, 904564368, 775165295, 743237986, 224951487, 231498521, 753491180, 834149106, 476778264, 297357201, 208084572, 545062759, 449046075, 991569871, 140626904, 628502101, 301240067, 176916147, 358422534, 614570287, 990157268, 429349498, 624748240, 324664171, 412316808, 858835874, 689800651, 736458419, 697561588, 680982850, 357277360, 684496641, 881243661, 945584551, 365150940, 434797101, 847244081, 971061685, 701151610, 990329021, 203429844, 231926630, 531206581, 870913318, 852314937, 414017269, 920166163, 533644455, 949630277, 572112912, 231195026, 6547397, 751428992, 586739435, 244707134, 300870928, 479483326, 963517796, 834663459, 358486783, 240875851, 169553993, 597095033, 327158193, 728962210, 914207635, 886034071, 514158321, 688597229, 680080438, 583585706, 578485912, 252001814, 982561599, 381397579, 89003898, 785736960, 250074484, 950336619, 476079419, 126977934, 928180152, 698519071, 973472936, 444975283, 789488361, 977784573, 257761103, 476487317, 410981030, 287844304, 561054345, 32056223, 20390499, 910021845, 928114181, 127088141, 69004961, 371051794, 511946710, 390598468, 163987748, 544478383, 388165546, 869529674, 192840898, 130685722, 806858826, 350290982, 672024404, 753612687, 876829043, 840521663, 43183007, 814832806, 658046986, 438777730, 101941879, 222157127, 159572245, 660394665, 81381710, 570606131, 685143200, 153447097, 155436544, 611098425, 718478673, 502098346, 894053727, 898352106, 633116794, 129603206, 599021002, 297204959, 708762932, 874306112, 132197909, 832678501, 411984339, 615008456, 838195410, 66777327, 252858184, 296207305, 843384107, 184420926, 233945654, 66890118, 319725592, 984513001, 205440368, 279745939, 922547380, 184631112, 42138175, 96301681, 181742900, 84297565, 428897318, 997652112, 545342626, 932308124, 407750118, 49575286, 982127167, 212169293, 926147900, 870358469, 130369738, 472604697, 310224195, 304817587, 877637123, 742415409, 224025537, 982468267, 960271444, 820025516, 411598905, 231547028, 287750448, 720316206, 57029250, 856937080, 774948365, 581289135, 857678711, 93388707, 837698265, 576382813, 866022419, 839308297, 922125107, 787114483, 75328672, 16489896, 585704118, 660826884, 916719848, 663239902, 396522650, 441173602, 722781607, 277883038, 218317500, 379506775, 894481454, 461235399, 451639295, 322178138, 981976819, 423925532, 249335646, 341039591, 999210597, 326902352, 664833066, 760927049, 976070355, 594535747, 831216937, 560466311, 911540174, 905281270, 492728966, 950295655, 398622966, 953635405, 558309174, 139904339, 20671135, 247541452, 713666265, 8361519, 710798900, 116485804, 193857390, 597377179, 258902848, 948579454, 69440731, 946579319, 2265382, 193749702, 229376411, 776853730, 533974475, 409631752, 847430402, 757443839, 520404804, 103764451, 473733428, 558999885, 500923996, 954216038, 867248129, 477270663, 954769145, 817819321, 240560408, 695913312, 780032670, 527425795, 173136576, 739018705, 714606181, 673339781, 45497745, 230739980, 543189635, 342970792, 362867680, 533823151, 249312475, 78215746, 33915453, 376571212, 101033465, 656125773, 130095038, 411341071, 755180452, 698409281, 102561700, 702309645, 64613070, 702874085, 388112741, 885591709, 812702224, 715539839, 300308961, 900732268, 600389889, 775392901, 556118828, 88168195, 466574043, 80856153, 842994392, 4583641, 827205363, 978758205, 660620716, 441209059, 324296670, 892489584, 940667338, 639369629, 296063492, 986386841, 830754825, 704528420, 693108722, 113311715, 511435803, 893242780, 535783395, 289063858, 568071469, 652699778, 716231519, 333335304, 758177376, 27591879, 423768880, 39719083, 879564778, 238625534, 177397666, 231099984, 32568932, 482934095, 99860028, 227161885, 991001605, 408479976, 716847061, 215184617, 866043713, 865890565, 139484981, 797963486, 569219643, 725019594, 776853298, 992921007, 705858682, 771937860, 396605623, 220433436, 47852181, 390324219, 272969931, 131066577, 224532035, 741271075, 370437321, 129375791, 816589975, 422458173, 319300426, 353635387, 563732529, 906104335, 970766096, 97648631, 142639115, 743680399, 527157912, 239648124, 239005714, 645791763, 125356798, 144519145, 467259023, 498076991, 999340242, 197636970, 409844576, 202797846, 682601535, 217157478, 656419401, 48141233, 165232869, 667004928, 503059641, 357543579, 873575232, 426531783, 42941538, 376939492, 675657597, 758124157, 640179225, 336396543, 514740064, 22964574, 767287186, 821756396, 815012776, 813279315, 761752103, 968238889, 195750726, 730971856, 792088753, 129294017, 683088283, 35414246, 255002724, 431016147, 671931477, 728147022, 977271626, 959356496, 4790344, 609603076, 208809922, 400700337, 171824719, 425465024, 670776606, 172005012, 516337363, 686256572, 907370327, 91085675, 436388137, 488145393, 880734659, 610511286, 751464567, 563707442, 836282811, 253265744, 245676338, 30201573, 913626696, 831023606, 326086253, 743151376, 282206626, 504392870, 655660368, 892568218, 611402257, 115556955, 604876345, 171738241, 54155100, 736313902, 474010192, 956666935, 388306085, 459128566, 263603474, 243530457, 289113459, 155384095, 725314131, 774874993, 635129362, 746605728, 393081803, 208309629, 165808091, 761123838, 997182866, 599474840, 507240992, 224067826, 242923200, 205280086, 150532660, 147932279, 528378440, 805160862, 667946629, 930600936, 189470815, 567338284, 86845250, 326431625, 180882533, 518970143, 872213402, 888348464, 129048875, 210878772, 16489676, 278697808, 584778734, 221442637, 202020118, 584949486, 316104414, 359652295, 368472798, 787025214, 236584960, 264449329, 86527102, 154567192, 664733880, 896096046, 62268156, 436256321, 178587196, 681236936, 69210478, 253842376, 540141637, 258532435, 818578741, 594434060, 608332089, 303931207, 59429220, 822907584, 583621975, 407298574, 581165429, 297681723, 331824607, 11534055, 597065996, 202085062, 771477527, 608681042, 255178734, 928094380, 23656829, 724936428, 556624904, 914237019, 82648936, 858026497, 246644599, 999277441, 210515651, 122506320, 982960323, 278207728, 258231321, 225809205, 429708661, 883409137, 504554342, 26484258, 675376588, 844767712, 768854266, 202947894, 930225779, 214026472, 505129119, 162995393, 528048897, 496316111, 105749096, 185910192, 477059644, 506201771, 596288283, 392816614, 582809600, 348188207, 65921209, 584463722, 346011727, 375965092, 934433319, 659191893, 841640733, 308455791, 471054405, 803925837, 966548518, 960831385, 689892992, 507728723, 461713105, 757181735, 159639657, 753543514, 618794641, 870737604, 493271536, 235388545, 304465697, 993215322, 205568908, 855615744, 283319489, 478511729, 217902688, 824862135, 907807679, 720178684, 757285318, 245007131, 181357259, 35828153, 604205358, 128848126, 660869581, 888251322, 634781437, 217917617, 990262202, 179936655, 685350063, 132111885, 946376281, 459047745, 699483582, 257256485, 637147668, 367002290, 266218943, 2030007, 118947520, 986055110, 435197532, 730483786, 214399429, 893617634, 613674228, 259298255, 650614957, 973260394, 490327956, 713185070, 379033658, 263586113, 738941625, 387911232, 71769011, 54236225, 933027517, 677098429, 518263429, 103914124, 810897849, 445091269, 827969670, 682765138, 801651313, 540961625, 473820476, 278216777, 16974755, 837642412, 31723303, 330476297, 195427826, 285660518, 153410032, 972460180, 749062324, 650544434, 677270911, 766604115, 73763290, 114958429, 598959321, 730858523, 885179050, 842067913, 861612634, 649588136, 662899544, 760558481, 149427074, 550284434, 294587954, 751762644, 646957877, 354612797, 235974218, 276053720, 126313430, 566837170, 191204178, 446907343, 586293832, 672793530, 796865014, 955462722, 657228627, 862814843, 830698159, 809619681, 183095272, 19828736, 634608843, 985359047, 928216511, 183863892, 594618098, 453635506, 325001219, 528880264, 362443933, 190746277, 255970892, 309764971, 544585284, 417749964, 801161656, 760782002, 891272485, 172757584, 381177656, 517155189, 751572616, 967107908, 962876253, 527913821, 125134241, 291489580, 768393388, 62924278, 562973971, 633728639, 499881522, 337610463, 158522706, 395671048, 220381046, 926001752, 952603843, 506660338, 543728434, 121885088, 172974342, 245731622, 558223148, 913682676, 164003565, 332682473, 300476371, 638046018, 188028594, 867998990, 584064436, 703115840, 961139001, 46141899, 858559334, 265683289, 393919242, 636879368, 192222184, 201458499, 658044687, 953591673, 116464143, 554663729, 223627057, 550386785, 84688652, 646363983, 48320923, 105122489, 935221857, 20742484, 904894418, 250687797, 113535881, 381689593, 932999097, 187944340, 213849002, 312079026, 641501017, 261273056, 89366730, 889342046, 121060035, 351154985, 793476450, 248724500, 303403362, 163784503, 26514412, 649795769, 585371711, 585674874, 512599993, 285150422, 432638017, 355681071, 326808211, 684666386, 684478616, 960206505, 240456660, 304251295, 664444170, 388128966, 257182884, 158712343, 998290218, 466309530, 174396443, 507206860, 87041084, 692106863, 878449246, 735077689, 781091348, 998375954, 431304402, 383523386, 117085999, 723289199, 135978866, 533100373, 340800733, 205195002, 63079632, 182657404, 591776657, 310536285, 312340017, 792483122, 846364382, 24769924, 691101149, 81944241, 252404931, 237949466, 656399950, 490285228, 576342256, 398137459, 35874901, 561538045, 221455055, 282832928, 54404898, 284522292, 951875996, 117099568, 601782802, 908093649, 724981066, 577986176, 646343213, 468532819, 686786871, 631255094, 938859714, 622292471, 372023813, 356007941, 346854247, 411159386, 255903176, 353580089, 257617468, 770713534, 152585464, 78517329, 857443150, 938547916, 677658491, 693810380, 951895216, 308503521, 746236973, 186845928, 762532657, 166236847, 696099633, 966811116, 721317042, 16687430, 264318217, 883262188, 706911033, 638565565, 942541098, 567585761, 609179505, 508948191, 650677937, 759548383, 144639776, 749081164, 952788006, 377413675, 486821855, 466762933, 7904996, 666493491, 92908356, 247221583, 329306874, 636223487, 527914997, 242635218, 46580241, 643053436, 317703974, 249856518, 276660651, 942692175, 679837872, 569182751, 674262998, 731472254, 405366348, 536196085, 259662745, 727623563, 974974856, 565204518, 635521448, 853245751, 385657278, 67599265, 244982914, 667048266, 89828829, 842302405, 142472648, 626057012, 413353883, 122994850, 409758938, 961483048, 378365297, 378603784, 846038770, 952304517, 201403446, 308642801, 175745593, 759720426, 73939504, 449160393, 877998196, 861521679, 673840279, 994807827, 624707379, 972330811, 655553591, 260731553, 579376455, 887451000, 172410285, 436744762, 62361816, 77697038, 933582610, 501773340, 701582842, 387129712, 474410874, 997108228, 428447626, 740553556, 224198377, 566358723, 149452225, 243958603, 751593673, 152855701, 680140825, 594997425, 412025102, 589632526, 867811928, 110395156, 98908655, 130658659, 100438662, 991359944, 532578635, 548712132, 271879011, 940433787, 990912221, 458657071, 606871004, 983458964, 211567948, 159020399, 821999299, 520780283, 496978056, 252487482, 324286927, 681048351, 128935634, 891596724, 634460530, 718957372, 707769172, 143098210, 633197994, 313131853, 483448494, 597232117, 467521193, 395023894, 739179124, 149548917, 169202442, 928107995, 705839061, 464143899, 664310763, 259313177, 155391582, 620281021, 425795624, 864585616, 787087402, 960917107, 95956244, 563744231, 447571574, 959322408, 151269062, 541906624, 415395072, 583261216, 417375611, 640088268, 316479606, 375655096, 995985898, 807861076, 876572136, 333019152, 805541028, 583967885, 82599347, 420058816, 904910933, 368127611, 647897735, 581203968, 662248775, 402438291, 791426, 752615004, 797738805, 174167875, 195533990, 142772538, 816530397, 719338174, 916369238, 338012455, 986458160, 635640315, 914722406, 238641187, 389168399, 530758178, 809873696, 505113560, 675141831, 215478921, 128449689, 311253996, 399957825, 883812367, 18525101, 437693952, 823008097, 468600903, 257222792, 769885503, 443750931, 946438791, 334558418, 439860810, 698972947, 119822696, 852464937, 530697642, 463623763, 652372130, 12503148, 212032010, 631734877, 973519499, 26985490, 787691389, 324907895, 557313724, 621353897, 755975122, 656726262, 213040043, 815047995, 728944243, 815412185, 575456948, 622788678, 50702850, 436441612, 546392695, 447601757, 173388295, 44015111, 300993893, 988817910, 481025588, 593567388, 174005837, 828472843, 733846271, 650822019, 673763646, 503729649, 897066870, 783661845, 39591037, 133644090, 480984905, 181913774, 65910435, 637895007, 998970277, 313323352, 945400323, 67467005, 806557254, 768482091, 105421703, 913562329, 176580161, 479459106, 842893292, 818922330, 523552584, 215215395, 633548905, 131128515, 813382015, 149370537, 222501577, 929078373, 971193332, 191749431, 142662075, 84861139, 753718623, 930122460, 360244109, 308197949, 750054106, 786402460, 777591590, 200754227, 607443968, 546876224, 822975154, 563561304, 303723025, 908668409, 565709736, 792559169, 188609733, 857194742, 435265637, 615300871, 607343890, 497332375, 413573408, 169117975, 295987183, 748292576, 183503048, 785331492, 310680085, 277836283, 198729122, 924617785, 393475358, 350007516, 896490708, 319491765, 224514190, 2244179, 628425806, 714461220, 331064990, 964914635, 614053586, 428998099, 84768388, 843417146, 627569821, 458224064, 64341650, 896633472, 134988301, 595879806, 848286477, 366981137, 172553581, 548247118, 601086680, 559954555, 655056565, 132070085, 733145632, 545190418, 259411746, 93534363, 158888992, 977745237, 193327966, 436954392, 412977656, 386520370, 363635025, 136833040, 518206252, 464385622, 131338816, 368825276, 99228806, 57735726, 167091471, 299662790, 684656492, 339505011, 610128620, 494801078, 92169095, 918551074, 797224624, 972607493, 703468036, 175465361, 156940041, 958014526, 409138230, 564339900, 285950188, 380228517, 337485284, 48215442, 126500935, 873282743, 193551333, 895221629, 252172404, 441930173, 789548329, 169068967, 120521563, 537013000, 319956407, 189519569, 467666654, 852223363, 374365455, 429923210, 17109350, 337363407, 752437955, 591146271, 542104638, 61065793, 158461478, 392268394, 643411740, 876067556, 459223846, 709188482, 177112092, 977934806, 743052813, 642493831, 362309016, 780337072, 339653041, 933105726, 110588023, 779453876, 942906819, 356312447, 645937833, 957905313, 142537746, 218295348, 164778989, 415067747, 884208885, 898749069, 739327510, 58402606, 304702499, 966536765, 34810346, 158816648, 706103168, 328829402, 857472788, 890322036, 295174417, 123424822, 630335052, 971008174, 5962862, 812927726, 101995930, 151908502, 942858141, 804386572, 998564097, 731157474, 247284541, 720379115, 441372935, 551414666, 674672810, 247156893, 388070725, 383672980, 782395868, 315587523, 448740364, 279915448, 979557971, 466573195, 814674644, 557018322, 755349395, 846618941, 832238825, 959926420, 522010053, 587485939, 877198731, 273589818, 279438433, 886370588, 731106472, 461412299, 761900806, 677138265, 721154867, 107385697, 717218822, 522873606, 39393126, 942970627, 342712961, 329320973, 941289585, 220045125, 144687520, 284525048, 450111548, 181252647, 432964854, 457666288, 454184833, 615131103, 841555969, 437863201, 853189516, 239304563, 269944162, 607336332, 94449398, 247211991, 121114092, 793087106, 50745671, 274351343, 723846053, 49461613, 104895632, 831643846, 972162556, 628419106, 493740685, 624637223, 743371046, 773741067, 314115526, 365920237, 213239792, 538713922, 477159564, 859798467, 955872177, 791114268, 360661326, 798918244, 784216563, 701734029, 543828757, 980784506, 341725015, 574226595, 370672130, 503996345, 627759717, 626615912, 25309475, 141883114, 290096428, 758555150, 829128704, 507032790, 25658708, 845084210, 121384412, 175442665, 959910730, 192674811, 776885307, 745144536, 681536390, 174993133, 468859420, 456246618, 369145726, 263303725, 870688668, 890030725, 584181315, 806405378, 334246033, 750713037, 145046838, 742361286, 820260797, 169752662, 127368007, 754654377, 389361616, 384609262, 539444572, 596046591, 626223301, 568055249, 288912139, 518256272, 281356767, 203216585, 325014354, 286207707, 658201844, 266195238, 598521066, 590461074, 783772991, 401708925, 430481673, 539841505, 773436513, 233498060, 422277795, 864989643, 836449864, 961565292, 761431806, 138287974, 170380238, 405278146, 582274497, 189093472, 477947325, 219653398, 246553760, 827192980, 972534592, 895231209, 842039219, 744985857, 893554263, 334680011, 159361077, 370533659, 93619643, 499398106, 884680624, 335426477, 69322060, 789831287, 979645120, 293506005, 64495216, 198941211, 308584588, 845859581, 493575756, 327450637, 481513585, 819674394, 102590798, 827043683, 338481934, 548713702, 80973578, 744659208, 874530852, 788817964, 50496128, 703864005, 751254264, 319258050, 866745972, 647942991, 322422552, 183348227, 569870962, 621305480, 459278329, 564764967, 463711175, 305858631, 653584497, 234746936, 845208297, 814633153, 458167417, 600679385, 170112023, 287262089, 385258931, 546191209, 904583437, 539161604, 769059042, 906840682, 873367196, 411950787, 998849925, 381651628, 413617061, 649426797, 866521887, 565242590, 549208504, 853435732, 530959414, 983783958, 326914526, 763873004, 720740440, 178922211, 306693568, 978377083, 138848429, 549685882, 221306447, 232554368, 485445435, 955348492, 717188464, 448492786, 115469346, 216387767, 764015467, 215531644, 926847709, 570358890, 522393445, 853739, 111103992, 289921689, 738542232, 513946463, 520298127, 574356567, 782181535, 937011048, 235108186, 295495151, 530650995, 89702949, 352493012, 218487634, 643367652, 525885121, 141101852, 651516952, 424823885, 274360992, 806669385, 794747213, 316451635, 400714526, 745483921, 57265155, 24982603, 361901919, 4737655, 810896435, 562578250, 698860851, 469316463, 302904096, 117214244, 902238408, 361674970, 400810564, 297898975, 861629489, 740449360, 850908405, 198330082, 810770121, 614266093, 232107245, 606262852, 334867234, 560048641, 329573235, 346411283, 661721154, 274692714, 726903505, 825137908, 622976149, 823505319, 32810553, 232531199, 866152979, 734136526, 859480332, 942800226, 7153107, 968228989, 154902776, 541582336, 169830147, 181273712, 179512599, 531224343, 628732263, 768260503, 288797258, 592253467, 635506678, 754973838, 415905195, 202612748, 755253247, 689436370, 967589429, 660518026, 129664544, 117472939, 644409709, 731414642, 132115770, 533289134, 944115783, 909209525, 73470343, 215183593, 321147986, 309846033, 642315052, 126486322, 521206386, 291426235, 963018295, 20465841, 663285167, 945891627, 346206756, 703053126, 440142878, 406561447, 465111349, 48664009, 167041344, 86431088, 301335882, 644872042, 52242895, 177775725, 851029877, 288499645, 271631512, 932551404, 190593505, 422120690, 934930127, 950297726, 568736467, 871070914, 844017942, 737315713, 20575436, 986951957, 622789491, 39583761, 729135380, 109619235, 614327285, 51752509, 355684888, 815687872, 484322302, 770252156, 550900099, 750666116, 202139856, 917972383, 589409699, 471115307, 145167852, 557989326, 351985360, 953731481, 664896143, 528011444, 488691514, 621192711, 665597507, 149225138, 758265986, 83017286, 458115745, 678107504, 825953533, 807619662, 632727853, 584733843, 401463539, 743225504, 148141053, 454910494, 209195338, 131716276, 256098217, 216749994, 993740807, 366381820, 522371386, 316018640, 556371389, 838668598, 587806595, 861687630, 771579248, 167224033, 230309360, 152197753, 539614239, 779682238, 733314522, 435299098, 326573149, 285014679, 192059825, 637231904, 65464501, 938098326, 901229196, 550139775, 813110011, 528342268, 746446510, 435005143, 417341914, 471278839, 396529525, 2627076, 830724496, 928724398, 191805228, 420553618, 466158267, 214167145, 218504574, 444404526, 735256525, 849411596, 905295612, 405977840, 819153461, 595572690, 707301784, 256655234, 306002130, 880714313, 636501580, 715649249, 211137122, 614662823, 563552520, 603997177, 733360919, 350902106, 743351612, 362641885, 410394994, 430616473, 114462731, 101238854, 495943423, 932293144, 536308927, 478348848, 971710965, 29962645, 889568683, 151185501, 459396014, 613754311, 52394723, 438441005, 466132452, 553661000, 636152105, 959122673, 193840568, 442729893, 740719532, 158931552, 593832366, 429565246, 557228392, 99304557, 181354334, 831843470, 386504914, 21559952, 614678631, 60083211, 898736266, 270817460, 652394179, 753926987, 771434950, 44501840, 275663357, 464994494, 991369692, 252372361, 489662766, 690699051, 421705790, 7470375, 451609651, 101299289, 460345475, 691119508, 646618256, 288760045, 39748848, 5743626, 740537895, 544802593, 545721824, 840721759, 539187143, 141936480, 194294253, 981103303, 465206404, 197697062, 190222230, 119297222, 181504308, 956810496, 505368549, 370509172, 500654514, 902551329, 100436795, 393086393, 873634402, 669326663, 348468349, 628894953, 259102612, 413292379, 94632345, 72916033, 346751931, 841394974, 274884044, 480840414, 676024199, 456780828, 801388224, 789298559, 444602494, 602318915, 591668592, 80074587, 706519487, 325284838, 959200964, 593237364, 450288562, 628419127, 860250642, 128152403, 57657749, 868258284, 976340552, 571889947, 707586207, 73182795, 645742003, 684859682, 421132205, 580382406, 499201812, 779829416, 375882910, 54176516, 188934718, 508559386, 459977065, 103866442, 747134338, 689297497, 148544343, 180794737, 14341331, 113465712, 150038487, 725284000, 425729847, 807311060, 956900427, 197811010, 770587654, 780280533, 137016213, 837023328, 133874021, 687090966, 325235448, 630726725, 552532103, 272791088, 901311803, 968948806, 30839863, 990527283, 534256670, 573793679, 627666829, 45995611, 11109619, 16849733, 548737634, 830317635, 350353982, 141317434, 897750595, 72613797, 112741206, 527465768, 870094723, 409560662, 154606187, 21938647, 118821619, 619712843, 517319215, 735349381, 289797185, 339352827, 415742677, 75260423, 785264315, 369465240, 430534707, 631951502, 716199324, 16488996, 685373444, 2877591, 119030759, 669887540, 960239192, 528750316, 881472056, 220195386, 410661651, 338669930, 181937133, 978410037, 213789121, 692829169, 663730769, 741777298, 184076747, 654925677, 436645088, 922165772, 829186026, 525096446, 150411283, 346613834, 671403212, 843911030, 416885211, 89863809, 536159889, 615217759, 892463855, 226732654, 142741749, 872013870, 864448683, 946136910, 103269706, 868116113, 264886381, 746275135, 829333054, 427548354, 477680613, 932549092, 358974343, 314442511, 434810435, 947554756, 47923588, 822165155, 982664057, 413076584, 587182937, 302984611, 20757216, 29125441, 82531793, 661217113, 875003140, 325844534, 685012081, 68293586, 343404996, 49225946, 914430259, 831551384, 717643785, 828786205, 508668436, 465967376, 144194522, 979985513, 941528577, 388762272, 726981805, 827770825, 270076823, 674731963, 264096065, 274421643, 198016494, 66242410, 63350194, 404000475, 907681618, 241192778, 506557291, 564279729, 95457551, 963998366, 567854704, 615016701, 990670966, 468382590, 111451528, 795257419, 339102272, 851810766, 371035944, 815262426, 940595095, 452765834, 989971486, 929105431, 514290353, 373170295, 536024525, 961135240, 269789795, 309598165, 327836224, 138882171, 72828520, 47787389, 316679950, 441613455, 420043499, 549477794, 538167257, 129087441, 540922229, 934774164, 171855368, 874581432, 16622156, 147217969, 727745544, 878579559, 118453723, 829166760, 914201931, 115166107, 325563038, 463362812, 315248796, 43296241, 869739128, 546083265, 22513753, 752165012, 607162166, 620084854, 842461706, 187537188, 37363477, 214170882, 331329336, 21005904, 788470879, 570727811, 859900401, 621664669, 916429056, 172886242, 422203086, 585351866, 105292202, 277607130, 503678078, 747906688, 766080511, 255927778, 431201937, 954362634, 660807046, 788340311, 269037105, 458782521, 83801759, 204813945, 727550346, 312245443, 979606967, 52004912, 935286523, 777755119, 352743009, 751060940, 387245785, 688615950, 929695423, 154102448, 716673543, 79663763, 518702118, 901588032, 319928671, 952511640, 149309383, 679870737, 346550891, 586324363, 822024899, 947240675, 162389555, 904357107, 197309507, 522087079, 581830824, 586974102, 537168117, 314110734, 316838111, 618667922, 251168594, 585324691, 208201453, 280832909, 648162242, 26859057, 875175172, 757334893, 365311049, 665598081, 365582079, 441325199, 601795940, 455714207, 262039916, 217485414, 519449982, 849603818, 887709771, 833087600, 909550820, 355947602, 81408759, 783961663, 244467389, 361468458, 177497912, 741781218, 531146511, 289635621, 899110168, 963011166, 240651926, 113836320, 618493890, 376948136, 225287364, 551800668, 32688357, 682359132, 76304232, 603244608, 850784949, 200759360, 179716805, 700871007, 802658332, 595608058, 592789360, 807741722, 68131619, 902746364, 643679015, 884912380, 739598325, 727022501, 641793969, 572448094, 802253187, 533172935, 847158917, 227941778, 918878588, 457949103, 344956064, 699666679, 254038811, 452536876, 409949772, 540393636, 479153689, 75439491, 900440892, 241762773, 954844348, 367779914, 538429390, 669785515, 317461580, 512990662, 629333311, 933266394, 791573978, 932257725, 921746311, 712836142, 403474052, 687173646, 229127912, 239999530, 890985974, 319119785, 36771551, 861658058, 344872863, 604159979, 739569778, 15654272, 511973201, 488150537, 960106308, 548931370, 336292002, 131842387, 785956747, 227787855, 134366959, 412518803, 498764262, 549284893, 641315581, 797043675, 254306853, 130427884, 190600619, 323433549, 409888699, 913107385, 306894514, 596847722, 866393787, 699029097, 444273975, 644568396, 471017618, 461670858, 372537135, 305175287, 83781078, 577654327, 623193451, 421948393, 269306381, 783966711, 654722732, 276118630, 381177751, 184566476, 969741446, 275789386, 456327119, 392213800, 289901064, 358607435, 813708908, 928314488, 814528223, 412589121, 638753282, 424428451, 408763556, 947439453, 758295027, 394732887, 197184585, 79256854, 533944113, 593797274, 757742336, 991340677, 906591748, 225077069, 949783825, 143356105, 868326389, 192727091, 542691120, 166680775, 212245978, 720878729, 161056629, 295246892, 215323058, 326985961, 399139764, 993153400, 404845016, 679976609, 519401072, 613152225, 165965846, 341174855, 629998434, 769749989, 87077985, 985113631, 475752635, 921511717, 698792562, 832972305, 401314147, 181383545, 780649826, 13085128, 573896159, 988195839, 316013560, 923462150, 418933895, 549787974, 139908908, 914166306, 367824198, 756074872, 597234401, 678497645, 354496905, 376157725, 422084685, 559121096, 192157508, 920340913, 104901711, 90163223, 918800546, 29115650, 960845916, 952755347, 788467909, 113956728, 620257760, 785482845, 372992547, 936942359, 605760016, 927629616, 471020967, 873145504, 324258919, 998758237, 459467854, 865886513, 302300383, 410265511, 908214432, 277479988, 895868713, 384158409, 727028018, 438204259, 223668395, 602480799, 999426217, 506352167, 794118678, 230587671, 353225888, 888195253, 175151588, 648289296, 305977148, 450540864, 320842921, 504790523, 242562020, 887519656, 519666531, 89322557, 160732675, 543019500, 430323795, 807613916, 127074014, 191181194, 230872284, 428125890, 893606969, 354472203, 447373100, 48166532, 882092182, 942735866, 481469787, 715775897, 160322641, 736223122, 302162358, 596900408, 735638781, 132532822, 674950412, 668283746, 123835930, 127171058, 676694702, 948808616, 701423865, 500625346, 974153809, 914213329, 181205293, 356742045, 260761290, 545585113, 660489377, 439349542, 272167281, 274183678, 761976410, 625138659, 410274641, 934055842, 47714786, 420877730, 947696704, 996092583, 753311142, 94635809, 454916563, 967982819, 60548134, 160807970, 624791628, 183393205, 790456615, 340473558, 81663857, 845682299, 192973625, 303436887, 304865088, 560943847, 254386708, 147596651, 699854319, 88880178, 247916007, 18964486, 178946150, 940314453, 169595135, 870894850, 124026733, 839570591, 508998220, 689552129, 31681527, 475768797, 924892398, 501968857, 641316133, 344754866, 90607618, 538384276, 277658119, 735416269, 404626197, 692513823, 473260434, 343680555, 12312109, 530406109, 432525188, 935893072, 313788278, 512085583, 279115030, 800578530, 461156465, 637133064, 990420627, 160200225, 326825222, 417823062, 288954402, 96555727, 976852925, 332603462, 246441058, 922815734, 512198099, 990397379, 707149747, 213038901, 871661857, 469938364, 177746394, 491552381, 998586932, 92259956, 727145732, 80369400, 707472045, 775109530, 724986907, 760768233, 293302960, 976647394, 177016908, 149737975, 324028284, 150114275, 681949511, 705869691, 842503826, 699808942, 693579953, 843340671, 358809523, 28659506, 125670565, 235627311, 408529811, 138818855, 193594469, 146337092, 229874193, 316803033, 551182431, 463424129, 192415274, 311865130, 198953761, 405216258, 314797525, 576915589, 879129942, 377868128, 54506857, 388651794, 642325687, 395058623, 151365917, 63870550, 699817049, 744301244, 724724496, 9666164, 950420139, 334099322, 602069305, 889435736, 895153999, 10282864, 395766527, 679905923, 527071700, 912214970, 931935610, 367656764, 75987772, 424243672, 847054420, 872252203, 684979647, 340066791, 611403172, 480749420, 881962143, 183812548, 609543822, 468964084, 889405028, 720181851, 269283963, 855719611, 472302992, 322360473, 921725993, 100329888, 402537828, 805095898, 519554503, 112895155, 269885046, 902821957, 477772492, 567059000, 770850486, 735208791, 352690002, 503706261, 584935129, 993752253, 788191794, 44681444, 393282730, 337873257, 109772433, 680412512, 26204889, 166506587, 203748675, 946700192, 756456040, 913427730, 3615651, 684490122, 304466977, 334775583, 917826145, 60217477, 677830981, 564821243, 723922728, 734875684, 315469540, 537393247, 916646879, 377642093, 628110058, 660013110, 563704072, 778006160, 628785807, 923389953, 130702155, 471914575, 82331532, 875114014, 616621796, 579639457, 520199715, 932368842, 881674892, 665903014, 61128882, 300908540, 638172281, 402535120, 142439745, 262432800, 392383833, 953000789, 482523765, 375830844, 729274912, 939368709, 253726383, 964192517, 837021348, 837934597, 155444513, 299933712, 6798970, 952201715, 646648241, 847530450, 176545425, 640395776, 1956547, 288880621, 150199988, 859309997, 462829714, 83848504, 91637542, 799559516, 376942808, 825240391, 500518686, 538456724, 426344925, 491191236, 236381643, 209161127, 787894205, 784559519, 792991914, 48993557, 882360186, 759127568, 313379095, 818252285, 634663767, 601074197, 958879486, 47998662, 211645198, 780211006, 687978460, 72602399, 887755443, 243736772, 747728151, 342285822, 328817824, 770196786, 390614964, 472424487, 64314848, 682106422, 831428417, 138611188, 337352285, 261781195, 584343870, 316466252, 341261583, 712536940, 224636164, 803445590, 625120755, 566418653, 86665993, 237663966, 46217356, 123348654, 473778326, 360366500, 583389286, 856141810, 374054236, 383971397, 421270857, 100439299, 944273254, 784231351, 704107603, 86627673, 23618491, 703622910, 726293523, 898571464, 118579772, 673394470, 491507936, 711735232, 810595158, 67577292, 135991198, 952421494, 375112807, 715070444, 512057050, 552395853, 185940886, 172574624, 611402965, 877612612, 391398924, 645543338, 788987499, 759596453, 413837352, 2885420, 336695164, 807050035, 49452872, 460954738, 191282507, 917992370, 401394790, 301108300, 731543493, 775516595, 40351447, 192105082, 229667630, 508183298, 862703844, 952579426, 712806990, 915478760, 774027266, 438891129, 171187278, 186737512, 725147281, 110402708, 373093984, 94713189, 370456300, 365141738, 984697356, 237993867, 46735451, 258608771, 857938646, 17624044, 718959211, 556994049, 750555379, 527586640, 330434504, 753457059, 430627708, 362892648, 372776073, 502100902, 782520525, 726264368, 868016193, 281468682, 672499774, 629927119, 619054996, 174388558, 688951829, 122006526, 246230355, 14524334, 788886982, 30831766, 276665863, 396915085, 786705274, 242986313, 640043495, 230275065, 171158094, 916640917, 378809607, 286328287, 44855905, 543067207, 137820567, 930278593, 219285539, 829359897, 151190144, 825651536, 444185228, 729146673, 603511173, 920895146, 136617132, 530290508, 135934218, 98699166, 313379038, 227181684, 737032675, 415506966, 930413156, 552836877, 298496639, 566459136, 881177507, 944438100, 562994463, 325655277, 88948604, 660883233, 735728283, 999109523, 257754491, 345801110, 539005280, 295665155, 122245756, 174691523, 499367339, 365632733, 814352600, 336301130, 926217957, 176961989, 386201353, 376471812, 501495921, 237242933, 519548860, 94256833, 273859056, 933763467, 304095459, 751810065, 738305218, 527588156, 275568276, 372012, 262398842, 762437545, 617229475, 339158805, 797237408, 785004616, 393014543, 768180536, 271971604, 269291779, 784335101, 681177510, 40350843, 58246155, 342203463, 361741483, 151482761, 471298074, 867285502, 416973774, 424979090, 713771305, 713546411, 218503224, 116987871, 182499737, 473647817, 76273257, 138787776, 849256662, 471338445, 594714234, 248586442, 129946827, 871722861, 484096535, 993033441, 631366806, 526631096, 837261222, 853669801, 215736040, 986645103, 4914218, 455613109, 760685509, 941150132, 684292749, 33525134, 593575766, 455887630, 107669730, 884030127, 205251825, 186536133, 383521667, 66580248, 595501894, 207013429, 83348270, 801013787, 196777577, 423233750, 869389262, 192420777, 181908765, 8422901, 727276764, 693182483, 658992287, 199164436, 494246208, 966384986, 57721583, 938246207, 65725173, 407709018, 543873597, 217118732, 806835118, 865376004, 966938055, 270169764, 149080572, 419481052, 372758725, 739298999, 209064354, 990166688, 458831014, 317562800, 92949887, 869491262, 373646743, 541653980, 901861952, 931614890, 429572049, 435456465, 421629947, 136020639, 142804180, 477201840, 754725298, 414725743, 307963727, 515795071, 114986689, 992323, 376521940, 338790056, 592629652, 819147625, 324732929, 999798513, 880951247, 742510255, 158893213, 611346908, 580809534, 885983868, 845584241, 380634165, 776018170, 974159768, 589116888, 785381606, 62146784, 380129127, 27860705, 465038131, 884372676, 597182176, 294398421, 349042002, 976615022, 315065140, 105006035, 545974619, 10208282, 309036832, 36212274, 953204016, 597244968, 239266647, 952793741, 464880887, 108242470, 884163197, 204915493, 790739639, 754890842, 211950644, 548708371, 960287069, 892088468, 76916663, 301626296, 810296949, 770926670, 206512653, 226993334, 729411531, 752124298, 223445066, 802319281, 326669784, 746032559, 394050817, 767875935, 853388312, 770719015, 913386644, 765829690, 93761599, 791337502, 942322531, 104716432, 710405889, 561352234, 604466246, 634187641, 929477060, 287876558, 26087208, 243974599, 910119850, 271789616, 642191028, 632328932, 618663093, 699402808, 495168488, 653709472, 961494578, 821931807, 573921315, 42888063, 634778372, 456626194, 628905692, 38887077, 135696723, 101325765, 590635837, 946629552, 181545714, 883345478, 208545194, 272723230, 341542013, 773796517, 459548726, 694648299, 200171756, 517887328, 331033844, 678156844, 396497515, 62754839, 763793424, 81599112, 151280141, 444364091, 951106570, 811192590, 605413294, 26513804, 956069870, 532235383, 689221262, 553578307, 120245291, 608821977, 941937598, 934841202, 254393521, 382758379, 345245268, 704036394, 639518658, 473470450, 809180692, 237910794, 981176620, 259003662, 576007807, 287691547, 56163304, 900081133, 252236379, 14752525, 273137790, 457973120, 235294149, 804678950, 731080927, 994556380, 789025069, 507024902, 791732181, 223210029, 499772258, 871322199, 990296484, 906448601, 300255874, 506619858, 381143169, 135308249, 365770291, 177795472, 264238246, 495997167, 186797332, 237701146, 27666352, 701819911, 569307961, 900484412, 735871657, 853005264, 283535597, 931026633, 649571650, 359056609, 542545681, 612339744, 590795619, 718241402, 775986830, 520814993, 565664214, 762728911, 304768581, 7313875, 299006998, 765087663, 124590689, 864974384, 202718742, 194890505, 712280347, 32817373, 255444056, 666632477, 788502014, 535511786, 530662496, 409585297, 397748763, 477491158, 431340345, 355605035, 819961992, 32255573, 338135299, 551747828, 832617296, 353398909, 140236588, 941256098, 160802059, 531085214, 540993057, 788665963, 530119418, 975718330, 153141431, 633225132, 308035980, 314070998, 824261728, 207319734, 905121953, 57923763, 899307212, 467004072, 99601493, 590616737, 374323259, 152953484, 969868003, 518772056, 478900827, 910349040, 314605119, 156297807, 259177400, 866412059, 451516165, 70877028, 322306693, 186381353, 239402502, 790269558, 388471649, 748133324, 862012485, 664449630, 808128165, 120970013, 852028389, 104235219, 911346119, 33761453, 831532681, 147042200, 990756120, 286951307, 626292685, 849005791, 607298625, 157432941, 440970673, 559495313, 408935189, 57995451, 843035287, 571750645, 286119608, 502044789, 334038134, 949704149, 814090493, 805991752, 724636103, 4587560, 964446880, 541800198, 663797770, 168699816, 211978570, 159406913, 581073854, 707562734, 573458966, 888667241, 182453064, 879103086, 284644597, 205975780, 241737227, 804902443, 990049951, 634786814, 112849588, 330044515, 714914825, 114267597, 201142490, 357156383, 637536976, 829618676, 873493131, 849830201, 816473056, 71392157, 527699750, 745132784, 199779433, 249075522, 637007348, 82637666, 427096326, 378331946, 385350878, 775282091, 831292162, 270866229, 482096438, 214410093, 253620154, 912948118, 244088974, 691864261, 569981584, 896832800, 914743392, 45002267, 803935515, 415605381, 675354466, 26080649, 602737610, 416763942, 343110965, 345030691, 772306307, 839836615, 385921511, 558759223, 101466178, 326240756, 207269412, 405840089, 635464418, 590721727, 127392795, 645702479, 958288691, 187313551, 777849488, 652482100, 549984361, 833686089, 754136042, 778651409, 918527182, 179771546, 485221477, 204388099, 910885247, 228973099, 259717906, 555259689, 289669792, 226714179, 358176701, 848150471, 329815981, 540574161, 255102602, 58166196, 669923991, 311236644, 412371512, 367955719, 485100520, 501886509, 784052577, 716710554, 857139808, 720668533, 556254451, 378463430, 476267260, 604295540, 552591090, 456248600, 205874450, 806336018, 601263713, 676567446, 9442386, 382649765, 969201602, 896809781, 721074323, 28121151, 771581951, 801327951, 832848162, 905545522, 236678222, 939988475, 378313683, 140673058, 626504702, 178873974, 733143157, 97274587, 223502346, 155204962, 240399674, 752768760, 123789099, 578854107, 7444331, 891757728, 703640970, 169371708, 683083511, 229228096, 77419721, 389264920, 620173188, 515294776, 415852243, 805082671, 554914257, 582167766, 171403295, 349968117, 613975716, 428185775, 827579785, 370160366, 465105177, 237404357, 447396329, 240162917, 995738793, 656945449, 332701730, 175242203, 347262078, 920901506, 503090525, 774417249, 545213176, 856606694, 457252811, 467617663, 125162286, 198814098, 309852671, 92215562, 580268884, 873260460, 793424480, 443402725, 153902316, 469407049, 983480064, 249165287, 293576598, 343136530, 172169631, 326403464, 839095860, 287104698, 179613981, 43948693, 892418729, 478645955, 491138180, 645926627, 597154895, 645817896, 216526744, 447691449, 408355278, 287994056, 203968329, 896357016, 877492960, 951310279, 267087312, 699143588, 20539555, 908820970, 760231885, 575462028, 920137277, 833552345, 868336664, 105254839, 282690405, 205548294, 472667358, 258736635, 573228772, 223465605, 449531253, 888838928, 95673224, 825080152, 665668300, 99781803, 479939391, 566606889, 228438593, 920878755, 597675623, 151436478, 905282028, 859233933, 520107841, 267032602, 282243486, 252264878, 572714316, 916971433, 961709880, 182702696, 178445516, 836311216, 85629650, 220524993, 611697526, 339523310, 889803214, 640823362, 886481734, 309408876, 97576202, 431216254, 337618855, 939237228, 955260724, 194537470, 56038507, 402934104, 928376516, 791863442, 351371552, 293346346, 57047079, 423652916, 89510866, 299990286, 945100680, 906910103, 865222987, 248013778, 630150106, 537025816, 385294073, 197578486, 763361467, 663367038, 609281549, 684877882, 337656717, 649821425, 388293814, 584994918, 643938521, 97324064, 713808647, 967711632, 3395693, 964827155, 974849892, 700861782, 93127903, 121477454, 484581181, 928497277, 62221606, 185710357, 432713673, 181045482, 496878979, 320046853, 493179406, 26112252, 709280981, 985963586, 458695724, 856640647, 788138686, 164894759, 820376376, 906947261, 562672759, 645882179, 757586995, 867781958, 802687080, 975207206, 963022606, 942165040, 495047945, 1504573, 351824833, 713308977, 387897343, 185246631, 327814896, 323902266, 314893479, 382433169, 414882838, 139068335, 153083277, 171484797, 625301333, 616080570, 625801550, 158539397, 248016032, 328855542, 289624536, 251491061, 403539005, 836322830, 800618075, 143976315, 705330085, 509074129, 757895742, 926458057, 224869722, 931034609, 390899503, 922156469, 141152569, 683524517, 150893544, 280579269, 147218000, 521857280, 167609799, 17914079, 620787339, 132357334, 61601600, 238586507, 45629643, 102152732, 821170766, 208703248, 159766147, 484449928, 505552238, 379380008, 228587197, 603774848, 699953769, 657316544, 372821, 216074584, 41018246, 783629480, 657406481, 746845856, 810578997, 914491702, 504224587, 895192678, 422677607, 543176451, 869924199, 245339899, 174793453, 49951952, 345722199, 72777699, 456905943, 808058729, 324546553, 419513612, 371221289, 284717787, 850806656, 61236726, 519319943, 613620869, 439520515, 115016355, 418333075, 12061291, 383679592, 220538288, 416522606, 243009237, 365349903, 954765949, 229568623, 884721941, 877836813, 533103751, 573826904, 598496750, 670425572, 564911332, 130823096, 956252039, 293806455, 111570046, 279207145, 556556181, 714014139, 332380638, 91246365, 30150456, 344067426, 38856282, 14237389, 601990628, 407353571, 820077112, 808108920, 727582414, 769526884, 212288199, 810205547, 353473252, 791492757, 226247201, 632337538, 263857755, 554127143, 622713614, 297485140, 620708684, 994322224, 695951748, 818152905, 87674193, 527761261, 939894257, 307362385, 659451735, 536325247, 95754249, 415956227, 658288902, 691825548, 674057941, 520891562, 289980888, 648984759, 560940792, 891665731, 106233823, 926689394, 329129779, 242817101, 193697171, 936484210, 364308069, 695991856, 776824383, 535805755, 154275014, 258673877, 904762987, 716775611, 215162880, 161305473, 248432617, 878370349, 896561422, 104002674, 938656913, 324145392, 416568441, 124663447, 789745658, 289063349, 470509708, 139917844, 846276698, 226811013, 130942360, 606220346, 22530780, 929516407, 797494762, 658683672, 6986308, 252670113, 805282607, 86686937, 677933113, 513513908, 98622615, 89652746, 224751147, 837755818, 807768117, 310613565, 617082899, 537418318, 4134118, 710157814, 794306582, 448905965, 517967020, 936954586, 784872579, 144606058, 962947608, 471366053, 331457474, 390915784, 62156171, 33321293, 865251235, 266538183, 8459375, 766182480, 156190575, 760019598, 63506255, 125007781, 389852384, 699722155, 440203467, 872710488, 357267816, 259729758, 205514184, 439402602, 631738837, 491684812, 182819323, 161465270, 455559575, 925649197, 577278028, 362062172, 519027755, 3270253, 98272518, 781033781, 268039697, 1846533, 464265790, 688050731, 20557560, 658813202, 530023768, 553395471, 817189845, 858777757, 646389206, 717593400, 713102841, 116976438, 200845757, 295790337, 259044413, 562121246, 320096905, 118889687, 776461277, 14601997, 725104673, 145892003, 534389231, 871723476, 131377674, 981111597, 889418596, 85591897, 926040587, 503696399, 141283241, 123411165, 621758251, 585945044, 586284982, 199828918, 39250313, 690828684, 751455343, 201882737, 757901999, 728720347, 163520942, 573874588, 933913159, 512471595, 702603380, 651411019, 600950824, 444025915, 315584350, 956955947, 698347204, 239381653, 84380248, 151952143, 960958628, 51634748, 410814706, 474793953, 56890026, 645494610, 265592079, 194339634, 766090419, 960528549, 475345756, 88183859, 343663189, 218558339, 520978918, 184503810, 472908066, 460373763, 867669611, 13454612, 571004490, 951926369, 170005553, 824778841, 645972678, 67961878, 588189774, 657461541, 833113487, 474332486, 241776880, 106419000, 924428368, 989037493, 955214381, 760310533, 992739335, 791488996, 136119729, 60157725, 949773577, 974137997, 669213532, 964187200, 591918504, 113557698, 416214775, 930843717, 938801921, 314789116, 242546951, 999225423, 33867101, 700401312, 340931275, 419003822, 221572896, 123416314, 656165742, 984308322, 223860304, 736578596, 489009377, 443735920, 12018624, 697355676, 722758463, 638734352, 258433343, 354669228, 257684169, 725011442, 776974101, 254164923, 352746512, 482608460, 63023762, 162833258, 643621928, 910374833, 911777661, 187756570, 228885213, 976248038, 214846621, 707804208, 697746596, 966940040, 473042169, 73224731, 702228414, 564275540, 127027431, 193269049, 128428320, 953675249, 523669293, 802543981, 878733750, 905560550, 784847264, 290427345, 667140138, 101648642, 455713374, 766981911, 9142085, 771337649, 912571312, 894884891, 427615753, 806158361, 128979997, 741167308, 539332113, 692801385, 382980939, 384741383, 513184062, 994241173, 302350049, 903482551, 591628190, 541790461, 311081027, 775437392, 696009732, 355399915, 596476214, 942390761, 549101017, 347745428, 550893842, 592799648, 880110577, 225485701, 39743675, 568888865, 288732625, 547393067, 784548925, 54170258, 588572063, 41676615, 55138962, 15012402, 348385340, 285089904, 360888987, 657307706, 499398789, 715808243, 403682386, 180002000, 945216270, 862967598, 913157750, 865354108, 452069204, 482923762, 932471370, 670927914, 790279475, 706103969, 677010393, 818458278, 203246551, 826382258, 366798765, 233460769, 294326007, 45924953, 981827966, 974494975, 742463771, 806675411, 501125228, 818311635, 694606381, 53324851, 832233628, 625895537, 528857460, 342211176, 35498564, 38297229, 973287141, 493120434, 202237212, 634873150, 867239726, 377869123, 455306133, 284703008, 176535019, 782434241, 171571099, 722887362, 377258426, 4154460, 260871360, 919901540, 695908688, 436849244, 418378250, 828185413, 125898842, 832491679, 708910895, 887426023, 862730073, 310480932, 684131512, 402223803, 893036179, 255166655, 986047839, 22055464, 135011949, 209149277, 217316074, 549847153, 938920427, 879981431, 796119321, 482159764, 934814530, 291831512, 478819785, 960253826, 201970382, 425064539, 701003771, 130970941, 227693294, 34719882, 317729233, 96235876, 706961389, 403679126, 640216641, 733227104, 796116015, 302033241, 952221878, 654135588, 444648477, 106507965, 915542424, 201539598, 938254349, 310735429, 605095353, 505245125, 434067332, 909341527, 280244167, 370984750, 570174459, 346639119, 16905948, 932597468, 541845989, 697814881, 677413178, 474130346, 210170805, 699125372, 885294885, 986423048, 453482371, 299018441, 744953930, 904680097, 598302544, 977360732, 237760650, 570200881, 408566630, 720501884, 204659079, 572810123, 720947381, 151746220, 81170650, 881000515, 64229301, 9807743, 830448081, 920507653, 20440000, 907367215, 560005650, 743047881, 849483941, 131990064, 927715272, 48123565, 405273602, 454155972, 971459074, 971699892, 717936561, 78111355, 704972358, 610828065, 904625364, 911925342, 969384794, 101498438, 363434489, 609546889, 123831374, 254891318, 833986888, 762050258, 811087191, 254455958, 983729255, 75681232, 608443467, 79873414, 294771072, 292620136, 652882539, 258780750, 172909325, 253503425, 471477425, 762376316, 236506641, 487822925, 137604771, 446371719, 636091293, 889209363, 306613418, 51380135, 694439137, 180892170, 362717187, 222727792, 772471922, 615857663, 978174032, 115929919, 927883407, 986341387, 726439721, 432250307, 384306124, 955766445, 596689876, 308886265, 564665351, 316255, 965020314, 417558005, 498029540, 912457114, 87859887, 699938730, 159579006, 740477793, 304516831, 638308288, 37961341, 915418069, 669796865, 489694534, 548329010, 313787125, 614233943, 435378321, 567776807, 30703271, 25797979, 23453493, 961843904, 292063062, 370892751, 995817736, 209925794, 886947081, 539328572, 696484787, 115177220, 212415843, 396083845, 795130184, 808167681, 327202493, 286208858, 218003346, 369997914, 954031254, 362047662, 797257567, 541934559, 505390680, 287094237, 110156749, 304000377, 478125255, 561190655, 318408948, 814710706, 239400802, 339735911, 980728346, 664051492, 473794101, 861357450, 823746987, 232435378, 785876675, 873192402, 915288291, 523913420, 424556723, 689237716, 775923074, 331756238, 531555225, 903223969, 481102286, 567389112, 721650901, 363853646, 738231710, 138458246, 75728355, 63237493, 104750595, 529663810, 944552807, 389594753, 177460440, 595352420, 521277443, 786056842, 562884034, 610003877, 72854823, 236323991, 763585138, 294751759, 902797506, 497658787, 625578566, 641685162, 154384558, 754068668, 213255835, 978641084, 888984706, 712867872, 871311298, 289561119, 610653866, 396915208, 56293834, 395982308, 596706149, 123564246, 548789409, 573860345, 689733948, 313643647, 366672684, 960413844, 565411222, 975100467, 325366291, 946632396, 426369481, 400451094, 959574585, 314823210, 59741204, 876261286, 359421600, 928515330, 820144861, 801790995, 973837868, 332631374, 597898841, 472244594, 214637382, 7458302, 6817733, 780408255, 461424384, 150769187, 516925605, 585652697, 802888390, 555636319, 260805368, 833425788, 485948190, 365393206, 307241353, 36222724, 166089814, 682798356, 246736859, 236161384, 260896728, 565877583, 901601220, 211208841, 20584234, 6822862, 424883095, 952059485, 389421490, 932866680, 951433754, 357429689, 356309165, 416964398, 910192943, 59305312, 563696038, 45892308, 475139562, 494077068, 6820029, 358235997, 641953838, 671467974, 716586427, 356778792, 315550694, 281649561, 406869450, 245175384, 446671087, 36190430, 852533212, 76256778, 331106980, 947001072, 609674374, 937378312, 167660056, 568994426, 59554159, 309752375, 56023916, 397231557, 994275779, 942316094, 369042555, 78008996, 558565729, 226582492, 187766576, 740881761, 80860775, 858389500, 854982749, 306271154, 521979524, 584340850, 235111005, 698177749, 804687832, 15503227, 922577589, 658363254, 177344091, 629847245, 396163309, 12837044, 185013399, 608466375, 71265446, 893547270, 669123283, 111891468, 892593722, 22661980, 10251996, 673541937, 472638154, 776578201, 791806730, 500411234, 443437399, 443607008, 94239179, 341510468, 74887199, 954335994, 733032950, 636691985, 154733186, 322529402, 308276260, 931904373, 324079242, 497067573, 403646645, 581915143, 746462712, 562422149, 745090428, 688226497, 804125202, 964120229, 12745100, 430450179, 197030688, 474409174, 57325081, 579640748, 644519162, 427181236, 421198413, 280473650, 673025089, 13864323, 339177643, 217955832, 319586731, 807045707, 865924085, 855574481, 344415184, 564713450, 804537417, 444298647, 892882525, 805854436, 701990902, 796105059, 772533292, 990899538, 230931829, 811627047, 450901718, 918798819, 265905607, 62578089, 633438608, 529868298, 989640200, 190005034, 550983099, 608026712, 522507756, 570105295, 875775293, 477274760, 946742675, 627389047, 679925368, 855034247, 284724223, 353070005, 96944456, 318001339, 195212678, 808230425, 2433715, 325946281, 249333275, 350509540, 407108858, 322305630, 339011221, 133846674, 952899167, 225960215, 579047269, 371466709, 705816139, 57673706, 246933594, 204392378, 305550879, 175598572, 594871901, 92712778, 531132027, 997551630, 460477996, 723639982, 345983903, 271923253, 555758924, 403439679, 374124090, 656188945, 581089121, 801888540, 11266098, 448934515, 917114162, 347640936, 406266988, 379419801, 659239453, 303073030, 246075381, 177107380, 121053523, 207024004, 470403823, 533332605, 126123291, 700602307, 271134909, 154017857, 352545543, 949473883, 774171764, 62320321, 374251213, 737638526, 304316692, 256246050, 981400000, 256517632, 964324901, 946694185, 70648938, 932960316, 201305237, 985562709, 924616806, 417721362, 804582687, 138600229, 562597431, 624893096, 14733085, 876635100, 403427407, 252561324, 638052621, 335705344, 11747165, 348744000, 853710100, 493910165, 126527486, 893317180, 889699512, 478090235, 799803178, 348172281, 526014520, 934081634, 489845835, 613847515, 974993260, 252428690, 989091507, 241568763, 10827326, 324167243, 77595227, 494337205, 977361362, 836194413, 949088699, 190098866, 133693866, 885870081, 463668278, 612846358, 895356413, 517196550, 111403257, 626163053, 706573810, 705956174, 907471110, 627526216, 579592102, 947661453, 793359752, 723879082, 474625864, 914252020, 604225035, 341397779, 392699668, 65433856, 621881549, 14653305, 198309961, 753734628, 151846391, 676187920, 928582544, 752297502, 512840634, 119732638, 146900933, 540948748, 671321808, 883420913, 597201025, 700976519, 233225014, 998893372, 588954543, 869114210, 27644986, 691131870, 439063330, 611252820, 893506356, 11578695, 800798689, 165687439, 248454236, 826052173, 402585769, 731220436, 311664395, 328795078, 583663980, 890827449, 552441556, 664065148, 199194532, 508701612, 68734970, 653114298, 928600156, 176182686, 300175969, 155274340, 734942032, 771352059, 705299197, 66474671, 653611013, 363116042, 446553661, 668797438, 524684719, 936787459, 398129152, 234426706, 755816438, 477461221, 112000374, 608402434, 151876011, 226341423, 932659143, 652049562, 509330784, 113201460, 880894732, 881641006, 436672538, 800530753, 819493236, 633609275, 119259541, 356008931, 821073190, 675297770, 823344412, 853862904, 228147691, 960409470, 805059806, 862716142, 585305505, 382362010, 640285611, 849340885, 518665995, 35859351, 109564632, 135997293, 193633221, 194617382, 319265859, 614731428, 326828373, 616277000, 518519135, 646669482, 197793816, 101921824, 129837157, 870186849, 98185004, 903408767, 213844020, 751675610, 911087706, 295327191, 781798427, 380650001, 894506430, 896911698, 49971329, 435620292, 916428879, 335834658, 30758085, 705645796, 118501316, 571542545, 895719804, 838560158, 224562826, 918149416, 535159136, 685219550, 445004608, 851940756, 328436970, 732697295, 168197617, 980669939, 623298169, 989854101, 963453948, 827740283, 45785531, 942810068, 778619977, 8418977, 241999720, 940856754, 753263181, 336631868, 470942662, 30255695, 439677279, 290836922, 206329334, 486542422, 105895775, 114964427, 41859758, 587332388, 428660849, 435675320, 509304236, 74088034, 663635837, 638375467, 225452138, 582937952, 104269758, 383409173, 805413634, 436155962, 41245429, 110858100, 708677733, 365084945, 545329251, 40463469, 554123806, 93374906, 901336008, 481605268, 801709771, 837543525, 911643985, 788143531, 556151185, 718350878, 519477768, 491852218, 218818303, 444854793, 665326470, 378488013, 906938341, 36379512, 918419536, 980312197, 582019564, 665999460, 779785194, 142956391, 213957663, 869094942, 473315816, 890339250, 212635277, 633377124, 594664294, 243493340, 382770292, 556976702, 924813761, 930152838, 578751664, 974480037, 628458484, 913508647, 527857243, 359473805, 440936102, 910910842, 826967740, 704928136, 28174244, 560483716, 434419519, 784499119, 506332523, 52870000, 618198303, 359347187, 813132905, 157453785, 840593891, 680343273, 567231394, 560507204, 77445550, 895826393, 323627642, 306854445, 114859864, 705032940, 800537057, 991903661, 973177252, 465425498, 631434297, 353137235, 321192443, 562514435, 773344453, 682356298, 928982825, 197083596, 702193589, 11002540, 248421439, 350004237, 720041324, 706132327, 975829122, 444284286, 706177915, 962603182, 258557201, 609684552, 2896511, 329632252, 81110616, 167861770, 791589, 648471073, 219361086, 356793122, 925057628, 242791153, 765188655, 761394364, 105726167, 300615339, 3747070, 137937613, 988527099, 256407117, 520452293, 751413650, 840546717, 633783864, 919782553, 178282240, 431923415, 517599661, 7796124, 739048004, 580532899, 194892864, 404011606, 727798415, 854976858, 582417683, 405186544, 541290208, 530632161, 50931028, 967022228, 202761394, 192541841, 818759618, 959089449, 263211989, 285704507, 112786558, 211305044, 593625528, 319898520, 425374903, 618243410, 977164746, 872014201, 403388794, 10823592, 248337558, 83635536, 665130305, 423348476, 332285348, 454375820, 310887044, 259630252, 590504522, 453125338, 199007713, 593854804, 841112958, 114691775, 771113696, 505282437, 669145, 702416287, 807686003, 922294882, 556780255, 26179184, 143277020, 650345054, 508156945, 54561557, 226198585, 63135800, 614772651, 321087921, 710622619, 51071867, 328394369, 516818369, 225622631, 361178815, 302259847, 756912806, 664527317, 871634130, 595420314, 538261183, 958595869, 454511154, 458044223, 890276723, 657831757, 558385100, 749886943, 250339747, 638816250, 110956717, 852322618, 112631338, 798822232, 621093292, 912365636, 998743543, 294911276, 889032293, 820911368, 515464798, 741601914, 160428145, 603562979, 50440736, 937405428, 540137652, 210362747, 55576648, 716819771, 988865135, 208326498, 563309721, 463253793, 127135143, 900768181, 658872146, 941443225, 336003552, 326154132, 934978339, 220592882, 660145183, 829993742, 371963233, 484369325, 307439855, 286489036, 239018394, 314711452, 947942901, 587469444, 487862557, 105673474, 71904700, 980830962, 947968888, 32582185, 362578587, 867976463, 944928685, 721954145, 392904149, 350960572, 98494446, 679977159, 435759482, 108756229, 38421160, 176723545, 422716430, 240462645, 941759291, 823185568, 219421983, 402548676, 911606407, 228215285, 322535396, 367851767, 821534164, 705218449, 45568956, 479457299, 750678928, 110785691, 481467258, 792375774, 705358185, 923553062, 199517672, 39891569, 432866342, 460657346, 620520316, 478652508, 42451404, 968794446, 713452169, 601366779, 147775900, 911623745, 664767403, 269040152, 558540456, 660602208, 371746992, 399423512, 69189104, 59442762, 633360046, 28532473, 969424532, 464560264, 902428551, 317706088, 485889295, 58671790, 952657354, 221032547, 332045024, 536101527, 422058571, 281426357, 49625477, 837466387, 410721148, 164946929, 159698778, 332921834, 504789150, 575117015, 624660226, 872219680, 821818933, 50663622, 912604837, 674645721, 842070195, 798029965, 32893477, 119368675, 386052574, 640628066, 716679776, 460642831, 191195157, 861189658, 100919506, 198441504, 130544061, 860338523, 23024086, 338846285, 972326938, 70672003, 873677698, 617958591, 587147852, 457393790, 451858227, 546930962, 442193623, 389400692, 833438007, 767235435, 547470468, 115870271, 387419901, 82711564, 214358652, 360301261, 788978185, 507129944, 788212879, 28516731, 801984405, 432048181, 74892321, 191084239, 930178587, 921710288, 315159113, 864923683, 459953159, 294870749, 831895220, 106611178, 313937902, 496270530, 39544179, 18471874, 193170144, 334923678, 842413068, 297098478, 398973695, 291559130, 971099099, 933738929, 505287163, 33936642, 57742284, 287698109, 438504005, 167709526, 262782198, 491099578, 187098574, 567871380, 971464300, 750372247, 814874077, 30974887, 643060176, 939517102, 301570799, 462540035, 344515379, 834054281, 846598504, 360101341, 126748706, 292705869, 680025260, 801617422, 387006015, 600981605, 880856530, 37860015, 30961705, 977987532, 992046572, 285881764, 658111837, 78049493, 120428873, 352719373, 957903700, 131708481, 62045239, 485804762, 583313524, 515089281, 581872480, 424044679, 64574189, 225549073, 638903950, 149525976, 16236402, 72135486, 162289369, 933765676, 792282022, 403168540, 147400838, 29944895, 719685169, 862883956, 678810452, 73161798, 111460998, 928677229, 99217599, 208523482, 288194519, 394515312, 536779610, 257871477, 645580565, 882741989, 331490921, 987584344, 262482121, 529843214, 483393144, 629448533, 40709505, 337913581, 461452163, 386250247, 913741909, 713119222, 945308869, 568134643, 138742083, 859438358, 295578946, 736621869, 877679803, 414964502, 671478840, 590085251, 98539329, 564822377, 927677124, 837560569, 78559781, 456636979, 788541947, 935518558, 226522677, 628896149, 340757995, 233072840, 246394198, 405211791, 785078946, 639227618, 301882692, 890682743, 605463547, 115003333, 509927026, 666971901, 180780717, 813706375, 779794300, 613139626, 780040612, 910704633, 602530635, 998202482, 365352694, 8421493, 224773592, 411985799, 601579431, 322641174, 506086512, 219916754, 926361742, 229777038, 608016522, 777604960, 320327223, 159046451, 787891933, 329677631, 457307490, 410860993, 191631682, 703646535, 664063875, 305964838, 56181993, 644633278, 624948972, 986400000, 841605567, 555782500, 791752394, 786143880, 688023384, 736058731, 877258890, 873331342, 619970296, 728676536, 715159841, 95035162, 662150393, 777452086, 387376887, 501610543, 451214530, 692432932, 124096606, 191489660, 228237128, 364499154, 453749312, 892902081, 359551577, 883835333, 173259436, 432390023, 921809694, 184035225, 256879606, 199338413, 765193542, 383927338, 789035854, 440116828, 626839483, 39963058, 515106432, 856337199, 11294381, 901858061, 571400412, 232748898, 63796240, 869425022, 972676005, 811784078, 191717840, 447772627, 577456161, 428802692, 395539679, 255526750, 183303109, 228447122, 448671048, 619274748, 997194509, 309494244, 992157686, 537630420, 822205639, 448578544, 190035917, 67982726, 313350906, 32511685, 204519695, 14727940, 960400093, 356443828, 157947990, 56308903, 158405104, 433876461, 305405318, 826178625, 260853720, 671589012, 620744624, 248590153, 798393023, 737923696, 782808389, 409175784, 366230747, 96554353, 992947199, 740250327, 520520392, 962616784, 941205318, 60909676, 785906371, 513959018, 759857384, 803126526, 890266595, 907757877, 373311845, 325890256, 627795295, 160668764, 985205257, 151864316, 228682104, 706896519, 423391884, 289228468, 45864934, 402706046, 539788697, 21442281, 1672063, 944635601, 152086735, 223107686, 180074708, 500483183, 296773860, 100227682, 802420, 103722614, 827975973, 911165693, 204967825, 653348287, 163917138, 475974161, 533568448, 624912891, 220810129, 965791132, 194277843, 525555100, 364787648, 684053336, 659485016, 153706464, 122691804, 849161677, 437221153, 750501513, 841478789, 557940394, 112712138, 783655906, 735627926, 10433577, 441551534, 242956080, 631677618, 378537751, 736680377, 359335943, 603052950, 162971263, 642682193, 453882010, 259515301, 55905804, 321304373, 407704394, 556377695, 529666175, 775110319, 697318256, 941773104, 660239778, 218384860, 713640264, 222932951, 646389180, 901387282, 780658150, 746459595, 670437999, 771627949, 747747188, 43309217, 188540234, 970522994, 123633849, 643799010, 907811627, 748985820, 352730666, 174175784, 353270135, 918152395, 150690387, 135023182, 831082723, 635819776, 932661733, 244873981, 885919084, 668048007, 218695582, 201331957, 236590206, 942737556, 638886701, 454569159, 675211633, 886171285, 562678125, 83798051, 751933920, 356120266, 518517310, 506163592, 346967922, 771038705, 967614452, 563013570, 529689803, 825309636, 920615089, 270325149, 728516152, 55200889, 198623677, 240160886, 881520310, 748209495, 551912620, 284739116, 830349484, 270506627, 851213098, 192390595, 914661513, 514066018, 245455251, 685656862, 111056197, 457616726, 927892129, 168115286, 389751679, 432262019, 500253009, 663140801, 189160441, 127254305, 919058802, 21216382, 157290485, 612600482, 747899567, 129624873, 889436039, 344889008, 688000959, 899017473, 681999071, 481317841, 364940848, 241572588, 475686051, 793434370, 11571669, 309466253, 195467540, 884823961, 163894618, 642142214, 99795696, 428697059, 708602081, 787376221, 940817620, 279227194, 749747257, 991342722, 562154467, 951288249, 193987896, 124587166, 200889999, 538569896, 760101880, 782068876, 944548401, 206053404, 269472958, 76329983, 225781796, 107055211, 582592725, 479373261, 635244641, 425952186, 559645658, 120299299, 942965602, 714986539, 553400962, 208669486, 864388718, 726138132, 178558931, 5230383, 581142733, 513188702, 137517076, 262276255, 225528093, 754204409, 241237664, 637418859, 280924563, 821507774, 543518143, 94474232, 210315956, 223582515, 314673168, 380642031, 299747830, 594591562, 599447956, 843257672, 403656747, 201935505, 644671880, 228991568, 843448556, 196185998, 940350730, 89607113, 312235937, 816471094, 309941249, 374241345, 157297211, 192817541, 857228996, 437228966, 121341707, 316944066, 588508253, 628915835, 698675095, 309806459, 600375776, 40766610, 753263432, 801074546, 889669974, 454372591, 782189255, 87663819, 41081436, 669337203, 637283067, 941294443, 611741732, 266839626, 727733717, 954893075, 860458219, 712756669, 185804779, 766649716, 102585076, 713981701, 894468268, 107104481, 83958531, 388834566, 706465474, 781672966, 165392837, 65249308, 303992456, 163930867, 249845653, 167901306, 853154544, 740156405, 496537489, 63557369, 965823678, 495477540, 482076264, 453173351, 265651110, 840490446, 114730922, 275458267, 855955592, 827358817, 262130164, 831528530, 341212945, 901638454, 709463956, 94313225, 886156361, 618715858, 503236732, 404434227, 425140239, 81476279, 445359319, 118860541, 14396764, 987526624, 80958778, 916242971, 3146654, 615551281, 410946518, 245550354, 46197941, 718828383, 299389816, 787043939, 2860815, 750513850, 904872916, 416479325, 650162859, 636644485, 906268495, 788577695, 699207780, 816014185, 931463695, 866550665, 454828185, 432080736, 956798729, 429952822, 375217537, 430270421, 314734597, 780450884, 304366803, 688054828, 980354252, 969584237, 397124998, 321102820, 467241756, 73302283, 326047368, 732219487, 914748705, 96686947, 567436414, 230999763, 690002898, 109749608, 671414875, 421353736, 557408152, 572859943, 428681194, 179775507, 227056047, 780693620, 799745862, 689825828, 152017291, 624057497, 943895275, 235643017, 64354483, 891031532, 43758217, 804727600, 110400916, 794928749, 220390356, 524181423, 206150240, 313121373, 518075728, 824519979, 967990446, 60178502, 913824865, 158956838, 466287286, 235013603, 132361729, 349825160, 591390437, 366684410, 805777694, 874985871, 602541580, 669852417, 989572838, 522456778, 737714092, 933825022, 967236779, 602552439, 653889227, 746283648, 645256871, 714726736, 251047623, 647293292, 254182929, 427591235, 874892423, 688945418, 303176096, 993853003, 378425589, 144563857, 760135594, 668179085, 933228983, 439321212, 393816885, 933930343, 221454711, 511951201, 497554587, 50563854, 444553027, 985732914, 478664178, 847747748, 825670359, 970603469, 106880642, 67993113, 262143429, 919658418, 832197784, 786492599, 205620916, 851230428, 404162642, 805666987, 546650945, 610110774, 831078894, 905756392, 875312579, 279704890, 566421218, 451149663, 559069892, 927495102, 821821548, 723875362, 549334341, 253005013, 700964520, 140719178, 264139827, 159715763, 58055964, 986587779, 964833484, 330349881, 359464570, 226981153, 804421991, 390786795, 527935481, 364634650, 787052673, 129136187, 52975326, 102135834, 963577772, 638712408, 209823917, 588093761, 233611474, 574197566, 130725444, 51599050, 271493072, 149385805, 350960787, 328947216, 722990515, 307702797, 556633978, 45552207, 603686063, 721498815, 815866986, 781829339, 396518783, 597814820, 692039821, 358439087, 381995152, 314525840, 240473861, 303967235, 160766944, 292818513, 706206914, 630155464, 98464758, 547739301, 174915674, 174460926, 210287740, 573666233, 254620114, 581945368, 809631073, 872204785, 996516499, 292824823, 872909761, 206698861, 159418252, 518505943, 162804443, 877172487, 356260992, 653525526, 218948090, 804364149, 319527091, 563542431, 899070820, 575582665, 315404329, 241181519, 721042358, 474816443, 742704705, 802668770, 13023433, 410511950, 888780154, 969011895, 601423310, 347327637, 146814502, 525376769, 388924125, 340929687, 242713648, 569449111, 247374196, 440230149, 702205992, 381641883, 835722490, 499582808, 637505574, 288476745, 2690549, 570317282, 407263872, 564896512, 840110851, 443906764, 50717114, 938595136, 572035247, 994022390, 246250403, 200397762, 568777958, 774316009, 861457371, 938908627, 621679751, 655652678, 612002242, 314646221, 814711552, 8004297, 357461093, 99664156, 218943883, 372670028, 752194750, 574447786, 667672147, 83493180, 649912990, 199395557, 479050568, 490831266, 82457961, 935616511, 352533441, 387698385, 553922257, 687056968, 136537461, 775903445, 542713869, 884344363, 662119504, 971397778, 476454636, 295205168, 20773645, 605231504, 54041583, 771438540, 56184343, 335122280, 424645476, 421581073, 834677772, 637291139, 725316658, 536847710, 427564618, 14300506, 335892903, 485533546, 593907645, 648751986, 962761048, 632761489, 567386521, 983301030, 88610534, 314424383, 726831751, 335152619, 197868394, 263811507, 767653652, 856765690, 881157847, 979830858, 950879156, 801808029, 261155303, 343405497, 137325318, 797854595, 958674909, 784227272, 671588771, 291139614, 40237683, 367251836, 34037418, 127797962, 230651698, 211461102, 298942378, 731491818, 547563549, 810893642, 129278110, 809415492, 821167142, 242098342, 281694793, 66789969, 706770139, 410440936, 855241978, 4579832, 507227441, 169513212, 290700387, 946112974, 323201329, 370771025, 234093576, 889899550, 352609860, 800548631, 943154166, 336899786, 87674876, 957452059, 347156490, 364165528, 671150521, 435580783, 350767316, 302790097, 574553597, 153887988, 787471464, 607133667, 139053934, 540622927, 508290873, 916357815, 498235817, 789910737, 162948547, 907057468, 112348632, 64953067, 612129318, 318539398, 986969220, 832404783, 268582213, 651555360, 519167466, 292812377, 895460177, 268374175, 396125011, 829573885, 845350318, 652147843, 205209441, 436616341, 604473675, 508885819, 671617153, 214655123, 181161611, 193810134, 234466307, 278315360, 849671242, 291539939, 910345625, 630091676, 179521180, 663348822, 81419230, 562926943, 791084281, 135030714, 394103868, 117146226, 649652174, 559963689, 407362243, 344722819, 141387745, 57552106, 642014367, 402125188, 1075685, 814181657, 77931151, 672220085, 241748241, 553397971, 263663914, 325883922, 39416560, 557350546, 622478396, 490343233, 467716657, 292148825, 262821491, 404536730, 574726912, 555532376, 325480851, 412823614, 662693527, 415242613, 784909082, 523492060, 973377827, 547021663, 47475676, 63475157, 59279186, 93931561, 809799525, 367243639, 205783141, 705794159, 729919038, 684359921, 268841243, 707568938, 522507785, 418253675, 969088568, 415240647, 77387489, 186515458, 868840452, 521558304, 866359039, 415789909, 474603092, 242761163, 205991679, 836453926, 412676184, 942778972, 494184587, 836021067, 640251050, 352569830, 442830792, 203944210, 344201819, 590000718, 559216550, 127790296, 319601498, 614480192, 69298622, 785507764, 249443698, 438045397, 253366753, 318012902, 9259702, 98814678, 930705342, 242030368, 877493629, 302356025, 999302694, 655264986, 343322203, 980382933, 425256916, 415631867, 961651637, 688043129, 760448317, 803966508, 696860523, 932653483, 909279123, 546783526, 442335736, 630743382, 792993611, 616076685, 741540105, 828648409, 309014291, 371080545, 150447332, 269088355, 967170263, 596427707, 977151167, 526238146, 414687438, 593255848, 84428499, 431296565, 485676029, 78507371, 944659833, 802329855, 1005378, 813731046, 535417919, 51971057, 857948650, 229557370, 43607922, 645059761, 493902036, 659214528, 138840148, 213315125, 109777191, 402522256, 746824410, 53852611, 797937782, 862741189, 722510766, 855897239, 551552766, 245214423, 590530509, 887952579, 933701503, 912731127, 283478113, 98885082, 657371628, 253837484, 394908082, 547416383, 623697413, 372446353, 507497483, 376646490, 805749114, 443454666, 440121233, 145323247, 870552751, 863501362, 711763426, 310607073, 506354042, 507304842, 184304851, 471657098, 734229088, 702177378, 364296659, 406086367, 449681751, 716034741, 223743826, 145104469, 781269586, 691941192, 409759588, 172886219, 639878481, 967128813, 810553206, 40475405, 636806679, 613111193, 557826151, 227567700, 982865222, 703089860, 498808612, 411396247, 980994247, 133769746, 433801999, 115795547, 762581854, 91652430, 290458769, 674906470, 339219368, 164147952, 83039673, 49244579, 823208128, 451594316, 746758047, 998285274, 365667202, 573491204, 923295477, 602802164, 287408398, 387151552, 436592098, 311097439, 290197978, 420756390, 640244967, 567499971, 632783601, 256428167, 114012971, 177500217, 737972881, 189507033, 980653598, 67949978, 578024926, 990264619, 149425435, 716311585, 87395976, 800634531, 198841401, 629310150, 436158331, 811801516, 847646616, 194325306, 46884280, 284530354, 201693694, 905752774, 189335536, 70031641, 320281380, 908869388, 185884519, 882679569, 847342238, 956384084, 217086947, 992319606, 408469041, 134189252, 712559520, 585275991, 387206219, 376333140, 650728697, 292478675, 63468803, 216817963, 772134084, 142789709, 666808714, 662326412, 877438101, 527697459, 749117085, 859056929, 307502586, 313465320, 523034548, 643569441, 902329334, 462347164, 924246627, 605128397, 250735482, 238404597, 587986144, 990415136, 509120727, 570521221, 103627436, 451808377, 71785160, 605490616, 185234823, 454138836, 51092847, 293800659, 448121372, 57122522, 196085232, 973273557, 555348690, 557550923, 500325612, 626453041, 46266570, 847988042, 623170890, 816340207, 643399719, 772921979, 503148625, 977112882, 978780117, 282708741, 532500915, 610643447, 960508649, 553324617, 930194932, 720506730, 169510150, 467995572, 815593524, 497592042, 890483314, 916399092, 315069577, 959796714, 776879039, 875260690, 867249960, 136590417, 618254675, 57386739, 75203678, 147986938, 985080975, 333560219, 441069885, 45349815, 224620645, 103368064, 939226340, 934672401, 843917261, 92706438, 784941667, 249565953, 460678823, 517709612, 87395706, 384898878, 513775205, 861791133, 912188445, 594064994, 482764752, 540937440, 452183682, 712633804, 603797913, 718948270, 749564448, 966948234, 944511579, 523691588, 28954887, 23587991, 268329780, 218625960, 476037283, 198537673, 399684002, 764292947, 833267579, 501728606, 580793506, 53061021, 601135758, 274342614, 233910298, 208695725, 144373783, 951855595, 260551101, 304597936, 885224723, 512548784, 497569079, 811735930, 285400692, 140820268, 86351114, 264596018, 845855748, 41478823, 550015508, 787743173, 410596297, 205955023, 29741123, 642673736, 398134052, 620213362, 417759106, 991787167, 788617353, 283551472, 687434649, 289227471, 664182494, 522497930, 394368807, 543575964, 998493395, 407985986, 989445420, 385757514, 615813409, 703093297, 712482131, 341809736, 913254820, 671688201, 413482569, 290555274, 543298141, 293665474, 999603453, 671451844, 237246412, 893030571, 63366705, 693381281, 336706139, 792674291, 243128660, 330689988, 124864876, 814895656, 665316972, 576244964, 371939785, 581650122, 967783949, 503000189, 993944892, 286306058, 160281311, 782830022, 849029771, 153069499, 130224054, 758062933, 66859044, 409328250, 82387539, 116627709, 444336399, 388235728, 939710437, 398134346, 249109548, 978372327, 236721480, 437103905, 293981775, 86748208, 517853932, 983879565, 897630716, 766033484, 795414049, 85898468, 336350059, 945078983, 789818699, 98105023, 395393181, 51178565, 353099947, 641984513, 884756874, 16268276, 187310297, 947607956, 905490683, 972693767, 371948393, 11117819, 878279216, 613270449, 893846591, 227849214, 890554122, 65967689, 94268192, 675809369, 944583916, 7506631, 925710029, 931913995, 347447073, 374618767, 76313394, 542989374, 444676118, 488967157, 399610196, 251034751, 451915446, 256087977, 841144935, 662458882, 614623542, 426015610, 124265561, 696543816, 724932433, 881137975, 689335273, 629116224, 696835531, 820749406, 964710466, 358426597, 108236532, 172992307, 491969379, 490491732, 47651486, 825878665, 992923814, 33265737, 576519115, 91395186, 909293366, 817347616, 848475140, 449609424, 119239433, 424835061, 174432577, 191412201, 200463308, 951090953, 742459175, 482731839, 501006026, 149301368, 239338614, 296671887, 822499875, 626216408, 952282315, 709849832, 813373162, 70403258, 614360492, 136504272, 574351136, 110336015, 711095560, 739091214, 846130230, 694633184, 379418475, 850484780, 978872035, 264055927, 849814404, 903285680, 597580810, 596957922, 272447248, 720490090, 938294902, 183782834, 129905943, 12120872, 118890321, 527735032, 145328260, 756142795, 696313674, 654909757, 864152441, 35279309, 958659532, 807054521, 584106985, 165474972, 971345431, 434495645, 478462309, 84005592, 429092475, 314560358, 352833251, 706756853, 139374172, 545137491, 243320176, 473106385, 964837480, 254675666, 874246498, 473305904, 568221769, 803899923, 21281910, 281849234, 650361816, 197820612, 891258546, 297895173, 379451935, 792456877, 191910113, 408909000, 341140215, 47645108, 986257271, 229080503, 537863534, 652458830, 782962918, 394454370, 565553781, 79599260, 26583657, 24043416, 560253041, 734360887, 754044996, 60422702, 391543863, 545390230, 960680372, 347966152, 932179441, 976224566, 35023663, 29422650, 323362034, 606899421, 243520020, 817345135, 740753433, 84507776, 440378833, 755585724, 722156702, 427057666, 569025811, 956186970, 371006259, 32541102, 958174850, 88395979, 802468315, 903732907, 887154715, 646388387, 797674093, 151034542, 509238624, 569663549, 210039965, 917273158, 294044856, 811005223, 733660272, 374446275, 540766587, 529828258, 231301543, 616155271, 950638040, 854875387, 189829085, 261452910, 34819302, 161751394, 277107476, 826279691, 544481650, 873590726, 458190154, 370794884, 706560862, 848998353, 194916928, 315857887, 943018956, 507733699, 106913955, 346691415, 9932628, 134680594, 364512972, 591668427, 520209381, 799748675, 567511902, 994453726, 816573004, 426415564, 915532079, 571285633, 29626723, 228368565, 716442307, 302799883, 700704891, 376131445, 686565938, 190980854, 118788085, 896536077, 763868296, 385486858, 644375966, 582954456, 47362626, 379091791, 773862633, 456047714, 565956041, 48454905, 404158437, 607249165, 145328547, 344336854, 487479344, 513697344, 617280471, 789039147, 499422963, 904184572, 88375581, 530489260, 72542607, 282665587, 180633604, 528326453, 119981394, 351098496, 21459714, 745490361, 523576418, 607068089, 398481008, 842391552, 116751761, 875716419, 949456677, 258607917, 217220280, 984127794, 347863, 978621913, 346258607, 280792120, 81083299, 340955458, 827924514, 31475589, 596146933, 836176178, 243999663, 359554468, 149337993, 934637016, 431067697, 915839508, 541042774, 160377142, 661022030, 369241043, 189123748, 907938384, 691886670, 447171649, 830934437, 188427557, 31381768, 724685185, 383091185, 656613918, 431458561, 564492623, 832595525, 492451997, 308241308, 411250253, 202464373, 123244773, 718732458, 764399561, 797264480, 609038523, 457190910, 846188220, 347615467, 288433627, 299428606, 869334514, 757910351, 882671097, 437453791, 825785953, 143182916, 668814661, 818839639, 449912668, 22959214, 187562327, 511713946, 712407887, 743492229, 33303701, 350240624, 385488376, 310883613, 275864510, 168424498, 277177239, 965437104, 740148353, 163615707, 790735292, 334384172, 94594288, 204349511, 494158527, 602617859, 59078266, 312968552, 605082072, 405802714, 902331755, 493519536, 759019722, 467360686, 517554513, 802950117, 139467914, 302316379, 698487249, 760890119, 156004847, 950273521, 76477897, 407663443, 478992914, 943375035, 273973284, 595890505, 794768690, 270614593, 397995572, 44797634, 325926160, 610727753, 162256845, 186260157, 587096683, 498955479, 216517776, 601273482, 788013512, 876587421, 694380356, 502611802, 595065772, 82460973, 846575428, 367562834, 410558836, 513685182, 684099557, 601286261, 896400384, 209899111, 732155119, 307314656, 108947665, 193492021, 398814279, 365105194, 16347327, 544880351, 327633493, 167892465, 583588160, 466174538, 868901730, 831221598, 285500724, 713206037, 369789200, 565856335, 666836427, 310654392, 195715703, 577047383, 988696357, 253049635, 133285677, 366423935, 237615967, 836986567, 118319565, 693764210, 110712756, 55294469, 100794770, 332723758, 341087729, 603490468, 303773791, 891147211, 45471977, 182536724, 605462038, 315917328, 683481273, 735583150, 982291303, 16983773, 498085126, 653254411, 380705692, 347882162, 18859258, 287143991, 645365471, 282367581, 433208131, 561091538, 791060691, 834174786, 392509100, 842421256, 69581188, 823738280, 279766090, 813746709, 224565850, 141784151, 20184269, 812491441, 525359494, 113176441, 52441382, 747759511, 3966751, 582387318, 945275233, 236337307, 548548201, 81340389, 282014788, 762551212, 939274835, 809015741, 822372120, 605798590, 660478163, 919457387, 179592287, 153052307, 629645792, 889805857, 423108279, 666539673, 413804480, 602181373, 33053259, 844027259, 454823162, 62085847, 75883868, 341399385, 967347918, 911263340, 554551946, 376365980, 495013914, 986465069, 654757700, 148162587, 314934858, 409449500, 281613395, 243669367, 795351850, 275127407, 194174969, 846113854, 298602109, 915732550, 292995870, 363804542, 796559355, 509186935, 669365077, 504114780, 810822611, 865883777, 197907236, 158511131, 496387412, 593409356, 322311223, 725951832, 29930936, 465975395, 640772238, 623615292, 647757485, 354340568, 198630897, 161007072, 898004743, 728294073, 923057729, 529104503, 522403517, 13921695, 83132498, 136964168, 301758360, 412646462, 150080756, 129229727, 519783369, 930066983, 771019695, 645117139, 224020244, 154139722, 184835555, 458728129, 347676741, 671053158, 886894558, 73639145, 717522797, 217255675, 824591358, 995777973, 437432088, 784747468, 637174047, 108421622, 549730009, 830817583, 954544849, 408384848, 343149389, 832574350, 305997268, 285124265, 319191781, 777081280, 416431778, 726888669, 512707912, 212964476, 143611270, 428898252, 557864469, 709587053, 535962603, 221244078, 48640230, 259895443, 836805582, 426705097, 616066656, 168787322, 306704597, 951026050, 923566045, 661375411, 57129731, 460824039, 25613836, 271113431, 606408238, 982095813, 141775140, 529209241, 461754317, 601721580, 33662989, 780316696, 930708649, 11950212, 122348384, 994832602, 844313961, 270112498, 696930199, 498383307, 674192298, 353282412, 971315591, 976968347, 963870671, 439708898, 310279085, 556088075, 496601759, 9689962, 42496822, 102058149, 895276078, 680810689, 597994795, 618542449, 473584931, 387923049, 638291459, 728247113, 407910951, 513060056, 224497369, 913520535, 803161161, 851408706, 776291473, 598818386, 747238450, 108898336, 461063654, 609158622, 262638402, 304410145, 127576875, 535808235, 302864589, 230327528, 386393818, 222331859, 338278500, 669100887, 680247608, 758801078, 338605190, 575295322, 435336770, 147466053, 637894052, 725923309, 496579549, 205884300, 773710842, 524916088, 114694357, 477900818, 997491728, 179083773, 759407089, 989411961, 507366003, 257269159, 67614894, 512350594, 621110906, 484663941, 980130106, 540809255, 248944843, 980073984, 301838214, 863908376, 386804491, 468398309, 829815676, 34767981, 122691745, 112232714, 619477955, 200561907, 909270487, 145724888, 931842726, 70294964, 314093497, 3987040, 102772742, 271636640, 98958432, 477090484, 945965864, 622374960, 856614950, 484202218, 432193096, 732608492, 721106396, 468678814, 471540176, 938451518, 719749698, 184620592, 480021669, 5162492, 637217209, 457821619, 752496268, 981937709, 265489860, 223335238, 598615360, 790550189, 423630953, 660408443, 411438466, 237804333, 884475442, 764086327, 356933854, 850877587, 50894433, 428881422, 677316628, 888186820, 666530056, 848135875, 748689355, 372759827, 794719223, 898402642, 582422419, 871180539, 572570070, 330081532, 990926819, 338146599, 65380491, 460791839, 937961590, 343619157, 66605887, 229725038, 475062791, 426456870, 811989419, 535412797, 809741636, 509163576, 817918882, 679088252, 534899365, 324108325, 103659404, 59946609, 431944455, 153392545, 174477333, 653453570, 760269222, 493633273, 817680189, 18603832, 393784894, 767341691, 861086136, 600947469, 899568508, 457964086, 381598232, 288335161, 536404462, 629245306, 685826105, 956773348, 939417333, 942213160, 988078374, 648155026, 22514667, 201338804, 868859497, 368855359, 903534989, 479371387, 376865938, 801406303, 224922319, 295558290, 928431753, 415265228, 675132958, 28363386, 651162074, 307354311, 929993921, 137088534, 677451651, 883477108, 170265573, 469473601, 651694805, 801592417, 334978884, 426509459, 437727152, 945725294, 401288528, 469051727, 876890567, 336058639, 772880510, 165313014, 208150399, 513248818, 387011319, 855874898, 158471400, 122467879, 159888256, 50123873, 40597789, 575518185, 748566048, 218658629, 337903618, 635321908, 208785281, 203137096, 543832444, 395677405, 826211115, 943119771, 379603284, 84285730, 394102068, 374064287, 725496693, 843951372, 155442890, 530955050, 224212075, 440914919, 805471702, 790699094, 585196544, 430556272, 831933169, 12110425, 550640532, 346201263, 485507893, 368238441, 97970779, 566102684, 826088057, 712421906, 196399324, 428166833, 630458031, 805374039, 883449384, 387363162, 642749140, 670626631, 630370467, 929548417, 638387890, 412338696, 129689821, 310758212, 696594663, 379317375, 962466040, 910846038, 324416431, 355435689, 393017813, 82532629, 777415730, 308935479, 429786573, 622946332, 670960652, 573603404, 228950953, 923946981, 181896015, 952103194, 400596191, 912177830, 609660594, 19101817, 146328276, 790108076, 80600035, 284759084, 710277468, 154610829, 822247897, 663873843, 184436162, 402987697, 644427762, 417659583, 846734255, 440349024, 615144274, 744504618, 334246875, 939889285, 401480085, 315022912, 377554154, 720462705, 461011189, 328227840, 979573030, 847722010, 36320566, 46896067, 418546237, 12410429, 435574951, 154598117, 371570545, 121173927, 973997744, 927564873, 149383486, 606366164, 518996896, 803669546, 490499201, 870837475, 991741834, 143315581, 848788010, 733676362, 64132095, 727225003, 814149834, 349299974, 157010354, 845482566, 19492271, 26646585, 53448601, 826068741, 775660102, 45996241, 847789337, 351468439, 934109868, 557895326, 909500044, 563526699, 347678684, 385238831, 466439686, 502518189, 903783848, 590624922, 899184853, 178238691, 327257338, 588800523, 218495176, 73989354, 80487431, 850642840, 135125406, 630573952, 537741486, 667546123, 468552865, 349107920, 97965139, 42113865, 221864803, 728045304, 552763627, 424213943, 535657254, 496651885, 900239395, 186094913, 597979083, 985583520, 175708774, 551314656, 693720122, 217594805, 233457177, 792636615, 71378051, 976511786, 185576154, 415219325, 598342278, 681210203, 658659846, 173111988, 83866544, 745132485, 350610777, 999469185, 317433846, 103037689, 735641994, 667874720, 883964253, 930336007, 22417704, 697839083, 249760032, 93531733, 705110156, 521730255, 339378710, 216930458, 472963822, 768693928, 618702939, 333608223, 772597361, 700063665, 16972505, 336735107, 612759376, 803629007, 935329664, 972619501, 330488588, 653214112, 801131365, 724222451, 490859160, 807162623, 916074021, 52387136, 338258478, 472609309, 996660296, 262895664, 65821344, 66000750, 298261833, 921058879, 567635487, 588343892, 74556284, 70328532, 579460314, 299176032, 742187528, 744490540, 928965138, 618833515, 787741980, 322001136, 4123987, 418565516, 470377562, 328792449, 489101731, 868842715, 535683930, 79599301, 367144024, 653392859, 148574884, 312868472, 890199035, 854314620, 93782319, 154435584, 849870256, 423897825, 538436402, 649058086, 483024149, 984889592, 563071083, 357288989, 110756066, 6408961, 185292338, 13688847, 123442758, 788913421, 758455979, 183597742, 464805692, 363020014, 78274874, 5520544, 664558247, 244498434, 293081245, 739411826, 148805585, 138434839, 68138979, 443093316, 281977180, 978724444, 81503692, 269188288, 12518665, 999494380, 910354081, 776327108, 670146813, 108117056, 201542633, 429216365, 277479587, 563711771, 359172089, 873343719, 834026032, 818704364, 398444250, 99236756, 711413052, 771348365, 627405766, 967450311, 151712458, 869602267, 406521529, 366319364, 690644288, 780237559, 276812477, 901540133, 813266409, 736717760, 201948363, 939592258, 516492333, 670666685, 263008842, 782271439, 624645363, 417826457, 599066371, 900592915, 625522408, 238465785, 942806792, 362682139, 935906548, 289629557, 877277015, 779607290, 217444278, 637653090, 684885100, 663914698, 131920961, 410164089, 974956936, 201249381, 138526099, 153878738, 545804730, 524858002, 310734007, 817121617, 120482620, 591870798, 494544908, 240886188, 612037450, 109814526, 625955886, 680767652, 824369515, 105466232, 559755905, 801766947, 418437266, 54678474, 426321224, 586657791, 633046578, 630436365, 642575957, 43726052, 22797869, 83968889, 978825989, 904821988, 603066503, 76702536, 203767259, 895981640, 597936105, 586100644, 168107513, 235057813, 70321518, 638154563, 911979963, 923035360, 47778756, 871433643, 615677925, 407557584, 432990081, 774435197, 722743445, 347195489, 543102096, 186960209, 849523402, 282339071, 807974310, 866826935, 796902139, 80787841, 837195509, 714460752, 910377122, 18436391, 471912878, 788450218, 454598318, 983664318, 128728274, 386823166, 888030376, 877535897, 65582647, 989835248, 986013865, 951746070, 831006644, 575032239, 992170165, 193064325, 805158324, 402144348, 356379128, 750344260, 738271646, 751669685, 229437904, 91445590, 222387769, 35545458, 148489506, 544204783, 688283036, 401848006, 238186138, 962744086, 560515878, 797154780, 716672807, 936484, 461202778, 601025203, 18529777, 15576739, 78012365, 775302008, 480647112, 586153040, 163064755, 492263832, 827782319, 808806787, 139288949, 917232125, 820942875, 867634126, 16065623, 868484046, 986005650, 375563965, 452767246, 649296721, 162409754, 841356740, 789049169, 828486442, 838685099, 78426048, 183662123, 258239780, 294060671, 20979799, 454989175, 166545504, 846071557, 517227276, 326305977, 26080471, 963165010, 728423175, 160002735, 523965043, 762273001, 466452161, 971888003, 409885579, 492930938, 53301087, 451713327, 379658906, 862608600, 462398869, 921933718, 739244400, 301951600, 780040772, 872717229, 4524074, 232361261, 917916681, 797220425, 947324321, 583459451, 240204199, 289092910, 288165859, 608874319, 863203281, 954927846, 102262005, 585807145, 947065021, 128014296, 193439606, 490071170, 100938616, 199865270, 969385554, 242493275, 683118363, 769130156, 981839654, 298793674, 341214971, 471675182, 812863813, 847189106, 184301437, 447840898, 117719879, 268266435, 486697672, 639922270, 321877076, 817143022, 101089006, 23551392, 68178755, 807587310, 880948555, 230669766, 403679709, 998597629, 984571716, 420951197, 401655312, 322469222, 180315325, 404681586, 669024091, 743023273, 693379037, 976098424, 7636801, 833504799, 55130539, 171432822, 829687795, 52531769, 896000145, 126879972, 553807202, 863239497, 197070040, 809743989, 261179355, 442651008, 617744252, 329244319, 647453569, 561354314, 505241411, 9140431, 815090472, 463049781, 590398988, 456264950, 4329335, 994824237, 254004051, 106486494, 102865263, 921102658, 847305570, 268291183, 163536428, 591304199, 620060169, 319424412, 767779123, 827594481, 918823373, 304518924, 418396237, 317178285, 74430343, 75523683, 652764060, 863207901, 511829535, 205665321, 259324753, 209277542, 266935574, 378515115, 278827052, 874263006, 933221012, 575727447, 579960355, 876243193, 319341226, 211077653, 391024828, 395298841, 928894726, 438929233, 509621424, 871378720, 877234434, 513383778, 349723846, 564799735, 739154067, 320702017, 581338019, 637706019, 493265986, 161470655, 29813098, 182878646, 728701672, 315968510, 585221585, 177083514, 774404803, 94326072, 784002230, 223909709, 999985760, 550903883, 715296186, 920544989, 282436375, 246005306, 195953808, 104335600, 670061049, 154926901, 210387137, 627121777, 49998413, 207988705, 149080560, 826586630, 994467836, 940245381, 148604501, 247430842, 516573800, 266811358, 761784847, 482741469, 122707037, 525273493, 287159245, 349497658, 695855301, 509527772, 265796211, 567045144, 447540323, 101837604, 730149471, 539916531, 594324824, 797374369, 783991437, 277909652, 317295700, 605175306, 968724959, 988691807, 343977974, 936061490, 357486411, 592629334, 500329856, 409785286, 580471028, 237966786, 370175731, 887414311, 491903484, 695540208, 270245365, 482341057, 854047921, 547583163, 422660038, 107814013, 749221068, 630994604, 702243231, 784126310, 724419014, 743121461, 95157315, 119255860, 9237124, 26179161, 351554327, 394020399, 159386913, 402090011, 261319307, 796422192, 433964388, 579060194, 242715897, 984036331, 701671232, 828516185, 607276600, 481794376, 222498897, 322337785, 71636254, 186825190, 461965213, 966234858, 322612855, 206954613, 735144012, 133524202, 912713144, 731490372, 298088560, 576867214, 723352406, 876979166, 636635549, 781572313, 386042316, 996815074, 51563912, 826759796, 92951438, 236093506, 752925081, 284432604, 889398056, 375232319, 493264149, 719877130, 54200703, 33777527, 579817310, 357528509, 722467351, 403544045, 884279616, 395811877, 556671322, 783555353, 875357099, 821708114, 971899046, 275682085, 185581589, 8556525, 286448354, 890834163, 765432224, 412254337, 891309208, 8604955, 878872233, 738712161, 765001922, 553825741, 37844962, 532970735, 991781728, 127366756, 575845657, 656344740, 700090223, 337563385, 107662400, 48853721, 14425424, 494923714, 82550111, 461088874, 239326293, 932897574, 887903242, 149432492, 806700986, 656825431, 478204269, 540211292, 44404958, 35141237, 807109814, 174070999, 908498764, 316071196, 697124636, 749516506, 945721959, 860208249, 161619960, 118078262, 464767599, 182598010, 987493062, 792238691, 320447989, 274748523, 329689934, 347476841, 589567929, 4096105, 967183421, 737718805, 280882510, 313136529, 137723806, 953594126, 514977250, 300825056, 578122097, 189406287, 201973412, 849506309, 420137236, 591478071, 638987638, 38442904, 93089957, 267378356, 139894479, 410175087, 243606689, 300010432, 18151431, 717033064, 935354411, 520863887, 622236943, 793408299, 500693384, 976047467, 429544895, 855459195, 465022173, 243306119, 199968597, 363059636, 488777934, 738437924, 896544899, 711037247, 266257485, 558936471, 719361005, 669546125, 616370293, 754279547, 422967548, 571580337, 511615919, 401263786, 828411907, 261103026, 802347793, 213333062, 506364970, 826988980, 79455934, 320123466, 852877041, 685889387, 672439858, 185035289, 303860913, 341202283, 391189294, 191678116, 445579128, 531121547, 844525294, 361128511, 610001726, 863997351, 307985701, 295278473, 388063176, 244409985, 423691954, 487639413, 39376293, 516388941, 381694586, 235306534, 558757211, 637975501, 351316627, 653933989, 742676291, 583733309, 465963499, 392277794, 378287668, 596365499, 584511701, 922056624, 639711838, 429518633, 131311565, 258901377, 592862772, 719742759, 333410217, 992594293, 191678836, 887394511, 513965590, 374001140, 28566797, 157861811, 391094931, 584296532, 5247222, 574331447, 991709444, 281251376, 261680923, 888916560, 920286662, 778777499, 952337393, 489458975, 589258387, 144337879, 491828934, 955539988, 961540452, 885919866, 736165560, 445427161, 940907083, 389844818, 413139169, 506018830, 443489510, 375856766, 857777841, 923010832, 14909579, 207782989, 949830815, 153422606, 133819805, 517616860, 363863591, 277844010, 961716734, 144107084, 413985969, 970060308, 927828921, 486055613, 568310513, 446134366, 849105854, 358582980, 66883406, 311128683, 175419040, 414909727, 939970500, 565027690, 368900744, 624807787, 994685337, 336250879, 956511706, 451270024, 218119224, 581641736, 383229333, 805167588, 254399281, 316128555, 556332925, 139553121, 121867242, 42016189, 283398289, 804790856, 832146847, 129413303, 862346662, 286970797, 152130137, 419800166, 667873152, 240215753, 803455190, 469588018, 474772250, 462603781, 317161270, 323878041, 33917004, 884220448, 762345830, 398878589, 84130477, 292794401, 272855421, 492518647, 35862762, 486985222, 588583416, 374765302, 238455662, 537723549, 131843264, 88500476, 416834967, 625561347, 553783961, 25283361, 20363237, 846338810, 982930934, 420934177, 673265831, 79238673, 816226457, 174871257, 265174983, 653859864, 313926511, 429433779, 856165059, 361905504, 897246370, 163620640, 897550399, 725378238, 618625220, 616023662, 841588897, 420834232, 52262780, 594777113, 679184310, 446533604, 963518319, 804117695, 902561563, 784786033, 786808529, 244157786, 720216605, 123831243, 271331481, 840118133, 183273163, 190523733, 3372965, 575938739, 821222088, 450608956, 366348016, 901987092, 384936113, 704363661, 578849106, 911300876, 342800789, 999203844, 898395860, 771432022, 258867325, 281462847, 572451312, 485455721, 73344049, 78126699, 702552247, 47485421, 451216690, 232078420, 381979623, 261395758, 36577790, 351154741, 203115932, 492517869, 898081338, 163755811, 546215369, 951841831, 720070402, 556174653, 296785625, 15915395, 628961541, 541421813, 560282935, 280130291, 605277185, 101632439, 708538536, 801277295, 948356046, 638026578, 891262643, 554673016, 766852550, 469324843, 716636177, 333923631, 842569570, 392279409, 478089655, 878576879, 513237667, 132227323, 550319076, 709614676, 960965335, 989321792, 317734511, 846905564, 764016103, 269077250, 771693809, 668023891, 718320948, 17845312, 242892707, 217764333, 173366104, 765853192, 438851416, 944927892, 689113739, 755163853, 657313133, 534941544, 421995978, 271930356, 201110399, 209912261, 86891718, 418461288, 723963847, 584982465, 615832724, 154271385, 764499749, 632099730, 834862963, 229225280, 145860679, 969525773, 604437777, 178294642, 225238111, 228867356, 190321538, 610749455, 939581404, 500981036, 814818406, 975184275, 484817942, 968482455, 283215693, 110602294, 669111406, 404381980, 161358908, 619832972, 554494012, 578019611, 643238421, 628709118, 817636497, 169274079, 5597879, 584682566, 476956905, 149367530, 643123959, 691610642, 550782422, 294840761, 900446102, 302306706, 659782398, 418614087, 563653621, 962162892, 384135323, 436189055, 398858424, 44832561, 773822420, 736375423, 801225368, 103766458, 400510797, 157109722, 184498707, 534149964, 104937533, 243854782, 744572970, 110480511, 943378267, 187209744, 633243723, 525416358, 672556668, 156394410, 940897409, 917965644, 298580261, 365713556, 782865921, 320597591, 62864650, 573842847, 650549493, 308907602, 457066922, 131863500, 867895200, 27825942, 49539545, 820585186, 71700831, 724030285, 846023481, 57374155, 892751228, 412485658, 537678316, 945568942, 953592077, 793418500, 592251398, 954103735, 836335514, 884487470, 287179248, 83425689, 127786812, 450150061, 703608216, 697319890, 513965640, 180029563, 911261762, 362712662, 250850519, 430618077, 517760775, 806550662, 378729964, 958761280, 544265621, 812076810, 880442949, 800797520, 806771369, 759142202, 873344620, 831789376, 321438559, 496629041, 990392722, 815059235, 549863978, 653317248, 644999850, 109487167, 30232388, 49784214, 442986635, 195852789, 66041272, 861315957, 696431148, 876952999, 730852423, 803726480, 684097437, 418065633, 76070518, 620702584, 634371385, 788940927, 860155167, 659765377, 701695061, 551442195, 735019185, 84468333, 866615788, 123232178, 819524220, 132037906, 249149459, 425441268, 197011815, 565468631, 927441989, 122954698, 190170939, 354432555, 971877723, 801997508, 512819683, 702616622, 957331565, 849411906, 823430134, 820029382, 620995344, 917380117, 118686093, 733951071, 855077863, 278113365, 767962149, 451945740, 999182383, 786736326, 933696854, 298912769, 859268448, 439043894, 415981209, 229314092, 59743618, 213478216, 179079607, 6162895, 431052867, 432301996, 122336473, 549233459, 861070231, 222893842, 978734802, 721510393, 85261900, 728071565, 335004592, 767233901, 940800236, 943411826, 422576822, 840364908, 480917499, 645455515, 116365661, 921857974, 41264683, 404262830, 832032648, 415487997, 936127820, 453008573, 470293350, 782967474, 713684305, 728539270, 967072079, 200613918, 562850069, 847125515, 333349593, 969260053, 889558711, 690048030, 234340535, 726289463, 409596050, 183853501, 62045033, 183507178, 197473173, 578826907, 976827601, 775229792, 474904969, 84120265, 947784406, 172779198, 369701802, 362513935, 568849434, 951984989, 674052112, 933351158, 500402092, 606176493, 181447123, 867156150, 168418795, 612750536, 156768477, 257134441, 48385654, 245236004, 556476090, 460884301, 489045631, 652970556, 116384916, 610265134, 761817584, 838188377, 409888493, 466625044, 609531243, 139444578, 257637003, 222429542, 207095685, 107572615, 569281601, 953661217, 639441124, 327403565, 696605945, 348846116, 208131829, 562507831, 206743113, 209311526, 703238640, 740502660, 949935400, 521335597, 94608654, 540087767, 33737161, 843555187, 284047888, 487660797, 129056303, 243290942, 696560015, 657392149, 188405634, 985681206, 558381657, 928797328, 352070537, 207812910, 96789933, 559692706, 15918248, 403870587, 287596990, 35186102, 251925342, 766754334, 268066046, 995014233, 863695384, 868449346, 110157128, 16240724, 108127664, 763478049, 761725997, 485870986, 799595413, 532717028, 795574135, 183928918, 355378601, 561315087, 488051473, 101287299, 64629597, 125335019, 7478478, 456288585, 253175404, 385861953, 243056268, 563654606, 296569983, 237129077, 721504331, 337436291, 883441470, 449774448, 676385798, 987859115, 978993455, 663574553, 956199933, 853606037, 730448184, 510982157, 890354502, 939326005, 230898073, 635733667, 799200087, 298511589, 889748049, 734057670, 124708997, 763335831, 383132467, 157064659, 713691951, 987949411, 372730684, 73578093, 926834716, 163016361, 31885884, 557481471, 502568879, 544502231, 50124045, 325286851, 468433981, 952913463, 479400807, 197155145, 317453234, 462063132, 230167601, 258043263, 768541267, 809849904, 268166794, 60857939, 440940890, 855749095, 941818913, 737784204, 668429686, 623865670, 689919975, 536983636, 866713490, 880808232, 530606974, 308821331, 839211749, 39031277, 249049801, 980618152, 975432198, 295805205, 253512141, 919682687, 436669509, 3804605, 936315543, 645432078, 922679957, 248735911, 244213199, 954027389, 851692056, 722532916, 114054733, 342542645, 943620996, 516744219, 461887824, 546804334, 734876356, 7875718, 175265944, 207775127, 973992521, 472672309, 413310457, 636018083, 507218601, 172783130, 92331011, 459467397, 23034552, 439707464, 736683516, 401674814, 625816809, 505245917, 73478986, 961013274, 444409303, 499876956, 299244208, 626989940, 418692475, 338133810, 305822499, 829160868, 497570075, 858917452, 596662583, 454978612, 252438303, 846504755, 533636028, 628640951, 243406706, 396814814, 602069395, 408062565, 139501049, 218180870, 595396917, 853046775, 738972202, 302201509, 178308982, 286610589, 56821173, 752515074, 289823477, 421124067, 90495585, 998546506, 811643781, 978905097, 778393505, 814415800, 47526016, 72868536, 301035723, 959759305, 244278310, 463490645, 273282480, 854584564, 81429874, 591759653, 123668808, 927200554, 649841196, 743693281, 108945510, 780567274, 908365358, 183801884, 906512693, 317290432, 100720277, 570766736, 925529738, 42878123, 385098741, 92468211, 34794978, 624989961, 946802048, 160571289, 686885976, 474534754, 565433872, 620006839, 859988294, 61751658, 621879080, 295105925, 74185541, 248582034, 800385790, 147700441, 590875925, 409074247, 746148383, 948897946, 72565427, 624938689, 742193194, 844666512, 431429349, 896909005, 334946258, 124004284, 200358189, 132630360, 419216711, 225446069, 580106066, 643226801, 878861394, 715458167, 45734933, 537148144, 822297631, 346184696, 107177718, 691319141, 34139004, 903870792, 866906590, 905230451, 147427354, 426957858, 51313831, 155462093, 195609577, 176492027, 750943227, 644886038, 52318934, 72924094, 314810869, 154362719, 576994184, 541908616, 674199706, 295200778, 924386683, 977785318, 527463893, 944105023, 8095163, 166552500, 126288286, 472374301, 333544159, 791454926, 839879825, 552886248, 889497317, 812341796, 115608056, 573861727, 804546687, 947872377, 665993884, 793000925, 764061000, 910057083, 963983997, 692807526, 746568372, 555869688, 582112343, 525747555, 207485400, 383887236, 641080256, 602867203, 566022551, 74472867, 954024735, 82098407, 405696863, 789728792, 890604045, 414619500, 79788409, 415548088, 458935442, 113056429, 420050521, 283213453, 301210948, 336137586, 403534285, 457734818, 513294509, 34250360, 54957247, 772406310, 941326679, 181224083, 248982496, 556436093, 962181719, 331903936, 46887916, 246662018, 678602924, 999323789, 255698616, 8558411, 811220948, 833262509, 301118183, 169758274, 255911512, 794695992, 78557618, 984590089, 768930126, 21165481, 334301450, 615767864, 966840695, 992946270, 605997756, 980507834, 33213224, 155246337, 202309857, 437590829, 173324727, 821886591, 824928290, 832128188, 397584202, 385195185, 463286923, 98074274, 771558632, 945790032, 428653060, 882365327, 553498533, 305449813, 374619232, 85430302, 650713983, 382275507, 85078794, 130015550, 650166113, 6201216, 335325541, 755736633, 135333549, 728893253, 692522038, 898422507, 443037697, 645244974, 801876382, 920310914, 935958324, 469578948, 15566871, 352505724, 858454279, 546829745, 742346719, 939321019, 329466560, 13522095, 373348625, 454497819, 211751866, 168974789, 367292447, 450272358, 213258689, 199908230, 741435466, 493822465, 243853864, 759168970, 414291331, 945134823, 164233710, 921643418, 5929120, 476898788, 164255149, 755327720, 687088597, 39585946, 442299022, 778179212, 250801581, 949479253, 932661019, 350186734, 345082494, 560863108, 238799548, 972396438, 774812769, 708386005, 147922554, 74014704, 326026433, 954381278, 111962723, 825276442, 58967580, 533232524, 400581102, 465912835, 766426244, 521316891, 756361548, 879053351, 797922313, 804176060, 278440433, 269909561, 697584476, 706061807, 417013061, 178407323, 400342717, 594740490, 273338771, 922430628, 342399176, 688423261, 799932899, 914066218, 925911917, 452208887, 680083162, 843754594, 713904796, 663797351, 436169849, 917141765, 2652603, 509299879, 218294413, 300847260, 351015122, 662108549, 12965733, 705562977, 942467260, 580396858, 711716061, 118432294, 382856319, 466675083, 12970803, 895387451, 64507559, 603293605, 639305727, 606299645, 928992497, 646070233, 661917590, 560953732, 653257056, 696731539, 35661514, 383837410, 238609731, 352127954, 233442359, 687715815, 219004375, 217669976, 325852825, 809722632, 689961391, 63293844, 861303418, 919696031, 449087827, 542864064, 166828580, 707811570, 37063869, 729080780, 217421941, 623809801, 594099522, 485199498, 971370574, 419186435, 570507835, 931703628, 263306277, 428892602, 755934349, 6628687, 837119993, 56797133, 313549293, 511998193, 7762095, 234343482, 688122709, 363824650, 618971162, 279627069, 466990694, 801533782, 116556583, 456279368, 814066343, 836855593, 760457572, 720112241, 348473513, 724070327, 780756895, 872083732, 72794103, 676336314, 181140680, 854824445, 43606405, 637610718, 997242111, 450226058, 440564875, 665817734, 929003123, 670404019, 227246140, 845788645, 654269213, 762602539, 933628803, 656551083, 842016208, 256368928, 479747124, 24086819, 189462506, 129696251, 866156487, 537327116, 780348620, 671915829, 437222280, 331340968, 444783267, 10205821, 48949948, 746046131, 166279234, 410671114, 434463101, 535925376, 657981290, 870025143, 857544737, 284441812, 646473599, 58430625, 414427662, 910453504, 771083079, 730834392, 585564890, 784351443, 885539225, 798236981, 978864711, 497994456, 906710962, 535199469, 746730811, 677965339, 13136873, 827828841, 722699150, 400759494, 455740864, 347338412, 297067885, 964118094, 187004499, 38092144, 346593569, 853330196, 408954545, 462313971, 245750055, 930943944, 359601558, 706386049, 46256831, 225561784, 25993673, 935329410, 614762920, 164529965, 532177559, 194772865, 542557078, 705570508, 121335378, 104971078, 76966474, 434197583, 552807438, 845904310, 650894330, 471112340, 825446750, 79208803, 650138781, 670019194, 86550945, 653849213, 541843129, 117097236, 943558622, 971667633, 207637216, 202680745, 529155198, 548004412, 221713777, 975324996, 172525278, 726763881, 970382372, 441965570, 286511314, 180745587, 128099331, 522288363, 179101348, 113009332, 693278239, 165787884, 977493478, 444869868, 124951969, 795974439, 672117329, 206621603, 925978891, 14962991, 822415659, 407450499, 168616147, 799890467, 678076709, 459555230, 982374811, 949668304, 610558457, 981665622, 856374610, 227338689, 54031241, 778488867, 922420537, 855382644, 792212049, 908681085, 541636110, 484845447, 875980199, 105656496, 893730031, 529722935, 379247771, 727283938, 68254597, 627431350, 533801937, 49583619, 274135423, 983900460, 163710934, 246660878, 491802029, 49046494, 273446252, 204392428, 206684991, 4578761, 17663093, 270854126, 257135498, 306587470, 71062784, 9816227, 797040122, 566231691, 393459895, 620932404, 894175182, 203988344, 960828116, 961669090, 360960043, 466846970, 993046924, 192986390, 217078014, 751437754, 377461085, 579993475, 189707328, 380385976, 334735631, 984564433, 364808186, 644011595, 454679267, 369788286, 743210347, 658789193, 694526276, 614603658, 903002374, 757449894, 971184838, 785591698, 653665953, 792382800, 815287806, 207586578, 313689024, 425373826, 756758845, 134367537, 864922394, 268398028, 522474130, 445043819, 58084183, 504205277, 732069665, 241572395, 925876602, 824406913, 621506162, 676912276, 562099521, 739583204, 18488016, 250453822, 80846471, 351854943, 380350429, 624189390, 191330553, 351313879, 943851726, 739786039, 966536393, 144475294, 282953210, 155354222, 7287840, 146532134, 607362900, 629858231, 250631671, 824688097, 669089139, 567543809, 246429470, 197696936, 300628375, 146332001, 499898988, 214459409, 607666965, 74018661, 462462893, 881045838, 963271030, 691631338, 12727226, 410980531, 973322754, 527226655, 218879406, 448263772, 502877244, 192007210, 667346480, 376086720, 895906829, 833714489, 148179263, 450185447, 874750415, 242716745, 978868163, 503553280, 432688840, 197651162, 218847137, 175064772, 880450131, 579415321, 300810001, 192879343, 104792208, 492996823, 904127001, 974780321, 125767132, 750216332, 264306583, 178141899, 765180974, 675328182, 716087755, 578965274, 472386596, 318015858, 158966756, 63733962, 791892501, 223656314, 265976494, 878456606, 213421455, 866713523, 825718545, 672506322, 534711986, 161162629, 631302531, 497351843, 8439044, 80478016, 723946442, 723395439, 271348903, 410139887, 526457438, 811302139, 692980289, 110577805, 351022341, 819604592, 480705590, 615772641, 354527060, 683392286, 370788517, 640131565, 282030410, 440405407, 628448625, 575915755, 543031344, 893990428, 717218619, 259439708, 92789436, 779004654, 173745660, 656907218, 340310153, 366820675, 822567322, 560341182, 115733588, 824867576, 998439053, 796114459, 210111855, 60687100, 995132197, 261004456, 13750573, 809836371, 165206773, 79970778, 943322939, 569104477, 47501225, 394927677, 552906513, 618998660, 550643197, 156764583, 402102413, 966850485, 501922337, 515823547, 891358954, 879467292, 955039174, 404929938, 729965317, 348510848, 282864289, 382423141, 17036075, 278820701, 196297297, 461072446, 19184476, 948364848, 146217083, 235520490, 341262156, 598562796, 79241743, 116609585, 801860138, 480914248, 452952770, 708932564, 296745275, 318419927, 600616414, 473082920, 159917889, 16757747, 440862318, 358826586, 400786425, 231626177, 7735213, 815291196, 630832271, 910996084, 349747096, 150299641, 339116648, 77372967, 51497529, 553258274, 980490692, 608489580, 791456404, 296314152, 686872572, 539024317, 817560304, 641951104, 590740350, 556997991, 347397734, 607705182, 915097141, 504005080, 845639289, 768237469, 373113132, 314019770, 578172262, 609049096, 788275931, 976215950, 978169548, 85945465, 989663555, 522847441, 286288656, 487905210, 909098820, 82666892, 731144327, 886796223, 194967197, 317454095, 947349737, 242505510, 114810106, 740578844, 941279459, 528674846, 914529414, 890510287, 420493411, 953075953, 451736139, 266453626, 491027008, 119927396, 306688395, 168352063, 106523159, 245719944, 867133775, 721641820, 882012296, 137061773, 691720869, 894806121, 594717944, 903726117, 189079980, 374092187, 945457526, 160046074, 767557840, 689446690, 666042143, 696527251, 690075064, 205648252, 681661951, 77921661, 493144152, 74746597, 76989354, 193236912, 766151468, 354614079, 204177585, 650823609, 379288522, 654025221, 455892255, 648357859, 448436498, 956053523, 428336872, 936432983, 953836563, 541865142, 109707853, 238884552, 163425570, 986834532, 589149591, 230873182, 398135720, 280266549, 52910961, 904131833, 94091961, 144934266, 916318280, 97958124, 38949822, 189686929, 704558308, 300450679, 554035460, 515078442, 119632502, 825360395, 175642358, 676262299, 818907157, 435668438, 971509964, 489116101, 770173068, 227949212, 808871571, 514847647, 822474886, 169796024, 288199152, 505655071, 739989862, 584555640, 400994438, 300911934, 386476998, 988778110, 337922499, 332660827, 801782390, 479799996, 282333138, 915794252, 62017469, 334863339, 909097702, 203258927, 186959648, 265206872, 370589352, 909673335, 499327078, 626959299, 873309880, 669697616, 386521521, 619736043, 198461789, 600174355, 934732559, 966470133, 913755170, 423672963, 862826369, 325472397, 874444800, 643669456, 962678750, 954503394, 402254465, 103028876, 376237258, 214529824, 64597247, 906338055, 437683209, 118542070, 637018216, 782550038, 215950498, 447255083, 285804080, 433924860, 716732131, 940196737, 138341656, 860083261, 555855611, 471579496, 40956568, 309420585, 84020966, 536862747, 483286917, 230045491, 669909639, 696793956, 901908841, 428959095, 862449859, 720189470, 553832007, 763106483, 958394517, 266697754, 634700928, 93450699, 699757174, 1236756, 80209889, 821439550, 758098335, 83698989, 536335401, 124616361, 444682767, 174369346, 774900222, 121989720, 690835004, 785951764, 884444315, 907769479, 30059305, 834800342, 186742732, 611936055, 101817761, 811737636, 314879424, 384779724, 909781740, 574532978, 984287514, 927588438, 359958715, 340767270, 638348081, 403670044, 626307051, 23436111, 73316136, 401465721, 795588872, 478477820, 702437102, 545692632, 467806591, 996967940, 897500450, 682802401, 765481351, 710043687, 319051325, 39922262, 995669596, 138706274, 266676083, 321088176, 661753060, 972744218, 373433058, 905655924, 731475762, 705263431, 582750656, 775727996, 6365715, 273481143, 660232970, 822423964, 241389091, 60851580, 492074119, 315054189, 874960831, 208860537, 979207445, 472556415, 567228785, 800417189, 746387127, 382635070, 639841053, 895099229, 285449882, 660100692, 403453130, 27801134, 356287860, 104009573, 750002438, 729723099, 598862415, 732856919, 310516040, 8101315, 307440247, 219069662, 699028441, 403337292, 949321796, 809114398, 892648037, 335656568, 670425946, 947213227, 811762012, 424133097, 203731677, 908170785, 721559591, 317613389, 993233448, 373357967, 139282786, 521880737, 123339193, 571886739, 317186037, 135212103, 417734581, 977627737, 364937615, 978921962, 156239464, 563791768, 640789078, 287836092, 537964254, 797500280, 4440258, 41048332, 970601650, 750944188, 391867333, 184714407, 301228262, 146979952, 834631876, 369080693, 496515306, 944351880, 989776084, 187330250, 8167202, 791976295, 102195594, 619575137, 910511755, 836305618, 963246860, 452986793, 959561968, 725526930, 814213751, 93690484, 803741083, 968161403, 317197725, 818656078, 347820135, 789806746, 382422782, 734281795, 262884942, 837005540, 875551361, 534431227, 834417925, 654081637, 700389015, 781949332, 909633330, 815570906, 795894209, 289673092, 278655860, 310673605, 993142230, 163133793, 545461522, 654031109, 550415517, 715607215, 843947064, 684054210, 856593546, 20274196, 50789503, 304389733, 612604798, 802423189, 286595364, 801374858, 779683852, 995794767, 235462030, 474510385, 189220466, 410523952, 946575086, 147697134, 277850701, 267951298, 689434684, 822654322, 531964371, 416471884, 336798978, 725067588, 52030588, 733785817, 395772533, 703368170, 49159908, 32728991, 497810933, 324214565, 756725234, 381326173, 867816326, 905638539, 436447340, 52523550, 942578443, 425987673, 74187705, 703354778, 825983989, 332387281, 949748996, 224676085, 280715228, 94304049, 61278628, 335585287, 165832928, 220764788, 749282578, 914372883, 67692816, 149049114, 141608277, 645794457, 316334236, 964682642, 974509714, 923009523, 255809125, 836718596, 132339233, 485568360, 657609869, 347073417, 243385171, 213162942, 342462718, 592258773, 86671451, 720921845, 718042916, 881218186, 191768021, 250996136, 557589009, 317296218, 445492507, 398155083, 719773830, 478631251, 919789123, 589866998, 260642440, 841441684, 712301690, 417463099, 152781457, 373471801, 657593486, 241684893, 486805976, 435335888, 441991350, 891469106, 349418427, 732241146, 572822893, 303612568, 816290496, 974078508, 931215742, 743194496, 503946945, 475615291, 12456864, 189371356, 470222481, 469152966, 651000766, 193630569, 152461251, 359046256, 973278037, 584228693, 773387499, 932495345, 866707735, 789804234, 496683790, 812272029, 306899430, 298187289, 247129060, 247008818, 355536802, 222349942, 677763378, 378875920, 75073122, 681049325, 946457984, 876476052, 830664032, 589036556, 629377258, 44428593, 203964677, 178889179, 653866818, 775984081, 442148536, 850953586, 259076482, 645691049, 27448680, 40156886, 134859064, 695546903, 407548299, 95527540, 659832308, 457581632, 573874349, 368057934, 933627926, 672777422, 763906721, 704577779, 782793815, 423458705, 373956576, 578364895, 647699906, 950124315, 926383391, 422591386, 239729150, 558311348, 106744042, 309636916, 864142021, 928381937, 787822412, 852228934, 701122273, 390286308, 94950740, 423503716, 627055856, 511796751, 901240054, 720557623, 735072999, 167828683, 854600472, 496137356, 20660568, 84772960, 451028393, 439110555, 781624359, 424728155, 513019228, 400000636, 743713825, 18970878, 723909827, 203056609, 525623317, 875194197, 749555863, 684172336, 24407556, 944680175, 133248312, 150238702, 547194921, 943248123, 413435746, 848980464, 592335638, 174447938, 100106850, 616600603, 12794595, 431208445, 389076223, 219160822, 434943510, 504415255, 41266623, 285679679, 988901301, 674037084, 493429866, 231403155, 28954116, 373005736, 63280773, 610939165, 988900661, 132133253, 385769659, 163667909, 338655267, 4067179, 899373888, 163255095, 357811721, 677643272, 972024935, 930051403, 653848955, 533414507, 194543728, 775693471, 988722718, 293686712, 35591166, 66095682, 66306144, 428755622, 99135291, 441782257, 802466408, 870694989, 154321623, 709291978, 284575678, 770029750, 107018798, 725153709, 771224092, 320481809, 820450784, 642053016, 478640892, 196098170, 102751416, 198956033, 682832363, 145869774, 232168683, 641090339, 268306989, 104315768, 7354143, 643504940, 75235978, 445360696, 996486773, 913755064, 213590226, 596982211, 473504938, 863480076, 234844774, 957625757, 624990814, 479526525, 5590528, 766841147, 816505621, 102504021, 170082704, 888266136, 852130227, 528909769, 288462566, 471725252, 107686847, 493899220, 125722322, 635984931, 86003703, 95357300, 601633188, 909590040, 820211742, 65054299, 722303207, 649346116, 724855364, 880447433, 728669376, 695220438, 172119530, 533925315, 455607037, 877541319, 604496941, 667642581, 520504441, 29009015, 825396203, 57759893, 640451912, 783674331, 429759662, 449138412, 113352880, 599812999, 65704196, 925121524, 791715365, 608725065, 284917132, 54138865, 30862170, 53657308, 212599566, 563444918, 964534420, 935703283, 829251031, 893003271, 169808015, 155428663, 167087659, 35344852, 596321234, 832510968, 819587668, 555403878, 30259132, 725413103, 713393962, 136795407, 464432778, 519366103, 448078855, 938055293, 152910998, 318913640, 317645060, 592850464, 899971453, 198027760, 598305984, 348431110, 528192490, 237480630, 692655669, 660092011, 128299817, 681391453, 580779621, 433921791, 201149580, 168603407, 435883424, 907376248, 343066938, 873196659, 799087991, 491701719, 11564598, 919395371, 822886643, 126105916, 384318087, 442896165, 151199677, 930589150, 499847118, 214763799, 397527786, 974062521, 486396083, 250637579, 443348067, 576715206, 253049951, 288914364, 98147863, 779109225, 774354435, 938731915, 710389443, 446955149, 788217236, 413756022, 780806723, 758804456, 718216333, 426156411, 575689750, 546412972, 107653160, 494606107, 963680678, 848494462, 894673914, 462868846, 158769946, 313183401, 827763679, 394784443, 248344209, 316394860, 67470265, 933534947, 318813484, 111174373, 599409171, 767409115, 351855847, 127460263, 152772616, 956927000, 867313284, 162531527, 330725343, 622901758, 223890279, 633119811, 96056534, 655522552, 194525639, 751902760, 687324670, 970838215, 131522230, 746507864, 700356297, 494539796, 774785587, 498896998, 481382411, 825668624, 909361760, 7457147, 802059158, 102255389, 154166426, 810100323, 281264667, 472557158, 298603294, 25143554, 984201305, 146393915, 289639113, 200319119, 613257795, 624287718, 433009713, 45005359, 73274698, 510211450, 877004748, 859870584, 152890274, 850923364, 684461976, 880496, 324585317, 490449837, 509825596, 477030854, 971750042, 331460579, 622684558, 423551124, 875698385, 946937880, 808678675, 604714394, 809999417, 112389563, 226077598, 769266731, 591190396, 97424371, 905239848, 553405389, 606862842, 418319366, 143681859, 92733734, 529107161, 834087454, 196913484, 463489618, 692107483, 188844911, 74604738, 27860121, 854198376, 26391865, 798551382, 323110952, 722174126, 797084659, 222394618, 86538865, 612236855, 796455545, 569760988, 872607310, 764170533, 786739197, 405076716, 500004732, 808794696, 577932534, 643923834, 82299639, 513732821, 485909858, 249901196, 874936970, 460518139, 777129052, 724836886, 605742508, 219279401, 790259961, 254135564, 694628141, 816853822, 966776732, 267471992, 13458085, 574971776, 531932443, 4818253, 40172936, 694789194, 626656994, 35408279, 361255166, 877792071, 189320466, 387617649, 16069640, 209455546, 70388185, 963007372, 977820330, 586862061, 276482680, 712494876, 855427380, 45726951, 455283386, 610569655, 802664662, 697747105, 489044838, 852738828, 379784401, 687741320, 921368838, 651183374, 226344489, 373511397, 340410211, 214897689, 556554258, 224148574, 346623795, 88675565, 898911294, 232629051, 378635064, 105013222, 440986770, 410927406, 653053994, 227673258, 246580918, 763996226, 348993156, 65142319, 530627679, 167663144, 462383703, 692713940, 176238350, 463980259, 768699685, 587416612, 598480930, 537581661, 113658627, 98201425, 485885398, 316003758, 381713408, 264487271, 873425727, 944961086, 721526110, 949325388, 951101263, 616076593, 382220640, 30777869, 3168257, 564139850, 452910778, 574766463, 692114612, 487475223, 132563861, 574151066, 890876778, 487783291, 971615745, 917987124, 52240610, 902105131, 992925825, 561748116, 172847723, 941912045, 99944516, 317604375, 446138140, 954871616, 817866343, 909701956, 412733987, 360459587, 814749942, 86555695, 343483995, 517623141, 833611004, 131854129, 494734280, 265948127, 88313348, 666238834, 902004294, 506520668, 40936417, 342913172, 517456918, 830813664, 110860926, 911251171, 938790291, 438165474, 496285392, 177936496, 158548061, 486356558, 201029348, 638559282, 512826351, 233370683, 652457100, 403721265, 761970550, 281715457, 565044959, 350054736, 717222616, 977261494, 803764535, 979573912, 599672367, 191620606, 869764072, 50336676, 728554200, 127279175, 542163654, 838508776, 115729617, 353206582, 727685303, 170411327, 472578987, 32013835, 565600632, 491918635, 433413257, 298654468, 60274073, 16882783, 871938279, 746979894, 274003201, 984370693, 646489085, 164421541, 947272914, 45289765, 448213255, 970906906, 481648284, 461643210, 838997837, 305200063, 726218274, 331859055, 596767013, 667096755, 272587498, 689617076, 992920000, 748258280, 622024340, 275171663, 379366387, 775592762, 596045052, 434642822, 819024614, 909963923, 760097139, 290482650, 485420568, 939570800, 17890222, 806145645, 72822345, 526901060, 379800801, 514213706, 72571014, 889595375, 606085104, 187026985, 546940690, 290902351, 986007183, 862912330, 161553589, 458294517, 68494764, 550730050, 722700923, 751487948, 765172994, 474534842, 38583523, 697625598, 12206365, 968205697, 34681167, 777638048, 543699693, 13875814, 218767550, 890639454, 963917894, 650889689, 920533829, 83498887, 287006127, 689787285, 990684227, 820589508, 998411816, 775913947, 146510283, 838151828, 518561657, 508530968, 323072534, 986274307, 604031912, 395147426, 658770480, 512773090, 306945442, 97256366, 373075764, 975155277, 585666971, 796914028, 768731069, 344555435, 738439050, 463617061, 556911270, 987051894, 4498123, 717336722, 973130755, 102121001, 661081443, 848207785, 75981910, 817559078, 490248723, 961223122, 58778908, 535377781, 55046975, 70674516, 217134094, 413286507, 685319853, 219193110, 75698763, 963531920, 40367850, 832303279, 617048679, 831885599, 657734333, 923333579, 306043356, 933296586, 245504287, 468288874, 167395808, 831653421, 412587017, 370878678, 582676505, 64252387, 349796576, 273733727, 937317973, 812715432, 802375537, 221657285, 550257245, 119120780, 403203033, 37177413, 726897481, 639708383, 43140106, 758193577, 911198232, 345081946, 528357085, 9917646, 4148322, 469999989, 407331899, 192629793, 981707038, 505856837, 952483424, 657166367, 188484443, 367415379, 127345133, 950581188, 234077728, 237258323, 685992730, 344097921, 15021090, 30972830, 233161337, 409123244, 332396540, 160447272, 339608227, 564157051, 773016649, 205025574, 602975117, 877976129, 995350127, 989700002, 412922387, 566357207, 76412890, 823481338, 44479968, 691823922, 175909022, 707723249, 566472804, 961730941, 617340763, 893213126, 629730962, 471615950, 554711763, 312925943, 112669562, 705944599, 469943763, 284653987, 946865711, 982651946, 302254213, 705184433, 129135317, 569196065, 599035261, 443668168, 325014765, 438527605, 395773057, 133317463, 261653237, 622276760, 820756639, 781512883, 784745449, 395750058, 502419310, 934566580, 98090477, 209549976, 464639176, 862494731, 864037461, 967183911, 787407386, 227325530, 18108484, 820791662, 470701668, 341237268, 832145174, 89084311, 286209506, 47971365, 593325000, 484008363, 653479368, 411997811, 88243270, 412450491, 880704155, 805712662, 742514230, 799364774, 484164856, 546165162, 286849410, 431460559, 460298623, 642838100, 48456860, 131434284, 415431802, 715882416, 879213596, 319791618, 49828244, 717408163, 660433408, 723198982, 97852925, 203046229, 286547315, 308037825, 948430024, 738592353, 896387586, 647263513, 662473365, 449542258, 389973145, 358360699, 967184600, 416534370, 139871406, 651364087, 970436569, 404955779, 258775609, 520262959, 658091840, 130485845, 875611888, 194322738, 266763933, 421983241, 807806673, 919816682, 48431913, 830858289, 175528597, 43399270, 677750897, 705242415, 24111842, 850372875, 198169171, 510353766, 93112121, 950180671, 341096798, 946859504, 890142829, 600202144, 772695708, 153580239, 877223051, 897892711, 180659443, 749106570, 797365589, 875532280, 349049182, 360407202, 255728045, 193640327, 109180568, 701335160, 452250587, 129824050, 801205545, 635897084, 792260895, 898592435, 834378483, 541956981, 28802334, 273613697, 563384834, 171944030, 999340349, 341275254, 23186906, 655086696, 632368397, 154057649, 539651476, 484068784, 756901915, 712088439, 124034078, 270256750, 91369235, 181496742, 133458346, 689214704, 157194771, 694460389, 274592929, 346642420, 966938937, 265035214, 881594055, 114932159, 623574278, 765264342, 760000863, 45103871, 261864841, 5503927, 933212497, 441269663, 614463211, 971389798, 681418904, 891830892, 877042874, 272959425, 28459414, 751859112, 37760641, 817126776, 923937956, 358752299, 341165093, 523121678, 328700014, 481503398, 116179679, 251870377, 912612795, 868940509, 514133740, 1970405, 233202905, 773552036, 797609922, 10362259, 889833754, 411269402, 800533570, 269471876, 37879503, 95000296, 810818043, 623252189, 395626280, 614017192, 315091510, 14313414, 290254618, 538258271, 445830063, 46873178, 805416118, 474497278, 948380868, 672445291, 253956012, 729314214, 50567519, 348613944, 373014093, 332033389, 916401256, 571230958, 673954119, 725767726, 672777307, 430330882, 915171121, 471220596, 419563962, 927476478, 457041863, 366862623, 995855471, 251225797, 546909658, 923509705, 897751190, 281071699, 652679803, 632382711, 257581422, 710493566, 330333603, 508758543, 581569486, 205858597, 270913684, 532763672, 818230440, 835841573, 105141387, 311711080, 542270487, 683133326, 6980431, 597279440, 450032293, 617792164, 238900116, 287657604, 954977072, 136972758, 149391769, 794036973, 150162109, 358961962, 733466502, 901620466, 749793763, 815096283, 675827877, 176821411, 768002300, 835183207, 502911220, 368542183, 141842349, 903496463, 527643819, 974188048, 663986323, 856543531, 469423782, 781836403, 754315376, 94213979, 371071329, 1316610, 195017395, 543923615, 681820675, 39391348, 749104323, 296207124, 43093796, 617856064, 55406624, 708967471, 50431801, 915157653, 133245421, 897903248, 965194145, 259706706, 926938224, 56575777, 949576759, 138551599, 969669951, 347339879, 261837250, 104497471, 827250103, 43897842, 402526525, 373308424, 581317660, 724504200, 552542932, 231888410, 390233835, 329190053, 689094898, 183956510, 469255215, 140333076, 309475399, 884666513, 119198642, 449054415, 281924074, 926260443, 42631901, 926001388, 475304579, 765037093, 6438145, 594604512, 750477746, 606094692, 907894227, 438918047, 283877131, 65734055, 855526048, 96957690, 696341210, 226083577, 479368626, 514065101, 174724869, 75388768, 566173845, 220530819, 23736856, 410341975, 135384743, 773288517, 814815313, 85265523, 191709138, 808153245, 47921022, 968866992, 439788405, 319589902, 436552430, 524381706, 79404648, 825467694, 823527233, 786508279, 529191807, 10165901, 763600287, 678930025, 80169550, 521965370, 197259318, 789811034, 14439031, 214500670, 269015475, 724594652, 308776097, 7670197, 947954564, 642624071, 981592033, 750501744, 548096245, 266865277, 236360947, 723843999, 202668492, 44584609, 74401476, 538498512, 714186575, 114746649, 451370516, 305856619, 364615529, 710401962, 251706891, 636300770, 181453707, 773023365, 393171603, 721837888, 96252225, 416765062, 841278659, 767335387, 412418791, 148250558, 777807300, 766761237, 163555148, 80763503, 2737106, 211218679, 678886996, 380066157, 18577479, 127192112, 281916693, 680629615, 765352083, 827528148, 358211100, 145914483, 344048550, 434735519, 36908940, 276405446, 27348280, 112776060, 719202052, 637645005, 965353925, 372985286, 41761977, 44503051, 138187935, 233471821, 109741843, 54922450, 916397018, 464299321, 669150103, 234216715, 908073232, 142983075, 711751412, 778333594, 526547850, 848009963, 559201816, 810141080, 831910450, 110814048, 981950159, 140998325, 533723610, 397777580, 579768942, 328490897, 531236197, 137346858, 59424363, 991197162, 329117519, 561537485, 497718683, 150713324, 378928835, 528270402, 297491572, 50089058, 700303299, 742417071, 275864563, 504300042, 720016579, 988481327, 73429388, 704916999, 367543739, 669010648, 893624678, 89971742, 14842503, 470491616, 493891107, 759225570, 732342924, 592194626, 941495125, 915224278, 920895766, 638724576, 347542041, 228744458, 702763508, 265023541, 989822708, 51701485, 63219543, 501682306, 424310352, 492520883, 968922778, 988420579, 867397865, 764034408, 154781071, 738407893, 476260282, 537993627, 658203200, 745181486, 221523705, 271716719, 921447416, 120722234, 803309431, 468791627, 68072104, 298602548, 696502035, 196856715, 514218715, 114247915, 683898622, 872295825, 672472801, 692326496, 897645256, 848486317, 307770191, 817515655, 397321599, 885002469, 663426234, 822801814, 718819945, 519950887, 941230139, 386079113, 680326722, 368299923, 437243459, 685827268, 290810592, 534973769, 154978538, 214643205, 118176599, 347718657, 289617223, 770451300, 202800495, 244581635, 720644936, 278092806, 382692836, 438701926, 670458626, 176087717, 439883283, 782819438, 192844910, 591610103, 960366848, 822898260, 652257797, 47316683, 560849940, 614177497, 374414120, 227290499, 729930616, 21948186, 997368798, 40611421, 691035085, 514576271, 980927708, 142309771, 808831934, 768071310, 866585599, 421600085, 900436442, 108850642, 617216699, 408065566, 157221091, 925801267, 5617338, 756914613, 686785083, 101178017, 859694734, 867917031, 248122301, 903919994, 706831543, 709859247, 484698029, 581690685, 134833367, 673437567, 708016181, 787536478, 238357146, 569681666, 408269635, 891145582, 734573626, 616244254, 190461878, 788889252, 146703039, 524612155, 532370602, 987648864, 9018393, 788705793, 179046914, 588437425, 923679692, 838047897, 667492524, 660128920, 356677759, 103899350, 863318947, 982053234, 115869048, 567524331, 464721935, 42410382, 245467070, 78490721, 258553547, 674581261, 983948466, 405199512, 155762744, 441838906, 501531318, 802870633, 590312127, 821782219, 347569781, 415712290, 31109200, 171257836, 619847499, 768041128, 314763680, 440412564, 363210004, 545806461, 636318999, 829331436, 300683890, 953375912, 905251356, 504294927, 665171987, 237297245, 988878292, 734420188, 919076553, 444473613, 394521693, 831787003, 379453908, 792405247, 215954927, 195241136, 793077251, 827863115, 267085839, 977895077, 81561756, 153224494, 149417436, 624304262, 324763030, 130252350, 594495220, 343560416, 745457038, 496652094, 863818787, 901750367, 883959769, 337497160, 816388909, 384921392, 453820973, 819689792, 242487557, 539116220, 178874226, 531158902, 772924977, 229496616, 674796612, 959998829, 468921387, 697930942, 691817025, 829829401, 374940838, 164221087, 14930773, 567793336, 56627899, 925717709, 418215651, 233118096, 401586593, 924419293, 886918815, 357105668, 830862284, 123911693, 432929676, 766969645, 611495329, 371053444, 777413087, 778934170, 601713304, 186665767, 754816806, 133244777, 991618068, 977987378, 179905931, 971735464, 342742219, 910996424, 684729080, 990680548, 304530643, 244802373, 581090715, 129063176, 581437836, 300332263, 103359525, 50032450, 73773091, 439026009, 623850712, 369308227, 489073193, 496075115, 266787226, 236660115, 341943026, 63750476, 94527946, 708765198, 878542688, 872942845, 917698350, 189275839, 955170901, 660019766, 136261019, 647979263, 750986970, 708608765, 160557648, 865867572, 515140523, 628714076, 809658462, 177952284, 512233758, 53654388, 943837592, 230417699, 484213668, 542943601, 261204298, 37658903, 460632034, 825776215, 402332980, 768967622, 430076510, 920223559, 158697157, 783508328, 314403692, 55745093, 275665620, 871029850, 215138995, 966852847, 183924343, 400818095, 654072476, 509334769, 442219126, 232266083, 982358155, 94851516, 644089331, 690238816, 286090937, 352755601, 569719933, 152596289, 546623690, 39989454, 807341497, 379795879, 869982748, 55141919, 257017260, 677726165, 46499889, 624512236, 261648467, 158798023, 439542246, 201811768, 53644571, 932961689, 747695595, 573025611, 884098106, 339097933, 236403062, 895557057, 486656244, 335154799, 188987622, 485492771, 710766465, 689256142, 498483319, 9405401, 487050960, 534240739, 418549058, 291501987, 688465524, 195689497, 978102680, 955379829, 223529790, 600643775, 255284981, 227707871, 100536182, 283430484, 742444706, 430631631, 555543803, 19290594, 307357829, 37670511, 95625112, 426907832, 952945046, 436498150, 448337959, 298549293, 893907254, 430128135, 161939013, 239052969, 60008360, 145402807, 768430704, 278342968, 814713941, 157686947, 189801711, 48198584, 526666267, 324653930, 694168834, 866023847, 554404573, 370095199, 556418836, 296978423, 757836855, 131225425, 135896693, 787134212, 944955504, 312682768, 486293413, 612478445, 768639885, 991923312, 6763721, 472087332, 192307355, 667160570, 219989471, 105106124, 752539239, 198945025, 218602241, 551771209, 627979213, 710323035, 487896864, 981289489, 257831416, 985384337, 531971355, 398871594, 776220523, 975451754, 214354586, 982239221, 469215437, 385775779, 558938292, 991667434, 213251313, 360886552, 921505982, 825774909, 97846832, 847103005, 904814259, 810437180, 645174226, 647340000, 203901156, 483476132, 28447765, 729646318, 555747654, 513902370, 54643224, 336960731, 440335775, 470444114, 542371106, 396929985, 706033310, 956840255, 106670433, 160879776, 638477817, 975807067, 103097937, 920471228, 96711693, 872909371, 463495369, 558113353, 943365590, 451043598, 186937143, 343807503, 440446218, 302586551, 543588425, 95501816, 120747913, 548134379, 695075688, 50512656, 350523563, 267939209, 760051873, 413890262, 812805673, 997292214, 139548323, 634374832, 778589124, 175885553, 334174773, 566969127, 489790944, 707120367, 353580332, 165546598, 60940531, 787332413, 564063717, 191603166, 232136137, 288564323, 61288503, 817232083, 282598676, 666619870, 395883096, 172577630, 498291878, 852215754, 987679443, 332270687, 691907945, 904043668, 931736285, 461191838, 11856438, 475659896, 29459464, 528751751, 571655694, 358209836, 114037379, 858145865, 699900382, 309728506, 18255697, 579821519, 828531446, 278833876, 862220531, 937539416, 179153328, 429671677, 709732223, 456497267, 322496975, 353877735, 426899911, 134385382, 943603392, 25481269, 395559177, 26534565, 485757983, 715302078, 520617866, 907382902, 907895473, 293570445, 526777860, 899358605, 81029462, 163504416, 444066531, 308108797, 558579252, 762102747, 885391125, 350389127, 598845290, 410066483, 472131014, 11312324, 520972125, 241608288, 368751762, 837229058, 566034683, 672687608, 927265321, 358279026, 855290509, 416144465, 953744838, 136320887, 65539199, 522438873, 46904582, 26512159, 731049075, 823119958, 874738725, 186844469, 313219551, 693805927, 93781613, 997834136, 295565803, 729503941, 555145012, 413518548, 927205134, 293472036, 843114207, 713112942, 482677323, 823515329, 725616759, 886453943, 305401037, 615697406, 251912382, 158494648, 581134588, 412751612, 277467603, 580877623, 699862873, 757647484, 363158101, 563724332, 718898075, 358733260, 335161888, 114775721, 854345489, 352108753, 176890356, 611420256, 664360440, 371373184, 493590328, 57145597, 505674188, 131568831, 851263796, 773294493, 708674433, 713582964, 930782408, 678774637, 823044960, 672349536, 850010460, 857908490, 919851762, 280780344, 819910044, 568861277, 168043380, 649079391, 819789897, 11879246, 300830337, 920652581, 9946580, 764012373, 691572737, 340990525, 510731131, 273766907, 522235910, 592309591, 2436070, 140631884, 713323322, 245820310, 924323146, 776562227, 877248271, 275687173, 919332742, 473529332, 383219686, 378253146, 340949644, 377990952, 800097358, 804145260, 319937370, 200557651, 30547964, 412177859, 813920244, 403776855, 559867214, 771199312, 225025143, 734504121, 945839396, 142717964, 175239797, 442883168, 865762039, 208599029, 934089945, 522753532, 820109153, 116871111, 83057939, 180814758, 532674936, 195664337, 775993087, 820085825, 448153887, 92384935, 656214871, 542809135, 746435163, 89830203, 817186679, 521354898, 673579949, 496421398, 914176675, 437909713, 205043425, 613075111, 935524248, 553537722, 687189888, 10544160, 818757740, 379971109, 607699552, 40098352, 257947748, 190602171, 254155466, 474871620, 396321529, 148412573, 250276117, 52218149, 282268310, 990358540, 16384727, 689596762, 386143644, 696144937, 571122970, 783617458, 622058750, 147556841, 512917839, 2727838, 639052376, 313161076, 281125401, 546407492, 385318844, 928085303, 742240304, 778073498, 111750515, 361297653, 39264401, 492909143, 502611504, 725080272, 474322581, 213127273, 800463587, 590339400, 442677176, 965404035, 726489392, 988556417, 868366355, 805105135, 303036950, 506742584, 968797527, 723953985, 900756376, 173824776, 16369228, 652222317, 958065775, 358678636, 547280179, 134372702, 956824841, 923853173, 232624728, 746908661, 632270176, 419280228, 835859911, 773614049, 756664050, 259454338, 228874743, 829356312, 269939055, 320071837, 850419981, 846854432, 594132263, 328166360, 458984248, 591369004, 739880660, 694125248, 712058207, 601349797, 650211045, 925295170, 641580391, 747955687, 89277206, 626657422, 6273475, 679266943, 338401425, 589706352, 100864936, 617217062, 133562633, 104461850, 904769506, 268259967, 706078114, 999550301, 898479960, 121855865, 190661509, 216193345, 695657203, 376202817, 961784652, 134084208, 260861736, 616879103, 297298079, 243438330, 453384057, 574811871, 326170271, 460532484, 119374174, 958495039, 744942219, 110973470, 88997276, 710644253, 814122644, 939356502, 462326029, 627421211, 627880219, 506022879, 252132655, 165335937, 442017318, 289526753, 611581310, 458405474, 142304915, 532451635, 177391573, 282902620, 431214435, 937244783, 862366339, 915470635, 424306023, 427998406, 67985558, 664866723, 123075556, 930074299, 198209225, 119044392, 919442504, 236530245, 259877986, 948304034, 354853659, 174372424, 895838292, 945395764, 681549659, 693197762, 715655589, 830322132, 50813373, 158047447, 368494283, 133524077, 554548782, 448967439, 493975751, 834192082, 142685204, 618704812, 861104128, 182325392, 690893553, 396995320, 355854880, 442112411, 88710756, 43403325, 637267543, 474751373, 359539708, 787092416, 533567970, 111794677, 241405962, 931893714, 311468889, 758334819, 587432386, 537538431, 719736303, 433454689, 561731908, 307762351, 340986803, 703198063, 681882760, 481966703, 284826128, 447925378, 611802114, 209293372, 743438365, 59346458, 306093235, 200057788, 224288854, 639188237, 974306566, 907285469, 816145496, 17762047, 292361165, 37511554, 435636703, 443325234, 692038689, 167298360, 805339378, 412236502, 497147699, 793642473, 176368783, 805246037, 235642314, 485143328, 688014882, 23875816, 817268097, 421669154, 701117240, 260122063, 164496585, 523895625, 708020883, 43463174, 590015176, 871929551, 654889870, 934093689, 393473487, 30803283, 590033057, 814882076, 617793879, 994548036, 926009124, 952764853, 498526402, 114395127, 147921078, 610105935, 865089298, 946077822, 449534496, 280766205, 124750285, 561472617, 435394012, 894447952, 963756987, 529830364, 656001838, 407590700, 253448243, 591898529, 664402825, 23116396, 439655233, 764303688, 913427406, 143449811, 71959065, 893975915, 491242151, 689796386, 555528615, 513299703, 139632149, 814773939, 903184400, 161468880, 980866662, 933107386, 978020882, 295187193, 193228819, 99216158, 131046233, 261429787, 530654354, 808644581, 684008831, 417339761, 120237442, 255751147, 598166894, 161687853, 662652330, 191012701, 796571683, 889185574, 931310373, 35059729, 770295611, 419841463, 213944018, 10439799, 464367303, 387277303, 971351313, 970911657, 839161230, 886335771, 500969274, 477940556, 499591482, 309348561, 820474079, 353855382, 968602701, 665254821, 900088060, 222477537, 539833058, 245905918, 28992313, 369166808, 675897669, 234730947, 206143779, 48099064, 775863376, 332547022, 689548089, 863248238, 742231482, 929781642, 265038512, 603372394, 677726568, 931449671, 39384051, 985762445, 15364417, 828547409, 892444252, 556711503, 662120617, 163873497, 787381465, 7504420, 451112456, 275629377, 150420065, 437639242, 122079914, 923495090, 622158744, 846114815, 73452876, 482975907, 546006422, 459829127, 53275721, 176169593, 166507288, 614794237, 533942405, 600214842, 181894535, 651520923, 387439728, 514337693, 343438347, 45963069, 844612185, 645036137, 418077217, 296318475, 900252518, 211525729, 134283108, 320418458, 267337764, 818544463, 3340377, 502810084, 277963207, 905065833, 43101073, 17622129, 241393633, 669158495, 645903405, 675757308, 80182622, 294363373, 980352816, 185276981, 766452668, 641856489, 623988676, 724973826, 351074332, 375012392, 452458287, 49557148, 700005350, 300924094, 748402418, 509967954, 198109850, 978782478, 102904011, 603693610, 905653517, 473885416, 29590404, 351873627, 849467141, 677373803, 935073429, 554503771, 596697723, 860223195, 197447638, 276510287, 244071654, 368328479, 956186332, 579750871, 345451278, 788699535, 833456186, 321190365, 527143897, 90493969, 472148305, 363552487, 115455100, 447673948, 571008816, 362667158, 372328084, 337167313, 691903798, 521550585, 852306792, 767240072, 321479310, 10012442, 234028273, 575914132, 578257885, 671457680, 407535544, 649522332, 376163258, 522724027, 643655176, 497723795, 708808809, 729566418, 854556393, 515983831, 570792350, 135840848, 367564120, 686046681, 550958956, 796667930, 601970576, 669050808, 398157007, 802359437, 875968612, 515845169, 192777702, 670755199, 457245813, 50557768, 931285441, 704058958, 999099923, 383793064, 529629010, 114664641, 83285356, 765463717, 410623315, 311450781, 491293941, 360393775, 237894288, 132819500, 312851880, 902658374, 968718397, 269482839, 745622136, 672921436, 643362118, 970109215, 633541396, 78158470, 296263404, 946374253, 953004789, 659339083, 531979702, 842547778, 902516466, 64994960, 492935540, 243281787, 494579980, 255002513, 581913285, 57491333, 197598346, 937549612, 709561000, 488023603, 386629844, 43579523, 994953627, 676471218, 459019977, 174326941, 207940658, 391808228, 215319623, 312497148, 324650571, 352001782, 715633302, 687050867, 968201518, 568541994, 392978258, 186687471, 822908529, 951859439, 266297459, 689472919, 620047676, 77882662, 138348727, 749340941, 167554698, 764920222, 603649376, 725844433, 398599353, 394289782, 116835159, 709828562, 45406119, 593020516, 933108727, 49221278, 109922937, 308986664, 45477833, 578119755, 747002232, 300456770, 176379225, 102258976, 996556059, 786526445, 303431462, 88698092, 29351381, 268785644, 449316434, 191286144, 802443302, 311323972, 658702861, 463754978, 695652547, 451537792, 421477460, 304831653, 957970109, 568596396, 334534781, 229589341, 371749092, 823676175, 702149404, 912826234, 223209013, 658123768, 626521019, 557403963, 463006296, 45700663, 402549091, 585844960, 622250607, 734687145, 844639586, 673496489, 682263198, 501385125, 235547493, 557091133, 82727985, 54432695, 559233563, 186639887, 996223803, 519274681, 372284166, 924968861, 567659428, 682094655, 438264093, 580862548, 639800250, 932389890, 212468472, 870295074, 874860276, 930731645, 307358816, 112533648, 797644456, 117584390, 663665946, 908121006, 789042031, 655320168, 779275366, 910026146, 988681892, 377391414, 880827085, 416099498, 393336156, 70117862, 132136637, 326273488, 891674782, 667800596, 974025406, 532212856, 188949372, 536514973, 621968256, 333354966, 320555724, 323989498, 971019060, 377165338, 601203721, 719047665, 289460078, 285844820, 900118967, 916745931, 453926918, 82617471, 72022506, 260935899, 16443016, 793197341, 363181668, 62198219, 993444430, 949627984, 810130019, 371102977, 950191648, 738679130, 133113030, 189947990, 563065136, 507281339, 446783185, 407941167, 665195614, 984184169, 649316869, 29691431, 970980021, 199739843, 160056059, 579722585, 789521664, 725144726, 965652644, 44098505, 404429578, 241887645, 455398547, 280964501, 435364685, 667532991, 92869575, 394277976, 982869675, 471133133, 821406811, 156937062, 946424338, 309558338, 855951955, 196371991, 342484868, 796895832, 985808683, 452205886, 573124406, 544767284, 570208140, 612552564, 961652113, 640164714, 340585878, 569825817, 829757186, 656638278, 996376859, 892648481, 192451552, 596470334, 457667476, 389165382, 784569978, 695764368, 563747066, 806280297, 107587730, 426198460, 391260686, 594721308, 118310010, 632434225, 998372265, 596989249, 520252399, 909625312, 488818444, 493713800, 932390173, 939841550, 960401554, 894565724, 451101182, 594982728, 156822453, 456430316, 554947124, 374141958, 849016411, 587542111, 507251098, 908645421, 915668743, 679651287, 114648474, 88510339, 110235259, 218288760, 473743588, 14544168, 854915858, 358988777, 976936999, 959411193, 924871600, 520381374, 300531814, 340265495, 188264440, 414713627, 322401167, 794621, 659462743, 331375786, 496179310, 15151206, 926782605, 691673765, 905063987, 140383706, 584768144, 51392656, 873937549, 429747552, 117959748, 294752181, 378621827, 116639293, 221453298, 259697474, 906573135, 106866921, 756375215, 55742426, 174211672, 672800182, 629139123, 370228745, 466816099, 680525478, 856135246, 576349930, 14531741, 157722685, 691326905, 614758305, 250479467, 486615437, 222594807, 9412181, 715458046, 98430658, 639246221, 355962266, 625944320, 404771964, 860585745, 923483401, 810396488, 383014094, 212480408, 158399446, 109377355, 614732404, 384685829, 999291616, 422575329, 850571430, 430099182, 490209610, 295101680, 414801901, 145611499, 144407228, 204776580, 957614532, 466080984, 416126399, 31264660, 841173612, 124150187, 354423893, 744191129, 466235540, 217077380, 638155761, 165324502, 726817028, 839122224, 933130400, 680461679, 482978855, 627829115, 98807905, 567554870, 395477772, 144483135, 852169179, 972642989, 138267992, 580376807, 632692337, 520766756, 322380248, 161068534, 676011512, 581026784, 281832760, 90769876, 708212224, 537006662, 683293206, 591411258, 743466813, 28063238, 284337363, 726465809, 90647679, 93404190, 950545737, 759017538, 531290635, 384724025, 598928941, 200167822, 133519209, 276098544, 552101433, 607424898, 401730879, 568034274, 664467861, 974080272, 776716362, 518666882, 790756833, 77423367, 540343226, 555656380, 822435563, 207830663, 962754220, 348940094, 603422466, 592571585, 744102196, 40991762, 859282274, 673651028, 538666300, 697108991, 509653414, 61438264, 78696341, 591197360, 228970148, 629403922, 520772433, 371818219, 309990824, 378797516, 251581470, 391391721, 294486813, 277285456, 86348520, 380229041, 283133695, 256944714, 774618487, 405259664, 485845935, 775203277, 20701052, 772054454, 210132048, 612088739, 118639908, 566394409, 635062535, 610832348, 93625448, 196881782, 39998974, 769821360, 147996432, 487689654, 869589624, 278776823, 996153821, 635585673, 324923317, 899554738, 159689954, 699511557, 586373010, 291478383, 526017070, 361938044, 50258098, 942903972, 343548080, 515201066, 560887019, 661974362, 661512994, 965575126, 931184620, 729132311, 748383473, 187075558, 896212530, 429593579, 408892032, 708885594, 949025307, 873299199, 987106633, 304964539, 697071821, 502006800, 640708587, 15047978, 323578529, 341596608, 395541597, 402058968, 557494453, 195379644, 230552149, 876799671, 674532763, 852453543, 408804577, 234426991, 70272547, 514606777, 118528905, 876058002, 533158020, 648163549, 948204704, 20207946, 920483507, 757607355, 452579736, 519841838, 110439878, 659781620, 696254672, 709218762, 78552974, 842476428, 66625939, 868521130, 890996398, 141463339, 742668951, 531834533, 465213726, 83297802, 534033003, 632684922, 710060002, 239442156, 295806362, 700367184, 944269261, 368549210, 130690893, 669822264, 974703662, 134887321, 583261285, 825398006, 457097879, 199644800, 170966953, 364158770, 611689294, 623815700, 542962789, 211448875, 73239338, 516425600, 336308991, 309300973, 179113936, 130936069, 793287503, 494900759, 436505150, 571184072, 234690918, 483487732, 530049882, 467228345, 298937349, 204475338, 732538048, 957904466, 658527854, 450609868, 189090077, 588476217, 172141159, 717317677, 474191560, 470114717, 956179104, 955420784, 796895742, 862620412, 115836183, 883612696, 565616701, 5996336, 470051697, 552701840, 711000701, 29821996, 313400341, 829727097, 826220729, 298848938, 624822809, 222141354, 254467669, 332743175, 695208013, 847899511, 977625406, 250897505, 205020574, 791901262, 956323844, 373628124, 63669340, 696026324, 31642699, 841754616, 881005740, 637821593, 423411663, 840392185, 326248799, 949517516, 898394816, 333522642, 984489376, 235397186, 637885098, 401617197, 1797154, 818107759, 209849570, 458840713, 774001987, 854745894, 735376263, 434165671, 316003502, 74804656, 353815344, 346962833, 252936233, 827522137, 586262653, 102914040, 412032963, 498081646, 12505073, 545080906, 853396372, 274539682, 92660507, 834433112, 562178155, 297017299, 625758837, 3150431, 545919916, 694095041, 86019459, 617643103, 534045221, 287305507, 65115113, 31658574, 450355052, 642120233, 284585432, 65681893, 999559058, 132822509, 58809857, 793002613, 983460186, 603006046, 702076832, 927324798, 927059367, 586953796, 124384607, 295636025, 593558182, 623649461, 26418370, 500953461, 507437309, 936435026, 637191837, 346420103, 805347468, 284662934, 80846853, 368278706, 191530089, 484735977, 491341510, 753441494, 666061716, 557472917, 470146159, 194534730, 324079187, 429799215, 783556963, 974880864, 137913623, 74285820, 992825088, 396088850, 899572253, 192090554, 49459453, 930021566, 992532755, 143491523, 980225433, 193453267, 479183017, 89878834, 828798175, 543822310, 14640307, 553519211, 341242485, 746420024, 365020767, 348895789, 175096745, 833697712, 617773282, 681367974, 779339989, 122773990, 340377004, 706824935, 501051812, 826672971, 648436708, 373680704, 371303589, 566143497, 555722481, 984040125, 80586527, 456227009, 74332137, 847897584, 854735715, 10812549, 730097732, 102508835, 666585983, 424005176, 517625409, 730181480, 622361541, 295178755, 300487687, 522223518, 481365496, 753759904, 803807027, 217633660, 705669248, 993490863, 437999584, 848389423, 839295386, 242236813, 585113962, 515920298, 909273217, 330737438, 687336469, 518248451, 847283828, 898464759, 709171505, 189102773, 552007502, 614120278, 452849399, 554189772, 296593982, 254116977, 85047247, 256130327, 316537182, 361585859, 149742691, 723734096, 608220640, 376176493, 415829886, 862552409, 621400262, 391397386, 942591596, 503787283, 859880209, 498137152, 823535175, 112126343, 674748527, 469626257, 263532230, 735944953, 207947627, 623609057, 440458472, 288265716, 505698817, 93170153, 282658893, 698376238, 527445675, 961589370, 546625094, 209208316, 820572512, 542673896, 810457200, 405989146, 712289675, 854730071, 446214276, 716257618, 183940055, 650837088, 856280409, 802810779, 48692094, 465929335, 425155525, 340824886, 898283804, 347177830, 329122183, 690780900, 45232402, 832515021, 619960333, 599608543, 519084213, 381174976, 909766750, 59939985, 238537278, 941738070, 731932511, 262997668, 30517088, 888923662, 744880138, 241133959, 671615712, 243253755, 833235422, 81914818, 916041091, 945583971, 861061227, 562911782, 537429837, 37401759, 121671974, 228622343, 508341865, 310956768, 790096676, 907661151, 963786827, 985056073, 755336439, 16837437, 369101265, 823459205, 528730739, 779298396, 743935258, 303056893, 894812785, 785460053, 666838305, 154921874, 918582995, 692238643, 94415266, 872562023, 376386504, 998123227, 165279838, 923024841, 731142205, 693428044, 378467872, 774707826, 33581147, 200975901, 879638990, 21549895, 202309048, 92113926, 376313719, 947461335, 799193596, 828350906, 356889207, 702745639, 943309751, 252999218, 806196514, 271143101, 317909191, 543769570, 12422262, 339340707, 135072750, 186402641, 18742356, 668497481, 121448196, 86639227, 582228056, 402355849, 447198304, 242593653, 190650398, 851704194, 923851898, 704508180, 215949573, 395552057, 81986263, 344171735, 86008787, 974186785, 730665711, 299304259, 887075793, 53616667, 944887660, 474870053, 995161295, 923552748, 948530629, 464514360, 378914135, 646755438, 655916329, 562128526, 612359608, 592473129, 331375817, 484129834, 838823389, 679525546, 1680339, 810120984, 535741789, 644511722, 158797145, 800422313, 192983231, 539547790, 280731108, 879941261, 402230440, 234424725, 319184960, 348842475, 374478527, 918703354, 200031297, 275559602, 225673458, 651340360, 45352691, 524652781, 498051474, 364008001, 630929322, 499454706, 547424155, 546410223, 513620152, 28913335, 325011903, 104783047, 599266109, 879140158, 119966931, 897635139, 407817165, 611779819, 671199212, 192731169, 70972000, 206397303, 682274274, 715918335, 140706073, 231105639, 66535150, 650910320, 76898398, 620649587, 570050713, 250124442, 441319572, 643931851, 441059993, 58837813, 961158498, 293375663, 797027734, 180176032, 710775077, 645327044, 609442561, 301207852, 810123385, 780170456, 978602982, 530421262, 374669541, 751733445, 681294831, 768916811, 33760074, 526811765, 732722219, 854592577, 12969035, 821429353, 997971753, 257866407, 277923858, 132277112, 820106493, 540172505, 967806304, 857536889, 876126026, 41022616, 719412419, 69877354, 251726584, 771817579, 139553939, 994087682, 957488222, 705268602, 944582769, 305233971, 799003067, 709553715, 153818983, 410877299, 236881465, 246076890, 777800521, 466365458, 981042592, 52690830, 594101862, 640740876, 35294199, 798045783, 985652264, 545516133, 249023676, 870276081, 915919345, 23406071, 582307534, 626156200, 792275036, 324736790, 692894681, 941239202, 837641093, 466452365, 475350156, 37426637, 109072518, 460487131, 903977607, 17867211, 123580168, 762356883, 878172064, 371166709, 695250967, 231307395, 748198453, 875220937, 684126931, 620322965, 144162978, 985878811, 701406981, 791019267, 760453191, 693782122, 329267461, 41231634, 47623581, 47122754, 810285920, 599114889, 589463530, 397226107, 548078346, 199514849, 199283630, 9472699, 745020181, 58697272, 31182929, 23027952, 280724347, 319836817, 361255333, 797031361, 381837951, 93114137, 682537948, 362756311, 4879833, 749452711, 425718709, 233105326, 611326178, 969830595, 4660949, 764445563, 885605392, 647311785, 517339125, 751840540, 231599611, 877504198, 388587074, 755499141, 279263669, 385369335, 925119892, 582201141, 678451090, 463183168, 367844801, 227409104, 423258773, 560232450, 998070013, 496308801, 236806869, 289477466, 609411491, 819732073, 877282759, 70105510, 487782181, 669899483, 950796213, 352323608, 89223525, 617843240, 318445641, 553869488, 482696537, 39982837, 241150104, 264030100, 161531680, 492941238, 599982056, 247981272, 793404966, 209394769, 914343527, 395517595, 183647548, 534743273, 593337338, 259139964, 707687143, 668115973, 463258034, 260420524, 465544067, 428304035, 486230616, 991579791, 898801494, 10702557, 783122596, 792650998, 44360016, 551100599, 567654992, 316301905, 6134907, 136729991, 770125321, 686339299, 287395842, 756741566, 90721801, 5117595, 354215864, 726607146, 810472222, 41750077, 773530170, 404304482, 272365872, 4923774, 721273073, 156051324, 388046185, 420217505, 793013705, 636767281, 914633112, 587911444, 93182208, 798981847, 460329253, 909480207, 108068070, 62902042, 132988275, 622163434, 861420899, 959068891, 745025560, 244102413, 215102173, 228768888, 477383522, 768642922, 729915718, 699960303, 606911447, 752493242, 770888051, 551343868, 453236240, 737108569, 893645619, 977748716, 196689903, 706570615, 277183150, 962093219, 108834621, 129471641, 444044930, 466839412, 321584316, 791905433, 882859111, 637683253, 132182589, 14149102, 859252364, 472008163, 556856268, 618264419, 335618584, 606266640, 765105681, 908921474, 332159071, 825537298, 642433057, 945417683, 426652350, 140575952, 367897217, 150562075, 597496483, 718163422, 956527269, 392937464, 478550718, 858441865, 974327847, 322097774, 899957790, 529879741, 627598637, 341068180, 359421362, 602647096, 684179382, 963519070, 559113369, 835259845, 537922869, 46130712, 612058178, 22960183, 629155291, 894765021, 436790667, 910264354, 294799425, 663351324, 26742403, 277771649, 254964269, 812339889, 237441327, 641308184, 726579069, 750436844, 568703833, 180219498, 749594292, 614745172, 340008055, 600674080, 379755990, 993289962, 806083503, 664191458, 561404823, 15721927, 883211891, 765118514, 422721401, 926139941, 841820324, 357052818, 297629143, 978322040, 736768335, 799168950, 503317696, 764521480, 943673443, 184783585, 612271351, 975113729, 706530211, 781333630, 759855742, 319458865, 389227875, 906121655, 109164213, 291711462, 13328003, 629031183, 19990913, 75714140, 438359915, 626187380, 236999684, 965437326, 48739387, 864924859, 991792312, 496770410, 967277543, 445823897, 74131655, 23848206, 537038161, 53027077, 487910135, 90479784, 53992245, 466636967, 415027454, 390572350, 172523069, 116296548, 752531058, 654711765, 946393462, 221869667, 383443864, 987010343, 691236, 507048549, 41218946, 846165698, 357877235, 266143929, 806138064, 891728487, 421798667, 233214804, 697129983, 857296700, 596916171, 392124855, 27026002, 672699276, 512711749, 722170854, 62555094, 209122302, 224553471, 296231079, 397387446, 229294623, 90154847, 5111137, 979076865, 226187551, 799524309, 125951753, 224086565, 142521302, 749390889, 156769381, 760073082, 832550237, 656593161, 447007298, 968945905, 736474415, 222511143, 167349531, 647289894, 740479789, 919216718, 173949183, 184081228, 820093972, 833493196, 237897377, 229122116, 484065571, 168230968, 413163970, 38254976, 129550653, 502587323, 842510868, 502095648, 99706349, 629537402, 33310874, 529068963, 822530822, 14773104, 629178168, 105603836, 53051591, 248670782, 814980293, 139328062, 462332703, 925870208, 494097026, 708305767, 671681490, 752259971, 47281980, 761684372, 105186473, 466971218, 370685942, 75066927, 210241307, 714998825, 756737950, 743798842, 355007982, 319486030, 958657129, 642533894, 767424949, 8351106, 881388994, 704748752, 109833027, 810684323, 747468585, 577949943, 262546202, 642082048, 725424889, 935832671, 862005312, 84964707, 716512053, 554365412, 786445221, 187828852, 439071487, 796446678, 410958933, 701340248, 498652498, 800799176, 731997553, 843226106, 301813316, 13512656, 954557698, 1491724, 795223613, 746122228, 50011813, 864538590, 742828738, 319972398, 95433504, 651111105, 181800406, 597057285, 760838950, 935643167, 256888899, 745176523, 838316097, 67289508, 832156030, 499859595, 858031621, 783416371, 776378879, 369000549, 105718292, 115732978, 27227585, 18575219, 82346475, 926473140, 404962221, 450133476, 622168955, 422179426, 897655183, 285563518, 586126831, 887242953, 720490886, 146995771, 499326792, 613242238, 954385401, 821419736, 746726029, 13284752, 316591077, 825722072, 635881702, 807125714, 92129434, 32310356, 44068717, 749011786, 616881626, 698757873, 50367271, 870110559, 176735352, 202877292, 848059245, 180086016, 262223326, 740250844, 655342919, 372098546, 90878112, 49825974, 240033719, 520781891, 49457849, 551782087, 665029829, 394959715, 304940671, 290905139, 921391045, 412132942, 784120595, 94735754, 433289424, 225297664, 20151042, 217722973, 672290796, 999812176, 539829963, 97475730, 176683477, 722374443, 271059819, 223774346, 339167210, 370128551, 635335202, 247283685, 194285824, 232710378, 816261292, 795742783, 906894309, 490512335, 853734024, 621502806, 308964004, 190946894, 798606957, 819158731, 644954413, 991168141, 918539877, 826624053, 444629927, 885945987, 818934714, 778382309, 25994973, 950504907, 604099227, 235705107, 966535820, 464096495, 910327903, 93548465, 760582920, 83412384, 233869668, 455506730, 51245688, 33307649, 506099868, 963159321, 768933466, 603226211, 890926976, 899253345, 653989491, 715371521, 850101967, 970907463, 959529094, 455459735, 827218831, 561094764, 577101765, 198679309, 780384843, 678555127, 401096113, 476483820, 870269765, 833065150, 604251056, 751344885, 950537541, 366881593, 195134499, 645201344, 626424202, 114604121, 350500132, 189617449, 252161217, 339194615, 463567635, 216748963, 820307448, 837081972, 775631604, 230203576, 170465630, 792619677, 623653876, 65015567, 985306917, 203904351, 407382082, 887419218, 451001184, 133336443, 715192505, 456518380, 916867416, 129614346, 835231115, 273675611, 863474794, 629364259, 827485799, 198226655, 564046517, 91462018, 87214183, 695777628, 38464440, 395582728, 181264397, 444964267, 211992279, 815437502, 207478010, 383342408, 959984111, 692382286, 669865170, 279767833, 651883819, 793174049, 455371014, 983682811, 500412246, 645935527, 545341071, 861090030, 54526420, 954511960, 924085948, 134934373, 354601089, 411228237, 535654783, 245577872, 773060511, 674095607, 261547873, 842658978, 718730747, 719462238, 590337673, 609742986, 917435120, 834050062, 439281701, 614378768, 166427411, 992241918, 587316907, 487255159, 383706018, 354875559, 97632375, 549364464, 858915785, 391292088, 189204543, 225983608, 419770077, 29166270, 506297632, 58628814, 891435972, 979294910, 981926883, 465888196, 514120105, 35116154, 850620160, 224793759, 752177445, 136630206, 841891717, 597618937, 713308579, 641622706, 937639687, 636799841, 274469257, 512468500, 839056900, 164407187, 958238674, 964097505, 306979178, 649297599, 233184647, 403615965, 511339241, 376184289, 573956660, 498314745, 440255748, 262149411, 140549444, 622776471, 157066713, 951563668, 926310286, 987375942, 858967836, 863982444, 225581476, 524303105, 732754679, 834374363, 554731209, 734671075, 986992300, 913505376, 331307596, 835509725, 969574111, 244342393, 905482238, 719807628, 900249975, 636037012, 332858577, 252109365, 201531060, 650627946, 172977670, 273877004, 764740427, 490817800, 12687250, 774965289, 862023316, 378473558, 775924078, 447207402, 625980553, 359906764, 284631024, 266234103, 777358435, 240695898, 61024759, 536623892, 689715626, 840253840, 286454110, 972350342, 257305500, 412319966, 69204211, 534181184, 360971166, 196449316, 186079054, 422946388, 231748282, 105195801, 683850979, 769847243, 21025003, 583693993, 137874717, 366913049, 569564383, 72689865, 943122528, 750185246, 701835028, 633317990, 364592414, 587208468, 582683869, 381647003, 106396640, 855754026, 626872186, 634038021, 794656060, 167891124, 21975326, 846842342, 283478846, 125929444, 456201218, 45941024, 226592358, 999118111, 587495772, 407543451, 661304104, 883120039, 813292359, 979931720, 528379543, 119335403, 308342214, 721734055, 58099258, 865826916, 804920137, 282044913, 880977404, 515036407, 281219964, 36932158, 379320826, 14338406, 524450151, 743665187, 137106312, 620288203, 199405833, 724666286, 727452953, 127947768, 444313295, 97490331, 86239900, 548730983, 144254967, 743470112, 836372238, 876501692, 628102171, 94595662, 698040835, 604010809, 774169025, 564203424, 144750569, 539036285, 219203627, 445334930, 65776411, 62112819, 498732381, 803387110, 908969097, 108056859, 32404743, 329600614, 406773672, 324055804, 34142934, 350480587, 902388369, 902772513, 274218634, 486704920, 149969373, 454954486, 866547997, 947521335, 29441626, 326109883, 842121971, 248003552, 460712237, 276531038, 355337282, 169945343, 24960954, 461949911, 949392770, 661875423, 331073779, 383794504, 725062357, 52172009, 545709631, 105964406, 997594279, 187408260, 557217307, 656221591, 20487713, 72982534, 620452158, 812237244, 977592607, 787028901, 746146100, 837653793, 704416536, 896537423, 379335167, 26287434, 457823646, 551659532, 227610282, 806591958, 277771400, 972579859, 529288448, 114962676, 725116987, 655326800, 202839523, 728811543, 2860318, 506400793, 587972728, 712509644, 613191614, 116960264, 422840769, 717929522, 475979803, 632206917, 818103980, 162535509, 848560940, 118600435, 819903354, 273287721, 356308103, 47838675, 861344826, 924039612, 205803724, 7927292, 365967613, 378263096, 111701571, 911157729, 97016384, 855317619, 755498855, 98899383, 201049777, 367088921, 947584364, 825482301, 437918682, 68173812, 246085252, 958478612, 701480971, 349122143, 629568241, 830630151, 903629637, 156531366, 588204481, 517339490, 453431188, 372480248, 330326030, 481496685, 670196162, 318473126, 485049648, 984631308, 360695743, 160313973, 721000573, 140088218, 771194397, 291435103, 255071816, 161051858, 765914298, 508593816, 559653924, 312905510, 206273855, 957598354, 161892069, 771626763, 959817853, 844060340, 958043027, 782511172, 771464332, 497894464, 295456063, 195234336, 781386672, 372267149, 60258815, 450474443, 82724670, 298963323, 325705026, 828168741, 197485707, 318369070, 41449838, 774173422, 12362556, 477340165, 36888803, 794884023, 522317833, 337049447, 48704825, 861421809, 611438907, 274882047, 875911659, 272794679, 187142678, 104914404, 528184040, 38597203, 859459307, 966509647, 897681274, 92037911, 199117322, 853639296, 754615320, 566921719, 397475397, 11936331, 737971110, 862311889, 294535809, 678741953, 512493433, 494153841, 96660717, 313897410, 878400004, 317286762, 574975438, 267460257, 883178404, 112989360, 471626822, 704317048, 323027497, 247897895, 724985896, 726939481, 408986655, 594614023, 408780433, 160790090, 581551269, 956040585, 789578088, 889179493, 796544857, 179310486, 41422879, 100861180, 849699185, 129521498, 504044124, 806322668, 531601025, 15859472, 192551340, 251947064, 719810340, 552190158, 675160641, 100516254, 883207423, 181776001, 415761664, 517459588, 705389957, 132559368, 587607842, 901609915, 455373469, 530740800, 648487842, 320755613, 743850820, 863837947, 311619412, 251706554, 46893600, 477092994, 209899576, 976292360, 105662493, 830295555, 947266597, 532444951, 91564772, 82318429, 391533751, 605904604, 855716801, 432683919, 485944946, 998900179, 750952035, 799833549, 109639299, 92992390, 557318777, 99321872, 676824847, 937205346, 677966998, 596715509, 976981907, 701819023, 407795460, 833200401, 87328619, 257747685, 865528649, 545799933, 239790776, 819901218, 585637672, 99799825, 490192492, 290524294, 534673869, 347112378, 921041510, 117511446, 957245083, 132632385, 720221790, 645654763, 72216378, 300081691, 419893376, 186591238, 135617419, 172605276, 97535638, 575310118, 142770850, 365413400, 754552705, 848389575, 568998872, 41944301, 279770377, 578549640, 298828138, 655308447, 759981540, 387199488, 156323823, 862094981, 874772972, 495962399, 710385462, 505207779, 677996362, 872611786, 435970635, 803779386, 110042614, 490898308, 10713256, 23265029, 109351821, 156260443, 467403096, 54321050, 732578499, 545385253, 910246355, 839704529, 39204084, 291736043, 889664813, 122861058, 425170348, 660518076, 459915377, 745291870, 980424673, 495780133, 234400248, 670097063, 435552581, 447522349, 571885448, 273440813, 582521520, 745416772, 191313859, 939312388, 561152226, 997745784, 564863557, 801619808, 815298837, 375466074, 747901072, 312260233, 517433821, 795233811, 997341423, 83331700, 3261570, 312098197, 181396669, 966401336, 416580089, 420021685, 268010416, 653750512, 368818502, 222360009, 229088480, 364583869, 252981029, 142095395, 638853062, 840464164, 668999084, 427485993, 471501916, 164310334, 486088440, 554314068, 591266053, 671317598, 261064612, 545135399, 564269614, 722989184, 3723735, 341041315, 120450193, 216280495, 256628949, 256761398, 203260417, 762480541, 495859780, 900249177, 669312879, 435175699, 627521520, 500681589, 892266019, 209199303, 339700384, 542902793, 151736126, 616692353, 959085982, 300788015, 964653192, 739170658, 115832171, 558470990, 318226594, 401967606, 628386829, 609452106, 586071821, 604904783, 387333944, 65945728, 297154910, 558921081, 55753251, 6750111, 357418067, 644704557, 834307663, 161940737, 14308661, 154778247, 316826584, 156821476, 303665753, 298012533, 223616460, 4175143, 292090987, 540550567, 988134497, 804504738, 392711434, 378191539, 395478243, 243624775, 154154598, 865914339, 186237623, 700629021, 486385772, 824291604, 199407554, 604864053, 308164987, 862065495, 291086269, 917340641, 470807977, 346188670, 826746279, 738893249, 933004865, 921997801, 561430121, 625899687, 105645062, 335411985, 685108564, 739716248, 124294734, 723522279, 404022427, 298101854, 319747426, 249674621, 906240915, 88366932, 698290456, 949901664, 227980643, 746901323, 292839432, 585082212, 338962081, 151303724, 938069804, 574990130, 701845448, 923935246, 328619149, 530907290, 682793860, 718435270, 108190781, 378352907, 217720458, 705152442, 499576408, 447134214, 706847987, 288859729, 40335358, 356892277, 196735349, 904445843, 333174259, 60344455, 452389858, 248833236, 463958893, 839258026, 547637350, 769980844, 790583361, 530531651, 38136722, 717333580, 546612954, 815812072, 419620491, 880693086, 770887188, 211502629, 846228516, 966587858, 366008025, 664647717, 265165933, 204286860, 187313839, 185356177, 869165399, 717994400, 968941549, 408329925, 273978822, 615788617, 446033230, 728718527, 678671369, 341537224, 146863854, 846210668, 749951101, 41127605, 84313806, 445714363, 157082192, 742091168, 860536527, 597239367, 482310304, 372586806, 342400225, 39668092, 759830539, 618190040, 221240450, 839843308, 978003052, 809441294, 210429339, 640536189, 272539245, 482016733, 506282788, 626920168, 171914401, 50322909, 732862233, 112688052, 698145509, 592189503, 346465957, 387553821, 343087594, 947289238, 176140639, 187021875, 188692132, 736979547, 740466857, 144482677, 893674954, 707561560, 858360068, 899189280, 568949459, 33116481, 33471377, 470372568, 235512677, 903983291, 489521189, 618065080, 584120854, 555276832, 303923194, 329963570, 337962878, 48444033, 868837210, 418645319, 337300930, 125469388, 331881376, 692426323, 503752180, 459333105, 886952261, 575272814, 541064007, 597944999, 936764939, 637385531, 425458319, 650692226, 59644309, 177265369, 352769605, 980753036, 738358787, 524792686, 78861963, 34807217, 200370398, 961967043, 792987714, 183638365, 545678062, 455490104, 488446460, 425276518, 781815973, 527930384, 731317168, 992391068, 883159420, 632359208, 653371015, 238888697, 654354361, 426837636, 294543525, 688868567, 894486980, 222534746, 922893463, 759435657, 651182102, 322888982, 346947317, 260252024, 305032131, 47952584, 722884477, 568244432, 489462147, 748902280, 597665884, 128853579, 913045055, 517336814, 234266824, 701290425, 930145460, 377204145, 153461283, 1095630, 407452112, 679946893, 132463495, 143737769, 514219643, 492954712, 581892964, 572833603, 219133282, 440792453, 198197102, 561201874, 707261031, 508792674, 77978029, 169647771, 555624434, 664386374, 681300537, 431089076, 880752158, 3147782, 24381835, 243818235, 78559858, 273090880, 796931207, 551344573, 586011330, 181328257, 890356963, 967624705, 61914219, 11675945, 126646063, 876467584, 376162733, 244903121, 828713975, 410368651, 103041656, 824167871, 41099790, 901214705, 351408075, 975044755, 878290958, 545009542, 522116464, 964573013, 16034055, 419407813, 689825450, 356067991, 253186141, 648923082, 968255083, 29703176, 209857110, 773086896, 554750933, 192820804, 858508338, 846190623, 266389510, 351373629, 684713664, 534024981, 559741790, 795050401, 715234290, 663034877, 246910834, 956435704, 344154831, 738743329, 458289979, 123694318, 455094272, 13562151, 671399711, 256693985, 888774190, 947510956, 726803357, 508229022, 566481367, 682442424, 126129754, 804432337, 957788260, 354013624, 532739265, 867411850, 379827039, 88256590, 215396585, 16037508, 84826507, 381755008, 662765759, 279909595, 370762445, 893840975, 831176154, 720782682, 935918423, 522373263, 666135252, 779123160, 365909055, 641613805, 100871186, 258487855, 424452555, 762939374, 939734844, 495332934, 538605175, 163303710, 808095934, 45558148, 793570363, 592241912, 798399245, 714575315, 388373339, 547968326, 246257817, 411079920, 683570976, 527247037, 512639072, 969875898, 766763433, 344719285, 519632817, 96933746, 573941210, 781819712, 736998759, 739358945, 352542974, 61956203, 986292173, 313490498, 168901470, 983547051, 509133785, 372912428, 445347055, 907362145, 587726943, 933925687, 532562183, 698194218, 223816027, 933244286, 312870083, 29959429, 193798395, 351873412, 667888264, 44536789, 186594188, 901296548, 439177424, 24183118, 531536661, 780206443, 143709411, 505015658, 855778538, 378757790, 471911133, 623923769, 738927331, 939491032, 801698517, 450375591, 719735601, 466057124, 324901735, 650200140, 928810018, 739779084, 507017658, 54545556, 697432973, 129610003, 651694160, 739633712, 191517100, 987847943, 879781887, 161172822, 847076808, 180126251, 242364869, 228035933, 189707114, 557836910, 692663641, 170127936, 308865023, 69049079, 68878647, 494861039, 662524042, 809918951, 444371812, 887023751, 672468937, 413561080, 319471577, 185221882, 639387095, 41694541, 882226983, 456561554, 940891370, 582825812, 749314330, 259459229, 761922010, 319451713, 949742778, 117844383, 356946423, 650466400, 403919867, 306940490, 849127155, 587874113, 202967092, 395411420, 863891979, 405993665, 965569081, 304318334, 963778813, 520103741, 93088466, 720224791, 783872888, 721941804, 907649452, 81640831, 798091021, 343973773, 305560445, 390021589, 33791989, 261907827, 465422503, 68916790, 584888849, 751099901, 467242320, 475131544, 309014187, 718641464, 809157832, 827714880, 369708591, 748632156, 849687893, 261434176, 201559462, 950105944, 626724540, 723702836, 136968452, 538853547, 757199766, 218741394, 101618381, 38520794, 855024762, 952790609, 220219313, 800733040, 852083306, 190248241, 477831310, 599222218, 186445566, 611869926, 733169305, 183363037, 200184483, 993601016, 924154130, 139436822, 926270241, 812435523, 550032966, 884192674, 406789361, 349749046, 142911994, 838620140, 398723110, 443383793, 106099360, 483960764, 604816277, 37189487, 753177308, 423984302, 629015987, 797112121, 805654726, 383442971, 256772493, 641060442, 914545439, 210332478, 660282181, 886664644, 901354938, 719997198, 264044795, 759038039, 93016843, 234349229, 973194292, 458971981, 128092254, 920013899, 598792656, 993412751, 618745216, 975962778, 664855638, 910328949, 347049553, 312349429, 410501983, 143507416, 489172283, 625052685, 868174145, 461158722, 978288495, 159387933, 322700760, 762656495, 49790272, 855970758, 820407191, 975578504, 519390051, 866583177, 740035430, 586200568, 337462915, 264070598, 521116745, 745040176, 910107418, 612054962, 83518745, 712248614, 987286113, 935686508, 389630175, 752537521, 232337152, 716909580, 326932519, 818426548, 298545583, 990083061, 71465299, 790454795, 354462693, 726189152, 535237306, 978021842, 668515401, 71948675, 66191559, 895988173, 585403406, 781892690, 846577528, 269280329, 246437308, 131065294, 923716172, 229634967, 171528049, 99667360, 336781202, 978737443, 505048216, 634277060, 455266315, 592351015, 386927689, 77901858, 729298942, 253107590, 230470272, 701059372, 549950717, 48254797, 802908069, 314233507, 335231554, 907955797, 197605405, 309404290, 721829222, 570232402, 49199856, 212819039, 660680563, 336988564, 425227417, 431031773, 599346165, 79979867, 738567401, 756412632, 512789700, 815635254, 697205454, 480574071, 705335058, 723088028, 520193378, 890407763, 723073371, 317139630, 79922627, 989957429, 427768211, 768105412, 317060556, 727819619, 821226940, 422408508, 257771689, 325488453, 581163704, 134407247, 620812911, 845461204, 389880249, 654816141, 530815441, 242462778, 533391180, 524389240, 35084578, 419071102, 391992943, 164353274, 414111232, 380303508, 424052854, 419923896, 395238599, 731078836, 578555510, 829968505, 583866973, 994372966, 399759381, 930872568, 952765354, 600643448, 502660911, 39076767, 357120182, 721263696, 332059551, 941579869, 454207187, 139821949, 977359160, 409102435, 744573552, 836367619, 318385951, 299129916, 95374646, 422199163, 835082819, 161471116, 928427339, 514788321, 545998361, 36255148, 714887248, 347448233, 213016939, 609928607, 255492277, 439206641, 974655100, 683847923, 531235156, 946687570, 561756830, 443488656, 283996760, 83230296, 600688642, 322694005, 354752724, 579809241, 15580192, 898036383, 624029052, 854250371, 318511558, 704429550, 931917225, 712549557, 523430283, 763787769, 280008178, 657585815, 371933423, 384874785, 548870528, 269305321, 816036827, 219683223, 175785002, 497037607, 203538965, 596326508, 811446225, 213283406, 264299084, 402552764, 901790497, 533942014, 839047449, 198375675, 52481232, 111456297, 28894812, 261403536, 556600344, 603669865, 752431666, 793976837, 967352878, 40574769, 937846162, 559221835, 350648387, 295253508, 946135051, 417678686, 164963672, 532732629, 322070264, 174412049, 507155736, 319036946, 86666063, 781263852, 894725578, 360897280, 417143334, 411928923, 869759562, 242575389, 763038168, 836793491, 456937527, 693949106, 206117973, 802227133, 901622468, 420549936, 955966033, 618134790, 357940186, 972731035, 102498462, 716976902, 711023775, 186635288, 70059122, 645808890, 825762778, 970290049, 199374580, 599556943, 695942847, 124522093, 118805966, 907092248, 105412836, 94635839, 386027652, 364253684, 560225243, 121891741, 372628907, 71780312, 100851946, 291564087, 473121605, 674792966, 427241927, 340125638, 692177127, 999502252, 61146924, 121736589, 253644944, 506581644, 285836574, 706532553, 689154466, 765706654, 986326784, 322676502, 827250815, 850585895, 706834397, 598167928, 333088519, 903115112, 375717998, 453481196, 82067861, 854630876, 816668884, 651431995, 30154004, 596449484, 859796979, 271052475, 313129243, 821230758, 562906797, 705867676, 18888723, 406955378, 909125324, 349158847, 88753710, 403767295, 728715747, 78755917, 653413064, 512189263, 867247447, 472794908, 372898, 665187838, 581972168, 859342843, 431337603, 89974818, 260276911, 315215307, 172362495, 538135248, 167883157, 763622179, 880074979, 62656001, 63585410, 719021732, 447135649, 881352652, 627498422, 173441201, 918137178, 131471354, 998779555, 409488395, 483663169, 15232083, 613011581, 801453823, 560620299, 261094367, 4393845, 35352229, 698005016, 869399394, 189110729, 141417418, 709972236, 717556995, 664722355, 228538760, 266313382, 180619510, 745148477, 374082332, 909102571, 639529624, 129807974, 895013016, 470095294, 833579883, 224243450, 836701381, 557420593, 925396921, 444099219, 724313370, 993669193, 22889999, 7891443, 959610015, 503155006, 175481176, 695700647, 849636068, 489593831, 601232992, 616640777, 191369434, 9164759, 151673642, 822515999, 452873062, 915075248, 334505991, 232265439, 431991304, 582922804, 908890882, 680111665, 145135816, 186640660, 918753665, 647749582, 890504661, 744001723, 128387687, 910228546, 610944935, 152827818, 473666401, 290660373, 282572519, 409096142, 296603757, 409631401, 109518067, 511661437, 834064138, 362804691, 389808110, 984769771, 526836026, 234929974, 59769886, 835844344, 659756784, 263522309, 52943948, 874085328, 225519763, 743086501, 664272630, 546846764, 673180317, 399499896, 495785233, 464663757, 54404582, 672210573, 671571654, 602790695, 988940021, 513258417, 955787914, 919963129, 782077325, 740713839, 579659805, 579408390, 230881450, 115012721, 889484618, 786073475, 762772321, 49046059, 126521589, 590897265, 63049655, 432298519, 341991554, 317148484, 123668059, 799376442, 462983175, 414715550, 198041110, 714129933, 458994362, 577486043, 405385997, 969202975, 759831935, 827059886, 104338057, 876827300, 439262438, 581583741, 160405830, 15844473, 709337792, 804676508, 301650494, 212888249, 108083495, 236543489, 117723844, 679067406, 671944489, 403818878, 529112884, 105766317, 283520339, 231965922, 313282907, 329442690, 945822010, 860555464, 919834735, 540898610, 46608380, 398892474, 577324208, 222210386, 995711405, 826962562, 947219564, 694166844, 70871922, 209903705, 375953225, 176273590, 260067150, 753742133, 52371775, 820969995, 999996982, 669333616, 827384741, 328986906, 190617836, 792410939, 800720584, 632391986, 515829367, 115487487, 838538087, 393724083, 444456579, 872462157, 659055049, 78242826, 707574246, 624862433, 65731973, 920767706, 140309160, 850471087, 205758814, 489977844, 615796843, 46694145, 222753050, 111012012, 830881498, 434449512, 72823586, 987251836, 791350773, 527166879, 111899540, 397399778, 812798455, 385422846, 61247007, 663362460, 720726675, 97208693, 743963190, 834465188, 95101916, 447880371, 717997507, 272140162, 82907846, 601896280, 490605698, 215771023, 317598403, 73448745, 315388291, 811113193, 519140062, 455872427, 870757522, 742399056, 560999666, 599500345, 172692667, 304856329, 909765608, 128232822, 544679353, 679814273, 103448005, 534076175, 673611539, 385254869, 532846862, 41758370, 594711565, 604719321, 235473425, 726959415, 649292063, 131017937, 391667110, 23296559, 3534003, 69388087, 880845847, 572958029, 408354184, 530000745, 943698292, 48499660, 336484283, 102255705, 498418008, 631656850, 980743384, 767945847, 19875762, 301245381, 190092519, 522247624, 312957436, 365462583, 409888116, 253738158, 684743885, 423574072, 481035580, 596928351, 324267177, 717180123, 859151846, 688669450, 295583000, 242171062, 979631026, 997506755, 505029540, 445589899, 676404029, 256797667, 1650225, 566134803, 255128378, 149701099, 102333500, 230971533, 347602777, 370831242, 129225072, 415410669, 396625220, 957264399, 610597909, 740983400, 396917663, 345887786, 853960503, 438516953, 458370223, 21824836, 474086292, 724111934, 130858600, 69712337, 721328587, 693676517, 197634184, 268494038, 207464397, 145082388, 399562063, 475030448, 388679912, 995401601, 122653744, 360683176, 383566463, 609993768, 868678524, 724698656, 872742194, 102145470, 835457758, 810066233, 667531224, 487000766, 832047108, 484097786, 800083566, 818184992, 82470001, 813929682, 506371978, 292469690, 550599519, 178509594, 384010688, 761523294, 755347110, 345612619, 483034192, 254757941, 404190760, 434738119, 987187616, 920320692, 960380548, 26273095, 953206112, 836359935, 261584227, 948733434, 443571740, 809961228, 221293100, 336715401, 928462392, 360186236, 216873326, 105809474, 955241188, 802535637, 905928343, 30750564, 445492605, 119594479, 604654460, 854369697, 237788910, 386176323, 104618553, 788054521, 259658166, 553090563, 758606815, 687847463, 783336429, 239668475, 770044432, 811451392, 318406762, 151729152, 612443625, 530863391, 949200146, 916988909, 594726718, 212210583, 378949648, 421909843, 679572040, 366264770, 87410793, 428388307, 205144628, 652013244, 570746974, 416555460, 475459526, 484201593, 817856603, 460127708, 69255171, 248372452, 275332789, 360317378, 599299148, 872417688, 742873715, 174782324, 815706816, 975291668, 650970090, 149304638, 722405652, 94842007, 78994654, 532607493, 88718970, 532485478, 345180046, 345269933, 704541883, 970130167, 813274007, 337028440, 106534329, 626997108, 989573888, 765558860, 258423991, 451674575, 52826617, 548001704, 769937070, 344239077, 101548614, 776626142, 764299478, 992909557, 670869570, 384785721, 888477291, 233089545, 205844417, 598025399, 560212319, 78249344, 616286142, 228218193, 248739037, 25571177, 384825554, 61403992, 719715672, 114209911, 411809134, 706204413, 43134642, 375647169, 678605767, 2671870, 701363158, 293725529, 413561817, 886687385, 934013868, 866659999, 617638621, 82988447, 783968196, 604790839, 304042271, 965761315, 470590406, 755435321, 157608536, 727574980, 185594445, 257359595, 209965830, 752014390, 590447695, 3402764, 63594816, 172363965, 49893744, 839773403, 748951590, 638608415, 922887883, 346695786, 590257934, 88412931, 310507041, 437345230, 325091120, 50255109, 405405583, 544699408, 262338276, 929111443, 914354145, 119826432, 525268100, 547245567, 921171387, 196622777, 194825561, 648177924, 205597524, 987275530, 52139337, 282514005, 862384596, 799037533, 699648391, 54596746, 242812258, 874627481, 85921710, 944200026, 2018626, 744705709, 44476936, 777246743, 440848931, 735417372, 339561993, 258039659, 485230039, 70552443, 831098798, 56052861, 425501103, 215053429, 509733614, 191453977, 225406822, 432949132, 247444163, 173549710, 326442194, 89094661, 839097077, 985344469, 279640188, 380544351, 598705869, 537085502, 800093763, 720917886, 749163924, 418716985, 668434652, 965246570, 177860907, 30487233, 753677961, 79632496, 288656469, 237997531, 252522988, 50021406, 881465360, 48966453, 159968026, 75392075, 970043570, 831519656, 737888850, 188639168, 885939292, 387813324, 241492673, 846053554, 234303025, 304678268, 13267729, 526089715, 464320149, 230141689, 723835528, 508276438, 915188131, 257491078, 101469927, 290186849, 943243202, 850845943, 782274616, 63564660, 722651966, 759519135, 528108427, 594489928, 27356845, 459450104, 222714862, 303710401, 367261035, 372205789, 341699563, 536150984, 554825118, 120767917, 51250643, 914981695, 264207078, 824327534, 953556233, 389870703, 81824035, 653381884, 236893848, 887275041, 342952689, 292055296, 450162130, 33598530, 631621914, 697770632, 642048549, 369173394, 696616468, 766002618, 296895264, 613242201, 992280295, 737881766, 417836934, 178541242, 840060022, 422609959, 39603037, 418714247, 313621552, 228187358, 924638083, 385158954, 821982833, 123557592, 319340133, 162352404, 2342318, 889889828, 285715310, 706901798, 940428360, 783879537, 27518925, 833666549, 393689950, 586819012, 394817441, 187808058, 424118909, 47311241, 327137046, 129544936, 104866259, 741153038, 504698273, 89707907, 722486815, 876753725, 91797978, 341719270, 83249633, 718072214, 421003451, 517512547, 44627680, 691499871, 56468315, 105831960, 75122602, 95829126, 347196580, 518812397, 842444719, 429502351, 484151352, 348137161, 730117700, 861686782, 830919036, 492359372, 275778975, 178903237, 731221863, 749846289, 24048234, 48904026, 316985701, 985727043, 497722975, 172359681, 879361403, 902455173, 169903998, 414144023, 655932558, 520406027, 578051116, 542737471, 518027286, 809060716, 75669825, 243727238, 303411677, 735607634, 633626397, 737724397, 634671823, 72412192, 644180076, 750861539, 507814891, 219733512, 729923706, 763835899, 186587675, 28068700, 641114979, 768496979, 52164440, 909530000, 350225319, 862091787, 649309049, 726220679, 497565456, 450864534, 482700613, 102463084, 824158686, 22657408, 471689625, 437827243, 649116687, 802187503, 90626334, 568713763, 801966284, 850885578, 726967300, 94788137, 855941025, 640077080, 717068170, 757227008, 287662441, 680631973, 780748519, 388160790, 993334261, 344019956, 863473382, 93922154, 787939696, 487287925, 473834959, 463064499, 306795974, 32088907, 771194914, 327864914, 528772405, 307555417, 648979085, 207884046, 74961981, 491847241, 911623206, 375061672, 163026376, 12486992, 84691166, 611383951, 34094906, 177193338, 920447603, 836638672, 656615288, 768346363, 508584477, 546543152, 876160355, 820323886, 751750719, 252834448, 319714712, 435322756, 584351189, 189008637, 839134467, 98177316, 581974780, 66949826, 356791570, 647626598, 37157636, 328963912, 357756759, 400372777, 911931917, 268566568, 84861016, 967934002, 458215311, 598877576, 941827875, 517011509, 250063723, 809964940, 36257291, 529267515, 29142664, 824623280, 294252644, 955631204, 130109830, 848106187, 371827454, 484340639, 93965846, 452132758, 660705432, 178456607, 524386412, 628198751, 679917379, 528116811, 61026807, 324286329, 33634218, 303439933, 200016730, 447203821, 388094527, 398759766, 223769858, 583825156, 411804733, 193024990, 225471649, 480411300, 83042106, 945792901, 460554563, 503485095, 678080483, 546710056, 535032427, 187192884, 964406671, 76123698, 596943680, 433531106, 327608385, 47780128, 215615499, 484452353, 998347911, 319781811, 524837244, 600118591, 153043503, 178056951, 327957109, 398715202, 302382118, 280546841, 300110754, 651640486, 946040757, 477238647, 277172453, 484806324, 818705376, 587200096, 9125245, 408176905, 881675824, 999183099, 172961028, 676545488, 668718175, 952782824, 380376225, 390371391, 39423770, 867895177, 628413115, 937051462, 660923106, 520597791, 140084534, 692355068, 61433819, 832062439, 794425153, 206970607, 205516339, 482972159, 280866128, 954057474, 902611405, 908891276, 214209489, 353706236, 355395029, 268296834, 166669153, 457083160, 756620875, 608957229, 377126781, 972309990, 68402540, 978543115, 389770425, 521036058, 662452572, 485637065, 628912063, 246272271, 533302593, 241280536, 880581254, 251930773, 663441781, 652421763, 955779203, 743300051, 711771230, 133088946, 900357432, 95353964, 228174227, 886934736, 7658668, 934783908, 103554774, 93522963, 24648463, 392024939, 390391957, 49588890, 422946642, 989498181, 977290975, 788112934, 963224251, 348168077, 817456968, 239023873, 544631421, 496254256, 103312004, 676784636, 574712606, 115550185, 210614844, 876888575, 254559026, 423441276, 568432965, 91000930, 190479327, 532858024, 5281324, 899909165, 151496613, 253363193, 540078014, 914568377, 746376700, 443255282, 236562221, 460282441, 73611269, 731645777, 514737187, 703437386, 492145025, 761419216, 825728927, 948182057, 621670575, 549451309, 525675063, 698595071, 890257754, 435412331, 604508856, 645521882, 226426792, 812025140, 150203693, 217927437, 208619047, 171123078, 716596126, 771735701, 18947874, 374343668, 66729190, 947964443, 57816197, 908866059, 494693401, 589051746, 566109125, 164499884, 50117209, 561961515, 264753046, 850661695, 262385978, 766329844, 662852226, 822964570, 881308619, 608201549, 955293579, 962733020, 917178025, 942329256, 808388730, 567101410, 465036839, 6991756, 905082739, 321459705, 573354481, 764392607, 90483185, 421092786, 209773309, 239605402, 661163158, 17374556, 130837669, 76621781, 729795073, 907531783, 304250218, 957724873, 674172728, 352694235, 236906041, 463683738, 413958487, 90756044, 384673705, 152555242, 290580251, 126456587, 414334558, 21306479, 550013284, 515312269, 729305759, 177707754, 744302028, 437075046, 179550219, 292414355, 167267291, 991508771, 221420837, 754229560, 375860455, 506778532, 723089875, 224897364, 301784465, 553677314, 425842314, 567737143, 664889080, 222757704, 309001575, 867842369, 427279625, 676571647, 797521634, 127816149, 3109278, 592478720, 688646673, 549299749, 215277404, 142617382, 652018783, 247806225, 855071759, 910917179, 634595817, 507809020, 995215753, 915337478, 356323510, 49090203, 520326987, 235561183, 713993944, 120778390, 563100940, 913911779, 951540294, 627687235, 899226640, 362137629, 582196539, 887775688, 234292274, 32242738, 990322082, 240746839, 194931740, 818774288, 188471172, 506044808, 458598200, 544969930, 559896478, 611546139, 834788773, 607324920, 408959357, 781978098, 558005474, 592172663, 67668155, 819610019, 701734020, 948390279, 412318275, 156256295, 714694291, 939809700, 67701813, 113198345, 858477534, 698645398, 788973512, 342806816, 935923767, 367672302, 79485115, 749110694, 145863141, 435670255, 917332532, 82794640, 771757545, 353776325, 664632436, 89597072, 960382272, 323077167, 693188813, 973704525, 163582686, 592490797, 844142328, 57461657, 295621537, 510649735, 189234137, 382821587, 584536039, 740295300, 596645344, 692436164, 75539920, 507872026, 452031696, 430458614, 614791782, 460224732, 286279247, 35154666, 419360263, 92843087, 853975719, 144480203, 607744424, 871137497, 912504824, 472138754, 788106131, 897442307, 292949742, 85998704, 580777058, 244701991, 141744722, 276532502, 1495487, 236975373, 329577345, 538618261, 510002070, 495850503, 977989183, 723118091, 388235645, 144614376, 829632675, 799763410, 788017820, 466920301, 93181424, 527914899, 648885842, 59848225, 126746173, 269585022, 393855407, 278060604, 985130959, 910930599, 754532982, 38333161, 491315460, 432755908, 979811024, 882571705, 90453049, 382540760, 409285342, 357373578, 494890410, 589831195, 650912493, 644368734, 721965708, 98891881, 213627374, 196769643, 358490087, 600635622, 893704541, 99471701, 308892439, 481841181, 960811995, 557783375, 583185394, 22394185, 268794314, 283101524, 945253445, 162616011, 465959516, 427295571, 26638164, 498675101, 781468173, 171170814, 38481278, 814769036, 106348061, 354222657, 211348876, 191266044, 533299299, 717326319, 441137194, 387197081, 941277690, 208111437, 397074350, 945183945, 66937522, 986013154, 263602664, 647730307, 873451144, 823784802, 777582339, 422597074, 158965063, 163750409, 84995862, 311704563, 167811370, 471137506, 859457649, 936134016, 991250797, 410834023, 632341562, 637879940, 539431719, 354838480, 433544982, 731427616, 689415096, 478600963, 454026357, 739616421, 733519698, 127105612, 625093606, 811173171, 945815065, 804006872, 88064578, 204519896, 721979549, 924573560, 104876427, 69215777, 326215368, 582783236, 440381900, 151962608, 99325694, 47679241, 446611496, 226997121, 762284563, 766168598, 546338875, 508576747, 653114287, 925511032, 23120616, 92551311, 358071461, 942768619, 123505026, 228902655, 280034197, 78612775, 611370980, 192901983, 26036, 215746753, 50441869, 188908664, 375256090, 542261968, 586873969, 770699542, 786866583, 788617792, 177180609, 56955029, 109458384, 211716274, 384407203, 992208806, 226608138, 485692711, 993060753, 403335474, 709525498, 780179320, 319001028, 725546136, 966506413, 518657238, 449900733, 769064060, 855563276, 725747209, 809436345, 890541436, 477118347, 619114449, 834058294, 597002281, 375375547, 556319952, 616677626, 379810771, 353550211, 463335103, 101422245, 276919981, 592482266, 125860404, 900446453, 339948004, 743339421, 768084508, 948434551, 527426652, 660084351, 580717552, 145589603, 473238280, 636863678, 196761271, 751985525, 438699257, 51747036, 695751762, 335366478, 987641326, 984747777, 578451500, 755228151, 874842485, 446870133, 888018711, 489263973, 554304183, 711651439, 117729859, 912829974, 677798380, 135710030, 78139217, 750343080, 510171305, 847790760, 184639468, 596418509, 901899860, 188188799, 123290390, 660958128, 355446857, 700466832, 965875845, 839938394, 818897102, 470127643, 999769094, 241147951, 618179901, 682983669, 234415531, 86310763, 862703659, 680774796, 54767017, 57952021, 216664597, 644421917, 923272825, 605703896, 744195142, 646635499, 841616482, 542081270, 588910367, 346914978, 193082408, 783472870, 339221511, 557726011, 48421716, 24856838, 43889836, 430855065, 635806566, 909989350, 933879576, 543854807, 765902652, 670713368, 259560462, 81252867, 330409093, 656698396, 668709219, 142043981, 129940058, 567872689, 235423569, 628939831, 386150526, 90757305, 134187095, 243344130, 80837664, 898888522, 513119498, 386270156, 896930593, 302154637, 385306917, 737445820, 824701393, 214963597, 447162609, 425558023, 278390762, 346499597, 297355135, 448698901, 949743003, 69354388, 851831105, 959469720, 337979721, 517745123, 353282680, 581827467, 795632181, 633829459, 829747623, 162645459, 169449790, 417656539, 363556519, 309427173, 531867510, 994301295, 77657741, 909164010, 836702150, 829336591, 892537555, 94180231, 338773745, 904041519, 454753135, 794394798, 676940805, 767353079, 511701301, 671676539, 831737242, 878277183, 961589009, 200741029, 182300277, 931856077, 46253946, 567069690, 529578698, 993200544, 614053535, 215485621, 376452097, 142182660, 398997980, 838578877, 671142030, 882031007, 52112920, 608820622, 849460376, 507345170, 872079046, 762472294, 318219730, 965317905, 560406947, 434349739, 68578918, 668943713, 16073095, 108683563, 420780333, 266603726, 904602270, 458188044, 527128471, 129939495, 665920131, 162466740, 210618995, 730756996, 882117278, 948288465, 480431087, 957152029, 627421573, 750824950, 596765144, 320465765, 524970793, 367044359, 888159540, 389044022, 693738071, 702857650, 865332418, 101586978, 870266501, 457561754, 530125374, 142381631, 19431376, 375644672, 820002749, 710441658, 215135123, 860330575, 88443439, 498393344, 525970654, 458055147, 370323920, 705430619, 519362337, 899377704, 618131245, 83624497, 210366715, 502482505, 965679861, 9065665, 850050245, 7327752, 339902838, 251860156, 510661127, 567511303, 524516887, 440428693, 364072422, 758391131, 993195182, 600303449, 731238823, 857373706, 763294089, 683984466, 280182074, 704323019, 415463738, 359441929, 248527897, 121845962, 195646676, 78233525, 218977609, 487408251, 674918878, 434078715, 657115197, 370443637, 654991696, 317696995, 223793434, 443988053, 884846704, 705084594, 530543484, 214669718, 771169746, 188005758, 226770059, 380012141, 304656833, 27327370, 79536577, 471561430, 630859130, 549951158, 336652199, 13811289, 162307209, 582430957, 700723812, 313403481, 346424683, 699126553, 885153455, 934285686, 69113086, 991307157, 829020814, 848915106, 835637915, 52021235, 429323856, 231871093, 195507387, 421862293, 823135454, 601577825, 958231503, 987414823, 325311331, 414850935, 198039352, 126073977, 274378949, 355985858, 326763332, 973307523, 914363322, 717932504, 326774783, 527013412, 825122405, 213568687, 69745613, 429566414, 839413435, 310089975, 862589608, 620573730, 846377703, 627286065, 1888732, 653552868, 762884209, 857485792, 967898246, 774351578, 415788916, 716503460, 457804209, 184087383, 639920548, 768180766, 497211030, 812454922, 495710517, 363964132, 336895998, 657696081, 531235732, 959171025, 702922062, 702956566, 591782829, 826883913, 873993354, 304377710, 354059250, 631683342, 102327001, 917047371, 582532158, 207976514, 119580778, 708500227, 33943800, 816096621, 427388309, 328747888, 508035503, 684936035, 717182256, 918113031, 74721272, 922776646, 101810377, 908665549, 243417801, 986723554, 402925971, 56453243, 962321757, 878931831, 625454231, 357164452, 283632934, 978696252, 749522435, 377308085, 243303998, 211364361, 738669039, 83258216, 264818892, 392170734, 389387623, 583277532, 638196439, 892556999, 855820358, 960453427, 508328721, 755677629, 159935276, 381982927, 654541659, 552575097, 313511133, 580999289, 900671422, 18073300, 889562082, 345487217, 119255902, 713038296, 94379443, 592715660, 491208804, 76443974, 62999497, 762000737, 203837454, 27171334, 427429964, 850525670, 911010346, 630219803, 95046605, 298944135, 552114381, 237473824, 322523122, 288141206, 925224848, 910049691, 115670016, 748254954, 364286225, 797885448, 123931862, 923171812, 90129415, 46695269, 33128325, 887530465, 234135959, 191163874, 12202196, 603599375, 609994860, 663368756, 502400412, 253596544, 924749585, 19224044, 512142712, 290220781, 506450626, 300547483, 62865262, 639745684, 621223272, 160537966, 740800658, 183556345, 455180178, 344046623, 570112054, 895834873, 285909775, 961825178, 295983908, 925862740, 279255893, 956946138, 19054979, 891093550, 73938226, 622615910, 611083443, 1165580, 831310131, 385982142, 648637328, 946245010, 49621575, 130982277, 936735628, 178976172, 69251324, 643472288, 355287230, 642254775, 516972318, 904423263, 848094031, 485922829, 284948509, 914442529, 925070221, 748812139, 535456264, 947437389, 516850792, 860523700, 9410657, 483919338, 455469569, 668896075, 48356697, 525595133, 110285321, 125811651, 925258378, 148375697, 733066452, 25624358, 594059629, 673210779, 245620015, 100530591, 673769400, 876038948, 675936582, 304214931, 785719780, 35778200, 780793300, 133943078, 1966141, 431644941, 979285681, 302923782, 114664868, 670959107, 569845474, 881653127, 137770857, 721213809, 45399308, 890496510, 456718014, 853705827, 95287101, 627665035, 500054812, 388920767, 326562759, 972413317, 428622540, 278641439, 888599855, 285148673, 633104139, 443290594, 824324015, 323034672, 384197903, 961967773, 989765547, 862867231, 637494257, 177541752, 212437489, 511239151, 945342198, 391678463, 957578924, 952042074, 660909556, 240081755, 22533955, 1028343, 715229560, 426035843, 907660391, 973420493, 239593932, 396001112, 330178325, 580564965, 797477831, 448633448, 861233626, 109272377, 135574121, 951744119, 798992854, 583629709, 513391926, 652003262, 159260541, 470495835, 817807816, 337208753, 874988692, 811428250, 538234414, 264448064, 168648029, 942537442, 832035740, 329301985, 61273035, 668582909, 823947404, 84362641, 862557220, 972512770, 87863505, 475345972, 70669731, 796324942, 169966842, 916565447, 883815789, 457665554, 516075297, 584879382, 907754116, 599357060, 660194216, 189601135, 800760526, 691724980, 873258446, 531756357, 459866148, 472563952, 933870880, 380653470, 273906476, 26672549, 52849345, 427719994, 284477485, 946874581, 658661615, 666461096, 130374214, 391232054, 639915291, 390002213, 813572152, 285889408, 398870727, 222463224, 255281910, 853476320, 606603458, 933919856, 761215528, 39974354, 497323804, 514439835, 770876898, 334078, 839278336, 255656536, 784528467, 421686567, 964741454, 443344045, 321737921, 978924733, 144215236, 891970202, 802394891, 471268202, 351807271, 145768226, 612955316, 642914161, 497383159, 389733916, 904729052, 877367464, 943755158, 342978249, 642954937, 660508247, 450108287, 477310505, 942414599, 959828586, 994593040, 638356866, 450545199, 784396245, 487986446, 460234323, 836725732, 400264669, 353558782, 116603558, 339706401, 877955189, 818883364, 624796924, 800951213, 854367201, 477273632, 322996671, 491312994, 553904745, 853199831, 845962831, 481487704, 11426150, 859749759, 427358651, 788383692, 777785480, 229779556, 115014861, 811306475, 785919896, 996946757, 719975119, 603983568, 256201328, 977902766, 7440283, 947333445, 636405621, 807224660, 386786682, 301419557, 782545502, 604904017, 309653725, 859762787, 800767782, 106379708, 295580274, 694729804, 243375651, 315489968, 397337060, 121620424, 150229044, 300914097, 78751841, 709143668, 581547971, 323112272, 639257591, 523424867, 404005936, 434906244, 938369503, 65540771, 481675354, 103184702, 1098163, 805664912, 274247101, 586102124, 491147296, 842382968, 166410182, 529704692, 464586462, 878159372, 853954355, 264046159, 738748218, 767549561, 781053688, 274485392, 864898569, 250328056, 776991858, 748883109, 628610439, 369809381, 809688812, 942261629, 742587007, 259787428, 615651577, 584976201, 807822900, 362999165, 592884341, 51059116, 897971732, 616030093, 84948332, 604263700, 748839267, 217871993, 917586164, 688720659, 795011093, 51955834, 750645055, 673050234, 476567037, 441739295, 315125392, 207707464, 205928495, 578943572, 434602971, 519606421, 736433450, 194392980, 351216782, 234904858, 321453226, 666284547, 95882908, 973636632, 283032172, 651432086, 892917860, 402630896, 69280258, 339618816, 125690562, 394391250, 676638879, 229443260, 187189151, 370602532, 743238444, 108568231, 774149975, 957058042, 994765030, 541478986, 792425664, 181704875, 627370291, 516173691, 287251978, 810754683, 908880667, 581230980, 930618929, 560720603, 652972935, 240731588, 101372917, 934110130, 813624147, 661755097, 260281980, 622009836, 858848053, 311042253, 23366797, 95909006, 819457635, 942460110, 648498789, 272194872, 500432327, 840085818, 671313827, 188011457, 667422675, 694790373, 557152631, 870003964, 706687502, 836703999, 113965753, 447954340, 367737567, 379470192, 418715179, 488565812, 990442785, 508411726, 379381078, 231485082, 263428363, 223564634, 264978000, 162805830, 866857834, 366246780, 708436635, 871862243, 245898897, 289307912, 543207861, 102934361, 832034856, 426846878, 834299980, 224808141, 970658314, 768784565, 943058167, 796939733, 383517573, 466906659, 247393123, 682181833, 908547550, 132478432, 595524300, 912109951, 849849598, 185044145, 389649682, 297942064, 10182062, 606920838, 960439548, 217727942, 946073478, 464064206, 67254641, 856255316, 366109589, 12567798, 155491247, 823059675, 666559413, 163102721, 503281725, 857781053, 514478345, 609667518, 825135629, 975445027, 877000140, 47688585, 107206190, 504111613, 289950890, 106617217, 872716972, 622449247, 313755585, 709930983, 760199014, 952748007, 56355922, 343312621, 235843590, 687051032, 739447375, 873940757, 198587397, 32392784, 473370337, 409277114, 476378006, 492018993, 207702347, 910711785, 137114159, 362742265, 973443148, 598815870, 469135740, 205499338, 540111508, 612386274, 121474961, 938818118, 769528119, 751996086, 567747221, 767850316, 308728291, 734866333, 438065889, 166490604, 904590528, 409465815, 320047287, 667982296, 190171119, 507550136, 798457362, 553211191, 356672582, 606268668, 478804354, 47203777, 127280495, 25516222, 732047164, 401197202, 243860899, 689710111, 394225727, 137550252, 538168754, 664939948, 928085748, 423867317, 624251084, 102160316, 817687806, 281998419, 277988966, 393686482, 140703455, 840945154, 527014183, 293261360, 226734744, 746629318, 517339894, 997847638, 965069275, 594319491, 765155808, 675486237, 507052647, 136714384, 791400693, 712640002, 520220302, 93461099, 720994709, 952542928, 410065434, 323111770, 827746234, 192034357, 550509706, 565762358, 134819601, 88888551, 152187120, 364291796, 352123329, 602535479, 977944379, 618724463, 184619113, 428412391, 754975157, 739069845, 936465247, 209721450, 716317710, 4188306, 218377452, 585521389, 790459379, 663504067, 966939364, 133722859, 796346353, 513788699, 895327060, 29635995, 602812781, 92202466, 353794498, 645896162, 832760127, 331766431, 320384551, 246870335, 883360105, 5848852, 41059512, 472748923, 855803024, 476918663, 147537216, 525581335, 883104772, 840360688, 987419849, 870929881, 315653499, 952733993, 485953536, 187466558, 522052536, 442626324, 673934690, 627906842, 302096161, 932892449, 846848586, 429943163, 571335910, 719219091, 992807222, 380527252, 693376241, 746472318, 525345210, 977593779, 230205437, 988889550, 397887978, 770786448, 82328616, 357606822, 520695059, 305291030, 543876104, 136638675, 245847714, 44515894, 138238431, 507657035, 718769083, 793813149, 829469702, 449478054, 753941267, 372551315, 440471480, 24940, 242212109, 964904521, 168847223, 470222939, 47633522, 361147175, 282426115, 135791314, 343178702, 323839221, 502451863, 712475880, 644577593, 583511876, 232381162, 960371824, 391525251, 559324849, 91549098, 129863523, 229720900, 962016388, 851342909, 161822457, 569428616, 88565703, 919039319, 720375293, 332912398, 483898332, 208582260, 469808877, 393187012, 341137945, 588672726, 221927027, 345141620, 241833454, 795905283, 671965368, 766583046, 141807523, 840250014, 53518572, 339681893, 707774390, 191952220, 742626702, 147146612, 382849800, 492455648, 821179214, 576818134, 155168057, 296390786, 896042701, 199718825, 911545066, 76119435, 508833725, 523234233, 803237122, 656406228, 810094481, 331733805, 633967295, 253904004, 250609359, 87539403, 685248810, 6418454, 52352929, 905393749, 719244826, 489232197, 199234272, 530878785, 668315543, 662743427, 461299305, 920026574, 891863382, 347253295, 682119946, 495529585, 866247786, 671869699, 20499471, 628232780, 390694392, 231975692, 633813421, 343513450, 20072692, 51460238, 136055599, 731658927, 918834338, 961238467, 884897683, 207669651, 789415845, 920910935, 612416267, 883565685, 100912263, 387714161, 666990117, 103459914, 927746793, 553621173, 142046214, 838048794, 815499772, 419232578, 110716969, 911641798, 198921687, 321942170, 366531394, 322076878, 72384183, 866393230, 83878557, 110652958, 28333431, 700901040, 963023879, 932821935, 994289207, 498744401, 993448155, 555073432, 429285295, 373247401, 514729996, 315727727, 693981618, 322151501, 234564479, 74421502, 81785933, 251002753, 559556063, 167473120, 371403404, 423441242, 733257665, 90853427, 350093816, 784471902, 12384651, 742525874, 380061785, 745244039, 565667928, 607956955, 951014559, 142140492, 761794969, 754883430, 604307485, 587439400, 466313768, 931906510, 694263992, 724514058, 17462146, 114846468, 528935047, 209738047, 134687807, 426382209, 451821589, 638779316, 956289388, 90992803, 417229486, 363005139, 747872944, 791424351, 610068997, 88176060, 92247633, 470968223, 794017241, 763940401, 304431328, 857963858, 128794707, 264584551, 885521087, 211013553, 80084940, 518734679, 474382334, 928126696, 693240042, 165027653, 137032804, 398831152, 125991532, 525179276, 263687566, 838386196, 674967682, 923173749, 17957306, 951854791, 214711180, 470723746, 187780355, 229517152, 975030011, 323281825, 641625797, 334968168, 163920259, 119887506, 465068176, 568402912, 331731980, 120710225, 14547637, 665200883, 228657950, 412052619, 212268050, 4807008, 236300213, 670580420, 33608630, 523740286, 707107964, 830422675, 810670811, 286535300, 877908187, 607232729, 308352537, 781264774, 991904679, 502728752, 963284840, 273253638, 133997572, 294836092, 438876949, 951644862, 608399932, 123529704, 223273147, 992043298, 389023298, 951428383, 179908166, 927684274, 831365568, 393156678, 497362081, 452358393, 593919686, 307764932, 909071674, 752290586, 296437174, 595823415, 742220589, 270347491, 147752572, 554181330, 197223514, 234702365, 494398757, 431521977, 900158784, 248903920, 675331639, 490593635, 372341198, 103082676, 303722993, 364529599, 165061037, 344706847, 582912840, 935146754, 380062713, 342881530, 23980722, 571226492, 611435428, 580597914, 171563752, 591912477, 345564234, 518198696, 690901149, 992450146, 414668976, 173203164, 587133073, 363114695, 13719611, 444382391, 105431558, 774589531, 613042803, 708573527, 788189331, 192286676, 770128235, 163943610, 653514303, 432128914, 626898328, 119765397, 281286366, 628221841, 702002845, 524104238, 539990548, 496981730, 8169805, 30785901, 13020961, 339897607, 182321149, 86646505, 589817197, 443324022, 90767834, 932927558, 602035712, 255993037, 771325796, 759253441, 813352362, 775819044, 904456711, 591064808, 132171073, 290216332, 227054577, 752879648, 768226800, 152218918, 982359080, 682939186, 101198536, 618017775, 523747198, 439386817, 912328539, 368270069, 647121311, 296472825, 385052403, 797495567, 337374151, 967951528, 791398630, 9049021, 226216362, 168411722, 345313885, 373528863, 751677710, 150911051, 45417571, 827953547, 653032376, 17630224, 742914173, 844552189, 412855473, 496884377, 446910574, 297812677, 309597211, 492716684, 341726408, 697959196, 848182497, 473653887, 336988457, 445724621, 714009823, 444553877, 983877887, 758276088, 238422592, 931912658, 479691505, 335996718, 966680836, 576803066, 759461285, 470138473, 405515418, 494720408, 169464842, 826468161, 928143475, 140326542, 347004593, 337504532, 12754725, 325340425, 150539242, 221150204, 71008359, 319828825, 123654172, 411304508, 408826630, 692932353, 345081837, 155946575, 455878397, 193569223, 721701376, 502572016, 128017763, 738847447, 936053523, 920866694, 684430374, 112736968, 841021802, 659192415, 202895454, 123775623, 905359169, 105827106, 692104231, 359889706, 692293109, 21686919, 600928700, 470556819, 961259998, 155719526, 55272142, 321405269, 602762222, 349962868, 362181769, 458418536, 666268756, 146224222, 855371705, 561536763, 242420234, 294151761, 478780741, 673479778, 404553110, 338803479, 506344744, 523049354, 613034920, 302372011, 152551728, 618046755, 495915892, 399922654, 229404329, 453941504, 35310492, 35486688, 893654805, 489343006, 816026387, 130340400, 518906927, 881969180, 675015154, 240873603, 325650465, 362465638, 71685006, 685809573, 142207941, 876863041, 372677442, 978337506, 618810569, 418958851, 208450182, 227539829, 767221246, 404529135, 251405368, 298197344, 3524086, 131742379, 329166908, 440523432, 958615676, 886745092, 51833856, 592643667, 711524363, 450331533, 494138086, 999343835, 25978590, 960864612, 642830033, 32818812, 568926323, 42311609, 678131799, 358505736, 537800517, 721302662, 667285010, 195477286, 58159879, 898815880, 937767472, 225089275, 544703866, 301457687, 155777588, 600447506, 3651469, 955808316, 724517494, 767687635, 712628430, 496926882, 356398135, 679708692, 859188393, 928401026, 661825977, 540234280, 157489853, 910926399, 957022181, 851505434, 351219868, 481221099, 990220958, 458550338, 213046726, 720078183, 407919246, 443948726, 634754279, 102161868, 814123270, 429306726, 554735457, 184534909, 607675030, 679478172, 47481877, 318422487, 123130737, 418016291, 366150790, 325072651, 302285412, 123790462, 650147825, 724964728, 602519836, 698597440, 173924322, 25436818, 945987217, 640523431, 592809321, 613792758, 835178440, 453227769, 41652103, 940135515, 922516944, 963771116, 567088492, 601275442, 746690840, 380261022, 808123596, 297636161, 346246259, 707248454, 193142818, 346388160, 920952196, 252266187, 110100873, 27636407, 956056622, 416080506, 704806509, 62395527, 659185310, 275359308, 318943773, 653495505, 765522485, 119430561, 730046307, 435402591, 284710821, 30955763, 640445551, 96883848, 411300178, 804834777, 19641951, 385228658, 176989716, 133682480, 435487793, 804754351, 200265028, 884845050, 311579716, 720506156, 254553821, 914161046, 890572659, 463737847, 894782049, 344546034, 131129992, 721589015, 569989932, 190655263, 65656082, 843555853, 2022651, 509407390, 953194720, 683134157, 40679504, 176527776, 869642836, 652937394, 727228240, 507883962, 374538604, 287541822, 85711629, 520366169, 35249891, 587452728, 406699780, 118806685, 5313153, 292873030, 407826705, 895973588, 561842804, 280706209, 888824762, 571444031, 118978453, 361511485, 84111865, 68561408, 468179999, 54856255, 312264400, 485559343, 990498537, 573771690, 7380797, 465874700, 831057446, 833855776, 976303335, 410790170, 794417412, 30309244, 724062315, 535534333, 13825317, 708095964, 563186258, 575751324, 88659204, 570224908, 936430834, 428314263, 517072564, 144719469, 207620055, 89090297, 123172051, 246649418, 313247487, 50653783, 389525080, 606695262, 139180865, 791014620, 98800767, 225706089, 474891091, 272061355, 982221241, 264081171, 783986773, 605027676, 2037658, 456025639, 188866822, 577412603, 709481575, 906020091, 385160692, 520880144, 477007529, 713910587, 215779598, 947505057, 623667427, 539370933, 5887740, 338648206, 889515457, 210052940, 337271459, 492539657, 775447275, 258854243, 59320490, 32864246, 330429121, 230393408, 320690893, 712936718, 490268371, 716946790, 34853818, 989665560, 381942677, 390827044, 120655055, 14878308, 931143755, 707688627, 484537549, 336981071, 372702647, 307249779, 286913718, 602347807, 845380343, 339962744, 335410273, 728762422, 386243460, 86616151, 763416696, 37995814, 706912336, 204786753, 703118517, 733842982, 102064530, 421708459, 423215617, 786012432, 659106982, 197762164, 586133640, 182766242, 414255763, 853919876, 607563935, 274441398, 431706924, 948155671, 438672867, 112102398, 489843865, 805388270, 943919400, 676450328, 502138590, 949234366, 738433452, 125912926, 669956556, 580764586, 830909005, 32047590, 126279355, 20173795, 326005568, 312783071, 699161436, 29668566, 932578891, 95127557, 532456724, 33821422, 733526651, 659557213, 719903616, 577135368, 992300634, 825319486, 243483137, 161612415, 542761058, 600688201, 821169460, 750389158, 639428713, 933337371, 477980782, 103525569, 424285947, 438734248, 6926145, 360531635, 963704247, 495629122, 326498723, 98704114, 641040728, 583800219, 529374894, 338009668, 607898688, 690239095, 467373171, 565748408, 508581794, 104004208, 611356294, 492522573, 571991848, 330276882, 820607273, 406901449, 27026921, 72026978, 42575789, 424167809, 692172166, 45989833, 202292082, 244946442, 798903942, 350157572, 704702380, 542367696, 239245048, 740218803, 702153333, 654729934, 590644421, 477646747, 774963474, 171928079, 182263126, 899082969, 200216092, 66591328, 228018176, 971717524, 892778089, 941025232, 588301154, 749178269, 190384691, 939797602, 215413803, 729757371, 539939207, 874246145, 99940735, 589834264, 127003758, 604003463, 687786912, 470411564, 516255853, 151922752, 170342345, 536029307, 103141260, 897057543, 618078411, 961134150, 626297176, 864026601, 122235127, 864281887, 246190388, 119026724, 454806457, 426445263, 376626842, 424763942, 832579295, 104969722, 319753592, 463396086, 209473300, 399848667, 392678257, 130290489, 865207460, 995016827, 238662745, 505399092, 854885111, 917711307, 290810218, 333128810, 775457734, 68199925, 809376247, 584641751, 149665281, 106322322, 218666913, 603080354, 308960736, 664415794, 524139908, 54011496, 181227101, 146051533, 377409482, 929974878, 315416041, 742149657, 472850729, 724146592, 4069474, 384835628, 958157043, 243018917, 217339795, 462493596, 227207349, 470366475, 216927029, 612792118, 696822870, 286535015, 379321958, 697084188, 111786881, 697034613, 177292358, 520147593, 774854596, 484224215, 726925670, 9663076, 644106563, 232558925, 842456210, 581737514, 664820030, 64955720, 25187863, 972122633, 703608390, 768790332, 917849821, 668711465, 325785651, 554940589, 508206655, 434314252, 566142271, 235786214, 646523534, 284861768, 216938190, 482143183, 530723615, 121102850, 510862018, 619063055, 152612429, 400992343, 715168361, 21420388, 954508484, 441737268, 914601800, 848481401, 29512204, 237077516, 812176279, 617436967, 17148674, 795061897, 783372985, 744604996, 640875640, 642607308, 240720895, 664439405, 459958097, 882861256, 969682106, 1041110, 294502005, 104019065, 750497523, 326261811, 497279544, 429127004, 116218301, 427546791, 39371276, 563770458, 633158070, 240454904, 426535061, 142931246, 803566787, 438968818, 626305691, 610167101, 247931646, 783132143, 267786804, 310269445, 299503970, 240584484, 19251120, 122873403, 847906459, 479675994, 590005384, 861192002, 713406552, 399973375, 650503573, 492072339, 453097714, 343568410, 176915843, 843260706, 76481650, 874339931, 273525077, 740311713, 790007713, 12828243, 543768292, 966181957, 458267190, 222354140, 517539966, 732750707, 101285585, 991903262, 883044219, 923424978, 758704734, 303299326, 880493110, 726476247, 130884340, 822617207, 257743544, 488694065, 402854095, 646491741, 388543583, 908485137, 630452574, 489599101, 3329733, 531974387, 646016151, 172588460, 807780312, 894946014, 166604796, 421467004, 424913942, 468657129, 659912372, 891342294, 115067278, 733143267, 416911313, 475149635, 318802055, 630579525, 336671387, 514273039, 481196171, 86503806, 970560964, 340515401, 767226785, 502153153, 193936581, 201055442, 168490135, 246266108, 875951851, 239849016, 627180264, 376452873, 169133948, 730304238, 798078203, 308243395, 28833340, 776780904, 173271564, 268399529, 971908598, 669028328, 923933284, 984638135, 544318920, 969235847, 985350671, 871805843, 608112434, 635999229, 71233299, 163628489, 790077940, 303885048, 285543342, 791873161, 556869555, 617665929, 35978256, 371159340, 781355582, 75184511, 74124918, 795459560, 743071538, 730527988, 426645649, 669622687, 131053022, 940374729, 608213734, 584290918, 804077245, 101801290, 639124065, 95177239, 907534813, 969589131, 904474614, 727318292, 429680838, 131862055, 403892484, 95025006, 664990765, 774537203, 236511829, 930284161, 26412125, 527074125, 957656648, 165375261, 317176188, 35608369, 765514758, 221580740, 268343360, 43049430, 246794102, 790026416, 432629815, 405518431, 546639128, 958466114, 1224519, 449744535, 154228077, 849647196, 871723078, 274375807, 459494039, 700260242, 811994779, 59974173, 49533976, 552173452, 534958548, 9642348, 14689194, 658778132, 962253151, 948734021, 263594259, 175597386, 665523264, 913950597, 535168479, 109310141, 682102550, 496750925, 437505093, 793979106, 363974542, 622466060, 914615275, 289149487, 654696747, 104219466, 713633098, 752798359, 420574748, 968712055, 428378580, 544690796, 114494616, 841317597, 997051278, 660125030, 641982395, 915539437, 982522763, 382522604, 761092933, 995114653, 33661045, 833711631, 139095696, 912604534, 399496525, 322106659, 802099363, 91161701, 689526662, 677466743, 201144838, 38888587, 218679150, 275895668, 789697268, 73964685, 719248025, 845129194, 213650091, 853230614, 17848654, 405239025, 669780196, 738281577, 871129751, 801955460, 493891882, 556622522, 277980119, 859930371, 246312235, 145671882, 2760359, 338266508, 529423306, 919622621, 640148610, 476596359, 727227125, 917120679, 153349590, 971968687, 188686150, 706059966, 227540414, 632444448, 906677793, 759394570, 611088365, 383381825, 792717758, 112989233, 876603170, 212012733, 38674523, 50618272, 107065135, 9809756, 561652526, 89276651, 501960910, 485938360, 118490142, 343448965, 262874247, 579404098, 523331099, 263956982, 21356431, 908053659, 241169005, 551609402, 585573815, 938047659, 248642460, 780384704, 782578863, 89998899, 373043726, 309918543, 124767386, 725961158, 292990942, 451027146, 49336189, 795257616, 897901033, 596093100, 8799285, 373549856, 470600574, 557622606, 445608741, 748186358, 709310588, 174114332, 794428362, 402914045, 562879464, 361461882, 969597482, 87824811, 973309070, 581098411, 458884208, 232142142, 866552586, 499965710, 815637061, 870247820, 212912908, 494341386, 520228467, 968098791, 649503021, 853404031, 888039695, 431678117, 264647970, 739524864, 580063295, 448436203, 808125858, 339232972, 479008640, 523252839, 66343961, 748266357, 823129001, 203503764, 164647317, 709655481, 879495898, 71897531, 683719130, 200262217, 709560476, 447932180, 71258827, 510481117, 984798971, 372646481, 803769258, 63873935, 835351283, 652821569, 370299891, 567141940, 575721889, 529834701, 654144879, 742477128, 33033002, 328474472, 946472835, 474601462, 396443844, 187508512, 302959168, 454682202, 108416999, 210995667, 345772426, 18530, 785850992, 304179583, 867807524, 26030144, 548108230, 671583330, 141692761, 433896818, 921247110, 427262089, 138384103, 637642559, 117652175, 691162714, 744326440, 51291310, 738593511, 340003318, 913315437, 362667547, 973902457, 40416056, 538923898, 412701392, 211467713, 621862357, 69780778, 11561777, 122964644, 731589915, 688461315, 843853336, 482923125, 687362842, 675090143, 535284330, 385627701, 27435112, 510194139, 109022170, 191475894, 776305335, 257557364, 754493549, 204315940, 914452646, 937256995, 689920944, 6737433, 64013845, 682185352, 126435125, 413944807, 769101546, 730574205, 278936328, 245985776, 735242291, 471281894, 377478094, 923633723, 656864070, 197309208, 854282555, 178906898, 44354890, 978153547, 895150756, 358262357, 821312006, 543692462, 202426756, 4068491, 686291232, 933326284, 850003477, 579305903, 887373674, 371299766, 235448960, 15827580, 553953310, 716958766, 129661688, 425790419, 29274240, 459436972, 389988888, 691398376, 91242044, 318264137, 667432377, 532444739, 295644700, 715929976, 677880978, 684923789, 903601901, 632822545, 111342669, 17281100, 234616115, 902296951, 11773578, 850047545, 74016447, 976097070, 305954532, 396889216, 473913408, 927619908, 128416671, 692720612, 312081227, 575407376, 586020036, 387329985, 923292561, 873507710, 558051539, 991332940, 847979528, 277471983, 214413452, 186959309, 836085993, 494050885, 222324401, 490820866, 741967530, 181747791, 831221194, 570582098, 7834774, 282261634, 813780387, 325132777, 760568825, 663432201, 610585797, 551842712, 441270691, 276702801, 260369435, 960112125, 431076591, 914008744, 344046373, 813076422, 904777167, 306631102, 433951257, 526955999, 134234032, 578209458, 791462894, 150309691, 608231982, 715233401, 546173386, 854446659, 45131623, 55474879, 630759598, 569232297, 830886429, 357873870, 626396635, 552454862, 135396739, 749543237, 913161262, 650008438, 618420119, 252964239, 912822316, 942572899, 336171083, 44013765, 195672031, 411379071, 320229284, 807807445, 956810224, 439045094, 826660034, 873935898, 942422885, 989638329, 382224448, 973957100, 193144046, 308579055, 778454605, 30185344, 891253374, 633020507, 555224969, 11751931, 409082939, 496898354, 829131134, 543942755, 673369477, 43456787, 265702015, 346121778, 991907567, 297376080, 285606561, 362674112, 728869982, 416296242, 378578381, 747941958, 445397937, 598981611, 53858628, 923870535, 693788211, 59628075, 587519445, 344081797, 484790213, 670759738, 812177811, 420954668, 468741329, 72184602, 872935609, 446397518, 426373831, 188423341, 648607780, 809064859, 720702955, 195522094, 998091310, 389779524, 62872621, 148280141, 962811157, 682843964, 273115497, 771313540, 810160007, 339650335, 734526828, 816439707, 800626946, 492946773, 692162695, 194734261, 448261492, 154440413, 34877827, 714509902, 692404240, 143809815, 659608663, 975740375, 330382980, 266689048, 681327361, 183167710, 15163623, 84879639, 30300282, 213092586, 941746381, 292944780, 722948879, 365046046, 497963476, 938270941, 884888328, 102023798, 665806562, 244141356, 730905539, 21429494, 149539502, 799598716, 939473505, 405038412, 151264333, 507304284, 846634656, 177921214, 697582735, 957059048, 616759522, 225366405, 226544194, 690898749, 773541355, 949689448, 246496967, 26165654, 240966021, 131120701, 497329495, 441314721, 742836165, 143273679, 462242018, 391712814, 905004277, 72413102, 171211620, 472980093, 348331437, 273739821, 25471443, 814300142, 550112551, 637968743, 759498564, 268464335, 871710375, 444362830, 216546629, 41536679, 309233986, 843043364, 521629017, 619518810, 152842849, 453802898, 918266798, 680798416, 886500264, 986003967, 914146409, 767189794, 437198686, 449630253, 755455079, 12608140, 514823554, 628782663, 945165626, 20322293, 934894228, 37694312, 667302673, 321952330, 719166253, 535040009, 766428312, 622686085, 417438496, 934600895, 107317433, 767305543, 460698161, 141421058, 686274852, 94364026, 243304861, 630387641, 349230283, 301831118, 746266973, 524773717, 598336821, 678506650, 893132164, 715807911, 723670143, 636267817, 830804461, 629320577, 319533453, 660231974, 72445243, 585477089, 714455425, 778731396, 723538295, 46801922, 346732203, 760475675, 741988352, 254472226, 347518104, 805996375, 320757954, 124416511, 666393032, 869212063, 920390550, 657525090, 320807995, 870580008, 635789426, 275427124, 627754166, 229157998, 986399292, 325501064, 664664483, 962506971, 67667832, 953353815, 704286447, 78225407, 228466835, 111614475, 529954375, 461945273, 938634153, 130758656, 106090233, 359555182, 290019857, 7118360, 115268612, 146611521, 710659818, 216368865, 604243769, 290124988, 748907808, 633864624, 950563636, 480904183, 864819786, 452523723, 314417081, 45802299, 846249953, 279435834, 891657388, 771589753, 156074307, 97994903, 990522950, 949049264, 786506379, 461590823, 583695749, 660085767, 266145883, 799439632, 753936226, 761837402, 209793883, 568970625, 751593656, 442019380, 866759641, 35370487, 687108159, 659451903, 829004736, 510530019, 513966581, 426465897, 768052991, 265588445, 960118443, 182979137, 865695839, 769197308, 6698224, 134045066, 612624014, 800485719, 410183158, 224717708, 584792004, 399761207, 107394371, 707471401, 516761457, 797083468, 320200602, 446100269, 310851243, 117438379, 327054190, 92551586, 238489200, 659389781, 102070513, 809498413, 354957601, 73482125, 684464902, 792060356, 802146472, 776084742, 970212790, 613557524, 23800378, 761304309, 426185196, 731863745, 669601226, 259624033, 467990132, 582180845, 169334460, 456351287, 469677472, 735801020, 893430061, 735567602, 454777473, 822554304, 209478137, 547618566, 710414994, 907468164, 914351712, 453719207, 492254269, 845692446, 921494596, 695999504, 371575017, 107677965, 723254840, 96016651, 886612151, 88155040, 386403127, 224887504, 345246953, 679896526, 493227493, 375781330, 252286705, 353476212, 24072328, 717510008, 167870832, 711532329, 912645685, 790436901, 49251933, 244802225, 553837769, 396248463, 988693721, 826555734, 294628268, 359853149, 906963495, 462808565, 808105917, 711194784, 238459595, 404022825, 498736484, 77150571, 501446385, 410711980, 15666521, 784071146, 923279399, 142219943, 187675238, 995263802, 724934600, 186559374, 419534035, 993962218, 151288661, 506414217, 461406420, 983737408, 795731812, 446307306, 456755758, 776774760, 258809651, 655261129, 511707359, 709393760, 501771234, 920960993, 972063174, 441003547, 441259713, 303189217, 862305340, 851780536, 564270933, 259922972, 995192208, 222609704, 983231898, 849844276, 381827129, 457124976, 670343401, 371053360, 300469439, 906462218, 324614046, 707035575, 728533561, 993367762, 952627445, 493885004, 236302601, 542158971, 672520601, 239535576, 924599098, 712165988, 19904829, 779009421, 592230632, 75621032, 698772352, 675137089, 281104422, 593505130, 553222477, 693517828, 562541228, 636658101, 155385232, 202489571, 802032030, 825629512, 22770446, 956073582, 453484487, 662332670, 677120842, 406464662, 830423373, 224813876, 91581784, 206750700, 857654161, 587193262, 255451784, 631127207, 525274464, 436206540, 675185694, 940559808, 122248145, 839396724, 423452018, 816207938, 508781250, 501306791, 241721766, 335352317, 798323585, 948033537, 380023077, 361641007, 759562345, 85860715, 669035865, 936721428, 843430896, 492439242, 151332828, 692403587, 475895699, 144316118, 615172888, 964828528, 981162419, 155953107, 640990229, 252125784, 434566464, 41208, 208257012, 368262766, 119735506, 170326811, 945257471, 653295170, 530271361, 158485036, 479736043, 230558349, 696661492, 327113456, 856201321, 365462381, 642308072, 310844230, 902219575, 533883045, 825269425, 970209391, 904827206, 170505947, 826326392, 165648655, 759295674, 381985998, 405551915, 413412411, 354319774, 406424717, 765591343, 87361676, 191442811, 566985870, 599379174, 699818537, 792890162, 926729437, 390787060, 943324225, 321688943, 222464251, 849966653, 358616602, 300180004, 146404252, 585823725, 833141262, 384446139, 758668549, 548779898, 733478665, 238792449, 853830083, 747236690, 727265465, 173332144, 672063546, 263079998, 650172553, 408265386, 477370522, 575439930, 817211519, 568054768, 50296442, 800291334, 778156720, 478298589, 983885625, 298142198, 594603575, 984465297, 131871731, 395658777, 371042257, 196021060, 702809493, 612679277, 124525885, 880295826, 942867659, 257206532, 431596684, 310678305, 55820918, 499826474, 924217554, 188303625, 66941551, 48024791, 757293206, 884362573, 763583330, 76952731, 932384288, 687865716, 342914587, 566998189, 194234968, 819464960, 624638274, 434149214, 629548295, 195179873, 336147091, 875298312, 522822282, 765652649, 165817972, 261369096, 821572905, 255455080, 919397936, 998222869, 64009685, 690442151, 274594360, 464833183, 924117063, 785861752, 606383875, 526799706, 750738274, 64734303, 660446530, 911496541, 343207487, 53372924, 531990213, 167644201, 822547601, 95925630, 935056668, 294684512, 2014076, 487947565, 894842981, 199512249, 761351689, 790080031, 624264178, 357049255, 651837911, 321565208, 737930238, 283760668, 438167273, 53821186, 151388569, 19281245, 259880443, 698738001, 128082774, 528230055, 915764212, 940967532, 15467067, 508777482, 169881826, 446796509, 747880287, 771912194, 225667153, 150947440, 803647616, 926274980, 947570537, 282456874, 539793179, 983509086, 237166421, 423796729, 974989696, 418083957, 916860747, 900353239, 849147823, 134308620, 524090653, 973803066, 313743598, 287961126, 882172525, 966472549, 191812564, 911421106, 9182341, 182665949, 978712379, 270347791, 123927931, 916251546, 352354411, 679110414, 32269220, 174629530, 812615352, 502987963, 655501762, 272586310, 609847208, 220307215, 256756638, 491755466, 218901137, 494127186, 478072283, 340309886, 328405333, 1721409, 733051022, 730888251, 430690086, 588158130, 532447087, 168600586, 700467392, 211568746, 477904411, 186322663, 157594888, 319195650, 247774201, 459245013, 801912639, 657319964, 154541367, 684307562, 285363049, 114632570, 808660253, 829767445, 386752080, 845382293, 786950355, 123250178, 386190423, 248663679, 7502367, 866062730, 724109242, 206693615, 710119971, 203839263, 437187843, 568477655, 577778950, 371061179, 969826943, 477174139, 885346561, 693242177, 27940704, 297788164, 777018398, 758850100, 772118518, 714170271, 980141324, 993711552, 502541776, 804685129, 219005263, 147412345, 275845066, 381218617, 627034906, 676400799, 142393313, 458263576, 513961566, 702957691, 623755860, 597560943, 264968446, 780772263, 897101980, 305733343, 947121642, 519014089, 132298262, 234427186, 465129906, 80697380, 125137122, 409596118, 795173708, 10159429, 592259352, 250782314, 262861592, 879980219, 411906290, 197864355, 790711551, 103240508, 531769957, 266411307, 555881530, 485504602, 643587857, 784689434, 708227514, 437725146, 223705858, 578413381, 832222277, 3590010, 833564763, 651561399, 40828987, 743424363, 390872585, 120699116, 132288653, 740641798, 396686724, 537605102, 910727286, 507185962, 69808549, 601007416, 371230624, 919230906, 427865538, 20058406, 949651307, 692572003, 484084568, 418578672, 670916501, 715928211, 875705820, 412924028, 682069186, 305025353, 218611140, 818025664, 637553549, 927265640, 770547940, 743217817, 976584433, 289841517, 259001051, 193512255, 60863413, 74403401, 71768057, 560492314, 575897418, 598398537, 121985796, 427202751, 292340773, 586253271, 595367030, 675333227, 412615822, 697838879, 267009210, 976915107, 703703869, 746039381, 588394451, 586438786, 587095576, 743019174, 739525583, 569367526, 961465718, 617707860, 721387237, 859587243, 294674429, 978838739, 815232172, 908957551, 48435937, 490276527, 488954513, 16334137, 404381486, 516974497, 262984130, 570258063, 702655850, 845095254, 101730750, 797766044, 15418439, 20053048, 443543052, 384705673, 816956976, 245865730, 150450230, 644928474, 952216396, 718684488, 245833027, 532812325, 759061790, 782864593, 29828916, 397961322, 192331712, 514736308, 79053561, 208159277, 364524261, 818905745, 245290022, 586158306, 354945631, 767901929, 372801794, 240797753, 823584113, 780569380, 24221015, 123940170, 24066195, 634851166, 882855184, 869720813, 138509827, 89630215, 505660674, 161497280, 853000282, 990313786, 226584503, 668288692, 865415906, 903997264, 168819338, 645838717, 495501645, 337009086, 601543864, 585883412, 198568432, 795277670, 828749217, 822897388, 484899687, 385128589, 20597312, 810875371, 924072897, 788193121, 771221952, 378137426, 262355090, 512597709, 491786895, 865795898, 123245254, 945015574, 748708721, 833840285, 733175823, 636313025, 946124219, 276581415, 222936765, 90772088, 133156059, 906808125, 989360636, 124120096, 687865771, 623084039, 908754491, 636252375, 154379776, 235870942, 113298499, 764616288, 531856900, 181705984, 766853598, 363398708, 386064569, 820144844, 759349461, 789187532, 207962824, 578181441, 808282780, 544029, 990674329, 972404901, 180375233, 675845056, 944051786, 783009508, 27713117, 503674239, 981679974, 857304622, 128703190, 538565041, 135162812, 432099058, 498571915, 3613153, 160602111, 525888673, 409156487, 863358494, 696879590, 858580319, 384614553, 417177328, 988281380, 384480837, 785330362, 847090444, 94548574, 88497166, 309676188, 527956950, 318429933, 273604993, 409326523, 128756121, 621560366, 402788437, 182578371, 767486669, 14334543, 845304265, 483332688, 89558508, 447567948, 883954828, 764713441, 430716377, 979434368, 107469583, 945907257, 823548547, 509994814, 557518841, 23505951, 853762432, 501306881, 784521251, 964710226, 255344554, 936937437, 877099497, 159181937, 792246262, 943344879, 410324030, 253433519, 305994141, 203087257, 76203011, 730971626, 596437195, 672721078, 459903133, 686346829, 171728115, 291693189, 871637461, 656000833, 648257181, 348345083, 626102442, 145840902, 808919873, 918851118, 471232152, 33648290, 11117648, 467147946, 705252798, 860943446, 402402614, 205792208, 481284719, 947527108, 571748062, 359346893, 440694725, 495342601, 763317, 999970905, 47316993, 259479154, 310383749, 2614749, 405177021, 954088084, 287993400, 974114495, 645132366, 296881558, 81226610, 467458362, 998707197, 628089666, 432246386, 613072626, 600616638, 352112257, 882608647, 750042171, 477712168, 71066117, 333752131, 623132623, 938396877, 395482909, 274263202, 92709376, 444753459, 760275314, 369882062, 836904646, 200034881, 382069729, 1339011, 892642009, 219197411, 485855732, 532355823, 921332046, 73145160, 500622283, 542139908, 907044013, 235055240, 269122369, 654933099, 762507892, 639009667, 857721171, 256944360, 786189937, 950857859, 783153104, 236366558, 447250044, 42969322, 667958178, 43678936, 672022317, 159236155, 673721653, 642053157, 673308646, 342781656, 379562041, 190210348, 216501393, 156549892, 489187100, 479776456, 826661007, 993972198, 83420795, 689512710, 91984550, 879953974, 940285483, 535720215, 90012165, 870998279, 221461658, 571899042, 782705803, 395732308, 600889524, 163107488, 719417032, 301766533, 136714439, 626818680, 146188293, 737655309, 535336384, 699883643, 571004842, 442561098, 66622859, 577302144, 179641424, 370658131, 874622822, 196614929, 540610274, 804302832, 342671762, 490459640, 852423478, 652601438, 684534197, 826180268, 563577345, 178653127, 730240304, 814086179, 710226292, 539247600, 582170047, 743155371, 93336962, 637560496, 74970128, 912914162, 320276811, 818646054, 109064922, 118021191, 417390296, 833350512, 81000122, 138678701, 125296963, 527308416, 503960614, 872128289, 434999983, 741177609, 306761722, 299933362, 896990400, 688256524, 939490918, 370970534, 74987849, 418654776, 151414302, 58737292, 175850471, 552910856, 239514478, 37608235, 256379260, 524774304, 259431203, 908892702, 73540743, 394615419, 553805548, 131181460, 640587823, 3280255, 300426273, 53287970, 379645508, 104037596, 226292597, 142215165, 18177047, 365386258, 883161212, 695726706, 435989910, 541676153, 133106736, 437821190, 941429437, 191226311, 770001143, 893446285, 723584780, 518799868, 890417084, 492442448, 676649415, 617837044, 720422729, 967066013, 635687241, 476722095, 302644944, 517199064, 531502671, 171336383, 317808730, 982505432, 243958544, 517497276, 442563122, 60288944, 829989935, 178122632, 299758368, 589256734, 317856139, 798394197, 493161381, 789720144, 368207551, 443334103, 634888510, 566298172, 966893646, 878202940, 116742313, 586224421, 456975028, 655133109, 875837831, 943450759, 432722450, 949929896, 22809585, 345535422, 877997905, 84392429, 829534352, 419078682, 16130188, 633848084, 592194232, 74549498, 162835520, 707309972, 599993839, 439812711, 331533101, 744949085, 953781712, 112281792, 385321287, 609744553, 417324866, 680430668, 482250125, 423442453, 436836708, 428811245, 795459160, 415625308, 254966673, 763765832, 250770072, 283697896, 67055866, 709960413, 636041160, 106325397, 542036276, 270856991, 534148067, 786982805, 341241497, 548019852, 455558316, 258703519, 120047702, 748893318, 540561376, 196705973, 393816768, 587900699, 332152945, 299373226, 205343701, 109056179, 562081492, 820336901, 739593124, 237380282, 865842745, 461980972, 905760734, 18176931, 182722121, 998193127, 221640893, 416619339, 875996903, 632599598, 631777563, 828276908, 132092073, 929112446, 666121069, 29591440, 291962299, 595240017, 868241712, 911618396, 27610754, 378896710, 805543670, 556302163, 773076545, 361320003, 834278229, 922460587, 552502167, 913678600, 573508110, 880112351, 306587061, 299825927, 387799288, 972819263, 355924460, 160679437, 338629221, 948864152, 249574029, 260078053, 912025260, 801342176, 313981722, 334487789, 777825427, 417112472, 904845780, 548812815, 231225515, 175599998, 606050547, 271842704, 256338360, 383277686, 209424710, 79717531, 428730702, 167505148, 499776045, 506392691, 942275566, 851990446, 592150794, 120647803, 541355601, 179959363, 428201896, 860389174, 913773592, 667562188, 775674639, 713194717, 539884840, 551545393, 846812900, 301481926, 466566272, 30983847, 22497175, 281328146, 427823150, 306393346, 138064898, 132328122, 872727382, 296873879, 840248455, 583891876, 98007726, 896739779, 684673317, 921466433, 51930907, 656978241, 563817505, 365263146, 209066144, 688173301, 238994998, 392936093, 939340441, 138228808, 475795679, 256144685, 97074599, 283102157, 620124631, 919037051, 364531005, 895470346, 380501523, 262553684, 871153019, 856634157, 687020331, 260301249, 596639347, 191796068, 903666544, 592301751, 730253286, 405688107, 131303707, 265371305, 870765344, 885634125, 528164591, 125044444, 770491765, 691069972, 861422429, 274959747, 97467612, 209664783, 87469639, 568483998, 399886272, 774124230, 7402395, 522380953, 723833103, 765485262, 738143863, 934130000, 719358437, 201868466, 94175836, 33280008, 525861099, 917129445, 682507720, 874538658, 329332893, 414061206, 998322968, 719757557, 89608350, 519353357, 2438775, 714730136, 585630052, 839964852, 859031685, 345440991, 268937925, 347790884, 539742803, 90378112, 905333323, 112808374, 160372956, 732637085, 925485361, 17554188, 892218777, 700611455, 126198473, 492069340, 956735071, 581696824, 76343628, 41355909, 223892477, 311152834, 755597971, 683906554, 158401379, 359236295, 590839315, 579829413, 665260655, 381143813, 337089760, 535690344, 71443618, 890708502, 777193409, 75079290, 951692323, 913808382, 371303372, 929015072, 819880446, 525309845, 522919902, 650627055, 618913278, 595640824, 831675905, 520936262, 121940591, 403530007, 169627048, 516996233, 336658297, 121566947, 81158638, 451397124, 438394037, 515198028, 308991885, 526581597, 285976428, 722499595, 990562995, 260957679, 547532676, 273181803, 277585449, 390915714, 441414515, 167271202, 878615553, 125559476, 934918189, 986472492, 301774233, 10147637, 589427777, 246117641, 922641736, 188111460, 594866547, 507137733, 282658381, 714402083, 992779665, 865297438, 263782200, 136765003, 857358745, 467315277, 791915235, 914021620, 649774619, 129989524, 313399052, 350366644, 957625434, 109198652, 697146913, 529585632, 551556163, 439285096, 788992882, 339562578, 446067266, 540257832, 900075252, 648919288, 979675, 99050974, 92316552, 823662016, 120259852, 266268638, 54533649, 610717688, 957462688, 994135779, 693886939, 654274304, 879909287, 70419785, 740354734, 955971891, 604807218, 487236389, 113804165, 383873480, 704744570, 772170397, 886763893, 891107339, 51966409, 409885139, 612379561, 439451049, 258709355, 503603491, 194400794, 176684150, 934068973, 979509350, 801406653, 96252281, 486151132, 743235438, 641061892, 186182917, 334371269, 976695648, 798336978, 738992985, 315856307, 406735901, 288544080, 102294547, 153503737, 680451224, 432466939, 929316689, 61338595, 576302307, 191954821, 154718279, 485348009, 779610991, 68560264, 961628006, 544932203, 982839804, 69166639, 403080748, 758893217, 162340705, 801246761, 620089935, 750190950, 812121405, 304044035, 847134930, 903158457, 217975862, 293166814, 369599641, 387541649, 996305205, 793507629, 185247582, 148679491, 175042220, 379287223, 46843022, 601112824, 479641619, 328123773, 153437019, 373098657, 996579472, 462819514, 144084750, 797934280, 619928713, 829570579, 262541280, 976062091, 640152247, 369694282, 616560178, 8661552, 773823288, 99029407, 100960418, 675235635, 658632969, 234276654, 85902731, 386132265, 10515082, 90400294, 331232494, 751543842, 996018483, 992502932, 645985657, 460038254, 958354199, 760304178, 133950543, 374744282, 975234435, 614484528, 844869056, 46799716, 97873244, 710410244, 1823501, 262186662, 426789474, 200697415, 419942391, 764426220, 394680723, 879725606, 414823002, 221377866, 252741772, 160521344, 525175804, 651056313, 497579885, 127206211, 651241892, 909767536, 636223755, 354019803, 223581633, 613546712, 807590128, 962910604, 910574829, 787639026, 626377269, 457110634, 95393473, 189804860, 627073885, 907317644, 500937225, 384631824, 417736363, 454419252, 786459171, 281494507, 183845443, 125638231, 84268046, 331754036, 543784004, 552656176, 681947313, 215789345, 107710495, 444453015, 404088473, 18961349, 68251596, 27433579, 621004466, 249607514, 949578703, 531645277, 358851110, 549779594, 146320109, 260793285, 293787765, 454250490, 703770469, 733142605, 850155243, 415913708, 204439698, 670220331, 904196249, 343906545, 353835519, 812559623, 703399928, 378510723, 175846482, 264458359, 343859218, 589266072, 311979176, 49985512, 691485588, 884960124, 102669113, 420459209, 694086603, 967829713, 817321280, 508290657, 490237437, 494804584, 777508193, 974934133, 138453003, 30871246, 988954610, 155488873, 340342167, 469736196, 700913232, 271996086, 803646618, 209547600, 418860615, 981668031, 262021827, 767685825, 29711545, 909555645, 98327846, 768007844, 944415769, 583774406, 410370400, 108669687, 682870703, 330001371, 9777291, 594614376, 924277801, 866512515, 191216570, 368652506, 811250658, 991816621, 246285881, 359450016, 277484985, 461597388, 288158553, 369779248, 168796420, 844162201, 533094771, 976153188, 974631967, 349279952, 724266392, 71275242, 448938264, 131854611, 557903168, 332585562, 744736085, 549213350, 44995043, 228115639, 183003467, 12540178, 13386973, 643638310, 437406258, 323733554, 275505142, 747478755, 387790968, 630292539, 291931333, 223414412, 407948125, 861671672, 128240506, 652178044, 142723904, 138731774, 818946780, 718918530, 995871553, 761721109, 580614582, 15475275, 904011435, 117159686, 737781709, 352004555, 317709116, 307604733, 901794874, 625687652, 604108030, 474550283, 574219070, 26000124, 339668666, 28598317, 174057876, 814743745, 937428282, 175302892, 396323834, 984284078, 619650090, 628616196, 762740181, 904999776, 190828436, 285089374, 334268811, 633344523, 936293994, 194518446, 739537681, 884626317, 678467420, 290880003, 980552277, 873647998, 441802860, 921357089, 106051165, 769225062, 720593594, 90327146, 347863691, 776751739, 328265804, 234480812, 900778832, 250337234, 896512928, 838018766, 275617058, 807363917, 562730231, 100924552, 660360541, 570030517, 410958897, 474123409, 858987471, 273792123, 215902709, 850567741, 784498750, 302333120, 260505006, 562278977, 700904102, 926931167, 95201818, 700603353, 818366118, 399195157, 652507070, 285503313, 249281792, 135629567, 539032522, 654521384, 22659508, 80994404, 275019891, 391068096, 129492637, 562233274, 77892890, 53991306, 97627690, 80568328, 934459310, 93968602, 718460568, 83792388, 195135093, 68337598, 517948190, 243313013, 663745235, 200187146, 347032767, 781028150, 632191449, 361057744, 204882503, 58906725, 632664747, 994345982, 399770098, 455811171, 713105687, 238326549, 27193718, 348515056, 905775576, 283592125, 656071480, 516497949, 384051485, 490455026, 815457144, 513998959, 187871127, 641125116, 869469847, 611369142, 181829803, 879362149, 360245930, 92955790, 256037492, 428731648, 694352869, 27349129, 95388340, 634958692, 860392823, 375596605, 489554499, 162658447, 194835205, 603110140, 509036167, 288951410, 669478005, 602872590, 538148510, 802140855, 342521038, 108638132, 134266289, 283458756, 401958045, 59204532, 762163933, 407247176, 828900659, 688383040, 766866456, 480689982, 602535929, 409185306, 204494620, 638727243, 385810848, 50184925, 427483588, 791250260, 996459379, 626905927, 605940571, 735399731, 669722422, 57335403, 741676278, 622284424, 12009942, 255926061, 177663380, 393189427, 489698198, 689498813, 800981532, 1633100, 832311126, 145498809, 892682411, 84060584, 62544690, 880123913, 678081939, 452850232, 342487049, 802665806, 718440092, 591153255, 146068641, 90906272, 582230239, 997676908, 179672997, 989104862, 657032328, 322485294, 753846567, 560129124, 919520481, 168648371, 803898470, 231392621, 137076288, 265972775, 634534326, 425230918, 414049259, 573206630, 65633376, 376156206, 695016625, 352792438, 618883515, 299862341, 592668425, 343897595, 59992272, 150725189, 277006459, 157971800, 501687746, 50860845, 667232318, 202831486, 749579413, 615258264, 868391363, 148307136, 586418307, 248185652, 328860308, 537502098, 988400535, 578305945, 469437792, 203337568, 143954932, 720996915, 822578504, 169237780, 495210124, 687426281, 806211530, 675054457, 1325788, 251066951, 531650468, 951846456, 965844289, 577945744, 520452286, 789920681, 793770764, 877886389, 58506764, 888297957, 253036905, 884694840, 711370512, 747884494, 398276390, 264462767, 563574369, 624254108, 295170446, 914344260, 354529951, 602679037, 80493845, 962584056, 997567651, 670193886, 431989859, 58976161, 561009926, 891360166, 917209651, 261989749, 816793459, 182432542, 835337502, 609893912, 569675502, 228888945, 980929340, 339916993, 620921350, 298417421, 28913936, 488457280, 610148153, 198421861, 265613517, 342943607, 416376202, 684692386, 835118746, 654283556, 27847985, 715688380, 277847428, 740899616, 533341514, 845585146, 147552215, 666541803, 488029037, 294882354, 457459760, 237537321, 23364300, 478424722, 996416516, 603199560, 534435288, 459513488, 730046613, 138650838, 93925958, 650794759, 137307680, 617345994, 115769516, 990487410, 587477145, 678079223, 510784925, 468212879, 736017817, 144176749, 11023210, 199983607, 204345067, 926629333, 391336356, 286101531, 766159038, 434455992, 14645992, 420859288, 735638993, 199706613, 120779761, 838863347, 47941544, 883024490, 23007635, 129352391, 225712377, 196348169, 359846854, 663652486, 592730189, 654895595, 135757043, 375982966, 382095780, 831054004, 340484329, 254035210, 348763001, 615837008, 408152096, 173431920, 174300753, 291097204, 572768634, 171204177, 365677254, 728856295, 16085352, 435174045, 374169643, 407792554, 865106997, 889341068, 112191846, 493374417, 435632918, 706037568, 597627440, 919325546, 261029316, 99068256, 554696404, 585089387, 530637850, 328730890, 608428135, 879500778, 59347565, 478390832, 596879473, 114067695, 143616647, 956566891, 654761510, 297660125, 648430276, 425291906, 711345700, 27467826, 197517954, 7454877, 431079328, 446382034, 549341588, 166795735, 585125120, 282832758, 643799474, 591740366, 850784568, 300229605, 165384544, 890574460, 54962319, 381530678, 827215681, 553941864, 135655110, 345260263, 584765925, 769120736, 639492103, 23178835, 531973975, 342206219, 991725437, 933178247, 80202947, 275706691, 885616805, 974990988, 414364193, 983181449, 835594399, 545784206, 873488445, 269749725, 202168130, 244073821, 54052175, 596813819, 666259366, 14814908, 299847373, 977078132, 805770400, 961583975, 151260573, 242183890, 641568163, 316646148, 200956276, 559615583, 444947409, 617771447, 997709265, 483446303, 785368763, 389983572, 592559766, 185587020, 197787381, 136640392, 407696567, 717815347, 751939739, 969881409, 908086209, 247765957, 687843272, 645161970, 602147057, 998885575, 605608010, 281141113, 453027552, 652210229, 444223518, 731671555, 952470718, 682631867, 325714128, 640168265, 870545777, 79732432, 42598325, 238870402, 225261791, 685876051, 626379578, 865531297, 610553815, 737291188, 896400545, 806647967, 459228580, 808044131, 982618818, 983491719, 294655329, 662374890, 193690091, 961002515, 595649856, 784713510, 870031545, 211338069, 680367005, 609394098, 104443280, 56727519, 104131874, 859133107, 612617153, 287944297, 480591359, 535887872, 957025109, 5782070, 402969122, 934137447, 106686665, 220293290, 531990253, 127363969, 366418088, 306237584, 763856769, 887225705, 180051123, 675661326, 687333451, 149289179, 991646023, 12981229, 392694435, 807362337, 942631753, 163188739, 681662157, 931331127, 685864179, 226999431, 436705771, 776592741, 889305765, 432463107, 477197791, 225987802, 833727179, 140859799, 241628560, 699040433, 752447978, 782902969, 800417771, 77445157, 987484475, 572030691, 331030155, 49163460, 360150823, 928096949, 591269191, 498682963, 619974993, 54370706, 659499447, 143019474, 53164629, 848049792, 982761765, 330366248, 974409080, 2014390, 830675311, 416936279, 82423508, 495310893, 439268416, 875502167, 431863102, 410509156, 864534005, 667013272, 922185482, 47828278, 668019743, 832135725, 93247691, 836590390, 659356925, 151544049, 872024175, 387636725, 402359993, 107280435, 675851455, 662694535, 538327177, 399202128, 717474376, 698408909, 480517578, 641905385, 696068596, 39827464, 674322032, 165965019, 705032536, 703329039, 50597325, 998655910, 725568935, 177686053, 228743896, 205798512, 266040967, 152866703, 848085639, 495749691, 689458381, 641696345, 480710529, 388294365, 855835834, 396635888, 138449892, 328037989, 937588874, 614868665, 714977376, 799397950, 641056709, 350215657, 155611947, 690600809, 498788505, 277232405, 111450443, 907112150, 596979434, 710811201, 475896288, 49155824, 808232198, 347323026, 41904446, 577040839, 772389056, 492117337, 440274093, 418126449, 627106455, 719380780, 221617386, 20957139, 208130128, 269037179, 268820134, 115308599, 392828869, 342765237, 666807417, 679768322, 804470931, 49800093, 439178894, 3958132, 908234765, 808749973, 410124080, 911071049, 819925436, 576898336, 653032054, 682665098, 457118072, 488749549, 550773536, 675439525, 602202280, 641373619, 71623983, 347940531, 643094785, 359258159, 943053484, 16791655, 471912400, 258678864, 719758911, 939513395, 479455502, 617838209, 139760928, 481059140, 181702797, 588653254, 195758456, 172932151, 782612068, 512606023, 383280466, 597912937, 54095521, 909621266, 323462931, 485707432, 434580767, 962385258, 43349614, 704934773, 187323758, 614434849, 276224474, 709880313, 373482855, 708774826, 686289041, 292641205, 388419905, 589592021, 169534998, 769266226, 307348767, 332675970, 761275401, 373239712, 629633977, 749513824, 283218915, 814146290, 119516826, 311097616, 57829146, 535192693, 90118768, 276076238, 978643948, 390151584, 376221942, 237623168, 422670617, 466686437, 270144963, 787234830, 895831236, 735183046, 55588311, 494778076, 30488448, 232232094, 373454363, 847309083, 927690556, 656502489, 206825336, 115637797, 439727001, 338090842, 193624014, 588686781, 251018978, 196775094, 767684689, 194087414, 640446967, 515391657, 633024526, 906502002, 584425313, 464048470, 674262495, 965444937, 146779725, 505691408, 886049965, 942402409, 503763684, 11047358, 60148457, 257344699, 994029236, 694306543, 673813311, 507606339, 660275975, 597011, 987553027, 494997519, 826893498, 688387262, 318882712, 948561780, 398762702, 275660209, 175507024, 99176830, 890120818, 683443847, 926931156, 866016109, 47856386, 670249228, 38177563, 28378691, 843650206, 373412461, 46477341, 10683591, 728621833, 819605360, 212015278, 653773738, 771741517, 925941674, 225485183, 502527001, 383022051, 895256839, 885148289, 109614663, 213659062, 68739466, 632320877, 831481787, 748961592, 503100545, 191164071, 656991120, 626933992, 872594215, 258252063, 34736260, 895437413, 165900431, 45010267, 436876363, 141384026, 371368940, 86767922, 454486357, 980128724, 551041023, 26070791, 773870807, 451749938, 869203010, 697692556, 668261040, 260646467, 175368998, 408331443, 802324818, 267127611, 93235922, 173490773, 420424726, 868750768, 293459630, 459118334, 860827319, 262462517, 263724558, 173924339, 79524147, 864005594, 303461317, 846579157, 749800546, 381688841, 934118861, 566915523, 3459775, 580858151, 681837831, 935057178, 48874594, 879026881, 289021892, 700566727, 962339255, 89485660, 913197721, 953728449, 710621448, 342983147, 860715308, 919909291, 187982098, 25102128, 252914206, 384182479, 37863525, 594573802, 24062272, 930684594, 210142240, 994673024, 330780308, 523404834, 890656556, 482775947, 167354516, 951996445, 330829568, 74584382, 531381430, 154774757, 374629668, 136946811, 796803618, 132439326, 768918122, 40721036, 188894777, 62988120, 352210465, 880704879, 692298254, 52963522, 540489945, 711558905, 340373110, 648915818, 201031, 341586655, 834452696, 723691312, 466590279, 927277598, 5981143, 399451386, 428749212, 481705027, 937715903, 213400383, 728336890, 159234685, 486414443, 377192079, 617956816, 130057700, 661397586, 804986150, 301747530, 675101516, 875021351, 574448768, 640817279, 270004710, 901553242, 250126827, 14651429, 696697975, 52663737, 184082934, 246308182, 457388541, 385206192, 639406179, 148881191, 787405456, 945237350, 277068846, 693733685, 434667618, 193915066, 479424364, 151704023, 14509783, 514040498, 384496404, 795970104, 360566647, 134548279, 601593073, 282923586, 837850710, 277939786, 126582376, 854770724, 124460020, 930396783, 191725927, 867288302, 306219818, 2039271, 688922134, 140833603, 71616132, 624661152, 357520266, 688304443, 811701828, 416339050, 263934480, 20594060, 79597971, 645262510, 999463806, 163611894, 172340982, 177228678, 932303957, 355736438, 697913565, 157326153, 938947582, 615846240, 384144909, 987742763, 538681286, 604920978, 379768582, 666650695, 670356493, 332237236, 943146146, 426442380, 300186137, 675397915, 660440966, 288090667, 691090353, 276266039, 496383916, 499757573, 166797993, 143798657, 731171546, 23821376, 830740007, 716356032, 824226870, 20077288, 426316098, 199706811, 774695599, 880485755, 876748798, 212820720, 66941216, 966326600, 931854359, 850632635, 148378966, 882512403, 955101491, 473979246, 885349799, 865270688, 890698809, 150751117, 835404900, 881420924, 71883471, 723380043, 509845732, 766980494, 948261037, 123750247, 994524797, 44434474, 637724565, 328311116, 949260078, 85729984, 634597551, 144565992, 623223987, 474496804, 820521321, 660899350, 65880535, 752810495, 384170888, 96730292, 631802962, 635668403, 419576616, 372408525, 522714468, 535950508, 972881922, 287507059, 977916994, 487053550, 471359667, 947611439, 758624036, 579785169, 45616298, 848994538, 830157267, 254429560, 69215662, 549862867, 887585334, 606268800, 167126287, 868044599, 218563713, 215165024, 737547865, 466855745, 285249072, 835642615, 439179564, 78585880, 439118671, 129272123, 31011487, 669617703, 389379135, 331031812, 759674164, 384260666, 986330554, 306939590, 68500349, 142992978, 878826608, 525808953, 899039905, 146589151, 292575530, 773065762, 481928029, 687752418, 891456099, 501591162, 626036336, 911149564, 844373454, 146113466, 967831751, 708329335, 528211702, 735786678, 673563101, 792118626, 766265480, 840975056, 143946334, 923566971, 126008140, 298412821, 174830437, 153781866, 708858720, 693188498, 322399651, 299551475, 375767481, 293378077, 624275598, 579548530, 493836054, 880619984, 469042759, 474595257, 590630370, 134629131, 193830185, 786942306, 160444309, 33487395, 367738524, 800431378, 673870290, 179968807, 946604747, 888991798, 384846, 696497260, 146675652, 413121505, 691754020, 904267483, 48270589, 410658361, 634911429, 82864058, 485760529, 907856865, 616043360, 339397222, 156854274, 331083178, 397935231, 330437194, 21580406, 803713667, 970261295, 275437607, 885788210, 620728361, 452931487, 353696083, 949635432, 261153396, 348808166, 457543084, 390992459, 531531767, 935188013, 313063930, 875919032, 507951036, 489114304, 469239242, 91897815, 483075238, 504367290, 692908142, 947304769, 8832665, 519421901, 836782003, 248193428, 565540344, 581339931, 70490795, 67226504, 497993956, 863792312, 700470104, 72179764, 2186182, 867413469, 443829609, 13780567, 776635131, 258857797, 480300450, 294560994, 931661127, 811680096, 859166470, 666226526, 854342276, 485080799, 394543032, 265402760, 159768969, 358311593, 405099677, 136542975, 837387752, 637667179, 222545048, 373358642, 272916633, 207723430, 489151452, 959452989, 513584295, 408333986, 296839067, 638806589, 896093292, 930252142, 148868309, 622043532, 979767771, 554069402, 517318241, 613277029, 455456977, 660299735, 158303556, 279702262, 269895793, 703314467, 753733502, 10255476, 33031221, 253186868, 724932344, 696037988, 651290278, 78917107, 46708089, 212727317, 43881480, 664718608, 863140720, 84344151, 201438943, 672198451, 876724222, 474091613, 575625615, 946268538, 218946712, 588019962, 419505025, 572432081, 892568294, 598415440, 340169516, 321735548, 761535400, 283468589, 281731008, 279038669, 544982619, 656879373, 834029372, 608744394, 150337893, 760534247, 448591043, 967939315, 125600451, 275243355, 224145353, 219287113, 485469535, 52114339, 861127594, 530650354, 122016543, 935940377, 662270916, 836054896, 620897896, 296103446, 674961386, 597055861, 144739419, 903713500, 940496305, 362639754, 403074047, 64139928, 593572756, 802469841, 789003439, 410383010, 395846930, 726830145, 613954380, 294844112, 934611054, 631257292, 486871290, 223584825, 392557777, 12906818, 815017677, 660235933, 347368521, 681900819, 602420655, 1041449, 720407290, 941009742, 397676555, 846810538, 274881344, 96528473, 254538034, 55397112, 354484807, 326123285, 922428822, 79435621, 17295466, 438556335, 727432350, 662612020, 379831947, 427105856, 253991515, 777090917, 964961755, 178408868, 931986347, 502231743, 167283839, 291715130, 646237292, 435934348, 709626589, 277211497, 398013050, 161205389, 634856950, 973344008, 627821701, 991411383, 671817519, 336362047, 355190845, 307045924, 926811081, 496234531, 866057640, 236059344, 934711325, 577024029, 240944896, 803570745, 997383725, 236916123, 814755232, 818631973, 381516602, 932843000, 302405268, 382645341, 268305808, 589602736, 517344680, 969176398, 729303155, 388676665, 369201518, 885569727, 255438367, 988604070, 2567325, 151321762, 5581894, 778663980, 874704913, 149646449, 807935587, 617690432, 65246242, 984222792, 754503896, 710651030, 65065985, 712289686, 40738416, 14271147, 133064928, 347871247, 29793092, 526177256, 884153118, 448131341, 555873392, 779372484, 818375543, 317654424, 592762079, 434234733, 223566615, 86948739, 524966234, 651491278, 493710601, 452595070, 962694145, 477146523, 923125636, 752773735, 465309795, 647448505, 168837660, 376449419, 882426957, 391653635, 878785904, 19298557, 405258243, 847461500, 727896001, 840402424, 286093965, 281202539, 924218957, 842715580, 706833676, 937898727, 800810661, 557264383, 993362684, 195424952, 16409043, 346904020, 593424815, 19924525, 580810086, 486718045, 910903689, 846930870, 862599400, 238058410, 863988914, 27631309, 303790066, 358649638, 826340175, 219880405, 677071298, 152847778, 793464398, 700242890, 626683663, 386785612, 431040857, 432111981, 856955445, 251051155, 175130463, 504032796, 616568855, 47267294, 820148593, 245602312, 181953817, 138050840, 133358390, 554048780, 230249260, 103669720, 961469478, 228139268, 924159163, 860278273, 371221095, 85919778, 752683875, 923834429, 855460244, 718074614, 933493586, 789896494, 266662714, 610299207, 807480015, 896074226, 11558692, 173874529, 732245785, 992670585, 325416314, 274424664, 975765146, 781991712, 196502608, 258733005, 474394889, 858160560, 934870904, 235200612, 587219893, 296687929, 61001237, 586994894, 801451562, 193139367, 509887599, 226021777, 282407830, 623727826, 641016065, 160381771, 922680112, 724960127, 860300026, 681006121, 565795844, 712745896, 180766437, 195744154, 78147513, 801162585, 1094974, 113117303, 910392905, 101564287, 161967540, 803994459, 620704732, 31527980, 467435028, 204051190, 799665426, 631397265, 23472644, 339128509, 381050272, 841369018, 874700393, 946207580, 562429342, 159646360, 456524111, 510258932, 850258296, 288460535, 113952689, 958015911, 332787671, 200704893, 403598585, 812920495, 186392243, 682106821, 443416434, 127211602, 182904466, 41033785, 972338459, 866983111, 423611648, 714386412, 917768350, 355470400, 972869079, 606371129, 151648788, 396174216, 431615001, 93807047, 740364204, 927556421, 556212893, 686637387, 206256218, 369919394, 252878167, 379861333, 738647912, 40544889, 256851566, 437791681, 83477339, 359120222, 181868412, 158278643, 99816120, 949711578, 457396896, 281840178, 714392657, 814753100, 257735609, 516594700, 970422756, 681478753, 598859349, 160063313, 51772142, 654684073, 10739419, 55666524, 630517193, 401488796, 899704503, 882352845, 597553770, 640784645, 90867196, 55531418, 124145808, 715111025, 418339509, 579474045, 404625232, 837396659, 238937036, 981028610, 8316562, 160264261, 848783961, 732931200, 26335232, 435442955, 663384971, 680432260, 560652744, 848399038, 516676468, 260550241, 483223803, 791977669, 720026261, 754649972, 647031768, 485247393, 659753144, 569665014, 631031882, 250307808, 78625651, 518740881, 718712768, 514524618, 758377402, 692384094, 311553696, 44325355, 546637691, 695292131, 163014261, 329879331, 462947822, 12318136, 917771048, 492856103, 217262143, 168131085, 562479870, 621954772, 768426762, 397416095, 921565637, 482161428, 648754102, 742790287, 221566299, 404761398, 897417180, 133234256, 904629136, 334319627, 393113730, 553440689, 544202916, 977704238, 27676179, 498555195, 792365063, 622448097, 344750348, 327761270, 335101677, 919343115, 476456766, 331417419, 484797417, 519821275, 138314628, 788650574, 570796693, 878612159, 363624950, 673629605, 171094609, 754081677, 294795962, 434289764, 287574842, 548037701, 184961116, 968594312, 939205336, 363627010, 636374044, 883154309, 407274222, 47450929, 423126271, 423712323, 661491065, 287268949, 291445339, 658608324, 142750995, 912880466, 803145883, 370045842, 581907521, 490984974, 613976636, 457778719, 102075538, 906683004, 395708771, 110850089, 513380702, 325410268, 777757303, 187722658, 685131911, 202425967, 352439257, 726925692, 766643441, 883968566, 38548594, 379989475, 765479916, 430028344, 160452614, 269245127, 799514869, 696972603, 59297366, 291188133, 567781147, 475287654, 794643020, 398124286, 773055766, 356855205, 71170277, 323252334, 682564665, 592704236, 622887859, 697020353, 731810410, 653479081, 495499100, 501133109, 131860213, 44862027, 703398313, 804654379, 199010659, 8583771, 101880760, 354250661, 757481310, 260835972, 4544487, 65778295, 14912404, 719446922, 70499331, 879805167, 950491269, 456753529, 71462700, 333075044, 28686783, 14910737, 778843964, 904481559, 956535708, 100416449, 698524436, 181479891, 856493372, 165953756, 411768279, 777666856, 672188778, 229123415, 442251670, 574712949, 420679626, 851194713, 857712388, 251447780, 364992280, 943745420, 888997414, 788020378, 672070503, 445715691, 898200318, 701678911, 606016176, 980846013, 79350581, 150695393, 293753069, 713518994, 345021350, 379282892, 472601471, 549952913, 562389711, 300602995, 534160374, 55246051, 275966677, 361343041, 636602554, 673856444, 214387328, 730980184, 343365214, 435103291, 521122947, 853409242, 896206107, 478140759, 523486388, 610634911, 833387497, 230445555, 321285953, 54002160, 352930139, 233113580, 414827899, 413428901, 488503133, 885496803, 904719668, 642915605, 503966933, 641503822, 559832786, 396971520, 22217857, 742224321, 944663361, 720595962, 286959965, 375171136, 277531630, 960671575, 375713031, 154416661, 215525419, 806825737, 800527168, 761761557, 749987116, 406674037, 106994538, 922148480, 894870108, 528367451, 717127899, 635890970, 595244610, 81392695, 319427638, 913902015, 127813646, 89201536, 869482232, 318679930, 852353623, 712696266, 947303168, 95205568, 89452595, 266007237, 357927090, 18082624, 563128155, 798850011, 830535603, 250998184, 851441381, 426209788, 121407550, 104039593, 771720348, 431904882, 763231038, 130991909, 914585759, 285364109, 913509545, 484078416, 852930463, 350061622, 280339332, 218002632, 716951875, 107198466, 653792985, 775904484, 440412315, 851413144, 33482942, 777826466, 798962810, 481549393, 398764820, 917314088, 953929527, 244333348, 482076730, 354587667, 454742307, 14640733, 373146230, 259680439, 333710267, 195444811, 291402290, 591853382, 399062150, 886887044, 732599440, 166992305, 261101842, 107974355, 993305792, 801740167, 665288531, 207946416, 498879582, 394323384, 628881122, 137192607, 651334598, 524988789, 707913869, 778946973, 95568718, 889823059, 217829131, 999297882, 710544216, 751102182, 712338628, 49441456, 630724367, 41623965, 54360536, 798904394, 888118131, 344351595, 451565284, 354757846, 328917871, 107757216, 603296653, 855352816, 756597100, 991319134, 778301737, 595351238, 118674892, 110941953, 68166878, 800220754, 94621568, 431691338, 835270546, 27724065, 938202388, 192540681, 580535240, 605788813, 501621317, 224332667, 395851233, 711904016, 961115570, 878238864, 840724005, 441352581, 461489231, 498362471, 212709057, 169177745, 385871197, 336412255, 283309340, 910557803, 21574694, 680283771, 745148890, 675689991, 831252911, 234848390, 926239433, 205382812, 448745733, 565286928, 856288173, 955463822, 270190758, 470199011, 978827159, 511740522, 22177677, 558847396, 648886335, 915358790, 411585584, 824764663, 993416812, 889512265, 133802020, 576302287, 318524817, 898497828, 573753746, 242206944, 327861380, 837759694, 751672045, 672221574, 649775795, 256053120, 393177963, 535158385, 935691190, 769795014, 139956169, 20471305, 999801197, 810218446, 724097519, 330660793, 589743899, 217256636, 495898048, 905884015, 626218612, 419844684, 678046743, 512053451, 845589264, 442441765, 672820412, 471431746, 983805571, 385191619, 281510920, 467197263, 678037802, 150657937, 948772913, 938448487, 225769040, 118775339, 896873798, 245861167, 30787018, 352084029, 631966995, 937058403, 676804267, 484939873, 707971908, 388461901, 306668708, 429880745, 53305417, 98325331, 956587771, 174760269, 593866456, 401453048, 680806304, 157824295, 987230924, 186136886, 149527774, 185969126, 54612910, 853927258, 647297331, 250877875, 240687127, 224711065, 963181923, 1099098, 562365293, 141507586, 201786692, 627384059, 794855265, 784775138, 149657805, 823562604, 679138727, 432451146, 303651495, 517153610, 522287061, 315342463, 236244352, 755981330, 11109972, 703862001, 128218681, 627558878, 213364383, 977838516, 919130000, 906637147, 43855264, 999167747, 90765589, 89501449, 924250619, 745895590, 449491165, 534729527, 356110878, 996128177, 949103025, 735866496, 347653302, 72765206, 742425822, 985995894, 840184479, 775745680, 747510902, 555449138, 552800080, 910839341, 759047168, 491144542, 903535866, 178312851, 411225471, 367751394, 670799138, 250720416, 447338911, 270744719, 565388996, 805901002, 932808341, 824638191, 478948939, 750288904, 978204594, 709559009, 500955986, 864253425, 918093471, 494651463, 136691092, 137828381, 407291260, 832586240, 338887976, 184715509, 445736171, 542381051, 699090156, 99512600, 301519097, 76894786, 179840745, 809879659, 905295703, 16038239, 319158480, 480223417, 538340557, 842615971, 482895795, 61080093, 805470810, 874807104, 606274329, 809187625, 132206631, 174663048, 243910489, 366998969, 85476810, 496528577, 413025730, 681740126, 611562286, 544351105, 110068024, 386442509, 565441897, 77958597, 276260123, 770517656, 87290461, 684497265, 796328933, 869783803, 949864991, 278421483, 407245644, 754900173, 670500449, 655116307, 18320569, 165361533, 332986312, 851763922, 693962563, 286670676, 297260989, 526283809, 34092574, 177575684, 700598395, 987174081, 871571191, 42888041, 615736455, 366018821, 868123353, 33273134, 401582704, 885912202, 215514351, 768806750, 811476769, 825335800, 395727225, 252829458, 178012488, 293965286, 821684775, 991070374, 292753693, 501884141, 655031049, 252119369, 637947384, 549533773, 775714705, 686560296, 528364528, 701051587, 395675241, 129981144, 816570154, 473173928, 43467264, 948471763, 239041971, 670927110, 773425489, 997278576, 958604333, 830717289, 164333297, 109011842, 914348664, 125023356, 863997854, 457556742, 63614310, 642078242, 951457437, 828813857, 189927329, 434102512, 881546023, 737823483, 825140079, 555142520, 537661516, 766073842, 523096065, 892283041, 441409378, 702558654, 640170051, 64016625, 762484578, 190358076, 930880246, 812330720, 291775257, 61190083, 990928159, 101158220, 304633449, 351464625, 125752397, 413897199, 552284952, 672642999, 770122377, 530605823, 408610852, 285708512, 335494753, 693217019, 469165463, 347248473, 366272690, 926535883, 189825197, 373780413, 694260614, 569720071, 240463801, 106421257, 894525726, 921475612, 721251935, 848637549, 880833277, 648238576, 927978973, 116719779, 261397855, 865640336, 442917426, 640728645, 447651401, 399577732, 990982427, 898443245, 359653490, 219917698, 269969394, 74991204, 698588489, 77772298, 962335212, 239669104, 360188959, 231416309, 258273881, 571148519, 399421490, 349393153, 982718056, 247086452, 241183807, 192499660, 560349440, 829727362, 736342442, 5358292, 55727192, 330887799, 477966193, 486045892, 371815390, 713837883, 382265116, 129093837, 799150465, 13966764, 180371236, 888052345, 698121410, 189437599, 863596409, 5318405, 110229878, 540020247, 36366518, 635324173, 19746052, 493268841, 167323125, 429086929, 20809061, 77680384, 780325134, 526288158, 754589746, 977721398, 678245558, 759034501, 589437112, 653657375, 692599826, 278860672, 155523813, 262672578, 185581979, 651209780, 759456098, 155705025, 9794004, 960127895, 486237566, 912442616, 20415619, 326130128, 726801642, 890643317, 172681513, 872266373, 448452770, 861863713, 798856263, 447387706, 64787594, 827630092, 571334892, 573278556, 768090476, 168463749, 614155732, 436892125, 291777689, 515874252, 791058394, 4138674, 763175550, 571840909, 261456803, 970468725, 702196428, 485836968, 147416438, 242838973, 660843820, 927259043, 464119842, 814622042, 207705455, 815510852, 377538479, 982031020, 827952999, 425370878, 3576782, 27556627, 435643037, 275207459, 852183726, 21040266, 370592056, 763700485, 132637265, 939035029, 151303473, 361737247, 859165678, 648534539, 67695077, 549431117, 65909090, 937360682, 513414666, 563281313, 127417707, 153413879, 637607166, 830840776, 949051137, 720553253, 255228491, 564422231, 986204658, 728551774, 447393921, 754852458, 940185341, 313511647, 912457706, 891933059, 521887125, 396153917, 362277025, 179237549, 711063529, 351937117, 518620552, 62184822, 249678633, 385056306, 418408008, 811302959, 278805042, 915722329, 334128701, 374236988, 16308004, 229035539, 534514487, 234223410, 208441629, 618525808, 881796450, 445756939, 784076762, 19516987, 110953616, 767306694, 56590056, 501900594, 340851473, 133283712, 654721156, 90119987, 654056486, 293418836, 424385915, 834411835, 204052509, 142117852, 42935814, 598467717, 725710429, 246544780, 273346304, 364972875, 294929948, 712143362, 854622622, 645149641, 771374984, 191986087, 822571839, 789487212, 252165133, 961945037, 145656226, 260173514, 474706173, 525998002, 504237448, 899986952, 802358662, 186059899, 534476382, 144723023, 713610558, 790510685, 109078443, 265436920, 906431327, 808687437, 48028500, 840776183, 348253664, 290240149, 658440490, 79167243, 740494067, 536072298, 438227980, 410274930, 842979690, 911843023, 142237124, 985843321, 149727884, 337729805, 612337217, 84746517, 741595361, 19150049, 480937233, 275070734, 756028688, 838230618, 113325150, 557059313, 365896773, 410764977, 638000614, 563160942, 218098482, 392410640, 82748780, 669528727, 79514102, 403094165, 423197035, 812181607, 632574445, 33421932, 546520320, 58078198, 94152415, 467789010, 885346316, 948830708, 951936338, 629731646, 184268046, 905062981, 686356095, 137231898, 770550480, 325994451, 808009053, 65475058, 803243152, 786553119, 222913324, 352044683, 900200117, 307924633, 888099091, 448515144, 951996109, 874810525, 839935087, 58972076, 192721817, 561890345, 411657845, 141117661, 829552540, 175577685, 358612785, 372428414, 870786916, 876031609, 566009337, 155552626, 769282928, 769051674, 31940407, 388264470, 477311120, 294908571, 52288474, 154132118, 763944263, 793855404, 276296938, 337377561, 51454261, 357645530, 604609849, 226737687, 887135927, 804882754, 934813408, 133855562, 344990147, 512195988, 401281913, 194447041, 530280927, 543521241, 57702267, 246393352, 813458394, 104004183, 949119284, 151231096, 9338620, 998289807, 171865454, 740208251, 588782785, 18651712, 736429911, 864432608, 736712488, 801376682, 110558614, 72505376, 424673106, 292647338, 989535276, 935952229, 992448797, 340450376, 426241028, 171926013, 902475767, 875394674, 647642745, 110298832, 456753524, 938571454, 603427428, 244995548, 89001129, 841141740, 702082557, 596633280, 463005290, 18779844, 153975755, 129561888, 660147316, 698427283, 535438682, 114233460, 546495039, 766203064, 391586041, 755370820, 124085120, 53434331, 549056824, 252028156, 988048540, 417847108, 530290931, 943659283, 761138846, 181094850, 228004287, 667630705, 106671120, 419034632, 630734936, 624523261, 259098410, 614187158, 607284906, 633435225, 522552639, 605414011, 227784834, 807515202, 598137875, 62150178, 157964933, 463778678, 70435991, 724603795, 996086752, 562788359, 588983374, 778125228, 7215854, 560801498, 892349679, 834254197, 385973317, 682831339, 487111680, 31381543, 65775730, 222535316, 3789966, 594009224, 722522866, 327837967, 519468380, 161064991, 816007518, 52532857, 748805813, 160063674, 552454176, 25358195, 481752154, 623674620, 225642094, 543339318, 338982079, 661451366, 464756154, 139609085, 69837133, 960286966, 117017928, 12754040, 497998259, 25316440, 761256664, 738996574, 109235641, 910023243, 294273705, 219336255, 119341084, 289555181, 626427632, 699421559, 773562141, 817191311, 114597445, 982438529, 793157693, 953720020, 359242205, 540336007, 735235029, 208285333, 752598325, 637794615, 43658678, 767684450, 163336818, 1398397, 323592336, 712273038, 179023562, 240554599, 987313852, 440293492, 81904187, 33197542, 499718072, 516990258, 368945854, 97066766, 982650399, 269560062, 327920380, 657224612, 496498551, 312375668, 727891248, 235166026, 906691546, 463710895, 677211410, 323391689, 802940330, 953159349, 328977196, 65269779, 882848055, 570015463, 98462305, 33949778, 70821755, 444617038, 892911314, 482897933, 747271213, 610431337, 785675371, 397475204, 11865622, 171935546, 663720596, 687076971, 981987752, 716770347, 136442158, 2388354, 943712684, 921019496, 371648373, 725764763, 205708759, 346448248, 61673904, 394917270, 128489297, 432533089, 657673754, 233001042, 252657175, 822309021, 808328409, 749417827, 266960715, 532470405, 803590480, 106705310, 959292663, 356382227, 939001323, 482575573, 760197350, 602457173, 449747334, 638978386, 938632619, 572045493, 378653082, 225443961, 283368752, 95082363, 8139715, 269229416, 601518258, 170903682, 428131926, 136897102, 203242030, 198688115, 752098560, 175659306, 7116465, 477085579, 150787196, 53525666, 356146507, 4572020, 634929596, 693360278, 517000737, 263747718, 907824678, 324646068, 806479093, 334389142, 844616931, 175108352, 794567860, 555279048, 894215745, 582774323, 22846584, 90540438, 931481185, 681711105, 486901869, 651931223, 823669102, 263478802, 866348777, 758525147, 116173515, 688107842, 967012499, 35245492, 326283640, 955400366, 272310185, 800611935, 702243507, 365501597, 766963917, 228654844, 691187672, 239026241, 754852207, 457441079, 990437848, 325538483, 625530670, 48055450, 417744575, 79245870, 373892819, 369050324, 415650013, 835067549, 308688092, 850541315, 840916158, 966327422, 576268489, 166140004, 455248192, 507387025, 428805396, 499990843, 859610236, 567102239, 495445122, 947898305, 764711145, 547662212, 226829228, 619523876, 358336662, 195014796, 721792396, 432298894, 902875517, 188464395, 5201808, 343554993, 366129543, 193558331, 70796216, 495075645, 489832547, 494227044, 96910674, 214400523, 691402184, 61750315, 489582091, 106667148, 279281512, 794542079, 628573983, 403198658, 183531854, 196242291, 324520264, 674448843, 654807762, 223635359, 160463577, 575609405, 370751012, 409939448, 578341755, 566864002, 763536443, 381037277, 787966635, 616577822, 652856391, 439664931, 82403395, 543938317, 724193940, 755206711, 903897925, 933364703, 972800897, 786973236, 763609127, 320756357, 123557051, 581141449, 52953131, 774758658, 440475952, 613594305, 997945548, 207164168, 71352146, 88819475, 752496229, 732153766, 914434501, 395090267, 404261842, 159093159, 428947159, 953575883, 671975034, 70414199, 602076507, 194607499, 145886096, 381651854, 399241115, 199652705, 947359261, 30626059, 413051914, 417456009, 944475638, 692088370, 268977193, 789958979, 794834819, 239102967, 385626799, 883049282, 203082407, 416006952, 247931277, 288481335, 701927281, 264831980, 551295332, 26147534, 832710227, 758152825, 898648458, 327235948, 738187112, 163620631, 912973111, 459031049, 44665553, 479922720, 842945, 473237185, 69764698, 673065362, 295109015, 964099364, 727990764, 59052022, 420953035, 746887829, 531624414, 325477727, 733968539, 813261745, 908593540, 836797419, 53742122, 885953781, 825537169, 728419936, 557499438, 824911859, 326213855, 752267860, 233662280, 428552714, 736844947, 387887762, 782387134, 964832387, 673294989, 403952788, 605133369, 405713041, 716833606, 304325977, 529032353, 263851809, 44664755, 954426910, 968156943, 49272770, 82654186, 849902201, 428728385, 571932452, 814877942, 335647832, 569328198, 674815026, 681698669, 371013068, 532232884, 694755925, 267023298, 250975261, 385208534, 868625155, 221501683, 888562459, 973761854, 123127947, 804079442, 30199171, 54801730, 127458771, 834716842, 999436394, 681972977, 601702706, 23536746, 957637597, 595401438, 201244248, 635256300, 823779664, 705662752, 890632361, 374072902, 676642542, 116144998, 290866220, 270908439, 873274570, 136625594, 812858245, 285095864, 671545872, 26939556, 962697764, 68612912, 160501947, 364893322, 656775732, 548299357, 848382155, 654677684, 359692454, 137469137, 188383890, 692204106, 191833869, 144360298, 947196400, 767053279, 220086311, 78427214, 18330686, 441633853, 338272239, 745291467, 529281700, 623063374, 48324166, 494856976, 769889854, 498039411, 993679559, 347309653, 786707147, 465928995, 988405606, 262082292, 534286855, 249177585, 164176214, 504984256, 103965517, 930320172, 254432377, 132129933, 451465462, 960169283, 632853990, 809324807, 567209970, 577509329, 683363677, 207848111, 320800512, 361708309, 686600872, 702836548, 578672769, 159954930, 333437761, 7236927, 178606408, 225997300, 579385500, 445948691, 166842014, 600653377, 310018272, 93079133, 263236511, 394108138, 55168834, 649546176, 348177823, 574818971, 438486751, 19859309, 897341935, 981252174, 526733910, 797686634, 113725643, 373189023, 793974374, 780614874, 193036204, 326175147, 873154039, 357240102, 250708111, 111611278, 187330611, 468720454, 45872525, 290745838, 414425167, 157990107, 425170127, 147757233, 180209039, 703740122, 308872569, 875450420, 553705679, 998973230, 780216556, 261378656, 838718229, 251447489, 58336679, 41261457, 58787959, 27274963, 433687091, 929576661, 111203999, 307495612, 577632764, 618855650, 382685429, 641929321, 184531590, 465521829, 589256088, 295868738, 536441070, 181931919, 124511595, 446718142, 361640141, 703231058, 955364095, 507054718, 181270574, 704388543, 817645658, 263729173, 87917447, 679371926, 148244511, 18990178, 80956074, 358507303, 497081634, 16709754, 467394264, 535451743, 392640635, 426008296, 961451645, 981136125, 707569851, 585523517, 10864639, 184018549, 13617331, 17992613, 848529752, 765921208, 42925735, 457486140, 785770478, 82087703, 493233308, 949747050, 211328273, 297557011, 617253655, 366588368, 340891096, 865041021, 275932061, 820654782, 275405792, 771508355, 848914972, 332728724, 640470841, 913968584, 740370181, 793169206, 425181938, 982842950, 633096911, 311883953, 873222577, 249703415, 464997401, 247040002, 103635137, 39515529, 122659861, 343911825, 997499158, 326226766, 633300040, 635085509, 751818063, 202007207, 825328127, 741716564, 881633115, 54438841, 344572184, 933583850, 940329555, 537911156, 205904346, 976594311, 919163271, 299800331, 114477696, 992836194, 884440543, 787245285, 884561463, 853087294, 110643811, 652647884, 530993785, 763998165, 227608832, 154266875, 603056070, 829685531, 492838508, 691033376, 440773663, 547174894, 174602924, 440686394, 549967898, 195631784, 146670431, 680715385, 353911584, 673785931, 991693908, 876126188, 48627627, 902537860, 186760279, 880941548, 566558449, 614981401, 226798760, 297562633, 751796284, 381285658, 689053987, 975908005, 156972340, 696227618, 454785198, 704614286, 537036747, 252593951, 336748387, 14829218, 900761043, 902607553, 887497990, 338267498, 815464042, 964086564, 196213486, 476481800, 197217470, 947019165, 157146908, 234550346, 38540091, 305321714, 149035530, 594668154, 687643199, 429841109, 856973058, 971630517, 572072365, 735278549, 866718961, 175500578, 899850512, 56391214, 813508, 343956260, 603835806, 430720615, 175742905, 46410619, 226706682, 772150860, 205431532, 540967779, 535966852, 793757908, 393141537, 990293519, 588653943, 697680042, 66035348, 153854952, 258516646, 814733190, 305161430, 810462649, 977304947, 314731645, 88104753, 48363377, 17696952, 281454139, 873275078, 492203329, 210484700, 282953791, 76219653, 797944222, 88983778, 323345627, 299223645, 451282644, 514134678, 516781717, 207311547, 698469759, 87127806, 253941508, 51743569, 119113371, 50403801, 286651841, 255965745, 75024682, 622685056, 581630195, 467646472, 159893193, 948214373, 972898173, 571200221, 57133824, 231208375, 860042588, 778339367, 331152334, 777433074, 334600756, 791494090, 690078515, 166821691, 822678642, 439160251, 636784486, 309645994, 541222884, 502968268, 347968256, 699473163, 813398350, 504481768, 797945196, 341508669, 94418986, 489885831, 551499038, 750273757, 548152887, 836549334, 512727928, 489745808, 294770807, 556724328, 157867194, 551398538, 274646844, 289731334, 641392432, 442798164, 311377065, 292363786, 721094534, 896187135, 450818478, 312886684, 19496531, 431734016, 285008867, 18168143, 32247575, 217991301, 472953436, 315250223, 751458330, 524213304, 751726855, 492781780, 944768001, 962082544, 986855988, 798056912, 311497581, 61218780, 912369929, 932794158, 239790658, 727054585, 450611421, 748463387, 708421943, 445452980, 819513845, 203715238, 247629234, 114511779, 970383159, 694706152, 672822665, 36945992, 932045289, 329716505, 849266117, 531913357, 429748986, 184931244, 386366405, 161115290, 176020911, 212128320, 456291203, 110258190, 572813837, 17060154, 539009813, 345328928, 143028930, 927168953, 996884225, 682889219, 447404893, 989740009, 289384377, 920789156, 729619975, 166896608, 605878044, 820131125, 477070471, 944223766, 274922955, 273961641, 814516483, 933077485, 707984567, 311530350, 614271689, 350013598, 424174598, 915070586, 349510218, 196439403, 288807318, 428460282, 892642697, 255980059, 25134794, 518594696, 534255274, 180777696, 394067720, 842610390, 886250928, 236753722, 655201528, 345416198, 500452618, 150448252, 905433906, 580568534, 769862457, 174435886, 526169327, 963283391, 851269765, 837874665, 309124373, 940526895, 34409737, 246868510, 356191859, 519090747, 542188263, 680968717, 896712692, 463105136, 803791583, 794923968, 946620377, 897619098, 213797877, 54768263, 997953611, 651593567, 669117717, 43783142, 616665080, 868493946, 231230220, 824531028, 567198967, 167451435, 643858592, 122167965, 517771394, 983220986, 614452995, 39315651, 625642460, 521320214, 15765103, 676630117, 340412972, 513427231, 724868546, 410002671, 869618954, 189390658, 563744031, 561044793, 551650894, 642365927, 276261348, 934032396, 142589619, 642213346, 579943153, 742173998, 186539764, 26768361, 241622783, 52442991, 674611418, 877441907, 279641050, 378593252, 426513637, 155931948, 734076292, 519632740, 884359285, 215355928, 409243316, 506906821, 650480601, 625555946, 438005291, 168572765, 394131323, 111945195, 333894433, 758696056, 47880295, 975324869, 783395602, 829867929, 627564057, 301037681, 154969198, 830566451, 491688805, 554288855, 85608443, 46431295, 978893035, 26677749, 689044617, 828398937, 488338330, 862207587, 958203991, 644992486, 75972030, 112107298, 966044578, 960723965, 677619740, 644548044, 923023470, 52664980, 893689798, 489551171, 188528324, 27466040, 255252674, 984470088, 322428922, 331587871, 810660230, 562695041, 938853382, 941890583, 574510738, 945482717, 542447570, 60792247, 37875237, 820660359, 755532927, 582077290, 328755435, 889079605, 903583715, 725694747, 782096047, 182644422, 923555563, 570744386, 442400119, 986461704, 130670760, 13345805, 987450495, 881702817, 45536433, 692028913, 420669715, 956615466, 843449240, 458785681, 475368140, 573579076, 482011529, 684730276, 940069420, 67299300, 572211289, 925981595, 776548046, 263360674, 192490751, 730049159, 530196351, 747485585, 757107424, 764463615, 94323569, 78286693, 411642293, 931858551, 185441384, 685402233, 355777771, 756692961, 860985063, 897243197, 841735811, 311358556, 77881617, 255249591, 347999964, 44961567, 650416230, 878238900, 77029025, 998277057, 784573316, 384695947, 11656226, 972945300, 259365903, 482882632, 286577450, 466358865, 313700472, 340850640, 648132831, 447844298, 427222751, 877699593, 129522579, 905971000, 794642912, 539442003, 530730837, 280917730, 294569019, 370444583, 174692100, 848881417, 996217694, 87170840, 197541943, 825837995, 931722768, 124505261, 500750995, 742062775, 973284953, 863299534, 117925975, 583669357, 112937383, 305110434, 379704474, 318330492, 463248184, 151461806, 372596274, 604937601, 73283358, 507734968, 678016138, 475941660, 671313696, 690836470, 519417486, 296655623, 58941918, 318490703, 236762542, 765133389, 324783161, 260046564, 166030437, 892625293, 588571020, 151272230, 815703404, 243950072, 566934454, 970195833, 112685022, 220046971, 906921622, 414503528, 485153499, 939332116, 753199667, 903938547, 702313413, 989584935, 570770301, 253828339, 157798006, 874118072, 459375419, 750928870, 15976451, 207010017, 50015208, 643188896, 724985086, 136394563, 793337833, 32667993, 935924022, 488354520, 616857487, 343359722, 483834516, 900073447, 435331192, 572359832, 357798205, 426051369, 850270602, 148977029, 106119768, 237792673, 943667320, 69961233, 50420321, 510021496, 804785412, 953465166, 976878167, 861896930, 815336160, 416068411, 742594217, 812863182, 272618516, 916327517, 543243110, 821566713, 189023445, 893388728, 813157850, 380935691, 441187481, 900209210, 898609976, 471456293, 122498771, 583352534, 862613292, 461191924, 545190966, 806196153, 406854070, 244983571, 502777017, 894119104, 820814032, 305800268, 440613162, 452026238, 921825307, 234722347, 563601828, 63302446, 181834445, 401951515, 347948638, 479467396, 760159656, 645131718, 186133407, 163193779, 120668268, 901101080, 89876195, 975628704, 860671555, 633599616, 613146835, 96955976, 224677746, 105355462, 916570963, 992700981, 960719783, 404469808, 602996951, 62559889, 569356580, 944611864, 738641089, 706955149, 910212790, 642686092, 692138388, 947161676, 575206715, 325009476, 825163263, 275765488, 849501756, 598504809, 675553298, 61246551, 776769547, 897736906, 711944554, 426678446, 557962594, 125580611, 509655198, 899378415, 383039716, 325288186, 853343538, 152950840, 289733142, 817029490, 820095381, 387698862, 473193145, 800739096, 334769368, 307038357, 550017444, 220878124, 287160447, 34658094, 891086419, 784797974, 538743706, 33460991, 751505489, 748024303, 262850177, 697479702, 620262917, 719829902, 14642046, 797190538, 156591352, 129534357, 829496403, 905550208, 494053757, 650730751, 678908531, 108134722, 284723855, 781600649, 566888435, 38525749, 463859949, 628472510, 21218862, 721377886, 750044008, 157876341, 457086222, 81547051, 673612858, 248901131, 392162894, 613140826, 395219378, 519787093, 717295545, 66544949, 994443376, 661627422, 163382422, 986348562, 118037084, 849679026, 263573870, 166039845, 135218396, 889397508, 332637073, 813297181, 487749965, 30372480, 611371556, 32313827, 983577258, 619738473, 626314248, 420707090, 111311795, 360396690, 300092298, 704539892, 912865116, 983913594, 588149006, 938214990, 269397305, 792747856, 273782504, 239813486, 54423239, 415710402, 522174704, 842973648, 365779657, 710508304, 980395904, 125401796, 426889457, 705275118, 127034107, 66426656, 588447899, 218345010, 543445943, 751178188, 65069993, 526617098, 873199024, 623764791, 329469407, 626941533, 481516600, 118900475, 47493103, 668243224, 434375289, 560309099, 422684831, 213522253, 268086770, 922980842, 754631419, 509636696, 390417779, 306358433, 717020745, 521835236, 281462249, 785216703, 81927521, 639981757, 694314155, 100219231, 908781137, 792230952, 114888929, 440458182, 208480433, 306361009, 48858634, 301586143, 557367040, 911947280, 994677268, 7876736, 370195480, 553755409, 462539243, 39281466, 63770282, 783226417, 695704759, 575416731, 518519188, 981156957, 261297412, 429748941, 291159367, 759633260, 149371108, 891304602, 835075924, 333992589, 643740396, 40374203, 849135807, 247808513, 166474444, 181223925, 155526495, 847653298, 411769882, 479273332, 561338520, 210339336, 183107674, 27449572, 445731331, 633792135, 932754401, 674937488, 991739333, 977912883, 89321428, 83592766, 569889171, 893449820, 8947801, 965222760, 352913482, 323834662, 995802163, 654242923, 524515106, 157082747, 589965084, 269398480, 737638553, 773081839, 392656200, 49846663, 925875355, 684441046, 343602439, 175540446, 611628183, 759466280, 461911226, 824134971, 178607519, 56858140, 822183847, 34377216, 664262889, 986070037, 103753220, 292553887, 101998435, 394528212, 483450096, 690043511, 53196782, 156575694, 66373885, 626696138, 348259752, 414319847, 176218734, 575651805, 559950068, 33969266, 653412717, 257160794, 627866707, 227063561, 847284148, 193392504, 677728116, 633450338, 5698338, 347178420, 261127899, 581342532, 778032818, 762463550, 552086564, 174501739, 334005675, 772065918, 330378677, 588614478, 545220510, 976048778, 804804227, 682317679, 529160948, 517196050, 396121275, 653658984, 924650311, 684883623, 506451250, 977497215, 43173621, 873087646, 415263690, 110129827, 977524361, 592196693, 360211387, 488035669, 842914200, 686225702, 897500939, 223512448, 683951399, 315278797, 184827235, 980022696, 439571830, 763993705, 511921620, 490610442, 597921414, 887102205, 952935950, 475564226, 540572830, 106091092, 84277503, 834653999, 321335825, 105698634, 204185782, 48462238, 628169517, 982199446, 917498549, 857720067, 224605171, 686075729, 647772489, 170299522, 952733030, 817329617, 256954321, 388996047, 340987822, 293651798, 959446784, 914063468, 645518447, 298401081, 503282107, 827924980, 704207596, 492855371, 330594544, 763228522, 146148217, 601430582, 108774712, 328674608, 209178452, 209806738, 474254561, 653350370, 546645637, 347749004, 928860827, 993567020, 271812990, 659078554, 160965708, 793208749, 396426681, 775618418, 104162475, 420436950, 701835077, 88264693, 612336412, 692716750, 894000610, 920365231, 740957148, 157550687, 308787498, 954176376, 694367396, 30515476, 646375010, 54062468, 620692857, 811161368, 592601387, 389214742, 416499114, 10782911, 393753071, 86443915, 346183110, 454915180, 300788968, 569363932, 410742647, 921170652, 705711100, 946266792, 639293806, 642091532, 217142027, 294337657, 489633594, 49955634, 761822873, 968359309, 198811267, 641294581, 878211044, 990732139, 736941315, 976318399, 383131107, 6110840, 26570108, 252766712, 68225090, 446411323, 55786112, 988846076, 52089686, 482150621, 622905892, 366593338, 506240848, 930010581, 559954622, 63048860, 673853979, 204211193, 162498244, 739374970, 209907369, 685632101, 374574931, 592164976, 438619935, 286400220, 409568528, 479990960, 431176868, 746602156, 162137083, 659394427, 666098011, 922672288, 27393175, 942924698, 905961257, 430849811, 317016394, 564614180, 623264098, 326418716, 384905518, 424291239, 801070470, 229398005, 432875675, 104720682, 9905141, 318191333, 108154375, 653256075, 657639134, 74862471, 502348828, 730326599, 266667701, 616581296, 42744349, 276847665, 15726298, 821800031, 296239014, 885509117, 410286676, 700835219, 345034529, 74140310, 518519896, 930033881, 560710661, 800962416, 828879163, 201249462, 775863757, 743711642, 672553012, 140798620, 457304298, 937380824, 890831894, 575579749, 256167297, 310399604, 868763857, 800419186, 768787578, 727517169, 541602361, 564120530, 791103420, 94965401, 327683586, 704385655, 359399512, 364765146, 46546216, 604005560, 144490996, 584725662, 160248013, 339300077, 655000074, 318260999, 571538033, 807709166, 106189529, 893181459, 821550941, 302773953, 253961019, 88082158, 181702937, 418543109, 505723113, 918606140, 215021248, 650555039, 521597540, 258494945, 815764481, 266204730, 94953113, 101623305, 733554107, 872062695, 375330301, 570283273, 273351469, 564593226, 687896571, 872329398, 92235769, 788298600, 710170993, 712275329, 597576740, 74129426, 4270417, 304166772, 554579320, 781569165, 909212867, 749141067, 64500236, 841286832, 180251227, 355916666, 103137850, 808812142, 712690371, 679386571, 792452053, 511350052, 600144716, 345852459, 828245305, 534737990, 662828684, 852010024, 114878965, 70671411, 849978077, 843024815, 996793722, 428214846, 953879103, 629385477, 88059969, 740819290, 581681155, 370844858, 607121077, 361278781, 801388488, 134532474, 64029574, 531275942, 116848167, 194079819, 489843546, 709012957, 295104008, 996380070, 589325997, 438018345, 144138656, 179416116, 602528282, 861202572, 955308202, 778990832, 366596840, 93159716, 60239946, 778396494, 297874058, 495996995, 701393799, 73866425, 463101287, 803060476, 701781968, 392148855, 22282879, 394892937, 417635380, 968162501, 818415966, 261544047, 778794860, 882448503, 848247106, 365023073, 349419156, 392009204, 937141035, 422675964, 764240502, 225713748, 301209103, 953226149, 134137832, 10707997, 225591333, 193062167, 464849379, 23230042, 694219109, 92563056, 723203136, 843716655, 767129467, 777884474, 197795915, 928097352, 164607212, 448530020, 43693829, 870427503, 898761697, 394070379, 83783754, 108884963, 630310083, 588416604, 409775575, 54807803, 313562368, 164116626, 799098765, 898560259, 255019756, 909870721, 841090877, 783199033, 43596717, 512725464, 757570488, 119836865, 979998526, 593718128, 613946405, 492138146, 249659373, 466474642, 733190213, 215077534, 859828586, 780237537, 550060624, 792837884, 33424593, 853411697, 24742604, 528906745, 210547119, 341082622, 243050558, 472916363, 109509479, 842991448, 52723870, 138637622, 45855803, 719994792, 749488507, 856739723, 708280481, 225134761, 940255111, 500071940, 366999802, 787711412, 196687526, 204739590, 158993137, 145151829, 557060549, 724487159, 388364920, 459468558, 34478254, 214710631, 803941651, 737382773, 259727450, 751651145, 859117295, 197741409, 149810276, 909093802, 880362448, 723376170, 526861502, 515909231, 194259242, 110880015, 547245470, 685656670, 266353347, 778708971, 61230107, 611860238, 825766598, 697055703, 110529071, 526215481, 167606800, 383463245, 515248920, 908234423, 186833202, 917585373, 984403233, 841783816, 948343172, 333401736, 839215694, 913311298, 670509905, 424526394, 579520306, 598516278, 267819553, 591455871, 166597066, 329301012, 519172921, 626576671, 766297484, 260907942, 585073735, 949607194, 689085835, 671967602, 609547162, 521783104, 525026987, 866322906, 97486566, 813398020, 191216403, 465420562, 549967850, 858127161, 27682177, 574065105, 841261039, 835331527, 738052913, 380684644, 968220180, 114008392, 560048419, 321780648, 815449894, 9653548, 498891050, 436853877, 115035125, 849112460, 57167796, 864989031, 192742472, 270580111, 10774511, 371361544, 750463093, 165044659, 548340030, 744561337, 917824245, 183834005, 831442179, 990871195, 151660434, 203239788, 838033834, 150782800, 385100102, 335766570, 471147237, 647230246, 320271407, 691724132, 473242837, 838324867, 685931158, 129919942, 19728100, 356989489, 920927561, 129154779, 975415286, 365143754, 343297784, 674844363, 1838179, 389247064, 636721740, 951442001, 397843310, 522381437, 435302411, 515977894, 816944186, 265063965, 716220113, 344865409, 975642492, 925068033, 575183788, 785677609, 240944538, 631196632, 922510679, 431896832, 75421370, 374858841, 113667262, 383029859, 169415828, 835508622, 912712442, 812472702, 845801198, 782797524, 19705479, 436174916, 886726495, 295446224, 416771323, 942561632, 402783970, 927574620, 471648921, 16670922, 26793555, 753355904, 384944216, 185752414, 82615799, 574948440, 550474836, 366694882, 768175595, 492894146, 149413296, 988360207, 802189259, 549422642, 727507886, 847955474, 541086523, 216269026, 987277321, 993861752, 138631198, 526298888, 138549192, 57633230, 922277170, 910486454, 223504403, 996621520, 417564022, 234766282, 842980161, 436337896, 90790598, 260087485, 622885954, 305142987, 441907543, 436642505, 594903605, 936974885, 173893437, 50611503, 597480982, 174681900, 76916543, 268571995, 486191583, 114290949, 829756925, 166615261, 418581371, 866752217, 954041722, 103277647, 124075850, 964482861, 180939367, 807914268, 444286312, 752019174, 614445610, 525062728, 700718394, 185388649, 408112451, 651434297, 482153324, 593033099, 498818117, 560228948, 16375645, 637944239, 877533486, 676636585, 865489663, 675680678, 730972803, 96618534, 749837583, 411379422, 577497696, 656208245, 179526959, 866355994, 552931151, 887184814, 211883540, 837559977, 241756298, 72440279, 220481620, 713612813, 751780991, 556001246, 760124431, 669333740, 300179950, 31262084, 227194500, 25084803, 684276115, 768023672, 915594439, 373650946, 746528062, 409948602, 644372702, 171002528, 721205391, 245581421, 848353266, 934315253, 244489208, 899854039, 632906824, 441283543, 46797674, 861896409, 492712961, 285858812, 602734595, 99843083, 871924857, 982355847, 919625476, 462807907, 344410885, 333770603, 538209559, 977350644, 210816034, 905112248, 336082824, 65341704, 359506916, 852714296, 969386405, 404345037, 757215259, 815414249, 562086163, 998373283, 317634559, 28155621, 612211046, 837080322, 457882640, 552475613, 418226626, 416167644, 920606666, 400006615, 907883532, 173024158, 262671646, 401870958, 9017183, 469150426, 70686015, 317406110, 704240722, 585894175, 14555475, 478851395, 815896645, 883317501, 275866563, 998399064, 73987465, 503581686, 390318210, 279767832, 90400524, 169792542, 363608668, 963585284, 21395758, 126446174, 951683669, 272775295, 661909474, 8991693, 616386852, 728811794, 19103754, 26736799, 601052158, 738968942, 371374196, 695766427, 700615488, 513290202, 42857011, 871514051, 635206940, 856449014, 608865491, 988627153, 91016601, 417964628, 167691035, 579795546, 587213147, 964558433, 442414828, 311986694, 263019878, 194617478, 260645883, 307917426, 698179819, 749010749, 857047696, 685416026, 587359209, 703200481, 283339830, 995500189, 449006047, 991016270, 454995979, 869323493, 228062887, 301384289, 102951776, 454196273, 431907754, 269904591, 609719641, 560859434, 366135207, 224533144, 714122705, 683385112, 381310297, 765874102, 405774836, 783155634, 415319159, 446858862, 553261198, 462232796, 730245680, 6916527, 5766296, 552996883, 330774279, 509378920, 522877820, 9399111, 339762605, 536890973, 923855820, 61969718, 427001373, 832149122, 380954462, 947097180, 928389456, 145486229, 305794296, 222110109, 466718359, 864781605, 534390588, 159777135, 1384306, 191723552, 722123910, 4060242, 978531597, 838018434, 953539618, 809317265, 833688742, 493538929, 151817317, 129044184, 983203797, 807968160, 587789133, 278695076, 38784027, 723533934, 451361368, 903099026, 762665683, 770308074, 538071136, 985263579, 696522494, 151921546, 478985958, 458989273, 345325290, 659429994, 937427210, 711727967, 437025209, 925995883, 708121249, 707622359, 792680826, 562139036, 502919337, 257065592, 127099783, 573161628, 694666499, 328883275, 702609557, 512645437, 332053983, 140800450, 505240512, 158873887, 332676452, 247022662, 455864308, 15000202, 560955006, 797223950, 238074627, 85477019, 76263279, 537284433, 988194375, 116531797, 566470106, 351696162, 574428957, 719199292, 470349832, 558489712, 376419022, 192142092, 769718386, 660331855, 506078047, 459543734, 945449734, 269996941, 627423118, 387274714, 276508992, 929815517, 489575407, 482878311, 924880457, 67713149, 599113720, 224037415, 481164219, 183044730, 488273409, 722578288, 723795886, 229951555, 502305806, 449174190, 43364095, 992023296, 930693786, 300685342, 323916141, 666898459, 740082535, 207062170, 861662838, 320789173, 498854732, 295943721, 305227858, 399258253, 717191049, 909395454, 345846980, 957185786, 860680870, 815631825, 788940650, 3336578, 482293221, 529696567, 24430445, 270799506, 11612693, 67749930, 915897901, 189699614, 973640418, 639476365, 604837913, 487460878, 87851269, 608173547, 32426309, 548168563, 863574394, 974771865, 87345085, 387800895, 936529433, 148593763, 801634412, 675836555, 745356541, 848466229, 152284066, 190719464, 119433139, 977582763, 552582064, 971102547, 860511397, 588692542, 479289769, 658964176, 153683059, 202852355, 102347509, 62496214, 729731954, 346971729, 408621383, 723752067, 831921825, 166210958, 628089992, 988255352, 344489612, 129384662, 152351098, 386775752, 107693625, 765203718, 314544689, 668252518, 872205019, 66377859, 687271065, 907792636, 403403379, 758679198, 605053985, 362749422, 370323367, 885302373, 737954805, 859015253, 49619956, 661037182, 76802835, 347916300, 469533480, 738506940, 793835594, 528792483, 15511777, 302829981, 675761849, 697040315, 277656155, 163754629, 458774865, 103387765, 110913304, 29976412, 653688502, 960883098, 925075011, 169014702, 500390343, 869408431, 964436583, 325385428, 372651661, 970060574, 90677298, 464081682, 609678493, 269863922, 457405364, 607398093, 315185156, 951695421, 272174947, 311639030, 260593423, 139718288, 162226401, 645687592, 971056251, 396870513, 802914623, 748291721, 872217498, 671556659, 43700886, 654773040, 638532431, 22333896, 132685654, 626071541, 826050658, 66286723, 952143196, 443590828, 841076140, 246345907, 152531582, 469802534, 579808023, 391631512, 33281522, 643130823, 257026698, 356218354, 684529248, 513869810, 189568400, 117656915, 908472343, 720725476, 648297224, 460814936, 290154991, 17465583, 250897266, 641730602, 442448475, 72852076, 359591584, 296326178, 538522121, 625235982, 549966162, 759583010, 893123928, 863233185, 632745005, 926922337, 281107815, 894540771, 795491819, 206158927, 132651506, 655584258, 606546375, 148925312, 259039502, 126652683, 157546280, 980536152, 13912165, 616716003, 141244707, 875893377, 974379074, 692685252, 434211919, 790801824, 878427419, 621759048, 346912652, 28592973, 913248433, 571637649, 12503771, 152921256, 764693592, 254419795, 100034296, 812130696, 904952855, 998735563, 459275169, 409451555, 690861357, 417705109, 555739937, 96991682, 100942052, 592036130, 337567279, 334739940, 212639872, 674515873, 560527706, 910991629, 196765359, 620658620, 573833871, 850481064, 672652749, 43031350, 45671775, 392283826, 454179423, 218093641, 11823154, 806937147, 480772319, 229681729, 146374176, 331535793, 339860792, 652977602, 589185054, 798566053, 534025094, 949886250, 983113774, 740527721, 229060279, 397655894, 995926806, 568644524, 508547243, 340542714, 662645021, 969547858, 154776643, 836185747, 440865124, 215743928, 335789778, 980178177, 514117167, 266364301, 39061863, 236711370, 896821653, 723189179, 493988554, 749804510, 991985130, 621354328, 410205230, 738517704, 735130250, 402229741, 579647416, 575079404, 108289554, 936148033, 885915772, 245617405, 562649645, 891108481, 741399525, 156683589, 680875526, 607985982, 361141905, 60212231, 803695495, 424676190, 349595745, 643307821, 672351572, 973411041, 383069103, 474452843, 634240467, 83365266, 523914385, 790869528, 666424483, 777554033, 425228578, 390069528, 432276188, 890794949, 770451094, 350981653, 565216400, 212196962, 514245799, 499164005, 580652208, 832281742, 162055117, 310382587, 604209178, 50362939, 821651285, 520283098, 67178217, 484466674, 164055188, 148838184, 645739968, 999822782, 172538516, 31094909, 189373067, 938676097, 216161856, 289951668, 4251839, 324473212, 652748562, 217129805, 263503258, 367086255, 663453820, 656244560, 660996852, 562031099, 79212698, 885738836, 594007310, 160840969, 428175149, 117926391, 690308341, 369718672, 199882765, 400814355, 204383143, 613900922, 138035861, 559779532, 186580757, 6260978, 932294308, 544398186, 968549876, 252668033, 181228291, 359789060, 55529699, 98776314, 818961184, 368102837, 315494725, 303922934, 719914975, 816104422, 438462445, 675315800, 572723017, 240686315, 876906025, 563323427, 7092449, 413074012, 904627489, 340077292, 463829079, 129734652, 420351307, 996014803, 314660891, 212794085, 164747562, 392112404, 574692104, 506939879, 330718878, 557006965, 219458740, 117744967, 275182482, 635410121, 940438773, 318912017, 898798658, 964395862, 483922119, 890075934, 572702009, 217253134, 448916160, 7903052, 476233385, 397860188, 757547404, 273372372, 589378269, 540046778, 763481459, 282869601, 136000820, 236618931, 114385563, 993021353, 679744630, 731939554, 848534464, 488591717, 814527447, 465575890, 889972057, 632863598, 518257058, 871794852, 107634141, 668091336, 202512004, 928106234, 537605348, 601017495, 42187869, 871275212, 181180004, 981777732, 326669020, 160854559, 618495502, 566628263, 927990316, 979699025, 881898432, 398444388, 267785188, 23491330, 989478338, 548211982, 148546634, 80776851, 490286196, 558549690, 70597943, 569059002, 445382493, 377800005, 549607952, 91994173, 829429594, 85986803, 312317991, 456156899, 706488256, 48494168, 212626549, 683274536, 980269249, 721995041, 719906873, 70999992, 349387423, 679230120, 401991701, 234270097, 985131417, 913097352, 674317925, 115032255, 100674890, 434625664, 104294439, 697014197, 469628189, 154591830, 368975783, 234076511, 660966083, 310536540, 588676627, 605931561, 983509145, 520397692, 433973832, 139162439, 937128470, 440644183, 368645762, 558504847, 336768920, 805030807, 502824886, 646065878, 512608705, 402829381, 893602877, 243626635, 796178629, 682012123, 126954825, 283845360, 488583517, 354827224, 747050334, 328202277, 904160937, 713037291, 737206022, 615377670, 570814912, 516635208, 561922721, 355149499, 415559029, 552739778, 971559773, 984466942, 508662640, 595848082, 474469152, 555806791, 266070943, 438144250, 73389374, 951727432, 720353896, 26817068, 891242136, 992731834, 455062271, 359578399, 852826645, 39997622, 183547465, 417690130, 713749408, 739309498, 819147053, 582070505, 900966995, 941624837, 936640066, 926375160, 605110707, 599510412, 852429483, 868607838, 791384498, 948976724, 308596834, 589230902, 682073329, 211236297, 793483975, 896378, 984170983, 824146492, 586800630, 104007474, 450523116, 229124508, 550453120, 93326801, 298889179, 254604446, 99970027, 879446376, 124831827, 587098558, 247788552, 376737571, 476375515, 36114040, 405415849, 538948450, 154223496, 499372573, 65306895, 938009229, 616290540, 375076952, 120946245, 373494387, 473495652, 189945306, 412979020, 468553802, 709286641, 197434544, 874267312, 927823766, 621642320, 739352016, 686381918, 414910426, 175517986, 460655887, 793726072, 456334308, 828333350, 463170695, 477638588, 365937191, 47469332, 467863479, 96250814, 841640592, 549364707, 92516474, 197194371, 434329746, 53694706, 307902362, 386852634, 229510368, 506205658, 887720117, 62220664, 400551883, 98378032, 386383282, 972871750, 676649436, 82378436, 701133854, 380592004, 431528105, 513236155, 527769994, 14542992, 962702316, 268291140, 839149614, 773357896, 627880009, 45806752, 643734407, 188752047, 205034715, 619169710, 39097078, 536953023, 684733717, 576482791, 724042703, 202211894, 873279042, 653414764, 450050581, 828262623, 48631805, 15494336, 188740875, 828981393, 764691214, 71217831, 543390535, 386632623, 312653827, 238357819, 665307704, 896104060, 145853434, 290739809, 796432420, 721834537, 464386419, 617694422, 878067052, 388852635, 797630914, 661634969, 365305322, 232154923, 460739384, 259578354, 376734612, 306421951, 251830781, 313192162, 800144083, 975348732, 77272371, 388417415, 500691581, 444430414, 658988957, 150785750, 568100002, 119083929, 75766219, 977946756, 619688362, 786736958, 607767423, 289942051, 938489563, 907631401, 867976261, 889334845, 678036615, 483387125, 35743262, 675271672, 887205355, 230244507, 27784321, 335453237, 298632730, 262424471, 661488435, 559061877, 532976080, 432942019, 962256242, 671929046, 56496944, 966467146, 759570503, 83793661, 940950304, 727410846, 36828330, 692608364, 911961115, 339445571, 299104900, 4836289, 831936307, 774148754, 702504968, 433801876, 944155748, 732928834, 243502001, 445989963, 160979706, 992026609, 106512982, 521339775, 968833281, 353173925, 518161646, 38338653, 886372155, 99131316, 112679982, 429085741, 782702032, 817156772, 751551207, 782810355, 860101631, 442235018, 202038950, 761342287, 323493627, 423974924, 948574960, 964640402, 752516523, 384438304, 367615795, 714582749, 833736386, 192519742, 790658626, 752006042, 280422161, 354264324, 849167390, 855805802, 331992101, 628920669, 631034361, 824786941, 136789653, 404585933, 579643612, 944470604, 636207159, 126462881, 965067037, 655920049, 122708607, 482412751, 674017334, 256483579, 31808514, 16298052, 587563616, 847633343, 396891430, 647521341, 563621987, 119237218, 826537169, 85909610, 218527109, 548024800, 2248659, 688746991, 558162172, 206425430, 186314709, 860064401, 486934929, 422049255, 318284335, 749215736, 905220128, 322278017, 205028756, 419908500, 661910078, 365269839, 499612249, 23105252, 386754111, 617402569, 872472667, 22043891, 579106761, 981715367, 83083536, 532422863, 12167060, 915684378, 969300238, 582369037, 502758768, 820389594, 524405442, 939141831, 802039493, 517539080, 34670677, 779045977, 959528264, 361615290, 78221131, 811826612, 37568196, 130525720, 957751471, 355387792, 568485065, 803691191, 353955106, 431029782, 542475389, 353920789, 737600533, 257401518, 301254360, 544776731, 396111923, 421398600, 81035680, 734202198, 645419078, 560322889, 709050341, 658472807, 110044820, 963657834, 217367168, 689723932, 647637990, 373237097, 59140405, 907313997, 393727060, 212663828, 674835886, 496884040, 682834902, 401335678, 974020905, 314756204, 732244496, 95221082, 509300082, 898843242, 270350163, 26190080, 70169716, 417995958, 60243799, 314759427, 465195001, 44886899, 906728638, 965019554, 677595922, 652788195, 206764895, 866765976, 749083663, 600086600, 437116843, 325532509, 630957084, 261856088, 587681252, 605301669, 143344038, 713753766, 628048648, 766810058, 822836755, 419846388, 292042302, 499484249, 739595089, 943685700, 796926553, 683102486, 993792654, 725168866, 896889457, 642529971, 647333225, 65277665, 155448734, 875181501, 73350229, 426705250, 269957505, 557162863, 968865383, 971310432, 745431386, 374436933, 746885602, 884389605, 447922439, 656623137, 228757711, 523708600, 840968979, 948597432, 38957162, 996351415, 424778518, 666606065, 83943421, 546130765, 871416139, 697680507, 772847200, 395272182, 264219071, 677978547, 924207205, 25329630, 363655471, 187388888, 190901291, 872280819, 430754505, 762048283, 369802855, 693762486, 126182284, 776752293, 863929895, 476650150, 296815976, 362588906, 27910507, 36433182, 998505765, 900325472, 273756108, 708261149, 458169636, 588860415, 966914446, 164089474, 91613469, 432459810, 763744289, 600333342, 690597689, 7282821, 892350177, 644400388, 201722705, 134950946, 907627607, 806290374, 991128420, 862293605, 235607023, 243505933, 969797891, 65917317, 259793518, 773528351, 978668774, 776267053, 654119615, 270813658, 18980463, 762842202, 734625151, 138036352, 28303374, 975241023, 681376413, 890140900, 225369053, 338046035, 362037602, 181538912, 546514426, 136796915, 25830847, 464672650, 843146803, 559751470, 425941654, 37860306, 370038287, 952886975, 37002610, 64636395, 960097297, 736643599, 647105080, 243063442, 395734594, 663336572, 995390998, 393405909, 691776456, 422117172, 166658825, 257566268, 934021886, 299087445, 516420748, 70889038, 104674462, 906785667, 683979968, 66899980, 182963872, 792889972, 501382318, 501954913, 883860055, 645367427, 748929389, 737222469, 891283411, 594480289, 759962749, 904983625, 779973490, 934124433, 453715352, 250163089, 474954847, 466901425, 903722011, 616535854, 386949004, 328674625, 920253484, 850593184, 711805290, 611191375, 758111760, 4509853, 73372698, 157294599, 60541934, 185527899, 646256152, 215963059, 293353777, 252890574, 687499467, 503271944, 741948419, 708942663, 766670535, 439813180, 42590749, 883452627, 404475737, 536766041, 708348344, 597835251, 797523547, 160207896, 313245344, 324726500, 68719176, 997724611, 623980538, 908041958, 413726315, 424795919, 767974974, 14227017, 946692364, 187823583, 779921808, 791077101, 463762187, 254687508, 383330731, 519790096, 342822301, 455435177, 25686054, 637092033, 873373678, 912806436, 376848775, 95227314, 194867920, 592322018, 337967277, 682213140, 481982866, 20303743, 144265202, 536331652, 894062037, 838499852, 342498111, 533277273, 252802722, 638336626, 848432335, 652516397, 293891365, 521814360, 583916446, 403759465, 923033114, 969454894, 964149934, 486055474, 85947483, 151412017, 956113290, 742725748, 383995349, 565121770, 546509044, 145683998, 215953768, 72774679, 105167075, 634086960, 948156379, 735953830, 931975256, 643998651, 212985993, 516451188, 391950010, 91051820, 856183663, 987718831, 489476603, 730128840, 962471336, 716055738, 508269496, 397883645, 957875799, 428085702, 996971891, 135043248, 294654068, 590526873, 205053334, 566075221, 664689791, 450179937, 949575091, 190327932, 990212288, 990390586, 466862015, 486692838, 62758053, 390178058, 272091202, 445971010, 768626053, 76600271, 276541881, 518383059, 841775856, 166446376, 607892786, 90998916, 179420281, 738393634, 263469717, 36739877, 149276708, 568455443, 265102444, 287314927, 786833923, 152276024, 81647155, 938027081, 408452540, 615957777, 989918213, 681017597, 482621854, 702976438, 348662922, 555212427, 516047032, 808302315, 203472845, 635183958, 316219611, 68308971, 405455386, 149403210, 763619355, 893614880, 776401368, 726296428, 513963137, 310198975, 146925177, 580695709, 856224608, 555059276, 382380397, 507246001, 911188739, 901073934, 268601317, 792963343, 835165285, 924106459, 518522172, 463610907, 78933316, 548407134, 783877800, 735883257, 557362530, 702462402, 693443229, 762780559, 652678297, 238312465, 2632137, 221424330, 980180590, 402198012, 791751864, 487817399, 763411408, 364801774, 274179704, 629473378, 783114624, 476646331, 863046275, 196114821, 628705084, 687313974, 500156472, 12425604, 782338022, 115712067, 254191254, 296645443, 497765127, 461847744, 829091285, 114459744, 426997766, 490266118, 902807049, 244438972, 526066416, 446300138, 971807736, 652328699, 101317819, 723149228, 344495344, 730326295, 823658034, 898406517, 207724458, 693348091, 844533394, 424315321, 961560054, 238463648, 719472220, 569784397, 439016019, 802459849, 343543834, 406627638, 884484531, 505260464, 481002830, 484359539, 327868163, 259638561, 847211519, 5218671, 150172432, 246475446, 620821457, 929663302, 709735356, 266534042, 547371916, 420251764, 885648468, 593918362, 77175731, 579625756, 29364370, 599534785, 735531797, 37669764, 120143450, 735022659, 323781491, 818561041, 588945157, 340728854, 960992660, 11585523, 990523436, 275774172, 440577160, 454760680, 544716736, 275969038, 591919975, 703167951, 790290205, 646153053, 788627076, 723625680, 514019870, 266640413, 327930429, 310750695, 227540522, 305848294, 249522804, 38482176, 398083746, 355344458, 142828104, 761043203, 547155311, 730089620, 853438163, 254176779, 713369403, 579918072, 138461071, 43852597, 168333485, 253517427, 962503445, 748146411, 971355284, 428823908, 580411243, 572044662, 897492325, 731853903, 303407100, 709391462, 363709666, 152220378, 731810522, 837376675, 785094615, 102388313, 844674279, 318842725, 156744346, 910109046, 697107957, 500931875, 784665388, 695540737, 255190944, 451315017, 30841714, 849938222, 796224072, 525562904, 288646099, 368724206, 756431042, 942170046, 537313347, 706771161, 51289236, 267691069, 512105143, 502225823, 232410081, 667146991, 311461586, 676041157, 15786124, 947651313, 22543873, 318038401, 166570719, 110273373, 64078708, 308928908, 942757645, 402156318, 279991373, 273508875, 206741253, 536755085, 22910415, 906049115, 606694935, 90015842, 94771702, 672692408, 633209591, 592544906, 950392387, 25589610, 197303496, 880744502, 897037079, 384463435, 865202677, 251083251, 737907679, 633001275, 86407817, 68218042, 54792351, 814906749, 612273528, 681916035, 867951916, 72587439, 569660473, 915528513, 768192665, 926627995, 413140562, 76022556, 778382819, 8101116, 99695010, 947127970, 170853739, 862233993, 324594688, 634278902, 484772857, 179707110, 284128706, 401121542, 391729917, 29764937, 133035170, 350631274, 107024027, 472137181, 824556822, 860672687, 569334878, 595602384, 541633521, 180491075, 925170263, 184462690, 526126925, 558071148, 496874253, 543037713, 835280656, 858344312, 578477911, 145028502, 345833469, 816377711, 319971041, 726517375, 737197664, 114679774, 805606019, 893763440, 246083801, 679453313, 15651110, 960251253, 455295085, 996336518, 514981247, 20631004, 773316009, 813003517, 242499182, 973979289, 797337185, 599560818, 367171294, 927313578, 946837365, 361760587, 293776318, 380546608, 920918402, 468912410, 842179774, 169083333, 465460783, 989956078, 485098189, 566897791, 543819153, 460042172, 865104964, 158376032, 180996268, 681325132, 634330874, 389385208, 642463513, 961796167, 685774359, 220213900, 856335121, 912436726, 317271884, 642323930, 82871638, 852372398, 641570237, 72264650, 10060949, 307683097, 904411524, 709804748, 762396731, 318267625, 599207280, 531496393, 697995526, 415881345, 435380953, 345279835, 102152085, 26899970, 693660201, 390649112, 863981825, 110656598, 201370834, 828610260, 492985128, 30919784, 672413459, 807475623, 523915843, 57691438, 602204900, 674263328, 887231475, 83063369, 882025482, 961830008, 46845108, 705208265, 44545182, 569601541, 971213886, 618321737, 109856345, 160181986, 413171757, 597495791, 332701476, 691178232, 686666603, 817969527, 503126622, 379818975, 428247721, 991281244, 990508617, 357355285, 665116981, 273132501, 768991281, 486968866, 252907425, 378880549, 8133263, 582276989, 720550921, 753811132, 159944873, 377648528, 662035329, 701241228, 336237666, 790610434, 180529169, 693786815, 653238888, 792971209, 773751913, 425435171, 216600121, 567546185, 921975649, 326074763, 844301972, 896273179, 825185996, 57493959, 529421447, 74469366, 373631552, 909768965, 976725710, 13638231, 301622659, 5939751, 398122182, 420874154, 328668213, 887924356, 489223040, 855792670, 464511111, 107294562, 488092556, 397634166, 398842491, 248363547, 900982222, 600130097, 50791776, 255331110, 17423623, 429428270, 200166748, 639744214, 284073976, 129049543, 619792773, 109750964, 308895491, 28095315, 734173643, 235340507, 855434862, 421971795, 179513655, 857487047, 87615259, 390110931, 873661334, 455144559, 692795316, 402529129, 26660797, 619898919, 31245527, 706958136, 19469739, 994795059, 538068839, 630861936, 60723709, 756046670, 854008554, 245863833, 27547577, 462412504, 924319462, 626068033, 701129273, 156697179, 889949486, 664567877, 363939970, 448775884, 502529867, 936874701, 935785728, 840905781, 514852084, 698985376, 97740176, 675987420, 835712926, 186098913, 846213644, 972401078, 798620261, 494399314, 401157684, 110801689, 788772005, 744796102, 187790533, 354946958, 362811160, 316099640, 342819665, 948483312, 438498061, 982723420, 719233752, 281701649, 485979744, 843970869, 460893356, 782933847, 308009640, 237252435, 415883985, 949234037, 64881454, 225332257, 393299794, 997748585, 389310572, 651823602, 975618933, 704661760, 941129102, 50848669, 309256619, 257544040, 95765227, 775622356, 964447246, 319720633, 224965814, 719278127, 269244793, 192653790, 436631982, 777191258, 95008301, 352914827, 525975483, 735821127, 291348225, 161119511, 457471832, 966928579, 877913971, 881484159, 255671463, 969066063, 275681689, 272420272, 219732687, 631994974, 85195620, 11023999, 152854460, 173910873, 13285076, 541556335, 448312480, 331850200, 50653985, 513097895, 694524561, 746892324, 818080571, 733969479, 451477915, 993709443, 536288507, 497937668, 891115046, 95496072, 119080906, 172904708, 926680291, 540690381, 363357003, 676620564, 1758733, 496979148, 736228039, 395741831, 90952263, 640692511, 89007129, 145882830, 312497370, 606681265, 431537171, 237618753, 375817431, 847173229, 486905847, 281668804, 626889246, 312947055, 245303408, 181238472, 361899305, 209152117, 428185279, 562882390, 457583386, 660807733, 341796475, 402528534, 541899935, 985272500, 503607931, 785466125, 399121878, 663783371, 353734152, 404551288, 771265064, 986381730, 881609249, 288128185, 587499330, 933794148, 469333368, 228472871, 431017481, 610049622, 506200790, 890957123, 243000962, 161747027, 611077885, 472795663, 17239719, 524340778, 589705181, 173887862, 887286082, 176445984, 85317394, 12743728, 519172781, 128130017, 874106320, 456663910, 318339488, 793165975, 382129403, 24075079, 170043854, 267640784, 351063958, 168281169, 632499250, 152958913, 404904943, 344446924, 15135720, 221730118, 247471337, 312020336, 531339608, 769403997, 937577230, 508700293, 15191778, 467100440, 706172442, 300547988, 764838287, 830282782, 918340234, 106952725, 585517412, 475743825, 118255869, 749105574, 681710211, 169937749, 47684831, 338626080, 314241171, 929376892, 921206896, 117048823, 956454013, 190806632, 634245381, 845265716, 181826172, 434712231, 650545600, 603357221, 34691827, 259085947, 643874511, 717373822, 545894094, 681445101, 851962212, 938788123, 365220090, 899600033, 591812602, 644113685, 646660110, 787194784, 300034734, 530309400, 557816035, 288439875, 236647360, 640883515, 708286550, 4646198, 232843365, 513594192, 917298775, 54920998, 883811728, 434747495, 512130925, 988828616, 67069098, 356703450, 684966119, 976460644, 493460824, 932615970, 406220196, 27051318, 806196117, 111629488, 730589194, 790442207, 974356762, 839717700, 756470151, 811448195, 261046173, 71673742, 725976697, 950031710, 293324406, 391394969, 915263300, 621878244, 815672754, 790825726, 682010804, 300617610, 144433331, 214842205, 277414550, 875412287, 137155559, 902450766, 21302494, 794618982, 208967901, 913917632, 783472044, 802341521, 795681846, 356366759, 754283947, 356806609, 595912763, 672838930, 968561746, 222669230, 210171149, 6225343, 306808600, 819270805, 339457006, 950872345, 609195548, 682507276, 643549067, 762312108, 504232651, 145465751, 559723437, 208699395, 865235187, 603696355, 332881003, 875042688, 984169565, 649946264, 688170202, 771898468, 47590220, 574935285, 65810188, 893409570, 479932798, 353701213, 129050968, 335075353, 148282963, 713325653, 417995396, 76316998, 677436979, 77889450, 494888081, 87533215, 659453527, 172051971, 392904890, 845042945, 424428743, 643532159, 668677720, 902081160, 537839685, 202202241, 434807826, 75676667, 309531405, 157969002, 329070253, 385226691, 456267802, 618318122, 439741031, 768161816, 665773988, 953538297, 314182804, 750339761, 754229092, 675968217, 973037606, 394480402, 902825210, 150960678, 70663533, 340404186, 111924542, 30865796, 882748292, 597258925, 574724170, 387086561, 19262345, 586778125, 506236834, 166822998, 977027823, 950952431, 344797476, 594532906, 442064131, 495002897, 794433109, 806275524, 995970236, 732046707, 394026321, 223082819, 943091256, 92326129, 33407102, 765513603, 485681089, 579159190, 327428031, 460554976, 397672289, 150561667, 68526146, 449439345, 421630445, 997254850, 740812398, 70227550, 514609173, 618445376, 560127845, 590100211, 92898767, 311163798, 128007808, 420682283, 795701022, 542184622, 69037152, 5309724, 95543222, 463411409, 590054792, 834193871, 519834149, 70427215, 954332927, 952723066, 483554933, 553678823, 854250777, 925894185, 507077142, 160938195, 378222745, 418599133, 34668139, 693199007, 611076835, 871799978, 878799540, 217907366, 966256855, 239103730, 867442666, 633399956, 609978713, 147358989, 339063050, 590207852, 995885980, 589081811, 210089225, 732298819, 350352843, 512005232, 554450715, 894444041, 562155638, 495744387, 326737138, 904041255, 965429770, 113900915, 688767149, 58633684, 375385780, 588638131, 753139470, 142434780, 41225997, 358105715, 919677555, 119196211, 493297755, 829881501, 690960267, 265655355, 761261209, 273556302, 881716033, 746093242, 977498924, 464225760, 34832243, 816373656, 952980205, 322550817, 167735663, 47475170, 556171237, 406983426, 341839341, 657173072, 142926851, 588710113, 763271593, 403014477, 697226863, 3969634, 545643482, 97001756, 619158611, 310000956, 134604147, 904485332, 211845552, 247240855, 650083312, 977015688, 356424267, 251223976, 664660454, 762018059, 656348259, 382294810, 299840566, 855479601, 173780211, 174826099, 647003834, 836366632, 484123093, 889344545, 938455276, 946976856, 178489809, 549885331, 644784273, 574052108, 50477085, 928004192, 157738408, 990397744, 597901509, 61480564, 318179838, 759628550, 231548092, 391287726, 71087417, 458546137, 412559299, 200008202, 137761413, 637819618, 226001220, 818482215, 626238932, 491448116, 946337792, 747431848, 722683031, 200320137, 524553429, 624018488, 780053732, 348203413, 471114745, 236487324, 198063973, 593065394, 835792972, 865040604, 343461697, 111462490, 881917279, 503847678, 426897920, 541851367, 924212712, 710270826, 854210374, 169988987, 863328221, 641736210, 649830423, 63076456, 236605226, 854377249, 440439112, 692376326, 816954064, 236457003, 777475852, 479824629, 778793034, 154076880, 873390665, 474263463, 772819162, 266278586, 355449050, 923427540, 789330836, 367359431, 25275120, 47590186, 324429521, 589357140, 435348776, 894962018, 207347220, 731373995, 280849586, 646227655, 711206332, 992406859, 590706392, 347596867, 946400114, 317654812, 107936908, 373409538, 975745385, 494886856, 890531859, 598069047, 920401507, 909132167, 252209297, 479325105, 686854173, 78906200, 785901609, 323456198, 106964390, 338279677, 66895619, 400370161, 213174216, 334614096, 709175269, 275161571, 584305236, 190729188, 651268712, 875852061, 474134439, 936643301, 282480862, 605723595, 318505511, 877371101, 408921324, 816101414, 615152273, 289107722, 123976126, 439027989, 724003024, 103760229, 677514746, 654891694, 516721856, 185892335, 171767233, 612356422, 498832017, 140125076, 304663394, 318705489, 317370804, 847595599, 255779047, 467544979, 274986647, 386452941, 354882043, 992749232, 132579316, 811756889, 604701019, 25707457, 236973531, 513694089, 456702132, 964172231, 575072446, 49881227, 307271775, 327114815, 385442498, 121975423, 564823081, 351875545, 714078786, 322979806, 306082363, 571717971, 917362892, 68516689, 867613081, 94817322, 581399662, 479896631, 269177720, 246956474, 913086578, 874619369, 626080015, 990930133, 525819622, 466539300, 959235446, 121626528, 499277979, 792039331, 367578993, 585677756, 310491710, 172059084, 662855788, 111155023, 778366234, 374133520, 355994921, 228097892, 650459417, 736686020, 859227683, 139738741, 178244983, 338593213, 968833164, 675377677, 965185949, 198178646, 102990597, 532181501, 174081960, 86299720, 942608631, 936859573, 689663369, 337993931, 778046286, 983846772, 279187737, 206741465, 782787473, 264235742, 928228339, 193971288, 358776532, 845612978, 727600374, 330020975, 573887324, 570461604, 822673045, 955051541, 154129159, 342388121, 967148454, 303606456, 570347494, 529661687, 790799473, 569219105, 529114446, 800468668, 253390337, 874861972, 913659428, 523318068, 429015335, 121112767, 474475715, 739367794, 13844054, 118190843, 718157138, 126023824, 973536483, 65694329, 533161349, 219138121, 237884452, 549482451, 577956174, 114954288, 106554142, 599949749, 597037951, 848567558, 696161055, 227302930, 464694309, 877689507, 689419743, 515891665, 4522584, 234342735, 317778733, 314628287, 723707810, 318833561, 837981018, 128368194, 537700629, 455145513, 273994204, 292305637, 533589709, 45200123, 576757119, 496116684, 652296231, 568763164, 604286980, 996317433, 381680411, 198670297, 584777966, 166014072, 478702391, 331427001, 273978214, 370822219, 85522871, 720293630, 204229545, 851755420, 965486945, 805911014, 439382094, 571063459, 266941664, 45063093, 646572392, 686832659, 34066044, 352708080, 241484343, 830866069, 70925392, 186364966, 162399646, 247794524, 3414524, 565166678, 359295015, 266834074, 741682211, 988087297, 480432056, 852370170, 632215483, 714225019, 998139952, 776786130, 246858706, 203100900, 262459132, 479547394, 189852047, 543158987, 150191207, 959783329, 492300815, 214599799, 960403615, 20703293, 912456231, 168911964, 263493838, 416072524, 66905836, 561512595, 930224071, 651173650, 414274174, 9362420, 140017940, 536282299, 711367929, 724530222, 611521312, 793782977, 774862913, 960999892, 266066618, 370705232, 774932619, 765822038, 31078862, 772278425, 190465436, 279549626, 641334562, 456744880, 101520025, 51672943, 745942786, 92416630, 701548872, 675927558, 491720319, 535341338, 716492413, 349155312, 183983772, 565319104, 229214578, 263185809, 59221931, 246636994, 501098761, 990882217, 709267963, 695032833, 308991960, 418902473, 114444149, 188487352, 611704835, 612505261, 711990208, 790192008, 165777316, 557083161, 420578371, 185026301, 205450386, 773785818, 320526878, 366375221, 60154317, 320873671, 278572554, 897875656, 800676605, 992541356, 467996739, 302946817, 777521853, 206090951, 679041900, 639698820, 669930876, 551744119, 149360031, 806079512, 529833142, 543819551, 856997894, 126163502, 654437906, 556958359, 228535537, 403812558, 964683355, 39736826, 269364970, 496027428, 85085444, 124030675, 870403127, 373214449, 118667506, 972354382, 545423250, 113669485, 557388277, 97803396, 335334358, 961068146, 962744649, 303801595, 742333206, 933327158, 368050249, 144888769, 969313787, 281110611, 633659016, 35458332, 23961032, 282614366, 150066721, 177472637, 214949293, 283861940, 576513760, 209887468, 544491419, 113478557, 648597255, 920896561, 345130111, 972708563, 669635047, 43315550, 183542470, 100027942, 728168161, 550474753, 509342346, 625850101, 256293406, 80185320, 862829068, 832798985, 674676426, 771333965, 136564967, 746749843, 429500500, 129945409, 169649327, 958195004, 567698292, 110576602, 978745528, 614234757, 886240362, 358677014, 903624599, 340076754, 463510112, 879722099, 783049242, 740889350, 120842721, 841452795, 429984070, 857577834, 980545289, 175932379, 99827638, 865432432, 902377567, 735792991, 911901445, 511961457, 687583329, 158885229, 257250593, 545689225, 530122012, 511713531, 938703620, 737344378, 739711102, 33109526, 484984760, 562762727, 803436840, 675757723, 552743496, 434275685, 203019224, 158328354, 762797171, 78429495, 439683597, 272131478, 35987382, 675586571, 278511701, 679465887, 89141699, 333860558, 532146896, 686780158, 138661250, 211050651, 453879218, 88488474, 546574257, 170430901, 466739837, 874327345, 271500363, 240476571, 795937236, 881694464, 764357174, 420549035, 323264991, 741175428, 966015390, 340878306, 771994551, 654421938, 487463149, 790854992, 480250715, 35563884, 740179484, 500636026, 538762932, 121872662, 175297284, 161474450, 783012362, 365637481, 609503981, 376628368, 822417587, 484156999, 236991884, 703678216, 199868050, 457593016, 204258030, 382050181, 195638466, 353607216, 474043376, 94181300, 255444150, 712179394, 616880311, 497217427, 853065017, 607848552, 546915251, 281548110, 602786293, 761961534, 737458755, 950310293, 916045777, 835352581, 823718435, 446381277, 832514486, 358544672, 443471199, 433979936, 647717683, 723228300, 799803443, 751492052, 976289573, 703504502, 156343123, 95177094, 493709306, 9325728, 688399670, 278851717, 7543809, 435665592, 653503062, 67719299, 692302116, 321573530, 475482589, 102118336, 257758478, 634544238, 635411545, 802761660, 842297413, 282219454, 374267867, 374639746, 638653260, 600923154, 621916973, 443549004, 429551008, 258991438, 231561850, 836886931, 452291895, 949420063, 577402695, 82615400, 823531927, 599120760, 311764406, 850395430, 653133963, 291205896, 884958447, 387518184, 481198651] 38071)," 84446 (countComponents [642098517, 592136333, 10316544, 270915225, 156082777, 230622305, 377603774, 295038140, 782504847, 259761538, 732552807, 796809407, 177162785, 695185260, 504820816, 217873219, 71373544, 885967978, 682483183, 61103833, 731028053, 668778591, 422745032, 370956633, 179375807, 537702512, 81479209, 858492597, 306119301, 108635884, 572032210, 559122068, 707647073, 75440080, 562595526, 398490308, 974028265, 491718480, 834435029, 992084533, 70142459, 855717664, 262338528, 590918581, 473300705, 838203235, 120713016, 623724806, 940235327, 460680611, 392899463, 240448852, 823958180, 506196035, 598102532, 880015372, 658948519, 412041542, 522650892, 286270559, 949259642, 248023424, 361850980, 849337477, 929679411, 550670838, 996942113, 556224194, 592054348, 821188986, 806503888, 280550326, 8094778, 153233216, 663101930, 215946965, 640362453, 495149788, 55572546, 929189449, 192636404, 999503992, 499938186, 940602578, 875101637, 273453179, 387286907, 513734716, 234195495, 666679810, 800693454, 385053787, 375056218, 899001280, 891913807, 830321625, 223580958, 148685608, 460378236, 963991895, 505248549, 442573382, 14830872, 580995323, 814318666, 13254122, 736735612, 750977137, 919396293, 701773318, 245856642, 909908034, 910258120, 612897678, 231984535, 18681413, 199991590, 606071400, 69850167, 25161787, 360309092, 10724803, 775042419, 242893242, 461765814, 998842974, 981605400, 316072036, 209058370, 486318686, 562233201, 461682238, 726929513, 945430062, 65650546, 97836419, 208101247, 56127349, 645891706, 289245055, 159412246, 853018591, 167076330, 825350544, 599385472, 5444315, 871826833, 664367645, 262777784, 671193015, 244229709, 917584252, 505600109, 131149007, 449913494, 822360693, 815769984, 836379615, 99570302, 546553201, 944138371, 147771540, 563361411, 617089031, 643350509, 684259162, 34602335, 595837851, 548477448, 806760276, 916787923, 590546026, 112029797, 991969630, 205736713, 538254048, 999289731, 60135316, 699729421, 896913787, 345711153, 168619996, 252492570, 52198673, 789855994, 536997493, 514728251, 601837717, 395342622, 351877133, 482827253, 347891100, 192917097, 719629948, 77119207, 679046394, 203086520, 643718486, 626414235, 864313118, 70364418, 781316787, 440681875, 681200897, 414762461, 728903002, 363844750, 50453206, 574583915, 526329157, 462612880, 74553937, 768785013, 435152113, 630299777, 404565709, 28229013, 725627961, 901752966, 911368511, 216295792, 86228641, 527014291, 155161286, 205266610, 332767047, 251668878, 377619816, 804113231, 987207513, 378262469, 609548413, 183495015, 322783757, 809145465, 986087186, 224849961, 628829716, 393942291, 908795219, 641778623, 111996763, 331353459, 555376015, 279065316, 622029867, 800957187, 509834250, 347423708, 858889869, 764898942, 635297486, 509523319, 933946968, 922165778, 25205773, 503349490, 714888621, 365567213, 194223499, 489935297, 484689577, 335053423, 632367838, 479239193, 793835890, 289309193, 242967245, 522727858, 903151, 556109055, 424572684, 410260844, 5639416, 429145304, 689651060, 304604682, 596991409, 712690242, 96345831, 279008715, 178350675, 581106402, 594230401, 7747701, 379640404, 967616610, 703113228, 614030073, 537559326, 576167389, 724564244, 72360361, 164466728, 867777604, 484785272, 342938499, 31204004, 91522137, 936457519, 779461098, 358702063, 571409863, 328220266, 232777354, 478420591, 163846191, 170682001, 219334654, 684381000, 663291989, 847548952, 755562663, 83532563, 605892658, 962597553, 22407620, 330526936, 842010406, 591598582, 194493029, 641378991, 554053177, 6300318, 209826312, 85148483, 912982088, 317878553, 745723311, 273756808, 182520502, 40364134, 131869003, 691222608, 796008007, 922250227, 414590656, 565400941, 566106067, 647883066, 461654503, 222550263, 306392262, 474213539, 41781760, 660265197, 357039379, 492269774, 778183575, 749385700, 671851314, 468308264, 879349826, 212699919, 944479714, 33882767, 761364392, 982865084, 746464150, 671444757, 853802934, 219405066, 622627339, 939588726, 295931570, 796761005, 196198707, 591378927, 740754791, 309868041, 797636383, 725379526, 4974186, 567021559, 16373549, 479113471, 905686896, 763759369, 178776839, 756116141, 131668603, 776187222, 369938981, 546091291, 691154248, 927834803, 480539736, 932384171, 529667016, 806236895, 997010444, 271587794, 98762920, 679727432, 796020760, 568444836, 831565337, 830064922, 447931005, 324019174, 154162512, 50656183, 699823043, 539713301, 792660328, 598440475, 456776120, 2725973, 55453140, 318714506, 704354613, 287984059, 5149074, 84092103, 22364627, 856086179, 848497304, 644950870, 301819382, 844848904, 227238292, 683713275, 328537552, 109160751, 912834243, 502978415, 449966463, 844152378, 920645292, 887694582, 272808266, 418396255, 295049073, 609156712, 527239528, 218432518, 466699299, 302226045, 903794424, 173691988, 881330617, 621482754, 315189109, 849416123, 997390539, 6400790, 49808428, 757487448, 191950604, 306986536, 233511162, 241833907, 751189194, 87709550, 509887122, 32964839, 195584917, 265765244, 45323392, 399622194, 472530066, 24442182, 808082987, 687953010, 534808101, 726412335, 817476904, 448908977, 705585359, 296318178, 305005992, 806952681, 107089293, 294870562, 496049971, 282222210, 640004487, 144784698, 85401522, 891400536, 946987892, 560365228, 695449613, 543097580, 689012289, 622096443, 361838134, 352118710, 480779653, 381320933, 35951226, 817538562, 989682152, 980833703, 770198700, 882118190, 409290669, 955843649, 471267135, 657914168, 611566017, 868660572, 77231255, 11014379, 365927336, 815772619, 729736584, 992541381, 76360548, 725659272, 684174094, 726455083, 910414402, 587396844, 134693600, 677231026, 784671874, 808364320, 661653836, 959204542, 705240586, 695760245, 758856025, 380494368, 804818065, 667216180, 324513631, 337885696, 17383115, 582150497, 420795139, 426801058, 924046023, 689475974, 814077523, 372259350, 430280436, 933032503, 353407901, 816832729, 516547748, 609549026, 870952782, 391691572, 540509433, 364893117, 588065677, 5933043, 699188804, 994800774, 38509104, 996726549, 745862755, 513835505, 971623791, 574902566, 25740357, 438435902, 369243558, 549834159, 175461238, 574206698, 917896145, 798348663, 249613073, 694411277, 519329398, 383939956, 319845424, 495291616, 543091201, 952584724, 510919167, 77552145, 61709722, 573424310, 654882640, 239348497, 135332613, 636552061, 323739395, 190380681, 39484128, 757974747, 670819775, 875906052, 710878058, 887308228, 180160601, 221244651, 974892049, 789676982, 979884428, 37865623, 332132550, 377692409, 795247077, 909747998, 776644770, 233745248, 152255092, 638988303, 242878561, 880430503, 866700486, 160028571, 461454051, 171359815, 331267045, 922227396, 333066890, 151967787, 678315666, 210912737, 508994220, 992757461, 282196545, 605019929, 370561405, 994153893, 72195023, 16287422, 551745501, 65544330, 331983800, 669730303, 250713743, 563389895, 852583831, 628985758, 153569757, 253704450, 354668211, 890158219, 538802247, 219087982, 439438800, 475234663, 426455377, 20840425, 854063085, 398046493, 113863731, 416667592, 635204945, 983349939, 833347329, 929224750, 125998890, 937977436, 703291940, 298139545, 211682649, 513248956, 589114207, 263825975, 148549888, 685055088, 866807002, 411216675, 325649892, 164313588, 898312787, 24916267, 892488319, 927942303, 963935465, 470490548, 169256013, 507417953, 374600977, 187879020, 53160834, 93101764, 670668858, 73401040, 643733865, 634982974, 268290956, 575390180, 948059502, 317545825, 363693139, 326397065, 458996748, 568531076, 966670599, 470952481, 237368204, 138273466, 959428828, 320625239, 979173520, 375317945, 512338642, 774191305, 348718798, 176765018, 688445449, 688574866, 742361586, 978105304, 319117516, 502100473, 855113626, 434871951, 169682821, 117529688, 379707645, 479054490, 268507463, 97889908, 543223310, 761603638, 192430411, 611731937, 673840575, 248893058, 769087110, 965546262, 746115671, 537130749, 794612442, 677490611, 138949309, 177414182, 76633417, 298620590, 853650468, 95216332, 866723306, 837577422, 347709313, 157737430, 94555387, 526768800, 742224674, 714415190, 324298734, 585430189, 684115479, 27066113, 373243816, 361721999, 95577100, 642354718, 80338033, 720824272, 954368799, 310088522, 289742984, 45168789, 504018395, 30358835, 969366231, 945718637, 181316862, 61477330, 74169517, 266366177, 942166363, 639691340, 569618588, 604841149, 105639076, 14982689, 179417952, 767082564, 586756946, 109966759, 462976163, 780295823, 208953432, 54305947, 739967325, 715202864, 408214882, 135978865, 868913127, 37194446, 672508503, 610626882, 694625620, 720598252, 262000145, 882789797, 457646281, 709998258, 343486472, 609642223, 10755425, 688353873, 439075294, 458284839, 567877044, 65728780, 587795102, 993020048, 93464050, 86751094, 594306258, 735350905, 788710243, 803792293, 422334519, 46941845, 398753411, 246849308, 208121671, 353482635, 308871639, 145853004, 580026666, 716363178, 63345856, 72416542, 227037223, 986451694, 527935943, 846838345, 798939603, 899029687, 665669444, 827776671, 117569163, 848461659, 81248906, 714785945, 218147225, 863423455, 795194452, 792612220, 799918790, 915873441, 479753687, 523419672, 806753663, 627187953, 884129979, 844649855, 871293211, 519833514, 866564289, 58610648, 363189796, 838897052, 853635871, 783069009, 856616146, 975849205, 503825756, 479906639, 803775237, 92231613, 637212139, 612931197, 78901013, 217045074, 675529951, 541360956, 279921115, 124328332, 399387644, 814430349, 650224373, 44534524, 834585382, 829922906, 39022714, 503039406, 819864707, 855263408, 206103874, 558577061, 912758335, 927454285, 7179860, 861017046, 605767844, 532717779, 692700379, 590255633, 156822586, 441502581, 550302566, 960512171, 259505703, 43957185, 250076777, 462715878, 97404416, 386801641, 733235860, 765924409, 805605747, 210601251, 371845173, 320896111, 287639811, 565203925, 873316610, 881064380, 700834777, 820869392, 488124589, 704069816, 516853487, 208043979, 891737733, 493790308, 97515117, 818265374, 669688470, 374406134, 182236019, 830923114, 632371173, 15434043, 499884891, 805587284, 639293542, 740904383, 519478616, 447799941, 755054014, 537121318, 984445535, 855540467, 184648972, 631332772, 969605060, 974770527, 882743982, 458756720, 111662212, 163854099, 169674392, 764514601, 387192714, 829496257, 715080424, 904635534, 512541616, 485706662, 349864430, 80057128, 96391222, 929663613, 522958121, 736024228, 902954459, 878774044, 425692334, 161254860, 85846546, 595024050, 551510909, 641302532, 904898730, 446714944, 366210419, 709275184, 672141149, 211296519, 783322339, 59939318, 543873981, 388850179, 559504801, 299690228, 593931981, 100679126, 260901683, 904300406, 608622559, 824668610, 669751033, 681641191, 239220701, 292189485, 101789405, 830350738, 55400677, 786280131, 635771128, 155463486, 52276572, 965872536, 644318539, 183722643, 114982394, 856212023, 395507021, 375009569, 134298688, 837953936, 665497923, 767878084, 376304129, 743099788, 969590133, 992835864, 439223597, 120036646, 508111710, 472407820, 92263812, 861367916, 694985998, 542438845, 683428520, 997101466, 267773733, 693487579, 459020424, 653560137, 141870658, 434284217, 744188184, 651569038, 634515317, 898550793, 334144814, 637486664, 3092898, 821894556, 78622536, 20054593, 564495460, 247848814, 3774099, 40877095, 552928464, 596551053, 230255581, 47926554, 446759463, 318309095, 223559453, 16460719, 801268201, 296286981, 276827969, 592715785, 723065119, 201156155, 182330437, 410771645, 855534609, 737552147, 394363455, 747293627, 833222469, 692883931, 84835137, 771917989, 811790547, 956088612, 56489045, 808772206, 284478769, 815828506, 826085292, 150419422, 791151571, 10758771, 292317244, 258395915, 491847971, 238025775, 792277994, 543651904, 785559343, 721043161, 305234995, 544931880, 906763254, 69358646, 259614104, 480868663, 369232731, 80590574, 164053986, 944797694, 12612136, 474291023, 956542940, 696253988, 110360430, 462355226, 161161350, 72035550, 656351263, 156851124, 32554170, 12345792, 182807943, 287116197, 479874724, 429322276, 916014104, 563300810, 577605613, 899515833, 483684242, 85269803, 727447048, 515632441, 148525181, 588065260, 898850144, 133195090, 65506827, 975400605, 362529790, 879700959, 144081112, 33161698, 488315269, 686886438, 727459716, 965875163, 208609068, 828031795, 269378903, 753947390, 177264054, 95556202, 335638262, 194842733, 365799470, 438965235, 759541476, 266420404, 353430460, 970103269, 636927163, 862246741, 511221611, 919628570, 114826933, 194443455, 710928315, 532472584, 836528613, 588569113, 801009720, 167628089, 487152718, 433606662, 120404204, 272748845, 347617604, 512476038, 252219225, 370222559, 571708296, 637688524, 698950887, 298071832, 332472970, 768964655, 31020210, 691785800, 62129713, 772369522, 515728601, 47457038, 125041571, 568845872, 164748963, 487198487, 872126294, 742060311, 371308816, 394247981, 987746682, 95064046, 587894942, 590733193, 262933275, 374683022, 4044468, 584971686, 332968964, 602876483, 73185053, 15407555, 342299341, 613581546, 790518391, 933938302, 387291621, 684911975, 308718539, 118107925, 186823976, 856665508, 609853140, 919440747, 230564845, 398172119, 99256484, 326238053, 113064991, 990712260, 928491820, 752231299, 179116299, 322155438, 458788574, 967681278, 151546322, 771562007, 855412304, 78789051, 631907543, 357383440, 84640576, 999580634, 482734388, 793266903, 780625245, 287452546, 692846653, 777606701, 907508019, 481269268, 454412694, 850308261, 479856420, 922740446, 816474033, 846943734, 195359636, 731006329, 205873167, 897396242, 304887252, 652075088, 476369243, 457785672, 416517445, 79208493, 282054377, 266015274, 519366564, 770838611, 981348768, 831807406, 774100283, 543660850, 391366726, 340528924, 594058366, 586717763, 425719958, 524102957, 817641725, 958865684, 450423946, 500044095, 875499785, 316544453, 275169398, 901673749, 63779648, 868074557, 834831230, 341818456, 180253007, 809357738, 497228607, 411169604, 96108848, 127237104, 605102921, 363655920, 555119001, 982797747, 185754717, 38981358, 692428957, 48072041, 276180911, 305618585, 290348302, 963388357, 182566300, 222013348, 293986609, 619075950, 202923834, 257287584, 468770571, 289340259, 607555829, 191629227, 13208433, 27558011, 144941037, 811167300, 579875783, 97857029, 124985382, 342950684, 200654088, 735961874, 585821534, 655707830, 558798782, 457953651, 998149435, 255942607, 574086739, 154502726, 277229124, 790040035, 756712250, 156217275, 587374304, 687515185, 811079396, 203334019, 707420598, 721914968, 637659257, 87520266, 707553856, 863692008, 161778203, 187829827, 943661241, 707561167, 407281857, 65308058, 283352593, 493192646, 300558259, 296467494, 618519823, 337337714, 383908881, 510379116, 734211838, 830413411, 731018643, 690078271, 714207674, 922452673, 521398114, 559267704, 522999652, 271942249, 825714170, 132513977, 160994478, 249899150, 355298549, 180343126, 827463639, 649851141, 376134804, 224405846, 409957079, 735851379, 393196104, 629819747, 698908433, 943004024, 796458170, 543671907, 868460704, 204512971, 218096952, 273150185, 712001480, 180408498, 185825785, 569980878, 490217981, 546557058, 556242663, 560727840, 123282731, 137938907, 472911446, 584048270, 993772928, 373604148, 361173817, 55358456, 300410008, 515587755, 341072379, 171257168, 783916563, 436919406, 758705776, 211671883, 596115541, 420021956, 866376986, 541459727, 646204126, 183017318, 982521122, 761497812, 43236886, 165790919, 754431818, 6632687, 446371028, 701472912, 313313550, 472335288, 127188261, 647887021, 119763576, 675475991, 383649623, 351395102, 160701791, 206125693, 157025755, 586226934, 839123652, 231666958, 635187886, 737644363, 78268132, 615928068, 957621154, 747669537, 798319953, 671029650, 775125714, 7887464, 540694214, 871006473, 817922172, 844624304, 571927017, 489497208, 596233040, 841763070, 219432305, 475445584, 712942241, 724322548, 648027661, 96570923, 535574988, 384023279, 509674761, 380718442, 586203107, 41701369, 996369280, 52837211, 517144563, 981626949, 356230341, 336666888, 718033083, 494771554, 39242573, 248087457, 474034219, 553813455, 857420591, 566452979, 755461294, 295264144, 495853729, 204544837, 220445255, 742918082, 707356527, 770843653, 102925782, 605520531, 565932304, 933058434, 708432083, 179701145, 696616656, 444810568, 513488974, 196873283, 246029956, 310042837, 902357957, 456004372, 779279251, 623044080, 442107680, 104968369, 130157736, 819340726, 75560735, 820472013, 51862015, 92560997, 766406407, 622969184, 697668091, 854548502, 256691140, 195363963, 473989162, 170384239, 139731735, 711563153, 404352818, 452231087, 246367910, 297379826, 918179617, 273457094, 933028678, 667155660, 396795766, 788901889, 635098145, 886072151, 242324847, 966275206, 750555931, 733256183, 380138801, 492976311, 294327705, 32446493, 909202134, 138302860, 969670587, 598497873, 896723778, 79736477, 346155756, 240643256, 330639902, 325544082, 133492833, 885951402, 3313878, 283758250, 689790849, 335404296, 471762276, 16040743, 320984340, 885756819, 182068628, 706646072, 265778701, 182717407, 113779932, 405876752, 393113930, 200895332, 335864428, 40139684, 256357760, 962482441, 246256104, 744548269, 610171599, 259858164, 175493486, 310998148, 709067580, 256851886, 372779164, 127141725, 143905209, 202316163, 372575029, 402183043, 85236533, 453351653, 849393943, 10241150, 351742855, 950740886, 265128880, 599832210, 853377750, 69399959, 279177250, 109703604, 777929263, 193634406, 276722110, 613362682, 791523110, 951880697, 616120169, 280277635, 35519046, 160536608, 508877024, 940990602, 151259521, 678014493, 323631542, 265852896, 378710933, 209201143, 836872692, 55557408, 136110859, 277179713, 476670913, 822056648, 756539252, 942622256, 726096249, 658183511, 861798173, 263321906, 393652869, 33390784, 824420810, 970611284, 910054597, 947275376, 884922106, 306874118, 717997363, 9729884, 948776972, 935744587, 300242830, 986748444, 693552715, 897662750, 338459944, 624564929, 578531732, 521983361, 788381939, 243145523, 185292258, 339030751, 364072321, 825205600, 338000196, 910796891, 72625376, 962457324, 568478477, 344541521, 992844753, 318069789, 569654582, 599828920, 873140767, 145298732, 706123105, 599401891, 474535047, 299420942, 15954459, 194408799, 134166329, 974592126, 475422642, 799784358, 565449112, 178613858, 854118412, 100882076, 25576675, 906321664, 220153191, 199911917, 550839495, 882792100, 267943580, 286300221, 137368303, 647244255, 631345469, 35640570, 824804690, 895421671, 744910211, 608599589, 539149592, 913076516, 105043794, 146194386, 728866996, 125145430, 584321251, 632403282, 895574543, 112409599, 397260207, 415736501, 903991441, 657536608, 907615030, 613259973, 218274461, 409658721, 210504286, 640581831, 656571634, 895404227, 911297711, 774458356, 739988287, 630082805, 92702894, 757721521, 655909343, 117986742, 971989319, 546268806, 377597740, 692617264, 466440342, 453013965, 865128795, 595781800, 599778539, 546124725, 620227023, 127538663, 466856898, 605030967, 619583697, 682663638, 225014857, 90899088, 830967575, 53751523, 182786647, 568785589, 823410635, 811652080, 310174044, 954194243, 338683711, 94358939, 103825203, 810892575, 273729975, 79731319, 485506985, 64844212, 666544220, 305658437, 191310440, 239661306, 296746208, 64289449, 267509845, 859447377, 662732147, 709878666, 167534665, 492099958, 741830134, 18948265, 753782424, 846601572, 762078643, 77177220, 107549073, 787267312, 935825802, 943035071, 485376493, 737987401, 99540628, 627681013, 125564905, 349757636, 600682637, 92576158, 624580290, 393514, 166464895, 618240020, 626602649, 665119140, 275672918, 698489642, 494733236, 879787610, 26108844, 129100961, 916503432, 771838472, 704225929, 302817591, 455134284, 328250631, 133771757, 368618143, 819293688, 748248266, 740435311, 852170933, 162638483, 65422998, 615864448, 707930351, 746015428, 599183503, 894242765, 488858986, 299378161, 425799656, 964817668, 412921097, 756470205, 438223878, 385049180, 653313961, 231794893, 485413998, 325994781, 934755358, 858963146, 91502825, 807942930, 993252323, 939225989, 485536338, 702059475, 684596157, 293851995, 858325255, 540726080, 670522262, 660971462, 137837050, 693076939, 902394802, 712080282, 879789298, 270226313, 166983700, 249096736, 297720960, 678181521, 995423525, 298889188, 956251109, 272009237, 295302874, 155586079, 70037980, 938860059, 572856622, 915623263, 894574492, 609152938, 820789504, 590010949, 32797070, 296151461, 958892622, 761242631, 735217784, 16959209, 910145547, 879838100, 3637783, 391699293, 521927927, 163370813, 339276674, 415396280, 663105601, 263898203, 552554566, 187138528, 107443875, 739312015, 590628872, 587364671, 364482278, 67886636, 95873019, 605985631, 165712384, 200612635, 432525244, 990363843, 528879635, 774719273, 528658543, 709684809, 914007329, 145466877, 705251522, 676640602, 419799671, 129866571, 61124559, 817219789, 947124549, 221623982, 565221434, 445824293, 35070377, 188866127, 323807815, 458266396, 194234787, 872037438, 458017110, 896840840, 67729638, 637461242, 176246297, 130502588, 889861940, 932836140, 422996609, 22700448, 289780785, 688802205, 478175905, 824613017, 92617090, 450147207, 563113014, 442943177, 305769504, 667871017, 330639476, 728009626, 456352675, 172910328, 641877078, 820282492, 214555998, 349432619, 767123620, 509467170, 516689815, 104727523, 602717975, 60974015, 499100747, 61483554, 544409140, 358953276, 62058381, 445489104, 665742697, 884247948, 116036268, 106455368, 821933855, 21336107, 558694240, 925407311, 164499037, 288846143, 223034454, 442397985, 451779015, 659064563, 596631270, 61971560, 155240908, 645492861, 776227173, 852663106, 418940917, 45673483, 474840510, 89185048, 475531109, 903523008, 413572504, 183613150, 845422041, 37254651, 637020591, 692442894, 776081084, 595579112, 349367101, 313303217, 839180704, 695631510, 402031611, 1223314, 165412050, 670416842, 140679101, 750862171, 221986481, 609246124, 793501614, 857873030, 346437643, 812492968, 722947344, 696244952, 287940468, 608126407, 615245661, 23216568, 434256984, 281000839, 30976833, 737587531, 900048919, 244051271, 447978947, 392614980, 114707068, 945891925, 962547663, 966293903, 704569832, 694550538, 808890429, 332082758, 516004789, 645187693, 37418596, 305887255, 369289049, 442021683, 643218321, 188086722, 48833288, 20935461, 810309261, 404665939, 991809344, 805381806, 601925404, 148951623, 239746149, 913164002, 27586625, 815785632, 199988165, 838543258, 188491616, 697862043, 609560445, 985514706, 671070442, 250913447, 927540697, 25939167, 51543930, 774107486, 394815297, 16866388, 810081132, 259972617, 911114530, 780410351, 318032308, 112473618, 139981601, 785703931, 828168341, 528372902, 119147674, 860346905, 339550719, 307810594, 205951824, 914129734, 333859485, 181869107, 104179405, 361852230, 845027979, 159235720, 476075008, 974492418, 476627489, 981363116, 892109842, 774114028, 649513838, 286285262, 638549101, 144824203, 448316762, 100740715, 278937446, 808323193, 238158508, 744414330, 465489738, 349944965, 255507503, 275743085, 59502181, 143685380, 516573478, 755908019, 630746383, 533064820, 434574333, 496529819, 308040213, 624991462, 419185959, 26988422, 187590100, 572462838, 726602578, 350123746, 391964568, 781880406, 434002635, 517313271, 24640888, 760297267, 252437933, 91894803, 254831178, 893126678, 302288229, 830709466, 234668481, 951929927, 208814825, 309259977, 249604091, 279128843, 152380637, 190356760, 166562029, 901352563, 445630386, 737243865, 144904473, 333095821, 73844661, 984527598, 210400245, 633143154, 197428059, 803107449, 274084718, 402452372, 276847372, 8457685, 114139669, 759038897, 884580004, 689799774, 411995458, 56496547, 764629085, 350240178, 841835345, 903003958, 603292600, 358387144, 228925140, 866699461, 464435793, 492029257, 3100184, 282825084, 709303707, 477846098, 306506875, 499401337, 651025184, 682092709, 950249789, 909200587, 492137016, 209538393, 253179707, 386100779, 496065789, 508388669, 995799463, 104062846, 120479122, 649277646, 796480988, 567999616, 39979167, 969909610, 735216964, 465368541, 468273845, 702208269, 348701402, 497713751, 261334755, 455163400, 334133166, 357001604, 905748968, 772611845, 410439643, 657816830, 481391684, 347706660, 131184934, 997874929, 731903224, 800995303, 428833444, 608578454, 481651242, 285492413, 47200487, 102591028, 915100928, 262098839, 962078764, 221489212, 915310537, 384271843, 735128527, 451936862, 624211663, 167598582, 95625570, 39529108, 141227375, 514822607, 65916336, 933928467, 538764044, 922903518, 124914483, 14876634, 691912315, 216808620, 950452847, 200085741, 574542421, 696599657, 46466518, 414244941, 466288670, 69373783, 744375158, 637935025, 969550851, 276651385, 506573379, 919844505, 124559408, 473336239, 922340045, 717429543, 403982897, 835228160, 187427549, 56064944, 266022926, 394618947, 845173483, 537946522, 230185345, 524478708, 137532556, 353782692, 825968475, 634344740, 608900118, 851637421, 911118845, 499531921, 963560734, 646248475, 530610123, 66459849, 808568077, 651131529, 569674461, 744724046, 978343704, 896767094, 212031373, 949569950, 877218033, 504410195, 505803123, 900860450, 890806203, 51251339, 480200964, 677153149, 525778412, 422812885, 553689081, 802797897, 790100482, 36743037, 159786866, 956477494, 164726146, 231906186, 923186756, 52831444, 545196226, 101927142, 602958280, 286752778, 453874155, 211257077, 769406131, 126536545, 831576207, 449415831, 233778065, 308016544, 119298694, 924604362, 115517470, 224146787, 521804482, 258760239, 144487075, 943966084, 4582418, 183710561, 89827190, 833930782, 322897342, 70442982, 947524130, 19848108, 695104967, 683732909, 429741679, 954715676, 994046041, 673835242, 711090666, 214880888, 781878745, 96171567, 986439312, 43807971, 386047209, 714671404, 251655929, 593910156, 381913548, 353726155, 599170219, 796427822, 960661708, 221313958, 50665980, 771975148, 468030233, 271184033, 813664699, 918913956, 448732408, 167471363, 443036034, 841033152, 757257893, 980299270, 382377431, 434599671, 859645251, 675578548, 215428066, 244048016, 896784609, 890270485, 332686137, 679589753, 434423446, 283682248, 737451538, 183342003, 893258078, 85973181, 666600143, 394503962, 736954135, 664021774, 769494378, 206213808, 938621444, 66420723, 964119644, 579923392, 747581050, 360312659, 169526823, 143351204, 369426648, 555123437, 871845699, 812305971, 48338666, 61100073, 542870335, 370767056, 149437220, 549404299, 190109923, 829700123, 872116446, 321165701, 415254565, 682769790, 234626971, 7097699, 246403882, 800166606, 726517513, 965373237, 203164005, 666585774, 998084053, 873375756, 407292643, 955646891, 554571714, 10396461, 915817636, 956816254, 132869289, 39478981, 234307360, 475164948, 626227524, 118167896, 932050922, 159066181, 723372754, 355109915, 597957672, 183585185, 208546582, 574003227, 658080290, 631185395, 121839234, 906535329, 72329588, 573956246, 67262275, 111435673, 918123871, 936857045, 535424620, 999052429, 515347068, 95875585, 239183449, 959011272, 57511777, 390876707, 341591261, 651398581, 115852372, 998285254, 371265702, 23480300, 513375710, 666059524, 985071803, 700424643, 294982580, 761041052, 59293368, 306242071, 68160145, 702241979, 161838010, 104321113, 120764369, 528255978, 440424703, 461014895, 629657521, 744941321, 780479957, 398240988, 47497073, 402672361, 10902242, 698363628, 16523987, 737630208, 404201215, 67286064, 792146528, 875175974, 170668620, 799129572, 16630821, 213182251, 591391506, 411310258, 761976421, 293359167, 747099206, 990652351, 458831988, 43920231, 847621574, 610779825, 176457300, 288773856, 346231327, 452806784, 745741997, 532929269, 663892808, 371441015, 769101907, 71704031, 628808908, 961704190, 105663352, 262961258, 705541955, 456734117, 37989969, 251483605, 509631827, 435076642, 311024185, 456011998, 924533986, 122726797, 458746693, 794222737, 968262522, 293197431, 460265041, 254550762, 800169758, 880977252, 567643443, 107212748, 870270488, 312706780, 958289206, 22748164, 653872022, 413573315, 70075162, 166410201, 503620930, 280071687, 341709425, 808722327, 967966465, 837069953, 274493833, 764500156, 339963171, 583990961, 218412772, 112308963, 173177804, 294160099, 979233632, 593077618, 387580191, 424832696, 515825141, 74305049, 258596314, 778008377, 451085027, 743544428, 371696287, 59262635, 863986950, 860163531, 734665658, 445219708, 570913426, 511347088, 338147246, 361591254, 752268473, 94437314, 490229067, 402578799, 859223181, 649804612, 423808028, 120127023, 545732847, 659856268, 336415588, 370871996, 175701184, 979892717, 816452365, 24216506, 484781843, 803730213, 89309058, 447615434, 977755095, 574701557, 217364708, 670017660, 506341037, 249013568, 310253746, 812732671, 660524710, 78290565, 996498855, 241098410, 156236972, 132466672, 564805975, 496805582, 69595909, 182299960, 98563715, 889444748, 815745341, 115733735, 904911269, 25784932, 876144653, 380470595, 714173313, 857190089, 165608, 154503822, 216065223, 238262217, 837016868, 24124509, 66348239, 960056232, 326432066, 515058023, 888151594, 582988252, 367053507, 147014491, 221066552, 825852651, 197594336, 729654325, 460344606, 323773409, 440455373, 184527482, 640187592, 327822016, 879598632, 590404496, 334485076, 855622451, 385552456, 618603339, 496981960, 289414274, 505792049, 363297081, 810030527, 146150223, 342712164, 934188352, 874566907, 783021291, 508346080, 409071564, 126478740, 644456037, 599651172, 354119193, 544029819, 24875071, 318402939, 226058630, 121336329, 239027574, 83221697, 214144855, 394764571, 643048913, 216549489, 187413070, 986834499, 179806972, 955378058, 950690589, 965098213, 593452248, 350150898, 926723242, 317536475, 399722214, 648463794, 172654013, 923746986, 753587688, 920530017, 87707880, 947032967, 657310988, 876283715, 556805744, 672763720, 628532766, 872500339, 759431381, 861080667, 783785988, 820963922, 815196629, 947982614, 50595032, 188268613, 327560582, 129226560, 740929614, 900240093, 81742643, 639332409, 209474893, 36785700, 95999725, 43198109, 145395084, 237782334, 452087722, 152830237, 900607431, 117842617, 303565575, 458940403, 874736072, 421648623, 770493909, 635414817, 70272251, 631237166, 639095125, 396618822, 510205949, 119484886, 882369852, 12457365, 324227247, 989888852, 695145868, 218787391, 352497619, 159430492, 683733589, 108424198, 259925123, 102467299, 462330267, 831922230, 14708719, 655859221, 230509418, 754153692, 974001044, 143146969, 702634857, 612583376, 129024066, 175412995, 969914380, 661024643, 122010387, 37357592, 889963194, 79669534, 988177019, 146889399, 468035279, 981208907, 698412096, 56685500, 823256141, 805567913, 994095226, 871405564, 598445323, 375098668, 448024146, 870497313, 321829806, 405533848, 172136247, 748025421, 18574479, 870027782, 396208300, 819533051, 797823540, 689083308, 119769199, 490776097, 980706794, 419899331, 851245387, 279513858, 372994446, 443556586, 236633336, 206796737, 429479264, 203372514, 712541912, 186700899, 90558010, 606418541, 819728329, 692637252, 390302923, 646650677, 750955933, 643622973, 732118110, 707334683, 52228436, 29173477, 562459116, 971148541, 588627979, 392782872, 776990351, 802964331, 292925819, 289612197, 495169008, 408987255, 420302589, 280637937, 959706337, 821443259, 895964535, 193797285, 560160363, 785472662, 14399982, 109772356, 947375361, 752788402, 185201107, 799126607, 57684950, 426211775, 487126110, 634111629, 346810293, 172546949, 988857438, 681113344, 998850926, 910042046, 789915785, 623285750, 826823558, 149096709, 198639098, 370938981, 746473603, 933952760, 555469572, 994888718, 205223098, 390970463, 567496632, 391443781, 738489494, 318088900, 222966123, 342525283, 26193798, 859043330, 872664547, 891326108, 755330995, 501125338, 769703079, 439792282, 793149410, 71630163, 86589773, 284854625, 892126887, 268048642, 442002647, 526411047, 817000448, 879950808, 709653680, 884845898, 907090713, 259202331, 165154441, 829359537, 856947676, 995599602, 224377033, 340579684, 431474208, 133832492, 719911125, 77504166, 917769796, 104829418, 942138930, 106576599, 198852831, 314015679, 54875450, 351662889, 419528525, 242386272, 345781680, 504253725, 258310877, 932238120, 242925165, 978162345, 307424284, 828918469, 508114705, 209883078, 71085266, 113182799, 574475438, 60345924, 379566368, 254380365, 156185110, 23462518, 684722232, 849020737, 530307470, 115647868, 75403230, 321012273, 574558647, 378921396, 297088420, 164374158, 342279509, 351750041, 367722745, 293601725, 293600409, 51189102, 58016984, 808037164, 705088238, 650970738, 746398692, 820357528, 220110489, 394913675, 684570201, 854355598, 314606615, 870663987, 683272593, 114159779, 117300944, 204335217, 777319099, 37158157, 274454211, 484631381, 973050956, 201958678, 96123755, 751554030, 385142321, 380995461, 907249582, 662968376, 487573113, 121770841, 601572157, 71812570, 489377757, 962606532, 426077270, 766705964, 926973162, 3294769, 940731524, 289913566, 668552518, 582275335, 341690976, 179083882, 671407974, 779259406, 804636924, 166537498, 374941974, 981871854, 346979588, 644372059, 563035873, 339803363, 585011526, 910120345, 683288235, 849584750, 955614464, 604532160, 818282636, 953188678, 158073207, 165879257, 46205601, 25010074, 612998720, 279701636, 772721638, 523717244, 333336753, 34506613, 685925674, 43879224, 821155439, 985235780, 161483395, 571598381, 581747359, 918206771, 780958084, 725118435, 43313332, 65680054, 84097765, 298135390, 540848121, 171734188, 108658166, 241643760, 769099046, 250873199, 409322778, 417030538, 974668205, 565133646, 367168045, 79396743, 184759624, 699909601, 518684157, 471599591, 273157560, 222713295, 9800218, 799271569, 701627099, 925385618, 276887590, 717721728, 323795386, 981145057, 427277303, 175982909, 618139521, 628853911, 296858868, 562260508, 601817105, 281060155, 716756797, 72890084, 934626076, 821177298, 758030264, 61130588, 286940774, 955501124, 426275159, 978137909, 248735333, 318583483, 397717922, 497824531, 524584339, 855063951, 421090887, 425718337, 390437505, 592671606, 862033023, 582277808, 534684744, 513910805, 491428896, 25619097, 76115951, 355175551, 906801393, 100136107, 989990175, 717567900, 441888345, 801891734, 544415958, 539566581, 385314666, 413961873, 655563076, 357052755, 209328609, 290044469, 419578119, 252164584, 853316379, 760714775, 129972415, 629567782, 834131323, 938190649, 455004058, 956582245, 300988963, 307289824, 660837816, 968484182, 507109192, 175656384, 166006965, 328053315, 802909860, 601767540, 726321297, 222888379, 691233927, 92730017, 758762901, 113532636, 37476494, 945425063, 500327238, 933707653, 755491775, 590943417, 720865425, 501947213, 947415190, 28738207, 1005835, 71724929, 363398119, 786648558, 681137760, 722136839, 306847453, 396980747, 900945640, 648985987, 300393031, 364095525, 382333179, 633633801, 51078798, 213295790, 92068314, 39779329, 577022580, 98630184, 645565778, 307664370, 310975202, 574961764, 996272569, 812110789, 514342491, 840119933, 201289836, 612475554, 167371420, 586113296, 58876513, 390799714, 447549985, 809181552, 437224853, 834683932, 405431404, 874045475, 472730247, 229966182, 1031538, 977408069, 436530677, 696436944, 937431600, 677921352, 816279044, 309260838, 787420398, 892999776, 508614046, 41477637, 982372950, 173081830, 751704261, 823407899, 293065451, 428514106, 427678546, 370149206, 878745286, 77486311, 371206770, 654832050, 74656688, 101294326, 276595844, 56284555, 1979362, 754793992, 519069653, 910180633, 834900594, 324061301, 689282958, 297529524, 976778368, 687672234, 345183193, 640693166, 809830260, 453724352, 150270104, 932837778, 185677304, 474129474, 854870611, 651181321, 467959004, 549200553, 536433883, 188611438, 142985171, 831001934, 327399583, 768226613, 32018566, 998726463, 751314610, 262825350, 972291413, 124580988, 260841542, 915797172, 790735083, 503456418, 263346820, 587941791, 538027947, 333153792, 885051065, 460694359, 299059901, 344098304, 302694738, 480678092, 708187954, 371236365, 265207622, 143928725, 546153392, 134142547, 222818925, 798360191, 969661293, 622645541, 925752103, 65843963, 287489046, 716638765, 77672169, 893937442, 867702396, 745397676, 12853731, 113220665, 420002688, 241085834, 420448283, 719216965, 902644348, 309450774, 499010568, 800358195, 783864820, 819773992, 215615485, 159810945, 190450925, 820271307, 469879951, 747113844, 981220260, 534470714, 562106451, 739622330, 495462255, 490943079, 971672954, 539380843, 174971018, 719026202, 92835352, 815032906, 147840543, 960243357, 19957881, 36339797, 861558066, 782392968, 431493139, 323705104, 667514647, 148080074, 22817289, 300014926, 62138425, 740978585, 225074441, 996550536, 313336877, 349917351, 740889558, 515614356, 162675445, 391571940, 980965281, 245595250, 934644288, 660044927, 233698219, 601822391, 790431514, 320201024, 274923731, 358337355, 493347210, 977731110, 450837180, 910739262, 811360054, 39443469, 161123761, 7147542, 532586585, 75406369, 292023701, 269116707, 739085841, 617555252, 241253046, 310320626, 749611297, 488812719, 85605615, 741977204, 278379589, 552513191, 618297799, 604535751, 21247390, 817156948, 297937288, 317426638, 389737886, 395669055, 476562544, 514573395, 880816858, 742718344, 240796100, 652209674, 373648078, 159290133, 214466358, 110459445, 389275213, 494177894, 193546793, 644365948, 465242052, 504598244, 402968233, 751974139, 810275130, 788228812, 11285416, 375518615, 482844914, 27592887, 168308086, 60206935, 756443364, 814593353, 891194459, 380537516, 386989782, 926536942, 602360053, 969032888, 634741593, 55436522, 640177510, 810143645, 249650844, 157551021, 722234661, 8490373, 101076613, 42105946, 291715146, 489168931, 169871434, 376972961, 569521790, 985003234, 570232999, 209223933, 279788024, 763405668, 421837401, 257826878, 922408913, 108203885, 287075059, 14728699, 977338412, 412576812, 403833845, 951775049, 58411460, 521933107, 801729479, 472434908, 345580685, 999453840, 742367752, 734282614, 468190961, 580871487, 871559600, 432408027, 305410683, 169275718, 498686574, 732561817, 659047187, 389927224, 522267240, 155687192, 892255002, 940188470, 243003481, 84870817, 809104064, 48784331, 480137071, 644452350, 425158885, 625795635, 249446015, 605351759, 40662966, 806150781, 733479326, 656422520, 782373424, 649131078, 860973475, 26176694, 172686466, 599198634, 314912556, 596017159, 599006, 306334750, 718129218, 130058593, 933478427, 807943898, 335847787, 811083459, 912627921, 601141214, 897531742, 100167856, 924579155, 496815330, 705588502, 698734999, 15592815, 142223532, 525519884, 60511616, 252769131, 936099609, 341361617, 858697117, 659947947, 264660142, 337802404, 298879220, 702762957, 23700032, 173548377, 845890325, 335408468, 340976954, 288487024, 578393984, 581463659, 122327280, 350992688, 746848789, 369793163, 632614749, 954165372, 185093521, 723398379, 191100151, 29517982, 808564794, 107955130, 294412286, 779345221, 597498869, 36046262, 752126578, 867151322, 696698567, 723244969, 946323958, 94809995, 226183488, 216100348, 577402977, 659300565, 270828332, 714678976, 810733527, 361578129, 986905033, 734170319, 158621591, 298808070, 122958513, 261868954, 148441049, 281961420, 672439192, 35615906, 590601241, 239956466, 301603226, 723574491, 378512753, 409700079, 702170455, 132768655, 218320117, 549267754, 283614336, 619986605, 520123842, 195143020, 188457836, 818012859, 738772618, 44299172, 776380556, 436173622, 567676194, 601406459, 28955049, 870007171, 652768799, 249274819, 708296520, 391688693, 140182185, 410291733, 376986492, 850385782, 189445558, 743146806, 984514739, 277318519, 76361684, 582395428, 242120589, 505011333, 405931642, 490733998, 29785453, 110544376, 518942389, 725018586, 287007060, 971796549, 483181323, 614005282, 281384781, 740892883, 978985656, 951027371, 738474605, 544812803, 245740747, 928438392, 490560054, 272268087, 478396648, 71663567, 481885603, 582234028, 531727139, 65927566, 448132258, 241486357, 426466552, 900847292, 319681016, 795185742, 876966553, 395782365, 597890707, 520853043, 677369086, 25279627, 386772068, 548506897, 221268337, 20638878, 830822141, 243782461, 342369802, 672938934, 177093186, 447943353, 205455607, 818385155, 433938779, 578905100, 172916284, 542902143, 114955125, 41158113, 832432568, 559181816, 938773329, 735234649, 237450111, 725476648, 158732758, 611484341, 500742467, 310937091, 864921962, 8973763, 736977528, 893555186, 952096941, 867836910, 944769721, 836223816, 588061913, 924225269, 955621391, 415945601, 907371236, 609792624, 77286002, 985239132, 500722882, 132850903, 340385682, 832336257, 133150046, 482251428, 518347202, 328724279, 513856531, 568791971, 139244494, 871821540, 797848791, 216871586, 959847622, 583953760, 658832368, 547120037, 424739427, 545889240, 763740202, 564630904, 117185761, 190703836, 604654636, 993789981, 197492929, 360714031, 293071706, 845738610, 120661086, 557532887, 499374537, 401625268, 557791321, 112302182, 726413953, 165092490, 541632577, 880300443, 546090248, 746461205, 361187193, 454809342, 674034658, 237637322, 331612902, 636341138, 956607670, 557516215, 913226363, 912557006, 458230740, 218175403, 194811171, 43579889, 313022076, 518649240, 65562823, 693277248, 528116909, 120991070, 928849834, 577017283, 162453980, 630084390, 772426852, 458497178, 93715155, 674039933, 91453390, 527476595, 861034007, 832215908, 167547238, 609340782, 331769838, 375243680, 390722132, 214951196, 771616645, 701855998, 3530299, 112393733, 994104818, 130637757, 274058916, 131602480, 47799468, 504691910, 309865857, 892549937, 10427027, 853447106, 973776357, 60331779, 597825036, 571676192, 713001904, 930743768, 957817991, 523999862, 92237064, 262507051, 447468532, 618823336, 745110100, 34909962, 508714331, 549473425, 246643712, 914331003, 7871936, 901843872, 93921525, 382033318, 613387756, 591290914, 80091175, 661459035, 341756317, 435401983, 760810404, 365112853, 580078567, 67730740, 880387934, 734822137, 921373169, 2801129, 777942510, 752409120, 283298641, 467372921, 396747321, 898280736, 453013594, 162349862, 76235176, 736763052, 619105144, 397455696, 467335349, 607948557, 47947392, 852274321, 888041368, 199387652, 256998841, 831234706, 151371095, 492664963, 942513998, 513118478, 655184576, 174808601, 212073767, 29123051, 826544103, 479369017, 752483898, 588274055, 338572740, 765249045, 685571915, 60963688, 439844963, 694333133, 643710225, 602309307, 829847053, 11633903, 948520153, 753698161, 276334988, 504250684, 264242954, 796573973, 475748178, 333582280, 152869057, 180598313, 119798804, 561705958, 902577479, 716338503, 618649471, 605555729, 675425809, 740551665, 296554398, 899284808, 763538813, 395452389, 563157488, 654973901, 228166586, 706980889, 702445055, 320260660, 94783673, 331775027, 1650138, 51469412, 20854351, 497652166, 903888527, 957764575, 132133341, 83224075, 98935883, 395254462, 85175116, 890091258, 244709640, 408299626, 311741518, 704510306, 844476256, 780636450, 100104370, 924017549, 776000426, 31809610, 996984897, 890903183, 165148946, 818566900, 15378093, 309910342, 203305305, 345888938, 910964759, 399094926, 544362202, 811482389, 967890076, 541909471, 545911049, 67990266, 954423897, 17487207, 162652413, 970980318, 216780587, 220340929, 698613383, 712093604, 743078551, 509401776, 905787824, 763691091, 291421918, 187325901, 863309326, 330074981, 753233300, 455212130, 112551138, 706766271, 361598579, 954258076, 229814205, 126348724, 919409928, 97723224, 724133771, 989128805, 32805358, 518593410, 46336671, 360247541, 679655437, 508138288, 929283691, 37578231, 805588125, 382244681, 981103857, 938839349, 913423026, 439265284, 470598068, 305511223, 444627470, 610972161, 814880401, 901538944, 938114093, 689916804, 949671677, 574626442, 606866523, 177404156, 282817523, 339889095, 340286835, 376707618, 187164743, 963042165, 617224182, 902342824, 660715465, 430199166, 557718493, 948000731, 84452469, 937777041, 926893640, 679006878, 659088030, 786685289, 543235720, 854299856, 644676960, 18651418, 872719571, 922534700, 462328784, 807880056, 111464552, 37371573, 547500361, 568700187, 551680785, 315606611, 201692843, 571868746, 433295234, 822477128, 686883522, 682622356, 987841015, 220286958, 433842314, 331161828, 470616737, 47499516, 828009809, 578330384, 762485736, 513779704, 486499101, 144935835, 783344054, 719060833, 440960282, 208752744, 455784676, 554217564, 80398585, 582548504, 840834585, 888450365, 153610137, 744821924, 898290618, 142151233, 735936340, 197881504, 273785218, 52706298, 800120834, 565199052, 130999638, 908013946, 812456358, 401979825, 158585013, 105135148, 839956198, 367358619, 585719025, 329770301, 5905581, 342678972, 219514892, 374187977, 533559502, 725642383, 890886413, 534262717, 869819893, 426611561, 680568992, 820459218, 703536757, 175174257, 270926955, 421622702, 22885777, 394213726, 112932420, 639575273, 614898387, 389395341, 295872978, 624819949, 212064223, 220775004, 728031792, 313941812, 663710880, 921616428, 867677589, 673571287, 259774134, 68507761, 674043010, 100013721, 139209938, 663684046, 865667531, 747358952, 675223895, 516257569, 151078375, 96709443, 995890210, 411144764, 778830652, 620260805, 945955261, 315405751, 905815971, 379878624, 216096215, 144893060, 339020288, 894736529, 415066836, 597587597, 58997104, 509474576, 359085229, 745427757, 214750089, 629908776, 68026553, 275515316, 87811767, 975565230, 740098166, 506146708, 183613070, 724317350, 870629919, 39035845, 476057281, 529680009, 60215069, 745011381, 294028923, 886367631, 212322274, 902749855, 925207767, 561782679, 38660602, 370655525, 154387399, 988533443, 136747977, 265451894, 133168531, 238590006, 330297661, 800103000, 940009322, 581637996, 382523155, 180973, 661719761, 154164966, 625313249, 473973257, 854790042, 260719890, 540481593, 540227347, 97362743, 927282998, 77901715, 454487254, 72246558, 784876938, 521029027, 51371553, 807533160, 461688882, 257181604, 998628349, 810877828, 55461097, 612358075, 329851904, 805980226, 65909044, 143788696, 174939705, 524293693, 601666945, 699529652, 450287539, 530350696, 830668660, 941463731, 223132087, 957249352, 761596763, 717734560, 615207891, 184675620, 845791834, 339121538, 647168446, 887185012, 922292381, 430057503, 295215442, 598962789, 488393662, 133604648, 374329769, 201091810, 176377924, 384046233, 530084199, 785018274, 859794057, 775327799, 117345321, 113258248, 169020669, 481004446, 206908786, 24115116, 468220742, 419095596, 957738287, 157751254, 121847324, 338122781, 313771061, 625923315, 596797748, 173531894, 84512799, 999683268, 92588929, 761021476, 362079616, 287302715, 915238102, 942293680, 233434860, 604487399, 591982239, 365152377, 661707394, 550445071, 488403574, 633821246, 954633223, 861788589, 92917278, 617434187, 275202628, 574649109, 406961183, 781482450, 261304739, 364920056, 932371337, 559685789, 680839953, 874831869, 835029573, 649892674, 419996197, 133935566, 467621785, 209668598, 770838620, 784300757, 194607587, 571793690, 663051877, 335986150, 639574425, 675463826, 14771968, 704361034, 729631814, 411504128, 626991241, 747704331, 650974946, 528582809, 48128457, 42645428, 472387398, 329752506, 361258540, 591133650, 463117037, 501046005, 817100347, 94272805, 806781061, 142351767, 486489598, 347345319, 987491136, 974070095, 299739106, 933085411, 283829253, 553660857, 563170308, 834933781, 283876363, 675195263, 577349531, 466337289, 627242964, 101399922, 933522338, 91614133, 490329557, 922532447, 259467355, 586759835, 11701347, 471308032, 65284159, 535174495, 165575035, 207778248, 223113633, 265971025, 952157876, 97643863, 785969017, 831470437, 730975446, 199486153, 821100865, 883651514, 1222074, 118905693, 874876058, 159176879, 969697109, 814504296, 216575194, 317614362, 530806565, 860545412, 921762050, 112272649, 892957330, 454970285, 506661394, 851329644, 602416668, 567541476, 104531301, 81208170, 482331308, 747560953, 583345209, 725885900, 366949774, 472431410, 650630710, 527425358, 276126896, 564241568, 455896074, 976571645, 689086805, 980630519, 2163863, 4028450, 381332051, 768028739, 621862568, 629607608, 981254569, 239151046, 523439731, 679923869, 15874998, 838950211, 767609356, 723179525, 235410860, 162139374, 93105162, 748852276, 890599634, 418316914, 742415816, 25977889, 562813526, 523374937, 940197834, 663323767, 388576303, 354638438, 130476234, 365177113, 625361191, 240067163, 601515120, 406172823, 886687638, 795994878, 247718277, 779070325, 924850851, 602024265, 743737851, 261912030, 255348098, 723250150, 437765585, 307050793, 597702005, 975101235, 544767393, 224207160, 722825217, 472006466, 373804340, 368982716, 737583923, 554614854, 772727856, 868219083, 436069492, 816078696, 231128319, 878817567, 173811384, 837565489, 643129536, 319902383, 574293983, 236959623, 714165276, 330783510, 467881960, 508501371, 712446244, 523107366, 162824731, 689082499, 560237546, 371322180, 872191521, 614863442, 348308704, 866655652, 745742751, 998956475, 463554193, 681972548, 945969189, 762765777, 371635011, 62590433, 748169891, 173393355, 611162694, 551305601, 387759769, 155252312, 392229620, 467932592, 328026508, 546777858, 659165425, 91326333, 963724826, 80020462, 162290733, 669123715, 294647785, 398050541, 608526144, 997879889, 664823336, 45819509, 207176391, 529940208, 103018891, 617163701, 890566211, 380094036, 993289405, 591862962, 726927876, 792691719, 316806240, 684506107, 838532388, 905963225, 75460168, 512836314, 362223162, 872795177, 473873392, 497204030, 723750465, 481553312, 503021823, 16684048, 225380548, 55331816, 830846958, 791521518, 59783803, 86587372, 921142481, 322585951, 899729248, 312734252, 222491678, 156776895, 928003006, 974391041, 201097854, 780618052, 766442424, 620114816, 872231517, 940060086, 105807199, 81868230, 641687945, 672148374, 167610766, 71973049, 679440288, 254612729, 756375182, 634170271, 834825014, 5101504, 772095832, 540828689, 10408654, 779255431, 150774523, 830574875, 539686295, 712668189, 267394789, 345789173, 156845122, 961438810, 882218547, 797303981, 956139987, 124753881, 937977990, 128689726, 291652481, 57179998, 777807436, 653358839, 725016254, 463340663, 609377795, 523597218, 930882862, 609195001, 590627434, 203918480, 851204035, 934266220, 984032134, 647102602, 493931891, 462717223, 402092717, 962587333, 269585940, 148761000, 666738976, 490800481, 389642574, 663352993, 768404396, 863500242, 934920951, 74080019, 958647779, 146942338, 442586288, 209266470, 643525298, 17675803, 989349645, 611928325, 727184042, 903238954, 243513088, 964271055, 451825478, 200390939, 892305307, 491385621, 639140497, 618929821, 926426095, 257571628, 859455578, 604130669, 591117998, 672081781, 500680298, 727418861, 736163207, 115881572, 505014087, 700764724, 604906074, 855711193, 400883427, 254294203, 569971249, 13880675, 732714269, 727314876, 650550625, 649093150, 839592102, 587713604, 314515657, 374837009, 401475564, 849376437, 448427562, 910698510, 484943168, 466502879, 39857859, 239619298, 140303540, 22628780, 608622827, 908608395, 869992182, 606719558, 825400931, 328479771, 817105800, 158918321, 466240889, 874200369, 508363514, 608957630, 223411772, 20481233, 900655052, 263868770, 317108434, 300753412, 33514466, 480086933, 669498764, 990650481, 760608127, 351969553, 61894792, 982157260, 447301336, 118301850, 678537131, 954305460, 816553206, 563748257, 220425258, 720004832, 626426431, 695375344, 562758807, 198456541, 979476345, 501661418, 162595998, 413143052, 10244401, 584186433, 928379955, 628992302, 790844614, 680448201, 118778276, 296513420, 768558621, 467315163, 363122589, 791615190, 98208282, 896412080, 266103725, 841810423, 650395783, 660582697, 952867192, 462236650, 670596827, 611290672, 903481074, 110163759, 542316147, 320264585, 806824390, 91414029, 846241052, 270675454, 862700148, 840533845, 75844601, 577414644, 369907995, 359420864, 278561712, 65930061, 640754608, 620646632, 650348939, 432007560, 195295139, 673063847, 18149788, 401047959, 781649346, 470895357, 173747634, 762701784, 671079780, 536503999, 353585093, 705604442, 123121723, 171208424, 888698192, 398119890, 274623641, 879911472, 537581144, 998105370, 689741174, 791014498, 589249369, 86301217, 230613313, 940283519, 924655410, 836820292, 442983125, 297784056, 648485101, 719321526, 607348109, 785970178, 998985752, 499182897, 410611447, 752819629, 337997257, 317389761, 705154031, 305585563, 657124777, 877879246, 305064774, 651862128, 443850655, 600925908, 945184721, 412028643, 257275607, 93986540, 170082116, 750845965, 844489896, 526341943, 165364687, 415789775, 611188363, 286091802, 546163571, 358695362, 701756997, 934408359, 205980988, 601144711, 235917391, 716762628, 349743980, 406437105, 77820442, 397454837, 869708284, 583022802, 809381989, 901101577, 256517081, 599096740, 491273570, 717781146, 720453615, 425768107, 804006938, 666582971, 418850767, 188153499, 201569622, 991481599, 110690294, 989435814, 41294472, 875038518, 734842517, 145506705, 864541709, 292186626, 791622565, 679741031, 346264944, 572554015, 194538460, 409303609, 343973256, 46032097, 312509444, 512773117, 465328190, 738521770, 146811957, 643369503, 672037308, 50842902, 702555408, 476897526, 93295034, 241481855, 43652177, 650987180, 519487455, 759287590, 582125127, 450491897, 199996855, 283937441, 149730671, 555353723, 788597574, 9092212, 378861436, 963444283, 109486076, 73348496, 66476245, 593687781, 660215268, 831138157, 536177519, 1246629, 174619695, 327719904, 315967995, 665343500, 478950594, 673632248, 842541502, 50529238, 986221234, 115366706, 126787974, 418410772, 944661158, 407166048, 811215238, 530853028, 684291233, 136340296, 984529135, 567670262, 110955116, 269935250, 888689306, 620529560, 284525080, 500770227, 111888521, 215906729, 74892311, 291312182, 680953530, 521528937, 450860877, 759233096, 466213360, 222065780, 617590597, 235902207, 725278935, 898288689, 903178047, 916639178, 932146577, 370568826, 338352871, 18169524, 31470869, 498934158, 753862416, 85360844, 541760724, 859293689, 459183307, 765510494, 450505009, 679346119, 358846252, 296449687, 125240150, 359868965, 584384685, 832351178, 786703821, 281306320, 650944920, 974677800, 560795785, 502322482, 671928149, 787721743, 594054474, 132182855, 375301990, 880072652, 699163732, 709839774, 687110741, 497633980, 665341103, 944709408, 425168841, 821479954, 698301058, 215004785, 829119608, 810604242, 137669520, 714583561, 377168085, 368749833, 946288294, 41032424, 829096840, 465856899, 339667473, 395946012, 797050324, 570917426, 597315945, 518714736, 185250560, 842721214, 895738603, 195463950, 706820396, 264980530, 311075758, 438656662, 322370866, 680324402, 238250002, 252387731, 423133393, 61170514, 468098019, 414966587, 511201508, 554211317, 480632376, 815472643, 361440602, 761072609, 733211398, 320203815, 851304024, 834521096, 182968241, 240141924, 211216983, 458345448, 177216957, 504048474, 753677543, 708898810, 857534367, 834604401, 4685390, 63786352, 592163154, 93964487, 735455537, 154686354, 198082807, 207082056, 460630433, 910089044, 454018805, 77246526, 206032320, 700855688, 316300767, 886523015, 846503878, 996149649, 648576077, 346103511, 944576769, 863721823, 90673597, 950434699, 596831601, 160960764, 634900499, 763998070, 763113859, 127499027, 167424531, 871738682, 614021837, 207169115, 213044923, 23547684, 121768198, 127882952, 897058615, 960097893, 202398111, 310828807, 717257269, 538680310, 817380010, 27087547, 349503450, 333952566, 819486278, 831619676, 718233818, 996297677, 820210226, 155272381, 276731005, 356691658, 189134210, 15433848, 542241673, 731442361, 782221126, 821065228, 282949520, 203363190, 781170687, 560360206, 915051402, 534672338, 559092636, 178997168, 136727697, 379610110, 327578084, 566541232, 728691589, 994113493, 415080387, 359263095, 596471742, 191170501, 655991985, 512183749, 588488520, 240988592, 248380477, 178074930, 91071701, 161170903, 957019664, 666103803, 86999117, 489532314, 767066786, 864785741, 415144135, 940912276, 497078625, 427478182, 393090672, 319641763, 839039237, 820102524, 468034698, 289134430, 525462372, 46273575, 404033085, 563740682, 895593419, 958188203, 881513951, 755370135, 94731648, 726693771, 612690786, 590738103, 597503986, 423368349, 405759620, 973440878, 963676592, 208853493, 108865494, 336113051, 529149573, 275730850, 722689552, 663585259, 141916407, 79405427, 915909429, 579834765, 834709587, 993327591, 702711163, 665711851, 137344603, 763149396, 343955240, 473626864, 335639929, 823895860, 547289356, 693574718, 490641813, 459088426, 313387011, 141981545, 148631966, 575455848, 408024880, 652411198, 724782803, 101102997, 236493209, 558439588, 845022977, 892498275, 813234515, 306518155, 253483975, 868667801, 121921525, 310780752, 88805925, 50997039, 945870451, 201145694, 227170230, 13381163, 953467379, 891900827, 918918159, 243756497, 546324226, 231966623, 909933035, 7039571, 698130889, 257415131, 786760019, 697921473, 422690305, 473500579, 969716906, 861909692, 971785295, 521988187, 26270368, 329863336, 955663920, 587648322, 804062073, 996106121, 340847426, 945776580, 420771406, 924311845, 499829738, 117709093, 831265223, 529819504, 112172952, 216620911, 22448771, 444639092, 636179115, 250342417, 138395878, 246992659, 593246725, 822195816, 130299868, 247870624, 602705896, 737987196, 833057671, 640568443, 228100207, 119932934, 317091051, 342449526, 795845182, 255217875, 692986919, 584630098, 958998244, 791214036, 883492369, 989463117, 657874689, 373606655, 539179730, 575827950, 84180742, 781776372, 427492225, 177792897, 819149663, 833115406, 93793502, 375142248, 279659577, 192047286, 443137866, 588797384, 359990979, 249079784, 283191991, 971151744, 282307114, 444627390, 818724144, 538857406, 125598584, 925165558, 884465746, 846078850, 572943691, 609899852, 677328821, 712500193, 626408075, 845022359, 912158558, 354569676, 733370328, 221331537, 393064371, 934572843, 573530433, 192358805, 439756709, 773706509, 834282862, 7753320, 408739810, 415229960, 325513422, 53936305, 336936786, 409308169, 43409819, 431364403, 195730873, 593915152, 878606093, 919239632, 464878693, 891736246, 708369385, 915000381, 880761133, 23286815, 789075158, 79250597, 352321864, 217434203, 276684859, 394293061, 947499845, 852398019, 405202172, 93066539, 544467967, 263517925, 73487374, 390542140, 49647809, 679351210, 595655029, 806582869, 383678400, 724039547, 105918094, 104552875, 429150038, 148804763, 656297714, 234166013, 923350423, 514136027, 83025993, 997188231, 713290525, 500875055, 88900529, 874404941, 959583449, 516379014, 226450271, 80335809, 289538157, 378846883, 343344729, 254969772, 279210198, 862328359, 348326459, 714980885, 822965830, 985626418, 142334500, 864621132, 72408554, 370780072, 386810604, 541547333, 478609022, 596092560, 878165680, 898777443, 333096984, 520015564, 729804897, 57513117, 605366539, 269786832, 587198779, 525082745, 684275632, 332217778, 401454618, 912698114, 765399749, 620604533, 315839989, 368363402, 74179779, 898091367, 679369537, 483866925, 380903407, 487728754, 47639114, 973986363, 253008626, 135641147, 99416278, 870595988, 400761834, 375355112, 902559529, 526425307, 916142876, 121273145, 605213469, 514094746, 833245688, 39006986, 450427219, 253982092, 663519201, 62326612, 302966240, 586463077, 562205107, 2682349, 345349994, 614290379, 54033993, 247915120, 972844326, 441565091, 507246362, 272514495, 315528109, 574372437, 714919, 54362464, 227515567, 457203091, 387063740, 726860678, 35439141, 753315440, 699159070, 320063011, 695978059, 465305319, 204582047, 899029057, 278887663, 542124130, 563914440, 761800593, 3046326, 786954531, 392911800, 478583049, 725099052, 42478771, 610412069, 34418631, 121197272, 361329576, 32304976, 809185109, 464135752, 936628070, 73803035, 479750342, 458227678, 126710672, 811509258, 621685997, 121424723, 715286785, 156051336, 810461447, 572889571, 764213994, 138778460, 15239821, 796135989, 113060517, 262494952, 279033150, 103839173, 801104971, 609403196, 935478306, 365720011, 732600487, 275701202, 890853908, 70046252, 980492934, 905792696, 119747158, 646161697, 817665259, 492608068, 997058188, 92006521, 584904766, 356137403, 116081303, 348893542, 819288965, 156686886, 162122464, 542760692, 249611274, 447233718, 590118117, 614452564, 683873095, 141453252, 134839494, 509308099, 13833966, 33907153, 281600719, 210882475, 73961478, 212247593, 97496964, 156365401, 187298374, 966770203, 224295487, 34752107, 925435970, 407439114, 379833385, 855921022, 524983752, 656138134, 697264452, 378352802, 362824508, 379238316, 95919858, 229316156, 520252535, 699262339, 51196991, 312380093, 166540334, 556968731, 822721646, 826255076, 754093261, 268578633, 542063042, 454583708, 311648828, 940966707, 742157065, 356428417, 335222277, 816117042, 948514163, 614213187, 830135065, 556820240, 854519511, 25412982, 91982611, 512038183, 967837061, 105679689, 576633580, 196794921, 828911987, 903849544, 35542585, 144886216, 595846933, 105234103, 792045933, 333977548, 201684211, 764426202, 240469575, 21884302, 66954225, 135971416, 901881059, 563168923, 36262022, 240191548, 735342427, 15164853, 515392901, 781523956, 230372145, 534818607, 163469993, 726488993, 352282917, 245908820, 138582284, 320791091, 231330085, 184605551, 256927234, 342919675, 220306227, 767947177, 424919955, 453090892, 550779050, 773116261, 150314450, 848166575, 838182249, 779906790, 756607345, 366733862, 445751919, 287981999, 831382499, 840938860, 579380470, 924435714, 72497118, 425064729, 925653559, 652184819, 945227693, 101167067, 99565514, 149647278, 754786382, 572416631, 684642552, 623848832, 453875531, 242143457, 562437437, 581554410, 323761796, 495097335, 837719691, 739559554, 339884355, 115698324, 837279136, 310207973, 81544442, 791335909, 750518901, 297447980, 92159638, 996562563, 59602849, 562344738, 60080284, 660032341, 257658224, 891744091, 433370439, 546036845, 656261379, 458342204, 482078909, 909283664, 84085585, 398948410, 479046987, 673257055, 205983376, 942107814, 550947127, 893061991, 407457955, 889601781, 352256110, 14651570, 122461354, 242965056, 554569045, 167606822, 211049943, 683902339, 846195931, 211223044, 682632282, 240600303, 488202201, 983556551, 977799808, 373139666, 548721020, 761019865, 737109185, 179852549, 372794284, 648764011, 759738622, 471758247, 744662014, 21612519, 324407876, 53748308, 847412392, 101118069, 969905361, 387225991, 825728303, 145525422, 271951847, 601597742, 122471313, 320975842, 788211437, 540314602, 414115397, 528941733, 951622631, 989573184, 212104480, 712250376, 652003802, 879360899, 331313435, 182734667, 542616573, 758031829, 9889336, 950769590, 218419849, 533555493, 981120171, 790534788, 240098922, 432953499, 148528152, 818396217, 969956146, 356624254, 728897799, 86866592, 789136264, 355094257, 965282575, 49509918, 564735126, 650239266, 58716868, 808306033, 397792085, 869327137, 245902221, 740960535, 28524319, 999499101, 698516898, 504059826, 696748098, 739097945, 460430742, 455952310, 372277133, 904168608, 510639491, 846851972, 835345463, 926721760, 408779227, 727268102, 231048453, 24651623, 721882273, 868581470, 507861701, 404081604, 400117978, 823835226, 521580138, 379450769, 612350696, 255648508, 86586446, 138816751, 559145470, 399926752, 871809023, 408119050, 678697524, 32612253, 370899453, 427254357, 187090453, 207617837, 628232054, 612919652, 115838379, 209846461, 357306828, 978486691, 145465500, 261401397, 349156602, 141759435, 234358762, 307313968, 362296252, 804277853, 649533094, 123492868, 649003905, 590290274, 579857231, 667272362, 762617518, 953280763, 282750149, 187349475, 235006534, 999326241, 646059124, 709950180, 67540494, 350351651, 442169168, 561687584, 831122534, 75283762, 157089267, 329648548, 382899233, 980583690, 75114835, 926127487, 971933027, 646473831, 537115420, 990840410, 645051701, 134571438, 857873090, 640181268, 148220497, 345296680, 333904400, 646017956, 314090353, 913217941, 71560199, 913762821, 749242502, 197443970, 722801638, 477278872, 460968134, 703669372, 366089522, 497978837, 94188094, 974876027, 450049330, 898589666, 406935331, 690009754, 905406120, 354762513, 121890988, 956891270, 713577382, 179622925, 254801116, 77685268, 565695376, 729784735, 446052714, 693084143, 881579577, 409722303, 950052309, 52569774, 136204996, 990901312, 393730439, 983427234, 121999679, 740003551, 103488525, 444602590, 649856942, 721332246, 379210221, 808571282, 958942582, 311772023, 184245521, 245047214, 380306165, 832296474, 808776205, 453509453, 815852376, 668642576, 93597834, 136179082, 158065894, 145564908, 571717436, 345762153, 453108330, 408585557, 360319633, 557904599, 542731011, 691887659, 260009996, 281462332, 470199840, 412565818, 22231531, 112616822, 104188676, 785897199, 305841790, 610353314, 968499268, 924675229, 881863638, 302127755, 81536743, 361133088, 93354319, 528065966, 286103608, 356785935, 978129114, 785975433, 395197764, 739431001, 133719643, 446760453, 117556105, 722793657, 810748952, 853231878, 757860510, 685347863, 925359239, 827566340, 90021340, 387811935, 957675647, 556536369, 618736637, 548577243, 273737190, 574360447, 151555735, 246342599, 789406476, 338653974, 743911741, 568829819, 720550812, 559015744, 549171538, 933685741, 406844115, 85444189, 364612841, 346132857, 933079852, 358007502, 390472236, 381512168, 22960746, 346245216, 3093192, 600857434, 511205107, 109240211, 791899536, 780821585, 764020619, 826052474, 350757721, 794417793, 678316131, 780057938, 144833324, 574357260, 819479192, 414020762, 609857644, 963661139, 814879916, 543733915, 392221859, 445397672, 48228030, 362770997, 261371435, 77887626, 603486717, 308537042, 207884698, 869910041, 517865316, 426744511, 306122785, 91302085, 49636547, 69290935, 907147413, 614066327, 856605662, 112924618, 793458430, 281851328, 560831547, 627918396, 358780886, 773153260, 300476326, 93010145, 760233894, 742734780, 711665726, 530178614, 386213762, 789047667, 962777430, 147872790, 945231959, 114107114, 128250966, 492903631, 292656929, 124175810, 659929955, 483124531, 235272138, 265829332, 90195673, 552399516, 207313613, 320577433, 687293386, 575230767, 613051873, 970235014, 802327496, 513374445, 334794470, 47011698, 32642315, 779233094, 827795442, 719778348, 661202466, 69179034, 719278994, 544966657, 243333835, 292366435, 567779932, 626986002, 258515116, 209156864, 352828036, 512693454, 614787226, 385620918, 198777086, 801404312, 360114984, 991934231, 71240165, 801906699, 748742908, 822964543, 816304188, 150964597, 278618397, 514018498, 185516189, 343546773, 489955952, 528611059, 456600463, 703017808, 724786354, 378669321, 655280414, 945215678, 704856863, 553598686, 871959812, 243917087, 945648804, 402730223, 11650230, 883843564, 91192457, 213997990, 85240553, 632768215, 25599184, 33123388, 367331407, 465075599, 537482331, 978833489, 205083671, 49096354, 700061442, 446848472, 13067459, 211774076, 933775963, 438342120, 245758773, 893913443, 181476928, 653042824, 98797292, 115639604, 600212196, 304038199, 313170700, 640088815, 433437996, 381119611, 425891882, 500788454, 698504655, 886737540, 338930353, 265573893, 923620162, 540212694, 842230764, 472261301, 954491576, 335160610, 709226073, 241703432, 856464950, 366938206, 348833149, 649944870, 813496724, 562326786, 540687202, 46452020, 674097212, 780454820, 942405725, 928945310, 667078188, 377332128, 275361510, 462608712, 959531794, 870959667, 659418106, 992079095, 211655989, 761942554, 228131058, 124841149, 920986006, 455545360, 249416456, 528293254, 902594832, 611941085, 52332182, 613812467, 411789468, 382707297, 586141534, 643149203, 728776189, 407447608, 308028936, 925478399, 43322460, 519535007, 752416281, 9330930, 633268409, 518593549, 933543404, 210671714, 69659386, 44637718, 991269727, 551693891, 350601140, 546939936, 458212772, 671514971, 994040001, 991068661, 668548070, 356719956, 789921000, 198181726, 581131759, 319381354, 331551587, 547872191, 960030930, 785198919, 360903550, 391354521, 340987346, 566634746, 687998072, 65158529, 453788719, 889080868, 869106415, 4690799, 152569425, 835923137, 579107843, 571493870, 281325834, 827170811, 319716627, 569519927, 440677616, 11574802, 557542095, 480267728, 683980326, 233770783, 682618332, 900763841, 257670652, 544516723, 543728385, 897010371, 195942551, 181226046, 291071254, 742582182, 804091130, 91343997, 216772844, 910540344, 22414860, 114139838, 217266194, 946392781, 929399217, 935291608, 643524411, 86668079, 255853770, 371960652, 874042777, 818899628, 296929728, 630528633, 550408786, 562725799, 33787076, 639287185, 648519968, 925770017, 290970199, 435017970, 578765389, 696193692, 159308267, 327080351, 524934623, 595993989, 777668119, 595055419, 721981244, 706567068, 630347615, 251533496, 871597424, 620427572, 106014862, 668689294, 321622162, 723519251, 1556720, 909149165, 648688053, 805185803, 726236503, 436984554, 162702740, 7162078, 574241669, 53738476, 680732917, 777745922, 380904348, 819007793, 330187329, 220048740, 139806335, 467666050, 404978828, 774800919, 301180190, 999813337, 588713503, 310795291, 769457459, 177172932, 472465640, 390726677, 36371235, 889197272, 460460446, 448012099, 817335758, 968087690, 486606536, 110255295, 670945696, 26544241, 808930018, 467152299, 812206155, 58535094, 352614992, 903780023, 684000649, 102371010, 376096881, 947545573, 211639272, 470300995, 633517279, 615811433, 78202307, 790819029, 470664822, 310217139, 870076811, 223503857, 708598931, 59950079, 516966253, 745510413, 179191453, 764286683, 354578287, 778447064, 998373053, 712602159, 774031017, 690139674, 930250557, 865478614, 938943379, 110518645, 445976544, 874685482, 225108983, 165576366, 22298115, 424005022, 393194574, 242272170, 246758435, 432904030, 65280604, 972099772, 214752109, 224957165, 404755769, 10313408, 922143921, 692037207, 91436397, 132875300, 928935649, 126732217, 560984488, 699188021, 553902813, 515191580, 829567212, 481621209, 962995481, 213409882, 560726035, 603150972, 157760348, 198909360, 246348347, 903148052, 35892158, 714058906, 67879385, 845376806, 835415107, 75777586, 188929428, 509232180, 247684816, 269521946, 754855485, 430481595, 156743658, 531262347, 947764210, 852076044, 870789194, 421852759, 621235130, 375263059, 957536020, 929923517, 849160690, 566381465, 186539876, 830395214, 524212032, 968619675, 321500692, 679524202, 581935765, 742327779, 261310319, 634346284, 756394006, 626237811, 465153126, 982807948, 361653957, 766568183, 433367726, 939531874, 248285265, 769379939, 682642079, 120659985, 737153318, 79751335, 190305059, 317349566, 956341769, 248462654, 191997300, 661532200, 44944027, 614117607, 96546061, 555798366, 493166899, 314159583, 142474830, 954195897, 468580419, 425947686, 490749818, 843824870, 602821869, 41148550, 857125133, 252883192, 649834282, 497174359, 328379348, 223130735, 986511960, 784065231, 790028278, 93051171, 858321564, 994431760, 257014271, 115169174, 886789435, 311944858, 445001274, 682796339, 774872409, 375640067, 533990521, 103331881, 653413678, 980622516, 63927897, 129989690, 752205339, 285625575, 119034266, 281176003, 86473071, 756152859, 501359583, 696758963, 694080852, 657017228, 690284082, 988725908, 975940279, 605448531, 119538936, 385874898, 668667215, 418949591, 349189688, 189129785, 720212763, 471085617, 133501132, 889462820, 378786929, 818312573, 5165823, 87274487, 110519108, 549929419, 900918833, 879331783, 358698541, 579161793, 402095656, 383566383, 876444, 231684622, 250277734, 837987862, 465566899, 972433169, 51667107, 335578727, 863686071, 596188812, 356813868, 603345789, 41237765, 801919257, 674238995, 45956181, 292335139, 501355037, 975394276, 915043849, 903777844, 698044965, 235542077, 721443796, 359058087, 558922350, 684212396, 332834950, 961002358, 960605740, 880986868, 423407538, 642273327, 761052242, 563208263, 777625293, 686640775, 880325199, 613688102, 965180940, 664536508, 187534205, 745366084, 204326617, 303538653, 527428802, 504767172, 323647190, 667759807, 286263028, 226211066, 130652374, 819863061, 863391585, 905516886, 90438273, 551162239, 409937157, 378894701, 568118363, 409972284, 399259655, 814565510, 451111148, 753446503, 899991803, 516250539, 603206644, 240761246, 274387549, 598317795, 506561702, 757972172, 316894480, 921026187, 626508184, 956657521, 448509775, 848363880, 785428896, 504781846, 557910090, 53850157, 718890135, 600617559, 178938466, 51452283, 175724663, 33086134, 463226804, 560471094, 942882410, 660997914, 976294081, 571436242, 390202084, 581171391, 23099505, 688642180, 564762034, 97179392, 470274608, 381438926, 711411155, 294186920, 958837661, 548684108, 820226916, 13539711, 123750530, 23009086, 547981087, 817509847, 265473633, 500592338, 409272069, 96939994, 352229777, 253301076, 633476017, 540202501, 929130953, 816721399, 278505057, 228512726, 447457078, 861318578, 48350549, 787491255, 372865505, 330020612, 895842105, 612893141, 984052217, 708629237, 133129531, 631616384, 181707205, 60566897, 598147374, 143900101, 690996054, 260706181, 297509519, 589831992, 516606361, 135972620, 479802990, 367303783, 2551368, 354948256, 33318991, 380744929, 255927285, 215533510, 793763140, 97228839, 61102509, 816265068, 96593818, 503425300, 923101236, 661418162, 224822710, 873673600, 833614667, 538080620, 476601084, 970417157, 267226692, 216104221, 316448963, 203609920, 350222985, 911153557, 79147956, 248238761, 48449357, 767033038, 703360608, 606107937, 565775004, 120672322, 947347509, 532764345, 37007764, 211628752, 30259131, 577389113, 508041875, 132234141, 717900104, 115893831, 828267222, 667141454, 429430082, 936730065, 645118245, 91601150, 683668299, 520398788, 620248837, 851378561, 834174472, 917756376, 169336858, 220970167, 472086840, 496198427, 647963881, 234483401, 553726790, 113238341, 90068209, 372806482, 480581161, 824366934, 884893186, 625592248, 207879360, 326598975, 70550679, 687281730, 603113535, 74962141, 899542332, 284949104, 368076970, 975080736, 860868255, 966587862, 16318443, 452359427, 715314524, 377918315, 796296676, 19074826, 632401594, 203793467, 452711856, 644559980, 63866082, 691200037, 125937862, 374864235, 990548248, 796133928, 6629407, 376818794, 357024114, 463287467, 398427609, 923539640, 455510608, 906502089, 505723893, 107924022, 543965963, 479335266, 246912842, 329872180, 577195216, 696657714, 426416293, 411780809, 943978915, 768398931, 108573563, 778133452, 94815540, 371575185, 406343135, 387462182, 117812886, 439751911, 164515468, 808154279, 8541990, 564899298, 508633519, 988958023, 874376065, 133638498, 132479969, 8122098, 419431287, 428358029, 132405551, 786529011, 630734264, 384418500, 59074148, 150102056, 826128092, 657273532, 566875095, 830350676, 966111066, 94968969, 235572153, 9513617, 635869507, 29242389, 354073753, 153770851, 342839629, 467617374, 365433964, 43553778, 89995664, 291391514, 225217739, 877616405, 98818534, 165366118, 317098726, 24742127, 814672861, 855204987, 436638518, 358861089, 560877342, 889871886, 349657123, 344958157, 858632311, 54197305, 951345083, 580002897, 717017571, 25411912, 632803917, 688359959, 376273966, 2542869, 170152371, 846715681, 301669113, 137088155, 783758398, 897003637, 293743620, 383114699, 426266711, 875800043, 702133310, 714395108, 314522362, 902058406, 855318623, 705025649, 311125587, 945759977, 179438994, 819602942, 587482702, 205131276, 860077672, 808504569, 671053102, 206424079, 613805623, 417447713, 494101136, 20539121, 783627954, 514645195, 509833373, 326588346, 144472051, 795891728, 294977759, 782224365, 688998917, 951693349, 308626423, 441608730, 574019346, 322269425, 651583597, 952456231, 553384523, 832846088, 936761560, 557541583, 996643237, 103898168, 931828990, 883381685, 936176075, 296437147, 691202425, 95825059, 240392243, 692054919, 723490385, 568152567, 373736476, 375109827, 689369773, 78751681, 968094914, 985489439, 655199708, 652819687, 101130160, 725973600, 7760638, 931432587, 135798554, 911924111, 586892309, 34524147, 521507435, 806163717, 378446532, 896492398, 467604322, 615724278, 396388721, 246243689, 630504722, 900196996, 738326405, 912208410, 93611752, 349557532, 649517436, 277335262, 403034414, 724936708, 967099115, 49950487, 100025120, 982903703, 582193686, 942661811, 488838784, 826926278, 636684674, 848744425, 110833528, 509902581, 953623509, 475108530, 758583379, 817900012, 347033530, 615187265, 767435264, 763085270, 134472285, 122270977, 606716439, 670661297, 569196198, 849314426, 292501832, 119005579, 381769464, 327755975, 805367129, 12070053, 872365848, 165110215, 212336157, 359092369, 383465187, 196824992, 610925839, 663826386, 898681139, 876610689, 715221210, 963259333, 43948610, 371516692, 607568577, 624533451, 169486144, 87857942, 551162894, 502902312, 131355212, 384740279, 560545191, 579198664, 623646398, 199648814, 72442911, 571185011, 865599303, 515862748, 462271566, 716140405, 982730896, 689465727, 948999047, 224058446, 154366227, 688447727, 288352927, 993122790, 332246582, 682799733, 746158589, 216236490, 124109957, 767410044, 286370440, 864593627, 335938902, 982159983, 308076342, 593980185, 55072370, 312160135, 825103987, 393048156, 292507008, 677052454, 687011566, 127800486, 672731001, 319324743, 214873772, 743512429, 743093365, 39322183, 772943647, 917706511, 998969427, 759734665, 288196013, 818530205, 798224070, 917552832, 839320987, 547282557, 969194963, 220701797, 550588091, 27671827, 367627075, 91061142, 367831653, 490968631, 395512261, 847784846, 174049742, 464037385, 967655543, 370985751, 228927013, 837082962, 972009010, 9254655, 598650536, 496226191, 498540609, 638918038, 953935183, 143668140, 263628889, 284123240, 377686872, 937382935, 34422553, 873267308, 86088627, 456296298, 726200256, 451067542, 739150867, 315934513, 4000514, 605828020, 903230631, 942504626, 316590855, 71156099, 285563722, 142680732, 806017397, 171531415, 484379691, 898836484, 525119830, 766455331, 428524871, 232494899, 447279954, 229571576, 191201338, 975789927, 659888793, 806946630, 666085686, 402980606, 318139979, 295527752, 460299102, 209316928, 584797066, 830971790, 436007035, 537773816, 357196239, 208006976, 392825063, 104980655, 807940813, 48977619, 969522308, 167083796, 336626823, 735763455, 871809819, 729016621, 978982369, 83485474, 149445452, 314851077, 194682818, 627778224, 39469967, 103737125, 760600891, 294251781, 542134014, 76279178, 740889731, 67399435, 700891514, 723424813, 221597963, 512194559, 677251645, 742947414, 717028449, 809988192, 910584249, 396250032, 330192262, 326813031, 461244333, 681976479, 471399611, 668424751, 251411014, 525315625, 113914575, 270930396, 516990749, 56308035, 6061374, 518772366, 854695166, 22538978, 107203833, 699448496, 778695993, 581967791, 196548312, 970944847, 120971702, 904864463, 344567809, 62278466, 359775363, 500912923, 884699687, 502475399, 422253867, 619424294, 66261453, 891787909, 120348233, 595026147, 968323464, 230094641, 631574873, 319163590, 682662674, 59129669, 149369699, 843587926, 643983766, 906848989, 254877268, 362272277, 538464910, 484895678, 321630806, 234234384, 731757936, 733055177, 667606345, 376598929, 369646725, 335521626, 727157445, 890968419, 513012017, 151902432, 549068638, 936336287, 533802919, 189716704, 436181320, 152311107, 196825445, 811763745, 353265339, 33007136, 173156842, 105196295, 599225579, 650619325, 53650868, 518731716, 177347343, 674710038, 765372011, 819695953, 235521238, 645774014, 917101770, 394178804, 354862121, 835933486, 596858009, 522263949, 165336946, 267069744, 932971383, 110597717, 148892166, 35297221, 511408975, 780690707, 389314616, 766255410, 688354166, 269269492, 278276593, 516385166, 943864023, 852466325, 997962699, 980152082, 664592276, 961864102, 654258841, 460779767, 135364133, 625304452, 585192094, 120017831, 866161595, 374849918, 709728596, 77236350, 492543438, 259835141, 526361020, 343597715, 125949979, 22006062, 168593664, 246749502, 748971699, 795902724, 898390605, 603929888, 546001111, 154594768, 762220273, 437419277, 14330542, 781335066, 246292592, 159636962, 161540819, 712887399, 262614908, 798260010, 194838580, 868974336, 80628900, 635173730, 174199447, 962649496, 865336173, 419781164, 474266760, 559341503, 398059624, 905604229, 802573622, 17575041, 343034632, 677333928, 268002434, 398494733, 343212772, 539018414, 528787327, 234796146, 686060179, 818693756, 305729521, 951442307, 584675840, 667721365, 569316501, 626181230, 914499560, 939465843, 988095153, 234705332, 464707961, 796907395, 349059196, 431055896, 395821679, 355676993, 410427771, 63487840, 899643882, 373031952, 81948777, 16892464, 199393470, 833121786, 984269034, 419824135, 748053356, 700353887, 938951259, 699661108, 734359617, 772576250, 236958077, 988494146, 354796062, 881266563, 645354984, 893564057, 789839987, 840844879, 400981650, 990421478, 172603144, 166370054, 611667795, 188687222, 677478373, 662765655, 919746323, 92059413, 128426545, 586020135, 430117166, 473826457, 147527941, 159490092, 140293512, 915105547, 998961064, 259035236, 495804551, 240455213, 724814227, 331229373, 432334087, 4370711, 836427578, 158805712, 91200122, 345231242, 114572465, 758658815, 369616335, 719777276, 5682049, 165686025, 833977707, 524511165, 279583475, 521478455, 233774361, 963872064, 233626432, 182942792, 377650687, 170093378, 684219041, 593427759, 940792596, 784776059, 139703093, 211255365, 268954659, 716117540, 78180453, 233933975, 21586318, 809261875, 251784899, 366330443, 42568682, 290768493, 11159641, 301818753, 208335975, 790268383, 601823764, 22082731, 215367397, 408438979, 591270316, 20694527, 429155544, 427143537, 676664661, 755077987, 546406376, 407350138, 83536801, 778645993, 64413560, 900675138, 533982612, 370718105, 335606827, 24082360, 8953845, 999877343, 975011191, 704858083, 2367760, 958627727, 394381369, 583603999, 433326959, 657058275, 712725571, 407063006, 92866495, 458739670, 70409519, 256859425, 489930615, 82795738, 536928212, 868465114, 711396637, 916103348, 683155777, 146904210, 411243923, 274711574, 364310891, 433530240, 102991077, 284008998, 488107310, 459536725, 434136492, 727915088, 282033728, 171984203, 420831174, 224207356, 242526372, 788104925, 33987242, 940362480, 576562126, 422483815, 886101250, 667159246, 145555853, 609557310, 793132202, 885598629, 534504488, 807910841, 959829197, 930055586, 550720760, 301615063, 763149536, 812436271, 687951352, 477207253, 233071624, 867193563, 598693517, 270588481, 465307504, 298561340, 84259122, 536135688, 309519075, 423038152, 318545790, 973988304, 799226275, 885213530, 941737768, 734869885, 904669663, 614562134, 599447058, 32923805, 754994982, 771880123, 135266352, 731801269, 819085719, 149538832, 691894210, 687966340, 424936382, 665006700, 442162811, 623216931, 556396088, 938312019, 994338790, 419605763, 107644975, 202571803, 608697068, 166903614, 473068262, 609880493, 58004202, 677159044, 318786589, 35147390, 684434865, 703724335, 467154123, 883626949, 76965386, 871391738, 368758006, 751566079, 431956341, 58641275, 425987765, 575049193, 908989511, 361648222, 741345242, 523300168, 299928046, 276654728, 50544983, 124554572, 965721057, 837553342, 526935328, 983778659, 555534419, 318886248, 824718354, 915809228, 846530330, 632067341, 313024744, 542912052, 284952307, 358546227, 991390535, 631440805, 481500959, 999392647, 97601582, 483043224, 271184591, 907711642, 343577025, 335754014, 141903109, 528886904, 304368397, 828106314, 997408664, 563568381, 995399052, 946123019, 657328621, 988021846, 37207296, 680730210, 960521466, 929505408, 890591590, 161021019, 513280007, 697006764, 136932569, 509334324, 983969677, 38453521, 344600897, 483228078, 758484966, 306275651, 453425197, 341703063, 673007337, 829950341, 712876435, 30178246, 315611507, 507565988, 772705656, 823743639, 320163708, 93786983, 613977749, 984797759, 38615902, 15879381, 416294080, 165667886, 714000678, 809335369, 475359505, 178584970, 467937319, 109907340, 253676021, 249472398, 361319231, 149818511, 14453872, 812947432, 137124894, 248293961, 748213859, 870109388, 675001820, 701478961, 406587108, 355477963, 171203444, 426145583, 856008514, 775363819, 539430292, 729862612, 618005096, 689605960, 854659009, 436890585, 893423670, 798687323, 507609777, 139074648, 105116209, 211592788, 490628474, 984643355, 574389524, 829961870, 15037688, 625959181, 294615738, 15390189, 926326111, 269535225, 963425931, 246627508, 740861566, 37709058, 480041102, 939524286, 235117207, 879487841, 308736359, 347605201, 922104388, 787578600, 773648976, 520293153, 530641166, 960456802, 903817647, 600177731, 531661369, 58922961, 623745957, 85233761, 346519823, 593956844, 412042249, 956228493, 712482164, 321110731, 729583752, 703633602, 24081079, 528279493, 905106882, 679520892, 349552289, 466463153, 886400857, 84670549, 549936686, 847270725, 361881260, 742233395, 911742258, 154939035, 838241011, 769879160, 206444320, 395361456, 517112128, 173531350, 790762826, 459831711, 644593458, 660232352, 833450446, 261197865, 206168371, 997082692, 547091223, 553085270, 127426139, 720656775, 758572853, 130863410, 206467639, 385161573, 471215499, 371925953, 630360883, 828736615, 790786562, 405680332, 795081261, 488865311, 990638795, 104657314, 955423810, 175971340, 808632571, 481803725, 789051902, 985631295, 174200392, 486220642, 124579045, 119939074, 907321957, 133893903, 302562290, 806703425, 631298254, 505304988, 301134358, 757217138, 86949714, 749985622, 834354879, 688133997, 781615034, 455657127, 433768381, 289615129, 254728950, 938633034, 451576706, 664619973, 960967876, 650921238, 345492714, 838969053, 531269142, 655062160, 726658544, 602984200, 382600134, 412367368, 679130455, 864509726, 301054792, 87658014, 229026797, 968792987, 560953459, 738542696, 941869073, 766391255, 296260300, 607064058, 985378399, 508937316, 337727835, 529305255, 148771733, 951540966, 370198439, 914584280, 883675847, 106324077, 703010155, 443710149, 64077123, 592882447, 704411343, 886655528, 600893732, 936331787, 245392632, 380772524, 199500505, 145267492, 518036836, 897269107, 191717942, 313511239, 44756377, 394112150, 397241341, 558706934, 78294539, 770209075, 24269751, 472023210, 475281921, 213149740, 804856006, 934197765, 931674340, 984513321, 660520928, 266835325, 771825114, 961603498, 870064470, 564391719, 617826553, 542495432, 500031488, 329240823, 755670121, 407522630, 535901960, 966548777, 543406455, 941826779, 394858038, 286585255, 871163286, 476954948, 569949933, 246536707, 710302304, 198381727, 546256564, 120318914, 646526098, 240730985, 439370610, 225017988, 776634037, 119665025, 208677381, 884432463, 324965831, 730080999, 28962128, 620720130, 198771578, 10615820, 368473212, 927001313, 423278683, 930152908, 453498588, 357991840, 538284692, 611894986, 340633509, 443715814, 925964938, 865810699, 257934181, 170904219, 906346476, 438573111, 927265483, 786285184, 383966987, 93942076, 951824532, 170766860, 545427812, 962492101, 194696316, 37379179, 360553026, 516746554, 932425164, 735444313, 357629555, 397322180, 279089111, 325073030, 223098866, 160901050, 635087582, 194304132, 226100920, 593043831, 462085475, 424582413, 112288873, 16174062, 115332415, 904668351, 819937881, 835899434, 524781089, 494503542, 208112900, 576708561, 142789837, 526047135, 929817280, 529827045, 525155149, 947190450, 627888574, 426505815, 870882123, 398136399, 193899535, 85450635, 659161054, 917415247, 703733723, 414235630, 452719771, 840863101, 741758499, 426714767, 726553489, 700956123, 693437010, 52507051, 23532020, 865023058, 786591231, 51293403, 383937177, 394621175, 354099602, 277800366, 72647644, 310458942, 866338066, 514191244, 373706038, 841907433, 930926746, 595186244, 430795131, 756876993, 775020168, 319493067, 15489494, 711599701, 501400508, 709445405, 779766130, 598639633, 763584841, 803509296, 117264945, 48116167, 7247153, 215705221, 370167120, 83371950, 446057410, 157450732, 406883357, 767489755, 94364178, 919557327, 301793365, 396686762, 866301893, 319837448, 720449703, 437930888, 413348192, 349419837, 724620138, 500965159, 779089795, 685618076, 572618959, 675487330, 841792495, 434929375, 143879056, 561437673, 658022526, 169491613, 659367720, 337160845, 228117137, 342936436, 936953293, 419939227, 991434020, 494784153, 184987698, 299852449, 23854400, 478829678, 680331077, 864841004, 536801020, 797290930, 773781289, 457627321, 998974773, 730010060, 416559531, 847255818, 72858893, 123721623, 628329113, 929116080, 191548279, 956891224, 715708935, 789622250, 269818153, 143132721, 319676013, 261544385, 50748080, 194931327, 203449884, 793439282, 231222603, 764996540, 110217476, 433084427, 19443640, 594887190, 204889188, 185839714, 316339472, 693042324, 133457835, 382540328, 871868804, 375908946, 795081963, 155037022, 808684506, 406131874, 697110607, 863403865, 268032038, 765717559, 676805718, 351330532, 511702693, 629137979, 223989050, 706850930, 382296301, 197193120, 349401896, 928744234, 732558973, 498713950, 865324942, 318418131, 873173986, 550895404, 89118638, 154178615, 560114414, 127651469, 278721159, 714547076, 16791021, 638005196, 918747693, 775750493, 710666528, 969091300, 861121320, 555668148, 456429450, 2374488, 769612282, 393694214, 638356203, 429132354, 106641719, 656737074, 716944608, 29315072, 966197205, 396084053, 127835630, 529576502, 226997937, 124071522, 260598745, 346781395, 777495903, 879365009, 480913041, 323539234, 931109786, 1902677, 533069665, 44330443, 96012078, 111772324, 994629606, 525924500, 566481604, 521520669, 585703083, 937848557, 141522406, 508844144, 127023041, 758972755, 575088215, 808181158, 18656950, 546617134, 860238259, 450767829, 115001241, 301360536, 263150389, 24664210, 230977086, 324860216, 829180157, 828416363, 199914505, 440509634, 171258599, 910065907, 334845839, 398312837, 650070658, 779828158, 591466473, 761609378, 236582255, 903571047, 593246062, 911882067, 744687616, 240710878, 305483963, 442953338, 549415551, 164695547, 905556609, 773043519, 605737308, 978923802, 883201209, 285659340, 563892504, 733832803, 925802478, 199693188, 489079941, 40675145, 133031606, 639895823, 890902496, 355861978, 128541163, 547605907, 493333177, 476841975, 389131767, 943391532, 429801578, 946729959, 846244997, 169390869, 219596066, 275877246, 489637209, 655461688, 739882108, 481523263, 471713361, 950913300, 803793131, 377786256, 72836215, 27021260, 444578617, 429185908, 127062732, 175302399, 711912917, 873114622, 885240812, 697360626, 36368554, 55915454, 48584642, 224654929, 995253286, 622837395, 172413882, 542460283, 168304981, 751496773, 177538723, 456904136, 13529156, 77089986, 760969858, 836966542, 464667331, 973561523, 840617976, 974826204, 615655869, 442979450, 854598516, 105976116, 140262785, 992460494, 364373042, 384457494, 576677666, 486631778, 246344131, 669906079, 577476305, 643631575, 52576857, 107582553, 442176828, 668466251, 658758871, 538167805, 462429021, 121140647, 18910346, 729515733, 266808930, 714533587, 526650045, 948318211, 833503516, 946388482, 310463158, 900726484, 823134304, 559872024, 181675961, 798134078, 84532509, 392903926, 678540213, 416729830, 949415688, 385913774, 166975063, 309950661, 579914086, 583381531, 634576055, 811284310, 383056512, 32101245, 654861963, 847053436, 61475265, 433746751, 623422074, 805765856, 230783448, 805498380, 827413821, 440108774, 158217126, 768683444, 171765642, 449082619, 598259577, 100768995, 725630518, 703583676, 236883576, 47867840, 737934418, 879788459, 476457371, 678275607, 230538111, 183616501, 696991113, 734553170, 990554958, 740347789, 915329279, 635671320, 17469054, 61918261, 930671248, 369376013, 458215077, 996691264, 920431364, 97430877, 992047777, 928857862, 582002388, 1253926, 179519499, 858971844, 631454824, 472329494, 678255594, 457799122, 346763796, 292466159, 81945428, 751934132, 353362163, 816115003, 82620108, 488584591, 782983383, 976105750, 733282660, 169062083, 296350077, 845686391, 699742123, 988498281, 865548504, 75361390, 630247313, 911111887, 900917960, 859477795, 376728227, 624802040, 803155647, 625644438, 497505053, 803271937, 403187761, 110794730, 617377914, 317268464, 215046463, 5912925, 154055801, 476937909, 940840737, 273436332, 148606984, 810812885, 306119718, 370967454, 309799070, 332857379, 585569565, 335767237, 13831091, 80394545, 191435826, 517215877, 624986860, 449884512, 846684755, 716971624, 83268232, 979797783, 211001592, 707084505, 427255050, 945064418, 336736382, 867771194, 260119961, 711569889, 935123718, 713692553, 483751411, 642765632, 830092217, 260053519, 632816350, 16639279, 433529981, 856363171, 929438461, 334940577, 873687319, 803493358, 260655874, 345938950, 81551012, 321952459, 242096921, 371802344, 306328239, 646889485, 616589454, 409629020, 406916219, 291868958, 886021497, 213278826, 80230482, 564387692, 479454533, 778359785, 288836457, 167340051, 88370178, 201188953, 110230262, 995691367, 269408673, 415152335, 560488035, 466256669, 718821796, 847014228, 309918280, 430901848, 430075411, 687909009, 334106892, 892131143, 500453989, 234417459, 676020671, 547669919, 716591436, 929806221, 338768244, 600069222, 918468504, 61142360, 714135327, 782116806, 277495269, 354178286, 139267265, 844092362, 394941103, 286436434, 872127148, 973791708, 583303634, 115629528, 356652848, 821606697, 217810417, 692567353, 175556370, 918712077, 740957478, 110416561, 211689831, 260165036, 419297180, 757094183, 686241788, 753330439, 696892947, 618474215, 666920166, 811567522, 461477985, 31501993, 851787802, 894431519, 235516462, 717275242, 742557085, 962704634, 179879817, 77455929, 553243918, 50794493, 332261022, 147347544, 555170893, 218037601, 876622468, 793341335, 291436395, 407479393, 695787874, 588628558, 590328843, 671097218, 694135178, 459257943, 626777444, 999949715, 234120153, 435307388, 71919945, 635525432, 869720954, 547687668, 720461358, 908574122, 998035761, 121319216, 533390465, 645938717, 527993633, 242276080, 90473044, 424269671, 73508389, 473497710, 846321946, 759188605, 990193800, 177856742, 545216988, 373778099, 273715538, 824310261, 252751639, 499296857, 191116986, 353955731, 227275389, 177893153, 158277420, 590476406, 710970557, 191627665, 835445648, 895977083, 647820355, 298908484, 167036983, 482409781, 386128681, 865948667, 82215307, 66179681, 675539764, 421022493, 958393484, 277458584, 886326957, 46718127, 86409513, 500292639, 809996058, 357641080, 382970633, 259297196, 757939379, 35071264, 815314189, 13809137, 469632868, 350213795, 107518450, 332473779, 314540221, 379402235, 141902849, 620017992, 547801391, 873124694, 18035705, 318560951, 825996616, 221136639, 729109688, 809091738, 858853288, 322555561, 409325832, 412297129, 73653670, 363404303, 289665564, 309921388, 890700560, 49008031, 809041750, 341289557, 381953136, 456104540, 22186363, 465495151, 103801780, 70957042, 719112237, 207009705, 799061581, 471684072, 144356824, 712473031, 973597891, 350669849, 556929814, 474561070, 699074165, 625319140, 345496295, 310683737, 250743516, 204814282, 89261381, 451868561, 839577913, 646360353, 560925586, 444311196, 57370550, 633917699, 472696523, 268965327, 244215871, 217066768, 974229885, 524625443, 57390091, 940123041, 897714256, 333345176, 614308853, 578712167, 339490060, 903438075, 594511561, 438939777, 396616842, 840138362, 569346574, 544305280, 712774049, 78442644, 92183658, 160850761, 581247818, 220576915, 856541929, 297699217, 377261166, 624795500, 17783679, 457983138, 379280004, 430178413, 199808652, 779135375, 360359589, 228760044, 729578593, 680700138, 867140860, 855228908, 328490516, 843869447, 956260248, 5130675, 688954066, 314033157, 761520274, 177143588, 28846650, 23454164, 620044513, 957159272, 108354239, 475613963, 925836751, 607695027, 344862296, 731559264, 831396880, 354504409, 217121708, 813537616, 150237482, 441192990, 625806559, 518326735, 59159868, 645327494, 529672256, 780884592, 21162375, 843176127, 222418939, 27343287, 973464209, 203937203, 256231252, 10138381, 177948275, 859937892, 874757298, 278588883, 460307708, 55066361, 510327240, 426642860, 422960457, 100372742, 182697730, 779160195, 338139533, 701611848, 84909141, 69346458, 809408079, 987596288, 127481151, 744197125, 960847014, 222399306, 383411529, 521496186, 468941830, 824808826, 248354802, 315252599, 62136451, 287648545, 157477349, 412621140, 879780266, 639306059, 437743558, 899247408, 639201155, 676056651, 153462240, 728768272, 710664593, 351516201, 420421864, 900744347, 867217281, 352863026, 452055940, 256595853, 268694648, 352431802, 238053780, 562476531, 421810587, 137836072, 485201216, 54103154, 36916525, 879763912, 447104750, 918807248, 692339199, 965733786, 178746149, 581639410, 962300067, 48308764, 375158175, 602441199, 572824890, 248020892, 56443894, 257957380, 161610609, 933897080, 114051666, 346829105, 514379297, 654230362, 852698664, 553321035, 553913521, 720508201, 341596656, 504405276, 692224112, 538433434, 279183151, 835613662, 399769721, 605083829, 235224583, 711159669, 934065499, 213591612, 986963735, 354690045, 2220541, 445984663, 981922695, 316013027, 524650958, 636010752, 642300682, 924633181, 590023122, 788823270, 457333199, 886394446, 912092933, 758153979, 756635638, 409778518, 757889509, 579298109, 253638118, 501247366, 408625212, 238639575, 552482040, 879900382, 107324729, 780868769, 156538433, 751986215, 592134429, 472913786, 961837364, 145186696, 692967039, 637567508, 747105141, 667178067, 256332391, 806036161, 593358372, 432954458, 308596542, 373505780, 720005882, 349498848, 651762790, 222641175, 542729390, 548174644, 426493243, 678356148, 718207767, 132511976, 640683875, 123979194, 370264916, 734983301, 896889269, 371189507, 409896036, 399244780, 626204800, 238225944, 147502026, 260954821, 477790827, 991321477, 726145685, 163734130, 711445650, 808436599, 530253334, 401592448, 60924042, 389368563, 70387088, 323240434, 948005835, 757604857, 301074771, 398290803, 71685072, 807814345, 164951632, 778243601, 964388442, 656263194, 160443081, 353812459, 176091735, 960734313, 837598386, 662192280, 201287250, 817598187, 744792154, 64722730, 801198629, 257415428, 759920091, 370977685, 804909288, 66636510, 555007579, 709339913, 415712160, 752702654, 155738521, 18854747, 215101216, 813292655, 374024012, 2282256, 878896880, 472496380, 882385668, 202892317, 628801658, 355364973, 651674429, 486120749, 971533863, 518823357, 715729803, 945347944, 105169138, 15634643, 861753270, 652233221, 952923201, 781505715, 505956681, 756808779, 648163037, 84812723, 428268312, 893924579, 81012694, 810865845, 830423404, 162528390, 142326938, 694009613, 53850413, 927358995, 702607616, 300648547, 482874505, 238290981, 240887162, 803149214, 927302809, 761595455, 939176332, 433550953, 656922296, 416901014, 257638214, 392587635, 911884121, 312500599, 495215930, 2558805, 868828097, 661516664, 487664447, 143053803, 672624436, 457061891, 941288155, 185927210, 340921814, 460007976, 181067114, 280696646, 526941761, 717642712, 608574919, 266398050, 907163833, 523453504, 49563755, 400308411, 918499720, 461801330, 727261059, 132212094, 704733398, 165419168, 608450746, 355251531, 393980762, 491541616, 94922851, 534675953, 432271985, 161715295, 11256274, 569405707, 336757433, 941002078, 359192981, 495278581, 652244689, 672886563, 532477626, 120282971, 908535368, 698337944, 120645819, 363934194, 241236941, 74747525, 118398044, 705954236, 98725505, 75116898, 557624209, 329395331, 411085182, 143542810, 995192828, 499291443, 399394154, 416952618, 786141656, 271739967, 131417353, 565444983, 865652171, 880262211, 983561581, 440311188, 558505094, 263442251, 573416058, 430959782, 389685318, 222294897, 553361709, 844843706, 939388649, 949859160, 89487304, 29744931, 400575842, 621134287, 194716389, 929692852, 712075050, 754829204, 428267858, 27469562, 754983658, 866285876, 918554042, 959305443, 413032518, 743166267, 966167313, 384065337, 322595690, 197599694, 794448658, 978036293, 808045756, 936647866, 354374683, 38072896, 761698838, 734249829, 283929914, 643709767, 657335293, 426847741, 73006926, 533351878, 356189423, 787844493, 972372455, 473707275, 454059489, 244235827, 808684748, 10168770, 45707857, 371668291, 804896946, 642323422, 660903797, 38103518, 684280208, 954800207, 760789484, 166039907, 430508460, 966203367, 562807897, 812516991, 176611737, 172840343, 195927807, 909831846, 254011668, 823646764, 505440566, 641619817, 984213883, 489613670, 338484567, 411924488, 957045950, 813511039, 123950990, 899460628, 189102253, 20366672, 81027961, 129258872, 597597550, 649195644, 472177321, 897971529, 234842772, 815508983, 973191202, 721595636, 468677711, 792869821, 944957504, 390365114, 42098542, 432800842, 213679185, 983576903, 54151156, 426628988, 240098934, 435805476, 170202763, 303688215, 101392619, 497115266, 683661329, 44636380, 80328173, 773164836, 819321945, 14610924, 304340544, 296856384, 237852020, 262143488, 364208784, 709889869, 399273002, 707982421, 787056118, 48912218, 990778416, 595034544, 996263191, 35947630, 19705991, 69401667, 135632576, 780020797, 445243314, 905708078, 948974110, 507684514, 685899914, 174114684, 588459824, 892243768, 8859895, 538150098, 130566433, 167051357, 887155467, 878800391, 780214997, 789398547, 875587040, 561311815, 168760146, 817322767, 434915554, 917478723, 878750803, 545229308, 891724001, 162433712, 764003450, 761741865, 831421500, 315192293, 851325391, 137919883, 931928094, 318024636, 465137067, 324824683, 655382869, 289367659, 120529508, 41702954, 831178486, 773704975, 834789395, 704167162, 691890888, 685958633, 550774960, 95437434, 947830350, 788283793, 230482272, 213820310, 493281378, 657077205, 483554115, 993061373, 117258101, 776909809, 757162616, 704551974, 877470708, 394756459, 345389495, 463596223, 815446317, 165355345, 653023752, 678778355, 154128087, 271236894, 364565340, 194669857, 427480606, 19794568, 734924374, 677234634, 838557395, 972191058, 349552823, 975978655, 818405164, 7451850, 840874005, 507426578, 527556166, 798534732, 68825362, 729354181, 991814397, 686176701, 773902937, 738744988, 802679161, 658183096, 972050623, 346016104, 365455169, 779753223, 403763145, 788045966, 678710902, 961270424, 56028422, 792787802, 554877083, 82357995, 968692375, 152944259, 119519963, 170454158, 39840138, 952813509, 184692585, 371330735, 333072344, 959801486, 160434814, 712808476, 480318267, 561131209, 789787861, 705517455, 144920092, 897621801, 495458786, 177102648, 326077467, 380812705, 595064150, 5712157, 237295199, 62634213, 493949241, 688395884, 305944990, 389549905, 970286824, 354675078, 784206169, 827865411, 955272897, 782443638, 76036320, 556631031, 702174333, 125327761, 667633541, 795333506, 659248438, 621004812, 498396916, 637936935, 531606865, 671962830, 422731957, 509907931, 948860749, 277256396, 49575366, 424316926, 191123892, 530420632, 979845228, 296720853, 262720136, 25954510, 989133649, 403900635, 694326225, 845515237, 974298760, 305484674, 313066021, 116750788, 310688998, 516539158, 128822184, 648130597, 800044882, 928937370, 320135837, 952500261, 549976333, 18593540, 122532557, 8890796, 75317921, 966521909, 327203788, 697188513, 749557784, 745942911, 77619358, 113993096, 463236827, 440412122, 283717340, 189147924, 483988885, 321326685, 590975028, 484545722, 920738122, 754833, 982211377, 995560017, 980390983, 778718830, 348961249, 750328423, 12007730, 533089901, 415835773, 726419849, 606466780, 228371956, 750899780, 134538395, 54607764, 935569944, 679888366, 782612640, 691543046, 408007018, 454441016, 346965505, 65495990, 403068254, 380063489, 851295683, 535206421, 881473202, 528032687, 684045345, 603082128, 113446569, 295939377, 333766066, 5970178, 296202880, 303072247, 486148766, 810228949, 898308878, 74426728, 641705233, 947442501, 959641285, 831571171, 338165466, 61752294, 305620847, 32473753, 318087924, 939239942, 728130817, 768507788, 831157904, 444443001, 965606369, 216060981, 595687880, 451120602, 148389065, 317712093, 442418526, 708547631, 623690453, 706644807, 452891664, 846006951, 337994988, 750129226, 156545307, 718513897, 133115136, 973504356, 385802269, 909370023, 329559751, 522957425, 564774229, 848746565, 654108467, 17074662, 231253945, 80964423, 480485533, 343332415, 674052381, 355945435, 641529708, 815097717, 835576171, 657857682, 314296121, 824167590, 633110108, 686648606, 634827667, 316787749, 416374561, 394098279, 251810021, 917179668, 974621436, 904360336, 313093781, 232889431, 169957884, 452990117, 448195227, 662504931, 197572305, 517912323, 712404348, 906592787, 508395675, 634066735, 934052578, 880732303, 882161855, 55646598, 614430567, 363419900, 508274464, 7668063, 887500260, 949074662, 969375005, 924240912, 211907878, 940734428, 720586854, 695833181, 23496588, 493209266, 543004438, 447905624, 786583412, 332763561, 855652617, 624428335, 642636122, 387184169, 285817722, 922239021, 628410172, 334685754, 816074368, 893150041, 308468179, 651790507, 555225321, 527582898, 814436071, 176506648, 250451928, 408858996, 555390085, 728700573, 448025963, 918713593, 950505447, 582282034, 792766719, 42577361, 255770817, 380429214, 736490440, 109412426, 463569522, 358106228, 107555804, 596034077, 548309469, 231278553, 802686712, 872575652, 400982920, 470422299, 707797789, 808126937, 973860763, 885328923, 474209574, 262160643, 244385947, 196809517, 757564092, 237621371, 213911250, 524272096, 167447916, 19056449, 302474251, 243610493, 690420167, 931425181, 652034213, 360336826, 702691711, 561947867, 295633127, 292115732, 215240751, 404679336, 30233537, 371443490, 190127273, 434101804, 571299473, 755079452, 934973079, 817770373, 455757685, 450656636, 720447131, 270480080, 309893600, 82441280, 739157134, 136269710, 158356684, 33528363, 90207960, 761385843, 403709303, 306966780, 959341550, 514437511, 808940210, 419544765, 503484372, 685087860, 461286099, 103523423, 979722293, 287756751, 752039131, 360871260, 440124185, 291508074, 941737330, 43691435, 690892617, 778605332, 543666081, 31183210, 504334853, 256495403, 466358817, 925747866, 524619133, 869420065, 837052616, 319676619, 499450338, 850207885, 395991059, 845825592, 115183063, 789782565, 832184368, 46350009, 266095955, 946807136, 23007553, 263987948, 561836651, 649168323, 137944923, 131459687, 781319219, 181525024, 151487336, 478284706, 606509757, 893984055, 153417928, 41584497, 56272536, 496414429, 945094231, 761384256, 157040644, 450610847, 179340145, 235901713, 495157460, 873770569, 769418554, 660064623, 816664872, 922314650, 365823358, 237173403, 213547903, 502282843, 506827713, 207466990, 526473139, 107009857, 627564612, 73309359, 758584185, 375518326, 765683135, 113996679, 188563657, 76618443, 89454314, 158700033, 358507432, 749683291, 24436332, 242619558, 277540396, 317684279, 517863358, 575961753, 307026325, 354505885, 803674415, 687995767, 496247436, 624758142, 89333872, 154654121, 958234854, 85942307, 875656385, 930715345, 768287922, 230858223, 616239674, 819416771, 732223508, 235334358, 921043069, 459715141, 905061436, 1319108, 500485962, 455546615, 812227855, 394279103, 17920504, 785962751, 429027680, 569458387, 963176884, 983928366, 601841273, 497059802, 934142231, 345012380, 307429794, 155233922, 634507711, 742802718, 702622138, 91637856, 929655897, 853119833, 605334112, 146367830, 587757027, 192697519, 94104672, 417853936, 595119137, 599971971, 183183537, 873367499, 300447234, 869504742, 94797755, 644628255, 669099037, 170838716, 26087392, 978861745, 555784020, 932583406, 282699924, 631981495, 663269739, 212667506, 870101130, 869594692, 767138221, 476464817, 533253408, 415395067, 235048331, 206260874, 317443211, 1482100, 13469314, 718394857, 744690066, 430081407, 882921918, 933433378, 285716711, 147883709, 302807528, 566554128, 80882524, 566911300, 911696095, 56083731, 834853313, 642583390, 964534982, 324498617, 874857810, 554614036, 393313570, 419106522, 778685884, 950487443, 896870014, 225221415, 463547658, 565240526, 641897162, 599185784, 966809598, 208880677, 623048360, 161290639, 349979869, 468820869, 619009887, 358584435, 164853030, 843712906, 73357450, 99292686, 5171960, 886166183, 456518890, 589311730, 488688272, 813853983, 209270973, 857748581, 871144362, 401458388, 904866452, 147574973, 12620255, 846217440, 166574415, 97022735, 288374362, 345424054, 20050575, 231777173, 282256669, 315334019, 508123227, 502518887, 732672828, 421866781, 348854462, 175551791, 100328170, 116278993, 303033789, 770232902, 774223336, 983607250, 360063697, 507049623, 3702860, 707944815, 504456356, 884766420, 362869764, 359551354, 990157604, 546211858, 597723104, 895172179, 409646793, 151171247, 338677762, 131959508, 705804470, 981799685, 741879585, 836591702, 312279967, 459320559, 854324588, 342087070, 911563309, 505477273, 217675110, 386010075, 953870681, 950713213, 878991313, 542911095, 196573905, 813613079, 616976066, 822470088, 171680555, 144576685, 878858579, 540881816, 327897104, 755794812, 856011206, 774021796, 50608894, 273581245, 657391070, 948865084, 211947122, 924485641, 5251805, 918259047, 298293154, 715419656, 272224483, 570126536, 717940217, 313526234, 77201804, 920532864, 731433633, 600112251, 953841580, 402246945, 810115594, 187552120, 267828202, 674105035, 530254555, 667338123, 915548023, 788345215, 570590348, 588324635, 507670595, 497344759, 704999433, 781316387, 578334697, 282635632, 634541812, 580418235, 618951821, 693388713, 211951575, 113248746, 839456566, 653980190, 692760802, 830542052, 465230534, 825996291, 315829781, 323221643, 70192854, 121135827, 883576921, 999206898, 961273276, 211903274, 68025861, 782923446, 914954115, 737750472, 73775496, 613158997, 271182014, 673050228, 892825858, 939809118, 625243904, 717457196, 24439541, 622179043, 946012269, 857961288, 412577520, 948087039, 466158479, 931292476, 85439748, 579957238, 657600796, 858710251, 174475184, 286723633, 740578195, 706087361, 218919952, 510567755, 702635151, 385830453, 458006698, 304778149, 459938603, 899060747, 144589003, 998769741, 605274949, 310707190, 484449012, 235939541, 188081668, 166992195, 583621957, 878632708, 239574470, 960432227, 757983174, 154948391, 116378206, 536983774, 615343401, 881469834, 48160195, 541832297, 330065961, 787313521, 88419890, 232655173, 514528413, 688197355, 323274257, 477934531, 117682512, 707574782, 331653321, 292580429, 442373295, 234802138, 251642357, 14019559, 813465218, 603481373, 348620261, 629787496, 821297478, 59463608, 459509738, 252313836, 835719494, 384619666, 709928185, 374306678, 890859529, 46344902, 692857306, 886668894, 900036191, 2821774, 565860142, 871707440, 699016642, 530706490, 424351801, 328600493, 739141161, 467303561, 504620263, 40050941, 725186887, 538600945, 889950843, 645850728, 607393864, 965131269, 31329842, 654403309, 61331377, 407498553, 329139157, 540599598, 467837655, 49069273, 394100180, 345554919, 25916562, 348552910, 155210145, 146753388, 479388403, 590705014, 576188984, 825072532, 978052541, 89549175, 378162244, 563961726, 850388314, 55522678, 693921701, 105626466, 353887018, 464664743, 32994739, 251852184, 398039755, 374223000, 889900542, 865770347, 964128995, 139043046, 528024547, 371739322, 233426456, 992831145, 56830233, 104924615, 574573591, 712927159, 159653349, 499805535, 924445991, 850734147, 337965360, 988782660, 92999631, 753169166, 332068689, 248097686, 122485067, 576739262, 62806421, 695074690, 215242014, 722552522, 914632698, 892100405, 740383346, 458467437, 587562731, 363673896, 420145778, 644215140, 361835120, 426555552, 503862133, 469548805, 977612881, 929312239, 738465822, 584632987, 187197154, 505346601, 19720430, 979544425, 703452678, 783683308, 313218490, 654071927, 407991146, 300643125, 809281136, 598574998, 308176260, 737419001, 780952245, 414070116, 170203038, 76168830, 942778438, 168431932, 543961647, 36809133, 585965383, 813802249, 618903747, 908700373, 821760461, 949024217, 510663406, 688985865, 386284843, 436367845, 293507065, 656304027, 566858797, 142316831, 948911822, 61142102, 310928018, 859814271, 435521692, 389879198, 112814899, 516905353, 138945373, 935922001, 99248505, 296292949, 889750139, 305692452, 657837017, 884563285, 863350408, 894369674, 63296757, 361756857, 131802778, 288104883, 944236912, 556337907, 255320253, 367179263, 612795335, 54798866, 794068952, 516112637, 745156208, 143680210, 958867204, 998854964, 804132001, 300196213, 630443265, 511818909, 97844321, 488069333, 379567066, 916736557, 144074372, 443817310, 756095337, 248862189, 527584504, 803738991, 117015989, 296352887, 541633468, 579602323, 142812012, 977035981, 128100487, 386633476, 231844763, 603793710, 258001937, 501747199, 66011513, 890302449, 773879757, 833240726, 537135662, 950970225, 764692346, 859286247, 232776594, 400120558, 20975298, 97854607, 884351013, 921148926, 270416189, 767041330, 180305985, 703375899, 224157665, 556595276, 601697501, 56001694, 919438240, 649519677, 559711610, 150600899, 6280171, 997100208, 604292208, 464344334, 23224479, 52815574, 601950838, 180547192, 873661138, 830430573, 370948768, 759448470, 745341221, 189744482, 787807083, 113212691, 495118645, 720211088, 963189592, 725873791, 60065219, 859854374, 215197737, 484455454, 6152804, 982995182, 34369122, 479805347, 489351602, 688750202, 63533818, 652421428, 664891156, 614782558, 870502244, 373222302, 23867478, 435649633, 204692456, 955197834, 340429997, 311761749, 507406133, 865481597, 163967819, 666625216, 540544527, 27758227, 579963227, 13081977, 699882023, 143653518, 571982262, 464623804, 731577776, 856970208, 82305025, 921365278, 68122836, 63521078, 18414939, 99950028, 752035338, 850595619, 92446010, 232567492, 821729284, 541708422, 22224494, 588798638, 558282697, 752262523, 967705022, 73875805, 955066944, 594706704, 340570477, 80949072, 619891738, 225531980, 206261297, 758020066, 244757101, 464627691, 494953358, 20649158, 203936405, 570083560, 984144802, 482397358, 844193936, 947798888, 948082289, 969174868, 883194474, 877324695, 834884648, 416001058, 638358918, 579972635, 818374308, 224826432, 325910627, 176570309, 3335413, 896967471, 675983155, 791724669, 481076088, 382473933, 688600666, 774495617, 880451356, 378167960, 461748351, 47065043, 831467028, 743093820, 936916284, 233315281, 588471036, 908420085, 145716329, 323513835, 700424602, 456638115, 887423385, 550734485, 907290118, 829470033, 555801436, 870307833, 351211587, 795505155, 213496157, 128928195, 614271129, 73115536, 786710214, 500373766, 29756367, 769597235, 39942947, 681837807, 904529050, 884993766, 402878164, 296906525, 374451100, 512966023, 366620782, 280482004, 170480304, 771857922, 446760628, 168175892, 568307136, 78172362, 933753386, 781812842, 493168346, 716768560, 961744200, 214310688, 224340946, 758161177, 469812669, 201444272, 785436511, 831290925, 40779217, 98816559, 570550343, 820984961, 141584739, 751517354, 769968700, 150684871, 644403461, 379116075, 26386795, 261296736, 497867032, 790882789, 805276326, 257317669, 876132154, 825837193, 942397569, 849220798, 341627001, 95875616, 280106013, 382221880, 144030861, 772056847, 340419869, 506461391, 537215507, 132856170, 873075436, 513766327, 96960314, 402543725, 851089019, 63370587, 302707000, 755668687, 43845540, 906987282, 357440369, 733059624, 368068938, 185391945, 448775646, 981961842, 461565840, 520773159, 970520857, 263862012, 703146949, 874813216, 500585598, 963709891, 555296532, 667837324, 760183639, 362671152, 186050990, 546993346, 580173277, 573636568, 440136806, 176194, 477630931, 877606410, 987267142, 954143163, 748850479, 739284123, 73463130, 895688886, 92754290, 987477055, 201533558, 564098152, 184081995, 760486264, 825834230, 330780585, 920571074, 786143949, 759709811, 644835817, 821835440, 443225869, 973570364, 934328480, 296639640, 76877758, 140880542, 612959897, 709406586, 228493729, 158239526, 57058580, 451455467, 863392916, 20750681, 376915196, 753256087, 269762892, 1674215, 453085086, 356791788, 95615689, 946608061, 502169386, 66699833, 937907625, 800519292, 247040091, 475249256, 361683325, 485528911, 953514044, 229198374, 859315097, 558644486, 1505370, 566351002, 516478076, 876873018, 859322924, 166557958, 622851016, 325136550, 241823951, 324962973, 365444636, 929258139, 861704083, 714592494, 690846113, 120091710, 489156783, 224718598, 596206950, 534834442, 828112054, 241055602, 975110712, 881586995, 249907040, 860726812, 328413108, 758663837, 251246969, 155824363, 694979081, 940321780, 270942328, 18641736, 728923789, 430415588, 165006384, 130739938, 442400317, 125047155, 94690529, 187502694, 947063316, 43425757, 160105716, 676363460, 476365718, 476978905, 853886824, 910630860, 880269378, 287128014, 664617930, 980173456, 731625524, 484570943, 134295136, 712897057, 259836786, 938554700, 204463712, 367565236, 114215436, 651592857, 289924282, 302813120, 491815661, 14787301, 778836836, 921600176, 833995066, 678870815, 775863273, 219678774, 497238061, 213158967, 585643045, 420291905, 156841946, 677839588, 609735181, 318458417, 634135481, 96067912, 788904911, 793063156, 708225798, 160518161, 614223683, 896154406, 359893274, 739146964, 943509579, 668483966, 328749992, 770601270, 111677867, 488517199, 685926556, 863540002, 117653885, 143601501, 650402988, 803030990, 344306650, 136964002, 532805871, 252744639, 764117474, 806644631, 578520750, 950384296, 390365551, 528209697, 831854828, 480760290, 708926729, 651799239, 694189833, 913118198, 235414135, 888769344, 469521680, 804892874, 756117545, 267461624, 246890970, 644900652, 650253414, 618222521, 303261930, 830909749, 550915976, 219540445, 66779344, 162735965, 457783055, 282827711, 946700608, 62179560, 916661668, 572062733, 132913061, 260675660, 842732715, 586772537, 219075080, 585339534, 504479777, 951588281, 129935171, 218014539, 754356942, 506556880, 965987219, 113499696, 403532028, 413732139, 904241295, 786699702, 926976187, 149645627, 868145254, 506462989, 233712177, 950643680, 882062219, 155517278, 459392413, 456717603, 203658784, 667179331, 321167325, 495129992, 856019856, 517289621, 410733701, 462023471, 782003938, 804835986, 187003814, 918477453, 477343847, 408849934, 730371575, 79594344, 537431261, 985791258, 956371603, 803380287, 115373914, 510923834, 897177387, 100706525, 371558809, 327733208, 925592991, 868232513, 275782629, 335173158, 155776162, 465588674, 116105420, 764648206, 279438626, 16244019, 579086518, 987682510, 469287624, 532258544, 589114092, 564419042, 717802490, 406140120, 819622277, 380928086, 557242024, 648383434, 690601492, 158373417, 828218461, 339309769, 578740825, 192624726, 970045572, 293897653, 989945600, 262901448, 399775841, 2054534, 910018011, 944341085, 192126485, 285265501, 664506258, 180893732, 655143684, 814408795, 892039531, 766658219, 405976343, 968884061, 347627999, 536627453, 188925613, 195334295, 692873344, 190999920, 760210350, 377941026, 588278302, 162376617, 634440993, 875686089, 542542655, 224200581, 589496859, 755485767, 69342149, 317740923, 983680568, 694469562, 345794106, 925699238, 943359014, 23447033, 103412423, 490482174, 137548718, 849356088, 871932103, 618507059, 881613555, 8518248, 437376862, 391330847, 600143596, 235134436, 958770390, 478770370, 518975449, 718936772, 602272937, 179943542, 826538946, 74311279, 476579115, 362974244, 77611297, 332120474, 644868420, 953898068, 303956032, 457444154, 747783398, 540040411, 984895330, 907516272, 736760530, 124217414, 434836767, 344155529, 979738311, 18381930, 895102529, 158342917, 275743487, 105100226, 149289421, 551318928, 682521960, 189907645, 771550809, 488083868, 212479506, 328530307, 380665238, 74593393, 492730958, 66936373, 629213940, 367513137, 988364000, 776690932, 678528861, 387460164, 516717936, 277164799, 609758117, 201483021, 858076193, 825075928, 496218949, 356547610, 236243735, 95134776, 546555885, 559755824, 869378030, 453633632, 17616857, 570227873, 431206526, 596864162, 124920040, 46405106, 501332314, 421584055, 37957767, 572557705, 664799140, 549190276, 849709931, 836046748, 488971615, 134880574, 914238906, 170554850, 591158346, 351602227, 377335390, 374858894, 9523045, 671083030, 659234520, 311486335, 970956634, 567073473, 917815645, 518773124, 956815816, 8632415, 649110699, 767260027, 360770537, 527117199, 252207381, 183947631, 945746923, 758318436, 514872837, 591959365, 548833412, 913742980, 905755128, 659021256, 507003143, 621482520, 282060706, 931627896, 609069886, 87099479, 333957755, 614699587, 897831887, 263930232, 413070420, 691229866, 891467604, 935915184, 82047175, 122751624, 271190216, 332617955, 503349532, 878827140, 556966301, 803349132, 250034665, 815851624, 624188492, 883729074, 568300655, 56268922, 552821126, 160019922, 153173500, 209384954, 898680247, 874266539, 811470293, 406785272, 871668111, 566679375, 4828143, 138135661, 760436595, 674205737, 721764495, 143283337, 29683015, 121741538, 471132158, 81031448, 337827175, 381250513, 804216176, 950131489, 314596499, 415349909, 743378111, 404151806, 898813248, 171704879, 500190426, 196964094, 4958125, 89636995, 788564443, 763445734, 513380336, 429010303, 712791110, 403378752, 648642765, 291996415, 434788888, 839745440, 495863329, 910803115, 644693143, 573826967, 150692820, 479858213, 210877964, 695948571, 316721400, 976894392, 924083488, 361395548, 791891466, 650991673, 314790862, 534407118, 780435190, 665910683, 99083007, 871179858, 456064667, 30160105, 358560142, 397764497, 725774694, 348666811, 401221525, 880800817, 458672456, 554544688, 926725942, 16527307, 958567506, 161133422, 65452044, 890378952, 3758371, 441073043, 257850937, 865637377, 540637540, 391728551, 213306319, 355376473, 610127369, 602051102, 484841029, 11773789, 14034266, 529765130, 319033345, 951726401, 858204943, 148530879, 820285329, 535927928, 343260283, 226659140, 575060005, 437730, 184465583, 252469361, 387170833, 130247970, 270838315, 327593313, 977416981, 464148700, 700960755, 599121117, 612540011, 375009399, 258863337, 102151207, 856770998, 42782490, 324806614, 636491657, 684752541, 128447158, 506900876, 220198729, 323564557, 936450548, 210387960, 317370277, 402703018, 481245120, 455919778, 636589904, 114937651, 674568278, 443046205, 844098732, 106014543, 966961433, 283833039, 387688988, 732553637, 153205209, 836935852, 864676391, 190954668, 614641361, 350709559, 766313601, 752384156, 900797010, 641238049, 691273727, 13510575, 83154496, 948602252, 344368788, 882631754, 96504063, 762963760, 7336492, 440559624, 445875364, 577628254, 991265117, 574355097, 938815004, 944094110, 419820019, 90433566, 163699356, 896781729, 720227282, 754116616, 285476791, 758997015, 424457036, 674120965, 365971192, 63467606, 688661046, 636325404, 121471342, 671621983, 782395568, 416449847, 985419227, 505875985, 719758572, 720310861, 313245788, 404900282, 529214776, 154439743, 109770261, 151625539, 619588509, 934451915, 899737312, 181148106, 599353822, 381341371, 414132297, 64785202, 242355012, 141224233, 57416907, 474991372, 240263482, 248271845, 262605527, 218652686, 309573609, 545739545, 852326696, 157825393, 153967149, 706063532, 241290155, 760820396, 824102186, 497114580, 108462116, 939519185, 993103483, 569457239, 621134993, 896619775, 231400569, 475881764, 835434335, 588640748, 928189570, 317075667, 723199693, 462714843, 323060552, 772046557, 478280016, 275911773, 909712890, 569896006, 136179769, 230125505, 361780816, 195554699, 485944954, 689719197, 335391441, 912338636, 565682128, 942944523, 217359688, 36246609, 814074876, 901884492, 733519995, 208946948, 584659520, 671849538, 768409800, 211008050, 862639359, 401204437, 701115793, 666517481, 605326371, 109313854, 989926253, 104007972, 969281134, 626772692, 21962268, 101905928, 938088111, 569516698, 842066010, 821214824, 538593877, 9687540, 337895324, 607280559, 979998927, 929480720, 63475895, 876908072, 46559768, 226279444, 782477793, 223658679, 721467961, 265776352, 105522078, 285405960, 629083427, 28206011, 525568375, 363761826, 94034746, 339378139, 820110612, 224941470, 580739572, 934835550, 118697302, 674043604, 303116927, 88335194, 178145017, 738204836, 4113716, 470534023, 916765379, 885997145, 549954693, 236350926, 120885074, 740652727, 196202427, 477747845, 847745005, 773693058, 468521497, 479688637, 242570761, 978455222, 84414279, 25328181, 900119134, 292135155, 150864013, 869568394, 517954424, 50890309, 873686204, 167907943, 92921548, 495578714, 80876270, 273763543, 862119291, 832580040, 917502348, 60798557, 942479423, 284944756, 828192794, 421952177, 273463859, 70713914, 240502862, 661176464, 282155384, 369894786, 569825798, 586420889, 646202853, 437503649, 587526804, 330772233, 994247942, 884706389, 886144920, 908418851, 274151731, 650159897, 52341940, 281881570, 702745472, 81263271, 738735726, 231830933, 466582115, 533049139, 828644292, 168431692, 158346431, 459527614, 583005887, 948663541, 219072450, 490166919, 869046946, 82150724, 711421511, 219979049, 822812058, 814490364, 149959395, 700384701, 196208915, 448321373, 390593012, 806296809, 4079385, 623791898, 7003170, 402043493, 871013756, 902482473, 644318420, 391879006, 407123560, 560134125, 920651496, 873436595, 931553373, 263588630, 590702424, 861566860, 423905765, 358634498, 364471675, 281047625, 557989212, 455672707, 361242348, 813701623, 476401740, 125834864, 545648825, 698957719, 771422640, 757240515, 100809586, 621493286, 503740195, 415850734, 594579519, 701797160, 712261701, 854719163, 938948068, 594199475, 21148848, 790497898, 940204274, 97272102, 854602999, 399499119, 802070197, 964154892, 656512412, 760454487, 672714820, 196000047, 283332664, 661582271, 865147181, 580926189, 863415376, 414843995, 22356721, 60620421, 28083521, 764129226, 283958276, 588785431, 932283556, 458462, 831852965, 687100047, 169947016, 514204272, 975417057, 782076887, 687553115, 142325146, 16728410, 297395008, 331636525, 918659731, 836063061, 171973638, 866497244, 587576705, 888047479, 530770816, 735903149, 387450800, 360065101, 478900905, 670152988, 49676893, 505248019, 819043567, 232663653, 737889305, 859452437, 148541871, 857636188, 930778244, 308185282, 73267437, 574903866, 798592341, 15074764, 889776270, 902161850, 196080698, 267287154, 19845356, 267381760, 54891982, 268931559, 512985765, 636304709, 417234542, 224033288, 480273305, 498906390, 540090381, 50784063, 549691836, 975140984, 375871180, 655125186, 939773205, 768453267, 119535587, 524025045, 700076711, 408781683, 89306562, 973408843, 904478537, 421669619, 509973387, 718424575, 400331003, 782232614, 585848778, 914356811, 750266753, 386127753, 126260029, 491717445, 308709784, 227136846, 728432744, 828868944, 757878208, 688172010, 953168724, 567992964, 465749962, 421595884, 17139414, 805259040, 883851067, 654482723, 826648754, 173044528, 642632653, 167101647, 161050749, 789945235, 306238760, 990246111, 720214485, 4545089, 638461639, 120302951, 199053355, 316827397, 503475663, 502781732, 124649255, 752062869, 644263448, 733670286, 299883959, 108793542, 889027541, 223115357, 82610437, 538004759, 85422044, 50067832, 993432076, 759659780, 87324175, 769923379, 762714966, 795069093, 193721905, 249891946, 663296778, 520819456, 665147741, 1937238, 160379612, 603462531, 385962621, 893282077, 100050719, 145227798, 136506598, 786350453, 112664473, 363185617, 627674225, 970521162, 789503585, 412764558, 656096947, 399767337, 788421648, 373018288, 319912747, 890998055, 249091221, 527546610, 563401012, 801252157, 461376757, 623619266, 454398078, 91539322, 826739855, 88802255, 643615029, 35186935, 701007684, 331964555, 617398128, 134804881, 174021591, 445799876, 203452334, 289138626, 568065694, 119131308, 552612668, 398892888, 133338885, 121220399, 811659539, 621822662, 437659325, 832172760, 76284770, 614129239, 523198241, 818072481, 216326853, 958394716, 20268877, 248340674, 791954567, 827821481, 912828399, 546394361, 721662423, 668587225, 602544910, 380372506, 507987202, 841621375, 499036311, 476882021, 248533767, 565508955, 44455217, 332848909, 986691621, 146890496, 718784567, 888512513, 576471482, 387739704, 902367379, 289976350, 868234097, 46688925, 404541626, 648533250, 883422698, 645120252, 175089719, 554958371, 612159762, 271261411, 692967975, 64598175, 2820640, 134980595, 272213846, 883638634, 190926031, 486430237, 955899363, 234541534, 385661103, 97807232, 851898505, 214453514, 194081879, 821145403, 644759553, 884526566, 527496365, 413485325, 135892696, 463241937, 917613339, 375349358, 688123865, 331605842, 518035241, 771849684, 549066247, 772266993, 469868606, 867605238, 776391869, 158739456, 326271687, 475728373, 300725625, 16256545, 800137712, 728619304, 59190181, 903182291, 314552748, 456802173, 328789450, 748840870, 264811840, 704750738, 559160698, 594057667, 698704646, 756082029, 889294982, 968058162, 797886699, 139801704, 996172271, 940971143, 542237633, 720504527, 285747909, 930538764, 836105668, 180049479, 207232963, 330410932, 255539422, 869877823, 13128480, 3620884, 169911027, 214900402, 53964675, 607923830, 530066594, 487417064, 150501246, 544527839, 666266945, 994377780, 439716476, 139029143, 730536661, 227544466, 901667981, 202019403, 980744436, 805705382, 310427110, 999020583, 722796705, 313581420, 716097429, 67288818, 151154542, 482037739, 927366960, 230087448, 675341761, 938357858, 838968173, 522405378, 243587638, 847232798, 619971109, 148720602, 595587140, 712660509, 858263525, 519799915, 767518761, 570358477, 947520057, 78623160, 625064159, 642695135, 324241880, 419701569, 298264760, 90347299, 859852950, 321986142, 412431732, 194652890, 5270362, 971277157, 255108736, 400311504, 366064212, 463197529, 210912144, 930297731, 205066523, 25974137, 577167078, 357706492, 872279015, 369044968, 175578671, 4028216, 82839381, 291179595, 681538150, 777264463, 169486182, 751129595, 494911920, 215923085, 371690395, 118123038, 679161507, 387335040, 202751979, 298240738, 478696368, 836710186, 847855456, 15076166, 64554607, 343775906, 262606149, 436994326, 374395959, 398513017, 692074910, 717456693, 67901797, 267166045, 82312147, 98123116, 925427651, 588444741, 158069171, 106697054, 720326501, 543133018, 812305136, 29167833, 663305862, 904959860, 730471834, 348950056, 549087283, 596940609, 456247750, 105127330, 471425451, 820253384, 614453142, 538871786, 653029522, 54356775, 584759746, 387219464, 47510862, 663029699, 340580490, 722057672, 989808836, 777100687, 525409643, 448678908, 907511932, 525523976, 606662391, 784174641, 509145123, 139445505, 567599636, 906908793, 482190161, 501040169, 883549445, 934014135, 398390902, 838096439, 255279212, 183413069, 491555543, 412519688, 904538267, 908248564, 987494904, 273229911, 60531080, 504376314, 631144216, 957525593, 80244481, 54787900, 854190689, 763904667, 617698774, 325381569, 282280737, 354418218, 996060262, 772936344, 64146104, 623019324, 691074092, 784031944, 883096194, 220260614, 167748481, 882007418, 130535836, 910886151, 436192278, 213367230, 622193177, 807852327, 768218349, 180772503, 431199706, 772104093, 703625037, 698304177, 231977285, 284609490, 804047141, 662586804, 792515836, 284383291, 76000920, 216952984, 211477367, 209349443, 578775936, 746099840, 419839618, 618168838, 456254971, 101175840, 744242623, 921835712, 82278784, 326364099, 860901458, 418105713, 957705653, 410086429, 125821986, 496901143, 185410247, 906458480, 832965891, 825539716, 355694240, 688671146, 351121800, 464998641, 252905582, 572172170, 474685867, 4823547, 630652917, 104084175, 193806260, 64956027, 726135407, 802430831, 661185401, 535375876, 935465300, 862740068, 740799833, 215364002, 817695046, 601378689, 504370547, 595690431, 620621138, 995248101, 288021052, 319597200, 585178219, 126780151, 982502347, 560272310, 757826987, 491508973, 318493791, 457127237, 157453144, 112162221, 33872931, 892474866, 879040176, 783460845, 67519419, 604544431, 150203244, 352473811, 478350315, 520355040, 378132203, 474311854, 68004041, 642330498, 588051654, 734238799, 966604573, 248769495, 570586883, 791929889, 6878267, 879456920, 479547230, 21178382, 689080051, 658958760, 950307722, 355897507, 978742252, 603796951, 902773980, 978224064, 182831019, 35423611, 838227435, 345706468, 290824700, 868634825, 491986843, 654803841, 878674737, 343725312, 566008162, 688283902, 471416519, 872299835, 511212210, 715035464, 694872308, 134248806, 454354509, 181742252, 534095736, 503765368, 585489937, 360300044, 635581710, 20161558, 201211447, 110826290, 217352463, 173649927, 90232948, 465874976, 648438066, 154910808, 269330804, 876899727, 314918187, 579629379, 792682206, 434016070, 122488893, 889019232, 787051430, 497028971, 248294481, 591678872, 906511479, 39726171, 24596150, 45890139, 241331402, 71929206, 693121013, 105223656, 178299148, 752592922, 975819303, 320929013, 409528236, 343434286, 274774004, 290949340, 101133950, 993296924, 414037385, 101484732, 467316179, 56165880, 295474737, 544650593, 336241662, 756169508, 868340959, 327113395, 453138566, 134164982, 632856048, 168132310, 846006136, 716250169, 760595328, 674298069, 156423928, 718230899, 561240395, 658691178, 814675652, 971384252, 117265765, 389565397, 630426641, 132615211, 497968837, 934399637, 459476725, 129557893, 659575011, 951970674, 805476150, 780442063, 802517901, 423405612, 704494646, 492923686, 910998911, 280050222, 507667134, 276119063, 989949516, 708398249, 679287777, 286579926, 869250423, 669762906, 642214445, 126684722, 153510613, 410387283, 935199744, 444828116, 306096430, 582302202, 727965797, 689991968, 415708936, 98497626, 459578787, 696141699, 238400318, 528105630, 737469897, 31847444, 26019367, 110431349, 419532347, 14210791, 515319752, 351714222, 978575347, 226747329, 487213812, 703388884, 518214356, 33118861, 734325295, 942662154, 744004203, 314780236, 281559197, 608449360, 360757429, 59925257, 639797858, 447240239, 513444569, 264190467, 427239918, 786698589, 876269470, 651384406, 931926921, 981009769, 548041286, 242927316, 26000343, 278961311, 267893285, 642070969, 601688646, 180644015, 22361258, 634499225, 971072793, 843481460, 544187010, 876706744, 496463878, 397462518, 108306376, 16965838, 932217374, 495759390, 390991554, 9559084, 171524185, 880104767, 684881030, 197862999, 396588674, 272663555, 490931009, 283478149, 644134528, 879910400, 250242677, 809593010, 676223285, 136079338, 266693232, 375435496, 258602949, 579804620, 731134055, 480814195, 303563658, 279876945, 43363248, 579782363, 541214667, 700408798, 267930448, 2549421, 383836328, 535148725, 539851463, 955850283, 911381736, 630626478, 51621565, 569208222, 45648983, 671743760, 965506210, 305017180, 201647576, 66872315, 679775039, 67220315, 873722217, 491649622, 538510423, 472187697, 39406995, 374471511, 347716185, 244443963, 770802682, 990758691, 255469233, 794753368, 138097167, 663162809, 727595992, 348041305, 23772522, 914035941, 265851667, 555017743, 258964051, 940631053, 122447123, 674116200, 669739987, 799611705, 23549277, 743957238, 83908842, 814076760, 69997368, 729296571, 158116936, 36185421, 109960708, 718047053, 428589450, 471896992, 348958081, 627475554, 18178358, 227102048, 54269131, 853831814, 295620004, 212375976, 372063273, 339429913, 35447202, 741214992, 848345206, 543017939, 65930120, 930297914, 337066391, 204417023, 78343685, 166720539, 752895078, 149910086, 404690442, 830311042, 797896558, 263299450, 965916475, 657689540, 922754980, 771516279, 713958985, 838353626, 460137604, 566488492, 902811995, 793041063, 274027838, 892687275, 952206605, 247109218, 975294234, 817400613, 440141799, 517186611, 948554299, 230802990, 437450633, 177346900, 318065521, 884616598, 973860604, 420112817, 899807056, 263045559, 628685838, 397925805, 523725719, 611872551, 687256920, 301415714, 24984511, 953139189, 90603543, 736263242, 814697123, 440383706, 465617858, 903178421, 187496695, 562016553, 289566505, 7024893, 240531270, 140460705, 222203173, 388312020, 898423790, 529631254, 255737856, 106945517, 604933973, 461725368, 637589801, 928796397, 91775572, 432158554, 886257329, 961397719, 774294566, 100145682, 684824419, 349778307, 199409037, 713210385, 753722851, 619150404, 41944147, 101793909, 33791723, 438036415, 761545929, 917538350, 963872383, 26500324, 303656326, 647062558, 736066498, 718526469, 394892389, 143465692, 403381124, 970039736, 732300771, 392754524, 918240287, 825559496, 195955284, 289661110, 134411508, 326604042, 929572005, 129623431, 496643203, 275191337, 799269573, 777315833, 12426244, 597925430, 363074599, 684937822, 673903768, 496698079, 952850070, 870282841, 534781193, 17690806, 439814839, 662746829, 625442434, 726508427, 631150513, 667833145, 270082640, 801922837, 477639161, 694894133, 5752651, 99159913, 141472416, 134720751, 593789968, 288982239, 65588080, 226945503, 920168676, 144434643, 650204568, 843381107, 811900477, 823206174, 51094670, 13462314, 806939314, 370632820, 97872634, 352424604, 329847015, 713691368, 241457895, 709589416, 365359740, 241064343, 220862739, 474405125, 715691534, 273435140, 804482853, 645690066, 986154502, 358655507, 67744008, 801171965, 47471660, 501939832, 901824636, 892837208, 672640666, 882123440, 361481075, 245184307, 901126888, 29809538, 778396644, 832591340, 813902214, 290194740, 80926431, 989625906, 216913487, 633446219, 101847378, 13802235, 196652527, 924935491, 9906858, 415464813, 966736534, 302385443, 876207792, 976599403, 477746229, 900370586, 282147013, 601635851, 852812853, 321758588, 431306091, 654747846, 406410, 13500093, 221291675, 980836459, 364722268, 10062676, 500704345, 431934552, 707843627, 440544674, 591578966, 279611040, 398178787, 690379657, 281386232, 283378827, 780150400, 612454979, 244433205, 591667134, 4034775, 922087116, 901569762, 388713121, 445736467, 310138835, 932491458, 426064054, 175074600, 728829222, 613006258, 929607351, 334362879, 523847094, 728228120, 302108289, 532901075, 6610420, 821629804, 801033904, 19581123, 113846461, 47999436, 929468106, 515420864, 195829015, 29860729, 172491647, 784632919, 243342788, 329189950, 905015279, 189568650, 771918175, 995981018, 407718036, 672728629, 596573610, 679425827, 711509620, 21585974, 137632765, 700460956, 371453517, 682781147, 740594766, 843444366, 847485943, 981614270, 13648020, 317490477, 109223349, 614231644, 58295018, 588259565, 340676645, 328470788, 913035384, 848567218, 250660387, 881865073, 25867019, 477661064, 664861651, 224056746, 657714016, 560586688, 425809419, 980470761, 678763846, 509829302, 989382915, 593822291, 785641686, 871608101, 446060676, 283025930, 197651600, 583015031, 606727529, 728250451, 221279052, 528764849, 32667369, 578846485, 240602213, 626021913, 512032121, 120474389, 49133020, 29443145, 769821558, 353847347, 929086814, 229930572, 285207096, 427787371, 971833517, 142483256, 250334115, 222684631, 628761467, 628269414, 124315867, 258505775, 356163837, 412577864, 154093042, 35181945, 828522410, 736639813, 207641274, 503782642, 560200443, 450696390, 571933738, 916430627, 547371204, 100217106, 199900259, 951515858, 500680176, 912191494, 53910343, 6207914, 256141498, 536304428, 101387440, 248871372, 150830203, 268349566, 212802479, 929175954, 901179871, 886188257, 267261495, 512109666, 397581735, 875052542, 915830446, 984917328, 337038307, 251957359, 470541380, 955417014, 776310247, 171304126, 676594217, 151604311, 703070622, 710261692, 481247756, 201782733, 352484383, 490330547, 592033103, 234307697, 450103949, 864561853, 553930681, 151816833, 436767411, 382859095, 872132262, 592889787, 285315545, 210815765, 169298909, 341909190, 298855004, 357063316, 451309517, 149506472, 496981619, 281002408, 571138849, 130580019, 199785065, 333877402, 715336488, 474296754, 896630853, 592012129, 663193799, 830373338, 104678510, 154989383, 272195466, 647552439, 695949047, 698923433, 110747305, 903772, 415088620, 789598719, 599731218, 368741683, 561354459, 168299598, 297086607, 12084869, 355906520, 997019020, 614602817, 504611351, 653226305, 41577402, 360560423, 659999792, 65273003, 432381907, 215535299, 530888832, 47112656, 743615950, 472683274, 445880226, 23044955, 485218467, 322137816, 947047919, 884041203, 139941753, 183019778, 785557864, 646684579, 685881260, 976052338, 569997552, 74666677, 466589196, 318858724, 698502655, 318842156, 606544083, 898656043, 88602982, 949303594, 386067694, 343794004, 317839790, 546506823, 414819429, 891091327, 670238410, 524409445, 488590777, 132319976, 443407588, 181548758, 493649450, 910870652, 686168621, 254486837, 596165531, 437878876, 26012020, 301496288, 804251267, 585584659, 532539659, 523492847, 724901628, 555783287, 268765429, 314903131, 971816343, 5600470, 614500512, 113395343, 717795739, 804418742, 198382184, 573781768, 855523677, 128707914, 626268738, 421187745, 866569825, 625004194, 72314495, 77913644, 106655187, 102473576, 764997125, 734114546, 909356529, 315592647, 409718469, 976653179, 728315483, 950832856, 11104841, 245175846, 552256210, 42159926, 390670590, 420364533, 897194273, 893263122, 807989749, 506209016, 89769700, 506094006, 903353245, 239896138, 312803798, 969131178, 774802039, 595663819, 464368633, 722809056, 541174684, 850294083, 445961064, 997968925, 888489785, 877207949, 393691736, 110400075, 248455838, 931114696, 6814915, 703043333, 148070337, 343912969, 854523540, 208627387, 893231847, 885706554, 313195589, 923982335, 981671907, 533082519, 548935707, 307123064, 485699406, 647655452, 688985042, 392406998, 886423628, 927539247, 56628771, 521509860, 820513279, 657235942, 48089352, 164669376, 369835481, 770729203, 224349441, 67714787, 120499402, 783086672, 848303861, 621279783, 898003928, 426864200, 710946422, 430366720, 915935920, 245144908, 844150600, 624339580, 253742657, 729187759, 933903189, 383673405, 774423558, 297530604, 24212343, 218582329, 624371091, 970382629, 596423621, 562776657, 377125560, 133306277, 907462213, 174318706, 244570044, 853262047, 835310455, 687263423, 439762541, 804746706, 701625595, 570911768, 829466803, 942077548, 830991069, 904570750, 520817375, 555357544, 344614901, 335579783, 925955901, 630078993, 761949163, 160249882, 236579199, 205804335, 285827756, 651452427, 423367957, 878266767, 467683003, 497264161, 3738691, 646800467, 340104798, 293472390, 256470702, 592402322, 711154184, 916329899, 957582035, 890842713, 848977003, 480238871, 636629471, 46715098, 109840257, 651735093, 736896914, 537693536, 636912359, 397762974, 426670866, 631538404, 664891881, 116018168, 803359738, 30394301, 685268143, 697690186, 779472177, 780305806, 320191702, 944170508, 468480174, 672431297, 815401663, 992336836, 942629308, 397101126, 82945595, 382785593, 127011223, 906093428, 596840232, 891666661, 919767844, 825901025, 964245836, 254819461, 640418041, 562859132, 977297579, 354976502, 324260940, 316370212, 186880013, 314062929, 381691692, 371796397, 296459960, 920340075, 684106991, 812691334, 36853363, 625995847, 789113340, 648909831, 373627732, 90798795, 930412677, 993175184, 97033463, 290305274, 229930580, 913488833, 75000495, 823703951, 676851634, 884856727, 976933714, 62692133, 25507558, 54378892, 368962408, 375046505, 611134918, 128366273, 768046492, 732716458, 944011695, 632684297, 498927470, 847906835, 985729454, 596852276, 496378783, 635426674, 354081329, 476053099, 969985647, 424191930, 213490409, 835779966, 73675880, 530338639, 552647513, 368623932, 317920630, 688773572, 338121649, 511242608, 758268165, 450458045, 847363816, 622849857, 396911814, 362784042, 496822747, 421468636, 892415538, 672904062, 261499768, 976313126, 259412286, 610577038, 108261473, 450917805, 549564328, 597229130, 268019787, 378005665, 200374409, 352409047, 179876989, 70517400, 220748080, 173612190, 524161847, 40343285, 582411435, 476117932, 692487182, 208833647, 997935929, 561609414, 850305582, 541173767, 12528738, 171560036, 276143152, 304664568, 830865453, 199382752, 971350534, 504200419, 217984022, 912314208, 572200047, 32734560, 752886152, 113299861, 167385886, 456678407, 483698235, 567341540, 475987977, 135486627, 943020051, 573232690, 603899454, 978495566, 201320712, 867476679, 472295030, 12716628, 37476725, 170281127, 733275023, 433421803, 940662105, 643334419, 954322516, 201826167, 384392655, 698986407, 324329358, 711876388, 329444459, 274579651, 769609590, 120106925, 754771235, 402868471, 892855612, 235583371, 834515798, 74154071, 677443439, 347595839, 857332173, 23277234, 446046763, 724273839, 476820921, 792888853, 631659447, 260099247, 490243760, 631547591, 467897861, 637190492, 255700340, 610607476, 706286446, 80770767, 54855922, 296718853, 605267923, 535561112, 684216540, 322363963, 994348557, 655832272, 980431260, 152882054, 479916949, 220435432, 210865070, 955655939, 924638966, 430522499, 47020151, 964059219, 284083551, 527713309, 832551832, 316393172, 349510375, 700734897, 885274055, 989157697, 391100294, 626153744, 151589998, 652229916, 701701224, 572142772, 40509172, 710152546, 507437847, 350797319, 528226621, 958305086, 870914504, 799234927, 884259638, 890262862, 765493028, 222851674, 336224809, 58888275, 995003680, 121202633, 864580354, 201230470, 7956512, 452850693, 845423887, 953794811, 371551932, 348118014, 269425804, 947145596, 421222828, 894721270, 944428142, 539423785, 610860160, 339924773, 854605339, 117118095, 6102426, 118013899, 818407080, 575767689, 537840089, 946877360, 798254067, 624177736, 789735543, 103744293, 504429942, 141063907, 409355421, 469778673, 434892617, 211371878, 383883012, 528583976, 808709429, 322462891, 219541136, 592345907, 384254567, 178504178, 644743890, 162481199, 849117964, 353277551, 471689206, 642512803, 575453872, 510215480, 5272942, 389159343, 373036992, 208649232, 67822488, 465724141, 287367677, 334153349, 587364833, 167361181, 499812135, 49967940, 947625369, 682696641, 273023817, 548219862, 440407747, 458447655, 768281741, 520136503, 211727482, 826232636, 195388415, 584351183, 334939151, 680157021, 576059840, 599511064, 825718156, 788672736, 133799408, 215396378, 708710235, 223380722, 916195236, 722633856, 351886501, 685933563, 709425836, 300079134, 646424086, 610165972, 170209932, 314847293, 945206164, 833627434, 523562509, 9702390, 710038160, 907972899, 514308611, 750476640, 701884796, 882705321, 472997167, 557371671, 51252972, 576946329, 862978023, 514457736, 238069544, 253637316, 980812846, 265360171, 755430853, 302362801, 379932300, 586024432, 920975497, 5513807, 905621865, 38121450, 497922676, 773489383, 875266429, 712320923, 651485897, 594282144, 616960405, 176928703, 836839340, 392667128, 838303594, 552013145, 792359613, 691098043, 307030384, 26943578, 769002075, 853738176, 61401857, 769623103, 140188217, 976071064, 198821648, 243831609, 968169179, 654175791, 453936703, 184691658, 548024130, 464913074, 158399434, 522970407, 636728869, 167480912, 216023781, 86916969, 647194647, 224217006, 130421189, 22881524, 728693046, 690033243, 298582738, 36730780, 705784560, 758445773, 479473259, 129252222, 419890239, 313932090, 100523810, 484771768, 870315763, 291179653, 451714107, 630633301, 168653964, 759501210, 604331493, 654698171, 74656742, 761079748, 593524566, 626506493, 199905514, 339969788, 141174017, 420446652, 486084650, 240861729, 260134769, 163305734, 978792804, 306378874, 973144943, 113361024, 324667435, 78866400, 635568236, 287091625, 334728519, 662270761, 23320254, 280143819, 71897565, 558462930, 831620890, 480284674, 494870726, 154120359, 949645488, 379444659, 990026260, 947518614, 508228940, 35609039, 614230411, 131623115, 294880381, 608149416, 28114648, 560524693, 118551457, 114276899, 262386728, 160875440, 282100609, 179199133, 11185037, 205948751, 295159117, 651087967, 572617114, 579443662, 801910723, 52536736, 566265370, 687309188, 741458739, 270724674, 467839551, 182065450, 906241534, 264297824, 138310589, 597782208, 294868109, 619557072, 664674440, 440920074, 140258888, 116626762, 874558313, 441898009, 285823559, 249417679, 274090349, 981633235, 479894687, 436661375, 926435130, 647181458, 958233893, 125275671, 115297141, 95029483, 745745665, 273365815, 545316456, 129491783, 634716184, 620807205, 267267985, 257378700, 258715993, 924085443, 774142631, 936480336, 864535885, 743017276, 352384068, 624430883, 71530978, 252307180, 871583195, 709397228, 73285081, 89054529, 151709353, 895123084, 356622153, 837243282, 420072164, 997596087, 458721341, 191614729, 464964307, 692344626, 621613501, 733008702, 42202482, 26091959, 526823219, 430156122, 819768221, 578133590, 32535954, 163677537, 267662430, 641268095, 473744132, 422550550, 5174157, 138213949, 162585261, 84933925, 595344810, 286820751, 758376964, 353821667, 746431747, 107614308, 420594917, 586204617, 740618346, 382376148, 533289256, 247904648, 560680999, 509492962, 257872592, 437599987, 349325665, 4174263, 99058247, 773713767, 283760919, 821905403, 229500062, 37114134, 879161921, 187797962, 612968254, 877974099, 587440011, 79540501, 615571205, 228125638, 494016682, 904613557, 622590392, 187890208, 755447728, 145432250, 930671654, 29513253, 670076647, 826627667, 548295234, 248048782, 402023195, 457957708, 251011299, 141905123, 100008381, 688621931, 644694337, 304760357, 614808130, 540791376, 17789278, 691894622, 337984354, 253144203, 926626054, 469654404, 434655016, 949034133, 874759620, 445511373, 220549883, 771618247, 886978818, 307064512, 508868964, 790112296, 458290612, 672319274, 475361018, 876286992, 942597408, 997275885, 854369851, 692662455, 190819766, 642513398, 507054568, 932942825, 249175083, 889833566, 841845818, 441507931, 761235244, 291722742, 544462597, 287465974, 833980613, 567751317, 667435026, 145611072, 852932719, 365638792, 977751884, 737221584, 597039218, 935974755, 677164662, 529152736, 403440664, 147405648, 664820902, 530753765, 546785326, 797316940, 109340516, 547373807, 264849075, 625899014, 667469990, 148342682, 922992590, 84236500, 429239807, 271706437, 467336503, 578998769, 570899862, 980522778, 122541759, 28313030, 536429912, 98092744, 340356438, 938049698, 899363293, 648718434, 204372614, 382710600, 972351849, 727208885, 628329662, 98249285, 238418492, 770024156, 661189599, 944381308, 404934125, 390986283, 208851321, 105038046, 425815191, 468946604, 66446542, 296040806, 462703092, 797748367, 374528433, 147111337, 587606390, 931328508, 45804416, 72938439, 885812614, 607855778, 234766681, 204359760, 788913523, 250551884, 966327734, 377841850, 235348015, 934006257, 237184828, 632231039, 655893373, 884196231, 343286595, 427199570, 748093532, 744449761, 676072872, 217250848, 527723519, 243832027, 380926477, 961558978, 750696022, 715953758, 374240408, 944160800, 429766942, 653543752, 391087406, 444264667, 451588802, 672511901, 386565535, 511951329, 155657223, 499731757, 784251242, 932970889, 205576429, 417606372, 540892734, 324614079, 334783680, 996804630, 536527368, 475288785, 854193938, 21373057, 687791999, 267029801, 244001137, 771789628, 115345489, 587268284, 437980469, 195362645, 381628476, 528060900, 448698045, 291212858, 801685939, 777032228, 337829064, 376654516, 410147876, 336219652, 383774559, 228417368, 446448047, 832832907, 727262142, 695463705, 480657423, 710189740, 585884402, 506065114, 602274131, 656879238, 394024815, 10001243, 625677608, 551745653, 907444621, 171418984, 703481589, 521441664, 844995023, 966860155, 389561151, 415124012, 720998693, 998628859, 694259064, 655870106, 88376876, 345905414, 885674815, 484010017, 270644642, 27581055, 415735108, 813607201, 399579380, 686477674, 338998877, 242736231, 115887029, 541236935, 179550317, 78631476, 77763165, 606215250, 697907445, 638270160, 908490745, 974448997, 915561652, 124317007, 753610812, 182776941, 753761638, 117239322, 594342283, 926044814, 768819405, 704395283, 153777916, 510166084, 982848370, 92696560, 719090908, 882829329, 289687715, 829398943, 984684036, 572536809, 749414495, 282461067, 429099495, 53745605, 661014980, 149542800, 21472247, 330105341, 525819285, 926411700, 449531534, 69980154, 481027515, 923518638, 29466109, 156250295, 146064641, 146634894, 373442239, 54286335, 316191876, 622961829, 654340582, 424175122, 121063, 426657071, 261171183, 136567417, 324155165, 503882699, 59837800, 751822260, 607065505, 131369607, 895853438, 614916675, 417779743, 702997674, 944685434, 712563528, 597468269, 935679248, 921049658, 355136087, 503122569, 419010847, 954223075, 368380543, 117958622, 741537150, 73140090, 978336835, 752184622, 832894935, 625157395, 770237287, 762957227, 185856413, 896214511, 116750232, 711877948, 926832776, 360998838, 937877541, 735710387, 240246967, 603149368, 331691152, 817636520, 627862555, 708336007, 526945176, 534435142, 697181908, 486638210, 313473207, 248342465, 805689722, 770181939, 694886933, 212469099, 698939731, 519911367, 673554557, 983729023, 354185604, 647754138, 541368483, 51498747, 624950279, 938633366, 775969545, 336227968, 100510656, 489375118, 67578594, 203015547, 258528092, 891896273, 936223297, 321067688, 991618573, 606667462, 246099054, 942444763, 617503062, 988956550, 978866180, 116187294, 148717142, 198753024, 330920335, 751927558, 339120736, 135828131, 897901284, 10922540, 931276873, 858728762, 862631004, 952328117, 707063008, 789149668, 311724821, 507960207, 339194859, 548449222, 501123480, 60773894, 72013787, 50422332, 734704273, 4167753, 496240279, 901667545, 90236828, 839153907, 142907001, 903181200, 745341678, 173018321, 833231210, 65435836, 927376284, 777954101, 219336160, 42944973, 423069902, 25359664, 877091062, 756242378, 851566635, 486946240, 813271462, 245307741, 969676229, 383336967, 961855516, 695917212, 367754192, 855704188, 250812397, 790487240, 129309613, 449040025, 667112856, 463073308, 930751342, 666390844, 811846384, 991594419, 748898776, 927664906, 835790216, 856220389, 703354466, 306747041, 356509919, 324255947, 571245230, 908708999, 993090824, 76179220, 974253674, 408314106, 298456502, 828051229, 517381248, 65985501, 717238667, 99852105, 530673390, 798498313, 2508879, 969615071, 865488189, 23853219, 792820567, 882444736, 452815369, 950108319, 517077734, 229331250, 228187117, 208434106, 11428584, 49696750, 972733695, 311176559, 505852747, 579858075, 891282820, 202447131, 245205010, 111381693, 966465979, 17114103, 14320389, 784033276, 292926238, 880496530, 504667729, 835739144, 745770510, 663005826, 903725271, 703981270, 167730615, 596243716, 784646465, 100024023, 791551773, 427103519, 723082318, 511780241, 328052759, 178406953, 857054993, 193605009, 219878888, 294312871, 305682215, 783641339, 915140904, 162712123, 510633484, 596156338, 25424085, 315904127, 355448037, 899261544, 698949946, 655669285, 329982889, 640652789, 365559081, 744179109, 556902298, 760752994, 729458614, 237830573, 965781297, 956803906, 505587655, 943092740, 765738373, 649586455, 952422587, 273597809, 254531296, 120644739, 821420293, 894684285, 502273951, 357917093, 596025089, 942096422, 210337013, 94835227, 879050618, 578862057, 406849290, 76023791, 607477662, 11477820, 945056314, 373548060, 252424407, 732614084, 876372756, 807432161, 136214250, 383561225, 859936414, 254744038, 523392795, 843931019, 410096441, 612270875, 414548968, 618168645, 373551427, 862785295, 544760992, 207072817, 471975447, 137711126, 878473638, 662839835, 550845416, 47593614, 550450202, 917520089, 317894288, 87415563, 711989628, 404808679, 532074246, 795606683, 314898849, 923636259, 294341622, 236966093, 408400223, 976088619, 174512753, 257915435, 162697695, 385213891, 478730995, 60745303, 954683569, 63071121, 764393839, 665195322, 375864852, 802025515, 300678877, 645428596, 833883579, 825959537, 923381564, 576975416, 407789216, 479462339, 581904026, 610610128, 870467862, 62921254, 824345241, 65880651, 587489490, 81510259, 952723356, 361533958, 747767532, 523336107, 962247733, 506242918, 429769605, 308509867, 652019599, 723264142, 722530902, 332825171, 927970164, 551556739, 591818717, 493650683, 205730211, 893094684, 120392663, 528362149, 244189413, 382090157, 626953202, 18762469, 152306309, 900165467, 984540667, 959062802, 147279091, 180763528, 801030356, 689803589, 769776597, 61350759, 663525319, 884959407, 523333063, 201035320, 372144839, 594486906, 373929415, 698576688, 74245039, 112147921, 65679713, 903287000, 873086362, 942369151, 457667082, 987574841, 380918116, 445569724, 504257939, 569144669, 975919759, 669654990, 690329180, 638066110, 189901136, 953940049, 903659729, 333374331, 744246780, 324760979, 326265984, 752550998, 767153252, 868728021, 591666940, 559089552, 397256827, 518642672, 919899452, 481467668, 84573614, 140099884, 199960638, 77943248, 751147415, 870423077, 562974605, 898017139, 412911426, 571271596, 613045371, 735206132, 826163821, 333239241, 236689750, 500551767, 286337279, 80917504, 168286671, 140652547, 791317109, 890988820, 506966903, 601832069, 501538006, 752379969, 685999084, 255788307, 560552311, 230422602, 97422672, 253352493, 978013272, 444032255, 389097231, 798326856, 807027217, 36074760, 122822099, 386692690, 460395806, 506513381, 545003564, 781691042, 390495527, 598865228, 644316776, 353951830, 178061711, 287801183, 32770755, 371233714, 850366122, 252957475, 577371197, 898508291, 174394339, 83409366, 639024102, 915577774, 455969209, 710090826, 543372927, 848676372, 416106404, 698447348, 325400708, 290405784, 104110837, 55649465, 299580935, 477713519, 439947788, 326968540, 633153367, 743082516, 879300971, 873895715, 668753971, 83125016, 91719118, 529833026, 934024816, 635739492, 987351158, 667953432, 651991275, 966954826, 687766795, 980716237, 813850968, 628759943, 700025664, 45709294, 25468454, 513300281, 745004617, 102308332, 372383887, 129576552, 93349490, 732492326, 686679029, 739763922, 783931776, 390540920, 104974586, 575288855, 751392191, 583332262, 255704892, 503971847, 675252470, 334544394, 804132453, 520888218, 580757093, 438742309, 59450848, 215467160, 558099518, 467302561, 801599105, 297472598, 747840352, 19946497, 874359752, 183755520, 451812020, 661724020, 293464606, 319255463, 596208100, 39081736, 205519719, 337876957, 109388785, 836254949, 152721453, 527047080, 975537811, 173538856, 901478654, 265800274, 341385784, 235896071, 306254025, 137526176, 107204603, 788093797, 414386840, 307032696, 918429903, 624031528, 517103802, 695132773, 958591486, 457946191, 720261742, 688192970, 701966454, 281655347, 121511983, 904708788, 316571658, 456372429, 816602659, 276506757, 599172533, 395104878, 549976117, 887548771, 143256698, 436999564, 25422439, 537840965, 893856560, 23892223, 228604049, 882607575, 144972333, 523335803, 329332915, 966817470, 29634209, 352304737, 520429714, 755740940, 272087697, 411855787, 22957447, 490405392, 305802015, 116520940, 97780089, 20686990, 269684937, 412361895, 307252825, 170282913, 545384050, 196059069, 389727849, 488088663, 369746862, 373325536, 921079338, 158230405, 386427689, 281870335, 886839653, 949814435, 133082443, 68139695, 596205858, 537253909, 294776786, 419393729, 832577293, 81584745, 476305028, 564767833, 313471107, 338033979, 228555240, 940536485, 733335124, 304277033, 939123587, 688109404, 399595367, 548521716, 596820333, 603384973, 115479420, 958005032, 818256706, 169701896, 941205227, 106671865, 106337891, 990252174, 333937550, 501802029, 522164960, 710240392, 176446408, 242087257, 669259753, 848804068, 854471824, 447805576, 938972146, 292269451, 975694401, 586698361, 162837142, 298052736, 987512108, 994439701, 248933278, 680831841, 657753657, 819485376, 867743054, 412784270, 119920307, 484477657, 699202984, 580837721, 133478771, 54340380, 301722637, 674064074, 159792442, 149928056, 225620331, 991747563, 157399949, 784720634, 247251019, 6153777, 443079160, 320662236, 348891170, 278525457, 117927971, 566811282, 232260799, 770263888, 785883648, 52054854, 619589606, 960388622, 910183155, 800953264, 837774250, 812819175, 178673534, 163254872, 215735283, 725794681, 178182874, 320576213, 758293236, 587956485, 375152476, 860804053, 586943422, 236722805, 842395471, 221338353, 731744948, 173343387, 300993737, 594576489, 693114531, 335668353, 541291946, 486600493, 496449269, 883148380, 969068938, 216700557, 966299524, 719998566, 497323892, 29174940, 627804480, 462878260, 554251893, 691804784, 7347115, 193153312, 41538441, 641153598, 530604134, 213980070, 377344703, 389627213, 917195198, 694169077, 692896055, 137332178, 195055619, 359598802, 7732582, 532844903, 309727155, 906243658, 124034972, 218508943, 569589519, 930884185, 863902580, 196963037, 818682132, 840476154, 450808459, 617499747, 421969621, 850302052, 576057102, 780673934, 930935093, 508512693, 776326141, 867934110, 806046998, 284762929, 239219647, 936011497, 673982107, 942280757, 630817006, 911802824, 446537049, 313082962, 806528533, 441306227, 424451104, 375846482, 26169113, 673744824, 278941113, 281587331, 338361576, 385020340, 825260855, 160810166, 734209156, 111165409, 960825901, 380197858, 567699189, 820172863, 151498874, 66760806, 469929557, 129714332, 635608734, 945571780, 780248052, 295312188, 331267876, 716920590, 853712795, 686799749, 100315733, 189230610, 905152170, 181560115, 722637730, 731875555, 235652745, 130138374, 953046713, 900813452, 88056566, 816185640, 932974237, 886645359, 999809019, 717369394, 486493253, 509542233, 954974182, 128613501, 544291384, 108851936, 145814504, 284804131, 27658935, 606358197, 413997504, 948002288, 947705626, 244307990, 779652479, 801115186, 157530291, 918945925, 587723176, 391911230, 376349695, 450103793, 3936988, 750898987, 295076028, 36611374, 268015075, 638284896, 750380538, 511151525, 263693563, 139030094, 517716059, 683665672, 556271849, 956714443, 563260410, 671753803, 66175494, 969554864, 293082412, 84149097, 680648187, 18453864, 612508654, 477595462, 863627202, 336028994, 897771135, 503230969, 89737514, 586424857, 165166693, 499352855, 761106970, 836933218, 759973366, 584195303, 134932657, 259829666, 216506658, 226490316, 95524773, 355618869, 863055795, 392544546, 322805384, 200434342, 856795704, 165889191, 56771723, 104784048, 968386601, 898248049, 738105843, 587489820, 958910706, 655061228, 794435943, 582971041, 674221402, 757304738, 742155220, 59418117, 990799441, 343564130, 364426084, 261207896, 108194414, 499756507, 718116669, 395644004, 283038333, 39213335, 820138872, 421020411, 772592493, 627735632, 42238719, 266396414, 405530442, 164646546, 286420761, 952386657, 959083330, 253907888, 912965907, 915876935, 753233604, 457001970, 9587917, 262773764, 53240510, 315616821, 214869315, 727486253, 964768913, 173270374, 707492911, 235456261, 265148821, 81296343, 533702875, 77253954, 760023212, 586845393, 934501410, 560101380, 627788396, 932869342, 731418150, 181331789, 783018825, 678012310, 76061662, 841979472, 67231811, 761520686, 872894575, 912975914, 165915474, 730889249, 309238106, 295132591, 668186528, 720936384, 36330019, 99104154, 872585556, 524155218, 127072648, 860379534, 610585950, 341699592, 119666411, 545745754, 479883683, 646916772, 938677822, 45228687, 611781676, 644799971, 941326357, 205076214, 480638315, 480211494, 956080729, 155900291, 807527665, 846142154, 711835850, 473980611, 706323251, 6021399, 778171596, 740389862, 980252440, 990975077, 882395341, 75594961, 164215605, 498833123, 342517570, 923841311, 908025663, 821126090, 561797694, 429747726, 271794402, 426455954, 972678732, 802864769, 272815669, 174134310, 450860836, 776203965, 8647512, 773132199, 357887044, 777568052, 647555599, 118683982, 587871365, 597839250, 700534959, 876101466, 435423682, 826930742, 514540068, 248311628, 252947793, 608063959, 890299399, 128918379, 437388267, 613880352, 272129110, 621401433, 878511171, 480923045, 565897426, 425032171, 850364432, 414365329, 284387406, 760988158, 325578536, 431187980, 354492253, 51849740, 156566901, 876138639, 242653034, 168123949, 867394770, 586402620, 220829005, 675643943, 245975352, 908270942, 941060774, 794851046, 252777466, 501846844, 280150833, 945248488, 839349074, 163211566, 152332959, 210601922, 787375226, 518381, 943512578, 169851669, 831912103, 747179674, 821543898, 30882849, 34753654, 545363084, 805481626, 759824387, 717633724, 395458476, 285569543, 203858783, 151950463, 702414908, 811344309, 867339513, 915765764, 164499146, 790332054, 279251877, 689919225, 61050283, 456203994, 757916281, 852295712, 630968399, 479474288, 256426011, 570442363, 882180977, 249133270, 971508464, 84201876, 138428149, 365442239, 201689572, 793198465, 368982935, 379396560, 543351383, 545328293, 204970377, 83799043, 825980014, 516296239, 623298935, 734385132, 699272447, 44145601, 254225203, 948099249, 440583948, 507039478, 589242261, 756840814, 496717407, 793305171, 152618442, 120137866, 410198833, 164696772, 698570670, 530100923, 192362585, 590560632, 333019204, 881035906, 128561025, 844731296, 240871709, 86820057, 107209706, 892524713, 723182634, 865560705, 949290163, 156174453, 488287445, 797802591, 544559989, 176835898, 809485572, 494824570, 96270618, 730356528, 461885849, 941129739, 24319866, 430382270, 251414909, 342169121, 3480852, 824494556, 271875761, 597788303, 831890081, 114435245, 90774411, 188632621, 694773154, 302791053, 912968075, 303479037, 190497686, 552542586, 134874496, 162446886, 272635097, 319460489, 542059169, 752365535, 416257183, 729220665, 914933869, 203695061, 65247929, 20187557, 497405632, 823791764, 255362976, 987887276, 808349446, 573902944, 186184973, 828209419, 660027173, 138273849, 602675918, 700782217, 257595171, 128446088, 281445805, 896162054, 983690214, 311651062, 722741921, 757947379, 465793788, 99025732, 782714795, 685860308, 561201033, 711389947, 185868323, 117808374, 12659934, 182979864, 303991751, 799579175, 621361150, 733815213, 430809815, 511648371, 888938556, 959826199, 974510563, 949575404, 574991167, 533640061, 860221536, 418913826, 96397779, 488588031, 600121113, 83898095, 116827868, 517852645, 614161728, 825637547, 78516437, 212867588, 123965757, 711097601, 599858194, 498755268, 757683956, 229499711, 11502516, 400153609, 353762624, 327086710, 266227440, 706320298, 438969535, 194541416, 177645588, 756057826, 175727045, 177277130, 13939263, 878440524, 771850554, 269529129, 443408312, 367257450, 110429800, 946365256, 941358813, 825030944, 25030817, 361542926, 101603182, 21446657, 276809149, 281270560, 645751651, 375437505, 882662747, 925445295, 167502818, 392125266, 837892240, 241022065, 59614092, 455783918, 176385645, 164860487, 38813666, 992572266, 851718645, 848386037, 906327189, 659919244, 973054859, 150564016, 159346486, 603851911, 447496709, 401866216, 749653509, 588046474, 808317048, 261443174, 967738960, 918667886, 716316664, 877132414, 34280644, 953775892, 590763545, 553430173, 73671292, 488617260, 461453534, 371306481, 107622128, 226510788, 615358482, 435014954, 632067902, 359952163, 151250428, 718711594, 553492136, 333838095, 208085206, 318125360, 638424383, 414380627, 508852665, 805801797, 143981429, 934429874, 625198385, 340059553, 869566563, 217778102, 320390713, 248401847, 816235271, 236091629, 811766786, 951452816, 887447827, 205302428, 383352362, 389040341, 432906030, 229939833, 928719694, 788284337, 117692471, 154643092, 256562778, 253064393, 289689432, 545992748, 447886502, 308797722, 241612501, 356437931, 70852734, 189876883, 757400652, 761895276, 854462052, 277865098, 662590351, 842029432, 819997342, 62666745, 443637247, 74933102, 235204182, 225819163, 202634598, 906271162, 984911307, 387638353, 798974363, 682274684, 189939081, 128810669, 631209296, 987230764, 503947648, 461151298, 362898028, 160745168, 155073730, 230512562, 586455190, 407452007, 281253331, 334428244, 827556721, 929538043, 911240978, 812700185, 450088687, 794865907, 209932866, 927717305, 603382877, 606939667, 803645303, 95314133, 737482394, 371592353, 67843178, 54202348, 967599368, 561617321, 650870318, 653846745, 195855861, 707053879, 65262751, 727553083, 422069779, 861019865, 53971078, 590180201, 479791590, 444606492, 768126575, 250770105, 55366090, 557461616, 959515460, 727251830, 36608258, 748978377, 356742922, 247618424, 869422411, 209536472, 134822944, 273015899, 174268380, 466685412, 102990610, 502957888, 220341732, 4974584, 759337174, 514805025, 298789889, 101171623, 612120628, 159481658, 336732667, 680640139, 986437498, 150470855, 898754594, 478716867, 223827838, 99671545, 596584008, 559436843, 416037224, 560110682, 112296447, 659380527, 738674586, 10114422, 647726650, 806427661, 586489004, 990449310, 917499801, 166152044, 998502264, 301634293, 912818938, 722724517, 618606549, 911182541, 995305492, 138822990, 367895005, 252229047, 658969923, 34267409, 769524831, 383325593, 366302369, 377724985, 991414673, 958542607, 531252965, 747077252, 112712976, 827138316, 578529491, 63819107, 229983019, 819474010, 139672396, 393862954, 415958629, 515963819, 169895917, 199048033, 915065038, 685876802, 659660951, 941034076, 211501338, 646809574, 249999335, 208570952, 929765614, 277339755, 321032424, 773073816, 977283000, 996625913, 139368932, 985536663, 121254152, 701288007, 155892817, 923458012, 589710977, 152501027, 56984121, 296354121, 25579211, 937494850, 286655508, 568419112, 1259577, 826754108, 12740259, 250428550, 847631218, 37516630, 219843911, 851280733, 441193945, 779193822, 2227921, 571738432, 509729281, 735725734, 191676575, 273010405, 207621090, 435438269, 406904429, 175494357, 249934750, 649342899, 155722506, 113961494, 338534515, 238448160, 669025611, 194643748, 123739064, 132130403, 687042956, 453464778, 407753794, 408137799, 554947854, 606902495, 776914053, 804456791, 654618274, 686639006, 172774709, 283683046, 240108797, 616216591, 221615296, 582837217, 14404079, 815159657, 939944040, 433311577, 891162046, 44455037, 606242558, 741428062, 489306511, 437201858, 61391895, 15990011, 421931051, 672503789, 134270203, 590261814, 319535772, 439451340, 219461259, 123966945, 983802622, 946682097, 662127520, 622620647, 587746938, 275048894, 884861771, 654927941, 308402647, 868946320, 715339293, 605631156, 337953435, 482657479, 264030905, 92423503, 503576915, 138646205, 562411478, 370612612, 50676286, 231807589, 418915451, 215768385, 714549493, 945806198, 307886152, 147982532, 393842458, 419781815, 995062506, 620512972, 156418339, 520875395, 361757258, 187265501, 412531784, 884629437, 982106497, 916756386, 430881479, 418563182, 425225654, 738489894, 660177118, 371607738, 987329962, 412596827, 674259944, 359699633, 263537825, 166398045, 778342456, 435215287, 750145506, 570235185, 336650486, 134177089, 546300642, 143934032, 258813355, 832878352, 88148753, 28660531, 979012583, 335324256, 895901747, 196059404, 957633693, 133642695, 974067434, 916533682, 137488337, 627560626, 55395961, 872970910, 438699494, 576883341, 829218911, 481795242, 394075832, 958244207, 237635886, 399573710, 514057719, 273133138, 547396918, 607913491, 826729861, 563810342, 327035649, 79911583, 819422298, 233202190, 883138409, 569451198, 621254625, 358406114, 155712449, 774141188, 15573377, 535177235, 955299867, 703347262, 216593517, 714505726, 811701086, 510616134, 362380872, 19655641, 692945442, 646477224, 970057678, 520568348, 296488162, 419448040, 363815579, 4626447, 49224277, 57610204, 682905680, 969705364, 842217798, 99235851, 160784673, 833907818, 771715050, 990424541, 662121267, 745790214, 912651229, 135174212, 528032449, 607385816, 951659960, 617821682, 37654401, 341824586, 182912597, 713330412, 937535703, 832293347, 532814680, 645562036, 115189129, 685040393, 186348807, 403719419, 532559258, 305306559, 760869167, 16631826, 423871789, 184658805, 526807060, 809389313, 996653205, 484781829, 447484898, 162885793, 588587872, 455997802, 902484503, 968639187, 895891432, 237575133, 53240534, 26099617, 253621323, 153183482, 356798857, 416246295, 302088554, 157632391, 201832481, 666788382, 246298481, 481510685, 241732013, 440584432, 354903651, 186376325, 253814770, 361745001, 320797921, 864761616, 213939765, 751217632, 582796581, 518386137, 96194298, 592479978, 777103835, 340421254, 387080631, 93990624, 605146271, 35809317, 698815079, 916860947, 70301374, 671889010, 798095799, 332481333, 388951204, 867475509, 598762351, 36702284, 567013981, 32261238, 525365539, 727074930, 665367154, 495416461, 19641625, 124963409, 82572646, 700820109, 583582495, 865398976, 557607773, 940561332, 387508074, 93136074, 268957080, 320692666, 57964992, 198307748, 645527661, 388964666, 163058711, 659381964, 724218791, 248902616, 990307343, 801164202, 818391812, 956171507, 608937158, 134963914, 33794216, 266610851, 713761650, 704931882, 213377618, 958701686, 90217961, 242776519, 837178185, 262589912, 230435345, 739231912, 960181114, 900466596, 335443674, 495478156, 76010677, 755314606, 756622425, 309643853, 215140406, 241691601, 371207164, 963418680, 556808466, 655480532, 850123748, 586839105, 706365970, 975132516, 306305531, 395754287, 380868958, 239696927, 462353770, 993824432, 300152817, 767108517, 27708445, 53527084, 314960950, 728297061, 390123720, 932101006, 271213955, 295336532, 445720007, 154427832, 237067261, 627109326, 637233393, 922029285, 949670365, 193090984, 396644842, 245850932, 203098489, 312689540, 128989877, 336159993, 197440367, 899119539, 41716413, 798054190, 379295385, 52917751, 643684987, 956040529, 939261594, 439783837, 34875409, 862960494, 432680647, 862584127, 497577488, 58675498, 706117312, 761517502, 878284394, 594285469, 935282850, 642424813, 230228393, 140523677, 931029802, 83003580, 203238091, 36990884, 114494172, 703982795, 680511010, 986072402, 151054305, 679165786, 712045336, 462150010, 584581720, 166210617, 701636338, 773736304, 502213492, 525541796, 397447068, 148877688, 122977358, 15695162, 503327602, 918504668, 470750362, 68045712, 511084203, 157185475, 56398151, 463486120, 706932477, 723442170, 369726044, 850150461, 683562592, 718100622, 471926063, 480321749, 868874218, 901572986, 177031012, 934977736, 261723186, 576342966, 708840977, 927299013, 626699863, 923495783, 250747389, 72256219, 36774048, 253580880, 478967575, 116234035, 796270929, 583427994, 472496522, 392239424, 311777005, 266524211, 807475341, 235506609, 36414040, 236848202, 1621700, 823695646, 147514867, 972831329, 460241614, 309960995, 217528234, 961649744, 385117374, 221570813, 122439384, 613391289, 175420173, 233328380, 818151481, 386528273, 858648363, 513806192, 569128923, 704773832, 548635063, 951990473, 731126853, 503459001, 136835003, 611418421, 786378016, 342825145, 322870520, 884751914, 834158, 893116051, 814769789, 180386681, 553325635, 54949946, 447564141, 376125603, 18891653, 921317913, 62009545, 803736146, 49591445, 688916890, 6449812, 446280884, 121261843, 549210344, 632888375, 132703681, 565142042, 475460521, 871759291, 525066009, 858089100, 550416261, 74825200, 356892938, 988457785, 96602396, 716449732, 165292419, 502288858, 667685155, 362008118, 77042241, 740478036, 791886174, 683646044, 250361963, 395791882, 316811565, 498566202, 367924045, 221236781, 586077933, 709905411, 31646383, 604967287, 106361363, 9815411, 793646625, 20449172, 172400664, 41696834, 689305334, 887906484, 79161381, 766839422, 131631736, 990639503, 648925393, 401176951, 169041291, 403194246, 307994454, 244516492, 121842841, 297582107, 165764575, 110689301, 707938344, 507585446, 131564823, 99031418, 566263319, 412397861, 246165934, 637617469, 34728402, 796630018, 242567121, 308801926, 77278406, 593938013, 647070826, 555162935, 466127099, 272245309, 362644166, 55983004, 146187625, 809408580, 381326636, 249662235, 969850768, 881895285, 977837013, 536002255, 557862195, 133879029, 722522029, 673985288, 83399362, 943186330, 271499309, 869215971, 696356104, 645107258, 926235621, 278237042, 27155985, 495028087, 502317871, 862226798, 64797760, 96709537, 985787190, 840923162, 669802952, 165745913, 170380926, 788508514, 359080226, 94054938, 126706091, 540841293, 568655193, 489140684, 524390910, 241898706, 549642931, 264993225, 261261360, 902640886, 160330874, 220493213, 565781831, 925422148, 514240734, 773198734, 960940978, 574245958, 974826429, 246914280, 394923358, 586075821, 98410036, 486626048, 158785771, 963420576, 187273676, 790507568, 604893785, 570680100, 425001297, 160809783, 612110845, 748935210, 26249989, 917309290, 30250364, 82455739, 986034454, 658715611, 79092922, 422150, 398005204, 124629286, 283689033, 704601261, 873099933, 660181210, 825024500, 392713988, 518397918, 136866645, 18740502, 140139137, 350177170, 270485620, 568082197, 554075640, 478672099, 857126308, 391053769, 946959617, 426941871, 852297892, 196112267, 178424918, 322412005, 573089882, 867110964, 435411215, 729174996, 604553895, 500169141, 149103995, 564477679, 991491276, 956622701, 957652842, 13326136, 675802353, 716041271, 401444328, 254241441, 503713555, 932627327, 258468212, 920537467, 349155074, 253763050, 642703689, 523173399, 874181774, 142892254, 601273595, 95514609, 159622906, 964672210, 380689302, 801456873, 29596914, 404104619, 84160792, 487526056, 399731745, 968790984, 778571363, 291742241, 367159536, 957087347, 265692492, 96908088, 175848357, 493240979, 556473718, 55315277, 874495945, 433907776, 714471612, 688241347, 760258452, 567712594, 733121291, 754200620, 358028371, 244178894, 330392084, 710474102, 389443991, 987309621, 661099649, 14551026, 969551263, 528108260, 411757136, 268810878, 131955197, 207666874, 32282129, 503857517, 468122360, 2096399, 822198379, 858398687, 533156753, 935999970, 434490254, 958066630, 737676683, 344781608, 122371285, 810632760, 922765592, 70336928, 897952283, 796500744, 854522270, 626417742, 480874631, 122011863, 686554425, 659876614, 88598444, 198652156, 488002308, 872035813, 18522576, 60209394, 882594474, 800172760, 470183441, 695288405, 383697648, 180506689, 93865794, 435173522, 402930679, 951414741, 273742431, 229725546, 244345455, 885225936, 650815246, 967063348, 812167658, 127142839, 861560726, 110964828, 937950576, 509329807, 992141428, 44456350, 168038655, 303555790, 503299515, 341968047, 415841205, 567584902, 309890371, 878297179, 625831112, 954176421, 317848207, 275278120, 929490219, 408885047, 362124902, 408558987, 424278545, 809946461, 337026675, 790386140, 59550813, 515149443, 71907408, 655971323, 320675378, 530600794, 851838825, 184184242, 242850548, 470535847, 332124302, 186223658, 116364933, 445725698, 630459095, 653222011, 141160536, 409559110, 214009636, 496541855, 501817755, 778211330, 924549291, 321179214, 167422737, 225796685, 498299249, 226682939, 229368737, 18140452, 473729732, 410484898, 239087562, 347342381, 504064050, 779221618, 292389508, 155406182, 222468064, 804275226, 809038119, 404652089, 562950581, 578482656, 993592713, 138944334, 78575999, 235193577, 761120874, 166524951, 107058457, 998490400, 862987481, 563865748, 803418349, 445110247, 688815393, 754612769, 347913883, 637916230, 510782515, 493113188, 699322111, 482817333, 444679564, 518131230, 930650484, 677264332, 739644283, 57580555, 452053739, 464544388, 810252122, 458358615, 57532318, 452809599, 670451973, 248036790, 898417731, 705026421, 770255139, 483525946, 926716025, 182478603, 663211721, 609230155, 260568595, 398234441, 347457649, 544974104, 684135245, 947393399, 531913556, 332412965, 269045873, 512977311, 877441353, 847570256, 118597822, 952177070, 542653608, 785272996, 631533228, 727715458, 9430451, 264117438, 343498628, 778780766, 712700669, 623330019, 889150486, 77948443, 479434158, 439659382, 290258434, 334082366, 671803316, 962025934, 793123416, 744385544, 967916616, 282148752, 350606331, 390853178, 731429273, 339048711, 218288996, 237928593, 867022674, 674765955, 961094633, 814241216, 108950867, 332172947, 466045129, 757440520, 813347781, 644942728, 223991302, 974316495, 586698951, 538360187, 202568965, 868496722, 121338898, 627166290, 892380459, 307778822, 497433093, 271376141, 539165967, 169739971, 716359102, 377527371, 844493220, 999108659, 395265904, 675103802, 36719103, 90579616, 946502853, 1870113, 29636895, 545818107, 849911264, 83691403, 386472006, 636560045, 816259553, 19156925, 82734310, 982172706, 229814071, 638995259, 629673147, 867456561, 981959160, 466948162, 87438948, 109040969, 968704443, 790394668, 430725449, 169604452, 349069203, 187135874, 266612434, 369038881, 558748393, 2167218, 325605863, 845295654, 499340891, 542126034, 741446959, 644099949, 767441494, 87929566, 796404698, 900602123, 510019814, 917151294, 521631264, 861431091, 662923645, 733898580, 997536439, 358561639, 773324823, 897572194, 811643995, 924900222, 867134997, 903715896, 551744590, 662123416, 704694604, 674211031, 146676134, 583006957, 671013566, 738955638, 221777844, 792889428, 540862294, 56443047, 353263933, 710750027, 386774640, 854825990, 860757106, 713488359, 949734562, 205650659, 358394600, 514313964, 686851240, 915286879, 19837892, 922449408, 131113693, 467856441, 542938797, 538336745, 384870933, 301359763, 159197785, 430284056, 437677070, 729744752, 398163064, 876188742, 302319293, 938448815, 513983646, 582326136, 862820588, 370944426, 369948661, 739142095, 679284280, 705449553, 65187039, 843652014, 5838032, 744333185, 681406568, 421560831, 826736006, 833134752, 374635804, 917056143, 34623613, 336297035, 123835320, 885835023, 161176944, 564406912, 845135137, 437410831, 972012565, 143950187, 641349353, 713530802, 246996485, 863004216, 217560090, 724770229, 111994522, 775022493, 201827834, 572532171, 96352135, 480958732, 444526518, 856378988, 777701076, 799712602, 219133589, 239289555, 654693230, 755189387, 260166475, 355347678, 75045694, 934751079, 69300598, 579641073, 653428482, 573976021, 797002509, 39670437, 219269192, 231487678, 959864461, 66454658, 450895327, 604479000, 825735685, 321073724, 164764304, 943768237, 898056682, 765503896, 823998491, 618699010, 368518391, 356496044, 905496346, 154451659, 321475137, 632282360, 790861491, 291340112, 342418090, 132153352, 909644081, 28747995, 804138703, 814245989, 454358399, 340982964, 516123055, 460402220, 542933237, 469429442, 148830708, 721604081, 222668860, 613131171, 691934788, 99091488, 848050498, 60094179, 71477799, 352541436, 82243852, 609386559, 245479521, 565060927, 47149771, 228735453, 6581690, 845825130, 208146500, 624839494, 15709241, 494070502, 831777088, 476386270, 580617461, 139684343, 555877770, 398089134, 488251706, 239719221, 808211235, 753876188, 901169485, 389386988, 757012817, 813267991, 390639218, 176096993, 423205366, 586045255, 318635332, 410660476, 784676579, 793880968, 794388805, 330478028, 254993845, 910240970, 573655964, 486869914, 31942728, 610204527, 260239947, 156985997, 840771323, 220461555, 969443174, 361644141, 616190109, 518482704, 122732765, 344178546, 496759504, 819024699, 838640527, 249102712, 948365092, 949841310, 116477840, 266347593, 2298691, 999282771, 901736044, 203059334, 486108963, 262651366, 226765553, 929351844, 38382603, 696520263, 765318683, 757784286, 696435484, 973428739, 491549637, 747822192, 935064248, 153790079, 634718974, 843279091, 302188555, 661792657, 366975577, 659421564, 155362576, 89960194, 550595268, 239015803, 612528645, 88785169, 685103314, 120704863, 166036874, 553239780, 563284244, 669126316, 722712147, 329807981, 618171665, 371370129, 636915973, 76837487, 316973886, 854944324, 344871088, 867851596, 59922136, 795643393, 432325097, 747235283, 788175184, 313722207, 773550865, 761904602, 730038692, 229128541, 849934376, 107553622, 220915838, 900828667, 579296294, 906041376, 707813323, 428112499, 711803545, 923459706, 793881674, 959213414, 21425202, 282951992, 79046466, 45902439, 598838860, 436851453, 279486292, 622216750, 462414212, 831612898, 450164185, 617105642, 203944207, 1648066, 722573131, 135171280, 585320280, 944782289, 34020102, 574935943, 261871342, 197636296, 642033071, 680867212, 229604059, 226152274, 911035892, 985434731, 211336455, 439937386, 399727084, 194624987, 440856193, 329235952, 792796909, 324920720, 335308412, 136435663, 175256847, 719135528, 67571197, 857962481, 170259372, 206211518, 428934409, 937626322, 732060613, 717812273, 275189376, 484692241, 466019874, 95997751, 879994813, 348788866, 942308568, 420757895, 6635507, 422376151, 793723481, 58778692, 821596714, 934079767, 490174259, 377623803, 954973405, 242527416, 642709539, 938753366, 328888245, 547216122, 792772352, 613350940, 653167233, 749495581, 872169733, 400214379, 447137053, 918888491, 670849849, 265472231, 556639947, 591248025, 233209301, 254167765, 983690647, 127298261, 248215309, 164418157, 414459993, 45469879, 729130992, 625867548, 491167947, 242639528, 328331477, 149097010, 606333430, 384760496, 568569566, 500743331, 766038112, 414266428, 663222285, 275127042, 113593486, 306642360, 187845127, 625850587, 103232750, 742855702, 597306114, 631816597, 843659989, 214946958, 644178036, 42024831, 39855762, 275974843, 372169792, 642987397, 96198426, 227851691, 17859300, 356420528, 766177787, 517348662, 462756787, 214739898, 167777550, 353686058, 523873171, 660284771, 697534105, 303192007, 382750052, 516765990, 267516377, 120202025, 971260014, 513538512, 802693193, 738417929, 749747101, 926322537, 533577925, 52865376, 748682465, 881111389, 477280, 492379048, 178302066, 764319921, 418528857, 492808642, 574711201, 944531575, 926781795, 508287088, 829533965, 224073059, 224490226, 965072871, 733956916, 532921644, 581467849, 916237902, 520574743, 6521137, 409442455, 428617303, 282128973, 260270592, 695313585, 606743726, 599839175, 998369446, 503071182, 711727791, 923079682, 376234982, 83508723, 39666946, 252497030, 857815927, 523162639, 654594219, 871933272, 838738739, 170462384, 774824464, 321323109, 673882768, 550550277, 149177753, 173910018, 540075905, 755592285, 109539670, 803580808, 116877202, 950542632, 195995748, 52241548, 657921216, 354671176, 244682556, 46174967, 49526080, 788226425, 528278361, 149668938, 398806938, 806738937, 939227850, 336483523, 535015107, 356434914, 995190185, 55842587, 812896981, 642917948, 583783892, 68034980, 917865087, 909813191, 955424164, 544481779, 143760853, 229365863, 776485111, 621914271, 348301490, 62197167, 469638880, 415574217, 819263356, 455900542, 362302032, 751136208, 173308239, 61795258, 976911004, 570155033, 324501790, 848349013, 289062671, 811242516, 968862867, 972571006, 421521930, 283500477, 42721340, 576874310, 359023122, 332776858, 680493313, 685388670, 714301453, 332994652, 667067869, 566306364, 873381686, 574456625, 469654252, 155410096, 25016091, 128099873, 817576623, 196191287, 647558464, 70407975, 418521706, 190216177, 304636583, 271018930, 830365370, 905248849, 534027951, 767118411, 919630722, 822904255, 543624677, 270148837, 15739290, 413847892, 707939197, 126995305, 371005453, 355874695, 656187001, 590726488, 580937327, 733476256, 489426963, 518222606, 939652707, 837520726, 829642043, 337095910, 87574898, 369719343, 327408418, 749217512, 632585809, 360279800, 265377621, 541589181, 826119430, 736539326, 429824035, 286871677, 732791595, 421855628, 832749438, 672795322, 627646964, 830864039, 812062053, 767602654, 69647918, 527365860, 226083954, 335639095, 781588385, 682430957, 324520460, 604530081, 737101935, 842425470, 642077473, 143911348, 872713353, 478776385, 921782995, 594617257, 121278691, 126836262, 438984868, 975689567, 708394629, 13046918, 746857095, 402139006, 559690061, 990036127, 267730780, 4924510, 439486085, 990545989, 696868817, 352014536, 926190404, 597502414, 750930651, 277123584, 32531865, 650104586, 871544921, 629970186, 253417647, 612827199, 626802869, 637379159, 90554676, 580870784, 840108061, 432024639, 597615808, 921819508, 850571743, 828302344, 275903218, 120121697, 294731973, 109650926, 592233220, 146760595, 255813433, 995158033, 366033574, 538561899, 818929437, 284671696, 669269635, 967913901, 799896894, 791088451, 112018883, 938438938, 978325519, 786014357, 294896492, 475302792, 226530837, 47822048, 219432695, 530342239, 415672056, 609107080, 512198772, 278350096, 776358226, 903967310, 227125355, 790738242, 989821838, 399646492, 501688106, 426912941, 53714056, 325926489, 603392369, 7956186, 513365468, 448817747, 356189116, 682755191, 785278994, 302930560, 4887645, 32495136, 420771325, 253557488, 150498276, 331929647, 229662115, 647151712, 211253215, 798943930, 107688214, 613344529, 949639545, 253399043, 91237755, 39764918, 106340123, 738576695, 251874521, 91617134, 902661074, 103435815, 420992693, 138996151, 727238082, 124060158, 761560072, 703720014, 787542549, 578564928, 530796477, 997880675, 852388324, 711655673, 801866248, 378425566, 151910180, 833275358, 180140184, 27665622, 601611700, 496425808, 322959666, 69762767, 207295020, 509128360, 864202187, 909533482, 167735924, 786882221, 848511718, 495581100, 882194427, 866622712, 945523744, 361338881, 886680048, 581548004, 355562426, 561238054, 935591228, 371791931, 158700258, 240630484, 988331346, 519866645, 335769380, 972864435, 88413753, 405940929, 922686190, 414951792, 72995797, 675687445, 318722720, 818678721, 122126149, 22559903, 849572990, 725502602, 805059845, 249596072, 118978433, 484370301, 174973556, 425165449, 568358061, 145649023, 906300620, 900266496, 832883587, 561522816, 416917852, 541203065, 187629512, 754463146, 356559754, 350434905, 427864503, 455247638, 105883613, 453809778, 546167750, 520292635, 772592913, 96531603, 768810868, 376268470, 926986227, 19195772, 877086506, 148445098, 378613876, 928206358, 58139468, 359885518, 121074146, 920402789, 485944931, 589299886, 301655780, 707094477, 292438097, 934386777, 201213970, 302482617, 845443583, 299243505, 365339985, 354429735, 467274881, 185254092, 941212596, 857868759, 278677370, 522804119, 204576323, 760282905, 372608801, 885662332, 64349328, 775452077, 406371629, 927111191, 501940897, 778455861, 90917601, 226602612, 526668808, 937147964, 80965348, 752257531, 774339413, 582233645, 937196562, 160747008, 806093001, 787775377, 225037055, 301852918, 595482702, 891790917, 461643635, 618006774, 450086405, 379600332, 828460204, 70264913, 555014408, 35327232, 771591231, 524436999, 75166704, 220154689, 398408658, 125723811, 930279628, 241245905, 432646563, 873622225, 439954122, 614544646, 68723745, 243882743, 388916921, 888959334, 403606451, 227769267, 787390332, 288331330, 935990516, 773428685, 866573175, 992451479, 807471575, 9630840, 818977831, 786835433, 889458372, 323987081, 572269927, 122399180, 197109812, 457892904, 794550984, 946648280, 338800747, 402109, 372674033, 237417690, 553444013, 788790919, 543372422, 715594293, 649334507, 695331910, 320474450, 647063193, 195875221, 294732771, 292278120, 412268070, 185569163, 23358477, 106305299, 936751091, 58577085, 173337605, 257723273, 741957898, 915388308, 871345814, 454760250, 878266335, 823525375, 475769769, 119318069, 205121151, 840624614, 826681570, 711177158, 618532778, 788365825, 230718286, 50067526, 762135413, 322691607, 805734674, 485324985, 919011950, 635605742, 43148077, 690481169, 127259432, 24141686, 184588493, 718586144, 790200303, 35297275, 658827629, 168759643, 302950434, 17984640, 240521752, 813568413, 468670956, 409809617, 572313525, 181650630, 464462276, 47027368, 713667032, 995976151, 262884129, 996611323, 970132270, 114069014, 125921261, 135507660, 951663487, 177495197, 374712150, 211678970, 952300344, 530295753, 126271459, 373277154, 778258194, 132458376, 101457785, 753378331, 647677507, 442736585, 519112814, 917178424, 148150892, 473279736, 853813014, 401914543, 387834387, 592932528, 858253879, 748345644, 411663133, 564808682, 725557251, 520959003, 175704925, 656831785, 394019522, 558085860, 561437676, 599596041, 104316987, 794808098, 260938874, 672085096, 948737337, 709954591, 335812289, 850083654, 219945515, 227797614, 345255454, 924304698, 481917706, 137831853, 472136179, 3906831, 108459911, 644253295, 455130133, 53305638, 889672366, 748572372, 495855437, 436806444, 204190161, 463459432, 24542956, 999754144, 427944850, 209605557, 26219687, 51379023, 184713512, 924613916, 289720717, 380785617, 942116830, 507057178, 323435703, 731974243, 484265032, 847082463, 900060031, 853655519, 134387895, 240825415, 297306275, 681141580, 567251326, 755267055, 915025151, 445899255, 947670732, 442190176, 733015426, 609745755, 565461526, 879504960, 736191441, 376640501, 912508120, 610463044, 604977494, 206885862, 1715149, 720632122, 184460621, 80372358, 720198923, 589960288, 817352042, 938331286, 340155319, 105913402, 637975947, 328665705, 618403389, 226787666, 597559520, 128199468, 47231306, 264163492, 485919102, 234904141, 942568019, 827540545, 905092303, 911317425, 840240904, 497644600, 494939415, 663343559, 918279072, 384570810, 586630523, 65985594, 170084352, 890542203, 59381112, 740821848, 268559242, 500157664, 254732374, 984705593, 372159649, 371642549, 755583692, 433477416, 368924644, 601239758, 670473318, 961630644, 155028377, 236033264, 99016381, 68759617, 590471092, 472573122, 126440634, 380431413, 940357931, 783455596, 235846233, 943517116, 982191222, 80766092, 633461530, 872816251, 176574802, 352875640, 399256339, 263715568, 832902545, 414752285, 841779340, 195713556, 78443801, 325158883, 177917222, 161269184, 142097928, 177223049, 580851494, 889440444, 352897578, 27266498, 908335008, 127602225, 292431051, 919024252, 427800126, 938335764, 564955411, 10476307, 541527624, 705165648, 808526134, 832695451, 175843264, 746701052, 511146, 625248271, 788594390, 653414038, 581722401, 212299953, 909796205, 405127185, 548799840, 475876390, 554050990, 347433827, 409274913, 605635433, 441401602, 79939981, 22311452, 67476254, 984803615, 8423383, 652237951, 7306549, 692263885, 220775034, 166029117, 145706597, 277948123, 457924232, 890893748, 596296250, 493135915, 52359655, 407675721, 870236379, 124708305, 267525123, 827538706, 568527938, 926521585, 879304852, 994684964, 945303813, 257107914, 198182002, 192109938, 146000239, 431576917, 757259720, 44917291, 959948146, 228022185, 699463125, 869841302, 295318798, 138057060, 521100918, 81409604, 628168317, 537329240, 742522972, 424909703, 21482618, 713468212, 88476623, 639271767, 601225161, 995012428, 808958790, 207926790, 967986682, 473124863, 746554706, 388344110, 925771202, 25399934, 559124622, 37412049, 942306407, 499614746, 594341873, 101170032, 875729191, 669391768, 47510460, 98611226, 152691145, 94955927, 957419216, 431643211, 663239629, 37293646, 548727501, 612650620, 52514238, 124382652, 326089653, 598990124, 508803046, 896444182, 714993175, 526377589, 450395952, 416753620, 238263106, 647799027, 746821957, 882738510, 611705653, 303626627, 205348039, 140994111, 348265196, 687038492, 622535202, 883050635, 90014530, 208981682, 940776351, 334740123, 157029250, 839564794, 299445314, 192198503, 482039339, 715977953, 626980648, 178628143, 512322651, 572182416, 124236312, 996422068, 665608666, 710103110, 733634540, 14679406, 911975454, 12850290, 348920, 220787217, 274450813, 430241, 517960577, 928621007, 739821169, 606819494, 923154202, 454306819, 877220310, 193243933, 850007471, 936668266, 657078809, 731384961, 920906473, 604261325, 118453075, 553506464, 826484465, 388720869, 155816885, 302063168, 360764504, 932486431, 601265047, 911781188, 274259394, 462132747, 326790901, 89797499, 308668208, 905594962, 488982636, 948896163, 385579913, 665246785, 838834952, 281768147, 964252780, 824638738, 948929820, 95609220, 840401152, 341263717, 65633847, 114562448, 965340085, 251386721, 872894789, 965247770, 854402734, 659495457, 697315318, 573609889, 627888422, 41268959, 511148575, 514441669, 510284970, 212140725, 969797648, 952857793, 208917240, 414373949, 195288766, 637284547, 502003415, 275091721, 116789432, 16268619, 234106550, 634823566, 600195552, 415019485, 521223749, 20503395, 732988482, 786701485, 780473204, 521918870, 859960745, 355201868, 731050004, 761376684, 270371230, 501660506, 31426368, 905645327, 724981854, 926225199, 520551587, 975597783, 455471675, 134711879, 587937241, 879083501, 532346064, 651929500, 653999017, 242875617, 633268313, 605326650, 913622372, 568424081, 945830236, 804863826, 184591923, 134272382, 313400572, 249696720, 387577701, 480809799, 90379593, 625096151, 907623960, 963116800, 283852841, 151487885, 652995246, 308495526, 667190813, 672457804, 854519824, 656493142, 598678353, 677742322, 866100767, 995299318, 5441336, 453386657, 530794739, 996438297, 405317869, 768083333, 94053451, 949767889, 284346687, 56910636, 626212228, 307254047, 313460148, 81845638, 702926330, 82921795, 788214251, 801754087, 175666172, 662055809, 444946448, 873291, 133908176, 145721947, 875783435, 490242130, 607644266, 954302047, 968722814, 594404712, 777988557, 565074695, 15756580, 740064545, 126799192, 394790768, 192870557, 94939267, 16159240, 320471373, 230118543, 660901678, 811120686, 146555500, 119299896, 331410887, 978171190, 377081306, 887050231, 850974501, 920864142, 99797674, 777227052, 393240077, 154838872, 697004024, 686680665, 348743475, 668178099, 916756140, 728839801, 440672671, 205184323, 751989559, 750918571, 930567482, 44610575, 262546703, 239066386, 39461743, 948532565, 436473144, 533334424, 926038615, 369734225, 687321319, 140375707, 233562565, 202775662, 413557845, 477907511, 977538846, 932700439, 994543297, 144363855, 41077759, 938382635, 450328719, 286843880, 259363220, 851690963, 219288483, 101053916, 145906278, 341626459, 385962357, 6714421, 617962845, 84696079, 630969124, 967235563, 799922085, 723615158, 519685527, 10718197, 13208133, 598313565, 649082218, 401593284, 207002530, 769402649, 207888241, 932189213, 945265418, 677398103, 134199381, 65823175, 945697642, 739475539, 866281538, 629397285, 178558513, 399078838, 91574856, 958679726, 28573789, 76782457, 362490425, 689006157, 534228665, 403881214, 393232767, 366901064, 21894306, 810318200, 141676310, 220541944, 127538699, 490639858, 570099338, 601087001, 158340453, 420264139, 574478657, 221742408, 790013401, 109342712, 10446304, 245097414, 479259504, 448917005, 715014646, 940249453, 261996878, 346967624, 85745964, 589927206, 747251040, 316502276, 850151804, 788355209, 231832611, 623911943, 508059149, 847712446, 915855913, 276585233, 583947638, 949275539, 834979726, 645668088, 796443919, 542503830, 208521861, 954189473, 712110660, 973082448, 296091585, 168851824, 389181249, 174666474, 518901764, 726989917, 318136596, 701799474, 341418912, 515971830, 455983266, 46395050, 264871800, 342701478, 355344961, 657059471, 827892016, 779055696, 22279918, 248539200, 536668314, 84509287, 76948671, 993771609, 626241566, 283639544, 141061412, 196966662, 193070139, 306952458, 715198105, 552301356, 660660812, 545276118, 677986683, 971912660, 299016581, 815364193, 481252447, 173803035, 522363709, 348288060, 604647236, 399456502, 995716331, 385613838, 823140621, 478581614, 929773671, 154526467, 427598931, 241290062, 476694180, 399683528, 652126863, 631411758, 851735582, 913718443, 416413042, 573929557, 253553541, 157172760, 56260036, 656645748, 121930001, 400200215, 951597618, 86484406, 779032273, 491112844, 49314393, 890080582, 860966307, 569629823, 552397335, 188657426, 364835770, 17239143, 457750836, 110970573, 205846746, 398922545, 137617103, 432265080, 957264541, 65050423, 251461280, 312185153, 647136771, 907075018, 821858743, 284928303, 688633487, 217481955, 491888410, 776098483, 207635796, 864834501, 464061678, 128302564, 70486774, 246564277, 856899198, 2050855, 689062054, 101731176, 917919223, 316205638, 400132221, 961559241, 325586271, 482758023, 943300703, 488610143, 187427415, 516354666, 26193857, 698294257, 629876325, 831860690, 571892050, 611553982, 843661894, 1182789, 881430494, 955982284, 719494103, 405241794, 601289748, 789601857, 887398869, 277691690, 217258262, 23216072, 922413047, 719433567, 409020255, 649450805, 163909418, 975909729, 766611252, 644366293, 153648842, 752925087, 326346668, 5188858, 685623909, 352089058, 641118373, 441795604, 572428529, 958221734, 280855149, 503777071, 690791281, 315481627, 534070105, 344212740, 808598172, 953584388, 691811153, 24706791, 923605569, 534659610, 958274210, 577190526, 138138656, 137717428, 717506530, 183960185, 625421620, 878746949, 209668786, 464536495, 61237058, 454336265, 57617916, 870179965, 441405371, 219075041, 291060840, 881938908, 109933709, 572084170, 436220987, 73987128, 759053835, 639333770, 944061782, 878774815, 186851177, 990566985, 487013443, 699612634, 222514554, 463078926, 956494867, 109266135, 754921553, 674911727, 872935517, 684147289, 625062747, 358189424, 531386549, 106751365, 481149362, 994008199, 42699368, 170879805, 43634397, 498743932, 337998452, 905408477, 386451773, 699304789, 25922102, 637006311, 884304512, 667254602, 588268529, 814507814, 881999137, 138304788, 671635863, 893760002, 990361081, 274901961, 209088730, 345696207, 983929652, 182294352, 176675658, 472257674, 553847394, 297418712, 565036123, 707937199, 245584258, 412108917, 98650995, 154654211, 400526203, 10890228, 347495463, 785899238, 775316076, 259193905, 534732550, 250568374, 883668454, 545778387, 212422406, 271985852, 935459793, 187961387, 82496432, 386031416, 283607997, 411531761, 861541950, 560479714, 229463852, 970652137, 515822223, 177700926, 439043014, 973672303, 984636667, 988980601, 912369282, 743203086, 866603292, 939869358, 494768150, 573412822, 912563141, 710904053, 913016717, 6515024, 404130631, 440381106, 704923174, 271073401, 628671003, 356049428, 693678517, 70259849, 345728275, 543556011, 637818098, 303137938, 547285197, 869158514, 92536957, 999784608, 747072333, 692763646, 773618211, 960975627, 500318951, 34612665, 541380411, 297916027, 372342690, 433976213, 105300526, 304583507, 334667869, 750022425, 973216652, 212638837, 128867026, 427510060, 837122243, 548250557, 972569213, 980183484, 593042800, 21396341, 40422421, 684027476, 986777196, 441330325, 452239514, 416822655, 160639182, 229706301, 699970831, 243901674, 552877891, 856929582, 773478426, 752192240, 581396474, 872867115, 323114628, 775309025, 659944452, 274788617, 129622636, 636871750, 624368398, 153342923, 349531907, 531827937, 916819914, 396034353, 934153520, 184510796, 831489295, 17082292, 710816369, 922644054, 971528559, 527816215, 926282172, 629047397, 520647739, 787047873, 628955041, 54468972, 895989416, 690433023, 139548081, 831362604, 97413460, 18649673, 409124904, 628352990, 963397789, 977528473, 363413722, 166109445, 814529530, 594475352, 989000117, 159310563, 43837844, 370144256, 512301061, 666933833, 838581428, 258350545, 788690143, 323761104, 41357671, 773090349, 751496547, 105042960, 462048564, 89726979, 118102612, 25428148, 541781741, 125728118, 846383032, 712818241, 377981031, 184890230, 981846015, 947010855, 418140804, 445841219, 420163411, 151034654, 271613448, 966665601, 56202849, 782855700, 221861879, 869450258, 395089608, 823126955, 175641533, 378475737, 605081560, 163062239, 595606364, 632571054, 521124462, 517792514, 175239021, 207155712, 884965761, 8586737, 447999066, 17977821, 260645690, 221477241, 770417626, 435759670, 574437152, 101838036, 589094863, 686797419, 63579588, 264463546, 961956550, 875216834, 398712495, 228219316, 667736271, 917595534, 578759047, 518400126, 410317599, 610335603, 916562072, 898839232, 455481361, 589143194, 431588890, 106519373, 568699843, 828336526, 983754866, 747392296, 308133340, 122836531, 845080956, 877407155, 615848834, 334828729, 177839767, 379178903, 103926398, 581133903, 567443869, 600063793, 227196810, 362743726, 986133151, 44396796, 899155391, 570950370, 899836696, 767388173, 385197429, 561753084, 949605647, 867512129, 778117587, 828016641, 905340293, 55960632, 993383297, 595664062, 512134181, 586457460, 412433211, 867666284, 71713066, 512968936, 809760134, 101085435, 923159461, 6819683, 438984595, 27826632, 39800580, 657754197, 58569416, 933249317, 2690275, 823073049, 931345312, 445113488, 863648490, 69953646, 151462367, 654577396, 429830514, 801535492, 735952463, 617511611, 132480503, 735343281, 497706613, 591878596, 276593348, 995747400, 416960307, 204007258, 318839615, 303431033, 41689177, 194919114, 795787007, 280921338, 440267514, 32545236, 381045797, 6770100, 609475973, 906381448, 48693314, 522800881, 591636986, 889662514, 6100235, 356398334, 843388302, 100086373, 714160096, 696521533, 521610585, 902485292, 259673504, 208339885, 190261163, 73102046, 823768584, 270485498, 935883778, 173193621, 688066401, 795359252, 836181013, 238656878, 819340310, 974433535, 989446140, 558692587, 393358511, 53011418, 425278858, 787718042, 585572963, 403173298, 317580240, 283266852, 144101223, 162787619, 309154980, 247040339, 3368455, 51965706, 449036048, 388539715, 528566181, 857636245, 724605956, 237349280, 991422141, 537759443, 546398519, 720731825, 478100643, 367083464, 479919895, 925377621, 297967490, 210256789, 106110223, 953688469, 592189651, 195582276, 658811166, 855578041, 719141271, 90449736, 402905433, 284447758, 326135067, 913673176, 400981662, 459211699, 498321658, 517431790, 108129349, 155014677, 404703569, 495928706, 728950782, 972585969, 495120035, 380963621, 587021389, 661159021, 145104168, 252718924, 45805087, 234731360, 325493200, 81077786, 832499336, 628068016, 617699844, 686755878, 796785178, 923815903, 245072478, 492135025, 107638678, 340116166, 382450333, 80050284, 894159766, 364991254, 604377731, 199186791, 323370717, 227802644, 94309775, 165220923, 848240331, 209869926, 257189571, 760036776, 382701550, 917476958, 367749629, 148600165, 702508123, 951424341, 152312078, 519583576, 772447421, 556820305, 91525046, 525915282, 677553844, 154787874, 537764504, 470594095, 461280919, 668688740, 851276577, 940633949, 156106315, 746856376, 958255973, 302352143, 770812793, 477043978, 226989267, 900636467, 651662362, 287172676, 441360273, 44320295, 184898870, 506369387, 200380804, 364745006, 926617135, 570464915, 403256599, 80279611, 88485626, 345478187, 554190755, 91135373, 161015977, 451458876, 462680139, 684213805, 788903312, 968733548, 613621186, 119572943, 786579169, 793701495, 590309264, 611502356, 624552399, 495344544, 999411182, 427835742, 933119862, 972951908, 35323387, 213475904, 982325262, 408866992, 304659319, 119455416, 293298056, 867887469, 561559231, 119176066, 360132905, 940942245, 151499284, 98044921, 684261055, 278708252, 393101886, 429349115, 640544834, 61703533, 965015924, 103424050, 846456717, 682626560, 79417367, 35499750, 967961172, 776539247, 803669700, 805645150, 268727392, 781363232, 331492689, 809461314, 63667041, 15113178, 647388287, 716614109, 608846626, 814649927, 216587766, 15895250, 849074986, 567311084, 809865402, 483115800, 85436865, 190227283, 403181128, 328762899, 64635761, 230699082, 384374359, 392198749, 654659380, 511492386, 8261837, 468545482, 370910023, 751189102, 202578643, 319859448, 166509376, 381402281, 399581777, 203050958, 390848273, 924149181, 572770190, 916831689, 881931010, 375570791, 297157452, 881246479, 838650969, 361957791, 995194093, 742801090, 947715406, 444775264, 367670303, 358679877, 129985934, 137645315, 147216470, 882879584, 274946167, 604446949, 957838378, 970088171, 710703794, 946547474, 808017761, 700260464, 688877634, 532679128, 870096788, 585335243, 594743934, 269399795, 813392753, 899156403, 459868641, 454475505, 530390940, 267176234, 140749580, 132625900, 60549984, 367804692, 920390939, 310680690, 623160203, 467704095, 737302971, 420829982, 948622892, 947415292, 687876561, 573626649, 774268741, 49572996, 431361956, 235649131, 779571079, 889413543, 204347610, 863302869, 846115575, 966032899, 890145595, 268929189, 70754622, 678896765, 814846791, 14548519, 304659666, 142246278, 273797157, 362313820, 577201316, 766301943, 106685373, 285394556, 376500765, 507439464, 617426872, 22879892, 394538838, 181417403, 876816753, 30387125, 992202546, 919991937, 902071518, 515318114, 1059852, 329111672, 770878140, 149547388, 826096947, 154691253, 249287527, 384101600, 261450697, 578049803, 960977432, 792148538, 937389608, 271733214, 796013121, 741657481, 694423696, 693914047, 858841962, 383657527, 268356418, 198761258, 700372242, 95966106, 107087605, 432065239, 585230335, 451614388, 877949392, 287419829, 871751834, 165172268, 402874766, 912850080, 533308948, 215791481, 138713861, 913497045, 339160856, 793008263, 129032920, 873820268, 745175841, 66150160, 963285932, 340010957, 40878725, 636504670, 897915569, 491238046, 617549166, 804061239, 486484576, 772452289, 815584815, 430287286, 548802968, 91530546, 686027891, 139003391, 999359957, 983948274, 663454730, 95871686, 566578711, 808754596, 587999581, 863865408, 783177955, 145424188, 480007288, 337450341, 37393905, 933680126, 880077856, 438097797, 472470798, 273897809, 844044585, 868773254, 42307163, 189569907, 648083160, 311634682, 468253462, 345103692, 314175262, 722707303, 662355038, 714658556, 975930319, 246977605, 767784076, 478279787, 258015557, 713775499, 825554060, 71470336, 278403446, 232375367, 575125219, 146575970, 13773578, 266369937, 301244673, 467172972, 171957986, 992768440, 641740481, 971633130, 783202585, 850858201, 11256748, 294552372, 750452727, 751428480, 133933360, 231394219, 809158607, 884024513, 11362210, 743953365, 342192148, 522939906, 699558908, 871851941, 808232446, 479754230, 772006260, 414662401, 569217425, 943617322, 660626488, 410132538, 143812972, 837931403, 838132811, 450263039, 955098207, 813787939, 755205740, 857541392, 335386297, 82739394, 953379170, 66020544, 736184959, 737656005, 545441064, 945162291, 873802150, 792943570, 399245394, 694400207, 487829117, 418220810, 81584365, 745110083, 471453484, 648133228, 639154197, 513241314, 404407984, 546722566, 276598157, 109151470, 769157756, 441158931, 236223649, 88129963, 724660420, 334416708, 861014211, 618753717, 958239184, 130282370, 693178295, 987113478, 279725303, 745774745, 892962575, 283340369, 813170030, 553963556, 552862036, 99724373, 406935123, 441461957, 435056097, 724400043, 50347933, 569017004, 464042317, 185585103, 373648331, 68306931, 759375084, 3841604, 182878240, 919332928, 400991142, 717812057, 853173155, 460620615, 656474422, 946831278, 909885643, 960609044, 366301162, 634466199, 791269108, 553306612, 494388421, 746868018, 71705120, 887536500, 183614337, 282851424, 197426410, 73721955, 137409710, 434486243, 490125152, 675048717, 931774365, 409127782, 181458242, 733932445, 755116229, 26062224, 677845260, 243888246, 245546205, 529056446, 313195284, 654623083, 495862987, 914880133, 698591935, 295863622, 266556133, 859909029, 669733615, 831772320, 274515078, 371930555, 724864355, 744840063, 277508600, 624309693, 418055288, 786763550, 287158800, 899903578, 708118608, 203758567, 574010417, 730236226, 220262487, 183733415, 943699337, 303780039, 306767957, 346308383, 736292226, 565940949, 309581765, 772468270, 7214876, 857473247, 688204424, 62410289, 327952533, 922707632, 756713112, 548404596, 421716831, 939887079, 342730404, 218071173, 726496369, 885298208, 658027083, 963776278, 563477038, 647769370, 486392528, 239277797, 515977528, 530141643, 171139250, 414162750, 908046510, 878100126, 291371724, 769171918, 288982303, 163697399, 685602824, 437250739, 714131477, 27909576, 116984877, 550862822, 932750208, 735521394, 434043715, 707565081, 107427190, 776749556, 820050095, 271022127, 303869068, 483021444, 138509457, 802323643, 685585641, 266934294, 812228309, 321127533, 62154538, 172060243, 994572538, 25709904, 575074174, 599332407, 438677803, 476834407, 167067390, 476799562, 589329167, 677629955, 975522432, 190589821, 527532598, 850472297, 349959010, 326546290, 377983412, 395594675, 21165271, 399299478, 898513340, 221868595, 230262559, 615767834, 713250791, 268702264, 13727810, 809316093, 250222828, 590261560, 330760508, 110188371, 777043603, 844572469, 73042559, 392085044, 838258845, 879194744, 372466821, 871812394, 510749461, 435528755, 594022863, 89279577, 591981386, 208915358, 985352102, 66178814, 863279776, 146661555, 461907096, 700590815, 189858459, 258087156, 590754543, 717515583, 697022445, 628153830, 714665099, 344218867, 801931435, 96495485, 269687502, 995442480, 78753365, 221487790, 446153923, 148283959, 309400976, 639948121, 864310306, 23424325, 398140994, 247748018, 289319778, 640329208, 201128997, 160651322, 482325540, 614068913, 807227290, 215449083, 393038817, 998764381, 175156728, 681824744, 846451946, 197523682, 814903615, 986219527, 51077386, 35905083, 413530752, 949152814, 432788568, 761925954, 419212736, 392769389, 988892025, 65339814, 806854514, 76753058, 963284530, 425508961, 546816711, 108440031, 236674492, 632622119, 915299919, 569185160, 525557985, 41461567, 885862532, 537287850, 370291171, 163942632, 50876788, 173264177, 133015792, 497170486, 214834194, 101210582, 477739835, 131865727, 129524064, 648831121, 539668436, 90593012, 919402568, 982951161, 653905965, 54615067, 952348534, 704951248, 538844261, 829586061, 541886848, 646948957, 218291737, 310074261, 254011648, 213832745, 812717983, 668566606, 285878433, 929537688, 832988703, 316088976, 705193296, 961808277, 644493953, 695787486, 387667054, 203663212, 204373503, 966691111, 653024446, 419082045, 875027331, 598042730, 244075887, 703662369, 71894421, 738489076, 365163701, 83525944, 366868352, 621829428, 937832281, 786104398, 907029830, 912418161, 764686537, 184720420, 315780738, 285468305, 851882451, 913053192, 644886513, 621587363, 661823266, 22945360, 543680065, 158115927, 281326590, 861050258, 306258994, 601534791, 967643244, 530871452, 960931421, 894643477, 144502065, 517346544, 446620504, 597314088, 812058974, 605365434, 471455382, 93499537, 220360112, 983177257, 969898986, 178699232, 519051754, 51031083, 308877234, 675737690, 546503614, 93999552, 179058000, 641432921, 628996169, 128832939, 557757370, 701309795, 190206105, 707366397, 805336835, 428616069, 751230835, 201007530, 742285783, 68687374, 11588900, 22814601, 203883159, 470399704, 28339016, 227423214, 645415317, 699204445, 921085599, 415045220, 248889411, 493034534, 855350235, 603258196, 776502608, 410191046, 931127039, 538463248, 168263989, 96650984, 119818006, 682142937, 300077199, 617132200, 193442148, 338953326, 312924207, 522159256, 381890710, 287917363, 563843254, 51497200, 416268136, 399213547, 433299193, 295128955, 332275834, 861020598, 811953023, 251593731, 287217734, 542230055, 911202702, 252536280, 364139096, 403925326, 627503363, 304837820, 151611439, 673661779, 472681756, 92604741, 239665886, 845613147, 5922688, 210789945, 569537699, 527697525, 620411758, 206237264, 724086414, 598512780, 40127745, 87925313, 535866858, 503995397, 99963941, 987451339, 887964559, 678542895, 977122363, 172143498, 723980675, 413419244, 83413487, 505347219, 78552349, 729022285, 12794246, 288642184, 592231440, 783863498, 701824430, 699115275, 650819526, 50816889, 877437255, 860772557, 517724710, 710677278, 420752911, 464973634, 737492783, 311118161, 168290582, 593886218, 704684522, 396591522, 451473043, 546941113, 107092913, 646128287, 110226340, 389675593, 117998775, 223766253, 355902106, 508689642, 813848824, 109714810, 42753381, 63954624, 672570454, 84534792, 402365662, 514782426, 378568138, 961754063, 170712689, 454746522, 623860784, 764154399, 197506730, 747537539, 769923023, 349598953, 727458796, 84360593, 89596604, 503514351, 882920737, 207264222, 523391721, 798846048, 850417842, 807880170, 828828228, 223165092, 161707346, 483348599, 631155933, 363514227, 458683892, 171334719, 64221051, 410238258, 392131616, 754767663, 258749276, 358396245, 293036754, 910918146, 299971556, 838954987, 359569404, 39253040, 843796175, 159210038, 532273357, 616408529, 792245146, 717295240, 951500280, 567334898, 382708481, 560435877, 367786696, 381962942, 308943066, 788597006, 349076435, 381361534, 609482523, 850896255, 350646136, 782217656, 72940292, 300422594, 985970971, 316039595, 129606542, 324457039, 843870914, 292190912, 604587014, 853920710, 172859488, 473109467, 850926147, 661222998, 465012564, 235796468, 550307145, 952248485, 140925651, 147970383, 225606943, 416718723, 588611569, 119479393, 254537601, 628796630, 285613523, 596645124, 635469536, 457786176, 762447246, 995010526, 459998899, 303572176, 864875606, 30468728, 516174273, 943368389, 727023167, 541509485, 642305806, 963109209, 997797842, 545498164, 624092152, 664682000, 909324904, 907422171, 988674161, 177403603, 40099347, 26934013, 223283197, 242208111, 615974757, 599285417, 623348057, 926784551, 217151987, 648235958, 422878269, 96657394, 685392133, 639166190, 483880898, 210898057, 832303106, 371301049, 550974951, 669555676, 915365181, 901540764, 207168708, 46090267, 341546914, 279456203, 734944639, 723894391, 415732806, 910310589, 912137729, 881350618, 888137511, 748195240, 927115890, 204066183, 633424468, 333023044, 978821038, 250857730, 203737689, 558445804, 905136105, 531356755, 78969217, 513862888, 151951979, 789741765, 895126691, 397231137, 859564064, 309272428, 353125528, 31685493, 34072998, 656575181, 385764873, 131837974, 154465129, 517394650, 930432894, 392494331, 376754227, 482780431, 932829354, 922870255, 180007934, 429742806, 408899558, 291832999, 825317842, 747687549, 296334780, 380342318, 708012142, 893629895, 696196434, 134509608, 999717276, 773301800, 959796830, 243199472, 57574752, 503686128, 851404921, 732630063, 325766470, 621159145, 392723494, 510659942, 592528705, 100339498, 591756442, 171853709, 652598034, 351342881, 129312887, 960819107, 768516871, 588101872, 866045733, 912829908, 54693228, 879945108, 571609699, 994493804, 813718507, 969428335, 84722531, 409837266, 806422071, 462159280, 828951470, 472810746, 577842375, 756705140, 715245821, 828509579, 778567957, 118518173, 963945212, 725552992, 785552687, 43680705, 530706053, 833108142, 151377616, 101538644, 305234831, 23665082, 998187760, 581644882, 892337367, 804173161, 462612304, 440160384, 339576732, 491100803, 134690174, 31243397, 362586530, 278835854, 579250815, 486275083, 639224200, 914018650, 715706285, 137219425, 885502048, 560205282, 185793390, 371048065, 134380076, 618912763, 970009536, 847099121, 38720002, 936165391, 828343507, 674098449, 362761478, 554193457, 905775023, 713706823, 893029655, 396617207, 117848732, 814350729, 152382617, 838624053, 676714790, 622257310, 14383278, 673313023, 401978132, 803059449, 661277968, 8042891, 698217368, 190070776, 196725433, 258255671, 922905851, 316133228, 736159396, 170278432, 257799441, 661651605, 132282928, 381917464, 843088373, 618845049, 301127487, 497129530, 904086460, 942866548, 412142648, 856432786, 241568596, 910406469, 157845484, 513729069, 416506746, 364337658, 989930375, 259229998, 182018816, 938514843, 899234858, 934036829, 806768267, 741750234, 922142296, 174529802, 165905913, 174143089, 635344475, 998332365, 509696239, 971505338, 766079920, 199440007, 679794752, 809951764, 924305885, 946671204, 83426162, 424775231, 949184293, 183222696, 544414020, 57979797, 403690591, 365215651, 107097932, 393145168, 683519033, 904329414, 258189685, 356763470, 594358707, 551933268, 440309210, 996581897, 502240956, 153822354, 354174021, 523946322, 508680343, 615844542, 32683502, 796533335, 273578382, 552190829, 712467425, 686006469, 206915379, 983709798, 223867577, 778957540, 759588672, 232742260, 174109129, 672209974, 946813457, 680888875, 340115107, 603349891, 334800646, 135421778, 193507160, 123254854, 568257356, 871795454, 699547098, 869843020, 252379213, 857817366, 340497749, 940040948, 728711806, 193860755, 855956032, 332851525, 909596063, 255943010, 515957560, 327562454, 728132480, 954841084, 772945331, 18263102, 521370819, 235783283, 668192779, 703064354, 559145097, 201501072, 499704188, 267483229, 496519146, 683720088, 101839192, 402466395, 882433733, 265367576, 778868580, 436039231, 755594353, 418319821, 337303586, 232520948, 718807521, 351643655, 979853297, 291580839, 723618984, 124415738, 601483173, 14462233, 133674746, 597079583, 230040139, 526353509, 348308792, 646526895, 371557652, 951024070, 215905802, 244634791, 936430060, 353352372, 231450690, 159886510, 208596308, 342004231, 924806393, 461205471, 690272011, 285666194, 643771651, 143968032, 301360764, 45824427, 707464700, 116662694, 164923975, 16546762, 217913943, 814969149, 415776296, 898705625, 180596603, 46897682, 768629511, 39133582, 991204995, 611672306, 75263188, 943520573, 373887023, 927251756, 364406100, 680361270, 22064558, 996078406, 298263292, 23517486, 898240428, 707489260, 375809543, 902844942, 271357998, 57947658, 75976555, 907870040, 953896609, 119400525, 502663930, 6996816, 41719862, 532839834, 438224881, 315406421, 908449871, 745449082, 870544952, 840820221, 346907742, 602187919, 360113991, 631725551, 764625993, 534134503, 360718340, 564006098, 802919317, 106158814, 648180442, 387359965, 625039402, 734435846, 674321416, 488522907, 957105092, 575232206, 145795220, 440358061, 421378656, 433280784, 101537795, 256049145, 117567052, 330811934, 6847838, 151633273, 550662792, 79709923, 723709884, 160575177, 812111291, 485178864, 126521568, 267357764, 37581622, 494606043, 256140304, 188878319, 4774073, 495255513, 455498805, 476584138, 390046444, 455283997, 665476020, 457537730, 613586503, 181575424, 562783445, 158793950, 310594420, 690766644, 336063589, 599199604, 872483111, 781075417, 922928097, 749650485, 595366532, 571411194, 793101024, 852350565, 252415350, 62158545, 762252064, 786384981, 655357537, 760938929, 213577556, 173280012, 603776701, 956392882, 896255246, 535227181, 521023106, 588563688, 193973971, 67443690, 862562836, 656234680, 458557671, 655226439, 717920980, 130628628, 776240506, 737881500, 59556924, 786015065, 964505349, 319107630, 905472645, 270819549, 290196844, 704023096, 863869189, 21088412, 563152184, 690265926, 255748124, 991297660, 441861075, 602003705, 735941688, 732807094, 894334525, 528981973, 383274066, 365490677, 25097615, 629401215, 329227277, 823245622, 330595453, 165365790, 756376642, 713308881, 143546162, 865837382, 663940040, 842670874, 997551040, 508907327, 158366562, 473604571, 850070490, 547886982, 597354176, 681732011, 416975176, 293033493, 250703000, 941881330, 688107425, 334201078, 521682954, 15885768, 146226820, 339814823, 734995533, 262002152, 74653982, 604930099, 853279783, 413149948, 248424850, 773809623, 924722280, 943044461, 206041673, 280867008, 643564807, 48249045, 100314220, 966924959, 7901570, 110422804, 213236024, 764137280, 8258574, 452171295, 7622833, 881947997, 42962038, 880015607, 358485997, 871829951, 657513728, 501148680, 555335814, 770137372, 514542256, 829859917, 989810548, 744149819, 663251374, 898928047, 872580228, 14324957, 192431019, 498845014, 32412271, 465365519, 463083322, 279127106, 224967479, 642202937, 123389093, 907936769, 595266967, 326834991, 295785213, 149962410, 636414122, 571242994, 422445419, 936162072, 436347124, 417985995, 14738890, 359780992, 59593988, 141575390, 191584218, 928278491, 684714814, 119480768, 279348935, 501027278, 820504070, 809753921, 277900423, 58740722, 145866059, 442926406, 168051327, 817975096, 665045850, 176634391, 517133440, 120729815, 324417881, 798538813, 160956680, 154033486, 287092462, 463461357, 868765160, 963126537, 133840376, 789497998, 293229304, 307002936, 11570748, 395088361, 1300803, 106574614, 743089727, 604193650, 601220219, 165186500, 95126329, 732082786, 987156637, 706234953, 169383532, 142901127, 719762136, 169600641, 856776395, 808903609, 816097649, 320614639, 109141690, 729533712, 433808343, 121742942, 457427442, 567097656, 664484708, 637705864, 734293762, 433047709, 446259993, 595043388, 745119428, 891258450, 340817908, 33892859, 507593750, 110531423, 923712939, 748252840, 413765182, 629646406, 243193243, 321972129, 7929182, 364657612, 339353010, 509283580, 856696566, 161009396, 988810979, 311107578, 991644138, 232682323, 486300847, 408398193, 35480116, 71269724, 365916299, 238088600, 133047673, 897903696, 739605032, 262153249, 569052888, 511626833, 524496949, 702836771, 100152665, 696203961, 584900587, 235241377, 245517800, 427527533, 557504709, 655364342, 127396906, 188910871, 674716548, 935482248, 476856966, 735255996, 690225821, 424171307, 696618115, 147345714, 272874390, 541660325, 214205802, 833151071, 10014428, 819327909, 129304772, 24066567, 973527028, 548035996, 458026122, 545594507, 93747696, 490220648, 684232716, 659027820, 992629713, 919872863, 918719788, 425938150, 234170230, 917105696, 63590566, 816777027, 794853478, 852387919, 413239459, 259294274, 914413842, 589120606, 420857566, 147095538, 269665463, 320739840, 464803875, 703979905, 891326809, 305381863, 193046044, 96733198, 60191906, 688770558, 967637750, 297332027, 284578298, 272222198, 647460240, 784242032, 97941211, 874054170, 124628244, 133795749, 773851240, 861764750, 498056246, 905935821, 924005346, 566652934, 243220114, 157102414, 221762843, 303936095, 147078518, 147721443, 848807112, 873547788, 909972210, 225061777, 586649724, 369840788, 632403932, 148320057, 101783184, 20523269, 522466069, 643961487, 14594846, 653926535, 270342839, 189508076, 300055328, 482832145, 402479170, 668333891, 325649057, 678296320, 718086501, 384678056, 186637540, 42943970, 495348437, 944120154, 200178303, 471300712, 297307511, 759584370, 40024218, 414376237, 732696059, 739300462, 863559440, 563246481, 515308897, 152075636, 137841113, 649463631, 509711905, 249221079, 572522641, 907249256, 951726451, 843053126, 551406299, 787760970, 484546978, 405758702, 49990940, 594586496, 389313517, 833039881, 119760776, 646029339, 900754990, 840419568, 950373416, 39950360, 908953461, 315234650, 276476741, 817253120, 309656017, 351273697, 432033780, 290511059, 611343162, 572847016, 818126751, 705706060, 685807438, 606652274, 827980234, 886587574, 747626041, 742969812, 199536700, 784454313, 197682784, 385804631, 926804216, 13187137, 658730842, 232046471, 374330456, 282715759, 733300074, 6183055, 185028803, 513174731, 189263949, 62908406, 613767051, 868363592, 93200185, 613426023, 705026655, 897563116, 849240922, 825108882, 59632573, 1220792, 83975626, 246887713, 949571329, 499734869, 225663610, 123189071, 601377659, 415351511, 256816179, 11690387, 155806305, 39607412, 636953664, 584506750, 762407674, 435819236, 118911696, 717694375, 388359794, 482830292, 626080804, 98572427, 123938826, 614112802, 222926000, 500764441, 691936724, 446657887, 614139310, 48041361, 620172996, 222541754, 939419192, 892411506, 130956228, 981681550, 636009626, 148518338, 872657688, 870353537, 116400056, 948275660, 879039151, 245457394, 261745358, 217327692, 167291357, 115632361, 471677543, 897424778, 18417987, 733014909, 919478417, 630125759, 250270814, 799845404, 227950276, 325743164, 420168253, 737035608, 877075713, 721597095, 661737474, 744640562, 422728809, 266993149, 791855678, 934190183, 735459602, 883623500, 559578379, 214282619, 724766370, 37365708, 979648113, 462372119, 350232953, 545288789, 780988526, 407918765, 668917316, 100770822, 842906599, 644158046, 353833242, 938444886, 573871060, 164405609, 935687518, 546905870, 30664762, 808147035, 423177950, 598652671, 560676469, 471361493, 584127000, 250030869, 695039381, 100450429, 887866683, 607838398, 681336103, 895560897, 772998876, 48785617, 38611162, 30785646, 405356437, 289855193, 688107686, 898040229, 331595598, 904572055, 552688140, 750803482, 670901090, 298475089, 290414414, 203797697, 999340422, 772709731, 988690148, 305549185, 97267704, 532361206, 110580694, 997969352, 882980032, 959480377, 401638133, 642989112, 376850623, 685544893, 720434766, 282078772, 695740827, 859476237, 509759655, 905542406, 885339569, 999612644, 139882040, 501229740, 294060557, 152647494, 538884736, 700286864, 342681295, 479516952, 455594109, 533222976, 653339102, 136178697, 357103525, 374884431, 303500095, 422309456, 588247768, 944656717, 14166441, 3982330, 957807825, 889525681, 317211858, 981640813, 501776854, 263587858, 395324788, 887356134, 15908467, 599984121, 10830672, 536792052, 448440880, 113372917, 346098460, 240826971, 92543970, 470391073, 394331281, 121790866, 618029732, 37786150, 911589337, 890274411, 806597465, 418092957, 917005714, 273115630, 954800027, 967009297, 866845139, 261186775, 220768333, 592555923, 105030749, 602262099, 884327001, 560387810, 255035958, 518607333, 180133851, 538023810, 309382151, 979361195, 872390655, 723998671, 194438297, 975828599, 506379167, 734507451, 244596245, 253311507, 445510116, 386288160, 504251089, 159352116, 985665360, 270492888, 711073104, 778149885, 265875922, 983806983, 458826496, 555553470, 762517164, 658243495, 631480486, 28437227, 946863682, 67206537, 664147175, 365334332, 93537429, 641443079, 625689445, 149883885, 442756933, 904225624, 851628422, 775803261, 450149577, 260182841, 454142456, 188574942, 346253696, 409671695, 276456740, 371588043, 579973983, 506274165, 768767283, 678433329, 248201960, 247507572, 587134974, 178609856, 64078413, 680921003, 140433240, 218624084, 435777867, 260969664, 159377767, 929471277, 732523876, 360034814, 428915586, 628437115, 992995203, 97350470, 928106443, 919205602, 853108643, 399532540, 632493135, 756952422, 938588853, 720819844, 381529824, 286790864, 530273473, 162849597, 679084531, 867039219, 410164415, 633014668, 506500547, 202883072, 14918023, 795205523, 431328887, 24481868, 896170148, 667220181, 117776057, 35747490, 720314362, 757084741, 258307641, 541670355, 911009329, 75245634, 19775428, 228956188, 81892116, 421401558, 911415914, 885490212, 983042836, 42621733, 755141765, 87613396, 798537668, 735931738, 911474832, 201828558, 124208053, 580090202, 335764913, 780169248, 159563633, 642060595, 153357735, 8594344, 239294915, 921348385, 90108617, 13373336, 6414141, 349434505, 6439810, 657310260, 917690035, 370155152, 226825875, 951044709, 546448856, 391412632, 361008820, 640910250, 254652133, 537424490, 985512451, 24457064, 261946801, 292409091, 852123912, 633786178, 924074646, 770189477, 926622648, 58047152, 838124692, 92122121, 281761248, 256817250, 570815218, 729919964, 547459210, 643814862, 763510947, 618540074, 598722060, 200529340, 339668179, 101617501, 464461555, 475804834, 243558360, 55178282, 380829753, 819455194, 455863137, 268455693, 506210088, 130884912, 294534607, 523049214, 805970520, 164576423, 455351230, 716311494, 205626654, 179839211, 633951912, 725956021, 785359944, 308435056, 564333547, 563836441, 57243744, 769394133, 299267356, 333757073, 722282383, 955578642, 678746716, 670027433, 472501894, 241303962, 863260161, 238357775, 551617303, 533291473, 880421351, 980606331, 558841148, 236585269, 49122266, 687348004, 923131657, 179630528, 982143497, 517199596, 684556999, 581180643, 345354096, 982089197, 772210758, 296783123, 467977529, 928997386, 164875054, 332596007, 941819079, 930578269, 601106716, 217638501, 120934937, 662402571, 861363288, 643971903, 727397951, 513473365, 359595236, 220340401, 289794499, 622913974, 210020632, 335869884, 770325299, 232336340, 492567582, 85173695, 566043307, 401358849, 422574585, 887311187, 604286654, 783800395, 568055327, 971478760, 411612470, 20323261, 531965472, 4900696, 45881115, 355662085, 274014509, 457989185, 644654414, 751313051, 519218877, 860060141, 937777879, 535041500, 565970958, 355659336, 546573178, 64024947, 330287248, 177870255, 956002621, 759796738, 218583565, 681916480, 966275333, 897640660, 488271582, 662298963, 777987809, 709677397, 237427771, 142530141, 937692477, 899326099, 970417154, 925678920, 862648993, 681267203, 131154267, 437428586, 270659484, 527308161, 459811234, 187882376, 755037997, 737409510, 716429497, 429547450, 905708805, 812530333, 299327277, 268047322, 774301521, 445792792, 741891787, 519602971, 764190779, 979267124, 425912947, 493248174, 410807991, 784900975, 162721368, 910026612, 111281109, 819399562, 457040688, 74225146, 758289163, 726658869, 996888226, 995871292, 455465220, 691778404, 426099607, 686370226, 687615758, 918641025, 788682513, 961745825, 716222999, 110406950, 931901678, 356777328, 399326146, 136595367, 475201669, 292185865, 23190019, 501656531, 4666190, 981606015, 179218638, 675391591, 226878614, 900240769, 891273899, 579324538, 220478902, 524823607, 629479118, 932211373, 955632762, 223928290, 612096863, 615628347, 115303156, 446899337, 257533319, 519649691, 184469609, 306139195, 967624169, 858156252, 628305493, 187176703, 201871616, 23767438, 941042145, 886014149, 771232964, 135310625, 504975733, 994203510, 183614059, 209591595, 83768923, 978774687, 600346080, 612635131, 733764433, 174239424, 208195014, 181078763, 22369909, 176259275, 395629179, 747920398, 257647155, 595990860, 650672685, 983751149, 503671477, 325809512, 337397130, 577121806, 92595913, 913536031, 197760340, 492317245, 254804537, 45824438, 92707509, 916539624, 689230593, 778235112, 176558491, 623655885, 407127281, 758067283, 631696287, 204617876, 967328030, 141436249, 198551313, 21033218, 739415200, 898536922, 97086930, 243460564, 613992604, 936633761, 550976161, 493889706, 864247143, 734639976, 545110171, 610522426, 672992954, 347095147, 939606022, 739784565, 852372300, 158141934, 857486876, 511458419, 493352451, 660042713, 377868939, 998877403, 624118472, 799556644, 797886893, 385946405, 226089134, 156567628, 875248229, 372666782, 547859522, 137754922, 359536384, 659017017, 837698999, 959508063, 111712465, 137261818, 704525428, 269615118, 746721217, 432065123, 260632406, 943400581, 797923546, 750203227, 245544349, 389635224, 936971647, 515910523, 680636052, 852454365, 200896797, 35341576, 124125628, 12793244, 916107624, 53082714, 433384053, 853651107, 53071409, 409746633, 110762151, 650893857, 69134748, 85564271, 145954712, 193842829, 217319257, 709327839, 196949296, 450325206, 429506677, 881999766, 122404269, 497071724, 372258099, 336601315, 180029745, 387474570, 650674840, 340182712, 431908376, 702831636, 745709143, 486242854, 364348842, 254705321, 788412840, 717964276, 172036366, 866843219, 895983557, 710794522, 39494214, 249791774, 78520434, 420065288, 803060862, 55312984, 440564699, 498846422, 6402697, 726098213, 964968829, 944962844, 777697764, 506352556, 229402866, 149899553, 833811785, 38012804, 379991054, 200443461, 988397943, 415815606, 450530126, 838974844, 852765901, 487193591, 614955143, 20468477, 171768627, 688735154, 602352556, 861724600, 639275199, 69045568, 337630961, 799625561, 283849880, 908578470, 372186334, 589957054, 173230736, 31342453, 430049293, 973261547, 884592408, 561548570, 638869134, 26202648, 723391171, 420443424, 807537089, 232554772, 558780050, 813876729, 376171258, 615734799, 450537502, 163729212, 673740660, 398378143, 339264443, 638206459, 397322088, 904946152, 180543496, 680427318, 931587537, 588322065, 519481352, 231769863, 606423552, 714025609, 91046269, 591769477, 80301195, 820924993, 899750678, 437667395, 817102513, 506705224, 961997528, 411541183, 732074620, 698439439, 21682791, 132447577, 776049377, 598299017, 182813220, 618549376, 902783632, 589564343, 850507037, 784728439, 753576768, 975719817, 740256914, 441577616, 7325827, 796634450, 676055076, 900577470, 919269752, 672417868, 710835681, 533118227, 245859260, 21826672, 303444562, 820969869, 649788029, 775659464, 435091754, 705339226, 888613071, 97541611, 663347403, 136135850, 928318429, 665512368, 812037107, 964110644, 643668812, 441652405, 591409870, 23604015, 148028436, 463343738, 590339875, 969695880, 414134782, 963130823, 921767781, 977845717, 41470882, 383141598, 243603295, 260896011, 863937314, 507522442, 648158642, 874472007, 468199263, 102077144, 500697298, 477874793, 712924121, 469126672, 998329691, 176728498, 199870977, 655889113, 312989487, 539609653, 680780893, 833170980, 201272404, 311209467, 314486128, 532931548, 715771647, 904995602, 323383431, 937847604, 563552582, 575162907, 783168542, 804259914, 338354883, 160093998, 18573070, 652560303, 542151658, 407516420, 745030949, 711778382, 394111303, 861616681, 139835406, 700338481, 851684105, 838933571, 91057011, 386590180, 995246777, 104252782, 20174872, 729127017, 84892207, 185616800, 483334539, 815322370, 527850509, 947163784, 991759670, 256353380, 529533312, 481856074, 714871468, 427914548, 54242299, 638818795, 995496789, 900557299, 175028962, 501444814, 248211296, 781172003, 697157152, 816390955, 867899982, 720062362, 80181770, 154014599, 215613630, 889599489, 302707033, 786544322, 945446119, 478436989, 411370020, 806780221, 693057110, 264665634, 317114751, 366404988, 647970943, 953884730, 900577237, 315834182, 717344140, 881785177, 520207652, 732564577, 407113309, 796455400, 301470139, 354517918, 509657552, 42524220, 488565252, 959020020, 171560400, 221125591, 258065069, 327980125, 794438009, 834220478, 690301144, 67801964, 642463048, 922082994, 919891533, 396693781, 263937415, 52992128, 421727355, 42288330, 189575793, 24657578, 622503636, 710906426, 450913687, 421166284, 840555524, 84312934, 58727316, 888538053, 947921205, 975476903, 811448795, 351471991, 926241480, 572132522, 899555291, 268080481, 94984639, 800157806, 213307438, 471591885, 535974022, 899744159, 547540376, 723814962, 591824409, 450260919, 487344657, 818316110, 813411773, 780183491, 137257374, 52947560, 99345860, 132659886, 171080580, 735053791, 471877449, 741863388, 653818454, 510345672, 704152776, 466533509, 819000751, 62959406, 617327004, 897949122, 994562975, 902892801, 940236148, 164699349, 427725374, 908050117, 386514886, 123934207, 441130736, 934267785, 608120306, 28751231, 279279995, 451895627, 712418635, 399587544, 585139981, 720539365, 441435865, 657807828, 202973355, 557622584, 985028219, 858089051, 610775313, 333633198, 78719984, 593912902, 431227733, 510979674, 835793775, 758334797, 602405857, 935102940, 29930707, 229906617, 534335909, 933709750, 680860291, 117950250, 891063637, 433215013, 383940244, 761548574, 131615051, 491385837, 304327036, 365161066, 330570590, 556017719, 767683235, 314611575, 281842725, 71363408, 747777222, 356537389, 958166025, 781650369, 614189887, 656731484, 659094737, 297890316, 182676583, 68157217, 524551447, 746561301, 486238689, 415571394, 727249704, 306078764, 759665765, 853837237, 332202506, 222084171, 911739487, 460834601, 472644666, 748196354, 508642287, 875575211, 111131346, 788946809, 555511930, 107755827, 333011740, 498777401, 180647238, 996632442, 647174930, 952630737, 728421037, 981677700, 951299451, 930871277, 445740, 357780741, 38072191, 881541040, 368272402, 120986608, 787276787, 383591513, 970760554, 990081841, 645771702, 87568826, 205674625, 192910040, 536736273, 192303639, 787605087, 545827650, 202808878, 523800681, 158315108, 912058226, 231494255, 861634046, 457998596, 324568242, 736908063, 505580432, 302982823, 562969149, 892668746, 117334499, 226690078, 473391243, 43344806, 745594287, 50395765, 943904755, 432238170, 665808410, 94501695, 679472760, 873208797, 481191362, 757947667, 358232462, 915291175, 222492321, 624430190, 341490343, 640301805, 547105675, 799723163, 821397818, 927184669, 764544890, 328461790, 997861006, 331845069, 991848170, 285902371, 51005004, 270203896, 885897664, 688221320, 541623812, 682478725, 654336422, 415834778, 488124195, 413539589, 978935415, 653890504, 108536028, 7985709, 843708648, 952861717, 542549009, 822502713, 408192388, 694002216, 749292342, 409372857, 319477506, 843142101, 889849420, 826150411, 619289448, 208738416, 381049023, 565284298, 331610661, 387326444, 41229746, 53758963, 498543447, 621426863, 164767606, 654199821, 556961258, 859171106, 494232459, 751651138, 780283051, 888931061, 846867870, 815344923, 652879208, 104753949, 640222287, 642260040, 324562356, 161664647, 761133868, 973310437, 492538289, 856406972, 695073429, 89351933, 951620971, 414736724, 15970072, 621342431, 923701010, 516701817, 902124472, 236010106, 702798599, 87351865, 801920204, 354388803, 94685133, 305950010, 980959770, 829073920, 990699902, 549823594, 961025204, 321640172, 938887149, 540339177, 740738371, 412484117, 723578844, 27620327, 813274226, 888979969, 426454313, 583843148, 391381407, 17706140, 614266674, 226943963, 844649112, 302133021, 131695603, 339116213, 139582164, 341249147, 620545885, 655893819, 678114593, 600847612, 532121397, 50724985, 178078868, 640815160, 898350275, 990398901, 543044846, 493845405, 776092308, 785524965, 429900838, 404439078, 188838733, 28900775, 593011002, 488542822, 116908303, 414819116, 656004654, 611801802, 251792569, 74625288, 56064364, 351209483, 784126168, 432116092, 21328417, 387345369, 331038403, 360974524, 769208653, 589761739, 169525861, 522374081, 263810446, 351431270, 563471980, 648164780, 866673001, 341408283, 193188168, 62099611, 858733953, 820376359, 142173466, 885033995, 260914998, 325553605, 509663289, 4927170, 362270931, 937937701, 634994132, 144074158, 773276045, 561000138, 284321913, 601991776, 291536203, 536543243, 659222810, 377724890, 37899396, 972873205, 97008432, 418607702, 801091935, 208461496, 326808060, 728835287, 128424715, 623542076, 539205523, 815932269, 28504999, 191183503, 434141476, 286287334, 599328652, 960333634, 71726554, 203207114, 461777470, 222891187, 54594736, 808909444, 313660293, 728045064, 927983134, 335132290, 520029325, 995764318, 942820460, 985711791, 467124712, 28851358, 253042102, 27512975, 141427796, 212163493, 721729871, 661876421, 282091179, 452804804, 931300290, 722728230, 736526808, 711420048, 189735562, 834983924, 190982168, 526883042, 575565883, 531408425, 628340591, 857570823, 534358759, 421223884, 433547896, 881412350, 991824702, 83215738, 436685152, 194864333, 699379072, 441385074, 19691638, 524033792, 99834721, 722244720, 366887693, 23015911, 223787149, 911816155, 589741828, 969318911, 506866626, 149211804, 929963830, 721815753, 319619404, 760564460, 31345484, 570087382, 209792233, 111164644, 288356179, 149484066, 127514048, 42719303, 90965231, 406576582, 998433325, 698268911, 280940264, 602754289, 899117988, 635757709, 785380488, 286527893, 346057025, 534157552, 313525782, 586917744, 673201865, 775267591, 840755113, 374393079, 732804672, 355173826, 143650946, 642700751, 134748985, 669988586, 967385472, 93846916, 602928729, 290225888, 932356274, 915802416, 908400350, 469171255, 166447888, 706874748, 673662601, 71373057, 949294032, 952088800, 416159387, 37787384, 658470524, 345761379, 479888658, 768896587, 552821685, 234955322, 323919497, 969519067, 950771921, 240656760, 77619888, 452067229, 908417921, 531558986, 305872882, 368583342, 217982838, 400394180, 137853525, 290690395, 795821999, 395109438, 786237852, 717002038, 935957634, 819411985, 672661868, 615319358, 214166977, 982093864, 828370021, 701423295, 703721494, 943315552, 497689717, 171642851, 720451136, 23148655, 69263281, 877449576, 28038136, 754050116, 75522063, 353850042, 617208494, 950645645, 680266040, 583140054, 894693306, 560449445, 915596885, 796015156, 590002495, 38644575, 71325682, 176195511, 10058295, 274889718, 427407872, 20691643, 589432011, 244139059, 571855113, 370524148, 587358909, 346846845, 280331246, 956599337, 398621972, 222833875, 392803283, 807438340, 727746755, 143130380, 116421657, 320049500, 911267188, 96411272, 301961671, 413535796, 836221649, 612230409, 491904381, 882345605, 916094045, 452064006, 249009244, 427074528, 725525954, 221298418, 706935808, 487449839, 857931927, 18062010, 893251016, 842804157, 85907171, 239833249, 227172084, 130464832, 478662367, 319849989, 402749984, 419284621, 720777353, 385196122, 974542067, 942163215, 301108172, 220689347, 980982088, 81643257, 881108459, 83810718, 120684509, 9244906, 988310554, 233061535, 209657986, 823498659, 71550637, 913416741, 646893343, 608680322, 477790438, 200485049, 252340468, 22627070, 426908388, 324403985, 15003760, 833075911, 707443774, 50653283, 233385910, 651616792, 493305744, 524062225, 108922185, 708454978, 279394881, 623834166, 962975382, 11351233, 448409581, 428523104, 901927983, 324731795, 704340758, 157874016, 951976205, 585144728, 582182910, 807112053, 587616383, 594886332, 965369683, 982230037, 196360077, 95320118, 992602205, 232414880, 999140310, 889330191, 905905246, 729271737, 664228406, 165458940, 244414424, 580666334, 407947074, 385613913, 34387382, 215621423, 145817288, 335159981, 829421001, 777872990, 485661598, 12534209, 396415492, 281003883, 140141064, 951952654, 375523767, 208050670, 427682243, 826909615, 201438538, 466185416, 29072876, 679575598, 375872933, 163317173, 337212837, 181591637, 405129802, 116515440, 967794972, 308785603, 636453845, 184974242, 66985775, 464290754, 921910888, 18006788, 226195937, 772315898, 585817243, 512563380, 855555498, 29749480, 419492744, 5369413, 860705326, 232541692, 634773185, 481007345, 544273223, 400813308, 571946770, 713101436, 804943676, 600905718, 487667312, 111610905, 175947456, 376271567, 272171630, 824463657, 665561854, 705115764, 296292656, 948315858, 32725435, 788224104, 895533301, 725910839, 617657393, 366356573, 695677599, 170377653, 552583445, 97728371, 345085139, 632401824, 843442071, 251101461, 668104334, 697050452, 580928558, 361865065, 516907326, 168434685, 186790844, 873433167, 888419600, 382196154, 97585769, 22585195, 107800255, 840599044, 370285897, 852911737, 685647801, 233116894, 595613298, 625416474, 925772264, 237793032, 560021901, 531394545, 822182904, 538392072, 891927705, 235872966, 550237258, 422370311, 560494449, 809085767, 854859817, 419874782, 229869581, 451862108, 845202019, 606687449, 865300862, 938453754, 89071399, 130478405, 56139336, 969975169, 138554710, 376748221, 310299831, 725080526, 127664061, 728208655, 308283461, 289122078, 22826752, 79269600, 89118824, 119641566, 74003123, 429652585, 798578670, 894131595, 321019626, 268386354, 219823935, 674359021, 804344835, 135571767, 909817544, 618249522, 498606259, 236473282, 901964823, 526739950, 584555799, 591883990, 954260025, 73944392, 568247015, 238076474, 549647287, 184960350, 937835001, 321618151, 20247828, 180630526, 639520746, 696835719, 950828707, 220976910, 396733174, 117470038, 336851340, 439682345, 803595856, 721656552, 846487044, 472850709, 505493819, 734594416, 870614983, 283362385, 397748022, 199543433, 573704580, 486503987, 756215703, 13027333, 592998894, 704802120, 60322763, 2647977, 739767247, 277006754, 813016551, 629145634, 738118785, 618373855, 199061353, 937215770, 550555827, 896413615, 830512509, 652508919, 759884580, 496066411, 265890221, 470971123, 193069802, 925504938, 99001646, 327498507, 536785454, 830652616, 749397804, 21201113, 644739952, 558035130, 7163687, 745218352, 216788468, 92749968, 657502334, 116941001, 308882729, 800614581, 298293658, 873937533, 627935522, 72445794, 799984397, 719498884, 289755299, 811693282, 350709817, 841734465, 998919048, 900449439, 624536685, 388436084, 692576081, 768651135, 135970632, 983862812, 851818849, 307826451, 387793482, 360201574, 450724501, 642560285, 544143977, 352100999, 221802382, 55227733, 901993959, 780576113, 653908849, 951905673, 408736378, 772213594, 928704024, 46399022, 743409631, 26220794, 927286051, 382803747, 281188661, 906652760, 814555162, 955953984, 913912333, 743576167, 748630322, 693533641, 369623093, 766593923, 894182940, 535504644, 652202646, 124887747, 905347639, 243571484, 579621921, 209510596, 90620473, 711601593, 495190273, 540074656, 294724105, 850526281, 12001506, 939216752, 946554616, 46082468, 678278973, 959955210, 155810837, 189139386, 638845738, 661901545, 473208690, 596650701, 687764212, 387746941, 31642453, 512649184, 135478796, 482744428, 324549431, 571498769, 9244934, 833080056, 497436617, 669402377, 747116512, 127396480, 536783433, 851077154, 724284296, 712571845, 343487853, 55717559, 604189860, 274307033, 892673075, 487216129, 736921019, 950842014, 862268678, 707869868, 112216474, 555874376, 582623990, 348817302, 391530919, 193750913, 255594642, 147536159, 51368026, 352917622, 411089383, 407168963, 980418437, 407175946, 568078336, 800808584, 458731848, 377368069, 155557546, 496751954, 109446814, 896439502, 510974819, 183106404, 546147745, 931934468, 619590296, 925854466, 919776937, 536122735, 633326471, 578704696, 53578079, 705593203, 834834961, 259919712, 543947850, 919839308, 781558276, 443916577, 358411173, 154966074, 595411711, 783404630, 698119095, 525514634, 152271659, 362526611, 319616841, 256236988, 212553419, 288521956, 862897596, 648251608, 929210758, 600280773, 406803219, 605306326, 340548794, 955554704, 9439602, 289013168, 915276215, 366705004, 66234393, 719223865, 952151868, 771552551, 673606291, 373880475, 525234608, 248967887, 395343443, 302943680, 792928807, 585332012, 825310965, 836537027, 654552034, 633140506, 226350523, 38919362, 127090499, 263802994, 476315572, 439141327, 261117172, 992557526, 393275439, 996416430, 669420988, 34956570, 758408608, 324398483, 633918144, 160701479, 329932021, 198146780, 419511701, 477324944, 173543152, 299816797, 63459367, 405905963, 239237302, 479442561, 555536506, 277426831, 649111906, 716923949, 973841271, 767128689, 557559767, 410750486, 489498632, 844518014, 76935111, 3249790, 690119644, 323647634, 810948552, 494332262, 444566971, 951368665, 361990686, 916378768, 645895476, 299813549, 86846546, 159671553, 129500982, 838600875, 265855307, 38534156, 504179220, 766985887, 21010417, 140468800, 579648217, 207079932, 476535372, 761229234, 354159370, 229776286, 457261701, 556233907, 774857681, 730467840, 609153769, 855865839, 851129885, 40401885, 864331866, 758291037, 329218980, 749362494, 222096643, 120956974, 443726678, 113057970, 817161470, 41474910, 248109067, 173387581, 786385617, 768119153, 678939506, 948424260, 461749244, 915895665, 936629083, 666706935, 179279612, 234690826, 530376858, 775138056, 522699290, 102469963, 736007166, 623310934, 710444719, 323811181, 368558786, 643657255, 854065093, 343027768, 367411022, 465304001, 998087881, 568247315, 647893121, 568066184, 541588484, 50630943, 794605156, 971328077, 277496805, 772745149, 588719296, 925753429, 192662297, 295993565, 258538769, 576407755, 379138672, 456973585, 623328169, 823090495, 636630557, 900419, 395143083, 563127824, 580443392, 640995634, 677430728, 140891212, 913326543, 141625256, 441837850, 274179348, 204009555, 416031053, 78053123, 494395237, 957769564, 996911748, 632207268, 46119560, 874885128, 361608711, 870275995, 883162946, 466917053, 257439726, 279066812, 4360997, 815611406, 96550410, 313767646, 545293893, 199056896, 150739017, 123931678, 76305759, 573111597, 368049643, 97138515, 447194518, 545789308, 497950774, 135168741, 489979706, 134691633, 692901443, 41001731, 933991006, 732407442, 912620526, 615559238, 46274077, 633459448, 499468540, 958716376, 699552560, 565247238, 380841653, 614218518, 510885205, 187294273, 918272890, 878948104, 396840258, 349434974, 170749821, 23667768, 943507265, 580865133, 558008412, 606217429, 955318018, 262646965, 117445848, 318419337, 139739501, 907721373, 762651374, 692824169, 48210484, 148809517, 677020881, 562424604, 935636399, 531490160, 344700666, 819423796, 23346940, 338155188, 375511435, 997928598, 267532868, 672533589, 809016529, 929848038, 879095016, 719356995, 973810570, 679008121, 74174449, 972246565, 227920302, 66047482, 796810304, 227523830, 38742919, 734440310, 789390769, 787556435, 667228243, 541331190, 868037458, 513788100, 253049411, 859786601, 52657128, 460875829, 507699958, 740346199, 962213258, 394864410, 451119203, 477601253, 926535124, 134033514, 614959100, 649699383, 409869025, 665443106, 759071567, 959098674, 723575628, 191775156, 781375759, 5573596, 121948711, 131279485, 887003659, 829941236, 307186188, 705759730, 173860778, 893164703, 583647588, 14188737, 250578326, 790567242, 890058814, 158710840, 488178887, 445127147, 931978519, 590544243, 47211093, 684528176, 821443376, 46763242, 658589978, 174755942, 34774797, 511652879, 402857599, 536227990, 810820379, 847920508, 828356507, 795758448, 317433157, 269297892, 439203275, 116880711, 29105088, 437067779, 895840695, 479702712, 995894282, 203755614, 805905915, 35122240, 540031356, 907818705, 325806082, 521910517, 986386215, 323662002, 551486723, 761129396, 556854891, 515661113, 567625510, 285437225, 118527356, 248248042, 65116696, 867757218, 838139100, 242177317, 987397725, 931918277, 511226488, 838243692, 358508549, 954523702, 778210335, 701946101, 939515260, 187513558, 430070653, 764656274, 654080506, 724310828, 410282933, 666899242, 284667426, 947016936, 786859231, 591737777, 837216599, 984750981, 418745051, 57486430, 575829629, 100046766, 78888598, 501058448, 293094846, 61735153, 334161116, 767386799, 936019045, 408929102, 314335992, 255435004, 224693722, 107212904, 892387031, 671445433, 642602863, 528251402, 971606499, 628259492, 176257153, 476129818, 451825182, 729017422, 552980341, 204596899, 121380710, 689245318, 968278562, 398998607, 733107778, 347463690, 595388406, 929827313, 621800054, 63307031, 847000415, 316464577, 6127117, 563504861, 845703953, 334134534, 762798057, 886414956, 574743549, 603062392, 423968474, 829079332, 274132616, 727584064, 408621553, 967513818, 817625072, 907760160, 966143587, 690370088, 574026679, 668893320, 37607216, 967735282, 592688366, 615629577, 310094426, 919242268, 506474488, 923759231, 398108188, 983120995, 680780702, 394878460, 915292460, 418158209, 914458717, 739382176, 542655604, 454307052, 876940753, 566092688, 684456377, 941907643, 104106423, 340176451, 351880903, 457723203, 776869657, 361511284, 532199723, 89078865, 178108326, 721648247, 261961863, 620031260, 960678682, 590491539, 296239665, 881048149, 100480198, 716293306, 14092734, 415730186, 250624970, 786589130, 289716708, 245562372, 671996744, 132263033, 506592420, 418294036, 374369032, 180804452, 117801967, 918074565, 436163574, 670359408, 124961256, 607856587, 932377859, 342176972, 998303006, 228878501, 336588759, 523975031, 129721230, 678720452, 879622563, 337341503, 699841215, 268553747, 352306461, 25131766, 624840127, 368386399, 512693603, 730170597, 539064711, 532634998, 971857155, 214993208, 325339471, 325746191, 525446415, 465627840, 158792857, 973257424, 560463989, 205114402, 974981000, 948824273, 980764528, 135578843, 247426593, 618000870, 26050572, 285007201, 215846397, 572798642, 487915963, 261098467, 889276309, 274033301, 390833257, 584117209, 807156507, 355927351, 713222292, 830350871, 393744385, 478577594, 739894130, 890035928, 283047256, 858528292, 791727111, 159434798, 196138214, 258198031, 839283439, 429508003, 175218908, 831293180, 582065156, 856586843, 203302839, 224296453, 967249609, 226413662, 970956651, 877157598, 172818761, 947590951, 677374540, 828974486, 884220350, 179109015, 362966199, 2634888, 494266043, 961249865, 494300555, 214613597, 84797206, 748489752, 367621530, 810281561, 51158026, 354360944, 794090368, 84701650, 448296321, 864045124, 624405361, 357170987, 297967828, 873875861, 645473558, 316637470, 696215875, 330544413, 870722358, 530283863, 357546048, 104826320, 255899734, 284524896, 35766710, 200686474, 560006959, 804162419, 40841975, 802710549, 231428741, 634293466, 711391219, 90002255, 258321962, 936780173, 213438754, 859921348, 420747664, 830659239, 129171470, 166754034, 467343866, 122458482, 890857968, 619587852, 941633569, 273557614, 588600122, 751295242, 55110469, 709230212, 180789000, 749278103, 775281782, 393468168, 489284703, 42060226, 72129006, 266226745, 116468398, 612564846, 869282854, 567261581, 906881791, 582352739, 390640990, 234195328, 717456247, 947821279, 903522535, 31855014, 413581656, 366003869, 83049478, 72028756, 726384230, 200878275, 303803434, 892038584, 251409749, 243756462, 527382320, 648223480, 557451629, 815707339, 510754485, 904509651, 401846263, 3492741, 942357430, 382470633, 265636208, 277982260, 190912159, 139004893, 66791571, 898783788, 590367175, 882415099, 427790296, 282360028, 741542408, 563068690, 79830859, 795314106, 954461872, 258004, 296889395, 370077959, 140601598, 17598809, 468936393, 39546358, 106718247, 377712547, 883158186, 198277998, 658587836, 515012586, 440912988, 625432656, 863859064, 777265773, 593428200, 808452247, 616948960, 852892653, 533546829, 333625045, 287642368, 498401187, 87523491, 299043159, 407738719, 884966588, 893226901, 4059790, 281773206, 619539700, 844818271, 353148457, 466206504, 302357695, 570305765, 607412275, 249517391, 703583743, 838685120, 709510326, 149221187, 744654444, 921612414, 865447420, 785776150, 189676483, 748885062, 899450390, 331870190, 94740530, 665039744, 335894600, 546485829, 129748496, 142487553, 572886753, 611839513, 459112159, 992741916, 744361400, 855275714, 542463825, 744959992, 926131146, 458741344, 894315438, 816200154, 930864793, 463303204, 318934579, 228327083, 903423371, 946769932, 128945644, 881652014, 513696494, 594119363, 304961255, 200820376, 73290408, 74379785, 975631319, 393708542, 71343137, 399912129, 117293889, 252355558, 70992091, 304387369, 128238664, 107220944, 383242283, 204188416, 891102289, 631620126, 868885691, 223659177, 453013837, 743236019, 661155174, 431738318, 836566181, 328496901, 420697684, 27855055, 643041399, 780780205, 886690492, 901673943, 325347753, 253354274, 842927175, 855631919, 766865065, 125794970, 984799763, 320766761, 680231877, 859068463, 872171668, 924935632, 515168229, 197085264, 463673950, 692228379, 145416915, 239165683, 513830591, 222555578, 734241113, 66756685, 568368536, 330444105, 257064098, 963984472, 702427742, 682442085, 407945285, 575520786, 744257517, 797748894, 127093662, 279751132, 391563808, 582619902, 929294663, 373398461, 827868475, 865846810, 165995110, 591996340, 307130676, 422789499, 18202383, 978087073, 508942217, 486127607, 902378533, 47059928, 645379711, 374121424, 721594949, 858677188, 290594664, 923490038, 379487415, 495769588, 420758518, 762060748, 535992051, 161208765, 112786903, 22807517, 928302806, 761238533, 71634063, 728483570, 934156392, 212960027, 497118115, 8274934, 441610415, 256012515, 460750646, 310229126, 52171022, 698032665, 296490255, 907670644, 826600338, 195433532, 787778792, 972564536, 664489109, 330545361, 608911977, 79287585, 262373338, 857529219, 230225218, 319016677, 809178604, 84243178, 203188562, 482443461, 866431881, 804221933, 334232669, 417582891, 166420040, 487841023, 139284381, 650790759, 220718398, 205896670, 514887379, 813108519, 37382147, 648318637, 821413896, 174520656, 516971110, 997522549, 341428964, 983308867, 256723955, 227329441, 616397664, 64720463, 508623918, 268380507, 181047103, 769528656, 800415260, 363910816, 585945320, 96903801, 290881702, 172357588, 82437998, 324881840, 370606113, 804261979, 805362904, 145456527, 400777381, 610360842, 743180228, 282089702, 227043180, 432739705, 798635676, 647619283, 525650436, 253364876, 675795532, 397700038, 284125968, 177867972, 701680423, 588623692, 80363117, 198999596, 507895147, 584406076, 283386302, 672742722, 31256114, 832037263, 540073726, 900027261, 629511894, 415774839, 685425637, 337273895, 651018598, 853323600, 175211359, 27321073, 578518158, 371397336, 48123662, 235734268, 386662990, 365897223, 884643181, 609253804, 552448300, 382063134, 143366784, 938760165, 279863663, 474652479, 205897392, 283040483, 493283115, 392788178, 210149104, 378731907, 306719608, 734052553, 552003708, 434190459, 356913024, 742443520, 649438592, 865184128, 221615024, 208710337, 349514076, 37857788, 498024147, 656440622, 990646499, 624571301, 588813492, 499618578, 341482793, 309105047, 638556639, 975166478, 791688155, 958872449, 180063146, 356185987, 366290508, 956103591, 691005518, 745986465, 503779291, 507888683, 951200338, 861064243, 99938028, 540214643, 721551740, 791955874, 160633300, 549450037, 740335646, 971650430, 589896766, 685495799, 281606809, 834729429, 900601855, 159007618, 958637866, 733985808, 448055937, 540501229, 9384772, 263152306, 499070866, 311191607, 716084316, 334435793, 971979740, 257337187, 797562927, 233098309, 127466494, 967434677, 499756701, 832488699, 684788665, 83569289, 881242171, 650750490, 717326103, 643304649, 790752963, 990710618, 263019542, 905092594, 341851902, 923293887, 279576753, 617754258, 34340550, 823244802, 554535751, 139261845, 899615264, 726110540, 326779672, 377035766, 675409410, 112124157, 549472038, 646777608, 531248687, 811825972, 480373436, 683548229, 367471607, 610484047, 902735255, 487806277, 340351286, 462210591, 428537541, 892053211, 841807144, 85184352, 813245400, 206222488, 459266717, 353381199, 871667130, 781387191, 427288030, 837835540, 149232030, 674492631, 200618920, 487128850, 760405853, 348490537, 488435491, 353279425, 917384283, 757787892, 299750702, 759873166, 230011498, 534081999, 806113057, 263153225, 76014776, 782695548, 283540184, 639810331, 220198581, 877850989, 747018716, 953850013, 161943812, 808295301, 801584475, 24149046, 326869649, 883428571, 456140021, 778029791, 632019586, 925266969, 752142410, 823814919, 313738635, 229483957, 805795199, 672864978, 931621031, 167764190, 839000119, 851337187, 681956453, 911902338, 633675967, 149692468, 629713423, 237054277, 85738807, 709882119, 841825190, 124881867, 37116474, 175121350, 280312745, 468635503, 324814814, 236484819, 57531195, 797751342, 204800999, 457790433, 393064438, 327896433, 171751319, 958533507, 626730292, 727994482, 260653974, 816705899, 724270294, 653657044, 461669813, 813646, 136466292, 401858342, 320236590, 32861942, 141238856, 582257687, 760386189, 638361286, 948521045, 794926627, 710199372, 363798524, 420667047, 596491275, 316549928, 875555957, 817518916, 805362541, 806119905, 389732473, 12915354, 833704261, 78269812, 927694616, 933121961, 959171060, 37926987, 670066036, 552966928, 989331695, 678129588, 754690029, 293617299, 62799842, 219518507, 44940016, 805380169, 285011142, 174206567, 940798064, 70491589, 23970287, 86471574, 291733781, 214320150, 983189061, 505947355, 868350508, 657975124, 370565057, 616295944, 472344361, 936654407, 820158394, 502187380, 287810982, 313617791, 612017183, 748190405, 994635174, 659057603, 498466909, 935957584, 238684408, 948899316, 854941183, 492528432, 899740461, 531726088, 414283771, 529525037, 589874368, 781522967, 630850451, 345705490, 125198979, 629291366, 363427339, 771001328, 698152653, 529540555, 337108301, 931062697, 649519637, 748381910, 466357956, 554138898, 813070279, 563628873, 486502004, 837031677, 77707657, 978679720, 258057744, 184226282, 417637171, 261450665, 436449979, 31642978, 562101633, 434122254, 391707015, 442610997, 862874181, 499517989, 881867396, 456593628, 585938440, 785850321, 195085074, 691905142, 782097174, 734183438, 348149005, 915766146, 91974002, 565400849, 866078328, 442235163, 503530795, 332583640, 379987408, 11690038, 249500886, 983879567, 211193410, 932902254, 36737707, 572939424, 723930142, 313435629, 749421779, 121411862, 91290147, 490333968, 7848785, 464208749, 763191065, 278164312, 621476907, 467562342, 266555968, 263587405, 765198274, 461886827, 598114386, 62496413, 840377405, 137028849, 184052015, 10070135, 115783683, 511226570, 639272720, 697866444, 897249329, 329501312, 271443899, 432740480, 101613970, 722658542, 58805691, 353520531, 751971596, 225052976, 725512122, 447495226, 690530328, 325914694, 397121854, 371920398, 329213935, 38527717, 910221663, 674240779, 178835496, 571716605, 186062941, 541608509, 726438919, 567768705, 745033292, 768740776, 878159476, 438278958, 74822276, 473974949, 188576704, 29758218, 364175398, 629237836, 443789685, 728374189, 511417840, 86339296, 324454158, 143733929, 703639397, 134270856, 328236401, 616357711, 576035911, 278140523, 679626897, 533512229, 758480901, 363405411, 286878081, 786715912, 44464375, 719696123, 381052899, 784888990, 235209051, 504931397, 191151045, 148025151, 209344048, 790344085, 190585686, 761971418, 216540418, 241239291, 769508414, 4739741, 247646040, 571561039, 56664766, 663637171, 645307470, 749303755, 106015730, 728900761, 536867853, 592613333, 11612891, 818019916, 947367424, 412032862, 440349566, 729169387, 120405759, 787465449, 71006527, 661171258, 416317053, 143580191, 117597421, 620255689, 442919725, 390277627, 585480575, 699125976, 432193321, 130567915, 483778327, 638052696, 381542688, 2916827, 734498277, 403416487, 990826705, 787819566, 233876497, 541102912, 827742526, 390504729, 346933037, 820466244, 768090554, 773663331, 830388414, 312893986, 215055921, 147085348, 354088384, 130458340, 173009510, 116803489, 670803097, 917782654, 687712044, 781194960, 974329994, 662037023, 52229017, 154937009, 402230717, 77914906, 152361998, 35777553, 260078499, 948061136, 171414439, 778149665, 653265258, 431756181, 615355670, 998317783, 963775154, 636057812, 904351941, 52833074, 302691063, 961998910, 778906452, 550858539, 838931294, 273112087, 659276115, 701198441, 609077194, 759104086, 71084930, 598681608, 506321557, 902134715, 240669519, 144774645, 412178312, 115752735, 837555131, 729507814, 931380244, 375246432, 67250557, 861172506, 923370376, 775733972, 511101429, 354938466, 292688617, 800797500, 444560902, 890428972, 225377320, 541491455, 891707801, 643555613, 298525197, 802171947, 436399053, 792422714, 55292907, 795487300, 827515962, 953002910, 969137133, 713770194, 544976274, 989928080, 472353523, 414718381, 978438415, 130910830, 735941006, 810100194, 767608267, 887536181, 838417175, 197002477, 743913585, 824182619, 695948345, 576547666, 115751708, 604824072, 21593608, 876876067, 461934028, 981583438, 340178840, 87600331, 646159880, 231038230, 552920855, 285547322, 92173262, 226981083, 424973171, 28627233, 80493195, 383275891, 694238520, 499362598, 395485787, 466849405, 169603844, 953363516, 818395539, 609000886, 516080016, 432407638, 589612132, 731987252, 816660977, 834734419, 766364137, 214240130, 344377256, 503582121, 893353464, 423650594, 763330327, 756630419, 53574986, 484166842, 351426550, 21557218, 587059174, 765589065, 809309488, 492241439, 244886268, 294188810, 661391300, 360549978, 907719214, 966492712, 350761020, 629290771, 345708009, 666401097, 429940847, 244804603, 77924915, 506196051, 430381503, 339096965, 710187383, 818268825, 52541100, 957161584, 891582442, 216592681, 170012570, 303217090, 73133023, 305428221, 214018162, 782344169, 248849595, 219691411, 811562763, 496936812, 46276668, 447433584, 206962610, 352135379, 601641555, 185014863, 51874823, 989527212, 740327296, 327550319, 945433035, 908318515, 947903226, 913486448, 875129054, 545643516, 949415909, 88382491, 563466929, 739976251, 230132571, 923867062, 860205541, 198402573, 36306683, 155688120, 646899170, 543666764, 86077108, 912855202, 281204454, 228420978, 371395268, 931799174, 4836107, 258638553, 562555871, 863422121, 228370878, 623596149, 821534578, 123213860, 436747326, 809313706, 71064871, 818739657, 913996527, 576982829, 621508690, 100149274, 747577132, 478095536, 943731594, 958724713, 741824645, 96041024, 352404043, 474451292, 191438782, 424561844, 975164359, 920343920, 928258475, 157908715, 50018102, 642970611, 513861840, 465294097, 251369213, 446886695, 271462699, 723982219, 534325202, 735228176, 818208394, 651383826, 752846330, 779557764, 816686056, 253897874, 604514830, 873941774, 843159986, 446984112, 990781355, 276238063, 962586480, 133143016, 598694053, 858895208, 640236638, 209813699, 899679842, 445776370, 862714528, 575737228, 240618232, 64761139, 605595100, 320323975, 541315317, 344639092, 842594778, 352825752, 398288447, 992729602, 663601866, 821688697, 483372102, 49509123, 796452663, 584917312, 856858577, 506942945, 713992493, 647140213, 465025961, 437711783, 863475646, 52197793, 698106064, 585510377, 858007292, 962158590, 415268121, 818968109, 260407694, 406318872, 586842542, 399451720, 780083034, 87031165, 911909329, 261576107, 189018806, 176795966, 576686327, 970920379, 778025396, 323092277, 157086103, 400136485, 208365209, 991193150, 275956935, 481155883, 242032094, 29784559, 207849626, 76946738, 939808585, 911759494, 595524053, 579253083, 473586638, 280537479, 306626991, 94890555, 88215268, 658607948, 722521868, 760414883, 412889696, 854532900, 550138808, 251597314, 630733227, 947305461, 582001734, 596839827, 605378274, 182959109, 231118336, 505210569, 397353609, 25431407, 764619246, 888310965, 772189516, 53052675, 598736809, 854669364, 478997662, 11447004, 957208177, 688751281, 940606053, 416905297, 696321369, 186315727, 888505203, 991224430, 104950910, 419993373, 395993911, 231777941, 611333337, 27547075, 339202565, 985054626, 366905575, 383209919, 368031007, 996548775, 167314173, 492084592, 33045618, 380198622, 35658739, 310284540, 184683611, 436846326, 752607794, 314412721, 180888058, 146394891, 371397019, 379170445, 607801771, 948633406, 789787878, 785619015, 886867872, 325860941, 105360558, 296238836, 58594956, 573594796, 561786768, 672369929, 642080208, 8703282, 439890350, 286650064, 951071630, 582985908, 53703484, 28285082, 484599297, 841334272, 99379370, 153411046, 725318103, 372303241, 422591330, 594678971, 664832216, 493047472, 937357814, 145621617, 183048913, 68204203, 991873576, 570435213, 171175723, 474379042, 806967307, 146872785, 690584618, 242225011, 882757771, 354428581, 196075259, 986182982, 843973629, 265892145, 461885001, 832142437, 284626834, 210845447, 719550011, 608973691, 87902119, 110015030, 805782332, 945967926, 123636101, 635608582, 363941811, 140996793, 714502086, 314731281, 673194229, 251449985, 667012046, 906564436, 553140927, 850239426, 326812578, 879280193, 719585419, 754323870, 174438644, 144214836, 71002455, 984605118, 780381952, 242727016, 848338390, 868374828, 290597157, 469455807, 262982434, 507457311, 614984462, 927688215, 500296410, 868982924, 502177036, 987396864, 744124445, 70360857, 442305265, 848360963, 37731380, 997341733, 405517961, 314742446, 447864808, 34428867, 647564223, 209835680, 789607737, 189294866, 821359626, 405848208, 597124559, 682974701, 567540149, 223100220, 1846015, 86337741, 804433804, 346860458, 637523074, 467199648, 178065329, 697516455, 244762604, 678823336, 113370105, 959515390, 217234083, 818105041, 715665700, 41312873, 63041107, 316087850, 948788833, 665192155, 630891931, 727493287, 770995506, 770832041, 160512010, 752393269, 295858426, 81798315, 93046472, 11969776, 422341402, 738747028, 741601331, 499147105, 383106442, 904734577, 923798519, 275223077, 947059179, 483986632, 990504613, 120272607, 988842758, 868471394, 501312730, 762265017, 267423668, 12397088, 664857226, 644387983, 508806081, 784084092, 784425386, 885191920, 14426594, 143037806, 289360319, 96368869, 7429589, 21193326, 633373119, 912351814, 5253158, 508715484, 244846469, 244128578, 581011486, 886690952, 486585812, 111246254, 620846233, 881978660, 972135209, 929640475, 513073534, 272041526, 455050455, 907522660, 403610523, 529729715, 65640434, 500871271, 758394991, 395238495, 520493878, 269239134, 387513075, 345351057, 215889750, 706242924, 365672609, 83065494, 651453081, 180885366, 764588474, 393289388, 569412810, 750520105, 285197883, 19581253, 722963780, 988944427, 468591395, 832287787, 656593873, 803013323, 341554808, 134929240, 875731243, 398144812, 984157615, 824908513, 14699809, 862846987, 414127957, 78010867, 851869899, 751018821, 609440764, 432560086, 8063612, 632906712, 756539408, 259300606, 471019509, 450440789, 79902253, 327094395, 581562450, 367027398, 203952219, 161098230, 888639857, 148505027, 983873968, 371822810, 940839757, 269967221, 284398261, 370845188, 184715805, 285108706, 815721967, 279684963, 542341026, 334246574, 492619090, 231417924, 89585287, 53957923, 939439573, 762613829, 854692852, 597497599, 667090920, 422049235, 334936078, 112898321, 936201808, 992585607, 660202938, 405317772, 710956853, 352680174, 688789832, 179862406, 312919423, 819846403, 797320523, 483039156, 527249531, 732851699, 13884065, 3968033, 876578607, 188913350, 513352060, 563155417, 315978268, 992001814, 512954736, 490730938, 996919179, 238719469, 407603369, 988480430, 618141794, 589847194, 71729118, 756336394, 687304241, 664937844, 431896733, 813507955, 212154872, 425227889, 935122972, 149136725, 302680738, 150003515, 380426159, 154503916, 495773707, 10712159, 986267749, 443588717, 641475524, 771174610, 321740327, 590480854, 506153772, 490927723, 120887896, 722261672, 959463791, 278586752, 479212955, 423920698, 293340782, 543717577, 956733381, 189907393, 155653311, 545932045, 258094666, 761041760, 949184211, 946484815, 967238490, 683411082, 860501349, 890521812, 776810228, 743741342, 958965693, 281122961, 735237549, 144563431, 950086100, 303506934, 225786054, 142770399, 734693040, 927028832, 344015362, 521943604, 605718192, 326637562, 654422160, 82650777, 56082144, 212880922, 800955830, 876903546, 985600580, 177952974, 545857992, 432990180, 820079343, 174907790, 14658399, 650267407, 754670123, 309508224, 147763736, 152310882, 537198933, 391492543, 822623327, 128281547, 843339115, 761782898, 786635461, 77724356, 461747118, 175634419, 382731839, 513771429, 923871426, 301446672, 989359782, 124992418, 927147796, 662809558, 992806554, 348932878, 107055229, 767352842, 301876572, 354907501, 485876292, 661960023, 241892978, 810481933, 391419550, 589712556, 301638219, 154242044, 303513496, 550840207, 351175686, 496456459, 150375317, 220856201, 556964503, 990277394, 929179214, 471788231, 262695408, 529475429, 185363918, 123167153, 192587963, 383577813, 843752, 798766633, 222142342, 910724491, 105083188, 369522759, 993153495, 949927818, 781698445, 282646107, 595072593, 429115936, 747831845, 782384345, 785265664, 446637922, 347145496, 838578786, 567687965, 639853120, 952816852, 420802417, 616229039, 984442210, 380312568, 383014865, 418645764, 177938136, 886443903, 779678855, 219813336, 939347110, 14133078, 201088558, 620359399, 160075462, 511558949, 354266256, 440744253, 850875728, 120483694, 276868542, 681439264, 614456803, 21105146, 589251391, 374907696, 546053551, 619216973, 575123329, 791643101, 459142252, 67431258, 792169492, 158313642, 240357163, 35309009, 120887209, 907530237, 751020037, 766758639, 866119910, 842645654, 15154524, 946836633, 729272852, 574992224, 424000414, 973346267, 5639356, 704495084, 114619663, 698267145, 472478947, 295002916, 423627000, 974935461, 908847168, 32068237, 148365010, 241367487, 248230661, 280194551, 642097800, 642276282, 479682142, 220360894, 865918454, 875572408, 85463236, 64382256, 925905484, 913964014, 905970967, 410216101, 411630608, 244480697, 341976149, 608747373, 15808639, 463222069, 598754434, 528881364, 486552921, 602787516, 485750753, 190114275, 428413732, 3420374, 635794779, 907242622, 607948808, 430483256, 413747927, 291349506, 116633681, 86487866, 151178703, 503248761, 439255888, 996097651, 89779996, 721897289, 346817769, 593421453, 55069752, 756778646, 33903462, 112634295, 473268551, 901615071, 119686753, 24294466, 428134250, 916482042, 538747613, 645126199, 422518151, 762868021, 896698705, 547329322, 956254700, 117137033, 258374750, 519995477, 190587447, 816014668, 783479441, 269362510, 599384451, 436622717, 97673898, 370202892, 276810355, 575741844, 114672431, 128402290, 217814429, 164637693, 539385223, 843108636, 661566726, 813894224, 405619405, 334661507, 824246404, 396059948, 136338157, 45244378, 764139621, 964054417, 936203201, 555708015, 829405734, 62531212, 716586266, 992348523, 861500209, 182197124, 590471667, 730474635, 328198087, 726134226, 769903437, 386262650, 128854866, 45399622, 414725222, 687564774, 327579179, 524822050, 952853151, 177057104, 686811822, 897723853, 162638275, 279119872, 489610359, 352172476, 710026269, 300317909, 76788936, 280477920, 314207621, 669772604, 121219283, 380589248, 5917941, 570196198, 289742165, 329527935, 288579640, 807603555, 876389872, 58785469, 867284097, 746528064, 924333619, 250066897, 865784919, 850363982, 466337491, 589497717, 4481151, 980152931, 744001304, 146547912, 108882698, 481692819, 630069609, 486620802, 356509948, 273788093, 635557264, 836059338, 650996631, 541185954, 557733556, 312541097, 344311844, 410976863, 118643842, 154508822, 106868785, 936684201, 343805101, 419625654, 512337378, 632110631, 247026968, 259371360, 409497847, 976035816, 442049421, 464115830, 54821076, 462703738, 998583950, 802487189, 115615558, 440539378, 447268685, 865514851, 483228150, 463115025, 353156965, 949055603, 802723806, 660026318, 874346649, 196976126, 234508625, 774217584, 487332028, 373783183, 910162765, 917694760, 92025403, 193753854, 718471244, 821807247, 956010331, 991020032, 340505556, 664233621, 853028075, 638504147, 515351987, 185005310, 137296920, 171369736, 316991231, 90462744, 236899516, 554836865, 923722172, 171686884, 46598150, 47366287, 339046437, 191989774, 728029644, 519413282, 407615749, 511688199, 71141098, 255712661, 382757112, 712648946, 408487556, 280426183, 666999736, 931179472, 318016280, 294857594, 394120623, 253268538, 38704109, 943605429, 910120205, 513667733, 181788577, 197862026, 768854377, 785298412, 591610739, 833177105, 234652211, 469631799, 136746343, 107540871, 114093759, 97858266, 829385309, 756280464, 14504148, 839927690, 942301152, 200886340, 778111472, 146427427, 383784805, 402765925, 836189904, 929600292, 628175572, 890948490, 527635642, 244318461, 728657850, 949457598, 402568329, 741462761, 680105956, 743009864, 786517206, 24312218, 484257516, 240781366, 754623701, 347096670, 933593935, 151449218, 760505952, 217001136, 212304028, 554557671, 457882556, 899805672, 554608357, 3941911, 549831167, 963020648, 776323880, 395874823, 206032105, 13121425, 617817695, 358036219, 846066519, 410964101, 106444334, 88060326, 666210371, 431702913, 304061062, 268601098, 70765262, 169440883, 503430641, 666070173, 301073862, 913915388, 970057664, 769081116, 920087740, 102417893, 284577072, 695006583, 613388324, 552018731, 651003882, 200827560, 144918260, 806525469, 924660109, 158982333, 937971775, 99338323, 435527481, 917048797, 387562190, 495591383, 838642432, 783871607, 30271948, 436969781, 176347140, 752455454, 918562187, 855773965, 926138247, 317976351, 719349476, 764846908, 48010882, 661820743, 18793362, 314063880, 523185492, 482948281, 570019555, 512635481, 872112960, 302855801, 961823991, 36215477, 907403068, 474308168, 552071700, 305348994, 681144968, 733383852, 837925303, 633617274, 238807637, 484731762, 370672060, 575343042, 537278802, 223663241, 543284471, 919916034, 13484286, 379203192, 152347553, 700343680, 16201801, 816318982, 437315152, 65581360, 591799224, 967659542, 895758435, 215853713, 397067267, 780690227, 674816270, 187783838, 920462682, 464667979, 590867370, 671868920, 72288991, 321936477, 271455477, 443977940, 21781348, 736060957, 184394096, 77162619, 167129115, 187891318, 288043847, 396468551, 229124173, 413533315, 821061470, 846147758, 595353899, 102507684, 169821336, 502514253, 979665482, 247823153, 177902716, 204479601, 67668431, 221051680, 102909210, 16394334, 620291693, 398951629, 43742292, 407544805, 21673865, 827559542, 213886733, 29144967, 115153054, 881880651, 241737358, 647058986, 131523377, 827794204, 82241505, 141526510, 243479444, 162616980, 430187690, 842832747, 808811904, 852907225, 961415116, 995803757, 62604013, 116857993, 301108956, 3859181, 382187773, 235549618, 744112981, 519498992, 42820985, 880990774, 272402012, 1163732, 477922976, 332955871, 567934293, 104352708, 514496867, 625741817, 92401496, 106888872, 174174334, 947535557, 185587062, 152067355, 565323675, 619446069, 65556239, 867529866, 642453443, 398362616, 242976412, 825212853, 814764124, 16837441, 610888116, 967451002, 887920058, 330168627, 912687921, 151249921, 964228953, 337810027, 661630628, 229489407, 951884315, 292005390, 675148261, 260225738, 917876835, 560045256, 735638020, 748818070, 960608581, 950384084, 712805869, 653861593, 728540199, 160064761, 821716542, 262711632, 143371404, 106740126, 560962424, 201524235, 389123393, 981933929, 314870508, 223269293, 482886748, 577258979, 580441513, 353876762, 732511067, 552519408, 720762595, 888926732, 568453453, 278202810, 276913819, 138413228, 740037201, 603902232, 430326908, 949249259, 928260951, 766277914, 1689579, 714590056, 767514668, 751013038, 699334906, 356698149, 164363967, 461055317, 920106895, 393584582, 74801868, 610292181, 119510105, 246961566, 207297988, 842214217, 403563627, 340566201, 553799347, 512674597, 366381294, 355330670, 797328081, 234499812, 125528366, 831706557, 830356961, 622975373, 236019912, 546363234, 599286198, 200713598, 525546031, 33841874, 47924081, 96007698, 533348384, 491836210, 140496048, 302483045, 673139311, 77414345, 254229544, 708193724, 803408296, 367326915, 975194461, 457850693, 670651904, 969943785, 939758797, 90870425, 473460525, 971227895, 611153385, 776392428, 976950120, 906314177, 470544669, 431968388, 583623034, 290180537, 845310667, 95804162, 349330434, 821527572, 632951900, 153795782, 254673390, 59195050, 964783551, 965157965, 668133847, 256735062, 222945730, 293139977, 489712763, 296561528, 827576341, 558068410, 487421855, 957435081, 624404826, 996426328, 628074870, 716806181, 447761345, 86322818, 235615756, 984433533, 143197528, 126524377, 171610579, 548477747, 549826370, 935944711, 896816640, 273878369, 387475377, 195175293, 667101412, 328619066, 462821977, 647728228, 36849105, 347609702, 988390957, 675851882, 312820272, 356880659, 753473900, 905428146, 576569603, 642804033, 515503388, 428089006, 115387591, 116303715, 479636697, 244485057, 136162163, 422790598, 402609781, 287152659, 594985507, 727395736, 821856598, 334663871, 194812932, 873243633, 359459438, 597811558, 279933520, 959030495, 896049361, 509491020, 366277498, 478030297, 958148515, 521223506, 743778210, 831423234, 701228232, 605436882, 792616129, 827874428, 410576201, 906266605, 480091720, 385508263, 995815174, 207658834, 980208955, 196900395, 766698491, 607991290, 692055561, 34789450, 213614008, 517638899, 442285150, 893849255, 565665433, 303422053, 140545832, 83251635, 46733735, 914257692, 352185626, 850223416, 659969631, 366083909, 741884861, 57565907, 646725856, 706143704, 413847058, 863321897, 789121897, 807936180, 584112572, 772414893, 371129962, 649671303, 319462087, 16096540, 839424340, 989431923, 515795522, 572643630, 90359331, 955354061, 182496142, 986051163, 59422459, 632921247, 60631899, 794194894, 612644953, 583750154, 279783195, 468970166, 242008396, 399005478, 964687953, 659983079, 638900475, 776455299, 387061020, 144623645, 147267071, 405799345, 845936004, 890759348, 526614566, 979305624, 254941947, 911570970, 729978559, 913645630, 870927167, 623977917, 757545329, 225820875, 589768459, 21055629, 55071088, 676388702, 535444678, 999115128, 936807016, 333938773, 298696712, 931567215, 761209986, 186487718, 810528241, 531711278, 734801664, 452165037, 726783493, 855842831, 339477830, 5271806, 10582389, 459059343, 506676761, 35196975, 863831034, 3318283, 477099298, 349016890, 361365211, 804192662, 430906995, 232959563, 826731729, 831614785, 922655957, 984684158, 579062316, 822270593, 19180654, 217763017, 882537324, 251738961, 715160360, 452375304, 873794226, 176100400, 917576532, 203157008, 644653150, 160359400, 546132774, 946127956, 17729020, 741345074, 447241629, 529808224, 632729735, 767731589, 870727141, 644684540, 205539476, 933241442, 889541683, 345385680, 971529878, 507693956, 281773121, 984085917, 842193866, 533712759, 793224065, 532230406, 389489503, 485638916, 844441799, 555359155, 812718300, 41329270, 340054923, 63065514, 569884599, 712507991, 279903184, 199359964, 779699071, 283606186, 209298844, 571602257, 8396013, 366870285, 319750522, 97357701, 240031074, 544606753, 879338556, 904486554, 889937285, 881786060, 837639436, 479085130, 21765387, 736692644, 732941273, 165041619, 705011403, 856471540, 504275451, 604959893, 12243066, 773302609, 885870762, 815311362, 146893063, 628888450, 834475700, 789847010, 661414553, 489901407, 712845501, 342071803, 136554159, 167902073, 74237085, 563193183, 942547191, 420252301, 880187855, 909082735, 1995438, 768620498, 247774302, 634602891, 670676313, 80806113, 821821968, 947019614, 838304457, 291007430, 538466378, 921770443, 713766180, 373630574, 253364979, 603189437, 105816872, 395588462, 780476736, 509883957, 3788413, 559820018, 318910630, 49806154, 537944363, 475547372, 102781904, 968457734, 383421350, 855115302, 944317986, 111241619, 372904298, 968800042, 981609711, 30547761, 883677383, 516509799, 367973182, 458396797, 106510335, 219291802, 106895727, 857879075, 469871055, 479843879, 58388688, 382389451, 730120568, 430766925, 586830662, 566649746, 925782107, 992529241, 44495205, 545770799, 359112028, 72118829, 512544695, 138977014, 417620012, 371922667, 631742526, 607013224, 724173234, 705099702, 829882741, 64801345, 494247498, 733086790, 305091876, 704962828, 807879871, 150610743, 514260164, 212653757, 77912027, 982631191, 989928938, 745294454, 466218884, 763495787, 348689874, 121534102, 460394454, 46218897, 355920187, 447765439, 334649493, 661181819, 227889919, 234818440, 862210136, 839242780, 223378545, 136698728, 282687448, 260253392, 817683807, 521086780, 72794340, 738126427, 946764463, 304227389, 518068233, 836928124, 473721255, 496130684, 403891487, 435055229, 486161878, 581269592, 41731005, 339483805, 230252012, 880197170, 397542349, 157440455, 993586154, 723092326, 735536530, 854573035, 719037813, 651250156, 359847442, 800201812, 710966721, 717499124, 584815302, 583463185, 629421443, 526521253, 312518808, 335259150, 655988833, 941063833, 117848194, 759327779, 162851711, 99291939, 518103558, 431119860, 953502083, 592741498, 390199164, 94959738, 51911315, 707419685, 943880319, 679805912, 859289720, 173419922, 624194631, 79588441, 502963863, 364094251, 698570396, 909794808, 397072502, 56989909, 971804104, 925131442, 311429799, 205389018, 841418934, 950055454, 57077943, 163575829, 459657292, 422200023, 485286489, 553858965, 855162779, 227182075, 788334934, 119117939, 499113644, 947514239, 517996950, 125116750, 422681781, 659450409, 333132816, 938099520, 965105401, 201371328, 805392974, 458584652, 838594318, 5985751, 671098331, 479230885, 563827317, 705821242, 47240510, 608794984, 129229554, 643273136, 517007012, 250716389, 464220925, 342874960, 654196498, 628692574, 259426969, 219108263, 732155227, 679450747, 436321258, 580984758, 510948119, 407250198, 65030975, 881454522, 169556409, 401604162, 889050529, 651057466, 215440634, 153510092, 998072582, 732377713, 574281404, 82146558, 328246724, 156109946, 718482581, 348569768, 388085809, 343355808, 72801272, 324737326, 900583948, 503881687, 169176997, 404091890, 700028503, 491804646, 214641092, 699446337, 399506676, 640749492, 371458245, 272412374, 961062158, 321113751, 431846646, 830174960, 134462455, 126557500, 677532948, 965731086, 282682297, 418963909, 448743909, 66080964, 276271688, 750767137, 345284643, 699006091, 926129518, 453650110, 740167408, 166516319, 698252720, 688280832, 342673316, 188589296, 9611, 784531740, 495027967, 630933091, 837331979, 658090402, 196268908, 42781914, 202255604, 732060300, 347924631, 399909515, 206461338, 32862381, 857131881, 664467724, 512982283, 138652390, 978345919, 526657158, 613021429, 921735581, 994959698, 87058938, 296836554, 637886410, 937263534, 801731540, 301913362, 951172918, 8534397, 16734935, 204635803, 300605820, 674176850, 639060810, 322595207, 28113732, 446453055, 300024881, 688518519, 196569425, 767761252, 733325053, 662166211, 900353057, 588072414, 244273204, 426071962, 549368753, 584425510, 557767224, 502766014, 896362576, 857021232, 147182015, 987294832, 74437864, 683422098, 942180434, 407162688, 541951486, 314589576, 905651311, 219022524, 728790040, 548106974, 230081771, 327765905, 934465451, 586886657, 905741473, 591312547, 794504756, 885076230, 855706530, 7602182, 537381556, 263289197, 603048570, 423607630, 838548775, 407972017, 102867085, 98503717, 729456688, 584407074, 129899718, 809476232, 927416575, 54509034, 220393433, 848840123, 315598378, 887904887, 363598026, 983944271, 438062904, 64439101, 859914350, 340472707, 624289354, 611671932, 786590871, 991218604, 225144943, 775727078, 784294742, 810208481, 328549207, 958399420, 654632575, 746393328, 115917075, 473169458, 94501836, 650093732, 262842251, 121371377, 811163691, 649954193, 697307320, 361307587, 579616032, 951415655, 565556094, 445543476, 640424781, 148954089, 836947197, 431594953, 790537259, 663316200, 183548489, 717668733, 897785723, 954155055, 845134203, 836269035, 249119065, 398755092, 618369449, 211323958, 969635422, 449504997, 346441861, 416660845, 175825398, 983476777, 697055389, 111537623, 392129584, 841254267, 220451960, 864074956, 675926767, 973779030, 338506765, 44757965, 673575167, 117506084, 995534485, 156637532, 680993362, 713809345, 901869517, 412520249, 694360714, 234445022, 862417911, 60401379, 678654037, 562580443, 567641580, 498320255, 297888196, 402337509, 907014735, 464404106, 382552917, 263394231, 87703109, 5377567, 81951987, 995796712, 553546738, 348305486, 60362656, 218297748, 744082989, 145791499, 634245441, 338339962, 739047768, 282932074, 386103420, 626035867, 810848458, 542904037, 956622870, 81882094, 786682250, 324990133, 303121415, 166504572, 230406866, 865643328, 280260083, 562404532, 408709989, 748118088, 408490815, 392552678, 429479873, 95315291, 732603561, 610675318, 312222876, 532721737, 180169036, 474101671, 183411642, 73543143, 318078917, 728695192, 813006106, 230993263, 669684009, 52344400, 589243197, 209227620, 407310917, 259139588, 597209693, 170521465, 721264432, 946995911, 94156246, 740319759, 86721298, 823101826, 895375787, 858465396, 957115790, 961022783, 799851394, 536312990, 665185816, 892313345, 60840015, 843789009, 49049551, 712342688, 499726037, 96188568, 326285484, 337987790, 648971750, 933190417, 760112476, 541601435, 433818659, 365366276, 638633806, 482528933, 348367172, 9688129, 398101223, 919461543, 42246127, 275671832, 968367187, 811245359, 417204590, 640403999, 275141657, 876478445, 624894479, 559092433, 230907392, 644854844, 741860993, 205747280, 137348347, 898238410, 395410255, 328574187, 160866687, 642114253, 210385002, 889461373, 476167515, 965509119, 797434138, 366833098, 322640033, 857763728, 795650060, 255426454, 68194037, 904843464, 720350304, 357510384, 787666319, 695013302, 203154892, 107548351, 781316411, 525058760, 392770341, 106358196, 269241568, 606697493, 588797734, 964730036, 450689367, 766927214, 648036550, 554955088, 574661021, 433920726, 582489213, 649423317, 219094782, 371920451, 435104849, 106160634, 893522632, 629068122, 12085009, 487441069, 390752175, 558615914, 952320720, 817443779, 469712096, 25655265, 390496455, 63368195, 176279182, 94607276, 623278630, 747647707, 222747152, 576754212, 524055099, 580489782, 493355250, 344454875, 58882168, 997213989, 327610100, 391028602, 644370007, 152626432, 607130676, 955589263, 354320582, 643860146, 122646442, 667712468, 710455120, 571570057, 494341195, 326653621, 612109743, 995488346, 135389170, 972837943, 412038343, 869105488, 501245917, 870508633, 879724337, 159244625, 69820239, 528960505, 2800192, 618942510, 819883858, 65715307, 219192986, 236622584, 423574729, 541402875, 577297344, 304603511, 607071246, 455777857, 221855199, 254449891, 151208694, 462336727, 899494108, 637690715, 965568311, 918587161, 943635608, 618322444, 425857759, 488728323, 318397401, 796020704, 426325029, 460646479, 858849600, 614815736, 190862311, 572832192, 237036635, 688419179, 214883414, 81848710, 838058760, 839320185, 953598407, 899830349, 478290467, 387492049, 261758299, 896995248, 394869698, 753839997, 230638667, 146848688, 745858881, 276237871, 880048602, 974748396, 737637901, 131319744, 349636724, 892257640, 687457056, 690137464, 840246943, 631564601, 949866691, 962453777, 469874663, 80929067, 860260622, 904838584, 732566614, 251732580, 332402208, 631169319, 178113421, 387483467, 507536263, 107061992, 33754894, 909902499, 367808239, 871653610, 349391046, 743850397, 64575696, 913790013, 260002177, 737445604, 514195002, 594871952, 727918706, 140174942, 443851891, 633293518, 9669218, 632691847, 615699670, 123074008, 199774024, 605703274, 659749236, 864805360, 816535742, 966059459, 837098095, 124277266, 739772353, 650654881, 68679204, 102477681, 201778384, 169969219, 308528021, 600659744, 826279710, 495984388, 489803474, 437458498, 605936725, 697596654, 278115911, 60557101, 898831167, 501727011, 338431807, 4414505, 597590498, 626843665, 431763653, 627695484, 544614895, 931291250, 183317064, 722330485, 907205256, 45929184, 694266174, 706078395, 430431778, 134494647, 525546607, 455352920, 938555780, 492648074, 925213310, 262947580, 846830183, 346320862, 441957787, 917995158, 648095194, 56781410, 351278014, 767274328, 13082199, 462679200, 544256975, 586399284, 413034501, 635656762, 622258630, 116438749, 981928833, 614392908, 963903684, 782854058, 453633062, 207647013, 41494500, 265695678, 84061943, 212516957, 611503938, 999454209, 241105907, 82414221, 164815987, 36533961, 646301914, 5750017, 530179769, 357567496, 328335992, 265182920, 850050560, 248242669, 643899333, 635469859, 667381999, 174714888, 442635446, 835398850, 73680848, 145736338, 158582911, 158000297, 380696536, 465097370, 424504456, 555907986, 418360660, 82037, 4216738, 169733839, 647849478, 733768236, 381884496, 552108950, 695530135, 652981744, 802070399, 522978841, 239297897, 799861706, 536463268, 80706352, 974787249, 594327057, 664184532, 292405207, 637991102, 695346070, 45841097, 998443797, 116973349, 39928314, 310647794, 414277194, 344883235, 843573553, 581082675, 228137349, 382854275, 427430600, 380969085, 100887043, 736319818, 899063202, 977415037, 401802693, 782634125, 614221080, 87080725, 421673127, 365522253, 399275627, 588965516, 903118737, 773592914, 253870839, 929210055, 558080183, 854913286, 424537832, 527991758, 265430045, 383334908, 127010690, 452004722, 44391826, 63189850, 205542254, 759071302, 994107507, 768994010, 892236068, 654174034, 721182771, 706697780, 11556082, 127160320, 989938913, 936267522, 739634266, 75842574, 886049631, 194554304, 629905497, 694900385, 836198433, 882247136, 568386373, 756423655, 686573250, 430427265, 281529459, 99522002, 96404864, 276526699, 993755506, 958120680, 146000018, 290311486, 796377052, 242466403, 266891403, 700721767, 420240546, 155812826, 940574563, 678235785, 129587077, 255590327, 469317424, 648009965, 416720026, 571304189, 268206342, 717614444, 982564692, 808371524, 28078495, 188399229, 146804029, 558042073, 553151155, 626427306, 389153967, 171816663, 515351994, 22985166, 665555470, 395821824, 716851824, 76880566, 22987034, 633031860, 912522738, 771671996, 667147699, 347995992, 281600182, 634418332, 723824642, 334530183, 426184612, 953188488, 814362313, 977651438, 718953800, 177131128, 601728300, 681134746, 315549845, 48007334, 731589717, 245553641, 713520595, 686515693, 113583807, 565947281, 839604927, 401170775, 908823250, 543348755, 327742244, 645265925, 317985332, 101943286, 542000665, 499276633, 469536426, 163336520, 216772705, 53939102, 810060305, 508381526, 412540975, 972015181, 559860385, 169009749, 190572866, 166845603, 252493662, 792932284, 338462183, 596931213, 368035385, 338610409, 191422267, 159846818, 388749724, 114401770, 51367961, 6218493, 226588582, 616985094, 781295752, 958534628, 683766196, 75821672, 345708026, 323186321, 574496664, 386139485, 726949291, 107346837, 710194553, 246024847, 552673161, 967765757, 529331590, 911444034, 309426285, 730291402, 618398672, 865707051, 55748693, 220710347, 874359408, 579992738, 613420334, 153422207, 168280023, 958957066, 82389944, 846889965, 500864746, 719229116, 491404072, 788746111, 151860353, 93686487, 850319525, 464361800, 746884561, 898777222, 609792245, 621711187, 266630180, 114725772, 654656772, 680263709, 290155826, 929266809, 584625045, 843860683, 426492351, 237265089, 637872413, 892006713, 47641792, 730834884, 225706467, 303094013, 282436604, 940001825, 240461115, 155271321, 543717956, 668735594, 468209563, 292082622, 413869798, 757019550, 828693665, 141933091, 209308403, 611704930, 910584013, 340516744, 272784622, 970923990, 196629554, 739687486, 860077038, 105828520, 628207070, 385522320, 188571433, 980368969, 807368682, 587217272, 902757235, 155443843, 955864749, 113215221, 774185169, 10280638, 541093412, 700983464, 76733085, 174794761, 683447166, 335374579, 858923408, 691935637, 429287040, 376094774, 815185553, 995182299, 681084358, 429839519, 607488707, 876345987, 513809822, 380172054, 972906721, 727994996, 436267625, 714699857, 106591097, 355946192, 171122869, 133157180, 643226687, 536321151, 520285311, 96769612, 937389058, 223552665, 755407743, 550037865, 535729456, 924789374, 822325679, 759264441, 965058031, 930613290, 353442724, 938293886, 809104905, 184824282, 731493560, 706777278, 209211989, 33282003, 404749630, 898874068, 153412023, 925482408, 661889881, 270734881, 664064300, 633630093, 813098923, 445445950, 854997607, 830646334, 148180486, 340673758, 104832568, 299660505, 711392429, 100788674, 807047564, 268421768, 715296570, 190305381, 443231568, 832225536, 269840080, 510701265, 282637166, 861348405, 381149131, 492248858, 936882449, 732564422, 439264705, 806532298, 492921658, 24422655, 310863419, 167176654, 175761472, 615795419, 124858677, 71064786, 843591469, 728806680, 390455938, 630633363, 716571758, 911415260, 83835412, 921676774, 440138509, 337637652, 383179451, 436930679, 748665777, 374991412, 87893374, 725950336, 791003097, 603640373, 722851513, 209598310, 418821309, 944742264, 162529191, 607091808, 600996285, 163693971, 476551688, 98537635, 609946838, 379674978, 194601055, 261535816, 150959352, 706255476, 311732951, 227779131, 276782136, 749996612, 637933579, 252685632, 826005972, 432190427, 898522653, 398586674, 659924352, 240606699, 605131435, 18360212, 101409664, 827201715, 86683296, 355004065, 946185208, 119851411, 692819801, 502233768, 233213801, 730659263, 342915550, 131929341, 255895929, 275765536, 213378664, 568522022, 126358582, 112644788, 641408612, 576018351, 52868212, 957095530, 349335350, 522962071, 981263746, 457367517, 628533501, 881644481, 506563343, 878269187, 881327422, 167498828, 304516088, 354705335, 735156465, 270348724, 286998709, 18124972, 403727661, 849482014, 365248580, 268669278, 475728279, 698899193, 924293464, 247976676, 637131790, 336571926, 326986566, 306634153, 272020552, 272653443, 112657518, 631836417, 896627493, 766676206, 625748599, 658574365, 270576139, 294906950, 616552184, 281359935, 33720847, 988285743, 249558277, 14860098, 804260711, 97216577, 513815014, 583222149, 819873397, 811343388, 144635492, 951042603, 112278366, 377158128, 774984685, 769022268, 374922556, 109942825, 682003020, 999540017, 402132093, 894685153, 508409259, 245449159, 990884046, 867994945, 786144719, 289540111, 400033045, 621867854, 537690587, 662493558, 837954632, 190455819, 856089658, 22366165, 545491834, 128052998, 576687592, 884025610, 350940500, 967340811, 191129310, 636671675, 251672598, 656404406, 256321489, 444848688, 51039353, 69651790, 286370919, 244038395, 360488413, 553502645, 686947078, 200459420, 729914270, 563316652, 547893883, 152735778, 503043220, 436647694, 621237481, 797983703, 585254950, 419923334, 817757317, 933561644, 441729310, 432165774, 891998462, 507075159, 267096343, 479350864, 386561792, 70695205, 728120989, 801691063, 693814568, 297364012, 940666776, 31447003, 294713896, 368847592, 162064922, 261033832, 394020574, 835691375, 484618667, 281235964, 918027300, 754111630, 835911400, 776790581, 794401896, 429786764, 402017919, 910602664, 697869572, 950284288, 765264238, 605437445, 616042383, 223380280, 865208167, 314018769, 820922569, 43891596, 67103114, 475120293, 839158025, 502393864, 732372832, 927034019, 170436225, 148527940, 703325329, 750470422, 438788063, 835250929, 606788296, 291309115, 157880234, 593990547, 919264683, 141917379, 812476307, 701420231, 713302795, 431070150, 66937139, 430294684, 852923237, 554855058, 979400022, 61284263, 347301885, 528129422, 161488366, 279051794, 859602756, 551993846, 380797151, 85694099, 398680997, 287463661, 258917882, 164750329, 491307001, 132407179, 422783144, 734864381, 692875759, 947496685, 308990082, 893671593, 411751534, 803014550, 356025412, 600245131, 205611994, 545159693, 319210335, 388949930, 461887222, 419495943, 683456510, 462758775, 970494550, 827475600, 673723351, 733379794, 683272554, 481937248, 95884559, 525779369, 680322556, 570026241, 103094296, 175642793, 943734347, 651593505, 462164404, 584556181, 512518242, 686962722, 621739082, 977007182, 815345094, 734222632, 599483890, 753884549, 960182092, 915437943, 455994541, 265267370, 386996778, 105786871, 511871962, 757013626, 138861006, 373012006, 849582509, 527173347, 681022417, 716907489, 188973052, 696703378, 639429089, 258897959, 212004240, 427879732, 25472837, 583436371, 580606791, 885892258, 128241369, 213116331, 822044426, 457591846, 362430284, 86857567, 433642503, 588357804, 715001928, 283513590, 732362454, 762294576, 392225892, 166749298, 657634612, 364888386, 21580881, 33099770, 746170843, 380390086, 292012551, 314592364, 43904488, 102662189, 461354381, 622029313, 401608188, 296334406, 349894971, 730705317, 949375375, 314481667, 284576318, 30821261, 915386926, 472520236, 751027135, 442551503, 837782564, 176387468, 991266243, 379462922, 401336480, 734093764, 416936778, 34718767, 728330587, 307665365, 362090188, 213851566, 911816903, 890355629, 932652180, 117865699, 559619881, 299531802, 96264037, 426812125, 446693696, 621938143, 11383760, 799580174, 796416567, 467854240, 531706617, 768732202, 214583689, 694637338, 387551456, 924731725, 429414192, 795508424, 875520708, 330935882, 400158540, 775038146, 693503935, 83093198, 266144664, 351300449, 311879168, 725055911, 874440522, 911485004, 968976784, 530921409, 346426572, 223169799, 528309515, 396633967, 416370212, 793299867, 833791036, 955514736, 698611768, 237171584, 473760587, 174888088, 484057627, 178507448, 737920691, 217955112, 800954789, 763537089, 888100756, 475315638, 297774054, 368534258, 1720268, 541957973, 638998806, 656435073, 963446243, 981042793, 313007957, 194205338, 561148725, 262482921, 730492185, 34159645, 167272210, 985835216, 728586816, 95238025, 514219583, 733383009, 285174185, 862611347, 473464708, 549416230, 948715887, 842572147, 793702048, 754760392, 162238097, 223759154, 200020829, 587603588, 907998172, 176729456, 887331714, 121551416, 67351609, 527871062, 528841854, 233486032, 418894727, 755445596, 651497938, 528896700, 345836829, 54827737, 636372394, 209727435, 330541304, 428315266, 759909366, 310684002, 341207016, 301352727, 445831062, 64486351, 935038276, 564413620, 811973069, 428120413, 806492043, 395622498, 836708325, 865442319, 877849738, 453663370, 869457411, 513239841, 299827825, 107965865, 752640701, 402360047, 788196590, 400546888, 919027457, 460290741, 562096011, 672395920, 555683420, 976875651, 373108972, 410425616, 107032971, 101585343, 265118413, 640209737, 595560018, 554952829, 940474560, 328293865, 416960300, 117164210, 856426131, 19065032, 822060131, 706802757, 191376123, 963938616, 633508904, 890566179, 342784911, 975317568, 386741310, 286230172, 138110470, 588951294, 967590386, 556709983, 427466447, 242978819, 17770074, 66015492, 429700332, 774573923, 761116382, 617921907, 840497380, 125112494, 126577286, 62620293, 516088437, 580549548, 409547954, 204624106, 496300122, 417182291, 701527603, 71177530, 178572700, 834732469, 787897824, 595062631, 344623008, 786816704, 134819850, 488929745, 322782283, 671725185, 464938354, 623431485, 875720955, 13314789, 263668336, 726236060, 594062863, 781584485, 817766359, 367678428, 993814043, 371421104, 187065170, 467588918, 471944493, 594442240, 600700890, 654852018, 223467843, 458540600, 535353808, 799582935, 166360684, 970447151, 284567766, 680417264, 257935388, 23788130, 731150132, 933983274, 341394442, 214025696, 53429401, 824379263, 603477484, 501091301, 433911646, 731793745, 771968207, 15749874, 891527351, 373608043, 868752248, 208622433, 93337472, 376471080, 728110243, 378904348, 196358113, 310823412, 173182789, 193662374, 487628501, 82486470, 550700386, 976135617, 322870233, 679632122, 449634613, 988093939, 167960867, 36525842, 88636333, 251624116, 264016494, 65590489, 319532464, 515764388, 277940838, 578644800, 330589390, 353656280, 570562647, 427426713, 499686928, 140939904, 233132789, 858756840, 978018257, 148392839, 120055241, 364926819, 272505105, 355648083, 966753184, 861210134, 32140945, 880971108, 127064732, 27472108, 83695903, 679503947, 884970346, 730591739, 969304544, 960031434, 547884844, 745677344, 503546732, 585315284, 865389915, 481120539, 361181309, 885686237, 8426229, 671728089, 665225170, 866864483, 423157632, 502853815, 949578511, 866095118, 314377091, 160053613, 847408130, 922097759, 304802348, 898751970, 700158164, 708770434, 783195008, 780778665, 370783117, 742960456, 545287500, 161359019, 787091049, 662347380, 12987165, 836718749, 169697688, 326890778, 661983668, 306858093, 357684376, 414512033, 222892586, 340237220, 911854777, 622804449, 419817385, 297471825, 629000351, 664896542, 226136320, 157944560, 94129555, 862286365, 706712502, 734687343, 267329386, 83485967, 305612072, 493808700, 861485712, 428820957, 865330469, 630359148, 995765845, 450457785, 487398972, 203904810, 717967195, 13241521, 414240845, 123196151, 574286375, 698300976, 577050137, 970178458, 655765315, 159049625, 996837163, 665423608, 232580514, 678433806, 823171871, 821611820, 738729067, 576976891, 369751090, 922959801, 406888679, 948401267, 561340100, 260720558, 425138105, 509368551, 439663019, 810620437, 979293753, 117336558, 431978653, 435610503, 417964244, 433587485, 115319505, 171412580, 679508607, 164686579, 532258357, 373225860, 66001073, 713491075, 123953225, 824750787, 533968550, 293521034, 545330664, 398116112, 400006521, 16210012, 444786994, 205481305, 981938833, 661106640, 337008705, 310524705, 614424640, 42000120, 289925693, 404922011, 595787976, 318014964, 469074467, 587491806, 438923108, 606140872, 398185822, 326394540, 145717030, 210980735, 727336149, 674220635, 62920728, 278956905, 371417190, 135618948, 664468271, 107157758, 17305839, 936713776, 905961938, 827510718, 688645544, 548215550, 713131299, 240760086, 237435764, 717431271, 87172114, 328839358, 195296194, 864543315, 901874621, 980124732, 654571850, 551797484, 725952062, 733121418, 403783522, 591402969, 59536165, 475732253, 274507430, 957540883, 683340213, 337249865, 868622334, 190887787, 314990005, 275109510, 559851969, 367564768, 737565449, 32388243, 357599551, 591407618, 16902936, 313774025, 504999649, 604721842, 664989337, 107639379, 13845142, 263475651, 590271413, 936284896, 905729821, 492800949, 926508730, 700083406, 686338517, 341183192, 842350717, 966954751, 206929085, 749049517, 302515916, 361122183, 457556049, 287683514, 774289294, 869591607, 320709805, 161394009, 311989403, 4808849, 637740063, 614208658, 205819006, 821420498, 478668784, 773955442, 427701236, 578521607, 930625514, 281380278, 482368798, 439347579, 712460028, 816445593, 134148033, 344653547, 649316219, 695813037, 680721754, 494774960, 533496814, 29227331, 112714115, 595567052, 712413245, 787013517, 682385388, 935554598, 870373229, 787948763, 349252587, 254738650, 911830024, 221421391, 752748532, 112204673, 16306974, 956106736, 380370407, 968936322, 101911457, 512258920, 864005316, 752795925, 176049202, 664836080, 772510359, 364876923, 205517288, 771088511, 774767135, 40942403, 233091708, 893990342, 882972225, 313219305, 542138973, 817385437, 198700570, 921653468, 949905067, 643586389, 272718512, 81701464, 688301529, 344617951, 750648465, 882046431, 541245211, 320810274, 104701876, 492094946, 880083868, 851077628, 125830015, 416907850, 565889912, 128522153, 823066256, 351725419, 892686240, 550209617, 848753004, 921794028, 890691725, 26915706, 394627828, 324015781, 857907590, 664982118, 611311114, 84765080, 356998515, 912607296, 579887733, 211298706, 27877958, 381508209, 540373409, 136768950, 238146557, 4619081, 969212173, 204203076, 146402041, 161638133, 882587275, 277847438, 189441891, 957060814, 591719778, 832274675, 804331967, 661382921, 475221117, 638929294, 669194435, 70155344, 442656394, 667639463, 424903695, 628025187, 537378798, 212537417, 497429894, 204168644, 824483748, 84481707, 464504742, 91307032, 843771366, 664249810, 90169370, 428634695, 805668845, 643024905, 776792911, 497129468, 155792179, 839002633, 203601809, 707952142, 484598038, 327713580, 481056414, 622497626, 273351494, 549503352, 851841009, 422216329, 395619021, 984737824, 447460198, 616121532, 63664154, 979231198, 739523099, 298703350, 65407579, 818779199, 505819174, 204270486, 97529214, 99912421, 61920555, 790268091, 509790537, 910974252, 323689857, 829052620, 426540057, 935538033, 195369513, 923675425, 33447410, 65426762, 54153529, 776904956, 284084202, 207246276, 52063948, 6006776, 274433568, 495724189, 334168391, 993488949, 155005479, 328193587, 923903263, 507498322, 794543223, 291129105, 789379942, 508456430, 529490737, 534451707, 500914921, 214041594, 423420291, 151059524, 263963822, 190039547, 61742905, 477437635, 754393308, 726263073, 12734914, 440707878, 76784962, 769546933, 757720945, 162864160, 363798047, 520321854, 840716339, 319979782, 483467146, 100292790, 595566425, 532088670, 391241113, 557032680, 717019583, 618444543, 413401142, 622092570, 943800254, 53691717, 327330149, 361175903, 928943329, 13148104, 898652331, 944446504, 907808507, 626319706, 221756546, 526986138, 337787080, 974374029, 626708361, 98475453, 109589058, 345422044, 720941418, 133107102, 693817928, 981612727, 357181537, 768614871, 100307145, 719412985, 854649650, 669130771, 133426106, 694034756, 932843646, 306552663, 965187258, 522486216, 990689478, 731790923, 228792295, 260990666, 612175662, 89764835, 557418046, 559822700, 682435678, 736018345, 114446761, 219906109, 185079061, 87398364, 382250549, 674297056, 830359811, 103032759, 878713628, 289659457, 777608708, 816227546, 677099604, 770189807, 298768309, 604405259, 835538774, 384282252, 483169347, 244405043, 195185268, 806214631, 857797315, 899272006, 68056353, 283453813, 142919673, 101858764, 811778290, 685422233, 999897749, 267578618, 798528860, 948657851, 379069403, 378198026, 439854062, 416054742, 686386547, 112820040, 244723191, 683500003, 99414092, 576638962, 951377941, 638656056, 458176416, 92270209, 984803659, 190760847, 966187018, 792887812, 952344635, 786872381, 874015671, 779839508, 62196257, 70455722, 227713800, 702667736, 617291483, 954360172, 371111099, 403741567, 337962612, 513737487, 231501376, 626831520, 768026277, 944684997, 744327035, 168558216, 105222950, 920427925, 616459507, 502991910, 933092195, 105608466, 639295865, 424843829, 702139544, 823185233, 203533591, 546543137, 823133293, 850567124, 9000803, 768618289, 207970299, 738303292, 56970624, 631381991, 720751095, 187681528, 471805501, 496434571, 797538264, 787377280, 184474952, 394904292, 135022931, 291981866, 414438017, 218170077, 222889650, 669971286, 276433697, 676938786, 816117981, 990129040, 642284167, 719281269, 427619331, 479587718, 127929455, 563041384, 448482090, 713685600, 808727446, 725218347, 218107668, 506444756, 191874882, 923821557, 446232516, 560354455, 42467479, 830381871, 861414854, 693707398, 842379769, 323078366, 325996991, 760363768, 914363208, 817994220, 306120918, 296604730, 276470972, 745503789, 246850028, 893673164, 900913862, 731222876, 575739468, 248014306, 664671472, 51072001, 239112958, 11276755, 86708599, 988084949, 22434890, 975077714, 802247792, 339810362, 969590040, 37782724, 761463894, 981667582, 899718677, 169056353, 218213144, 728056835, 897650681, 328739573, 489960980, 188917379, 832501786, 333499598, 939145312, 607254640, 176583050, 199824080, 989767746, 790342282, 130026743, 72194757, 881717436, 732834575, 628349666, 724686760, 936289446, 988998461, 688595419, 402633151, 265592644, 808812411, 854605419, 913919838, 851402594, 312033622, 321250516, 311834184, 847383232, 584290574, 740014048, 206021243, 335984636, 84319204, 876087174, 113429224, 132706352, 162369285, 293285399, 214616122, 469940437, 696671086, 982023718, 136335095, 550118706, 390257061, 640245930, 931000863, 728131047, 203107621, 183335551, 202820496, 37593042, 804531119, 791597020, 554831335, 936387493, 499588895, 958325169, 145937411, 849282675, 93419201, 209248250, 443465530, 904214035, 958972962, 542956340, 554846622, 458916097, 886230148, 800881740, 506403011, 4865360, 374099768, 102476894, 340407083, 444019349, 184419690, 647128146, 985244473, 320150555, 258342874, 454199013, 781197767, 922616093, 608333117, 398011729, 671472975, 854823821, 145939077, 512531904, 848762672, 618822228, 607435784, 327479511, 501750532, 99833177, 781710187, 361991934, 368264647, 317609255, 562730835, 562114360, 427496981, 206417460, 317207162, 56528319, 919883817, 421536636, 390368704, 767485443, 661512956, 30989696, 552837580, 43189917, 917112531, 670638812, 332983909, 200701835, 590125801, 5886770, 569831677, 671626238, 289890414, 17018978, 222105847, 11327690, 202570805, 118043150, 23295916, 494463161, 793854746, 359575816, 248732520, 326658812, 497700325, 589305969, 391814316, 729028940, 637928964, 447205693, 809982310, 201970047, 824035614, 723274776, 482420731, 528301204, 490860057, 611313260, 157158962, 260456288, 254394737, 391248362, 376302498, 612291622, 447041057, 143725749, 945158374, 16307228, 601995873, 658803534, 665360337, 945714670, 354570539, 631405761, 81261281, 909294123, 677817340, 667616384, 755786891, 129199823, 295777258, 948027410, 118580233, 307546377, 390800918, 618144090, 241331972, 418156853, 759516516, 774392882, 646998373, 82968443, 429717252, 483814650, 345752339, 331328511, 298539792, 988041391, 919307596, 240668677, 814370977, 616395329, 780649300, 977466491, 498552098, 823460416, 132892296, 543144699, 856209586, 943520334, 976985343, 767505393, 796720222, 990326908, 572088605, 759965686, 384910480, 100793896, 783071015, 924602960, 322425561, 966283574, 374251032, 589647524, 489663655, 629303642, 19271497, 822997909, 91383833, 453893093, 662697952, 661525785, 540604478, 144749113, 17274516, 530304763, 140042833, 757696101, 755705305, 707316277, 152739185, 595092650, 174711058, 389092128, 658382967, 554841401, 360583892, 48286341, 720914802, 289938676, 739194663, 872469459, 355232781, 644700390, 291482705, 918508013, 544858478, 215645637, 532544617, 222421603, 198914463, 427438002, 840341328, 334963469, 930886383, 585234300, 956016131, 352102341, 631812271, 552293835, 384939690, 234213847, 740674009, 720108586, 439371345, 319244395, 735692308, 904644528, 385956310, 25562107, 204739891, 93571276, 379729938, 483072022, 804155108, 859502361, 630086030, 422562316, 742041874, 535215821, 864569852, 980035049, 47871277, 626649719, 117051553, 347278214, 231555778, 610991335, 669751983, 871166786, 484615365, 460126362, 446073077, 26969642, 501857708, 171354483, 443716670, 392044487, 927757141, 184743451, 818173889, 55604910, 536862257, 807119425, 429265609, 559882399, 97575335, 65642656, 339331, 23804253, 627790515, 503795769, 214136282, 289566779, 499403756, 257364346, 798566747, 272476565, 291879651, 898135150, 517560716, 714002839, 824849205, 219547787, 660203669, 978574576, 17358427, 654057164, 950375092, 320126783, 857559375, 616274688, 424073530, 938572247, 25175076, 773346009, 148411536, 243481177, 305857503, 109060601, 74234239, 258265619, 19062809, 491484259, 913553319, 915906284, 659690196, 292668945, 837690426, 258957490, 615274669, 237866683, 953320443, 26481871, 660330326, 333455718, 867940495, 198685460, 828198347, 937846336, 720540467, 452617681, 695914565, 444096385, 483437160, 39590284, 482193061, 148511963, 588195137, 314236606, 445260262, 108639029, 772600875, 700791486, 719373539, 772487397, 138314729, 561976704, 237871161, 52584604, 510401948, 987756183, 364778135, 56187101, 971405597, 648958296, 601845484, 225218837, 66182370, 720135732, 408641812, 108327384, 805090597, 793767461, 600851479, 716965037, 721582051, 268896875, 914433939, 885830992, 532435797, 706803459, 58365371, 153506572, 127189805, 633796197, 760178210, 37987366, 49292266, 896128047, 694607640, 49674886, 636768625, 759412882, 555326417, 700743694, 691281095, 943539881, 128961912, 675383411, 354641078, 734089704, 474801586, 830746485, 480494626, 310914966, 615431829, 866218440, 599325339, 547290567, 442257840, 614241534, 451715120, 168220626, 859613149, 356344814, 59847954, 399671657, 675797429, 649267703, 888620399, 258410703, 313155985, 134957747, 857292221, 760618575, 761477397, 754788927, 511342487, 746201079, 647335536, 429985598, 293900870, 863809841, 188114276, 153644533, 716440379, 488301780, 513071431, 426474167, 75696817, 158383377, 929161281, 502603338, 187292778, 961841134, 554435356, 456889976, 175747660, 934033347, 850161475, 874791423, 892795707, 599742285, 681063253, 9164078, 714845353, 513059045, 572879221, 916776139, 173429271, 18691349, 282976994, 653369384, 73040846, 829736147, 494855500, 755891848, 277195803, 526875958, 10865451, 695287423, 46404343, 265057739, 446706707, 177525315, 152326694, 216931346, 38244568, 17396289, 530446602, 198102593, 507643436, 412655784, 334886810, 403944335, 52864117, 256549974, 368704997, 216230644, 642204721, 266175645, 919311843, 353863687, 833846960, 188932136, 674843967, 334916317, 997455029, 976610667, 987704926, 567299681, 624395116, 381265453, 839785104, 288382500, 31985075, 674377035, 517214971, 925531415, 719669426, 231662481, 627194120, 98469900, 169078183, 528505533, 152594486, 881089188, 559412326, 541398610, 890004882, 765889542, 667485755, 317419625, 777094394, 539885438, 453551912, 80345676, 925357538, 382708476, 366253055, 389789406, 635628030, 682635463, 257651747, 562039252, 135492170, 327518451, 888231952, 175895742, 556965564, 65116901, 877736186, 440533104, 754909484, 716450307, 331053517, 494143345, 740718247, 16066568, 853100021, 147000981, 251657090, 759880201, 1809734, 458906948, 804314224, 756617782, 385270893, 924455307, 608266367, 796139787, 104358867, 728340756, 395832875, 724300286, 676723997, 587989748, 819730069, 240864765, 394720596, 97241247, 8211692, 925916063, 363715316, 852401481, 999958825, 811477329, 195296365, 805592184, 227548878, 4230400, 415325139, 437646645, 997571434, 875797753, 138946283, 524892397, 773059611, 826507078, 584943172, 517815567, 271346352, 900253940, 803625369, 56813922, 467659189, 737829033, 101845701, 713102, 462293332, 256791261, 457100729, 113839967, 837564883, 606039665, 913790212, 823797315, 754421518, 682279692, 740204101, 245010298, 606060840, 991185291, 394500079, 956607329, 593438994, 60568657, 158096722, 378951035, 525985619, 564392473, 452845518, 203530079, 954409765, 366502965, 895339095, 219188263, 213571085, 366908646, 845210721, 349949596, 226090627, 604880097, 445838551, 472751816, 248488485, 831033981, 307146000, 126870744, 775565905, 315287762, 578775633, 684651682, 532594583, 161665205, 878897032, 848775940, 188272734, 469679650, 238793464, 393721992, 900868375, 760489204, 591250171, 501195257, 507467072, 479326142, 883686048, 172924814, 759655221, 499246587, 450273133, 70534712, 83660020, 443181803, 663065003, 603749729, 649057124, 908286883, 314724403, 448219679, 79198242, 298515258, 488314464, 338849412, 560924114, 674088175, 297391875, 208746871, 754492806, 325752813, 706696286, 686886039, 962881652, 132441272, 211518573, 629340770, 485491291, 983727599, 991073669, 294907703, 115950491, 364508287, 747369351, 483218360, 901209257, 967399592, 827233975, 21192208, 122943255, 114038323, 827611887, 39833087, 417099677, 655961550, 841517542, 529982085, 292738195, 710254465, 529285197, 185585, 542784773, 883122006, 56352603, 970500724, 22475583, 31883246, 937090549, 437466180, 876038129, 973344195, 120605070, 855265282, 432853873, 399930404, 524886748, 282668677, 730031527, 818685395, 138819956, 126863315, 334703175, 440803528, 16989218, 147537739, 130320043, 333260230, 991307720, 160221877, 516474618, 883554868, 127472660, 330661633, 451203802, 374479679, 789506435, 152887040, 626233189, 415458231, 82305033, 150020376, 888172662, 716766216, 194123031, 557137544, 641475335, 708181977, 235146726, 146808207, 233278250, 881825663, 264369334, 740106023, 661364512, 793738418, 842972132, 260170433, 233834282, 791439359, 60149634, 841015982, 807933599, 608418785, 442080234, 771189693, 106940467, 856237075, 245900297, 836125784, 293193815, 776613967, 112563274, 851135521, 746503573, 585325797, 176371376, 419249459, 944384047, 807329730, 619442983, 663747533, 557740934, 529804537, 635664967, 611374211, 987532921, 825339509, 379857345, 724062721, 286940437, 349813045, 833898568, 864705172, 980979778, 558560725, 392211393, 906109080, 937482696, 349431119, 453907392, 941858533, 462513021, 195879152, 530141952, 746959080, 161679477, 69182030, 112447987, 879193441, 842206019, 861664253, 703174944, 385022709, 899593552, 48396802, 659658358, 654138408, 133314890, 802181586, 756795142, 230038113, 326027316, 11208727, 124583564, 251113442, 632535825, 846253308, 947797797, 871185214, 86746218, 907748941, 220650919, 586250136, 812811255, 899747745, 310180555, 784641296, 549115548, 832127122, 559265452, 73905438, 527869579, 321588776, 612788146, 862844345, 497072760, 775086244, 838107442, 903716401, 775315667, 749902937, 586392151, 819857903, 321030007, 195277621, 288455044, 525904865, 684597091, 44596712, 454877548, 381609277, 579957399, 689316243, 181960884, 981882818, 402604958, 178250131, 797538580, 830056965, 689557378, 598782151, 634831824, 77080261, 983782792, 36953838, 229040817, 129774843, 633675542, 148991387, 981769796, 338436496, 329254890, 917910095, 774431111, 121089814, 25120099, 894768627, 353712279, 151161059, 803363710, 256145826, 255474817, 202121975, 469520521, 182028414, 443936114, 327476906, 201769575, 361726365, 812651687, 40015660, 526929481, 650016085, 94270255, 544181058, 475176551, 276247186, 317863191, 385763013, 964382133, 994540662, 386704036, 875477101, 842608728, 928053163, 793108301, 45453437, 137046777, 66123986, 539098959, 8963537, 86225618, 662712895, 637246923, 458332998, 66460530, 363947369, 668059037, 507373558, 407171901, 323791869, 427613465, 436268725, 883617698, 798706834, 736971193, 538460257, 481122202, 52352514, 802703929, 310514436, 426269702, 693374439, 26917092, 640676735, 365376358, 668572154, 475739592, 490768265, 243593602, 879222331, 205681313, 466252731, 137067203, 424506098, 653713164, 374089961, 639773167, 149453261, 55077789, 175303874, 180421663, 309370193, 715088546, 697965017, 568149095, 809682861, 541886009, 547863165, 717325992, 506050714, 312384973, 646352079, 297008533, 448263027, 297990724, 191617601, 623234869, 542452677, 338736797, 621221351, 592839404, 67035808, 304892796, 227966134, 499244569, 747634040, 342700146, 310975388, 355315564, 309004787, 744143387, 764161545, 469686041, 880724078, 296677321, 627905523, 945489729, 102675550, 804356945, 676506794, 541661016, 657904475, 634720468, 508604704, 434203522, 444699398, 324722012, 896545952, 534835573, 759655719, 739063205, 330429336, 44098070, 452590177, 933395799, 603700601, 741475026, 477030675, 130573838, 944715745, 787283638, 288776633, 697378146, 580821068, 513109039, 312821682, 704815193, 89358438, 277747956, 591232690, 556591507, 716049034, 60820407, 276576031, 393714098, 810433531, 32936779, 403638808, 945247050, 309334388, 585307733, 823020012, 554578493, 941614317, 325101190, 228649421, 611741148, 617364015, 740210271, 190891920, 280929408, 920021860, 835200648, 819083553, 906778136, 667043874, 793862354, 350904805, 442066893, 391982738, 70243920, 508030354, 73815445, 681424400, 164009228, 573651956, 281500716, 932848095, 172130761, 203963760, 445462117, 537513904, 734176525, 661837075, 474503328, 497283789, 847141409, 990612589, 284517453, 34968382, 285801644, 862176870, 313612021, 906553202, 468676784, 197378374, 360626094, 976039769, 107320028, 809549583, 308425595, 731481205, 702448995, 977768667, 776386689, 867660019, 512462945, 759109751, 52474684, 641003925, 208349136, 326209195, 37273425, 842616282, 549010842, 529410458, 817508986, 14236698, 278059981, 1987407, 57024863, 170669759, 105965395, 331809002, 808295205, 888426748, 977841872, 817440845, 61008923, 872259565, 797591007, 942883129, 453971972, 993084833, 282940101, 283075491, 257223232, 711456932, 150101845, 59698328, 696878646, 14862142, 477099981, 828393869, 166158604, 65578080, 351730056, 902487960, 810193390, 497334712, 798437339, 621810283, 74666207, 996276597, 946337712, 29458108, 734238029, 645820822, 422106305, 710383772, 131084114, 536960506, 135531781, 249103682, 24650598, 469680540, 932322203, 451890232, 718475581, 373951740, 562634011, 13188312, 238033372, 30357683, 901933519, 817831946, 501647742, 374819988, 593379452, 11882404, 622851564, 820712364, 848394617, 713331297, 933911652, 643738117, 843166622, 158344719, 320017157, 83363701, 880429952, 201325197, 946046637, 338025113, 409623645, 350129446, 633069426, 844224613, 677163037, 865694497, 81215657, 502698604, 350950658, 911568969, 799209924, 323851494, 929635044, 790097873, 447766101, 811192023, 922860149, 392704192, 764872759, 530953370, 31205327, 916404646, 972569493, 534422371, 19173348, 268339023, 486225729, 533710239, 814789860, 18310263, 616869790, 557262805, 890052375, 606239077, 621944459, 234545983, 400938145, 658184314, 225151905, 357081412, 8042026, 931618648, 826071791, 832867690, 286891324, 487670191, 73929385, 471393620, 824385131, 25130990, 776037761, 749103976, 562089886, 529165931, 503382358, 410129898, 342090348, 67361057, 930428083, 153220402, 644579021, 46989371, 877827643, 978323160, 546654340, 12696478, 764101501, 440219810, 982308833, 376837875, 11214426, 955493442, 914443335, 134124716, 898190954, 275894326, 421744163, 981058992, 802378737, 511623240, 614497707, 906352067, 335589126, 656192769, 890211044, 750041186, 668462555, 145139547, 593778760, 978050204, 198929405, 144751999, 944227400, 849412491, 816534452, 129482696, 899971031, 551142647, 104292314, 740836332, 784629181, 625824944, 722610372, 239477442, 336224022, 817512922, 361396978, 235328988, 46710416, 886381518, 638229379, 28681220, 958831774, 225398486, 799635289, 663658653, 644277404, 496961693, 883187685, 249174893, 301548749, 412766452, 63136860, 618928570, 925898561, 496941420, 603647776, 377658822, 55287374, 539544798, 940111959, 395384663, 299586838, 285568606, 728738630, 404566894, 894698906, 298716547, 170638656, 265795392, 938526321, 604165543, 648925700, 317411782, 987906381, 706638858, 443553595, 806490199, 990954126, 581748928, 762433417, 329647610, 608631856, 470471084, 133160565, 292585740, 541069883, 699595415, 754162243, 726343029, 360059692, 867504175, 194954734, 427647535, 426068924, 269228349, 791675967, 468609297, 274677636, 57575155, 786036431, 460538645, 816987315, 351991572, 800686151, 870793318, 335544140, 233821333, 598280367, 27092874, 372050713, 744955181, 800831555, 228566537, 876262144, 882634011, 776391647, 482908362, 945611496, 46240215, 667116364, 77863347, 143127636, 981771192, 862763081, 8481632, 795170202, 712939798, 851025647, 684260963, 708788338, 428023345, 424697111, 113606260, 618779229, 748467131, 698898659, 389766170, 526254278, 896394934, 680860241, 611188535, 476545070, 716737698, 512888057, 726307809, 45192577, 369858213, 821182258, 698747876, 926725986, 810297461, 76074900, 337270568, 310947272, 738609862, 85531331, 756531549, 732902061, 507925027, 20957759, 727324437, 828565822, 827713550, 848643401, 800591179, 188929944, 150941765, 722766339, 957641204, 568363530, 212260123, 272986710, 67015474, 716024740, 901636028, 43776957, 325803177, 984990716, 857357692, 294178314, 63319663, 41476972, 621894633, 550213662, 337643329, 346689688, 408828232, 333504510, 486914681, 463887360, 724726224, 173304840, 450353217, 42213763, 682800151, 580322222, 175122432, 915967115, 924045084, 215148173, 989433627, 881137412, 999035169, 373643345, 496132641, 785959341, 560778037, 543101751, 648052125, 170757094, 911296223, 448758928, 366987433, 351546884, 45866053, 627940118, 467063636, 917357734, 649739073, 66856893, 680017785, 341789239, 935743886, 187654208, 853284982, 569259858, 90129072, 950399859, 770794908, 675843585, 746895477, 378861509, 697993463, 857856870, 26650486, 198125331, 63240735, 736992230, 632584792, 207966037, 765079848, 845078004, 807769719, 225217447, 155819633, 890961301, 351621878, 204758018, 698293346, 919652435, 503725248, 540237828, 298799319, 115112145, 640573578, 606475760, 18079835, 252940359, 970304967, 765440882, 144521136, 23941531, 606894043, 830347462, 770737725, 577399218, 881561026, 460390691, 71983769, 265497243, 840704757, 941890489, 891259265, 40528045, 895909935, 142589115, 603137876, 393583426, 895261875, 880283990, 503501920, 258864170, 507364342, 245181083, 896219236, 887187308, 724430120, 359762388, 566508221, 241853854, 480858967, 906355375, 27775089, 36876645, 280956971, 128476952, 293647130, 942610434, 121365325, 168843609, 681038289, 623972177, 197004061, 271982401, 476740322, 249624259, 385021934, 749016105, 861901569, 504311242, 702983671, 847433860, 515092661, 184662680, 987803217, 617780096, 899856043, 100069214, 79613718, 599089593, 478872624, 195628971, 570488174, 541950669, 356946322, 698925937, 750339449, 788186764, 334371846, 265706856, 77964802, 463169665, 649170239, 407852703, 28804562, 592917028, 611306380, 282433886, 394357400, 187060052, 868739951, 650340344, 784390429, 897360714, 303626616, 402571693, 779407905, 219740039, 223672955, 205354462, 291551672, 721878805, 886894624, 541527513, 365542214, 741041943, 768964033, 432045895, 457457735, 798470815, 887618953, 533680931, 586008764, 455021326, 155283575, 424851806, 896525753, 405342114, 291035430, 879451927, 344781907, 91164255, 745482420, 257829273, 668796144, 776584420, 393075637, 111155500, 435252435, 391178369, 103182200, 826611015, 380148410, 799862994, 438311239, 817860367, 267658578, 721461036, 845249138, 388105055, 121483108, 444826344, 370112971, 425526445, 484388344, 829704328, 808762851, 935112323, 29728568, 321651372, 203795988, 667225139, 193104596, 191356718, 972021141, 143127667, 417990892, 455118414, 577642715, 477521355, 181627527, 887439300, 90019650, 713840866, 892553609, 653524922, 714514872, 80608449, 199249498, 527649937, 319394058, 435867045, 261607760, 412421231, 507210056, 795287082, 276602096, 646725343, 613613539, 880825152, 997464358, 868011278, 651391356, 54039497, 486682700, 248884937, 180225216, 190117682, 203196686, 933508517, 28456336, 570593339, 993273583, 877418735, 176307800, 391890745, 849824216, 133976166, 625198528, 971674954, 994664201, 750222657, 802452689, 230366835, 942297879, 706061654, 242719516, 829788299, 388947664, 821519099, 313446649, 365945522, 647490772, 205193244, 353761203, 55150366, 816288280, 290470003, 75138164, 928408258, 816801629, 59793186, 335399828, 592093519, 91665066, 792787287, 513447878, 641486546, 4556091, 870455630, 637064729, 244698502, 569670871, 751963915, 804271780, 169227087, 316635435, 347289116, 962828111, 698337781, 27307935, 400696295, 441544669, 675687007, 469825746, 465353085, 498526625, 188712917, 977705102, 68029052, 915710936, 182775756, 360275536, 126866241, 904935632, 326937803, 563474859, 462699519, 698287100, 937314634, 58305058, 730477732, 983068578, 283124904, 589002280, 117639927, 649803002, 442339727, 392692236, 694923631, 193020724, 809556691, 997570014, 574382008, 48739106, 394011792, 531761231, 96380076, 655095343, 865690180, 758099469, 52505047, 554206154, 207136971, 81424471, 325541873, 696612877, 547647321, 68179794, 224345897, 50085109, 223907829, 429134903, 257815006, 879743371, 101348912, 511334874, 501612300, 847532625, 872312910, 321890109, 558435026, 2031752, 115131957, 503027982, 800539055, 911882184, 651607975, 332807913, 893711612, 518009194, 921331002, 760974476, 720508603, 153541031, 358148658, 448130581, 123430145, 661935881, 221036260, 973170166, 201845477, 59975546, 674859118, 634267528, 276893607, 170372134, 62156160, 92276100, 495108381, 428307191, 659043603, 520189978, 798591227, 170779752, 420418110, 571815856, 360718595, 525842365, 569133845, 257791494, 406803354, 961309601, 319491399, 476029244, 924342640, 572020494, 709789966, 56344533, 590305796, 911722302, 533568824, 248031758, 868703568, 615925709, 634637387, 899282316, 399679289, 208990502, 516253288, 612626014, 501516217, 525415953, 586829945, 21068381, 726586390, 230823896, 748836874, 551842537, 161184406, 648439109, 327937728, 978433766, 407646274, 367562326, 632282609, 184464867, 821293639, 883084039, 236592764, 683636023, 509262694, 67081089, 393515101, 551448563, 661620820, 959328528, 131406706, 159071961, 144910121, 526409032, 839429304, 591063170, 452271070, 771825104, 105516880, 735056263, 260240956, 393984224, 366598946, 970365789, 850992788, 591432387, 731690630, 743779280, 963372751, 233553209, 989856347, 718309892, 622119615, 603644966, 481199586, 219653252, 278468640, 317106875, 815758299, 852077618, 98287481, 663446814, 150983397, 77175628, 114014387, 431825358, 600368639, 777057837, 347013131, 102963028, 246905170, 594606532, 602387872, 491537522, 456448700, 24256290, 482344213, 786536374, 124813252, 558709525, 235691064, 985530259, 659489177, 723947546, 195438293, 76558956, 985749123, 305676604, 725350097, 735766122, 482219264, 755115054, 865498191, 221848004, 524820948, 237523807, 295108055, 762526345, 843177949, 395148341, 206676719, 769910394, 757708638, 387330509, 409748897, 184688784, 912669778, 757043015, 308542298, 107307594, 553494769, 21779265, 877213410, 963260335, 174516390, 142730963, 752935888, 75394273, 144987946, 49849569, 520404288, 530382378, 216650130, 72316692, 303893455, 296702671, 687678354, 645207597, 166169878, 867274862, 114353081, 187895692, 397705997, 909159607, 134097978, 176622847, 37830029, 654280695, 217670723, 191922749, 779980441, 576567194, 489119861, 850404899, 425583773, 730622558, 730982146, 392792273, 848959159, 220281769, 386220694, 466336010, 218808556, 958802145, 543844513, 465689348, 385229497, 214035318, 227598686, 539346086, 415267083, 381241383, 231370450, 765440219, 648601716, 430394296, 959959129, 761740602, 106802270, 378302961, 871213517, 496571739, 694546527, 584592883, 498514642, 84833265, 229071302, 576132387, 882582977, 317938062, 794988064, 109156552, 730966334, 99302612, 450179482, 942867244, 293887332, 322697311, 292022487, 975046793, 896577308, 977610668, 611349098, 906085084, 266256322, 17969424, 38067721, 4424569, 307796332, 999280968, 789298425, 254490990, 262064353, 3900027, 751929560, 244882186, 203663313, 672291107, 577498309, 503741648, 699364602, 693776334, 839646898, 914199533, 867825086, 112120876, 320309235, 628520152, 755410863, 979283026, 469510452, 398937838, 488907413, 925182784, 763557164, 419896393, 33780361, 912203282, 660967823, 751389261, 98211276, 797031731, 382930177, 33018821, 529273621, 743847781, 157028330, 440221868, 108718501, 935088977, 784671438, 175795471, 529237957, 423097216, 208111056, 460000426, 714044332, 943927055, 230170008, 244620530, 230970517, 103560824, 735593327, 865971598, 16093832, 244862243, 359225011, 110653881, 747489688, 228068320, 219867296, 175117945, 24603431, 897636635, 145277815, 320577605, 532563857, 888081246, 532401909, 829826597, 590572705, 409925370, 682560455, 719446387, 110543620, 524378532, 641514459, 812391823, 111298630, 320545723, 606855178, 3854817, 475861338, 730204432, 14360383, 157292089, 769807164, 376561244, 12746343, 201386004, 54000252, 44541027, 243257565, 974091308, 914545147, 553386506, 562919777, 550624975, 49311461, 337548694, 921712079, 22137543, 994080618, 459552042, 373067999, 231413810, 585909031, 103386518, 968814188, 126195404, 184224714, 298042493, 124126983, 899531398, 154738845, 121504545, 447823559, 876329224, 224428834, 456879694, 522232921, 741173342, 295443096, 275359460, 94739037, 754329336, 584665599, 717711686, 861764699, 887007703, 638640838, 380944633, 343347467, 695021637, 297240078, 841764019, 589385620, 78910558, 217826283, 756561474, 861810760, 263518001, 70864686, 105526655, 859131601, 576058515, 63391453, 46124878, 602062017, 679905550, 943583844, 604288239, 532798555, 533286909, 173141365, 652512898, 26299511, 659290846, 56770376, 447744524, 734780561, 581193203, 611804930, 537884341, 626406, 365313138, 539811642, 359653959, 257238460, 934655795, 114233905, 358576545, 323927538, 690057583, 115929734, 972056736, 690450452, 22507905, 385914551, 773993172, 422295841, 593240956, 683021199, 415717073, 198217038, 652451353, 419548776, 48749797, 638316639, 608083864, 944303272, 89286586, 336860232, 126730805, 626371185, 460485773, 562586145, 414013192, 934857486, 876006539, 206041391, 722913726, 425266743, 448940687, 428860415, 166365137, 608644956, 590662506, 218423464, 222894877, 500089507, 26444448, 731061493, 782414900, 228064124, 894102884, 294102698, 434957798, 993714748, 51818231, 549990158, 111673304, 175083850, 539435990, 580245260, 171336203, 552204183, 390514327, 149634002, 450976413, 601054149, 291806122, 707236351, 44732601, 368180200, 704701386, 293349777, 82637470, 730093927, 366400803, 358441677, 929981248, 275056638, 390471767, 641513148, 400929618, 608146868, 648021242, 480780255, 382887734, 758946617, 717821739, 821575240, 456867796, 515161879, 374112793, 303218681, 458273084, 882843397, 971134083, 381456111, 915998348, 195646015, 771474736, 700411907, 391541653, 665886600, 7997522, 466054934, 290438237, 422161580, 579846209, 972177808, 672821117, 244438682, 357967009, 508829973, 923256975, 658088542, 18761019, 280951300, 993436924, 424872327, 225928781, 600915579, 908473379, 931122296, 835500756, 894928537, 730354798, 783529315, 70443676, 63215133, 95297755, 645402643, 52656722, 49777601, 280196018, 680530535, 477300460, 466005130, 636418637, 365331663, 725703020, 945447127, 977406354, 267212515, 863629610, 515225793, 569026405, 957290146, 626743667, 154330338, 904057169, 432414992, 685245919, 482883647, 794834582, 511055569, 973689024, 584904716, 860433178, 907157805, 981679639, 980946629, 90579129, 179183956, 698907009, 696787442, 533638606, 511212390, 670862379, 575803399, 349687071, 324760493, 99972804, 878174754, 379537414, 364480326, 938757076, 983838032, 581509226, 180351213, 708550357, 881514134, 890802762, 973720316, 519136984, 594333095, 453692701, 204364, 928107307, 231675776, 320026393, 610039675, 868905174, 268556808, 396184331, 491502917, 775292206, 206666209, 266200195, 426683055, 804784051, 12303846, 910818243, 834295879, 71790729, 835727271, 531754035, 503523634, 946677725, 421520073, 381467924, 762438437, 537209081, 673951930, 105539275, 153097382, 244413153, 925635436, 886668864, 495639055, 291089382, 158307140, 342385897, 720135278, 93207280, 410814806, 328738839, 258762029, 242714390, 259924511, 249511635, 169164697, 727291437, 720849690, 672164074, 412741181, 829927731, 429869407, 566805115, 85760801, 982267232, 232859023, 432683183, 56093702, 953846637, 689166045, 176998408, 966575340, 703652740, 70453597, 843245273, 518308813, 305278753, 690668819, 2831124, 105852071, 52499588, 272646744, 96626390, 359884012, 314979696, 116639975, 97791459, 846724622, 905207513, 287871066, 606157424, 804266878, 927661754, 216652173, 78210296, 960861178, 107934509, 30771710, 441182759, 496140342, 369158450, 584166011, 293208185, 466908349, 356907009, 986730859, 192411610, 277897909, 120328522, 834567691, 415942053, 907026330, 305895700, 158445177, 766926261, 765068432, 368020881, 90824711, 711923807, 350694885, 422762680, 659023383, 564698385, 916869315, 689334181, 18124455, 145920433, 277655475, 13692455, 699481640, 516480855, 344782801, 571216155, 306183838, 362320336, 399747888, 249186416, 165610020, 998520783, 279128662, 38163520, 717163035, 335716217, 259870407, 54575352, 508660550, 749530506, 778854893, 861817984, 849700081, 764497739, 695435001, 925975158, 596408360, 265084060, 260378758, 449194117, 452166605, 349815125, 285755613, 430280, 784980949, 460860622, 709312197, 602287690, 481171880, 332364457, 616517796, 981158834, 671929625, 550400612, 884698733, 852561927, 830692996, 794210173, 46494473, 267285202, 821422125, 503696031, 929170699, 943167287, 595239672, 61240892, 707311483, 390258216, 894454333, 642338631, 938940985, 137645687, 120442981, 32437627, 550476493, 133354517, 758194460, 507755339, 55297781, 642527206, 99321447, 761733018, 976620562, 775205247, 159676858, 572731757, 258198830, 687473705, 513538297, 420688729, 268795334, 258432746, 190215804, 961883541, 766957029, 443421564, 506810286, 779747995, 651633090, 921733604, 67894075, 657416718, 797662212, 349197265, 915967252, 491103114, 345072612, 540419288, 684187759, 607711067, 658141816, 585190385, 903606579, 951140999, 918771446, 278690479, 311141500, 75643138, 193807531, 986711192, 887025032, 6694499, 227368429, 342623521, 347721813, 200570150, 295030946, 141132639, 587401569, 411559241, 234674303, 846622938, 869171994, 415674374, 122808115, 846064563, 974763065, 735784928, 268341614, 190453545, 833468998, 273076748, 4797894, 554115679, 111843181, 192239391, 179073923, 785927807, 669489026, 973682394, 293409280, 58954635, 53002351, 366028702, 753593056, 762483730, 727553690, 58962134, 904823378, 252462804, 411531278, 767704664, 288508806, 774458413, 650866962, 657752208, 696625665, 577910896, 705484890, 501948289, 925977928, 324666791, 920778008, 957255542, 642941636, 823077853, 809860426, 998963296, 304164612, 378563253, 265476605, 490686486, 870023756, 607309926, 52999115, 331880241, 720395619, 777068431, 907165104, 608350082, 254462519, 850237022, 692670589, 886410869, 558993925, 147160252, 992092269, 829077685, 431881955, 464689812, 156129540, 869786865, 281480341, 390271009, 630340117, 361623581, 453961536, 102591587, 622281272, 754687536, 832017779, 990342336, 991418532, 876736476, 572938046, 857089332, 804185065, 57582962, 637671725, 740566215, 691609519, 947118581, 670754806, 583704787, 65839764, 501058879, 974692710, 454722964, 74854058, 680248748, 81051063, 132440334, 145870712, 987792906, 193557911, 544565839, 879333925, 507231455, 721939207, 141925047, 433555245, 670844965, 300567706, 291138788, 207744245, 503495240, 345670742, 57959714, 978373737, 478291778, 386496481, 119053575, 985956536, 968776179, 525850445, 904282407, 545472937, 25677068, 990318678, 683269829, 738738423, 387606008, 416988781, 311005030, 19568397, 225849341, 547996134, 742856908, 104536642, 618336254, 580956342, 285802122, 94235780, 974917223, 540866660, 597550264, 255095714, 857505034, 319582557, 854825720, 374579233, 672125777, 620844701, 89095646, 407787905, 428170481, 501862013, 31793639, 248781086, 891516722, 516954460, 479413290, 186146575, 255217966, 6730289, 845579139, 437857107, 903268522, 656523552, 683790526, 97957095, 549946843, 585689017, 793027328, 684014095, 691295561, 958879834, 84732929, 3121485, 397121338, 458476771, 324873834, 242440412, 25906115, 727934911, 614581165, 16730440, 65325847, 103172132, 535592710, 54697772, 112837219, 553179190, 19968452, 478714421, 775461738, 695067793, 118791693, 597092602, 511653548, 452894773, 507779108, 763196617, 77664764, 160282244, 598804480, 954316702, 478446535, 588725169, 23633867, 601907173, 866688516, 29737606, 114211470, 950216598, 955429454, 956594319, 298984422, 144990367, 772498720, 411894863, 973805645, 510838639, 580701588, 569732524, 758041995, 278458355, 152541458, 757900449, 461146299, 863948036, 851199191, 688228841, 176361345, 543750802, 518019706, 693291535, 663212440, 532248197, 86034246, 178902489, 831504762, 189173465, 815738024, 393520358, 211196506, 777231746, 38879262, 960197514, 846174404, 476278151, 595981653, 746152434, 751586822, 456024083, 672178564, 230435687, 990726486, 232801950, 314252542, 759773936, 245492662, 91400343, 9670254, 908656832, 492884065, 225641830, 389576955, 894961089, 312152665, 782463509, 844125228, 300164572, 518931619, 973817795, 763719090, 994081176, 338597252, 253073968, 955279570, 595032317, 68723327, 12135412, 1669022, 900353904, 681271960, 21125489, 173294586, 15300799, 882966434, 2387852, 561809975, 347828257, 454908293, 125744152, 537942576, 718527506, 20454104, 961276695, 895235423, 522994199, 817405751, 957419367, 924351729, 376824314, 414921082, 820084339, 177075860, 117838736, 993203684, 492403675, 955002184, 499760241, 252017869, 325905327, 97025179, 235386407, 269353647, 443758718, 686453790, 455935167, 23496772, 703591842, 955591509, 64228977, 715712645, 444689049, 901333639, 315336432, 299331755, 915105161, 345125840, 865607414, 146742914, 478349193, 568903434, 777091990, 863759055, 750879, 847352108, 723678858, 706428270, 208964143, 355713632, 2159431, 605419634, 450271942, 790997314, 922035874, 528128837, 867669563, 899260336, 696188729, 838509928, 171607847, 451726637, 100174076, 4215688, 449613022, 125909177, 857243139, 996632145, 129494642, 853397052, 358284306, 812559692, 44956109, 88916302, 473037800, 283777864, 706777620, 670460952, 11094493, 176001755, 263267950, 157700174, 870448301, 577735246, 558163593, 707265250, 569990767, 2930770, 258988166, 721559266, 816881015, 856544818, 653684810, 50037112, 925682383, 736674403, 893937474, 498459792, 839098473, 100430279, 294566800, 242573402, 297087416, 378809035, 158053352, 861542662, 434416946, 743198750, 264590462, 150505978, 794794793, 654789204, 579653555, 599516637, 651731053, 831684675, 613908357, 190003939, 165348776, 299436895, 277217086, 244829835, 322429636, 980428536, 307742637, 605775236, 60093830, 534201571, 998869757, 631846353, 26515467, 381383576, 140978286, 573476739, 554056095, 203421899, 961903609, 886370292, 19459005, 385628899, 701192516, 29239212, 797034330, 763237306, 516640905, 43977434, 769928425, 610059462, 723515190, 776550927, 108194811, 255622681, 485257616, 879512868, 306090503, 633464972, 137707241, 931975581, 557771366, 983051261, 203250316, 241086206, 309736514, 285638102, 214114922, 227810730, 391192034, 902478494, 978991437, 869150880, 151383125, 116195201, 360471630, 354327561, 683381705, 263158731, 250943527, 410388644, 138305675, 334379589, 587615537, 903003656, 389354353, 116501788, 243747130, 556517446, 773525411, 808066990, 325277840, 914792240, 7990674, 124144313, 161590467, 601534982, 135428052, 824639841, 523817537, 699050254, 118725019, 788365222, 827633891, 400186560, 928905736, 333371214, 208167951, 434203273, 390426843, 548963881, 150935714, 124788529, 255618394, 335516196, 439234363, 648214516, 859906497, 735620451, 103088933, 621438681, 474937566, 547943312, 747182301, 477788430, 377976242, 522974242, 94925387, 661690835, 381074501, 458709086, 211933984, 26663722, 973711586, 915910836, 151159715, 438866683, 272286928, 304841731, 893805040, 972243941, 154808568, 795438766, 621804150, 584285768, 521758253, 199143311, 32403352, 932931903, 264063449, 590817436, 408217384, 424410087, 503210293, 425143213, 847425771, 366438147, 635018998, 557362823, 54782803, 737179410, 455578569, 744072935, 996521953, 83021616, 768655742, 41267967, 593890281, 970570872, 755917543, 254391107, 434926233, 783746407, 397240837, 188637270, 615018185, 562623798, 635656874, 685835899, 390488266, 831053555, 866916411, 957492358, 494623880, 370624494, 984327718, 582525288, 657387610, 228068608, 338044635, 653607045, 281830962, 809946327, 487785944, 687313859, 39758138, 623671476, 681166556, 640940178, 195338022, 439619739, 284427716, 966250249, 841862695, 953137229, 218375606, 952638309, 157533460, 946612336, 962130819, 172670824, 338381395, 39436521, 411028269, 188328757, 979214239, 512003733, 921400262, 519750107, 596546267, 411309760, 259535045, 783045153, 288562238, 633813989, 657153074, 763157481, 848693031, 901280066, 214699774, 909285610, 288942086, 749001375, 96707900, 814637540, 785595311, 467378297, 247597532, 536092981, 992575993, 985302152, 173520996, 252761309, 235909727, 440998848, 659070605, 666419341, 257792079, 282083574, 672290564, 475323017, 268661696, 400495164, 975570864, 150401358, 564606819, 934327344, 94143987, 347754475, 828035576, 27698902, 83554314, 215561651, 367361282, 493941376, 684615265, 155620220, 900380412, 399963440, 665692274, 659448279, 173222151, 607995211, 307385120, 820757666, 406471044, 983911936, 206898343, 663315820, 624562560, 903004859, 327889475, 60292207, 860740915, 802802326, 742663933, 127526271, 199313061, 16437510, 681301758, 146949605, 331623204, 425352992, 102128610, 291446657, 988241314, 79697136, 455882215, 759864715, 99341544, 629922134, 458634598, 816316616, 681602008, 6629207, 841743384, 940159389, 146571356, 595981335, 263625798, 803603681, 956970914, 49791724, 771766219, 735000449, 995424244, 218683107, 647292831, 242229035, 373857138, 980516403, 545824493, 463608131, 595374920, 944603250, 549394493, 333687316, 979637009, 353651949, 442526236, 595927234, 44986759, 966073972, 708866183, 158065805, 163603725, 717083883, 922350699, 738977995, 143036394, 212483984, 319779627, 441189737, 64805080, 663606454, 673074293, 138789102, 811884716, 474826037, 72276378, 875482725, 131603078, 527247170, 771026714, 993986738, 24512030, 660996881, 673291868, 973544672, 830538677, 203945874, 35163156, 777567022, 669480115, 175850921, 763169332, 10583411, 744785286, 168247389, 413679251, 61596426, 675388153, 435980796, 50872359, 432229235, 241867509, 337116478, 267861202, 130132517, 525736618, 554443999, 247257085, 32410569, 203279699, 287738456, 775486221, 938259213, 762430019, 610232142, 608499706, 290035148, 213712877, 178244329, 791825509, 101927327, 929905881, 387044904, 527767321, 204507249, 825421655, 757326931, 898882650, 259296837, 435978168, 307005400, 407533204, 261207816, 432754812, 626227598, 803299735, 488936528, 164860289, 768373455, 600417062, 773425339, 8034558, 263475909, 942775368, 950817284, 918881940, 920701840, 28834849, 868200978, 471025993, 298275969, 940653977, 21510172, 808120999, 825061372, 927609489, 504301035, 791394475, 629828071, 975329610, 634387255, 208677753, 411230352, 393516860, 752443404, 535390815, 171353196, 714599000, 975368717, 786121932, 57147318, 775478376, 175558612, 322140678, 92345239, 754065117, 320159836, 515688769, 197636972, 433165476, 29688458, 237771340, 276085948, 742984273, 569261563, 512723022, 479134408, 224417625, 714229022, 86021400, 760173461, 392491207, 715437226, 179118309, 333008198, 851686124, 392098016, 587770063, 188107812, 376683313, 360231006, 390376192, 139320656, 371458538, 512779323, 38465022, 515239212, 21392184, 221610887, 502109998, 614933009, 264105845, 300584259, 580015844, 924672038, 640421565, 510076778, 890748678, 693372356, 694760722, 502744518, 231713069, 536941537, 644955709, 340063652, 285707564, 298666925, 881193814, 290274300, 979279078, 214149766, 960390164, 418253178, 873683671, 590567965, 667265728, 306321168, 441176529, 861179754, 829306227, 445609205, 470733681, 259713823, 72222857, 57954273, 884936900, 470634114, 550059204, 8866628, 520291932, 850376034, 768454421, 470386522, 689480216, 531459252, 379081442, 141490027, 47222435, 877706725, 657364232, 266490807, 811203632, 532295160, 354317598, 649400057, 772077503, 957495071, 919349282, 732848672, 75313789, 469699368, 162275424, 639777749, 71575889, 467580748, 85419926, 231720265, 884619533, 955933243, 225046271, 443851092, 585236583, 415902732, 227577985, 344618518, 148324289, 841585193, 579256362, 188788222, 789352211, 306418562, 755385944, 330757694, 799889633, 829126812, 173585365, 80633192, 432923482, 543076408, 162494436, 174237631, 427004041, 698384261, 641803657, 285523311, 939751793, 481575908, 695490914, 433438806, 398460142, 172524446, 733793439, 613161095, 702227302, 23814249, 563075947, 364316833, 487811140, 286387188, 986773467, 270409345, 556634986, 993749197, 397538688, 155281104, 895581057, 37978797, 490465549, 257284818, 629893098, 242704557, 226906760, 809864855, 634509572, 661508846, 198749306, 703786978, 57868055, 299718017, 308009344, 907451710, 711878379, 509522304, 775364341, 43333253, 997325050, 503297519, 167870188, 771573556, 840306658, 729170900, 259137327, 381781043, 336994613, 178488815, 775850410, 84122777, 738079137, 26642421, 319767753, 63397054, 475960158, 842040595, 220792827, 229726519, 633474461, 229728258, 290092649, 418192203, 209967373, 372112105, 644802248, 74820526, 763935006, 228949892, 188499931, 831826850, 220833846, 638612816, 529512605, 462629272, 547465546, 237716238, 460289629, 448215058, 885906167, 888309928, 877716108, 520298022, 644363924, 722135114, 825723903, 880495754, 746832754, 865739552, 258437719, 60830548, 192443586, 637403574, 512129646, 278817081, 614504625, 375665870, 248367312, 765279915, 374120276, 215567576, 266491390, 266935386, 818983769, 612550411, 467168226, 93483006, 871091785, 628902395, 536850791, 421794811, 393399575, 782261642, 72558103, 381589356, 263392129, 313949094, 843345429, 570577101, 445830991, 844128439, 132051073, 249261348, 45204498, 332032815, 724568537, 899552580, 421709820, 782641281, 651111803, 930552875, 2679461, 539807344, 109642029, 438262009, 368837655, 626409832, 636955189, 739129051, 13568393, 520690850, 367754991, 598888145, 74290255, 589948853, 758886213, 151973907, 696686498, 630340326, 348042292, 587356458, 228929153, 851522497, 105997465, 610954520, 905691959, 309070085, 989708609, 702988873, 647035304, 713100243, 564065405, 227312394, 630525227, 201230164, 549966016, 305213138, 876195925, 479535739, 44329804, 305181373, 425814450, 996475041, 382540000, 71063856, 477479692, 387498635, 166044312, 320238253, 339642578, 62791092, 517927561, 887575391, 906522419, 436245454, 972711997, 499924855, 365902069, 849509387, 656734334, 634466238, 53141443, 41232122, 995211050, 11924518, 233159478, 96997312, 550981630, 667703821, 301523965, 995441836, 703286088, 7011305, 424787194, 462902439, 754006025, 892383087, 75619318, 40176812, 892583619, 916829817, 73922813, 709819149, 991857967, 940304116, 827837423, 917142609, 16524909, 835120928, 445176549, 505833612, 200392786, 792241851, 958687719, 728517059, 964311885, 207014490, 710379152, 745706357, 974151056, 641021735, 75089153, 716826196, 33224905, 133247627, 726300932, 206880245, 35153419, 939109583, 847571558, 331215293, 356223081, 238329789, 858252425, 18652020, 908534225, 28193965, 163922160, 388503148, 401434099, 930108102, 744440779, 676264720, 835390557, 239387794, 293034370, 342688371, 846672623, 966206224, 734480197, 422509051, 774994519, 262739428, 60565170, 488272006, 332635300, 812840927, 226150734, 189218548, 152342778, 567923967, 158572506, 396430992, 6926143, 816665181, 340632637, 293024193, 88539527, 793121989, 361425852, 201555702, 612920359, 437477820, 934578770, 852950064, 113770354, 365677328, 897074522, 576760234, 967194609, 454642865, 637998388, 44623198, 689850370, 770727482, 204249025, 940665820, 767653025, 465115084, 986486093, 561715663, 330348980, 598651199, 952688228, 823709420, 95861150, 180027040, 2086471, 655488438, 228745927, 95579005, 696640845, 738981954, 669107370, 441908404, 572139563, 373935617, 949591797, 142003299, 883464946, 441827966, 119011839, 657704739, 368309264, 861659098, 60930145, 531277293, 488238720, 969192064, 562104463, 641047757, 319989817, 978940188, 699928275, 682122544, 21460893, 498893287, 432245586, 311572888, 408508673, 695791964, 872981557, 348566690, 495147524, 957816678, 402083928, 613183198, 386029879, 973712640, 272443677, 447936716, 459014341, 835730303, 124958676, 44592307, 997444082, 928000107, 91990713, 335522139, 658494047, 497865541, 724468515, 178253790, 194641246, 370580995, 616287472, 65325351, 948840147, 442767996, 190589105, 358921393, 168900734, 26456397, 80174750, 949299533, 538959864, 333394445, 819397848, 294964679, 866727431, 3112193, 864753649, 137722982, 232926335, 37318100, 973322952, 175028911, 885635874, 232870941, 47158652, 38628898, 577428373, 817631326, 803747309, 598657786, 434193850, 77331937, 866574461, 768715129, 234013590, 535458482, 703826796, 565633018, 710274450, 313850492, 719289487, 993077943, 328733046, 935434574, 344802090, 587578452, 257013553, 720128646, 394701694, 700791527, 397332729, 461015257, 907814818, 556983255, 572390202, 986463795, 381875526, 336304134, 389129082, 169947494, 915127523, 200302173, 315604138, 79666394, 770200891, 56823689, 194780539, 865578116, 716832878, 545278607, 850444314, 511604782, 256898495, 169451432, 679284824, 297305271, 195197361, 924807549, 106041372, 573690985, 608688032, 118552161, 510935711, 16170279, 501939907, 736285326, 246674047, 399292179, 610273782, 34980231, 862640145, 813151105, 980754676, 341160461, 492376095, 823357358, 79667564, 863240671, 719223342, 810948813, 656879575, 837569369, 344683535, 294869761, 998822023, 916851950, 647033040, 467506799, 593255156, 609459328, 627593114, 238168647, 473632791, 330538577, 22043009, 615306787, 852231414, 517012228, 614767014, 706728579, 217154244, 459110826, 883447787, 947505036, 212503011, 529561393, 52199771, 518061166, 197974447, 425033033, 920044350, 146330962, 662126683, 455598714, 933768053, 149045703, 98270001, 920817014, 654139827, 916706261, 419453027, 322303439, 812632321, 595033399, 114918017, 873342405, 984587384, 975321912, 980855746, 913520833, 89091936, 153069558, 891218029, 120536426, 271688464, 584690788, 770808401, 699363142, 776064698, 599729176, 5364316, 401284579, 41135880, 632061536, 933837366, 703225448, 76247991, 460776954, 963718425, 617311349, 673916635, 632183401, 164592766, 105699332, 340716335, 361304221, 285551667, 461953109, 431193109, 301571297, 928953453, 665292393, 319027477, 524990186, 827927568, 507344508, 940865676, 48074752, 644682634, 979663326, 184760031, 118066519, 111192005, 586839083, 35176670, 950309788, 764837087, 965903170, 98394249, 234786883, 150495783, 991562690, 887226104, 711653614, 247744403, 945691588, 747295490, 630827959, 703569015, 262580535, 8577608, 450455260, 918418917, 96673331, 112460973, 288389141, 581439288, 133979535, 344325172, 46952391, 71170542, 250904963, 643545823, 903503680, 57734459, 987485344, 395398630, 479198587, 86516541, 17811982, 375953995, 690325330, 38015799, 158489049, 9558264, 641548203, 810452537, 464397714, 427660253, 543349044, 142061719, 998587284, 647528657, 562544801, 496342702, 248301924, 630776070, 773007102, 850137748, 417311570, 892434876, 750186514, 307699846, 759009309, 807231041, 40211335, 248760572, 799113380, 652139811, 2681392, 250381405, 870437072, 185043862, 323606039, 677791691, 209007438, 637344120, 635191697, 428182573, 872956133, 62203732, 520760586, 155223769, 379153601, 996816567, 124564546, 906079050, 494257069, 510027594, 234165046, 721305105, 257517931, 271546967, 648015154, 227017563, 320299997, 291180985, 192923222, 480450135, 195033599, 820378006, 87581176, 656922824, 269736953, 741927462, 130874937, 986460849, 29160223, 535096358, 170315378, 828521350, 361298825, 385103418, 102671714, 990748099, 786878820, 869416196, 539709571, 303032102, 975505945, 179583907, 79823267, 940970958, 146762928, 29806147, 521502075, 563281924, 728042076, 25115466, 419597864, 228230250, 772197974, 654917147, 368835750, 25903805, 676545218, 449307362, 853726946, 272791345, 557575219, 508566723, 8234012, 145428351, 102626906, 376478134, 591691064, 398876072, 54975923, 485992892, 617817178, 713243907, 96755949, 348813689, 606379949, 165273080, 664942500, 47570263, 63839235, 214829281, 500942480, 474712502, 579841841, 280355868, 189506740, 813509496, 258066751, 14117707, 141786817, 260399396, 863102231, 547318034, 887942025, 898647821, 176288457, 481045549, 136785595, 463940361, 551425004, 734461784, 316934154, 499257357, 570456436, 502621690, 271703168, 587165459, 309951128, 775860470, 254398035, 155328970, 430237939, 355217567, 306835173, 355383630, 426173938, 970225664, 776158524, 995925960, 479144538, 818213036, 377320468, 754268536, 22146714, 347995279, 699492714, 585389677, 965746560, 472119539, 934823036, 241787974, 334165625, 697127254, 739482069, 610221236, 254840187, 912992329, 493581977, 874839863, 254066448, 217916299, 343639067, 729123164, 120745501, 24349134, 803108725, 814028545, 570327794, 354817751, 467496600, 139427222, 206724383, 789105936, 745446988, 630912478, 293029427, 255441773, 403647976, 438820483, 206770657, 515358626, 655304722, 519512556, 477438931, 401833845, 809062587, 614379670, 610237958, 904389168, 780277142, 800253715, 829715247, 456645855, 345776386, 131621643, 988587223, 200032177, 5391444, 455786982, 211091846, 653363984, 229083610, 272988426, 691486056, 172020421, 958987590, 910535090, 802465948, 739574202, 372464559, 654833542, 399714079, 327327061, 703461148, 796830980, 426263280, 597502471, 659187244, 880750720, 237151947, 514978658, 480955960, 242448727, 433311349, 304983335, 4479778, 419606983, 981758641, 660319473, 274720325, 638051599, 84064480, 307109205, 612209826, 566355589, 526869351, 801906074, 415182816, 499363109, 92582928, 183909021, 966719507, 762366173, 268146218, 26022108, 125201607, 615108093, 648406416, 939139957, 421582523, 146101911, 67303893, 592488802, 899860720, 388493082, 128125488, 406395370, 291198267, 435749395, 89854723, 521659741, 369805924, 874023176, 945505847, 536005789, 230121560, 651873045, 548431085, 427156196, 481332835, 315052824, 756872587, 396467011, 41678639, 201087349, 431230086, 207769569, 980496259, 233025900, 467040815, 874089403, 806952760, 807888211, 966794342, 904390922, 727866002, 118057239, 817827201, 645192373, 5834717, 210136693, 648771371, 953114166, 802240444, 245063535, 460390368, 198271398, 753233432, 409808431, 536053883, 352812506, 651277105, 268353035, 342778373, 970840948, 6265716, 162137517, 499289137, 439432891, 728566907, 911751834, 738470466, 250854728, 213286460, 833372456, 825475479, 559495828, 13325421, 23136649, 713633278, 871085014, 277742508, 334934567, 807300357, 391848952, 695958567, 755351230, 467126530, 832482762, 913839468, 201724300, 531126937, 362713655, 402575599, 78793153, 67769332, 224275755, 897262839, 187430224, 472299793, 428917964, 262945308, 934375484, 303220399, 140168440, 97523656, 422296534, 252454041, 218660442, 195325920, 291259646, 777815022, 554775112, 775800232, 73225534, 688194419, 999972533, 617084358, 641753643, 74543715, 118630050, 544538230, 184169229, 466149380, 565990789, 242377914, 98708216, 563906848, 184400092, 551981479, 215154634, 808582625, 202080355, 177931676, 440620618, 411574467, 6793899, 263016209, 985285710, 844147323, 724289974, 596729698, 909561242, 509629626, 151440661, 355263617, 861896159, 629724358, 433284572, 473481045, 664504285, 644718781, 304807583, 400950977, 782843442, 753392570, 662898397, 515390917, 340596394, 574232625, 873007675, 850320469, 653230936, 806810397, 343584569, 699440777, 557451616, 347262914, 344190304, 855406003, 645858150, 998497020, 70393960, 345856057, 940461541, 796220258, 487855385, 931203294, 711052740, 37403071, 80138979, 953442162, 698373924, 352429001, 469241154, 732635200, 230938742, 565318629, 3679972, 736577560, 158697187, 319422163, 427609936, 806544426, 416667007, 321555293, 288649873, 126104168, 933504539, 347085769, 659963641, 454375883, 488729633, 343665644, 339080736, 404806714, 971895097, 226188650, 672720513, 623711531, 919929639, 642725943, 491039542, 636961374, 56855559, 712299151, 265838945, 465373642, 146876610, 983506474, 859550378, 78211889, 191744604, 528390169, 411279151, 278112159, 352103482, 706265683, 55896226, 923969372, 216619715, 845719000, 773008449, 72020114, 343452421, 892372093, 888161596, 152350064, 191009326, 244130672, 198268676, 281310905, 323542954, 193817470, 22400121, 885152115, 309589263, 58682192, 732375774, 752528746, 326733411, 444449654, 608571449, 500185557, 166781141, 848753268, 388834487, 849608491, 726017960, 539432509, 868282899, 628120503, 125433796, 527373070, 99288257, 81999086, 84795307, 829033267, 684276103, 938868435, 424647101, 808140992, 225381156, 355299695, 208704216, 159261112, 581424602, 405189588, 348305342, 418946270, 952066790, 697338285, 352488833, 344532725, 337868199, 897258614, 352566591, 989633364, 139018679, 918000197, 348248076, 523823064, 307989169, 19265768, 28115445, 546348902, 205601852, 131470497, 743951971, 760064271, 504588919, 30648794, 213053418, 410889131, 776862154, 370066955, 307109002, 451636480, 948982059, 834394861, 963425498, 158844759, 525412245, 952774668, 54804711, 571829219, 722535638, 417301354, 941991514, 26205051, 61388039, 544254026, 462438464, 315965470, 166243688, 120094893, 589523775, 218036765, 634433539, 687413199, 279941262, 699188172, 494205934, 229592999, 886639712, 96577961, 870024558, 85256017, 808193182, 669571737, 886256555, 396645958, 915210481, 786721631, 880336275, 448067988, 48248149, 293293823, 615858635, 852057264, 796599392, 311155216, 584659029, 364419407, 991088902, 17664315, 519533755, 818186796, 875768365, 946340376, 737205390, 883455824, 155320163, 488296191, 51633363, 652208993, 51466141, 527667206, 58530884, 669140364, 656869318, 408655252, 485840124, 254570215, 88537697, 87318531, 471351734, 24188761, 739346760, 946630926, 292724713, 254103096, 612809836, 96680610, 307003899, 116566247, 61706729, 833086196, 441357514, 950874776, 495784712, 622525880, 229244195, 465243535, 64363735, 766618776, 456726902, 795686178, 827512441, 579848016, 67897218, 321732263, 112766009, 825592865, 508096728, 289884615, 238328479, 102182432, 211350645, 715323272, 275344687, 654186745, 263139406, 949199317, 616948393, 198757765, 973172997, 795402086, 993336054, 139018669, 594986356, 523489140, 637451858, 872483455, 757374889, 892502725, 738368686, 36768814, 907644547, 718985279, 414935137, 846551312, 847966146, 392912469, 485449111, 693116068, 209517691, 76278361, 728248185, 706539860, 962080262, 960658318, 805513088, 962266643, 419639959, 179968518, 752474159, 167875359, 858054718, 313170509, 840421043, 782196266, 670469479, 594858499, 224652248, 972005530, 100731359, 55453011, 342589568, 391013695, 800714699, 578499847, 114896505, 160286650, 752084926, 711011985, 93165626, 841700917, 239727225, 804041268, 365988491, 145869965, 558033604, 413564401, 183277132, 515950984, 750134135, 759297896, 495237429, 334726561, 445004592, 82936854, 722011149, 901559038, 355481809, 132277929, 811618758, 999898644, 17103993, 436038364, 82907271, 137386145, 406600288, 634018375, 419595509, 191978795, 347470204, 722589854, 736781379, 13434260, 746895171, 376933141, 458995674, 514557072, 596943260, 386980281, 338692439, 988003319, 319550044, 129255987, 933870920, 105588893, 625549649, 959356132, 27273779, 802490993, 4692897, 188943049, 385069188, 976822688, 522386221, 690295221, 403623623, 108719527, 855612612, 443701986, 646915803, 649318540, 953532757, 132022241, 194143108, 755072790, 351171314, 741804067, 757931370, 219645223, 358038962, 37549893, 415372539, 101608703, 583052706, 733382009, 799185253, 299273170, 654772682, 50640681, 476163751, 864265593, 47942661, 376154840, 854673861, 129354507, 552056560, 702536270, 963940306, 138857958, 955739317, 396101385, 746039678, 380503187, 511839791, 237093318, 854257910, 215596428, 941365387, 41081184, 394740005, 364151278, 466318159, 242047723, 259442694, 116731631, 294739187, 945030769, 232136203, 529568238, 207627916, 858693843, 664840223, 825567605, 865176858, 198981677, 235815318, 362187715, 44498219, 360452527, 151838470, 581734016, 260561023, 157410652, 499596845, 148744719, 309771926, 650838533, 27342326, 950377651, 449285852, 330199453, 755303857, 702102498, 409315885, 738023525, 558993544, 863206248, 523305718, 915555024, 666646613, 231312505, 102723992, 784383809, 870180807, 592577344, 26941216, 99283639, 319366716, 529855386, 857981722, 606162974, 445062688, 197722979, 680382236, 156338906, 411982164, 673580159, 840822292, 136222633, 195685053, 357174364, 239687356, 790399180, 680019776, 66573425, 526069421, 40704575, 115322733, 534466535, 545882156, 973182377, 593351054, 612835464, 168308973, 363178758, 989318718, 692142224, 26158011, 37930403, 216786423, 379100108, 518866430, 635234117, 688779470, 671264374, 249107709, 569447564, 176928123, 640333564, 521740707, 851556857, 667535966, 954268607, 489670611, 489172091, 781118750, 523136649, 453354008, 310106678, 625256141, 491547580, 374552319, 99770376, 891016140, 611419378, 105941560, 836852052, 899177736, 201036849, 904042070, 812413680, 193741933, 342371961, 75057053, 475183255, 877434298, 647245144, 828005379, 754851065, 145541535, 268616448, 242731102, 171096912, 184984276, 857196540, 685876040, 479026753, 668646497, 701594712, 623871315, 602137172, 958542630, 62128210, 247420543, 949071723, 650401983, 207477719, 330741036, 654739769, 323503237, 657309466, 419866702, 93824938, 44130737, 235134422, 693442025, 571422571, 545017854, 903982948, 671040344, 587886701, 500544164, 429149480, 848916848, 396497294, 477805773, 249412474, 425923188, 522260758, 928123037, 36551338, 520886997, 284258245, 574337435, 329580070, 954952165, 699574969, 107430435, 94480091, 37396683, 990122724, 894317586, 256007281, 77167797, 605605440, 265039657, 151863816, 294748397, 222717290, 18577840, 166049791, 239903625, 349743865, 448309677, 481586332, 672725153, 866012459, 294865060, 762909174, 699907090, 636342563, 990470298, 48422477, 749713716, 857997131, 392065538, 6403079, 378301042, 659430452, 192314756, 464352462, 39431274, 63625227, 631440436, 623715321, 374088591, 274322641, 420333785, 153505084, 820345901, 719462880, 850404728, 402450394, 514165144, 670130547, 209774160, 101215273, 996236131, 269218744, 265553829, 424812966, 820629038, 638004001, 692395156, 782856708, 824346497, 96652014, 770026610, 466180464, 74741968, 225220816, 889701605, 745811549, 308231276, 870648965, 783363059, 532299911, 823416702, 837586287, 796851868, 415640207, 571275738, 261273964, 371513970, 25449252, 275926258, 543870230, 473570710, 795017509, 309998764, 741083605, 582203496, 801570730, 208445567, 856213769, 554536396, 268392296, 482373448, 161611289, 595595760, 905203053, 946168430, 863021237, 68482262, 782411333, 286380145, 944478889, 796571628, 526725209, 495886535, 672746134, 881888691, 488006031, 442303627, 277859045, 490987211, 108822841, 135269700, 296171446, 293443169, 309076561, 945603270, 622278907, 847689313, 219041822, 103039336, 594556289, 77007245, 595309094, 103358977, 470753939, 369041575, 305868364, 514170852, 285646279, 202378672, 173309617, 504873868, 467554317, 781943126, 5881471, 533457565, 715092740, 328078539, 376630978, 777512330, 599676293, 576282906, 68818027, 340436400, 304639981, 701524270, 611627285, 847854002, 755484265, 153893751, 871477433, 748174760, 925798880, 954764682, 828321038, 854574599, 225344521, 403961395, 849153494, 662459742, 526129071, 420161326, 311367559, 324274813, 866713612, 823123217, 8123625, 323778746, 638041324, 624262762, 118846555, 919765551, 757931285, 301695224, 534873143, 175407206, 432365335, 256356256, 268181054, 977457931, 204981598, 951912340, 319600807, 370786960, 561603188, 731497068, 165959075, 814855591, 824175528, 721923471, 937652865, 990742674, 33204834, 680883027, 310959713, 584889853, 987572311, 558707837, 111781593, 608597075, 713116627, 44134059, 995003946, 159643980, 578558384, 160495551, 230608433, 250375254, 723798418, 442760793, 483620270, 291826209, 114067673, 699261704, 122430316, 488601918, 727095015, 364008078, 942412072, 998504081, 251215128, 14759237, 453010732, 420406642, 844370371, 62103623, 300679598, 761061957, 189678229, 435265157, 712912374, 687412453, 208258188, 427582061, 235447655, 513784961, 923862543, 470281236, 826775686, 722981210, 305817249, 655382107, 864503997, 755829015, 424463153, 882619882, 897481908, 770567976, 101864891, 178637667, 77450368, 498315525, 389339026, 513697848, 505821866, 928591212, 150981850, 863369146, 410479373, 993034671, 386497683, 7370332, 340336071, 568030258, 377733044, 965491060, 210914206, 862878426, 416164246, 769496925, 730539965, 759987218, 438942609, 9037457, 428136472, 118590949, 956425992, 38285370, 332338674, 297905295, 153213802, 325641190, 806422046, 662328405, 477272694, 799469922, 605010272, 759911171, 979869767, 848721034, 526962808, 57465923, 53542014, 107741530, 792799393, 841710, 796394734, 209798566, 298211787, 123319445, 541664716, 751333378, 551030789, 963729785, 589841038, 144867554, 202473936, 939769727, 559720595, 675209824, 333193927, 552854278, 235365727, 297666146, 667766310, 551420618, 107002878, 271801876, 3908461, 385724866, 335886756, 651100735, 875550108, 668997635, 315701228, 293943137, 367011763, 686072776, 309472187, 578276843, 663133020, 820734653, 102894679, 624565306, 899665876, 91022266, 882123688, 677752070, 355315254, 691548534, 369766993, 95674694, 522046551, 200296086, 252675550, 255644618, 40753517, 81640776, 834975944, 769373532, 526133437, 292881401, 939467917, 567648856, 292431825, 267346998, 427890185, 961297722, 138568069, 24979642, 770064173, 175559410, 871953715, 100863394, 366687088, 753021525, 859633312, 423891558, 524439530, 565443784, 891484423, 992753488, 843061250, 384260228, 621569621, 988956495, 606506324, 648771022, 830254379, 188663407, 43428331, 507799839, 981162121, 964966168, 451295298, 309843186, 554741823, 301733130, 47452302, 429889442, 228270156, 251992130, 934961140, 270338725, 941778312, 480287374, 195334239, 644705841, 849947748, 710944316, 542236820, 682295538, 871669189, 575812371, 167601196, 805599394, 820600013, 716569756, 883325680, 15144899, 702125163, 465354882, 726924394, 419893692, 582770027, 221843493, 691072031, 665374472, 161659296, 858105312, 492088009, 82517854, 822355990, 576440798, 824037241, 773968725, 882307988, 354092399, 387482772, 23417004, 236631993, 941815773, 351801418, 803862481, 536938305, 956518074, 338028413, 700669941, 598588033, 170170878, 93101897, 191474775, 650092320, 891116417, 936219242, 302799593, 921902203, 207849407, 925767039, 552966552, 128354274, 176964572, 895013050, 848848811, 923385321, 965849674, 574898248, 733084334, 39568389, 836354816, 103728208, 8777332, 43625857, 632389472, 862740020, 669677481, 987526230, 859108471, 819805772, 759599347, 943094834, 656559212, 945486697, 900866019, 454696411, 305656422, 444884544, 774350932, 718156335, 768068095, 510398391, 921155134, 173025774, 87363377, 463824238, 880942403, 421067684, 882932739, 608569773, 697627502, 11475703, 488541260, 632619786, 649701214, 636827146, 395280675, 500444573, 223778371, 625408861, 502691676, 498275675, 170522955, 509437996, 626627704, 914943351, 322197590, 931081039, 488170067, 462279995, 975017322, 711548589, 972489581, 372143849, 374174400, 963462358, 652714690, 539874581, 900428163, 379737010, 164942226, 280542447, 745626033, 189672244, 838922079, 949535251, 901185941, 979453525, 385368004, 936441502, 566136801, 506570912, 923301741, 626595351, 137092804, 273548556, 539474235, 528667215, 673713500, 523917394, 996094962, 321580186, 813601366, 710448755, 472062910, 496965780, 925841356, 668455789, 538611067, 880468411, 48535077, 851276193, 752199289, 596422237, 875164080, 752071922, 823981324, 294420088, 433525857, 839004586, 999784764, 110694686, 308437135, 226256410, 826396101, 388435270, 649146620, 3811072, 688874359, 233759384, 449582915, 534259863, 765961208, 283673746, 520062517, 830997441, 824197126, 447091583, 674535957, 979500606, 795424478, 628872496, 15917434, 126807517, 686118405, 552434293, 867842964, 959610799, 850888141, 802210517, 476572034, 358153179, 414021371, 578507411, 345938540, 824377581, 977306944, 338912091, 499750676, 318173352, 853747961, 739400547, 121796227, 602361110, 181997404, 40736322, 340402547, 939120315, 330865771, 6231157, 243295867, 562981071, 544011412, 128692606, 681512738, 717931343, 143799117, 762121739, 14286348, 473574424, 416229199, 709756809, 404229402, 662126944, 204042938, 843369383, 91098504, 886096385, 431821135, 515008143, 88118203, 891019948, 759736008, 289287066, 93482894, 688143114, 731939273, 198468991, 774231289, 810498271, 370529664, 939096983, 165769679, 393173736, 262513454, 211420449, 174653461, 586471434, 973464807, 475677110, 344994331, 312570358, 239701058, 427673036, 523948822, 557242590, 515357458, 331932316, 513414916, 161961629, 820423772, 528799114, 5377903, 261412035, 74854121, 256992327, 456508919, 766746432, 363347495, 884398293, 578413899, 416973929, 361647275, 626376611, 586162088, 64346876, 947852695, 703302308, 834206614, 693492580, 673184467, 256470327, 231756861, 190317459, 35637089, 428504455, 464391108, 821866001, 248327462, 332612003, 709209459, 830300521, 931478928, 2263362, 150005264, 302067623, 602570511, 70578878, 431896179, 543647934, 134504115, 749697310, 515710948, 354284599, 1931323, 483517386, 10460734, 675225238, 104014437, 531347060, 788049625, 78878347, 361069502, 661242625, 840082613, 368627299, 694545342, 557600539, 71164307, 524169040, 886885078, 435214834, 430954914, 874290492, 456542203, 14975533, 87794465, 769740673, 613875245, 429207757, 754030801, 393972172, 54233949, 387910902, 492339002, 320233681, 834804554, 174801643, 797037004, 472641662, 529565779, 855195338, 443244900, 742514711, 873159097, 249723530, 951631600, 690299676, 346152221, 428815551, 403578232, 921444859, 651333735, 449984413, 209693021, 179851777, 504783934, 957735954, 543220354, 446623093, 664042212, 591135816, 442899407, 220995495, 646647161, 176242800, 119762178, 430787231, 257776834, 791829700, 357837926, 319797441, 282157659, 31928713, 223082505, 623315295, 498787279, 997185581, 776387343, 715600993, 58564946, 205013782, 208182188, 442259692, 383433583, 206960425, 779792135, 785640987, 933412121, 684349842, 456832660, 645830591, 186488963, 648256046, 699985952, 855973187, 585043388, 660667840, 659340248, 83149654, 713460620, 98933794, 548630178, 498255063, 51981994, 809779099, 543268294, 485323592, 521352044, 467392840, 7465506, 130269600, 325709831, 94183989, 940149338, 421692164, 501928550, 270695516, 570255267, 216368545, 356278699, 274598219, 778442306, 959031297, 493889970, 651241324, 224013655, 679867399, 212891458, 261779640, 455215449, 275023240, 240217757, 866612044, 766068383, 730829678, 99892489, 140105529, 329432481, 545090718, 560690031, 603030837, 107330241, 362294203, 101662019, 259788622, 252699350, 73318833, 858533991, 778120970, 536239009, 91223073, 431076085, 190121658, 899210745, 799792701, 895018913, 131628423, 832834571, 290770248, 379042023, 828201826, 231727992, 639151314, 337511011, 536812173, 77099816, 96365228, 885564923, 252505948, 220213418, 891185636, 43972643, 223494654, 341507188, 383571857, 909347538, 783054861, 236566325, 90770266, 837270464, 534088699, 406703909, 292039967, 855709538, 527993355, 500890699, 132595619, 588712511, 237841287, 317405990, 357084601, 214145334, 957607403, 615587784, 636759849, 604380471, 808285239, 212089294, 446254600, 533617347, 183187074, 289250335, 227111367, 254630257, 505388070, 134177319, 234591814, 806453177, 968044939, 8364889, 897629663, 846110986, 740650791, 575958587, 71730656, 424012164, 516343857, 411777991, 534934698, 765223280, 527405997, 259133103, 923667748, 629181425, 841831383, 743959373, 642030419, 4916235, 386265821, 1182237, 28393389, 138133924, 564255288, 456978464, 867530161, 505403946, 156259279, 554144780, 663317728, 495223770, 942786135, 189526691, 198772750, 634324748, 897351674, 806485195, 612647725, 616272407, 414494414, 695361632, 105070053, 84846413, 844073398, 641898331, 43113792, 514040707, 334379123, 610685009, 835270057, 798058857, 277813659, 360710280, 76130623, 700414716, 46378438, 400810410, 284160807, 451907301, 184212942, 7190422, 807187951, 958524121, 667065992, 999939825, 615018519, 916873415, 917477873, 20103749, 370917692, 979135196, 664881151, 536021647, 703848614, 935220720, 48909794, 396116655, 923446001, 502323898, 958344675, 607540921, 41835164, 161091260, 265089221, 41098994, 999764167, 846510658, 160913136, 283852372, 413210258, 40099731, 255718593, 696136104, 173019175, 303329281, 679588155, 162268705, 216328431, 93799790, 786438377, 569549463, 366031823, 159868826, 4920083, 871868360, 687642785, 178464096, 9827097, 832010520, 376885788, 35355497, 184220881, 391136577, 917755111, 112782282, 852999779, 95641177, 198506623, 876630932, 250927127, 155762709, 166992956, 886203151, 815251831, 533756551, 364573731, 156652349, 374912392, 234629450, 769709417, 106445852, 638420532, 726327916, 113917309, 980427242, 953414182, 286871319, 604198529, 431893250, 258232373, 330812775, 839637605, 248672153, 351703149, 59166656, 622639168, 934414588, 788713999, 232521845, 628312339, 978064865, 857575177, 543412025, 299857514, 856956076, 255119451, 559339306, 649842844, 544220623, 864188268, 156192037, 367694189, 107035076, 856303924, 542216879, 162600181, 753784287, 99836788, 578484539, 470832506, 396936293, 745135177, 583741141, 240348851, 842516227, 975387862, 812012036, 291254503, 915147922, 426035897, 901655110, 28960219, 149613894, 166743417, 498323252, 884544290, 99406238, 512561088, 597325408, 870098046, 448482005, 30209127, 907780250, 627072177, 112775355, 862777125, 114300097, 680644936, 747049826, 453741277, 390315853, 889949681, 805284923, 555994693, 153834112, 893753564, 333871504, 821981015, 4369930, 830118259, 763476394, 39931221, 863948795, 979582558, 97250582, 989435752, 679933004, 544298664, 421403171, 385304260, 358351084, 797968478, 672690463, 35247906, 828385553, 955232519, 185600889, 57870900, 446735145, 919568978, 599180232, 103844761, 717751626, 551597618, 410033770, 866189488, 640897309, 393927850, 42909733, 39864737, 273327327, 709787785, 247348298, 956276453, 309451927, 412172697, 754106559, 257145915, 260569813, 267655876, 693608380, 69686111, 599024884, 175059265, 785121658, 412625657, 797991140, 357291311, 940931919, 112977253, 697063760, 634549816, 449273627, 787818218, 31636387, 902913740, 757510474, 154842704, 344559051, 676909726, 727144675, 537304560, 480028197, 116895024, 628560986, 356237799, 102155273, 863537160, 145351565, 753292708, 54691355, 768039463, 191304478, 453966067, 665517637, 402573891, 988189877, 414314744, 670935177, 306076687, 570104271, 769397570, 93878902, 188790333, 963044617, 81586365, 153874938, 160340052, 170921122, 313532171, 580386492, 701879423, 793707761, 508545278, 580796451, 905758981, 231542096, 630487723, 953260814, 795084491, 741293391, 486351114, 434406779, 440693116, 406545516, 627442397, 10221200, 196388327, 91408511, 159001299, 379076170, 846462085, 718302894, 252726052, 989770586, 396265721, 635364591, 579689716, 977573641, 884265036, 146393813, 634956042, 497676721, 456180303, 569809319, 239462242, 575214543, 279376542, 838750322, 76242497, 462784092, 258033610, 209350601, 777976596, 640281973, 320060563, 981084842, 448098721, 828431900, 531100990, 205014301, 827986844, 608241486, 643512828, 458506869, 375033508, 359149114, 58942307, 899466401, 963168616, 227741880, 640619391, 498787773, 277946334, 334114090, 622034727, 604049720, 698471264, 725175888, 723225601, 48507635, 726562654, 573258253, 533908703, 615130075, 63555120, 474189923, 954731021, 269960210, 49714668, 844440698, 713172505, 822597718, 728070354, 475448318, 487336030, 980690129, 189610759, 873982978, 654236733, 736822636, 376137182, 691709428, 389842796, 366230346, 426668386, 597843914, 704290367, 470928389, 163765319, 721484655, 837688040, 260340879, 500635330, 835726440, 165955961, 584673650, 753654707, 577660881, 656198577, 291263473, 699560476, 202453664, 562452471, 579904277, 502541308, 769536657, 872482975, 976851126, 309974893, 987198132, 785383237, 641586394, 865110402, 16408611, 855707506, 495806106, 909127156, 597368020, 395085007, 371981801, 991451026, 57034370, 781221065, 66948244, 600346111, 798744021, 699827365, 725148710, 629973676, 271884613, 194632810, 198340141, 788031731, 217361027, 166694200, 36817281, 970468503, 688337244, 407339907, 692217310, 814793398, 333806473, 569275090, 384165231, 944097613, 900538421, 314075643, 939529697, 464270495, 506917932, 729420379, 415373425, 854866657, 968343258, 884981369, 617899418, 225731757, 710495865, 733811699, 84483762, 260896989, 821777446, 149268670, 932359084, 968456365, 813826918, 639940560, 723230392, 492465978, 454478069, 908519366, 597847519, 870929113, 676454642, 716052122, 704548798, 687867742, 787322493, 779275810, 286525829, 212593230, 225989593, 252700597, 159041053, 654550821, 819716559, 273226506, 261280497, 526513043, 274026068, 610473214, 940292484, 370892092, 578050466, 412716099, 437379318, 187181158, 158145814, 150917307, 926528407, 140069761, 346813085, 314087022, 261727764, 23876482, 949996815, 431317732, 43414437, 291122323, 509478579, 64673333, 469723606, 700803519, 618113628, 187006380, 841232106, 713795399, 527770577, 559589126, 737392344, 545551594, 975473832, 884726258, 539278561, 415016853, 649616018, 694755103, 888998950, 671128705, 577204223, 933797816, 94270777, 116110724, 592648897, 234547852, 349693058, 739247599, 941581865, 709369677, 278861846, 563399872, 729807554, 993859651, 247193122, 286004509, 523298592, 226227190, 550626033, 31757392, 902084678, 474882397, 294315983, 785459280, 94254904, 446792647, 340516323, 263710723, 68966576, 684417400, 699974420, 681558276, 407688196, 912924146, 233755377, 846119761, 533357245, 245590348, 690879663, 844334223, 699674773, 801930545, 438231653, 307040749, 55814209, 720849253, 299512224, 99614243, 827653529, 357647925, 244761219, 220673475, 461804246, 292790060, 234521721, 252530355, 101005523, 924536532, 915771054, 405053630, 594717366, 885142911, 407788945, 491442072, 332972954, 894043294, 255029077, 800682002, 887722907, 93250857, 83991044, 701836244, 600406261, 248767085, 652167411, 711151540, 159086017, 730126677, 782955330, 818085774, 812137442, 982746150, 982427194, 638159679, 117001665, 227053230, 259816729, 599032825, 959935578, 544062700, 100952771, 96568870, 408676532, 280189694, 386966121, 14113992, 948815935, 940161071, 34829292, 825532527, 253187701, 706390293, 139063545, 573266673, 193645024, 991182013, 196873437, 985420451, 900723439, 371329424, 892342034, 473462153, 189195987, 873318341, 414461621, 422958796, 400457047, 577794189, 768895185, 20596293, 141495547, 278427289, 153694587, 586446199, 729460618, 996515887, 205204929, 273292089, 569572611, 249470463, 43052271, 104614221, 46258139, 781384892, 345805627, 945695451, 371606064, 270625085, 562056660, 464871386, 47777158, 299314231, 316444424, 490594352, 524479817, 306721615, 453332066, 908902272, 21058549, 400881111, 282540810, 733256737, 338711496, 60014355, 741552531, 705817797, 563120335, 535440955, 612092594, 398871667, 690631467, 837221453, 459428643, 919210873, 950258415, 494194380, 450967894, 246250482, 188643556, 693850373, 634923558, 668403861, 483005146, 286619712, 63153333, 882526274, 356185586, 150519809, 886973507, 822860650, 79804727, 787747315, 648081796, 178093503, 516248360, 459613274, 859861091, 469434483, 808831540, 151669300, 648174761, 530032266, 643982373, 861345898, 768299723, 483970763, 934868085, 826630478, 783458054, 188457185, 989402824, 503949594, 946389920, 609686296, 455755725, 813687262, 49379769, 727112383, 399543588, 617862973, 494656334, 906126935, 541007257, 572304365, 763558517, 90153446, 876943378, 218439085, 635011912, 355769731, 536549755, 560551518, 334113944, 875879999, 155864052, 783368583, 382090958, 533953951, 330554332, 424460244, 841660314, 944285842, 610146561, 611369541, 938749917, 530233920, 614559661, 576127376, 898699766, 848296885, 616068594, 579664928, 18372419, 620370434, 140525614, 834869683, 690538244, 31453294, 383287134, 421184773, 593996649, 657075606, 789701756, 943412762, 394718953, 950145883, 564458659, 102278367, 885550660, 447783162, 737190647, 850761064, 879841768, 691680965, 980183402, 666710041, 99528691, 319851539, 502729389, 529069900, 298542030, 733853418, 715194952, 716182655, 769747586, 245530187, 751059238, 429503208, 390545891, 672955786, 565372244, 318723483, 97009509, 105972664, 13710113, 554262738, 932329064, 126706756, 625157597, 200364530, 888585509, 21886408, 546863925, 402434768, 604113152, 343346003, 735672924, 853073163, 109110467, 702082477, 239162593, 166307739, 97893747, 797216670, 669669252, 110022779, 163791251, 248202725, 513725166, 455199422, 809487769, 988876946, 832776542, 314803147, 971530487, 570401022, 771756333, 543723081, 219233567, 91704329, 494287603, 272916621, 42305907, 420538827, 79936449, 559490958, 506071491, 114235310, 711948210, 114580237, 926786862, 551749218, 134764505, 586256253, 417319283, 386433030, 877786990, 347434400, 180008501, 140304293, 473958887, 965464378, 413943060, 850427132, 739741525, 150448083, 229104271, 168590187, 316105894, 582974526, 742433343, 182540592, 862279947, 521834954, 336748523, 337940151, 89504672, 731165639, 484733899, 380991609, 947179528, 960001003, 149347620, 664868812, 915188254, 720707664, 734547519, 547966286, 177164512, 978822403, 225572028, 872871499, 916969806, 178223487, 899445521, 745354801, 228590618, 825215546, 582514703, 852221202, 396042667, 553515876, 869630242, 130607772, 670647878, 475702298, 112991981, 753517085, 527567775, 956624604, 455373201, 446102147, 742578273, 765134126, 214126508, 565859966, 455902835, 512033782, 241808488, 836742676, 908533652, 201029179, 892531807, 657414724, 549620735, 127916214, 158860916, 270271435, 488783364, 632108492, 739000162, 697780915, 889173787, 751734899, 718143365, 407210782, 251138986, 113824476, 820255127, 356438891, 817369873, 445206225, 506344595, 549073849, 44528180, 853583379, 181779930, 931157187, 853430426, 6687315, 144401715, 447570865, 251876616, 354332349, 115317254, 835794831, 255332488, 761074127, 948781907, 319656251, 650673980, 457777584, 345903778, 577434011, 479757223, 471147577, 288553478, 930264526, 120766090, 759735723, 581748914, 635187756, 169205856, 816127143, 42099850, 827568154, 418276799, 551545842, 403205596, 690426657, 663623663, 945420203, 301475633, 451950722, 583653923, 507960098, 795831908, 832998073, 183903460, 300667915, 384985737, 963124285, 83343486, 580773487, 315948157, 123126273, 925309036, 188561970, 88872252, 753165386, 242064615, 219982935, 653844880, 867670210, 812496640, 116029932, 72335508, 379249975, 39561283, 420594812, 637494837, 573007339, 456995093, 667208335, 414015607, 50599492, 267802827, 223886184, 557794930, 24772349, 308227706, 746927332, 720087986, 564222085, 485995608, 779172711, 268763997, 174283702, 246675929, 853768412, 173590861, 693241809, 313254057, 989499523, 17377670, 881311161, 783433113, 439442106, 854906332, 565174807, 839495579, 402268307, 784017619, 489619602, 98984236, 602048702, 735622279, 32136763, 437122713, 100854593, 876540522, 491430923, 574787960, 410448975, 721637795, 674960384, 672602594, 67279181, 947181183, 426952075, 710736246, 462903900, 451521013, 42767304, 343118765, 183501254, 763642473, 237667986, 521190583, 546707457, 774601199, 196553806, 549854591, 456695901, 506915172, 376788013, 254427, 771337332, 289385936, 376775367, 789181456, 76711696, 527216121, 216678119, 484533131, 605909224, 483596971, 322479129, 96843513, 270903172, 387893469, 269430874, 363095377, 23317770, 658684610, 768651224, 726837862, 617749928, 917044949, 731211855, 806395120, 446404940, 507449797, 121418191, 999735111, 504775422, 882008386, 105744680, 687137004, 107679921, 798629518, 457745349, 328360604, 471871539, 46245097, 611768327, 623396098, 510069683, 153391699, 87987550, 944193016, 710696616, 336899875, 697657045, 638756716, 972210912, 906638765, 341155153, 7233795, 988514903, 495494024, 423050300, 161969240, 797076891, 303455882, 706690619, 30322434, 190355255, 986474214, 672469036, 769210173, 77636131, 741268226, 211870574, 881415250, 444700936, 149975557, 902978842, 504556769, 473735187, 871513159, 572261013, 624858639, 878332497, 617612176, 395870551, 934013539, 760388790, 546601555, 28465802, 81697431, 697476259, 241746233, 984018966, 54283723, 258688506, 947595008, 815835349, 476739866, 608503786, 836653724, 328905883, 359337238, 371656638, 772160121, 517340624, 696125481, 414620573, 105955670, 890421382, 296353460, 667636007, 241270097, 712179935, 825106199, 793675314, 153167152, 458101597, 807192322, 987431400, 856675930, 323686354, 185236059, 313352299, 363453968, 757776861, 927284749, 321332271, 742911876, 565727925, 872724608, 862242100, 463925644, 899675639, 229110333, 982887488, 824719211, 27485879, 487322539, 430851158, 946993551, 495513639, 34711916, 191829964, 764594266, 505717616, 432889213, 562990773, 506209767, 962997931, 451252762, 309042263, 481474075, 64266045, 412825347, 553935019, 748454855, 22075060, 596576812, 960894729, 254890721, 337525106, 353930960, 987133315, 57979631, 635421802, 575330606, 189676911, 721913557, 968787293, 797030531, 805516940, 456573140, 838441522, 890877341, 934912074, 125625418, 743688281, 201993562, 801913850, 382274791, 619366826, 26659563, 429694521, 607504814, 84906139, 537040861, 939037834, 545210324, 330259863, 962081559, 753542033, 241235780, 903267635, 851339787, 844866415, 142911149, 641939142, 769253829, 233538568, 613047922, 292277082, 94214753, 890894138, 688505132, 520191725, 316739090, 951435287, 209278605, 963802839, 569013837, 410871052, 762902999, 928563557, 719627743, 963183584, 23210867, 795399333, 434289344, 248480886, 230554598, 490427643, 84256267, 734971773, 132983253, 465306520, 598916906, 277621599, 173249957, 733091201, 359825956, 938959519, 725818281, 908507701, 393569923, 594712545, 199130100, 778494315, 206025593, 59659300, 673543802, 583267027, 196655425, 233156294, 102598744, 190115901, 11580447, 386224178, 160045851, 210272706, 864886274, 420482585, 419377329, 104752968, 42156510, 104814772, 60265062, 232334204, 758137191, 486535505, 502291421, 616169688, 833404797, 150867329, 704568562, 900302921, 899762963, 294519992, 929887214, 806365287, 891769447, 809720221, 201303687, 997854939, 455827435, 444834231, 376722969, 509648434, 795738695, 674176788, 432977664, 663225894, 643647176, 124434036, 269857856, 566551404, 828488207, 890084872, 289707188, 203167270, 695980470, 261339329, 995066270, 907222303, 143634813, 894802773, 122796690, 464005881, 884543445, 185484861, 746943101, 134128499, 551011875, 645964665, 757758461, 630322490, 540478229, 891065262, 435351361, 326460677, 683206026, 252763016, 462401492, 789369405, 219334370, 733502495, 652202588, 505499877, 304260962, 214950499, 860637954, 665538759, 980692911, 477774309, 463323100, 134989000, 625741435, 650787373, 692729201, 164212820, 1212944, 939273672, 855232449, 191355596, 18593517, 537305906, 511128788, 567510903, 52741132, 648126698, 37011370, 690026102, 849583273, 487747803, 62217845, 433097261, 375209705, 344509831, 371693833, 943110395, 290116039, 209758002, 56168111, 483841938, 789187370, 990225465, 43772030, 222218767, 702107422, 900101783, 951624047, 946177154, 906026476, 810347966, 631831630, 394346546, 420993269, 74412467, 633863311, 162041525, 670131135, 606724303, 642589146, 382078434, 33422759, 953210494, 397129054, 563325429, 110135375, 244414148, 619678970, 87679241, 126610127, 680112333, 646714739, 739302686, 620299787, 335432322, 946571494, 779875190, 464257546, 99359366, 372225979, 860049990, 440325758, 265766619, 384540277, 123174749, 497977502, 765405308, 473493849, 372647608, 689009297, 462401230, 697864175, 265719307, 73415986, 26024368, 211745118, 454621376, 201225426, 657945077, 750717048, 302304320, 615620792, 721422906, 661303041, 590839077, 136400721, 549561192, 261702042, 609361559, 929881225, 614951111, 49736433, 662918486, 100760150, 763750361, 647056922, 127907391, 64174595, 213507485, 645366695, 833662405, 521562955, 395574083, 379272315, 696297910, 363033992, 590043365, 718897644, 780043037, 981755891, 402328855, 245340525, 824354609, 279794643, 143384295, 636517127, 105333072, 587754437, 255492241, 933069684, 497009065, 251974135, 911934951, 419619189, 25834934, 964562262, 348656863, 798479253, 659763246, 319496696, 777116176, 515872833, 123521019, 434386303, 705901768, 640034019, 583590217, 709470131, 613970490, 131092840, 107224137, 30760600, 154722718, 128957775, 734666111, 354745977, 829624246, 986551524, 29422292, 211403935, 913487332, 937818896, 760765349, 763225394, 651648600, 559178597, 602356569, 290204325, 510578014, 558488693, 424748053, 369054475, 483722014, 715450505, 155268303, 585859363, 867746106, 516384887, 106157303, 812281867, 18219744, 671873821, 976493121, 832837666, 600007058, 197011929, 333336330, 918865262, 367947091, 657380867, 41798778, 305638369, 789778715, 766091180, 187289326, 312472265, 32213762, 815447943, 118798795, 24090217, 920220573, 983590575, 774349579, 418919061, 589804912, 94129847, 124610796, 653643661, 661119479, 538361784, 438424246, 242726398, 489266678, 301015570, 949496179, 885303417, 663101597, 587336347, 95908176, 754354794, 184324286, 799333166, 62249703, 887470877, 136983826, 712456719, 401223545, 919975037, 689334652, 986383678, 682729152, 11052967, 965657675, 366257258, 553680045, 381509241, 829444509, 918352361, 20294584, 84708278, 588131906, 33558896, 809398737, 22978482, 484721928, 911360228, 891891903, 733144229, 276798521, 392564164, 179005059, 377648475, 64116466, 36357013, 727720485, 877717775, 208137023, 32643473, 750955308, 432192744, 162243643, 738392805, 779033585, 618784988, 518642258, 505137328, 355209562, 605323967, 866804072, 10162190, 366804638, 652767141, 491758350, 713819503, 464584958, 806339353, 256435487, 195169968, 576633405, 369182669, 138883584, 338826979, 502580764, 104406869, 696301940, 299824852, 16578950, 357340328, 962686455, 825767270, 28154310, 889527861, 419390761, 182385742, 68119511, 951178178, 150454231, 507178373, 763500779, 30062467, 407432252, 459457771, 450178657, 378021565, 799450792, 386271699, 240021368, 622973358, 360224584, 227243842, 436129032, 502912154, 874172953, 988533807, 196032008, 303924587, 438211452, 666344740, 837704136, 749427149, 261532604, 571730397, 548305126, 105772831, 537593282, 242081139, 785675240, 683390857, 645452782, 546880829, 990901583, 232448203, 745375381, 209699746, 600831019, 883467121, 605925649, 58890296, 309415101, 525076308, 149233781, 652431202, 642902748, 313384853, 678535212, 533902942, 104387408, 571170677, 294817416, 381920308, 93735775, 801211671, 320425322, 968965176, 759619674, 165192267, 856758314, 177914887, 238825261, 119937606, 515305038, 656560468, 605395145, 319138098, 446814109, 837407418, 132124104, 726217393, 114261151, 323669141, 154431908, 762224958, 6197220, 454041306, 411139639, 157102062, 960327789, 803486557, 674134916, 940063499, 397822997, 94250089, 433967818, 580171216, 410325600, 145912840, 83120796, 216784244, 646001600, 301157194, 517337322, 317475265, 911681935, 50365982, 158080713, 201481837, 13744417, 291320795, 377920027, 485742521, 71279571, 212267967, 958785662, 953830554, 689743781, 490287637, 898377079, 64347012, 573461743, 94911338, 909946826, 658801495, 527539088, 951660045, 227597608, 942473503, 176543873, 89239099, 645290010, 446072917, 320334930, 386681524, 827658575, 966774978, 247293255, 299510148, 5349545, 103284470, 378082922, 660778681, 319807825, 432184125, 155373016, 725650439, 838856947, 280595769, 210245750, 773940602, 179753634, 541630236, 471080738, 925528597, 967379152, 748689779, 861097823, 703405602, 31263594, 733280188, 398950645, 780497107, 662212745, 296027375, 480241168, 792801146, 204400470, 510066365, 406467631, 989713586, 409251142, 779042685, 11601666, 880403912, 463258768, 960221215, 560125291, 745281398, 955999098, 494290083, 980145946, 755166342, 393599973, 79581752, 283905169, 864651078, 722039239, 773166186, 744603669, 68249917, 689518216, 26414906, 266190093, 75451017, 298328475, 583200608, 959138772, 343594575, 637843213, 376166102, 405810670, 392015003, 92172640, 899045566, 331906248, 49776227, 546137606, 967524129, 828951030, 143988366, 502858806, 583583319, 780565990, 974435190, 685581604, 442873013, 508333113, 509602886, 536409019, 352442052, 392496068, 452845460, 384136556, 654079624, 782216294, 526472504, 506667529, 421656762, 545207402, 411686181, 356850445, 613022870, 257525333, 455456229, 76162353, 662811953, 568471540, 323107665, 54018105, 104636787, 838423380, 343571956, 215538207, 335079184, 559286921, 498023610, 797747628, 241204905, 606706139, 70627856, 536699745, 502553301, 873017390, 63028952, 224864670, 726114901, 63373022, 721829863, 203222533, 747112756, 859181350, 967764339, 254820727, 872918306, 476993202, 365739963, 774755721, 504840827, 263676674, 314453346, 287987966, 415570674, 422744299, 483263307, 990120282, 952547590, 131679922, 315327626, 509569221, 844093902, 653291263, 897441729, 662909097, 914002889, 380037716, 164647109, 684792068, 934426240, 176007785, 206871077, 81947583, 923980147, 730732010, 495174116, 712150535, 234665658, 267160858, 277157605, 322618727, 756479524, 126758779, 440074666, 135257891, 477948642, 23854318, 26747678, 336592841, 822569571, 774439940, 740850541, 930027455, 344263261, 332794446, 782230897, 148153485, 36705772, 809394940, 558634639, 732456220, 537863719, 559948773, 169139715, 523405692, 397653051, 804322053, 573640262, 88493401, 100553834, 298331862, 388688480, 993960016, 807134846, 390333880, 711580476, 458640084, 795042052, 246412772, 508188779, 939751469, 105936570, 798736289, 304745599, 240453228, 556341989, 378482413, 8340371, 137454826, 923350527, 973417873, 30520474, 844467552, 414995380, 117637579, 963197069, 292086628, 690366219, 189568581, 722494615, 649029800, 252282830, 845671284, 743453392, 349095150, 357736562, 971841105, 909249728, 457757398, 185420450, 464116436, 442282774, 138518187, 634271954, 105825410, 234042788, 880117579, 5089785, 46572765, 412799188, 358741643, 229532740, 248425231, 300386428, 560950875, 841275643, 54544916, 307567094, 720926394, 437212127, 549050568, 77652180, 294755320, 620871794, 393858784, 835279334, 458441360, 246568006, 917944091, 846114638, 743443445, 539617477, 944404092, 970602029, 990135705, 154080273, 70140759, 514622573, 574267441, 90563018, 429338948, 572121977, 596824311, 444249817, 881742282, 366847561, 575579103, 671274286, 42278773, 208813785, 880320525, 12701983, 453445549, 626092161, 634747048, 126745619, 862023894, 949487270, 964536394, 334273464, 724535065, 799779530, 73707829, 15054143, 588030372, 47972005, 941770612, 698182349, 349235818, 893035767, 232545915, 533410053, 277183246, 924175478, 880306596, 950747663, 385231349, 876443727, 436785051, 14375572, 998082200, 563524356, 48617894, 908732767, 63133996, 897549459, 80754829, 785280864, 75663398, 303722845, 166385363, 100727115, 101464897, 521490095, 812879215, 535434275, 77776733, 6824088, 261328568, 108692483, 462829917, 325377197, 417163769, 736923353, 683589800, 119947455, 654307017, 488111694, 493891727, 821362987, 911662844, 295379849, 102298554, 70131804, 59686073, 32078554, 34053232, 79379196, 903433144, 44647178, 21307382, 941370686, 690334251, 68436284, 22036489, 819353158, 139968009, 812484175, 149615141, 908999210, 791533656, 205677382, 313941009, 536840839, 640464883, 839811443, 520470689, 724098377, 196388276, 107471670, 208829204, 568660991, 732368703, 985274771, 605402021, 199387520, 530912327, 374860418, 85064193, 747296797, 560220170, 576691872, 416461167, 792356387, 222724834, 279886591, 706828056, 282708568, 924613138, 257935102, 531287631, 329790613, 834009545, 379633041, 796652175, 535344387, 299043914, 500729997, 215283322, 895498085, 190900807, 60063262, 537312104, 560252451, 620327494, 32948409, 306110043, 948719165, 967501696, 991064736, 979987033, 536966414, 981058984, 608945755, 914408004, 939013355, 158735507, 583622022, 329203276, 197153178, 93975184, 489638608, 729935785, 231165676, 3168804, 283640314, 93747166, 700356867, 693625847, 205405001, 693837141, 169911002, 837734377, 525797480, 688217606, 636393411, 373220902, 735144432, 162258847, 103175567, 253387751, 551477232, 123056503, 517291122, 732394842, 390430487, 463638060, 560515348, 517234190, 978092886, 389592965, 205684291, 60566266, 692152774, 306867476, 282060699, 598367163, 394605508, 196880008, 69275484, 882771845, 185438448, 757828909, 288972798, 488182383, 260704919, 416807389, 429082164, 714609757, 748016284, 93529036, 574093273, 948338714, 753911531, 95180761, 909089631, 737272996, 693029103, 263202178, 507089747, 797609603, 775329320, 710265373, 349706402, 755718614, 295995591, 558141090, 790715567, 638162167, 828194840, 569833087, 348778049, 242604593, 29228048, 819339322, 376983174, 875930491, 806432361, 648570317, 233890858, 571807636, 691184604, 653126668, 895499515, 671392804, 158001455, 121420379, 759384148, 292631029, 65102502, 614419199, 854850075, 388920467, 452907818, 468638373, 307708884, 774176391, 527311315, 250366321, 631582172, 919555010, 801559525, 586365583, 603234467, 950610555, 537208058, 575919837, 760413952, 907721633, 751612175, 3328971, 513054565, 219913780, 49789054, 158339606, 6994861, 424931435, 433473536, 938112161, 191220304, 333176583, 171646413, 957648895, 868378313, 68161864, 517356070, 312271439, 476762128, 474011532, 46372651, 564145438, 117811726, 457762875, 532352217, 832068510, 561403379, 211050029, 224231387, 590063888, 127686756, 40022217, 616665610, 844201701, 714288911, 797717696, 707748549, 108239856, 139473435, 662114802, 184784814, 635534586, 227501896, 976767916, 183443074, 325342513, 541819388, 132939873, 454122776, 531317610, 13579540, 932737837, 299033244, 294605919, 419093656, 831028193, 42068373, 982799313, 650620788, 192205325, 123924252, 595181040, 591792798, 137408038, 94054858, 24822678, 454710665, 407424322, 394693338, 644503332, 742903169, 133910768, 180029639, 989975908, 198739239, 256454034, 893233580, 571182696, 948690404, 42075902, 200994199, 560244358, 494457112, 476116098, 328276990, 543054776, 683861786, 388927192, 426356650, 300838624, 241708024, 692701977, 715565850, 84639827, 366619377, 984294672, 474279794, 76562117, 571869795, 471405767, 467270164, 629424592, 413063134, 73404517, 70595989, 734344209, 316531770, 635677943, 320794212, 701890546, 511764371, 738711165, 604331653, 372426156, 285108378, 353097465, 69839760, 14197929, 960384616, 112894688, 538269017, 346777933, 640211134, 157058755, 244044818, 509835628, 283992935, 745848210, 994844691, 546615893, 358304859, 112411529, 464413272, 986319534, 113573545, 773618028, 107514879, 743923051, 787979837, 236967807, 129044732, 708776217, 906495600, 868965172, 479380642, 449255117, 342694496, 461835827, 877259367, 622599363, 771346653, 755239444, 600292243, 444021041, 735916163, 455446051, 718433698, 835255314, 579297479, 252948723, 428908903, 948367235, 112084414, 610969267, 906433160, 649233198, 993622156, 564564975, 760936712, 766675071, 630224457, 267271209, 633661446, 265855356, 473717626, 528806810, 559089531, 416366744, 105880721, 870397120, 166808763, 222543976, 92113194, 279546047, 750525537, 410904, 331369846, 882098525, 857702767, 341514119, 503197511, 985500692, 623877441, 598307650, 754251552, 344284721, 671721749, 118589471, 74058660, 343999645, 567101552, 695775288, 484659992, 843383979, 809388188, 428864439, 14683558, 935977992, 887369897, 346616460, 177200625, 634010950, 857540849, 9151935, 520957879, 425408838, 809042774, 396687629, 139434851, 755418991, 616451391, 381328771, 337551329, 426577448, 709381894, 244369358, 561811265, 80971685, 965190376, 40455523, 995008316, 138579867, 284632828, 337059797, 523499310, 507455013, 986438089, 307008377, 731925955, 405393121, 272688484, 334987508, 574175838, 747497821, 658212798, 16708711, 588232210, 348204459, 908753050, 487646105, 218272155, 968019734, 575660488, 964718799, 982195111, 614912591, 40217338, 760999571, 813648491, 694427887, 618746504, 889626679, 586103092, 939905362, 128669636, 763957858, 397351083, 928606918, 396868979, 521879743, 977580021, 273486787, 833936450, 804239332, 539718687, 714878471, 647329895, 338638003, 895333737, 171381310, 584323272, 429938959, 651657448, 493498841, 880463732, 283196145, 755403706, 420156719, 46534728, 161526233, 241256886, 536278697, 714055427, 410620008, 997279468, 494841600, 456148540, 679144108, 472568458, 709788816, 430275607, 865499935, 226718029, 948239655, 471268749, 420231357, 142866788, 577209171, 661832865, 352561373, 345528853, 270288604, 566696753, 785529236, 963896575, 318786103, 311779254, 496386519, 999989859, 453048008, 834312966, 245990274, 669018325, 725589070, 987592761, 918588092, 499158367, 383320300, 746235987, 156231073, 408335266, 268333063, 970772428, 641144549, 45712980, 142771890, 92510915, 454415232, 408635584, 29434966, 27366107, 677068690, 192601615, 201133908, 380779650, 452268269, 290937731, 614801690, 480515546, 410080793, 193289877, 116079036, 27507966, 224180621, 537902355, 288793925, 332208895, 34567110, 124529247, 873913265, 799672484, 46539068, 777129226, 126692631, 859757821, 773516760, 373380293, 864382886, 556292191, 614906249, 632721333, 690060344, 437435561, 72744380, 781671014, 485421998, 318564742, 414794758, 503832597, 488473309, 151807850, 305417910, 48839240, 54219992, 941153722, 855323422, 651689021, 407847032, 40248278, 175914609, 799976141, 619106221, 416212258, 706512677, 303300563, 899803214, 521606745, 289090488, 191023901, 902098487, 34688850, 569156580, 145668973, 344941224, 934668010, 638393500, 700396597, 618252607, 783411177, 565149389, 549329692, 743476635, 61248006, 313455447, 35225185, 80138795, 957647980, 119341537, 142531876, 626095366, 491130599, 51036641, 92424501, 732715633, 753882031, 132375409, 898130357, 272078879, 798816602, 838914928, 128956871, 54716154, 746794657, 952860706, 428527048, 303920886, 813916607, 241973846, 44185261, 56936727, 505797398, 936526283, 953055702, 594170477, 288859465, 9813528, 423031268, 528323364, 470721517, 371057824, 434410781, 376208292, 408123093, 509710910, 498915287, 648474107, 646420756, 435459281, 239570247, 745069712, 338639664, 334404881, 203409055, 976981381, 467216453, 218494036, 705264283, 887174041, 658737176, 7255966, 707415972, 377138573, 146962951, 43502199, 978419440, 719482362, 843075897, 582030792, 78673796, 428726585, 844489942, 256621058, 488824910, 843225726, 69918626, 214812903, 486768799, 207113429, 255833951, 1388851, 601170140, 83485439, 558225020, 958304069, 811748077, 520567813, 110630361, 573414694, 591197251, 71165965, 163778696, 831889138, 142304841, 708870135, 7798665, 888467322, 374291873, 884183874, 279254888, 96169424, 798951687, 749817033, 33209461, 791279617, 769301954, 518561928, 838630987, 795319538, 795284144, 436497018, 825744869, 699128068, 292486490, 185998834, 979717105, 990488423, 662161330, 747280188, 912795487, 424566970, 114947397, 476382592, 100137648, 809353140, 275576652, 523468707, 655182550, 727143303, 236409827, 565850486, 422717109, 73605070, 336667312, 204146641, 108068960, 143873989, 273847297, 218357401, 452847328, 330334264, 455497754, 486685225, 994759108, 699358554, 893771677, 83129869, 468577358, 756793935, 121465228, 778348040, 146569673, 450653058, 45864344, 127577816, 422410872, 669990437, 78944630, 212923629, 844407834, 275356858, 241285597, 895760922, 669264078, 568021595, 336199191, 45730611, 54462714, 625520337, 838896210, 45329440, 7856316, 28458047, 619081575, 919098728, 148970842, 926941229, 732667567, 658314841, 454274469, 50137840, 330142771, 50255517, 892682405, 370963868, 33951577, 787792858, 621604949, 968779848, 757280728, 241777929, 183658122, 197755025, 56225352, 817205605, 800262932, 336928249, 677949848, 169287943, 480140928, 199542539, 294860744, 243506291, 55500408, 631069993, 595388381, 951382463, 555525173, 23764706, 322720032, 25841650, 500149540, 32366794, 620267167, 288615381, 508898892, 454012425, 270552078, 272396174, 641312307, 826438819, 393932476, 584769545, 305848553, 604272512, 417080383, 219540525, 231640586, 381433710, 972551777, 861519407, 52651895, 920788573, 650781281, 645464950, 407606265, 320819105, 799891629, 620765074, 500904125, 107573305, 309102650, 191435789, 849206908, 59777870, 550367551, 214866118, 990366485, 9671137, 228440145, 292719583, 52570937, 829586725, 609314182, 29710350, 513793565, 865983296, 177358497, 741890879, 776839410, 932633672, 550624736, 754092589, 244941052, 585692177, 102709693, 740272831, 420804590, 583792132, 991813654, 908535778, 786034484, 369037267, 592038314, 749120717, 429623051, 716237303, 213694377, 233279163, 638747305, 916145763, 145664962, 964894140, 857993997, 653356842, 468152650, 356357584, 931845525, 522824818, 482721352, 601301617, 891497100, 13198821, 958644852, 661599345, 118722282, 84821546, 279771115, 999653629, 354260188, 118563850, 770595937, 810401836, 423010364, 357971689, 379754658, 632009740, 63418984, 599742936, 627456369, 954055997, 800932814, 355933199, 232120696, 381457522, 871311621, 811939426, 106492828, 362899445, 182223598, 423742728, 407273027, 728404768, 75873123, 996571414, 640211875, 773081744, 359252635, 159382157, 3687325, 589039077, 126611047, 183412657, 237529434, 945549778, 371099183, 680812319, 463743565, 223660039, 773481044, 79507372, 375371747, 199182163, 535747497, 982791297, 167330453, 178857109, 284589676, 137804402, 322911192, 633485595, 851906180, 507832659, 520719279, 267615971, 943181503, 956415466, 741677440, 589985757, 827135392, 624579237, 437658199, 700049216, 253405417, 80584766, 253556274, 269363495, 55107094, 774211520, 397907245, 878718541, 461601126, 787556808, 14806699, 807524245, 95939217, 82514374, 26077804, 136291200, 251602424, 958665867, 10605997, 332371464, 827080430, 68626133, 259786691, 431800005, 307578812, 205347281, 145538966, 563244128, 510666049, 838491630, 549353608, 812322847, 669603525, 803052775, 773777061, 478328156, 112346227, 529836634, 226951424, 633189210, 894723884, 172959217, 836492235, 947627568, 38804640, 215377012, 699290449, 758748885, 856581737, 576440887, 852828693, 902014570, 93570207, 202488049, 901380603, 971026432, 641250301, 535993116, 343538407, 172981247, 884540344, 831281918, 615363225, 123000792, 246733749, 388908119, 835493172, 398418390, 50672790, 828084724, 336700460, 43996308, 15165688, 81373240, 310496913, 4592279, 528337845, 310221605, 870960539, 7079634, 455412864, 767572759, 715937457, 333995281, 41697241, 393964725, 723184476, 852702906, 800069533, 366225531, 511292990, 931912378, 815488587, 219076241, 809013661, 655058479, 247447883, 737698439, 520103541, 424904799, 521776129, 769971610, 865547718, 907577169, 730560383, 987598908, 258961922, 662013050, 268652208, 15372299, 916869330, 143678317, 674544718, 511899139, 152622112, 815587520, 620825449, 162548579, 901452079, 229959951, 346737559, 266767154, 248242286, 962778393, 34778641, 444780170, 899567874, 448105691, 183982995, 994731404, 137432305, 705188748, 718366354, 307817795, 29593818, 323187597, 823286136, 772552531, 640621679, 325953595, 308457120, 953091115, 5511219, 363573832, 470311330, 248959411, 969076388, 411638925, 995879226, 233081673, 462761963, 588264599, 190701776, 608114499, 300082295, 345773845, 473680636, 297671790, 182645163, 54409362, 100808003, 145742338, 557679701, 3031836, 187787385, 910488591, 853391354, 232232721, 872552948, 766842368, 635754715, 697486084, 681004594, 368862127, 136390285, 431689651, 294562511, 890310315, 117062216, 526344253, 980002034, 40549376, 296280458, 703542081, 688184597, 1027745, 903003438, 155076229, 856138734, 350532299, 539415547, 929559103, 423976958, 528388870, 91169525, 25908062, 430236560, 944699641, 373387276, 609118278, 34901908, 774443143, 611797362, 556850082, 584136829, 388760105, 793563055, 382227192, 815555315, 796410187, 452174032, 323343346, 125729128, 296426631, 844383025, 96657907, 278823956, 55805219, 240365530, 564044496, 496999014, 783946249, 670040828, 620911318, 913944915, 765392845, 594479733, 10065982, 74689815, 87399729, 113636752, 722646202, 536542266, 960349701, 738810522, 754716081, 64650145, 796380789, 76956852, 576859601, 371493616, 815580568, 462312056, 575477757, 308082787, 684841439, 810910451, 383501775, 70898186, 671577539, 542847831, 301336437, 966389230, 793484872, 383654341, 189658057, 3483658, 824618195, 520828046, 461240445, 36632364, 334411948, 528548919, 738199859, 455515863, 55164712, 826134473, 8662399, 818558970, 143964413, 375721842, 536587865, 129969131, 552560920, 650752829, 345257621, 225119572, 80537844, 893958050, 900420030, 728645439, 16681465, 552793959, 592672704, 130355827, 778861698, 656047698, 270584295, 699429354, 7997461, 973668251, 420874269, 268062914, 493160314, 527729498, 248785190, 99866129, 895996731, 990889603, 347706795, 901691542, 383143706, 672520606, 82021874, 231694634, 264428121, 668274616, 500022099, 638619188, 22067187, 835521860, 349376494, 667337702, 183965239, 418290134, 417057935, 205340853, 744299569, 236188369, 305672874, 176346694, 520300645, 997993853, 453157096, 259395259, 125530573, 487031409, 324385946, 816512763, 704540741, 24912712, 923032541, 745397411, 350852946, 713326943, 606258845, 149932872, 264537320, 329312370, 975342143, 230146559, 585639918, 717506579, 636790240, 795978028, 400849577, 671505219, 352329482, 152217038, 650557122, 378375416, 117341409, 267046334, 354260900, 14146212, 786599795, 211038832, 490595322, 855306883, 352166213, 985279478, 489988532, 863141365, 177696058, 353095954, 460287141, 599199987, 573704017, 233306284, 847694475, 19126402, 611609558, 996664894, 483317566, 775034732, 434216462, 293233850, 970242779, 825824256, 817164971, 297112692, 631488457, 417338472, 232449903, 130881944, 573089066, 282539670, 311187089, 324021596, 519531952, 635494994, 50183096, 915959812, 741835540, 921014608, 421944044, 759914083, 453267964, 954757042, 369585003, 831272859, 664568101, 145229243, 504694511, 836390705, 583409999, 73888140, 648219356, 618920331, 44820803, 856037030, 736548123, 232136850, 991728968, 849351301, 446615681, 976037520, 929028464, 46526754, 345171667, 895589390, 9922045, 999708346, 308746157, 834730459, 260285403, 875729895, 877074889, 357629201, 153508195, 149325909, 324927517, 49047373, 804173737, 895820802, 131928443, 125226299, 110288576, 89011777, 86960382, 101685355, 494645297, 53790777, 985102221, 199464693, 923491647, 86718731, 11627963, 581722368, 632261557, 274081663, 970270095, 220680066, 371658244, 359165823, 524372236, 145147504, 968267996, 875479422, 780431917, 886987574, 18144310, 842947417, 984995303, 985653470, 470543195, 130353982, 195778977, 689066071, 297460495, 771727448, 781157887, 916552804, 445699519, 625756506, 358979002, 572124922, 472399772, 432073462, 457270012, 400243818, 394948306, 353263960, 857544779, 170690766, 277117944, 830712090, 568937839, 289017364, 984964558, 797591581, 446848659, 655823470, 188964279, 934882685, 584192623, 882317951, 953844665, 917601639, 728462037, 84528616, 408325630, 940391946, 611284706, 563863467, 870769934, 108838098, 11966125, 529941992, 446175445, 7695607, 676691626, 99384860, 758808979, 84694675, 19950171, 973645172, 931364105, 767077064, 368318738, 428908597, 507726227, 811944415, 300920595, 831339130, 766190942, 688562521, 371054465, 829534188, 192271346, 752671152, 812436411, 53697226, 144275962, 55081136, 968356367, 333845116, 850120874, 599630958, 299355449, 218689643, 375141097, 402620827, 322805138, 829987168, 653754394, 548315836, 618272707, 536946517, 902152573, 9427618, 535819541, 436119677, 531086987, 5141024, 231400505, 649391071, 520739784, 57372527, 951929624, 851458139, 577186997, 979708023, 872361964, 64434434, 351838948, 267090463, 365810608, 896769895, 380648793, 825865574, 844074162, 406536043, 760219042, 467154113, 204834944, 190945533, 925481669, 771501256, 901167715, 758342015, 311526952, 528178594, 94155758, 335883792, 474435919, 736575996, 666220320, 675910479, 254919697, 362150037, 821299042, 538600188, 261442198, 487169742, 292726538, 972066820, 12202514, 197071554, 633829648, 289034966, 274195893, 983247636, 128665221, 134373853, 445264749, 527989556, 440791861, 571763961, 967107514, 415443654, 60327259, 419241826, 645269012, 866880703, 547998979, 435768089, 557337225, 961774118, 141504341, 349866703, 936565486, 810798910, 563711752, 824617366, 779872488, 359778051, 916725083, 230002018, 680951855, 277833225, 921340759, 387698919, 628047365, 874250804, 741905328, 718799087, 6060132, 204532489, 827081120, 774003356, 978085920, 761710268, 476023442, 955571075, 713542688, 656581900, 395350047, 853464461, 375923505, 143916530, 525746467, 359519676, 139947779, 317505928, 715123940, 408932698, 10837757, 159659408, 920993769, 236773611, 472534362, 484830450, 923009055, 97975857, 525688852, 701636761, 181402884, 136327728, 386205305, 907345687, 884456004, 842461028, 392818986, 33016111, 110670340, 146178983, 333462474, 31104121, 109210700, 553521365, 43595379, 59481065, 334995613, 262170602, 526937256, 462094154, 936285954, 731374144, 654025112, 77212012, 778214635, 123577655, 735183064, 527934011, 658523737, 239880946, 208104801, 526268963, 561201712, 919021230, 697582256, 646742893, 673807057, 404357444, 119682119, 128894318, 609179959, 540696361, 571331969, 575514531, 906956684, 895245590, 638208433, 253457487, 509156412, 559719704, 833253760, 920673479, 324719912, 882705921, 720515369, 179273980, 436030051, 779545825, 402363064, 511198255, 875661027, 770097226, 394196000, 810067250, 782930946, 751182569, 215905056, 192372257, 328201034, 616818832, 488998342, 237138703, 551679845, 497621898, 192007577, 654781727, 212179647, 151109891, 671155921, 190657880, 690946120, 19254082, 776500286, 226589716, 132111283, 312444106, 507695576, 980793888, 250964653, 435144973, 315970132, 282476760, 178750535, 467080850, 184329995, 105729191, 603941481, 421626969, 448119028, 179708447, 196499949, 599824625, 339354955, 911263178, 170790791, 268400948, 793334390, 587162647, 434772101, 272753390, 696930534, 376723232, 132435811, 894018476, 731321913, 996577868, 218510875, 992722762, 464323995, 169185207, 634211397, 383981433, 632990982, 488591354, 626757656, 660349170, 325427660, 479735299, 337976591, 231961588, 593089743, 485993298, 529615720, 963662609, 346047176, 422010177, 5941042, 998255356, 279920227, 818206936, 901787845, 173755200, 376356859, 485894120, 846282402, 413175220, 826893137, 638304579, 72822914, 809677879, 206372926, 343965051, 594752084, 817206842, 122253544, 133507133, 436542930, 265078803, 215526034, 936321987, 909355672, 450938898, 203573166, 380726936, 522939162, 56004851, 990862784, 886170441, 594384094, 332473353, 929017737, 138185330, 561521627, 463567272, 895393434, 734140713, 59460074, 323047240, 908178026, 522688900, 618814369, 272223107, 392267487, 155376034, 351931658, 262440996, 551501175, 157187437, 251373311, 288938448, 973096886, 291397428, 320585930, 372770173, 877431231, 890283008, 407711735, 374091394, 287322695, 815542372, 77896937, 762548292, 53803145, 771655329, 761789944, 681944354, 169265733, 838235481, 497599906, 304722661, 470226442, 605324206, 358818773, 177821812, 150830020, 155151784, 240706642, 14901562, 82863301, 700420986, 956088010, 321719547, 822046556, 633198975, 247687560, 126628731, 901014309, 747519389, 853428805, 836292487, 419933908, 838066401, 805976065, 748520788, 205578867, 165927670, 255545235, 788679219, 96972230, 889623437, 365222406, 111001272, 215675978, 480601889, 353109674, 530945353, 938634564, 11533978, 335485720, 776393370, 90525105, 874363040, 55432624, 70107374, 959788465, 364877016, 623845181, 839493981, 954074712, 804773125, 240634123, 189377752, 508702284, 349536848, 227810379, 264895498, 924105986, 656312407, 531391368, 957392689, 227749209, 237562270, 286877188, 926465865, 799670670, 601460606, 658787088, 179165427, 14235844, 407590217, 731545385, 892116689, 764529961, 177488891, 971188455, 640772347, 10258033, 215263048, 811682510, 979555352, 454970716, 799498630, 935448666, 696151320, 138053597, 127749603, 904370569, 161999216, 203153608, 977472217, 294160880, 236677382, 462240787, 774681928, 610666770, 737228109, 949746887, 673532838, 430842215, 847601289, 578909239, 658254157, 697854350, 475827810, 917593433, 563704706, 230750287, 500862236, 898857675, 50900017, 910418055, 416207988, 918549399, 812899250, 454750741, 791224013, 638937204, 835575161, 20259761, 630352108, 577283043, 490527714, 844066627, 283918368, 738722667, 577030330, 116677184, 906410708, 542001186, 597858005, 930162384, 3068810, 596474389, 260414685, 375384982, 858488153, 671949230, 702670725, 257673907, 466454109, 949352009, 28290194, 640057456, 560833227, 410744612, 656409326, 562002535, 312669577, 447477556, 642789535, 361055988, 588259495, 895021571, 858789413, 55088588, 287460718, 934350667, 800978541, 467938050, 547328250, 387394343, 61657901, 617042915, 221536228, 972737043, 196260401, 270450144, 488473376, 873449307, 162746303, 636051044, 824068912, 714540367, 235592104, 176662094, 56812358, 105670214, 45174657, 791511841, 662197923, 457410652, 940629374, 369774275, 711316344, 61731863, 346961085, 384708751, 214965337, 238054718, 55163977, 327014056, 510852184, 940672989, 529634287, 691917270, 144436985, 497060240, 269482230, 923491468, 444275464, 638586388, 626149829, 863172450, 715383549, 571906145, 328812508, 434994117, 12230513, 54340017, 616490420, 913034973, 245326661, 537342627, 620996213, 957284051, 424552733, 551845896, 622870638, 476587990, 259562440, 778265689, 322006753, 20093732, 985648579, 913690766, 889685997, 629029625, 888698152, 709137337, 104465318, 792636094, 635230633, 764580744, 189125745, 244334938, 912844778, 713243395, 613803698, 223876885, 758897729, 57168861, 472225995, 884820667, 6748908, 768335549, 271442752, 902718016, 983780535, 802791262, 878964283, 498935941, 22407729, 998749281, 917994440, 542604839, 95216942, 578540968, 811539640, 147878367, 635990283, 714447113, 931933364, 611232922, 732080208, 744330249, 379159273, 764453916, 517817824, 692735242, 512481074, 494873489, 963567204, 370464954, 929952825, 916343606, 366901160, 702653559, 10455136, 59771811, 891589843, 634296665, 697576456, 396025762, 749687669, 362881273, 60407379, 836394503, 515520803, 94705041, 180074929, 788002289, 63002105, 769573922, 536016384, 246086959, 870574369, 286968866, 478319294, 792919910, 176114133, 949887189, 813671752, 345878450, 276987979, 792069209, 409565740, 991043605, 708965931, 199802341, 744151302, 764848304, 711644559, 261510940, 749942346, 299377997, 594854482, 783660430, 793059588, 366420693, 589537729, 617433956, 441996077, 885258429, 752320066, 560825312, 319616604, 678656396, 478778420, 445662144, 979634048, 774387730, 846763775, 543561343, 296973942, 976802807, 988551572, 451016262, 206661163, 588153052, 786432829, 696434794, 73331570, 966080695, 993681154, 38925179, 766593492, 366447842, 723894538, 190369290, 329781584, 887819327, 159036329, 817858178, 945231891, 505763362, 304866824, 41843992, 233758108, 80016739, 195432547, 906288763, 722659948, 775968350, 739027259, 347152070, 354303442, 122116684, 791564447, 295545938, 461123312, 655231074, 738175650, 200704301, 768617332, 772620417, 757215097, 591822009, 246028852, 30030230, 667786155, 569489099, 649721828, 322172807, 844477581, 440574397, 368677249, 843291298, 650058034, 694077294, 713830460, 805526954, 458602171, 659042733, 693913566, 785719833, 733292947, 23914404, 749545784, 962171939, 360545674, 568581684, 752877689, 899910676, 641980163, 518831049, 171203219, 650545125, 586509656, 617125067, 748878853, 756632892, 216148192, 382728569, 773327213, 5962518, 339226024, 62058798, 403540929, 924762348, 336047105, 447220530, 134034129, 629289014, 674435927, 418711447, 696933914, 640780943, 366385033, 741892950, 958169459, 701328180, 158003122, 117760584, 488736438, 37895260, 496797939, 698919416, 319912815, 847926312, 443469467, 370213944, 867793068, 750788239, 914416701, 274332780, 816773578, 733529044, 826531407, 946255377, 381841144, 26904141, 933772359, 102523071, 22953158, 909220795, 604819470, 968804576, 741017076, 313479661, 407681839, 925125230, 785622469, 36431987, 963378185, 898948021, 525308770, 908630100, 483366675, 207067897, 820960907, 317034794, 776196126, 547233862, 863212033, 35068583, 330460706, 277391884, 706861216, 7116349, 44925800, 990284402, 1734839, 787272384, 547451450, 784571590, 661488999, 38234430, 573754356, 298463966, 576183606, 144146169, 894703451, 762609397, 809789742, 664175833, 231098046, 515634360, 236881125, 602696331, 424200686, 181013270, 262632898, 917183959, 457939727, 899860428, 358715536, 790914959, 745126544, 687110221, 591141716, 169087129, 220112537, 132667196, 67307675, 224660623, 989709306, 815563863, 616648537, 367642620, 647693034, 332885157, 546273654, 449450033, 973679709, 842175715, 481373170, 920874065, 729535291, 314515760, 535240676, 329530327, 835587317, 915207390, 971297354, 835725860, 39720755, 112494793, 108117127, 14127780, 250658569, 792074115, 560445008, 698787283, 376563809, 313109621, 237679725, 647497002, 60201124, 306355037, 896688071, 396588833, 625107635, 599946929, 107209168, 650137160, 363711013, 828049946, 697710929, 745696243, 289010777, 756361405, 380039830, 925008651, 158840903, 416244312, 391179536, 719374276, 922613005, 824297878, 903366917, 872626275, 499159437, 594570751, 592155195, 298199767, 424470547, 983262850, 492538961, 277436209, 536207358, 787049856, 822694992, 656466198, 53281088, 489849504, 883799570, 554733207, 376858373, 681416782, 810492280, 936328995, 818606417, 155031658, 361214270, 335492759, 188389194, 66316185, 29303506, 451182158, 662942661, 980237904, 343382239, 844225608, 939275394, 565854431, 938430279, 442446790, 538326160, 923472419, 89203773, 647631048, 219198595, 570852031, 968860875, 355913905, 716161935, 83071939, 661417013, 754516033, 444908162, 215440268, 29155649, 34861762, 602737133, 910752928, 380795277, 646155811, 64686712, 648428704, 806232893, 578089383, 415030819, 357221222, 259922983, 997986620, 372364068, 170959349, 582893898, 899563107, 576034864, 356600098, 451033467, 136104545, 618517298, 352027055, 949739986, 198811920, 145073772, 745177127, 804731155, 280448017, 823579429, 550461699, 324689935, 995395928, 564206776, 524043163, 887683851, 440725135, 169484956, 810902038, 33141268, 643917037, 457774675, 601394463, 493118035, 100867434, 857917320, 840996815, 360957527, 897723622, 603755815, 302795436, 601548596, 226399722, 911508357, 65141238, 746993895, 835538249, 941932525, 933897010, 427918813, 213960920, 167983238, 154488951, 277161146, 628330767, 439337863, 436998418, 62466499, 646349989, 355634607, 273725579, 335082877, 213728931, 405075718, 727576748, 342440976, 774415422, 478714697, 125792180, 284393959, 834056793, 645985450, 463215393, 313026848, 989569077, 84045596, 296783794, 438781556, 873548637, 928120632, 69884229, 185636158, 51349959, 579037409, 167100416, 979904421, 493319626, 53719174, 725764374, 455996602, 131526235, 192076103, 190844462, 222258184, 936946894, 575529791, 823211773, 616648084, 752602961, 739029283, 51595366, 210010248, 129540100, 800582717, 969459207, 880020024, 76733560, 115013855, 964190254, 236264308, 457894547, 340439486, 435574295, 831721285, 215897970, 40300747, 934284011, 773352207, 313843421, 967314086, 474139992, 412591936, 339583851, 966798793, 193555291, 47576208, 806507315, 21347474, 192678711, 45979727, 708269315, 468072096, 707928509, 769624785, 317961352, 897313377, 674744462, 200681598, 348138817, 691012202, 488434752, 902950869, 178233463, 939509685, 97532440, 283352776, 249026767, 375826828, 505321768, 197077641, 3405445, 474334284, 873391239, 160890042, 675012167, 431293826, 507143402, 968816744, 236711956, 837896766, 311784695, 970797577, 361864196, 237755107, 949465501, 422176348, 145718248, 100315510, 855943342, 242987038, 478739064, 623352799, 760516234, 414956613, 719592722, 281863145, 628089052, 488184800, 959235941, 504138393, 308158547, 8371917, 32627652, 256863895, 897441071, 355541552, 407875421, 24184283, 516390665, 952761761, 543021436, 446131684, 58545054, 436710887, 974482231, 349455543, 990582395, 480217259, 12156138, 696224706, 717618863, 143804240, 198013598, 115580655, 904137836, 283039027, 690563300, 758972084, 645543969, 591623439, 222587012, 269851412, 479734759, 917625789, 556867899, 904664567, 713886164, 863833868, 43102017, 720415107, 104699948, 411073360, 191485505, 797227010, 447391593, 707903637, 52330871, 869124412, 284976958, 346974744, 615904125, 939707889, 432900923, 942758554, 8652164, 940665632, 787044968, 161561460, 807238109, 169451054, 17692206, 159147068, 960559645, 513491584, 34939719, 677230270, 337574595, 661739559, 171217361, 244879205, 252027345, 21973330, 857432172, 634179589, 769884231, 851191102, 113009220, 898593536, 954228072, 814344901, 246069895, 962274895, 270990358, 273501485, 339503463, 527789107, 166052688, 987306659, 216181473, 94342402, 417996095, 16497999, 868337154, 568424606, 227148197, 298102012, 863128523, 867547737, 260853230, 982131418, 438631456, 546489998, 321538914, 907533712, 441379382, 508727760, 146070503, 624927159, 497480571, 229539710, 667338267, 511833687, 321960306, 741676734, 790458937, 390330083, 149813130, 820382108, 668185062, 671764330, 745215957, 125224127, 888635182, 490721974, 561721617, 683144541, 615239342, 317838146, 132194457, 869220648, 921122008, 839660590, 740152631, 423281446, 815265165, 881583833, 868581699, 733838036, 668746119, 72690499, 997871932, 259180178, 745652179, 661524511, 9640554, 211723017, 111149287, 22869529, 633715775, 239936137, 666168216, 189980301, 752959494, 347341484, 461903997, 832294952, 448049507, 119921048, 422689914, 990767842, 999632446, 241907381, 577580149, 282465622, 667624188, 178430171, 253607819, 203601252, 513803749, 944211511, 568626626, 760282131, 396469282, 213656459, 206779780, 152103151, 850332829, 960273386, 698983159, 981798954, 738822501, 20353800, 783281806, 128642983, 900943406, 119588139, 684804245, 47821921, 32670649, 872232416, 22660921, 996065896, 483108164, 793901295, 852383506, 193519770, 231684774, 115806906, 305739025, 843717018, 729269911, 897749962, 609770279, 840361052, 120496098, 601936842, 4916380, 259201778, 664360271, 437872, 180617511, 950039794, 268249776, 352515362, 264173016, 239280727, 72673140, 60600943, 301694757, 562274243, 705514105, 876524517, 355633507, 702808072, 690457431, 990635412, 468819983, 326068019, 898700450, 609795908, 179860687, 22974936, 45556863, 848783204, 367037480, 128839083, 857547504, 232865496, 763286446, 626468125, 173819723, 887586224, 774179308, 258542402, 136162087, 407926197, 525687089, 789592269, 44855038, 400153451, 160123589, 24254679, 30488512, 528128234, 661809676, 536429773, 411095141, 99981146, 600770040, 280640431, 524881644, 620604040, 683986861, 74532098, 921309971, 404898472, 121393553, 187638388, 923504746, 110648018, 528373417, 433572526, 187405934, 901188683, 161049505, 364359165, 651948030, 451483222, 772687861, 438831744, 852437307, 395635000, 271405683, 318743648, 530361344, 477581957, 817692939, 276814311, 647743565, 167038011, 592120158, 376157292, 221082490, 795509031, 894696953, 854532663, 88017337, 333202724, 113322877, 90658435, 932672474, 883990526, 275596000, 819825326, 850014006, 809524098, 187630905, 587585099, 516662716, 985639234, 627050393, 637193670, 792070072, 25480330, 143792285, 542444778, 844387879, 384646318, 30148495, 419955563, 589257669, 973417119, 605603125, 272353277, 681836150, 313907337, 626056591, 825209374, 924723393, 853019680, 827506106, 695894756, 499959021, 544275964, 74943081, 720512717, 903483380, 145997797, 813987893, 450120779, 77330617, 524658672, 760808235, 755138920, 852205547, 726105009, 952355691, 693876605, 730711169, 460710322, 935221147, 827324521, 69585671, 694554697, 938819124, 769844794, 86833762, 536181876, 69448288, 678898834, 311399642, 230412665, 684989042, 791467009, 94972118, 665458724, 31247042, 560693290, 408763539, 160412143, 899218985, 895875228, 357213957, 33883541, 971362243, 541860566, 869852236, 43482126, 615480443, 129605068, 736577438, 30257078, 613813186, 768070156, 465401629, 71546248, 856962854, 554349991, 450784225, 345776202, 228730514, 968928855, 978547736, 892817832, 612624480, 488339228, 766810318, 861527052, 120527878, 850941187, 884599226, 747672508, 467678580, 156139828, 313253327, 85342106, 757559605, 649452221, 329406806, 801760563, 216682990, 991320922, 6281099, 727032612, 952934150, 434104737, 103242279, 748509702, 521820581, 501688467, 520700825, 29029426, 627223756, 791118476, 653537425, 767288454, 409420356, 849179757, 327387295, 826393915, 223229611, 593433483, 198901310, 272224885, 217181552, 696522204, 766129321, 659407771, 387710203, 195260830, 74991758, 367913199, 336150636, 540403592, 682155902, 374217874, 486246966, 826772621, 994432720, 910397445, 730691262, 510954302, 951234635, 527771919, 250389301, 189690068, 607503065, 413299307, 294779795, 946901258, 361490056, 844892094, 788907396, 105549397, 815472454, 486262159, 702976048, 607009721, 842548856, 648231017, 143038321, 481132795, 14224298, 332081171, 13162114, 173168404, 220885706, 792825805, 402594401, 234816345, 198123813, 652736719, 20244263, 233797938, 322948563, 802888999, 155275860, 187934341, 338845685, 220242422, 645525746, 245297577, 429757419, 534887541, 141970437, 738482378, 175794090, 859323688, 718798543, 34588019, 716713098, 698725857, 53865638, 416598266, 963657467, 262969928, 199415919, 326427252, 546618268, 411563819, 322988772, 7374986, 532819312, 865279689, 220467576, 513401616, 718608655, 562799573, 638675805, 185565974, 372464995, 306540260, 905739017, 132056275, 738225508, 409808802, 30713696, 225496576, 295915994, 627574693, 325217563, 174859626, 73184086, 325533991, 523327517, 875794772, 175383507, 770994072, 434284225, 752115571, 915338561, 821623779, 712929654, 344342622, 97792574, 278863930, 58975217, 78721977, 380058728, 894568157, 854094824, 916381974, 218738219, 466732445, 701731510, 885358251, 559618032, 156631115, 852419192, 853045333, 4472945, 313422868, 615240284, 493761984, 310768477, 845750876, 532714799, 124402519, 819203684, 807253548, 941911047, 686518214, 36101981, 607205867, 808676446, 745961804, 99933187, 427218857, 92279124, 252676990, 282901652, 555602343, 258866887, 236109693, 686813890, 370205748, 899256245, 206195035, 147234678, 829652481, 151826164, 283139327, 926069050, 568501350, 622435954, 833698369, 631886999, 300585659, 704285813, 680841763, 575202068, 183353366, 566870616, 165720712, 710800351, 433257799, 846074855, 282677028, 154094300, 941990514, 612999074, 575966452, 525488306, 40523623, 345969700, 950177736, 439694914, 174894666, 233040122, 607467896, 845203141, 132443822, 179188796, 512383277, 918902206, 669750635, 864125370, 441576635, 849339708, 879524370, 816522108, 429905658, 290515572, 525032899, 607354036, 248890647, 591708342, 443786844, 236454427, 72814655, 766402564, 761598427, 455698867, 494637190, 273466232, 650462700, 774602712, 914596966, 554717772, 833396485, 166466060, 278325701, 816025065, 747262838, 186331659, 871385691, 746946658, 282413883, 330548991, 862775962, 477695443, 613242027, 247134737, 689648168, 941070735, 436882030, 921385781, 165749406, 575017751, 388487671, 125973459, 909257453, 120318782, 731074499, 751850834, 571921440, 480588137, 901480337, 176404483, 524011942, 737165875, 675188618, 915826754, 363758806, 373601309, 241361855, 881279692, 855133932, 621893165, 957932427, 138792251, 354776775, 605614225, 820927437, 634341526, 934942870, 842932102, 334286967, 219202812, 407135040, 352277742, 148516948, 413820763, 117778045, 843236671, 880375103, 433605107, 173863603, 897022375, 36271762, 367874490, 169135275, 804851907, 578253476, 202136032, 22304807, 177950156, 741418431, 799233093, 35937071, 854868354, 212350646, 57692891, 845227246, 717194037, 86706194, 949285631, 126504205, 629838623, 624260119, 14186658, 421812094, 344707219, 260701741, 84150456, 2717715, 264098781, 495494752, 299017492, 89118651, 696757714, 702379928, 199299040, 935979784, 597431021, 81040381, 384164339, 979653602, 199359525, 744215440, 186520173, 398125773, 868383113, 248636834, 746101957, 206387837, 247718630, 579184577, 602375421, 235933017, 664851397, 25348662, 291416063, 769186123, 513339048, 605877696, 69812180, 50447749, 837275454, 745988944, 664978541, 342545172, 595704012, 157831287, 151749631, 452477397, 355296658, 180459322, 754776535, 841601745, 796071510, 686130599, 286040328, 496219447, 344203145, 753041082, 983880366, 954747424, 634373166, 590936400, 239338401, 341515141, 383089805, 756615379, 95099037, 861573234, 532845804, 593126304, 885715532, 569960922, 397294193, 935191835, 946067625, 935033996, 89783331, 928162607, 428478088, 800032143, 844605413, 544127902, 781062048, 542335339, 107943552, 256877508, 686948454, 633249758, 484164254, 89153913, 277942908, 507133572, 716159422, 201157197, 171906529, 769762205, 666110787, 467795687, 862754349, 874911066, 950142906, 833166557, 857901174, 919842914, 862468644, 887306888, 624832656, 408752796, 686651415, 617550370, 119664180, 19736714, 753944591, 599743052, 555769219, 940081443, 153604677, 407312545, 139310424, 589743365, 177723322, 235403842, 7182900, 377136934, 431032867, 38961680, 900481911, 917748787, 998292208, 382212835, 958748627, 521419036, 52178837, 244622841, 319573168, 478088771, 621001265, 407760601, 543736324, 153744016, 34701015, 246340362, 246758761, 965905694, 932564124, 572780851, 462150438, 371984873, 802668705, 449124806, 460820319, 383233556, 416292004, 936121309, 435738999, 641696659, 575212592, 165351226, 826939086, 992114073, 602813016, 681278593, 310121588, 714120220, 275567182, 464111395, 647559727, 314573129, 120296512, 163392106, 827928815, 958779767, 461364631, 851470025, 692109892, 577465088, 722918937, 845249554, 92279949, 356311577, 983103060, 120983922, 116317705, 12806449, 890194943, 884421969, 699881086, 386341867, 757054852, 246117576, 344802331, 208460116, 86316015, 59112106, 598215573, 46559873, 222236114, 705132913, 236031470, 350199672, 689196268, 396080785, 394420037, 914757386, 865169328, 367244624, 570661855, 527947790, 432362569, 984354056, 444742143, 988825258, 631931761, 149904432, 986965835, 175030240, 312252897, 116249241, 360098638, 25073709, 228197180, 12366815, 649999810, 521660858, 275934848, 513527209, 391196475, 376783994, 818868204, 216918552, 921181615, 418273777, 287613761, 311580728, 146990891, 596613466, 531621426, 514094283, 433299505, 689923795, 977568521, 108281625, 487160668, 478740586, 966032852, 970031246, 669779508, 36679575, 607693081, 686707021, 248260439, 521467396, 227117659, 374608518, 323920137, 574872967, 184246529, 271683505, 976319123, 218010693, 905455691, 357648455, 213647979, 882324344, 12733529, 431231678, 685530389, 494701835, 849517910, 317552985, 495425465, 340556046, 268905556, 362060579, 914159950, 954280095, 241953692, 742396251, 769008296, 244430723, 608938189, 337203166, 394263101, 151237291, 644583783, 281730742, 753053360, 267372106, 243121260, 222284020, 35302026, 911133168, 285783858, 882440252, 87582115, 556322346, 702641402, 623368190, 979337979, 965274570, 356353446, 427405348, 411384529, 502741217, 268203367, 380414885, 223521601, 378983118, 627636558, 624111022, 898902657, 234652091, 420317686, 439175565, 511875190, 79984530, 395982530, 111271157, 596494739, 706222910, 103291753, 481334215, 977313091, 853999849, 81606222, 432998383, 716907305, 137075327, 634011436, 351408096, 587161218, 538741587, 843018396, 64059428, 665670127, 684898090, 346157328, 609753649, 585523780, 456127455, 532971100, 41218749, 698250860, 356186915, 972458725, 563239908, 166596531, 222582548, 934131555, 586925078, 206678380, 890412611, 418757939, 123514343, 570868743, 829244119, 980064376, 224996881, 235664157, 916200780, 298937144, 945758062, 678284364, 51985440, 767149419, 223154399, 950061593, 437071600, 850788496, 476167090, 350010040, 351946587, 933384661, 50008732, 62405726, 117979192, 30049765, 217048062, 541008535, 563057765, 856348864, 304821855, 590401123, 299064786, 442432842, 510570090, 660821956, 4964557, 861033052, 541326123, 845386675, 232741772, 820163323, 631529520, 810058303, 421073534, 331106005, 312929973, 172229458, 294138938, 28171341, 130696248, 935440617, 793102260, 722902359, 806734344, 993652033, 517250005, 36672434, 833848814, 692505775, 773178197, 948802465, 387731614, 703062138, 224690648, 292871820, 610613008, 797629148, 730960335, 930023668, 858529568, 775736766, 708094534, 646958219, 775248726, 156777207, 107405023, 219416292, 868220260, 806993929, 149872840, 653693496, 777200365, 815566611, 197528182, 566236082, 939227235, 66955824, 987309226, 2091569, 105001442, 436533362, 56367467, 994800488, 561656351, 132006796, 284859349, 950884219, 217691010, 311431704, 561216675, 171436028, 612521042, 926914541, 702578780, 502247346, 892243583, 219288843, 341955396, 117669210, 101132717, 805439236, 306412372, 147309262, 302514912, 270343565, 967900348, 443361747, 41979896, 748397635, 116303998, 190018286, 865684982, 297993819, 996267007, 932550619, 286160066, 781676992, 365084957, 361411620, 479855663, 611464198, 193581443, 808767381, 75282101, 473368345, 95876631, 33828432, 336189331, 948194378, 646826075, 98721595, 147244066, 954126939, 129002378, 173069897, 715928578, 164957963, 523400660, 6015517, 587082552, 580982093, 31330620, 976661749, 409351992, 679088189, 565697598, 18888346, 968157302, 348648235, 533913024, 23762342, 138587218, 277110461, 639305374, 715038810, 505836156, 116924839, 409151937, 688893658, 323759422, 829592002, 599542341, 23013119, 822405893, 814138629, 148647764, 113791825, 868261475, 613113095, 255805643, 26469933, 785449305, 646970500, 651947977, 742686877, 837272312, 815910591, 277433234, 163947519, 777804401, 212777420, 118693197, 440581537, 77869834, 981067754, 362544164, 292500334, 74980662, 527002721, 859824749, 24334750, 582614925, 468308583, 456019310, 619491774, 5064649, 162805608, 226984084, 864509038, 643260220, 275597745, 996587791, 528332391, 233081109, 593143012, 312227587, 74642120, 400921331, 214734911, 20674390, 1717047, 809245312, 454464360, 490585615, 270882186, 121544412, 870943774, 432562777, 682265443, 305581124, 736372763, 877520151, 580085326, 359465190, 369961479, 701187328, 792267790, 394668511, 838698386, 541300941, 241737988, 161927693, 729929916, 795074507, 915712558, 964199864, 220537734, 646313732, 778465166, 625740645, 100974815, 733973768, 570425362, 748747250, 417121181, 767075700, 955012320, 992463626, 403498912, 986896518, 907446635, 903858339, 483180327, 475407905, 955068277, 480901271, 587500623, 915258069, 97729327, 88572781, 457025442, 732789615, 654478043, 65302740, 820282165, 442476894, 673975989, 106464854, 139838501, 140240680, 308855996, 411405252, 955883247, 755029497, 806505624, 547001383, 324529985, 413514569, 480923334, 496193440, 774391069, 772799790, 744112705, 82667574, 846119399, 692366682, 571126757, 630977263, 178224835, 274997746, 708318951, 623267636, 106044546, 186050700, 123553020, 207884516, 251912181, 246485012, 842750039, 89323672, 607939118, 884905823, 206464462, 963938513, 176616171, 490810870, 108693738, 676094558, 770625615, 995078169, 999794922, 345974597, 899005406, 974418235, 152880379, 178007185, 286010920, 721168599, 634083520, 473172153, 500803999, 755225792, 76436218, 962235276, 817682404, 375497486, 443157596, 536832860, 142782495, 83314244, 14586407, 771018356, 888613609, 710276957, 539981600, 687059081, 644644295, 901405402, 869714047, 970432802, 625195168, 584130877, 831095355, 970291313, 835450497, 826343357, 888670561, 565929183, 413297503, 994471111, 554491383, 836955395, 227858546, 781916028, 766262881, 139878195, 615027652, 467533766, 541794428, 699479186, 103268152, 614477050, 315067271, 140373883, 740407404, 6548450, 102432031, 409493280, 603261698, 961785326, 999658078, 800864442, 201992210, 267819472, 197560278, 306027910, 366654547, 995030813, 570739262, 467320968, 131424441, 685996041, 773390443, 947717790, 784451293, 848349808, 24267247, 893415066, 315710573, 510761228, 630511750, 232603050, 174629274, 280868970, 842541077, 138825793, 914715819, 105981293, 670433584, 242043375, 605732760, 220487849, 66241582, 45105139, 924132190, 6509145, 4922976, 33141619, 115927273, 640970852, 259722634, 636414838, 770124493, 575541753, 910590485, 114087077, 899684715, 750678761, 345336683, 712735610, 195793842, 846347189, 567517491, 414541528, 827344953, 515126198, 883784250, 210838402, 845690294, 581122058, 85954714, 23038872, 636880830, 178213255, 933438522, 159478328, 679304190, 671279797, 469868964, 662469075, 386743594, 289555206, 456153265, 825415900, 319793544, 446299444, 913175780, 384164560, 262710451, 725912447, 9886378, 820427377, 74896905, 257892113, 927620563, 946158514, 340323418, 322718475, 773844338, 307672526, 294031356, 119028605, 555496892, 486128257, 753240559, 462401817, 883353970, 271483705, 42861915, 507721629, 761357357, 457501488, 31365029, 340848977, 864826721, 815224486, 80010223, 31543667, 517667007, 873817147, 981745555, 666664852, 950784229, 813018102, 274998454, 988849548, 598600362, 99685913, 599459852, 45317599, 470058262, 741331190, 364564303, 239426108, 377163928, 707455204, 557771211, 715232970, 97245548, 914781902, 958863260, 812298071, 828252941, 122886904, 600570520, 636230700, 131898408, 401768102, 105172822, 250002422, 878431799, 662144459, 638096517, 186514201, 229806570, 893668594, 846524613, 895032708, 873194474, 541499277, 666834099, 892025406, 140394206, 423500683, 821930679, 529466460, 163190960, 825889159, 687285275, 811440083, 224635170, 410605019, 99238643, 638059331, 810323209, 440802645, 749496239, 686932608, 457377557, 641396788, 868219913, 530578182, 284536524, 702833567, 362618990, 808155091, 149745926, 537849013, 280941609, 806391315, 526958782, 146808553, 490930675, 749963514, 960643770, 472554826, 597286755, 700828532, 250169194, 38086407, 494160198, 541242382, 109424292, 727109049, 983105306, 105764869, 209721351, 906116029, 661439790, 504675360, 249710812, 605526061, 933841925, 602548068, 332090163, 986660516, 5088325, 849365861, 938610250, 64393556, 769791556, 710652792, 10578803, 279245960, 71393075, 236278130, 284138533, 52587481, 448529671, 671034983, 98338689, 181534741, 758821664, 646628783, 343025352, 572202175, 49246484, 769388680, 220507972, 614722882, 502596496, 809483147, 671147993, 618543324, 781685744, 293240842, 832354961, 298715423, 650984087, 47265215, 194502504, 695580748, 137862837, 761280558, 622936436, 380490722, 541045940, 914915909, 28422945, 158955702, 473012971, 389714176, 408043003, 791704791, 761304572, 918927801, 434042042, 340563850, 471923504, 384955718, 706181154, 211492771, 673375629, 38593328, 312485329, 203231423, 527171304, 725546652, 88521705, 91308756, 879734253, 664242009, 998705526, 463573536, 975520840, 364290146, 945926720, 458303508, 426130317, 51891742, 825701999, 802224851, 902454171, 263041305, 605996077, 838431432, 369438015, 157082761, 247363198, 706595497, 790899742, 130076678, 37572325, 984331931, 829637640, 475528160, 344541573, 125856359, 68441109, 282300608, 327820449, 847853613, 210585933, 569476344, 572754876, 832561089, 414634765, 441532801, 522782829, 524318319, 938317852, 822210071, 400438644, 689881704, 431079039, 688129858, 446037625, 137549685, 689108339, 133232504, 334402545, 926366559, 593018956, 910745454, 758874845, 89489782, 392378320, 845765894, 558381600, 358065198, 289743633, 206950975, 895581372, 712606287, 387515511, 289370672, 116737904, 816706094, 544441521, 58077167, 743524189, 809245754, 703575867, 370853375, 614180473, 495653696, 643549654, 605497169, 342093438, 459630328, 563609796, 981969960, 99732662, 950784356, 534620786, 778339626, 494303695, 266696634, 653640989, 377287325, 168023406, 782962798, 862868314, 325101249, 518204737, 117682779, 339737301, 412163107, 768620482, 307154426, 729412713, 474620106, 700561563, 86331798, 256945389, 991908617, 103111246, 771808556, 600271815, 60651990, 92390910, 721659166, 573807754, 896951129, 478365222, 735904476, 808789243, 86602953, 715515109, 490821357, 598244088, 614327838, 770313436, 439510688, 26867320, 385907648, 381852675, 188657094, 160472293, 637828165, 733970932, 811577064, 542984602, 238739998, 934852298, 314684020, 491726419, 160045412, 207035987, 593736087, 680898383, 32680287, 355869012, 307276531, 749259716, 783418467, 944375241, 327401372, 652709115, 882536696, 764095916, 670162198, 200379361, 129370702, 208640870, 632422481, 339059579, 935943424, 799059525, 490227881, 319664898, 423765576, 873773445, 493582900, 189433759, 638768848, 217732291, 4624015, 886491985, 646737680, 231968180, 727172809, 558887841, 547586858, 886313997, 806327891, 72433899, 10069160, 582697889, 882137781, 40663238, 84084187, 652733701, 404647208, 909568880, 999991734, 221764910, 785827085, 912498653, 151511199, 216427262, 66427795, 694589677, 111904324, 341316008, 67771941, 298234751, 599002964, 318177836, 393992072, 321068173, 679946809, 846910760, 646207854, 265967019, 320161206, 35464922, 857671815, 668768091, 377975736, 562778792, 208528852, 628945298, 945423081, 378891618, 802634035, 343712030, 514965605, 373510085, 723074842, 901114883, 983797142, 382921329, 25949337, 841498118, 746515717, 974885379, 431064605, 321887624, 871496249, 378510193, 811527147, 387000842, 101556979, 23026339, 882642703, 340777674, 743930550, 870263262, 440370633, 513837974, 648673097, 246722587, 615672071, 432461513, 651193919, 562790620, 136069159, 409528036, 587578181, 432520556, 328328748, 32291084, 546310012, 478143573, 103085872, 979880333, 216961800, 961100986, 873771314, 247821383, 354209043, 709221399, 280562658, 312824503, 525533549, 776022534, 236198198, 788891701, 953806248, 893330663, 382918699, 726263274, 311535508, 404160320, 262239818, 959761964, 711018014, 50391255, 751526247, 954913283, 400238457, 798049512, 329471888, 427301077, 889856559, 410730388, 671356749, 899383039, 147352189, 351813831, 556248580, 728068987, 381320104, 320688725, 506546379, 576355257, 505526438, 114326341, 953200154, 290696304, 238081480, 363159598, 153710768, 305296233, 925050772, 308684606, 206970381, 368632538, 881996646, 330206703, 582390783, 635759191, 227253780, 299795311, 165146296, 363366404, 814630473, 480741791, 721925033, 79863854, 153079781, 486513821, 703199835, 873189558, 217595200, 439499793, 519314140, 736520455, 231843782, 982372981, 757134060, 125072848, 341997911, 980946424, 74284260, 263984642, 621919768, 495459547, 930604849, 265985081, 540240295, 103364074, 516275848, 657398777, 211882512, 659769469, 633550247, 908804775, 260619738, 137851597, 892864460, 323179327, 374441018, 62835208, 768304336, 874293902, 44426854, 761822870, 458143378, 434093962, 467056352, 89645964, 792746326, 480127564, 525663814, 643596443, 931954609, 713243725, 849417161, 637255178, 349558901, 266540085, 944851953, 761084280, 885844543, 845608781, 8462391, 587569983, 670962886, 927158234, 541949318, 948097763, 403905670, 409953969, 183599367, 836206810, 131371949, 790455416, 934858454, 102381027, 373088918, 463635375, 888535495, 515437504, 568848097, 185927750, 701222473, 630745923, 789182183, 729145077, 793659368, 322997005, 784844137, 316691183, 171113934, 750621944, 675436433, 802298666, 416122226, 35654156, 211306035, 743425143, 245750922, 393343873, 602883048, 598359235, 346518522, 714517408, 231228466, 651599928, 729576055, 395259076, 492166071, 431436421, 102346592, 450984122, 264474807, 641900279, 921951628, 878574806, 249891198, 874862391, 469092213, 709464906, 434035167, 974450948, 9557851, 61816594, 333736661, 374690289, 450551269, 57959122, 473908083, 560178668, 922237321, 68194007, 78812739, 638448520, 476793658, 229699111, 52226256, 913243619, 935479815, 808243412, 182147673, 16726979, 475515729, 484445989, 224078834, 132105833, 170022389, 189460450, 519398382, 60758893, 465941498, 186389922, 507590300, 676831948, 89744684, 334878972, 620984443, 394139961, 789228136, 341068746, 189814933, 621374692, 984459553, 800902188, 746450381, 607483455, 836048694, 215270265, 769206563, 798303283, 58183350, 757754967, 730810667, 650601597, 880558174, 238008606, 885591277, 558099299, 385790389, 429110123, 619863037, 240625372, 454379221, 584373557, 492330565, 996630065, 794413620, 20037928, 399821508, 79170535, 152872836, 340874005, 693290951, 612878825, 280600542, 337723433, 40451232, 831451284, 82350276, 338646028, 714156629, 832289290, 151243030, 811702, 700034395, 980010365, 594438522, 181134977, 898123088, 242488226, 78339006, 264151129, 901373916, 514949128, 806944784, 594550288, 302457217, 6933693, 129250090, 956015417, 802993532, 468442940, 951691549, 799664153, 916305998, 893012967, 851813136, 662383348, 265661093, 387244355, 864786046, 864988868, 361560232, 333305284, 35345849, 447507463, 750308864, 84983100, 433466714, 334537465, 8988431, 861975319, 993030011, 92689578, 345629756, 836351922, 154653958, 628858977, 454183963, 789463954, 832018827, 852044580, 836601726, 425062043, 870340001, 351673616, 733510030, 450689370, 664603640, 362468116, 156445735, 674596494, 118017187, 640375952, 319225918, 689606034, 785521551, 325579041, 222774664, 89117734, 160785478, 533683126, 343421335, 765696332, 131438412, 21711604, 327474349, 915147432, 950846119, 337298242, 552555489, 490111683, 335952250, 871184966, 701070713, 755976242, 399648771, 321068727, 581877524, 35076580, 864804052, 366131312, 894224773, 763688814, 490501026, 325400256, 16443047, 975940201, 983805592, 164983621, 589900921, 474848999, 455322597, 730275005, 196991211, 93889698, 427178898, 514146962, 455948145, 714602089, 274667048, 517135663, 389187661, 442486611, 635546737, 716528756, 319942059, 901071381, 443379099, 288250246, 982194568, 250711079, 353526999, 109325652, 924661291, 520741942, 920324770, 965088811, 381821991, 476413151, 503990461, 563128778, 819386104, 593442171, 95014949, 370209850, 340898373, 460456228, 615230967, 204455824, 57922365, 383225023, 357787256, 55041494, 181251427, 993854680, 496179880, 734422709, 910148492, 106406704, 679032587, 205969630, 1473085, 213182477, 127123119, 945532222, 871435658, 202698572, 494859873, 777557915, 907747072, 162692375, 876536606, 615338581, 162643046, 163188892, 575957366, 241990447, 682599259, 59149989, 288129148, 331715868, 299176420, 228077100, 327821512, 415030130, 9109064, 727971255, 907451897, 977742441, 608991142, 589282381, 922122671, 264632660, 366262125, 870783701, 143628086, 466908875, 744930578, 393275900, 541758370, 686934962, 285975965, 123915191, 624388965, 440234127, 86223196, 835644185, 600016250, 204049532, 553643518, 7790886, 837618184, 837192102, 955016285, 474634939, 486487675, 896936472, 364419129, 166429610, 435157261, 106476745, 599052208, 643214569, 516096213, 885079687, 498074227, 806274815, 991964646, 987245081, 943485661, 844827833, 407049587, 368803501, 65120997, 896111051, 884171629, 203430059, 365058477, 824132663, 383420134, 993279910, 181841936, 786622851, 375651386, 710383766, 261191524, 125275645, 634760435, 396541716, 886763281, 156173482, 586401663, 382138048, 961491291, 182011887, 182060739, 432096757, 837774796, 81055543, 791229577, 184907735, 804750067, 963458749, 47994319, 656140759, 627299958, 243344913, 132594256, 264284863, 628166229, 423267347, 642403783, 615694146, 37971352, 791718304, 898866229, 608800699, 600232053, 494398240, 584242221, 519392954, 142625015, 260142606, 189427845, 686895283, 726450101, 147307668, 358202367, 804003455, 943053075, 844080898, 571165157, 872452957, 594707825, 369158948, 370504425, 968105866, 375460735, 184131532, 660026821, 320132134, 113942923, 146952466, 62316988, 410701966, 767367148, 585050232, 232819349, 481376207, 736686545, 452465019, 1594857, 752493095, 524731517, 248397858, 420218912, 790970232, 814373244, 568691525, 579452297, 550418862, 358082863, 840642052, 363864025, 472660475, 99598510, 557831020, 145334390, 609983554, 35316532, 797844676, 532803822, 646580426, 234900408, 85839940, 247931727, 219520002, 505862468, 949965984, 212399166, 610641789, 678310286, 174557548, 30205154, 912631779, 606988299, 42708209, 223760655, 293567395, 487867592, 203922433, 193005358, 178596632, 853861119, 370096905, 881689437, 27985052, 210114368, 722424563, 212716681, 803303147, 366753341, 93827864, 203347340, 232158874, 857889947, 511371339, 465294442, 678610637, 497702124, 214583922, 911078508, 625482359, 405187322, 713723784, 527514552, 698857263, 855990089, 666049934, 696543590, 799376011, 626119516, 159876381, 156072730, 426341106, 592636987, 837936318, 841501069, 512757904, 427097423, 646385216, 504905954, 882388125, 406554639, 6549926, 350162210, 618431281, 637347908, 705838577, 102472438, 141724060, 432216970, 732159160, 241994950, 59091009, 407749704, 586366053, 694220299, 780010409, 150150310, 339659611, 648728575, 991816096, 620033758, 299753640, 642236637, 89853455, 894736316, 966896574, 500140079, 798545437, 784316629, 459171531, 117636504, 810107677, 534487604, 301136322, 342363877, 463963274, 747043535, 568707998, 795887637, 561730452, 176017027, 724321930, 104575555, 44361019, 75564261, 691042961, 91613731, 458381012, 11047747, 69773607, 541783569, 112104450, 630490552, 281492866, 542048739, 744309783, 463931716, 226931452, 860166566, 33704112, 940433055, 546876688, 634981406, 138148050, 963738957, 668721793, 904125503, 715632749, 33973900, 108408964, 934237604, 871948336, 961199170, 548899580, 98407511, 870848156, 369324686, 470149639, 460797153, 744723267, 818246066, 419314951, 467972848, 551991705, 506257491, 592871740, 168693206, 498602104, 150714618, 263872903, 854697910, 992811863, 22121691, 599758693, 858166272, 948816246, 464554481, 341307748, 810763772, 330135761, 634667228, 881450323, 341569640, 346516408, 480491977, 571175093, 40999451, 82320595, 337826839, 402475003, 967449439, 838217512, 547475729, 766662025, 404798778, 228491050, 307912181, 291093875, 989601997, 382987653, 578954045, 177890679, 902263382, 468397471, 927920631, 472962753, 221303845, 289914143, 635290200, 291112065, 657831473, 938268744, 895622682, 397449355, 444530197, 451711155, 917415163, 586145278, 943013619, 347357813, 592202220, 547372376, 981031932, 554129171, 298163013, 75548863, 789934035, 264015884, 195176251, 760981046, 682513018, 638154964, 540353442, 926586424, 735801284, 495470516, 659863533, 544293670, 236384977, 172558051, 592257834, 153745099, 775009087, 217806336, 401200982, 834647561, 273022818, 497936631, 377617803, 477664292, 200274232, 578028211, 110047657, 921365630, 248060465, 485625801, 769978219, 935928475, 429880846, 99619147, 822510485, 960808888, 892616296, 378516413, 22806623, 504201113, 592272048, 535525551, 660994523, 66768340, 513210618, 596870759, 675326374, 506390044, 603697888, 128631891, 165719948, 773009208, 416238425, 797391405, 742433817, 146021504, 141645015, 442632883, 591467061, 686408276, 908353937, 794759910, 566880150, 176598852, 53509098, 752206419, 754926129, 35773446, 925126663, 241632301, 340551754, 96333231, 911338034, 302272424, 607383452, 804556631, 969683137, 481034119, 862558706, 736174245, 473022408, 851766599, 27730271, 531775089, 986776071, 506865631, 998230796, 200772179, 988108393, 861210273, 517825208, 379202496, 304054691, 763488990, 13297912, 167232794, 600750241, 317225040, 464021976, 997187776, 34789914, 647431773, 922256433, 823742194, 792839868, 385751937, 787308400, 55191033, 180633490, 889438819, 684134544, 394210397, 981592482, 11416387, 836575872, 744290171, 275323215, 544260185, 211177445, 624691353, 566865083, 594550828, 990505188, 958531627, 986135103, 183302762, 822676727, 479772269, 295249961, 573008031, 176317009, 73964140, 71560969, 487622264, 13974977, 258023868, 586587374, 351971683, 728793296, 568606739, 117859925, 186902706, 719265967, 574749648, 481413345, 158580295, 198420235, 540091171, 901661819, 153093862, 501351007, 351246179, 234953018, 913962910, 824969484, 740199420, 569554593, 861377489, 29085495, 69644599, 973214034, 345462304, 895805641, 295003440, 793350109, 573624736, 901223715, 363873081, 991154815, 492913492, 74138759, 891300893, 414232421, 873813730, 831404613, 41874274, 832509043, 296634459, 719503430, 766558247, 584307045, 138050480, 388000074, 903586988, 265622673, 465149462, 559823350, 998771006, 608259773, 245861409, 67683202, 726624681, 115463672, 27828916, 162777456, 956638820, 662024422, 880022110, 173515551, 299794751, 500968308, 122976199, 5984755, 182141407, 517812528, 464082195, 214345755, 833473359, 315228392, 886805446, 633406400, 701338116, 946935456, 278467058, 440820742, 534638906, 757376226, 940903395, 233185231, 420585888, 122247467, 466423017, 139483922, 134738791, 62466117, 682518284, 82572212, 140125132, 988660223, 125069369, 874351823, 173890975, 913727384, 953674904, 268086051, 850048855, 668210341, 181341143, 618617484, 828340387, 980454740, 947167104, 533575640, 606201896, 348932017, 820680242, 47013459, 831126264, 721962260, 378542126, 481328195, 795323453, 499181646, 859067676, 776519514, 624881100, 517104616, 265142817, 578841295, 706957782, 467233763, 614512075, 313134334, 216093761, 5059008, 204104029, 856110913, 481311654, 431686824, 637330184, 363211505, 780497764, 926947710, 891508882, 753959243, 288004955, 916609973, 609209132, 410728001, 889682248, 538683632, 95378204, 837732251, 753439757, 172199323, 73539544, 976822221, 912772349, 827709143, 228561940, 321163830, 700382117, 179629356, 802380242, 157655159, 136482184, 718874533, 806671533, 905900562, 339717994, 400140054, 710291052, 130665908, 510306894, 582245849, 872563333, 505035314, 559106029, 755303682, 36200439, 67869595, 416472564, 118303469, 662181529, 471509001, 64653851, 826676203, 825260021, 171809903, 610133622, 904443933, 185254754, 829920139, 435488261, 436861508, 149477454, 148627776, 226104369, 823542290, 164048053, 278609969, 283053480, 359633991, 716396555, 643628770, 426444930, 518681130, 910777684, 114109247, 857629106, 138524196, 384488753, 504296224, 204443765, 883426780, 181498807, 951089773, 871861342, 289450586, 450279027, 630685801, 849968837, 266515223, 96790234, 848948322, 404986180, 491087263, 463118944, 289978030, 295088777, 827051533, 575008555, 928865371, 847028869, 403812060, 901216218, 406909165, 525703608, 875900797, 854530619, 524404984, 871399420, 46459564, 730379582, 40980151, 101208218, 286718624, 638761333, 205359354, 970787378, 947803292, 222487976, 617265660, 476122369, 662498095, 380874073, 789663867, 604134982, 848519929, 393888403, 657297045, 444396223, 819845065, 857858182, 766166571, 343583032, 477445277, 625737509, 105337692, 48914282, 781823814, 621725392, 521440471, 954861703, 365039873, 194615952, 2052474, 3130336, 866216969, 34105122, 544476219, 91018503, 759274708, 753675807, 933910797, 766688615, 70905309, 47157904, 985876055, 214869461, 491508056, 526769371, 758879585, 396578462, 464665071, 758769341, 596116226, 438804878, 646503664, 970167676, 360954191, 844226975, 832939060, 828421952, 821051688, 730131563, 165578602, 913744245, 380897874, 775255951, 152749873, 417811936, 592034236, 710106698, 982276054, 754958391, 793041028, 40265288, 648465245, 729351484, 842750196, 203667496, 316560468, 207154958, 795526543, 100302813, 417159244, 575841088, 340962138, 75318612, 149557524, 532223403, 675459721, 333337843, 724895587, 47501697, 85836367, 294917341, 713606562, 221045417, 616004379, 950538947, 736688346, 993831065, 771816869, 132302179, 812509100, 423672716, 268261646, 447550677, 171096990, 17238268, 955666915, 624525773, 142810985, 68958305, 631192415, 670010969, 563595673, 721174124, 311796219, 612328942, 469466851, 156201517, 837355378, 107281925, 280748946, 732209823, 109434748, 729256729, 954053468, 646510406, 422010540, 815049772, 108276779, 508163910, 606973591, 634606769, 848207532, 829640735, 25922924, 668395669, 871850742, 538853395, 946670481, 31976777, 864725967, 231309575, 302319299, 612006145, 327357098, 262346963, 610465444, 813716458, 893630566, 108486846, 917130207, 802107597, 298126345, 167753165, 187395668, 369532762, 139472315, 186843682, 303465833, 209069354, 152654457, 531959281, 346790607, 150166255, 848992220, 884146482, 888885299, 104304865, 261786257, 776377519, 509602101, 808040746, 782535468, 654635420, 451948874, 127953552, 444950989, 778379282, 567429799, 538281016, 669083122, 503301231, 281053660, 849538819, 40759152, 601514138, 523863341, 198181387, 162490605, 604767779, 234583576, 457842429, 533956397, 157106526, 833153818, 607936068, 801415064, 62431424, 931143948, 814859806, 780043233, 858448928, 328526207, 754723733, 779977652, 23580008, 977038398, 750285211, 562714563, 234934664, 526004260, 641599632, 209009288, 608364233, 399417148, 72253006, 688883679, 160763134, 62393845, 736609556, 433112449, 668851313, 413511525, 917355683, 510898642, 412884387, 732314389, 394976635, 459433084, 83275404, 544674274, 777320052, 212980350, 120971239, 455982337, 606103265, 822005288, 632091111, 931550251, 568531252, 890530396, 416476095, 11548598, 45230662, 378220311, 119628133, 766602209, 27150365, 96559479, 879391755, 606579408, 836784294, 817960871, 211441281, 101727982, 73127355, 80476523, 817091416, 625784516, 566033612, 370634296, 284652231, 770497363, 7761295, 792104197, 635439549, 666875927, 911431373, 691298469, 545327568, 288934838, 349511085, 460725834, 670136182, 350027130, 634926857, 841092292, 560426148, 522997212, 943191733, 916185039, 889417351, 891193417, 767232458, 757969413, 194825567, 607540714, 352592382, 894179670, 248799343, 124765119, 944552686, 253404685, 713946632, 330809043, 957032512, 907911325, 21733118, 260329656, 558097167, 19966050, 187418053, 853351566, 181719469, 799485106, 52656556, 753448127, 763195487, 591826229, 679441821, 379794309, 68028530, 612264412, 400845548, 479402806, 300723689, 141752462, 952676832, 916939975, 900371764, 728095923, 633673503, 271822165, 390110161, 137984250, 663930043, 652894995, 638429662, 333908746, 3868692, 457360001, 617547344, 195912946, 903027050, 865896971, 934824262, 437706004, 989537600, 584213511, 107318246, 301914651, 160417246, 488993280, 944196935, 265324063, 882369388, 278822287, 58844907, 961704674, 658644176, 899567458, 595921961, 694313826, 146973430, 672439715, 569265871, 991436395, 150840903, 271520207, 178145651, 41565958, 681555026, 599093429, 43465770, 231694086, 330123499, 305209339, 915728358, 364414862, 696776574, 43228756, 121979769, 275670486, 527647971, 285238234, 427533658, 42110028, 938521145, 949912384, 440039175, 872041772, 279110898, 543178136, 251771478, 705471971, 703965107, 665401902, 333586435, 675382856, 910235522, 487759944, 786522662, 535281603, 710109016, 770499752, 520292123, 412312749, 736469748, 27007102, 138994829, 487742949, 276513858, 510517743, 271253521, 295235215, 47366166, 919430101, 432182650, 134694394, 929763420, 6660292, 827612185, 282252986, 408639877, 427370473, 410182710, 232741607, 462382277, 238339744, 193739106, 706051620, 436362394, 240348602, 682685255, 797965060, 63727529, 536121411, 468313704, 498431217, 676914327, 515171142, 795880893, 356297298, 155122623, 710829930, 811152648, 345362700, 879899206, 291430928, 312299502, 769964964, 823486234, 290056479, 411836626, 860962232, 358192746, 4705190, 970931519, 662386329, 128281560, 875167950, 171683378, 774011582, 314032456, 59184600, 574047311, 715903153, 246515552, 234854803, 366849093, 58201980, 70198622, 151927874, 212279751, 532345458, 16904294, 420403507, 116459530, 131424759, 83417322, 979596542, 706861640, 995654808, 457308567, 472842975, 429293048, 843856010, 406930432, 271306986, 476947008, 52016414, 308068350, 281324287, 718882398, 716784502, 167635880, 888134847, 708770419, 375558334, 140055066, 315613442, 436941691, 460084188, 981759090, 836682861, 622467841, 946071166, 795574240, 529707186, 250227913, 360434517, 450988743, 604973354, 514957988, 779444253, 697823540, 708523925, 925745183, 695678373, 612862473, 319816312, 382531564, 52081791, 203714515, 486384576, 229025383, 83384610, 252564805, 347130613, 944240316, 784112251, 513091594, 657184169, 234507575, 871813333, 461606654, 644703064, 85949410, 778712989, 55486482, 187542890, 169721757, 264797300, 796391159, 949740535, 515553215, 437680851, 559020067, 673466411, 888874804, 307562646, 773036429, 825961, 837654417, 311140473, 119534442, 53731277, 843166179, 371310634, 188047367, 637648371, 425009302, 806552048, 592068322, 764604594, 47305576, 886205002, 513241315, 964164056, 911400748, 903973495, 177718287, 340059559, 137770038, 685305756, 628350412, 405892683, 643743379, 832065789, 31583905, 334745495, 270016185, 986500111, 328373713, 764017310, 861330376, 207205379, 797069244, 921216749, 946668642, 580149293, 260695108, 754015947, 750150365, 543252530, 198165469, 368305579, 765443281, 139581147, 236926163, 153747176, 435561650, 166767943, 153444754, 311053991, 938494313, 33736877, 378724170, 111936915, 391368439, 366344893, 561186809, 543234338, 936230702, 622989122, 391500141, 670342298, 494920087, 977255380, 29072592, 967666292, 510457590, 382839583, 753359534, 229209135, 672153751, 604921009, 816626432, 941674791, 7914079, 950832140, 712106919, 31279010, 781174955, 226265953, 397960091, 701945927, 791136646, 625366074, 741821133, 152284250, 536463950, 389803819, 812487489, 92312999, 901707421, 856680802, 215656539, 130045840, 612572292, 751005934, 714371524, 215334057, 205235903, 241471002, 578441951, 41882332, 563849641, 840502731, 342283856, 25919611, 834523674, 830787727, 117950528, 659341706, 319954081, 481522004, 559454607, 511879386, 829357707, 24399770, 309346540, 313816725, 264489372, 725909751, 675409756, 379284700, 734963479, 567058011, 581433204, 713974397, 51851867, 752387517, 647801196, 870031783, 203290927, 448295487, 347741452, 94008111, 843827575, 586221914, 153591374, 783953576, 319365887, 812564933, 607580466, 197823193, 563564239, 398747377, 467012935, 297452161, 419303821, 433387452, 164941483, 919699252, 123097908, 653996073, 718285760, 97636441, 496529649, 311473499, 618936906, 899136404, 754433735, 716317643, 54977060, 151144135, 578254488, 143550916, 495925941, 262147351, 800700334, 998953166, 315550565, 911300957, 743864102, 21233998, 692355565, 40327130, 78544196, 511036881, 215162872, 526271639, 880471224, 239820376, 680628659, 247427326, 698375909, 986020035, 591643689, 668208471, 890558764, 750609808, 758726021, 72117490, 383225638, 805564978, 417709469, 976138923, 89003330, 14312876, 200660867, 684945398, 550062226, 929622203, 945140576, 384270949, 305563478, 910400821, 328505446, 842771516, 606169871, 223361040, 670190366, 156659834, 291481115, 438214388, 420066838, 364243327, 949277916, 589228926, 870020981, 594202351, 778635607, 869786779, 844048802, 722504589, 252304410, 269101127, 127269432, 868391499, 581980557, 72867042, 995701258, 93327298, 282281711, 497651364, 693110841, 390002819, 233896180, 248090065, 758532962, 133189820, 733218523, 465068585, 161278063, 149284729, 410188601, 578232119, 903296451, 135809465, 907344850, 924610036, 881235798, 876826991, 13121331, 659088958, 204662660, 578436246, 365548613, 271107601, 484255631, 533190509, 309599330, 192450768, 179105846, 365859656, 987101542, 482560398, 553010573, 447147978, 203369512, 922894201, 213146152, 710661195, 82019320, 300120583, 41407126, 711646376, 428715240, 490753918, 404981198, 710765410, 937948357, 27482372, 601039904, 79917589, 810835323, 832480659, 626822690, 285517308, 103026738, 743701095, 297327774, 701750766, 8344390, 380831617, 828453026, 541003035, 717502157, 128769655, 792577924, 955622397, 723508997, 751107343, 962659225, 473320402, 995365872, 100981630, 274771503, 697687133, 629570550, 61320656, 181742487, 743959944, 759757497, 119357020, 605759587, 521322546, 566254860, 613238893, 310289773, 71114940, 328077478, 747094657, 582297843, 824169743, 537909943, 859427259, 661327810, 382876479, 290206696, 980716678, 150794959, 759717594, 239204092, 37164844, 362169543, 103379705, 805330417, 516359252, 398477858, 893187058, 320198241, 73986009, 707291836, 506755546, 321435046, 332693336, 415072743, 151099409, 761958845, 23699271, 313471997, 332928291, 966636604, 965717374, 144034504, 963472398, 407417402, 16129991, 60321763, 760052878, 744270226, 80547170, 455027495, 532439913, 417025557, 743521190, 795450932, 587606704, 235465176, 575713169, 621315490, 50138100, 77735897, 913821780, 915196975, 967031099, 127697499, 208283439, 20916368, 792156902, 108936294, 733835608, 677346438, 783745500, 939466787, 718272764, 704756498, 110635577, 674060239, 626291540, 687241048, 468448292, 113852806, 442657614, 462127270, 791584150, 505195897, 262922256, 651280526, 98620063, 366253185, 443443711, 934905135, 927981297, 275680474, 607326878, 772731263, 626239739, 487772242, 246279959, 673986743, 631598091, 209730527, 702121681, 865699188, 384773658, 772604728, 720551862, 617412434, 338211747, 377077946, 803721125, 544217225, 699679204, 607517920, 660535016, 29657971, 586007808, 962825336, 925498566, 772174964, 264055488, 500924066, 955030313, 207826419, 88697010, 461692395, 890633843, 616527673, 947924389, 140346164, 245299817, 207767227, 690345829, 377175823, 272961726, 467983663, 691101301, 353464471, 356126580, 628934641, 661140537, 779155113, 591551044, 779940063, 946787464, 613675034, 348478589, 203982715, 146297355, 151255694, 525669086, 35919068, 523041579, 96684077, 75572896, 29138510, 136461305, 216498237, 702078857, 835146614, 246128864, 44096056, 733710085, 352457842, 992661946, 112058277, 363305741, 772253448, 408102553, 351875697, 239074289, 723116228, 543885579, 688885865, 589429200, 679404965, 671756211, 589445077, 101777200, 534935549, 206039647, 87739002, 600664306, 78063017, 233233708, 892765853, 284711954, 257535145, 520761449, 654962128, 974824518, 629132639, 694429209, 537486324, 935827341, 746895778, 574985536, 595235706, 131381916, 361532003, 327731310, 310590927, 220458319, 152939098, 567418547, 267206521, 29126018, 750113096, 6550830, 177209079, 705711136, 373122387, 438796062, 603365183, 237041058, 731682055, 543520733, 705962706, 93265229, 737799339, 648962808, 613336341, 368022360, 612058107, 168612607, 740098068, 473255762, 17753024, 126633214, 860713209, 206533640, 786616525, 575635555, 481538624, 732781021, 250175855, 918536692, 509839188, 64856786, 674243333, 850325349, 334882472, 961132927, 773632737, 814729463, 396284523, 16124388, 582402467, 534766829, 906730464, 90991423, 891360413, 199539387, 457338363, 299735117, 240263546, 504562327, 797422303, 773054717, 142021578, 72212492, 7445058, 338568852, 951304434, 776412321, 141045858, 904132283, 705991570, 19690327, 730721180, 143872495, 291533963, 767245588, 335460589, 35509458, 191683478, 783552540, 687609281, 192958864, 959935383, 382196175, 176928978, 965339308, 789928334, 15000586, 174724444, 447359195, 485667142, 824975282, 154891394, 664213084, 748644367, 228360072, 948257037, 276768827, 301670090, 141450706, 196617594, 587089176, 753277281, 482338517, 51322964, 10945942, 484073490, 722640025, 703154104, 396346638, 42310283, 217019345, 853282171, 401135313, 864539516, 835919284, 695053440, 692104504, 307730355, 487770413, 389339119, 659385662, 427454007, 294055709, 684372783, 676117148, 307826489, 790149543, 828684033, 973812442, 689673047, 562343108, 872423465, 147788661, 759389481, 482818873, 846576095, 659886983, 836302273, 274237026, 721441088, 436104907, 430791615, 105152135, 181838353, 404333656, 803532260, 274333249, 531871566, 455289070, 245266094, 686710820, 875284087, 609193680, 399098402, 305968904, 445769775, 271595487, 207042857, 241972519, 462586562, 386795680, 435387083, 114578882, 989015496, 93834446, 394019151, 132480282, 917221539, 391337857, 164887194, 775442799, 313058432, 136632184, 741495689, 290048478, 18592929, 881724033, 882822656, 985936355, 274967145, 293622706, 819031656, 635152377, 570297741, 704991901, 200729726, 273172856, 313736375, 445702669, 411437415, 324791537, 454172564, 94351576, 112702769, 395284802, 991331537, 163436372, 202219981, 435048310, 743543899, 828023606, 153889120, 863026958, 984505110, 798407996, 604074387, 423047908, 948463951, 396038529, 282712532, 758941356, 857889373, 774821247, 743775072, 453638239, 702924887, 362092796, 777333394, 986644090, 802357549, 18411561, 924193558, 9003312, 292589645, 808651178, 684748901, 400135533, 536169635, 952502120, 910148282, 540667885, 801360983, 962770904, 893078421, 869921911, 729669481, 428754887, 750535329, 282319956, 353556619, 34137808, 935631757, 318364232, 867047752, 286634982, 414389254, 741714763, 840097089, 209263799, 583045874, 107224985, 500324249, 984430620, 800981403, 518338947, 716369271, 71549375, 976535764, 944934751, 483693858, 871381482, 35918035, 420802618, 119242755, 770521228, 392084173, 63704560, 141093795, 644941485, 757272918, 179328182, 790748419, 602221355, 810480741, 412296007, 956823110, 902762314, 54387504, 298789347, 603980954, 490832177, 683739892, 866460626, 205809426, 738612865, 275278746, 770063822, 600805980, 632930959, 650355416, 849014368, 34868416, 881321912, 753407620, 809237182, 413915183, 106022455, 379593657, 405031864, 581620643, 408795750, 813043482, 674673308, 614445567, 349104607, 880529980, 864883686, 74234849, 324832206, 587430801, 793582743, 184840561, 157468333, 585710775, 686441194, 754556419, 691119763, 70762440, 336137893, 983333609, 939318498, 624052482, 466615419, 437740720, 420342747, 421150505, 60108146, 491686901, 244386895, 872140036, 995168768, 242676931, 919834595, 253004417, 869829540, 579846273, 344163271, 315014605, 399082996, 214913153, 483789690, 284412423, 693288607, 325320542, 630376545, 938273286, 567162941, 500369201, 518263689, 761066743, 109393255, 515227741, 845179678, 742938176, 665978439, 887247053, 87423133, 711822190, 920841806, 181631950, 886296531, 769284642, 871175389, 378813789, 548287798, 902819446, 121697943, 645984212, 553235351, 129255446, 2005898, 924084177, 44068255, 772256295, 358741801, 453249401, 221321222, 925374243, 199082821, 114842572, 953266800, 861875192, 772175453, 583002189, 186842903, 788711537, 588831714, 874821714, 545403384, 595675136, 177858888, 28907595, 7432490, 605684305, 417092244, 362709856, 608722773, 980736041, 349848040, 558112767, 172950333, 796900261, 474090327, 810302236, 922283126, 926180643, 373257931, 403606746, 345108411, 511463678, 908680911, 790542389, 109554804, 565040053, 178131332, 796870898, 556457545, 587929733, 874641383, 738458853, 692214405, 998955320, 276059054, 24084449, 437909344, 370793992, 602480052, 182699462, 951002343, 958250665, 449858068, 618946121, 59703091, 916419851, 502696059, 432956789, 5321711, 449169484, 986767381, 423219471, 405309625, 995337267, 601053182, 751197231, 550767424, 833858969, 913382736, 307126318, 225831692, 831770797, 593027839, 884592782, 215124319, 242690401, 977059862, 432122953, 390750219, 363250897, 999642429, 451530548, 831383177, 67978845, 280644709, 906878462, 959283417, 270314655, 359877090, 571302505, 273195987, 478339850, 495181961, 7342514, 520785324, 74380801, 780239217, 492850118, 376931010, 723069238, 922770547, 545938125, 138085572, 905125703, 502757137, 11612895, 20929424, 802936606, 346651230, 891477198, 146491859, 554276148, 457382138, 327845273, 250788577, 873798309, 593369578, 55127037, 654304037, 963113662, 637693028, 944925264, 864247595, 292771132, 394865986, 773539812, 751889554, 860099507, 165840459, 122459990, 373669637, 103057448, 277397970, 806750534, 571678650, 418353258, 721219722, 12540564, 913778547, 962751574, 924583624, 148944819, 323995819, 966737494, 574285330, 679292627, 507000047, 472582652, 804785842, 282380258, 585243756, 252023238, 591397975, 679728356, 517502347, 451610482, 650897008, 543401150, 410611287, 942997181, 853668624, 545620646, 464520981, 35216388, 988662339, 884980003, 302939009, 858733480, 914032411, 403232374, 964196795, 303948764, 200861382, 235262336, 779159037, 792619413, 903470827, 455868923, 609577312, 348675565, 256502428, 485252609, 607686329, 908963439, 298909343, 733436143, 353167543, 697162993, 235899951, 726133182, 584077781, 610641737, 783674301, 462768593, 683439255, 303017320, 394785946, 73934605, 891234004, 969458716, 115166, 808793960, 93864622, 174266953, 158329885, 823497632, 755852113, 174904068, 948684255, 798912043, 398100214, 610970927, 967785272, 106481026, 712143359, 223498207, 433867256, 261643175, 87827985, 637301057, 368355267, 956951492, 798553355, 638005967, 874436935, 945068190, 654544723, 414455320, 868975605, 979631491, 14239201, 819590801, 508485799, 959537834, 572635018, 978099362, 651370615, 236642041, 912573328, 569080725, 909849955, 186290806, 418653777, 310610196, 265573731, 230164408, 222234172, 330316175, 472005628, 140086200, 604818304, 819662145, 883357154, 514846981, 129386941, 975512387, 57506491, 59070894, 387107260, 821423433, 627142012, 114633913, 988152255, 203007718, 302664960, 918843443, 267061414, 441620121, 915904390, 495305525, 898140666, 586845494, 206441261, 675710009, 307755085, 213245461, 65794512, 696526925, 454192961, 982940760, 373568585, 599524433, 453229260, 274412031, 649348104, 435311071, 604800876, 753440617, 731359049, 25157803, 843782452, 676155885, 240623939, 515304660, 55122522, 515042358, 625827559, 656341970, 991949657, 997979498, 734832789, 872756851, 343212826, 680472501, 890757729, 18196517, 595341561, 598088328, 42201945, 318862527, 454892538, 183161821, 428823562, 891677430, 104481697, 676951926, 235762400, 637988379, 966167341, 564424345, 833293232, 374231671, 450027312, 96111248, 493729539, 183588558, 27943134, 212907866, 177044296, 243579684, 569241764, 93851338, 91562937, 567814391, 942740573, 756927288, 539875161, 436264093, 854800868, 586344914, 879616164, 90739381, 42682123, 138682071, 733044496, 884058973, 613691022, 318208344, 415170670, 644160752, 546484718, 329091041, 988034811, 877131942, 491520609, 601559481, 570233073, 184104926, 418478950, 267110260, 930263581, 240177623, 249198974, 925053325, 518641561, 111025709, 906635354, 837921442, 798579036, 943187593, 757915305, 643280584, 572177428, 190330366, 969003500, 548714671, 88569478, 414895960, 70107616, 827941820, 496927608, 24452616, 700232619, 985596379, 243540544, 962361302, 376436190, 386290540, 173970914, 253166726, 832519639, 569738332, 299402596, 102077152, 325320263, 733589976, 537396670, 438341199, 433174279, 568439668, 320991687, 634446740, 908107311, 751468446, 948136991, 683364983, 439012847, 453435747, 266923601, 984346047, 190475326, 415858679, 979338106, 908359163, 514413635, 918141913, 604463262, 288005446, 71011258, 538770873, 400981639, 421677478, 994467398, 556950278, 135644643, 139202320, 568589178, 458247503, 397683661, 797170372, 547439995, 567518170, 462177498, 702900342, 101471612, 38560130, 193627275, 387783675, 804922683, 700288556, 959071491, 598471191, 216472848, 948879298, 83455865, 112910844, 50573862, 357433874, 64558013, 922823149, 779069504, 128619802, 838564097, 795658450, 479823865, 763734851, 771255458, 660298486, 206087498, 241971126, 332063220, 95259955, 564965017, 521140826, 874678061, 45877451, 454422953, 328743204, 104658906, 396029010, 105964673, 438013953, 513777319, 980167852, 501978368, 884243015, 98183142, 674594560, 245257926, 842095420, 790786275, 131731976, 540064262, 789646672, 816348976, 63492267, 756813582, 867718841, 88769113, 503069986, 154078396, 676880540, 148102623, 765541837, 372501706, 294760059, 207023901, 171518157, 695134584, 532778844, 770557261, 630938969, 141140533, 788861976, 714317702, 811870814, 336051275, 490625025, 867529972, 537367003, 426733704, 442065264, 221442369, 747782246, 89532466, 830505491, 388577143, 584300168, 919262603, 248038224, 132310548, 836549546, 126095099, 901137218, 978963564, 184502151, 464271549, 927237329, 345124003, 438290752, 160700531, 299091292, 201380213, 854278620, 465693915, 881242077, 94313715, 380381478, 356687041, 951462625, 499040227, 78759796, 473477436, 94096698, 622549106, 536914977, 927077031, 833190509, 368680321, 34407326, 922802950, 329510561, 956825256, 983229904, 802458358, 849654007, 530545294, 565510792, 572272786, 135262411, 794229535, 179342424, 108042707, 71993563, 71811083, 544110719, 255702521, 965129321, 909204497, 206768507, 154226119, 190047038, 989653496, 112285905, 120002680, 176308944, 659995515, 411103495, 565878974, 159250160, 294190920, 924889478, 514721993, 357901646, 30821566, 387828455, 362093862, 6896451, 901156288, 606773506, 9746219, 998838241, 278455175, 672390697, 315107510, 672273397, 930727536, 676243916, 492044277, 506982084, 255656753, 817167628, 542721976, 484340125, 702479220, 609061011, 776578985, 476355379, 855725010, 689755171, 854843222, 161599834, 723640238, 619622469, 772348248, 109967449, 883400523, 120402821, 504235943, 695926997, 684600792, 440331575, 680792197, 677891183, 411182149, 693740568, 785145165, 186738852, 805855305, 407494192, 313442270, 679698359, 821491418, 131906940, 163255047, 82782892, 786180124, 26414774, 298825877, 26756887, 457714590, 210204449, 831444815, 879965185, 211778441, 759589772, 871699106, 429348409, 893917235, 652410518, 85375410, 856150652, 888412781, 518460398, 152031781, 321410325, 719845567, 31883788, 552694295, 887243302, 94834588, 821586353, 68703152, 625268110, 468803383, 953245563, 288008489, 396172431, 526973128, 793341622, 528272954, 516239836, 533970357, 566847940, 931350618, 202554862, 643777563, 399539341, 565196583, 272750745, 329255442, 874982652, 857462506, 749538552, 401784890, 37104601, 106320639, 459597180, 490020509, 947663949, 754224123, 107584986, 808503104, 467041635, 4864442, 579356489, 80501979, 582718740, 89847144, 431682305, 992394623, 126089716, 310582295, 223706443, 814096251, 221420429, 54790196, 988130237, 115717636, 862376693, 569514918, 517312787, 169347009, 846429666, 798679419, 511076827, 41411736, 829977461, 215555918, 678634502, 520540277, 998837265, 131063436, 158418201, 879867393, 13165882, 501319320, 693190244, 818582218, 443702280, 573552695, 357800559, 783268543, 794847764, 246420654, 221237617, 654140575, 333268141, 479403034, 435717525, 533726016, 848046783, 280862518, 416274981, 258685698, 98834056, 699968722, 928484282, 66452964, 831515058, 526791754, 403822428, 438086334, 334715696, 871810315, 368677829, 955562847, 690731618, 117752506, 411364174, 620948379, 300476092, 781683118, 936530461, 799504950, 615218766, 721967171, 377471943, 191431724, 70766285, 477064656, 681173253, 358563137, 965405293, 796420214, 50100517, 253384826, 876606737, 603132813, 611008827, 482214823, 298111892, 354142973, 95634060, 540909883, 990282962, 80332514, 573910743, 735872863, 502831703, 34764304, 214592871, 604220387, 339347780, 877337465, 91358992, 142794384, 964147993, 476910023, 423894235, 163404039, 928074242, 954578382, 287644745, 149247153, 233426647, 39775741, 698972182, 28736722, 668318540, 691492797, 98016621, 382742954, 967443227, 446441025, 416320839, 708147052, 768758344, 815061974, 499949333, 138012014, 509599692, 530755039, 408991124, 271711334, 25689868, 759246457, 516834351, 499516457, 973707668, 464068615, 936996624, 369596484, 42726009, 114513765, 835366193, 902331162, 443965288, 823203806, 772853332, 672331824, 600788068, 833294804, 847054714, 822941959, 23339901, 472016844, 958983477, 22669083, 410553230, 832846017, 805899642, 810874266, 692758820, 685279280, 714239879, 27760126, 768206901, 433744484, 592504452, 819786460, 155814801, 762743619, 188979599, 154763157, 430342193, 369728776, 328600782, 628963804, 74984063, 364196191, 83239371, 149165839, 270101988, 947465008, 365780420, 272759088, 429372586, 166133824, 731401631, 968679773, 640812873, 501359934, 14945672, 890581556, 636796978, 233747541, 305445500, 63405663, 666705030, 867870082, 905151936, 867388368, 959196697, 221431554, 501082518, 991646302, 77044942, 542877638, 35648335, 231303530, 916763538, 581792839, 544891190, 471198157, 415674773, 761245488, 298994950, 891816427, 840244642, 398740095, 712360312, 680943831, 891720041, 334811738, 979321028, 201390863, 951783674, 208299640, 917371475, 176508540, 153525022, 182468823, 869756992, 130069212, 795571901, 726167924, 95061399, 367827522, 677502758, 492092941, 838908174, 42819328, 523009853, 4283377, 427605523, 848674793, 686701136, 564076733, 761746374, 456763700, 794885729, 404841422, 819103866, 97111838, 36318716, 30432481, 190748200, 528014033, 723389800, 814712617, 440795455, 900330032, 313662331, 354826803, 607951532, 782996716, 478347149, 340505099, 444539617, 938993780, 330677399, 660277779, 946084198, 30636077, 676894384, 653015644, 609828713, 175988975, 610988077, 999706826, 668410877, 716926142, 110791990, 205223448, 484496509, 565418560, 787368328, 569323670, 110723386, 252024200, 288249049, 443070219, 943811559, 786703011, 404258895, 969433927, 462213926, 557977212, 298143317, 800379849, 377473551, 503155782, 38619994, 952662197, 835460009, 55917577, 466506970, 563849198, 653219534, 971682916, 619758726, 74796268, 847457008, 227885229, 137877848, 447598665, 252115312, 562361721, 213863388, 743598668, 33064582, 835317004, 836660888, 277195053, 835968160, 736223493, 898457533, 243199709, 652631320, 889534781, 894526636, 720668501, 600205753, 465720383, 675125944, 329662348, 959506811, 127195572, 90785345, 147426624, 449607010, 155204205, 34518525, 920077101, 503569867, 472609343, 784538816, 631119536, 182135814, 866418858, 556951473, 293240769, 402018275, 241374064, 88191295, 840717757, 378308836, 975770170, 18552440, 788770795, 122549168, 807473635, 88403694, 250843372, 692447385, 984359332, 60528874, 977228062, 318113619, 845613693, 255278096, 364189378, 253336231, 676301497, 366990474, 804343791, 207932515, 414276070, 241321716, 563161830, 39714668, 870483659, 175294393, 264982522, 653042841, 672588116, 874888894, 8735406, 554895268, 559701874, 797259169, 396187225, 846698528, 698084690, 203257753, 559263185, 4049148, 60190320, 443577445, 15121863, 581544509, 377090084, 512378303, 589966584, 572479874, 839910845, 63478105, 453832427, 994088980, 396689515, 95987733, 239307226, 350495475, 236576129, 68895894, 463450430, 880849826, 875049099, 159393002, 860748736, 131044676, 144847559, 44409983, 648706069, 963504767, 347633837, 186805059, 30203123, 854742562, 631417340, 16158731, 146396470, 198229772, 154143730, 499640253, 921610633, 336289251, 206745865, 547737651, 750581578, 268276934, 202241176, 441828413, 341949042, 26851474, 919260434, 256093114, 32089129, 72065935, 648177141, 34335978, 303114259, 839787482, 507920519, 700017649, 22133772, 592630159, 491278839, 674677542, 148119647, 358800012, 708663720, 805068822, 355573677, 481269618, 20932169, 528209038, 312727571, 399349519, 893557255, 592476611, 932656595, 648965451, 371822453, 815370084, 372772707, 263462870, 36315339, 18161503, 922356142, 563522394, 979522663, 390851478, 102198565, 242672615, 854341661, 207734559, 485388445, 547422943, 684782336, 316759710, 709892829, 115991649, 738574821, 791589190, 690612380, 702406191, 427534678, 718619493, 518595242, 763248907, 465655346, 133438718, 602921993, 449819139, 158887595, 82263507, 220643274, 454428769, 56566852, 329942306, 167206135, 895957150, 986623624, 362544147, 339591198, 549702184, 676796436, 153100736, 401312129, 531675194, 328998165, 580008827, 566190783, 485423642, 552844073, 728769452, 185886569, 591604433, 265011464, 889790768, 369003790, 956127200, 335562759, 155731951, 553731991, 930007667, 706355140, 515304610, 932531852, 225347644, 296668335, 672448281, 343133143, 904194338, 891192611, 847903075, 190337272, 309394176, 685317370, 810507783, 470806865, 432849215, 825813822, 793617464, 658939270, 377442203, 2305651, 755746644, 816706632, 617323918, 897434505, 449300299, 828528141, 785333122, 424938149, 100822890, 725303071, 651986594, 88887971, 45487762, 589285616, 163924927, 777345292, 820878606, 305384827, 975453383, 875679886, 423615061, 39058627, 750461539, 739419612, 131977333, 439889666, 883855800, 140850654, 927592295, 755259297, 855469397, 362751532, 607426629, 943377403, 937672320, 205286047, 375438347, 20923226, 771711033, 93270809, 210612783, 387960034, 279805686, 999050376, 74210189, 227465742, 1268255, 337972028, 714806794, 613383025, 114928757, 984651275, 563770358, 776385846, 453757794, 328018607, 303781, 498460409, 321905389, 18988968, 757501801, 705250713, 606266102, 672793007, 839791967, 1116682, 117883890, 811885780, 377321554, 357015549, 183493229, 241898554, 624800100, 104130858, 31744696, 76854606, 474593965, 811566652, 885226325, 456947796, 683942148, 796251361, 561026010, 381523480, 23206012, 565282053, 287272266, 101827915, 506255352, 784222874, 214513242, 919415388, 191918233, 729664682, 414463500, 289778162, 661040956, 790180898, 768986758, 526229016, 165775198, 36086608, 154960867, 557152203, 801531037, 443953478, 3999022, 858374861, 277947054, 87754115, 730967390, 441544123, 890707421, 124603906, 240697246, 578843352, 95632016, 821303074, 537357689, 257227001, 909110611, 241631495, 589042317, 881857350, 388771642, 221341165, 606454218, 555916017, 680028805, 102816783, 550453094, 589455187, 492505692, 780401834, 909852563, 756642246, 20182895, 123482676, 271589655, 65050646, 492075966, 647146919, 504485598, 848058673, 641159936, 161125472, 293517083, 506990829, 236865823, 159125742, 390400203, 795809980, 41531447, 611926498, 347719342, 981652528, 836956954, 733855488, 784618224, 784738230, 665119219, 424214617, 112032507, 33092102, 86392028, 85146431, 924386913, 835794725, 635835792, 147425836, 536667651, 407320457, 586656608, 492753212, 908420754, 63417852, 593540094, 754311972, 122719737, 915600487, 874375779, 299559448, 83708675, 649386352, 813712166, 701832616, 507636631, 262708252, 426679941, 215403940, 842774335, 842154790, 373808833, 238188924, 366698062, 747934728, 120379048, 890246339, 374446716, 216410524, 948246450, 941428366, 507030627, 40408970, 344630483, 462618273, 772916226, 476708634, 177503950, 125875816, 145983044, 339011681, 813655437, 434628067, 336101909, 888150495, 908405647, 927435721, 721818550, 952034495, 996227386, 447466930, 389036776, 996387048, 172055817, 430582111, 315734525, 343107562, 460811225, 151873705, 47429207, 641187872, 650034342, 668657404, 875706690, 510185099, 77454330, 403085339, 400389209, 116677637, 179653507, 186231011, 464157010, 743119452, 158251434, 770623968, 992572537, 636268936, 554775105, 472422327, 724728483, 463527483, 933721039, 188168466, 737336369, 130657553, 893128058, 232835901, 607893468, 644007978, 584638705, 57938395, 485310217, 818055794, 353190156, 416996189, 441561152, 160449046, 792226572, 679446618, 36716245, 630929358, 276169975, 947306760, 530529665, 874334135, 388051980, 275978536, 895392635, 561271796, 232460263, 924845579, 788881366, 256123854, 392371924, 598760829, 451357492, 116371404, 324055487, 28213892, 850411546, 944591518, 550970986, 745232739, 226552489, 719581837, 151641182, 27987218, 979510639, 301751686, 391640876, 415456653, 411139338, 632895581, 826197393, 515901019, 179437059, 117699395, 215995871, 55801105, 371093530, 721523026, 703974712, 95544390, 561787282, 139019092, 620273833, 23702472, 979581035, 697647190, 331933167, 452920056, 8753261, 366391787, 603998497, 900906987, 19434087, 828101844, 932729841, 898969648, 901928971, 325504806, 551341443, 481502988, 71130191, 799278450, 718734062, 469273172, 228450793, 654538570, 586974236, 59048397, 663386197, 98422426, 116225640, 913685051, 674498510, 888351355, 941553192, 364397042, 956044540, 990558399, 486791024, 124208034, 225958507, 394044363, 64182287, 8129514, 408343339, 128932941, 453128422, 279372209, 488862244, 625240843, 864655832, 582503560, 33887641, 17750255, 516033079, 278105169, 376376834, 591784987, 887077112, 472402267, 882548815, 64215752, 191617776, 170251269, 887554093, 942698504, 960352471, 500683236, 466443458, 735517470, 299695965, 34152143, 70907636, 724804219, 796830738, 525875647, 208895860, 194901215, 897065528, 83834078, 914234306, 44833898, 455755314, 14940457, 563070308, 842011108, 775899537, 631648070, 790818452, 965627219, 425333157, 580136, 437916879, 872931623, 773671356, 939689956, 505294945, 765675061, 195513907, 128351721, 473347135, 541544396, 471351080, 960719731, 340042954, 423818063, 27586641, 450253475, 188350198, 309735667, 343809525, 412060737, 488694667, 225823736, 176925126, 948447019, 120292959, 517180178, 648913753, 912612669, 19310051, 364928227, 525005611, 44664959, 415580729, 206342662, 774388242, 856698892, 636549594, 125307258, 939359771, 57797461, 955161776, 908108941, 640119532, 637472888, 821576251, 559481804, 871077925, 774069793, 515358118, 832995313, 976400514, 51087169, 349357299, 275234389, 400060815, 848308307, 642275910, 294512680, 996415410, 701247651, 839719903, 707829716, 423359442, 940895136, 625026859, 67621275, 463677184, 999341479, 12879248, 961113344, 909195655, 593510617, 5967819, 656039480, 616208122, 259406857, 283841963, 540718336, 168849928, 866866855, 594634693, 535749554, 290012321, 577242257, 161412914, 992113594, 466056839, 285982764, 572884844, 677864412, 498320369, 357285095, 548553493, 615584316, 361541010, 630755396, 466020089, 560491423, 288399517, 430638563, 380013079, 791226085, 209037035, 599829480, 29081649, 778040448, 692896957, 778990709, 839870318, 90786003, 550344664, 16916425, 275261673, 624902558, 440587684, 810573, 324238403, 84189107, 698338206, 281649777, 242197630, 368078664, 207900624, 910137206, 879597772, 773454403, 786947828, 768476585, 483421786, 408477948, 825299100, 381265108, 842967769, 352865611, 83880036, 836207215, 857783081, 21235091, 431113056, 571114055, 818000352, 565204715, 164167420, 853232598, 785939065, 198678345, 893899717, 754404785, 553507971, 771769152, 561685258, 652272569, 775571082, 647883511, 437888503, 206820085, 713932805, 501325400, 901373931, 768265774, 353451480, 471846233, 482195989, 383696593, 662289349, 815722130, 516586989, 168167170, 446015929, 30130835, 422759410, 685322951, 974706018, 247208109, 791247538, 500946663, 681869892, 216129977, 510328708, 296762846, 264088812, 808258034, 393751270, 297595712, 313668136, 457786149, 43461897, 740512172, 84338241, 382962713, 759364519, 907941563, 451650900, 450811145, 673470387, 255114717, 303754499, 218159363, 894315155, 842362679, 679728283, 978209959, 216099285, 40356556, 903649842, 269720453, 532211978, 142225627, 657062676, 698169251, 345886427, 311649318, 426893543, 371148292, 311382455, 428838081, 135024847, 219130112, 279213727, 454470531, 915357408, 401298167, 65583313, 587434510, 399384109, 176029607, 372742087, 525660936, 255304758, 782012157, 9011452, 773570878, 21028578, 907461049, 662789542, 578418026, 36902621, 248512162, 620245880, 297199865, 303610140, 763327956, 465962999, 121697087, 805959417, 951275565, 512183113, 625894058, 982171156, 418109299, 869844056, 563200479, 169661728, 910441741, 354440901, 671179465, 849997857, 669826292, 271707668, 805982046, 724499231, 683178455, 356676505, 74157933, 413495246, 799066031, 40046541, 662465596, 423929015, 389949861, 980105202, 408959224, 984160312, 480635174, 618597355, 695425287, 588760069, 583453534, 542508859, 419799256, 213932330, 8643687, 814861177, 396435353, 651203969, 868395098, 699532390, 720261718, 612491203, 647562544, 579208372, 220634313, 315311953, 824357709, 632258471, 426956052, 219687281, 34671055, 595375787, 382388442, 927180820, 660955077, 182959543, 672143748, 66595710, 953444978, 330006148, 27746340, 171239307, 32166187, 921637519, 63466762, 3339317, 441645427, 176590475, 222351055, 579518477, 10012232, 779897911, 464426285, 781127748, 616155205, 771682937, 820518741, 312645194, 628692996, 636034350, 873127189, 466499859, 409039714, 946900374, 849101288, 134356794, 724109984, 393463864, 636579569, 756591124, 563229328, 570807519, 597216967, 273542796, 721137608, 704536553, 420526937, 524234986, 715676190, 195687628, 203752367, 43358446, 412530558, 758751047, 48483053, 624751516, 33880733, 249511792, 96800096, 124321198, 585473444, 57701122, 726847955, 574943490, 263564354, 194385592, 86454658, 598753090, 132437080, 787035712, 30001713, 637141180, 790485856, 203251672, 760969709, 212945118, 254981126, 341441288, 34770413, 319758764, 974518210, 838749749, 810446463, 425621607, 548512440, 728930928, 743397904, 615089276, 572287466, 555686945, 52189051, 256500307, 413998665, 686778084, 890461428, 141992740, 540233362, 992417793, 288661757, 876827172, 243127279, 309984927, 632998535, 737081529, 824494921, 757494221, 496203689, 392568938, 565165534, 278516159, 294506339, 418976927, 426104948, 811960094, 343478195, 456844066, 611107040, 518449068, 785247200, 263219756, 952775763, 910379672, 90449435, 46081735, 611878562, 938340067, 961104739, 631945960, 243604018, 149705628, 195221447, 3061831, 340698516, 818262304, 808249262, 966753055, 841378219, 147418038, 14129621, 30162600, 825814824, 308098123, 228375914, 403620280, 684898930, 590465274, 188067642, 842423638, 110720409, 551645013, 549568145, 445864597, 307546937, 817916992, 251073534, 8032193, 253162275, 67436182, 169750472, 857566061, 607705019, 401446327, 465563113, 897202006, 417454251, 164643626, 245210896, 192955801, 583775874, 144718244, 96605261, 787970366, 336505643, 636137556, 556249495, 980900108, 413047423, 998525436, 931453139, 760303301, 521340177, 198848221, 384899893, 433043213, 148318336, 229614181, 2582189, 45469173, 459060383, 855161702, 585148922, 10791633, 922923134, 285923713, 298981758, 793736102, 370180102, 769429427, 440780396, 414469002, 252385909, 881729842, 933814081, 92056971, 666992735, 184096658, 450628014, 669916028, 139907838, 395010687, 540908001, 641065208, 151043087, 778492517, 821640574, 454379935, 464988014, 937644880, 999630292, 909292548, 2579849, 495086563, 470282896, 907146609, 133664693, 109246268, 570262410, 127918292, 359401932, 515271308, 477135596, 379570938, 501970867, 139096358, 341404891, 196752512, 585659897, 663238544, 788540220, 588197905, 586209281, 316341798, 941680086, 617253023, 898220576, 494661481, 825884352, 702997451, 555981148, 170131099, 578832515, 165904106, 317494353, 969231326, 690886721, 527396626, 724874334, 100235636, 906382809, 311892656, 221817800, 387216460, 34104408, 40878074, 202542971, 623875262, 909426109, 426183883, 616857314, 724440450, 740625086, 730480203, 403011752, 493810445, 769812165, 514481015, 813486836, 15802125, 409271363, 977960080, 218126077, 248189171, 491431231, 304376474, 815898346, 202152379, 403340541, 262170068, 254509753, 788656358, 917241557, 988846036, 717036079, 390717446, 749230941, 711202046, 544476347, 70509453, 976768724, 790349319, 735849018, 423040551, 14605140, 772180733, 375747488, 414925477, 186763583, 218095116, 702490742, 412473473, 418861913, 629103523, 838203252, 539195667, 787596674, 946598468, 240720339, 231505011, 361059534, 902609799, 37994510, 262976412, 649055226, 624879088, 663185921, 556285788, 662285347, 821681275, 12863540, 576441717, 329475529, 277062085, 79029091, 299299285, 395872566, 658574246, 953447348, 351006683, 89611814, 60206541, 103405859, 836432971, 469252974, 780666449, 814296382, 728948830, 853036333, 722392942, 561519600, 449253190, 41818700, 229136847, 850723433, 809319993, 124134781, 9002161, 65337125, 725079700, 28880621, 225114648, 379028788, 791897681, 340503195, 561045531, 257984834, 726536872, 148905877, 960592006, 469280412, 632652013, 431509516, 701477939, 606696499, 181610353, 488352809, 263110993, 891871645, 236459852, 683268319, 845732189, 710752307, 315371304, 900577660, 654038186, 766174482, 886546786, 345898414, 417351772, 33509268, 451077959, 862614106, 676367637, 563075939, 167421104, 643597829, 227257177, 411554272, 411916388, 169653106, 846262391, 674292159, 880781802, 113406469, 415923712, 67289826, 817534347, 752318002, 581784948, 774415495, 493480697, 2177000, 141255479, 647189745, 64498281, 172483460, 138502177, 155446097, 447662658, 410010960, 38422079, 870977683, 82462212, 360413815, 836784935, 293465002, 641089035, 94831316, 440059262, 582056935, 74046395, 319825133, 210539154, 862874597, 979751846, 30002100, 853604242, 754405787, 440428644, 814888379, 166345478, 623293527, 244233244, 216095932, 430045764, 940188185, 523606603, 116746322, 961055891, 30069652, 860443994, 515446500, 198988340, 248035553, 225977667, 685401464, 656924463, 694307082, 660963961, 207367595, 233423570, 360010384, 724378471, 550401873, 822120650, 660574860, 767611986, 663459719, 244573147, 234935120, 244354060, 760976468, 687115622, 433638413, 102880840, 886564706, 78519374, 539340908, 462211009, 29359473, 19170077, 392161306, 334437894, 834669520, 800400698, 920596460, 9025251, 723554118, 210867287, 88792086, 80721053, 818320994, 308080616, 305613239, 115972457, 312194839, 813861994, 411462860, 828212416, 496122786, 726368986, 494400428, 147720882, 179783223, 683623564, 551291573, 880767669, 187346003, 571152193, 491290678, 259663355, 771186384, 921004188, 269420726, 80458009, 398482115, 698229276, 329083188, 706201460, 764960730, 132301797, 462741103, 169906614, 214581362, 182859956, 842055992, 342894935, 539476110, 203599468, 767828667, 631004921, 844117678, 450717622, 400108890, 233308024, 622577868, 518623838, 100728699, 174987463, 724593353, 515921152, 18039214, 76051471, 814529731, 381636987, 676388061, 316579746, 525291974, 611771326, 274752293, 32717869, 988882110, 493624134, 800841954, 970510112, 461608312, 63414427, 853405355, 707535590, 822840512, 509000954, 126870985, 556054722, 141027506, 874842525, 83022421, 8200131, 165514777, 76990695, 782933060, 654143602, 775887814, 817471654, 111989377, 577163012, 321830285, 173277958, 629181721, 17790322, 933661029, 919530084, 96503730, 982017031, 768493892, 455240516, 948959330, 717594632, 252005177, 208381686, 843104002, 796861666, 962157933, 160732538, 132731859, 449094748, 429040118, 88634277, 500707624, 979801207, 759885599, 152493206, 488660341, 537924432, 140489734, 339072139, 149623819, 130283630, 354122973, 671711688, 301550686, 895399108, 558849034, 569808368, 824182801, 865523720, 788458455, 735703000, 10568571, 240683204, 276726133, 796220765, 559991828, 507166325, 790382572, 274536088, 387626008, 116583533, 296697509, 518749339, 807401367, 975473724, 561738008, 293144231, 202736168, 745235232, 176750577, 84204830, 588237475, 456791725, 293312151, 39694872, 259402509, 47182480, 384263456, 494233992, 77516173, 411234139, 101003865, 710884593, 817213643, 116204085, 810271281, 81415430, 721571408, 195271496, 787066300, 272761297, 581539111, 424703638, 107979782, 721703277, 854446800, 187608269, 631944532, 282492124, 254910542, 993681355, 187835099, 601590233, 627366792, 924916822, 447020738, 508487690, 345069753, 663005892, 499071883, 75399835, 364869780, 791809253, 797096619, 730806615, 978853795, 655740669, 391899124, 37975085, 506761701, 283411781, 203374710, 227978704, 122544730, 714281832, 197438581, 295443852, 758477991, 351581011, 137484285, 37161799, 649017324, 648804367, 846713234, 525154739, 124984989, 163087310, 404324589, 815081682, 555498329, 953725348, 223031923, 416473385, 528790477, 276846986, 953783144, 952628408, 556407986, 325752794, 344218503, 719227376, 959923210, 793274098, 983923790, 697108235, 265310693, 404720754, 44139422, 483736786, 292459936, 962752245, 544577401, 888928735, 862177486, 468895410, 886828110, 529949708, 96092881, 282916314, 530341716, 582066523, 114986439, 576192328, 733860319, 539929671, 473478458, 318837864, 505100290, 366452576, 784334530, 659178321, 260087396, 986685455, 457758940, 178844902, 738007407, 245869692, 658680650, 811774328, 810181000, 632374001, 320700726, 230826924, 462996142, 898464292, 546596011, 600771612, 755022215, 790754446, 266591909, 944863966, 577956231, 954640760, 454068861, 532174227, 169095822, 711892608, 114248890, 459315759, 808512630, 749886440, 94742275, 394207388, 992660922, 342985192, 572022877, 950556727, 923167011, 179616816, 231879435, 753387450, 238079908, 288243583, 985970301, 140637864, 9504250, 560881854, 581521400, 398458109, 912303414, 532173617, 352570509, 503313846, 722456985, 117494218, 162426200, 534014561, 899399455, 447129307, 593863173, 281841464, 715279813, 238422422, 172612409, 402245863, 401355235, 652782823, 404618737, 798751679, 429200568, 758911660, 44437031, 702730124, 516307547, 352339629, 672782362, 590148917, 999361859, 389602203, 434816927, 868211829, 675727185, 718987071, 405222641, 778402502, 450322078, 117512669, 244026588, 977487672, 500142249, 955574746, 10861916, 273413149, 193000533, 95772810, 179980337, 349674918, 703803790, 35598750, 788647964, 663698566, 527076483, 866139219, 808290781, 548544271, 638362472, 288824016, 758393689, 85282862, 278310644, 233623285, 208986608, 111120644, 789722816, 95981640, 201994558, 128732883, 406551882, 870118241, 672608057, 348562063, 231513793, 293576728, 503278418, 447888319, 270776247, 920720381, 352514479, 136414011, 532670740, 794223464, 211362627, 691754247, 724727059, 214293145, 956510411, 744625042, 571401990, 272095621, 597204452, 16828928, 83902937, 748299971, 465466756, 34634147, 84266669, 589527187, 227095065, 426742861, 183565500, 577735672, 723044908, 954716349, 188311505, 830346594, 276096704, 250518825, 881432564, 186792128, 678508875, 449661413, 74008136, 95423968, 438630292, 336557730, 660948072, 382147456, 560731262, 805430957, 266927074, 543319393, 624478606, 840534347, 294583758, 740022724, 206566618, 447741252, 299737949, 483142021, 726415450, 501879384, 903230244, 610597170, 695475385, 356759405, 663711067, 101841923, 931380993, 572742866, 908784891, 667344845, 455093150, 369581172, 633090755, 644599209, 863805416, 473881037, 106120135, 166098859, 690879040, 119494979, 967626036, 357488285, 835347323, 147378587, 789166911, 19235328, 777873214, 559228789, 897590686, 213470044, 108915499, 318275288, 599974987, 358763508, 112452660, 48104222, 736299058, 20489008, 559577273, 620085229, 952091718, 729314896, 581834304, 629813481, 574064684, 779864617, 354735048, 650629066, 30981779, 50727842, 583206444, 949221324, 177667594, 315946869, 701719977, 259663674, 928427555, 949102760, 541260356, 794329960, 579274067, 65518619, 537025668, 236893691, 995627310, 940273301, 3901838, 409022992, 138431263, 548317399, 994051029, 703165661, 134241488, 414793353, 767160354, 304919941, 897413320, 189753199, 484927317, 425726994, 618064931, 46876132, 203462417, 596731304, 371915057, 312466292, 279454686, 121653217, 93705838, 313179854, 651975682, 867210021, 829585057, 901623117, 235038108, 721238029, 567946228, 91194320, 302634956, 809056387, 786348745, 73008074, 277191255, 893014390, 596764934, 947420968, 232402695, 481061460, 90628629, 425736735, 61654078, 59962164, 58314976, 863580494, 580317282, 618292233, 834322330, 933461765, 317034256, 714945337, 145167922, 976234042, 31986512, 974270992, 605553118, 448823526, 705397578, 154899755, 504272328, 521364885, 773889368, 966916205, 341791784, 663342523, 229374478, 130460265, 234192731, 888793426, 194184564, 102807860, 33238818, 115680199, 569597755, 477818553, 376190193, 443762310, 735028629, 333536615, 855056969, 237741135, 377202321, 221749523, 513973620, 905017975, 137856677, 910109293, 676975962, 770015277, 62309629, 65953657, 797232774, 349895042, 717634834, 280183802, 359801146, 305491878, 439240201, 26230667, 963920483, 63712039, 13583747, 800348720, 732387598, 751173252, 38960386, 929846532, 888449209, 419380081, 95193949, 248183356, 454984523, 417296528, 80582932, 979535658, 479380823, 403987511, 118964322, 183801898, 744135384, 508318972, 666920368, 759485853, 880818251, 661424271, 782285987, 352723466, 270274594, 523036480, 487979865, 663310676, 96096692, 680285644, 794322777, 144578117, 486354083, 686417615, 151371347, 170116335, 209776545, 54339070, 659792876, 829702559, 919213529, 584340672, 516059771, 220638357, 798206523, 411520364, 690939630, 413847117, 808540988, 62979264, 576604770, 705566279, 886073465, 543557869, 461418464, 200632556, 652174546, 899391019, 123781323, 337587948, 68534660, 241615372, 280994538, 900679336, 272306999, 945373627, 699564586, 521844557, 904860895, 747937048, 470619494, 995787323, 700730228, 943351466, 963317606, 836364144, 404590236, 924140044, 702635514, 614058325, 832761297, 640360526, 992059929, 411450845, 859420335, 944852745, 124809907, 344640917, 750844222, 419586445, 778585715, 310076770, 428311714, 705061788, 174119278, 893056803, 522521728, 910838071, 883787428, 601919907, 680829881, 559011323, 352674462, 290767239, 710319241, 555354473, 379007892, 661168964, 911828803, 868899997, 103442888, 550138067, 467901154, 535854078, 260066394, 412704447, 370896649, 769632253, 673381724, 969147735, 839490289, 676249707, 828186090, 620306904, 102366314, 377814806, 558563673, 108897336, 919382641, 228147118, 673779203, 192730001, 989275344, 687837117, 157790344, 601791245, 15798837, 799752151, 77968997, 920059769, 173007398, 941786268, 491779409, 772869645, 538831595, 963055693, 448883987, 977508948, 923037516, 960849953, 668851966, 226222929, 146526469, 477015853, 376747863, 585124086, 531056056, 790461173, 966376655, 976441833, 208002088, 49672773, 4791451, 105930053, 190771975, 433072759, 361551152, 480072436, 223613749, 827270192, 411524188, 202758019, 18480584, 807789216, 200226609, 2860422, 251390858, 864996130, 679892369, 642199542, 978188339, 198562756, 245661466, 330499230, 479627841, 155860184, 303413071, 946411448, 413972042, 117899022, 310460470, 136827382, 785719471, 692849138, 784760658, 466852914, 486242496, 66242223, 682341831, 271783142, 458724435, 798706468, 89070881, 163553974, 693222016, 410399458, 228314531, 767042885, 807728695, 437385389, 306292555, 22566490, 429312854, 22011847, 71282920, 844006501, 87646040, 245919225, 180690359, 952116932, 388396480, 29030569, 510155380, 529560454, 645952058, 225416807, 775240211, 729305065, 576196984, 110138107, 628042443, 901352199, 256138823, 483111562, 126130692, 764337100, 973093967, 72797892, 944814347, 213586818, 103561025, 269445897, 759791575, 932676608, 44216165, 600944864, 486412735, 428754895, 101254884, 477912234, 764292074, 3516551, 22429168, 883204373, 605922335, 769750547, 344572666, 195191237, 438003284, 259030451, 612443299, 54819093, 968387423, 559601696, 185879608, 429187605, 276672112, 257979272, 308662830, 900767478, 635417982, 689671034, 11304027, 513413011, 521692634, 962340196, 255300023, 476478602, 307726630, 539416601, 43164275, 578969782, 244803069, 720181562, 636513054, 479244876, 280309924, 7115857, 378467143, 589828990, 252458810, 65267202, 364109519, 983602406, 495169667, 486992415, 578432068, 313500925, 439324451, 599186314, 212634131, 503929819, 845681449, 166747247, 846859321, 381319275, 850149526, 827638855, 538742074, 370276253, 130968778, 421137521, 573270541, 396758304, 41113427, 179772268, 463209814, 604749598, 136422838, 439724604, 498140360, 106806322, 627613073, 215377627, 594216010, 701739762, 319238864, 431966425, 988273868, 164245501, 285446455, 25034565, 228840130, 963646409, 271568193, 500825984, 384530117, 523337908, 774964526, 294576219, 950952973, 637312582, 112034915, 840398827, 36834684, 774536317, 175478396, 120174302, 528130161, 730702288, 978647342, 669099148, 920151462, 27930654, 509617895, 683175854, 601502711, 74571205, 903361251, 954067769, 983205403, 205095045, 580482117, 576583434, 234637551, 477554203, 838154481, 730542169, 182591158, 925433733, 511387584, 158903370, 989547091, 787919260, 850595911, 92034041, 781701220, 547384309, 469206482, 893595478, 464144977, 201516085, 857229361, 624792050, 626520800, 184824116, 546176386, 439744665, 573230524, 922517123, 737271886, 796252672, 936745320, 402027112, 434569920, 627211712, 555169493, 527561537, 946114175, 905653840, 143550703, 25266019, 969912466, 740396556, 973082032, 566138770, 566545061, 765480380, 250708753, 964886742, 185170595, 493396046, 854208341, 869612176, 387317831, 427431985, 444026373, 198508010, 700968270, 688083495, 117827530, 630047419, 178824650, 597076992, 869138931, 57844993, 991663014, 713011877, 504355248, 325397389, 243071463, 269726319, 133250924, 111708797, 838846004, 695168163, 52137310, 989468991, 816408474, 543667706, 285658311, 135092100, 332483021, 85362677, 689938277, 391940250, 533815822, 948661260, 419383803, 53690236, 101518099, 452164178, 820467747, 877903144, 564644962, 486028785, 76681602, 110808404, 440751928, 9924868, 509120360, 34545680, 545490737, 445799530, 80624805, 364188698, 168401080, 882057358, 903972610, 508477283, 266687740, 711100718, 622826673, 641945487, 187958779, 538931492, 625327000, 960507405, 76865169, 644466347, 391080510, 710872748, 528277301, 701091070, 902118677, 179453981, 334557079, 367166860, 601577544, 553211979, 608858958, 695873786, 951870982, 840747702, 662809648, 885829514, 540272316, 804759339, 71771433, 171507608, 856532923, 25692439, 873616803, 596735392, 213979840, 207099713, 700401249, 703538105, 941400269, 121028933, 401622057, 867600449, 461992973, 831448761, 619180490, 318408659, 810853951, 15699090, 93771994, 26445953, 513121188, 534173943, 515217038, 122291984, 798598673, 291354308, 381102164, 610351020, 754818442, 912894609, 34390003, 871517160, 465451759, 880782233, 29972461, 199623863, 646743877, 264494003, 794577212, 257719444, 570343137, 459080358, 25705581, 331884432, 861392687, 695141068, 492410070, 158967899, 559574745, 722078183, 899345702, 345357312, 354954507, 32777666, 670661412, 749752109, 611322541, 453890715, 685486984, 882949055, 48697640, 268933258, 394498650, 951988124, 622785898, 697430666, 117193516, 213829500, 295826137, 210624723, 387780650, 599453291, 94045955, 437894977, 768371716, 338378596, 731236624, 849227367, 115765446, 633339373, 981596187, 577442880, 226163036, 432943738, 84933605, 801790983, 545463793, 864218580, 185419017, 972151223, 641761148, 854050357, 532562527, 121911710, 5628947, 53289304, 710681464, 668932726, 881403224, 435331972, 348605021, 104938044, 928489927, 11997723, 321051807, 300999633, 201134388, 660254743, 892891857, 175905890, 10492044, 696907713, 997445259, 67482268, 964871519, 737459556, 57275605, 426144278, 865134106, 20074769, 803251610, 256856955, 581284472, 562769697, 623671977, 230847893, 81254851, 428265132, 637397588, 722488845, 178597562, 977860425, 819593020, 308528470, 903870553, 193615216, 473006289, 664003798, 329470986, 325648638, 519640764, 363477517, 392126363, 94607268, 683231627, 210128665, 782588749, 94838347, 805360134, 795410076, 474374934, 426128104, 425711706, 611089603, 266189389, 784971389, 225292746, 947594984, 48549135, 148970009, 598649718, 448086793, 25962779, 148464330, 652957239, 443639431, 263670363, 687064086, 600962701, 646768800, 637376096, 448035814, 855700045, 141673177, 422968144, 347677448, 364203717, 582815417, 863585784, 690623172, 470501374, 393836744, 487168594, 451695584, 871484213, 874666789, 638205836, 947955791, 399614869, 61533799, 908831315, 558850734, 511472831, 515851967, 840485484, 477941874, 132145915, 417716690, 869910028, 168422414, 249946142, 284421652, 297763502, 586902969, 210933381, 1156154, 669370136, 637736779, 844377470, 91468566, 718392768, 769425515, 132149276, 755032739, 612897386, 451533363, 883632889, 494532231, 900514892, 731622510, 599341147, 174707601, 523930199, 291027602, 243208906, 262632820, 527244695, 247515976, 302450497, 115666650, 358816039, 495070280, 962920736, 156240293, 868843717, 179245845, 983372886, 326134989, 313156130, 913680854, 586068735, 533851084, 207575159, 519417057, 602408244, 399776073, 428067493, 227881681, 252007211, 169960909, 494333046, 760115073, 351247376, 320571348, 846055574, 933048829, 299643878, 565407261, 246665464, 965784352, 697304678, 926488395, 928324757, 722883873, 253652711, 667993303, 449157704, 442628343, 597496595, 795988899, 600853882, 895493328, 20445204, 546289095, 742779853, 886310565, 730466232, 66279109, 479688354, 731309848, 986095224, 810917717, 305794872, 400695181, 400912494, 179054887, 528043912, 206679441, 739000794, 173001664, 428144302, 272853532, 414671965, 143475478, 31928757, 11503511, 362055813, 152789652, 407184299, 259729289, 43580292, 425059846, 547692511, 567297410, 710079880, 79988748, 462076167, 674543417, 961067691, 805993517, 972638913, 376350210, 237030673, 738594550, 171546872, 419737328, 694416054, 520533162, 572425147, 653952873, 649084687, 306030432, 462286474, 372047814, 252697273, 759309020, 144907194, 932538600, 995197368, 214236873, 801282093, 509210026, 31807390, 382640880, 45228587, 218686312, 608911654, 946799916, 413338860, 190233128, 153525804, 947562890, 892263407, 171564791, 710023747, 228818746, 47578663, 725003332, 699398466, 8683587, 35067507, 592947621, 790389772, 65439916, 754025463, 660880465, 371321023, 557242266, 714529571, 117343452, 450835423, 150481825, 857478412, 675809722, 580496654, 450858109, 48827831, 729998320, 234589661, 153343855, 867152837, 799049930, 451073759, 325596485, 242681192, 197336163, 917318280, 480969978, 702390961, 248216, 434232457, 394657670, 566962667, 121898952, 81432681, 881343385, 847921104, 479365949, 553909441, 879195426, 136440547, 47126634, 807514226, 278210706, 690273690, 629414226, 327731816, 54430737, 688124998, 53836437, 674075321, 964562130, 187714683, 466797662, 81706431, 126229159, 611608901, 665904314, 308391100, 18587676, 110784624, 223952928, 898887290, 925043241, 333585156, 942087983, 271114931, 507817341, 721481499, 545644316, 683419310, 917327226, 475788720, 759617293, 105879078, 819418995, 358329382, 722024308, 556380451, 274502323, 480570439, 495381628, 461771187, 91312962, 610618958, 436642496, 126705273, 593397154, 101026635, 721346792, 909001997, 344485431, 564919464, 783799194, 448036692, 143556156, 595271889, 989027286, 866154185, 691287366, 711594547, 961897644, 232501526, 227306168, 745180368, 430541743, 628387298, 802615751, 358797422, 748359697, 728569367, 224036801, 776664567, 772008978, 26322519, 605425600, 767883587, 944301683, 525662722, 591489777, 871268383, 130042778, 972315045, 812944702, 956480390, 39623081, 857646946, 249832656, 739812897, 954634519, 489002657, 153759972, 869045404, 954314654, 680591021, 747490561, 604825668, 753150976, 682525761, 774246809, 945319225, 574928092, 333120240, 720641613, 600033602, 366954723, 780523932, 220400116, 121654443, 922752345, 31803624, 578424649, 550668614, 856169871, 77274811, 892799375, 642358194, 364087927, 433473848, 894650990, 133703039, 939093040, 467740210, 566788767, 643626544, 916114396, 576813902, 470379452, 14211833, 462064472, 129580827, 650717434, 617244512, 414904135, 628058957, 700966571, 603654042, 174306158, 221009206, 712183828, 154151305, 610148481, 578575494, 768526856, 867335285, 381247701, 553841836, 910818295, 170182227, 457704718, 651902084, 189300056, 190826064, 176810672, 148411603, 439451943, 912578056, 709545490, 738723395, 662558191, 587953390, 498315437, 922289274, 484789630, 426192320, 396531559, 429340545, 625402045, 170814372, 729875822, 233969432, 27299324, 558652451, 326742562, 577841023, 855350606, 324401439, 997125464, 35386300, 294590501, 41804992, 476581710, 6637947, 589961075, 161781054, 832359117, 139329894, 831689460, 167636667, 815478285, 375714242, 74334883, 480715580, 670898743, 341505638, 19747055, 120321121, 679633909, 552611150, 964558544, 19940353, 204547131, 765521380, 193702710, 290171103, 868817717, 851446117, 421538681, 216957735, 943118447, 137536686, 909422977, 929484571, 788316903, 408034007, 83099214, 723262976, 516576027, 460357797, 667427624, 76524848, 560265057, 345749542, 162296878, 606051742, 973490837, 131406258, 472765379, 429486857, 95304176, 231162905, 931476799, 625873742, 900760060, 608751432, 826961667, 652738404, 702698447, 800761313, 378553597, 360017559, 456236644, 156665215, 84127665, 369861427, 101556795, 582068012, 504637092, 741070667, 45248480, 961900374, 759680249, 577030996, 535973801, 810727977, 3840583, 981347410, 144913142, 132028491, 218789800, 494683110, 264801289, 288913597, 854386384, 241616422, 548891665, 580719803, 740025423, 782026590, 657565741, 895164696, 612702795, 675791256, 367759968, 434879707, 279702856, 984969518, 532686206, 202075904, 368779738, 560494809, 450839372, 700905867, 444440025, 784467830, 87056622, 718320845, 512644339, 715296344, 442012785, 829882279, 376889777, 79496618, 193960064, 186544717, 225850156, 9074067, 859248463, 675177186, 908585829, 41237244, 334074562, 790990196, 633853973, 690465111, 197973191, 479958463, 782585481, 698950942, 441725401, 823556347, 215732978, 686335202, 68626046, 668262698, 770945634, 836950677, 864652040, 395640268, 787475114, 242500562, 228857704, 127213657, 445301684, 638524724, 613021823, 652695503, 237476145, 981645071, 880698749, 75421941, 5492010, 691884966, 210825114, 768166822, 335508746, 27478980, 379643026, 351775061, 235073325, 984074496, 326294251, 248889196, 536438566, 773859187, 415605045, 265939463, 864191664, 28623703, 328503581, 310953135, 95383606, 530797299, 964097034, 492359887, 659739020, 422577247, 854143284, 987301563, 321166843, 548230749, 314296791, 490772354, 205554116, 848288096, 755732017, 118568201, 477712273, 292178449, 962803867, 312977789, 171507524, 980901509, 894039075, 145571514, 31138781, 256751074, 165569646, 465616386, 231671399, 610807127, 671284491, 252489274, 156829556, 295395866, 92441513, 773300696, 158442953, 677075423, 797725661, 249122586, 309495206, 526557072, 544488885, 608286326, 589444790, 614130143, 899243535, 280781721, 603307230, 743372497, 254004058, 964700538, 304205022, 14714540, 98048161, 632679511, 347510911, 960130045, 33099891, 644436543, 588614402, 780664825, 406140662, 698186265, 70125663, 562258207, 368962405, 842669283, 559803610, 691189125, 337869920, 286049016, 414844772, 434987914, 985417858, 851404408, 858433519, 890557585, 968451462, 949364370, 166066017, 438539124, 803197041, 173182023, 255356774, 928055846, 677975733, 616185057, 323854785, 205780361, 689319816, 223091845, 131127622, 604669257, 924091873, 943808803, 465493416, 597995518, 92417245, 664151597, 781928005, 37945675, 866785777, 384896645, 37464132, 862111480, 107545301, 412432735, 900982060, 828405559, 747283962, 689491450, 813809007, 217352229, 534359782, 519313035, 273460208, 936159606, 415675590, 984448223, 259307925, 315550506, 5780658, 333750190, 213024605, 630829488, 662571179, 826324455, 780456462, 972475962, 150224944, 540685368, 247904879, 770825722, 992827476, 369837187, 297545077, 143042133, 380448478, 483433565, 657924235, 743244452, 806798554, 797257444, 771905401, 864571357, 856139432, 414695413, 365109261, 318410005, 351585402, 774920050, 67382692, 421764554, 634397436, 334690404, 939909143, 427462897, 116009658, 8401472, 409974400, 923291879, 694244901, 446092897, 230669785, 372725226, 69803875, 260009841, 985928763, 952700138, 746618692, 243649950, 224182497, 613354273, 904756432, 874595750, 744254487, 646464030, 392637008, 70092952, 625771497, 69306656, 830994441, 100248443, 238059633, 45562279, 654957596, 774880560, 456589885, 889085739, 839459664, 147964170, 578937096, 33639381, 527448395, 249585147, 414763777, 386473608, 859880947, 876477409, 721326082, 242907016, 556137561, 249444327, 852609167, 416370985, 335844313, 575322487, 146020582, 690559955, 314713618, 571013196, 324027556, 660868535, 758659363, 761295869, 230846772, 746089087, 771977973, 571654176, 635358778, 447081574, 766173475, 669435032, 491730110, 967770540, 388024560, 738844454, 112607810, 715799590, 273825282, 889760818, 535318681, 88548573, 150479395, 234286415, 334249582, 258567320, 525892756, 361845067, 6964407, 629921941, 42923491, 442869644, 537343507, 193355033, 411707383, 728419604, 978635933, 565265114, 122584855, 551076695, 630371872, 232017501, 980583050, 129054490, 590246190, 329319586, 451295541, 804224832, 146024936, 402626912, 246303328, 556368024, 426797618, 820458411, 430288917, 658826211, 694010163, 788979825, 990478302, 436477353, 187875219, 351642700, 17869924, 258790782, 595321821, 388330234, 319320729, 698589887, 266395266, 992732519, 386112942, 799413185, 399557112, 829164509, 900482804, 154000772, 367801340, 698691776, 241042800, 312632835, 293280755, 112907646, 937494170, 169968061, 940390841, 641092301, 200341701, 97430665, 154358170, 936321902, 415457786, 510371340, 104225857, 949789834, 617919909, 205132253, 597867006, 253590488, 674354035, 573935844, 689558384, 197938415, 436196167, 719163671, 224603971, 653863141, 530867042, 333649366, 922336222, 702668981, 686347446, 463661607, 733862690, 845121230, 461492165, 740809575, 745739848, 160492264, 129627767, 827271231, 410851551, 125208955, 848655168, 314528309, 339626697, 675042648, 251407587, 893634565, 477486336, 464407576, 688132364, 307773252, 526254792, 296458285, 572275700, 830166799, 448740975, 588223473, 932513160, 194666563, 100768906, 558494451, 950667989, 978270217, 408477181, 779657295, 158630823, 8829812, 275590709, 624513130, 269668546, 23161534, 275174735, 404332188, 424915566, 764253098, 950236758, 796376178, 169259031, 278374383, 995297944, 663152731, 64916629, 191249560, 994383740, 169632400, 473595379, 962927586, 255665471, 184500193, 892542634, 605828929, 690348886, 271484538, 308339834, 813065874, 511513403, 340738508, 649035121, 313247186, 567958995, 169563978, 537828918, 752124955, 215480394, 127079856, 748578632, 673200254, 674919863, 165790669, 162108838, 72894062, 395935275, 923032237, 331416390, 351417061, 234937162, 620783362, 519786681, 990740993, 867711578, 787576359, 275280376, 629140373, 613847385, 492450228, 761796489, 433658017, 997518560, 320573249, 125019308, 90343146, 950564624, 690006571, 572105172, 956631491, 280507366, 513516427, 144688095, 482327088, 924771918, 727549500, 558053371, 503322025, 816908658, 519493724, 103467081, 948615844, 307976882, 884526176, 78904274, 828375052, 949673729, 727154767, 732825379, 938331034, 114108315, 745740783, 783930688, 426480113, 946464150, 151550022, 386145853, 133705807, 573782449, 905431814, 646930369, 167175585, 929329401, 538128334, 781864218, 930909254, 785975823, 799204552, 965442393, 945480088, 8345764, 954601866, 156350573, 678596787, 787893862, 452785055, 144744441, 986631532, 348106278, 923308989, 918517842, 669996235, 550781033, 252512826, 790154251, 693347352, 649440325, 59826233, 377453722, 84574553, 97161012, 543924666, 971319894, 785416825, 331080949, 467697426, 177994561, 30815459, 97269807, 524434508, 313055189, 967726237, 520288657, 586613114, 191343287, 99880741, 882306362, 418219961, 267801145, 98942382, 536659539, 861657828, 67069392, 621072913, 2397588, 565320454, 957253473, 27887139, 706335418, 523475213, 71387226, 431226100, 276266845, 246183289, 995898632, 126508441, 837919589, 622590056, 3154665, 521727603, 617850311, 830596081, 320312701, 275533765, 712298181, 380977808, 325970795, 403084788, 288117096, 483641350, 727964603, 385385463, 555665323, 709075059, 224863005, 130186774, 772906619, 623353526, 953380508, 414311926, 455350224, 730828363, 143080146, 575823400, 349376896, 371966405, 992058283, 930295935, 593879624, 615520852, 624376070, 265094981, 995383878, 553212155, 678450915, 238889661, 552381485, 60813839, 499146335, 346613773, 536158330, 384240743, 120636582, 71918633, 291520161, 187918405, 490458348, 914456038, 979611111, 788477113, 299931132, 431042437, 703588870, 661912569, 512093129, 100659307, 656886712, 794643923, 360693874, 529929658, 175607243, 533437780, 780981743, 174793678, 110522940, 696726699, 563623924, 461178364, 620411851, 344911500, 233187715, 2323161, 811886165, 73112891, 415536279, 7940590, 622178830, 88653950, 530791915, 687995189, 639328111, 596458385, 766712121, 209568009, 849476493, 630458280, 843999743, 63555446, 881265831, 876660109, 832999831, 221072679, 278144305, 960690631, 116554453, 951761854, 28669337, 208100771, 430324550, 130232913, 814890068, 330742662, 656731293, 392069183, 707969302, 885982830, 588233051, 871831894, 291049289, 59975159, 519135276, 109297166, 570669387, 745559504, 360989548, 48242713, 596357397, 711852687, 353676433, 847991472, 560129780, 62708252, 495536821, 848126499, 866395252, 83618012, 989624657, 110242585, 919472468, 183447171, 635118640, 867185925, 527481619, 3083140, 42377151, 23459389, 592912724, 841197391, 12334554, 590497098, 263363643, 508941218, 539415310, 742461561, 494464151, 9982644, 106778074, 918212941, 686181490, 833385476, 790438558, 423963844, 476150909, 893416173, 623979796, 366335553, 369097972, 307403465, 606881222, 620818784, 226068376, 940756822, 34336993, 309717592, 239435285, 647927719, 579702822, 463396257, 670272700, 786315083, 525851384, 416978574, 220592292, 157311823, 842763419, 803512621, 174332919, 969628702, 942213308, 852333943, 101147602, 427050888, 381803288, 316252846, 952740585, 133705249, 818541735, 606337134, 955639861, 605867969, 885707709, 499662981, 680533127, 259872601, 746546685, 497087798, 132191538, 866467701, 633503729, 125185645, 6474702, 867339936, 958540236, 916983642, 623709831, 83917056, 479971129, 223288269, 931802130, 338326570, 937047066, 642208011, 703032869, 906588406, 853375656, 811071920, 551933852, 153109105, 679163929, 563289652, 787034030, 19486885, 371014170, 131299417, 340996993, 159635223, 668828752, 708155875, 788136697, 266990918, 20997460, 764740850, 455524179, 325450287, 277103721, 637265565, 472974141, 399584283, 886335153, 996083716, 411608202, 482733270, 647841266, 314796219, 211330709, 667406149, 142500224, 525323892, 942364020, 645984261, 57248352, 237497923, 592475480, 263026902, 505253505, 826074972, 257162337, 86606638, 913124541, 99564866, 806888118, 850400228, 716637976, 626508592, 526337948, 506887327, 571635641, 874949214, 995615596, 242435369, 846606026, 605373660, 376751249, 454437464, 300489107, 607967473, 202524951, 61537372, 573285775, 677889619, 896299426, 446809791, 825931285, 43956612, 967207274, 181324695, 908710812, 947423062, 586141368, 153677039, 140320997, 48411612, 156360998, 620428948, 106748152, 334973020, 662740287, 160232025, 699806711, 295377960, 764960927, 257295203, 266360550, 303512604, 306579112, 144699555, 491707957, 422148326, 483781305, 677516991, 180020848, 965614186, 307731304, 181092620, 534577383, 43607445, 354605448, 248268163, 908722923, 716467109, 257273315, 440925671, 681198596, 850957738, 919074663, 210506587, 516250711, 575676305, 893032858, 670974538, 552070885, 769950498, 682564189, 868924175, 2533289, 1409204, 845132236, 589395179, 174211220, 846453981, 479526365, 271384104, 68834659, 439898202, 257661865, 389874486, 251159510, 323503606, 262956850, 5428366, 692646952, 966233114, 316948455, 551996548, 470253318, 75157477, 199107733, 435265181, 684299089, 802631579, 709637179, 18209037, 965159500, 805486626, 543261364, 671875950, 420471802, 498345709, 955414687, 202525420, 272502457, 629404228, 212370327, 321986589, 244778402, 817994276, 231367576, 247560553, 259038150, 690546494, 197428194, 70015140, 872382937, 155413515, 16741470, 503062816, 302385650, 556193091, 320035641, 154448958, 958681198, 583079126, 763020628, 699011197, 919799515, 339284020, 50583000, 67684848, 779233670, 84820989, 116853612, 216439168, 55106664, 510753841, 149837882, 735190203, 954465390, 892704819, 355210786, 649555502, 121235486, 143617219, 326844153, 854827572, 424752801, 599872105, 421342488, 561165640, 825209010, 107471400, 585393840, 769100860, 749859437, 859834728, 818267072, 496799722, 668779780, 343371796, 844506720, 382633061, 942315656, 49728654, 829991148, 289608421, 661830158, 127715196, 285537374, 708591034, 833598459, 859338915, 989509608, 507551194, 836435541, 589860505, 540697388, 424580528, 228129534, 765348488, 631528405, 923293653, 116582298, 8385396, 285976034, 468164383, 222922791, 188729839, 137548469, 810136893, 523018197, 533467432, 230925143, 91574910, 15479772, 607175795, 301799161, 802926256, 257844461, 714084892, 253847175, 811475316, 168917598, 665277924, 953050023, 718768048, 480611699, 686230717, 51972892, 299191202, 312041423, 973543274, 392675129, 591698166, 173314622, 872798714, 80522902, 913624460, 410855714, 752140261, 620657710, 458273265, 377989034, 873352482, 452858310, 274394118, 716886554, 307915960, 574252220, 304001803, 862405552, 713730588, 789109758, 227245349, 983834320, 342207049, 430303056, 820857612, 875151784, 514267551, 562448032, 739758062, 34493495, 563105568, 488136356, 685671873, 172153170, 333676722, 850808693, 853035444, 460148054, 847129645, 495162410, 326651678, 877994679, 769928711, 534895681, 83900697, 585652271, 832878917, 7239948, 744990657, 350653542, 69885948, 790956702, 581226041, 318640005, 557890167, 333098977, 434585517, 348620469, 96710977, 493210713, 957332457, 378637790, 395864174, 983386604, 907398370, 521681559, 274543118, 106402327, 698780487, 966373238, 65843212, 626467479, 37628731, 862549163, 424596151, 443800732, 13914882, 643815834, 32001660, 775948622, 251472896, 119839134, 304969922, 544723830, 567504818, 101309317, 478822173, 408676121, 362338973, 81725688, 639224561, 538788389, 723446692, 685542309, 699007108, 656898430, 444309894, 681707381, 865092311, 881051306, 771871491, 564704111, 993591974, 915284514, 477989559, 197571345, 876069716, 168045196, 303637752, 270143460, 40326263, 574093466, 814809686, 824026861, 537161721, 43478803, 3176567, 101921703, 78756634, 290004791, 407649718, 723739602, 119304407, 400503624, 913549310, 368511676, 536608510, 592217714, 16634385, 895905544, 357658866, 675583647, 212934394, 694596044, 778469980, 740435304, 105605950, 437018375, 803018100, 612126451, 193297579, 700511050, 76227316, 416270495, 997938444, 154465676, 928336432, 594596625, 237520826, 522099910, 701556309, 98128119, 894867217, 606092687, 750963305, 46863058, 967429169, 226504091, 231008426, 207595265, 871902051, 458312402, 477694624, 557719658, 652225979, 351895450, 535032744, 869432629, 374162808, 725897735, 914394839, 969671800, 635621101, 229410446, 522195085, 627552776, 948842768, 129858932, 743521783, 264371186, 578507804, 829228762, 610823817, 546092200, 876607103, 258083972, 886755687, 352450265, 893728041, 688744602, 543813959, 272778996, 369426150, 858901791, 373354910, 915984626, 393340221, 488219928, 95700468, 161991761, 131361555, 99608815, 442989995, 21492834, 951263780, 336188836, 80146702, 888897625, 233465944, 733383468, 485825039, 240717881, 4311453, 372985575, 358674911, 952992588, 478479311, 854469858, 471225707, 999430023, 457389761, 527499506, 357923585, 492208384, 41114516, 173643743, 275212771, 217484831, 10650016, 472052138, 361182038, 655000838, 826893606, 341190376, 18333223, 818326703, 244561484, 628439966, 972892662, 549738724, 794179241, 793090927, 433768911, 959619578, 114099635, 512296165, 111675350, 652285479, 235075448, 423941982, 451877776, 621641794, 464818261, 97374473, 851659097, 711439140, 488052287, 281479288, 463481372, 124072077, 626815750, 212898757, 344787834, 591005050, 291601539, 345999405, 18328754, 566588724, 105429428, 965209041, 441705310, 479742328, 187928039, 946690242, 813256680, 478236163, 12429108, 126727582, 705921916, 723558885, 532141331, 600306720, 656654004, 823492481, 948202578, 399612572, 213821786, 286803203, 10116710, 255493580, 283370034, 597578798, 24313459, 107533616, 994310717, 886869428, 345738276, 916780161, 774251059, 44787241, 457971273, 710694199, 125964266, 530027564, 193512197, 763609664, 908109801, 31727032, 540283455, 421780329, 977409113, 774063186, 637575033, 171439682, 719497025, 700458193, 263808325, 511101499, 371429904, 907928939, 10959042, 642113606, 377769980, 352540295, 772321037, 376347183, 130159082, 43851794, 211785308, 654459092, 744332931, 377526332, 731091166, 775923243, 396673883, 717143635, 447854313, 667409415, 699619255, 62098946, 649486433, 336559117, 707979379, 703827626, 769971112, 514540441, 991347687, 227818427, 972141858, 345614011, 456957163, 664917990, 565448379, 360214035, 955574396, 787471562, 928445156, 470434131, 701855376, 194773866, 979825189, 535843429, 201321027, 7960565, 589698727, 447712211, 65006202, 168561338, 722556027, 838145337, 257902887, 750687505, 805764128, 980618143, 512434767, 23998517, 121892576, 221696315, 760555310, 794673576, 90572706, 733123241, 888305332, 720071260, 461969553, 168906821, 520071345, 681962928, 280346648, 267828462, 615865984, 703513591, 777569244, 848520305, 993089106, 981748962, 723404348, 227632004, 711704313, 870099790, 347193780, 772226390, 892556450, 85295172, 12516194, 558498424, 12654008, 938281250, 651109010, 551125480, 716121016, 17552593, 896427123, 196973614, 410341607, 546625731, 484348242, 703896002, 839733277, 854512192, 945711000, 791974626, 216653598, 702983017, 959817539, 316101239, 766965341, 646129881, 931538107, 632554914, 493207158, 390511437, 664569204, 345142316, 972369946, 978220118, 810594240, 341740414, 576132636, 614377509, 711452574, 593803426, 963441880, 976562182, 230694730, 420941207, 721059215, 207464697, 833722085, 173122348, 488113177, 325369205, 405923928, 409836988, 235548630, 619953327, 4877099, 702034825, 930024284, 497564804, 779689734, 516544001, 601433391, 421112235, 878998937, 99971189, 476729648, 689992981, 382326274, 702889078, 523065055, 954663570, 282383474, 891290276, 839686765, 949245205, 860734833, 255753374, 861837879, 849987131, 457783069, 640437876, 68497687, 816417624, 82803213, 939363318, 259392244, 840014587, 343725509, 608689989, 834024824, 788542161, 465074, 42580260, 642138576, 490792804, 117946571, 278112362, 148539495, 538073162, 952948445, 6945218, 305111009, 220896122, 861621661, 156198187, 96712280, 745098398, 665167132, 896879607, 585142108, 452984674, 959960215, 871375242, 10645293, 719051662, 838987985, 70279710, 273392699, 112392824, 179357311, 615076970, 346301992, 17441968, 284461964, 13769820, 289558744, 531461323, 936049918, 238134292, 856389950, 310777717, 340534240, 77127073, 928605807, 187444089, 149701190, 693357431, 709864642, 397282603, 892868917, 705177687, 778052271, 466699639, 557216740, 857514403, 698911886, 881080100, 497490063, 187477759, 690672469, 209661657, 769426971, 528777212, 522392124, 268202432, 875857100, 723738431, 619906337, 378388546, 569621697, 364869012, 551698362, 406546210, 648058043, 807163414, 425959365, 982906782, 873040664, 889814173, 325482327, 906771975, 310562571, 117658305, 689838729, 50675355, 683655508, 894377373, 543438546, 791198510, 76428109, 471002277, 793763131, 131871347, 581696547, 864894987, 322457867, 685318283, 824070738, 788001587, 176346615, 44240519, 116281780, 249017024, 44393366, 249471337, 942972621, 579154145, 4175503, 214004605, 932074352, 593370561, 451656025, 255690127, 496762188, 173059507, 611266631, 175416379, 92814563, 221635434, 669369328, 74717402, 298843424, 35720522, 225591443, 246796230, 726851773, 726637949, 918701962, 755663528, 938957937, 159075733, 272142104, 122876481, 110437830, 389587318, 493603555, 453056441, 964676372, 363290082, 949829622, 577155223, 14271531, 277042258, 320768108, 832306956, 642864349, 197226029, 217842481, 359827870, 733464102, 512016890, 794239364, 745260718, 331781809, 791074124, 685306426, 685105079, 107789538, 436125904, 165754615, 119018059, 353315536, 878351776, 631461380, 755103043, 795347746, 136294711, 385890043, 190201502, 105488917, 59537165, 478711281, 101873108, 582793478, 530330601, 720701797, 442646859, 975899426, 882265414, 92959722, 743326214, 384312569, 700236136, 718290900, 753193646, 601846551, 87700710, 890161437, 19579263, 251195930, 738286614, 633443353, 98860733, 805524044, 528501635, 385401470, 846057787, 900729157, 420436843, 491512831, 273047175, 341932010, 885178583, 579783947, 107225423, 381038847, 307855032, 222511534, 432498000, 856497362, 40513, 744169099, 228983269, 406094650, 239065685, 825377167, 27008440, 957373541, 77594822, 728777450, 247236760, 438402497, 4196247, 123247458, 106138119, 260180394, 284725875, 226669964, 861052008, 134406631, 987658246, 324523537, 273142363, 682131146, 286788895, 219955628, 666115669, 963194087, 278001930, 933988657, 805662515, 633364397, 875015846, 644649994, 109775058, 474274049, 950759607, 796216881, 381260156, 419365866, 160370272, 202144626, 530495175, 221910153, 212042772, 1193209, 476189967, 630292464, 104318846, 736545767, 640587909, 76511940, 70181175, 476340068, 623772037, 904970989, 271618393, 922750469, 175707852, 986609199, 45321214, 673912642, 584375019, 324167698, 545365790, 986023577, 19420931, 91166002, 675762618, 974347936, 963389846, 124290937, 637077201, 285762274, 642215810, 737032458, 273004243, 808873146, 942516832, 590569766, 716143464, 975303417, 91642336, 453874032, 439581122, 527678896, 443897592, 861585775, 427659301, 130697443, 977026226, 22462540, 378989746, 152082206, 406966828, 222224194, 346018149, 739194190, 475148479, 210205484, 94439314, 322002136, 583071547, 46758344, 143901156, 645883612, 432871070, 462809337, 14639918, 90898975, 592222154, 27785636, 76306192, 912756327, 504865217, 741190925, 851027319, 106664181, 163322282, 358273756, 875270140, 361475205, 280089538, 686593739, 48381613, 578027008, 22689842, 908770552, 436062911, 581969161, 121141517, 391687516, 250784853, 527478533, 559175976, 975999753, 924586011, 626756651, 679614372, 53335103, 176327736, 262709879, 105901889, 659015291, 388795251, 790199844, 618305858, 174129342, 807311767, 242894347, 659403243, 542913509, 268929276, 46119511, 886665056, 261544414, 635737480, 856659075, 274359584, 400974749, 2358338, 97481619, 524192656, 832300435, 447620780, 608851006, 185002234, 144691943, 249151870, 865758449, 615923397, 548841078, 711792264, 376665767, 856229451, 2081583, 982831652, 977354764, 406209993, 562855988, 934850561, 807856719, 830479294, 973798721, 161511252, 331581207, 964219675, 522202865, 121505525, 716781839, 967510039, 503081216, 728391664, 302920176, 541913225, 977000247, 623771927, 152514925, 223299493, 649069457, 901838444, 427396426, 206787395, 278429292, 290014884, 305017319, 610151155, 255735219, 800478186, 733555276, 509311905, 687403857, 692530707, 614503107, 601744471, 708592327, 169333922, 932040101, 489826847, 208338244, 360564094, 827626356, 745212309, 799549407, 161498817, 751804784, 246016, 479006176, 317013885, 527603185, 764830550, 449864645, 122327406, 455962331, 617355603, 618600918, 498448656, 867979029, 231074394, 397092279, 664250881, 461703583, 660712241, 172773424, 491759517, 448489103, 645255563, 97665890, 167624978, 469280408, 718860617, 729460291, 459352920, 945580825, 366170638, 727606832, 699790135, 730273350, 662893402, 416948838, 25448580, 834260072, 793285724, 593359044, 126632653, 526685226, 502348465, 156763444, 843215301, 123856298, 990577675, 921734592, 742390534, 998878139, 747365358, 221032288, 856214159, 481776870, 663681122, 861797762, 89196708, 879600438, 132156465, 53629474, 404844087, 533219233, 94288338, 253094639, 459269382, 915709783, 418956178, 358959990, 604716912, 500551584, 85410865, 924558562, 316624453, 80454826, 517651930, 180841101, 363180947, 141476354, 808514925, 332712035, 687799383, 183006280, 348684372, 374149357, 584123973, 363264017, 395736783, 871556152, 842951286, 549745458, 368431802, 921019845, 18833248, 345929952, 29911730, 811108839, 266009616, 990416841, 187855071, 336120395, 867714961, 494838297, 922005033, 273189316, 27365745, 757771186, 738643625, 115365731, 405274203, 31479675, 605730832, 9529061, 581459265, 20372725, 757831904, 767825818, 793342197, 91676519, 398344875, 165959908, 397877792, 862511006, 851443834, 646302194, 680976836, 705894849, 704207092, 507407391, 50911916, 711657107, 244146091, 482332031, 220668856, 479381049, 352514220, 817864313, 813914691, 550604966, 36208758, 528186622, 819325079, 608529523, 155309853, 424334410, 20501848, 59632882, 515572646, 132559514, 89986671, 240592425, 535384009, 891932829, 400221506, 408615279, 27315502, 944509235, 318277108, 188191902, 943009582, 287229500, 592961676, 865904527, 368534857, 598679743, 226431971, 338658038, 926016144, 603685921, 616489064, 760375732, 241322878, 977055520, 85100040, 671804180, 265362525, 855814190, 312129736, 585690239, 138694584, 549659745, 692058504, 139534387, 313763024, 142334056, 751922899, 400637783, 901973232, 271358182, 887998251, 446785912, 245902513, 311218196, 770199528, 994318036, 740605571, 212596502, 498135853, 969248877, 628408895, 417521079, 26762749, 468673157, 668638610, 435437363, 579166175, 271062715, 232252055, 703190746, 544471043, 703742266, 322841107, 51264627, 655555531, 375060797, 200101503, 360831288, 628278573, 45469154, 874633939, 760311658, 764548134, 881761118, 111338798, 704393416, 40422478, 347906176, 173452709, 927678483, 267666971, 406050806, 674717575, 672338600, 914707105, 835538746, 604513870, 892168337, 482394495, 661446848, 681558411, 988541516, 999185192, 411357039, 517319631, 119598003, 243722886, 733228555, 49812755, 470485951, 341603413, 822264342, 586755458, 565556945, 710574578, 149515, 707179476, 535959350, 202224696, 423062280, 21518805, 813229392, 791167196, 382737121, 577007669, 917223151, 681195435, 494498177, 117720548, 691677058, 665646387, 385676426, 742674243, 493063507, 407090217, 449894366, 941213308, 898326058, 537151975, 704095033, 800365460, 496485285, 454267412, 25484359, 981276436, 629144502, 927238599, 110490393, 213840140, 303341220, 559872720, 49174871, 177888986, 565457596, 224185923, 293260683, 325692850, 713577957, 528382477, 861324702, 736682777, 282649085, 455510217, 43432099, 297822634, 105512708, 74842719, 113293360, 243591766, 499900911, 721636272, 890883804, 803940598, 132936700, 949882633, 111258954, 680655738, 764107453, 317686002, 987595000, 84228499, 691596146, 551191801, 521900865, 743840733, 815470132, 279834461, 605026016, 716399819, 534826422, 322732062, 915276834, 281023855, 56295408, 744602834, 388502559, 71091467, 663801126, 238090351, 220611950, 448652886, 950607188, 969872436, 294216738, 655172340, 390321870, 169643219, 20968811, 538993008, 896612396, 383471576, 185687421, 166315023, 440672831, 503972916, 259181517, 582374952, 861745086, 694912074, 15984428, 220240312, 83642949, 386569824, 650376510, 936522795, 705294341, 978980096, 985546013, 379077802, 717871492, 151281514, 101082162, 84747929, 444806870, 127453849, 538034677, 449601113, 696181021, 244184836, 436820738, 472874631, 375097475, 510451508, 944966927, 563196592, 309426677, 996293879, 647253948, 405073987, 592717870, 323656925, 964588435, 94556934, 110958211, 27285486, 677422729, 87805868, 731705859, 807187279, 801619417, 208979631, 465030053, 436455905, 470089412, 738920287, 569709180, 15560370, 585386481, 557910388, 930765732, 765048716, 214916441, 549189167, 899756892, 382582087, 600640217, 763731696, 110075293, 181688167, 534968650, 918843608, 944999659, 19307862, 767586751, 926675200, 247089117, 56224627, 34592497, 17456976, 441035263, 657431015, 126737023, 916173512, 388024367, 806447469, 190742572, 631696413, 606193375, 268549212, 759647280, 758556039, 712378284, 643030520, 444522032, 48811573, 243778453, 189890624, 90513791, 457906836, 215559399, 131185088, 494119367, 909622896, 584210792, 496675471, 289139571, 610222868, 916195039, 485283370, 726398645, 714132442, 686448092, 99308617, 841735174, 662141549, 333333856, 732977749, 807399948, 797056195, 770275472, 333995807, 145755213, 606827910, 938884955, 231953733, 162320961, 481385491, 209517425, 925744882, 719213758, 590432892, 890547760, 688963074, 233195749, 168734538, 187377860, 402821264, 303173408, 117808158, 357997451, 556359768, 46352890, 204239170, 192766419, 557344412, 277913889, 895224501, 595536922, 660064212, 54819818, 415989639, 750970411, 14924531, 713572696, 844397219, 433635398, 305990323, 686102370, 61882231, 775306465, 942520898, 343089537, 891639874, 650746501, 402524776, 348727160, 910305734, 249220382, 669064852, 370731944, 398119319, 561274578, 791446724, 463206497, 24570615, 459257340, 132019381, 91058006, 489817096, 499021142, 593827459, 941102106, 90163495, 818855173, 977681131, 515324281, 904148077, 14547432, 118449948, 194137091, 472084997, 10583235, 519374910, 58105328, 340005006, 417636488, 986800934, 208911700, 603640646, 859137537, 246260654, 604682254, 967601312, 937667933, 587342075, 873384022, 570140284, 186434901, 635617694, 166242132, 296424464, 762406222, 29224141, 855027071, 140253628, 132587592, 60899340, 81665032, 801548740, 298970014, 775675712, 797496434, 171852997, 152145385, 444171111, 333633350, 617449861, 864304811, 968616599, 135429047, 438547390, 195394328, 885216866, 489722064, 844274619, 267035409, 317787648, 628804423, 978597252, 916582154, 518413849, 183506295, 170532453, 20905738, 346432231, 399867131, 149236401, 517695785, 277830662, 138200738, 290143337, 954965360, 574401244, 672036946, 828547910, 414411029, 288723824, 908100252, 907358790, 921755277, 471324250, 933303828, 922507144, 385889772, 477495817, 551976594, 479727437, 657157343, 491475149, 449896480, 445396000, 728571078, 772904976, 367865843, 993591036, 722119036, 601054927, 379455891, 35650105, 706811227, 878824855, 477093641, 234122982, 460522874, 859348892, 392724201, 442655496, 214410519, 88521476, 706509533, 98941863, 925984075, 10407681, 540424733, 722515712, 322462280, 600787400, 819446604, 654838812, 877134758, 467307117, 100221168, 279007038, 591706097, 174180959, 335384604, 646736161, 424675518, 728984887, 675297679, 628418734, 859726215, 729614966, 336046972, 405680775, 587521269, 827759116, 251529321, 264173792, 17771379, 69915343, 512834647, 578839161, 744942962, 567114460, 267627349, 938905094, 22812670, 975854415, 491624466, 69695820, 239982258, 438584506, 412397679, 687403584, 580567651, 754189811, 231911078, 967679347, 439621451, 348744680, 228586321, 61121040, 522395298, 307921696, 325586656, 761764344, 749316065, 651420623, 600619494, 444498551, 426704822, 455477242, 467678545, 646342599, 281012821, 49084226, 556964474, 726128057, 23175683, 897189459, 618429245, 761702823, 908317346, 497184566, 799800044, 74437495, 503230997, 108135763, 219022357, 161006958, 55898386, 323448166, 26165207, 413839211, 442187539, 636352068, 778084267, 811173025, 203763735, 22934533, 742593615, 136852146, 69859396, 111946835, 38925668, 671449426, 36670164, 96620124, 916264991, 38301182, 742438949, 551633236, 448287485, 156917187, 685531085, 633458449, 443627679, 960276651, 510023310, 768587593, 345466633, 172992616, 913358981, 133786307, 153371050, 82677510, 804976580, 671718307, 657406869, 511499884, 415497480, 159951887, 840937264, 546066865, 362260903, 794951024, 213492855, 316581357, 337311942, 986856776, 127746403, 591811643, 991153802, 241803528, 10828176, 375935113, 600244274, 648161205, 963542411, 465020785, 48711746, 30697833, 695315561, 719440440, 801634124, 161124609, 731929799, 802370950, 956290145, 41997852, 533978645, 511144905, 390133654, 887236238, 587721155, 353441564, 119701364, 788384393, 509483268, 441879516, 940512643, 114659245, 611765202, 791954695, 64757545, 232290390, 194953491, 108254003, 514170594, 502338457, 589774719, 331378401, 241645736, 747105600, 746019964, 166493694, 681453406, 745202381, 396954668, 595592231, 706576467, 362892907, 610577516, 141760476, 992996867, 429786228, 540781058, 453464937, 177217848, 83353022, 215494847, 531343452, 347482029, 326625081, 335637324, 698388102, 19655393, 609033207, 673889585, 99464791, 926977749, 671988086, 104424475, 274651310, 218082051, 204172499, 939097622, 290469916, 680217806, 280663749, 157154627, 729417252, 560155416, 243990561, 113415343, 710633672, 318221222, 562430572, 433669885, 292664930, 763277842, 233930329, 65557672, 917305314, 105954592, 717323979, 752365042, 928446069, 690629415, 745440638, 685567379, 305261277, 921107262, 521952804, 280596955, 643567686, 573068451, 819383935, 140881518, 972936392, 928996103, 383852540, 649824819, 361060235, 480227141, 349472885, 180680627, 988517991, 457773244, 339753008, 939721385, 500037865, 198195133, 198291087, 607083979, 937639448, 527882598, 341757699, 239334677, 815144238, 135291706, 904482792, 535895225, 353177691, 733364631, 858398899, 602658219, 24835513, 521939942, 631484735, 476205163, 262780436, 981792766, 812408140, 686911055, 453893299, 796362244, 423292149, 996809678, 74132164, 197214243, 860957867, 873576574, 468300935, 879589377, 457736403, 651448843, 431701074, 847488201, 552605035, 531487521, 160021815, 495192855, 714543018, 653011162, 75426838, 665077507, 582966259, 988391256, 666456165, 103819673, 792350922, 595612151, 489626545, 861588087, 314166061, 934563690, 369426138, 717221114, 284751259, 431875722, 115494253, 735155805, 658487269, 673880534, 268050787, 861372446, 291998252, 214786081, 738951392, 600180476, 762880599, 1024374, 453689156, 37690504, 827851588, 835861293, 868906030, 16563290, 439698186, 325228194, 368498813, 289772187, 308039509, 330933941, 429918546, 673294333, 544072654, 72959448, 72028651, 911167067, 562210796, 586419533, 37984326, 797386669, 871571624, 68972610, 43550197, 341127064, 972451225, 427801025, 640215926, 388584727, 819820955, 394650459, 751529448, 252919590, 716977543, 214529984, 878189587, 815794560, 206746704, 41315542, 461919126, 313263316, 390823021, 901933248, 572704297, 601050309, 58996725, 514312632, 402932609, 437830771, 68953280, 80280522, 373379824, 21975835, 989627454, 150358703, 26538070, 449613852, 666605452, 53821906, 155280344, 702142334, 246529528, 253515515, 160358415, 162183643, 355828183, 250748528, 629463965, 110578321, 299974079, 275002986, 350102530, 359422431, 843571022, 834895535, 320377224, 661737198, 342039328, 851026884, 972567772, 405161709, 278981741, 277544170, 92918076, 353714640, 356765746, 757253527, 830193245, 839841382, 859976845, 163114195, 528550649, 682239624, 436311088, 112404123, 463414547, 721067767, 94120043, 244167147, 495767534, 621546367, 452167060, 594756818, 190337319, 97050716, 895311832, 436878737, 550619627, 141117616, 817452678, 794080574, 943389572, 670049456, 399142356, 4583722, 462531539, 756296709, 748496083, 887357168, 698178924, 375371602, 107801275, 292824672, 936466477, 681948964, 254591002, 620839175, 737164441, 947033084, 172997302, 127953302, 86847796, 73903786, 886983815, 89897199, 789027757, 249037660, 768731350, 847530835, 662253921, 338913152, 179517885, 286758477, 193582299, 323019146, 626290913, 359017592, 378298496, 624977736, 549091650, 47366752, 989620136, 799125110, 69658453, 344792789, 323772038, 650075279, 490614286, 254731513, 314562940, 250120397, 423522612, 70087565, 188487930, 834651432, 768465459, 470537657, 663913016, 43045852, 582325905, 59076158, 961225737, 945194185, 713890089, 435241340, 537289437, 390607418, 208276625, 893617927, 586410318, 974115566, 97276794, 906387099, 478198809, 796732167, 996386676, 272969406, 536577583, 603672416, 808216851, 76923553, 255260878, 290857970, 520534604, 606567815, 216342667, 779769461, 453683860, 148579320, 190760870, 111718317, 601420510, 852670244, 703190639, 634823452, 370928769, 29910391, 139733591, 836924632, 28438397, 88155626, 277132394, 957302227, 841769546, 960801896, 378127311, 263473882, 150343388, 17457020, 66034634, 32454002, 50669562, 525829410, 885854764, 189508788, 880301324, 324192848, 711098835, 369007517, 169754616, 656052898, 447244001, 235415106, 175132999, 690932938, 598243673, 830071105, 614543562, 87820501, 139305607, 797462941, 895103535, 630238695, 131363737, 270268729, 792732460, 816689588, 607317081, 526832560, 147822532, 505279939, 515836858, 295003839, 75087770, 98698463, 572407874, 914925355, 917481480, 317847787, 583255761, 941104527, 184535345, 168711723, 754681378, 784286493, 307286110, 255745780, 218837630, 195479897, 869621067, 473482843, 940488548, 921390806, 8792033, 96711364, 405831716, 752251686, 962756822, 282790886, 891179633, 244486672, 500425952, 631642879, 564637390, 785868591, 222451684, 511123952, 352789503, 873990836, 817348963, 881078120, 68518902, 253533307, 920737052, 115452709, 948388443, 21833726, 772542396, 638985176, 142062061, 578629291, 801399777, 310014524, 167005107, 453388275, 435808033, 887201016, 541278491, 243256817, 457103356, 379536078, 400283541, 316733346, 273284400, 498911083, 245416273, 201799116, 61264423, 376804104, 610028324, 387172869, 697448288, 960992965, 177121655, 70816331, 138509624, 842564685, 979258009, 796772991, 337751988, 543618221, 619616357, 941734319, 426067338, 880940113, 434366953, 683773283, 616835560, 251918733, 195489427, 74281826, 846998252, 51184803, 8067733, 295194660, 448258130, 744409309, 238009993, 333070573, 269739822, 240803893, 347462047, 801955095, 313569148, 987709451, 942719662, 874348342, 475653444, 853984176, 835185562, 804520355, 864496714, 278925905, 690388797, 483820616, 820418763, 996023516, 698562518, 265361433, 937448220, 713515561, 854019688, 246061360, 660755858, 573222969, 835710442, 372906787, 614318159, 416720442, 644260288, 737354125, 793259894, 421767685, 158391391, 811163458, 175838279, 372672817, 936567075, 153479359, 832585299, 272387106, 936560609, 880393150, 957863842, 617591214, 234552544, 889619659, 294814695, 431914995, 615148363, 360169556, 241732440, 354367819, 227376313, 772096764, 282564545, 890205121, 360768691, 397772546, 384617623, 255793326, 500130742, 329166790, 968955153, 384187486, 681817988, 386870564, 929400975, 620229409, 479648094, 82764116, 444649851, 514242337, 738610225, 625113800, 901401146, 589472271, 839912224, 866873963, 911217328, 103140497, 385521505, 644606772, 397320505, 675449505, 254149819, 97594961, 396679478, 640510534, 666649222, 436723106, 549062798, 273252321, 556819221, 707539973, 720959772, 895831320, 588571834, 124328088, 749313648, 605754398, 450487059, 925806477, 52051771, 692933059, 411069946, 488729285, 892354248, 327771364, 632748861, 930771322, 324337387, 297528170, 657395518, 337164766, 360841138, 386471820, 411333073, 886510309, 587375411, 519026087, 925962455, 143360143, 226656857, 428790357, 384433990, 899246789, 780210278, 7050897, 296105175, 111758016, 360313543, 898768793, 950623262, 715116039, 786091276, 759037930, 562731931, 478500024, 60689187, 237764127, 517128148, 187034840, 662177050, 994748723, 283123138, 327586414, 266048361, 804022624, 611955051, 776691177, 845250088, 986413461, 558991943, 707393145, 398842434, 433671356, 251566913, 349249313, 426383146, 225749956, 435486132, 537484719, 792013633, 922892120, 229071607, 17463369, 574798898, 136717553, 974418251, 967410101, 783125419, 99059182, 235878123, 772098598, 634956507, 221013695, 165296802, 860906185, 186446184, 395963092, 293283616, 359243216, 203982711, 793908499, 944789147, 647024685, 536079623, 528891609, 280202562, 386829053, 148078511, 163996894, 51407996, 676193598, 733993688, 905815721, 254410723, 638272410, 167601242, 922061391, 806834247, 48039887, 812555951, 376107111, 227770024, 362289182, 789046064, 75379231, 153121635, 499253167, 512092035, 337683087, 890664230, 472180796, 70182053, 19951568, 42359488, 730338269, 973353089, 373002658, 994994593, 786818619, 301115874, 279989441, 144789429, 407659652, 478735016, 917757291, 69553243, 626558168, 687805424, 746140936, 762567192, 375634414, 486651775, 178762489, 922331914, 268774964, 56620855, 172591412, 979633325, 658482876, 489377589, 190722863, 579242012, 116642307, 753054395, 486918661, 153897800, 750922828, 630497738, 882975474, 384557157, 56990482, 4759156, 920286552, 799106834, 231689417, 864704165, 168264251, 834048766, 148336051, 491716402, 621405242, 973344434, 613875981, 907643008, 239060708, 603253771, 207417560, 447993627, 516351237, 871144060, 548543182, 392894385, 751137580, 133821604, 272476374, 370100377, 621070111, 222424786, 273309037, 507382691, 703279380, 568641636, 761099028, 137837070, 942651578, 866048902, 178146494, 211038560, 170962786, 960453718, 988585374, 113206094, 61427115, 458178441, 295498871, 206995807, 575326032, 974634332, 834476416, 76166577, 238786952, 494704004, 436740772, 613792715, 61780590, 500423413, 155712628, 304725442, 303300267, 567663283, 465429420, 864727112, 716812793, 949340086, 117500566, 728538718, 521305126, 13579541, 107875520, 407998811, 188432666, 601180837, 761245462, 272975581, 154574844, 599839976, 115663342, 996128050, 604833527, 248959274, 305246017, 464317193, 274929220, 681971498, 338692757, 245533195, 387359562, 764414542, 230701683, 995996567, 954558630, 997171809, 684845133, 899287100, 455167210, 164526436, 284847387, 332024904, 87161242, 109411999, 426984230, 405175629, 870389147, 445064463, 644223782, 864912535, 768250728, 814233879, 75628754, 40751368, 906174057, 397257125, 163268249, 128454706, 915757465, 482222017, 78130408, 118524061, 145994523, 803866131, 920993034, 571273601, 540623652, 259436680, 793557100, 884492321, 770980566, 826915121, 999693163, 573234435, 36804669, 76615130, 746370818, 113933311, 318544250, 836052815, 625035980, 934567584, 91886017, 909509509, 958123961, 14737057, 704332384, 727923600, 972861293, 760508982, 134868375, 116513256, 337180185, 396945670, 21767762, 754822925, 746909091, 790680141, 755413248, 151936747, 30810107, 144774189, 197067203, 114994520, 181801007, 684005564, 696154896, 68781487, 199237500, 724180192, 524915434, 308947107, 993959527, 699821128, 222636023, 988006838, 474908248, 259854204, 987726543, 649011728, 499275615, 28081832, 408713258, 227135682, 111973130, 331589567, 526803909, 816237485, 636254484, 82374774, 355029334, 488002891, 609854970, 675614846, 948411400, 559262569, 936195674, 771670016, 921198042, 525511190, 276311874, 246781344, 418646551, 645976674, 196685938, 439168551, 939521508, 165223573, 997024676, 692408387, 651458861, 762008721, 90864999, 112566773, 461702120, 894812730, 784552634, 819518940, 270344047, 633951748, 336068447, 161025708, 827636500, 629319960, 42707573, 957049053, 885284887, 364662058, 836710411, 201212288, 444112709, 36019187, 30537419, 241668625, 277113271, 823252064, 82392048, 299725198, 527296718, 404209471, 204228822, 803985672, 708905846, 750541612, 365348735, 468632771, 462715084, 296872683, 523269615, 112265037, 985433973, 950398004, 972056125, 178309246, 217124022, 295559664, 705169414, 634467997, 92424186, 807892662, 380318638, 28486113, 141163297, 918239299, 419289636, 130528383, 515275633, 736555816, 243240129, 417694135, 124752244, 989093402, 955707158, 116245797, 151105897, 101510875, 889002161, 613384043, 492018044, 631858215, 255312592, 697572606, 245254267, 118544559, 706032055, 287773020, 623413969, 358732970, 731361997, 931488916, 385448515, 319821404, 873063279, 96908903, 47038245, 838130872, 314430916, 495539895, 68596014, 644168771, 572307130, 538594158, 484600595, 830128619, 948671310, 785229024, 568959555, 138586135, 539183856, 874360213, 173735754, 477577703, 495836390, 257851262, 179219092, 623818308, 870825928, 685693319, 535633714, 897061364, 952183888, 722737746, 599195583, 422605845, 923633794, 613753359, 481584708, 390321108, 144571490, 723224454, 87075985, 319499956, 315658195, 542270055, 112348050, 616050177, 776051954, 276146162, 307307723, 455311856, 676001650, 512588921, 642281996, 150497167, 440110191, 380799186, 367488668, 654835904, 402094106, 395367077, 402560104, 695640448, 762691885, 510521927, 138568317, 661864642, 669121434, 254896025, 629516763, 823188326, 290509733, 525258188, 401836554, 237640663, 480174807, 972799590, 440104933, 963084966, 898021752, 565719489, 584886281, 19717183, 93110788, 683488174, 647585121, 216923122, 706962825, 154246700, 954681570, 937596224, 421303786, 478622391, 399921453, 693133599, 315487055, 595913420, 748459783, 461828738, 977746654, 285738756, 973374674, 793895665, 925768911, 839048953, 500365682, 899397019, 537532412, 914335551, 873285026, 592591986, 766530880, 839987726, 478372790, 20321861, 360103611, 993891066, 116086813, 542545388, 911069811, 764257681, 649155176, 538756021, 831353138, 260046372, 223588830, 985851866, 678331746, 929112007, 850340472, 276272444, 732012678, 465462868, 394910760, 438847111, 589089342, 182095027, 322500613, 769715217, 399231690, 288960620, 970271192, 30910874, 846257122, 755262746, 420729340, 721579078, 330702559, 488441320, 798257176, 901032602, 146282523, 406057990, 290124719, 672639645, 665677167, 422752082, 445789130, 658708727, 481403747, 914243257, 19349446, 908958684, 774595148, 440802032, 740533022, 427366192, 265461493, 675127533, 185896816, 11474515, 595764273, 531245600, 169481168, 753813990, 53604067, 594400209, 256702959, 259488070, 136995538, 281748483, 185332884, 82603977, 710429695, 426177168, 336653350, 346706578, 174294405, 399491398, 719639276, 123081315, 177607521, 884670950, 771459306, 782806631, 955798223, 295083028, 342298637, 528153379, 70696261, 373860590, 494449705, 476146842, 577919990, 505601195, 752889311, 665474035, 478182392, 578965138, 917142938, 247534482, 228794794, 345165840, 623590363, 317386694, 4661750, 283243248, 211695035, 850363871, 347175949, 10997663, 902719343, 379541129, 882364503, 315327511, 850317367, 844818500, 630944784, 602320765, 416604774, 330246739, 844906676, 568745911, 979520794, 955070616, 803718182, 485971536, 876225609, 32648287, 607968234, 238442019, 552171029, 159252625, 931907728, 210181116, 375915268, 324420915, 844287630, 740447418, 255717783, 967928314, 727005336, 289945298, 19536491, 936084893, 106660224, 624511279, 926366662, 924566802, 998846243, 570576817, 554047338, 823252976, 143900542, 333465762, 892372903, 309892072, 900656557, 493144214, 832997023, 696042863, 368752300, 745197843, 90889505, 191542357, 359350776, 816827251, 354362266, 932781683, 988852853, 451778520, 158699049, 297906652, 984512537, 61883583, 866776690, 467275989, 317093036, 59917717, 832535205, 524440513, 316908649, 314068263, 6646797, 574893793, 169351405, 535525129, 737221083, 744486041, 841193971, 500062083, 960998256, 218928449, 387167999, 980807296, 3527067, 940487001, 431075887, 584464530, 443742703, 778018433, 728018017, 789218818, 636250107, 77487044, 351630865, 239106660, 770109341, 262186543, 890373720, 32817659, 692352267, 973333055, 562008715, 641134855, 658237024, 434164752, 484801446, 902654826, 891296473, 139853894, 593071601, 19324281, 214229613, 701730584, 255107679, 386947267, 88933647, 531149775, 244804734, 20052556, 272787217, 446207517, 189168529, 383133965, 292226531, 537440297, 421544395, 121329772, 108621076, 844923828, 420662844, 12003039, 512673191, 160687695, 125324886, 309178427, 439564187, 477578639, 50169406, 537098199, 60189262, 942271996, 423816343, 773264804, 331420549, 190992562, 243002164, 962947045, 950372898, 320042686, 787298293, 728392124, 447571580, 590027133, 136986208, 388444032, 372264621, 877824039, 888913131, 907638449, 760791179, 979533460, 629396461, 970185913, 319576918, 956819705, 512456939, 713993415, 509451185, 119105630, 321239161, 472667792, 950476775, 549725522, 715585334, 524546396, 381746146, 472936415, 174532762, 177823636, 305148775, 886481836, 413881421, 265001050, 288824636, 554383339, 430848904, 118876670, 260271901, 259905104, 907410142, 442763880, 862520204, 634536377, 209761623, 504889345, 76987290, 556301839, 42751213, 672549692, 309491374, 960396627, 948278817, 343097549, 339037812, 843300881, 567785735, 59868732, 567073785, 528314845, 379869490, 158813971, 379533474, 199279294, 503446866, 138287096, 32840355, 510112892, 685284952, 551470282, 806038713, 251760254, 210320509, 846318927, 968290662, 929734591, 938036733, 678553920, 12888783, 95239588, 824639639, 820381274, 42264173, 134143645, 512062321, 275155074, 530340805, 518312881, 625235421, 114278173, 845075291, 437224248, 197153976, 342515320, 900618263, 841817450, 224872258, 328881230, 489581437, 564809303, 387554081, 564029934, 791640994, 356304147, 274799470, 136630698, 516738417, 348972330, 735892972, 661544886, 357933446, 458402954, 457297053, 724695403, 702742952, 126989414, 322229627, 472462882, 541870552, 375995506, 80438189, 871612165, 292945664, 612905957, 529593863, 462118677, 401310769, 446084283, 837289242, 587257951, 576728210, 534706795, 144088707, 28261086, 230091996, 861232675, 94242956, 180240844, 314750225, 120819132, 460868794, 131566611, 123966216, 235761066, 444573755, 164203832, 687300703, 893313484, 302221288, 413012870, 163159510, 428017955, 956724714, 855439035, 591849626, 212270001, 829008132, 319542067, 711754210, 816911126, 921685461, 136122915, 539667234, 609599999, 584626553, 696816561, 769498436, 657810994, 610760095, 731669099, 353490503, 393022432, 747908833, 847246360, 222318081, 763058796, 369472956, 214775057, 121818269, 705754989, 955060656, 968262316, 734992163, 17479005, 965251975, 65161240, 529520365, 625840140, 774157228, 240261084, 38379960, 794520797, 588399161, 313597850, 389123513, 553975624, 572753307, 506136794, 91809356, 778279114, 943456760, 941135361, 895064115, 665798567, 9474220, 743583488, 733930543, 852928890, 449771867, 794601266, 680310390, 637379685, 823362414, 209886594, 313407019, 119969430, 805901591, 382710127, 272788972, 609038603, 761442869, 337240803, 358926121, 198780579, 573804441, 310314146, 979191476, 140850920, 447401664, 953822093, 816935745, 876850469, 357652142, 418485353, 923788268, 998818097, 790694592, 827067516, 576634112, 537350238, 121254704, 801642252, 126833197, 767327655, 589652247, 338943467, 34471123, 407700279, 898963540, 656042238, 843246964, 443216371, 447037409, 644220109, 74868739, 73574092, 788427898, 617033313, 83465920, 303254583, 200152294, 716709480, 906739069, 607092278, 936274178, 218215672, 18316897, 678339165, 382882070, 332891232, 492720415, 931423845, 139790093, 140247474, 739573267, 350596566, 253450566, 905894747, 448784057, 669011213, 293899986, 983242507, 852894555, 103297766, 977638307, 181544008, 594201243, 965037366, 119123896, 810998089, 616856222, 405963614, 45799732, 559618721, 197057967, 706311546, 30968852, 660792745, 552710060, 746353934, 614685476, 705228267, 828882530, 939752075, 478293578, 514288005, 814486878, 227766435, 363079919, 670426000, 827562339, 568567430, 829056078, 983366359, 950077673, 719189868, 16906496, 292384770, 917969318, 701467664, 961815491, 668554007, 86515270, 585322234, 858197303, 962839939, 327300242, 265267474, 117588535, 805633759, 753869183, 136586747, 508500187, 740987619, 498175774, 526038998, 332468307, 295499793, 939027902, 378035605, 470556576, 775207929, 874624229, 642017101, 980431934, 360026225, 237072326, 936710911, 380120873, 282420109, 608731087, 438725169, 817174706, 670944964, 829858379, 704796134, 504419258, 329000126, 952966445, 612616743, 560540027, 763293927, 203433739, 511149779, 208505259, 614336895, 707381057, 17380255, 281881719, 655411885, 697485324, 647181278, 105943436, 448233965, 879225423, 59561095, 616186873, 625377840, 37107638, 604192286, 594193138, 194626538, 923916020, 396542613, 604013726, 9089045, 699207306, 460816657, 626509010, 456858475, 19863732, 505790343, 253668109, 599628723, 719928492, 21461030, 529432811, 555841803, 962594292, 211402718, 33911395, 421337751, 208242873, 323715418, 540855928, 434439509, 521362356, 449056644, 746067051, 573544964, 458855961, 344175578, 473900600, 977516335, 66054961, 910089269, 931801858, 622025316, 924712911, 554005299, 43564386, 344988429, 401352356, 104061615, 242042604, 933028275, 736140463, 10376582, 85425172, 672357168, 590612125, 301600569, 811632378, 872311386, 272230661, 344536569, 909471881, 127432507, 858380674, 292082738, 414333646, 155687166, 92153296, 525280322, 492335924, 801469238, 296115792, 622288534, 42371828, 754536310, 495972346, 707889267, 761485505, 264835680, 292490171, 425615379, 19001657, 520168099, 651978901, 311861560, 122634317, 151003281, 662052221, 770020239, 894467555, 414114818, 270857553, 928365400, 374649330, 788694470, 536785119, 110654461, 168559734, 958951631, 927515241, 437352819, 166754925, 943504265, 3456380, 73852676, 85285831, 241684747, 334440199, 975858453, 886202535, 872656792, 589652312, 422560097, 298918837, 115808176, 457436413, 32806884, 319769148, 893598249, 62774379, 970912321, 509933774, 16807833, 216806555, 214269155, 94663606, 608018555, 777301399, 884471408, 211274834, 508002722, 72743859, 397836886, 890703366, 706329009, 750455599, 317252298, 735893498, 799598821, 407257788, 76801055, 476383556, 286895440, 587160337, 281215669, 897567298, 574240908, 605952044, 223952342, 106465312, 643869545, 954236454, 989711612, 520499882, 841463917, 953632595, 876897156, 496494932, 589166944, 167341648, 629488775, 782920198, 150991196, 745728825, 280553544, 737669059, 19722636, 213999915, 594658881, 984703004, 919063622, 593364555, 276055561, 988408350, 767060826, 595487498, 129906809, 118840945, 49743896, 367702137, 523151041, 798424889, 556921243, 255752686, 304377195, 947008231, 379959755, 389676322, 658227442, 489570949, 961175330, 449473946, 635185090, 671370112, 117637025, 162083988, 680715876, 415165701, 993955494, 39776626, 440678953, 995759861, 654150041, 511317860, 417070550, 464659669, 16627766, 871452884, 767499349, 909125655, 300098418, 54784258, 487114695, 169844953, 456373928, 570541313, 96453647, 531173990, 677705676, 937505127, 735904743, 466716664, 613044791, 72012012, 500735372, 988011909, 26503495, 527290221, 725320435, 723890646, 505872496, 698283492, 167649691, 127235192, 262742761, 66234906, 433544311, 210973443, 646612414, 495099278, 326884014, 870385813, 725037754, 606001076, 209375299, 252986338, 748663927, 365802401, 752626084, 663903448, 367967872, 728425461, 837895258, 400920172, 832544346, 963505516, 357670240, 14069842, 694548792, 727863102, 283869855, 380740249, 739607262, 270766305, 834537292, 887571098, 673977118, 398658349, 770309042, 860905553, 833995115, 539724279, 387740670, 15009121, 382351535, 176234089, 620085220, 634199964, 189729327, 391202357, 635950347, 562579472, 394715882, 312526924, 953199651, 662691281, 748287884, 409548899, 646815218, 389735985, 791678874, 948180363, 847587670, 340938857, 42354647, 942470530, 684907726, 259396383, 323126562, 870785710, 499501250, 568936371, 159888018, 89919967, 302321427, 543897362, 397827937, 341223417, 580204459, 32191927, 694875825, 299873756, 444465547, 459790645, 975055249, 776311677, 894815433, 749756494, 265756612, 844566808, 233122092, 168694353, 661508734, 263592607, 670947755, 988289877, 293879949, 519747596, 50690273, 519271478, 814153649, 860134525, 88967048, 348463667, 634726172, 514426775, 949294054, 201770076, 176722050, 383902001, 864127616, 498420276, 440679845, 765996895, 775384622, 200187198, 731312688, 801828132, 481119151, 987499032, 716086548, 158830889, 208012948, 313229015, 789069749, 851779925, 810559556, 123209494, 307684693, 568298717, 744707090, 862527111, 983839741, 812040754, 793473796, 917921805, 491061501, 772184029, 476819839, 136769232, 952792296, 733934918, 472477164, 829525868, 996041839, 667928608, 52951158, 113102474, 65162229, 711834498, 719380551, 676962431, 209162771, 790480985, 56775836, 261907199, 364205075, 203515756, 184871732, 552183643, 223954064, 387463730, 701915798, 477312042, 522437510, 572125833, 492311510, 485567228, 985766284, 752892933, 415324510, 358102237, 424399613, 691834597, 292711342, 542667246, 699612423, 64032175, 798894363, 844859285, 556659731, 74993008, 25198003, 283348449, 105419381, 783184744, 912620368, 113896508, 152777657, 334825973, 186216599, 264163493, 744158051, 576324185, 110336049, 18974964, 207447704, 702575764, 195200199, 31844510, 278084465, 307337573, 616283203, 601701427, 936242429, 245231326, 58693595, 153266980, 549203128, 670997360, 453361687, 945905011, 440756522, 700836432, 431255832, 111737475, 760236799, 964085148, 951421095, 949029122, 845191306, 680605132, 157524109, 730728427, 709821462, 726335831, 492561223, 134807987, 428285660, 639238773, 875518155, 78967557, 939693877, 248442692, 51446926, 10998912, 641821046, 161671545, 467280024, 772049530, 575841616, 735933201, 566388801, 616327462, 532141466, 521257886, 177993979, 421758155, 17802888, 796610267, 187034529, 981258019, 821331196, 509154733, 597322524, 153919047, 884970387, 895497975, 832101019, 117581389, 976291067, 966534806, 299026495, 129356675, 5818909, 342765905, 339600184, 165395244, 688824342, 480830283, 520684446, 988880509, 89312132, 178893900, 641001770, 695173731, 412310043, 652830049, 323289097, 598061656, 675424529, 345461978, 20823439, 275926227, 951519769, 683793662, 97217058, 748061266, 386845504, 908942231, 181025529, 86876218, 413440800, 697344152, 886619665, 839196470, 840898144, 335129071, 628770823, 862749306, 295150407, 898615729, 749900075, 289559154, 198367798, 976250975, 354960738, 850867860, 488331872, 591569066, 22896690, 376876201, 128836410, 42136424, 657474327, 507912653, 81791438, 883648238, 394747124, 801897350, 665459910, 981289283, 294231312, 49031760, 77168514, 756871752, 927508627, 539553312, 66692381, 501295162, 762155907, 974348476, 21031084, 76183684, 452588937, 90636392, 313456596, 437934469, 665439972, 658612137, 309610586, 854234786, 917667022, 302398375, 354071821, 504521603, 543363965, 939486967, 775958910, 30703227, 447238924, 104330661, 905085644, 806946854, 970478783, 965833679, 307543502, 411745880, 353427383, 953357640, 189504129, 952247052, 999691273, 993276315, 591700806, 801413969, 329148210, 656089409, 919666413, 177126969, 427789775, 267620511, 959462209, 735522570, 540372697, 109587578, 862872237, 738154972, 326867338, 533495768, 838816978, 960316461, 238207155, 532093214, 88919516, 535670419, 753502208, 697249605, 324701783, 563691398, 951097853, 427380284, 615646693, 494167449, 149853606, 631940720, 53826251, 775466556, 399239360, 48541802, 549091645, 765313129, 61631504, 316507683, 811462309, 165780186, 464246213, 388506750, 975381897, 854423181, 3832316, 297603942, 576581324, 372810348, 806367912, 153808054, 771377633, 181312057, 532846232, 52800938, 886578992, 111567688, 233730802, 914282162, 198062828, 398597791, 32132391, 501164413, 295058888, 884315583, 856440689, 435916795, 961651325, 314816350, 255522728, 534444691, 199814546, 899779560, 549318404, 33201038, 76711720, 917523440, 908911063, 265420465, 341480311, 896114998, 671932549, 169661761, 989036940, 764970741, 212563717, 180281423, 681382287, 626497904, 274617382, 869322036, 308970361, 347471631, 105780051, 420023801, 449324919, 182977725, 948476640, 597370398, 50581747, 541572586, 510420901, 297810406, 463384078, 874543502, 657551718, 919549513, 257046369, 195660502, 115803531, 388485913, 988237150, 298750973, 45402467, 557009491, 887259326, 399539000, 887466576, 452607896, 815423193, 50416057, 503538481, 31489283, 243306490, 579484906, 920013508, 641244232, 407436955, 285619924, 421979579, 787009301, 339921633, 734946252, 470309029, 807465034, 757897450, 997561397, 799393666, 476813807, 336074591, 304030358, 764199890, 85488184, 881519675, 335957660, 74100036, 246738318, 430314301, 744498098, 706262217, 281184288, 440266348, 233245696, 225011729, 218463424, 245072491, 55156607, 325962466, 430268119, 247412279, 310078473, 115163566, 943566906, 850486489, 319383969, 435752985, 952041643, 831236324, 362929165, 178815701, 193715204, 608562716, 612144481, 843801521, 708703992, 648749127, 879557372, 727437662, 392863858, 330527862, 712276079, 561752202, 720741022, 849956928, 339104700, 202661144, 208243673, 524947696, 853848724, 764046427, 10451583, 213125396, 990776445, 78436484, 175708678, 208415856, 666613330, 657704138, 674367450, 993652323, 427093987, 76826584, 479651708, 200415452, 803638180, 594779928, 14013312, 491499439, 490419606, 511467463, 172157368, 537886784, 248237671, 128899613, 403052109, 48108103, 590322893, 555097030, 6982678, 564845428, 516073798, 733998867, 379919991, 664869936, 442882582, 637677187, 46772222, 813061764, 455906540, 930213246, 559262793, 186228559, 410530, 420276354, 986909077, 151483941, 3918323, 845017547, 677573426, 924826481, 195356761, 808727273, 765365060, 778706428, 952265263, 299929128, 409626500, 897385338, 114950722, 223696209, 813568703, 773327079, 314700851, 269940919, 398935294, 588553622, 972412570, 116158976, 279612612, 110284227, 335325164, 335251975, 898805729, 711925048, 553878034, 438267568, 922030264, 669048392, 640419337, 13087180, 237202447, 943993508, 331764904, 831691971, 565569418, 659925996, 624042387, 470940420, 708584800, 547325076, 848562825, 407222878, 970647451, 602019092, 772208154, 287991988, 428531152, 673226748, 582340100, 941000006, 135181148, 295686637, 118909667, 382497408, 670611281, 460557006, 667184502, 385216500, 546631044, 947411876, 995555829, 202243752, 572556772, 465949551, 809063938, 684194368, 411727905, 706506704, 888054021, 455546833, 888756068, 677011133, 904199963, 949535512, 301058532, 190812401, 578847929, 813249122, 12402735, 418465032, 883039223, 413941665, 883408459, 213217690, 345883260, 671514030, 992813289, 678698834, 132408081, 295700142, 64499671, 588794581, 502135396, 863144694, 730072597, 206592169, 282693915, 697094390, 214384265, 228077924, 298062847, 836102934, 623645989, 587780051, 404925604, 982223647, 438884234, 275260743, 431197651, 404908205, 134819485, 848182753, 886142478, 730422273, 571368671, 181092026, 173413661, 468196834, 902673714, 257168444, 136004693, 242210225, 982479605, 849032285, 956370012, 598127051, 954542171, 81608244, 687571178, 563009011, 116387902, 96395766, 345154254, 406176090, 813915760, 644422750, 140728378, 92189649, 345103929, 568622030, 311815213, 931958103, 140180290, 898642094, 455536612, 933737728, 835083550, 256764888, 263802264, 893051120, 31590884, 271046022, 808647107, 739608540, 676704071, 136562482, 120922724, 475656411, 378987843, 501016765, 571002473, 629942005, 904303191, 517243735, 62962148, 706906512, 481998149, 896616220, 465799441, 691534758, 342395904, 740619128, 882237675, 723933292, 491606319, 919855247, 958916657, 233841753, 30781325, 816046539, 956065566, 812773827, 803738485, 754723016, 358339386, 570321752, 209403986, 567178185, 898456465, 840969043, 653960783, 133080805, 421598208, 848144514, 458779491, 289761176, 69967895, 881910540, 414687916, 377841436, 891132650, 610386319, 303578580, 346147752, 918222155, 70297189, 563506478, 618243336, 211089380, 208452275, 891653927, 107146633, 72636391, 722732596, 367517688, 293504737, 757390286, 567429788, 63029707, 596276398, 722918089, 107691254, 362885634, 520990466, 377148566, 880409355, 104721762, 84337840, 299956637, 14092779, 14101165, 446075610, 137258784, 874571163, 987261751, 212417112, 977284308, 49105255, 767407021, 479615213, 406714707, 369880693, 888022377, 890550491, 54254083, 904867026, 973196385, 829105535, 811540190, 643086893, 204013914, 114490695, 212905301, 544359199, 732354624, 200870107, 182175375, 130118343, 417034757, 784421585, 650157368, 891138741, 303800177, 329359530, 194119030, 382036242, 894145575, 410601938, 434023843, 570363059, 291592184, 313876594, 45946079, 592888162, 564142667, 899398333, 497502058, 647633237, 733514723, 842514679, 518042238, 311261412, 119670341, 928180788, 252354424, 447600815, 716819779, 256909960, 412344450, 637518729, 430600721, 891141303, 565101836, 135332897, 126977049, 728613646, 751178370, 597304832, 468885014, 271820322, 301701380, 471185475, 286225438, 963301994, 871136876, 673481309, 815064331, 604139034, 964468134, 746692563, 119441016, 18691994, 285049147, 743925712, 28545379, 460216703, 62528231, 197424425, 775876770, 560475081, 771381290, 884804448, 250617066, 451967927, 904564368, 775165295, 743237986, 224951487, 231498521, 753491180, 834149106, 476778264, 297357201, 208084572, 545062759, 449046075, 991569871, 140626904, 628502101, 301240067, 176916147, 358422534, 614570287, 990157268, 429349498, 624748240, 324664171, 412316808, 858835874, 689800651, 736458419, 697561588, 680982850, 357277360, 684496641, 881243661, 945584551, 365150940, 434797101, 847244081, 971061685, 701151610, 990329021, 203429844, 231926630, 531206581, 870913318, 852314937, 414017269, 920166163, 533644455, 949630277, 572112912, 231195026, 6547397, 751428992, 586739435, 244707134, 300870928, 479483326, 963517796, 834663459, 358486783, 240875851, 169553993, 597095033, 327158193, 728962210, 914207635, 886034071, 514158321, 688597229, 680080438, 583585706, 578485912, 252001814, 982561599, 381397579, 89003898, 785736960, 250074484, 950336619, 476079419, 126977934, 928180152, 698519071, 973472936, 444975283, 789488361, 977784573, 257761103, 476487317, 410981030, 287844304, 561054345, 32056223, 20390499, 910021845, 928114181, 127088141, 69004961, 371051794, 511946710, 390598468, 163987748, 544478383, 388165546, 869529674, 192840898, 130685722, 806858826, 350290982, 672024404, 753612687, 876829043, 840521663, 43183007, 814832806, 658046986, 438777730, 101941879, 222157127, 159572245, 660394665, 81381710, 570606131, 685143200, 153447097, 155436544, 611098425, 718478673, 502098346, 894053727, 898352106, 633116794, 129603206, 599021002, 297204959, 708762932, 874306112, 132197909, 832678501, 411984339, 615008456, 838195410, 66777327, 252858184, 296207305, 843384107, 184420926, 233945654, 66890118, 319725592, 984513001, 205440368, 279745939, 922547380, 184631112, 42138175, 96301681, 181742900, 84297565, 428897318, 997652112, 545342626, 932308124, 407750118, 49575286, 982127167, 212169293, 926147900, 870358469, 130369738, 472604697, 310224195, 304817587, 877637123, 742415409, 224025537, 982468267, 960271444, 820025516, 411598905, 231547028, 287750448, 720316206, 57029250, 856937080, 774948365, 581289135, 857678711, 93388707, 837698265, 576382813, 866022419, 839308297, 922125107, 787114483, 75328672, 16489896, 585704118, 660826884, 916719848, 663239902, 396522650, 441173602, 722781607, 277883038, 218317500, 379506775, 894481454, 461235399, 451639295, 322178138, 981976819, 423925532, 249335646, 341039591, 999210597, 326902352, 664833066, 760927049, 976070355, 594535747, 831216937, 560466311, 911540174, 905281270, 492728966, 950295655, 398622966, 953635405, 558309174, 139904339, 20671135, 247541452, 713666265, 8361519, 710798900, 116485804, 193857390, 597377179, 258902848, 948579454, 69440731, 946579319, 2265382, 193749702, 229376411, 776853730, 533974475, 409631752, 847430402, 757443839, 520404804, 103764451, 473733428, 558999885, 500923996, 954216038, 867248129, 477270663, 954769145, 817819321, 240560408, 695913312, 780032670, 527425795, 173136576, 739018705, 714606181, 673339781, 45497745, 230739980, 543189635, 342970792, 362867680, 533823151, 249312475, 78215746, 33915453, 376571212, 101033465, 656125773, 130095038, 411341071, 755180452, 698409281, 102561700, 702309645, 64613070, 702874085, 388112741, 885591709, 812702224, 715539839, 300308961, 900732268, 600389889, 775392901, 556118828, 88168195, 466574043, 80856153, 842994392, 4583641, 827205363, 978758205, 660620716, 441209059, 324296670, 892489584, 940667338, 639369629, 296063492, 986386841, 830754825, 704528420, 693108722, 113311715, 511435803, 893242780, 535783395, 289063858, 568071469, 652699778, 716231519, 333335304, 758177376, 27591879, 423768880, 39719083, 879564778, 238625534, 177397666, 231099984, 32568932, 482934095, 99860028, 227161885, 991001605, 408479976, 716847061, 215184617, 866043713, 865890565, 139484981, 797963486, 569219643, 725019594, 776853298, 992921007, 705858682, 771937860, 396605623, 220433436, 47852181, 390324219, 272969931, 131066577, 224532035, 741271075, 370437321, 129375791, 816589975, 422458173, 319300426, 353635387, 563732529, 906104335, 970766096, 97648631, 142639115, 743680399, 527157912, 239648124, 239005714, 645791763, 125356798, 144519145, 467259023, 498076991, 999340242, 197636970, 409844576, 202797846, 682601535, 217157478, 656419401, 48141233, 165232869, 667004928, 503059641, 357543579, 873575232, 426531783, 42941538, 376939492, 675657597, 758124157, 640179225, 336396543, 514740064, 22964574, 767287186, 821756396, 815012776, 813279315, 761752103, 968238889, 195750726, 730971856, 792088753, 129294017, 683088283, 35414246, 255002724, 431016147, 671931477, 728147022, 977271626, 959356496, 4790344, 609603076, 208809922, 400700337, 171824719, 425465024, 670776606, 172005012, 516337363, 686256572, 907370327, 91085675, 436388137, 488145393, 880734659, 610511286, 751464567, 563707442, 836282811, 253265744, 245676338, 30201573, 913626696, 831023606, 326086253, 743151376, 282206626, 504392870, 655660368, 892568218, 611402257, 115556955, 604876345, 171738241, 54155100, 736313902, 474010192, 956666935, 388306085, 459128566, 263603474, 243530457, 289113459, 155384095, 725314131, 774874993, 635129362, 746605728, 393081803, 208309629, 165808091, 761123838, 997182866, 599474840, 507240992, 224067826, 242923200, 205280086, 150532660, 147932279, 528378440, 805160862, 667946629, 930600936, 189470815, 567338284, 86845250, 326431625, 180882533, 518970143, 872213402, 888348464, 129048875, 210878772, 16489676, 278697808, 584778734, 221442637, 202020118, 584949486, 316104414, 359652295, 368472798, 787025214, 236584960, 264449329, 86527102, 154567192, 664733880, 896096046, 62268156, 436256321, 178587196, 681236936, 69210478, 253842376, 540141637, 258532435, 818578741, 594434060, 608332089, 303931207, 59429220, 822907584, 583621975, 407298574, 581165429, 297681723, 331824607, 11534055, 597065996, 202085062, 771477527, 608681042, 255178734, 928094380, 23656829, 724936428, 556624904, 914237019, 82648936, 858026497, 246644599, 999277441, 210515651, 122506320, 982960323, 278207728, 258231321, 225809205, 429708661, 883409137, 504554342, 26484258, 675376588, 844767712, 768854266, 202947894, 930225779, 214026472, 505129119, 162995393, 528048897, 496316111, 105749096, 185910192, 477059644, 506201771, 596288283, 392816614, 582809600, 348188207, 65921209, 584463722, 346011727, 375965092, 934433319, 659191893, 841640733, 308455791, 471054405, 803925837, 966548518, 960831385, 689892992, 507728723, 461713105, 757181735, 159639657, 753543514, 618794641, 870737604, 493271536, 235388545, 304465697, 993215322, 205568908, 855615744, 283319489, 478511729, 217902688, 824862135, 907807679, 720178684, 757285318, 245007131, 181357259, 35828153, 604205358, 128848126, 660869581, 888251322, 634781437, 217917617, 990262202, 179936655, 685350063, 132111885, 946376281, 459047745, 699483582, 257256485, 637147668, 367002290, 266218943, 2030007, 118947520, 986055110, 435197532, 730483786, 214399429, 893617634, 613674228, 259298255, 650614957, 973260394, 490327956, 713185070, 379033658, 263586113, 738941625, 387911232, 71769011, 54236225, 933027517, 677098429, 518263429, 103914124, 810897849, 445091269, 827969670, 682765138, 801651313, 540961625, 473820476, 278216777, 16974755, 837642412, 31723303, 330476297, 195427826, 285660518, 153410032, 972460180, 749062324, 650544434, 677270911, 766604115, 73763290, 114958429, 598959321, 730858523, 885179050, 842067913, 861612634, 649588136, 662899544, 760558481, 149427074, 550284434, 294587954, 751762644, 646957877, 354612797, 235974218, 276053720, 126313430, 566837170, 191204178, 446907343, 586293832, 672793530, 796865014, 955462722, 657228627, 862814843, 830698159, 809619681, 183095272, 19828736, 634608843, 985359047, 928216511, 183863892, 594618098, 453635506, 325001219, 528880264, 362443933, 190746277, 255970892, 309764971, 544585284, 417749964, 801161656, 760782002, 891272485, 172757584, 381177656, 517155189, 751572616, 967107908, 962876253, 527913821, 125134241, 291489580, 768393388, 62924278, 562973971, 633728639, 499881522, 337610463, 158522706, 395671048, 220381046, 926001752, 952603843, 506660338, 543728434, 121885088, 172974342, 245731622, 558223148, 913682676, 164003565, 332682473, 300476371, 638046018, 188028594, 867998990, 584064436, 703115840, 961139001, 46141899, 858559334, 265683289, 393919242, 636879368, 192222184, 201458499, 658044687, 953591673, 116464143, 554663729, 223627057, 550386785, 84688652, 646363983, 48320923, 105122489, 935221857, 20742484, 904894418, 250687797, 113535881, 381689593, 932999097, 187944340, 213849002, 312079026, 641501017, 261273056, 89366730, 889342046, 121060035, 351154985, 793476450, 248724500, 303403362, 163784503, 26514412, 649795769, 585371711, 585674874, 512599993, 285150422, 432638017, 355681071, 326808211, 684666386, 684478616, 960206505, 240456660, 304251295, 664444170, 388128966, 257182884, 158712343, 998290218, 466309530, 174396443, 507206860, 87041084, 692106863, 878449246, 735077689, 781091348, 998375954, 431304402, 383523386, 117085999, 723289199, 135978866, 533100373, 340800733, 205195002, 63079632, 182657404, 591776657, 310536285, 312340017, 792483122, 846364382, 24769924, 691101149, 81944241, 252404931, 237949466, 656399950, 490285228, 576342256, 398137459, 35874901, 561538045, 221455055, 282832928, 54404898, 284522292, 951875996, 117099568, 601782802, 908093649, 724981066, 577986176, 646343213, 468532819, 686786871, 631255094, 938859714, 622292471, 372023813, 356007941, 346854247, 411159386, 255903176, 353580089, 257617468, 770713534, 152585464, 78517329, 857443150, 938547916, 677658491, 693810380, 951895216, 308503521, 746236973, 186845928, 762532657, 166236847, 696099633, 966811116, 721317042, 16687430, 264318217, 883262188, 706911033, 638565565, 942541098, 567585761, 609179505, 508948191, 650677937, 759548383, 144639776, 749081164, 952788006, 377413675, 486821855, 466762933, 7904996, 666493491, 92908356, 247221583, 329306874, 636223487, 527914997, 242635218, 46580241, 643053436, 317703974, 249856518, 276660651, 942692175, 679837872, 569182751, 674262998, 731472254, 405366348, 536196085, 259662745, 727623563, 974974856, 565204518, 635521448, 853245751, 385657278, 67599265, 244982914, 667048266, 89828829, 842302405, 142472648, 626057012, 413353883, 122994850, 409758938, 961483048, 378365297, 378603784, 846038770, 952304517, 201403446, 308642801, 175745593, 759720426, 73939504, 449160393, 877998196, 861521679, 673840279, 994807827, 624707379, 972330811, 655553591, 260731553, 579376455, 887451000, 172410285, 436744762, 62361816, 77697038, 933582610, 501773340, 701582842, 387129712, 474410874, 997108228, 428447626, 740553556, 224198377, 566358723, 149452225, 243958603, 751593673, 152855701, 680140825, 594997425, 412025102, 589632526, 867811928, 110395156, 98908655, 130658659, 100438662, 991359944, 532578635, 548712132, 271879011, 940433787, 990912221, 458657071, 606871004, 983458964, 211567948, 159020399, 821999299, 520780283, 496978056, 252487482, 324286927, 681048351, 128935634, 891596724, 634460530, 718957372, 707769172, 143098210, 633197994, 313131853, 483448494, 597232117, 467521193, 395023894, 739179124, 149548917, 169202442, 928107995, 705839061, 464143899, 664310763, 259313177, 155391582, 620281021, 425795624, 864585616, 787087402, 960917107, 95956244, 563744231, 447571574, 959322408, 151269062, 541906624, 415395072, 583261216, 417375611, 640088268, 316479606, 375655096, 995985898, 807861076, 876572136, 333019152, 805541028, 583967885, 82599347, 420058816, 904910933, 368127611, 647897735, 581203968, 662248775, 402438291, 791426, 752615004, 797738805, 174167875, 195533990, 142772538, 816530397, 719338174, 916369238, 338012455, 986458160, 635640315, 914722406, 238641187, 389168399, 530758178, 809873696, 505113560, 675141831, 215478921, 128449689, 311253996, 399957825, 883812367, 18525101, 437693952, 823008097, 468600903, 257222792, 769885503, 443750931, 946438791, 334558418, 439860810, 698972947, 119822696, 852464937, 530697642, 463623763, 652372130, 12503148, 212032010, 631734877, 973519499, 26985490, 787691389, 324907895, 557313724, 621353897, 755975122, 656726262, 213040043, 815047995, 728944243, 815412185, 575456948, 622788678, 50702850, 436441612, 546392695, 447601757, 173388295, 44015111, 300993893, 988817910, 481025588, 593567388, 174005837, 828472843, 733846271, 650822019, 673763646, 503729649, 897066870, 783661845, 39591037, 133644090, 480984905, 181913774, 65910435, 637895007, 998970277, 313323352, 945400323, 67467005, 806557254, 768482091, 105421703, 913562329, 176580161, 479459106, 842893292, 818922330, 523552584, 215215395, 633548905, 131128515, 813382015, 149370537, 222501577, 929078373, 971193332, 191749431, 142662075, 84861139, 753718623, 930122460, 360244109, 308197949, 750054106, 786402460, 777591590, 200754227, 607443968, 546876224, 822975154, 563561304, 303723025, 908668409, 565709736, 792559169, 188609733, 857194742, 435265637, 615300871, 607343890, 497332375, 413573408, 169117975, 295987183, 748292576, 183503048, 785331492, 310680085, 277836283, 198729122, 924617785, 393475358, 350007516, 896490708, 319491765, 224514190, 2244179, 628425806, 714461220, 331064990, 964914635, 614053586, 428998099, 84768388, 843417146, 627569821, 458224064, 64341650, 896633472, 134988301, 595879806, 848286477, 366981137, 172553581, 548247118, 601086680, 559954555, 655056565, 132070085, 733145632, 545190418, 259411746, 93534363, 158888992, 977745237, 193327966, 436954392, 412977656, 386520370, 363635025, 136833040, 518206252, 464385622, 131338816, 368825276, 99228806, 57735726, 167091471, 299662790, 684656492, 339505011, 610128620, 494801078, 92169095, 918551074, 797224624, 972607493, 703468036, 175465361, 156940041, 958014526, 409138230, 564339900, 285950188, 380228517, 337485284, 48215442, 126500935, 873282743, 193551333, 895221629, 252172404, 441930173, 789548329, 169068967, 120521563, 537013000, 319956407, 189519569, 467666654, 852223363, 374365455, 429923210, 17109350, 337363407, 752437955, 591146271, 542104638, 61065793, 158461478, 392268394, 643411740, 876067556, 459223846, 709188482, 177112092, 977934806, 743052813, 642493831, 362309016, 780337072, 339653041, 933105726, 110588023, 779453876, 942906819, 356312447, 645937833, 957905313, 142537746, 218295348, 164778989, 415067747, 884208885, 898749069, 739327510, 58402606, 304702499, 966536765, 34810346, 158816648, 706103168, 328829402, 857472788, 890322036, 295174417, 123424822, 630335052, 971008174, 5962862, 812927726, 101995930, 151908502, 942858141, 804386572, 998564097, 731157474, 247284541, 720379115, 441372935, 551414666, 674672810, 247156893, 388070725, 383672980, 782395868, 315587523, 448740364, 279915448, 979557971, 466573195, 814674644, 557018322, 755349395, 846618941, 832238825, 959926420, 522010053, 587485939, 877198731, 273589818, 279438433, 886370588, 731106472, 461412299, 761900806, 677138265, 721154867, 107385697, 717218822, 522873606, 39393126, 942970627, 342712961, 329320973, 941289585, 220045125, 144687520, 284525048, 450111548, 181252647, 432964854, 457666288, 454184833, 615131103, 841555969, 437863201, 853189516, 239304563, 269944162, 607336332, 94449398, 247211991, 121114092, 793087106, 50745671, 274351343, 723846053, 49461613, 104895632, 831643846, 972162556, 628419106, 493740685, 624637223, 743371046, 773741067, 314115526, 365920237, 213239792, 538713922, 477159564, 859798467, 955872177, 791114268, 360661326, 798918244, 784216563, 701734029, 543828757, 980784506, 341725015, 574226595, 370672130, 503996345, 627759717, 626615912, 25309475, 141883114, 290096428, 758555150, 829128704, 507032790, 25658708, 845084210, 121384412, 175442665, 959910730, 192674811, 776885307, 745144536, 681536390, 174993133, 468859420, 456246618, 369145726, 263303725, 870688668, 890030725, 584181315, 806405378, 334246033, 750713037, 145046838, 742361286, 820260797, 169752662, 127368007, 754654377, 389361616, 384609262, 539444572, 596046591, 626223301, 568055249, 288912139, 518256272, 281356767, 203216585, 325014354, 286207707, 658201844, 266195238, 598521066, 590461074, 783772991, 401708925, 430481673, 539841505, 773436513, 233498060, 422277795, 864989643, 836449864, 961565292, 761431806, 138287974, 170380238, 405278146, 582274497, 189093472, 477947325, 219653398, 246553760, 827192980, 972534592, 895231209, 842039219, 744985857, 893554263, 334680011, 159361077, 370533659, 93619643, 499398106, 884680624, 335426477, 69322060, 789831287, 979645120, 293506005, 64495216, 198941211, 308584588, 845859581, 493575756, 327450637, 481513585, 819674394, 102590798, 827043683, 338481934, 548713702, 80973578, 744659208, 874530852, 788817964, 50496128, 703864005, 751254264, 319258050, 866745972, 647942991, 322422552, 183348227, 569870962, 621305480, 459278329, 564764967, 463711175, 305858631, 653584497, 234746936, 845208297, 814633153, 458167417, 600679385, 170112023, 287262089, 385258931, 546191209, 904583437, 539161604, 769059042, 906840682, 873367196, 411950787, 998849925, 381651628, 413617061, 649426797, 866521887, 565242590, 549208504, 853435732, 530959414, 983783958, 326914526, 763873004, 720740440, 178922211, 306693568, 978377083, 138848429, 549685882, 221306447, 232554368, 485445435, 955348492, 717188464, 448492786, 115469346, 216387767, 764015467, 215531644, 926847709, 570358890, 522393445, 853739, 111103992, 289921689, 738542232, 513946463, 520298127, 574356567, 782181535, 937011048, 235108186, 295495151, 530650995, 89702949, 352493012, 218487634, 643367652, 525885121, 141101852, 651516952, 424823885, 274360992, 806669385, 794747213, 316451635, 400714526, 745483921, 57265155, 24982603, 361901919, 4737655, 810896435, 562578250, 698860851, 469316463, 302904096, 117214244, 902238408, 361674970, 400810564, 297898975, 861629489, 740449360, 850908405, 198330082, 810770121, 614266093, 232107245, 606262852, 334867234, 560048641, 329573235, 346411283, 661721154, 274692714, 726903505, 825137908, 622976149, 823505319, 32810553, 232531199, 866152979, 734136526, 859480332, 942800226, 7153107, 968228989, 154902776, 541582336, 169830147, 181273712, 179512599, 531224343, 628732263, 768260503, 288797258, 592253467, 635506678, 754973838, 415905195, 202612748, 755253247, 689436370, 967589429, 660518026, 129664544, 117472939, 644409709, 731414642, 132115770, 533289134, 944115783, 909209525, 73470343, 215183593, 321147986, 309846033, 642315052, 126486322, 521206386, 291426235, 963018295, 20465841, 663285167, 945891627, 346206756, 703053126, 440142878, 406561447, 465111349, 48664009, 167041344, 86431088, 301335882, 644872042, 52242895, 177775725, 851029877, 288499645, 271631512, 932551404, 190593505, 422120690, 934930127, 950297726, 568736467, 871070914, 844017942, 737315713, 20575436, 986951957, 622789491, 39583761, 729135380, 109619235, 614327285, 51752509, 355684888, 815687872, 484322302, 770252156, 550900099, 750666116, 202139856, 917972383, 589409699, 471115307, 145167852, 557989326, 351985360, 953731481, 664896143, 528011444, 488691514, 621192711, 665597507, 149225138, 758265986, 83017286, 458115745, 678107504, 825953533, 807619662, 632727853, 584733843, 401463539, 743225504, 148141053, 454910494, 209195338, 131716276, 256098217, 216749994, 993740807, 366381820, 522371386, 316018640, 556371389, 838668598, 587806595, 861687630, 771579248, 167224033, 230309360, 152197753, 539614239, 779682238, 733314522, 435299098, 326573149, 285014679, 192059825, 637231904, 65464501, 938098326, 901229196, 550139775, 813110011, 528342268, 746446510, 435005143, 417341914, 471278839, 396529525, 2627076, 830724496, 928724398, 191805228, 420553618, 466158267, 214167145, 218504574, 444404526, 735256525, 849411596, 905295612, 405977840, 819153461, 595572690, 707301784, 256655234, 306002130, 880714313, 636501580, 715649249, 211137122, 614662823, 563552520, 603997177, 733360919, 350902106, 743351612, 362641885, 410394994, 430616473, 114462731, 101238854, 495943423, 932293144, 536308927, 478348848, 971710965, 29962645, 889568683, 151185501, 459396014, 613754311, 52394723, 438441005, 466132452, 553661000, 636152105, 959122673, 193840568, 442729893, 740719532, 158931552, 593832366, 429565246, 557228392, 99304557, 181354334, 831843470, 386504914, 21559952, 614678631, 60083211, 898736266, 270817460, 652394179, 753926987, 771434950, 44501840, 275663357, 464994494, 991369692, 252372361, 489662766, 690699051, 421705790, 7470375, 451609651, 101299289, 460345475, 691119508, 646618256, 288760045, 39748848, 5743626, 740537895, 544802593, 545721824, 840721759, 539187143, 141936480, 194294253, 981103303, 465206404, 197697062, 190222230, 119297222, 181504308, 956810496, 505368549, 370509172, 500654514, 902551329, 100436795, 393086393, 873634402, 669326663, 348468349, 628894953, 259102612, 413292379, 94632345, 72916033, 346751931, 841394974, 274884044, 480840414, 676024199, 456780828, 801388224, 789298559, 444602494, 602318915, 591668592, 80074587, 706519487, 325284838, 959200964, 593237364, 450288562, 628419127, 860250642, 128152403, 57657749, 868258284, 976340552, 571889947, 707586207, 73182795, 645742003, 684859682, 421132205, 580382406, 499201812, 779829416, 375882910, 54176516, 188934718, 508559386, 459977065, 103866442, 747134338, 689297497, 148544343, 180794737, 14341331, 113465712, 150038487, 725284000, 425729847, 807311060, 956900427, 197811010, 770587654, 780280533, 137016213, 837023328, 133874021, 687090966, 325235448, 630726725, 552532103, 272791088, 901311803, 968948806, 30839863, 990527283, 534256670, 573793679, 627666829, 45995611, 11109619, 16849733, 548737634, 830317635, 350353982, 141317434, 897750595, 72613797, 112741206, 527465768, 870094723, 409560662, 154606187, 21938647, 118821619, 619712843, 517319215, 735349381, 289797185, 339352827, 415742677, 75260423, 785264315, 369465240, 430534707, 631951502, 716199324, 16488996, 685373444, 2877591, 119030759, 669887540, 960239192, 528750316, 881472056, 220195386, 410661651, 338669930, 181937133, 978410037, 213789121, 692829169, 663730769, 741777298, 184076747, 654925677, 436645088, 922165772, 829186026, 525096446, 150411283, 346613834, 671403212, 843911030, 416885211, 89863809, 536159889, 615217759, 892463855, 226732654, 142741749, 872013870, 864448683, 946136910, 103269706, 868116113, 264886381, 746275135, 829333054, 427548354, 477680613, 932549092, 358974343, 314442511, 434810435, 947554756, 47923588, 822165155, 982664057, 413076584, 587182937, 302984611, 20757216, 29125441, 82531793, 661217113, 875003140, 325844534, 685012081, 68293586, 343404996, 49225946, 914430259, 831551384, 717643785, 828786205, 508668436, 465967376, 144194522, 979985513, 941528577, 388762272, 726981805, 827770825, 270076823, 674731963, 264096065, 274421643, 198016494, 66242410, 63350194, 404000475, 907681618, 241192778, 506557291, 564279729, 95457551, 963998366, 567854704, 615016701, 990670966, 468382590, 111451528, 795257419, 339102272, 851810766, 371035944, 815262426, 940595095, 452765834, 989971486, 929105431, 514290353, 373170295, 536024525, 961135240, 269789795, 309598165, 327836224, 138882171, 72828520, 47787389, 316679950, 441613455, 420043499, 549477794, 538167257, 129087441, 540922229, 934774164, 171855368, 874581432, 16622156, 147217969, 727745544, 878579559, 118453723, 829166760, 914201931, 115166107, 325563038, 463362812, 315248796, 43296241, 869739128, 546083265, 22513753, 752165012, 607162166, 620084854, 842461706, 187537188, 37363477, 214170882, 331329336, 21005904, 788470879, 570727811, 859900401, 621664669, 916429056, 172886242, 422203086, 585351866, 105292202, 277607130, 503678078, 747906688, 766080511, 255927778, 431201937, 954362634, 660807046, 788340311, 269037105, 458782521, 83801759, 204813945, 727550346, 312245443, 979606967, 52004912, 935286523, 777755119, 352743009, 751060940, 387245785, 688615950, 929695423, 154102448, 716673543, 79663763, 518702118, 901588032, 319928671, 952511640, 149309383, 679870737, 346550891, 586324363, 822024899, 947240675, 162389555, 904357107, 197309507, 522087079, 581830824, 586974102, 537168117, 314110734, 316838111, 618667922, 251168594, 585324691, 208201453, 280832909, 648162242, 26859057, 875175172, 757334893, 365311049, 665598081, 365582079, 441325199, 601795940, 455714207, 262039916, 217485414, 519449982, 849603818, 887709771, 833087600, 909550820, 355947602, 81408759, 783961663, 244467389, 361468458, 177497912, 741781218, 531146511, 289635621, 899110168, 963011166, 240651926, 113836320, 618493890, 376948136, 225287364, 551800668, 32688357, 682359132, 76304232, 603244608, 850784949, 200759360, 179716805, 700871007, 802658332, 595608058, 592789360, 807741722, 68131619, 902746364, 643679015, 884912380, 739598325, 727022501, 641793969, 572448094, 802253187, 533172935, 847158917, 227941778, 918878588, 457949103, 344956064, 699666679, 254038811, 452536876, 409949772, 540393636, 479153689, 75439491, 900440892, 241762773, 954844348, 367779914, 538429390, 669785515, 317461580, 512990662, 629333311, 933266394, 791573978, 932257725, 921746311, 712836142, 403474052, 687173646, 229127912, 239999530, 890985974, 319119785, 36771551, 861658058, 344872863, 604159979, 739569778, 15654272, 511973201, 488150537, 960106308, 548931370, 336292002, 131842387, 785956747, 227787855, 134366959, 412518803, 498764262, 549284893, 641315581, 797043675, 254306853, 130427884, 190600619, 323433549, 409888699, 913107385, 306894514, 596847722, 866393787, 699029097, 444273975, 644568396, 471017618, 461670858, 372537135, 305175287, 83781078, 577654327, 623193451, 421948393, 269306381, 783966711, 654722732, 276118630, 381177751, 184566476, 969741446, 275789386, 456327119, 392213800, 289901064, 358607435, 813708908, 928314488, 814528223, 412589121, 638753282, 424428451, 408763556, 947439453, 758295027, 394732887, 197184585, 79256854, 533944113, 593797274, 757742336, 991340677, 906591748, 225077069, 949783825, 143356105, 868326389, 192727091, 542691120, 166680775, 212245978, 720878729, 161056629, 295246892, 215323058, 326985961, 399139764, 993153400, 404845016, 679976609, 519401072, 613152225, 165965846, 341174855, 629998434, 769749989, 87077985, 985113631, 475752635, 921511717, 698792562, 832972305, 401314147, 181383545, 780649826, 13085128, 573896159, 988195839, 316013560, 923462150, 418933895, 549787974, 139908908, 914166306, 367824198, 756074872, 597234401, 678497645, 354496905, 376157725, 422084685, 559121096, 192157508, 920340913, 104901711, 90163223, 918800546, 29115650, 960845916, 952755347, 788467909, 113956728, 620257760, 785482845, 372992547, 936942359, 605760016, 927629616, 471020967, 873145504, 324258919, 998758237, 459467854, 865886513, 302300383, 410265511, 908214432, 277479988, 895868713, 384158409, 727028018, 438204259, 223668395, 602480799, 999426217, 506352167, 794118678, 230587671, 353225888, 888195253, 175151588, 648289296, 305977148, 450540864, 320842921, 504790523, 242562020, 887519656, 519666531, 89322557, 160732675, 543019500, 430323795, 807613916, 127074014, 191181194, 230872284, 428125890, 893606969, 354472203, 447373100, 48166532, 882092182, 942735866, 481469787, 715775897, 160322641, 736223122, 302162358, 596900408, 735638781, 132532822, 674950412, 668283746, 123835930, 127171058, 676694702, 948808616, 701423865, 500625346, 974153809, 914213329, 181205293, 356742045, 260761290, 545585113, 660489377, 439349542, 272167281, 274183678, 761976410, 625138659, 410274641, 934055842, 47714786, 420877730, 947696704, 996092583, 753311142, 94635809, 454916563, 967982819, 60548134, 160807970, 624791628, 183393205, 790456615, 340473558, 81663857, 845682299, 192973625, 303436887, 304865088, 560943847, 254386708, 147596651, 699854319, 88880178, 247916007, 18964486, 178946150, 940314453, 169595135, 870894850, 124026733, 839570591, 508998220, 689552129, 31681527, 475768797, 924892398, 501968857, 641316133, 344754866, 90607618, 538384276, 277658119, 735416269, 404626197, 692513823, 473260434, 343680555, 12312109, 530406109, 432525188, 935893072, 313788278, 512085583, 279115030, 800578530, 461156465, 637133064, 990420627, 160200225, 326825222, 417823062, 288954402, 96555727, 976852925, 332603462, 246441058, 922815734, 512198099, 990397379, 707149747, 213038901, 871661857, 469938364, 177746394, 491552381, 998586932, 92259956, 727145732, 80369400, 707472045, 775109530, 724986907, 760768233, 293302960, 976647394, 177016908, 149737975, 324028284, 150114275, 681949511, 705869691, 842503826, 699808942, 693579953, 843340671, 358809523, 28659506, 125670565, 235627311, 408529811, 138818855, 193594469, 146337092, 229874193, 316803033, 551182431, 463424129, 192415274, 311865130, 198953761, 405216258, 314797525, 576915589, 879129942, 377868128, 54506857, 388651794, 642325687, 395058623, 151365917, 63870550, 699817049, 744301244, 724724496, 9666164, 950420139, 334099322, 602069305, 889435736, 895153999, 10282864, 395766527, 679905923, 527071700, 912214970, 931935610, 367656764, 75987772, 424243672, 847054420, 872252203, 684979647, 340066791, 611403172, 480749420, 881962143, 183812548, 609543822, 468964084, 889405028, 720181851, 269283963, 855719611, 472302992, 322360473, 921725993, 100329888, 402537828, 805095898, 519554503, 112895155, 269885046, 902821957, 477772492, 567059000, 770850486, 735208791, 352690002, 503706261, 584935129, 993752253, 788191794, 44681444, 393282730, 337873257, 109772433, 680412512, 26204889, 166506587, 203748675, 946700192, 756456040, 913427730, 3615651, 684490122, 304466977, 334775583, 917826145, 60217477, 677830981, 564821243, 723922728, 734875684, 315469540, 537393247, 916646879, 377642093, 628110058, 660013110, 563704072, 778006160, 628785807, 923389953, 130702155, 471914575, 82331532, 875114014, 616621796, 579639457, 520199715, 932368842, 881674892, 665903014, 61128882, 300908540, 638172281, 402535120, 142439745, 262432800, 392383833, 953000789, 482523765, 375830844, 729274912, 939368709, 253726383, 964192517, 837021348, 837934597, 155444513, 299933712, 6798970, 952201715, 646648241, 847530450, 176545425, 640395776, 1956547, 288880621, 150199988, 859309997, 462829714, 83848504, 91637542, 799559516, 376942808, 825240391, 500518686, 538456724, 426344925, 491191236, 236381643, 209161127, 787894205, 784559519, 792991914, 48993557, 882360186, 759127568, 313379095, 818252285, 634663767, 601074197, 958879486, 47998662, 211645198, 780211006, 687978460, 72602399, 887755443, 243736772, 747728151, 342285822, 328817824, 770196786, 390614964, 472424487, 64314848, 682106422, 831428417, 138611188, 337352285, 261781195, 584343870, 316466252, 341261583, 712536940, 224636164, 803445590, 625120755, 566418653, 86665993, 237663966, 46217356, 123348654, 473778326, 360366500, 583389286, 856141810, 374054236, 383971397, 421270857, 100439299, 944273254, 784231351, 704107603, 86627673, 23618491, 703622910, 726293523, 898571464, 118579772, 673394470, 491507936, 711735232, 810595158, 67577292, 135991198, 952421494, 375112807, 715070444, 512057050, 552395853, 185940886, 172574624, 611402965, 877612612, 391398924, 645543338, 788987499, 759596453, 413837352, 2885420, 336695164, 807050035, 49452872, 460954738, 191282507, 917992370, 401394790, 301108300, 731543493, 775516595, 40351447, 192105082, 229667630, 508183298, 862703844, 952579426, 712806990, 915478760, 774027266, 438891129, 171187278, 186737512, 725147281, 110402708, 373093984, 94713189, 370456300, 365141738, 984697356, 237993867, 46735451, 258608771, 857938646, 17624044, 718959211, 556994049, 750555379, 527586640, 330434504, 753457059, 430627708, 362892648, 372776073, 502100902, 782520525, 726264368, 868016193, 281468682, 672499774, 629927119, 619054996, 174388558, 688951829, 122006526, 246230355, 14524334, 788886982, 30831766, 276665863, 396915085, 786705274, 242986313, 640043495, 230275065, 171158094, 916640917, 378809607, 286328287, 44855905, 543067207, 137820567, 930278593, 219285539, 829359897, 151190144, 825651536, 444185228, 729146673, 603511173, 920895146, 136617132, 530290508, 135934218, 98699166, 313379038, 227181684, 737032675, 415506966, 930413156, 552836877, 298496639, 566459136, 881177507, 944438100, 562994463, 325655277, 88948604, 660883233, 735728283, 999109523, 257754491, 345801110, 539005280, 295665155, 122245756, 174691523, 499367339, 365632733, 814352600, 336301130, 926217957, 176961989, 386201353, 376471812, 501495921, 237242933, 519548860, 94256833, 273859056, 933763467, 304095459, 751810065, 738305218, 527588156, 275568276, 372012, 262398842, 762437545, 617229475, 339158805, 797237408, 785004616, 393014543, 768180536, 271971604, 269291779, 784335101, 681177510, 40350843, 58246155, 342203463, 361741483, 151482761, 471298074, 867285502, 416973774, 424979090, 713771305, 713546411, 218503224, 116987871, 182499737, 473647817, 76273257, 138787776, 849256662, 471338445, 594714234, 248586442, 129946827, 871722861, 484096535, 993033441, 631366806, 526631096, 837261222, 853669801, 215736040, 986645103, 4914218, 455613109, 760685509, 941150132, 684292749, 33525134, 593575766, 455887630, 107669730, 884030127, 205251825, 186536133, 383521667, 66580248, 595501894, 207013429, 83348270, 801013787, 196777577, 423233750, 869389262, 192420777, 181908765, 8422901, 727276764, 693182483, 658992287, 199164436, 494246208, 966384986, 57721583, 938246207, 65725173, 407709018, 543873597, 217118732, 806835118, 865376004, 966938055, 270169764, 149080572, 419481052, 372758725, 739298999, 209064354, 990166688, 458831014, 317562800, 92949887, 869491262, 373646743, 541653980, 901861952, 931614890, 429572049, 435456465, 421629947, 136020639, 142804180, 477201840, 754725298, 414725743, 307963727, 515795071, 114986689, 992323, 376521940, 338790056, 592629652, 819147625, 324732929, 999798513, 880951247, 742510255, 158893213, 611346908, 580809534, 885983868, 845584241, 380634165, 776018170, 974159768, 589116888, 785381606, 62146784, 380129127, 27860705, 465038131, 884372676, 597182176, 294398421, 349042002, 976615022, 315065140, 105006035, 545974619, 10208282, 309036832, 36212274, 953204016, 597244968, 239266647, 952793741, 464880887, 108242470, 884163197, 204915493, 790739639, 754890842, 211950644, 548708371, 960287069, 892088468, 76916663, 301626296, 810296949, 770926670, 206512653, 226993334, 729411531, 752124298, 223445066, 802319281, 326669784, 746032559, 394050817, 767875935, 853388312, 770719015, 913386644, 765829690, 93761599, 791337502, 942322531, 104716432, 710405889, 561352234, 604466246, 634187641, 929477060, 287876558, 26087208, 243974599, 910119850, 271789616, 642191028, 632328932, 618663093, 699402808, 495168488, 653709472, 961494578, 821931807, 573921315, 42888063, 634778372, 456626194, 628905692, 38887077, 135696723, 101325765, 590635837, 946629552, 181545714, 883345478, 208545194, 272723230, 341542013, 773796517, 459548726, 694648299, 200171756, 517887328, 331033844, 678156844, 396497515, 62754839, 763793424, 81599112, 151280141, 444364091, 951106570, 811192590, 605413294, 26513804, 956069870, 532235383, 689221262, 553578307, 120245291, 608821977, 941937598, 934841202, 254393521, 382758379, 345245268, 704036394, 639518658, 473470450, 809180692, 237910794, 981176620, 259003662, 576007807, 287691547, 56163304, 900081133, 252236379, 14752525, 273137790, 457973120, 235294149, 804678950, 731080927, 994556380, 789025069, 507024902, 791732181, 223210029, 499772258, 871322199, 990296484, 906448601, 300255874, 506619858, 381143169, 135308249, 365770291, 177795472, 264238246, 495997167, 186797332, 237701146, 27666352, 701819911, 569307961, 900484412, 735871657, 853005264, 283535597, 931026633, 649571650, 359056609, 542545681, 612339744, 590795619, 718241402, 775986830, 520814993, 565664214, 762728911, 304768581, 7313875, 299006998, 765087663, 124590689, 864974384, 202718742, 194890505, 712280347, 32817373, 255444056, 666632477, 788502014, 535511786, 530662496, 409585297, 397748763, 477491158, 431340345, 355605035, 819961992, 32255573, 338135299, 551747828, 832617296, 353398909, 140236588, 941256098, 160802059, 531085214, 540993057, 788665963, 530119418, 975718330, 153141431, 633225132, 308035980, 314070998, 824261728, 207319734, 905121953, 57923763, 899307212, 467004072, 99601493, 590616737, 374323259, 152953484, 969868003, 518772056, 478900827, 910349040, 314605119, 156297807, 259177400, 866412059, 451516165, 70877028, 322306693, 186381353, 239402502, 790269558, 388471649, 748133324, 862012485, 664449630, 808128165, 120970013, 852028389, 104235219, 911346119, 33761453, 831532681, 147042200, 990756120, 286951307, 626292685, 849005791, 607298625, 157432941, 440970673, 559495313, 408935189, 57995451, 843035287, 571750645, 286119608, 502044789, 334038134, 949704149, 814090493, 805991752, 724636103, 4587560, 964446880, 541800198, 663797770, 168699816, 211978570, 159406913, 581073854, 707562734, 573458966, 888667241, 182453064, 879103086, 284644597, 205975780, 241737227, 804902443, 990049951, 634786814, 112849588, 330044515, 714914825, 114267597, 201142490, 357156383, 637536976, 829618676, 873493131, 849830201, 816473056, 71392157, 527699750, 745132784, 199779433, 249075522, 637007348, 82637666, 427096326, 378331946, 385350878, 775282091, 831292162, 270866229, 482096438, 214410093, 253620154, 912948118, 244088974, 691864261, 569981584, 896832800, 914743392, 45002267, 803935515, 415605381, 675354466, 26080649, 602737610, 416763942, 343110965, 345030691, 772306307, 839836615, 385921511, 558759223, 101466178, 326240756, 207269412, 405840089, 635464418, 590721727, 127392795, 645702479, 958288691, 187313551, 777849488, 652482100, 549984361, 833686089, 754136042, 778651409, 918527182, 179771546, 485221477, 204388099, 910885247, 228973099, 259717906, 555259689, 289669792, 226714179, 358176701, 848150471, 329815981, 540574161, 255102602, 58166196, 669923991, 311236644, 412371512, 367955719, 485100520, 501886509, 784052577, 716710554, 857139808, 720668533, 556254451, 378463430, 476267260, 604295540, 552591090, 456248600, 205874450, 806336018, 601263713, 676567446, 9442386, 382649765, 969201602, 896809781, 721074323, 28121151, 771581951, 801327951, 832848162, 905545522, 236678222, 939988475, 378313683, 140673058, 626504702, 178873974, 733143157, 97274587, 223502346, 155204962, 240399674, 752768760, 123789099, 578854107, 7444331, 891757728, 703640970, 169371708, 683083511, 229228096, 77419721, 389264920, 620173188, 515294776, 415852243, 805082671, 554914257, 582167766, 171403295, 349968117, 613975716, 428185775, 827579785, 370160366, 465105177, 237404357, 447396329, 240162917, 995738793, 656945449, 332701730, 175242203, 347262078, 920901506, 503090525, 774417249, 545213176, 856606694, 457252811, 467617663, 125162286, 198814098, 309852671, 92215562, 580268884, 873260460, 793424480, 443402725, 153902316, 469407049, 983480064, 249165287, 293576598, 343136530, 172169631, 326403464, 839095860, 287104698, 179613981, 43948693, 892418729, 478645955, 491138180, 645926627, 597154895, 645817896, 216526744, 447691449, 408355278, 287994056, 203968329, 896357016, 877492960, 951310279, 267087312, 699143588, 20539555, 908820970, 760231885, 575462028, 920137277, 833552345, 868336664, 105254839, 282690405, 205548294, 472667358, 258736635, 573228772, 223465605, 449531253, 888838928, 95673224, 825080152, 665668300, 99781803, 479939391, 566606889, 228438593, 920878755, 597675623, 151436478, 905282028, 859233933, 520107841, 267032602, 282243486, 252264878, 572714316, 916971433, 961709880, 182702696, 178445516, 836311216, 85629650, 220524993, 611697526, 339523310, 889803214, 640823362, 886481734, 309408876, 97576202, 431216254, 337618855, 939237228, 955260724, 194537470, 56038507, 402934104, 928376516, 791863442, 351371552, 293346346, 57047079, 423652916, 89510866, 299990286, 945100680, 906910103, 865222987, 248013778, 630150106, 537025816, 385294073, 197578486, 763361467, 663367038, 609281549, 684877882, 337656717, 649821425, 388293814, 584994918, 643938521, 97324064, 713808647, 967711632, 3395693, 964827155, 974849892, 700861782, 93127903, 121477454, 484581181, 928497277, 62221606, 185710357, 432713673, 181045482, 496878979, 320046853, 493179406, 26112252, 709280981, 985963586, 458695724, 856640647, 788138686, 164894759, 820376376, 906947261, 562672759, 645882179, 757586995, 867781958, 802687080, 975207206, 963022606, 942165040, 495047945, 1504573, 351824833, 713308977, 387897343, 185246631, 327814896, 323902266, 314893479, 382433169, 414882838, 139068335, 153083277, 171484797, 625301333, 616080570, 625801550, 158539397, 248016032, 328855542, 289624536, 251491061, 403539005, 836322830, 800618075, 143976315, 705330085, 509074129, 757895742, 926458057, 224869722, 931034609, 390899503, 922156469, 141152569, 683524517, 150893544, 280579269, 147218000, 521857280, 167609799, 17914079, 620787339, 132357334, 61601600, 238586507, 45629643, 102152732, 821170766, 208703248, 159766147, 484449928, 505552238, 379380008, 228587197, 603774848, 699953769, 657316544, 372821, 216074584, 41018246, 783629480, 657406481, 746845856, 810578997, 914491702, 504224587, 895192678, 422677607, 543176451, 869924199, 245339899, 174793453, 49951952, 345722199, 72777699, 456905943, 808058729, 324546553, 419513612, 371221289, 284717787, 850806656, 61236726, 519319943, 613620869, 439520515, 115016355, 418333075, 12061291, 383679592, 220538288, 416522606, 243009237, 365349903, 954765949, 229568623, 884721941, 877836813, 533103751, 573826904, 598496750, 670425572, 564911332, 130823096, 956252039, 293806455, 111570046, 279207145, 556556181, 714014139, 332380638, 91246365, 30150456, 344067426, 38856282, 14237389, 601990628, 407353571, 820077112, 808108920, 727582414, 769526884, 212288199, 810205547, 353473252, 791492757, 226247201, 632337538, 263857755, 554127143, 622713614, 297485140, 620708684, 994322224, 695951748, 818152905, 87674193, 527761261, 939894257, 307362385, 659451735, 536325247, 95754249, 415956227, 658288902, 691825548, 674057941, 520891562, 289980888, 648984759, 560940792, 891665731, 106233823, 926689394, 329129779, 242817101, 193697171, 936484210, 364308069, 695991856, 776824383, 535805755, 154275014, 258673877, 904762987, 716775611, 215162880, 161305473, 248432617, 878370349, 896561422, 104002674, 938656913, 324145392, 416568441, 124663447, 789745658, 289063349, 470509708, 139917844, 846276698, 226811013, 130942360, 606220346, 22530780, 929516407, 797494762, 658683672, 6986308, 252670113, 805282607, 86686937, 677933113, 513513908, 98622615, 89652746, 224751147, 837755818, 807768117, 310613565, 617082899, 537418318, 4134118, 710157814, 794306582, 448905965, 517967020, 936954586, 784872579, 144606058, 962947608, 471366053, 331457474, 390915784, 62156171, 33321293, 865251235, 266538183, 8459375, 766182480, 156190575, 760019598, 63506255, 125007781, 389852384, 699722155, 440203467, 872710488, 357267816, 259729758, 205514184, 439402602, 631738837, 491684812, 182819323, 161465270, 455559575, 925649197, 577278028, 362062172, 519027755, 3270253, 98272518, 781033781, 268039697, 1846533, 464265790, 688050731, 20557560, 658813202, 530023768, 553395471, 817189845, 858777757, 646389206, 717593400, 713102841, 116976438, 200845757, 295790337, 259044413, 562121246, 320096905, 118889687, 776461277, 14601997, 725104673, 145892003, 534389231, 871723476, 131377674, 981111597, 889418596, 85591897, 926040587, 503696399, 141283241, 123411165, 621758251, 585945044, 586284982, 199828918, 39250313, 690828684, 751455343, 201882737, 757901999, 728720347, 163520942, 573874588, 933913159, 512471595, 702603380, 651411019, 600950824, 444025915, 315584350, 956955947, 698347204, 239381653, 84380248, 151952143, 960958628, 51634748, 410814706, 474793953, 56890026, 645494610, 265592079, 194339634, 766090419, 960528549, 475345756, 88183859, 343663189, 218558339, 520978918, 184503810, 472908066, 460373763, 867669611, 13454612, 571004490, 951926369, 170005553, 824778841, 645972678, 67961878, 588189774, 657461541, 833113487, 474332486, 241776880, 106419000, 924428368, 989037493, 955214381, 760310533, 992739335, 791488996, 136119729, 60157725, 949773577, 974137997, 669213532, 964187200, 591918504, 113557698, 416214775, 930843717, 938801921, 314789116, 242546951, 999225423, 33867101, 700401312, 340931275, 419003822, 221572896, 123416314, 656165742, 984308322, 223860304, 736578596, 489009377, 443735920, 12018624, 697355676, 722758463, 638734352, 258433343, 354669228, 257684169, 725011442, 776974101, 254164923, 352746512, 482608460, 63023762, 162833258, 643621928, 910374833, 911777661, 187756570, 228885213, 976248038, 214846621, 707804208, 697746596, 966940040, 473042169, 73224731, 702228414, 564275540, 127027431, 193269049, 128428320, 953675249, 523669293, 802543981, 878733750, 905560550, 784847264, 290427345, 667140138, 101648642, 455713374, 766981911, 9142085, 771337649, 912571312, 894884891, 427615753, 806158361, 128979997, 741167308, 539332113, 692801385, 382980939, 384741383, 513184062, 994241173, 302350049, 903482551, 591628190, 541790461, 311081027, 775437392, 696009732, 355399915, 596476214, 942390761, 549101017, 347745428, 550893842, 592799648, 880110577, 225485701, 39743675, 568888865, 288732625, 547393067, 784548925, 54170258, 588572063, 41676615, 55138962, 15012402, 348385340, 285089904, 360888987, 657307706, 499398789, 715808243, 403682386, 180002000, 945216270, 862967598, 913157750, 865354108, 452069204, 482923762, 932471370, 670927914, 790279475, 706103969, 677010393, 818458278, 203246551, 826382258, 366798765, 233460769, 294326007, 45924953, 981827966, 974494975, 742463771, 806675411, 501125228, 818311635, 694606381, 53324851, 832233628, 625895537, 528857460, 342211176, 35498564, 38297229, 973287141, 493120434, 202237212, 634873150, 867239726, 377869123, 455306133, 284703008, 176535019, 782434241, 171571099, 722887362, 377258426, 4154460, 260871360, 919901540, 695908688, 436849244, 418378250, 828185413, 125898842, 832491679, 708910895, 887426023, 862730073, 310480932, 684131512, 402223803, 893036179, 255166655, 986047839, 22055464, 135011949, 209149277, 217316074, 549847153, 938920427, 879981431, 796119321, 482159764, 934814530, 291831512, 478819785, 960253826, 201970382, 425064539, 701003771, 130970941, 227693294, 34719882, 317729233, 96235876, 706961389, 403679126, 640216641, 733227104, 796116015, 302033241, 952221878, 654135588, 444648477, 106507965, 915542424, 201539598, 938254349, 310735429, 605095353, 505245125, 434067332, 909341527, 280244167, 370984750, 570174459, 346639119, 16905948, 932597468, 541845989, 697814881, 677413178, 474130346, 210170805, 699125372, 885294885, 986423048, 453482371, 299018441, 744953930, 904680097, 598302544, 977360732, 237760650, 570200881, 408566630, 720501884, 204659079, 572810123, 720947381, 151746220, 81170650, 881000515, 64229301, 9807743, 830448081, 920507653, 20440000, 907367215, 560005650, 743047881, 849483941, 131990064, 927715272, 48123565, 405273602, 454155972, 971459074, 971699892, 717936561, 78111355, 704972358, 610828065, 904625364, 911925342, 969384794, 101498438, 363434489, 609546889, 123831374, 254891318, 833986888, 762050258, 811087191, 254455958, 983729255, 75681232, 608443467, 79873414, 294771072, 292620136, 652882539, 258780750, 172909325, 253503425, 471477425, 762376316, 236506641, 487822925, 137604771, 446371719, 636091293, 889209363, 306613418, 51380135, 694439137, 180892170, 362717187, 222727792, 772471922, 615857663, 978174032, 115929919, 927883407, 986341387, 726439721, 432250307, 384306124, 955766445, 596689876, 308886265, 564665351, 316255, 965020314, 417558005, 498029540, 912457114, 87859887, 699938730, 159579006, 740477793, 304516831, 638308288, 37961341, 915418069, 669796865, 489694534, 548329010, 313787125, 614233943, 435378321, 567776807, 30703271, 25797979, 23453493, 961843904, 292063062, 370892751, 995817736, 209925794, 886947081, 539328572, 696484787, 115177220, 212415843, 396083845, 795130184, 808167681, 327202493, 286208858, 218003346, 369997914, 954031254, 362047662, 797257567, 541934559, 505390680, 287094237, 110156749, 304000377, 478125255, 561190655, 318408948, 814710706, 239400802, 339735911, 980728346, 664051492, 473794101, 861357450, 823746987, 232435378, 785876675, 873192402, 915288291, 523913420, 424556723, 689237716, 775923074, 331756238, 531555225, 903223969, 481102286, 567389112, 721650901, 363853646, 738231710, 138458246, 75728355, 63237493, 104750595, 529663810, 944552807, 389594753, 177460440, 595352420, 521277443, 786056842, 562884034, 610003877, 72854823, 236323991, 763585138, 294751759, 902797506, 497658787, 625578566, 641685162, 154384558, 754068668, 213255835, 978641084, 888984706, 712867872, 871311298, 289561119, 610653866, 396915208, 56293834, 395982308, 596706149, 123564246, 548789409, 573860345, 689733948, 313643647, 366672684, 960413844, 565411222, 975100467, 325366291, 946632396, 426369481, 400451094, 959574585, 314823210, 59741204, 876261286, 359421600, 928515330, 820144861, 801790995, 973837868, 332631374, 597898841, 472244594, 214637382, 7458302, 6817733, 780408255, 461424384, 150769187, 516925605, 585652697, 802888390, 555636319, 260805368, 833425788, 485948190, 365393206, 307241353, 36222724, 166089814, 682798356, 246736859, 236161384, 260896728, 565877583, 901601220, 211208841, 20584234, 6822862, 424883095, 952059485, 389421490, 932866680, 951433754, 357429689, 356309165, 416964398, 910192943, 59305312, 563696038, 45892308, 475139562, 494077068, 6820029, 358235997, 641953838, 671467974, 716586427, 356778792, 315550694, 281649561, 406869450, 245175384, 446671087, 36190430, 852533212, 76256778, 331106980, 947001072, 609674374, 937378312, 167660056, 568994426, 59554159, 309752375, 56023916, 397231557, 994275779, 942316094, 369042555, 78008996, 558565729, 226582492, 187766576, 740881761, 80860775, 858389500, 854982749, 306271154, 521979524, 584340850, 235111005, 698177749, 804687832, 15503227, 922577589, 658363254, 177344091, 629847245, 396163309, 12837044, 185013399, 608466375, 71265446, 893547270, 669123283, 111891468, 892593722, 22661980, 10251996, 673541937, 472638154, 776578201, 791806730, 500411234, 443437399, 443607008, 94239179, 341510468, 74887199, 954335994, 733032950, 636691985, 154733186, 322529402, 308276260, 931904373, 324079242, 497067573, 403646645, 581915143, 746462712, 562422149, 745090428, 688226497, 804125202, 964120229, 12745100, 430450179, 197030688, 474409174, 57325081, 579640748, 644519162, 427181236, 421198413, 280473650, 673025089, 13864323, 339177643, 217955832, 319586731, 807045707, 865924085, 855574481, 344415184, 564713450, 804537417, 444298647, 892882525, 805854436, 701990902, 796105059, 772533292, 990899538, 230931829, 811627047, 450901718, 918798819, 265905607, 62578089, 633438608, 529868298, 989640200, 190005034, 550983099, 608026712, 522507756, 570105295, 875775293, 477274760, 946742675, 627389047, 679925368, 855034247, 284724223, 353070005, 96944456, 318001339, 195212678, 808230425, 2433715, 325946281, 249333275, 350509540, 407108858, 322305630, 339011221, 133846674, 952899167, 225960215, 579047269, 371466709, 705816139, 57673706, 246933594, 204392378, 305550879, 175598572, 594871901, 92712778, 531132027, 997551630, 460477996, 723639982, 345983903, 271923253, 555758924, 403439679, 374124090, 656188945, 581089121, 801888540, 11266098, 448934515, 917114162, 347640936, 406266988, 379419801, 659239453, 303073030, 246075381, 177107380, 121053523, 207024004, 470403823, 533332605, 126123291, 700602307, 271134909, 154017857, 352545543, 949473883, 774171764, 62320321, 374251213, 737638526, 304316692, 256246050, 981400000, 256517632, 964324901, 946694185, 70648938, 932960316, 201305237, 985562709, 924616806, 417721362, 804582687, 138600229, 562597431, 624893096, 14733085, 876635100, 403427407, 252561324, 638052621, 335705344, 11747165, 348744000, 853710100, 493910165, 126527486, 893317180, 889699512, 478090235, 799803178, 348172281, 526014520, 934081634, 489845835, 613847515, 974993260, 252428690, 989091507, 241568763, 10827326, 324167243, 77595227, 494337205, 977361362, 836194413, 949088699, 190098866, 133693866, 885870081, 463668278, 612846358, 895356413, 517196550, 111403257, 626163053, 706573810, 705956174, 907471110, 627526216, 579592102, 947661453, 793359752, 723879082, 474625864, 914252020, 604225035, 341397779, 392699668, 65433856, 621881549, 14653305, 198309961, 753734628, 151846391, 676187920, 928582544, 752297502, 512840634, 119732638, 146900933, 540948748, 671321808, 883420913, 597201025, 700976519, 233225014, 998893372, 588954543, 869114210, 27644986, 691131870, 439063330, 611252820, 893506356, 11578695, 800798689, 165687439, 248454236, 826052173, 402585769, 731220436, 311664395, 328795078, 583663980, 890827449, 552441556, 664065148, 199194532, 508701612, 68734970, 653114298, 928600156, 176182686, 300175969, 155274340, 734942032, 771352059, 705299197, 66474671, 653611013, 363116042, 446553661, 668797438, 524684719, 936787459, 398129152, 234426706, 755816438, 477461221, 112000374, 608402434, 151876011, 226341423, 932659143, 652049562, 509330784, 113201460, 880894732, 881641006, 436672538, 800530753, 819493236, 633609275, 119259541, 356008931, 821073190, 675297770, 823344412, 853862904, 228147691, 960409470, 805059806, 862716142, 585305505, 382362010, 640285611, 849340885, 518665995, 35859351, 109564632, 135997293, 193633221, 194617382, 319265859, 614731428, 326828373, 616277000, 518519135, 646669482, 197793816, 101921824, 129837157, 870186849, 98185004, 903408767, 213844020, 751675610, 911087706, 295327191, 781798427, 380650001, 894506430, 896911698, 49971329, 435620292, 916428879, 335834658, 30758085, 705645796, 118501316, 571542545, 895719804, 838560158, 224562826, 918149416, 535159136, 685219550, 445004608, 851940756, 328436970, 732697295, 168197617, 980669939, 623298169, 989854101, 963453948, 827740283, 45785531, 942810068, 778619977, 8418977, 241999720, 940856754, 753263181, 336631868, 470942662, 30255695, 439677279, 290836922, 206329334, 486542422, 105895775, 114964427, 41859758, 587332388, 428660849, 435675320, 509304236, 74088034, 663635837, 638375467, 225452138, 582937952, 104269758, 383409173, 805413634, 436155962, 41245429, 110858100, 708677733, 365084945, 545329251, 40463469, 554123806, 93374906, 901336008, 481605268, 801709771, 837543525, 911643985, 788143531, 556151185, 718350878, 519477768, 491852218, 218818303, 444854793, 665326470, 378488013, 906938341, 36379512, 918419536, 980312197, 582019564, 665999460, 779785194, 142956391, 213957663, 869094942, 473315816, 890339250, 212635277, 633377124, 594664294, 243493340, 382770292, 556976702, 924813761, 930152838, 578751664, 974480037, 628458484, 913508647, 527857243, 359473805, 440936102, 910910842, 826967740, 704928136, 28174244, 560483716, 434419519, 784499119, 506332523, 52870000, 618198303, 359347187, 813132905, 157453785, 840593891, 680343273, 567231394, 560507204, 77445550, 895826393, 323627642, 306854445, 114859864, 705032940, 800537057, 991903661, 973177252, 465425498, 631434297, 353137235, 321192443, 562514435, 773344453, 682356298, 928982825, 197083596, 702193589, 11002540, 248421439, 350004237, 720041324, 706132327, 975829122, 444284286, 706177915, 962603182, 258557201, 609684552, 2896511, 329632252, 81110616, 167861770, 791589, 648471073, 219361086, 356793122, 925057628, 242791153, 765188655, 761394364, 105726167, 300615339, 3747070, 137937613, 988527099, 256407117, 520452293, 751413650, 840546717, 633783864, 919782553, 178282240, 431923415, 517599661, 7796124, 739048004, 580532899, 194892864, 404011606, 727798415, 854976858, 582417683, 405186544, 541290208, 530632161, 50931028, 967022228, 202761394, 192541841, 818759618, 959089449, 263211989, 285704507, 112786558, 211305044, 593625528, 319898520, 425374903, 618243410, 977164746, 872014201, 403388794, 10823592, 248337558, 83635536, 665130305, 423348476, 332285348, 454375820, 310887044, 259630252, 590504522, 453125338, 199007713, 593854804, 841112958, 114691775, 771113696, 505282437, 669145, 702416287, 807686003, 922294882, 556780255, 26179184, 143277020, 650345054, 508156945, 54561557, 226198585, 63135800, 614772651, 321087921, 710622619, 51071867, 328394369, 516818369, 225622631, 361178815, 302259847, 756912806, 664527317, 871634130, 595420314, 538261183, 958595869, 454511154, 458044223, 890276723, 657831757, 558385100, 749886943, 250339747, 638816250, 110956717, 852322618, 112631338, 798822232, 621093292, 912365636, 998743543, 294911276, 889032293, 820911368, 515464798, 741601914, 160428145, 603562979, 50440736, 937405428, 540137652, 210362747, 55576648, 716819771, 988865135, 208326498, 563309721, 463253793, 127135143, 900768181, 658872146, 941443225, 336003552, 326154132, 934978339, 220592882, 660145183, 829993742, 371963233, 484369325, 307439855, 286489036, 239018394, 314711452, 947942901, 587469444, 487862557, 105673474, 71904700, 980830962, 947968888, 32582185, 362578587, 867976463, 944928685, 721954145, 392904149, 350960572, 98494446, 679977159, 435759482, 108756229, 38421160, 176723545, 422716430, 240462645, 941759291, 823185568, 219421983, 402548676, 911606407, 228215285, 322535396, 367851767, 821534164, 705218449, 45568956, 479457299, 750678928, 110785691, 481467258, 792375774, 705358185, 923553062, 199517672, 39891569, 432866342, 460657346, 620520316, 478652508, 42451404, 968794446, 713452169, 601366779, 147775900, 911623745, 664767403, 269040152, 558540456, 660602208, 371746992, 399423512, 69189104, 59442762, 633360046, 28532473, 969424532, 464560264, 902428551, 317706088, 485889295, 58671790, 952657354, 221032547, 332045024, 536101527, 422058571, 281426357, 49625477, 837466387, 410721148, 164946929, 159698778, 332921834, 504789150, 575117015, 624660226, 872219680, 821818933, 50663622, 912604837, 674645721, 842070195, 798029965, 32893477, 119368675, 386052574, 640628066, 716679776, 460642831, 191195157, 861189658, 100919506, 198441504, 130544061, 860338523, 23024086, 338846285, 972326938, 70672003, 873677698, 617958591, 587147852, 457393790, 451858227, 546930962, 442193623, 389400692, 833438007, 767235435, 547470468, 115870271, 387419901, 82711564, 214358652, 360301261, 788978185, 507129944, 788212879, 28516731, 801984405, 432048181, 74892321, 191084239, 930178587, 921710288, 315159113, 864923683, 459953159, 294870749, 831895220, 106611178, 313937902, 496270530, 39544179, 18471874, 193170144, 334923678, 842413068, 297098478, 398973695, 291559130, 971099099, 933738929, 505287163, 33936642, 57742284, 287698109, 438504005, 167709526, 262782198, 491099578, 187098574, 567871380, 971464300, 750372247, 814874077, 30974887, 643060176, 939517102, 301570799, 462540035, 344515379, 834054281, 846598504, 360101341, 126748706, 292705869, 680025260, 801617422, 387006015, 600981605, 880856530, 37860015, 30961705, 977987532, 992046572, 285881764, 658111837, 78049493, 120428873, 352719373, 957903700, 131708481, 62045239, 485804762, 583313524, 515089281, 581872480, 424044679, 64574189, 225549073, 638903950, 149525976, 16236402, 72135486, 162289369, 933765676, 792282022, 403168540, 147400838, 29944895, 719685169, 862883956, 678810452, 73161798, 111460998, 928677229, 99217599, 208523482, 288194519, 394515312, 536779610, 257871477, 645580565, 882741989, 331490921, 987584344, 262482121, 529843214, 483393144, 629448533, 40709505, 337913581, 461452163, 386250247, 913741909, 713119222, 945308869, 568134643, 138742083, 859438358, 295578946, 736621869, 877679803, 414964502, 671478840, 590085251, 98539329, 564822377, 927677124, 837560569, 78559781, 456636979, 788541947, 935518558, 226522677, 628896149, 340757995, 233072840, 246394198, 405211791, 785078946, 639227618, 301882692, 890682743, 605463547, 115003333, 509927026, 666971901, 180780717, 813706375, 779794300, 613139626, 780040612, 910704633, 602530635, 998202482, 365352694, 8421493, 224773592, 411985799, 601579431, 322641174, 506086512, 219916754, 926361742, 229777038, 608016522, 777604960, 320327223, 159046451, 787891933, 329677631, 457307490, 410860993, 191631682, 703646535, 664063875, 305964838, 56181993, 644633278, 624948972, 986400000, 841605567, 555782500, 791752394, 786143880, 688023384, 736058731, 877258890, 873331342, 619970296, 728676536, 715159841, 95035162, 662150393, 777452086, 387376887, 501610543, 451214530, 692432932, 124096606, 191489660, 228237128, 364499154, 453749312, 892902081, 359551577, 883835333, 173259436, 432390023, 921809694, 184035225, 256879606, 199338413, 765193542, 383927338, 789035854, 440116828, 626839483, 39963058, 515106432, 856337199, 11294381, 901858061, 571400412, 232748898, 63796240, 869425022, 972676005, 811784078, 191717840, 447772627, 577456161, 428802692, 395539679, 255526750, 183303109, 228447122, 448671048, 619274748, 997194509, 309494244, 992157686, 537630420, 822205639, 448578544, 190035917, 67982726, 313350906, 32511685, 204519695, 14727940, 960400093, 356443828, 157947990, 56308903, 158405104, 433876461, 305405318, 826178625, 260853720, 671589012, 620744624, 248590153, 798393023, 737923696, 782808389, 409175784, 366230747, 96554353, 992947199, 740250327, 520520392, 962616784, 941205318, 60909676, 785906371, 513959018, 759857384, 803126526, 890266595, 907757877, 373311845, 325890256, 627795295, 160668764, 985205257, 151864316, 228682104, 706896519, 423391884, 289228468, 45864934, 402706046, 539788697, 21442281, 1672063, 944635601, 152086735, 223107686, 180074708, 500483183, 296773860, 100227682, 802420, 103722614, 827975973, 911165693, 204967825, 653348287, 163917138, 475974161, 533568448, 624912891, 220810129, 965791132, 194277843, 525555100, 364787648, 684053336, 659485016, 153706464, 122691804, 849161677, 437221153, 750501513, 841478789, 557940394, 112712138, 783655906, 735627926, 10433577, 441551534, 242956080, 631677618, 378537751, 736680377, 359335943, 603052950, 162971263, 642682193, 453882010, 259515301, 55905804, 321304373, 407704394, 556377695, 529666175, 775110319, 697318256, 941773104, 660239778, 218384860, 713640264, 222932951, 646389180, 901387282, 780658150, 746459595, 670437999, 771627949, 747747188, 43309217, 188540234, 970522994, 123633849, 643799010, 907811627, 748985820, 352730666, 174175784, 353270135, 918152395, 150690387, 135023182, 831082723, 635819776, 932661733, 244873981, 885919084, 668048007, 218695582, 201331957, 236590206, 942737556, 638886701, 454569159, 675211633, 886171285, 562678125, 83798051, 751933920, 356120266, 518517310, 506163592, 346967922, 771038705, 967614452, 563013570, 529689803, 825309636, 920615089, 270325149, 728516152, 55200889, 198623677, 240160886, 881520310, 748209495, 551912620, 284739116, 830349484, 270506627, 851213098, 192390595, 914661513, 514066018, 245455251, 685656862, 111056197, 457616726, 927892129, 168115286, 389751679, 432262019, 500253009, 663140801, 189160441, 127254305, 919058802, 21216382, 157290485, 612600482, 747899567, 129624873, 889436039, 344889008, 688000959, 899017473, 681999071, 481317841, 364940848, 241572588, 475686051, 793434370, 11571669, 309466253, 195467540, 884823961, 163894618, 642142214, 99795696, 428697059, 708602081, 787376221, 940817620, 279227194, 749747257, 991342722, 562154467, 951288249, 193987896, 124587166, 200889999, 538569896, 760101880, 782068876, 944548401, 206053404, 269472958, 76329983, 225781796, 107055211, 582592725, 479373261, 635244641, 425952186, 559645658, 120299299, 942965602, 714986539, 553400962, 208669486, 864388718, 726138132, 178558931, 5230383, 581142733, 513188702, 137517076, 262276255, 225528093, 754204409, 241237664, 637418859, 280924563, 821507774, 543518143, 94474232, 210315956, 223582515, 314673168, 380642031, 299747830, 594591562, 599447956, 843257672, 403656747, 201935505, 644671880, 228991568, 843448556, 196185998, 940350730, 89607113, 312235937, 816471094, 309941249, 374241345, 157297211, 192817541, 857228996, 437228966, 121341707, 316944066, 588508253, 628915835, 698675095, 309806459, 600375776, 40766610, 753263432, 801074546, 889669974, 454372591, 782189255, 87663819, 41081436, 669337203, 637283067, 941294443, 611741732, 266839626, 727733717, 954893075, 860458219, 712756669, 185804779, 766649716, 102585076, 713981701, 894468268, 107104481, 83958531, 388834566, 706465474, 781672966, 165392837, 65249308, 303992456, 163930867, 249845653, 167901306, 853154544, 740156405, 496537489, 63557369, 965823678, 495477540, 482076264, 453173351, 265651110, 840490446, 114730922, 275458267, 855955592, 827358817, 262130164, 831528530, 341212945, 901638454, 709463956, 94313225, 886156361, 618715858, 503236732, 404434227, 425140239, 81476279, 445359319, 118860541, 14396764, 987526624, 80958778, 916242971, 3146654, 615551281, 410946518, 245550354, 46197941, 718828383, 299389816, 787043939, 2860815, 750513850, 904872916, 416479325, 650162859, 636644485, 906268495, 788577695, 699207780, 816014185, 931463695, 866550665, 454828185, 432080736, 956798729, 429952822, 375217537, 430270421, 314734597, 780450884, 304366803, 688054828, 980354252, 969584237, 397124998, 321102820, 467241756, 73302283, 326047368, 732219487, 914748705, 96686947, 567436414, 230999763, 690002898, 109749608, 671414875, 421353736, 557408152, 572859943, 428681194, 179775507, 227056047, 780693620, 799745862, 689825828, 152017291, 624057497, 943895275, 235643017, 64354483, 891031532, 43758217, 804727600, 110400916, 794928749, 220390356, 524181423, 206150240, 313121373, 518075728, 824519979, 967990446, 60178502, 913824865, 158956838, 466287286, 235013603, 132361729, 349825160, 591390437, 366684410, 805777694, 874985871, 602541580, 669852417, 989572838, 522456778, 737714092, 933825022, 967236779, 602552439, 653889227, 746283648, 645256871, 714726736, 251047623, 647293292, 254182929, 427591235, 874892423, 688945418, 303176096, 993853003, 378425589, 144563857, 760135594, 668179085, 933228983, 439321212, 393816885, 933930343, 221454711, 511951201, 497554587, 50563854, 444553027, 985732914, 478664178, 847747748, 825670359, 970603469, 106880642, 67993113, 262143429, 919658418, 832197784, 786492599, 205620916, 851230428, 404162642, 805666987, 546650945, 610110774, 831078894, 905756392, 875312579, 279704890, 566421218, 451149663, 559069892, 927495102, 821821548, 723875362, 549334341, 253005013, 700964520, 140719178, 264139827, 159715763, 58055964, 986587779, 964833484, 330349881, 359464570, 226981153, 804421991, 390786795, 527935481, 364634650, 787052673, 129136187, 52975326, 102135834, 963577772, 638712408, 209823917, 588093761, 233611474, 574197566, 130725444, 51599050, 271493072, 149385805, 350960787, 328947216, 722990515, 307702797, 556633978, 45552207, 603686063, 721498815, 815866986, 781829339, 396518783, 597814820, 692039821, 358439087, 381995152, 314525840, 240473861, 303967235, 160766944, 292818513, 706206914, 630155464, 98464758, 547739301, 174915674, 174460926, 210287740, 573666233, 254620114, 581945368, 809631073, 872204785, 996516499, 292824823, 872909761, 206698861, 159418252, 518505943, 162804443, 877172487, 356260992, 653525526, 218948090, 804364149, 319527091, 563542431, 899070820, 575582665, 315404329, 241181519, 721042358, 474816443, 742704705, 802668770, 13023433, 410511950, 888780154, 969011895, 601423310, 347327637, 146814502, 525376769, 388924125, 340929687, 242713648, 569449111, 247374196, 440230149, 702205992, 381641883, 835722490, 499582808, 637505574, 288476745, 2690549, 570317282, 407263872, 564896512, 840110851, 443906764, 50717114, 938595136, 572035247, 994022390, 246250403, 200397762, 568777958, 774316009, 861457371, 938908627, 621679751, 655652678, 612002242, 314646221, 814711552, 8004297, 357461093, 99664156, 218943883, 372670028, 752194750, 574447786, 667672147, 83493180, 649912990, 199395557, 479050568, 490831266, 82457961, 935616511, 352533441, 387698385, 553922257, 687056968, 136537461, 775903445, 542713869, 884344363, 662119504, 971397778, 476454636, 295205168, 20773645, 605231504, 54041583, 771438540, 56184343, 335122280, 424645476, 421581073, 834677772, 637291139, 725316658, 536847710, 427564618, 14300506, 335892903, 485533546, 593907645, 648751986, 962761048, 632761489, 567386521, 983301030, 88610534, 314424383, 726831751, 335152619, 197868394, 263811507, 767653652, 856765690, 881157847, 979830858, 950879156, 801808029, 261155303, 343405497, 137325318, 797854595, 958674909, 784227272, 671588771, 291139614, 40237683, 367251836, 34037418, 127797962, 230651698, 211461102, 298942378, 731491818, 547563549, 810893642, 129278110, 809415492, 821167142, 242098342, 281694793, 66789969, 706770139, 410440936, 855241978, 4579832, 507227441, 169513212, 290700387, 946112974, 323201329, 370771025, 234093576, 889899550, 352609860, 800548631, 943154166, 336899786, 87674876, 957452059, 347156490, 364165528, 671150521, 435580783, 350767316, 302790097, 574553597, 153887988, 787471464, 607133667, 139053934, 540622927, 508290873, 916357815, 498235817, 789910737, 162948547, 907057468, 112348632, 64953067, 612129318, 318539398, 986969220, 832404783, 268582213, 651555360, 519167466, 292812377, 895460177, 268374175, 396125011, 829573885, 845350318, 652147843, 205209441, 436616341, 604473675, 508885819, 671617153, 214655123, 181161611, 193810134, 234466307, 278315360, 849671242, 291539939, 910345625, 630091676, 179521180, 663348822, 81419230, 562926943, 791084281, 135030714, 394103868, 117146226, 649652174, 559963689, 407362243, 344722819, 141387745, 57552106, 642014367, 402125188, 1075685, 814181657, 77931151, 672220085, 241748241, 553397971, 263663914, 325883922, 39416560, 557350546, 622478396, 490343233, 467716657, 292148825, 262821491, 404536730, 574726912, 555532376, 325480851, 412823614, 662693527, 415242613, 784909082, 523492060, 973377827, 547021663, 47475676, 63475157, 59279186, 93931561, 809799525, 367243639, 205783141, 705794159, 729919038, 684359921, 268841243, 707568938, 522507785, 418253675, 969088568, 415240647, 77387489, 186515458, 868840452, 521558304, 866359039, 415789909, 474603092, 242761163, 205991679, 836453926, 412676184, 942778972, 494184587, 836021067, 640251050, 352569830, 442830792, 203944210, 344201819, 590000718, 559216550, 127790296, 319601498, 614480192, 69298622, 785507764, 249443698, 438045397, 253366753, 318012902, 9259702, 98814678, 930705342, 242030368, 877493629, 302356025, 999302694, 655264986, 343322203, 980382933, 425256916, 415631867, 961651637, 688043129, 760448317, 803966508, 696860523, 932653483, 909279123, 546783526, 442335736, 630743382, 792993611, 616076685, 741540105, 828648409, 309014291, 371080545, 150447332, 269088355, 967170263, 596427707, 977151167, 526238146, 414687438, 593255848, 84428499, 431296565, 485676029, 78507371, 944659833, 802329855, 1005378, 813731046, 535417919, 51971057, 857948650, 229557370, 43607922, 645059761, 493902036, 659214528, 138840148, 213315125, 109777191, 402522256, 746824410, 53852611, 797937782, 862741189, 722510766, 855897239, 551552766, 245214423, 590530509, 887952579, 933701503, 912731127, 283478113, 98885082, 657371628, 253837484, 394908082, 547416383, 623697413, 372446353, 507497483, 376646490, 805749114, 443454666, 440121233, 145323247, 870552751, 863501362, 711763426, 310607073, 506354042, 507304842, 184304851, 471657098, 734229088, 702177378, 364296659, 406086367, 449681751, 716034741, 223743826, 145104469, 781269586, 691941192, 409759588, 172886219, 639878481, 967128813, 810553206, 40475405, 636806679, 613111193, 557826151, 227567700, 982865222, 703089860, 498808612, 411396247, 980994247, 133769746, 433801999, 115795547, 762581854, 91652430, 290458769, 674906470, 339219368, 164147952, 83039673, 49244579, 823208128, 451594316, 746758047, 998285274, 365667202, 573491204, 923295477, 602802164, 287408398, 387151552, 436592098, 311097439, 290197978, 420756390, 640244967, 567499971, 632783601, 256428167, 114012971, 177500217, 737972881, 189507033, 980653598, 67949978, 578024926, 990264619, 149425435, 716311585, 87395976, 800634531, 198841401, 629310150, 436158331, 811801516, 847646616, 194325306, 46884280, 284530354, 201693694, 905752774, 189335536, 70031641, 320281380, 908869388, 185884519, 882679569, 847342238, 956384084, 217086947, 992319606, 408469041, 134189252, 712559520, 585275991, 387206219, 376333140, 650728697, 292478675, 63468803, 216817963, 772134084, 142789709, 666808714, 662326412, 877438101, 527697459, 749117085, 859056929, 307502586, 313465320, 523034548, 643569441, 902329334, 462347164, 924246627, 605128397, 250735482, 238404597, 587986144, 990415136, 509120727, 570521221, 103627436, 451808377, 71785160, 605490616, 185234823, 454138836, 51092847, 293800659, 448121372, 57122522, 196085232, 973273557, 555348690, 557550923, 500325612, 626453041, 46266570, 847988042, 623170890, 816340207, 643399719, 772921979, 503148625, 977112882, 978780117, 282708741, 532500915, 610643447, 960508649, 553324617, 930194932, 720506730, 169510150, 467995572, 815593524, 497592042, 890483314, 916399092, 315069577, 959796714, 776879039, 875260690, 867249960, 136590417, 618254675, 57386739, 75203678, 147986938, 985080975, 333560219, 441069885, 45349815, 224620645, 103368064, 939226340, 934672401, 843917261, 92706438, 784941667, 249565953, 460678823, 517709612, 87395706, 384898878, 513775205, 861791133, 912188445, 594064994, 482764752, 540937440, 452183682, 712633804, 603797913, 718948270, 749564448, 966948234, 944511579, 523691588, 28954887, 23587991, 268329780, 218625960, 476037283, 198537673, 399684002, 764292947, 833267579, 501728606, 580793506, 53061021, 601135758, 274342614, 233910298, 208695725, 144373783, 951855595, 260551101, 304597936, 885224723, 512548784, 497569079, 811735930, 285400692, 140820268, 86351114, 264596018, 845855748, 41478823, 550015508, 787743173, 410596297, 205955023, 29741123, 642673736, 398134052, 620213362, 417759106, 991787167, 788617353, 283551472, 687434649, 289227471, 664182494, 522497930, 394368807, 543575964, 998493395, 407985986, 989445420, 385757514, 615813409, 703093297, 712482131, 341809736, 913254820, 671688201, 413482569, 290555274, 543298141, 293665474, 999603453, 671451844, 237246412, 893030571, 63366705, 693381281, 336706139, 792674291, 243128660, 330689988, 124864876, 814895656, 665316972, 576244964, 371939785, 581650122, 967783949, 503000189, 993944892, 286306058, 160281311, 782830022, 849029771, 153069499, 130224054, 758062933, 66859044, 409328250, 82387539, 116627709, 444336399, 388235728, 939710437, 398134346, 249109548, 978372327, 236721480, 437103905, 293981775, 86748208, 517853932, 983879565, 897630716, 766033484, 795414049, 85898468, 336350059, 945078983, 789818699, 98105023, 395393181, 51178565, 353099947, 641984513, 884756874, 16268276, 187310297, 947607956, 905490683, 972693767, 371948393, 11117819, 878279216, 613270449, 893846591, 227849214, 890554122, 65967689, 94268192, 675809369, 944583916, 7506631, 925710029, 931913995, 347447073, 374618767, 76313394, 542989374, 444676118, 488967157, 399610196, 251034751, 451915446, 256087977, 841144935, 662458882, 614623542, 426015610, 124265561, 696543816, 724932433, 881137975, 689335273, 629116224, 696835531, 820749406, 964710466, 358426597, 108236532, 172992307, 491969379, 490491732, 47651486, 825878665, 992923814, 33265737, 576519115, 91395186, 909293366, 817347616, 848475140, 449609424, 119239433, 424835061, 174432577, 191412201, 200463308, 951090953, 742459175, 482731839, 501006026, 149301368, 239338614, 296671887, 822499875, 626216408, 952282315, 709849832, 813373162, 70403258, 614360492, 136504272, 574351136, 110336015, 711095560, 739091214, 846130230, 694633184, 379418475, 850484780, 978872035, 264055927, 849814404, 903285680, 597580810, 596957922, 272447248, 720490090, 938294902, 183782834, 129905943, 12120872, 118890321, 527735032, 145328260, 756142795, 696313674, 654909757, 864152441, 35279309, 958659532, 807054521, 584106985, 165474972, 971345431, 434495645, 478462309, 84005592, 429092475, 314560358, 352833251, 706756853, 139374172, 545137491, 243320176, 473106385, 964837480, 254675666, 874246498, 473305904, 568221769, 803899923, 21281910, 281849234, 650361816, 197820612, 891258546, 297895173, 379451935, 792456877, 191910113, 408909000, 341140215, 47645108, 986257271, 229080503, 537863534, 652458830, 782962918, 394454370, 565553781, 79599260, 26583657, 24043416, 560253041, 734360887, 754044996, 60422702, 391543863, 545390230, 960680372, 347966152, 932179441, 976224566, 35023663, 29422650, 323362034, 606899421, 243520020, 817345135, 740753433, 84507776, 440378833, 755585724, 722156702, 427057666, 569025811, 956186970, 371006259, 32541102, 958174850, 88395979, 802468315, 903732907, 887154715, 646388387, 797674093, 151034542, 509238624, 569663549, 210039965, 917273158, 294044856, 811005223, 733660272, 374446275, 540766587, 529828258, 231301543, 616155271, 950638040, 854875387, 189829085, 261452910, 34819302, 161751394, 277107476, 826279691, 544481650, 873590726, 458190154, 370794884, 706560862, 848998353, 194916928, 315857887, 943018956, 507733699, 106913955, 346691415, 9932628, 134680594, 364512972, 591668427, 520209381, 799748675, 567511902, 994453726, 816573004, 426415564, 915532079, 571285633, 29626723, 228368565, 716442307, 302799883, 700704891, 376131445, 686565938, 190980854, 118788085, 896536077, 763868296, 385486858, 644375966, 582954456, 47362626, 379091791, 773862633, 456047714, 565956041, 48454905, 404158437, 607249165, 145328547, 344336854, 487479344, 513697344, 617280471, 789039147, 499422963, 904184572, 88375581, 530489260, 72542607, 282665587, 180633604, 528326453, 119981394, 351098496, 21459714, 745490361, 523576418, 607068089, 398481008, 842391552, 116751761, 875716419, 949456677, 258607917, 217220280, 984127794, 347863, 978621913, 346258607, 280792120, 81083299, 340955458, 827924514, 31475589, 596146933, 836176178, 243999663, 359554468, 149337993, 934637016, 431067697, 915839508, 541042774, 160377142, 661022030, 369241043, 189123748, 907938384, 691886670, 447171649, 830934437, 188427557, 31381768, 724685185, 383091185, 656613918, 431458561, 564492623, 832595525, 492451997, 308241308, 411250253, 202464373, 123244773, 718732458, 764399561, 797264480, 609038523, 457190910, 846188220, 347615467, 288433627, 299428606, 869334514, 757910351, 882671097, 437453791, 825785953, 143182916, 668814661, 818839639, 449912668, 22959214, 187562327, 511713946, 712407887, 743492229, 33303701, 350240624, 385488376, 310883613, 275864510, 168424498, 277177239, 965437104, 740148353, 163615707, 790735292, 334384172, 94594288, 204349511, 494158527, 602617859, 59078266, 312968552, 605082072, 405802714, 902331755, 493519536, 759019722, 467360686, 517554513, 802950117, 139467914, 302316379, 698487249, 760890119, 156004847, 950273521, 76477897, 407663443, 478992914, 943375035, 273973284, 595890505, 794768690, 270614593, 397995572, 44797634, 325926160, 610727753, 162256845, 186260157, 587096683, 498955479, 216517776, 601273482, 788013512, 876587421, 694380356, 502611802, 595065772, 82460973, 846575428, 367562834, 410558836, 513685182, 684099557, 601286261, 896400384, 209899111, 732155119, 307314656, 108947665, 193492021, 398814279, 365105194, 16347327, 544880351, 327633493, 167892465, 583588160, 466174538, 868901730, 831221598, 285500724, 713206037, 369789200, 565856335, 666836427, 310654392, 195715703, 577047383, 988696357, 253049635, 133285677, 366423935, 237615967, 836986567, 118319565, 693764210, 110712756, 55294469, 100794770, 332723758, 341087729, 603490468, 303773791, 891147211, 45471977, 182536724, 605462038, 315917328, 683481273, 735583150, 982291303, 16983773, 498085126, 653254411, 380705692, 347882162, 18859258, 287143991, 645365471, 282367581, 433208131, 561091538, 791060691, 834174786, 392509100, 842421256, 69581188, 823738280, 279766090, 813746709, 224565850, 141784151, 20184269, 812491441, 525359494, 113176441, 52441382, 747759511, 3966751, 582387318, 945275233, 236337307, 548548201, 81340389, 282014788, 762551212, 939274835, 809015741, 822372120, 605798590, 660478163, 919457387, 179592287, 153052307, 629645792, 889805857, 423108279, 666539673, 413804480, 602181373, 33053259, 844027259, 454823162, 62085847, 75883868, 341399385, 967347918, 911263340, 554551946, 376365980, 495013914, 986465069, 654757700, 148162587, 314934858, 409449500, 281613395, 243669367, 795351850, 275127407, 194174969, 846113854, 298602109, 915732550, 292995870, 363804542, 796559355, 509186935, 669365077, 504114780, 810822611, 865883777, 197907236, 158511131, 496387412, 593409356, 322311223, 725951832, 29930936, 465975395, 640772238, 623615292, 647757485, 354340568, 198630897, 161007072, 898004743, 728294073, 923057729, 529104503, 522403517, 13921695, 83132498, 136964168, 301758360, 412646462, 150080756, 129229727, 519783369, 930066983, 771019695, 645117139, 224020244, 154139722, 184835555, 458728129, 347676741, 671053158, 886894558, 73639145, 717522797, 217255675, 824591358, 995777973, 437432088, 784747468, 637174047, 108421622, 549730009, 830817583, 954544849, 408384848, 343149389, 832574350, 305997268, 285124265, 319191781, 777081280, 416431778, 726888669, 512707912, 212964476, 143611270, 428898252, 557864469, 709587053, 535962603, 221244078, 48640230, 259895443, 836805582, 426705097, 616066656, 168787322, 306704597, 951026050, 923566045, 661375411, 57129731, 460824039, 25613836, 271113431, 606408238, 982095813, 141775140, 529209241, 461754317, 601721580, 33662989, 780316696, 930708649, 11950212, 122348384, 994832602, 844313961, 270112498, 696930199, 498383307, 674192298, 353282412, 971315591, 976968347, 963870671, 439708898, 310279085, 556088075, 496601759, 9689962, 42496822, 102058149, 895276078, 680810689, 597994795, 618542449, 473584931, 387923049, 638291459, 728247113, 407910951, 513060056, 224497369, 913520535, 803161161, 851408706, 776291473, 598818386, 747238450, 108898336, 461063654, 609158622, 262638402, 304410145, 127576875, 535808235, 302864589, 230327528, 386393818, 222331859, 338278500, 669100887, 680247608, 758801078, 338605190, 575295322, 435336770, 147466053, 637894052, 725923309, 496579549, 205884300, 773710842, 524916088, 114694357, 477900818, 997491728, 179083773, 759407089, 989411961, 507366003, 257269159, 67614894, 512350594, 621110906, 484663941, 980130106, 540809255, 248944843, 980073984, 301838214, 863908376, 386804491, 468398309, 829815676, 34767981, 122691745, 112232714, 619477955, 200561907, 909270487, 145724888, 931842726, 70294964, 314093497, 3987040, 102772742, 271636640, 98958432, 477090484, 945965864, 622374960, 856614950, 484202218, 432193096, 732608492, 721106396, 468678814, 471540176, 938451518, 719749698, 184620592, 480021669, 5162492, 637217209, 457821619, 752496268, 981937709, 265489860, 223335238, 598615360, 790550189, 423630953, 660408443, 411438466, 237804333, 884475442, 764086327, 356933854, 850877587, 50894433, 428881422, 677316628, 888186820, 666530056, 848135875, 748689355, 372759827, 794719223, 898402642, 582422419, 871180539, 572570070, 330081532, 990926819, 338146599, 65380491, 460791839, 937961590, 343619157, 66605887, 229725038, 475062791, 426456870, 811989419, 535412797, 809741636, 509163576, 817918882, 679088252, 534899365, 324108325, 103659404, 59946609, 431944455, 153392545, 174477333, 653453570, 760269222, 493633273, 817680189, 18603832, 393784894, 767341691, 861086136, 600947469, 899568508, 457964086, 381598232, 288335161, 536404462, 629245306, 685826105, 956773348, 939417333, 942213160, 988078374, 648155026, 22514667, 201338804, 868859497, 368855359, 903534989, 479371387, 376865938, 801406303, 224922319, 295558290, 928431753, 415265228, 675132958, 28363386, 651162074, 307354311, 929993921, 137088534, 677451651, 883477108, 170265573, 469473601, 651694805, 801592417, 334978884, 426509459, 437727152, 945725294, 401288528, 469051727, 876890567, 336058639, 772880510, 165313014, 208150399, 513248818, 387011319, 855874898, 158471400, 122467879, 159888256, 50123873, 40597789, 575518185, 748566048, 218658629, 337903618, 635321908, 208785281, 203137096, 543832444, 395677405, 826211115, 943119771, 379603284, 84285730, 394102068, 374064287, 725496693, 843951372, 155442890, 530955050, 224212075, 440914919, 805471702, 790699094, 585196544, 430556272, 831933169, 12110425, 550640532, 346201263, 485507893, 368238441, 97970779, 566102684, 826088057, 712421906, 196399324, 428166833, 630458031, 805374039, 883449384, 387363162, 642749140, 670626631, 630370467, 929548417, 638387890, 412338696, 129689821, 310758212, 696594663, 379317375, 962466040, 910846038, 324416431, 355435689, 393017813, 82532629, 777415730, 308935479, 429786573, 622946332, 670960652, 573603404, 228950953, 923946981, 181896015, 952103194, 400596191, 912177830, 609660594, 19101817, 146328276, 790108076, 80600035, 284759084, 710277468, 154610829, 822247897, 663873843, 184436162, 402987697, 644427762, 417659583, 846734255, 440349024, 615144274, 744504618, 334246875, 939889285, 401480085, 315022912, 377554154, 720462705, 461011189, 328227840, 979573030, 847722010, 36320566, 46896067, 418546237, 12410429, 435574951, 154598117, 371570545, 121173927, 973997744, 927564873, 149383486, 606366164, 518996896, 803669546, 490499201, 870837475, 991741834, 143315581, 848788010, 733676362, 64132095, 727225003, 814149834, 349299974, 157010354, 845482566, 19492271, 26646585, 53448601, 826068741, 775660102, 45996241, 847789337, 351468439, 934109868, 557895326, 909500044, 563526699, 347678684, 385238831, 466439686, 502518189, 903783848, 590624922, 899184853, 178238691, 327257338, 588800523, 218495176, 73989354, 80487431, 850642840, 135125406, 630573952, 537741486, 667546123, 468552865, 349107920, 97965139, 42113865, 221864803, 728045304, 552763627, 424213943, 535657254, 496651885, 900239395, 186094913, 597979083, 985583520, 175708774, 551314656, 693720122, 217594805, 233457177, 792636615, 71378051, 976511786, 185576154, 415219325, 598342278, 681210203, 658659846, 173111988, 83866544, 745132485, 350610777, 999469185, 317433846, 103037689, 735641994, 667874720, 883964253, 930336007, 22417704, 697839083, 249760032, 93531733, 705110156, 521730255, 339378710, 216930458, 472963822, 768693928, 618702939, 333608223, 772597361, 700063665, 16972505, 336735107, 612759376, 803629007, 935329664, 972619501, 330488588, 653214112, 801131365, 724222451, 490859160, 807162623, 916074021, 52387136, 338258478, 472609309, 996660296, 262895664, 65821344, 66000750, 298261833, 921058879, 567635487, 588343892, 74556284, 70328532, 579460314, 299176032, 742187528, 744490540, 928965138, 618833515, 787741980, 322001136, 4123987, 418565516, 470377562, 328792449, 489101731, 868842715, 535683930, 79599301, 367144024, 653392859, 148574884, 312868472, 890199035, 854314620, 93782319, 154435584, 849870256, 423897825, 538436402, 649058086, 483024149, 984889592, 563071083, 357288989, 110756066, 6408961, 185292338, 13688847, 123442758, 788913421, 758455979, 183597742, 464805692, 363020014, 78274874, 5520544, 664558247, 244498434, 293081245, 739411826, 148805585, 138434839, 68138979, 443093316, 281977180, 978724444, 81503692, 269188288, 12518665, 999494380, 910354081, 776327108, 670146813, 108117056, 201542633, 429216365, 277479587, 563711771, 359172089, 873343719, 834026032, 818704364, 398444250, 99236756, 711413052, 771348365, 627405766, 967450311, 151712458, 869602267, 406521529, 366319364, 690644288, 780237559, 276812477, 901540133, 813266409, 736717760, 201948363, 939592258, 516492333, 670666685, 263008842, 782271439, 624645363, 417826457, 599066371, 900592915, 625522408, 238465785, 942806792, 362682139, 935906548, 289629557, 877277015, 779607290, 217444278, 637653090, 684885100, 663914698, 131920961, 410164089, 974956936, 201249381, 138526099, 153878738, 545804730, 524858002, 310734007, 817121617, 120482620, 591870798, 494544908, 240886188, 612037450, 109814526, 625955886, 680767652, 824369515, 105466232, 559755905, 801766947, 418437266, 54678474, 426321224, 586657791, 633046578, 630436365, 642575957, 43726052, 22797869, 83968889, 978825989, 904821988, 603066503, 76702536, 203767259, 895981640, 597936105, 586100644, 168107513, 235057813, 70321518, 638154563, 911979963, 923035360, 47778756, 871433643, 615677925, 407557584, 432990081, 774435197, 722743445, 347195489, 543102096, 186960209, 849523402, 282339071, 807974310, 866826935, 796902139, 80787841, 837195509, 714460752, 910377122, 18436391, 471912878, 788450218, 454598318, 983664318, 128728274, 386823166, 888030376, 877535897, 65582647, 989835248, 986013865, 951746070, 831006644, 575032239, 992170165, 193064325, 805158324, 402144348, 356379128, 750344260, 738271646, 751669685, 229437904, 91445590, 222387769, 35545458, 148489506, 544204783, 688283036, 401848006, 238186138, 962744086, 560515878, 797154780, 716672807, 936484, 461202778, 601025203, 18529777, 15576739, 78012365, 775302008, 480647112, 586153040, 163064755, 492263832, 827782319, 808806787, 139288949, 917232125, 820942875, 867634126, 16065623, 868484046, 986005650, 375563965, 452767246, 649296721, 162409754, 841356740, 789049169, 828486442, 838685099, 78426048, 183662123, 258239780, 294060671, 20979799, 454989175, 166545504, 846071557, 517227276, 326305977, 26080471, 963165010, 728423175, 160002735, 523965043, 762273001, 466452161, 971888003, 409885579, 492930938, 53301087, 451713327, 379658906, 862608600, 462398869, 921933718, 739244400, 301951600, 780040772, 872717229, 4524074, 232361261, 917916681, 797220425, 947324321, 583459451, 240204199, 289092910, 288165859, 608874319, 863203281, 954927846, 102262005, 585807145, 947065021, 128014296, 193439606, 490071170, 100938616, 199865270, 969385554, 242493275, 683118363, 769130156, 981839654, 298793674, 341214971, 471675182, 812863813, 847189106, 184301437, 447840898, 117719879, 268266435, 486697672, 639922270, 321877076, 817143022, 101089006, 23551392, 68178755, 807587310, 880948555, 230669766, 403679709, 998597629, 984571716, 420951197, 401655312, 322469222, 180315325, 404681586, 669024091, 743023273, 693379037, 976098424, 7636801, 833504799, 55130539, 171432822, 829687795, 52531769, 896000145, 126879972, 553807202, 863239497, 197070040, 809743989, 261179355, 442651008, 617744252, 329244319, 647453569, 561354314, 505241411, 9140431, 815090472, 463049781, 590398988, 456264950, 4329335, 994824237, 254004051, 106486494, 102865263, 921102658, 847305570, 268291183, 163536428, 591304199, 620060169, 319424412, 767779123, 827594481, 918823373, 304518924, 418396237, 317178285, 74430343, 75523683, 652764060, 863207901, 511829535, 205665321, 259324753, 209277542, 266935574, 378515115, 278827052, 874263006, 933221012, 575727447, 579960355, 876243193, 319341226, 211077653, 391024828, 395298841, 928894726, 438929233, 509621424, 871378720, 877234434, 513383778, 349723846, 564799735, 739154067, 320702017, 581338019, 637706019, 493265986, 161470655, 29813098, 182878646, 728701672, 315968510, 585221585, 177083514, 774404803, 94326072, 784002230, 223909709, 999985760, 550903883, 715296186, 920544989, 282436375, 246005306, 195953808, 104335600, 670061049, 154926901, 210387137, 627121777, 49998413, 207988705, 149080560, 826586630, 994467836, 940245381, 148604501, 247430842, 516573800, 266811358, 761784847, 482741469, 122707037, 525273493, 287159245, 349497658, 695855301, 509527772, 265796211, 567045144, 447540323, 101837604, 730149471, 539916531, 594324824, 797374369, 783991437, 277909652, 317295700, 605175306, 968724959, 988691807, 343977974, 936061490, 357486411, 592629334, 500329856, 409785286, 580471028, 237966786, 370175731, 887414311, 491903484, 695540208, 270245365, 482341057, 854047921, 547583163, 422660038, 107814013, 749221068, 630994604, 702243231, 784126310, 724419014, 743121461, 95157315, 119255860, 9237124, 26179161, 351554327, 394020399, 159386913, 402090011, 261319307, 796422192, 433964388, 579060194, 242715897, 984036331, 701671232, 828516185, 607276600, 481794376, 222498897, 322337785, 71636254, 186825190, 461965213, 966234858, 322612855, 206954613, 735144012, 133524202, 912713144, 731490372, 298088560, 576867214, 723352406, 876979166, 636635549, 781572313, 386042316, 996815074, 51563912, 826759796, 92951438, 236093506, 752925081, 284432604, 889398056, 375232319, 493264149, 719877130, 54200703, 33777527, 579817310, 357528509, 722467351, 403544045, 884279616, 395811877, 556671322, 783555353, 875357099, 821708114, 971899046, 275682085, 185581589, 8556525, 286448354, 890834163, 765432224, 412254337, 891309208, 8604955, 878872233, 738712161, 765001922, 553825741, 37844962, 532970735, 991781728, 127366756, 575845657, 656344740, 700090223, 337563385, 107662400, 48853721, 14425424, 494923714, 82550111, 461088874, 239326293, 932897574, 887903242, 149432492, 806700986, 656825431, 478204269, 540211292, 44404958, 35141237, 807109814, 174070999, 908498764, 316071196, 697124636, 749516506, 945721959, 860208249, 161619960, 118078262, 464767599, 182598010, 987493062, 792238691, 320447989, 274748523, 329689934, 347476841, 589567929, 4096105, 967183421, 737718805, 280882510, 313136529, 137723806, 953594126, 514977250, 300825056, 578122097, 189406287, 201973412, 849506309, 420137236, 591478071, 638987638, 38442904, 93089957, 267378356, 139894479, 410175087, 243606689, 300010432, 18151431, 717033064, 935354411, 520863887, 622236943, 793408299, 500693384, 976047467, 429544895, 855459195, 465022173, 243306119, 199968597, 363059636, 488777934, 738437924, 896544899, 711037247, 266257485, 558936471, 719361005, 669546125, 616370293, 754279547, 422967548, 571580337, 511615919, 401263786, 828411907, 261103026, 802347793, 213333062, 506364970, 826988980, 79455934, 320123466, 852877041, 685889387, 672439858, 185035289, 303860913, 341202283, 391189294, 191678116, 445579128, 531121547, 844525294, 361128511, 610001726, 863997351, 307985701, 295278473, 388063176, 244409985, 423691954, 487639413, 39376293, 516388941, 381694586, 235306534, 558757211, 637975501, 351316627, 653933989, 742676291, 583733309, 465963499, 392277794, 378287668, 596365499, 584511701, 922056624, 639711838, 429518633, 131311565, 258901377, 592862772, 719742759, 333410217, 992594293, 191678836, 887394511, 513965590, 374001140, 28566797, 157861811, 391094931, 584296532, 5247222, 574331447, 991709444, 281251376, 261680923, 888916560, 920286662, 778777499, 952337393, 489458975, 589258387, 144337879, 491828934, 955539988, 961540452, 885919866, 736165560, 445427161, 940907083, 389844818, 413139169, 506018830, 443489510, 375856766, 857777841, 923010832, 14909579, 207782989, 949830815, 153422606, 133819805, 517616860, 363863591, 277844010, 961716734, 144107084, 413985969, 970060308, 927828921, 486055613, 568310513, 446134366, 849105854, 358582980, 66883406, 311128683, 175419040, 414909727, 939970500, 565027690, 368900744, 624807787, 994685337, 336250879, 956511706, 451270024, 218119224, 581641736, 383229333, 805167588, 254399281, 316128555, 556332925, 139553121, 121867242, 42016189, 283398289, 804790856, 832146847, 129413303, 862346662, 286970797, 152130137, 419800166, 667873152, 240215753, 803455190, 469588018, 474772250, 462603781, 317161270, 323878041, 33917004, 884220448, 762345830, 398878589, 84130477, 292794401, 272855421, 492518647, 35862762, 486985222, 588583416, 374765302, 238455662, 537723549, 131843264, 88500476, 416834967, 625561347, 553783961, 25283361, 20363237, 846338810, 982930934, 420934177, 673265831, 79238673, 816226457, 174871257, 265174983, 653859864, 313926511, 429433779, 856165059, 361905504, 897246370, 163620640, 897550399, 725378238, 618625220, 616023662, 841588897, 420834232, 52262780, 594777113, 679184310, 446533604, 963518319, 804117695, 902561563, 784786033, 786808529, 244157786, 720216605, 123831243, 271331481, 840118133, 183273163, 190523733, 3372965, 575938739, 821222088, 450608956, 366348016, 901987092, 384936113, 704363661, 578849106, 911300876, 342800789, 999203844, 898395860, 771432022, 258867325, 281462847, 572451312, 485455721, 73344049, 78126699, 702552247, 47485421, 451216690, 232078420, 381979623, 261395758, 36577790, 351154741, 203115932, 492517869, 898081338, 163755811, 546215369, 951841831, 720070402, 556174653, 296785625, 15915395, 628961541, 541421813, 560282935, 280130291, 605277185, 101632439, 708538536, 801277295, 948356046, 638026578, 891262643, 554673016, 766852550, 469324843, 716636177, 333923631, 842569570, 392279409, 478089655, 878576879, 513237667, 132227323, 550319076, 709614676, 960965335, 989321792, 317734511, 846905564, 764016103, 269077250, 771693809, 668023891, 718320948, 17845312, 242892707, 217764333, 173366104, 765853192, 438851416, 944927892, 689113739, 755163853, 657313133, 534941544, 421995978, 271930356, 201110399, 209912261, 86891718, 418461288, 723963847, 584982465, 615832724, 154271385, 764499749, 632099730, 834862963, 229225280, 145860679, 969525773, 604437777, 178294642, 225238111, 228867356, 190321538, 610749455, 939581404, 500981036, 814818406, 975184275, 484817942, 968482455, 283215693, 110602294, 669111406, 404381980, 161358908, 619832972, 554494012, 578019611, 643238421, 628709118, 817636497, 169274079, 5597879, 584682566, 476956905, 149367530, 643123959, 691610642, 550782422, 294840761, 900446102, 302306706, 659782398, 418614087, 563653621, 962162892, 384135323, 436189055, 398858424, 44832561, 773822420, 736375423, 801225368, 103766458, 400510797, 157109722, 184498707, 534149964, 104937533, 243854782, 744572970, 110480511, 943378267, 187209744, 633243723, 525416358, 672556668, 156394410, 940897409, 917965644, 298580261, 365713556, 782865921, 320597591, 62864650, 573842847, 650549493, 308907602, 457066922, 131863500, 867895200, 27825942, 49539545, 820585186, 71700831, 724030285, 846023481, 57374155, 892751228, 412485658, 537678316, 945568942, 953592077, 793418500, 592251398, 954103735, 836335514, 884487470, 287179248, 83425689, 127786812, 450150061, 703608216, 697319890, 513965640, 180029563, 911261762, 362712662, 250850519, 430618077, 517760775, 806550662, 378729964, 958761280, 544265621, 812076810, 880442949, 800797520, 806771369, 759142202, 873344620, 831789376, 321438559, 496629041, 990392722, 815059235, 549863978, 653317248, 644999850, 109487167, 30232388, 49784214, 442986635, 195852789, 66041272, 861315957, 696431148, 876952999, 730852423, 803726480, 684097437, 418065633, 76070518, 620702584, 634371385, 788940927, 860155167, 659765377, 701695061, 551442195, 735019185, 84468333, 866615788, 123232178, 819524220, 132037906, 249149459, 425441268, 197011815, 565468631, 927441989, 122954698, 190170939, 354432555, 971877723, 801997508, 512819683, 702616622, 957331565, 849411906, 823430134, 820029382, 620995344, 917380117, 118686093, 733951071, 855077863, 278113365, 767962149, 451945740, 999182383, 786736326, 933696854, 298912769, 859268448, 439043894, 415981209, 229314092, 59743618, 213478216, 179079607, 6162895, 431052867, 432301996, 122336473, 549233459, 861070231, 222893842, 978734802, 721510393, 85261900, 728071565, 335004592, 767233901, 940800236, 943411826, 422576822, 840364908, 480917499, 645455515, 116365661, 921857974, 41264683, 404262830, 832032648, 415487997, 936127820, 453008573, 470293350, 782967474, 713684305, 728539270, 967072079, 200613918, 562850069, 847125515, 333349593, 969260053, 889558711, 690048030, 234340535, 726289463, 409596050, 183853501, 62045033, 183507178, 197473173, 578826907, 976827601, 775229792, 474904969, 84120265, 947784406, 172779198, 369701802, 362513935, 568849434, 951984989, 674052112, 933351158, 500402092, 606176493, 181447123, 867156150, 168418795, 612750536, 156768477, 257134441, 48385654, 245236004, 556476090, 460884301, 489045631, 652970556, 116384916, 610265134, 761817584, 838188377, 409888493, 466625044, 609531243, 139444578, 257637003, 222429542, 207095685, 107572615, 569281601, 953661217, 639441124, 327403565, 696605945, 348846116, 208131829, 562507831, 206743113, 209311526, 703238640, 740502660, 949935400, 521335597, 94608654, 540087767, 33737161, 843555187, 284047888, 487660797, 129056303, 243290942, 696560015, 657392149, 188405634, 985681206, 558381657, 928797328, 352070537, 207812910, 96789933, 559692706, 15918248, 403870587, 287596990, 35186102, 251925342, 766754334, 268066046, 995014233, 863695384, 868449346, 110157128, 16240724, 108127664, 763478049, 761725997, 485870986, 799595413, 532717028, 795574135, 183928918, 355378601, 561315087, 488051473, 101287299, 64629597, 125335019, 7478478, 456288585, 253175404, 385861953, 243056268, 563654606, 296569983, 237129077, 721504331, 337436291, 883441470, 449774448, 676385798, 987859115, 978993455, 663574553, 956199933, 853606037, 730448184, 510982157, 890354502, 939326005, 230898073, 635733667, 799200087, 298511589, 889748049, 734057670, 124708997, 763335831, 383132467, 157064659, 713691951, 987949411, 372730684, 73578093, 926834716, 163016361, 31885884, 557481471, 502568879, 544502231, 50124045, 325286851, 468433981, 952913463, 479400807, 197155145, 317453234, 462063132, 230167601, 258043263, 768541267, 809849904, 268166794, 60857939, 440940890, 855749095, 941818913, 737784204, 668429686, 623865670, 689919975, 536983636, 866713490, 880808232, 530606974, 308821331, 839211749, 39031277, 249049801, 980618152, 975432198, 295805205, 253512141, 919682687, 436669509, 3804605, 936315543, 645432078, 922679957, 248735911, 244213199, 954027389, 851692056, 722532916, 114054733, 342542645, 943620996, 516744219, 461887824, 546804334, 734876356, 7875718, 175265944, 207775127, 973992521, 472672309, 413310457, 636018083, 507218601, 172783130, 92331011, 459467397, 23034552, 439707464, 736683516, 401674814, 625816809, 505245917, 73478986, 961013274, 444409303, 499876956, 299244208, 626989940, 418692475, 338133810, 305822499, 829160868, 497570075, 858917452, 596662583, 454978612, 252438303, 846504755, 533636028, 628640951, 243406706, 396814814, 602069395, 408062565, 139501049, 218180870, 595396917, 853046775, 738972202, 302201509, 178308982, 286610589, 56821173, 752515074, 289823477, 421124067, 90495585, 998546506, 811643781, 978905097, 778393505, 814415800, 47526016, 72868536, 301035723, 959759305, 244278310, 463490645, 273282480, 854584564, 81429874, 591759653, 123668808, 927200554, 649841196, 743693281, 108945510, 780567274, 908365358, 183801884, 906512693, 317290432, 100720277, 570766736, 925529738, 42878123, 385098741, 92468211, 34794978, 624989961, 946802048, 160571289, 686885976, 474534754, 565433872, 620006839, 859988294, 61751658, 621879080, 295105925, 74185541, 248582034, 800385790, 147700441, 590875925, 409074247, 746148383, 948897946, 72565427, 624938689, 742193194, 844666512, 431429349, 896909005, 334946258, 124004284, 200358189, 132630360, 419216711, 225446069, 580106066, 643226801, 878861394, 715458167, 45734933, 537148144, 822297631, 346184696, 107177718, 691319141, 34139004, 903870792, 866906590, 905230451, 147427354, 426957858, 51313831, 155462093, 195609577, 176492027, 750943227, 644886038, 52318934, 72924094, 314810869, 154362719, 576994184, 541908616, 674199706, 295200778, 924386683, 977785318, 527463893, 944105023, 8095163, 166552500, 126288286, 472374301, 333544159, 791454926, 839879825, 552886248, 889497317, 812341796, 115608056, 573861727, 804546687, 947872377, 665993884, 793000925, 764061000, 910057083, 963983997, 692807526, 746568372, 555869688, 582112343, 525747555, 207485400, 383887236, 641080256, 602867203, 566022551, 74472867, 954024735, 82098407, 405696863, 789728792, 890604045, 414619500, 79788409, 415548088, 458935442, 113056429, 420050521, 283213453, 301210948, 336137586, 403534285, 457734818, 513294509, 34250360, 54957247, 772406310, 941326679, 181224083, 248982496, 556436093, 962181719, 331903936, 46887916, 246662018, 678602924, 999323789, 255698616, 8558411, 811220948, 833262509, 301118183, 169758274, 255911512, 794695992, 78557618, 984590089, 768930126, 21165481, 334301450, 615767864, 966840695, 992946270, 605997756, 980507834, 33213224, 155246337, 202309857, 437590829, 173324727, 821886591, 824928290, 832128188, 397584202, 385195185, 463286923, 98074274, 771558632, 945790032, 428653060, 882365327, 553498533, 305449813, 374619232, 85430302, 650713983, 382275507, 85078794, 130015550, 650166113, 6201216, 335325541, 755736633, 135333549, 728893253, 692522038, 898422507, 443037697, 645244974, 801876382, 920310914, 935958324, 469578948, 15566871, 352505724, 858454279, 546829745, 742346719, 939321019, 329466560, 13522095, 373348625, 454497819, 211751866, 168974789, 367292447, 450272358, 213258689, 199908230, 741435466, 493822465, 243853864, 759168970, 414291331, 945134823, 164233710, 921643418, 5929120, 476898788, 164255149, 755327720, 687088597, 39585946, 442299022, 778179212, 250801581, 949479253, 932661019, 350186734, 345082494, 560863108, 238799548, 972396438, 774812769, 708386005, 147922554, 74014704, 326026433, 954381278, 111962723, 825276442, 58967580, 533232524, 400581102, 465912835, 766426244, 521316891, 756361548, 879053351, 797922313, 804176060, 278440433, 269909561, 697584476, 706061807, 417013061, 178407323, 400342717, 594740490, 273338771, 922430628, 342399176, 688423261, 799932899, 914066218, 925911917, 452208887, 680083162, 843754594, 713904796, 663797351, 436169849, 917141765, 2652603, 509299879, 218294413, 300847260, 351015122, 662108549, 12965733, 705562977, 942467260, 580396858, 711716061, 118432294, 382856319, 466675083, 12970803, 895387451, 64507559, 603293605, 639305727, 606299645, 928992497, 646070233, 661917590, 560953732, 653257056, 696731539, 35661514, 383837410, 238609731, 352127954, 233442359, 687715815, 219004375, 217669976, 325852825, 809722632, 689961391, 63293844, 861303418, 919696031, 449087827, 542864064, 166828580, 707811570, 37063869, 729080780, 217421941, 623809801, 594099522, 485199498, 971370574, 419186435, 570507835, 931703628, 263306277, 428892602, 755934349, 6628687, 837119993, 56797133, 313549293, 511998193, 7762095, 234343482, 688122709, 363824650, 618971162, 279627069, 466990694, 801533782, 116556583, 456279368, 814066343, 836855593, 760457572, 720112241, 348473513, 724070327, 780756895, 872083732, 72794103, 676336314, 181140680, 854824445, 43606405, 637610718, 997242111, 450226058, 440564875, 665817734, 929003123, 670404019, 227246140, 845788645, 654269213, 762602539, 933628803, 656551083, 842016208, 256368928, 479747124, 24086819, 189462506, 129696251, 866156487, 537327116, 780348620, 671915829, 437222280, 331340968, 444783267, 10205821, 48949948, 746046131, 166279234, 410671114, 434463101, 535925376, 657981290, 870025143, 857544737, 284441812, 646473599, 58430625, 414427662, 910453504, 771083079, 730834392, 585564890, 784351443, 885539225, 798236981, 978864711, 497994456, 906710962, 535199469, 746730811, 677965339, 13136873, 827828841, 722699150, 400759494, 455740864, 347338412, 297067885, 964118094, 187004499, 38092144, 346593569, 853330196, 408954545, 462313971, 245750055, 930943944, 359601558, 706386049, 46256831, 225561784, 25993673, 935329410, 614762920, 164529965, 532177559, 194772865, 542557078, 705570508, 121335378, 104971078, 76966474, 434197583, 552807438, 845904310, 650894330, 471112340, 825446750, 79208803, 650138781, 670019194, 86550945, 653849213, 541843129, 117097236, 943558622, 971667633, 207637216, 202680745, 529155198, 548004412, 221713777, 975324996, 172525278, 726763881, 970382372, 441965570, 286511314, 180745587, 128099331, 522288363, 179101348, 113009332, 693278239, 165787884, 977493478, 444869868, 124951969, 795974439, 672117329, 206621603, 925978891, 14962991, 822415659, 407450499, 168616147, 799890467, 678076709, 459555230, 982374811, 949668304, 610558457, 981665622, 856374610, 227338689, 54031241, 778488867, 922420537, 855382644, 792212049, 908681085, 541636110, 484845447, 875980199, 105656496, 893730031, 529722935, 379247771, 727283938, 68254597, 627431350, 533801937, 49583619, 274135423, 983900460, 163710934, 246660878, 491802029, 49046494, 273446252, 204392428, 206684991, 4578761, 17663093, 270854126, 257135498, 306587470, 71062784, 9816227, 797040122, 566231691, 393459895, 620932404, 894175182, 203988344, 960828116, 961669090, 360960043, 466846970, 993046924, 192986390, 217078014, 751437754, 377461085, 579993475, 189707328, 380385976, 334735631, 984564433, 364808186, 644011595, 454679267, 369788286, 743210347, 658789193, 694526276, 614603658, 903002374, 757449894, 971184838, 785591698, 653665953, 792382800, 815287806, 207586578, 313689024, 425373826, 756758845, 134367537, 864922394, 268398028, 522474130, 445043819, 58084183, 504205277, 732069665, 241572395, 925876602, 824406913, 621506162, 676912276, 562099521, 739583204, 18488016, 250453822, 80846471, 351854943, 380350429, 624189390, 191330553, 351313879, 943851726, 739786039, 966536393, 144475294, 282953210, 155354222, 7287840, 146532134, 607362900, 629858231, 250631671, 824688097, 669089139, 567543809, 246429470, 197696936, 300628375, 146332001, 499898988, 214459409, 607666965, 74018661, 462462893, 881045838, 963271030, 691631338, 12727226, 410980531, 973322754, 527226655, 218879406, 448263772, 502877244, 192007210, 667346480, 376086720, 895906829, 833714489, 148179263, 450185447, 874750415, 242716745, 978868163, 503553280, 432688840, 197651162, 218847137, 175064772, 880450131, 579415321, 300810001, 192879343, 104792208, 492996823, 904127001, 974780321, 125767132, 750216332, 264306583, 178141899, 765180974, 675328182, 716087755, 578965274, 472386596, 318015858, 158966756, 63733962, 791892501, 223656314, 265976494, 878456606, 213421455, 866713523, 825718545, 672506322, 534711986, 161162629, 631302531, 497351843, 8439044, 80478016, 723946442, 723395439, 271348903, 410139887, 526457438, 811302139, 692980289, 110577805, 351022341, 819604592, 480705590, 615772641, 354527060, 683392286, 370788517, 640131565, 282030410, 440405407, 628448625, 575915755, 543031344, 893990428, 717218619, 259439708, 92789436, 779004654, 173745660, 656907218, 340310153, 366820675, 822567322, 560341182, 115733588, 824867576, 998439053, 796114459, 210111855, 60687100, 995132197, 261004456, 13750573, 809836371, 165206773, 79970778, 943322939, 569104477, 47501225, 394927677, 552906513, 618998660, 550643197, 156764583, 402102413, 966850485, 501922337, 515823547, 891358954, 879467292, 955039174, 404929938, 729965317, 348510848, 282864289, 382423141, 17036075, 278820701, 196297297, 461072446, 19184476, 948364848, 146217083, 235520490, 341262156, 598562796, 79241743, 116609585, 801860138, 480914248, 452952770, 708932564, 296745275, 318419927, 600616414, 473082920, 159917889, 16757747, 440862318, 358826586, 400786425, 231626177, 7735213, 815291196, 630832271, 910996084, 349747096, 150299641, 339116648, 77372967, 51497529, 553258274, 980490692, 608489580, 791456404, 296314152, 686872572, 539024317, 817560304, 641951104, 590740350, 556997991, 347397734, 607705182, 915097141, 504005080, 845639289, 768237469, 373113132, 314019770, 578172262, 609049096, 788275931, 976215950, 978169548, 85945465, 989663555, 522847441, 286288656, 487905210, 909098820, 82666892, 731144327, 886796223, 194967197, 317454095, 947349737, 242505510, 114810106, 740578844, 941279459, 528674846, 914529414, 890510287, 420493411, 953075953, 451736139, 266453626, 491027008, 119927396, 306688395, 168352063, 106523159, 245719944, 867133775, 721641820, 882012296, 137061773, 691720869, 894806121, 594717944, 903726117, 189079980, 374092187, 945457526, 160046074, 767557840, 689446690, 666042143, 696527251, 690075064, 205648252, 681661951, 77921661, 493144152, 74746597, 76989354, 193236912, 766151468, 354614079, 204177585, 650823609, 379288522, 654025221, 455892255, 648357859, 448436498, 956053523, 428336872, 936432983, 953836563, 541865142, 109707853, 238884552, 163425570, 986834532, 589149591, 230873182, 398135720, 280266549, 52910961, 904131833, 94091961, 144934266, 916318280, 97958124, 38949822, 189686929, 704558308, 300450679, 554035460, 515078442, 119632502, 825360395, 175642358, 676262299, 818907157, 435668438, 971509964, 489116101, 770173068, 227949212, 808871571, 514847647, 822474886, 169796024, 288199152, 505655071, 739989862, 584555640, 400994438, 300911934, 386476998, 988778110, 337922499, 332660827, 801782390, 479799996, 282333138, 915794252, 62017469, 334863339, 909097702, 203258927, 186959648, 265206872, 370589352, 909673335, 499327078, 626959299, 873309880, 669697616, 386521521, 619736043, 198461789, 600174355, 934732559, 966470133, 913755170, 423672963, 862826369, 325472397, 874444800, 643669456, 962678750, 954503394, 402254465, 103028876, 376237258, 214529824, 64597247, 906338055, 437683209, 118542070, 637018216, 782550038, 215950498, 447255083, 285804080, 433924860, 716732131, 940196737, 138341656, 860083261, 555855611, 471579496, 40956568, 309420585, 84020966, 536862747, 483286917, 230045491, 669909639, 696793956, 901908841, 428959095, 862449859, 720189470, 553832007, 763106483, 958394517, 266697754, 634700928, 93450699, 699757174, 1236756, 80209889, 821439550, 758098335, 83698989, 536335401, 124616361, 444682767, 174369346, 774900222, 121989720, 690835004, 785951764, 884444315, 907769479, 30059305, 834800342, 186742732, 611936055, 101817761, 811737636, 314879424, 384779724, 909781740, 574532978, 984287514, 927588438, 359958715, 340767270, 638348081, 403670044, 626307051, 23436111, 73316136, 401465721, 795588872, 478477820, 702437102, 545692632, 467806591, 996967940, 897500450, 682802401, 765481351, 710043687, 319051325, 39922262, 995669596, 138706274, 266676083, 321088176, 661753060, 972744218, 373433058, 905655924, 731475762, 705263431, 582750656, 775727996, 6365715, 273481143, 660232970, 822423964, 241389091, 60851580, 492074119, 315054189, 874960831, 208860537, 979207445, 472556415, 567228785, 800417189, 746387127, 382635070, 639841053, 895099229, 285449882, 660100692, 403453130, 27801134, 356287860, 104009573, 750002438, 729723099, 598862415, 732856919, 310516040, 8101315, 307440247, 219069662, 699028441, 403337292, 949321796, 809114398, 892648037, 335656568, 670425946, 947213227, 811762012, 424133097, 203731677, 908170785, 721559591, 317613389, 993233448, 373357967, 139282786, 521880737, 123339193, 571886739, 317186037, 135212103, 417734581, 977627737, 364937615, 978921962, 156239464, 563791768, 640789078, 287836092, 537964254, 797500280, 4440258, 41048332, 970601650, 750944188, 391867333, 184714407, 301228262, 146979952, 834631876, 369080693, 496515306, 944351880, 989776084, 187330250, 8167202, 791976295, 102195594, 619575137, 910511755, 836305618, 963246860, 452986793, 959561968, 725526930, 814213751, 93690484, 803741083, 968161403, 317197725, 818656078, 347820135, 789806746, 382422782, 734281795, 262884942, 837005540, 875551361, 534431227, 834417925, 654081637, 700389015, 781949332, 909633330, 815570906, 795894209, 289673092, 278655860, 310673605, 993142230, 163133793, 545461522, 654031109, 550415517, 715607215, 843947064, 684054210, 856593546, 20274196, 50789503, 304389733, 612604798, 802423189, 286595364, 801374858, 779683852, 995794767, 235462030, 474510385, 189220466, 410523952, 946575086, 147697134, 277850701, 267951298, 689434684, 822654322, 531964371, 416471884, 336798978, 725067588, 52030588, 733785817, 395772533, 703368170, 49159908, 32728991, 497810933, 324214565, 756725234, 381326173, 867816326, 905638539, 436447340, 52523550, 942578443, 425987673, 74187705, 703354778, 825983989, 332387281, 949748996, 224676085, 280715228, 94304049, 61278628, 335585287, 165832928, 220764788, 749282578, 914372883, 67692816, 149049114, 141608277, 645794457, 316334236, 964682642, 974509714, 923009523, 255809125, 836718596, 132339233, 485568360, 657609869, 347073417, 243385171, 213162942, 342462718, 592258773, 86671451, 720921845, 718042916, 881218186, 191768021, 250996136, 557589009, 317296218, 445492507, 398155083, 719773830, 478631251, 919789123, 589866998, 260642440, 841441684, 712301690, 417463099, 152781457, 373471801, 657593486, 241684893, 486805976, 435335888, 441991350, 891469106, 349418427, 732241146, 572822893, 303612568, 816290496, 974078508, 931215742, 743194496, 503946945, 475615291, 12456864, 189371356, 470222481, 469152966, 651000766, 193630569, 152461251, 359046256, 973278037, 584228693, 773387499, 932495345, 866707735, 789804234, 496683790, 812272029, 306899430, 298187289, 247129060, 247008818, 355536802, 222349942, 677763378, 378875920, 75073122, 681049325, 946457984, 876476052, 830664032, 589036556, 629377258, 44428593, 203964677, 178889179, 653866818, 775984081, 442148536, 850953586, 259076482, 645691049, 27448680, 40156886, 134859064, 695546903, 407548299, 95527540, 659832308, 457581632, 573874349, 368057934, 933627926, 672777422, 763906721, 704577779, 782793815, 423458705, 373956576, 578364895, 647699906, 950124315, 926383391, 422591386, 239729150, 558311348, 106744042, 309636916, 864142021, 928381937, 787822412, 852228934, 701122273, 390286308, 94950740, 423503716, 627055856, 511796751, 901240054, 720557623, 735072999, 167828683, 854600472, 496137356, 20660568, 84772960, 451028393, 439110555, 781624359, 424728155, 513019228, 400000636, 743713825, 18970878, 723909827, 203056609, 525623317, 875194197, 749555863, 684172336, 24407556, 944680175, 133248312, 150238702, 547194921, 943248123, 413435746, 848980464, 592335638, 174447938, 100106850, 616600603, 12794595, 431208445, 389076223, 219160822, 434943510, 504415255, 41266623, 285679679, 988901301, 674037084, 493429866, 231403155, 28954116, 373005736, 63280773, 610939165, 988900661, 132133253, 385769659, 163667909, 338655267, 4067179, 899373888, 163255095, 357811721, 677643272, 972024935, 930051403, 653848955, 533414507, 194543728, 775693471, 988722718, 293686712, 35591166, 66095682, 66306144, 428755622, 99135291, 441782257, 802466408, 870694989, 154321623, 709291978, 284575678, 770029750, 107018798, 725153709, 771224092, 320481809, 820450784, 642053016, 478640892, 196098170, 102751416, 198956033, 682832363, 145869774, 232168683, 641090339, 268306989, 104315768, 7354143, 643504940, 75235978, 445360696, 996486773, 913755064, 213590226, 596982211, 473504938, 863480076, 234844774, 957625757, 624990814, 479526525, 5590528, 766841147, 816505621, 102504021, 170082704, 888266136, 852130227, 528909769, 288462566, 471725252, 107686847, 493899220, 125722322, 635984931, 86003703, 95357300, 601633188, 909590040, 820211742, 65054299, 722303207, 649346116, 724855364, 880447433, 728669376, 695220438, 172119530, 533925315, 455607037, 877541319, 604496941, 667642581, 520504441, 29009015, 825396203, 57759893, 640451912, 783674331, 429759662, 449138412, 113352880, 599812999, 65704196, 925121524, 791715365, 608725065, 284917132, 54138865, 30862170, 53657308, 212599566, 563444918, 964534420, 935703283, 829251031, 893003271, 169808015, 155428663, 167087659, 35344852, 596321234, 832510968, 819587668, 555403878, 30259132, 725413103, 713393962, 136795407, 464432778, 519366103, 448078855, 938055293, 152910998, 318913640, 317645060, 592850464, 899971453, 198027760, 598305984, 348431110, 528192490, 237480630, 692655669, 660092011, 128299817, 681391453, 580779621, 433921791, 201149580, 168603407, 435883424, 907376248, 343066938, 873196659, 799087991, 491701719, 11564598, 919395371, 822886643, 126105916, 384318087, 442896165, 151199677, 930589150, 499847118, 214763799, 397527786, 974062521, 486396083, 250637579, 443348067, 576715206, 253049951, 288914364, 98147863, 779109225, 774354435, 938731915, 710389443, 446955149, 788217236, 413756022, 780806723, 758804456, 718216333, 426156411, 575689750, 546412972, 107653160, 494606107, 963680678, 848494462, 894673914, 462868846, 158769946, 313183401, 827763679, 394784443, 248344209, 316394860, 67470265, 933534947, 318813484, 111174373, 599409171, 767409115, 351855847, 127460263, 152772616, 956927000, 867313284, 162531527, 330725343, 622901758, 223890279, 633119811, 96056534, 655522552, 194525639, 751902760, 687324670, 970838215, 131522230, 746507864, 700356297, 494539796, 774785587, 498896998, 481382411, 825668624, 909361760, 7457147, 802059158, 102255389, 154166426, 810100323, 281264667, 472557158, 298603294, 25143554, 984201305, 146393915, 289639113, 200319119, 613257795, 624287718, 433009713, 45005359, 73274698, 510211450, 877004748, 859870584, 152890274, 850923364, 684461976, 880496, 324585317, 490449837, 509825596, 477030854, 971750042, 331460579, 622684558, 423551124, 875698385, 946937880, 808678675, 604714394, 809999417, 112389563, 226077598, 769266731, 591190396, 97424371, 905239848, 553405389, 606862842, 418319366, 143681859, 92733734, 529107161, 834087454, 196913484, 463489618, 692107483, 188844911, 74604738, 27860121, 854198376, 26391865, 798551382, 323110952, 722174126, 797084659, 222394618, 86538865, 612236855, 796455545, 569760988, 872607310, 764170533, 786739197, 405076716, 500004732, 808794696, 577932534, 643923834, 82299639, 513732821, 485909858, 249901196, 874936970, 460518139, 777129052, 724836886, 605742508, 219279401, 790259961, 254135564, 694628141, 816853822, 966776732, 267471992, 13458085, 574971776, 531932443, 4818253, 40172936, 694789194, 626656994, 35408279, 361255166, 877792071, 189320466, 387617649, 16069640, 209455546, 70388185, 963007372, 977820330, 586862061, 276482680, 712494876, 855427380, 45726951, 455283386, 610569655, 802664662, 697747105, 489044838, 852738828, 379784401, 687741320, 921368838, 651183374, 226344489, 373511397, 340410211, 214897689, 556554258, 224148574, 346623795, 88675565, 898911294, 232629051, 378635064, 105013222, 440986770, 410927406, 653053994, 227673258, 246580918, 763996226, 348993156, 65142319, 530627679, 167663144, 462383703, 692713940, 176238350, 463980259, 768699685, 587416612, 598480930, 537581661, 113658627, 98201425, 485885398, 316003758, 381713408, 264487271, 873425727, 944961086, 721526110, 949325388, 951101263, 616076593, 382220640, 30777869, 3168257, 564139850, 452910778, 574766463, 692114612, 487475223, 132563861, 574151066, 890876778, 487783291, 971615745, 917987124, 52240610, 902105131, 992925825, 561748116, 172847723, 941912045, 99944516, 317604375, 446138140, 954871616, 817866343, 909701956, 412733987, 360459587, 814749942, 86555695, 343483995, 517623141, 833611004, 131854129, 494734280, 265948127, 88313348, 666238834, 902004294, 506520668, 40936417, 342913172, 517456918, 830813664, 110860926, 911251171, 938790291, 438165474, 496285392, 177936496, 158548061, 486356558, 201029348, 638559282, 512826351, 233370683, 652457100, 403721265, 761970550, 281715457, 565044959, 350054736, 717222616, 977261494, 803764535, 979573912, 599672367, 191620606, 869764072, 50336676, 728554200, 127279175, 542163654, 838508776, 115729617, 353206582, 727685303, 170411327, 472578987, 32013835, 565600632, 491918635, 433413257, 298654468, 60274073, 16882783, 871938279, 746979894, 274003201, 984370693, 646489085, 164421541, 947272914, 45289765, 448213255, 970906906, 481648284, 461643210, 838997837, 305200063, 726218274, 331859055, 596767013, 667096755, 272587498, 689617076, 992920000, 748258280, 622024340, 275171663, 379366387, 775592762, 596045052, 434642822, 819024614, 909963923, 760097139, 290482650, 485420568, 939570800, 17890222, 806145645, 72822345, 526901060, 379800801, 514213706, 72571014, 889595375, 606085104, 187026985, 546940690, 290902351, 986007183, 862912330, 161553589, 458294517, 68494764, 550730050, 722700923, 751487948, 765172994, 474534842, 38583523, 697625598, 12206365, 968205697, 34681167, 777638048, 543699693, 13875814, 218767550, 890639454, 963917894, 650889689, 920533829, 83498887, 287006127, 689787285, 990684227, 820589508, 998411816, 775913947, 146510283, 838151828, 518561657, 508530968, 323072534, 986274307, 604031912, 395147426, 658770480, 512773090, 306945442, 97256366, 373075764, 975155277, 585666971, 796914028, 768731069, 344555435, 738439050, 463617061, 556911270, 987051894, 4498123, 717336722, 973130755, 102121001, 661081443, 848207785, 75981910, 817559078, 490248723, 961223122, 58778908, 535377781, 55046975, 70674516, 217134094, 413286507, 685319853, 219193110, 75698763, 963531920, 40367850, 832303279, 617048679, 831885599, 657734333, 923333579, 306043356, 933296586, 245504287, 468288874, 167395808, 831653421, 412587017, 370878678, 582676505, 64252387, 349796576, 273733727, 937317973, 812715432, 802375537, 221657285, 550257245, 119120780, 403203033, 37177413, 726897481, 639708383, 43140106, 758193577, 911198232, 345081946, 528357085, 9917646, 4148322, 469999989, 407331899, 192629793, 981707038, 505856837, 952483424, 657166367, 188484443, 367415379, 127345133, 950581188, 234077728, 237258323, 685992730, 344097921, 15021090, 30972830, 233161337, 409123244, 332396540, 160447272, 339608227, 564157051, 773016649, 205025574, 602975117, 877976129, 995350127, 989700002, 412922387, 566357207, 76412890, 823481338, 44479968, 691823922, 175909022, 707723249, 566472804, 961730941, 617340763, 893213126, 629730962, 471615950, 554711763, 312925943, 112669562, 705944599, 469943763, 284653987, 946865711, 982651946, 302254213, 705184433, 129135317, 569196065, 599035261, 443668168, 325014765, 438527605, 395773057, 133317463, 261653237, 622276760, 820756639, 781512883, 784745449, 395750058, 502419310, 934566580, 98090477, 209549976, 464639176, 862494731, 864037461, 967183911, 787407386, 227325530, 18108484, 820791662, 470701668, 341237268, 832145174, 89084311, 286209506, 47971365, 593325000, 484008363, 653479368, 411997811, 88243270, 412450491, 880704155, 805712662, 742514230, 799364774, 484164856, 546165162, 286849410, 431460559, 460298623, 642838100, 48456860, 131434284, 415431802, 715882416, 879213596, 319791618, 49828244, 717408163, 660433408, 723198982, 97852925, 203046229, 286547315, 308037825, 948430024, 738592353, 896387586, 647263513, 662473365, 449542258, 389973145, 358360699, 967184600, 416534370, 139871406, 651364087, 970436569, 404955779, 258775609, 520262959, 658091840, 130485845, 875611888, 194322738, 266763933, 421983241, 807806673, 919816682, 48431913, 830858289, 175528597, 43399270, 677750897, 705242415, 24111842, 850372875, 198169171, 510353766, 93112121, 950180671, 341096798, 946859504, 890142829, 600202144, 772695708, 153580239, 877223051, 897892711, 180659443, 749106570, 797365589, 875532280, 349049182, 360407202, 255728045, 193640327, 109180568, 701335160, 452250587, 129824050, 801205545, 635897084, 792260895, 898592435, 834378483, 541956981, 28802334, 273613697, 563384834, 171944030, 999340349, 341275254, 23186906, 655086696, 632368397, 154057649, 539651476, 484068784, 756901915, 712088439, 124034078, 270256750, 91369235, 181496742, 133458346, 689214704, 157194771, 694460389, 274592929, 346642420, 966938937, 265035214, 881594055, 114932159, 623574278, 765264342, 760000863, 45103871, 261864841, 5503927, 933212497, 441269663, 614463211, 971389798, 681418904, 891830892, 877042874, 272959425, 28459414, 751859112, 37760641, 817126776, 923937956, 358752299, 341165093, 523121678, 328700014, 481503398, 116179679, 251870377, 912612795, 868940509, 514133740, 1970405, 233202905, 773552036, 797609922, 10362259, 889833754, 411269402, 800533570, 269471876, 37879503, 95000296, 810818043, 623252189, 395626280, 614017192, 315091510, 14313414, 290254618, 538258271, 445830063, 46873178, 805416118, 474497278, 948380868, 672445291, 253956012, 729314214, 50567519, 348613944, 373014093, 332033389, 916401256, 571230958, 673954119, 725767726, 672777307, 430330882, 915171121, 471220596, 419563962, 927476478, 457041863, 366862623, 995855471, 251225797, 546909658, 923509705, 897751190, 281071699, 652679803, 632382711, 257581422, 710493566, 330333603, 508758543, 581569486, 205858597, 270913684, 532763672, 818230440, 835841573, 105141387, 311711080, 542270487, 683133326, 6980431, 597279440, 450032293, 617792164, 238900116, 287657604, 954977072, 136972758, 149391769, 794036973, 150162109, 358961962, 733466502, 901620466, 749793763, 815096283, 675827877, 176821411, 768002300, 835183207, 502911220, 368542183, 141842349, 903496463, 527643819, 974188048, 663986323, 856543531, 469423782, 781836403, 754315376, 94213979, 371071329, 1316610, 195017395, 543923615, 681820675, 39391348, 749104323, 296207124, 43093796, 617856064, 55406624, 708967471, 50431801, 915157653, 133245421, 897903248, 965194145, 259706706, 926938224, 56575777, 949576759, 138551599, 969669951, 347339879, 261837250, 104497471, 827250103, 43897842, 402526525, 373308424, 581317660, 724504200, 552542932, 231888410, 390233835, 329190053, 689094898, 183956510, 469255215, 140333076, 309475399, 884666513, 119198642, 449054415, 281924074, 926260443, 42631901, 926001388, 475304579, 765037093, 6438145, 594604512, 750477746, 606094692, 907894227, 438918047, 283877131, 65734055, 855526048, 96957690, 696341210, 226083577, 479368626, 514065101, 174724869, 75388768, 566173845, 220530819, 23736856, 410341975, 135384743, 773288517, 814815313, 85265523, 191709138, 808153245, 47921022, 968866992, 439788405, 319589902, 436552430, 524381706, 79404648, 825467694, 823527233, 786508279, 529191807, 10165901, 763600287, 678930025, 80169550, 521965370, 197259318, 789811034, 14439031, 214500670, 269015475, 724594652, 308776097, 7670197, 947954564, 642624071, 981592033, 750501744, 548096245, 266865277, 236360947, 723843999, 202668492, 44584609, 74401476, 538498512, 714186575, 114746649, 451370516, 305856619, 364615529, 710401962, 251706891, 636300770, 181453707, 773023365, 393171603, 721837888, 96252225, 416765062, 841278659, 767335387, 412418791, 148250558, 777807300, 766761237, 163555148, 80763503, 2737106, 211218679, 678886996, 380066157, 18577479, 127192112, 281916693, 680629615, 765352083, 827528148, 358211100, 145914483, 344048550, 434735519, 36908940, 276405446, 27348280, 112776060, 719202052, 637645005, 965353925, 372985286, 41761977, 44503051, 138187935, 233471821, 109741843, 54922450, 916397018, 464299321, 669150103, 234216715, 908073232, 142983075, 711751412, 778333594, 526547850, 848009963, 559201816, 810141080, 831910450, 110814048, 981950159, 140998325, 533723610, 397777580, 579768942, 328490897, 531236197, 137346858, 59424363, 991197162, 329117519, 561537485, 497718683, 150713324, 378928835, 528270402, 297491572, 50089058, 700303299, 742417071, 275864563, 504300042, 720016579, 988481327, 73429388, 704916999, 367543739, 669010648, 893624678, 89971742, 14842503, 470491616, 493891107, 759225570, 732342924, 592194626, 941495125, 915224278, 920895766, 638724576, 347542041, 228744458, 702763508, 265023541, 989822708, 51701485, 63219543, 501682306, 424310352, 492520883, 968922778, 988420579, 867397865, 764034408, 154781071, 738407893, 476260282, 537993627, 658203200, 745181486, 221523705, 271716719, 921447416, 120722234, 803309431, 468791627, 68072104, 298602548, 696502035, 196856715, 514218715, 114247915, 683898622, 872295825, 672472801, 692326496, 897645256, 848486317, 307770191, 817515655, 397321599, 885002469, 663426234, 822801814, 718819945, 519950887, 941230139, 386079113, 680326722, 368299923, 437243459, 685827268, 290810592, 534973769, 154978538, 214643205, 118176599, 347718657, 289617223, 770451300, 202800495, 244581635, 720644936, 278092806, 382692836, 438701926, 670458626, 176087717, 439883283, 782819438, 192844910, 591610103, 960366848, 822898260, 652257797, 47316683, 560849940, 614177497, 374414120, 227290499, 729930616, 21948186, 997368798, 40611421, 691035085, 514576271, 980927708, 142309771, 808831934, 768071310, 866585599, 421600085, 900436442, 108850642, 617216699, 408065566, 157221091, 925801267, 5617338, 756914613, 686785083, 101178017, 859694734, 867917031, 248122301, 903919994, 706831543, 709859247, 484698029, 581690685, 134833367, 673437567, 708016181, 787536478, 238357146, 569681666, 408269635, 891145582, 734573626, 616244254, 190461878, 788889252, 146703039, 524612155, 532370602, 987648864, 9018393, 788705793, 179046914, 588437425, 923679692, 838047897, 667492524, 660128920, 356677759, 103899350, 863318947, 982053234, 115869048, 567524331, 464721935, 42410382, 245467070, 78490721, 258553547, 674581261, 983948466, 405199512, 155762744, 441838906, 501531318, 802870633, 590312127, 821782219, 347569781, 415712290, 31109200, 171257836, 619847499, 768041128, 314763680, 440412564, 363210004, 545806461, 636318999, 829331436, 300683890, 953375912, 905251356, 504294927, 665171987, 237297245, 988878292, 734420188, 919076553, 444473613, 394521693, 831787003, 379453908, 792405247, 215954927, 195241136, 793077251, 827863115, 267085839, 977895077, 81561756, 153224494, 149417436, 624304262, 324763030, 130252350, 594495220, 343560416, 745457038, 496652094, 863818787, 901750367, 883959769, 337497160, 816388909, 384921392, 453820973, 819689792, 242487557, 539116220, 178874226, 531158902, 772924977, 229496616, 674796612, 959998829, 468921387, 697930942, 691817025, 829829401, 374940838, 164221087, 14930773, 567793336, 56627899, 925717709, 418215651, 233118096, 401586593, 924419293, 886918815, 357105668, 830862284, 123911693, 432929676, 766969645, 611495329, 371053444, 777413087, 778934170, 601713304, 186665767, 754816806, 133244777, 991618068, 977987378, 179905931, 971735464, 342742219, 910996424, 684729080, 990680548, 304530643, 244802373, 581090715, 129063176, 581437836, 300332263, 103359525, 50032450, 73773091, 439026009, 623850712, 369308227, 489073193, 496075115, 266787226, 236660115, 341943026, 63750476, 94527946, 708765198, 878542688, 872942845, 917698350, 189275839, 955170901, 660019766, 136261019, 647979263, 750986970, 708608765, 160557648, 865867572, 515140523, 628714076, 809658462, 177952284, 512233758, 53654388, 943837592, 230417699, 484213668, 542943601, 261204298, 37658903, 460632034, 825776215, 402332980, 768967622, 430076510, 920223559, 158697157, 783508328, 314403692, 55745093, 275665620, 871029850, 215138995, 966852847, 183924343, 400818095, 654072476, 509334769, 442219126, 232266083, 982358155, 94851516, 644089331, 690238816, 286090937, 352755601, 569719933, 152596289, 546623690, 39989454, 807341497, 379795879, 869982748, 55141919, 257017260, 677726165, 46499889, 624512236, 261648467, 158798023, 439542246, 201811768, 53644571, 932961689, 747695595, 573025611, 884098106, 339097933, 236403062, 895557057, 486656244, 335154799, 188987622, 485492771, 710766465, 689256142, 498483319, 9405401, 487050960, 534240739, 418549058, 291501987, 688465524, 195689497, 978102680, 955379829, 223529790, 600643775, 255284981, 227707871, 100536182, 283430484, 742444706, 430631631, 555543803, 19290594, 307357829, 37670511, 95625112, 426907832, 952945046, 436498150, 448337959, 298549293, 893907254, 430128135, 161939013, 239052969, 60008360, 145402807, 768430704, 278342968, 814713941, 157686947, 189801711, 48198584, 526666267, 324653930, 694168834, 866023847, 554404573, 370095199, 556418836, 296978423, 757836855, 131225425, 135896693, 787134212, 944955504, 312682768, 486293413, 612478445, 768639885, 991923312, 6763721, 472087332, 192307355, 667160570, 219989471, 105106124, 752539239, 198945025, 218602241, 551771209, 627979213, 710323035, 487896864, 981289489, 257831416, 985384337, 531971355, 398871594, 776220523, 975451754, 214354586, 982239221, 469215437, 385775779, 558938292, 991667434, 213251313, 360886552, 921505982, 825774909, 97846832, 847103005, 904814259, 810437180, 645174226, 647340000, 203901156, 483476132, 28447765, 729646318, 555747654, 513902370, 54643224, 336960731, 440335775, 470444114, 542371106, 396929985, 706033310, 956840255, 106670433, 160879776, 638477817, 975807067, 103097937, 920471228, 96711693, 872909371, 463495369, 558113353, 943365590, 451043598, 186937143, 343807503, 440446218, 302586551, 543588425, 95501816, 120747913, 548134379, 695075688, 50512656, 350523563, 267939209, 760051873, 413890262, 812805673, 997292214, 139548323, 634374832, 778589124, 175885553, 334174773, 566969127, 489790944, 707120367, 353580332, 165546598, 60940531, 787332413, 564063717, 191603166, 232136137, 288564323, 61288503, 817232083, 282598676, 666619870, 395883096, 172577630, 498291878, 852215754, 987679443, 332270687, 691907945, 904043668, 931736285, 461191838, 11856438, 475659896, 29459464, 528751751, 571655694, 358209836, 114037379, 858145865, 699900382, 309728506, 18255697, 579821519, 828531446, 278833876, 862220531, 937539416, 179153328, 429671677, 709732223, 456497267, 322496975, 353877735, 426899911, 134385382, 943603392, 25481269, 395559177, 26534565, 485757983, 715302078, 520617866, 907382902, 907895473, 293570445, 526777860, 899358605, 81029462, 163504416, 444066531, 308108797, 558579252, 762102747, 885391125, 350389127, 598845290, 410066483, 472131014, 11312324, 520972125, 241608288, 368751762, 837229058, 566034683, 672687608, 927265321, 358279026, 855290509, 416144465, 953744838, 136320887, 65539199, 522438873, 46904582, 26512159, 731049075, 823119958, 874738725, 186844469, 313219551, 693805927, 93781613, 997834136, 295565803, 729503941, 555145012, 413518548, 927205134, 293472036, 843114207, 713112942, 482677323, 823515329, 725616759, 886453943, 305401037, 615697406, 251912382, 158494648, 581134588, 412751612, 277467603, 580877623, 699862873, 757647484, 363158101, 563724332, 718898075, 358733260, 335161888, 114775721, 854345489, 352108753, 176890356, 611420256, 664360440, 371373184, 493590328, 57145597, 505674188, 131568831, 851263796, 773294493, 708674433, 713582964, 930782408, 678774637, 823044960, 672349536, 850010460, 857908490, 919851762, 280780344, 819910044, 568861277, 168043380, 649079391, 819789897, 11879246, 300830337, 920652581, 9946580, 764012373, 691572737, 340990525, 510731131, 273766907, 522235910, 592309591, 2436070, 140631884, 713323322, 245820310, 924323146, 776562227, 877248271, 275687173, 919332742, 473529332, 383219686, 378253146, 340949644, 377990952, 800097358, 804145260, 319937370, 200557651, 30547964, 412177859, 813920244, 403776855, 559867214, 771199312, 225025143, 734504121, 945839396, 142717964, 175239797, 442883168, 865762039, 208599029, 934089945, 522753532, 820109153, 116871111, 83057939, 180814758, 532674936, 195664337, 775993087, 820085825, 448153887, 92384935, 656214871, 542809135, 746435163, 89830203, 817186679, 521354898, 673579949, 496421398, 914176675, 437909713, 205043425, 613075111, 935524248, 553537722, 687189888, 10544160, 818757740, 379971109, 607699552, 40098352, 257947748, 190602171, 254155466, 474871620, 396321529, 148412573, 250276117, 52218149, 282268310, 990358540, 16384727, 689596762, 386143644, 696144937, 571122970, 783617458, 622058750, 147556841, 512917839, 2727838, 639052376, 313161076, 281125401, 546407492, 385318844, 928085303, 742240304, 778073498, 111750515, 361297653, 39264401, 492909143, 502611504, 725080272, 474322581, 213127273, 800463587, 590339400, 442677176, 965404035, 726489392, 988556417, 868366355, 805105135, 303036950, 506742584, 968797527, 723953985, 900756376, 173824776, 16369228, 652222317, 958065775, 358678636, 547280179, 134372702, 956824841, 923853173, 232624728, 746908661, 632270176, 419280228, 835859911, 773614049, 756664050, 259454338, 228874743, 829356312, 269939055, 320071837, 850419981, 846854432, 594132263, 328166360, 458984248, 591369004, 739880660, 694125248, 712058207, 601349797, 650211045, 925295170, 641580391, 747955687, 89277206, 626657422, 6273475, 679266943, 338401425, 589706352, 100864936, 617217062, 133562633, 104461850, 904769506, 268259967, 706078114, 999550301, 898479960, 121855865, 190661509, 216193345, 695657203, 376202817, 961784652, 134084208, 260861736, 616879103, 297298079, 243438330, 453384057, 574811871, 326170271, 460532484, 119374174, 958495039, 744942219, 110973470, 88997276, 710644253, 814122644, 939356502, 462326029, 627421211, 627880219, 506022879, 252132655, 165335937, 442017318, 289526753, 611581310, 458405474, 142304915, 532451635, 177391573, 282902620, 431214435, 937244783, 862366339, 915470635, 424306023, 427998406, 67985558, 664866723, 123075556, 930074299, 198209225, 119044392, 919442504, 236530245, 259877986, 948304034, 354853659, 174372424, 895838292, 945395764, 681549659, 693197762, 715655589, 830322132, 50813373, 158047447, 368494283, 133524077, 554548782, 448967439, 493975751, 834192082, 142685204, 618704812, 861104128, 182325392, 690893553, 396995320, 355854880, 442112411, 88710756, 43403325, 637267543, 474751373, 359539708, 787092416, 533567970, 111794677, 241405962, 931893714, 311468889, 758334819, 587432386, 537538431, 719736303, 433454689, 561731908, 307762351, 340986803, 703198063, 681882760, 481966703, 284826128, 447925378, 611802114, 209293372, 743438365, 59346458, 306093235, 200057788, 224288854, 639188237, 974306566, 907285469, 816145496, 17762047, 292361165, 37511554, 435636703, 443325234, 692038689, 167298360, 805339378, 412236502, 497147699, 793642473, 176368783, 805246037, 235642314, 485143328, 688014882, 23875816, 817268097, 421669154, 701117240, 260122063, 164496585, 523895625, 708020883, 43463174, 590015176, 871929551, 654889870, 934093689, 393473487, 30803283, 590033057, 814882076, 617793879, 994548036, 926009124, 952764853, 498526402, 114395127, 147921078, 610105935, 865089298, 946077822, 449534496, 280766205, 124750285, 561472617, 435394012, 894447952, 963756987, 529830364, 656001838, 407590700, 253448243, 591898529, 664402825, 23116396, 439655233, 764303688, 913427406, 143449811, 71959065, 893975915, 491242151, 689796386, 555528615, 513299703, 139632149, 814773939, 903184400, 161468880, 980866662, 933107386, 978020882, 295187193, 193228819, 99216158, 131046233, 261429787, 530654354, 808644581, 684008831, 417339761, 120237442, 255751147, 598166894, 161687853, 662652330, 191012701, 796571683, 889185574, 931310373, 35059729, 770295611, 419841463, 213944018, 10439799, 464367303, 387277303, 971351313, 970911657, 839161230, 886335771, 500969274, 477940556, 499591482, 309348561, 820474079, 353855382, 968602701, 665254821, 900088060, 222477537, 539833058, 245905918, 28992313, 369166808, 675897669, 234730947, 206143779, 48099064, 775863376, 332547022, 689548089, 863248238, 742231482, 929781642, 265038512, 603372394, 677726568, 931449671, 39384051, 985762445, 15364417, 828547409, 892444252, 556711503, 662120617, 163873497, 787381465, 7504420, 451112456, 275629377, 150420065, 437639242, 122079914, 923495090, 622158744, 846114815, 73452876, 482975907, 546006422, 459829127, 53275721, 176169593, 166507288, 614794237, 533942405, 600214842, 181894535, 651520923, 387439728, 514337693, 343438347, 45963069, 844612185, 645036137, 418077217, 296318475, 900252518, 211525729, 134283108, 320418458, 267337764, 818544463, 3340377, 502810084, 277963207, 905065833, 43101073, 17622129, 241393633, 669158495, 645903405, 675757308, 80182622, 294363373, 980352816, 185276981, 766452668, 641856489, 623988676, 724973826, 351074332, 375012392, 452458287, 49557148, 700005350, 300924094, 748402418, 509967954, 198109850, 978782478, 102904011, 603693610, 905653517, 473885416, 29590404, 351873627, 849467141, 677373803, 935073429, 554503771, 596697723, 860223195, 197447638, 276510287, 244071654, 368328479, 956186332, 579750871, 345451278, 788699535, 833456186, 321190365, 527143897, 90493969, 472148305, 363552487, 115455100, 447673948, 571008816, 362667158, 372328084, 337167313, 691903798, 521550585, 852306792, 767240072, 321479310, 10012442, 234028273, 575914132, 578257885, 671457680, 407535544, 649522332, 376163258, 522724027, 643655176, 497723795, 708808809, 729566418, 854556393, 515983831, 570792350, 135840848, 367564120, 686046681, 550958956, 796667930, 601970576, 669050808, 398157007, 802359437, 875968612, 515845169, 192777702, 670755199, 457245813, 50557768, 931285441, 704058958, 999099923, 383793064, 529629010, 114664641, 83285356, 765463717, 410623315, 311450781, 491293941, 360393775, 237894288, 132819500, 312851880, 902658374, 968718397, 269482839, 745622136, 672921436, 643362118, 970109215, 633541396, 78158470, 296263404, 946374253, 953004789, 659339083, 531979702, 842547778, 902516466, 64994960, 492935540, 243281787, 494579980, 255002513, 581913285, 57491333, 197598346, 937549612, 709561000, 488023603, 386629844, 43579523, 994953627, 676471218, 459019977, 174326941, 207940658, 391808228, 215319623, 312497148, 324650571, 352001782, 715633302, 687050867, 968201518, 568541994, 392978258, 186687471, 822908529, 951859439, 266297459, 689472919, 620047676, 77882662, 138348727, 749340941, 167554698, 764920222, 603649376, 725844433, 398599353, 394289782, 116835159, 709828562, 45406119, 593020516, 933108727, 49221278, 109922937, 308986664, 45477833, 578119755, 747002232, 300456770, 176379225, 102258976, 996556059, 786526445, 303431462, 88698092, 29351381, 268785644, 449316434, 191286144, 802443302, 311323972, 658702861, 463754978, 695652547, 451537792, 421477460, 304831653, 957970109, 568596396, 334534781, 229589341, 371749092, 823676175, 702149404, 912826234, 223209013, 658123768, 626521019, 557403963, 463006296, 45700663, 402549091, 585844960, 622250607, 734687145, 844639586, 673496489, 682263198, 501385125, 235547493, 557091133, 82727985, 54432695, 559233563, 186639887, 996223803, 519274681, 372284166, 924968861, 567659428, 682094655, 438264093, 580862548, 639800250, 932389890, 212468472, 870295074, 874860276, 930731645, 307358816, 112533648, 797644456, 117584390, 663665946, 908121006, 789042031, 655320168, 779275366, 910026146, 988681892, 377391414, 880827085, 416099498, 393336156, 70117862, 132136637, 326273488, 891674782, 667800596, 974025406, 532212856, 188949372, 536514973, 621968256, 333354966, 320555724, 323989498, 971019060, 377165338, 601203721, 719047665, 289460078, 285844820, 900118967, 916745931, 453926918, 82617471, 72022506, 260935899, 16443016, 793197341, 363181668, 62198219, 993444430, 949627984, 810130019, 371102977, 950191648, 738679130, 133113030, 189947990, 563065136, 507281339, 446783185, 407941167, 665195614, 984184169, 649316869, 29691431, 970980021, 199739843, 160056059, 579722585, 789521664, 725144726, 965652644, 44098505, 404429578, 241887645, 455398547, 280964501, 435364685, 667532991, 92869575, 394277976, 982869675, 471133133, 821406811, 156937062, 946424338, 309558338, 855951955, 196371991, 342484868, 796895832, 985808683, 452205886, 573124406, 544767284, 570208140, 612552564, 961652113, 640164714, 340585878, 569825817, 829757186, 656638278, 996376859, 892648481, 192451552, 596470334, 457667476, 389165382, 784569978, 695764368, 563747066, 806280297, 107587730, 426198460, 391260686, 594721308, 118310010, 632434225, 998372265, 596989249, 520252399, 909625312, 488818444, 493713800, 932390173, 939841550, 960401554, 894565724, 451101182, 594982728, 156822453, 456430316, 554947124, 374141958, 849016411, 587542111, 507251098, 908645421, 915668743, 679651287, 114648474, 88510339, 110235259, 218288760, 473743588, 14544168, 854915858, 358988777, 976936999, 959411193, 924871600, 520381374, 300531814, 340265495, 188264440, 414713627, 322401167, 794621, 659462743, 331375786, 496179310, 15151206, 926782605, 691673765, 905063987, 140383706, 584768144, 51392656, 873937549, 429747552, 117959748, 294752181, 378621827, 116639293, 221453298, 259697474, 906573135, 106866921, 756375215, 55742426, 174211672, 672800182, 629139123, 370228745, 466816099, 680525478, 856135246, 576349930, 14531741, 157722685, 691326905, 614758305, 250479467, 486615437, 222594807, 9412181, 715458046, 98430658, 639246221, 355962266, 625944320, 404771964, 860585745, 923483401, 810396488, 383014094, 212480408, 158399446, 109377355, 614732404, 384685829, 999291616, 422575329, 850571430, 430099182, 490209610, 295101680, 414801901, 145611499, 144407228, 204776580, 957614532, 466080984, 416126399, 31264660, 841173612, 124150187, 354423893, 744191129, 466235540, 217077380, 638155761, 165324502, 726817028, 839122224, 933130400, 680461679, 482978855, 627829115, 98807905, 567554870, 395477772, 144483135, 852169179, 972642989, 138267992, 580376807, 632692337, 520766756, 322380248, 161068534, 676011512, 581026784, 281832760, 90769876, 708212224, 537006662, 683293206, 591411258, 743466813, 28063238, 284337363, 726465809, 90647679, 93404190, 950545737, 759017538, 531290635, 384724025, 598928941, 200167822, 133519209, 276098544, 552101433, 607424898, 401730879, 568034274, 664467861, 974080272, 776716362, 518666882, 790756833, 77423367, 540343226, 555656380, 822435563, 207830663, 962754220, 348940094, 603422466, 592571585, 744102196, 40991762, 859282274, 673651028, 538666300, 697108991, 509653414, 61438264, 78696341, 591197360, 228970148, 629403922, 520772433, 371818219, 309990824, 378797516, 251581470, 391391721, 294486813, 277285456, 86348520, 380229041, 283133695, 256944714, 774618487, 405259664, 485845935, 775203277, 20701052, 772054454, 210132048, 612088739, 118639908, 566394409, 635062535, 610832348, 93625448, 196881782, 39998974, 769821360, 147996432, 487689654, 869589624, 278776823, 996153821, 635585673, 324923317, 899554738, 159689954, 699511557, 586373010, 291478383, 526017070, 361938044, 50258098, 942903972, 343548080, 515201066, 560887019, 661974362, 661512994, 965575126, 931184620, 729132311, 748383473, 187075558, 896212530, 429593579, 408892032, 708885594, 949025307, 873299199, 987106633, 304964539, 697071821, 502006800, 640708587, 15047978, 323578529, 341596608, 395541597, 402058968, 557494453, 195379644, 230552149, 876799671, 674532763, 852453543, 408804577, 234426991, 70272547, 514606777, 118528905, 876058002, 533158020, 648163549, 948204704, 20207946, 920483507, 757607355, 452579736, 519841838, 110439878, 659781620, 696254672, 709218762, 78552974, 842476428, 66625939, 868521130, 890996398, 141463339, 742668951, 531834533, 465213726, 83297802, 534033003, 632684922, 710060002, 239442156, 295806362, 700367184, 944269261, 368549210, 130690893, 669822264, 974703662, 134887321, 583261285, 825398006, 457097879, 199644800, 170966953, 364158770, 611689294, 623815700, 542962789, 211448875, 73239338, 516425600, 336308991, 309300973, 179113936, 130936069, 793287503, 494900759, 436505150, 571184072, 234690918, 483487732, 530049882, 467228345, 298937349, 204475338, 732538048, 957904466, 658527854, 450609868, 189090077, 588476217, 172141159, 717317677, 474191560, 470114717, 956179104, 955420784, 796895742, 862620412, 115836183, 883612696, 565616701, 5996336, 470051697, 552701840, 711000701, 29821996, 313400341, 829727097, 826220729, 298848938, 624822809, 222141354, 254467669, 332743175, 695208013, 847899511, 977625406, 250897505, 205020574, 791901262, 956323844, 373628124, 63669340, 696026324, 31642699, 841754616, 881005740, 637821593, 423411663, 840392185, 326248799, 949517516, 898394816, 333522642, 984489376, 235397186, 637885098, 401617197, 1797154, 818107759, 209849570, 458840713, 774001987, 854745894, 735376263, 434165671, 316003502, 74804656, 353815344, 346962833, 252936233, 827522137, 586262653, 102914040, 412032963, 498081646, 12505073, 545080906, 853396372, 274539682, 92660507, 834433112, 562178155, 297017299, 625758837, 3150431, 545919916, 694095041, 86019459, 617643103, 534045221, 287305507, 65115113, 31658574, 450355052, 642120233, 284585432, 65681893, 999559058, 132822509, 58809857, 793002613, 983460186, 603006046, 702076832, 927324798, 927059367, 586953796, 124384607, 295636025, 593558182, 623649461, 26418370, 500953461, 507437309, 936435026, 637191837, 346420103, 805347468, 284662934, 80846853, 368278706, 191530089, 484735977, 491341510, 753441494, 666061716, 557472917, 470146159, 194534730, 324079187, 429799215, 783556963, 974880864, 137913623, 74285820, 992825088, 396088850, 899572253, 192090554, 49459453, 930021566, 992532755, 143491523, 980225433, 193453267, 479183017, 89878834, 828798175, 543822310, 14640307, 553519211, 341242485, 746420024, 365020767, 348895789, 175096745, 833697712, 617773282, 681367974, 779339989, 122773990, 340377004, 706824935, 501051812, 826672971, 648436708, 373680704, 371303589, 566143497, 555722481, 984040125, 80586527, 456227009, 74332137, 847897584, 854735715, 10812549, 730097732, 102508835, 666585983, 424005176, 517625409, 730181480, 622361541, 295178755, 300487687, 522223518, 481365496, 753759904, 803807027, 217633660, 705669248, 993490863, 437999584, 848389423, 839295386, 242236813, 585113962, 515920298, 909273217, 330737438, 687336469, 518248451, 847283828, 898464759, 709171505, 189102773, 552007502, 614120278, 452849399, 554189772, 296593982, 254116977, 85047247, 256130327, 316537182, 361585859, 149742691, 723734096, 608220640, 376176493, 415829886, 862552409, 621400262, 391397386, 942591596, 503787283, 859880209, 498137152, 823535175, 112126343, 674748527, 469626257, 263532230, 735944953, 207947627, 623609057, 440458472, 288265716, 505698817, 93170153, 282658893, 698376238, 527445675, 961589370, 546625094, 209208316, 820572512, 542673896, 810457200, 405989146, 712289675, 854730071, 446214276, 716257618, 183940055, 650837088, 856280409, 802810779, 48692094, 465929335, 425155525, 340824886, 898283804, 347177830, 329122183, 690780900, 45232402, 832515021, 619960333, 599608543, 519084213, 381174976, 909766750, 59939985, 238537278, 941738070, 731932511, 262997668, 30517088, 888923662, 744880138, 241133959, 671615712, 243253755, 833235422, 81914818, 916041091, 945583971, 861061227, 562911782, 537429837, 37401759, 121671974, 228622343, 508341865, 310956768, 790096676, 907661151, 963786827, 985056073, 755336439, 16837437, 369101265, 823459205, 528730739, 779298396, 743935258, 303056893, 894812785, 785460053, 666838305, 154921874, 918582995, 692238643, 94415266, 872562023, 376386504, 998123227, 165279838, 923024841, 731142205, 693428044, 378467872, 774707826, 33581147, 200975901, 879638990, 21549895, 202309048, 92113926, 376313719, 947461335, 799193596, 828350906, 356889207, 702745639, 943309751, 252999218, 806196514, 271143101, 317909191, 543769570, 12422262, 339340707, 135072750, 186402641, 18742356, 668497481, 121448196, 86639227, 582228056, 402355849, 447198304, 242593653, 190650398, 851704194, 923851898, 704508180, 215949573, 395552057, 81986263, 344171735, 86008787, 974186785, 730665711, 299304259, 887075793, 53616667, 944887660, 474870053, 995161295, 923552748, 948530629, 464514360, 378914135, 646755438, 655916329, 562128526, 612359608, 592473129, 331375817, 484129834, 838823389, 679525546, 1680339, 810120984, 535741789, 644511722, 158797145, 800422313, 192983231, 539547790, 280731108, 879941261, 402230440, 234424725, 319184960, 348842475, 374478527, 918703354, 200031297, 275559602, 225673458, 651340360, 45352691, 524652781, 498051474, 364008001, 630929322, 499454706, 547424155, 546410223, 513620152, 28913335, 325011903, 104783047, 599266109, 879140158, 119966931, 897635139, 407817165, 611779819, 671199212, 192731169, 70972000, 206397303, 682274274, 715918335, 140706073, 231105639, 66535150, 650910320, 76898398, 620649587, 570050713, 250124442, 441319572, 643931851, 441059993, 58837813, 961158498, 293375663, 797027734, 180176032, 710775077, 645327044, 609442561, 301207852, 810123385, 780170456, 978602982, 530421262, 374669541, 751733445, 681294831, 768916811, 33760074, 526811765, 732722219, 854592577, 12969035, 821429353, 997971753, 257866407, 277923858, 132277112, 820106493, 540172505, 967806304, 857536889, 876126026, 41022616, 719412419, 69877354, 251726584, 771817579, 139553939, 994087682, 957488222, 705268602, 944582769, 305233971, 799003067, 709553715, 153818983, 410877299, 236881465, 246076890, 777800521, 466365458, 981042592, 52690830, 594101862, 640740876, 35294199, 798045783, 985652264, 545516133, 249023676, 870276081, 915919345, 23406071, 582307534, 626156200, 792275036, 324736790, 692894681, 941239202, 837641093, 466452365, 475350156, 37426637, 109072518, 460487131, 903977607, 17867211, 123580168, 762356883, 878172064, 371166709, 695250967, 231307395, 748198453, 875220937, 684126931, 620322965, 144162978, 985878811, 701406981, 791019267, 760453191, 693782122, 329267461, 41231634, 47623581, 47122754, 810285920, 599114889, 589463530, 397226107, 548078346, 199514849, 199283630, 9472699, 745020181, 58697272, 31182929, 23027952, 280724347, 319836817, 361255333, 797031361, 381837951, 93114137, 682537948, 362756311, 4879833, 749452711, 425718709, 233105326, 611326178, 969830595, 4660949, 764445563, 885605392, 647311785, 517339125, 751840540, 231599611, 877504198, 388587074, 755499141, 279263669, 385369335, 925119892, 582201141, 678451090, 463183168, 367844801, 227409104, 423258773, 560232450, 998070013, 496308801, 236806869, 289477466, 609411491, 819732073, 877282759, 70105510, 487782181, 669899483, 950796213, 352323608, 89223525, 617843240, 318445641, 553869488, 482696537, 39982837, 241150104, 264030100, 161531680, 492941238, 599982056, 247981272, 793404966, 209394769, 914343527, 395517595, 183647548, 534743273, 593337338, 259139964, 707687143, 668115973, 463258034, 260420524, 465544067, 428304035, 486230616, 991579791, 898801494, 10702557, 783122596, 792650998, 44360016, 551100599, 567654992, 316301905, 6134907, 136729991, 770125321, 686339299, 287395842, 756741566, 90721801, 5117595, 354215864, 726607146, 810472222, 41750077, 773530170, 404304482, 272365872, 4923774, 721273073, 156051324, 388046185, 420217505, 793013705, 636767281, 914633112, 587911444, 93182208, 798981847, 460329253, 909480207, 108068070, 62902042, 132988275, 622163434, 861420899, 959068891, 745025560, 244102413, 215102173, 228768888, 477383522, 768642922, 729915718, 699960303, 606911447, 752493242, 770888051, 551343868, 453236240, 737108569, 893645619, 977748716, 196689903, 706570615, 277183150, 962093219, 108834621, 129471641, 444044930, 466839412, 321584316, 791905433, 882859111, 637683253, 132182589, 14149102, 859252364, 472008163, 556856268, 618264419, 335618584, 606266640, 765105681, 908921474, 332159071, 825537298, 642433057, 945417683, 426652350, 140575952, 367897217, 150562075, 597496483, 718163422, 956527269, 392937464, 478550718, 858441865, 974327847, 322097774, 899957790, 529879741, 627598637, 341068180, 359421362, 602647096, 684179382, 963519070, 559113369, 835259845, 537922869, 46130712, 612058178, 22960183, 629155291, 894765021, 436790667, 910264354, 294799425, 663351324, 26742403, 277771649, 254964269, 812339889, 237441327, 641308184, 726579069, 750436844, 568703833, 180219498, 749594292, 614745172, 340008055, 600674080, 379755990, 993289962, 806083503, 664191458, 561404823, 15721927, 883211891, 765118514, 422721401, 926139941, 841820324, 357052818, 297629143, 978322040, 736768335, 799168950, 503317696, 764521480, 943673443, 184783585, 612271351, 975113729, 706530211, 781333630, 759855742, 319458865, 389227875, 906121655, 109164213, 291711462, 13328003, 629031183, 19990913, 75714140, 438359915, 626187380, 236999684, 965437326, 48739387, 864924859, 991792312, 496770410, 967277543, 445823897, 74131655, 23848206, 537038161, 53027077, 487910135, 90479784, 53992245, 466636967, 415027454, 390572350, 172523069, 116296548, 752531058, 654711765, 946393462, 221869667, 383443864, 987010343, 691236, 507048549, 41218946, 846165698, 357877235, 266143929, 806138064, 891728487, 421798667, 233214804, 697129983, 857296700, 596916171, 392124855, 27026002, 672699276, 512711749, 722170854, 62555094, 209122302, 224553471, 296231079, 397387446, 229294623, 90154847, 5111137, 979076865, 226187551, 799524309, 125951753, 224086565, 142521302, 749390889, 156769381, 760073082, 832550237, 656593161, 447007298, 968945905, 736474415, 222511143, 167349531, 647289894, 740479789, 919216718, 173949183, 184081228, 820093972, 833493196, 237897377, 229122116, 484065571, 168230968, 413163970, 38254976, 129550653, 502587323, 842510868, 502095648, 99706349, 629537402, 33310874, 529068963, 822530822, 14773104, 629178168, 105603836, 53051591, 248670782, 814980293, 139328062, 462332703, 925870208, 494097026, 708305767, 671681490, 752259971, 47281980, 761684372, 105186473, 466971218, 370685942, 75066927, 210241307, 714998825, 756737950, 743798842, 355007982, 319486030, 958657129, 642533894, 767424949, 8351106, 881388994, 704748752, 109833027, 810684323, 747468585, 577949943, 262546202, 642082048, 725424889, 935832671, 862005312, 84964707, 716512053, 554365412, 786445221, 187828852, 439071487, 796446678, 410958933, 701340248, 498652498, 800799176, 731997553, 843226106, 301813316, 13512656, 954557698, 1491724, 795223613, 746122228, 50011813, 864538590, 742828738, 319972398, 95433504, 651111105, 181800406, 597057285, 760838950, 935643167, 256888899, 745176523, 838316097, 67289508, 832156030, 499859595, 858031621, 783416371, 776378879, 369000549, 105718292, 115732978, 27227585, 18575219, 82346475, 926473140, 404962221, 450133476, 622168955, 422179426, 897655183, 285563518, 586126831, 887242953, 720490886, 146995771, 499326792, 613242238, 954385401, 821419736, 746726029, 13284752, 316591077, 825722072, 635881702, 807125714, 92129434, 32310356, 44068717, 749011786, 616881626, 698757873, 50367271, 870110559, 176735352, 202877292, 848059245, 180086016, 262223326, 740250844, 655342919, 372098546, 90878112, 49825974, 240033719, 520781891, 49457849, 551782087, 665029829, 394959715, 304940671, 290905139, 921391045, 412132942, 784120595, 94735754, 433289424, 225297664, 20151042, 217722973, 672290796, 999812176, 539829963, 97475730, 176683477, 722374443, 271059819, 223774346, 339167210, 370128551, 635335202, 247283685, 194285824, 232710378, 816261292, 795742783, 906894309, 490512335, 853734024, 621502806, 308964004, 190946894, 798606957, 819158731, 644954413, 991168141, 918539877, 826624053, 444629927, 885945987, 818934714, 778382309, 25994973, 950504907, 604099227, 235705107, 966535820, 464096495, 910327903, 93548465, 760582920, 83412384, 233869668, 455506730, 51245688, 33307649, 506099868, 963159321, 768933466, 603226211, 890926976, 899253345, 653989491, 715371521, 850101967, 970907463, 959529094, 455459735, 827218831, 561094764, 577101765, 198679309, 780384843, 678555127, 401096113, 476483820, 870269765, 833065150, 604251056, 751344885, 950537541, 366881593, 195134499, 645201344, 626424202, 114604121, 350500132, 189617449, 252161217, 339194615, 463567635, 216748963, 820307448, 837081972, 775631604, 230203576, 170465630, 792619677, 623653876, 65015567, 985306917, 203904351, 407382082, 887419218, 451001184, 133336443, 715192505, 456518380, 916867416, 129614346, 835231115, 273675611, 863474794, 629364259, 827485799, 198226655, 564046517, 91462018, 87214183, 695777628, 38464440, 395582728, 181264397, 444964267, 211992279, 815437502, 207478010, 383342408, 959984111, 692382286, 669865170, 279767833, 651883819, 793174049, 455371014, 983682811, 500412246, 645935527, 545341071, 861090030, 54526420, 954511960, 924085948, 134934373, 354601089, 411228237, 535654783, 245577872, 773060511, 674095607, 261547873, 842658978, 718730747, 719462238, 590337673, 609742986, 917435120, 834050062, 439281701, 614378768, 166427411, 992241918, 587316907, 487255159, 383706018, 354875559, 97632375, 549364464, 858915785, 391292088, 189204543, 225983608, 419770077, 29166270, 506297632, 58628814, 891435972, 979294910, 981926883, 465888196, 514120105, 35116154, 850620160, 224793759, 752177445, 136630206, 841891717, 597618937, 713308579, 641622706, 937639687, 636799841, 274469257, 512468500, 839056900, 164407187, 958238674, 964097505, 306979178, 649297599, 233184647, 403615965, 511339241, 376184289, 573956660, 498314745, 440255748, 262149411, 140549444, 622776471, 157066713, 951563668, 926310286, 987375942, 858967836, 863982444, 225581476, 524303105, 732754679, 834374363, 554731209, 734671075, 986992300, 913505376, 331307596, 835509725, 969574111, 244342393, 905482238, 719807628, 900249975, 636037012, 332858577, 252109365, 201531060, 650627946, 172977670, 273877004, 764740427, 490817800, 12687250, 774965289, 862023316, 378473558, 775924078, 447207402, 625980553, 359906764, 284631024, 266234103, 777358435, 240695898, 61024759, 536623892, 689715626, 840253840, 286454110, 972350342, 257305500, 412319966, 69204211, 534181184, 360971166, 196449316, 186079054, 422946388, 231748282, 105195801, 683850979, 769847243, 21025003, 583693993, 137874717, 366913049, 569564383, 72689865, 943122528, 750185246, 701835028, 633317990, 364592414, 587208468, 582683869, 381647003, 106396640, 855754026, 626872186, 634038021, 794656060, 167891124, 21975326, 846842342, 283478846, 125929444, 456201218, 45941024, 226592358, 999118111, 587495772, 407543451, 661304104, 883120039, 813292359, 979931720, 528379543, 119335403, 308342214, 721734055, 58099258, 865826916, 804920137, 282044913, 880977404, 515036407, 281219964, 36932158, 379320826, 14338406, 524450151, 743665187, 137106312, 620288203, 199405833, 724666286, 727452953, 127947768, 444313295, 97490331, 86239900, 548730983, 144254967, 743470112, 836372238, 876501692, 628102171, 94595662, 698040835, 604010809, 774169025, 564203424, 144750569, 539036285, 219203627, 445334930, 65776411, 62112819, 498732381, 803387110, 908969097, 108056859, 32404743, 329600614, 406773672, 324055804, 34142934, 350480587, 902388369, 902772513, 274218634, 486704920, 149969373, 454954486, 866547997, 947521335, 29441626, 326109883, 842121971, 248003552, 460712237, 276531038, 355337282, 169945343, 24960954, 461949911, 949392770, 661875423, 331073779, 383794504, 725062357, 52172009, 545709631, 105964406, 997594279, 187408260, 557217307, 656221591, 20487713, 72982534, 620452158, 812237244, 977592607, 787028901, 746146100, 837653793, 704416536, 896537423, 379335167, 26287434, 457823646, 551659532, 227610282, 806591958, 277771400, 972579859, 529288448, 114962676, 725116987, 655326800, 202839523, 728811543, 2860318, 506400793, 587972728, 712509644, 613191614, 116960264, 422840769, 717929522, 475979803, 632206917, 818103980, 162535509, 848560940, 118600435, 819903354, 273287721, 356308103, 47838675, 861344826, 924039612, 205803724, 7927292, 365967613, 378263096, 111701571, 911157729, 97016384, 855317619, 755498855, 98899383, 201049777, 367088921, 947584364, 825482301, 437918682, 68173812, 246085252, 958478612, 701480971, 349122143, 629568241, 830630151, 903629637, 156531366, 588204481, 517339490, 453431188, 372480248, 330326030, 481496685, 670196162, 318473126, 485049648, 984631308, 360695743, 160313973, 721000573, 140088218, 771194397, 291435103, 255071816, 161051858, 765914298, 508593816, 559653924, 312905510, 206273855, 957598354, 161892069, 771626763, 959817853, 844060340, 958043027, 782511172, 771464332, 497894464, 295456063, 195234336, 781386672, 372267149, 60258815, 450474443, 82724670, 298963323, 325705026, 828168741, 197485707, 318369070, 41449838, 774173422, 12362556, 477340165, 36888803, 794884023, 522317833, 337049447, 48704825, 861421809, 611438907, 274882047, 875911659, 272794679, 187142678, 104914404, 528184040, 38597203, 859459307, 966509647, 897681274, 92037911, 199117322, 853639296, 754615320, 566921719, 397475397, 11936331, 737971110, 862311889, 294535809, 678741953, 512493433, 494153841, 96660717, 313897410, 878400004, 317286762, 574975438, 267460257, 883178404, 112989360, 471626822, 704317048, 323027497, 247897895, 724985896, 726939481, 408986655, 594614023, 408780433, 160790090, 581551269, 956040585, 789578088, 889179493, 796544857, 179310486, 41422879, 100861180, 849699185, 129521498, 504044124, 806322668, 531601025, 15859472, 192551340, 251947064, 719810340, 552190158, 675160641, 100516254, 883207423, 181776001, 415761664, 517459588, 705389957, 132559368, 587607842, 901609915, 455373469, 530740800, 648487842, 320755613, 743850820, 863837947, 311619412, 251706554, 46893600, 477092994, 209899576, 976292360, 105662493, 830295555, 947266597, 532444951, 91564772, 82318429, 391533751, 605904604, 855716801, 432683919, 485944946, 998900179, 750952035, 799833549, 109639299, 92992390, 557318777, 99321872, 676824847, 937205346, 677966998, 596715509, 976981907, 701819023, 407795460, 833200401, 87328619, 257747685, 865528649, 545799933, 239790776, 819901218, 585637672, 99799825, 490192492, 290524294, 534673869, 347112378, 921041510, 117511446, 957245083, 132632385, 720221790, 645654763, 72216378, 300081691, 419893376, 186591238, 135617419, 172605276, 97535638, 575310118, 142770850, 365413400, 754552705, 848389575, 568998872, 41944301, 279770377, 578549640, 298828138, 655308447, 759981540, 387199488, 156323823, 862094981, 874772972, 495962399, 710385462, 505207779, 677996362, 872611786, 435970635, 803779386, 110042614, 490898308, 10713256, 23265029, 109351821, 156260443, 467403096, 54321050, 732578499, 545385253, 910246355, 839704529, 39204084, 291736043, 889664813, 122861058, 425170348, 660518076, 459915377, 745291870, 980424673, 495780133, 234400248, 670097063, 435552581, 447522349, 571885448, 273440813, 582521520, 745416772, 191313859, 939312388, 561152226, 997745784, 564863557, 801619808, 815298837, 375466074, 747901072, 312260233, 517433821, 795233811, 997341423, 83331700, 3261570, 312098197, 181396669, 966401336, 416580089, 420021685, 268010416, 653750512, 368818502, 222360009, 229088480, 364583869, 252981029, 142095395, 638853062, 840464164, 668999084, 427485993, 471501916, 164310334, 486088440, 554314068, 591266053, 671317598, 261064612, 545135399, 564269614, 722989184, 3723735, 341041315, 120450193, 216280495, 256628949, 256761398, 203260417, 762480541, 495859780, 900249177, 669312879, 435175699, 627521520, 500681589, 892266019, 209199303, 339700384, 542902793, 151736126, 616692353, 959085982, 300788015, 964653192, 739170658, 115832171, 558470990, 318226594, 401967606, 628386829, 609452106, 586071821, 604904783, 387333944, 65945728, 297154910, 558921081, 55753251, 6750111, 357418067, 644704557, 834307663, 161940737, 14308661, 154778247, 316826584, 156821476, 303665753, 298012533, 223616460, 4175143, 292090987, 540550567, 988134497, 804504738, 392711434, 378191539, 395478243, 243624775, 154154598, 865914339, 186237623, 700629021, 486385772, 824291604, 199407554, 604864053, 308164987, 862065495, 291086269, 917340641, 470807977, 346188670, 826746279, 738893249, 933004865, 921997801, 561430121, 625899687, 105645062, 335411985, 685108564, 739716248, 124294734, 723522279, 404022427, 298101854, 319747426, 249674621, 906240915, 88366932, 698290456, 949901664, 227980643, 746901323, 292839432, 585082212, 338962081, 151303724, 938069804, 574990130, 701845448, 923935246, 328619149, 530907290, 682793860, 718435270, 108190781, 378352907, 217720458, 705152442, 499576408, 447134214, 706847987, 288859729, 40335358, 356892277, 196735349, 904445843, 333174259, 60344455, 452389858, 248833236, 463958893, 839258026, 547637350, 769980844, 790583361, 530531651, 38136722, 717333580, 546612954, 815812072, 419620491, 880693086, 770887188, 211502629, 846228516, 966587858, 366008025, 664647717, 265165933, 204286860, 187313839, 185356177, 869165399, 717994400, 968941549, 408329925, 273978822, 615788617, 446033230, 728718527, 678671369, 341537224, 146863854, 846210668, 749951101, 41127605, 84313806, 445714363, 157082192, 742091168, 860536527, 597239367, 482310304, 372586806, 342400225, 39668092, 759830539, 618190040, 221240450, 839843308, 978003052, 809441294, 210429339, 640536189, 272539245, 482016733, 506282788, 626920168, 171914401, 50322909, 732862233, 112688052, 698145509, 592189503, 346465957, 387553821, 343087594, 947289238, 176140639, 187021875, 188692132, 736979547, 740466857, 144482677, 893674954, 707561560, 858360068, 899189280, 568949459, 33116481, 33471377, 470372568, 235512677, 903983291, 489521189, 618065080, 584120854, 555276832, 303923194, 329963570, 337962878, 48444033, 868837210, 418645319, 337300930, 125469388, 331881376, 692426323, 503752180, 459333105, 886952261, 575272814, 541064007, 597944999, 936764939, 637385531, 425458319, 650692226, 59644309, 177265369, 352769605, 980753036, 738358787, 524792686, 78861963, 34807217, 200370398, 961967043, 792987714, 183638365, 545678062, 455490104, 488446460, 425276518, 781815973, 527930384, 731317168, 992391068, 883159420, 632359208, 653371015, 238888697, 654354361, 426837636, 294543525, 688868567, 894486980, 222534746, 922893463, 759435657, 651182102, 322888982, 346947317, 260252024, 305032131, 47952584, 722884477, 568244432, 489462147, 748902280, 597665884, 128853579, 913045055, 517336814, 234266824, 701290425, 930145460, 377204145, 153461283, 1095630, 407452112, 679946893, 132463495, 143737769, 514219643, 492954712, 581892964, 572833603, 219133282, 440792453, 198197102, 561201874, 707261031, 508792674, 77978029, 169647771, 555624434, 664386374, 681300537, 431089076, 880752158, 3147782, 24381835, 243818235, 78559858, 273090880, 796931207, 551344573, 586011330, 181328257, 890356963, 967624705, 61914219, 11675945, 126646063, 876467584, 376162733, 244903121, 828713975, 410368651, 103041656, 824167871, 41099790, 901214705, 351408075, 975044755, 878290958, 545009542, 522116464, 964573013, 16034055, 419407813, 689825450, 356067991, 253186141, 648923082, 968255083, 29703176, 209857110, 773086896, 554750933, 192820804, 858508338, 846190623, 266389510, 351373629, 684713664, 534024981, 559741790, 795050401, 715234290, 663034877, 246910834, 956435704, 344154831, 738743329, 458289979, 123694318, 455094272, 13562151, 671399711, 256693985, 888774190, 947510956, 726803357, 508229022, 566481367, 682442424, 126129754, 804432337, 957788260, 354013624, 532739265, 867411850, 379827039, 88256590, 215396585, 16037508, 84826507, 381755008, 662765759, 279909595, 370762445, 893840975, 831176154, 720782682, 935918423, 522373263, 666135252, 779123160, 365909055, 641613805, 100871186, 258487855, 424452555, 762939374, 939734844, 495332934, 538605175, 163303710, 808095934, 45558148, 793570363, 592241912, 798399245, 714575315, 388373339, 547968326, 246257817, 411079920, 683570976, 527247037, 512639072, 969875898, 766763433, 344719285, 519632817, 96933746, 573941210, 781819712, 736998759, 739358945, 352542974, 61956203, 986292173, 313490498, 168901470, 983547051, 509133785, 372912428, 445347055, 907362145, 587726943, 933925687, 532562183, 698194218, 223816027, 933244286, 312870083, 29959429, 193798395, 351873412, 667888264, 44536789, 186594188, 901296548, 439177424, 24183118, 531536661, 780206443, 143709411, 505015658, 855778538, 378757790, 471911133, 623923769, 738927331, 939491032, 801698517, 450375591, 719735601, 466057124, 324901735, 650200140, 928810018, 739779084, 507017658, 54545556, 697432973, 129610003, 651694160, 739633712, 191517100, 987847943, 879781887, 161172822, 847076808, 180126251, 242364869, 228035933, 189707114, 557836910, 692663641, 170127936, 308865023, 69049079, 68878647, 494861039, 662524042, 809918951, 444371812, 887023751, 672468937, 413561080, 319471577, 185221882, 639387095, 41694541, 882226983, 456561554, 940891370, 582825812, 749314330, 259459229, 761922010, 319451713, 949742778, 117844383, 356946423, 650466400, 403919867, 306940490, 849127155, 587874113, 202967092, 395411420, 863891979, 405993665, 965569081, 304318334, 963778813, 520103741, 93088466, 720224791, 783872888, 721941804, 907649452, 81640831, 798091021, 343973773, 305560445, 390021589, 33791989, 261907827, 465422503, 68916790, 584888849, 751099901, 467242320, 475131544, 309014187, 718641464, 809157832, 827714880, 369708591, 748632156, 849687893, 261434176, 201559462, 950105944, 626724540, 723702836, 136968452, 538853547, 757199766, 218741394, 101618381, 38520794, 855024762, 952790609, 220219313, 800733040, 852083306, 190248241, 477831310, 599222218, 186445566, 611869926, 733169305, 183363037, 200184483, 993601016, 924154130, 139436822, 926270241, 812435523, 550032966, 884192674, 406789361, 349749046, 142911994, 838620140, 398723110, 443383793, 106099360, 483960764, 604816277, 37189487, 753177308, 423984302, 629015987, 797112121, 805654726, 383442971, 256772493, 641060442, 914545439, 210332478, 660282181, 886664644, 901354938, 719997198, 264044795, 759038039, 93016843, 234349229, 973194292, 458971981, 128092254, 920013899, 598792656, 993412751, 618745216, 975962778, 664855638, 910328949, 347049553, 312349429, 410501983, 143507416, 489172283, 625052685, 868174145, 461158722, 978288495, 159387933, 322700760, 762656495, 49790272, 855970758, 820407191, 975578504, 519390051, 866583177, 740035430, 586200568, 337462915, 264070598, 521116745, 745040176, 910107418, 612054962, 83518745, 712248614, 987286113, 935686508, 389630175, 752537521, 232337152, 716909580, 326932519, 818426548, 298545583, 990083061, 71465299, 790454795, 354462693, 726189152, 535237306, 978021842, 668515401, 71948675, 66191559, 895988173, 585403406, 781892690, 846577528, 269280329, 246437308, 131065294, 923716172, 229634967, 171528049, 99667360, 336781202, 978737443, 505048216, 634277060, 455266315, 592351015, 386927689, 77901858, 729298942, 253107590, 230470272, 701059372, 549950717, 48254797, 802908069, 314233507, 335231554, 907955797, 197605405, 309404290, 721829222, 570232402, 49199856, 212819039, 660680563, 336988564, 425227417, 431031773, 599346165, 79979867, 738567401, 756412632, 512789700, 815635254, 697205454, 480574071, 705335058, 723088028, 520193378, 890407763, 723073371, 317139630, 79922627, 989957429, 427768211, 768105412, 317060556, 727819619, 821226940, 422408508, 257771689, 325488453, 581163704, 134407247, 620812911, 845461204, 389880249, 654816141, 530815441, 242462778, 533391180, 524389240, 35084578, 419071102, 391992943, 164353274, 414111232, 380303508, 424052854, 419923896, 395238599, 731078836, 578555510, 829968505, 583866973, 994372966, 399759381, 930872568, 952765354, 600643448, 502660911, 39076767, 357120182, 721263696, 332059551, 941579869, 454207187, 139821949, 977359160, 409102435, 744573552, 836367619, 318385951, 299129916, 95374646, 422199163, 835082819, 161471116, 928427339, 514788321, 545998361, 36255148, 714887248, 347448233, 213016939, 609928607, 255492277, 439206641, 974655100, 683847923, 531235156, 946687570, 561756830, 443488656, 283996760, 83230296, 600688642, 322694005, 354752724, 579809241, 15580192, 898036383, 624029052, 854250371, 318511558, 704429550, 931917225, 712549557, 523430283, 763787769, 280008178, 657585815, 371933423, 384874785, 548870528, 269305321, 816036827, 219683223, 175785002, 497037607, 203538965, 596326508, 811446225, 213283406, 264299084, 402552764, 901790497, 533942014, 839047449, 198375675, 52481232, 111456297, 28894812, 261403536, 556600344, 603669865, 752431666, 793976837, 967352878, 40574769, 937846162, 559221835, 350648387, 295253508, 946135051, 417678686, 164963672, 532732629, 322070264, 174412049, 507155736, 319036946, 86666063, 781263852, 894725578, 360897280, 417143334, 411928923, 869759562, 242575389, 763038168, 836793491, 456937527, 693949106, 206117973, 802227133, 901622468, 420549936, 955966033, 618134790, 357940186, 972731035, 102498462, 716976902, 711023775, 186635288, 70059122, 645808890, 825762778, 970290049, 199374580, 599556943, 695942847, 124522093, 118805966, 907092248, 105412836, 94635839, 386027652, 364253684, 560225243, 121891741, 372628907, 71780312, 100851946, 291564087, 473121605, 674792966, 427241927, 340125638, 692177127, 999502252, 61146924, 121736589, 253644944, 506581644, 285836574, 706532553, 689154466, 765706654, 986326784, 322676502, 827250815, 850585895, 706834397, 598167928, 333088519, 903115112, 375717998, 453481196, 82067861, 854630876, 816668884, 651431995, 30154004, 596449484, 859796979, 271052475, 313129243, 821230758, 562906797, 705867676, 18888723, 406955378, 909125324, 349158847, 88753710, 403767295, 728715747, 78755917, 653413064, 512189263, 867247447, 472794908, 372898, 665187838, 581972168, 859342843, 431337603, 89974818, 260276911, 315215307, 172362495, 538135248, 167883157, 763622179, 880074979, 62656001, 63585410, 719021732, 447135649, 881352652, 627498422, 173441201, 918137178, 131471354, 998779555, 409488395, 483663169, 15232083, 613011581, 801453823, 560620299, 261094367, 4393845, 35352229, 698005016, 869399394, 189110729, 141417418, 709972236, 717556995, 664722355, 228538760, 266313382, 180619510, 745148477, 374082332, 909102571, 639529624, 129807974, 895013016, 470095294, 833579883, 224243450, 836701381, 557420593, 925396921, 444099219, 724313370, 993669193, 22889999, 7891443, 959610015, 503155006, 175481176, 695700647, 849636068, 489593831, 601232992, 616640777, 191369434, 9164759, 151673642, 822515999, 452873062, 915075248, 334505991, 232265439, 431991304, 582922804, 908890882, 680111665, 145135816, 186640660, 918753665, 647749582, 890504661, 744001723, 128387687, 910228546, 610944935, 152827818, 473666401, 290660373, 282572519, 409096142, 296603757, 409631401, 109518067, 511661437, 834064138, 362804691, 389808110, 984769771, 526836026, 234929974, 59769886, 835844344, 659756784, 263522309, 52943948, 874085328, 225519763, 743086501, 664272630, 546846764, 673180317, 399499896, 495785233, 464663757, 54404582, 672210573, 671571654, 602790695, 988940021, 513258417, 955787914, 919963129, 782077325, 740713839, 579659805, 579408390, 230881450, 115012721, 889484618, 786073475, 762772321, 49046059, 126521589, 590897265, 63049655, 432298519, 341991554, 317148484, 123668059, 799376442, 462983175, 414715550, 198041110, 714129933, 458994362, 577486043, 405385997, 969202975, 759831935, 827059886, 104338057, 876827300, 439262438, 581583741, 160405830, 15844473, 709337792, 804676508, 301650494, 212888249, 108083495, 236543489, 117723844, 679067406, 671944489, 403818878, 529112884, 105766317, 283520339, 231965922, 313282907, 329442690, 945822010, 860555464, 919834735, 540898610, 46608380, 398892474, 577324208, 222210386, 995711405, 826962562, 947219564, 694166844, 70871922, 209903705, 375953225, 176273590, 260067150, 753742133, 52371775, 820969995, 999996982, 669333616, 827384741, 328986906, 190617836, 792410939, 800720584, 632391986, 515829367, 115487487, 838538087, 393724083, 444456579, 872462157, 659055049, 78242826, 707574246, 624862433, 65731973, 920767706, 140309160, 850471087, 205758814, 489977844, 615796843, 46694145, 222753050, 111012012, 830881498, 434449512, 72823586, 987251836, 791350773, 527166879, 111899540, 397399778, 812798455, 385422846, 61247007, 663362460, 720726675, 97208693, 743963190, 834465188, 95101916, 447880371, 717997507, 272140162, 82907846, 601896280, 490605698, 215771023, 317598403, 73448745, 315388291, 811113193, 519140062, 455872427, 870757522, 742399056, 560999666, 599500345, 172692667, 304856329, 909765608, 128232822, 544679353, 679814273, 103448005, 534076175, 673611539, 385254869, 532846862, 41758370, 594711565, 604719321, 235473425, 726959415, 649292063, 131017937, 391667110, 23296559, 3534003, 69388087, 880845847, 572958029, 408354184, 530000745, 943698292, 48499660, 336484283, 102255705, 498418008, 631656850, 980743384, 767945847, 19875762, 301245381, 190092519, 522247624, 312957436, 365462583, 409888116, 253738158, 684743885, 423574072, 481035580, 596928351, 324267177, 717180123, 859151846, 688669450, 295583000, 242171062, 979631026, 997506755, 505029540, 445589899, 676404029, 256797667, 1650225, 566134803, 255128378, 149701099, 102333500, 230971533, 347602777, 370831242, 129225072, 415410669, 396625220, 957264399, 610597909, 740983400, 396917663, 345887786, 853960503, 438516953, 458370223, 21824836, 474086292, 724111934, 130858600, 69712337, 721328587, 693676517, 197634184, 268494038, 207464397, 145082388, 399562063, 475030448, 388679912, 995401601, 122653744, 360683176, 383566463, 609993768, 868678524, 724698656, 872742194, 102145470, 835457758, 810066233, 667531224, 487000766, 832047108, 484097786, 800083566, 818184992, 82470001, 813929682, 506371978, 292469690, 550599519, 178509594, 384010688, 761523294, 755347110, 345612619, 483034192, 254757941, 404190760, 434738119, 987187616, 920320692, 960380548, 26273095, 953206112, 836359935, 261584227, 948733434, 443571740, 809961228, 221293100, 336715401, 928462392, 360186236, 216873326, 105809474, 955241188, 802535637, 905928343, 30750564, 445492605, 119594479, 604654460, 854369697, 237788910, 386176323, 104618553, 788054521, 259658166, 553090563, 758606815, 687847463, 783336429, 239668475, 770044432, 811451392, 318406762, 151729152, 612443625, 530863391, 949200146, 916988909, 594726718, 212210583, 378949648, 421909843, 679572040, 366264770, 87410793, 428388307, 205144628, 652013244, 570746974, 416555460, 475459526, 484201593, 817856603, 460127708, 69255171, 248372452, 275332789, 360317378, 599299148, 872417688, 742873715, 174782324, 815706816, 975291668, 650970090, 149304638, 722405652, 94842007, 78994654, 532607493, 88718970, 532485478, 345180046, 345269933, 704541883, 970130167, 813274007, 337028440, 106534329, 626997108, 989573888, 765558860, 258423991, 451674575, 52826617, 548001704, 769937070, 344239077, 101548614, 776626142, 764299478, 992909557, 670869570, 384785721, 888477291, 233089545, 205844417, 598025399, 560212319, 78249344, 616286142, 228218193, 248739037, 25571177, 384825554, 61403992, 719715672, 114209911, 411809134, 706204413, 43134642, 375647169, 678605767, 2671870, 701363158, 293725529, 413561817, 886687385, 934013868, 866659999, 617638621, 82988447, 783968196, 604790839, 304042271, 965761315, 470590406, 755435321, 157608536, 727574980, 185594445, 257359595, 209965830, 752014390, 590447695, 3402764, 63594816, 172363965, 49893744, 839773403, 748951590, 638608415, 922887883, 346695786, 590257934, 88412931, 310507041, 437345230, 325091120, 50255109, 405405583, 544699408, 262338276, 929111443, 914354145, 119826432, 525268100, 547245567, 921171387, 196622777, 194825561, 648177924, 205597524, 987275530, 52139337, 282514005, 862384596, 799037533, 699648391, 54596746, 242812258, 874627481, 85921710, 944200026, 2018626, 744705709, 44476936, 777246743, 440848931, 735417372, 339561993, 258039659, 485230039, 70552443, 831098798, 56052861, 425501103, 215053429, 509733614, 191453977, 225406822, 432949132, 247444163, 173549710, 326442194, 89094661, 839097077, 985344469, 279640188, 380544351, 598705869, 537085502, 800093763, 720917886, 749163924, 418716985, 668434652, 965246570, 177860907, 30487233, 753677961, 79632496, 288656469, 237997531, 252522988, 50021406, 881465360, 48966453, 159968026, 75392075, 970043570, 831519656, 737888850, 188639168, 885939292, 387813324, 241492673, 846053554, 234303025, 304678268, 13267729, 526089715, 464320149, 230141689, 723835528, 508276438, 915188131, 257491078, 101469927, 290186849, 943243202, 850845943, 782274616, 63564660, 722651966, 759519135, 528108427, 594489928, 27356845, 459450104, 222714862, 303710401, 367261035, 372205789, 341699563, 536150984, 554825118, 120767917, 51250643, 914981695, 264207078, 824327534, 953556233, 389870703, 81824035, 653381884, 236893848, 887275041, 342952689, 292055296, 450162130, 33598530, 631621914, 697770632, 642048549, 369173394, 696616468, 766002618, 296895264, 613242201, 992280295, 737881766, 417836934, 178541242, 840060022, 422609959, 39603037, 418714247, 313621552, 228187358, 924638083, 385158954, 821982833, 123557592, 319340133, 162352404, 2342318, 889889828, 285715310, 706901798, 940428360, 783879537, 27518925, 833666549, 393689950, 586819012, 394817441, 187808058, 424118909, 47311241, 327137046, 129544936, 104866259, 741153038, 504698273, 89707907, 722486815, 876753725, 91797978, 341719270, 83249633, 718072214, 421003451, 517512547, 44627680, 691499871, 56468315, 105831960, 75122602, 95829126, 347196580, 518812397, 842444719, 429502351, 484151352, 348137161, 730117700, 861686782, 830919036, 492359372, 275778975, 178903237, 731221863, 749846289, 24048234, 48904026, 316985701, 985727043, 497722975, 172359681, 879361403, 902455173, 169903998, 414144023, 655932558, 520406027, 578051116, 542737471, 518027286, 809060716, 75669825, 243727238, 303411677, 735607634, 633626397, 737724397, 634671823, 72412192, 644180076, 750861539, 507814891, 219733512, 729923706, 763835899, 186587675, 28068700, 641114979, 768496979, 52164440, 909530000, 350225319, 862091787, 649309049, 726220679, 497565456, 450864534, 482700613, 102463084, 824158686, 22657408, 471689625, 437827243, 649116687, 802187503, 90626334, 568713763, 801966284, 850885578, 726967300, 94788137, 855941025, 640077080, 717068170, 757227008, 287662441, 680631973, 780748519, 388160790, 993334261, 344019956, 863473382, 93922154, 787939696, 487287925, 473834959, 463064499, 306795974, 32088907, 771194914, 327864914, 528772405, 307555417, 648979085, 207884046, 74961981, 491847241, 911623206, 375061672, 163026376, 12486992, 84691166, 611383951, 34094906, 177193338, 920447603, 836638672, 656615288, 768346363, 508584477, 546543152, 876160355, 820323886, 751750719, 252834448, 319714712, 435322756, 584351189, 189008637, 839134467, 98177316, 581974780, 66949826, 356791570, 647626598, 37157636, 328963912, 357756759, 400372777, 911931917, 268566568, 84861016, 967934002, 458215311, 598877576, 941827875, 517011509, 250063723, 809964940, 36257291, 529267515, 29142664, 824623280, 294252644, 955631204, 130109830, 848106187, 371827454, 484340639, 93965846, 452132758, 660705432, 178456607, 524386412, 628198751, 679917379, 528116811, 61026807, 324286329, 33634218, 303439933, 200016730, 447203821, 388094527, 398759766, 223769858, 583825156, 411804733, 193024990, 225471649, 480411300, 83042106, 945792901, 460554563, 503485095, 678080483, 546710056, 535032427, 187192884, 964406671, 76123698, 596943680, 433531106, 327608385, 47780128, 215615499, 484452353, 998347911, 319781811, 524837244, 600118591, 153043503, 178056951, 327957109, 398715202, 302382118, 280546841, 300110754, 651640486, 946040757, 477238647, 277172453, 484806324, 818705376, 587200096, 9125245, 408176905, 881675824, 999183099, 172961028, 676545488, 668718175, 952782824, 380376225, 390371391, 39423770, 867895177, 628413115, 937051462, 660923106, 520597791, 140084534, 692355068, 61433819, 832062439, 794425153, 206970607, 205516339, 482972159, 280866128, 954057474, 902611405, 908891276, 214209489, 353706236, 355395029, 268296834, 166669153, 457083160, 756620875, 608957229, 377126781, 972309990, 68402540, 978543115, 389770425, 521036058, 662452572, 485637065, 628912063, 246272271, 533302593, 241280536, 880581254, 251930773, 663441781, 652421763, 955779203, 743300051, 711771230, 133088946, 900357432, 95353964, 228174227, 886934736, 7658668, 934783908, 103554774, 93522963, 24648463, 392024939, 390391957, 49588890, 422946642, 989498181, 977290975, 788112934, 963224251, 348168077, 817456968, 239023873, 544631421, 496254256, 103312004, 676784636, 574712606, 115550185, 210614844, 876888575, 254559026, 423441276, 568432965, 91000930, 190479327, 532858024, 5281324, 899909165, 151496613, 253363193, 540078014, 914568377, 746376700, 443255282, 236562221, 460282441, 73611269, 731645777, 514737187, 703437386, 492145025, 761419216, 825728927, 948182057, 621670575, 549451309, 525675063, 698595071, 890257754, 435412331, 604508856, 645521882, 226426792, 812025140, 150203693, 217927437, 208619047, 171123078, 716596126, 771735701, 18947874, 374343668, 66729190, 947964443, 57816197, 908866059, 494693401, 589051746, 566109125, 164499884, 50117209, 561961515, 264753046, 850661695, 262385978, 766329844, 662852226, 822964570, 881308619, 608201549, 955293579, 962733020, 917178025, 942329256, 808388730, 567101410, 465036839, 6991756, 905082739, 321459705, 573354481, 764392607, 90483185, 421092786, 209773309, 239605402, 661163158, 17374556, 130837669, 76621781, 729795073, 907531783, 304250218, 957724873, 674172728, 352694235, 236906041, 463683738, 413958487, 90756044, 384673705, 152555242, 290580251, 126456587, 414334558, 21306479, 550013284, 515312269, 729305759, 177707754, 744302028, 437075046, 179550219, 292414355, 167267291, 991508771, 221420837, 754229560, 375860455, 506778532, 723089875, 224897364, 301784465, 553677314, 425842314, 567737143, 664889080, 222757704, 309001575, 867842369, 427279625, 676571647, 797521634, 127816149, 3109278, 592478720, 688646673, 549299749, 215277404, 142617382, 652018783, 247806225, 855071759, 910917179, 634595817, 507809020, 995215753, 915337478, 356323510, 49090203, 520326987, 235561183, 713993944, 120778390, 563100940, 913911779, 951540294, 627687235, 899226640, 362137629, 582196539, 887775688, 234292274, 32242738, 990322082, 240746839, 194931740, 818774288, 188471172, 506044808, 458598200, 544969930, 559896478, 611546139, 834788773, 607324920, 408959357, 781978098, 558005474, 592172663, 67668155, 819610019, 701734020, 948390279, 412318275, 156256295, 714694291, 939809700, 67701813, 113198345, 858477534, 698645398, 788973512, 342806816, 935923767, 367672302, 79485115, 749110694, 145863141, 435670255, 917332532, 82794640, 771757545, 353776325, 664632436, 89597072, 960382272, 323077167, 693188813, 973704525, 163582686, 592490797, 844142328, 57461657, 295621537, 510649735, 189234137, 382821587, 584536039, 740295300, 596645344, 692436164, 75539920, 507872026, 452031696, 430458614, 614791782, 460224732, 286279247, 35154666, 419360263, 92843087, 853975719, 144480203, 607744424, 871137497, 912504824, 472138754, 788106131, 897442307, 292949742, 85998704, 580777058, 244701991, 141744722, 276532502, 1495487, 236975373, 329577345, 538618261, 510002070, 495850503, 977989183, 723118091, 388235645, 144614376, 829632675, 799763410, 788017820, 466920301, 93181424, 527914899, 648885842, 59848225, 126746173, 269585022, 393855407, 278060604, 985130959, 910930599, 754532982, 38333161, 491315460, 432755908, 979811024, 882571705, 90453049, 382540760, 409285342, 357373578, 494890410, 589831195, 650912493, 644368734, 721965708, 98891881, 213627374, 196769643, 358490087, 600635622, 893704541, 99471701, 308892439, 481841181, 960811995, 557783375, 583185394, 22394185, 268794314, 283101524, 945253445, 162616011, 465959516, 427295571, 26638164, 498675101, 781468173, 171170814, 38481278, 814769036, 106348061, 354222657, 211348876, 191266044, 533299299, 717326319, 441137194, 387197081, 941277690, 208111437, 397074350, 945183945, 66937522, 986013154, 263602664, 647730307, 873451144, 823784802, 777582339, 422597074, 158965063, 163750409, 84995862, 311704563, 167811370, 471137506, 859457649, 936134016, 991250797, 410834023, 632341562, 637879940, 539431719, 354838480, 433544982, 731427616, 689415096, 478600963, 454026357, 739616421, 733519698, 127105612, 625093606, 811173171, 945815065, 804006872, 88064578, 204519896, 721979549, 924573560, 104876427, 69215777, 326215368, 582783236, 440381900, 151962608, 99325694, 47679241, 446611496, 226997121, 762284563, 766168598, 546338875, 508576747, 653114287, 925511032, 23120616, 92551311, 358071461, 942768619, 123505026, 228902655, 280034197, 78612775, 611370980, 192901983, 26036, 215746753, 50441869, 188908664, 375256090, 542261968, 586873969, 770699542, 786866583, 788617792, 177180609, 56955029, 109458384, 211716274, 384407203, 992208806, 226608138, 485692711, 993060753, 403335474, 709525498, 780179320, 319001028, 725546136, 966506413, 518657238, 449900733, 769064060, 855563276, 725747209, 809436345, 890541436, 477118347, 619114449, 834058294, 597002281, 375375547, 556319952, 616677626, 379810771, 353550211, 463335103, 101422245, 276919981, 592482266, 125860404, 900446453, 339948004, 743339421, 768084508, 948434551, 527426652, 660084351, 580717552, 145589603, 473238280, 636863678, 196761271, 751985525, 438699257, 51747036, 695751762, 335366478, 987641326, 984747777, 578451500, 755228151, 874842485, 446870133, 888018711, 489263973, 554304183, 711651439, 117729859, 912829974, 677798380, 135710030, 78139217, 750343080, 510171305, 847790760, 184639468, 596418509, 901899860, 188188799, 123290390, 660958128, 355446857, 700466832, 965875845, 839938394, 818897102, 470127643, 999769094, 241147951, 618179901, 682983669, 234415531, 86310763, 862703659, 680774796, 54767017, 57952021, 216664597, 644421917, 923272825, 605703896, 744195142, 646635499, 841616482, 542081270, 588910367, 346914978, 193082408, 783472870, 339221511, 557726011, 48421716, 24856838, 43889836, 430855065, 635806566, 909989350, 933879576, 543854807, 765902652, 670713368, 259560462, 81252867, 330409093, 656698396, 668709219, 142043981, 129940058, 567872689, 235423569, 628939831, 386150526, 90757305, 134187095, 243344130, 80837664, 898888522, 513119498, 386270156, 896930593, 302154637, 385306917, 737445820, 824701393, 214963597, 447162609, 425558023, 278390762, 346499597, 297355135, 448698901, 949743003, 69354388, 851831105, 959469720, 337979721, 517745123, 353282680, 581827467, 795632181, 633829459, 829747623, 162645459, 169449790, 417656539, 363556519, 309427173, 531867510, 994301295, 77657741, 909164010, 836702150, 829336591, 892537555, 94180231, 338773745, 904041519, 454753135, 794394798, 676940805, 767353079, 511701301, 671676539, 831737242, 878277183, 961589009, 200741029, 182300277, 931856077, 46253946, 567069690, 529578698, 993200544, 614053535, 215485621, 376452097, 142182660, 398997980, 838578877, 671142030, 882031007, 52112920, 608820622, 849460376, 507345170, 872079046, 762472294, 318219730, 965317905, 560406947, 434349739, 68578918, 668943713, 16073095, 108683563, 420780333, 266603726, 904602270, 458188044, 527128471, 129939495, 665920131, 162466740, 210618995, 730756996, 882117278, 948288465, 480431087, 957152029, 627421573, 750824950, 596765144, 320465765, 524970793, 367044359, 888159540, 389044022, 693738071, 702857650, 865332418, 101586978, 870266501, 457561754, 530125374, 142381631, 19431376, 375644672, 820002749, 710441658, 215135123, 860330575, 88443439, 498393344, 525970654, 458055147, 370323920, 705430619, 519362337, 899377704, 618131245, 83624497, 210366715, 502482505, 965679861, 9065665, 850050245, 7327752, 339902838, 251860156, 510661127, 567511303, 524516887, 440428693, 364072422, 758391131, 993195182, 600303449, 731238823, 857373706, 763294089, 683984466, 280182074, 704323019, 415463738, 359441929, 248527897, 121845962, 195646676, 78233525, 218977609, 487408251, 674918878, 434078715, 657115197, 370443637, 654991696, 317696995, 223793434, 443988053, 884846704, 705084594, 530543484, 214669718, 771169746, 188005758, 226770059, 380012141, 304656833, 27327370, 79536577, 471561430, 630859130, 549951158, 336652199, 13811289, 162307209, 582430957, 700723812, 313403481, 346424683, 699126553, 885153455, 934285686, 69113086, 991307157, 829020814, 848915106, 835637915, 52021235, 429323856, 231871093, 195507387, 421862293, 823135454, 601577825, 958231503, 987414823, 325311331, 414850935, 198039352, 126073977, 274378949, 355985858, 326763332, 973307523, 914363322, 717932504, 326774783, 527013412, 825122405, 213568687, 69745613, 429566414, 839413435, 310089975, 862589608, 620573730, 846377703, 627286065, 1888732, 653552868, 762884209, 857485792, 967898246, 774351578, 415788916, 716503460, 457804209, 184087383, 639920548, 768180766, 497211030, 812454922, 495710517, 363964132, 336895998, 657696081, 531235732, 959171025, 702922062, 702956566, 591782829, 826883913, 873993354, 304377710, 354059250, 631683342, 102327001, 917047371, 582532158, 207976514, 119580778, 708500227, 33943800, 816096621, 427388309, 328747888, 508035503, 684936035, 717182256, 918113031, 74721272, 922776646, 101810377, 908665549, 243417801, 986723554, 402925971, 56453243, 962321757, 878931831, 625454231, 357164452, 283632934, 978696252, 749522435, 377308085, 243303998, 211364361, 738669039, 83258216, 264818892, 392170734, 389387623, 583277532, 638196439, 892556999, 855820358, 960453427, 508328721, 755677629, 159935276, 381982927, 654541659, 552575097, 313511133, 580999289, 900671422, 18073300, 889562082, 345487217, 119255902, 713038296, 94379443, 592715660, 491208804, 76443974, 62999497, 762000737, 203837454, 27171334, 427429964, 850525670, 911010346, 630219803, 95046605, 298944135, 552114381, 237473824, 322523122, 288141206, 925224848, 910049691, 115670016, 748254954, 364286225, 797885448, 123931862, 923171812, 90129415, 46695269, 33128325, 887530465, 234135959, 191163874, 12202196, 603599375, 609994860, 663368756, 502400412, 253596544, 924749585, 19224044, 512142712, 290220781, 506450626, 300547483, 62865262, 639745684, 621223272, 160537966, 740800658, 183556345, 455180178, 344046623, 570112054, 895834873, 285909775, 961825178, 295983908, 925862740, 279255893, 956946138, 19054979, 891093550, 73938226, 622615910, 611083443, 1165580, 831310131, 385982142, 648637328, 946245010, 49621575, 130982277, 936735628, 178976172, 69251324, 643472288, 355287230, 642254775, 516972318, 904423263, 848094031, 485922829, 284948509, 914442529, 925070221, 748812139, 535456264, 947437389, 516850792, 860523700, 9410657, 483919338, 455469569, 668896075, 48356697, 525595133, 110285321, 125811651, 925258378, 148375697, 733066452, 25624358, 594059629, 673210779, 245620015, 100530591, 673769400, 876038948, 675936582, 304214931, 785719780, 35778200, 780793300, 133943078, 1966141, 431644941, 979285681, 302923782, 114664868, 670959107, 569845474, 881653127, 137770857, 721213809, 45399308, 890496510, 456718014, 853705827, 95287101, 627665035, 500054812, 388920767, 326562759, 972413317, 428622540, 278641439, 888599855, 285148673, 633104139, 443290594, 824324015, 323034672, 384197903, 961967773, 989765547, 862867231, 637494257, 177541752, 212437489, 511239151, 945342198, 391678463, 957578924, 952042074, 660909556, 240081755, 22533955, 1028343, 715229560, 426035843, 907660391, 973420493, 239593932, 396001112, 330178325, 580564965, 797477831, 448633448, 861233626, 109272377, 135574121, 951744119, 798992854, 583629709, 513391926, 652003262, 159260541, 470495835, 817807816, 337208753, 874988692, 811428250, 538234414, 264448064, 168648029, 942537442, 832035740, 329301985, 61273035, 668582909, 823947404, 84362641, 862557220, 972512770, 87863505, 475345972, 70669731, 796324942, 169966842, 916565447, 883815789, 457665554, 516075297, 584879382, 907754116, 599357060, 660194216, 189601135, 800760526, 691724980, 873258446, 531756357, 459866148, 472563952, 933870880, 380653470, 273906476, 26672549, 52849345, 427719994, 284477485, 946874581, 658661615, 666461096, 130374214, 391232054, 639915291, 390002213, 813572152, 285889408, 398870727, 222463224, 255281910, 853476320, 606603458, 933919856, 761215528, 39974354, 497323804, 514439835, 770876898, 334078, 839278336, 255656536, 784528467, 421686567, 964741454, 443344045, 321737921, 978924733, 144215236, 891970202, 802394891, 471268202, 351807271, 145768226, 612955316, 642914161, 497383159, 389733916, 904729052, 877367464, 943755158, 342978249, 642954937, 660508247, 450108287, 477310505, 942414599, 959828586, 994593040, 638356866, 450545199, 784396245, 487986446, 460234323, 836725732, 400264669, 353558782, 116603558, 339706401, 877955189, 818883364, 624796924, 800951213, 854367201, 477273632, 322996671, 491312994, 553904745, 853199831, 845962831, 481487704, 11426150, 859749759, 427358651, 788383692, 777785480, 229779556, 115014861, 811306475, 785919896, 996946757, 719975119, 603983568, 256201328, 977902766, 7440283, 947333445, 636405621, 807224660, 386786682, 301419557, 782545502, 604904017, 309653725, 859762787, 800767782, 106379708, 295580274, 694729804, 243375651, 315489968, 397337060, 121620424, 150229044, 300914097, 78751841, 709143668, 581547971, 323112272, 639257591, 523424867, 404005936, 434906244, 938369503, 65540771, 481675354, 103184702, 1098163, 805664912, 274247101, 586102124, 491147296, 842382968, 166410182, 529704692, 464586462, 878159372, 853954355, 264046159, 738748218, 767549561, 781053688, 274485392, 864898569, 250328056, 776991858, 748883109, 628610439, 369809381, 809688812, 942261629, 742587007, 259787428, 615651577, 584976201, 807822900, 362999165, 592884341, 51059116, 897971732, 616030093, 84948332, 604263700, 748839267, 217871993, 917586164, 688720659, 795011093, 51955834, 750645055, 673050234, 476567037, 441739295, 315125392, 207707464, 205928495, 578943572, 434602971, 519606421, 736433450, 194392980, 351216782, 234904858, 321453226, 666284547, 95882908, 973636632, 283032172, 651432086, 892917860, 402630896, 69280258, 339618816, 125690562, 394391250, 676638879, 229443260, 187189151, 370602532, 743238444, 108568231, 774149975, 957058042, 994765030, 541478986, 792425664, 181704875, 627370291, 516173691, 287251978, 810754683, 908880667, 581230980, 930618929, 560720603, 652972935, 240731588, 101372917, 934110130, 813624147, 661755097, 260281980, 622009836, 858848053, 311042253, 23366797, 95909006, 819457635, 942460110, 648498789, 272194872, 500432327, 840085818, 671313827, 188011457, 667422675, 694790373, 557152631, 870003964, 706687502, 836703999, 113965753, 447954340, 367737567, 379470192, 418715179, 488565812, 990442785, 508411726, 379381078, 231485082, 263428363, 223564634, 264978000, 162805830, 866857834, 366246780, 708436635, 871862243, 245898897, 289307912, 543207861, 102934361, 832034856, 426846878, 834299980, 224808141, 970658314, 768784565, 943058167, 796939733, 383517573, 466906659, 247393123, 682181833, 908547550, 132478432, 595524300, 912109951, 849849598, 185044145, 389649682, 297942064, 10182062, 606920838, 960439548, 217727942, 946073478, 464064206, 67254641, 856255316, 366109589, 12567798, 155491247, 823059675, 666559413, 163102721, 503281725, 857781053, 514478345, 609667518, 825135629, 975445027, 877000140, 47688585, 107206190, 504111613, 289950890, 106617217, 872716972, 622449247, 313755585, 709930983, 760199014, 952748007, 56355922, 343312621, 235843590, 687051032, 739447375, 873940757, 198587397, 32392784, 473370337, 409277114, 476378006, 492018993, 207702347, 910711785, 137114159, 362742265, 973443148, 598815870, 469135740, 205499338, 540111508, 612386274, 121474961, 938818118, 769528119, 751996086, 567747221, 767850316, 308728291, 734866333, 438065889, 166490604, 904590528, 409465815, 320047287, 667982296, 190171119, 507550136, 798457362, 553211191, 356672582, 606268668, 478804354, 47203777, 127280495, 25516222, 732047164, 401197202, 243860899, 689710111, 394225727, 137550252, 538168754, 664939948, 928085748, 423867317, 624251084, 102160316, 817687806, 281998419, 277988966, 393686482, 140703455, 840945154, 527014183, 293261360, 226734744, 746629318, 517339894, 997847638, 965069275, 594319491, 765155808, 675486237, 507052647, 136714384, 791400693, 712640002, 520220302, 93461099, 720994709, 952542928, 410065434, 323111770, 827746234, 192034357, 550509706, 565762358, 134819601, 88888551, 152187120, 364291796, 352123329, 602535479, 977944379, 618724463, 184619113, 428412391, 754975157, 739069845, 936465247, 209721450, 716317710, 4188306, 218377452, 585521389, 790459379, 663504067, 966939364, 133722859, 796346353, 513788699, 895327060, 29635995, 602812781, 92202466, 353794498, 645896162, 832760127, 331766431, 320384551, 246870335, 883360105, 5848852, 41059512, 472748923, 855803024, 476918663, 147537216, 525581335, 883104772, 840360688, 987419849, 870929881, 315653499, 952733993, 485953536, 187466558, 522052536, 442626324, 673934690, 627906842, 302096161, 932892449, 846848586, 429943163, 571335910, 719219091, 992807222, 380527252, 693376241, 746472318, 525345210, 977593779, 230205437, 988889550, 397887978, 770786448, 82328616, 357606822, 520695059, 305291030, 543876104, 136638675, 245847714, 44515894, 138238431, 507657035, 718769083, 793813149, 829469702, 449478054, 753941267, 372551315, 440471480, 24940, 242212109, 964904521, 168847223, 470222939, 47633522, 361147175, 282426115, 135791314, 343178702, 323839221, 502451863, 712475880, 644577593, 583511876, 232381162, 960371824, 391525251, 559324849, 91549098, 129863523, 229720900, 962016388, 851342909, 161822457, 569428616, 88565703, 919039319, 720375293, 332912398, 483898332, 208582260, 469808877, 393187012, 341137945, 588672726, 221927027, 345141620, 241833454, 795905283, 671965368, 766583046, 141807523, 840250014, 53518572, 339681893, 707774390, 191952220, 742626702, 147146612, 382849800, 492455648, 821179214, 576818134, 155168057, 296390786, 896042701, 199718825, 911545066, 76119435, 508833725, 523234233, 803237122, 656406228, 810094481, 331733805, 633967295, 253904004, 250609359, 87539403, 685248810, 6418454, 52352929, 905393749, 719244826, 489232197, 199234272, 530878785, 668315543, 662743427, 461299305, 920026574, 891863382, 347253295, 682119946, 495529585, 866247786, 671869699, 20499471, 628232780, 390694392, 231975692, 633813421, 343513450, 20072692, 51460238, 136055599, 731658927, 918834338, 961238467, 884897683, 207669651, 789415845, 920910935, 612416267, 883565685, 100912263, 387714161, 666990117, 103459914, 927746793, 553621173, 142046214, 838048794, 815499772, 419232578, 110716969, 911641798, 198921687, 321942170, 366531394, 322076878, 72384183, 866393230, 83878557, 110652958, 28333431, 700901040, 963023879, 932821935, 994289207, 498744401, 993448155, 555073432, 429285295, 373247401, 514729996, 315727727, 693981618, 322151501, 234564479, 74421502, 81785933, 251002753, 559556063, 167473120, 371403404, 423441242, 733257665, 90853427, 350093816, 784471902, 12384651, 742525874, 380061785, 745244039, 565667928, 607956955, 951014559, 142140492, 761794969, 754883430, 604307485, 587439400, 466313768, 931906510, 694263992, 724514058, 17462146, 114846468, 528935047, 209738047, 134687807, 426382209, 451821589, 638779316, 956289388, 90992803, 417229486, 363005139, 747872944, 791424351, 610068997, 88176060, 92247633, 470968223, 794017241, 763940401, 304431328, 857963858, 128794707, 264584551, 885521087, 211013553, 80084940, 518734679, 474382334, 928126696, 693240042, 165027653, 137032804, 398831152, 125991532, 525179276, 263687566, 838386196, 674967682, 923173749, 17957306, 951854791, 214711180, 470723746, 187780355, 229517152, 975030011, 323281825, 641625797, 334968168, 163920259, 119887506, 465068176, 568402912, 331731980, 120710225, 14547637, 665200883, 228657950, 412052619, 212268050, 4807008, 236300213, 670580420, 33608630, 523740286, 707107964, 830422675, 810670811, 286535300, 877908187, 607232729, 308352537, 781264774, 991904679, 502728752, 963284840, 273253638, 133997572, 294836092, 438876949, 951644862, 608399932, 123529704, 223273147, 992043298, 389023298, 951428383, 179908166, 927684274, 831365568, 393156678, 497362081, 452358393, 593919686, 307764932, 909071674, 752290586, 296437174, 595823415, 742220589, 270347491, 147752572, 554181330, 197223514, 234702365, 494398757, 431521977, 900158784, 248903920, 675331639, 490593635, 372341198, 103082676, 303722993, 364529599, 165061037, 344706847, 582912840, 935146754, 380062713, 342881530, 23980722, 571226492, 611435428, 580597914, 171563752, 591912477, 345564234, 518198696, 690901149, 992450146, 414668976, 173203164, 587133073, 363114695, 13719611, 444382391, 105431558, 774589531, 613042803, 708573527, 788189331, 192286676, 770128235, 163943610, 653514303, 432128914, 626898328, 119765397, 281286366, 628221841, 702002845, 524104238, 539990548, 496981730, 8169805, 30785901, 13020961, 339897607, 182321149, 86646505, 589817197, 443324022, 90767834, 932927558, 602035712, 255993037, 771325796, 759253441, 813352362, 775819044, 904456711, 591064808, 132171073, 290216332, 227054577, 752879648, 768226800, 152218918, 982359080, 682939186, 101198536, 618017775, 523747198, 439386817, 912328539, 368270069, 647121311, 296472825, 385052403, 797495567, 337374151, 967951528, 791398630, 9049021, 226216362, 168411722, 345313885, 373528863, 751677710, 150911051, 45417571, 827953547, 653032376, 17630224, 742914173, 844552189, 412855473, 496884377, 446910574, 297812677, 309597211, 492716684, 341726408, 697959196, 848182497, 473653887, 336988457, 445724621, 714009823, 444553877, 983877887, 758276088, 238422592, 931912658, 479691505, 335996718, 966680836, 576803066, 759461285, 470138473, 405515418, 494720408, 169464842, 826468161, 928143475, 140326542, 347004593, 337504532, 12754725, 325340425, 150539242, 221150204, 71008359, 319828825, 123654172, 411304508, 408826630, 692932353, 345081837, 155946575, 455878397, 193569223, 721701376, 502572016, 128017763, 738847447, 936053523, 920866694, 684430374, 112736968, 841021802, 659192415, 202895454, 123775623, 905359169, 105827106, 692104231, 359889706, 692293109, 21686919, 600928700, 470556819, 961259998, 155719526, 55272142, 321405269, 602762222, 349962868, 362181769, 458418536, 666268756, 146224222, 855371705, 561536763, 242420234, 294151761, 478780741, 673479778, 404553110, 338803479, 506344744, 523049354, 613034920, 302372011, 152551728, 618046755, 495915892, 399922654, 229404329, 453941504, 35310492, 35486688, 893654805, 489343006, 816026387, 130340400, 518906927, 881969180, 675015154, 240873603, 325650465, 362465638, 71685006, 685809573, 142207941, 876863041, 372677442, 978337506, 618810569, 418958851, 208450182, 227539829, 767221246, 404529135, 251405368, 298197344, 3524086, 131742379, 329166908, 440523432, 958615676, 886745092, 51833856, 592643667, 711524363, 450331533, 494138086, 999343835, 25978590, 960864612, 642830033, 32818812, 568926323, 42311609, 678131799, 358505736, 537800517, 721302662, 667285010, 195477286, 58159879, 898815880, 937767472, 225089275, 544703866, 301457687, 155777588, 600447506, 3651469, 955808316, 724517494, 767687635, 712628430, 496926882, 356398135, 679708692, 859188393, 928401026, 661825977, 540234280, 157489853, 910926399, 957022181, 851505434, 351219868, 481221099, 990220958, 458550338, 213046726, 720078183, 407919246, 443948726, 634754279, 102161868, 814123270, 429306726, 554735457, 184534909, 607675030, 679478172, 47481877, 318422487, 123130737, 418016291, 366150790, 325072651, 302285412, 123790462, 650147825, 724964728, 602519836, 698597440, 173924322, 25436818, 945987217, 640523431, 592809321, 613792758, 835178440, 453227769, 41652103, 940135515, 922516944, 963771116, 567088492, 601275442, 746690840, 380261022, 808123596, 297636161, 346246259, 707248454, 193142818, 346388160, 920952196, 252266187, 110100873, 27636407, 956056622, 416080506, 704806509, 62395527, 659185310, 275359308, 318943773, 653495505, 765522485, 119430561, 730046307, 435402591, 284710821, 30955763, 640445551, 96883848, 411300178, 804834777, 19641951, 385228658, 176989716, 133682480, 435487793, 804754351, 200265028, 884845050, 311579716, 720506156, 254553821, 914161046, 890572659, 463737847, 894782049, 344546034, 131129992, 721589015, 569989932, 190655263, 65656082, 843555853, 2022651, 509407390, 953194720, 683134157, 40679504, 176527776, 869642836, 652937394, 727228240, 507883962, 374538604, 287541822, 85711629, 520366169, 35249891, 587452728, 406699780, 118806685, 5313153, 292873030, 407826705, 895973588, 561842804, 280706209, 888824762, 571444031, 118978453, 361511485, 84111865, 68561408, 468179999, 54856255, 312264400, 485559343, 990498537, 573771690, 7380797, 465874700, 831057446, 833855776, 976303335, 410790170, 794417412, 30309244, 724062315, 535534333, 13825317, 708095964, 563186258, 575751324, 88659204, 570224908, 936430834, 428314263, 517072564, 144719469, 207620055, 89090297, 123172051, 246649418, 313247487, 50653783, 389525080, 606695262, 139180865, 791014620, 98800767, 225706089, 474891091, 272061355, 982221241, 264081171, 783986773, 605027676, 2037658, 456025639, 188866822, 577412603, 709481575, 906020091, 385160692, 520880144, 477007529, 713910587, 215779598, 947505057, 623667427, 539370933, 5887740, 338648206, 889515457, 210052940, 337271459, 492539657, 775447275, 258854243, 59320490, 32864246, 330429121, 230393408, 320690893, 712936718, 490268371, 716946790, 34853818, 989665560, 381942677, 390827044, 120655055, 14878308, 931143755, 707688627, 484537549, 336981071, 372702647, 307249779, 286913718, 602347807, 845380343, 339962744, 335410273, 728762422, 386243460, 86616151, 763416696, 37995814, 706912336, 204786753, 703118517, 733842982, 102064530, 421708459, 423215617, 786012432, 659106982, 197762164, 586133640, 182766242, 414255763, 853919876, 607563935, 274441398, 431706924, 948155671, 438672867, 112102398, 489843865, 805388270, 943919400, 676450328, 502138590, 949234366, 738433452, 125912926, 669956556, 580764586, 830909005, 32047590, 126279355, 20173795, 326005568, 312783071, 699161436, 29668566, 932578891, 95127557, 532456724, 33821422, 733526651, 659557213, 719903616, 577135368, 992300634, 825319486, 243483137, 161612415, 542761058, 600688201, 821169460, 750389158, 639428713, 933337371, 477980782, 103525569, 424285947, 438734248, 6926145, 360531635, 963704247, 495629122, 326498723, 98704114, 641040728, 583800219, 529374894, 338009668, 607898688, 690239095, 467373171, 565748408, 508581794, 104004208, 611356294, 492522573, 571991848, 330276882, 820607273, 406901449, 27026921, 72026978, 42575789, 424167809, 692172166, 45989833, 202292082, 244946442, 798903942, 350157572, 704702380, 542367696, 239245048, 740218803, 702153333, 654729934, 590644421, 477646747, 774963474, 171928079, 182263126, 899082969, 200216092, 66591328, 228018176, 971717524, 892778089, 941025232, 588301154, 749178269, 190384691, 939797602, 215413803, 729757371, 539939207, 874246145, 99940735, 589834264, 127003758, 604003463, 687786912, 470411564, 516255853, 151922752, 170342345, 536029307, 103141260, 897057543, 618078411, 961134150, 626297176, 864026601, 122235127, 864281887, 246190388, 119026724, 454806457, 426445263, 376626842, 424763942, 832579295, 104969722, 319753592, 463396086, 209473300, 399848667, 392678257, 130290489, 865207460, 995016827, 238662745, 505399092, 854885111, 917711307, 290810218, 333128810, 775457734, 68199925, 809376247, 584641751, 149665281, 106322322, 218666913, 603080354, 308960736, 664415794, 524139908, 54011496, 181227101, 146051533, 377409482, 929974878, 315416041, 742149657, 472850729, 724146592, 4069474, 384835628, 958157043, 243018917, 217339795, 462493596, 227207349, 470366475, 216927029, 612792118, 696822870, 286535015, 379321958, 697084188, 111786881, 697034613, 177292358, 520147593, 774854596, 484224215, 726925670, 9663076, 644106563, 232558925, 842456210, 581737514, 664820030, 64955720, 25187863, 972122633, 703608390, 768790332, 917849821, 668711465, 325785651, 554940589, 508206655, 434314252, 566142271, 235786214, 646523534, 284861768, 216938190, 482143183, 530723615, 121102850, 510862018, 619063055, 152612429, 400992343, 715168361, 21420388, 954508484, 441737268, 914601800, 848481401, 29512204, 237077516, 812176279, 617436967, 17148674, 795061897, 783372985, 744604996, 640875640, 642607308, 240720895, 664439405, 459958097, 882861256, 969682106, 1041110, 294502005, 104019065, 750497523, 326261811, 497279544, 429127004, 116218301, 427546791, 39371276, 563770458, 633158070, 240454904, 426535061, 142931246, 803566787, 438968818, 626305691, 610167101, 247931646, 783132143, 267786804, 310269445, 299503970, 240584484, 19251120, 122873403, 847906459, 479675994, 590005384, 861192002, 713406552, 399973375, 650503573, 492072339, 453097714, 343568410, 176915843, 843260706, 76481650, 874339931, 273525077, 740311713, 790007713, 12828243, 543768292, 966181957, 458267190, 222354140, 517539966, 732750707, 101285585, 991903262, 883044219, 923424978, 758704734, 303299326, 880493110, 726476247, 130884340, 822617207, 257743544, 488694065, 402854095, 646491741, 388543583, 908485137, 630452574, 489599101, 3329733, 531974387, 646016151, 172588460, 807780312, 894946014, 166604796, 421467004, 424913942, 468657129, 659912372, 891342294, 115067278, 733143267, 416911313, 475149635, 318802055, 630579525, 336671387, 514273039, 481196171, 86503806, 970560964, 340515401, 767226785, 502153153, 193936581, 201055442, 168490135, 246266108, 875951851, 239849016, 627180264, 376452873, 169133948, 730304238, 798078203, 308243395, 28833340, 776780904, 173271564, 268399529, 971908598, 669028328, 923933284, 984638135, 544318920, 969235847, 985350671, 871805843, 608112434, 635999229, 71233299, 163628489, 790077940, 303885048, 285543342, 791873161, 556869555, 617665929, 35978256, 371159340, 781355582, 75184511, 74124918, 795459560, 743071538, 730527988, 426645649, 669622687, 131053022, 940374729, 608213734, 584290918, 804077245, 101801290, 639124065, 95177239, 907534813, 969589131, 904474614, 727318292, 429680838, 131862055, 403892484, 95025006, 664990765, 774537203, 236511829, 930284161, 26412125, 527074125, 957656648, 165375261, 317176188, 35608369, 765514758, 221580740, 268343360, 43049430, 246794102, 790026416, 432629815, 405518431, 546639128, 958466114, 1224519, 449744535, 154228077, 849647196, 871723078, 274375807, 459494039, 700260242, 811994779, 59974173, 49533976, 552173452, 534958548, 9642348, 14689194, 658778132, 962253151, 948734021, 263594259, 175597386, 665523264, 913950597, 535168479, 109310141, 682102550, 496750925, 437505093, 793979106, 363974542, 622466060, 914615275, 289149487, 654696747, 104219466, 713633098, 752798359, 420574748, 968712055, 428378580, 544690796, 114494616, 841317597, 997051278, 660125030, 641982395, 915539437, 982522763, 382522604, 761092933, 995114653, 33661045, 833711631, 139095696, 912604534, 399496525, 322106659, 802099363, 91161701, 689526662, 677466743, 201144838, 38888587, 218679150, 275895668, 789697268, 73964685, 719248025, 845129194, 213650091, 853230614, 17848654, 405239025, 669780196, 738281577, 871129751, 801955460, 493891882, 556622522, 277980119, 859930371, 246312235, 145671882, 2760359, 338266508, 529423306, 919622621, 640148610, 476596359, 727227125, 917120679, 153349590, 971968687, 188686150, 706059966, 227540414, 632444448, 906677793, 759394570, 611088365, 383381825, 792717758, 112989233, 876603170, 212012733, 38674523, 50618272, 107065135, 9809756, 561652526, 89276651, 501960910, 485938360, 118490142, 343448965, 262874247, 579404098, 523331099, 263956982, 21356431, 908053659, 241169005, 551609402, 585573815, 938047659, 248642460, 780384704, 782578863, 89998899, 373043726, 309918543, 124767386, 725961158, 292990942, 451027146, 49336189, 795257616, 897901033, 596093100, 8799285, 373549856, 470600574, 557622606, 445608741, 748186358, 709310588, 174114332, 794428362, 402914045, 562879464, 361461882, 969597482, 87824811, 973309070, 581098411, 458884208, 232142142, 866552586, 499965710, 815637061, 870247820, 212912908, 494341386, 520228467, 968098791, 649503021, 853404031, 888039695, 431678117, 264647970, 739524864, 580063295, 448436203, 808125858, 339232972, 479008640, 523252839, 66343961, 748266357, 823129001, 203503764, 164647317, 709655481, 879495898, 71897531, 683719130, 200262217, 709560476, 447932180, 71258827, 510481117, 984798971, 372646481, 803769258, 63873935, 835351283, 652821569, 370299891, 567141940, 575721889, 529834701, 654144879, 742477128, 33033002, 328474472, 946472835, 474601462, 396443844, 187508512, 302959168, 454682202, 108416999, 210995667, 345772426, 18530, 785850992, 304179583, 867807524, 26030144, 548108230, 671583330, 141692761, 433896818, 921247110, 427262089, 138384103, 637642559, 117652175, 691162714, 744326440, 51291310, 738593511, 340003318, 913315437, 362667547, 973902457, 40416056, 538923898, 412701392, 211467713, 621862357, 69780778, 11561777, 122964644, 731589915, 688461315, 843853336, 482923125, 687362842, 675090143, 535284330, 385627701, 27435112, 510194139, 109022170, 191475894, 776305335, 257557364, 754493549, 204315940, 914452646, 937256995, 689920944, 6737433, 64013845, 682185352, 126435125, 413944807, 769101546, 730574205, 278936328, 245985776, 735242291, 471281894, 377478094, 923633723, 656864070, 197309208, 854282555, 178906898, 44354890, 978153547, 895150756, 358262357, 821312006, 543692462, 202426756, 4068491, 686291232, 933326284, 850003477, 579305903, 887373674, 371299766, 235448960, 15827580, 553953310, 716958766, 129661688, 425790419, 29274240, 459436972, 389988888, 691398376, 91242044, 318264137, 667432377, 532444739, 295644700, 715929976, 677880978, 684923789, 903601901, 632822545, 111342669, 17281100, 234616115, 902296951, 11773578, 850047545, 74016447, 976097070, 305954532, 396889216, 473913408, 927619908, 128416671, 692720612, 312081227, 575407376, 586020036, 387329985, 923292561, 873507710, 558051539, 991332940, 847979528, 277471983, 214413452, 186959309, 836085993, 494050885, 222324401, 490820866, 741967530, 181747791, 831221194, 570582098, 7834774, 282261634, 813780387, 325132777, 760568825, 663432201, 610585797, 551842712, 441270691, 276702801, 260369435, 960112125, 431076591, 914008744, 344046373, 813076422, 904777167, 306631102, 433951257, 526955999, 134234032, 578209458, 791462894, 150309691, 608231982, 715233401, 546173386, 854446659, 45131623, 55474879, 630759598, 569232297, 830886429, 357873870, 626396635, 552454862, 135396739, 749543237, 913161262, 650008438, 618420119, 252964239, 912822316, 942572899, 336171083, 44013765, 195672031, 411379071, 320229284, 807807445, 956810224, 439045094, 826660034, 873935898, 942422885, 989638329, 382224448, 973957100, 193144046, 308579055, 778454605, 30185344, 891253374, 633020507, 555224969, 11751931, 409082939, 496898354, 829131134, 543942755, 673369477, 43456787, 265702015, 346121778, 991907567, 297376080, 285606561, 362674112, 728869982, 416296242, 378578381, 747941958, 445397937, 598981611, 53858628, 923870535, 693788211, 59628075, 587519445, 344081797, 484790213, 670759738, 812177811, 420954668, 468741329, 72184602, 872935609, 446397518, 426373831, 188423341, 648607780, 809064859, 720702955, 195522094, 998091310, 389779524, 62872621, 148280141, 962811157, 682843964, 273115497, 771313540, 810160007, 339650335, 734526828, 816439707, 800626946, 492946773, 692162695, 194734261, 448261492, 154440413, 34877827, 714509902, 692404240, 143809815, 659608663, 975740375, 330382980, 266689048, 681327361, 183167710, 15163623, 84879639, 30300282, 213092586, 941746381, 292944780, 722948879, 365046046, 497963476, 938270941, 884888328, 102023798, 665806562, 244141356, 730905539, 21429494, 149539502, 799598716, 939473505, 405038412, 151264333, 507304284, 846634656, 177921214, 697582735, 957059048, 616759522, 225366405, 226544194, 690898749, 773541355, 949689448, 246496967, 26165654, 240966021, 131120701, 497329495, 441314721, 742836165, 143273679, 462242018, 391712814, 905004277, 72413102, 171211620, 472980093, 348331437, 273739821, 25471443, 814300142, 550112551, 637968743, 759498564, 268464335, 871710375, 444362830, 216546629, 41536679, 309233986, 843043364, 521629017, 619518810, 152842849, 453802898, 918266798, 680798416, 886500264, 986003967, 914146409, 767189794, 437198686, 449630253, 755455079, 12608140, 514823554, 628782663, 945165626, 20322293, 934894228, 37694312, 667302673, 321952330, 719166253, 535040009, 766428312, 622686085, 417438496, 934600895, 107317433, 767305543, 460698161, 141421058, 686274852, 94364026, 243304861, 630387641, 349230283, 301831118, 746266973, 524773717, 598336821, 678506650, 893132164, 715807911, 723670143, 636267817, 830804461, 629320577, 319533453, 660231974, 72445243, 585477089, 714455425, 778731396, 723538295, 46801922, 346732203, 760475675, 741988352, 254472226, 347518104, 805996375, 320757954, 124416511, 666393032, 869212063, 920390550, 657525090, 320807995, 870580008, 635789426, 275427124, 627754166, 229157998, 986399292, 325501064, 664664483, 962506971, 67667832, 953353815, 704286447, 78225407, 228466835, 111614475, 529954375, 461945273, 938634153, 130758656, 106090233, 359555182, 290019857, 7118360, 115268612, 146611521, 710659818, 216368865, 604243769, 290124988, 748907808, 633864624, 950563636, 480904183, 864819786, 452523723, 314417081, 45802299, 846249953, 279435834, 891657388, 771589753, 156074307, 97994903, 990522950, 949049264, 786506379, 461590823, 583695749, 660085767, 266145883, 799439632, 753936226, 761837402, 209793883, 568970625, 751593656, 442019380, 866759641, 35370487, 687108159, 659451903, 829004736, 510530019, 513966581, 426465897, 768052991, 265588445, 960118443, 182979137, 865695839, 769197308, 6698224, 134045066, 612624014, 800485719, 410183158, 224717708, 584792004, 399761207, 107394371, 707471401, 516761457, 797083468, 320200602, 446100269, 310851243, 117438379, 327054190, 92551586, 238489200, 659389781, 102070513, 809498413, 354957601, 73482125, 684464902, 792060356, 802146472, 776084742, 970212790, 613557524, 23800378, 761304309, 426185196, 731863745, 669601226, 259624033, 467990132, 582180845, 169334460, 456351287, 469677472, 735801020, 893430061, 735567602, 454777473, 822554304, 209478137, 547618566, 710414994, 907468164, 914351712, 453719207, 492254269, 845692446, 921494596, 695999504, 371575017, 107677965, 723254840, 96016651, 886612151, 88155040, 386403127, 224887504, 345246953, 679896526, 493227493, 375781330, 252286705, 353476212, 24072328, 717510008, 167870832, 711532329, 912645685, 790436901, 49251933, 244802225, 553837769, 396248463, 988693721, 826555734, 294628268, 359853149, 906963495, 462808565, 808105917, 711194784, 238459595, 404022825, 498736484, 77150571, 501446385, 410711980, 15666521, 784071146, 923279399, 142219943, 187675238, 995263802, 724934600, 186559374, 419534035, 993962218, 151288661, 506414217, 461406420, 983737408, 795731812, 446307306, 456755758, 776774760, 258809651, 655261129, 511707359, 709393760, 501771234, 920960993, 972063174, 441003547, 441259713, 303189217, 862305340, 851780536, 564270933, 259922972, 995192208, 222609704, 983231898, 849844276, 381827129, 457124976, 670343401, 371053360, 300469439, 906462218, 324614046, 707035575, 728533561, 993367762, 952627445, 493885004, 236302601, 542158971, 672520601, 239535576, 924599098, 712165988, 19904829, 779009421, 592230632, 75621032, 698772352, 675137089, 281104422, 593505130, 553222477, 693517828, 562541228, 636658101, 155385232, 202489571, 802032030, 825629512, 22770446, 956073582, 453484487, 662332670, 677120842, 406464662, 830423373, 224813876, 91581784, 206750700, 857654161, 587193262, 255451784, 631127207, 525274464, 436206540, 675185694, 940559808, 122248145, 839396724, 423452018, 816207938, 508781250, 501306791, 241721766, 335352317, 798323585, 948033537, 380023077, 361641007, 759562345, 85860715, 669035865, 936721428, 843430896, 492439242, 151332828, 692403587, 475895699, 144316118, 615172888, 964828528, 981162419, 155953107, 640990229, 252125784, 434566464, 41208, 208257012, 368262766, 119735506, 170326811, 945257471, 653295170, 530271361, 158485036, 479736043, 230558349, 696661492, 327113456, 856201321, 365462381, 642308072, 310844230, 902219575, 533883045, 825269425, 970209391, 904827206, 170505947, 826326392, 165648655, 759295674, 381985998, 405551915, 413412411, 354319774, 406424717, 765591343, 87361676, 191442811, 566985870, 599379174, 699818537, 792890162, 926729437, 390787060, 943324225, 321688943, 222464251, 849966653, 358616602, 300180004, 146404252, 585823725, 833141262, 384446139, 758668549, 548779898, 733478665, 238792449, 853830083, 747236690, 727265465, 173332144, 672063546, 263079998, 650172553, 408265386, 477370522, 575439930, 817211519, 568054768, 50296442, 800291334, 778156720, 478298589, 983885625, 298142198, 594603575, 984465297, 131871731, 395658777, 371042257, 196021060, 702809493, 612679277, 124525885, 880295826, 942867659, 257206532, 431596684, 310678305, 55820918, 499826474, 924217554, 188303625, 66941551, 48024791, 757293206, 884362573, 763583330, 76952731, 932384288, 687865716, 342914587, 566998189, 194234968, 819464960, 624638274, 434149214, 629548295, 195179873, 336147091, 875298312, 522822282, 765652649, 165817972, 261369096, 821572905, 255455080, 919397936, 998222869, 64009685, 690442151, 274594360, 464833183, 924117063, 785861752, 606383875, 526799706, 750738274, 64734303, 660446530, 911496541, 343207487, 53372924, 531990213, 167644201, 822547601, 95925630, 935056668, 294684512, 2014076, 487947565, 894842981, 199512249, 761351689, 790080031, 624264178, 357049255, 651837911, 321565208, 737930238, 283760668, 438167273, 53821186, 151388569, 19281245, 259880443, 698738001, 128082774, 528230055, 915764212, 940967532, 15467067, 508777482, 169881826, 446796509, 747880287, 771912194, 225667153, 150947440, 803647616, 926274980, 947570537, 282456874, 539793179, 983509086, 237166421, 423796729, 974989696, 418083957, 916860747, 900353239, 849147823, 134308620, 524090653, 973803066, 313743598, 287961126, 882172525, 966472549, 191812564, 911421106, 9182341, 182665949, 978712379, 270347791, 123927931, 916251546, 352354411, 679110414, 32269220, 174629530, 812615352, 502987963, 655501762, 272586310, 609847208, 220307215, 256756638, 491755466, 218901137, 494127186, 478072283, 340309886, 328405333, 1721409, 733051022, 730888251, 430690086, 588158130, 532447087, 168600586, 700467392, 211568746, 477904411, 186322663, 157594888, 319195650, 247774201, 459245013, 801912639, 657319964, 154541367, 684307562, 285363049, 114632570, 808660253, 829767445, 386752080, 845382293, 786950355, 123250178, 386190423, 248663679, 7502367, 866062730, 724109242, 206693615, 710119971, 203839263, 437187843, 568477655, 577778950, 371061179, 969826943, 477174139, 885346561, 693242177, 27940704, 297788164, 777018398, 758850100, 772118518, 714170271, 980141324, 993711552, 502541776, 804685129, 219005263, 147412345, 275845066, 381218617, 627034906, 676400799, 142393313, 458263576, 513961566, 702957691, 623755860, 597560943, 264968446, 780772263, 897101980, 305733343, 947121642, 519014089, 132298262, 234427186, 465129906, 80697380, 125137122, 409596118, 795173708, 10159429, 592259352, 250782314, 262861592, 879980219, 411906290, 197864355, 790711551, 103240508, 531769957, 266411307, 555881530, 485504602, 643587857, 784689434, 708227514, 437725146, 223705858, 578413381, 832222277, 3590010, 833564763, 651561399, 40828987, 743424363, 390872585, 120699116, 132288653, 740641798, 396686724, 537605102, 910727286, 507185962, 69808549, 601007416, 371230624, 919230906, 427865538, 20058406, 949651307, 692572003, 484084568, 418578672, 670916501, 715928211, 875705820, 412924028, 682069186, 305025353, 218611140, 818025664, 637553549, 927265640, 770547940, 743217817, 976584433, 289841517, 259001051, 193512255, 60863413, 74403401, 71768057, 560492314, 575897418, 598398537, 121985796, 427202751, 292340773, 586253271, 595367030, 675333227, 412615822, 697838879, 267009210, 976915107, 703703869, 746039381, 588394451, 586438786, 587095576, 743019174, 739525583, 569367526, 961465718, 617707860, 721387237, 859587243, 294674429, 978838739, 815232172, 908957551, 48435937, 490276527, 488954513, 16334137, 404381486, 516974497, 262984130, 570258063, 702655850, 845095254, 101730750, 797766044, 15418439, 20053048, 443543052, 384705673, 816956976, 245865730, 150450230, 644928474, 952216396, 718684488, 245833027, 532812325, 759061790, 782864593, 29828916, 397961322, 192331712, 514736308, 79053561, 208159277, 364524261, 818905745, 245290022, 586158306, 354945631, 767901929, 372801794, 240797753, 823584113, 780569380, 24221015, 123940170, 24066195, 634851166, 882855184, 869720813, 138509827, 89630215, 505660674, 161497280, 853000282, 990313786, 226584503, 668288692, 865415906, 903997264, 168819338, 645838717, 495501645, 337009086, 601543864, 585883412, 198568432, 795277670, 828749217, 822897388, 484899687, 385128589, 20597312, 810875371, 924072897, 788193121, 771221952, 378137426, 262355090, 512597709, 491786895, 865795898, 123245254, 945015574, 748708721, 833840285, 733175823, 636313025, 946124219, 276581415, 222936765, 90772088, 133156059, 906808125, 989360636, 124120096, 687865771, 623084039, 908754491, 636252375, 154379776, 235870942, 113298499, 764616288, 531856900, 181705984, 766853598, 363398708, 386064569, 820144844, 759349461, 789187532, 207962824, 578181441, 808282780, 544029, 990674329, 972404901, 180375233, 675845056, 944051786, 783009508, 27713117, 503674239, 981679974, 857304622, 128703190, 538565041, 135162812, 432099058, 498571915, 3613153, 160602111, 525888673, 409156487, 863358494, 696879590, 858580319, 384614553, 417177328, 988281380, 384480837, 785330362, 847090444, 94548574, 88497166, 309676188, 527956950, 318429933, 273604993, 409326523, 128756121, 621560366, 402788437, 182578371, 767486669, 14334543, 845304265, 483332688, 89558508, 447567948, 883954828, 764713441, 430716377, 979434368, 107469583, 945907257, 823548547, 509994814, 557518841, 23505951, 853762432, 501306881, 784521251, 964710226, 255344554, 936937437, 877099497, 159181937, 792246262, 943344879, 410324030, 253433519, 305994141, 203087257, 76203011, 730971626, 596437195, 672721078, 459903133, 686346829, 171728115, 291693189, 871637461, 656000833, 648257181, 348345083, 626102442, 145840902, 808919873, 918851118, 471232152, 33648290, 11117648, 467147946, 705252798, 860943446, 402402614, 205792208, 481284719, 947527108, 571748062, 359346893, 440694725, 495342601, 763317, 999970905, 47316993, 259479154, 310383749, 2614749, 405177021, 954088084, 287993400, 974114495, 645132366, 296881558, 81226610, 467458362, 998707197, 628089666, 432246386, 613072626, 600616638, 352112257, 882608647, 750042171, 477712168, 71066117, 333752131, 623132623, 938396877, 395482909, 274263202, 92709376, 444753459, 760275314, 369882062, 836904646, 200034881, 382069729, 1339011, 892642009, 219197411, 485855732, 532355823, 921332046, 73145160, 500622283, 542139908, 907044013, 235055240, 269122369, 654933099, 762507892, 639009667, 857721171, 256944360, 786189937, 950857859, 783153104, 236366558, 447250044, 42969322, 667958178, 43678936, 672022317, 159236155, 673721653, 642053157, 673308646, 342781656, 379562041, 190210348, 216501393, 156549892, 489187100, 479776456, 826661007, 993972198, 83420795, 689512710, 91984550, 879953974, 940285483, 535720215, 90012165, 870998279, 221461658, 571899042, 782705803, 395732308, 600889524, 163107488, 719417032, 301766533, 136714439, 626818680, 146188293, 737655309, 535336384, 699883643, 571004842, 442561098, 66622859, 577302144, 179641424, 370658131, 874622822, 196614929, 540610274, 804302832, 342671762, 490459640, 852423478, 652601438, 684534197, 826180268, 563577345, 178653127, 730240304, 814086179, 710226292, 539247600, 582170047, 743155371, 93336962, 637560496, 74970128, 912914162, 320276811, 818646054, 109064922, 118021191, 417390296, 833350512, 81000122, 138678701, 125296963, 527308416, 503960614, 872128289, 434999983, 741177609, 306761722, 299933362, 896990400, 688256524, 939490918, 370970534, 74987849, 418654776, 151414302, 58737292, 175850471, 552910856, 239514478, 37608235, 256379260, 524774304, 259431203, 908892702, 73540743, 394615419, 553805548, 131181460, 640587823, 3280255, 300426273, 53287970, 379645508, 104037596, 226292597, 142215165, 18177047, 365386258, 883161212, 695726706, 435989910, 541676153, 133106736, 437821190, 941429437, 191226311, 770001143, 893446285, 723584780, 518799868, 890417084, 492442448, 676649415, 617837044, 720422729, 967066013, 635687241, 476722095, 302644944, 517199064, 531502671, 171336383, 317808730, 982505432, 243958544, 517497276, 442563122, 60288944, 829989935, 178122632, 299758368, 589256734, 317856139, 798394197, 493161381, 789720144, 368207551, 443334103, 634888510, 566298172, 966893646, 878202940, 116742313, 586224421, 456975028, 655133109, 875837831, 943450759, 432722450, 949929896, 22809585, 345535422, 877997905, 84392429, 829534352, 419078682, 16130188, 633848084, 592194232, 74549498, 162835520, 707309972, 599993839, 439812711, 331533101, 744949085, 953781712, 112281792, 385321287, 609744553, 417324866, 680430668, 482250125, 423442453, 436836708, 428811245, 795459160, 415625308, 254966673, 763765832, 250770072, 283697896, 67055866, 709960413, 636041160, 106325397, 542036276, 270856991, 534148067, 786982805, 341241497, 548019852, 455558316, 258703519, 120047702, 748893318, 540561376, 196705973, 393816768, 587900699, 332152945, 299373226, 205343701, 109056179, 562081492, 820336901, 739593124, 237380282, 865842745, 461980972, 905760734, 18176931, 182722121, 998193127, 221640893, 416619339, 875996903, 632599598, 631777563, 828276908, 132092073, 929112446, 666121069, 29591440, 291962299, 595240017, 868241712, 911618396, 27610754, 378896710, 805543670, 556302163, 773076545, 361320003, 834278229, 922460587, 552502167, 913678600, 573508110, 880112351, 306587061, 299825927, 387799288, 972819263, 355924460, 160679437, 338629221, 948864152, 249574029, 260078053, 912025260, 801342176, 313981722, 334487789, 777825427, 417112472, 904845780, 548812815, 231225515, 175599998, 606050547, 271842704, 256338360, 383277686, 209424710, 79717531, 428730702, 167505148, 499776045, 506392691, 942275566, 851990446, 592150794, 120647803, 541355601, 179959363, 428201896, 860389174, 913773592, 667562188, 775674639, 713194717, 539884840, 551545393, 846812900, 301481926, 466566272, 30983847, 22497175, 281328146, 427823150, 306393346, 138064898, 132328122, 872727382, 296873879, 840248455, 583891876, 98007726, 896739779, 684673317, 921466433, 51930907, 656978241, 563817505, 365263146, 209066144, 688173301, 238994998, 392936093, 939340441, 138228808, 475795679, 256144685, 97074599, 283102157, 620124631, 919037051, 364531005, 895470346, 380501523, 262553684, 871153019, 856634157, 687020331, 260301249, 596639347, 191796068, 903666544, 592301751, 730253286, 405688107, 131303707, 265371305, 870765344, 885634125, 528164591, 125044444, 770491765, 691069972, 861422429, 274959747, 97467612, 209664783, 87469639, 568483998, 399886272, 774124230, 7402395, 522380953, 723833103, 765485262, 738143863, 934130000, 719358437, 201868466, 94175836, 33280008, 525861099, 917129445, 682507720, 874538658, 329332893, 414061206, 998322968, 719757557, 89608350, 519353357, 2438775, 714730136, 585630052, 839964852, 859031685, 345440991, 268937925, 347790884, 539742803, 90378112, 905333323, 112808374, 160372956, 732637085, 925485361, 17554188, 892218777, 700611455, 126198473, 492069340, 956735071, 581696824, 76343628, 41355909, 223892477, 311152834, 755597971, 683906554, 158401379, 359236295, 590839315, 579829413, 665260655, 381143813, 337089760, 535690344, 71443618, 890708502, 777193409, 75079290, 951692323, 913808382, 371303372, 929015072, 819880446, 525309845, 522919902, 650627055, 618913278, 595640824, 831675905, 520936262, 121940591, 403530007, 169627048, 516996233, 336658297, 121566947, 81158638, 451397124, 438394037, 515198028, 308991885, 526581597, 285976428, 722499595, 990562995, 260957679, 547532676, 273181803, 277585449, 390915714, 441414515, 167271202, 878615553, 125559476, 934918189, 986472492, 301774233, 10147637, 589427777, 246117641, 922641736, 188111460, 594866547, 507137733, 282658381, 714402083, 992779665, 865297438, 263782200, 136765003, 857358745, 467315277, 791915235, 914021620, 649774619, 129989524, 313399052, 350366644, 957625434, 109198652, 697146913, 529585632, 551556163, 439285096, 788992882, 339562578, 446067266, 540257832, 900075252, 648919288, 979675, 99050974, 92316552, 823662016, 120259852, 266268638, 54533649, 610717688, 957462688, 994135779, 693886939, 654274304, 879909287, 70419785, 740354734, 955971891, 604807218, 487236389, 113804165, 383873480, 704744570, 772170397, 886763893, 891107339, 51966409, 409885139, 612379561, 439451049, 258709355, 503603491, 194400794, 176684150, 934068973, 979509350, 801406653, 96252281, 486151132, 743235438, 641061892, 186182917, 334371269, 976695648, 798336978, 738992985, 315856307, 406735901, 288544080, 102294547, 153503737, 680451224, 432466939, 929316689, 61338595, 576302307, 191954821, 154718279, 485348009, 779610991, 68560264, 961628006, 544932203, 982839804, 69166639, 403080748, 758893217, 162340705, 801246761, 620089935, 750190950, 812121405, 304044035, 847134930, 903158457, 217975862, 293166814, 369599641, 387541649, 996305205, 793507629, 185247582, 148679491, 175042220, 379287223, 46843022, 601112824, 479641619, 328123773, 153437019, 373098657, 996579472, 462819514, 144084750, 797934280, 619928713, 829570579, 262541280, 976062091, 640152247, 369694282, 616560178, 8661552, 773823288, 99029407, 100960418, 675235635, 658632969, 234276654, 85902731, 386132265, 10515082, 90400294, 331232494, 751543842, 996018483, 992502932, 645985657, 460038254, 958354199, 760304178, 133950543, 374744282, 975234435, 614484528, 844869056, 46799716, 97873244, 710410244, 1823501, 262186662, 426789474, 200697415, 419942391, 764426220, 394680723, 879725606, 414823002, 221377866, 252741772, 160521344, 525175804, 651056313, 497579885, 127206211, 651241892, 909767536, 636223755, 354019803, 223581633, 613546712, 807590128, 962910604, 910574829, 787639026, 626377269, 457110634, 95393473, 189804860, 627073885, 907317644, 500937225, 384631824, 417736363, 454419252, 786459171, 281494507, 183845443, 125638231, 84268046, 331754036, 543784004, 552656176, 681947313, 215789345, 107710495, 444453015, 404088473, 18961349, 68251596, 27433579, 621004466, 249607514, 949578703, 531645277, 358851110, 549779594, 146320109, 260793285, 293787765, 454250490, 703770469, 733142605, 850155243, 415913708, 204439698, 670220331, 904196249, 343906545, 353835519, 812559623, 703399928, 378510723, 175846482, 264458359, 343859218, 589266072, 311979176, 49985512, 691485588, 884960124, 102669113, 420459209, 694086603, 967829713, 817321280, 508290657, 490237437, 494804584, 777508193, 974934133, 138453003, 30871246, 988954610, 155488873, 340342167, 469736196, 700913232, 271996086, 803646618, 209547600, 418860615, 981668031, 262021827, 767685825, 29711545, 909555645, 98327846, 768007844, 944415769, 583774406, 410370400, 108669687, 682870703, 330001371, 9777291, 594614376, 924277801, 866512515, 191216570, 368652506, 811250658, 991816621, 246285881, 359450016, 277484985, 461597388, 288158553, 369779248, 168796420, 844162201, 533094771, 976153188, 974631967, 349279952, 724266392, 71275242, 448938264, 131854611, 557903168, 332585562, 744736085, 549213350, 44995043, 228115639, 183003467, 12540178, 13386973, 643638310, 437406258, 323733554, 275505142, 747478755, 387790968, 630292539, 291931333, 223414412, 407948125, 861671672, 128240506, 652178044, 142723904, 138731774, 818946780, 718918530, 995871553, 761721109, 580614582, 15475275, 904011435, 117159686, 737781709, 352004555, 317709116, 307604733, 901794874, 625687652, 604108030, 474550283, 574219070, 26000124, 339668666, 28598317, 174057876, 814743745, 937428282, 175302892, 396323834, 984284078, 619650090, 628616196, 762740181, 904999776, 190828436, 285089374, 334268811, 633344523, 936293994, 194518446, 739537681, 884626317, 678467420, 290880003, 980552277, 873647998, 441802860, 921357089, 106051165, 769225062, 720593594, 90327146, 347863691, 776751739, 328265804, 234480812, 900778832, 250337234, 896512928, 838018766, 275617058, 807363917, 562730231, 100924552, 660360541, 570030517, 410958897, 474123409, 858987471, 273792123, 215902709, 850567741, 784498750, 302333120, 260505006, 562278977, 700904102, 926931167, 95201818, 700603353, 818366118, 399195157, 652507070, 285503313, 249281792, 135629567, 539032522, 654521384, 22659508, 80994404, 275019891, 391068096, 129492637, 562233274, 77892890, 53991306, 97627690, 80568328, 934459310, 93968602, 718460568, 83792388, 195135093, 68337598, 517948190, 243313013, 663745235, 200187146, 347032767, 781028150, 632191449, 361057744, 204882503, 58906725, 632664747, 994345982, 399770098, 455811171, 713105687, 238326549, 27193718, 348515056, 905775576, 283592125, 656071480, 516497949, 384051485, 490455026, 815457144, 513998959, 187871127, 641125116, 869469847, 611369142, 181829803, 879362149, 360245930, 92955790, 256037492, 428731648, 694352869, 27349129, 95388340, 634958692, 860392823, 375596605, 489554499, 162658447, 194835205, 603110140, 509036167, 288951410, 669478005, 602872590, 538148510, 802140855, 342521038, 108638132, 134266289, 283458756, 401958045, 59204532, 762163933, 407247176, 828900659, 688383040, 766866456, 480689982, 602535929, 409185306, 204494620, 638727243, 385810848, 50184925, 427483588, 791250260, 996459379, 626905927, 605940571, 735399731, 669722422, 57335403, 741676278, 622284424, 12009942, 255926061, 177663380, 393189427, 489698198, 689498813, 800981532, 1633100, 832311126, 145498809, 892682411, 84060584, 62544690, 880123913, 678081939, 452850232, 342487049, 802665806, 718440092, 591153255, 146068641, 90906272, 582230239, 997676908, 179672997, 989104862, 657032328, 322485294, 753846567, 560129124, 919520481, 168648371, 803898470, 231392621, 137076288, 265972775, 634534326, 425230918, 414049259, 573206630, 65633376, 376156206, 695016625, 352792438, 618883515, 299862341, 592668425, 343897595, 59992272, 150725189, 277006459, 157971800, 501687746, 50860845, 667232318, 202831486, 749579413, 615258264, 868391363, 148307136, 586418307, 248185652, 328860308, 537502098, 988400535, 578305945, 469437792, 203337568, 143954932, 720996915, 822578504, 169237780, 495210124, 687426281, 806211530, 675054457, 1325788, 251066951, 531650468, 951846456, 965844289, 577945744, 520452286, 789920681, 793770764, 877886389, 58506764, 888297957, 253036905, 884694840, 711370512, 747884494, 398276390, 264462767, 563574369, 624254108, 295170446, 914344260, 354529951, 602679037, 80493845, 962584056, 997567651, 670193886, 431989859, 58976161, 561009926, 891360166, 917209651, 261989749, 816793459, 182432542, 835337502, 609893912, 569675502, 228888945, 980929340, 339916993, 620921350, 298417421, 28913936, 488457280, 610148153, 198421861, 265613517, 342943607, 416376202, 684692386, 835118746, 654283556, 27847985, 715688380, 277847428, 740899616, 533341514, 845585146, 147552215, 666541803, 488029037, 294882354, 457459760, 237537321, 23364300, 478424722, 996416516, 603199560, 534435288, 459513488, 730046613, 138650838, 93925958, 650794759, 137307680, 617345994, 115769516, 990487410, 587477145, 678079223, 510784925, 468212879, 736017817, 144176749, 11023210, 199983607, 204345067, 926629333, 391336356, 286101531, 766159038, 434455992, 14645992, 420859288, 735638993, 199706613, 120779761, 838863347, 47941544, 883024490, 23007635, 129352391, 225712377, 196348169, 359846854, 663652486, 592730189, 654895595, 135757043, 375982966, 382095780, 831054004, 340484329, 254035210, 348763001, 615837008, 408152096, 173431920, 174300753, 291097204, 572768634, 171204177, 365677254, 728856295, 16085352, 435174045, 374169643, 407792554, 865106997, 889341068, 112191846, 493374417, 435632918, 706037568, 597627440, 919325546, 261029316, 99068256, 554696404, 585089387, 530637850, 328730890, 608428135, 879500778, 59347565, 478390832, 596879473, 114067695, 143616647, 956566891, 654761510, 297660125, 648430276, 425291906, 711345700, 27467826, 197517954, 7454877, 431079328, 446382034, 549341588, 166795735, 585125120, 282832758, 643799474, 591740366, 850784568, 300229605, 165384544, 890574460, 54962319, 381530678, 827215681, 553941864, 135655110, 345260263, 584765925, 769120736, 639492103, 23178835, 531973975, 342206219, 991725437, 933178247, 80202947, 275706691, 885616805, 974990988, 414364193, 983181449, 835594399, 545784206, 873488445, 269749725, 202168130, 244073821, 54052175, 596813819, 666259366, 14814908, 299847373, 977078132, 805770400, 961583975, 151260573, 242183890, 641568163, 316646148, 200956276, 559615583, 444947409, 617771447, 997709265, 483446303, 785368763, 389983572, 592559766, 185587020, 197787381, 136640392, 407696567, 717815347, 751939739, 969881409, 908086209, 247765957, 687843272, 645161970, 602147057, 998885575, 605608010, 281141113, 453027552, 652210229, 444223518, 731671555, 952470718, 682631867, 325714128, 640168265, 870545777, 79732432, 42598325, 238870402, 225261791, 685876051, 626379578, 865531297, 610553815, 737291188, 896400545, 806647967, 459228580, 808044131, 982618818, 983491719, 294655329, 662374890, 193690091, 961002515, 595649856, 784713510, 870031545, 211338069, 680367005, 609394098, 104443280, 56727519, 104131874, 859133107, 612617153, 287944297, 480591359, 535887872, 957025109, 5782070, 402969122, 934137447, 106686665, 220293290, 531990253, 127363969, 366418088, 306237584, 763856769, 887225705, 180051123, 675661326, 687333451, 149289179, 991646023, 12981229, 392694435, 807362337, 942631753, 163188739, 681662157, 931331127, 685864179, 226999431, 436705771, 776592741, 889305765, 432463107, 477197791, 225987802, 833727179, 140859799, 241628560, 699040433, 752447978, 782902969, 800417771, 77445157, 987484475, 572030691, 331030155, 49163460, 360150823, 928096949, 591269191, 498682963, 619974993, 54370706, 659499447, 143019474, 53164629, 848049792, 982761765, 330366248, 974409080, 2014390, 830675311, 416936279, 82423508, 495310893, 439268416, 875502167, 431863102, 410509156, 864534005, 667013272, 922185482, 47828278, 668019743, 832135725, 93247691, 836590390, 659356925, 151544049, 872024175, 387636725, 402359993, 107280435, 675851455, 662694535, 538327177, 399202128, 717474376, 698408909, 480517578, 641905385, 696068596, 39827464, 674322032, 165965019, 705032536, 703329039, 50597325, 998655910, 725568935, 177686053, 228743896, 205798512, 266040967, 152866703, 848085639, 495749691, 689458381, 641696345, 480710529, 388294365, 855835834, 396635888, 138449892, 328037989, 937588874, 614868665, 714977376, 799397950, 641056709, 350215657, 155611947, 690600809, 498788505, 277232405, 111450443, 907112150, 596979434, 710811201, 475896288, 49155824, 808232198, 347323026, 41904446, 577040839, 772389056, 492117337, 440274093, 418126449, 627106455, 719380780, 221617386, 20957139, 208130128, 269037179, 268820134, 115308599, 392828869, 342765237, 666807417, 679768322, 804470931, 49800093, 439178894, 3958132, 908234765, 808749973, 410124080, 911071049, 819925436, 576898336, 653032054, 682665098, 457118072, 488749549, 550773536, 675439525, 602202280, 641373619, 71623983, 347940531, 643094785, 359258159, 943053484, 16791655, 471912400, 258678864, 719758911, 939513395, 479455502, 617838209, 139760928, 481059140, 181702797, 588653254, 195758456, 172932151, 782612068, 512606023, 383280466, 597912937, 54095521, 909621266, 323462931, 485707432, 434580767, 962385258, 43349614, 704934773, 187323758, 614434849, 276224474, 709880313, 373482855, 708774826, 686289041, 292641205, 388419905, 589592021, 169534998, 769266226, 307348767, 332675970, 761275401, 373239712, 629633977, 749513824, 283218915, 814146290, 119516826, 311097616, 57829146, 535192693, 90118768, 276076238, 978643948, 390151584, 376221942, 237623168, 422670617, 466686437, 270144963, 787234830, 895831236, 735183046, 55588311, 494778076, 30488448, 232232094, 373454363, 847309083, 927690556, 656502489, 206825336, 115637797, 439727001, 338090842, 193624014, 588686781, 251018978, 196775094, 767684689, 194087414, 640446967, 515391657, 633024526, 906502002, 584425313, 464048470, 674262495, 965444937, 146779725, 505691408, 886049965, 942402409, 503763684, 11047358, 60148457, 257344699, 994029236, 694306543, 673813311, 507606339, 660275975, 597011, 987553027, 494997519, 826893498, 688387262, 318882712, 948561780, 398762702, 275660209, 175507024, 99176830, 890120818, 683443847, 926931156, 866016109, 47856386, 670249228, 38177563, 28378691, 843650206, 373412461, 46477341, 10683591, 728621833, 819605360, 212015278, 653773738, 771741517, 925941674, 225485183, 502527001, 383022051, 895256839, 885148289, 109614663, 213659062, 68739466, 632320877, 831481787, 748961592, 503100545, 191164071, 656991120, 626933992, 872594215, 258252063, 34736260, 895437413, 165900431, 45010267, 436876363, 141384026, 371368940, 86767922, 454486357, 980128724, 551041023, 26070791, 773870807, 451749938, 869203010, 697692556, 668261040, 260646467, 175368998, 408331443, 802324818, 267127611, 93235922, 173490773, 420424726, 868750768, 293459630, 459118334, 860827319, 262462517, 263724558, 173924339, 79524147, 864005594, 303461317, 846579157, 749800546, 381688841, 934118861, 566915523, 3459775, 580858151, 681837831, 935057178, 48874594, 879026881, 289021892, 700566727, 962339255, 89485660, 913197721, 953728449, 710621448, 342983147, 860715308, 919909291, 187982098, 25102128, 252914206, 384182479, 37863525, 594573802, 24062272, 930684594, 210142240, 994673024, 330780308, 523404834, 890656556, 482775947, 167354516, 951996445, 330829568, 74584382, 531381430, 154774757, 374629668, 136946811, 796803618, 132439326, 768918122, 40721036, 188894777, 62988120, 352210465, 880704879, 692298254, 52963522, 540489945, 711558905, 340373110, 648915818, 201031, 341586655, 834452696, 723691312, 466590279, 927277598, 5981143, 399451386, 428749212, 481705027, 937715903, 213400383, 728336890, 159234685, 486414443, 377192079, 617956816, 130057700, 661397586, 804986150, 301747530, 675101516, 875021351, 574448768, 640817279, 270004710, 901553242, 250126827, 14651429, 696697975, 52663737, 184082934, 246308182, 457388541, 385206192, 639406179, 148881191, 787405456, 945237350, 277068846, 693733685, 434667618, 193915066, 479424364, 151704023, 14509783, 514040498, 384496404, 795970104, 360566647, 134548279, 601593073, 282923586, 837850710, 277939786, 126582376, 854770724, 124460020, 930396783, 191725927, 867288302, 306219818, 2039271, 688922134, 140833603, 71616132, 624661152, 357520266, 688304443, 811701828, 416339050, 263934480, 20594060, 79597971, 645262510, 999463806, 163611894, 172340982, 177228678, 932303957, 355736438, 697913565, 157326153, 938947582, 615846240, 384144909, 987742763, 538681286, 604920978, 379768582, 666650695, 670356493, 332237236, 943146146, 426442380, 300186137, 675397915, 660440966, 288090667, 691090353, 276266039, 496383916, 499757573, 166797993, 143798657, 731171546, 23821376, 830740007, 716356032, 824226870, 20077288, 426316098, 199706811, 774695599, 880485755, 876748798, 212820720, 66941216, 966326600, 931854359, 850632635, 148378966, 882512403, 955101491, 473979246, 885349799, 865270688, 890698809, 150751117, 835404900, 881420924, 71883471, 723380043, 509845732, 766980494, 948261037, 123750247, 994524797, 44434474, 637724565, 328311116, 949260078, 85729984, 634597551, 144565992, 623223987, 474496804, 820521321, 660899350, 65880535, 752810495, 384170888, 96730292, 631802962, 635668403, 419576616, 372408525, 522714468, 535950508, 972881922, 287507059, 977916994, 487053550, 471359667, 947611439, 758624036, 579785169, 45616298, 848994538, 830157267, 254429560, 69215662, 549862867, 887585334, 606268800, 167126287, 868044599, 218563713, 215165024, 737547865, 466855745, 285249072, 835642615, 439179564, 78585880, 439118671, 129272123, 31011487, 669617703, 389379135, 331031812, 759674164, 384260666, 986330554, 306939590, 68500349, 142992978, 878826608, 525808953, 899039905, 146589151, 292575530, 773065762, 481928029, 687752418, 891456099, 501591162, 626036336, 911149564, 844373454, 146113466, 967831751, 708329335, 528211702, 735786678, 673563101, 792118626, 766265480, 840975056, 143946334, 923566971, 126008140, 298412821, 174830437, 153781866, 708858720, 693188498, 322399651, 299551475, 375767481, 293378077, 624275598, 579548530, 493836054, 880619984, 469042759, 474595257, 590630370, 134629131, 193830185, 786942306, 160444309, 33487395, 367738524, 800431378, 673870290, 179968807, 946604747, 888991798, 384846, 696497260, 146675652, 413121505, 691754020, 904267483, 48270589, 410658361, 634911429, 82864058, 485760529, 907856865, 616043360, 339397222, 156854274, 331083178, 397935231, 330437194, 21580406, 803713667, 970261295, 275437607, 885788210, 620728361, 452931487, 353696083, 949635432, 261153396, 348808166, 457543084, 390992459, 531531767, 935188013, 313063930, 875919032, 507951036, 489114304, 469239242, 91897815, 483075238, 504367290, 692908142, 947304769, 8832665, 519421901, 836782003, 248193428, 565540344, 581339931, 70490795, 67226504, 497993956, 863792312, 700470104, 72179764, 2186182, 867413469, 443829609, 13780567, 776635131, 258857797, 480300450, 294560994, 931661127, 811680096, 859166470, 666226526, 854342276, 485080799, 394543032, 265402760, 159768969, 358311593, 405099677, 136542975, 837387752, 637667179, 222545048, 373358642, 272916633, 207723430, 489151452, 959452989, 513584295, 408333986, 296839067, 638806589, 896093292, 930252142, 148868309, 622043532, 979767771, 554069402, 517318241, 613277029, 455456977, 660299735, 158303556, 279702262, 269895793, 703314467, 753733502, 10255476, 33031221, 253186868, 724932344, 696037988, 651290278, 78917107, 46708089, 212727317, 43881480, 664718608, 863140720, 84344151, 201438943, 672198451, 876724222, 474091613, 575625615, 946268538, 218946712, 588019962, 419505025, 572432081, 892568294, 598415440, 340169516, 321735548, 761535400, 283468589, 281731008, 279038669, 544982619, 656879373, 834029372, 608744394, 150337893, 760534247, 448591043, 967939315, 125600451, 275243355, 224145353, 219287113, 485469535, 52114339, 861127594, 530650354, 122016543, 935940377, 662270916, 836054896, 620897896, 296103446, 674961386, 597055861, 144739419, 903713500, 940496305, 362639754, 403074047, 64139928, 593572756, 802469841, 789003439, 410383010, 395846930, 726830145, 613954380, 294844112, 934611054, 631257292, 486871290, 223584825, 392557777, 12906818, 815017677, 660235933, 347368521, 681900819, 602420655, 1041449, 720407290, 941009742, 397676555, 846810538, 274881344, 96528473, 254538034, 55397112, 354484807, 326123285, 922428822, 79435621, 17295466, 438556335, 727432350, 662612020, 379831947, 427105856, 253991515, 777090917, 964961755, 178408868, 931986347, 502231743, 167283839, 291715130, 646237292, 435934348, 709626589, 277211497, 398013050, 161205389, 634856950, 973344008, 627821701, 991411383, 671817519, 336362047, 355190845, 307045924, 926811081, 496234531, 866057640, 236059344, 934711325, 577024029, 240944896, 803570745, 997383725, 236916123, 814755232, 818631973, 381516602, 932843000, 302405268, 382645341, 268305808, 589602736, 517344680, 969176398, 729303155, 388676665, 369201518, 885569727, 255438367, 988604070, 2567325, 151321762, 5581894, 778663980, 874704913, 149646449, 807935587, 617690432, 65246242, 984222792, 754503896, 710651030, 65065985, 712289686, 40738416, 14271147, 133064928, 347871247, 29793092, 526177256, 884153118, 448131341, 555873392, 779372484, 818375543, 317654424, 592762079, 434234733, 223566615, 86948739, 524966234, 651491278, 493710601, 452595070, 962694145, 477146523, 923125636, 752773735, 465309795, 647448505, 168837660, 376449419, 882426957, 391653635, 878785904, 19298557, 405258243, 847461500, 727896001, 840402424, 286093965, 281202539, 924218957, 842715580, 706833676, 937898727, 800810661, 557264383, 993362684, 195424952, 16409043, 346904020, 593424815, 19924525, 580810086, 486718045, 910903689, 846930870, 862599400, 238058410, 863988914, 27631309, 303790066, 358649638, 826340175, 219880405, 677071298, 152847778, 793464398, 700242890, 626683663, 386785612, 431040857, 432111981, 856955445, 251051155, 175130463, 504032796, 616568855, 47267294, 820148593, 245602312, 181953817, 138050840, 133358390, 554048780, 230249260, 103669720, 961469478, 228139268, 924159163, 860278273, 371221095, 85919778, 752683875, 923834429, 855460244, 718074614, 933493586, 789896494, 266662714, 610299207, 807480015, 896074226, 11558692, 173874529, 732245785, 992670585, 325416314, 274424664, 975765146, 781991712, 196502608, 258733005, 474394889, 858160560, 934870904, 235200612, 587219893, 296687929, 61001237, 586994894, 801451562, 193139367, 509887599, 226021777, 282407830, 623727826, 641016065, 160381771, 922680112, 724960127, 860300026, 681006121, 565795844, 712745896, 180766437, 195744154, 78147513, 801162585, 1094974, 113117303, 910392905, 101564287, 161967540, 803994459, 620704732, 31527980, 467435028, 204051190, 799665426, 631397265, 23472644, 339128509, 381050272, 841369018, 874700393, 946207580, 562429342, 159646360, 456524111, 510258932, 850258296, 288460535, 113952689, 958015911, 332787671, 200704893, 403598585, 812920495, 186392243, 682106821, 443416434, 127211602, 182904466, 41033785, 972338459, 866983111, 423611648, 714386412, 917768350, 355470400, 972869079, 606371129, 151648788, 396174216, 431615001, 93807047, 740364204, 927556421, 556212893, 686637387, 206256218, 369919394, 252878167, 379861333, 738647912, 40544889, 256851566, 437791681, 83477339, 359120222, 181868412, 158278643, 99816120, 949711578, 457396896, 281840178, 714392657, 814753100, 257735609, 516594700, 970422756, 681478753, 598859349, 160063313, 51772142, 654684073, 10739419, 55666524, 630517193, 401488796, 899704503, 882352845, 597553770, 640784645, 90867196, 55531418, 124145808, 715111025, 418339509, 579474045, 404625232, 837396659, 238937036, 981028610, 8316562, 160264261, 848783961, 732931200, 26335232, 435442955, 663384971, 680432260, 560652744, 848399038, 516676468, 260550241, 483223803, 791977669, 720026261, 754649972, 647031768, 485247393, 659753144, 569665014, 631031882, 250307808, 78625651, 518740881, 718712768, 514524618, 758377402, 692384094, 311553696, 44325355, 546637691, 695292131, 163014261, 329879331, 462947822, 12318136, 917771048, 492856103, 217262143, 168131085, 562479870, 621954772, 768426762, 397416095, 921565637, 482161428, 648754102, 742790287, 221566299, 404761398, 897417180, 133234256, 904629136, 334319627, 393113730, 553440689, 544202916, 977704238, 27676179, 498555195, 792365063, 622448097, 344750348, 327761270, 335101677, 919343115, 476456766, 331417419, 484797417, 519821275, 138314628, 788650574, 570796693, 878612159, 363624950, 673629605, 171094609, 754081677, 294795962, 434289764, 287574842, 548037701, 184961116, 968594312, 939205336, 363627010, 636374044, 883154309, 407274222, 47450929, 423126271, 423712323, 661491065, 287268949, 291445339, 658608324, 142750995, 912880466, 803145883, 370045842, 581907521, 490984974, 613976636, 457778719, 102075538, 906683004, 395708771, 110850089, 513380702, 325410268, 777757303, 187722658, 685131911, 202425967, 352439257, 726925692, 766643441, 883968566, 38548594, 379989475, 765479916, 430028344, 160452614, 269245127, 799514869, 696972603, 59297366, 291188133, 567781147, 475287654, 794643020, 398124286, 773055766, 356855205, 71170277, 323252334, 682564665, 592704236, 622887859, 697020353, 731810410, 653479081, 495499100, 501133109, 131860213, 44862027, 703398313, 804654379, 199010659, 8583771, 101880760, 354250661, 757481310, 260835972, 4544487, 65778295, 14912404, 719446922, 70499331, 879805167, 950491269, 456753529, 71462700, 333075044, 28686783, 14910737, 778843964, 904481559, 956535708, 100416449, 698524436, 181479891, 856493372, 165953756, 411768279, 777666856, 672188778, 229123415, 442251670, 574712949, 420679626, 851194713, 857712388, 251447780, 364992280, 943745420, 888997414, 788020378, 672070503, 445715691, 898200318, 701678911, 606016176, 980846013, 79350581, 150695393, 293753069, 713518994, 345021350, 379282892, 472601471, 549952913, 562389711, 300602995, 534160374, 55246051, 275966677, 361343041, 636602554, 673856444, 214387328, 730980184, 343365214, 435103291, 521122947, 853409242, 896206107, 478140759, 523486388, 610634911, 833387497, 230445555, 321285953, 54002160, 352930139, 233113580, 414827899, 413428901, 488503133, 885496803, 904719668, 642915605, 503966933, 641503822, 559832786, 396971520, 22217857, 742224321, 944663361, 720595962, 286959965, 375171136, 277531630, 960671575, 375713031, 154416661, 215525419, 806825737, 800527168, 761761557, 749987116, 406674037, 106994538, 922148480, 894870108, 528367451, 717127899, 635890970, 595244610, 81392695, 319427638, 913902015, 127813646, 89201536, 869482232, 318679930, 852353623, 712696266, 947303168, 95205568, 89452595, 266007237, 357927090, 18082624, 563128155, 798850011, 830535603, 250998184, 851441381, 426209788, 121407550, 104039593, 771720348, 431904882, 763231038, 130991909, 914585759, 285364109, 913509545, 484078416, 852930463, 350061622, 280339332, 218002632, 716951875, 107198466, 653792985, 775904484, 440412315, 851413144, 33482942, 777826466, 798962810, 481549393, 398764820, 917314088, 953929527, 244333348, 482076730, 354587667, 454742307, 14640733, 373146230, 259680439, 333710267, 195444811, 291402290, 591853382, 399062150, 886887044, 732599440, 166992305, 261101842, 107974355, 993305792, 801740167, 665288531, 207946416, 498879582, 394323384, 628881122, 137192607, 651334598, 524988789, 707913869, 778946973, 95568718, 889823059, 217829131, 999297882, 710544216, 751102182, 712338628, 49441456, 630724367, 41623965, 54360536, 798904394, 888118131, 344351595, 451565284, 354757846, 328917871, 107757216, 603296653, 855352816, 756597100, 991319134, 778301737, 595351238, 118674892, 110941953, 68166878, 800220754, 94621568, 431691338, 835270546, 27724065, 938202388, 192540681, 580535240, 605788813, 501621317, 224332667, 395851233, 711904016, 961115570, 878238864, 840724005, 441352581, 461489231, 498362471, 212709057, 169177745, 385871197, 336412255, 283309340, 910557803, 21574694, 680283771, 745148890, 675689991, 831252911, 234848390, 926239433, 205382812, 448745733, 565286928, 856288173, 955463822, 270190758, 470199011, 978827159, 511740522, 22177677, 558847396, 648886335, 915358790, 411585584, 824764663, 993416812, 889512265, 133802020, 576302287, 318524817, 898497828, 573753746, 242206944, 327861380, 837759694, 751672045, 672221574, 649775795, 256053120, 393177963, 535158385, 935691190, 769795014, 139956169, 20471305, 999801197, 810218446, 724097519, 330660793, 589743899, 217256636, 495898048, 905884015, 626218612, 419844684, 678046743, 512053451, 845589264, 442441765, 672820412, 471431746, 983805571, 385191619, 281510920, 467197263, 678037802, 150657937, 948772913, 938448487, 225769040, 118775339, 896873798, 245861167, 30787018, 352084029, 631966995, 937058403, 676804267, 484939873, 707971908, 388461901, 306668708, 429880745, 53305417, 98325331, 956587771, 174760269, 593866456, 401453048, 680806304, 157824295, 987230924, 186136886, 149527774, 185969126, 54612910, 853927258, 647297331, 250877875, 240687127, 224711065, 963181923, 1099098, 562365293, 141507586, 201786692, 627384059, 794855265, 784775138, 149657805, 823562604, 679138727, 432451146, 303651495, 517153610, 522287061, 315342463, 236244352, 755981330, 11109972, 703862001, 128218681, 627558878, 213364383, 977838516, 919130000, 906637147, 43855264, 999167747, 90765589, 89501449, 924250619, 745895590, 449491165, 534729527, 356110878, 996128177, 949103025, 735866496, 347653302, 72765206, 742425822, 985995894, 840184479, 775745680, 747510902, 555449138, 552800080, 910839341, 759047168, 491144542, 903535866, 178312851, 411225471, 367751394, 670799138, 250720416, 447338911, 270744719, 565388996, 805901002, 932808341, 824638191, 478948939, 750288904, 978204594, 709559009, 500955986, 864253425, 918093471, 494651463, 136691092, 137828381, 407291260, 832586240, 338887976, 184715509, 445736171, 542381051, 699090156, 99512600, 301519097, 76894786, 179840745, 809879659, 905295703, 16038239, 319158480, 480223417, 538340557, 842615971, 482895795, 61080093, 805470810, 874807104, 606274329, 809187625, 132206631, 174663048, 243910489, 366998969, 85476810, 496528577, 413025730, 681740126, 611562286, 544351105, 110068024, 386442509, 565441897, 77958597, 276260123, 770517656, 87290461, 684497265, 796328933, 869783803, 949864991, 278421483, 407245644, 754900173, 670500449, 655116307, 18320569, 165361533, 332986312, 851763922, 693962563, 286670676, 297260989, 526283809, 34092574, 177575684, 700598395, 987174081, 871571191, 42888041, 615736455, 366018821, 868123353, 33273134, 401582704, 885912202, 215514351, 768806750, 811476769, 825335800, 395727225, 252829458, 178012488, 293965286, 821684775, 991070374, 292753693, 501884141, 655031049, 252119369, 637947384, 549533773, 775714705, 686560296, 528364528, 701051587, 395675241, 129981144, 816570154, 473173928, 43467264, 948471763, 239041971, 670927110, 773425489, 997278576, 958604333, 830717289, 164333297, 109011842, 914348664, 125023356, 863997854, 457556742, 63614310, 642078242, 951457437, 828813857, 189927329, 434102512, 881546023, 737823483, 825140079, 555142520, 537661516, 766073842, 523096065, 892283041, 441409378, 702558654, 640170051, 64016625, 762484578, 190358076, 930880246, 812330720, 291775257, 61190083, 990928159, 101158220, 304633449, 351464625, 125752397, 413897199, 552284952, 672642999, 770122377, 530605823, 408610852, 285708512, 335494753, 693217019, 469165463, 347248473, 366272690, 926535883, 189825197, 373780413, 694260614, 569720071, 240463801, 106421257, 894525726, 921475612, 721251935, 848637549, 880833277, 648238576, 927978973, 116719779, 261397855, 865640336, 442917426, 640728645, 447651401, 399577732, 990982427, 898443245, 359653490, 219917698, 269969394, 74991204, 698588489, 77772298, 962335212, 239669104, 360188959, 231416309, 258273881, 571148519, 399421490, 349393153, 982718056, 247086452, 241183807, 192499660, 560349440, 829727362, 736342442, 5358292, 55727192, 330887799, 477966193, 486045892, 371815390, 713837883, 382265116, 129093837, 799150465, 13966764, 180371236, 888052345, 698121410, 189437599, 863596409, 5318405, 110229878, 540020247, 36366518, 635324173, 19746052, 493268841, 167323125, 429086929, 20809061, 77680384, 780325134, 526288158, 754589746, 977721398, 678245558, 759034501, 589437112, 653657375, 692599826, 278860672, 155523813, 262672578, 185581979, 651209780, 759456098, 155705025, 9794004, 960127895, 486237566, 912442616, 20415619, 326130128, 726801642, 890643317, 172681513, 872266373, 448452770, 861863713, 798856263, 447387706, 64787594, 827630092, 571334892, 573278556, 768090476, 168463749, 614155732, 436892125, 291777689, 515874252, 791058394, 4138674, 763175550, 571840909, 261456803, 970468725, 702196428, 485836968, 147416438, 242838973, 660843820, 927259043, 464119842, 814622042, 207705455, 815510852, 377538479, 982031020, 827952999, 425370878, 3576782, 27556627, 435643037, 275207459, 852183726, 21040266, 370592056, 763700485, 132637265, 939035029, 151303473, 361737247, 859165678, 648534539, 67695077, 549431117, 65909090, 937360682, 513414666, 563281313, 127417707, 153413879, 637607166, 830840776, 949051137, 720553253, 255228491, 564422231, 986204658, 728551774, 447393921, 754852458, 940185341, 313511647, 912457706, 891933059, 521887125, 396153917, 362277025, 179237549, 711063529, 351937117, 518620552, 62184822, 249678633, 385056306, 418408008, 811302959, 278805042, 915722329, 334128701, 374236988, 16308004, 229035539, 534514487, 234223410, 208441629, 618525808, 881796450, 445756939, 784076762, 19516987, 110953616, 767306694, 56590056, 501900594, 340851473, 133283712, 654721156, 90119987, 654056486, 293418836, 424385915, 834411835, 204052509, 142117852, 42935814, 598467717, 725710429, 246544780, 273346304, 364972875, 294929948, 712143362, 854622622, 645149641, 771374984, 191986087, 822571839, 789487212, 252165133, 961945037, 145656226, 260173514, 474706173, 525998002, 504237448, 899986952, 802358662, 186059899, 534476382, 144723023, 713610558, 790510685, 109078443, 265436920, 906431327, 808687437, 48028500, 840776183, 348253664, 290240149, 658440490, 79167243, 740494067, 536072298, 438227980, 410274930, 842979690, 911843023, 142237124, 985843321, 149727884, 337729805, 612337217, 84746517, 741595361, 19150049, 480937233, 275070734, 756028688, 838230618, 113325150, 557059313, 365896773, 410764977, 638000614, 563160942, 218098482, 392410640, 82748780, 669528727, 79514102, 403094165, 423197035, 812181607, 632574445, 33421932, 546520320, 58078198, 94152415, 467789010, 885346316, 948830708, 951936338, 629731646, 184268046, 905062981, 686356095, 137231898, 770550480, 325994451, 808009053, 65475058, 803243152, 786553119, 222913324, 352044683, 900200117, 307924633, 888099091, 448515144, 951996109, 874810525, 839935087, 58972076, 192721817, 561890345, 411657845, 141117661, 829552540, 175577685, 358612785, 372428414, 870786916, 876031609, 566009337, 155552626, 769282928, 769051674, 31940407, 388264470, 477311120, 294908571, 52288474, 154132118, 763944263, 793855404, 276296938, 337377561, 51454261, 357645530, 604609849, 226737687, 887135927, 804882754, 934813408, 133855562, 344990147, 512195988, 401281913, 194447041, 530280927, 543521241, 57702267, 246393352, 813458394, 104004183, 949119284, 151231096, 9338620, 998289807, 171865454, 740208251, 588782785, 18651712, 736429911, 864432608, 736712488, 801376682, 110558614, 72505376, 424673106, 292647338, 989535276, 935952229, 992448797, 340450376, 426241028, 171926013, 902475767, 875394674, 647642745, 110298832, 456753524, 938571454, 603427428, 244995548, 89001129, 841141740, 702082557, 596633280, 463005290, 18779844, 153975755, 129561888, 660147316, 698427283, 535438682, 114233460, 546495039, 766203064, 391586041, 755370820, 124085120, 53434331, 549056824, 252028156, 988048540, 417847108, 530290931, 943659283, 761138846, 181094850, 228004287, 667630705, 106671120, 419034632, 630734936, 624523261, 259098410, 614187158, 607284906, 633435225, 522552639, 605414011, 227784834, 807515202, 598137875, 62150178, 157964933, 463778678, 70435991, 724603795, 996086752, 562788359, 588983374, 778125228, 7215854, 560801498, 892349679, 834254197, 385973317, 682831339, 487111680, 31381543, 65775730, 222535316, 3789966, 594009224, 722522866, 327837967, 519468380, 161064991, 816007518, 52532857, 748805813, 160063674, 552454176, 25358195, 481752154, 623674620, 225642094, 543339318, 338982079, 661451366, 464756154, 139609085, 69837133, 960286966, 117017928, 12754040, 497998259, 25316440, 761256664, 738996574, 109235641, 910023243, 294273705, 219336255, 119341084, 289555181, 626427632, 699421559, 773562141, 817191311, 114597445, 982438529, 793157693, 953720020, 359242205, 540336007, 735235029, 208285333, 752598325, 637794615, 43658678, 767684450, 163336818, 1398397, 323592336, 712273038, 179023562, 240554599, 987313852, 440293492, 81904187, 33197542, 499718072, 516990258, 368945854, 97066766, 982650399, 269560062, 327920380, 657224612, 496498551, 312375668, 727891248, 235166026, 906691546, 463710895, 677211410, 323391689, 802940330, 953159349, 328977196, 65269779, 882848055, 570015463, 98462305, 33949778, 70821755, 444617038, 892911314, 482897933, 747271213, 610431337, 785675371, 397475204, 11865622, 171935546, 663720596, 687076971, 981987752, 716770347, 136442158, 2388354, 943712684, 921019496, 371648373, 725764763, 205708759, 346448248, 61673904, 394917270, 128489297, 432533089, 657673754, 233001042, 252657175, 822309021, 808328409, 749417827, 266960715, 532470405, 803590480, 106705310, 959292663, 356382227, 939001323, 482575573, 760197350, 602457173, 449747334, 638978386, 938632619, 572045493, 378653082, 225443961, 283368752, 95082363, 8139715, 269229416, 601518258, 170903682, 428131926, 136897102, 203242030, 198688115, 752098560, 175659306, 7116465, 477085579, 150787196, 53525666, 356146507, 4572020, 634929596, 693360278, 517000737, 263747718, 907824678, 324646068, 806479093, 334389142, 844616931, 175108352, 794567860, 555279048, 894215745, 582774323, 22846584, 90540438, 931481185, 681711105, 486901869, 651931223, 823669102, 263478802, 866348777, 758525147, 116173515, 688107842, 967012499, 35245492, 326283640, 955400366, 272310185, 800611935, 702243507, 365501597, 766963917, 228654844, 691187672, 239026241, 754852207, 457441079, 990437848, 325538483, 625530670, 48055450, 417744575, 79245870, 373892819, 369050324, 415650013, 835067549, 308688092, 850541315, 840916158, 966327422, 576268489, 166140004, 455248192, 507387025, 428805396, 499990843, 859610236, 567102239, 495445122, 947898305, 764711145, 547662212, 226829228, 619523876, 358336662, 195014796, 721792396, 432298894, 902875517, 188464395, 5201808, 343554993, 366129543, 193558331, 70796216, 495075645, 489832547, 494227044, 96910674, 214400523, 691402184, 61750315, 489582091, 106667148, 279281512, 794542079, 628573983, 403198658, 183531854, 196242291, 324520264, 674448843, 654807762, 223635359, 160463577, 575609405, 370751012, 409939448, 578341755, 566864002, 763536443, 381037277, 787966635, 616577822, 652856391, 439664931, 82403395, 543938317, 724193940, 755206711, 903897925, 933364703, 972800897, 786973236, 763609127, 320756357, 123557051, 581141449, 52953131, 774758658, 440475952, 613594305, 997945548, 207164168, 71352146, 88819475, 752496229, 732153766, 914434501, 395090267, 404261842, 159093159, 428947159, 953575883, 671975034, 70414199, 602076507, 194607499, 145886096, 381651854, 399241115, 199652705, 947359261, 30626059, 413051914, 417456009, 944475638, 692088370, 268977193, 789958979, 794834819, 239102967, 385626799, 883049282, 203082407, 416006952, 247931277, 288481335, 701927281, 264831980, 551295332, 26147534, 832710227, 758152825, 898648458, 327235948, 738187112, 163620631, 912973111, 459031049, 44665553, 479922720, 842945, 473237185, 69764698, 673065362, 295109015, 964099364, 727990764, 59052022, 420953035, 746887829, 531624414, 325477727, 733968539, 813261745, 908593540, 836797419, 53742122, 885953781, 825537169, 728419936, 557499438, 824911859, 326213855, 752267860, 233662280, 428552714, 736844947, 387887762, 782387134, 964832387, 673294989, 403952788, 605133369, 405713041, 716833606, 304325977, 529032353, 263851809, 44664755, 954426910, 968156943, 49272770, 82654186, 849902201, 428728385, 571932452, 814877942, 335647832, 569328198, 674815026, 681698669, 371013068, 532232884, 694755925, 267023298, 250975261, 385208534, 868625155, 221501683, 888562459, 973761854, 123127947, 804079442, 30199171, 54801730, 127458771, 834716842, 999436394, 681972977, 601702706, 23536746, 957637597, 595401438, 201244248, 635256300, 823779664, 705662752, 890632361, 374072902, 676642542, 116144998, 290866220, 270908439, 873274570, 136625594, 812858245, 285095864, 671545872, 26939556, 962697764, 68612912, 160501947, 364893322, 656775732, 548299357, 848382155, 654677684, 359692454, 137469137, 188383890, 692204106, 191833869, 144360298, 947196400, 767053279, 220086311, 78427214, 18330686, 441633853, 338272239, 745291467, 529281700, 623063374, 48324166, 494856976, 769889854, 498039411, 993679559, 347309653, 786707147, 465928995, 988405606, 262082292, 534286855, 249177585, 164176214, 504984256, 103965517, 930320172, 254432377, 132129933, 451465462, 960169283, 632853990, 809324807, 567209970, 577509329, 683363677, 207848111, 320800512, 361708309, 686600872, 702836548, 578672769, 159954930, 333437761, 7236927, 178606408, 225997300, 579385500, 445948691, 166842014, 600653377, 310018272, 93079133, 263236511, 394108138, 55168834, 649546176, 348177823, 574818971, 438486751, 19859309, 897341935, 981252174, 526733910, 797686634, 113725643, 373189023, 793974374, 780614874, 193036204, 326175147, 873154039, 357240102, 250708111, 111611278, 187330611, 468720454, 45872525, 290745838, 414425167, 157990107, 425170127, 147757233, 180209039, 703740122, 308872569, 875450420, 553705679, 998973230, 780216556, 261378656, 838718229, 251447489, 58336679, 41261457, 58787959, 27274963, 433687091, 929576661, 111203999, 307495612, 577632764, 618855650, 382685429, 641929321, 184531590, 465521829, 589256088, 295868738, 536441070, 181931919, 124511595, 446718142, 361640141, 703231058, 955364095, 507054718, 181270574, 704388543, 817645658, 263729173, 87917447, 679371926, 148244511, 18990178, 80956074, 358507303, 497081634, 16709754, 467394264, 535451743, 392640635, 426008296, 961451645, 981136125, 707569851, 585523517, 10864639, 184018549, 13617331, 17992613, 848529752, 765921208, 42925735, 457486140, 785770478, 82087703, 493233308, 949747050, 211328273, 297557011, 617253655, 366588368, 340891096, 865041021, 275932061, 820654782, 275405792, 771508355, 848914972, 332728724, 640470841, 913968584, 740370181, 793169206, 425181938, 982842950, 633096911, 311883953, 873222577, 249703415, 464997401, 247040002, 103635137, 39515529, 122659861, 343911825, 997499158, 326226766, 633300040, 635085509, 751818063, 202007207, 825328127, 741716564, 881633115, 54438841, 344572184, 933583850, 940329555, 537911156, 205904346, 976594311, 919163271, 299800331, 114477696, 992836194, 884440543, 787245285, 884561463, 853087294, 110643811, 652647884, 530993785, 763998165, 227608832, 154266875, 603056070, 829685531, 492838508, 691033376, 440773663, 547174894, 174602924, 440686394, 549967898, 195631784, 146670431, 680715385, 353911584, 673785931, 991693908, 876126188, 48627627, 902537860, 186760279, 880941548, 566558449, 614981401, 226798760, 297562633, 751796284, 381285658, 689053987, 975908005, 156972340, 696227618, 454785198, 704614286, 537036747, 252593951, 336748387, 14829218, 900761043, 902607553, 887497990, 338267498, 815464042, 964086564, 196213486, 476481800, 197217470, 947019165, 157146908, 234550346, 38540091, 305321714, 149035530, 594668154, 687643199, 429841109, 856973058, 971630517, 572072365, 735278549, 866718961, 175500578, 899850512, 56391214, 813508, 343956260, 603835806, 430720615, 175742905, 46410619, 226706682, 772150860, 205431532, 540967779, 535966852, 793757908, 393141537, 990293519, 588653943, 697680042, 66035348, 153854952, 258516646, 814733190, 305161430, 810462649, 977304947, 314731645, 88104753, 48363377, 17696952, 281454139, 873275078, 492203329, 210484700, 282953791, 76219653, 797944222, 88983778, 323345627, 299223645, 451282644, 514134678, 516781717, 207311547, 698469759, 87127806, 253941508, 51743569, 119113371, 50403801, 286651841, 255965745, 75024682, 622685056, 581630195, 467646472, 159893193, 948214373, 972898173, 571200221, 57133824, 231208375, 860042588, 778339367, 331152334, 777433074, 334600756, 791494090, 690078515, 166821691, 822678642, 439160251, 636784486, 309645994, 541222884, 502968268, 347968256, 699473163, 813398350, 504481768, 797945196, 341508669, 94418986, 489885831, 551499038, 750273757, 548152887, 836549334, 512727928, 489745808, 294770807, 556724328, 157867194, 551398538, 274646844, 289731334, 641392432, 442798164, 311377065, 292363786, 721094534, 896187135, 450818478, 312886684, 19496531, 431734016, 285008867, 18168143, 32247575, 217991301, 472953436, 315250223, 751458330, 524213304, 751726855, 492781780, 944768001, 962082544, 986855988, 798056912, 311497581, 61218780, 912369929, 932794158, 239790658, 727054585, 450611421, 748463387, 708421943, 445452980, 819513845, 203715238, 247629234, 114511779, 970383159, 694706152, 672822665, 36945992, 932045289, 329716505, 849266117, 531913357, 429748986, 184931244, 386366405, 161115290, 176020911, 212128320, 456291203, 110258190, 572813837, 17060154, 539009813, 345328928, 143028930, 927168953, 996884225, 682889219, 447404893, 989740009, 289384377, 920789156, 729619975, 166896608, 605878044, 820131125, 477070471, 944223766, 274922955, 273961641, 814516483, 933077485, 707984567, 311530350, 614271689, 350013598, 424174598, 915070586, 349510218, 196439403, 288807318, 428460282, 892642697, 255980059, 25134794, 518594696, 534255274, 180777696, 394067720, 842610390, 886250928, 236753722, 655201528, 345416198, 500452618, 150448252, 905433906, 580568534, 769862457, 174435886, 526169327, 963283391, 851269765, 837874665, 309124373, 940526895, 34409737, 246868510, 356191859, 519090747, 542188263, 680968717, 896712692, 463105136, 803791583, 794923968, 946620377, 897619098, 213797877, 54768263, 997953611, 651593567, 669117717, 43783142, 616665080, 868493946, 231230220, 824531028, 567198967, 167451435, 643858592, 122167965, 517771394, 983220986, 614452995, 39315651, 625642460, 521320214, 15765103, 676630117, 340412972, 513427231, 724868546, 410002671, 869618954, 189390658, 563744031, 561044793, 551650894, 642365927, 276261348, 934032396, 142589619, 642213346, 579943153, 742173998, 186539764, 26768361, 241622783, 52442991, 674611418, 877441907, 279641050, 378593252, 426513637, 155931948, 734076292, 519632740, 884359285, 215355928, 409243316, 506906821, 650480601, 625555946, 438005291, 168572765, 394131323, 111945195, 333894433, 758696056, 47880295, 975324869, 783395602, 829867929, 627564057, 301037681, 154969198, 830566451, 491688805, 554288855, 85608443, 46431295, 978893035, 26677749, 689044617, 828398937, 488338330, 862207587, 958203991, 644992486, 75972030, 112107298, 966044578, 960723965, 677619740, 644548044, 923023470, 52664980, 893689798, 489551171, 188528324, 27466040, 255252674, 984470088, 322428922, 331587871, 810660230, 562695041, 938853382, 941890583, 574510738, 945482717, 542447570, 60792247, 37875237, 820660359, 755532927, 582077290, 328755435, 889079605, 903583715, 725694747, 782096047, 182644422, 923555563, 570744386, 442400119, 986461704, 130670760, 13345805, 987450495, 881702817, 45536433, 692028913, 420669715, 956615466, 843449240, 458785681, 475368140, 573579076, 482011529, 684730276, 940069420, 67299300, 572211289, 925981595, 776548046, 263360674, 192490751, 730049159, 530196351, 747485585, 757107424, 764463615, 94323569, 78286693, 411642293, 931858551, 185441384, 685402233, 355777771, 756692961, 860985063, 897243197, 841735811, 311358556, 77881617, 255249591, 347999964, 44961567, 650416230, 878238900, 77029025, 998277057, 784573316, 384695947, 11656226, 972945300, 259365903, 482882632, 286577450, 466358865, 313700472, 340850640, 648132831, 447844298, 427222751, 877699593, 129522579, 905971000, 794642912, 539442003, 530730837, 280917730, 294569019, 370444583, 174692100, 848881417, 996217694, 87170840, 197541943, 825837995, 931722768, 124505261, 500750995, 742062775, 973284953, 863299534, 117925975, 583669357, 112937383, 305110434, 379704474, 318330492, 463248184, 151461806, 372596274, 604937601, 73283358, 507734968, 678016138, 475941660, 671313696, 690836470, 519417486, 296655623, 58941918, 318490703, 236762542, 765133389, 324783161, 260046564, 166030437, 892625293, 588571020, 151272230, 815703404, 243950072, 566934454, 970195833, 112685022, 220046971, 906921622, 414503528, 485153499, 939332116, 753199667, 903938547, 702313413, 989584935, 570770301, 253828339, 157798006, 874118072, 459375419, 750928870, 15976451, 207010017, 50015208, 643188896, 724985086, 136394563, 793337833, 32667993, 935924022, 488354520, 616857487, 343359722, 483834516, 900073447, 435331192, 572359832, 357798205, 426051369, 850270602, 148977029, 106119768, 237792673, 943667320, 69961233, 50420321, 510021496, 804785412, 953465166, 976878167, 861896930, 815336160, 416068411, 742594217, 812863182, 272618516, 916327517, 543243110, 821566713, 189023445, 893388728, 813157850, 380935691, 441187481, 900209210, 898609976, 471456293, 122498771, 583352534, 862613292, 461191924, 545190966, 806196153, 406854070, 244983571, 502777017, 894119104, 820814032, 305800268, 440613162, 452026238, 921825307, 234722347, 563601828, 63302446, 181834445, 401951515, 347948638, 479467396, 760159656, 645131718, 186133407, 163193779, 120668268, 901101080, 89876195, 975628704, 860671555, 633599616, 613146835, 96955976, 224677746, 105355462, 916570963, 992700981, 960719783, 404469808, 602996951, 62559889, 569356580, 944611864, 738641089, 706955149, 910212790, 642686092, 692138388, 947161676, 575206715, 325009476, 825163263, 275765488, 849501756, 598504809, 675553298, 61246551, 776769547, 897736906, 711944554, 426678446, 557962594, 125580611, 509655198, 899378415, 383039716, 325288186, 853343538, 152950840, 289733142, 817029490, 820095381, 387698862, 473193145, 800739096, 334769368, 307038357, 550017444, 220878124, 287160447, 34658094, 891086419, 784797974, 538743706, 33460991, 751505489, 748024303, 262850177, 697479702, 620262917, 719829902, 14642046, 797190538, 156591352, 129534357, 829496403, 905550208, 494053757, 650730751, 678908531, 108134722, 284723855, 781600649, 566888435, 38525749, 463859949, 628472510, 21218862, 721377886, 750044008, 157876341, 457086222, 81547051, 673612858, 248901131, 392162894, 613140826, 395219378, 519787093, 717295545, 66544949, 994443376, 661627422, 163382422, 986348562, 118037084, 849679026, 263573870, 166039845, 135218396, 889397508, 332637073, 813297181, 487749965, 30372480, 611371556, 32313827, 983577258, 619738473, 626314248, 420707090, 111311795, 360396690, 300092298, 704539892, 912865116, 983913594, 588149006, 938214990, 269397305, 792747856, 273782504, 239813486, 54423239, 415710402, 522174704, 842973648, 365779657, 710508304, 980395904, 125401796, 426889457, 705275118, 127034107, 66426656, 588447899, 218345010, 543445943, 751178188, 65069993, 526617098, 873199024, 623764791, 329469407, 626941533, 481516600, 118900475, 47493103, 668243224, 434375289, 560309099, 422684831, 213522253, 268086770, 922980842, 754631419, 509636696, 390417779, 306358433, 717020745, 521835236, 281462249, 785216703, 81927521, 639981757, 694314155, 100219231, 908781137, 792230952, 114888929, 440458182, 208480433, 306361009, 48858634, 301586143, 557367040, 911947280, 994677268, 7876736, 370195480, 553755409, 462539243, 39281466, 63770282, 783226417, 695704759, 575416731, 518519188, 981156957, 261297412, 429748941, 291159367, 759633260, 149371108, 891304602, 835075924, 333992589, 643740396, 40374203, 849135807, 247808513, 166474444, 181223925, 155526495, 847653298, 411769882, 479273332, 561338520, 210339336, 183107674, 27449572, 445731331, 633792135, 932754401, 674937488, 991739333, 977912883, 89321428, 83592766, 569889171, 893449820, 8947801, 965222760, 352913482, 323834662, 995802163, 654242923, 524515106, 157082747, 589965084, 269398480, 737638553, 773081839, 392656200, 49846663, 925875355, 684441046, 343602439, 175540446, 611628183, 759466280, 461911226, 824134971, 178607519, 56858140, 822183847, 34377216, 664262889, 986070037, 103753220, 292553887, 101998435, 394528212, 483450096, 690043511, 53196782, 156575694, 66373885, 626696138, 348259752, 414319847, 176218734, 575651805, 559950068, 33969266, 653412717, 257160794, 627866707, 227063561, 847284148, 193392504, 677728116, 633450338, 5698338, 347178420, 261127899, 581342532, 778032818, 762463550, 552086564, 174501739, 334005675, 772065918, 330378677, 588614478, 545220510, 976048778, 804804227, 682317679, 529160948, 517196050, 396121275, 653658984, 924650311, 684883623, 506451250, 977497215, 43173621, 873087646, 415263690, 110129827, 977524361, 592196693, 360211387, 488035669, 842914200, 686225702, 897500939, 223512448, 683951399, 315278797, 184827235, 980022696, 439571830, 763993705, 511921620, 490610442, 597921414, 887102205, 952935950, 475564226, 540572830, 106091092, 84277503, 834653999, 321335825, 105698634, 204185782, 48462238, 628169517, 982199446, 917498549, 857720067, 224605171, 686075729, 647772489, 170299522, 952733030, 817329617, 256954321, 388996047, 340987822, 293651798, 959446784, 914063468, 645518447, 298401081, 503282107, 827924980, 704207596, 492855371, 330594544, 763228522, 146148217, 601430582, 108774712, 328674608, 209178452, 209806738, 474254561, 653350370, 546645637, 347749004, 928860827, 993567020, 271812990, 659078554, 160965708, 793208749, 396426681, 775618418, 104162475, 420436950, 701835077, 88264693, 612336412, 692716750, 894000610, 920365231, 740957148, 157550687, 308787498, 954176376, 694367396, 30515476, 646375010, 54062468, 620692857, 811161368, 592601387, 389214742, 416499114, 10782911, 393753071, 86443915, 346183110, 454915180, 300788968, 569363932, 410742647, 921170652, 705711100, 946266792, 639293806, 642091532, 217142027, 294337657, 489633594, 49955634, 761822873, 968359309, 198811267, 641294581, 878211044, 990732139, 736941315, 976318399, 383131107, 6110840, 26570108, 252766712, 68225090, 446411323, 55786112, 988846076, 52089686, 482150621, 622905892, 366593338, 506240848, 930010581, 559954622, 63048860, 673853979, 204211193, 162498244, 739374970, 209907369, 685632101, 374574931, 592164976, 438619935, 286400220, 409568528, 479990960, 431176868, 746602156, 162137083, 659394427, 666098011, 922672288, 27393175, 942924698, 905961257, 430849811, 317016394, 564614180, 623264098, 326418716, 384905518, 424291239, 801070470, 229398005, 432875675, 104720682, 9905141, 318191333, 108154375, 653256075, 657639134, 74862471, 502348828, 730326599, 266667701, 616581296, 42744349, 276847665, 15726298, 821800031, 296239014, 885509117, 410286676, 700835219, 345034529, 74140310, 518519896, 930033881, 560710661, 800962416, 828879163, 201249462, 775863757, 743711642, 672553012, 140798620, 457304298, 937380824, 890831894, 575579749, 256167297, 310399604, 868763857, 800419186, 768787578, 727517169, 541602361, 564120530, 791103420, 94965401, 327683586, 704385655, 359399512, 364765146, 46546216, 604005560, 144490996, 584725662, 160248013, 339300077, 655000074, 318260999, 571538033, 807709166, 106189529, 893181459, 821550941, 302773953, 253961019, 88082158, 181702937, 418543109, 505723113, 918606140, 215021248, 650555039, 521597540, 258494945, 815764481, 266204730, 94953113, 101623305, 733554107, 872062695, 375330301, 570283273, 273351469, 564593226, 687896571, 872329398, 92235769, 788298600, 710170993, 712275329, 597576740, 74129426, 4270417, 304166772, 554579320, 781569165, 909212867, 749141067, 64500236, 841286832, 180251227, 355916666, 103137850, 808812142, 712690371, 679386571, 792452053, 511350052, 600144716, 345852459, 828245305, 534737990, 662828684, 852010024, 114878965, 70671411, 849978077, 843024815, 996793722, 428214846, 953879103, 629385477, 88059969, 740819290, 581681155, 370844858, 607121077, 361278781, 801388488, 134532474, 64029574, 531275942, 116848167, 194079819, 489843546, 709012957, 295104008, 996380070, 589325997, 438018345, 144138656, 179416116, 602528282, 861202572, 955308202, 778990832, 366596840, 93159716, 60239946, 778396494, 297874058, 495996995, 701393799, 73866425, 463101287, 803060476, 701781968, 392148855, 22282879, 394892937, 417635380, 968162501, 818415966, 261544047, 778794860, 882448503, 848247106, 365023073, 349419156, 392009204, 937141035, 422675964, 764240502, 225713748, 301209103, 953226149, 134137832, 10707997, 225591333, 193062167, 464849379, 23230042, 694219109, 92563056, 723203136, 843716655, 767129467, 777884474, 197795915, 928097352, 164607212, 448530020, 43693829, 870427503, 898761697, 394070379, 83783754, 108884963, 630310083, 588416604, 409775575, 54807803, 313562368, 164116626, 799098765, 898560259, 255019756, 909870721, 841090877, 783199033, 43596717, 512725464, 757570488, 119836865, 979998526, 593718128, 613946405, 492138146, 249659373, 466474642, 733190213, 215077534, 859828586, 780237537, 550060624, 792837884, 33424593, 853411697, 24742604, 528906745, 210547119, 341082622, 243050558, 472916363, 109509479, 842991448, 52723870, 138637622, 45855803, 719994792, 749488507, 856739723, 708280481, 225134761, 940255111, 500071940, 366999802, 787711412, 196687526, 204739590, 158993137, 145151829, 557060549, 724487159, 388364920, 459468558, 34478254, 214710631, 803941651, 737382773, 259727450, 751651145, 859117295, 197741409, 149810276, 909093802, 880362448, 723376170, 526861502, 515909231, 194259242, 110880015, 547245470, 685656670, 266353347, 778708971, 61230107, 611860238, 825766598, 697055703, 110529071, 526215481, 167606800, 383463245, 515248920, 908234423, 186833202, 917585373, 984403233, 841783816, 948343172, 333401736, 839215694, 913311298, 670509905, 424526394, 579520306, 598516278, 267819553, 591455871, 166597066, 329301012, 519172921, 626576671, 766297484, 260907942, 585073735, 949607194, 689085835, 671967602, 609547162, 521783104, 525026987, 866322906, 97486566, 813398020, 191216403, 465420562, 549967850, 858127161, 27682177, 574065105, 841261039, 835331527, 738052913, 380684644, 968220180, 114008392, 560048419, 321780648, 815449894, 9653548, 498891050, 436853877, 115035125, 849112460, 57167796, 864989031, 192742472, 270580111, 10774511, 371361544, 750463093, 165044659, 548340030, 744561337, 917824245, 183834005, 831442179, 990871195, 151660434, 203239788, 838033834, 150782800, 385100102, 335766570, 471147237, 647230246, 320271407, 691724132, 473242837, 838324867, 685931158, 129919942, 19728100, 356989489, 920927561, 129154779, 975415286, 365143754, 343297784, 674844363, 1838179, 389247064, 636721740, 951442001, 397843310, 522381437, 435302411, 515977894, 816944186, 265063965, 716220113, 344865409, 975642492, 925068033, 575183788, 785677609, 240944538, 631196632, 922510679, 431896832, 75421370, 374858841, 113667262, 383029859, 169415828, 835508622, 912712442, 812472702, 845801198, 782797524, 19705479, 436174916, 886726495, 295446224, 416771323, 942561632, 402783970, 927574620, 471648921, 16670922, 26793555, 753355904, 384944216, 185752414, 82615799, 574948440, 550474836, 366694882, 768175595, 492894146, 149413296, 988360207, 802189259, 549422642, 727507886, 847955474, 541086523, 216269026, 987277321, 993861752, 138631198, 526298888, 138549192, 57633230, 922277170, 910486454, 223504403, 996621520, 417564022, 234766282, 842980161, 436337896, 90790598, 260087485, 622885954, 305142987, 441907543, 436642505, 594903605, 936974885, 173893437, 50611503, 597480982, 174681900, 76916543, 268571995, 486191583, 114290949, 829756925, 166615261, 418581371, 866752217, 954041722, 103277647, 124075850, 964482861, 180939367, 807914268, 444286312, 752019174, 614445610, 525062728, 700718394, 185388649, 408112451, 651434297, 482153324, 593033099, 498818117, 560228948, 16375645, 637944239, 877533486, 676636585, 865489663, 675680678, 730972803, 96618534, 749837583, 411379422, 577497696, 656208245, 179526959, 866355994, 552931151, 887184814, 211883540, 837559977, 241756298, 72440279, 220481620, 713612813, 751780991, 556001246, 760124431, 669333740, 300179950, 31262084, 227194500, 25084803, 684276115, 768023672, 915594439, 373650946, 746528062, 409948602, 644372702, 171002528, 721205391, 245581421, 848353266, 934315253, 244489208, 899854039, 632906824, 441283543, 46797674, 861896409, 492712961, 285858812, 602734595, 99843083, 871924857, 982355847, 919625476, 462807907, 344410885, 333770603, 538209559, 977350644, 210816034, 905112248, 336082824, 65341704, 359506916, 852714296, 969386405, 404345037, 757215259, 815414249, 562086163, 998373283, 317634559, 28155621, 612211046, 837080322, 457882640, 552475613, 418226626, 416167644, 920606666, 400006615, 907883532, 173024158, 262671646, 401870958, 9017183, 469150426, 70686015, 317406110, 704240722, 585894175, 14555475, 478851395, 815896645, 883317501, 275866563, 998399064, 73987465, 503581686, 390318210, 279767832, 90400524, 169792542, 363608668, 963585284, 21395758, 126446174, 951683669, 272775295, 661909474, 8991693, 616386852, 728811794, 19103754, 26736799, 601052158, 738968942, 371374196, 695766427, 700615488, 513290202, 42857011, 871514051, 635206940, 856449014, 608865491, 988627153, 91016601, 417964628, 167691035, 579795546, 587213147, 964558433, 442414828, 311986694, 263019878, 194617478, 260645883, 307917426, 698179819, 749010749, 857047696, 685416026, 587359209, 703200481, 283339830, 995500189, 449006047, 991016270, 454995979, 869323493, 228062887, 301384289, 102951776, 454196273, 431907754, 269904591, 609719641, 560859434, 366135207, 224533144, 714122705, 683385112, 381310297, 765874102, 405774836, 783155634, 415319159, 446858862, 553261198, 462232796, 730245680, 6916527, 5766296, 552996883, 330774279, 509378920, 522877820, 9399111, 339762605, 536890973, 923855820, 61969718, 427001373, 832149122, 380954462, 947097180, 928389456, 145486229, 305794296, 222110109, 466718359, 864781605, 534390588, 159777135, 1384306, 191723552, 722123910, 4060242, 978531597, 838018434, 953539618, 809317265, 833688742, 493538929, 151817317, 129044184, 983203797, 807968160, 587789133, 278695076, 38784027, 723533934, 451361368, 903099026, 762665683, 770308074, 538071136, 985263579, 696522494, 151921546, 478985958, 458989273, 345325290, 659429994, 937427210, 711727967, 437025209, 925995883, 708121249, 707622359, 792680826, 562139036, 502919337, 257065592, 127099783, 573161628, 694666499, 328883275, 702609557, 512645437, 332053983, 140800450, 505240512, 158873887, 332676452, 247022662, 455864308, 15000202, 560955006, 797223950, 238074627, 85477019, 76263279, 537284433, 988194375, 116531797, 566470106, 351696162, 574428957, 719199292, 470349832, 558489712, 376419022, 192142092, 769718386, 660331855, 506078047, 459543734, 945449734, 269996941, 627423118, 387274714, 276508992, 929815517, 489575407, 482878311, 924880457, 67713149, 599113720, 224037415, 481164219, 183044730, 488273409, 722578288, 723795886, 229951555, 502305806, 449174190, 43364095, 992023296, 930693786, 300685342, 323916141, 666898459, 740082535, 207062170, 861662838, 320789173, 498854732, 295943721, 305227858, 399258253, 717191049, 909395454, 345846980, 957185786, 860680870, 815631825, 788940650, 3336578, 482293221, 529696567, 24430445, 270799506, 11612693, 67749930, 915897901, 189699614, 973640418, 639476365, 604837913, 487460878, 87851269, 608173547, 32426309, 548168563, 863574394, 974771865, 87345085, 387800895, 936529433, 148593763, 801634412, 675836555, 745356541, 848466229, 152284066, 190719464, 119433139, 977582763, 552582064, 971102547, 860511397, 588692542, 479289769, 658964176, 153683059, 202852355, 102347509, 62496214, 729731954, 346971729, 408621383, 723752067, 831921825, 166210958, 628089992, 988255352, 344489612, 129384662, 152351098, 386775752, 107693625, 765203718, 314544689, 668252518, 872205019, 66377859, 687271065, 907792636, 403403379, 758679198, 605053985, 362749422, 370323367, 885302373, 737954805, 859015253, 49619956, 661037182, 76802835, 347916300, 469533480, 738506940, 793835594, 528792483, 15511777, 302829981, 675761849, 697040315, 277656155, 163754629, 458774865, 103387765, 110913304, 29976412, 653688502, 960883098, 925075011, 169014702, 500390343, 869408431, 964436583, 325385428, 372651661, 970060574, 90677298, 464081682, 609678493, 269863922, 457405364, 607398093, 315185156, 951695421, 272174947, 311639030, 260593423, 139718288, 162226401, 645687592, 971056251, 396870513, 802914623, 748291721, 872217498, 671556659, 43700886, 654773040, 638532431, 22333896, 132685654, 626071541, 826050658, 66286723, 952143196, 443590828, 841076140, 246345907, 152531582, 469802534, 579808023, 391631512, 33281522, 643130823, 257026698, 356218354, 684529248, 513869810, 189568400, 117656915, 908472343, 720725476, 648297224, 460814936, 290154991, 17465583, 250897266, 641730602, 442448475, 72852076, 359591584, 296326178, 538522121, 625235982, 549966162, 759583010, 893123928, 863233185, 632745005, 926922337, 281107815, 894540771, 795491819, 206158927, 132651506, 655584258, 606546375, 148925312, 259039502, 126652683, 157546280, 980536152, 13912165, 616716003, 141244707, 875893377, 974379074, 692685252, 434211919, 790801824, 878427419, 621759048, 346912652, 28592973, 913248433, 571637649, 12503771, 152921256, 764693592, 254419795, 100034296, 812130696, 904952855, 998735563, 459275169, 409451555, 690861357, 417705109, 555739937, 96991682, 100942052, 592036130, 337567279, 334739940, 212639872, 674515873, 560527706, 910991629, 196765359, 620658620, 573833871, 850481064, 672652749, 43031350, 45671775, 392283826, 454179423, 218093641, 11823154, 806937147, 480772319, 229681729, 146374176, 331535793, 339860792, 652977602, 589185054, 798566053, 534025094, 949886250, 983113774, 740527721, 229060279, 397655894, 995926806, 568644524, 508547243, 340542714, 662645021, 969547858, 154776643, 836185747, 440865124, 215743928, 335789778, 980178177, 514117167, 266364301, 39061863, 236711370, 896821653, 723189179, 493988554, 749804510, 991985130, 621354328, 410205230, 738517704, 735130250, 402229741, 579647416, 575079404, 108289554, 936148033, 885915772, 245617405, 562649645, 891108481, 741399525, 156683589, 680875526, 607985982, 361141905, 60212231, 803695495, 424676190, 349595745, 643307821, 672351572, 973411041, 383069103, 474452843, 634240467, 83365266, 523914385, 790869528, 666424483, 777554033, 425228578, 390069528, 432276188, 890794949, 770451094, 350981653, 565216400, 212196962, 514245799, 499164005, 580652208, 832281742, 162055117, 310382587, 604209178, 50362939, 821651285, 520283098, 67178217, 484466674, 164055188, 148838184, 645739968, 999822782, 172538516, 31094909, 189373067, 938676097, 216161856, 289951668, 4251839, 324473212, 652748562, 217129805, 263503258, 367086255, 663453820, 656244560, 660996852, 562031099, 79212698, 885738836, 594007310, 160840969, 428175149, 117926391, 690308341, 369718672, 199882765, 400814355, 204383143, 613900922, 138035861, 559779532, 186580757, 6260978, 932294308, 544398186, 968549876, 252668033, 181228291, 359789060, 55529699, 98776314, 818961184, 368102837, 315494725, 303922934, 719914975, 816104422, 438462445, 675315800, 572723017, 240686315, 876906025, 563323427, 7092449, 413074012, 904627489, 340077292, 463829079, 129734652, 420351307, 996014803, 314660891, 212794085, 164747562, 392112404, 574692104, 506939879, 330718878, 557006965, 219458740, 117744967, 275182482, 635410121, 940438773, 318912017, 898798658, 964395862, 483922119, 890075934, 572702009, 217253134, 448916160, 7903052, 476233385, 397860188, 757547404, 273372372, 589378269, 540046778, 763481459, 282869601, 136000820, 236618931, 114385563, 993021353, 679744630, 731939554, 848534464, 488591717, 814527447, 465575890, 889972057, 632863598, 518257058, 871794852, 107634141, 668091336, 202512004, 928106234, 537605348, 601017495, 42187869, 871275212, 181180004, 981777732, 326669020, 160854559, 618495502, 566628263, 927990316, 979699025, 881898432, 398444388, 267785188, 23491330, 989478338, 548211982, 148546634, 80776851, 490286196, 558549690, 70597943, 569059002, 445382493, 377800005, 549607952, 91994173, 829429594, 85986803, 312317991, 456156899, 706488256, 48494168, 212626549, 683274536, 980269249, 721995041, 719906873, 70999992, 349387423, 679230120, 401991701, 234270097, 985131417, 913097352, 674317925, 115032255, 100674890, 434625664, 104294439, 697014197, 469628189, 154591830, 368975783, 234076511, 660966083, 310536540, 588676627, 605931561, 983509145, 520397692, 433973832, 139162439, 937128470, 440644183, 368645762, 558504847, 336768920, 805030807, 502824886, 646065878, 512608705, 402829381, 893602877, 243626635, 796178629, 682012123, 126954825, 283845360, 488583517, 354827224, 747050334, 328202277, 904160937, 713037291, 737206022, 615377670, 570814912, 516635208, 561922721, 355149499, 415559029, 552739778, 971559773, 984466942, 508662640, 595848082, 474469152, 555806791, 266070943, 438144250, 73389374, 951727432, 720353896, 26817068, 891242136, 992731834, 455062271, 359578399, 852826645, 39997622, 183547465, 417690130, 713749408, 739309498, 819147053, 582070505, 900966995, 941624837, 936640066, 926375160, 605110707, 599510412, 852429483, 868607838, 791384498, 948976724, 308596834, 589230902, 682073329, 211236297, 793483975, 896378, 984170983, 824146492, 586800630, 104007474, 450523116, 229124508, 550453120, 93326801, 298889179, 254604446, 99970027, 879446376, 124831827, 587098558, 247788552, 376737571, 476375515, 36114040, 405415849, 538948450, 154223496, 499372573, 65306895, 938009229, 616290540, 375076952, 120946245, 373494387, 473495652, 189945306, 412979020, 468553802, 709286641, 197434544, 874267312, 927823766, 621642320, 739352016, 686381918, 414910426, 175517986, 460655887, 793726072, 456334308, 828333350, 463170695, 477638588, 365937191, 47469332, 467863479, 96250814, 841640592, 549364707, 92516474, 197194371, 434329746, 53694706, 307902362, 386852634, 229510368, 506205658, 887720117, 62220664, 400551883, 98378032, 386383282, 972871750, 676649436, 82378436, 701133854, 380592004, 431528105, 513236155, 527769994, 14542992, 962702316, 268291140, 839149614, 773357896, 627880009, 45806752, 643734407, 188752047, 205034715, 619169710, 39097078, 536953023, 684733717, 576482791, 724042703, 202211894, 873279042, 653414764, 450050581, 828262623, 48631805, 15494336, 188740875, 828981393, 764691214, 71217831, 543390535, 386632623, 312653827, 238357819, 665307704, 896104060, 145853434, 290739809, 796432420, 721834537, 464386419, 617694422, 878067052, 388852635, 797630914, 661634969, 365305322, 232154923, 460739384, 259578354, 376734612, 306421951, 251830781, 313192162, 800144083, 975348732, 77272371, 388417415, 500691581, 444430414, 658988957, 150785750, 568100002, 119083929, 75766219, 977946756, 619688362, 786736958, 607767423, 289942051, 938489563, 907631401, 867976261, 889334845, 678036615, 483387125, 35743262, 675271672, 887205355, 230244507, 27784321, 335453237, 298632730, 262424471, 661488435, 559061877, 532976080, 432942019, 962256242, 671929046, 56496944, 966467146, 759570503, 83793661, 940950304, 727410846, 36828330, 692608364, 911961115, 339445571, 299104900, 4836289, 831936307, 774148754, 702504968, 433801876, 944155748, 732928834, 243502001, 445989963, 160979706, 992026609, 106512982, 521339775, 968833281, 353173925, 518161646, 38338653, 886372155, 99131316, 112679982, 429085741, 782702032, 817156772, 751551207, 782810355, 860101631, 442235018, 202038950, 761342287, 323493627, 423974924, 948574960, 964640402, 752516523, 384438304, 367615795, 714582749, 833736386, 192519742, 790658626, 752006042, 280422161, 354264324, 849167390, 855805802, 331992101, 628920669, 631034361, 824786941, 136789653, 404585933, 579643612, 944470604, 636207159, 126462881, 965067037, 655920049, 122708607, 482412751, 674017334, 256483579, 31808514, 16298052, 587563616, 847633343, 396891430, 647521341, 563621987, 119237218, 826537169, 85909610, 218527109, 548024800, 2248659, 688746991, 558162172, 206425430, 186314709, 860064401, 486934929, 422049255, 318284335, 749215736, 905220128, 322278017, 205028756, 419908500, 661910078, 365269839, 499612249, 23105252, 386754111, 617402569, 872472667, 22043891, 579106761, 981715367, 83083536, 532422863, 12167060, 915684378, 969300238, 582369037, 502758768, 820389594, 524405442, 939141831, 802039493, 517539080, 34670677, 779045977, 959528264, 361615290, 78221131, 811826612, 37568196, 130525720, 957751471, 355387792, 568485065, 803691191, 353955106, 431029782, 542475389, 353920789, 737600533, 257401518, 301254360, 544776731, 396111923, 421398600, 81035680, 734202198, 645419078, 560322889, 709050341, 658472807, 110044820, 963657834, 217367168, 689723932, 647637990, 373237097, 59140405, 907313997, 393727060, 212663828, 674835886, 496884040, 682834902, 401335678, 974020905, 314756204, 732244496, 95221082, 509300082, 898843242, 270350163, 26190080, 70169716, 417995958, 60243799, 314759427, 465195001, 44886899, 906728638, 965019554, 677595922, 652788195, 206764895, 866765976, 749083663, 600086600, 437116843, 325532509, 630957084, 261856088, 587681252, 605301669, 143344038, 713753766, 628048648, 766810058, 822836755, 419846388, 292042302, 499484249, 739595089, 943685700, 796926553, 683102486, 993792654, 725168866, 896889457, 642529971, 647333225, 65277665, 155448734, 875181501, 73350229, 426705250, 269957505, 557162863, 968865383, 971310432, 745431386, 374436933, 746885602, 884389605, 447922439, 656623137, 228757711, 523708600, 840968979, 948597432, 38957162, 996351415, 424778518, 666606065, 83943421, 546130765, 871416139, 697680507, 772847200, 395272182, 264219071, 677978547, 924207205, 25329630, 363655471, 187388888, 190901291, 872280819, 430754505, 762048283, 369802855, 693762486, 126182284, 776752293, 863929895, 476650150, 296815976, 362588906, 27910507, 36433182, 998505765, 900325472, 273756108, 708261149, 458169636, 588860415, 966914446, 164089474, 91613469, 432459810, 763744289, 600333342, 690597689, 7282821, 892350177, 644400388, 201722705, 134950946, 907627607, 806290374, 991128420, 862293605, 235607023, 243505933, 969797891, 65917317, 259793518, 773528351, 978668774, 776267053, 654119615, 270813658, 18980463, 762842202, 734625151, 138036352, 28303374, 975241023, 681376413, 890140900, 225369053, 338046035, 362037602, 181538912, 546514426, 136796915, 25830847, 464672650, 843146803, 559751470, 425941654, 37860306, 370038287, 952886975, 37002610, 64636395, 960097297, 736643599, 647105080, 243063442, 395734594, 663336572, 995390998, 393405909, 691776456, 422117172, 166658825, 257566268, 934021886, 299087445, 516420748, 70889038, 104674462, 906785667, 683979968, 66899980, 182963872, 792889972, 501382318, 501954913, 883860055, 645367427, 748929389, 737222469, 891283411, 594480289, 759962749, 904983625, 779973490, 934124433, 453715352, 250163089, 474954847, 466901425, 903722011, 616535854, 386949004, 328674625, 920253484, 850593184, 711805290, 611191375, 758111760, 4509853, 73372698, 157294599, 60541934, 185527899, 646256152, 215963059, 293353777, 252890574, 687499467, 503271944, 741948419, 708942663, 766670535, 439813180, 42590749, 883452627, 404475737, 536766041, 708348344, 597835251, 797523547, 160207896, 313245344, 324726500, 68719176, 997724611, 623980538, 908041958, 413726315, 424795919, 767974974, 14227017, 946692364, 187823583, 779921808, 791077101, 463762187, 254687508, 383330731, 519790096, 342822301, 455435177, 25686054, 637092033, 873373678, 912806436, 376848775, 95227314, 194867920, 592322018, 337967277, 682213140, 481982866, 20303743, 144265202, 536331652, 894062037, 838499852, 342498111, 533277273, 252802722, 638336626, 848432335, 652516397, 293891365, 521814360, 583916446, 403759465, 923033114, 969454894, 964149934, 486055474, 85947483, 151412017, 956113290, 742725748, 383995349, 565121770, 546509044, 145683998, 215953768, 72774679, 105167075, 634086960, 948156379, 735953830, 931975256, 643998651, 212985993, 516451188, 391950010, 91051820, 856183663, 987718831, 489476603, 730128840, 962471336, 716055738, 508269496, 397883645, 957875799, 428085702, 996971891, 135043248, 294654068, 590526873, 205053334, 566075221, 664689791, 450179937, 949575091, 190327932, 990212288, 990390586, 466862015, 486692838, 62758053, 390178058, 272091202, 445971010, 768626053, 76600271, 276541881, 518383059, 841775856, 166446376, 607892786, 90998916, 179420281, 738393634, 263469717, 36739877, 149276708, 568455443, 265102444, 287314927, 786833923, 152276024, 81647155, 938027081, 408452540, 615957777, 989918213, 681017597, 482621854, 702976438, 348662922, 555212427, 516047032, 808302315, 203472845, 635183958, 316219611, 68308971, 405455386, 149403210, 763619355, 893614880, 776401368, 726296428, 513963137, 310198975, 146925177, 580695709, 856224608, 555059276, 382380397, 507246001, 911188739, 901073934, 268601317, 792963343, 835165285, 924106459, 518522172, 463610907, 78933316, 548407134, 783877800, 735883257, 557362530, 702462402, 693443229, 762780559, 652678297, 238312465, 2632137, 221424330, 980180590, 402198012, 791751864, 487817399, 763411408, 364801774, 274179704, 629473378, 783114624, 476646331, 863046275, 196114821, 628705084, 687313974, 500156472, 12425604, 782338022, 115712067, 254191254, 296645443, 497765127, 461847744, 829091285, 114459744, 426997766, 490266118, 902807049, 244438972, 526066416, 446300138, 971807736, 652328699, 101317819, 723149228, 344495344, 730326295, 823658034, 898406517, 207724458, 693348091, 844533394, 424315321, 961560054, 238463648, 719472220, 569784397, 439016019, 802459849, 343543834, 406627638, 884484531, 505260464, 481002830, 484359539, 327868163, 259638561, 847211519, 5218671, 150172432, 246475446, 620821457, 929663302, 709735356, 266534042, 547371916, 420251764, 885648468, 593918362, 77175731, 579625756, 29364370, 599534785, 735531797, 37669764, 120143450, 735022659, 323781491, 818561041, 588945157, 340728854, 960992660, 11585523, 990523436, 275774172, 440577160, 454760680, 544716736, 275969038, 591919975, 703167951, 790290205, 646153053, 788627076, 723625680, 514019870, 266640413, 327930429, 310750695, 227540522, 305848294, 249522804, 38482176, 398083746, 355344458, 142828104, 761043203, 547155311, 730089620, 853438163, 254176779, 713369403, 579918072, 138461071, 43852597, 168333485, 253517427, 962503445, 748146411, 971355284, 428823908, 580411243, 572044662, 897492325, 731853903, 303407100, 709391462, 363709666, 152220378, 731810522, 837376675, 785094615, 102388313, 844674279, 318842725, 156744346, 910109046, 697107957, 500931875, 784665388, 695540737, 255190944, 451315017, 30841714, 849938222, 796224072, 525562904, 288646099, 368724206, 756431042, 942170046, 537313347, 706771161, 51289236, 267691069, 512105143, 502225823, 232410081, 667146991, 311461586, 676041157, 15786124, 947651313, 22543873, 318038401, 166570719, 110273373, 64078708, 308928908, 942757645, 402156318, 279991373, 273508875, 206741253, 536755085, 22910415, 906049115, 606694935, 90015842, 94771702, 672692408, 633209591, 592544906, 950392387, 25589610, 197303496, 880744502, 897037079, 384463435, 865202677, 251083251, 737907679, 633001275, 86407817, 68218042, 54792351, 814906749, 612273528, 681916035, 867951916, 72587439, 569660473, 915528513, 768192665, 926627995, 413140562, 76022556, 778382819, 8101116, 99695010, 947127970, 170853739, 862233993, 324594688, 634278902, 484772857, 179707110, 284128706, 401121542, 391729917, 29764937, 133035170, 350631274, 107024027, 472137181, 824556822, 860672687, 569334878, 595602384, 541633521, 180491075, 925170263, 184462690, 526126925, 558071148, 496874253, 543037713, 835280656, 858344312, 578477911, 145028502, 345833469, 816377711, 319971041, 726517375, 737197664, 114679774, 805606019, 893763440, 246083801, 679453313, 15651110, 960251253, 455295085, 996336518, 514981247, 20631004, 773316009, 813003517, 242499182, 973979289, 797337185, 599560818, 367171294, 927313578, 946837365, 361760587, 293776318, 380546608, 920918402, 468912410, 842179774, 169083333, 465460783, 989956078, 485098189, 566897791, 543819153, 460042172, 865104964, 158376032, 180996268, 681325132, 634330874, 389385208, 642463513, 961796167, 685774359, 220213900, 856335121, 912436726, 317271884, 642323930, 82871638, 852372398, 641570237, 72264650, 10060949, 307683097, 904411524, 709804748, 762396731, 318267625, 599207280, 531496393, 697995526, 415881345, 435380953, 345279835, 102152085, 26899970, 693660201, 390649112, 863981825, 110656598, 201370834, 828610260, 492985128, 30919784, 672413459, 807475623, 523915843, 57691438, 602204900, 674263328, 887231475, 83063369, 882025482, 961830008, 46845108, 705208265, 44545182, 569601541, 971213886, 618321737, 109856345, 160181986, 413171757, 597495791, 332701476, 691178232, 686666603, 817969527, 503126622, 379818975, 428247721, 991281244, 990508617, 357355285, 665116981, 273132501, 768991281, 486968866, 252907425, 378880549, 8133263, 582276989, 720550921, 753811132, 159944873, 377648528, 662035329, 701241228, 336237666, 790610434, 180529169, 693786815, 653238888, 792971209, 773751913, 425435171, 216600121, 567546185, 921975649, 326074763, 844301972, 896273179, 825185996, 57493959, 529421447, 74469366, 373631552, 909768965, 976725710, 13638231, 301622659, 5939751, 398122182, 420874154, 328668213, 887924356, 489223040, 855792670, 464511111, 107294562, 488092556, 397634166, 398842491, 248363547, 900982222, 600130097, 50791776, 255331110, 17423623, 429428270, 200166748, 639744214, 284073976, 129049543, 619792773, 109750964, 308895491, 28095315, 734173643, 235340507, 855434862, 421971795, 179513655, 857487047, 87615259, 390110931, 873661334, 455144559, 692795316, 402529129, 26660797, 619898919, 31245527, 706958136, 19469739, 994795059, 538068839, 630861936, 60723709, 756046670, 854008554, 245863833, 27547577, 462412504, 924319462, 626068033, 701129273, 156697179, 889949486, 664567877, 363939970, 448775884, 502529867, 936874701, 935785728, 840905781, 514852084, 698985376, 97740176, 675987420, 835712926, 186098913, 846213644, 972401078, 798620261, 494399314, 401157684, 110801689, 788772005, 744796102, 187790533, 354946958, 362811160, 316099640, 342819665, 948483312, 438498061, 982723420, 719233752, 281701649, 485979744, 843970869, 460893356, 782933847, 308009640, 237252435, 415883985, 949234037, 64881454, 225332257, 393299794, 997748585, 389310572, 651823602, 975618933, 704661760, 941129102, 50848669, 309256619, 257544040, 95765227, 775622356, 964447246, 319720633, 224965814, 719278127, 269244793, 192653790, 436631982, 777191258, 95008301, 352914827, 525975483, 735821127, 291348225, 161119511, 457471832, 966928579, 877913971, 881484159, 255671463, 969066063, 275681689, 272420272, 219732687, 631994974, 85195620, 11023999, 152854460, 173910873, 13285076, 541556335, 448312480, 331850200, 50653985, 513097895, 694524561, 746892324, 818080571, 733969479, 451477915, 993709443, 536288507, 497937668, 891115046, 95496072, 119080906, 172904708, 926680291, 540690381, 363357003, 676620564, 1758733, 496979148, 736228039, 395741831, 90952263, 640692511, 89007129, 145882830, 312497370, 606681265, 431537171, 237618753, 375817431, 847173229, 486905847, 281668804, 626889246, 312947055, 245303408, 181238472, 361899305, 209152117, 428185279, 562882390, 457583386, 660807733, 341796475, 402528534, 541899935, 985272500, 503607931, 785466125, 399121878, 663783371, 353734152, 404551288, 771265064, 986381730, 881609249, 288128185, 587499330, 933794148, 469333368, 228472871, 431017481, 610049622, 506200790, 890957123, 243000962, 161747027, 611077885, 472795663, 17239719, 524340778, 589705181, 173887862, 887286082, 176445984, 85317394, 12743728, 519172781, 128130017, 874106320, 456663910, 318339488, 793165975, 382129403, 24075079, 170043854, 267640784, 351063958, 168281169, 632499250, 152958913, 404904943, 344446924, 15135720, 221730118, 247471337, 312020336, 531339608, 769403997, 937577230, 508700293, 15191778, 467100440, 706172442, 300547988, 764838287, 830282782, 918340234, 106952725, 585517412, 475743825, 118255869, 749105574, 681710211, 169937749, 47684831, 338626080, 314241171, 929376892, 921206896, 117048823, 956454013, 190806632, 634245381, 845265716, 181826172, 434712231, 650545600, 603357221, 34691827, 259085947, 643874511, 717373822, 545894094, 681445101, 851962212, 938788123, 365220090, 899600033, 591812602, 644113685, 646660110, 787194784, 300034734, 530309400, 557816035, 288439875, 236647360, 640883515, 708286550, 4646198, 232843365, 513594192, 917298775, 54920998, 883811728, 434747495, 512130925, 988828616, 67069098, 356703450, 684966119, 976460644, 493460824, 932615970, 406220196, 27051318, 806196117, 111629488, 730589194, 790442207, 974356762, 839717700, 756470151, 811448195, 261046173, 71673742, 725976697, 950031710, 293324406, 391394969, 915263300, 621878244, 815672754, 790825726, 682010804, 300617610, 144433331, 214842205, 277414550, 875412287, 137155559, 902450766, 21302494, 794618982, 208967901, 913917632, 783472044, 802341521, 795681846, 356366759, 754283947, 356806609, 595912763, 672838930, 968561746, 222669230, 210171149, 6225343, 306808600, 819270805, 339457006, 950872345, 609195548, 682507276, 643549067, 762312108, 504232651, 145465751, 559723437, 208699395, 865235187, 603696355, 332881003, 875042688, 984169565, 649946264, 688170202, 771898468, 47590220, 574935285, 65810188, 893409570, 479932798, 353701213, 129050968, 335075353, 148282963, 713325653, 417995396, 76316998, 677436979, 77889450, 494888081, 87533215, 659453527, 172051971, 392904890, 845042945, 424428743, 643532159, 668677720, 902081160, 537839685, 202202241, 434807826, 75676667, 309531405, 157969002, 329070253, 385226691, 456267802, 618318122, 439741031, 768161816, 665773988, 953538297, 314182804, 750339761, 754229092, 675968217, 973037606, 394480402, 902825210, 150960678, 70663533, 340404186, 111924542, 30865796, 882748292, 597258925, 574724170, 387086561, 19262345, 586778125, 506236834, 166822998, 977027823, 950952431, 344797476, 594532906, 442064131, 495002897, 794433109, 806275524, 995970236, 732046707, 394026321, 223082819, 943091256, 92326129, 33407102, 765513603, 485681089, 579159190, 327428031, 460554976, 397672289, 150561667, 68526146, 449439345, 421630445, 997254850, 740812398, 70227550, 514609173, 618445376, 560127845, 590100211, 92898767, 311163798, 128007808, 420682283, 795701022, 542184622, 69037152, 5309724, 95543222, 463411409, 590054792, 834193871, 519834149, 70427215, 954332927, 952723066, 483554933, 553678823, 854250777, 925894185, 507077142, 160938195, 378222745, 418599133, 34668139, 693199007, 611076835, 871799978, 878799540, 217907366, 966256855, 239103730, 867442666, 633399956, 609978713, 147358989, 339063050, 590207852, 995885980, 589081811, 210089225, 732298819, 350352843, 512005232, 554450715, 894444041, 562155638, 495744387, 326737138, 904041255, 965429770, 113900915, 688767149, 58633684, 375385780, 588638131, 753139470, 142434780, 41225997, 358105715, 919677555, 119196211, 493297755, 829881501, 690960267, 265655355, 761261209, 273556302, 881716033, 746093242, 977498924, 464225760, 34832243, 816373656, 952980205, 322550817, 167735663, 47475170, 556171237, 406983426, 341839341, 657173072, 142926851, 588710113, 763271593, 403014477, 697226863, 3969634, 545643482, 97001756, 619158611, 310000956, 134604147, 904485332, 211845552, 247240855, 650083312, 977015688, 356424267, 251223976, 664660454, 762018059, 656348259, 382294810, 299840566, 855479601, 173780211, 174826099, 647003834, 836366632, 484123093, 889344545, 938455276, 946976856, 178489809, 549885331, 644784273, 574052108, 50477085, 928004192, 157738408, 990397744, 597901509, 61480564, 318179838, 759628550, 231548092, 391287726, 71087417, 458546137, 412559299, 200008202, 137761413, 637819618, 226001220, 818482215, 626238932, 491448116, 946337792, 747431848, 722683031, 200320137, 524553429, 624018488, 780053732, 348203413, 471114745, 236487324, 198063973, 593065394, 835792972, 865040604, 343461697, 111462490, 881917279, 503847678, 426897920, 541851367, 924212712, 710270826, 854210374, 169988987, 863328221, 641736210, 649830423, 63076456, 236605226, 854377249, 440439112, 692376326, 816954064, 236457003, 777475852, 479824629, 778793034, 154076880, 873390665, 474263463, 772819162, 266278586, 355449050, 923427540, 789330836, 367359431, 25275120, 47590186, 324429521, 589357140, 435348776, 894962018, 207347220, 731373995, 280849586, 646227655, 711206332, 992406859, 590706392, 347596867, 946400114, 317654812, 107936908, 373409538, 975745385, 494886856, 890531859, 598069047, 920401507, 909132167, 252209297, 479325105, 686854173, 78906200, 785901609, 323456198, 106964390, 338279677, 66895619, 400370161, 213174216, 334614096, 709175269, 275161571, 584305236, 190729188, 651268712, 875852061, 474134439, 936643301, 282480862, 605723595, 318505511, 877371101, 408921324, 816101414, 615152273, 289107722, 123976126, 439027989, 724003024, 103760229, 677514746, 654891694, 516721856, 185892335, 171767233, 612356422, 498832017, 140125076, 304663394, 318705489, 317370804, 847595599, 255779047, 467544979, 274986647, 386452941, 354882043, 992749232, 132579316, 811756889, 604701019, 25707457, 236973531, 513694089, 456702132, 964172231, 575072446, 49881227, 307271775, 327114815, 385442498, 121975423, 564823081, 351875545, 714078786, 322979806, 306082363, 571717971, 917362892, 68516689, 867613081, 94817322, 581399662, 479896631, 269177720, 246956474, 913086578, 874619369, 626080015, 990930133, 525819622, 466539300, 959235446, 121626528, 499277979, 792039331, 367578993, 585677756, 310491710, 172059084, 662855788, 111155023, 778366234, 374133520, 355994921, 228097892, 650459417, 736686020, 859227683, 139738741, 178244983, 338593213, 968833164, 675377677, 965185949, 198178646, 102990597, 532181501, 174081960, 86299720, 942608631, 936859573, 689663369, 337993931, 778046286, 983846772, 279187737, 206741465, 782787473, 264235742, 928228339, 193971288, 358776532, 845612978, 727600374, 330020975, 573887324, 570461604, 822673045, 955051541, 154129159, 342388121, 967148454, 303606456, 570347494, 529661687, 790799473, 569219105, 529114446, 800468668, 253390337, 874861972, 913659428, 523318068, 429015335, 121112767, 474475715, 739367794, 13844054, 118190843, 718157138, 126023824, 973536483, 65694329, 533161349, 219138121, 237884452, 549482451, 577956174, 114954288, 106554142, 599949749, 597037951, 848567558, 696161055, 227302930, 464694309, 877689507, 689419743, 515891665, 4522584, 234342735, 317778733, 314628287, 723707810, 318833561, 837981018, 128368194, 537700629, 455145513, 273994204, 292305637, 533589709, 45200123, 576757119, 496116684, 652296231, 568763164, 604286980, 996317433, 381680411, 198670297, 584777966, 166014072, 478702391, 331427001, 273978214, 370822219, 85522871, 720293630, 204229545, 851755420, 965486945, 805911014, 439382094, 571063459, 266941664, 45063093, 646572392, 686832659, 34066044, 352708080, 241484343, 830866069, 70925392, 186364966, 162399646, 247794524, 3414524, 565166678, 359295015, 266834074, 741682211, 988087297, 480432056, 852370170, 632215483, 714225019, 998139952, 776786130, 246858706, 203100900, 262459132, 479547394, 189852047, 543158987, 150191207, 959783329, 492300815, 214599799, 960403615, 20703293, 912456231, 168911964, 263493838, 416072524, 66905836, 561512595, 930224071, 651173650, 414274174, 9362420, 140017940, 536282299, 711367929, 724530222, 611521312, 793782977, 774862913, 960999892, 266066618, 370705232, 774932619, 765822038, 31078862, 772278425, 190465436, 279549626, 641334562, 456744880, 101520025, 51672943, 745942786, 92416630, 701548872, 675927558, 491720319, 535341338, 716492413, 349155312, 183983772, 565319104, 229214578, 263185809, 59221931, 246636994, 501098761, 990882217, 709267963, 695032833, 308991960, 418902473, 114444149, 188487352, 611704835, 612505261, 711990208, 790192008, 165777316, 557083161, 420578371, 185026301, 205450386, 773785818, 320526878, 366375221, 60154317, 320873671, 278572554, 897875656, 800676605, 992541356, 467996739, 302946817, 777521853, 206090951, 679041900, 639698820, 669930876, 551744119, 149360031, 806079512, 529833142, 543819551, 856997894, 126163502, 654437906, 556958359, 228535537, 403812558, 964683355, 39736826, 269364970, 496027428, 85085444, 124030675, 870403127, 373214449, 118667506, 972354382, 545423250, 113669485, 557388277, 97803396, 335334358, 961068146, 962744649, 303801595, 742333206, 933327158, 368050249, 144888769, 969313787, 281110611, 633659016, 35458332, 23961032, 282614366, 150066721, 177472637, 214949293, 283861940, 576513760, 209887468, 544491419, 113478557, 648597255, 920896561, 345130111, 972708563, 669635047, 43315550, 183542470, 100027942, 728168161, 550474753, 509342346, 625850101, 256293406, 80185320, 862829068, 832798985, 674676426, 771333965, 136564967, 746749843, 429500500, 129945409, 169649327, 958195004, 567698292, 110576602, 978745528, 614234757, 886240362, 358677014, 903624599, 340076754, 463510112, 879722099, 783049242, 740889350, 120842721, 841452795, 429984070, 857577834, 980545289, 175932379, 99827638, 865432432, 902377567, 735792991, 911901445, 511961457, 687583329, 158885229, 257250593, 545689225, 530122012, 511713531, 938703620, 737344378, 739711102, 33109526, 484984760, 562762727, 803436840, 675757723, 552743496, 434275685, 203019224, 158328354, 762797171, 78429495, 439683597, 272131478, 35987382, 675586571, 278511701, 679465887, 89141699, 333860558, 532146896, 686780158, 138661250, 211050651, 453879218, 88488474, 546574257, 170430901, 466739837, 874327345, 271500363, 240476571, 795937236, 881694464, 764357174, 420549035, 323264991, 741175428, 966015390, 340878306, 771994551, 654421938, 487463149, 790854992, 480250715, 35563884, 740179484, 500636026, 538762932, 121872662, 175297284, 161474450, 783012362, 365637481, 609503981, 376628368, 822417587, 484156999, 236991884, 703678216, 199868050, 457593016, 204258030, 382050181, 195638466, 353607216, 474043376, 94181300, 255444150, 712179394, 616880311, 497217427, 853065017, 607848552, 546915251, 281548110, 602786293, 761961534, 737458755, 950310293, 916045777, 835352581, 823718435, 446381277, 832514486, 358544672, 443471199, 433979936, 647717683, 723228300, 799803443, 751492052, 976289573, 703504502, 156343123, 95177094, 493709306, 9325728, 688399670, 278851717, 7543809, 435665592, 653503062, 67719299, 692302116, 321573530, 475482589, 102118336, 257758478, 634544238, 635411545, 802761660, 842297413, 282219454, 374267867, 374639746, 638653260, 600923154, 621916973, 443549004, 429551008, 258991438, 231561850, 836886931, 452291895, 949420063, 577402695, 82615400, 823531927, 599120760, 311764406, 850395430, 653133963, 291205896, 884958447, 387518184, 481198651] 38071))
+
+test5 :: Test
+test5 = TestCase (assertEqual "for (countComponents [521267470, 349112930, 327767978, 144434200, 938889644, 624728236, 632831418, 182141945, 548184191, 248969840, 475656481, 28955409, 381493877, 945624349, 705350395, 363867693, 574069134, 300771941, 671379554, 31831684, 923942370, 132289610, 639211434, 368988384, 720924152, 206387981, 573365604, 540375598, 313966100, 678237416, 856705104, 607073634, 237390764, 870178961, 504367394, 905165317, 284775365, 149810016, 741175150, 496120106, 67926486, 537178934, 86314708, 568422180, 234610537, 307149697, 160277513, 630948987, 328289736, 752215971, 933006100, 366061976, 183974977, 563592163, 188608520, 247217863, 141271872, 544439109, 463868062, 849816210, 317817894, 937223067, 355626617, 457840934, 520490588, 221043372, 666899741, 923189558, 478619002, 203128207, 189518840, 926977189, 999451677, 130965777, 165612764, 569416599, 232211673, 38381556, 733535656, 752890330, 124877836, 2488532, 520744415, 66679407, 846886951, 611516821, 127817719, 196674408, 880071519, 291938760, 362694826, 910464532, 375508509, 820385313, 58550558, 585658893, 425196995, 547812642, 718716617, 258769749, 602781267, 385781008, 980126464, 653933496, 201934402, 803343938, 956024740, 182166514, 174714761, 818673604, 795893865, 140998970, 12088263, 42937776, 644698568, 113252815, 170895206, 992662840, 643017263, 978438058, 523774838, 115345432, 360818233, 206409550, 448712313, 362782233, 970284354, 298815707, 211706570, 645742619, 815784172, 21343402, 248940053, 915907812, 725132969, 308590893, 871520416, 651889247, 183098506, 916896529, 323065695, 443633564, 623521467, 51701208, 658345087, 101406330, 731119531, 636139162, 856174358, 827887461, 667465344, 219042700, 256402396, 768496153, 631098337, 207158470, 363390327, 82344083, 918102826, 558415800, 926995654, 775582234, 667082451, 624520438, 201212278, 668494087, 696642037, 227173484, 597780595, 999169645, 617637457, 786001454, 630340270, 544745571, 722797278, 137166821, 710873764, 664081039, 919335974, 669347960, 388075876, 878932358, 259187835, 506741059, 323883252, 210386341, 594060706, 22544364, 80901305, 657636623, 978623752, 851133332, 519901538, 24733707, 770475910, 302840995, 133137238, 172862833, 815456216, 939016223, 692667491, 328758058, 15106791, 502777702, 864047441, 797793653, 409251017, 971194196, 756449187, 354467712, 437006958, 251601727, 653623532, 61875306, 139083293, 369695240, 726116166, 711949604, 514116474, 320737101, 265630093, 103604704, 828048681, 827881856, 56157281, 280323416, 625981973, 544808226, 32464994, 174021489, 709401361, 280268699, 565865373, 65207663, 329595471, 121337693, 919905016, 77133153, 818926306, 360574727, 546397637, 855873031, 114733259, 831649663, 781807407, 79738381, 498985502, 910971579, 502889391, 172597746, 148484529, 360763553, 210653660, 763623770, 508099157, 347415831, 235385010, 960504701, 584111298, 727909859, 306601593, 556992958, 290107811, 84569338, 146717363, 154926141, 90312189, 757656419, 98578784, 39349232, 583439763, 305296439, 541772182, 118794726, 410558081, 303567272, 777100011, 57495211, 908109567, 14921046, 121245082, 919958683, 985360384, 867875038, 449810879, 575282326, 859876130, 510952773, 316246901, 753113747, 522173911, 560430995, 441724916, 796970605, 792274184, 844868550, 907796090, 36239133, 223735884, 140226142, 887611348, 834164644, 113276379, 294066062, 415018201, 501475900, 582059623, 734247021, 112944668, 327180226, 429344762, 964375823, 140297483, 378326467, 354906973, 93019781, 217669462, 396050557, 455289404, 334667686, 840285038, 888251490, 671661910, 379654205, 993988223, 322359071, 357159809, 847682003, 115942326, 244575278, 258789567, 102100811, 263251122, 15911569, 451919078, 559346470, 719544143, 692997143, 581168520, 872827108, 954447146, 825605871, 717941983, 185080393, 874832322, 469978741, 73697592, 722167702, 970268707, 205770259, 303162273, 713609208, 250529723, 519151305, 968808197, 3974435, 588653423, 234447723, 462274634, 767795429, 681805752, 638037100, 910518158, 775928729, 533909659, 759045554, 899616592, 475280234, 948008974, 60457996, 244397408, 98672372, 989268694, 781784147, 507226425, 617379023, 976239602, 17823800, 807511242, 914170676, 310771995, 499224273, 321010983, 546243960, 144573230, 36118238, 140862537, 345183053, 371151395, 476920739, 380565101, 344250648, 363097960, 685727542, 957606835, 625105449, 360714277, 828972850, 356646646, 976568443, 896218798, 508668496, 820489261, 297290710, 983960284, 524170197, 116595476, 997668486, 278678982, 731961750, 952742604, 548553472, 455007661, 424610636, 751381793, 53501265, 635452736, 736430908, 525527923, 193104627, 712163685, 138852090, 498778831, 668711329, 935602669, 835791241, 259936639, 510814896, 845080202, 891589648, 431513456, 606035519, 375765871, 927923123, 652698684, 735166691, 515032117, 903312454, 87904456, 503037048, 920835456, 265415526, 678210686, 731320004, 893298838, 136794621, 85497868, 982398076, 748904899, 795346351, 499435285, 727413789, 313230984, 794005108, 520250327, 256708793, 8518586, 495480522, 138736651, 36730321, 193392455, 545650298, 689026978, 432669381, 282854067, 400737271, 43574819, 941668399, 335716761, 687150962, 11775519, 428493632, 445838290, 532567963, 690128130, 465007988, 837364378, 501559189, 515839390, 426701548, 246540197, 411711823, 559892740, 439709528, 181929120, 629741855, 883385576, 669757494, 84410511, 172348671, 437404499, 563280065, 814830736, 287335211, 161124565, 156882533, 841210495, 636339444, 507037072, 103321723, 875174669, 830467217, 440221197, 115355964, 515872050, 128584234, 973876693, 541418529, 828175308, 761165035, 666167914, 589454133, 71971381, 355863832, 204885386, 498015059, 938169628, 445703088, 372839077, 715482175, 539041817, 961921638, 274678448, 403959624, 96657922, 51122521, 492414907, 530192284, 436687089, 323672879, 149124314, 945978926, 670589374, 793394484, 328678534, 286918033, 532832481, 822606814, 95724424, 986062512, 828022692, 350562665, 714352423, 519486705, 603188825, 702843631, 99955558, 625569040, 638140698, 554224026, 449093388, 468834778, 925477776, 20884534, 75845682, 493467062, 773016737, 132725683, 699446161, 603666504, 110502981, 418013704, 72980389, 176236941, 626834132, 750857836, 980519532, 273417683, 615905332, 236991750, 950118256, 583352254, 133152977, 744036215, 888408298, 195845709, 687302098, 267054735, 673360422, 840495847, 958487874, 647823040, 972951501, 650749219, 459386369, 907826537, 677438076, 220430336, 550090257, 4333115, 132479685, 556999521, 309030812, 476859750, 938275448, 111328711, 517289780, 280329561, 224770110, 183829500, 157206583, 720367386, 334389050, 757852226, 934087315, 843047720, 172933225, 375176148, 134185421, 106652571, 724117517, 434956256, 916131122, 96410747, 141976232, 478852320, 902202043, 453519930, 843532384, 525821789, 919022196, 769009460, 939435032, 66337368, 471803996, 22297010, 683556239, 247732309, 452205043, 448366974, 387131234, 744437354, 319603045, 927030522, 522933325, 539361770, 942753426, 451153130, 113719401, 833059911, 230713203, 70990863, 695897973, 858225170, 628072910, 108049212, 719618073, 513308515, 843729037, 535150320, 821425272, 435218656, 802851136, 261661159, 962735322, 193171217, 7654925, 696948992, 926191346, 522212721, 191500920, 560603763, 995358531, 542750580, 553433573, 617487892, 26299006, 283386021, 783200818, 972279643, 214878432, 813777360, 766539612, 750138922, 111218877, 959429255, 313247687, 641974373, 750438527, 917653369, 112201386, 186845841, 616763929, 155507791, 638638808, 845904386, 617340657, 136696587, 742657055, 879221076, 276303393, 928244454, 162125667, 108767295, 157042096, 984835943, 232794825, 89576322, 256304054, 151064833, 944612354, 281897146, 349172284, 520431211, 699501188, 760104970, 250716873, 767161936, 246931190, 404367730, 720001831, 578753578, 877767638, 880020336, 175605840, 272945787, 186573321, 215817009, 512755627, 928451003, 54411463, 652319703, 442985190, 877928529, 623424725, 216628990, 527914413, 91790039, 457404361, 270500, 36078358, 529903221, 386883480, 710886657, 661811048, 153140673, 221091605, 335293345, 5175037, 659528509, 890270432, 716134831, 993696671, 374043737, 162804874, 128981846, 995882863, 145753965, 322513106, 689288959, 841938338, 448195087, 182409959, 248389885, 343629764, 680098962, 598949518, 680528778, 702637990, 973329239, 854916066, 353874394, 900361727, 102662291, 399103923, 781363138, 837826134, 960585614, 145082378, 63998789, 62490006, 136153969, 448747257, 858731846, 992493232, 821376643, 280171361, 389230198, 734619103, 134200759, 459551862, 549054682, 658617715, 403812152, 549706342, 448187720, 197172318, 267441764, 615679820, 571554035, 141035648, 714244542, 886013930, 310944578, 615626908, 952442170, 861177841, 516413999, 465635344, 137122638, 32236304, 1159320, 813099691, 800407273, 622876762, 115294281, 667091436, 844678095, 374426468, 196430699, 11356866, 520338154, 937569746, 420171321, 300471379, 751711914, 112816248, 375908257, 870912016, 879754446, 807262280, 628134382, 34560457, 73246086, 102290832, 869792634, 270172521, 337635777, 210142492, 812436229, 113647037, 607420050, 860543752, 912457405, 138976430, 719466173, 134625641, 882447540, 907905538, 537714023, 848634907, 731454485, 683700984, 474282253, 25136780, 736772755, 44384959, 158582706, 153786128, 314095124, 392397039, 709990221, 402287456, 544120731, 633601904, 423535335, 327757355, 663822192, 608502789, 223650602, 201455103, 459175729, 173848248, 521017549, 124068578, 881529975, 637750445, 534158048, 807778385, 513136785, 29506434, 142720748, 944901030, 772350526, 696226339, 72026360, 856622469, 121298798, 158922370, 310973548, 879983019, 400152497, 728354256, 499234626, 264616777, 767116646, 674603870, 323999300, 233664295, 496210286, 890868429, 600129642, 596335237, 499034037, 670345195, 955032238, 280832840, 610050387, 363756264, 221070894, 988407348, 906607120, 131838592, 500409731, 990055222, 225586295, 96361390, 109680985, 316018567, 848311336, 636403444, 265106603, 376278297, 532009518, 532172247, 798384200, 710000786, 517993482, 31041896, 804313100, 925101611, 437745439, 681134057, 559410262, 380055784, 619435371, 895600067, 780557280, 679014280, 450285069, 340211196, 52794021, 330836740, 271305923, 9776, 549296573, 893692395, 141428154, 67830183, 356585923, 683344006, 350399686, 170465335, 385880872, 48278765, 808335187, 920219188, 82955971, 540146220, 722222219, 652300089, 584949710, 296215495, 508408639, 728051841, 750261099, 439317906, 890827973, 755558067, 182092791, 623365203, 690818848, 605538702, 391191539, 771374536, 517418576, 434851486, 784957438, 471817791, 509026077, 930155172, 985855497, 188328004, 254467198, 852766581, 40968985, 283588995, 375987812, 429316781, 110034666, 548861632, 404882130, 706415437, 251935647, 877275252, 932370155, 855875425, 46180662, 970546572, 959607243, 938867241, 314697773, 537607290, 335802037, 570926875, 790421301, 75121456, 435299253, 927924614, 639662552, 998902282, 386254493, 759658292, 755743908, 893518528, 932983215, 621088300, 757725879, 217108943, 537241152, 258772510, 921843755, 719026542, 306361913, 487768002, 275741342, 193646267, 704295646, 799382312, 624010526, 269520323, 228068599, 655392479, 45394872, 869922100, 541282785, 343093073, 420809123, 779273937, 379682310, 965030808, 779023007, 160993442, 465054037, 151359993, 922207376, 319446490, 98613163, 740004165, 825213551, 201318495, 82062008, 944642196, 923967682, 475984729, 90529253, 466646924, 745612577, 833415069, 187586399, 161841985, 204780733, 202212856, 821859938, 976900500, 228206935, 28048325, 107477692, 851128217, 303788350, 273903978, 728962095, 980378989, 683625417, 868712025, 47344293, 101170680, 533739208, 444515472, 231297612, 117768066, 241719615, 135398543, 890102607, 122103679, 855324897, 293663, 86187649, 234230018, 852808062, 366621317, 147120965, 627409287, 827705569, 198019366, 112335973, 960234718, 821517698, 813739973, 579951810, 803465256, 529085120, 93473212, 865907123, 194558992, 327097170, 517650648, 456290477, 742309698, 741976106, 874671779, 737245842, 594062940, 922888771, 421381435, 363480037, 900332077, 117114123, 212383249, 334247419, 341276264, 354174931, 800142972, 387270323, 28492171, 87521779, 281036652, 710644581, 562042027, 889985964, 99958602, 78116150, 58358321, 130463226, 201493329, 849462522, 530023994, 142300007, 513198975, 552465398, 232686201, 941383211, 98712250, 502110518, 602728074, 803108485, 526158446, 471281899, 648513048, 316088070, 294887972, 853077874, 11110195, 652350458, 416914385, 39059034, 215438924, 574698289, 341564767, 381421777, 141635565, 756639606, 382057812, 471087337, 820376606, 278494659, 211454869, 175790702, 780904758, 287541454, 843079161, 230085807, 187615503, 432016458, 559107431, 190765655, 79380439, 261415072, 890180431, 145303074, 420644754, 810053215, 969972115, 288178659, 722908591, 649707667, 259477757, 750408071, 709804692, 710671234, 641000562, 324593808, 296948551, 262491174, 596129518, 340883998, 677993504, 625833624, 429600480, 108440688, 20499747, 308154133, 543522083, 850721045, 403162130, 142279709, 570338177, 650596139, 46650173, 338160934, 615033555, 684102265, 617280823, 972244654, 840478447, 970348554, 145101938, 865033161, 236260567, 969119956, 934301688, 424554547, 231038758, 850198538, 969200732, 852023402, 690138012, 866915705, 738939698, 614021507, 467595535, 343611568, 188729245, 821632245, 425043174, 366948317, 151625973, 793583559, 265338824, 330655206, 63212393, 444145135, 355263180, 311513232, 437738974, 442641814, 188351797, 150360878, 777469855, 842688191, 865811534, 282418070, 855508034, 153117456, 782098371, 439883400, 471617596, 642971844, 142086980, 30241699, 145175291, 394091787, 748554806, 473225953, 498367013, 831334985, 975795070, 998058026, 689417371, 26504817, 300450336, 300229093, 851931284, 508346609, 51831346, 846549905, 345123479, 43817505, 501510236, 779207948, 338615833, 439284032, 74037966, 197260423, 985053579, 955778936, 831574073, 476202648, 781421599, 450997196, 673289160, 777206007, 797238290, 589433718, 831364788, 819112735, 680025370, 703327362, 491117414, 970230411, 827826581, 837476683, 98861148, 913120371, 525906049, 219551069, 259722068, 798222415, 328021215, 777432333, 257826397, 390295618, 644651150, 978262810, 538651310, 948429124, 895217652, 373839311, 161604807, 844862838, 471584257, 433837937, 285251855, 815555705, 33899226, 513406178, 737661851, 707917190, 336843845, 93006104, 932838409, 871506684, 257053559, 624282968, 418437372, 387814074, 229452884, 677364527, 133960332, 326366663, 747612198, 721312213, 532974921, 759517103, 617132033, 870993502, 675363307, 306892335, 741085638, 202167093, 536410810, 778007463, 949174412, 241944772, 188476817, 503506561, 255941798, 481916219, 550023056, 103239680, 153453829, 42189439, 438824312, 286319066, 709177403, 929652186, 538418352, 329676810, 50176482, 887910225, 864717866, 581715900, 785216566, 372667512, 980797110, 132939210, 93478208, 248804691, 221851837, 246667619, 359377104, 863624795, 900222516, 579040363, 185151274, 803910113, 729005420, 444710353, 989637206, 242239113, 2864095, 987893096, 622069670, 210071449, 211704754, 422991762, 283795902, 279167175, 646543357, 342558070, 41103059, 40203798, 5643678, 497448458, 906033419, 133719611, 847818348, 619097592, 858928381, 646469185, 671824437, 491647510, 99985984, 814275056, 818001639, 420174296, 608962048, 428568743, 384141194, 342694414, 450487464, 203921073, 559248495, 598388348, 399069546, 622303471, 30756007, 254653238, 839101585, 119467502, 531847461, 321644773, 810398900, 709226391, 984659568, 589722167, 263217431, 393353415, 245326053, 444331822, 370464995, 44244791, 879238094, 940513793, 58817100, 173750590, 799112783, 777971125, 630346234, 938646010, 209420741, 231192630, 981474879, 601498273, 884889040, 574743078, 266696005, 398531161, 316874335, 712831986, 627886360, 248193998, 589446125, 818609513, 263899588, 200832713, 803812478, 49812038, 750287182, 235639792, 328818861, 413207590, 519055604, 225496589, 442466862, 791306309, 556099682, 411758447, 501772685, 237668207, 762067977, 473800492, 803856418, 790599671, 313644366, 216570317, 748740124, 297048886, 920113354, 250859693, 580535218, 810312058, 782777929, 998278798, 366897263, 970731892, 936233423, 752440502, 966183397, 722111554, 331231808, 890998103, 195884450, 120907567, 754493751, 676889588, 920919027, 301441636, 976313964, 540111647, 807638119, 22760713, 146213660, 492228022, 109145417, 523040265, 749763308, 494637233, 542741172, 74667181, 137028037, 163067444, 215373926, 878179931, 164766908, 250569816, 795679826, 438208677, 990464244, 565716901, 336435764, 34061006, 190710694, 465843787, 825470194, 349604543, 19094694, 291902544, 524760940, 535033750, 696383214, 371409514, 26618118, 248759549, 34668033, 884681506, 499807951, 984262433, 572387855, 983185158, 968453796, 503427135, 888367363, 898090300, 742699280, 849925688, 153037320, 600600906, 331318245, 770601213, 935471641, 497125448, 735760750, 601636613, 857555770, 690643212, 535129403, 816664832, 564531732, 506421734, 998790858, 240737894, 119907989, 731756356, 215844143, 23931830, 631262442, 760552468, 36212607, 578898666, 347113932, 153977143, 239663501, 667509174, 497026076, 655986877, 860297992, 263290336, 235774843, 872200575, 91684046, 332327082, 112988598, 658352531, 198011757, 331430707, 588864819, 858211864, 12918301, 909901480, 398481216, 296428882, 967185852, 32188641, 811911821, 870808912, 173284637, 123603124, 60185946, 603177950, 631555949, 530830139, 251613182, 681513344, 355936113, 570828732, 424954061, 377644961, 343059754, 852467790, 637454698, 739433280, 340893177, 637838607, 128145759, 487147793, 781176189, 488151841, 671085629, 902972633, 763978518, 799029189, 719486763, 371866328, 349912616, 178187435, 530065888, 906289926, 234456068, 822624941, 805531907, 764879707, 902891714, 237892057, 86469822, 505239214, 302675875, 930707353, 824506233, 51472519, 478044302, 265816554, 431183257, 517921388, 117269343, 281160758, 983778522, 196748917, 731893803, 797567396, 813354719, 227067309, 630340, 633277786, 850643853, 668040576, 503884949, 760564710, 371286175, 337594921, 281653205, 706545753, 229970009, 116808469, 827523936, 233204382, 777298577, 369294056, 905023959, 328265551, 651510416, 112116582, 499420343, 743805372, 794884967, 605753246, 775934990, 143335906, 103029437, 500088667, 129906725, 748701010, 467711809, 274582719, 76199214, 324032623, 671280300, 298789393, 312923431, 974099790, 544965748, 316104002, 768375730, 478317938, 37830617, 390370026, 69598189, 371692033, 882624144, 69689032, 818499045, 898225053, 32659554, 5461130, 23063269, 229349123, 309172856, 361233652, 46165466, 194967633, 243860994, 626701702, 97091088, 633835796, 79499246, 113520056, 12068671, 909414351, 695535232, 756936319, 79097795, 376957699, 497558287, 994275809, 855892469, 667162977, 560483352, 709722308, 828894998, 824808219, 344464029, 234703445, 496155301, 733629195, 537394635, 564096527, 513518610, 547849218, 154717286, 743724482, 780981055, 704136436, 754894323, 591891440, 973069789, 967231679, 480500899, 886866749, 10990672, 607878976, 490133812, 708918441, 319858879, 636746716, 957857063, 574420466, 206755404, 367023621, 804671986, 52891863, 467051447, 550560888, 20408558, 482663404, 711319695, 595783288, 22500008, 339554333, 815247286, 601543751, 345712862, 136291977, 305014018, 152209466, 663025283, 693381969, 692258789, 866956987, 625886897, 69780252, 192450751, 517213704, 107499777, 461413548, 11406803, 99959165, 883431162, 472921325, 440278027, 634312965, 685055655, 888116579, 447606400, 317159470, 610183080, 262211283, 760251155, 642903632, 573683775, 429734816, 276860178, 616526788, 529317626, 823790328, 515579165, 57594904, 619929708, 662575412, 166503448, 865909879, 692914109, 253621992, 508109696, 77677683, 255772867, 501912656, 275252344, 397436086, 428049022, 422170525, 84224987, 524413275, 864853274, 89322645, 902774564, 418041614, 225220581, 840222805, 216020222, 478255104, 955071245, 142681, 531286923, 984865068, 740260095, 215627877, 788889535, 615772860, 492918750, 281069023, 877746931, 652128834, 103319581, 702396619, 505088536, 576548912, 146045169, 799512292, 452981791, 271958026, 222987491, 785790149, 993996620, 122586624, 491550354, 101742675, 215170085, 347215435, 803733489, 125689377, 994920110, 310187285, 811143603, 501301307, 99916358, 580811364, 632116085, 570511259, 998058431, 990190833, 423823206, 158620868, 667027373, 51038050, 868235047, 496814115, 509696383, 199294089, 273440729, 146725763, 245994685, 75709260, 712085886, 782053889, 372182921, 56334055, 514972704, 255282037, 138082992, 888036856, 361783968, 747445946, 513123062, 890236891, 52246329, 653619919, 744102898, 670522359, 625335363, 618756269, 676183624, 281844583, 159800656, 467630446, 446244338, 374230338, 970774999, 532744456, 91717268, 406039554, 470933678, 756549196, 745451052, 852519116, 584640574, 714506155, 576205120, 226156114, 901035370, 641954919, 521893756, 103827318, 781127950, 968216297, 795157486, 525197647, 314378744, 532075542, 882953688, 872146726, 319843780, 329710585, 911521437, 809860752, 564615591, 262344337, 261319688, 377661065, 878230816, 654587459, 619352602, 428083275, 2795780, 879920139, 921006040, 936417158, 837707744, 362046872, 538125601, 371574544, 323379782, 925506022, 311401460, 304632895, 154169924, 312819908, 53827496, 362615174, 317538593, 125459684, 903815854, 555390241, 760017419, 927471002, 220349169, 780911656, 827454619, 979803002, 365811303, 343627097, 848267610, 354053710, 63212208, 54038363, 503358615, 705010872, 27555106, 371341793, 903152381, 988813898, 276299458, 929531200, 845364210, 229224164, 234487480, 799331267, 472839479, 119702250, 395869068, 964134267, 632643245, 926111977, 351674799, 707697067, 712151097, 400487954, 612951713, 262017009, 484221032, 581763681, 784322647, 255307201, 382200887, 484332630, 955348032, 227491397, 436643050, 857555241, 858603399, 594629097, 426682155, 969052352, 34100701, 806001478, 814790344, 260512894, 641223443, 990543429, 90914121, 996917671, 170545754, 872067347, 330639090, 128447820, 877150426, 43315129, 291981100, 971724575, 588139766, 712327762, 284602232, 921685857, 734106450, 386405369, 91251359, 694036424, 320514118, 693318303, 552900210, 776667958, 565159253, 758991274, 393313596, 419108296, 787852084, 668928529, 643691203, 213160442, 184927739, 607727777, 35273121, 825319576, 332555747, 18098459, 988707552, 183074684, 36318189, 822493159, 554232990, 776674007, 597917812, 266787910, 903717062, 197304693, 271406077, 635372084, 437480370, 489348542, 694237230, 121029008, 784670537, 286198474, 634197283, 474815210, 863203811, 743847157, 536478818, 382698040, 639503007, 300641250, 979219752, 108443146, 811727982, 755364616, 871183457, 119977866, 213220615, 50730481, 475641180, 378772294, 165001599, 956756421, 241950481, 218450135, 275584713, 255687197, 729295436, 778032076, 134829581, 422907716, 751413351, 173689452, 383578174, 385496670, 774429996, 445233279, 749212509, 228812580, 413093362, 125287109, 975402716, 533989186, 260690346, 645525555, 408162657, 551538769, 685659478, 596393516, 837348972, 406752185, 372312455, 311782792, 851195184, 185611996, 559071501, 922324696, 702371018, 170159349, 176487994, 118813211, 571170359, 742270506, 618500585, 424128396, 946432128, 209528839, 604069090, 286333629, 210024258, 957474135, 616293180, 563796093, 505352880, 552429540, 826918186, 173040427, 20040720, 181801159, 596764871, 861688899, 701152991, 780000031, 579633702, 373457387, 724512713, 34458565, 416813712, 926588587, 236409300, 143811910, 706144150, 764321792, 918839781, 725868025, 536276421, 997160266, 316581030, 511319269, 66696226, 119739865, 410249163, 42494031, 583716246, 812338081, 152828439, 869188602, 459884289, 438488740, 622408910, 748020944, 770929580, 960594567, 41861988, 161247562, 751275595, 526332751, 442851952, 798349823, 644573181, 161506827, 440689897, 19793413, 281368357, 846456739, 798807863, 968512975, 766518433, 66337629, 125886006, 983867218, 729708003, 381425934, 468960210, 565197275, 745090208, 172047826, 77232874, 526167202, 655410396, 310695606, 91170143, 276966586, 204284692, 675536445, 204471028, 117096962, 885607212, 803011598, 651499073, 531996252, 491141778, 975091404, 526059036, 744151201, 950213420, 116436628, 380302527, 797968512, 689958385, 806962438, 48109498, 811300242, 591045502, 432041405, 829714682, 168478440, 461251506, 728421683, 445372623, 787752183, 665704593, 834465245, 605486887, 696057511, 834482669, 76483047, 798746696, 547483561, 868753678, 631821583, 542754445, 904360778, 436112669, 813406635, 305908610, 629183638, 502614015, 616168447, 189386269, 208146332, 581308162, 836186632, 589400499, 40692101, 447035607, 463266807, 177351592, 285817382, 443376122, 913008587, 118191231, 238174920, 317506285, 550319298, 151988598, 409645099, 623151893, 178310679, 150768164, 210472462, 372121516, 315453554, 465721731, 424310306, 546647699, 40337884, 928458826, 236300590, 957964142, 626797580, 830941102, 686931802, 841017788, 582020149, 213681350, 175444520, 762803112, 192196207, 299902053, 121963311, 977233833, 459951411, 225309830, 175908338, 475275820, 272582659, 707962870, 991345415, 769833206, 927899680, 555162315, 275872890, 884660776, 565553192, 881772265, 39448331, 977716016, 23464873, 50669945, 911414744, 4323320, 948731368, 368443884, 533410955, 825061733, 254804319, 2880941, 858938655, 682669188, 420171455, 629573867, 781234134, 126414821, 214377244, 19582606, 142149746, 108214613, 236899053, 871918654, 31499526, 659163155, 860845070, 658521096, 888010469, 12270872, 52678270, 691146273, 211647427, 282093601, 141041611, 842621006, 888833988, 789683911, 365400252, 908474603, 846720278, 57111794, 375531281, 565854564, 434240728, 53215296, 394827307, 885311552, 250261842, 14380640, 278521592, 211618697, 71017966, 425674561, 300685705, 71182492, 199943527, 867128667, 646107420, 246590884, 435130901, 798226122, 18411871, 3289051, 975850710, 339389418, 152717327, 697084191, 888437079, 809986806, 512865204, 576435150, 944611832, 652753079, 501954951, 187460169, 836030567, 775218082, 621831763, 448154494, 882870037, 373370171, 267059002, 349282218, 294712109, 218063345, 423355393, 498573998, 620217787, 370994050, 136512081, 991698740, 970848069, 155500522, 997637549, 743868871, 955423197, 956046580, 700011637, 261081526, 267978102, 434579734, 958247010, 193641941, 767051989, 618783184, 8068367, 812355756, 439513507, 787934316, 587398278, 539360333, 208331661, 397596349, 661432686, 742146866, 21828093, 414728190, 304145797, 407647214, 13211031, 918532721, 257850744, 317941087, 397332093, 143629647, 880557616, 718133532, 523584487, 179795400, 64022320, 905860322, 375647265, 163335103, 596876473, 170580943, 169902506, 95859091, 627257108, 882787049, 796436854, 252594074, 708940538, 832500365, 652396892, 179395594, 943536416, 103907844, 619856713, 928897202, 729710731, 718978081, 637660907, 450939572, 888122157, 743113760, 154083161, 424345138, 716671043, 429530522, 666874572, 942181696, 126564601, 228952466, 534860484, 593408362, 482155855, 932963583, 368437, 222508679, 410237308, 37455989, 352703765, 400778056, 719273488, 899300398, 25342284, 857276696, 285047252, 6147696, 254646420, 374676251, 237926022, 697379244, 101518045, 339439559, 903462687, 98923915, 339315435, 478520317, 467656159, 402456753, 108230219, 667327474, 114093793, 364538607, 895868372, 404553087, 337914177, 395600661, 602938551, 634068218, 716619738, 204391617, 180032210, 416283612, 279677483, 913970193, 253607356, 514547322, 483616649, 324887702, 342713741, 134026038, 326824727, 790472455, 457298423, 224501786, 537989516, 148743140, 588113442, 298278248, 646593607, 321769178, 72053698, 322460492, 331635396, 258865748, 824170795, 479797291, 681534257, 180674406, 514969179, 143411129, 83749643, 989640772, 823477331, 471839709, 599710495, 358344148, 474159103, 785150739, 714632587, 493544496, 678795997, 420818577, 371971991, 561666517, 58463873, 440712192, 869049663, 988975076, 270552238, 932137016, 29459773, 287131493, 917145446, 158093017, 101701440, 701091931, 857281745, 399158136, 785068361, 606689894, 904062017, 339324502, 616796886, 366797514, 358871345, 353745987, 289900049, 954911196, 651489337, 864944128, 726581846, 774480194, 442281690, 180807937, 876060947, 12224797, 899249948, 670881937, 383877002, 612900491, 543504865, 120832555, 581890892, 364374870, 355549899, 660103963, 619064087, 988179677, 726991886, 276850311, 773616545, 54785983, 873265998, 429857800, 692505823, 40629313, 937120548, 148787413, 407868713, 336058119, 531560557, 714504806, 710438856, 539813791, 680172561, 962345675, 869012730, 879134687, 679771714, 268789329, 827512346, 276055750, 980823225, 595282913, 937417905, 437085005, 898745479, 25949650, 944485837, 616040701, 701894248, 43443131, 726770090, 429199934, 815557470, 17857513, 403513463, 632340240, 652412477, 360074276, 344434692, 173768931, 20277137, 320892821, 515557308, 847122333, 158313642, 212885176, 91385674, 404189287, 481535425, 229869225, 568823604, 367926582, 856931560, 838059738, 7847131, 278450610, 335072418, 91465550, 532367186, 581511813, 452963827, 337821529, 901944639, 834787475, 742936703, 33256558, 858349837, 317380616, 936815415, 931615405, 913534669, 674692767, 775068345, 30359620, 522957583, 663429335, 868487744, 326124836, 840272897, 303170627, 455918, 782198443, 722692065, 936621434, 276132998, 611668389, 420797703, 763926569, 249370819, 946336308, 569513483, 588359411, 585681317, 28485706, 557427220, 914222108, 545815348, 789340202, 41152066, 322809456, 420257253, 989040813, 18827002, 811899701, 548526209, 607462815, 796919300, 150077781, 45658272, 148862726, 926040257, 220482481, 400851389, 972398012, 254067064, 573360529, 446608164, 880687714, 546883883, 662947343, 498575284, 825086531, 220278427, 51440645, 705414915, 767875200, 756046347, 141446377, 810246264, 965373308, 360307446, 922012195, 859211979, 882849644, 640058753, 550239147, 655339609, 484171624, 464160632, 238049051, 792522303, 992998832, 971907804, 133639984, 302861755, 208003986, 874386102, 566349097, 431842243, 419785848, 631111556, 362505992, 279072434, 523907137, 987403368, 249253592, 672492841, 836206726, 522277839, 274459003, 399642957, 903197028, 714174136, 951771484, 60096420, 112236326, 118653517, 382709035, 465632877, 222224434, 738674438, 105246882, 907588782, 773822451, 743126306, 204081120, 367987177, 805546845, 900681352, 611573827, 869777292, 376399627, 787912790, 413963812, 542538690, 169086383, 139959926, 340148655, 447505822, 814159003, 590666823, 400957063, 240077505, 274864680, 295386410, 70236921, 777063864, 734416861, 833495945, 767363819, 58176336, 262207351, 454375154, 714644349, 615116286, 259148972, 158932955, 188881819, 370359473, 502831508, 105503785, 372959175, 428271890, 758496682, 789563659, 35485380, 39463152, 991165003, 453991917, 436555808, 632268450, 602447889, 896178293, 17522236, 345416788, 976049140, 836228043, 722446972, 391614156, 154508852, 891828608, 214443610, 429522970, 317259564, 893035972, 297843454, 109363963, 761630620, 490645821, 127574546, 172257414, 116064687, 584650577, 884613575, 640700180, 412351035, 372916743, 590338938, 168446846, 390143570, 66537223, 670384486, 850114465, 43574825, 386529829, 970273736, 798585566, 457823213, 331045874, 284803949, 370875250, 133325912, 827153550, 538497688, 768261962, 467152019, 777235520, 727454819, 5699568, 72533577, 273942205, 423917077, 782609636, 266737212, 681295660, 807767806, 347710386, 741429210, 676455464, 768903769, 183151395, 846222414, 47407938, 101682460, 780296536, 580287597, 769008567, 919967696, 813109367, 854356494, 811835132, 187058231, 31996689, 593552265, 890336895, 366288381, 992236447, 572637964, 985584302, 543544569, 432029627, 486157257, 443535286, 215439170, 731660772, 260962792, 710112607, 909134777, 61681817, 536271275, 963401966, 546824527, 770303133, 325125132, 857342051, 763639671, 504386673, 121783562, 456308712, 175156507, 897410553, 270917420, 133791449, 249440009, 159326706, 809794384, 871926236, 346306765, 473343844, 122887336, 776577948, 56317536, 598663298, 497570494, 547465010, 439478610, 983909675, 638283177, 916705849, 239480120, 458014087, 727319543, 200744976, 515361760, 244724755, 222814170, 699691191, 961900094, 513517306, 536003141, 143362448, 422711081, 322589415, 431968534, 366164395, 770235346, 440909351, 354787124, 908650253, 973800951, 872654162, 320406381, 512704036, 949735249, 258222230, 387935464, 535026542, 25253882, 929988499, 387315838, 688469552, 559693564, 872120833, 291344749, 892408165, 78991936, 801178947, 593910251, 976287508, 958269430, 636836060, 200096150, 300462256, 544975549, 494947606, 261450743, 946241448, 459475586, 357889859, 491754179, 617229260, 232315933, 920645114, 874358482, 300704991, 22919234, 647492420, 656267174, 705305519, 805256465, 249344912, 593260711, 384348870, 946011411, 678664105, 553864849, 747156527, 832596263, 806549708, 389938777, 427184391, 906483995, 408274950, 786200314, 143444075, 776220285, 16191598, 141352554, 983554637, 724529320, 534343334, 215109787, 733824022, 683210703, 805299721, 950465958, 697973565, 197256415, 975898075, 518796798, 522405126, 195985636, 222213833, 628138895, 668528107, 637228698, 971735329, 942980477, 461340969, 731804857, 148298446, 429289714, 661237640, 68266836, 106810772, 452539973, 736471333, 140185872, 899493870, 373825177, 199081333, 163792313, 507579555, 941068818, 814073585, 322240841, 868214202, 611544012, 400656611, 785404595, 638052840, 474060207, 730762622, 79867067, 194651042, 680484422, 584928618, 468430184, 460553559, 672129979, 865431646, 69601133, 53383385, 745515016, 92372363, 525067294, 710341385, 972876177, 479393216, 68139347, 425079528, 627276110, 382992882, 974487710, 710330226, 743942782, 324572644, 57321192, 834046092, 659955508, 787352957, 762131349, 739037929, 698116314, 145517960, 689304064, 111570577, 591734246, 207647871, 595090827, 833981257, 272346488, 3522485, 741702334, 947440403, 123328918, 762677509, 809315883, 741770002, 681495318, 344770709, 456250385, 583550736, 388654594, 910016366, 884705109, 16983083, 173103359, 167646244, 205022806, 908689319, 103444271, 693061445, 550282293, 283534230, 71818933, 360606660, 541817852, 203021125, 334157951, 343369189, 53471893, 159123973, 297354754, 279375201, 93119048, 439984728, 826443271, 18840097, 435540494, 82982118, 211544082, 692375572, 242277898, 40243692, 871191499, 811457067, 501142676, 367978570, 183278586, 250017918, 830164344, 355615206, 597259975, 200619794, 700634017, 284193920, 256959032, 397754207, 407380323, 196203587, 563349366, 406189032, 2327265, 316695121, 997448234, 390461093, 710683145, 170506618, 266140763, 952051468, 963627322, 986243042, 792502826, 920700885, 282170987, 608627114, 397832026, 996231328, 683525539, 475793449, 295922669, 994259596, 862589978, 319826471, 140007719, 767303045, 318687100, 372857123, 198532439, 641276129, 602329429, 226943688, 635111726, 223233601, 437408182, 753012106, 943304873, 643924205, 982461930, 313198168, 866610207, 91619465, 688083694, 386919843, 688716281, 453967596, 115689595, 662797484, 309069756, 578881267, 952060609, 436522517, 83905110, 547678098, 220734859, 786315526, 786279860, 283520951, 996697347, 829910782, 366487998, 788411325, 253316459, 952017276, 574623537, 757824343, 504324841, 48298395, 654474861, 557695399, 848680671, 460640374, 43258148, 443229598, 6357316, 392099108, 396758006, 143201233, 263904994, 852737553, 935259338, 445442469, 107280798, 791481425, 749473758, 256772443, 626327744, 961336476, 309036579, 90128836, 570245001, 170563569, 945235616, 873706833, 555146383, 47434288, 401217112, 745564999, 15298917, 4131313, 417384315, 795865587, 67051082, 39931674, 460625095, 319881255, 544769538, 285789128, 655939320, 594856759, 270300842, 624527551, 883991607, 764862459, 10484629, 785346116, 518259719, 780804556, 966640520, 828242718, 637470836, 783684573, 615006977, 359002341, 654384109, 690355711, 126399365, 91409158, 647530802, 142431343, 334140906, 350133118, 891301826, 400807955, 259801781, 663568000, 22352086, 296966333, 939484307, 347678276, 545181186, 374690973, 255093275, 885052984, 396231042, 348502768, 288190611, 756657527, 515209647, 147268087, 933112020, 939470878, 485657697, 58859510, 327873449, 243876161, 867499283, 731047531, 768221507, 362690300, 132985292, 715344436, 109712611, 840742796, 924025675, 155590177, 603078198, 967216950, 790068178, 896933426, 562983098, 400543784, 165725773, 233787789, 359469618, 365953162, 810038480, 587306656, 829083749, 663288640, 672295399, 968963740, 124516453, 368277826, 972255894, 43012805, 746350567, 712911545, 161557169, 129884066, 394231187, 545422458, 206009581, 908075922, 509798742, 732700452, 24690879, 616332353, 895984550, 4770727, 120653278, 387232774, 438299461, 764507979, 416984615, 154054603, 855861676, 771003532, 163428386, 263897657, 461247474, 117429767, 204007610, 62965816, 583072996, 149189711, 510269943, 177362624, 920251828, 711022409, 801232988, 532894659, 282233372, 911030331, 847554371, 996689148, 145250781, 241430691, 912000451, 566460897, 840431371, 281806903, 431951765, 721343201, 680144859, 230939986, 264956519, 223103815, 757762376, 93805148, 234522368, 485691960, 600319502, 584730011, 29559825, 778255475, 982600817, 449605630, 595656860, 130434982, 349094078, 421447514, 709088667, 980868362, 269427366, 541104537, 736447833, 77168967, 532700369, 390626510, 685701301, 699997554, 444354094, 617177156, 702470650, 964203114, 278554455, 99567205, 658569419, 781160509, 284590554, 269168959, 838946801, 856767321, 17867624, 780611961, 711952369, 468397262, 327410813, 357778234, 165355953, 356438252, 722053626, 767413315, 232138172, 978664734, 596246614, 286116562, 137926675, 134522661, 922037968, 17939769, 657060579, 277544575, 988101228, 671639274, 165762147, 298156963, 254766764, 464067695, 916232775, 641340747, 226103292, 432707531, 800602278, 851966973, 527187812, 718223896, 211588928, 615284938, 934559557, 422952165, 203019455, 863209754, 163574735, 670787651, 900399860, 118064192, 196379677, 839498588, 922494074, 274248942, 760210785, 858357263, 891081060, 614515246, 415536672, 489355563, 473708800, 207704700, 840518597, 577732826, 971962782, 649696584, 746290340, 54473914, 547941165, 877775479, 597742913, 61913401, 451071575, 203265728, 360015991, 247359537, 779904336, 484596643, 248350550, 498796586, 244571582, 422611872, 533246602, 336377534, 155879724, 379046423, 243332101, 345988859, 504295960, 72304327, 972651997, 510875745, 475811172, 123505199, 707936037, 475231575, 639482779, 521542952, 24777214, 464458098, 746266043, 817348704, 425880458, 448923302, 658202140, 439785667, 35306575, 646055003, 552022910, 813071893, 127987656, 97146394, 534149939, 743114995, 472885464, 891888633, 263081670, 297590382, 303408783, 445033274, 913303644, 834143416, 661131204, 552502347, 917341930, 901835399, 108980672, 877002743, 70249578, 4234414, 63994150, 724863468, 509463182, 444128621, 30137059, 660637400, 90210640, 217543264, 202421877, 769788016, 107303712, 58694592, 871956065, 588556031, 127410502, 14042320, 442615387, 96190709, 252505837, 616095264, 35085281, 683353955, 312160271, 873584435, 243091095, 751046857, 966584167, 673063855, 863834287, 869914883, 656909260, 195615088, 589192276, 97497114, 322647097, 427131737, 73536653, 996873422, 445991206, 768798145, 880697609, 978894266, 842442771, 627690785, 899555142, 317630926, 348455553, 389548681, 357193849, 582535597, 26059540, 376400732, 643725269, 459052874, 974623987, 639241308, 566453209, 383480565, 789919332, 176570539, 469885712, 454436046, 677569269, 348197933, 91326010, 968947311, 156735873, 439877863, 116375791, 166427524, 430792509, 169485007, 103049444, 257327417, 970994447, 757754314, 543286055, 755274968, 740719504, 714458751, 417277969, 956330019, 797603403, 975127617, 999470406, 719170732, 631784302, 137081584, 547699250, 694601327, 323684128, 57536855, 186268930, 999786899, 338453591, 532293698, 296128340, 451406596, 400944588, 790272202, 520073254, 542487438, 47418610, 56206844, 499197679, 265249198, 528991568, 131583244, 271451856, 741712770, 942553524, 383240685, 814001316, 646360007, 658714098, 787666769, 454581175, 674583098, 924261075, 186563125, 905466110, 216422120, 442692857, 842809066, 9605195, 436595247, 961377633, 773793243, 707171363, 98070206, 555788716, 192460208, 817297343, 790586793, 254911203, 168221284, 618230782, 492386185, 934927577, 572529409, 18088981, 219557178, 918547815, 643604426, 775812156, 163297413, 797766815, 275839108, 859378706, 233907285, 749006176, 757851736, 466256136, 763641233, 925376163, 725379046, 369616023, 26824321, 28705503, 810769397, 144523072, 461715790, 621879917, 278419214, 607625440, 104272492, 933696375, 628792732, 639478457, 563711868, 942884423, 642460659, 555007165, 497569399, 621151180, 560646343, 523664767, 286769174, 982564214, 260676319, 814917682, 852172714, 469296671, 626900044, 430456340, 143518430, 460407135, 777382218, 765778718, 734324040, 97774266, 305365408, 832332337, 676358486, 889340731, 756052524, 637853159, 263054172, 170319221, 753122953, 727504943, 807385127, 911046678, 581553705, 250558429, 469604323, 520608583, 664868910, 680354980, 897533243, 43382196, 349240281, 412702829, 934405894, 972466568, 309212663, 755763111, 480529892, 408027774, 338525860, 192394416, 171212725, 423317745, 833066378, 579698309, 548379393, 401341208, 81154964, 684995295, 273695823, 227000911, 899435580, 247776257, 342555044, 580593074, 36849714, 879818045, 267778990, 969346140, 574977498, 554752487, 863385776, 365182432, 612248801, 764957437, 653886797, 938295064, 284561525, 833129415, 271068518, 361348147, 340525938, 888383436, 558595832, 679957308, 346608423, 646186699, 585126701, 951270067, 694399351, 961917552, 489205577, 972170568, 572699734, 188095862, 717771987, 668542172, 327789797, 922671330, 712158524, 577481433, 86656204, 30697784, 295762512, 112373085, 136998322, 615166007, 358850280, 696361603, 665161287, 958639364, 399746239, 671411731, 990376711, 902494721, 349799049, 118623463, 565222828, 500100700, 130632487, 903697713, 697767099, 634243785, 911275641, 449335537, 37907393, 377627541, 536688347, 365000841, 702758125, 786824116, 210774790, 567486520, 995538005, 608448676, 576943447, 741576263, 933230446, 780309820, 311090339, 795178000, 571171359, 924087624, 425646235, 349125180, 711595898, 180077013, 804045427, 457639765, 85396834, 304349672, 305313028, 428983890, 794603168, 270120004, 778608784, 644446989, 267938209, 878991847, 168816165, 257522921, 24226725, 153647477, 943891624, 529006777, 18114559, 676102770, 7800410, 915459691, 553017996, 988002301, 389938543, 433284578, 831326291, 371331994, 170266272, 851590796, 214035762, 203623717, 492574008, 119105845, 243711329, 517569598, 985671396, 10021815, 986940766, 287189953, 440184040, 462040111, 916826261, 885806804, 222942943, 720622183, 718032344, 588890642, 242840369, 690910748, 535235836, 254240007, 609616198, 792337902, 183734330, 631382279, 306303793, 184738844, 682713146, 702015125, 94806936, 555213323, 621604439, 774160992, 119424271, 41333500, 190494311, 329390437, 148513839, 879018929, 725506441, 231124767, 817331693, 635631497, 743825175, 88108013, 41759199, 942558192, 731803606, 920825166, 155786455, 329943804, 376178297, 944963783, 773618681, 522859043, 804720318, 908377302, 540410087, 130139196, 24777907, 175682313, 911928861, 931621679, 821956718, 342040993, 504130967, 311270136, 361760544, 81892987, 255800260, 168659575, 726173062, 64657014, 152163372, 52980509, 868347486, 638920481, 343446734, 99175864, 445655267, 316741936, 982468025, 970953178, 936314792, 926764780, 897709084, 715032392, 704537435, 507633036, 529788153, 994975904, 270126030, 596651175, 244283501, 254850756, 364968072, 458377977, 75106517, 7395615, 567257185, 277127041, 977642343, 606734540, 40011335, 340608922, 155195099, 289217908, 502910127, 744320964, 424130371, 192202770, 15151739, 567481463, 671411179, 869282917, 104386012, 862442434, 693487344, 524570118, 318889216, 780699294, 452271297, 812718039, 63518833, 776417743, 917105311, 153590268, 20857904, 579378280, 274882928, 558335518, 897608198, 383194904, 983496343, 831057811, 733374710, 838759815, 385891757, 759753262, 128970579, 945483233, 921485969, 305301558, 183001793, 185594426, 991003100, 756217592, 386363330, 230838413, 416534383, 350082452, 197724966, 612916443, 287973602, 708544489, 727013685, 422421497, 68825011, 391385436, 621033619, 276592090, 497657395, 46804291, 498117069, 907617954, 848726448, 257487934, 759515880, 277937946, 205942566, 900787006, 675281475, 194728754, 766822993, 300635541, 690015805, 233714950, 697717176, 644796291, 120489891, 213741762, 607489980, 177900233, 716567127, 682303337, 100458453, 826297076, 815552433, 248084355, 628211939, 511355817, 358514581, 744511457, 156074869, 794408101, 634495748, 121174579, 828004984, 235864438, 266812276, 707928336, 350350560, 24126282, 53943519, 267987126, 129774202, 26336377, 530138186, 510585720, 393827141, 303900378, 978744368, 269949496, 723427256, 458838678, 56216438, 665103479, 597179555, 605181729, 578306763, 865495388, 453522888, 192765333, 650067994, 504379183, 733009758, 557182873, 716408516, 982364887, 786257845, 31741692, 727019288, 410635403, 520557523, 911419990, 4781431, 147086788, 744835121, 447928465, 721907001, 640713648, 13869514, 90484037, 57515108, 297438223, 363415155, 35588486, 334577040, 457246855, 558956012, 488287392, 522400670, 719018991, 36576392, 622707419, 842644451, 474214367, 66652407, 29647896, 160754891, 328237207, 300788995, 818203222, 224887916, 459969850, 985423340, 561360973, 962140592, 384303958, 973342123, 657388043, 730804627, 162192527, 954465380, 443863673, 904556921, 203828251, 870342886, 767248815, 254633151, 476319236, 283604851, 853849777, 440326324, 241306554, 702881910, 601386580, 127571661, 979455899, 373691278, 858211234, 748219960, 199046939, 895711040, 503137818, 176235618, 6107970, 882972342, 41706211, 76356818, 170152163, 541423742, 829253286, 322975998, 572187246, 64554280, 634801415, 89674283, 335945397, 686852049, 183934092, 572137357, 20395716, 339746901, 631163243, 40054652, 169198122, 345805087, 516787422, 281985702, 138831955, 802201370, 821981710, 670862497, 792437906, 973270219, 402279892, 580074850, 28470443, 294678437, 767837875, 666157517, 225286907, 629381967, 126929007, 876264889, 820050334, 148617563, 920695940, 889651832, 424959694, 76967514, 537651045, 581831804, 413093988, 976967770, 928128534, 469385066, 296335668, 279838962, 727704784, 863431082, 742460653, 588756293, 628539664, 639896981, 497167398, 726467792, 453077301, 61926836, 832944687, 755057103, 340841357, 902257375, 978508643, 431650228, 755083116, 549384447, 615983895, 998485087, 806391992, 157398537, 551791298, 172077677, 889992171, 995889562, 179325556, 2604890, 177176481, 387561075, 668160900, 139648047, 471518380, 245351149, 585620851, 525384925, 99757806, 267974883, 782779608, 130171586, 504932171, 64170142, 927047031, 466645461, 690448696, 337787984, 682118373, 413919003, 173463555, 797273837, 537648353, 57601736, 835568007, 965172304, 310047734, 197760389, 934908852, 64917302, 338833261, 630486669, 310031663, 875552561, 405959629, 431857558, 200790950, 638729128, 91296865, 44658467, 631192838, 918418216, 789740590, 649359888, 877467407, 255702025, 352178982, 171996349, 778410362, 553243596, 872599035, 250467462, 696594705, 762346301, 907330380, 745206846, 730845978, 367992143, 573590003, 355359281, 712854001, 875441318, 572069201, 23052423, 486166173, 976222521, 955512928, 623042720, 250625547, 341691761, 936397535, 80165198, 360513119, 642427096, 213083188, 834481540, 835500110, 755692571, 29201389, 333527001, 439989955, 516448820, 691929278, 863461009, 911833041, 437672716, 535585353, 278448366, 980740587, 856237435, 333390978, 454192659, 852527356, 904804907, 423220256, 496016439, 651971087, 700901, 958078363, 108924788, 611117147, 381774619, 445130709, 716455396, 56338148, 356817670, 362253702, 768566966, 281428052, 174301504, 474873482, 152316487, 835580046, 785149601, 545754252, 34993526, 12011501, 118218204, 240842785, 702537664, 602382325, 216492473, 435355044, 406443737, 283204045, 531493364, 962993339, 981395260, 947066097, 4059524, 576617064, 956450004, 689369625, 960382740, 491105480, 626717502, 421248911, 433074936, 28861474, 146592960, 352452955, 78614301, 822381867, 70756099, 809964430, 800047746, 34381548, 362927374, 608455362, 318918967, 144414598, 262850354, 165230848, 754463432, 606086005, 857407300, 682754062, 571832804, 544417452, 334537845, 931847641, 659593186, 265367318, 47293492, 978010288, 605319352, 545029145, 790723264, 73085148, 132959688, 901658391, 614783529, 998934895, 288316961, 304852023, 485825437, 929167419, 504635470, 837575280, 90545524, 224551240, 940481968, 424446184, 601001219, 414597404, 830057916, 727742360, 964924450, 311821323, 139444911, 477648643, 24700440, 423945998, 868766183, 455587976, 566129154, 655332874, 814142023, 200141864, 904509952, 969122161, 343726034, 86790786, 961613400, 891346299, 150755273, 930731382, 670156454, 243630116, 550181847, 591571658, 522284572, 452634054, 53743323, 196748469, 315380666, 410938838, 821744408, 167592523, 287170228, 702215823, 144514462, 846510517, 412261940, 200625246, 819381487, 600688065, 349200084, 19759660, 87516437, 588885812, 154408157, 920347023, 635010514, 586392527, 865426436, 295519548, 111029150, 778450130, 385300978, 382626667, 813373137, 409764208, 958171502, 340479144, 363739073, 545705705, 75497186, 741533639, 675280557, 424317331, 908738459, 549421214, 378230457, 158242803, 469924451, 6177935, 628808993, 65045331, 191494121, 728780809, 513701298, 454783632, 592806690, 242720746, 259155372, 500102868, 397560132, 902956921, 274738281, 475320970, 71588723, 297527418, 450825495, 495667462, 951623820, 336977294, 113142984, 646678947, 652844280, 118453548, 200761819, 960471231, 501271043, 160334372, 311145853, 173787183, 159438043, 523528585, 889975151, 487318740, 57254259, 643295205, 154341906, 535443547, 663821618, 568445518, 527523745, 561310191, 923858135, 908232400, 488411401, 832508153, 386923586, 534820788, 522407574, 798563299, 64030481, 795569164, 480048236, 375567808, 160150781, 769603856, 198533346, 505259538, 905548608, 327093215, 827579205, 249704842, 472635677, 770040817, 85477994, 443523990, 657792468, 425296878, 595385719, 317942676, 725853512, 465252131, 218099089, 705054, 189568513, 726470478, 365648532, 612388366, 811525072, 540375361, 615840006, 577154897, 777281281, 642830325, 812060225, 928820766, 210533236, 773392495, 623419704, 566265502, 709362190, 291271263, 896985589, 99787511, 250404862, 420195462, 565918755, 591617575, 406500555, 441552765, 675446165, 958344472, 744058684, 229524113, 218475141, 509792994, 515073569, 51551067, 333615149, 41322704, 690884914, 432339237, 132437040, 560813722, 247085662, 608727907, 852036050, 335975096, 619881476, 71333852, 522649657, 75872936, 83722080, 198131173, 896856851, 952773685, 386813300, 873498036, 289997298, 610760549, 619911109, 170160678, 861594146, 39273220, 539534008, 105233657, 730674321, 385388520, 615089087, 897337232, 356155520, 406138593, 333671440, 942246931, 801494710, 4120080, 584702335, 372176942, 397815743, 767710951, 784141291, 226820120, 250115662, 541453983, 159142298, 943042269, 162700271, 876413718, 169465739, 822838603, 340080354, 462146861, 549135681, 578150049, 794826753, 992795978, 742822609, 984317786, 51197607, 231360903, 138909107, 547354653, 543705958, 874542995, 690479397, 202082483, 321214090, 803081978, 952641827, 921407352, 123027351, 477919578, 19140859, 658740889, 633869382, 478640404, 100867785, 303256535, 176888726, 797346737, 975425898, 661984911, 987057642, 627873379, 867555691, 185846823, 992266496, 514781328, 992318456, 529417863, 960587118, 37206595, 38297826, 228688385, 928759026, 855594350, 784038908, 751568010, 624704074, 290964, 512158666, 756228946, 126289736, 77302910, 562419321, 358269700, 543630966, 778334011, 22683459, 737107129, 896013322, 551935554, 908965003, 351055034, 503361267, 737478571, 357500016, 863568852, 492298716, 391027924, 941081770, 330726947, 435373132, 590693342, 677144019, 61924122, 512326338, 649345286, 739931672, 696276660, 730926652, 455072581, 251213407, 317001464, 426831391, 163074272, 352034146, 885631603, 823401408, 839324474, 164736470, 171189762, 209269343, 951386166, 630702730, 580276660, 314496432, 495301365, 126590567, 721309108, 643751542, 74025182, 34983243, 826351431, 855317208, 608942744, 803444273, 470517642, 799179403, 578399573, 709965601, 907809184, 251410911, 883109424, 266574726, 257756132, 787234940, 32748326, 794259646, 526957746, 869862223, 73518072, 700460549, 83687874, 673671207, 149293762, 924896353, 497796117, 28372042, 800069309, 342560078, 819628707, 373107386, 696126745, 268413483, 733001076, 740887083, 380467706, 194020813, 529126220, 84965155, 129875456, 116890587, 971203760, 127235037, 69085143, 298737690, 188335071, 314865854, 589641717, 747748276, 539448021, 383748323, 317330346, 986667577, 888699616, 599597108, 441545260, 835351333, 707053625, 519216700, 968774804, 528148921, 701162327, 662780380, 136034885, 131193164, 311656144, 278069159, 423611668, 83175724, 886411988, 868461960, 535561865, 154715308, 126476658, 761584605, 508157755, 780964783, 578438764, 784907196, 810493643, 319344623, 934097122, 950730014, 233378193, 770851486, 820213640, 226653078, 990331214, 788840505, 624886710, 417020519, 396677451, 857552048, 856709133, 336848997, 423196902, 632255361, 908713778, 813179845, 750634041, 543394676, 694929623, 313405362, 998085627, 432988323, 804637208, 626343325, 727743351, 757092586, 451503777, 225412119, 201512209, 240494171, 433847081, 953729888, 655811283, 399525382, 851835654, 717258918, 997272263, 207937468, 724045947, 803016675, 54705206, 962618832, 405823559, 100225569, 674366455, 64006322, 343918918, 897221070, 714562208, 202817637, 501332406, 370549948, 592030726, 118725806, 288348745, 375746054, 724215258, 457633661, 101020780, 731825489, 956241354, 820096851, 828391358, 894760706, 840551440, 314132703, 931385116, 151230097, 879288068, 639678603, 628383055, 410560469, 527187686, 12605914, 974912442, 924786505, 20921218, 230992610, 514965935, 122055530, 844289072, 671330347, 125964402, 37902695, 746384611, 582195695, 758142356, 622962180, 591360856, 506819248, 137909753, 560216901, 765256092, 114236881, 882427992, 961949079, 146535275, 582711199, 202209855, 818923970, 774884387, 24333071, 189366088, 234402725, 134163236, 815552718, 337594193, 316910632, 358816972, 218068132, 180810902, 147825493, 631488830, 147737707, 277267878, 124283016, 90930478, 259252168, 624755642, 899109229, 697608415, 178211228, 895231257, 992850214, 603162046, 53455555, 175953316, 746878052, 975345231, 540572804, 405121256, 27732428, 669954120, 245189188, 376647321, 412475764, 605339312, 535601986, 427686239, 914977365, 279458623, 642067549, 681037429, 595312007, 725559960, 199454015, 121635426, 260577104, 629768912, 194080867, 416695724, 246114941, 504033317, 194601033, 330554718, 853449713, 949867839, 114932817, 356106426, 613249763, 658905631, 613386236, 403175775, 321130277, 376324166, 417457546, 667741739, 815692405, 228259015, 624135050, 564186149, 695432898, 574666375, 526532560, 498115027, 372278812, 7727561, 511308575, 242087746, 464051819, 246505391, 423086075, 616700050, 492990517, 133788229, 824226825, 69234797, 928799746, 289551014, 200173157, 176009453, 944312294, 135547703, 24488174, 732934251, 391812405, 622538928, 577259244, 657620238, 961792822, 66187534, 644749521, 755611118, 828862965, 591511693, 297776507, 418298199, 970229760, 86503116, 705372603, 469292937, 319287645, 336995750, 374076496, 964586261, 919194311, 118243589, 821497761, 681541185, 375430224, 260261703, 154644123, 253177812, 535326923, 431303305, 955673695, 299454667, 434081946, 491150828, 429189500, 978614793, 776792041, 985284732, 766423117, 601943728, 290207775, 506812579, 403169809, 794155018, 415405, 903776754, 839193958, 242770784, 862439863, 737849157, 311581973, 726765688, 693762856, 31512841, 15579464, 765663724, 61849510, 50726119, 947395547, 163450694, 525000671, 293039129, 906418274, 719921104, 259327682, 950975882, 139378647, 614357141, 820600477, 624473122, 9408227, 877181186, 471330509, 724452026, 86703313, 545776863, 940982256, 742670220, 105519120, 750264387, 838369258, 533105243, 315771829, 942999087, 574702319, 788429699, 677225158, 365253533, 406637792, 427697095, 586739556, 732198879, 656332976, 941835194, 202346879, 286039190, 565211070, 409597322, 233774446, 921798090, 414433109, 949675376, 406384374, 185054736, 790733272, 547161465, 918214342, 368187126, 380935095, 864094745, 646595366, 474616023, 185294330, 398227420, 956208202, 402277860, 265466830, 926416422, 79080340, 35299046, 899887845, 9526831, 152158877, 824453413, 126920506, 150452625, 469480072, 238887138, 149442044, 347550549, 141569298, 164677866, 678834942, 851746971, 471422455, 108176005, 209123483, 202628636, 603888704, 849750407, 288154727, 348556111, 494199525, 695851211, 175080592, 602932370, 34303971, 613574163, 410093582, 108117230, 234090436, 89998477, 649048422, 640826544, 113382235, 699023193, 582470305, 197956832, 138837971, 730453869, 474174302, 352421859, 283886190, 782519776, 171956232, 155850150, 130769413, 321139183, 565906079, 49757443, 142234494, 697529175, 251684752, 232518772, 82947305, 50535765, 183809465, 728452414, 24032832, 720683564, 142387931, 917141818, 481130299, 676376988, 517304075, 156042179, 696944877, 564029962, 263638907, 217428551, 930980902, 680137458, 392807777, 512494295, 690243300, 667647889, 505998927, 856687480, 738645857, 678751717, 866058117, 780135339, 784838188, 702603419, 17105595, 249784234, 528800829, 93534993, 273506386, 683199891, 325447503, 223338059, 8265545, 531023032, 455574005, 977267932, 92344167, 192160674, 931965355, 67770660, 698868887, 643642850, 383044672, 247544000, 497271945, 185798269, 175324870, 397367464, 125567706, 513166548, 84567067, 616326232, 336493621, 919684409, 64925713, 793235103, 365022448, 979927117, 831464007, 731348313, 380709117, 709566532, 651535143, 196260793, 342132233, 207311182, 543283187, 551098948, 121567081, 806742262, 984638522, 998001469, 999417468, 520969805, 333903235, 32512358, 756922238, 730235261, 533699174, 708690837, 520332418, 803282075, 920157210, 405079619, 641228911, 70074278, 620574899, 20968495, 522976351, 700390664, 269105211, 21678015, 274757111, 293688839, 82062350, 968773718, 575269443, 158967304, 275284975, 434505148, 202350135, 935271855, 33413976, 768681657, 961109970, 315404144, 923894334, 134546447, 64646766, 31090918, 737992492, 446312522, 113308839, 628578612, 565794622, 343801071, 603238358, 979667576, 491549214, 832482343, 180072822, 547024792, 956872275, 765502541, 940600942, 401808343, 293256234, 850390273, 673679213, 821596318, 948238974, 636923023, 137371896, 45898770, 817358635, 469477107, 936636741, 103208212, 321885243, 198635852, 23371076, 427230094, 650262291, 400300486, 137594044, 211180301, 559929363, 907836429, 328420775, 182600249, 461364705, 278849730, 793476624, 563577616, 685118134, 941758252, 845015724, 634838956, 752376782, 931716742, 268397414, 217349443, 235860783, 827900084, 487829123, 850884957, 903706722, 771613593, 480434187, 255443998, 325489680, 424279809, 684079785, 669830102, 74025625, 912460424, 687669380, 647576064, 425369016, 516153265, 695721127, 819488634, 437999277, 12963098, 867405007, 7498983, 208553903, 385217138, 315687902, 249850982, 419194351, 552142600, 406386085, 898692344, 2662604, 624912101, 91437844, 309402665, 477072635, 377600630, 608824486, 7786634, 299218348, 253719825, 775622181, 68326222, 103865252, 979278021, 346289587, 449496091, 811645909, 574655061, 837091039, 879967327, 848736675, 378318335, 83542480, 373426715, 280175265, 482083917, 486587048, 270113166, 68508327, 705682728, 587848617, 520335404, 161880367, 258672953, 331647088, 748665793, 209653984, 158930208, 318402259, 960826397, 317526241, 401547949, 447416065, 372531586, 821275512, 251922897, 897257606, 443832057, 246893762, 452591330, 600136783, 688561648, 31684396, 687482216, 597444421, 24034858, 387840055, 163668691, 343599673, 572063422, 705617061, 728561102, 863539041, 752005226, 732256184, 288757780, 932115710, 17394274, 544408516, 50989098, 605196639, 369634728, 822583967, 255840353, 303785123, 384401609, 165990747, 390330213, 416445613, 722594946, 151481507, 738647415, 351585560, 275225368, 228451316, 820163468, 878763577, 828686579, 17461285, 950238102, 94134171, 594130375, 323600119, 38075227, 708699998, 139504429, 215364801, 711631123, 102630263, 315532435, 784435467, 591667084, 267624038, 59630857, 745799824, 473083978, 819268307, 784624091, 422046738, 4216212, 742837978, 248513419, 436775638, 795620782, 183437409, 893126891, 116014514, 198305610, 410708927, 782160736, 89521100, 165061324, 534607477, 887310525, 943863286, 658001724, 790257772, 370952595, 193648741, 36203756, 152519624, 677638875, 907651381, 57923267, 428986110, 438298377, 682256430, 354986489, 244435468, 818199317, 29981320, 548064123, 143254720, 403391793, 847198534, 533273690, 58189499, 409982106, 833002656, 522800927, 640327993, 289296703, 815386006, 131200760, 515757343, 370574165, 711613060, 550213577, 171972236, 497130686, 974648646, 955302159, 506415002, 734247939, 851855264, 833272054, 515765177, 954130028, 214154924, 273308466, 364667274, 106844338, 190010993, 59827501, 236573610, 566438266, 616198923, 963899702, 146570219, 113870308, 546136684, 831247413, 930952511, 868366094, 550210026, 477883539, 605337437, 715142864, 792818788, 326157455, 183848184, 176665209, 924384776, 44531447, 110160511, 931172538, 299745188, 322661935, 139385333, 589448661, 491365508, 278343965, 858293871, 96341655, 656110011, 223545834, 177092505, 589947800, 60712867, 332229069, 873171372, 374248896, 797599449, 636050839, 734516137, 301700164, 251269648, 79090129, 225382579, 331227823, 54006882, 349696393, 603087201, 563529399, 269743098, 799052262, 800118559, 399790660, 202567323, 596487814, 313072145, 947544859, 68539131, 542900224, 473226000, 182306060, 871464491, 453467963, 442382862, 877318451, 749163460, 98986231, 867206807, 642597006, 81602435, 444678488, 313067910, 62386612, 987424121, 128887366, 682112778, 414210889, 612098699, 226918101, 611806031, 364392081, 16699034, 498101111, 672181048, 393066269, 406332283, 819004337, 848170744, 540378327, 998570575, 615679719, 950897498, 928218251, 172976681, 950440528, 234874226, 483619711, 286695727, 635882714, 231349928, 996706257, 22981726, 257150007, 79243909, 878179204, 596977486, 240711048, 945301069, 983882240, 734765933, 307976446, 703957625, 943604562, 253791937, 661522100, 535837789, 112945044, 57354062, 407083637, 515497492, 397514746, 24352347, 852966529, 301735962, 214009547, 525310703, 187379553, 687900022, 309180816, 946955706, 705625111, 975829487, 553682089, 560561988, 126523088, 539689798, 522462280, 581699007, 703526528, 945605939, 270528195, 399687030, 492835884, 505548398, 556616713, 343425114, 421526877, 533979517, 657975019, 271328068, 671471900, 116325994, 987072037, 200364830, 675417246, 973154515, 765398132, 932264661, 649120479, 974000978, 680402562, 265343241, 217763389, 373698062, 790505008, 519287141, 134646122, 914549418, 645310428, 888473785, 392226056, 449177070, 640787682, 57345555, 398857167, 448602848, 972789569, 987960013, 211166607, 41299247, 259015342, 302714797, 823202630, 663851544, 850922084, 971424952, 930413363, 189221628, 939945993, 591367176, 360561690, 565664208, 128705798, 74907474, 518255001, 344070371, 512948506, 349146299, 218246554, 850680963, 894934852, 279025769, 238635886, 662408191, 484512700, 861613732, 708424484, 725789583, 98255014, 167657146, 154249334, 212308774, 384838180, 434407700, 31391074, 958767669, 834368987, 463910354, 257482639, 842169804, 744848872, 185918212, 668396636, 449126379, 987290610, 690719316, 709586492, 93006451, 211022181, 555484726, 751572356, 55237875, 755690387, 194170978, 618430963, 85698337, 601265409, 552151649, 218551892, 325943833, 670896061, 118205874, 756880236, 281050901, 248617432, 591800751, 366292634, 4932964, 235147459, 650432203, 877494240, 488969159, 622620137, 26503990, 780508089, 978361855, 721418587, 717968341, 527835386, 92215891, 905084425, 328151481, 676654149, 946912592, 396130811, 591967609, 179573544, 936160617, 668824711, 238971896, 325988109, 866174663, 694457254, 446698134, 487478940, 30287861, 246161394, 759291233, 532941199, 159528912, 50509598, 113866253, 350335516, 234551926, 69960810, 912494342, 78475569, 536779704, 410340610, 97372670, 848637612, 658037951, 681452994, 587163678, 824313293, 553915283, 11260361, 261847762, 530409468, 355103105, 93962105, 415214171, 734697784, 716785481, 138703878, 117701111, 123697767, 253928188, 344157822, 947345256, 923586126, 701871396, 203014190, 798279844, 355223152, 43787443, 287725125, 715598256, 51483785, 575343231, 145555713, 412814726, 19050425, 796582363, 930232999, 849286502, 407388139, 492449645, 634380254, 654411862, 923156807, 172753796, 249577097, 87172210, 11941715, 982107472, 588318134, 738579825, 675004245, 652776914, 434152541, 499111855, 453115583, 99082749, 839051154, 460821086, 637487806, 41566379, 664935788, 125354211, 962469884, 834664671, 689280706, 142587756, 997038011, 889480268, 680197223, 496287720, 935800554, 528076208, 758862137, 505545782, 863105649, 910103008, 603998387, 837599847, 708785822, 621936967, 637929249, 849611426, 829140836, 875349175, 817065022, 362558505, 700706164, 127276853, 266399255, 926782317, 459162289, 817711199, 168081304, 816143692, 800123647, 431731, 513368493, 257161676, 284695876, 244087899, 602191513, 339688035, 632295853, 675061346, 202805860, 63338263, 133286892, 312891353, 628349817, 742148189, 50312017, 849625658, 77756547, 713243426, 929099616, 904500654, 458102894, 411759289, 830842409, 321479280, 163557756, 542132423, 86497716, 92549959, 662774537, 79003683, 710608932, 914550564, 65822981, 165880760, 819505013, 86033283, 73985869, 254138696, 552962168, 547812952, 755207050, 89228694, 46152719, 178709678, 960091044, 149071757, 874276489, 35102733, 480928664, 880676261, 921731900, 461709567, 250494309, 760873322, 766097362, 401765418, 241738747, 944705895, 440266390, 993242396, 217217287, 425824421, 322382762, 271715424, 984665876, 443636390, 45073777, 630398800, 463527890, 699285772, 261445910, 361127267, 986655367, 552443266, 625976509, 239267508, 703676733, 18908159, 170171417, 571434884, 46930286, 870303851, 289129754, 107652894, 976576501, 262732157, 948792696, 235942723, 557374156, 363772201, 61382406, 553110543, 61332652, 439667948, 355735563, 922059559, 970570432, 38786591, 737366860, 496992842, 986301417, 499876384, 404490372, 548071903, 859972303, 565774278, 215740184, 957869483, 961797760, 603105381, 140812719, 305574439, 512468874, 316366056, 210399817, 166397468, 350135655, 188702016, 521209061, 550064245, 493734073, 734324737, 721979216, 341818965, 592008862, 68127306, 697081703, 798561444, 665377664, 549126337, 218559346, 56939457, 884808162, 374279544, 494308664, 675081714, 306455216, 758039052, 378776656, 766274312, 268862088, 424585912, 321403851, 74172857, 546928338, 748110955, 69420111, 259006221, 29654096, 950183379, 587656964, 121343238, 229016931, 525245078, 170762495, 135320142, 25471919, 409327078, 482351459, 57105968, 400665115, 586461433, 990233607, 599982658, 983229122, 772243280, 271293935, 543399714, 562956348, 401122663, 565344421, 585481424, 576479398, 350731842, 485680485, 20714071, 8158187, 603676268, 516963904, 50419445, 443382140, 675259130, 578897710, 886055104, 883905960, 843769997, 356448838, 165054711, 873422703, 674858914, 566484751, 290384255, 418280121, 252680321, 313721456, 127494952, 110816777, 978162164, 911708194, 461526613, 51237904, 343087656, 964695900, 567799989, 330915468, 52021458, 769071566, 79680948, 682535765, 782771203, 943275162, 783291822, 107048562, 410718487, 899898952, 612269357, 212422294, 598059048, 47785784, 368137559, 706853767, 856172856, 501722227, 594136918, 632941179, 696935904, 588309848, 344197568, 227597154, 343123605, 150960171, 428348498, 107312392, 615388455, 20862536, 221770846, 108398306, 975393037, 812563636, 479292310, 191962891, 900276884, 64332642, 19070170, 874028993, 693596412, 613502393, 240689082, 745636412, 473039836, 61229543, 272777730, 783616413, 143536322, 267303673, 505572297, 541148583, 453046592, 932204121, 695930429, 469234640, 40394889, 245678506, 379342040, 447331352, 193723249, 794770747, 637835888, 677551742, 183765102, 8654870, 24622899, 318737956, 114809644, 524590776, 190981785, 869145324, 35138376, 427210398, 906571999, 133831917, 582464945, 379813583, 13744075, 930564563, 948909520, 592320547, 694986509, 254468528, 607105249, 756103791, 932423961, 727289900, 664605864, 868744448, 309037550, 940669590, 459649335, 223557976, 8258357, 38442305, 311834126, 156954810, 304138234, 607755580, 812273179, 217330753, 991156956, 146846528, 302229092, 401669001, 410053765, 951295470, 364290625, 913710434, 749703765, 797036850, 714396025, 829199445, 404738333, 528537805, 298177475, 243302524, 747828111, 899957329, 777663512, 188019740, 498959514, 723192952, 853563821, 606229842, 961608924, 696914372, 466518493, 344994555, 648187584, 638455375, 885947283, 781574994, 656881615, 59637376, 558578472, 773306181, 56699458, 985621298, 896680941, 540104372, 422039908, 910719887, 593862686, 668579274, 481737766, 94051045, 346792485, 651272987, 22359606, 383474730, 726717221, 649031134, 432795925, 410664462, 524002439, 99812955, 193828939, 266002287, 178289011, 262754856, 604558007, 989182052, 471003761, 272789026, 366747885, 775426656, 308769796, 652642055, 635966732, 257175713, 774653352, 546910763, 272356229, 356376140, 203289750, 423046787, 206579249, 835424306, 730121193, 462414453, 700330421, 177515153, 60301805, 460688654, 950788134, 435368871, 606354863, 313410660, 527708973, 396637894, 577007460, 363797918, 755174113, 123250931, 144985875, 385709565, 839625686, 984837532, 180311821, 527706273, 42391451, 557203115, 484096602, 898705583, 553582617, 741739114, 673598814, 239463861, 713654674, 111050640, 51658146, 385201111, 95695593, 531401488, 245024545, 929399419, 345707508, 189930506, 191328985, 512707801, 648311112, 562011241, 521399246, 964497228, 574815795, 447240566, 746892336, 544465477, 553348939, 945530537, 690980210, 74454684, 630027257, 780492865, 53856595, 17026426, 74870726, 623770904, 932504723, 572320755, 738723578, 607311149, 763068014, 732871592, 649275364, 345338234, 434322986, 114154691, 711701309, 689627961, 419506969, 512390721, 508982830, 176789545, 44906278, 271579538, 70268286, 693726780, 309926130, 804231666, 414253983, 559828682, 697862796, 3778915, 252628133, 23241813, 270754971, 750412039, 245980495, 968703190, 789817007, 6251983, 877812817, 226199837, 975130951, 388748940, 350512225, 736086463, 787082228, 874832353, 453842604, 110796318, 184017920, 221623260, 343504960, 429844866, 206788428, 395920679, 93959303, 692274984, 411563523, 673142937, 131589711, 535122062, 883315828, 143341025, 774217777, 716717381, 23539174, 223799562, 709433558, 119567082, 214994059, 937693727, 112703971, 160419920, 731684129, 41098667, 166426309, 697905247, 233428649, 815236761, 891973120, 130432203, 307053374, 686813041, 875985183, 4918738, 20507707, 566355485, 647665177, 456579864, 60555248, 625746080, 118340438, 707546649, 247840598, 461884660, 566259807, 462415898, 785756956, 380275960, 492404430, 806376471, 578418707, 30841689, 143900994, 114286563, 434207907, 982869204, 885199219, 920457131, 192183126, 873206887, 26238450, 374540113, 287993364, 153154730, 700603522, 226023494, 460531469, 424322482, 580489217, 256733353, 906778071, 272013555, 116897625, 605725435, 523281744, 462184848, 322828585, 656849773, 394116152, 21285649, 862474623, 717063658, 169305474, 168438110, 531852797, 172252049, 456277359, 34421450, 646106489, 508395412, 801312816, 55907344, 762171340, 380297471, 523107905, 817103656, 522347744, 352163557, 77179319, 384523508, 45585339, 780296523, 494310111, 725626749, 748697565, 48383335, 779749254, 428900227, 6658212, 561674379, 799251486, 360515735, 338863992, 396623630, 331695, 844338722, 445019569, 29666646, 934220527, 66502905, 437550334, 520202354, 509341053, 821259954, 814346797, 757189385, 431956245, 56929632, 658485912, 8357721, 909711014, 339290901, 499076660, 266279089, 223717098, 37751706, 1728890, 907967359, 750783681, 724860040, 407197324, 760824278, 964524285, 82046809, 388018140, 918324391, 726118200, 29996354, 9380144, 295953960, 686909753, 542705021, 359056682, 755129788, 350038063, 919554315, 540661580, 960127137, 121931752, 11118137, 211703671, 817177376, 2661744, 38825172, 311905539, 448759978, 243133301, 281412852, 965823694, 356525410, 415268195, 549662188, 83132684, 442666214, 776128451, 950499786, 522035840, 100723188, 321148136, 286709266, 189944699, 349864806, 896204910, 113157177, 213195841, 417395056, 489687015, 35210791, 713528315, 537471643, 401535692, 763975871, 214908443, 351603337, 61237212, 28865552, 537061595, 181576615, 685528103, 871991101, 979308856, 578656584, 35554205, 225614562, 900546210, 66473668, 878701536, 218940833, 261521587, 111358037, 573297272, 98599596, 915288573, 230255082, 629646637, 424094332, 346194316, 131145885, 756207610, 687602388, 55766433, 895172319, 841927962, 313673634, 292877870, 667308047, 878775560, 162837794, 562416202, 92045264, 818036011, 929987863, 530473273, 811053805, 719368497, 845461559, 877745019, 751235032, 852524671, 389003894, 383205130, 52646362, 60578696, 620122364, 769771437, 39381799, 872314928, 66816587, 709548016, 27925488, 969175485, 668922779, 560443124, 684527438, 328886561, 167084686, 769005581, 354658832, 88908411, 865689838, 481778871, 820927809, 714663045, 295844489, 613831254, 348975326, 663923887, 853837690, 189903833, 327588584, 687161946, 753641374, 845151885, 384826080, 329915404, 430121917, 941496684, 261607823, 183314611, 520019659, 263944485, 130634314, 872787, 238042364, 877606485, 84404041, 582513996, 189519503, 386450742, 367874448, 698670327, 666999420, 690425136, 65267809, 709309218, 318699847, 903377587, 498432870, 528491104, 945823542, 896759259, 446982621, 600171670, 420083788, 311041532, 83304583, 594527982, 288437408, 277737395, 635738579, 307552404, 385211341, 415493180, 35697067, 119675855, 987959555, 240584917, 624550772, 420751874, 86227025, 121316817, 458693555, 991732539, 919001148, 375167404, 591159125, 282201837, 130422424, 100388887, 207959193, 696460574, 838192688, 852763222, 421514642, 508265629, 549545362, 674950255, 182777539, 499915270, 860953605, 373759875, 432886072, 910819976, 521640642, 561091051, 840421145, 408432244, 917135491, 249315080, 261506157, 363952905, 663640240, 723466234, 205531865, 669822494, 21876031, 813176273, 184769950, 367911529, 125863173, 114934624, 365890778, 920909997, 807716698, 332276656, 332749903, 702352183, 143041463, 496236023, 760043273, 168055081, 61020287, 199978162, 374583590, 822291687, 658954229, 434618063, 781217975, 954930537, 751556139, 916422992, 326306085, 402393464, 18667929, 841811129, 285855218, 514285335, 324364429, 362743859, 830871767, 218379793, 951017713, 951689173, 158584461, 807551076, 999189161, 154008093, 325089994, 569823715, 811391354, 552799698, 26280529, 512495238, 554863509, 377075141, 115138239, 482893755, 755545361, 304612032, 312537843, 425073309, 189723504, 371558443, 36574975, 484986659, 712354879, 210026958, 747911299, 534230244, 332820218, 415636681, 86289236, 898552573, 220861434, 451118745, 587881320, 154434133, 601801484, 265047208, 274762967, 686394454, 144350284, 877688366, 374301917, 145602695, 447585333, 359937878, 838305936, 613361381, 274725185, 217792425, 373451437, 250927783, 260171575, 938872856, 21437271, 170809202, 899489778, 809823537, 317012194, 985326788, 878588780, 799392552, 4934238, 324132319, 845530403, 599236814, 466634522, 503859688, 146188597, 53917762, 512071289, 620819783, 597953203, 543238421, 839694423, 848114156, 864284005, 896961857, 807475003, 759115530, 567673424, 362946846, 604767132, 989120261, 524475174, 513159186, 330415433, 728366575, 933690396, 695341736, 465951693, 295006006, 632583914, 14983593, 487817771, 784170905, 710615450, 683119849, 784350027, 496430467, 219643886, 732961852, 486951659, 694591832, 694824637, 222490997, 173613156, 718492168, 202161623, 885140984, 204506014, 349678354, 822685403, 349457981, 685398579, 291080126, 683327822, 52732731, 405053892, 23543348, 578287457, 64082934, 413951990, 381416853, 233576448, 230360833, 53758285, 327395934, 885144938, 651017990, 747396091, 365564289, 124013641, 750619858, 132763357, 29854342, 838812953, 94328745, 717767140, 198065884, 950887307, 782940931, 297294555, 581829592, 864136611, 950554453, 197415377, 181111687, 586746390, 405897371, 780269887, 305942561, 968711522, 244244661, 416501381, 862266926, 765984223, 245269177, 165498167, 315093106, 81409142, 259370363, 65637981, 950545110, 257381870, 223836198, 878631831, 938006494, 43880989, 61201126, 203617417, 613175784, 428782739, 131875174, 405080742, 891122095, 821417052, 687660900, 358138278, 489870236, 689712328, 400270774, 619805867, 536900762, 435365278, 880692543, 237163045, 169361821, 994314126, 296607951, 868170894, 180768836, 138417339, 450530638, 765055046, 273247174, 314214022, 430432513, 776590919, 367024946, 426314224, 582647665, 690538559, 259710790, 771754731, 184135998, 667750596, 47636022, 971587743, 198785152, 514781554, 245264396, 700931820, 66048997, 339139206, 290416775, 70116860, 351759459, 846894401, 545832846, 256427620, 560891510, 922114160, 938361373, 280641589, 942816877, 977895706, 485438426, 656306356, 538372101, 180623411, 896196692, 794740517, 531465919, 302607307, 789512781, 274129314, 107016173, 750069739, 432495397, 578547134, 869148622, 46192056, 46334032, 273574203, 150779227, 845062735, 588551180, 604343165, 55742112, 214537073, 762334920, 356834937, 701820653, 406995612, 876477147, 388689781, 849720036, 629731987, 277691047, 266176600, 77659538, 562592753, 298980416, 877566984, 217618207, 257701403, 219564653, 896455196, 864526819, 70408858, 831878750, 514868154, 12899219, 259912985, 86932715, 8563658, 148614601, 723231372, 539277362, 873553185, 347901431, 160823547, 785064769, 351096949, 676906630, 79690309, 796844738, 697174687, 497018836, 434242159, 949795157, 520145698, 897040079, 179273768, 782498847, 769382713, 988033389, 417896305, 413455361, 444204363, 609389692, 69342151, 367654414, 429922949, 217961276, 116941643, 708309891, 703189216, 369201005, 711810771, 65614368, 528811453, 113822010, 367406620, 124416315, 301271796, 606038984, 205997049, 510257498, 84053768, 383892497, 406113146, 145942585, 426336322, 815452245, 792429943, 587064788, 252454678, 470923821, 660007045, 624847658, 640809297, 125517432, 722536656, 818691426, 467378630, 271321185, 611378365, 468646381, 966168732, 222967743, 112536028, 646632216, 662188505, 167603254, 244337172, 300477869, 404770766, 72585516, 858459397, 946164984, 346890506, 523971352, 480301545, 268292189, 521905968, 861522981, 284565166, 519944945, 475724432, 753955726, 888335941, 185012652, 213414829, 224437823, 862528153, 206338038, 248743648, 761402470, 370185122, 121158772, 420427003, 279987929, 478107622, 722641635, 850475312, 490475316, 840856887, 126876447, 965820404, 543986006, 215687696, 25956857, 910050289, 369305157, 24942000, 542428127, 95031873, 751132042, 417633554, 310586793, 449237304, 617214295, 248729894, 167458930, 630006532, 458851289, 857295365, 558811477, 776265, 976931079, 800604583, 39399996, 110944822, 332323409, 12095625, 901137708, 300401295, 913905974, 16122227, 674102295, 952615665, 178711321, 571929609, 548720624, 635561004, 359047088, 50641179, 910890567, 748044204, 808856025, 129229417, 773165872, 409447219, 55618586, 510137712, 614633163, 442467802, 170576051, 298969052, 466422086, 605276991, 120534409, 836066551, 404565887, 679458451, 283554252, 197465322, 983417191, 256177056, 277526981, 765260435, 650952023, 19903544, 615600241, 924737028, 495826036, 381211630, 512430504, 540048781, 499526274, 159107525, 5413883, 584422894, 731764100, 232164170, 853887149, 601689114, 650769987, 668300823, 409252900, 712462036, 770127873, 656634687, 187777558, 735209169, 999143003, 615801848, 572881079, 432638249, 665022854, 230906551, 63508398, 410646782, 941874677, 295964775, 808525294, 32679618, 411358931, 208867206, 592127562, 822989680, 937989587, 170531640, 318167739, 145769901, 949667639, 250873623, 567930176, 72321639, 158991171, 674818870, 423093211, 943592910, 487340746, 947920454, 826983299, 239166348, 598369272, 174185005, 882209603, 185517608, 99080310, 72348259, 366725399, 108464983, 614642930, 785753219, 962287660, 150782326, 884609036, 660535412, 581916489, 296782782, 694735773, 36235419, 215566006, 963587474, 118286340, 214059770, 476651334, 99133352, 695765763, 829269107, 659637080, 273856951, 927769042, 127271375, 238503829, 330272908, 539667428, 364337670, 434680890, 529518877, 619416117, 35132230, 160323275, 981080119, 844318143, 185591791, 598315885, 794712759, 105425459, 97379288, 197337536, 265170907, 99928724, 746848687, 872601362, 453161332, 469471192, 877806362, 720501964, 922586090, 492629735, 134912199, 67168688, 213731441, 798349422, 998890761, 176867290, 153186379, 624045329, 301905529, 220383855, 28189031, 183750130, 694572531, 50343701, 788684043, 600276545, 823585307, 562851058, 199495035, 119867246, 850025791, 61128722, 529606131, 167819420, 600788434, 299678692, 914329048, 600595731, 789045891, 891289083, 100733957, 160146335, 611481528, 827753166, 540222732, 708935553, 323427185, 159748804, 63197827, 760657751, 480013216, 376979093, 896546557, 585262432, 991188187, 740848261, 572977484, 536165505, 523855464, 733725086, 491140463, 195610245, 844478034, 728699422, 349282592, 158780039, 877868550, 283867985, 58521291, 993177621, 583734649, 103565534, 169652900, 564411989, 689645110, 1533611, 614595114, 247778655, 48599069, 493548127, 32897936, 592164744, 441844677, 467870817, 933418849, 594840896, 240917870, 583403432, 121601316, 628476740, 862343177, 381757668, 98629155, 204425327, 202952056, 976161289, 977808256, 879544439, 407933949, 950330919, 188724296, 705085701, 31453403, 682007080, 868801999, 467549638, 593949245, 408738941, 588245962, 448019488, 742447798, 963157846, 935413814, 429924168, 658174187, 182264808, 688558134, 952571995, 461265591, 925188062, 528889323, 11064091, 259275366, 32119858, 30432206, 267503453, 458239572, 68444226, 531846178, 223389033, 195362035, 120292389, 636196092, 259184711, 640129234, 901023248, 394790214, 310427564, 689428464, 829078308, 111725331, 400878138, 656564040, 658087224, 842079567, 110579815, 574068387, 920033670, 742504942, 436127525, 195780557, 592911766, 9416138, 358285017, 492228509, 291127324, 942857387, 844960321, 262400943, 385728889, 643162539, 765288484, 632375536, 571153014, 939053349, 792420813, 737890999, 203010379, 426766236, 299216826, 134736664, 189711224, 630654819, 723399775, 628770994, 658182226, 4058544, 153725706, 717628793, 772507681, 799623569, 523301668, 189023944, 139974167, 545164092, 393216306, 173381793, 376257153, 614799914, 929575207, 304489855, 334411820, 489756240, 959147827, 738679048, 292082097, 574926321, 168520655, 511930320, 993046079, 437982977, 996095348, 936349716, 648842781, 861031851, 354128366, 856589128, 29085145, 379983102, 414442852, 971614060, 630706859, 562871178, 139127978, 583215027, 295086763, 606401951, 621836657, 798739083, 917182621, 343876138, 300477326, 90398221, 101896086, 184455352, 797527355, 579165055, 337391083, 277951447, 318306522, 382644679, 777363394, 560511777, 310392293, 738456664, 273261366, 124245111, 866276238, 99934603, 607033550, 481063372, 761065930, 888503477, 114110125, 875744250, 162017530, 259216605, 589793584, 246292870, 479349499, 747591847, 108551535, 308755541, 520028160, 687163596, 59151798, 545969478, 63585526, 797768975, 499760726, 752869166, 39752645, 744322426, 585001371, 515394472, 183244930, 167029417, 114779130, 982957742, 753256643, 628316842, 740378422, 2027954, 382355544, 53951470, 743243053, 767604541, 449622611, 907907071, 30707614, 759422750, 67637343, 552599256, 459766319, 772172070, 718369526, 414338738, 453202409, 337059909, 89592364, 971329176, 676186953, 510889646, 330369918, 334111287, 801573469, 879884157, 552660118, 364802502, 752183584, 17874315, 706673070, 558283197, 801524078, 350829511, 368147351, 139513204, 253452926, 834687742, 800567258, 356885627, 348544354, 898302605, 190596217, 953608492, 973822753, 787271464, 655581456, 521033309, 838695696, 684596291, 824948530, 992276650, 641008830, 642233855, 430800291, 174298000, 911258137, 190485553, 413348943, 473548470, 293964500, 588978473, 409900822, 977768515, 379940153, 480209723, 852904816, 606087528, 818511725, 371007780, 577649741, 303578315, 127932593, 78544456, 798731180, 15237331, 327967434, 464880394, 112309970, 566300324, 588832068, 319440621, 153289697, 453198750, 768676800, 828473514, 245795779, 498013547, 498211783, 69173996, 595334864, 222304316, 444003629, 846536785, 124148629, 976080768, 739560882, 185798414, 757798843, 409965399, 530709891, 57930881, 956281373, 376684460, 297444329, 316295904, 312518639, 363901132, 165059002, 979734332, 273643903, 982308181, 597618736, 566936150, 528915318, 516833609, 724593231, 480520465, 660504364, 578694436, 445340850, 693373982, 955385739, 204061962, 647984161, 824324300, 666955088, 571800474, 148511766, 423588494, 534312447, 778328859, 872562414, 855046988, 621811509, 504788836, 86785736, 557257572, 22897601, 723062743, 583643984, 934380544, 648927714, 545209256, 732764599, 680446021, 757509985, 737278030, 638414152, 1214291, 198222652, 923907883, 193638251, 93705892, 284031625, 867664338, 37845168, 454150966, 151339405, 242773860, 573712096, 38391023, 800118638, 244265174, 726838150, 520038475, 853551509, 179445331, 132360175, 7369379, 963204562, 374192296, 502494073, 425307162, 570394195, 10459095, 435808796, 690426381, 546333304, 459728838, 415523895, 133486069, 858554333, 287372380, 63136164, 818754172, 202864425, 300530506, 6450224, 414585615, 296430451, 947754972, 759397959, 397675451, 497887705, 970209777, 810435615, 425938762, 870710945, 521212099, 187752187, 977547905, 948426932, 641705414, 67635016, 569099712, 814499919, 512994412, 198629530, 116238625, 758808420, 36017286, 425560913, 671751288, 729738777, 603341323, 220073169, 598147354, 919959, 340291349, 833922027, 362023278, 78930717, 545915735, 909090643, 815862568, 458058744, 143745223, 37744273, 702834885, 375278874, 589654141, 33636296, 957200449, 288517268, 30823353, 837670361, 457662146, 315944146, 671503212, 322885081, 129682175, 431636834, 179805875, 491573730, 584518209, 146622908, 960075829, 406567036, 685824198, 468315804, 734723528, 980218131, 758070148, 470597019, 115142637, 114228856, 915581659, 134674529, 490065982, 104214706, 423063033, 553273502, 539884901, 966657260, 609800658, 216607861, 814941360, 795309417, 543452944, 627743983, 461086432, 946153924, 510296485, 605162018, 342824250, 43740625, 38954722, 559621050, 469487029, 237982838, 903998895, 891679371, 159427471, 277273192, 921779750, 834505910, 393146706, 213415981, 373355557, 420954066, 583549766, 793635607, 418047927, 411916018, 238969118, 851944164, 909847365, 661702454, 516222919, 623294525, 30143499, 939731007, 599044067, 142903640, 363960132, 267428763, 371590926, 914548268, 219842146, 428887395, 257151950, 711618105, 877908623, 534030844, 582269835, 983698452, 427957552, 12111220, 870854918, 23706137, 801083396, 594032768, 351124482, 70953550, 86788898, 25274713, 709977307, 709316098, 999840766, 503738444, 916742166, 77959589, 492588270, 950261329, 378005946, 211860623, 792361535, 907900445, 389679769, 627835877, 136538023, 728573296, 861299752, 245398841, 277404641, 537800397, 867227241, 844916797, 239878657, 52714352, 891112467, 929826750, 689410313, 48910825, 477002823, 224300422, 659458179, 238430863, 765582150, 472184286, 984099087, 534257016, 266947514, 206590708, 625706528, 564282005, 140083365, 573192872, 963331165, 15623242, 547066392, 481017265, 710891238, 340390228, 780361868, 297199286, 796594654, 163595567, 665686490, 756708467, 104246213, 737953036, 163364663, 58664509, 492107948, 46487483, 353050082, 210340377, 57257547, 688505227, 899370883, 824232588, 766317629, 896674625, 426733082, 670716510, 488154896, 401085342, 593451583, 513940855, 15482769, 505423549, 279222097, 655233380, 716270801, 59018384, 805196575, 454084373, 657057714, 481463858, 284431622, 984555986, 961821355, 232383867, 571923875, 623274428, 862518352, 696749064, 134519053, 530228646, 675059259, 707985558, 238543718, 824162726, 825737278, 408497004, 296038145, 791474235, 537992299, 261438515, 45084588, 289783077, 847334641, 431523663, 613249357, 656851900, 927402735, 606074870, 933328277, 638485227, 99624000, 352416290, 310970706, 867737805, 778800435, 540311006, 402344881, 953333850, 806501901, 685720559, 871072449, 649293385, 294333033, 72866937, 164744537, 388006741, 227918787, 655036844, 578138910, 329076828, 619661272, 236105720, 352881648, 342740701, 774085954, 698732813, 65037844, 838746928, 900962730, 962141548, 693355421, 741628680, 711415204, 324419292, 126539327, 544076891, 639471822, 767461465, 873673240, 660562625, 81629058, 189331155, 491127248, 694868888, 928056999, 758498938, 649556729, 229410528, 791822461, 533321457, 636103595, 595953987, 514221718, 619807724, 899444609, 275206777, 409554691, 154279855, 860218530, 648200561, 238169554, 620616000, 142559600, 547004150, 514059865, 631647171, 698073901, 947128962, 970496862, 629687078, 247113610, 809787074, 469184040, 334403355, 726497272, 469530751, 496291618, 889111728, 744095151, 947811046, 988485775, 170521966, 773424492, 323848429, 978659268, 305070490, 790704139, 27231278, 458229452, 983204647, 63226304, 42612458, 874443964, 643449069, 171243836, 278750334, 85017385, 329406012, 15270339, 364740862, 675937569, 395672618, 724096013, 12502450, 824864288, 581484405, 977927315, 842193516, 667828918, 364926556, 458123196, 168122643, 970395515, 540819611, 890207029, 727923737, 415893190, 941853400, 76271895, 739543160, 574776383, 562215379, 971072588, 809335561, 114154226, 466864144, 618663814, 602904244, 714260192, 925506155, 149927714, 804421433, 315067191, 675101275, 59475841, 882203674, 427308819, 749906023, 511041305, 950269805, 96576108, 479579711, 102273421, 510246830, 795418135, 207658390, 912160831, 855210906, 679043168, 874945995, 293381060, 211407402, 878001928, 222781019, 367632513, 228431513, 145464720, 559409158, 622904152, 826146760, 561824854, 222906803, 241458734, 640915391, 415692609, 796587845, 708469400, 670816114, 406705493, 518068540, 401577631, 65526375, 137403846, 236059002, 557783343, 638364160, 47095975, 69820818, 981633385, 896206472, 123092250, 741619026, 867382035, 1949662, 26684641, 163983355, 643091938, 320067345, 978329306, 520980101, 122622274, 762610903, 873413840, 620507985, 94991179, 862153071, 139316564, 790653299, 8927022, 576825674, 350764703, 111568323, 40543676, 236624912, 925996318, 624061982, 320567480, 422432922, 347830632, 457413145, 309087405, 139695156, 314016399, 267575266, 66765395, 438727031, 781039994, 80614100, 379779472, 90459489, 31839648, 258479096, 914027953, 998194048, 48786152, 836175572, 47573258, 467504262, 939551997, 671468729, 779950601, 574938858, 591246318, 58227353, 272636086, 759617236, 628547269, 790047160, 424948345, 814139514, 948522291, 60075633, 554037758, 289841710, 681222391, 411313928, 846527128, 783707525, 972878770, 388963468, 386493429, 480086319, 984948645, 529608444, 986655259, 111985259, 205332683, 430679034, 705016471, 192825334, 230375339, 538417743, 677572048, 695125813, 449209354, 912533141, 304529464, 92984389, 957791236, 756501090, 88818682, 247955314, 859505709, 249514245, 89115638, 307041445, 754167282, 426480920, 116270046, 784212147, 694435990, 296956151, 367985478, 914100350, 941052531, 136982, 359743230, 205144920, 235109249, 540636747, 30061122, 873062708, 44242402, 366796101, 118605618, 293378085, 657121495, 140682345, 475550826, 917913081, 466825628, 329035135, 105167095, 766462129, 97776871, 868205004, 801879445, 987708796, 440166758, 381727972, 760257057, 543911015, 433548637, 845083831, 823542944, 488263369, 75988127, 689999068, 99482074, 123375841, 121440459, 387886156, 486210498, 768984432, 549555938, 612886888, 295159325, 972062841, 145429663, 113767870, 158222256, 273927596, 634090071, 783903541, 389503717, 581102771, 138295290, 556087286, 487464011, 366918754, 193442721, 830530307, 607926608, 861658795, 848533641, 188503927, 384974699, 868280943, 680652271, 146465334, 663054763, 841738133, 666246438, 178826090, 396363594, 265641705, 283812463, 188161780, 715029399, 155774543, 160473528, 336241749, 255485127, 411674921, 600097480, 210604935, 159260622, 996086446, 615106354, 542216704, 654351952, 743404506, 262415273, 514765045, 749837080, 918352110, 232620737, 216289287, 459344280, 473115012, 209428014, 699568657, 4440123, 67537376, 646873824, 441223810, 625870539, 536821478, 466825839, 714884655, 458406412, 558625704, 918822008, 865442114, 273901288, 12039614, 99710422, 810712763, 945645688, 237659362, 368252680, 397953396, 794402798, 734397137, 991924697, 993852934, 675841369, 366459584, 560073004, 394815081, 158148045, 204934587, 169831004, 488991870, 699131644, 353248010, 194631456, 585567707, 300032566, 765573951, 649240773, 644101326, 25771487, 962555423, 707751252, 265702303, 278167151, 886858466, 182818803, 31369491, 5376545, 304212576, 127732349, 539058241, 478920656, 871908501, 791343182, 472708407, 211307449, 637661237, 173202466, 102993691, 778195223, 898882170, 72282712, 820598584, 105246141, 642201664, 25376389, 55234287, 220702628, 142286558, 965720663, 211412129, 725711647, 423174024, 542725208, 135180088, 590453968, 243060473, 742719623, 963752491, 698897382, 417710568, 769386230, 877632888, 398687843, 451839707, 696841940, 409484180, 771781940, 355812747, 578931537, 279876175, 117325713, 526538791, 22257760, 44276378, 69419609, 830526473, 584356163, 715756085, 824756271, 376968888, 724776276, 8259082, 538314108, 982585626, 794984215, 528028268, 782200636, 613666396, 800965717, 365385027, 653699921, 590735574, 328022502, 295563511, 465699321, 516203799, 188699845, 664641034, 756527473, 860552642, 847164189, 329397430, 500454927, 718018543, 58840868, 902447836, 889944620, 305564650, 575304542, 638935476, 42624369, 528680537, 697472062, 140374827, 44328040, 725162738, 291721800, 406575644, 296559083, 440378768, 224981015, 318899123, 284052810, 375926313, 109614323, 597758701, 54905137, 436709465, 849780756, 151876755, 857927180, 389683028, 662546428, 540365370, 922496848, 284559867, 62245089, 95199327, 890921207, 195336697, 834148333, 478602826, 491284957, 313659049, 373184231, 601503105, 117793073, 675299773, 513957978, 440309445, 7977602, 884815091, 20092688, 526720658, 228845328, 780257656, 422257097, 995431723, 291401225, 645996083, 68163274, 685630179, 617311165, 264151746, 545202334, 215498196, 750228282, 728271540, 145102388, 415376789, 780002686, 87746319, 832009090, 98336406, 434249618, 403745764, 197306243, 316028497, 903542896, 752403536, 571848279, 79796613, 664520685, 730088374, 167532627, 692612459, 98335549, 734347801, 625110784, 901372976, 193716235, 283110382, 478853645, 748179663, 142940222, 415723372, 724180608, 429620142, 222000170, 311660070, 369436885, 395803672, 579871425, 212306160, 715780561, 229903077, 820235070, 70021172, 812023048, 990688897, 505462930, 232333441, 534270392, 852673, 695274144, 483732727, 780686255, 715078842, 610341240, 559614017, 326751587, 542881806, 867193934, 906987618, 931389762, 322610356, 441365179, 391990260, 763204720, 312373824, 827094754, 364199755, 73746047, 936411667, 910207316, 732380294, 316028555, 830603904, 274388153, 198874156, 452550444, 676810498, 136119352, 92081970, 535200929, 27910830, 596745836, 426246101, 282866252, 57698372, 903740530, 523623569, 103774237, 956219328, 583041042, 209214637, 180339134, 177823704, 301718940, 435096505, 697211442, 190765120, 502150022, 509956671, 202076702, 661598182, 825207295, 680505895, 776157476, 180643594, 704267037, 381342353, 905078228, 48216395, 42849214, 498611356, 109352451, 113683189, 65091463, 451571902, 780978035, 985554365, 258452844, 35343937, 492330622, 742209904, 446142893, 344317192, 30505760, 792465518, 965444017, 771490422, 440702176, 290615122, 479848074, 922382407, 869675822, 223349807, 211456085, 599973113, 402798, 238130726, 932053449, 981715822, 724870580, 467426640, 837867912, 71715443, 31207558, 422727593, 496841487, 425533862, 508492525, 533524572, 652063573, 656858525, 262770631, 375466626, 263822411, 217553486, 307772224, 264755573, 39124, 334693220, 657293731, 487133977, 118647577, 350538533, 516735880, 542704668, 491915140, 651275093, 587131477, 426195109, 160030384, 9841926, 701330204, 263671541, 443004061, 309214006, 722377482, 774919832, 88582332, 272161368, 685111713, 639515534, 632716052, 376616028, 286936010, 400757016, 828864318, 672807971, 783173816, 879905600, 38194155, 866170350, 96595201, 369256200, 727248850, 368424750, 906014132, 219683020, 654952997, 147953957, 298568138, 104549374, 414471482, 599350856, 537802671, 227382107, 580145664, 361977857, 150890521, 618648805, 990972884, 137446692, 179565321, 904654167, 319881053, 327702401, 660141341, 721119841, 151648156, 427293633, 116820349, 429801245, 34748451, 843712393, 632494634, 229679772, 815474356, 858391268, 306302830, 301751301, 500555793, 157787152, 593918146, 160792723, 942921307, 241298175, 649009391, 25036940, 873121601, 870014326, 785454944, 566416761, 700001353, 102709575, 381699621, 936040845, 784934112, 187639066, 132740079, 736207542, 80448453, 653425814, 846498564, 704080577, 163132468, 359513625, 179865051, 946014624, 307012626, 923860441, 143423338, 834503650, 289907199, 286617529, 47466563, 983264075, 332025196, 719276404, 428944702, 855386300, 607517613, 812189552, 133927540, 463714893, 54914629, 479844508, 663574632, 550733649, 740912709, 428250166, 517916201, 10684357, 250833441, 34948504, 957946529, 974096607, 744512176, 569223593, 912519689, 460066348, 624437732, 602968857, 482135474, 775162983, 394458371, 175979013, 25632154, 412737715, 448693958, 939204468, 489233109, 733014321, 806951415, 231590243, 238359377, 749155026, 706557446, 149596781, 68077212, 557003077, 256341146, 190705861, 38329707, 318556630, 114406561, 445415432, 762142915, 696117785, 922382282, 142283172, 388892873, 849499513, 174965506, 928602633, 407971776, 762987708, 97246560, 289951754, 677836204, 182835762, 654603124, 869095080, 766931395, 307074170, 405214019, 101079522, 880303484, 367271887, 995153432, 482626852, 679531852, 210892077, 305219786, 265838258, 986196998, 25393238, 571158333, 320425358, 340209049, 592723385, 233632448, 890756448, 273171795, 34790186, 914133286, 307113989, 321298734, 276649880, 888181093, 670883590, 287789822, 30601672, 256333932, 226234935, 794460237, 133795886, 394144425, 152076448, 569807357, 605482260, 88765926, 747591257, 493521135, 368373664, 654918587, 134501077, 820304693, 25103623, 884655767, 222119935, 180024790, 80751863, 826164091, 691639727, 964330529, 589539930, 251944489, 303420555, 525608645, 571170245, 286354488, 92711622, 839302778, 670936423, 778838425, 325900424, 816859953, 630549945, 733064090, 786045337, 162474097, 337867716, 482372307, 252759413, 360522761, 840520291, 486607674, 832092087, 267835301, 511464971, 555830464, 606237884, 971712921, 85423390, 465328042, 518538267, 265820771, 46157406, 758857789, 672647464, 143007274, 780991565, 38647176, 959660306, 639027561, 783009375, 288898906, 916668282, 756684619, 629918362, 17162212, 50931740, 424637264, 980326520, 144294922, 571029663, 464849705, 404851910, 768025090, 21253725, 396021473, 183865816, 745064740, 183048056, 773542939, 109019269, 594149135, 143445861, 946713514, 762280895, 180692897, 260756975, 899823450, 823061461, 393567419, 163895552, 761539145, 505239929, 143291373, 599128082, 739239086, 798262685, 425345972, 944625585, 434815719, 818791191, 174442434, 667109214, 343233560, 522801000, 181841411, 707487444, 816002369, 895137783, 576933678, 140421621, 769867853, 647899750, 196094109, 809709411, 832034807, 203231625, 447683053, 458413079, 784604105, 621065622, 209342679, 84146082, 255334290, 664457671, 947143008, 984396563, 894661311, 648699249, 495394933, 609381485, 167411555, 568754832, 43710852, 422283183, 246156515, 725641291, 476603360, 451779494, 606234691, 935384974, 504292651, 564614539, 752897129, 60480486, 838085593, 221278822, 16126502, 615764762, 174396373, 521397910, 387532609, 846783131, 380747044, 986968620, 264828038, 941875012, 375529543, 735071920, 567851410, 655388200, 312800675, 564239059, 638542043, 451847067, 465244057, 280222968, 45284330, 292999533, 233375565, 879329730, 569328038, 323094695, 673274030, 846272799, 781926751, 520752535, 514637639, 779955153, 339976522, 370066033, 608323998, 790215900, 740934478, 400425126, 49700418, 102287162, 603905597, 822072635, 734622132, 592983400, 79702933, 659743460, 625629853, 747267171, 85216853, 724232394, 269885138, 178619843, 170652363, 331611068, 468339328, 543331258, 740361589, 369559374, 141836517, 653960123, 435601815, 720775349, 945833113, 171895181, 611226822, 526037108, 903801070, 833653680, 861455907, 153278751, 460326148, 721783495, 282481981, 589662868, 429457431, 925306652, 152183793, 117032816, 375637533, 763298997, 536382010, 216236545, 613896964, 857414814, 200718727, 324028467, 494854817, 613679292, 698809419, 999556058, 398369641, 990217840, 181890210, 402105941, 909151817, 886935977, 798802173, 771361523, 72587033, 188254565, 696721208, 322951932, 383181304, 888083169, 986309138, 346713478, 475842980, 789067797, 502010232, 315216929, 471617113, 430458048, 492970971, 289930147, 751466499, 88074475, 561639, 684199818, 87046760, 158587843, 875723324, 441273418, 495965768, 12542162, 873760427, 35667809, 481895550, 28699101, 16902817, 959074921, 42897220, 202014916, 225857912, 373250835, 118843499, 199899554, 566489901, 735048369, 433100197, 918100846, 276352245, 850980122, 122593653, 599930159, 832022205, 58770240, 728992837, 761904419, 997736342, 265454761, 711427032, 145853104, 487258868, 743164002, 739097152, 903360953, 88230100, 569481731, 606077915, 982380824, 234516663, 102235191, 857737414, 926736257, 459751993, 756652772, 598602499, 178364587, 207170860, 481937286, 689841238, 359569413, 684975581, 699383794, 130607781, 133414837, 34044318, 921976533, 130321819, 20899901, 30930109, 987400111, 11867723, 991702148, 438208538, 283671463, 708298459, 376107210, 713559989, 791399811, 946479833, 162401245, 129960071, 470656344, 862284987, 840130336, 608239784, 247094874, 83527554, 860191428, 530424961, 528857762, 866697707, 327666472, 845333967, 451565283, 122839324, 463365109, 152385382, 894179163, 382934423, 401043958, 42834453, 806294825, 819588790, 700309497, 514106930, 831781772, 85839279, 885959423, 863066934, 897375959, 708930051, 295326048, 61241821, 237977952, 597327018, 781523516, 49011548, 720066741, 85185473, 865019359, 654462772, 976770079, 866925805, 889920280, 368163321, 70449500, 704135265, 868818086, 304656817, 72922887, 168154860, 764074688, 217537029, 38618288, 256916063, 113212626, 186588357, 188425508, 356049328, 264802931, 307109827, 936651755, 308137279, 468920299, 169361973, 221089425, 922996336, 864758132, 976430482, 148120798, 653794145, 33526550, 809125683, 259517875, 141371086, 407538264, 56786657, 692689250, 674477027, 276558482, 53211307, 443718493, 9879434, 939215855, 69736720, 45849567, 556266304, 383172947, 427222508, 656118064, 852130633, 666024846, 400202178, 266923373, 199125149, 131142403, 714066371, 346427107, 562528509, 719685222, 966788590, 594473442, 402294027, 404859150, 534148951, 585411484, 602566864, 761484214, 960764566, 312874455, 397814317, 144567044, 430874816, 309881986, 330809037, 548456194, 330274093, 866887976, 144349350, 331449650, 766693783, 888375632, 233316887, 607414209, 693070200, 71744500, 488807200, 629168227, 174076723, 851241068, 739159044, 430190185, 479749554, 609355086, 294021713, 111825755, 200642829, 764319225, 152222502, 676640300, 124715511, 705343078, 556324524, 866657469, 81912063, 552545034, 141922945, 717091078, 933464836, 318760873, 237450764, 370450144, 141534582, 437988518, 934545766, 46056396, 534704659, 880252898, 447174484, 115134637, 788220596, 737477865, 763331850, 714586314, 294214464, 94542428, 62115265, 112018879, 19735561, 322885497, 911814011, 326921798, 515254732, 989564432, 450274077, 875892910, 700327364, 184001601, 192465149, 784285996, 784393573, 983291647, 238125202, 781184924, 344923506, 819452127, 528209134, 246941079, 949108763, 75722503, 194423801, 561771022, 142923901, 741683952, 756690123, 16429013, 750394400, 528752324, 55895575, 549473964, 700537762, 986404361, 562498987, 975334460, 110956066, 886810283, 223878568, 558846461, 205059708, 991237658, 949666311, 925749103, 899498722, 365480545, 138661989, 990892817, 419889516, 533551716, 46516542, 577307608, 739237526, 627516391, 749666445, 796246753, 133565940, 369578699, 253450732, 317685255, 745666455, 902291049, 466209812, 221280371, 617141610, 259453519, 235744733, 734780698, 528763944, 968047166, 745918082, 348785794, 146223299, 596884092, 628040098, 363627146, 188402279, 302447826, 406511761, 291179566, 240085718, 12707210, 597556429, 756507126, 161279072, 601338868, 954071074, 809934823, 251684471, 81344244, 305458159, 590794359, 134874375, 275124609, 237827635, 547445429, 827327017, 428273896, 816751872, 703284718, 658403035, 700865596, 674914211, 437291373, 737342048, 7078599, 572238123, 399450607, 537932181, 734651005, 482719951, 948839332, 343479440, 365734304, 971687152, 161928400, 282764973, 210304273, 491900674, 575938277, 401516756, 66100141, 263701116, 377230788, 889435482, 516758578, 398483913, 97861489, 298383629, 174610119, 527281065, 937447771, 385596361, 692367448, 98489754, 686493098, 742457633, 915575991, 814665086, 931390952, 131969114, 851423303, 560640485, 438414599, 601835178, 56432440, 656864534, 696228648, 415976580, 784254880, 575614467, 400153772, 200498418, 527054802, 263610484, 641899080, 108453750, 774660779, 297945906, 41729725, 279318285, 288766182, 302305771, 502598073, 495094403, 546225744, 872070484, 26456430, 402714849, 812305297, 148493994, 222761732, 86997371, 4331819, 755659176, 348902343, 601657573, 62666404, 469258440, 146283276, 441099883, 239208656, 435255935, 94856757, 694221014, 471589265, 246824425, 800124104, 556092152, 61390178, 228503137, 250738315, 770603334, 527475056, 462012134, 880310102, 629732292, 873128845, 682224484, 536620001, 358091146, 825006301, 507550393, 561231572, 616551766, 285505164, 338852875, 731656187, 921454926, 807246590, 541682426, 330013369, 972868535, 705620788, 16645105, 250611793, 385509580, 84958733, 256441431, 676899378, 575270661, 35159589, 834570264, 741036386, 579276090, 631332009, 534833461, 574313231, 400863339, 920647357, 869421170, 322203804, 536240554, 861226072, 71367064, 277160788, 935534992, 88387493, 490671711, 574511162, 642346575, 768560220, 476727337, 661089159, 220118164, 238583867, 593852555, 307073711, 95426798, 684541283, 249461953, 768047376, 982405807, 16419895, 239379039, 810787605, 525904434, 719919432, 813067888, 985553946, 954600675, 279887168, 104904037, 554451858, 787988655, 554350247, 343748570, 342051899, 672203811, 918613181, 910176158, 109943034, 821661088, 894410430, 751609971, 669268269, 21205897, 560670389, 546252168, 362555644, 399593530, 5912378, 120233055, 634009335, 698604377, 584622832, 24697666, 19645565, 846617830, 40783902, 971899692, 898473895, 917316877, 926545649, 105357248, 2754764, 629280984, 302230772, 692107791, 597741751, 621285381, 411171284, 818551185, 120540814, 591252730, 328243889, 41549998, 399616147, 104308789, 500333854, 179798397, 746517113, 396640092, 631645740, 376447731, 384309064, 446180102, 447346782, 881470181, 700406615, 386381758, 672616574, 878015205, 807526410, 463354839, 548052019, 887444032, 726839419, 2655772, 885729920, 320241822, 649743556, 995187365, 842371475, 439233232, 532292684, 249422420, 175506725, 976915232, 29494108, 323100159, 835713193, 845328088, 545775040, 871937733, 291360317, 435109735, 785320583, 607053696, 600495807, 209992385, 934204294, 960363462, 634328486, 706040794, 493036317, 295035816, 918106398, 624006407, 960147513, 174798607, 614902197, 188132150, 395917887, 120178111, 722032769, 488244653, 633681622, 148990445, 6141693, 246756914, 350381440, 419718276, 64592799, 206357322, 785666251, 568050512, 465232777, 687659992, 864519537, 195568853, 626754408, 867818992, 223451740, 880552233, 80805858, 446326761, 632444749, 733042741, 327578479, 43473716, 416719214, 761176268, 716618870, 827758630, 775389104, 384130761, 745788244, 631903432, 883634705, 15900069, 420538529, 403086817, 921609798, 283290171, 135419645, 50146634, 701304712, 777454693, 386101378, 974327447, 38985355, 123864198, 640662728, 351415246, 923497426, 469782567, 320133533, 952961028, 253395301, 277362936, 445606442, 607031344, 191683632, 571055776, 264814143, 170784779, 208784328, 249676149, 407033794, 273376912, 558477690, 486374474, 896154163, 607121942, 786180366, 189287426, 369840101, 59748136, 215395245, 279837753, 393357063, 500930554, 743169837, 491772583, 949407475, 112687920, 131285437, 268644085, 210742844, 519604469, 833932891, 638104579, 863561880, 955145053, 859401017, 651923670, 617613941, 395007138, 339015760, 482848658, 220910172, 754349810, 589685126, 809626074, 237503870, 58596511, 9108285, 241498204, 879941494, 597801523, 303384146, 13612337, 570352658, 783518443, 69540949, 327039166, 32907897, 244297018, 41104804, 415074896, 65467481, 463711264, 89471570, 380690782, 646331256, 199821452, 835409028, 839394885, 800754735, 55755813, 435551463, 115678340, 823026057, 700079867, 110370956, 346177276, 295991467, 624291524, 729523637, 917461649, 528991189, 107338942, 777740377, 195992804, 203951023, 307486830, 45637064, 687651244, 351634657, 962132333, 786649593, 748587819, 343489993, 890321221, 619606459, 577494504, 740416282, 961811648, 410615541, 182794272, 95226327, 981822049, 773012863, 257933769, 949339390, 799182709, 801473772, 292109006, 869826955, 88434374, 744655270, 324835758, 576653180, 139682284, 868819694, 976373111, 881528083, 987785101, 672669817, 641179505, 84671759, 502437761, 358745321, 354201252, 223757731, 137759270, 190592683, 895199958, 369510645, 726092842, 150084157, 993580146, 29836509, 563681097, 273641385, 401646904, 631431305, 322153747, 814675608, 414336739, 524777678, 168707447, 194140005, 176190815, 519763209, 763041219, 494908732, 989050452, 431995324, 202237604, 862456958, 642895564, 530128065, 931652380, 504661114, 524139528, 385431398, 808468090, 759040777, 906036585, 807806282, 735148906, 321087079, 75122743, 120837557, 221055670, 549745641, 410597918, 270951451, 91665690, 896970490, 336007564, 511564117, 826002007, 7041832, 471499496, 182844138, 790052504, 737180413, 147043793, 592124432, 601565234, 366148581, 963134581, 410339190, 386078784, 809218070, 478462692, 260293619, 121208069, 242223274, 5209081, 152252623, 38668597, 410022603, 610397060, 533952468, 151678681, 996410305, 839818570, 504932969, 686340697, 818220994, 41623051, 797940721, 113244328, 742853747, 270119264, 795788772, 218726021, 65991555, 850828526, 694899678, 797051082, 542575830, 74526830, 392047761, 714634198, 638913965, 55106872, 547973591, 742241575, 859732311, 838467909, 112151861, 222260355, 180396888, 687157040, 7896075, 818836628, 608149538, 973006428, 655392328, 997224107, 277279675, 594206688, 386664878, 374922612, 822903321, 485035393, 169555, 186498448, 866727699, 784596347, 685951782, 442106436, 535645735, 679730917, 590402842, 236634364, 673522931, 997198881, 484308717, 732231369, 370802184, 352520076, 954332393, 761206351, 881197853, 240625885, 20022613, 789771946, 190006549, 774269491, 244493071, 213640983, 876432773, 447391683, 244769414, 442892356, 883795035, 31076617, 967514531, 766250691, 728686699, 567166338, 516894911, 935369984, 430719197, 210868886, 875584398, 321313953, 864019708, 638316886, 465979379, 622131417, 184640981, 598202173, 38750572, 211814545, 403962257, 500036420, 719701717, 750133151, 78067260, 720082010, 53020998, 111463034, 862382906, 601287705, 210319878, 423240770, 924966467, 82677823, 700023930, 866363424, 486334258, 543008159, 316067192, 189949209, 643067739, 917804550, 340715813, 639014490, 836790308, 857840416, 260827165, 657383725, 306522840, 304203605, 278402073, 137834220, 225019241, 135073761, 407185150, 204153313, 747928831, 926520619, 179107226, 518726094, 366737231, 714299037, 210217629, 775588301, 692140763, 46935496, 625237423, 961979206, 319824429, 601494526, 336182834, 159894952, 282744141, 99752662, 547098688, 234559632, 391623943, 620636213, 218074140, 952305231, 948609498, 10188176, 929632710, 94010464, 169396635, 743829634, 947462175, 79801804, 243247259, 727658883, 552933516, 860814203, 872287387, 637857899, 233249073, 502305880, 292778831, 439449547, 472851299, 849853, 7299251, 565856001, 410407325, 562110144, 106393434, 588731432, 133719734, 260755361, 279678286, 492000780, 335008057, 438484302, 950177194, 918822949, 234695348, 47178008, 14277520, 252454719, 757846910, 641658275, 365816521, 854934254, 370998558, 340958834, 131709062, 488217955, 104404561, 349284417, 300954755, 540737693, 859785281, 188189688, 662597068, 776362622, 210970332, 839135496, 323915321, 651572985, 507195280, 956113648, 937010989, 877550045, 951900250, 270028550, 462321302, 379927562, 785300560, 514815540, 746342188, 728808726, 561270710, 853300561, 318072297, 21771093, 509665326, 725905284, 167329788, 309785886, 869171617, 261402981, 107236015, 110398674, 296302864, 130476993, 774868043, 139281566, 546719273, 824427531, 212838973, 718543567, 325695711, 992857506, 275781954, 978957827, 802007034, 126134662, 314321753, 526636509, 669860978, 297617464, 971963755, 308736211, 264137658, 693969935, 641242481, 229105422, 608031116, 811489123, 295262517, 562487393, 380466626, 65365086, 122236785, 696024238, 455993045, 11733920, 182303105, 451753704, 821480930, 988903438, 423166622, 714298799, 469935244, 470688778, 907163775, 207366779, 118229048, 652973173, 129866562, 645653421, 910126417, 107139217, 496129142, 776399470, 965807421, 255450856, 487356227, 640647638, 458605059, 798926944, 851461505, 718815019, 510526688, 825873168, 253960434, 73103550, 876997621, 992239786, 266571918, 738216878, 1375081, 147889034, 254261510, 963369701, 458215256, 177922449, 732903216, 456918709, 152241006, 493832756, 807776793, 710620781, 715316346, 451972215, 476588272, 366284705, 728354934, 24904837, 338695963, 160363176, 850299682, 589835789, 966868326, 462897894, 835786827, 208498597, 71762643, 870803947, 948222062, 61304794, 361728285, 126326102, 799657218, 303266305, 227952506, 617083974, 408620562, 552050758, 818807126, 589410944, 29019827, 924104101, 320908838, 670085586, 695989428, 744484653, 169634875, 658212059, 575511330, 364555432, 531451066, 695726061, 323714037, 585115196, 31782947, 444958923, 510863434, 702912923, 105287083, 919933837, 857982724, 108004002, 662443213, 639442141, 921725922, 60995178, 414607692, 731108687, 715190633, 397275464, 552409625, 736490631, 706967803, 550327560, 825423070, 878250286, 570310929, 740698009, 829249315, 201314289, 359009898, 270131622, 353857927, 389236591, 181370266, 279517306, 676871420, 343499823, 350500369, 82031725, 657004104, 252916064, 385428852, 181389092, 230321601, 26121821, 383018349, 240263786, 542043884, 235954224, 674224711, 775078512, 612447007, 144107551, 756371550, 795035020, 499136675, 276252081, 625833759, 625527013, 649183668, 258642108, 859903211, 44326388, 955169702, 496340542, 344479010, 955110460, 855910031, 266330786, 647646288, 681003327, 565459915, 94778947, 798882640, 338089335, 337975687, 118527076, 632776555, 706287228, 886348480, 115304455, 190149520, 720783547, 522908592, 802612348, 617647495, 380037975, 9275579, 976542375, 515722503, 351126144, 327853877, 993938931, 17963358, 346746055, 760284185, 344771643, 584655391, 970726446, 530756969, 621164508, 487446146, 73913117, 523067188, 315021817, 962001016, 4571229, 742405672, 153488361, 617251213, 276044189, 750851639, 689664226, 189060915, 889194475, 225717708, 561536243, 33303088, 932729914, 79508745, 717346465, 879732119, 679095167, 29621170, 82282959, 533685587, 587323060, 713563732, 179508384, 515852382, 10669718, 910885137, 633757626, 628224683, 845372655, 601124275, 416007900, 911712173, 274939084, 598614441, 452356232, 7187469, 470963314, 294638974, 215155621, 818576168, 539458785, 435402659, 661076742, 680241039, 398299729, 517753279, 947646511, 834215052, 933470564, 717089161, 469993466, 165846411, 533905831, 638646525, 883159158, 185693176, 518970910, 358746826, 261303567, 829935364, 535242099, 677597869, 999703173, 915258333, 263018838, 160676234, 544303462, 916818114, 531010686, 398444184, 891721116, 893715794, 579005272, 538602718, 919428312, 654860481, 128090283, 743998301, 682909219, 178945427, 410909759, 357996537, 817983747, 161979026, 707755396, 269292698, 393867890, 406191170, 296539328, 383682038, 453930745, 536047511, 546686029, 276434832, 272082653, 631092961, 634571427, 210488800, 801067367, 177981288, 719015570, 125539399, 251855903, 994705173, 341361739, 276146614, 82199174, 659981136, 558342002, 116755006, 297249287, 913159686, 303136843, 937745784, 784183380, 555561488, 425906525, 92724957, 425214373, 485185586, 428893281, 23223360, 38058443, 700551914, 227060915, 37363308, 87721013, 800389259, 41022705, 713234463, 508604378, 215325852, 809524671, 301117904, 111646954, 453866200, 264587275, 396738076, 117758842, 386171946, 454883455, 290563973, 467767840, 712662989, 329093813, 102775695, 271054045, 527256497, 307019937, 821887339, 297378124, 328508735, 810225467, 20408038, 486842188, 31522925, 550204525, 282565850, 644453729, 944390158, 72845079, 868308766, 719274088, 176073676, 72970343, 139736213, 351401737, 187744379, 198409080, 887560928, 976385115, 864901825, 5564848, 541157876, 153769828, 813424570, 941961047, 827362414, 949130709, 57027455, 916103893, 830609531, 802658822, 56299606, 171693696, 771987940, 565253003, 323365363, 494712100, 30779239, 169084275, 292087147, 891484244, 273416585, 973485526, 267020504, 965469925, 26299763, 991634741, 826732324, 998110427, 499068064, 23413794, 601099391, 256189684, 821798415, 963195896, 629035232, 152633339, 936845606, 636391192, 803087834, 19894896, 183114796, 194460448, 741898640, 8342455, 93352496, 393842187, 758200816, 620128134, 532211616, 595145050, 15689877, 880297306, 788937730, 570586234, 230424526, 124179774, 194374088, 671031263, 739191386, 485135553, 505403115, 941636908, 960520204, 418966204, 650341855, 716685841, 141736642, 818493450, 69563126, 474632263, 68307837, 563830748, 618750014, 266543293, 759699263, 453181824, 840004145, 204024078, 86540361, 208902777, 691792282, 886511813, 116219663, 46411681, 832014022, 359094075, 64134909, 993470927, 742311554, 225919967, 848724655, 525681207, 528891207, 799523923, 92049203, 455900072, 91458261, 369331454, 78742737, 28069006, 239878992, 97794540, 33703532, 831430579, 803127495, 264207707, 555939307, 68322705, 123518913, 713128915, 686115540, 734040383, 922625459, 909968794, 811448019, 525455843, 639502889, 25699212, 870037211, 90813063, 529570352, 346436063, 712606885, 241447369, 857749279, 437205689, 21498960, 611153400, 508258366, 93726319, 399783462, 631765452, 693787518, 50153541, 847016957, 82775299, 741096315, 796247180, 669651402, 380246574, 595630377, 954299210, 435792508, 357223623, 772568411, 531605304, 806018098, 57995778, 530551219, 307910701, 559711369, 714985976, 182931473, 672643381, 851895046, 870319726, 161363907, 812549936, 445216924, 690020917, 700966970, 193282016, 732064891, 43272853, 883572421, 473833110, 34203716, 934232129, 719530125, 374840976, 273993565, 735316309, 822312474, 676647787, 911562237, 327830898, 592102013, 548365690, 554853413, 808737576, 377591458, 384585393, 523580915, 419011759, 264374682, 539462488, 875402358, 356787493, 315555272, 964085714, 40246856, 6243552, 209510561, 788113175, 851270858, 353978800, 991483711, 934575132, 24386351, 842527654, 356939058, 22408288, 239519546, 842592009, 778293400, 847548252, 891561398, 969533079, 897478586, 669886259, 783920624, 988475799, 366503348, 742733088, 729425327, 658449745, 854025912, 906082842, 62495707, 934813315, 145190307, 421908935, 203116381, 143640867, 46680903, 594878773, 447567912, 121457103, 936630347, 352145124, 913881730, 80312387, 780962178, 269335817, 664854131, 676542027, 296764363, 283477597, 924579130, 335085470, 684336152, 430916840, 780694770, 547851502, 352261680, 610914443, 339878090, 680087415, 639583589, 122498260, 237179440, 710969136, 40359050, 229704329, 442351808, 804186786, 122241693, 917307097, 546362416, 829427602, 399554192, 143110850, 998667132, 819505067, 543802178, 287277226, 871972010, 151472222, 171004576, 85130237, 653005060, 627575183, 777557794, 346560129, 162718526, 420626391, 59236782, 439403647, 861996503, 217289855, 281376210, 904964820, 520381013, 525031363, 91692156, 495203860, 815128593, 406566378, 11266340, 758603919, 219187740, 557489293, 731526802, 18744001, 617073411, 309651030, 430449720, 669993154, 697884863, 120820049, 876774213, 907115413, 248098795, 575235869, 35379767, 755467889, 434543014, 234192509, 615921324, 887405522, 366102119, 685859676, 784607748, 419966684, 928397480, 861558625, 187983083, 974326369, 338477263, 958505512, 641100895, 989544155, 23913741, 252561321, 444580750, 944409133, 639662556, 294371860, 786932201, 442566150, 921197656, 365148667, 812317898, 310329971, 860637639, 920710184, 491064847, 959495882, 265268460, 225861147, 571696218, 5404041, 47735754, 620275470, 129157865, 413168397, 953831516, 583764091, 136968006, 271771695, 728768627, 358303247, 260211836, 933471744, 542692276, 230796793, 445784015, 487786534, 950323771, 964744355, 997439775, 333175923, 890341113, 148811853, 480157892, 746301130, 506688530, 145646757, 251394130, 872958974, 611283421, 566303944, 827215649, 971571594, 132768738, 547561093, 317051704, 882471113, 201335464, 771103559, 388162270, 774454413, 376863328, 413025136, 94921660, 59391628, 824782658, 393658787, 278057219, 534885517, 534772265, 186568253, 309200702, 941395772, 508120872, 97641933, 949750951, 785100801, 404474966, 453483995, 845091948, 91197145, 677095299, 955160548, 420774463, 369290759, 611870109, 304565764, 501911687, 819013130, 310336333, 901361930, 558744514, 271607686, 54347015, 241490591, 847206630, 260370227, 537985455, 736009850, 383980738, 548435383, 294434121, 199540861, 122811977, 176244726, 320842723, 262711529, 65823133, 29283379, 834612427, 285234575, 573240709, 677598353, 276354307, 542743797, 907557082, 143852868, 577959723, 310253865, 289666608, 891352601, 979835329, 802845983, 283029458, 118315522, 578009677, 790411964, 690118698, 788056541, 811797576, 610078615, 565050925, 774000899, 130731440, 906956590, 997046984, 304578271, 241637289, 731399282, 204108316, 944202020, 714404957, 810227679, 849907578, 334355905, 325632228, 14566567, 105171950, 435632243, 369585943, 928377037, 207725636, 911716335, 30869448, 811572500, 248081847, 692292651, 164302292, 568916793, 344878366, 284543490, 737544984, 341864192, 876981260, 94647613, 75222313, 129394418, 781354012, 221598625, 648182192, 640559334, 359026062, 354700173, 805157812, 40782512, 196882057, 272280910, 778709126, 344972737, 68330259, 408250921, 246605947, 946771296, 433636257, 909392039, 325496018, 298748500, 56953816, 823003917, 958168810, 9541866, 230577253, 685188114, 251268919, 317477694, 191299712, 711154458, 58890721, 669924457, 734892139, 61353781, 779988, 348136958, 269152445, 416417584, 547455994, 333412538, 774804732, 557884854, 457960775, 559550771, 964623637, 446411790, 52638783, 384006102, 300204118, 632469915, 225958723, 307509915, 962561344, 897904292, 537821878, 959017631, 726262197, 636385621, 565835405, 619020054, 836700996, 566803210, 974930871, 16975952, 989870812, 213423539, 851144827, 405341063, 697118616, 214395242, 361066618, 580458617, 5221794, 558988907, 422756936, 945073203, 423733749, 382668863, 187408479, 891334723, 413148079, 278602107, 231527956, 335758300, 81289662, 476317404, 136262830, 189514592, 750881152, 886526176, 429394378, 172883541, 750115880, 855965673, 219819337, 856919509, 282759120, 424371409, 194301600, 704570442, 414368857, 225175944, 854786117, 661800299, 267582165, 973827785, 935746043, 119025703, 375826152, 167671996, 6398890, 150324727, 528361403, 310458536, 899917391, 430851672, 135547737, 882417873, 857624967, 90589157, 39992501, 357759786, 542102174, 415611582, 753539943, 135222518, 894411466, 183421645, 984113271, 474331115, 690732637, 201659087, 696909678, 21132876, 524478043, 327061975, 959744814, 571526279, 937816917, 598659408, 497653251, 141638524, 351586949, 215110912, 935218243, 832516689, 616027018, 922226879, 55220666, 157344164, 555408120, 750647932, 932634192, 708928621, 207249184, 215479972, 860431283, 362459276, 564717194, 947371969, 941834931, 646158162, 976944479, 187228228, 870543127, 632492888, 614569443, 380169002, 38341678, 812823504, 730399909, 204690945, 531310017, 344729053, 184850244, 974413185, 672280081, 264179666, 811337522, 493543024, 576394721, 490871735, 903444248, 986613870, 913304807, 898408543, 427725323, 332368236, 772777539, 164155401, 289707109, 82096190, 662310243, 352066194, 841016805, 353829053, 762792839, 595288568, 628699308, 380535985, 20305745, 429011670, 734798547, 389365147, 304045049, 713118298, 44410935, 539333489, 375117558, 68328407, 30170131, 991031913, 178910188, 94860104, 782739254, 570333005, 853509233, 599862036, 503734688, 705259944, 931944323, 292894250, 80627451, 86312249, 413958063, 210153798, 979977702, 771213653, 671791074, 54964648, 265425696, 133306298, 180668760, 135625195, 832626817, 252267562, 567692363, 85381260, 957616151, 113331547, 599192533, 961860707, 391827925, 301321565, 862207091, 845568852, 739563421, 474706635, 304516028, 42637061, 334885998, 354940404, 1719222, 875672902, 642687139, 772001670, 665354507, 824626600, 270935628, 690232002, 276318998, 246095545, 575333751, 129175898, 303770946, 726672337, 783857958, 941706232, 955378151, 63924872, 792930631, 722905446, 745450827, 485787148, 268349961, 235392690, 315325927, 901148976, 494746259, 767590375, 98270474, 585818449, 870875753, 587770973, 840656029, 901652582, 512254514, 84344079, 255089462, 826805329, 579187312, 418446258, 29487442, 108981377, 34923416, 98794812, 409158643, 630545356, 597162263, 685777681, 849351557, 849606262, 460014023, 224094996, 43316631, 407367476, 207004355, 153036516, 842946386, 831695317, 357003132, 690887785, 668171390, 872557577, 360189009, 724418582, 915528218, 985024557, 244534191, 972173571, 316107735, 599071964, 846282930, 587839869, 238741997, 843058312, 3369353, 135023941, 449899003, 993968406, 118827906, 513233890, 48408843, 118022303, 206459577, 714101876, 750169203, 286351403, 919816044, 984222967, 248387733, 551951027, 216366838, 215457709, 80731084, 643236504, 660007475, 366277747, 234615819, 818383125, 258898316, 19916588, 651171404, 206424432, 624981059, 743648908, 448282329, 5967644, 791318197, 831381867, 966689781, 814016847, 634403025, 471448289, 631807341, 376106983, 689434176, 545841396, 346624276, 843666283, 296459283, 645359355, 496936455, 980051858, 362241315, 884709747, 462267120, 730784247, 802768717, 514923059, 20465144, 534034357, 780788169, 888232686, 947447381, 846718405, 19348440, 885017539, 993340934, 880332533, 841711301, 756901875, 476768409, 115802192, 975469182, 996496983, 4500667, 693026071, 940238928, 282303168, 551650820, 991107947, 166413227, 626662327, 537484846, 593304494, 264333047, 472830406, 383967915, 131937640, 469593211, 518690204, 109701262, 433724001, 589460911, 87981419, 503321189, 917411481, 973646916, 769623415, 344380507, 17475889, 303160370, 501314843, 406540502, 501332983, 582592948, 828682035, 409090508, 5096288, 789077346, 875370153, 782615462, 369077364, 147559651, 669617953, 890531186, 313826988, 862508804, 486539360, 177740430, 836211554, 401875267, 56666153, 492809936, 379994429, 553000670, 443324051, 350137230, 4305752, 143478941, 456067512, 953190388, 280861565, 785690235, 98438175, 480932944, 624936617, 557986742, 145939091, 221442793, 40986745, 414725586, 408582435, 595277840, 492736829, 543156446, 819057905, 358873319, 498389677, 172060803, 70772757, 26242108, 199881932, 274079032, 898814596, 289676181, 533829535, 793293851, 367543661, 113908991, 535493540, 345604814, 809558797, 749615480, 312694439, 614084502, 448597595, 343247423, 425288156, 677268857, 780209943, 132331046, 92112570, 360196024, 238655288, 284471350, 731640510, 515319310, 779792351, 328153275, 645266220, 486343587, 94932265, 865586668, 817905630, 112572052, 202733685, 610974189, 432440725, 432919444, 691207598, 771017932, 462012136, 432040145, 381256815, 497699787, 233385663, 816514085, 916654549, 259485038, 380312838, 271389650, 212783904, 417594977, 863018988, 772461893, 7617187, 892160380, 566661907, 764768368, 642119063, 336006724, 949438074, 284349253, 137287150, 884170777, 748100958, 736060352, 337305632, 801563752, 486453347, 72967801, 748469757, 674261723, 891905913, 615597512, 57932076, 289020223, 461888916, 414544691, 537402870, 770889654, 990672959, 279116354, 832281891, 362207441, 457570169, 772418008, 75867607, 371405197, 624503861, 323026788, 407251650, 93104946, 972515739, 92866565, 617347585, 969311280, 583658661, 733494047, 653091902, 136930117, 453391555, 554203533, 986487270, 928831968, 763184928, 296902285, 486138549, 937659648, 266459876, 54901662, 812864548, 285773187, 947027852, 680598722, 712377095, 687800365, 672211695, 519141717, 773417867, 119112401, 705923771, 313047743, 512817645, 449023675, 486127354, 511560984, 556462065, 463320325, 343093303, 109194568, 451642632, 622191424, 154287664, 796271695, 145452454, 233018199, 909118807, 255425758, 754978504, 444019809, 688719103, 468963057, 416846633, 530997359, 883610607, 671185383, 802976975, 4500307, 165397552, 915081004, 275100848, 606196810, 23486438, 505495268, 863597601, 895063910, 831132052, 509246778, 405176683, 754456529, 646627772, 560774272, 793282277, 77816885, 579171183, 529860868, 490565024, 26534071, 170604191, 785597936, 989586010, 677732534, 48352813, 859591841, 510324837, 156803171, 47686090, 239543673, 531598895, 449555864, 575173934, 726495206, 147069523, 238537394, 61452640, 957023357, 385918561, 677320443, 806363938, 7814936, 206649674, 423225445, 821030225, 448372214, 136100379, 296356022, 661486443, 906413276, 784203158, 247644959, 930267668, 688588161, 365427069, 208863267, 672113025, 631218283, 755216456, 670089457, 569257262, 16200509, 498566061, 49713782, 596520222, 925378792, 974510742, 770854638, 297585748, 223491854, 187582702, 418791274, 516625989, 538385676, 89615050, 844533137, 516329735, 214240330, 365126145, 465883115, 576659309, 179026899, 765577307, 290615921, 615078017, 752242600, 418685875, 510656246, 525347499, 427735625, 468807969, 134995509, 82772618, 415280443, 254199146, 279220277, 595746343, 674107127, 718444758, 401323524, 910630263, 398660112, 839065158, 270784345, 961649470, 502796884, 126020878, 95393876, 845130707, 721416808, 67530076, 325318528, 676686614, 804581255, 299390919, 670013888, 87388469, 35759274, 917008584, 971718005, 337413261, 514364432, 642898363, 508583322, 246235294, 235615374, 924922752, 136022411, 203174583, 832841299, 770791366, 922913899, 959383851, 666210855, 167431395, 91402907, 20587823, 335513097, 567480071, 82717344, 785653203, 513849598, 183467388, 994261295, 247161324, 403559225, 294477355, 943192325, 543161378, 730109648, 576425090, 954447041, 270128720, 668458120, 896332990, 87607988, 790164452, 696785515, 229355478, 197806556, 569616993, 641576670, 895925023, 663459100, 143078560, 127336301, 88510827, 788157234, 833218305, 980549907, 772052164, 795244338, 242187725, 942373095, 765435929, 858916355, 699092547, 860427314, 487994043, 105051576, 688777719, 89784309, 485065415, 110980909, 808168469, 970001152, 594761413, 309872970, 356955795, 292609604, 963025087, 632307480, 81032523, 583803511, 840612188, 29090396, 592161409, 273981860, 667724431, 211649705, 913410629, 482867182, 927919625, 55233069, 821406593, 998948869, 992619346, 999198931, 194067075, 346878615, 56254897, 867094785, 36263848, 791474823, 158483638, 563777600, 97952479, 336447091, 616455520, 7362021, 512297112, 735967015, 371929046, 153694027, 964500955, 900298692, 889401559, 752822205, 6125937, 939435985, 46956846, 792303429, 347302504, 760018027, 520198783, 507670523, 20829309, 165304242, 471673037, 579521387, 965463976, 707263955, 812116507, 264053525, 476752441, 770855613, 779644806, 715945750, 611723901, 117910549, 805339295, 904496433, 775549978, 184373119, 911695104, 674689582, 253532277, 553703900, 313552433, 733230331, 889961096, 838621457, 699518217, 307068898, 257083158, 737503126, 777679320, 842948827, 637286793, 250200453, 15797973, 750210889, 668291598, 551684764, 393437616, 314241045, 927932561, 323736421, 303701698, 296044151, 860382434, 173682170, 977873913, 249686031, 243332738, 199893966, 875059640, 122923305, 457610143, 60256117, 682415887, 727539977, 694434339, 910080011, 399262402, 51699252, 90920368, 202215213, 752475764, 769386196, 509530168, 686779724, 345969097, 598510252, 55499498, 660317491, 739568830, 301650443, 343650531, 895327468, 403239016, 227330832, 327743530, 903004206, 311117856, 886148154, 484756820, 362369387, 612752013, 430813052, 231656418, 638444662, 983825475, 826490989, 213870029, 962666843, 792623902, 23649969, 392764778, 797871356, 706385603, 710905535, 269568104, 662107726, 347430571, 702743133, 529211999, 509981149, 254271961, 974971159, 711428612, 571655825, 988714872, 779172762, 13664719, 831349816, 954734364, 344676554, 610365324, 197947438, 648518018, 402851045, 805476574, 288580926, 204885950, 253845024, 318356305, 827561476, 219716212, 659859623, 462287738, 757426837, 36720267, 929012646, 783394162, 615413122, 261706855, 342556399, 519304064, 540461710, 943295167, 918530384, 332017966, 705110528, 556943552, 835983525, 954447211, 248930518, 117595237, 485723544, 342419732, 356259654, 842406303, 798480043, 340835173, 617349099, 399613220, 600244197, 972368947, 334432598, 103253519, 473253948, 732306984, 814318857, 810693351, 365519488, 910849473, 367721009, 522352433, 114563449, 38870652, 550532313, 646901359, 214232496, 920524785, 158509407, 794816912, 506543406, 785116585, 546110348, 105272397, 997519761, 309795874, 989729625, 748084946, 240358763, 276631747, 412556727, 865949420, 53761367, 178274222, 939756931, 440083746, 522844609, 77119991, 182552196, 897129301, 432641518, 198850030, 366267709, 933060804, 753365699, 264999867, 756956573, 469957960, 559484009, 4266208, 636546056, 186310408, 182027535, 625069334, 682203171, 720012359, 749624604, 609983373, 386710595, 432239806, 236311761, 580286941, 690907134, 369142480, 626687655, 205585395, 906565457, 803745949, 498171348, 760290705, 787786766, 830531037, 925173483, 487891035, 987297557, 59215575, 20769092, 250135009, 976238968, 790772291, 805083052, 806396454, 594704633, 288560962, 145541499, 521907580, 491519453, 247673616, 571132005, 733141567, 730933455, 778897108, 359579755, 68466049, 579003222, 707101543, 656287215, 545022096, 422053942, 665503788, 528780078, 399678565, 658689696, 761024555, 732751616, 170616825, 839316990, 956429187, 525211418, 300376851, 9898817, 11383671, 899815184, 739008369, 877439583, 796645450, 726825066, 571308819, 755245313, 867197099, 63389959, 594567357, 85931579, 415495614, 180055875, 497958171, 455922426, 787659457, 735825871, 577233683, 352131438, 686282707, 789046768, 783138324, 555005932, 542379988, 901408331, 933813169, 467911078, 525120983, 855086647, 492324499, 25675325, 871416107, 164612722, 566388776, 12562722, 81804684, 575356764, 13511367, 249432296, 540996593, 809633555, 342657439, 697587365, 749862402, 463418766, 861941421, 222968348, 726777411, 749106555, 115601651, 662325101, 496516296, 18334620, 684937062, 727953365, 343488912, 193115753, 440114157, 758284384, 990787281, 104572646, 885376555, 296727717, 706914847, 849871526, 507244771, 813895292, 816484695, 780859975, 428739734, 405911389, 188349365, 936628881, 904363908, 764772969, 89752943, 987592405, 865305804, 106047971, 595408855, 449988669, 726461509, 515473586, 969182481, 213560543, 296283141, 907813464, 171757454, 462104448, 235080325, 876720956, 358030164, 739844436, 276936022, 55960014, 26088784, 898230683, 225643428, 139459704, 886182421, 622982186, 232761498, 710489081, 580652926, 788670925, 254083429, 942911550, 583407404, 728711664, 170072243, 516639685, 496085600, 866565926, 395540308, 898000122, 444031981, 435935805, 328401000, 207887438, 989552997, 985847202, 774411296, 53167338, 426250215, 763371444, 804615082, 626490060, 605605170, 132251931, 67649823, 848954847, 419670752, 207825938, 392295079, 548000673, 42429760, 604800706, 797802706, 962085226, 897190187, 921925874, 760425581, 290423185, 166163783, 825672364, 6713485, 684059677, 8419834, 403527755, 469156436, 949948042, 602704421, 38716367, 725561252, 998057412, 61101667, 975001881, 541782309, 130796403, 726688918, 808518526, 923022808, 21150994, 229122192, 821888544, 591428827, 743863937, 961174352, 22750573, 704138530, 46788953, 45935340, 530470500, 279823311, 925349940, 212333333, 532912829, 455473581, 172215604, 369028370, 577646372, 286889341, 205660003, 410788662, 370504363, 141151960, 59018782, 631880725, 768262308, 904938209, 85478873, 373102843, 421430573, 698818109, 551572187, 570204574, 249437998, 708643, 901132144, 688547404, 71009153, 581066120, 480063901, 203620586, 616785624, 303726635, 504502642, 573830689, 275533772, 316366597, 80682264, 448689955, 800201082, 876805830, 574554214, 105082484, 55954660, 70094763, 306816268, 687254175, 53854307, 83106778, 686696, 641684079, 291047976, 58379835, 833941126, 345500274, 554338609, 382694550, 383803809, 750483985, 673955806, 432583122, 227744346, 224029491, 887622722, 204258038, 154084067, 487140198, 348359842, 584052760, 698206274, 305460694, 497394898, 738303200, 504234052, 608287883, 719698017, 393209783, 17385114, 815728969, 282259367, 245772510, 690652899, 53339185, 405261634, 161366633, 140385065, 879606595, 139439680, 747347693, 26417831, 54738248, 314833934, 609455518, 220763549, 270100102, 147078450, 346855728, 562961767, 395074048, 853736639, 386304935, 817675408, 933510296, 202175673, 135357307, 327917189, 362850661, 213841750, 710947845, 105622302, 41872917, 689537153, 182394903, 552414990, 175363164, 114787242, 961188596, 998974854, 740450445, 9083605, 546030522, 855334584, 659662713, 737173930, 825385596, 271027346, 245695392, 928854482, 862338873, 483040692, 23692170, 128177301, 305863176, 389491960, 90769336, 821211871, 576083911, 47542990, 274495495, 764699506, 187655266, 205419765, 375173597, 328318181, 211646820, 971409765, 570953513, 354342547, 246966750, 890567494, 557397332, 383201960, 229085446, 811607466, 345763423, 11986719, 829045671, 999471732, 421634081, 889411439, 644968734, 53660411, 91313377, 16929652, 823380898, 819183172, 648101253, 561157404, 312748477, 110483646, 933237154, 435157820, 811228160, 476483445, 632515588, 432097843, 207799233, 660467126, 887565306, 541294230, 665048106, 170845024, 591487723, 350802608, 160664566, 800222610, 370351331, 541464368, 505131480, 151884758, 284286877, 193096955, 878493517, 684903128, 643288958, 163078194, 474543227, 831826148, 399026398, 136829610, 350999456, 614667827, 103553756, 73321182, 186849133, 31454869, 342355254, 505664364, 590460524, 704942005, 635564077, 334980094, 625136921, 701543243, 203047774, 595409129, 545836816, 50075356, 925036463, 846047006, 646204132, 791848067, 549409574, 562364691, 809213599, 586034525, 346843122, 246683622, 783409868, 922578890, 151583997, 791308990, 37194480, 61408837, 803455292, 832704356, 475001707, 522899646, 62039277, 177629078, 730193790, 643945700, 773571405, 518324145, 207487092, 565316067, 674593909, 909337768, 768917398, 675647930, 758883523, 767540368, 620430564, 942759806, 403945327, 520176660, 124808790, 496162816, 350501435, 865227257, 134929849, 377200141, 677914553, 263764068, 360702404, 724636592, 497899931, 259483559, 888700387, 10458533, 391350312, 457419212, 811655387, 132233871, 918250949, 74136581, 903307818, 459916970, 350975567, 245077558, 848086846, 985007836, 457000827, 448811766, 122087960, 476337890, 97056114, 608967275, 433075898, 739920601, 371247586, 467166786, 979142265, 901919792, 440587266, 995712385, 507947093, 444534756, 609248456, 716942354, 47888372, 693299033, 343202992, 42779610, 561907648, 642901941, 676576765, 292649027, 239241028, 605631088, 519507128, 201699105, 972006763, 731124468, 248133586, 209070310, 614547606, 981846504, 167230510, 246282401, 529295927, 184320428, 383421895, 666805314, 358432604, 966528447, 83441642, 60011108, 676546031, 551338292, 601761459, 901043988, 975953023, 431548759, 342466411, 604207686, 21875053, 288155041, 103418912, 89334888, 12555284, 596769503, 138391148, 993454811, 88318927, 493930980, 207848269, 189357144, 22067128, 589495235, 184255474, 595181908, 208971865, 153896827, 997172864, 853081084, 528915528, 104667591, 563399752, 83118423, 291348622, 990415192, 499160486, 713118196, 894464804, 45502702, 236360403, 505150168, 99803465, 107071202, 352185991, 595671876, 771654888, 699141514, 315633343, 594631057, 797536825, 48029112, 992166506, 415904645, 759312368, 210385978, 292050552, 233258366, 898728296, 795027529, 964465944, 111164909, 646821703, 625060675, 957034864, 561988731, 204610520, 707212035, 395682366, 25920146, 476787506, 87482312, 485549237, 186160049, 179302162, 163182711, 333263287, 919635114, 877337941, 834475925, 152975673, 646781753, 878711055, 780234815, 614881801, 831151129, 943134201, 321139905, 969334923, 559092429, 380198113, 933639423, 461325062, 422843351, 854073687, 49419605, 504078934, 111955963, 415170263, 38650302, 686693251, 135586958, 23493053, 664491870, 518227303, 628045416, 620994574, 61616235, 611080856, 952151375, 759722188, 984580843, 837077964, 609956170, 95634477, 95796808, 570991056, 429530541, 296768816, 737652942, 968297061, 858953520, 54112108, 697463124, 37987413, 801806446, 161095160, 975104182, 571728230, 481712265, 11512819, 902771966, 866963141, 685863987, 390684715, 574387507, 694027107, 629642233, 757778801, 10144421, 931126402, 242358115, 962143504, 13858696, 840672802, 99727675, 785574328, 63272665, 184845125, 498474392, 449813723, 972715483, 29232658, 244141088, 676197717, 729901544, 482210559, 322227599, 768961061, 383477101, 164225770, 549481736, 309512660, 965173888, 839016175, 725105715, 858511131, 45427299, 723481299, 846760649, 545946020, 313524166, 790612044, 396297300, 267823972, 936254925, 755531026, 448514838, 267793697, 718045081, 356758135, 572108603, 939514762, 775411656, 859165480, 773618846, 407398645, 872425553, 899646299, 944256491, 44779806, 580896659, 19003864, 751468882, 947744145, 409029983, 649475774, 279569892, 264427736, 570715680, 860643193, 925111653, 541635981, 941250119, 252457551, 714651518, 956978188, 925257029, 88743025, 701436727, 652366595, 681515031, 112318348, 108572528, 204956102, 189184351, 952066187, 415091063, 429454917, 643396113, 510370119, 664575188, 448331803, 214738505, 812294225, 241146626, 708432799, 665879693, 679551978, 880811234, 917509064, 545908826, 321505246, 446031650, 545953083, 831932481, 858504429, 489144701, 268760130, 872392, 233527966, 779646034, 117697036, 623311004, 288470086, 77831640, 35195372, 392362692, 923481935, 546209786, 97994387, 772965268, 30792951, 124695046, 766184388, 39361032, 487916874, 604071110, 476730629, 193938851, 466810735, 287371208, 876563956, 557330367, 495272807, 971548461, 683063871, 864525657, 773067139, 796406703, 844345435, 247555291, 642200088, 776659916, 550135054, 776324901, 887310163, 57772673, 877064328, 653730578, 91662808, 255536401, 498291418, 714439882, 194595018, 994659638, 924552944, 815513449, 807134062, 982014591, 61853628, 102189243, 173761436, 569169992, 198958579, 837609314, 970011333, 17677091, 289399603, 379468479, 34109686, 81658783, 683476273, 454271922, 513301325, 77949203, 316570132, 121227334, 332984923, 390741998, 929098339, 976616368, 109271781, 582771117, 848501683, 481202738, 708016390, 979229349, 78481563, 997558487, 707390793, 717378701, 382657388, 958391483, 411213423, 229257131, 602068585, 297494410, 912350860, 512374303, 727852679, 605460353, 90502330, 817166237, 783165775, 858585602, 18282917, 323603266, 774822860, 859171651, 423717931, 803523197, 158693726, 983611409, 552725018, 455770092, 722868964, 289844225, 706682463, 255136931, 892291965, 796272613, 309981067, 859128367, 232960312, 701378182, 457587102, 867562680, 602344303, 773758909, 933870320, 192417995, 895279567, 209586163, 854187701, 60108579, 736143589, 431773513, 548628841, 434938430, 918831885, 482197613, 525675128, 473310824, 789890632, 820069011, 615010916, 428621372, 186757229, 763441814, 887744965, 594454304, 581625741, 856378149, 935068701, 946858221, 671271265, 44413276, 628833150, 643087583, 99894542, 60176056, 822613396, 752611624, 455120173, 244836249, 234578166, 282575501, 528270058, 322510099, 759725086, 65714701, 661716429, 723191814, 475051290, 843184526, 39900039, 987294105, 291777593, 619683026, 414632695, 470937352, 348115112, 903841167, 593325537, 240202443, 583453704, 368949397, 830020313, 121957709, 209321633, 867575260, 885310180, 422211234, 2641133, 651005368, 898822038, 745993150, 787123800, 443791284, 150027441, 124561815, 914630877, 264484755, 479696245, 435891189, 594204747, 590842507, 969147318, 678747477, 23199013, 300817173, 732242196, 118447569, 941161386, 700005236, 655874249, 560793058, 997854885, 112994178, 840349888, 746701650, 71156430, 948784330, 118448347, 604325084, 110106836, 936137147, 780121459, 361368979, 690250955, 364328295, 80805165, 385717308, 945526231, 807663146, 318016229, 648537355, 55770168, 476431208, 993273221, 44076136, 742022820, 72517462, 113507335, 826958212, 525289092, 974038159, 951843227, 554918444, 471444445, 747584729, 693889210, 487669718, 979136150, 663855291, 252845200, 147422588, 407094936, 813895708, 385426508, 826806820, 450785882, 626892601, 907111269, 254020682, 767642529, 116918911, 668919615, 612741561, 900100653, 150014387, 509734007, 998669096, 957542112, 251778160, 532942420, 412691963, 549790111, 62176423, 995933553, 748079686, 97981664, 449994622, 276031337, 862341648, 373574504, 843628481, 268890781, 600452084, 340315270, 407512144, 1329411, 458165557, 471506017, 82414572, 196558451, 810582409, 804816876, 649059371, 634988969, 476400294, 56469993, 971717657, 99368802, 998398846, 60929036, 226034176, 912001745, 643176412, 981808081, 392095148, 152086177, 885687035, 44700428, 530403429, 889092263, 138812406, 428896079, 955080170, 644861170, 108582646, 200432687, 694586155, 396821803, 662380823, 127219626, 17858523, 633376749, 14780415, 242164105, 595744254, 699879808, 946757126, 585919303, 618862828, 584568855, 28027870, 414498555, 139235783, 194921222, 990898262, 57251306, 440133639, 555873589, 467429735, 966371832, 500184173, 714425956, 247010690, 673443885, 939918066, 956461347, 719485267, 787811116, 756667399, 201712173, 721372744, 511963427, 792233691, 593340850, 916410000, 809408897, 339901535, 132189684, 679295711, 814549104, 144713825, 294602061, 279901202, 101378743, 182970055, 24452680, 45055849, 14119302, 245064664, 704547032, 299299260, 146773603, 151961302, 271940410, 960319745, 768140321, 607896720, 46519303, 477552386, 71595804, 172220594, 71002299, 248791693, 485483305, 618189094, 685230663, 61483724, 595661006, 486471424, 941160765, 612230502, 566023006, 895164424, 922957543, 472420564, 620654302, 88601193, 413439084, 608948145, 385545505, 992146387, 842488929, 865510840, 864968603, 948512445, 78895699, 140740802, 511508485, 204424490, 173239222, 941981371, 592570263, 34745176, 195354720, 837153978, 310789239, 604918657, 992986443, 102594708, 932636782, 674394673, 879215877, 922562830, 593994457, 177534020, 10272555, 698685629, 171507059, 790262364, 670580768, 335959752, 90746200, 889845222, 720803260, 796519866, 697587922, 918697805, 715902096, 678675060, 821809107, 421667928, 952458057, 613725873, 504731913, 469323196, 328527485, 227418367, 919197450, 194406569, 190109913, 916918695, 515565634, 54895417, 745991696, 876013856, 224988066, 451690385, 577605961, 344834780, 46258355, 317531404, 329025255, 809618646, 571431770, 662205491, 383973219, 403480493, 388967623, 783474605, 124617260, 947088465, 976395627, 813192415, 550599754, 407407947, 952496857, 865121248, 202462496, 751796203, 708338566, 865619296, 267537218, 439931681, 341084981, 637176833, 489383277, 371601211, 213822748, 305909556, 839315735, 626519603, 928813355, 129609306, 504859713, 394471893, 209107364, 589847200, 560709712, 731886552, 167289168, 793133463, 903743007, 697390346, 821565011, 721158835, 709632063, 804265935, 208523038, 381098767, 604050963, 516440604, 202636716, 106620197, 748220561, 119574280, 595295810, 402039031, 239325116, 542326372, 326772217, 864555993, 423958046, 899378816, 228134811, 752103908, 536544258, 343000204, 895062699, 55557501, 203982547, 767790868, 75114946, 739674288, 448846414, 100765064, 864519937, 305255778, 358122819, 990218570, 69754280, 963465136, 383811843, 280120055, 970992489, 865697063, 84104743, 424421395, 300055903, 905640034, 881922817, 291814239, 903688197, 161894559, 381609509, 592521316, 759231791, 190776832, 397406154, 42931730, 626522472, 750229914, 419133438, 803428531, 228368525, 275475313, 92485485, 260190579, 92329127, 220207340, 35662511, 802977306, 599819130, 491436614, 478703706, 516556181, 772266087, 842372644, 422738779, 110256799, 393958935, 389272895, 337757816, 84255081, 658280557, 582893514, 925068855, 807223658, 271750849, 890837587, 780395572, 103538159, 725152237, 220522296, 541029122, 566838099, 510396990, 792724696, 510097847, 810113985, 716948359, 569541741, 3023804, 258158621, 401704589, 274143020, 971453130, 753893494, 896643305, 581560751, 326211828, 982526031, 708230025, 475787263, 982002500, 205934439, 227666472, 696964132, 369844404, 122432369, 495243942, 419489068, 307734490, 974593486, 36725987, 298246654, 348990409, 394057097, 2786486, 735801066, 382837631, 419989165, 23701461, 748608127, 275884141, 554797964, 133758004, 836444908, 492451873, 331736152, 867493475, 450023261, 576555765, 655220867, 21593980, 623980420, 576599540, 310619731, 596680570, 289447559, 499500537, 319131546, 504583220, 389021097, 254606556, 252658807, 826483041, 969807883, 34367081, 242116580, 832824943, 919797302, 113532783, 743747050, 757799375, 654944929, 971335668, 643887467, 711002654, 900655421, 702449077, 910058983, 802460385, 475369177, 10741247, 785805811, 775040093, 700356181, 796677884, 779959709, 715810985, 884671386, 417337750, 220807304, 865886544, 477056250, 577664737, 68925009, 136868212, 190975622, 875280118, 951179737, 459433252, 983917875, 474766325, 894478720, 37273750, 814987465, 169989999, 714821820, 794841, 828440582, 531269736, 20569809, 541119638, 130069881, 941080887, 527558609, 94640387, 131681373, 319962873, 702013311, 328969387, 877777740, 803863540, 975049700, 83869754, 14093554, 843176424, 754759874, 779305107, 172113250, 761146533, 266513518, 838342729, 182226455, 508006928, 815203679, 906027839, 162113935, 395624419, 650025600, 230451383, 951270549, 85659075, 526091052, 810040628, 11200983, 810442402, 357805452, 673566025, 406636203, 259537353, 440237835, 407065371, 660524425, 652038862, 694571422, 681722925, 158326977, 967337341, 451221296, 184224209, 324719200, 460177457, 396425683, 284255770, 552702991, 408071954, 884892277, 7901743, 100427216, 107703962, 159981312, 843536010, 583607187, 552869016, 559421936, 66356939, 163771528, 546309856, 541844826, 958489886, 603630858, 451851355, 134260856, 821171975, 545182456, 146497066, 215234552, 990834533, 186596040, 821359910, 444813287, 387117019, 350759176, 932898113, 802447920, 879540951, 551464289, 548549272, 73174144, 434501708, 539006582, 203655582, 720883083, 100709932, 549483988, 761473908, 813848127, 602007015, 252303141, 944232956, 287985574, 930572454, 691371334, 395730574, 963837164, 439363229, 579140561, 198612214, 13445409, 416819845, 55750954, 364905413, 223013901, 886565741, 478580145, 478500637, 350899618, 889202261, 781233422, 287389574, 394340402, 319848269, 669854356, 501950886, 883271346, 844012345, 435289404, 320318959, 668777077, 724574715, 167300692, 754106187, 907488635, 345578753, 442567435, 350558513, 668716267, 643945010, 912942827, 382184294, 559386253, 226375460, 50040751, 737475457, 710558516, 55854795, 559911430, 879327153, 113118707, 150719794, 229315261, 291129049, 754506819, 429106361, 322493315, 498779559, 458327748, 914449163, 961088520, 210977920, 90442453, 399105428, 999583599, 851030152, 647039241, 400635897, 643054431, 728447570, 887530925, 413339524, 861518404, 653272735, 999473813, 34901830, 511317503, 827451593, 244971271, 228153947, 451452385, 9037157, 254811443, 575270936, 940826707, 720486994, 396112627, 140056885, 196538326, 413594893, 761454701, 858218144, 881348503, 713504965, 653817267, 618544743, 213021543, 518762843, 444875091, 908642103, 137250910, 258125039, 690100902, 405905062, 414756750, 71769558, 428140671, 526332933, 85133335, 730933687, 832138582, 58720139, 394362229, 212258082, 453349142, 414656152, 118673272, 245975582, 451692378, 601282657, 630058723, 909676391, 800224666, 771207837, 735205076, 774822432, 443486965, 839050364, 716159010, 561270799, 746657652, 475769725, 794167656, 860827574, 120536162, 444974639, 743407154, 324057252, 854548070, 349566878, 439313996, 566690745, 164924819, 457936467, 241227083, 16171653, 577662290, 544560539, 590821587, 349748325, 583602090, 686738901, 147462014, 879809806, 901642081, 263489326, 190077539, 775535556, 24402729, 815199937, 352712592, 179232934, 109481153, 214256699, 724292132, 785990824, 437572991, 176184009, 678276495, 930231172, 352778339, 135930886, 92761768, 118988749, 736995298, 424648408, 637642828, 489393871, 634025789, 714285003, 988438922, 75978681, 255351042, 79206951, 257901648, 40074518, 219032585, 584925252, 939923479, 196757843, 859854596, 636427655, 97879863, 33684561, 980597530, 558661079, 57117657, 344460797, 142593844, 987902892, 869209120, 122234616, 749283238, 950901164, 899194798, 131616325, 619026362, 939107753, 524771529, 781625423, 933844456, 424259196, 898759239, 197161498, 986318065, 607318739, 357706756, 555307956, 410323347, 629032015, 400923080, 15065954, 672753120, 832845301, 104755791, 778330144, 279000089, 132969591, 493222388, 877320333, 379625506, 618847258, 814356723, 494850904, 749075656, 198060506, 240801117, 104199744, 400317747, 22820194, 426207975, 343791495, 149804862, 162580728, 27062603, 822281473, 189657568, 524705389, 475720618, 878516501, 271149938, 199300514, 748882072, 272045003, 504883189, 171553653, 425231487, 948820722, 891272141, 21177837, 353991384, 393936678, 633753728, 245252678, 620282971, 624389305, 103533775, 763460598, 515331182, 671671151, 373316057, 497370153, 916469340, 336357793, 996707222, 546072867, 542031768, 972426234, 795100718, 875896012, 487676499, 35797539, 800717176, 822283671, 294523487, 340163986, 570415045, 319849017, 894035630, 601119760, 182301904, 375260737, 170871767, 928559289, 345700226, 341322688, 449716836, 954447572, 642388355, 629820219, 949364961, 787403640, 927669919, 940889170, 990679220, 585617551, 562228298, 750898977, 844945463, 134225355, 533050307, 807838556, 278247481, 338731752, 551686340, 59997120, 934854036, 256414190, 335108956, 41465820, 889875970, 699466918, 58965196, 458347823, 966481447, 124024790, 840672689, 707265936, 15404437, 623899576, 750548226, 472971531, 811290605, 829053191, 284910755, 698470663, 175165138, 127235108, 190385844, 427171305, 12099992, 468898129, 554932948, 21377939, 923056535, 813898582, 810935527, 247281910, 135282375, 297156046, 614714216, 752477697, 442944796, 799218288, 187136934, 316294053, 182869377, 826061229, 296776855, 213576255, 651919028, 690406721, 576332624, 202542555, 596691315, 684436877, 488406567, 518835158, 390779057, 850684288, 416230437, 763035220, 833281526, 356974854, 344096913, 471478652, 95942919, 326547357, 808080561, 906756829, 641188896, 369270666, 170624893, 637487138, 933782114, 904799511, 330621039, 113482499, 600862343, 350180919, 311241567, 665817105, 539329410, 310302961, 440257329, 628027656, 661549043, 96667437, 901040414, 200768539, 893277076, 430707340, 38673971, 84131062, 178119750, 11668008, 758204438, 598297076, 962663458, 289074421, 431461907, 793142485, 883500559, 324705887, 536407723, 153571976, 533337199, 166728779, 923343090, 568944850, 344986357, 171256685, 632976079, 163478577, 436492158, 42212548, 436073308, 989574194, 764573423, 188179081, 592679098, 234390532, 323417087, 564937631, 706236169, 212453708, 584842534, 836841782, 361155009, 541068171, 868102507, 471971121, 833572095, 501390994, 729613784, 83132207, 89066022, 354569367, 900775022, 905112560, 20718081, 560676146, 953304346, 597655840, 327652757, 881412384, 196670850, 833387187, 336934587, 921810301, 706303441, 251748221, 418333527, 209621914, 964978675, 320509439, 366962536, 245542878, 765796046, 941769569, 975748155, 802501194, 145413374, 113584460, 272945407, 602794686, 586757392, 350820086, 106168322, 881665012, 568592911, 893681204, 874937405, 896470728, 162867657, 928866889, 113674500, 534785807, 878201404, 786247854, 585050877, 754544784, 551554153, 840186294, 163341410, 625566404, 490910240, 772404135, 302417729, 522887400, 890255552, 578052910, 811620906, 838876829, 21524460, 584811422, 926436081, 860754274, 558668669, 423395304, 462746705, 781028931, 533295576, 935404087, 739950738, 277030631, 119763211, 997951760, 560518640, 759036582, 523349335, 477694450, 540551617, 931591158, 301087010, 654206653, 92293537, 375306915, 437038442, 38317818, 661177354, 188749829, 139015533, 887399788, 612089273, 833224281, 382553730, 133070189, 50124971, 985914618, 611652417, 181715538, 876781430, 185431854, 515353051, 919365518, 609290814, 178982122, 75309598, 793866485, 562176631, 872113301, 979141278, 495148819, 150132811, 779537010, 955509542, 931809707, 955095996, 136424099, 349261259, 194122170, 217586866, 506140454, 933314780, 371527645, 880813839, 594649790, 917411460, 596699532, 639405623, 717968049, 912064709, 529042949, 65569514, 490421692, 313601926, 437682548, 267733863, 142902942, 696363893, 855204976, 653541532, 984531725, 242590226, 286083828, 63380264, 380377852, 478663106, 679800258, 66381828, 682039609, 104229654, 23715404, 485879821, 697061653, 556497628, 53795034, 302224389, 309796740, 382766296, 968437222, 548060435, 891938134, 279855590, 277324888, 23420718, 797752831, 207176306, 983300268, 65133250, 642119104, 941268159, 311754938, 224773903, 870455510, 652236867, 538503780, 881806149, 400820041, 582497578, 698970657, 2984282, 387920844, 470861011, 576010341, 759646153, 381096562, 892444759, 628285642, 217542065, 260938057, 640884025, 741003699, 556073948, 625109849, 572303526, 158375503, 912113933, 700340432, 166023442, 759256617, 128785069, 468028330, 546001799, 601925755, 909017601, 790356300, 393564253, 252050694, 262353248, 513605719, 842592166, 741753178, 319875184, 810555147, 884958291, 92670700, 579901998, 942741597, 467837290, 66746374, 990297463, 200032891, 297649187, 684265086, 99368513, 161463159, 729538622, 276614057, 816248730, 913723441, 544784125, 979111556, 511331748, 514896006, 766066957, 150476083, 199588985, 598917988, 268538295, 778787620, 104157131, 284821062, 796481434, 739106593, 132579999, 484596789, 702821955, 448837150, 485776162, 942170498, 352969036, 465287801, 397878092, 449648295, 96058806, 231235979, 944267063, 165273419, 5155714, 116783794, 103392629, 259959193, 468599731, 57326750, 621881622, 517542925, 698529685, 252339972, 672864139, 808983904, 648896833, 451858592, 269472821, 409889030, 354207785, 330032129, 49770941, 866658395, 165570082, 724423792, 231222369, 917989366, 575759457, 997198600, 834501124, 470658967, 417045576, 989367511, 55172805, 96535040, 578444223, 20322923, 102061371, 788051498, 122716661, 572928125, 500879524, 330711536, 392542420, 913231398, 371362590, 537176084, 971418369, 137688630, 694979537, 425511557, 427385680, 250630649, 520946984, 553919037, 248495249, 951343499, 899979392, 431628813, 612579948, 584777005, 790474908, 797512467, 745913338, 42044527, 294162918, 534813079, 995488801, 323272261, 479940534, 535081526, 411582636, 111042164, 162791362, 583430134, 652251352, 311420095, 78012278, 291890107, 229602221, 291058002, 538823134, 418172690, 518702044, 557686794, 999712210, 845011931, 371900650, 461042993, 512643447, 92210445, 308585285, 444502606, 477416752, 593815276, 337894249, 491608006, 365121044, 402326166, 534013098, 603369065, 91496985, 694937816, 306744559, 199265163, 843346668, 633760660, 155227180, 707557127, 988798460, 948390827, 154790374, 240254720, 934214452, 344827521, 828099832, 555098156, 606698625, 323870345, 506338969, 993710898, 273824346, 732191798, 305726381, 617087334, 102110761, 443049820, 854436779, 428405220, 645868244, 278360205, 359040868, 594172953, 665258846, 306767944, 719181338, 136349658, 305184573, 928816956, 971765879, 302053316, 500435373, 761319151, 902641042, 889734445, 387175620, 734548635, 114956509, 51734574, 976739327, 334505281, 554586356, 745054216, 105664814, 527969455, 336882327, 854197819, 352847249, 182875790, 714908152, 590629359, 227571771, 390925996, 486960881, 734201708, 757045598, 951331161, 823009739, 876822404, 434099528, 57426746, 992227647, 684381624, 61620083, 371478999, 111623366, 734919686, 471953360, 666947574, 244091370, 323826657, 263190693, 357224690, 415020767, 125888743, 59352390, 733450870, 900946258, 974746880, 898736392, 809460826, 586713672, 917761349, 849153202, 100792363, 206688777, 564781379, 399282440, 176576921, 379932809, 688285573, 884071619, 737009458, 445033823, 809517068, 143969606, 721150611, 777245706, 595773489, 593070065, 795366906, 568949298, 198311755, 240017931, 882677389, 13245923, 274722202, 119615204, 995255432, 322476698, 284854773, 394532899, 541359432, 591630320, 544056017, 224781154, 730112956, 252828332, 477396147, 141739292, 606941836, 601494288, 589271157, 650111531, 3433091, 186240242, 279912409, 417579975, 329200345, 249292690, 963806180, 721781770, 361306826, 918095943, 875331306, 907490245, 156270876, 183275261, 496483552, 378090958, 14038504, 993528078, 632299361, 502832133, 352132703, 478571949, 951507312, 883193118, 165264880, 843904919, 923851808, 25157131, 293366377, 32544365, 355421933, 762594502, 758717400, 346607789, 461063005, 220205829, 65157733, 345960092, 560842535, 860963191, 787582252, 367809066, 395483058, 303697261, 993870846, 322483618, 751578556, 190024205, 114259273, 528934808, 704290925, 141088397, 239203182, 733914436, 340031947, 888719713, 899525991, 804840830, 254474362, 831258980, 121594164, 999569523, 310191286, 496434282, 35147808, 378072002, 866312483, 533382213, 618611296, 183019083, 368287432, 204105800, 819386438, 279324277, 718939657, 933121, 258323837, 744403943, 694752055, 628532119, 881049478, 188135167, 449678771, 938048531, 168992399, 439240098, 663870912, 281846477, 131553881, 408509100, 188236572, 97851701, 845276357, 908176272, 488423886, 699635023, 448883586, 246159230, 366742709, 693673411, 221536311, 225169906, 723221956, 115836215, 86373342, 520361309, 193666470, 92504514, 775177783, 674083483, 891678918, 674890783, 464999978, 123186675, 811071478, 858000520, 438935887, 905672487, 686881302, 110872023, 300860229, 751504082, 506169716, 469290206, 947854206, 477153798, 482685314, 445890970, 245029648, 243913733, 299007486, 830208913, 208466297, 685744624, 758540833, 158302403, 765292873, 125209025, 248034631, 630477772, 891781018, 425034895, 88808018, 872010626, 52471343, 14277290, 296799198, 674775183, 120530846, 6260288, 922853104, 751757206, 40849151, 167553326, 278722096, 506882224, 543463410, 645368127, 600882481, 884195512, 778396209, 748934172, 650538920, 763846008, 909691104, 208224978, 901022246, 999164642, 313555827, 57780624, 765266267, 954814737, 332550994, 682921783, 575346480, 911709722, 96986837, 599829041, 131752315, 946668631, 413328722, 619532677, 818058567, 989354954, 794077582, 733865007, 956298273, 559054799, 158398047, 95232206, 805318792, 203384710, 765890552, 6603520, 546907495, 999302123, 328049054, 865743011, 423454567, 161210184, 791354310, 27797825, 630461146, 409187898, 981658578, 621992937, 992319033, 8566474, 525465458, 126872583, 773740100, 581088152, 33755131, 903848800, 882051125, 786952868, 349660660, 784901051, 339993688, 787397843, 866691542, 199124919, 71870684, 595894779, 965449891, 729941239, 963955249, 911204846, 2745999, 756754924, 124960276, 60408673, 912884635, 719962379, 389695681, 356578439, 967728392, 902325744, 142420890, 950361711, 953715698, 427686673, 939262849, 75759800, 959397259, 868686814, 527458170, 812641453, 458011702, 631735248, 866711448, 622768905, 754454506, 627165058, 906250855, 362448082, 341340499, 986114018, 711857726, 141463316, 222635556, 431001347, 956114831, 607270558, 338896831, 929446668, 44527860, 228827978, 761269020, 946903789, 310653483, 316028687, 922303120, 532010047, 831518210, 490670249, 887202345, 349374675, 808791576, 97152966, 904268229, 461952565, 258761240, 417917454, 128530119, 811739069, 127167246, 265788294, 718057965, 649530920, 929152170, 995592113, 976480300, 956265691, 461424656, 963420002, 425639568, 178524643, 814852233, 33067176, 230668915, 551695064, 685814137, 291499881, 394830071, 752849158, 193115016, 365884349, 116947508, 527015130, 610438144, 785810218, 576219941, 775616427, 748323612, 658261543, 537082162, 615752103, 140696628, 612398632, 728092126, 127384999, 179184335, 146748611, 596708335, 608418715, 601407608, 139249089, 933201200, 670180459, 489826034, 869217074, 870327941, 33836224, 291828458, 880450522, 475031415, 399591494, 979605590, 409168070, 595296352, 870236280, 775639866, 778109380, 377636744, 884700558, 948928592, 333335301, 125434861, 733078828, 342776295, 275689012, 891129393, 525450252, 143701404, 297992905, 556557197, 748935989, 935863747, 295146664, 248667479, 39047781, 735412224, 810680993, 938742706, 634788505, 526267755, 449022968, 663773806, 641953294, 52341551, 380373722, 877726794, 795541842, 60215301, 986080756, 790289633, 930549785, 791780571, 936205069, 358657469, 451371038, 203907886, 895222130, 997203971, 768714236, 306178351, 64151251, 905063841, 983419930, 962967578, 345369356, 909242801, 330719036, 925275463, 978832263, 268038043, 951569932, 344158497, 667895252, 300714231, 738607519, 862324579, 135819606, 82013958, 751011454, 67118706, 725129592, 784252533, 111028769, 104909970, 348262411, 282474413, 712068189, 801847957, 873461670, 913048945, 457922595, 313475243, 892269817, 613740044, 247066694, 622744046, 325273686, 815678268, 31934846, 253801982, 464763526, 233058798, 250984268, 153534932, 372289488, 366517455, 29222045, 135441411, 861850979, 131060284, 427483513, 811949897, 513676148, 305716068, 310342023, 627263675, 834277738, 829390973, 176750604, 348785887, 332986978, 682434062, 766337307, 483906013, 820486624, 821006283, 78946727, 373989155, 50102157, 592105652, 647977957, 761809692, 195190113, 243311058, 818384871, 437933828, 791661094, 784140752, 281851610, 556452230, 438361672, 665527401, 863974826, 170055962, 303422593, 799664894, 247439869, 536427189, 793415313, 309072247, 480532685, 837418030, 995928153, 258281236, 418688407, 876404586, 555076895, 770910423, 437067639, 13307604, 472648032, 984808083, 673743066, 980046382, 873506446, 575817041, 375583187, 742733313, 863712513, 55956287, 528506372, 934027786, 362765840, 232612953, 914326772, 380397098, 333256862, 747520361, 596695592, 536098531, 831441784, 69623499, 357741138, 573607460, 884255008, 459434903, 650168103, 912910821, 781160677, 726845577, 895068589, 670444969, 904636729, 378477439, 429886088, 840950466, 62368264, 59153283, 133335810, 767000574, 35628086, 250226089, 665763852, 838353659, 598147355, 296755035, 81385713, 738701460, 223243676, 598272589, 461126752, 206197463, 214450040, 918143085, 445858141, 773418510, 198109918, 266633215, 256332518, 662363792, 218261083, 504524031, 866062042, 394285545, 852478706, 118512392, 667866725, 843237278, 914240448, 588422332, 250752795, 142865584, 3105827, 641673110, 470661060, 356287662, 65588966, 853875602, 838003598, 412156798, 755515670, 667861755, 788182232, 165913367, 895271314, 771206906, 587279421, 693026967, 910313906, 6954388, 357479550, 82041624, 912284532, 995302584, 239445465, 115968057, 656627492, 118093169, 807509292, 161592241, 268836236, 756696245, 74693897, 545729846, 524731338, 712357147, 541603196, 258255003, 779944257, 997127077, 560845713, 534695066, 403929249, 694998194, 558091278, 312642499, 289928148, 149834486, 870211997, 592893660, 628991435, 913954899, 8133140, 974001072, 702618310, 741534242, 33317359, 775193102, 187930463, 87531656, 251800146, 635386886, 367239043, 468545546, 224096859, 396890478, 471945352, 183227512, 355427020, 101511262, 605264324, 754018241, 247227613, 684310093, 605893824, 858257254, 941100514, 178343213, 108533974, 653180991, 305391668, 375335765, 447858387, 632210709, 261867630, 490043962, 241941542, 345509494, 519802983, 44999142, 587545522, 766490349, 147677440, 788915985, 643130836, 859444174, 412808274, 987792040, 879792148, 407472380, 386602534, 350747173, 602894171, 65505334, 493288762, 683094188, 319746720, 446564586, 681525667, 945782287, 732890120, 432064234, 303599455, 23772264, 985175851, 235228708, 591100900, 371062064, 376329593, 361928763, 233510272, 98248068, 299116429, 53397499, 80411171, 715755904, 38723206, 717243297, 691713137, 130662319, 713938247, 918525286, 76923585, 302577071, 638114916, 641968244, 874659870, 663265658, 42061168, 275146281, 687618279, 513984128, 151436536, 65446483, 942668450, 47536872, 969100252, 450103390, 40230893, 763156426, 738793011, 494997502, 371114966, 585936016, 776713625, 446430368, 456777552, 398596649, 562280422, 118845452, 975278577, 730793050, 782142559, 950752097, 642239184, 503604767, 410279011, 867923368, 356110605, 301645515, 40027134, 212546064, 349102318, 866965260, 897572479, 958885575, 536393686, 732766090, 645773899, 986116384, 718651542, 591657406, 21764979, 163776412, 390230572, 283667590, 370094761, 236251703, 561054751, 211535106, 254568885, 805866927, 769098343, 552525565, 186924693, 197068170, 422891587, 591079185, 685457956, 127178470, 804945852, 237488464, 494634764, 58809174, 168221713, 608105732, 255815895, 132342264, 137686561, 468583061, 20261376, 67216118, 561353300, 402910558, 919831024, 520883539, 295485675, 779435506, 736489664, 290929122, 569358429, 730217245, 275502172, 575242751, 250983511, 852052635, 540030441, 560073293, 507127598, 203366989, 684299920, 503777214, 147161021, 894406921, 733055601, 205078937, 185582206, 625341194, 266117973, 620744249, 716905142, 555773269, 840275200, 337165380, 707247806, 89763728, 812808793, 363968014, 796036366, 123657650, 425811618, 719539443, 642551278, 116976545, 95875601, 604807350, 940428990, 703943904, 51460901, 8253576, 803819645, 333522964, 988842024, 430671827, 425405204, 329174860, 640020082, 54360306, 139877090, 932631034, 357574839, 637931079, 446940938, 599591805, 723904263, 224473596, 602956544, 662413693, 948051877, 290594705, 179704231, 687351225, 396642196, 89729793, 961209816, 524432333, 469377729, 878615981, 11906554, 200486221, 367341624, 380911146, 614949383, 691938876, 987346951, 267883777, 775474674, 894803303, 215081396, 11249849, 744032029, 748692669, 278779939, 840687955, 990608749, 176713945, 257935606, 942391570, 281506970, 364123307, 3993207, 876663191, 378508989, 8575927, 230671663, 788308925, 579046713, 343793141, 431754391, 527557325, 799790002, 867023558, 10996566, 831454774, 564537906, 372511577, 394799118, 313737422, 368563816, 926680002, 193857423, 505764563, 922197122, 560487602, 192754643, 218893784, 679234851, 103481834, 333977054, 477319154, 72699350, 240917805, 214008248, 903956753, 480455695, 800654395, 404230405, 371725874, 122714175, 888299612, 666645164, 51562767, 697070726, 397656325, 948413228, 99099537, 572248862, 116574516, 332346642, 613108598, 368142623, 241715286, 645291230, 349509472, 132525162, 346703557, 241787344, 171959498, 360800549, 445575938, 778386807, 458526055, 602665390, 332456641, 962962190, 67097169, 245533978, 932900327, 474836595, 357695848, 975054492, 303788651, 443381150, 99116175, 642540263, 764238377, 135855792, 258970677, 46517214, 399471162, 702258157, 543686002, 73026283, 430862499, 673675252, 230480219, 148403514, 448322631, 617647672, 500442037, 138370751, 591455240, 181478977, 513019733, 432327169, 151580408, 157716263, 306973895, 403001442, 765054462, 44103214, 779194334, 624922391, 18001134, 64110324, 881582035, 904864469, 457293686, 975106299, 394848447, 277441267, 504233781, 456301029, 797379236, 981354874, 944328580, 232021438, 251832547, 657883462, 188909245, 248702699, 570031840, 57610040, 391691953, 167681020, 388757005, 287535806, 643718504, 391286745, 699602259, 201833320, 688233440, 537633596, 659525747, 525262602, 133736011, 695072510, 898418393, 962965609, 891384908, 382229176, 168003686, 74708949, 773917545, 332571828, 9462686, 296087917, 440412278, 763400576, 569432128, 429366662, 219347369, 701714604, 269045231, 362927872, 952468892, 738935399, 193430585, 445172031, 260565869, 848539839, 566454547, 290246210, 675348677, 64822471, 136726136, 689290692, 988173116, 310162951, 814971898, 431479640, 783378862, 531162273, 478468545, 842442236, 833514029, 72798965, 278759683, 789223795, 648706807, 403101516, 333181768, 754852897, 110099963, 423510538, 266956385, 4337631, 765905916, 414333952, 702565616, 629954251, 611784705, 749167944, 942891976, 340846468, 94188327, 676972029, 929264846, 830520046, 332680858, 828017477, 77942134, 48686981, 312323693, 13153710, 734790416, 895025536, 394853004, 435606239, 978068013, 327133375, 972996501, 181035222, 368618057, 470592792, 683912500, 36740101, 605901826, 467726353, 599402245, 167325363, 286543679, 110186666, 390857229, 97371848, 925150344, 500285598, 600247732, 522362536, 132795342, 216570977, 564250955, 667517802, 36350663, 689356535, 481568932, 327707598, 645508834, 776641799, 567084479, 825024403, 495095930, 231725781, 430609036, 31892469, 393674747, 1257721, 717245861, 306966363, 922817577, 264263510, 23365918, 155830316, 973262752, 730976458, 961971463, 153614949, 42000731, 273060639, 520984907, 433509703, 947172884, 944288925, 789690233, 607930078, 620339918, 987067316, 991418517, 542546966, 491381726, 581700455, 431412496, 329799107, 605754309, 340652686, 508621958, 547454691, 923484727, 356354262, 214665958, 323940201, 667943020, 383275041, 872943835, 948754789, 312752035, 823673098, 713964426, 861921773, 457473357, 656358527, 30933257, 425398949, 971684947, 25036945, 821359572, 546708482, 892762570, 424533083, 794723983, 277887978, 155824397, 221680371, 287321049, 765154902, 888802737, 690180115, 308708981, 138936178, 441205235, 604014447, 180493144, 178003064, 961720150, 888727733, 131803589, 990187424, 925098705, 274428497, 306486168, 653846003, 294586536, 751928317, 152118185, 247152296, 76567207, 563024628, 832389655, 83185573, 994175715, 36528973, 594586913, 468243214, 826148032, 109040441, 233345036, 225802653, 547983791, 555599950, 848921260, 867704311, 729448940, 292134671, 285281598, 92188500, 41908105, 278473489, 674337216, 313407958, 851383468, 225736328, 729622225, 502965285, 612809210, 668777384, 450712349, 492803928, 698574990, 255570285, 442452548, 40523903, 815584183, 860527053, 483532754, 674289877, 784300177, 788619153, 940367740, 728646079, 299388217, 707184641, 382885055, 694454811, 664938437, 760792485, 813925399, 97246413, 700692169, 695488053, 78936708, 941724192, 806576824, 642290043, 238798671, 178428677, 845815856, 795748303, 750240184, 388011132, 430392407, 596746395, 19455451, 882841423, 410569499, 66968591, 696686121, 563932282, 753072940, 241222604, 523657957, 608658896, 429192836, 884903852, 645994867, 66829466, 182464260, 790425936, 404255533, 859809107, 181437413, 145526160, 733978631, 969531751, 35488612, 892963113, 968363361, 655374068, 895338374, 778854043, 379091283, 304550779, 36893984, 7134575, 277269755, 100317856, 633817270, 306184293, 881961203, 825557208, 71828454, 280773420, 438998756, 912508223, 466100305, 912912395, 599022525, 424857236, 84772134, 237928915, 996421436, 9372130, 200753273, 870955585, 230240588, 215456764, 549569984, 590159328, 874851886, 40461857, 530200796, 386676914, 227685916, 653719460, 480343437, 793336857, 309313968, 663261943, 652841199, 903267218, 584552577, 108658028, 993940674, 480238460, 535263629, 592007516, 428773978, 702819834, 735986503, 460998158, 267315853, 182483845, 770280089, 247204185, 528366191, 373382904, 39074358, 724714246, 387807568, 171041116, 987152638, 970031755, 147495525, 977882383, 713324116, 225233295, 617476968, 419913584, 794547177, 256151645, 228171504, 669971684, 794805072, 139649035, 448407078, 376482459, 156069620, 391481988, 655625562, 76793190, 217532540, 14815398, 475391174, 615576556, 1516817, 711457029, 401659081, 620255522, 884460547, 662230228, 935976844, 966701584, 811104768, 610323338, 547867563, 655289822, 449355502, 435928775, 422945308, 224371490, 963462380, 31012144, 187258824, 470528589, 691940048, 597081516, 547484056, 886537752, 633674874, 448669092, 706883366, 980259352, 853187554, 357910718, 798467700, 94679960, 343767502, 619819151, 65617961, 108728586, 973721250, 959897757, 500756741, 360203468, 886915042, 629168606, 88274325, 964300653, 612452166, 386179096, 520285123, 938069700, 656734795, 859717192, 852712573, 494234661, 801213852, 206965846, 132684111, 943036337, 385131277, 620169362, 230024746, 823641924, 677727606, 632447161, 478167879, 671064490, 779720904, 182099814, 652621789, 594754256, 433179749, 316829926, 232554049, 188355686, 305545914, 618378023, 532396846, 620211101, 84473382, 213131650, 147720814, 340507434, 919224329, 615030944, 426884710, 896971953, 572952753, 116384040, 393514546, 294362836, 569697491, 344472566, 754543082, 38788573, 524171616, 228460549, 298209698, 416086478, 987392137, 731356922, 875006089, 903356496, 722860278, 117134933, 845869630, 155640439, 73886058, 599889646, 160544775, 314680253, 267115569, 616828020, 124488912, 103970839, 797472247, 428304837, 405147437, 773709001, 351123986, 415141224, 385289827, 501876917, 928287124, 910644913, 998167074, 923874368, 647210360, 451540832, 520848854, 107778206, 695090751, 978306852, 12086, 882049491, 281666410, 396649036, 741191563, 314515472, 375187282, 13796196, 190900026, 481659455, 411086109, 455456744, 827499222, 309454398, 390485258, 112818509, 599834466, 548769460, 210738268, 882203257, 42668532, 584700893, 984963473, 163139090, 261424597, 572096736, 529446107, 621952390, 604994176, 627999913, 369351143, 538416568, 80172902, 115439258, 771466193, 95766457, 620550204, 958236746, 44795224, 79513460, 385190769, 64749443, 751297830, 313848211, 143429852, 335416381, 867653254, 139985084, 267778175, 279371403, 63175884, 645829078, 507607104, 853437874, 956745893, 422026774, 315837029, 375902560, 133136097, 168617876, 433180356, 61822234, 621468288, 830553876, 491207660, 715723895, 883681633, 72884622, 872661392, 765898910, 519608122, 899941300, 758008301, 223948268, 775764249, 351072964, 460374003, 190758990, 510244924, 492913810, 57090086, 809753966, 775034838, 250566477, 906328372, 931072514, 40480711, 97202790, 710222894, 346644401, 425914141, 746617369, 827742947, 738154781, 60353964, 116495118, 719713410, 867756253, 359128627, 443968505, 168433107, 967169399, 568716550, 781466023, 818046517, 421015, 881608204, 210355587, 549652366, 617166627, 109169876, 525806720, 976832965, 932650479, 118965579, 648175215, 509119811, 805760849, 906414270, 904925286, 856194588, 922508369, 4656734, 808154747, 228807691, 7702012, 620499002, 733735196, 397262170, 1260754, 215654107, 311184960, 647933980, 973062741, 868213092, 573992748, 220763636, 463199603, 367857640, 667197371, 474620030, 802323571, 913985212, 605015922, 632537152, 489807262, 149242528, 799016648, 42736888, 623173819, 977083388, 397098792, 240820628, 348226661, 584861186, 434911009, 865033173, 898649206, 844147468, 702896183, 486893973, 974102867, 606538165, 244885398, 690079586, 659900123, 769149585, 990129572, 154902320, 543795719, 1891435, 921848468, 65301090, 466885026, 181887821, 976830167, 519079614, 153439391, 500529763, 457980981, 915814327, 328431588, 778220412, 31286648, 946591069, 301938778, 352470164, 984179947, 639046998, 320574748, 486905320, 453307156, 678014287, 246371881, 865246162, 373221028, 228932701, 392031533, 548557554, 756331519, 517800898, 755902700, 268251997, 523885304, 655841039, 77624400, 509792596, 101362097, 258289852, 495798753, 236591647, 80735649, 241946538, 823814176, 300056889, 941887619, 677063421, 32811406, 840669136, 593239014, 733211751, 150233002, 812565290, 863187852, 39946601, 31097295, 747491678, 790975617, 727481211, 504543455, 47940281, 786635950, 246274573, 622183086, 729297947, 717418335, 465593369, 930057088, 906665855, 932644386, 754568546, 129446057, 158917815, 444860916, 527418719, 822697785, 512581896, 423210483, 263681611, 291180357, 319068692, 315502419, 161052127, 580468119, 598470658, 345600235, 811801567, 144008905, 456080694, 147341103, 157554131, 788784002, 787339179, 14671194, 938685784, 33932361, 659975819, 215751365, 903655146, 269874837, 449162838, 222998057, 967616018, 985452623, 622652925, 527187776, 101467613, 688777029, 831044399, 563035914, 938819671, 630780116, 354309813, 231232404, 379996245, 965741363, 286964257, 602653566, 344306970, 218126702, 962237583, 57706835, 74578235, 367046031, 473939427, 647680645, 993436217, 361018561, 899118879, 439255773, 616909221, 11977291, 883898262, 368369417, 18227856, 880853178, 487203488, 768900600, 612982831, 810832503, 527652934, 58793550, 575066578, 839008956, 112117966, 625039417, 222173297, 693978244, 267747636, 547370783, 786995298, 983942701, 997100306, 914062512, 294796229, 781911041, 898855097, 212967346, 994381500, 488776340, 924144649, 489912526, 763521116, 178308344, 873549071, 548252662, 94111160, 538236834, 392997042, 173048469, 978261528, 308424503, 696290009, 168775690, 999597429, 798668236, 488450386, 767334433, 682002488, 253941335, 911050575, 64780117, 188955627, 768938068, 596658988, 399819623, 9869915, 188438445, 184689486, 322340246, 528636515, 407836738, 493542973, 956202424, 331519334, 94206550, 503788430, 804951846, 782203618, 618493028, 562746887, 800620075, 370949589, 751424952, 230945019, 441515301, 552436125, 591955580, 924820230, 740874988, 659602563, 449505351, 366819176, 300830619, 400275457, 536640579, 965748254, 646058961, 602325224, 735853238, 877298613, 483087461, 966547135, 375799660, 611678694, 326834172, 457643534, 43400648, 436402164, 747597793, 208809992, 71201758, 534174491, 697385848, 811032284, 170797201, 408032202, 380146317, 200973291, 761166793, 538651569, 478485725, 391977807, 347135660, 861476728, 299347493, 731763348, 264300692, 429872287, 652920678, 942415086, 792664123, 991146168, 465579930, 350295954, 166360920, 459748067, 883674353, 996502801, 820059315, 942533450, 487234080, 814717118, 95711573, 546465354, 639353804, 470828520, 157584498, 216589922, 230615686, 7721825, 508147073, 838838774, 731500828, 677105121, 245470873, 369100669, 312268398, 439042142, 672536399, 941524612, 61360878, 545168076, 937544815, 8477470, 247511609, 770287854, 694729028, 357640257, 426152436, 552685733, 720368183, 797984919, 962958010, 577356908, 996314321, 120258477, 740913298, 406607879, 41369763, 330884939, 850876000, 921627117, 345068433, 420875747, 802284275, 583064520, 14941406, 751246984, 298762574, 552635491, 308313087, 703157381, 633955688, 50056389, 783701465, 555118056, 243413042, 921429111, 913962471, 38592278, 214604176, 223488024, 821480610, 887092049, 248628817, 113871107, 302489624, 83751365, 226540713, 462235301, 405868338, 298177850, 974710187, 842741459, 912866963, 576251955, 78769654, 563827543, 476754928, 626293922, 100540663, 379808991, 755811419, 296440317, 593303631, 294186397, 503119349, 224384203, 549135457, 900681472, 386458365, 100079709, 228934035, 648184363, 49983783, 677408434, 821317594, 355287106, 879636079, 463618328, 340958586, 402569451, 999168288, 974260828, 769316867, 230578605, 964388314, 302881166, 506403015, 679220244, 426065793, 83431392, 240976972, 850320991, 153637260, 484486752, 709662195, 683667816, 845057703, 958056884, 20392426, 393683685, 947789491, 76749389, 968572522, 344264808, 637903667, 385757481, 390760854, 534588096, 785188253, 203735053, 740155799, 412737049, 131420107, 298021351, 767523983, 163221755, 973283734, 216380053, 415691477, 30720081, 187960290, 212391470, 812459980, 420960533, 458941151, 573453801, 406188889, 97596865, 735215934, 740222041, 438975437, 617087030, 877332320, 934020633, 295637638, 973919848, 505165097, 481283775, 212506125, 432303648, 38527548, 886230623, 279220635, 156816412, 1756979, 632690117, 547865082, 180171534, 397138230, 209400329, 830622188, 970694442, 192701583, 19918039, 254404594, 572861590, 263876482, 308764194, 601997874, 590744072, 408101412, 703065188, 199560581, 682522049, 387378279, 114719648, 116943506, 245042652, 407931518, 983021179, 434176332, 972007556, 283879928, 252570370, 168025094, 469442379, 531775888, 814156437, 904550017, 667058054, 115217277, 959708330, 765447069, 333601781, 276421283, 120816714, 527460465, 535505433, 189321986, 19300090, 809205879, 453464424, 548743990, 144483583, 402214354, 417636642, 814720668, 922275473, 946970634, 370895484, 849022307, 429908929, 619681552, 694684435, 941106897, 298408339, 839324578, 627699919, 311048187, 27851728, 353238773, 581662321, 33778419, 383042417, 762644241, 455807304, 883003341, 556195585, 215433814, 666606069, 919792999, 316764418, 633741846, 396698945, 546761023, 30133577, 880951603, 231051277, 763922440, 113896663, 677592735, 881715177, 65957910, 861675066, 323690011, 320704888, 824126416, 201617129, 407836158, 652681816, 752128380, 877292628, 805934358, 362183644, 80743903, 4318266, 730973748, 719483797, 519755629, 974338827, 772067913, 464790734, 267325958, 485324157, 58840636, 842898617, 259336837, 272499301, 750426889, 703041969, 893093975, 506893668, 624090734, 543693238, 201694674, 67506904, 3592932, 7001314, 458699826, 393747114, 515635133, 900547932, 766660076, 107284824, 210429665, 894924822, 895917588, 55569562, 15116267, 727209247, 842952738, 314058120, 176702155, 372978418, 801546055, 481329363, 423673168, 833331762, 552882637, 653352918, 235722980, 849534767, 453995298, 985297651, 949487413, 776926470, 993189634, 84902449, 850623013, 440778752, 813053614, 695637937, 846234625, 569848248, 904367026, 912075369, 971095569, 12412253, 743854840, 503007547, 769530189, 4257946, 942925499, 899156300, 502740283, 347578563, 817930606, 347828121, 711123468, 826213690, 239259552, 550857097, 282834209, 462390950, 452825448, 592076005, 335374214, 24119345, 211607393, 218897450, 860905672, 919854964, 298366157, 318569385, 999624834, 559004666, 13171609, 729517316, 232030203, 294363422, 662897304, 106931184, 166951357, 923837093, 691950008, 962182328, 862276795, 516777336, 409550849, 779951341, 163399929, 397592798, 823576169, 801574884, 864599244, 516948460, 227351718, 830771925, 841079929, 320247270, 814134421, 534123950, 621921089, 203389147, 752393814, 168484130, 548498413, 128552966, 579493673, 649875760, 945351628, 51612888, 667788987, 499527397, 258371430, 84181119, 142851478, 125816006, 654750897, 441523212, 551530514, 18184521, 584029380, 999470139, 715047346, 774649402, 677241616, 521787747, 767353505, 30968022, 125595426, 785647662, 899399946, 891133111, 723806107, 234895341, 451548893, 854469418, 876850946, 284037863, 190557719, 207817212, 206208870, 327092156, 988964300, 207498312, 203341197, 724389965, 448027111, 13589931, 415568209, 389732985, 316473845, 98509817, 947272001, 286130782, 316735233, 183034885, 72996969, 620639764, 339257110, 411194678, 371454352, 398417820, 823108423, 164331451, 207918197, 102575881, 451946650, 185144738, 898508188, 856632253, 782609168, 366963772, 684326687, 834275769, 173684561, 8154327, 406404203, 684945939, 450548998, 536909871, 85028527, 108035071, 616326904, 861006395, 165120586, 597039380, 274283855, 398509014, 911156883, 532243517, 83892118, 418146004, 827029891, 284662837, 871965168, 338278603, 618324842, 242077731, 157647220, 756593371, 78402794, 492150167, 759275724, 838596041, 38743243, 415812269, 521325572, 578585610, 574959955, 615275522, 314060557, 836071300, 2339188, 179605202, 932086826, 242452663, 251449593, 867904366, 498212234, 470958394, 455148848, 787415182, 343469815, 814830896, 395043810, 165694966, 366110785, 60664865, 391193555, 657120463, 872093958, 963086498, 111115360, 562250377, 495636971, 768495495, 47653852, 859088325, 507977642, 673508965, 538597124, 425152018, 815518094, 948801210, 706833783, 52591138, 931285886, 32111380, 950652425, 227147084, 545759979, 202699821, 781538903, 170320307, 874208843, 183889175, 638333682, 741991509, 258453739, 147807279, 364233646, 584538300, 942779114, 978768542, 465731801, 234049035, 42875425, 584715265, 643361757, 367301681, 903718465, 738704663, 382253318, 435397466, 46077086, 309530190, 202221590, 332926285, 115401913, 696334309, 820555399, 355844608, 864478081, 204658288, 433049235, 409341894, 394313302, 481122650, 6684651, 302583389, 140193605, 703383928, 159797011, 859509233, 455520237, 744306791, 679943006, 260542129, 463165982, 304319232, 143109580, 332523016, 902620603, 395889683, 555438659, 127158354, 314123905, 128717377, 289673769, 23198671, 605022319, 685103788, 232962158, 568942202, 72152240, 400152288, 234104841, 390993823, 411479888, 95923074, 296565795, 295646569, 493394408, 123723353, 70039603, 886483369, 729733412, 277942153, 734451416, 932513543, 244620364, 627352070, 46754720, 199243096, 547402341, 309234691, 374183490, 755908218, 995937461, 201951265, 299919111, 888195760, 336981538, 408598958, 436556308, 409505419, 702963393, 611070920, 584163463, 226381428, 163931021, 560794801, 362512685, 419168017, 631022980, 36938884, 217168776, 838879355, 450201730, 149723716, 968395540, 201527224, 57344778, 63169048, 767732596, 367642229, 822400735, 649061962, 636919971, 933341618, 697167313, 412473410, 333781746, 626823163, 855278367, 258887183, 525176459, 570653261, 771470818, 342851403, 784340882, 437306862, 949999695, 854730877, 904007589, 541818290, 224367362, 62456633, 330210753, 46574656, 777431849, 927216872, 659555219, 447489236, 912570033, 570732806, 97202045, 859120753, 566474640, 56017787, 321065974, 903212267, 739279862, 632297605, 759753701, 999037624, 226531452, 832759840, 773989089, 347449440, 153165523, 360803860, 813997830, 59620989, 678721393, 789702627, 81629307, 219813243, 535770078, 969267692, 846292156, 523606917, 569223915, 750034659, 357337603, 528886829, 168205980, 814798613, 358463836, 981963606, 761385401, 277641607, 911936287, 682978515, 216440026, 789541254, 662251009, 487871692, 184053586, 590659797, 241116408, 339269789, 370361481, 398080232, 832944734, 594701938, 698338279, 588647084, 112272332, 860659377, 287212805, 523750613, 926134392, 371278966, 366063725, 904136188, 188975063, 494869469, 617932779, 437713959, 786024117, 769020258, 415080014, 598328898, 229210911, 601434543, 325494736, 561050209, 631586585, 406695321, 325426953, 920470267, 896422953, 626902111, 720595138, 487581249, 546581437, 505992325, 78667005, 233838696, 330358709, 388146018, 780251472, 251866449, 281482377, 71352835, 528893662, 658069524, 625507993, 418601661, 248472878, 15675041, 320853535, 680355031, 251600531, 818405152, 495036455, 29573899, 655318835, 747571653, 138804251, 316195221, 645694026, 356310225, 739271223, 124019712, 630687779, 507564732, 476165912, 465761866, 792741046, 566655307, 876839446, 494199330, 769383778, 724916965, 709696379, 121242515, 856713782, 88315935, 932677196, 476344392, 161210052, 258187186, 882506502, 830055368, 527038183, 376955880, 253395744, 785580485, 375954333, 166698281, 865642662, 156045273, 607989143, 603034301, 545441332, 998254438, 415117718, 302869489, 473072131, 903363946, 593579201, 477357719, 195223426, 97230496, 93254456, 863698717, 375117362, 336325253, 448629317, 961988370, 155727730, 608447273, 135602751, 294221267, 381042728, 221789115, 782899563, 490471255, 125377782, 658689480, 442764274, 417021018, 688070411, 344024034, 159396790, 15826687, 53636285, 785347389, 302397507, 679035652, 356465732, 113253012, 548485666, 561328350, 194688083, 319427109, 598064080, 884532714, 169999150, 183197286, 805466771, 198831135, 638154735, 763173558, 231075345, 764273671, 931113586, 935290469, 917912748, 355745691, 238016416, 583569680, 272883838, 420188976, 802885743, 720670072, 164246244, 444070231, 945063348, 204893722, 286729522, 556847542, 707315213, 264361898, 919523129, 977333787, 374512943, 938677583, 642241989, 683469895, 481993993, 87033542, 70572472, 943355642, 674327082, 655142456, 404397320, 702105431, 225434864, 899949339, 100321008, 334848061, 158322691, 887967819, 924491975, 783371369, 155976404, 292801585, 763195119, 336893351, 924068755, 171181731, 478358559, 53743475, 5019531, 610318609, 396884661, 58109789, 696604538, 481954639, 589044167, 376623464, 132245078, 567023603, 138257364, 661533656, 724430596, 490240824, 293835032, 991993155, 593121824, 451989726, 449302216, 882540370, 781974597, 784396625, 949208912, 354239251, 361450398, 217373056, 562699440, 737564507, 958247242, 950777522, 621006736, 315637511, 70934650, 64152552, 222951693, 295836098, 687187059, 482417148, 885367422, 912051908, 388888360, 127803616, 982962529, 375015885, 831878098, 999911262, 559980541, 963740092, 651078174, 383390751, 28622743, 444862041, 670954905, 505045557, 901936023, 198692533, 663801654, 10791540, 831479128, 674464447, 291711223, 523860848, 988249658, 780125605, 638911478, 706858565, 412537914, 780694985, 821716679, 573453966, 334271287, 557660598, 148051438, 35747442, 996363993, 534556280, 487992720, 964113796, 495527634, 120169312, 923069288, 322856222, 343030168, 4353021, 791798662, 75972976, 50745814, 493411117, 251871427, 769108953, 1830167, 998653807, 197530510, 370470548, 344580346, 914479782, 667666956, 813625989, 880670270, 208873204, 892615100, 763667364, 313982559, 620137920, 457844265, 785881346, 521310212, 449375767, 930655622, 684372674, 906910170, 334592331, 47461155, 206780290, 54240289, 347540117, 800047739, 373672431, 637407973, 697186277, 698578625, 863155251, 450404376, 830991929, 882031738, 954294422, 156743793, 950751298, 640979246, 768721208, 126033963, 417436627, 380677515, 809690424, 126301186, 248253950, 943317463, 975345359, 775699623, 240898295, 933048969, 12151538, 266237322, 440933224, 367279254, 756948239, 789365719, 976669794, 559893050, 382346321, 408855585, 991316834, 326172927, 458718362, 783970371, 70021841, 78019357, 15940, 890570995, 523070789, 529359306, 130457931, 979240078, 626208836, 335696652, 106192968, 312170063, 721778628, 281874201, 908259990, 881290802, 661184313, 274539864, 439817387, 416674701, 19436738, 889559209, 251287726, 756031507, 457953289, 314296647, 802821623, 363118759, 445224392, 129999549, 778357686, 138350778, 15975563, 898580469, 725766572, 38733313, 449234774, 290458996, 317299578, 565675095, 66813373, 23362394, 864979446, 150024160, 947479756, 277466217, 526459271, 979373166, 376922731, 362327221, 202256283, 634859325, 62843125, 268938260, 347532959, 190827554, 500848498, 884829461, 344909578, 586367451, 126960461, 427818765, 878158683, 776082252, 409581937, 400339927, 648748770, 839706944, 720920773, 226130928, 285784949, 956046148, 989322690, 189946489, 462274584, 465398190, 679857637, 21491353, 777178684, 283532502, 303449580, 129156083, 36947046, 501379779, 392244143, 312423690, 823830576, 197941051, 867132636, 786808479, 261360706, 411360343, 715352745, 965595881, 726131168, 916474327, 401091453, 601058440, 348944925, 807781979, 482916954, 336725478, 191289356, 332748087, 91258240, 240422, 588244910, 17760236, 820242003, 411066210, 150430074, 252525952, 588705946, 49171973, 507955409, 660389811, 295651118, 707509144, 17729211, 533560429, 73897110, 612378115, 75135866, 55108116, 787320962, 536007020, 552470122, 21254650, 626547434, 292705777, 708523653, 671692149, 736090819, 223716846, 306921467, 37032817, 95379204, 793597155, 967736532, 176221913, 975335108, 319640645, 523234938, 31378790, 529831808, 950384788, 818282563, 919169992, 102323869, 659773173, 519081880, 175081171, 63164743, 358837526, 705925970, 906882791, 132463089, 966888317, 655484996, 625725257, 185472276, 509995405, 385582972, 48561661, 621014401, 601439134, 712009301, 894079665, 336346769, 435967794, 10943930, 952236648, 752267625, 612187934, 405744613, 664544572, 821600570, 683417910, 17737757, 159319709, 232027566, 452549279, 346686077, 152987170, 922646522, 318550144, 67172207, 851086097, 396809730, 179877736, 980620363, 30524133, 157043665, 502460618, 598773814, 237934086, 727867429, 82410665, 245330241, 10380430, 722428542, 254330731, 941967739, 614450536, 101568275, 147458664, 819578422, 828261485, 509043855, 912136619, 61353469, 464577941, 253784643, 531230250, 281196158, 616852168, 1997499, 447543327, 316318749, 318914721, 817471854, 142324816, 659326197, 242759629, 911668106, 893633822, 56237848, 241510803, 798510719, 200450415, 4355289, 813064633, 568401816, 375165986, 299860019, 910639212, 633430293, 543685102, 331039280, 818286038, 52900836, 623146385, 996696196, 583978787, 603914453, 529414122, 980597437, 419871816, 658547236, 297241564, 428205378, 560851540, 299393199, 939760400, 647277633, 368607520, 360103423, 562083334, 640844865, 476392880, 519232518, 394163946, 397749868, 818759378, 998968859, 321693423, 776597825, 164687108, 669260786, 922786766, 692603886, 5248202, 960915953, 371843097, 141240029, 642924551, 64321847, 449053088, 815952325, 24972487, 747759735, 630192654, 810250933, 674517762, 476193035, 89309940, 50888641, 307377631, 605145012, 673027793, 467166865, 285127660, 307888984, 146223324, 841123889, 889632869, 692924763, 433985437, 347193081, 973271803, 160850650, 188547151, 266050425, 197710732, 786098553, 321263008, 625995937, 381940223, 519670454, 409304172, 547628320, 805524470, 888445663, 126984062, 701667701, 877719426, 378406358, 540553858, 161047600, 218462148, 899439021, 565662587, 46484938, 712782585, 418161501, 473486717, 275185290, 573907744, 961421933, 431857955, 598518320, 875463044, 936923023, 913283712, 538459625, 978614157, 707994986, 656575399, 361629923, 707619018, 962287484, 284053524, 236941040, 855057410, 883414630, 74302862, 571836095, 621851038, 199520372, 9073562, 195658376, 831610340, 454865692, 176611108, 371931424, 527032599, 91752634, 265729061, 893145620, 500152358, 516880740, 996462482, 470554026, 978553421, 394242029, 892767074, 171794555, 599769862, 712669366, 553157008, 646968444, 123020230, 618888432, 929109385, 882996682, 728512998, 651877313, 928374180, 67778053, 929682028, 982971396, 210443400, 617086954, 713188838, 241347694, 193358637, 782462318, 453747147, 306037923, 654258382, 4694977, 848057445, 395122624, 974053022, 470841252, 678472737, 802898454, 696104155, 516650411, 937195012, 825967663, 241322578, 842794283, 3191248, 145683604, 578912077, 251877298, 325676059, 751715306, 658874554, 495980486, 436528971, 995132738, 583819138, 350675016, 404253719, 494599430, 741580632, 218030427, 726595501, 66499087, 504290310, 329572213, 370944242, 373679262, 189435361, 608402743, 16853698, 623612939, 621595164, 170777312, 264517254, 697696321, 243504400, 295640769, 542992780, 302376110, 633955593, 47472549, 464918748, 701331326, 186759647, 874182294, 442698257, 329457511, 12874621, 814442017, 882827401, 381526023, 309860352, 415854682, 615215183, 684820792, 152455761, 161461765, 997658784, 264556769, 755279397, 56875984, 563091553, 480705049, 665517946, 803128266, 800838003, 466482227, 228821700, 602180153, 277769807, 329483093, 605044949, 554982428, 758494520, 729050536, 203898452, 423357159, 411839388, 445705024, 658328197, 213819008, 388877573, 719734905, 462545306, 697374920, 944294274, 425675572, 459227225, 993713801, 459882329, 227575828, 577958049, 417775872, 953402477, 385927748, 588735660, 296054133, 355362961, 288551915, 830210542, 5360736, 50636751, 581394276, 15915463, 945360654, 613890886, 472463053, 538496357, 724258887, 347538213, 477998314, 529321210, 733718086, 883962321, 59015706, 238494513, 374795979, 582317350, 162034908, 778914753, 977758682, 772554974, 418429560, 891003387, 308322883, 181829443, 772208826, 475031047, 12529901, 292813215, 665327789, 345738314, 287351347, 447973727, 645213267, 728683408, 477928576, 532728849, 274430586, 834894398, 572466094, 910137546, 40777104, 635567955, 365513906, 914644900, 221961545, 832761713, 775449899, 587297685, 251488554, 956324587, 640405125, 65188156, 679755017, 841710673, 780928655, 902211088, 668052749, 441077375, 363275117, 37892438, 456708831, 373389396, 734008004, 99261975, 811813177, 744629157, 482669667, 435610274, 142372425, 731104331, 860342048, 761704172, 597514387, 759349116, 479880499, 319989288, 953002665, 108920670, 503851327, 561805772, 696096822, 878961971, 612912113, 206177014, 169062086, 577117337, 165064825, 203929347, 886637437, 336928503, 256822734, 25480670, 557016768, 746330700, 462413242, 281661962, 64264774, 674445681, 933093468, 531199708, 388306129, 993194043, 273621355, 290263347, 557365978, 712588949, 171624823, 763004339, 57013262, 498697164, 876521815, 12251393, 841735760, 155273578, 200210473, 558338247, 42926282, 515939470, 824112871, 951856072, 402079888, 496169247, 455542018, 395839784, 499100356, 859709781, 282586894, 40658857, 291937094, 909123253, 637588904, 767369814, 446311933, 103970661, 499490185, 850205569, 788282011, 73197825, 147576527, 352034314, 695202124, 325580794, 458569526, 695773231, 239466862, 763542170, 81782242, 949706793, 543729552, 773945909, 105265484, 411772806, 651616223, 543544424, 873784151, 355843866, 666331887, 824149228, 340316971, 745977306, 893148025, 996129076, 861699977, 874454484, 405751371, 534656627, 108179447, 53958479, 189224707, 167583554, 250524624, 85696867, 642013350, 551845950, 457702337, 726836496, 639688268, 288495829, 893677614, 580039453, 345924496, 528819504, 486653930, 284074229, 407752249, 601984563, 332748089, 441327568, 556316582, 392653249, 413297265, 540695324, 613349230, 771151600, 530840282, 341469194, 44948688, 179329778, 966075264, 821049389, 861276623, 204469104, 424022680, 239605710, 289303450, 158284200, 362766613, 299019661, 322650725, 732262458, 130003617, 939823345, 847969994, 600269249, 915341281, 276845663, 541487624, 340185774, 595194601, 436688032, 512587166, 576401943, 508403390, 60707456, 545016555, 721996916, 429190836, 154277369, 981493506, 671885265, 904249053, 656199446, 117593065, 312898168, 759871551, 422644771, 862148368, 680022288, 919784945, 443708887, 251306030, 712495645, 525182832, 699867506, 661410509, 197567613, 69983407, 294103016, 653982593, 627179926, 912414734, 716159908, 839310758, 33107169, 209752847, 554428112, 410950184, 870112115, 446078529, 839302000, 523079641, 524126696, 739402920, 77382068, 477110194, 739555299, 410058390, 139229712, 384870699, 65205055, 276858671, 223998862, 520702390, 538692023, 931321310, 857237772, 219418799, 377306206, 278435484, 370387251, 495727186, 406455462, 662194530, 148919692, 725615816, 694008609, 14665900, 802456960, 273348720, 308188638, 879297908, 175364019, 995330902, 351814625, 825543737, 686121284, 455192168, 563954925, 28290424, 24685396, 239183276, 13494348, 163480677, 495614620, 169088575, 999409434, 851655256, 174429253, 59595700, 623345672, 302953168, 460513354, 93403647, 715454825, 947243325, 468734495, 254305903, 139815652, 333269463, 350201641, 800345320, 507567531, 481008212, 693331886, 412938405, 162712205, 518775794, 250073148, 517019323, 67944129, 911832038, 161897622, 514102214, 453477407, 885660548, 412069355, 861423483, 640322433, 174274089, 624516000, 704889413, 177673967, 941077300, 888151781, 405274825, 930038441, 537049158, 872159025, 940604639, 214138801, 599627019, 158693150, 190875594, 204390016, 679943601, 755584856, 315129817, 219403359, 668699986, 323909839, 733964551, 215918121, 684752758, 482284745, 618041677, 3435354, 825522892, 615906638, 916814104, 852147250, 184649224, 357591651, 141644735, 565819610, 399644807, 945531723, 768221983, 964821148, 670885558, 107712879, 764021082, 126570848, 12318178, 823833718, 118487153, 562309420, 777107429, 665365652, 384205441, 391172882, 25080556, 546547469, 307663474, 941597606, 223249658, 792354788, 241091199, 734034760, 738329668, 145059251, 18394715, 669449102, 923221209, 150229794, 999202393, 115327248, 328963306, 281315118, 511421718, 508758886, 977769930, 12604142, 296832240, 505120665, 148197208, 889568782, 398384695, 308172356, 979636547, 11011494, 392855848, 939327186, 889299521, 288279849, 922955234, 103734537, 218840921, 427124883, 919153697, 235455162, 514104919, 580934414, 283488605, 363306326, 913842644, 168848845, 653809988, 857651346, 160355103, 560571129, 447110639, 600949437, 844090893, 117127840, 456293695, 558973740, 959104035, 162085599, 335642201, 815877354, 94198586, 795741296, 875925348, 714705593, 354076878, 87121559, 930327297, 38730416, 741391414, 799850952, 100960516, 412728401, 923600306, 401737041, 776321591, 337130696, 23543856, 249685300, 557008749, 772847921, 212072099, 131775648, 662259481, 897139141, 557262125, 510269308, 76651687, 457272547, 5798165, 325179829, 254919674, 770849121, 587642847, 145858238, 105800291, 483319943, 272450025, 171214798, 736023355, 482646786, 652873913, 310234962, 202204862, 874091347, 700072094, 45513515, 842267809, 227243728, 696299174, 675158878, 88836308, 900286868, 759046116, 605261051, 95455350, 163027669, 567863141, 493945882, 835770593, 726376338, 1526382, 370209649, 715269965, 449802706, 945061414, 788240905, 843508992, 107669048, 110167114, 388677009, 775794125, 960409590, 162896182, 151703234, 681080572, 362684253, 699562375, 312039983, 391948124, 281127605, 972656762, 20734652, 379508309, 675512554, 486684460, 538832512, 860892017, 880078449, 354415964, 14557508, 744096368, 190362756, 488010857, 17648120, 294299296, 379023392, 68497781, 418249287, 850272948, 572138085, 712080271, 219783834, 588972498, 951339848, 617091032, 708186561, 105667321, 583200149, 490597274, 522524479, 665430981, 106589638, 234120119, 574734875, 447267050, 145590116, 155937758, 829864412, 962446287, 117978188, 759488072, 377532595, 115401010, 527875659, 451571562, 168516090, 99385140, 840000941, 34868335, 528635140, 689533200, 961905280, 451123383, 541088244, 825547709, 366240377, 237938070, 847681824, 400864212, 169628052, 485119222, 132288737, 417287573, 459894925, 541741964, 788805819, 663651480, 971873198, 960033525, 762917174, 633561413, 571145465, 316231530, 933761490, 152935429, 331851085, 100729933, 784719430, 148947475, 441583551, 185389464, 983371952, 43335914, 860761812, 485458890, 559395960, 559491418, 56516309, 806075825, 284388744, 148057509, 851827770, 354085165, 561804263, 317597282, 571083216, 525366804, 786701414, 530585368, 514264278, 581387297, 418857400, 605543422, 632890811, 439124409, 764288167, 102075128, 143750867, 644347630, 540724971, 185544625, 628710327, 252248780, 991059356, 170339815, 190411876, 765942755, 100946896, 871372880, 355543856, 657595789, 292197688, 632866784, 760466774, 360507744, 536400849, 451944267, 635005415, 647500718, 805725273, 909028300, 264393432, 324650312, 611141440, 235289381, 960680242, 386369235, 730936101, 312379546, 105388133, 794925525, 977913869, 611812867, 799290060, 294556263, 371828801, 88330516, 741729065, 502766620, 649137433, 593806888, 860844584, 878127700, 141200963, 284964174, 478574760, 194518459, 258466668, 816354191, 296731601, 34353347, 353706983, 737884274, 4911065, 301211326, 569960292, 310433588, 803314751, 870313545, 982209763, 28445299, 980649128, 787496913, 276637176, 935675071, 735491436, 312145063, 155075520, 377526313, 138414600, 499553038, 198001190, 716431820, 72521474, 564862061, 519672195, 929381052, 513633205, 707042450, 874811944, 400712562, 786766072, 717644659, 387343100, 869148091, 617794637, 167305770, 915922944, 277347283, 994559327, 354070038, 763186482, 52407080, 234443397, 418394549, 813893031, 133491652, 545919443, 376703627, 828957371, 185041982, 829329238, 327846245, 287711399, 395058137, 959344138, 250180734, 26666179, 730057271, 645685822, 743972687, 141126691, 819080264, 142037092, 63762388, 303855967, 522102976, 733949094, 770477710, 568203275, 622126257, 7550802, 75712796, 442970114, 41670815, 378605300, 458149254, 331311094, 778435471, 914417493, 840170945, 491516104, 936656974, 739047077, 350197497, 579763060, 743313784, 812099594, 310077431, 899558362, 914988589, 842648048, 621445224, 614433595, 176388386, 707644184, 20598691, 431855210, 703501362, 789228878, 814722981, 465984859, 364915780, 963701518, 682040014, 900846958, 260535423, 497265502, 559759070, 252570869, 71995537, 170608451, 318956868, 489097262, 734922670, 785493319, 252576542, 295028962, 793566534, 10651983, 630289375, 462221089, 910679673, 642841198, 433214715, 712766417, 761794044, 944140706, 661138252, 969479421, 40790036, 50571438, 198795499, 986045828, 529648733, 247759367, 291103284, 890391384, 984348458, 124007586, 773447272, 334765860, 714088579, 281598355, 176015718, 307549040, 864852999, 222429048, 460905359, 681290352, 698457413, 969133324, 899001554, 547619525, 373201942, 938928561, 89526561, 792653409, 992935703, 262362659, 255870725, 811611415, 705720502, 174620481, 799386425, 303450332, 7873955, 699160566, 369366681, 2474679, 197723321, 593635933, 396669258, 902967515, 675236040, 890631341, 401373734, 693398650, 971437007, 142741962, 473622419, 527439081, 433771514, 119178041, 531839208, 516026901, 846942108, 526415185, 510518427, 259177371, 617087168, 116440386, 840670464, 984512127, 732934511, 110850145, 740097406, 190710142, 578757864, 887115760, 468348777, 327713730, 72880606, 539379599, 529203864, 84262379, 949847517, 847371801, 703818148, 343550785, 948360207, 477564873, 829626010, 109909240, 169691997, 476884325, 953698872, 364467864, 791843851, 590446904, 355636228, 678415041, 111719294, 586341749, 48360746, 218411108, 473755132, 183311546, 814913381, 693220524, 826835906, 957578579, 931665860, 637539495, 850566279, 859109750, 930424641, 215937175, 137809079, 617904390, 706858124, 645046418, 611091145, 309763410, 606420996, 202734355, 198182881, 344439099, 76525850, 174418408, 500483168, 735862305, 707320593, 805212388, 170699062, 656153137, 492170103, 270519858, 688943769, 957231980, 532937565, 834222402, 423501862, 743888695, 634023421, 309788295, 39542292, 586738017, 724879786, 143445050, 374388062, 601481553, 720583093, 309210190, 404689844, 127544920, 152766144, 703889695, 79849681, 275986920, 150196588, 139236581, 850256080, 325136312, 959649286, 857883850, 462332104, 90324946, 343289442, 222996348, 972535292, 868228455, 746018766, 762889760, 982921480, 499049080, 55161352, 732598418, 228882604, 177401978, 180580659, 319826956, 169253813, 886089430, 15536837, 359468089, 61298295, 661928892, 802321373, 844804561, 183121530, 947216527, 205137319, 17995028, 689555449, 275124822, 8713256, 953007222, 146512414, 342964177, 163630573, 16764832, 124628510, 628117674, 143862652, 551194055, 484297190, 458180912, 412701087, 455242001, 555211658, 989524413, 965316100, 732105282, 672283734, 358166268, 785031071, 882966127, 654189914, 513514324, 224699497, 266477357, 886144093, 178755035, 506283231, 818690286, 678640468, 215198843, 836090963, 472803084, 735281759, 252878445, 459004288, 916520269, 177448076, 561703808, 696269152, 235655341, 12606421, 759865931, 297080814, 702200737, 252366063, 931853579, 176525872, 676346305, 469325496, 332803508, 847463864, 177136602, 900434826, 557159470, 990501169, 60926341, 703630793, 99228213, 459899028, 906753988, 491289755, 822451864, 739203645, 5858793, 235112883, 374580375, 8662767, 636633440, 646658649, 806242864, 150927605, 125868006, 402777229, 745144994, 184815711, 733858511, 152837008, 114862920, 523784893, 989315648, 592007415, 926941860, 78320889, 425689814, 717256881, 646862374, 27915112, 320949792, 910081608, 562447533, 609782283, 844701304, 620739250, 259531905, 452820937, 991340508, 279427326, 980586723, 584275150, 786749207, 291031631, 214439005, 332767819, 586544418, 866922823, 63843679, 119526828, 965304224, 455171271, 824311651, 40500807, 149106730, 20043408, 920845480, 954702724, 182435974, 493233036, 550477529, 472016410, 545928396, 277518422, 695622094, 433307594, 456053144, 957389972, 57562915, 153294488, 40405725, 609140246, 143349349, 960809655, 433162794, 47345201, 121186686, 836009184, 219047930, 33727503, 386931362, 264339107, 458522461, 501319279, 438619287, 575411272, 178070069, 453471359, 943320253, 435583234, 431910414, 840228373, 566411597, 163994965, 306330297, 820123923, 854179355, 884993408, 548163740, 690308067, 499090195, 112035239, 447111945, 747738584, 975313659, 587227974, 136835710, 748830319, 813696141, 646846891, 602698183, 952757102, 486091417, 189822433, 213236002, 137424592, 337748194, 265724999, 557356790, 602562575, 863504465, 838455442, 505095453, 115426626, 597626839, 531764291, 100384687, 698970151, 257376610, 777692267, 362400650, 316162674, 203403628, 867599344, 189604163, 988296320, 970361203, 247538065, 540535655, 690728030, 837236277, 763975486, 909016501, 769465505, 518524652, 102432828, 607489895, 494403552, 47235786, 358762665, 15584613, 2405043, 595116929, 557888363, 750799476, 687571070, 710490299, 848929667, 79105677, 658513976, 822558274, 245851478, 237338035, 348801511, 322445644, 667806017, 82043799, 701195341, 81947579, 309603532, 963240591, 631341299, 924976161, 721598492, 367662786, 221855576, 729400595, 666411154, 751987490, 229727345, 309229059, 493287664, 356268539, 85781733, 932650185, 81922499, 59104910, 459645222, 754876598, 956542515, 983146760, 893624823, 515578015, 736970421, 782684931, 806851485, 372550091, 723298610, 925125839, 855910321, 195602770, 787922675, 963742402, 999386755, 69703853, 58586618, 364935333, 912976591, 823085661, 773873823, 279813750, 622789295, 143833813, 446347346, 257501743, 202755948, 289322966, 707588455, 670443408, 203056534, 619348511, 134796471, 264513436, 13614748, 555743804, 922602413, 341254839, 262357656, 249187368, 712606359, 120863943, 951572437, 729339024, 589596742, 2841536, 320933025, 427305939, 794277539, 257717634, 749553211, 10709703, 996279959, 155267618, 569924476, 483760060, 634165605, 826017159, 58393859, 449995504, 543019914, 84153992, 225688438, 912147421, 774559517, 143774933, 455389765, 652760379, 971662357, 584949213, 844602390, 511475121, 169644831, 844614011, 386122427, 262970796, 74389883, 376722554, 158370840, 922149046, 349512470, 550239846, 172991023, 411909072, 689422810, 655494443, 214920279, 50896729, 301631911, 164970705, 905172978, 567166927, 967676099, 124421397, 526672863, 755071253, 380417315, 215941977, 990297227, 529955289, 480183922, 952607439, 263999757, 872043151, 853192664, 366895735, 811864456, 823084166, 729225008, 181455498, 632654326, 79404825, 917904371, 659064048, 91379214, 904394719, 235801595, 438526460, 547558712, 30196765, 203155819, 17991549, 602962461, 342307573, 979596064, 492289822, 542561792, 606305232, 661917555, 804047505, 963232614, 32615712, 110953015, 901140224, 240979174, 104244348, 451262383, 23279427, 848593573, 499413711, 918836126, 33016957, 477256233, 463640675, 853247269, 949040112, 468406100, 984026819, 22772087, 856496955, 194822105, 711013847, 522078548, 822079776, 497812330, 492953773, 156316854, 108916561, 408949163, 184844598, 176265332, 418229459, 121637141, 190908312, 599511986, 32895727, 350337792, 89998494, 878706491, 759310095, 976222029, 976660046, 524264667, 402219689, 985687362, 422370055, 329672842, 766774824, 21652133, 643784514, 677561029, 107355396, 359069717, 351325790, 890872965, 389319690, 6565538, 999953146, 497843127, 814921996, 190094868, 296978149, 354380498, 890449191, 80407136, 541304413, 608182474, 942239611, 722148484, 716929890, 530103369, 305929842, 151395821, 170217767, 410313162, 737368322, 841234004, 518091171, 396402776, 905081861, 932086326, 471913961, 884071478, 631170155, 651408521, 26928797, 465174323, 114303487, 382473259, 315728395, 427775273, 707131083, 276925993, 428184636, 273932846, 391715262, 411060004, 768633108, 495726712, 825978759, 154624655, 163544732, 292108356, 308802435, 454314463, 112842220, 506544557, 707643981, 750528244, 135597339, 526408955, 519629300, 11280976, 376269475, 133305291, 89768053, 408617304, 883926724, 933349135, 555514718, 603407782, 23325719, 659235531, 910922199, 289140920, 12104167, 578451838, 631143755, 195715054, 137056494, 336595730, 690201543, 467707924, 588731483, 495710916, 633161558, 407577957, 718070962, 19925074, 122097858, 731265727, 995163855, 374257935, 731972101, 54604948, 689028846, 442824030, 197976339, 973359195, 410251057, 480595099, 56866515, 767089881, 33401747, 672178818, 48197206, 913792, 727032904, 993623383, 596770377, 363405858, 185561935, 125013900, 141368970, 409380135, 88267837, 650468108, 866603771, 535108667, 534946432, 330975157, 305662040, 611245957, 547310781, 838950267, 493863397, 811205039, 95003048, 861491291, 176177251, 794573553, 439796810, 579353501, 565060560, 920593385, 868461145, 503827085, 77724411, 728417238, 295806855, 940614096, 280906770, 365846596, 776890580, 964647879, 783596569, 513247368, 114620906, 882601060, 427836983, 679916828, 852695247, 148861743, 986498168, 352266416, 985916669, 652017749, 709591055, 874974646, 566445853, 357642337, 702014001, 801063828, 567261315, 11470572, 85135262, 732989271, 67926608, 199163808, 63687428, 25245082, 322575024, 223196361, 160666369, 922446460, 898360371, 354036576, 634417912, 187149337, 732814523, 13835062, 676342979, 310770116, 566113481, 214446356, 927877431, 838310157, 556076448, 105819049, 593572591, 910301797, 285766549, 699535686, 830722684, 495804604, 129209092, 701191952, 205501705, 90897418, 453305625, 740519881, 27457210, 764587544, 165461484, 57539651, 477722591, 149812261, 80353964, 912630871, 221181739, 853492534, 752871100, 162219079, 481579898, 293216497, 553775392, 248640371, 559014311, 591966276, 273893118, 204400012, 247536059, 764212126, 123874500, 593001833, 11634751, 358942083, 637459322, 732424428, 215314775, 677425500, 352725133, 396318265, 267515553, 574103791, 178530672, 542636332, 337839669, 744396101, 29368329, 337432599, 179743137, 720226076, 501124164, 546191095, 370674727, 844956155, 254866866, 646054737, 631487284, 903373219, 730371302, 396860176, 363021206, 565002663, 930397641, 442080096, 972874303, 132836582, 615123352, 888658420, 648355179, 216465616, 320586323, 842062813, 697532147, 449464060, 45142399, 513188820, 46416811, 293190006, 388414223, 161919892, 993683468, 30379599, 546816474, 870307514, 523006001, 260892373, 164416107, 573470417, 516919234, 197071347, 817356039, 739364265, 301957627, 34742305, 559653530, 30865404, 700109696, 133183233, 873729749, 962610844, 764417656, 441524245, 222592732, 195041599, 283244062, 910509793, 243568174, 906683246, 497320814, 858338325, 932693334, 787552191, 906402165, 369759882, 653500546, 195442439, 495221576, 813233399, 65709419, 439227158, 492985508, 149798835, 334615565, 129949767, 418501976, 733035684, 493119959, 654959801, 678810273, 209344948, 544674684, 171622965, 353218316, 481727029, 270777534, 20731699, 722852040, 919140547, 955589875, 259984489, 6453520, 53896497, 134362781, 626242441, 995256729, 903941197, 664564310, 655800866, 133244779, 183571048, 426102469, 565665893, 947933672, 158616926, 111761810, 203201249, 784374403, 845197879, 34357679, 276703780, 642164060, 833153053, 260221401, 847571421, 131943785, 926838220, 85963711, 679896711, 501310404, 501325379, 88354002, 474025038, 934322724, 343269549, 494087071, 673368412, 648351704, 894746275, 633866342, 167392667, 264159315, 441272410, 527590073, 148643623, 918797375, 695138336, 458044845, 122864298, 747203836, 933042041, 600230160, 636674197, 349446483, 437978640, 465956402, 291512814, 124466530, 928872930, 488278654, 53872748, 546259306, 117551080, 574928834, 907947162, 14749164, 214989385, 612353992, 210167493, 522564853, 535240523, 735229229, 921329369, 594628446, 386547265, 669193514, 443218463, 290155190, 435088755, 628123750, 699178265, 122543337, 495544033, 918004202, 101477384, 88421449, 956667488, 776912728, 606167299, 272437467, 308774802, 229099064, 293213414, 35166568, 477235357, 337665998, 268831320, 90882125, 121376360, 434814671, 471593001, 536589323, 801943831, 486459199, 664552691, 294200309, 801530022, 595152633, 94721352, 460233508, 653086962, 679399879, 719140486, 687485616, 899485138, 947329450, 856553367, 612153016, 926411765, 90583888, 600212259, 808981060, 514597524, 213710519, 715564950, 794808633, 111135595, 258255490, 681283958, 597070845, 714017180, 718378574, 32780333, 3222012, 582324141, 860339288, 778025208, 361879751, 203662324, 827647991, 96385094, 545956210, 780388468, 890032886, 436931751, 700074108, 243510700, 329059853, 222441481, 289659798, 575885895, 810865470, 781102236, 630644645, 635871400, 947390982, 645025890, 992346977, 925024486, 911859689, 244647383, 910379443, 469168775, 301396836, 302627898, 633375194, 39370122, 18426791, 547946712, 500816421, 629677990, 703578969, 764680437, 940785755, 816937066, 914710103, 384931875, 318792944, 890876885, 520707653, 861514240, 355875966, 779631847, 952294244, 487178716, 737971024, 61169692, 729086077, 523941870, 232168892, 153174997, 552857140, 54739707, 657596169, 426611496, 934002355, 908265091, 969518971, 833076671, 621849132, 596142262, 780274055, 539164070, 631028869, 500516323, 588126907, 949484879, 604767803, 772147036, 51039622, 201799950, 428033665, 388660210, 140109040, 748550186, 954088648, 461368151, 852922067, 66841619, 106769652, 620174280, 166765596, 143204652, 199525500, 919520619, 231114673, 607945170, 597912461, 994288925, 832332272, 138680003, 712205854, 615640042, 245099530, 421874650, 357726798, 863448753, 622671106, 776217467, 625312898, 283184948, 262443364, 275877332, 267124479, 390735741, 528156549, 630489400, 582202167, 803592811, 434668671, 901775202, 741033568, 600650178, 887933168, 229148456, 224941260, 613994887, 199695401, 612658478, 604533882, 763142960, 62711138, 242923316, 382975977, 560513967, 677359127, 843101985, 303382470, 796975517, 233771105, 878819800, 701406465, 478107134, 63319323, 142590833, 237377419, 231873321, 881503137, 386863553, 720248335, 675209901, 168241125, 214592853, 36064197, 130459023, 370133367, 454120634, 14919924, 330897123, 754037527, 271964003, 983486154, 232188707, 111036723, 179818025, 410356699, 232431830, 841173521, 106519908, 848181938, 345316866, 288268910, 214765267, 166916875, 127325717, 743693047, 640032526, 895809428, 974156352, 730112217, 383575080, 815297307, 14273087, 439890017, 511586064, 916657022, 538102496, 364142217, 594878823, 774879907, 684166230, 37586632, 948261165, 296781548, 873813254, 107029435, 675059737, 982029416, 223754859, 860251327, 995268795, 14659015, 323907104, 288906690, 311033334, 275710044, 354711660, 949431260, 498301854, 94558715, 146481731, 968406230, 728662717, 460881516, 350117731, 756934866, 593305539, 490580602, 158262762, 443212096, 887935566, 641712366, 899436149, 27591938, 834817727, 496782917, 347922878, 995841948, 381188184, 330833491, 332920217, 767153952, 367346158, 74890566, 734866856, 301792267, 840812775, 731346168, 72173101, 799520864, 326763840, 293687477, 553199919, 979804009, 956225842, 267407139, 535465446, 624600645, 794626622, 666753206, 479442748, 754797315, 143289200, 625895693, 953106849, 41345217, 947149702, 198325891, 857077007, 327415073, 235371338, 453291512, 771343042, 98018842, 815085164, 527099219, 549891934, 935931419, 516155337, 375123953, 850191429, 897620815, 324335429, 1649374, 32248570, 686225746, 542217498, 825767017, 970859526, 630459300, 579791820, 646989011, 315107731, 911563377, 616039984, 103557410, 516150984, 229402531, 418542918, 981352133, 863707420, 780456987, 864558547, 691517047, 303327691, 754044050, 70142708, 353850175, 666795147, 629745746, 599805737, 635460208, 560158271, 214399602, 111130508, 212421291, 217521859, 649056586, 757864817, 3452078, 970029448, 609634658, 661784361, 115053786, 501351101, 810600819, 190870112, 529305629, 225335229, 44006857, 179739124, 475716711, 803578790, 338277934, 912376321, 575469366, 910444515, 330853694, 910272698, 207792578, 290726863, 707232368, 196011107, 135289830, 872063225, 99626454, 561436066, 305794694, 94392524, 114488019, 710349682, 451698894, 353037845, 279314903, 175124368, 883395808, 669083018, 45186461, 182734143, 499136371, 156777496, 596483787, 907135675, 493179365, 987249077, 981369105, 953462150, 599413941, 251082062, 470540542, 626611355, 116227755, 447744240, 399636425, 503272690, 805926968, 24466833, 996139703, 326957805, 10741788, 884040511, 224504583, 353726011, 419992108, 738833458, 61135159, 20541696, 833583901, 42408795, 836029201, 190039026, 135444698, 223516062, 900726520, 511154806, 673622448, 851415953, 550157764, 660039666, 336214991, 831308017, 238868168, 919133949, 453679987, 899033636, 336816427, 119736864, 172771242, 879216032, 887419074, 637660002, 255063705, 873155697, 646369511, 149448907, 786936197, 517623686, 907980897, 498132228, 936895198, 627019194, 567700800, 197815167, 101566708, 601331088, 926031945, 619737071, 488811596, 580737605, 244583892, 628593537, 611872221, 813346767, 520841366, 787516027, 370559403, 246337843, 545665791, 153428125, 697566776, 589918385, 201880005, 413772512, 458113618, 675571208, 576388109, 34738217, 385295073, 580264557, 184487058, 144039152, 411592542, 66962707, 753396797, 565388915, 258334408, 274416625, 675733805, 456565621, 257491676, 340996631, 172357956, 296342418, 940647589, 104219885, 133358855, 674278521, 588750566, 989477312, 494560280, 608128334, 263174517, 717141339, 573909321, 968377967, 672280468, 437788073, 326778855, 730036825, 767637110, 496180085, 657077231, 917455833, 676008137, 768285029, 365533240, 352183456, 628074651, 215816997, 533437585, 113985999, 746945743, 641521529, 172199495, 522996959, 953836768, 934866550, 378628680, 688193439, 877877141, 499256154, 209439785, 643520079, 636585567, 628641494, 56207176, 845329303, 540842853, 52988685, 881486700, 745358431, 140715437, 572756758, 15258358, 19474007, 906259955, 46431264, 359093529, 448006013, 674127394, 674667526, 570473160, 411542792, 156783886, 612649237, 899836, 100423055, 200959126, 960482637, 405843843, 427674277, 279036306, 838505910, 81051435, 918158412, 501978957, 879446653, 474098956, 234088907, 690764281, 709979643, 444956423, 205450554, 877184250, 578811117, 36888443, 732923291, 74834001, 319237048, 79745004, 225877847, 885219922, 640104242, 574406947, 892642305, 34961746, 669091351, 627708980, 740755110, 794328725, 456990156, 97289467, 894611106, 78562430, 688509661, 968163854, 447905316, 853973920, 158366601, 311148252, 299533588, 592082683, 652380199, 382469648, 638748451, 445520912, 395347055, 937896847, 742047170, 986730842, 260165596, 513974115, 28363704, 862829982, 737307986, 20443619, 969757375, 619862070, 161065465, 696891519, 740305796, 140362555, 802567388, 655005341, 90677083, 187154496, 640173253, 695979475, 115801350, 105421674, 639704703, 30050937, 211402230, 816563217, 137441378, 404993700, 588906649, 883469987, 785918594, 781124440, 90145992, 863199552, 828431766, 992238130, 236595981, 714810552, 137993861, 265406720, 985928905, 393144577, 831647826, 130681793, 998089489, 471391106, 709250606, 145312431, 827242432, 55124563, 622312837, 258242724, 726865860, 308670805, 276467426, 146261023, 546469154, 204012845, 210388444, 183885267, 495138784, 375672635, 564400826, 343308828, 574510383, 99030266, 963607341, 723909940, 215616215, 493448233, 610446573, 686112612, 837594940, 16638967, 213043718, 902055459, 285636841, 479712110, 164308927, 341888747, 762682427, 502002607, 7407055, 733946903, 281265954, 178263320, 232510146, 377423319, 345959869, 895417640, 172822686, 762743337, 588403320, 306221733, 165095990, 583662717, 4925941, 563182668, 103003371, 681718422, 248017380, 323580196, 872385320, 897478094, 297636429, 997971047, 372088313, 928349760, 52436432, 415182521, 404200925, 184544773, 842985402, 502355725, 854453136, 757050563, 277776969, 415935671, 572042740, 778542793, 193653403, 697685619, 359732222, 231743693, 399641667, 396837674, 934558180, 376545673, 133393933, 944997753, 918145792, 346357218, 455036939, 321733827, 638898940, 393099467, 508575799, 786040115, 318047169, 333555706, 826115781, 771405945, 727552607, 327541280, 596931615, 967836190, 864793335, 412342226, 456048842, 122303758, 622369311, 622129336, 748489257, 665392987, 880834646, 486007342, 403871882, 261455925, 955976405, 395944590, 311814604, 746390573, 812357956, 43732593, 834842067, 546386982, 365629921, 14548522, 958733974, 920674652, 728626451, 150981220, 120134333, 901943206, 803204929, 867958502, 332312959, 165248232, 385139586, 733737753, 777560311, 820524207, 693410798, 498210590, 764161997, 192199534, 732153244, 777326234, 981088735, 866547333, 351209291, 456994596, 356951974, 543279704, 725854375, 249123103, 225223084, 835161822, 93019175, 674694940, 426378133, 69062484, 816288175, 70268735, 484372259, 528734038, 277013210, 928700014, 910509066, 474997007, 229470646, 310666702, 645707066, 848988951, 126329460, 267860366, 42531843, 183232119, 15871468, 936944790, 186705853, 142710470, 799134875, 815757241, 859323450, 564880, 698970529, 398415806, 390918891, 367767048, 619148991, 627063297, 272001313, 785154460, 47132793, 514444918, 167941135, 839355541, 506719536, 640203947, 994288611, 624227427, 819638960, 405535317, 996374189, 363131972, 373059374, 320490286, 783584176, 596192111, 33104761, 691825868, 631513306, 293856890, 800388963, 942590458, 154874296, 362292765, 242667797, 267585675, 242523310, 381869386, 949412116, 368601991, 497895803, 636737865, 381363439, 483163333, 42300324, 602082731, 524252387, 590618901, 573776766, 144429509, 440333553, 614066259, 459317633, 387171502, 964243405, 955578378, 447018505, 725378191, 671539291, 171521850, 365222816, 833094722, 194359663, 929244362, 806506771, 222607988, 479698723, 180136314, 838437272, 339561189, 369217505, 723236882, 30821859, 884621270, 461996321, 168607460, 28188837, 343321369, 624135646, 11244044, 322627178, 381979628, 928373632, 160038851, 613608372, 396304427, 21753143, 302474655, 453728335, 605257175, 560161489, 398605107, 488768417, 861793110, 224332111, 687990910, 737409372, 149573951, 694872193, 261258209, 491167557, 471617475, 547539154, 801920511, 236408513, 478953495, 112013377, 761424091, 765729385, 487961548, 708021482, 425908804, 321808907, 745104914, 501999417, 531896166, 232784327, 499082401, 417751103, 646282742, 620796105, 833692901, 156774796, 330256715, 62987182, 905928590, 302513530, 340089458, 867142401, 963776483, 848005115, 127533692, 592791053, 408685363, 81471184, 185289324, 695184027, 334842344, 631354011, 488361642, 977534390, 382285758, 966487099, 439986987, 649930094, 678033940, 723638596, 620047643, 571355753, 966591325, 940731116, 340846003, 315068780, 539667698, 793626309, 689906935, 624494435, 118621001, 859315645, 988348428, 79612577, 35419723, 232358171, 889278869, 314453679, 631355417, 172334882, 321313144, 826007599, 963790616, 25303263, 142398843, 172788994, 21804565, 978132624, 307106299, 53213042, 419294756, 411089807, 160933303, 238420995, 269545119, 302421714, 313238156, 191063843, 374221166, 816981877, 813725438, 764652321, 44130977, 347931143, 612165750, 702776961, 499619743, 6999731, 197347305, 227682882, 699306476, 187657969, 826239312, 81197197, 476667386, 529171044, 631930766, 895338445, 943361341, 845186189, 234169314, 534510025, 999126273, 929752689, 214065027, 379859578, 17872238, 569223182, 818412158, 980619124, 762316465, 576764567, 716551087, 968828825, 763279102, 555966675, 953563021, 781310818, 270316833, 880794985, 120822541, 644612746, 907315695, 766109468, 113732905, 182533172, 139013901, 757422143, 50247210, 927975581, 162742420, 981491098, 732837404, 892692711, 933862681, 373752938, 748450783, 101319803, 226701838, 226801036, 751637083, 696246952, 436672491, 323930102, 372126921, 420297624, 135940511, 261054862, 332553636, 590846350, 663223544, 99796635, 328542992, 851164653, 824575719, 265576962, 202269699, 840734816, 947282404, 952526289, 75975564, 689916464, 232060765, 106791822, 878621817, 278311250, 129292773, 520532282, 604672155, 333776697, 713131280, 973442179, 207297851, 834494998, 77210131, 640206256, 483633436, 270021700, 409980557, 666260690, 904808926, 158493789, 54819873, 854049281, 115460891, 858475445, 975267779, 103875042, 541691888, 278437846, 490576916, 819556623, 845575157, 281399927, 173026660, 810836689, 720297903, 787978043, 188856739, 791949758, 957421141, 733517421, 295932094, 160929688, 494159774, 232308061, 892848290, 657857710, 207459256, 217597163, 513947947, 413946637, 834387735, 789756100, 209413090, 752486469, 60238632, 694869415, 904015086, 145942076, 986804685, 817947313, 289256821, 317886480, 240571932, 153079609, 103385253, 831515767, 245389313, 583571856, 33997872, 200563886, 298974505, 898619050, 438040263, 929045068, 708633254, 949471226, 8229058, 738455147, 658006174, 403350976, 305614950, 667289368, 322467725, 913862726, 912914903, 117958124, 621276689, 580479552, 910914973, 411314445, 101680586, 210410191, 457590022, 62542017, 257552021, 641818031, 16017634, 990621492, 923372767, 426091274, 511289974, 392806239, 94662174, 900328249, 946766534, 640153503, 482635363, 761303444, 777627068, 664206104, 14356124, 980403711, 855125964, 695448957, 860621571, 829526400, 393809994, 488024606, 408335302, 959801533, 78554041, 252477986, 644173182, 509825920, 144691595, 34387223, 385970334, 24470806, 650829587, 476805601, 946360634, 43120591, 552505165, 278610753, 496719984, 316741574, 727214172, 49659832, 676044731, 679863741, 268141854, 693996277, 960104418, 61847292, 334304778, 569575415, 81962728, 733761228, 392122718, 935384889, 392990520, 97110440, 265703284, 416201677, 747116146, 241999764, 714903526, 763481934, 441920918, 205742787, 762178792, 68716198, 468438694, 547759714, 414607286, 137987031, 888807539, 684209911, 664441193, 896185638, 121558418, 91903993, 610743813, 372178161, 26482883, 82458944, 434059965, 538877954, 456629758, 302280172, 155200925, 161167453, 874992141, 260553170, 564337810, 79791592, 382893262, 125203762, 489670707, 407202899, 78140089, 287182565, 150436493, 317439328, 815533595, 95274508, 547118784, 438359418, 971065332, 352785366, 609100083, 950630821, 249311483, 227960278, 233360547, 319823050, 395052033, 915696582, 528544624, 813622735, 965277769, 643798833, 170720110, 171656839, 553540902, 751919483, 492698775, 719148701, 333962719, 239554692, 118189128, 550894999, 64318751, 623014373, 316686429, 816725235, 892643388, 366583230, 337490649, 835176052, 488491044, 7636355, 597871195, 256180623, 248389504, 151022564, 193960540, 514459693, 106806400, 678089534, 508287092, 16783879, 868441333, 27136694, 442599246, 807054118, 329924246, 95811582, 960551585, 598443193, 856033561, 434610406, 993974775, 941113096, 746632424, 449306729, 843499837, 548197422, 506878243, 692938439, 78736781, 349662860, 916806343, 8740828, 54859696, 918255858, 600351316, 665382784, 184162465, 728482020, 623254294, 151599806, 447915112, 69457739, 601339731, 442477054, 749295379, 332382063, 356215319, 610710613, 382348431, 371087585, 189004842, 991411107, 393213270, 584660399, 345875841, 144550126, 136003682, 136522242, 777261161, 53254028, 701295780, 589809952, 677865356, 444245331, 456926708, 149673037, 324321106, 940430605, 453394984, 710758109, 231018491, 232860932, 420259110, 728437976, 701846356, 857367175, 351161602, 316791454, 761806055, 317923727, 320413491, 201048559, 827576871, 4865372, 603660978, 503289946, 213996922, 121422578, 890294764, 344025208, 894445705, 610107708, 610699041, 781443829, 772146959, 325895006, 78701576, 606196957, 555156224, 158604061, 59538855, 304755242, 741290133, 535681823, 390038046, 624489002, 852971670, 446930197, 305553748, 247019653, 422951562, 474574087, 349581485, 779499029, 895943703, 190549395, 271806639, 614947824, 75308074, 574962091, 12185014, 18512956, 895114206, 945082389, 78734702, 559491086, 648677171, 829809694, 526492914, 712495965, 315743418, 665417107, 725159398, 696874635, 90268539, 401258681, 678876179, 223472047, 7129781, 778058656, 720405547, 18261862, 18584842, 572755960, 754165583, 580123442, 331192777, 469250948, 134233901, 292220334, 99143529, 623068113, 840075504, 835052960, 819355532, 573900298, 338491101, 899012726, 412962569, 544672376, 482322172, 382190490, 764142661, 846369524, 8548046, 825740780, 490897414, 218313553, 257377230, 41625702, 746351602, 507408492, 135114490, 905689082, 129501056, 941040708, 310107270, 388917301, 710180193, 77279026, 198932232, 103979392, 422413105, 737791420, 314499696, 489686011, 304609523, 240188838, 79473093, 602364287, 163559403, 553438716, 176888713, 68791411, 41537846, 122771343, 617785548, 999195789, 480642047, 629352023, 569619453, 722913355, 424821874, 40898114, 341855833, 997957819, 551649056, 930350872, 509304663, 987475656, 801901316, 421974169, 296973135, 762474289, 727305768, 215323576, 696439124, 593548749, 64230422, 437402477, 438667858, 904631107, 622898362, 265380611, 519909519, 852113519, 353000294, 499789345, 57704680, 442773215, 725550445, 431901993, 811940960, 750503078, 113971957, 888443766, 999362899, 997234137, 729839789, 253843810, 10752953, 215254607, 204415918, 592050459, 961853866, 573812919, 517944513, 249042770, 943537627, 216869072, 269810071, 769290470, 736287768, 407886382, 608162851, 176556005, 69675828, 113257610, 935911109, 752162095, 659444503, 294669968, 526542956, 522166687, 173497546, 893606697, 398364014, 736037141, 355134795, 392119107, 450743421, 574287397, 552918074, 709202625, 119895224, 595076893, 317324889, 321988763, 798225582, 301223381, 621320828, 662413538, 873082242, 813156101, 847647114, 260119130, 5321742, 323430278, 444523052, 212414270, 537485162, 230555240, 600701671, 97753135, 470646508, 276020996, 398835219, 577386341, 737990549, 359878002, 425449448, 204942758, 99935644, 796457950, 239403193, 935945579, 276781106, 748002182, 636146900, 7907075, 66417975, 446327393, 485104756, 600922541, 67165256, 246104563, 284875447, 885617568, 93746876, 430003545, 895979538, 157370256, 541267637, 579331603, 792345401, 231460723, 480489846, 885101392, 253383780, 65612224, 175357974, 557313242, 407939831, 38494991, 817398830, 910558551, 171935256, 811625034, 572601280, 973756649, 726782183, 244012637, 483963880, 713304084, 844697008, 223220629, 271031028, 73995981, 532607513, 525434143, 933536733, 228843344, 157773962, 871734987, 901081431, 890210060, 254577291, 653191426, 516049386, 631782722, 924948901, 615690358, 502939276, 509238249, 465385333, 581899600, 349882115, 95251199, 840834151, 620414867, 483279083, 313543515, 664381049, 843577376, 649290721, 847559116, 629916351, 705357207, 119832285, 991646069, 672818310, 688820227, 161784617, 847912973, 456515453, 711165328, 559077415, 491557954, 62874373, 970094169, 510138956, 940988898, 232762883, 246127145, 502326188, 154077381, 329608368, 41071573, 892357894, 992023721, 21503845, 867244747, 755250433, 210836742, 622670548, 614913904, 622725063, 106585234, 640810906, 928893001, 209377109, 143499400, 490271516, 931743157, 595187912, 789437350, 534719115, 767075351, 441516045, 374328522, 7144276, 272691427, 488211150, 35416843, 232005120, 172638590, 192640508, 325242748, 479442880, 624553558, 877055869, 213783643, 758970946, 683751298, 867667351, 569551627, 536099666, 429196815, 78646653, 230097671, 958845023, 83477960, 766868115, 186539194, 560581125, 569507022, 774449519, 451407739, 959479699, 146796180, 926986346, 107397073, 639648253, 171889664, 152509930, 593870108, 920284406, 453993606, 526920626, 482370724, 849549178, 175797662, 703945188, 678130827, 303160918, 293782270, 309378314, 247612626, 669968029, 895579013, 911150887, 612666006, 858332170, 710185587, 703219738, 91727101, 5651961, 265824615, 159704376, 765704111, 279644856, 362356031, 530811148, 93115749, 211945953, 766598486, 658205586, 261421918, 655621278, 637105919, 991498814, 765639250, 14269671, 233482958, 530727206, 371116860, 581069172, 524608143, 91374798, 581106628, 899703171, 521370731, 991528905, 393415028, 79222073, 726030108, 933214040, 992279032, 163514388, 681958185, 802431878, 41986906, 48635122, 39225168, 435884632, 871942352, 547258983, 995519376, 499938514, 347097129, 491184862, 630953719, 417117450, 522791608, 346050613, 333133419, 780908411, 578031941, 880361815, 888736921, 432016569, 431489286, 343967467, 850310708, 222680319, 294002426, 141460357, 670956260, 146617965, 29885916, 10777899, 132816247, 933249069, 639069371, 636495915, 62454862, 549460138, 331241046, 466664156, 233084921, 316839709, 867830128, 49296216, 200540344, 41470884, 74101206, 149037875, 976097078, 356876632, 590370121, 601570924, 108288881, 268738150, 804281181, 377707925, 355207263, 340148047, 575161158, 124042071, 383938037, 727441020, 226983379, 903229226, 857889911, 813447137, 98803652, 651090382, 753742517, 719350555, 839335829, 607328930, 559011195, 219864231, 832830783, 759681931, 474129673, 94656977, 637982213, 858576344, 362347640, 242186701, 509865102, 843720555, 107702094, 312455647, 141176378, 878094179, 820332250, 750493184, 764130304, 662927732, 321998538, 453594106, 339672822, 355534885, 697610263, 504259899, 565959841, 714836121, 229297733, 37664807, 575582193, 536923605, 898916654, 901747484, 664376684, 738360900, 384633833, 686625398, 494724319, 935199042, 773481841, 312931235, 266324271, 989534371, 241778416, 943307620, 61296506, 216136751, 712950600, 564737841, 384487146, 202022955, 380778028, 583232494, 97916651, 904395632, 700244780, 535499375, 530899094, 644744834, 520965459, 741435663, 80821323, 466778101, 323248111, 147576537, 135442475, 719833993, 911943223, 615900973, 35427271, 725769294, 343701017, 669136440, 998085666, 304706267, 83772052, 823126299, 131225309, 635803911, 423836796, 620968405, 187470897, 611833104, 876070376, 896514327, 830805753, 962302483, 583703543, 776556093, 768308998, 375826610, 708244261, 24896596, 796038706, 228511549, 443799247, 683761814, 880697842, 170232163, 187867032, 159852589, 526578450, 79638983, 861626526, 870905448, 18955156, 152781926, 66918037, 337929154, 418639342, 84883043, 383915527, 849840613, 331129306, 962520441, 746629503, 291592385, 563093688, 946116833, 166794407, 468155712, 572681684, 564990485, 994199915, 877021745, 340910226, 696085449, 16476970, 995585523, 723380171, 900107463, 571712623, 382770739, 678784004, 651313731, 849437085, 865015316, 638473999, 187579566, 90477295, 69087948, 232790103, 487123881, 970954373, 712931580, 940707282, 976075043, 410792455, 810830106, 570512063, 915745236, 145440308, 226865833, 719874397, 441028524, 182813143, 109279400, 603776107, 904274645, 832994060, 151823134, 672255765, 161110102, 147838348, 915726971, 30940601, 443820985, 168182586, 971668815, 683603472, 428643690, 781118363, 388890929, 504720153, 522711324, 284034289, 369449266, 800294689, 10928038, 318202903, 291495097, 910699093, 500661913, 672799980, 617635321, 996311392, 402995659, 430178337, 192244638, 329116648, 252009893, 509899993, 276947751, 605380729, 294440203, 991169179, 863003810, 283378103, 340780656, 353102744, 818604165, 916343608, 94125401, 28042916, 540153628, 689165923, 59368178, 68002625, 276024717, 510341182, 538546444, 363726489, 842898878, 930218866, 497683051, 746482032, 397390528, 869620672, 426259208, 6024448, 889534222, 251316340, 819814932, 134725778, 271667458, 890431182, 950611356, 622343990, 678320635, 92773326, 425143547, 279558720, 609036730, 735649564, 64142788, 303827271, 391438158, 417163291, 155546765, 916763847, 310614413, 138348249, 9775137, 456739521, 311127424, 701782619, 92919320, 602235295, 541862056, 292092679, 631805064, 502496813, 737415706, 465656872, 782955118, 670413782, 195047974, 488584983, 207850582, 356637263, 679218402, 980578042, 881096002, 597970843, 213520772, 797092810, 839904550, 8389834, 715189040, 643367873, 53572180, 418019094, 155508627, 729490914, 172248372, 866150098, 370981775, 85810727, 12471974, 498091235, 42723649, 385338132, 300678215, 998579403, 1700941, 843578654, 937874827, 448836585, 717979223, 301861307, 108258677, 696291362, 184525272, 456105002, 479305057, 279165170, 514070395, 970822886, 402946038, 386050827, 470284688, 777525097, 972549646, 118159725, 212124016, 568816084, 576018686, 629839290, 625758167, 463180601, 812359714, 866245330, 961879107, 103549273, 516735946, 890485881, 383381527, 984818223, 942564899, 887628153, 831146883, 861571857, 70549810, 924608314, 140942890, 904454289, 989621920, 193528800, 999892005, 881439621, 679256100, 101912196, 324051074, 776060610, 596797948, 215064649, 682575897, 473540502, 420689316, 178170054, 730813232, 863121716, 414404748, 820249884, 978775512, 273400079, 428078541, 267189964, 145997124, 307381314, 706443757, 994073360, 315086180, 666495940, 806788821, 433636167, 389628414, 335596604, 739267692, 688548208, 529555344, 486438747, 409459988, 459234229, 698213423, 951688572, 225687652, 418090140, 596202001, 277658171, 714515848, 24391047, 458618247, 516891721, 989984454, 878491708, 245934903, 744256819, 184390841, 435946104, 675225902, 890283734, 616829102, 587156114, 54560863, 683635321, 741333877, 595985686, 547150676, 491597883, 269008020, 872846593, 572804086, 940408563, 999598917, 498809400, 962010664, 742382958, 162214708, 742435274, 406014036, 322955459, 871118830, 826577774, 840334259, 312794600, 349152423, 496130235, 37978401, 473544071, 678255435, 769215574, 772502490, 541138068, 826327765, 396580156, 973131008, 231514272, 334099066, 246283271, 711822878, 198715050, 426760613, 524141621, 184851984, 766364561, 561071154, 532857926, 181906267, 623210470, 116256481, 227554856, 83211685, 219019899, 653109558, 313955304, 486799291, 795193301, 713617502, 586923817, 710544867, 193902382, 783432960, 559703288, 324821673, 530503068, 291871466, 672830263, 849940690, 603805933, 705792707, 916319617, 888384664, 641001820, 341050532, 187037453, 546091835, 275297625, 564104367, 463180282, 784722069, 584942062, 341923879, 3489153, 475074851, 495115094, 656458314, 20128243, 752421141, 988264768, 544102855, 18128901, 131378904, 97643145, 854379361, 60053912, 842307853, 341772812, 278150259, 460405886, 521454280, 944201776, 803732858, 377271797, 874631813, 536087468, 734346183, 746516611, 796755960, 393147094, 326723044, 920439442, 396426027, 674167606, 662889825, 593251148, 289040796, 417907799, 627974396, 278799179, 478850999, 593192586, 437320574, 423976339, 561582254, 791024360, 975862645, 932391315, 123689544, 771916785, 110252300, 29294742, 665231590, 142815076, 344131347, 953609809, 552278451, 478033529, 319952960, 375671731, 342216473, 945999919, 898859699, 820255695, 186761236, 50326337, 187472448, 124163904, 516618233, 423154385, 553476844, 567543921, 896091077, 970453356, 382821092, 249235245, 853576460, 131011972, 94527242, 1355084, 458112238, 905692900, 70658899, 700365171, 524459006, 691078340, 722804191, 790883511, 143357515, 507580634, 637530398, 223725425, 182122933, 972104792, 107568155, 887035537, 25879792, 986187950, 346762295, 598693016, 886459485, 236481060, 927507371, 718851671, 188142923, 286467095, 682057828, 870490782, 410163308, 81029433, 999498387, 579539172, 80639512, 734451190, 15574047, 93814500, 951963784, 933481032, 876872171, 518678669, 97081635, 163687585, 530640774, 777939813, 757163439, 574496208, 800546349, 769637953, 837272741, 522244768, 547657808, 154007475, 498467380, 525567777, 905547136, 145347763, 756667113, 244735620, 544873407, 37976493, 321171669, 991486944, 152487871, 763994272, 972439462, 475357225, 718977214, 898314247, 624287587, 88513267, 162487938, 360775922, 940361067, 140543189, 558786589, 438634163, 912471662, 345451647, 905114593, 814988496, 149853100, 185701091, 561205514, 485400172, 616945562, 443663906, 865432836, 488724305, 883418701, 760165759, 452724848, 12899815, 389768126, 379549121, 638157172, 721273471, 566207117, 139898843, 592726450, 312706360, 107553009, 968729256, 558606802, 641940685, 235639306, 50027686, 392050413, 807847974, 559184642, 911178411, 552287320, 805637890, 61284429, 518844330, 430809997, 574693906, 21061751, 439421477, 484504699, 52743663, 535927420, 274852109, 704803012, 682928028, 355615917, 714162277, 715505404, 417254520, 810991045, 918380099, 82867554, 967279580, 650977245, 784319998, 915564074, 689457030, 241922114, 508311938, 285418421, 506641266, 805034364, 722126109, 229046862, 345637713, 731987455, 533360316, 443472183, 212204045, 803494783, 952043508, 66088339, 617688852, 119316282, 683845431, 422183000, 713858907, 860516283, 502513942, 71442630, 575369426, 394835005, 788228731, 759906814, 457738452, 636401874, 683205930, 150048214, 686140176, 311981570, 130836156, 241354992, 647413944, 968653157, 716540934, 117384102, 872964726, 986550571, 467408717, 130463135, 830734994, 65773923, 61370221, 278569657, 444775961, 403997273, 395301638, 104742584, 11968191, 843323641, 138187857, 512221530, 35173674, 545115359, 298808903, 87371169, 421848423, 764264048, 979381378, 92961053, 539683916, 787987200, 145700147, 100003188, 199023398, 918954815, 212234660, 194397924, 420206909, 508358846, 73574443, 984962027, 296388172, 8690839, 841680610, 540381861, 121464824, 405576644, 817426821, 551134297, 359570770, 783353855, 203117019, 554526064, 661842416, 530427192, 959753893, 420872561, 682988564, 523638607, 744941988, 794032054, 586430676, 799344947, 535423014, 998203863, 702604419, 722556747, 550188054, 94948457, 458097836, 806992742, 73049073, 144951662, 19080529, 538413875, 530081416, 227108769, 236713265, 155780961, 843444931, 949292308, 480694261, 304966942, 406125430, 51254732, 521065996, 64278667, 938004265, 934747804, 657058478, 128090878, 390111318, 115117382, 176012673, 332001993, 446834311, 182536689, 356786778, 525201809, 486999740, 995498191, 362978690, 10552201, 268797295, 78776580, 888235492, 146436894, 874892133, 345003973, 186502407, 521870448, 238584343, 913620456, 891284313, 951952946, 295679090, 815559882, 572645564, 210576651, 216938439, 600921841, 730533947, 579701858, 601217122, 402164843, 924006099, 45836387, 9828771, 825398335, 309474364, 518596526, 792229020, 581625830, 453053100, 770173387, 885553446, 621442437, 350232752, 623071010, 308858999, 536214528, 542625749, 954708232, 758548395, 631306004, 317498119, 8410491, 766122052, 177669786, 210211550, 828559832, 401076137, 300840239, 37915371, 153215358, 510385402, 37760394, 719578100, 30344642, 453951774, 429573297, 838789252, 149002569, 121451612, 362591346, 190109087, 974530800, 463282011, 598041796, 180258075, 762197533, 978532245, 67263693, 234963224, 171046101, 910325810, 589191256, 48991600, 277411683, 189333576, 810182629, 302788034, 879871715, 590692919, 121943822, 250482288, 705459566, 752911404, 229150308, 928063871, 459136965, 536305927, 244891417, 152268904, 508055829, 705904613, 749850644, 601172646, 643599840, 840161363, 603405405, 573541612, 945249983, 30909684, 795330802, 224883936, 682056967, 38991786, 964583650, 362135811, 743373518, 637797320, 992054423, 290526593, 959178720, 863692717, 412666728, 271853299, 400860334, 968672221, 396258832, 821260059, 731863596, 754574212, 525363689, 323065140, 4088488, 586382276, 445621905, 566551907, 862296066, 410854320, 658957109, 125297003, 914395831, 212144341, 915214572, 197448175, 784671279, 725395900, 769356497, 801309274, 517994611, 517187704, 44545261, 470053405, 909088299, 389798082, 57241632, 665866302, 314117592, 675714658, 114019963, 984278617, 242651054, 775226050, 543927116, 56579493, 415657204, 12972109, 201195065, 8632463, 905849857, 863196224, 345253763, 37819315, 526931775, 597236925, 790603802, 836838025, 288360536, 759318131, 523331578, 684832224, 500598276, 747480756, 48930598, 865035093, 252755858, 407845141, 801564584, 603579699, 508527010, 924158254, 57870647, 114318268, 852326769, 988346137, 761315736, 923224857, 454979486, 708747760, 132949871, 461235066, 868026551, 829049975, 303353158, 833288071, 399136979, 916367539, 341907726, 419503313, 495818967, 266053262, 223092067, 546167535, 926931616, 356286256, 232171099, 450758172, 477665403, 751866359, 639462603, 883553192, 186729678, 736760533, 173969964, 965887747, 656461771, 763838997, 290647796, 329889857, 430219616, 444746212, 951701839, 363899299, 497448627, 247355551, 20275675, 499540657, 534343360, 826650240, 223595710, 667582886, 612349901, 136558590, 638945436, 251315599, 623058784, 810070019, 158890854, 338254089, 29739023, 751126680, 561208428, 36570919, 451267198, 148016563, 237633076, 12524147, 978965853, 372016599, 647675917, 965231134, 743975954, 801705853, 169081077, 700875710, 708338016, 126878585, 76361776, 71922371, 689017066, 810791059, 937919849, 191408990, 284438904, 900143405, 787359364, 581951559, 68841395, 371878050, 828534145, 555964458, 185496663, 4358020, 765223338, 884264328, 302919640, 14689283, 673987956, 42987120, 145156708, 952973303, 670174895, 552197270, 40683916, 317319084, 372659891, 399993019, 768692580, 628636136, 198015564, 702779129, 678162538, 65319531, 790255951, 225740287, 454689493, 927652214, 69015832, 194813891, 791397442, 865227174, 281793132, 664819379, 894979034, 193020911, 229750944, 876873120, 56777381, 601630431, 563193518, 586916511, 755738252, 536288670, 998911301, 755004023, 29027188, 159536489, 261850575, 441839582, 193504714, 822722425, 782379260, 208907237, 364102837, 495489008, 751875671, 627442910, 438090726, 776551283, 817857784, 230158780, 76447796, 433299929, 11620888, 822333187, 342971568, 327609676, 947461902, 156062886, 504543553, 105765841, 977908833, 896538014, 660603742, 27811837, 33726274, 63837407, 304401173, 463098975, 124111127, 523974617, 326942457, 883124710, 386402127, 441160449, 289946168, 696077275, 91311401, 874491636, 515853551, 671613354, 936079669, 905717541, 400281798, 779506464, 508838970, 406352710, 419240432, 312709546, 189274595, 269589274, 18852057, 311945161, 448477544, 987964743, 532584149, 931668961, 628628441, 486878516, 991118868, 168097704, 334707487, 423906852, 929680067, 490653503, 687307340, 72983908, 6803547, 600272083, 385336848, 209061654, 38228256, 974116049, 712542625, 907271553, 348441874, 603010476, 938579681, 75790459, 406431493, 43733600, 116593978, 475515837, 595201427, 909702357, 505138931, 682272584, 850397062, 784624215, 9747543, 843948673, 227940961, 613461553, 495969713, 157838619, 938381587, 397188214, 506025923, 457105546, 444600612, 252302882, 971867251, 478640153, 249084924, 630517837, 516838805, 43266909, 476654385, 234448657, 755143461, 110054091, 435966675, 254156594, 227874161, 711406829, 625003204, 233338166, 676749261, 440198298, 659523940, 736376940, 769879237, 146408934, 406317068, 199525069, 692931931, 281228802, 161676244, 997573093, 334571521, 322044743, 870697509, 885697303, 259056028, 970238459, 148885454, 296312493, 758838123, 199923816, 623688137, 721838438, 40218616, 399830301, 391930481, 325030937, 781764557, 116256492, 262584526, 990552960, 476110346, 381768516, 277502315, 34874241, 312107272, 432961204, 615451726, 172449863, 966741881, 198442774, 157868066, 66272226, 216340730, 73163303, 595829465, 400474141, 638023204, 72310961, 512972902, 285011573, 482651680, 861658973, 568452594, 950917913, 132870966, 679469130, 590921866, 877180562, 280567177, 817175508, 856441791, 650585175, 641793562, 562685965, 151286556, 868935174, 832815760, 590356050, 273083639, 981622808, 541628731, 208842350, 396259516, 29066410, 8713287, 856917460, 64395641, 452033090, 411397413, 965104745, 820227979, 375163404, 771878840, 487031196, 453733438, 606067223, 986785548, 938545459, 185082361, 285570049, 151888180, 574624671, 631596589, 736127807, 52527646, 860737791, 186029609, 695240098, 927211334, 535525781, 305380527, 905081126, 170949891, 223834187, 449593706, 918888273, 274459487, 572195336, 784326963, 896353142, 821530423, 355847790, 556320279, 603187900, 663932519, 972398396, 893409576, 128951052, 230173618, 544166699, 955930702, 565160021, 974968472, 802244010, 557855967, 248166725, 541271692, 240897911, 600190089, 758998943, 183159066, 987510231, 356614970, 618485659, 188306693, 769795361, 700222751, 475162737, 332391459, 492406813, 447170277, 728875312, 505126057, 102441411, 133099565, 653047302, 563492376, 320460709, 725887805, 286186256, 731318330, 923561143, 572518687, 19637124, 749501323, 61977033, 394195168, 298255240, 807866912, 495356365, 848218027, 146641430, 151390526, 395463103, 239802934, 138851921, 417098761, 160935770, 813117992, 595718116, 821293996, 888828793, 75418845, 475939797, 313132136, 732124829, 942969534, 816948498, 359060491, 476314593, 575410067, 739557464, 223142078, 499946564, 174390050, 855147609, 446683368, 62219803, 356162592, 451389937, 56577965, 551309101, 733117620, 286256398, 819181740, 85986862, 483892693, 636690609, 764637244, 897340269, 516230629, 914251081, 956623015, 495490580, 235000261, 657921193, 259645857, 699226433, 665413284, 87322628, 816344505, 801175249, 934303264, 584452353, 767690559, 612509692, 235832003, 6267347, 178580303, 341540826, 605312784, 298880313, 327518171, 53649303, 473999042, 668845244, 890324693, 382036888, 674715115, 488740833, 792142350, 298387026, 372890559, 775878047, 989756771, 236756447, 322033017, 126405280, 703544667, 718949955, 655431459, 920240745, 399592239, 996750888, 541373982, 733151752, 648407796, 433786232, 68122803, 387598330, 374537667, 782694623, 352827953, 756667776, 607385725, 942033084, 634868506, 991054652, 428084681, 568258184, 19019013, 999753917, 732909061, 622079309, 61961621, 785562458, 99522807, 525690666, 944350696, 427269635, 645391316, 959469439, 496280046, 531572770, 123849291, 502716121, 991137586, 765142977, 532064219, 147082419, 511818698, 884039504, 551663707, 909063908, 172774893, 252172921, 326668906, 55335694, 296388397, 371737241, 555546449, 637014144, 860648895, 130173481, 189758871, 785551289, 708960005, 946956990, 212919712, 222318584, 692379719, 771065111, 989909488, 142342944, 252000971, 93135354, 863134826, 417879277, 321378678, 864967727, 805574323, 227050956, 126695779, 435439686, 137115152, 603300503, 644844368, 954895843, 283763482, 786052862, 84897429, 765985458, 262104129, 2155960, 273553746, 362143442, 425821982, 636084453, 74850028, 37752612, 315887962, 790317171, 387720869, 20813448, 801755326, 153714341, 14784710, 462897360, 843757853, 410721199, 759525316, 662657941, 746529066, 976028787, 40779032, 102421984, 96072038, 593523372, 92381238, 393273068, 446491528, 711475904, 501815223, 682015419, 895903399, 418820165, 345238808, 771010673, 644562251, 705810246, 627423795, 344845267, 651378187, 998645832, 555597465, 323830914, 910940115, 417310574, 552467033, 674564925, 669225558, 861201132, 656599654, 98439193, 61744407, 896190296, 604321754, 840725772, 192870258, 50708362, 21133891, 233940701, 573685723, 982813607, 834161672, 747008730, 612763067, 150757854, 815135626, 573722338, 403809594, 917379644, 665490137, 347710393, 455574384, 43000315, 48132335, 846205858, 406924652, 77400199, 227756367, 323274915, 208436195, 13489271, 766990827, 231257870, 19964225, 990668710, 111059100, 84938389, 879931902, 414695952, 305518805, 151065436, 225934598, 813717974, 636216518, 413230273, 920025527, 305303263, 774988105, 262096066, 418376943, 256646860, 224998361, 100151367, 750673664, 292153916, 758749571, 900284793, 228164331, 160388373, 687575757, 636409388, 648491231, 380721303, 783593115, 583723079, 603871490, 969427100, 315248649, 305922399, 485034462, 844396855, 596161314, 281947096, 313510011, 55142441, 216056019, 202030548, 298341865, 896997320, 377533245, 967074741, 473513351, 880141749, 798767470, 271306582, 369878538, 471219779, 677553824, 803605248, 433877650, 911199321, 701135839, 110243119, 292069579, 115688289, 514832370, 300868938, 763332033, 620201733, 20407197, 369340577, 217567120, 319481034, 238164674, 896221719, 427103622, 944447622, 141463601, 695231159, 48962050, 619012880, 668702293, 52486206, 401569477, 241617277, 646837029, 433450945, 830540846, 962726206, 674840256, 131646355, 784564580, 331821926, 633928993, 220826258, 298266145, 951987231, 572889175, 204993520, 903007162, 579033074, 564125358, 107669210, 599277167, 181806924, 259553443, 413757181, 25852834, 755138947, 688758721, 909465699, 322339095, 134860422, 29342667, 865617590, 791221401, 310629316, 707484859, 408716182, 531695879, 341521551, 679132446, 585808512, 468409907, 154553811, 534451441, 981018760, 989948915, 586618227, 237109296, 945550765, 907808714, 42855721, 189352214, 718478652, 511066200, 243338029, 933202772, 68300815, 398108655, 537857208, 258796064, 995959632, 936563714, 194753457, 767487580, 891451370, 843867231, 696237193, 127338822, 873977523, 477195222, 254531626, 687513623, 73069234, 908839578, 445537551, 101388002, 173986794, 134694511, 726831932, 571542177, 199023144, 38201268, 316726965, 331884972, 125980530, 446320365, 143381728, 382283578, 475160363, 579116204, 629140064, 24862597, 843771349, 20832518, 771592702, 842458730, 546430212, 559331570, 898431889, 232320012, 928907067, 378931236, 939795936, 873652013, 555170488, 932610079, 909887216, 205152908, 497809357, 160272158, 336111517, 168200925, 712236151, 415886955, 443654175, 11084778, 369552258, 632106468, 578578555, 266822424, 487144365, 54407623, 761081806, 75733911, 789758106, 948742601, 108875959, 964283318, 19106669, 73876307, 476103775, 675310299, 293486746, 276177652, 627781323, 353228612, 157964066, 678246846, 934355300, 755052503, 121748664, 188147673, 222575270, 450637608, 271693548, 259022538, 137016718, 320040148, 698003484, 395466197, 721661126, 123765861, 233112867, 603457072, 379352752, 233001350, 414572431, 324927657, 548126417, 421273237, 793673331, 904351239, 359290430, 175378322, 368499643, 864562636, 632192407, 247284288, 769779717, 740492322, 597614301, 831332274, 873357538, 761310568, 31836991, 743669651, 368212674, 601213655, 189510685, 893499218, 424636418, 104212090, 116366125, 981758294, 544187161, 827478653, 447252479, 189312643, 397832467, 525544933, 696817909, 367480957, 64561222, 596890671, 505428501, 328912283, 462864455, 79325186, 16173149, 789505313, 649254555, 40356727, 176518095, 24293704, 709649558, 260746562, 742915104, 998321975, 176422211, 343381236, 835715391, 983231524, 918862471, 645478617, 904608068, 162657115, 313477234, 919173278, 475071859, 548889926, 85284333, 856703885, 124868962, 831866606, 589981252, 658177679, 38325542, 981847785, 711427386, 287136089, 464252765, 807642852, 257516899, 245390431, 156136153, 971072313, 124419439, 537254843, 865757717, 65648627, 619892058, 927928675, 353140806, 524332951, 380232347, 147573923, 405514173, 987156483, 6373447, 871895509, 306430975, 792380654, 114385636, 275525220, 505042659, 302585248, 260256837, 530719097, 914134183, 256295031, 589743909, 623055842, 495043866, 917301324, 343631369, 769648565, 649311434, 590741039, 435943232, 768351388, 57048669, 262715689, 25142025, 318729056, 467001603, 757469976, 128859522, 885718313, 901954562, 947165018, 474981970, 346568049, 545499484, 541312233, 407020244, 846446784, 147201069, 837076671, 284521281, 527202646, 604037953, 513841382, 935446092, 576051654, 137148501, 248995757, 293893362, 460016008, 314963385, 353732372, 318897554, 938358386, 629937785, 583024616, 315204426, 782465319, 553256794, 699480163, 428459188, 187815792, 163178093, 99619346, 66558017, 216311451, 15778449, 862843751, 616468275, 221719369, 910669099, 622753387, 113798359, 102334179, 959474530, 504625143, 906338616, 942641799, 442673352, 628771656, 735073952, 442644049, 399023450, 504887914, 91636188, 61765783, 703489382, 310245295, 524009590, 857663167, 907610869, 226324379, 548834579, 404742332, 698216191, 805489293, 21399253, 590228759, 470189333, 131737023, 702297389, 449346182, 898030176, 925165658, 908690527, 6625962, 9945310, 539632300, 383376139, 434363149, 768283036, 673143640, 800908317, 210358154, 754143030, 63987555, 22017131, 938705115, 660365746, 237661053, 776886275, 972058792, 497996606, 406366776, 214704499, 643844103, 804949656, 884284094, 670608025, 60734642, 776112857, 48277279, 343740758, 706380942, 168708980, 597854699, 507077451, 23972635, 573519763, 863169867, 531133728, 803213497, 239585265, 687451888, 904558976, 163449883, 631991729, 718985075, 480565206, 500709762, 26659910, 469191195, 183376299, 429616918, 896730620, 561104980, 508425031, 661123137, 65589640, 513633806, 729759740, 617722605, 982517442, 395294519, 798049162, 279186603, 351420085, 805401103, 449310657, 369446688, 325454934, 530972183, 89392517, 323068244, 591308537, 332477404, 856982411, 530932298, 829063808, 354107839, 19340164, 494141633, 538586602, 43395100, 312166099, 364309906, 285063814, 306228114, 906561159, 128289064, 301723572, 790024577, 632288651, 433132441, 519511445, 477326550, 840838219, 869840651, 231215483, 212530824, 128701354, 268382435, 827862289, 988879734, 440463511, 442800967, 160613923, 388000, 689308981, 812996255, 75853467, 501171477, 323493238, 86187426, 26876077, 486914617, 9453761, 185749142, 543072533, 905066873, 246544158, 698292568, 293972975, 781572618, 144727586, 628073201, 518293714, 944995217, 399991027, 199232460, 492520495, 356034354, 413693259, 772000211, 833477781, 448929217, 406993988, 331425182, 903561593, 565362278, 798690694, 379497461, 469847028, 637466695, 540120971, 616690916, 955230283, 56200999, 164653518, 121292497, 140507780, 265688082, 751012087, 908719073, 147295075, 234320633, 969600079, 655886938, 419553648, 184927803, 707205588, 62754338, 164091525, 627945009, 485596606, 900730640, 30490513, 623697653, 490133297, 973256675, 234573993, 319035587, 166385617, 901469068, 694755680, 952520998, 844688321, 725205172, 916821682, 632457294, 806969122, 317879055, 383969381, 578244613, 811324769, 289348319, 140102775, 309876393, 945656012, 760069597, 536299759, 651801869, 187493731, 960612237, 193513262, 357997814, 901822078, 697269301, 48889644, 619354788, 629349913, 15431752, 220869758, 600411598, 53515304, 420509262, 800727003, 686025485, 732092901, 941884259, 741773655, 795913751, 251880864, 139108061, 14875756, 361514290, 452265289, 653603642, 783402374, 728061342, 690131602, 502604874, 331125071, 98087117, 157531549, 518135383, 954115107, 899558751, 520625224, 146787254, 191417036, 880793264, 891058956, 610250243, 500540603, 373404673, 784433529, 493996244, 710138449, 138260420, 589456098, 19687724, 132944186, 961637089, 212524293, 227631628, 286647924, 429028196, 575615042, 767722227, 716323191, 662154413, 884389155, 279093157, 595881369, 494248470, 202092183, 498881220, 288859121, 567774235, 173005794, 835904962, 162203032, 26703734, 553859594, 880523001, 757803788, 411201340, 895049790, 453726967, 919194579, 683403741, 601944553, 968699840, 650749735, 522985395, 965202744, 634090338, 709233765, 583963764, 861425251, 588099412, 676800999, 652609144, 51082514, 910264445, 832148200, 987632168, 328263285, 963948665, 174904242, 105434577, 185130125, 176210899, 790525232, 746060002, 998843334, 555273209, 670083359, 277277772, 775814977, 268308285, 340115472, 146509585, 914385013, 716193106, 75929793, 276282698, 191670021, 860878913, 357534460, 761720033, 476712829, 739090826, 817310613, 179773445, 503484419, 405661582, 828847852, 404468093, 125313182, 562182094, 54833929, 398254709, 39196756, 715495507, 262123852, 914049327, 491518148, 887050515, 749602204, 291474896, 45749227, 717127860, 836006005, 654799283, 300297893, 299616891, 866596849, 205001287, 369576553, 372351718, 981389446, 915808859, 644559122, 583718630, 298141947, 557261006, 652186100, 828293965, 865649797, 728048746, 887206812, 488759111, 857173031, 640195775, 231219715, 283651663, 429893785, 472819060, 646587096, 498861453, 460402922, 72424117, 469971613, 304697044, 416853079, 510954533, 752531048, 380187779, 928741930, 545431238, 381956548, 209681366, 528750686, 945690092, 15652209, 328534637, 400372633, 896022116, 518634025, 677970067, 145573182, 757514379, 293377330, 328395888, 10145141, 810834676, 292794818, 937114932, 561900305, 469023198, 254764507, 707180501, 749536626, 544035268, 851683243, 773661953, 707491694, 209501620, 50236291, 118136241, 589314896, 73216123, 74108341, 897007925, 102768342, 648839991, 158296083, 211089292, 461106250, 803991154, 57062077, 312031827, 481622223, 168665438, 332486400, 390008332, 181979577, 54497737, 371304867, 392581563, 896268607, 962460227, 793607473, 630287943, 80935751, 57247287, 766558458, 261444243, 500756429, 425245386, 863851333, 237707722, 314049360, 89372115, 987384407, 379376359, 941720168, 615039759, 186770256, 795372996, 35362500, 311195338, 174609434, 33218062, 632618956, 647742644, 400516423, 483910514, 327664990, 733492876, 372897744, 591437967, 555762772, 615853669, 651955055, 164500082, 65463807, 77136709, 787128143, 972419859, 693620512, 415155995, 361783720, 539858790, 772191111, 327027061, 434144137, 577746917, 588810221, 127291182, 384136933, 128785218, 765140586, 952789923, 219862718, 666365774, 486815479, 265209369, 793362141, 485680921, 772346026, 996687965, 378851240, 292879552, 220200534, 770826181, 397689373, 843420929, 456775619, 285869918, 273569450, 741563025, 973022609, 562226396, 329949901, 470873239, 312322965, 456009976, 360521482, 937509803, 108999236, 964982973, 612136156, 513097338, 851066221, 493701309, 17233481, 433679354, 726150595, 576272032, 345746556, 22191460, 843005828, 21317663, 653628865, 377284833, 880955930, 967823739, 700722402, 856356026, 761605154, 388551018, 149875600, 303663662, 29776536, 637283560, 280135925, 238048369, 711481104, 127555515, 271976193, 280442141, 260199898, 492478259, 217452575, 192649288, 734975681, 986209604, 631127640, 71696904, 941794739, 780141072, 810784114, 165167304, 8761889, 364387224, 422886951, 186820651, 857602638, 465750857, 908721823, 43489582, 602480354, 101935562, 226548310, 956088965, 664257661, 568327457, 960997675, 514878264, 75714256, 587689060, 42603898, 261219621, 943043308, 687787339, 37470684, 580208208, 68884198, 378945244, 178425907, 54385222, 598891955, 244328181, 215409697, 574548620, 850559233, 430521456, 963772889, 158427287, 497046559, 913255195, 554266062, 487022874, 972705379, 578152302, 310293953, 138610873, 941137897, 885219512, 250708336, 950939729, 144240851, 263823082, 386666159, 382848751, 713871842, 428294160, 145935090, 403617600, 474187766, 171428120, 320403543, 269350981, 699767074, 790453987, 884532616, 226416931, 40006263, 634661437, 708407870, 572933644, 737922421, 723191819, 862303223, 147473646, 762388528, 210976162, 293926159, 743638087, 662747484, 744007195, 441580777, 506164802, 393807920, 124048571, 502663388, 30971345, 640994239, 825295629, 219622582, 765139451, 308828709, 409216351, 34791381, 666753933, 947726354, 269505629, 8585522, 525329118, 696829786, 90556606, 773888808, 696453636, 838761940, 669187381, 817986588, 181813947, 540769797, 637727638, 937576748, 335004511, 594517902, 276569281, 474899263, 657310403, 505540045, 194292202, 575574567, 171068744, 18506401, 739465379, 369583500, 510654211, 451580271, 723579956, 720348065, 137118157, 656215601, 445458187, 500255906, 566721177, 447860714, 362436145, 94804242, 300876299, 431920564, 138711060, 982243566, 354303222, 612230403, 859509267, 810742011, 946333571, 496806810, 666053456, 625808022, 886643754, 427872690, 398825451, 732939956, 190932803, 457763208, 545257434, 592723265, 116109640, 212281348, 164654854, 183873433, 163831627, 879945165, 692573515, 375104974, 421077363, 350645752, 6312368, 613330578, 877858816, 497281589, 16950760, 456455681, 30130950, 912522531, 238580462, 882904555, 129643684, 154940508, 299453983, 546917112, 403532596, 815283929, 587022746, 868421030, 452059382, 962137852, 678628951, 812058731, 320444906, 136826811, 440788134, 962820781, 425519856, 163744395, 194456334, 78600187, 157144708, 58994926, 51111279, 423563783, 39902106, 878284096, 510071607, 760230148, 846814684, 478850881, 706228807, 969017271, 70968123, 907772544, 745058589, 197581345, 354340994, 691513855, 659484547, 889781749, 136252707, 268683188, 419901160, 343047015, 7340351, 236095707, 852965279, 203158839, 67938418, 577035977, 355416404, 746049834, 547231469, 906438808, 21082535, 932282039, 997089263, 788914633, 66235231, 159963316, 990328335, 765772769, 655574098, 231536005, 329047017, 258638426, 911519890, 248305477, 152588662, 900619682, 772735521, 116648079, 918019920, 400110875, 91491591, 620167873, 933516959, 251051096, 880808594, 450028393, 39299516, 522579071, 956053355, 216190769, 321452512, 573309027, 515474466, 127864990, 451926809, 160212869, 11887583, 501095497, 886539232, 464080926, 806936582, 604580753, 139142819, 322627872, 313035398, 229813688, 878124443, 636406812, 534244398, 311446211, 555998089, 318571775, 272562797, 828123600, 238857610, 939553310, 768715299, 259963920, 247067825, 484375184, 802326949, 323362558, 948177639, 129905642, 218049296, 340688182, 803375644, 345686167, 424275904, 733315615, 938799823, 108392299, 495423818, 869485021, 189920562, 141435892, 373296055, 119736283, 354238445, 83876594, 879695540, 869564235, 337240515, 322628257, 81349829, 246668161, 724715609, 780530411, 457138178, 390796048, 681546480, 69208109, 627077453, 205247518, 768348433, 513700234, 599617381, 480681675, 128700341, 306463671, 190803876, 386260260, 724954927, 199891709, 408572417, 862854906, 103872570, 535438005, 685514481, 121022045, 758063081, 949333691, 752160590, 300232002, 777371278, 177973135, 320910861, 840808042, 40168060, 131059786, 322054151, 553161432, 996035624, 727892008, 22253353, 649570136, 710096554, 173762459, 404902448, 484490982, 306936133, 556252002, 506575094, 756081191, 175661383, 208610169, 657054912, 974869601, 50277360, 598558625, 633139550, 131022763, 761504607, 183256546, 195659159, 756239853, 75387723, 618738034, 199480506, 527430250, 405644314, 668679586, 606235797, 294817182, 404094547, 797939993, 727409504, 301345021, 366195756, 988283527, 219178569, 402310580, 848553933, 172587936, 456894628, 427632061, 799166121, 495293555, 558841189, 586617521, 499256171, 776804732, 427616805, 251639045, 426035276, 282316048, 176318669, 804907462, 135313869, 659303858, 817211573, 529239299, 523805118, 553861499, 570704850, 85271018, 938449471, 204987093, 24700818, 876382318, 726360022, 315448320, 562330741, 161374641, 410677861, 902460809, 87771953, 580974507, 234722282, 550237035, 735861410, 828627782, 532481983, 698423843, 892508252, 10956261, 841612622, 653297909, 410687699, 128477611, 513930047, 64831000, 702083745, 716478045, 523840311, 459525991, 767753371, 569461013, 224544602, 383974990, 338838096, 704538046, 229335855, 738247492, 650294265, 829823588, 12276052, 987153614, 264652049, 889377351, 63544658, 693154675, 237202121, 696674415, 883864302, 41459045, 36196160, 319332558, 999124452, 139710128, 503916944, 658081730, 596944893, 797128759, 37755923, 487662048, 95727806, 851322072, 691480726, 836163846, 424610862, 570907344, 119175425, 342610762, 916559067, 467711760, 395379720, 914567725, 117157724, 39778105, 841497178, 89663272, 480619227, 74429759, 154699575, 197590665, 62526912, 526828976, 351399017, 360951168, 353036060, 935786441, 796630190, 579777792, 595352996, 231140383, 121490314, 767174730, 19363604, 101047409, 671051914, 199944849, 553416322, 251339417, 931852211, 438021624, 194791323, 459304302, 248807003, 149536218, 45529850, 642515137, 837667775, 191893184, 406164392, 253024165, 891602156, 461347111, 880927208, 871174322, 771164643, 33481756, 129794074, 445842795, 664077340, 409939942, 615819738, 362927164, 107332045, 355018605, 582342898, 645234328, 561385097, 766842832, 636103271, 655430127, 323227423, 278579215, 262468739, 273610398, 310372267, 786296061, 338511493, 352990772, 18634701, 977013444, 553275522, 878190699, 781979984, 349463562, 580901607, 732970113, 189362045, 80597694, 638195681, 597670532, 168953979, 225419295, 94798963, 377903894, 780319216, 677785557, 674581432, 118633732, 192172140, 181200311, 365252862, 637074511, 457598943, 89320358, 992050613, 132435926, 122368034, 54801829, 643397308, 767605139, 523378457, 580141013, 586710101, 727419003, 50511410, 164303561, 542762318, 418093234, 984959494, 553093424, 678757705, 139846245, 834767165, 373320781, 128361123, 763702936, 553796946, 953500327, 940342004, 4183648, 879972937, 707919278, 571918108, 993876153, 795814888, 323272194, 20295520, 863819202, 716130684, 389386335, 700363962, 149139242, 589461749, 59412118, 780673401, 540482143, 738160670, 625926903, 994841500, 409914282, 835122939, 866529208, 159671973, 368198850, 445681412, 100961458, 672931323, 82417745, 172456352, 168613069, 309347364, 447409314, 137909190, 80866149, 8399592, 676877253, 191367769, 933157113, 500083035, 236417511, 305944537, 484665425, 812057196, 507721248, 994393112, 766959038, 285792593, 551956135, 959085960, 24341364, 998193017, 6596033, 32252119, 734896599, 157274220, 154102997, 969185329, 912759863, 900658591, 524203518, 977770848, 276354484, 924530790, 280707894, 39055128, 645632710, 698797328, 739728930, 55600005, 912411748, 889517172, 774938752, 782090743, 564862759, 171044733, 168970230, 285568945, 514603193, 238704057, 434979402, 191028454, 517933133, 749268365, 109142681, 357584958, 368915267, 130629682, 51472110, 638772960, 767714405, 929474500, 945790951, 769512661, 698963592, 320478658, 890078499, 941150152, 668756853, 340300990, 876186640, 154264217, 384329648, 666355835, 539619155, 491870978, 72494552, 477678643, 935404354, 21778655, 335658181, 17360355, 543205112, 432411168, 973837284, 411451039, 800474346, 923085832, 701625757, 674878510, 362701604, 460500539, 588261230, 525099603, 16787351, 784139095, 560285814, 207054996, 924128598, 994499360, 614913626, 310586858, 406485065, 300771108, 427901056, 461215164, 323216537, 53703443, 788588711, 8197663, 602202107, 960366157, 253022223, 361709561, 920644230, 383142425, 946207999, 732418981, 383574765, 147262769, 542836797, 558795100, 595575434, 983830550, 916653231, 632383058, 265162214, 984241494, 645664235, 510373042, 975521227, 928502834, 394154339, 754678570, 352979291, 57528582, 494534264, 973600748, 724845621, 996196832, 875213472, 841782194, 967019867, 504876478, 42686482, 742644708, 166850656, 961259421, 904681841, 36776422, 584803355, 559061348, 441570773, 737318716, 447151914, 625135933, 619125467, 647639937, 562824119, 427237120, 704710622, 462878586, 447324642, 133936723, 200755400, 629029752, 78949913, 142616979, 819415265, 578833938, 88261575, 650561792, 608161774, 271595766, 666350049, 370048511, 64351668, 591020374, 26069474, 932242906, 505780852, 550432875, 323521144, 636769551, 372940709, 394106285, 257020626, 608841015, 962134873, 622232991, 155267365, 930259568, 998211668, 939888569, 346520916, 524256093, 651140450, 15567039, 982385880, 931420432, 266029561, 386211520, 585369236, 758210908, 245039630, 223388233, 806685795, 552737022, 317540203, 120137661, 227601277, 646839095, 733815331, 755639277, 186781299, 503543105, 234579257, 987843824, 700361682, 830805021, 396475394, 917270052, 37617417, 211082266, 467077338, 680827494, 823758295, 322153422, 916812815, 545632002, 337772619, 682139372, 552980253, 136292298, 390982353, 537172819, 610227510, 269541342, 22284098, 604757121, 580765818, 253904677, 567212873, 10768840, 929026366, 640795783, 748569236, 385119926, 312521363, 938758484, 579427160, 777926745, 3927531, 337793737, 259911325, 419739074, 407674917, 396939519, 957562532, 256174611, 333578009, 700361498, 183882646, 520937447, 797404807, 131397927, 154887708, 784630195, 32692724, 646977475, 772648148, 825849551, 151118125, 995611238, 693884025, 60202524, 678263183, 466845845, 204186603, 349303364, 470097670, 406004957, 196791821, 673337265, 583460206, 58896508, 245359349, 197473240, 380774646, 412432430, 695515811, 273309107, 596898538, 172259275, 534479619, 433213650, 836219562, 381420143, 49245390, 413490385, 376570547, 279601842, 535975417, 596809611, 221438825, 973764379, 857438744, 263665851, 247554227, 308373283, 574243597, 123616505, 404074596, 650717427, 962248120, 131494419, 120920228, 566479325, 491321281, 211862945, 500294698, 204251712, 421158394, 532784202, 721830015, 966965225, 875551489, 455163374, 667412811, 136103510, 637947625, 806582673, 426623315, 98648012, 769437718, 181135309, 203096315, 320062610, 322530795, 737448863, 257821664, 397824839, 388353484, 164838928, 25633283, 834669668, 461892684, 189236817, 4464975, 737115376, 27706235, 362345490, 577910613, 637674903, 446489281, 696472259, 859138360, 807395527, 696344438, 417773486, 291621986, 303840619, 758679278, 214791802, 862059226, 857283608, 170688984, 814273260, 162630590, 986871985, 205770279, 221141296, 238154981, 714663856, 74040707, 20714015, 936091635, 613718902, 105174081, 895837118, 189075908, 820519028, 181240769, 932963567, 552297264, 404397565, 326442618, 972953223, 785009909, 399871883, 516983690, 610906108, 971289318, 413373779, 389905403, 513613356, 444347023, 55918279, 354959323, 802657542, 364147626, 466912244, 875115590, 397325159, 401980039, 149314165, 795768412, 599421512, 160930989, 852949990, 630638597, 758523753, 163348687, 226185350, 993493521, 474578820, 770639870, 626996736, 10472192, 967101508, 229745620, 875323662, 181009361, 877825050, 175588760, 467748496, 835602301, 894948039, 932913701, 510226278, 935269805, 561679508, 442619135, 192847582, 833184362, 568930157, 839451789, 573431087, 865999333, 935769708, 794876723, 467016019, 8652512, 113562078, 41403045, 781731827, 310674864, 745581887, 176497327, 480003277, 477664746, 326926537, 534819590, 374303967, 528994632, 710599153, 558580158, 41502516, 720689851, 400399304, 638434898, 907465112, 73357115, 693543280, 823925617, 470063308, 733497863, 661945774, 144377635, 22249114, 808582175, 515442966, 415485857, 97062706, 119518223, 12336357, 518964736, 807823616, 933286641, 933031127, 107116719, 413923274, 183222616, 79480381, 682977967, 218853323, 766470573, 190261602, 429756580, 408870511, 968208809, 860060219, 186683053, 579629916, 489923466, 650045113, 584261945, 42447339, 281000834, 898750686, 794879578, 134561450, 116910365, 289212134, 963644406, 856223738, 809756471, 315847869, 827508118, 682134345, 284608479, 736161417, 981655967, 264674155, 654705962, 752144654, 299445881, 10646084, 75526251, 589986519, 876581891, 624683036, 240722315, 348053585, 898755116, 493969837, 661591005, 490340180, 442330175, 339319017, 607023279, 138878646, 710137891, 691542515, 229712918, 285304457, 765350051, 948929802, 933365493, 792094831, 635111327, 486660618, 475609161, 955619547, 614630290, 760430979, 56078162, 855645460, 823281295, 805904021, 126717473, 965134177, 366624448, 20960814, 117771723, 451508642, 395978917, 340281138, 734869026, 422448661, 796107396, 250859250, 161715052, 803030143, 72210573, 279566898, 284448463, 605321005, 713515163, 170775591, 953379473, 699422669, 128726386, 779099228, 726956270, 158339008, 66207862, 728031329, 951416622, 714406831, 183078149, 384664434, 921248888, 210138933, 859656626, 280974059, 204686558, 104337349, 16294688, 216516303, 151739488, 213062784, 451930935, 659178894, 536928275, 603987172, 822889155, 600208753, 662320576, 679809676, 483803738, 873861298, 395285567, 654799648, 386508427, 182183692, 842160713, 899092582, 556306976, 782750731, 411676671, 943735145, 516944939, 995145430, 730488224, 60014765, 889559825, 835553560, 27250803, 532504305, 700169077, 475633068, 460791162, 854955474, 195450564, 417802583, 599381496, 948204587, 270187878, 17217139, 24621173, 108231201, 80643754, 509940303, 236612152, 790398983, 442624197, 620960037, 562919343, 271350341, 873375523, 942331886, 735465177, 624918626, 719956377, 902639805, 646307129, 459602675, 839472113, 857418602, 43504997, 115584011, 589965105, 820582691, 596712193, 987694063, 370122846, 397662158, 930297823, 729213747, 639441016, 177952767, 155423021, 298557728, 879995347, 674414268, 897005059, 165209869, 707380492, 489779915, 40693562, 751835002, 510660185, 271104458, 338539643, 286855575, 29921556, 690254979, 417014479, 623013351, 776202367, 950383609, 307331529, 278332176, 436733225, 749912948, 793186501, 770201209, 90676013, 121513273, 284797446, 243581592, 107691175, 595278435, 475371185, 688107716, 182393913, 32400570, 744479400, 859167681, 572668243, 233415206, 565017098, 211680078, 595658948, 414459977, 317995628, 598604039, 498524461, 175152513, 239774273, 180827738, 870630298, 179051958, 716635927, 291983041, 696129281, 84034712, 555578145, 462874075, 644187392, 802242043, 776454470, 945872445, 965994107, 808060460, 792381116, 961045682, 274313303, 802843895, 918437295, 738704703, 858870311, 983140247, 92663178, 932599245, 466386197, 629049731, 920580006, 947192746, 918849901, 844175644, 101118314, 331249963, 247572502, 637258541, 225488570, 69954072, 173277623, 580738499, 811179023, 778236355, 133712282, 591784194, 764754520, 650855788, 42132775, 869280791, 527711862, 846598048, 192602092, 66057901, 745586594, 781453, 371255632, 541568260, 422934592, 936951273, 839118706, 316200453, 228883428, 537835842, 510735146, 227146891, 736296054, 269919861, 492801572, 922627128, 133455104, 134409498, 361150133, 570789857, 643741303, 765575694, 880225049, 717050112, 596314766, 208959069, 26360401, 199438643, 810296612, 435587823, 948531910, 94109073, 699812877, 482914410, 301355734, 162962174, 295532151, 426837953, 476584324, 138400439, 103394574, 120401832, 727602021, 267579337, 114931976, 266908070, 42945721, 644538234, 786502644, 127001179, 374803105, 14579337, 919032976, 815307772, 864278189, 820955505, 872708251, 621622536, 240871354, 12736716, 567836978, 961539828, 193919309, 656569988, 712607470, 973131587, 643597329, 499052692, 389759567, 793339029, 549087025, 273596396, 352765, 622364621, 813606885, 453714395, 771084997, 591542946, 320761102, 453174735, 366293527, 803601563, 52642844, 73294134, 836878878, 836767237, 997720353, 35936626, 64298632, 682028977, 470490824, 594617928, 502033454, 136957232, 959048683, 176775108, 829577238, 427554671, 643765051, 379256461, 238428958, 520671283, 16487958, 757504669, 547533820, 507541865, 571779845, 34150098, 885867856, 60462246, 996181878, 517541214, 790610917, 65023176, 935157178, 840363495, 549838493, 380016920, 693201917, 705168154, 90870223, 404002726, 124802836, 196547375, 911040897, 589059545, 913159895, 760996721, 859620273, 178881793, 994280667, 39723116, 434288829, 723577492, 290824618, 114247389, 838211272, 946838480, 711578250, 84119386, 421484284, 564283944, 252397174, 502234972, 693474840, 415779282, 764784301, 885798346, 538827162, 520137113, 534583666, 951113046, 507109550, 442129838, 556477125, 728320668, 886950570, 368198590, 403851149, 880213680, 477796439, 356778572, 835253001, 326191490, 435243195, 502878850, 355909256, 491518982, 534528937, 647619735, 911976872, 229581301, 51787757, 469831949, 376887402, 763218094, 929895234, 791373425, 920956372, 955746443, 628122820, 297894809, 710950989, 200251632, 900507833, 431052742, 30163267, 218514627, 448302370, 230007869, 53996601, 488091985, 157401778, 658141946, 755524514, 466816696, 331302804, 588720394, 810020376, 860665978, 408513601, 840308740, 310600596, 307548689, 211880277, 709566934, 464562678, 172745107, 287404015, 614375253, 518255827, 132176290, 940846948, 662312688, 9718199, 82208123, 923682765, 262283933, 149765988, 108888338, 190433948, 109927639, 210856503, 727333301, 496198295, 739162985, 261344372, 788460404, 419683806, 678086198, 285320455, 289900561, 984313277, 880781333, 882497617, 900977192, 248652147, 689809266, 210061341, 115476518, 677837082, 326854967, 425703118, 677276047, 536570022, 942308146, 30582325, 368778741, 100700745, 21064635, 578823701, 725075833, 533901938, 710188261, 402909298, 147066878, 334980698, 646273094, 361092010, 134185853, 471364374, 64966949, 575841447, 197373496, 446865252, 970450302, 542093008, 47959928, 544804217, 255314589, 520704067, 905120949, 261591047, 163872193, 976481507, 958301836, 736028195, 154647439, 761551568, 65846320, 611775527, 998375166, 126355099, 701401622, 812549227, 20296806, 669728839, 176270891, 702694022, 666972923, 201993158, 405862569, 575053282, 76576468, 647296002, 308190376, 926147779, 525526069, 864042983, 249798314, 388281115, 830264177, 418756658, 495201450, 923938741, 379822751, 590348485, 835974678, 533109927, 541002496, 161465598, 58872235, 111313637, 225206202, 102573384, 940399552, 267052425, 809178713, 48421597, 102536359, 535043976, 765149280, 547170707, 709786862, 552189229, 826915011, 85186718, 173993851, 539030974, 477539006, 355879051, 802320374, 449211701, 637604992, 313722660, 342785739, 274167521, 436107798, 860378702, 554835652, 827261429, 66359739, 927439684, 588798191, 465310774, 540169613, 823541599, 229216457, 331940407, 577019085, 76636608, 672718331, 697289576, 891153184, 112434260, 985421473, 629646688, 893058551, 68144651, 668887141, 794584629, 41166114, 977355616, 714830811, 402578639, 789036955, 373386569, 575333281, 664421702, 228459766, 648059972, 883837234, 224525472, 182613696, 294083906, 103905540, 603551732, 928670062, 366941791, 144734012, 639965116, 492060431, 978721791, 720553174, 207863620, 977952331, 224107319, 569186403, 840673319, 958063644, 880072434, 717909045, 27007016, 246761975, 630724129, 58843394, 422585129, 956672679, 891608011, 264319145, 23299356, 712431703, 321782114, 993038844, 159329469, 175640403, 594528281, 943763328, 96260535, 562728177, 470360280, 940566537, 472876, 366983315, 944454690, 309286271, 356139148, 437016890, 285732342, 806921107, 153283063, 978627955, 58009793, 909141309, 464712375, 908661830, 206790059, 285070844, 204071331, 387359561, 147553310, 442922635, 142654674, 232597880, 854744977, 374773185, 383993457, 349521881, 501925749, 419849323, 941314030, 389144720, 182571634, 345272078, 125145197, 198923462, 932985425, 334766022, 915237270, 253217273, 305654550, 74453899, 541329471, 781639180, 912905992, 215916503, 218862627, 42333342, 784490334, 144801258, 51049194, 508579597, 70700572, 348901936, 431174008, 177953162, 397707126, 618789065, 297631506, 472595615, 272259312, 287581743, 786882785, 370419120, 661731989, 434479461, 847593536, 975683515, 933071512, 138801761, 434742445, 32771454, 105729941, 996332217, 110165217, 501303236, 932529891, 531498456, 779508669, 704751232, 781089983, 656912459, 103504122, 893235003, 849099932, 121137678, 484971142, 756214026, 242683816, 421347892, 994864034, 311351979, 754584662, 206336552, 544293189, 240890730, 648419890, 624118385, 577024841, 565809794, 516732205, 98792776, 396003684, 436852393, 177464134, 721310752, 911646398, 811241564, 492030053, 506400062, 123688271, 805274681, 407362882, 103447785, 636996557, 244581246, 870701049, 547544481, 275646204, 745609777, 157411920, 233738288, 121103372, 462416054, 113841165, 400997204, 927170195, 517267474, 480440820, 213778329, 782291550, 403310713, 46663739, 563572937, 240663127, 222475689, 342653982, 196893049, 647156452, 513938549, 436814370, 49332682, 926434095, 409325754, 853423339, 524710611, 999751172, 986597195, 671480488, 324423967, 477216766, 46889853, 174245324, 365079135, 887963704, 437208353, 326463167, 688953622, 707565767, 690366617, 548759027, 154075426, 889663013, 441802363, 237656048, 977396566, 586734818, 824063678, 17834528, 333899707, 514874876, 539332123, 396801017, 196108430, 301921182, 893035305, 759134597, 108876314, 80598084, 158429178, 232505510, 960719689, 681105172, 773752384, 765211765, 951408883, 771295028, 118499607, 875213235, 780927311, 962063980, 302094086, 165331563, 395570403, 924081414, 333883695, 587168749, 696274802, 473007134, 320685292, 143983241, 321793248, 602221354, 703497474, 60080208, 870520684, 387657692, 100457693, 456429309, 837392544, 356057722, 796288575, 995686189, 938780151, 736083082, 981094026, 2793476, 147633121, 675043462, 713088318, 589749557, 869520690, 282070510, 721753701, 625746202, 645307913, 519794244, 6053827, 613583974, 456339013, 785061842, 267031287, 821960016, 457243950, 86348857, 238673711, 397969972, 734829138, 242528335, 986357288, 796211531, 298004584, 850936022, 182342103, 214179230, 442414958, 22582945, 463738333, 467110772, 852187239, 91695522, 925293185, 16038330, 592401632, 393550936, 833283080, 503292747, 985059401, 898691017, 991145080, 403808150, 955096409, 613903854, 81905600, 816931925, 549754411, 45252363, 355197378, 66955569, 396330206, 711554685, 893616117, 372804991, 743549041, 295778936, 730469956, 472175397, 419084066, 541176456, 718852986, 239543075, 424400508, 23970944, 962269480, 767836881, 802455697, 45306298, 212051222, 201843724, 289426998, 529104659, 466258460, 614610779, 771421516, 101481718, 565829184, 651551790, 903607046, 139601856, 402235338, 915658076, 666963691, 5832892, 507446568, 45080848, 399306288, 516786035, 784578355, 589335276, 734594619, 712969592, 273898707, 901285968, 655825979, 236521275, 295800950, 827750292, 811630377, 825610475, 454447280, 469302480, 988143493, 68656025, 34278192, 841941553, 501390072, 508355067, 407760703, 186968029, 828636100, 801919254, 221650492, 310983999, 5794059, 719225917, 901564942, 196576458, 746133013, 75291735, 495465343, 130811733, 57526167, 862244860, 305520885, 477875386, 140999878, 333955351, 473530165, 469748936, 718357850, 519003721, 377337665, 96705152, 608990060, 948755083, 337048521, 497022376, 646579646, 792065589, 368880889, 939989801, 303246689, 589913531, 152759939, 812685446, 860894628, 620770780, 955240897, 245757993, 369584310, 913896107, 681594683, 655481566, 163959622, 310620449, 230558298, 124110099, 252033142, 962331457, 633956414, 432995474, 765527432, 392055829, 17446450, 408631066, 187569078, 378048779, 514926094, 557011780, 701997376, 863505320, 8926049, 159217456, 436685949, 247373320, 640727736, 62402197, 416284497, 689337452, 385012866, 925296563, 797460399, 733827304, 1193695, 625507542, 64973988, 711368681, 368192368, 764037547, 37948133, 748872636, 144023991, 760700821, 258495693, 799190680, 381869630, 153390685, 454206955, 222272837, 145725876, 520547246, 427475399, 565893971, 446602864, 875509593, 52160462, 164609546, 519549483, 228720816, 757122892, 395952416, 522936272, 948287469, 752934674, 622007755, 629445638, 537988553, 627832411, 665305735, 67660518, 618714187, 285401075, 577988819, 462292210, 285675881, 821789982, 350730257, 814810069, 475884279, 103867332, 739602209, 332227908, 968157957, 722281619, 239136839, 259428968, 930428747, 237699320, 904395332, 539309685, 543034172, 657276452, 912737793, 992694852, 895936021, 960563632, 302631384, 517844609, 665081408, 429303332, 39720300, 340397105, 736760690, 833482651, 340890135, 299355498, 618273018, 335281777, 680505364, 368288392, 242307717, 101191902, 784755806, 550801909, 346299619, 669133593, 66477697, 924913978, 372354401, 774168198, 567420330, 122871510, 711013500, 651351744, 419656821, 878785170, 602072423, 428692110, 39350922, 150596574, 857589340, 828865943, 60040902, 529986752, 435470142, 762836153, 935539428, 4802307, 284268787, 673598737, 367578328, 38612275, 979814284, 684529018, 534809661, 904097725, 208984946, 456218715, 575811274, 990588614, 463625216, 161222316, 298490874, 974474299, 375555608, 568072288, 716108201, 620180696, 343665891, 380340801, 659169540, 740092231, 720566392, 387625745, 207162497, 215518424, 619925020, 187073802, 258232909, 651333825, 266308528, 640784907, 655694364, 218251067, 906012735, 950439711, 211445044, 412390170, 541824538, 907936425, 247839983, 183972384, 518349947, 112648158, 340495922, 965518708, 308251645, 687554930, 285662837, 194895923, 837173644, 284763081, 626043711, 607820827, 729566671, 831128767, 193114722, 682429007, 553262367, 763752379, 875460867, 254411768, 579699747, 558899805, 671455324, 832795100, 280863078, 744171643, 117068727, 370920695, 976153595, 401217468, 151953639, 257327530, 263883950, 783672357, 323929608, 935620945, 846492700, 123146687, 415814092, 560881600, 3991857, 273480912, 453120194, 238240488, 936111242, 856303562, 7644233, 519936353, 387000783, 338191527, 546820005, 75177315, 65124302, 480645349, 786551942, 412581174, 59461083, 926409613, 720590178, 35272585, 143350018, 621772613, 922751210, 574036068, 431939795, 54124739, 696945565, 294188382, 293340995, 397233682, 912741701, 30406065, 733802617, 249722913, 44865810, 754772972, 242693772, 293564760, 133673619, 426610279, 177304480, 407110377, 135932652, 706294229, 561106990, 55511636, 187185806, 405797453, 128188821, 974980421, 205952485, 457727710, 732266303, 421986842, 641047531, 994488708, 756040816, 582860889, 231915190, 773383932, 822437895, 353349100, 104897494, 849141574, 264391508, 996142556, 104418230, 49734819, 756841102, 911407052, 418719239, 942833876, 760320620, 229540072, 933138700, 316694851, 945422628, 646693491, 207110158, 983941144, 258165777, 150519386, 602443396, 619947569, 544283335, 978242904, 466717601, 803850077, 74894559, 353076006, 750311517, 153337859, 150167016, 458052838, 115257949, 687008060, 910671019, 42748979, 614836430, 82480672, 923927156, 166878321, 502117924, 827445687, 284870275, 261570818, 768211092, 788838353, 810777884, 481837565, 523642693, 589997393, 17203542, 806367996, 635981501, 128668421, 590537595, 923438389, 975792477, 294607559, 952213015, 924721544, 157446823, 300664963, 434011597, 286514135, 869612244, 873433537, 647881644, 115114555, 585200252, 506873343, 401518490, 379233521, 336589831, 183172176, 227059945, 994159304, 405424254, 41117055, 543609715, 397836567, 156671032, 632968239, 202143882, 390445666, 194888586, 980814348, 793875485, 423884747, 624642224, 868317189, 998450820, 550340394, 537721325, 561421958, 647969027, 665945278, 634754443, 604860616, 278583613, 228494338, 583966472, 748989216, 418776391, 313700965, 512030215, 154681988, 743043964, 237840775, 945950417, 742995376, 830439909, 979435679, 527658120, 828449623, 808367763, 704616860, 900865932, 887991597, 143234949, 674505219, 493810197, 649819198, 118947658, 457801244, 628520493, 849707019, 384544402, 153729184, 393069468, 874384221, 290213781, 238348554, 321723739, 56586742, 50230279, 179159940, 604277297, 814654924, 995245955, 252240740, 220032820, 446453828, 958702055, 155750870, 947812913, 745426296, 633898840, 198207679, 45374497, 184638947, 327033023, 978915476, 744969211, 668747325, 959813499, 667927148, 250608740, 38659090, 144222399, 984043591, 382094721, 255143605, 124760875, 203370583, 289159581, 584324797, 512099448, 209120089, 905590981, 281897441, 856522343, 61577622, 627308581, 908932478, 314985117, 144421138, 632388718, 568259194, 363071559, 121592107, 757566026, 103129110, 800328974, 594449283, 309490379, 611676946, 144614466, 418815408, 155848340, 784416012, 650224958, 705628286, 891576678, 70342689, 723534826, 268799076, 693077186, 776324466, 875342252, 385262395, 946474574, 463458033, 70014245, 240067223, 189295013, 847533142, 164046848, 538090039, 515121190, 773146282, 645264916, 205293323, 676906549, 573538466, 792340430, 660373050, 891396778, 596832390, 989005540, 29652289, 443391041, 100670343, 800338476, 561618367, 338645545, 35202073, 843056459, 82790303, 794548454, 704147200, 487973816, 592083843, 34675896, 242672025, 880250151, 838779806, 632282815, 670904003, 230484043, 306640065, 841792243, 910542351, 669665801, 82052994, 847439224, 359963836, 375243897, 624154789, 248417881, 968074985, 911480831, 895812970, 300780310, 404687478, 136400637, 497033842, 669907152, 477721691, 361996085, 284970485, 225282552, 806987066, 889403683, 951198535, 500531593, 360478217, 283827341, 436347347, 31302822, 507983616, 260815120, 954923541, 71340859, 529732962, 501653905, 874593478, 851395376, 264895623, 582089644, 954053838, 744446657, 493749522, 113518067, 144594133, 365640625, 18130301, 809442217, 11207842, 234004184, 696297715, 514761799, 807230564, 36328980, 39700391, 231149316, 18064507, 651611815, 546041760, 817037726, 347064688, 774036137, 859786333, 265540840, 353856361, 997026536, 129823597, 435977661, 150223230, 317194513, 301678519, 814452313, 844664836, 412583721, 911475457, 922263570, 806518726, 918294876, 415955103, 237623264, 460597496, 677988501, 482998516, 445479577, 697724707, 14808990, 194398264, 90966160, 145599529, 424602986, 96654322, 381930956, 576193533, 885960116, 567145019, 402226685, 542248453, 345353682, 878078773, 337925236, 865584721, 831952211, 732321093, 241633459, 640424570, 780355520, 623831128, 813442794, 687636655, 126292559, 813662828, 301723211, 876848131, 736424695, 77496000, 234032109, 249829429, 849916963, 809337455, 397140279, 448088375, 382107518, 354234631, 962895835, 927481771, 55451686, 254874534, 351798784, 217137783, 315868572, 534515687, 588568789, 472860032, 443737499, 586769766, 534207192, 254966234, 400472664, 431728474, 213250959, 175042558, 324357848, 739522736, 527163074, 938563502, 783538572, 453145549, 614645418, 206201808, 168396233, 116791324, 547016365, 203437688, 599377654, 969383448, 164294779, 319499378, 229371080, 335884469, 406382940, 410219827, 615973198, 584158665, 243302392, 835798316, 153781753, 20903831, 824326927, 726740685, 675709199, 447573752, 964687153, 576977804, 252441643, 533287654, 132944580, 118167129, 867694458, 575694499, 534439195, 908478581, 502345405, 650703275, 554936555, 51760717, 100814895, 768106403, 390885347, 716315205, 243079373, 288066687, 526492685, 672784385, 811677508, 138184663, 13693438, 899148132, 914461154, 118421779, 445317097, 696256070, 956194016, 508481169, 912627883, 118183665, 728855987, 851570548, 481934129, 230045991, 744003813, 329543670, 654952527, 322162024, 873986855, 934179525, 810159644, 835700833, 16027128, 859684335, 316642576, 343077268, 108451230, 682360212, 583724351, 240604295, 710484087, 780411286, 433120857, 965348358, 446906942, 437622381, 628450915, 581888462, 687241241, 831476535, 534935045, 298242349, 712029669, 558270108, 531804746, 312325895, 558476011, 204456695, 842100698, 613160363, 787279703, 606349312, 904281079, 698260500, 533440465, 563742701, 481358421, 588705084, 65527985, 413312243, 627356088, 395029480, 563523107, 693065333, 949100474, 416039860, 108409761, 433378420, 726227301, 892693072, 232810880, 536914252, 37026766, 298429012, 829091204, 894643477, 15940625, 606594391, 694450726, 510706380, 165596972, 167071808, 969702324, 516030389, 302109295, 936887434, 754873576, 943862504, 949899267, 174253734, 3108970, 97748463, 336664605, 155270916, 471888966, 795142439, 450687484, 359388707, 943104595, 782395865, 269271627, 512940852, 757418351, 36467427, 87371355, 871588058, 34028695, 603941849, 317377478, 293298466, 885122269, 713946783, 736310024, 175664261, 503293890, 601006753, 726062768, 373036221, 6063070, 169159914, 115801363, 707977592, 369119611, 187072166, 949283166, 306700010, 795062011, 403941024, 411546421, 689735118, 666520638, 872236372, 575442180, 569697653, 769987331, 335245832, 264855169, 799283824, 182781095, 992281684, 515476718, 556716880, 237750144, 627174107, 263678370, 503468798, 647038649, 375794762, 850778043, 797898808, 376477828, 249013784, 357044414, 122126012, 228549580, 704472295, 879201742, 702704773, 652871983, 722965087, 873292417, 756929690, 829378899, 806784061, 963414658, 80384831, 678288748, 91914533, 807282213, 214292268, 537910766, 186921747, 352368655, 365440267, 519925350, 369865977, 954611734, 697896880, 905295359, 465837409, 508959211, 819165676, 144992894, 78018595, 361827788, 233671526, 922596687, 230530531, 871961088, 497140762, 446334253, 129566194, 788916640, 762036823, 12046877, 364468063, 965329084, 369241096, 442968897, 664583378, 101796603, 425653555, 727698540, 533200985, 328424283, 582775569, 323067566, 753540414, 673286129, 763795799, 492189313, 18507494, 336762300, 400389817, 337541459, 765566755, 48952969, 534459278, 839102557, 377810596, 209294694, 106090984, 680208121, 235643674, 731971814, 742312736, 783993729, 730581808, 201356634, 480587774, 260057795, 282112234, 277053041, 168329236, 783411050, 649330235, 811531032, 473377694, 454975029, 563685804, 301262770, 53084590, 728236257, 534525642, 419783613, 635624659, 919351449, 845807195, 812238494, 444248674, 244184224, 119560892, 291706946, 903318415, 645660962, 308289402, 646243415, 879279591, 982163266, 629350379, 988355585, 508114388, 120215868, 665619593, 408394997, 953757838, 4438714, 808306054, 340043825, 344080777, 189972376, 13283552, 957753634, 171110823, 627327061, 317259444, 113857526, 980902080, 288532164, 715056672, 728398021, 516339319, 733453199, 906048568, 932434332, 917493486, 63080104, 491432924, 374417928, 78201145, 153201386, 677608404, 464345028, 621593374, 475476638, 702186914, 588367677, 652153260, 325221470, 38008980, 918584149, 490710691, 303003854, 784480772, 863335109, 192983505, 858922543, 484757052, 917990118, 495815875, 811954038, 297432688, 392883017, 204669258, 602527301, 102230239, 338952360, 686341760, 933132885, 926969208, 300943993, 492321200, 953756451, 115040287, 538749949, 264891490, 757687087, 374850377, 283104914, 321448383, 637564038, 381798206, 919348300, 719165317, 897656621, 766949641, 209694980, 883668600, 85103866, 326626077, 354882370, 294819223, 103678815, 628297439, 552815128, 746880060, 882716310, 639761826, 853313845, 227267776, 33989281, 205082115, 172038197, 127604684, 87774336, 10899006, 510660920, 847949808, 803379096, 268046698, 325484960, 65979647, 195624623, 381305220, 814387134, 721896604, 193134081, 474576004, 332337948, 963021663, 436686832, 51683011, 747900642, 184632977, 206896071, 492762433, 247388661, 338193259, 699455085, 827874340, 707620250, 870121395, 30906712, 11787926, 331881157, 82483534, 289213892, 324337894, 496626657, 50161209, 630162071, 856062231, 635277408, 808763182, 65296468, 25262602, 3767520, 254519520, 254268981, 961108266, 381075511, 352664122, 851482442, 924035567, 950621230, 178288430, 348301474, 252976146, 467330905, 855842886, 648246342, 277367609, 927160171, 805549444, 843076577, 750172152, 274112028, 871610556, 277401074, 444870619, 560695474, 552736261, 259184367, 504148864, 576377476, 280537286, 567861281, 954490495, 459256201, 128707966, 346636733, 740938798, 467486468, 632303238, 864901315, 680107539, 206449012, 188035820, 64744175, 305024357, 716309557, 343008536, 300911047, 73822015, 612086326, 594305338, 993845689, 679787210, 195983225, 128940269, 146413954, 443687704, 438215444, 58300467, 413529351, 304234267, 894208746, 48378180, 626499087, 584811010, 717583272, 548535748, 334736821, 820768741, 532984475, 835983705, 303415415, 953455535, 698533565, 150549788, 960120544, 59702004, 633482569, 756241910, 681140655, 121688483, 537417261, 659383894, 15021880, 223408979, 230133973, 28074229, 415857550, 304950947, 697203444, 825836110, 805732962, 794292730, 378730326, 661235959, 447282449, 19518359, 310802095, 270324007, 92442866, 617023302, 769587208, 169984450, 182981653, 322637971, 717165814, 875327362, 508359935, 400645173, 257579302, 369971922, 160255885, 7016573, 11799058, 196195886, 296750807, 286032662, 846677082, 379118996, 126965336, 339453246, 59716049, 99289953, 643219682, 578636445, 552668930, 336030355, 823547909, 271452127, 600885957, 229411451, 47785971, 475194378, 427455022, 368678254, 654320682, 785873685, 548793391, 183239987, 589537820, 159005013, 757387065, 900586607, 760581402, 926202279, 105527598, 679199382, 692477947, 27181177, 937577548, 513153667, 940079219, 35891005, 599213012, 679647386, 970140226, 21250292, 941271297, 672417865, 809343157, 41160052, 470512203, 276603028, 61565991, 189612081, 887627573, 262687492, 770436910, 610939149, 212573174, 844855670, 280487479, 796747033, 715329777, 941186839, 174743968, 228446617, 960030734, 365622811, 216637546, 113585009, 292258686, 835292152, 306469024, 83534904, 236211293, 962832425, 606078287, 268241261, 942574769, 452320400, 986074289, 105093698, 751053933, 53758322, 693296661, 420700933, 858555678, 50582589, 732479344, 580664013, 422531450, 932062437, 181058589, 511576288, 133903503, 71388391, 896626975, 482104660, 626188672, 245217261, 19717046, 41292287, 245207821, 74966520, 441594880, 787613402, 895042505, 136186710, 674081634, 188530931, 125636461, 84440225, 774311446, 882476031, 27392959, 255282924, 406748899, 444581406, 211192628, 920095225, 79522482, 688953002, 440176436, 780772934, 646618926, 595236364, 938011100, 168013279, 614989118, 269040294, 765460843, 445281348, 355254399, 665795, 708303183, 491095610, 328408917, 350611458, 230289568, 339486688, 146843547, 722881734, 105108031, 24646485, 512099739, 200315563, 726780592, 17570844, 98584838, 463038204, 724990875, 588241938, 499108151, 89456034, 823542398, 572034302, 930774928, 215347835, 704858759, 660719094, 182347835, 545428907, 534682088, 741787255, 226726207, 296405244, 426826182, 435443979, 82566895, 339544578, 277740970, 388941744, 400405845, 367306231, 266902570, 855203964, 798398284, 656964346, 673422561, 258108666, 202818634, 718276335, 581278836, 601752559, 731103069, 943778872, 348097247, 535435780, 681868887, 464396921, 43306191, 967364568, 46165167, 304461698, 643876511, 994870574, 724430623, 484265295, 148587362, 554902237, 480293953, 59149104, 81571052, 82894637, 893773552, 708360924, 427410034, 934247113, 246579071, 153311302, 852984162, 651742304, 342301214, 641569483, 919633354, 827838933, 520203536, 62063412, 219610108, 575009845, 486891079, 576411028, 25035993, 260039527, 945040022, 342814573, 15038414, 563069370, 265492216, 854909312, 425715089, 7312182, 160414451, 501151700, 116185754, 729517819, 492502860, 864681677, 669402779, 957120379, 956190681, 415036510, 7168406, 708582529, 688303823, 353500738, 724806770, 992291835, 683316612, 661672379, 834875499, 573935244, 311091693, 155794692, 889382447, 246927400, 998839783, 353928997, 618015609, 780379588, 893652074, 858171861, 728920467, 202063755, 105621341, 973094180, 95684960, 448025414, 120870548, 872451962, 842407973, 113745871, 682631973, 142955529, 150961511, 975153999, 893298679, 224047600, 39021643, 23513478, 920448488, 176356826, 873617071, 998099427, 537894294, 440599711, 623015105, 809540076, 572620848, 989775166, 767682747, 415059066, 795931215, 634293464, 944160485, 653383078, 840348212, 20065611, 771390462, 865070256, 249325093, 81750223, 259055231, 292400521, 780609578, 900087624, 608924976, 680931600, 244301010, 116264116, 908388246, 543210499, 348216392, 689016443, 34402737, 460524049, 368536909, 704487932, 726774950, 294262593, 473176168, 783571453, 262635158, 148408095, 748675252, 458361632, 437538694, 248519321, 972710737, 220884532, 857219994, 454844708, 994546343, 442661707, 780713887, 387742729, 605141096, 453870867, 80767973, 921152760, 564692519, 379182152, 650350565, 283763023, 632136009, 3820281, 859140923, 396982241, 885294665, 900933627, 742179726, 481063048, 508989898, 146210427, 113641228, 482552296, 989670047, 805479053, 241092406, 124529105, 574048866, 282685659, 532238276, 720771035, 607714901, 596474847, 1781768, 146265104, 959084191, 350207063, 314467144, 517153484, 693569617, 373224808, 866065808, 796464088, 457369630, 8873383, 487229057, 663554605, 370053071, 745915116, 127350434, 862064211, 660056718, 281061990, 83435542, 82075278, 598496020, 826688932, 111339314, 595256565, 316743706, 385594008, 684172223, 811268401, 402015638, 784495892, 850742706, 969958744, 137151325, 96712663, 851666935, 974646403, 51833400, 307592549, 494934099, 695661124, 448027007, 249559987, 449414605, 713257418, 130881283, 71141823, 792027626, 133031449, 26488061, 778884292, 584963881, 179284628, 922064100, 358780027, 732682382, 462171048, 811242121, 514386418, 528859441, 690180411, 679717980, 727133883, 261757462, 865865763, 431948558, 405487241, 961136187, 224727539, 255527553, 99667325, 664955934, 768409539, 188983014, 957202401, 890893894, 913538661, 300669547, 274594102, 597827896, 881338729, 729822124, 45386857, 631115358, 40842902, 25938396, 666386895, 575011086, 490073765, 544867506, 734859126, 336725789, 169675644, 421334219, 384620497, 843852821, 358066200, 309719649, 108393897, 228028505, 486121019, 345339287, 542682729, 310867404, 423540847, 663645133, 759390697, 764299113, 37808624, 892555688, 896601795, 13690094, 872381213, 970710090, 963038257, 755462006, 84072561, 983897578, 308133804, 420160238, 958683710, 113034574, 815704874, 370323485, 406527666, 870922075, 434845692, 636816884, 811547090, 698281749, 596357824, 716958921, 162155978, 275295238, 103043650, 355711561, 244094511, 631025740, 809085202, 952099203, 83172811, 274988253, 394313770, 352820204, 518776934, 363603495, 438961493, 514096380, 969435990, 682780563, 823091874, 134685642, 130452995, 751063459, 958571449, 23345338, 995253873, 214678490, 711133836, 144932374, 803924615, 443583003, 558254520, 523877439, 384148839, 933322257, 591264140, 134291574, 903292187, 261832821, 233382846, 366166700, 873726095, 656235450, 504177539, 426272523, 959281141, 440839251, 312448184, 323980711, 451008760, 917385292, 770160704, 470998472, 650314856, 430521219, 929798902, 70659692, 29480159, 288573656, 871267256, 171511445, 681260144, 760187652, 452527457, 355783537, 86881506, 247186638, 174963499, 223050579, 577246348, 608636138, 693392316, 20574132, 722646215, 124612712, 31672255, 851544468, 635475987, 614670256, 877749934, 703598450, 507074116, 735038233, 150483813, 18978101, 694782160, 658632304, 470792003, 998107286, 498355441, 349877929, 733978060, 251089559, 352806062, 701414409, 213972313, 832037450, 601341552, 732282782, 897675718, 905212063, 380507821, 62120416, 507628272, 437856689, 49627731, 857042565, 613596556, 663702564, 729041855, 171241421, 973570079, 819916160, 239669058, 569742844, 367097394, 830025860, 229465586, 312539523, 19664213, 47933129, 539319102, 776961809, 946121563, 870826034, 46749273, 399482674, 334606827, 184626442, 308657933, 970941447, 891269516, 94391288, 978715416, 406271999, 259382609, 756406334, 330200373, 193727753, 393419871, 775407599, 461365360, 464103125, 786128833, 916926448, 235882001, 841198733, 509655914, 372002773, 339304834, 593995517, 758719272, 223542671, 686890013, 465660139, 793321777, 224062282, 646718370, 976278797, 122503101, 203912406, 101697150, 931674481, 281156834, 466143016, 644348211, 622839994, 243066626, 516598277, 672991768, 799059258, 942216583, 945900216, 831159334, 303785044, 706286618, 963628425, 519171046, 191985955, 787255127, 934433642, 592697185, 561306966, 29913294, 251806591, 742135859, 82211934, 669167917, 712820871, 359358533, 859664913, 388965083, 458929828, 41175878, 510828554, 840975647, 112153538, 567884001, 837171357, 653677241, 798557586, 755305963, 172917933, 150506344, 298067273, 110729584, 32969612, 351183824, 655025602, 472428427, 600154255, 858504041, 177472574, 416664127, 780179398, 504409527, 754660786, 703386130, 203957410, 676997786, 411783755, 728559736, 751147244, 819142544, 618658491, 956500712, 451510122, 273697213, 936583661, 317814279, 383291422, 558385221, 878438045, 111578599, 950984603, 296992288, 559856435, 481060273, 761338859, 181682618, 338780478, 822320755, 301168549, 491943617, 266845303, 317158248, 114245461, 289475559, 401479073, 678610178, 713326874, 623515322, 654405924, 128321204, 648081926, 445615432, 103245214, 568857767, 290075454, 796503340, 422312040, 519270647, 605759917, 274121160, 138540329, 583942722, 704735406, 304375686, 70765281, 266962566, 345403157, 747247310, 229144213, 5373097, 11871834, 496674330, 776260516, 656214823, 840563742, 594485587, 549506304, 574660766, 896874573, 179015048, 181739678, 31893773, 843600719, 453849124, 248244431, 526484048, 821245928, 627017326, 985496537, 174512332, 826613425, 159217907, 726811709, 422262969, 718091203, 286774509, 250058432, 837788620, 484748739, 749630982, 750115337, 163098613, 198909872, 595334537, 434094205, 936824435, 307259895, 987825968, 426398009, 623609676, 46085578, 962518112, 641044731, 467834485, 57374341, 771759223, 502409423, 357774837, 360330261, 301301054, 93682885, 297499738, 520110842, 732683046, 33488871, 547194519, 587926043, 353710019, 311844942, 938010141, 969930655, 949138604, 406622077, 74937740, 480984270, 651598252, 55583047, 633230862, 157427386, 652658967, 170775794, 232370255, 867315435, 692764443, 910350939, 554346685, 730806829, 300281833, 304074345, 258346470, 170848625, 11613533, 860789665, 587406732, 829835378, 569147519, 881847531, 876467169, 318828522, 293637619, 251678228, 381727216, 832674655, 649161339, 455325306, 169297450, 210990136, 67731262, 226711117, 767468635, 774316268, 723018462, 640607414, 108058279, 121424430, 57199766, 703736430, 958161237, 141765290, 314761570, 414461323, 1231153, 114700817, 717134355, 934432334, 996338179, 370412334, 602406485, 292790006, 682874739, 410661655, 261573983, 518326990, 157112606, 970814016, 646350220, 633155103, 719877753, 976196212, 424706742, 533889451, 968181748, 199391582, 329474775, 568122520, 494972275, 312369364, 954741176, 285877173, 244158578, 245892364, 997973006, 52116554, 470920086, 99927298, 357222231, 76390466, 681630621, 934074697, 405761637, 369757984, 160879567, 813366205, 677422180, 619877714, 654132550, 421693334, 808585047, 265741156, 920317744, 995068417, 838743609, 332282297, 577258110, 956888852, 813486548, 232822380, 395383049, 714153767, 265813676, 742131324, 284338336, 589631520, 652477333, 703675271, 41528806, 558780146, 567384888, 932346004, 994238882, 289245571, 947041312, 66367101, 922099539, 795340355, 862693735, 618385196, 752558159, 487721279, 257470785, 834764416, 54829083, 559659257, 474302871, 130779795, 282153904, 220308051, 885843428, 637626638, 419281414, 206249770, 378899601, 738829982, 297908515, 395109480, 739743860, 892205137, 956056604, 278213315, 649312642, 860654458, 334452914, 37221954, 643914142, 337957712, 597146261, 216235590, 341013, 789649024, 809173601, 316347734, 281857012, 170005339, 655737045, 843869752, 932998072, 931807506, 997687843, 5895813, 170152013, 744762959, 414559294, 99458093, 743997308, 812294053, 564071815, 568538826, 508973071, 939967931, 117523653, 229367451, 408935578, 27537148, 814186644, 628513347, 377883978, 234398318, 877334362, 562694378, 964684225, 658261132, 736383336, 303212459, 442795130, 857889170, 461677261, 431204421, 117596768, 461059168, 577259033, 914495275, 456805053, 683238857, 603511774, 812087907, 716025595, 10146600, 76403700, 999049031, 976919228, 19455816, 544824346, 139311333, 614618462, 147431115, 85687581, 837380127, 272340430, 536423682, 503823717, 49007269, 280915949, 476395825, 176747929, 260374775, 999189189, 953019311, 441978388, 311017252, 834025142, 143191813, 645866401, 559084800, 474564176, 448386988, 365500802, 877563140, 113121358, 822625385, 886027393, 311318908, 822906529, 28947146, 418550552, 146950270, 295592606, 938016497, 463583518, 940983433, 978693077, 787048262, 964685181, 698750767, 724265409, 661344041, 426994353, 348930929, 41819263, 414355087, 971730888, 314687001, 683884758, 114571895, 867502439, 931397323, 507545058, 624094240, 671421177, 724560795, 822958448, 231590035, 473827694, 190520749, 315986829, 445063744, 741872452, 164477431, 884548734, 523504575, 987951823, 283999748, 345962315, 503850240, 755887438, 275961784, 235259381, 590921588, 96402556, 336069867, 683360093, 414457128, 66235392, 955716698, 567546851, 708308433, 49695402, 269776183, 544864253, 853373543, 575334471, 929745204, 51391672, 307363956, 171622695, 147316091, 608387908, 310176424, 1394797, 219126835, 530713330, 201066835, 660500419, 406253714, 5298484, 525813998, 470644525, 815558539, 361109438, 739867301, 524306983, 906483663, 560101393, 538817564, 144459068, 756626186, 163982673, 534457718, 240577903, 205122778, 695891472, 574478912, 128831030, 209270740, 220731744, 817622360, 136049378, 567405395, 672559640, 852149942, 161224065, 541619051, 4140767, 887840986, 86344208, 781847785, 791979936, 563814593, 747812457, 179683856, 732573277, 8012583, 113280601, 701711283, 281405462, 234484386, 986971548, 613582442, 755928160, 870177522, 420404434, 385387079, 525465864, 746835156, 86112358, 805143360, 87614086, 264309690, 479542244, 901546727, 757966374, 71505854, 119065037, 356267616, 943035147, 457075098, 537364678, 778228279, 86760706, 990637298, 675747099, 212775441, 776128940, 502863331, 624936014, 232755318, 671363842, 824227936, 555426542, 163643256, 247832749, 478255076, 252246041, 780242865, 146724841, 676028237, 273318819, 898624354, 17118941, 548032327, 642012435, 746672410, 868445473, 511220916, 456308463, 962046814, 69052136, 328940311, 529108862, 382239274, 719803978, 13380483, 626197484, 755958216, 381140886, 91195987, 949616007, 588800781, 239754403, 184354164, 437727307, 411882831, 477061208, 133143624, 688422495, 618713301, 950540653, 738269626, 79109279, 712077402, 343528758, 557672670, 817664751, 396288942, 388250202, 615133732, 937320599, 457460892, 247569409, 285446341, 348134294, 154523187, 319806933, 314209174, 211788541, 319869810, 58580367, 632028124, 598915575, 20589989, 594932592, 894036293, 782870138, 805190602, 508846732, 37189913, 985177519, 143320987, 71546484, 91725654, 601634861, 118745137, 711642627, 981198655, 19076893, 771950628, 663244906, 530468593, 400810872, 936065299, 980750762, 769960072, 50875341, 949320195, 497202663, 724506753, 74898945, 784616279, 939125484, 587964061, 888483115, 845309527, 293541380, 677487618, 715913923, 696606735, 623914302, 706285501, 697926545, 865367171, 2260525, 17623687, 427107899, 952455269, 487852425, 849522563, 310828363, 230442133, 11904631, 329880248, 390939478, 217030279, 578339172, 155252167, 576746105, 331872372, 500160465, 815875265, 807376603, 854338713, 856156583, 965676433, 264663088, 448835037, 663792988, 512271889, 843133792, 823279228, 452058650, 922760800, 751148109, 492056562, 871499095, 713864422, 167217467, 899965212, 460164429, 109912322, 367328915, 441055036, 662027050, 57931493, 482449011, 92932139, 879544383, 381417942, 579803085, 375391274, 168526460, 419342148, 429402853, 568411552, 316562614, 820690813, 740252352, 854371440, 725884366, 138416144, 431894350, 676222451, 440173517, 44964849, 128660320, 424850388, 859952894, 187361962, 311724788, 220260058, 750434919, 38441932, 530637940, 892249107, 69241158, 611866252, 870911800, 431917970, 652775570, 730437539, 693176764, 782131924, 826499267, 656468739, 34013606, 276863490, 808125368, 496010142, 571568834, 957920477, 100107837, 185387397, 484157809, 828635340, 350774354, 441639091, 868581448, 490522560, 810610614, 169001940, 344682003, 833509258, 553711313, 603108897, 447482067, 164291439, 473341391, 74945428, 515701197, 824016324, 134265505, 568236274, 295318119, 967338382, 550917044, 217477370, 240895936, 724650227, 609125545, 928996916, 114877175, 321425652, 625701434, 136503648, 714140983, 305326744, 719690972, 522718258, 633637011, 617205657, 695099808, 731708818, 621805192, 63441095, 692145738, 589820550, 223179659, 794967342, 23815935, 175902725, 869059125, 545210286, 971988929, 20063225, 653255871, 261837209, 470108589, 763821991, 510836673, 625837876, 542166331, 267612376, 877763274, 450287219, 636910749, 672213937, 589923727, 152830154, 990283364, 116391117, 766339349, 499438456, 372650456, 552496177, 345751481, 337170349, 777750869, 900669647, 312324834, 14275486, 845152122, 547879523, 521544163, 78659278, 112166107, 553466046, 570479008, 205487084, 605725481, 681766731, 785727674, 491256220, 219361728, 426027840, 799367136, 846143222, 631891486, 232764369, 681053075, 994288090, 932242604, 757218317, 548126981, 341289461, 6298758, 194181230, 965573430, 100768608, 734209639, 193285256, 975096978, 137036929, 487230087, 810143575, 737225621, 856237063, 756059796, 329070780, 302892146, 564303820, 139337790, 995890789, 531096749, 638350439, 529792389, 191102576, 406696840, 332455896, 962425938, 860498904, 891168468, 614888218, 547557729, 547795401, 702760083, 505258090, 464146831, 424415551, 401420245, 528725804, 334151445, 391512840, 716372627, 475925914, 118722588, 505452021, 338248000, 520888368, 22349060, 590484916, 843541055, 339469615, 381199592, 124326027, 24217575, 999815362, 897814078, 728223823, 738271851, 482666358, 593663127, 460672264, 652374478, 780685445, 621794834, 50767091, 86505102, 912612522, 190767517, 1871985, 397328264, 298579322, 833724824, 729541775, 233848373, 303361785, 935421926, 53414866, 742741467, 51763967, 611385144, 144029340, 654041418, 148224019, 530372062, 193356300, 437284137, 670368995, 484946693, 416329547, 825887630, 584356030, 570348692, 279726222, 577811089, 447846434, 213234759, 974359258, 425724360, 994570925, 71071742, 425263332, 826908911, 904726513, 227040531, 839107015, 300469658, 195060859, 2289429, 837470505, 350711754, 401185823, 438738899, 390901401, 52337168, 785674700, 584370534, 419256595, 748409, 495722458, 81024645, 468978278, 217949975, 424965044, 571432751, 690286860, 909154736, 491676861, 364581496, 157484010, 271364696, 922354483, 96606874, 962421800, 771876577, 406338478, 418761804, 450592159, 974973624, 661910088, 48411278, 175618490, 194575908, 272245316, 293579277, 920645060, 828718350, 453479968, 215212762, 205888153, 823163658, 215401550, 517134773, 268499232, 882334105, 959158582, 490774657, 20640556, 700835131, 147486728, 899706058, 883223294, 857265149, 251792819, 897561659, 386020418, 325383383, 709181159, 844596424, 846784220, 349001843, 129532931, 267118554, 915418214, 296057519, 547177171, 898517196, 435889354, 710688690, 90916040, 283877776, 3350216, 615791703, 957298136, 108526394, 942993268, 103804371, 849035531, 483568755, 597558494, 746637604, 338432128, 875013466, 747730800, 653684280, 331465656, 460066004, 54287379, 711223124, 65753215, 743891315, 441137911, 376144881, 336459375, 247756129, 264110684, 679541878, 342970285, 123591471, 525242846, 881937584, 38731636, 709839649, 415346612, 607520142, 998165722, 708008452, 230974031, 613439657, 881921259, 8554481, 665581745, 464310696, 931786718, 241662857, 648143259, 125643562, 807852034, 214697729, 500312834, 477466167, 36795400, 969167952, 792352203, 61191577, 377550700, 694973649, 542255720, 341555370, 497570807, 323967320, 394608009, 117566171, 52287123, 892997003, 233474931, 429997905, 711395347, 91233613, 867160743, 612099306, 962643056, 180282770, 87987125, 379344409, 626006254, 645309262, 216083745, 861855162, 434955730, 673311330, 600728610, 935517234, 342750454, 313391281, 450330793, 10074268, 578117356, 56631480, 891393404, 188353175, 601901882, 284275573, 99418601, 665687883, 119905934, 442208130, 734278507, 364742715, 392296036, 858537667, 79888001, 624751109, 605632567, 648904217, 217257553, 93375929, 929223456, 51070403, 881562652, 691344005, 620618520, 537644698, 87823694, 83566536, 627498574, 842618166, 770195778, 27820926, 245542445, 92049370, 787116375, 585243722, 796115912, 400432045, 676757414, 228915034, 377934221, 493615788, 825221803, 754187462, 538531721, 498196200, 528495315, 572651704, 263072857, 750750746, 251927228, 388043031, 473526657, 813800355, 257800136, 7064253, 172974928, 271587659, 624048083, 244381206, 200378611, 892584536, 922320537, 40532543, 789895858, 114256685, 599358385, 480784817, 752630222, 721248970, 394367649, 950417504, 182377730, 638681502, 521463666, 30922932, 49797574, 875264020, 126136055, 629344373, 333625827, 826236193, 180572353, 328919137, 921656748, 738531263, 71768939, 78738035, 127555293, 97703599, 79293824, 122791375, 959540402, 795529976, 474042132, 952786914, 799606439, 813653015, 915917101, 293366330, 439795088, 298468440, 538904183, 757771561, 25762048, 722119705, 640887895, 216264085, 237918750, 950312672, 882779638, 427047827, 117315150, 552089515, 152969248, 921694485, 527838112, 902578968, 807255100, 996536900, 303682615, 582310999, 562189493, 996752140, 510173610, 63239799, 939074807, 128145299, 645302997, 845454144, 502909388, 675649846, 137930630, 331521371, 816282875, 235064446, 272905120, 705436347, 769870389, 913333125, 256708758, 342033540, 910429185, 669977877, 169372784, 880651391, 894490237, 808132898, 920894164, 557799650, 310170262, 947213333, 461716995, 201173011, 298350369, 430298321, 65133590, 283041943, 106592939, 191477739, 917887830, 639517787, 278177311, 619412603, 404840084, 184220544, 39435002, 919160857, 582470169, 621629562, 264481097, 56626290, 85660658, 583993093, 983181265, 111074458, 905843658, 183908312, 182191419, 36770165, 126322922, 717246190, 85779368, 179168427, 819257474, 245180384, 185926034, 918095720, 849784382, 709230022, 190256467, 84978328, 691013072, 684879058, 840426196, 534196961, 538225751, 766533403, 107624636, 341103079, 721952656, 300930542, 729795832, 771455433, 398344626, 227654387, 591686375, 170487770, 300734072, 526166348, 976116815, 405933305, 408533814, 429611754, 386154102, 960093924, 935780113, 768829298, 553506647, 359482490, 908711177, 639227274, 754835694, 106744368, 158747716, 584157048, 633829307, 738183213, 434470907, 480492356, 949610515, 219547608, 912787970, 468109622, 529006236, 451630133, 85279789, 140277119, 229226059, 74800824, 843496904, 49853335, 557702905, 239571507, 45033050, 127574088, 999090142, 164885134, 701035946, 207456138, 736257152, 370769939, 322938402, 248011321, 211843674, 763903787, 411589190, 845851958, 894946414, 596897057, 729354895, 835976391, 588453981, 419004337, 573405858, 357168519, 256924132, 38478278, 516612557, 109634085, 186550141, 519654072, 687467730, 401975577, 412390480, 734347103, 595464727, 790054555, 586210219, 266820253, 115017989, 818436829, 19466335, 423489876, 611167695, 184906221, 443986363, 363648720, 697968759, 183753675, 208886706, 978605291, 199230167, 668306440, 862943055, 393121474, 399491488, 716811188, 95904918, 150815534, 634221940, 572819325, 516701567, 247729308, 628237311, 950237566, 895932832, 798344156, 361477293, 200768694, 453130992, 449359752, 258566437, 46243827, 340415465, 797314729, 225027123, 347926855, 549462741, 470933245, 784801966, 52544954, 266884719, 842243224, 310448042, 234059330, 198200386, 584267595, 877184380, 532463005, 623505077, 341146720, 371333353, 780785134, 584962338, 328478384, 904400789, 604022682, 54632598, 15002393, 814393242, 97911828, 859263515, 341602409, 202651471, 802440966, 393875666, 798141569, 657216905, 475473344, 305570648, 879895344, 311182816, 503007520, 204679800, 112800049, 552372186, 103507485, 568935452, 471900255, 776813248, 135644437, 430242592, 355121162, 124079247, 183749289, 202908076, 459297077, 378944189, 84006778, 59606441, 362429368, 408957821, 426612448, 366222960, 704525349, 440217321, 526590265, 306525505, 545564690, 571423800, 200747844, 92587980, 649924512, 357848956, 201065780, 475542486, 166751374, 80874539, 872454924, 248687765, 966651965, 38318885, 843776131, 899727307, 249155291, 936925224, 600114357, 811574873, 714596718, 316068261, 740873555, 939931805, 489505624, 318524570, 757761760, 41051871, 818421349, 754888238, 474363894, 680246990, 160309972, 714772285, 652697849, 39597100, 737910767, 77723564, 603530388, 160143507, 392356694, 956440454, 726704272, 716666577, 801021845, 679512910, 433248880, 404969841, 86362730, 213482433, 42799231, 884818915, 942564501, 915415562, 62731113, 541350910, 372020485, 477893897, 558680170, 377409722, 833501189, 248150898, 819450718, 243891765, 264492000, 525003063, 701819086, 19334263, 277229924, 211826003, 665873900, 821325759, 291892742, 859145006, 941116593, 854211834, 49937437, 477993915, 596850374, 867500576, 375515708, 707920793, 264420889, 143076388, 953149265, 474535451, 557728834, 512914972, 545772394, 180787804, 330944778, 937371596, 941638649, 33431675, 562461142, 484413156, 845083520, 628496244, 518307208, 711735032, 647474433, 779503618, 635841755, 445296913, 728014794, 277855213, 216312927, 474362320, 665940801, 87577400, 373281666, 724019670, 773558086, 668379183, 795613988, 672700403, 262339129, 526533009, 929889794, 372247405, 521229665, 4632829, 948506, 107082948, 884305588, 720569008, 486753038, 295092185, 187592101, 272527783, 77424524, 895752952, 524405439, 179788361, 691524025, 314874400, 423003750, 100239226, 567008113, 122943429, 658319050, 290175079, 528294576, 3284332, 729376166, 189551993, 253735662, 43654149, 525657884, 918903276, 758259463, 737754704, 748725568, 765330318, 374820142, 430426123, 666352461, 795536991, 751210171, 147885981, 797782296, 210486817, 979519939, 640514836, 978898136, 805150856, 975538087, 25129244, 317196567, 837769484, 946120896, 171142271, 175534373, 71875114, 818527879, 897417158, 14683206, 368318848, 362495724, 942696340, 287220134, 740682767, 672587971, 994514346, 352200106, 901341120, 741634352, 365523242, 175830274, 205559885, 932239511, 223459315, 391035836, 745033133, 556014105, 860808847, 620555889, 936529086, 736923056, 15347472, 152299892, 626848976, 488011092, 872214716, 788083000, 712731518, 46402150, 283812667, 287152900, 999509079, 91787056, 54353312, 535770711, 398031351, 973077100, 628658777, 319751113, 608596887, 25426624, 29218354, 848240022, 381779503, 183002637, 596317682, 612654818, 311798927, 890192279, 162592348, 682405072, 280452552, 649296498, 161946195, 704866058, 373301125, 24240648, 811162765, 455055324, 943545661, 898432924, 625404904, 536175613, 995558019, 424925242, 339906459, 275353578, 932953614, 530991748, 228930954, 210502813, 638593549, 721528215, 521436039, 592242112, 803456272, 467243049, 440681158, 914004253, 941588067, 868373972, 473313108, 589745916, 82387606, 512805510, 935015966, 801510420, 831895402, 917256196, 395199427, 918303299, 910341028, 603262277, 990717177, 864715753, 34221122, 237512276, 707359434, 323871154, 285521034, 413451141, 922395076, 785651558, 58178508, 78137318, 40046964, 721228884, 956932624, 193175243, 473142134, 964829678, 508130174, 547083159, 474063868, 708204551, 459900798, 874856054, 177083647, 513680207, 479823632, 73483348, 220716025, 716082181, 583996669, 33717053, 291771460, 598739176, 842531951, 493533534, 382094005, 330203219, 88590176, 342566941, 9592778, 18093974, 653463570, 685705472, 867324153, 956270324, 645749104, 51861396, 961231909, 610754073, 754862549, 169709719, 136828942, 178757699, 892866063, 326505142, 432572518, 932483226, 545929556, 527796754, 350090601, 248487775, 214528456, 278770827, 313083325, 69793354, 263457751, 726233065, 498902895, 317041374, 297736231, 173687318, 507374740, 74477233, 176050302, 593156642, 753312573, 815150917, 4468228, 655891926, 291431029, 35927850, 874937759, 59595969, 620758349, 718351367, 118335202, 830834324, 115709406, 173060826, 961959088, 392600159, 920457934, 108856859, 522411877, 521943986, 848136016, 940563981, 575466256, 288396962, 101114054, 277295774, 261787053, 905187805, 967223851, 637223235, 784266452, 489649076, 242306845, 328819445, 21926824, 136719492, 242119020, 562125452, 283268844, 178526812, 777233781, 894999284, 733248658, 776374270, 110291347, 546114823, 464958665, 806651957, 393154550, 979194432, 973520603, 734781196, 532334153, 719467841, 156383950, 961993688, 407337297, 435191286, 703870102, 114555249, 726116751, 773366271, 549377833, 206796906, 543399476, 260806595, 642247550, 899107805, 575897200, 99377833, 479604758, 757030463, 768098324, 27408988, 958373561, 757336917, 291971670, 445652874, 505102552, 511158675, 702804435, 519867211, 785592050, 453934677, 68938951, 529886133, 860768787, 930354649, 313821678, 138443453, 574687727, 59494932, 940197275, 955745471, 271515512, 404220934, 964328296, 21271689, 357153880, 915273959, 794913664, 477194292, 608605657, 560006383, 731600758, 838122492, 335765952, 865721008, 753533842, 489905335, 744883646, 175790601, 895751673, 561101417, 386205128, 204850883, 122651173, 6980006, 658010484, 609713378, 95507699, 873253258, 806885202, 450189163, 896703812, 197717430, 327433104, 218755084, 220939685, 433196353, 155861496, 695322850, 353991352, 19768805, 454431501, 133124424, 605539343, 405596993, 95348945, 240494858, 833362727, 957335754, 823100326, 534367323, 545945619, 709760797, 125664656, 823397621, 643351656, 380162738, 979125987, 527873317, 820468285, 209334965, 929023173, 42862342, 852546808, 54861866, 552272376, 861786554, 571973991, 947192210, 730801856, 845194667, 49469063, 417307132, 958547960, 72624546, 1615670, 513297278, 768882981, 78047438, 240298192, 977542793, 549251586, 575861556, 636683100, 909928448, 169149185, 990655181, 849870187, 408169156, 594646729, 596661911, 943421839, 50316642, 659854218, 455971298, 517878897, 88537811, 337629864, 10095268, 123067280, 881920341, 581910567, 443676615, 36732507, 947554109, 298655534, 99682003, 6338124, 608330718, 699608619, 823207827, 975165820, 19055661, 803593791, 636448246, 257007534, 731561686, 553613969, 714123021, 455007095, 34216505, 273681166, 197794327, 111769864, 616046687, 211044401, 977248232, 723644529, 224485885, 229803778, 573233630, 168252492, 349833700, 654205146, 937269452, 827267318, 327353755, 428966758, 130841196, 936438713, 505584436, 940895692, 766748863, 881740393, 600263027, 239042789, 691448086, 74488244, 286176939, 647685433, 976544472, 850615956, 591885995, 455812892, 104092954, 818246440, 321176214, 105165122, 87063581, 40485329, 837957204, 898619448, 36785218, 311746264, 238772474, 906811361, 453503012, 225162938, 162998782, 73041937, 777832344, 518548902, 837811393, 256956581, 604986846, 254338530, 19730164, 102736048, 358195062, 407143528, 692285653, 172933155, 77761503, 453826384, 878595209, 922399691, 792091082, 236100727, 580304777, 6562353, 502591782, 326046719, 652721772, 945237834, 963886226, 403348706, 690617148, 37315395, 316877355, 184089679, 908880885, 997552146, 577313311, 810084723, 516359279, 830603774, 497500869, 724178579, 164876799, 975585527, 561703278, 825228897, 959068306, 878290811, 172607591, 510619271, 539372515, 753431969, 849782015, 537607990, 926848895, 304671465, 593056874, 855071316, 725025220, 68686497, 149862062, 242379471, 103263006, 638554558, 124567681, 404333717, 911179297, 601100921, 399694760, 718571763, 907577221, 656676362, 282000413, 12562007, 663362026, 704535831, 188198683, 100851040, 913916849, 119740804, 358635698, 826711351, 105520426, 236646803, 372097656, 772859598, 296411656, 239349222, 592121508, 302831716, 390198882, 305052638, 403775234, 333927932, 723031554, 919822512, 632309115, 613184520, 641937895, 571070410, 759793360, 975078764, 853667276, 88526843, 770268827, 839480365, 117821186, 94635994, 992113888, 305034069, 273297759, 752608560, 78722986, 241993087, 173289405, 78317812, 205977220, 454901351, 764905261, 971364602, 916690310, 638312248, 126766843, 743074026, 925888321, 352629267, 463735957, 34816479, 3405342, 871058522, 639133405, 799352916, 523345661, 19362118, 748750382, 347773985, 700159445, 143928232, 667672679, 666643528, 150551777, 566155617, 370512425, 667572994, 396010995, 347832460, 926650446, 84560958, 163476398, 598327923, 489894370, 359027408, 782208897, 991901518, 66050267, 352340904, 538523599, 768038896, 466054734, 187134244, 751355089, 649245498, 673754174, 782828867, 963409318, 967569407, 643505415, 284547763, 669039635, 240011413, 250940020, 576638830, 746430385, 311466718, 534006138, 853821118, 288436271, 166870935, 883171759, 923801905, 320575222, 752682378, 133149804, 498490236, 230433147, 896279537, 620219198, 386934472, 552714381, 516739010, 970156993, 57028625, 550877074, 878750343, 57559223, 186060524, 961677821, 95433859, 704122766, 153648710, 21472409, 66013748, 455282519, 920309781, 106778149, 120196164, 963593818, 971567182, 731937135, 970373346, 525680266, 822268993, 349609301, 374967580, 863221182, 861916047, 189594999, 592097472, 776482170, 869139499, 367185231, 904816384, 244335500, 932857703, 404164279, 198966603, 630206346, 282157196, 930047612, 697844710, 750101564, 668779516, 446298847, 482597831, 984373493, 24750675, 402347750, 102601815, 961890668, 865434554, 374693206, 166136396, 923608089, 527964188, 851504373, 240655036, 301862257, 13062665, 161782623, 417449301, 375937632, 450195536, 306960900, 713820791, 478632366, 658923821, 465252155, 758662530, 99723019, 861415296, 685091871, 334060223, 611488398, 943561373, 799199301, 138651306, 855760524, 969730306, 890169940, 734065651, 932284186, 160443, 282964102, 769839276, 792455972, 820575709, 718861953, 323363753, 500768088, 578280288, 28946047, 582302665, 668392270, 534821373, 179471288, 66366308, 942404528, 705791162, 983144551, 964275701, 56456866, 794770249, 240041924, 576502758, 926295074, 250198881, 996961917, 643493386, 918402940, 98769416, 325568479, 343399564, 569483609, 600390597, 610067734, 48383376, 540799309, 34100504, 860128890, 483005372, 703634131, 506067433, 885902400, 179422739, 815442619, 402251067, 836530935, 333010591, 659249276, 523597233, 961700762, 790248442, 254967599, 530017937, 895684710, 270965132, 272939117, 498342746, 927728691, 705553687, 931844217, 365042270, 731160388, 996812689, 169616221, 62050209, 348021200, 391207424, 71710288, 112175417, 771427141, 809924849, 709593667, 14896628, 665664289, 218396341, 300312302, 880130758, 131346774, 944317605, 377584193, 889711098, 928102970, 50483107, 695181718, 398212174, 565249741, 307458973, 196442762, 162778488, 706451985, 515753091, 643824570, 622036267, 107365184, 413315744, 581871801, 928859392, 114713743, 65035698, 477227887, 382801976, 551605897, 29510124, 800185131, 646794887, 537423042, 872929793, 610402848, 181758001, 913096392, 201614655, 147946010, 14778735, 184781999, 21898672, 826710595, 924806876, 441024743, 189692857, 69127222, 88521536, 413864624, 587571748, 388355164, 716652181, 268449697, 669353210, 540030946, 439981494, 669157691, 888848494, 129139164, 150427790, 64684672, 30917080, 995019983, 556577852, 815114813, 377776763, 274749292, 990610415, 857547148, 568042489, 261654836, 765905201, 780836563, 76088551, 412448612, 953660936, 689219834, 715573239, 321125180, 805138467, 714727928, 748052370, 182319095, 339779140, 788301948, 659879246, 59914901, 335678071, 484196702, 916798614, 533324291, 861789009, 779941012, 130953975, 816528133, 177148151, 976440530, 591558949, 906874509, 81770228, 460526135, 188938249, 302367797, 877541017, 926234483, 535357490, 977969258, 952410322, 184022386, 39003411, 903852188, 85348276, 547648490, 54057130, 328089676, 464778990, 496054058, 230688743, 185530620, 310662461, 165649843, 424527480, 835736114, 588254525, 234436256, 777484902, 451683784, 58206789, 116631165, 659549711, 629132646, 383176279, 994688823, 962737996, 616662218, 430400519, 476607525, 975522109, 331607755, 360697667, 686121701, 301329398, 437586673, 827898356, 388474262, 757602532, 931154599, 916092646, 283025757, 36207078, 194145142, 137873138, 135284158, 319664097, 742773209, 922731064, 844804024, 583132138, 852487272, 133302308, 179386548, 762960727, 203975619, 226450564, 753831170, 300856526, 114100917, 274075126, 22332310, 610052763, 934197148, 463322851, 783030817, 794901807, 23841582, 838265008, 120972924, 281476004, 744153504, 675784872, 750629951, 175226288, 382271713, 526433287, 379075880, 677105847, 730234073, 510123284, 330204216, 752407682, 764816887, 566453116, 103960971, 935922841, 363446576, 920437435, 740381461, 936363920, 176130055, 42115500, 255378193, 439292300, 732265865, 770218684, 701485694, 583083870, 735804884, 587427334, 17117225, 972806332, 719025108, 434910647, 613162157, 835113624, 829399728, 172602352, 385842623, 452998941, 430351154, 45639022, 674194338, 657504549, 940680639, 332055642, 599173631, 255608157, 548671573, 560388145, 746442031, 927018562, 278156379, 110621879, 533205333, 34865517, 269345854, 905837859, 753900063, 294355904, 11788576, 625789132, 233510107, 749343468, 446022177, 971084039, 102298594, 106710124, 871943636, 203014562, 777996490, 696273653, 234742677, 872765220, 528966788, 650351613, 603726936, 727194423, 631536945, 256405696, 313613488, 353758850, 454020547, 898318780, 246364530, 522641296, 389487116, 484669193, 632706081, 644035728, 753215495, 221810580, 741894816, 793097232, 417698328, 258524998, 649464364, 375945182, 311060359, 406508178, 954803508, 619018236, 296427474, 269710041, 30501269, 570102791, 210375862, 302082492, 574780808, 173975181, 472334998, 28942551, 984195213, 161853795, 831483579, 221920641, 109977589, 702058424, 174411089, 128827548, 789837512, 375120260, 413241082, 567470001, 304998304, 320734351, 318633376, 731305850, 160137804, 868018015, 765738958, 741753847, 803794131, 133797182, 466579134, 339549015, 609612095, 956596358, 647034370, 580669127, 920440489, 826931134, 598813719, 183457646, 509255987, 476024676, 300576722, 466456056, 325069564, 862338800, 315114886, 757911634, 845276726, 960986799, 896058008, 662862477, 825149990, 88481152, 376930138, 718400439, 898992816, 105268843, 947679959, 592654934, 165796903, 444951888, 196690548, 775181734, 794517924, 337391605, 347551587, 757013287, 861921337, 776271821, 494029462, 42715250, 768490002, 164486353, 818318162, 453956191, 277639886, 818373611, 28978154, 168069102, 71722770, 761885729, 68161779, 584541940, 457844970, 779461685, 245894470, 551361999, 472165826, 892135874, 46979102, 989097519, 918195393, 531440010, 889178970, 233894267, 105411490, 557532964, 944475503, 112412588, 451794403, 981580368, 769680952, 154713865, 75224331, 50284558, 849876240, 717682888, 537900712, 291837346, 867781677, 534507495, 453860107, 349813936, 762289525, 342065168, 313756921, 319201357, 968554905, 635754486, 765545184, 783717681, 238825992, 625690441, 159361982, 715852723, 601592795, 326948880, 952289191, 674878583, 67355948, 321144043, 9936221, 580490255, 818489650, 391836916, 979544037, 213208289, 33951904, 277958276, 609853875, 434822608, 404856557, 21601325, 483582949, 919693768, 701564212, 210157547, 174381896, 612389734, 205121927, 203720636, 853245521, 948045410, 545371629, 721234825, 887059697, 480681120, 207730081, 289037493, 149395535, 534086548, 130958388, 636980011, 333502630, 618462554, 386238441, 873850259, 647412661, 662068861, 667670376, 743391487, 85828842, 268098833, 800878494, 98573479, 902505563, 524152884, 556060348, 472546043, 117578773, 915773206, 8555030, 737673538, 30244433, 171666314, 640122062, 24423426, 472991661, 581217350, 868494291, 567023143, 600965503, 683701715, 211404615, 365942840, 199098416, 817193507, 660776678, 323156226, 796062709, 142353573, 486646916, 865666700, 640090457, 384798734, 347537822, 905839951, 993142021, 106480410, 25296711, 505098034, 911677609, 667831823, 123235749, 565498799, 825407999, 902158133, 636442840, 142866107, 494151391, 549852349, 189070258, 679892935, 722305453, 551494510, 487215855, 131801618, 292234966, 220034291, 748848409, 724290421, 594843650, 787943224, 667595084, 784894615, 968075740, 930168039, 980773346, 92167655, 257361651, 324873234, 987669240, 47617470, 759947825, 440448856, 767156798, 361916814, 177800884, 189604022, 423544098, 693663371, 890366692, 930173043, 830535563, 536282282, 842465026, 343678125, 829854422, 160323270, 96022391, 478426562, 978496738, 379037804, 185935994, 695532848, 484364274, 448181091, 889629770, 558111319, 545003977, 955067283, 314738226, 328065816, 618732281, 441638445, 269496552, 462019346, 352226698, 896218658, 897653854, 329596019, 471841760, 457629249, 137822287, 927848639, 546545773, 110848430, 780863664, 268982599, 552677624, 266216467, 457107380, 748232602, 968590703, 678588137, 720381924, 290493803, 704497957, 935813201, 847324213, 992708790, 103040611, 678808499, 660143173, 700592283, 441239217, 553754414, 832407718, 750942746, 578892009, 502935668, 778606553, 918382193, 685394886, 438571867, 516820459, 840969406, 863895459, 879151230, 224170300, 350795422, 741192125, 648700340, 983376217, 609869586, 124321095, 264170742, 612338647, 875376010, 273104598, 55469953, 21310456, 63275679, 84295111, 497532948, 53499514, 277590663, 339320499, 752064798, 999585609, 752899672, 580277162, 141656967, 252294374, 377530023, 512120666, 656466646, 907522652, 566777593, 650573552, 557346807, 515608530, 178937673, 502623202, 277323611, 84607385, 997029522, 229552075, 915080767, 526775168, 66255853, 65014126, 616026555, 614087484, 807772040, 844040435, 335848688, 738442708, 749264525, 651537639, 119584462, 501973050, 847204192, 467030377, 896541033, 232450752, 116343004, 263881077, 428175706, 878574352, 110761895, 717004533, 504761031, 309475093, 572191966, 69183634, 733235884, 615058715, 519868840, 557775964, 287085427, 210730684, 471562795, 447170604, 860982372, 995540584, 819962002, 265992196, 300105269, 972892972, 332522689, 870951354, 531904469, 622923672, 513010038, 572444061, 740686290, 571108905, 58291933, 465133906, 467259103, 731008374, 979987240, 36438480, 188664775, 494522612, 753598047, 620740733, 768411919, 335205688, 701699997, 790020474, 508623558, 921533586, 522150636, 41857457, 526617665, 913392228, 864632768, 153685883, 292614187, 18986731, 688479330, 177014293, 830498920, 482889229, 503500942, 505867971, 910278109, 438834476, 167173459, 665204976, 42237748, 485387415, 220831468, 338903369, 588418937, 30961685, 326481409, 240642078, 877067029, 434014034, 724065998, 619920727, 780044785, 698189275, 878481530, 702225458, 287624002, 471253142, 818059799, 297188677, 161291664, 306435471, 566912987, 253311258, 71457220, 835702091, 347401503, 572896298, 292926076, 218397318, 452049578, 73320953, 992702335, 691524291, 857036978, 933660122, 497794194, 717129134, 813691244, 285952473, 995264232, 391554424, 696159076, 479560480, 769944023, 230794430, 725777449, 587612929, 901254839, 369082330, 464209121, 655798949, 318185087, 890189610, 289346903, 776610939, 967639160, 785361405, 878758230, 345456882, 6093387, 132944636, 427168083, 641378858, 693761019, 368131791, 844617147, 477914254, 556233469, 636941104, 196964278, 155596067, 875822115, 375228013, 984787188, 989784883, 226221989, 760208878, 424456308, 676617333, 977234816, 564304024, 679076100, 652006578, 697578632, 313674732, 849749714, 65557754, 594429022, 806412244, 710877855, 259733352, 755069648, 5277325, 930128962, 655219464, 319770783, 209452798, 699074050, 448707029, 773818901, 904579381, 779181345, 645242447, 794808570, 982796513, 871325512, 568303944, 567315196, 972093624, 346378613, 786802427, 909682846, 388367411, 284577980, 992416232, 642526398, 814628054, 949031496, 987973933, 409303230, 144255513, 754427299, 878533894, 763920283, 61095963, 794043034, 518633983, 736318935, 694593537, 607249969, 1271247, 882715382, 80304485, 478492014, 117757178, 247838470, 205877633, 505390633, 389839486, 411112323, 304299930, 179254695, 196098447, 799195422, 361144692, 725736892, 147774128, 130589577, 457177302, 714741813, 763897760, 321654602, 298100798, 337977052, 257357393, 897413694, 366993999, 155103024, 15258190, 762598697, 54997736, 453491171, 407417400, 906048473, 708606338, 692658014, 293904962, 775670308, 707729863, 805725591, 419436661, 968829389, 483360002, 732386186, 607098718, 570882192, 313131750, 631302622, 427414251, 132062469, 795950052, 98547364, 994920237, 499844070, 764842890, 795204780, 450664424, 694903676, 903642934, 284031782, 977861733, 299998851, 569283937, 726681526, 496707598, 984314538, 793242284, 995971396, 166579315, 902787910, 951842526, 434055251, 892231770, 582579108, 83581085, 347956689, 860999320, 671773164, 491476234, 734682256, 676937856, 901046134, 653517894, 739057599, 59658027, 861815162, 195672917, 824794507, 90875796, 291462604, 916025392, 169370666, 643797238, 66780642, 658242365, 133250696, 23825063, 359165262, 576547351, 45912378, 623727067, 570730876, 183685105, 884373251, 571958123, 788044057, 2680890, 3070028, 145965328, 273229439, 176293222, 970903491, 776188672, 179216860, 105537985, 866338524, 886790454, 505677907, 926192207, 228941840, 567509910, 612110366, 266425996, 494798659, 818069063, 705536643, 42748009, 998500268, 189531764, 564649762, 479886835, 771222749, 929247156, 716644657, 712124746, 843192698, 801793941, 801475626, 111825321, 804367251, 452944764, 500194708, 262189289, 813548096, 914341953, 335496653, 717103655, 436111796, 443585642, 678431559, 611136861, 373071016, 391231650, 981091484, 594912070, 737337302, 87162128, 544972234, 305468137, 747728665, 679772905, 148288668, 310220689, 60297795, 396602078, 792350915, 875709448, 311997068, 846704297, 57149446, 258839941, 937899439, 930554090, 573009559, 398544864, 10050845, 412253436, 902526869, 673890562, 555300862, 490903134, 110621368, 319581203, 715032450, 620505756, 421470962, 241062075, 504431927, 214288513, 665081715, 653648325, 741507325, 355241793, 25759565, 520549527, 630713436, 754920658, 186885459, 637690277, 221764616, 754474771, 380741349, 896174987, 45177104, 382101513, 691999147, 653146504, 831658771, 622252475, 859718133, 430013823, 103698667, 735284122, 850895488, 932875160, 336581064, 78487463, 574323020, 341034898, 215138568, 107496130, 912392956, 926313541, 653145079, 893689622, 340335917, 185649751, 998136694, 589680291, 469739273, 616029938, 725713241, 739672944, 101318080, 635284397, 602403562, 940545552, 638758720, 555827852, 448249907, 927071018, 822265606, 197373369, 471954425, 551078915, 876772729, 469054824, 828308954, 811180982, 886662211, 283062891, 827918806, 169464777, 551298984, 950292521, 805150079, 918539117, 291771299, 770958556, 743706983, 848063333, 482833928, 35728510, 461053347, 571059803, 602684727, 193036830, 184621126, 24666953, 753954932, 14224950, 888748067, 998158070, 253552256, 185335919, 838662911, 113404379, 40284411, 773761877, 733963562, 773549164, 614504827, 776460785, 141704955, 267981608, 761903232, 327374516, 11330856, 811485921, 88898305, 749793651, 900924322, 573719106, 125296467, 682770712, 400405580, 362676768, 50953117, 342388622, 726036155, 376910752, 912176386, 828714871, 122833583, 368987390, 106514874, 503123914, 788066321, 105113445, 377647593, 742625317, 649671568, 896213779, 576115577, 46067107, 479030747, 165433004, 289816627, 925767884, 268803925, 544412991, 927878449, 177243323, 722114015, 677537804, 623902546, 242397283, 194692662, 86008206, 620092641, 887194408, 849278251, 283205046, 229145691, 96896353, 44516211, 464601228, 427876043, 41426318, 513539191, 882570642, 822570179, 655903783, 972926188, 476103312, 484847365, 985024823, 253990032, 211772454, 715982760, 991240993, 46986042, 410103078, 344371320, 452890703, 713099151, 76576262, 278466043, 206212847, 665216699, 896146751, 874333428, 742150518, 302210184, 652834669, 860796055, 887515468, 376144853, 175445437, 952213381, 658958345, 590702620, 643186069, 354414481, 266949514, 584873411, 117105688, 65713067, 452994669, 53679, 455106984, 138218568, 812920764, 745269901, 589856538, 493770319, 669615895, 373280721, 177685069, 691178922, 182653948, 439321596, 59867403, 787952248, 334041625, 591233035, 350916093, 536876422, 734060502, 4211162, 670311631, 181251941, 736086484, 77224255, 876573273, 452877524, 284082997, 660973246, 318396497, 168958041, 389556127, 541589573, 205511137, 549483164, 146148431, 281932693, 646709951, 826053333, 721697803, 296070907, 410560904, 431390746, 407432130, 164915777, 585577737, 491239779, 819046152, 335665184, 837447130, 763543207, 436002401, 705158149, 792295200, 182341974, 166967906, 212930681, 58410046, 740609478, 366313945, 182177429, 957104833, 171705573, 148129519, 159055207, 514786695, 943665081, 239227067, 100506423, 853928606, 473684019, 864766403, 795470231, 594630915, 962196519, 637826696, 649248043, 167439512, 208142841, 542691442, 346039149, 761230490, 26898055, 190033614, 776648294, 86970289, 868597812, 66639564, 934019227, 892018911, 220131971, 945714197, 769812612, 169455256, 485415371, 565031152, 805898803, 158187456, 962936974, 15853578, 144793015, 723598672, 943741511, 842567337, 196485038, 907548386, 113392127, 796876345, 302944116, 79752413, 592027769, 957949462, 108503217, 766518043, 698139510, 775504746, 160281013, 691942067, 848775337, 484403958, 126880566, 611713254, 972915279, 709014776, 401884021, 951895380, 110478626, 847786266, 213952236, 467269652, 717479912, 471412382, 419321005, 366810721, 779089534, 64914746, 186445091, 529615278, 914506580, 855204894, 393029752, 699948300, 721873083, 102293909, 236772272, 739417176, 812195641, 642530335, 78782118, 801626464, 685821963, 527299527, 593599558, 570125711, 2653453, 189979468, 912069478, 726969084, 972659275, 807477263, 645761604, 333523306, 801984700, 339952175, 994152832, 747780270, 761507954, 547190333, 662978006, 567510828, 573661445, 414151418, 503559728, 811969299, 952091197, 868795974, 394922786, 465410541, 989469663, 402142908, 159142970, 774825721, 840502385, 311390149, 462907874, 493100017, 422805829, 306961184, 740250980, 120890767, 19106612, 700362487, 604174148, 7506198, 381874734, 105578558, 840037108, 485472957, 146148128, 661492535, 341195893, 477174863, 59464885, 977754338, 732873151, 974157214, 961241404, 292609110, 851777330, 390178547, 831899799, 959087197, 268402630, 847362771, 583491851, 443763810, 267404795, 498875669, 732515132, 709802434, 760137428, 595054103, 71927525, 414732908, 46950745, 456280563, 936196843, 136365610, 200788395, 937570602, 457293959, 879647112, 288697091, 356961859, 593910129, 249461301, 990405248, 672771650, 62852216, 157980548, 563096531, 406762033, 186089415, 749736347, 16009610, 494564073, 714995306, 658973320, 884789123, 744367417, 474606454, 604771830, 374742159, 494829014, 709821981, 464755258, 782656124, 819643035, 686143508, 984251819, 636051509, 218445110, 558637240, 648582135, 147228284, 25323628, 931605647, 472194706, 861576313, 790150595, 104549897, 39458183, 820812127, 657219438, 213044598, 284877192, 148395261, 99225910, 718865311, 672628968, 687046513, 90709667, 926059656, 572249180, 744960414, 55099427, 237351901, 449645960, 712433600, 915669555, 752567560, 442244610, 299434120, 792753217, 692210385, 827695004, 23913731, 986408396, 417429258, 170097551, 428473981, 733528182, 661360843, 908795473, 315812758, 355261487, 193721255, 905669129, 666331780, 744975596, 498165769, 478144980, 468502167, 960982535, 228771734, 523539212, 578217251, 178110371, 593528730, 950934799, 460448041, 45150977, 298075393, 859973307, 15503901, 779445355, 280409033, 905760541, 238981913, 610041531, 992487550, 926963088, 450795553, 617306191, 984303791, 380793333, 674698485, 516330620, 643893716, 949394482, 207372270, 778731506, 268330873, 595237237, 432619123, 890174599, 435174640, 674402656, 641149228, 21613916, 411404993, 751601714, 240295885, 727173243, 237651434, 187805758, 933659211, 401574245, 977624560, 906875753, 82757334, 675098405, 501306633, 17428134, 389758934, 34076391, 36837551, 531122744, 211962428, 297051217, 904808326, 354548428, 553629340, 355075038, 293972337, 452312386, 605055035, 370809409, 463041340, 119621750, 787225007, 836330818, 772616387, 499000835, 239957944, 9812012, 56731767, 359194976, 117283830, 950416114, 272291447, 990226846, 395281006, 907833250, 889323778, 574080818, 979999778, 39460057, 837626861, 954735096, 829566910, 903055362, 936625452, 667717457, 770960621, 599286523, 109083636, 232349308, 464070087, 131480569, 791476700, 474812138, 693736583, 808335082, 438000284, 591623626, 212756597, 646434137, 769601750, 848431856, 674705700, 739596515, 6948533, 205664169, 80897877, 971828432, 70049486, 646279027, 21103455, 332543453, 321964913, 728024241, 878937128, 378347811, 933599640, 4182155, 429241141, 204978255, 599786456, 888122884, 221528750, 560720420, 620656832, 476211656, 799448569, 365297764, 118990317, 249595256, 301621777, 486401336, 315078488, 18130280, 616246780, 857020572, 34352609, 495460534, 769176726, 935219068, 99924617, 110548405, 576656707, 530193443, 201836478, 3101160, 310938411, 86771508, 745430877, 3394048, 918937654, 54598597, 155994831, 914554147, 651459496, 732594078, 39636927, 776732410, 856681086, 137376088, 907983438, 203969735, 425629108, 445364956, 425943659, 763432141, 747278175, 238057915, 499339142, 818229856, 945452772, 809316337, 50086403, 485485004, 644136459, 824884308, 798077648, 984616129, 970565812, 229676494, 972539516, 656874767, 533133748, 132039529, 77225170, 523935940, 646153814, 489012052, 836791961, 482405359, 445540909, 207495986, 49190739, 657367870, 16383303, 447493480, 68146397, 807583118, 911401677, 820039001, 820136353, 417895819, 60294119, 115874475, 856642328, 39287955, 414406680, 166878415, 450534430, 377348741, 994235314, 251003020, 39584227, 983204520, 289837856, 166848445, 292261610, 223699859, 270227962, 733145937, 387347639, 720815342, 316653051, 269538555, 411303967, 411997422, 895550275, 411474902, 509496011, 534546505, 168000885, 3984887, 503362386, 779788844, 95897269, 17000062, 918203573, 337544448, 955415918, 476834938, 864424068, 82078580, 499164303, 771795884, 228339568, 789738251, 608229084, 749047971, 389496945, 977699058, 80889384, 403020954, 260836961, 632059505, 255699681, 407722513, 894628690, 983531391, 432787051, 18591328, 315061487, 994177310, 61460056, 195103149, 20293248, 514826914, 941600627, 940392190, 836940654, 613346428, 962583834, 935504500, 970615883, 692303611, 650315631, 439047488, 483350350, 989687017, 386649121, 506671037, 497383833, 798433202, 717689056, 279301103, 223341110, 555107866, 228947595, 419159980, 501751093, 936536927, 26571232, 478855213, 249385324, 679142845, 461862401, 632598405, 132594859, 294068472, 26035590, 243747682, 776107656, 256103734, 765484076, 777973936, 395374318, 659413687, 87136976, 426290453, 961858887, 23364496, 412090147, 54021212, 385167232, 885467003, 864443912, 67259056, 697888545, 754265805, 591657785, 354909268, 554521367, 826163416, 994735244, 955512580, 740672088, 127318542, 43310528, 612637534, 69732749, 37230000, 276180277, 56623089, 765235422, 82553225, 481672050, 24198031, 977896518, 113389523, 491454170, 717149700, 451778500, 229633204, 206755465, 946243619, 850622300, 230347037, 652934379, 908805079, 501995077, 923862771, 740429973, 442322721, 595008835, 511409158, 134319136, 556544542, 850802033, 953725032, 299787663, 711814138, 617616138, 67122274, 838745274, 577298901, 396198553, 211039392, 703216753, 92842409, 329200582, 195568760, 944297660, 865953743, 562319499, 768185960, 241198618, 40965140, 13913889, 201871112, 481448062, 262049161, 603272931, 214336030, 154231470, 826497754, 480134919, 122526251, 804143696, 721769557, 128092637, 143217467, 320869435, 418173564, 319873710, 660136357, 7169900, 656518641, 914983157, 727707508, 60991683, 63852993, 433793150, 638860510, 581013005, 764744843, 812735988, 623965512, 667660249, 108392049, 807111623, 989019715, 115771606, 646013316, 863906765, 506947823, 86203375, 416689636, 463914537, 952004180, 246796338, 292630576, 513090144, 521730329, 648539285, 153265481, 532590999, 887943189, 351057430, 116565190, 86070812, 994711196, 530731134, 567684244, 48087224, 510014736, 67901396, 283891011, 371762650, 925895584, 638737709, 665136144, 149498008, 287883131, 280904265, 647399103, 862454503, 124333520, 675212239, 267525215, 966274790, 831234407, 499985566, 209156376, 404972868, 49948392, 120832540, 254788212, 439283170, 846092120, 26969693, 25844012, 203086775, 589391788, 100866582, 806827983, 676444851, 180230374, 846841252, 161232423, 560851217, 609964441, 437358314, 481653379, 629649214, 819821716, 158644049, 216655960, 823306681, 353115758, 852439939, 736311970, 685158445, 991237831, 652584945, 861383505, 769052992, 730477882, 393218227, 640800707, 713778160, 5552684, 556466041, 356469590, 399091405, 927374984, 424070164, 692550676, 13227574, 644259740, 934334967, 922174415, 961503373, 22024400, 898430086, 423108783, 604478137, 76580624, 793285391, 226799164, 445730559, 6294901, 702642278, 257231718, 699679426, 184751461, 617569570, 837255358, 803344297, 604498291, 502902443, 600688365, 639881229, 669868820, 241305005, 456556173, 302289881, 855678463, 501467613, 518292358, 990506389, 485485332, 873066079, 255065841, 745864632, 168995233, 321909498, 581251669, 488160985, 764708341, 292785782, 544696824, 149619874, 957016037, 717284535, 788808178, 74212381, 925315889, 253659983, 43509695, 130266263, 363518685, 877887363, 666263963, 222414090, 757257805, 572919394, 493706190, 146518349, 815628967, 853677535, 601954338, 506358994, 424283051, 246724586, 138734608, 622976103, 838555993, 241986125, 581453811, 440706213, 946007036, 564867991, 772371103, 260094941, 547539677, 43996176, 295111046, 548042698, 13962546, 180486749, 957502195, 127669467, 294460849, 272730713, 489685971, 591400085, 735563726, 779720617, 358478579, 624358205, 780132323, 686612103, 873542935, 720515698, 185064070, 300087047, 839011944, 149572550, 295815496, 603885672, 917021606, 414082388, 521738803, 203300703, 348215925, 116099581, 352629246, 353304501, 369216719, 946088514, 184640974, 643905704, 437912962, 798665912, 398183591, 449151843, 87946862, 448506432, 817697753, 177067442, 313913735, 110783374, 295267326, 971813259, 609856722, 32164854, 871986681, 980347146, 639324921, 694047628, 988716139, 915332739, 514596768, 871867612, 565852235, 628392365, 657646223, 937808209, 375465550, 301109488, 783535206, 199251614, 388463637, 3865366, 310403211, 877522588, 631547565, 5018972, 459922951, 655107514, 705308011, 964830916, 546640101, 786021234, 532813113, 634846117, 31129823, 902943133, 429974110, 828588628, 300381263, 182893946, 363419269, 484875056, 146650511, 533887161, 911616556, 341065797, 644119757, 768778729, 408593662, 49199417, 184690575, 561725593, 273633026, 310723415, 900099750, 366593905, 480529231, 922739507, 73132761, 137076018, 14708892, 617667628, 889328840, 606225980, 404342534, 859675108, 268274085, 302213796, 44158247, 912298945, 219171767, 278151498, 702466333, 409419218, 542825783, 456365145, 973910623, 992233859, 654995197, 352500085, 592390880, 642648819, 731271784, 319297078, 749845716, 122108465, 679222202, 132933464, 376718582, 621940373, 511285732, 544758082, 617434462, 405983337, 923942527, 646073233, 266579699, 440621222, 96004245, 907807522, 620049590, 624075338, 299456245, 47957838, 308236532, 157222307, 10343310, 250308047, 260802725, 95793170, 647939016, 97568977, 701331229, 655088502, 617317111, 506997225, 763337808, 717582220, 992670633, 499241059, 469826038, 17077860, 560407681, 351902232, 308881280, 649732920, 440776218, 766780710, 551853280, 381121564, 507885306, 458825772, 204975624, 855299456, 189003106, 622467510, 609057646, 65728776, 123306720, 449293907, 612154490, 280466121, 761038812, 208918815, 629134572, 108525612, 745049727, 592778672, 753611024, 107520382, 871048152, 414412344, 192617658, 921581582, 999869645, 247557928, 773535624, 563020333, 553150466, 593658260, 850903300, 525537637, 340942201, 228008220, 125527053, 994306249, 763468305, 85560615, 423560567, 442549253, 382930794, 831994303, 165167457, 359493328, 329662991, 733819026, 908234088, 666081217, 342367152, 15132885, 702317012, 648481368, 520164515, 97180115, 260221092, 559568062, 871089952, 925937437, 154303280, 701334732, 404659632, 636891150, 951267357, 629333650, 944246952, 580597673, 78055241, 856810488, 477805699, 731969315, 204682893, 109992108, 778151915, 115770976, 689171401, 120906154, 123996606, 147716327, 136680864, 173937892, 569832116, 151709189, 246212236, 397487906, 973989188, 553612009, 494226101, 573877720, 486269350, 459241148, 86477203, 812943643, 572014844, 555282393, 503018292, 321650419, 410206773, 167190645, 108899801, 753415461, 118701214, 179866417, 280804700, 662224560, 501341299, 261019242, 801773188, 74612897, 670960423, 459363167, 738231747, 349795684, 838020994, 185251762, 26617359, 593113799, 794463024, 965467550, 583568705, 446543618, 281210830, 408230189, 3539388, 35128258, 285369269, 961146219, 469712485, 742184870, 476576928, 143182740, 915881935, 378307583, 533362693, 392477192, 490985950, 756250671, 535513278, 319226503, 18906907, 700371670, 789903475, 643305906, 526375300, 2673856, 536850485, 342794545, 370630932, 884337475, 513955333, 80292123, 1726500, 27862116, 742117197, 855824058, 295093008, 675051482, 363945524, 880648382, 723705005, 11010698, 444221518, 719316066, 893207102, 960134020, 679735490, 205117700, 208388042, 834210329, 609232129, 829590829, 774970727, 7089602, 756330325, 410357501, 135487423, 588135627, 408897585, 621271474, 472429713, 26230876, 313276069, 989711135, 36873105, 122715109, 605960128, 138394012, 426263249, 355183138, 263895978, 268353025, 200655032, 520007609, 884842087, 42208253, 180620594, 319702508, 161110077, 301586865, 809243863, 32390174, 289396281, 429067186, 356747720, 81239289, 303022055, 715083606, 293975056, 317736876, 234032830, 576039051, 803878934, 791129708, 397060449, 849256412, 80718481, 793659981, 942300393, 504252934, 932351010, 606945720, 378877054, 26600683, 711518376, 353813975, 835803117, 55293950, 595335948, 893020965, 425625646, 705303072, 749401167, 471615068, 964862255, 952795470, 682232938, 970371526, 546443476, 732913427, 711241381, 504130959, 49852693, 699977618, 887246086, 973663198, 633969403, 473122641, 901028311, 937050049, 8326036, 84987475, 271173046, 619985133, 702217448, 712138702, 653162252, 279055351, 555298182, 528117855, 302437404, 502683603, 693845295, 227463507, 855783874, 503168930, 626104974, 667165114, 328818166, 795346169, 769823362, 151226163, 939215598, 198558276, 228308197, 286976351, 465101389, 991390690, 170509010, 572136638, 840039170, 422078079, 526097325, 204929178, 737621111, 497962645, 334136768, 291158505, 135338225, 841977554, 16142890, 317783291, 546419130, 113575715, 572076053, 584649112, 995762349, 665477245, 888331730, 524354589, 345161853, 216620589, 584595309, 866402245, 294764903, 739016492, 855556364, 124831363, 33510444, 870328035, 407456339, 29177427, 699712217, 741780225, 503635200, 858709846, 512878558, 274172794, 587342928, 302182443, 542557362, 899057048, 355671723, 611086949, 736775992, 805568240, 146847863, 527338367, 393092656, 584371487, 279525574, 390456815, 55347954, 919011172, 526113948, 504193727, 920066906, 790612622, 445700100, 465058779, 465043720, 81488934, 279226864, 352371777, 370826423, 869907934, 648382569, 871994111, 232639009, 535928928, 300708931, 113571516, 528085011, 438106083, 206375462, 309863234, 931094543, 163034087, 259061012, 584218221, 69707548, 415525766, 645448776, 888511450, 198464904, 945576069, 504918839, 344469732, 931484126, 646962145, 398644178, 254723908, 473781894, 551784666, 566471220, 286776158, 774945905, 921653875, 459678440, 532091399, 493195183, 373385401, 568089804, 798626585, 964619051, 73311730, 375931729, 783434309, 757908169, 272232474, 159065052, 952780695, 942336954, 958990293, 760364668, 969135731, 202800662, 267005750, 731044339, 106887442, 370557802, 64887556, 743869826, 731563002, 709838394, 880015870, 120473736, 727379347, 957699336, 629044422, 866880228, 352986104, 370169954, 543757962, 201567437, 253830842, 410818738, 908650543, 432716644, 452779944, 725409325, 89148888, 843972870, 415564788, 404481706, 340245348, 265238602, 817760903, 744267823, 327974198, 495139924, 149722661, 274375398, 59866767, 698652677, 725485741, 592492095, 267038273, 799649266, 29336147, 864962427, 326503959, 373039426, 527140300, 959942995, 236366025, 303549300, 936894780, 403412789, 278617058, 656242276, 950086998, 584008393, 915477969, 601799002, 30375215, 59569688, 241662237, 522336655, 881195838, 351715411, 927346939, 334636799, 14351265, 735572486, 337092342, 142789283, 282439964, 848326510, 144257343, 101091580, 387780639, 413564761, 80196493, 837436920, 457146393, 88662920, 131747522, 517794435, 544825673, 806763809, 271650888, 501191296, 513685466, 414583246, 18221477, 937109853, 136216074, 710111483, 178137733, 118109682, 686138300, 906550707, 118994330, 894015818, 554427071, 409303424, 190999274, 368678275, 665854874, 447742775, 988032277, 511143892, 693186812, 826233869, 312932993, 246086169, 367130917, 473511358, 700374251, 141375099, 287709068, 180583141, 361280501, 908885541, 301656885, 171838714, 283364689, 186288593, 578238765, 254938013, 132171662, 413788027, 265873276, 816510956, 492061927, 90033168, 687939009, 790483706, 429376578, 97378474, 581361790, 559487365, 886980552, 964689924, 964193638, 437159848, 322904202, 794714094, 812432139, 199641430, 624795231, 524064438, 636984610, 352568137, 417586671, 53057488, 151351828, 458338710, 122223881, 615833855, 560583564, 594973747, 931910677, 152916692, 2198747, 99155309, 859653827, 60556257, 404796065, 256250827, 903774458, 659241091, 971301285, 523699417, 836328309, 204851858, 721198813, 873223765, 872991811, 42985039, 820672257, 521097349, 983705168, 696412394, 24634413, 429173059, 962401625, 296250796, 333115263, 654472391, 889977841, 302057090, 709283223, 349729640, 455283332, 288419362, 618526346, 919886037, 831767972, 797791122, 683192894, 640914350, 765161421, 236941945, 431797163, 679169594, 830275485, 102787781, 599112548, 991400317, 771435364, 481875131, 138681778, 297507758, 32859383, 343094000, 372403952, 495860823, 6063850, 426374325, 595954892, 699126103, 913527277, 450584240, 892113233, 961002987, 404797432, 872378472, 484858896, 863376203, 559136619, 850869233, 112915045, 354522032, 89770019, 220365496, 138448608, 646563684, 236695916, 164087081, 657220420, 654689802, 306459676, 693306306, 110466307, 112607541, 881408403, 349787490, 18273441, 180397794, 187207626, 67488736, 611245625, 978288457, 934115642, 434398675, 122216171, 608494099, 179140053, 651920066, 23497077, 325024647, 39108916, 213161562, 601764182, 798573900, 845670490, 302580948, 961037859, 48256379, 996481812, 501141409, 841317546, 761317275, 568382470, 884250101, 946701970, 159625159, 367316430, 993047680, 573058492, 874884044, 61417725, 315067218, 978061346, 280791810, 981802774, 76354613, 533724355, 602835786, 94349633, 664358977, 100468465, 167900764, 206315591, 825094072, 395399318, 544710705, 497159488, 625104774, 930212978, 712947216, 575802511, 368512119, 283716525, 250805005, 125434817, 416131896, 425081619, 121271719, 806852465, 403034946, 480038054, 146003310, 300375818, 700313172, 453914927, 873167245, 631673837, 180985237, 338810196, 239682360, 196314312, 721682480, 426067295, 798103825, 146997810, 325606398, 308733150, 352740276, 599030834, 268654615, 82576267, 846118717, 59921668, 565982863, 443074524, 159304258, 91227999, 230764164, 744308286, 146808886, 984409828, 192673578, 707198450, 42879151, 435883214, 898891403, 502249300, 272225018, 283904662, 378041610, 764365459, 222830183, 488472223, 189075088, 809181247, 490360297, 321960291, 799823552, 308365238, 383174172, 759228085, 565090296, 80242367, 118083118, 367220048, 790671741, 720302899, 295244137, 130045031, 633828752, 610388779, 823690797, 378996360, 131342854, 558302228, 567410341, 119478802, 896930406, 211636129, 702946770, 207065762, 373265197, 318592848, 768966995, 991646083, 741223567, 182959366, 856092244, 361397457, 512671247, 499024618, 597652550, 119370568, 158778817, 486913496, 328762661, 355851774, 526360066, 591682830, 42173534, 238255549, 126601710, 375274982, 140428215, 84667916, 840841327, 205362832, 892959092, 914949086, 176520755, 209737749, 954446673, 660068782, 606770781, 435236472, 186661056, 857587336, 964986007, 936673888, 740825188, 78543334, 418857300, 420535386, 79530435, 714237435, 812034856, 407993167, 151494414, 311950554, 588895778, 14869345, 978574616, 101265122, 956507429, 998344941, 788538900, 495457688, 694669083, 671016583, 343807866, 295277754, 962397987, 744201206, 52876295, 739771753, 241299494, 318332665, 915375556, 201796456, 511716771, 27078927, 975616478, 243157317, 984498639, 647157261, 829491353, 213781822, 561877089, 229833463, 498490359, 470800166, 211155613, 711994595, 100760127, 493458346, 998103155, 216605636, 886372080, 392776061, 106522695, 900253775, 159310900, 559171977, 671807980, 456591680, 363886509, 371409079, 849192731, 877119078, 298062836, 776633319, 92520987, 930933947, 155418880, 637148930, 69699242, 666470878, 795887486, 343567233, 246963352, 878960146, 245241705, 260804408, 676070549, 244812935, 92474248, 416837623, 836959310, 822806217, 574194202, 498031533, 507931558, 287614896, 406109749, 991061210, 16993934, 513421742, 737374153, 94059331, 238699841, 629537022, 800464783, 218802069, 899304638, 137865237, 596242226, 879620874, 102956676, 199443016, 41798972, 863938838, 967793340, 759759571, 322388270, 602765425, 180164320, 491235317, 267123708, 25053695, 769684258, 582351567, 96813800, 798265439, 307706074, 582465356, 802975338, 126747309, 858202170, 506871869, 560374069, 840240316, 142327749, 752929483, 124991468, 294931113, 83169768, 880416227, 722931361, 103677953, 504039475, 568420970, 285399245, 787321242, 886974870, 686941056, 300765171, 217242329, 272595247, 819260995, 243164774, 468884805, 166806807, 714645489, 977259272, 670312618, 743583981, 800060240, 972641031, 551288245, 373713622, 402027449, 321510002, 278599421, 572709446, 635579207, 45164374, 478507365, 660583244, 21577246, 331477857, 419404351, 486672326, 163146961, 905796223, 919366597, 658579851, 798048065, 260227731, 674940560, 313836161, 778836250, 931475874, 411843895, 470963126, 23715129, 511530997, 383608675, 602075422, 852642105, 15877414, 608343244, 728947328, 820386715, 913881049, 535735149, 416027923, 621034933, 724012622, 464562056, 454903330, 515964498, 661760794, 905396227, 205850389, 245462905, 579669209, 129374630, 737517786, 314662802, 113230534, 590416899, 278477834, 26306853, 844558225, 373985838, 873577869, 495812491, 222849042, 82846800, 919355180, 183449150, 695661154, 990106156, 704399455, 246574663, 978019813, 351694013, 657786656, 867307467, 91944344, 458911521, 850231494, 570642517, 489745623, 48683575, 859079564, 997765309, 408147356, 472620093, 950499859, 898139797, 364777884, 239931188, 703101004, 253125118, 679598026, 413072909, 585419369, 377252952, 56581638, 816893625, 189948382, 72254800, 39269695, 27528279, 449738624, 208543034, 403170805, 959053014, 818754818, 654937978, 32743293, 409436887, 621035385, 950632447, 408918714, 757340161, 860791817, 893466801, 891123938, 488104136, 59650041, 792931199, 691684104, 201159600, 388326056, 311053621, 240369669, 823339435, 262779201, 489508489, 80690852, 495517355, 397971646, 584837958, 994719377, 573616960, 264435450, 263725323, 796084932, 107393340, 956110583, 411549381, 347056262, 767127785, 680936669, 569642269, 522799171, 326818466, 332887342, 946857957, 39334699, 965530261, 167967704, 333876549, 810527244, 691450277, 682984368, 860020574, 667212088, 847972605, 686521540, 825277185, 493264583, 84474482, 768446423, 982980244, 562741899, 652442335, 602178961, 417508255, 162074572, 244901151, 52009984, 719616590, 740936589, 585796772, 583154116, 106460112, 465341424, 221132482, 282973328, 324764078, 496211785, 741019781, 119949340, 98453009, 865806373, 444834782, 68790096, 332424810, 867042990, 202319559, 413750249, 14940457, 894893613, 798826956, 572435525, 40951998, 166696774, 108473807, 569001743, 603883743, 475061605, 90550102, 198012968, 537134305, 93623875, 171937613, 31015258, 967632941, 393999077, 416460052, 340342618, 619937967, 972329299, 382913511, 570902693, 24461553, 606812820, 335522214, 429455477, 676665385, 233136942, 599490549, 375866552, 757366306, 593813034, 907002989, 480751123, 199644336, 151144094, 276360240, 470508311, 667728830, 915504026, 634024908, 223064395, 248380672, 444205002, 603413377, 366440769, 501353189, 399822011, 660546944, 349610826, 59325545, 643361154, 924070634, 359648088, 196994735, 202897297, 545293181, 540175107, 856492404, 59424381, 422002708, 752141918, 718744392, 331857734, 720997095, 261768532, 291907083, 112765911, 856308768, 393285502, 425955678, 26573608, 974803418, 534867948, 398736786, 720696785, 531595248, 71823181, 274285795, 342981679, 788195390, 719118424, 388564065, 557154289, 458056468, 652780224, 259849222, 965606091, 402444661, 835122475, 748407465, 709060558, 771947366, 997390405, 160423841, 608546222, 252985875, 359945960, 635060797, 159559231, 936843296, 32027086, 653139179, 59240317, 765178937, 488839024, 27353250, 263663117, 722279105, 325328280, 100889666, 940899966, 405495355, 604281355, 273177590, 548811702, 862046244, 920152435, 854470973, 225254474, 115282960, 612010240, 554581514, 994776902, 707538462, 441355136, 31817971, 169061790, 621740274, 523510285, 109071984, 168992929, 618025991, 478218288, 618056724, 15641368, 272935098, 125848401, 374231910, 991053583, 643804197, 460725960, 295899014, 388904313, 600863192, 228806144, 182881163, 117105449, 241588463, 350424292, 314022264, 925807462, 734170000, 594191306, 958058352, 150305783, 486674653, 805208880, 822176902, 965982427, 723398431, 659775813, 228115008, 851697838, 140557923, 821031788, 735135532, 66985602, 943613934, 391861274, 402668383, 643196300, 815053007, 719428440, 346385297, 661169416, 658604216, 221178850, 556495935, 997295028, 490607860, 426758990, 985853178, 359009437, 946055949, 720906959, 505869927, 20222559, 168384677, 391004469, 560693760, 724648995, 148557277, 241502392, 427841392, 132950892, 147113489, 873556918, 817642983, 212159355, 868561693, 109792804, 6308825, 303436535, 585493997, 646271187, 150704647, 539035516, 226832563, 624941667, 149756128, 442992011, 909163860, 599941272, 600170762, 329886043, 662126414, 715089543, 133535378, 111422098, 651996272, 529347928, 903700685, 2325875, 8637151, 945734852, 939013112, 391515287, 992271743, 297297467, 843180659, 187461403, 899358455, 742543244, 43731000, 866281231, 52516796, 548580327, 532863338, 794857779, 54768160, 392974807, 979800045, 572901764, 51990062, 628450692, 998995491, 881485497, 89840097, 15126116, 558684234, 7351245, 342842976, 694884608, 157324788, 886500390, 993709305, 557906767, 801673340, 826091635, 454328444, 711514083, 162655239, 845189114, 860305629, 891583943, 549690035, 574523792, 6004479, 572241986, 451952907, 372862318, 836728461, 705897884, 929303406, 937422149, 377121323, 917102247, 941026831, 597068965, 52733151, 26267212, 852814801, 591264251, 226166392, 3023178, 693112987, 416112239, 981329332, 201836954, 184445134, 497780772, 276423462, 156775602, 578430067, 189535703, 747297757, 876593176, 934557737, 328613357, 351818244, 111352528, 353759224, 252537646, 390712609, 83921431, 856680694, 368549026, 979152360, 131495170, 471516207, 805450106, 281374666, 641170235, 388636599, 86558298, 319110126, 121657656, 586698950, 418197663, 589974307, 363931195, 993105063, 131907687, 673301293, 584447897, 500457295, 182948852, 452618868, 613546608, 90712736, 261657965, 650753346, 330089149, 899420936, 439824492, 991070442, 249882081, 565149357, 287217084, 802683013, 12882903, 271156363, 896567990, 714971796, 99264923, 652392717, 523562858, 279005230, 798078785, 530246521, 87840739, 432344551, 834720921, 391388167, 922125398, 897356189, 362930649, 854939974, 561262630, 909507819, 960930341, 256337274, 108273168, 729764858, 711029092, 400481434, 614271188, 348519381, 180067482, 606151378, 414937008, 767180266, 615925646, 813593250, 662377338, 193905634, 400701574, 778933021, 23918040, 970263131, 232340232, 541212829, 476573116, 707674013, 600731048, 769109013, 404183322, 938740730, 5891335, 189199690, 912954707, 123235487, 183035707, 171530396, 368490314, 588515721, 60560136, 232006513, 31340813, 45612197, 209786294, 915465287, 758984532, 931313139, 516650927, 431221508, 222455022, 220156389, 516125209, 982957378, 791466187, 184306140, 362964186, 695623695, 324453957, 656052630, 635027868, 824561249, 49376774, 157308322, 21496736, 724616349, 322508356, 910579842, 471904797, 197011591, 211394552, 651743568, 112307294, 298918257, 868672684, 206786908, 892304335, 505986036, 523401877, 500484407, 506269246, 836067703, 420010829, 334348633, 676512033, 423331165, 531162365, 103249453, 499018178, 867964301, 519101625, 976215400, 903971205, 627295400, 631876048, 268000481, 291759055, 399119324, 315449051, 229688316, 671803415, 550602123, 655646193, 995864726, 315954872, 60968769, 773114103, 922966994, 550211105, 210843739, 954189703, 841693374, 662598276, 366213350, 917097815, 663157632, 112047479, 129300019, 399485699, 983375668, 24274858, 408572254, 225573215, 384790028, 140769458, 711920876, 467386646, 530646532, 947129029, 127507863, 822900516, 915392686, 56938487, 387524289, 486873271, 395979263, 100570498, 160631377, 491820245, 742555898, 958366567, 374849074, 144896166, 789532424, 477399642, 498898935, 410418796, 388540294, 990232602, 536148721, 579037268, 136796057, 593331044, 389708610, 188259530, 153696722, 47135937, 309304342, 58165808, 980974810, 510688264, 79526395, 958682345, 576654603, 24843911, 413689345, 905924419, 675296084, 721952441, 533147511, 513706556, 769213189, 909865638, 814558234, 57967642, 380744243, 672808666, 342712919, 520440946, 490990709, 990745155, 678390060, 596226116, 127954604, 235449846, 323462089, 193666184, 839405301, 866595813, 98076489, 904990303, 804748094, 320925966, 676207317, 516945621, 451327438, 267622297, 557917497, 427905237, 795192120, 744705315, 527581041, 637838568, 853887252, 178020243, 768389779, 582831529, 596689859, 327795952, 433125884, 710206147, 776754279, 750975880, 439684669, 222363893, 227878210, 852890258, 814210666, 416673706, 906769877, 901625111, 118383181, 782307223, 246132706, 30897415, 306818121, 712610925, 801566209, 902892319, 194217502, 318193116, 680256920, 124503219, 669870257, 731990872, 773883205, 669167417, 594092053, 95151030, 197484136, 355476302, 186150239, 754132358, 566099267, 451970638, 718361766, 992829447, 523672823, 54087868, 613114370, 684564990, 767158756, 954145034, 822423682, 43470241, 844235798, 999735495, 639320617, 383943105, 232938658, 740206456, 20675911, 50710488, 125578888, 822694048, 777791748, 418037050, 944786626, 657973809, 734270863, 200237713, 230080531, 864529254, 454274880, 557649513, 446171417, 123126153, 176960671, 392796004, 34759813, 694702768, 527534163, 699403776, 618702266, 142036628, 814606824, 356919671, 546135229, 168212994, 46807739, 268849627, 614313527, 330189193, 701102688, 394575420, 140978715, 555276187, 427421309, 743979214, 381777644, 300750352, 856369892, 876011138, 101961180, 850565009, 715560127, 639907029, 998057569, 463807658, 166994382, 447659680, 121867020, 797212240, 35793395, 723234229, 904813971, 580482687, 637575543, 246411368, 572887874, 4275760, 782719659, 975844922, 383981291, 545438731, 870063717, 91456117, 373729936, 497057682, 712593286, 454554392, 778473938, 81572430, 298198454, 997402583, 784344267, 936678366, 73996605, 366042423, 703674549, 841607232, 234375723, 131095914, 751525812, 915295978, 83365399, 959313078, 405091367, 181279104, 422026469, 531838489, 44869458, 915802851, 576923891, 417403860, 781334362, 633237703, 268161871, 94381262, 639053829, 397417424, 151176782, 527613961, 611935537, 756982580, 806079637, 673281350, 580902384, 131456781, 764209493, 69191821, 657069923, 427825941, 678456165, 339580984, 633726255, 342091250, 339774173, 630684632, 623279142, 904296472, 738534180, 392968727, 62027530, 351592186, 708895814, 350812118, 144986931, 81122546, 572611771, 713975334, 85016025, 249268949, 34226, 395892677, 727196383, 816884506, 725486739, 988899247, 994013018, 276192936, 44585060, 354655055, 15082635, 55753608, 534216902, 167285952, 521142626, 872477067, 176592882, 350034908, 22734133, 525501021, 955806275, 287287442, 623155639, 578633753, 259553226, 724091138, 316744014, 473855948, 85802487, 475478487, 223817870, 251030200, 393202071, 808815835, 341475978, 586488103, 360185254, 277986901, 475540156, 659726127, 276025260, 557888931, 716722816, 500082135, 639754363, 922047017, 79467045, 365075228, 914451350, 291639989, 396298329, 6437665, 654953806, 757453131, 329706426, 202005856, 895447159, 135633542, 517053876, 325551404, 21985924, 176174306, 894925477, 677188909, 205237654, 813693886, 622626599, 60428101, 158541297, 149465821, 47057506, 788579195, 881268745, 830841990, 814699725, 603120345, 290504531, 159785608, 660920765, 5902030, 418704595, 654251501, 610519634, 512605077, 771592549, 86862085, 894538417, 47433569, 992398823, 427886999, 761258648, 184280418, 139387249, 497312931, 118083734, 353100092, 467711649, 742991289, 129576287, 132711532, 955710915, 936619149, 979088229, 846190171, 510414803, 431727636, 930420794, 821692021, 750736306, 410216883, 936463832, 180322634, 75569957, 636819137, 158107835, 124087264, 504899409, 993444054, 409791272, 796729256, 357406056, 935430969, 777739535, 808322616, 558312857, 888213709, 340548077, 186726084, 356853292, 350873266, 111823383, 217319208, 936443688, 272037631, 959516106, 687884596, 796377802, 499090835, 314901737, 999897839, 290762394, 843798222, 295021746, 229322014, 542056375, 619323067, 538241346, 683151400, 668677524, 587368053, 398104369, 648170330, 493248665, 430881803, 506273186, 327870417, 259260330, 992042236, 18702365, 669728551, 265001534, 690722071, 579459514, 788334689, 580200271, 870784126, 66155026, 443871158, 43423939, 203215949, 68261002, 59674979, 100788057, 148735354, 502075191, 8344688, 342994424, 232194492, 379441292, 48826567, 204783306, 590385348, 572918452, 851859062, 897514029, 943361823, 453416525, 902413822, 422001094, 666673150, 586502175, 652875278, 603662018, 629635226, 161657619, 608166838, 555374320, 443244967, 820110627, 255939266, 868319200, 633068948, 940856662, 837316417, 145926799, 886309074, 769441267, 447832083, 49361330, 440611393, 487475331, 162423694, 807609919, 108600679, 660326109, 518804404, 417672899, 63208750, 980230948, 692598526, 443466276, 524230845, 16608929, 561909070, 188749259, 146995758, 927532165, 722964898, 394600750, 818826428, 39400451, 150911860, 359142875, 198664162, 494989409, 370536953, 247066426, 583351932, 411793822, 62022436, 313648604, 988631639, 41576021, 172913448, 666579058, 394868018, 57993484, 452934117, 746204966, 170959559, 815136662, 896254367, 958086581, 884812708, 361113035, 64973588, 90428872, 569593514, 392881399, 28801037, 365841140, 234865311, 672967511, 801935144, 132825884, 181318420, 320815500, 317287632, 762962907, 898213426, 385799965, 877532896, 61899438, 439095773, 696083422, 805804891, 817310363, 70705806, 514579364, 480330958, 214914666, 809666811, 48580263, 153443282, 582759690, 735698122, 84108730, 263021530, 812620295, 671149817, 191534650, 238413316, 248714983, 595486275, 599720210, 786369463, 388768414, 283995155, 508717273, 789048008, 491937615, 409837602, 264508225, 472126006, 807264995, 241991236, 652713154, 430526913, 445933351, 25712305, 954390904, 595548495, 933874882, 306923409, 567025643, 938140827, 758550946, 976250208, 989379077, 24061260, 259653361, 176164612, 212181678, 302110452, 343274233, 480098148, 658479891, 877711152, 731685676, 887622339, 557021925, 295476944, 555222052, 487256263, 884527899, 426713668, 36130830, 250992121, 476009964, 333728505, 402940800, 790602567, 606548761, 940441187, 688716920, 180684783, 516458081, 293119249, 267466579, 959676219, 697790331, 113088084, 868354631, 532623296, 192964708, 621625786, 893194558, 673938370, 797331585, 23920721, 183578869, 587235354, 485634450, 617618254, 651501612, 552154282, 531110951, 812339984, 270634989, 441200221, 486855843, 618535471, 736885981, 46856256, 801408575, 369861537, 937783589, 657180320, 320388947, 986397959, 186466908, 63134905, 957162956, 992099126, 106677942, 866959794, 522069225, 179282694, 661494034, 885260353, 999498412, 856565880, 765973355, 353152978, 777114681, 950859225, 492924316, 130320574, 366514264, 982385324, 284300012, 827755988, 447533349, 638990046, 810456510, 151889685, 382693110, 224110833, 51967719, 669492260, 134069335, 265489758, 756490250, 836589206, 171377998, 708330323, 620821065, 753027392, 584223672, 49990920, 753583365, 180228596, 74686053, 753490373, 738089245, 278379146, 145593808, 608050936, 118898295, 877771249, 329642666, 580740753, 27398338, 823178900, 261862933, 936920244, 155453577, 664742754, 300373443, 612207902, 505995592, 555133123, 489985767, 693064492, 701022420, 696392364, 729145707, 809492082, 146480418, 939280559, 558594812, 411364284, 437955992, 152325838, 684285555, 621552928, 36557641, 879331336, 230915855, 512250103, 229365648, 145118842, 753889969, 285159790, 413759832, 29980131, 783111919, 628784318, 415674721, 753935040, 427219517, 421469639, 332286884, 251914159, 903148085, 716086947, 560968897, 459329735, 500995025, 621371203, 56094541, 692347521, 319070582, 984396420, 911866381, 574132216, 123709685, 498361507, 45295875, 329002661, 276575322, 300770330, 323660057, 605462860, 403338358, 561482492, 413687776, 222205952, 823236402, 88629997, 478758896, 242702907, 608009868, 753905657, 470478787, 720336325, 988646986, 249902289, 619521333, 517151755, 309426714, 428899578, 549391501, 649855412, 160191982, 439311455, 424890429, 807662367, 201252273, 896800567, 207954634, 702579233, 740440550, 490664776, 353687077, 438334389, 28609988, 962715167, 986464142, 629689902, 590915480, 780627383, 60381040, 722809086, 82222845, 723393056, 797961280, 241636874, 271021382, 260532308, 149698132, 511320618, 4995319, 245957051, 647243286, 758062011, 251552131, 644595214, 629011528, 995864644, 157393737, 836756976, 286167240, 943880966, 294723074, 521672980, 534205914, 503404297, 768288266, 291978785, 685489279, 400375337, 892013757, 327917564, 461437027, 248607419, 663749207, 162828101, 853147086, 211508313, 677729949, 421231950, 818899414, 588059177, 22617740, 867868932, 482884878, 678473444, 561158108, 410923237, 372195459, 860212439, 271001186, 448677564, 457051041, 75823803, 619216159, 527325734, 754478724, 230373210, 10741419, 352695754, 725745774, 992327056, 432641409, 36484372, 118562594, 254646835, 759231417, 153935740, 609799739, 470203875, 195340831, 803204064, 883094461, 600034, 77350047, 581160646, 382493213, 715864088, 3580829, 140043210, 799417440, 540678759, 315935749, 990616678, 205472032, 354327244, 855160096, 268204898, 118501166, 556324008, 800337170, 371955419, 952451875, 36907726, 666569152, 579498125, 293915607, 124942407, 986896191, 264255848, 211014336, 553069114, 492249812, 503689752, 806660108, 842491517, 61558632, 530990277, 671300769, 660823096, 61427922, 46513981, 830108485, 219880904, 645362487, 584529316, 993111001, 235302244, 368395703, 97084752, 593381816, 591654009, 221096589, 680704591, 14637069, 494275037, 730609224, 865975318, 726797044, 599665717, 160423002, 105085013, 554238624, 556531931, 159237504, 283638415, 612450184, 186580631, 932710345, 502803379, 999266569, 201856256, 52618669, 877820930, 696964998, 60914583, 661165745, 852747133, 529112080, 666292866, 562642421, 930776341, 997528143, 750821686, 282125498, 177087332, 114266011, 52059385, 97821116, 339258535, 910592845, 112094333, 467692326, 801226977, 764093867, 372677958, 81574094, 210252775, 799893582, 659430092, 507609195, 619554783, 7827656, 948237389, 481738070, 909463594, 351943181, 961290833, 20431758, 15293146, 310357942, 111586957, 154717832, 450204757, 661192727, 758529132, 149109739, 293647452, 132055644, 962570085, 393942297, 110431689, 18439703, 451335262, 650166285, 933087403, 664309430, 706439977, 521445136, 699558570, 742233918, 559491376, 376645580, 473566136, 709930549, 446526633, 753023247, 107239148, 736017648, 194077896, 744129255, 540100558, 214671313, 862512473, 883296670, 976015484, 836226233, 882592171, 91584138, 354856021, 477520248, 614852988, 940249651, 145474686, 222945405, 196571164, 506825641, 840944659, 741934860, 476187466, 82381886, 646247407, 760494846, 283307033, 178641558, 249004229, 483369576, 550604263, 609177578, 137007471, 16595717, 67646731, 597422085, 383131345, 570122256, 893370199, 837084174, 325249565, 887177385, 569052168, 424830902, 617314301, 809363056, 222029380, 124372301, 660746320, 577375620, 936020238, 473013903, 56104062, 723329105, 184590230, 300553059, 618309991, 327199226, 73942776, 528323246, 78967605, 391323990, 54630118, 757653292, 441500261, 395631316, 151799420, 643359118, 916928701, 875545019, 403844298, 769407302, 557137044, 696805549, 392470985, 947410253, 212193484, 235969685, 423449264, 659810470, 773221518, 838751803, 419292958, 352086664, 715947982, 884381237, 997244300, 707823657, 342354551, 49463538, 184129331, 530223709, 142835437, 360805330, 407102283, 919679778, 220777852, 894248922, 276290725, 528969927, 48335033, 639076198, 835424246, 960530220, 927150665, 667048111, 659632219, 764374461, 90057287, 502580398, 912250061, 482158625, 705096443, 996153989, 452574747, 462137297, 70668097, 432657709, 801533379, 321745306, 955663020, 207742916, 428104227, 570619744, 900982604, 47477596, 274557241, 236061473, 323675263, 915847602, 682745356, 928278329, 642068277, 529118086, 908827445, 955983754, 282935795, 82489519, 773943949, 2819006, 397187856, 105844392, 711466529, 541895008, 863259388, 517266326, 681622498, 639645370, 125676670, 774853568, 754435867, 925508216, 833357628, 793169820, 359427603, 667543736, 795720688, 237140924, 990349249, 281019669, 444851044, 150804787, 848524527, 606911152, 520142296, 855006513, 155724303, 889816264, 325463686, 300163200, 152373702, 238965264, 232607550, 88044616, 718163581, 547951039, 57781938, 475560559, 422877382, 560029854, 484129064, 491068509, 278577910, 189203938, 315884497, 444972238, 670584210, 866799282, 820926217, 980128468, 485865404, 94348104, 389096101, 627610021, 295153911, 964055135, 710645630, 259368219, 607291118, 630085579, 223571417, 253987908, 637750709, 55313317, 913516111, 342149646, 389616956, 709715064, 554375192, 868742715, 337203628, 402457471, 676890516, 281709944, 867713824, 220861363, 799871620, 167446791, 150148269, 994231553, 977188967, 468725017, 115524140, 162361047, 689234872, 52219245, 773800558, 334289288, 844148869, 45623860, 806036481, 739748630, 300952897, 922852170, 116018016, 174285557, 2287585, 794410716, 637984119, 741888489, 503613048, 916690266, 709307749, 185840065, 547100919, 998004363, 297256190, 782445206, 559533730, 345989111, 40670455, 850101106, 259184241, 479080994, 11634115, 633724607, 161969137, 594336326, 498239134, 460981570, 276348321, 875071337, 350410544, 744870459, 868713622, 731013472, 179992321, 778679295, 894642518, 284870849, 966380065, 278078567, 579747731, 22513351, 137537139, 529766518, 76618, 600661751, 607172567, 21292702, 44205533, 515065372, 145232634, 77824840, 923372569, 345825687, 167458169, 981538412, 216836109, 277992318, 81481048, 191091398, 645824908, 417734431, 116660000, 608900511, 127140975, 871562096, 687641917, 328350817, 259714496, 133031704, 932162015, 400017682, 533579269, 656752382, 726512797, 292925831, 110880572, 454509452, 703440021, 378792368, 603791574, 557535013, 769156454, 793508201, 679617812, 592100614, 149437316, 653430205, 583222668, 166095222, 246760206, 119997050, 284046968, 644991328, 378081825, 178851478, 521524755, 679052041, 72937081, 710544099, 584435320, 598560378, 516947282, 256862533, 361311074, 463808340, 918728099, 945269930, 921609050, 643399875, 784354136, 421683757, 949092619, 841301287, 759439874, 558947832, 538617009, 86682903, 850370187, 781372513, 536096620, 969855300, 111205372, 242081965, 618277691, 272647515, 824633147, 519683434, 433349874, 195775257, 954951647, 209114353, 591231024, 749536914, 215256206, 480734254, 354242939, 911040929, 412684243, 520535839, 915485745, 527696537, 823171861, 527558539, 4379960, 225666571, 191577787, 82107162, 253534973, 281361997, 947309920, 911349134, 840017937, 445215841, 185741470, 575557944, 797238643, 4179304, 513560177, 478179391, 774404560, 660045698, 753435434, 470180411, 796578440, 893271945, 330876324, 913785296, 141064854, 103389786, 744254322, 573545345, 382669039, 309413656, 333908546, 921508830, 439457290, 284559657, 493924372, 482300736, 758654259, 212280328, 947006753, 871114184, 289251116, 277313774, 32698387, 222566853, 397651149, 110894404, 630927139, 614656290, 642246938, 407103064, 313579989, 940708876, 202962665, 65539408, 302031904, 815038172, 198962579, 197173654, 594532308, 279104510, 442019648, 656291183, 997179003, 72510906, 976909549, 775107305, 26036256, 51675531, 410707130, 579588957, 270515645, 891375587, 6536685, 341027098, 237016075, 23310506, 349804289, 860052940, 547892442, 192474720, 761943114, 644031251, 425013163, 327053897, 304641256, 222938098, 10484049, 966984826, 450054358, 459824267, 191055912, 358346237, 563591434, 67555672, 136787728, 656817425, 791721275, 36990448, 496440385, 946359240, 988396153, 136171933, 809601772, 977473210, 73343617, 691009575, 343840847, 555370765, 787459455, 367694974, 864175789, 623651814, 594052165, 113766822, 621038547, 469827672, 191649366, 141296905, 240243129, 194017610, 8755186, 570939614, 543650775, 672249848, 303775367, 111975652, 348646452, 83244090, 59995880, 34681530, 546456650, 756177681, 417815719, 951775434, 663111118, 323683604, 78902994, 493599497, 904475821, 821678951, 665241724, 608379921, 358161343, 165421785, 156615253, 430169975, 328491829, 247629193, 267482962, 922891133, 850282534, 95555063, 875650178, 95087713, 946133727, 884936609, 76314786, 369772014, 221268352, 780401942, 540977194, 296397337, 233676820, 206669947, 47093847, 844025873, 139517271, 718710567, 278072627, 510069963, 373867677, 528589056, 856582215, 515542993, 887973414, 353763340, 388287937, 365101191, 441306664, 751748529, 42429472, 372176243, 867418623, 255315151, 419249488, 926169875, 726798365, 973548139, 573824927, 279935084, 811142769, 822808700, 903144307, 740472745, 684199885, 97582391, 320851317, 327099424, 441429327, 102504599, 686736371, 54412650, 692641691, 11800911, 829279358, 267901048, 530109215, 615333880, 940732265, 33452731, 347050429, 949983274, 209009686, 240885731, 245888679, 945953456, 568963399, 349747434, 114489695, 631375179, 564079477, 714801172, 68162918, 743977202, 48814783, 527547084, 859749982, 533608958, 223529178, 72137367, 264231756, 576368619, 990420712, 202678815, 605041066, 650842613, 968210352, 859380582, 331992695, 34240640, 407311433, 662840008, 804368831, 137065469, 828636242, 570685125, 215366510, 561323865, 891007771, 733289060, 839910736, 951315610, 22323306, 681789418, 552006549, 478633926, 617832196, 368107615, 470938120, 750223434, 875444320, 669536648, 743829118, 411519695, 437041348, 898766274, 953072981, 619793135, 928730321, 828921174, 893336847, 835393590, 913545355, 980434974, 445053938, 453719482, 674005302, 540293853, 818271394, 694889588, 697336737, 994880221, 968577900, 614082176, 886918369, 850842119, 751522884, 627700519, 919322046, 688907832, 596459079, 864971832, 861737595, 813558695, 776066126, 700959782, 60765245, 306342813, 878613143, 942828073, 659204178, 259378308, 203857822, 997887748, 315287313, 406846151, 944099144, 551117428, 164020406, 888977792, 66272007, 185885174, 302729276, 293646531, 502272869, 745524988, 121802932, 414762221, 702894998, 922699273, 288852168, 876108732, 670036109, 396024391, 524252941, 913227638, 897325644, 906374264, 984531100, 337319531, 490060150, 881302391, 845716640, 194353033, 125028051, 439253230, 857797888, 560666416, 86964844, 318165775, 497551216, 883048534, 753299786, 116097444, 298278578, 51173894, 379308215, 265072057, 921628202, 542672193, 435368861, 269507235, 527559402, 407062666, 493179202, 247443160, 594517433, 369579399, 676727065, 671159776, 56877591, 630967811, 911952040, 769454119, 770607290, 678806605, 900326803, 527539256, 881502562, 155080468, 309180940, 572195921, 955917758, 269583454, 768875775, 10086631, 187368319, 916426254, 694205625, 89863231, 743253529, 546227346, 476202041, 740324502, 834809898, 219627644, 784025357, 886081041, 67417974, 188663523, 516673717, 371228263, 175573608, 268269744, 478447528, 346285449, 604594208, 514127090, 569413517, 155337138, 393771175, 355200593, 348986438, 62913819, 655893684, 556071389, 153601924, 465010498, 886917465, 588068786, 188890060, 367859310, 556207754, 379587336, 635118559, 661400504, 871723435, 296658395, 186292412, 823246950, 455537442, 774101615, 582237107, 392889088, 741860963, 330652998, 425969381, 68096326, 947321500, 402496583, 751761880, 674841357, 468227704, 712744484, 402460150, 726523560, 254805643, 73553239, 276312962, 589163815, 753518377, 354235374, 602187768, 75963482, 769137985, 476787045, 800488955, 578635900, 603710725, 682070459, 216278470, 205083008, 42083539, 877223710, 147545173, 640392356, 791176479, 150449779, 657972594, 44118810, 132313251, 517953586, 832166472, 793727432, 842714729, 572265670, 148885979, 962503967, 192845918, 109106403, 586426351, 749205811, 298529524, 32095520, 82808479, 356457069, 156827333, 679536359, 997137879, 427965995, 247826703, 521580214, 529664322, 668608847, 431250608, 75150387, 644774841, 83321876, 195127749, 475068182, 755931871, 223548131, 571754703, 364307403, 900189688, 717630524, 491186789, 958718926, 406072862, 111705903, 566215935, 982214143, 923725084, 598834514, 471573116, 633487941, 497111166, 831017676, 864588613, 480334157, 890164970, 172310617, 140181378, 477048035, 821977836, 729034735, 338705051, 159449562, 569481924, 822871970, 597635261, 164891734, 840329758, 932457873, 328129449, 600834563, 190082078, 789144875, 665175879, 540015099, 752345535, 595274791, 422645046, 534464480, 595603784, 678770380, 841330523, 253676866, 908927305, 289824566, 845789366, 436910907, 503766127, 210666463, 317543316, 376176790, 823636855, 732612583, 40319495, 320975995, 846422356, 646682072, 7579772, 477136233, 640417310, 373878894, 495330345, 29006963, 13158780, 477711137, 734168629, 888346665, 924565339, 635632226, 456010053, 799700633, 941682121, 618155847, 437007220, 338530460, 962798210, 733906343, 243355045, 247112158, 83039330, 246571139, 210158333, 340304048, 712886985, 214299047, 243263798, 590183867, 307732230, 581707078, 886613905, 268069269, 530833912, 910919605, 230842836, 232571086, 449839350, 645870304, 624289363, 839032284, 48412052, 491938989, 536306262, 233753369, 171943468, 520354223, 787513536, 685330014, 157186422, 282051913, 92954136, 265440024, 36942864, 191120823, 146407147, 750936660, 276759948, 692953354, 35578238, 850090443, 457596296, 119609213, 645860426, 743420838, 436251506, 990003331, 323302751, 806884701, 652371783, 892909122, 24513900, 941344122, 284669545, 357921578, 959368868, 9811513, 758290409, 373133974, 921764419, 467994437, 396737625, 596665819, 866114607, 231058691, 248875961, 865675353, 801678772, 674581033, 798984114, 96589446, 288615808, 177604295, 254592458, 74671818, 604108290, 401001302, 422891382, 762252019, 631001011, 272453800, 844901993, 446395910, 551983368, 119734090, 750060143, 874745100, 85821413, 140604450, 912974634, 413595389, 550204302, 544643190, 574107074, 933109756, 508946564, 688023428, 444372005, 619732458, 573546650, 753368228, 310567866, 628137106, 635702444, 708371771, 171853990, 310327260, 908258853, 775419886, 212248206, 759658459, 415579078, 546560074, 224778819, 311655959, 361135509, 197071920, 710690868, 279089116, 614049319, 841954442, 499071844, 874718223, 527796171, 137544529, 348999598, 993766027, 428510064, 884929493, 229119934, 553475663, 423393201, 540099903, 182302334, 121959653, 892384948, 845711645, 699492174, 884921778, 26495563, 182529918, 74836107, 514784064, 560567231, 225794819, 275090891, 123306188, 450418761, 298853234, 45874114, 57359741, 833064149, 193587324, 826022520, 365835361, 515922203, 116140253, 558062331, 255122546, 694119896, 82187312, 755088093, 429077320, 54253876, 221242014, 452155379, 720575586, 501170, 567329486, 502661034, 444579035, 562345070, 676982490, 112063828, 829401994, 23940390, 796946128, 381892775, 305256150, 814919304, 385222119, 981376805, 781349314, 685426767, 705515865, 406976936, 302290533, 148528208, 541759310, 159806708, 244221174, 562914589, 920885318, 812935286, 381170237, 354787104, 71201061, 893196229, 781070220, 892504383, 370229028, 13912898, 750169183, 789233815, 943203976, 49452623, 403862285, 634083109, 212667378, 569465954, 672999646, 597469153, 975684416, 716478159, 231643490, 111875716, 860601392, 873407917, 556103158, 433235432, 54895197, 951753626, 388149249, 241265364, 188147521, 874782663, 774911518, 618562191, 778629647, 401882405, 768956670, 573273057, 463846311, 732649235, 342316033, 583137428, 951883833, 667884794, 852704264, 33072629, 457120095, 947891975, 319994697, 844577231, 808144845, 335752444, 850426663, 884260539, 747014304, 343519360, 422772256, 703553762, 460126974, 410633846, 773610737, 304009281, 798899126, 83968913, 448812096, 337444038, 569733629, 728919476, 512740011, 618756992, 206220377, 967429880, 57082907, 519582179, 304830316, 70922465, 351157186, 326209371, 31257379, 603797347, 327051239, 7542758, 782638475, 579415940, 651013599, 205612507, 378530870, 517937477, 663100997, 533658989, 810888792, 689305247, 396163528, 605815931, 477577860, 131925445, 846203053, 517608246, 346888875, 466561871, 645958608, 131489810, 535458103, 747406617, 52611144, 31096303, 737681785, 655100931, 843873661, 914253358, 431857371, 828451809, 833736215, 31850621, 146627638, 625726409, 741387028, 998973186, 286681584, 669048895, 974982144, 521984973, 120554664, 799899319, 428778142, 691298298, 17643445, 511098184, 117831017, 569891436, 271604219, 781399328, 987350510, 703238910, 564801918, 872730769, 964457143, 31515737, 782281872, 281968258, 361228486, 22319132, 153789328, 901584255, 478516351, 117084688, 235921623, 690601133, 813059459, 120208711, 452092324, 975085664, 688038071, 543417823, 871821204, 369248896, 100329581, 30077079, 218597450, 966860599, 101442070, 959536481, 531600638, 320926495, 831601080, 530713178, 879325917, 509893523, 618317610, 744407779, 711265351, 600635514, 502525311, 761743099, 13103321, 959683826, 485768364, 378994470, 115650182, 668925300, 707386518, 647353798, 351056979, 202163577, 775197361, 140790130, 581183885, 66423281, 665868173, 136313166, 547683796, 690211631, 859964729, 574890967, 987120474, 288335650, 176088066, 800212288, 445349490, 744574800, 956609008, 493787814, 390644678, 454141956, 461778065, 326478243, 435211218, 906841688, 642736021, 844214336, 609350318, 473907595, 446540649, 895763398, 893174118, 715055181, 768728243, 725324899, 655902273, 631862248, 887209426, 196572349, 919088601, 929922208, 354517158, 291508411, 552535253, 906405704, 972060268, 285758109, 597876239, 433761121, 311587985, 652962248, 45765545, 81510484, 944105924, 375443410, 153457504, 896886363, 907691485, 707051187, 359194502, 360573576, 329813518, 150124634, 851558251, 214255643, 687723226, 673174796, 201853964, 325159293, 118149262, 421573798, 189496280, 844478901, 1752693, 499818908, 352658282, 190011463, 158829707, 239317775, 151220177, 712940703, 980109089, 255101571, 777969960, 880670513, 655141856, 844508741, 499481037, 349878324, 552710067, 547717910, 777400145, 119565286, 744315990, 101731756, 864558260, 997618108, 287575347, 215361788, 889507431, 328091706, 875598765, 713834957, 282137803, 192345657, 513728306, 458193509, 909589667, 824034861, 909778159, 508065577, 404991904, 800448396, 622132641, 301831625, 789665673, 47175779, 969734857, 129088337, 928611875, 622066093, 994293286, 936984126, 326463764, 425652393, 762410998, 588670516, 6574330, 752113948, 22217051, 456748464, 908948343, 879876797, 774900405, 672306380, 749146120, 236008364, 413288299, 361684848, 723242033, 290821408, 337773027, 614420206, 120417053, 616716066, 191913445, 537547347, 651261445, 575852344, 11032506, 554646885, 912852307, 960770988, 163988373, 235626893, 955652989, 676419975, 809067058, 561560974, 93787238, 559318063, 427773364, 258189024, 192468168, 97265678, 455475514, 844349786, 716887379, 945874675, 319458461, 147303140, 770006175, 564668396, 898902957, 275239674, 742371559, 776624528, 809844228, 725239894, 155204984, 20357638, 185750123, 348361725, 386466714, 868431079, 164355366, 426456353, 823093754, 239194553, 642069986, 775067489, 284188368, 57673155, 927338389, 519209758, 868489620, 904274224, 135390781, 469018262, 451233267, 428178251, 361978636, 854303594, 400272293, 208677581, 973808888, 251011816, 38967631, 712368468, 776340741, 836042022, 321260524, 569654673, 463697428, 992568872, 600013145, 281965427, 189899738, 487247560, 343509068, 261361279, 682834885, 81748730, 120541796, 147149360, 901746748, 436309617, 503252671, 800750948, 449532639, 698151823, 699643129, 969975173, 370044722, 70916765, 583941681, 866271365, 997729481, 915074441, 181507711, 336640855, 723238170, 483732841, 458639110, 427121226, 666546390, 724578017, 940834741, 689506362, 624063900, 921362379, 158791266, 721911321, 811438957, 91313918, 458124482, 140415040, 970150508, 487869886, 233677998, 664793872, 677762412, 247763626, 131802842, 449845280, 375968785, 50208996, 665936326, 394130986, 460633414, 80271394, 82629818, 968242212, 292498752, 945970104, 547884705, 164778889, 287934646, 627048215, 595949578, 356800522, 67394680, 884978858, 117687388, 811372712, 440319325, 449804027, 399805179, 279112736, 496271995, 84236218, 203773993, 300717412, 589270661, 46403112, 595871293, 294838763, 612312104, 933532700, 559385316, 158247489, 92149751, 371742869, 957832736, 302783648, 570017557, 965402327, 270163764, 5041226, 590226041, 390349606, 505568591, 138681833, 332407286, 538315229, 53531125, 225388141, 482635924, 695417437, 620905321, 100047466, 918964739, 305892280, 650136655, 441492436, 215405087, 853523862, 463859659, 309725161, 557727753, 429025208, 954534414, 163524123, 936400858, 936606811, 619552390, 356781342, 229118611, 300651993, 842464074, 874668299, 216388874, 777168152, 525374877, 621955386, 170416724, 611932291, 200106155, 149458749, 666193393, 318007975, 634942245, 212743253, 989755794, 571768385, 343623598, 427016018, 111080460, 185735096, 483718367, 62273688, 622212324, 861363519, 363014936, 910757444, 583207672, 633851489, 751908807, 244634027, 555576373, 454738217, 405089358, 26079049, 614660948, 738619783, 45964092, 641533460, 166414320, 275387110, 327610524, 658803145, 816965509, 692321059, 312014050, 844051684, 927905977, 818908436, 638081756, 405768233, 772227538, 826029501, 377221447, 894228782, 175770350, 69348752, 923948540, 785350564, 16238, 200837087, 870339416, 435286975, 427958154, 434522715, 81726038, 697751881, 329273576, 269173949, 790259848, 686022838, 639341740, 723770367, 533054757, 466727745, 94271882, 782338770, 644012421, 242512352, 390348417, 611809924, 433555657, 933446393, 367408186, 259109908, 471707193, 177716663, 849462583, 609500703, 286612615, 906713819, 62356533, 205530472, 845396565, 85351524, 51895229, 783712656, 830096010, 760248399, 176724384, 125570823, 203388791, 91394027, 12822245, 712843056, 124358401, 994393697, 472217026, 125436565, 355632410, 850350294, 177801945, 757252903, 485011791, 126607022, 437417256, 496986583, 283018709, 428473099, 441420669, 577159413, 414583850, 5015517, 404215921, 479852811, 827853177, 531887606, 374655388, 154630820, 786399081, 500526298, 513409391, 410015824, 693468643, 469951036, 133559175, 878222525, 598992187, 201296459, 322859562, 703112345, 245984296, 286849745, 110387986, 663773680, 167743178, 130036056, 8995959, 460161605, 755294449, 601330730, 638350682, 879036187, 452136042, 495105104, 817018161, 156536575, 167182137, 142223705, 9344262, 530425933, 775635752, 351287109, 363016374, 956577785, 603527063, 251362453, 288883292, 579080421, 544188768, 313604807, 255993005, 891635462, 464370967, 582671832, 688295370, 518232275, 904867632, 724541539, 572685500, 560055870, 721543274, 332785845, 396543613, 907967810, 274986941, 906717107, 160974861, 626110113, 534837346, 461824503, 825912352, 837544626, 579991102, 646912647, 91793832, 71584642, 402795953, 650615686, 971820809, 926372741, 505139478, 217163301, 31918509, 435625230, 875326843, 595315891, 144455854, 843176758, 7737186, 882361243, 347209808, 449560433, 931265597, 554920839, 625022748, 459911929, 230639344, 742075215, 302694687, 257568308, 455939139, 418599094, 472754410, 474830792, 605715171, 48655407, 803555048, 783420344, 756847770, 743226896, 208090155, 759262998, 264223055, 995371552, 353029533, 115085333, 197438099, 4207726, 495279643, 696440910, 379238764, 921650278, 465701068, 490675829, 517907955, 874911363, 733871056, 588640997, 911583278, 550176734, 480596898, 160653778, 699307714, 736477963, 727861004, 516920415, 594489392, 219397468, 357970670, 957607928, 364952803, 167378949, 168950517, 398911508, 671426527, 142840599, 917009356, 492072161, 374179053, 694469445, 492259165, 879128333, 817568206, 673987623, 49991064, 627950149, 268534457, 141965334, 975132721, 316045157, 641161177, 793516165, 21171881, 203884661, 247358731, 837825833, 302964416, 287303231, 652041415, 623579216, 285115074, 782053026, 496110601, 734605632, 871865648, 285119653, 334352546, 121806422, 632279135, 885333350, 46359742, 763579594, 813127928, 137700446, 411078569, 362125137, 219097698, 32141136, 366415958, 892928698, 232018231, 516830193, 548989134, 772273893, 67024374, 381403202, 13828728, 827698634, 166749585, 290113105, 759913851, 219681827, 242178386, 997494566, 826299101, 66171455, 520356175, 636001977, 811276742, 915634948, 358540614, 315742661, 700115705, 692206914, 154517086, 878595995, 196230286, 912469287, 367788200, 663252017, 142612705, 465747876, 175809317, 514931082, 994141634, 901786935, 591089222, 619747431, 662396984, 512509478, 682361692, 443321413, 921375657, 797347736, 431992778, 675040704, 782208224, 394630989, 827557701, 115869082, 674149695, 643873606, 212037961, 911077058, 63725009, 163504157, 212771176, 868047473, 236898837, 598144528, 265404266, 502830958, 573372501, 224005185, 54470817, 464877102, 605582500, 760952687, 847684682, 73913756, 347614760, 498348300, 640735811, 615424183, 633560026, 107493531, 736766843, 479812803, 404432197, 861390642, 351537701, 417698116, 717867885, 943471362, 697033642, 757511783, 249571299, 93728002, 297998025, 660858186, 639751509, 692804474, 31538837, 33826166, 194751463, 798130574, 812320494, 433159564, 842570404, 203332505, 773477614, 955934620, 781720651, 293373171, 959242791, 585028926, 223968145, 379094795, 755211468, 842521724, 884529178, 92862323, 702830967, 118119101, 520060026, 762906698, 340300025, 3902933, 668041815, 91968580, 861595888, 43126869, 403759260, 962915156, 343343438, 902980184, 867151923, 303807371, 222899905, 259613873, 953370762, 12293043, 548322081, 397088239, 569581851, 5849043, 185604279, 137956348, 393116168, 673735286, 849863953, 465277685, 963068814, 181022150, 374085770, 360728575, 266292159, 696827163, 960951827, 68859919, 856531881, 846981037, 500839700, 8106293, 570784901, 640782652, 614385229, 884630773, 359801589, 841150909, 602823744, 846923734, 484822118, 46518910, 174454606, 44623845, 339512643, 908440531, 350283883, 323107877, 623577357, 44645455, 639402199, 574403312, 975989468, 34847117, 963287520, 310203217, 10044735, 990995208, 571149222, 59239961, 341641588, 721540892, 998982205, 203839562, 400143564, 219440357, 108817080, 807094706, 640834822, 791669153, 260645016, 420603574, 411639678, 143718245, 173003961, 192549277, 960232427, 494297723, 148276053, 24640177, 483454402, 7553210, 235477121, 262480152, 367160290, 1825236, 442696670, 130674784, 608579388, 941963687, 255089158, 796589197, 229225071, 314432695, 442740094, 664271392, 930154433, 115527459, 575295867, 185796968, 692432100, 16135787, 308176839, 955726933, 694029103, 339818461, 774898866, 632429881, 953694798, 276461649, 86292088, 997528677, 715531599, 675357146, 238895933, 552457439, 577229618, 924933658, 396913926, 162333796, 789419577, 63107104, 904329941, 58329287, 292550122, 245285036, 99065883, 491803690, 286854395, 963922960, 688775905, 763866563, 181634754, 600636291, 402528100, 324461437, 444960653, 735401551, 404886010, 958881485, 501408743, 917243293, 777472632, 876965390, 251273456, 73151667, 437902628, 861599367, 358756004, 133899668, 443125475, 485586416, 988606018, 320683714, 133639674, 21472407, 781547055, 704570794, 366906295, 836028636, 602552589, 874657046, 538329332, 809204568, 551945499, 439474834, 387963377, 367621502, 147310836, 492725145, 955978985, 91500424, 810922748, 948805688, 904209543, 767088219, 124858002, 816953987, 371797318, 949123014, 416138612, 875614067, 473866042, 145671975, 798001090, 193036276, 507127438, 383230588, 313862707, 802842749, 748130338, 13266802, 181448685, 416197581, 350727983, 252353106, 936796630, 815559863, 764617858, 701033378, 205007534, 374729944, 21032886, 856113246, 526712642, 853862437, 410099241, 217940821, 2041628, 74784411, 551040586, 547176857, 361160527, 669424896, 538836594, 473161245, 524926732, 537947849, 604036515, 394181122, 274713209, 10123810, 828219685, 226406523, 869124622, 423615212, 606701704, 958411319, 810214953, 553754808, 855197439, 825984014, 874633097, 204826987, 645864741, 46127285, 375562342, 587575537, 476201175, 781634866, 485718396, 613939502, 703401624, 40276902, 376095400, 711387573, 508334470, 173979462, 115869031, 496855543, 165787301, 36942537, 816208971, 82392311, 398594343, 677394042, 896950985, 571507723, 122237380, 986711606, 458305511, 120034345, 580058725, 581433529, 873386679, 338404979, 184207281, 800745631, 798647110, 334877105, 246035549, 518196351, 637914690, 641579091, 523612283, 828953812, 382010816, 991596086, 361482704, 211353775, 449631948, 977293652, 235136089, 939565846, 496274545, 566159454, 407850099, 551577670, 432023840, 399704507, 223475326, 659349283, 803815517, 832215533, 913136617, 517961060, 874580997, 374895296, 498535966, 640164536, 818107356, 591111184, 3141411, 868675079, 391751557, 609644095, 640883740, 701761151, 946331720, 410766566, 690815676, 198085339, 61799216, 672700044, 144833024, 311046510, 510238082, 249168018, 654508673, 893303328, 519390626, 690096167, 960703454, 856780850, 283624203, 225141435, 375280867, 157673134, 830660392, 304460606, 353195612, 857587602, 334995241, 593570294, 538689689, 56852069, 250456261, 831982339, 701406008, 396361454, 337781793, 228251810, 956913757, 47722332, 721188294, 942340221, 928026166, 733121938, 65465300, 266435014, 765888162, 804763027, 987117314, 200846579, 31427262, 886844658, 671948392, 407532961, 820629802, 478329535, 358648806, 297403431, 382014093, 409424916, 706311093, 437928871, 940029016, 359987384, 420912647, 854946583, 95952127, 200124908, 504483858, 899110816, 460965092, 929352943, 985566144, 532008583, 5273382, 427793332, 38557452, 841537694, 986509162, 642277363, 907253653, 444002231, 844569704, 61289990, 724614929, 187711963, 114478887, 222232884, 254159869, 373403004, 443521198, 563899018, 560259573, 387348497, 36840607, 238728735, 966277534, 261413774, 155727516, 258600039, 977943598, 475627525, 539569380, 23885997, 237706470, 369811186, 988141008, 421202096, 873720667, 629241170, 626588892, 815842298, 840637966, 307128308, 732470682, 563151463, 896297029, 797196154, 996960170, 108948894, 60588566, 288323446, 793885547, 232413808, 300646344, 161565990, 533959614, 528037881, 575464632, 147580271, 310465339, 447064614, 514149879, 168733770, 103244689, 424316799, 7429167, 756774625, 680721770, 150215299, 525421338, 723886679, 591484776, 861278019, 263501068, 824353600, 700681966, 92638876, 732522143, 76261896, 210266496, 324849612, 983360877, 933894139, 654269943, 811345492, 988354118, 844471374, 747502471, 325351974, 784463480, 283960333, 823395377, 996652323, 273509087, 436361014, 332883079, 127115633, 862442667, 524016645, 731033459, 695915808, 796408937, 330950568, 745649256, 406125627, 289216763, 987576148, 984964643, 910731682, 949641787, 192565000, 277247067, 608079708, 134678089, 135475945, 953445529, 659552938, 961149533, 154432506, 728460326, 884832003, 930628775, 702168321, 925433687, 532044042, 816098445, 856958273, 206828633, 657776167, 740963010, 43447408, 450897573, 698477979, 271359705, 138906726, 282619050, 395524169, 869714790, 387447812, 250334613, 913937295, 676868239, 953917063, 457927176, 500367259, 229485516, 680687901, 144775710, 80592020, 666290593, 323233303, 610591478, 312214936, 785895607, 858982562, 232777142, 189690884, 25280192, 9630468, 472496692, 139226624, 842832545, 730417665, 395855768, 73846714, 297552565, 742610747, 658849978, 574041485, 900869944, 396460609, 552379567, 572823241, 452807500, 344822832, 558526818, 283126010, 923257907, 244296103, 906885824, 338379886, 548178166, 590443093, 306016118, 408805593, 108163256, 600387371, 156263378, 796826328, 582910961, 65983559, 875052694, 209094552, 17448871, 406844493, 804345057, 977058870, 997161295, 875220124, 792326965, 4919035, 182190921, 131510268, 543603871, 998054780, 932768854, 742515042, 275110472, 713063634, 45861022, 621079516, 688303993, 139774444, 466115661, 23266090, 328275100, 399417804, 69185884, 205013294, 69759923, 711739169, 347845891, 720396096, 655429301, 721187031, 598767029, 617464213, 725597549, 395726602, 649124361, 237048644, 984577892, 796412836, 322857583, 693180692, 600582461, 767187277, 904872569, 980893776, 278417317, 375482422, 524884423, 889352985, 492811041, 261636853, 947866773, 953003271, 945549495, 768187178, 854902119, 35402567, 473044660, 862579706, 119218015, 172819223, 77046422, 917073154, 316113488, 366108456, 162452228, 162286755, 398504923, 981802837, 802502186, 25717762, 735497339, 746942402, 212452642, 117194702, 761787772, 144957076, 717706279, 990912073, 691362454, 933251244, 396178494, 503060526, 112897552, 763573699, 970216071, 991468873, 25881360, 2963222, 138628926, 759611103, 318362734, 378465806, 273957489, 925135240, 738232998, 562339114, 158907362, 398471979, 100225912, 911062736, 621926627, 80693138, 325580576, 689750379, 452539419, 513407922, 801839844, 534447486, 36374977, 882820853, 61066838, 683662338, 943980798, 646994655, 784839600, 572038034, 34101761, 799609958, 103948577, 8759094, 772116942, 666163752, 943544713, 73018995, 465604035, 245743424, 490937442, 337703811, 267926464, 84088381, 201173083, 177609821, 246469025, 42172635, 743310465, 829876134, 906525006, 147950959, 850977072, 162934796, 174916225, 635361363, 639604996, 338755089, 957451065, 456040705, 890915727, 113451246, 637777806, 326373387, 839517765, 291965578, 228912342, 130731758, 282994972, 269482580, 191955077, 272281179, 609938331, 949716061, 788396731, 593580319, 998617145, 911697201, 563624938, 225480998, 321289869, 578079613, 743948944, 363018279, 776636957, 891852880, 897047446, 839823075, 487054560, 241076378, 47631847, 225058044, 186985053, 828046161, 130749296, 822127020, 542670985, 267710634, 934175764, 166490702, 532035678, 980681492, 209941147, 748360803, 953726368, 586282629, 30235370, 670116837, 530279413, 560633349, 438530745, 750586984, 620252648, 267842427, 610573173, 442840222, 322530972, 861139553, 179340877, 685728204, 355381194, 604515846, 524373780, 652533368, 402144723, 674868418, 487641151, 914058839, 857834696, 714841559, 688164857, 727572347, 225140802, 894796360, 852638754, 532226044, 219634096, 258022168, 236837132, 186976952, 89098750, 773549052, 857182112, 919596226, 417541512, 995383184, 401455519, 128007927, 952732799, 972421489, 23031727, 416008363, 141379864, 395866402, 907239237, 643810600, 584551834, 897618435, 49512082, 242948742, 440406895, 422621064, 249006871, 496748122, 802205124, 959181771, 366156134, 334211937, 93831682, 641171473, 965611822, 559741220, 779395084, 286022831, 860134022, 102352634, 723811320, 132327375, 424774769, 927760290, 586248806, 208454225, 360490230, 127089328, 868524828, 653365377, 20936423, 450478439, 294453705, 479173080, 370532250, 466556242, 271553710, 223275500, 699626112, 683559607, 781955659, 975901506, 956432798, 955449935, 789916472, 268563864, 777275253, 169796323, 357775179, 570367455, 851792431, 85999682, 151601513, 357357820, 431089811, 810057076, 592114492, 270282112, 260835001, 195519779, 939799583, 947587247, 678034512, 408988632, 450171004, 848162809, 568251411, 294905953, 928000617, 683425604, 329443483, 572252736, 152193482, 84330188, 633471246, 847528322, 194345932, 193868614, 609512822, 611170304, 534590061, 118698809, 988082403, 696282092, 946516755, 85086091, 613467574, 913156391, 644754326, 775370386, 292842722, 376355322, 269201598, 460750239, 238039697, 980309779, 902959363, 410347767, 588774998, 607770118, 777146746, 14613609, 154388076, 483498388, 55547940, 948876661, 927405152, 527900954, 739865911, 108011880, 617169012, 537216451, 450750827, 109416774, 3982072, 249090566, 37469245, 963322961, 409187212, 14041518, 623971935, 441090921, 330802076, 194714752, 806432676, 555834432, 576978514, 208745067, 895395649, 877211042, 728784725, 742316760, 508339039, 514599921, 955981445, 277129655, 201565098, 359006626, 903573540, 998435772, 860982657, 172599776, 542156974, 377256668, 214064087, 199231909, 929824934, 187939699, 717004852, 20442425, 303705673, 684193605, 294280950, 946379652, 66266967, 859911663, 509279122, 199265879, 850023953, 611380061, 614995068, 863681833, 771057186, 740306034, 473245952, 262402558, 597874889, 473293236, 694537561, 913767531, 864279968, 700304257, 774424050, 6628322, 373282772, 891093310, 396167822, 354222126, 21680055, 805139729, 712320495, 671813589, 842871706, 494331628, 693839284, 796678515, 458280733, 176912659, 83447258, 105570591, 968973426, 341503047, 169367492, 711480567, 121678466, 210490608, 817027984, 772686561, 321924905, 386611252, 520836587, 602151815, 535988212, 631925112, 421550381, 953064865, 645944676, 532140593, 928510291, 316210919, 140800304, 511952826, 872400130, 77337742, 495533479, 770196138, 802077370, 376704738, 182726262, 823822763, 729632564, 366867590, 109944611, 764483743, 746587956, 296362238, 954820667, 15483719, 284054345, 595711030, 810717953, 646045369, 10494140, 477513904, 331899266, 816819773, 623402520, 310066077, 439324333, 736030366, 781268999, 562253080, 487104625, 233168656, 403554199, 537576743, 711169012, 644955646, 881209424, 722269955, 441866362, 592422743, 58270764, 512265634, 737437923, 957795918, 55499277, 42310661, 744985961, 409519651, 189364810, 662901790, 879581122, 143297428, 855319468, 665081702, 998496931, 724759847, 532089435, 515468759, 595532935, 973195676, 145862136, 696010793, 244532759, 282315183, 453900866, 639268967, 619201639, 397168312, 712201792, 444947322, 60356159, 598411137, 917100403, 261189048, 688096057, 22701841, 624272127, 618707225, 929041585, 636553424, 931389949, 708391650, 162376660, 893345458, 524436903, 807398744, 129727526, 909122628, 883970898, 876101513, 351552515, 940706542, 549140205, 810591717, 381709508, 235413611, 297708135, 169661863, 632177045, 733084413, 859675056, 253286024, 724055846, 326801436, 847696483, 238719485, 222719596, 640762726, 568916706, 522617229, 464294368, 986457366, 666956961, 877056924, 394109171, 86330393, 218071833, 668236393, 555248148, 904145517, 596771466, 256734147, 785573268, 243770615, 72792748, 40647522, 786239805, 958402889, 834557773, 270697892, 367001965, 802268058, 463931550, 869624566, 348848987, 100050777, 537502065, 890761890, 65115949, 709264241, 203223327, 704883110, 584175111, 357375202, 948025364, 391187736, 504936236, 365557988, 897754138, 963548147, 551518638, 763782870, 82920314, 563571086, 482914450, 777577898, 874233207, 802817779, 128390461, 203322875, 596731034, 178850749, 917633116, 480795644, 832593493, 68111923, 5815884, 796488219, 70736348, 186825799, 952433848, 812017572, 523305151, 181412727, 276199294, 872515106, 698668281, 400840184, 248257060, 978566673, 397403466, 21555423, 519583403, 73172221, 556061231, 82959064, 86667016, 715757195, 340757639, 124262513, 17183804, 353526319, 418534476, 261634980, 746947567, 199761963, 138727202, 187856656, 916426964, 325671254, 851986035, 720695449, 939537971, 820056911, 941714756, 953752173, 611259660, 158803202, 228723346, 557805378, 977911906, 653922379, 722656685, 583906133, 519339144, 818548772, 232849168, 267508959, 563586388, 210896472, 87361957, 355870338, 878028287, 164906524, 126506455, 896888215, 659719371, 434984502, 86815397, 691548777, 265309830, 998625294, 655095928, 174638638, 238497731, 671214739, 437085462, 661901548, 69719508, 356749178, 890778141, 25600822, 401158769, 396478448, 490256424, 476780070, 900723275, 753963998, 892359374, 767845774, 324062122, 598620718, 394047345, 367310168, 331362473, 422282222, 761586949, 49424511, 41733869, 40662555, 509334461, 197853442, 347632526, 588005536, 220841481, 601573015, 150536558, 330708785, 505488087, 738925192, 566830016, 488969575, 751421432, 348952006, 465252940, 546945995, 811462635, 282493357, 195777327, 589861484, 152920727, 421433790, 383758390, 734860339, 538528052, 144892893, 679229470, 293416162, 716821762, 648358763, 119944563, 504601789, 586851166, 354512880, 295003940, 248602121, 942070940, 584110570, 206237258, 820069805, 748777055, 770245284, 445604668, 690291223, 782790728, 207214294, 950782540, 925889648, 726156530, 940346688, 341433146, 189012710, 162055332, 484085864, 857816210, 100921963, 173287266, 795838714, 513967600, 688671493, 886512426, 962609216, 754101180, 455691849, 486648921, 181948813, 171469411, 97247034, 436592529, 582448368, 381032413, 281844479, 984412631, 166223654, 756065498, 117125865, 210665128, 837043143, 908728103, 680847529, 943360940, 607318691, 798183545, 869948758, 736142619, 658378803, 176375618, 510386185, 839159141, 848324775, 906856117, 634807338, 322803047, 669997417, 959419799, 468034414, 914708119, 790178895, 903113787, 244635081, 917621184, 441183274, 657404415, 35403057, 454823761, 676286558, 124549855, 752776483, 857925485, 985830420, 951484240, 351668080, 908656548, 32858774, 1506246, 14349081, 91997450, 518305385, 183729850, 970052368, 275173648, 768491076, 974284950, 14349141, 587276860, 944459991, 666217656, 591743582, 241296039, 721030454, 88274423, 951760600, 162431468, 260963665, 236248220, 638738789, 210167902, 573285754, 269846718, 541522081, 436704642, 752418794, 744473414, 494846565, 991867402, 713505998, 30317490, 258049603, 191302900, 91514439, 542875252, 225812823, 959262154, 74410834, 692404020, 268647796, 271880341, 724259351, 407590333, 620261935, 620300418, 710401431, 181213671, 239700514, 926373423, 298331279, 867305590, 524064364, 632344715, 32076714, 11320481, 479507989, 668944066, 404012138, 383363787, 691084127, 484685122, 763973998, 519928259, 954152574, 607916368, 715350068, 15534805, 74165598, 809405241, 309070591, 117875256, 381012444, 510654673, 871582164, 580479848, 295702343, 730280391, 382309120, 16383915, 308464264, 611933373, 481458963, 372070145, 274285433, 525753640, 149117125, 772513055, 437030364, 249866578, 856092536, 69825776, 166464077, 519941920, 303858022, 888561772, 585412675, 541996247, 449382276, 936339121, 982390405, 83370289, 861127480, 434830403, 547279072, 622781498, 721786423, 91940653, 500594766, 392206545, 466629321, 708107261, 497529962, 849763769, 999567917, 983053093, 826952134, 109906470, 303892113, 632862316, 658337428, 636805844, 301274566, 124709870, 453177483, 498125013, 331235156, 794283057, 443797259, 917412230, 314208015, 30730963, 488889083, 665014548, 897752994, 549018358, 707055334, 119597845, 907552365, 53798165, 289143928, 416117719, 126024144, 850970348, 843085639, 606560158, 611594439, 908217526, 921513090, 973034331, 632600828, 919930029, 848508709, 313764126, 342992073, 991380941, 72539747, 654091490, 112285215, 223332828, 435994616, 345530337, 738547235, 166769255, 834475189, 544363047, 740124302, 543531328, 678489699, 833585858, 442711447, 605394947, 130040040, 27775316, 444535486, 728630371, 910085113, 873276940, 711423088, 206296603, 362020150, 42463696, 990710449, 339860276, 427021558, 530241257, 847151287, 465696042, 534199454, 547370061, 488846347, 55591438, 41304795, 847827830, 864386120, 746010853, 467024471, 58682017, 344152640, 944820122, 660045355, 466838922, 323392117, 834300661, 782270658, 955071833, 851143951, 86064444, 507965367, 404963002, 850315340, 344937568, 405419051, 388943156, 164556509, 630415863, 233240533, 637430360, 870272456, 331345771, 322417439, 226833155, 512977917, 731964953, 916270575, 387473663, 193936613, 350643302, 139725739, 129291296, 203351947, 592109987, 451714835, 887629405, 580008958, 630674901, 68363024, 330063149, 70436774, 453313862, 894150249, 917652099, 165512893, 604220702, 54701883, 529945474, 980617958, 891919608, 927131801, 912141198, 714954201, 247304314, 515729277, 446988372, 650028985, 239497413, 881398037, 91514124, 410228293, 637796978, 165532339, 811249776, 179250419, 891608455, 723331760, 46311845, 648955644, 139619795, 334728991, 341315829, 167966084, 502599113, 160057412, 15098866, 747003153, 547553755, 152492583, 945750228, 762798210, 287986192, 900427813, 669148856, 851233942, 450085835, 761684473, 382294173, 784286169, 20942582, 312518796, 368390925, 4927666, 612833985, 598213206, 350859384, 552200019, 499903411, 406581340, 528349714, 819147673, 66472108, 171377736, 553584979, 891849241, 741522463, 352639219, 820552660, 697072854, 483993197, 592392364, 821882139, 846421733, 60734140, 502140419, 34301546, 829637455, 551846356, 535204997, 418804615, 634196400, 864262035, 803162150, 449588139, 643580763, 193557631, 35831741, 273408931, 343801220, 631977488, 684518485, 282458566, 585649656, 620829705, 79229083, 763701754, 815267592, 499401983, 834086107, 253187930, 846400465, 749874071, 579007085, 100401723, 415327439, 54619750, 363106171, 589905273, 295586019, 389219628, 648544776, 523322750, 255751399, 949746318, 115540225, 553795677, 718154854, 771463250, 374680156, 719944881, 51570151, 119844381, 614397240, 203107027, 826020923, 191917789, 643216319, 963246355, 689056987, 295496017, 306950173, 294444082, 717551858, 687246477, 531304446, 3492311, 786912327, 835207454, 444640817, 479269424, 5437719, 588622092, 85996613, 275482516, 123711742, 686984834, 607097121, 117123610, 831783987, 509193525, 168653457, 950872653, 663244855, 15928634, 435927582, 395555203, 157982922, 833700521, 513363443, 784196888, 179291296, 603764728, 687031478, 760777821, 56089051, 867946582, 675274306, 195635699, 189311600, 422933062, 688887381, 295826703, 312825296, 626440947, 260359851, 798764662, 866763211, 56770677, 534664998, 709597771, 184401164, 482362568, 812357451, 196607498, 49605496, 201868586, 250902563, 141462695, 935090704, 815209315, 537400543, 891939321, 185977538, 592273149, 275420355, 898756721, 964500831, 735717312, 885138, 984586239, 699516510, 660922665, 224082706, 665530512, 159921151, 329408605, 687186202, 330097984, 878958388, 325733034, 10291982, 199323008, 212816774, 791916046, 312845248, 826228097, 959569820, 448179906, 449190419, 712551883, 833699083, 966398000, 186143355, 877177285, 999938686, 26017365, 442342465, 883896521, 440424658, 267619975, 465951978, 664624989, 299042692, 595591966, 386136182, 89792616, 848139562, 19672176, 494838808, 634537502, 101164497, 832549880, 432086186, 383089923, 855122806, 712445207, 915594702, 133331185, 863652247, 917038040, 48027556, 236561162, 263102318, 247717590, 875517013, 128287081, 906815039, 462850964, 773412785, 283633873, 635008650, 768272543, 656474622, 473349924, 175634675, 112782919, 289471108, 752995986, 46059815, 190695732, 284493886, 255630062, 671103044, 776728374, 767446726, 392008182, 959431860, 886639172, 615851130, 299942484, 743116391, 228778633, 504144248, 598850612, 869632977, 512582092, 909234637, 901068834, 476295116, 324700189, 412598508, 676318573, 694259549, 968864729, 299876212, 138895729, 182295366, 106615855, 587369289, 708541072, 718215717, 90899054, 899965675, 136607697, 489851689, 640677228, 295647282, 336346167, 847471118, 589953600, 592839122, 559254864, 112930240, 903486638, 167332361, 393869011, 639799904, 344873831, 707526218, 74207976, 5175062, 307388942, 936431621, 835891525, 599048961, 483721499, 799267277, 738637640, 15062430, 179205394, 768306018, 958168162, 945580534, 697050016, 497792333, 748903620, 645739942, 578365894, 478565742, 748965486, 121384656, 346536663, 639688883, 904652456, 980856847, 37664498, 227411250, 422877328, 301584762, 203832437, 787544148, 710928709, 318399702, 148222233, 822382037, 483230348, 534163538, 344738125, 50547162, 334248065, 287349101, 658584762, 215913886, 339346551, 581981220, 696633690, 264507267, 206558282, 234048911, 551327635, 93115989, 661864384, 642663255, 896620984, 80697637, 269864560, 910829229, 82168999, 315621530, 661531592, 414235342, 842372231, 434326609, 15240906, 661914579, 4650920, 926853121, 684360249, 280447397, 372717697, 608764776, 276895983, 265236380, 267168071, 524471479, 828772307, 764275587, 606931836, 563057026, 68301430, 270980977, 97915247, 564097741, 936411433, 46380004, 367180294, 717626391, 568564763, 786259288, 913724030, 796435598, 890572176, 196144229, 37216350, 552478188, 191737766, 476966169, 258341903, 342619193, 714299144, 192734452, 909747286, 837374659, 789924871, 335124886, 15624242, 768672032, 734205899, 243970583, 796545948, 34214135, 694832835, 399427135, 204317913, 877861763, 280302719, 550375894, 503736582, 719593552, 311173752, 119575915, 752322610, 396537229, 513731810, 630890093, 57841950, 56900484, 950152751, 839618881, 161761630, 809732804, 444386411, 452389022, 907443093, 1391751, 332251276, 424213221, 285708103, 686821521, 511665754, 969075625, 485250804, 121283641, 570376055, 824078606, 316359454, 631152633, 554343547, 60251934, 604341, 586358220, 509084087, 772050516, 201027587, 631226448, 522840730, 144021355, 803658167, 263031165, 405717315, 96995508, 910734833, 982988669, 36825560, 185096635, 808726090, 774885514, 617305448, 828117395, 976587617, 183453311, 65392466, 387958993, 685116280, 697355083, 930378969, 117251101, 800746064, 145790964, 244507716, 374554482, 429361614, 410151781, 638234432, 431636266, 740382815, 131984591, 9392136, 851524031, 734867445, 282788910, 232648129, 463587071, 798290088, 140606911, 344264554, 718901731, 919187911, 744050255, 136885732, 112516910, 419306866, 534871188, 178446380, 39539686, 509676793, 318554883, 650584689, 354516615, 33581666, 12198623, 807377652, 966100808, 279182475, 95305434, 554266475, 162015383, 843824260, 426934857, 898806281, 138371782, 649978841, 680115658, 455077057, 728218655, 619714486, 656344625, 905268842, 834971552, 603721621, 874366233, 307984766, 339829210, 422667052, 620132635, 340397913, 30985706, 151628181, 674001127, 232378282, 504068506, 735687902, 307651127, 117805605, 531054023, 146468469, 864901516, 367256332, 114630411, 636402678, 642548364, 941746551, 65760878, 396063267, 628165892, 299496053, 868601493, 282692062, 923034561, 724683053, 178523404, 371632126, 726573067, 815865501, 215585858, 637434040, 774084973, 261411126, 889965768, 450401141, 217450280, 343428974, 557042755, 245155688, 107377082, 280520421, 872995441, 420585212, 311494534, 491939271, 249501157, 884237251, 306009106, 618911855, 2484201, 414578285, 758940369, 576996529, 9258122, 439302539, 824906065, 205905908, 538798224, 465000157, 579247995, 804072660, 397306706, 146700580, 526937547, 216956026, 82801974, 35826971, 84147959, 234614628, 268469398, 466806490, 9162947, 42205273, 660691617, 179261351, 87116431, 252881569, 394949657, 186781121, 753239912, 734034393, 381247094, 684123566, 872385092, 952948561, 121872674, 382240258, 748239274, 761237575, 766697993, 898423399, 311731305, 960339366, 946775088, 751902447, 179105362, 176044436, 782572795, 83392402, 770369993, 900936162, 92731948, 702277387, 309746124, 144405434, 344281161, 415216070, 473944369, 654521652, 330138840, 73089882, 594497082, 497874402, 346092601, 402119148, 569961999, 269840240, 817493325, 579757508, 681591997, 86384733, 252370557, 124868848, 386131734, 28739189, 67603269, 580668524, 479349374, 863843369, 332321231, 178388321, 554693607, 531230268, 90462722, 766459692, 489630827, 610068621, 574482193, 460798033, 57884403, 339010201, 751397939, 648783224, 729076029, 520220152, 607399914, 464753076, 944830946, 252457919, 920818507, 998768808, 325740480, 129850392, 190124766, 525738414, 739462817, 850598937, 673837504, 827503002, 971029978, 710893617, 931341953, 2535884, 559614825, 400660351, 292841935, 805457312, 464792942, 584007230, 73599852, 850446127, 689644434, 295078816, 404695231, 133687563, 827395483, 490203648, 719880540, 89594641, 538398032, 525036726, 506933230, 151636498, 100097018, 286136769, 921585248, 987752537, 324028447, 741129530, 98504756, 54475209, 648319437, 477937707, 456597573, 655598154, 643064782, 692192553, 665722633, 131727875, 133559032, 763460037, 633704276, 484789877, 145682024, 198813507, 172848986, 571583380, 3210347, 381246316, 195805580, 954111980, 516086638, 527624933, 772415993, 974212136, 568882555, 858830192, 933901684, 636752120, 213926105, 778214259, 879260654, 802705839, 782875037, 646926868, 155823554, 51883981, 920288210, 644750154, 486885960, 600488752, 992853085, 360719200, 666505856, 3816485, 732914031, 866575593, 824953234, 405933580, 562680998, 827246449, 700993252, 411952807, 265497736, 699231489, 602375787, 99998399, 397657981, 966293156, 116670334, 381729918, 577517585, 202841368, 291535506, 104409298, 601778804, 351100947, 231375815, 521635954, 248646312, 571978379, 675054083, 243662114, 832505939, 667811674, 367043666, 411871899, 47073226, 172139738, 588038695, 943756643, 631672388, 830423020, 720197364, 81810279, 789998953, 568284314, 438398679, 141723922, 252337765, 970279300, 592368772, 809193271, 388129130, 973400100, 288410523, 972926195, 370749066, 824609937, 331077979, 771030749, 923475607, 202576257, 529021772, 46805907, 746925193, 263076130, 712547943, 276506990, 346291832, 950649603, 323685359, 684957702, 381149646, 802310423, 12352738, 82792382, 738712855, 999579615, 870578944, 524292741, 367214536, 790874901, 799135277, 551388206, 975174642, 996499928, 847938990, 515558409, 736640262, 378896218, 178192071, 907079999, 870286846, 987805279, 231957286, 985307710, 575659599, 967913645, 653798305, 475741801, 247791508, 976675539, 446779714, 402156648, 716545860, 866363355, 478549672, 317994635, 794711411, 861139312, 408393975, 461481156, 219707892, 604012914, 875587440, 799893454, 287473959, 524250322, 188554573, 587072645, 997290273, 431087615, 643399992, 846195563, 757548829, 33352468, 163744505, 891574266, 976423327, 525722636, 618316920, 912764690, 267922450, 595467782, 68382715, 9855068, 195011060, 37809955, 994454887, 56977910, 485723225, 676753476, 364512039, 934331021, 68773212, 642316349, 906500016, 38196009, 953560841, 254554815, 546789419, 996009456, 533918880, 206938797, 355210751, 159501385, 18345311, 713580475, 478174431, 723778838, 122134860, 989610196, 96543495, 959139055, 800435578, 230690081, 133682979, 743132367, 746744921, 580115168, 840588, 525221880, 93436947, 750587045, 89934712, 500046657, 90165532, 225420180, 165971328, 22355917, 428805992, 889977193, 758589326, 344887379, 137017034, 643135821, 95861974, 246131172, 468038300, 767317554, 482016324, 138845811, 782029127, 126461440, 676491132, 969335900, 459781796, 838876131, 6856313, 116856132, 348228214, 183279631, 620284082, 675136444, 987985335, 978419346, 787270139, 775259006, 373714075, 852058348, 632955776, 265009162, 349854682, 843896103, 477234760, 292834660, 109505604, 599743081, 73807077, 271809493, 409467811, 704950788, 772594632, 1041619, 56616132, 478824025, 630012270, 827773404, 852726767, 70651035, 845009472, 32873981, 249394409, 257748767, 908951628, 734136981, 972452123, 406052184, 624755073, 330168392, 22018815, 40841463, 290644758, 318163214, 124330540, 274222286, 900080206, 493977557, 54996806, 251144961, 717191814, 663304317, 426740739, 752701480, 818243773, 625351191, 68663706, 869889291, 821680679, 634669906, 215356693, 937667289, 767441625, 267315076, 744843220, 149669558, 742811640, 40528603, 383955195, 244845835, 473353745, 389111982, 915474604, 724276687, 595786629, 492467083, 732778872, 639636219, 488103132, 753058923, 271370896, 307448401, 875865949, 827239911, 938752291, 435137364, 774537432, 963681016, 822702018, 860231214, 702396588, 955366699, 626207509, 411033153, 634377543, 889042075, 737819494, 746748448, 552218070, 872664564, 1159741, 491580017, 948167236, 734265765, 114294859, 413109705, 107793664, 521247423, 904831042, 798013512, 787659386, 615213623, 64226434, 822892454, 955633082, 988019489, 984581179, 156616882, 391259235, 620341928, 516586751, 833656488, 736994761, 992362695, 39069031, 882644608, 693905745, 974599661, 546734660, 477052396, 792420539, 590390668, 619235984, 375338018, 320892738, 689167099, 741676088, 378125490, 937016033, 911319838, 577469036, 208357368, 681565718, 932131635, 676951436, 181008518, 399908309, 280046588, 359169956, 82673171, 469847954, 577019564, 550291152, 525003806, 162938236, 890220701, 660452505, 684878849, 483335695, 504939785, 238454155, 687523857, 385574489, 527773853, 722175781, 337088350, 934091852, 123536285, 243976006, 610833726, 898563172, 887379781, 287584551, 642080690, 74853262, 703386103, 258251868, 150123893, 926593120, 819170954, 173546634, 337780929, 513708188, 890178688, 68682794, 280434961, 157095380, 271838639, 518769869, 429147456, 5705362, 151245315, 652862004, 744879985, 831852115, 851635897, 307838891, 316154845, 994017635, 584265930, 187556703, 760209230, 956261499, 174574348, 326209271, 79122, 706436789, 360589342, 991113686, 549135386, 326252350, 538211165, 910697172, 556587112, 565778125, 120230534, 966028253, 340187527, 560301132, 35240009, 962359542, 562036837, 527786140, 147487358, 296768858, 26316042, 248572665, 952332740, 830325988, 124737148, 8505585, 355688943, 378563084, 288481917, 920613116, 201292563, 922655223, 209773712, 323519013, 620477341, 103274570, 532871668, 133456014, 606628010, 172810088, 108941706, 362204432, 885385430, 729992869, 308500640, 72228269, 135308259, 492674149, 378011988, 966988412, 873511425, 936686447, 921480542, 529898215, 413919386, 290394807, 714050838, 185365842, 826672503, 54064953, 903966247, 964501660, 532838753, 479187371, 192214022, 795464917, 629810312, 227943178, 823780627, 769003202, 155041286, 111407999, 199720556, 136621070, 484933851, 288465394, 811225326, 701773021, 476041904, 960601095, 258996685, 264737704, 724509703, 400444300, 736655871, 932677177, 795681769, 937603203, 911987357, 634687367, 873958935, 698965830, 305366456, 19803735, 161441774, 562359752, 457286091, 309006622, 375249973, 679289355, 460479420, 787018627, 906458364, 267809902, 787050023, 114575006, 610279886, 679448511, 213778236, 338253575, 821115196, 211923936, 890427304, 331313682, 885864819, 5453562, 23707825, 173659010, 582273714, 33178110, 570179403, 729187234, 9405674, 413843857, 369630823, 142699832, 241230258, 360031061, 434986408, 568888627, 814404512, 779159263, 851507145, 67732688, 302280429, 991260520, 390526778, 374113960, 66038503, 625689442, 896620200, 151317150, 417847853, 289565885, 511377907, 708547031, 481548721, 124212876, 22542903, 478620515, 103563217, 432629456, 890459373, 959059379, 740603843, 491300401, 767412050, 239417051, 350639363, 156801608, 965455077, 920057493, 235944770, 350298446, 672635335, 441380877, 205876914, 889652762, 241868250, 72036784, 877053651, 670442574, 329311358, 109842371, 133450088, 677386667, 348881005, 145156907, 273936515, 527312627, 369864371, 561043138, 113227528, 134103938, 120683196, 325534756, 926553523, 827327215, 551704339, 385487755, 17174452, 545511232, 978285992, 402737373, 791330151, 388077377, 989286544, 797174223, 581699019, 211512093, 921175231, 612340823, 464989853, 81026366, 546329967, 582791599, 984581706, 805193238, 448641139, 799613458, 719188063, 970527002, 599053738, 82283392, 167997659, 547929358, 552276369, 588013446, 106971161, 546019779, 271552856, 298928239, 135366773, 869570252, 974406296, 85335516, 158952795, 716952456, 941005223, 19274901, 981158, 174825051, 122985613, 387571853, 336516150, 696870527, 593065522, 34475140, 906968269, 266052111, 122469322, 224445101, 31541696, 358525024, 486902975, 850396610, 32662413, 533943081, 165820472, 397579280, 813776624, 762836359, 873713950, 500164954, 979946550, 661182530, 545599927, 221752234, 546633839, 898515261, 701661394, 280669097, 95850756, 728407933, 341333662, 31980350, 563578525, 360242750, 913689113, 231266584, 754791317, 433896817, 61075676, 963392839, 382980220, 330052816, 782432992, 226144269, 704250136, 38380484, 503493888, 567219349, 585448038, 496353483, 326679769, 554227850, 812965999, 589114934, 315388004, 413973113, 984531656, 801628120, 700374975, 917586041, 210424748, 446684643, 332512242, 272457682, 825908513, 441386807, 689343974, 804091094, 748310390, 189235880, 96907350, 107417257, 610569627, 433902871, 79610949, 137438381, 396704648, 988753184, 262788807, 207345187, 951015223, 695095555, 84136551, 695429333, 60023457, 740530933, 997686854, 266575748, 575234223, 397716176, 72803130, 425163261, 162832811, 269030348, 534424572, 320618898, 20933226, 395107369, 601127253, 745605462, 339713536, 357753424, 531618530, 26372339, 731646418, 894698095, 360038327, 408968069, 598403575, 314897183, 287260491, 439886564, 623926712, 61582451, 402618477, 13518162, 187509961, 336897993, 24524719, 981678879, 50249795, 776462820, 264868286, 576206011, 15684554, 361881470, 45534309, 874166596, 753457623, 572032048, 573807774, 449581554, 278316921, 805342646, 337904743, 545189146, 228089866, 617865894, 904088819, 69334192, 453534887, 349985210, 137923618, 368325430, 85890214, 124526915, 535143560, 878616998, 875650179, 591372313, 369151321, 254594925, 378480339, 387356793, 381370421, 851845805, 648817490, 990443714, 136869651, 503018039, 491992242, 567004945, 793980805, 410634244, 932341106, 333286533, 755146682, 487614603, 35924468, 620573307, 944424425, 806130366, 844098135, 379695948, 90548238, 55645865, 757290482, 589653527, 766264590, 72478911, 348212807, 776923655, 848256488, 568913003, 649532535, 124529826, 283783202, 776958666, 316663530, 74580147, 482332436, 465600777, 426191612, 55234424, 913978023, 161421171, 826323402, 250710728, 520870593, 454189886, 371891853, 38802115, 454536881, 270204093, 772473481, 385726016, 669129701, 852727578, 128771419, 547246663, 60729838, 181073189, 305680451, 13017407, 45839352, 204787150, 430300033, 295895077, 101930350, 695858306, 775976754, 344008060, 138633062, 919836980, 582789107, 752165487, 906834355, 338888216, 882588540, 480425669, 528745174, 511627831, 971806493, 160673578, 372289627, 738442948, 477973356, 501009055, 909350355, 668227671, 460778664, 852330108, 744541473, 488555325, 419857369, 692512089, 617642937, 110112783, 307363068, 863751151, 1447608, 959334389, 531501603, 44139339, 474272631, 571679581, 925304341, 221361482, 534955563, 805463351, 655185011, 505002670, 86044079, 328499405, 463462121, 677894247, 528740682, 124268113, 840488457, 951978875, 312065423, 837445832, 58226297, 53044416, 82246449, 249887554, 518159238, 883407627, 7849526, 716847828, 886619562, 432160187, 462291703, 148317326, 733180248, 421349849, 520607604, 219716361, 400141489, 118357155, 20639412, 285371294, 578570566, 879570664, 496533416, 214847314, 747858419, 963494974, 912153714, 434324674, 234891888, 754514670, 42289592, 334799094, 445913903, 338516523, 809534789, 842668065, 707096712, 139412831, 534997929, 960781460, 265967200, 802438533, 614873287, 966516549, 14752526, 4553697, 954971002, 609674689, 937688596, 444036390, 490681480, 802673031, 25859832, 813669079, 206800383, 69568688, 248266765, 132497283, 680975176, 625881759, 508097747, 345502820, 72169190, 133923783, 632764471, 350818248, 107320963, 98488265, 29724274, 958310493, 745673391, 467129737, 20868356, 175497480, 570702526, 618436497, 212645650, 813529173, 436104158, 440203768, 90033519, 453889964, 444252672, 841197546, 653078115, 177340232, 523284249, 513389141, 961124927, 118743836, 227956376, 707680575, 588683884, 8755296, 822573650, 975878983, 912853716, 267555969, 348417031, 79020878, 189614065, 189013407, 581605596, 753662522, 893929475, 228861199, 699304566, 276885846, 633992863, 411756166, 455425746, 401822381, 938161422, 628854130, 237250690, 11939637, 124410959, 225988139, 891132505, 13940280, 262353710, 79407917, 925341747, 552742799, 273919668, 8053763, 275270543, 166401585, 634810056, 153111134, 773751713, 931644558, 486472593, 624343855, 21469817, 315507227, 86475231, 384741390, 828914098, 506745114, 937222146, 901704405, 624700169, 991250500, 674669195, 54061698, 330374485, 571543775, 815696003, 851567923, 886304427, 449159739, 625922420, 189469244, 552768445, 691555397, 786166000, 165818026, 442334066, 82941899, 611763274, 307065493, 799495490, 835537519, 428298934, 530543377, 421331558, 230074366, 192179005, 481105149, 822456149, 137860590, 679959447, 605853313, 513325575, 839133663, 5012960, 594531748, 810562457, 7222375, 355637679, 831427223, 209552520, 571270673, 567547129, 683286461, 45372272, 621503756, 736819250, 781185613, 438402858, 344748808, 261854859, 178565024, 686059580, 607129871, 744980032, 653329935, 216601686, 226451531, 432079645, 462321448, 782117269, 78489638, 752038950, 487856526, 275360437, 447467971, 873385689, 525289458, 51879292, 510108697, 453410219, 844897504, 743053358, 865999154, 841137710, 860328702, 232668189, 351867913, 54278853, 308547240, 823141600, 114362676, 725377682, 772630751, 366599782, 228513379, 218422279, 69414101, 595890512, 359241876, 395180852, 140131713, 482222932, 356415641, 131575781, 29763142, 803288994, 808057998, 232145592, 326097652, 960019834, 530753656, 535230202, 911511482, 553048979, 864027039, 767905353, 663379639, 95811887, 973869658, 74719863, 665035376, 947391820, 600846923, 903316650, 616115287, 728138541, 143859896, 131569039, 638842588, 939376144, 609199266, 712474870, 976378214, 80410996, 679284008, 68814635, 292604630, 798429976, 600410497, 738393739, 664836611, 22932340, 80220205, 148284049, 129450424, 316785994, 188515381, 349946981, 212143611, 767741442, 382503238, 506881210, 129542149, 640652572, 698438683, 613783707, 103298355, 392851256, 210484362, 757293917, 556694565, 272880179, 498007795, 805953854, 411190882, 961686384, 871879934, 971670183, 540059325, 319119826, 245194742, 137016364, 689834430, 669699112, 582551303, 48483185, 909868583, 937463919, 275178739, 804037067, 952260631, 717810465, 534838750, 65212307, 844442872, 657252666, 640330635, 992297569, 41497591, 21699716, 706580614, 865827450, 231449865, 587444198, 909420183, 948864341, 64736037, 76298314, 345962695, 732572905, 997310541, 257197859, 734096866, 283734366, 289431307, 934687473, 862059054, 956442874, 796683351, 335003696, 813113650, 691500456, 295329745, 123739235, 190112610, 655846702, 369065685, 661545385, 631149790, 764469756, 56019207, 724033446, 399166225, 779765787, 593766765, 722425284, 885199999, 616291439, 280298548, 86991438, 800791868, 700912518, 460739753, 511754930, 737335757, 345345301, 584172521, 947939222, 636911050, 927841860, 77509006, 777435858, 950309721, 929698561, 461878526, 60005082, 239431894, 547657817, 366473912, 467170798, 340578699, 242539315, 164784456, 958702629, 97435162, 377359355, 986044673, 375187076, 410767411, 715766715, 852098860, 387786482, 712387373, 942120461, 777185840, 272803232, 426258414, 574659989, 537544574, 914350395, 638819825, 559634184, 804300147, 443451807, 834335621, 293815848, 675856122, 972432447, 798307309, 495259127, 407733525, 40227695, 106716353, 632525450, 203709622, 650389576, 984533309, 826067313, 39485975, 435180393, 438079250, 400051783, 238641530, 307606039, 907249920, 345819271, 806400662, 30674637, 487651260, 903182771, 350481639, 90532022, 397702209, 830225250, 268582192, 818792105, 597241211, 975929546, 858820611, 454558133, 311864639, 19927239, 176999836, 917611889, 969899867, 922186649, 278144840, 616878938, 231189100, 790499486, 727272140, 1961273, 636547689, 857923506, 215080597, 113918948, 72269748, 650214060, 262126426, 6176448, 298721374, 597372298, 443260441, 615952960, 70077411, 159098349, 134580593, 222980809, 365726266, 244259854, 122666939, 746945654, 450981277, 472592896, 53898738, 788877193, 741540536, 946734412, 624482677, 559074070, 671237673, 904718522, 623322881, 788777540, 908242305, 420223573, 376148869, 839586101, 640533263, 320200969, 205588544, 467774129, 976488091, 836766497, 644346344, 247306792, 420187986, 163377792, 69881889, 93190282, 878688893, 155218612, 620706564, 854872642, 146113486, 862583675, 804563916, 929128161, 287221110, 198244310, 148245469, 572593352, 698396269, 264341305, 251650000, 838237617, 272588331, 487390330, 422064790, 350583903, 372562957, 472652903, 735189453, 501360236, 405878538, 966653939, 998885500, 642176095, 476627082, 708830996, 360274068, 838892110, 798334322, 142427196, 978095457, 17992263, 41574629, 799275501, 492896473, 198273533, 800523512, 537706086, 476510492, 206762318, 569273941, 224124570, 945607428, 425641197, 963806478, 219407941, 378524029, 255753723, 381043168, 898288954, 886873035, 423181353, 367096716, 148407387, 778251759, 270411613, 708551440, 139453167, 445656934, 734007270, 263718896, 604101657, 68241842, 714007771, 669332774, 508001, 862082528, 332356135, 168839930, 339249674, 177686172, 199357320, 417521206, 419630802, 552292856, 700891213, 244975303, 415212072, 931796605, 792032697, 918049756, 781643325, 202103348, 725920338, 303341798, 322230233, 75513096, 563932694, 306355232, 696914750, 306481613, 31446844, 428780994, 512436264, 60209654, 491457704, 843542864, 186189162, 983928500, 441594824, 4891933, 895199735, 283527807, 843281881, 462681375, 311162304, 155782901, 181157064, 430934853, 746522898, 137833858, 692268971, 264583830, 974428361, 436603720, 484573174, 350059510, 557797637, 845211974, 210387632, 520496793, 37367338, 870998384, 712469909, 66828114, 647633889, 832209170, 468492115, 563148428, 393943235, 244381293, 819328393, 309312399, 633421683, 203280541, 548529200, 420491974, 82984834, 995732646, 585183599, 204999194, 582680039, 106562907, 264303683, 793346692, 128251008, 553973951, 714475023, 936070275, 364781945, 455766826, 666063539, 348347577, 700948950, 816048805, 594972918, 507564341, 27992697, 31524973, 737352936, 775245829, 517705268, 1922386, 633081293, 633921596, 802603496, 731930499, 770278750, 691266134, 897434542, 315598532, 253445888, 413884076, 543501812, 756735826, 697543230, 755762954, 845674663, 321139894, 927884991, 593243914, 827460046, 462013796, 285875788, 352808098, 950980589, 444042564, 847410176, 838832483, 712275798, 122796785, 185211204, 831952987, 170128834, 403724282, 119800220, 195559355, 197714644, 111237079, 136581880, 231599060, 637783205, 512682161, 387632277, 8336665, 209466589, 144473361, 605505327, 822802006, 580477647, 323642351, 243792953, 668474395, 999366990, 848894028, 21450052, 598498913, 287363025, 923100538, 195317859, 897477525, 935805091, 768453817, 608979558, 578103615, 239686680, 339765174, 865456432, 144611561, 362677971, 302900125, 817050466, 485597313, 594137322, 928803423, 574875210, 105751880, 600449685, 989028387, 439156132, 949331543, 745433945, 568470460, 940246830, 972318833, 882145227, 341662167, 784481036, 424683063, 190114049, 376665321, 216448882, 561697268, 596501268, 37973918, 686546910, 203133026, 4466524, 633336662, 103306881, 920698259, 186933187, 543405525, 598356321, 177847163, 428608711, 994363723, 574284092, 543694813, 983888165, 967979200, 903027071, 836236007, 985068847, 31215914, 212978243, 773250206, 776536611, 777332350, 831907444, 597727070, 629540101, 642115575, 686761728, 84713709, 198306627, 419618362, 538211073, 816359523, 108501702, 198366424, 462533973, 524966452, 570570775, 982080880, 382703983, 583279326, 327653858, 927344742, 881105135, 133686985, 301134736, 374479736, 305323990, 914110124, 273978812, 476049492, 41180147, 176706403, 670034118, 565864320, 209021600, 371481263, 856343139, 834233824, 114724709, 111580425, 830191851, 835028877, 129024282, 75496351, 68908731, 642264541, 672032898, 583249325, 377761045, 36652410, 568572077, 511323917, 198440481, 408000570, 172900494, 986039263, 636537369, 688750587, 413671302, 312046722, 535813113, 227245945, 957702822, 409844186, 423418460, 368963695, 618496940, 636436006, 966342252, 740271180, 996265305, 786866557, 489404689, 375505437, 567752620, 203210946, 804618442, 158900769, 258946233, 539923776, 534384833, 943918848, 54249270, 480078670, 218387459, 135665424, 272600663, 195085515, 69687380, 900347260, 91221115, 245810552, 719008211, 798036912, 430982285, 536575114, 627189432, 786593572, 527110278, 729333143, 308395652, 925245500, 528564804, 470517389, 399652296, 69839608, 300929562, 69056538, 635776036, 438664137, 752453612, 576537063, 767792442, 491746052, 166415417, 266659529, 175144647, 466232653, 313134543, 65115237, 121559649, 365898740, 728853153, 559795947, 861956452, 860878978, 691247107, 705378607, 46846056, 108483622, 690414214, 297676780, 326745205, 286477879, 218724074, 828932739, 65014987, 849251248, 747046902, 9621090, 206930772, 684333466, 159928478, 287066560, 371586922, 886083689, 591794896, 980243312, 598664882, 80410288, 206167430, 851852132, 88388196, 699643248, 552278988, 56282823, 817221015, 431462141, 700587231, 625638021, 257038838, 188883400, 662294237, 514395161, 810919165, 415766050, 883552184, 932034104, 138320460, 284179340, 101483105, 636295128, 262036150, 298091674, 75092247, 659523097, 252340810, 928234324, 171038508, 411675346, 578460601, 953212709, 489280202, 194841826, 255446378, 422206581, 927991677, 332519653, 350661818, 268583286, 810590780, 206062643, 781623870, 63313711, 689821789, 983742120, 652504242, 180393067, 417664077, 708773387, 201129452, 277870372, 385245874, 853323431, 890451581, 93341336, 604448528, 511262046, 831948740, 899744315, 370502948, 63681474, 154987933, 267563754, 653748455, 598164464, 331733831, 286428234, 676194268, 100108238, 405802122, 75220939, 591800689, 567419625, 944638405, 17205638, 856921194, 424396398, 466801746, 927200777, 528019913, 272812452, 376228276, 201367764, 350741931, 203328151, 700016751, 195702440, 772022107, 8320863, 386426, 313503887, 92410942, 995879457, 754069172, 825643889, 733145539, 79322273, 21957047, 578703471, 935244424, 757139453, 138009701, 119600131, 814055303, 226841689, 610027666, 534307053, 224159347, 619560249, 108997754, 42652397, 644086053, 30175842, 556988850, 420082450, 343867334, 946763397, 264229086, 890909272, 654253990, 866541835, 252861435, 900267562, 533923841, 279872989, 784772261, 851390523, 18690832, 207994765, 379317468, 919336491, 975078385, 399349361, 189204659, 366305102, 618799244, 682626847, 272750762, 143343994, 309703469, 152766168, 158221771, 904053575, 543755378, 307098326, 614087474, 663099156, 471936419, 547712260, 318124867, 349020021, 552583734, 936841634, 25974905, 453127862, 720434456, 635930619, 511906650, 813266692, 878463427, 825817979, 255457328, 398296242, 214435157, 864500621, 260254662, 631248332, 136058945, 12453428, 693866224, 668368501, 620130529, 691363401, 691985005, 668705511, 737401128, 108977358, 787968296, 436114486, 54525754, 294889309, 69589804, 754640814, 105557736, 657901278, 185516396, 810361182, 31550195, 134728225, 618878495, 798940353, 839246903, 444470298, 564862424, 208629951, 490181115, 121312554, 751599500, 519639838, 242605994, 996837354, 713212314, 151206251, 268952982, 840874019, 938412010, 986467170, 833912254, 745472722, 779005612, 284469094, 170825974, 646731853, 828423607, 694894476, 559343372, 792508370, 949808978, 591918081, 993990044, 392359153, 72800446, 285279474, 66321408, 943541203, 461871708, 927358803, 405744261, 307384034, 50719574, 535888765, 485543633, 16212170, 208824311, 93908400, 113186290, 701813075, 589804077, 303190377, 597534624, 583024554, 388031480, 657095094, 34011360, 640670219, 159639616, 440964585, 896577440, 440528646, 778482391, 121361008, 202173089, 901677020, 911985628, 554373052, 277808590, 826683761, 237808235, 205695375, 961328252, 82211032, 239135974, 979465230, 60626259, 831541315, 166180727, 906096658, 710994408, 127541073, 861284513, 815555814, 753264634, 911935705, 196182329, 312308903, 371250139, 421458544, 789137682, 658192881, 653803109, 34882213, 487144690, 79953411, 226257853, 309058801, 849179651, 821527279, 669973354, 781191483, 233505654, 567859489, 834579685, 83413742, 34802854, 253728892, 620739400, 153661969, 916252607, 928272224, 165667176, 581259271, 751925005, 478298238, 866690906, 427400049, 893190015, 342363992, 652414230, 230926326, 359348744, 185192250, 904160346, 790536721, 660896822, 581677596, 438800389, 186583773, 612311920, 174210524, 604846351, 801082202, 601037012, 682345864, 151627841, 421367743, 14525815, 995992565, 303237336, 839900005, 729544337, 749649494, 369954468, 988379436, 612288922, 631132124, 550890517, 53140728, 55988090, 116074028, 245839468, 905783369, 499553354, 451291245, 24518000, 236284679, 149675383, 10497216, 345658134, 635897414, 48072218, 311963419, 336628427, 615771035, 145650780, 677214509, 341801980, 703982818, 880031556, 914614858, 849218851, 730167645, 607971564, 566182921, 43246000, 33464255, 572873236, 426847329, 439479175, 445634058, 250301016, 443123242, 30725035, 72625472, 172357470, 22549591, 327767722, 14268429, 259726091, 254516980, 921950886, 291815902, 18555383, 918180053, 663828049, 328949865, 398358853, 714044598, 901584856, 998460996, 762158820, 459971104, 185662779, 712601901, 926538843, 144079199, 958090997, 666031046, 752711923, 14124367, 313791363, 229631279, 479583564, 930766798, 483586160, 73537236, 415407325, 491397461, 386360130, 526526192, 159467929, 539095006, 150648586, 396635797, 727395624, 261934581, 288102668, 231041829, 62875481, 782985017, 247088010, 907234694, 388699689, 128683523, 950127101, 573720545, 193478133, 317300974, 507943708, 751909568, 9907918, 844863057, 883605908, 778041390, 1093562, 439382128, 962327399, 253886607, 292753351, 605839560, 127642105, 579962237, 754683846, 880091043, 130069306, 166385596, 275367505, 163466372, 671688377, 579145090, 211716816, 895208301, 35009133, 778353337, 750099602, 781766091, 752041478, 195244873, 229122565, 208140929, 704838518, 832529824, 754792682, 836792433, 51759322, 975644224, 875219458, 698441065, 390409087, 152973090, 63845751, 19905348, 412410137, 246272475, 93990719, 513064975, 774875958, 100822227, 2714459, 641194947, 736251214, 627792918, 918676545, 465051356, 392385538, 359616750, 151441822, 118800524, 272463606, 643885343, 239752610, 668713608, 42130227, 249301780, 228733330, 362167983, 793806923, 530589947, 713802976, 134951934, 145976104, 590221035, 391998822, 312029344, 971262361, 249410506, 984154759, 744075650, 60244093, 134823896, 938890682, 118685150, 918968426, 359018048, 600464016, 653753166, 943977685, 308898406, 283637438, 289742161, 138285298, 209051768, 171074970, 8226407, 680566652, 180837031, 344939513, 371920508, 517360807, 102145048, 953936082, 644789176, 54155301, 284830998, 295706794, 879874541, 862725577, 162486402, 213241018, 989529389, 826572479, 377774515, 250042914, 307054518, 160887601, 744522832, 671671866, 314904943, 130864883, 237237892, 445153305, 575673934, 468011023, 424512739, 411984974, 241008703, 691963185, 94668731, 608461239, 815042878, 452057377, 334244662, 108467681, 467266809, 677038014, 34196708, 871681575, 968956805, 323804203, 806125782, 640734383, 254794983, 43690638, 979585099, 123244794, 941567815, 84027861, 229116254, 385186252, 466210049, 789590174, 579743991, 820555819, 83023023, 786996092, 931133353, 191182651, 36582587, 444755354, 898526031, 855418226, 800282335, 41082954, 323107, 402535947, 166602441, 481319094, 609178058, 404193924, 189292129, 102881452, 382720973, 599804845, 361615965, 825649687, 297991492, 460667973, 866461792, 943136280, 609336653, 109569063, 939204154, 944573452, 452161609, 364754423, 175586826, 369040599, 874084647, 858369120, 959962885, 702890970, 905899939, 932512600, 474202131, 567873543, 811112591, 264933853, 980438195, 585177618, 302643886, 16285793, 296238229, 11872393, 701935453, 595031254, 593219237, 11670212, 181607755, 527517887, 726527067, 129875931, 751167505, 847985546, 56212787, 810914387, 753810240, 643647851, 396637389, 11175177, 232158458, 724872544, 404205256, 387965732, 585830428, 923244457, 531090589, 135843768, 370043854, 367636182, 428029098, 568527776, 443741709, 387747895, 838997412, 70682355, 494011171, 172659233, 208443454, 15793373, 137873455, 522013826, 389641218, 652239865, 239702755, 495260323, 720500782, 112895383, 568513704, 513336827, 567377225, 335996170, 178477375, 458074773, 790744123, 86294914, 525377176, 778204754, 850770078, 782610430, 745920540, 783041815, 215581692, 396761602, 370613198, 434236088, 600561103, 522242646, 909540871, 540240114, 953162344, 892156814, 870677339, 60906764, 91353584, 661899591, 955818182, 816017064, 517105630, 779455065, 956437775, 416863415, 660623273, 632349796, 980210938, 183167141, 5442015, 799734659, 379616047, 653901485, 934275222, 176701990, 960074882, 734846257, 983097126, 169439060, 603425147, 77724952, 241357833, 654394135, 471172650, 138753074, 507054713, 889427340, 198583212, 421996500, 999773608, 944260686, 688157670, 164188568, 612979418, 983051517, 465830499, 454596952, 869714957, 819397474, 864349014, 791201366, 74634990, 174395487, 108598786, 316902872, 46529151, 349685531, 154623868, 149148477, 170253399, 845824907, 233201818, 191334901, 552330327, 878304891, 960700260, 639155602, 983508290, 726579804, 166664110, 162816621, 375692369, 145423389, 375935561, 45885463, 809416613, 657490386, 820932541, 441424558, 116579167, 282018889, 886845984, 844357663, 212019857, 430578851, 753703318, 510515825, 520123186, 625587405, 554416987, 609580651, 996735949, 9493740, 438188666, 982821706, 829400313, 305506578, 322640710, 336526043, 585604085, 396866872, 981888407, 605116270, 720310340, 756051897, 170305090, 374195331, 465222637, 265398398, 237829681, 597006434, 296294658, 209266001, 702535828, 138481351, 750822628, 509728051, 316736139, 811924978, 913113520, 94244431, 194958469, 963348709, 731146413, 443757372, 205030778, 724436708, 872587590, 867183290, 348681945, 22950433, 717414294, 852250777, 306132248, 666666226, 741416291, 54025551, 55416008, 990813827, 274235571, 357975927, 575378920, 115775612, 45081500, 667903114, 132494539, 241669907, 145013371, 352417304, 863803041, 658372236, 11056610, 965340322, 724034261, 338031467, 276139286, 648165143, 971639463, 401223246, 2404939, 515590604, 650436812, 873838425, 20463058, 183170721, 656354371, 857678050, 389736937, 454342940, 759226980, 631987147, 307238666, 329292295, 811816215, 437994795, 436874341, 920858430, 421502683, 889227270, 767182758, 515589234, 801901200, 213297507, 633196696, 807144768, 507374807, 131324985, 678063555, 849581204, 910860844, 528044507, 676399175, 630890778, 308233900, 458790479, 614539535, 616546998, 3564554, 579278302, 93023724, 14855544, 604637474, 501146012, 604086363, 69419217, 242116224, 407895895, 649379158, 575458271, 788997872, 393585196, 166318692, 964949280, 378894549, 536581998, 227098158, 215484166, 107546677, 652690631, 363039231, 860836383, 557969782, 872981034, 225569, 467955048, 756428349, 196892441, 706963577, 258047533, 770021860, 912290130, 76567936, 576515367, 72902226, 759467716, 790195268, 275478940, 280974208, 340264026, 225600875, 190672550, 199114040, 96333038, 946039660, 308929204, 621631642, 118784596, 367611243, 257987378, 298651653, 964197617, 499854537, 305897758, 559607228, 378907790, 526936795, 150426601, 506384968, 731603534, 46328496, 364385594, 115839086, 795774454, 387712424, 152327352, 618108894, 231490886, 764803815, 841995208, 861691984, 199347455, 319304435, 303198814, 345735965, 227253985, 5881154, 777882334, 112359454, 41866552, 105439924, 981821754, 165177768, 814580076, 60896461, 967367820, 31621597, 590694182, 84049114, 785438275, 370253982, 517032051, 735001225, 435909050, 366117047, 68209503, 958400681, 810751348, 958554571, 250360766, 592174144, 543534612, 386427725, 967859149, 921022349, 14029152, 815805969, 812263150, 340765632, 586950100, 137139235, 441325421, 75186726, 468441661, 614825502, 858619477, 66803343, 970545109, 166740434, 852724686, 670028318, 538623293, 23461048, 768366648, 577875431, 806151240, 372281134, 65513993, 451499665, 780292967, 915432484, 629355315, 580394864, 349856506, 141527490, 465416831, 258387647, 380600444, 426881273, 612857229, 228094606, 141262140, 782239196, 815583103, 75313470, 698257931, 938255222, 844610452, 485391639, 194060417, 769663684, 339301623, 102510619, 641821645, 388563377, 432817699, 55083719, 413034153, 40869442, 780986734, 415282591, 227757760, 767472124, 525797225, 540608500, 248114948, 880838110, 853000316, 191070580, 500879315, 701023287, 963320089, 538692113, 397618950, 136060588, 498043044, 602193323, 214133231, 221088334, 554165514, 914053153, 32307067, 771886360, 67567548, 696004137, 513607653, 81307829, 663050561, 154416634, 66937569, 663674984, 904474767, 861723176, 361058290, 425761970, 538735386, 952003959, 367643922, 664496178, 660100932, 670737357, 81888384, 633718813, 479936708, 689883802, 668796961, 676452647, 198144222, 981280233, 766125746, 814417616, 75170535, 101673854, 214506718, 214169385, 766437142, 890030208, 297996935, 529334328, 490534141, 42541721, 357475858, 168716144, 905075059, 871052719, 106822399, 880579162, 610821005, 967188956, 401222596, 914154940, 477329030, 70247587, 945325977, 490028993, 31751989, 673631934, 629903017, 547953231, 91945538, 684904560, 319155437, 761736637, 943381052, 693561127, 306034987, 714309191, 491036861, 70622707, 131769292, 498945872, 526306783, 599306127, 202911692, 42760171, 386296766, 803122504, 548545756, 742480212, 601660363, 41053970, 181396178, 312488833, 180936844, 775403673, 352644391, 334674271, 541447630, 421180732, 804413909, 459875651, 866043081, 27714607, 923021745, 333082619, 724648991, 942989482, 569062124, 459201568, 817404383, 473025465, 60076239, 435401112, 516352870, 222540358, 486916207, 189920164, 518716565, 204579136, 619592167, 239868337, 229159284, 890340004, 596575806, 792148201, 171171377, 953746844, 372621403, 554624458, 902230087, 688495003, 864506190, 457383135, 433389317, 216620615, 937844747, 641297844, 624647585, 169871470, 415111757, 528707507, 560773965, 271660380, 603324185, 490055477, 402837211, 550618110, 664686927, 783040410, 372179787, 322082422, 106906794, 683710519, 562149067, 622169723, 189060190, 378791123, 860202921, 520339561, 515132908, 614575631, 888816123, 571326628, 977358978, 795118468, 694064685, 481181072, 606710926, 606610477, 560211819, 249279396, 427106705, 120368078, 246410745, 94511466, 653314913, 10709566, 390412508, 542892953, 637905530, 880464729, 201687561, 60858709, 377958462, 379939474, 489644540, 819091622, 175188164, 399244063, 520893848, 621142161, 711195199, 272523069, 696787124, 812309465, 930058292, 980874889, 792848869, 134090756, 457634031, 275766066, 747269540, 826660629, 997317868, 616391181, 597880588, 443649146, 898306124, 591976729, 42720077, 547433961, 45470915, 626047165, 431479958, 778212262, 782638777, 406566826, 55323098, 858085695, 109288792, 688636767, 494828001, 95307471, 372797332, 514180354, 92443314, 582051311, 918415160, 179528834, 696385299, 286283770, 684355153, 639344840, 470683449, 198663459, 718968202, 550270741, 157829324, 57431117, 419252712, 89045804, 693082840, 6780245, 3621366, 75291048, 414859778, 35549069, 606583451, 247868559, 339289203, 34251548, 754517335, 399130638, 846315122, 816556369, 448599703, 574984077, 635036806, 555752112, 832804880, 280441708, 384239152, 180042089, 649477845, 869840011, 132106452, 846483140, 339980526, 367570006, 78461503, 367442166, 95024484, 27110901, 33213355, 375677434, 934463353, 116578324, 850892590, 305260007, 416536063, 686182430, 781447676, 856894359, 249334565, 732844565, 347120656, 132858917, 723064056, 84795158, 982642397, 881925399, 917103853, 584143661, 679999825, 877475931, 877754882, 710179866, 958216782, 437384071, 87105978, 928708136, 873976863, 81990291, 736924313, 234174590, 25868228, 931713705, 566481101, 822598774, 343100115, 128149930, 272521140, 760806357, 454166720, 380947278, 902592603, 772088385, 100594174, 27206995, 161851220, 823311246, 258322543, 256338038, 58414151, 723756764, 235970522, 206197170, 311117523, 668215705, 317033771, 888566100, 238699461, 132782513, 362378471, 970565825, 854781914, 581124242, 701114280, 776824580, 568306771, 386177561, 230681992, 876211754, 964481470, 172366469, 286842093, 637880367, 473594761, 893626561, 706226787, 680642395, 931133196, 269522916, 924217960, 255060645, 198839936, 441242250, 143810034, 583434462, 783179318, 631992814, 198149226, 812840635, 879598502, 175470633, 101474661, 904404526, 199636820, 462807928, 158588575, 963068915, 527379918, 938536101, 95212575, 215603972, 819955741, 779882005, 502080173, 221880901, 584707643, 398586331, 150048399, 623736457, 860093544, 214646645, 51085086, 888396103, 229334911, 685720359, 654281063, 527376042, 859069644, 695143092, 440176403, 5980806, 319948728, 124652688, 548550756, 997979106, 497282222, 177587949, 782353528, 986465548, 620611376, 262621910, 636413324, 448599070, 163682015, 561837454, 658462425, 274789795, 283914410, 379556132, 697283171, 303002149, 162031972, 860823653, 322074249, 195743461, 674776106, 914030220, 890451059, 844976141, 357425594, 257098024, 270167509, 460664262, 798871159, 514485793, 834025774, 621506281, 913277254, 775041679, 431164694, 320660484, 713103379, 712323751, 219206714, 58820189, 45683455, 140288921, 916855353, 71308357, 996087832, 130132852, 821479149, 645986801, 21222439, 38086862, 114935016, 162485584, 548180187, 393173355, 184440366, 732918459, 935950285, 497884687, 866354310, 176384850, 783278640, 382925732, 604171709, 659168328, 105392023, 626683728, 649367330, 915483454, 601786131, 326430749, 571460660, 425203655, 24981064, 296248920, 737268865, 126881624, 194498799, 770900015, 500789564, 616043241, 35133721, 971701226, 153026863, 56873832, 536831183, 843729934, 407865579, 405033451, 515329731, 443648151, 513299444, 143852563, 449880909, 942546304, 21150685, 229060019, 311867606, 80987638, 549973103, 947604661, 352923324, 366159466, 561129752, 780617045, 477218181, 680326974, 872522522, 863088187, 997866210, 178663329, 332089591, 449610258, 31636157, 317981205, 126350196, 951300063, 668828418, 879207686, 883585681, 606828373, 650724859, 615338212, 157184175, 716693453, 99849823, 7169342, 327647869, 458410726, 206727462, 7182229, 325436855, 392197201, 850412786, 362217309, 717785307, 770311677, 632825237, 831419178, 484732703, 817034379, 355370779, 887139749, 268539782, 358393859, 757164772, 124613356, 326668256, 911048848, 618417523, 487870233, 745912608, 399238097, 637077800, 164687104, 798620013, 609435745, 981797079, 211553642, 834177296, 943922482, 760468445, 881028518, 11129700, 673278385, 680956102, 299970033, 977269800, 525594973, 47306885, 754680291, 647597250, 944391891, 825535381, 99724416, 846153062, 213540514, 933839983, 373576412, 677041091, 787704655, 999746406, 11349512, 502710368, 401101373, 436525883, 32298080, 681837955, 852671979, 581004028, 844664300, 633252979, 760405289, 203715871, 922496657, 481826689, 443994771, 244462326, 677693944, 795526850, 488466224, 31971580, 101252102, 710126470, 981724658, 939705123, 3183071, 255075652, 694823768, 675205718, 834662780, 340300118, 164514027, 314037039, 523717816, 543362663, 947658845, 522986227, 729184044, 694366663, 260477039, 142028887, 461766599, 721107002, 600839977, 795851501, 121006922, 783845607, 929013642, 89474726, 195477526, 225652358, 657975237, 109422626, 454188697, 218764240, 826524144, 609490278, 869136133, 489863506, 287337861, 672940596, 568263257, 76853373, 573722307, 816703433, 649254494, 17558056, 536995935, 540704326, 835512170, 494314860, 556695432, 550570112, 34316203, 554794367, 577761474, 835385012, 642819600, 950230760, 153100174, 197296660, 60107438, 53281543, 271687279, 72033219, 773784138, 660849448, 432997300, 168399653, 509227199, 503448148, 466934725, 505329951, 268141357, 865703265, 13347065, 211381468, 30448540, 271732324, 290337995, 148969330, 433003235, 425901148, 857286259, 601023496, 509112015, 951721826, 344812601, 113321366, 618748951, 230118976, 983475176, 635559630, 691074272, 224416042, 900342194, 129550662, 472755439, 762812370, 647539363, 158279807, 68087714, 904360412, 490297794, 414558241, 318111683, 212400041, 389681959, 203150665, 94962263, 809098932, 501862796, 531026267, 681213844, 71624252, 610911134, 732327763, 340630500, 39569349, 124254379, 201938083, 19726039, 689155766, 983571024, 354259425, 449435006, 95716820, 242616367, 674877622, 76588488, 541717676, 282073658, 139825841, 131508656, 519310046, 314063532, 366253692, 573235462, 238536902, 938656207, 809180007, 218551554, 623966253, 541182487, 246377898, 842280341, 202140362, 214270984, 373217605, 877609738, 576597295, 419444629, 744963714, 648014040, 236306638, 687203047, 127527592, 132068073, 894732628, 662962259, 324689864, 167071773, 65035715, 463808216, 393497237, 602523072, 31141618, 799827533, 961495511, 675814075, 937066747, 643174807, 385756232, 885076732, 85799026, 717482474, 19026215, 903670249, 995327254, 629400400, 436433300, 622746272, 709176715, 520760751, 561126485, 861734740, 720345123, 650704174, 736872631, 92044404, 944669334, 671402791, 463600180, 23736559, 716591793, 201385078, 780756408, 647387180, 538410609, 165812043, 182690896, 375446227, 911389110, 609080477, 796689004, 819294916, 820236141, 394644850, 423589142, 206314674, 755126988, 420583002, 832483889, 369735715, 273804984, 18926370, 164434299, 41321390, 952212692, 330240753, 258387385, 615392184, 161258923, 543965705, 510670343, 782195965, 689736125, 249249268, 180554357, 401039868, 627854928, 729539022, 73845980, 152217454, 932922501, 754779917, 195221702, 791250755, 803484505, 354934329, 457870556, 884173687, 103716580, 312787245, 743349457, 591844074, 772925815, 144025415, 423521950, 147280259, 796055188, 577741509, 60520096, 296201652, 266628088, 264444703, 598909544, 479064957, 910348648, 489757766, 246481696, 553713422, 118090275, 453618269, 897603289, 482889650, 731052976, 402366856, 302926983, 131232616, 802424533, 767724223, 333270752, 519315424, 110209612, 892862390, 339460475, 549119638, 550270963, 94832758, 257807012, 514521332, 793349531, 519974528, 833018608, 317243684, 167655381, 748650431, 445048712, 32194054, 431531911, 164526904, 275660610, 400450302, 456482752, 289187183, 68231670, 304797767, 778505739, 649076066, 998156665, 398538831, 535337411, 770416532, 415738763, 97801474, 944273829, 893965525, 11715331, 429311013, 253621739, 536983219, 664808800, 355578587, 604853718, 171383685, 475818301, 392192355, 463948676, 425938392, 949044557, 134231555, 124042254, 410295211, 21478145, 287290565, 259581912, 145428238, 632304713, 650840398, 1266550, 291060934, 927055338, 231526341, 104144056, 903192312, 846843538, 657811803, 429773174, 641000826, 985898369, 95708184, 159205417, 478235344, 87264783, 461017492, 421460284, 519448371, 774695530, 799905957, 445275955, 540622630, 255822723, 208816414, 290791919, 896849823, 191524676, 571220650, 372738243, 322804707, 863551114, 766933662, 259147584, 297567265, 488971925, 327246112, 223154232, 749211439, 940240310, 451726653, 835549090, 529808460, 221685042, 57842189, 968328538, 920627751, 827433584, 773314183, 412480300, 245862494, 547719878, 266569067, 933921770, 537085138, 919791543, 26795929, 233856529, 950988475, 130575613, 217079768, 173388938, 328775800, 862905763, 161812350, 612387956, 982491200, 905319221, 690388153, 263495617, 540664923, 141746379, 541395216, 510668942, 320599740, 508982472, 981590479, 885433515, 115233797, 497269047, 626021100, 268696463, 822821044, 959603999, 630278496, 442318046, 866253660, 526428278, 628587115, 576829418, 822374408, 671288772, 612569344, 38771227, 875009913, 696220848, 931182563, 212371677, 265671237, 652344210, 245567487, 310441268, 904397274, 399351172, 140348870, 936784819, 811633514, 450603679, 984077055, 177313640, 413913819, 359053323, 522297963, 106320417, 49392580, 292921004, 490830630, 771040824, 758930309, 871105201, 432897839, 824403118, 760356335, 194236202, 759164219, 119201508, 268831132, 121418904, 191421526, 308600222, 911644522, 880186934, 321043006, 743421036, 111167972, 123232071, 441642031, 257643698, 33197131, 240353090, 480689362, 840692722, 613943111, 997718822, 317871900, 240441426, 319838552, 70776849, 578654221, 867233943, 960092046, 29251925, 589755524, 916164976, 115420488, 322538247, 767305496, 744337274, 363068882, 975508943, 520274380, 890270204, 953053460, 952921257, 839236715, 79710743, 793077441, 665851652, 481644582, 604536552, 427966806, 497031005, 482089163, 291059402, 884514385, 149048331, 310879216, 791371026, 620094394, 671180145, 423531058, 743183728, 980007381, 125193392, 974844968, 626300670, 406461973, 306558402, 171180480, 149808255, 632829642, 466565696, 893301332, 405136113, 359439849, 407124420, 362840313, 136196363, 417359232, 139054955, 528555608, 675549654, 478110259, 853346610, 140156251, 43358118, 516195088, 885412790, 376389552, 798676200, 737737528, 671555811, 849223134, 377641109, 561302312, 77684324, 54004413, 15395951, 583819199, 971828377, 821159376, 595482289, 21858242, 463648951, 874750568, 605029023, 328071314, 951612915, 764546962, 888270258, 832563776, 387164142, 755249367, 185233849, 440951594, 83384767, 48559255, 3440624, 546816809, 181922576, 62957200, 720202345, 733270073, 759096522, 122506122, 910695810, 569388336, 729305332, 742573827, 674999380, 637086643, 174853876, 998540595, 863847723, 352992812, 649890413, 182404216, 66035981, 228983035, 170405571, 798581599, 449313456, 137870663, 523373552, 982173475, 729710929, 259903716, 430339961, 284648150, 60348900, 185526943, 615857902, 376235827, 921881177, 962270958, 337664993, 110691686, 723027516, 571712371, 184143877, 9016447, 77085170, 343443475, 509074694, 239362605, 670468239, 145461067, 391255406, 765023560, 674709989, 366354531, 701896698, 411117004, 491187900, 29946439, 429370065, 657765799, 707870466, 695629788, 570918648, 453667052, 811870010, 304680815, 877574831, 612032586, 218830940, 457092879, 318282161, 387671698, 516893174, 506497018, 306770445, 121868792, 214008423, 747335420, 261272962, 881424173, 461779364, 67082890, 381405720, 86428983, 570866920, 894194367, 715511996, 11462630, 459189186, 163327987, 469587679, 207324807, 188339951, 17739416, 660140767, 661737766, 736885192, 994395124, 300600486, 391099562, 349148236, 341828828, 875698248, 394288265, 540247188, 787094391, 269436692, 318097541, 795040025, 45370022, 963692832, 54386222, 432517084, 408967053, 402824904, 793328199, 24449125, 163663183, 320539657, 441491177, 767771613, 655031824, 440636882, 266295461, 71821923, 794043358, 317237090, 537832885, 812779081, 625965826, 372818712, 920353760, 794337424, 777961159, 823077856, 433588008, 125349009, 290930369, 884374608, 31308803, 279194743, 740284847, 476500260, 355255762, 493117181, 111398911, 644996351, 582290838, 326443255, 161825250, 81437950, 996115652, 163972371, 311710377, 208256729, 939811561, 415824058, 357971620, 412631, 875738313, 250298947, 75129731, 559284873, 901459775, 476877442, 949676649, 69132501, 140071071, 544067168, 626385645, 782115040, 585566508, 907275111, 841218273, 497237973, 806024381, 907460436, 929209598, 416609462, 880861147, 862773163, 839810980, 300687179, 846242580, 259264099, 44354248, 80680942, 557767017, 88144990, 542760423, 71322093, 365158368, 786761175, 603283429, 399762422, 44494407, 994481364, 488504036, 101731137, 895859939, 482813891, 938943343, 791810644, 556501914, 434786041, 804859600, 271573258, 629412978, 860134018, 30387083, 675673834, 597466136, 715624770, 232170294, 139227974, 654895306, 822490877, 184402613, 854100944, 759521746, 591576990, 733822536, 471511337, 922279115, 45613537, 780521355, 351940890, 50924228, 382335860, 61248060, 216721329, 735214422, 118704785, 564329559, 72673553, 617062568, 582711649, 79585059, 647810123, 543116874, 502020362, 554090548, 584048768, 949923166, 822084094, 526498102, 550933146, 374573573, 899823700, 175832182, 958496210, 928597835, 271340048, 944957592, 4048066, 211679890, 722993477, 418030340, 569998687, 273772515, 433106817, 913189695, 193861724, 493825489, 889172372, 68453033, 225369056, 707400890, 214142465, 686383652, 903224580, 522868980, 614259413, 698350894, 752157377, 857901937, 569976804, 180284340, 382512441, 446497220, 389890696, 143165447, 626008802, 96714041, 785413340, 400272787, 934161634, 578645594, 678868097, 160900310, 622225172, 749560048, 590998841, 843848421, 196633415, 612708743, 56353287, 813459900, 971032517, 279217342, 764650853, 725161513, 848412789, 384014871, 138023637, 384489365, 747872571, 634273356, 815687414, 902529389, 261890609, 674016330, 711613870, 780565560, 465777244, 12676649, 532915805, 764775762, 498492752, 88340986, 619896990, 644052369, 615661528, 557685364, 894216579, 156341673, 471400350, 129310789, 359273828, 842227223, 313436997, 177205479, 509211585, 149515714, 675888179, 947134585, 210300138, 964839244, 289836688, 860509148, 258890543, 989177502, 408563187, 79756673, 743444176, 41681336, 960679096, 712661842, 443363906, 180888833, 303642107, 830460296, 256211868, 387954266, 711450608, 381683491, 215461251, 768920769, 365286884, 953922346, 453885343, 432011702, 176340842, 525380640, 939084543, 958059942, 878367396, 220918389, 921305048, 704006275, 425683321, 531480897, 509641522, 974464965, 913241190, 724531967, 111539574, 233446634, 578414222, 269325239, 553370239, 659668076, 520995424, 256654426, 264353587, 300297038, 684909544, 54465737, 892375197, 294037095, 721969015, 555062759, 892251146, 458196956, 205516064, 832611947, 951372615, 99754502, 941402934, 607281591, 311760595, 998048930, 298045223, 334517721, 222079005, 719209980, 864371075, 933424832, 803571955, 27232015, 199530486, 371503423, 778169033, 282309907, 323995056, 883330894, 595839789, 569136949, 523414377, 173271261, 362265053, 480477800, 681464730, 593871769, 627637375, 33036832, 609528462, 511793622, 710914062, 829493293, 501923910, 249719000, 425574142, 782789111, 859562811, 338224939, 123676560, 21452658, 197528192, 254234602, 720425272, 902377740, 717131065, 992245148, 452482634, 309551684, 274090817, 146700444, 491761104, 343309851, 513575756, 872031642, 99040709, 356750698, 999944227, 448468104, 996962517, 789057748, 950097352, 552673246, 503264602, 698095927, 637776721, 183439731, 162842728, 956399001, 806967337, 994782507, 660590066, 909760464, 643885386, 874115833, 618013120, 300704801, 828006174, 411371260, 357879235, 849098554, 461697377, 544326055, 626463590, 353596644, 429981342, 176113196, 106107563, 876692145, 798809680, 887117051, 758233274, 203152370, 938994685, 351124123, 170033104, 963388625, 112221335, 136702517, 929639507, 321467624, 810042865, 458519735, 92289794, 61845488, 693686777, 905169756, 957857093, 414542852, 883234963, 541809761, 426096522, 781452508, 792055469, 311432951, 647327891, 229630435, 858305454, 451732842, 474980534, 582283276, 292795830, 702803118, 9268622, 198063400, 817104929, 228487011, 657234318, 892793747, 508342914, 889274388, 272184077, 365556765, 284366636, 234801166, 668064836, 765620267, 352131626, 57015191, 830993548, 80502376, 334601118, 633352895, 169582433, 126064622, 176374290, 641530701, 745844599, 515438249, 273862911, 459316285, 938736918, 748391462, 288547166, 838650981, 252630266, 434178381, 14649737, 258321782, 193664840, 849322523, 135081676, 520869650, 370063161, 691507395, 104514340, 100687491, 459031216, 991217949, 751443140, 122283446, 135904169, 484958173, 995773212, 190015502, 674138936, 66529490, 393006802, 684399215, 823572719, 164640222, 256619589, 783259210, 680093196, 927466192, 828327808, 360071339, 869162426, 643759116, 719176890, 413446641, 981475963, 464167130, 531778197, 152012660, 995240372, 341172237, 902914795, 447195740, 699191543, 47424924, 632849796, 525032146, 524667156, 604747693, 40594737, 287221397, 927233222, 660423872, 515454648, 521730875, 235107299, 264330613, 171480707, 998569178, 899531598, 130794967, 205906585, 664652328, 34465960, 88557940, 229766849, 475747987, 794743738, 57456170, 33579904, 145626984, 492641829, 526435357, 884436788, 892812083, 815126162, 298165628, 743601795, 884580048, 917503824, 927160947, 488390475, 151405037, 436287013, 86576325, 481282878, 99196531, 278104230, 364049995, 762215910, 688719329, 762438339, 123140266, 186381876, 550460322, 235178502, 270704451, 610643346, 794564874, 305423154, 177365503, 164814825, 383301093, 524748973, 888301926, 547481724, 874008851, 365923395, 860706298, 286806196, 134211500, 107147871, 525531843, 89903873, 107225459, 568149805, 681095977, 573732577, 795293059, 643285338, 969962195, 166501834, 276005190, 971506738, 403304333, 526904778, 832702288, 935371516, 170650055, 96528405, 621394990, 840311272, 65248626, 699203718, 331327785, 7961190, 171403261, 784510195, 213134161, 790644851, 839703874, 61767490, 754362991, 21728316, 88088015, 555190250, 524573256, 316610549, 37434572, 416193020, 992647315, 169239031, 67459414, 536326159, 872319403, 704908849, 569794591, 419486597, 246615906, 388416531, 383778513, 558365614, 837134469, 16679836, 129696204, 61337257, 975946644, 163326735, 931541855, 231780892, 805559230, 470456509, 882094687, 850465070, 10858615, 126080699, 237740777, 417976136, 845328193, 631403840, 94039237, 419133719, 877687432, 91235462, 30623274, 369296469, 572382227, 280027077, 819086470, 495426848, 274091119, 919243584, 727216110, 423945800, 377869132, 349823758, 581824582, 118397469, 515859172, 78649409, 978650195, 255093388, 907556774, 690245371, 141949666, 554296468, 913132846, 122677668, 188805586, 505889726, 602173902, 85647535, 651844118, 325045064, 521762946, 488688057, 616431563, 300096644, 736185309, 30259865, 562001084, 62687784, 510367654, 893552382, 88004227, 216605838, 737609998, 845760579, 1157117, 214653544, 476251871, 835938820, 281637573, 142507552, 545642196, 725232009, 136100162, 819859979, 311786301, 899716950, 594696858, 13352454, 377528521, 166144746, 547824856, 514288331, 869653549, 833309341, 347973954, 149589670, 715588268, 636470924, 684697369, 782243094, 95034949, 893227320, 364470207, 955607811, 133192923, 109969272, 552523742, 5995117, 219503329, 417061567, 613219677, 308302837, 635530205, 340160661, 132074331, 546858367, 60934613, 70611374, 7169425, 679328754, 305548724, 334659839, 895195737, 283399048, 357099512, 333915617, 505462244, 254613688, 425831868, 2760296, 879107127, 353000587, 328009631, 811377912, 695854716, 681339076, 159213010, 939783509, 347896169, 263176484, 563810548, 546669364, 685440188, 278244445, 627886820, 420159571, 642547917, 979110991, 34728795, 52836571, 306088640, 866553842, 394039057, 442405456, 460389350, 508641900, 842380414, 537112379, 274049380, 470853625, 250845215, 8517273, 222001670, 6627550, 17460521, 991054843, 21174576, 830321689, 402063537, 448810738, 437921673, 887592923, 954722084, 195380896, 965540390, 537439288, 869084659, 639558780, 655888439, 704627797, 633133368, 236676368, 670524054, 52154637, 679132885, 767780710, 708129169, 677076777, 668081659, 839507894, 193257720, 56172140, 776485510, 536509466, 686999578, 566150911, 147258473, 161186529, 936049067, 364553717, 476744643, 474044171, 108973914, 20825021, 142409683, 333994993, 449845940, 570418261, 682620574, 108950771, 98613996, 530817043, 813371633, 486602580, 344164713, 600293141, 434364390, 973282371, 797778902, 897458073, 302754260, 429080622, 599959973, 181748753, 288840372, 751479683, 643216068, 74294191, 665409994, 143272675, 555747413, 159840397, 822100337, 643727847, 991812779, 991493148, 986334728, 517165339, 285769638, 408318755, 809766245, 479384700, 319498737, 614819697, 940023347, 885558882, 278923732, 171890721, 408921590, 220541629, 441044743, 582995572, 267690382, 537828921, 16155411, 482825764, 984255641, 897226279, 28192348, 883985584, 322640874, 705478980, 877743912, 882337020, 81302222, 895458654, 241900450, 786569657, 235500687, 182300363, 212448496, 974877434, 683505303, 716453317, 855259419, 941498663, 444876950, 681347216, 883895945, 481759071, 486358587, 964686084, 272703417, 504162917, 263324580, 875442318, 30228077, 390573477, 585883902, 120785093, 78195974, 257428066, 262289646, 987144264, 840790790, 907453503, 872005358, 812273311, 429436709, 692299104, 210177125, 307781597, 572745950, 712994809, 843069526, 699309341, 4433931, 643705217, 375127981, 247005626, 891129848, 490917276, 476093369, 634188216, 723570309, 749871821, 943265132, 37962537, 394468880, 284453860, 798843749, 751775228, 306508487, 744083053, 848115036, 758072979, 658689162, 549549437, 757988133, 324220949, 729106723, 931252936, 387139280, 272698219, 372521513, 321322066, 690866597, 657771764, 835712121, 804659874, 679943049, 59471246, 798279133, 995082799, 120993866, 749617131, 277455032, 531467527, 884409550, 346746018, 779761031, 362618738, 649166311, 323896546, 710975025, 660922105, 133540166, 855590297, 437340372, 462171291, 720927726, 789493979, 148335156, 254372825, 596779159, 478980813, 851543224, 491059009, 909727399, 281931667, 945074163, 824964990, 741090303, 270389678, 103957332, 103623074, 985586631, 12955417, 41037068, 302949717, 441608574, 443798975, 7675545, 8813655, 980473184, 841023186, 836457550, 328689326, 462519548, 904700498, 561526741, 182467774, 610433850, 80460404, 335639221, 417781412, 326442249, 657723657, 524839372, 256329309, 454213097, 628306625, 807489817, 78041100, 825430200, 735179208, 763242709, 217800369, 249654121, 683806314, 404930748, 20533069, 34369626, 899778097, 48907212, 493950453, 102417385, 694440298, 374253780, 270890719, 293356744, 688533972, 68069713, 109616503, 305711726, 538566447, 272160224, 858163479, 971188330, 664451336, 422244809, 506691066, 797696601, 139161198, 823331996, 803568799, 753528845, 64642334, 768396011, 604446349, 116585185, 35561358, 872620637, 345268228, 464719110, 710192788, 128161693, 578049846, 642129818, 85762119, 646184559, 441761832, 918514956, 658113457, 977214209, 995204215, 583669732, 828966502, 258017456, 828017429, 795239429, 517910184, 809577762, 859453802, 46899095, 308972610, 637032480, 348442822, 899458726, 461143399, 477614712, 945572625, 392230029, 816891165, 983840916, 116219643, 984359210, 965608980, 405465779, 726071853, 552172772, 786393467, 788115179, 813729102, 423139100, 754921787, 564276609, 195609374, 994851523, 898587269, 49906996, 424225275, 912007387, 845031602, 755673166, 320827906, 836587013, 969674896, 426554167, 4511808, 206048430, 679136619, 423305702, 599179040, 444402951, 448979012, 358984940, 664209624, 486430089, 106701090, 198188231, 468074987, 827692816, 730469911, 45906520, 220358095, 264062402, 134227245, 291051642, 657851476, 530864997, 419406453, 463388418, 960197738, 555587931, 817157374, 235158913, 912431279, 325353660, 123016574, 7427866, 896773309, 839345630, 434536157, 217837845, 93306839, 173943805, 978264490, 601702067, 73939966, 938277742, 543959976, 251355763, 728060159, 671579007, 443599843, 808535447, 440852686, 696560783, 92109724, 231119047, 464747566, 658153400, 394245278, 46928340, 680227157, 828811337, 583141440, 369666256, 94311605, 624183995, 835077644, 528117627, 649508220, 955202804, 405936031, 499367101, 586851442, 956588593, 139327526, 116191849, 906126224, 127246893, 630239480, 964837581, 338612393, 248789751, 499413802, 786268935, 11950655, 488999892, 353566951, 118754703, 830530680, 506261916, 750118296, 996321693, 55912228, 148238116, 765649972, 153886358, 527004213, 539822766, 254286032, 696517554, 746528697, 478089530, 718398786, 915604917, 115261946, 34035357, 860499149, 438254298, 772928519, 549280011, 89815303, 667720032, 583264927, 418941853, 24335416, 905206045, 842266667, 320134468, 881859859, 63043328, 137932063, 713619929, 256015998, 52097886, 294380390, 227862797, 65695051, 717933945, 629346426, 470035492, 986731056, 584923476, 411913455, 448907321, 977793000, 777515902, 442943057, 365197923, 685158799, 748722444, 438294171, 837126041, 197678799, 627427917, 207860063, 11655585, 820572233, 188603101, 92977460, 729053491, 467364900, 776195443, 234916823, 103952475, 447146747, 687906716, 352525310, 162836230, 206998579, 776917130, 284989292, 65031468, 797417488, 260493291, 430423287, 945780017, 262410364, 798081668, 342302948, 902074209, 496112104, 747950543, 470770876, 150522200, 29673855, 109807053, 43718912, 214289226, 392740174, 867441455, 814044914, 655100505, 617563972, 218584255, 585064034, 747532032, 238649084, 914324012, 294310527, 948787574, 669390720, 843493503, 324494918, 386990196, 781506985, 758197613, 63423324, 200682577, 188375652, 523182199, 719422563, 193196443, 933596675, 105818262, 768073291, 569646589, 791455964, 298902807, 644395732, 18975837, 988254951, 630690354, 845695644, 240573471, 952858526, 959200561, 784418523, 789328314, 972243305, 583764643, 948413399, 140486492, 977790835, 815266074, 137003479, 535693808, 315252170, 629905630, 125669086, 65627198, 509579171, 64679676, 416132534, 60320173, 945465577, 425336294, 136179377, 880041549, 779897809, 813683302, 383324511, 660551728, 169829176, 744050070, 692933602, 266396703, 430227137, 637250450, 987849250, 666446463, 369174214, 911646475, 494704220, 244817398, 544780161, 521271810, 417531091, 505701516, 988039841, 904408150, 57107188, 811319857, 956058263, 497735188, 176292572, 758652151, 948745581, 647081870, 231799466, 535798916, 809854548, 845084124, 747944685, 141792714, 74712399, 969822359, 20115744, 986066772, 249352495, 63367605, 973026968, 295824338, 985806714, 494263813, 485843974, 756941374, 910108302, 95926861, 51251324, 690881939, 274544232, 973342638, 938558326, 767276793, 898270349, 527952571, 181872257, 646808449, 906035552, 975450429, 96474500, 625185841, 36188319, 14846339, 296281733, 120865850, 486658618, 762818671, 241112671, 116833949, 184052555, 854058623, 838275897, 974454876, 39694855, 543505560, 557907966, 427936117, 289237552, 886622020, 427691559, 964184140, 367451878, 333523299, 495047778, 569869753, 45540436, 545074560, 615956662, 388604354, 828202369, 556125839, 368003970, 888572458, 5858775, 145476153, 970773606, 983188985, 553167279, 733944680, 771068895, 184770250, 447566375, 837423115, 968008236, 281683794, 427701467, 107396387, 434812094, 738116985, 158101417, 105762118, 533341246, 486847654, 198616790, 818479010, 929373212, 18142870, 210996336, 798854545, 710335882, 851395426, 333715434, 607196343, 305778639, 816901860, 772358597, 698413898, 970657545, 858262688, 892730947, 983666100, 622924937, 119904638, 955575401, 733958313, 482639662, 53502327, 607389655, 938568938, 935814331, 51944993, 266712811, 559044583, 382614067, 788954857, 590316186, 172654078, 819360165, 88684421, 220411007, 386166177, 959696375, 573135619, 931327803, 580629545, 407963173, 848221775, 773644864, 333739389, 189650120, 420741864, 459389221, 945666885, 649401774, 741632207, 852854084, 7199555, 725125782, 517421187, 885478419, 734947249, 429779029, 625879600, 761043653, 397922340, 95235614, 226975128, 793457825, 239353351, 901576113, 93755885, 53414898, 749555874, 635502516, 776779452, 688801757, 710614938, 783836805, 808280959, 29098314, 260975724, 599264763, 418779912, 141472251, 90409258, 699976184, 249108839, 172423629, 388694503, 89475458, 483409169, 234895862, 205738362, 699926929, 372711683, 26007319, 721166120, 124699613, 950501991, 349874641, 586738631, 684900097, 511385858, 738761354, 915227544, 235216320, 906979746, 994042043, 267482829, 836571857, 140931864, 186767224, 59225474, 648129476, 455772731, 459391764, 320251633, 418913888, 330880173, 214159617, 49716276, 344962331, 555840894, 92990529, 181977363, 249164313, 110190937, 902609423, 726444331, 688690303, 635353715, 886678010, 246719724, 134509704, 110353197, 538140258, 437700283, 919298401, 523391007, 192995021, 995628766, 476644871, 398084477, 382049586, 836848368, 240936966, 708441207, 322783643, 836346835, 142922972, 540034316, 967505142, 483699061, 959908842, 705381647, 2632377, 488663489, 442803118, 993599107, 94666263, 176865987, 496148318, 421137740, 354236990, 65457568, 654085783, 541131495, 593434837, 364704332, 953707333, 953271713, 531515572, 190207463, 427030424, 683460981, 744770438, 752536165, 351155272, 301031823, 249154440, 303130026, 27875478, 3816014, 605550503, 342836019, 745783792, 663315346, 441572023, 655458936, 64100706, 570810664, 805299862, 304111028, 841690918, 846036322, 261232102, 248031846, 203707187, 997466244, 254522083, 710306903, 185638469, 987584485, 504157924, 609327669, 934456813, 339726689, 46509969, 595321884, 819710883, 81088509, 771809156, 404348063, 967527264, 396818412, 414394289, 914185757, 766601925, 367807864, 791392983, 321948235, 940906320, 609840378, 413308326, 278229530, 787235986, 147399850, 236535925, 824554907, 876177016, 96163549, 329403774, 555946502, 716401997, 896914482, 671612020, 841391612, 872988702, 586187297, 939826426, 319982195, 836550955, 896020779, 794634607, 345162615, 496519530, 216616408, 555211631, 532599910, 305354443, 494234935, 361696328, 523343269, 733256437, 249221769, 731695595, 792687111, 714966123, 123042746, 229407379, 20772035, 665363220, 55399020, 587422186, 675022794, 951214023, 668958800, 506462263, 761051157, 718727459, 944571752, 5288336, 946292403, 772773691, 707997358, 84370919, 624255258, 680248839, 227942722, 15151369, 223110728, 891328430, 490025767, 109469579, 11382337, 474744460, 497804224, 678045712, 141450798, 934519193, 785003353, 215598906, 114495816, 987624166, 961191703, 743326870, 236731201, 277744026, 90870273, 906132447, 97765923, 151503903, 431437639, 306514760, 476398923, 150960026, 124811428, 222013629, 418530101, 673522610, 562871679, 237594154, 170943795, 789087897, 178826697, 251202846, 308157942, 179565521, 55083755, 953323855, 671587368, 140603922, 344927004, 466027635, 219234711, 518961853, 226417851, 348111107, 586113091, 510816486, 361219700, 584777245, 889195826, 935756472, 899249380, 421190694, 44259573, 156082819, 59227880, 836441622, 110223531, 535135022, 934996840, 403809169, 1137941, 793258261, 274421474, 186593328, 906160682, 629221716, 405127997, 335794880, 660811214, 404736010, 748683818, 469936300, 287970676, 84752259, 220993705, 302921144, 467000475, 392856797, 603458739, 117528701, 382368304, 488132888, 136630976, 455303433, 30901926, 451860770, 748370270, 466252621, 567697960, 356640486, 350872009, 54770820, 752732435, 264639821, 806362904, 482732072, 853798181, 571945726, 769202965, 494829592, 732827178, 717616606, 634046328, 942410612, 42905703, 536667375, 840326766, 589698234, 377641362, 954298903, 94470595, 627173962, 231614720, 814395814, 120248063, 381520986, 324007952, 721039153, 323153699, 444686172, 727989434, 644977861, 892507345, 555888132, 720991502, 611215572, 443304126, 800413547, 492407143, 622392896, 389310138, 567188669, 719876724, 445744247, 978120332, 877875626, 432774507, 643060744, 399272444, 981871312, 115248343, 539979293, 737100522, 412467536, 5437906, 716929063, 811675586, 959548224, 881996397, 889266715, 195215262, 451413193, 557677878, 778622280, 984739180, 967928424, 199466131, 911481979, 468414209, 586471496, 879669951, 907466243, 858047416, 495475862, 788298151, 461614350, 314671177, 265244388, 12829631, 540952314, 59443303, 594375586, 354143177, 493502160, 265576433, 394203193, 993622757, 612135940, 117758606, 71290310, 381846330, 881647804, 421641167, 471710978, 499286850, 83260326, 308926319, 450378009, 251581515, 826556462, 889045655, 8290881, 267904802, 702629471, 425584815, 747312575, 47184379, 553242299, 246621126, 469599413, 740378115, 795294046, 906438579, 204170750, 807838743, 602619402, 501490128, 660732901, 594293703, 431307034, 129151861, 654924666, 900737744, 980045513, 364936662, 605869804, 925511249, 842772158, 527173846, 736528170, 625859607, 318585308, 483858642, 934658406, 920628558, 688820401, 368118733, 875933837, 582058572, 97707289, 985235785, 115749565, 474589103, 458653367, 807310520, 843667541, 478324075, 888144922, 554010982, 164047597, 407641572, 13483378, 865889011, 987934623, 165609174, 712993712, 140878389, 695703382, 586161231, 162364808, 921126203, 516457743, 295037735, 988667519, 584783921, 130264270, 991230134, 568135370, 411481760, 8758064, 180845784, 650270729, 480449573, 454375951, 982915932, 884083297, 364233186, 161470258, 283789650, 306266028, 999141699, 303803597, 770397782, 800045121, 755148874, 701503093, 255810048, 644669428, 573835058, 236397487, 788937765, 45948419, 71030683, 431759177, 611861706, 100977844, 82441970, 86991564, 374844529, 946242974, 660288002, 808358132, 107686930, 426311153, 908763159, 838958816, 170695792, 128271289, 456644664, 400045241, 682415650, 660724250, 420131653, 749690671, 886572054, 635337879, 923825637, 857152963, 970005010, 490199205, 791820884, 490484243, 704407956, 624438823, 879706577, 804727711, 3153664, 420818632, 513203828, 41428176, 232661009, 469165506, 624698612, 917409090, 593917189, 554622285, 187332479, 121883211, 690588822, 445727068, 561950942, 820847908, 938493639, 601539447, 399900780, 362856527, 954726172, 215321529, 737085207, 179888361, 279337070, 67302184, 143029930, 129963728, 484809559, 466821545, 121393019, 133782547, 878437998, 63476215, 397761258, 201316590, 192269536, 740610177, 507563279, 566322310, 181369762, 30173666, 187652931, 138354237, 935476796, 8780681, 239741591, 991437369, 373711364, 161269671, 482281521, 129832469, 294755138, 231934266, 448010302, 213219693, 138629540, 655847048, 737428562, 244368052, 62950844, 973052427, 666351142, 460374480, 503040025, 995801962, 327488146, 372731056, 44266612, 632459816, 266349369, 280748370, 274821280, 995837893, 887422516, 645052798, 708386676, 853459367, 586342905, 464589626, 98489205, 760576020, 910978607, 411950660, 706579837, 674905894, 14310684, 549360428, 226832822, 492999689, 356689254, 560899934, 418511228, 682876787, 622282517, 366726142, 508414563, 299813884, 919196915, 756116913, 502737979, 210048456, 636339325, 838041561, 443826950, 151385814, 642038395, 692595920, 737723998, 176185277, 884452977, 780876047, 710552819, 794536896, 779290817, 871895174, 26750433, 485963529, 870873495, 621849580, 120616641, 661687154, 178810985, 415861968, 195700127, 127381840, 642135556, 18951825, 25508720, 754615839, 282168651, 327720040, 35738954, 487133427, 650239582, 511169352, 66069776, 178710455, 263741792, 46432135, 496209827, 713971519, 712055978, 285321019, 58866341, 809131226, 229075925, 914348562, 97706203, 790431567, 120800020, 789927788, 532841133, 554270739, 899776583, 951261078, 72131865, 309986254, 364282158, 843976269, 639784895, 560875725, 44329305, 494539829, 746321758, 277344399, 234023212, 15784258, 204771330, 861971417, 270491032, 526013272, 849538400, 381533862, 291195883, 246384677, 981306201, 615239159, 792450829, 450387743, 63442147, 815789602, 306188088, 863514934, 745699606, 37300911, 931201368, 300139498, 255777419, 967132457, 353537003, 433692831, 820466728, 154471048, 767143670, 720361491, 586111850, 477581269, 545087755, 837656156, 413247448, 665901922, 902054802, 295365364, 119473206, 532704322, 855175002, 793417689, 900044876, 974890434, 423810070, 366344126, 951324535, 26326404, 90049046, 440740082, 44613281, 384400610, 152813044, 516623330, 849694254, 93236163, 118759501, 182719243, 665553685, 483157736, 64922448, 949340850, 985395474, 134849278, 490146189, 851340917, 536078522, 154624270, 244186366, 333452937, 709010876, 376242538, 99267675, 414177835, 919868306, 943445339, 224848233, 150929984, 133277070, 51625914, 609800377, 267036001, 319035858, 939479553, 190101621, 13079154, 504814338, 469404687, 579142910, 456149069, 125351160, 612294135, 924673613, 561008666, 88400542, 997439025, 191846495, 138879654, 865013386, 705371030, 438092779, 716823706, 552583395, 260813466, 450078209, 980237805, 414605819, 173416892, 475872690, 903023310, 402637346, 793909845, 330080115, 433148714, 80304735, 712275568, 981752633, 272978622, 556524113, 640586826, 338184844, 3040573, 199853516, 186003289, 516415799, 188252257, 939806645, 475782889, 282670470, 28794889, 834865958, 825144902, 7029396, 130845815, 764174936, 337658212, 759950662, 289132129, 529018942, 222819235, 309865284, 122314406, 588392674, 658163217, 33556503, 439425179, 158175104, 584334686, 94945531, 254779725, 813163192, 832449552, 795414548, 774593067, 301434524, 987689521, 832747192, 876589544, 136961641, 407630665, 775479490, 641384893, 88110687, 881662378, 740512845, 258917716, 594688817, 264576234, 781241065, 410268339, 949420451, 321148044, 348325062, 893689705, 308141038, 563401674, 290357458, 666922526, 865939280, 72844973, 38730927, 860381789, 296650746, 361118734, 62892734, 269114205, 782620088, 830912542, 284770953, 424503150, 936808174, 388561809, 344286558, 850927273, 485959518, 644750972, 727345965, 75272773, 42094192, 513940225, 270082597, 256633123, 148604443, 921129395, 307714827, 534620476, 452271079, 541727609, 212581587, 810061890, 793873370, 691994635, 745667256, 44492595, 863379850, 194629560, 850885397, 930433797, 442652872, 972701494, 841353504, 693406909, 27659534, 392289018, 558113670, 248765754, 142408251, 46647966, 203445969, 851186381, 414868398, 559046871, 317456543, 66598531, 256134395, 497688417, 936566966, 655670978, 205755247, 991155800, 661117898, 104138753, 931001648, 248488128, 974256343, 661087363, 999137777, 484583367, 160866319, 968602706, 844043439, 627413395, 250425814, 674191827, 4735450, 64000194, 620951347, 151108482, 237208187, 70275338, 159877126, 116711339, 745712862, 566830032, 457618723, 753430608, 903758135, 148101676, 812054400, 304811172, 153203829, 750998923, 731705402, 883445604, 789570353, 700013408, 574592434, 705798972, 844183132, 168943575, 75574957, 318056197, 996501070, 841355139, 398877656, 781134087, 483580934, 672785158, 833415526, 420242012, 266968338, 549515178, 965442900, 739178282, 189625155, 859536116, 119333128, 89895451, 212717906, 2060904, 246803264, 54082469, 724457263, 664730283, 96510988, 621312401, 249497128, 948454697, 535012142, 327426647, 99956734, 163655591, 74835939, 447290508, 625231130, 872737596, 141461354, 403637993, 856877447, 396876290, 360362793, 625788927, 735986079, 790781129, 992014210, 931576637, 667173804, 361646735, 917096715, 93759940, 165379837, 841775113, 249963791, 146328761, 485490862, 9429346, 816498822, 615292168, 974193656, 883277870, 905566470, 285373739, 653823764, 725471035, 673105248, 777693014, 409177581, 830100870, 633323595, 596573835, 431063267, 551707732, 624037513, 129726259, 500134901, 212045009, 705915049, 301151708, 616393363, 789771253, 516280073, 569575129, 616108146, 146511772, 743727439, 58036639, 619888430, 19223981, 584185472, 651866405, 693032402, 499139338, 275119477, 354792699, 696342333, 337260795, 500576614, 98316592, 118769863, 530240053, 208048618, 51399992, 995037123, 675844284, 273570119, 672469357, 970868784, 792063192, 447410628, 203043818, 118217382, 245638454, 86633604, 229334766, 456525918, 928860373, 268001777, 155138466, 674894430, 627280344, 336107390, 94809544, 73643520, 509988028, 570273325, 974450830, 149202259, 186158587, 548420245, 809375658, 168411086, 578630704, 977989728, 948555802, 94033005, 78343580, 825190587, 74447964, 935854439, 674018165, 43987440, 35646673, 93694902, 949245881, 806589037, 315856996, 301840436, 916136179, 973374203, 436458553, 134913483, 867208451, 106680227, 327145358, 245634754, 410411226, 62114564, 312222476, 665927500, 690331820, 796738252, 479523936, 926331941, 962956053, 623042696, 555644755, 723716155, 280840927, 255890146, 1638871, 53239888, 731146359, 277806554, 715516871, 575222744, 926826967, 470392694, 294188752, 190271003, 906987688, 973416524, 154423409, 564568275, 580957106, 353455569, 746246141, 588247534, 201466430, 895921917, 365669744, 512045123, 924861421, 456420350, 627583756, 627140835, 306301003, 56782053, 83737009, 590027040, 433532525, 289467186, 115365066, 394285475, 415581808, 73531010, 384411750, 540778271, 658386879, 52001458, 59518350, 172988246, 687070346, 624867540, 14372642, 83554520, 441599703, 37999163, 41870958, 562523420, 506360208, 379881447, 178371900, 88602882, 633294853, 332567973, 642594, 76593846, 572828060, 756046882, 316187599, 391330493, 95467632, 757987781, 408651048, 347746592, 510127385, 945677023, 766274079, 386527948, 419550642, 12994663, 862438456, 609776023, 881944771, 569829546, 617061, 368281494, 677971554, 64273348, 30205561, 869260686, 638897712, 984444005, 280306012, 476440768, 373332926, 533205119, 959357806, 556741759, 809638630, 471646523, 804553578, 616000282, 337023073, 955063091, 330325518, 287635833, 28476771, 887431568, 251575345, 609454764, 244504882, 824783975, 724160777, 705495365, 559026321, 81775089, 691518566, 471260894, 902858957, 991969237, 128037691, 522340123, 812085566, 430974390, 713149992, 846538292, 808065737, 253054856, 847427829, 687843360, 315944786, 845783078, 686590766, 636222568, 542377098, 818136641, 692592063, 506466775, 601330605, 615267687, 9535327, 578629335, 972435450, 304355294, 2588060, 132441386, 634757823, 813911312, 573909775, 395489761, 439066572, 899216158, 578350613, 809525397, 4760205, 822758429, 742127925, 735233013, 115285729, 352720567, 949461853, 474769993, 890999975, 535316527, 447342759, 725879785, 432906497, 476396639, 90523982, 628450583, 786867120, 229635773, 849722695, 55577762, 523912887, 886184054, 597236004, 169134502, 569619290, 351865111, 648020700, 406780930, 761809171, 286856128, 382516222, 656751526, 56957658, 132355164, 612108956, 32739669, 610652861, 842398289, 683217328, 855913775, 654822686, 616245914, 250331411, 715353709, 334234725, 641249116, 782224168, 781406626, 389348943, 936416449, 87569682, 536228984, 517389748, 671916404, 808894138, 338996864, 994107516, 876937234, 738136266, 547583345, 572443109, 93569076, 992645752, 403896138, 690945302, 994695831, 453593743, 882775309, 117113712, 474853338, 181237437, 559065378, 573150716, 456782582, 465589054, 411953404, 9672149, 187820401, 358621377, 463330095, 114208031, 149581979, 140069321, 297379973, 109503419, 565254649, 13081187, 583989979, 752750855, 308592024, 959356214, 862115922, 941307839, 299628396, 715133144, 876249108, 304940267, 396714228, 981231449, 148508902, 450154585, 252206909, 790200397, 496622215, 320747767, 948091207, 962899576, 510141197, 889139844, 841618406, 715772872, 884532525, 31885344, 657480667, 21397271, 416854327, 301470068, 250196570, 672360497, 548379332, 388738289, 998300232, 75693811, 938108220, 910222273, 959011876, 366759954, 618493466, 9498750, 167588245, 104818298, 118825516, 244205692, 498314386, 115700328, 343617637, 982525392, 550791573, 140274837, 827996919, 348046720, 834669263, 368207717, 311678149, 605240482, 259052572, 628351238, 247314513, 309564844, 88284357, 357623272, 858620666, 710252063, 921157429, 36656343, 653706688, 823879943, 77635226, 168072186, 463961184, 898900914, 394652437, 934019588, 239396203, 219186598, 287855363, 935927366, 540117135, 457502316, 348456650, 236998127, 265737927, 263030557, 731807511, 696824224, 123255390, 443889715, 779777239, 778156863, 825927226, 672625908, 866712596, 842942690, 819552826, 418374867, 743909818, 704593919, 336249296, 882413567, 899970400, 567660362, 634338319, 66741627, 133719384, 43145183, 151669207, 361820743, 819351561, 745359441, 574390115, 870182372, 537801873, 358406581, 886094264, 138154018, 547587886, 256612817, 870486732, 686038663, 861281538, 534784786, 21970482, 212475964, 350054463, 923166837, 733771484, 234222603, 574568315, 631779458, 155391078, 120430341, 64290476, 728641071, 588791732, 532394008, 657896001, 279459816, 280149606, 336370065, 864234462, 777946898, 584891225, 45879126, 17193600, 144942174, 205184258, 874759200, 736544353, 851218273, 848106933, 674707848, 907228151, 608556590, 752575817, 512445068, 318893986, 277699866, 423751588, 448937424, 426603413, 494124931, 283221868, 474609818, 797402690, 34734703, 302656582, 125854515, 662197259, 78398247, 67698016, 891105696, 893630677, 712663316, 98904529, 447586288, 756874602, 531274286, 821164506, 701826136, 819284855, 108507245, 839035379, 658503763, 763428400, 940563042, 19752261, 186535447, 376014621, 514371564, 434222781, 60127188, 788726524, 385389150, 106947548, 392365771, 58357194, 519872470, 465567789, 997841396, 867197108, 944256166, 88713747, 72315760, 476566013, 948723675, 208554484, 175989584, 114936176, 530176230, 728681623, 32040823, 915939140, 404834132, 406078808, 278432566, 548441830, 531288991, 561195352, 401838310, 688953499, 449772400, 363350380, 290262297, 335749251, 342832525, 940650323, 497080602, 127866545, 816899382, 849367584, 873196710, 233046848, 926700130, 201337995, 783919842, 248361253, 47817653, 609874791, 766683654, 885955436, 781284209, 987420002, 658717651, 636750366, 161906912, 403296602, 544887911, 979631687, 445904470, 861904174, 27868043, 831361673, 288173015, 871052774, 25469620, 833634136, 376717706, 296345702, 222212958, 671158798, 60948533, 269371559, 287658932, 245486913, 669535949, 180324707, 783822650, 195979391, 301386159, 383235424, 548037066, 732815917, 722594542, 731628083, 290622651, 716478290, 128384019, 862100381, 280622340, 157284828, 516133885, 685490487, 428500878, 906038762, 873461998, 262669490, 926641141, 456514266, 562734064, 740899842, 985652376, 658143354, 21796422, 844626445, 664819909, 905807060, 261017322, 329722841, 745748670, 514115268, 766976253, 960263574, 366072298, 64628382, 807297615, 941681675, 550526876, 974800521, 506661044, 251335827, 580479917, 417403417, 906139425, 442957768, 383239689, 451300010, 340893729, 778567634, 840345142, 897109122, 20914588, 387815976, 6127759, 396642295, 326626683, 759615298, 871345838, 896669942, 948701938, 493842932, 84277341, 552103312, 278771807, 395711846, 402359726, 100475468, 114671686, 733128160, 841314114, 306299815, 752605321, 521973090, 474835945, 812045115, 615281918, 968561871, 593020266, 99920862, 156317588, 166468669, 279250567, 463343100, 89356493, 552845385, 862202409, 716464511, 950265345, 983859693, 123560961, 935667690, 854298743, 774057457, 301966969, 38852420, 943585667, 595433212, 364262435, 405967603, 624079777, 634821354, 882365283, 629252529, 223540349, 451815603, 495651848, 761349068, 44930390, 559265888, 622079154, 469597355, 13623660, 494669600, 228668364, 425805422, 148571513, 951996110, 346593738, 440260097, 64835193, 819310127, 853187870, 2726080, 110659687, 38520502, 472912345, 852712823, 583233249, 806579636, 695852249, 382833836, 256163579, 194361751, 430825701, 585738364, 16824531, 342458111, 85677790, 655129429, 769808031, 717867343, 804487320, 221604571, 464820033, 148149350, 101572556, 623032936, 371221926, 409457969, 721275999, 371457007, 241353061, 515763453, 125866269, 815758100, 133874283, 357804650, 951681726, 699815220, 352279422, 778069690, 748169409, 979404583, 411137128, 844940040, 657815987, 254060190, 565875257, 668995239, 15332660, 617301834, 492722807, 48917032, 755500118, 633651668, 252402703, 461762242, 453373466, 817638900, 673892558, 992612184, 194907013, 990643190, 467737705, 809411082, 697328886, 636368639, 372404354, 261113117, 166777275, 45464720, 823976729, 496508821, 638495761, 979340022, 626951658, 697443645, 723699210, 371160528, 998341707, 108289916, 605869910, 274509395, 112072212, 481132982, 237474427, 422113799, 346943296, 616377340, 573912740, 425844738, 67585530, 57897350, 563900849, 926741479, 50838990, 396078150, 871888167, 491412285, 451856863, 254296593, 558722723, 700676472, 978998105, 305114166, 328462603, 545298224, 322791720, 370421269, 845136258, 121641192, 964214491, 898826593, 749988029, 28420075, 542513488, 356206473, 905199935, 676931373, 918930162, 496813493, 38562674, 588260828, 336364252, 809818209, 363223636, 365724929, 976003901, 868234557, 20788192, 420694314, 58042740, 906202796, 816300797, 490314340, 958553151, 546361097, 515586792, 585577585, 222710386, 109981207, 908821603, 959748876, 977278624, 312084861, 559405590, 734198283, 981930569, 206082986, 258278094, 802511220, 458914157, 829779912, 291082538, 939468938, 24969471, 784555600, 136190386, 923275160, 245697474, 997163233, 538815079, 645172957, 70997041, 17653677, 30589988, 160818584, 116604148, 605231755, 401271700, 239750542, 696435878, 514436300, 207419926, 211961811, 809429766, 771933914, 95977906, 618410492, 607995989, 537450381, 644179286, 785313163, 132075419, 578572362, 904951871, 120483398, 901495408, 138844629, 290636087, 830823985, 461010319, 882434401, 144812446, 845201683, 429386793, 986642885, 174859021, 117114804, 191194659, 639628364, 513499145, 711698714, 139639497, 372177999, 653607387, 983913656, 535405511, 254106996, 597801488, 764923159, 459139545, 349505430, 460368920, 627273752, 915469503, 576128159, 770037108, 760270845, 781566554, 638819318, 7921884, 895310454, 191540675, 947797245, 937298397, 80561742, 557799102, 183164394, 80802274, 384292397, 957642759, 290097368, 506871488, 983533801, 714473049, 444302333, 372928810, 17714988, 296283193, 595130169, 526836535, 341757577, 898013774, 361516299, 280314775, 133009025, 492867531, 186390949, 4866941, 521325172, 138243016, 818631907, 940112393, 516084485, 847287194, 303702719, 338911166, 990603273, 307953938, 227286806, 110978184, 456919115, 774573361, 878232458, 190985726, 432639060, 321806475, 644297743, 610218966, 214524488, 77178868, 471553760, 642754401, 767874635, 589805384, 186592638, 333553350, 824995940, 908263935, 721468824, 918315725, 521426666, 238863677, 550869532, 268249334, 747044401, 101199125, 169782770, 337989161, 284908081, 85451386, 798756971, 44676268, 147985457, 784636058, 516759410, 738665491, 355510736, 58342350, 340181371, 658769437, 913079188, 995055603, 21965722, 433316054, 519955501, 949400592, 616406956, 658341314, 409933772, 439122954, 626320759, 945214635, 543944839, 67739009, 200888264, 82022124, 910829559, 475226611, 883764077, 329985070, 708782563, 900956544, 460536155, 974793664, 223787932, 771686836, 342105477, 983946316, 527068823, 556602558, 469510110, 560233296, 332925185, 18526356, 230580901, 29675013, 653588897, 672157593, 347011087, 800374791, 281585632, 669555794, 259298048, 841212463, 925140076, 231600030, 120612061, 508276247, 477449903, 651019671, 472931036, 594209151, 617325783, 261881026, 4382264, 431371139, 263248189, 60941462, 954655301, 734614212, 43828713, 79124071, 341378793, 266325245, 151540590, 734762701, 140089307, 275624846, 60757477, 967045373, 757596208, 72515502, 68041302, 338952063, 529993775, 30789823, 965498466, 316600344, 374417777, 970844756, 816218081, 209402163, 604957515, 794926986, 898304783, 502189567, 530998731, 197379418, 546993012, 939422069, 775379345, 403289176, 168487087, 103629436, 549957978, 123556131, 763089199, 544767378, 556383417, 496140086, 289348677, 330107876, 375330289, 805884843, 632529493, 975861693, 948837625, 761209891, 216978530, 878951609, 379183797, 881237132, 876800215, 292388976, 803916473, 697511407, 129966183, 585315527, 595363685, 463419391, 529229871, 548650663, 47620513, 70490651, 405880401, 36391003, 635714808, 923932832, 837243384, 419120578, 143699994, 565782732, 29586688, 68395441, 397800657, 457766387, 60258288, 816257332, 835594192, 476080372, 949806250, 742006360, 905122712, 462987243, 500701520, 929500009, 655366986, 828084170, 664409453, 325245221, 995271069, 451052714, 21351085, 655973487, 539596685, 131291583, 157449375, 6807949, 750752571, 206377410, 701768908, 545376089, 451634583, 761301365, 566890394, 637409841, 461022961, 36618065, 368904080, 29630894, 877661356, 802703576, 800772261, 366488637, 73534485, 105874753, 533459734, 289061130, 347626778, 341400692, 78794592, 746809012, 693858655, 357851554, 64144200, 449104791, 287929799, 132590618, 812690272, 895897984, 336247141, 284556898, 530760809, 545531570, 635093168, 856357165, 577740991, 979683865, 652511118, 904476943, 818922946, 688633939, 890158059, 249548701, 527278556, 282704050, 854971519, 58333687, 657904768, 326810913, 501386582, 789123802, 470490356, 496754832, 513253574, 540382162, 781168052, 843073716, 422013927, 542202946, 505621664, 252127956, 625387993, 63109787, 645128792, 127287960, 501027134, 6697023, 285963908, 204239208, 588787484, 685984853, 889256092, 89071290, 987979730, 966001246, 30647766, 384084133, 635225924, 277395892, 521548594, 123593543, 86137168, 264586257, 236776020, 346089038, 859140165, 880634636, 290496578, 825162249, 949050142, 477711209, 842366809, 920108180, 872638852, 651189202, 355640761, 376119167, 795279774, 348101750, 811376519, 751294746, 343381691, 999476458, 101574969, 779652541, 149718984, 821558540, 69711320, 677843642, 454459098, 768870258, 465346991, 571981607, 795830973, 418484193, 129724026, 123014399, 524162207, 586244715, 242399287, 884222043, 650096041, 906724141, 777505812, 187344160, 37059848, 707361471, 738575703, 905568478, 55672369, 907286674, 788534291, 447412377, 767724228, 691723311, 117991945, 156827819, 926223323, 34743367, 528642320, 35986689, 62241730, 697639657, 80826729, 462209398, 627946250, 30269147, 949712928, 491199978, 488490658, 26056301, 286774748, 731457922, 33208806, 583966904, 398303347, 419222000, 434493291, 416533932, 644271630, 228276448, 887402439, 991845647, 440494325, 531628828, 403732940, 104087672, 27009716, 809933208, 966100405, 969032950, 685121569, 399383587, 461956266, 60011051, 595064745, 490310423, 410218309, 56342314, 139055116, 506821743, 534197493, 78839852, 778631437, 599325335, 757312066, 547745340, 944551755, 580686816, 789272214, 162456676, 584301260, 105792040, 350426097, 685568882, 357194973, 43645469, 565222640, 860037653, 720389072, 51537966, 307750685, 361567211, 891327654, 285661258, 643567568, 483830528, 1180825, 745959658, 858610288, 870791818, 489977959, 738108848, 61885962, 433197563, 860390213, 942927365, 979472776, 859271151, 505136733, 66125902, 36176538, 277524593, 38812111, 634942602, 260067207, 863972216, 460433199, 931395698, 188128588, 600028396, 885235076, 371927190, 801610001, 142196042, 259783385, 485983581, 454801209, 599418028, 903835575, 778483626, 276471688, 469263063, 740392436, 953279454, 481071025, 704180408, 303879789, 24584289, 146331736, 133007415, 463055167, 205470755, 854712867, 553690518, 809339539, 176185270, 709057218, 395655378, 407668316, 38618811, 522205780, 659015071, 192869933, 887170242, 94716615, 619497851, 909716392, 7849832, 145683737, 375790003, 48524976, 495183960, 988499230, 135519779, 506473540, 840198167, 562491511, 47608506, 213041337, 875643288, 520861074, 59574555, 70676550, 826541510, 226002580, 293364680, 702333092, 482086093, 573101520, 613095912, 395781133, 383427672, 356667528, 348657431, 418351318, 756608630, 78655432, 529425494, 218653185, 201900795, 676640662, 376876027, 916527280, 724357050, 91995795, 441739361, 440293859, 5341718, 495108504, 994322935, 790141241, 151299470, 548111138, 421809607, 146164399, 726762943, 784490032, 348809022, 792303271, 290076866, 553428337, 710192170, 9283808, 193990386, 470581024, 704800814, 102153470, 242317074, 79275155, 352081587, 639672189, 869387546, 371929689, 582886264, 10896083, 291789705, 755141909, 422549078, 522526159, 462143713, 966603041, 233714354, 263968030, 775569548, 517621721, 190321342, 256760769, 255580491, 96919231, 638895655, 932375054, 678207919, 924371055, 299568215, 262086337, 463720330, 780429501, 110553816, 544085401, 798867085, 993351797, 73115373, 295256749, 549672213, 599596513, 205355892, 878076019, 422707623, 587427244, 315980650, 903958245, 126562582, 226962455, 528783197, 602448675, 527413397, 102671893, 749039120, 891855789, 962365692, 642638618, 766964619, 61335851, 991268591, 965441064, 901861310, 880011970, 841198265, 179671198, 101073123, 128943039, 386456803, 639150059, 154101150, 820911314, 380892517, 691717139, 428641849, 131867546, 639740499, 934168680, 733999282, 835636751, 141887272, 701211426, 361639268, 713154702, 149330205, 261592240, 623594637, 577327313, 259753004, 934870888, 138974972, 481701715, 88212701, 390824452, 725095080, 216495931, 677954434, 464674029, 333454891, 158109672, 372611550, 178682310, 61720641, 261110643, 993419251, 524209645, 778373393, 454766807, 820252369, 885414638, 921760994, 446398936, 937483391, 894644323, 456457797, 936975126, 990755221, 459992648, 570840892, 100348020, 98080381, 688550824, 150801157, 921730218, 685354962, 328347218, 789741361, 431787394, 561051381, 24533749, 612199167, 813367972, 29281487, 188569300, 55460469, 174445999, 451734419, 219649278, 480991174, 921182130, 868830605, 385265774, 998919078, 400461057, 450118464, 473653307, 565577437, 130627130, 582284021, 336725967, 460231046, 356863320, 710793735, 337977003, 974983915, 848413382, 500103647, 496137457, 922945285, 760790504, 352209916, 408625167, 412576023, 703430085, 805298914, 81652381, 377281593, 892962383, 487569679, 892417842, 306057650, 417528605, 672083964, 650704841, 260732999, 777160714, 467042236, 305756132, 599122027, 676428806, 769623515, 251447075, 978977606, 547772878, 975620220, 820865600, 445409992, 530561569, 342510670, 554078268, 22790875, 357467436, 628429827, 782125760, 361548601, 138112163, 531590062, 117498778, 924650854, 546710167, 932164365, 310003367, 500457459, 501855707, 142238848, 468818243, 577253031, 43416147, 889552959, 696131578, 85251817, 741583135, 523333034, 719331816, 25999707, 756276710, 879426570, 193257954, 949052801, 874031168, 367516718, 958654477, 846272855, 363301295, 268839477, 206864755, 525527273, 651174091, 556836066, 330868459, 500562289, 182051223, 71755532, 606372241, 262991038, 838716376, 886902156, 338176863, 15827671, 167348812, 421768348, 629955793, 872583666, 139772211, 526907087, 548442504, 658765912, 783292588, 884613409, 655360754, 112901338, 972750311, 316466236, 549647612, 208801087, 385866178, 90766415, 402067597, 423105174, 795986883, 30191407, 287268717, 514410047, 54532003, 258771674, 327189336, 297893064, 396514461, 700125149, 834292286, 317559185, 645047710, 745440035, 685643898, 168988937, 904220570, 140608961, 414048856, 528829853, 9693683, 73946532, 112816024, 83764932, 487848328, 466686847, 77520914, 736060607, 812396179, 645494180, 917072898, 166938121, 105604535, 418371347, 481320764, 153856024, 709284074, 802449597, 462183596, 552595390, 319884616, 777838438, 688456480, 544330970, 575574124, 77716627, 78828198, 303546540, 304517815, 535279928, 787977151, 863930938, 899241013, 614566231, 487970242, 735966439, 270830275, 392677195, 31219739, 69649383, 377791082, 323873053, 126106650, 976743282, 640058515, 782321533, 758224153, 958757871, 878966573, 690761921, 342056872, 697096207, 373872902, 519150695, 587593130, 696930911, 690828155, 737606182, 493916726, 885726050, 852390135, 194134218, 42478926, 714361690, 63511326, 101511057, 96066870, 25163527, 920562649, 712782347, 700028187, 977484736, 525420941, 924155554, 607854489, 675355313, 654391067, 656165415, 156454887, 455478997, 384866586, 393239621, 31803571, 610105197, 26236060, 860029769, 328948009, 785459675, 317980312, 863691309, 273397566, 720641578, 532612290, 438400070, 775140933, 116130926, 745422411, 830560518, 949664460, 250283695, 32037076, 9713223, 987625308, 874797517, 739441331, 745559889, 776229593, 456694026, 392670908, 981186932, 670708243, 260458342, 60606233, 211050027, 621747005, 307356029, 252281653, 266847182, 755630324, 162462843, 171061107, 489039655, 694849806, 653175082, 53249337, 961033677, 762309540, 46451382, 43028157, 604547111, 853775831, 569656841, 377514097, 925852989, 192748758, 764147446, 84881742, 874581575, 744269521, 529140296, 803377778, 19346239, 988809776, 54564094, 130864897, 848980574, 14494783, 11891024, 448017364, 499708341, 711204744, 618561837, 373337428, 131630777, 337490287, 730848019, 579242334, 586856686, 523675027, 858797839, 739774426, 135800792, 895081908, 228298979, 884783056, 480892290, 96042413, 833871449, 944075684, 216155852, 464339778, 72813382, 949550079, 654803217, 80247501, 662015880, 759893340, 327106585, 892733806, 194319176, 611089924, 295346173, 449709061, 255279608, 883083516, 409926233, 670308514, 770279379, 319656039, 753224143, 296201462, 258618618, 734599442, 922562629, 693855908, 445426603, 39307751, 180608794, 924548817, 368082775, 160959249, 567171877, 371393446, 499085383, 508338820, 810282523, 724401422, 132215338, 473456356, 232411219, 536693983, 102038825, 763953878, 688705557, 540525786, 366683340, 587614838, 67422896, 519114487, 509077421, 233574000, 122705185, 295548127, 797884503, 724356579, 28064745, 236663069, 984830621, 632274272, 196015721, 405558074, 71726190, 997643954, 122911105, 669952116, 891776559, 603944452, 300380432, 440107743, 645475252, 307258657, 904313610, 205060034, 136341857, 415171623, 71034702, 358468501, 766555389, 731427542, 25939476, 724227430, 230077524, 940188917, 41448311, 669586442, 648075272, 480247820, 320833929, 93743950, 783450592, 760616539, 841530661, 81084712, 404150341, 353040517, 941738267, 680799914, 855459274, 419748286, 297491897, 322315339, 353517681, 360538205, 27116438, 233652477, 75536912, 245635505, 384610710, 398287244, 302159812, 687896367, 605405318, 2465282, 203389452, 375896685, 925760658, 767649936, 543833444, 156416724, 835932211, 57334827, 894218837, 674101667, 328455691, 300989429, 883712296, 229641315, 645691410, 833899368, 835612635, 692553095, 513838338, 225864124, 120842284, 162489809, 950844885, 587626056, 103894817, 415692077, 804674029, 205947991, 526991906, 284369333, 532817390, 313928476, 168956054, 140375161, 248914296, 806988403, 509242314, 172295748, 119367697, 846923040, 158793673, 254783238, 704977230, 285598138, 737202206, 551850352, 401867677, 91117728, 440291576, 19643573, 283545826, 930860139, 188466993, 799462141, 160014663, 426537782, 374652644, 207992753, 656612397, 385638960, 883842966, 592337582, 541863494, 101683513, 845251642, 790545551, 784844772, 607418480, 772603386, 444946770, 155196229, 61193259, 815401290, 82532233, 734751777, 634094680, 643511271, 987561970, 28642079, 524518728, 664744544, 870410857, 71088966, 442904776, 390913517, 803090930, 498878547, 818236902, 135930456, 278593894, 48428371, 962635275, 587872544, 428273562, 450210902, 893871113, 127442801, 407708682, 901144493, 700866032, 266418488, 588951562, 234826244, 724035608, 601017685, 272830168, 805735138, 75738246, 954255661, 858678522, 636672676, 343718286, 19103871, 196347570, 683202554, 557924879, 356914668, 868836001, 957074612, 3753467, 446040171, 270269657, 70998551, 896925639, 921858474, 621955820, 732822583, 624518681, 325268841, 660876273, 26066756, 777996265, 329112063, 144556529, 850163496, 429723366, 355081072, 527147899, 588300979, 743150433, 661447866, 664351290, 567802460, 620945466, 11431171, 669907857, 446079114, 77611006, 666278959, 544829859, 909534989, 650701187, 574738336, 659283318, 713467098, 43457724, 687828314, 591569968, 52773035, 212643311, 556983493, 969262732, 825513699, 616014654, 45760614, 682309042, 215059740, 388653344, 928259971, 952458297, 644550287, 521484515, 655383783, 430094519, 304919783, 939900851, 964225345, 433463680, 90171294, 599848275, 486531419, 415821566, 824184641, 899455868, 648252244, 950329669, 27591566, 202563794, 844202011, 41539415, 535663591, 426312649, 639315700, 847625002, 376948497, 390094559, 137940885, 999038598, 855419575, 764515494, 24383385, 938111772, 367707384, 535258515, 299814451, 958668189, 826322069, 808411154, 275333959, 121696083, 720432742, 241765246, 780725883, 139343809, 324587919, 768253769, 11514827, 987175746, 17963105, 918881938, 850229076, 770307584, 541504399, 784973971, 775462098, 700066449, 578310551, 165226769, 50225694, 100534069, 149165392, 276510274, 669782640, 194417949, 775330484, 863267000, 708285028, 874496724, 888888318, 329234243, 641814712, 361569061, 115812205, 529772852, 490685807, 980585359, 881402168, 804537375, 24292325, 987141144, 920381745, 188398396, 531378185, 286370038, 951525358, 438074324, 985318295, 662768657, 596443484, 920005782, 409256325, 58214417, 552941977, 247378964, 195476454, 771743475, 276561858, 879116872, 280995945, 824288028, 415123847, 247360634, 272882912, 27499546, 190769435, 844059990, 707740356, 102043550, 401428290, 791957814, 913396378, 363415784, 22778269, 225890428, 756001767, 784452284, 345373690, 792643765, 704824941, 376864792, 143423486, 669282586, 119650767, 138236693, 946523517, 504568714, 511286535, 548953952, 570962729, 182400608, 252745706, 846747613, 976017334, 707051419, 851457836, 373108667, 91035034, 652583988, 299089045, 286468675, 984239376, 387096800, 242514731, 889063155, 794129680, 900501199, 290010831, 331022456, 170157966, 932517717, 667634008, 303258950, 882385889, 771336221, 923312093, 618251121, 599611104, 449065900, 483335052, 626683078, 451772927, 858868323, 28508624, 777879850, 247256177, 385216029, 941370260, 164566533, 5404916, 121149285, 332381183, 624537323, 871735812, 988485670, 221504682, 881543570, 725665654, 350174032, 571358472, 640703237, 907810148, 449326955, 18750725, 112458690, 627223311, 107605037, 686317244, 274201771, 457686453, 480039111, 521136815, 688307354, 277179790, 558691027, 347562477, 251543461, 381857198, 600195893, 508069511, 856986974, 527984358, 855361441, 872416824, 723389520, 791249291, 490416041, 829100353, 837572768, 511236237, 492979919, 862831329, 501000613, 490615842, 887464291, 76829759, 586338359, 718683862, 409483894, 940587144, 364528062, 686821960, 410575668, 174324346, 436529653, 731180027, 947722518, 2842901, 696211608, 610962474, 271267196, 578917552, 106053062, 528021615, 144991863, 782914659, 514267937, 38899230, 912482071, 775719218, 544229688, 838453716, 478119701, 576208626, 403138020, 346849345, 937830072, 887973642, 554032542, 973593275, 919255731, 22425403, 349053501, 777839946, 207709918, 479919712, 23429955, 728742476, 537204336, 388461263, 340233476, 879372698, 124917129, 980273956, 483563057, 177346006, 381472754, 914814127, 244250853, 819448935, 34709933, 378061106, 376755521, 422205595, 599613252, 750426578, 605705463, 65104701, 748731003, 188477622, 687479160, 983872941, 404722786, 252344506, 929129980, 750203879, 900816783, 513680279, 873812617, 940408633, 622115788, 488489770, 435424943, 602113169, 310396285, 782303953, 558161004, 546201016, 897451704, 115704795, 940724050, 979100331, 387740215, 531133588, 995338154, 871811952, 278938069, 932779662, 677744523, 714491403, 179614093, 210732977, 627479656, 202301503, 477982620, 244275933, 320402025, 922319668, 896655288, 84356808, 579878104, 768474665, 560229584, 389050760, 467470404, 208958320, 58886003, 767111631, 724299733, 116232567, 400497456, 373995786, 478945410, 351550731, 964215715, 494204422, 234494954, 559740610, 6121377, 459722553, 400444518, 498185188, 490603894, 620981000, 22411861, 66618478, 871130029, 441614921, 279487149, 573484422, 460362422, 350577292, 291297258, 755658941, 458419366, 242191956, 881235898, 592337989, 795322890, 68663458, 287368512, 71226747, 941890588, 332808765, 85201701, 979813098, 651424383, 4125093, 717405173, 385129886, 134242763, 904266298, 935437243, 85899394, 540614912, 712904534, 812110746, 978387010, 609424553, 323093173, 522779031, 130087069, 749291670, 506972371, 496015781, 876159698, 236914366, 9686035, 504155106, 838237790, 593208807, 468021992, 503161747, 869800874, 779962525, 1407143, 700470578, 47813945, 730253071, 917305676, 128586163, 714080129, 446368825, 251359279, 431503868, 412465007, 976425706, 108893070, 712840652, 853347987, 223605327, 290448517, 720050784, 206812972, 726309109, 962210394, 388987236, 958659240, 26678563, 109897053, 960208679, 649789832, 155888106, 313627088, 905655937, 535846709, 650417951, 696912537, 259008643, 10712502, 170782472, 338446511, 364836758, 443247839, 381306796, 126689053, 273585021, 348144767, 493793132, 397699656, 37788275, 566307016, 29822733, 298196361, 636201008, 873494474, 934182029, 700886260, 516295853, 85065168, 579242296, 681421197, 607709231, 161591729, 981397507, 38602675, 42576977, 65675845, 961502276, 566148767, 172551324, 592416086, 937770186, 790798258, 619453171, 326564083, 382591549, 748640502, 885105083, 442475427, 146107629, 443463319, 586366745, 911483425, 261578515, 205918844, 780183705, 592230910, 589531596, 303992530, 307429710, 838746658, 616294573, 350219450, 722658168, 405218526, 661682110, 513389880, 398547350, 983476128, 53221453, 588455172, 94710026, 104938881, 672492554, 195923867, 647504693, 733441782, 712911257, 248344074, 717315030, 213164804, 310354577, 584340194, 497671817, 888556871, 141607469, 426270774, 949457659, 993879967, 19392306, 345992228, 772551107, 989441288, 780464995, 51019065, 184683652, 336694262, 206230709, 223023451, 389232684, 556481387, 417690414, 225964430, 845525004, 470440418, 278242498, 561540396, 335022417, 206491133, 245419248, 85449266, 656440435, 329412109, 625883297, 773092166, 89782405, 950002172, 913472376, 270850104, 779186456, 876303082, 740870130, 673707108, 278028562, 381950768, 82757295, 764938084, 876596212, 244291855, 786987913, 527931328, 383369286, 318089949, 607487625, 128081232, 548606862, 478910183, 784962156, 243411785, 89751889, 65690600, 999876664, 559329245, 649520883, 573670255, 43424468, 282821327, 686490787, 562748463, 747449758, 945684930, 355744426, 209004023, 225082700, 661933077, 380936841, 504457667, 338822153, 53895416, 74022312, 833727611, 551567482, 140050559, 959427051, 44536320, 701519847, 845158144, 969603441, 337985023, 266676862, 735471084, 15144009, 613573544, 249324013, 903121657, 886346155, 396038365, 617880642, 330373760, 721703096, 320809647, 202388532, 574871111, 772193860, 847764502, 863135079, 735077488, 124571543, 535683859, 799133587, 447550497, 453858485, 398622038, 621600194, 871362096, 365307237, 685740221, 69535519, 221885179, 685407800, 720519610, 833868975, 536173355, 863415350, 4421076, 636852585, 51251441, 737961887, 919386364, 233154864, 68557204, 202619491, 773610703, 6672183, 928752083, 935439689, 733518322, 945564946, 286057550, 462953607, 365197360, 965205772, 335873479, 700925570, 144000132, 246561718, 832645735, 179147425, 302463531, 452450843, 74914598, 272059632, 526086645, 868091081, 455406062, 194855302, 511435105, 997769587, 572020805, 882667558, 67042751, 632791279, 968751666, 740762247, 671061295, 470673939, 98950944, 817520846, 362958226, 305557693, 157805134, 63044662, 955681597, 684427700, 289174512, 163820625, 881800297, 614072494, 106844162, 276207809, 47836157, 355104122, 152829704, 587217936, 426912280, 514578430, 863544631, 374659904, 77214808, 340748257, 179890775, 43605192, 892055459, 314249556, 655163499, 311770315, 689253237, 275071129, 480412040, 820480221, 767982743, 915504366, 335326517, 974201352, 830993527, 384080573, 557728185, 782837348, 143179419, 827161944, 171459678, 40328742, 808283756, 211343471, 952313085, 550455384, 458842576, 179250134, 150338946, 853144840, 382091851, 993171846, 633942187, 829283648, 736358395, 313040780, 541049685, 18062870, 848291811, 7268117, 382662678, 46851101, 64851260, 671311682, 508651764, 388580365, 581146958, 420245741, 477197585, 856098202, 640244672, 309353007, 658473669, 608456173, 269149987, 818856873, 120962968, 164651368, 849005219, 332436466, 680010818, 642590867, 291109139, 264579401, 186700172, 446004565, 990522643, 794928171, 664481448, 754760928, 260256350, 432819891, 139123602, 322260281, 469558001, 176361611, 265568534, 373641300, 925248393, 346812205, 242412479, 867767184, 586552469, 391139182, 654031459, 858053660, 968278216, 5183962, 161250101, 121975842, 744162609, 906136205, 989763531, 75892109, 258910383, 552998052, 704350061, 990311637, 428597592, 460898779, 497978585, 389587451, 46691516, 329699202, 726893116, 633785312, 203164655, 986264950, 168368854, 563629890, 968093115, 885893101, 527563745, 139936794, 933798910, 800602360, 722524914, 930197149, 987828744, 373991274, 520626742, 820555240, 281863859, 988263658, 410163859, 183349716, 756858525, 357966970, 233200805, 23513873, 459980443, 18728698, 176423093, 442203849, 577373961, 405084393, 553045812, 886177542, 364555213, 401450602, 173078862, 327555385, 962876587, 268005727, 450430628, 611497381, 61652708, 765436219, 688023755, 251013765, 894021839, 632559360, 603750621, 406389532, 864943630, 971812500, 787996709, 711072352, 260415625, 348940047, 208128408, 511940864, 584298282, 442943054, 47425154, 390012634, 365999820, 53975482, 813159605, 833029801, 92272354, 204612333, 167515066, 667815601, 544177076, 874845556, 877274002, 515757471, 585730778, 32305849, 933770999, 637024288, 296718031, 756838961, 90128294, 403587139, 87290257, 879506051, 872432803, 262436476, 672121411, 726544433, 360245522, 285938325, 674817026, 501245318, 211094395, 804625333, 816411271, 791449640, 678447016, 584255396, 425058660, 98535211, 406928207, 57785682, 34168774, 107328352, 180250444, 998840921, 965618439, 100676053, 555741169, 860824141, 600263268, 336600312, 902973735, 618936316, 535077538, 82846280, 136274624, 15119374, 517019539, 660175037, 315091025, 726245270, 490190476, 834779907, 774677224, 607921765, 940008180, 672746710, 227670410, 125996754, 224294163, 820838959, 585886295, 927383243, 994384222, 947305763, 353465797, 370181351, 825238833, 732047627, 688513373, 984648114, 205145540, 177362370, 710324235, 384909270, 770184390, 506616450, 709653404, 597087809, 312880350, 900320272, 818564039, 838984953, 617179668, 956143290, 532210631, 940330651, 619230339, 981145788, 274533395, 664411518, 634912927, 570510091, 116643815, 931407854, 153410500, 971587428, 727429199, 958266931, 877936139, 540654540, 827498416, 504105889, 106029759, 279252520, 736936497, 556543195, 621242947, 42373308, 619611562, 24526057, 345046315, 788061929, 324528522, 503455513, 297433628, 593270225, 174568411, 947583541, 614508202, 630515978, 414636719, 358639658, 587807180, 793243924, 419202493, 316144280, 292835859, 708334753, 989069976, 823838937, 154078508, 698722996, 50125289, 974958693, 380885687, 409875387, 989549096, 671084032, 285256348, 419674464, 483308815, 299670262, 835105043, 347147562, 60109735, 102006353, 610509139, 342930116, 359442809, 676060362, 170549881, 973902033, 209296269, 493449548, 764592881, 4620809, 382196965, 507180620, 142070191, 840873499, 468222479, 52427852, 930507067, 425347631, 308066127, 553711581, 354299134, 381992843, 542164697, 267008595, 31751590, 192446440, 692754242, 515442204, 945912382, 781234482, 22034647, 391674310, 467954869, 54998391, 600968543, 701351247, 521428442, 7221346, 967734612, 418899152, 995444867, 424180007, 676360713, 983647721, 18210480, 507594949, 623632955, 81711878, 982625419, 665204459, 918459140, 18945829, 967594677, 794136490, 835201946, 863871457, 574534163, 69792634, 198142552, 511928234, 239127146, 184932352, 47661469, 105561993, 793757903, 7922574, 760414294, 984354905, 341824271, 205884027, 164843285, 659910946, 41278361, 212472502, 612294587, 745856068, 708898807, 977886360, 689110613, 938130713, 408954040, 39982683, 59259171, 3093743, 983233410, 443451062, 238160072, 72133548, 296643448, 605105507, 735500101, 256890510, 334096800, 750529413, 418312728, 433640482, 932946485, 511641935, 947398764, 820976153, 174009057, 521834194, 835882476, 124400383, 755160191, 599783450, 580704409, 285230504, 439672183, 557704828, 408944377, 345584555, 808492150, 919196227, 444590007, 952744387, 725646538, 266721330, 509070398, 190803528, 879664108, 580105624, 495817358, 250887247, 678630312, 65001249, 695956031, 252032703, 871313191, 854827072, 160704656, 485681817, 31683754, 567443064, 197971077, 695588909, 108573550, 261777728, 973292955, 199764655, 495799979, 310532635, 260801408, 565314132, 275458536, 470308835, 699715220, 719577007, 502346822, 4775649, 132354285, 291887498, 48816351, 912887865, 158136889, 804918348, 166644556, 524407172, 792473093, 352446024, 866958786, 397048127, 264739396, 310377642, 766566175, 8637954, 182161491, 508126268, 768535977, 257928149, 230472059, 928152858, 825357879, 930406856, 643313168, 291739843, 103348897, 90179708, 665542859, 639797746, 423791625, 90776075, 563904848, 761476059, 202517991, 460109347, 211303230, 983813607, 548487672, 908240532, 956530513, 844353896, 279917336, 109946072, 889644122, 427302296, 783333131, 315733760, 806400620, 586482617, 162305355, 456405528, 406178946, 184572640, 19974332, 456473152, 400094902, 136957039, 926128362, 347611075, 222853953, 400718994, 948145903, 544447873, 306051825, 289852094, 795622880, 917189164, 904760581, 187444945, 691227705, 413952358, 222224700, 706431859, 708171471, 288059925, 100607309, 110132456, 800557735, 611021105, 986044414, 785007580, 174712468, 198595624, 796573255, 920451867, 953844274, 570489560, 771321585, 590453144, 969472406, 825664219, 556562079, 725858806, 738756673, 741923152, 18635150, 659452642, 45883615, 107356921, 523355960, 378320115, 105634907, 323411956, 950664249, 344771393, 405979996, 698945535, 45141570, 213907426, 647449738, 872765824, 18183219, 272917244, 948524711, 916141328, 649253351, 329523688, 252944344, 438071795, 62029684, 652424087, 563151724, 792327085, 904448209, 646820646, 761539695, 733228074, 797656068, 780214041, 734396917, 156606991, 536750112, 878475014, 614063190, 545564829, 293296758, 934305086, 607939046, 659024717, 576519289, 310717832, 123382198, 919538728, 458571252, 833909947, 413288586, 109908385, 397771398, 547676099, 495017190, 6508941, 542376094, 498207946, 701975614, 88652288, 283398093, 876588937, 804897356, 430682772, 785613968, 132743877, 736592940, 476705676, 796038472, 177850419, 885226388, 139049930, 7087566, 588076645, 88923509, 630381578, 704587268, 502608219, 527002108, 477636557, 707887630, 824429315, 538326502, 540053509, 192741366, 794540233, 580577879, 289576387, 483945315, 669323102, 870050587, 829174713, 342140854, 965682100, 7702646, 615538111, 714317146, 151141038, 162908220, 693708353, 213906510, 751055746, 252587413, 675837456, 331762578, 146916268, 191922234, 559097079, 752062798, 572091883, 958594762, 499779045, 547194612, 884843557, 82854657, 838986087, 422916098, 970560577, 682950608, 897358460, 56586070, 674841757, 810038905, 917736001, 296206205, 38826013, 268417644, 121085635, 414322099, 329445268, 871899865, 61123184, 376344896, 824909441, 266583620, 553204898, 524894675, 137276231, 608014401, 53765513, 329586968, 802353770, 477024752, 983056318, 250732368, 828684058, 227110954, 280954623, 625515395, 961069112, 640844830, 718542990, 305895962, 869667777, 58061643, 212435748, 773460568, 900008526, 515313608, 218743341, 497935279, 725421373, 438244211, 6930711, 444682286, 651328575, 423718372, 675584966, 925267957, 405836066, 5418964, 709563469, 818555803, 287564808, 163836853, 137596888, 630068168, 197177063, 774912037, 785077696, 707741131, 736368125, 843131720, 603656685, 712590456, 907233009, 799764462, 527284416, 243598823, 179232021, 624926221, 753392759, 950228322, 616645344, 946615209, 787381153, 295166167, 706380934, 6111214, 838444370, 201674736, 246782668, 875897380, 953597148, 55884673, 913486225, 865277461, 255356520, 514691764, 749856601, 692850951, 501319749, 574102306, 923168604, 923575660, 491663013, 412271545, 890914073, 201436882, 376485886, 669323531, 440091536, 701660880, 585532823, 867613712, 551348295, 120748236, 122103104, 873953295, 121022999, 629943046, 784361916, 510753836, 466975960, 962046569, 557790954, 45886649, 992078485, 535822692, 42159159, 907981412, 20577051, 797013156, 8016372, 375678047, 690918700, 346481743, 781524167, 748663764, 912530741, 229168880, 631884411, 195816626, 174585756, 363032125, 917865438, 933059918, 739660641, 307375785, 257685633, 561140792, 608714402, 7107400, 623280639, 606056684, 942770824, 700666112, 375317986, 922532814, 675472314, 822398652, 875859378, 73672393, 803100941, 988406448, 107070690, 128168647, 719896694, 85715716, 805782574, 206498727, 188601810, 83167078, 378273865, 779551389, 226034071, 595601518, 258519084, 341628538, 649404910, 514872572, 270959264, 255324835, 577759587, 491500630, 939606697, 650252920, 510976273, 227676445, 701294580, 130445423, 312556697, 719585558, 958512169, 623449975, 194736198, 33687768, 603527094, 794344804, 928407235, 310524106, 773102113, 773971353, 342370403, 143152037, 508061574, 277484464, 610050742, 32924410, 413534921, 195188108, 56056192, 228437279, 73189911, 893912362, 167796721, 471904030, 76679014, 121677541, 90757724, 484269646, 155450944, 696124948, 807549843, 817338247, 87592424, 485670011, 402955975, 438161640, 611691778, 535378405, 308531485, 862884174, 167052813, 679273041, 321753633, 298596145, 423834936, 567318632, 259688530, 736349050, 18719870, 273823892, 607833889, 873846907, 790003693, 410545042, 777812096, 394544062, 208620584, 932114607, 81748294, 603626657, 957552697, 786707893, 259884503, 163414965, 150400043, 460489134, 872800124, 858443471, 78246767, 458636287, 238498657, 453691844, 843269435, 734906916, 383506483, 304468890, 225467346, 296834379, 164627725, 28594361, 549597966, 781776978, 769752792, 190564363, 995151381, 260662222, 881815177, 421825060, 628297220, 114476647, 360590675, 852670153, 777282659, 323031781, 299989022, 826190517, 556760027, 391222992, 998581881, 749363517, 925424304, 768514557, 763331376, 335126336, 283553648, 519713912, 827307257, 641095215, 510429869, 412809322, 598076192, 357837369, 922809557, 60185044, 358875797, 348297521, 559859452, 118180941, 955242984, 675096365, 669394776, 397690641, 616612731, 527784277, 132908533, 586889610, 781620401, 237564323, 467039512, 366000591, 306311302, 715449490, 626911295, 295230208, 33818322, 367573147, 152864404, 814548795, 299467832, 747210372, 8952219, 907686226, 35672829, 768355434, 551478645, 576465238, 538208866, 787986909, 48319943, 100095587, 124411763, 109428133, 265963359, 241093544, 579430737, 12793962, 848012263, 67355157, 538816520, 62936090, 75965180, 187487842, 652219773, 888171805, 274948674, 878554453, 188913325, 666600255, 883914038, 804625361, 259798997, 738813633, 264055746, 913717712, 498019011, 219110915, 21807429, 698734697, 877622961, 65321119, 292068344, 919105018, 983149118, 19838479, 161100742, 295717215, 391644559, 654488146, 149381954, 925331059, 414314293, 612462757, 465022123, 988294885, 837599753, 913641428, 429009761, 229405619, 867115482, 819183927, 88700324, 979303465, 371781146, 542072204, 609186061, 553794085, 655693594, 61108179, 644090237, 229218991, 423583973, 804835239, 968209745, 573069229, 885170816, 218122445, 211965130, 78301633, 485334378, 248094656, 940318723, 958568214, 479951754, 76962576, 955029126, 387765624, 598219288, 404780443, 451116738, 544254603, 356082942, 430112926, 293442128, 949250222, 415030540, 228232280, 207769639, 678311416, 592769073, 709582995, 701716116, 238554542, 616115046, 519177833, 691154603, 812337502, 546608149, 118976013, 54469287, 499714133, 451758142, 603355171, 513407418, 609943170, 166821615, 790218200, 92705361, 492954839, 632633421, 605677950, 373182523, 572970354, 951313427, 829425975, 260616427, 922280129, 537809752, 4069905, 216284539, 388239542, 995805852, 646306664, 82500429, 381552280, 653609459, 674714396, 398384235, 146800788, 583312536, 867199232, 327968905, 963101854, 984337914, 820516344, 18707451, 541215567, 95679896, 437487733, 566310620, 780189423, 241687451, 484945829, 919430611, 271425088, 965158352, 215108873, 544294109, 690704019, 53454793, 64959766, 902832340, 451707236, 455053264, 235418655, 867642854, 963436337, 827867348, 208091796, 896087392, 46038257, 489952437, 535859405, 379970998, 639787851, 124522312, 295273935, 805872744, 335931455, 918746351, 183412939, 199239636, 904152083, 712837918, 341905697, 957322363, 652974769, 594517814, 261883616, 906807946, 524910580, 448107716, 478910292, 608089057, 507367404, 58903488, 691947128, 55196687, 697527497, 700323890, 800025463, 76520927, 959094572, 867711557, 598690318, 88187597, 654050577, 459474306, 845038661, 134917622, 362087129, 828505864, 76144272, 692567905, 947386932, 761718451, 178907140, 825444213, 402566435, 565228552, 514078924, 839719580, 608756017, 91278897, 344284744, 692269699, 817974857, 306542584, 826743063, 345203667, 127252140, 887455655, 58495974, 446473567, 609962507, 658680658, 903271937, 697538052, 510908534, 545669706, 697326480, 275291625, 583852728, 194110032, 816792189, 872197743, 987315064, 229009682, 507789963, 28938430, 382905505, 397218569, 4793893, 344751265, 194725581, 38800826, 665877228, 880324839, 594471622, 890859178, 119610488, 578254693, 842032914, 295740764, 847833782, 735549267, 487395549, 824369491, 459308738, 89227733, 803706521, 571283430, 955707272, 847640669, 840959957, 17343555, 752187046, 479425454, 248983785, 175431375, 519273616, 5356081, 961815937, 497312810, 246484883, 595437398, 954871017, 627598819, 294431721, 936440898, 443192556, 908873174, 669118560, 934754699, 728304866, 357228352, 352816693, 639687823, 806657713, 361357947, 656545804, 354326015, 380446338, 70022081, 928219740, 472332507, 675718704, 640619700, 88944311, 769056009, 562271230, 991084687, 342685537, 528338264, 758143128, 920619891, 899306701, 674752229, 481893356, 671780228, 642013303, 931722285, 153621684, 957710950, 177940567, 38073085, 311017774, 909489314, 925830275, 272482075, 406280437, 882827433, 244549974, 364724774, 752943953, 165659759, 867292678, 304313879, 581420311, 723172626, 808790293, 91248665, 249150101, 3127693, 485461425, 738788584, 796335171, 159937833, 728684467, 258189584, 782056949, 126071983, 640160014, 733915657, 150593155, 493873585, 179655679, 392955035, 965192959, 928399309, 179130847, 393836238, 507420743, 196813588, 328354287, 157577886, 336439283, 466111754, 262261836, 756158446, 694518051, 52379863, 996319801, 8222515, 633209835, 810267582, 200812002, 579051873, 893747640, 857811631, 113059468, 996014113, 126440158, 164936769, 494493213, 239953286, 697429054, 380277147, 52373079, 133074248, 943661282, 578780752, 829715128, 786545791, 109067835, 149812667, 896617066, 499226494, 854842461, 331703646, 587783850, 636565832, 188357296, 57005403, 777934363, 769897587, 372990830, 968849595, 628992006, 830510636, 36633412, 634779796, 752899409, 773388011, 344045756, 761587644, 930356908, 758004425, 985512274, 448063315, 953138531, 770856951, 734554953, 189951718, 917331620, 31157219, 638463843, 166451344, 999732021, 380430662, 993779595, 63356578, 248221747, 843652632, 131448780, 268130610, 782374732, 310091708, 282983001, 446235411, 877151792, 215945278, 925128360, 655153086, 572208212, 319107390, 40820118, 594654916, 354282133, 390307524, 735155214, 579551989, 681124557, 379269214, 100171507, 63097313, 440956948, 940813497, 261623890, 142095950, 695357420, 605777184, 106135876, 351509495, 345024839, 26872173, 782937574, 634942691, 63642624, 419806298, 877040369, 214713871, 68889747, 537896021, 833110386, 11648596, 376064696, 493331901, 995567306, 251239977, 8259748, 757603210, 944169920, 130103695, 835131919, 503916001, 135307947, 648834366, 120886902, 795104209, 437425144, 369869345, 675850404, 903920856, 31828875, 417636941, 813285415, 581209506, 350159054, 726003234, 23779991, 982827982, 756060021, 855404159, 634211893, 930152240, 33531597, 561679364, 70990823, 967575584, 931907672, 942760596, 231194311, 636406236, 775024266, 629592592, 174467131, 403191661, 163583792, 860106686, 67992693, 50294792, 11965115, 742383574, 199137045, 235529705, 37645237, 220280926, 53808721, 70814331, 568215606, 694935184, 877594523, 908812519, 609102933, 587057299, 426845704, 795125443, 682948847, 958158273, 748031063, 757834368, 901458905, 489710138, 409763398, 161847056, 872955924, 975338084, 301292676, 331567925, 812637221, 189169086, 386329469, 519160062, 896509627, 364986975, 999106576, 739348237, 29646453, 226854989, 356961848, 451914088, 579103296, 430456646, 787940494, 595113746, 799579416, 64914472, 345812621, 4006791, 510818610, 142742069, 499226356, 567321790, 411721913, 354879074, 647444671, 817475482, 551650066, 992668397, 44232533, 183243721, 533786136, 432045902, 925461618, 952697802, 491057391, 639048509, 195346943, 251095528, 677006734, 351997137, 541086820, 54382954, 677816206, 275476146, 906053228, 75739074, 866566293, 18246503, 88722795, 901521755, 182527353, 747289676, 630870507, 549674715, 711095190, 361632717, 62756765, 76386006, 446474500, 541887138, 469572837, 739063557, 472476902, 250027042, 979334636, 409833698, 21002853, 35050304, 122390748, 892488839, 466467002, 214415364, 859351125, 763944842, 891578116, 131236841, 147352788, 110150642, 578189220, 187503236, 256651737, 592184762, 620123205, 506456988, 107192315, 23677368, 946859892, 650875146, 315527920, 66578573, 689147542, 335134960, 296988854, 435344455, 105971338, 956150408, 56311739, 425461289, 172021228, 974867886, 813517167, 965224958, 901581251, 650079096, 354618721, 426086315, 69208269, 713558590, 434350516, 264741886, 936417023, 47502154, 301937000, 102481741, 158591340, 336282764, 45044020, 566744493, 209675428, 435368608, 390076741, 865892422, 613592939, 491641197, 462928, 809656495, 35677515, 715925765, 21507283, 330269980, 992734019, 398253323, 275832632, 766350513, 682584132, 586132043, 113161090, 832431763, 19403291, 259370623, 343024961, 576602362, 963596280, 948285085, 150450888, 165093862, 661975729, 232092839, 381941956, 803495504, 348678252, 899511236, 422976098, 500999488, 566120232, 919403464, 959906247, 530888840, 189869865, 985094902, 493519488, 998097686, 204308394, 37638089, 848573261, 231812482, 265697750, 348064884, 470814214, 369191481, 57228660, 689898468, 904333906, 121068897, 89518765, 832501319, 522938431, 142929318, 172088131, 768166595, 679662301, 49644662, 486495027, 202207633, 633059341, 700876600, 941546248, 401850786, 288570043, 61294398, 518682138, 666283934, 663322989, 94529330, 578438418, 635357966, 287793115, 159553682, 700031027, 242944696, 782684085, 115800076, 953790950, 128449314, 937050816, 552257159, 980212825, 263963765, 767611824, 71264179, 304162931, 974928866, 883818570, 546658232, 206451319, 36080707, 201245687, 419192697, 988029233, 574525656, 23638665, 329440872, 141313642, 841585810, 903731625, 985112919, 380987190, 117820326, 896075204, 680397208, 733036711, 615974478, 95287610, 733721616, 258248264, 467104996, 190245977, 513350215, 227468378, 140179418, 888774230, 471478955, 463709540, 79322361, 144016204, 906817993, 336262675, 89282373, 523094687, 238261025, 26749241, 800506695, 528758485, 771015509, 543122969, 258139938, 781875356, 916496820, 489411537, 847456376, 138058756, 914911995, 782784965, 982207159, 653942178, 632874438, 70064152, 339087188, 566519575, 564250943, 848993160, 417212948, 266230869, 963804290, 982047834, 115913562, 14401313, 905095252, 717011328, 492909695, 125139954, 330356066, 282199164, 35765113, 206353897, 805575606, 397401965, 909845126, 853347574, 781618304, 844593381, 734721104, 747228631, 713324609, 270631926, 579904851, 813786094, 653892969, 187854369, 812166237, 456713349, 176935010, 607087798, 444921731, 849206269, 867027011, 694127544, 636216719, 856467730, 695228452, 844338262, 455690392, 228133114, 467791485, 815893519, 781436989, 782240613, 995519538, 601590860, 742144989, 730778169, 104355421, 67848071, 279578142, 390858395, 237579215, 937492749, 952776280, 631896088, 102152557, 960439290, 419906133, 775649585, 77808050, 477153109, 58517877, 451053263, 184447040, 813065418, 914805482, 252628098, 755806184, 64805517, 593045209, 310952295, 248460886, 626143652, 463620972, 391249156, 212809647, 104841842, 473154146, 580729504, 411737767, 402790115, 989190884, 6800004, 992290319, 238444378, 472676426, 699287733, 490496258, 699494221, 284990433, 569156474, 249772300, 323642291, 897412985, 933352481, 988721337, 58433697, 974484561, 746265893, 358239043, 869612001, 100809527, 703925695, 520632009, 690259470, 834774082, 194550962, 690907651, 606605195, 61688002, 818260579, 156774390, 66018680, 952237018, 319588785, 289478964, 807064376, 177581529, 695359173, 815810815, 600094628, 272135807, 866879837, 618304755, 217422914, 382253247, 23628722, 898309149, 628327890, 975834806, 33624296, 197028308, 756954448, 38901951, 455860670, 800707359, 501666402, 27921373, 184811457, 867088988, 538014898, 567622445, 460684324, 70614625, 185738342, 104551572, 498123299, 318339857, 844655045, 711064218, 350899817, 145913295, 524965996, 9937613, 436656128, 246118588, 822334117, 327766791, 245883747, 522883167, 884383979, 150396894, 27471286, 227876730, 954717004, 704348396, 66256947, 429977399, 644010630, 347428152, 998033596, 324780548, 51503204, 182737682, 648132216, 990163586, 943497382, 917365553, 218757339, 874212810, 31961922, 342629552, 793048361, 861539802, 112604799, 904398355, 200426110, 97877657, 361404164, 5072924, 830838247, 238536080, 352581982, 581240007, 975747903, 7436389, 844404956, 170824782, 441443892, 669871386, 3831792, 162882932, 514397655, 734904424, 143341839, 387468191, 129784472, 502438505, 987221587, 101518171, 327588282, 428335528, 117299809, 29993746, 231967086, 487131811, 352715862, 299610475, 743122216, 292709480, 773574938, 408160565, 81087708, 94450764, 979306820, 745882201, 995563704, 360487512, 951517816, 893522711, 329182049, 436127477, 911252845, 154539275, 675465576, 935026787, 922260832, 574608555, 668887102, 498994699, 521953341, 521603851, 76785449, 680473816, 723809280, 952387601, 235218666, 843261076, 517865188, 793692722, 177530029, 426872932, 583900630, 712857242, 64572431, 709868098, 668759893, 500938566, 633093450, 475033908, 685686195, 635755384, 707913360, 168801551, 872760272, 338421398, 958363781, 188588776, 554392124, 489262282, 208471348, 458437616, 309416259, 354361807, 439424117, 235120819, 266656139, 616440633, 185508691, 183383236, 656075230, 576368752, 954931064, 319995905, 628593827, 262213377, 684756242, 196902852, 751580722, 335435743, 452360598, 232846078, 503136118, 861075714, 747005347, 979134148, 279934785, 815107081, 482286462, 883428112, 915210951, 929517853, 806182135, 717090169, 573500810, 376222189, 158865909, 617911029, 741853997, 629079006, 809946768, 52137300, 976753412, 700918362, 381499938, 844827039, 386743341, 233451832, 205456051, 279232048, 684390745, 12519873, 827886608, 607412622, 183655608, 290002504, 962372666, 793928894, 383275822, 80903145, 102814432, 62875396, 842147986, 809942341, 515055197, 830377439, 933650505, 498457178, 782816731, 280949222, 458158617, 367018298, 700813003, 245479222, 281715672, 916019818, 326040864, 788121553, 503757235, 694971265, 553066121, 12460460, 912819270, 973362359, 662010775, 891025790, 785448736, 423082485, 72920013, 74867184, 782807346, 134433503, 796343010, 167105248, 971798657, 760811979, 639892429, 804068012, 752509287, 460889612, 656569741, 499563123, 392159393, 703934462, 132892443, 450456034, 815391892, 573330636, 247786324, 770572122, 179623612, 432819077, 308277223, 667111677, 669648358, 777026082, 482234013, 122415089, 556823203, 273437843, 785937384, 851585325, 697058440, 50237507, 366775167, 484063051, 325256153, 846645510, 995634805, 967232305, 702440942, 901773762, 3075844, 715525351, 192924878, 241988284, 373241186, 532180326, 414435191, 349509886, 272098714, 508142841, 248219834, 476284106, 575294477, 452146501, 658731194, 227590194, 57630611, 227190833, 408475268, 40133866, 738245725, 38022447, 411081748, 213485438, 707984155, 261243947, 42348829, 327212931, 474702679, 433898385, 255471881, 334750301, 820186088, 741326648, 773455556, 777903595, 355416872, 871992100, 54764425, 855020380, 63318178, 4087999, 589893419, 269082193, 535852320, 102798764, 506043429, 872037551, 889836293, 157170166, 834039886, 320507915, 293735449, 129601835, 716978029, 764591643, 232680425, 34766759, 33449714, 48275040, 852648021, 489818527, 617863557, 826730829, 728107865, 179834709, 531672432, 520895925, 713806105, 542309476, 655462854, 457110882, 658096300, 238062494, 894620622, 461439521, 270882783, 55830443, 559085865, 607976614, 46333872, 422592598, 888033537, 94430658, 615425792, 45442581, 185332734, 788858535, 177416873, 262082790, 239183566, 653129759, 390351672, 319991896, 7316796, 524894778, 376331572, 699330422, 684527187, 166056494, 860244022, 571014831, 282679118, 248807488, 991690884, 892272350, 455699717, 596820542, 731399426, 411003443, 834958961, 194249138, 706923914, 169063867, 106139097, 431572658, 505852072, 981644416, 988802696, 211089144, 290380755, 734897666, 750191527, 990387307, 659957074, 429966952, 886943784, 991447435, 781740540, 781749025, 410144556, 713249315, 526234953, 233048794, 225535916, 53982228, 329416247, 405768560, 418659992, 754138779, 579977486, 957411770, 2146865, 976578740, 147723123, 954334553, 147761157, 907813124, 73922143, 275492213, 16017612, 584615523, 112339472, 545783411, 311603734, 786210194, 832252489, 644196662, 688220729, 121025095, 143484176, 24620994, 99943861, 199485938, 237181059, 793860708, 607599082, 476733635, 790817292, 237691803, 291719531, 286664139, 801874463, 337483773, 555048233, 687164375, 278940407, 492465754, 958406561, 651998546, 736437081, 950807322, 18337182, 260882492, 214730896, 460029647, 131829650, 696714025, 614654930, 635339456, 505585437, 880025304, 500416852, 967699239, 683212316, 818373604, 447382347, 216968629, 718691255, 494563135, 770723521, 259950152, 885889832, 575374920, 112380237, 914211757, 53326925, 163807341, 777548228, 467807835, 895420686, 431427132, 458908042, 375511790, 367333489, 512059890, 771684194, 365464808, 414649369, 65953689, 45599596, 285436754, 498816946, 296485561, 995239011, 943212259, 824260676, 86207988, 239360749, 253873700, 430689496, 330194677, 755063345, 566779866, 986229301, 515102453, 824598052, 707916835, 939649958, 639838047, 794389826, 979998752, 500790176, 707069261, 852439917, 14922855, 795690598, 373070585, 544298212, 296356921, 190583592, 630434458, 419111452, 710078235, 410052769, 365348675, 664302425, 897054244, 127115820, 993430137, 119456891, 373531938, 186202389, 973804297, 259110884, 965782088, 453773924, 553411343, 329601978, 970051905, 971544578, 384700555, 736535369, 930478897, 857959718, 242353399, 502632282, 771728414, 551559016, 245367628, 866035449, 953266824, 594437003, 191032524, 744513204, 722743708, 98865500, 478771785, 578837701, 122846470, 183025351, 489774585, 393481692, 652817154, 203122020, 212638695, 906456898, 290862810, 78572502, 82692779, 197577064, 695774634, 518490714, 180444263, 205063864, 167210094, 387896495, 114047031, 67116558, 140993492, 309522107, 55477644, 525190568, 999813195, 106121291, 636251834, 864586891, 834262355, 802616860, 250403548, 595585098, 655829733, 654720228, 137595872, 368668079, 899413665, 306339958, 950978406, 637078907, 644288433, 355918890, 172926099, 311879582, 192448676, 844657036, 483742629, 95511055, 315403806, 845994186, 602024912, 475024554, 586582370, 421069174, 257277457, 821400329, 333848329, 308859713, 586289059, 914823460, 691139023, 460280871, 51907852, 942111921, 74025715, 146404027, 977175215, 419680782, 559881501, 792566106, 370062847, 234927790, 234108671, 416333763, 111896330, 844510380, 750332063, 750585977, 902383057, 30061102, 855151115, 553632244, 129822805, 296859239, 140130842, 596488606, 115749376, 970860332, 871444885, 517448266, 180253634, 956194545, 2775959, 57077513, 461639587, 999715927, 891093350, 260179595, 723281190, 165065518, 483047395, 756348075, 223898159, 138768875, 323051424, 134080041, 803205774, 730513900, 379476529, 197420831, 544799910, 452200968, 739659114, 386486442, 226846036, 559189421, 45576202, 20238102, 489334052, 40519882, 816198963, 528499412, 321361592, 346495622, 778852757, 784219404, 650470090, 143518359, 806326807, 155676215, 234968773, 530547214, 571266229, 580868690, 174480279, 97543020, 944207176, 971202172, 721070023, 539711599, 726461901, 943589793, 91853167, 440876918, 412282535, 292541583, 319499215, 937483205, 377870188, 281653404, 827654316, 827455607, 416074320, 374025865, 77630648, 289789868, 502277848, 572281850, 589969843, 708406502, 286833350, 971999155, 831511666, 994987278, 113288679, 350367344, 32885854, 356486095, 456235912, 332629966, 882277926, 885820797, 582533718, 234399130, 957210204, 165343820, 373740289, 740805684, 429472249, 989281096, 550752711, 795570271, 398322025, 347971691, 654817019, 910570201, 829343492, 352699284, 94712971, 410145581, 437789849, 120122771, 215691437, 713675187, 640086032, 905167175, 159886684, 787774201, 986671164, 442826650, 313529928, 935452198, 357339048, 153655696, 754028817, 540602631, 2514838, 752049936, 828786379, 747808867, 232825209, 343605490, 467676304, 775558064, 644844089, 713337540, 299792089, 339959953, 381593321, 221374524, 634560445, 819420011, 600303756, 158050687, 552237828, 793798495, 562655682, 63711119, 447539903, 700451696, 764949544, 19855188, 747064665, 881562562, 744502551, 683993111, 740966443, 284853284, 20559722, 236676520, 419991817, 428737126, 357578235, 177199067, 485890282, 544555701, 670126394, 498394376, 120065002, 756425497, 708469497, 146034727, 359825475, 223185592, 604741229, 784437523, 898646443, 766222117, 360558824, 669415077, 139286677, 5854091, 278273496, 794630634, 242285340, 490563535, 780708559, 506243604, 402800353, 357233311, 752272727, 144311061, 905226078, 676902930, 438286205, 998766459, 137577371, 959421812, 520341108, 77538361, 785851267, 880793947, 416051361, 414537096, 360979397, 62537711, 893607993, 68815330, 82303014, 473083171, 187192785, 831157316, 489459565, 737475505, 576102283, 832557512, 778701590, 604058410, 822163042, 482542779, 954643378, 748014520, 219540749, 263159153, 225005102, 770672875, 582862583, 76121527, 838451342, 438350099, 952591364, 354644263, 686269562, 631307882, 523567598, 160033227, 446317502, 472189923, 52389092, 341108890, 387088222, 107064544, 919956406, 678231171, 732278264, 242450226, 99116401, 621442245, 988705298, 705774304, 306004365, 64484671, 626353193, 911470324, 954861014, 304193957, 493914702, 973184163, 52691742, 184377257, 753695743, 286063924, 98921438, 691078922, 770193005, 438637025, 147571238, 132258009, 837498352, 471197506, 280182600, 754288716, 684031592, 289561805, 836208724, 706938806, 681398260, 606004817, 316518775, 921568585, 20131990, 963639395, 646036787, 468894425, 218399064, 521397594, 270136166, 456348669, 392546155, 233990032, 200654355, 30550915, 358720470, 366334576, 992261815, 856654460, 315332477, 689547616, 668301851, 840280230, 101121727, 348688299, 654049812, 166512341, 161909636, 369735005, 742918571, 460719686, 259914507, 194621524, 20442548, 256980583, 457838881, 557678272, 806199114, 808804554, 123744928, 354071525, 9245118, 862358000, 568107061, 639148481, 704848045, 864192849, 968791558, 374767465, 617337025, 332928450, 626035131, 671385807, 549258776, 542742929, 667194889, 789662829, 64243917, 272034004, 715305772, 342236553, 392592838, 841493384, 85160227, 842193138, 272236060, 170179268, 568860268, 403532344, 126253718, 871041781, 646418147, 696825946, 729264780, 438643484, 401161961, 330648734, 248216343, 416662316, 772344082, 983104643, 600224112, 26262033, 940754733, 374574730, 423607745, 901976894, 754183149, 957989820, 714709223, 389526567, 230418658, 692990544, 33936554, 117726084, 961198902, 486116219, 345532392, 345181469, 522158705, 666401972, 129130141, 228000917, 582819334, 207772070, 40831080, 243605472, 139942988, 125492012, 866951458, 707890980, 124928423, 488732076, 219007245, 335044936, 89136257, 474512717, 614726418, 573629007, 575803376, 293950301, 432137077, 341871597, 522093018, 641178194, 30229400, 266767552, 993301563, 625441873, 398687764, 733665453, 694032642, 476514327, 716745709, 279186695, 180840299, 77279632, 601003876, 142483063, 553188950, 308036207, 77974814, 923906956, 235129000, 786896834, 245002063, 167625193, 844213806, 954205635, 390957346, 300401305, 452640564, 773895467, 319508124, 76059796, 609254899, 563636075, 518449442, 101244618, 5030548, 723372530, 890572638, 407993955, 593139027, 613646666, 375271476, 404310516, 566742538, 775485298, 247379611, 997628211, 475532494, 961082785, 226565441, 436887733, 692845193, 649384165, 192792870, 656421471, 428343444, 383983293, 115894766, 733911555, 788110991, 594101776, 513120725, 757103159, 908946939, 900578872, 814891239, 734935059, 307399459, 845061388, 865477264, 120375541, 3612176, 269969451, 107514926, 227341573, 215404524, 207954921, 515854417, 529495773, 411070814, 602342776, 397285031, 951414494, 177087835, 750617632, 870605846, 603534876, 712191517, 847714645, 920227309, 706162014, 19143713, 723352614, 789681529, 437532825, 937393329, 653646445, 927781965, 336293180, 675408717, 665777767, 401951077, 943407761, 308706419, 340540607, 119172524, 729488897, 204044956, 350778106, 51616753, 573298500, 923739197, 219101490, 958265825, 474027791, 965462029, 912109515, 610731472, 792531093, 245329698, 637337803, 905224529, 710268853, 778954451, 877212627, 73673891, 309630178, 727027707, 377002318, 514275159, 930953452, 354429089, 665780225, 474473389, 768366661, 465723800, 337187642, 618962034, 885102169, 705758996, 648298496, 551508821, 874331419, 887319277, 219650240, 831563940, 65550396, 342677442, 753563326, 108114717, 30656478, 521903632, 32440225, 482118465, 264242193, 532071401, 449650226, 993520100, 972571249, 547152578, 743753828, 819183891, 824705194, 996951482, 89691488, 887880454, 698534927, 257387597, 570888620, 847107843, 989441131, 339960724, 457319761, 291798676, 596033, 827671452, 118538120, 503585220, 42092555, 69232690, 350212695, 159510087, 578246643, 938361796, 315963189, 305577834, 963880913, 187531663, 939534391, 994937532, 131168832, 709997621, 815331809, 257650817, 139733328, 984493425, 824875361, 114105163, 486160790, 607154117, 438214575, 728251795, 62528814, 861046843, 269890831, 908858672, 949423023, 587925326, 937640634, 168007938, 503557021, 753159547, 22236522, 10651204, 23053317, 546302543, 338883996, 753816659, 719371874, 670119839, 45270824, 870077416, 491518736, 374570843, 413159810, 559978263, 40185381, 980020684, 722013638, 222221614, 474219229, 962731403, 384796180, 424543438, 816169304, 925213057, 656529931, 143789688, 661261947, 464719113, 555385331, 828268031, 977083859, 663070514, 670356002, 219650394, 667358619, 239103014, 200083163, 740631825, 874233375, 597670211, 1484368, 470611452, 403067084, 427359820, 352624631, 397640942, 228586486, 412739480, 563471874, 193407494, 982839831, 518681898, 847945340, 540746084, 845117315, 445512572, 518776491, 391158407, 342053432, 703340096, 830287137, 919414686, 323557615, 316842487, 836132975, 246597249, 967705048, 484832645, 82749633, 958039312, 137623826, 911477757, 347784415, 623974496, 570465651, 327379191, 744593653, 211473804, 581237974, 548664032, 812471324, 482309189, 840783833, 16248350, 645909933, 293266991, 32976294, 430067426, 328062331, 145082568, 835371415, 281563627, 292340086, 440262136, 125863171, 430706342, 185503452, 208435864, 634479197, 268476991, 637275472, 338734951, 648918682, 783570410, 702334342, 13113634, 25899183, 704364941, 213992624, 230892243, 99939418, 427279692, 133370458, 702801633, 348134293, 877606186, 462447511, 805679547, 623035829, 238995894, 892227645, 314721626, 703623443, 640711499, 480250151, 917002974, 97473348, 471588829, 511053842, 36717728, 921005758, 566502505, 537269731, 690541246, 813650240, 598637549, 727947695, 788521638, 779652613, 281627413, 506086324, 247243296, 642250118, 373586879, 312509244, 346081236, 467476955, 171570271, 58907716, 938801952, 955658440, 598871547, 970302329, 298498440, 380094222, 970413377, 744472015, 107236022, 410181798, 184013065, 230838727, 232921282, 405516521, 526930145, 103862347, 594510283, 484091784, 660621499, 448013730, 961104676, 945968923, 85693537, 53560914, 929088625, 586062244, 503732944, 668160603, 142996886, 992145379, 377232596, 944204001, 486782802, 755958602, 457402829, 521402869, 116459916, 226397024, 27479571, 60597503, 885284648, 875042621, 87693502, 23605098, 861159092, 949674555, 551510746, 97310154, 109352038, 49379687, 857337704, 71082396, 679820227, 861124714, 835100405, 864503279, 212460075, 836866917, 285805184, 416148180, 818446192, 854849739, 366467324, 998359603, 717443815, 644372403, 930930409, 26640279, 269671341, 605118255, 488613749, 487250206, 356980942, 797804843, 836048364, 130399922, 885670693, 217345657, 202714246, 609477078, 737505181, 602384114, 676503364, 178091877, 366362534, 288275136, 468276690, 242047543, 624206963, 459420912, 348400353, 305554844, 433300059, 78715941, 427271968, 107206094, 604849598, 112815774, 402842627, 42498263, 376807386, 342292618, 297982898, 363412922, 210797413, 575664014, 481205821, 890474588, 869079920, 34394892, 156311857, 754978699, 623397642, 40379930, 769181979, 688411592, 807314317, 324034279, 539403029, 91476546, 671868783, 812623883, 935049361, 813928883, 887391997, 234522969, 624047843, 435514372, 406074369, 234739682, 46081724, 642827639, 723308434, 134219791, 463949204, 388946446, 450384238, 816304079, 628068196, 672767074, 97630155, 348089599, 49477069, 245220806, 94285451, 846806430, 438467734, 885183875, 24926022, 249107777, 785016464, 866550018, 808849120, 399117631, 361096191, 122160005, 308833481, 866244083, 537790715, 79237790, 669519194, 263107693, 246671815, 851682144, 468981153, 532991332, 903237514, 857147714, 650947830, 234535758, 850604938, 626972021, 733955658, 776198589, 488722482, 899266815, 862556396, 197849390, 621382237, 7034278, 527629037, 756910351, 316250734, 596905342, 813731254, 178143362, 304860711, 741184828, 470202952, 639780063, 757642270, 829060565, 588919026, 937979144, 118461618, 744550304, 698879385, 204952325, 670003054, 145286786, 490239552, 175228796, 604486508, 897078102, 656752795, 419648575, 643226939, 993793604, 793420767, 646294710, 976388177, 793695088, 5781587, 493671444, 438285451, 668627941, 126066307, 457433526, 603542657, 398663381, 254823738, 660262543, 841341906, 500634212, 424636793, 629949565, 300565265, 576676570, 931045658, 562317392, 850036750, 48935291, 651860158, 204353609, 218291327, 663976068, 101882759, 859800284, 591816, 811205101, 908843949, 444152345, 524202218, 361020968, 503088289, 663874138, 267094829, 798983632, 509836933, 282698247, 930617413, 648915981, 475270669, 520591647, 673416276, 739498815, 195005276, 701563091, 637438198, 980250945, 794584185, 906138439, 627361732, 961321807, 319960863, 615972390, 56631957, 724546250, 56996258, 897266740, 656402463, 941922612, 707695890, 946141029, 248207857, 214303966, 389562304, 722309623, 154582553, 140078919, 727328510, 605535990, 569054277, 891722252, 139520973, 271321810, 44920053, 371505823, 411670339, 173894629, 64024164, 891858314, 345602356, 346271882, 252890469, 116309681, 574794099, 294565966, 798784647, 876908811, 415797955, 469529982, 690119265, 187635958, 436721263, 345517082, 725365053, 31064838, 440761468, 228738496, 186374411, 895424367, 562823851, 752818177, 587081802, 794404197, 715745852, 74124747, 223633224, 369257882, 450582956, 61397950, 491676108, 246513455, 755212843, 572023640, 919563196, 854236375, 820351996, 937857280, 454920848, 38225285, 683859296, 294166941, 242452426, 985745101, 32091656, 869000403, 742209562, 224686534, 169255819, 64879969, 358218260, 953493444, 533221169, 214192945, 463408622, 891878624, 366863857, 529783740, 680758772, 946978853, 645037780, 422593746, 101261905, 647493476, 22906291, 346888326, 900135987, 120548267, 974158497, 613782454, 807840033, 304093802, 134562430, 52017369, 64850583, 435927445, 437467008, 286369396, 249154058, 296531436, 870582039, 400289881, 339651603, 811385503, 598940194, 331938209, 51526303, 741279605, 694800656, 86903949, 91193347, 993744568, 738551405, 807066062, 871896921, 662390841, 243555192, 310651567, 242266081, 759550174, 322920204, 168316629, 800922897, 440085941, 241349006, 947449962, 929574448, 5323195, 308860048, 251084237, 860537455, 558300586, 943776631, 902378541, 26763099, 697670072, 187000724, 630846296, 466182543, 843734093, 659456140, 826264315, 717647252, 739293072, 560100104, 985470399, 403946656, 859146130, 68054051, 263865615, 74582953, 354137901, 517236520, 327424998, 945364442, 110137059, 92194004, 228343488, 546194304, 912394778, 802097415, 195787222, 829225668, 748290559, 162578242, 137177259, 595018425, 65056280, 782115002, 837492137, 457990504, 280709650, 74466362, 224420145, 356579631, 79190831, 339475395, 789339923, 655206125, 843023266, 782321601, 963587644, 643370345, 851871898, 169633318, 100864648, 528885836, 874820137, 412724038, 363856929, 50660189, 358991146, 661377802, 931117886, 227678433, 215809941, 878153700, 528025056, 662243473, 843761203, 956546985, 293170864, 652452691, 858510280, 631646032, 85428297, 819077851, 246189723, 7399100, 301169646, 518891807, 579148651, 181826973, 704616673, 161986951, 614531094, 955626874, 386952583, 28756591, 938656297, 109232663, 762010860, 777258952, 568479434, 293352689, 126331296, 627240348, 755740168, 396738574, 538697445, 792519931, 231837982, 678633212, 102364019, 350017594, 460564258, 632737815, 777150321, 970033296, 981459719, 355436486, 229556338, 179058431, 169150097, 942097221, 457132930, 840406638, 97135077, 368564290, 748400437, 779312108, 960168231, 679452515, 54732069, 112070900, 551315545, 254136123, 510321012, 229884954, 157466021, 715793553, 873168015, 338307635, 691665811, 690358311, 250215744, 854659325, 113278304, 454892905, 29819904, 413855161, 592934874, 761078463, 26054544, 464284560, 141927296, 856068422, 609265978, 674807107, 609158451, 458503642, 626331565, 551394505, 303181848, 993810235, 488365636, 798466426, 610710413, 722720227, 317816086, 89685172, 526351115, 845067599, 47500690, 585602167, 894000689, 162647202, 474734667, 255373891, 798135133, 530977658, 618108944, 777701102, 993378048, 432532924, 486946861, 447583692, 421239440, 69170860, 313650676, 380535510, 406687244, 955759417, 246873510, 85163118, 28576760, 955717831, 973848943, 670216061, 449988200, 862801841, 445269791, 28216248, 459545967, 178320433, 778994280, 490380617, 603770653, 479828493, 691756906, 226977351, 604345796, 787027050, 460241954, 139990842, 891460525, 986679411, 905026035, 49712044, 789074218, 721360247, 65191073, 562064852, 716859120, 927675625, 210105212, 751606927, 192292876, 996017138, 649760464, 832146686, 358917416, 186632962, 864386921, 693144375, 613199413, 151741253, 803201680, 544672686, 860562075, 232128814, 867952358, 682617623, 452745490, 657702170, 538867257, 720218412, 947259542, 346892018, 987123185, 593885560, 842226805, 354115378, 525275879, 969876543, 205659993, 801463358, 164320711, 824449795, 245476189, 819407763, 251325179, 863273881, 563510550, 224766460, 490900494, 986882027, 786342472, 182121582, 340762571, 476472005, 713067963, 790337447, 90762366, 453105092, 205339823, 97703974, 512240215, 39442589, 733014501, 774066814, 139388337, 611329443, 539098574, 370965160, 883111109, 597504449, 3305163, 369909351, 906030966, 91327695, 852205140, 147625689, 538980068, 313808084, 648834032, 883719967, 677834186, 432377149, 188369690, 497541999, 563668136, 363079630, 880668266, 351630582, 829503636, 245076465, 832075154, 248658761, 284921819, 770268928, 383481902, 764766391, 427674804, 494865755, 174408634, 559033572, 947258820, 930354262, 182845367, 153344280, 477626388, 184999521, 824239136, 912446567, 883001973, 281593493, 198081708, 866616580, 216676271, 96522062, 684498859, 836900505, 974373653, 677077526, 218131253, 66700175, 296005816, 598932162, 813368390, 28219993, 662654629, 731882051, 644840001, 424549633, 654104559, 297555756, 749951480, 761431597, 838442576, 196985464, 720593595, 291054815, 9676449, 588009682, 207791689, 845634523, 108310544, 500241535, 677930179, 503212245, 755390518, 568136437, 493894394, 882605815, 403560195, 902374046, 889589332, 8003335, 222899256, 244355075, 559442517, 809729961, 178123535, 176884786, 195684593, 64395106, 685945223, 927724544, 515740489, 719551819, 70141848, 289880842, 423914124, 619790041, 504515033, 725552279, 414482609, 589003412, 924384031, 373214261, 962051628, 278654527, 801951534, 47184616, 887997779, 406866268, 381729653, 281444120, 481771167, 519944430, 466605640, 575964906, 665684128, 73432209, 276183495, 316439845, 141823714, 582050554, 475908057, 128285741, 780141569, 116810226, 925257559, 762693730, 141237113, 111092582, 788897421, 747985955, 533889598, 725168149, 165302189, 645598891, 92403604, 616680513, 932991418, 310519903, 637471029, 344279085, 677953636, 488660278, 98493435, 268542024, 916396950, 936350208, 58589824, 56004178, 819335475, 496990783, 234713856, 477040223, 797063959, 552069408, 291066000, 208059024, 680809150, 895850533, 38752004, 497653473, 407981310, 868868429, 949651329, 941703103, 863580618, 750988764, 908065942, 112889221, 565819309, 267946881, 796050728, 529775849, 471764235, 703137357, 789665895, 307759388, 127383016, 636513530, 694586885, 273496412, 244805842, 954186479, 543113226, 343001531, 171989887, 749639299, 681972353, 824015482, 527734940, 442026117, 278456576, 9572137, 540201522, 614404400, 594180340, 31426104, 210576469, 459297922, 14216729, 274536547, 484465597, 356759967, 610847209, 967389735, 315249434, 592516718, 276315745, 235410307, 369944681, 754988674, 223766541, 902680673, 418617767, 20003469, 925687561, 415482919, 819219529, 823587167, 12997758, 446737634, 722452881, 274401011, 732288266, 57667793, 768532431, 808790830, 999086416, 961712137, 489433053, 56665404, 221305979, 498285696, 612361240, 503702881, 229561271, 607046554, 326826716, 269853933, 547986116, 909369544, 357894107, 630438547, 930737522, 497748431, 323670112, 826844235, 723987390, 196431410, 792628023, 307365627, 278940374, 757384303, 671978819, 838359527, 536092968, 765887901, 145364276, 219438581, 97248482, 955588291, 724668241, 984338358, 212123481, 62682971, 706111405, 242737493, 383296851, 580519606, 368547562, 650792707, 93510382, 201443826, 316794838, 338664699, 21546567, 534709368, 368310795, 695780744, 340993049, 315201806, 52193914, 8347198, 990497673, 979514979, 722481094, 765191724, 391321859, 715827623, 622856639, 75192984, 159246644, 89083523, 561307140, 962064166, 632251255, 570516417, 382613516, 738934870, 683156939, 928012691, 896510021, 231269208, 605986708, 629899313, 49403443, 770897449, 665868716, 434750378, 638243543, 226612633, 793852167, 269907543, 188205862, 448645790, 285902416, 688789825, 701964516, 945428120, 355143461, 135456934, 986503770, 144854396, 517600999, 639411260, 990787321, 340009534, 960366986, 341054833, 111283593, 361900238, 138976175, 700605552, 241115721, 445021183, 943364927, 222024350, 296693700, 711675593, 87867175, 684238024, 326303357, 988071256, 192988306, 590172767, 575970443, 468686688, 267869755, 691362673, 674694706, 81620283, 219928009, 971501026, 40217459, 275128415, 9270797, 721737418, 940034963, 983907741, 679709395, 449712505, 632556383, 966391033, 519585862, 636170439, 783473588, 980844837, 732821565, 313077139, 710431897, 856627001, 906354028, 156839531, 305542883, 685806509, 724881187, 429741818, 14651192, 308610693, 754489694, 224787912, 581402462, 164052920, 895457641, 264153482, 626133751, 413643933, 743985216, 538066362, 361436188, 687791147, 543470441, 532601553, 827117384, 166819983, 11012858, 216147474, 17062921, 294905976, 658109697, 767972653, 678338479, 301372892, 580665087, 544270654, 401808234, 997233467, 459856807, 158266978, 675013934, 932322104, 548428672, 773948465, 894894882, 708531586, 31040345, 642608298, 34995373, 390067449, 63053419, 197616018, 331926630, 488042564, 776058523, 80621631, 341641762, 494186001, 857183010, 952343014, 611165752, 2245705, 359940898, 478810360, 79695835, 154420178, 568720163, 677157222, 38186918, 818490078, 939863454, 830255721, 527036550, 959579248, 587023419, 760762650, 753786195, 699568742, 578949913, 430732252, 669536584, 38774149, 857078894, 435973253, 929492522, 964042399, 781556235, 12141830, 237655646, 558402416, 251559634, 804335515, 249815776, 921601958, 273258097, 768003783, 17902772, 745436793, 53947366, 58511241, 105285184, 763315224, 416704268, 635256712, 518272459, 435761626, 522729645, 950032642, 547871406, 596306830, 427059028, 423281887, 293055997, 594124927, 885722869, 310621687, 962039575, 14934386, 993806932, 745788486, 796112228, 522184082, 396085926, 657189969, 800265182, 679857689, 540473584, 144232148, 205515528, 514381106, 88845681, 36971793, 726714504, 548064493, 943151987, 103382502, 258054878, 880373590, 223481990, 302551120, 918594265, 590460238, 400565763, 328989470, 655445081, 374563406, 33506136, 715202754, 17409568, 586273272, 628533328, 975529394, 174377640, 295514237, 938848860, 483188112, 114585872, 855272170, 800556477, 336795829, 733210022, 703976324, 537645182, 248330469, 901388093, 525102670, 864506262, 221576389, 927037192, 887514886, 97394412, 647689541, 67622768, 236530759, 833873787, 485241875, 563970420, 971706942, 963706445, 825134603, 6487151, 345206613, 864988302, 357295516, 48957279, 716437776, 316030925, 244182015, 692521764, 25289219, 704178683, 581544219, 358801486, 107814293, 743309851, 899474619, 160053376, 663143061, 888784802, 639881130, 923248083, 910890751, 367285318, 858846392, 896514850, 167708596, 618930404, 81001012, 686649980, 308989278, 447752909, 130596905, 894515534, 827482046, 28143031, 960798481, 220786320, 77361393, 991851681, 766215053, 215309010, 935045570, 671039253, 199975213, 60094121, 5202475, 843955545, 817757831, 650747551, 200787934, 313036089, 527148970, 929632140, 244574773, 40075231, 300307875, 241730303, 57128942, 185777397, 677799056, 192687659, 676023050, 149103328, 412733230, 222263995, 362437625, 922661089, 262747865, 170505482, 209663656, 422107067, 82091282, 541461963, 87157711, 67145244, 100006766, 483113324, 176097806, 904205330, 215712549, 256411401, 612010679, 688649214, 50272754, 664552874, 300678321, 146885681, 182515796, 338623032, 837662249, 274802416, 615580814, 546174286, 368208150, 652014594, 911774961, 992061850, 552988649, 88926644, 591000403, 724029540, 16704043, 114396556, 275222342, 88994804, 165512660, 147423646, 995888289, 570391300, 956228978, 114221063, 958145755, 962209245, 229457347, 208920063, 541287374, 947179785, 67203556, 149211202, 455327550, 406737057, 169041079, 277050285, 302673321, 174017503, 475465990, 865458525, 996149427, 242661858, 165944179, 504598716, 567824141, 883628029, 149158677, 534813460, 818347156, 400940976, 312182675, 173019178, 545384899, 9224880, 905495390, 261798435, 447147218, 451571358, 220796466, 485323877, 220008892, 836968487, 229131951, 760982603, 688938009, 293966313, 654902668, 34122064, 925075858, 967915095, 440496053, 781692308, 549520879, 318430537, 584278282, 847392696, 751899421, 473052483, 899388517, 478709601, 792442365, 593195546, 708534082, 886139784, 840577637, 816497590, 147143600, 262692628, 994511371, 464778833, 178118223, 422901639, 927161548, 836135821, 966275653, 314796385, 306026870, 747719799, 922179296, 144223893, 666111451, 384242853, 360818651, 778724052, 530334292, 969481117, 790452385, 944270936, 589568393, 923188650, 683682809, 720753069, 682249013, 30771092, 457813718, 789097827, 281425942, 95990936, 925212479, 415953530, 548112893, 135546443, 112789492, 98195008, 37189837, 859991580, 27323398, 991279720, 619366071, 686428835, 161543295, 848746634, 109799239, 564290994, 434958568, 673957661, 147940686, 521618059, 523280520, 590107280, 547916468, 904150562, 760278586, 139278273, 837097593, 436693413, 424552236, 628026840, 779618699, 846691869, 155705034, 253108518, 508611607, 429599854, 725709084, 978814595, 275169315, 965100587, 63443538, 114845902, 70429004, 731277397, 972899922, 77305442, 315882403, 669980441, 169162340, 505655336, 180540590, 278282944, 23617119, 755985404, 525050353, 531147915, 572154687, 660609195, 735755339, 801654521, 327828884, 242180128, 86806620, 626127995, 523254222, 6948488, 133956621, 289740615, 210787116, 387291434, 338350654, 210626770, 799297548, 391190137, 465492304, 748534739, 855918380, 644042829, 846445832, 998033968, 674617921, 530871375, 45803227, 974368804, 746634768, 98796195, 913574130, 299391385, 91442420, 380821420, 837939611, 38345865, 459232153, 234931589, 436824902, 205210644, 970002574, 988869171, 586026618, 235950015, 656406134, 585639525, 813193605, 321766155, 154072081, 694559189, 432372889, 754773627, 568664176, 976576801, 435350104, 442670860, 710672980, 65083290, 276891950, 350726329, 754446406, 122431415, 746737756, 484894889, 661213230, 757242805, 54270114, 983692691, 507507733, 541483342, 922930795, 877736125, 177734746, 340712113, 667434963, 36961831, 908166909, 779211597, 752637999, 306360040, 698487030, 317815227, 387528105, 884790793, 384831930, 535568963, 171774297, 18771762, 942802976, 414454284, 345440352, 763653490, 931816687, 516873092, 337346784, 291516284, 616006297, 726411519, 402123876, 415004358, 906034889, 699880751, 521233254, 574672021, 464573950, 613764248, 214676748, 129486560, 555665206, 789660807, 195914734, 499670964, 201175162, 157042394, 531207787, 564862942, 11268018, 827466919, 550443056, 954249790, 714754499, 590077878, 483474109, 615509255, 11792310, 759270292, 365405336, 652646063, 249099992, 253570584, 350607699, 326411856, 388932430, 316800413, 180499720, 735950644, 737823283, 972834709, 262737053, 76093206, 429650940, 724851739, 601724383, 577360833, 608494146, 319771678, 826404508, 529814956, 87694424, 767102729, 802985900, 555158031, 229767453, 764770361, 494351555, 205717898, 557042255, 579392130, 782508984, 988391910, 329534953, 516990530, 288512855, 289346345, 461044016, 143874971, 129135328, 940362536, 502568837, 119250575, 393109800, 200586193, 501820044, 95642026, 723024706, 332508898, 297305236, 73329783, 296472603, 231222139, 553468618, 168008673, 791677407, 245052909, 685085353, 137962744, 174862794, 842433735, 518477579, 121882621, 814651822, 487157052, 343978654, 324296246, 895713261, 292166885, 818929917, 15392186, 387901582, 927820639, 320270945, 961968735, 332262666, 210413126, 755219771, 952777514, 661364842, 221339388, 116131099, 825200751, 461014356, 108545759, 452651148, 396421123, 598114542, 340292426, 461870243, 30115866, 973102466, 891088832, 121017305, 616314904, 685453892, 292782398, 516635774, 762772982, 197356971, 435993982, 558075767, 251554811, 518304943, 807574862, 315926666, 419148023, 56638239, 400888467, 303065614, 216875420, 578395791, 334695224, 200622388, 506055781, 378276336, 338527666, 751746414, 953693382, 50442021, 783449625, 91519529, 120159651, 948833530, 138805985, 560365815, 147137791, 557268629, 969075246, 399472897, 698585162, 72380525, 727806493, 468773033, 538263980, 401268931, 676975959, 627527307, 534136573, 581942703, 105272615, 680728636, 490194050, 829042686, 986167597, 900352077, 490854803, 21427093, 785236114, 862332675, 973111893, 363297909, 102921489, 925554737, 146894779, 636127327, 880627151, 39677636, 239314679, 617533707, 864469843, 152760467, 771307264, 976653029, 989567834, 480785201, 846512766, 298834677, 135581750, 269940300, 179751231, 199192251, 176113710, 799889857, 10205414, 248380587, 427252927, 515924011, 509526697, 414756949, 185807696, 46816770, 897155060, 600180749, 512029450, 984931336, 717798089, 844621320, 3729352, 669356841, 484980858, 852540792, 249342168, 131540413, 383234298, 928901972, 421664459, 706193820, 253144005, 724904949, 2470335, 175881926, 166153887, 571433582, 897585336, 131140698, 860014683, 75802717, 716218866, 913693739, 765691888, 675819008, 242624914, 662827555, 516836242, 584629395, 829454359, 110877440, 354847394, 214227522, 558910038, 122259865, 881045079, 409917678, 793243773, 746706553, 881768757, 527878761, 565254329, 973258705, 940720397, 771768591, 966079743, 338453751, 205812495, 106441693, 83906275, 664773392, 325734215, 516486941, 917871244, 974804636, 440312853, 681732882, 517534532, 994526645, 688264595, 288921441, 837430214, 952961339, 432702526, 263516946, 203451117, 558314353, 407355188, 314628664, 418251119, 612319042, 142589390, 971534407, 614227685, 509962983, 112787127, 740128616, 18772880, 827706293, 43270452, 928463852, 442356724, 617832332, 80396156, 450959321, 468670731, 100847341, 580716694, 534497762, 489201957, 811029923, 259965098, 114783693, 191711118, 162058046, 409487770, 112326520, 966275292, 583657509, 745574827, 188761357, 163625196, 942410327, 844380357, 168740643, 314349926, 803623121, 98147542, 506272771, 305274167, 812580626, 111057808, 210840797, 426769427, 779187203, 595882698, 96940134, 441552709, 820512937, 784276631, 359000736, 169700445, 713063980, 327090460, 275795862, 259371625, 693408577, 684684810, 944612559, 94488248, 422608655, 328434642, 346129175, 59044065, 495775485, 136933292, 947963095, 41471825, 39687754, 557416847, 503917925, 167524413, 208321276, 479750822, 637255141, 223618468, 445960481, 370343274, 74302742, 923908288, 301824736, 683237747, 281584010, 883050540, 249732426, 760259995, 51255222, 419267742, 424113566, 412485308, 147281553, 996660814, 446644016, 489612849, 972527088, 643852593, 57024262, 942163239, 917836600, 422389790, 938471487, 533952839, 958643328, 14080045, 337167893, 627351775, 378064821, 704352606, 413765281, 530056280, 486220227, 264954138, 613960236, 740156266, 304279860, 294377737, 744421986, 387825769, 641627080, 859720240, 412817715, 421695887, 929267954, 419944713, 216961618, 83431237, 277668251, 704784154, 974085111, 187794981, 415783156, 954918584, 483300380, 847147343, 994169495, 976188468, 57263674, 324418480, 736314117, 240065489, 73168940, 592041471, 994987114, 164891536, 272411480, 800843233, 273807303, 377272076, 932112236, 632044734, 753850039, 62237876, 115477546, 911292529, 322794881, 296074749, 637001579, 682240518, 313087990, 816586817, 111239803, 528811232, 682189388, 818819407, 639902002, 904204823, 712288597, 388559764, 374803375, 729617209, 68603334, 504559616, 117257740, 745833658, 622175099, 981006399, 879865197, 916584897, 317426954, 446457822, 882858245, 725981868, 906019363, 302817183, 737049275, 755618774, 862210821, 289355423, 360593144, 402550564, 572452183, 891906993, 436190241, 265883991, 554917256, 536071083, 360584781, 552464786, 135442062, 339688433, 76330665, 672441393, 827641549, 224972222, 874313007, 544521914, 764805401, 477533022, 510501654, 990805095, 493150205, 574119591, 580060383, 876939672, 191907862, 330986057, 447164679, 708562467, 5867998, 876175777, 842394329, 23778797, 38965967, 673651693, 133350210, 394403515, 338023742, 463452527, 912520849, 57288537, 792966973, 879253690, 241541104, 17978743, 758488272, 50940689, 998540673, 79563660, 980251567, 189669858, 136765887, 404523600, 187149802, 871963681, 736498073, 968761468, 398436206, 888908558, 67157973, 342437300, 539156478, 32654563, 693747589, 677507921, 672424264, 551267378, 785364283, 905085600, 819846452, 496640037, 634926401, 934579317, 294223211, 637447639, 349799009, 493009157, 620381823, 843702858, 154300685, 360647417, 713908882, 379557681, 191254729, 87731133, 800747842, 6679968, 775788996, 653619376, 446495327, 816454065, 60656920, 183973964, 7979391, 287510211, 453085689, 73239066, 790385026, 548619047, 272295444, 480760654, 925328055, 719922610, 79363586, 854884227, 112043070, 161511194, 689449102, 547111505, 710627490, 903073517, 417910051, 648464345, 916653865, 446377476, 788719316, 829756811, 565198891, 466755622, 133785597, 979639873, 473356179, 721423630, 464018007, 539512083, 478922611, 999086288, 362486041, 387926611, 918153149, 5796605, 770405623, 778017526, 710115511, 172489996, 101481006, 928216127, 145665323, 151428851, 498014400, 292796516, 910539273, 560983109, 92083139, 509612890, 294889383, 454386593, 975263925, 228918134, 488110867, 181153525, 589454861, 859674573, 689975309, 219901187, 246210078, 220956838, 422191610, 376215468, 983086002, 546756317, 337204464, 925348255, 125902420, 730963415, 739264873, 808628812, 241144289, 669911318, 220558669, 867171476, 282963732, 595423117, 412934711, 557972266, 750035510, 446489633, 180737096, 278608958, 936633088, 896631444, 994675644, 814675754, 659351733, 235452016, 19807004, 655042108, 89415898, 69482895, 94932846, 954432673, 971634982, 214518331, 153413027, 58990090, 722495667, 875093796, 291611848, 209379077, 573543327, 988649853, 85832924, 288155134, 371238154, 334347038, 513485730, 585866472, 740090810, 145079062, 37680893, 618507666, 664183848, 996922460, 421311990, 713206292, 494095549, 34813323, 331676553, 931643249, 465556516, 708914047, 519419163, 287842720, 211173769, 259067916, 132877127, 585262456, 752409026, 493219706, 322996708, 220518718, 867437002, 450655943, 920603487, 313252537, 664692356, 577949099, 510949719, 732149750, 586404003, 885549563, 805190041, 854758915, 198719596, 547105574, 703347336, 401170552, 440614593, 160466627, 302180908, 525666474, 454269440, 822368614, 818826410, 654146592, 879368079, 232068938, 789009774, 757428572, 383872702, 210784510, 7689338, 537457366, 211754263, 715521892, 863108703, 231020805, 724609905, 930908802, 209166437, 835439151, 252523755, 692320919, 668660948, 763298537, 382875241, 359131055, 132577074, 742511275, 977615564, 734378841, 961798979, 893731998, 650435335, 653982578, 601938987, 425795122, 622412986, 197799891, 109872317, 147260283, 137974028, 616083601, 966076840, 924968810, 489102080, 41476709, 304632332, 371339029, 704204067, 238427715, 894033538, 535781796, 358122300, 664604136, 420270943, 718105792, 542642381, 989061537, 931635000, 704305295, 254754972, 727462653, 399655772, 923468438, 912291934, 4837188, 598718874, 977371910, 794625414, 882796444, 935669723, 956186125, 445197975, 319564913, 53014871, 336147888, 82899160, 443025626, 145070160, 121625871, 752663034, 433878326, 850033776, 438118958, 393941345, 919077109, 170726635, 597838429, 195390294, 352708189, 243162229, 216137516, 928467986, 399778286, 985502215, 151768436, 76874843, 315243881, 98935874, 621762811, 788879379, 823071509, 722078757, 638345391, 919638074, 660080629, 429510257, 874802241, 952054898, 744757811, 478567515, 336693762, 865187728, 30892163, 28296680, 171587997, 806380829, 696596727, 312595089, 459379398, 181187228, 287295388, 967926675, 335436848, 649930909, 519357711, 909482108, 83192698, 116224576, 535808027, 950717401, 547463169, 453275940, 744429790, 127311099, 34436549, 470487945, 650274705, 410614524, 467894956, 156062398, 391042837, 429366900, 231744524, 928960957, 7343520, 102383896, 278139523, 599651470, 439808007, 287849498, 589876587, 568068103, 805637681, 647405401, 948123766, 778967337, 222065126, 631915057, 853820273, 244516420, 759227120, 436507434, 470079161, 957118251, 4969016, 203540759, 354948578, 154594953, 31240383, 599794564, 872387051, 201084659, 422488080, 669085823, 551832901, 574425977, 890804388, 3865283, 587721859, 323288065, 345292123, 578383754, 902109424, 161167445, 842993588, 707740724, 476813120, 160164290, 763349998, 318739490, 24415413, 37551724, 395156300, 445441071, 804240749, 128008055, 761971917, 837579877, 744284295, 414017794, 771998141, 333223885, 536964819, 127844363, 136030955, 919615813, 805369368, 299438687, 555261413, 40543557, 806897994, 74892635, 142952642, 732285927, 747446124, 663669922, 225515098, 483744404, 607584744, 907216120, 767748755, 761556784, 327402779, 373288411, 510480324, 523684137, 892442821, 447792523, 972450457, 387426214, 384872016, 49072949, 960161553, 221522087, 921368455, 420223083, 419547812, 132629761, 570356495, 941252043, 983793922, 188749296, 953425507, 82655024, 878246505, 827293796, 950132654, 517138225, 223696620, 276363296, 283331543, 114380739, 101976535, 617323062, 279302442, 128826150, 408295462, 744496361, 166518911, 146737545, 854089873, 714521583, 926103323, 916080450, 939092404, 49206912, 935057892, 62528438, 205727104, 682887122, 552566059, 626060198, 604783708, 625185823, 287986312, 805007756, 141162542, 548735759, 827704115, 699650290, 170610030, 248857435, 267013517, 889102462, 707601588, 914266269, 980823702, 130951313, 111906349, 627585066, 516436118, 636762082, 92570234, 831493952, 16320237, 693284520, 968382462, 829440516, 406914538, 674928452, 236419604, 411624668, 856067016, 355414845, 752128447, 115802067, 719318848, 793716560, 869153427, 392243595, 948794190, 838057440, 252822175, 403116661, 902306756, 269094062, 198727838, 469643896, 948231971, 687167174, 619923260, 609081099, 76766684, 910269319, 885483434, 216806070, 313773328, 503146559, 816640854, 532861552, 930576567, 639358035, 396223791, 267068972, 706952880, 851754985, 789418783, 269341317, 140205575, 486757349, 793701151, 554721989, 438984014, 10216447, 446281372, 123723157, 902726085, 54530290, 211842476, 649803711, 66952214, 82673162, 306612372, 575320441, 276207684, 972085496, 736352481, 983156525, 787557981, 92777639, 961042687, 466038396, 784275035, 45975625, 949943914, 736365705, 463439409, 274845089, 89040899, 209059525, 438595770, 865888691, 586520579, 376925184, 575591468, 455484309, 744455137, 704761852, 825389732, 535422579, 199048910, 572893829, 413753698, 869667852, 6116559, 5471987, 104993154, 817479977, 457939504, 44606502, 548203710, 326763132, 99956212, 328614944, 651534940, 383073882, 368104356, 267618701, 738611137, 440975094, 142266846, 903658721, 130530158, 174299333, 520826157, 180468711, 178559585, 2658353, 41876510, 231876734, 521721897, 934165898, 513444081, 541968843, 693242100, 169745371, 102179066, 696521851, 313524355, 41935742, 701631385, 998493689, 352808208, 495950746, 704094963, 277829039, 939571470, 44908328, 578894831, 864041550, 24577032, 839088236, 772732284, 810745653, 155204776, 94024895, 761002682, 108939684, 688428306, 843184541, 290261237, 521985465, 270765198, 526918778, 69000944, 199543037, 706077419, 625263676, 469300454, 445007898, 869723906, 721388137, 855733771, 182273224, 24959699, 110938295, 964341287, 291942249, 973012277, 703632592, 717074987, 723823368, 462331888, 416383120, 748328492, 231404804, 873065933, 762664077, 967832170, 684994925, 312309101, 697862468, 319286164, 381519193, 718860804, 867211267, 654616150, 240392195, 873319705, 282768888, 808228735, 70649491, 998024280, 867161665, 674845870, 927454450, 385786343, 688639249, 575851579, 351030728, 4541559, 853626301, 255866949, 873812358, 479824210, 119674213, 603608551, 813697155, 184202798, 841964211, 292946858, 892894898, 16630489, 97694495, 691802712, 703004929, 258894087, 259434130, 765605861, 20384841, 968128064, 950575998, 864960071, 685882688, 412515519, 575944122, 290787059, 603053402, 515397910, 294360210, 717472973, 744023760, 21328014, 518353485, 394489272, 486063204, 837938254, 279010296, 93601160, 916583949, 438057099, 819891218, 793885918, 965811028, 883976095, 824676291, 609232672, 321167760, 548704125, 114017712, 664713229, 536511972, 414640831, 687228408, 750525755, 357701738, 969152496, 153780993, 88541667, 444815672, 765673963, 939023335, 763417656, 110966023, 354813427, 190389293, 986019514, 929179154, 79999466, 661672179, 273803925, 771575219, 999312286, 143131380, 621394090, 8721820, 419282, 797443538, 258501808, 335155507, 473145532, 482035287, 857215503, 160884593, 84297795, 96820923, 769020190, 456828493, 991451233, 225040743, 641287382, 862381893, 586842533, 687794214, 467356128, 357626687, 46129381, 432820217, 706521247, 447981255, 755852464, 373789663, 68003615, 230818633, 132215434, 408850494, 658477319, 721918948, 439027260, 857162340, 829222412, 43984961, 947313774, 26095678, 74533177, 368435244, 114907413, 716937977, 537420411, 958388668, 895296976, 84585302, 173594648, 745559863, 485763706, 578557224, 116625107, 610212449, 377268246, 593868473, 926383220, 246295691, 664953436, 389973466, 924842891, 638962273, 752814359, 292950629, 554982465, 472961028, 576480498, 87205770, 495897641, 391399712, 851646550, 575588055, 284659830, 159783396, 385693394, 847824955, 577624575, 423612143, 603348283, 37589497, 903680334, 922627927, 510825292, 633295969, 391563062, 651250869, 38764002, 661795106, 20165100, 778347469, 743349472, 45013276, 43687258, 805512459, 190412119, 285015394, 877464651, 822631185, 375981099, 872840089, 625355642, 834037895, 65197892, 517742638, 648806392, 285607607, 877371812, 619138354, 55800908, 553676044, 123268867, 377122068, 267186264, 457056790, 490931720, 114342983, 548934967, 382293428, 357385602, 418642561, 294334465, 52382937, 545096069, 939559089, 131801799, 545263959, 967928731, 242648829, 988574000, 342525326, 899465240, 73788900, 475164809, 153140503, 470260407, 254916926, 481869861, 895488935, 368571712, 577874643, 380940592, 20714136, 701025722, 934208817, 774701128, 73236847, 550052685, 303155156, 833128467, 644693452, 882015078, 782358043, 383046758, 287645738, 375961104, 193334393, 482703696, 367537654, 329956311, 886069908, 859653872, 25376100, 609248633, 266728884, 242759605, 131944644, 866201903, 319677310, 200419109, 787326760, 665368684, 32030909, 851699052, 357247872, 358299794, 738185910, 61596753, 568750693, 976680416, 460004871, 52278127, 594540343, 471077956, 917484792, 656794791, 452982181, 608421482, 201117580, 593370811, 830030532, 213890442, 11038564, 70049494, 628435993, 288335030, 965648242, 66049339, 853546938, 544455150, 621470114, 594966254, 605694029, 301483573, 423856933, 977275204, 289503991, 939200364, 445398810, 467705638, 624954250, 142769905, 555110697, 156373414, 54921517, 51335726, 537557994, 428021805, 919303551, 552639454, 778509703, 957910986, 296120480, 678796680, 905195905, 246769649, 916581238, 562813787, 844956446, 378230451, 411175856, 754488821, 832944167, 562526745, 525036470, 508966918, 849222570, 1849915, 727739668, 111811816, 28071383, 584053824, 366320441, 485231763, 801944594, 233727157, 585784340, 887222707, 465416160, 935598209, 723830137, 350379637, 150730361, 292709502, 957855975, 941277306, 917592704, 210991074, 597241125, 462678825, 965996337, 928080730, 533204851, 959224266, 441371604, 468984537, 120118022, 853822102, 497172923, 948596797, 823889230, 82335562, 395561897, 587940807, 557040343, 204796612, 43080445, 970057181, 497203694, 546220290, 787554702, 205860605, 560354507, 233573026, 348607864, 494599455, 862283527, 457315610, 940192814, 453563983, 5955140, 117159945, 821436242, 428874709, 810121690, 418714756, 111816822, 555391144, 611576602, 50705912, 322921652, 765090770, 710243852, 241625646, 530425577, 409012421, 887369519, 237742344, 778361253, 261239614, 904903317, 469558265, 190142295, 570420890, 421737521, 582564457, 783704429, 265401805, 567625601, 804971513, 663905970, 63939601, 998550634, 159065808, 912820587, 599667257, 92607556, 693401359, 375372419, 388985680, 343265018, 663024233, 359962433, 11208765, 617394486, 235892306, 2946842, 271960604, 648949176, 183167482, 827600027, 123521004, 524179556, 503920775, 506296889, 689937029, 766177020, 49586554, 927588688, 545745762, 754227928, 625903839, 122645065, 68581404, 873602522, 720733565, 774677183, 628299069, 541825200, 454109368, 448517666, 47646513, 362367061, 241623806, 634859318, 942772543, 714891201, 114332709, 678042325, 31571639, 759639963, 303807567, 868970888, 451386165, 941801446, 770282800, 37029400, 251734414, 974605129, 593438681, 201679725, 716030402, 922362832, 209733415, 886345803, 127763562, 1325821, 222191989, 974738292, 929400630, 242610889, 419453919, 412533186, 387259638, 246864141, 904151348, 50956967, 894319078, 588566538, 765423726, 626424779, 521949701, 852564629, 78753942, 242583367, 348192635, 258326401, 316727138, 278360379, 539409923, 5715504, 81963193, 433276008, 928552064, 228194293, 168482624, 894360473, 450082222, 974439339, 762626879, 825574204, 932210211, 601245711, 534922155, 519123137, 732901178, 78688160, 915473269, 652185631, 807596025, 276711682, 616149818, 910306342, 538133623, 137005556, 405625954, 111220861, 318675765, 575550025, 897782250, 340258313, 321278709, 242465132, 716564410, 303112827, 329546094, 875589755, 687498514, 262601236, 998058383, 113846655, 306221150, 833490833, 526294881, 457454801, 503013175, 116559314, 14840034, 683718202, 230968587, 457781576, 287922901, 270407249, 940309630, 111147472, 163419175, 263410242, 272132137, 106066375, 511614307, 482188937, 689538725, 984316571, 751032802, 389261497, 290988339, 36027478, 665733097, 356049445, 507071746, 28393107, 684073884, 582792594, 598836363, 490029854, 710007437, 912499820, 934962861, 119288623, 307257630, 753677909, 673556676, 30257755, 121694573, 130281334, 434027781, 219743549, 501009954, 751476758, 731883638, 266943631, 873578456, 157251798, 204209711, 68317877, 662110091, 507217526, 739701449, 787974083, 943897362, 425007958, 297197917, 861677445, 713097702, 42988357, 426066546, 577759805, 232667800, 848936501, 543102689, 697169837, 705205381, 311393703, 112149520, 306913932, 811393329, 140883896, 56102571, 259640932, 759072290, 213573626, 613283461, 813280763, 880690266, 664395918, 9437757, 312860425, 497042352, 417651958, 503743761, 871880422, 273657268, 849683630, 644029174, 559848921, 43845364, 739058552, 814011275, 709660786, 596189092, 68738255, 975247841, 707430611, 334893733, 371474802, 203594605, 796495907, 223094222, 269241264, 257719680, 968525084, 700149306, 383930689, 95442528, 752406413, 830221501, 845023926, 526249209, 737249765, 379543042, 778590777, 541997483, 805950102, 452343265, 422205939, 949371073, 701736867, 848511053, 17629408, 713007159, 567872254, 166211855, 135029327, 818121296, 287502092, 388849648, 615929776, 410974328, 297808061, 926570788, 887081220, 748495451, 835132250, 747266406, 285387791, 416606838, 559861423, 402478746, 435120779, 534641375, 969538243, 923033121, 593548638, 157608628, 947350678, 706494398, 496384175, 963607659, 657146370, 62450352, 628278488, 412374956, 527451644, 768168800, 282843494, 459822314, 525448471, 106122698, 206003545, 922727754, 578290401, 609926820, 406067789, 333499126, 943315234, 399447724, 994754502, 97872992, 597676998, 262825818, 721729019, 669213213, 584035442, 735658767, 466346917, 252157437, 579287834, 106106189, 812569756, 163244829, 528684170, 74176025, 97599839, 329714406, 544094296, 49496774, 865067115, 103957442, 581570118, 109750506, 709451390, 290370463, 419368039, 593777937, 707931354, 581909957, 767177368, 985359913, 885350920, 675376762, 391660552, 456089086, 227094366, 524234242, 127884838, 284304984, 646382691, 158840901, 196281916, 730229139, 634593968, 133621002, 790035234, 358516537, 990832612, 45831745, 957925524, 342143304, 112920828, 570463759, 665128362, 48973350, 646823830, 633705983, 628426022, 104619691, 934092789, 726509584, 880055576, 99538310, 747887453, 950424173, 251276236, 998669565, 225635439, 416656647, 292344434, 265460373, 407755473, 323348446, 20388220, 910349814, 286797875, 651066874, 459697349, 800930558, 36080363, 283380140, 371125672, 927135320, 427297093, 984614123, 669234883, 253045739, 178524104, 628928005, 779195896, 182865991, 78943504, 284736978, 376406380, 526681229, 998636141, 8314241, 279681011, 625222605, 244251821, 325300822, 968232969, 613896319, 506373932, 685743333, 124834113, 321674988, 439540079, 683308957, 637408101, 446581149, 615521279, 649244808, 94321378, 274718988, 697642290, 476380848, 222190143, 243041115, 571850906, 265977583, 271109503, 138237745, 363000630, 207900704, 767756767, 73966601, 977861021, 449170949, 621611548, 449498054, 89295044, 460771074, 804628650, 824941173, 621072239, 495295497, 96525512, 681669666, 128946969, 157734586, 78358288, 563941572, 479369174, 625067724, 268132843, 102764063, 852228038, 810608714, 539920594, 598686595, 963579920, 87490697, 359840011, 21511287, 291499121, 750976771, 213446014, 463867887, 692100885, 871053801, 853267818, 270788844, 556399895, 304576955, 138850807, 148285074, 896675119, 879947377, 691293699, 163309449, 950330842, 819236851, 359418876, 921237840, 307150168, 886112994, 899646646, 224477795, 745424926, 335128262, 405728369, 553938728, 769382677, 813506241, 997291654, 213883564, 468918233, 951223483, 720266473, 673716965, 722653918, 860770016, 783043857, 764488883, 706241035, 184526712, 805638031, 364171318, 611384869, 716594237, 957426529, 995757904, 75436482, 674623971, 715248540, 144413546, 505873460, 175642174, 485631789, 12106398, 426124297, 355622698, 367420133, 791972769, 24396919, 172367582, 315240841, 439903929, 483847551, 223287201, 820749319, 57179076, 15669015, 374888039, 777542341, 326212688, 835170082, 70331292, 644517030, 453259044, 111044650, 874223234, 986292802, 446014937, 666803670, 56804437, 757375450, 856031172, 158224744, 317201390, 952684302, 533873830, 394168746, 298257712, 546673603, 12517469, 308161786, 9634996, 322097294, 47058115, 714213742, 672873979, 109356815, 826259412, 773520690, 947034284, 994072058, 1296661, 916529786, 184846890, 933834209, 988753793, 794845590, 249461869, 557752906, 469704679, 892936167, 601657849, 520061031, 485667234, 95497035, 780575462, 684341798, 995762664, 186671667, 669262492, 795623196, 856102817, 349557818, 566807913, 868666336, 432732718, 897774508, 436196896, 239439365, 565250829, 756418695, 98483026, 812685073, 967281032, 485709094, 347057573, 733199907, 607857022, 777598616, 74293669, 522485133, 590673653, 767265247, 241844477, 887350460, 893011410, 43243527, 819480982, 655360170, 993644516, 274946534, 322635046, 920602623, 727674672, 231058965, 354356003, 100054654, 459964868, 445726761, 300339544, 281634268, 989146491, 282911126, 799176857, 423869564, 225014614, 675978462, 407726016, 975507771, 904270534, 292012268, 473698103, 766357544, 514578551, 684624588, 701518549, 950395808, 114800878, 463026118, 256697326, 559987387, 702332395, 46536461, 964082935, 391141918, 148377366, 164547861, 862165322, 519862589, 301355932, 912101669, 964500501, 953382869, 873045795, 515261244, 81825443, 371707741, 258018949, 25066841, 832307571, 888831968, 109305894, 929552774, 470969471, 28684853, 99724302, 957417005, 470394833, 958429233, 665847392, 310745855, 349248905, 444437304, 549783133, 248437561, 809545777, 696617742, 589755885, 281137526, 392867962, 684168317, 620596357, 101486861, 275500079, 247392225, 791059379, 393220707, 369894586, 359071323, 731144842, 129593984, 986702961, 221481848, 442642364, 28023918, 210031306, 944792282, 859418068, 916188592, 253073715, 251243188, 494968277, 79670124, 96755455, 798477019, 362256597, 880429727, 74184637, 532142454, 598454357, 31166616, 155924013, 605469235, 558540703, 488475068, 200508626, 931905570, 882694114, 333842168, 346452595, 208463016, 232184505, 733016968, 41426980, 169064128, 418711424, 993127042, 757553645, 317305392, 242004321, 135801447, 656897305, 629900591, 266461703, 777311897, 89454839, 575923650, 633027635, 950345380, 413536840, 147444682, 389298400, 539794750, 665101961, 896022753, 425433476, 141133219, 327871500, 176525377, 896391854, 996708334, 264782728, 64342997, 244406414, 690529967, 60691130, 799799189, 630409430, 469945309, 913463276, 722858750, 757017731, 755546708, 389015295, 137441446, 382627486, 99698372, 640606128, 506055804, 296983061, 937377110, 52596499, 921100155, 308507768, 147514651, 276337586, 424729198, 874907442, 521526350, 521089519, 951853129, 990844895, 112198924, 238031151, 38325918, 196472576, 455447530, 695717958, 757941066, 94916651, 850045702, 574841326, 791324632, 674356220, 806918042, 712411352, 433020232, 488951702, 562822009, 686508440, 735870277, 697066434, 808523828, 56975611, 536673711, 974226422, 553508493, 225426757, 957160474, 998989726, 128099191, 711361321, 668286655, 618275017, 384320743, 839798416, 750673974, 811682432, 987588670, 597080255, 826737403, 141176389, 234063857, 641019721, 201438095, 967839898, 592237903, 377707596, 386615904, 994268438, 522456418, 894358559, 711288554, 459750856, 787592001, 443070025, 697173402, 621331607, 716731266, 177122232, 236186309, 189979610, 545398282, 188304224, 879647433, 31772215, 857996767, 856422401, 725267711, 398479643, 29602201, 346406503, 894514540, 37147748, 545144290, 301677114, 714264959, 119822846, 551224270, 457479858, 284363737, 765543949, 610678950, 961637014, 816869739, 250213878, 100636415, 568560589, 554695778, 377416945, 388020661, 101344251, 780212906, 263866714, 601066941, 441628748, 71345366, 977905587, 733800010, 254961190, 574432023, 842077772, 726935989, 611035239, 149135449, 646642180, 163244262, 371443691, 408635147, 735485030, 309894310, 38354957, 815917696, 781383289, 960158883, 325674274, 577779405, 366843509, 85665050, 118167897, 197727417, 664655762, 489347382, 260763176, 722501747, 235104758, 10175030, 757334677, 521213392, 373861649, 434661453, 320001403, 558429534, 622596683, 841450784, 247941195, 839861888, 204773033, 991719280, 947250370, 1214170, 295002557, 26207871, 555128177, 988141918, 980549392, 888034913, 790875232, 207131838, 827574721, 10434120, 640868600, 230118974, 626380589, 269818941, 821000955, 166960708, 799509249, 266827702, 658459693, 551792516, 735293580, 364556126, 100472272, 634404813, 703509503, 897427264, 599811748, 587233062, 743966276, 946589505, 44323033, 242265515, 757351588, 221745757, 145369895, 553067423, 680337205, 27716801, 449467310, 521100163, 945156564, 13206884, 361917696, 146725184, 499208492, 922936759, 875480280, 835098318, 974949114, 218253154, 773364758, 670951653, 81284059, 464685090, 533636978, 256388483, 669601672, 53415985, 581273254, 33003595, 484122377, 127983122, 482648286, 133535745, 22382381, 895497301, 346502740, 662166293, 582606891, 327781972, 289704832, 148232133, 58809347, 187089504, 601580262, 439143383, 261040398, 887749030, 500093661, 265785621, 515609354, 876252140, 869262187, 922014402, 385333785, 743096258, 120965437, 189387454, 580146193, 898692772, 342277996, 121287248, 683534388, 382113686, 980088623, 831394782, 169566766, 674588467, 763584314, 132161699, 12029929, 499686236, 935453337, 675086461, 968638445, 729428404, 660599512, 420265200, 880051775, 607341046, 979455563, 634126423, 293431390, 157881884, 359345589, 809850989, 195182739, 222818235, 65049078, 434568413, 499221213, 865204650, 557141275, 33996536, 105769928, 20507123, 445205932, 388232586, 424435630, 800668909, 900319024, 43558815, 495203239, 978786271, 70133000, 281022687, 961017208, 299974481, 223909818, 401293690, 742562393, 737478370, 918842190, 916330175, 227254720, 958326663, 230764220, 427630206, 198593059, 357627225, 387002642, 528721131, 555526425, 699646461, 681479293, 822267224, 240888024, 301763560, 771378660, 376516495, 262215835, 853500064, 223560405, 640534592, 814240441, 935904531, 754411916, 104792781, 578148793, 130627397, 744349654, 25492715, 435258480, 432967942, 258217568, 330382262, 800116444, 703290496, 300366465, 48098109, 797783360, 676310332, 170982506, 139233071, 626449078, 227573474, 283264267, 126308796, 828261345, 639550508, 632412826, 248014696, 473567232, 934752063, 945533913, 820870657, 750871973, 985173545, 988804776, 500116857, 595769369, 626243305, 318993693, 56671564, 391143098, 728341421, 747063672, 997129469, 668139404, 197351509, 57502230, 702602813, 833463087, 646614063, 326772458, 827696771, 147217842, 360237084, 256542000, 438025934, 385611348, 425245599, 127503368, 725566611, 605032579, 864306708, 39480842, 245850891, 25923971, 871339263, 459426466, 388474894, 87162993, 147105928, 167096316, 665066314, 525060489, 509715358, 676483997, 505248258, 232928545, 279904683, 880361663, 263334060, 837383645, 525943870, 786232378, 592790934, 28384502, 747232696, 382552179, 575547093, 352541715, 544100933, 957386116, 279723293, 250510571, 685638301, 939304569, 420992364, 988768254, 940045867, 271906702, 560217759, 172353475, 394501906, 413346667, 711918452, 672253893, 76623293, 230023902, 947975695, 924327981, 104843725, 929558561, 91516436, 656597267, 137649465, 192072223, 722856436, 904028403, 695639856, 57069735, 868005513, 23802548, 726412698, 741792421, 308059486, 186161614, 303027708, 984803256, 463693381, 586960953, 235641417, 439497910, 501151530, 452191711, 902291953, 211410369, 41615308, 429365357, 587194092, 46196637, 922732850, 288302887, 795277362, 937545105, 397442070, 320395263, 232533498, 883142162, 766199973, 431890598, 508073252, 731161703, 327185492, 760603138, 985317650, 456819801, 454368361, 460113504, 688340321, 666285681, 963081786, 188983060, 566091184, 971834602, 241677294, 653156670, 105605026, 721942715, 752367067, 167846449, 298922641, 345395214, 757413474, 252258659, 516272732, 86612229, 765830441, 568689186, 591199598, 562083411, 378345818, 910500856, 783743955, 112402022, 353967979, 296193772, 718062304, 8685541, 676155037, 255761566, 139671100, 48767630, 539242908, 378771714, 348697930, 759151311, 417377883, 177982936, 922194056, 374428670, 251783133, 349847809, 967858699, 134658403, 192049390, 899638889, 103617964, 432189147, 528433712, 1777246, 765320906, 167699911, 841891684, 963267478, 415889520, 591804935, 88113212, 497732857, 302750596, 686849185, 934058786, 747623506, 120235638, 161160171, 859466630, 978373869, 277586507, 62538292, 649505314, 951272029, 112621654, 972519955, 182323364, 233597333, 424972898, 229477286, 362184260, 879334959, 162337178, 109440310, 696096290, 989249290, 61678022, 880623362, 917282368, 432632397, 951239511, 581643217, 739014516, 662709761, 404775191, 476374084, 393478767, 738774625, 188254166, 841047813, 138853858, 492440859, 688517956, 299179092, 868580088, 71494063, 364994318, 369417002, 314194684, 51833288, 917993842, 469258839, 35100969, 942903264, 759127277, 641147925, 555589946, 486340724, 722797831, 24648485, 388318519, 264509742, 6425244, 440788989, 690119533, 57657221, 280969968, 788959468, 605489439, 475955807, 476523134, 734265104, 27319897, 842349967, 593640124, 793235520, 455510416, 774589101, 228581958, 457746335, 722510791, 721529753, 6644640, 799016246, 457261100, 382545059, 554434940, 826564561, 305494328, 709506777, 158297220, 172531838, 2393870, 564790935, 530043080, 318433090, 227794941, 739054016, 116213046, 126472523, 282674204, 203044988, 977791206, 633639047, 518018438, 860648429, 814738927, 765379930, 917061637, 151546916, 186637834, 144106065, 116191069, 354533655, 792769175, 663396184, 910510131, 264188025, 647383387, 838724018, 444041343, 707035613, 800108284, 267674543, 491293399, 301017869, 996656794, 762718359, 734322010, 459941069, 622792031, 145632117, 675105038, 949522631, 106184097, 478856805, 88210844, 682288036, 994966509, 653912044, 73659605, 1912407, 2661714, 833870096, 788137224, 858194208, 137697732, 459028192, 962778666, 571450177, 876721346, 277959461, 399035602, 130037902, 38220704, 353704108, 85398389, 170032296, 340191443, 183611449, 495403658, 497027645, 754551204, 612285162, 319505799, 196699492, 133009882, 970879717, 864683653, 920871549, 190024591, 499031168, 58851182, 852815307, 375194729, 644500619, 788069474, 626033537, 347651772, 360318276, 796223263, 890134453, 792072140, 485463616, 810227629, 328646267, 126970487, 670840700, 143666474, 70193831, 650767311, 169890657, 2030060, 442230084, 751963315, 565113929, 595230101, 697692289, 902652588, 677041134, 238250820, 478689983, 519589874, 824107191, 428169115, 658276226, 957075333, 954836823, 603007738, 639378098, 319057097, 473727103, 833505084, 319695208, 787828110, 632265369, 525482501, 678739938, 503069605, 517191943, 15246729, 869529871, 491608415, 53659670, 209997514, 387474783, 57025151, 696755815, 701880770, 471717436, 736072688, 158020374, 259154271, 874221096, 829027927, 326258148, 79424145, 21756769, 197446415, 655657721, 885790778, 821997229, 377448524, 245242203, 495427986, 848144391, 907437376, 788355864, 7491320, 961263631, 288923951, 983019745, 442277415, 906082858, 567922387, 454484752, 988554574, 38099645, 913538950, 588222938, 425635453, 91225583, 965207401, 208118153, 693942046, 924821532, 730024873, 389444815, 76455799, 329099676, 52030234, 153070346, 262473952, 178994333, 411501568, 345333117, 566570470, 877698020, 174376087, 501486882, 99210610, 501737890, 358328309, 99621190, 938581990, 68664785, 356724217, 638575327, 927604874, 214595702, 120026865, 208641745, 691813727, 997862595, 324956969, 29220119, 960181891, 677893398, 823749933, 476388726, 147812724, 224734496, 455084878, 943825406, 724513245, 632300421, 884305810, 172770490, 441520455, 234773739, 840141592, 926014904, 227582589, 66636853, 291256411, 23974830, 945293105, 381978221, 180660151, 228868319, 610738466, 189815845, 895536248, 285937804, 499999477, 439259926, 866069845, 131026659, 891145121, 692161648, 866258726, 938357671, 534685431, 821683330, 336911141, 852911286, 190166515, 210662297, 600366817, 634564456, 750384173, 268290219, 631748027, 414699281, 238172274, 10469425, 790123900, 103832720, 478865535, 311513481, 361744907, 119194827, 815456896, 821787921, 660062483, 577665327, 983454689, 821778048, 505186674, 285803813, 771725860, 584615446, 252701539, 777399143, 528707024, 905793697, 266552818, 155245291, 539661269, 776539893, 960740637, 811465531, 248457050, 999100613, 132454562, 312926949, 751077056, 254286048, 616002637, 349955198, 464216170, 175428775, 770684308, 233160197, 455601602, 577515510, 983841764, 160162628, 383540701, 738713620, 208007465, 722958834, 264909464, 449913345, 344310730, 644356099, 654503790, 578554160, 758918236, 535419504, 629009925, 764027003, 65967628, 145076887, 745598630, 430128286, 290760580, 784540048, 500387520, 485543241, 564626207, 558864427, 467046621, 871135408, 834534836, 732042787, 876685908, 558895267, 228686098, 708203403, 636955802, 517067546, 647125695, 889013861, 781089942, 192707390, 762774705, 427146745, 903579676, 943772529, 678748098, 696511765, 637940088, 568609011, 774091729, 323442263, 656353519, 967776830, 472240162, 577502368, 421150894, 72502346, 172124067, 552602357, 455061464, 231091011, 471859478, 141310648, 337715110, 333108938, 134534571, 680427511, 141049784, 608492584, 25789644, 157836365, 607444356, 70378040, 507203925, 373292439, 953154067, 351163755, 796455864, 583975955, 776331986, 545200662, 805204767, 39984275, 122021941, 337274408, 877007499, 226541806, 825422700, 539133472, 438332858, 844345445, 943248598, 636139910, 416316756, 198190650, 101631508, 695649645, 753792877, 233909026, 433879531, 323377047, 534339809, 128886845, 234215071, 141406436, 275040696, 679769502, 359569669, 948023117, 577165120, 267461252, 689516259, 208860530, 222312290, 234730618, 383967805, 784124599, 357492476, 33332645, 336013946, 142871541, 875178182, 146812650, 7045063, 618535998, 119784852, 977639252, 283636846, 659041594, 353495098, 978522160, 369280691, 901289994, 4011482, 388236082, 63423571, 793114373, 960890577, 342892112, 498273868, 825216350, 602419025, 313553639, 146107542, 450465861, 765310208, 220653556, 528371559, 227654518, 734850209, 479534495, 495051968, 27850451, 500991028, 859051617, 222332494, 151774674, 881235070, 275059086, 934270411, 583627933, 440667915, 160524792, 394611319, 540566047, 352678894, 450015622, 429670187, 472270448, 582716630, 310253486, 625344781, 733628657, 943657684, 626361748, 383723155, 996635906, 698950680, 494839057, 209258573, 47310880, 250550123, 595923978, 412363929, 91361585, 318939105, 973156295, 945078016, 135672510, 616271749, 771886869, 338157334, 371127129, 759200845, 262870638, 319997388, 651706411, 362977386, 897980508, 88130861, 911322191, 55894420, 646932474, 883478127, 209198128, 845071738, 573499056, 187298261, 949496887, 809660319, 176201830, 730713149, 986469534, 121814457, 835432258, 23578646, 643046789, 981856518, 105702393, 11557192, 457756328, 778807076, 305975827, 845276829, 371266902, 788763359, 600157503, 597141448, 214730907, 462987119, 130853730, 781914733, 264901211, 828286872, 307088342, 91059958, 398040654, 238263914, 531346115, 217459062, 146778360, 918109272, 145843775, 847919945, 541009670, 472491007, 606501905, 360439585, 763232133, 229483481, 526052460, 592891086, 652432211, 899109757, 987645010, 707911113, 256074021, 105808765, 187507520, 425070785, 371507917, 571634873, 558730100, 684423157, 268468587, 729346852, 575487707, 714285355, 542110191, 409561665, 83758484, 705330315, 652163453, 216366387, 402879206, 266420734, 948261061, 975372857, 668964850, 890735448, 227542196, 876419231, 971304662, 438439847, 928411267, 592871364, 340334163, 296533743, 8259975, 735114319, 407779640, 164563695, 990960510, 719863636, 288323282, 31172539, 246338766, 182971555, 545615404, 118456522, 318755134, 382222293, 43241898, 548441699, 971998410, 896448362, 594075016, 859765140, 717380879, 59614863, 103275303, 81494707, 824689021, 962799957, 707856610, 115602957, 131377766, 156924362, 626325843, 107044030, 520177369, 672532352, 35542220, 736982854, 973778429, 299449096, 194590119, 241698499, 716541375, 29762613, 783556767, 702662211, 972637245, 83824584, 432338877, 767298936, 257137411, 415254061, 536357543, 820646171, 95598200, 481172798, 249095243, 141426120, 610949882, 624637117, 141972313, 859208992, 445304769, 854555904, 363702073, 188463683, 191011658, 483051565, 535702369, 979053237, 723567178, 733689771, 850011870, 114410427, 828398978, 480657242, 332683811, 80235055, 627883312, 611678530, 874800917, 626943499, 198009460, 747998513, 147090143, 315626870, 249176214, 236849924, 251731602, 261503083, 239042180, 432682220, 889464970, 498024088, 360080897, 116831003, 954044830, 293816539, 339021781, 205678551, 173650573, 671344127, 837275603, 80470904, 328566368, 299296251, 246850154, 281118807, 835905239, 324977274, 324099815, 185319571, 1315700, 835055942, 814879265, 460721074, 650853233, 918332760, 136157250, 804121069, 872117539, 481523297, 862551139, 470349723, 708941111, 406962696, 284687621, 384805430, 732769542, 716050279, 677444617, 94755273, 487246922, 744169122, 540980596, 162599401, 288932722, 736156579, 563552913, 309712226, 975505233, 431136423, 840745133, 918513963, 556901601, 882724956, 161154342, 162402041, 525762292, 225323484, 857131726, 410408696, 17427327, 592786575, 333278816, 543907795, 990575615, 504198250, 825872252, 62670675, 658774058, 20912579, 891529027, 292597506, 823615590, 105944217, 228053735, 107421983, 644412303, 767334082, 37148962, 13957312, 74364030, 870829311, 542673451, 359145841, 250098300, 56969225, 971779985, 924688803, 114696668, 26588233, 897006269, 433057475, 771719887, 834309862, 198427127, 152145449, 591001107, 216076311, 297850708, 555777773, 559842423, 239668752, 44880848, 545187866, 693629523, 97025032, 620760416, 884138014, 21501345, 208655194, 636816496, 704283264, 319898802, 689565220, 378226872, 859341445, 958210231, 164574548, 632499714, 718236270, 991959554, 977141558, 537419560, 608734174, 215651367, 327186599, 708980697, 720347629, 112194118, 828412538, 397946895, 337848744, 58807700, 820884629, 861689306, 739257606, 481980552, 684328839, 991475320, 412110124, 41815925, 678212273, 678291384, 43772936, 567999546, 701689068, 900526287, 929114101, 439355778, 144564106, 859577130, 81561940, 440752860, 471361049, 968157991, 671796373, 394940679, 898998666, 552515469, 262996474, 221745036, 118983607, 603557231, 847773985, 909117847, 233594595, 709126704, 926516280, 637710608, 4409874, 391504725, 717208333, 641511650, 346452549, 645869121, 270191856, 888633699, 936791550, 165767518, 561989771, 945480771, 60888789, 84254008, 107754521, 676959710, 411280671, 220278829, 890443714, 308761396, 30250911, 924740786, 624379939, 464894304, 565729261, 130927449, 250879943, 666090124, 713609359, 383946055, 193280896, 616038668, 209971308, 819528217, 221895673, 531074341, 940830818, 423869468, 589041194, 733101541, 90784215, 665605275, 174000186, 323477777, 966855465, 772134309, 365575654, 249515227, 61143579, 513562170, 690621859, 486392612, 78071904, 873706995, 324149378, 292357914, 802832384, 230028186, 15123074, 959060638, 340629762, 970942928, 767493011, 50744351, 365076670, 188472076, 327267073, 829103541, 79358530, 178114284, 511959911, 247818555, 941315662, 409265294, 379486487, 864641822, 288117218, 632532297, 765318601, 169791329, 630542112, 29705117, 225772617, 893014388, 13107443, 962554804, 624146372, 143421121, 740652187, 816732454, 594083739, 543993295, 515752911, 533543351, 270784849, 238074613, 978674514, 866926879, 623685699, 698904533, 547653892, 479538056, 152555278, 984344980, 244682158, 665535641, 348259948, 969139401, 409941098, 787343749, 418975191, 183560946, 87267258, 113573979, 815276968, 944106501, 96676140, 480057531, 225558312, 346855339, 551107962, 654329119, 985442676, 679974029, 899733886, 265153672, 868861374, 986347980, 209199868, 880211684, 893419664, 682981914, 115197339, 432758997, 222844657, 424223620, 189774851, 408002265, 672943118, 172323513, 129183180, 962673656, 833924785, 775618726, 186695986, 944380619, 976706147, 127286584, 131840168, 607269089, 47565052, 773014467, 869842489, 772827828, 268802230, 695011180, 734211340, 571751484, 795414942, 804160111, 536237127, 717747903, 902313728, 284878956, 74013813, 408951612, 392202757, 349881930, 880248984, 668691914, 243267771, 467695894, 952669433, 636712115, 987882515, 33947812, 678614539, 91992556, 617728345, 318626683, 348910740, 831006727, 307798718, 800029097, 240682491, 701610111, 735864983, 330195621, 793372942, 548411437, 950706689, 876430340, 241279238, 904988428, 430469894, 259273581, 466545195, 564807472, 851992698, 650701129, 339455309, 701107455, 492909735, 383840574, 109651525, 991880803, 401676904, 855009680, 998110504, 426807926, 325747550, 666266177, 398414550, 812401573, 334930562, 971678245, 713867756, 902781704, 635821692, 904743621, 133859733, 741493886, 836462521, 655722745, 632987717, 441217849, 904521859, 105244823, 444226970, 382192477, 184882874, 251687217, 943793524, 171144244, 879640355, 572301630, 877884828, 962243502, 641239545, 716966285, 545498295, 866599802, 530422269, 558614306, 591689297, 648204098, 161684663, 481343236, 755480214, 979415585, 608837546, 152212286, 161126629, 414076869, 991942674, 747474708, 905048374, 63028500, 590498975, 36468205, 257157597, 340862664, 28332678, 844525956, 17914531, 839532344, 846738743, 877095512, 758738, 204135509, 474064405, 259765531, 315738559, 212094468, 978063421, 118278864, 371813996, 933216216, 349741074, 819812960, 377093740, 2125623, 327923013, 861936712, 709766222, 218311785, 330723826, 839206970, 535474870, 608861185, 486736702, 141374513, 252963628, 187739600, 992617983, 282214991, 935202647, 780080666, 498256803, 222654901, 532815529, 147617032, 991521031, 825638940, 991550338, 390508796, 158059825, 857662316, 866520864, 661916352, 695750125, 357980818, 225326295, 707283006, 612802209, 347288494, 139805352, 810945152, 434331003, 73749721, 405271693, 873755611, 799449969, 331668677, 233464928, 632154896, 268083656, 473740454, 528503135, 299305008, 615876439, 759214880, 936634889, 179931152, 322321311, 298689076, 770579184, 944371175, 829404483, 213754189, 646082892, 133999295, 694370904, 20241228, 528682219, 578096429, 790190611, 619678050, 67966320, 69532313, 512755466, 492071322, 793046841, 661679242, 977207177, 867253813, 513411651, 647167736, 420378760, 592661299, 559895384, 281890792, 148495650, 150778369, 275648572, 449920678, 67357339, 798276350, 441295941, 574558217, 17448204, 739150347, 993963671, 335780257, 530365554, 332853517, 502545134, 63958082, 391968177, 910377568, 411392371, 507781704, 6237344, 375614687, 409923174, 795408504, 436300977, 603216661, 970516906, 333461297, 581005915, 58976720, 308336139, 474236052, 445328398, 983038030, 581666385, 426585669, 622163288, 656890638, 707388250, 907074476, 546509268, 355634986, 415300267, 242986098, 496003970, 50245401, 976412859, 825447177, 6503390, 321014634, 192616634, 471596113, 578238717, 47860704, 539663290, 249125214, 383730801, 173487122, 543670720, 337769896, 464927241, 996035594, 377706264, 305519920, 195784296, 901379682, 705463999, 486712094, 50867150, 394823646, 450145456, 461037035, 13536946, 941570615, 125794184, 654931181, 927133319, 614801570, 284351904, 953203088, 860424482, 497383401, 203330642, 653836544, 434206483, 389726606, 493119896, 79453441, 649518567, 624010958, 377760216, 369994070, 824534853, 450007118, 176056612, 138543645, 282689432, 826480659, 650352242, 536910062, 73994706, 521808340, 261432099, 530854889, 848886275, 530222254, 831024508, 501255198, 953510984, 730775546, 623891496, 954604575, 503457992, 439065488, 935504239, 839168746, 897965435, 539424312, 572116376, 437689976, 197406515, 822243275, 899412370, 760442036, 196985502, 321057112, 56460525, 93240379, 486221693, 257888389, 664627919, 278445866, 313543324, 393439113, 850263945, 204104102, 792845180, 109789855, 716753265, 884147455, 166412174, 654574261, 161790309, 694443508, 264620875, 497040712, 45143118, 649663304, 645773653, 398771737, 673291401, 440863730, 637045546, 338794502, 552548127, 777779967, 23398753, 561440739, 43996679, 468105627, 144643467, 651855066, 983497976, 227913833, 897704321, 292635921, 735111261, 815263961, 265321096, 298356568, 918284916, 297818687, 771644387, 714817752, 53897312, 17805621, 423330261, 298721697, 14839751, 107830463, 22321188, 161784481, 539782823, 461198315, 999595417, 240691835, 512912524, 223878415, 441946111, 668935167, 483224160, 713443879, 642370948, 797568564, 850018390, 287696217, 504651322, 623777318, 254904580, 221249339, 321130998, 371014035, 217888573, 275652227, 215763530, 369115701, 425903113, 604686643, 217204006, 435424496, 338189086, 94421116, 282120962, 552430087, 601978161, 824356320, 394504718, 971400932, 619362670, 272901384, 346077451, 849113100, 145886579, 432056885, 348870224, 703120894, 757932269, 300394882, 533871625, 138166913, 410377747, 857633832, 572071683, 565745679, 101183903, 683038891, 987518459, 904655752, 397767621, 691633806, 600489492, 275511078, 864889554, 884900466, 421825191, 934492875, 911554793, 623826195, 282804953, 913895482, 952623277, 730125776, 50982239, 963035137, 760459579, 906052371, 192270080, 79397246, 792533882, 981779608, 351732445, 692015883, 437910858, 610729170, 191640753, 567556789, 29724301, 426025529, 816485712, 958311253, 551189908, 404806445, 340264583, 600958933, 207545443, 428474611, 181429421, 589211544, 123721774, 444155803, 305988692, 224923359, 148026481, 71338183, 867440799, 157208898, 488739935, 477567487, 641445326, 229975323, 161536219, 8504947, 426734011, 417601221, 289809147, 233714899, 358392802, 829206776, 590679079, 175472999, 381552389, 546510019, 466463916, 656007555, 865492409, 620255874, 439030404, 396473763, 796637001, 734892135, 468951841, 612728478, 722547897, 43671685, 889122302, 221813208, 424932136, 186488193, 601596494, 809802005, 634596478, 336360351, 285171050, 709358193, 536630747, 848123990, 899804777, 809376028, 219898051, 248411672, 469001208, 909880577, 50259655, 513039169, 302482583, 483409290, 442619889, 278798975, 620512105, 894629688, 796013895, 42610668, 756318155, 984107847, 813464908, 300752278, 959781129, 460868254, 368716170, 802557800, 818187194, 732602198, 855590182, 837326148, 17279411, 642393730, 681266061, 81357046, 505820848, 276654258, 686505212, 71831818, 44856688, 753669877, 926114421, 876800541, 807657925, 564248496, 540395653, 378700994, 996737194, 633568756, 576658877, 499166919, 744223781, 139386874, 592218740, 776045628, 888829306, 238407161, 824037284, 957813927, 190231656, 635780504, 682780981, 560940728, 968207596, 68927031, 645137386, 3818313, 175924689, 523354260, 523267295, 62371822, 111929953, 465117534, 49850575, 800302485, 193309356, 761917650, 300117013, 386955072, 830666665, 142826527, 25981664, 955834694, 758272261, 725973563, 371085101, 724833972, 776661661, 389881414, 103849101, 323107977, 766152985, 4216148, 269837125, 928664179, 653433689, 927901847, 628403911, 809188351, 622369870, 200430098, 991015352, 911373293, 35076638, 589327157, 871829844, 270119599, 297460537, 872433300, 42318974, 840714869, 760112365, 349388198, 264843588, 713971446, 475833644, 46339778, 976509952, 877456497, 932328460, 738518068, 41361700, 956891378, 94331046, 825688288, 406738889, 208545348, 165742318, 427830327, 619519689, 750216639, 714500377, 400446400, 338978891, 643471391, 220644587, 817814455, 395201762, 36055217, 877718550, 25531172, 934578977, 138961546, 45148023, 991004635, 317992947, 575523064, 100352714, 790413216, 540205237, 279562059, 165253396, 7993283, 221862161, 91913759, 548314186, 35974764, 526834818, 543472533, 682652541, 834501689, 209320750, 298543394, 995172297, 930014979, 904581863, 229507352, 719272433, 37564745, 989761982, 516905366, 937684712, 649711362, 682923207, 757021029, 136965164, 475672759, 923340440, 160340757, 861244635, 848202307, 139721414, 389936673, 851935918, 350945578, 467131358, 455161727, 641169948, 791148506, 892902, 383956179, 515875448, 652649297, 354452410, 777998028, 194977211, 871946956, 957357750, 312559995, 555502731, 334314674, 182542928, 498598024, 127225934, 567785183, 78268656, 422865584, 99166093, 271942852, 838138392, 615537151, 305700311, 200227902, 636399591, 518370476, 743805611, 500687344, 63899200, 400729178, 770605382, 79132794, 217151884, 82447254, 374718897, 912734669, 570464000, 106955050, 370844878, 553737961, 906474917, 607940488, 787228170, 517462597, 889032805, 153097410, 928940863, 330281195, 886785216, 563922176, 367747182, 912794843, 847442488, 277369299, 32291856, 464273380, 586778139, 203153060, 593204912, 56599056, 347375159, 488620402, 667162706, 623204477, 113760382, 743211920, 541082043, 360738754, 36786846, 340084966, 471481115, 403400238, 76236419, 260836392, 705312818, 997588632, 598586034, 350838041, 385313414, 700396409, 757930200, 727874503, 574500987, 891115055, 244491239, 381203651, 520733655, 794529884, 580171285, 893675881, 351834958, 679370753, 976968389, 405951702, 401853075, 985596743, 498049008, 908384084, 251938819, 498337538, 446225192, 315216546, 972985027, 725673856, 88577220, 379263903, 660567346, 74090851, 603173008, 414687608, 86946375, 22186550, 211506277, 315558972, 817015752, 48515874, 421210339, 627579425, 168993639, 816432292, 492067653, 638686183, 686711925, 875165388, 965582732, 74399350, 735356293, 265920635, 432073755, 598096857, 917072060, 58372831, 120825715, 622242390, 661249347, 395016770, 575041806, 220579399, 751677597, 72213061, 848652081, 172105728, 478791362, 271370413, 4018861, 241705831, 586054834, 482818449, 482508238, 341642596, 972207951, 934098501, 26322311, 81645336, 139070575, 425046991, 192186943, 426661869, 573322151, 466483970, 171082753, 750311994, 948770384, 275968702, 421882723, 725135915, 315038429, 16979696, 144053784, 414933710, 139213876, 714290324, 732505268, 745796629, 540117951, 776437425, 786114160, 165574434, 546194227, 356726289, 833545610, 540588498, 222182273, 169210004, 709089195, 490982349, 598467665, 721690732, 543431031, 928940138, 575106746, 536612431, 5452230, 182218123, 126094430, 698565709, 926052481, 20522353, 885023051, 106007863, 313184052, 166018180, 51344282, 675571401, 279317528, 290857536, 991921619, 223112796, 730097303, 49409126, 698597866, 557437406, 988666934, 349409664, 798809911, 208572459, 119049912, 378082726, 468050545, 124010988, 775621581, 273598831, 192000108, 136826319, 414385176, 485261636, 966326290, 524708114, 291384394, 36825302, 266709129, 474786110, 197159404, 641038391, 351280489, 630943884, 492754074, 213533208, 671503819, 884809040, 200229550, 158153467, 165443927, 500469068, 740782949, 875482689, 796584183, 54965374, 45845621, 883382278, 683850236, 603189774, 634277393, 196621765, 869380778, 686217397, 620292433, 101182247, 631907231, 791365331, 879550741, 188699159, 86884885, 82146196, 137326802, 728820709, 358508448, 857907544, 94594218, 49968980, 407279079, 688421857, 573741543, 543821105, 373740237, 410581458, 830482613, 926948359, 508057111, 333124189, 100100161, 749495456, 392927080, 957628365, 180962487, 880154451, 804140543, 679425403, 263566557, 11645160, 837861416, 124915102, 180649185, 302567421, 828991465, 636460830, 200276036, 191217694, 499002820, 423633258, 286418696, 115688231, 661606569, 518727102, 967850598, 758286705, 867392259, 340101813, 155038790, 112979543, 177857649, 591600056, 553933980, 342567068, 417582751, 232116198, 674997088, 142367661, 460774198, 689612872, 342285918, 270834777, 68515988, 648415399, 570024196, 826894661, 434609996, 248591854, 745110444, 677201384, 255256248, 398974632, 584649506, 134717397, 941559695, 262716072, 119526698, 375362811, 641986452, 58625999, 523417171, 458767176, 412734515, 355165667, 527995430, 422243332, 535428501, 895980846, 998465326, 511736459, 282256618, 400784263, 27332422, 656204708, 755111742, 171360772, 500889267, 994670281, 542743441, 549268896, 759337126, 430272089, 683718379, 140843893, 304108499, 997495737, 666140092, 234401031, 355231851, 646294424, 20138891, 135084422, 432376611, 665590060, 679017325, 978196040, 861865847, 386057832, 256484605, 579706463, 847254232, 864540561, 155525790, 11824353, 700779585, 330411977, 57825484, 972206920, 61632298, 821546924, 191529261, 957898978, 121453556, 259106504, 682502117, 548911323, 525889843, 127880119, 165015470, 196343187, 706731689, 990315103, 860231298, 482553827, 230027030, 97291690, 176089409, 234919450, 269733109, 434980183, 495856173, 492179233, 58440907, 268809903, 762426531, 183716832, 711494481, 919995828, 549966689, 629839375, 961537951, 902458383, 399649738, 399398869, 132664905, 719156404, 515867982, 677289158, 864246995, 18328686, 253296837, 879410808, 850663281, 583067553, 211746927, 317586999, 261513340, 891419021, 195741215, 52965639, 668361749, 798882800, 447828644, 527936564, 30820147, 449704420, 882414806, 4305038, 62071798, 228468494, 909467693, 899182053, 386524664, 89332703, 219810915, 534198888, 866076925, 44986050, 961656565, 611610507, 877700126, 493044272, 707748853, 987889015, 503163432, 747897983, 825700030, 79884320, 741113730, 534016607, 301337407, 549324125, 772013098, 839846536, 528594785, 85981390, 659785966, 108029042, 530280284, 470643957, 190652846, 323523509, 322975150, 216636130, 163864457, 584643641, 481142597, 335881325, 945080226, 150633596, 187546954, 413700769, 634262994, 924292274, 4875734, 537605329, 611518496, 155076000, 205393977, 918903762, 736505628, 198166525, 115570051, 734703961, 263863795, 484195271, 428601323, 695634636, 713169665, 435665054, 855574968, 444225815, 759674538, 794397061, 235242093, 566165547, 654258115, 704283000, 539853898, 870738715, 438572670, 451887174, 855976755, 491790650, 418236546, 788299276, 902884178, 701070348, 867369794, 584190484, 462696891, 705776579, 631612566, 695307878, 956620825, 647329147, 685574836, 901334651, 360889235, 3374240, 996250035, 210221507, 688950530, 848060869, 292652863, 788426962, 509922518, 418713424, 366533405, 699001346, 880658195, 36617150, 225847008, 685179574, 538080725, 404736014, 85438551, 422123581, 55793065, 258391093, 808433291, 408232913, 29112866, 322501312, 13511859, 19916117, 857544200, 372835740, 414462663, 252079962, 998044476, 555624745, 509542851, 528778103, 889478421, 724475833, 775914011, 639748888, 544571185, 340867545, 96033548, 148586393, 687366301, 412250080, 203424139, 850250111, 909360926, 800356807, 160796737, 247434172, 424822908, 458715653, 804262932, 632631588, 737808543, 933879822, 410678994, 473412350, 317970310, 913022201, 283293242, 311439129, 599419072, 527319769, 370248744, 498031468, 333778961, 61273948, 557324226, 940883622, 969934824, 825742568, 888081058, 387420609, 180087760, 847108349, 437200886, 85030528, 298972273, 415096722, 597515787, 344910992, 902718072, 637699387, 43445115, 98985094, 345728067, 336882155, 815330813, 523541040, 501793755, 654951905, 3257393, 288559691, 333545528, 136107842, 268037538, 489617652, 554300622, 173622840, 131971567, 682951642, 370495868, 876842807, 108232738, 984269681, 841460706, 155091570, 223730401, 760752448, 294158245, 869007922, 75002725, 684122774, 316782787, 733909458, 467018766, 337154538, 262647990, 628536938, 333067932, 134816858, 255654138, 143885242, 656046200, 658308297, 395122897, 523463532, 536794349, 157294390, 627704944, 773103793, 843260204, 171918854, 383090178, 852558597, 701161846, 838720871, 228270620, 541747588, 469825794, 213114806, 431446029, 240659488, 445470827, 128453970, 131950480, 82013400, 478185290, 751036724, 327831377, 711205605, 817567386, 844027091, 622187712, 461189655, 84348151, 36420687, 180437202, 651087029, 947490038, 585943719, 175680124, 239837979, 464910864, 724016042, 180953214, 704909172, 720213902, 858721943, 685938257, 394913478, 523390760, 404214525, 164592142, 69027246, 40870573, 536755967, 706287798, 406248151, 191050637, 592106200, 187245365, 711963991, 539193840, 147760471, 556294608, 579117993, 931478803, 479828887, 333171518, 164550734, 436011356, 792154869, 56410557, 712945809, 123551008, 181273615, 524508088, 58075424, 790548574, 135932243, 419479816, 365116095, 120684060, 406823925, 256354089, 551315396, 677232844, 717910401, 120415701, 576289777, 311997089, 397951566, 434752342, 681844358, 880115873, 631940440, 226158987, 385247702, 814152565, 718173323, 401948286, 812964959, 810288389, 495420036, 874702787, 521710704, 889469144, 818628376, 703949560, 573953936, 566719076, 640191960, 619930474, 305580754, 700035041, 36249892, 542566171, 474372491, 828589966, 393647299, 311229898, 374449453, 743651404, 147334298, 943084522, 764179839, 753493275, 930193771, 203271380, 514282114, 336205861, 263772240, 220330715, 693344327, 808329108, 255472159, 755400820, 542684577, 392896639, 360875289, 56600579, 94031934, 181386725, 126511461, 435878470, 832240719, 240298838, 10902700, 848766754, 13755811, 292076093, 77610118, 443587700, 689362339, 744343488, 866700332, 505477828, 457515285, 838786475, 830927916, 379487086, 119914834, 32167366, 619516712, 151328449, 24921313, 751534590, 348400980, 435531159, 561492775, 645747490, 651986427, 644034489, 898815139, 640362798, 457233782, 824387409, 769777340, 336505727, 762514908, 774787810, 745315041, 361104881, 897457077, 969706218, 74594908, 598000398, 26609916, 761110908, 307953191, 63244681, 187709417, 470936397, 322636260, 855187750, 777841054, 212174350, 520085497, 686466829, 990515920, 521156303, 786252169, 605534489, 712757559, 478308221, 925700710, 610680500, 396711424, 442321905, 810901760, 983440283, 591908922, 410322331, 893714980, 414993017, 819483428, 833958379, 983907060, 528993509, 359447895, 369345995, 42089189, 605723686, 154592293, 75817414, 694186862, 261167045, 89536550, 196684283, 237006606, 243748195, 816612022, 875678651, 26909066, 595237195, 654079457, 722802737, 55390094, 459816455, 207642652, 11353313, 878566757, 756524403, 363667403, 558507875, 654572383, 522362142, 434851345, 472359008, 400366494, 438835406, 906351919, 212914893, 635638342, 25298946, 420409693, 268336201, 102429537, 712886198, 624737805, 639099234, 227522434, 192014503, 791810122, 582636099, 353645327, 514457961, 449444781, 726431049, 888370142, 59175589, 226097153, 541304853, 476338242, 502824653, 159885588, 911029126, 403248794, 435180682, 762710772, 369241528, 724918970, 697694744, 949253789, 26489141, 285762297, 734296236, 703610964, 17422329, 146578326, 600319383, 656918778, 729714592, 820013230, 784653156, 569705586, 430812359, 377674107, 489812274, 642171449, 534568775, 766086668, 467851121, 932814263, 420052367, 605085413, 156927523, 94460691, 863840283, 922930713, 428850423, 979484459, 171411160, 601689949, 244289415, 332848663, 355990470, 681667346, 384881874, 61920602, 884308226, 958420422, 355197635, 519374230, 342874827, 194066184, 460521735, 958090733, 162012933, 806855449, 352325942, 314439005, 237825249, 94886658, 609430373, 857888026, 209032838, 489486394, 575705463, 535290911, 586678010, 712465205, 236522673, 163126913, 48353344, 402470249, 204622938, 184860064, 45518925, 67254012, 502824076, 192366814, 508989828, 432619387, 514826256, 457253267, 540671112, 309981332, 715153567, 830588903, 881186426, 423984905, 127784074, 460903676, 739267697, 150901256, 33671190, 262932610, 205794031, 283969056, 478100051, 510520705, 375027603, 324939648, 278338199, 610494598, 63799724, 446848341, 448578293, 867709676, 654540611, 922548493, 144075088, 770290001, 421351469, 381838448, 941010748, 644555937, 724750254, 582694975, 717630330, 613751445, 414300789, 257765963, 634993777, 182969766, 426405192, 518511263, 368391997, 330139725, 240024606, 486614980, 817967630, 727328141, 731400492, 967246942, 524254477, 574190032, 592414340, 23248004, 679086651, 269953584, 526199020, 354774802, 607022600, 165845635, 847451343, 898568014, 448082817, 708548105, 184059614, 534896268, 743025909, 690276481, 760452445, 367035519, 946802329, 598562253, 826871280, 298101328, 389296003, 658788774, 384009753, 880302143, 297980821, 380490107, 353818894, 460811, 635193706, 540421377, 705734851, 868580362, 586914718, 43671867, 606271261, 536506282, 486699639, 312441433, 137732025, 716433603, 861219722, 795632647, 596281271, 822641716, 76139321, 755942337, 78413798, 924956134, 855908783, 61197861, 749992480, 617128652, 450189997, 612817327, 995199123, 852995457, 573758586, 437632207, 730357769, 934717391, 182200106, 495448983, 584658883, 988946344, 186359718, 229310434, 256573732, 884576325, 837580677, 599728333, 458171252, 514151297, 29033887, 893963958, 739537156, 229201298, 712016452, 714369147, 865237433, 987301282, 165769892, 510664467, 74880801, 252817364, 382727117, 533652541, 642270389, 208902350, 807999296, 254434502, 254804369, 483339997, 623129237, 244927891, 742335142, 814973275, 737000744, 724500090, 214073819, 657932698, 89878530, 924522114, 828430429, 62713711, 795839643, 1192772, 669034582, 247122989, 344862090, 968094448, 299468407, 457439033, 734394273, 203689140, 29655736, 464629672, 15163177, 420985325, 224614880, 143621982, 392238550, 651844253, 415639693, 381519711, 828896694, 820873069, 924463271, 626273689, 683872827, 440905917, 126725443, 153451480, 765694575, 632731259, 956530897, 13734633, 22354370, 519486939, 248090061, 45060587, 105289859, 831353836, 779347284, 880308485, 977979363, 433148829, 290640045, 663014338, 817082230, 101191528, 636827186, 408465574, 590047511, 345742228, 179486978, 59917527, 681285788, 211728990, 254497097, 697191628, 627634152, 244573707, 18784257, 79117565, 848258227, 924956683, 67913077, 223138299, 860185740, 477639882, 942545563, 791754842, 406883173, 765450795, 189618999, 165116488, 553721137, 57919860, 306608059, 352426842, 175633982, 136961632, 895741541, 97781265, 568556320, 336690239, 574441246, 260676526, 662034993, 416978893, 193491229, 919889015, 480630171, 699579276, 715782916, 851704350, 447534008, 584059699, 2171245, 834547351, 796296228, 242029344, 959258481, 395522478, 937793173, 346913577, 440384495, 367576072, 659594047, 118768671, 846392890, 859465518, 265843161, 275518421, 240380604, 828341248, 632346825, 267628702, 423383383, 484781648, 704462668, 369701323, 900274503, 956750192, 787639560, 399907891, 804032108, 214569841, 361508853, 234195457, 768329691, 116582363, 824490839, 645880888, 173724870, 399981378, 693581964, 486351877, 392387012, 691561495, 608418397, 840142288, 386175660, 891085709, 144450571, 255525968, 86967224, 716829478, 880741007, 621723825, 809165782, 84447622, 917674858, 242325775, 549474950, 677992553, 803021421, 658728117, 561217493, 502675151, 995348408, 398513718, 740455727, 87524993, 208665049, 689554057, 86836324, 598184816, 596613544, 987208588, 703357682, 448234291, 887615396, 152259869, 542827275, 588430881, 214680881, 671904922, 791848887, 716054061, 869202253, 992214072, 728478502, 607821942, 364747148, 928800079, 364520382, 251735924, 104922878, 46107204, 220339161, 98215213, 274537508, 989880107, 933602695, 255753104, 629850152, 863807328, 737455580, 497877072, 514000448, 90378191, 372397609, 666648152, 543463217, 481765604, 886373508, 536177410, 405043659, 971422879, 371621217, 167957684, 801001105, 759394740, 499568406, 867955789, 987210271, 398894086, 212824262, 683752444, 742843461, 577485470, 602950246, 762843705, 76902788, 285148928, 921736896, 147837526, 413123190, 287167271, 445343550, 371807786, 717309368, 183159323, 115378548, 27380371, 802265940, 185031175, 499049430, 142176028, 127945052, 54719775, 976964469, 600352100, 214635795, 769122986, 359852359, 947850858, 988496878, 798529971, 427872405, 432487299, 784402681, 961458605, 501835893, 670128713, 466869271, 683127794, 623111461, 452205569, 37048530, 445658754, 108861894, 656070719, 91910205, 479700680, 356058454, 385312428, 163948871, 881731389, 137316766, 161617942, 52432091, 289440062, 921790124, 276499486, 214147517, 492154504, 349288382, 183510756, 709956593, 364902773, 544994690, 694530457, 879688304, 778174405, 464859346, 524146049, 894746110, 361140356, 851268723, 376661137, 358547401, 236428587, 538445343, 791165770, 701081345, 834094250, 384730071, 419835974, 332460331, 151089564, 778719137, 78710442, 442299562, 427866968, 525261244, 442050335, 999712411, 410504174, 151598575, 355431190, 223699986, 359899408, 716823205, 786482787, 781167560, 653205142, 282903705, 316001533, 17342522, 314623570, 466042211, 229053264, 813239635, 166487045, 825338732, 664623093, 400529552, 566051381, 120223367, 103800003, 838253921, 103390879, 393932165, 730062961, 515984067, 442451632, 35431867, 171157557, 660382499, 969667023, 794537715, 845048433, 668917485, 833829168, 699700411, 788757636, 858409387, 569513017, 807536383, 52478397, 333302211, 207419130, 633583587, 2930710, 180881389, 23191578, 769939033, 281429931, 960273918, 859246877, 602963278, 147251439, 569212545, 960944371, 606171750, 573880468, 995093436, 875648604, 89057643, 469634735, 225934330, 345383057, 912770120, 101495270, 243085512, 859990187, 175211491, 617693412, 37860360, 668877412, 88318544, 682607122, 700227857, 170379562, 284871091, 793724576, 952337873, 713314899, 671947019, 514421220, 707284244, 36674121, 307668867, 714388148, 696061770, 285750647, 711124284, 841144623, 764067314, 755365601, 383667477, 206231727, 439944775, 510916424, 201045926, 614922975, 254356606, 181079149, 812847710, 859177201, 248790452, 233415094, 973129161, 980486444, 11402806, 382642641, 633824931, 561348392, 605919557, 422311258, 416948020, 464616490, 156999687, 515481781, 509694177, 484033741, 555124953, 572564133, 670902858, 715376368, 329583106, 736136138, 608178634, 352927819, 169222905, 422344488, 205411369, 761098729, 306652833, 251504599, 195595219, 403688640, 532063724, 894710774, 787139501, 728019377, 673563017, 735200692, 314988647, 237885394, 636256998, 191223059, 619008550, 642390983, 373598059, 452672034, 325111527, 557861659, 495471684, 207913677, 980142431, 426696565, 586258445, 767987726, 861146201, 93792466, 716777187, 181277599, 277058001, 148800635, 6053585, 153016017, 680304285, 767737667, 600937445, 984132721, 305685120, 113671927, 480087871, 335400086, 55236587, 13281790, 954411269, 518001287, 970489327, 180978330, 382113561, 990110298, 998017958, 377138280, 771430701, 901704265, 681907307, 145034133, 6198287, 120134231, 115792093, 415623340, 462526553, 300758345, 153082905, 296532424, 179366755, 25615807, 15077050, 454957684, 279878292, 869810918, 404202956, 642712670, 582970147, 174241369, 875973673, 3062201, 788451234, 801335832, 626345254, 366203908, 187596435, 707623728, 714680565, 679465210, 982727409, 577382497, 872983794, 563792758, 479607825, 39544890, 345371850, 29878703, 400450568, 591779137, 853942652, 935102132, 588879909, 750047604, 405730625, 851232134, 139997265, 875319016, 470337588, 359773424, 340912780, 112381312, 54244885, 47679516, 14698553, 542559091, 294082255, 135568973, 736836904, 311760823, 731690362, 327077297, 516964508, 216575271, 935974711, 81878621, 704390180, 491029196, 41070340, 462881647, 339544581, 65597498, 817036298, 109789402, 559455138, 711224631, 684058075, 799484213, 21824729, 627774594, 4237181, 240450412, 745548841, 59263664, 798083858, 368504148, 405801265, 836751015, 73001924, 856517249, 194008040, 38333721, 572445059, 671302840, 559117835, 104332491, 509596254, 977576457, 588343135, 974085592, 915148133, 657200791, 236191570, 110804634, 146610129, 60440094, 839981567, 615723953, 35786246, 33103709, 511522004, 302027156, 38202977, 810144059, 544091176, 379058339, 597804438, 916865225, 746668790, 168311111, 170408398, 84363013, 19185748, 925687578, 664816646, 494676776, 774350460, 752449035, 357393227, 483902613, 168611203, 910961353, 857435643, 452715688, 835177440, 35579065, 261560775, 356616649, 455228574, 314864339, 64175534, 635898254, 546526583, 651859369, 327264837, 282239031, 231891584, 687138604, 470638078, 800274116, 322889186, 149507650, 530978927, 28541289, 615737737, 3573, 248841714, 388644542, 235551185, 219846001, 824049834, 366703971, 237159295, 454888856, 327945731, 819003253, 101590541, 83719840, 977152789, 709650042, 575362303, 307855704, 77357477, 610917725, 853784556, 409769763, 688425169, 694553403, 72220016, 797205908, 66788517, 260866595, 932401554, 203752872, 193139036, 467420496, 729749283, 584610378, 527671803, 727957205, 245633546, 632025342, 920735502, 557276843, 924969320, 340605677, 330847926, 47996667, 793064494, 736993687, 225611288, 244478557, 854779766, 362360085, 759418349, 733188251, 538221383, 448660762, 871173418, 240598910, 215786274, 760597042, 60700231, 806596044, 624922358, 630466360, 335813961, 711671448, 456689342, 645100696, 535803411, 879889379, 560686544, 259267108, 31372850, 796062813, 684016970, 377683193, 661230062, 830662721, 705732116, 62945837, 600536908, 597946894, 927950447, 876691937, 261805040, 189383874, 449922641, 483359279, 52253209, 738598627, 953911355, 168726638, 418327304, 328484284, 72834778, 114789762, 731443783, 408933507, 801373547, 974792662, 944106675, 108116044, 21450059, 489125130, 662554883, 957314483, 307265563, 941592268, 66519929, 5097001, 155694929, 394423296, 602258804, 358457416, 497241172, 762750975, 122869199, 144601009, 733833079, 338957413, 810309414, 343633542, 152493084, 840033664, 369424927, 258443383, 767739516, 609758912, 656485289, 349831908, 320666402, 488263963, 397645147, 674279528, 345786229, 497318741, 627642439, 326773516, 400075029, 290011542, 927647629, 807755675, 315575269, 185830758, 497852588, 76652244, 47280101, 296818780, 862797509, 877913079, 678171413, 180130241, 286072329, 657115572, 859761768, 293601414, 557954823, 163303488, 343212444, 187854364, 75643768, 402108432, 438217710, 783037278, 930894628, 352444555, 483693425, 218718226, 704546156, 700586403, 335647971, 891253120, 509855830, 245224334, 559884358, 37386998, 799354826, 296899766, 778286016, 531477857, 307671700, 803473098, 966546896, 172796612, 210671818, 835447509, 275952121, 33357674, 629719656, 408809501, 930889738, 911044490, 583332228, 771624519, 671295344, 520764485, 50031514, 378838793, 426748224, 676363325, 519993981, 3495139, 374476060, 113738001, 467866381, 545769012, 414795869, 69005829, 789772844, 900291806, 964666528, 691977970, 195224267, 574522310, 255272579, 938151519, 191479402, 176045687, 436813479, 449440601, 166534938, 725740864, 446687690, 300358066, 988097390, 412186975, 765007887, 346608247, 652592048, 841964769, 118949129, 150325214, 596566863, 342819611, 298315869, 266464827, 616993008, 447012690, 78698846, 662624366, 954395726, 304717441, 46967251, 175530886, 389041333, 247786195, 8039987, 782316139, 158947844, 452210371, 797924827, 521640907, 191806876, 99105091, 956832692, 132390522, 541298400, 355531725, 178333861, 899503216, 832326518, 171597925, 227154420, 99957257, 909552625, 500614465, 734842226, 216345759, 902319643, 389394043, 922757613, 575434061, 755583538, 251448903, 569011548, 128795961, 868330100, 130916092, 531897322, 973092814, 226948352, 705596911, 626101651, 84470257, 751557650, 162238137, 21614334, 709726021, 321535591, 666576958, 712593436, 53675442, 255238273, 999026273, 444600876, 855760867, 146486765, 507399200, 550168777, 820532155, 777776264, 433319026, 511187151, 317529502, 363720694, 940180814, 470639064, 750784357, 63631599, 577546480, 941222013, 398369449, 298655055, 555309987, 474650496, 86097465, 84142596, 62461141, 977847963, 261857490, 490846531, 929039952, 980417683, 169125842, 465221360, 487597527, 107217220, 442015862, 490637841, 414897159, 845777779, 788544174, 555605341, 28684835, 635372115, 224267866, 537846971, 375559117, 975023604, 792956204, 101407949, 10427133, 25621536, 293871820, 871814616, 363245648, 171999514, 79406076, 963030226, 208557307, 414507487, 364526575, 950170759, 579383609, 208870509, 761595343, 970335246, 949438400, 618255618, 115950665, 862842120, 236700832, 892368779, 14998805, 508894872, 607579070, 143942217, 239587828, 924022451, 844715805, 93756169, 123650356, 426375244, 80942001, 951427560, 322926419, 158169298, 661849585, 484974336, 892734765, 60193043, 987850653, 936400586, 863943729, 649271742, 318455983, 443045080, 257861780, 53137110, 358713019, 942322468, 48278806, 882784285, 390410716, 395742452, 139467825, 251658737, 190343495, 630912837, 477158305, 226777091, 863372534, 515084324, 343992339, 986580941, 679039279, 432890517, 911410222, 512128749, 80576528, 601173486, 990021342, 480485208, 447305155, 176052705, 248944936, 264300989, 138245512, 959141617, 911580987, 415924049, 430310037, 177416107, 925088821, 587272388, 598666021, 716908803, 548636475, 100784980, 1360642, 701772538, 91940096, 769623680, 808140042, 715576039, 287489602, 565872856, 491856660, 661741083, 792103600, 892788570, 913818859, 31939145, 869080704, 293627945, 311447201, 193045262, 511273038, 556197070, 827879882, 506757073, 794924379, 550915210, 204691644, 690853225, 680320770, 39263222, 519710790, 180180329, 525065133, 548735228, 240848482, 203926056, 378505017, 158753830, 899965844, 566139648, 75689811, 267006903, 860137262, 471146097, 728704923, 722668892, 613277159, 691674566, 358635614, 789551951, 196882476, 480643314, 98696420, 646212428, 774096064, 414021463, 876970663, 235968364, 134540986, 63409177, 944043711, 619743501, 176118317, 45636217, 945728036, 626554828, 741940503, 695000496, 746868513, 21410563, 521015298, 851426751, 921132461, 21233523, 616674449, 90052620, 742143095, 302839176, 261347983, 466590804, 487774901, 49507144, 29524878, 22576918, 658162149, 254176722, 28788889, 492712236, 690234074, 281839324, 252809125, 430264624, 987918618, 11759088, 647087817, 265665089, 553528192, 169623267, 726531699, 247522209, 113152055, 437113956, 840984215, 753516135, 33521160, 417339403, 198254239, 679398331, 161676816, 680082825, 798339002, 713502787, 27400223, 220506525, 765047266, 603333799, 439594319, 269504100, 437821176, 4744650, 458965340, 244066099, 349818570, 614198838, 694173416, 186291246, 446761876, 806004558, 285930304, 464445146, 5280583, 637358156, 325222713, 993153448, 486209402, 385718185, 412422969, 607684139, 398460432, 370593545, 652971311, 34087627, 321262702, 715008822, 305239873, 99943857, 764982473, 34512300, 942076793, 558572452, 672667703, 436067940, 259479618, 736694571, 354404164, 239225809, 42007999, 58994502, 895405824, 570386049, 429352869, 32337586, 242757997, 547916848, 745931601, 337707821, 208831078, 954974090, 540567764, 370939032, 489262867, 641504441, 339088240, 139570138, 39975788, 389628869, 125545867, 631754717, 890086554, 255747877, 650581271, 848559023, 452416215, 573960961, 98374328, 616815509, 570074633, 163432936, 942333497, 873839258, 590925840, 889240704, 663174950, 675030995, 912886134, 774390409, 991836496, 240524428, 976949668, 640347945, 228353721, 735764927, 906787542, 639435973, 292962323, 248110421, 996966944, 973948916, 797434391, 898396612, 117197721, 961021201, 109217385, 569560969, 744482972, 550397446, 767214476, 242987413, 545485642, 559573786, 149513145, 844308837, 508766101, 788799181, 184147523, 226810346, 906256594, 655942795, 660447554, 905784792, 143272613, 59383058, 927852109, 216128762, 992102683, 820241999, 658439964, 283003184, 472607579, 696248562, 192982615, 542982395, 333517594, 89064946, 205922804, 268482853, 536584227, 412311207, 844163669, 463127743, 810726504, 595979237, 936739912, 496692821, 820537859, 504124126, 112724907, 392919504, 493344137, 537437725, 830032626, 196794722, 325985940, 400169727, 963700162, 718161562, 945350947, 78243112, 358538046, 479942671, 844378066, 576482595, 348138220, 490269139, 291306234, 648977504, 614041752, 811861866, 276655926, 84683425, 9872728, 818869778, 654412484, 896457787, 993726563, 89172553, 109553905, 281594303, 675432339, 291770361, 823475788, 358402538, 564991594, 535404474, 66170677, 342135077, 921755468, 285196994, 964385554, 587531250, 103695727, 334205577, 653446002, 914069467, 399807887, 475615329, 869544699, 102427048, 578510078, 362535288, 916633854, 829786751, 553272719, 699124170, 971248204, 942527502, 138998869, 16697140, 274930311, 334162476, 821108767, 663073812, 548675721, 173279238, 414163860, 146782856, 683813539, 109802674, 466484008, 148103876, 822370652, 613895230, 372233656, 66006756, 776227153, 955198845, 945501511, 609374615, 578464074, 197110206, 282974132, 669559480, 201371970, 202771568, 835117429, 556162787, 280127469, 742675046, 987797007, 906426621, 114624814, 289255121, 717260982, 572312822, 213346284, 512857493, 101887994, 929776574, 417081284, 760604937, 25245704, 333903036, 534598389, 62349129, 997399282, 712748471, 107964553, 710673175, 633831352, 30991380, 562108843, 620391674, 318272909, 979299146, 638709396, 681824248, 107582055, 42690860, 796078757, 624944489, 137138067, 21429297, 65739453, 596675190, 938917765, 549074731, 322527878, 591409889, 530593627, 3233756, 993745468, 70658604, 47157338, 985268155, 809040126, 391865965, 711351994, 166543387, 850948374, 735251309, 212986498, 190214438, 427699196, 670020912, 773428060, 778892559, 441147728, 590741746, 789633575, 943957243, 226223189, 520449200, 94762146, 396224766, 611776090, 973656532, 896242924, 281474435, 411275503, 964910705, 135493990, 675451088, 475728430, 74324318, 734527035, 957258534, 837121771, 127232386, 864693233, 756765070, 95474702, 905858850, 908740332, 794651537, 557876024, 396954218, 516096802, 54294518, 314213414, 832577329, 821016050, 590929501, 707214626, 475951878, 649166863, 662434178, 946628182, 545753919, 395420340, 892541196, 843546720, 183214569, 844365892, 405269996, 586787735, 199832190, 339925140, 743754755, 175359978, 807411017, 472098930, 191783827, 139644589, 989233827, 423436247, 135553528, 67817095, 955539991, 142049747, 958280088, 892121313, 382874392, 843526040, 646204734, 838406095, 125886195, 835354160, 611056074, 20277058, 916900413, 95073607, 91706156, 56661273, 777205695, 57628648, 521472447, 89576783, 769504764, 479674237, 959125512, 582386946, 455134902, 475983185, 925046077, 570130399, 828138542, 673621312, 979008660, 245841334, 524285539, 63083853, 122972279, 517440461, 509045925, 607908327, 397355730, 435804121, 205209039, 788956944, 582125018, 68505287, 104458505, 796082491, 462165163, 635497168, 599015235, 658468061, 220023930, 527907350, 657493801, 951012477, 848379362, 694927138, 193561733, 207068396, 82841902, 431783232, 514744392, 482852030, 795903127, 483831377, 995268437, 932292539, 441045059, 627981010, 405270732, 969426093, 806676502, 681191977, 219260770, 146867010, 651522346, 918151466, 163459986, 209046723, 294167673, 20656886, 136024234, 248724041, 513954735, 18523425, 541208146, 138990551, 438394793, 740462818, 234090294, 67165148, 333986232, 169630604, 719507281, 141649031, 319504367, 429741624, 287495023, 682055468, 160080299, 446366391, 379436198, 550303749, 782220533, 449038322, 112590394, 377047262, 533287253, 178809306, 758480831, 857665363, 122572198, 258004556, 62600360, 570404798, 486793511, 430960042, 493609311, 576530434, 409298454, 506342044, 279683401, 432597028, 737583969, 292331899, 414874901, 17791373, 772342548, 271727273, 129588661, 231399211, 626911524, 752228090, 752142604, 855024380, 546064805, 46887099, 870826243, 652502861, 977278858, 861756603, 160505917, 61430665, 326133433, 333449822, 47729688, 35727176, 189129278, 681205228, 986865710, 429437026, 41511090, 701621983, 410134708, 236971117, 868487644, 370509166, 554213, 470400394, 350122292, 673596418, 667228045, 316663976, 41060166, 414393937, 145297422, 924297278, 581743819, 617214286, 303843368, 691486036, 757560471, 757896034, 734605914, 68857053, 108646450, 764269819, 595166708, 220201725, 429664839, 548992493, 129079339, 928102866, 329945971, 934133719, 761764028, 388349404, 181856361, 699211096, 658436823, 427540768, 547662599, 617189756, 409757696, 241400767, 813900709, 655699415, 232413167, 437200344, 51401860, 32418709, 962967503, 630104596, 668131824, 546693127, 664551074, 534313626, 797005093, 523130070, 399515167, 756805421, 34011328, 481448069, 218895618, 169381967, 46409704, 901221443, 58039177, 549038300, 850513822, 56412086, 153831963, 866557863, 931191310, 517396245, 181846737, 466416566, 338465356, 796007632, 106455364, 946888009, 209014308, 707168651, 792575330, 629032591, 47679025, 781050678, 785238256, 538227052, 879896701, 217738180, 253791662, 762480753, 245171464, 764389591, 581681047, 322774705, 532917132, 753105093, 523444661, 784550086, 514467220, 791403971, 748642117, 181365974, 285304377, 482293796, 485620001, 661613529, 38031373, 775544608, 400144092, 909646689, 350968829, 259695447, 982760545, 866241139, 195514397, 488483995, 187311896, 339711676, 407783899, 594241761, 124421259, 414434293, 64532841, 283930340, 259017000, 629345386, 429048613, 861396670, 52093281, 283315268, 566284094, 162693184, 894535913, 102572532, 412464548, 64340553, 444790164, 495934924, 291440732, 395190591, 362763309, 659084356, 496590537, 116168631, 499595410, 822786921, 776895452, 295659896, 711357438, 203034752, 210997314, 986996638, 835426215, 822546507, 607319635, 667217741, 134968777, 286085633, 85731221, 984038956, 497614036, 67271738, 778532607, 57587601, 325091295, 918229246, 254341073, 410106517, 221380912, 858897593, 396143816, 678019342, 532432907, 697726239, 814259538, 470748205, 472060620, 887644791, 465487578, 781513287, 861973178, 330667380, 968406761, 886167965, 655525741, 236767716, 841059139, 83460858, 574915894, 83215115, 285579099, 966143268, 349189915, 165809005, 686915461, 82616313, 535327480, 364181228, 568286123, 140516566, 405076261, 485975280, 478648035, 882490062, 458303931, 404344913, 918495967, 641734934, 416634675, 840697065, 770214117, 345266311, 27825129, 360051847, 844919370, 49329882, 152228674, 323900221, 812060857, 868689092, 648827261, 132048981, 617668731, 354941562, 262946086, 253013815, 985413146, 527325542, 977031523, 692392895, 716954394, 269682980, 29885737, 611226974, 362619996, 432470285, 832235890, 362850712, 735475653, 234553226, 385704178, 576721725, 327797236, 748477529, 828150335, 363237269, 922194458, 793222160, 25127531, 310015557, 170406870, 907068535, 691338751, 114443775, 243987125, 836803451, 380375131, 918071256, 381460544, 627092272, 692731270, 144704260, 424303728, 364116871, 91821839, 827560282, 736655586, 376119809, 101361319, 156129810, 738058943, 634014753, 334432797, 143231237, 949154115, 144982224, 461925839, 291519093, 207917570, 843812429, 140119881, 575138008, 203132566, 447498151, 813378965, 385959157, 930673607, 570660541, 911755371, 858516720, 50115346, 84141585, 573920561, 379888947, 354724023, 519370296, 29047331, 338621591, 29568153, 597735719, 517175593, 736507199, 658794388, 654712995, 991098528, 107006615, 17648380, 992503858, 217747928, 873691135, 293371553, 548146832, 171170996, 966365006, 630645616, 642730119, 143960617, 280548936, 422368953, 619863741, 781404210, 285788577, 247238699, 331708623, 781111623, 594465235, 753088368, 442274175, 532116405, 395470522, 175374821, 586200984, 152417, 368532033, 560180092, 471867437, 688304610, 311729665, 453489050, 224198859, 629715442, 640403913, 408572993, 23549672, 110443535, 159406232, 897534699, 566112520, 882466928, 377270395, 318711675, 532817937, 985651527, 36712644, 263540646, 231945293, 139947589, 956478600, 346047033, 489552446, 555117442, 182094002, 678024655, 905324864, 886784440, 615060709, 394122571, 970266596, 37807338, 746961967, 390762139, 658848670, 82730646, 202681303, 648282461, 528215612, 10834436, 58018821, 668585065, 581591138, 808447740, 741483838, 705164819, 346004504, 966425610, 853763212, 721332480, 786095311, 84525197, 577843076, 404270476, 131154127, 727873172, 140215663, 292131725, 871031024, 306607222, 579313905, 520919305, 391692432, 558066587, 554389086, 141922006, 996895268, 164874220, 28024679, 196794922, 252525066, 194179895, 138700553, 20889534, 379152171, 885551078, 477547057, 877285267, 379340455, 163351116, 508240221, 232990254, 786451117, 237222858, 856528542, 930702212, 695787935, 357386028, 822549455, 145329061, 45005207, 775593544, 753622910, 259410350, 589261453, 847316010, 620351598, 98719215, 147409713, 885845418, 92953141, 475839332, 159613629, 464766512, 141470204, 137312810, 667478440, 364945614, 287148673, 584287504, 588440736, 846393647, 9219100, 288807033, 878235360, 645610631, 47959639, 257850963, 740814617, 36772026, 848432008, 646822939, 21016696, 807562957, 809930489, 365855088, 701137265, 591909064, 19103895, 319259713, 833679767, 161838233, 865807068, 710691362, 793688657, 633677347, 381566054, 575291253, 71316601, 408850303, 98175469, 821963379, 755604397, 212685248, 587770765, 736087695, 580478, 107767146, 995989274, 823421982, 905422028, 746333621, 374948811, 579280526, 657012595, 102470687, 726643469, 430339080, 374557723, 620014453, 268453628, 205587738, 930967710, 327385548, 504767594, 419639950, 259849838, 963794464, 959140873, 48000450, 525636415, 729501724, 930113726, 728566788, 539562667, 381405949, 469020161, 864975000, 522822393, 288663983, 989832967, 95985815, 129702497, 456863339, 714200460, 968164439, 169125100, 244725327, 832881689, 17159390, 449904665, 45147252, 226795721, 211058741, 202407387, 204194050, 977905600, 79599177, 782783756, 384318079, 171985481, 139879128, 798527139, 880851700, 748586792, 267748183, 234003478, 749092732, 723206164, 951005948, 368285423, 559733911, 908684668, 216264560, 420237196, 812611456, 960054909, 527571108, 886143236, 7071774, 8693149, 556057369, 607272322, 64810080, 470068144, 999094416, 429556180, 375423988, 565508167, 249842334, 914225126, 998922392, 179382442, 651434100, 146257214, 476772787, 712319663, 543482020, 386083325, 769999020, 180390862, 547079712, 52090884, 347244102, 957962067, 71488402, 948646343, 140068618, 680621552, 263034404, 375439472, 245140382, 810911244, 195994597, 271140265, 82859249, 963829027, 315219347, 946948192, 864767856, 464604234, 532706650, 261106510, 258504307, 932444514, 477485250, 873354886, 496623653, 760225738, 202255800, 154389741, 165065744, 590914440, 258385392, 150884991, 388815091, 711215884, 518167916, 692415650, 226175509, 323976120, 991939798, 865078889, 35642452, 411940880, 821875692, 381212242, 290232459, 490904944, 1407450, 406040276, 44280683, 133159237, 823164318, 992564108, 732308872, 470326020, 339763872, 913821955, 548349723, 678154625, 268532189, 220015664, 725750823, 380111283, 511300692, 780426346, 557132367, 836001182, 258436698, 390620164, 698314426, 433911590, 980796204, 811639663, 904325998, 474866276, 193780677, 625592141, 133913770, 929976234, 806383656, 93143164, 640355342, 171092491, 965896329, 388447804, 162673613, 719270371, 717758441, 29596570, 38452581, 593670998, 964153563, 146746491, 100445421, 133455962, 504849557, 227981878, 874459098, 861932652, 541348621, 168298263, 259585208, 87622990, 142156701, 448313407, 819392568, 11015933, 445991876, 93719616, 207395266, 464616412, 506721764, 983172656, 957967010, 774377459, 873416260, 414455526, 149461371, 289135835, 969272078, 999153117, 33484815, 974147073, 708261260, 187645423, 183963679, 914787523, 182679185, 337239552, 884568484, 324686496, 74027437, 737626465, 201780011, 35992320, 390327235, 795430768, 477781806, 889359984, 158011524, 771965315, 297672083, 985076039, 516521494, 907085004, 681232237, 818780629, 64017726, 432834742, 699237263, 168658277, 165669909, 356349048, 519750621, 214959054, 919076869, 687944029, 616710851, 278979387, 149613383, 99793501, 755177718, 396901934, 100119662, 780561105, 797031113, 507049993, 495464558, 282454406, 152909509, 733514454, 985614474, 660762402, 27500159, 780364676, 768843061, 962895763, 649634485, 894881667, 592687037, 492516522, 257947425, 188608335, 15482077, 769985813, 628568831, 301845929, 105554984, 530965215, 25764774, 482114743, 503646604, 843289064, 548178385, 955893424, 193993778, 155860988, 749696062, 887276489, 821672800, 201541544, 669479234, 342706050, 647517849, 77012944, 933164138, 372028747, 782725787, 662102275, 312842957, 457045723, 433573021, 304935158, 676772342, 708042406, 655590214, 29853011, 32162283, 651767331, 998382698, 44443900, 24031345, 342412328, 611475445, 388103168, 469618966, 226620018, 653400068, 918372100, 161637964, 273339154, 142434231, 540371819, 377943543, 602150005, 920403289, 78714989, 721606356, 237103604, 960755316, 771875217, 91531079, 758207026, 978770602, 647351805, 715241347, 787980764, 997359648, 923257810, 292631362, 341535664, 488107851, 794616143, 728023909, 679711176, 780857726, 931302714, 473906615, 211181369, 754408236, 767462075, 647290531, 598340187, 616824632, 245769265, 845344735, 775669233, 374848171, 298297997, 423098154, 868845880, 856598761, 225584755, 8570440, 115955611, 201324294, 540093180, 742042471, 695013982, 968624021, 742365406, 322616198, 420163284, 214555766, 224202494, 921259815, 413504961, 665404002, 502136909, 13996735, 427311614, 920364096, 352518400, 589254396, 797690558, 177046280, 796621248, 260896726, 537538480, 497958290, 989434996, 355495362, 5340975, 871419512, 348688467, 426306852, 543898606, 651456475, 448477062, 993085100, 31518167, 190169837, 602200899, 343074105, 227197018, 744661193, 199005193, 766934459, 988287532, 31273888, 106016487, 244664570, 196387891, 160224405, 281702326, 770078002, 783476714, 642643109, 328678605, 759141258, 101318181, 87571847, 232063176, 182385447, 129002617, 979543059, 116496592, 128561, 482548962, 226534041, 438037963, 632226951, 24187818, 711401956, 474963112, 151054121, 984513973, 96193316, 438539945, 20162629, 43325507, 274399939, 242201168, 185404073, 856419802, 985479083, 649367315, 113903647, 143447188, 727474955, 922772425, 431293850, 803780420, 758082715, 589982827, 211962448, 996573593, 876140579, 129116860, 927773370, 723689262, 894529371, 270268935, 174924723, 981834088, 530356675, 726115753, 239491265, 944622696, 252493658, 752325157, 170041767, 685787489, 304713645, 890177555, 712490271, 617680751, 523191657, 154594845, 876802622, 906702277, 470015673, 696240949, 928184447, 865493930, 355182458, 949876846, 635076645, 236746189, 461056925, 927674547, 862304461, 649393501, 402433306, 661640704, 231525170, 69840319, 675435537, 428490294, 926838401, 118485557, 582973756, 251524547, 994846897, 565322655, 422368073, 913980181, 946253730, 37141569, 303728194, 475970097, 747563796, 172946131, 963519182, 816526251, 247891336, 781524009, 437478984, 96665565, 364420912, 233297432, 801352528, 244855289, 991160613, 356869442, 131022908, 241723606, 781182096, 556634802, 80995046, 604677312, 639095775, 757617301, 747860744, 753667841, 309525322, 933265133, 485064810, 945096549, 913767132, 904255918, 899731535, 355540663, 721242881, 538098432, 256116225, 955561262, 343537452, 601949399, 344562064, 911127107, 282282333, 950656441, 404189206, 613865780, 152494926, 616201849, 729539347, 520075874, 553833551, 197550917, 353354682, 519527221, 661564796, 487798375, 552228187, 498432002, 319224056, 932904021, 971564071, 492944704, 768020464, 31116079, 325113081, 151209112, 942045199, 133354522, 526240205, 228641343, 541211746, 883299384, 484408871, 248464256, 41403665, 5592738, 590693383, 747116270, 854609159, 318044830, 882937258, 106331281, 771758496, 110293201, 551411611, 387843995, 810586929, 525155659, 603450933, 33824165, 214189884, 402398660, 260691938, 986575425, 492864974, 93895333, 507148147, 927013965, 748358555, 426943766, 849982494, 809884284, 653242951, 210629373, 461991386, 716219801, 808479312, 159399692, 413422871, 820785810, 999644153, 22300008, 203057624, 584341278, 117474133, 952413699, 464112417, 232724431, 926832080, 237403522, 130622039, 440172749, 845626328, 842291708, 689762911, 878667469, 765010167, 856992353, 319997564, 193202303, 347966783, 412781083, 497760063, 840676384, 775522703, 129386558, 213058334, 290387644, 318626469, 767012993, 419674953, 904591856, 753563270, 990323755, 83915961, 560827309, 691331824, 677711252, 469174786, 892641208, 549513336, 528245776, 924472810, 324477857, 348530289, 326263792, 249750577, 713161089, 897443099, 348724675, 208501362, 820614770, 851851623, 67265263, 416226234, 990089476, 412698872, 115617605, 949706213, 429408820, 899850607, 893010431, 782878034, 873321419, 430624273, 575962955, 925804707, 945817735, 141151777, 490234108, 739029818, 592836938, 857398879, 945635573, 309492931, 253153513, 1547157, 229732008, 933931849, 40496034, 644163648, 4973039, 351139662, 579348848, 900665097, 752606202, 20005639, 596139061, 510909576, 698312956, 411000142, 946018577, 128361769, 597947667, 873272315, 742023170, 256000771, 898987967, 849958295, 479625204, 199255169, 62090864, 568259375, 805423645, 369587798, 765634156, 186518455, 588529472, 925595762, 296786227, 163959932, 846987714, 145199359, 615230932, 442785622, 505545881, 722615141, 111046529, 872615462, 735388462, 807640035, 80747728, 650899878, 576640043, 734117891, 191899654, 957687339, 637125769, 401648559, 835670338, 342383928, 126111708, 247344650, 613820530, 708265162, 674031201, 960845389, 895318125, 646712201, 67586599, 628534531, 653081507, 240569376, 278929289, 819015653, 441470893, 441022352, 205666890, 82758357, 239421893, 19470622, 771460950, 15221807, 150306519, 902483852, 212175181, 133050532, 915217063, 20256946, 151983242, 126342818, 247516029, 398222792, 107566022, 527301453, 388507665, 621112232, 838168846, 709634957, 782260177, 882391882, 390639657, 857485359, 819763177, 307810943, 674320302, 673812244, 720146515, 695310336, 963312041, 704950977, 976779264, 409419826, 72221616, 201244527, 636768114, 203260720, 181153571, 632581751, 214142639, 406926819, 356703939, 513658605, 921768691, 68596680, 867438491, 687455210, 49675410, 992451208, 924861807, 333603494, 152549153, 802464894, 898795947, 150012056, 17242861, 75869438, 872422976, 302754664, 625122900, 725118563, 239107644, 97948576, 324475840, 410532790, 318917498, 970568114, 970105842, 753033718, 746992037, 482247597, 77270570, 887076573, 921075296, 433717297, 106527411, 10739840, 206322890, 505429606, 478687641, 793624192, 263657991, 934916082, 186144654, 68748866, 241174410, 338108163, 446531893, 78204403, 720735355, 785197721, 153840116, 647606065, 786779061, 82975732, 723169747, 942251794, 979547998, 800490452, 882253173, 926368676, 464365593, 503529597, 269160289, 253072388, 933130720, 935042861, 669545896, 140679259, 840377112, 364820494, 948656047, 508778319, 112774137, 686515534, 220796696, 790569820, 742819023, 631107300, 427275150, 753084268, 874910684, 595237650, 528845997, 369040243, 706701018, 751469831, 913815395, 793231092, 924516957, 964955140, 665535247, 73659304, 873769471, 52205546, 75640183, 424002834, 461425154, 342850683, 116718400, 410867861, 672839199, 766571630, 70576832, 389510974, 259238905, 142675419, 153860144, 592851505, 474680094, 728299931, 445174852, 190353462, 464543665, 987730938, 614046575, 231549505, 583690380, 9933570, 323587044, 558456970, 332869583, 570122814, 22943496, 702554138, 652879872, 484456073, 272248327, 199514577, 376328825, 738015364, 675012177, 909870187, 103101547, 605173310, 89922384, 274455393, 405797628, 600324207, 594042935, 138425612, 43250873, 408608355, 694940097, 84849658, 812955840, 295189074, 517165671, 701419514, 564862251, 529848233, 941994112, 105831371, 475631044, 223834261, 105806408, 459662178, 825054625, 209773285, 786110437, 762702130, 759730817, 402679799, 48938152, 198137906, 465166348, 93632897, 430988921, 656003393, 128385429, 206770568, 428883109, 604144377, 220661456, 438792780, 158239216, 6580504, 510214094, 211246417, 573260222, 626631167, 281333966, 503436437, 460377082, 58413167, 12347819, 640293717, 109448781, 351537761, 306646746, 907837507, 695463339, 640571747, 310942116, 162238985, 30472074, 625689213, 335394722, 988168357, 682665352, 512115735, 403233154, 749249794, 900653479, 3452698, 868809752, 343551795, 346866168, 515619623, 604017427, 745066806, 251827794, 832820755, 472988113, 749031577, 371127861, 541630462, 477288269, 965760100, 912186871, 732125972, 185487848, 218191643, 574014185, 277054511, 704782816, 810713342, 379841468, 567781684, 674797674, 820247441, 476769668, 715044029, 629942873, 42125571, 60611504, 792220027, 58775095, 829918081, 973155802, 332491452, 40758347, 318741171, 118423475, 569989085, 898209374, 344165459, 844590039, 244395599, 25707788, 537775694, 155419256, 664987795, 467801088, 334918894, 592626070, 167521021, 730001938, 324181399, 966325909, 613296675, 346222016, 957914852, 935119884, 36949473, 236641462, 574148442, 804788011, 250692110, 377840536, 969264937, 283116909, 99131678, 82884640, 545029275, 142064796, 288458490, 924747178, 385944163, 647328030, 201253059, 686635351, 758264065, 111797593, 469154286, 576509221, 99840491, 479542317, 203878465, 484553666, 364287254, 628541923, 300604552, 431730287, 892288970, 69659510, 992028380, 851301748, 509394386, 956346697, 953565075, 769708515, 624929033, 345409752, 254977344, 336724172, 868498283, 9949625, 95371944, 408889855, 5678294, 191874068, 637841315, 985170412, 294958063, 830012695, 232134630, 218403841, 698315369, 484287884, 993677609, 145844921, 30948706, 587676842, 307585365, 580388270, 107603577, 968120836, 282099036, 655411329, 116515711, 93432414, 312083228, 161289008, 63585744, 470470743, 380849202, 930719100, 5489334, 94981390, 10561062, 964408361, 843769215, 439437375, 298495329, 87644648, 941229116, 852242870, 846146132, 740201867, 991242706, 141941567, 32155208, 245932014, 493872421, 184989284, 661013745, 834720531, 662501225, 483620847, 173537887, 379485512, 480507486, 147513230, 346989242, 651910831, 682397320, 594012708, 840583128, 163007017, 554507692, 713268846, 801216019, 904389442, 913850110, 346890608, 486114739, 155860142, 106550774, 752865584, 266251270, 199268053, 50992587, 293629146, 219199302, 879664935, 481944718, 298743266, 149110792, 447487771, 513434651, 257670968, 411163484, 815261264, 327151051, 756093827, 383743201, 406158065, 586942438, 598159376, 953338691, 534385885, 984086712, 802539839, 568774155, 375214762, 404939601, 838946562, 348242709, 462038913, 644611046, 938318505, 454134060, 954020577, 721514693, 57876470, 172585251, 511887472, 576346902, 433615102, 161247042, 887650034, 922475829, 194421916, 729192090, 813757337, 422989599, 420725900, 842670193, 147960985, 366360614, 610705331, 529068758, 245979387, 320885595, 113432889, 644312719, 598413453, 397574167, 796753825, 824571152, 108654452, 671993842, 991065482, 83046734, 552664952, 514121778, 752001883, 751575429, 323148925, 195724064, 720807705, 272309867, 984514618, 751692308, 644478119, 918230478, 175857942, 655001231, 16236467, 116756811, 500181354, 505899639, 449526135, 165662046, 569240875, 212718095, 105870719, 242486867, 67358583, 909526625, 99834335, 772116664, 877007375, 29735686, 203850780, 729698656, 88253009, 664537643, 316612469, 66000101, 945949989, 971566713, 465156126, 466327192, 293008335, 830341128, 134138518, 486217140, 377245794, 852696879, 129037433, 837158344, 525789105, 684739031, 177355016, 645971150, 442816701, 672543596, 292724116, 540194570, 11547074, 539373897, 150126100, 140293354, 568442966, 140991611, 75662899, 142206280, 481581217, 591692025, 995944168, 137897969, 509215222, 41020776, 897363613, 103798584, 753157608, 967665616, 802420193, 630521304, 652054498, 746858380, 711937227, 389664413, 187503112, 56452317, 204095613, 934426610, 641436816, 744694860, 585609891, 170572551, 317432791, 622152526, 621950688, 960131307, 826157660, 849118357, 443168948, 267902951, 486843495, 215589771, 763149365, 526585546, 935878217, 815856864, 672421276, 929804616, 809871772, 80043523, 428399960, 598818922, 325429706, 223608652, 9759013, 343303133, 368185047, 324406196, 390477761, 890632197, 203199553, 623062676, 368919943, 61045529, 454665470, 634225351, 78158588, 898248405, 358928066, 150259685, 578365864, 888694896, 563258611, 653822968, 947561908, 21135500, 592209238, 322371934, 853508245, 337978941, 90722259, 396667990, 257316267, 724580684, 30243925, 525344942, 714739789, 459974406, 443576615, 956230120, 436271009, 779304411, 152556296, 348240283, 973455293, 999413787, 11210592, 544646829, 362815541, 147816530, 178165657, 502823960, 543789165, 805195365, 111107490, 67078418, 979178596, 149354512, 460429726, 138259169, 416744287, 689474310, 309998352, 259790010, 953637081, 823828973, 988678409, 757594397, 497917581, 907411875, 948395353, 863635737, 823907791, 636187909, 695076900, 931292149, 531839905, 277979451, 334853349, 188186669, 905097663, 345988140, 935257656, 252588359, 226326749, 856077500, 596265602, 610283051, 865389404, 722733603, 797431808, 525623699, 957281328, 334656148, 615369721, 256426723, 288008514, 227513678, 538561824, 697841587, 575135146, 707275604, 537138449, 604493845, 724105167, 229802032, 813750412, 68269876, 900673652, 670263599, 155633094, 46838459, 883402568, 209404948, 881681136, 121145588, 739631731, 110822163, 271599669, 783006423, 911366472, 836143383, 392192247, 967352177, 625758740, 144768253, 934152605, 831644969, 908978540, 608272398, 432669543, 668315353, 469338027, 777219556, 187592946, 416372276, 710079331, 521957661, 795049265, 523076796, 796922353, 225123564, 739496730, 182723363, 980276893, 896389075, 306908631, 991836041, 949168778, 581264774, 28196686, 672574560, 984281287, 671102670, 85930263, 587975844, 438276274, 978444004, 830112239, 400827027, 375839379, 760099459, 707510358, 999921960, 565034772, 299034700, 984808781, 255682093, 898092530, 445794625, 330780069, 232416841, 946680679, 530353592, 248873953, 905537847, 911648469, 291383340, 568012674, 145028028, 200674859, 371982575, 481955440, 216242895, 331268259, 851546983, 200921198, 384209780, 16639040, 778598266, 844619259, 137976342, 753522419, 742755167, 797403476, 796044063, 970890315, 936954398, 717269069, 783431082, 288786960, 113290666, 40597570, 902518435, 863370083, 319260211, 343121870, 711229445, 62473178, 56750743, 783191352, 387590076, 472277087, 680974383, 168111970, 282422902, 748174994, 209602643, 383062316, 416082822, 136075006, 566065769, 14238990, 411475706, 856631008, 375177358, 412906921, 853588652, 758656110, 484546579, 471885963, 522734932, 30508481, 296086885, 966643845, 591831357, 986668911, 688092229, 650257349, 439473748, 79903910, 3383775, 397266767, 379292585, 692250305, 73969434, 460590391, 486381233, 365512890, 679538200, 786192934, 407269657, 56976890, 473135234, 405307531, 956613804, 339070052, 481321007, 849366262, 515836252, 980737501, 381164233, 927520607, 606039556, 807810287, 684031068, 780771359, 900522437, 14488558, 861806889, 618495260, 558208064, 550775679, 461889668, 210963444, 160136524, 267582451, 611178150, 644681440, 82541707, 736678950, 193691444, 346929459, 895742054, 97478023, 805688501, 616563045, 288186568, 434196948, 666624414, 69285982, 354760546, 892604100, 88636388, 971813263, 702577602, 481916444, 726328334, 195113551, 484483591, 18047906, 527834471, 535706315, 981551641, 767094355, 382574314, 866727221, 746880109, 970317088, 959274053, 607223014, 258228015, 308781943, 167072260, 916002421, 304563939, 950303943, 699472785, 926671262, 885607874, 146885986, 159894085, 644343615, 802467284, 970871865, 3830987, 474108768, 234076817, 224790923, 302706292, 369259016, 77160329, 43750306, 532826086, 321758865, 938156922, 517675134, 408891506, 746545810, 509988080, 964518252, 961223791, 795156390, 978549271, 613162120, 250441867, 498940954, 652120594, 474029164, 366646277, 454985608, 4927120, 513372127, 252506289, 908085742, 658232871, 883462664, 348903282, 280628660, 297054171, 195136370, 564032366, 679003884, 60246184, 447110921, 715841910, 166043546, 516101629, 554216535, 59074950, 573138386, 293032144, 796098780, 49510914, 970209917, 877131302, 468020549, 693778350, 281293615, 695155013, 254342913, 317870606, 545168751, 611777514, 880952105, 119653122, 225337995, 930213346, 407292240, 488502578, 250869921, 272543839, 782712648, 2539727, 767597735, 932719970, 61318529, 86197349, 357874217, 819074971, 692609906, 895672582, 872731152, 902821830, 468183863, 105556474, 788163177, 74040927, 584166410, 507186554, 586760479, 984317772, 848970391, 494991454, 103973691, 124459131, 542945782, 416349179, 57055850, 51435631, 821351089, 455916754, 97530894, 822904638, 837199972, 666554337, 534811072, 321872633, 890548518, 11863822, 372375609, 814615862, 363510693, 513612892, 105628682, 652519540, 905495481, 160849493, 815442645, 94521492, 688813315, 990169761, 897526458, 192702916, 545276715, 486499885, 126423804, 624529028, 323106268, 276749589, 962857882, 381780674, 698203794, 162175158, 159714067, 818405866, 668567189, 476524533, 202447466, 311107450, 156900763, 689950779, 20656092, 339691020, 113068666, 167502445, 695720155, 185850363, 789477515, 931162747, 303664693, 77025847, 344441308, 14877792, 385943945, 469748289, 683586939, 839374405, 876832150, 74569086, 893293476, 572614078, 793642020, 897575861, 370638568, 576605872, 25549689, 767026165, 565371158, 204487247, 536454481, 195101049, 468532037, 672111571, 678584331, 568417029, 46367774, 269547958, 754866196, 951341167, 274328187, 172351686, 150208757, 142041474, 339264452, 294374676, 875898254, 730125966, 190644337, 641319707, 627640261, 921575483, 859923718, 770291741, 907371322, 567569906, 580454954, 814781907, 581784593, 319064536, 833123845, 952284081, 956124100, 184313832, 504432849, 367679281, 237791530, 714215107, 821263811, 284889452, 407847974, 370287771, 979595281, 291874097, 33812799, 221816765, 197877247, 455971066, 161344765, 365895393, 428613799, 640143061, 950413162, 220976528, 440223551, 913196166, 347892614, 633273256, 333048562, 578708157, 290695892, 198193541, 571275802, 518739863, 88253040, 71801888, 521626454, 42914740, 888850468, 400510217, 786811386, 505265937, 665414124, 116699090, 470277048, 423127613, 503364274, 776163351, 533319336, 913964215, 866110575, 774646494, 16064348, 265413255, 808265649, 379190526, 320274251, 670565942, 396084515, 916068558, 726835715, 457006600, 735764585, 861261541, 320494234, 813814862, 677272000, 466981749, 262726316, 554292563, 775172137, 286155026, 814824205, 992637032, 823520839, 996863918, 389937061, 234112346, 667440617, 207657643, 730929816, 601066343, 8043049, 96776870, 535048600, 912949322, 66390809, 65708312, 624482061, 52164257, 321842970, 255484174, 703195203, 398561472, 163487784, 851549688, 864873121, 480656507, 582845302, 813752889, 357767936, 493924769, 353084239, 927202229, 952705477, 7853379, 112043541, 110606753, 400638346, 518274109, 528240095, 225432705, 774180833, 984780578, 240180588, 76630252, 389874718, 54548500, 780135211, 987547183, 243802733, 172254023, 763165411, 392533180, 857985665, 196588010, 471076833, 789666335, 221845544, 732550253, 351562812, 590119415, 640146665, 791588949, 769755945, 325742953, 934210620, 662458572, 114524747, 425022854, 364692970, 714124086, 731159034, 899655345, 292521457, 851972293, 417715961, 642114140, 639251887, 107132869, 711704332, 570289469, 461763970, 421554140, 346906711, 929858781, 110509316, 500620643, 836093027, 62468449, 985247871, 511144896, 445059516, 295208034, 781351980, 315449395, 695850883, 402604029, 370348843, 571957250, 989985850, 105765090, 999943481, 709179748, 888037139, 917558103, 755584065, 134672592, 507289272, 910302404, 924858728, 188942378, 204027363, 282215419, 792613802, 417863021, 121969847, 710279246, 4595801, 755546478, 194635665, 187952915, 477923366, 941362653, 601581443, 485140183, 954732979, 285060378, 66506243, 733238641, 177856708, 373405843, 56845826, 121887298, 564819833, 658346435, 633919404, 417508033, 92056398, 842781271, 640832819, 298273277, 634463180, 556589452, 176538960, 687817959, 224004893, 447513643, 513177950, 172406076, 331715239, 187371872, 969055207, 953700548, 291718649, 20007529, 330540310, 391890088, 436380265, 106618311, 998141293, 256173877, 396366450, 789594887, 47204550, 385254091, 668527107, 81179671, 521946650, 960137809, 776442597, 41926497, 513667614, 26901795, 705482055, 175170223, 283977813, 633207380, 794793607, 619889671, 200499146, 451008284, 697063230, 825695717, 336198777, 457308077, 606769822, 346987973, 875104643, 884912912, 826161877, 256859770, 543132074, 675171473, 4739853, 190257080, 157922704, 864728094, 44007573, 608360831, 7466474, 352718365, 943318553, 758534786, 48806909, 300430354, 173931995, 315730619, 305359694, 188789515, 939367072, 506551009, 188661179, 196267266, 957548666, 603516395, 214804842, 65823341, 838488430, 42422448, 746683808, 841657371, 938619448, 678237037, 331354703, 775990532, 361829042, 56790237, 357811161, 165511975, 298209833, 602092199, 32412939, 226304135, 661772890, 168017618, 713741860, 225667866, 610869548, 787916132, 380708460, 272196490, 519375613, 773882438, 564468199, 243380107, 545273073, 585088210, 559560448, 481530538, 985479790, 670297634, 636216263, 733320158, 630331372, 868287059, 979740184, 228039970, 412660602, 29318342, 866259411, 826872522, 673815948, 152994720, 647586182, 275597016, 223691333, 813004665, 33338985, 26336380, 196752943, 170710146, 651212992, 572898906, 728188377, 273206207, 229366571, 773786958, 608059578, 737469530, 573325586, 157967581, 325378149, 89657791, 306578902, 26267739, 59951323, 162264743, 811793158, 218955036, 234728613, 978350689, 502391283, 414627632, 581004719, 481964463, 503177588, 623273958, 515762524, 958665856, 745016337, 938670822, 929901708, 857841141, 991965995, 132872714, 967027058, 926329257, 882206291, 225518800, 632873974, 846108341, 734869866, 79216024, 884719299, 425766286, 880723767, 852565045, 959043655, 806086733, 747464827, 860269158, 761449231, 163169121, 397503104, 552652012, 427368098, 294532438, 398398092, 859757078, 552900516, 656727606, 715922442, 800253083, 289492800, 803788544, 513912199, 858627066, 66494801, 648416182, 744359800, 780975456, 377020429, 234406108, 566852064, 775085555, 463026963, 712124099, 230763957, 705501257, 200807935, 655174056, 753814679, 464359622, 139885151, 190679639, 13385808, 579300460, 703061798, 547006495, 951495570, 533412846, 563228293, 535679899, 527404995, 231868091, 565923086, 686133749, 846261167, 655369702, 801026081, 325968015, 698417864, 112445859, 437090146, 428342993, 17260156, 2971987, 417978290, 962727323, 541852805, 640816950, 788221788, 259687010, 435702330, 46993806, 73644058, 846028147, 325539428, 402789280, 374473337, 335926996, 649351598, 991195894, 556563497, 495539098, 946705386, 591216794, 792360437, 965922841, 125462351, 478017126, 366898250, 289006042, 510256219, 997580757, 396608416, 638652087, 214157267, 745554920, 539632808, 215323488, 312885434, 67668948, 339865541, 4500306, 731691405, 568522187, 438318442, 355647726, 722145727, 878529665, 398758702, 297061900, 770689330, 549189589, 335148876, 646465055, 616688517, 687558930, 760356756, 249862403, 668514803, 580974128, 15222471, 471664909, 221030172, 197614313, 755377547, 86150392, 514227100, 937597968, 579533181, 414063233, 460291113, 654362756, 36694296, 215273498, 306317561, 753566644, 946549440, 708319452, 509276613, 135562864, 470125082, 7472704, 947176561, 362226529, 960608361, 523138562, 297727255, 832324665, 612769676, 214301724, 561045355, 792678864, 497003699, 455799316, 248124467, 775673424, 84328618, 810892143, 999935026, 439472871, 939717016, 964542614, 714032840, 917296995, 842553071, 891524831, 249173163, 371758335, 294413015, 242725373, 619189341, 942485790, 243007252, 369008414, 180291185, 538824766, 389467506, 902846795, 60092237, 557920568, 41455747, 855351292, 630845215, 363346443, 153925651, 405883037, 279656354, 624887966, 680963241, 27929697, 550528366, 616917298, 226755816, 456337620, 337959828, 56679551, 383172059, 159790687, 73608942, 642019111, 126402141, 49215843, 546640287, 786910323, 298568746, 307060030, 484433164, 122366332, 88896028, 638870247, 291530446, 168119178, 415428349, 638741436, 813032275, 72587618, 337242669, 281591488, 579540078, 537940643, 38109535, 471862293, 798447785, 411712280, 916335421, 196739563, 588360368, 48941332, 617715658, 994540076, 724096278, 459275029, 622619546, 155992868, 289436276, 85379287, 411738582, 629206008, 286385121, 262528790, 770590393, 916417640, 501513207, 469276038, 34797943, 775425482, 862271702, 460271812, 593384320, 106966539, 786832195, 432236696, 700617179, 646016441, 487332995, 533740706, 207910533, 772560750, 677144286, 139750799, 906007288, 832211795, 971101085, 2342181, 611045620, 50547735, 398544312, 487965529, 842151292, 767813976, 393089368, 952260988, 997855882, 785621401, 902340912, 864229347, 254475970, 511966575, 561140959, 193877616, 906119679, 165806965, 349282787, 888243586, 185560745, 142955756, 151783209, 60741261, 127653416, 436601548, 312268055, 181285041, 725589799, 673375062, 484438283, 450808716, 511419403, 140193506, 569450614, 637070234, 356715799, 924374080, 543433185, 442515469, 829270536, 167795592, 657458182, 651917484, 701586993, 269008382, 660509368, 348023024, 307598919, 390451191, 789131603, 923357303, 806946627, 213713163, 269178489, 73876988, 211118255, 415994634, 525183039, 476115693, 590688183, 460946750, 325981126, 786909566, 709892613, 877676056, 206700541, 81555907, 950930945, 713422494, 11432052, 530029688, 924644212, 452858539, 747198123, 259179749, 69520704, 690258644, 151610410, 76277782, 558586364, 863574974, 576701821, 816275322, 480364551, 710873174, 803656051, 613576376, 404702594, 246627622, 269793279, 215212593, 876841038, 646332546, 733980083, 195368891, 682449154, 145883845, 121574315, 931471873, 425408065, 677797924, 887080872, 125918861, 597690077, 857344985, 603196594, 683424863, 139875589, 16576840, 891373630, 797430476, 690148049, 881804089, 781697486, 825857742, 185532518, 741221247, 75192306, 695587954, 478481936, 847661627, 649741252, 969746773, 744797913, 532842567, 395240301, 833413010, 702356679, 568577746, 333149948, 328379250, 618555334, 203943428, 548641185, 556167743, 74948239, 556786245, 172086189, 853849650, 319030934, 614444754, 729877116, 64331871, 16446676, 322589714, 800660598, 419817948, 901126116, 497522627, 226029018, 341449913, 444576809, 779192338, 80702753, 793261906, 142896651, 385945900, 448907871, 316653546, 104980344, 282372895, 456531023, 458989402, 520740530, 952920261, 881986034, 844327970, 959136912, 243346501, 391584946, 535016610, 78576272, 144282709, 36405422, 901196619, 105604352, 207247822, 797962041, 153116165, 387693738, 684474374, 649276134, 57941686, 794733722, 558401053, 198847922, 29234033, 237708665, 394173955, 167880739, 508821797, 677500976, 343668778, 291521594, 359207740, 971074481, 169940348, 492640329, 468732870, 211083919, 365128403, 560744977, 281123918, 696003793, 157596743, 119683067, 406461433, 471624045, 929164149, 990486528, 997837027, 453837576, 755271353, 498236118, 437427002, 417749385, 732537243, 453445579, 828101685, 647871408, 322447340, 155349120, 568842411, 848091077, 221222658, 323266337, 426776811, 886577296, 8908979, 262578272, 193329368, 937834553, 514693063, 941171407, 467885314, 950997545, 63535210, 81053498, 353951314, 575212455, 339437270, 275485965, 51881774, 357972323, 401942311, 830918529, 417068681, 498607328, 380403725, 951420952, 974858578, 742750700, 95070620, 2151249, 521896932, 404990990, 337746684, 317701230, 439063184, 102744971, 5044691, 112590599, 267959685, 252620620, 812510024, 296264512, 839360575, 662998337, 658716606, 648835129, 844823198, 332835207, 83384055, 854009963, 742123123, 486509515, 231796569, 433574803, 101291575, 534489122, 464463659, 957335034, 80217972, 489109475, 284372965, 43494317, 956493254, 771914224, 787984559, 298119481, 719280820, 575814798, 962507740, 486933665, 202615337, 515477513, 706899062, 475987853, 948025661, 917700346, 887689834, 188508434, 338958219, 258271006, 390638669, 949070380, 691830744, 124581915, 802469937, 481399615, 185124797, 816187624, 547983215, 53969052, 852286278, 99507300, 432130737, 9876997, 516083190, 500519772, 758552010, 885287773, 765512551, 709057090, 90612982, 791039851, 563564736, 337324510, 136301212, 144890509, 784269293, 323717799, 64348033, 816111569, 907791957, 504076286, 961983973, 704396913, 372929826, 201371499, 566089041, 844099713, 822100104, 695967955, 16094191, 134598222, 334666275, 252811092, 727821817, 729856376, 854197532, 478291594, 599790732, 253039406, 313472477, 46294618, 644534575, 209697269, 142774856, 234992444, 93829240, 116916564, 868604579, 546289357, 765166553, 997968665, 205521262, 804965852, 869394939, 898670695, 53924070, 516616743, 776551133, 479042331, 388415330, 944828430, 380512368, 972765404, 121734290, 483621572, 922536183, 618377658, 617639226, 948477473, 930710119, 431989338, 337702891, 929951140, 855724542, 149940187, 903455747, 350303441, 144075780, 715826, 995910945, 951926371, 455182826, 508621339, 535175209, 739531894, 557722610, 758831802, 875478135, 343816242, 694262423, 57906236, 328801042, 266655362, 932221640, 23782857, 471375687, 753275655, 703972514, 271823077, 991876501, 549559507, 467879982, 54031170, 239779398, 950888725, 938434403, 232050506, 370509351, 936519252, 816783572, 299270382, 35718661, 665451963, 112026289, 311687785, 117441301, 967270790, 523472030, 4534533, 61447221, 877893635, 652986316, 654991639, 246587108, 841715663, 300455933, 780801180, 467478888, 285993307, 538756223, 68990773, 43209821, 626895356, 703059328, 954515271, 297136425, 916353849, 993269732, 90241896, 374008208, 385663764, 817537239, 227908271, 907444319, 833054679, 990041244, 888468755, 321255954, 175900145, 834184047, 342057996, 789738360, 63361796, 472952614, 454438705, 677126997, 585449418, 223730334, 624099179, 925328535, 914686784, 166851552, 513621152, 329357042, 61421359, 909831026, 305280794, 554928906, 809576309, 217245219, 473370483, 603169662, 586458775, 527915350, 343917358, 90504895, 413745098, 411252526, 741146258, 220105613, 905955799, 916326746, 144166500, 375436894, 699599431, 602694718, 64992061, 509443165, 10946709, 405455656, 921642713, 946073804, 837310937, 410790806, 9102445, 937422273, 316682795, 863900986, 651928937, 582632872, 3646459, 847072932, 707516077, 822337789, 61917590, 168001939, 853579593, 127602156, 404271305, 726592436, 392297445, 5172780, 561730119, 117612072, 676886139, 85880854, 88761982, 576081072, 962147578, 417753534, 8411936, 706270832, 69551874, 345412619, 753087757, 361813781, 276445820, 491062370, 148700130, 411127359, 115023615, 785914522, 736089485, 720902258, 909153161, 294543649, 329003736, 317361028, 283034474, 826627144, 266477866, 88568515, 10242253, 98491771, 125188863, 28244412, 638257175, 278922524, 48952565, 291594595, 9265656, 203778892, 107405383, 424288942, 804211086, 488864180, 895810556, 226176218, 421525026, 726169844, 247254683, 669872365, 199574869, 679020093, 777892446, 605588482, 631735160, 397205738, 465061750, 156863067, 597694630, 55508462, 702594785, 565370904, 532203382, 122696661, 66907250, 900468607, 415182427, 640810639, 132899533, 523918409, 966729515, 813924769, 174941861, 771266811, 480098983, 582494119, 242209431, 457025322, 271721954, 488501066, 920145796, 678262461, 962050863, 31919195, 433200554, 122986674, 486348472, 992118765, 901804976, 896230450, 614215002, 233435531, 174206361, 582340467, 523479400, 221363160, 96288667, 551295580, 504549813, 496309462, 883170934, 718368207, 944818287, 667724605, 972150330, 125064651, 298573422, 184785447, 559464903, 702786361, 281499975, 526676630, 696622694, 315770956, 356977612, 43419541, 382059126, 3970778, 302737971, 957340451, 525794834, 860634029, 600593936, 508053940, 201640333, 771842637, 517317269, 198017416, 720109389, 953572390, 533663440, 708917054, 21292953, 271620004, 958223773, 81113010, 581711844, 771172300, 104833217, 273971678, 403168749, 292097976, 969170964, 83515087, 225455842, 387703285, 882516594, 243323655, 825297703, 94334629, 611418781, 572822551, 340042572, 123400626, 812105285, 612661431, 487088530, 65036242, 868324200, 738172306, 14524605, 51020903, 148671066, 601893623, 422271772, 729100212, 674788374, 753819155, 634027478, 723333701, 743933032, 112484496, 271787500, 957132138, 531583249, 795446403, 95779824, 336440709, 778780755, 922424602, 344619920, 854421412, 236063227, 209254594, 890064134, 38516880, 791899574, 28179593, 347187858, 432370827, 985244780, 494964587, 769261857, 786653359, 821871087, 222699325, 283305842, 398790194, 400871385, 297250534, 448944542, 814442194, 334943202, 63471474, 271659312, 550270853, 94085208, 838680986, 843907559, 471668467, 119323626, 619493379, 531957701, 197853995, 285409402, 733158445, 130331798, 663920788, 674260263, 554697945, 61799083, 733406824, 327579271, 222036173, 692357160, 943681314, 21877340, 140229924, 715258409, 140004853, 570173293, 997760134, 879248189, 5284687, 552749201, 384272186, 991838220, 300385168, 765683772, 977431425, 92231964, 808174870, 95800409, 819668124, 552200691, 64232100, 643122856, 855163715, 464256510, 574355227, 475711218, 549824380, 157771808, 891763228, 483464755, 144432186, 984395665, 33712105, 457859883, 769934286, 502607320, 646725604, 133227430, 73493457, 678598210, 97294224, 387605969, 451949996, 643753398, 125141587, 971301868, 329892047, 428928898, 742462555, 910853298, 1566932, 242036209, 313127567, 441284035, 305962393, 514208894, 973776756, 694901373, 483377923, 535643780, 614328922, 730579051, 812489454, 913916531, 271119551, 290292947, 56825565, 649657727, 751918064, 704025072, 275753989, 342711474, 281603608, 749875336, 66051321, 857326631, 605673953, 268095739, 521299785, 121046083, 653194004, 322518513, 810946408, 921495890, 805888773, 283125173, 317037692, 983171497, 154760878, 313128698, 629029549, 812682422, 402256156, 576348581, 454104567, 278869480, 802546773, 475053341, 443730866, 935154361, 157666850, 102297374, 58220707, 216827979, 453326998, 122211568, 884334462, 7514246, 416729001, 393583170, 379605680, 212826790, 206759505, 491670490, 689635436, 140115302, 343243597, 469476046, 271126387, 17217784, 572635431, 80862927, 399768565, 978274491, 221378950, 912586594, 60528411, 799604429, 436473966, 347645809, 495282990, 725478685, 405972754, 735569993, 931886306, 965655546, 747604688, 414615847, 606026509, 974389765, 269295919, 610333075, 868392535, 718460500, 282182570, 130894624, 376903362, 585254615, 463520750, 88296198, 596795029, 732117690, 532522798, 173222809, 566389775, 323738623, 159422764, 594514955, 128086675, 780649992, 855265145, 690918542, 528706535, 992757548, 788373317, 333530694, 921613503, 541449366, 894209959, 147875461, 602090613, 685579840, 32445718, 125715580, 795343098, 97438146, 650717495, 20390724, 667164175, 782461147, 814501546, 210421505, 988452779, 113332673, 93282266, 125622567, 893196003, 992438232, 699764726, 175383892, 174302704, 328119968, 137120303, 363330140, 808518811, 44704938, 691836558, 414662204, 772516879, 623977061, 344258670, 767809232, 115101473, 535654611, 506907334, 270536297, 220615013, 639777915, 188901616, 768566610, 968882064, 571769675, 27612524, 612094333, 791683941, 781194226, 15950461, 517245035, 521171187, 797658757, 895947406, 271279872, 851534690, 508211059, 619195850, 641847717, 537485226, 686089710, 385055361, 30605065, 172439542, 888942466, 391900467, 621496231, 49840149, 614302770, 117739900, 466472157, 771278168, 572018458, 943198414, 73922637, 279210449, 515676008, 710714892, 962845067, 412076090, 216411567, 454869856, 688840862, 330664805, 814598522, 782689850, 972122247, 68559966, 854587839, 804192146, 563231475, 515260173, 586156928, 134766223, 346555112, 846762316, 623832079, 652443767, 840495962, 545320909, 480422324, 569292098, 680330031, 719349076, 586512850, 33018300, 561835224, 914084690, 471207026, 957975385, 790017190, 152619695, 367467186, 39018383, 985848917, 559989587, 290483532, 312071779, 928346961, 384626287, 897002325, 160703723, 51811515, 779179466, 862115494, 128202547, 570823315, 673530266, 626276841, 136357641, 481705069, 509662059, 283568505, 769681702, 337259538, 553284587, 140113918, 943115019, 955222484, 708894937, 432891711, 182165814, 190130330, 277855450, 637508896, 306870798, 451814760, 834530887, 862851385, 80325727, 870832720, 872568153, 696972663, 673564058, 266770838, 539319093, 26178017, 214369875, 78248572, 150871012, 918087615, 313853166, 868020781, 86495281, 159756659, 157294866, 805164058, 810547882, 869869669, 300755233, 390755258, 213771484, 449224516, 479642717, 452733643, 366441952, 24463826, 187094122, 5379524, 66367949, 648588905, 12426566, 928920529, 594558594, 944348133, 342371401, 166437065, 510726941, 164013421, 57526092, 867624622, 592014737, 579492629, 251423997, 198537277, 739492771, 491424686, 253462928, 487293668, 25921220, 937302926, 753333899, 829143488, 588140689, 519150495, 975388167, 732002831, 679155442, 79298100, 476263764, 41988372, 224701024, 594092693, 609324839, 337943370, 916187747, 96723301, 410714341, 299586661, 260301672, 846941594, 635600039, 509879211, 10992899, 508099753, 492318763, 746192327, 14337879, 473004710, 156438306, 398597232, 521206965, 634882256, 575064530, 148057638, 619360473, 852236103, 311508909, 103660997, 407509141, 502808452, 534967513, 255701286, 981138438, 257386237, 393848893, 683221940, 369366335, 871365221, 620171402, 323943408, 485840444, 484715676, 190682668, 855461118, 628155287, 277205981, 551688920, 111552989, 333049261, 707455833, 761555086, 628299688, 233692454, 95377610, 991653891, 545909539, 190041138, 952207221, 103675611, 808767630, 37486315, 558543966, 846732634, 82019018, 946514521, 109665898, 821520906, 156303178, 944684939, 229907185, 214354970, 222691632, 278278612, 292386015, 550099355, 90292847, 276814747, 507872963, 181194602, 215972812, 160301239, 171317594, 339757285, 568994153, 981717182, 833528336, 411513873, 169248100, 510251737, 92235481, 542844669, 441235923, 753417765, 586210745, 41447964, 874141513, 488505893, 723877828, 994020704, 957192940, 430741925, 706020572, 662885655, 35791231, 401140932, 199173982, 641223193, 125196204, 197837761, 958345426, 448442739, 186809282, 778413649, 665283626, 812281119, 706180444, 34503636, 602190871, 716957023, 679179227, 384304074, 845268234, 385718496, 954528167, 277866873, 96455559, 201716294, 278621028, 891032624, 249793220, 872109313, 972077786, 260219491, 192451565, 733090785, 218016896, 879228960, 660632691, 193542654, 148908146, 356706350, 437533788, 511735806, 55631802, 980094797, 732478130, 291903085, 50449648, 776903677, 884153208, 165436041, 966313245, 311343020, 947283619, 585701280, 42040880, 53901223, 883269414, 778087574, 371932919, 320845811, 588053191, 34875110, 378110208, 748986823, 816399339, 89475424, 378490069, 585569708, 59323142, 953714846, 866855533, 64900395, 136689297, 945874619, 310397012, 514867325, 880460379, 584264576, 661686490, 439755076, 822496923, 75433253, 438943049, 724729824, 550004708, 644197223, 238057281, 95288708, 743470978, 245434853, 114453758, 594257125, 337784564, 218276431, 507858792, 446357254, 901418288, 372070590, 900035357, 478534291, 575190293, 887711510, 206866996, 135497293, 846801676, 238506040, 614112873, 675671743, 798041770, 601329024, 921989064, 634372731, 986926892, 634436707, 118445490, 771053884, 919012185, 597591450, 490893568, 330119526, 667061805, 318771730, 652445728, 650514512, 462705905, 774886377, 478879402, 51867873, 393373322, 675465460, 517721018, 154221342, 372180394, 328492002, 135982084, 591027983, 187582652, 571845899, 350647475, 501495935, 264601960, 884028912, 293197801, 71556788, 587798559, 807537926, 437306332, 498498339, 93302689, 508535707, 944997513, 612525297, 202570876, 500497602, 180132296, 939952684, 362506090, 627807068, 49881899, 269874341, 766979748, 253143852, 862889138, 8461171, 611493943, 965250381, 948843053, 911875684, 202761869, 613440380, 868653780, 852275614, 599637160, 567421603, 604814940, 485919014, 552217996, 338973809, 482685910, 276396171, 703778325, 241695738, 693166373, 256013816, 928076690, 726130784, 345796410, 580095608, 567953012, 103861787, 56950728, 737157184, 254422697, 757770710, 233402090, 130452522, 68582336, 698339219, 482652072, 964933128, 644706740, 480891614, 815238855, 50169242, 991839737, 563520748, 230093696, 154640281, 599513661, 157245132, 371670596, 220513775, 297953557, 142320508, 380562459, 805133342, 879368170, 319752252, 207203477, 809432804, 54049362, 452833483, 954388466, 250364955, 67307284, 628813933, 172873513, 137117598, 465149047, 380346998, 996360617, 763441905, 171423635, 784983795, 152179101, 151605754, 326330907, 238503465, 895309803, 687920764, 620895171, 448599136, 689879026, 243033335, 337930811, 266715597, 102409665, 661654678, 944650965, 993812358, 675606096, 719039876, 805815157, 938271677, 103298384, 139210207, 599212275, 616627658, 292714673, 984494399, 246255938, 636412077, 658340850, 137646218, 599699577, 957525885, 643748347, 169275484, 351854421, 837771096, 776266871, 928104695, 47323636, 173577730, 248002255, 567682536, 93864722, 291774426, 783630604, 933122718, 542009398, 507789289, 367075229, 496968375, 588935785, 184393053, 343778632, 87037087, 477960610, 470611576, 650363224, 473547114, 223303679, 100320964, 634322747, 673497839, 914589042, 743384520, 819810315, 69271577, 609353181, 624440626, 704497400, 161211200, 234305750, 20772812, 872804853, 274973759, 175189125, 326910759, 736731783, 565840925, 499967377, 586603287, 535614560, 171528001, 351288907, 721760813, 318325791, 620351358, 51063930, 50987088, 360401745, 216223838, 570503407, 153743131, 809703552, 985207856, 852680800, 541955431, 654340865, 682538330, 271386423, 614792815, 538475254, 82658111, 211163223, 867869299, 879539846, 545487812, 770393689, 483811475, 424947414, 783937023, 962701233, 896652172, 388648948, 820587524, 942460965, 127023757, 160579985, 237980764, 454849225, 19084961, 370084032, 413002982, 287461941, 953440034, 734978031, 687306080, 232557081, 827005543, 698368621, 331224393, 701958122, 179819421, 835992729, 431655091, 384506030, 455852299, 325867805, 965591107, 472798237, 998694492, 226978383, 651264621, 794519396, 158213534, 129563797, 323801163, 956615004, 666820951, 422921958, 276960416, 209992496, 900282947, 459731404, 405070986, 476325128, 817625529, 628600862, 475772123, 18992803, 876219516, 737555429, 602355476, 72015210, 223015638, 543412757, 267643626, 818588674, 158372882, 173299042, 135361488, 290499277, 713422282, 715930004, 328453570, 957901963, 816551255, 112797849, 393718606, 451479041, 907984867, 747499911, 572163897, 501090363, 539049373, 747507184, 437195552, 947101723, 327242963, 19665147, 63638377, 741364457, 768028706, 813791803, 680788777, 847907889, 133483310, 38557023, 621598878, 212072180, 352005197, 59804850, 860517954, 563783841, 928820793, 727142529, 439205220, 386673786, 935024658, 387151579, 569183069, 797026744, 290342176, 323176794, 160119616, 436033315, 823418988, 376704276, 473091054, 526984199, 313630223, 966050126, 784250505, 449941832, 778951261, 766576070, 347715786, 46291364, 64619459, 100017336, 15939766, 138987694, 922424013, 772841267, 952546583, 610091107, 603775581, 799138450, 198313074, 428501955, 737383211, 731147424, 13192920, 552358437, 503567326, 798810785, 622185681, 773216520, 324593820, 482313974, 980186149, 110196922, 55523793, 601419452, 745152293, 758149452, 295445962, 957915810, 288876774, 860117477, 349557841, 444084145, 378621013, 619172375, 978296304, 472591399, 837907769, 37088019, 882086955, 820883640, 411192886, 120928443, 234602699, 233795521, 664841506, 355191436, 357706275, 477459566, 683806694, 494426294, 667494738, 102660090, 56685042, 540775674, 176882513, 513081730, 161939684, 117132968, 485673651, 337917438, 320170855, 69191037, 80095255, 388919046, 927973391, 437490021, 354092992, 483623756, 633900093, 97614546, 780072268, 163273809, 914591475, 136902241, 83212142, 28183675, 85122577, 884473659, 194891111, 247327301, 695387732, 197349412, 964725641, 355846317, 492258899, 233474492, 583029269, 411766047, 869010162, 464221300, 734408375, 265256571, 469299093, 997514255, 381818468, 722714723, 806583457, 33430232, 129804036, 738212396, 293305314, 166992535, 813935033, 931596271, 543899093, 248681151, 694087013, 330200646, 9706129, 334612597, 182644134, 849281388, 776262227, 85157134, 768554768, 72988627, 139031656, 639556383, 524310726, 669249749, 168333291, 773930007, 647772852, 497425182, 520622090, 868755546, 646126389, 176643234, 865250845, 79763786, 356575910, 174279610, 478263278, 223568875, 809624674, 496348606, 34720247, 96310255, 542399855, 842104715, 112483268, 652658060, 744460739, 809623264, 101536231, 456136988, 703167990, 204975778, 931310182, 91252360, 677354172, 85169944, 697051480, 268198452, 582363978, 269107224, 154409263, 133624094, 828232880, 523126357, 761244555, 513818155, 556212044, 216276922, 597154327, 502431676, 162886874, 568448130, 231558617, 534857671, 590713893, 182433847, 591652759, 669090240, 519893978, 60442057, 119482415, 190659070, 520057041, 228486010, 780226376, 295464539, 512984334, 73332806, 774853939, 713410152, 281476829, 188768817, 583216299, 892351120, 538328231, 395746232, 483678475, 75746554, 960625096, 244392213, 56262936, 241650800, 394857857, 623042727, 409395629, 284821141, 592692920, 167998535, 538331510, 744117606, 777473354, 947393637, 342533463, 681704391, 908825742, 105940896, 169010339, 787449339, 36854368, 128344544, 236043896, 859039246, 661084525, 522845775, 184758392, 480805669, 536265034, 549115405, 933768208, 265006462, 243275531, 557677989, 808005756, 734261579, 708142530, 779712021, 879796795, 220284916, 798174288, 294705541, 592329734, 746811563, 710754102, 174108552, 399943161, 599048166, 522848009, 291246146, 721866819, 554641493, 233034091, 539572365, 521074467, 589071326, 932142664, 45525889, 150901928, 806856795, 164941948, 396270256, 101054808, 129928067, 76630887, 134194847, 851450543, 257520077, 782202208, 983636142, 748153341, 640341645, 45858860, 777611508, 905004798, 133338531, 159420807, 737502762, 431800136, 761255512, 309599786, 789437874, 775537553, 919643590, 60724392, 138025640, 6644874, 816502046, 107554379, 516787390, 252589482, 34587593, 660643495, 740405066, 916672517, 836352210, 25520828, 852015160, 585946339, 315476184, 125053025, 765000114, 559900120, 179304059, 536204446, 3586611, 996197534, 724487731, 288807840, 469572770, 28646054, 305690919, 885697110, 120651633, 884823627, 90162350, 42718606, 720617242, 394847402, 43268215, 213483460, 655721684, 582434987, 155050489, 386288951, 22256052, 127262927, 370123255, 694434367, 540476314, 219412798, 400820268, 624646614, 349459886, 679083470, 670320873, 280433592, 632517063, 914589782, 890798299, 994987602, 890437948, 998379920, 659060873, 265176058, 713243920, 411268058, 969694778, 936484233, 147459258, 872918446, 848283770, 339272749, 213281682, 797629779, 829155509, 59468993, 957538127, 372314054, 969356184, 264214090, 399129875, 505106764, 725464666, 136758839, 700198949, 979612724, 488741359, 195651630, 603589580, 105757329, 893873170, 648103965, 340796727, 142705795, 693757542, 802237167, 250089012, 217789543, 25589483, 513077339, 470128137, 452777059, 850203212, 453233455, 177080421, 467620297, 370745448, 80478468, 419854022, 881793086, 42044755, 985864144, 30452167, 811210272, 106478526, 241240296, 486240230, 133797889, 420857579, 701254032, 311291517, 750877014, 283895698, 412239887, 477348564, 630232308, 536212608, 916679121, 146059142, 197976748, 503436761, 589483010, 668679584, 638090575, 449062126, 718518230, 844486425, 479941797, 915798744, 792891619, 700117263, 117643885, 269333100, 552449847, 580003107, 732188964, 103111309, 960610091, 587225043, 426081785, 671124364, 935771552, 85932917, 110522528, 844413353, 985016163, 575126400, 38448486, 239508100, 470195904, 449609907, 660037501, 919346739, 718599910, 558339488, 70531273, 20526756, 308732302, 346656323, 949411951, 449644925, 112046440, 757044924, 819553982, 229380061, 883318616, 810275561, 681247072, 74048252, 656340572, 572370917, 862624041, 339228084, 934283042, 895663868, 241527037, 256376050, 370765711, 796475219, 794270591, 630216886, 702367282, 145671740, 647609793, 145383052, 187762438, 437385261, 955159203, 824612419, 122319549, 778045837, 701792023, 291375916, 891074305, 24343752, 59038993, 672817182, 86030585, 62766249, 912555675, 43171735, 615320684, 268609263, 305894699, 495456584, 332244539, 479814752, 110500503, 180548824, 567162395, 11753516, 860829792, 907752567, 441014730, 194762170, 259512296, 480281098, 238257388, 271682198, 285839150, 652244882, 645480229, 659483281, 358965763, 426833568, 494209726, 196270902, 157646039, 752913308, 80787641, 3441158, 607513427, 659599700, 117481253, 503407209, 411703776, 342567372, 828750963, 278810949, 660823785, 367773760, 754210395, 631119733, 318953831, 483594264, 965031545, 349033600, 802210172, 275195919, 227608370, 262157778, 123471556, 819951692, 992376791, 220737883, 952802550, 213176311, 365214123, 679291605, 372977933, 909149061, 859326915, 528792474, 168508353, 416241291, 214791713, 274118008, 908084098, 91229035, 540144876, 875042256, 874977529, 522384835, 538034342, 143174228, 53784120, 937406190, 325879671, 593875247, 795295552, 843941061, 848467322, 939394714, 272157326, 474152239, 906934368, 152478420, 280075608, 760910672, 667419347, 876901528, 924670881, 718807836, 884238661, 975593608, 765043314, 876632915, 692868579, 763560996, 506740881, 468155932, 614206575, 996181102, 366779204, 633706898, 617383889, 52744834, 185870524, 156547400, 683163625, 532402287, 623898910, 680521733, 971232695, 381108143, 565516535, 924216711, 800723759, 811692258, 398604955, 439620996, 933771369, 187924883, 434742381, 231238837, 439088159, 875841663, 562489690, 880367023, 544916946, 557216861, 928063307, 814100052, 501597906, 106161190, 389475568, 180382664, 241744013, 470169848, 403751422, 584415188, 901009159, 763421717, 143448899, 413699558, 671093139, 850570780, 556818063, 178901581, 381718331, 239206378, 812736389, 953646350, 382843901, 603504032, 905588230, 84864977, 706007589, 273623700, 150865796, 112337167, 403721211, 533937337, 631334818, 629121742, 381832258, 242551062, 105121201, 82762650, 162206302, 802030441, 940518305, 209407458, 936120865, 276020057, 101172705, 71806331, 259028107, 962195134, 886205806, 694633319, 616305205, 140717228, 41890507, 109966366, 13245514, 884362910, 231484890, 78359648, 517285223, 831752224, 301711871, 955956359, 837608133, 79209986, 205227224, 474470662, 720883982, 738918195, 318244001, 882872932, 530045496, 332788305, 121140612, 390817768, 378274384, 581275680, 956798086, 284603334, 916148674, 780491529, 330696969, 392856666, 662891862, 799333438, 13607179, 140295257, 242883526, 984573823, 969473566, 577758896, 102522603, 105369903, 332033708, 572786881, 234256347, 589056973, 951506809, 97692753, 251771055, 773244996, 47962900, 815754056, 978154535, 536747203, 517544465, 741126695, 775823089, 861221821, 525840823, 474976579, 789743068, 667074201, 610452147, 547951612, 190652977, 520779452, 412354147, 312112086, 846347164, 657080940, 915556374, 449085557, 453366822, 63371175, 830801778, 34622099, 479221762, 3356101, 39082075, 229924821, 209891387, 608035861, 203002592, 971932150, 694234272, 89441354, 276608882, 632075849, 269239559, 363000121, 356869230, 739676063, 727115880, 766533489, 698475146, 79872015, 494053488, 59044299, 8476837, 679492505, 633769276, 142916846, 383289636, 199561488, 20411806, 138943530, 222997047, 664161602, 635944317, 36516068, 392684198, 138039349, 280219678, 829600769, 849304812, 126839851, 36548079, 999619527, 833887039, 964345427, 409001402, 16065452, 915934597, 770763527, 649705403, 30716127, 523665470, 65163792, 194219193, 138760471, 319275067, 712754555, 254031852, 477479491, 27264923, 171351782, 118760259, 698553004, 939311347, 208841520, 42328903, 876644731, 682413108, 378438126, 430133006, 698547492, 924434598, 457122325, 101099219, 5861350, 404636198, 63785940, 476898767, 424736672, 146022158, 302657778, 449562202, 173058939, 907368885, 863886797, 368835261, 240080094, 13248720, 25726, 816738842, 223982037, 510961795, 445731447, 447285521, 112951371, 53100499, 509970334, 703213857, 795766155, 551134454, 302449891, 378015240, 20761390, 927053975, 257612900, 574104613, 913639454, 313073927, 319708220, 296535043, 160847400, 507883858, 927132476, 909603554, 906071155, 88784825, 357209017, 287858816, 912996655, 162538003, 729292922, 268602183, 377281417, 415006831, 859932375, 895913598, 397803876, 269552379, 538992086, 327849083, 819061990, 48161870, 711353044, 597957203, 878433353, 488137426, 387193885, 40382089, 223893854, 38541869, 47368489, 227873207, 998641119, 604734245, 185378459, 208120641, 95789631, 102990957, 634304678, 8481864, 185776131, 946876183, 208744997, 480960541, 402901694, 444877508, 169423298, 841686772, 627142914, 315190398, 670248046, 886221519, 227773058, 844609711, 990897829, 322468454, 8742195, 149190506, 164381826, 370824592, 842691439, 204606856, 638942316, 176647970, 701444110, 538758184, 412922283, 418040945, 156223004, 301962760, 967118225, 797862038, 944535276, 872950927, 408655338, 673928485, 549493255, 230648193, 169300226, 329655823, 46433647, 819216082, 175135838, 982206428, 959926712, 29152280, 295177974, 298187568, 260474864, 706455861, 355128286, 903646637, 94819472, 256350544, 243067996, 818580400, 926534621, 426122262, 583350951, 309117203, 701222855, 803206182, 275132025, 962330784, 281707701, 667208939, 716018095, 869419506, 18708260, 675843429, 42488737, 518323842, 524690863, 657652243, 489828224, 94580977, 713104452, 595127782, 528781722, 190027479, 921152115, 938191806, 670608669, 642777941, 684340694, 373486542, 412145079, 407699234, 936139368, 74773068, 773224496, 150294237, 92027888, 146343043, 306289756, 150370494, 958358307, 788147569, 354874553, 652650507, 856929151, 521676900, 609242543, 426712300, 933418039, 584836706, 113291170, 621095027, 171816137, 739172124, 793842124, 98535234, 548379174, 533063636, 306432028, 439528259, 796097229, 439779301, 471155990, 98783298, 561027844, 94519496, 808752731, 991667042, 761573855, 103353168, 543575708, 742534800, 932511900, 477647503, 369441762, 976075500, 113474285, 341028337, 98699398, 469547540, 343978148, 823545148, 201087305, 221104206, 180955384, 835214633, 864300897, 5905220, 60714580, 595402983, 380740748, 936056297, 35942681, 915157503, 563444412, 591023554, 183688558, 331239150, 391381334, 3095623, 186253373, 670106997, 122963967, 593457865, 914119461, 693108227, 157614399, 159959067, 48353649, 328427412, 747667829, 954018479, 428169382, 123308849, 254224270, 205300047, 39533491, 66915422, 699244094, 958579133, 502927711, 547444456, 912852805, 718573775, 871233528, 5300588, 739794904, 628328212, 551753150, 940903121, 503022971, 815527274, 679407961, 201271739, 245408976, 301179669, 857686415, 143259129, 4472500, 937896074, 469460138, 871726839, 521832810, 452967474, 628985269, 160953416, 929756683, 225805736, 455764846, 662304585, 15213468, 245335652, 992462589, 750876046, 856736301, 732229786, 225998800, 144613370, 649242744, 940163538, 595638524, 618000692, 798023463, 566492497, 583681536, 606842320, 691251217, 364020114, 902576800, 151682315, 111109896, 81686301, 424161063, 891209636, 381774058, 41772216, 28331165, 767493826, 56308435, 20478207, 290450417, 821255823, 95291849, 581496169, 884137545, 70506956, 36607723, 824224272, 258723245, 897287947, 664400190, 973321376, 494950440, 903210693, 954141355, 269539173, 475682433, 180875871, 662757712, 178809724, 203817037, 927560467, 367202249, 884369673, 891120103, 562396236, 347942581, 465211973, 674392623, 663911949, 267772855, 972526965, 635808990, 900704772, 947690349, 976772386, 468483869, 666387860, 822976156, 838780716, 313261, 278112131, 597137791, 312891063, 512874977, 423653373, 476608625, 992441064, 421910902, 122830865, 321063880, 962287790, 177368787, 731325157, 310152810, 156544799, 119081801, 993968143, 539292858, 799650855, 866892612, 486547051, 571354833, 8980020, 941281839, 23339794, 359731019, 20382028, 432923641, 161564918, 717132336, 387392438, 678692188, 956541702, 907184699, 534647432, 686608972, 317422985, 485197325, 726450755, 538135805, 240787935, 312075893, 850135022, 586883518, 752402752, 134504281, 121527440, 42032232, 582626272, 974412136, 14044957, 954792282, 445631629, 958463660, 946730908, 810535975, 879683557, 547428748, 341426522, 17644150, 858224565, 953529385, 512954086, 107821363, 942085378, 464457923, 512307786, 470101993, 687991785, 790428871, 970295044, 418596101, 632176470, 742277922, 403121357, 990869479, 34538847, 615916259, 114802826, 71258624, 37433722, 549969402, 573215294, 364029857, 569007584, 639105966, 176353800, 700097799, 236866072, 243286942, 583713342, 709656539, 536779855, 667219873, 809601451, 605857725, 804844202, 329788003, 503952195, 604888152, 465821528, 133130707, 886025446, 727511216, 269089755, 419608722, 489078359, 706496673, 291280444, 409508757, 837226843, 792464390, 779991214, 318916112, 484694804, 113415840, 77368196, 342959939, 656426869, 143658968, 200565707, 336628882, 55697701, 610968564, 451844627, 913646726, 54702891, 863247906, 757928878, 677878423, 415409681, 655701965, 914440494, 182152296, 614236681, 84150499, 232057395, 244459909, 430989211, 492530287, 24476336, 685006873, 865148435, 388590470, 173384422, 822251841, 960563860, 114702993, 796173215, 226941505, 923344339, 675071268, 674680144, 152074129, 906021561, 156777422, 669745498, 811587637, 658218845, 961289267, 884935511, 635911203, 310513599, 282566810, 282938530, 568569013, 345186962, 134760154, 166996718, 123366033, 453108894, 394169316, 528139910, 93860641, 983350086, 863420790, 831748549, 641434391, 761632291, 900228549, 272977721, 279856177, 224923216, 219095615, 357748792, 541167392, 74405834, 25200667, 209368657, 209316408, 643210139, 741584239, 299443609, 620681644, 68703077, 587692080, 522152824, 764088662, 400454727, 17923002, 308301329, 968639305, 112527158, 494791605, 725343045, 774407417, 828738511, 896975148, 669164703, 203103088, 951955863, 85650258, 207481197, 972900579, 791851749, 189660588, 638764991, 886556893, 503261159, 396794215, 484139027, 779994531, 199061106, 465274695, 208159453, 143480579, 623337425, 503105161, 418726869, 448821989, 234232246, 69671485, 304798947, 662052961, 290167918, 773482714, 971747822, 438448839, 42683462, 666803455, 600372860, 78914748, 645038596, 485548388, 720159668, 940929585, 858358957, 177949067, 91939248, 778246220, 834265079, 806513702, 95437614, 52897974, 811657567, 652597520, 506937051, 291597836, 342793030, 62491732, 69690874, 772146408, 361965037, 932520165, 108526018, 634444892, 647684185, 858478147, 415460593, 695958466, 287371662, 183558421, 828509589, 450805623, 811435280, 948969476, 575594196, 31993631, 730204216, 984344094, 40659242, 842176186, 482194656, 204148200, 522269431, 598218529, 250314974, 851280201, 488748649, 704468893, 645632529, 888645627, 288665882, 988135990, 694224680, 768295192, 583118812, 153430331, 82954216, 411660206, 530896115, 318047845, 651750545, 419238304, 203387608, 801605549, 291272652, 175382252, 871092043, 670955498, 713116838, 383147464, 179775537, 307295660, 552713258, 835099423, 95421037, 324137932, 42340024, 465910157, 271689538, 547945850, 262358411, 604888151, 861862784, 522937682, 480307760, 971855518, 203550599, 611523083, 155448344, 769626047, 659332601, 591334951, 619414430, 94136980, 803750448, 298206680, 163771920, 196320296, 124312079, 570917559, 36805423, 568578456, 476903212, 242279068, 717886186, 265283574, 369874421, 949123882, 125766632, 453880387, 340911104, 716012596, 373491028, 209000685, 519926369, 575603163, 419740646, 459138559, 385263668, 412312376, 259542972, 280799263, 683598287, 73547723, 450881012, 193589113, 323085265, 488559384, 556424104, 700362689, 561575121, 609462871, 266032420, 817604964, 839881971, 698495225, 360211364, 682613098, 464184036, 974274605, 49046107, 882052673, 457498494, 987078230, 629248296, 989253939, 919388409, 671519499, 999670523, 493001074, 954410445, 785292858, 130143485, 656012446, 186703920, 929803489, 879228115, 617650867, 402655520, 585935618, 489279300, 748865014, 360368298, 365587304, 922337831, 669996027, 651757132, 421868050, 915909027, 768446691, 490369366, 512803097, 269826548, 398855503, 421234935, 859825646, 712031378, 381657279, 673234295, 143742269, 796499912, 163430523, 493696243, 974222667, 396484473, 993164105, 222723386, 11857719, 831806449, 625303285, 668604326, 281244907, 941483167, 156023907, 783706973, 759045305, 658845774, 761638237, 470465671, 106774912, 826685052, 765885327, 828803712, 923439084, 627755555, 492815529, 590766800, 967639241, 195298086, 599386229, 386412633, 865057096, 720499288, 124735499, 139449078, 713854084, 402253149, 728578797, 203210044, 191970535, 703481451, 812655852, 84729123, 241537663, 215085443, 795500400, 221417025, 818552186, 637240500, 385607335, 633396801, 302949470, 458997134, 552449852, 828946102, 350234001, 443539818, 466711985, 867905765, 99066410, 211035251, 900604607, 221864337, 605259002, 555388320, 391616032, 194800316, 899604023, 435369160, 505865773, 379216591, 559565443, 385660830, 929377869, 679071360, 314816156, 142265333, 143947827, 492376897, 924714665, 325196479, 335925061, 986517787, 712506942, 890756423, 994621792, 165761807, 70735827, 520353255, 656586073, 749320982, 447607553, 884757471, 808032531, 991816708, 280859880, 894437972, 233351065, 980823555, 428863493, 168348597, 434264553, 819024720, 413955127, 879755846, 181939260, 528592423, 867690221, 296848045, 254501954, 232615481, 811011108, 277631269, 86562230, 314050405, 738429304, 577347820, 28009173, 911249808, 460386443, 214942989, 303874016, 927615443, 412334511, 491253560, 218852695, 650179959, 622064822, 297755489, 7907559, 525868613, 837191592, 935385273, 186232438, 397030169, 34405123, 347657634, 507588504, 464198477, 888979117, 349441531, 736438706, 476956487, 166867736, 901172759, 781277805, 943458197, 672700360, 169111561, 171884466, 846899993, 780143412, 807479923, 910750875, 869778356, 161382647, 813454121, 420860717, 77499383, 741994834, 465662258, 105884862, 369885459, 864134312, 723952564, 208400572, 847323531, 298367523, 661712816, 749927193, 541274128, 200071426, 171396116, 355758761, 991790304, 406464569, 676563232, 158010768, 393458735, 984071144, 19059475, 868578312, 723281907, 340448860, 439595260, 873453565, 562311714, 59808716, 326886346, 460999072, 215220741, 172285533, 247635568, 497950554, 969604101, 684842336, 32864466, 695578271, 988977892, 594652294, 147988725, 75243603, 195026110, 895925962, 185918578, 181568319, 840071806, 507505751, 553549199, 572694295, 925962138, 530003222, 807300496, 530551200, 857869110, 771326743, 637627113, 751079219, 536090447, 157134603, 93860841, 894297035, 862756890, 94899912, 558414911, 238831255, 917003971, 322187528, 759205006, 228837456, 671355132, 701847207, 5634758, 823100463, 791087750, 100940904, 771534224, 66256578, 294367963, 991298927, 165333519, 684419641, 104021985, 669628342, 94004729, 438417522, 729551514, 81808503, 881691708, 847480824, 657838877, 374298177, 513482663, 559569942, 15279927, 8572570, 5365326, 685798296, 290192726, 685853305, 288503232, 90086360, 633787976, 908079049, 704691636, 527729406, 414728326, 626369945, 927429825, 915291710, 795058530, 734773997, 767186502, 262211348, 174551300, 105264256, 787204067, 493643306, 280283446, 759732056, 414454214, 348721356, 188987995, 913038040, 581378065, 511851168, 933349383, 644933944, 695936248, 508063698, 241795264, 724612813, 609301132, 441009280, 854859036, 745584696, 77516048, 472584958, 473070625, 982018437, 768711454, 670625937, 827823364, 590870083, 739816671, 736287079, 565914469, 785458129, 424474835, 999119635, 720044438, 403134453, 511317376, 164661117, 302926599, 232399831, 20941624, 114265424, 298393504, 955828238, 24435666, 484921662, 337240791, 944494419, 627888306, 124944667, 897790607, 996812646, 788471053, 940013313, 426224079, 617683992, 701133093, 127105818, 225692088, 119407368, 710493345, 322746963, 277874341, 700904696, 226414825, 32184627, 230616119, 536803012, 634372100, 897438984, 53747636, 959495334, 715847823, 879495671, 255696468, 558022409, 664501133, 201242418, 8178160, 908901650, 537804422, 998128457, 212926026, 253087964, 229413909, 91649330, 492218337, 189708637, 201731494, 903065783, 755955922, 794529725, 818835478, 141610813, 11109939, 241573541, 462742412, 635994990, 699883649, 590902129, 871312982, 979563653, 774325034, 401082308, 915623454, 628863356, 322655227, 74083614, 708951566, 916206482, 246070822, 831303344, 192956869, 651447545, 815359174, 445907877, 932062449, 924162017, 44909808, 29147391, 460548741, 743399392, 729539607, 615195043, 801086578, 871427925, 569881214, 308621676, 843382277, 542036766, 502650872, 203878867, 440029582, 883425739, 690874336, 591298906, 257314594, 216647931, 76420856, 109183749, 502984519, 827586469, 140462912, 48037457, 844533001, 604859664, 769516554, 632703416, 386294493, 658818520, 491011218, 437064538, 739456400, 199861446, 538389515, 712093815, 772693373, 400601029, 979539821, 208527539, 800490083, 694251932, 771758875, 445657568, 746130234, 570341786, 711797229, 704752330, 591018988, 241743862, 804031834, 513547280, 221775641, 72268921, 360693074, 326710760, 98163589, 922954665, 208804849, 697581580, 487304128, 374964408, 610501318, 89182365, 836731307, 199612412, 375985755, 573310291, 299388791, 96635974, 230439369, 545481365, 712126680, 271352039, 137428613, 977222500, 463466031, 505552192, 938131278, 321507100, 445661706, 590576439, 645921920, 36223366, 846836733, 468683408, 841637880, 118666952, 506499079, 685421487, 925381776, 152178958, 929428640, 57460135, 320856671, 543637577, 177682120, 91228849, 203491039, 300317057, 411885257, 394586355, 756362680, 933090600, 355940816, 371246465, 959967588, 326638719, 169549154, 581288005, 901135471, 534290102, 825657616, 635762784, 780778191, 974602198, 956541288, 166549533, 801160771, 237435826, 28148162, 763293118, 201022699, 281718555, 375026124, 508342621, 30783253, 488291977, 104143206, 156319871, 996649100, 612561985, 539134753, 343082855, 179155408, 538210155, 278735914, 272329225, 369342955, 735362822, 204231900, 996091990, 47143070, 268697245, 530401619, 876059965, 630475571, 727609395, 393827227, 356982702, 323774436, 422332057, 977475955, 482967783, 966850613, 157093884, 701555919, 344670793, 769184166, 29386630, 671213562, 263312462, 826383399, 920541656, 457882146, 762293629, 348763507, 163910104, 260690813, 714839033, 173261665, 827022534, 369872112, 520288939, 312882138, 967121646, 459157941, 124608000, 512304204, 96699728, 81863269, 86309950, 62085249, 687303148, 654221665, 914676510, 372955088, 79803930, 927647650, 668154035, 377118835, 903650975, 255087356, 184104021, 583522417, 159125252, 249837750, 853230425, 481044601, 554773505, 964008547, 366862510, 781331192, 133419249, 573855520, 74289007, 82062069, 54635643, 78573647, 889683844, 129007219, 724410491, 111276942, 495580201, 73871539, 287499787, 575452819, 745408700, 698089636, 107939839, 296612238, 595140171, 545046583, 736539201, 262548832, 867432754, 996945190, 491225384, 834617727, 615082843, 236872018, 273225819, 716244204, 656276686, 139098763, 311477312, 213160149, 278879183, 829964497, 959023204, 593164503, 357303248, 360913136, 727988863, 700862503, 459358490, 600471353, 792191227, 492827239, 765332317, 643685309, 233046953, 9430067, 646956555, 518730564, 346616300, 200647459, 769508920, 609277865, 938460854, 587560985, 228408132, 772426871, 991163231, 590400390, 826379154, 508342638, 236727535, 193960803, 124140421, 823589954, 256188923, 782492249, 136342342, 418286989, 75831440, 418351324, 595777390, 510889568, 207600146, 671715207, 761615385, 978794552, 525737966, 282190195, 293690161, 505105288, 669728708, 452762989, 417461577, 636582066, 452517703, 244675251, 350792833, 528020868, 241882908, 139804624, 550460970, 41162592, 533364790, 882150310, 380356575, 154586566, 930617282, 88698069, 489486740, 644709329, 126376644, 338317629, 520392627, 964573659, 433136421, 919616089, 610314797, 866471441, 619885288, 268405510, 24260862, 71536949, 88516952, 547055123, 610351925, 871121483, 630033128, 613414796, 113225753, 1907049, 312487540, 96453869, 93001728, 108208397, 668128352, 751502653, 47238674, 217472696, 306966731, 121206093, 119564686, 900609484, 545661127, 907359688, 163280950, 323941691, 394482464, 830360983, 982933210, 236525702, 732744194, 965903068, 369217792, 310869217, 130945518, 420673216, 119078559, 998027792, 433052527, 39883302, 462039260, 495752851, 574210806, 723496759, 13241944, 101639529, 830883017, 120091303, 689577972, 162055248, 77391136, 508490084, 167647433, 450132176, 101246035, 651478894, 384192873, 785782242, 56374806, 903755041, 225467170, 951086261, 455637303, 992609104, 586303529, 31057494, 898842695, 324611173, 609208362, 906604178, 222889736, 263312403, 146400537, 178199508, 631144465, 373547355, 358065454, 360677806, 905294016, 158892342, 413631856, 26570627, 796610658, 144822789, 77559329, 862037411, 578694931, 831376588, 423463491, 518560174, 387839245, 202398165, 232037675, 3587076, 63581166, 276035916, 739411195, 281065158, 175330030, 650165712, 758999584, 318348735, 807421188, 660478862, 578215710, 454006454, 885225580, 123059705, 426458104, 679310372, 384825926, 138600614, 545113760, 129683431, 593299129, 734067698, 280114255, 496521379, 956962315, 860414362, 533826871, 71941641, 942391775, 880816082, 858578494, 416430513, 324645707, 971492178, 346120810, 938629346, 828107774, 657441244, 281935728, 399163867, 804763058, 498121438, 933788419, 468509629, 665497491, 367180114, 505783112, 746515779, 617329034, 475978718, 640415101, 212340352, 381416205, 815293548, 423275842, 274862352, 641147690, 769759826, 675140502, 746218196, 444730010, 458857957, 176567942, 278690861, 68981330, 315417739, 187336007, 797034875, 807152528, 891617482, 860040184, 255165220, 631740028, 209435585, 278446352, 895853938, 942518547, 629155035, 985622161, 906477994, 493878985, 681638237, 833653283, 829218992, 62404261, 319174812, 793554254, 558833560, 81372070, 939199258, 285056233, 995211564, 347037104, 187028558, 405221688, 197569719, 21941762, 481888724, 696343911, 416628505, 387513618, 808183973, 267111189, 793473459, 54538344, 250150494, 29912930, 959872637, 143284386, 597878300, 109256650, 50297270, 206294795, 481162075, 993447708, 116552966, 695444277, 75777942, 372448220, 856505797, 525435589, 826679925, 761766744, 88021584, 784445127, 371604124, 80302652, 708508991, 601264132, 760197480, 321782486, 157786781, 746771879, 870251278, 651545163, 390939016, 929145319, 439431464, 437701583, 100613261, 829843879, 42362553, 673883806, 763386919, 211396693, 206019465, 512396141, 36040200, 824014326, 147534540, 994445462, 956676393, 667017454, 996633172, 616057582, 264940528, 50365869, 655415190, 670466503, 699476915, 422034462, 770406691, 897586286, 511916740, 232042745, 960841650, 396868639, 775932866, 826525888, 433023051, 543139852, 451569741, 105017378, 296873787, 187722871, 609407789, 824026634, 728311790, 714395784, 736758009, 632913944, 4691184, 802682299, 730880127, 84314748, 702242199, 17115905, 216751660, 921148743, 375619985, 920798350, 302942292, 292176843, 685629764, 315708998, 956417751, 183033848, 173294306, 293305319, 266729088, 261348780, 335590532, 933650114, 915302140, 953451387, 144730817, 226703352, 672899448, 468107557, 439103639, 580886659, 724704665, 467591017, 766366588, 211603168, 447954978, 318573308, 920590642, 379312052, 839540768, 586047629, 966969512, 178641389, 481869070, 84828071, 644231616, 511456039, 822369685, 567238970, 690897811, 179724567, 464339612, 59582744, 384205889, 794452810, 240460821, 337624658, 806110408, 55948669, 411668235, 352478842, 852362880, 508544272, 471407254, 225259002, 198851677, 924496987, 431043196, 659120535, 428701140, 942539458, 219844909, 112596779, 547902615, 359160431, 4508570, 204909036, 933525660, 965589463, 747779084, 502519175, 26012165, 841137597, 755363075, 825666701, 370121633, 389160434, 819812833, 68290252, 982498705, 868020461, 187887313, 12074751, 100769276, 456836795, 649992856, 801045150, 136486551, 708801554, 608408874, 186480063, 236513174, 648967198, 42140816, 875013376, 716846793, 164911127, 597837650, 161559649, 775390621, 859562912, 751368382, 492036325, 862529735, 515071607, 4884889, 797196543, 509227021, 77143342, 748522136, 12288441, 288771508, 949680210, 792622981, 348932795, 158558505, 296539059, 898972694, 556469626, 739166716, 746121091, 977120286, 797039855, 888298221, 858941279, 867758807, 817509777, 620763270, 95395399, 627545422, 601990866, 29773344, 892010602, 109257484, 687644821, 128899394, 897001598, 520102751, 805126501, 772526339, 593788342, 507875674, 915897935, 788629615, 428948750, 906454918, 110840061, 741487773, 669880831, 784522770, 697477690, 746702320, 389039569, 470897949, 738145362, 542626348, 606799907, 559545812, 335976433, 739760137, 572689539, 643623650, 616102740, 597544923, 757143131, 941128958, 600152952, 513605625, 876477118, 474430082, 606786918, 603405832, 726284124, 331613854, 100361991, 156327535, 106145370, 724276793, 925451534, 617788905, 835328792, 99758139, 139135096, 145198834, 415884348, 906974061, 983402866, 882008297, 609083584, 924379257, 445304949, 569356672, 671700103, 611064608, 48764393, 815664737, 216857330, 128668163, 900976131, 997360860, 460666685, 133361911, 640265896, 187920765, 590516667, 184295468, 127077283, 135592579, 256182441, 736184963, 742853961, 709627564, 254210641, 868951036, 625389810, 322286194, 24482995, 534285901, 889201206, 147397266, 37934250, 367183999, 802964727, 958892756, 576002910, 828892410, 794208423, 598349859, 648749361, 746857937, 728305319, 796257079, 509971994, 234626568, 31195417, 151888768, 545653065, 958143100, 349642640, 801456002, 64582428, 828775182, 536854759, 750380103, 410158129, 744805721, 132917529, 557411680, 231644047, 774421527, 963044217, 952226021, 721156729, 760782664, 224336896, 703954073, 212331747, 393799578, 126825886, 167634017, 654502341, 833313103, 972494650, 918479326, 868754923, 590129459, 276145351, 72188238, 372431986, 111681030, 378093042, 808057979, 524505149, 764285903, 143508058, 231205193, 818780196, 648771703, 660762020, 718954164, 72216969, 92759208, 506824524, 592996539, 975094958, 630648342, 625950793, 114061672, 223313286, 291231255, 68004777, 14679795, 194865226, 538907879, 172130478, 953054588, 22261844, 500707219, 678799720, 135553186, 698630462, 761640667, 476493906, 324690210, 829368149, 122988261, 252980588, 386748665, 473757967, 724330785, 440308846, 514451646, 248015205, 913998953, 914546678, 667866098, 74498599, 243509029, 586624242, 976443283, 412591500, 915191240, 890342730, 628657380, 572790999, 608364318, 575731892, 781924456, 101783571, 113682766, 932757171, 27198816, 408756980, 122928455, 781538594, 262124866, 50016916, 401045379, 626300813, 673864934, 507407695, 847099696, 699634612, 46500969, 693771715, 705661960, 19583846, 857716693, 237796982, 364143980, 775801722, 70266688, 410256564, 143930313, 661875559, 1602441, 798309731, 457980716, 489113421, 9093766, 294185988, 555317925, 576041143, 638190831, 880037414, 86837579, 942718849, 870113021, 434762720, 550935063, 268209881, 591136804, 810950619, 364629808, 932984643, 409423, 230433153, 310384605, 187213645, 344452564, 770634199, 119739377, 38930838, 212910152, 922436823, 264438708, 354113737, 555050007, 505761975, 531942855, 715003726, 6769665, 777712819, 957424109, 416645642, 330816538, 673133793, 383125881, 892130459, 45761245, 882566848, 952739725, 835965962, 992216620, 937810927, 858266268, 261640263, 540892210, 782332188, 895929646, 374694299, 861357023, 512130482, 487247799, 474466038, 615332381, 653620938, 502196797, 569975290, 746958445, 670406193, 168483957, 141377164, 625813457, 428780454, 648588813, 383792028, 936378614, 124358496, 224352884, 570021139, 965607251, 421806869, 125292193, 764703065, 867059093, 153518922, 901140693, 604164493, 651704766, 48748616, 117686008, 732046886, 544620932, 806846831, 728169500, 244393101, 110063515, 291103283, 195075431, 939021866, 712964358, 392709645, 375755946, 701919896, 142448393, 448877815, 161662764, 601467683, 388055313, 498816190, 718829053, 317946787, 713276904, 129851630, 84415380, 19481106, 702634665, 364336254, 106814926, 251600694, 186437567, 507442776, 657148964, 463215007, 635894894, 644900176, 227362305, 68055552, 242949609, 803232545, 221452835, 582752080, 367311583, 783958305, 400665052, 781774097, 501169702, 369759789, 422737577, 75815800, 327021088, 753124275, 822432631, 450826464, 287775126, 920767444, 668617961, 555971226, 293232537, 574523333, 917468610, 521469852, 562435736, 494470125, 404017732, 537208382, 35915292, 723370544, 863435950, 43230877, 593289998, 415792817, 141038020, 17504260, 256098245, 941878176, 674394992, 974976783, 430416817, 199149088, 98097085, 500828010, 669292946, 322550403, 385860114, 306969658, 977821126, 144556821, 858333758, 125998028, 211905837, 714309592, 30014042, 90408394, 201080940, 430314028, 37451274, 158133321, 303583889, 712321656, 482389046, 703259440, 444514950, 973644736, 335782130, 734987929, 236285552, 468396623, 434817218, 718091845, 679290020, 376873684, 962754552, 455685074, 146355648, 880733621, 510391172, 490405760, 685243943, 264959752, 365447984, 52558441, 483750692, 963073156, 410463201, 458805039, 945844850, 602528584, 410717389, 408416141, 985569581, 495991754, 771562947, 631996801, 171064386, 352474704, 190869354, 972559901, 870500648, 972834473, 491180762, 206749009, 64059742, 342010522, 408560391, 144476054, 430971118, 62098172, 496250785, 692312329, 199441367, 899856371, 699179645, 720140330, 355889509, 814951941, 328830219, 802540527, 690122251, 63477603, 473469237, 511256695, 515261618, 768545173, 768076163, 46336381, 656977824, 797301606, 355557671, 761339044, 442460747, 175130088, 822579407, 908725788, 397005993, 965457434, 871952253, 867869897, 440417420, 647244556, 392912864, 234998856, 617136943, 563763544, 271846858, 278659084, 901269782, 250635440, 874942914, 975587119, 957977702, 673860530, 297569463, 56448505, 969719219, 345367032, 755641156, 668689098, 894040547, 278247955, 857892747, 366911600, 592466273, 80847916, 961462764, 31486035, 620894849, 970652111, 821188624, 383808830, 11721493, 949375616, 517175691, 105796800, 568986140, 936786574, 894501983, 742391846, 911563099, 894238748, 281742058, 520479245, 169232327, 541238137, 306257780, 587905225, 45639336, 659155994, 134284802, 158503182, 415269594, 66080368, 125440182, 217065297, 608151430, 427415397, 310305634, 203755464, 710663037, 44661019, 34106456, 59215899, 295755216, 447855952, 10011094, 152746152, 89712400, 132174262, 770978879, 204364697, 915688129, 16217873, 852372715, 378459836, 580811484, 535721611, 448330117, 746484927, 905828794, 352439079, 825570424, 18636426, 995345344, 708427803, 564742988, 213353221, 141526779, 466350630, 774462361, 576804625, 18047411, 967323555, 681439761, 544870975, 976208180, 801161955, 542664576, 246137818, 314141202, 364405308, 37406932, 414283591, 361982090, 173306434, 566130015, 913741872, 171030096, 814670728, 106057609, 358093322, 64026639, 391637348, 328318535, 280039309, 161074187, 491932006, 732243329, 798993069, 624620619, 168738725, 27823948, 239410382, 663122287, 615792143, 168154382, 583679537, 284364453, 790754225, 128186543, 6675704, 190842017, 13400473, 848199588, 643444461, 394220915, 879376737, 157695214, 105225377, 846284117, 393289997, 793666644, 931193523, 683460798, 14998417, 943393519, 743333393, 631471605, 919236322, 615999667, 515683760, 154872964, 977958309, 565121288, 43284073, 714253543, 178126351, 293522727, 950648796, 175488515, 593428708, 257336895, 202092137, 812552579, 870135068, 776544003, 112272413, 292795159, 256725971, 27324312, 543614459, 971552217, 823845128, 45145827, 584753211, 823778766, 232620092, 626364890, 463331380, 616509456, 979225531, 48479820, 140120438, 800543504, 695488680, 151814594, 307800586, 456619602, 261694765, 488520945, 260600701, 155566246, 66506437, 237667418, 650269785, 153417837, 491769116, 142971637, 820853523, 373236451, 347943773, 252807905, 712624481, 451428785, 337141832, 678596586, 115176137, 410735766, 780015990, 785524261, 546867200, 822273100, 113475946, 792216594, 123592931, 836184045, 487825929, 374604796, 339615822, 897218451, 428764882, 463564810, 561247986, 660772722, 167358150, 582326274, 771349818, 173509647, 231893176, 427887984, 128498090, 124976693, 549663261, 712003470, 96427572, 445952031, 253892313, 874446484, 866129596, 738443325, 180568991, 384751043, 172679124, 408991219, 501673370, 309127310, 602718301, 129041723, 165321855, 445033358, 314571402, 268505730, 611601219, 411145075, 61498284, 369673959, 586967151, 738219852, 283482352, 982565838, 293111026, 168934406, 197492998, 479562322, 731109767, 162929139, 505666063, 359860746, 843658958, 480991898, 471945511, 333299990, 271743965, 825973216, 995413762, 281411091, 866818346, 319795525, 169993909, 390286381, 101817548, 587971832, 42903757, 912320721, 279695218, 924261616, 385770086, 285603783, 19804757, 714815783, 281807469, 237478240, 931140064, 343413607, 748024555, 998810380, 408467796, 229093472, 63019196, 343267381, 380723909, 104448401, 84660225, 184603655, 162617517, 420152716, 367846157, 281408529, 216633641, 758323319, 825826773, 599394272, 652980960, 456338597, 215034340, 336359679, 924157016, 953890961, 893097842, 55739355, 293409858, 592803352, 842115481, 566455674, 779223886, 567366463, 347952854, 52042711, 682271099, 753743144, 948875868, 980024223, 136069910, 989291515, 891935650, 887468472, 800650379, 512190603, 888293555, 554589388, 882976446, 458017777, 868877293, 364646374, 805120849, 104079928, 109928977, 575318525, 238006710, 9784497, 357525196, 854151306, 56713759, 641559953, 724657229, 924629676, 732590437, 296993711, 605060663, 663204712, 687501159, 448496036, 633379425, 908636634, 133589701, 322119414, 292210967, 140716911, 257946387, 32602403, 170492774, 568371635, 283757913, 302246533, 350669609, 550694968, 533344639, 681688046, 719513147, 238913895, 428925688, 681008582, 459472648, 620105000, 494245895, 717782001, 756709019, 362887255, 614079077, 95189474, 317671739, 130183824, 450228121, 195766760, 418256968, 408894093, 656463460, 972435131, 247875093, 421178787, 50861196, 558979737, 402694081, 238662273, 294230217, 193901048, 957021366, 59568958, 837226304, 272424080, 898402284, 390938752, 273736604, 621973865, 979073424, 166975565, 616807973, 948582808, 146531562, 617913109, 547391550, 700235034, 968418487, 317628029, 62677958, 191075626, 567388484, 930722477, 498665761, 726626805, 15804286, 36626825, 924699494, 167338036, 197789370, 10982554, 454405641, 744484169, 149054001, 672310972, 604837656, 123483561, 559592933, 938763575, 824410218, 228312326, 854734748, 74503697, 685734090, 562448258, 984206032, 766779754, 381994041, 827611273, 868407084, 423842274, 852374501, 556696951, 467377703, 525508824, 186063055, 326722698, 515005875, 515297075, 537180072, 91118735, 561255081, 792418050, 132946195, 879704389, 375319603, 981866038, 512596113, 325230891, 246150587, 997293053, 401015375, 771887529, 125327770, 880947608, 864857514, 740582949, 448220152, 435384492, 560466592, 893875193, 962717790, 288756787, 857456265, 111320772, 705726405, 756855911, 172027712, 842768058, 844227108, 5267370, 679155120, 100128866, 306983308, 113722975, 94596078, 943967555, 670789405, 592861885, 448230717, 570692144, 864569862, 239755591, 507571432, 331968089, 614396833, 272831980, 877339122, 695134481, 863472045, 506060738, 57925114, 183904252, 105030382, 725456121, 193421945, 612224893, 188182469, 935595760, 10202523, 876015087, 175068291, 475162318, 605519134, 270975194, 32729776, 521169438, 821563405, 466000775, 219649582, 490102626, 351567072, 356106393, 930231809, 419798900, 921095821, 125439479, 88557528, 328020590, 35786507, 718409475, 14200308, 845528039, 10893450, 928805853, 954362147, 272826054, 964298731, 895169032, 545261391, 913673117, 463106416, 687357079, 113524182, 131189338, 295891077, 855738169, 957325234, 170269805, 7243694, 223903866, 183743058, 163873923, 5289490, 954211155, 427094304, 441287796, 350585919, 466992471, 925590746, 699125297, 417420052, 783223976, 877930512, 6546517, 362894498, 313961283, 912914819, 170313486, 904336526, 256161006, 742872238, 575424788, 813932074, 148802517, 454952286, 461962420, 909224176, 182099633, 528507720, 338457517, 184437241, 56356091, 800770877, 511958202, 606923451, 850642286, 853906539, 285024366, 238349806, 818725518, 365281886, 852705474, 901751092, 973858496, 593898977, 431748280, 465587806, 941499963, 703897964, 492037100, 610455480, 529155475, 322823988, 531726781, 444179806, 174056726, 197203377, 655842414, 983299907, 737656837, 347372323, 62354171, 921221331, 865000940, 25648037, 920288089, 554934242, 760234089, 620047624, 227716716, 625646627, 62708526, 215943823, 966248403, 998697923, 66416495, 182806402, 946960539, 878898051, 921083097, 925652193, 420294796, 578221093, 940987435, 915435104, 768041674, 442924112, 691664286, 276592356, 327495770, 261143733, 176841817, 729744816, 954829147, 214209963, 141693065, 410414633, 819092676, 461481649, 201637879, 456103212, 826733702, 978390490, 470766199, 812104984, 193744343, 104208431, 744092496, 71058409, 207179799, 608691212, 993374746, 51311395, 511567823, 618707292, 785855547, 877125189, 604777042, 953006206, 972822793, 324878640, 531907602, 258524246, 900136995, 885990771, 480707967, 533107902, 121128836, 821395517, 946677157, 330556178, 323022461, 151189080, 533331702, 181080266, 266927895, 537839782, 8876201, 725821181, 494728712, 701004093, 769237786, 648808840, 907517880, 102666095, 585247137, 173363703, 759846852, 951167702, 71460761, 59944111, 982785998, 79359380, 970925272, 415330181, 919748448, 220628213, 836594849, 35683251, 13996441, 908394106, 957385161, 799602628, 105276881, 918722638, 491404202, 598376156, 301376486, 702580078, 983980381, 239432006, 986661673, 634920035, 46830095, 509776784, 851115841, 29772522, 275771409, 821482788, 78873882, 274741712, 593983061, 976396960, 472584527, 305937943, 544617244, 79723489, 2877801, 222836421, 127311740, 341130337, 514201857, 117884731, 6052544, 11653960, 410273702, 40451486, 835557000, 722043598, 883424865, 771708406, 805841002, 547390640, 318197360, 157573652, 288539457, 238875847, 962638725, 378597705, 61344819, 860898278, 552023731, 510261279, 481512558, 214658827, 687212563, 897757632, 810904806, 902533129, 124719986, 136261572, 62590939, 91038364, 80594357, 893664281, 474330120, 444338813, 457906052, 15073593, 187613736, 411390851, 44438477, 505814772, 339897062, 163569054, 908043145, 908524605, 801542263, 514408078, 654928769, 453090284, 669223167, 984168155, 167229498, 520357386, 870917981, 221230763, 147674848, 40015588, 926820374, 877121355, 499211795, 338649505, 551402782, 978674120, 408231324, 508918566, 71208798, 882455446, 832337796, 232453568, 190441539, 573990929, 857852329, 418623219, 369672652, 476775625, 820945154, 457862733, 44152341, 15836537, 997375358, 891994947, 90831656, 16756076, 136768558, 421431253, 65025604, 622529474, 3659555, 771176983, 50735472, 515203718, 163602480, 558566346, 776594586, 507947707, 39948798, 408582960, 353722667, 856826279, 243650430, 617504244, 576785957, 706621485, 648106415, 753212759, 511826108, 72404565, 912304444, 122039466, 834704958, 408277463, 559959624, 978467461, 899165586, 305961683, 607642240, 8788885, 74450257, 443991499, 541462547, 140882046, 342692593, 611382001, 57206174, 94149504, 532384641, 235738883, 853916514, 341787919, 69732085, 321889541, 569941756, 580466832, 388751722, 578535386, 449283192, 174407969, 277271878, 866041395, 180257749, 97862118, 799739083, 331536670, 291412670, 322365403, 359156637, 855139020, 962193216, 428764968, 862075976, 378010279, 169457255, 962016626, 209625710, 906244925, 261276586, 178672067, 718385436, 29210938, 540089002, 647189497, 920847589, 814352348, 950372668, 188338906, 352265892, 330021206, 498844044, 529951509, 409905442, 847809888, 484214202, 551090244, 917354463, 720918579, 609609718, 37878511, 420828023, 293390771, 467474906, 738966074, 469248810, 546935268, 324031634, 178271259, 349046950, 720567371, 673327228, 913833699, 178787138, 908818386, 861304581, 986767086, 378509432, 404130810, 73539003, 603900038, 888781109, 179666782, 313194207, 702756974, 292589752, 286561872, 92155100, 846339467, 393738006, 516852765, 641418173, 152290216, 773144099, 387819999, 207422505, 810486564, 438436804, 29744440, 256108175, 408450762, 245061940, 643277997, 209209816, 872603129, 622048063, 164780921, 643711443, 30104159, 750087556, 151725725, 596146556, 876359034, 84715937, 499101346, 289220144, 467229742, 122237187, 225252543, 558552302, 483803661, 724814848, 554697117, 105527521, 565774250, 437026198, 423615880, 465775032, 416164035, 742034431, 168271990, 30206889, 307246884, 849742626, 301566689, 410932429, 469663856, 569007674, 626923995, 115065027, 95615371, 106846935, 93310471, 646948771, 463861148, 871305445, 528105297, 366791674, 153537971, 899237888, 59481763, 202507538, 686100246, 700819948, 451082115, 488538021, 401770962, 175479257, 444279679, 513187673, 115831672, 236480016, 975482336, 558230948, 33504657, 873211493, 156613158, 268882189, 395994262, 641604792, 593638392, 527724980, 82514674, 562164280, 821317565, 26370092, 812789649, 683056325, 584263131, 557924195, 373712950, 264313309, 380798951, 87257375, 450203209, 944597933, 282688487, 686578116, 142339880, 754437900, 275203368, 556458175, 449806927, 551413320, 187783867, 328992601, 320030848, 491017550, 314507132, 227510989, 66262787, 456181224, 26766253, 312590687, 838065594, 369019969, 524967234, 718257015, 609506769, 367781567, 530239446, 984971082, 920434166, 806974042, 212749181, 933645115, 960798757, 441310699, 858235753, 993582159, 241966999, 422258154, 362331390, 897518403, 385705452, 26015865, 863516317, 296752868, 682462734, 640781021, 121539895, 522187296, 313074096, 780673386, 891822064, 732365576, 219698137, 490445830, 4633921, 323708260, 680071101, 834301823, 905788956, 919619345, 736684401, 802092006, 463033660, 629886165, 76606738, 811711774, 84127757, 405195200, 367483297, 934498271, 500915971, 160689541, 131930965, 219699011, 865727368, 900310040, 925461336, 186695108, 847400766, 548943696, 859948357, 384290470, 878476971, 864118597, 246949920, 928636614, 231722009, 53137893, 557608646, 653870741, 575116426, 105197460, 992941789, 195933535, 184975076, 971327712, 465568463, 240128932, 257882251, 659021744, 616230903, 592178382, 904828672, 883780255, 578150147, 995551973, 895253640, 282229589, 249800555, 564685023, 37527780, 473770202, 93335558, 827488589, 982063942, 616596973, 204258091, 578764224, 214944675, 545727748, 680383395, 338542468, 574377015, 881936460, 966878512, 185821274, 307279455, 917058920, 214741665, 866260239, 38073544, 249761401, 376805367, 772706729, 630095092, 743639623, 843532279, 993421935, 439820866, 69704808, 940719436, 863375194, 516610354, 177089434, 815452709, 344936273, 58079665, 538410545, 223855428, 221744061, 574721013, 715741533, 819497474, 913594494, 732936594, 427308377, 436217275, 569333583, 156032599, 68690734, 32723726, 653871268, 318757000, 164376688, 37654990, 499247777, 337042610, 361944950, 548782284, 336710454, 588551897, 512944116, 764677558, 863665119, 977771815, 626322696, 222501606, 957156432, 859095409, 74494255, 282439314, 57007817, 402911827, 201921550, 418688998, 414641132, 788414524, 276654782, 773454113, 349931919, 299264893, 365155792, 721283370, 979931184, 815608785, 307962197, 954906975, 911490012, 134194004, 683873333, 986958556, 656414364, 282118180, 442903925, 209897839, 152469654, 628643020, 818838327, 614840903, 310533939, 322121801, 841012302, 714495646, 105078030, 81732285, 609056032, 159900285, 40585981, 419831233, 327370690, 541910004, 161593823, 389393213, 216536409, 393359597, 912693877, 942672630, 14932390, 156251893, 457400212, 250083364, 616439288, 667256820, 936251008, 30069545, 372658412, 149707887, 227350838, 844287024, 151657138, 880631693, 257481042, 505011786, 711695197, 661044356, 711594114, 972634482, 986876160, 587278479, 849201032, 330635474, 277391447, 522124851, 787551676, 264862576, 820483367, 111246451, 921681294, 820887842, 286408294, 297496997, 440135667, 343577641, 755427285, 324920444, 837554705, 34473508, 772003277, 970905786, 594416769, 422546608, 191289121, 754233646, 800545585, 778440474, 52967533, 844862786, 452987144, 74916312, 186976862, 899904451, 637183962, 628880326, 319724001, 76249927, 32826677, 526468957, 903401811, 582906456, 436329313, 905245787, 255663992, 222928782, 941268381, 99384928, 784545862, 575468231, 941907858, 299397655, 835227176, 418734499, 379359460, 890884674, 189411381, 491439697, 267642018, 82384531, 155165936, 925456532, 257783334, 34310350, 731635737, 435401012, 137168193, 630363810, 549129372, 233692374, 402604069, 879076323, 741852211, 736674333, 806750067, 464888381, 208667019, 62744653, 140020597, 384270209, 729529675, 439332855, 643158514, 668318726, 350775565, 648193494, 185905204, 283426886, 422494727, 110087369, 736088227, 377378495, 625273957, 260570655, 296298811, 859936265, 458642230, 398199685, 137153252, 102997453, 769903734, 66739046, 814485285, 901537117, 189126625, 382021813, 325904888, 42874241, 177697296, 607314953, 824556891, 413993550, 218895000, 146414417, 986198028, 129623635, 817494863, 870592147, 519303547, 449440386, 261846448, 99375217, 301341879, 267332772, 487415323, 116300479, 269847107, 632646128, 901212849, 235847342, 873071523, 665315365, 247257109, 72545495, 343840820, 162189260, 929026424, 773075470, 997259918, 616274766, 747320401, 155298180, 40032942, 811974260, 697178546, 757267871, 120324972, 973383721, 155938017, 435595123, 542460396, 41849750, 167276099, 400716671, 375361944, 369750387, 860294909, 931802914, 740902109, 689318443, 589853800, 45944498, 685187760, 289127055, 39712097, 195075989, 75716633, 198027331, 935406844, 408588817, 472260981, 219099911, 258309584, 202891082, 180023235, 94707244, 772012134, 181117333, 244394367, 582082488, 126645631, 986797256, 993633410, 966847784, 754800437, 428126166, 47772836, 753831604, 698724928, 819752770, 676068333, 273818758, 797768836, 594247416, 189446097, 344060386, 479065496, 162223551, 233498216, 484168310, 754004095, 470957703, 57163791, 841974386, 150597297, 463649222, 782687709, 16417091, 750425854, 428324607, 960230271, 739675470, 874694376, 163287663, 428809251, 482515578, 55108058, 188891298, 103600401, 564537828, 179937918, 708799928, 339237061, 351007958, 154923909, 19867397, 79970903, 464928520, 670493003, 362627255, 273039041, 374420326, 916788157, 879700657, 442417300, 886590084, 880848242, 204077204, 737457247, 168520829, 144475013, 126310023, 943351957, 620097326, 676345642, 13431425, 332957063, 396362796, 922795494, 934977784, 95013620, 546092632, 276882345, 334078418, 740183391, 887496684, 376421862, 866910124, 581361500, 282152315, 906531042, 362286651, 440955165, 417381726, 776211628, 975987, 687107873, 374088664, 993588192, 500483928, 466197155, 152148389, 958596889, 139494177, 203024235, 606875070, 109441412, 917645715, 583796562, 454938498, 915883210, 173318880, 881800125, 312868301, 391745865, 898873132, 332257999, 439936986, 72730649, 250575306, 568752294, 678014325, 90937865, 534204352, 670301692, 793467472, 952991574, 562942800, 4152506, 192743164, 551380579, 153338169, 960002913, 915521740, 732018926, 16821431, 737030845, 609296986, 937518979, 256588559, 102726756, 463097628, 531214894, 506865406, 136173539, 501751505, 165007802, 962515691, 216813260, 404144840, 782183216, 43644191, 524206285, 874922259, 726571710, 355549130, 842065679, 838953089, 500010759, 461722832, 161755421, 664553302, 760489053, 79025410, 886405644, 250559656, 447999640, 634648327, 625426972, 833646675, 628729386, 195079144, 481902750, 435002358, 856887171, 179555956, 794715757, 772195390, 571445152, 466313949, 963857766, 320756054, 801350998, 347911481, 826800443, 71297879, 306921952, 492878381, 676184688, 710405806, 706874951, 701715596, 319896797, 75649027, 501398567, 703118741, 479118589, 124789737, 603848201, 119413651, 474684501, 20929662, 1368529, 346040433, 214041530, 175073279, 55231661, 671880756, 531610288, 111719836, 209198194, 95340255, 853122443, 540406322, 365293355, 209161916, 771363796, 659415961, 483845200, 789346000, 517124671, 380495885, 579510274, 568383810, 594326533, 713394092, 79624549, 724922125, 717324870, 406365556, 735074944, 915743078, 451885533, 729870318, 809328310, 887868687, 298622313, 749316843, 906200162, 977571862, 878160944, 240938200, 851038110, 203178152, 980312410, 335516530, 560820414, 79956815, 559235070, 897613252, 636496097, 613146039, 755603455, 505544422, 31299051, 749379500, 949955516, 321833766, 523706679, 675774414, 21805946, 350520555, 638041787, 759642784, 233037030, 97485550, 186898480, 111151789, 79952205, 359425591, 341746263, 124426881, 712819789, 745407437, 944661031, 910478563, 320313949, 852643024, 25512574, 760592649, 356673710, 65507439, 42081540, 768529573, 335043015, 487450870, 25937326, 217823426, 501670981, 905364646, 203175761, 74635404, 582215493, 36668159, 593120622, 217111731, 242055424, 383044680, 786613071, 603448299, 808269536, 327907818, 242828871, 677481098, 186816666, 182357067, 308834396, 970536407, 69494350, 990067248, 659659917, 724530792, 317768424, 542787356, 233658805, 765393483, 754887819, 752812085, 99604975, 292430934, 249754499, 877498797, 560869001, 752446491, 770183419, 830929823, 500335533, 813672467, 615294438, 484223100, 240233877, 554400176, 845520886, 405722079, 913951318, 343678473, 249362961, 908244380, 393877494, 385004274, 515140596, 797603022, 870532603, 46607111, 81280006, 369097501, 564752539, 743576787, 54795106, 739251279, 799245625, 503194332, 295947171, 739214667, 622681725, 656359150, 858439309, 930747268, 415142004, 534149446, 740307828, 837265136, 287928841, 837716798, 632857796, 897666147, 661988356, 935691623, 52828648, 922350275, 996198112, 329585590, 200818309, 418878225, 347106059, 13888366, 752666211, 825822209, 878662362, 760646933, 859194952, 649291631, 663299409, 182547655, 351750056, 262459621, 967657937, 723191939, 116729659, 557053945, 475800480, 635388675, 645375219, 229185610, 102546839, 754687932, 751368687, 909935137, 226659202, 188271111, 900199947, 319355171, 98600650, 305554208, 825518206, 143557032, 60629162, 91333540, 163574768, 149900498, 38814615, 129756997, 581278041, 535640995, 939085880, 374641031, 629699378, 727355605, 429031813, 745649308, 98751589, 830753852, 986719508, 244585113, 562676528, 100010564, 921750529, 325521690, 558499327, 306874874, 599815650, 53520781, 907542419, 960742990, 946239132, 466558910, 247299682, 619172808, 89640297, 529931857, 716284873, 383788763, 465853099, 229631854, 488158890, 225181371, 123679808, 202940831, 39148071, 534559227, 370007853, 878030139, 59237473, 750132963, 813811383, 894084635, 508517263, 498522816, 452347323, 401417963, 866713304, 690970285, 233767429, 401856640, 551411261, 114922650, 296847114, 144333456, 325092482, 471786969, 846851726, 438600651, 921281986, 104456173, 60394054, 316670963, 611174870, 671296686, 653754362, 80209464, 959817856, 405455330, 823112141, 980179111, 413854162, 874824715, 217411694, 787824848, 684296551, 106012774, 243247866, 463968478, 56019181, 496231303, 317588206, 621345608, 52236952, 501769936, 301244122, 722991958, 702024555, 552912278, 100379614, 44281503, 461565152, 744024426, 255433143, 31265636, 908085810, 25801299, 490331623, 537122675, 467483806, 63278586, 614458328, 496139710, 306878929, 570380481, 265750291, 579904967, 272803842, 556192315, 181398074, 742515868, 343418103, 276014766, 740664601, 801898515, 687352186, 390893365, 354296201, 841706607, 366794921, 993040985, 245252094, 938592599, 296438022, 734502912, 281462144, 767293725, 857322458, 782191840, 897546506, 256985560, 806906802, 918914397, 380207445, 815300491, 156623084, 257675224, 236882105, 118722001, 940803312, 96453024, 871927418, 135130569, 84112227, 800208800, 234829604, 496448996, 787590637, 565352259, 882867899, 36192786, 497253025, 765714393, 425855182, 464610825, 597768467, 628153364, 385545352, 17190974, 210721924, 117382915, 556212188, 699969619, 873632215, 392655029, 474320108, 537794, 470906933, 995409820, 803334050, 942424402, 512024463, 255277673, 669339814, 641082839, 624269128, 9475225, 184156521, 39871818, 311443033, 662322590, 780431474, 387188674, 531723181, 443080826, 804322967, 412939425, 723794112, 364327634, 681932765, 655277794, 684012425, 263345144, 310188627, 584355498, 956669649, 23232558, 147498678, 2460469, 563753750, 21866692, 730230007, 215591716, 888826165, 225357555, 279107501, 774033285, 101746394, 695783936, 360267892, 789608641, 103249160, 419865436, 81630194, 85214734, 568562081, 316325677, 645661811, 463573391, 171012575, 177376757, 166267944, 906878215, 250362421, 396017715, 836446763, 50631245, 616255833, 652246073, 690541018, 322027253, 53625500, 124704198, 103305376, 953579817, 258004616, 31785233, 684820717, 516286186, 688893032, 438554912, 624312695, 296708463, 767094164, 203251445, 388529802, 816769839, 589961075, 483262482, 519019255, 431858486, 217389187, 930949235, 321628648, 980588210, 890786698, 834761856, 985306580, 768253791, 943912154, 134728617, 977122639, 787426925, 300520268, 214781138, 803097121, 980325374, 267641119, 179320954, 507504098, 137858161, 748183619, 476054154, 646241322, 869170643, 53164753, 880245687, 246062909, 84047924, 802705913, 348152041, 827397955, 18234661, 287595992, 327930712, 533169367, 892326526, 695274337, 427537408, 460271341, 34192164, 91480844, 498027922, 823865017, 458150165, 507493005, 847260496, 850429663, 490237205, 253374362, 290071016, 789572965, 338646247, 33788990, 61052025, 833215270, 403543342, 185871291, 259385828, 739305579, 160179770, 104464836, 498402550, 919754098, 254970964, 895476188, 434450855, 307376102, 925667147, 26441490, 713311623, 863058835, 87412727, 993214071, 624081897, 897429357, 108269632, 894645190, 87900746, 603699715, 327996264, 791129699, 447687173, 81218137, 611503775, 9158296, 655594829, 852686700, 132694698, 270072096, 816405341, 156001790, 916231731, 630946420, 16751002, 952536738, 271005707, 86474739, 498535745, 155406686, 567405036, 803208175, 308155064, 78832770, 12728736, 254522064, 508931171, 843995836, 647441207, 34011532, 629799482, 576968475, 514877480, 368454184, 874336294, 347816075, 410240486, 837042798, 983396515, 314946711, 831594763, 858010042, 699220135, 760237225, 864042351, 423763431, 962238156, 441420412, 878441936, 110244073, 493424692, 290778252, 69871731, 416208662, 929402520, 372275976, 53770392, 391774771, 791129216, 743263299, 915525062, 57488186, 392562193, 474154454, 420596034, 533569830, 21433566, 521755085, 267916125, 205578755, 971308931, 451234504, 565216649, 406515847, 687522445, 256397969, 28992700, 189943523, 530703549, 138327525, 251229629, 347511977, 433088092, 45045426, 881669996, 611419234, 500939852, 441004220, 49816765, 632522370, 80709469, 619010957, 628942339, 285777735, 393103050, 357148200, 504076293, 631699434, 751571715, 241157287, 119162572, 934209217, 400977359, 761317599, 598662838, 314066408, 823516923, 269926465, 871720117, 609889797, 775669336, 464104088, 610848229, 355754634, 878125110, 876064618, 983001157, 569974750, 773336061, 661659174, 301966842, 777484254, 613557183, 56681246, 790055439, 132641447, 560671723, 770436815, 62248189, 158673162, 492036066, 761289393, 493751813, 207806764, 648978741, 38396582, 900401183, 737647993, 35544653, 636471551, 872756503, 132676222, 146237957, 453850051, 411893800, 270882430, 691626870, 458865534, 380962082, 947417096, 325892554, 716204171, 948942679, 274663154, 130852568, 408267302, 363133419, 742061504, 977062474, 733909715, 491168615, 428546748, 589044725, 446164874, 875987086, 896585385, 277249384, 779556388, 758609950, 623709720, 572295481, 229397554, 108659237, 988366671, 971214135, 943006119, 713306627, 998444511, 366523820, 126701325, 680641803, 576396799, 498421160, 944454439, 343685011, 913924244, 430089830, 178750843, 637144792, 442704890, 177200406, 494920915, 415431184, 393702902, 699918082, 307092434, 783611144, 299223674, 871279343, 449048076, 846441127, 366275459, 802691658, 614094134, 488148981, 892883431, 799709915, 233912073, 880579439, 814171868, 615349890, 783900493, 548531359, 900811752, 75917464, 116923281, 327164919, 840628519, 477491309, 27489982, 850931097, 979505335, 900218928, 495127257, 127552849, 427716721, 673225642, 601060715, 723196888, 257239326, 146339730, 978615707, 752665989, 690191464, 712851947, 260700237, 701327820, 173321010, 199228883, 280758181, 165339266, 982171785, 997894564, 293615785, 369330249, 702496027, 674120263, 877892201, 443516672, 69402535, 701551814, 868800212, 255881762, 476832280, 939741801, 202004492, 663550695, 395717622, 530566704, 336067536, 532688236, 534815639, 872408239, 992969186, 719525623, 826420416, 846300262, 769721745, 943519143, 648018199, 85703446, 30745398, 799737411, 17693812, 349185266, 296350920, 792233879, 983332621, 559117601, 814472143, 776675834, 270220259, 160651322, 518937137, 53528221, 445203437, 413330759, 495539926, 418924017, 220921790, 853770650, 18466521, 266674983, 707192007, 219542190, 856250976, 792144226, 754611453, 793363711, 448188974, 445232549, 269829202, 62549503, 323689878, 902450018, 983353638, 180196109, 722686257, 120206330, 326124605, 945954333, 102191900, 134154542, 741265842, 234652127, 718827295, 21178048, 583212064, 769086134, 445349163, 968820829, 602351677, 382857660, 654299396, 902826505, 601374948, 918816810, 423058687, 629290003, 72712827, 677892515, 810359493, 674661022, 416996977, 824607609, 825761619, 732107065, 797000417, 744918727, 399096651, 299818221, 69978051, 514165285, 715427086, 32182319, 713923579, 654669789, 480187422, 702106305, 86566591, 822642599, 850338625, 715480425, 27056408, 719576318, 300085679, 76869784, 621654878, 288787277, 474126954, 14892310, 744745235, 884930859, 339925233, 700275191, 949423433, 276429704, 727789902, 58934406, 863503803, 234763338, 464433579, 473304956, 623228338, 738189033, 227101225, 532657834, 627816751, 294289932, 276517069, 91860344, 232610126, 200148933, 189224608, 78119547, 734041777, 799728152, 476663797, 78512711, 375326602, 108459342, 515619756, 115198263, 957044975, 374344148, 666226063, 1600590, 98728568, 408889062, 912575601, 220155139, 667108378, 629260584, 19246054, 259330271, 815978657, 238626749, 48153479, 120418191, 800380586, 510061869, 59829262, 825524567, 334753491, 34182484, 936602892, 833706499, 591983559, 242723254, 760662256, 199325244, 45036472, 183441007, 640146560, 740127319, 864933869, 332039403, 178310561, 973970750, 240387920, 808401160, 414292993, 439582441, 865751640, 939498012, 49361673, 51927210, 404617638, 414163173, 505731489, 573480594, 233247500, 194760546, 183060041, 256795561, 13582226, 550014114, 8849244, 149791837, 310529261, 44801821, 736798497, 432697711, 562192691, 408872067, 153984389, 194021824, 138961305, 514372676, 935823804, 666266126, 849681544, 606657201, 424387001, 761474620, 812879676, 393448783, 538203230, 452054396, 466878369, 759825436, 672422854, 223326172, 911764386, 443436390, 995311906, 137106033, 300285165, 265400458, 364215853, 922428125, 779123225, 719147698, 223836003, 705021157, 352726029, 760720521, 814960860, 257198022, 737860752, 209414194, 763781059, 632059819, 343799235, 789747647, 106445651, 318427386, 236234803, 616775720, 639775602, 313354496, 806715643, 31497345, 167084440, 386618116, 702789042, 761591212, 216197526, 362938183, 54550875, 850858497, 524995796, 945250129, 664736955, 988934536, 120613890, 762316011, 344119144, 572751285, 183890153, 567999518, 692447457, 687567994, 950936643, 209137710, 33077232, 398415411, 110061699, 332748872, 73220783, 165170504, 940909220, 731925389, 127914722, 318352260, 32988496, 857932297, 429342231, 481137088, 799646091, 581722118, 174889926, 351278357, 351632326, 700117284, 950564425, 410218293, 868970903, 233915228, 923531760, 589440245, 199907514, 899105056, 323127938, 269322009, 95761148, 124327690, 784269523, 315149225, 412054353, 886541951, 206889028, 674010802, 571678612, 305960702, 254982613, 285715206, 952392165, 812666898, 433624205, 818383314, 618668175, 482909059, 757440184, 320018661, 653950442, 754047514, 841955649, 829334098, 382190621, 342711529, 473701402, 482938138, 265152614, 24009387, 300574237, 617904038, 590108627, 453624048, 37974221, 567996126, 51048494, 370101877, 325346993, 893917581, 392615754, 93160917, 44199000, 307010650, 196093831, 908867305, 407800066, 44865603, 612845302, 530307382, 685885, 210691028, 187925900, 444204554, 488491466, 923332400, 435269648, 27427247, 474377908, 901890259, 989815948, 671432298, 845335609, 374615957, 491933573, 360941401, 942284181, 365596956, 141300253, 701674290, 847812323, 848620229, 780293441, 243568056, 787350731, 74358681, 57443058, 606749178, 579993075, 405224296, 871158959, 797882869, 774403105, 914433945, 286594200, 559581679, 154287699, 125280598, 981058556, 65305596, 251028739, 813664571, 401337839, 378737585, 184514652, 987133982, 322119671, 147135969, 877842058, 996307569, 515760622, 582979985, 394237985, 899370039, 533032850, 210341471, 671034634, 705830040, 854157060, 278951559, 742332715, 23607953, 827662033, 759065017, 468964291, 453956896, 15174206, 482152279, 617856661, 162527246, 213196735, 408037515, 230783611, 954209428, 838454668, 481932851, 922671197, 23678015, 772793789, 390852589, 601511578, 169100334, 771121651, 251712859, 192907985, 757228352, 763318007, 708329173, 609824029, 238682037, 232026099, 258860069, 444187652, 349517767, 427893583, 169788331, 496628112, 5672294, 692965543, 495819154, 391983424, 95656280, 935648866, 302942668, 65033240, 104254655, 830981710, 136613469, 187842319, 410665587, 276758834, 962989290, 264826416, 612508309, 280979884, 700423206, 370507484, 244466154, 241626258, 694546640, 66251027, 307099839, 390890845, 875223133, 375529616, 834293097, 267324276, 440821328, 105408598, 993686696, 904297914, 293477102, 445840469, 311287477, 675974675, 200767904, 387997964, 173379272, 350056444, 879282800, 653908423, 180075225, 782261450, 107319619, 758818558, 159922406, 775106187, 803755345, 615533570, 944510643, 971322362, 627704043, 545048001, 385160763, 578077716, 703009002, 675523481, 874937653, 776446480, 88099381, 239727093, 935258708, 230741586, 338525743, 537315676, 59354417, 855548875, 807435254, 431986243, 632989971, 892219945, 754755280, 70067371, 284514624, 719351018, 44198882, 640623656, 965733499, 415728704, 907305052, 923008914, 631168405, 42203159, 588690831, 688621625, 531349905, 372801927, 283546586, 13232552, 97165959, 731716462, 12074829, 387169830, 645293362, 380421139, 441754349, 667043510, 150531927, 658951368, 500897328, 142288957, 644577107, 213964381, 240718608, 97925700, 932004908, 503619214, 495644587, 597288911, 790254371, 486860485, 825569836, 315719269, 771743532, 600474623, 397139070, 739685607, 789114040, 286886373, 297450027, 45978806, 740702015, 627621993, 931921539, 680550136, 400266646, 949560244, 506156072, 999180920, 796110279, 978251197, 551271934, 428764677, 45641402, 741456680, 986359182, 496355408, 835203971, 958512414, 713592504, 340998093, 195811602, 979310463, 949931422, 690309930, 836789619, 176054265, 312206492, 11067409, 742552586, 112409401, 60281045, 672976514, 648294606, 707172414, 246353787, 561121694, 235588415, 264068908, 26300437, 541403850, 632837896, 118270223, 901624101, 338474561, 303249274, 673702538, 786688202, 671572183, 542963937, 835873956, 647143318, 450086639, 541904793, 888374805, 495188646, 208587510, 345770005, 313975958, 724859485, 126909212, 184925580, 479129432, 621826479, 497938580, 870134092, 436586450, 11780588, 876582885, 948212796, 668863915, 766275375, 150672080, 669954560, 23084395, 126062278, 351778864, 746769545, 965631001, 603362929, 632337703, 822857926, 143756572, 453937299, 769912401, 887636088, 440568138, 318364336, 436635685, 750268478, 828235678, 969071365, 427827274, 150114450, 607264688, 733001213, 270809860, 943577766, 800082605, 485530452, 404418072, 472125259, 674385707, 64996111, 518075655, 946302178, 719029478, 145645571, 340653788, 829872729, 325167216, 403518970, 541409873, 724734131, 783910684, 798931227, 747982043, 485206967, 954523715, 554075946, 57312683, 199052213, 868675792, 252723287, 768122383, 150894509, 804997937, 612360070, 171480336, 382167316, 705954721, 616910229, 549306701, 542996526, 912195824, 187901075, 449604276, 826866656, 436779729, 897242120, 444478740, 458981018, 609407574, 316370429, 362376156, 589481380, 592147260, 376292830, 185358343, 473370953, 828041987, 63296194, 917922558, 729750960, 736084025, 938044773, 625420926, 112870648, 564391432, 16381208, 760761527, 602832826, 351800187, 64187541, 219166243, 796455831, 287689417, 532038708, 986015353, 741526619, 502810261, 610012890, 798271794, 46308333, 985884126, 130322935, 889179612, 341314415, 228870813, 317914827, 168354507, 538882416, 959480345, 649728931, 791680252, 889283558, 802949932, 396000078, 78056494, 461522951, 261780409, 47774504, 489004000, 265399221, 550758000, 108041910, 380887700, 593687913, 715206161, 603543508, 789062628, 682661236, 188608399, 76336998, 301748211, 211739260, 594161930, 129596254, 215578391, 228600044, 3767509, 410913980, 326024948, 743749140, 246612003, 204707149, 925769905, 702389991, 993956600, 467270767, 544561708, 644666700, 665344095, 359904661, 349660756, 707660032, 591463332, 588425034, 939217984, 133758613, 309390143, 153385741, 329697890, 832292420, 781676865, 637434004, 732445294, 329573238, 145239713, 622603824, 647611498, 163114030, 396852204, 546818190, 299342493, 269532080, 608193276, 878005805, 458884356, 102513655, 65550449, 904786989, 436304859, 185162967, 888600853, 974377868, 575761795, 118558543, 680567456, 3396895, 704046297, 191028410, 601204473, 687717284, 92911792, 390109227, 304775491, 124542043, 114036826, 27828518, 512509074, 118674233, 707616789, 201986773, 430643726, 356256934, 70560034, 969075432, 968056852, 45310630, 121104709, 510829573, 204252851, 549940169, 273478206, 333206802, 442317733, 852745329, 411670308, 319413458, 764215381, 739325104, 637460490, 39467442, 609060584, 221676077, 122682937, 957126850, 872511946, 825658066, 801154102, 774940083, 890105512, 230848774, 123319111, 719436104, 575960404, 629061208, 603083346, 291678404, 614343736, 205704106, 216765601, 938679900, 634509557, 231526641, 125897962, 581463998, 278259744, 231275204, 916495375, 768370372, 243220479, 374572699, 7157882, 508911371, 353159729, 366175092, 589436875, 710631172, 382815710, 970269987, 751940468, 183917709, 58906645, 510652065, 768085550, 271968412, 303658670, 171601419, 29874238, 996965066, 338699628, 690542305, 870528340, 654374694, 531250879, 160311798, 17236584, 401687281, 464178344, 933664420, 708231420, 503202854, 634257391, 553012445, 692247438, 451542590, 56382237, 882066975, 67655277, 595449847, 34763700, 311400761, 978623521, 591693693, 15240385, 844689755, 305413325, 264188266, 241636540, 388703149, 285102120, 283999842, 710904163, 214902933, 301396867, 872898619, 347466250, 743631263, 991706112, 42931496, 363287599, 314774407, 530985634, 825087607, 576621417, 972521187, 482186305, 773742107, 516466151, 733614788, 875125243, 323316249, 259162405, 135911599, 259538918, 637956185, 694603417, 230603275, 991461030, 786888200, 73357438, 403564147, 163309652, 814876870, 244247205, 79102002, 830119843, 953209727, 433791271, 656845136, 316316006, 755277949, 167904410, 69081264, 261899895, 526493218, 603048164, 178007485, 137344230, 872495411, 766412584, 117020219, 143635626, 76788561, 681311891, 124339292, 517040476, 474032056, 973614596, 442842779, 826325690, 813992305, 240096674, 649510024, 748043494, 757112534, 113542292, 944086176, 569980029, 238525494, 938931047, 23744919, 349637182, 694017955, 211763481, 346503420, 649881022, 143429102, 930421929, 466271766, 60960711, 966796474, 834179558, 536153966, 207639669, 87196843, 465417404, 421553033, 430705884, 41447667, 935659366, 757923948, 630450663, 971005297, 30828392, 665196309, 87948961, 886127588, 164426112, 923996271, 464932059, 637633389, 313763002, 422877887, 716489750, 232116879, 462076337, 576940926, 682597786, 240335037, 880503073, 652603192, 592021663, 181571625, 296938380, 337005346, 929825568, 926793478, 182220158, 424510097, 133857092, 992947883, 578549199, 463509046, 903201687, 793199929, 289802322, 816472557, 166566022, 389645647, 158639515, 990482284, 731172018, 738207844, 763228036, 22513586, 998994916, 379901146, 579287179, 834521737, 965663969, 55396291, 196716715, 965943909, 689857558, 621979295, 528690120, 703268180, 654759374, 20619702, 451276171, 588550591, 944820115, 815329799, 935795605, 317980894, 536599868, 968367089, 768168039, 461744106, 803707832, 979101903, 867804859, 441483474, 703532795, 88467165, 103597692, 71094464, 666885276, 525456314, 243784977, 389670181, 94138621, 879889677, 516007263, 333263282, 456393298, 221004615, 743296681, 155624335, 161128245, 647215463, 766498658, 960803225, 84933272, 630241664, 991571026, 770357410, 904130418, 733521569, 727832211, 852694071, 669704084, 694098864, 227723963, 392674809, 119860635, 4168820, 572505022, 373905928, 164967344, 431440542, 770780122, 185390140, 469527278, 136541539, 931202489, 31595800, 788036418, 494753275, 9342305, 345233340, 207768118, 631642390, 807455599, 555171652, 216658674, 579375603, 19775605, 110470256, 327945593, 213672889, 827089806, 555753125, 367205789, 478770215, 709740658, 676041298, 589617968, 785481680, 566097335, 330919812, 926229823, 586902317, 392238723, 663707051, 665107935, 848080829, 782703569, 219549043, 965702710, 134391210, 845085164, 699249776, 787993705, 629622315, 972655588, 305628998, 84097541, 8811571, 106161666, 981868860, 797763528, 143726876, 493655429, 752987783, 599651577, 162210054, 58933483, 230856786, 598747040, 877144049, 661811360, 225284628, 458543787, 654339814, 13157109, 740560214, 727430559, 863954136, 485501526, 962368825, 322219573, 200833413, 142947389, 283591638, 570100692, 7737307, 749487495, 4149207, 450999279, 250042974, 37380780, 322672803, 759674701, 511045076, 11473666, 518935233, 110082079, 282229697, 729257649, 822497840, 167019330, 161025906, 547021508, 637910048, 687204509, 630077980, 779239966, 472285107, 543502036, 55872763, 880884866, 741533579, 554900134, 914159750, 547190394, 982521668, 198596704, 228794250, 43127828, 595492274, 441361445, 39608589, 395735026, 157398301, 30305780, 243374928, 281175796, 315695378, 465511354, 324684766, 858993746, 849691769, 132439679, 876363694, 785171903, 329726665, 688475108, 850253610, 966239609, 439791882, 27180544, 329925951, 803459414, 361482984, 631552790, 32619919, 712872121, 63558317, 242763911, 920162015, 583040632, 281971969, 530280887, 698011835, 156950362, 727104879, 936435250, 230296227, 373871041, 777138156, 35960294, 486255272, 341779018, 229348049, 967424907, 388696724, 340494794, 312067732, 859793850, 770912778, 742472588, 685955861, 20566600, 768032193, 611514814, 54193724, 382875433, 911436284, 528237018, 292878066, 156269892, 87583106, 790404577, 372460379, 388197227, 6255139, 790584177, 95169355, 957022700, 495654957, 846050076, 257107641, 545489718, 485951687, 808086329, 761231173, 854681129, 807234, 437425964, 608870847, 248346072, 403860, 906846780, 743582380, 446460017, 515297756, 511921018, 584800972, 348930016, 880838527, 354445035, 7771535, 489551117, 462323639, 345271463, 648202410, 950753477, 358331229, 418193393, 997240525, 939026213, 827454764, 414511976, 728209187, 391030888, 133810220, 543665691, 403797045, 11219120, 489272770, 508917140, 181801933, 920419220, 69411298, 361488783, 593223512, 443152644, 392365043, 948304564, 632019300, 762415829, 896636296, 745780512, 826751661, 186640630, 491583121, 660077398, 420971635, 37568430, 823924211, 289761053, 115925352, 35916548, 949607777, 710610633, 708718622, 662071711, 792550656, 444002604, 149420553, 159949668, 428987584, 160794615, 495305290, 110434903, 415262303, 250393848, 853831260, 856392101, 879789312, 143282888, 482819310, 143342073, 999909182, 805518193, 48695426, 915250997, 171852131, 362427391, 811933799, 286479546, 83385632, 588562770, 251348667, 104999545, 832098390, 581479555, 329439349, 341620977, 292562458, 928268637, 923840140, 766062098, 634816803, 987652450, 670191742, 713888841, 365982540, 961928994, 276626091, 899599147, 591270430, 704313300, 627915045, 600468724, 341167275, 593423889, 810745483, 105499216, 650682265, 550590862, 155839984, 113217487, 544611474, 697834058, 782975334, 939834625, 43435512, 634251184, 675589527, 657864128, 855922905, 538226438, 98964628, 576444250, 845686828, 432660815, 443753174, 959402816, 29573725, 423138834, 723627300, 425602757, 647513525, 753978652, 786793767, 968568153, 559146423, 625126245, 602027863, 335328641, 51542195, 258264700, 399716668, 920291511, 546993452, 48995161, 3356725, 996329855, 556788924, 404795218, 787316597, 861141024, 182702668, 983955428, 853252196, 148718756, 71670279, 338538699, 195380491, 190354365, 999002704, 160746435, 395265851, 906626020, 171750964, 323183376, 266627758, 223305730, 344710249, 273034377, 241996050, 171202491, 880358597, 695842229, 147589228, 828589900, 23659793, 268784037, 656795842, 579503133, 499344055, 985787891, 477182505, 211541801, 391718876, 240223670, 459271332, 771451275, 865124133, 643514966, 33512727, 783087084, 545155336, 787661795, 37563336, 756765885, 35206598, 431209500, 348708312, 26774799, 272439509, 7618023, 124231292, 573630893, 725935305, 742124762, 158742427, 359735862, 752389136, 449437709, 585019951, 62293537, 538031699, 170548067, 433296452, 364979097, 388708495, 124443368, 983335647, 488699240, 737686982, 287999626, 53965822, 693852334, 911745175, 490070907, 386412679, 951391017, 125213674, 71475581, 154981751, 943853492, 892761585, 477670182, 191205994, 732013321, 153853057, 486070395, 821608743, 906951348, 381760434, 566668165, 98600557, 736068589, 910558742, 548291451, 217616705, 817293015, 141897321, 371589768, 852819181, 692525190, 916016128, 224422646, 509087593, 616500277, 558641268, 714424657, 812179941, 32420585, 16846505, 993012935, 630148708, 268037846, 54136216, 532608583, 279634453, 324266560, 675833805, 161172828, 359086414, 716344093, 888813554, 6005930, 618755419, 484602576, 129447364, 110685353, 309472998, 801791421, 924516170, 41102128, 816665545, 518370731, 673550540, 915810177, 491164789, 164378337, 713718190, 819685252, 213277228, 635208476, 983556376, 388243086, 924021954, 419703289, 986913789, 511342179, 258206925, 745839846, 956590819, 208339500, 909599933, 407363685, 383941468, 784797233, 388818044, 729075892, 531299775, 462945995, 801483078, 308654792, 915243228, 592562242, 41919015, 412138180, 640213203, 584194538, 651426654, 540133062, 663541422, 964499684, 993448501, 435259181, 39493032, 314785064, 844708428, 689436635, 648842666, 240320528, 397425876, 469610339, 233844560, 815283287, 555347923, 429807, 849587326, 152663166, 930658265, 300719915, 307320204, 178216402, 898299914, 797670056, 677609563, 603844815, 540404244, 471357353, 106525386, 824134824, 333796591, 468481090, 600425642, 898807231, 857333420, 443856775, 52499779, 660750500, 308004685, 581206002, 283957687, 471899429, 406239861, 704168945, 813532366, 896883706, 120711249, 552963915, 950325748, 329936763, 801604110, 507540795, 140650705, 89466553, 621667399, 417540477, 795624558, 715334153, 805839595, 758951670, 178117947, 336423896, 375616190, 677027767, 939439822, 96860510, 555233373, 494304960, 173056010, 100844376, 779330693, 993391781, 364166781, 74748382, 585354468, 349350902, 722766462, 935150781, 371021000, 897976304, 763187414, 919849924, 775419493, 361271750, 496199579, 931951467, 958212467, 816191773, 683867658, 631343031, 410014075, 937691198, 416455508, 454755009, 12462359, 770953389, 156889629, 953433813, 460833694, 152233697, 947243918, 980257580, 495541495, 220610336, 457097931, 168632034, 792480607, 477319616, 268707551, 235604062, 436817802, 558440414, 968633239, 123692569, 838960075, 158867352, 920739493, 739527219, 403096403, 804836129, 828643466, 46362913, 681279964, 646402349, 700103616, 69805598, 955337096, 462950303, 7607087, 712242077, 246531684, 365400083, 567590921, 976341566, 232669329, 726586668, 45265492, 425475939, 161699174, 300883035, 738708565, 14621275, 332495989, 897207180, 395066636, 747008840, 816699584, 778238104, 186224002, 796587175, 4158894, 286987188, 675195035, 490880177, 897603788, 907792974, 550363730, 136585637, 975325362, 869041207, 649018900, 99516455, 85262965, 239391237, 249774860, 586095740, 475595980, 369055926, 535753321, 143452058, 587832135, 842336885, 543448194, 476436853, 582503603, 498256788, 312120741, 855967026, 222933830, 233001639, 394172599, 134872196, 257010160, 420927957, 772847744, 19390675, 801800390, 435633620, 493144521, 839127155, 152243845, 271970455, 168208001, 805544992, 83416421, 547293502, 947464123, 764790807, 401431337, 328480530, 689631522, 11363123, 335168038, 705979847, 725680572, 33483946, 51567878, 739852194, 272825994, 442535306, 960064022, 297376489, 406526037, 892050960, 522681420, 832616530, 60612924, 708251066, 485100939, 910453602, 107026954, 579559727, 205359605, 987866142, 790297067, 582074190, 872333920, 266451943, 406634997, 447050396, 534403304, 956452662, 247256710, 729401516, 298915123, 651877914, 575401353, 162375727, 339469317, 581747241, 785719028, 104549478, 726681512, 352737441, 915079840, 25165009, 330630641, 392160831, 33863568, 225673661, 659391956, 857942366, 180436436, 442791913, 346616870, 144542051, 31523259, 944162208, 557079862, 249937203, 334199294, 979007056, 278040242, 913339001, 126899555, 466704942, 644497057, 433483171, 847689965, 109048847, 473284400, 851420085, 276724744, 776879171, 881960101, 333368688, 427124959, 57088053, 508846671, 201827255, 988473568, 686698208, 182218214, 295623279, 544955769, 221023238, 773311930, 483031404, 713123398, 679974289, 280009107, 737872230, 647081064, 316329706, 395314047, 377406846, 25221571, 895811504, 738236984, 142806801, 360125346, 911958661, 814724715, 373191487, 605509792, 157858264, 862558364, 129194333, 712368246, 312221417, 216039137, 353672351, 60467646, 406792128, 194732553, 993800619, 974287810, 380897054, 97672881, 406313554, 481516240, 374420894, 201517876, 235985091, 430863996, 782466585, 48259648, 905291545, 80856342, 97662594, 384385033, 81122443, 439516481, 736511130, 746448531, 581450238, 785314612, 98385747, 129956292, 945360693, 622143377, 785843583, 463743227, 679240266, 940591405, 755063535, 224056913, 343186950, 182678840, 255311995, 67600959, 790621325, 660043232, 6819772, 848193051, 711114104, 897923541, 764123158, 522395856, 898292476, 73517226, 425019400, 147463159, 503882238, 525266204, 695995115, 672573927, 845449581, 688005629, 763208031, 405186396, 981896382, 935586146, 77516672, 240815087, 731080090, 464782553, 981314444, 88340727, 855290677, 639268550, 385493711, 11190448, 700731042, 903355601, 926002596, 889621302, 69234478, 719414277, 606048315, 765007390, 946318782, 959939498, 93063390, 512163584, 654134670, 770865585, 30365499, 858591081, 500798540, 153968359, 363531817, 425136544, 899676977, 776911832, 823133263, 92705873, 877940426, 267052772, 557602408, 912658141, 86750286, 811378118, 296097589, 383485626, 59817847, 982547156, 900153072, 505180795, 21275948, 506888083, 732585268, 89278647, 618293526, 262255325, 941400918, 584575407, 749060240, 444064267, 820987627, 704903414, 626461180, 817201960, 171834279, 74604646, 121283758, 992263563, 460910495, 400597706, 455725101, 411008931, 516527768, 829358381, 344018243, 977604535, 59689102, 108797905, 800365431, 423208382, 495386972, 977143763, 626616080, 716926807, 64719283, 852788024, 221809651, 696578134, 817286529, 400991539, 351524281, 24266602, 46968621, 725075569, 586836731, 201147661, 554253614, 65874494, 727596868, 754628187, 67425605, 804662875, 792848082, 54473278, 287853946, 501642487, 828789132, 19541620, 338989290, 50695689, 915743194, 202646071, 705783158, 36958679, 870548563, 14292437, 614717936, 242604067, 607690470, 978544302, 648426801, 45309653, 361620169, 437126801, 941981638, 39824920, 79661263, 880489100, 228004676, 419452748, 801694196, 59608971, 234905532, 422687825, 487625557, 357447154, 233898433, 407051755, 824740817, 748809658, 826402654, 402892481, 678886820, 876343285, 468394047, 497550208, 38323218, 198752885, 754418217, 580484974, 483820475, 290272685, 781724781, 995698548, 404604673, 142055923, 956182259, 416433152, 398531419, 264511067, 645623111, 841424790, 148312175, 532399891, 268724076, 369459068, 684343396, 314373195, 828983269, 111619676, 7662910, 355111139, 642533848, 21016026, 62315891, 567074648, 919317966, 876046871, 253448015, 51915289, 588153842, 173321514, 865187699, 978626178, 169783745, 710528156, 717591518, 137111521, 340658680, 555778796, 782890577, 443650834, 188798393, 774738071, 330695673, 321675361, 620473603, 340977282, 347521535, 632730748, 964876436, 160393703, 565216333, 842083199, 318596065, 336168331, 555906511, 73443752, 907332517, 372935160, 813711032, 715770699, 36149539, 497813432, 894288948, 674556282, 459362753, 214123451, 348489507, 17852355, 925213529, 17529544, 338048677, 792093039, 419933027, 370286567, 257357855, 266021184, 944006371, 46674915, 309451841, 488924557, 800713723, 609896379, 836444277, 211707341, 98230700, 768840796, 979798564, 129121064, 280712443, 619990217, 11130082, 837948508, 739559321, 57465800, 608004873, 666459075, 845898813, 223457370, 472528872, 531621764, 29279944, 522792421, 336543131, 905187333, 46024672, 107072353, 328457427, 832874142, 882336075, 402419655, 529320923, 585525267, 815893680, 877678443, 532643905, 466082580, 978742697, 376222406, 458068290, 138116417, 829811254, 654930891, 457265162, 342691287, 872223390, 344463176, 32571698, 256148951, 615157529, 564457184, 860606876, 516872054, 392089963, 179060158, 229689762, 269642496, 787463870, 379200860, 295991778, 656123161, 633961048, 512779842, 811956641, 535037742, 2997335, 100935598, 987817936, 337110345, 257314643, 290992584, 93817220, 60209748, 427701104, 830196610, 176888976, 179778069, 175521926, 980396837, 804046857, 251772036, 300943356, 532396667, 871714905, 474049176, 59819795, 281400886, 585547379, 845570055, 830855551, 212268480, 235394616, 393276334, 595928035, 352587069, 351393386, 697714266, 681855036, 987297632, 963518829, 309589742, 86773862, 557526376, 195157768, 247703052, 892690172, 4199833, 410295355, 383064466, 854878223, 134333279, 240964078, 856522833, 15263575, 423219678, 233297551, 400816991, 316032860, 274141414, 733684335, 816719134, 477834456, 943850566, 700147931, 125002458, 685325385, 522960717, 681079623, 109986127, 64993603, 872152981, 942241349, 416511376, 825374260, 497323758, 23201383, 648278894, 402641614, 136554555, 395335423, 768364903, 492361353, 674991665, 17389976, 587226756, 91895288, 343271527, 856040514, 68977382, 773196804, 925855252, 903018444, 709828547, 141286526, 45957244, 683172582, 47100953, 138063688, 491068724, 732213179, 816132407, 909105039, 118249937, 448002243, 73602325, 254256855, 938880446, 805208308, 855601217, 544924206, 587841746, 854857580, 818618490, 673193472, 128931712, 552997707, 848715157, 828503375, 248027317, 386215663, 354500765, 324716201, 819355518, 829261690, 805388202, 620326294, 653490684, 741054021, 591605760, 953806258, 117585406, 286280957, 399586056, 980660298, 546521693, 716820708, 334756795, 111694327, 271404802, 836998218, 782042529, 147276262, 7677169, 658485749, 923950845, 244359184, 920636486, 290502322, 577436351, 564276948, 660969888, 253452486, 867809988, 174413202, 908595500, 396348657, 541350548, 209178731, 687710872, 324817927, 659051407, 319418047, 285997237, 362841790, 608237364, 12217535, 409440149, 479989024, 656554869, 325847936, 109985851, 333110893, 309557552, 210285231, 129805917, 595945604, 443716533, 318894336, 720404283, 844016489, 589155194, 852779580, 908955149, 674396047, 534470644, 278810778, 730443250, 572828061, 429600453, 634386910, 816385743, 993132877, 390866823, 117381883, 119024025, 908203457, 805294719, 517669194, 953791817, 785172839, 817527398, 39772327, 989106939, 186472009, 192813716, 519609129, 414865443, 254126120, 963540698, 40441423, 866073811, 445102080, 859346952, 950647758, 287603368, 261742732, 721815079, 635693217, 32076525, 828976387, 397087670, 889998324, 36317146, 733567102, 848569404, 881203989, 974512535, 26492291, 394058394, 488941429, 632281004, 679803308, 328529079, 640691296, 391347834, 674559034, 674126547, 755011671, 945953691, 53797537, 776684027, 916365427, 187798618, 206114232, 300886222, 916053968, 274715122, 850919399, 756202985, 72451314, 269110830, 874669004, 967766783, 132039368, 278027982, 313762256, 31623163, 353282822, 947944973, 944698824, 965967783, 426243148, 159269235, 507051579, 867837477, 318121670, 942260196, 613567996, 982501419, 135946625, 615312943, 451937063, 7683623, 147900879, 146195221, 272861848, 291408387, 503885184, 393259268, 850431754, 677949500, 341028741, 247150581, 360986992, 444028385, 61827456, 6406558, 952520439, 20255952, 462210094, 417443627, 398324581, 106787292, 680630559, 214142897, 742960325, 138081144, 260805984, 304537301, 90530715, 990238195, 59823318, 380701978, 461037411, 982790439, 856188688, 220131520, 889907207, 275730017, 720519355, 337985166, 756848041, 302271897, 976485628, 214978560, 737515882, 560767941, 717487728, 710456909, 130289659, 100057940, 534429544, 480479358, 103634381, 352410046, 928313611, 623165340, 220072637, 520784855, 962019007, 331065947, 17113759, 593627624, 143473152, 738554815, 200344486, 304826602, 896685771, 933840764, 203142557, 923875131, 80732131, 50088772, 575493136, 132336862, 546544037, 367376638, 71957059, 752618234, 473255647, 381226364, 638638122, 739168732, 323419739, 190873261, 3780677, 827284511, 211981755, 177924516, 754520422, 389769127, 971094158, 105419347, 972097288, 971886604, 551118864, 260258590, 868099821, 369032844, 144753468, 132575822, 945220236, 652597175, 554404733, 527738956, 48318165, 8064169, 13657214, 5647071, 918925011, 288350769, 292963352, 933563299, 18228484, 732054239, 503178888, 610217752, 953157977, 659969646, 777587518, 554201086, 408237442, 619976901, 39902127, 105465376, 977717283, 5892007, 576968647, 453764491, 815600361, 180334733, 451123853, 223504564, 51101736, 374020752, 265271317, 650564093, 503840841, 952995028, 997711072, 239910582, 275462993, 370997937, 261319384, 128917697, 451902011, 518339639, 376319334, 304772644, 365025749, 473460980, 786709977, 506662703, 988269922, 648673918, 18891032, 14109288, 702705711, 839611545, 174702095, 464987669, 559692211, 938414285, 505933585, 336670255, 443307951, 191470378, 363624042, 118892527, 176440251, 386060550, 160835230, 518165549, 251651019, 784694533, 669169475, 469528140, 423202130, 77531492, 60713394, 621880312, 128252228, 162721979, 942828133, 502577515, 222907649, 920302045, 38667760, 752002129, 749900194, 894113013, 711419715, 596426577, 971683072, 76925511, 657788748, 98820988, 850448161, 830302576, 835331420, 608242898, 669165886, 701028293, 351434082, 491097542, 609410349, 892109353, 728986047, 361770674, 830405764, 194877855, 583765695, 298454744, 823327748, 603946263, 27667454, 604586863, 360461779, 578192581, 776225551, 853464656, 970556118, 557957662, 853833156, 912520340, 961580344, 861686892, 152248074, 533107951, 168167849, 87490543, 809209417, 696907786, 231592595, 51579575, 354347921, 159819287, 358659029, 874507739, 310139292, 429897440, 843445291, 275936780, 104137487, 195308176, 237129086, 844035535, 209929269, 804729916, 887415938, 542434593, 100769645, 666856663, 814576711, 770240165, 228913962, 872538046, 226616662, 860731029, 853535633, 233943694, 337694649, 261043822, 479594507, 126081538, 986496655, 314487724, 220270148, 308802609, 444009265, 710928118, 283024651, 123028796, 646551151, 164358424, 107741359, 463327183, 859630171, 662843898, 710000080, 439017299, 58811514, 305142755, 47410106, 327159691, 52363453, 473315210, 489447282, 841416206, 92484295, 146848385, 923831415, 62930929, 426776320, 980940885, 452984169, 899813158, 764885614, 334852044, 56424105, 870225753, 550485522, 220740447, 781808016, 981501748, 917818265, 274122137, 296676465, 321617989, 789486395, 246462004, 544038688, 169188993, 449241355, 80471745, 698174352, 664457629, 920971148, 370818785, 159889570, 873075935, 221900362, 109163358, 434469268, 695777842, 822616892, 418446858, 301951329, 697623126, 75639094, 480417821, 735697831, 492239645, 310468166, 168620180, 791443621, 228463984, 279634686, 130836679, 618997945, 852615622, 657579292, 677999619, 871853670, 493238584, 345388287, 588998681, 112537252, 15270907, 997370782, 493059525, 222472147, 618670924, 576550074, 808611971, 922534957, 640523257, 996354618, 957366479, 958691696, 538777119, 135370590, 318497467, 389351649, 398428053, 628339583, 587368273, 826913204, 680136283, 117523185, 417451588, 258357823, 530224971, 447899892, 962227303, 384679760, 639608440, 921144859, 144918545, 684439535, 637479531, 567976751, 566893076, 220476081, 303571215, 530383679, 990725286, 287545148, 979102106, 326881730, 455090929, 1280656, 422664216, 157314346, 460926297, 363925166, 644759359, 515007176, 984879633, 5663881, 480653791, 629063997, 238200833, 28469649, 40257804, 494974225, 517964623, 700083229, 443563771, 180165459, 158973656, 808701318, 48039979, 358544177, 788056049, 267520714, 666708222, 327364902, 879331053, 507226520, 114756798, 50128822, 962402611, 40874168, 529089723, 369753455, 714299260, 706157662, 508692015, 483475191, 17992634, 457648437, 958531523, 63874900, 899784400, 532153822, 370863614, 335399548, 321108258, 312723, 59635638, 974513640, 518598402, 350110608, 587683989, 216171562, 602610627, 82775390, 116740889, 478796119, 397476280, 583362852, 807511005, 944481407, 243236170, 205440467, 578163722, 365282719, 544477167, 75425486, 814676440, 758828746, 181236212, 961192906, 974282107, 589346580, 32181524, 970812150, 634583316, 482087652, 877845772, 884472818, 812082864, 562517763, 335528557, 627701420, 466118042, 891184379, 617626321, 918762744, 223020617, 388079552, 591860500, 904093998, 718098849, 898608647, 679856458, 152903336, 160137082, 696616359, 359225246, 144451475, 772218766, 995790956, 396287064, 921334852, 184559342, 151494721, 353381883, 672321536, 456095344, 544383766, 600695951, 645140169, 851577320, 986689044, 419734157, 99230116, 360381782, 70020020, 430769884, 381009939, 861736168, 982333816, 841878698, 919308346, 617618311, 934255763, 529676131, 370225166, 644294346, 763235273, 918024902, 429366943, 825396100, 772669446, 847726374, 55962069, 966399894, 801986294, 708970036, 190132318, 901807702, 909428196, 848653621, 292377569, 167058430, 852484433, 496236629, 722785210, 889141615, 477310090, 444851446, 363862191, 94945747, 888532568, 514839716, 228206212, 82039690, 977672405, 242494985, 72875443, 574464764, 274357384, 496410389, 916692664, 826650271, 256103257, 837234478, 545444991, 874890656, 764987862, 747755691, 906573095, 803495276, 854958215, 269321606, 531086889, 500667661, 4035473, 261550429, 121271830, 63252087, 696241669, 552062892, 917326333, 871093384, 424637393, 688632278, 315188240, 292369122, 348589541, 309345874, 476613095, 234951419, 136467996, 769372877, 499794857, 68494044, 348135569, 593511316, 56882790, 188052132, 560435680, 212749735, 520113118, 867773833, 155116628, 75870331, 737101666, 263039769, 963329380, 374235441, 333799469, 747080776, 70384293, 916073679, 227776067, 65231239, 568007382, 812079501, 815434374, 739516900, 272287, 585914304, 646519178, 293783614, 895740393, 950624952, 120183820, 533293338, 386685441, 858760100, 41310982, 958250447, 404658254, 207343980, 439673341, 1943394, 261518238, 227699466, 862654782, 883074916, 414473459, 950280552, 562579873, 577205517, 803637049, 127066502, 208600445, 693944973, 124928871, 753993535, 517996580, 780979056, 913302824, 669080272, 771420149, 506930894, 279984489, 527744461, 942837432, 736628159, 585739673, 637744925, 699474887, 851176656, 608667970, 252456036, 961019404, 624169019, 828445010, 426406241, 596241276, 769480536, 212628254, 910542406, 719688443, 831770467, 189676096, 492247375, 169080332, 469063227, 93062866, 286028072, 959145129, 394731456, 53156127, 57028277, 252469628, 87547289, 377173966, 247291371, 415167470, 292778813, 628565765, 234497285, 83454926, 256513809, 5314440, 375475859, 520472464, 673375815, 9473777, 181578213, 602834628, 745075304, 194725716, 635273216, 403679472, 372362399, 37172903, 395444107, 22737680, 508201613, 804996465, 469884851, 665892616, 122913461, 120248809, 657321148, 998050512, 249587024, 93817838, 644573050, 945091251, 699250632, 141879759, 912387155, 644951909, 674936579, 843902846, 348258956, 988572189, 735405170, 259091200, 205202533, 1951491, 4232445, 816547400, 267203530, 28507642, 418645449, 540892307, 835742339, 141915879, 405938091, 575451034, 592895943, 464285196, 909890103, 669983172, 25576711, 158941299, 266103683, 243626547, 511234051, 21057860, 938031362, 467570918, 580179508, 431653329, 902650979, 933436438, 325419359, 730780486, 256057831, 505639510, 278044848, 379994068, 840898665, 51053545, 237319408, 215511581, 793559692, 914874588, 1094627, 197982832, 506510996, 160473442, 632188895, 198357953, 956795112, 756953126, 954763680, 45463056, 972892237, 787311015, 481584647, 845340547, 910887930, 135111774, 425719438, 892814312, 930083408, 892111140, 922477136, 396948086, 204770031, 227595033, 54518472, 325964159, 904814558, 837655424, 957290800, 412940544, 956358545, 92786543, 185097719, 478677999, 448784740, 354550172, 509455465, 744396851, 949861694, 197314625, 780181556, 398645153, 134817131, 930899411, 251825390, 726363590, 470019157, 860377929, 423385608, 411481973, 872813130, 24884623, 32491395, 535580979, 874508889, 767220651, 463621824, 140398558, 440751216, 517034338, 702975874, 708512388, 693338925, 29120300, 715405984, 329805173, 944955929, 622173589, 203786855, 139099811, 524440236, 383632595, 939764657, 172194298, 345826281, 42748552, 489353120, 107872727, 351388584, 551187996, 491541546, 512708920, 519352104, 252451540, 313937036, 811213958, 574482823, 316703432, 897586580, 847629622, 257562399, 575327105, 935846695, 176733929, 740390094, 400841212, 938431025, 791870134, 273556359, 973994345, 869847865, 455749913, 562380847, 89888754, 856363816, 613284095, 659941598, 805395310, 157084499, 127652618, 446086791, 10370021, 185764784, 713878481, 153705337, 501619045, 121814664, 11091284, 846093218, 719182150, 337141223, 347593582, 742164161, 690284948, 622551822, 286606612, 446210, 719001239, 918203986, 909980213, 331883327, 789626667, 101259172, 190087648, 950600571, 18050755, 525906712, 659039416, 33384097, 236449072, 33534545, 138962206, 718107344, 806422215, 824261968, 218256205, 996768238, 993100676, 699022060, 620711394, 582464030, 619535913, 762070836, 276652927, 378191893, 801377329, 190557085, 126132416, 251393177, 901937994, 787178051, 938746896, 568146203, 866110519, 418686081, 396742147, 757019357, 130306558, 382908004, 206818314, 541764847, 745021287, 250230400, 864339782, 134241472, 913124558, 124326888, 832970424, 137135039, 5785692, 717513349, 260327061, 611825756, 555288335, 721613180, 742934040, 101419921, 904549121, 74010659, 473054009, 464229208, 698481194, 54142265, 620401141, 517445194, 311694797, 325422729, 72457912, 90403756, 67055338, 939221538, 271530437, 259115256, 959263356, 516684217, 389801724, 376794260, 117993942, 161158465, 139211377, 397799625, 160030113, 524453476, 349593459, 279401592, 40343255, 12334782, 333241887, 804570072, 877464065, 380217772, 469474179, 917501460, 978168247, 691402587, 857638327, 884084341, 246123305, 556306887, 155772525, 342161189, 711649486, 589702851, 297888757, 267337949, 927327722, 965612958, 978667781, 644558866, 267395245, 706384198, 369997136, 384687400, 743630169, 441834143, 642819904, 729875747, 962004092, 630119184, 70123681, 337118701, 179450780, 899711082, 861414232, 81781527, 889671442, 31320345, 137292185, 708586790, 790204344, 646132596, 250402640, 290534484, 684464784, 775500094, 877144418, 670101792, 4474871, 491202341, 505493593, 529238338, 480896279, 393885599, 430524530, 420632630, 163635483, 705575376, 619716523, 134790166, 609551057, 401080035, 16670594, 857688338, 878277277, 973789166, 628926163, 323986736, 183892895, 263595232, 345354225, 651635999, 799491325, 171608801, 797329583, 984060262, 582497577, 742520811, 391326015, 191392077, 467864571, 235723808, 31426597, 631947915, 506041066, 281816586, 868841145, 423707874, 147914994, 772142739, 332890569, 144485789, 718889192, 772424611, 344628981, 884497426, 260476474, 592434890, 401387527, 423630, 218559811, 338115303, 875268143, 34826472, 990300487, 317705213, 575266709, 558372703, 164324678, 56564559, 157061810, 104671184, 372452807, 415588049, 835956724, 669643807, 104759804, 93959915, 552372737, 546669764, 122368049, 42446782, 157897736, 894866794, 528371789, 367012778, 117005840, 863642714, 460237183, 584591460, 254535521, 531818653, 437375255, 249618504, 37298994, 183399378, 679626906, 489001246, 558575568, 603739273, 966797369, 563292887, 4184379, 986030545, 387656251, 230427539, 376534779, 504309115, 85493565, 296130574, 88368811, 166029350, 396583850, 593061874, 641411660, 829538328, 996223017, 593957815, 673132470, 226691880, 257697670, 283949351, 697906169, 487240776, 649503798, 992150704, 932061855, 128597969, 872550803, 270248437, 781097690, 776397998, 510537394, 763568621, 445758956, 512646239, 386993488, 200075740, 544479270, 483278971, 234724401, 157904969, 162488344, 803860401, 641008318, 609577568, 525602237, 281913525, 473263453, 558138728, 922951199, 15187543, 863751465, 340606331, 292657850, 325039822, 134289711, 852215124, 42943814, 317285670, 876442413, 925844577, 262191607, 379839430, 287474054, 766910954, 419307687, 591510038, 978127969, 697290014, 794224082, 820137615, 77719845, 203796953, 273875555, 969105609, 772768124, 991741401, 98150014, 684169986, 879539554, 358494758, 42137445, 608030187, 980179790, 221932843, 942847944, 490581977, 839232630, 878508099, 573371708, 214278038, 43912760, 150050488, 834058578, 123998793, 274176319, 735882268, 567558251, 938673211, 178361260, 635205095, 337756860, 357194011, 437431536, 342821886, 356036033, 403836435, 960304831, 73410403, 532340925, 94335047, 250279570, 940677676, 511467228, 14975456, 120658082, 640514982, 855975230, 69501899, 118642111, 17418043, 44166202, 805733997, 216117768, 870908850, 631096037, 485832784, 880447192, 177062860, 193813785, 473434159, 244253720, 523008478, 95867147, 521440262, 251500155, 55274824, 383403316, 445277530, 51191396, 662622643, 347425798, 761180006, 564183117, 515990137, 308939666, 25431609, 150401565, 615132013, 826706429, 518490325, 974397609, 817308500, 752456616, 964373589, 663689176, 138825282, 520157279, 825930436, 142424798, 287917893, 979435616, 676207886, 198747809, 377155205, 860687525, 456052856, 514092015, 337087481, 922037446, 992358388, 764757053, 194531764, 634326214, 343088421, 298745049, 139126824, 155737347, 580186023, 989814866, 527486846, 963646525, 543082485, 375321850, 882987124, 253384358, 192012695, 869815685, 252486114, 314891160, 924841345, 196813849, 994604935, 123557703, 169044080, 101496769, 574184193, 451787377, 143128051, 670810850, 712920439, 415573814, 148700551, 289442177, 806947257, 709697961, 54202368, 708720828, 454867841, 660177991, 207126314, 904973678, 202939295, 85117949, 9305408, 950949022, 225296890, 402470425, 49280263, 120561412, 598356487, 910887126, 185840374, 814702670, 275310558, 442064512, 907469835, 723220495, 70588266, 762467962, 520280149, 82922093, 148118019, 198669022, 458144134, 150230669, 149239191, 304537830, 601873170, 78475706, 373174318, 535862738, 199840344, 154121383, 159140643, 218684991, 784575779, 456096836, 164534933, 980884104, 51354846, 348349965, 605545935, 637613725, 453888802, 59805517, 717817749, 439520279, 351488546, 86660316, 622506120, 32568234, 792079761, 788522925, 582303265, 482974058, 88264802, 370082528, 955102332, 262335537, 836454276, 576831913, 976284843, 570629690, 876091419, 646937324, 97512181, 172027820, 146936591, 396697293, 551898089, 153954392, 621110339, 363714491, 153652162, 417275209, 814465283, 889633094, 421907314, 858400669, 971842604, 811118314, 259704467, 489989640, 733702862, 822932175, 262919261, 217092478, 810044661, 77467106, 871422116, 926637659, 259934005, 79098876, 617649224, 140546399, 860076159, 583376179, 779844868, 7448778, 354875267, 405786402, 258841249, 437047621, 115060808, 689867288, 524764435, 471976245, 446160337, 183368852, 488139299, 310049115, 737398391, 568940751, 318828623, 876471228, 364751693, 396791309, 983350331, 347547088, 877780573, 347076383, 463508003, 689500839, 628536308, 497505762, 666593548, 968905937, 9369277, 855486775, 852081366, 529768020, 524212416, 647876534, 518160141, 918908465, 623496083, 938676480, 842595887, 451226582, 363702879, 968747941, 395671912, 94290106, 966006371, 305958876, 265921948, 676293331, 962972418, 266531274, 673148804, 13769973, 347931238, 816825604, 891214575, 15217574, 369630851, 180814907, 899233909, 956352938, 517086300, 463765015, 711454142, 533032656, 257023405, 192333132, 74936463, 226089146, 772599497, 369032039, 838834155, 415128983, 436683239, 773719901, 661718164, 701288862, 156515237, 910389644, 493119389, 464703025, 487211659, 563458350, 903596699, 821787634, 609622072, 569041890, 556118489, 269491515, 897991705, 599730454, 405045529, 887728101, 43191867, 871130780, 350203317, 171737219, 582946130, 128956319, 248174780, 565265518, 340377247, 117531732, 525708869, 394242390, 560095114, 78347876, 396733281, 198049335, 191244866, 559781334, 891900984, 312313527, 937204431, 589451427, 395276851, 599040731, 377959739, 860720323, 549696417, 350370094, 917659397, 824996947, 514622559, 33239111, 254711909, 61560335, 81848836, 472947059, 752975900, 358346578, 178577572, 159525692, 291855913, 248585642, 799534564, 810135006, 498316302, 675519873, 896350478, 264060389, 163369592, 895024566, 548233638, 809437287, 361284723, 89746037, 258536530, 674278866, 763514904, 519601518, 354804608, 972226048, 241895215, 245353612, 783528217, 437627813, 637226417, 192485877, 594568801, 184281591, 998454071, 988116973, 250015678, 536337126, 885199670, 189369241, 564818183, 167476183, 242025000, 422090441, 567049887, 967338158, 243882014, 101549792, 945456507, 957627413, 909599779, 577844437, 782964187, 619662136, 335610041, 437581291, 109800273, 485454949, 142880363, 814975647, 924588222, 621635167, 62544338, 979418295, 516086912, 199535386, 160474752, 560281822, 63148351, 7878033, 416337387, 934831693, 668722086, 95113647, 337629544, 306132628, 834301121, 223427116, 681397991, 449820445, 8455778, 757531043, 915587542, 486885657, 280347993, 64986332, 29670828, 141192507, 512412635, 696236215, 841582702, 435467426, 339981396, 245766425, 866506040, 96343301, 244861066, 51818224, 436106854, 698170268, 307968730, 370880793, 684052793, 828908217, 351545426, 689666425, 951562796, 200462978, 241483815, 310841361, 424810090, 522546067, 223345736, 555100946, 866944176, 574946997, 178185620, 456742828, 816920095, 750886470, 524716947, 598370923, 535443043, 611054006, 679903116, 846671094, 852112939, 107211797, 156949257, 285887649, 959817751, 512058237, 860134599, 246352067, 377986507, 614622636, 670966082, 205787863, 839182436, 300965888, 330785278, 899334530, 644554064, 338191907, 336290616, 563616085, 108881963, 682583966, 547402677, 219375019, 326903564, 705981264, 205236061, 763010950, 112865769, 127049984, 238027132, 620853120, 877755572, 165293666, 38832079, 695682961, 6713313, 534282835, 449218737, 950912380, 750476588, 795567668, 123096039, 397616813, 608103712, 246055547, 102609601, 334094649, 426298834, 555894189, 507974855, 900566764, 808816153, 901877694, 574572951, 158265330, 903571922, 485531716, 142717787, 271449190, 783173281, 947596484, 672561619, 48281208, 792379161, 181162740, 825328987, 242767570, 38388827, 108814705, 822909459, 732855541, 545957963, 783059204, 120477879, 631590658, 994991890, 18383966, 780351571, 98784032, 582496574, 427678928, 184188780, 391665082, 280849215, 812230753, 94064582, 553886677, 914930593, 470043400, 123467371, 178840526, 885539652, 310066268, 648294089, 394132378, 101205320, 159272760, 724333827, 607267316, 29801359, 497297139, 63925210, 389663463, 105775952, 122956303, 242938248, 121294414, 137855531, 757082840, 468169545, 529113055, 229142781, 265708582, 709064125, 439734844, 122124316, 589925877, 919406705, 920224567, 779987899, 713292565, 573664243, 840564264, 508680408, 851705822, 626159180, 605564890, 104007948, 278106254, 840499045, 56165957, 653161912, 120018917, 277658523, 821626374, 572191240, 606063658, 771630873, 4112846, 523606853, 702820426, 136385863, 759548455, 836453162, 443015855, 496352010, 113062728, 118914428, 393036095, 698302989, 501850493, 196028976, 588268163, 137372289, 786042732, 931917503, 118883512, 151316219, 628280809, 659305007, 19084581, 834085445, 942587954, 966420737, 289921233, 591848665, 456183129, 632412892, 390855156, 166607220, 759155645, 327386171, 68255510, 29692428, 774572866, 237592357, 275219173, 348620262, 258622023, 736588077, 35692614, 48022314, 955063080, 538976926, 193357590, 116097582, 906064015, 125031519, 110409289, 276376192, 939936098, 51694914, 621914921, 89009592, 746061801, 667170796, 563580643, 719433138, 212902097, 689521275, 778708477, 223559747, 162086288, 899193045, 308930050, 879826969, 41628287, 889653227, 549632279, 195990906, 214008074, 552427923, 174455934, 907848934, 307186644, 960136392, 675786077, 542206514, 902748752, 921073212, 382619488, 637721925, 442527608, 128450986, 662084332, 475415579, 925276599, 269616219, 327009092, 511714544, 650451911, 952583293, 388257416, 882673631, 867526072, 576712211, 786105386, 182752397, 672585314, 246222800, 125571923, 710460056, 963946894, 345691051, 396722779, 876355216, 829447457, 913463892, 803602097, 95970833, 706693229, 940344329, 470868758, 298210914, 705027049, 855801624, 14912024, 87629051, 86783886, 152086158, 143926846, 431343056, 609029153, 957976049, 35980321, 72943384, 412345639, 333700647, 619875835, 377562096, 104477930, 898579459, 502892938, 618432480, 897757275, 345734483, 827359104, 742733925, 492202267, 820517025, 184105306, 80559114, 583678390, 929931911, 643578004, 811463802, 571172374, 640777242, 973515030, 28545219, 717246445, 509546085, 718002665, 115957437, 798001706, 559994195, 973516163, 962830279, 240951562, 919053893, 191222998, 497178135, 219068805, 618468756, 283979015, 755875542, 869996706, 263817249, 429423142, 824504258, 647022043, 691270539, 782914276, 312538563, 419291126, 211999765, 857271394, 165653281, 944936361, 44767795, 580844279, 362761566, 79170684, 882294946, 961316711, 799119784, 808042187, 955663421, 46638811, 519133580, 593956158, 22933778, 561426092, 119321323, 59359113, 236972533, 222034686, 764261908, 332160809, 660167650, 764733450, 537312131, 373634525, 694556327, 378788341, 135293728, 464322799, 770952611, 610765867, 898047460, 547443125, 238266299, 44088047, 435180494, 133406444, 95374009, 675959384, 348623914, 564449067, 968664660, 129395480, 812172444, 601499078, 640270065, 682152182, 156029216, 136172043, 746433858, 592335344, 116947520, 526525046, 348980292, 889622847, 87040577, 934059652, 59006076, 928409840, 647048082, 705297356, 581573000, 142529770, 594620392, 501986146, 942575314, 703013273, 345871449, 349384676, 918079820, 769553231, 876471767, 136516205, 892023851, 686041314, 453092275, 111528556, 39369147, 498949279, 605399007, 910128115, 374895257, 255869534, 397282799, 37024591, 509944573, 551438302, 704982154, 444343107, 781549405, 810034449, 934819938, 642259505, 238714181, 483049786, 501014486, 253655840, 988486443, 681139557, 40474010, 60971471, 792492834, 501290017, 907979972, 227652094, 46405774, 683277225, 235660756, 159299269, 320120297, 172891522, 961873595, 498385054, 153576983, 635009471, 569023881, 878767201, 414963970, 548862331, 715904669, 697790156, 255514712, 561609848, 963061452, 773178910, 553397785, 367421313, 498699845, 475582083, 978643270, 788053226, 371759654, 906213258, 9190029, 424246335, 236673509, 712270461, 706119929, 502618433, 222831126, 7552115, 378129934, 534619705, 353737612, 990576831, 265303483, 110494116, 413465979, 878468107, 488311276, 740991831, 329025321, 121133987, 26720649, 210958985, 827962161, 819466984, 906149717, 912894747, 90217532, 186043400, 347908827, 380741279, 614170714, 793786865, 986531280, 702186135, 470093501, 279506533, 140450342, 711322654, 246991315, 814009780, 472897803, 873235296, 622085132, 896588173, 907037570, 650492691, 985561594, 283694996, 962154344, 881643107, 191570593, 383918102, 273819653, 685317810, 789590702, 837038561, 143794710, 917898786, 845389746, 508466425, 71182214, 658197570, 522200976, 908943180, 473852372, 342982504, 267742854, 151850971, 118292746, 856752791, 638402021, 187322845, 837179719, 490770383, 237132678, 743336856, 318670386, 709553153, 111752438, 38326276, 342207806, 426341127, 399517451, 191698738, 671934045, 418383124, 304384679, 504482095, 330157630, 171961696, 645382275, 911547683, 444823290, 894685796, 222617757, 888262127, 768848608, 753632865, 466417421, 292997948, 109502711, 649436768, 723024345, 451946725, 834838368, 425795292, 296884953, 211888353, 905722344, 596934994, 795368584, 919113547, 142330135, 101042390, 53508212, 482378811, 396492554, 544169178, 526089854, 385910627, 34755984, 883091525, 234252371, 5647154, 389817058, 715313199, 114627240, 499017615, 204103946, 580370819, 403252381, 621920353, 828519885, 664618651, 670157582, 960022638, 89112325, 506617429, 736910978, 623965211, 48015852, 723131460, 610348609, 287567214, 56549844, 557154672, 304004570, 233881959, 614821839, 212962317, 266079660, 92249765, 795580583, 960459795, 843953916, 930006891, 156259559, 655930271, 794963354, 643541053, 392396274, 146969729, 326598476, 267081555, 778678958, 303911224, 302641367, 958406197, 870645144, 312425235, 615308977, 189561974, 547203444, 352791704, 82714699, 925542649, 245239680, 119227192, 615859888, 125410691, 432730796, 376949424, 571071643, 20921575, 401647964, 509646232, 601994262, 404000900, 501342523, 378906892, 906164301, 41877915, 814000933, 786572051, 287629385, 683219304, 957363525, 393163582, 376547598, 80081313, 879907365, 215004473, 47965313, 632857724, 795106550, 932082893, 27411137, 845316869, 485824301, 518790797, 500582922, 625096409, 438688153, 687911275, 605580851, 303575999, 831153781, 191032479, 206358410, 496180467, 946930380, 72509031, 847165372, 746239771, 556538455, 880483537, 635840795, 228768838, 303368860, 322984293, 782979864, 466263072, 769158105, 948840480, 741132272, 920753794, 803610283, 433405224, 563652456, 670599438, 399475685, 904013321, 798569273, 172121183, 838107282, 554893329, 758570063, 541120225, 241455736, 895782188, 389334165, 892770989, 649771371, 778905376, 497327763, 403373950, 108213731, 493760006, 38021548, 871928119, 988775705, 567524738, 19591446, 39471147, 665514951, 12980283, 978430734, 342409420, 800397348, 634122336, 768453599, 788546306, 237097188, 584945450, 802086839, 362869463, 746237675, 717610054, 933141029, 905933621, 316225125, 727258946, 311410258, 121029650, 846918859, 511115208, 278155790, 520955855, 501624477, 649471801, 710801236, 533950390, 857912040, 749780370, 176899060, 650527766, 278582099, 30958992, 330912422, 356425536, 620664949, 870028611, 931605272, 279826621, 231850539, 769865764, 939279741, 23551886, 655499132, 766047358, 818808676, 838134432, 281207858, 565937027, 364469849, 24507562, 663422742, 22551540, 157157231, 117614503, 338815407, 375740070, 299475699, 172441071, 314140549, 947368178, 168325589, 214842719, 902700266, 756724642, 744183959, 127000406, 837296070, 608505558, 25880334, 907772448, 762308242, 50302096, 481406684, 161269949, 215537672, 555494590, 904695541, 435965163, 362819255, 164529251, 360222171, 120572999, 557696395, 726454999, 491263516, 662478712, 826695438, 663804639, 100933587, 205720501, 576599604, 215637955, 921981648, 261353893, 952590601, 825468449, 118189062, 522327292, 738227879, 248842566, 36477833, 697027444, 796980965, 793441402, 509558524, 418616011, 352139194, 52941438, 585453898, 827930448, 449468348, 625683145, 702011683, 837063632, 975844007, 520473638, 145085947, 102966505, 263522762, 697262540, 680142386, 834762888, 601585420, 906509637, 738294523, 401195485, 446019067, 33500151, 75881295, 937996938, 159329452, 130325451, 773084695, 631569967, 156181209, 927013080, 55194939, 616778582, 931407400, 988828778, 531151033, 345482074, 650932545, 210166551, 629597843, 567940759, 49744356, 868834650, 132995173, 23196303, 483064322, 445163515, 349118109, 458168884, 192504373, 218674295, 597218017, 986618715, 312382448, 807149545, 747333095, 243335710, 97971179, 816767425, 120524897, 80121300, 587560801, 524330970, 127260061, 427089094, 319187754, 527732948, 869805447, 461493809, 752328393, 778195436, 830824611, 23714080, 358413127, 675779042, 483326896, 884381304, 478848356, 911018526, 675509499, 381120027, 946036720, 702918352, 282223738, 806702692, 758295016, 928907208, 790058584, 618976736, 232229420, 676629066, 565866535, 473678929, 493455075, 313568331, 66594096, 902863747, 528478341, 269294800, 996161906, 546875039, 159093720, 840497592, 795139019, 350176285, 705081772, 199910061, 54679465, 765631896, 419962990, 398326138, 122893854, 447641626, 554492573, 915223844, 632830501, 544625432, 157930313, 471960341, 538714275, 864120104, 897749097, 535691274, 106476389, 106877581, 893972788, 181378162, 145971510, 73456963, 476904919, 910418760, 85957784, 695936392, 656965180, 527527239, 902047322, 119608068, 948841495, 426204776, 268819204, 218495684, 183349870, 717512776, 460094377, 445005507, 880984851, 687774286, 361681662, 238786366, 346728989, 973085893, 578128350, 431545957, 939411109, 310761842, 764175485, 368960372, 55897978, 888724105, 23758481, 185219039, 679242860, 508777788, 190914677, 904011158, 560935722, 980029626, 592947535, 444539096, 273879930, 919224421, 388730435, 259257905, 526362, 626245353, 771735888, 452936856, 685273410, 202066217, 165291195, 904627426, 601578489, 377627296, 424722792, 804329007, 977231319, 163795231, 746758017, 997314557, 542063347, 620787292, 448034918, 583546061, 44577233, 905381827, 954918506, 786274873, 3476481, 210049017, 494540760, 651913253, 435353860, 593768712, 705833314, 887884636, 329153944, 351082017, 552783480, 718203381, 927976858, 65968707, 209599289, 787293405, 738138729, 227412441, 325777879, 965486192, 550873385, 887696704, 315872700, 925661080, 224263066, 823583284, 560531135, 527315955, 251570848, 405847169, 649614524, 727509737, 166162958, 811163904, 166299, 365392832, 661821668, 462286214, 981438112, 177868726, 175383470, 275401939, 77266226, 702963290, 641655875, 124710794, 874258761, 310648083, 232475938, 363320067, 819676241, 631873575, 71968192, 115884005, 933711781, 745949753, 292476261, 850525276, 382086761, 147368356, 995334380, 99474233, 399147479, 372498167, 367301252, 607161253, 625507840, 502385732, 494697680, 496980027, 657252611, 255897226, 641729654, 736012888, 950314295, 358789406, 149445766, 546852779, 826456784, 344753021, 109980301, 192933822, 793515486, 287362202, 657442232, 125769471, 175983008, 451866, 770156201, 301572412, 504033560, 233447223, 677945265, 31240894, 617241985, 551246843, 714972861, 677624640, 846685852, 569047614, 672498489, 112722246, 547767217, 652805554, 594274486, 581652174, 736957898, 631934202, 12404390, 438254280, 455282155, 991302788, 431651388, 886740863, 993189399, 314739563, 216859134, 188102860, 330360398, 686199137, 295966973, 996661857, 777773949, 160923957, 901599501, 563565770, 12316576, 455189679, 793495827, 364850523, 136242659, 767795837, 59666278, 344944436, 773550780, 452593154, 372088510, 590367962, 193443867, 838114778, 431848703, 143611028, 72810444, 405912195, 125383134, 657471563, 418275611, 477006090, 528571431, 389129510, 453359468, 140631829, 799926501, 133602245, 935261864, 245277556, 203148188, 886279047, 315428914, 966387756, 266196220, 368201032, 262043451, 542220435, 670688723, 407517944, 89252308, 137644274, 549051752, 604486488, 274875614, 809102807, 271889654, 665852744, 775450333, 939222348, 579146471, 241095154, 954687598, 860517977, 590410446, 755417604, 695074651, 392111015, 989061023, 614900763, 941378862, 626232849, 241518691, 414973325, 446486076, 666917799, 528394618, 828613155, 412517430, 618201606, 302096443, 160560059, 208700530, 542917739, 663822100, 24530044, 583208273, 230681096, 189114892, 947660113, 193309002, 97787312, 818992680, 303550159, 273705180, 459133702, 636753802, 633170607, 697668193, 376995945, 98929425, 577492733, 34474083, 960009714, 800398676, 415288000, 379143865, 202383190, 583525295, 72767594, 634111798, 924017981, 797834582, 921008914, 78944131, 811021105, 860953098, 356683596, 289734461, 301078061, 158790039, 830580616, 750184084, 275619665, 528698855, 897559842, 491250644, 876769066, 499748584, 761943647, 552235532, 231127047, 547002668, 486190095, 620871479, 742369746, 48472180, 263816354, 219029880, 95523176, 482162502, 824611608, 489549594, 398772422, 465854223, 389479735, 140017136, 422228408, 953663377, 697100581, 107308605, 250000038, 553666803, 57059721, 200410088, 518922797, 554994963, 676143374, 880912053, 82906954, 221780733, 577742136, 572019888, 212360421, 604387525, 962971767, 200426970, 681844465, 652553979, 639249468, 51219877, 923951247, 387253895, 883129752, 454320657, 714566912, 33847405, 1156529, 69598096, 113924043, 399586091, 530808489, 622148588, 224820007, 857494391, 492756925, 940881292, 245172654, 861571695, 271535448, 336297996, 224451403, 47773343, 568259515, 39605035, 180143121, 48337294, 808337112, 26924358, 963050724, 255689811, 826990682, 611901125, 90500461, 957615891, 245734881, 161411520, 799526085, 67534750, 149069069, 581984231, 528847747, 118957500, 619697224, 498647029, 19180241, 127226253, 720431445, 115676931, 521101135, 946470940, 54845921, 422959706, 379459302, 711299489, 160034306, 990780042, 194925499, 891767568, 475577197, 977751154, 835655199, 466433331, 591179797, 394812381, 568808390, 507573435, 525344556, 797502243, 809305071, 317731462, 837230899, 441204905, 299635053, 827190522, 221898905, 919013599, 620627752, 885063741, 744241970, 158279729, 237490797, 333058100, 824082411, 276898817, 894478026, 506835526, 713578732, 140472377, 403373026, 329697389, 750008823, 132953021, 89249220, 61669008, 75632046, 788579566, 915176451, 351979723, 180751012, 298279488, 48523067, 597753667, 590476455, 7613731, 715475747, 429802376, 918520133, 41270175, 626707695, 890612422, 147724119, 701738422, 250746950, 877060065, 586986230, 137447391, 459808617, 889054453, 439893079, 161850765, 233112559, 391865574, 872155428, 189205646, 520699146, 506725178, 744506640, 996828691, 128724853, 688009486, 486436708, 232218154, 638606010, 896128836, 785912357, 61741378, 58560187, 459276831, 81665261, 722583434, 615450857, 897126085, 27366010, 497523694, 472038710, 551963130, 441562556, 9755918, 730133828, 848277609, 864349111, 710105292, 415957736, 309081633, 787772709, 151118454, 101232341, 645836869, 626720550, 303281839, 788696519, 249733016, 636054632, 8561534, 284104800, 959458455, 467032019, 816772043, 273588238, 220842592, 891875079, 744693970, 651890057, 285907451, 104012274, 923512326, 737188320, 696526199, 81747032, 600417717, 706253724, 214896933, 35128233, 624903214, 940363463, 354456154, 304869188, 835259060, 390591505, 113938407, 187945541, 670440580, 285478776, 365626599, 133082149, 329432359, 983929465, 659805729, 557157835, 879697967, 707898768, 555304588, 120126464, 541307924, 745746367, 847523897, 666365088, 266390511, 616271512, 272776173, 592480128, 875321601, 82028185, 33517666, 436256606, 921630236, 730740079, 707008514, 189838182, 259271760, 996117410, 381898334, 282250560, 33176084, 672466522, 624712741, 678137665, 214196927, 72347390, 458312824, 205249864, 241273713, 396562396, 244450533, 677911275, 395005270, 203019759, 691658934, 842172332, 147466337, 482095876, 453131423, 646686879, 662203932, 368622229, 786675044, 22179025, 734900962, 161362275, 340881209, 132569654, 97742332, 157114814, 854135560, 201808279, 224031590, 66426948, 977820774, 795022048, 801224, 503186295, 294870067, 509152038, 331531261, 367264134, 975748726, 929715407, 702955084, 902001373, 159571793, 44583727, 970172039, 510070600, 727325127, 504946797, 901524864, 102785101, 154464492, 874900640, 606850262, 491641793, 510561251, 570697589, 809677575, 507611340, 160927499, 560722359, 153720836, 691755432, 113944828, 668276899, 361676436, 509873114, 948352536, 792922194, 662469591, 54785969, 668575463, 605540535, 381376366, 833821481, 810216568, 124213344, 352827373, 269721494, 133819876, 800162697, 77004614, 934972617, 529069794, 604997299, 258775430, 788613302, 57179808, 472566308, 767515487, 584970225, 600577310, 177577044, 197918352, 595585700, 821171841, 881564637, 860837340, 71313305, 171244906, 313962523, 621687059, 506740561, 101429386, 250247448, 192760582, 959772401, 318855440, 320987910, 2315370, 597686539, 143615509, 686535207, 740675216, 927603413, 1995748, 947120490, 787244947, 74641171, 845540421, 395403866, 630735339, 35910545, 421951706, 65697012, 274439861, 770003684, 100338901, 580800811, 924775866, 693584198, 601063688, 715917285, 692212120, 888003079, 678461226, 158476550, 704368935, 764313649, 898495095, 272613919, 119755569, 977789129, 530601130, 510406511, 113209738, 280596709, 530200075, 262634378, 695854506, 572810635, 264421777, 636307887, 549914503, 335341548, 697440439, 461986730, 171818324, 676075696, 421686731, 474567442, 843744095, 434384348, 784535276, 592569303, 597708943, 145687414, 580293218, 78981143, 521013022, 756862994, 292903523, 804990977, 126851181, 537999459, 479197717, 252460070, 458445939, 888341594, 522048759, 418572458, 445974103, 526703211, 840031637, 99958436, 300586267, 666570827, 825967106, 362381316, 116537645, 425515262, 535995277, 340148467, 187469683, 285708174, 89511811, 318384214, 126379716, 561687077, 594741771, 979894104, 643724838, 822536887, 130593241, 283746160, 222204431, 8698992, 733761471, 834893607, 437746772, 260595941, 428691478, 714814317, 782757453, 588431443, 959682362, 925842382, 509847366, 873977704, 768810440, 291106679, 389643043, 582686712, 710371963, 279423146, 633222138, 66324509, 900136657, 52710586, 103436083, 12179412, 163879340, 329968750, 155396542, 104805373, 955981150, 588778093, 206680710, 916781435, 24724390, 585296436, 733421433, 190827512, 805821332, 482678865, 879537282, 676143178, 978603201, 382047971, 916139917, 919326407, 885432573, 740787526, 642484982, 641059682, 725638660, 585300445, 919543628, 955993401, 653651689, 947864521, 782451587, 32745140, 122393611, 423908349, 647423868, 397110567, 80037953, 271739409, 259025064, 521376259, 166191795, 912879691, 975124360, 710768206, 894487456, 192871709, 62276404, 577554103, 733180990, 595896823, 862294992, 95330817, 504455860, 774377111, 510095742, 684757602, 697823579, 401233218, 91099580, 3988556, 757432231, 26290580, 3014694, 446606386, 295376204, 847835702, 722377188, 538068288, 416846050, 256266546, 759070518, 360971392, 15579432, 940915128, 108736170, 646154719, 688613519, 228248295, 689458021, 551399114, 305127209, 5327045, 457523241, 72419062, 582429067, 570540272, 335427330, 809510345, 320555030, 885999496, 343307454, 834988612, 494359269, 551129992, 422277141, 594999629, 464348076, 727496258, 225439807, 857699059, 842928286, 185534856, 981017338, 442135016, 445684514, 151839006, 905954648, 925062644, 168352992, 677466283, 20746837, 627801348, 648197977, 979369882, 900937929, 179673856, 303267224, 171956527, 90809006, 419067129, 933161952, 213465187, 981516036, 982222618, 11651449, 513039593, 799127007, 356739647, 825292653, 393751058, 190195824, 687572493, 989709240, 623960623, 563156445, 916338632, 892714604, 865932551, 705116138, 63293527, 305028073, 586861709, 769777489, 32724162, 325816688, 379968154, 460846661, 104409533, 249152373, 580826412, 173242846, 622520596, 886089968, 80481497, 736301295, 300553987, 581420627, 579499433, 634400883, 82127978, 303480116, 223466414, 257054573, 704674584, 232079254, 562866867, 778282352, 513769027, 68869859, 292099243, 864321772, 125749647, 802718706, 520710889, 978503113, 64642361, 102601867, 174211599, 673865544, 526953641, 476775980, 974353062, 866984396, 341361459, 693081611, 493947992, 356573959, 243591316, 301047766, 936244423, 883518637, 22904263, 377232185, 132774453, 340023183, 724403779, 393053996, 597443758, 639116299, 739095604, 569788916, 65734731, 972418710, 859888842, 634651280, 46827514, 505670834, 537408616, 420573025, 925997952, 96585709, 26689168, 499826593, 554761156, 901544972, 7895931, 663186945, 836446897, 283092357, 150012018, 874203553, 641035020, 915551962, 428171689, 282474, 352024371, 214307177, 657762302, 181663942, 549150667, 12446742, 48011326, 658267043, 867012122, 982254867, 738829573, 402147885, 285470905, 29366623, 843924602, 105476721, 332691377, 301870031, 977476708, 291279837, 748688461, 671395525, 484857404, 288767353, 810968278, 40206921, 21327149, 322141126, 468345976, 389523556, 92566069, 370254404, 346754256, 771257079, 615559018, 706570366, 511048155, 545221285, 178028570, 669428449, 695454944, 888594469, 155197717, 651658655, 157353494, 36454264, 373146505, 116617082, 185464891, 383704768, 992577899, 579706058, 786618790, 598031334, 243231316, 202062328, 434446787, 663199526, 334503359, 439249446, 444952226, 890449447, 897597167, 781101584, 954279708, 426829590, 711161656, 517923876, 205471917, 963342159, 247412019, 178928830, 816555890, 769743867, 934977525, 350657911, 135213063, 591188799, 264014353, 20206061, 845040566, 553254500, 269511748, 949058429, 447778828, 48934971, 35562578, 328689694, 163955404, 523824960, 795281778, 384144866, 874386091, 606057928, 660724883, 343979695, 356312622, 375621142, 746997328, 92994313, 934053860, 692949496, 277366666, 366140563, 214880633, 526748466, 507328568, 922854238, 919433395, 920352353, 303066190, 785974913, 285977901, 938782491, 902237728, 771717412, 805353307, 566724159, 128479222, 342863599, 180868279, 791949161, 762060086, 515539164, 644853727, 486818923, 310762747, 962616919, 859604542, 676928353, 709778587, 952157897, 770060894, 248725834, 103443369, 721776233, 794942251, 837440991, 976997554, 627622625, 356450513, 557547249, 260520595, 949551284, 340394361, 27413993, 277797281, 24137687, 712557126, 260805011, 982198409, 538344451, 606469393, 175345922, 293217238, 614568183, 857199067, 989894012, 785995610, 682391849, 597751619, 926235276, 707776023, 958940960, 430191814, 289095471, 662541727, 138823815, 549000456, 791259980, 41997796, 574670398, 292105613, 393323743, 947651944, 745592823, 225135177, 367920201, 453874869, 207096550, 510166993, 487150394, 770158410, 608848411, 657347490, 992901741, 725154895, 215489763, 113565422, 883774996, 552973583, 259544997, 696825235, 629554809, 973955656, 35879835, 271592386, 928508730, 498783909, 164302418, 67843879, 42433150, 720217057, 3794552, 563426740, 962628400, 927405703, 112040589, 286562322, 621266919, 974792641, 945813110, 502940025, 358467640, 895105587, 789438995, 548451762, 1530134, 618517156, 828900371, 295371908, 714269470, 568363511, 681967157, 34212792, 841758427, 717068411, 615728869, 14678935, 342582830, 577862106, 917119661, 758748877, 740872001, 792022220, 208874992, 315451399, 946716020, 893752332, 275438654, 580984492, 223182026, 830072228, 322646024, 651560222, 349115999, 320364630, 681637583, 715499968, 17876615, 692413560, 283631858, 340595503, 173699330, 199229160, 341263837, 159446397, 81971484, 165936697, 850574449, 145965657, 559744047, 871654025, 82543366, 565202104, 257243895, 887129732, 172668638, 20606958, 781345625, 756247341, 11364851, 194364898, 297875638, 898770369, 712007258, 945871497, 514012240, 289695388, 628883595, 527407279, 204341933, 287854347, 936293262, 832900990, 13418918, 409892794, 103205672, 773198077, 957800316, 713623730, 746913424, 265611680, 812265642, 186086401, 283062201, 966937544, 799158777, 860207918, 920105146, 161506944, 697078362, 370998035, 540666930, 665685397, 944594890, 484523832, 787221360, 55021875, 937266935, 845111027, 779206560, 71773155, 915060186, 16573335, 747057252, 334378764, 514053112, 780919733, 509094351, 761490464, 213882210, 312246781, 544622605, 978442499, 217021446, 830547814, 691960397, 582563922, 254950401, 723995925, 813316745, 950443850, 727576708, 141104661, 109590282, 395112959, 773521191, 825331916, 214120773, 144624742, 228027120, 467957028, 64712708, 31703847, 190162833, 119734984, 619157757, 147750461, 133205643, 711484836, 998798683, 986321399, 993728917, 224298766, 464930001, 666534901, 678348363, 833673598, 243309740, 823075967, 217353881, 308250352, 399377793, 834828151, 348572894, 16508283, 861787247, 57231023, 318702663, 945133704, 640841987, 223562300, 40480134, 407197753, 295179850, 477633205, 410295430, 689956566, 848882891, 598110011, 265489020, 778939569, 817379574, 661589952, 955713776, 555902125, 396441300, 690465152, 580883909, 754964075, 176285695, 752221671, 721616648, 821426690, 140173532, 687991084, 782805928, 406147749, 370236422, 273616100, 39686916, 203405690, 70696631, 671011583, 345026126, 624681236, 157074135, 263704271, 226136737, 582824035, 563400158, 29701491, 876763846, 678048411, 861926398, 84751920, 479928452, 702088431, 888541494, 819780690, 317395779, 466053403, 870699608, 144025257, 688023722, 966979076, 212221389, 467843325, 543964668, 17822567, 892042480, 891608563, 861292811, 155096779, 710072475, 659085695, 473021311, 988215580, 626264270, 857835179, 599305396, 152247699, 499947659, 184213291, 711279672, 264177924, 819745819, 745609941, 936683580, 878856659, 331439072, 208575858, 613860032, 228718624, 514552250, 572731293, 15081416, 792916689, 468701751, 768136942, 372167859, 482694926, 493031432, 244815822, 405258286, 55446587, 408393279, 442499166, 305311214, 86817274, 725858625, 746135527, 69865617, 128371582, 866929865, 83442618, 430313371, 486269291, 886853156, 830380292, 959752867, 353828850, 248778377, 91892814, 327890086, 411240705, 375820587, 455194100, 174985268, 94416253, 971589056, 222982932, 411974279, 278339449, 202050182, 332245853, 810772721, 744971171, 341440767, 241587135, 722355173, 834795027, 809718059, 252803517, 307398397, 152193009, 314332226, 536381760, 992847976, 155539373, 35317306, 172439091, 240012059, 74669945, 492266404, 808776545, 318232704, 697615636, 266397343, 382767362, 708671341, 317421097, 123661046, 249131696, 681502607, 395423981, 114928601, 760201920, 938735258, 317697137, 459724860, 646578164, 611522494, 468638195, 1854662, 680234748, 744103915, 466931667, 474392785, 536202586, 816584681, 825553531, 984058365, 107061027, 954189571, 635730849, 292058212, 176335737, 554325395, 675294643, 832269567, 793504083, 830187794, 652540165, 369044566, 88181370, 602039641, 59241876, 586764142, 354801635, 6405127, 649861603, 365921046, 485520194, 906820278, 127873919, 790881804, 257653318, 826800363, 731438555, 389879028, 612836478, 207398936, 906053350, 486275423, 194409304, 597725320, 698054165, 612180953, 743191924, 736711743, 188587915, 532385812, 405774368, 302403804, 218765773, 266257463, 800510886, 132235176, 174795715, 319233089, 197595883, 229950836, 908533646, 457460677, 500676651, 790424437, 534573529, 342864930, 271053467, 836162051, 270977527, 519986645, 750113467, 338232842, 498427009, 848320192, 277450077, 706394110, 909903869, 928074691, 651720831, 346342835, 377554095, 795243410, 390503042, 563672043, 814326688, 570574654, 575191291, 805483863, 421757148, 28162102, 844237657, 1991790, 647553173, 439432176, 821119317, 764333935, 673086775, 594131293, 252477087, 454391710, 931260792, 650165162, 549314362, 788889057, 511084126, 217517276, 737208751, 382764778, 154440564, 379143862, 111549619, 517986271, 845912326, 317851637, 363955606, 719843864, 940442430, 432024959, 594837244, 406327814, 25938617, 250827382, 576094867, 163933286, 685951206, 315339530, 538815470, 569643756, 366308884, 906633840, 904224013, 715042908, 771965114, 737310318, 921730799, 288481206, 155430187, 397491054, 297106266, 776018875, 851678734, 572249298, 632525436, 53607565, 674803562, 910725628, 645666672, 161766311, 533996909, 604962353, 48534799, 407867535, 961218649, 283432496, 322058720, 36597976, 323367766, 804984216, 864697662, 37975319, 157960479, 746459406, 875725676, 549840261, 326624428, 489336102, 616359267, 387311544, 640359497, 101167905, 576877609, 273649955, 848869767, 554686283, 22653362, 757171973, 460528566, 539196835, 995664911, 515391802, 675779753, 991250581, 771199391, 161571391, 636768395, 572248419, 228551983, 636716252, 737135561, 971819820, 557415671, 286642727, 277049176, 755883769, 211906630, 517776545, 942227144, 660855103, 990223768, 835039533, 646402591, 824102205, 355923116, 725154378, 549476955, 615223376, 325720028, 756268928, 193551194, 809283905, 944063126, 257806473, 470376980, 274798126, 357076254, 949990165, 659659030, 641863217, 378062367, 17730179, 136212170, 305276017, 238235510, 284795408, 373488287, 679862501, 716417872, 83598023, 517046973, 827958502, 328936070, 781602101, 571755220, 247901674, 314242700, 132289496, 354393972, 820965162, 83172049, 562027669, 643297206, 82639602, 636565548, 84615658, 334220104, 348662152, 844847186, 173406497, 500467633, 484681964, 410673146, 742565483, 267017340, 284332481, 901081197, 564166127, 589439469, 175292980, 257590678, 702811382, 818884772, 503715275, 217633532, 791022228, 312246341, 989357090, 521756492, 262134535, 105642935, 432801918, 596675992, 496859091, 297256906, 408877621, 386166142, 4290524, 319813688, 15627152, 315207156, 673288236, 906806111, 54384962, 385698610, 923800751, 499532433, 945715388, 385197137, 207629934, 675169938, 893632928, 467445870, 781578391, 410252848, 103261855, 229859217, 553089460, 54664648, 347952700, 639371758, 235108761, 713801127, 730729082, 211185300, 302238196, 498137113, 778000793, 477342131, 730233284, 361433096, 161009475, 852182298, 573712444, 31153418, 790158705, 197661435, 883454361, 785169071, 257520377, 353617928, 740456572, 394029160, 502711542, 845720363, 203320423, 967554920, 199144058, 884284287, 110265979, 67931554, 63639436, 454658030, 932216927, 900613313, 111193378, 467781896, 534193305, 869783302, 900212883, 733669213, 470404843, 508578694, 335789014, 652483891, 104086534, 369335088, 746127589, 67866016, 625260345, 415464056, 200946066, 65909552, 340978146, 516875894, 49387393, 374115609, 45901489, 200848961, 388604384, 572719567, 752270925, 438020493, 935731773, 669298344, 199779505, 123934747, 414897597, 913865634, 228260899, 701905294, 297984966, 642496509, 852271626, 68698566, 112760731, 598038006, 679261908, 116099892, 104173047, 279483103, 67571355, 728201480, 647672145, 530200770, 464428772, 71512664, 618913015, 607701472, 685371798, 972508285, 819621323, 764475421, 596599190, 516200742, 434436130, 318940088, 625883690, 494943377, 310790292, 348538879, 566560178, 787117666, 497877634, 191934393, 954511863, 546697167, 104840297, 209560810, 719400460, 847524091, 674401279, 754463139, 95889631, 96197138, 361007834, 453859022, 853831673, 653975595, 493684790, 403703830, 463955874, 811189835, 964320605, 722345272, 31293217, 362503143, 518401187, 757683478, 294708719, 794392339, 30316327, 838400316, 913412795, 916297687, 250640324, 569615684, 92053113, 251351665, 970459404, 588211848, 510210991, 745505316, 294464909, 435777016, 231013847, 322718081, 968792066, 404442754, 448908388, 80226986, 547161788, 177150871, 621241066, 962252028, 94837914, 272478498, 718062637, 455836051, 518601575, 118840399, 517210302, 967363120, 780997120, 198440919, 559084376, 212413456, 545347028, 953537117, 218581277, 494273111, 783158014, 799414844, 712563737, 311627750, 115476262, 72372582, 801700595, 711269427, 723847236, 702052020, 956527860, 549942732, 746731724, 42264380, 347730330, 657885183, 573097179, 967929862, 419063242, 926809267, 350980656, 696127819, 178120684, 766013081, 588200855, 964361164, 18450253, 281865689, 768876845, 924444100, 268070505, 254252681, 163873640, 890348067, 311993813, 181653679, 547665791, 443735841, 348145564, 862662457, 45238597, 549287502, 263219637, 893160597, 347530798, 848137837, 106056563, 498216350, 15817316, 9645260, 429407608, 691186192, 395535327, 666147212, 422287214, 794744452, 288128277, 307563637, 997577085, 193402850, 56571292, 395187014, 194230954, 241090885, 627930114, 113084073, 641250353, 238029429, 711792969, 328390058, 733812770, 343624100, 328615609, 169710227, 748048973, 790914288, 208508728, 629531668, 568249790, 405646392, 602321864, 192573860, 263846915, 929777583, 950276528, 788763862, 887805252, 537167236, 132809330, 789933628, 409888027, 31736559, 539909784, 73745245, 517381026, 447997149, 950725101, 591207299, 694222536, 706708791, 647066729, 183926329, 697673364, 110624288, 725582627, 520783167, 293245143, 238438694, 876385001, 790834988, 193221511, 700299788, 208824403, 252369415, 911202964, 282243231, 866100249, 923683655, 945365465, 178005836, 566056792, 598239938, 333024230, 413840347, 304256207, 348191900, 742088882, 691374140, 184407203, 559963833, 423724110, 720975544, 260771129, 376895937, 677572567, 420642028, 746168357, 373228943, 754645651, 368284876, 515496542, 591283351, 454666223, 807243936, 891048513, 686829045, 222716902, 177157841, 447870149, 420605045, 580514831, 679826543, 949924851, 962877964, 130333438, 979219815, 128118383, 225512458, 565236301, 363828910, 647639227, 939365437, 636783066, 827483505, 973643554, 904084718, 425864941, 525128150, 289855619, 802629248, 766425539, 788825594, 282721114, 76350971, 427064014, 464022191, 774188234, 133729950, 402836263, 704127796, 94566802, 45976497, 685080324, 143976541, 959923322, 190238815, 829452672, 314925820, 495923216, 920581958, 63427845, 480594605, 213565255, 471348435, 961516968, 652133517, 383294033, 352100637, 861568083, 3468001, 874102504, 911197936, 215297797, 694437, 191561424, 40403745, 578820119, 43707344, 107314477, 339598317, 649946996, 125791547, 642732860, 972969413, 102677275, 655988188, 175806411, 484694396, 745185989, 846916478, 772015586, 294612294, 975910353, 354228766, 954320494, 260539007, 763781461, 8415028, 698607398, 459131011, 118881446, 220444021, 369506212, 550332540, 844348680, 293133100, 373115443, 178538750, 112647834, 904179786, 513436102, 770794106, 118894519, 928929025, 20944598, 193834414, 613654395, 930957660, 452343473, 924494018, 479485120, 776581783, 229535811, 423070060, 375115532, 116798662, 391267304, 50883048, 458589733, 260976166, 653397832, 505292190, 714192620, 771238979, 142615926, 356932216, 935464417, 864034404, 18433614, 491017449, 743561708, 440040432, 523503162, 454410270, 771076583, 845474746, 737578666, 133657028, 12699306, 384615245, 522243646, 808546038, 796830631, 555627538, 71065813, 373004584, 577515472, 621544376, 774325201, 789667499, 657724170, 427538845, 693769995, 841362183, 825532184, 151627212, 9419337, 76077832, 165731987, 928806090, 561238298, 52361742, 471979166, 682725266, 908577668, 276089460, 300636759, 421968705, 87149723, 573099286, 299215534, 659235295, 208969562, 515318930, 929296289, 36956355, 417096136, 313196338, 116334992, 436669844, 603127532, 206138712, 432942377, 827957891, 115054145, 330221647, 903511267, 871894704, 726677950, 973807896, 530650145, 256153058, 734182078, 892551096, 540371356, 561528834, 73665706, 933293994, 802633206, 27952049, 823170494, 432586201, 715884451, 177332712, 890220938, 358315005, 752185373, 126245651, 752737040, 277538485, 371647137, 213957590, 461266517, 488808380, 785856730, 437785319, 610637147, 396129005, 45093629, 468406803, 814385988, 474811386, 741747553, 428160914, 5991945, 55530004, 519225336, 151544968, 879908026, 14328480, 705902970, 814544736, 655819220, 409715516, 483790803, 623765673, 255531267, 858373663, 29945558, 60093827, 933933695, 76545127, 631322450, 290403623, 421603509, 50907775, 975762770, 520158699, 878449092, 209908452, 831918104, 793160839, 817108996, 622926589, 182678680, 640366288, 127159751, 771946782, 903127665, 998941442, 407506333, 981702741, 826022022, 995392670, 886144081, 911566537, 287512311, 473300880, 986554101, 562560799, 600188797, 120640013, 318494533, 984605726, 161334379, 435011613, 292180205, 876934514, 60457736, 422340067, 502710420, 165727850, 471614674, 808783343, 207899360, 894749357, 566149381, 113418443, 275272329, 674546275, 823469018, 862500366, 319351046, 75904297, 925333575, 521231150, 878715029, 623882281, 118458387, 820070802, 905840627, 785688389, 352004496, 690509058, 558590594, 224103000, 857196564, 510868699, 987535648, 84137275, 342730282, 112846342, 718085401, 110530863, 137856365, 676016104, 725975266, 108332155, 958818188, 481943654, 93422543, 280410621, 621816453, 467525565, 886355196, 929744391, 729028153, 553278630, 238482515, 879599482, 226654175, 209812378, 873380539, 234440336, 639466303, 110040835, 62549558, 439922604, 554072898, 821011438, 802343660, 791020583, 287357703, 485652626, 817328108, 221158491, 132468095, 399756767, 546488746, 482892185, 582806115, 871638938, 716534090, 277054576, 863707922, 44538445, 619382604, 571440323, 738812878, 202479926, 269671079, 85184165, 900282380, 51012882, 219130592, 542593891, 258803296, 208337015, 33161348, 681751072, 457855272, 590174991, 304001565, 380237618, 945535510, 347282549, 4920154, 228256630, 169345474, 141088276, 290487218, 248368679, 962440747, 330681289, 528387277, 975957065, 704870416, 42045233, 555016311, 174322603, 584510830, 781545090, 193390000, 173763117, 734462940, 441817185, 576775294, 412544121, 976726669, 552618617, 59702142, 212200116, 12089939, 11164344, 607716376, 5101408, 787309824, 548514615, 116555222, 642938835, 473779009, 648493554, 13444888, 758055765, 729941350, 625025361, 444450634, 129909799, 13986871, 951560491, 489712485, 295144142, 107721005, 844092328, 92491405, 718395844, 305203844, 846600577, 162356961, 346915946, 579250417, 775208824, 346956654, 70321756, 515159308, 316526052, 43929488, 917537415, 319064342, 282204505, 42533067, 75566318, 141592065, 481068164, 771264898, 800856331, 268268379, 331414098, 14284327, 977557403, 760939136, 669512382, 232698629, 575380269, 821915099, 385416520, 464062052, 81126052, 836359945, 591566666, 592507154, 511864171, 254757103, 12273620, 245043301, 921839163, 482202973, 315764828, 741102980, 28199219, 57737973, 710297287, 444349105, 849791269, 517793009, 662036636, 711654689, 2942711, 43552678, 958363642, 980910163, 675373444, 631666390, 398033665, 645585445, 508914426, 758236389, 725082805, 493017858, 219562958, 873875024, 259270358, 750913023, 426677037, 759075179, 314788942, 999881342, 135786717, 127723560, 611938686, 856864613, 14866455, 241655021, 797594839, 2056771, 381931045, 770392142, 928094538, 179572471, 887439994, 581348166, 979449932, 963040671, 226349909, 547746125, 291243353, 261995677, 856207301, 158698136, 623785665, 343398269, 259682081, 948707671, 475874103, 644204099, 228163156, 21199372, 387066834, 706670676, 522343519, 539820896, 398522064, 494652847, 788096823, 733095623, 901971898, 870471219, 313772793, 221914220, 108375387, 288468988, 795296607, 528157088, 87551215, 735092310, 591602600, 670894579, 378842350, 160481513, 759622159, 60673591, 93692170, 446804875, 185123647, 609282358, 908809496, 1252419, 993433124, 247669112, 420853936, 68891124, 581537293, 880589749, 53624976, 322536372, 93208731, 839028717, 749799827, 652761856, 515362028, 362649978, 584785944, 796711579, 202381225, 846623078, 800315255, 120011787, 328624981, 973986947, 854362412, 687238849, 463550144, 672752215, 701763593, 980243717, 496947445, 174739801, 784846733, 406018179, 109730233, 366337197, 306116112, 571922364, 22387836, 818442417, 421969418, 427482645, 42735953, 140316859, 653769902, 898301252, 786636228, 556880339, 840268950, 293765228, 662346114, 813656449, 85448221, 95632635, 496652131, 415532781, 605483727, 421218028, 448066313, 172027517, 738680133, 578778167, 820316816, 315277410, 345303094, 719420380, 501646550, 464265308, 489083582, 857200953, 211876204, 773311640, 973452103, 997120902, 451410330, 743708220, 511511829, 259092402, 803880863, 623299447, 689944925, 271887429, 357269533, 766553365, 9401042, 322235735, 153089306, 93918245, 817512017, 376337811, 918970296, 81763988, 981132668, 700473586, 633270640, 35837115, 575297631, 533965725, 454977399, 833401499, 169564209, 829794559, 182765729, 960069865, 450033865, 772817967, 572631590, 868658470, 538926323, 874638884, 11184608, 508851475, 919898542, 416484629, 958443558, 85265154, 581630870, 430724703, 443331220, 944988692, 216845162, 917742501, 159903258, 57479589, 530431858, 508892241, 273736157, 428872499, 590044403, 247322656, 70538894, 346198763, 847189169, 944316034, 839602075, 704364855, 154143753, 698158068, 992741737, 165180953, 832746231, 303042904, 132775682, 844450690, 251354475, 68905022, 772926383, 702032828, 694986414, 697363458, 289619011, 929489808, 74783845, 438994851, 565593667, 241522043, 35246457, 492152041, 373248241, 703132324, 583786775, 39765389, 587291049, 156853033, 453092298, 247280079, 221780298, 995911605, 196526018, 367472924, 340445183, 981154182, 153459210, 551615197, 68149747, 348847659, 25290284, 848476146, 809859851, 651772403, 404346449, 977651728, 661999839, 365928079, 146790370, 150723910, 813856425, 458142122, 113010103, 828543387, 495091749, 545699446, 886435210, 610202646, 545228981, 689879113, 84105597, 595008770, 729862013, 564176770, 121818043, 221056799, 798722725, 301731096, 258819421, 778841085, 935142332, 309875415, 31393595, 765425473, 145332597, 791850204, 868203002, 560100053, 624096375, 60183026, 710929848, 354174822, 743349370, 162165551, 474003721, 155913400, 432885353, 981255361, 137972496, 305533179, 522068549, 293712689, 885849333, 696941853, 774358276, 872567745, 384134832, 701312590, 254175629, 679479124, 493087728, 125316726, 596920633, 746410817, 904996466, 243162742, 759207539, 296531563, 842784359, 266478972, 264230011, 802550064, 284393687, 53063594, 544697342, 384253282, 447816125, 505757066, 929287600, 710873190, 659204240, 739365046, 557078926, 385785842, 244177272, 905680759, 549378756, 966342408, 236721841, 940135456, 459929023, 926288500, 397524218, 808940702, 383561642, 44221951, 204748025, 934797881, 257511912, 680664280, 987892815, 616374684, 885114520, 937660011, 168790959, 193174094, 468466421, 696565398, 873380989, 827928749, 75756108, 399764247, 920273290, 719984002, 926382536, 889157472, 877519998, 438750260, 163452138, 436107561, 416755845, 102874976, 76401873, 233241858, 86948292, 369549868, 372437602, 731251434, 818534691, 97594745, 973623772, 206956625, 821735775, 612358191, 470676389, 576900112, 678949674, 344303121, 10834079, 216932743, 17302022, 564618910, 52998117, 29268359, 488156299, 975470693, 1502106, 718523993, 297666427, 283672442, 50788865, 59313130, 291067827, 192963441, 376421866, 476916394, 801489335, 874728867, 474128950, 79323692, 941373700, 752169595, 195187932, 575168051, 248423554, 768153446, 645888458, 887383910, 939239417, 559657393, 754543143, 462384315, 991452832, 668049957, 636366033, 553483040, 231354725, 71728189, 75037728, 114243980, 839248936, 653229296, 636200355, 201582381, 167044209, 949929886, 914232441, 536662109, 335026276, 255500806, 307349828, 107122695, 48903752, 992067075, 297893562, 76962954, 250365978, 802469679, 107970932, 102371038, 357724610, 652771903, 658638822, 445041145, 424455294, 105590678, 701316246, 42309363, 851987562, 975657994, 528010561, 560034627, 315464852, 401551487, 508648799, 717541221, 320890888, 632712056, 761177915, 115779723, 984568590, 494717526, 751095584, 130044019, 79316658, 876723606, 399406995, 546324893, 828422655, 191720254, 68247787, 207732045, 221678708, 87906885, 303249251, 569915700, 330261249, 581592456, 996995871, 925326986, 697674964, 881936258, 85182234, 136565960, 842346990, 796471732, 683541370, 494603835, 655976890, 20368489, 325357595, 930850151, 554035772, 458580742, 863648025, 548590797, 412562134, 470806511, 235277822, 58375924, 641196406, 4231159, 489165630, 276460041, 600437086, 433183606, 541545767, 685030999, 333388466, 605307504, 877954812, 335578796, 510332439, 196273991, 704684397, 374033543, 954751538, 79217313, 76034277, 504074109, 834395722, 161867453, 513282232, 591794522, 393736725, 897575338, 225935483, 159313198, 778347146, 691168851, 17219653, 674161592, 65678853, 50073330, 354720022, 599342783, 225670172, 681537502, 749520052, 3808716, 226084374, 766419604, 575125208, 484874601, 756317471, 83133378, 1311203, 561417535, 969851506, 573754167, 359070838, 57438742, 921528217, 572370627, 233936936, 794934635, 33634211, 175402970, 969912837, 725746045, 12161898, 815020382, 896978407, 324357736, 272745001, 893173557, 830478608, 932558373, 298802990, 245615821, 874504668, 592632691, 707957526, 484013546, 984370140, 500714030, 832612626, 872913716, 587774601, 95489894, 671836917, 658826503, 526446501, 896445833, 947994177, 592902066, 258565394, 639480585, 865711684, 480126513, 304466516, 861702513, 410766534, 399624414, 621901884, 65454589, 566415005, 259382395, 573114714, 210820849, 939771922, 515846468, 23258736, 851218377, 473545663, 907258767, 270287093, 374464752, 247640801, 600436646, 74677031, 23140960, 114852327, 573475100, 904594298, 166560842, 772161620, 3732233, 858594556, 984715846, 497597339, 630757354, 553065107, 623372033, 196524764, 461980847, 415963920, 987466359, 308074546, 850317529, 401805913, 48445735, 969351944, 993627054, 296487757, 53882671, 449360282, 617415805, 205694452, 357963549, 334503843, 335719383, 293927888, 43669494, 569688283, 485845149, 499041216, 863939350, 238893514, 333268559, 726056052, 73850249, 213313698, 653409286, 189119886, 112151911, 584304996, 132737961, 158877749, 997830687, 982930991, 58855923, 664050170, 852247033, 186590437, 353832645, 968354759, 7619598, 702680624, 231758057, 818812025, 88837601, 674997910, 712288315, 972975397, 847999061, 142424439, 118653731, 638437470, 401051406, 44098904, 893451844, 532354833, 689270711, 304800744, 765778807, 745213953, 57320356, 842825098, 287016221, 134990352, 674920457, 723017631, 97960658, 336075331, 240833334, 211489067, 600219576, 196210508, 484513014, 4167025, 826501281, 491734912, 877265940, 794131702, 520500860, 100291892, 445169796, 164613404, 756316604, 887908923, 232928431, 285082494, 647791629, 898003312, 423678018, 87220126, 800521908, 541914278, 97992920, 415981798, 502244753, 659510754, 931924168, 700438918, 568367550, 157796831, 901123186, 458390923, 931480393, 410842018, 342009335, 57010099, 564707055, 766458836, 118284707, 738376625, 811155994, 858967361, 585901368, 580554909, 329608753, 485294875, 638338755, 447013244, 741579440, 166304704, 3402179, 522361550, 159688028, 973914312, 406376685, 751566224, 430563497, 38738435, 914847544, 391026311, 39579438, 575233787, 122013448, 942891618, 412040280, 555961277, 883605667, 756056115, 283080404, 874777832, 733872406, 341280375, 821632133, 739967094, 124514125, 950519385, 358750262, 463409879, 230823347, 900971687, 5249398, 870028528, 391325587, 383308822, 415556869, 66223196, 341382456, 135231439, 515175133, 254616383, 424933999, 776739053, 370336090, 950519428, 364938171, 624995001, 472428560, 804284906, 685420485, 329205037, 937310921, 814407189, 599431607, 507366875, 464892480, 404610790, 446963301, 586476506, 97663798, 465250387, 959033427, 976652302, 13511419, 903102055, 909113345, 730596273, 726268924, 515335101, 765099446, 954516543, 394496082, 256390220, 207089427, 614884980, 637383445, 340296956, 328942399, 19290898, 165738542, 187508372, 473134369, 389506528, 188237407, 165219471, 534758555, 845747565, 261402312, 309224982, 346337697, 442365000, 536612068, 644609390, 937051160, 320372584, 650290138, 309311621, 102670686, 880381837, 258225070, 525990995, 511387861, 98504648, 297632094, 369405958, 429267553, 506961725, 215268298, 92421904, 625044464, 778956753, 360088996, 954302971, 473377917, 408115030, 161599977, 365575883, 839127664, 316717059, 526633710, 357296151, 634901599, 27522561, 612215208, 815483171, 143628518, 45236162, 116825130, 667373397, 27288481, 50230790, 505313555, 571423696, 1659491, 883123239, 375382759, 526890250, 622127751, 243810382, 904430120, 790279955, 235872007, 47965728, 528113793, 624427609, 821453308, 553083326, 469907182, 152234846, 126552555, 37546830, 638603540, 150985559, 49993359, 797343229, 925354557, 672584832, 714394287, 118656056, 757731586, 164247789, 475706301, 798865053, 345555502, 93521497, 149806453, 770769649, 442429399, 213533340, 433672823, 210083083, 286031995, 916338084, 330747698, 660904261, 450725742, 526997423, 397470403, 225239222, 962614583, 915163132, 108700537, 237373453, 286203097, 724015158, 612547226, 173200802, 320889894, 167585766, 72633202, 190517415, 94624413, 788626593, 220557479, 297019297, 120862920, 397026731, 536804573, 417699015, 837892272, 423222715, 715721756, 670427432, 356343459, 687070266, 949189761, 478055746, 314954561, 839350791, 402105051, 101206613, 41661097, 819752897, 644579032, 604405242, 64596965, 917615724, 786033213, 516648207, 387541032, 12201179, 166794533, 238617832, 451636294, 117198069, 977942907, 235765682, 291905081, 409436547, 141229705, 902937711, 950942422, 329141116, 916560574, 978299470, 193992236, 927449416, 348663115, 359712678, 619327398, 765635763, 383048138, 725041628, 980814454, 253993441, 418845437, 557578136, 706932506, 269693663, 916041890, 487610681, 397991557, 19517597, 313225341, 964610773, 746093054, 263830809, 346111817, 155225334, 520942062, 374284486, 840661950, 727472807, 596301526, 486920281, 746267368, 355602262, 685068258, 688808680, 405047644, 74550114, 460430132, 983280893, 9620915, 18180097, 308021251, 538069659, 821226641, 866932973, 483273261, 71784690, 366605379, 2667991, 990507626, 650572295, 241088799, 877428277, 158715152, 989709013, 138983979, 720935951, 4010491, 923044524, 501015088, 16050875, 104447907, 113133406, 265713665, 942262843, 748072272, 689527296, 726435319, 460070322, 741632043, 494234951, 819845154, 757554022, 232120791, 367160544, 289954110, 131632113, 767480351, 183659114, 182955945, 878731369, 58576577, 301461163, 843756022, 544430032, 976551850, 714262463, 413723270, 770942258, 701806678, 481813458, 183378624, 609989275, 736423166, 19409658, 822776197, 845403130, 960983152, 979983712, 585504701, 816707103, 7758891, 119213959, 32458381, 134147402, 503989238, 101727031, 305801080, 183972152, 962068655, 372270121, 782390957, 382101943, 195817094, 644931382, 138757009, 570777205, 168425449, 431209105, 398627983, 942274586, 253675910, 332698764, 580839456, 268924867, 354442011, 176409227, 981707371, 14481036, 648279298, 238143076, 621905139, 911504375, 779096677, 646089788, 354478906, 136065831, 602355060, 875470356, 92518082, 1728567, 410656227, 301073914, 867511361, 655954162, 984885725, 959989409, 574270976, 103028623, 575792194, 433268722, 784648636, 76524128, 51959984, 135247333, 915700169, 98713786, 780811869, 181731845, 33846902, 579596058, 194541238, 794890843, 731041345, 396670933, 766354875, 658034045, 759299202, 410362403, 712418650, 18461654, 767508587, 665153615, 564855692, 372352782, 515511970, 110222346, 229585021, 539095368, 852787777, 795133910, 663038674, 334742621, 295343483, 348107967, 414632216, 661685797, 125675794, 466042811, 780367073, 996743280, 673551335, 451812183, 432710552, 947408654, 18804421, 785018337, 6667190, 313713723, 629849918, 633553200, 607055107, 715677524, 11310323, 390114580, 723713565, 992598619, 891563185, 985668319, 619773054, 229774941, 808022391, 239273236, 750522298, 525009267, 341941677, 242335082, 584401709, 596252850, 433149455, 523894263, 552231300, 478304397, 820771670, 63582188, 767518561, 404028328, 913982303, 89525265, 747430898, 20019634, 611632382, 109668609, 153096007, 76517535, 388436783, 388057105, 430652077, 444534128, 155603953, 645835608, 920509643, 379135936, 447915092, 576156465, 294358165, 382027792, 132374362, 761835853, 793632941, 954744329, 396897899, 740419464, 376163284, 117179028, 752977331, 880347853, 201062548, 932185573, 572457227, 389660321, 904175306, 728420089, 299268390, 620012356, 821839341, 704895759, 839469491, 746070616, 590915519, 160175099, 142201638, 280584986, 436822658, 102315841, 110440915, 906532905, 732740331, 154129355, 919975886, 687483336, 340324391, 40290198, 677959269, 554484340, 148137611, 416053173, 724276919, 81886725, 386362125, 320845895, 110307203, 888237767, 405013503, 336526470, 362542186, 154483633, 990092498, 365696748, 650050361, 582356115, 159889140, 11354630, 408600795, 381453483, 820131527, 425160241, 505480769, 894596646, 419780389, 344908227, 243573679, 709343127, 261515657, 460837132, 389166060, 270002106, 788947570, 474858721, 577515350, 748932850, 153544776, 164382414, 510345835, 342340304, 253690458, 711393588, 823315326, 623148280, 518905116, 307282281, 156353992, 32731283, 197657807, 205775688, 418781857, 10324990, 200054602, 940036809, 87385513, 200076075, 712515340, 765396858, 925894343, 653504196, 944501241, 753690580, 577589476, 867822704, 308904645, 597463157, 825829504, 875618050, 978073436, 500555319, 510915818, 584026402, 145830223, 912830814, 379444890, 674664289, 113110246, 424216623, 334179520, 937245523, 881899184, 145326880, 932284154, 510727958, 870138012, 815424934, 660787876, 966877303, 510959083, 493840030, 340598922, 596285018, 614105225, 699078868, 658006376, 484135158, 262289133, 594181665, 820652666, 746890471, 236818566, 428543200, 255782970, 266324071, 242829498, 525348868, 24503737, 169295086, 62902846, 938651192, 873277291, 625210134, 839187128, 71761822, 976205331, 152993479, 756581194, 998734529, 772418449, 439576405, 701229810, 375905829, 702079947, 794696839, 935410292, 22392785, 697762917, 654156462, 740885694, 125310509, 986393957, 16942186, 579100790, 177561130, 373162176, 905847619, 964644470, 478605520, 408535246, 182685491, 485057333, 304231152, 994485741, 520872150, 671389852, 404632905, 276804374, 337722109, 774141032, 251633934, 58065426, 550465011, 835579919, 807834616, 366359166, 730403452, 261483663, 444316046, 637593346, 311710221, 853771071, 967884077, 133332624, 224137450, 776753279, 763181004, 400570481, 176690883, 393539637, 148467106, 66463170, 918415064, 693144739, 27167664, 302978653, 1940475, 747198755, 412583034, 736425850, 457553886, 145500239, 291375106, 841558575, 172590964, 96491640, 515667043, 107564800, 948361865, 62760727, 455283733, 364108995, 392385544, 33923473, 218351148, 619835817, 847967489, 593782576, 480883734, 546129561, 378394268, 19496987, 453076301, 835226467, 52554433, 792148601, 600171488, 635026898, 19716453, 360338238, 935725588, 657694005, 285544769, 329999995, 539727930, 826408367, 407838487, 634223172, 473966046, 890260804, 973697639, 516393991, 408323053, 833901546, 760515941, 917195059, 106650349, 909371169, 961190395, 796966849, 376612552, 776383212, 331988435, 199150658, 985654492, 572228432, 721719972, 905913036, 180722448, 203782716, 245400510, 95948555, 566590479, 736068944, 794079069, 921655572, 834952098, 109977660, 955605720, 863344977, 845135078, 526871755, 614280199, 109768817, 569728994, 635795486, 801353343, 772030972, 822987168, 268992081, 373185792, 325249466, 831706953, 913740937, 753152698, 129661474, 245028480, 772271233, 300349984, 822464213, 97727785, 96393323, 316514116, 898245997, 232919860, 969680675, 982841237, 4457500, 586552152, 78137528, 96302296, 174237797, 161399131, 925363957, 545843334, 437619822, 391981882, 678225689, 388871371, 717033046, 233411239, 560480622, 523306940, 666619829, 997864063, 106764998, 533944949, 399566193, 792848211, 275651088, 169459918, 467108492, 714697069, 715941248, 870338173, 928298213, 795502686, 133319167, 651148103, 149969845, 432605630, 874277131, 577334168, 16555378, 869841517, 353291318, 250300597, 404664812, 754835489, 129029568, 578535191, 286628102, 85065266, 21483363, 673875927, 67651981, 369296329, 599915795, 288556086, 526681489, 579030149, 134468958, 950933243, 897117491, 100606148, 751972058, 234210350, 733103041, 753940152, 58647099, 726881853, 49444936, 148831561, 788990071, 186315464, 274743467, 435412444, 339622736, 748571750, 133790497, 923848120, 414776581, 925120064, 572313620, 650908761, 730576890, 730093332, 381809478, 694196614, 457222363, 149277173, 977596454, 723763054, 459508660, 897772152, 785339753, 320992726, 185308754, 138450012, 386564191, 485509325, 225484433, 644367691, 437051234, 237535724, 368308975, 523594133, 973181295, 146404129, 244733720, 244548877, 835115825, 842513976, 913574059, 74311073, 260834303, 931400442, 850425551, 716743797, 88823573, 420175167, 784997229, 775662465, 663584771, 997197307, 664338095, 183011008, 385043184, 931240379, 521733274, 836339138, 459402065, 82406364, 393123135, 154062054, 921231165, 286121514, 587032931, 510969042, 418549582, 407708737, 389142128, 250257378, 238528471, 343858539, 602291988, 436968529, 942314041, 856151538, 577708780, 979638516, 610343437, 742893684, 826629261, 183047549, 998082318, 705177162, 592608963, 185323036, 517399263, 343460395, 205939978, 917866098, 514298925, 180774553, 166036270, 651230569, 549900365, 630155464, 38018833, 185280789, 906755495, 652274265, 71112357, 157844821, 98335149, 334885058, 361590334, 736818126, 647197176, 680536075, 744430483, 109064997, 439507791, 948493190, 541246140, 131411436, 78776939, 441991705, 329425651, 808729076, 981054272, 308062446, 190094995, 990393503, 235965169, 714435048, 318453806, 614528044, 732424414, 183839877, 140206304, 436041308, 359209594, 893994358, 890334761, 234247343, 567303650, 787205768, 14736057, 918534334, 307189576, 875787191, 402311185, 665444400, 338184344, 359793320, 435228747, 460030930, 493135774, 692925148, 403655708, 666375126, 29107108, 522646635, 870808133, 21675809, 845837718, 600972496, 411271058, 456437684, 742873528, 506703571, 591575565, 674024077, 720342978, 660117903, 359714113, 550371207, 569857192, 545374426, 826347532, 930336680, 5657600, 43780320, 466820601, 940771089, 292200949, 670401250, 873319558, 466272802, 363189756, 217983973, 604280045, 307121041, 991320395, 575584250, 322295189, 588528317, 70325244, 474123954, 778161220, 794512142, 980273113, 334276788, 477300657, 527453812, 78927766, 759553169, 232553898, 841248847, 620982835, 819493168, 990983335, 469413832, 286474571, 845906817, 734239090, 917250320, 435547911, 766223430, 369971138, 856140627, 57101810, 959380206, 767529139, 902340109, 559814822, 699384402, 734050132, 903550272, 224741666, 781596007, 137326733, 61616616, 14151026, 5393223, 287420705, 602637871, 556807839, 962112228, 224134202, 747099334, 263439951, 707968154, 689789467, 567334238, 875267070, 152164172, 936381376, 391566114, 809394322, 323201099, 425917735, 695314135, 765012107, 424765131, 891234022, 669417448, 243165545, 109802078, 719293943, 263419428, 578585892, 493924683, 701640415, 995091590, 711210158, 231167208, 284922808, 567022943, 494965433, 747219013, 224356664, 569043262, 881445309, 104737187, 740305686, 352816225, 419971268, 683729272, 971366517, 950593596, 470549348, 280401679, 555334308, 280241319, 358893597, 219496298, 338703526, 217299075, 366915830, 939987436, 797593783, 672747627, 435291653, 247586746, 931259216, 23778976, 136088988, 898685828, 396267234, 24322979, 663862614, 921040152, 655523909, 277466729, 933597918, 125785888, 674006138, 646546601, 81286945, 926491796, 398267836, 173996293, 385363864, 183709137, 161628835, 843625521, 604983757, 421161155, 981032904, 956108965, 779469391, 766827368, 644251527, 697219021, 455130143, 137183222, 782203510, 752428572, 715399676, 926989480, 950125490, 224391645, 138310676, 854943037, 418760538, 475767779, 249361534, 408422018, 41692471, 818750346, 387254151, 210178623, 865743654, 89089611, 847556880, 63658169, 736975575, 30663775, 446786831, 820857608, 874679935, 679405505, 194911414, 104457032, 911418435, 61733860, 860413188, 944467504, 486330904, 207995892, 418442515, 249140373, 548014788, 149561748, 852683930, 9473052, 353189804, 560708481, 911586745, 707783377, 341914366, 941307353, 91316723, 597732991, 387672612, 90744580, 447676711, 180766358, 485157125, 988090511, 96892432, 696053135, 561157376, 22792207, 665264757, 107804728, 909326000, 91329617, 657767121, 755029130, 692932355, 838364068, 515053167, 591558665, 917698437, 639049323, 427615332, 56900052, 483953584, 23992014, 287898575, 9949292, 705182044, 34970515, 716715461, 949510671, 172789143, 603155907, 231886, 70421054, 135649023, 383326832, 952616766, 563980802, 873846131, 261873652, 456780651, 802712566, 147546977, 121656446, 438586945, 403092135, 206493940, 844736646, 74335615, 275414658, 174525487, 828145419, 350558550, 804925424, 622551691, 218941174, 107379742, 744423832, 7559847, 558114164, 332985914, 314667964, 375659009, 786357613, 978379038, 479798783, 722079568, 517571963, 875606622, 994901472, 553880495, 621435040, 315413787, 50037996, 872289859, 522798758, 581402585, 165216964, 804687460, 254327632, 744928515, 172206090, 826053027, 353402259, 242096086, 856314117, 26973726, 915065296, 52774488, 759850465, 112352304, 393732628, 764158817, 648209347, 673473371, 971189511, 136328055, 107930563, 956492838, 889536173, 316558534, 675166917, 610956309, 104769390, 654327961, 108838353, 647036557, 873800542, 700612189, 659438373, 558516925, 138774350, 218556455, 798918295, 125561074, 188886366, 489443545, 79459459, 54983277, 206055891, 233792486, 274023298, 209406649, 788490370, 404068681, 865575082, 722363258, 81340125, 26284238, 856490343, 320192139, 582658808, 292923205, 789341754, 386848990, 765796380, 682762532, 276093524, 422994252, 355611551, 157973709, 792572809, 443695409, 296137396, 396015076, 296512612, 889400900, 590969358, 871183537, 749006053, 672599854, 332697985, 650877522, 605865884, 465206236, 720992146, 74455881, 558946470, 990605522, 287732447, 3053524, 289639560, 614920072, 37035814, 83277331, 544381896, 693642631, 384534314, 597545003, 776074455, 9146011, 334565225, 464895963, 43667525, 541639767, 457427697, 705435270, 937901433, 447943505, 730376431, 358720930, 265322441, 697821814, 287464679, 431266504, 944531449, 889492616, 303386266, 356618228, 408618003, 962574993, 858123366, 567478036, 242820012, 553335739, 599841962, 643105015, 682376382, 855977043, 358095066, 474960064, 236147017, 435828826, 659163886, 37293999, 363871691, 20696559, 696256282, 697574683, 616646412, 864960336, 464439140, 543604698, 582689457, 571300615, 48759655, 403924660, 662400761, 952832857, 829025485, 337780517, 47906121, 980490631, 771156206, 755387640, 760746259, 280988150, 885775374, 141204894, 346740047, 942524974, 950378942, 591681918, 546889029, 887178997, 917526483, 192620307, 823083573, 700720342, 642577886, 416442357, 978660966, 397623242, 646457896, 44164668, 487369310, 648620360, 959728181, 935557233, 516637129, 238691257, 761270344, 469429305, 155741600, 423565393, 485019332, 160901278, 524866627, 391790249, 381269334, 384041437, 946381932, 649854223, 659038338, 883096616, 766923280, 403553075, 856691622, 246618520, 709882187, 600166208, 897909436, 550984841, 256611299, 165327588, 798744595, 144745379, 558260061, 824883353, 192503563, 726549183, 983537104, 276687212, 829279298, 296152181, 860192888, 883153403, 929450555, 694851068, 848731107, 267833163, 602401881, 363490050, 163476246, 807188744, 922625327, 435183921, 680807327, 540036653, 877031966, 586546401, 789859149, 340498193, 120248562, 842676230, 60151523, 426069769, 621401334, 113353229, 589960100, 270727150, 131191657, 425053837, 359574405, 186336917, 927524063, 629311919, 313066097, 122784603, 230985314, 696936048, 44277528, 802279527, 266477047, 24268073, 908828424, 971643899, 772964417, 118853387, 882068690, 617220591, 557101590, 586975489, 743597062, 620082074, 767133139, 799196600, 381856323, 641786629, 385440726, 185840772, 353470209, 144827024, 777310422, 9921363, 312362956, 666312840, 644592862, 775443026, 615381518, 529571726, 104248597, 931467721, 15707428, 988200931, 479805007, 970946195, 791455587, 641268013, 952089476, 778877811, 365671306, 730617530, 480950201, 303795539, 939684568, 649779051, 23338504, 486469763, 996394983, 74302768, 442483815, 512494370, 953485624, 831826773, 763162823, 154121035, 696126801, 672454447, 245147871, 821681276, 69009113, 834355604, 419253858, 71809209, 201151540, 299855576, 895602138, 730517924, 763809596, 921785478, 337595493, 46806044, 233095258, 909058194, 714209896, 56661569, 80638217, 625538053, 498301819, 1730151, 761192731, 935372030, 674621410, 597685181, 752311159, 615309365, 392536069, 352330034, 326964768, 536710181, 414397269, 55039154, 79752006, 592888039, 890978403, 323473786, 765242767, 725394121, 588755243, 272804457, 899872345, 336924154, 282244386, 86385590, 169297422, 446773014, 583208399, 798496412, 645944112, 20744284, 401749637, 13006388, 883705501, 616895171, 937647284, 498622630, 316973198, 681110488, 916811474, 326579589, 348661002, 682529904, 551720888, 140946151, 533148086, 149466581, 860437806, 572540318, 523190682, 516468042, 116904214, 774834542, 820641533, 583005875, 187206382, 437938308, 864554072, 934201422, 69452118, 641198310, 560499303, 248258066, 905549438, 886500906, 254251730, 139966061, 147825763, 208928292, 895713371, 633026128, 97296846, 135724335, 239072141, 39097168, 644282979, 776181356, 461865916, 286079451, 794758623, 768065967, 860745400, 145067540, 31082860, 91298698, 375088013, 802919751, 230249792, 533380001, 871959954, 574861278, 471578125, 893088589, 73210259, 406564087, 397280405, 379663961, 158947150, 1005415, 269890271, 252925648, 806659687, 573123761, 7674647, 261889515, 123604676, 471334712, 966565668, 992900418, 305393631, 348523224, 549781034, 893582268, 167940759, 915897590, 715586476, 649931736, 561291754, 70393025, 367252042, 229676279, 691024274, 482955298, 623685421, 689098615, 922746543, 863604428, 807033093, 889687166, 909046468, 864635191, 580152433, 277595946, 565549888, 666533472, 934849097, 74902765, 68766723, 369864232, 84450435, 390755113, 27754510, 93507685, 196843888, 465350352, 977377041, 194839969, 147635161, 518220193, 570812442, 749549013, 507166415, 350850236, 93476641, 502200910, 834057391, 977434251, 834568339, 402707837, 950334644, 499135644, 982670320, 480501236, 10177905, 771154138, 306189056, 689661255, 574007814, 532025111, 309125253, 677586139, 587154733, 217320654, 489362703, 298516385, 618283768, 7442103, 904910417, 666478797, 856339008, 619732460, 691536615, 630739869, 332557183, 930002158, 933362723, 128139896, 84186988, 959540292, 199362482, 166951603, 519219114, 110481222, 32836349, 933086818, 118538089, 213862802, 556821032, 980620460, 879016660, 542212775, 133297441, 109666288, 314335467, 910711200, 307464425, 890973622, 309315036, 751151232, 771323353, 201502855, 442252159, 538341040, 601072582, 776996160, 246016586, 325789692, 925952653, 931914245, 400674664, 549741959, 222974734, 407655553, 424284307, 565120360, 286089209, 427825245, 580155147, 218190670, 487122598, 506318738, 238185577, 410730532, 777500398, 805616217, 296904503, 669770359, 675786853, 723451152, 590334718, 358611022, 848234108, 446063120, 400250007, 576014812, 427836243, 513047471, 510879408, 328586132, 763121452, 973307437, 851080427, 199482198, 960164461, 601788309, 940659467, 165956266, 369819619, 448759071, 508260471, 764992929, 418324655, 441776144, 607374324, 500602937, 493749825, 233501385, 750965002, 791761198, 412822166, 748342985, 889192453, 677808210, 618968327, 886972954, 60777458, 760999053, 490247631, 837043279, 312108692, 192333468, 677068100, 669793965, 615285114, 996001585, 676729477, 278312596, 94916103, 778051547, 908926085, 611763004, 869548415, 613565697, 97774686, 494322644, 321312835, 986025058, 208664651, 284143416, 505195515, 394744438, 95126373, 286621622, 537790252, 851825139, 588885537, 371308247, 987306300, 813359169, 357205040, 423695529, 177025047, 561770479, 792407681, 798585349, 305583318, 600178455, 876670072, 730923198, 231886491, 122200082, 573421102, 513834393, 145104522, 786427086, 609783207, 217914802, 558588251, 692001808, 639118890, 362353620, 184942637, 221382142, 231981207, 302997021, 619687988, 185533215, 351271761, 478579493, 842054033, 74571546, 416208601, 253370907, 435311789, 595678882, 571274611, 994886737, 619291072, 532830347, 124025303, 771973617, 323692924, 929276167, 201043422, 237147870, 994357508, 408471700, 709844523, 910734877, 645708486, 716260149, 399338474, 161651842, 890954470, 537025788, 82857883, 210452283, 389258429, 918429357, 455499294, 396025739, 771751825, 257521085, 683189357, 94470850, 526576637, 16318017, 340359553, 452916444, 854574224, 987987641, 534005380, 549181980, 297650256, 118422763, 358587960, 291122188, 378792973, 631851078, 441637295, 535799400, 239169645, 641191883, 35626979, 107957574, 398416607, 449501456, 553469673, 509228821, 130514762, 606795173, 667896550, 988322433, 542648658, 171686842, 253153765, 214595451, 165008457, 913382244, 191051176, 148276817, 639512073, 236412038, 277839016, 458687707, 842886072, 806508409, 736000694, 597502039, 347020221, 904507495, 577376533, 588458953, 155888880, 418248974, 584223326, 255206628, 824962680, 499276735, 280303009, 184149651, 875397316, 556923237, 957384204, 631557983, 967235628, 285237420, 505496075, 508327558, 965827278, 326916651, 862360058, 86292246, 508571700, 637520411, 490243098, 657278388, 560871090, 57694492, 52709127, 690057583, 738316743, 825384514, 351310367, 110596439, 12393956, 718648135, 147335201, 3415784, 147565723, 880842535, 639196124, 313518589, 111691510, 320828057, 433495671, 42836989, 683961553, 80391499, 589372037, 799070436, 688320308, 811442098, 81154157, 616790811, 274296884, 704926018, 178494900, 709950277, 839865339, 238140363, 578548605, 802112756, 588939564, 260484156, 466963073, 462401095, 69824659, 121357385, 359727154, 125800962, 267407278, 695060006, 476440687, 922109215, 79141052, 120038833, 934445224, 908463557, 510102822, 511350220, 447014745, 933781468, 622503458, 25121785, 851096527, 476034914, 482166045, 860850196, 764693469, 125617815, 477402928, 626772414, 509324941, 401580871, 827093608, 432181338, 805538411, 927590615, 179508420, 538485088, 356533703, 906994068, 985544622, 385036850, 626627492, 217895249, 145894381, 207920897, 239765023, 974501499, 330864643, 635289299, 73519707, 565346037, 810562571, 753688236, 547396455, 781788705, 821282473, 434532711, 851601897, 678926027, 820867352, 507732354, 237303281, 884665566, 989923601, 169066843, 922718845, 196453905, 394121643, 575072280, 376083448, 168198104, 105129144, 24564504, 69383997, 70687, 65717852, 487704369, 646912696, 709173753, 777905568, 309733728, 540042881, 496200881, 371603412, 956742886, 562467363, 98579470, 544408095, 979256753, 427342916, 406720532, 932073642, 759231976, 616708073, 931923207, 171785271, 556868315, 188295108, 209351008, 550489858, 512916666, 183443676, 859856037, 659642344, 378320358, 8950987, 636137805, 652486531, 458550770, 820238210, 115017801, 655995537, 254704037, 957208016, 391762055, 917778551, 795870220, 351334888, 624046775, 461351834, 581246314, 64368171, 525932270, 940775405, 102464604, 347229983, 891023150, 169464852, 585908026, 675629420, 214119145, 540070470, 512872025, 530715141, 971187901, 28141797, 674592345, 688599078, 822536673, 170213393, 336300451, 990018225, 382728577, 59048386, 804557750, 879781878, 130827133, 865882045, 785241984, 103364524, 879359713, 136095660, 916213497, 394882676, 461569206, 551633579, 888200273, 871248855, 139961559, 899412624, 832211401, 664257599, 944969435, 181133862, 543834849, 66403703, 263285927, 419756599, 938723252, 872082362, 576224131, 128343412, 832379617, 826431318, 889421835, 536778909, 168573154, 34070649, 998295998, 725328004, 475791737, 86227437, 656573719, 185295769, 520922096, 35348177, 188802642, 358827146, 548843461, 590989935, 621264630, 628079944, 126394770, 151068434, 232272505, 362458343, 448532345, 428694233, 177285852, 642022083, 134010312, 853011091, 790600802, 40820809, 32178580, 375393108, 901645021, 646616042, 724818720, 873492982, 479660523, 777187694, 686550933, 79221807, 932622531, 767494415, 375443357, 669536350, 547808176, 966339805, 92438064, 329385926, 428091468, 251010350, 641186122, 678416679, 501632415, 646910223, 254427000, 543802465, 413197553, 114719486, 536972636, 698930215, 820452137, 95550119, 718123165, 746335212, 927253448, 749296707, 730034743, 214571230, 4261916, 481468486, 468810898, 555944954, 463326211, 32235592, 465058414, 343876280, 424382606, 772234116, 929704930, 277444047, 46693486, 594053641, 485195691, 849628563, 573101560, 946947700, 348737018, 248341823, 900737355, 21502610, 348174574, 397652977, 707937008, 782212998, 727520824, 721975514, 104131374, 32366399, 887331386, 844511136, 881885721, 116293782, 395006346, 614415918, 877061092, 395040161, 496270281, 430555784, 892655079, 866900450, 707509837, 543332489, 659439827, 319894264, 404513326, 76442082, 203360585, 972863982, 504621780, 109676832, 429686594, 698454192, 135741549, 309428194, 632159848, 82404209, 538863114, 380661036, 634561417, 399168554, 723974250, 524755110, 874930836, 308458969, 730209641, 41130089, 30477299, 521784735, 779951123, 786296051, 362220787, 366084086, 615052082, 511677879, 46488834, 174731076, 429105811, 308155699, 670835162, 263911432, 810660902, 350334229, 466661414, 292275495, 480633753, 647355614, 461823767, 452473557, 131934698, 347909773, 657015327, 670602147, 616073676, 146907591, 18622032, 330246166, 348814878, 468092818, 488466106, 725096698, 312501522, 625794415, 655892419, 170245285, 443448057, 754136814, 579344608, 476454347, 693392338, 815828019, 982868453, 534354666, 64373904, 556108480, 345913130, 321533054, 494943755, 366542215, 596123547, 304783554, 936691462, 950732160, 769580699, 889221304, 89565466, 532717612, 56006394, 656324835, 784507815, 941105899, 693335755, 996585578, 68729565, 285287873, 458932505, 752193908, 83581899, 652557986, 741778515, 605951082, 729482841, 984783528, 534841709, 734535555, 319314160, 895388480, 454712786, 216715603, 839096807, 786351871, 201929222, 660738289, 450135671, 248451035, 656738322, 225130357, 755958269, 608424449, 308148494, 153320536, 482094946, 55544958, 987559579, 511701269, 984953900, 469724756, 867935936, 954531443, 75824428, 108070793, 709770218, 999330638, 823813925, 829638080, 853743668, 154455998, 734592052, 243656611, 83696541, 976951556, 928628997, 586748015, 445092412, 700417052, 914838123, 857763944, 894243601, 547204158, 672359128, 993931219, 687269895, 914373488, 993200245, 668481297, 502324438, 400724049, 796285502, 287494465, 488409040, 784426050, 985242555, 255119680, 632842214, 536143431, 719550335, 707021313, 322266098, 231922499, 616389189, 100185946, 117222662, 386020543, 615683192, 708957105, 898737396, 93577426, 553003332, 997842836, 102466047, 571531589, 991453156, 637583346, 225395330, 193180768, 655895230, 237068903, 71016611, 990260609, 588490371, 209973741, 443154703, 689482011, 871246652, 758908495, 716874552, 489502690, 825790534, 146155788, 351176671, 298965036, 711672841, 482309832, 512923664, 549275820, 657462379, 668351644, 651302616, 342109739, 111332459, 148590674, 395935890, 885828005, 319923497, 120468910, 61938245, 967170829, 667866497, 731452469, 888719438, 902736257, 418391367, 442671842, 74951400, 778299834, 321051016, 631353257, 593943249, 434605205, 883998104, 827257482, 532697503, 528876271, 756217581, 57115783, 414818833, 435519832, 837670241, 623066521, 768094822, 358985642, 903619465, 614896855, 780907560, 798460008, 140662240, 933133416, 159287449, 910281683, 375431392, 514959593, 291503143, 329383113, 942263675, 743698095, 715736983, 589493603, 796805027, 840281163, 840475377, 520874446, 592944917, 145135421, 788664714, 445756795, 182955775, 547416607, 549952379, 319551578, 123384824, 255960699, 602300393, 425021145, 475510918, 387836074, 100721217, 417458908, 459714602, 725740644, 659828312, 664855084, 552042359, 223900371, 8354468, 42676713, 719617752, 506189282, 501337843, 226761572, 774446264, 963191022, 823466451, 506326090, 166350419, 288443319, 301405910, 438118828, 800467789, 454447233, 476063964, 147031412, 583225407, 511171719, 551828572, 795155316, 202134804, 300380877, 753171519, 983693034, 574139976, 141528897, 225341525, 353944913, 874629063, 216654199, 463395021, 115935568, 561020007, 464074247, 43083988, 439456497, 398772085, 298170461, 415723885, 112076938, 495390045, 639037316, 596121325, 217185501, 959163223, 680628596, 922591159, 925593847, 377030814, 184197207, 896867213, 902623829, 180653867, 530349972, 504369808, 985403678, 383863463, 52358534, 333705875, 624445713, 263966380, 364665733, 534295028, 598250418, 926830451, 86230847, 23057278, 111317750, 876575607, 142439376, 424682202, 598475801, 832087392, 961660471, 921233737, 382945726, 19581435, 851243411, 680075165, 886482642, 594097731, 167882363, 360109296, 128503479, 265754913, 500997299, 643076676, 644368348, 609129176, 117681237, 737419880, 718414403, 187293694, 810411694, 449598584, 899466994, 156942119, 251813725, 614063248, 281981061, 301759534, 9124967, 122181757, 860942615, 598788883, 452808319, 740462571, 604456305, 726592156, 218914696, 502149373, 34510756, 81267287, 816994986, 202300907, 641818223, 667852590, 567929157, 556392120, 713945183, 417913733, 977467215, 225600221, 258171524, 750608091, 532606668, 236996912, 177417684, 709928251, 723572133, 222490303, 635523663, 741230001, 49011079, 475295979, 402470883, 326234726, 608133130, 576414360, 794480954, 357464644, 580021879, 926236570, 429867503, 45965814, 626071727, 111907187, 388363118, 713273227, 381179970, 687602379, 42743215, 436627068, 213714020, 59814012, 47885629, 886636525, 359271417, 113804707, 494722585, 104624523, 285543840, 667925314, 824447278, 882456369, 94028924, 611877098, 818920553, 681181463, 509329900, 533251907, 795030066, 88551660, 364058556, 558069201, 440697503, 894813028, 692366833, 319582193, 263346909, 839881873, 716946728, 524243491, 210209322, 852180262, 510590414, 23611514, 895624776, 58889140, 637943534, 96899760, 515246024, 831305147, 450938102, 627061419, 237130411, 367799981, 686891986, 493350452, 584530166, 256129786, 257227906, 988799441, 510558282, 924721196, 348994091, 232092137, 920434138, 653368186, 34549981, 155457299, 27161108, 448966604, 458222164, 563500731, 581805105, 604209116, 277920349, 590777719, 41055373, 97540784, 242490664, 691205335, 76005069, 214490945, 195804801, 504050165, 634209479, 665071921, 962223654, 222683266, 907813320, 644652762, 198880224, 763278207, 848318634, 523653386, 731095628, 264462840, 298236729, 383521742, 441213475, 803171560, 700880255, 370161683, 672565354, 986469946, 279548551, 741040529, 366364944, 18327684, 242902982, 262821175, 978246142, 72660186, 910032515, 891915101, 453848765, 83569667, 184093617, 554179086, 558120636, 834975357, 773225156, 594394255, 387612584, 266789112, 742878358, 886440706, 679607410, 318036613, 205830020, 972841559, 392473176, 807388756, 835540282, 49883442, 657406177, 528932042, 157657047, 981367575, 575203048, 223484438, 981712055, 599873933, 285019029, 278966305, 502627592, 638166171, 311642272, 189451292, 100990947, 879887782, 373778631, 200425499, 824917146, 422090723, 384447878, 244174972, 569972088, 777177652, 909812734, 448887683, 808168383, 854760154, 404156095, 541531674, 18934510, 989624776, 898466914, 548354774, 326375917, 668974262, 665817169, 79330414, 371800792, 822857449, 225667938, 606733198, 27343945, 210191967, 68329896, 839091684, 89123684, 325595808, 340471581, 300087386, 102991284, 650601237, 367726563, 586646314, 455905510, 426912846, 775706501, 614540486, 698978941, 732767658, 587251988, 217953425, 642899073, 679256277, 382561591, 779996946, 924915282, 842776541, 86441030, 367410908, 399556619, 872081209, 356381074, 473477585, 458048488, 237785173, 886964781, 633415537, 917346689, 882256569, 229147539, 259926519, 485117058, 810442495, 71950392, 405389338, 754837500, 941242764, 718427168, 243204771, 223744730, 857876649, 348030019, 467970752, 694395164, 72470693, 435137189, 388985475, 547621956, 732467190, 830991330, 921724809, 920665405, 90207405, 679930084, 565193749, 143257443, 466252315, 124481198, 121019911, 970296729, 629199040, 257658451, 965818015, 698451909, 512586653, 204355815, 285663424, 997403546, 489611907, 818236999, 714003717, 598655164, 11137909, 512989373, 76870067, 124517308, 463059508, 588938566, 609299528, 166671240, 712755955, 891573928, 105732160, 147168478, 409406890, 187014622, 276884652, 20051298, 938103958, 645585264, 147443304, 684340533, 94375738, 491632615, 242673944, 518477804, 402542739, 419175952, 864884507, 806581551, 588634579, 552991672, 309264659, 948740857, 44256882, 657327043, 735194336, 221565470, 99547969, 370730844, 321210790, 51195320, 395463720, 545060931, 518748354, 30996130, 187150722, 68584530, 764629510, 869258357, 490011909, 899557285, 778627042, 499041907, 989657987, 328828007, 610511380, 684354826, 756179279, 883815267, 491509664, 240007486, 731949291, 285799042, 977549583, 142593529, 600033717, 257308933, 132879887, 328348622, 784502810, 53153449, 998020708, 112103285, 951369632, 476253145, 413557585, 97685423, 534475163, 457489243, 269370676, 237517101, 132362635, 135183981, 849753794, 229135504, 679269156, 515145292, 236961044, 217690325, 147606969, 281986285, 882128018, 144325193, 508410919, 862335819, 122354141, 251778549, 507972014, 505994324, 621985887, 464082905, 700393389, 585034312, 332976881, 251772306, 246586622, 119576811, 248022624, 723090128, 622887818, 953810355, 96152062, 967460961, 615228214, 891116449, 487417030, 335851140, 41591670, 455429880, 214895299, 56676257, 405117239, 346085036, 315256079, 773321651, 311474764, 406263297, 255519683, 912331449, 31264032, 759784214, 790434033, 118706857, 143952448, 558460993, 255769316, 872256303, 415715459, 450544193, 236853626, 903714872, 905441880, 76310598, 613958941, 665330215, 10119689, 905553846, 732015135, 624723245, 74389675, 354243452, 411482504, 308513919, 850996395, 580040172, 776095642, 983078060, 113119830, 286544148, 591446436, 910612613, 201031438, 899776463, 941414239, 983129985, 547398155, 173284732, 375116232, 39878658, 550531768, 869614245, 729369951, 400501185, 806323684, 376358072, 839302520, 195058031, 467327969, 136850279, 337984799, 279101112, 882561726, 527615354, 194736841, 575770707, 748847236, 768056696, 306650634, 443200073, 476113917, 667716132, 253531666, 513635668, 312202392, 34914895, 796740089, 438740175, 276601868, 660877, 111335488, 289494776, 794755611, 451464340, 446637932, 317321602, 730325754, 35686906, 133966608, 809862340, 886421669, 164587367, 548919068, 650797046, 805664753, 806871678, 946497522, 135126963, 524599269, 713383844, 22882777, 509497691, 172750259, 515378145, 395041789, 959018232, 79135405, 708991926, 210450655, 833124853, 851144818, 105156169, 784305228, 324266405, 789837947, 788699728, 798973179, 103143987, 223968901, 951879149, 579760720, 57260942, 77370017, 444921165, 308241983, 458998963, 340152485, 458388199, 791130406, 828873519, 132102833, 705699551, 503412990, 251154594, 132648375, 175971214, 225909215, 817439469, 769059127, 830366913, 196586184, 261342490, 686414703, 33400220, 494395384, 829961176, 591902466, 350261315, 122213932, 562099750, 282712456, 378449627, 884166693, 386222082, 702051812, 857591851, 163767546, 500176108, 114187841, 779927966, 397660301, 238266941, 5772478, 851586326, 126812877, 318538190, 730613602, 145334762, 156133377, 300274391, 844503262, 64324157, 997367168, 552995946, 533013028, 25187886, 793478287, 894529135, 200560336, 56667490, 382108262, 280236910, 467983840, 18000725, 688977475, 70508464, 149533528, 826258189, 935795149, 220883672, 165599405, 598513557, 900871755, 218232867, 127476162, 707899441, 96551572, 861995688, 455839363, 791574005, 731916331, 814211140, 695979255, 368363245, 459484017, 702477818, 754205227, 818376546, 993731420, 539629272, 587863348, 807261649, 323963539, 506471676, 936883719, 273672362, 260975744, 923676544, 999720678, 573802491, 693828058, 24439366, 814268639, 435376250, 80093581, 98987820, 559847121, 209848246, 36812458, 226272924, 607884774, 114740151, 912790500, 577804068, 51814524, 48878817, 343543444, 181034226, 846453531, 384349606, 208358110, 510593864, 113946563, 971017783, 121436328, 775812857, 964187319, 765948492, 738811504, 75290674, 182282532, 457897029, 770611224, 742819993, 341169748, 958068928, 535430835, 341348674, 248771149, 148937638, 513630772, 297331421, 223633866, 701722564, 418866499, 280258887, 379092707, 374968962, 26575956, 112421951, 407909519, 246357787, 530988960, 53002855, 290224095, 733847283, 636804581, 957335980, 737667839, 539560084, 123853324, 543584846, 645177091, 967300491, 671074595, 692527065, 269450792, 26668955, 16694991, 971777300, 900410380, 244381390, 961665099, 216200949, 992602167, 421792848, 126504338, 718583113, 199744673, 21382380, 721729787, 233403510, 725550736, 155164522, 941116081, 12003474, 484108618, 810738859, 874045367, 440692412, 216481608, 31497664, 152928560, 924032410, 274210217, 958959334, 141106668, 507838471, 730380857, 919072247, 742835852, 880042550, 536893185, 601092862, 831348650, 826671040, 270800284, 738314212, 550008039, 637044980, 416525215, 505944994, 670692903, 557524653, 582348180, 175566191, 742054263, 913514272, 473660368, 572883596, 930242122, 62565077, 898489195, 326311550, 892199189, 143179755, 356068873, 357034433, 133905442, 535471664, 269174406, 758576065, 269077424, 370702343, 727179914, 881628378, 169308935, 885432381, 58191510, 273234794, 228232365, 357463691, 930819875, 810121671, 668302639, 482796311, 819498749, 155132237, 609223488, 147812512, 302808055, 49643797, 58547737, 129665693, 993692513, 140808779, 735975428, 760924905, 614958254, 947374355, 252656532, 829610932, 255450406, 514685079, 900297982, 191913293, 743664675, 423504657, 40849096, 417340806, 324017911, 12219149, 875119591, 681806632, 768537993, 79850051, 554031132, 608887497, 71122239, 48493074, 33958108, 213678571, 648467648, 529338612, 825592758, 619435431, 992691799, 598495916, 580798234, 167335305, 761480860, 913913150, 982650142, 477121870, 8556990, 531572129, 192076113, 274798782, 763407879, 173031519, 255500660, 905364155, 888366823, 805933364, 599587061, 881911884, 986577537, 213668706, 521331755, 676959337, 686557183, 204904734, 12757667, 336389868, 344203496, 942443836, 802905638, 4530861, 682066672, 651677746, 320025644, 661853428, 408734848, 459522793, 932346953, 283364341, 528835145, 416885156, 368903054, 641078836, 538204795, 500119158, 597397694, 434334308, 750275227, 910669425, 702005646, 511015064, 619735921, 534216443, 511469831, 910665922, 715777333, 752893961, 234196401, 989870912, 623114954, 97208778, 384285421, 603083397, 116204964, 820845431, 236224749, 88495670, 12446326, 761798367, 40774067, 163235872, 735406084, 259865283, 791116118, 692789918, 683514258, 344738419, 852021495, 166690189, 798451892, 330490323, 521713090, 574738603, 709153808, 149453276, 469997302, 670889021, 143423247, 242208603, 357512760, 239315352, 518119870, 744502923, 814899346, 567065892, 995937584, 855063447, 898132022, 568233753, 969625278, 976725628, 955221831, 262094632, 3315382, 318380933, 231604857, 390693938, 693484096, 97918574, 428858921, 58310070, 919282626, 852983294, 598480230, 440049274, 277459999, 515211478, 685581997, 67913206, 579917248, 272619121, 772507598, 15768167, 261304378, 240033581, 351582016, 897305024, 247512573, 249304650, 23641354, 189184903, 452971851, 191866317, 88442500, 544431442, 781297214, 967006882, 229527335, 503628385, 232756639, 436430355, 777725972, 620434528, 327960648, 670711471, 69917412, 923676999, 664395725, 885672638, 950538831, 856292060, 515108069, 656254134, 411107072, 538942386, 591418166, 728063569, 838803821, 913112933, 206340705, 457097081, 240997597, 45005544, 403013080, 207124119, 788825434, 374709242, 532249346, 288245446, 841743583, 254104138, 378577240, 591060596, 338084120, 870112561, 279966183, 743918740, 896052289, 681615376, 451345266, 937718252, 882875820, 169823361, 570841107, 794852126, 55181682, 95225139, 775900362, 415815246, 93012766, 203514901, 155831885, 198679170, 573923482, 769847249, 162005600, 601393296, 389679512, 448615729, 29459247, 423970945, 750874173, 155219205, 139725532, 426240841, 729649930, 200206856, 237193611, 544197081, 388847441, 651932027, 514373508, 968674570, 839266332, 706428928, 806980381, 604175401, 61199737, 837183939, 678394144, 453896634, 801956516, 161791840, 737571467, 464282620, 630142746, 616263826, 163746533, 594372844, 667323043, 95209413, 236245392, 190023291, 295470128, 994041179, 717071290, 260769548, 199230378, 296230215, 79298786, 97914971, 461440989, 260407679, 150682064, 603978059, 143821430, 430795156, 620592135, 971060311, 781260719, 219774882, 20316101, 827063840, 823452259, 461885724, 656428877, 302848188, 715676624, 648354178, 730097864, 34641979, 714891961, 238999646, 566172706, 620747074, 449909325, 344309988, 879127791, 902710698, 216045666, 552569654, 472078638, 51184777, 560933452, 403786499, 871511869, 166181392, 864714027, 340775313, 888192625, 342504012, 14864556, 292801354, 830545636, 728608105, 283470662, 789827638, 962048304, 784566746, 398880098, 778753501, 310184730, 567753216, 530363800, 346267703, 589773766, 880960835, 856350618, 858833143, 939870373, 885258436, 651074739, 659011876, 959319381, 93617999, 964531491, 828801095, 114323993, 692879872, 405974941, 34026988, 841324122, 139056823, 890116964, 421964081, 100399703, 329898283, 69585533, 322684388, 537068927, 758713156, 972574368, 524477042, 260024278, 440270165, 879043864, 832284608, 993446584, 385285472, 822881642, 183005660, 748566864, 79332804, 861471671, 630071735, 399491529, 637348402, 231670596, 606168591, 635985530, 155149532, 716857158, 743372948, 678403928, 493454989, 650934963, 206225159, 126520429, 398179442, 569661237, 161657707, 842237312, 527032738, 216739244, 832031668, 226699693, 934964052, 58205987, 544296146, 673912120, 907362352, 891310903, 751552223, 368739413, 466010809, 347070206, 712113571, 951144661, 469750743, 111996432, 372458755, 353605243, 45010630, 347085752, 568534691, 620086666, 199791601, 255263327, 130454539, 860943325, 322166156, 368979576, 82382250, 321634804, 91064369, 98169140, 694165081, 709329375, 262388445, 810011014, 552693198, 810704, 164688532, 983420324, 715450598, 66919540, 387379186, 612595596, 939950991, 661822086, 74247218, 858224560, 110218745, 166429100, 227117175, 250249613, 914254695, 405489636, 358951283, 392105218, 609638932, 524866079, 955409992, 889685037, 278470709, 507800157, 255124984, 954609838, 501528944, 641988339, 259175834, 586154137, 194740967, 167160097, 828243318, 894314384, 945421755, 411619044, 122555774, 652051485, 14448811, 183627336, 271161545, 188807890, 114757178, 149140641, 222575007, 612139276, 46630582, 779681254, 149344395, 322032289, 431246809, 399064932, 187347825, 765749368, 673122246, 28972588, 585375298, 472284891, 768095462, 367713593, 554634859, 950963596, 272315288, 659599389, 365283988, 878900271, 563034095, 386519356, 530594164, 709741773, 971915476, 932073746, 463549115, 196682613, 241405772, 150634042, 796523869, 808581357, 614067467, 772824958, 673224393, 229433962, 212349888, 391845111, 297152454, 747659044, 845239400, 286217557, 767544853, 451960827, 638758314, 181559225, 380892460, 663828670, 126760574, 627654425, 124066900, 800071948, 397331496, 153080276, 483367839, 487892475, 460165599, 828535432, 421855386, 679868627, 969579846, 611159412, 892563505, 735427402, 370479043, 797778959, 450346771, 212736492, 961489691, 534942784, 390599148, 911518264, 704735549, 684187180, 13447575, 715985606, 571735834, 596650407, 766746861, 888782451, 583755602, 371437755, 529705616, 687158450, 728965152, 861464995, 641742970, 704520840, 219081531, 566238171, 543477620, 13356045, 44108989, 34734148, 729751757, 44652346, 387647513, 564288880, 43927939, 516897760, 173652145, 581634052, 465942519, 96026137, 238856646, 687656713, 516537043, 693300058, 99603544, 50055324, 7871166, 394797860, 628859045, 88116819, 544859258, 808220612, 507148297, 325680680, 286838216, 404753432, 128803063, 417289402, 874753082, 109049967, 550061564, 383725973, 531603754, 41936664, 382450411, 822632101, 981001588, 572518574, 305505121, 215097707, 116595223, 897698411, 108838848, 391322758, 185901751, 409066828, 590764960, 998767005, 234150567, 139715691, 520434355, 343634899, 811276617, 344133699, 765496411, 234505459, 327779039, 978800004, 725752514, 675688453, 935610571, 775142092, 318507303, 270704254, 635157804, 343880383, 19011841, 15446601, 176256253, 783346060, 747078761, 475731480, 505535505, 788751900, 811197269, 711082517, 665641278, 322093338, 284427774, 153715265, 595478729, 463299336, 217730409, 318134267, 663298125, 55622993, 137972942, 691961726, 498567101, 818463686, 97435919, 787863347, 791171511, 761753332, 13582325, 559355268, 883132265, 902974888, 943883784, 571891750, 39786177, 60223210, 744861888, 193105519, 497381868, 482585907, 407538856, 578835186, 823409616, 794207381, 729108682, 549704952, 516343790, 538994575, 968329577, 435662025, 538378444, 17192405, 110518416, 847841417, 792833873, 516056938, 861655591, 4442655, 942091345, 436134547, 245458506, 92752975, 145697865, 194492467, 701270342, 573882140, 922459036, 320333174, 585572450, 611922212, 238805016, 500177247, 406656776, 758265345, 908298537, 963971772, 885075695, 960946395, 160321109, 984906553, 607237, 186714080, 76394457, 325956999, 631540704, 41371780, 481719742, 214800210, 223486787, 513137025, 706771756, 614529929, 775630336, 883597904, 185655535, 767502080, 451143805, 782042471, 984401432, 613654712, 985503443, 889699381, 841211492, 743608964, 402451037, 110624239, 391067781, 481957785, 273478545, 356074430, 826335330, 489003332, 992258360, 199540282, 532663369, 249329694, 153455849, 861832451, 780241591, 559881452, 142249833, 756858485, 244875739, 402335186, 619851654, 488094148, 899209908, 339901643, 943275475, 215798761, 706847843, 348920072, 418638451, 610996221, 375933586, 659227171, 614578446, 130143072, 393158430, 781086641, 970256349, 589621273, 30304851, 738005539, 8891066, 757255555, 863166409, 627181393, 772577427, 592797964, 383317609, 52203264, 389831009, 177755799, 229217868, 944130418, 170422142, 268678210, 305023435, 333774160, 719537408, 449052657, 758510619, 134671411, 115556766, 245873509, 930498837, 208097722, 803696112, 839115758, 766869041, 375114781, 248985706, 40947273, 501346952, 85572586, 452800526, 983852309, 902817456, 394945290, 266552283, 695710669, 343573087, 756202192, 607870410, 595028661, 626254550, 829135822, 929826130, 820700209, 245142999, 89011927, 954246472, 434021289, 701986827, 193314792, 481011617, 425561483, 663245466, 507391489, 657094227, 448972366, 396814181, 325877902, 806135493, 461907553, 336768848, 456440141, 139579678, 728545134, 705959134, 642759883, 35948365, 71939262, 191098155, 345063761, 388941845, 892621988, 624147515, 323309107, 444700568, 766587839, 57896068, 613349928, 419438752, 72090356, 285533712, 385792181, 363651783, 554013782, 337534394, 643339212, 470845131, 840211044, 361778855, 317775505, 206824000, 993425128, 650959451, 938887144, 488852879, 307821497, 918079998, 896397867, 640441508, 757359481, 476952631, 843845899, 291603910, 21152621, 732590783, 424920301, 329449776, 944150729, 257308512, 786456715, 293156143, 927079914, 212372695, 45754425, 180364774, 728533225, 142985515, 26005200, 238439156, 196978127, 998048069, 318378297, 303380186, 343711972, 832249021, 904379717, 231878, 285300221, 928094073, 259612480, 738608446, 179323690, 640115758, 333871037, 817292539, 175246028, 928201699, 702154475, 607551231, 813047267, 276327147, 456488665, 27531617, 358346094, 960328166, 795378475, 563631759, 48301249, 330436850, 27688931, 756273451, 720423432, 465908422, 106718472, 117446323, 42226698, 710716183, 218270756, 168675578, 972717756, 161496227, 969615119, 945642392, 247669431, 573383454, 240967815, 303810417, 41078229, 918076213, 1477400, 90829388, 37587619, 329178565, 288357952, 461549642, 946138248, 196364267, 801939081, 853652982, 883267601, 482081508, 166261800, 556618129, 830567494, 141731823, 184237708, 301434266, 808918903, 295648927, 479179924, 389669866, 980192738, 765603160, 626586591, 321594921, 417456529, 735365662, 88221058, 4991544, 394403201, 860773634, 493727081, 16453863, 298140639, 499664440, 793999096, 257318084, 721523180, 517626570, 817974606, 890570778, 320582147, 230172641, 738880110, 559850427, 433976563, 619589137, 415636994, 548351198, 732654721, 678873145, 185831506, 233480818, 942731248, 270272163, 716214214, 467940001, 58402147, 79031677, 303711176, 42015396, 870737495, 800122885, 126423054, 962636128, 984461084, 789326693, 43536990, 968369098, 15280815, 337613628, 739341871, 584195901, 987306342, 329574085, 595509880, 330362028, 578353836, 179828773, 887652042, 646850926, 946104117, 216033854, 785329018, 658908723, 771867598, 246792310, 656442324, 481688414, 18018068, 191958416, 424705029, 720810934, 598517150, 152559131, 844847706, 434465687, 819461253, 102321202, 559996911, 804587429, 16543557, 356049640, 852784715, 606189603, 678455022, 773859268, 940410824, 933751914, 276474516, 436202627, 240774123, 514407588, 841918092, 154796136, 457059432, 173770379, 52148080, 716132016, 481972118, 137870154, 987622106, 990373774, 257830016, 128493546, 175748228, 554013532, 612153900, 934403256, 492179017, 70729176, 470554986, 306503966, 971443071, 348833635, 735772763, 663486354, 48900789, 904218893, 216497573, 92107053, 796774193, 285894066, 386445051, 583631025, 446844953, 4090955, 896517707, 435701128, 920517804, 26975825, 207025120, 925126594, 137007146, 32377012, 795460736, 517045296, 203067052, 524869435, 261526896, 980680415, 833657387, 364970602, 285339631, 677003119, 623397636, 734648886, 41328271, 786469657, 821667025, 337889477, 241679129, 664602214, 466981842, 544012360, 15498434, 774426075, 770867268, 147658861, 222360322, 64751011, 96475688, 634986822, 654404711, 542805807, 501294408, 822803160, 424829161, 299355145, 294652118, 111194194, 596763711, 623424690, 902677822, 4974420, 118258913, 678297557, 893715723, 20662489, 536178849, 925774756, 843626253, 702112692, 824794166, 45281672, 418408472, 641520994, 775181023, 821051870, 602459132, 746670069, 118466420, 52708026, 683013822, 637864884, 575287860, 548373719, 102081901, 240698182, 228216800, 806632577, 859790314, 711861046, 4165590, 801788185, 661718551, 713877881, 405089748, 739022065, 927127326, 220762351, 269257673, 192639018, 162224086, 496283990, 251179102, 84423294, 790846429, 788265217, 191718745, 878135279, 197622744, 803084907, 460310166, 50552701, 717804082, 310741015, 941981114, 503741771, 251993921, 563576372, 427165684, 967923634, 290220537, 199004514, 206608206, 121344302, 787995291, 768925763, 17120395, 9837205, 850909860, 678075452, 682541634, 849785297, 976753750, 732921105, 635107068, 611200367, 146294064, 288941358, 528759540, 530508515, 438398518, 138490500, 322910687, 771980508, 811544368, 472479002, 164149403, 745262348, 123123013, 731611706, 489993956, 140831318, 275876593, 932597673, 70941694, 275924094, 121828247, 601363001, 918245570, 287423486, 924284340, 383464645, 365292187, 476471343, 983281032, 943309341, 806395633, 342202912, 915234209, 918936251, 909865094, 474147117, 435041625, 959360392, 267423147, 774366803, 447681497, 212603240, 772674357, 326563927, 922788053, 74176524, 278473021, 891763748, 163050239, 965737721, 805986866, 743164466, 932256632, 521303213, 767844876, 631464881, 940782649, 181428146, 113234152, 358454316, 921391594, 759480370, 140665286, 532811719, 925542354, 754800573, 806660665, 224123288, 173184367, 654285836, 543581220, 261640434, 214676290, 64013064, 350332513, 123355899, 255714642, 312270378, 760255777, 99077591, 633650921, 661518722, 318131673, 178663783, 575744105, 318550824, 804010828, 667019214, 57108379, 661072613, 151453032, 776143233, 827672436, 187181443, 814571961, 221935538, 330001293, 519720319, 221590262, 755001959, 117857653, 699325363, 986979637, 639546517, 782306909, 176521002, 241720236, 596315745, 407722525, 855803235, 729383641, 123167396, 573759895, 102932796, 55207703, 308441380, 603029953, 684869362, 830882809, 762414581, 605105037, 419514581, 832073222, 790715713, 487713163, 434490113, 17960515, 102119843, 821124649, 830828574, 548487220, 51728474, 153156950, 985499722, 435660787, 552616880, 915089660, 515111583, 192321613, 536797864, 903864759, 157458865, 471044296, 884118369, 479375976, 262107733, 338725914, 941732855, 549246809, 429732625, 648597876, 173623854, 830983317, 149927719, 584223721, 995191346, 96544091, 181489560, 778289560, 821245469, 918959115, 481344556, 171584580, 481689493, 417579831, 276388942, 22813831, 429857360, 50855739, 522739285, 898766818, 239601006, 672573371, 833437102, 49062873, 168513442, 792505961, 133316076, 381012452, 90812940, 736238158, 862491112, 102572419, 842490365, 228963062, 736983942, 220842333, 671708583, 31573224, 648876069, 78108011, 828408280, 866919220, 956234973, 52768096, 606661922, 990408445, 174604465, 814401013, 528148817, 555417690, 911922472, 833144317, 536051275, 275680845, 286565545, 935972929, 415402221, 927057063, 589837773, 79424155, 637420244, 684590817, 171525012, 692166406, 564964574, 935596404, 45773044, 827395583, 252393217, 466091656, 206032773, 175242990, 166625640, 26840597, 709945752, 511463564, 247850243, 307780525, 307139287, 249929556, 49094594, 706190659, 240241535, 430888126, 439334639, 505835887, 360209630, 826989987, 216568361, 693903868, 758166877, 793036342, 295862418, 882211632, 64160649, 330497506, 126704669, 417099448, 681242471, 964149891, 753373407, 544010889, 174114803, 320523683, 63681793, 822784702, 52832909, 733708485, 768997839, 629714548, 479787320, 79936222, 580554249, 383190039, 554548165, 836919808, 485594548, 698639449, 283262005, 927653524, 755864841, 507261659, 126732515, 683949292, 590487030, 876421599, 420362632, 697371425, 94821042, 464234997, 732721352, 884466726, 822947034, 195581359, 322047452, 718240449, 60604828, 732312381, 59963834, 769933695, 395152386, 261856516, 483498669, 751052934, 176523822, 363913579, 666069473, 340839487, 157277897, 997592562, 792495015, 187045030, 351464454, 883809180, 921680247, 2149803, 650395090, 194159790, 197736041, 435853827, 67764255, 700019281, 142817386, 41063434, 311710901, 896407590, 366283350, 848094885, 420360258, 265320702, 451175727, 190708080, 887996470, 754377327, 891952080, 812742714, 955118389, 513100799, 246779096, 887439705, 596472821, 307536394, 591986677, 578520344, 558082132, 793788878, 350076278, 725820313, 342130801, 816303319, 790405431, 31988171, 358736180, 827916444, 493909970, 44604842, 912958946, 725563272, 332045644, 17119648, 664699490, 343086164, 605211252, 438477314, 348734657, 493898192, 895095024, 225102760, 958906488, 498012693, 182415524, 752647480, 504166011, 213218127, 480520369, 588218000, 497898923, 158372256, 659471447, 865835577, 315687483, 142137783, 984649049, 309362685, 203044485, 267472999, 301507310, 883471743, 999756311, 297107743, 971886763, 319486684, 444997809, 237182968, 859102783, 35551236, 688263415, 132987080, 5493416, 928691002, 290093347, 777059999, 745978270, 447086717, 965179594, 688444421, 483994814, 659197731, 532521913, 120826363, 550697046, 426476516, 188877217, 580594380, 574815624, 546819100, 620203118, 893215637, 319370070, 177314676, 523590868, 493371085, 332353682, 185622026, 720374327, 578939291, 764684261, 788433351, 137231737, 759668668, 317653438, 443401434, 510645113, 595279956, 881386912, 667953139, 286889111, 792681484, 844304842, 574436717, 725245713, 602254636, 726293246, 174385344, 417140752, 625671632, 443967490, 952543096, 248526439, 802742087, 221866289, 794843252, 496196553, 65612032, 217291763, 61076560, 581314, 787109550, 334534033, 386934900, 505041048, 551261993, 302732972, 679959018, 151048146, 616657619, 505686502, 488644093, 407520053, 336774592, 988287225, 506097042, 757605331, 208464343, 30229089, 416840653, 559844346, 407637176, 838724274, 923545167, 720350174, 8572395, 664094373, 671191947, 934279949, 121068193, 794290209, 247654834, 500978700, 797612828, 823992684, 709725874, 903377588, 401955563, 747089033, 583593381, 320802269, 491347955, 594233570, 897071922, 197822903, 575684590, 836231192, 968339846, 971607550, 136530560, 842011288, 357535585, 683102445, 92336384, 272124276, 171286050, 938928358, 922544905, 232771353, 419428957, 448813293, 252651355, 461904543, 424322486, 681954878, 544434535, 796882340, 309686150, 357441059, 836384759, 571958435, 922737044, 992221852, 67089059, 882596041, 981208235, 363264265, 422459799, 232305587, 977310750, 210645566, 146639136, 94852429, 754551959, 516512324, 162352095, 579319741, 765880112, 401496430, 690661211, 783273548, 588948783, 248455967, 473931874, 206572977, 445259859, 489897593, 304808300, 254635294, 559971895, 473766494, 58140968, 804923287, 182058123, 18858635, 415737334, 275738542, 65100574, 191542902, 917179393, 418188909, 981897596, 189170608, 417438175, 601547223, 710379363, 435519975, 332893226, 390392462, 390445866, 750633554, 230495869, 851082349, 619461324, 3403640, 112866463, 80524784, 905882801, 83735480, 855669766, 710823602, 632919904, 233058880, 601180580, 934996567, 527450719, 964834285, 15865598, 134498965, 397374175, 768133341, 599105366, 700762578, 703687203, 154268140, 998989217, 142256407, 942384730, 177611391, 888866410, 794286321, 151515643, 706343643, 748341433, 554833168, 578067401, 764412967, 762345609, 734853127, 655365596, 532151926, 929579085, 471374027, 293746065, 482878997, 956016772, 225737719, 768956375, 107089518, 307027538, 947218899, 12267907, 397263264, 965273368, 290674, 419393745, 528387341, 215999730, 100304823, 111796128, 724131630, 552595524, 899376157, 849484403, 258227667, 81022604, 405165528, 295095284, 758755591, 582178847, 901416776, 964045241, 158331640, 526816406, 258063086, 238430743, 523968299, 84629947, 716815889, 339707358, 799962707, 33649645, 721984024, 99859731, 529563350, 263755469, 380146839, 385668718, 105638071, 163236706, 407662953, 984416471, 395685789, 121252287, 384609527, 679722992, 676898870, 417815752, 666111663, 352942585, 154723559, 133933042, 942913808, 855012363, 134819523, 466056982, 913694720, 585335089, 204920307, 453002801, 124752185, 515823018, 129186008, 769964167, 817111555, 613979478, 492621202, 885276949, 966883318, 348836124, 333607024, 791722302, 181773349, 921897372, 21723477, 31820964, 204272178, 188670635, 894616158, 777924546, 929825380, 136694582, 213474906, 152351163, 10990171, 917609630, 148281934, 696483222, 214916435, 140920179, 860403229, 148662343, 606007177, 847578419, 222771483, 643129162, 436815369, 242620727, 940485138, 417533636, 511021103, 132392765, 134833836, 850714567, 399233411, 83856307, 723919842, 802947140, 342308229, 338154908, 368572768, 783862802, 61035256, 264535777, 424765175, 862516994, 163708395, 59498984, 444492908, 883060239, 850002863, 40339524, 72552779, 627393236, 643860567, 40021489, 426626504, 569830859, 710036898, 828393402, 38256997, 825946846, 439540503, 235953265, 448677154, 848372635, 752294255, 3230807, 901334636, 762266853, 459636575, 878842385, 857372868, 19516596, 282690041, 596946599, 309057188, 372283374, 556453179, 979623827, 775045280, 938001516, 334273553, 315718949, 206613457, 795051376, 839712451, 597945264, 642871006, 837478389, 952120244, 425397197, 660554503, 459652706, 995877263, 970718609, 380917980, 645143505, 306899646, 658269438, 828465373, 809314591, 111205059, 529296047, 994589780, 103986248, 919808782, 790007247, 556454165, 215511418, 265042626, 653330536, 997210702, 974409490, 359475866, 599214611, 882293903, 991733124, 425906937, 523925658, 433534788, 112425051, 979666847, 16929155, 993719840, 452252376, 173734883, 481681909, 849728722, 155237704, 365284160, 579879424, 687337744, 880408675, 287083657, 201926869, 433493579, 564256369, 813036615, 947598878, 33701087, 49830500, 314289972, 683639269, 419561596, 117672496, 286731552, 4157527, 503860535, 144298036, 255224021, 713533476, 838405983, 903120492, 710299870, 690084981, 299043857, 640877553, 721174613, 975892511, 986736989, 945291149, 561755658, 652085992, 477966735, 687211807, 838982544, 86478785, 495774986, 418631446, 518941482, 121892929, 63363503, 840986235, 451384284, 709118835, 24736291, 374860762, 384593990, 512297420, 285599534, 465145539, 608815979, 826187530, 237552723, 757014456, 714725218, 712291158, 97348421, 239486424, 779581200, 524473788, 375079410, 622728978, 892079262, 602877468, 207032056, 725399971, 590729340, 302196884, 718272893, 151476716, 367366817, 495212402, 233528890, 203337048, 108516721, 834851123, 711110190, 917764573, 439989809, 699992096, 313444456, 140861016, 292844703, 665738281, 576452933, 606154924, 482302715, 243537317, 278787136, 939258102, 804015732, 570636501, 998137453, 670819114, 497757205, 348457120, 528205573, 304208834, 926793519, 460972344, 268848677, 605970941, 177666230, 185613027, 916660867, 63982291, 585734623, 232940458, 791208140, 526534283, 332301125, 100674364, 751619808, 948950869, 707360533, 231203856, 146793596, 46809510, 631710321, 840368179, 472289754, 810016448, 888285907, 285140871, 547129197, 469764866, 57949351, 509697391, 880472804, 273222388, 315542038, 710732321, 971658256, 78936857, 473954542, 783404145, 329481146, 168384456, 147826805, 20215957, 546014666, 293918921, 463339377, 899121344, 866848528, 814159470, 64820323, 669918938, 311481169, 215849082, 972410310, 986996155, 573728562, 365799479, 113185645, 322522391, 153309721, 95029870, 286389352, 635659984, 907645676, 311695567, 689636959, 342739589, 528832457, 170055686, 464436691, 412283554, 505692787, 326915281, 349869659, 922455668, 332352622, 352915155, 523749069, 62465191, 682671512, 670550873, 343427762, 497753760, 698328978, 335557209, 607372763, 742866268, 276371406, 337842334, 925274874, 528207585, 821776990, 806901223, 514459510, 943358216, 421006404, 254524979, 414879422, 856050546, 897905307, 758684817, 167234272, 24530118, 300357302, 90443435, 665756791, 153399474, 793029612, 529424014, 114521388, 293741987, 940181362, 747532994, 469986402, 121504499, 707545341, 34820461, 764536774, 565928154, 7887824, 150974851, 584541152, 157137261, 379122075, 31765912, 517316826, 193377032, 989729091, 606896298, 251445874, 689276850, 505156593, 619303298, 484708738, 329193960, 522612097, 657253500, 97510937, 697615253, 268273290, 145735849, 510130243, 119417968, 981931609, 854927051, 345279710, 685218103, 805614216, 349315377, 347007679, 880923524, 390120610, 57615755, 56321311, 524629001, 909833389, 268903607, 225409324, 124016719, 108188125, 856286516, 241070647, 120136751, 165983852, 398490534, 33085982, 639010881, 787973559, 79224302, 898302451, 112723585, 853024271, 930577423, 283094449, 660967214, 450301764, 563263104, 363636546, 250083257, 140719962, 46602026, 14363563, 288870648, 240981756, 831204635, 538781355, 488098369, 389682539, 217361340, 312550023, 576953571, 756971621, 593599349, 154179540, 899656967, 261151782, 428478720, 15600720, 352588081, 951456602, 26402989, 427782519, 380744166, 908324005, 916123237, 151129374, 168434438, 174387616, 36381621, 546682282, 983420238, 11976997, 975132456, 942853761, 92834316, 593205186, 845204413, 86878622, 457619461, 889286598, 472547082, 424098265, 561595627, 230869056, 842807567, 430816007, 739359241, 879800723, 130738994, 832042851, 354896140, 911527413, 678731550, 411035287, 154499266, 998504683, 706839496, 714835217, 924779463, 364114030, 334773147, 185730419, 789025213, 619177562, 177304418, 34141240, 902297426, 741796741, 856851132, 60059714, 511205486, 352330115, 953308121, 639637460, 503110051, 95796384, 142997232, 565877096, 192815116, 232839793, 987942829, 456345574, 257764085, 177956290, 415784123, 13795326, 822539096, 708617821, 992072493, 439006059, 695808279, 266831548, 32446476, 159714122, 406892811, 71828781, 635529586, 593316116, 466323354, 681260084, 239208073, 25545584, 457397382, 123305509, 257335328, 857963328, 225286181, 431691879, 105110265, 773130878, 820056498, 31355590, 388572949, 619338423, 291492954, 330615933, 893484991, 412863198, 917015301, 187318121, 634730155, 840977731, 864675685, 678014653, 868301078, 98089611, 451435680, 719464865, 651406547, 771492340, 469710089, 859143091, 36457855, 995067007, 344905154, 35251772, 18597430, 241902292, 334431561, 268808023, 612662016, 384130811, 139739951, 151542675, 173972180, 436601366, 192124433, 917990866, 116666329, 538766429, 743186471, 751743392, 719962239, 16337764, 41480222, 324992704, 808664568, 226763615, 666948600, 117280551, 861144245, 956282540, 89036607, 520369358, 965814447, 290686980, 129292376, 18885421, 21901551, 308849829, 583659809, 884241509, 988969834, 215705588, 477903080, 264265405, 199813850, 774146845, 464219194, 816821775, 911283993, 709941721, 410193826, 82651911, 189194175, 608319440, 977843552, 264235447, 440816646, 5983730, 541962290, 483802175, 511822593, 671529442, 311806266, 440181733, 334485831, 135931357, 843424846, 414035857, 570625792, 235105209, 268631368, 842432364, 771563438, 196399638, 850710196, 650731895, 208010576, 857420609, 207672045, 435318743, 893205708, 877084299, 528393820, 402185594, 251737553, 107819435, 118167779, 444656226, 894275515, 696080660, 176062586, 312754136, 554598953, 569689921, 322838562, 663946348, 732070203, 456468471, 729396217, 518976887, 450975704, 47663291, 247480436, 181405139, 574843326, 909664080, 69773617, 909249346, 178095989, 700966395, 547618721, 133088831, 393205244, 485570522, 972938455, 122707267, 58810091, 295114126, 366449664, 184111934, 101894722, 622220013, 425240180, 850344835, 329245158, 849743218, 402289374, 336874079, 993694198, 76217107, 475001627, 437414921, 802717997, 287823199, 563442684, 32440021, 704062737, 317807224, 982016472, 671523816, 556384303, 975191673, 827376249, 277722148, 585381609, 877234587, 925793623, 712551211, 21158214, 556335243, 621385309, 277782866, 181687585, 523627435, 603306540, 468684662, 148638600, 194563076, 912216849, 608516602, 399544567, 988701751, 291961565, 180913104, 173690872, 714994765, 707205919, 809763845, 148995059, 373609720, 912244196, 886283250, 457566126, 265500878, 99943646, 674185036, 298965013, 254341996, 87437439, 587383532, 964177588, 239110474, 779056452, 720869039, 340724118, 476892151, 858714808, 894039422, 332348724, 8390325, 648345038, 802606539, 439920012, 220501700, 616836716, 289888810, 125093174, 330473491, 393455410, 661218326, 459611942, 65075449, 24069065, 999502187, 142027850, 928516348, 589435252, 187729790, 769328335, 56401197, 524217076, 710634200, 219825745, 507015605, 318299689, 526577914, 634413611, 805378336, 997804946, 754833954, 528540619, 653615275, 617494293, 907243958, 489311940, 327879423, 725624235, 505799373, 138450535, 714273411, 154445858, 814916667, 910474384, 574249612, 968438425, 337674800, 148694119, 663426867, 799542139, 177219278, 800960761, 10135554, 289834572, 564505953, 331456430, 43859718, 109097733, 810913628, 765047808, 416224011, 304848138, 882308016, 534014876, 484294484, 308665266, 944677062, 659218146, 967431894, 1940713, 703202475, 832910882, 604919622, 855925094, 638524285, 442697407, 658521489, 134267209, 315072180, 383992192, 711093885, 204024114, 443112774, 11105262, 521197550, 944574300, 81131625, 90260139, 941549130, 310207696, 318271801, 626631835, 191882824, 360203731, 8562646, 336999966, 458411772, 884522670, 892016966, 25393963, 724282549, 603778876, 364077301, 135068866, 25559052, 558086655, 784650584, 666350835, 571755067, 967522317, 932413382, 255745650, 986013362, 770283600, 853769353, 194958062, 157260435, 140472229, 68994286, 109746380, 329643698, 319694395, 673894136, 394750658, 584159689, 711804662, 518232029, 714286983, 119873864, 493793405, 483750368, 857401997, 662116030, 518268865, 651088395, 633290061, 800287007, 201075721, 847873049, 23937872, 723144440, 989710380, 745802260, 229236415, 607130338, 704641904, 546335601, 990302602, 319070337, 491265028, 842846755, 267466101, 879463036, 675501021, 474753866, 530003195, 836451732, 841654032, 223051001, 380372225, 726230502, 263123318, 584933554, 713157694, 336503985, 459721308, 979917129, 110514573, 622588172, 482691788, 23958305, 588877916, 592630875, 236973881, 239752132, 631326306, 881199064, 914411152, 268701596, 879915491, 462887790, 923721706, 335774758, 245444626, 594185548, 78028794, 519811473, 445456101, 398051168, 965666832, 855907877, 523779362, 47678763, 311591187, 349933468, 222641450, 241149410, 798610197, 16222735, 294327158, 895325834, 300306473, 409172812, 669207531, 878568696, 237072455, 818275292, 130980463, 240432359, 275188339, 580679523, 148645706, 129990462, 115008273, 708755679, 944484637, 200224791, 896796951, 37427218, 754782596, 507623136, 615200326, 540308229, 197059597, 443492871, 988326335, 804543674, 235178529, 920402113, 649658092, 721948591, 526846430, 412035419, 207808616, 430589353, 431093010, 599283869, 862478872, 702867205, 774159625, 388123276, 144654434, 21586143, 163599057, 201547155, 470528347, 367700761, 403449953, 267891424, 463209790, 9216131, 18447927, 555741220, 766921148, 285339314, 143423685, 742382357, 542953865, 916982645, 728673142, 4971797, 356153892, 615584810, 128220952, 3579846, 975853360, 45149011, 630751087, 889886707, 689971781, 936349572, 888679259, 335629486, 690131804, 662261423, 846940116, 225219914, 366695329, 692765650, 578549289, 954881396, 397132568, 803138148, 190032365, 263513304, 646584031, 21551344, 818503627, 760709773, 33591525, 298695019, 708102125, 424562487, 886707964, 142204627, 187566388, 104302901, 917699625, 968125085, 222118211, 449881119, 936159175, 932578405, 101445197, 187878231, 500461545, 978293503, 193688869, 451570347, 593528445, 627691452, 146068000, 922124301, 575926979, 573545732, 208952515, 951413756, 994655151, 887365579, 771983169, 637770662, 559527093, 158271701, 38169122, 812267862, 764547945, 63298440, 311570867, 141850310, 505508681, 848251605, 151809510, 800222223, 397858694, 687938467, 571780335, 630229605, 181167670, 368898236, 494937237, 406076681, 53605468, 779942793, 894017929, 417868169, 665922928, 600450418, 855644125, 73428705, 534773701, 294100631, 594986999, 634970878, 821463706, 492108542, 337647333, 612175928, 226563695, 882536830, 938334277, 412461405, 371092611, 555961193, 375533431, 87661928, 748372739, 446694944, 795790209, 928375875, 177485692, 290482547, 986909109, 726690443, 153728562, 227908055, 906726348, 852630922, 634396798, 863788594, 586245575, 139493989, 91962721, 967717609, 289406414, 875279941, 48798941, 199441932, 347883096, 172697298, 115465066, 939251527, 338738695, 455938246, 310861788, 506309933, 786658944, 336402959, 349236114, 665042393, 94120099, 220480474, 213363408, 104485882, 717321498, 328484592, 589356113, 786293621, 429891123, 958603905, 460273449, 884342032, 792557457, 88416052, 693842637, 82698884, 185368512, 435118530, 888790133, 910647560, 114399997, 647733323, 630139040, 70143457, 511063302, 428597177, 330214623, 151516964, 699234959, 442246063, 551213994, 956614831, 905521227, 560913925, 128616904, 245517469, 233768130, 501070827, 615716983, 366109296, 412308993, 85030221, 986177033, 95037967, 394256215, 460007447, 60084018, 63926098, 243072093, 750927912, 3889886, 406705041, 553809809, 293269121, 366999799, 358742040, 290494132, 608682335, 168769849, 968940541, 768714338, 737346271, 782354386, 575420468, 583254603, 290098086, 550083131, 233305158, 875091947, 135323476, 811809410, 376835737, 611582565, 642042651, 614647859, 375944312, 782870898, 205769221, 731523112, 197848003, 862633908, 49331184, 607424118, 296696327, 950478678, 291988783, 801950889, 430538156, 120211568, 300138004, 443180682, 26023199, 998402250, 691535749, 745905437, 587353590, 130726069, 738215212, 983823366, 942619098, 431656462, 690407495, 856260939, 440899434, 400991435, 347584069, 271399249, 677677244, 595022325, 743467716, 615365344, 154726926, 915548810, 221575545, 789973650, 939906134, 762921631, 762380802, 961283963, 277771717, 937031499, 907230923, 443457569, 191591141, 558489769, 905938571, 301676156, 882218008, 721676113, 404974763, 676402390, 559492093, 223604321, 895287947, 443243605, 706104309, 702577742, 230821765, 76284885, 477918443, 316274928, 984362297, 235894951, 599586779, 460206821, 393584362, 707641343, 157596940, 846084851, 324107453, 546378039, 37683841, 973591241, 447079337, 780019291, 916647376, 547502327, 285065356, 625354905, 818717513, 743076310, 470819199, 519757341, 513992298, 421692017, 883800419, 511237651, 782800328, 188397894, 104811742, 316511550, 544848829, 748437261, 192220238, 307191711, 604728751, 673973609, 20531090, 368583839, 401356325, 955967631, 122102392, 941892126, 288535341, 480593734, 44724948, 474500813, 764475066, 200598649, 586312425, 320403788, 585835975, 19892411, 631577017, 666357020, 309711504, 615608677, 111891236, 203836015, 521501450, 435558293, 878442699, 599313222, 358937702, 993282337, 426767369, 600132129, 449562352, 739981928, 388198418, 120842372, 63412876, 779870479, 986937435, 520892993, 218075546, 571198045, 192352038, 875063172, 575261156, 641812877, 300050025, 588855292, 384055818, 376743114, 292679703, 420040789, 30137698, 935719707, 523913422, 653656962, 529217845, 568294145, 734248073, 494076246, 739919237, 730172103, 259408039, 785240687, 405962349, 909885629, 849811961, 801563796, 804553466, 727620214, 368920639, 578599163, 820151042, 862731428, 446828905, 200044513, 987125864, 186217981, 469069368, 781988449, 471469825, 900697280, 437148369, 861535319, 284423792, 664218933, 613092718, 634642739, 567528129, 415443131, 921446901, 160313909, 599720175, 811223238, 852624687, 960414018, 639827437, 577186583, 738681294, 256253374, 289623149, 967925016, 24886189, 32589988, 161760265, 145570314, 67592331, 968049042, 861656329, 393401631, 9733845, 983513216, 910318966, 180906003, 874401966, 51294360, 140247338, 206552930, 640007707, 132578273, 562687280, 549609006, 322906697, 185015108, 917886003, 264445742, 570003144, 198020503, 565309910, 872012658, 125940856, 37226172, 650652309, 890016117, 20586593, 78997844, 615574266, 706751046, 871089983, 140128339, 780699043, 741741376, 899239408, 390671538, 378444526, 638630358, 107716070, 493555098, 809409354, 903155155, 410801919, 65897641, 407896971, 887484336, 94178267, 954269777, 235485106, 673498436, 926037876, 514665354, 893904706, 597024436, 481333444, 606204043, 36379158, 861572348, 715560280, 480284928, 926464193, 171905839, 873376591, 684104016, 954809036, 534970308, 275029596, 401996663, 855080192, 276241924, 877275346, 26991150, 739481499, 505849307, 88308425, 714649300, 271279279, 389093781, 91053265, 860412638, 697383292, 354128094, 758636659, 405014498, 664501976, 56323910, 761003295, 795024478, 418146918, 221722061, 493597974, 247030174, 937881722, 499759738, 217018043, 510522051, 479229949, 767641591, 983546449, 677702027, 365141275, 172057716, 341011700, 513971297, 911204041, 755429727, 41830333, 442520289, 385421670, 517748729, 793199317, 443458356, 980953893, 359319670, 283550371, 960217673, 929293038, 522454566, 276814735, 938290129, 735414643, 244215093, 281974679, 703093876, 91484161, 377979346, 551988870, 305877702, 869874608, 73137496, 841552554, 156363387, 825985185, 278036139, 43845088, 468411000, 242404126, 288296194, 149301712, 99054885, 431095471, 219292325, 116910852, 137768109, 345451185, 213279310, 865108938, 231822200, 32185774, 615376427, 356004856, 447094658, 821279017, 138693752, 379621811, 845273932, 16624400, 584819960, 292021331, 17755980, 337911253, 182709011, 711961787, 33460733, 281837017, 724405772, 333422932, 378558583, 198112622, 222582072, 992525301, 56916544, 786613438, 750478258, 217190321, 440926563, 581932272, 496848936, 986078658, 495154452, 7401488, 969970027, 442762081, 751468239, 540465782, 787784292, 945122860, 293133572, 129069016, 880483892, 837119945, 600786166, 913645032, 626153690, 477166156, 639642598, 521566498, 269791440, 871461897, 193507896, 539622883, 43830703, 792779703, 367925937, 916465616, 54738352, 827610228, 582661813, 80510151, 429181958, 253550646, 557664493, 275000299, 896678305, 603701310, 961448866, 116652558, 549185254, 255101209, 507693703, 212042582, 1519313, 873190130, 282563486, 899110275, 880919167, 19297657, 146311981, 694930031, 637560074, 16165961, 810570090, 379529060, 526156770, 959326212, 673839798, 309138010, 171289164, 505222186, 797925048, 921456232, 268217472, 955458422, 118849826, 930811204, 287307574, 462565962, 197210144, 281418235, 327538054, 504659613, 197910356, 49692475, 564535021, 749111332, 934307550, 683253165, 902089093, 225390984, 891600850, 53416933, 631920222, 475539854, 644045723, 181915177, 389666571, 972341651, 741124112, 58357839, 365531430, 752849159, 725379682, 672749601, 979862676, 968392740, 354770661, 366290257, 243881365, 233910023, 382439092, 292717277, 195964018, 123610781, 355334172, 161919993, 722344219, 329603951, 695281437, 197014569, 410162791, 363605522, 949620357, 861632573, 80283055, 94454871, 808530046, 335328581, 17480601, 71356352, 195059494, 857953212, 543901215, 178136321, 490879749, 804349811, 612964377, 675542764, 647464411, 131555067, 759920346, 64269581, 585608032, 822340567, 149139512, 549560649, 538683865, 85598694, 344240118, 535239509, 245596956, 16829957, 950286464, 639166385, 496753410, 871411577, 970768320, 199460605, 754462922, 989234888, 921487833, 404652829, 839473815, 4641374, 418951468, 597564926, 474898700, 953040005, 362356250, 366978918, 668498405, 196115332, 466665658, 955252888, 170516027, 616648384, 374303111, 385547132, 328292706, 230039521, 203068734, 893118060, 291608895, 570085829, 571839783, 707879242, 738283330, 265337298, 950224646, 734128002, 162151724, 232868636, 844470110, 297103864, 778011513, 295650340, 178029145, 296722855, 214598110, 226847892, 394823438, 317935491, 245135201, 386365083, 434773392, 42908235, 418076346, 831194370, 626783009, 463153804, 826374509, 917062433, 482661082, 37465370, 263636183, 500797406, 350049011, 545888907, 481198765, 559141483, 715812795, 822017004, 317432297, 876144086, 56180773, 913146547, 881213167, 540444491, 968113415, 73662420, 867280919, 121046653, 446856283, 498590407, 172905646, 762475338, 716879395, 270763180, 571793553, 175321439, 417060582, 183395839, 423204947, 816171258, 632827913, 24472439, 991280586, 489643652, 563847791, 412872233, 758234167, 680487501, 16130638, 471970503, 83433989, 715962312, 870238494, 712649056, 260250692, 807022609, 211628292, 379598111, 263061534, 920253597, 181534486, 147341646, 534733225, 300258386, 585848191, 446570760, 806201123, 92154910, 784838928, 191992014, 238239288, 427359701, 264305952, 944004751, 310897501, 771686947, 777417256, 565571969, 843159038, 734938665, 248883128, 310895574, 691878051, 324949268, 960954735, 30394666, 750711717, 828216698, 116838992, 833191116, 56248096, 499875152, 25802771, 175278050, 247217518, 213180732, 397173678, 523235173, 212933523, 820303471, 857949372, 730577561, 85720792, 652129248, 651353125, 732406455, 353226346, 349813117, 562819614, 23186102, 626952445, 412794653, 891242041, 832139480, 201054698, 66010849, 1660223, 607115908, 145352043, 624843531, 585126157, 279492165, 638187937, 621263726, 540019629, 982700049, 727676666, 102417204, 357129128, 3264020, 776988877, 992872179, 974577439, 328526248, 841650335, 783131371, 680836672, 295103574, 371593763, 700081443, 560580778, 540318609, 817587555, 144709511, 660657559, 867116914, 216344265, 589070428, 798015589, 262582252, 744009476, 310830661, 38801922, 578316387, 665983338, 394493280, 940758308, 25412292, 293360018, 715278017, 467134782, 444442165, 532553790, 265990548, 873974975, 314223733, 236125172, 124958116, 812162681, 842426137, 212301133, 179554952, 993163208, 260072016, 197096172, 418063072, 764312952, 955390186, 553810141, 641937219, 134935336, 441266963, 463461561, 704947717, 70402155, 3604215, 699333523, 407337431, 450536636, 857595432, 256357192, 509902719, 219575658, 153572682, 200004344, 138472121, 719262832, 162504210, 404511620, 465906357, 694098414, 149830783, 357740036, 4449334, 233717513, 486771155, 661298973, 937415059, 411399292, 181283507, 500594246, 276817631, 623005499, 50589768, 874889987, 194953382, 43321861, 803003868, 824783427, 756192342, 399322220, 505958429, 204570022, 540813658, 980326270, 124735615, 655973168, 995132079, 428093787, 402197030, 776335627, 137226996, 640130456, 249142087, 747053261, 946245858, 695777204, 276028469, 457673059, 236107335, 130176950, 657367695, 594057980, 880283763, 361054500, 952356849, 753058273, 517160287, 793053338, 317405910, 770952097, 446896176, 884167255, 881996667, 929808988, 617960353, 4655112, 596129703, 950232496, 199091289, 346186348, 186142990, 802597999, 715101774, 444188944, 528002430, 742210107, 729303864, 24645473, 327885973, 446721459, 331290120, 564745192, 742190644, 579894974, 222096104, 824926277, 484377127, 685797602, 714225829, 400503396, 169327535, 897174773, 818897074, 966496673, 458636373, 782139438, 323137854, 254474234, 64010969, 557036046, 537631043, 675075242, 892628583, 618657496, 480147441, 983255320, 330274149, 846059304, 860618256, 681565381, 18105820, 723478754, 344311865, 152831129, 684152149, 371911775, 669434740, 753640539, 357447363, 944943594, 320493963, 983303696, 710173931, 78286919, 354752332, 280747633, 83036025, 209830, 536413772, 385026986, 236971900, 105903987, 607149243, 263190919, 526275625, 941367891, 898878095, 771265676, 266358094, 204535326, 898209984, 275467881, 951162827, 951822170, 874299273, 408486640, 473932908, 988517313, 509092542, 697623879, 556232466, 548203695, 845914836, 779706423, 447277470, 490197674, 221911641, 112933398, 614206893, 689783376, 911835276, 152887932, 620406592, 367458756, 495226201, 57695635, 168996993, 156126721, 798722363, 752692033, 798540896, 328505344, 204522548, 588067598, 892639816, 417336897, 244447873, 314793173, 463214376, 970702763, 395292368, 514669354, 264614150, 939940990, 24086436, 145349870, 100304889, 747492006, 47590240, 790731475, 754551153, 269954751, 854682447, 358647113, 563891200, 686427296, 91730316, 605101250, 872619948, 469156406, 142041905, 401470059, 342972086, 565884105, 915550946, 896335540, 343469558, 503031847, 328396308, 585285154, 414639645, 616349916, 883655534, 789692568, 992683815, 658687627, 964563887, 291468331, 36210474, 802593180, 461752852, 647628005, 762638976, 25141781, 387777012, 157591855, 253672719, 885486660, 863172279, 571017271, 522549089, 380366964, 658939736, 192184781, 4873339, 111153999, 557837857, 746544868, 416871536, 666812063, 422788087, 520144418, 324081212, 129618413, 45982746, 364654394, 953547944, 84772748, 194385239, 508528909, 712323194, 429385112, 189618291, 577639826, 166208902, 130204687, 331568988, 37336997, 667063057, 885375263, 772041092, 833945978, 725127230, 649904031, 402707571, 66988341, 806067413, 519074354, 382181021, 258537777, 196532877, 577878685, 205173546, 954626691, 681996543, 594085226, 755066627, 71277009, 190757955, 446362479, 284870859, 831349179, 665139227, 994956838, 385305040, 351302571, 762230433, 97819321, 712937262, 764645952, 787270048, 17217667, 12716292, 545002432, 197238601, 308163819, 231160446, 27427045, 118748703, 132308380, 593406328, 719146473, 833473358, 159352151, 803907230, 272796733, 406528040, 878268705, 878606229, 858547895, 546432022, 645085249, 859531454, 724570604, 254125285, 692500735, 882203690, 503338483, 423726266, 421300541, 693415792, 532920182, 672674136, 400048925, 671996908, 448743287, 858890844, 207077523, 734279848, 562872067, 29223091, 703637812, 260697637, 606112276, 683137700, 816506090, 933778336, 45022069, 771111597, 413888885, 636097429, 621181372, 118466143, 275297351, 592284655, 586914654, 813893833, 951231505, 123852409, 678328048, 157812469, 585838286, 259944344, 421252250, 637779891, 346078446, 771260740, 476758160, 56455414, 818196726, 833781113, 465307201, 788832865, 623932879, 957188580, 398937787, 636203135, 917258238, 434133625, 951797147, 473053030, 338915270, 135077390, 16452531, 311394366, 613001250, 458791757, 906911837, 174259487, 255626074, 61087924, 924817742, 571103277, 101286638, 580899125, 456912129, 495675504, 345364473, 892915518, 765314379, 409938327, 958127486, 841185087, 455688255, 103177053, 569930626, 1315509, 253825146, 289325574, 715407714, 181511159, 433539943, 350473358, 279513170, 501066285, 229563056, 879195113, 980015728, 1494379, 921129862, 219571874, 222347755, 424489486, 286153404, 692415236, 608014692, 474863070, 216501921, 430081000, 12538559, 883335190, 198511027, 445735020, 438769701, 531237415, 654275420, 661621716, 377603743, 634942305, 986637611, 602112117, 489261902, 207144724, 395328973, 796281619, 168945028, 74832669, 95603872, 812994982, 257691099, 980939385, 730149164, 127026914, 693146757, 628286632, 265390138, 757066192, 763797917, 941926092, 202813113, 951539821, 410947626, 229432, 959476087, 750560365, 761332808, 82387660, 355464067, 747884889, 352180819, 438271883, 919059990, 892923135, 789780895, 355626960, 80555899, 368506987, 287540901, 729718896, 715646981, 461686451, 353436971, 871308232, 360446116, 554010131, 117094712, 941942447, 277491011, 389714011, 43877519, 146008960, 400176917, 899860728, 536922148, 846902737, 171955208, 184566229, 709865480, 255913198, 525324854, 777340234, 986236982, 764256369, 716108925, 436517040, 715113883, 412753702, 327778415, 55788581, 584901697, 638352327, 347918058, 302598412, 202000858, 357049483, 608257006, 36095216, 734700570, 825188056, 980055637, 133095404, 941944128, 419238775, 301810330, 795384828, 759110606, 271446053, 587068042, 215090547, 656574052, 227263772, 483606492, 205869042, 957772168, 197228583, 11804125, 360764109, 216833383, 95315956, 852499134, 364387626, 247670480, 495157725, 188707487, 164792604, 588285322, 929083091, 750161093, 874360519, 101123845, 285865646, 553587992, 484903977, 877323171, 46403358, 341686268, 556023550, 525067329, 225667342, 821006849, 516772150, 668926979, 509777173, 864038854, 765402054, 167809960, 760657126, 57674237, 644923891, 263554907, 158812418, 689472896, 6968811, 719902689, 463336871, 415043571, 118424044, 767398339, 983972616, 662519872, 379559554, 361385530, 228005065, 339907875, 833015305, 989327247, 31466552, 372304562, 45534413, 712505648, 50392700, 891407560, 999253162, 312601387, 811052517, 876050111, 591441739, 351233834, 778948366, 386789597, 26119509, 392468162, 968806573, 216864973, 768511140, 230607377, 846548562, 98589422, 416049842, 531860379, 230921727, 544208502, 727482465, 409535983, 339064831, 796157207, 20753579, 109012101, 899785869, 330426880, 90972256, 414563304, 45716729, 55829806, 476851207, 678071268, 195406278, 215451246, 63766178, 838123945, 464798958, 702987174, 746189392, 454723687, 276900805, 284577038, 911268589, 599024481, 516715752, 266212248, 355837794, 227309973, 904796071, 2225778, 150875469, 993784771, 704154567, 702773848, 950523556, 670971839, 494006010, 114438762, 400250127, 14481790, 460853290, 75452734, 792709602, 16202940, 760257843, 608938180, 353323362, 91778274, 738455293, 661458620, 73880093, 493327370, 13548908, 105874476, 252599765, 260859550, 480324987, 827579616, 299504247, 207900221, 346749092, 75857462, 371534173, 670938088, 325260468, 842458171, 419841310, 210616997, 942072306, 326410479, 568763115, 931839034, 367415193, 882959525, 611384750, 97566162, 604576224, 788544402, 150133491, 31389961, 818085707, 224191173, 319551095, 251201566, 260601082, 673576982, 772515096, 616603879, 494788112, 234393937, 263131740, 559498214, 541511862, 895207914, 217248475, 160534539, 29334175, 295126254, 108078933, 402376097, 233591836, 77953204, 905879924, 70017991, 884595096, 224511423, 377108252, 39671050, 125374733, 322549705, 738921124, 645486980, 275851530, 955633671, 382123043, 992778222, 300424281, 320201709, 611631771, 733292502, 932157210, 961994455, 643120345, 820403586, 614659060, 873021928, 597448627, 56035565, 256521802, 954955071, 560450881, 748624100, 957088483, 960616301, 76637089, 471123795, 192520577, 675496226, 732509456, 532239918, 361300355, 538330969, 272239667, 491780611, 650791947, 749178212, 4453809, 744619672, 625819632, 672048163, 445764610, 960930224, 194374275, 157992020, 619520675, 190167274, 302681877, 461895044, 81023449, 914346232, 867108092, 565601980, 184117960, 472364822, 513039860, 952846900, 455912421, 865200136, 329823748, 260131291, 786574063, 744719460, 41458125, 227629034, 917910273, 782225141, 439525064, 816671435, 639645725, 415529683, 82126710, 664313045, 190160442, 386071110, 2755153, 856591660, 409711727, 623726647, 76074697, 686005594, 723527767, 785821045, 257332980, 709907161, 881992720, 356271500, 175829016, 352743685, 582317604, 466112995, 370959575, 454310902, 848731778, 554405080, 359613215, 671251542, 296040164, 950272088, 647828864, 548412551, 552042060, 937020055, 952946509, 159649055, 761383371, 405386725, 944379658, 241054883, 956835951, 716863297, 410512092, 49486356, 3685005, 975807901, 148833254, 245632180, 280081344, 227341615, 191766988, 988821974, 36624897, 820585909, 891880925, 828984902, 44738532, 401527357, 210464926, 570941075, 164801286, 414855097, 355264182, 290881985, 413857833, 660432946, 219882274, 101446061, 540638936, 705873978, 496831863, 745913241, 706598252, 191638063, 159783697, 507958256, 668205749, 629233778, 347448226, 413659292, 629920746, 455235333, 766290558, 152706802, 85638176, 44109957, 495411711, 670095201, 737035058, 938270808, 505988587, 466791808, 721865221, 170212070, 481771705, 991564599, 105344547, 19606238, 859684009, 599342974, 825534298, 153742423, 190003582, 686860109, 665911892, 114878290, 982991891, 994275773, 64142355, 478577107, 960709790, 728448110, 431712635, 869610317, 796652220, 961395861, 649307629, 625101481, 495218511, 842043936, 684193850, 672337608, 669206923, 28990377, 65559918, 765573664, 323953388, 699063519, 871897772, 926607758, 292704051, 407291007, 86850819, 436122783, 151303767, 145335028, 164667745, 163758627, 661349530, 528475527, 954518659, 538765742, 855066046, 828527525, 167985723, 523887245, 316851426, 578423528, 341591455, 903307983, 99640416, 552313602, 438750613, 725093889, 986386822, 471605779, 230910283, 812819380, 606498717, 199958034, 587185447, 784954094, 790568870, 491185803, 24964609, 699090720, 962429119, 864787890, 227988039, 859810955, 804603738, 22077674, 131145149, 222310246, 110841383, 407326997, 543044827, 483993065, 217336797, 503421823, 893435420, 265211075, 170177748, 107737625, 834734044, 685150068, 829140878, 966542861, 461000225, 186425898, 136664391, 94074935, 786619549, 895482959, 480048515, 877578427, 590174312, 654478103, 727939021, 454826282, 844449012, 990634364, 198651560, 367435788, 371641536, 75756442, 542765661, 879434752, 213909579, 994449119, 893304567, 27363797, 123089928, 891007454, 37540132, 661442962, 134458234, 531164951, 944139833, 712533330, 664150413, 166252586, 630647117, 555851052, 758614475, 122294031, 222817925, 499646890, 422700556, 103312992, 681537736, 470585236, 637536229, 817650164, 931286245, 283459082, 543706654, 333947967, 537240053, 812223877, 359846870, 242812977, 729588628, 321184391, 672727341, 856186011, 210169085, 805821401, 975401652, 105204030, 639996427, 280253248, 61120497, 903804010, 9526818, 747975205, 294743908, 362043190, 102046228, 527182754, 202128952, 801181311, 71441204, 354717693, 112278962, 693253471, 636838881, 719917264, 799319148, 730162389, 218063651, 811397018, 505212720, 250758334, 349926044, 297186918, 374261588, 422946846, 873705219, 254385135, 70739601, 429425535, 969723988, 601407081, 86978262, 688888488, 702124558, 276216047, 291654898, 301563193, 362002172, 221926623, 833447916, 636900861, 597918112, 842775034, 72352314, 134887361, 7118253, 758931347, 990991488, 66413101, 153161623, 440006829, 735039830, 781111639, 340612375, 713706780, 426553463, 937871226, 196985892, 975090450, 397200453, 250096746, 82981755, 674500617, 537006911, 223131820, 267446954, 589986687, 310611207, 262849737, 52970203, 304643964, 931249218, 95606045, 802790435, 380199302, 473003405, 138456536, 258099170, 811825052, 151848499, 959922570, 619095290, 249216066, 391439695, 698604798, 435454080, 855649332, 896084675, 171744778, 776992994, 200043897, 434088909, 294799633, 811122638, 205387056, 289669557, 449127645, 367057017, 223362123, 250363863, 492718184, 626864309, 322307105, 598396145, 280022398, 725524883, 914940796, 576047966, 810991837, 881757488, 816432057, 503142987, 553970831, 181573480, 211242456, 7983219, 181454398, 627200812, 328441243, 871998857, 674264415, 229269012, 830212104, 866743051, 863546745, 899391637, 182626518, 732010697, 153341243, 336668787, 2412202, 147198651, 992051551, 44015092, 40216045, 938705487, 553674966, 492491457, 310490358, 319184791, 241735303, 421223140, 474253486, 521843320, 899204155, 965429131, 702161642, 860589504, 403671254, 868887465, 546727888, 236335851, 738329503, 104198353, 427706964, 159082927, 267959103, 277235800, 941565379, 263349280, 835354229, 537794163, 107383838, 164407922, 972567439, 473275337, 199507571, 592018312, 288169277, 313303160, 861354991, 277800033, 319877572, 569606240, 960046835, 45844465, 905899135, 57207637, 540663447, 916557360, 603365707, 379119263, 374881384, 99813519, 701743655, 533596095, 342039, 602907412, 851671970, 822627427, 663937589, 957094848, 775150026, 365308501, 272347201, 118014573, 227830677, 52267793, 807923005, 663835092, 742074137, 131171955, 416820044, 54909453, 387689201, 387574663, 68454297, 111780475, 561049035, 156969320, 766559117, 590762362, 827936196, 957338226, 59635737, 80278847, 584816470, 75495367, 477844050, 695729764, 842601079, 510338328, 942316751, 199859790, 25497970, 235800538, 449374333, 319436371, 47071180, 480123485, 30462300, 885934306, 947339877, 235522761, 148024787, 743412368, 405498745, 534213671, 45106725, 221258757, 19261391, 580335226, 759073675, 855885844, 772941085, 247104086, 703200024, 197523433, 659940732, 349950255, 654301085, 374559298, 923093772, 204653305, 734418709, 156797277, 741167018, 80243143, 725056845, 585924, 281945340, 883145228, 119817817, 730768099, 598510575, 65202128, 176375962, 424437587, 517694869, 694802516, 996505813, 773277553, 727941545, 24947366, 662905332, 305974950, 318423796, 112032678, 93177595, 490985466, 936276856, 142656171, 226391666, 323167149, 39745767, 423660463, 254833081, 35053513, 284990770, 557747312, 335922512, 430074818, 401738923, 53108124, 231752666, 58871770, 265611345, 618367018, 349805193, 702687246, 484712521, 961899785, 169445983, 60789160, 587943748, 408642387, 805170169, 196797700, 801482318, 836326334, 743840962, 526534188, 304302209, 438947444, 184037605, 151886284, 924213409, 27513709, 384822951, 861070049, 68088025, 137417764, 3696375, 991686845, 312991783, 189538009, 43981954, 514619080, 97066810, 376583399, 383524121, 314187079, 710506752, 411711783, 885922992, 109362289, 534989130, 622663847, 834846484, 241477214, 23400944, 15877963, 451576345, 582173574, 92904743, 6400460, 569015331, 273979895, 546259909, 249556793, 882906080, 817588074, 840529544, 723193701, 668096729, 206103732, 642332369, 274877058, 355211075, 547007875, 278093685, 458038061, 245299363, 345902274, 420661061, 495746013, 264973337, 889760882, 917764134, 45427628, 992489799, 617064525, 917859731, 876751904, 128234365, 611635580, 968570502, 821480615, 238360128, 634332851, 462541831, 679988747, 14288320, 120493, 611807730, 351807616, 121689121, 466260784, 779007775, 28275329, 147198633, 291150207, 121141598, 680547689, 525650852, 969092155, 669246191, 223376468, 575727072, 332521276, 549586920, 635124531, 660993665, 585649051, 755715368, 590574419, 291457736, 889167411, 606682305, 791644528, 836320368, 659816237, 842974521, 853176519, 659620970, 501357346, 858060405, 929013901, 281037683, 604570778, 630467529, 483325866, 116137072, 794184594, 145849323, 35764270, 946450108, 208516591, 524144183, 463437262, 614599940, 888858912, 185478198, 163425899, 669611862, 441886060, 187355048, 379210140, 186619532, 839035421, 639020532, 505973496, 372401590, 277641588, 164694704, 735316085, 776281177, 282439461, 274016392, 138491575, 891004497, 633683344, 414854510, 761180335, 285601082, 57255396, 78099921, 186620567, 64228967, 633203440, 90324033, 881182205, 457148172, 367455613, 534442081, 121367573, 608438617, 278952333, 999687115, 572362311, 119312455, 133234357, 4842717, 141181735, 874778242, 923068036, 5834675, 819784012, 382613752, 891357690, 501096593, 235199372, 281151895, 123961584, 227166318, 265483905, 323135317, 653850657, 973494698, 49304074, 227109896, 309400064, 255332284, 121876057, 415268679, 894823340, 811971919, 480744003, 34951711, 387230469, 525631687, 994215244, 828729794, 668998152, 2490294, 984605590, 630703345, 201344349, 749690706, 705901640, 44903966, 446314758, 937822275, 486978390, 330339162, 41179374, 869339328, 97154462, 937226172, 2879429, 446053547, 362951418, 778223041, 525016260, 731894208, 910401835, 906416363, 360515439, 105471890, 356975304, 237080114, 895950760, 662029394, 615672864, 939983231, 136359934, 128666883, 530715962, 108793885, 825969152, 738428309, 338983054, 729546845, 801983876, 886992480, 506626207, 393195031, 688986820, 490541067, 840096811, 895999325, 939433818, 611835332, 413588548, 757171443, 684932871, 72020722, 854926320, 984945160, 302336654, 114031603, 214349240, 70088155, 877350158, 626769709, 228404600, 534844835, 851086753, 215964093, 363157852, 331186057, 543147775, 911819849, 234966978, 87449812, 501121179, 530303472, 686387299, 891749422, 94835812, 604282420, 768041715, 629369937, 808159812, 869710834, 625328, 329793696, 876823415, 477789423, 410231420, 612216704, 706569550, 991889748, 857145736, 317051417, 752194834, 327919685, 155774898, 887014681, 156845782, 408626999, 390858007, 713602852, 607538133, 117244791, 377706737, 769837228, 360405345, 997981003, 792817119, 978608117, 9507872, 854824060, 530602045, 496501538, 303970013, 670711377, 693304784, 329016620, 749692055, 697597142, 5151269, 601641507, 728140389, 834905904, 891575811, 96021269, 651039365, 380746095, 403280110, 545624995, 369058720, 519488165, 504668224, 507166214, 648514671, 576961627, 883140995, 934119542, 55038331, 501808384, 186524628, 687138757, 489661887, 51894755, 678108197, 302387353, 385513652, 152155987, 540156914, 772354294, 981801043, 759590450, 334656531, 753808061, 401300835, 483683511, 454271784, 354622260, 887325298, 865414319, 377798753, 346974784, 198883484, 697386316, 471086096, 351979341, 561093512, 934245554, 955896740, 554415306, 378790615, 57603686, 334433345, 369379335, 452759261, 322763544, 502915688, 359911052, 775749538, 615834509, 289188568, 16524527, 376878642, 911259709, 216383501, 795560147, 99178516, 827273275, 631942244, 741243454, 475560309, 33340765, 970849053, 147939836, 687164004, 797170554, 464304697, 54565999, 243229327, 841822685, 723022133, 709416313, 162109756, 893706159, 900689468, 936356025, 826426282, 636485490, 889022728, 443806364, 800637286, 371975882, 99588416, 936058175, 731426302, 131169241, 169699844, 743253474, 276986155, 253076764, 963095364, 273386692, 144066283, 747646078, 959492399, 504871829, 241301357, 666934657, 420055690, 975413061, 171845394, 702962877, 322564340, 553956582, 397688809, 8979646, 536685952, 213733949, 682712227, 66977369, 917908541, 365882758, 460187264, 940355465, 121178853, 932034162, 950132754, 626187256, 983550931, 200315336, 291989153, 771112830, 67289800, 635791598, 256612613, 229817829, 65017285, 921576266, 81198848, 275981620, 406373888, 76511510, 291409056, 831298076, 716889542, 138111020, 956873687, 868208018, 655401080, 192455434, 38841089, 312546011, 869646430, 759019029, 174502630, 459879121, 784359517, 815696487, 531190286, 479449215, 220126553, 377894609, 34143382, 406011044, 863825094, 591508738, 242185140, 112083742, 767663300, 243808283, 824252828, 783331845, 702131338, 33791335, 987422927, 490327373, 300977432, 591486792, 142973173, 12379062, 589079282, 578883156, 666755491, 354231626, 94369930, 498392696, 950477457, 460893061, 772511189, 873560373, 857273940, 898915315, 36308411, 122869383, 118145787, 568668605, 510737237, 881440862, 647163302, 284072991, 903610719, 750176380, 71351745, 506301418, 122574170, 483210947, 541126186, 633899483, 944652625, 798263982, 984000284, 890908453, 624178456, 147068479, 848908417, 220121799, 477651047, 821267181, 448775301, 982491973, 52213314, 3230262, 156931347, 875219170, 457084357, 631004612, 782391435, 852572288, 554327240, 964023297, 364700031, 378502903, 793926466, 18672842, 423554816, 784128714, 347986270, 244950324, 669558768, 748923705, 841064204, 73667218, 140905472, 105801894, 221572331, 424601955, 494898106, 885117795, 55149752, 783360816, 44678262, 914617822, 791137221, 285888503, 920619000, 249329189, 399817159, 324243594, 175164587, 939696542, 432684183, 206113032, 21981931, 224437994, 330272900, 313046884, 657619817, 596794445, 112540355, 821157236, 767703843, 861639, 455968287, 394921059, 431111370, 561148384, 532333400, 338099933, 484462652, 290806767, 217044255, 195173032, 924150978, 565828231, 168103611, 938911510, 216896623, 542457021, 347447268, 772305347, 50237660, 967103321, 709059433, 884767477, 988031332, 385843474, 893940083, 563434534, 404554950, 729335057, 311436087, 101427905, 40797133, 306534097, 566282350, 491680695, 549467308, 994704196, 467665451, 408006268, 539312010, 681130215, 433500983, 296464716, 817850418, 733697624, 526959822, 848002291, 465787077, 861100508, 581205883, 369759679, 167985557, 240998181, 404073318, 128737613, 637653620, 698382493, 403207860, 537965536, 173364246, 568821712, 566589683, 710539772, 495829709, 917867072, 487504493, 613565230, 759992036, 628062190, 114096241, 560203200, 501569234, 905622353, 420847892, 321270128, 922815822, 411209840, 351069362, 534429020, 395579756, 981886645, 583756438, 109221353, 914842960, 849945098, 724472276, 827095534, 141106831, 971096937, 322384212, 394199220, 435071394, 240896190, 687800158, 567993014, 748083747, 29395138, 75459065, 833031690, 868892950, 354784762, 444142083, 33103917, 339530893, 517006990, 832387769, 547843736, 212490223, 111342608, 710136803, 716945846, 978441049, 992349039, 775446882, 171414295, 933151665, 753764873, 954335009, 626564984, 632932732, 955502813, 246580319, 929384883, 454577845, 110843846, 125287361, 540895749, 912089927, 908149857, 750187045, 256916776, 585109046, 925368580, 869953938, 818503485, 942203808, 471152472, 825891688, 379808805, 611315392, 865343909, 411620730, 657033964, 416177392, 338089478, 838048269, 462317943, 681190749, 366603404, 437237506, 629219751, 101392207, 830031234, 361805905, 228215393, 870984542, 229677963, 141689344, 760234749, 537418980, 374060179, 88783617, 466413901, 169372715, 82257595, 123093033, 969903152, 479083875, 595969362, 975997316, 512163009, 502037896, 485147462, 940566794, 68917904, 322890490, 195008460, 444112721, 137807686, 596245870, 334164066, 963914292, 993322219, 995510967, 16710089, 64917709, 187979166, 72221936, 355284870, 217455051, 106102715, 325605146, 450817701, 439616560, 540688787, 256543898, 980705226, 143519795, 449384347, 597848432, 166328467, 670458009, 936170934, 190364961, 576292537, 188972735, 929684547, 624926011, 551135064, 267689916, 44434869, 945696719, 66655812, 233701447, 914335748, 967601084, 472301697, 340421372, 186931175, 130258639, 960088679, 926003206, 870617644, 653884420, 664264788, 27032311, 129043300, 585527209, 536325558, 855995176, 53357895, 336840792, 429003200, 465352751, 473651520, 952151544, 496795668, 805312294, 219819380, 173632607, 210465429, 136307903, 490200655, 105402059, 249129026, 91749408, 33241489, 513969848, 464894093, 619545574, 143133689, 761761735, 762289120, 459625878, 664313438, 126599504, 860612535, 787246689, 179930628, 876883790, 880743015, 654786712, 87724838, 278358709, 528438789, 988010434, 882654640, 538016610, 469471139, 955981167, 232294652, 683760322, 435904659, 219309595, 868720147, 926226058, 172644146, 204336432, 522148866, 880278961, 854394910, 339877888, 857826580, 385224617, 558783306, 728590052, 640256537, 460290597, 129377857, 518112175, 187737228, 533596857, 723477644, 81026956, 703416113, 438225716, 987034038, 804265528, 350089283, 602055728, 328528472, 128962491, 623244190, 848464800, 934040805, 139837248, 593748304, 378218117, 126461522, 725300086, 966716379, 184714405, 383733821, 238545095, 325117946, 555180738, 347801948, 282916240, 980903654, 416034412, 305638584, 452667514, 949597011, 334321615, 150538143, 841534787, 357564997, 24163627, 723675677, 955484147, 410093870, 332057129, 676533052, 704625803, 53571749, 780549093, 277183153, 309734837, 205243553, 196452132, 242572202, 859307882, 868606712, 517522878, 455435511, 787565701, 26907019, 906069645, 664405988, 385422918, 456286026, 717678214, 778628921, 802049407, 349585366, 114349691, 333948582, 903130747, 905007522, 275619710, 936642878, 878721938, 498984970, 268855899, 176877411, 586452996, 72944934, 613052193, 77738958, 27042922, 513539567, 251856195, 289776545, 992340269, 689755400, 504408647, 354171046, 902766842, 145291259, 942436528, 925106434, 453862043, 193170784, 123923298, 868629873, 855644262, 978348380, 676824455, 722884816, 119351193, 722744367, 736093807, 27973030, 192516162, 338774510, 560472346, 679998257, 934119377, 817902625, 985651964, 86868631, 362516627, 221333654, 189079721, 266065297, 598225972, 663424668, 769370815, 931975291, 538943977, 932690957, 156386017, 65665985, 768591755, 354869425, 720552410, 785977267, 429882527, 874277644, 45525756, 488567967, 140705558, 362821141, 471788382, 485599419, 564816361, 718482442, 988853047, 624397405, 386721224, 304137210, 511803373, 204227658, 676517882, 157499246, 223591066, 705187862, 80610867, 707140484, 143767756, 984197820, 895128948, 417369859, 297447556, 197457960, 825653763, 412782311, 371156949, 730003927, 67811504, 585987895, 515480000, 938168773, 981860130, 112276732, 971817471, 828188847, 862754015, 931096454, 557606122, 964394211, 12271265, 844574245, 957071969, 671921624, 396610380, 623322169, 198451175, 967881746, 341285430, 597615317, 575730786, 992262695, 521755212, 975673582, 170636249, 199275056, 78784747, 887741579, 153735542, 59013554, 659658698, 930427845, 850165422, 543894754, 418590905, 438598385, 589827850, 83213969, 791305236, 176693149, 668710346, 330805513, 993059906, 861868209, 336555572, 320725327, 259235173, 789570480, 651823084, 44677960, 324916059, 117541251, 486254769, 10788141, 707843051, 292837121, 202450280, 501188277, 585860401, 747288135, 970056783, 189923019, 601766874, 169954394, 83063482, 44804898, 46201908, 833428332, 509005128, 74294687, 641365087, 447306846, 175620289, 39602965, 761321751, 105067756, 705344849, 516313187, 521838068, 71551687, 316557993, 438169030, 880395743, 776028270, 542717304, 592346305, 903757447, 505329549, 667522233, 97083405, 105013494, 548470613, 229139707, 615446139, 593189401, 289278307, 639870612, 381139892, 602609740, 817906354, 397463055, 403176820, 267212966, 924497601, 98388136, 893353226, 889917691, 754184941, 749969258, 608658153, 267282705, 36760594, 600956956, 610823143, 812622205, 369092508, 769499760, 731573691, 295012159, 167514214, 781573751, 251333472, 60688559, 466123967, 190016624, 285619620, 831905899, 385452481, 167331937, 226192452, 981354849, 768370133, 969747076, 440532519, 717334918, 199056306, 76020648, 111205386, 778740323, 704299608, 885147196, 390997032, 374727345, 575016833, 333129316, 587078358, 478673577, 15123608, 24536582, 199350769, 949185271, 328556816, 759041383, 748742965, 573459104, 1301493, 785588425, 141284527, 625903472, 592195350, 589847052, 884457124, 765649572, 26978511, 840815568, 102617035, 147132104, 423995130, 21605074, 440821313, 676122097, 233559211, 286517210, 286749107, 29704826, 591533879, 989435675, 965249952, 510102456, 791294799, 839818482, 469032853, 810258838, 795674119, 268366991, 259687309, 670863980, 842609420, 662983846, 962499955, 453446032, 290033951, 350308461, 200322874, 141098455, 402332199, 202146022, 496021563, 511303239, 267089548, 646782089, 864257368, 458692045, 799047822, 201188183, 103668066, 544498049, 822062289, 210264788, 88573690, 85076986, 768453708, 62897537, 701438173, 652578307, 343253095, 596615417, 117809341, 867268159, 790750778, 310235560, 862569074, 582890928, 780734338, 409335410, 6059523, 448404721, 208430354, 915221638, 407466340, 711751743, 690278403, 312243433, 529756436, 387323809, 307943936, 235589457, 89099766, 782331517, 273464472, 728971220, 528767666, 484323934, 690623882, 879395226, 819732193, 64935181, 921421646, 291588099, 681976493, 570768232, 126291041, 690526251, 633049040, 732504759, 350037710, 861353188, 320763709, 224951730, 557705183, 747349390, 9543738, 473275829, 724198958, 355928389, 304491225, 262980831, 455258717, 410345050, 267563978, 210149400, 320894116, 27283338, 907744652, 474655863, 720381045, 812980619, 450705594, 609011005, 86444821, 648042956, 651921875, 811494232, 156565232, 332532255, 311607671, 286231313, 822433646, 614487727, 193852484, 577874651, 686122027, 415551281, 638151422, 283645766, 953509261, 102565505, 891086335, 8142636, 443985871, 447422043, 873330543, 857865457, 953198989, 289353379, 64751471, 844356971, 687606643, 273154995, 502680493, 528624692, 66157082, 355602007, 152266733, 868619039, 915876991, 146631278, 603112690, 442146253, 274764021, 31607163, 869122340, 844422124, 806513927, 825519510, 923398939, 688620143, 393854432, 469398333, 186105960, 688862217, 995504140, 205839392, 770928682, 848591482, 775627134, 402584063, 353294985, 911481594, 370352365, 980719637, 479295659, 300925025, 785768934, 392473133, 602510564, 977419014, 530197163, 750391391, 198102805, 566287953, 791341484, 519763953, 465577407, 690312971, 277161412, 5601063, 711090026, 718809779, 425078463, 736601408, 248229868, 547202815, 864371708, 140288816, 515056414, 201077386, 671640947, 987796962, 964431920, 182554048, 238957616, 591573760, 985381599, 717962956, 991599118, 814242312, 784344795, 219977558, 214378167, 220765674, 720722139, 319665136, 74877098, 958430214, 327870715, 917229099, 773405395, 440450553, 275459126, 909710103, 52756464, 354825747, 829626668, 161535381, 511783424, 871683853, 223582986, 908225841, 199648439, 432203265, 756533481, 631420177, 240153424, 138774566, 705304911, 354613894, 617626227, 671333305, 395648269, 435172050, 850759845, 314078107, 685536371, 817771537, 140289960, 697341887, 969788909, 205689373, 323905306, 497645096, 988824328, 161322126, 549551235, 582100844, 340076044, 829407418, 758729122, 125256648, 224124534, 752966763, 324363155, 591130373, 254770196, 428758711, 541676573, 253040403, 520335945, 684990381, 898906309, 59136886, 267516105, 202729860, 320819592, 977506410, 984594373, 850418756, 107714626, 119895709, 71774894, 303850105, 529310094, 360719453, 254815353, 390734841, 733069781, 776354861, 245626087, 618282316, 271626508, 363272058, 671009138, 879648717, 214246770, 475274213, 40809827, 337055339, 520577968, 245368978, 385156454, 609269891, 974912993, 105412564, 54922841, 733160322, 774152493, 814047110, 572374535, 819938667, 374685187, 560350570, 99402061, 167421134, 293485067, 242474651, 461574802, 807669437, 218904032, 236963621, 779113234, 364978211, 994730608, 202567035, 75057956, 264032947, 978233826, 852776027, 688035565, 736377113, 431651816, 28340723, 718842545, 460963504, 948852727, 238617659, 228415949, 677175099, 24774470, 235637880, 939588859, 870014836, 60856895, 223878214, 437976818, 330730837, 404725849, 269168216, 39610891, 808230619, 510409126, 187375738, 646515614, 178667977, 475656976, 817376417, 679525636, 747708065, 702441013, 840081250, 972077139, 110154483, 962296365, 503342607, 918991509, 189704828, 666125750, 288495146, 487999890, 472427435, 158928542, 375391787, 466399070, 409695510, 264653127, 624565119, 505430453, 700722788, 931015989, 427590116, 953975275, 425610436, 551859413, 371068943, 756992449, 847456252, 873613256, 83401325, 563746924, 354409277, 538615516, 111816525, 263722436, 210915987, 515704310, 981804875, 766223693, 277368555, 500266262, 832032822, 286117108, 459489626, 488830818, 357224131, 90684121, 972992706, 945708561, 826451041, 383805857, 17314357, 787550287, 486781663, 900379737, 43903666, 970171853, 983721700, 863092916, 135544414, 6096240, 722145534, 563460568, 461728557, 160697075, 478440003, 925763723, 245211168, 947356087, 856825515, 505918951, 847723611, 43076655, 910082883, 277399345, 63366456, 505004529, 115207286, 26807934, 570385711, 496254610, 411708701, 913779137, 773268180, 106080991, 479891861, 233707626, 772276355, 847289049, 494315923, 292887234, 473211549, 15282937, 198784480, 416995632, 700678861, 206988572, 779558375, 172079872, 710426012, 897552019, 530629283, 903059475, 504967286, 474325867, 700402855, 329780462, 31132988, 443365293, 865676040, 919447487, 390068240, 531602202, 334036675, 622246728, 131556315, 753066302, 355106452, 262847283, 935304536, 662497833, 136669179, 605777386, 847139264, 449726566, 116597852, 472770092, 637166343, 103897010, 932928080, 406002254, 557445045, 405327773, 347740785, 647807163, 697323179, 418879465, 812931683, 507437104, 566264790, 236787033, 847174027, 763135528, 109136523, 693143898, 242209635] 147356)," 92554 (countComponents [521267470, 349112930, 327767978, 144434200, 938889644, 624728236, 632831418, 182141945, 548184191, 248969840, 475656481, 28955409, 381493877, 945624349, 705350395, 363867693, 574069134, 300771941, 671379554, 31831684, 923942370, 132289610, 639211434, 368988384, 720924152, 206387981, 573365604, 540375598, 313966100, 678237416, 856705104, 607073634, 237390764, 870178961, 504367394, 905165317, 284775365, 149810016, 741175150, 496120106, 67926486, 537178934, 86314708, 568422180, 234610537, 307149697, 160277513, 630948987, 328289736, 752215971, 933006100, 366061976, 183974977, 563592163, 188608520, 247217863, 141271872, 544439109, 463868062, 849816210, 317817894, 937223067, 355626617, 457840934, 520490588, 221043372, 666899741, 923189558, 478619002, 203128207, 189518840, 926977189, 999451677, 130965777, 165612764, 569416599, 232211673, 38381556, 733535656, 752890330, 124877836, 2488532, 520744415, 66679407, 846886951, 611516821, 127817719, 196674408, 880071519, 291938760, 362694826, 910464532, 375508509, 820385313, 58550558, 585658893, 425196995, 547812642, 718716617, 258769749, 602781267, 385781008, 980126464, 653933496, 201934402, 803343938, 956024740, 182166514, 174714761, 818673604, 795893865, 140998970, 12088263, 42937776, 644698568, 113252815, 170895206, 992662840, 643017263, 978438058, 523774838, 115345432, 360818233, 206409550, 448712313, 362782233, 970284354, 298815707, 211706570, 645742619, 815784172, 21343402, 248940053, 915907812, 725132969, 308590893, 871520416, 651889247, 183098506, 916896529, 323065695, 443633564, 623521467, 51701208, 658345087, 101406330, 731119531, 636139162, 856174358, 827887461, 667465344, 219042700, 256402396, 768496153, 631098337, 207158470, 363390327, 82344083, 918102826, 558415800, 926995654, 775582234, 667082451, 624520438, 201212278, 668494087, 696642037, 227173484, 597780595, 999169645, 617637457, 786001454, 630340270, 544745571, 722797278, 137166821, 710873764, 664081039, 919335974, 669347960, 388075876, 878932358, 259187835, 506741059, 323883252, 210386341, 594060706, 22544364, 80901305, 657636623, 978623752, 851133332, 519901538, 24733707, 770475910, 302840995, 133137238, 172862833, 815456216, 939016223, 692667491, 328758058, 15106791, 502777702, 864047441, 797793653, 409251017, 971194196, 756449187, 354467712, 437006958, 251601727, 653623532, 61875306, 139083293, 369695240, 726116166, 711949604, 514116474, 320737101, 265630093, 103604704, 828048681, 827881856, 56157281, 280323416, 625981973, 544808226, 32464994, 174021489, 709401361, 280268699, 565865373, 65207663, 329595471, 121337693, 919905016, 77133153, 818926306, 360574727, 546397637, 855873031, 114733259, 831649663, 781807407, 79738381, 498985502, 910971579, 502889391, 172597746, 148484529, 360763553, 210653660, 763623770, 508099157, 347415831, 235385010, 960504701, 584111298, 727909859, 306601593, 556992958, 290107811, 84569338, 146717363, 154926141, 90312189, 757656419, 98578784, 39349232, 583439763, 305296439, 541772182, 118794726, 410558081, 303567272, 777100011, 57495211, 908109567, 14921046, 121245082, 919958683, 985360384, 867875038, 449810879, 575282326, 859876130, 510952773, 316246901, 753113747, 522173911, 560430995, 441724916, 796970605, 792274184, 844868550, 907796090, 36239133, 223735884, 140226142, 887611348, 834164644, 113276379, 294066062, 415018201, 501475900, 582059623, 734247021, 112944668, 327180226, 429344762, 964375823, 140297483, 378326467, 354906973, 93019781, 217669462, 396050557, 455289404, 334667686, 840285038, 888251490, 671661910, 379654205, 993988223, 322359071, 357159809, 847682003, 115942326, 244575278, 258789567, 102100811, 263251122, 15911569, 451919078, 559346470, 719544143, 692997143, 581168520, 872827108, 954447146, 825605871, 717941983, 185080393, 874832322, 469978741, 73697592, 722167702, 970268707, 205770259, 303162273, 713609208, 250529723, 519151305, 968808197, 3974435, 588653423, 234447723, 462274634, 767795429, 681805752, 638037100, 910518158, 775928729, 533909659, 759045554, 899616592, 475280234, 948008974, 60457996, 244397408, 98672372, 989268694, 781784147, 507226425, 617379023, 976239602, 17823800, 807511242, 914170676, 310771995, 499224273, 321010983, 546243960, 144573230, 36118238, 140862537, 345183053, 371151395, 476920739, 380565101, 344250648, 363097960, 685727542, 957606835, 625105449, 360714277, 828972850, 356646646, 976568443, 896218798, 508668496, 820489261, 297290710, 983960284, 524170197, 116595476, 997668486, 278678982, 731961750, 952742604, 548553472, 455007661, 424610636, 751381793, 53501265, 635452736, 736430908, 525527923, 193104627, 712163685, 138852090, 498778831, 668711329, 935602669, 835791241, 259936639, 510814896, 845080202, 891589648, 431513456, 606035519, 375765871, 927923123, 652698684, 735166691, 515032117, 903312454, 87904456, 503037048, 920835456, 265415526, 678210686, 731320004, 893298838, 136794621, 85497868, 982398076, 748904899, 795346351, 499435285, 727413789, 313230984, 794005108, 520250327, 256708793, 8518586, 495480522, 138736651, 36730321, 193392455, 545650298, 689026978, 432669381, 282854067, 400737271, 43574819, 941668399, 335716761, 687150962, 11775519, 428493632, 445838290, 532567963, 690128130, 465007988, 837364378, 501559189, 515839390, 426701548, 246540197, 411711823, 559892740, 439709528, 181929120, 629741855, 883385576, 669757494, 84410511, 172348671, 437404499, 563280065, 814830736, 287335211, 161124565, 156882533, 841210495, 636339444, 507037072, 103321723, 875174669, 830467217, 440221197, 115355964, 515872050, 128584234, 973876693, 541418529, 828175308, 761165035, 666167914, 589454133, 71971381, 355863832, 204885386, 498015059, 938169628, 445703088, 372839077, 715482175, 539041817, 961921638, 274678448, 403959624, 96657922, 51122521, 492414907, 530192284, 436687089, 323672879, 149124314, 945978926, 670589374, 793394484, 328678534, 286918033, 532832481, 822606814, 95724424, 986062512, 828022692, 350562665, 714352423, 519486705, 603188825, 702843631, 99955558, 625569040, 638140698, 554224026, 449093388, 468834778, 925477776, 20884534, 75845682, 493467062, 773016737, 132725683, 699446161, 603666504, 110502981, 418013704, 72980389, 176236941, 626834132, 750857836, 980519532, 273417683, 615905332, 236991750, 950118256, 583352254, 133152977, 744036215, 888408298, 195845709, 687302098, 267054735, 673360422, 840495847, 958487874, 647823040, 972951501, 650749219, 459386369, 907826537, 677438076, 220430336, 550090257, 4333115, 132479685, 556999521, 309030812, 476859750, 938275448, 111328711, 517289780, 280329561, 224770110, 183829500, 157206583, 720367386, 334389050, 757852226, 934087315, 843047720, 172933225, 375176148, 134185421, 106652571, 724117517, 434956256, 916131122, 96410747, 141976232, 478852320, 902202043, 453519930, 843532384, 525821789, 919022196, 769009460, 939435032, 66337368, 471803996, 22297010, 683556239, 247732309, 452205043, 448366974, 387131234, 744437354, 319603045, 927030522, 522933325, 539361770, 942753426, 451153130, 113719401, 833059911, 230713203, 70990863, 695897973, 858225170, 628072910, 108049212, 719618073, 513308515, 843729037, 535150320, 821425272, 435218656, 802851136, 261661159, 962735322, 193171217, 7654925, 696948992, 926191346, 522212721, 191500920, 560603763, 995358531, 542750580, 553433573, 617487892, 26299006, 283386021, 783200818, 972279643, 214878432, 813777360, 766539612, 750138922, 111218877, 959429255, 313247687, 641974373, 750438527, 917653369, 112201386, 186845841, 616763929, 155507791, 638638808, 845904386, 617340657, 136696587, 742657055, 879221076, 276303393, 928244454, 162125667, 108767295, 157042096, 984835943, 232794825, 89576322, 256304054, 151064833, 944612354, 281897146, 349172284, 520431211, 699501188, 760104970, 250716873, 767161936, 246931190, 404367730, 720001831, 578753578, 877767638, 880020336, 175605840, 272945787, 186573321, 215817009, 512755627, 928451003, 54411463, 652319703, 442985190, 877928529, 623424725, 216628990, 527914413, 91790039, 457404361, 270500, 36078358, 529903221, 386883480, 710886657, 661811048, 153140673, 221091605, 335293345, 5175037, 659528509, 890270432, 716134831, 993696671, 374043737, 162804874, 128981846, 995882863, 145753965, 322513106, 689288959, 841938338, 448195087, 182409959, 248389885, 343629764, 680098962, 598949518, 680528778, 702637990, 973329239, 854916066, 353874394, 900361727, 102662291, 399103923, 781363138, 837826134, 960585614, 145082378, 63998789, 62490006, 136153969, 448747257, 858731846, 992493232, 821376643, 280171361, 389230198, 734619103, 134200759, 459551862, 549054682, 658617715, 403812152, 549706342, 448187720, 197172318, 267441764, 615679820, 571554035, 141035648, 714244542, 886013930, 310944578, 615626908, 952442170, 861177841, 516413999, 465635344, 137122638, 32236304, 1159320, 813099691, 800407273, 622876762, 115294281, 667091436, 844678095, 374426468, 196430699, 11356866, 520338154, 937569746, 420171321, 300471379, 751711914, 112816248, 375908257, 870912016, 879754446, 807262280, 628134382, 34560457, 73246086, 102290832, 869792634, 270172521, 337635777, 210142492, 812436229, 113647037, 607420050, 860543752, 912457405, 138976430, 719466173, 134625641, 882447540, 907905538, 537714023, 848634907, 731454485, 683700984, 474282253, 25136780, 736772755, 44384959, 158582706, 153786128, 314095124, 392397039, 709990221, 402287456, 544120731, 633601904, 423535335, 327757355, 663822192, 608502789, 223650602, 201455103, 459175729, 173848248, 521017549, 124068578, 881529975, 637750445, 534158048, 807778385, 513136785, 29506434, 142720748, 944901030, 772350526, 696226339, 72026360, 856622469, 121298798, 158922370, 310973548, 879983019, 400152497, 728354256, 499234626, 264616777, 767116646, 674603870, 323999300, 233664295, 496210286, 890868429, 600129642, 596335237, 499034037, 670345195, 955032238, 280832840, 610050387, 363756264, 221070894, 988407348, 906607120, 131838592, 500409731, 990055222, 225586295, 96361390, 109680985, 316018567, 848311336, 636403444, 265106603, 376278297, 532009518, 532172247, 798384200, 710000786, 517993482, 31041896, 804313100, 925101611, 437745439, 681134057, 559410262, 380055784, 619435371, 895600067, 780557280, 679014280, 450285069, 340211196, 52794021, 330836740, 271305923, 9776, 549296573, 893692395, 141428154, 67830183, 356585923, 683344006, 350399686, 170465335, 385880872, 48278765, 808335187, 920219188, 82955971, 540146220, 722222219, 652300089, 584949710, 296215495, 508408639, 728051841, 750261099, 439317906, 890827973, 755558067, 182092791, 623365203, 690818848, 605538702, 391191539, 771374536, 517418576, 434851486, 784957438, 471817791, 509026077, 930155172, 985855497, 188328004, 254467198, 852766581, 40968985, 283588995, 375987812, 429316781, 110034666, 548861632, 404882130, 706415437, 251935647, 877275252, 932370155, 855875425, 46180662, 970546572, 959607243, 938867241, 314697773, 537607290, 335802037, 570926875, 790421301, 75121456, 435299253, 927924614, 639662552, 998902282, 386254493, 759658292, 755743908, 893518528, 932983215, 621088300, 757725879, 217108943, 537241152, 258772510, 921843755, 719026542, 306361913, 487768002, 275741342, 193646267, 704295646, 799382312, 624010526, 269520323, 228068599, 655392479, 45394872, 869922100, 541282785, 343093073, 420809123, 779273937, 379682310, 965030808, 779023007, 160993442, 465054037, 151359993, 922207376, 319446490, 98613163, 740004165, 825213551, 201318495, 82062008, 944642196, 923967682, 475984729, 90529253, 466646924, 745612577, 833415069, 187586399, 161841985, 204780733, 202212856, 821859938, 976900500, 228206935, 28048325, 107477692, 851128217, 303788350, 273903978, 728962095, 980378989, 683625417, 868712025, 47344293, 101170680, 533739208, 444515472, 231297612, 117768066, 241719615, 135398543, 890102607, 122103679, 855324897, 293663, 86187649, 234230018, 852808062, 366621317, 147120965, 627409287, 827705569, 198019366, 112335973, 960234718, 821517698, 813739973, 579951810, 803465256, 529085120, 93473212, 865907123, 194558992, 327097170, 517650648, 456290477, 742309698, 741976106, 874671779, 737245842, 594062940, 922888771, 421381435, 363480037, 900332077, 117114123, 212383249, 334247419, 341276264, 354174931, 800142972, 387270323, 28492171, 87521779, 281036652, 710644581, 562042027, 889985964, 99958602, 78116150, 58358321, 130463226, 201493329, 849462522, 530023994, 142300007, 513198975, 552465398, 232686201, 941383211, 98712250, 502110518, 602728074, 803108485, 526158446, 471281899, 648513048, 316088070, 294887972, 853077874, 11110195, 652350458, 416914385, 39059034, 215438924, 574698289, 341564767, 381421777, 141635565, 756639606, 382057812, 471087337, 820376606, 278494659, 211454869, 175790702, 780904758, 287541454, 843079161, 230085807, 187615503, 432016458, 559107431, 190765655, 79380439, 261415072, 890180431, 145303074, 420644754, 810053215, 969972115, 288178659, 722908591, 649707667, 259477757, 750408071, 709804692, 710671234, 641000562, 324593808, 296948551, 262491174, 596129518, 340883998, 677993504, 625833624, 429600480, 108440688, 20499747, 308154133, 543522083, 850721045, 403162130, 142279709, 570338177, 650596139, 46650173, 338160934, 615033555, 684102265, 617280823, 972244654, 840478447, 970348554, 145101938, 865033161, 236260567, 969119956, 934301688, 424554547, 231038758, 850198538, 969200732, 852023402, 690138012, 866915705, 738939698, 614021507, 467595535, 343611568, 188729245, 821632245, 425043174, 366948317, 151625973, 793583559, 265338824, 330655206, 63212393, 444145135, 355263180, 311513232, 437738974, 442641814, 188351797, 150360878, 777469855, 842688191, 865811534, 282418070, 855508034, 153117456, 782098371, 439883400, 471617596, 642971844, 142086980, 30241699, 145175291, 394091787, 748554806, 473225953, 498367013, 831334985, 975795070, 998058026, 689417371, 26504817, 300450336, 300229093, 851931284, 508346609, 51831346, 846549905, 345123479, 43817505, 501510236, 779207948, 338615833, 439284032, 74037966, 197260423, 985053579, 955778936, 831574073, 476202648, 781421599, 450997196, 673289160, 777206007, 797238290, 589433718, 831364788, 819112735, 680025370, 703327362, 491117414, 970230411, 827826581, 837476683, 98861148, 913120371, 525906049, 219551069, 259722068, 798222415, 328021215, 777432333, 257826397, 390295618, 644651150, 978262810, 538651310, 948429124, 895217652, 373839311, 161604807, 844862838, 471584257, 433837937, 285251855, 815555705, 33899226, 513406178, 737661851, 707917190, 336843845, 93006104, 932838409, 871506684, 257053559, 624282968, 418437372, 387814074, 229452884, 677364527, 133960332, 326366663, 747612198, 721312213, 532974921, 759517103, 617132033, 870993502, 675363307, 306892335, 741085638, 202167093, 536410810, 778007463, 949174412, 241944772, 188476817, 503506561, 255941798, 481916219, 550023056, 103239680, 153453829, 42189439, 438824312, 286319066, 709177403, 929652186, 538418352, 329676810, 50176482, 887910225, 864717866, 581715900, 785216566, 372667512, 980797110, 132939210, 93478208, 248804691, 221851837, 246667619, 359377104, 863624795, 900222516, 579040363, 185151274, 803910113, 729005420, 444710353, 989637206, 242239113, 2864095, 987893096, 622069670, 210071449, 211704754, 422991762, 283795902, 279167175, 646543357, 342558070, 41103059, 40203798, 5643678, 497448458, 906033419, 133719611, 847818348, 619097592, 858928381, 646469185, 671824437, 491647510, 99985984, 814275056, 818001639, 420174296, 608962048, 428568743, 384141194, 342694414, 450487464, 203921073, 559248495, 598388348, 399069546, 622303471, 30756007, 254653238, 839101585, 119467502, 531847461, 321644773, 810398900, 709226391, 984659568, 589722167, 263217431, 393353415, 245326053, 444331822, 370464995, 44244791, 879238094, 940513793, 58817100, 173750590, 799112783, 777971125, 630346234, 938646010, 209420741, 231192630, 981474879, 601498273, 884889040, 574743078, 266696005, 398531161, 316874335, 712831986, 627886360, 248193998, 589446125, 818609513, 263899588, 200832713, 803812478, 49812038, 750287182, 235639792, 328818861, 413207590, 519055604, 225496589, 442466862, 791306309, 556099682, 411758447, 501772685, 237668207, 762067977, 473800492, 803856418, 790599671, 313644366, 216570317, 748740124, 297048886, 920113354, 250859693, 580535218, 810312058, 782777929, 998278798, 366897263, 970731892, 936233423, 752440502, 966183397, 722111554, 331231808, 890998103, 195884450, 120907567, 754493751, 676889588, 920919027, 301441636, 976313964, 540111647, 807638119, 22760713, 146213660, 492228022, 109145417, 523040265, 749763308, 494637233, 542741172, 74667181, 137028037, 163067444, 215373926, 878179931, 164766908, 250569816, 795679826, 438208677, 990464244, 565716901, 336435764, 34061006, 190710694, 465843787, 825470194, 349604543, 19094694, 291902544, 524760940, 535033750, 696383214, 371409514, 26618118, 248759549, 34668033, 884681506, 499807951, 984262433, 572387855, 983185158, 968453796, 503427135, 888367363, 898090300, 742699280, 849925688, 153037320, 600600906, 331318245, 770601213, 935471641, 497125448, 735760750, 601636613, 857555770, 690643212, 535129403, 816664832, 564531732, 506421734, 998790858, 240737894, 119907989, 731756356, 215844143, 23931830, 631262442, 760552468, 36212607, 578898666, 347113932, 153977143, 239663501, 667509174, 497026076, 655986877, 860297992, 263290336, 235774843, 872200575, 91684046, 332327082, 112988598, 658352531, 198011757, 331430707, 588864819, 858211864, 12918301, 909901480, 398481216, 296428882, 967185852, 32188641, 811911821, 870808912, 173284637, 123603124, 60185946, 603177950, 631555949, 530830139, 251613182, 681513344, 355936113, 570828732, 424954061, 377644961, 343059754, 852467790, 637454698, 739433280, 340893177, 637838607, 128145759, 487147793, 781176189, 488151841, 671085629, 902972633, 763978518, 799029189, 719486763, 371866328, 349912616, 178187435, 530065888, 906289926, 234456068, 822624941, 805531907, 764879707, 902891714, 237892057, 86469822, 505239214, 302675875, 930707353, 824506233, 51472519, 478044302, 265816554, 431183257, 517921388, 117269343, 281160758, 983778522, 196748917, 731893803, 797567396, 813354719, 227067309, 630340, 633277786, 850643853, 668040576, 503884949, 760564710, 371286175, 337594921, 281653205, 706545753, 229970009, 116808469, 827523936, 233204382, 777298577, 369294056, 905023959, 328265551, 651510416, 112116582, 499420343, 743805372, 794884967, 605753246, 775934990, 143335906, 103029437, 500088667, 129906725, 748701010, 467711809, 274582719, 76199214, 324032623, 671280300, 298789393, 312923431, 974099790, 544965748, 316104002, 768375730, 478317938, 37830617, 390370026, 69598189, 371692033, 882624144, 69689032, 818499045, 898225053, 32659554, 5461130, 23063269, 229349123, 309172856, 361233652, 46165466, 194967633, 243860994, 626701702, 97091088, 633835796, 79499246, 113520056, 12068671, 909414351, 695535232, 756936319, 79097795, 376957699, 497558287, 994275809, 855892469, 667162977, 560483352, 709722308, 828894998, 824808219, 344464029, 234703445, 496155301, 733629195, 537394635, 564096527, 513518610, 547849218, 154717286, 743724482, 780981055, 704136436, 754894323, 591891440, 973069789, 967231679, 480500899, 886866749, 10990672, 607878976, 490133812, 708918441, 319858879, 636746716, 957857063, 574420466, 206755404, 367023621, 804671986, 52891863, 467051447, 550560888, 20408558, 482663404, 711319695, 595783288, 22500008, 339554333, 815247286, 601543751, 345712862, 136291977, 305014018, 152209466, 663025283, 693381969, 692258789, 866956987, 625886897, 69780252, 192450751, 517213704, 107499777, 461413548, 11406803, 99959165, 883431162, 472921325, 440278027, 634312965, 685055655, 888116579, 447606400, 317159470, 610183080, 262211283, 760251155, 642903632, 573683775, 429734816, 276860178, 616526788, 529317626, 823790328, 515579165, 57594904, 619929708, 662575412, 166503448, 865909879, 692914109, 253621992, 508109696, 77677683, 255772867, 501912656, 275252344, 397436086, 428049022, 422170525, 84224987, 524413275, 864853274, 89322645, 902774564, 418041614, 225220581, 840222805, 216020222, 478255104, 955071245, 142681, 531286923, 984865068, 740260095, 215627877, 788889535, 615772860, 492918750, 281069023, 877746931, 652128834, 103319581, 702396619, 505088536, 576548912, 146045169, 799512292, 452981791, 271958026, 222987491, 785790149, 993996620, 122586624, 491550354, 101742675, 215170085, 347215435, 803733489, 125689377, 994920110, 310187285, 811143603, 501301307, 99916358, 580811364, 632116085, 570511259, 998058431, 990190833, 423823206, 158620868, 667027373, 51038050, 868235047, 496814115, 509696383, 199294089, 273440729, 146725763, 245994685, 75709260, 712085886, 782053889, 372182921, 56334055, 514972704, 255282037, 138082992, 888036856, 361783968, 747445946, 513123062, 890236891, 52246329, 653619919, 744102898, 670522359, 625335363, 618756269, 676183624, 281844583, 159800656, 467630446, 446244338, 374230338, 970774999, 532744456, 91717268, 406039554, 470933678, 756549196, 745451052, 852519116, 584640574, 714506155, 576205120, 226156114, 901035370, 641954919, 521893756, 103827318, 781127950, 968216297, 795157486, 525197647, 314378744, 532075542, 882953688, 872146726, 319843780, 329710585, 911521437, 809860752, 564615591, 262344337, 261319688, 377661065, 878230816, 654587459, 619352602, 428083275, 2795780, 879920139, 921006040, 936417158, 837707744, 362046872, 538125601, 371574544, 323379782, 925506022, 311401460, 304632895, 154169924, 312819908, 53827496, 362615174, 317538593, 125459684, 903815854, 555390241, 760017419, 927471002, 220349169, 780911656, 827454619, 979803002, 365811303, 343627097, 848267610, 354053710, 63212208, 54038363, 503358615, 705010872, 27555106, 371341793, 903152381, 988813898, 276299458, 929531200, 845364210, 229224164, 234487480, 799331267, 472839479, 119702250, 395869068, 964134267, 632643245, 926111977, 351674799, 707697067, 712151097, 400487954, 612951713, 262017009, 484221032, 581763681, 784322647, 255307201, 382200887, 484332630, 955348032, 227491397, 436643050, 857555241, 858603399, 594629097, 426682155, 969052352, 34100701, 806001478, 814790344, 260512894, 641223443, 990543429, 90914121, 996917671, 170545754, 872067347, 330639090, 128447820, 877150426, 43315129, 291981100, 971724575, 588139766, 712327762, 284602232, 921685857, 734106450, 386405369, 91251359, 694036424, 320514118, 693318303, 552900210, 776667958, 565159253, 758991274, 393313596, 419108296, 787852084, 668928529, 643691203, 213160442, 184927739, 607727777, 35273121, 825319576, 332555747, 18098459, 988707552, 183074684, 36318189, 822493159, 554232990, 776674007, 597917812, 266787910, 903717062, 197304693, 271406077, 635372084, 437480370, 489348542, 694237230, 121029008, 784670537, 286198474, 634197283, 474815210, 863203811, 743847157, 536478818, 382698040, 639503007, 300641250, 979219752, 108443146, 811727982, 755364616, 871183457, 119977866, 213220615, 50730481, 475641180, 378772294, 165001599, 956756421, 241950481, 218450135, 275584713, 255687197, 729295436, 778032076, 134829581, 422907716, 751413351, 173689452, 383578174, 385496670, 774429996, 445233279, 749212509, 228812580, 413093362, 125287109, 975402716, 533989186, 260690346, 645525555, 408162657, 551538769, 685659478, 596393516, 837348972, 406752185, 372312455, 311782792, 851195184, 185611996, 559071501, 922324696, 702371018, 170159349, 176487994, 118813211, 571170359, 742270506, 618500585, 424128396, 946432128, 209528839, 604069090, 286333629, 210024258, 957474135, 616293180, 563796093, 505352880, 552429540, 826918186, 173040427, 20040720, 181801159, 596764871, 861688899, 701152991, 780000031, 579633702, 373457387, 724512713, 34458565, 416813712, 926588587, 236409300, 143811910, 706144150, 764321792, 918839781, 725868025, 536276421, 997160266, 316581030, 511319269, 66696226, 119739865, 410249163, 42494031, 583716246, 812338081, 152828439, 869188602, 459884289, 438488740, 622408910, 748020944, 770929580, 960594567, 41861988, 161247562, 751275595, 526332751, 442851952, 798349823, 644573181, 161506827, 440689897, 19793413, 281368357, 846456739, 798807863, 968512975, 766518433, 66337629, 125886006, 983867218, 729708003, 381425934, 468960210, 565197275, 745090208, 172047826, 77232874, 526167202, 655410396, 310695606, 91170143, 276966586, 204284692, 675536445, 204471028, 117096962, 885607212, 803011598, 651499073, 531996252, 491141778, 975091404, 526059036, 744151201, 950213420, 116436628, 380302527, 797968512, 689958385, 806962438, 48109498, 811300242, 591045502, 432041405, 829714682, 168478440, 461251506, 728421683, 445372623, 787752183, 665704593, 834465245, 605486887, 696057511, 834482669, 76483047, 798746696, 547483561, 868753678, 631821583, 542754445, 904360778, 436112669, 813406635, 305908610, 629183638, 502614015, 616168447, 189386269, 208146332, 581308162, 836186632, 589400499, 40692101, 447035607, 463266807, 177351592, 285817382, 443376122, 913008587, 118191231, 238174920, 317506285, 550319298, 151988598, 409645099, 623151893, 178310679, 150768164, 210472462, 372121516, 315453554, 465721731, 424310306, 546647699, 40337884, 928458826, 236300590, 957964142, 626797580, 830941102, 686931802, 841017788, 582020149, 213681350, 175444520, 762803112, 192196207, 299902053, 121963311, 977233833, 459951411, 225309830, 175908338, 475275820, 272582659, 707962870, 991345415, 769833206, 927899680, 555162315, 275872890, 884660776, 565553192, 881772265, 39448331, 977716016, 23464873, 50669945, 911414744, 4323320, 948731368, 368443884, 533410955, 825061733, 254804319, 2880941, 858938655, 682669188, 420171455, 629573867, 781234134, 126414821, 214377244, 19582606, 142149746, 108214613, 236899053, 871918654, 31499526, 659163155, 860845070, 658521096, 888010469, 12270872, 52678270, 691146273, 211647427, 282093601, 141041611, 842621006, 888833988, 789683911, 365400252, 908474603, 846720278, 57111794, 375531281, 565854564, 434240728, 53215296, 394827307, 885311552, 250261842, 14380640, 278521592, 211618697, 71017966, 425674561, 300685705, 71182492, 199943527, 867128667, 646107420, 246590884, 435130901, 798226122, 18411871, 3289051, 975850710, 339389418, 152717327, 697084191, 888437079, 809986806, 512865204, 576435150, 944611832, 652753079, 501954951, 187460169, 836030567, 775218082, 621831763, 448154494, 882870037, 373370171, 267059002, 349282218, 294712109, 218063345, 423355393, 498573998, 620217787, 370994050, 136512081, 991698740, 970848069, 155500522, 997637549, 743868871, 955423197, 956046580, 700011637, 261081526, 267978102, 434579734, 958247010, 193641941, 767051989, 618783184, 8068367, 812355756, 439513507, 787934316, 587398278, 539360333, 208331661, 397596349, 661432686, 742146866, 21828093, 414728190, 304145797, 407647214, 13211031, 918532721, 257850744, 317941087, 397332093, 143629647, 880557616, 718133532, 523584487, 179795400, 64022320, 905860322, 375647265, 163335103, 596876473, 170580943, 169902506, 95859091, 627257108, 882787049, 796436854, 252594074, 708940538, 832500365, 652396892, 179395594, 943536416, 103907844, 619856713, 928897202, 729710731, 718978081, 637660907, 450939572, 888122157, 743113760, 154083161, 424345138, 716671043, 429530522, 666874572, 942181696, 126564601, 228952466, 534860484, 593408362, 482155855, 932963583, 368437, 222508679, 410237308, 37455989, 352703765, 400778056, 719273488, 899300398, 25342284, 857276696, 285047252, 6147696, 254646420, 374676251, 237926022, 697379244, 101518045, 339439559, 903462687, 98923915, 339315435, 478520317, 467656159, 402456753, 108230219, 667327474, 114093793, 364538607, 895868372, 404553087, 337914177, 395600661, 602938551, 634068218, 716619738, 204391617, 180032210, 416283612, 279677483, 913970193, 253607356, 514547322, 483616649, 324887702, 342713741, 134026038, 326824727, 790472455, 457298423, 224501786, 537989516, 148743140, 588113442, 298278248, 646593607, 321769178, 72053698, 322460492, 331635396, 258865748, 824170795, 479797291, 681534257, 180674406, 514969179, 143411129, 83749643, 989640772, 823477331, 471839709, 599710495, 358344148, 474159103, 785150739, 714632587, 493544496, 678795997, 420818577, 371971991, 561666517, 58463873, 440712192, 869049663, 988975076, 270552238, 932137016, 29459773, 287131493, 917145446, 158093017, 101701440, 701091931, 857281745, 399158136, 785068361, 606689894, 904062017, 339324502, 616796886, 366797514, 358871345, 353745987, 289900049, 954911196, 651489337, 864944128, 726581846, 774480194, 442281690, 180807937, 876060947, 12224797, 899249948, 670881937, 383877002, 612900491, 543504865, 120832555, 581890892, 364374870, 355549899, 660103963, 619064087, 988179677, 726991886, 276850311, 773616545, 54785983, 873265998, 429857800, 692505823, 40629313, 937120548, 148787413, 407868713, 336058119, 531560557, 714504806, 710438856, 539813791, 680172561, 962345675, 869012730, 879134687, 679771714, 268789329, 827512346, 276055750, 980823225, 595282913, 937417905, 437085005, 898745479, 25949650, 944485837, 616040701, 701894248, 43443131, 726770090, 429199934, 815557470, 17857513, 403513463, 632340240, 652412477, 360074276, 344434692, 173768931, 20277137, 320892821, 515557308, 847122333, 158313642, 212885176, 91385674, 404189287, 481535425, 229869225, 568823604, 367926582, 856931560, 838059738, 7847131, 278450610, 335072418, 91465550, 532367186, 581511813, 452963827, 337821529, 901944639, 834787475, 742936703, 33256558, 858349837, 317380616, 936815415, 931615405, 913534669, 674692767, 775068345, 30359620, 522957583, 663429335, 868487744, 326124836, 840272897, 303170627, 455918, 782198443, 722692065, 936621434, 276132998, 611668389, 420797703, 763926569, 249370819, 946336308, 569513483, 588359411, 585681317, 28485706, 557427220, 914222108, 545815348, 789340202, 41152066, 322809456, 420257253, 989040813, 18827002, 811899701, 548526209, 607462815, 796919300, 150077781, 45658272, 148862726, 926040257, 220482481, 400851389, 972398012, 254067064, 573360529, 446608164, 880687714, 546883883, 662947343, 498575284, 825086531, 220278427, 51440645, 705414915, 767875200, 756046347, 141446377, 810246264, 965373308, 360307446, 922012195, 859211979, 882849644, 640058753, 550239147, 655339609, 484171624, 464160632, 238049051, 792522303, 992998832, 971907804, 133639984, 302861755, 208003986, 874386102, 566349097, 431842243, 419785848, 631111556, 362505992, 279072434, 523907137, 987403368, 249253592, 672492841, 836206726, 522277839, 274459003, 399642957, 903197028, 714174136, 951771484, 60096420, 112236326, 118653517, 382709035, 465632877, 222224434, 738674438, 105246882, 907588782, 773822451, 743126306, 204081120, 367987177, 805546845, 900681352, 611573827, 869777292, 376399627, 787912790, 413963812, 542538690, 169086383, 139959926, 340148655, 447505822, 814159003, 590666823, 400957063, 240077505, 274864680, 295386410, 70236921, 777063864, 734416861, 833495945, 767363819, 58176336, 262207351, 454375154, 714644349, 615116286, 259148972, 158932955, 188881819, 370359473, 502831508, 105503785, 372959175, 428271890, 758496682, 789563659, 35485380, 39463152, 991165003, 453991917, 436555808, 632268450, 602447889, 896178293, 17522236, 345416788, 976049140, 836228043, 722446972, 391614156, 154508852, 891828608, 214443610, 429522970, 317259564, 893035972, 297843454, 109363963, 761630620, 490645821, 127574546, 172257414, 116064687, 584650577, 884613575, 640700180, 412351035, 372916743, 590338938, 168446846, 390143570, 66537223, 670384486, 850114465, 43574825, 386529829, 970273736, 798585566, 457823213, 331045874, 284803949, 370875250, 133325912, 827153550, 538497688, 768261962, 467152019, 777235520, 727454819, 5699568, 72533577, 273942205, 423917077, 782609636, 266737212, 681295660, 807767806, 347710386, 741429210, 676455464, 768903769, 183151395, 846222414, 47407938, 101682460, 780296536, 580287597, 769008567, 919967696, 813109367, 854356494, 811835132, 187058231, 31996689, 593552265, 890336895, 366288381, 992236447, 572637964, 985584302, 543544569, 432029627, 486157257, 443535286, 215439170, 731660772, 260962792, 710112607, 909134777, 61681817, 536271275, 963401966, 546824527, 770303133, 325125132, 857342051, 763639671, 504386673, 121783562, 456308712, 175156507, 897410553, 270917420, 133791449, 249440009, 159326706, 809794384, 871926236, 346306765, 473343844, 122887336, 776577948, 56317536, 598663298, 497570494, 547465010, 439478610, 983909675, 638283177, 916705849, 239480120, 458014087, 727319543, 200744976, 515361760, 244724755, 222814170, 699691191, 961900094, 513517306, 536003141, 143362448, 422711081, 322589415, 431968534, 366164395, 770235346, 440909351, 354787124, 908650253, 973800951, 872654162, 320406381, 512704036, 949735249, 258222230, 387935464, 535026542, 25253882, 929988499, 387315838, 688469552, 559693564, 872120833, 291344749, 892408165, 78991936, 801178947, 593910251, 976287508, 958269430, 636836060, 200096150, 300462256, 544975549, 494947606, 261450743, 946241448, 459475586, 357889859, 491754179, 617229260, 232315933, 920645114, 874358482, 300704991, 22919234, 647492420, 656267174, 705305519, 805256465, 249344912, 593260711, 384348870, 946011411, 678664105, 553864849, 747156527, 832596263, 806549708, 389938777, 427184391, 906483995, 408274950, 786200314, 143444075, 776220285, 16191598, 141352554, 983554637, 724529320, 534343334, 215109787, 733824022, 683210703, 805299721, 950465958, 697973565, 197256415, 975898075, 518796798, 522405126, 195985636, 222213833, 628138895, 668528107, 637228698, 971735329, 942980477, 461340969, 731804857, 148298446, 429289714, 661237640, 68266836, 106810772, 452539973, 736471333, 140185872, 899493870, 373825177, 199081333, 163792313, 507579555, 941068818, 814073585, 322240841, 868214202, 611544012, 400656611, 785404595, 638052840, 474060207, 730762622, 79867067, 194651042, 680484422, 584928618, 468430184, 460553559, 672129979, 865431646, 69601133, 53383385, 745515016, 92372363, 525067294, 710341385, 972876177, 479393216, 68139347, 425079528, 627276110, 382992882, 974487710, 710330226, 743942782, 324572644, 57321192, 834046092, 659955508, 787352957, 762131349, 739037929, 698116314, 145517960, 689304064, 111570577, 591734246, 207647871, 595090827, 833981257, 272346488, 3522485, 741702334, 947440403, 123328918, 762677509, 809315883, 741770002, 681495318, 344770709, 456250385, 583550736, 388654594, 910016366, 884705109, 16983083, 173103359, 167646244, 205022806, 908689319, 103444271, 693061445, 550282293, 283534230, 71818933, 360606660, 541817852, 203021125, 334157951, 343369189, 53471893, 159123973, 297354754, 279375201, 93119048, 439984728, 826443271, 18840097, 435540494, 82982118, 211544082, 692375572, 242277898, 40243692, 871191499, 811457067, 501142676, 367978570, 183278586, 250017918, 830164344, 355615206, 597259975, 200619794, 700634017, 284193920, 256959032, 397754207, 407380323, 196203587, 563349366, 406189032, 2327265, 316695121, 997448234, 390461093, 710683145, 170506618, 266140763, 952051468, 963627322, 986243042, 792502826, 920700885, 282170987, 608627114, 397832026, 996231328, 683525539, 475793449, 295922669, 994259596, 862589978, 319826471, 140007719, 767303045, 318687100, 372857123, 198532439, 641276129, 602329429, 226943688, 635111726, 223233601, 437408182, 753012106, 943304873, 643924205, 982461930, 313198168, 866610207, 91619465, 688083694, 386919843, 688716281, 453967596, 115689595, 662797484, 309069756, 578881267, 952060609, 436522517, 83905110, 547678098, 220734859, 786315526, 786279860, 283520951, 996697347, 829910782, 366487998, 788411325, 253316459, 952017276, 574623537, 757824343, 504324841, 48298395, 654474861, 557695399, 848680671, 460640374, 43258148, 443229598, 6357316, 392099108, 396758006, 143201233, 263904994, 852737553, 935259338, 445442469, 107280798, 791481425, 749473758, 256772443, 626327744, 961336476, 309036579, 90128836, 570245001, 170563569, 945235616, 873706833, 555146383, 47434288, 401217112, 745564999, 15298917, 4131313, 417384315, 795865587, 67051082, 39931674, 460625095, 319881255, 544769538, 285789128, 655939320, 594856759, 270300842, 624527551, 883991607, 764862459, 10484629, 785346116, 518259719, 780804556, 966640520, 828242718, 637470836, 783684573, 615006977, 359002341, 654384109, 690355711, 126399365, 91409158, 647530802, 142431343, 334140906, 350133118, 891301826, 400807955, 259801781, 663568000, 22352086, 296966333, 939484307, 347678276, 545181186, 374690973, 255093275, 885052984, 396231042, 348502768, 288190611, 756657527, 515209647, 147268087, 933112020, 939470878, 485657697, 58859510, 327873449, 243876161, 867499283, 731047531, 768221507, 362690300, 132985292, 715344436, 109712611, 840742796, 924025675, 155590177, 603078198, 967216950, 790068178, 896933426, 562983098, 400543784, 165725773, 233787789, 359469618, 365953162, 810038480, 587306656, 829083749, 663288640, 672295399, 968963740, 124516453, 368277826, 972255894, 43012805, 746350567, 712911545, 161557169, 129884066, 394231187, 545422458, 206009581, 908075922, 509798742, 732700452, 24690879, 616332353, 895984550, 4770727, 120653278, 387232774, 438299461, 764507979, 416984615, 154054603, 855861676, 771003532, 163428386, 263897657, 461247474, 117429767, 204007610, 62965816, 583072996, 149189711, 510269943, 177362624, 920251828, 711022409, 801232988, 532894659, 282233372, 911030331, 847554371, 996689148, 145250781, 241430691, 912000451, 566460897, 840431371, 281806903, 431951765, 721343201, 680144859, 230939986, 264956519, 223103815, 757762376, 93805148, 234522368, 485691960, 600319502, 584730011, 29559825, 778255475, 982600817, 449605630, 595656860, 130434982, 349094078, 421447514, 709088667, 980868362, 269427366, 541104537, 736447833, 77168967, 532700369, 390626510, 685701301, 699997554, 444354094, 617177156, 702470650, 964203114, 278554455, 99567205, 658569419, 781160509, 284590554, 269168959, 838946801, 856767321, 17867624, 780611961, 711952369, 468397262, 327410813, 357778234, 165355953, 356438252, 722053626, 767413315, 232138172, 978664734, 596246614, 286116562, 137926675, 134522661, 922037968, 17939769, 657060579, 277544575, 988101228, 671639274, 165762147, 298156963, 254766764, 464067695, 916232775, 641340747, 226103292, 432707531, 800602278, 851966973, 527187812, 718223896, 211588928, 615284938, 934559557, 422952165, 203019455, 863209754, 163574735, 670787651, 900399860, 118064192, 196379677, 839498588, 922494074, 274248942, 760210785, 858357263, 891081060, 614515246, 415536672, 489355563, 473708800, 207704700, 840518597, 577732826, 971962782, 649696584, 746290340, 54473914, 547941165, 877775479, 597742913, 61913401, 451071575, 203265728, 360015991, 247359537, 779904336, 484596643, 248350550, 498796586, 244571582, 422611872, 533246602, 336377534, 155879724, 379046423, 243332101, 345988859, 504295960, 72304327, 972651997, 510875745, 475811172, 123505199, 707936037, 475231575, 639482779, 521542952, 24777214, 464458098, 746266043, 817348704, 425880458, 448923302, 658202140, 439785667, 35306575, 646055003, 552022910, 813071893, 127987656, 97146394, 534149939, 743114995, 472885464, 891888633, 263081670, 297590382, 303408783, 445033274, 913303644, 834143416, 661131204, 552502347, 917341930, 901835399, 108980672, 877002743, 70249578, 4234414, 63994150, 724863468, 509463182, 444128621, 30137059, 660637400, 90210640, 217543264, 202421877, 769788016, 107303712, 58694592, 871956065, 588556031, 127410502, 14042320, 442615387, 96190709, 252505837, 616095264, 35085281, 683353955, 312160271, 873584435, 243091095, 751046857, 966584167, 673063855, 863834287, 869914883, 656909260, 195615088, 589192276, 97497114, 322647097, 427131737, 73536653, 996873422, 445991206, 768798145, 880697609, 978894266, 842442771, 627690785, 899555142, 317630926, 348455553, 389548681, 357193849, 582535597, 26059540, 376400732, 643725269, 459052874, 974623987, 639241308, 566453209, 383480565, 789919332, 176570539, 469885712, 454436046, 677569269, 348197933, 91326010, 968947311, 156735873, 439877863, 116375791, 166427524, 430792509, 169485007, 103049444, 257327417, 970994447, 757754314, 543286055, 755274968, 740719504, 714458751, 417277969, 956330019, 797603403, 975127617, 999470406, 719170732, 631784302, 137081584, 547699250, 694601327, 323684128, 57536855, 186268930, 999786899, 338453591, 532293698, 296128340, 451406596, 400944588, 790272202, 520073254, 542487438, 47418610, 56206844, 499197679, 265249198, 528991568, 131583244, 271451856, 741712770, 942553524, 383240685, 814001316, 646360007, 658714098, 787666769, 454581175, 674583098, 924261075, 186563125, 905466110, 216422120, 442692857, 842809066, 9605195, 436595247, 961377633, 773793243, 707171363, 98070206, 555788716, 192460208, 817297343, 790586793, 254911203, 168221284, 618230782, 492386185, 934927577, 572529409, 18088981, 219557178, 918547815, 643604426, 775812156, 163297413, 797766815, 275839108, 859378706, 233907285, 749006176, 757851736, 466256136, 763641233, 925376163, 725379046, 369616023, 26824321, 28705503, 810769397, 144523072, 461715790, 621879917, 278419214, 607625440, 104272492, 933696375, 628792732, 639478457, 563711868, 942884423, 642460659, 555007165, 497569399, 621151180, 560646343, 523664767, 286769174, 982564214, 260676319, 814917682, 852172714, 469296671, 626900044, 430456340, 143518430, 460407135, 777382218, 765778718, 734324040, 97774266, 305365408, 832332337, 676358486, 889340731, 756052524, 637853159, 263054172, 170319221, 753122953, 727504943, 807385127, 911046678, 581553705, 250558429, 469604323, 520608583, 664868910, 680354980, 897533243, 43382196, 349240281, 412702829, 934405894, 972466568, 309212663, 755763111, 480529892, 408027774, 338525860, 192394416, 171212725, 423317745, 833066378, 579698309, 548379393, 401341208, 81154964, 684995295, 273695823, 227000911, 899435580, 247776257, 342555044, 580593074, 36849714, 879818045, 267778990, 969346140, 574977498, 554752487, 863385776, 365182432, 612248801, 764957437, 653886797, 938295064, 284561525, 833129415, 271068518, 361348147, 340525938, 888383436, 558595832, 679957308, 346608423, 646186699, 585126701, 951270067, 694399351, 961917552, 489205577, 972170568, 572699734, 188095862, 717771987, 668542172, 327789797, 922671330, 712158524, 577481433, 86656204, 30697784, 295762512, 112373085, 136998322, 615166007, 358850280, 696361603, 665161287, 958639364, 399746239, 671411731, 990376711, 902494721, 349799049, 118623463, 565222828, 500100700, 130632487, 903697713, 697767099, 634243785, 911275641, 449335537, 37907393, 377627541, 536688347, 365000841, 702758125, 786824116, 210774790, 567486520, 995538005, 608448676, 576943447, 741576263, 933230446, 780309820, 311090339, 795178000, 571171359, 924087624, 425646235, 349125180, 711595898, 180077013, 804045427, 457639765, 85396834, 304349672, 305313028, 428983890, 794603168, 270120004, 778608784, 644446989, 267938209, 878991847, 168816165, 257522921, 24226725, 153647477, 943891624, 529006777, 18114559, 676102770, 7800410, 915459691, 553017996, 988002301, 389938543, 433284578, 831326291, 371331994, 170266272, 851590796, 214035762, 203623717, 492574008, 119105845, 243711329, 517569598, 985671396, 10021815, 986940766, 287189953, 440184040, 462040111, 916826261, 885806804, 222942943, 720622183, 718032344, 588890642, 242840369, 690910748, 535235836, 254240007, 609616198, 792337902, 183734330, 631382279, 306303793, 184738844, 682713146, 702015125, 94806936, 555213323, 621604439, 774160992, 119424271, 41333500, 190494311, 329390437, 148513839, 879018929, 725506441, 231124767, 817331693, 635631497, 743825175, 88108013, 41759199, 942558192, 731803606, 920825166, 155786455, 329943804, 376178297, 944963783, 773618681, 522859043, 804720318, 908377302, 540410087, 130139196, 24777907, 175682313, 911928861, 931621679, 821956718, 342040993, 504130967, 311270136, 361760544, 81892987, 255800260, 168659575, 726173062, 64657014, 152163372, 52980509, 868347486, 638920481, 343446734, 99175864, 445655267, 316741936, 982468025, 970953178, 936314792, 926764780, 897709084, 715032392, 704537435, 507633036, 529788153, 994975904, 270126030, 596651175, 244283501, 254850756, 364968072, 458377977, 75106517, 7395615, 567257185, 277127041, 977642343, 606734540, 40011335, 340608922, 155195099, 289217908, 502910127, 744320964, 424130371, 192202770, 15151739, 567481463, 671411179, 869282917, 104386012, 862442434, 693487344, 524570118, 318889216, 780699294, 452271297, 812718039, 63518833, 776417743, 917105311, 153590268, 20857904, 579378280, 274882928, 558335518, 897608198, 383194904, 983496343, 831057811, 733374710, 838759815, 385891757, 759753262, 128970579, 945483233, 921485969, 305301558, 183001793, 185594426, 991003100, 756217592, 386363330, 230838413, 416534383, 350082452, 197724966, 612916443, 287973602, 708544489, 727013685, 422421497, 68825011, 391385436, 621033619, 276592090, 497657395, 46804291, 498117069, 907617954, 848726448, 257487934, 759515880, 277937946, 205942566, 900787006, 675281475, 194728754, 766822993, 300635541, 690015805, 233714950, 697717176, 644796291, 120489891, 213741762, 607489980, 177900233, 716567127, 682303337, 100458453, 826297076, 815552433, 248084355, 628211939, 511355817, 358514581, 744511457, 156074869, 794408101, 634495748, 121174579, 828004984, 235864438, 266812276, 707928336, 350350560, 24126282, 53943519, 267987126, 129774202, 26336377, 530138186, 510585720, 393827141, 303900378, 978744368, 269949496, 723427256, 458838678, 56216438, 665103479, 597179555, 605181729, 578306763, 865495388, 453522888, 192765333, 650067994, 504379183, 733009758, 557182873, 716408516, 982364887, 786257845, 31741692, 727019288, 410635403, 520557523, 911419990, 4781431, 147086788, 744835121, 447928465, 721907001, 640713648, 13869514, 90484037, 57515108, 297438223, 363415155, 35588486, 334577040, 457246855, 558956012, 488287392, 522400670, 719018991, 36576392, 622707419, 842644451, 474214367, 66652407, 29647896, 160754891, 328237207, 300788995, 818203222, 224887916, 459969850, 985423340, 561360973, 962140592, 384303958, 973342123, 657388043, 730804627, 162192527, 954465380, 443863673, 904556921, 203828251, 870342886, 767248815, 254633151, 476319236, 283604851, 853849777, 440326324, 241306554, 702881910, 601386580, 127571661, 979455899, 373691278, 858211234, 748219960, 199046939, 895711040, 503137818, 176235618, 6107970, 882972342, 41706211, 76356818, 170152163, 541423742, 829253286, 322975998, 572187246, 64554280, 634801415, 89674283, 335945397, 686852049, 183934092, 572137357, 20395716, 339746901, 631163243, 40054652, 169198122, 345805087, 516787422, 281985702, 138831955, 802201370, 821981710, 670862497, 792437906, 973270219, 402279892, 580074850, 28470443, 294678437, 767837875, 666157517, 225286907, 629381967, 126929007, 876264889, 820050334, 148617563, 920695940, 889651832, 424959694, 76967514, 537651045, 581831804, 413093988, 976967770, 928128534, 469385066, 296335668, 279838962, 727704784, 863431082, 742460653, 588756293, 628539664, 639896981, 497167398, 726467792, 453077301, 61926836, 832944687, 755057103, 340841357, 902257375, 978508643, 431650228, 755083116, 549384447, 615983895, 998485087, 806391992, 157398537, 551791298, 172077677, 889992171, 995889562, 179325556, 2604890, 177176481, 387561075, 668160900, 139648047, 471518380, 245351149, 585620851, 525384925, 99757806, 267974883, 782779608, 130171586, 504932171, 64170142, 927047031, 466645461, 690448696, 337787984, 682118373, 413919003, 173463555, 797273837, 537648353, 57601736, 835568007, 965172304, 310047734, 197760389, 934908852, 64917302, 338833261, 630486669, 310031663, 875552561, 405959629, 431857558, 200790950, 638729128, 91296865, 44658467, 631192838, 918418216, 789740590, 649359888, 877467407, 255702025, 352178982, 171996349, 778410362, 553243596, 872599035, 250467462, 696594705, 762346301, 907330380, 745206846, 730845978, 367992143, 573590003, 355359281, 712854001, 875441318, 572069201, 23052423, 486166173, 976222521, 955512928, 623042720, 250625547, 341691761, 936397535, 80165198, 360513119, 642427096, 213083188, 834481540, 835500110, 755692571, 29201389, 333527001, 439989955, 516448820, 691929278, 863461009, 911833041, 437672716, 535585353, 278448366, 980740587, 856237435, 333390978, 454192659, 852527356, 904804907, 423220256, 496016439, 651971087, 700901, 958078363, 108924788, 611117147, 381774619, 445130709, 716455396, 56338148, 356817670, 362253702, 768566966, 281428052, 174301504, 474873482, 152316487, 835580046, 785149601, 545754252, 34993526, 12011501, 118218204, 240842785, 702537664, 602382325, 216492473, 435355044, 406443737, 283204045, 531493364, 962993339, 981395260, 947066097, 4059524, 576617064, 956450004, 689369625, 960382740, 491105480, 626717502, 421248911, 433074936, 28861474, 146592960, 352452955, 78614301, 822381867, 70756099, 809964430, 800047746, 34381548, 362927374, 608455362, 318918967, 144414598, 262850354, 165230848, 754463432, 606086005, 857407300, 682754062, 571832804, 544417452, 334537845, 931847641, 659593186, 265367318, 47293492, 978010288, 605319352, 545029145, 790723264, 73085148, 132959688, 901658391, 614783529, 998934895, 288316961, 304852023, 485825437, 929167419, 504635470, 837575280, 90545524, 224551240, 940481968, 424446184, 601001219, 414597404, 830057916, 727742360, 964924450, 311821323, 139444911, 477648643, 24700440, 423945998, 868766183, 455587976, 566129154, 655332874, 814142023, 200141864, 904509952, 969122161, 343726034, 86790786, 961613400, 891346299, 150755273, 930731382, 670156454, 243630116, 550181847, 591571658, 522284572, 452634054, 53743323, 196748469, 315380666, 410938838, 821744408, 167592523, 287170228, 702215823, 144514462, 846510517, 412261940, 200625246, 819381487, 600688065, 349200084, 19759660, 87516437, 588885812, 154408157, 920347023, 635010514, 586392527, 865426436, 295519548, 111029150, 778450130, 385300978, 382626667, 813373137, 409764208, 958171502, 340479144, 363739073, 545705705, 75497186, 741533639, 675280557, 424317331, 908738459, 549421214, 378230457, 158242803, 469924451, 6177935, 628808993, 65045331, 191494121, 728780809, 513701298, 454783632, 592806690, 242720746, 259155372, 500102868, 397560132, 902956921, 274738281, 475320970, 71588723, 297527418, 450825495, 495667462, 951623820, 336977294, 113142984, 646678947, 652844280, 118453548, 200761819, 960471231, 501271043, 160334372, 311145853, 173787183, 159438043, 523528585, 889975151, 487318740, 57254259, 643295205, 154341906, 535443547, 663821618, 568445518, 527523745, 561310191, 923858135, 908232400, 488411401, 832508153, 386923586, 534820788, 522407574, 798563299, 64030481, 795569164, 480048236, 375567808, 160150781, 769603856, 198533346, 505259538, 905548608, 327093215, 827579205, 249704842, 472635677, 770040817, 85477994, 443523990, 657792468, 425296878, 595385719, 317942676, 725853512, 465252131, 218099089, 705054, 189568513, 726470478, 365648532, 612388366, 811525072, 540375361, 615840006, 577154897, 777281281, 642830325, 812060225, 928820766, 210533236, 773392495, 623419704, 566265502, 709362190, 291271263, 896985589, 99787511, 250404862, 420195462, 565918755, 591617575, 406500555, 441552765, 675446165, 958344472, 744058684, 229524113, 218475141, 509792994, 515073569, 51551067, 333615149, 41322704, 690884914, 432339237, 132437040, 560813722, 247085662, 608727907, 852036050, 335975096, 619881476, 71333852, 522649657, 75872936, 83722080, 198131173, 896856851, 952773685, 386813300, 873498036, 289997298, 610760549, 619911109, 170160678, 861594146, 39273220, 539534008, 105233657, 730674321, 385388520, 615089087, 897337232, 356155520, 406138593, 333671440, 942246931, 801494710, 4120080, 584702335, 372176942, 397815743, 767710951, 784141291, 226820120, 250115662, 541453983, 159142298, 943042269, 162700271, 876413718, 169465739, 822838603, 340080354, 462146861, 549135681, 578150049, 794826753, 992795978, 742822609, 984317786, 51197607, 231360903, 138909107, 547354653, 543705958, 874542995, 690479397, 202082483, 321214090, 803081978, 952641827, 921407352, 123027351, 477919578, 19140859, 658740889, 633869382, 478640404, 100867785, 303256535, 176888726, 797346737, 975425898, 661984911, 987057642, 627873379, 867555691, 185846823, 992266496, 514781328, 992318456, 529417863, 960587118, 37206595, 38297826, 228688385, 928759026, 855594350, 784038908, 751568010, 624704074, 290964, 512158666, 756228946, 126289736, 77302910, 562419321, 358269700, 543630966, 778334011, 22683459, 737107129, 896013322, 551935554, 908965003, 351055034, 503361267, 737478571, 357500016, 863568852, 492298716, 391027924, 941081770, 330726947, 435373132, 590693342, 677144019, 61924122, 512326338, 649345286, 739931672, 696276660, 730926652, 455072581, 251213407, 317001464, 426831391, 163074272, 352034146, 885631603, 823401408, 839324474, 164736470, 171189762, 209269343, 951386166, 630702730, 580276660, 314496432, 495301365, 126590567, 721309108, 643751542, 74025182, 34983243, 826351431, 855317208, 608942744, 803444273, 470517642, 799179403, 578399573, 709965601, 907809184, 251410911, 883109424, 266574726, 257756132, 787234940, 32748326, 794259646, 526957746, 869862223, 73518072, 700460549, 83687874, 673671207, 149293762, 924896353, 497796117, 28372042, 800069309, 342560078, 819628707, 373107386, 696126745, 268413483, 733001076, 740887083, 380467706, 194020813, 529126220, 84965155, 129875456, 116890587, 971203760, 127235037, 69085143, 298737690, 188335071, 314865854, 589641717, 747748276, 539448021, 383748323, 317330346, 986667577, 888699616, 599597108, 441545260, 835351333, 707053625, 519216700, 968774804, 528148921, 701162327, 662780380, 136034885, 131193164, 311656144, 278069159, 423611668, 83175724, 886411988, 868461960, 535561865, 154715308, 126476658, 761584605, 508157755, 780964783, 578438764, 784907196, 810493643, 319344623, 934097122, 950730014, 233378193, 770851486, 820213640, 226653078, 990331214, 788840505, 624886710, 417020519, 396677451, 857552048, 856709133, 336848997, 423196902, 632255361, 908713778, 813179845, 750634041, 543394676, 694929623, 313405362, 998085627, 432988323, 804637208, 626343325, 727743351, 757092586, 451503777, 225412119, 201512209, 240494171, 433847081, 953729888, 655811283, 399525382, 851835654, 717258918, 997272263, 207937468, 724045947, 803016675, 54705206, 962618832, 405823559, 100225569, 674366455, 64006322, 343918918, 897221070, 714562208, 202817637, 501332406, 370549948, 592030726, 118725806, 288348745, 375746054, 724215258, 457633661, 101020780, 731825489, 956241354, 820096851, 828391358, 894760706, 840551440, 314132703, 931385116, 151230097, 879288068, 639678603, 628383055, 410560469, 527187686, 12605914, 974912442, 924786505, 20921218, 230992610, 514965935, 122055530, 844289072, 671330347, 125964402, 37902695, 746384611, 582195695, 758142356, 622962180, 591360856, 506819248, 137909753, 560216901, 765256092, 114236881, 882427992, 961949079, 146535275, 582711199, 202209855, 818923970, 774884387, 24333071, 189366088, 234402725, 134163236, 815552718, 337594193, 316910632, 358816972, 218068132, 180810902, 147825493, 631488830, 147737707, 277267878, 124283016, 90930478, 259252168, 624755642, 899109229, 697608415, 178211228, 895231257, 992850214, 603162046, 53455555, 175953316, 746878052, 975345231, 540572804, 405121256, 27732428, 669954120, 245189188, 376647321, 412475764, 605339312, 535601986, 427686239, 914977365, 279458623, 642067549, 681037429, 595312007, 725559960, 199454015, 121635426, 260577104, 629768912, 194080867, 416695724, 246114941, 504033317, 194601033, 330554718, 853449713, 949867839, 114932817, 356106426, 613249763, 658905631, 613386236, 403175775, 321130277, 376324166, 417457546, 667741739, 815692405, 228259015, 624135050, 564186149, 695432898, 574666375, 526532560, 498115027, 372278812, 7727561, 511308575, 242087746, 464051819, 246505391, 423086075, 616700050, 492990517, 133788229, 824226825, 69234797, 928799746, 289551014, 200173157, 176009453, 944312294, 135547703, 24488174, 732934251, 391812405, 622538928, 577259244, 657620238, 961792822, 66187534, 644749521, 755611118, 828862965, 591511693, 297776507, 418298199, 970229760, 86503116, 705372603, 469292937, 319287645, 336995750, 374076496, 964586261, 919194311, 118243589, 821497761, 681541185, 375430224, 260261703, 154644123, 253177812, 535326923, 431303305, 955673695, 299454667, 434081946, 491150828, 429189500, 978614793, 776792041, 985284732, 766423117, 601943728, 290207775, 506812579, 403169809, 794155018, 415405, 903776754, 839193958, 242770784, 862439863, 737849157, 311581973, 726765688, 693762856, 31512841, 15579464, 765663724, 61849510, 50726119, 947395547, 163450694, 525000671, 293039129, 906418274, 719921104, 259327682, 950975882, 139378647, 614357141, 820600477, 624473122, 9408227, 877181186, 471330509, 724452026, 86703313, 545776863, 940982256, 742670220, 105519120, 750264387, 838369258, 533105243, 315771829, 942999087, 574702319, 788429699, 677225158, 365253533, 406637792, 427697095, 586739556, 732198879, 656332976, 941835194, 202346879, 286039190, 565211070, 409597322, 233774446, 921798090, 414433109, 949675376, 406384374, 185054736, 790733272, 547161465, 918214342, 368187126, 380935095, 864094745, 646595366, 474616023, 185294330, 398227420, 956208202, 402277860, 265466830, 926416422, 79080340, 35299046, 899887845, 9526831, 152158877, 824453413, 126920506, 150452625, 469480072, 238887138, 149442044, 347550549, 141569298, 164677866, 678834942, 851746971, 471422455, 108176005, 209123483, 202628636, 603888704, 849750407, 288154727, 348556111, 494199525, 695851211, 175080592, 602932370, 34303971, 613574163, 410093582, 108117230, 234090436, 89998477, 649048422, 640826544, 113382235, 699023193, 582470305, 197956832, 138837971, 730453869, 474174302, 352421859, 283886190, 782519776, 171956232, 155850150, 130769413, 321139183, 565906079, 49757443, 142234494, 697529175, 251684752, 232518772, 82947305, 50535765, 183809465, 728452414, 24032832, 720683564, 142387931, 917141818, 481130299, 676376988, 517304075, 156042179, 696944877, 564029962, 263638907, 217428551, 930980902, 680137458, 392807777, 512494295, 690243300, 667647889, 505998927, 856687480, 738645857, 678751717, 866058117, 780135339, 784838188, 702603419, 17105595, 249784234, 528800829, 93534993, 273506386, 683199891, 325447503, 223338059, 8265545, 531023032, 455574005, 977267932, 92344167, 192160674, 931965355, 67770660, 698868887, 643642850, 383044672, 247544000, 497271945, 185798269, 175324870, 397367464, 125567706, 513166548, 84567067, 616326232, 336493621, 919684409, 64925713, 793235103, 365022448, 979927117, 831464007, 731348313, 380709117, 709566532, 651535143, 196260793, 342132233, 207311182, 543283187, 551098948, 121567081, 806742262, 984638522, 998001469, 999417468, 520969805, 333903235, 32512358, 756922238, 730235261, 533699174, 708690837, 520332418, 803282075, 920157210, 405079619, 641228911, 70074278, 620574899, 20968495, 522976351, 700390664, 269105211, 21678015, 274757111, 293688839, 82062350, 968773718, 575269443, 158967304, 275284975, 434505148, 202350135, 935271855, 33413976, 768681657, 961109970, 315404144, 923894334, 134546447, 64646766, 31090918, 737992492, 446312522, 113308839, 628578612, 565794622, 343801071, 603238358, 979667576, 491549214, 832482343, 180072822, 547024792, 956872275, 765502541, 940600942, 401808343, 293256234, 850390273, 673679213, 821596318, 948238974, 636923023, 137371896, 45898770, 817358635, 469477107, 936636741, 103208212, 321885243, 198635852, 23371076, 427230094, 650262291, 400300486, 137594044, 211180301, 559929363, 907836429, 328420775, 182600249, 461364705, 278849730, 793476624, 563577616, 685118134, 941758252, 845015724, 634838956, 752376782, 931716742, 268397414, 217349443, 235860783, 827900084, 487829123, 850884957, 903706722, 771613593, 480434187, 255443998, 325489680, 424279809, 684079785, 669830102, 74025625, 912460424, 687669380, 647576064, 425369016, 516153265, 695721127, 819488634, 437999277, 12963098, 867405007, 7498983, 208553903, 385217138, 315687902, 249850982, 419194351, 552142600, 406386085, 898692344, 2662604, 624912101, 91437844, 309402665, 477072635, 377600630, 608824486, 7786634, 299218348, 253719825, 775622181, 68326222, 103865252, 979278021, 346289587, 449496091, 811645909, 574655061, 837091039, 879967327, 848736675, 378318335, 83542480, 373426715, 280175265, 482083917, 486587048, 270113166, 68508327, 705682728, 587848617, 520335404, 161880367, 258672953, 331647088, 748665793, 209653984, 158930208, 318402259, 960826397, 317526241, 401547949, 447416065, 372531586, 821275512, 251922897, 897257606, 443832057, 246893762, 452591330, 600136783, 688561648, 31684396, 687482216, 597444421, 24034858, 387840055, 163668691, 343599673, 572063422, 705617061, 728561102, 863539041, 752005226, 732256184, 288757780, 932115710, 17394274, 544408516, 50989098, 605196639, 369634728, 822583967, 255840353, 303785123, 384401609, 165990747, 390330213, 416445613, 722594946, 151481507, 738647415, 351585560, 275225368, 228451316, 820163468, 878763577, 828686579, 17461285, 950238102, 94134171, 594130375, 323600119, 38075227, 708699998, 139504429, 215364801, 711631123, 102630263, 315532435, 784435467, 591667084, 267624038, 59630857, 745799824, 473083978, 819268307, 784624091, 422046738, 4216212, 742837978, 248513419, 436775638, 795620782, 183437409, 893126891, 116014514, 198305610, 410708927, 782160736, 89521100, 165061324, 534607477, 887310525, 943863286, 658001724, 790257772, 370952595, 193648741, 36203756, 152519624, 677638875, 907651381, 57923267, 428986110, 438298377, 682256430, 354986489, 244435468, 818199317, 29981320, 548064123, 143254720, 403391793, 847198534, 533273690, 58189499, 409982106, 833002656, 522800927, 640327993, 289296703, 815386006, 131200760, 515757343, 370574165, 711613060, 550213577, 171972236, 497130686, 974648646, 955302159, 506415002, 734247939, 851855264, 833272054, 515765177, 954130028, 214154924, 273308466, 364667274, 106844338, 190010993, 59827501, 236573610, 566438266, 616198923, 963899702, 146570219, 113870308, 546136684, 831247413, 930952511, 868366094, 550210026, 477883539, 605337437, 715142864, 792818788, 326157455, 183848184, 176665209, 924384776, 44531447, 110160511, 931172538, 299745188, 322661935, 139385333, 589448661, 491365508, 278343965, 858293871, 96341655, 656110011, 223545834, 177092505, 589947800, 60712867, 332229069, 873171372, 374248896, 797599449, 636050839, 734516137, 301700164, 251269648, 79090129, 225382579, 331227823, 54006882, 349696393, 603087201, 563529399, 269743098, 799052262, 800118559, 399790660, 202567323, 596487814, 313072145, 947544859, 68539131, 542900224, 473226000, 182306060, 871464491, 453467963, 442382862, 877318451, 749163460, 98986231, 867206807, 642597006, 81602435, 444678488, 313067910, 62386612, 987424121, 128887366, 682112778, 414210889, 612098699, 226918101, 611806031, 364392081, 16699034, 498101111, 672181048, 393066269, 406332283, 819004337, 848170744, 540378327, 998570575, 615679719, 950897498, 928218251, 172976681, 950440528, 234874226, 483619711, 286695727, 635882714, 231349928, 996706257, 22981726, 257150007, 79243909, 878179204, 596977486, 240711048, 945301069, 983882240, 734765933, 307976446, 703957625, 943604562, 253791937, 661522100, 535837789, 112945044, 57354062, 407083637, 515497492, 397514746, 24352347, 852966529, 301735962, 214009547, 525310703, 187379553, 687900022, 309180816, 946955706, 705625111, 975829487, 553682089, 560561988, 126523088, 539689798, 522462280, 581699007, 703526528, 945605939, 270528195, 399687030, 492835884, 505548398, 556616713, 343425114, 421526877, 533979517, 657975019, 271328068, 671471900, 116325994, 987072037, 200364830, 675417246, 973154515, 765398132, 932264661, 649120479, 974000978, 680402562, 265343241, 217763389, 373698062, 790505008, 519287141, 134646122, 914549418, 645310428, 888473785, 392226056, 449177070, 640787682, 57345555, 398857167, 448602848, 972789569, 987960013, 211166607, 41299247, 259015342, 302714797, 823202630, 663851544, 850922084, 971424952, 930413363, 189221628, 939945993, 591367176, 360561690, 565664208, 128705798, 74907474, 518255001, 344070371, 512948506, 349146299, 218246554, 850680963, 894934852, 279025769, 238635886, 662408191, 484512700, 861613732, 708424484, 725789583, 98255014, 167657146, 154249334, 212308774, 384838180, 434407700, 31391074, 958767669, 834368987, 463910354, 257482639, 842169804, 744848872, 185918212, 668396636, 449126379, 987290610, 690719316, 709586492, 93006451, 211022181, 555484726, 751572356, 55237875, 755690387, 194170978, 618430963, 85698337, 601265409, 552151649, 218551892, 325943833, 670896061, 118205874, 756880236, 281050901, 248617432, 591800751, 366292634, 4932964, 235147459, 650432203, 877494240, 488969159, 622620137, 26503990, 780508089, 978361855, 721418587, 717968341, 527835386, 92215891, 905084425, 328151481, 676654149, 946912592, 396130811, 591967609, 179573544, 936160617, 668824711, 238971896, 325988109, 866174663, 694457254, 446698134, 487478940, 30287861, 246161394, 759291233, 532941199, 159528912, 50509598, 113866253, 350335516, 234551926, 69960810, 912494342, 78475569, 536779704, 410340610, 97372670, 848637612, 658037951, 681452994, 587163678, 824313293, 553915283, 11260361, 261847762, 530409468, 355103105, 93962105, 415214171, 734697784, 716785481, 138703878, 117701111, 123697767, 253928188, 344157822, 947345256, 923586126, 701871396, 203014190, 798279844, 355223152, 43787443, 287725125, 715598256, 51483785, 575343231, 145555713, 412814726, 19050425, 796582363, 930232999, 849286502, 407388139, 492449645, 634380254, 654411862, 923156807, 172753796, 249577097, 87172210, 11941715, 982107472, 588318134, 738579825, 675004245, 652776914, 434152541, 499111855, 453115583, 99082749, 839051154, 460821086, 637487806, 41566379, 664935788, 125354211, 962469884, 834664671, 689280706, 142587756, 997038011, 889480268, 680197223, 496287720, 935800554, 528076208, 758862137, 505545782, 863105649, 910103008, 603998387, 837599847, 708785822, 621936967, 637929249, 849611426, 829140836, 875349175, 817065022, 362558505, 700706164, 127276853, 266399255, 926782317, 459162289, 817711199, 168081304, 816143692, 800123647, 431731, 513368493, 257161676, 284695876, 244087899, 602191513, 339688035, 632295853, 675061346, 202805860, 63338263, 133286892, 312891353, 628349817, 742148189, 50312017, 849625658, 77756547, 713243426, 929099616, 904500654, 458102894, 411759289, 830842409, 321479280, 163557756, 542132423, 86497716, 92549959, 662774537, 79003683, 710608932, 914550564, 65822981, 165880760, 819505013, 86033283, 73985869, 254138696, 552962168, 547812952, 755207050, 89228694, 46152719, 178709678, 960091044, 149071757, 874276489, 35102733, 480928664, 880676261, 921731900, 461709567, 250494309, 760873322, 766097362, 401765418, 241738747, 944705895, 440266390, 993242396, 217217287, 425824421, 322382762, 271715424, 984665876, 443636390, 45073777, 630398800, 463527890, 699285772, 261445910, 361127267, 986655367, 552443266, 625976509, 239267508, 703676733, 18908159, 170171417, 571434884, 46930286, 870303851, 289129754, 107652894, 976576501, 262732157, 948792696, 235942723, 557374156, 363772201, 61382406, 553110543, 61332652, 439667948, 355735563, 922059559, 970570432, 38786591, 737366860, 496992842, 986301417, 499876384, 404490372, 548071903, 859972303, 565774278, 215740184, 957869483, 961797760, 603105381, 140812719, 305574439, 512468874, 316366056, 210399817, 166397468, 350135655, 188702016, 521209061, 550064245, 493734073, 734324737, 721979216, 341818965, 592008862, 68127306, 697081703, 798561444, 665377664, 549126337, 218559346, 56939457, 884808162, 374279544, 494308664, 675081714, 306455216, 758039052, 378776656, 766274312, 268862088, 424585912, 321403851, 74172857, 546928338, 748110955, 69420111, 259006221, 29654096, 950183379, 587656964, 121343238, 229016931, 525245078, 170762495, 135320142, 25471919, 409327078, 482351459, 57105968, 400665115, 586461433, 990233607, 599982658, 983229122, 772243280, 271293935, 543399714, 562956348, 401122663, 565344421, 585481424, 576479398, 350731842, 485680485, 20714071, 8158187, 603676268, 516963904, 50419445, 443382140, 675259130, 578897710, 886055104, 883905960, 843769997, 356448838, 165054711, 873422703, 674858914, 566484751, 290384255, 418280121, 252680321, 313721456, 127494952, 110816777, 978162164, 911708194, 461526613, 51237904, 343087656, 964695900, 567799989, 330915468, 52021458, 769071566, 79680948, 682535765, 782771203, 943275162, 783291822, 107048562, 410718487, 899898952, 612269357, 212422294, 598059048, 47785784, 368137559, 706853767, 856172856, 501722227, 594136918, 632941179, 696935904, 588309848, 344197568, 227597154, 343123605, 150960171, 428348498, 107312392, 615388455, 20862536, 221770846, 108398306, 975393037, 812563636, 479292310, 191962891, 900276884, 64332642, 19070170, 874028993, 693596412, 613502393, 240689082, 745636412, 473039836, 61229543, 272777730, 783616413, 143536322, 267303673, 505572297, 541148583, 453046592, 932204121, 695930429, 469234640, 40394889, 245678506, 379342040, 447331352, 193723249, 794770747, 637835888, 677551742, 183765102, 8654870, 24622899, 318737956, 114809644, 524590776, 190981785, 869145324, 35138376, 427210398, 906571999, 133831917, 582464945, 379813583, 13744075, 930564563, 948909520, 592320547, 694986509, 254468528, 607105249, 756103791, 932423961, 727289900, 664605864, 868744448, 309037550, 940669590, 459649335, 223557976, 8258357, 38442305, 311834126, 156954810, 304138234, 607755580, 812273179, 217330753, 991156956, 146846528, 302229092, 401669001, 410053765, 951295470, 364290625, 913710434, 749703765, 797036850, 714396025, 829199445, 404738333, 528537805, 298177475, 243302524, 747828111, 899957329, 777663512, 188019740, 498959514, 723192952, 853563821, 606229842, 961608924, 696914372, 466518493, 344994555, 648187584, 638455375, 885947283, 781574994, 656881615, 59637376, 558578472, 773306181, 56699458, 985621298, 896680941, 540104372, 422039908, 910719887, 593862686, 668579274, 481737766, 94051045, 346792485, 651272987, 22359606, 383474730, 726717221, 649031134, 432795925, 410664462, 524002439, 99812955, 193828939, 266002287, 178289011, 262754856, 604558007, 989182052, 471003761, 272789026, 366747885, 775426656, 308769796, 652642055, 635966732, 257175713, 774653352, 546910763, 272356229, 356376140, 203289750, 423046787, 206579249, 835424306, 730121193, 462414453, 700330421, 177515153, 60301805, 460688654, 950788134, 435368871, 606354863, 313410660, 527708973, 396637894, 577007460, 363797918, 755174113, 123250931, 144985875, 385709565, 839625686, 984837532, 180311821, 527706273, 42391451, 557203115, 484096602, 898705583, 553582617, 741739114, 673598814, 239463861, 713654674, 111050640, 51658146, 385201111, 95695593, 531401488, 245024545, 929399419, 345707508, 189930506, 191328985, 512707801, 648311112, 562011241, 521399246, 964497228, 574815795, 447240566, 746892336, 544465477, 553348939, 945530537, 690980210, 74454684, 630027257, 780492865, 53856595, 17026426, 74870726, 623770904, 932504723, 572320755, 738723578, 607311149, 763068014, 732871592, 649275364, 345338234, 434322986, 114154691, 711701309, 689627961, 419506969, 512390721, 508982830, 176789545, 44906278, 271579538, 70268286, 693726780, 309926130, 804231666, 414253983, 559828682, 697862796, 3778915, 252628133, 23241813, 270754971, 750412039, 245980495, 968703190, 789817007, 6251983, 877812817, 226199837, 975130951, 388748940, 350512225, 736086463, 787082228, 874832353, 453842604, 110796318, 184017920, 221623260, 343504960, 429844866, 206788428, 395920679, 93959303, 692274984, 411563523, 673142937, 131589711, 535122062, 883315828, 143341025, 774217777, 716717381, 23539174, 223799562, 709433558, 119567082, 214994059, 937693727, 112703971, 160419920, 731684129, 41098667, 166426309, 697905247, 233428649, 815236761, 891973120, 130432203, 307053374, 686813041, 875985183, 4918738, 20507707, 566355485, 647665177, 456579864, 60555248, 625746080, 118340438, 707546649, 247840598, 461884660, 566259807, 462415898, 785756956, 380275960, 492404430, 806376471, 578418707, 30841689, 143900994, 114286563, 434207907, 982869204, 885199219, 920457131, 192183126, 873206887, 26238450, 374540113, 287993364, 153154730, 700603522, 226023494, 460531469, 424322482, 580489217, 256733353, 906778071, 272013555, 116897625, 605725435, 523281744, 462184848, 322828585, 656849773, 394116152, 21285649, 862474623, 717063658, 169305474, 168438110, 531852797, 172252049, 456277359, 34421450, 646106489, 508395412, 801312816, 55907344, 762171340, 380297471, 523107905, 817103656, 522347744, 352163557, 77179319, 384523508, 45585339, 780296523, 494310111, 725626749, 748697565, 48383335, 779749254, 428900227, 6658212, 561674379, 799251486, 360515735, 338863992, 396623630, 331695, 844338722, 445019569, 29666646, 934220527, 66502905, 437550334, 520202354, 509341053, 821259954, 814346797, 757189385, 431956245, 56929632, 658485912, 8357721, 909711014, 339290901, 499076660, 266279089, 223717098, 37751706, 1728890, 907967359, 750783681, 724860040, 407197324, 760824278, 964524285, 82046809, 388018140, 918324391, 726118200, 29996354, 9380144, 295953960, 686909753, 542705021, 359056682, 755129788, 350038063, 919554315, 540661580, 960127137, 121931752, 11118137, 211703671, 817177376, 2661744, 38825172, 311905539, 448759978, 243133301, 281412852, 965823694, 356525410, 415268195, 549662188, 83132684, 442666214, 776128451, 950499786, 522035840, 100723188, 321148136, 286709266, 189944699, 349864806, 896204910, 113157177, 213195841, 417395056, 489687015, 35210791, 713528315, 537471643, 401535692, 763975871, 214908443, 351603337, 61237212, 28865552, 537061595, 181576615, 685528103, 871991101, 979308856, 578656584, 35554205, 225614562, 900546210, 66473668, 878701536, 218940833, 261521587, 111358037, 573297272, 98599596, 915288573, 230255082, 629646637, 424094332, 346194316, 131145885, 756207610, 687602388, 55766433, 895172319, 841927962, 313673634, 292877870, 667308047, 878775560, 162837794, 562416202, 92045264, 818036011, 929987863, 530473273, 811053805, 719368497, 845461559, 877745019, 751235032, 852524671, 389003894, 383205130, 52646362, 60578696, 620122364, 769771437, 39381799, 872314928, 66816587, 709548016, 27925488, 969175485, 668922779, 560443124, 684527438, 328886561, 167084686, 769005581, 354658832, 88908411, 865689838, 481778871, 820927809, 714663045, 295844489, 613831254, 348975326, 663923887, 853837690, 189903833, 327588584, 687161946, 753641374, 845151885, 384826080, 329915404, 430121917, 941496684, 261607823, 183314611, 520019659, 263944485, 130634314, 872787, 238042364, 877606485, 84404041, 582513996, 189519503, 386450742, 367874448, 698670327, 666999420, 690425136, 65267809, 709309218, 318699847, 903377587, 498432870, 528491104, 945823542, 896759259, 446982621, 600171670, 420083788, 311041532, 83304583, 594527982, 288437408, 277737395, 635738579, 307552404, 385211341, 415493180, 35697067, 119675855, 987959555, 240584917, 624550772, 420751874, 86227025, 121316817, 458693555, 991732539, 919001148, 375167404, 591159125, 282201837, 130422424, 100388887, 207959193, 696460574, 838192688, 852763222, 421514642, 508265629, 549545362, 674950255, 182777539, 499915270, 860953605, 373759875, 432886072, 910819976, 521640642, 561091051, 840421145, 408432244, 917135491, 249315080, 261506157, 363952905, 663640240, 723466234, 205531865, 669822494, 21876031, 813176273, 184769950, 367911529, 125863173, 114934624, 365890778, 920909997, 807716698, 332276656, 332749903, 702352183, 143041463, 496236023, 760043273, 168055081, 61020287, 199978162, 374583590, 822291687, 658954229, 434618063, 781217975, 954930537, 751556139, 916422992, 326306085, 402393464, 18667929, 841811129, 285855218, 514285335, 324364429, 362743859, 830871767, 218379793, 951017713, 951689173, 158584461, 807551076, 999189161, 154008093, 325089994, 569823715, 811391354, 552799698, 26280529, 512495238, 554863509, 377075141, 115138239, 482893755, 755545361, 304612032, 312537843, 425073309, 189723504, 371558443, 36574975, 484986659, 712354879, 210026958, 747911299, 534230244, 332820218, 415636681, 86289236, 898552573, 220861434, 451118745, 587881320, 154434133, 601801484, 265047208, 274762967, 686394454, 144350284, 877688366, 374301917, 145602695, 447585333, 359937878, 838305936, 613361381, 274725185, 217792425, 373451437, 250927783, 260171575, 938872856, 21437271, 170809202, 899489778, 809823537, 317012194, 985326788, 878588780, 799392552, 4934238, 324132319, 845530403, 599236814, 466634522, 503859688, 146188597, 53917762, 512071289, 620819783, 597953203, 543238421, 839694423, 848114156, 864284005, 896961857, 807475003, 759115530, 567673424, 362946846, 604767132, 989120261, 524475174, 513159186, 330415433, 728366575, 933690396, 695341736, 465951693, 295006006, 632583914, 14983593, 487817771, 784170905, 710615450, 683119849, 784350027, 496430467, 219643886, 732961852, 486951659, 694591832, 694824637, 222490997, 173613156, 718492168, 202161623, 885140984, 204506014, 349678354, 822685403, 349457981, 685398579, 291080126, 683327822, 52732731, 405053892, 23543348, 578287457, 64082934, 413951990, 381416853, 233576448, 230360833, 53758285, 327395934, 885144938, 651017990, 747396091, 365564289, 124013641, 750619858, 132763357, 29854342, 838812953, 94328745, 717767140, 198065884, 950887307, 782940931, 297294555, 581829592, 864136611, 950554453, 197415377, 181111687, 586746390, 405897371, 780269887, 305942561, 968711522, 244244661, 416501381, 862266926, 765984223, 245269177, 165498167, 315093106, 81409142, 259370363, 65637981, 950545110, 257381870, 223836198, 878631831, 938006494, 43880989, 61201126, 203617417, 613175784, 428782739, 131875174, 405080742, 891122095, 821417052, 687660900, 358138278, 489870236, 689712328, 400270774, 619805867, 536900762, 435365278, 880692543, 237163045, 169361821, 994314126, 296607951, 868170894, 180768836, 138417339, 450530638, 765055046, 273247174, 314214022, 430432513, 776590919, 367024946, 426314224, 582647665, 690538559, 259710790, 771754731, 184135998, 667750596, 47636022, 971587743, 198785152, 514781554, 245264396, 700931820, 66048997, 339139206, 290416775, 70116860, 351759459, 846894401, 545832846, 256427620, 560891510, 922114160, 938361373, 280641589, 942816877, 977895706, 485438426, 656306356, 538372101, 180623411, 896196692, 794740517, 531465919, 302607307, 789512781, 274129314, 107016173, 750069739, 432495397, 578547134, 869148622, 46192056, 46334032, 273574203, 150779227, 845062735, 588551180, 604343165, 55742112, 214537073, 762334920, 356834937, 701820653, 406995612, 876477147, 388689781, 849720036, 629731987, 277691047, 266176600, 77659538, 562592753, 298980416, 877566984, 217618207, 257701403, 219564653, 896455196, 864526819, 70408858, 831878750, 514868154, 12899219, 259912985, 86932715, 8563658, 148614601, 723231372, 539277362, 873553185, 347901431, 160823547, 785064769, 351096949, 676906630, 79690309, 796844738, 697174687, 497018836, 434242159, 949795157, 520145698, 897040079, 179273768, 782498847, 769382713, 988033389, 417896305, 413455361, 444204363, 609389692, 69342151, 367654414, 429922949, 217961276, 116941643, 708309891, 703189216, 369201005, 711810771, 65614368, 528811453, 113822010, 367406620, 124416315, 301271796, 606038984, 205997049, 510257498, 84053768, 383892497, 406113146, 145942585, 426336322, 815452245, 792429943, 587064788, 252454678, 470923821, 660007045, 624847658, 640809297, 125517432, 722536656, 818691426, 467378630, 271321185, 611378365, 468646381, 966168732, 222967743, 112536028, 646632216, 662188505, 167603254, 244337172, 300477869, 404770766, 72585516, 858459397, 946164984, 346890506, 523971352, 480301545, 268292189, 521905968, 861522981, 284565166, 519944945, 475724432, 753955726, 888335941, 185012652, 213414829, 224437823, 862528153, 206338038, 248743648, 761402470, 370185122, 121158772, 420427003, 279987929, 478107622, 722641635, 850475312, 490475316, 840856887, 126876447, 965820404, 543986006, 215687696, 25956857, 910050289, 369305157, 24942000, 542428127, 95031873, 751132042, 417633554, 310586793, 449237304, 617214295, 248729894, 167458930, 630006532, 458851289, 857295365, 558811477, 776265, 976931079, 800604583, 39399996, 110944822, 332323409, 12095625, 901137708, 300401295, 913905974, 16122227, 674102295, 952615665, 178711321, 571929609, 548720624, 635561004, 359047088, 50641179, 910890567, 748044204, 808856025, 129229417, 773165872, 409447219, 55618586, 510137712, 614633163, 442467802, 170576051, 298969052, 466422086, 605276991, 120534409, 836066551, 404565887, 679458451, 283554252, 197465322, 983417191, 256177056, 277526981, 765260435, 650952023, 19903544, 615600241, 924737028, 495826036, 381211630, 512430504, 540048781, 499526274, 159107525, 5413883, 584422894, 731764100, 232164170, 853887149, 601689114, 650769987, 668300823, 409252900, 712462036, 770127873, 656634687, 187777558, 735209169, 999143003, 615801848, 572881079, 432638249, 665022854, 230906551, 63508398, 410646782, 941874677, 295964775, 808525294, 32679618, 411358931, 208867206, 592127562, 822989680, 937989587, 170531640, 318167739, 145769901, 949667639, 250873623, 567930176, 72321639, 158991171, 674818870, 423093211, 943592910, 487340746, 947920454, 826983299, 239166348, 598369272, 174185005, 882209603, 185517608, 99080310, 72348259, 366725399, 108464983, 614642930, 785753219, 962287660, 150782326, 884609036, 660535412, 581916489, 296782782, 694735773, 36235419, 215566006, 963587474, 118286340, 214059770, 476651334, 99133352, 695765763, 829269107, 659637080, 273856951, 927769042, 127271375, 238503829, 330272908, 539667428, 364337670, 434680890, 529518877, 619416117, 35132230, 160323275, 981080119, 844318143, 185591791, 598315885, 794712759, 105425459, 97379288, 197337536, 265170907, 99928724, 746848687, 872601362, 453161332, 469471192, 877806362, 720501964, 922586090, 492629735, 134912199, 67168688, 213731441, 798349422, 998890761, 176867290, 153186379, 624045329, 301905529, 220383855, 28189031, 183750130, 694572531, 50343701, 788684043, 600276545, 823585307, 562851058, 199495035, 119867246, 850025791, 61128722, 529606131, 167819420, 600788434, 299678692, 914329048, 600595731, 789045891, 891289083, 100733957, 160146335, 611481528, 827753166, 540222732, 708935553, 323427185, 159748804, 63197827, 760657751, 480013216, 376979093, 896546557, 585262432, 991188187, 740848261, 572977484, 536165505, 523855464, 733725086, 491140463, 195610245, 844478034, 728699422, 349282592, 158780039, 877868550, 283867985, 58521291, 993177621, 583734649, 103565534, 169652900, 564411989, 689645110, 1533611, 614595114, 247778655, 48599069, 493548127, 32897936, 592164744, 441844677, 467870817, 933418849, 594840896, 240917870, 583403432, 121601316, 628476740, 862343177, 381757668, 98629155, 204425327, 202952056, 976161289, 977808256, 879544439, 407933949, 950330919, 188724296, 705085701, 31453403, 682007080, 868801999, 467549638, 593949245, 408738941, 588245962, 448019488, 742447798, 963157846, 935413814, 429924168, 658174187, 182264808, 688558134, 952571995, 461265591, 925188062, 528889323, 11064091, 259275366, 32119858, 30432206, 267503453, 458239572, 68444226, 531846178, 223389033, 195362035, 120292389, 636196092, 259184711, 640129234, 901023248, 394790214, 310427564, 689428464, 829078308, 111725331, 400878138, 656564040, 658087224, 842079567, 110579815, 574068387, 920033670, 742504942, 436127525, 195780557, 592911766, 9416138, 358285017, 492228509, 291127324, 942857387, 844960321, 262400943, 385728889, 643162539, 765288484, 632375536, 571153014, 939053349, 792420813, 737890999, 203010379, 426766236, 299216826, 134736664, 189711224, 630654819, 723399775, 628770994, 658182226, 4058544, 153725706, 717628793, 772507681, 799623569, 523301668, 189023944, 139974167, 545164092, 393216306, 173381793, 376257153, 614799914, 929575207, 304489855, 334411820, 489756240, 959147827, 738679048, 292082097, 574926321, 168520655, 511930320, 993046079, 437982977, 996095348, 936349716, 648842781, 861031851, 354128366, 856589128, 29085145, 379983102, 414442852, 971614060, 630706859, 562871178, 139127978, 583215027, 295086763, 606401951, 621836657, 798739083, 917182621, 343876138, 300477326, 90398221, 101896086, 184455352, 797527355, 579165055, 337391083, 277951447, 318306522, 382644679, 777363394, 560511777, 310392293, 738456664, 273261366, 124245111, 866276238, 99934603, 607033550, 481063372, 761065930, 888503477, 114110125, 875744250, 162017530, 259216605, 589793584, 246292870, 479349499, 747591847, 108551535, 308755541, 520028160, 687163596, 59151798, 545969478, 63585526, 797768975, 499760726, 752869166, 39752645, 744322426, 585001371, 515394472, 183244930, 167029417, 114779130, 982957742, 753256643, 628316842, 740378422, 2027954, 382355544, 53951470, 743243053, 767604541, 449622611, 907907071, 30707614, 759422750, 67637343, 552599256, 459766319, 772172070, 718369526, 414338738, 453202409, 337059909, 89592364, 971329176, 676186953, 510889646, 330369918, 334111287, 801573469, 879884157, 552660118, 364802502, 752183584, 17874315, 706673070, 558283197, 801524078, 350829511, 368147351, 139513204, 253452926, 834687742, 800567258, 356885627, 348544354, 898302605, 190596217, 953608492, 973822753, 787271464, 655581456, 521033309, 838695696, 684596291, 824948530, 992276650, 641008830, 642233855, 430800291, 174298000, 911258137, 190485553, 413348943, 473548470, 293964500, 588978473, 409900822, 977768515, 379940153, 480209723, 852904816, 606087528, 818511725, 371007780, 577649741, 303578315, 127932593, 78544456, 798731180, 15237331, 327967434, 464880394, 112309970, 566300324, 588832068, 319440621, 153289697, 453198750, 768676800, 828473514, 245795779, 498013547, 498211783, 69173996, 595334864, 222304316, 444003629, 846536785, 124148629, 976080768, 739560882, 185798414, 757798843, 409965399, 530709891, 57930881, 956281373, 376684460, 297444329, 316295904, 312518639, 363901132, 165059002, 979734332, 273643903, 982308181, 597618736, 566936150, 528915318, 516833609, 724593231, 480520465, 660504364, 578694436, 445340850, 693373982, 955385739, 204061962, 647984161, 824324300, 666955088, 571800474, 148511766, 423588494, 534312447, 778328859, 872562414, 855046988, 621811509, 504788836, 86785736, 557257572, 22897601, 723062743, 583643984, 934380544, 648927714, 545209256, 732764599, 680446021, 757509985, 737278030, 638414152, 1214291, 198222652, 923907883, 193638251, 93705892, 284031625, 867664338, 37845168, 454150966, 151339405, 242773860, 573712096, 38391023, 800118638, 244265174, 726838150, 520038475, 853551509, 179445331, 132360175, 7369379, 963204562, 374192296, 502494073, 425307162, 570394195, 10459095, 435808796, 690426381, 546333304, 459728838, 415523895, 133486069, 858554333, 287372380, 63136164, 818754172, 202864425, 300530506, 6450224, 414585615, 296430451, 947754972, 759397959, 397675451, 497887705, 970209777, 810435615, 425938762, 870710945, 521212099, 187752187, 977547905, 948426932, 641705414, 67635016, 569099712, 814499919, 512994412, 198629530, 116238625, 758808420, 36017286, 425560913, 671751288, 729738777, 603341323, 220073169, 598147354, 919959, 340291349, 833922027, 362023278, 78930717, 545915735, 909090643, 815862568, 458058744, 143745223, 37744273, 702834885, 375278874, 589654141, 33636296, 957200449, 288517268, 30823353, 837670361, 457662146, 315944146, 671503212, 322885081, 129682175, 431636834, 179805875, 491573730, 584518209, 146622908, 960075829, 406567036, 685824198, 468315804, 734723528, 980218131, 758070148, 470597019, 115142637, 114228856, 915581659, 134674529, 490065982, 104214706, 423063033, 553273502, 539884901, 966657260, 609800658, 216607861, 814941360, 795309417, 543452944, 627743983, 461086432, 946153924, 510296485, 605162018, 342824250, 43740625, 38954722, 559621050, 469487029, 237982838, 903998895, 891679371, 159427471, 277273192, 921779750, 834505910, 393146706, 213415981, 373355557, 420954066, 583549766, 793635607, 418047927, 411916018, 238969118, 851944164, 909847365, 661702454, 516222919, 623294525, 30143499, 939731007, 599044067, 142903640, 363960132, 267428763, 371590926, 914548268, 219842146, 428887395, 257151950, 711618105, 877908623, 534030844, 582269835, 983698452, 427957552, 12111220, 870854918, 23706137, 801083396, 594032768, 351124482, 70953550, 86788898, 25274713, 709977307, 709316098, 999840766, 503738444, 916742166, 77959589, 492588270, 950261329, 378005946, 211860623, 792361535, 907900445, 389679769, 627835877, 136538023, 728573296, 861299752, 245398841, 277404641, 537800397, 867227241, 844916797, 239878657, 52714352, 891112467, 929826750, 689410313, 48910825, 477002823, 224300422, 659458179, 238430863, 765582150, 472184286, 984099087, 534257016, 266947514, 206590708, 625706528, 564282005, 140083365, 573192872, 963331165, 15623242, 547066392, 481017265, 710891238, 340390228, 780361868, 297199286, 796594654, 163595567, 665686490, 756708467, 104246213, 737953036, 163364663, 58664509, 492107948, 46487483, 353050082, 210340377, 57257547, 688505227, 899370883, 824232588, 766317629, 896674625, 426733082, 670716510, 488154896, 401085342, 593451583, 513940855, 15482769, 505423549, 279222097, 655233380, 716270801, 59018384, 805196575, 454084373, 657057714, 481463858, 284431622, 984555986, 961821355, 232383867, 571923875, 623274428, 862518352, 696749064, 134519053, 530228646, 675059259, 707985558, 238543718, 824162726, 825737278, 408497004, 296038145, 791474235, 537992299, 261438515, 45084588, 289783077, 847334641, 431523663, 613249357, 656851900, 927402735, 606074870, 933328277, 638485227, 99624000, 352416290, 310970706, 867737805, 778800435, 540311006, 402344881, 953333850, 806501901, 685720559, 871072449, 649293385, 294333033, 72866937, 164744537, 388006741, 227918787, 655036844, 578138910, 329076828, 619661272, 236105720, 352881648, 342740701, 774085954, 698732813, 65037844, 838746928, 900962730, 962141548, 693355421, 741628680, 711415204, 324419292, 126539327, 544076891, 639471822, 767461465, 873673240, 660562625, 81629058, 189331155, 491127248, 694868888, 928056999, 758498938, 649556729, 229410528, 791822461, 533321457, 636103595, 595953987, 514221718, 619807724, 899444609, 275206777, 409554691, 154279855, 860218530, 648200561, 238169554, 620616000, 142559600, 547004150, 514059865, 631647171, 698073901, 947128962, 970496862, 629687078, 247113610, 809787074, 469184040, 334403355, 726497272, 469530751, 496291618, 889111728, 744095151, 947811046, 988485775, 170521966, 773424492, 323848429, 978659268, 305070490, 790704139, 27231278, 458229452, 983204647, 63226304, 42612458, 874443964, 643449069, 171243836, 278750334, 85017385, 329406012, 15270339, 364740862, 675937569, 395672618, 724096013, 12502450, 824864288, 581484405, 977927315, 842193516, 667828918, 364926556, 458123196, 168122643, 970395515, 540819611, 890207029, 727923737, 415893190, 941853400, 76271895, 739543160, 574776383, 562215379, 971072588, 809335561, 114154226, 466864144, 618663814, 602904244, 714260192, 925506155, 149927714, 804421433, 315067191, 675101275, 59475841, 882203674, 427308819, 749906023, 511041305, 950269805, 96576108, 479579711, 102273421, 510246830, 795418135, 207658390, 912160831, 855210906, 679043168, 874945995, 293381060, 211407402, 878001928, 222781019, 367632513, 228431513, 145464720, 559409158, 622904152, 826146760, 561824854, 222906803, 241458734, 640915391, 415692609, 796587845, 708469400, 670816114, 406705493, 518068540, 401577631, 65526375, 137403846, 236059002, 557783343, 638364160, 47095975, 69820818, 981633385, 896206472, 123092250, 741619026, 867382035, 1949662, 26684641, 163983355, 643091938, 320067345, 978329306, 520980101, 122622274, 762610903, 873413840, 620507985, 94991179, 862153071, 139316564, 790653299, 8927022, 576825674, 350764703, 111568323, 40543676, 236624912, 925996318, 624061982, 320567480, 422432922, 347830632, 457413145, 309087405, 139695156, 314016399, 267575266, 66765395, 438727031, 781039994, 80614100, 379779472, 90459489, 31839648, 258479096, 914027953, 998194048, 48786152, 836175572, 47573258, 467504262, 939551997, 671468729, 779950601, 574938858, 591246318, 58227353, 272636086, 759617236, 628547269, 790047160, 424948345, 814139514, 948522291, 60075633, 554037758, 289841710, 681222391, 411313928, 846527128, 783707525, 972878770, 388963468, 386493429, 480086319, 984948645, 529608444, 986655259, 111985259, 205332683, 430679034, 705016471, 192825334, 230375339, 538417743, 677572048, 695125813, 449209354, 912533141, 304529464, 92984389, 957791236, 756501090, 88818682, 247955314, 859505709, 249514245, 89115638, 307041445, 754167282, 426480920, 116270046, 784212147, 694435990, 296956151, 367985478, 914100350, 941052531, 136982, 359743230, 205144920, 235109249, 540636747, 30061122, 873062708, 44242402, 366796101, 118605618, 293378085, 657121495, 140682345, 475550826, 917913081, 466825628, 329035135, 105167095, 766462129, 97776871, 868205004, 801879445, 987708796, 440166758, 381727972, 760257057, 543911015, 433548637, 845083831, 823542944, 488263369, 75988127, 689999068, 99482074, 123375841, 121440459, 387886156, 486210498, 768984432, 549555938, 612886888, 295159325, 972062841, 145429663, 113767870, 158222256, 273927596, 634090071, 783903541, 389503717, 581102771, 138295290, 556087286, 487464011, 366918754, 193442721, 830530307, 607926608, 861658795, 848533641, 188503927, 384974699, 868280943, 680652271, 146465334, 663054763, 841738133, 666246438, 178826090, 396363594, 265641705, 283812463, 188161780, 715029399, 155774543, 160473528, 336241749, 255485127, 411674921, 600097480, 210604935, 159260622, 996086446, 615106354, 542216704, 654351952, 743404506, 262415273, 514765045, 749837080, 918352110, 232620737, 216289287, 459344280, 473115012, 209428014, 699568657, 4440123, 67537376, 646873824, 441223810, 625870539, 536821478, 466825839, 714884655, 458406412, 558625704, 918822008, 865442114, 273901288, 12039614, 99710422, 810712763, 945645688, 237659362, 368252680, 397953396, 794402798, 734397137, 991924697, 993852934, 675841369, 366459584, 560073004, 394815081, 158148045, 204934587, 169831004, 488991870, 699131644, 353248010, 194631456, 585567707, 300032566, 765573951, 649240773, 644101326, 25771487, 962555423, 707751252, 265702303, 278167151, 886858466, 182818803, 31369491, 5376545, 304212576, 127732349, 539058241, 478920656, 871908501, 791343182, 472708407, 211307449, 637661237, 173202466, 102993691, 778195223, 898882170, 72282712, 820598584, 105246141, 642201664, 25376389, 55234287, 220702628, 142286558, 965720663, 211412129, 725711647, 423174024, 542725208, 135180088, 590453968, 243060473, 742719623, 963752491, 698897382, 417710568, 769386230, 877632888, 398687843, 451839707, 696841940, 409484180, 771781940, 355812747, 578931537, 279876175, 117325713, 526538791, 22257760, 44276378, 69419609, 830526473, 584356163, 715756085, 824756271, 376968888, 724776276, 8259082, 538314108, 982585626, 794984215, 528028268, 782200636, 613666396, 800965717, 365385027, 653699921, 590735574, 328022502, 295563511, 465699321, 516203799, 188699845, 664641034, 756527473, 860552642, 847164189, 329397430, 500454927, 718018543, 58840868, 902447836, 889944620, 305564650, 575304542, 638935476, 42624369, 528680537, 697472062, 140374827, 44328040, 725162738, 291721800, 406575644, 296559083, 440378768, 224981015, 318899123, 284052810, 375926313, 109614323, 597758701, 54905137, 436709465, 849780756, 151876755, 857927180, 389683028, 662546428, 540365370, 922496848, 284559867, 62245089, 95199327, 890921207, 195336697, 834148333, 478602826, 491284957, 313659049, 373184231, 601503105, 117793073, 675299773, 513957978, 440309445, 7977602, 884815091, 20092688, 526720658, 228845328, 780257656, 422257097, 995431723, 291401225, 645996083, 68163274, 685630179, 617311165, 264151746, 545202334, 215498196, 750228282, 728271540, 145102388, 415376789, 780002686, 87746319, 832009090, 98336406, 434249618, 403745764, 197306243, 316028497, 903542896, 752403536, 571848279, 79796613, 664520685, 730088374, 167532627, 692612459, 98335549, 734347801, 625110784, 901372976, 193716235, 283110382, 478853645, 748179663, 142940222, 415723372, 724180608, 429620142, 222000170, 311660070, 369436885, 395803672, 579871425, 212306160, 715780561, 229903077, 820235070, 70021172, 812023048, 990688897, 505462930, 232333441, 534270392, 852673, 695274144, 483732727, 780686255, 715078842, 610341240, 559614017, 326751587, 542881806, 867193934, 906987618, 931389762, 322610356, 441365179, 391990260, 763204720, 312373824, 827094754, 364199755, 73746047, 936411667, 910207316, 732380294, 316028555, 830603904, 274388153, 198874156, 452550444, 676810498, 136119352, 92081970, 535200929, 27910830, 596745836, 426246101, 282866252, 57698372, 903740530, 523623569, 103774237, 956219328, 583041042, 209214637, 180339134, 177823704, 301718940, 435096505, 697211442, 190765120, 502150022, 509956671, 202076702, 661598182, 825207295, 680505895, 776157476, 180643594, 704267037, 381342353, 905078228, 48216395, 42849214, 498611356, 109352451, 113683189, 65091463, 451571902, 780978035, 985554365, 258452844, 35343937, 492330622, 742209904, 446142893, 344317192, 30505760, 792465518, 965444017, 771490422, 440702176, 290615122, 479848074, 922382407, 869675822, 223349807, 211456085, 599973113, 402798, 238130726, 932053449, 981715822, 724870580, 467426640, 837867912, 71715443, 31207558, 422727593, 496841487, 425533862, 508492525, 533524572, 652063573, 656858525, 262770631, 375466626, 263822411, 217553486, 307772224, 264755573, 39124, 334693220, 657293731, 487133977, 118647577, 350538533, 516735880, 542704668, 491915140, 651275093, 587131477, 426195109, 160030384, 9841926, 701330204, 263671541, 443004061, 309214006, 722377482, 774919832, 88582332, 272161368, 685111713, 639515534, 632716052, 376616028, 286936010, 400757016, 828864318, 672807971, 783173816, 879905600, 38194155, 866170350, 96595201, 369256200, 727248850, 368424750, 906014132, 219683020, 654952997, 147953957, 298568138, 104549374, 414471482, 599350856, 537802671, 227382107, 580145664, 361977857, 150890521, 618648805, 990972884, 137446692, 179565321, 904654167, 319881053, 327702401, 660141341, 721119841, 151648156, 427293633, 116820349, 429801245, 34748451, 843712393, 632494634, 229679772, 815474356, 858391268, 306302830, 301751301, 500555793, 157787152, 593918146, 160792723, 942921307, 241298175, 649009391, 25036940, 873121601, 870014326, 785454944, 566416761, 700001353, 102709575, 381699621, 936040845, 784934112, 187639066, 132740079, 736207542, 80448453, 653425814, 846498564, 704080577, 163132468, 359513625, 179865051, 946014624, 307012626, 923860441, 143423338, 834503650, 289907199, 286617529, 47466563, 983264075, 332025196, 719276404, 428944702, 855386300, 607517613, 812189552, 133927540, 463714893, 54914629, 479844508, 663574632, 550733649, 740912709, 428250166, 517916201, 10684357, 250833441, 34948504, 957946529, 974096607, 744512176, 569223593, 912519689, 460066348, 624437732, 602968857, 482135474, 775162983, 394458371, 175979013, 25632154, 412737715, 448693958, 939204468, 489233109, 733014321, 806951415, 231590243, 238359377, 749155026, 706557446, 149596781, 68077212, 557003077, 256341146, 190705861, 38329707, 318556630, 114406561, 445415432, 762142915, 696117785, 922382282, 142283172, 388892873, 849499513, 174965506, 928602633, 407971776, 762987708, 97246560, 289951754, 677836204, 182835762, 654603124, 869095080, 766931395, 307074170, 405214019, 101079522, 880303484, 367271887, 995153432, 482626852, 679531852, 210892077, 305219786, 265838258, 986196998, 25393238, 571158333, 320425358, 340209049, 592723385, 233632448, 890756448, 273171795, 34790186, 914133286, 307113989, 321298734, 276649880, 888181093, 670883590, 287789822, 30601672, 256333932, 226234935, 794460237, 133795886, 394144425, 152076448, 569807357, 605482260, 88765926, 747591257, 493521135, 368373664, 654918587, 134501077, 820304693, 25103623, 884655767, 222119935, 180024790, 80751863, 826164091, 691639727, 964330529, 589539930, 251944489, 303420555, 525608645, 571170245, 286354488, 92711622, 839302778, 670936423, 778838425, 325900424, 816859953, 630549945, 733064090, 786045337, 162474097, 337867716, 482372307, 252759413, 360522761, 840520291, 486607674, 832092087, 267835301, 511464971, 555830464, 606237884, 971712921, 85423390, 465328042, 518538267, 265820771, 46157406, 758857789, 672647464, 143007274, 780991565, 38647176, 959660306, 639027561, 783009375, 288898906, 916668282, 756684619, 629918362, 17162212, 50931740, 424637264, 980326520, 144294922, 571029663, 464849705, 404851910, 768025090, 21253725, 396021473, 183865816, 745064740, 183048056, 773542939, 109019269, 594149135, 143445861, 946713514, 762280895, 180692897, 260756975, 899823450, 823061461, 393567419, 163895552, 761539145, 505239929, 143291373, 599128082, 739239086, 798262685, 425345972, 944625585, 434815719, 818791191, 174442434, 667109214, 343233560, 522801000, 181841411, 707487444, 816002369, 895137783, 576933678, 140421621, 769867853, 647899750, 196094109, 809709411, 832034807, 203231625, 447683053, 458413079, 784604105, 621065622, 209342679, 84146082, 255334290, 664457671, 947143008, 984396563, 894661311, 648699249, 495394933, 609381485, 167411555, 568754832, 43710852, 422283183, 246156515, 725641291, 476603360, 451779494, 606234691, 935384974, 504292651, 564614539, 752897129, 60480486, 838085593, 221278822, 16126502, 615764762, 174396373, 521397910, 387532609, 846783131, 380747044, 986968620, 264828038, 941875012, 375529543, 735071920, 567851410, 655388200, 312800675, 564239059, 638542043, 451847067, 465244057, 280222968, 45284330, 292999533, 233375565, 879329730, 569328038, 323094695, 673274030, 846272799, 781926751, 520752535, 514637639, 779955153, 339976522, 370066033, 608323998, 790215900, 740934478, 400425126, 49700418, 102287162, 603905597, 822072635, 734622132, 592983400, 79702933, 659743460, 625629853, 747267171, 85216853, 724232394, 269885138, 178619843, 170652363, 331611068, 468339328, 543331258, 740361589, 369559374, 141836517, 653960123, 435601815, 720775349, 945833113, 171895181, 611226822, 526037108, 903801070, 833653680, 861455907, 153278751, 460326148, 721783495, 282481981, 589662868, 429457431, 925306652, 152183793, 117032816, 375637533, 763298997, 536382010, 216236545, 613896964, 857414814, 200718727, 324028467, 494854817, 613679292, 698809419, 999556058, 398369641, 990217840, 181890210, 402105941, 909151817, 886935977, 798802173, 771361523, 72587033, 188254565, 696721208, 322951932, 383181304, 888083169, 986309138, 346713478, 475842980, 789067797, 502010232, 315216929, 471617113, 430458048, 492970971, 289930147, 751466499, 88074475, 561639, 684199818, 87046760, 158587843, 875723324, 441273418, 495965768, 12542162, 873760427, 35667809, 481895550, 28699101, 16902817, 959074921, 42897220, 202014916, 225857912, 373250835, 118843499, 199899554, 566489901, 735048369, 433100197, 918100846, 276352245, 850980122, 122593653, 599930159, 832022205, 58770240, 728992837, 761904419, 997736342, 265454761, 711427032, 145853104, 487258868, 743164002, 739097152, 903360953, 88230100, 569481731, 606077915, 982380824, 234516663, 102235191, 857737414, 926736257, 459751993, 756652772, 598602499, 178364587, 207170860, 481937286, 689841238, 359569413, 684975581, 699383794, 130607781, 133414837, 34044318, 921976533, 130321819, 20899901, 30930109, 987400111, 11867723, 991702148, 438208538, 283671463, 708298459, 376107210, 713559989, 791399811, 946479833, 162401245, 129960071, 470656344, 862284987, 840130336, 608239784, 247094874, 83527554, 860191428, 530424961, 528857762, 866697707, 327666472, 845333967, 451565283, 122839324, 463365109, 152385382, 894179163, 382934423, 401043958, 42834453, 806294825, 819588790, 700309497, 514106930, 831781772, 85839279, 885959423, 863066934, 897375959, 708930051, 295326048, 61241821, 237977952, 597327018, 781523516, 49011548, 720066741, 85185473, 865019359, 654462772, 976770079, 866925805, 889920280, 368163321, 70449500, 704135265, 868818086, 304656817, 72922887, 168154860, 764074688, 217537029, 38618288, 256916063, 113212626, 186588357, 188425508, 356049328, 264802931, 307109827, 936651755, 308137279, 468920299, 169361973, 221089425, 922996336, 864758132, 976430482, 148120798, 653794145, 33526550, 809125683, 259517875, 141371086, 407538264, 56786657, 692689250, 674477027, 276558482, 53211307, 443718493, 9879434, 939215855, 69736720, 45849567, 556266304, 383172947, 427222508, 656118064, 852130633, 666024846, 400202178, 266923373, 199125149, 131142403, 714066371, 346427107, 562528509, 719685222, 966788590, 594473442, 402294027, 404859150, 534148951, 585411484, 602566864, 761484214, 960764566, 312874455, 397814317, 144567044, 430874816, 309881986, 330809037, 548456194, 330274093, 866887976, 144349350, 331449650, 766693783, 888375632, 233316887, 607414209, 693070200, 71744500, 488807200, 629168227, 174076723, 851241068, 739159044, 430190185, 479749554, 609355086, 294021713, 111825755, 200642829, 764319225, 152222502, 676640300, 124715511, 705343078, 556324524, 866657469, 81912063, 552545034, 141922945, 717091078, 933464836, 318760873, 237450764, 370450144, 141534582, 437988518, 934545766, 46056396, 534704659, 880252898, 447174484, 115134637, 788220596, 737477865, 763331850, 714586314, 294214464, 94542428, 62115265, 112018879, 19735561, 322885497, 911814011, 326921798, 515254732, 989564432, 450274077, 875892910, 700327364, 184001601, 192465149, 784285996, 784393573, 983291647, 238125202, 781184924, 344923506, 819452127, 528209134, 246941079, 949108763, 75722503, 194423801, 561771022, 142923901, 741683952, 756690123, 16429013, 750394400, 528752324, 55895575, 549473964, 700537762, 986404361, 562498987, 975334460, 110956066, 886810283, 223878568, 558846461, 205059708, 991237658, 949666311, 925749103, 899498722, 365480545, 138661989, 990892817, 419889516, 533551716, 46516542, 577307608, 739237526, 627516391, 749666445, 796246753, 133565940, 369578699, 253450732, 317685255, 745666455, 902291049, 466209812, 221280371, 617141610, 259453519, 235744733, 734780698, 528763944, 968047166, 745918082, 348785794, 146223299, 596884092, 628040098, 363627146, 188402279, 302447826, 406511761, 291179566, 240085718, 12707210, 597556429, 756507126, 161279072, 601338868, 954071074, 809934823, 251684471, 81344244, 305458159, 590794359, 134874375, 275124609, 237827635, 547445429, 827327017, 428273896, 816751872, 703284718, 658403035, 700865596, 674914211, 437291373, 737342048, 7078599, 572238123, 399450607, 537932181, 734651005, 482719951, 948839332, 343479440, 365734304, 971687152, 161928400, 282764973, 210304273, 491900674, 575938277, 401516756, 66100141, 263701116, 377230788, 889435482, 516758578, 398483913, 97861489, 298383629, 174610119, 527281065, 937447771, 385596361, 692367448, 98489754, 686493098, 742457633, 915575991, 814665086, 931390952, 131969114, 851423303, 560640485, 438414599, 601835178, 56432440, 656864534, 696228648, 415976580, 784254880, 575614467, 400153772, 200498418, 527054802, 263610484, 641899080, 108453750, 774660779, 297945906, 41729725, 279318285, 288766182, 302305771, 502598073, 495094403, 546225744, 872070484, 26456430, 402714849, 812305297, 148493994, 222761732, 86997371, 4331819, 755659176, 348902343, 601657573, 62666404, 469258440, 146283276, 441099883, 239208656, 435255935, 94856757, 694221014, 471589265, 246824425, 800124104, 556092152, 61390178, 228503137, 250738315, 770603334, 527475056, 462012134, 880310102, 629732292, 873128845, 682224484, 536620001, 358091146, 825006301, 507550393, 561231572, 616551766, 285505164, 338852875, 731656187, 921454926, 807246590, 541682426, 330013369, 972868535, 705620788, 16645105, 250611793, 385509580, 84958733, 256441431, 676899378, 575270661, 35159589, 834570264, 741036386, 579276090, 631332009, 534833461, 574313231, 400863339, 920647357, 869421170, 322203804, 536240554, 861226072, 71367064, 277160788, 935534992, 88387493, 490671711, 574511162, 642346575, 768560220, 476727337, 661089159, 220118164, 238583867, 593852555, 307073711, 95426798, 684541283, 249461953, 768047376, 982405807, 16419895, 239379039, 810787605, 525904434, 719919432, 813067888, 985553946, 954600675, 279887168, 104904037, 554451858, 787988655, 554350247, 343748570, 342051899, 672203811, 918613181, 910176158, 109943034, 821661088, 894410430, 751609971, 669268269, 21205897, 560670389, 546252168, 362555644, 399593530, 5912378, 120233055, 634009335, 698604377, 584622832, 24697666, 19645565, 846617830, 40783902, 971899692, 898473895, 917316877, 926545649, 105357248, 2754764, 629280984, 302230772, 692107791, 597741751, 621285381, 411171284, 818551185, 120540814, 591252730, 328243889, 41549998, 399616147, 104308789, 500333854, 179798397, 746517113, 396640092, 631645740, 376447731, 384309064, 446180102, 447346782, 881470181, 700406615, 386381758, 672616574, 878015205, 807526410, 463354839, 548052019, 887444032, 726839419, 2655772, 885729920, 320241822, 649743556, 995187365, 842371475, 439233232, 532292684, 249422420, 175506725, 976915232, 29494108, 323100159, 835713193, 845328088, 545775040, 871937733, 291360317, 435109735, 785320583, 607053696, 600495807, 209992385, 934204294, 960363462, 634328486, 706040794, 493036317, 295035816, 918106398, 624006407, 960147513, 174798607, 614902197, 188132150, 395917887, 120178111, 722032769, 488244653, 633681622, 148990445, 6141693, 246756914, 350381440, 419718276, 64592799, 206357322, 785666251, 568050512, 465232777, 687659992, 864519537, 195568853, 626754408, 867818992, 223451740, 880552233, 80805858, 446326761, 632444749, 733042741, 327578479, 43473716, 416719214, 761176268, 716618870, 827758630, 775389104, 384130761, 745788244, 631903432, 883634705, 15900069, 420538529, 403086817, 921609798, 283290171, 135419645, 50146634, 701304712, 777454693, 386101378, 974327447, 38985355, 123864198, 640662728, 351415246, 923497426, 469782567, 320133533, 952961028, 253395301, 277362936, 445606442, 607031344, 191683632, 571055776, 264814143, 170784779, 208784328, 249676149, 407033794, 273376912, 558477690, 486374474, 896154163, 607121942, 786180366, 189287426, 369840101, 59748136, 215395245, 279837753, 393357063, 500930554, 743169837, 491772583, 949407475, 112687920, 131285437, 268644085, 210742844, 519604469, 833932891, 638104579, 863561880, 955145053, 859401017, 651923670, 617613941, 395007138, 339015760, 482848658, 220910172, 754349810, 589685126, 809626074, 237503870, 58596511, 9108285, 241498204, 879941494, 597801523, 303384146, 13612337, 570352658, 783518443, 69540949, 327039166, 32907897, 244297018, 41104804, 415074896, 65467481, 463711264, 89471570, 380690782, 646331256, 199821452, 835409028, 839394885, 800754735, 55755813, 435551463, 115678340, 823026057, 700079867, 110370956, 346177276, 295991467, 624291524, 729523637, 917461649, 528991189, 107338942, 777740377, 195992804, 203951023, 307486830, 45637064, 687651244, 351634657, 962132333, 786649593, 748587819, 343489993, 890321221, 619606459, 577494504, 740416282, 961811648, 410615541, 182794272, 95226327, 981822049, 773012863, 257933769, 949339390, 799182709, 801473772, 292109006, 869826955, 88434374, 744655270, 324835758, 576653180, 139682284, 868819694, 976373111, 881528083, 987785101, 672669817, 641179505, 84671759, 502437761, 358745321, 354201252, 223757731, 137759270, 190592683, 895199958, 369510645, 726092842, 150084157, 993580146, 29836509, 563681097, 273641385, 401646904, 631431305, 322153747, 814675608, 414336739, 524777678, 168707447, 194140005, 176190815, 519763209, 763041219, 494908732, 989050452, 431995324, 202237604, 862456958, 642895564, 530128065, 931652380, 504661114, 524139528, 385431398, 808468090, 759040777, 906036585, 807806282, 735148906, 321087079, 75122743, 120837557, 221055670, 549745641, 410597918, 270951451, 91665690, 896970490, 336007564, 511564117, 826002007, 7041832, 471499496, 182844138, 790052504, 737180413, 147043793, 592124432, 601565234, 366148581, 963134581, 410339190, 386078784, 809218070, 478462692, 260293619, 121208069, 242223274, 5209081, 152252623, 38668597, 410022603, 610397060, 533952468, 151678681, 996410305, 839818570, 504932969, 686340697, 818220994, 41623051, 797940721, 113244328, 742853747, 270119264, 795788772, 218726021, 65991555, 850828526, 694899678, 797051082, 542575830, 74526830, 392047761, 714634198, 638913965, 55106872, 547973591, 742241575, 859732311, 838467909, 112151861, 222260355, 180396888, 687157040, 7896075, 818836628, 608149538, 973006428, 655392328, 997224107, 277279675, 594206688, 386664878, 374922612, 822903321, 485035393, 169555, 186498448, 866727699, 784596347, 685951782, 442106436, 535645735, 679730917, 590402842, 236634364, 673522931, 997198881, 484308717, 732231369, 370802184, 352520076, 954332393, 761206351, 881197853, 240625885, 20022613, 789771946, 190006549, 774269491, 244493071, 213640983, 876432773, 447391683, 244769414, 442892356, 883795035, 31076617, 967514531, 766250691, 728686699, 567166338, 516894911, 935369984, 430719197, 210868886, 875584398, 321313953, 864019708, 638316886, 465979379, 622131417, 184640981, 598202173, 38750572, 211814545, 403962257, 500036420, 719701717, 750133151, 78067260, 720082010, 53020998, 111463034, 862382906, 601287705, 210319878, 423240770, 924966467, 82677823, 700023930, 866363424, 486334258, 543008159, 316067192, 189949209, 643067739, 917804550, 340715813, 639014490, 836790308, 857840416, 260827165, 657383725, 306522840, 304203605, 278402073, 137834220, 225019241, 135073761, 407185150, 204153313, 747928831, 926520619, 179107226, 518726094, 366737231, 714299037, 210217629, 775588301, 692140763, 46935496, 625237423, 961979206, 319824429, 601494526, 336182834, 159894952, 282744141, 99752662, 547098688, 234559632, 391623943, 620636213, 218074140, 952305231, 948609498, 10188176, 929632710, 94010464, 169396635, 743829634, 947462175, 79801804, 243247259, 727658883, 552933516, 860814203, 872287387, 637857899, 233249073, 502305880, 292778831, 439449547, 472851299, 849853, 7299251, 565856001, 410407325, 562110144, 106393434, 588731432, 133719734, 260755361, 279678286, 492000780, 335008057, 438484302, 950177194, 918822949, 234695348, 47178008, 14277520, 252454719, 757846910, 641658275, 365816521, 854934254, 370998558, 340958834, 131709062, 488217955, 104404561, 349284417, 300954755, 540737693, 859785281, 188189688, 662597068, 776362622, 210970332, 839135496, 323915321, 651572985, 507195280, 956113648, 937010989, 877550045, 951900250, 270028550, 462321302, 379927562, 785300560, 514815540, 746342188, 728808726, 561270710, 853300561, 318072297, 21771093, 509665326, 725905284, 167329788, 309785886, 869171617, 261402981, 107236015, 110398674, 296302864, 130476993, 774868043, 139281566, 546719273, 824427531, 212838973, 718543567, 325695711, 992857506, 275781954, 978957827, 802007034, 126134662, 314321753, 526636509, 669860978, 297617464, 971963755, 308736211, 264137658, 693969935, 641242481, 229105422, 608031116, 811489123, 295262517, 562487393, 380466626, 65365086, 122236785, 696024238, 455993045, 11733920, 182303105, 451753704, 821480930, 988903438, 423166622, 714298799, 469935244, 470688778, 907163775, 207366779, 118229048, 652973173, 129866562, 645653421, 910126417, 107139217, 496129142, 776399470, 965807421, 255450856, 487356227, 640647638, 458605059, 798926944, 851461505, 718815019, 510526688, 825873168, 253960434, 73103550, 876997621, 992239786, 266571918, 738216878, 1375081, 147889034, 254261510, 963369701, 458215256, 177922449, 732903216, 456918709, 152241006, 493832756, 807776793, 710620781, 715316346, 451972215, 476588272, 366284705, 728354934, 24904837, 338695963, 160363176, 850299682, 589835789, 966868326, 462897894, 835786827, 208498597, 71762643, 870803947, 948222062, 61304794, 361728285, 126326102, 799657218, 303266305, 227952506, 617083974, 408620562, 552050758, 818807126, 589410944, 29019827, 924104101, 320908838, 670085586, 695989428, 744484653, 169634875, 658212059, 575511330, 364555432, 531451066, 695726061, 323714037, 585115196, 31782947, 444958923, 510863434, 702912923, 105287083, 919933837, 857982724, 108004002, 662443213, 639442141, 921725922, 60995178, 414607692, 731108687, 715190633, 397275464, 552409625, 736490631, 706967803, 550327560, 825423070, 878250286, 570310929, 740698009, 829249315, 201314289, 359009898, 270131622, 353857927, 389236591, 181370266, 279517306, 676871420, 343499823, 350500369, 82031725, 657004104, 252916064, 385428852, 181389092, 230321601, 26121821, 383018349, 240263786, 542043884, 235954224, 674224711, 775078512, 612447007, 144107551, 756371550, 795035020, 499136675, 276252081, 625833759, 625527013, 649183668, 258642108, 859903211, 44326388, 955169702, 496340542, 344479010, 955110460, 855910031, 266330786, 647646288, 681003327, 565459915, 94778947, 798882640, 338089335, 337975687, 118527076, 632776555, 706287228, 886348480, 115304455, 190149520, 720783547, 522908592, 802612348, 617647495, 380037975, 9275579, 976542375, 515722503, 351126144, 327853877, 993938931, 17963358, 346746055, 760284185, 344771643, 584655391, 970726446, 530756969, 621164508, 487446146, 73913117, 523067188, 315021817, 962001016, 4571229, 742405672, 153488361, 617251213, 276044189, 750851639, 689664226, 189060915, 889194475, 225717708, 561536243, 33303088, 932729914, 79508745, 717346465, 879732119, 679095167, 29621170, 82282959, 533685587, 587323060, 713563732, 179508384, 515852382, 10669718, 910885137, 633757626, 628224683, 845372655, 601124275, 416007900, 911712173, 274939084, 598614441, 452356232, 7187469, 470963314, 294638974, 215155621, 818576168, 539458785, 435402659, 661076742, 680241039, 398299729, 517753279, 947646511, 834215052, 933470564, 717089161, 469993466, 165846411, 533905831, 638646525, 883159158, 185693176, 518970910, 358746826, 261303567, 829935364, 535242099, 677597869, 999703173, 915258333, 263018838, 160676234, 544303462, 916818114, 531010686, 398444184, 891721116, 893715794, 579005272, 538602718, 919428312, 654860481, 128090283, 743998301, 682909219, 178945427, 410909759, 357996537, 817983747, 161979026, 707755396, 269292698, 393867890, 406191170, 296539328, 383682038, 453930745, 536047511, 546686029, 276434832, 272082653, 631092961, 634571427, 210488800, 801067367, 177981288, 719015570, 125539399, 251855903, 994705173, 341361739, 276146614, 82199174, 659981136, 558342002, 116755006, 297249287, 913159686, 303136843, 937745784, 784183380, 555561488, 425906525, 92724957, 425214373, 485185586, 428893281, 23223360, 38058443, 700551914, 227060915, 37363308, 87721013, 800389259, 41022705, 713234463, 508604378, 215325852, 809524671, 301117904, 111646954, 453866200, 264587275, 396738076, 117758842, 386171946, 454883455, 290563973, 467767840, 712662989, 329093813, 102775695, 271054045, 527256497, 307019937, 821887339, 297378124, 328508735, 810225467, 20408038, 486842188, 31522925, 550204525, 282565850, 644453729, 944390158, 72845079, 868308766, 719274088, 176073676, 72970343, 139736213, 351401737, 187744379, 198409080, 887560928, 976385115, 864901825, 5564848, 541157876, 153769828, 813424570, 941961047, 827362414, 949130709, 57027455, 916103893, 830609531, 802658822, 56299606, 171693696, 771987940, 565253003, 323365363, 494712100, 30779239, 169084275, 292087147, 891484244, 273416585, 973485526, 267020504, 965469925, 26299763, 991634741, 826732324, 998110427, 499068064, 23413794, 601099391, 256189684, 821798415, 963195896, 629035232, 152633339, 936845606, 636391192, 803087834, 19894896, 183114796, 194460448, 741898640, 8342455, 93352496, 393842187, 758200816, 620128134, 532211616, 595145050, 15689877, 880297306, 788937730, 570586234, 230424526, 124179774, 194374088, 671031263, 739191386, 485135553, 505403115, 941636908, 960520204, 418966204, 650341855, 716685841, 141736642, 818493450, 69563126, 474632263, 68307837, 563830748, 618750014, 266543293, 759699263, 453181824, 840004145, 204024078, 86540361, 208902777, 691792282, 886511813, 116219663, 46411681, 832014022, 359094075, 64134909, 993470927, 742311554, 225919967, 848724655, 525681207, 528891207, 799523923, 92049203, 455900072, 91458261, 369331454, 78742737, 28069006, 239878992, 97794540, 33703532, 831430579, 803127495, 264207707, 555939307, 68322705, 123518913, 713128915, 686115540, 734040383, 922625459, 909968794, 811448019, 525455843, 639502889, 25699212, 870037211, 90813063, 529570352, 346436063, 712606885, 241447369, 857749279, 437205689, 21498960, 611153400, 508258366, 93726319, 399783462, 631765452, 693787518, 50153541, 847016957, 82775299, 741096315, 796247180, 669651402, 380246574, 595630377, 954299210, 435792508, 357223623, 772568411, 531605304, 806018098, 57995778, 530551219, 307910701, 559711369, 714985976, 182931473, 672643381, 851895046, 870319726, 161363907, 812549936, 445216924, 690020917, 700966970, 193282016, 732064891, 43272853, 883572421, 473833110, 34203716, 934232129, 719530125, 374840976, 273993565, 735316309, 822312474, 676647787, 911562237, 327830898, 592102013, 548365690, 554853413, 808737576, 377591458, 384585393, 523580915, 419011759, 264374682, 539462488, 875402358, 356787493, 315555272, 964085714, 40246856, 6243552, 209510561, 788113175, 851270858, 353978800, 991483711, 934575132, 24386351, 842527654, 356939058, 22408288, 239519546, 842592009, 778293400, 847548252, 891561398, 969533079, 897478586, 669886259, 783920624, 988475799, 366503348, 742733088, 729425327, 658449745, 854025912, 906082842, 62495707, 934813315, 145190307, 421908935, 203116381, 143640867, 46680903, 594878773, 447567912, 121457103, 936630347, 352145124, 913881730, 80312387, 780962178, 269335817, 664854131, 676542027, 296764363, 283477597, 924579130, 335085470, 684336152, 430916840, 780694770, 547851502, 352261680, 610914443, 339878090, 680087415, 639583589, 122498260, 237179440, 710969136, 40359050, 229704329, 442351808, 804186786, 122241693, 917307097, 546362416, 829427602, 399554192, 143110850, 998667132, 819505067, 543802178, 287277226, 871972010, 151472222, 171004576, 85130237, 653005060, 627575183, 777557794, 346560129, 162718526, 420626391, 59236782, 439403647, 861996503, 217289855, 281376210, 904964820, 520381013, 525031363, 91692156, 495203860, 815128593, 406566378, 11266340, 758603919, 219187740, 557489293, 731526802, 18744001, 617073411, 309651030, 430449720, 669993154, 697884863, 120820049, 876774213, 907115413, 248098795, 575235869, 35379767, 755467889, 434543014, 234192509, 615921324, 887405522, 366102119, 685859676, 784607748, 419966684, 928397480, 861558625, 187983083, 974326369, 338477263, 958505512, 641100895, 989544155, 23913741, 252561321, 444580750, 944409133, 639662556, 294371860, 786932201, 442566150, 921197656, 365148667, 812317898, 310329971, 860637639, 920710184, 491064847, 959495882, 265268460, 225861147, 571696218, 5404041, 47735754, 620275470, 129157865, 413168397, 953831516, 583764091, 136968006, 271771695, 728768627, 358303247, 260211836, 933471744, 542692276, 230796793, 445784015, 487786534, 950323771, 964744355, 997439775, 333175923, 890341113, 148811853, 480157892, 746301130, 506688530, 145646757, 251394130, 872958974, 611283421, 566303944, 827215649, 971571594, 132768738, 547561093, 317051704, 882471113, 201335464, 771103559, 388162270, 774454413, 376863328, 413025136, 94921660, 59391628, 824782658, 393658787, 278057219, 534885517, 534772265, 186568253, 309200702, 941395772, 508120872, 97641933, 949750951, 785100801, 404474966, 453483995, 845091948, 91197145, 677095299, 955160548, 420774463, 369290759, 611870109, 304565764, 501911687, 819013130, 310336333, 901361930, 558744514, 271607686, 54347015, 241490591, 847206630, 260370227, 537985455, 736009850, 383980738, 548435383, 294434121, 199540861, 122811977, 176244726, 320842723, 262711529, 65823133, 29283379, 834612427, 285234575, 573240709, 677598353, 276354307, 542743797, 907557082, 143852868, 577959723, 310253865, 289666608, 891352601, 979835329, 802845983, 283029458, 118315522, 578009677, 790411964, 690118698, 788056541, 811797576, 610078615, 565050925, 774000899, 130731440, 906956590, 997046984, 304578271, 241637289, 731399282, 204108316, 944202020, 714404957, 810227679, 849907578, 334355905, 325632228, 14566567, 105171950, 435632243, 369585943, 928377037, 207725636, 911716335, 30869448, 811572500, 248081847, 692292651, 164302292, 568916793, 344878366, 284543490, 737544984, 341864192, 876981260, 94647613, 75222313, 129394418, 781354012, 221598625, 648182192, 640559334, 359026062, 354700173, 805157812, 40782512, 196882057, 272280910, 778709126, 344972737, 68330259, 408250921, 246605947, 946771296, 433636257, 909392039, 325496018, 298748500, 56953816, 823003917, 958168810, 9541866, 230577253, 685188114, 251268919, 317477694, 191299712, 711154458, 58890721, 669924457, 734892139, 61353781, 779988, 348136958, 269152445, 416417584, 547455994, 333412538, 774804732, 557884854, 457960775, 559550771, 964623637, 446411790, 52638783, 384006102, 300204118, 632469915, 225958723, 307509915, 962561344, 897904292, 537821878, 959017631, 726262197, 636385621, 565835405, 619020054, 836700996, 566803210, 974930871, 16975952, 989870812, 213423539, 851144827, 405341063, 697118616, 214395242, 361066618, 580458617, 5221794, 558988907, 422756936, 945073203, 423733749, 382668863, 187408479, 891334723, 413148079, 278602107, 231527956, 335758300, 81289662, 476317404, 136262830, 189514592, 750881152, 886526176, 429394378, 172883541, 750115880, 855965673, 219819337, 856919509, 282759120, 424371409, 194301600, 704570442, 414368857, 225175944, 854786117, 661800299, 267582165, 973827785, 935746043, 119025703, 375826152, 167671996, 6398890, 150324727, 528361403, 310458536, 899917391, 430851672, 135547737, 882417873, 857624967, 90589157, 39992501, 357759786, 542102174, 415611582, 753539943, 135222518, 894411466, 183421645, 984113271, 474331115, 690732637, 201659087, 696909678, 21132876, 524478043, 327061975, 959744814, 571526279, 937816917, 598659408, 497653251, 141638524, 351586949, 215110912, 935218243, 832516689, 616027018, 922226879, 55220666, 157344164, 555408120, 750647932, 932634192, 708928621, 207249184, 215479972, 860431283, 362459276, 564717194, 947371969, 941834931, 646158162, 976944479, 187228228, 870543127, 632492888, 614569443, 380169002, 38341678, 812823504, 730399909, 204690945, 531310017, 344729053, 184850244, 974413185, 672280081, 264179666, 811337522, 493543024, 576394721, 490871735, 903444248, 986613870, 913304807, 898408543, 427725323, 332368236, 772777539, 164155401, 289707109, 82096190, 662310243, 352066194, 841016805, 353829053, 762792839, 595288568, 628699308, 380535985, 20305745, 429011670, 734798547, 389365147, 304045049, 713118298, 44410935, 539333489, 375117558, 68328407, 30170131, 991031913, 178910188, 94860104, 782739254, 570333005, 853509233, 599862036, 503734688, 705259944, 931944323, 292894250, 80627451, 86312249, 413958063, 210153798, 979977702, 771213653, 671791074, 54964648, 265425696, 133306298, 180668760, 135625195, 832626817, 252267562, 567692363, 85381260, 957616151, 113331547, 599192533, 961860707, 391827925, 301321565, 862207091, 845568852, 739563421, 474706635, 304516028, 42637061, 334885998, 354940404, 1719222, 875672902, 642687139, 772001670, 665354507, 824626600, 270935628, 690232002, 276318998, 246095545, 575333751, 129175898, 303770946, 726672337, 783857958, 941706232, 955378151, 63924872, 792930631, 722905446, 745450827, 485787148, 268349961, 235392690, 315325927, 901148976, 494746259, 767590375, 98270474, 585818449, 870875753, 587770973, 840656029, 901652582, 512254514, 84344079, 255089462, 826805329, 579187312, 418446258, 29487442, 108981377, 34923416, 98794812, 409158643, 630545356, 597162263, 685777681, 849351557, 849606262, 460014023, 224094996, 43316631, 407367476, 207004355, 153036516, 842946386, 831695317, 357003132, 690887785, 668171390, 872557577, 360189009, 724418582, 915528218, 985024557, 244534191, 972173571, 316107735, 599071964, 846282930, 587839869, 238741997, 843058312, 3369353, 135023941, 449899003, 993968406, 118827906, 513233890, 48408843, 118022303, 206459577, 714101876, 750169203, 286351403, 919816044, 984222967, 248387733, 551951027, 216366838, 215457709, 80731084, 643236504, 660007475, 366277747, 234615819, 818383125, 258898316, 19916588, 651171404, 206424432, 624981059, 743648908, 448282329, 5967644, 791318197, 831381867, 966689781, 814016847, 634403025, 471448289, 631807341, 376106983, 689434176, 545841396, 346624276, 843666283, 296459283, 645359355, 496936455, 980051858, 362241315, 884709747, 462267120, 730784247, 802768717, 514923059, 20465144, 534034357, 780788169, 888232686, 947447381, 846718405, 19348440, 885017539, 993340934, 880332533, 841711301, 756901875, 476768409, 115802192, 975469182, 996496983, 4500667, 693026071, 940238928, 282303168, 551650820, 991107947, 166413227, 626662327, 537484846, 593304494, 264333047, 472830406, 383967915, 131937640, 469593211, 518690204, 109701262, 433724001, 589460911, 87981419, 503321189, 917411481, 973646916, 769623415, 344380507, 17475889, 303160370, 501314843, 406540502, 501332983, 582592948, 828682035, 409090508, 5096288, 789077346, 875370153, 782615462, 369077364, 147559651, 669617953, 890531186, 313826988, 862508804, 486539360, 177740430, 836211554, 401875267, 56666153, 492809936, 379994429, 553000670, 443324051, 350137230, 4305752, 143478941, 456067512, 953190388, 280861565, 785690235, 98438175, 480932944, 624936617, 557986742, 145939091, 221442793, 40986745, 414725586, 408582435, 595277840, 492736829, 543156446, 819057905, 358873319, 498389677, 172060803, 70772757, 26242108, 199881932, 274079032, 898814596, 289676181, 533829535, 793293851, 367543661, 113908991, 535493540, 345604814, 809558797, 749615480, 312694439, 614084502, 448597595, 343247423, 425288156, 677268857, 780209943, 132331046, 92112570, 360196024, 238655288, 284471350, 731640510, 515319310, 779792351, 328153275, 645266220, 486343587, 94932265, 865586668, 817905630, 112572052, 202733685, 610974189, 432440725, 432919444, 691207598, 771017932, 462012136, 432040145, 381256815, 497699787, 233385663, 816514085, 916654549, 259485038, 380312838, 271389650, 212783904, 417594977, 863018988, 772461893, 7617187, 892160380, 566661907, 764768368, 642119063, 336006724, 949438074, 284349253, 137287150, 884170777, 748100958, 736060352, 337305632, 801563752, 486453347, 72967801, 748469757, 674261723, 891905913, 615597512, 57932076, 289020223, 461888916, 414544691, 537402870, 770889654, 990672959, 279116354, 832281891, 362207441, 457570169, 772418008, 75867607, 371405197, 624503861, 323026788, 407251650, 93104946, 972515739, 92866565, 617347585, 969311280, 583658661, 733494047, 653091902, 136930117, 453391555, 554203533, 986487270, 928831968, 763184928, 296902285, 486138549, 937659648, 266459876, 54901662, 812864548, 285773187, 947027852, 680598722, 712377095, 687800365, 672211695, 519141717, 773417867, 119112401, 705923771, 313047743, 512817645, 449023675, 486127354, 511560984, 556462065, 463320325, 343093303, 109194568, 451642632, 622191424, 154287664, 796271695, 145452454, 233018199, 909118807, 255425758, 754978504, 444019809, 688719103, 468963057, 416846633, 530997359, 883610607, 671185383, 802976975, 4500307, 165397552, 915081004, 275100848, 606196810, 23486438, 505495268, 863597601, 895063910, 831132052, 509246778, 405176683, 754456529, 646627772, 560774272, 793282277, 77816885, 579171183, 529860868, 490565024, 26534071, 170604191, 785597936, 989586010, 677732534, 48352813, 859591841, 510324837, 156803171, 47686090, 239543673, 531598895, 449555864, 575173934, 726495206, 147069523, 238537394, 61452640, 957023357, 385918561, 677320443, 806363938, 7814936, 206649674, 423225445, 821030225, 448372214, 136100379, 296356022, 661486443, 906413276, 784203158, 247644959, 930267668, 688588161, 365427069, 208863267, 672113025, 631218283, 755216456, 670089457, 569257262, 16200509, 498566061, 49713782, 596520222, 925378792, 974510742, 770854638, 297585748, 223491854, 187582702, 418791274, 516625989, 538385676, 89615050, 844533137, 516329735, 214240330, 365126145, 465883115, 576659309, 179026899, 765577307, 290615921, 615078017, 752242600, 418685875, 510656246, 525347499, 427735625, 468807969, 134995509, 82772618, 415280443, 254199146, 279220277, 595746343, 674107127, 718444758, 401323524, 910630263, 398660112, 839065158, 270784345, 961649470, 502796884, 126020878, 95393876, 845130707, 721416808, 67530076, 325318528, 676686614, 804581255, 299390919, 670013888, 87388469, 35759274, 917008584, 971718005, 337413261, 514364432, 642898363, 508583322, 246235294, 235615374, 924922752, 136022411, 203174583, 832841299, 770791366, 922913899, 959383851, 666210855, 167431395, 91402907, 20587823, 335513097, 567480071, 82717344, 785653203, 513849598, 183467388, 994261295, 247161324, 403559225, 294477355, 943192325, 543161378, 730109648, 576425090, 954447041, 270128720, 668458120, 896332990, 87607988, 790164452, 696785515, 229355478, 197806556, 569616993, 641576670, 895925023, 663459100, 143078560, 127336301, 88510827, 788157234, 833218305, 980549907, 772052164, 795244338, 242187725, 942373095, 765435929, 858916355, 699092547, 860427314, 487994043, 105051576, 688777719, 89784309, 485065415, 110980909, 808168469, 970001152, 594761413, 309872970, 356955795, 292609604, 963025087, 632307480, 81032523, 583803511, 840612188, 29090396, 592161409, 273981860, 667724431, 211649705, 913410629, 482867182, 927919625, 55233069, 821406593, 998948869, 992619346, 999198931, 194067075, 346878615, 56254897, 867094785, 36263848, 791474823, 158483638, 563777600, 97952479, 336447091, 616455520, 7362021, 512297112, 735967015, 371929046, 153694027, 964500955, 900298692, 889401559, 752822205, 6125937, 939435985, 46956846, 792303429, 347302504, 760018027, 520198783, 507670523, 20829309, 165304242, 471673037, 579521387, 965463976, 707263955, 812116507, 264053525, 476752441, 770855613, 779644806, 715945750, 611723901, 117910549, 805339295, 904496433, 775549978, 184373119, 911695104, 674689582, 253532277, 553703900, 313552433, 733230331, 889961096, 838621457, 699518217, 307068898, 257083158, 737503126, 777679320, 842948827, 637286793, 250200453, 15797973, 750210889, 668291598, 551684764, 393437616, 314241045, 927932561, 323736421, 303701698, 296044151, 860382434, 173682170, 977873913, 249686031, 243332738, 199893966, 875059640, 122923305, 457610143, 60256117, 682415887, 727539977, 694434339, 910080011, 399262402, 51699252, 90920368, 202215213, 752475764, 769386196, 509530168, 686779724, 345969097, 598510252, 55499498, 660317491, 739568830, 301650443, 343650531, 895327468, 403239016, 227330832, 327743530, 903004206, 311117856, 886148154, 484756820, 362369387, 612752013, 430813052, 231656418, 638444662, 983825475, 826490989, 213870029, 962666843, 792623902, 23649969, 392764778, 797871356, 706385603, 710905535, 269568104, 662107726, 347430571, 702743133, 529211999, 509981149, 254271961, 974971159, 711428612, 571655825, 988714872, 779172762, 13664719, 831349816, 954734364, 344676554, 610365324, 197947438, 648518018, 402851045, 805476574, 288580926, 204885950, 253845024, 318356305, 827561476, 219716212, 659859623, 462287738, 757426837, 36720267, 929012646, 783394162, 615413122, 261706855, 342556399, 519304064, 540461710, 943295167, 918530384, 332017966, 705110528, 556943552, 835983525, 954447211, 248930518, 117595237, 485723544, 342419732, 356259654, 842406303, 798480043, 340835173, 617349099, 399613220, 600244197, 972368947, 334432598, 103253519, 473253948, 732306984, 814318857, 810693351, 365519488, 910849473, 367721009, 522352433, 114563449, 38870652, 550532313, 646901359, 214232496, 920524785, 158509407, 794816912, 506543406, 785116585, 546110348, 105272397, 997519761, 309795874, 989729625, 748084946, 240358763, 276631747, 412556727, 865949420, 53761367, 178274222, 939756931, 440083746, 522844609, 77119991, 182552196, 897129301, 432641518, 198850030, 366267709, 933060804, 753365699, 264999867, 756956573, 469957960, 559484009, 4266208, 636546056, 186310408, 182027535, 625069334, 682203171, 720012359, 749624604, 609983373, 386710595, 432239806, 236311761, 580286941, 690907134, 369142480, 626687655, 205585395, 906565457, 803745949, 498171348, 760290705, 787786766, 830531037, 925173483, 487891035, 987297557, 59215575, 20769092, 250135009, 976238968, 790772291, 805083052, 806396454, 594704633, 288560962, 145541499, 521907580, 491519453, 247673616, 571132005, 733141567, 730933455, 778897108, 359579755, 68466049, 579003222, 707101543, 656287215, 545022096, 422053942, 665503788, 528780078, 399678565, 658689696, 761024555, 732751616, 170616825, 839316990, 956429187, 525211418, 300376851, 9898817, 11383671, 899815184, 739008369, 877439583, 796645450, 726825066, 571308819, 755245313, 867197099, 63389959, 594567357, 85931579, 415495614, 180055875, 497958171, 455922426, 787659457, 735825871, 577233683, 352131438, 686282707, 789046768, 783138324, 555005932, 542379988, 901408331, 933813169, 467911078, 525120983, 855086647, 492324499, 25675325, 871416107, 164612722, 566388776, 12562722, 81804684, 575356764, 13511367, 249432296, 540996593, 809633555, 342657439, 697587365, 749862402, 463418766, 861941421, 222968348, 726777411, 749106555, 115601651, 662325101, 496516296, 18334620, 684937062, 727953365, 343488912, 193115753, 440114157, 758284384, 990787281, 104572646, 885376555, 296727717, 706914847, 849871526, 507244771, 813895292, 816484695, 780859975, 428739734, 405911389, 188349365, 936628881, 904363908, 764772969, 89752943, 987592405, 865305804, 106047971, 595408855, 449988669, 726461509, 515473586, 969182481, 213560543, 296283141, 907813464, 171757454, 462104448, 235080325, 876720956, 358030164, 739844436, 276936022, 55960014, 26088784, 898230683, 225643428, 139459704, 886182421, 622982186, 232761498, 710489081, 580652926, 788670925, 254083429, 942911550, 583407404, 728711664, 170072243, 516639685, 496085600, 866565926, 395540308, 898000122, 444031981, 435935805, 328401000, 207887438, 989552997, 985847202, 774411296, 53167338, 426250215, 763371444, 804615082, 626490060, 605605170, 132251931, 67649823, 848954847, 419670752, 207825938, 392295079, 548000673, 42429760, 604800706, 797802706, 962085226, 897190187, 921925874, 760425581, 290423185, 166163783, 825672364, 6713485, 684059677, 8419834, 403527755, 469156436, 949948042, 602704421, 38716367, 725561252, 998057412, 61101667, 975001881, 541782309, 130796403, 726688918, 808518526, 923022808, 21150994, 229122192, 821888544, 591428827, 743863937, 961174352, 22750573, 704138530, 46788953, 45935340, 530470500, 279823311, 925349940, 212333333, 532912829, 455473581, 172215604, 369028370, 577646372, 286889341, 205660003, 410788662, 370504363, 141151960, 59018782, 631880725, 768262308, 904938209, 85478873, 373102843, 421430573, 698818109, 551572187, 570204574, 249437998, 708643, 901132144, 688547404, 71009153, 581066120, 480063901, 203620586, 616785624, 303726635, 504502642, 573830689, 275533772, 316366597, 80682264, 448689955, 800201082, 876805830, 574554214, 105082484, 55954660, 70094763, 306816268, 687254175, 53854307, 83106778, 686696, 641684079, 291047976, 58379835, 833941126, 345500274, 554338609, 382694550, 383803809, 750483985, 673955806, 432583122, 227744346, 224029491, 887622722, 204258038, 154084067, 487140198, 348359842, 584052760, 698206274, 305460694, 497394898, 738303200, 504234052, 608287883, 719698017, 393209783, 17385114, 815728969, 282259367, 245772510, 690652899, 53339185, 405261634, 161366633, 140385065, 879606595, 139439680, 747347693, 26417831, 54738248, 314833934, 609455518, 220763549, 270100102, 147078450, 346855728, 562961767, 395074048, 853736639, 386304935, 817675408, 933510296, 202175673, 135357307, 327917189, 362850661, 213841750, 710947845, 105622302, 41872917, 689537153, 182394903, 552414990, 175363164, 114787242, 961188596, 998974854, 740450445, 9083605, 546030522, 855334584, 659662713, 737173930, 825385596, 271027346, 245695392, 928854482, 862338873, 483040692, 23692170, 128177301, 305863176, 389491960, 90769336, 821211871, 576083911, 47542990, 274495495, 764699506, 187655266, 205419765, 375173597, 328318181, 211646820, 971409765, 570953513, 354342547, 246966750, 890567494, 557397332, 383201960, 229085446, 811607466, 345763423, 11986719, 829045671, 999471732, 421634081, 889411439, 644968734, 53660411, 91313377, 16929652, 823380898, 819183172, 648101253, 561157404, 312748477, 110483646, 933237154, 435157820, 811228160, 476483445, 632515588, 432097843, 207799233, 660467126, 887565306, 541294230, 665048106, 170845024, 591487723, 350802608, 160664566, 800222610, 370351331, 541464368, 505131480, 151884758, 284286877, 193096955, 878493517, 684903128, 643288958, 163078194, 474543227, 831826148, 399026398, 136829610, 350999456, 614667827, 103553756, 73321182, 186849133, 31454869, 342355254, 505664364, 590460524, 704942005, 635564077, 334980094, 625136921, 701543243, 203047774, 595409129, 545836816, 50075356, 925036463, 846047006, 646204132, 791848067, 549409574, 562364691, 809213599, 586034525, 346843122, 246683622, 783409868, 922578890, 151583997, 791308990, 37194480, 61408837, 803455292, 832704356, 475001707, 522899646, 62039277, 177629078, 730193790, 643945700, 773571405, 518324145, 207487092, 565316067, 674593909, 909337768, 768917398, 675647930, 758883523, 767540368, 620430564, 942759806, 403945327, 520176660, 124808790, 496162816, 350501435, 865227257, 134929849, 377200141, 677914553, 263764068, 360702404, 724636592, 497899931, 259483559, 888700387, 10458533, 391350312, 457419212, 811655387, 132233871, 918250949, 74136581, 903307818, 459916970, 350975567, 245077558, 848086846, 985007836, 457000827, 448811766, 122087960, 476337890, 97056114, 608967275, 433075898, 739920601, 371247586, 467166786, 979142265, 901919792, 440587266, 995712385, 507947093, 444534756, 609248456, 716942354, 47888372, 693299033, 343202992, 42779610, 561907648, 642901941, 676576765, 292649027, 239241028, 605631088, 519507128, 201699105, 972006763, 731124468, 248133586, 209070310, 614547606, 981846504, 167230510, 246282401, 529295927, 184320428, 383421895, 666805314, 358432604, 966528447, 83441642, 60011108, 676546031, 551338292, 601761459, 901043988, 975953023, 431548759, 342466411, 604207686, 21875053, 288155041, 103418912, 89334888, 12555284, 596769503, 138391148, 993454811, 88318927, 493930980, 207848269, 189357144, 22067128, 589495235, 184255474, 595181908, 208971865, 153896827, 997172864, 853081084, 528915528, 104667591, 563399752, 83118423, 291348622, 990415192, 499160486, 713118196, 894464804, 45502702, 236360403, 505150168, 99803465, 107071202, 352185991, 595671876, 771654888, 699141514, 315633343, 594631057, 797536825, 48029112, 992166506, 415904645, 759312368, 210385978, 292050552, 233258366, 898728296, 795027529, 964465944, 111164909, 646821703, 625060675, 957034864, 561988731, 204610520, 707212035, 395682366, 25920146, 476787506, 87482312, 485549237, 186160049, 179302162, 163182711, 333263287, 919635114, 877337941, 834475925, 152975673, 646781753, 878711055, 780234815, 614881801, 831151129, 943134201, 321139905, 969334923, 559092429, 380198113, 933639423, 461325062, 422843351, 854073687, 49419605, 504078934, 111955963, 415170263, 38650302, 686693251, 135586958, 23493053, 664491870, 518227303, 628045416, 620994574, 61616235, 611080856, 952151375, 759722188, 984580843, 837077964, 609956170, 95634477, 95796808, 570991056, 429530541, 296768816, 737652942, 968297061, 858953520, 54112108, 697463124, 37987413, 801806446, 161095160, 975104182, 571728230, 481712265, 11512819, 902771966, 866963141, 685863987, 390684715, 574387507, 694027107, 629642233, 757778801, 10144421, 931126402, 242358115, 962143504, 13858696, 840672802, 99727675, 785574328, 63272665, 184845125, 498474392, 449813723, 972715483, 29232658, 244141088, 676197717, 729901544, 482210559, 322227599, 768961061, 383477101, 164225770, 549481736, 309512660, 965173888, 839016175, 725105715, 858511131, 45427299, 723481299, 846760649, 545946020, 313524166, 790612044, 396297300, 267823972, 936254925, 755531026, 448514838, 267793697, 718045081, 356758135, 572108603, 939514762, 775411656, 859165480, 773618846, 407398645, 872425553, 899646299, 944256491, 44779806, 580896659, 19003864, 751468882, 947744145, 409029983, 649475774, 279569892, 264427736, 570715680, 860643193, 925111653, 541635981, 941250119, 252457551, 714651518, 956978188, 925257029, 88743025, 701436727, 652366595, 681515031, 112318348, 108572528, 204956102, 189184351, 952066187, 415091063, 429454917, 643396113, 510370119, 664575188, 448331803, 214738505, 812294225, 241146626, 708432799, 665879693, 679551978, 880811234, 917509064, 545908826, 321505246, 446031650, 545953083, 831932481, 858504429, 489144701, 268760130, 872392, 233527966, 779646034, 117697036, 623311004, 288470086, 77831640, 35195372, 392362692, 923481935, 546209786, 97994387, 772965268, 30792951, 124695046, 766184388, 39361032, 487916874, 604071110, 476730629, 193938851, 466810735, 287371208, 876563956, 557330367, 495272807, 971548461, 683063871, 864525657, 773067139, 796406703, 844345435, 247555291, 642200088, 776659916, 550135054, 776324901, 887310163, 57772673, 877064328, 653730578, 91662808, 255536401, 498291418, 714439882, 194595018, 994659638, 924552944, 815513449, 807134062, 982014591, 61853628, 102189243, 173761436, 569169992, 198958579, 837609314, 970011333, 17677091, 289399603, 379468479, 34109686, 81658783, 683476273, 454271922, 513301325, 77949203, 316570132, 121227334, 332984923, 390741998, 929098339, 976616368, 109271781, 582771117, 848501683, 481202738, 708016390, 979229349, 78481563, 997558487, 707390793, 717378701, 382657388, 958391483, 411213423, 229257131, 602068585, 297494410, 912350860, 512374303, 727852679, 605460353, 90502330, 817166237, 783165775, 858585602, 18282917, 323603266, 774822860, 859171651, 423717931, 803523197, 158693726, 983611409, 552725018, 455770092, 722868964, 289844225, 706682463, 255136931, 892291965, 796272613, 309981067, 859128367, 232960312, 701378182, 457587102, 867562680, 602344303, 773758909, 933870320, 192417995, 895279567, 209586163, 854187701, 60108579, 736143589, 431773513, 548628841, 434938430, 918831885, 482197613, 525675128, 473310824, 789890632, 820069011, 615010916, 428621372, 186757229, 763441814, 887744965, 594454304, 581625741, 856378149, 935068701, 946858221, 671271265, 44413276, 628833150, 643087583, 99894542, 60176056, 822613396, 752611624, 455120173, 244836249, 234578166, 282575501, 528270058, 322510099, 759725086, 65714701, 661716429, 723191814, 475051290, 843184526, 39900039, 987294105, 291777593, 619683026, 414632695, 470937352, 348115112, 903841167, 593325537, 240202443, 583453704, 368949397, 830020313, 121957709, 209321633, 867575260, 885310180, 422211234, 2641133, 651005368, 898822038, 745993150, 787123800, 443791284, 150027441, 124561815, 914630877, 264484755, 479696245, 435891189, 594204747, 590842507, 969147318, 678747477, 23199013, 300817173, 732242196, 118447569, 941161386, 700005236, 655874249, 560793058, 997854885, 112994178, 840349888, 746701650, 71156430, 948784330, 118448347, 604325084, 110106836, 936137147, 780121459, 361368979, 690250955, 364328295, 80805165, 385717308, 945526231, 807663146, 318016229, 648537355, 55770168, 476431208, 993273221, 44076136, 742022820, 72517462, 113507335, 826958212, 525289092, 974038159, 951843227, 554918444, 471444445, 747584729, 693889210, 487669718, 979136150, 663855291, 252845200, 147422588, 407094936, 813895708, 385426508, 826806820, 450785882, 626892601, 907111269, 254020682, 767642529, 116918911, 668919615, 612741561, 900100653, 150014387, 509734007, 998669096, 957542112, 251778160, 532942420, 412691963, 549790111, 62176423, 995933553, 748079686, 97981664, 449994622, 276031337, 862341648, 373574504, 843628481, 268890781, 600452084, 340315270, 407512144, 1329411, 458165557, 471506017, 82414572, 196558451, 810582409, 804816876, 649059371, 634988969, 476400294, 56469993, 971717657, 99368802, 998398846, 60929036, 226034176, 912001745, 643176412, 981808081, 392095148, 152086177, 885687035, 44700428, 530403429, 889092263, 138812406, 428896079, 955080170, 644861170, 108582646, 200432687, 694586155, 396821803, 662380823, 127219626, 17858523, 633376749, 14780415, 242164105, 595744254, 699879808, 946757126, 585919303, 618862828, 584568855, 28027870, 414498555, 139235783, 194921222, 990898262, 57251306, 440133639, 555873589, 467429735, 966371832, 500184173, 714425956, 247010690, 673443885, 939918066, 956461347, 719485267, 787811116, 756667399, 201712173, 721372744, 511963427, 792233691, 593340850, 916410000, 809408897, 339901535, 132189684, 679295711, 814549104, 144713825, 294602061, 279901202, 101378743, 182970055, 24452680, 45055849, 14119302, 245064664, 704547032, 299299260, 146773603, 151961302, 271940410, 960319745, 768140321, 607896720, 46519303, 477552386, 71595804, 172220594, 71002299, 248791693, 485483305, 618189094, 685230663, 61483724, 595661006, 486471424, 941160765, 612230502, 566023006, 895164424, 922957543, 472420564, 620654302, 88601193, 413439084, 608948145, 385545505, 992146387, 842488929, 865510840, 864968603, 948512445, 78895699, 140740802, 511508485, 204424490, 173239222, 941981371, 592570263, 34745176, 195354720, 837153978, 310789239, 604918657, 992986443, 102594708, 932636782, 674394673, 879215877, 922562830, 593994457, 177534020, 10272555, 698685629, 171507059, 790262364, 670580768, 335959752, 90746200, 889845222, 720803260, 796519866, 697587922, 918697805, 715902096, 678675060, 821809107, 421667928, 952458057, 613725873, 504731913, 469323196, 328527485, 227418367, 919197450, 194406569, 190109913, 916918695, 515565634, 54895417, 745991696, 876013856, 224988066, 451690385, 577605961, 344834780, 46258355, 317531404, 329025255, 809618646, 571431770, 662205491, 383973219, 403480493, 388967623, 783474605, 124617260, 947088465, 976395627, 813192415, 550599754, 407407947, 952496857, 865121248, 202462496, 751796203, 708338566, 865619296, 267537218, 439931681, 341084981, 637176833, 489383277, 371601211, 213822748, 305909556, 839315735, 626519603, 928813355, 129609306, 504859713, 394471893, 209107364, 589847200, 560709712, 731886552, 167289168, 793133463, 903743007, 697390346, 821565011, 721158835, 709632063, 804265935, 208523038, 381098767, 604050963, 516440604, 202636716, 106620197, 748220561, 119574280, 595295810, 402039031, 239325116, 542326372, 326772217, 864555993, 423958046, 899378816, 228134811, 752103908, 536544258, 343000204, 895062699, 55557501, 203982547, 767790868, 75114946, 739674288, 448846414, 100765064, 864519937, 305255778, 358122819, 990218570, 69754280, 963465136, 383811843, 280120055, 970992489, 865697063, 84104743, 424421395, 300055903, 905640034, 881922817, 291814239, 903688197, 161894559, 381609509, 592521316, 759231791, 190776832, 397406154, 42931730, 626522472, 750229914, 419133438, 803428531, 228368525, 275475313, 92485485, 260190579, 92329127, 220207340, 35662511, 802977306, 599819130, 491436614, 478703706, 516556181, 772266087, 842372644, 422738779, 110256799, 393958935, 389272895, 337757816, 84255081, 658280557, 582893514, 925068855, 807223658, 271750849, 890837587, 780395572, 103538159, 725152237, 220522296, 541029122, 566838099, 510396990, 792724696, 510097847, 810113985, 716948359, 569541741, 3023804, 258158621, 401704589, 274143020, 971453130, 753893494, 896643305, 581560751, 326211828, 982526031, 708230025, 475787263, 982002500, 205934439, 227666472, 696964132, 369844404, 122432369, 495243942, 419489068, 307734490, 974593486, 36725987, 298246654, 348990409, 394057097, 2786486, 735801066, 382837631, 419989165, 23701461, 748608127, 275884141, 554797964, 133758004, 836444908, 492451873, 331736152, 867493475, 450023261, 576555765, 655220867, 21593980, 623980420, 576599540, 310619731, 596680570, 289447559, 499500537, 319131546, 504583220, 389021097, 254606556, 252658807, 826483041, 969807883, 34367081, 242116580, 832824943, 919797302, 113532783, 743747050, 757799375, 654944929, 971335668, 643887467, 711002654, 900655421, 702449077, 910058983, 802460385, 475369177, 10741247, 785805811, 775040093, 700356181, 796677884, 779959709, 715810985, 884671386, 417337750, 220807304, 865886544, 477056250, 577664737, 68925009, 136868212, 190975622, 875280118, 951179737, 459433252, 983917875, 474766325, 894478720, 37273750, 814987465, 169989999, 714821820, 794841, 828440582, 531269736, 20569809, 541119638, 130069881, 941080887, 527558609, 94640387, 131681373, 319962873, 702013311, 328969387, 877777740, 803863540, 975049700, 83869754, 14093554, 843176424, 754759874, 779305107, 172113250, 761146533, 266513518, 838342729, 182226455, 508006928, 815203679, 906027839, 162113935, 395624419, 650025600, 230451383, 951270549, 85659075, 526091052, 810040628, 11200983, 810442402, 357805452, 673566025, 406636203, 259537353, 440237835, 407065371, 660524425, 652038862, 694571422, 681722925, 158326977, 967337341, 451221296, 184224209, 324719200, 460177457, 396425683, 284255770, 552702991, 408071954, 884892277, 7901743, 100427216, 107703962, 159981312, 843536010, 583607187, 552869016, 559421936, 66356939, 163771528, 546309856, 541844826, 958489886, 603630858, 451851355, 134260856, 821171975, 545182456, 146497066, 215234552, 990834533, 186596040, 821359910, 444813287, 387117019, 350759176, 932898113, 802447920, 879540951, 551464289, 548549272, 73174144, 434501708, 539006582, 203655582, 720883083, 100709932, 549483988, 761473908, 813848127, 602007015, 252303141, 944232956, 287985574, 930572454, 691371334, 395730574, 963837164, 439363229, 579140561, 198612214, 13445409, 416819845, 55750954, 364905413, 223013901, 886565741, 478580145, 478500637, 350899618, 889202261, 781233422, 287389574, 394340402, 319848269, 669854356, 501950886, 883271346, 844012345, 435289404, 320318959, 668777077, 724574715, 167300692, 754106187, 907488635, 345578753, 442567435, 350558513, 668716267, 643945010, 912942827, 382184294, 559386253, 226375460, 50040751, 737475457, 710558516, 55854795, 559911430, 879327153, 113118707, 150719794, 229315261, 291129049, 754506819, 429106361, 322493315, 498779559, 458327748, 914449163, 961088520, 210977920, 90442453, 399105428, 999583599, 851030152, 647039241, 400635897, 643054431, 728447570, 887530925, 413339524, 861518404, 653272735, 999473813, 34901830, 511317503, 827451593, 244971271, 228153947, 451452385, 9037157, 254811443, 575270936, 940826707, 720486994, 396112627, 140056885, 196538326, 413594893, 761454701, 858218144, 881348503, 713504965, 653817267, 618544743, 213021543, 518762843, 444875091, 908642103, 137250910, 258125039, 690100902, 405905062, 414756750, 71769558, 428140671, 526332933, 85133335, 730933687, 832138582, 58720139, 394362229, 212258082, 453349142, 414656152, 118673272, 245975582, 451692378, 601282657, 630058723, 909676391, 800224666, 771207837, 735205076, 774822432, 443486965, 839050364, 716159010, 561270799, 746657652, 475769725, 794167656, 860827574, 120536162, 444974639, 743407154, 324057252, 854548070, 349566878, 439313996, 566690745, 164924819, 457936467, 241227083, 16171653, 577662290, 544560539, 590821587, 349748325, 583602090, 686738901, 147462014, 879809806, 901642081, 263489326, 190077539, 775535556, 24402729, 815199937, 352712592, 179232934, 109481153, 214256699, 724292132, 785990824, 437572991, 176184009, 678276495, 930231172, 352778339, 135930886, 92761768, 118988749, 736995298, 424648408, 637642828, 489393871, 634025789, 714285003, 988438922, 75978681, 255351042, 79206951, 257901648, 40074518, 219032585, 584925252, 939923479, 196757843, 859854596, 636427655, 97879863, 33684561, 980597530, 558661079, 57117657, 344460797, 142593844, 987902892, 869209120, 122234616, 749283238, 950901164, 899194798, 131616325, 619026362, 939107753, 524771529, 781625423, 933844456, 424259196, 898759239, 197161498, 986318065, 607318739, 357706756, 555307956, 410323347, 629032015, 400923080, 15065954, 672753120, 832845301, 104755791, 778330144, 279000089, 132969591, 493222388, 877320333, 379625506, 618847258, 814356723, 494850904, 749075656, 198060506, 240801117, 104199744, 400317747, 22820194, 426207975, 343791495, 149804862, 162580728, 27062603, 822281473, 189657568, 524705389, 475720618, 878516501, 271149938, 199300514, 748882072, 272045003, 504883189, 171553653, 425231487, 948820722, 891272141, 21177837, 353991384, 393936678, 633753728, 245252678, 620282971, 624389305, 103533775, 763460598, 515331182, 671671151, 373316057, 497370153, 916469340, 336357793, 996707222, 546072867, 542031768, 972426234, 795100718, 875896012, 487676499, 35797539, 800717176, 822283671, 294523487, 340163986, 570415045, 319849017, 894035630, 601119760, 182301904, 375260737, 170871767, 928559289, 345700226, 341322688, 449716836, 954447572, 642388355, 629820219, 949364961, 787403640, 927669919, 940889170, 990679220, 585617551, 562228298, 750898977, 844945463, 134225355, 533050307, 807838556, 278247481, 338731752, 551686340, 59997120, 934854036, 256414190, 335108956, 41465820, 889875970, 699466918, 58965196, 458347823, 966481447, 124024790, 840672689, 707265936, 15404437, 623899576, 750548226, 472971531, 811290605, 829053191, 284910755, 698470663, 175165138, 127235108, 190385844, 427171305, 12099992, 468898129, 554932948, 21377939, 923056535, 813898582, 810935527, 247281910, 135282375, 297156046, 614714216, 752477697, 442944796, 799218288, 187136934, 316294053, 182869377, 826061229, 296776855, 213576255, 651919028, 690406721, 576332624, 202542555, 596691315, 684436877, 488406567, 518835158, 390779057, 850684288, 416230437, 763035220, 833281526, 356974854, 344096913, 471478652, 95942919, 326547357, 808080561, 906756829, 641188896, 369270666, 170624893, 637487138, 933782114, 904799511, 330621039, 113482499, 600862343, 350180919, 311241567, 665817105, 539329410, 310302961, 440257329, 628027656, 661549043, 96667437, 901040414, 200768539, 893277076, 430707340, 38673971, 84131062, 178119750, 11668008, 758204438, 598297076, 962663458, 289074421, 431461907, 793142485, 883500559, 324705887, 536407723, 153571976, 533337199, 166728779, 923343090, 568944850, 344986357, 171256685, 632976079, 163478577, 436492158, 42212548, 436073308, 989574194, 764573423, 188179081, 592679098, 234390532, 323417087, 564937631, 706236169, 212453708, 584842534, 836841782, 361155009, 541068171, 868102507, 471971121, 833572095, 501390994, 729613784, 83132207, 89066022, 354569367, 900775022, 905112560, 20718081, 560676146, 953304346, 597655840, 327652757, 881412384, 196670850, 833387187, 336934587, 921810301, 706303441, 251748221, 418333527, 209621914, 964978675, 320509439, 366962536, 245542878, 765796046, 941769569, 975748155, 802501194, 145413374, 113584460, 272945407, 602794686, 586757392, 350820086, 106168322, 881665012, 568592911, 893681204, 874937405, 896470728, 162867657, 928866889, 113674500, 534785807, 878201404, 786247854, 585050877, 754544784, 551554153, 840186294, 163341410, 625566404, 490910240, 772404135, 302417729, 522887400, 890255552, 578052910, 811620906, 838876829, 21524460, 584811422, 926436081, 860754274, 558668669, 423395304, 462746705, 781028931, 533295576, 935404087, 739950738, 277030631, 119763211, 997951760, 560518640, 759036582, 523349335, 477694450, 540551617, 931591158, 301087010, 654206653, 92293537, 375306915, 437038442, 38317818, 661177354, 188749829, 139015533, 887399788, 612089273, 833224281, 382553730, 133070189, 50124971, 985914618, 611652417, 181715538, 876781430, 185431854, 515353051, 919365518, 609290814, 178982122, 75309598, 793866485, 562176631, 872113301, 979141278, 495148819, 150132811, 779537010, 955509542, 931809707, 955095996, 136424099, 349261259, 194122170, 217586866, 506140454, 933314780, 371527645, 880813839, 594649790, 917411460, 596699532, 639405623, 717968049, 912064709, 529042949, 65569514, 490421692, 313601926, 437682548, 267733863, 142902942, 696363893, 855204976, 653541532, 984531725, 242590226, 286083828, 63380264, 380377852, 478663106, 679800258, 66381828, 682039609, 104229654, 23715404, 485879821, 697061653, 556497628, 53795034, 302224389, 309796740, 382766296, 968437222, 548060435, 891938134, 279855590, 277324888, 23420718, 797752831, 207176306, 983300268, 65133250, 642119104, 941268159, 311754938, 224773903, 870455510, 652236867, 538503780, 881806149, 400820041, 582497578, 698970657, 2984282, 387920844, 470861011, 576010341, 759646153, 381096562, 892444759, 628285642, 217542065, 260938057, 640884025, 741003699, 556073948, 625109849, 572303526, 158375503, 912113933, 700340432, 166023442, 759256617, 128785069, 468028330, 546001799, 601925755, 909017601, 790356300, 393564253, 252050694, 262353248, 513605719, 842592166, 741753178, 319875184, 810555147, 884958291, 92670700, 579901998, 942741597, 467837290, 66746374, 990297463, 200032891, 297649187, 684265086, 99368513, 161463159, 729538622, 276614057, 816248730, 913723441, 544784125, 979111556, 511331748, 514896006, 766066957, 150476083, 199588985, 598917988, 268538295, 778787620, 104157131, 284821062, 796481434, 739106593, 132579999, 484596789, 702821955, 448837150, 485776162, 942170498, 352969036, 465287801, 397878092, 449648295, 96058806, 231235979, 944267063, 165273419, 5155714, 116783794, 103392629, 259959193, 468599731, 57326750, 621881622, 517542925, 698529685, 252339972, 672864139, 808983904, 648896833, 451858592, 269472821, 409889030, 354207785, 330032129, 49770941, 866658395, 165570082, 724423792, 231222369, 917989366, 575759457, 997198600, 834501124, 470658967, 417045576, 989367511, 55172805, 96535040, 578444223, 20322923, 102061371, 788051498, 122716661, 572928125, 500879524, 330711536, 392542420, 913231398, 371362590, 537176084, 971418369, 137688630, 694979537, 425511557, 427385680, 250630649, 520946984, 553919037, 248495249, 951343499, 899979392, 431628813, 612579948, 584777005, 790474908, 797512467, 745913338, 42044527, 294162918, 534813079, 995488801, 323272261, 479940534, 535081526, 411582636, 111042164, 162791362, 583430134, 652251352, 311420095, 78012278, 291890107, 229602221, 291058002, 538823134, 418172690, 518702044, 557686794, 999712210, 845011931, 371900650, 461042993, 512643447, 92210445, 308585285, 444502606, 477416752, 593815276, 337894249, 491608006, 365121044, 402326166, 534013098, 603369065, 91496985, 694937816, 306744559, 199265163, 843346668, 633760660, 155227180, 707557127, 988798460, 948390827, 154790374, 240254720, 934214452, 344827521, 828099832, 555098156, 606698625, 323870345, 506338969, 993710898, 273824346, 732191798, 305726381, 617087334, 102110761, 443049820, 854436779, 428405220, 645868244, 278360205, 359040868, 594172953, 665258846, 306767944, 719181338, 136349658, 305184573, 928816956, 971765879, 302053316, 500435373, 761319151, 902641042, 889734445, 387175620, 734548635, 114956509, 51734574, 976739327, 334505281, 554586356, 745054216, 105664814, 527969455, 336882327, 854197819, 352847249, 182875790, 714908152, 590629359, 227571771, 390925996, 486960881, 734201708, 757045598, 951331161, 823009739, 876822404, 434099528, 57426746, 992227647, 684381624, 61620083, 371478999, 111623366, 734919686, 471953360, 666947574, 244091370, 323826657, 263190693, 357224690, 415020767, 125888743, 59352390, 733450870, 900946258, 974746880, 898736392, 809460826, 586713672, 917761349, 849153202, 100792363, 206688777, 564781379, 399282440, 176576921, 379932809, 688285573, 884071619, 737009458, 445033823, 809517068, 143969606, 721150611, 777245706, 595773489, 593070065, 795366906, 568949298, 198311755, 240017931, 882677389, 13245923, 274722202, 119615204, 995255432, 322476698, 284854773, 394532899, 541359432, 591630320, 544056017, 224781154, 730112956, 252828332, 477396147, 141739292, 606941836, 601494288, 589271157, 650111531, 3433091, 186240242, 279912409, 417579975, 329200345, 249292690, 963806180, 721781770, 361306826, 918095943, 875331306, 907490245, 156270876, 183275261, 496483552, 378090958, 14038504, 993528078, 632299361, 502832133, 352132703, 478571949, 951507312, 883193118, 165264880, 843904919, 923851808, 25157131, 293366377, 32544365, 355421933, 762594502, 758717400, 346607789, 461063005, 220205829, 65157733, 345960092, 560842535, 860963191, 787582252, 367809066, 395483058, 303697261, 993870846, 322483618, 751578556, 190024205, 114259273, 528934808, 704290925, 141088397, 239203182, 733914436, 340031947, 888719713, 899525991, 804840830, 254474362, 831258980, 121594164, 999569523, 310191286, 496434282, 35147808, 378072002, 866312483, 533382213, 618611296, 183019083, 368287432, 204105800, 819386438, 279324277, 718939657, 933121, 258323837, 744403943, 694752055, 628532119, 881049478, 188135167, 449678771, 938048531, 168992399, 439240098, 663870912, 281846477, 131553881, 408509100, 188236572, 97851701, 845276357, 908176272, 488423886, 699635023, 448883586, 246159230, 366742709, 693673411, 221536311, 225169906, 723221956, 115836215, 86373342, 520361309, 193666470, 92504514, 775177783, 674083483, 891678918, 674890783, 464999978, 123186675, 811071478, 858000520, 438935887, 905672487, 686881302, 110872023, 300860229, 751504082, 506169716, 469290206, 947854206, 477153798, 482685314, 445890970, 245029648, 243913733, 299007486, 830208913, 208466297, 685744624, 758540833, 158302403, 765292873, 125209025, 248034631, 630477772, 891781018, 425034895, 88808018, 872010626, 52471343, 14277290, 296799198, 674775183, 120530846, 6260288, 922853104, 751757206, 40849151, 167553326, 278722096, 506882224, 543463410, 645368127, 600882481, 884195512, 778396209, 748934172, 650538920, 763846008, 909691104, 208224978, 901022246, 999164642, 313555827, 57780624, 765266267, 954814737, 332550994, 682921783, 575346480, 911709722, 96986837, 599829041, 131752315, 946668631, 413328722, 619532677, 818058567, 989354954, 794077582, 733865007, 956298273, 559054799, 158398047, 95232206, 805318792, 203384710, 765890552, 6603520, 546907495, 999302123, 328049054, 865743011, 423454567, 161210184, 791354310, 27797825, 630461146, 409187898, 981658578, 621992937, 992319033, 8566474, 525465458, 126872583, 773740100, 581088152, 33755131, 903848800, 882051125, 786952868, 349660660, 784901051, 339993688, 787397843, 866691542, 199124919, 71870684, 595894779, 965449891, 729941239, 963955249, 911204846, 2745999, 756754924, 124960276, 60408673, 912884635, 719962379, 389695681, 356578439, 967728392, 902325744, 142420890, 950361711, 953715698, 427686673, 939262849, 75759800, 959397259, 868686814, 527458170, 812641453, 458011702, 631735248, 866711448, 622768905, 754454506, 627165058, 906250855, 362448082, 341340499, 986114018, 711857726, 141463316, 222635556, 431001347, 956114831, 607270558, 338896831, 929446668, 44527860, 228827978, 761269020, 946903789, 310653483, 316028687, 922303120, 532010047, 831518210, 490670249, 887202345, 349374675, 808791576, 97152966, 904268229, 461952565, 258761240, 417917454, 128530119, 811739069, 127167246, 265788294, 718057965, 649530920, 929152170, 995592113, 976480300, 956265691, 461424656, 963420002, 425639568, 178524643, 814852233, 33067176, 230668915, 551695064, 685814137, 291499881, 394830071, 752849158, 193115016, 365884349, 116947508, 527015130, 610438144, 785810218, 576219941, 775616427, 748323612, 658261543, 537082162, 615752103, 140696628, 612398632, 728092126, 127384999, 179184335, 146748611, 596708335, 608418715, 601407608, 139249089, 933201200, 670180459, 489826034, 869217074, 870327941, 33836224, 291828458, 880450522, 475031415, 399591494, 979605590, 409168070, 595296352, 870236280, 775639866, 778109380, 377636744, 884700558, 948928592, 333335301, 125434861, 733078828, 342776295, 275689012, 891129393, 525450252, 143701404, 297992905, 556557197, 748935989, 935863747, 295146664, 248667479, 39047781, 735412224, 810680993, 938742706, 634788505, 526267755, 449022968, 663773806, 641953294, 52341551, 380373722, 877726794, 795541842, 60215301, 986080756, 790289633, 930549785, 791780571, 936205069, 358657469, 451371038, 203907886, 895222130, 997203971, 768714236, 306178351, 64151251, 905063841, 983419930, 962967578, 345369356, 909242801, 330719036, 925275463, 978832263, 268038043, 951569932, 344158497, 667895252, 300714231, 738607519, 862324579, 135819606, 82013958, 751011454, 67118706, 725129592, 784252533, 111028769, 104909970, 348262411, 282474413, 712068189, 801847957, 873461670, 913048945, 457922595, 313475243, 892269817, 613740044, 247066694, 622744046, 325273686, 815678268, 31934846, 253801982, 464763526, 233058798, 250984268, 153534932, 372289488, 366517455, 29222045, 135441411, 861850979, 131060284, 427483513, 811949897, 513676148, 305716068, 310342023, 627263675, 834277738, 829390973, 176750604, 348785887, 332986978, 682434062, 766337307, 483906013, 820486624, 821006283, 78946727, 373989155, 50102157, 592105652, 647977957, 761809692, 195190113, 243311058, 818384871, 437933828, 791661094, 784140752, 281851610, 556452230, 438361672, 665527401, 863974826, 170055962, 303422593, 799664894, 247439869, 536427189, 793415313, 309072247, 480532685, 837418030, 995928153, 258281236, 418688407, 876404586, 555076895, 770910423, 437067639, 13307604, 472648032, 984808083, 673743066, 980046382, 873506446, 575817041, 375583187, 742733313, 863712513, 55956287, 528506372, 934027786, 362765840, 232612953, 914326772, 380397098, 333256862, 747520361, 596695592, 536098531, 831441784, 69623499, 357741138, 573607460, 884255008, 459434903, 650168103, 912910821, 781160677, 726845577, 895068589, 670444969, 904636729, 378477439, 429886088, 840950466, 62368264, 59153283, 133335810, 767000574, 35628086, 250226089, 665763852, 838353659, 598147355, 296755035, 81385713, 738701460, 223243676, 598272589, 461126752, 206197463, 214450040, 918143085, 445858141, 773418510, 198109918, 266633215, 256332518, 662363792, 218261083, 504524031, 866062042, 394285545, 852478706, 118512392, 667866725, 843237278, 914240448, 588422332, 250752795, 142865584, 3105827, 641673110, 470661060, 356287662, 65588966, 853875602, 838003598, 412156798, 755515670, 667861755, 788182232, 165913367, 895271314, 771206906, 587279421, 693026967, 910313906, 6954388, 357479550, 82041624, 912284532, 995302584, 239445465, 115968057, 656627492, 118093169, 807509292, 161592241, 268836236, 756696245, 74693897, 545729846, 524731338, 712357147, 541603196, 258255003, 779944257, 997127077, 560845713, 534695066, 403929249, 694998194, 558091278, 312642499, 289928148, 149834486, 870211997, 592893660, 628991435, 913954899, 8133140, 974001072, 702618310, 741534242, 33317359, 775193102, 187930463, 87531656, 251800146, 635386886, 367239043, 468545546, 224096859, 396890478, 471945352, 183227512, 355427020, 101511262, 605264324, 754018241, 247227613, 684310093, 605893824, 858257254, 941100514, 178343213, 108533974, 653180991, 305391668, 375335765, 447858387, 632210709, 261867630, 490043962, 241941542, 345509494, 519802983, 44999142, 587545522, 766490349, 147677440, 788915985, 643130836, 859444174, 412808274, 987792040, 879792148, 407472380, 386602534, 350747173, 602894171, 65505334, 493288762, 683094188, 319746720, 446564586, 681525667, 945782287, 732890120, 432064234, 303599455, 23772264, 985175851, 235228708, 591100900, 371062064, 376329593, 361928763, 233510272, 98248068, 299116429, 53397499, 80411171, 715755904, 38723206, 717243297, 691713137, 130662319, 713938247, 918525286, 76923585, 302577071, 638114916, 641968244, 874659870, 663265658, 42061168, 275146281, 687618279, 513984128, 151436536, 65446483, 942668450, 47536872, 969100252, 450103390, 40230893, 763156426, 738793011, 494997502, 371114966, 585936016, 776713625, 446430368, 456777552, 398596649, 562280422, 118845452, 975278577, 730793050, 782142559, 950752097, 642239184, 503604767, 410279011, 867923368, 356110605, 301645515, 40027134, 212546064, 349102318, 866965260, 897572479, 958885575, 536393686, 732766090, 645773899, 986116384, 718651542, 591657406, 21764979, 163776412, 390230572, 283667590, 370094761, 236251703, 561054751, 211535106, 254568885, 805866927, 769098343, 552525565, 186924693, 197068170, 422891587, 591079185, 685457956, 127178470, 804945852, 237488464, 494634764, 58809174, 168221713, 608105732, 255815895, 132342264, 137686561, 468583061, 20261376, 67216118, 561353300, 402910558, 919831024, 520883539, 295485675, 779435506, 736489664, 290929122, 569358429, 730217245, 275502172, 575242751, 250983511, 852052635, 540030441, 560073293, 507127598, 203366989, 684299920, 503777214, 147161021, 894406921, 733055601, 205078937, 185582206, 625341194, 266117973, 620744249, 716905142, 555773269, 840275200, 337165380, 707247806, 89763728, 812808793, 363968014, 796036366, 123657650, 425811618, 719539443, 642551278, 116976545, 95875601, 604807350, 940428990, 703943904, 51460901, 8253576, 803819645, 333522964, 988842024, 430671827, 425405204, 329174860, 640020082, 54360306, 139877090, 932631034, 357574839, 637931079, 446940938, 599591805, 723904263, 224473596, 602956544, 662413693, 948051877, 290594705, 179704231, 687351225, 396642196, 89729793, 961209816, 524432333, 469377729, 878615981, 11906554, 200486221, 367341624, 380911146, 614949383, 691938876, 987346951, 267883777, 775474674, 894803303, 215081396, 11249849, 744032029, 748692669, 278779939, 840687955, 990608749, 176713945, 257935606, 942391570, 281506970, 364123307, 3993207, 876663191, 378508989, 8575927, 230671663, 788308925, 579046713, 343793141, 431754391, 527557325, 799790002, 867023558, 10996566, 831454774, 564537906, 372511577, 394799118, 313737422, 368563816, 926680002, 193857423, 505764563, 922197122, 560487602, 192754643, 218893784, 679234851, 103481834, 333977054, 477319154, 72699350, 240917805, 214008248, 903956753, 480455695, 800654395, 404230405, 371725874, 122714175, 888299612, 666645164, 51562767, 697070726, 397656325, 948413228, 99099537, 572248862, 116574516, 332346642, 613108598, 368142623, 241715286, 645291230, 349509472, 132525162, 346703557, 241787344, 171959498, 360800549, 445575938, 778386807, 458526055, 602665390, 332456641, 962962190, 67097169, 245533978, 932900327, 474836595, 357695848, 975054492, 303788651, 443381150, 99116175, 642540263, 764238377, 135855792, 258970677, 46517214, 399471162, 702258157, 543686002, 73026283, 430862499, 673675252, 230480219, 148403514, 448322631, 617647672, 500442037, 138370751, 591455240, 181478977, 513019733, 432327169, 151580408, 157716263, 306973895, 403001442, 765054462, 44103214, 779194334, 624922391, 18001134, 64110324, 881582035, 904864469, 457293686, 975106299, 394848447, 277441267, 504233781, 456301029, 797379236, 981354874, 944328580, 232021438, 251832547, 657883462, 188909245, 248702699, 570031840, 57610040, 391691953, 167681020, 388757005, 287535806, 643718504, 391286745, 699602259, 201833320, 688233440, 537633596, 659525747, 525262602, 133736011, 695072510, 898418393, 962965609, 891384908, 382229176, 168003686, 74708949, 773917545, 332571828, 9462686, 296087917, 440412278, 763400576, 569432128, 429366662, 219347369, 701714604, 269045231, 362927872, 952468892, 738935399, 193430585, 445172031, 260565869, 848539839, 566454547, 290246210, 675348677, 64822471, 136726136, 689290692, 988173116, 310162951, 814971898, 431479640, 783378862, 531162273, 478468545, 842442236, 833514029, 72798965, 278759683, 789223795, 648706807, 403101516, 333181768, 754852897, 110099963, 423510538, 266956385, 4337631, 765905916, 414333952, 702565616, 629954251, 611784705, 749167944, 942891976, 340846468, 94188327, 676972029, 929264846, 830520046, 332680858, 828017477, 77942134, 48686981, 312323693, 13153710, 734790416, 895025536, 394853004, 435606239, 978068013, 327133375, 972996501, 181035222, 368618057, 470592792, 683912500, 36740101, 605901826, 467726353, 599402245, 167325363, 286543679, 110186666, 390857229, 97371848, 925150344, 500285598, 600247732, 522362536, 132795342, 216570977, 564250955, 667517802, 36350663, 689356535, 481568932, 327707598, 645508834, 776641799, 567084479, 825024403, 495095930, 231725781, 430609036, 31892469, 393674747, 1257721, 717245861, 306966363, 922817577, 264263510, 23365918, 155830316, 973262752, 730976458, 961971463, 153614949, 42000731, 273060639, 520984907, 433509703, 947172884, 944288925, 789690233, 607930078, 620339918, 987067316, 991418517, 542546966, 491381726, 581700455, 431412496, 329799107, 605754309, 340652686, 508621958, 547454691, 923484727, 356354262, 214665958, 323940201, 667943020, 383275041, 872943835, 948754789, 312752035, 823673098, 713964426, 861921773, 457473357, 656358527, 30933257, 425398949, 971684947, 25036945, 821359572, 546708482, 892762570, 424533083, 794723983, 277887978, 155824397, 221680371, 287321049, 765154902, 888802737, 690180115, 308708981, 138936178, 441205235, 604014447, 180493144, 178003064, 961720150, 888727733, 131803589, 990187424, 925098705, 274428497, 306486168, 653846003, 294586536, 751928317, 152118185, 247152296, 76567207, 563024628, 832389655, 83185573, 994175715, 36528973, 594586913, 468243214, 826148032, 109040441, 233345036, 225802653, 547983791, 555599950, 848921260, 867704311, 729448940, 292134671, 285281598, 92188500, 41908105, 278473489, 674337216, 313407958, 851383468, 225736328, 729622225, 502965285, 612809210, 668777384, 450712349, 492803928, 698574990, 255570285, 442452548, 40523903, 815584183, 860527053, 483532754, 674289877, 784300177, 788619153, 940367740, 728646079, 299388217, 707184641, 382885055, 694454811, 664938437, 760792485, 813925399, 97246413, 700692169, 695488053, 78936708, 941724192, 806576824, 642290043, 238798671, 178428677, 845815856, 795748303, 750240184, 388011132, 430392407, 596746395, 19455451, 882841423, 410569499, 66968591, 696686121, 563932282, 753072940, 241222604, 523657957, 608658896, 429192836, 884903852, 645994867, 66829466, 182464260, 790425936, 404255533, 859809107, 181437413, 145526160, 733978631, 969531751, 35488612, 892963113, 968363361, 655374068, 895338374, 778854043, 379091283, 304550779, 36893984, 7134575, 277269755, 100317856, 633817270, 306184293, 881961203, 825557208, 71828454, 280773420, 438998756, 912508223, 466100305, 912912395, 599022525, 424857236, 84772134, 237928915, 996421436, 9372130, 200753273, 870955585, 230240588, 215456764, 549569984, 590159328, 874851886, 40461857, 530200796, 386676914, 227685916, 653719460, 480343437, 793336857, 309313968, 663261943, 652841199, 903267218, 584552577, 108658028, 993940674, 480238460, 535263629, 592007516, 428773978, 702819834, 735986503, 460998158, 267315853, 182483845, 770280089, 247204185, 528366191, 373382904, 39074358, 724714246, 387807568, 171041116, 987152638, 970031755, 147495525, 977882383, 713324116, 225233295, 617476968, 419913584, 794547177, 256151645, 228171504, 669971684, 794805072, 139649035, 448407078, 376482459, 156069620, 391481988, 655625562, 76793190, 217532540, 14815398, 475391174, 615576556, 1516817, 711457029, 401659081, 620255522, 884460547, 662230228, 935976844, 966701584, 811104768, 610323338, 547867563, 655289822, 449355502, 435928775, 422945308, 224371490, 963462380, 31012144, 187258824, 470528589, 691940048, 597081516, 547484056, 886537752, 633674874, 448669092, 706883366, 980259352, 853187554, 357910718, 798467700, 94679960, 343767502, 619819151, 65617961, 108728586, 973721250, 959897757, 500756741, 360203468, 886915042, 629168606, 88274325, 964300653, 612452166, 386179096, 520285123, 938069700, 656734795, 859717192, 852712573, 494234661, 801213852, 206965846, 132684111, 943036337, 385131277, 620169362, 230024746, 823641924, 677727606, 632447161, 478167879, 671064490, 779720904, 182099814, 652621789, 594754256, 433179749, 316829926, 232554049, 188355686, 305545914, 618378023, 532396846, 620211101, 84473382, 213131650, 147720814, 340507434, 919224329, 615030944, 426884710, 896971953, 572952753, 116384040, 393514546, 294362836, 569697491, 344472566, 754543082, 38788573, 524171616, 228460549, 298209698, 416086478, 987392137, 731356922, 875006089, 903356496, 722860278, 117134933, 845869630, 155640439, 73886058, 599889646, 160544775, 314680253, 267115569, 616828020, 124488912, 103970839, 797472247, 428304837, 405147437, 773709001, 351123986, 415141224, 385289827, 501876917, 928287124, 910644913, 998167074, 923874368, 647210360, 451540832, 520848854, 107778206, 695090751, 978306852, 12086, 882049491, 281666410, 396649036, 741191563, 314515472, 375187282, 13796196, 190900026, 481659455, 411086109, 455456744, 827499222, 309454398, 390485258, 112818509, 599834466, 548769460, 210738268, 882203257, 42668532, 584700893, 984963473, 163139090, 261424597, 572096736, 529446107, 621952390, 604994176, 627999913, 369351143, 538416568, 80172902, 115439258, 771466193, 95766457, 620550204, 958236746, 44795224, 79513460, 385190769, 64749443, 751297830, 313848211, 143429852, 335416381, 867653254, 139985084, 267778175, 279371403, 63175884, 645829078, 507607104, 853437874, 956745893, 422026774, 315837029, 375902560, 133136097, 168617876, 433180356, 61822234, 621468288, 830553876, 491207660, 715723895, 883681633, 72884622, 872661392, 765898910, 519608122, 899941300, 758008301, 223948268, 775764249, 351072964, 460374003, 190758990, 510244924, 492913810, 57090086, 809753966, 775034838, 250566477, 906328372, 931072514, 40480711, 97202790, 710222894, 346644401, 425914141, 746617369, 827742947, 738154781, 60353964, 116495118, 719713410, 867756253, 359128627, 443968505, 168433107, 967169399, 568716550, 781466023, 818046517, 421015, 881608204, 210355587, 549652366, 617166627, 109169876, 525806720, 976832965, 932650479, 118965579, 648175215, 509119811, 805760849, 906414270, 904925286, 856194588, 922508369, 4656734, 808154747, 228807691, 7702012, 620499002, 733735196, 397262170, 1260754, 215654107, 311184960, 647933980, 973062741, 868213092, 573992748, 220763636, 463199603, 367857640, 667197371, 474620030, 802323571, 913985212, 605015922, 632537152, 489807262, 149242528, 799016648, 42736888, 623173819, 977083388, 397098792, 240820628, 348226661, 584861186, 434911009, 865033173, 898649206, 844147468, 702896183, 486893973, 974102867, 606538165, 244885398, 690079586, 659900123, 769149585, 990129572, 154902320, 543795719, 1891435, 921848468, 65301090, 466885026, 181887821, 976830167, 519079614, 153439391, 500529763, 457980981, 915814327, 328431588, 778220412, 31286648, 946591069, 301938778, 352470164, 984179947, 639046998, 320574748, 486905320, 453307156, 678014287, 246371881, 865246162, 373221028, 228932701, 392031533, 548557554, 756331519, 517800898, 755902700, 268251997, 523885304, 655841039, 77624400, 509792596, 101362097, 258289852, 495798753, 236591647, 80735649, 241946538, 823814176, 300056889, 941887619, 677063421, 32811406, 840669136, 593239014, 733211751, 150233002, 812565290, 863187852, 39946601, 31097295, 747491678, 790975617, 727481211, 504543455, 47940281, 786635950, 246274573, 622183086, 729297947, 717418335, 465593369, 930057088, 906665855, 932644386, 754568546, 129446057, 158917815, 444860916, 527418719, 822697785, 512581896, 423210483, 263681611, 291180357, 319068692, 315502419, 161052127, 580468119, 598470658, 345600235, 811801567, 144008905, 456080694, 147341103, 157554131, 788784002, 787339179, 14671194, 938685784, 33932361, 659975819, 215751365, 903655146, 269874837, 449162838, 222998057, 967616018, 985452623, 622652925, 527187776, 101467613, 688777029, 831044399, 563035914, 938819671, 630780116, 354309813, 231232404, 379996245, 965741363, 286964257, 602653566, 344306970, 218126702, 962237583, 57706835, 74578235, 367046031, 473939427, 647680645, 993436217, 361018561, 899118879, 439255773, 616909221, 11977291, 883898262, 368369417, 18227856, 880853178, 487203488, 768900600, 612982831, 810832503, 527652934, 58793550, 575066578, 839008956, 112117966, 625039417, 222173297, 693978244, 267747636, 547370783, 786995298, 983942701, 997100306, 914062512, 294796229, 781911041, 898855097, 212967346, 994381500, 488776340, 924144649, 489912526, 763521116, 178308344, 873549071, 548252662, 94111160, 538236834, 392997042, 173048469, 978261528, 308424503, 696290009, 168775690, 999597429, 798668236, 488450386, 767334433, 682002488, 253941335, 911050575, 64780117, 188955627, 768938068, 596658988, 399819623, 9869915, 188438445, 184689486, 322340246, 528636515, 407836738, 493542973, 956202424, 331519334, 94206550, 503788430, 804951846, 782203618, 618493028, 562746887, 800620075, 370949589, 751424952, 230945019, 441515301, 552436125, 591955580, 924820230, 740874988, 659602563, 449505351, 366819176, 300830619, 400275457, 536640579, 965748254, 646058961, 602325224, 735853238, 877298613, 483087461, 966547135, 375799660, 611678694, 326834172, 457643534, 43400648, 436402164, 747597793, 208809992, 71201758, 534174491, 697385848, 811032284, 170797201, 408032202, 380146317, 200973291, 761166793, 538651569, 478485725, 391977807, 347135660, 861476728, 299347493, 731763348, 264300692, 429872287, 652920678, 942415086, 792664123, 991146168, 465579930, 350295954, 166360920, 459748067, 883674353, 996502801, 820059315, 942533450, 487234080, 814717118, 95711573, 546465354, 639353804, 470828520, 157584498, 216589922, 230615686, 7721825, 508147073, 838838774, 731500828, 677105121, 245470873, 369100669, 312268398, 439042142, 672536399, 941524612, 61360878, 545168076, 937544815, 8477470, 247511609, 770287854, 694729028, 357640257, 426152436, 552685733, 720368183, 797984919, 962958010, 577356908, 996314321, 120258477, 740913298, 406607879, 41369763, 330884939, 850876000, 921627117, 345068433, 420875747, 802284275, 583064520, 14941406, 751246984, 298762574, 552635491, 308313087, 703157381, 633955688, 50056389, 783701465, 555118056, 243413042, 921429111, 913962471, 38592278, 214604176, 223488024, 821480610, 887092049, 248628817, 113871107, 302489624, 83751365, 226540713, 462235301, 405868338, 298177850, 974710187, 842741459, 912866963, 576251955, 78769654, 563827543, 476754928, 626293922, 100540663, 379808991, 755811419, 296440317, 593303631, 294186397, 503119349, 224384203, 549135457, 900681472, 386458365, 100079709, 228934035, 648184363, 49983783, 677408434, 821317594, 355287106, 879636079, 463618328, 340958586, 402569451, 999168288, 974260828, 769316867, 230578605, 964388314, 302881166, 506403015, 679220244, 426065793, 83431392, 240976972, 850320991, 153637260, 484486752, 709662195, 683667816, 845057703, 958056884, 20392426, 393683685, 947789491, 76749389, 968572522, 344264808, 637903667, 385757481, 390760854, 534588096, 785188253, 203735053, 740155799, 412737049, 131420107, 298021351, 767523983, 163221755, 973283734, 216380053, 415691477, 30720081, 187960290, 212391470, 812459980, 420960533, 458941151, 573453801, 406188889, 97596865, 735215934, 740222041, 438975437, 617087030, 877332320, 934020633, 295637638, 973919848, 505165097, 481283775, 212506125, 432303648, 38527548, 886230623, 279220635, 156816412, 1756979, 632690117, 547865082, 180171534, 397138230, 209400329, 830622188, 970694442, 192701583, 19918039, 254404594, 572861590, 263876482, 308764194, 601997874, 590744072, 408101412, 703065188, 199560581, 682522049, 387378279, 114719648, 116943506, 245042652, 407931518, 983021179, 434176332, 972007556, 283879928, 252570370, 168025094, 469442379, 531775888, 814156437, 904550017, 667058054, 115217277, 959708330, 765447069, 333601781, 276421283, 120816714, 527460465, 535505433, 189321986, 19300090, 809205879, 453464424, 548743990, 144483583, 402214354, 417636642, 814720668, 922275473, 946970634, 370895484, 849022307, 429908929, 619681552, 694684435, 941106897, 298408339, 839324578, 627699919, 311048187, 27851728, 353238773, 581662321, 33778419, 383042417, 762644241, 455807304, 883003341, 556195585, 215433814, 666606069, 919792999, 316764418, 633741846, 396698945, 546761023, 30133577, 880951603, 231051277, 763922440, 113896663, 677592735, 881715177, 65957910, 861675066, 323690011, 320704888, 824126416, 201617129, 407836158, 652681816, 752128380, 877292628, 805934358, 362183644, 80743903, 4318266, 730973748, 719483797, 519755629, 974338827, 772067913, 464790734, 267325958, 485324157, 58840636, 842898617, 259336837, 272499301, 750426889, 703041969, 893093975, 506893668, 624090734, 543693238, 201694674, 67506904, 3592932, 7001314, 458699826, 393747114, 515635133, 900547932, 766660076, 107284824, 210429665, 894924822, 895917588, 55569562, 15116267, 727209247, 842952738, 314058120, 176702155, 372978418, 801546055, 481329363, 423673168, 833331762, 552882637, 653352918, 235722980, 849534767, 453995298, 985297651, 949487413, 776926470, 993189634, 84902449, 850623013, 440778752, 813053614, 695637937, 846234625, 569848248, 904367026, 912075369, 971095569, 12412253, 743854840, 503007547, 769530189, 4257946, 942925499, 899156300, 502740283, 347578563, 817930606, 347828121, 711123468, 826213690, 239259552, 550857097, 282834209, 462390950, 452825448, 592076005, 335374214, 24119345, 211607393, 218897450, 860905672, 919854964, 298366157, 318569385, 999624834, 559004666, 13171609, 729517316, 232030203, 294363422, 662897304, 106931184, 166951357, 923837093, 691950008, 962182328, 862276795, 516777336, 409550849, 779951341, 163399929, 397592798, 823576169, 801574884, 864599244, 516948460, 227351718, 830771925, 841079929, 320247270, 814134421, 534123950, 621921089, 203389147, 752393814, 168484130, 548498413, 128552966, 579493673, 649875760, 945351628, 51612888, 667788987, 499527397, 258371430, 84181119, 142851478, 125816006, 654750897, 441523212, 551530514, 18184521, 584029380, 999470139, 715047346, 774649402, 677241616, 521787747, 767353505, 30968022, 125595426, 785647662, 899399946, 891133111, 723806107, 234895341, 451548893, 854469418, 876850946, 284037863, 190557719, 207817212, 206208870, 327092156, 988964300, 207498312, 203341197, 724389965, 448027111, 13589931, 415568209, 389732985, 316473845, 98509817, 947272001, 286130782, 316735233, 183034885, 72996969, 620639764, 339257110, 411194678, 371454352, 398417820, 823108423, 164331451, 207918197, 102575881, 451946650, 185144738, 898508188, 856632253, 782609168, 366963772, 684326687, 834275769, 173684561, 8154327, 406404203, 684945939, 450548998, 536909871, 85028527, 108035071, 616326904, 861006395, 165120586, 597039380, 274283855, 398509014, 911156883, 532243517, 83892118, 418146004, 827029891, 284662837, 871965168, 338278603, 618324842, 242077731, 157647220, 756593371, 78402794, 492150167, 759275724, 838596041, 38743243, 415812269, 521325572, 578585610, 574959955, 615275522, 314060557, 836071300, 2339188, 179605202, 932086826, 242452663, 251449593, 867904366, 498212234, 470958394, 455148848, 787415182, 343469815, 814830896, 395043810, 165694966, 366110785, 60664865, 391193555, 657120463, 872093958, 963086498, 111115360, 562250377, 495636971, 768495495, 47653852, 859088325, 507977642, 673508965, 538597124, 425152018, 815518094, 948801210, 706833783, 52591138, 931285886, 32111380, 950652425, 227147084, 545759979, 202699821, 781538903, 170320307, 874208843, 183889175, 638333682, 741991509, 258453739, 147807279, 364233646, 584538300, 942779114, 978768542, 465731801, 234049035, 42875425, 584715265, 643361757, 367301681, 903718465, 738704663, 382253318, 435397466, 46077086, 309530190, 202221590, 332926285, 115401913, 696334309, 820555399, 355844608, 864478081, 204658288, 433049235, 409341894, 394313302, 481122650, 6684651, 302583389, 140193605, 703383928, 159797011, 859509233, 455520237, 744306791, 679943006, 260542129, 463165982, 304319232, 143109580, 332523016, 902620603, 395889683, 555438659, 127158354, 314123905, 128717377, 289673769, 23198671, 605022319, 685103788, 232962158, 568942202, 72152240, 400152288, 234104841, 390993823, 411479888, 95923074, 296565795, 295646569, 493394408, 123723353, 70039603, 886483369, 729733412, 277942153, 734451416, 932513543, 244620364, 627352070, 46754720, 199243096, 547402341, 309234691, 374183490, 755908218, 995937461, 201951265, 299919111, 888195760, 336981538, 408598958, 436556308, 409505419, 702963393, 611070920, 584163463, 226381428, 163931021, 560794801, 362512685, 419168017, 631022980, 36938884, 217168776, 838879355, 450201730, 149723716, 968395540, 201527224, 57344778, 63169048, 767732596, 367642229, 822400735, 649061962, 636919971, 933341618, 697167313, 412473410, 333781746, 626823163, 855278367, 258887183, 525176459, 570653261, 771470818, 342851403, 784340882, 437306862, 949999695, 854730877, 904007589, 541818290, 224367362, 62456633, 330210753, 46574656, 777431849, 927216872, 659555219, 447489236, 912570033, 570732806, 97202045, 859120753, 566474640, 56017787, 321065974, 903212267, 739279862, 632297605, 759753701, 999037624, 226531452, 832759840, 773989089, 347449440, 153165523, 360803860, 813997830, 59620989, 678721393, 789702627, 81629307, 219813243, 535770078, 969267692, 846292156, 523606917, 569223915, 750034659, 357337603, 528886829, 168205980, 814798613, 358463836, 981963606, 761385401, 277641607, 911936287, 682978515, 216440026, 789541254, 662251009, 487871692, 184053586, 590659797, 241116408, 339269789, 370361481, 398080232, 832944734, 594701938, 698338279, 588647084, 112272332, 860659377, 287212805, 523750613, 926134392, 371278966, 366063725, 904136188, 188975063, 494869469, 617932779, 437713959, 786024117, 769020258, 415080014, 598328898, 229210911, 601434543, 325494736, 561050209, 631586585, 406695321, 325426953, 920470267, 896422953, 626902111, 720595138, 487581249, 546581437, 505992325, 78667005, 233838696, 330358709, 388146018, 780251472, 251866449, 281482377, 71352835, 528893662, 658069524, 625507993, 418601661, 248472878, 15675041, 320853535, 680355031, 251600531, 818405152, 495036455, 29573899, 655318835, 747571653, 138804251, 316195221, 645694026, 356310225, 739271223, 124019712, 630687779, 507564732, 476165912, 465761866, 792741046, 566655307, 876839446, 494199330, 769383778, 724916965, 709696379, 121242515, 856713782, 88315935, 932677196, 476344392, 161210052, 258187186, 882506502, 830055368, 527038183, 376955880, 253395744, 785580485, 375954333, 166698281, 865642662, 156045273, 607989143, 603034301, 545441332, 998254438, 415117718, 302869489, 473072131, 903363946, 593579201, 477357719, 195223426, 97230496, 93254456, 863698717, 375117362, 336325253, 448629317, 961988370, 155727730, 608447273, 135602751, 294221267, 381042728, 221789115, 782899563, 490471255, 125377782, 658689480, 442764274, 417021018, 688070411, 344024034, 159396790, 15826687, 53636285, 785347389, 302397507, 679035652, 356465732, 113253012, 548485666, 561328350, 194688083, 319427109, 598064080, 884532714, 169999150, 183197286, 805466771, 198831135, 638154735, 763173558, 231075345, 764273671, 931113586, 935290469, 917912748, 355745691, 238016416, 583569680, 272883838, 420188976, 802885743, 720670072, 164246244, 444070231, 945063348, 204893722, 286729522, 556847542, 707315213, 264361898, 919523129, 977333787, 374512943, 938677583, 642241989, 683469895, 481993993, 87033542, 70572472, 943355642, 674327082, 655142456, 404397320, 702105431, 225434864, 899949339, 100321008, 334848061, 158322691, 887967819, 924491975, 783371369, 155976404, 292801585, 763195119, 336893351, 924068755, 171181731, 478358559, 53743475, 5019531, 610318609, 396884661, 58109789, 696604538, 481954639, 589044167, 376623464, 132245078, 567023603, 138257364, 661533656, 724430596, 490240824, 293835032, 991993155, 593121824, 451989726, 449302216, 882540370, 781974597, 784396625, 949208912, 354239251, 361450398, 217373056, 562699440, 737564507, 958247242, 950777522, 621006736, 315637511, 70934650, 64152552, 222951693, 295836098, 687187059, 482417148, 885367422, 912051908, 388888360, 127803616, 982962529, 375015885, 831878098, 999911262, 559980541, 963740092, 651078174, 383390751, 28622743, 444862041, 670954905, 505045557, 901936023, 198692533, 663801654, 10791540, 831479128, 674464447, 291711223, 523860848, 988249658, 780125605, 638911478, 706858565, 412537914, 780694985, 821716679, 573453966, 334271287, 557660598, 148051438, 35747442, 996363993, 534556280, 487992720, 964113796, 495527634, 120169312, 923069288, 322856222, 343030168, 4353021, 791798662, 75972976, 50745814, 493411117, 251871427, 769108953, 1830167, 998653807, 197530510, 370470548, 344580346, 914479782, 667666956, 813625989, 880670270, 208873204, 892615100, 763667364, 313982559, 620137920, 457844265, 785881346, 521310212, 449375767, 930655622, 684372674, 906910170, 334592331, 47461155, 206780290, 54240289, 347540117, 800047739, 373672431, 637407973, 697186277, 698578625, 863155251, 450404376, 830991929, 882031738, 954294422, 156743793, 950751298, 640979246, 768721208, 126033963, 417436627, 380677515, 809690424, 126301186, 248253950, 943317463, 975345359, 775699623, 240898295, 933048969, 12151538, 266237322, 440933224, 367279254, 756948239, 789365719, 976669794, 559893050, 382346321, 408855585, 991316834, 326172927, 458718362, 783970371, 70021841, 78019357, 15940, 890570995, 523070789, 529359306, 130457931, 979240078, 626208836, 335696652, 106192968, 312170063, 721778628, 281874201, 908259990, 881290802, 661184313, 274539864, 439817387, 416674701, 19436738, 889559209, 251287726, 756031507, 457953289, 314296647, 802821623, 363118759, 445224392, 129999549, 778357686, 138350778, 15975563, 898580469, 725766572, 38733313, 449234774, 290458996, 317299578, 565675095, 66813373, 23362394, 864979446, 150024160, 947479756, 277466217, 526459271, 979373166, 376922731, 362327221, 202256283, 634859325, 62843125, 268938260, 347532959, 190827554, 500848498, 884829461, 344909578, 586367451, 126960461, 427818765, 878158683, 776082252, 409581937, 400339927, 648748770, 839706944, 720920773, 226130928, 285784949, 956046148, 989322690, 189946489, 462274584, 465398190, 679857637, 21491353, 777178684, 283532502, 303449580, 129156083, 36947046, 501379779, 392244143, 312423690, 823830576, 197941051, 867132636, 786808479, 261360706, 411360343, 715352745, 965595881, 726131168, 916474327, 401091453, 601058440, 348944925, 807781979, 482916954, 336725478, 191289356, 332748087, 91258240, 240422, 588244910, 17760236, 820242003, 411066210, 150430074, 252525952, 588705946, 49171973, 507955409, 660389811, 295651118, 707509144, 17729211, 533560429, 73897110, 612378115, 75135866, 55108116, 787320962, 536007020, 552470122, 21254650, 626547434, 292705777, 708523653, 671692149, 736090819, 223716846, 306921467, 37032817, 95379204, 793597155, 967736532, 176221913, 975335108, 319640645, 523234938, 31378790, 529831808, 950384788, 818282563, 919169992, 102323869, 659773173, 519081880, 175081171, 63164743, 358837526, 705925970, 906882791, 132463089, 966888317, 655484996, 625725257, 185472276, 509995405, 385582972, 48561661, 621014401, 601439134, 712009301, 894079665, 336346769, 435967794, 10943930, 952236648, 752267625, 612187934, 405744613, 664544572, 821600570, 683417910, 17737757, 159319709, 232027566, 452549279, 346686077, 152987170, 922646522, 318550144, 67172207, 851086097, 396809730, 179877736, 980620363, 30524133, 157043665, 502460618, 598773814, 237934086, 727867429, 82410665, 245330241, 10380430, 722428542, 254330731, 941967739, 614450536, 101568275, 147458664, 819578422, 828261485, 509043855, 912136619, 61353469, 464577941, 253784643, 531230250, 281196158, 616852168, 1997499, 447543327, 316318749, 318914721, 817471854, 142324816, 659326197, 242759629, 911668106, 893633822, 56237848, 241510803, 798510719, 200450415, 4355289, 813064633, 568401816, 375165986, 299860019, 910639212, 633430293, 543685102, 331039280, 818286038, 52900836, 623146385, 996696196, 583978787, 603914453, 529414122, 980597437, 419871816, 658547236, 297241564, 428205378, 560851540, 299393199, 939760400, 647277633, 368607520, 360103423, 562083334, 640844865, 476392880, 519232518, 394163946, 397749868, 818759378, 998968859, 321693423, 776597825, 164687108, 669260786, 922786766, 692603886, 5248202, 960915953, 371843097, 141240029, 642924551, 64321847, 449053088, 815952325, 24972487, 747759735, 630192654, 810250933, 674517762, 476193035, 89309940, 50888641, 307377631, 605145012, 673027793, 467166865, 285127660, 307888984, 146223324, 841123889, 889632869, 692924763, 433985437, 347193081, 973271803, 160850650, 188547151, 266050425, 197710732, 786098553, 321263008, 625995937, 381940223, 519670454, 409304172, 547628320, 805524470, 888445663, 126984062, 701667701, 877719426, 378406358, 540553858, 161047600, 218462148, 899439021, 565662587, 46484938, 712782585, 418161501, 473486717, 275185290, 573907744, 961421933, 431857955, 598518320, 875463044, 936923023, 913283712, 538459625, 978614157, 707994986, 656575399, 361629923, 707619018, 962287484, 284053524, 236941040, 855057410, 883414630, 74302862, 571836095, 621851038, 199520372, 9073562, 195658376, 831610340, 454865692, 176611108, 371931424, 527032599, 91752634, 265729061, 893145620, 500152358, 516880740, 996462482, 470554026, 978553421, 394242029, 892767074, 171794555, 599769862, 712669366, 553157008, 646968444, 123020230, 618888432, 929109385, 882996682, 728512998, 651877313, 928374180, 67778053, 929682028, 982971396, 210443400, 617086954, 713188838, 241347694, 193358637, 782462318, 453747147, 306037923, 654258382, 4694977, 848057445, 395122624, 974053022, 470841252, 678472737, 802898454, 696104155, 516650411, 937195012, 825967663, 241322578, 842794283, 3191248, 145683604, 578912077, 251877298, 325676059, 751715306, 658874554, 495980486, 436528971, 995132738, 583819138, 350675016, 404253719, 494599430, 741580632, 218030427, 726595501, 66499087, 504290310, 329572213, 370944242, 373679262, 189435361, 608402743, 16853698, 623612939, 621595164, 170777312, 264517254, 697696321, 243504400, 295640769, 542992780, 302376110, 633955593, 47472549, 464918748, 701331326, 186759647, 874182294, 442698257, 329457511, 12874621, 814442017, 882827401, 381526023, 309860352, 415854682, 615215183, 684820792, 152455761, 161461765, 997658784, 264556769, 755279397, 56875984, 563091553, 480705049, 665517946, 803128266, 800838003, 466482227, 228821700, 602180153, 277769807, 329483093, 605044949, 554982428, 758494520, 729050536, 203898452, 423357159, 411839388, 445705024, 658328197, 213819008, 388877573, 719734905, 462545306, 697374920, 944294274, 425675572, 459227225, 993713801, 459882329, 227575828, 577958049, 417775872, 953402477, 385927748, 588735660, 296054133, 355362961, 288551915, 830210542, 5360736, 50636751, 581394276, 15915463, 945360654, 613890886, 472463053, 538496357, 724258887, 347538213, 477998314, 529321210, 733718086, 883962321, 59015706, 238494513, 374795979, 582317350, 162034908, 778914753, 977758682, 772554974, 418429560, 891003387, 308322883, 181829443, 772208826, 475031047, 12529901, 292813215, 665327789, 345738314, 287351347, 447973727, 645213267, 728683408, 477928576, 532728849, 274430586, 834894398, 572466094, 910137546, 40777104, 635567955, 365513906, 914644900, 221961545, 832761713, 775449899, 587297685, 251488554, 956324587, 640405125, 65188156, 679755017, 841710673, 780928655, 902211088, 668052749, 441077375, 363275117, 37892438, 456708831, 373389396, 734008004, 99261975, 811813177, 744629157, 482669667, 435610274, 142372425, 731104331, 860342048, 761704172, 597514387, 759349116, 479880499, 319989288, 953002665, 108920670, 503851327, 561805772, 696096822, 878961971, 612912113, 206177014, 169062086, 577117337, 165064825, 203929347, 886637437, 336928503, 256822734, 25480670, 557016768, 746330700, 462413242, 281661962, 64264774, 674445681, 933093468, 531199708, 388306129, 993194043, 273621355, 290263347, 557365978, 712588949, 171624823, 763004339, 57013262, 498697164, 876521815, 12251393, 841735760, 155273578, 200210473, 558338247, 42926282, 515939470, 824112871, 951856072, 402079888, 496169247, 455542018, 395839784, 499100356, 859709781, 282586894, 40658857, 291937094, 909123253, 637588904, 767369814, 446311933, 103970661, 499490185, 850205569, 788282011, 73197825, 147576527, 352034314, 695202124, 325580794, 458569526, 695773231, 239466862, 763542170, 81782242, 949706793, 543729552, 773945909, 105265484, 411772806, 651616223, 543544424, 873784151, 355843866, 666331887, 824149228, 340316971, 745977306, 893148025, 996129076, 861699977, 874454484, 405751371, 534656627, 108179447, 53958479, 189224707, 167583554, 250524624, 85696867, 642013350, 551845950, 457702337, 726836496, 639688268, 288495829, 893677614, 580039453, 345924496, 528819504, 486653930, 284074229, 407752249, 601984563, 332748089, 441327568, 556316582, 392653249, 413297265, 540695324, 613349230, 771151600, 530840282, 341469194, 44948688, 179329778, 966075264, 821049389, 861276623, 204469104, 424022680, 239605710, 289303450, 158284200, 362766613, 299019661, 322650725, 732262458, 130003617, 939823345, 847969994, 600269249, 915341281, 276845663, 541487624, 340185774, 595194601, 436688032, 512587166, 576401943, 508403390, 60707456, 545016555, 721996916, 429190836, 154277369, 981493506, 671885265, 904249053, 656199446, 117593065, 312898168, 759871551, 422644771, 862148368, 680022288, 919784945, 443708887, 251306030, 712495645, 525182832, 699867506, 661410509, 197567613, 69983407, 294103016, 653982593, 627179926, 912414734, 716159908, 839310758, 33107169, 209752847, 554428112, 410950184, 870112115, 446078529, 839302000, 523079641, 524126696, 739402920, 77382068, 477110194, 739555299, 410058390, 139229712, 384870699, 65205055, 276858671, 223998862, 520702390, 538692023, 931321310, 857237772, 219418799, 377306206, 278435484, 370387251, 495727186, 406455462, 662194530, 148919692, 725615816, 694008609, 14665900, 802456960, 273348720, 308188638, 879297908, 175364019, 995330902, 351814625, 825543737, 686121284, 455192168, 563954925, 28290424, 24685396, 239183276, 13494348, 163480677, 495614620, 169088575, 999409434, 851655256, 174429253, 59595700, 623345672, 302953168, 460513354, 93403647, 715454825, 947243325, 468734495, 254305903, 139815652, 333269463, 350201641, 800345320, 507567531, 481008212, 693331886, 412938405, 162712205, 518775794, 250073148, 517019323, 67944129, 911832038, 161897622, 514102214, 453477407, 885660548, 412069355, 861423483, 640322433, 174274089, 624516000, 704889413, 177673967, 941077300, 888151781, 405274825, 930038441, 537049158, 872159025, 940604639, 214138801, 599627019, 158693150, 190875594, 204390016, 679943601, 755584856, 315129817, 219403359, 668699986, 323909839, 733964551, 215918121, 684752758, 482284745, 618041677, 3435354, 825522892, 615906638, 916814104, 852147250, 184649224, 357591651, 141644735, 565819610, 399644807, 945531723, 768221983, 964821148, 670885558, 107712879, 764021082, 126570848, 12318178, 823833718, 118487153, 562309420, 777107429, 665365652, 384205441, 391172882, 25080556, 546547469, 307663474, 941597606, 223249658, 792354788, 241091199, 734034760, 738329668, 145059251, 18394715, 669449102, 923221209, 150229794, 999202393, 115327248, 328963306, 281315118, 511421718, 508758886, 977769930, 12604142, 296832240, 505120665, 148197208, 889568782, 398384695, 308172356, 979636547, 11011494, 392855848, 939327186, 889299521, 288279849, 922955234, 103734537, 218840921, 427124883, 919153697, 235455162, 514104919, 580934414, 283488605, 363306326, 913842644, 168848845, 653809988, 857651346, 160355103, 560571129, 447110639, 600949437, 844090893, 117127840, 456293695, 558973740, 959104035, 162085599, 335642201, 815877354, 94198586, 795741296, 875925348, 714705593, 354076878, 87121559, 930327297, 38730416, 741391414, 799850952, 100960516, 412728401, 923600306, 401737041, 776321591, 337130696, 23543856, 249685300, 557008749, 772847921, 212072099, 131775648, 662259481, 897139141, 557262125, 510269308, 76651687, 457272547, 5798165, 325179829, 254919674, 770849121, 587642847, 145858238, 105800291, 483319943, 272450025, 171214798, 736023355, 482646786, 652873913, 310234962, 202204862, 874091347, 700072094, 45513515, 842267809, 227243728, 696299174, 675158878, 88836308, 900286868, 759046116, 605261051, 95455350, 163027669, 567863141, 493945882, 835770593, 726376338, 1526382, 370209649, 715269965, 449802706, 945061414, 788240905, 843508992, 107669048, 110167114, 388677009, 775794125, 960409590, 162896182, 151703234, 681080572, 362684253, 699562375, 312039983, 391948124, 281127605, 972656762, 20734652, 379508309, 675512554, 486684460, 538832512, 860892017, 880078449, 354415964, 14557508, 744096368, 190362756, 488010857, 17648120, 294299296, 379023392, 68497781, 418249287, 850272948, 572138085, 712080271, 219783834, 588972498, 951339848, 617091032, 708186561, 105667321, 583200149, 490597274, 522524479, 665430981, 106589638, 234120119, 574734875, 447267050, 145590116, 155937758, 829864412, 962446287, 117978188, 759488072, 377532595, 115401010, 527875659, 451571562, 168516090, 99385140, 840000941, 34868335, 528635140, 689533200, 961905280, 451123383, 541088244, 825547709, 366240377, 237938070, 847681824, 400864212, 169628052, 485119222, 132288737, 417287573, 459894925, 541741964, 788805819, 663651480, 971873198, 960033525, 762917174, 633561413, 571145465, 316231530, 933761490, 152935429, 331851085, 100729933, 784719430, 148947475, 441583551, 185389464, 983371952, 43335914, 860761812, 485458890, 559395960, 559491418, 56516309, 806075825, 284388744, 148057509, 851827770, 354085165, 561804263, 317597282, 571083216, 525366804, 786701414, 530585368, 514264278, 581387297, 418857400, 605543422, 632890811, 439124409, 764288167, 102075128, 143750867, 644347630, 540724971, 185544625, 628710327, 252248780, 991059356, 170339815, 190411876, 765942755, 100946896, 871372880, 355543856, 657595789, 292197688, 632866784, 760466774, 360507744, 536400849, 451944267, 635005415, 647500718, 805725273, 909028300, 264393432, 324650312, 611141440, 235289381, 960680242, 386369235, 730936101, 312379546, 105388133, 794925525, 977913869, 611812867, 799290060, 294556263, 371828801, 88330516, 741729065, 502766620, 649137433, 593806888, 860844584, 878127700, 141200963, 284964174, 478574760, 194518459, 258466668, 816354191, 296731601, 34353347, 353706983, 737884274, 4911065, 301211326, 569960292, 310433588, 803314751, 870313545, 982209763, 28445299, 980649128, 787496913, 276637176, 935675071, 735491436, 312145063, 155075520, 377526313, 138414600, 499553038, 198001190, 716431820, 72521474, 564862061, 519672195, 929381052, 513633205, 707042450, 874811944, 400712562, 786766072, 717644659, 387343100, 869148091, 617794637, 167305770, 915922944, 277347283, 994559327, 354070038, 763186482, 52407080, 234443397, 418394549, 813893031, 133491652, 545919443, 376703627, 828957371, 185041982, 829329238, 327846245, 287711399, 395058137, 959344138, 250180734, 26666179, 730057271, 645685822, 743972687, 141126691, 819080264, 142037092, 63762388, 303855967, 522102976, 733949094, 770477710, 568203275, 622126257, 7550802, 75712796, 442970114, 41670815, 378605300, 458149254, 331311094, 778435471, 914417493, 840170945, 491516104, 936656974, 739047077, 350197497, 579763060, 743313784, 812099594, 310077431, 899558362, 914988589, 842648048, 621445224, 614433595, 176388386, 707644184, 20598691, 431855210, 703501362, 789228878, 814722981, 465984859, 364915780, 963701518, 682040014, 900846958, 260535423, 497265502, 559759070, 252570869, 71995537, 170608451, 318956868, 489097262, 734922670, 785493319, 252576542, 295028962, 793566534, 10651983, 630289375, 462221089, 910679673, 642841198, 433214715, 712766417, 761794044, 944140706, 661138252, 969479421, 40790036, 50571438, 198795499, 986045828, 529648733, 247759367, 291103284, 890391384, 984348458, 124007586, 773447272, 334765860, 714088579, 281598355, 176015718, 307549040, 864852999, 222429048, 460905359, 681290352, 698457413, 969133324, 899001554, 547619525, 373201942, 938928561, 89526561, 792653409, 992935703, 262362659, 255870725, 811611415, 705720502, 174620481, 799386425, 303450332, 7873955, 699160566, 369366681, 2474679, 197723321, 593635933, 396669258, 902967515, 675236040, 890631341, 401373734, 693398650, 971437007, 142741962, 473622419, 527439081, 433771514, 119178041, 531839208, 516026901, 846942108, 526415185, 510518427, 259177371, 617087168, 116440386, 840670464, 984512127, 732934511, 110850145, 740097406, 190710142, 578757864, 887115760, 468348777, 327713730, 72880606, 539379599, 529203864, 84262379, 949847517, 847371801, 703818148, 343550785, 948360207, 477564873, 829626010, 109909240, 169691997, 476884325, 953698872, 364467864, 791843851, 590446904, 355636228, 678415041, 111719294, 586341749, 48360746, 218411108, 473755132, 183311546, 814913381, 693220524, 826835906, 957578579, 931665860, 637539495, 850566279, 859109750, 930424641, 215937175, 137809079, 617904390, 706858124, 645046418, 611091145, 309763410, 606420996, 202734355, 198182881, 344439099, 76525850, 174418408, 500483168, 735862305, 707320593, 805212388, 170699062, 656153137, 492170103, 270519858, 688943769, 957231980, 532937565, 834222402, 423501862, 743888695, 634023421, 309788295, 39542292, 586738017, 724879786, 143445050, 374388062, 601481553, 720583093, 309210190, 404689844, 127544920, 152766144, 703889695, 79849681, 275986920, 150196588, 139236581, 850256080, 325136312, 959649286, 857883850, 462332104, 90324946, 343289442, 222996348, 972535292, 868228455, 746018766, 762889760, 982921480, 499049080, 55161352, 732598418, 228882604, 177401978, 180580659, 319826956, 169253813, 886089430, 15536837, 359468089, 61298295, 661928892, 802321373, 844804561, 183121530, 947216527, 205137319, 17995028, 689555449, 275124822, 8713256, 953007222, 146512414, 342964177, 163630573, 16764832, 124628510, 628117674, 143862652, 551194055, 484297190, 458180912, 412701087, 455242001, 555211658, 989524413, 965316100, 732105282, 672283734, 358166268, 785031071, 882966127, 654189914, 513514324, 224699497, 266477357, 886144093, 178755035, 506283231, 818690286, 678640468, 215198843, 836090963, 472803084, 735281759, 252878445, 459004288, 916520269, 177448076, 561703808, 696269152, 235655341, 12606421, 759865931, 297080814, 702200737, 252366063, 931853579, 176525872, 676346305, 469325496, 332803508, 847463864, 177136602, 900434826, 557159470, 990501169, 60926341, 703630793, 99228213, 459899028, 906753988, 491289755, 822451864, 739203645, 5858793, 235112883, 374580375, 8662767, 636633440, 646658649, 806242864, 150927605, 125868006, 402777229, 745144994, 184815711, 733858511, 152837008, 114862920, 523784893, 989315648, 592007415, 926941860, 78320889, 425689814, 717256881, 646862374, 27915112, 320949792, 910081608, 562447533, 609782283, 844701304, 620739250, 259531905, 452820937, 991340508, 279427326, 980586723, 584275150, 786749207, 291031631, 214439005, 332767819, 586544418, 866922823, 63843679, 119526828, 965304224, 455171271, 824311651, 40500807, 149106730, 20043408, 920845480, 954702724, 182435974, 493233036, 550477529, 472016410, 545928396, 277518422, 695622094, 433307594, 456053144, 957389972, 57562915, 153294488, 40405725, 609140246, 143349349, 960809655, 433162794, 47345201, 121186686, 836009184, 219047930, 33727503, 386931362, 264339107, 458522461, 501319279, 438619287, 575411272, 178070069, 453471359, 943320253, 435583234, 431910414, 840228373, 566411597, 163994965, 306330297, 820123923, 854179355, 884993408, 548163740, 690308067, 499090195, 112035239, 447111945, 747738584, 975313659, 587227974, 136835710, 748830319, 813696141, 646846891, 602698183, 952757102, 486091417, 189822433, 213236002, 137424592, 337748194, 265724999, 557356790, 602562575, 863504465, 838455442, 505095453, 115426626, 597626839, 531764291, 100384687, 698970151, 257376610, 777692267, 362400650, 316162674, 203403628, 867599344, 189604163, 988296320, 970361203, 247538065, 540535655, 690728030, 837236277, 763975486, 909016501, 769465505, 518524652, 102432828, 607489895, 494403552, 47235786, 358762665, 15584613, 2405043, 595116929, 557888363, 750799476, 687571070, 710490299, 848929667, 79105677, 658513976, 822558274, 245851478, 237338035, 348801511, 322445644, 667806017, 82043799, 701195341, 81947579, 309603532, 963240591, 631341299, 924976161, 721598492, 367662786, 221855576, 729400595, 666411154, 751987490, 229727345, 309229059, 493287664, 356268539, 85781733, 932650185, 81922499, 59104910, 459645222, 754876598, 956542515, 983146760, 893624823, 515578015, 736970421, 782684931, 806851485, 372550091, 723298610, 925125839, 855910321, 195602770, 787922675, 963742402, 999386755, 69703853, 58586618, 364935333, 912976591, 823085661, 773873823, 279813750, 622789295, 143833813, 446347346, 257501743, 202755948, 289322966, 707588455, 670443408, 203056534, 619348511, 134796471, 264513436, 13614748, 555743804, 922602413, 341254839, 262357656, 249187368, 712606359, 120863943, 951572437, 729339024, 589596742, 2841536, 320933025, 427305939, 794277539, 257717634, 749553211, 10709703, 996279959, 155267618, 569924476, 483760060, 634165605, 826017159, 58393859, 449995504, 543019914, 84153992, 225688438, 912147421, 774559517, 143774933, 455389765, 652760379, 971662357, 584949213, 844602390, 511475121, 169644831, 844614011, 386122427, 262970796, 74389883, 376722554, 158370840, 922149046, 349512470, 550239846, 172991023, 411909072, 689422810, 655494443, 214920279, 50896729, 301631911, 164970705, 905172978, 567166927, 967676099, 124421397, 526672863, 755071253, 380417315, 215941977, 990297227, 529955289, 480183922, 952607439, 263999757, 872043151, 853192664, 366895735, 811864456, 823084166, 729225008, 181455498, 632654326, 79404825, 917904371, 659064048, 91379214, 904394719, 235801595, 438526460, 547558712, 30196765, 203155819, 17991549, 602962461, 342307573, 979596064, 492289822, 542561792, 606305232, 661917555, 804047505, 963232614, 32615712, 110953015, 901140224, 240979174, 104244348, 451262383, 23279427, 848593573, 499413711, 918836126, 33016957, 477256233, 463640675, 853247269, 949040112, 468406100, 984026819, 22772087, 856496955, 194822105, 711013847, 522078548, 822079776, 497812330, 492953773, 156316854, 108916561, 408949163, 184844598, 176265332, 418229459, 121637141, 190908312, 599511986, 32895727, 350337792, 89998494, 878706491, 759310095, 976222029, 976660046, 524264667, 402219689, 985687362, 422370055, 329672842, 766774824, 21652133, 643784514, 677561029, 107355396, 359069717, 351325790, 890872965, 389319690, 6565538, 999953146, 497843127, 814921996, 190094868, 296978149, 354380498, 890449191, 80407136, 541304413, 608182474, 942239611, 722148484, 716929890, 530103369, 305929842, 151395821, 170217767, 410313162, 737368322, 841234004, 518091171, 396402776, 905081861, 932086326, 471913961, 884071478, 631170155, 651408521, 26928797, 465174323, 114303487, 382473259, 315728395, 427775273, 707131083, 276925993, 428184636, 273932846, 391715262, 411060004, 768633108, 495726712, 825978759, 154624655, 163544732, 292108356, 308802435, 454314463, 112842220, 506544557, 707643981, 750528244, 135597339, 526408955, 519629300, 11280976, 376269475, 133305291, 89768053, 408617304, 883926724, 933349135, 555514718, 603407782, 23325719, 659235531, 910922199, 289140920, 12104167, 578451838, 631143755, 195715054, 137056494, 336595730, 690201543, 467707924, 588731483, 495710916, 633161558, 407577957, 718070962, 19925074, 122097858, 731265727, 995163855, 374257935, 731972101, 54604948, 689028846, 442824030, 197976339, 973359195, 410251057, 480595099, 56866515, 767089881, 33401747, 672178818, 48197206, 913792, 727032904, 993623383, 596770377, 363405858, 185561935, 125013900, 141368970, 409380135, 88267837, 650468108, 866603771, 535108667, 534946432, 330975157, 305662040, 611245957, 547310781, 838950267, 493863397, 811205039, 95003048, 861491291, 176177251, 794573553, 439796810, 579353501, 565060560, 920593385, 868461145, 503827085, 77724411, 728417238, 295806855, 940614096, 280906770, 365846596, 776890580, 964647879, 783596569, 513247368, 114620906, 882601060, 427836983, 679916828, 852695247, 148861743, 986498168, 352266416, 985916669, 652017749, 709591055, 874974646, 566445853, 357642337, 702014001, 801063828, 567261315, 11470572, 85135262, 732989271, 67926608, 199163808, 63687428, 25245082, 322575024, 223196361, 160666369, 922446460, 898360371, 354036576, 634417912, 187149337, 732814523, 13835062, 676342979, 310770116, 566113481, 214446356, 927877431, 838310157, 556076448, 105819049, 593572591, 910301797, 285766549, 699535686, 830722684, 495804604, 129209092, 701191952, 205501705, 90897418, 453305625, 740519881, 27457210, 764587544, 165461484, 57539651, 477722591, 149812261, 80353964, 912630871, 221181739, 853492534, 752871100, 162219079, 481579898, 293216497, 553775392, 248640371, 559014311, 591966276, 273893118, 204400012, 247536059, 764212126, 123874500, 593001833, 11634751, 358942083, 637459322, 732424428, 215314775, 677425500, 352725133, 396318265, 267515553, 574103791, 178530672, 542636332, 337839669, 744396101, 29368329, 337432599, 179743137, 720226076, 501124164, 546191095, 370674727, 844956155, 254866866, 646054737, 631487284, 903373219, 730371302, 396860176, 363021206, 565002663, 930397641, 442080096, 972874303, 132836582, 615123352, 888658420, 648355179, 216465616, 320586323, 842062813, 697532147, 449464060, 45142399, 513188820, 46416811, 293190006, 388414223, 161919892, 993683468, 30379599, 546816474, 870307514, 523006001, 260892373, 164416107, 573470417, 516919234, 197071347, 817356039, 739364265, 301957627, 34742305, 559653530, 30865404, 700109696, 133183233, 873729749, 962610844, 764417656, 441524245, 222592732, 195041599, 283244062, 910509793, 243568174, 906683246, 497320814, 858338325, 932693334, 787552191, 906402165, 369759882, 653500546, 195442439, 495221576, 813233399, 65709419, 439227158, 492985508, 149798835, 334615565, 129949767, 418501976, 733035684, 493119959, 654959801, 678810273, 209344948, 544674684, 171622965, 353218316, 481727029, 270777534, 20731699, 722852040, 919140547, 955589875, 259984489, 6453520, 53896497, 134362781, 626242441, 995256729, 903941197, 664564310, 655800866, 133244779, 183571048, 426102469, 565665893, 947933672, 158616926, 111761810, 203201249, 784374403, 845197879, 34357679, 276703780, 642164060, 833153053, 260221401, 847571421, 131943785, 926838220, 85963711, 679896711, 501310404, 501325379, 88354002, 474025038, 934322724, 343269549, 494087071, 673368412, 648351704, 894746275, 633866342, 167392667, 264159315, 441272410, 527590073, 148643623, 918797375, 695138336, 458044845, 122864298, 747203836, 933042041, 600230160, 636674197, 349446483, 437978640, 465956402, 291512814, 124466530, 928872930, 488278654, 53872748, 546259306, 117551080, 574928834, 907947162, 14749164, 214989385, 612353992, 210167493, 522564853, 535240523, 735229229, 921329369, 594628446, 386547265, 669193514, 443218463, 290155190, 435088755, 628123750, 699178265, 122543337, 495544033, 918004202, 101477384, 88421449, 956667488, 776912728, 606167299, 272437467, 308774802, 229099064, 293213414, 35166568, 477235357, 337665998, 268831320, 90882125, 121376360, 434814671, 471593001, 536589323, 801943831, 486459199, 664552691, 294200309, 801530022, 595152633, 94721352, 460233508, 653086962, 679399879, 719140486, 687485616, 899485138, 947329450, 856553367, 612153016, 926411765, 90583888, 600212259, 808981060, 514597524, 213710519, 715564950, 794808633, 111135595, 258255490, 681283958, 597070845, 714017180, 718378574, 32780333, 3222012, 582324141, 860339288, 778025208, 361879751, 203662324, 827647991, 96385094, 545956210, 780388468, 890032886, 436931751, 700074108, 243510700, 329059853, 222441481, 289659798, 575885895, 810865470, 781102236, 630644645, 635871400, 947390982, 645025890, 992346977, 925024486, 911859689, 244647383, 910379443, 469168775, 301396836, 302627898, 633375194, 39370122, 18426791, 547946712, 500816421, 629677990, 703578969, 764680437, 940785755, 816937066, 914710103, 384931875, 318792944, 890876885, 520707653, 861514240, 355875966, 779631847, 952294244, 487178716, 737971024, 61169692, 729086077, 523941870, 232168892, 153174997, 552857140, 54739707, 657596169, 426611496, 934002355, 908265091, 969518971, 833076671, 621849132, 596142262, 780274055, 539164070, 631028869, 500516323, 588126907, 949484879, 604767803, 772147036, 51039622, 201799950, 428033665, 388660210, 140109040, 748550186, 954088648, 461368151, 852922067, 66841619, 106769652, 620174280, 166765596, 143204652, 199525500, 919520619, 231114673, 607945170, 597912461, 994288925, 832332272, 138680003, 712205854, 615640042, 245099530, 421874650, 357726798, 863448753, 622671106, 776217467, 625312898, 283184948, 262443364, 275877332, 267124479, 390735741, 528156549, 630489400, 582202167, 803592811, 434668671, 901775202, 741033568, 600650178, 887933168, 229148456, 224941260, 613994887, 199695401, 612658478, 604533882, 763142960, 62711138, 242923316, 382975977, 560513967, 677359127, 843101985, 303382470, 796975517, 233771105, 878819800, 701406465, 478107134, 63319323, 142590833, 237377419, 231873321, 881503137, 386863553, 720248335, 675209901, 168241125, 214592853, 36064197, 130459023, 370133367, 454120634, 14919924, 330897123, 754037527, 271964003, 983486154, 232188707, 111036723, 179818025, 410356699, 232431830, 841173521, 106519908, 848181938, 345316866, 288268910, 214765267, 166916875, 127325717, 743693047, 640032526, 895809428, 974156352, 730112217, 383575080, 815297307, 14273087, 439890017, 511586064, 916657022, 538102496, 364142217, 594878823, 774879907, 684166230, 37586632, 948261165, 296781548, 873813254, 107029435, 675059737, 982029416, 223754859, 860251327, 995268795, 14659015, 323907104, 288906690, 311033334, 275710044, 354711660, 949431260, 498301854, 94558715, 146481731, 968406230, 728662717, 460881516, 350117731, 756934866, 593305539, 490580602, 158262762, 443212096, 887935566, 641712366, 899436149, 27591938, 834817727, 496782917, 347922878, 995841948, 381188184, 330833491, 332920217, 767153952, 367346158, 74890566, 734866856, 301792267, 840812775, 731346168, 72173101, 799520864, 326763840, 293687477, 553199919, 979804009, 956225842, 267407139, 535465446, 624600645, 794626622, 666753206, 479442748, 754797315, 143289200, 625895693, 953106849, 41345217, 947149702, 198325891, 857077007, 327415073, 235371338, 453291512, 771343042, 98018842, 815085164, 527099219, 549891934, 935931419, 516155337, 375123953, 850191429, 897620815, 324335429, 1649374, 32248570, 686225746, 542217498, 825767017, 970859526, 630459300, 579791820, 646989011, 315107731, 911563377, 616039984, 103557410, 516150984, 229402531, 418542918, 981352133, 863707420, 780456987, 864558547, 691517047, 303327691, 754044050, 70142708, 353850175, 666795147, 629745746, 599805737, 635460208, 560158271, 214399602, 111130508, 212421291, 217521859, 649056586, 757864817, 3452078, 970029448, 609634658, 661784361, 115053786, 501351101, 810600819, 190870112, 529305629, 225335229, 44006857, 179739124, 475716711, 803578790, 338277934, 912376321, 575469366, 910444515, 330853694, 910272698, 207792578, 290726863, 707232368, 196011107, 135289830, 872063225, 99626454, 561436066, 305794694, 94392524, 114488019, 710349682, 451698894, 353037845, 279314903, 175124368, 883395808, 669083018, 45186461, 182734143, 499136371, 156777496, 596483787, 907135675, 493179365, 987249077, 981369105, 953462150, 599413941, 251082062, 470540542, 626611355, 116227755, 447744240, 399636425, 503272690, 805926968, 24466833, 996139703, 326957805, 10741788, 884040511, 224504583, 353726011, 419992108, 738833458, 61135159, 20541696, 833583901, 42408795, 836029201, 190039026, 135444698, 223516062, 900726520, 511154806, 673622448, 851415953, 550157764, 660039666, 336214991, 831308017, 238868168, 919133949, 453679987, 899033636, 336816427, 119736864, 172771242, 879216032, 887419074, 637660002, 255063705, 873155697, 646369511, 149448907, 786936197, 517623686, 907980897, 498132228, 936895198, 627019194, 567700800, 197815167, 101566708, 601331088, 926031945, 619737071, 488811596, 580737605, 244583892, 628593537, 611872221, 813346767, 520841366, 787516027, 370559403, 246337843, 545665791, 153428125, 697566776, 589918385, 201880005, 413772512, 458113618, 675571208, 576388109, 34738217, 385295073, 580264557, 184487058, 144039152, 411592542, 66962707, 753396797, 565388915, 258334408, 274416625, 675733805, 456565621, 257491676, 340996631, 172357956, 296342418, 940647589, 104219885, 133358855, 674278521, 588750566, 989477312, 494560280, 608128334, 263174517, 717141339, 573909321, 968377967, 672280468, 437788073, 326778855, 730036825, 767637110, 496180085, 657077231, 917455833, 676008137, 768285029, 365533240, 352183456, 628074651, 215816997, 533437585, 113985999, 746945743, 641521529, 172199495, 522996959, 953836768, 934866550, 378628680, 688193439, 877877141, 499256154, 209439785, 643520079, 636585567, 628641494, 56207176, 845329303, 540842853, 52988685, 881486700, 745358431, 140715437, 572756758, 15258358, 19474007, 906259955, 46431264, 359093529, 448006013, 674127394, 674667526, 570473160, 411542792, 156783886, 612649237, 899836, 100423055, 200959126, 960482637, 405843843, 427674277, 279036306, 838505910, 81051435, 918158412, 501978957, 879446653, 474098956, 234088907, 690764281, 709979643, 444956423, 205450554, 877184250, 578811117, 36888443, 732923291, 74834001, 319237048, 79745004, 225877847, 885219922, 640104242, 574406947, 892642305, 34961746, 669091351, 627708980, 740755110, 794328725, 456990156, 97289467, 894611106, 78562430, 688509661, 968163854, 447905316, 853973920, 158366601, 311148252, 299533588, 592082683, 652380199, 382469648, 638748451, 445520912, 395347055, 937896847, 742047170, 986730842, 260165596, 513974115, 28363704, 862829982, 737307986, 20443619, 969757375, 619862070, 161065465, 696891519, 740305796, 140362555, 802567388, 655005341, 90677083, 187154496, 640173253, 695979475, 115801350, 105421674, 639704703, 30050937, 211402230, 816563217, 137441378, 404993700, 588906649, 883469987, 785918594, 781124440, 90145992, 863199552, 828431766, 992238130, 236595981, 714810552, 137993861, 265406720, 985928905, 393144577, 831647826, 130681793, 998089489, 471391106, 709250606, 145312431, 827242432, 55124563, 622312837, 258242724, 726865860, 308670805, 276467426, 146261023, 546469154, 204012845, 210388444, 183885267, 495138784, 375672635, 564400826, 343308828, 574510383, 99030266, 963607341, 723909940, 215616215, 493448233, 610446573, 686112612, 837594940, 16638967, 213043718, 902055459, 285636841, 479712110, 164308927, 341888747, 762682427, 502002607, 7407055, 733946903, 281265954, 178263320, 232510146, 377423319, 345959869, 895417640, 172822686, 762743337, 588403320, 306221733, 165095990, 583662717, 4925941, 563182668, 103003371, 681718422, 248017380, 323580196, 872385320, 897478094, 297636429, 997971047, 372088313, 928349760, 52436432, 415182521, 404200925, 184544773, 842985402, 502355725, 854453136, 757050563, 277776969, 415935671, 572042740, 778542793, 193653403, 697685619, 359732222, 231743693, 399641667, 396837674, 934558180, 376545673, 133393933, 944997753, 918145792, 346357218, 455036939, 321733827, 638898940, 393099467, 508575799, 786040115, 318047169, 333555706, 826115781, 771405945, 727552607, 327541280, 596931615, 967836190, 864793335, 412342226, 456048842, 122303758, 622369311, 622129336, 748489257, 665392987, 880834646, 486007342, 403871882, 261455925, 955976405, 395944590, 311814604, 746390573, 812357956, 43732593, 834842067, 546386982, 365629921, 14548522, 958733974, 920674652, 728626451, 150981220, 120134333, 901943206, 803204929, 867958502, 332312959, 165248232, 385139586, 733737753, 777560311, 820524207, 693410798, 498210590, 764161997, 192199534, 732153244, 777326234, 981088735, 866547333, 351209291, 456994596, 356951974, 543279704, 725854375, 249123103, 225223084, 835161822, 93019175, 674694940, 426378133, 69062484, 816288175, 70268735, 484372259, 528734038, 277013210, 928700014, 910509066, 474997007, 229470646, 310666702, 645707066, 848988951, 126329460, 267860366, 42531843, 183232119, 15871468, 936944790, 186705853, 142710470, 799134875, 815757241, 859323450, 564880, 698970529, 398415806, 390918891, 367767048, 619148991, 627063297, 272001313, 785154460, 47132793, 514444918, 167941135, 839355541, 506719536, 640203947, 994288611, 624227427, 819638960, 405535317, 996374189, 363131972, 373059374, 320490286, 783584176, 596192111, 33104761, 691825868, 631513306, 293856890, 800388963, 942590458, 154874296, 362292765, 242667797, 267585675, 242523310, 381869386, 949412116, 368601991, 497895803, 636737865, 381363439, 483163333, 42300324, 602082731, 524252387, 590618901, 573776766, 144429509, 440333553, 614066259, 459317633, 387171502, 964243405, 955578378, 447018505, 725378191, 671539291, 171521850, 365222816, 833094722, 194359663, 929244362, 806506771, 222607988, 479698723, 180136314, 838437272, 339561189, 369217505, 723236882, 30821859, 884621270, 461996321, 168607460, 28188837, 343321369, 624135646, 11244044, 322627178, 381979628, 928373632, 160038851, 613608372, 396304427, 21753143, 302474655, 453728335, 605257175, 560161489, 398605107, 488768417, 861793110, 224332111, 687990910, 737409372, 149573951, 694872193, 261258209, 491167557, 471617475, 547539154, 801920511, 236408513, 478953495, 112013377, 761424091, 765729385, 487961548, 708021482, 425908804, 321808907, 745104914, 501999417, 531896166, 232784327, 499082401, 417751103, 646282742, 620796105, 833692901, 156774796, 330256715, 62987182, 905928590, 302513530, 340089458, 867142401, 963776483, 848005115, 127533692, 592791053, 408685363, 81471184, 185289324, 695184027, 334842344, 631354011, 488361642, 977534390, 382285758, 966487099, 439986987, 649930094, 678033940, 723638596, 620047643, 571355753, 966591325, 940731116, 340846003, 315068780, 539667698, 793626309, 689906935, 624494435, 118621001, 859315645, 988348428, 79612577, 35419723, 232358171, 889278869, 314453679, 631355417, 172334882, 321313144, 826007599, 963790616, 25303263, 142398843, 172788994, 21804565, 978132624, 307106299, 53213042, 419294756, 411089807, 160933303, 238420995, 269545119, 302421714, 313238156, 191063843, 374221166, 816981877, 813725438, 764652321, 44130977, 347931143, 612165750, 702776961, 499619743, 6999731, 197347305, 227682882, 699306476, 187657969, 826239312, 81197197, 476667386, 529171044, 631930766, 895338445, 943361341, 845186189, 234169314, 534510025, 999126273, 929752689, 214065027, 379859578, 17872238, 569223182, 818412158, 980619124, 762316465, 576764567, 716551087, 968828825, 763279102, 555966675, 953563021, 781310818, 270316833, 880794985, 120822541, 644612746, 907315695, 766109468, 113732905, 182533172, 139013901, 757422143, 50247210, 927975581, 162742420, 981491098, 732837404, 892692711, 933862681, 373752938, 748450783, 101319803, 226701838, 226801036, 751637083, 696246952, 436672491, 323930102, 372126921, 420297624, 135940511, 261054862, 332553636, 590846350, 663223544, 99796635, 328542992, 851164653, 824575719, 265576962, 202269699, 840734816, 947282404, 952526289, 75975564, 689916464, 232060765, 106791822, 878621817, 278311250, 129292773, 520532282, 604672155, 333776697, 713131280, 973442179, 207297851, 834494998, 77210131, 640206256, 483633436, 270021700, 409980557, 666260690, 904808926, 158493789, 54819873, 854049281, 115460891, 858475445, 975267779, 103875042, 541691888, 278437846, 490576916, 819556623, 845575157, 281399927, 173026660, 810836689, 720297903, 787978043, 188856739, 791949758, 957421141, 733517421, 295932094, 160929688, 494159774, 232308061, 892848290, 657857710, 207459256, 217597163, 513947947, 413946637, 834387735, 789756100, 209413090, 752486469, 60238632, 694869415, 904015086, 145942076, 986804685, 817947313, 289256821, 317886480, 240571932, 153079609, 103385253, 831515767, 245389313, 583571856, 33997872, 200563886, 298974505, 898619050, 438040263, 929045068, 708633254, 949471226, 8229058, 738455147, 658006174, 403350976, 305614950, 667289368, 322467725, 913862726, 912914903, 117958124, 621276689, 580479552, 910914973, 411314445, 101680586, 210410191, 457590022, 62542017, 257552021, 641818031, 16017634, 990621492, 923372767, 426091274, 511289974, 392806239, 94662174, 900328249, 946766534, 640153503, 482635363, 761303444, 777627068, 664206104, 14356124, 980403711, 855125964, 695448957, 860621571, 829526400, 393809994, 488024606, 408335302, 959801533, 78554041, 252477986, 644173182, 509825920, 144691595, 34387223, 385970334, 24470806, 650829587, 476805601, 946360634, 43120591, 552505165, 278610753, 496719984, 316741574, 727214172, 49659832, 676044731, 679863741, 268141854, 693996277, 960104418, 61847292, 334304778, 569575415, 81962728, 733761228, 392122718, 935384889, 392990520, 97110440, 265703284, 416201677, 747116146, 241999764, 714903526, 763481934, 441920918, 205742787, 762178792, 68716198, 468438694, 547759714, 414607286, 137987031, 888807539, 684209911, 664441193, 896185638, 121558418, 91903993, 610743813, 372178161, 26482883, 82458944, 434059965, 538877954, 456629758, 302280172, 155200925, 161167453, 874992141, 260553170, 564337810, 79791592, 382893262, 125203762, 489670707, 407202899, 78140089, 287182565, 150436493, 317439328, 815533595, 95274508, 547118784, 438359418, 971065332, 352785366, 609100083, 950630821, 249311483, 227960278, 233360547, 319823050, 395052033, 915696582, 528544624, 813622735, 965277769, 643798833, 170720110, 171656839, 553540902, 751919483, 492698775, 719148701, 333962719, 239554692, 118189128, 550894999, 64318751, 623014373, 316686429, 816725235, 892643388, 366583230, 337490649, 835176052, 488491044, 7636355, 597871195, 256180623, 248389504, 151022564, 193960540, 514459693, 106806400, 678089534, 508287092, 16783879, 868441333, 27136694, 442599246, 807054118, 329924246, 95811582, 960551585, 598443193, 856033561, 434610406, 993974775, 941113096, 746632424, 449306729, 843499837, 548197422, 506878243, 692938439, 78736781, 349662860, 916806343, 8740828, 54859696, 918255858, 600351316, 665382784, 184162465, 728482020, 623254294, 151599806, 447915112, 69457739, 601339731, 442477054, 749295379, 332382063, 356215319, 610710613, 382348431, 371087585, 189004842, 991411107, 393213270, 584660399, 345875841, 144550126, 136003682, 136522242, 777261161, 53254028, 701295780, 589809952, 677865356, 444245331, 456926708, 149673037, 324321106, 940430605, 453394984, 710758109, 231018491, 232860932, 420259110, 728437976, 701846356, 857367175, 351161602, 316791454, 761806055, 317923727, 320413491, 201048559, 827576871, 4865372, 603660978, 503289946, 213996922, 121422578, 890294764, 344025208, 894445705, 610107708, 610699041, 781443829, 772146959, 325895006, 78701576, 606196957, 555156224, 158604061, 59538855, 304755242, 741290133, 535681823, 390038046, 624489002, 852971670, 446930197, 305553748, 247019653, 422951562, 474574087, 349581485, 779499029, 895943703, 190549395, 271806639, 614947824, 75308074, 574962091, 12185014, 18512956, 895114206, 945082389, 78734702, 559491086, 648677171, 829809694, 526492914, 712495965, 315743418, 665417107, 725159398, 696874635, 90268539, 401258681, 678876179, 223472047, 7129781, 778058656, 720405547, 18261862, 18584842, 572755960, 754165583, 580123442, 331192777, 469250948, 134233901, 292220334, 99143529, 623068113, 840075504, 835052960, 819355532, 573900298, 338491101, 899012726, 412962569, 544672376, 482322172, 382190490, 764142661, 846369524, 8548046, 825740780, 490897414, 218313553, 257377230, 41625702, 746351602, 507408492, 135114490, 905689082, 129501056, 941040708, 310107270, 388917301, 710180193, 77279026, 198932232, 103979392, 422413105, 737791420, 314499696, 489686011, 304609523, 240188838, 79473093, 602364287, 163559403, 553438716, 176888713, 68791411, 41537846, 122771343, 617785548, 999195789, 480642047, 629352023, 569619453, 722913355, 424821874, 40898114, 341855833, 997957819, 551649056, 930350872, 509304663, 987475656, 801901316, 421974169, 296973135, 762474289, 727305768, 215323576, 696439124, 593548749, 64230422, 437402477, 438667858, 904631107, 622898362, 265380611, 519909519, 852113519, 353000294, 499789345, 57704680, 442773215, 725550445, 431901993, 811940960, 750503078, 113971957, 888443766, 999362899, 997234137, 729839789, 253843810, 10752953, 215254607, 204415918, 592050459, 961853866, 573812919, 517944513, 249042770, 943537627, 216869072, 269810071, 769290470, 736287768, 407886382, 608162851, 176556005, 69675828, 113257610, 935911109, 752162095, 659444503, 294669968, 526542956, 522166687, 173497546, 893606697, 398364014, 736037141, 355134795, 392119107, 450743421, 574287397, 552918074, 709202625, 119895224, 595076893, 317324889, 321988763, 798225582, 301223381, 621320828, 662413538, 873082242, 813156101, 847647114, 260119130, 5321742, 323430278, 444523052, 212414270, 537485162, 230555240, 600701671, 97753135, 470646508, 276020996, 398835219, 577386341, 737990549, 359878002, 425449448, 204942758, 99935644, 796457950, 239403193, 935945579, 276781106, 748002182, 636146900, 7907075, 66417975, 446327393, 485104756, 600922541, 67165256, 246104563, 284875447, 885617568, 93746876, 430003545, 895979538, 157370256, 541267637, 579331603, 792345401, 231460723, 480489846, 885101392, 253383780, 65612224, 175357974, 557313242, 407939831, 38494991, 817398830, 910558551, 171935256, 811625034, 572601280, 973756649, 726782183, 244012637, 483963880, 713304084, 844697008, 223220629, 271031028, 73995981, 532607513, 525434143, 933536733, 228843344, 157773962, 871734987, 901081431, 890210060, 254577291, 653191426, 516049386, 631782722, 924948901, 615690358, 502939276, 509238249, 465385333, 581899600, 349882115, 95251199, 840834151, 620414867, 483279083, 313543515, 664381049, 843577376, 649290721, 847559116, 629916351, 705357207, 119832285, 991646069, 672818310, 688820227, 161784617, 847912973, 456515453, 711165328, 559077415, 491557954, 62874373, 970094169, 510138956, 940988898, 232762883, 246127145, 502326188, 154077381, 329608368, 41071573, 892357894, 992023721, 21503845, 867244747, 755250433, 210836742, 622670548, 614913904, 622725063, 106585234, 640810906, 928893001, 209377109, 143499400, 490271516, 931743157, 595187912, 789437350, 534719115, 767075351, 441516045, 374328522, 7144276, 272691427, 488211150, 35416843, 232005120, 172638590, 192640508, 325242748, 479442880, 624553558, 877055869, 213783643, 758970946, 683751298, 867667351, 569551627, 536099666, 429196815, 78646653, 230097671, 958845023, 83477960, 766868115, 186539194, 560581125, 569507022, 774449519, 451407739, 959479699, 146796180, 926986346, 107397073, 639648253, 171889664, 152509930, 593870108, 920284406, 453993606, 526920626, 482370724, 849549178, 175797662, 703945188, 678130827, 303160918, 293782270, 309378314, 247612626, 669968029, 895579013, 911150887, 612666006, 858332170, 710185587, 703219738, 91727101, 5651961, 265824615, 159704376, 765704111, 279644856, 362356031, 530811148, 93115749, 211945953, 766598486, 658205586, 261421918, 655621278, 637105919, 991498814, 765639250, 14269671, 233482958, 530727206, 371116860, 581069172, 524608143, 91374798, 581106628, 899703171, 521370731, 991528905, 393415028, 79222073, 726030108, 933214040, 992279032, 163514388, 681958185, 802431878, 41986906, 48635122, 39225168, 435884632, 871942352, 547258983, 995519376, 499938514, 347097129, 491184862, 630953719, 417117450, 522791608, 346050613, 333133419, 780908411, 578031941, 880361815, 888736921, 432016569, 431489286, 343967467, 850310708, 222680319, 294002426, 141460357, 670956260, 146617965, 29885916, 10777899, 132816247, 933249069, 639069371, 636495915, 62454862, 549460138, 331241046, 466664156, 233084921, 316839709, 867830128, 49296216, 200540344, 41470884, 74101206, 149037875, 976097078, 356876632, 590370121, 601570924, 108288881, 268738150, 804281181, 377707925, 355207263, 340148047, 575161158, 124042071, 383938037, 727441020, 226983379, 903229226, 857889911, 813447137, 98803652, 651090382, 753742517, 719350555, 839335829, 607328930, 559011195, 219864231, 832830783, 759681931, 474129673, 94656977, 637982213, 858576344, 362347640, 242186701, 509865102, 843720555, 107702094, 312455647, 141176378, 878094179, 820332250, 750493184, 764130304, 662927732, 321998538, 453594106, 339672822, 355534885, 697610263, 504259899, 565959841, 714836121, 229297733, 37664807, 575582193, 536923605, 898916654, 901747484, 664376684, 738360900, 384633833, 686625398, 494724319, 935199042, 773481841, 312931235, 266324271, 989534371, 241778416, 943307620, 61296506, 216136751, 712950600, 564737841, 384487146, 202022955, 380778028, 583232494, 97916651, 904395632, 700244780, 535499375, 530899094, 644744834, 520965459, 741435663, 80821323, 466778101, 323248111, 147576537, 135442475, 719833993, 911943223, 615900973, 35427271, 725769294, 343701017, 669136440, 998085666, 304706267, 83772052, 823126299, 131225309, 635803911, 423836796, 620968405, 187470897, 611833104, 876070376, 896514327, 830805753, 962302483, 583703543, 776556093, 768308998, 375826610, 708244261, 24896596, 796038706, 228511549, 443799247, 683761814, 880697842, 170232163, 187867032, 159852589, 526578450, 79638983, 861626526, 870905448, 18955156, 152781926, 66918037, 337929154, 418639342, 84883043, 383915527, 849840613, 331129306, 962520441, 746629503, 291592385, 563093688, 946116833, 166794407, 468155712, 572681684, 564990485, 994199915, 877021745, 340910226, 696085449, 16476970, 995585523, 723380171, 900107463, 571712623, 382770739, 678784004, 651313731, 849437085, 865015316, 638473999, 187579566, 90477295, 69087948, 232790103, 487123881, 970954373, 712931580, 940707282, 976075043, 410792455, 810830106, 570512063, 915745236, 145440308, 226865833, 719874397, 441028524, 182813143, 109279400, 603776107, 904274645, 832994060, 151823134, 672255765, 161110102, 147838348, 915726971, 30940601, 443820985, 168182586, 971668815, 683603472, 428643690, 781118363, 388890929, 504720153, 522711324, 284034289, 369449266, 800294689, 10928038, 318202903, 291495097, 910699093, 500661913, 672799980, 617635321, 996311392, 402995659, 430178337, 192244638, 329116648, 252009893, 509899993, 276947751, 605380729, 294440203, 991169179, 863003810, 283378103, 340780656, 353102744, 818604165, 916343608, 94125401, 28042916, 540153628, 689165923, 59368178, 68002625, 276024717, 510341182, 538546444, 363726489, 842898878, 930218866, 497683051, 746482032, 397390528, 869620672, 426259208, 6024448, 889534222, 251316340, 819814932, 134725778, 271667458, 890431182, 950611356, 622343990, 678320635, 92773326, 425143547, 279558720, 609036730, 735649564, 64142788, 303827271, 391438158, 417163291, 155546765, 916763847, 310614413, 138348249, 9775137, 456739521, 311127424, 701782619, 92919320, 602235295, 541862056, 292092679, 631805064, 502496813, 737415706, 465656872, 782955118, 670413782, 195047974, 488584983, 207850582, 356637263, 679218402, 980578042, 881096002, 597970843, 213520772, 797092810, 839904550, 8389834, 715189040, 643367873, 53572180, 418019094, 155508627, 729490914, 172248372, 866150098, 370981775, 85810727, 12471974, 498091235, 42723649, 385338132, 300678215, 998579403, 1700941, 843578654, 937874827, 448836585, 717979223, 301861307, 108258677, 696291362, 184525272, 456105002, 479305057, 279165170, 514070395, 970822886, 402946038, 386050827, 470284688, 777525097, 972549646, 118159725, 212124016, 568816084, 576018686, 629839290, 625758167, 463180601, 812359714, 866245330, 961879107, 103549273, 516735946, 890485881, 383381527, 984818223, 942564899, 887628153, 831146883, 861571857, 70549810, 924608314, 140942890, 904454289, 989621920, 193528800, 999892005, 881439621, 679256100, 101912196, 324051074, 776060610, 596797948, 215064649, 682575897, 473540502, 420689316, 178170054, 730813232, 863121716, 414404748, 820249884, 978775512, 273400079, 428078541, 267189964, 145997124, 307381314, 706443757, 994073360, 315086180, 666495940, 806788821, 433636167, 389628414, 335596604, 739267692, 688548208, 529555344, 486438747, 409459988, 459234229, 698213423, 951688572, 225687652, 418090140, 596202001, 277658171, 714515848, 24391047, 458618247, 516891721, 989984454, 878491708, 245934903, 744256819, 184390841, 435946104, 675225902, 890283734, 616829102, 587156114, 54560863, 683635321, 741333877, 595985686, 547150676, 491597883, 269008020, 872846593, 572804086, 940408563, 999598917, 498809400, 962010664, 742382958, 162214708, 742435274, 406014036, 322955459, 871118830, 826577774, 840334259, 312794600, 349152423, 496130235, 37978401, 473544071, 678255435, 769215574, 772502490, 541138068, 826327765, 396580156, 973131008, 231514272, 334099066, 246283271, 711822878, 198715050, 426760613, 524141621, 184851984, 766364561, 561071154, 532857926, 181906267, 623210470, 116256481, 227554856, 83211685, 219019899, 653109558, 313955304, 486799291, 795193301, 713617502, 586923817, 710544867, 193902382, 783432960, 559703288, 324821673, 530503068, 291871466, 672830263, 849940690, 603805933, 705792707, 916319617, 888384664, 641001820, 341050532, 187037453, 546091835, 275297625, 564104367, 463180282, 784722069, 584942062, 341923879, 3489153, 475074851, 495115094, 656458314, 20128243, 752421141, 988264768, 544102855, 18128901, 131378904, 97643145, 854379361, 60053912, 842307853, 341772812, 278150259, 460405886, 521454280, 944201776, 803732858, 377271797, 874631813, 536087468, 734346183, 746516611, 796755960, 393147094, 326723044, 920439442, 396426027, 674167606, 662889825, 593251148, 289040796, 417907799, 627974396, 278799179, 478850999, 593192586, 437320574, 423976339, 561582254, 791024360, 975862645, 932391315, 123689544, 771916785, 110252300, 29294742, 665231590, 142815076, 344131347, 953609809, 552278451, 478033529, 319952960, 375671731, 342216473, 945999919, 898859699, 820255695, 186761236, 50326337, 187472448, 124163904, 516618233, 423154385, 553476844, 567543921, 896091077, 970453356, 382821092, 249235245, 853576460, 131011972, 94527242, 1355084, 458112238, 905692900, 70658899, 700365171, 524459006, 691078340, 722804191, 790883511, 143357515, 507580634, 637530398, 223725425, 182122933, 972104792, 107568155, 887035537, 25879792, 986187950, 346762295, 598693016, 886459485, 236481060, 927507371, 718851671, 188142923, 286467095, 682057828, 870490782, 410163308, 81029433, 999498387, 579539172, 80639512, 734451190, 15574047, 93814500, 951963784, 933481032, 876872171, 518678669, 97081635, 163687585, 530640774, 777939813, 757163439, 574496208, 800546349, 769637953, 837272741, 522244768, 547657808, 154007475, 498467380, 525567777, 905547136, 145347763, 756667113, 244735620, 544873407, 37976493, 321171669, 991486944, 152487871, 763994272, 972439462, 475357225, 718977214, 898314247, 624287587, 88513267, 162487938, 360775922, 940361067, 140543189, 558786589, 438634163, 912471662, 345451647, 905114593, 814988496, 149853100, 185701091, 561205514, 485400172, 616945562, 443663906, 865432836, 488724305, 883418701, 760165759, 452724848, 12899815, 389768126, 379549121, 638157172, 721273471, 566207117, 139898843, 592726450, 312706360, 107553009, 968729256, 558606802, 641940685, 235639306, 50027686, 392050413, 807847974, 559184642, 911178411, 552287320, 805637890, 61284429, 518844330, 430809997, 574693906, 21061751, 439421477, 484504699, 52743663, 535927420, 274852109, 704803012, 682928028, 355615917, 714162277, 715505404, 417254520, 810991045, 918380099, 82867554, 967279580, 650977245, 784319998, 915564074, 689457030, 241922114, 508311938, 285418421, 506641266, 805034364, 722126109, 229046862, 345637713, 731987455, 533360316, 443472183, 212204045, 803494783, 952043508, 66088339, 617688852, 119316282, 683845431, 422183000, 713858907, 860516283, 502513942, 71442630, 575369426, 394835005, 788228731, 759906814, 457738452, 636401874, 683205930, 150048214, 686140176, 311981570, 130836156, 241354992, 647413944, 968653157, 716540934, 117384102, 872964726, 986550571, 467408717, 130463135, 830734994, 65773923, 61370221, 278569657, 444775961, 403997273, 395301638, 104742584, 11968191, 843323641, 138187857, 512221530, 35173674, 545115359, 298808903, 87371169, 421848423, 764264048, 979381378, 92961053, 539683916, 787987200, 145700147, 100003188, 199023398, 918954815, 212234660, 194397924, 420206909, 508358846, 73574443, 984962027, 296388172, 8690839, 841680610, 540381861, 121464824, 405576644, 817426821, 551134297, 359570770, 783353855, 203117019, 554526064, 661842416, 530427192, 959753893, 420872561, 682988564, 523638607, 744941988, 794032054, 586430676, 799344947, 535423014, 998203863, 702604419, 722556747, 550188054, 94948457, 458097836, 806992742, 73049073, 144951662, 19080529, 538413875, 530081416, 227108769, 236713265, 155780961, 843444931, 949292308, 480694261, 304966942, 406125430, 51254732, 521065996, 64278667, 938004265, 934747804, 657058478, 128090878, 390111318, 115117382, 176012673, 332001993, 446834311, 182536689, 356786778, 525201809, 486999740, 995498191, 362978690, 10552201, 268797295, 78776580, 888235492, 146436894, 874892133, 345003973, 186502407, 521870448, 238584343, 913620456, 891284313, 951952946, 295679090, 815559882, 572645564, 210576651, 216938439, 600921841, 730533947, 579701858, 601217122, 402164843, 924006099, 45836387, 9828771, 825398335, 309474364, 518596526, 792229020, 581625830, 453053100, 770173387, 885553446, 621442437, 350232752, 623071010, 308858999, 536214528, 542625749, 954708232, 758548395, 631306004, 317498119, 8410491, 766122052, 177669786, 210211550, 828559832, 401076137, 300840239, 37915371, 153215358, 510385402, 37760394, 719578100, 30344642, 453951774, 429573297, 838789252, 149002569, 121451612, 362591346, 190109087, 974530800, 463282011, 598041796, 180258075, 762197533, 978532245, 67263693, 234963224, 171046101, 910325810, 589191256, 48991600, 277411683, 189333576, 810182629, 302788034, 879871715, 590692919, 121943822, 250482288, 705459566, 752911404, 229150308, 928063871, 459136965, 536305927, 244891417, 152268904, 508055829, 705904613, 749850644, 601172646, 643599840, 840161363, 603405405, 573541612, 945249983, 30909684, 795330802, 224883936, 682056967, 38991786, 964583650, 362135811, 743373518, 637797320, 992054423, 290526593, 959178720, 863692717, 412666728, 271853299, 400860334, 968672221, 396258832, 821260059, 731863596, 754574212, 525363689, 323065140, 4088488, 586382276, 445621905, 566551907, 862296066, 410854320, 658957109, 125297003, 914395831, 212144341, 915214572, 197448175, 784671279, 725395900, 769356497, 801309274, 517994611, 517187704, 44545261, 470053405, 909088299, 389798082, 57241632, 665866302, 314117592, 675714658, 114019963, 984278617, 242651054, 775226050, 543927116, 56579493, 415657204, 12972109, 201195065, 8632463, 905849857, 863196224, 345253763, 37819315, 526931775, 597236925, 790603802, 836838025, 288360536, 759318131, 523331578, 684832224, 500598276, 747480756, 48930598, 865035093, 252755858, 407845141, 801564584, 603579699, 508527010, 924158254, 57870647, 114318268, 852326769, 988346137, 761315736, 923224857, 454979486, 708747760, 132949871, 461235066, 868026551, 829049975, 303353158, 833288071, 399136979, 916367539, 341907726, 419503313, 495818967, 266053262, 223092067, 546167535, 926931616, 356286256, 232171099, 450758172, 477665403, 751866359, 639462603, 883553192, 186729678, 736760533, 173969964, 965887747, 656461771, 763838997, 290647796, 329889857, 430219616, 444746212, 951701839, 363899299, 497448627, 247355551, 20275675, 499540657, 534343360, 826650240, 223595710, 667582886, 612349901, 136558590, 638945436, 251315599, 623058784, 810070019, 158890854, 338254089, 29739023, 751126680, 561208428, 36570919, 451267198, 148016563, 237633076, 12524147, 978965853, 372016599, 647675917, 965231134, 743975954, 801705853, 169081077, 700875710, 708338016, 126878585, 76361776, 71922371, 689017066, 810791059, 937919849, 191408990, 284438904, 900143405, 787359364, 581951559, 68841395, 371878050, 828534145, 555964458, 185496663, 4358020, 765223338, 884264328, 302919640, 14689283, 673987956, 42987120, 145156708, 952973303, 670174895, 552197270, 40683916, 317319084, 372659891, 399993019, 768692580, 628636136, 198015564, 702779129, 678162538, 65319531, 790255951, 225740287, 454689493, 927652214, 69015832, 194813891, 791397442, 865227174, 281793132, 664819379, 894979034, 193020911, 229750944, 876873120, 56777381, 601630431, 563193518, 586916511, 755738252, 536288670, 998911301, 755004023, 29027188, 159536489, 261850575, 441839582, 193504714, 822722425, 782379260, 208907237, 364102837, 495489008, 751875671, 627442910, 438090726, 776551283, 817857784, 230158780, 76447796, 433299929, 11620888, 822333187, 342971568, 327609676, 947461902, 156062886, 504543553, 105765841, 977908833, 896538014, 660603742, 27811837, 33726274, 63837407, 304401173, 463098975, 124111127, 523974617, 326942457, 883124710, 386402127, 441160449, 289946168, 696077275, 91311401, 874491636, 515853551, 671613354, 936079669, 905717541, 400281798, 779506464, 508838970, 406352710, 419240432, 312709546, 189274595, 269589274, 18852057, 311945161, 448477544, 987964743, 532584149, 931668961, 628628441, 486878516, 991118868, 168097704, 334707487, 423906852, 929680067, 490653503, 687307340, 72983908, 6803547, 600272083, 385336848, 209061654, 38228256, 974116049, 712542625, 907271553, 348441874, 603010476, 938579681, 75790459, 406431493, 43733600, 116593978, 475515837, 595201427, 909702357, 505138931, 682272584, 850397062, 784624215, 9747543, 843948673, 227940961, 613461553, 495969713, 157838619, 938381587, 397188214, 506025923, 457105546, 444600612, 252302882, 971867251, 478640153, 249084924, 630517837, 516838805, 43266909, 476654385, 234448657, 755143461, 110054091, 435966675, 254156594, 227874161, 711406829, 625003204, 233338166, 676749261, 440198298, 659523940, 736376940, 769879237, 146408934, 406317068, 199525069, 692931931, 281228802, 161676244, 997573093, 334571521, 322044743, 870697509, 885697303, 259056028, 970238459, 148885454, 296312493, 758838123, 199923816, 623688137, 721838438, 40218616, 399830301, 391930481, 325030937, 781764557, 116256492, 262584526, 990552960, 476110346, 381768516, 277502315, 34874241, 312107272, 432961204, 615451726, 172449863, 966741881, 198442774, 157868066, 66272226, 216340730, 73163303, 595829465, 400474141, 638023204, 72310961, 512972902, 285011573, 482651680, 861658973, 568452594, 950917913, 132870966, 679469130, 590921866, 877180562, 280567177, 817175508, 856441791, 650585175, 641793562, 562685965, 151286556, 868935174, 832815760, 590356050, 273083639, 981622808, 541628731, 208842350, 396259516, 29066410, 8713287, 856917460, 64395641, 452033090, 411397413, 965104745, 820227979, 375163404, 771878840, 487031196, 453733438, 606067223, 986785548, 938545459, 185082361, 285570049, 151888180, 574624671, 631596589, 736127807, 52527646, 860737791, 186029609, 695240098, 927211334, 535525781, 305380527, 905081126, 170949891, 223834187, 449593706, 918888273, 274459487, 572195336, 784326963, 896353142, 821530423, 355847790, 556320279, 603187900, 663932519, 972398396, 893409576, 128951052, 230173618, 544166699, 955930702, 565160021, 974968472, 802244010, 557855967, 248166725, 541271692, 240897911, 600190089, 758998943, 183159066, 987510231, 356614970, 618485659, 188306693, 769795361, 700222751, 475162737, 332391459, 492406813, 447170277, 728875312, 505126057, 102441411, 133099565, 653047302, 563492376, 320460709, 725887805, 286186256, 731318330, 923561143, 572518687, 19637124, 749501323, 61977033, 394195168, 298255240, 807866912, 495356365, 848218027, 146641430, 151390526, 395463103, 239802934, 138851921, 417098761, 160935770, 813117992, 595718116, 821293996, 888828793, 75418845, 475939797, 313132136, 732124829, 942969534, 816948498, 359060491, 476314593, 575410067, 739557464, 223142078, 499946564, 174390050, 855147609, 446683368, 62219803, 356162592, 451389937, 56577965, 551309101, 733117620, 286256398, 819181740, 85986862, 483892693, 636690609, 764637244, 897340269, 516230629, 914251081, 956623015, 495490580, 235000261, 657921193, 259645857, 699226433, 665413284, 87322628, 816344505, 801175249, 934303264, 584452353, 767690559, 612509692, 235832003, 6267347, 178580303, 341540826, 605312784, 298880313, 327518171, 53649303, 473999042, 668845244, 890324693, 382036888, 674715115, 488740833, 792142350, 298387026, 372890559, 775878047, 989756771, 236756447, 322033017, 126405280, 703544667, 718949955, 655431459, 920240745, 399592239, 996750888, 541373982, 733151752, 648407796, 433786232, 68122803, 387598330, 374537667, 782694623, 352827953, 756667776, 607385725, 942033084, 634868506, 991054652, 428084681, 568258184, 19019013, 999753917, 732909061, 622079309, 61961621, 785562458, 99522807, 525690666, 944350696, 427269635, 645391316, 959469439, 496280046, 531572770, 123849291, 502716121, 991137586, 765142977, 532064219, 147082419, 511818698, 884039504, 551663707, 909063908, 172774893, 252172921, 326668906, 55335694, 296388397, 371737241, 555546449, 637014144, 860648895, 130173481, 189758871, 785551289, 708960005, 946956990, 212919712, 222318584, 692379719, 771065111, 989909488, 142342944, 252000971, 93135354, 863134826, 417879277, 321378678, 864967727, 805574323, 227050956, 126695779, 435439686, 137115152, 603300503, 644844368, 954895843, 283763482, 786052862, 84897429, 765985458, 262104129, 2155960, 273553746, 362143442, 425821982, 636084453, 74850028, 37752612, 315887962, 790317171, 387720869, 20813448, 801755326, 153714341, 14784710, 462897360, 843757853, 410721199, 759525316, 662657941, 746529066, 976028787, 40779032, 102421984, 96072038, 593523372, 92381238, 393273068, 446491528, 711475904, 501815223, 682015419, 895903399, 418820165, 345238808, 771010673, 644562251, 705810246, 627423795, 344845267, 651378187, 998645832, 555597465, 323830914, 910940115, 417310574, 552467033, 674564925, 669225558, 861201132, 656599654, 98439193, 61744407, 896190296, 604321754, 840725772, 192870258, 50708362, 21133891, 233940701, 573685723, 982813607, 834161672, 747008730, 612763067, 150757854, 815135626, 573722338, 403809594, 917379644, 665490137, 347710393, 455574384, 43000315, 48132335, 846205858, 406924652, 77400199, 227756367, 323274915, 208436195, 13489271, 766990827, 231257870, 19964225, 990668710, 111059100, 84938389, 879931902, 414695952, 305518805, 151065436, 225934598, 813717974, 636216518, 413230273, 920025527, 305303263, 774988105, 262096066, 418376943, 256646860, 224998361, 100151367, 750673664, 292153916, 758749571, 900284793, 228164331, 160388373, 687575757, 636409388, 648491231, 380721303, 783593115, 583723079, 603871490, 969427100, 315248649, 305922399, 485034462, 844396855, 596161314, 281947096, 313510011, 55142441, 216056019, 202030548, 298341865, 896997320, 377533245, 967074741, 473513351, 880141749, 798767470, 271306582, 369878538, 471219779, 677553824, 803605248, 433877650, 911199321, 701135839, 110243119, 292069579, 115688289, 514832370, 300868938, 763332033, 620201733, 20407197, 369340577, 217567120, 319481034, 238164674, 896221719, 427103622, 944447622, 141463601, 695231159, 48962050, 619012880, 668702293, 52486206, 401569477, 241617277, 646837029, 433450945, 830540846, 962726206, 674840256, 131646355, 784564580, 331821926, 633928993, 220826258, 298266145, 951987231, 572889175, 204993520, 903007162, 579033074, 564125358, 107669210, 599277167, 181806924, 259553443, 413757181, 25852834, 755138947, 688758721, 909465699, 322339095, 134860422, 29342667, 865617590, 791221401, 310629316, 707484859, 408716182, 531695879, 341521551, 679132446, 585808512, 468409907, 154553811, 534451441, 981018760, 989948915, 586618227, 237109296, 945550765, 907808714, 42855721, 189352214, 718478652, 511066200, 243338029, 933202772, 68300815, 398108655, 537857208, 258796064, 995959632, 936563714, 194753457, 767487580, 891451370, 843867231, 696237193, 127338822, 873977523, 477195222, 254531626, 687513623, 73069234, 908839578, 445537551, 101388002, 173986794, 134694511, 726831932, 571542177, 199023144, 38201268, 316726965, 331884972, 125980530, 446320365, 143381728, 382283578, 475160363, 579116204, 629140064, 24862597, 843771349, 20832518, 771592702, 842458730, 546430212, 559331570, 898431889, 232320012, 928907067, 378931236, 939795936, 873652013, 555170488, 932610079, 909887216, 205152908, 497809357, 160272158, 336111517, 168200925, 712236151, 415886955, 443654175, 11084778, 369552258, 632106468, 578578555, 266822424, 487144365, 54407623, 761081806, 75733911, 789758106, 948742601, 108875959, 964283318, 19106669, 73876307, 476103775, 675310299, 293486746, 276177652, 627781323, 353228612, 157964066, 678246846, 934355300, 755052503, 121748664, 188147673, 222575270, 450637608, 271693548, 259022538, 137016718, 320040148, 698003484, 395466197, 721661126, 123765861, 233112867, 603457072, 379352752, 233001350, 414572431, 324927657, 548126417, 421273237, 793673331, 904351239, 359290430, 175378322, 368499643, 864562636, 632192407, 247284288, 769779717, 740492322, 597614301, 831332274, 873357538, 761310568, 31836991, 743669651, 368212674, 601213655, 189510685, 893499218, 424636418, 104212090, 116366125, 981758294, 544187161, 827478653, 447252479, 189312643, 397832467, 525544933, 696817909, 367480957, 64561222, 596890671, 505428501, 328912283, 462864455, 79325186, 16173149, 789505313, 649254555, 40356727, 176518095, 24293704, 709649558, 260746562, 742915104, 998321975, 176422211, 343381236, 835715391, 983231524, 918862471, 645478617, 904608068, 162657115, 313477234, 919173278, 475071859, 548889926, 85284333, 856703885, 124868962, 831866606, 589981252, 658177679, 38325542, 981847785, 711427386, 287136089, 464252765, 807642852, 257516899, 245390431, 156136153, 971072313, 124419439, 537254843, 865757717, 65648627, 619892058, 927928675, 353140806, 524332951, 380232347, 147573923, 405514173, 987156483, 6373447, 871895509, 306430975, 792380654, 114385636, 275525220, 505042659, 302585248, 260256837, 530719097, 914134183, 256295031, 589743909, 623055842, 495043866, 917301324, 343631369, 769648565, 649311434, 590741039, 435943232, 768351388, 57048669, 262715689, 25142025, 318729056, 467001603, 757469976, 128859522, 885718313, 901954562, 947165018, 474981970, 346568049, 545499484, 541312233, 407020244, 846446784, 147201069, 837076671, 284521281, 527202646, 604037953, 513841382, 935446092, 576051654, 137148501, 248995757, 293893362, 460016008, 314963385, 353732372, 318897554, 938358386, 629937785, 583024616, 315204426, 782465319, 553256794, 699480163, 428459188, 187815792, 163178093, 99619346, 66558017, 216311451, 15778449, 862843751, 616468275, 221719369, 910669099, 622753387, 113798359, 102334179, 959474530, 504625143, 906338616, 942641799, 442673352, 628771656, 735073952, 442644049, 399023450, 504887914, 91636188, 61765783, 703489382, 310245295, 524009590, 857663167, 907610869, 226324379, 548834579, 404742332, 698216191, 805489293, 21399253, 590228759, 470189333, 131737023, 702297389, 449346182, 898030176, 925165658, 908690527, 6625962, 9945310, 539632300, 383376139, 434363149, 768283036, 673143640, 800908317, 210358154, 754143030, 63987555, 22017131, 938705115, 660365746, 237661053, 776886275, 972058792, 497996606, 406366776, 214704499, 643844103, 804949656, 884284094, 670608025, 60734642, 776112857, 48277279, 343740758, 706380942, 168708980, 597854699, 507077451, 23972635, 573519763, 863169867, 531133728, 803213497, 239585265, 687451888, 904558976, 163449883, 631991729, 718985075, 480565206, 500709762, 26659910, 469191195, 183376299, 429616918, 896730620, 561104980, 508425031, 661123137, 65589640, 513633806, 729759740, 617722605, 982517442, 395294519, 798049162, 279186603, 351420085, 805401103, 449310657, 369446688, 325454934, 530972183, 89392517, 323068244, 591308537, 332477404, 856982411, 530932298, 829063808, 354107839, 19340164, 494141633, 538586602, 43395100, 312166099, 364309906, 285063814, 306228114, 906561159, 128289064, 301723572, 790024577, 632288651, 433132441, 519511445, 477326550, 840838219, 869840651, 231215483, 212530824, 128701354, 268382435, 827862289, 988879734, 440463511, 442800967, 160613923, 388000, 689308981, 812996255, 75853467, 501171477, 323493238, 86187426, 26876077, 486914617, 9453761, 185749142, 543072533, 905066873, 246544158, 698292568, 293972975, 781572618, 144727586, 628073201, 518293714, 944995217, 399991027, 199232460, 492520495, 356034354, 413693259, 772000211, 833477781, 448929217, 406993988, 331425182, 903561593, 565362278, 798690694, 379497461, 469847028, 637466695, 540120971, 616690916, 955230283, 56200999, 164653518, 121292497, 140507780, 265688082, 751012087, 908719073, 147295075, 234320633, 969600079, 655886938, 419553648, 184927803, 707205588, 62754338, 164091525, 627945009, 485596606, 900730640, 30490513, 623697653, 490133297, 973256675, 234573993, 319035587, 166385617, 901469068, 694755680, 952520998, 844688321, 725205172, 916821682, 632457294, 806969122, 317879055, 383969381, 578244613, 811324769, 289348319, 140102775, 309876393, 945656012, 760069597, 536299759, 651801869, 187493731, 960612237, 193513262, 357997814, 901822078, 697269301, 48889644, 619354788, 629349913, 15431752, 220869758, 600411598, 53515304, 420509262, 800727003, 686025485, 732092901, 941884259, 741773655, 795913751, 251880864, 139108061, 14875756, 361514290, 452265289, 653603642, 783402374, 728061342, 690131602, 502604874, 331125071, 98087117, 157531549, 518135383, 954115107, 899558751, 520625224, 146787254, 191417036, 880793264, 891058956, 610250243, 500540603, 373404673, 784433529, 493996244, 710138449, 138260420, 589456098, 19687724, 132944186, 961637089, 212524293, 227631628, 286647924, 429028196, 575615042, 767722227, 716323191, 662154413, 884389155, 279093157, 595881369, 494248470, 202092183, 498881220, 288859121, 567774235, 173005794, 835904962, 162203032, 26703734, 553859594, 880523001, 757803788, 411201340, 895049790, 453726967, 919194579, 683403741, 601944553, 968699840, 650749735, 522985395, 965202744, 634090338, 709233765, 583963764, 861425251, 588099412, 676800999, 652609144, 51082514, 910264445, 832148200, 987632168, 328263285, 963948665, 174904242, 105434577, 185130125, 176210899, 790525232, 746060002, 998843334, 555273209, 670083359, 277277772, 775814977, 268308285, 340115472, 146509585, 914385013, 716193106, 75929793, 276282698, 191670021, 860878913, 357534460, 761720033, 476712829, 739090826, 817310613, 179773445, 503484419, 405661582, 828847852, 404468093, 125313182, 562182094, 54833929, 398254709, 39196756, 715495507, 262123852, 914049327, 491518148, 887050515, 749602204, 291474896, 45749227, 717127860, 836006005, 654799283, 300297893, 299616891, 866596849, 205001287, 369576553, 372351718, 981389446, 915808859, 644559122, 583718630, 298141947, 557261006, 652186100, 828293965, 865649797, 728048746, 887206812, 488759111, 857173031, 640195775, 231219715, 283651663, 429893785, 472819060, 646587096, 498861453, 460402922, 72424117, 469971613, 304697044, 416853079, 510954533, 752531048, 380187779, 928741930, 545431238, 381956548, 209681366, 528750686, 945690092, 15652209, 328534637, 400372633, 896022116, 518634025, 677970067, 145573182, 757514379, 293377330, 328395888, 10145141, 810834676, 292794818, 937114932, 561900305, 469023198, 254764507, 707180501, 749536626, 544035268, 851683243, 773661953, 707491694, 209501620, 50236291, 118136241, 589314896, 73216123, 74108341, 897007925, 102768342, 648839991, 158296083, 211089292, 461106250, 803991154, 57062077, 312031827, 481622223, 168665438, 332486400, 390008332, 181979577, 54497737, 371304867, 392581563, 896268607, 962460227, 793607473, 630287943, 80935751, 57247287, 766558458, 261444243, 500756429, 425245386, 863851333, 237707722, 314049360, 89372115, 987384407, 379376359, 941720168, 615039759, 186770256, 795372996, 35362500, 311195338, 174609434, 33218062, 632618956, 647742644, 400516423, 483910514, 327664990, 733492876, 372897744, 591437967, 555762772, 615853669, 651955055, 164500082, 65463807, 77136709, 787128143, 972419859, 693620512, 415155995, 361783720, 539858790, 772191111, 327027061, 434144137, 577746917, 588810221, 127291182, 384136933, 128785218, 765140586, 952789923, 219862718, 666365774, 486815479, 265209369, 793362141, 485680921, 772346026, 996687965, 378851240, 292879552, 220200534, 770826181, 397689373, 843420929, 456775619, 285869918, 273569450, 741563025, 973022609, 562226396, 329949901, 470873239, 312322965, 456009976, 360521482, 937509803, 108999236, 964982973, 612136156, 513097338, 851066221, 493701309, 17233481, 433679354, 726150595, 576272032, 345746556, 22191460, 843005828, 21317663, 653628865, 377284833, 880955930, 967823739, 700722402, 856356026, 761605154, 388551018, 149875600, 303663662, 29776536, 637283560, 280135925, 238048369, 711481104, 127555515, 271976193, 280442141, 260199898, 492478259, 217452575, 192649288, 734975681, 986209604, 631127640, 71696904, 941794739, 780141072, 810784114, 165167304, 8761889, 364387224, 422886951, 186820651, 857602638, 465750857, 908721823, 43489582, 602480354, 101935562, 226548310, 956088965, 664257661, 568327457, 960997675, 514878264, 75714256, 587689060, 42603898, 261219621, 943043308, 687787339, 37470684, 580208208, 68884198, 378945244, 178425907, 54385222, 598891955, 244328181, 215409697, 574548620, 850559233, 430521456, 963772889, 158427287, 497046559, 913255195, 554266062, 487022874, 972705379, 578152302, 310293953, 138610873, 941137897, 885219512, 250708336, 950939729, 144240851, 263823082, 386666159, 382848751, 713871842, 428294160, 145935090, 403617600, 474187766, 171428120, 320403543, 269350981, 699767074, 790453987, 884532616, 226416931, 40006263, 634661437, 708407870, 572933644, 737922421, 723191819, 862303223, 147473646, 762388528, 210976162, 293926159, 743638087, 662747484, 744007195, 441580777, 506164802, 393807920, 124048571, 502663388, 30971345, 640994239, 825295629, 219622582, 765139451, 308828709, 409216351, 34791381, 666753933, 947726354, 269505629, 8585522, 525329118, 696829786, 90556606, 773888808, 696453636, 838761940, 669187381, 817986588, 181813947, 540769797, 637727638, 937576748, 335004511, 594517902, 276569281, 474899263, 657310403, 505540045, 194292202, 575574567, 171068744, 18506401, 739465379, 369583500, 510654211, 451580271, 723579956, 720348065, 137118157, 656215601, 445458187, 500255906, 566721177, 447860714, 362436145, 94804242, 300876299, 431920564, 138711060, 982243566, 354303222, 612230403, 859509267, 810742011, 946333571, 496806810, 666053456, 625808022, 886643754, 427872690, 398825451, 732939956, 190932803, 457763208, 545257434, 592723265, 116109640, 212281348, 164654854, 183873433, 163831627, 879945165, 692573515, 375104974, 421077363, 350645752, 6312368, 613330578, 877858816, 497281589, 16950760, 456455681, 30130950, 912522531, 238580462, 882904555, 129643684, 154940508, 299453983, 546917112, 403532596, 815283929, 587022746, 868421030, 452059382, 962137852, 678628951, 812058731, 320444906, 136826811, 440788134, 962820781, 425519856, 163744395, 194456334, 78600187, 157144708, 58994926, 51111279, 423563783, 39902106, 878284096, 510071607, 760230148, 846814684, 478850881, 706228807, 969017271, 70968123, 907772544, 745058589, 197581345, 354340994, 691513855, 659484547, 889781749, 136252707, 268683188, 419901160, 343047015, 7340351, 236095707, 852965279, 203158839, 67938418, 577035977, 355416404, 746049834, 547231469, 906438808, 21082535, 932282039, 997089263, 788914633, 66235231, 159963316, 990328335, 765772769, 655574098, 231536005, 329047017, 258638426, 911519890, 248305477, 152588662, 900619682, 772735521, 116648079, 918019920, 400110875, 91491591, 620167873, 933516959, 251051096, 880808594, 450028393, 39299516, 522579071, 956053355, 216190769, 321452512, 573309027, 515474466, 127864990, 451926809, 160212869, 11887583, 501095497, 886539232, 464080926, 806936582, 604580753, 139142819, 322627872, 313035398, 229813688, 878124443, 636406812, 534244398, 311446211, 555998089, 318571775, 272562797, 828123600, 238857610, 939553310, 768715299, 259963920, 247067825, 484375184, 802326949, 323362558, 948177639, 129905642, 218049296, 340688182, 803375644, 345686167, 424275904, 733315615, 938799823, 108392299, 495423818, 869485021, 189920562, 141435892, 373296055, 119736283, 354238445, 83876594, 879695540, 869564235, 337240515, 322628257, 81349829, 246668161, 724715609, 780530411, 457138178, 390796048, 681546480, 69208109, 627077453, 205247518, 768348433, 513700234, 599617381, 480681675, 128700341, 306463671, 190803876, 386260260, 724954927, 199891709, 408572417, 862854906, 103872570, 535438005, 685514481, 121022045, 758063081, 949333691, 752160590, 300232002, 777371278, 177973135, 320910861, 840808042, 40168060, 131059786, 322054151, 553161432, 996035624, 727892008, 22253353, 649570136, 710096554, 173762459, 404902448, 484490982, 306936133, 556252002, 506575094, 756081191, 175661383, 208610169, 657054912, 974869601, 50277360, 598558625, 633139550, 131022763, 761504607, 183256546, 195659159, 756239853, 75387723, 618738034, 199480506, 527430250, 405644314, 668679586, 606235797, 294817182, 404094547, 797939993, 727409504, 301345021, 366195756, 988283527, 219178569, 402310580, 848553933, 172587936, 456894628, 427632061, 799166121, 495293555, 558841189, 586617521, 499256171, 776804732, 427616805, 251639045, 426035276, 282316048, 176318669, 804907462, 135313869, 659303858, 817211573, 529239299, 523805118, 553861499, 570704850, 85271018, 938449471, 204987093, 24700818, 876382318, 726360022, 315448320, 562330741, 161374641, 410677861, 902460809, 87771953, 580974507, 234722282, 550237035, 735861410, 828627782, 532481983, 698423843, 892508252, 10956261, 841612622, 653297909, 410687699, 128477611, 513930047, 64831000, 702083745, 716478045, 523840311, 459525991, 767753371, 569461013, 224544602, 383974990, 338838096, 704538046, 229335855, 738247492, 650294265, 829823588, 12276052, 987153614, 264652049, 889377351, 63544658, 693154675, 237202121, 696674415, 883864302, 41459045, 36196160, 319332558, 999124452, 139710128, 503916944, 658081730, 596944893, 797128759, 37755923, 487662048, 95727806, 851322072, 691480726, 836163846, 424610862, 570907344, 119175425, 342610762, 916559067, 467711760, 395379720, 914567725, 117157724, 39778105, 841497178, 89663272, 480619227, 74429759, 154699575, 197590665, 62526912, 526828976, 351399017, 360951168, 353036060, 935786441, 796630190, 579777792, 595352996, 231140383, 121490314, 767174730, 19363604, 101047409, 671051914, 199944849, 553416322, 251339417, 931852211, 438021624, 194791323, 459304302, 248807003, 149536218, 45529850, 642515137, 837667775, 191893184, 406164392, 253024165, 891602156, 461347111, 880927208, 871174322, 771164643, 33481756, 129794074, 445842795, 664077340, 409939942, 615819738, 362927164, 107332045, 355018605, 582342898, 645234328, 561385097, 766842832, 636103271, 655430127, 323227423, 278579215, 262468739, 273610398, 310372267, 786296061, 338511493, 352990772, 18634701, 977013444, 553275522, 878190699, 781979984, 349463562, 580901607, 732970113, 189362045, 80597694, 638195681, 597670532, 168953979, 225419295, 94798963, 377903894, 780319216, 677785557, 674581432, 118633732, 192172140, 181200311, 365252862, 637074511, 457598943, 89320358, 992050613, 132435926, 122368034, 54801829, 643397308, 767605139, 523378457, 580141013, 586710101, 727419003, 50511410, 164303561, 542762318, 418093234, 984959494, 553093424, 678757705, 139846245, 834767165, 373320781, 128361123, 763702936, 553796946, 953500327, 940342004, 4183648, 879972937, 707919278, 571918108, 993876153, 795814888, 323272194, 20295520, 863819202, 716130684, 389386335, 700363962, 149139242, 589461749, 59412118, 780673401, 540482143, 738160670, 625926903, 994841500, 409914282, 835122939, 866529208, 159671973, 368198850, 445681412, 100961458, 672931323, 82417745, 172456352, 168613069, 309347364, 447409314, 137909190, 80866149, 8399592, 676877253, 191367769, 933157113, 500083035, 236417511, 305944537, 484665425, 812057196, 507721248, 994393112, 766959038, 285792593, 551956135, 959085960, 24341364, 998193017, 6596033, 32252119, 734896599, 157274220, 154102997, 969185329, 912759863, 900658591, 524203518, 977770848, 276354484, 924530790, 280707894, 39055128, 645632710, 698797328, 739728930, 55600005, 912411748, 889517172, 774938752, 782090743, 564862759, 171044733, 168970230, 285568945, 514603193, 238704057, 434979402, 191028454, 517933133, 749268365, 109142681, 357584958, 368915267, 130629682, 51472110, 638772960, 767714405, 929474500, 945790951, 769512661, 698963592, 320478658, 890078499, 941150152, 668756853, 340300990, 876186640, 154264217, 384329648, 666355835, 539619155, 491870978, 72494552, 477678643, 935404354, 21778655, 335658181, 17360355, 543205112, 432411168, 973837284, 411451039, 800474346, 923085832, 701625757, 674878510, 362701604, 460500539, 588261230, 525099603, 16787351, 784139095, 560285814, 207054996, 924128598, 994499360, 614913626, 310586858, 406485065, 300771108, 427901056, 461215164, 323216537, 53703443, 788588711, 8197663, 602202107, 960366157, 253022223, 361709561, 920644230, 383142425, 946207999, 732418981, 383574765, 147262769, 542836797, 558795100, 595575434, 983830550, 916653231, 632383058, 265162214, 984241494, 645664235, 510373042, 975521227, 928502834, 394154339, 754678570, 352979291, 57528582, 494534264, 973600748, 724845621, 996196832, 875213472, 841782194, 967019867, 504876478, 42686482, 742644708, 166850656, 961259421, 904681841, 36776422, 584803355, 559061348, 441570773, 737318716, 447151914, 625135933, 619125467, 647639937, 562824119, 427237120, 704710622, 462878586, 447324642, 133936723, 200755400, 629029752, 78949913, 142616979, 819415265, 578833938, 88261575, 650561792, 608161774, 271595766, 666350049, 370048511, 64351668, 591020374, 26069474, 932242906, 505780852, 550432875, 323521144, 636769551, 372940709, 394106285, 257020626, 608841015, 962134873, 622232991, 155267365, 930259568, 998211668, 939888569, 346520916, 524256093, 651140450, 15567039, 982385880, 931420432, 266029561, 386211520, 585369236, 758210908, 245039630, 223388233, 806685795, 552737022, 317540203, 120137661, 227601277, 646839095, 733815331, 755639277, 186781299, 503543105, 234579257, 987843824, 700361682, 830805021, 396475394, 917270052, 37617417, 211082266, 467077338, 680827494, 823758295, 322153422, 916812815, 545632002, 337772619, 682139372, 552980253, 136292298, 390982353, 537172819, 610227510, 269541342, 22284098, 604757121, 580765818, 253904677, 567212873, 10768840, 929026366, 640795783, 748569236, 385119926, 312521363, 938758484, 579427160, 777926745, 3927531, 337793737, 259911325, 419739074, 407674917, 396939519, 957562532, 256174611, 333578009, 700361498, 183882646, 520937447, 797404807, 131397927, 154887708, 784630195, 32692724, 646977475, 772648148, 825849551, 151118125, 995611238, 693884025, 60202524, 678263183, 466845845, 204186603, 349303364, 470097670, 406004957, 196791821, 673337265, 583460206, 58896508, 245359349, 197473240, 380774646, 412432430, 695515811, 273309107, 596898538, 172259275, 534479619, 433213650, 836219562, 381420143, 49245390, 413490385, 376570547, 279601842, 535975417, 596809611, 221438825, 973764379, 857438744, 263665851, 247554227, 308373283, 574243597, 123616505, 404074596, 650717427, 962248120, 131494419, 120920228, 566479325, 491321281, 211862945, 500294698, 204251712, 421158394, 532784202, 721830015, 966965225, 875551489, 455163374, 667412811, 136103510, 637947625, 806582673, 426623315, 98648012, 769437718, 181135309, 203096315, 320062610, 322530795, 737448863, 257821664, 397824839, 388353484, 164838928, 25633283, 834669668, 461892684, 189236817, 4464975, 737115376, 27706235, 362345490, 577910613, 637674903, 446489281, 696472259, 859138360, 807395527, 696344438, 417773486, 291621986, 303840619, 758679278, 214791802, 862059226, 857283608, 170688984, 814273260, 162630590, 986871985, 205770279, 221141296, 238154981, 714663856, 74040707, 20714015, 936091635, 613718902, 105174081, 895837118, 189075908, 820519028, 181240769, 932963567, 552297264, 404397565, 326442618, 972953223, 785009909, 399871883, 516983690, 610906108, 971289318, 413373779, 389905403, 513613356, 444347023, 55918279, 354959323, 802657542, 364147626, 466912244, 875115590, 397325159, 401980039, 149314165, 795768412, 599421512, 160930989, 852949990, 630638597, 758523753, 163348687, 226185350, 993493521, 474578820, 770639870, 626996736, 10472192, 967101508, 229745620, 875323662, 181009361, 877825050, 175588760, 467748496, 835602301, 894948039, 932913701, 510226278, 935269805, 561679508, 442619135, 192847582, 833184362, 568930157, 839451789, 573431087, 865999333, 935769708, 794876723, 467016019, 8652512, 113562078, 41403045, 781731827, 310674864, 745581887, 176497327, 480003277, 477664746, 326926537, 534819590, 374303967, 528994632, 710599153, 558580158, 41502516, 720689851, 400399304, 638434898, 907465112, 73357115, 693543280, 823925617, 470063308, 733497863, 661945774, 144377635, 22249114, 808582175, 515442966, 415485857, 97062706, 119518223, 12336357, 518964736, 807823616, 933286641, 933031127, 107116719, 413923274, 183222616, 79480381, 682977967, 218853323, 766470573, 190261602, 429756580, 408870511, 968208809, 860060219, 186683053, 579629916, 489923466, 650045113, 584261945, 42447339, 281000834, 898750686, 794879578, 134561450, 116910365, 289212134, 963644406, 856223738, 809756471, 315847869, 827508118, 682134345, 284608479, 736161417, 981655967, 264674155, 654705962, 752144654, 299445881, 10646084, 75526251, 589986519, 876581891, 624683036, 240722315, 348053585, 898755116, 493969837, 661591005, 490340180, 442330175, 339319017, 607023279, 138878646, 710137891, 691542515, 229712918, 285304457, 765350051, 948929802, 933365493, 792094831, 635111327, 486660618, 475609161, 955619547, 614630290, 760430979, 56078162, 855645460, 823281295, 805904021, 126717473, 965134177, 366624448, 20960814, 117771723, 451508642, 395978917, 340281138, 734869026, 422448661, 796107396, 250859250, 161715052, 803030143, 72210573, 279566898, 284448463, 605321005, 713515163, 170775591, 953379473, 699422669, 128726386, 779099228, 726956270, 158339008, 66207862, 728031329, 951416622, 714406831, 183078149, 384664434, 921248888, 210138933, 859656626, 280974059, 204686558, 104337349, 16294688, 216516303, 151739488, 213062784, 451930935, 659178894, 536928275, 603987172, 822889155, 600208753, 662320576, 679809676, 483803738, 873861298, 395285567, 654799648, 386508427, 182183692, 842160713, 899092582, 556306976, 782750731, 411676671, 943735145, 516944939, 995145430, 730488224, 60014765, 889559825, 835553560, 27250803, 532504305, 700169077, 475633068, 460791162, 854955474, 195450564, 417802583, 599381496, 948204587, 270187878, 17217139, 24621173, 108231201, 80643754, 509940303, 236612152, 790398983, 442624197, 620960037, 562919343, 271350341, 873375523, 942331886, 735465177, 624918626, 719956377, 902639805, 646307129, 459602675, 839472113, 857418602, 43504997, 115584011, 589965105, 820582691, 596712193, 987694063, 370122846, 397662158, 930297823, 729213747, 639441016, 177952767, 155423021, 298557728, 879995347, 674414268, 897005059, 165209869, 707380492, 489779915, 40693562, 751835002, 510660185, 271104458, 338539643, 286855575, 29921556, 690254979, 417014479, 623013351, 776202367, 950383609, 307331529, 278332176, 436733225, 749912948, 793186501, 770201209, 90676013, 121513273, 284797446, 243581592, 107691175, 595278435, 475371185, 688107716, 182393913, 32400570, 744479400, 859167681, 572668243, 233415206, 565017098, 211680078, 595658948, 414459977, 317995628, 598604039, 498524461, 175152513, 239774273, 180827738, 870630298, 179051958, 716635927, 291983041, 696129281, 84034712, 555578145, 462874075, 644187392, 802242043, 776454470, 945872445, 965994107, 808060460, 792381116, 961045682, 274313303, 802843895, 918437295, 738704703, 858870311, 983140247, 92663178, 932599245, 466386197, 629049731, 920580006, 947192746, 918849901, 844175644, 101118314, 331249963, 247572502, 637258541, 225488570, 69954072, 173277623, 580738499, 811179023, 778236355, 133712282, 591784194, 764754520, 650855788, 42132775, 869280791, 527711862, 846598048, 192602092, 66057901, 745586594, 781453, 371255632, 541568260, 422934592, 936951273, 839118706, 316200453, 228883428, 537835842, 510735146, 227146891, 736296054, 269919861, 492801572, 922627128, 133455104, 134409498, 361150133, 570789857, 643741303, 765575694, 880225049, 717050112, 596314766, 208959069, 26360401, 199438643, 810296612, 435587823, 948531910, 94109073, 699812877, 482914410, 301355734, 162962174, 295532151, 426837953, 476584324, 138400439, 103394574, 120401832, 727602021, 267579337, 114931976, 266908070, 42945721, 644538234, 786502644, 127001179, 374803105, 14579337, 919032976, 815307772, 864278189, 820955505, 872708251, 621622536, 240871354, 12736716, 567836978, 961539828, 193919309, 656569988, 712607470, 973131587, 643597329, 499052692, 389759567, 793339029, 549087025, 273596396, 352765, 622364621, 813606885, 453714395, 771084997, 591542946, 320761102, 453174735, 366293527, 803601563, 52642844, 73294134, 836878878, 836767237, 997720353, 35936626, 64298632, 682028977, 470490824, 594617928, 502033454, 136957232, 959048683, 176775108, 829577238, 427554671, 643765051, 379256461, 238428958, 520671283, 16487958, 757504669, 547533820, 507541865, 571779845, 34150098, 885867856, 60462246, 996181878, 517541214, 790610917, 65023176, 935157178, 840363495, 549838493, 380016920, 693201917, 705168154, 90870223, 404002726, 124802836, 196547375, 911040897, 589059545, 913159895, 760996721, 859620273, 178881793, 994280667, 39723116, 434288829, 723577492, 290824618, 114247389, 838211272, 946838480, 711578250, 84119386, 421484284, 564283944, 252397174, 502234972, 693474840, 415779282, 764784301, 885798346, 538827162, 520137113, 534583666, 951113046, 507109550, 442129838, 556477125, 728320668, 886950570, 368198590, 403851149, 880213680, 477796439, 356778572, 835253001, 326191490, 435243195, 502878850, 355909256, 491518982, 534528937, 647619735, 911976872, 229581301, 51787757, 469831949, 376887402, 763218094, 929895234, 791373425, 920956372, 955746443, 628122820, 297894809, 710950989, 200251632, 900507833, 431052742, 30163267, 218514627, 448302370, 230007869, 53996601, 488091985, 157401778, 658141946, 755524514, 466816696, 331302804, 588720394, 810020376, 860665978, 408513601, 840308740, 310600596, 307548689, 211880277, 709566934, 464562678, 172745107, 287404015, 614375253, 518255827, 132176290, 940846948, 662312688, 9718199, 82208123, 923682765, 262283933, 149765988, 108888338, 190433948, 109927639, 210856503, 727333301, 496198295, 739162985, 261344372, 788460404, 419683806, 678086198, 285320455, 289900561, 984313277, 880781333, 882497617, 900977192, 248652147, 689809266, 210061341, 115476518, 677837082, 326854967, 425703118, 677276047, 536570022, 942308146, 30582325, 368778741, 100700745, 21064635, 578823701, 725075833, 533901938, 710188261, 402909298, 147066878, 334980698, 646273094, 361092010, 134185853, 471364374, 64966949, 575841447, 197373496, 446865252, 970450302, 542093008, 47959928, 544804217, 255314589, 520704067, 905120949, 261591047, 163872193, 976481507, 958301836, 736028195, 154647439, 761551568, 65846320, 611775527, 998375166, 126355099, 701401622, 812549227, 20296806, 669728839, 176270891, 702694022, 666972923, 201993158, 405862569, 575053282, 76576468, 647296002, 308190376, 926147779, 525526069, 864042983, 249798314, 388281115, 830264177, 418756658, 495201450, 923938741, 379822751, 590348485, 835974678, 533109927, 541002496, 161465598, 58872235, 111313637, 225206202, 102573384, 940399552, 267052425, 809178713, 48421597, 102536359, 535043976, 765149280, 547170707, 709786862, 552189229, 826915011, 85186718, 173993851, 539030974, 477539006, 355879051, 802320374, 449211701, 637604992, 313722660, 342785739, 274167521, 436107798, 860378702, 554835652, 827261429, 66359739, 927439684, 588798191, 465310774, 540169613, 823541599, 229216457, 331940407, 577019085, 76636608, 672718331, 697289576, 891153184, 112434260, 985421473, 629646688, 893058551, 68144651, 668887141, 794584629, 41166114, 977355616, 714830811, 402578639, 789036955, 373386569, 575333281, 664421702, 228459766, 648059972, 883837234, 224525472, 182613696, 294083906, 103905540, 603551732, 928670062, 366941791, 144734012, 639965116, 492060431, 978721791, 720553174, 207863620, 977952331, 224107319, 569186403, 840673319, 958063644, 880072434, 717909045, 27007016, 246761975, 630724129, 58843394, 422585129, 956672679, 891608011, 264319145, 23299356, 712431703, 321782114, 993038844, 159329469, 175640403, 594528281, 943763328, 96260535, 562728177, 470360280, 940566537, 472876, 366983315, 944454690, 309286271, 356139148, 437016890, 285732342, 806921107, 153283063, 978627955, 58009793, 909141309, 464712375, 908661830, 206790059, 285070844, 204071331, 387359561, 147553310, 442922635, 142654674, 232597880, 854744977, 374773185, 383993457, 349521881, 501925749, 419849323, 941314030, 389144720, 182571634, 345272078, 125145197, 198923462, 932985425, 334766022, 915237270, 253217273, 305654550, 74453899, 541329471, 781639180, 912905992, 215916503, 218862627, 42333342, 784490334, 144801258, 51049194, 508579597, 70700572, 348901936, 431174008, 177953162, 397707126, 618789065, 297631506, 472595615, 272259312, 287581743, 786882785, 370419120, 661731989, 434479461, 847593536, 975683515, 933071512, 138801761, 434742445, 32771454, 105729941, 996332217, 110165217, 501303236, 932529891, 531498456, 779508669, 704751232, 781089983, 656912459, 103504122, 893235003, 849099932, 121137678, 484971142, 756214026, 242683816, 421347892, 994864034, 311351979, 754584662, 206336552, 544293189, 240890730, 648419890, 624118385, 577024841, 565809794, 516732205, 98792776, 396003684, 436852393, 177464134, 721310752, 911646398, 811241564, 492030053, 506400062, 123688271, 805274681, 407362882, 103447785, 636996557, 244581246, 870701049, 547544481, 275646204, 745609777, 157411920, 233738288, 121103372, 462416054, 113841165, 400997204, 927170195, 517267474, 480440820, 213778329, 782291550, 403310713, 46663739, 563572937, 240663127, 222475689, 342653982, 196893049, 647156452, 513938549, 436814370, 49332682, 926434095, 409325754, 853423339, 524710611, 999751172, 986597195, 671480488, 324423967, 477216766, 46889853, 174245324, 365079135, 887963704, 437208353, 326463167, 688953622, 707565767, 690366617, 548759027, 154075426, 889663013, 441802363, 237656048, 977396566, 586734818, 824063678, 17834528, 333899707, 514874876, 539332123, 396801017, 196108430, 301921182, 893035305, 759134597, 108876314, 80598084, 158429178, 232505510, 960719689, 681105172, 773752384, 765211765, 951408883, 771295028, 118499607, 875213235, 780927311, 962063980, 302094086, 165331563, 395570403, 924081414, 333883695, 587168749, 696274802, 473007134, 320685292, 143983241, 321793248, 602221354, 703497474, 60080208, 870520684, 387657692, 100457693, 456429309, 837392544, 356057722, 796288575, 995686189, 938780151, 736083082, 981094026, 2793476, 147633121, 675043462, 713088318, 589749557, 869520690, 282070510, 721753701, 625746202, 645307913, 519794244, 6053827, 613583974, 456339013, 785061842, 267031287, 821960016, 457243950, 86348857, 238673711, 397969972, 734829138, 242528335, 986357288, 796211531, 298004584, 850936022, 182342103, 214179230, 442414958, 22582945, 463738333, 467110772, 852187239, 91695522, 925293185, 16038330, 592401632, 393550936, 833283080, 503292747, 985059401, 898691017, 991145080, 403808150, 955096409, 613903854, 81905600, 816931925, 549754411, 45252363, 355197378, 66955569, 396330206, 711554685, 893616117, 372804991, 743549041, 295778936, 730469956, 472175397, 419084066, 541176456, 718852986, 239543075, 424400508, 23970944, 962269480, 767836881, 802455697, 45306298, 212051222, 201843724, 289426998, 529104659, 466258460, 614610779, 771421516, 101481718, 565829184, 651551790, 903607046, 139601856, 402235338, 915658076, 666963691, 5832892, 507446568, 45080848, 399306288, 516786035, 784578355, 589335276, 734594619, 712969592, 273898707, 901285968, 655825979, 236521275, 295800950, 827750292, 811630377, 825610475, 454447280, 469302480, 988143493, 68656025, 34278192, 841941553, 501390072, 508355067, 407760703, 186968029, 828636100, 801919254, 221650492, 310983999, 5794059, 719225917, 901564942, 196576458, 746133013, 75291735, 495465343, 130811733, 57526167, 862244860, 305520885, 477875386, 140999878, 333955351, 473530165, 469748936, 718357850, 519003721, 377337665, 96705152, 608990060, 948755083, 337048521, 497022376, 646579646, 792065589, 368880889, 939989801, 303246689, 589913531, 152759939, 812685446, 860894628, 620770780, 955240897, 245757993, 369584310, 913896107, 681594683, 655481566, 163959622, 310620449, 230558298, 124110099, 252033142, 962331457, 633956414, 432995474, 765527432, 392055829, 17446450, 408631066, 187569078, 378048779, 514926094, 557011780, 701997376, 863505320, 8926049, 159217456, 436685949, 247373320, 640727736, 62402197, 416284497, 689337452, 385012866, 925296563, 797460399, 733827304, 1193695, 625507542, 64973988, 711368681, 368192368, 764037547, 37948133, 748872636, 144023991, 760700821, 258495693, 799190680, 381869630, 153390685, 454206955, 222272837, 145725876, 520547246, 427475399, 565893971, 446602864, 875509593, 52160462, 164609546, 519549483, 228720816, 757122892, 395952416, 522936272, 948287469, 752934674, 622007755, 629445638, 537988553, 627832411, 665305735, 67660518, 618714187, 285401075, 577988819, 462292210, 285675881, 821789982, 350730257, 814810069, 475884279, 103867332, 739602209, 332227908, 968157957, 722281619, 239136839, 259428968, 930428747, 237699320, 904395332, 539309685, 543034172, 657276452, 912737793, 992694852, 895936021, 960563632, 302631384, 517844609, 665081408, 429303332, 39720300, 340397105, 736760690, 833482651, 340890135, 299355498, 618273018, 335281777, 680505364, 368288392, 242307717, 101191902, 784755806, 550801909, 346299619, 669133593, 66477697, 924913978, 372354401, 774168198, 567420330, 122871510, 711013500, 651351744, 419656821, 878785170, 602072423, 428692110, 39350922, 150596574, 857589340, 828865943, 60040902, 529986752, 435470142, 762836153, 935539428, 4802307, 284268787, 673598737, 367578328, 38612275, 979814284, 684529018, 534809661, 904097725, 208984946, 456218715, 575811274, 990588614, 463625216, 161222316, 298490874, 974474299, 375555608, 568072288, 716108201, 620180696, 343665891, 380340801, 659169540, 740092231, 720566392, 387625745, 207162497, 215518424, 619925020, 187073802, 258232909, 651333825, 266308528, 640784907, 655694364, 218251067, 906012735, 950439711, 211445044, 412390170, 541824538, 907936425, 247839983, 183972384, 518349947, 112648158, 340495922, 965518708, 308251645, 687554930, 285662837, 194895923, 837173644, 284763081, 626043711, 607820827, 729566671, 831128767, 193114722, 682429007, 553262367, 763752379, 875460867, 254411768, 579699747, 558899805, 671455324, 832795100, 280863078, 744171643, 117068727, 370920695, 976153595, 401217468, 151953639, 257327530, 263883950, 783672357, 323929608, 935620945, 846492700, 123146687, 415814092, 560881600, 3991857, 273480912, 453120194, 238240488, 936111242, 856303562, 7644233, 519936353, 387000783, 338191527, 546820005, 75177315, 65124302, 480645349, 786551942, 412581174, 59461083, 926409613, 720590178, 35272585, 143350018, 621772613, 922751210, 574036068, 431939795, 54124739, 696945565, 294188382, 293340995, 397233682, 912741701, 30406065, 733802617, 249722913, 44865810, 754772972, 242693772, 293564760, 133673619, 426610279, 177304480, 407110377, 135932652, 706294229, 561106990, 55511636, 187185806, 405797453, 128188821, 974980421, 205952485, 457727710, 732266303, 421986842, 641047531, 994488708, 756040816, 582860889, 231915190, 773383932, 822437895, 353349100, 104897494, 849141574, 264391508, 996142556, 104418230, 49734819, 756841102, 911407052, 418719239, 942833876, 760320620, 229540072, 933138700, 316694851, 945422628, 646693491, 207110158, 983941144, 258165777, 150519386, 602443396, 619947569, 544283335, 978242904, 466717601, 803850077, 74894559, 353076006, 750311517, 153337859, 150167016, 458052838, 115257949, 687008060, 910671019, 42748979, 614836430, 82480672, 923927156, 166878321, 502117924, 827445687, 284870275, 261570818, 768211092, 788838353, 810777884, 481837565, 523642693, 589997393, 17203542, 806367996, 635981501, 128668421, 590537595, 923438389, 975792477, 294607559, 952213015, 924721544, 157446823, 300664963, 434011597, 286514135, 869612244, 873433537, 647881644, 115114555, 585200252, 506873343, 401518490, 379233521, 336589831, 183172176, 227059945, 994159304, 405424254, 41117055, 543609715, 397836567, 156671032, 632968239, 202143882, 390445666, 194888586, 980814348, 793875485, 423884747, 624642224, 868317189, 998450820, 550340394, 537721325, 561421958, 647969027, 665945278, 634754443, 604860616, 278583613, 228494338, 583966472, 748989216, 418776391, 313700965, 512030215, 154681988, 743043964, 237840775, 945950417, 742995376, 830439909, 979435679, 527658120, 828449623, 808367763, 704616860, 900865932, 887991597, 143234949, 674505219, 493810197, 649819198, 118947658, 457801244, 628520493, 849707019, 384544402, 153729184, 393069468, 874384221, 290213781, 238348554, 321723739, 56586742, 50230279, 179159940, 604277297, 814654924, 995245955, 252240740, 220032820, 446453828, 958702055, 155750870, 947812913, 745426296, 633898840, 198207679, 45374497, 184638947, 327033023, 978915476, 744969211, 668747325, 959813499, 667927148, 250608740, 38659090, 144222399, 984043591, 382094721, 255143605, 124760875, 203370583, 289159581, 584324797, 512099448, 209120089, 905590981, 281897441, 856522343, 61577622, 627308581, 908932478, 314985117, 144421138, 632388718, 568259194, 363071559, 121592107, 757566026, 103129110, 800328974, 594449283, 309490379, 611676946, 144614466, 418815408, 155848340, 784416012, 650224958, 705628286, 891576678, 70342689, 723534826, 268799076, 693077186, 776324466, 875342252, 385262395, 946474574, 463458033, 70014245, 240067223, 189295013, 847533142, 164046848, 538090039, 515121190, 773146282, 645264916, 205293323, 676906549, 573538466, 792340430, 660373050, 891396778, 596832390, 989005540, 29652289, 443391041, 100670343, 800338476, 561618367, 338645545, 35202073, 843056459, 82790303, 794548454, 704147200, 487973816, 592083843, 34675896, 242672025, 880250151, 838779806, 632282815, 670904003, 230484043, 306640065, 841792243, 910542351, 669665801, 82052994, 847439224, 359963836, 375243897, 624154789, 248417881, 968074985, 911480831, 895812970, 300780310, 404687478, 136400637, 497033842, 669907152, 477721691, 361996085, 284970485, 225282552, 806987066, 889403683, 951198535, 500531593, 360478217, 283827341, 436347347, 31302822, 507983616, 260815120, 954923541, 71340859, 529732962, 501653905, 874593478, 851395376, 264895623, 582089644, 954053838, 744446657, 493749522, 113518067, 144594133, 365640625, 18130301, 809442217, 11207842, 234004184, 696297715, 514761799, 807230564, 36328980, 39700391, 231149316, 18064507, 651611815, 546041760, 817037726, 347064688, 774036137, 859786333, 265540840, 353856361, 997026536, 129823597, 435977661, 150223230, 317194513, 301678519, 814452313, 844664836, 412583721, 911475457, 922263570, 806518726, 918294876, 415955103, 237623264, 460597496, 677988501, 482998516, 445479577, 697724707, 14808990, 194398264, 90966160, 145599529, 424602986, 96654322, 381930956, 576193533, 885960116, 567145019, 402226685, 542248453, 345353682, 878078773, 337925236, 865584721, 831952211, 732321093, 241633459, 640424570, 780355520, 623831128, 813442794, 687636655, 126292559, 813662828, 301723211, 876848131, 736424695, 77496000, 234032109, 249829429, 849916963, 809337455, 397140279, 448088375, 382107518, 354234631, 962895835, 927481771, 55451686, 254874534, 351798784, 217137783, 315868572, 534515687, 588568789, 472860032, 443737499, 586769766, 534207192, 254966234, 400472664, 431728474, 213250959, 175042558, 324357848, 739522736, 527163074, 938563502, 783538572, 453145549, 614645418, 206201808, 168396233, 116791324, 547016365, 203437688, 599377654, 969383448, 164294779, 319499378, 229371080, 335884469, 406382940, 410219827, 615973198, 584158665, 243302392, 835798316, 153781753, 20903831, 824326927, 726740685, 675709199, 447573752, 964687153, 576977804, 252441643, 533287654, 132944580, 118167129, 867694458, 575694499, 534439195, 908478581, 502345405, 650703275, 554936555, 51760717, 100814895, 768106403, 390885347, 716315205, 243079373, 288066687, 526492685, 672784385, 811677508, 138184663, 13693438, 899148132, 914461154, 118421779, 445317097, 696256070, 956194016, 508481169, 912627883, 118183665, 728855987, 851570548, 481934129, 230045991, 744003813, 329543670, 654952527, 322162024, 873986855, 934179525, 810159644, 835700833, 16027128, 859684335, 316642576, 343077268, 108451230, 682360212, 583724351, 240604295, 710484087, 780411286, 433120857, 965348358, 446906942, 437622381, 628450915, 581888462, 687241241, 831476535, 534935045, 298242349, 712029669, 558270108, 531804746, 312325895, 558476011, 204456695, 842100698, 613160363, 787279703, 606349312, 904281079, 698260500, 533440465, 563742701, 481358421, 588705084, 65527985, 413312243, 627356088, 395029480, 563523107, 693065333, 949100474, 416039860, 108409761, 433378420, 726227301, 892693072, 232810880, 536914252, 37026766, 298429012, 829091204, 894643477, 15940625, 606594391, 694450726, 510706380, 165596972, 167071808, 969702324, 516030389, 302109295, 936887434, 754873576, 943862504, 949899267, 174253734, 3108970, 97748463, 336664605, 155270916, 471888966, 795142439, 450687484, 359388707, 943104595, 782395865, 269271627, 512940852, 757418351, 36467427, 87371355, 871588058, 34028695, 603941849, 317377478, 293298466, 885122269, 713946783, 736310024, 175664261, 503293890, 601006753, 726062768, 373036221, 6063070, 169159914, 115801363, 707977592, 369119611, 187072166, 949283166, 306700010, 795062011, 403941024, 411546421, 689735118, 666520638, 872236372, 575442180, 569697653, 769987331, 335245832, 264855169, 799283824, 182781095, 992281684, 515476718, 556716880, 237750144, 627174107, 263678370, 503468798, 647038649, 375794762, 850778043, 797898808, 376477828, 249013784, 357044414, 122126012, 228549580, 704472295, 879201742, 702704773, 652871983, 722965087, 873292417, 756929690, 829378899, 806784061, 963414658, 80384831, 678288748, 91914533, 807282213, 214292268, 537910766, 186921747, 352368655, 365440267, 519925350, 369865977, 954611734, 697896880, 905295359, 465837409, 508959211, 819165676, 144992894, 78018595, 361827788, 233671526, 922596687, 230530531, 871961088, 497140762, 446334253, 129566194, 788916640, 762036823, 12046877, 364468063, 965329084, 369241096, 442968897, 664583378, 101796603, 425653555, 727698540, 533200985, 328424283, 582775569, 323067566, 753540414, 673286129, 763795799, 492189313, 18507494, 336762300, 400389817, 337541459, 765566755, 48952969, 534459278, 839102557, 377810596, 209294694, 106090984, 680208121, 235643674, 731971814, 742312736, 783993729, 730581808, 201356634, 480587774, 260057795, 282112234, 277053041, 168329236, 783411050, 649330235, 811531032, 473377694, 454975029, 563685804, 301262770, 53084590, 728236257, 534525642, 419783613, 635624659, 919351449, 845807195, 812238494, 444248674, 244184224, 119560892, 291706946, 903318415, 645660962, 308289402, 646243415, 879279591, 982163266, 629350379, 988355585, 508114388, 120215868, 665619593, 408394997, 953757838, 4438714, 808306054, 340043825, 344080777, 189972376, 13283552, 957753634, 171110823, 627327061, 317259444, 113857526, 980902080, 288532164, 715056672, 728398021, 516339319, 733453199, 906048568, 932434332, 917493486, 63080104, 491432924, 374417928, 78201145, 153201386, 677608404, 464345028, 621593374, 475476638, 702186914, 588367677, 652153260, 325221470, 38008980, 918584149, 490710691, 303003854, 784480772, 863335109, 192983505, 858922543, 484757052, 917990118, 495815875, 811954038, 297432688, 392883017, 204669258, 602527301, 102230239, 338952360, 686341760, 933132885, 926969208, 300943993, 492321200, 953756451, 115040287, 538749949, 264891490, 757687087, 374850377, 283104914, 321448383, 637564038, 381798206, 919348300, 719165317, 897656621, 766949641, 209694980, 883668600, 85103866, 326626077, 354882370, 294819223, 103678815, 628297439, 552815128, 746880060, 882716310, 639761826, 853313845, 227267776, 33989281, 205082115, 172038197, 127604684, 87774336, 10899006, 510660920, 847949808, 803379096, 268046698, 325484960, 65979647, 195624623, 381305220, 814387134, 721896604, 193134081, 474576004, 332337948, 963021663, 436686832, 51683011, 747900642, 184632977, 206896071, 492762433, 247388661, 338193259, 699455085, 827874340, 707620250, 870121395, 30906712, 11787926, 331881157, 82483534, 289213892, 324337894, 496626657, 50161209, 630162071, 856062231, 635277408, 808763182, 65296468, 25262602, 3767520, 254519520, 254268981, 961108266, 381075511, 352664122, 851482442, 924035567, 950621230, 178288430, 348301474, 252976146, 467330905, 855842886, 648246342, 277367609, 927160171, 805549444, 843076577, 750172152, 274112028, 871610556, 277401074, 444870619, 560695474, 552736261, 259184367, 504148864, 576377476, 280537286, 567861281, 954490495, 459256201, 128707966, 346636733, 740938798, 467486468, 632303238, 864901315, 680107539, 206449012, 188035820, 64744175, 305024357, 716309557, 343008536, 300911047, 73822015, 612086326, 594305338, 993845689, 679787210, 195983225, 128940269, 146413954, 443687704, 438215444, 58300467, 413529351, 304234267, 894208746, 48378180, 626499087, 584811010, 717583272, 548535748, 334736821, 820768741, 532984475, 835983705, 303415415, 953455535, 698533565, 150549788, 960120544, 59702004, 633482569, 756241910, 681140655, 121688483, 537417261, 659383894, 15021880, 223408979, 230133973, 28074229, 415857550, 304950947, 697203444, 825836110, 805732962, 794292730, 378730326, 661235959, 447282449, 19518359, 310802095, 270324007, 92442866, 617023302, 769587208, 169984450, 182981653, 322637971, 717165814, 875327362, 508359935, 400645173, 257579302, 369971922, 160255885, 7016573, 11799058, 196195886, 296750807, 286032662, 846677082, 379118996, 126965336, 339453246, 59716049, 99289953, 643219682, 578636445, 552668930, 336030355, 823547909, 271452127, 600885957, 229411451, 47785971, 475194378, 427455022, 368678254, 654320682, 785873685, 548793391, 183239987, 589537820, 159005013, 757387065, 900586607, 760581402, 926202279, 105527598, 679199382, 692477947, 27181177, 937577548, 513153667, 940079219, 35891005, 599213012, 679647386, 970140226, 21250292, 941271297, 672417865, 809343157, 41160052, 470512203, 276603028, 61565991, 189612081, 887627573, 262687492, 770436910, 610939149, 212573174, 844855670, 280487479, 796747033, 715329777, 941186839, 174743968, 228446617, 960030734, 365622811, 216637546, 113585009, 292258686, 835292152, 306469024, 83534904, 236211293, 962832425, 606078287, 268241261, 942574769, 452320400, 986074289, 105093698, 751053933, 53758322, 693296661, 420700933, 858555678, 50582589, 732479344, 580664013, 422531450, 932062437, 181058589, 511576288, 133903503, 71388391, 896626975, 482104660, 626188672, 245217261, 19717046, 41292287, 245207821, 74966520, 441594880, 787613402, 895042505, 136186710, 674081634, 188530931, 125636461, 84440225, 774311446, 882476031, 27392959, 255282924, 406748899, 444581406, 211192628, 920095225, 79522482, 688953002, 440176436, 780772934, 646618926, 595236364, 938011100, 168013279, 614989118, 269040294, 765460843, 445281348, 355254399, 665795, 708303183, 491095610, 328408917, 350611458, 230289568, 339486688, 146843547, 722881734, 105108031, 24646485, 512099739, 200315563, 726780592, 17570844, 98584838, 463038204, 724990875, 588241938, 499108151, 89456034, 823542398, 572034302, 930774928, 215347835, 704858759, 660719094, 182347835, 545428907, 534682088, 741787255, 226726207, 296405244, 426826182, 435443979, 82566895, 339544578, 277740970, 388941744, 400405845, 367306231, 266902570, 855203964, 798398284, 656964346, 673422561, 258108666, 202818634, 718276335, 581278836, 601752559, 731103069, 943778872, 348097247, 535435780, 681868887, 464396921, 43306191, 967364568, 46165167, 304461698, 643876511, 994870574, 724430623, 484265295, 148587362, 554902237, 480293953, 59149104, 81571052, 82894637, 893773552, 708360924, 427410034, 934247113, 246579071, 153311302, 852984162, 651742304, 342301214, 641569483, 919633354, 827838933, 520203536, 62063412, 219610108, 575009845, 486891079, 576411028, 25035993, 260039527, 945040022, 342814573, 15038414, 563069370, 265492216, 854909312, 425715089, 7312182, 160414451, 501151700, 116185754, 729517819, 492502860, 864681677, 669402779, 957120379, 956190681, 415036510, 7168406, 708582529, 688303823, 353500738, 724806770, 992291835, 683316612, 661672379, 834875499, 573935244, 311091693, 155794692, 889382447, 246927400, 998839783, 353928997, 618015609, 780379588, 893652074, 858171861, 728920467, 202063755, 105621341, 973094180, 95684960, 448025414, 120870548, 872451962, 842407973, 113745871, 682631973, 142955529, 150961511, 975153999, 893298679, 224047600, 39021643, 23513478, 920448488, 176356826, 873617071, 998099427, 537894294, 440599711, 623015105, 809540076, 572620848, 989775166, 767682747, 415059066, 795931215, 634293464, 944160485, 653383078, 840348212, 20065611, 771390462, 865070256, 249325093, 81750223, 259055231, 292400521, 780609578, 900087624, 608924976, 680931600, 244301010, 116264116, 908388246, 543210499, 348216392, 689016443, 34402737, 460524049, 368536909, 704487932, 726774950, 294262593, 473176168, 783571453, 262635158, 148408095, 748675252, 458361632, 437538694, 248519321, 972710737, 220884532, 857219994, 454844708, 994546343, 442661707, 780713887, 387742729, 605141096, 453870867, 80767973, 921152760, 564692519, 379182152, 650350565, 283763023, 632136009, 3820281, 859140923, 396982241, 885294665, 900933627, 742179726, 481063048, 508989898, 146210427, 113641228, 482552296, 989670047, 805479053, 241092406, 124529105, 574048866, 282685659, 532238276, 720771035, 607714901, 596474847, 1781768, 146265104, 959084191, 350207063, 314467144, 517153484, 693569617, 373224808, 866065808, 796464088, 457369630, 8873383, 487229057, 663554605, 370053071, 745915116, 127350434, 862064211, 660056718, 281061990, 83435542, 82075278, 598496020, 826688932, 111339314, 595256565, 316743706, 385594008, 684172223, 811268401, 402015638, 784495892, 850742706, 969958744, 137151325, 96712663, 851666935, 974646403, 51833400, 307592549, 494934099, 695661124, 448027007, 249559987, 449414605, 713257418, 130881283, 71141823, 792027626, 133031449, 26488061, 778884292, 584963881, 179284628, 922064100, 358780027, 732682382, 462171048, 811242121, 514386418, 528859441, 690180411, 679717980, 727133883, 261757462, 865865763, 431948558, 405487241, 961136187, 224727539, 255527553, 99667325, 664955934, 768409539, 188983014, 957202401, 890893894, 913538661, 300669547, 274594102, 597827896, 881338729, 729822124, 45386857, 631115358, 40842902, 25938396, 666386895, 575011086, 490073765, 544867506, 734859126, 336725789, 169675644, 421334219, 384620497, 843852821, 358066200, 309719649, 108393897, 228028505, 486121019, 345339287, 542682729, 310867404, 423540847, 663645133, 759390697, 764299113, 37808624, 892555688, 896601795, 13690094, 872381213, 970710090, 963038257, 755462006, 84072561, 983897578, 308133804, 420160238, 958683710, 113034574, 815704874, 370323485, 406527666, 870922075, 434845692, 636816884, 811547090, 698281749, 596357824, 716958921, 162155978, 275295238, 103043650, 355711561, 244094511, 631025740, 809085202, 952099203, 83172811, 274988253, 394313770, 352820204, 518776934, 363603495, 438961493, 514096380, 969435990, 682780563, 823091874, 134685642, 130452995, 751063459, 958571449, 23345338, 995253873, 214678490, 711133836, 144932374, 803924615, 443583003, 558254520, 523877439, 384148839, 933322257, 591264140, 134291574, 903292187, 261832821, 233382846, 366166700, 873726095, 656235450, 504177539, 426272523, 959281141, 440839251, 312448184, 323980711, 451008760, 917385292, 770160704, 470998472, 650314856, 430521219, 929798902, 70659692, 29480159, 288573656, 871267256, 171511445, 681260144, 760187652, 452527457, 355783537, 86881506, 247186638, 174963499, 223050579, 577246348, 608636138, 693392316, 20574132, 722646215, 124612712, 31672255, 851544468, 635475987, 614670256, 877749934, 703598450, 507074116, 735038233, 150483813, 18978101, 694782160, 658632304, 470792003, 998107286, 498355441, 349877929, 733978060, 251089559, 352806062, 701414409, 213972313, 832037450, 601341552, 732282782, 897675718, 905212063, 380507821, 62120416, 507628272, 437856689, 49627731, 857042565, 613596556, 663702564, 729041855, 171241421, 973570079, 819916160, 239669058, 569742844, 367097394, 830025860, 229465586, 312539523, 19664213, 47933129, 539319102, 776961809, 946121563, 870826034, 46749273, 399482674, 334606827, 184626442, 308657933, 970941447, 891269516, 94391288, 978715416, 406271999, 259382609, 756406334, 330200373, 193727753, 393419871, 775407599, 461365360, 464103125, 786128833, 916926448, 235882001, 841198733, 509655914, 372002773, 339304834, 593995517, 758719272, 223542671, 686890013, 465660139, 793321777, 224062282, 646718370, 976278797, 122503101, 203912406, 101697150, 931674481, 281156834, 466143016, 644348211, 622839994, 243066626, 516598277, 672991768, 799059258, 942216583, 945900216, 831159334, 303785044, 706286618, 963628425, 519171046, 191985955, 787255127, 934433642, 592697185, 561306966, 29913294, 251806591, 742135859, 82211934, 669167917, 712820871, 359358533, 859664913, 388965083, 458929828, 41175878, 510828554, 840975647, 112153538, 567884001, 837171357, 653677241, 798557586, 755305963, 172917933, 150506344, 298067273, 110729584, 32969612, 351183824, 655025602, 472428427, 600154255, 858504041, 177472574, 416664127, 780179398, 504409527, 754660786, 703386130, 203957410, 676997786, 411783755, 728559736, 751147244, 819142544, 618658491, 956500712, 451510122, 273697213, 936583661, 317814279, 383291422, 558385221, 878438045, 111578599, 950984603, 296992288, 559856435, 481060273, 761338859, 181682618, 338780478, 822320755, 301168549, 491943617, 266845303, 317158248, 114245461, 289475559, 401479073, 678610178, 713326874, 623515322, 654405924, 128321204, 648081926, 445615432, 103245214, 568857767, 290075454, 796503340, 422312040, 519270647, 605759917, 274121160, 138540329, 583942722, 704735406, 304375686, 70765281, 266962566, 345403157, 747247310, 229144213, 5373097, 11871834, 496674330, 776260516, 656214823, 840563742, 594485587, 549506304, 574660766, 896874573, 179015048, 181739678, 31893773, 843600719, 453849124, 248244431, 526484048, 821245928, 627017326, 985496537, 174512332, 826613425, 159217907, 726811709, 422262969, 718091203, 286774509, 250058432, 837788620, 484748739, 749630982, 750115337, 163098613, 198909872, 595334537, 434094205, 936824435, 307259895, 987825968, 426398009, 623609676, 46085578, 962518112, 641044731, 467834485, 57374341, 771759223, 502409423, 357774837, 360330261, 301301054, 93682885, 297499738, 520110842, 732683046, 33488871, 547194519, 587926043, 353710019, 311844942, 938010141, 969930655, 949138604, 406622077, 74937740, 480984270, 651598252, 55583047, 633230862, 157427386, 652658967, 170775794, 232370255, 867315435, 692764443, 910350939, 554346685, 730806829, 300281833, 304074345, 258346470, 170848625, 11613533, 860789665, 587406732, 829835378, 569147519, 881847531, 876467169, 318828522, 293637619, 251678228, 381727216, 832674655, 649161339, 455325306, 169297450, 210990136, 67731262, 226711117, 767468635, 774316268, 723018462, 640607414, 108058279, 121424430, 57199766, 703736430, 958161237, 141765290, 314761570, 414461323, 1231153, 114700817, 717134355, 934432334, 996338179, 370412334, 602406485, 292790006, 682874739, 410661655, 261573983, 518326990, 157112606, 970814016, 646350220, 633155103, 719877753, 976196212, 424706742, 533889451, 968181748, 199391582, 329474775, 568122520, 494972275, 312369364, 954741176, 285877173, 244158578, 245892364, 997973006, 52116554, 470920086, 99927298, 357222231, 76390466, 681630621, 934074697, 405761637, 369757984, 160879567, 813366205, 677422180, 619877714, 654132550, 421693334, 808585047, 265741156, 920317744, 995068417, 838743609, 332282297, 577258110, 956888852, 813486548, 232822380, 395383049, 714153767, 265813676, 742131324, 284338336, 589631520, 652477333, 703675271, 41528806, 558780146, 567384888, 932346004, 994238882, 289245571, 947041312, 66367101, 922099539, 795340355, 862693735, 618385196, 752558159, 487721279, 257470785, 834764416, 54829083, 559659257, 474302871, 130779795, 282153904, 220308051, 885843428, 637626638, 419281414, 206249770, 378899601, 738829982, 297908515, 395109480, 739743860, 892205137, 956056604, 278213315, 649312642, 860654458, 334452914, 37221954, 643914142, 337957712, 597146261, 216235590, 341013, 789649024, 809173601, 316347734, 281857012, 170005339, 655737045, 843869752, 932998072, 931807506, 997687843, 5895813, 170152013, 744762959, 414559294, 99458093, 743997308, 812294053, 564071815, 568538826, 508973071, 939967931, 117523653, 229367451, 408935578, 27537148, 814186644, 628513347, 377883978, 234398318, 877334362, 562694378, 964684225, 658261132, 736383336, 303212459, 442795130, 857889170, 461677261, 431204421, 117596768, 461059168, 577259033, 914495275, 456805053, 683238857, 603511774, 812087907, 716025595, 10146600, 76403700, 999049031, 976919228, 19455816, 544824346, 139311333, 614618462, 147431115, 85687581, 837380127, 272340430, 536423682, 503823717, 49007269, 280915949, 476395825, 176747929, 260374775, 999189189, 953019311, 441978388, 311017252, 834025142, 143191813, 645866401, 559084800, 474564176, 448386988, 365500802, 877563140, 113121358, 822625385, 886027393, 311318908, 822906529, 28947146, 418550552, 146950270, 295592606, 938016497, 463583518, 940983433, 978693077, 787048262, 964685181, 698750767, 724265409, 661344041, 426994353, 348930929, 41819263, 414355087, 971730888, 314687001, 683884758, 114571895, 867502439, 931397323, 507545058, 624094240, 671421177, 724560795, 822958448, 231590035, 473827694, 190520749, 315986829, 445063744, 741872452, 164477431, 884548734, 523504575, 987951823, 283999748, 345962315, 503850240, 755887438, 275961784, 235259381, 590921588, 96402556, 336069867, 683360093, 414457128, 66235392, 955716698, 567546851, 708308433, 49695402, 269776183, 544864253, 853373543, 575334471, 929745204, 51391672, 307363956, 171622695, 147316091, 608387908, 310176424, 1394797, 219126835, 530713330, 201066835, 660500419, 406253714, 5298484, 525813998, 470644525, 815558539, 361109438, 739867301, 524306983, 906483663, 560101393, 538817564, 144459068, 756626186, 163982673, 534457718, 240577903, 205122778, 695891472, 574478912, 128831030, 209270740, 220731744, 817622360, 136049378, 567405395, 672559640, 852149942, 161224065, 541619051, 4140767, 887840986, 86344208, 781847785, 791979936, 563814593, 747812457, 179683856, 732573277, 8012583, 113280601, 701711283, 281405462, 234484386, 986971548, 613582442, 755928160, 870177522, 420404434, 385387079, 525465864, 746835156, 86112358, 805143360, 87614086, 264309690, 479542244, 901546727, 757966374, 71505854, 119065037, 356267616, 943035147, 457075098, 537364678, 778228279, 86760706, 990637298, 675747099, 212775441, 776128940, 502863331, 624936014, 232755318, 671363842, 824227936, 555426542, 163643256, 247832749, 478255076, 252246041, 780242865, 146724841, 676028237, 273318819, 898624354, 17118941, 548032327, 642012435, 746672410, 868445473, 511220916, 456308463, 962046814, 69052136, 328940311, 529108862, 382239274, 719803978, 13380483, 626197484, 755958216, 381140886, 91195987, 949616007, 588800781, 239754403, 184354164, 437727307, 411882831, 477061208, 133143624, 688422495, 618713301, 950540653, 738269626, 79109279, 712077402, 343528758, 557672670, 817664751, 396288942, 388250202, 615133732, 937320599, 457460892, 247569409, 285446341, 348134294, 154523187, 319806933, 314209174, 211788541, 319869810, 58580367, 632028124, 598915575, 20589989, 594932592, 894036293, 782870138, 805190602, 508846732, 37189913, 985177519, 143320987, 71546484, 91725654, 601634861, 118745137, 711642627, 981198655, 19076893, 771950628, 663244906, 530468593, 400810872, 936065299, 980750762, 769960072, 50875341, 949320195, 497202663, 724506753, 74898945, 784616279, 939125484, 587964061, 888483115, 845309527, 293541380, 677487618, 715913923, 696606735, 623914302, 706285501, 697926545, 865367171, 2260525, 17623687, 427107899, 952455269, 487852425, 849522563, 310828363, 230442133, 11904631, 329880248, 390939478, 217030279, 578339172, 155252167, 576746105, 331872372, 500160465, 815875265, 807376603, 854338713, 856156583, 965676433, 264663088, 448835037, 663792988, 512271889, 843133792, 823279228, 452058650, 922760800, 751148109, 492056562, 871499095, 713864422, 167217467, 899965212, 460164429, 109912322, 367328915, 441055036, 662027050, 57931493, 482449011, 92932139, 879544383, 381417942, 579803085, 375391274, 168526460, 419342148, 429402853, 568411552, 316562614, 820690813, 740252352, 854371440, 725884366, 138416144, 431894350, 676222451, 440173517, 44964849, 128660320, 424850388, 859952894, 187361962, 311724788, 220260058, 750434919, 38441932, 530637940, 892249107, 69241158, 611866252, 870911800, 431917970, 652775570, 730437539, 693176764, 782131924, 826499267, 656468739, 34013606, 276863490, 808125368, 496010142, 571568834, 957920477, 100107837, 185387397, 484157809, 828635340, 350774354, 441639091, 868581448, 490522560, 810610614, 169001940, 344682003, 833509258, 553711313, 603108897, 447482067, 164291439, 473341391, 74945428, 515701197, 824016324, 134265505, 568236274, 295318119, 967338382, 550917044, 217477370, 240895936, 724650227, 609125545, 928996916, 114877175, 321425652, 625701434, 136503648, 714140983, 305326744, 719690972, 522718258, 633637011, 617205657, 695099808, 731708818, 621805192, 63441095, 692145738, 589820550, 223179659, 794967342, 23815935, 175902725, 869059125, 545210286, 971988929, 20063225, 653255871, 261837209, 470108589, 763821991, 510836673, 625837876, 542166331, 267612376, 877763274, 450287219, 636910749, 672213937, 589923727, 152830154, 990283364, 116391117, 766339349, 499438456, 372650456, 552496177, 345751481, 337170349, 777750869, 900669647, 312324834, 14275486, 845152122, 547879523, 521544163, 78659278, 112166107, 553466046, 570479008, 205487084, 605725481, 681766731, 785727674, 491256220, 219361728, 426027840, 799367136, 846143222, 631891486, 232764369, 681053075, 994288090, 932242604, 757218317, 548126981, 341289461, 6298758, 194181230, 965573430, 100768608, 734209639, 193285256, 975096978, 137036929, 487230087, 810143575, 737225621, 856237063, 756059796, 329070780, 302892146, 564303820, 139337790, 995890789, 531096749, 638350439, 529792389, 191102576, 406696840, 332455896, 962425938, 860498904, 891168468, 614888218, 547557729, 547795401, 702760083, 505258090, 464146831, 424415551, 401420245, 528725804, 334151445, 391512840, 716372627, 475925914, 118722588, 505452021, 338248000, 520888368, 22349060, 590484916, 843541055, 339469615, 381199592, 124326027, 24217575, 999815362, 897814078, 728223823, 738271851, 482666358, 593663127, 460672264, 652374478, 780685445, 621794834, 50767091, 86505102, 912612522, 190767517, 1871985, 397328264, 298579322, 833724824, 729541775, 233848373, 303361785, 935421926, 53414866, 742741467, 51763967, 611385144, 144029340, 654041418, 148224019, 530372062, 193356300, 437284137, 670368995, 484946693, 416329547, 825887630, 584356030, 570348692, 279726222, 577811089, 447846434, 213234759, 974359258, 425724360, 994570925, 71071742, 425263332, 826908911, 904726513, 227040531, 839107015, 300469658, 195060859, 2289429, 837470505, 350711754, 401185823, 438738899, 390901401, 52337168, 785674700, 584370534, 419256595, 748409, 495722458, 81024645, 468978278, 217949975, 424965044, 571432751, 690286860, 909154736, 491676861, 364581496, 157484010, 271364696, 922354483, 96606874, 962421800, 771876577, 406338478, 418761804, 450592159, 974973624, 661910088, 48411278, 175618490, 194575908, 272245316, 293579277, 920645060, 828718350, 453479968, 215212762, 205888153, 823163658, 215401550, 517134773, 268499232, 882334105, 959158582, 490774657, 20640556, 700835131, 147486728, 899706058, 883223294, 857265149, 251792819, 897561659, 386020418, 325383383, 709181159, 844596424, 846784220, 349001843, 129532931, 267118554, 915418214, 296057519, 547177171, 898517196, 435889354, 710688690, 90916040, 283877776, 3350216, 615791703, 957298136, 108526394, 942993268, 103804371, 849035531, 483568755, 597558494, 746637604, 338432128, 875013466, 747730800, 653684280, 331465656, 460066004, 54287379, 711223124, 65753215, 743891315, 441137911, 376144881, 336459375, 247756129, 264110684, 679541878, 342970285, 123591471, 525242846, 881937584, 38731636, 709839649, 415346612, 607520142, 998165722, 708008452, 230974031, 613439657, 881921259, 8554481, 665581745, 464310696, 931786718, 241662857, 648143259, 125643562, 807852034, 214697729, 500312834, 477466167, 36795400, 969167952, 792352203, 61191577, 377550700, 694973649, 542255720, 341555370, 497570807, 323967320, 394608009, 117566171, 52287123, 892997003, 233474931, 429997905, 711395347, 91233613, 867160743, 612099306, 962643056, 180282770, 87987125, 379344409, 626006254, 645309262, 216083745, 861855162, 434955730, 673311330, 600728610, 935517234, 342750454, 313391281, 450330793, 10074268, 578117356, 56631480, 891393404, 188353175, 601901882, 284275573, 99418601, 665687883, 119905934, 442208130, 734278507, 364742715, 392296036, 858537667, 79888001, 624751109, 605632567, 648904217, 217257553, 93375929, 929223456, 51070403, 881562652, 691344005, 620618520, 537644698, 87823694, 83566536, 627498574, 842618166, 770195778, 27820926, 245542445, 92049370, 787116375, 585243722, 796115912, 400432045, 676757414, 228915034, 377934221, 493615788, 825221803, 754187462, 538531721, 498196200, 528495315, 572651704, 263072857, 750750746, 251927228, 388043031, 473526657, 813800355, 257800136, 7064253, 172974928, 271587659, 624048083, 244381206, 200378611, 892584536, 922320537, 40532543, 789895858, 114256685, 599358385, 480784817, 752630222, 721248970, 394367649, 950417504, 182377730, 638681502, 521463666, 30922932, 49797574, 875264020, 126136055, 629344373, 333625827, 826236193, 180572353, 328919137, 921656748, 738531263, 71768939, 78738035, 127555293, 97703599, 79293824, 122791375, 959540402, 795529976, 474042132, 952786914, 799606439, 813653015, 915917101, 293366330, 439795088, 298468440, 538904183, 757771561, 25762048, 722119705, 640887895, 216264085, 237918750, 950312672, 882779638, 427047827, 117315150, 552089515, 152969248, 921694485, 527838112, 902578968, 807255100, 996536900, 303682615, 582310999, 562189493, 996752140, 510173610, 63239799, 939074807, 128145299, 645302997, 845454144, 502909388, 675649846, 137930630, 331521371, 816282875, 235064446, 272905120, 705436347, 769870389, 913333125, 256708758, 342033540, 910429185, 669977877, 169372784, 880651391, 894490237, 808132898, 920894164, 557799650, 310170262, 947213333, 461716995, 201173011, 298350369, 430298321, 65133590, 283041943, 106592939, 191477739, 917887830, 639517787, 278177311, 619412603, 404840084, 184220544, 39435002, 919160857, 582470169, 621629562, 264481097, 56626290, 85660658, 583993093, 983181265, 111074458, 905843658, 183908312, 182191419, 36770165, 126322922, 717246190, 85779368, 179168427, 819257474, 245180384, 185926034, 918095720, 849784382, 709230022, 190256467, 84978328, 691013072, 684879058, 840426196, 534196961, 538225751, 766533403, 107624636, 341103079, 721952656, 300930542, 729795832, 771455433, 398344626, 227654387, 591686375, 170487770, 300734072, 526166348, 976116815, 405933305, 408533814, 429611754, 386154102, 960093924, 935780113, 768829298, 553506647, 359482490, 908711177, 639227274, 754835694, 106744368, 158747716, 584157048, 633829307, 738183213, 434470907, 480492356, 949610515, 219547608, 912787970, 468109622, 529006236, 451630133, 85279789, 140277119, 229226059, 74800824, 843496904, 49853335, 557702905, 239571507, 45033050, 127574088, 999090142, 164885134, 701035946, 207456138, 736257152, 370769939, 322938402, 248011321, 211843674, 763903787, 411589190, 845851958, 894946414, 596897057, 729354895, 835976391, 588453981, 419004337, 573405858, 357168519, 256924132, 38478278, 516612557, 109634085, 186550141, 519654072, 687467730, 401975577, 412390480, 734347103, 595464727, 790054555, 586210219, 266820253, 115017989, 818436829, 19466335, 423489876, 611167695, 184906221, 443986363, 363648720, 697968759, 183753675, 208886706, 978605291, 199230167, 668306440, 862943055, 393121474, 399491488, 716811188, 95904918, 150815534, 634221940, 572819325, 516701567, 247729308, 628237311, 950237566, 895932832, 798344156, 361477293, 200768694, 453130992, 449359752, 258566437, 46243827, 340415465, 797314729, 225027123, 347926855, 549462741, 470933245, 784801966, 52544954, 266884719, 842243224, 310448042, 234059330, 198200386, 584267595, 877184380, 532463005, 623505077, 341146720, 371333353, 780785134, 584962338, 328478384, 904400789, 604022682, 54632598, 15002393, 814393242, 97911828, 859263515, 341602409, 202651471, 802440966, 393875666, 798141569, 657216905, 475473344, 305570648, 879895344, 311182816, 503007520, 204679800, 112800049, 552372186, 103507485, 568935452, 471900255, 776813248, 135644437, 430242592, 355121162, 124079247, 183749289, 202908076, 459297077, 378944189, 84006778, 59606441, 362429368, 408957821, 426612448, 366222960, 704525349, 440217321, 526590265, 306525505, 545564690, 571423800, 200747844, 92587980, 649924512, 357848956, 201065780, 475542486, 166751374, 80874539, 872454924, 248687765, 966651965, 38318885, 843776131, 899727307, 249155291, 936925224, 600114357, 811574873, 714596718, 316068261, 740873555, 939931805, 489505624, 318524570, 757761760, 41051871, 818421349, 754888238, 474363894, 680246990, 160309972, 714772285, 652697849, 39597100, 737910767, 77723564, 603530388, 160143507, 392356694, 956440454, 726704272, 716666577, 801021845, 679512910, 433248880, 404969841, 86362730, 213482433, 42799231, 884818915, 942564501, 915415562, 62731113, 541350910, 372020485, 477893897, 558680170, 377409722, 833501189, 248150898, 819450718, 243891765, 264492000, 525003063, 701819086, 19334263, 277229924, 211826003, 665873900, 821325759, 291892742, 859145006, 941116593, 854211834, 49937437, 477993915, 596850374, 867500576, 375515708, 707920793, 264420889, 143076388, 953149265, 474535451, 557728834, 512914972, 545772394, 180787804, 330944778, 937371596, 941638649, 33431675, 562461142, 484413156, 845083520, 628496244, 518307208, 711735032, 647474433, 779503618, 635841755, 445296913, 728014794, 277855213, 216312927, 474362320, 665940801, 87577400, 373281666, 724019670, 773558086, 668379183, 795613988, 672700403, 262339129, 526533009, 929889794, 372247405, 521229665, 4632829, 948506, 107082948, 884305588, 720569008, 486753038, 295092185, 187592101, 272527783, 77424524, 895752952, 524405439, 179788361, 691524025, 314874400, 423003750, 100239226, 567008113, 122943429, 658319050, 290175079, 528294576, 3284332, 729376166, 189551993, 253735662, 43654149, 525657884, 918903276, 758259463, 737754704, 748725568, 765330318, 374820142, 430426123, 666352461, 795536991, 751210171, 147885981, 797782296, 210486817, 979519939, 640514836, 978898136, 805150856, 975538087, 25129244, 317196567, 837769484, 946120896, 171142271, 175534373, 71875114, 818527879, 897417158, 14683206, 368318848, 362495724, 942696340, 287220134, 740682767, 672587971, 994514346, 352200106, 901341120, 741634352, 365523242, 175830274, 205559885, 932239511, 223459315, 391035836, 745033133, 556014105, 860808847, 620555889, 936529086, 736923056, 15347472, 152299892, 626848976, 488011092, 872214716, 788083000, 712731518, 46402150, 283812667, 287152900, 999509079, 91787056, 54353312, 535770711, 398031351, 973077100, 628658777, 319751113, 608596887, 25426624, 29218354, 848240022, 381779503, 183002637, 596317682, 612654818, 311798927, 890192279, 162592348, 682405072, 280452552, 649296498, 161946195, 704866058, 373301125, 24240648, 811162765, 455055324, 943545661, 898432924, 625404904, 536175613, 995558019, 424925242, 339906459, 275353578, 932953614, 530991748, 228930954, 210502813, 638593549, 721528215, 521436039, 592242112, 803456272, 467243049, 440681158, 914004253, 941588067, 868373972, 473313108, 589745916, 82387606, 512805510, 935015966, 801510420, 831895402, 917256196, 395199427, 918303299, 910341028, 603262277, 990717177, 864715753, 34221122, 237512276, 707359434, 323871154, 285521034, 413451141, 922395076, 785651558, 58178508, 78137318, 40046964, 721228884, 956932624, 193175243, 473142134, 964829678, 508130174, 547083159, 474063868, 708204551, 459900798, 874856054, 177083647, 513680207, 479823632, 73483348, 220716025, 716082181, 583996669, 33717053, 291771460, 598739176, 842531951, 493533534, 382094005, 330203219, 88590176, 342566941, 9592778, 18093974, 653463570, 685705472, 867324153, 956270324, 645749104, 51861396, 961231909, 610754073, 754862549, 169709719, 136828942, 178757699, 892866063, 326505142, 432572518, 932483226, 545929556, 527796754, 350090601, 248487775, 214528456, 278770827, 313083325, 69793354, 263457751, 726233065, 498902895, 317041374, 297736231, 173687318, 507374740, 74477233, 176050302, 593156642, 753312573, 815150917, 4468228, 655891926, 291431029, 35927850, 874937759, 59595969, 620758349, 718351367, 118335202, 830834324, 115709406, 173060826, 961959088, 392600159, 920457934, 108856859, 522411877, 521943986, 848136016, 940563981, 575466256, 288396962, 101114054, 277295774, 261787053, 905187805, 967223851, 637223235, 784266452, 489649076, 242306845, 328819445, 21926824, 136719492, 242119020, 562125452, 283268844, 178526812, 777233781, 894999284, 733248658, 776374270, 110291347, 546114823, 464958665, 806651957, 393154550, 979194432, 973520603, 734781196, 532334153, 719467841, 156383950, 961993688, 407337297, 435191286, 703870102, 114555249, 726116751, 773366271, 549377833, 206796906, 543399476, 260806595, 642247550, 899107805, 575897200, 99377833, 479604758, 757030463, 768098324, 27408988, 958373561, 757336917, 291971670, 445652874, 505102552, 511158675, 702804435, 519867211, 785592050, 453934677, 68938951, 529886133, 860768787, 930354649, 313821678, 138443453, 574687727, 59494932, 940197275, 955745471, 271515512, 404220934, 964328296, 21271689, 357153880, 915273959, 794913664, 477194292, 608605657, 560006383, 731600758, 838122492, 335765952, 865721008, 753533842, 489905335, 744883646, 175790601, 895751673, 561101417, 386205128, 204850883, 122651173, 6980006, 658010484, 609713378, 95507699, 873253258, 806885202, 450189163, 896703812, 197717430, 327433104, 218755084, 220939685, 433196353, 155861496, 695322850, 353991352, 19768805, 454431501, 133124424, 605539343, 405596993, 95348945, 240494858, 833362727, 957335754, 823100326, 534367323, 545945619, 709760797, 125664656, 823397621, 643351656, 380162738, 979125987, 527873317, 820468285, 209334965, 929023173, 42862342, 852546808, 54861866, 552272376, 861786554, 571973991, 947192210, 730801856, 845194667, 49469063, 417307132, 958547960, 72624546, 1615670, 513297278, 768882981, 78047438, 240298192, 977542793, 549251586, 575861556, 636683100, 909928448, 169149185, 990655181, 849870187, 408169156, 594646729, 596661911, 943421839, 50316642, 659854218, 455971298, 517878897, 88537811, 337629864, 10095268, 123067280, 881920341, 581910567, 443676615, 36732507, 947554109, 298655534, 99682003, 6338124, 608330718, 699608619, 823207827, 975165820, 19055661, 803593791, 636448246, 257007534, 731561686, 553613969, 714123021, 455007095, 34216505, 273681166, 197794327, 111769864, 616046687, 211044401, 977248232, 723644529, 224485885, 229803778, 573233630, 168252492, 349833700, 654205146, 937269452, 827267318, 327353755, 428966758, 130841196, 936438713, 505584436, 940895692, 766748863, 881740393, 600263027, 239042789, 691448086, 74488244, 286176939, 647685433, 976544472, 850615956, 591885995, 455812892, 104092954, 818246440, 321176214, 105165122, 87063581, 40485329, 837957204, 898619448, 36785218, 311746264, 238772474, 906811361, 453503012, 225162938, 162998782, 73041937, 777832344, 518548902, 837811393, 256956581, 604986846, 254338530, 19730164, 102736048, 358195062, 407143528, 692285653, 172933155, 77761503, 453826384, 878595209, 922399691, 792091082, 236100727, 580304777, 6562353, 502591782, 326046719, 652721772, 945237834, 963886226, 403348706, 690617148, 37315395, 316877355, 184089679, 908880885, 997552146, 577313311, 810084723, 516359279, 830603774, 497500869, 724178579, 164876799, 975585527, 561703278, 825228897, 959068306, 878290811, 172607591, 510619271, 539372515, 753431969, 849782015, 537607990, 926848895, 304671465, 593056874, 855071316, 725025220, 68686497, 149862062, 242379471, 103263006, 638554558, 124567681, 404333717, 911179297, 601100921, 399694760, 718571763, 907577221, 656676362, 282000413, 12562007, 663362026, 704535831, 188198683, 100851040, 913916849, 119740804, 358635698, 826711351, 105520426, 236646803, 372097656, 772859598, 296411656, 239349222, 592121508, 302831716, 390198882, 305052638, 403775234, 333927932, 723031554, 919822512, 632309115, 613184520, 641937895, 571070410, 759793360, 975078764, 853667276, 88526843, 770268827, 839480365, 117821186, 94635994, 992113888, 305034069, 273297759, 752608560, 78722986, 241993087, 173289405, 78317812, 205977220, 454901351, 764905261, 971364602, 916690310, 638312248, 126766843, 743074026, 925888321, 352629267, 463735957, 34816479, 3405342, 871058522, 639133405, 799352916, 523345661, 19362118, 748750382, 347773985, 700159445, 143928232, 667672679, 666643528, 150551777, 566155617, 370512425, 667572994, 396010995, 347832460, 926650446, 84560958, 163476398, 598327923, 489894370, 359027408, 782208897, 991901518, 66050267, 352340904, 538523599, 768038896, 466054734, 187134244, 751355089, 649245498, 673754174, 782828867, 963409318, 967569407, 643505415, 284547763, 669039635, 240011413, 250940020, 576638830, 746430385, 311466718, 534006138, 853821118, 288436271, 166870935, 883171759, 923801905, 320575222, 752682378, 133149804, 498490236, 230433147, 896279537, 620219198, 386934472, 552714381, 516739010, 970156993, 57028625, 550877074, 878750343, 57559223, 186060524, 961677821, 95433859, 704122766, 153648710, 21472409, 66013748, 455282519, 920309781, 106778149, 120196164, 963593818, 971567182, 731937135, 970373346, 525680266, 822268993, 349609301, 374967580, 863221182, 861916047, 189594999, 592097472, 776482170, 869139499, 367185231, 904816384, 244335500, 932857703, 404164279, 198966603, 630206346, 282157196, 930047612, 697844710, 750101564, 668779516, 446298847, 482597831, 984373493, 24750675, 402347750, 102601815, 961890668, 865434554, 374693206, 166136396, 923608089, 527964188, 851504373, 240655036, 301862257, 13062665, 161782623, 417449301, 375937632, 450195536, 306960900, 713820791, 478632366, 658923821, 465252155, 758662530, 99723019, 861415296, 685091871, 334060223, 611488398, 943561373, 799199301, 138651306, 855760524, 969730306, 890169940, 734065651, 932284186, 160443, 282964102, 769839276, 792455972, 820575709, 718861953, 323363753, 500768088, 578280288, 28946047, 582302665, 668392270, 534821373, 179471288, 66366308, 942404528, 705791162, 983144551, 964275701, 56456866, 794770249, 240041924, 576502758, 926295074, 250198881, 996961917, 643493386, 918402940, 98769416, 325568479, 343399564, 569483609, 600390597, 610067734, 48383376, 540799309, 34100504, 860128890, 483005372, 703634131, 506067433, 885902400, 179422739, 815442619, 402251067, 836530935, 333010591, 659249276, 523597233, 961700762, 790248442, 254967599, 530017937, 895684710, 270965132, 272939117, 498342746, 927728691, 705553687, 931844217, 365042270, 731160388, 996812689, 169616221, 62050209, 348021200, 391207424, 71710288, 112175417, 771427141, 809924849, 709593667, 14896628, 665664289, 218396341, 300312302, 880130758, 131346774, 944317605, 377584193, 889711098, 928102970, 50483107, 695181718, 398212174, 565249741, 307458973, 196442762, 162778488, 706451985, 515753091, 643824570, 622036267, 107365184, 413315744, 581871801, 928859392, 114713743, 65035698, 477227887, 382801976, 551605897, 29510124, 800185131, 646794887, 537423042, 872929793, 610402848, 181758001, 913096392, 201614655, 147946010, 14778735, 184781999, 21898672, 826710595, 924806876, 441024743, 189692857, 69127222, 88521536, 413864624, 587571748, 388355164, 716652181, 268449697, 669353210, 540030946, 439981494, 669157691, 888848494, 129139164, 150427790, 64684672, 30917080, 995019983, 556577852, 815114813, 377776763, 274749292, 990610415, 857547148, 568042489, 261654836, 765905201, 780836563, 76088551, 412448612, 953660936, 689219834, 715573239, 321125180, 805138467, 714727928, 748052370, 182319095, 339779140, 788301948, 659879246, 59914901, 335678071, 484196702, 916798614, 533324291, 861789009, 779941012, 130953975, 816528133, 177148151, 976440530, 591558949, 906874509, 81770228, 460526135, 188938249, 302367797, 877541017, 926234483, 535357490, 977969258, 952410322, 184022386, 39003411, 903852188, 85348276, 547648490, 54057130, 328089676, 464778990, 496054058, 230688743, 185530620, 310662461, 165649843, 424527480, 835736114, 588254525, 234436256, 777484902, 451683784, 58206789, 116631165, 659549711, 629132646, 383176279, 994688823, 962737996, 616662218, 430400519, 476607525, 975522109, 331607755, 360697667, 686121701, 301329398, 437586673, 827898356, 388474262, 757602532, 931154599, 916092646, 283025757, 36207078, 194145142, 137873138, 135284158, 319664097, 742773209, 922731064, 844804024, 583132138, 852487272, 133302308, 179386548, 762960727, 203975619, 226450564, 753831170, 300856526, 114100917, 274075126, 22332310, 610052763, 934197148, 463322851, 783030817, 794901807, 23841582, 838265008, 120972924, 281476004, 744153504, 675784872, 750629951, 175226288, 382271713, 526433287, 379075880, 677105847, 730234073, 510123284, 330204216, 752407682, 764816887, 566453116, 103960971, 935922841, 363446576, 920437435, 740381461, 936363920, 176130055, 42115500, 255378193, 439292300, 732265865, 770218684, 701485694, 583083870, 735804884, 587427334, 17117225, 972806332, 719025108, 434910647, 613162157, 835113624, 829399728, 172602352, 385842623, 452998941, 430351154, 45639022, 674194338, 657504549, 940680639, 332055642, 599173631, 255608157, 548671573, 560388145, 746442031, 927018562, 278156379, 110621879, 533205333, 34865517, 269345854, 905837859, 753900063, 294355904, 11788576, 625789132, 233510107, 749343468, 446022177, 971084039, 102298594, 106710124, 871943636, 203014562, 777996490, 696273653, 234742677, 872765220, 528966788, 650351613, 603726936, 727194423, 631536945, 256405696, 313613488, 353758850, 454020547, 898318780, 246364530, 522641296, 389487116, 484669193, 632706081, 644035728, 753215495, 221810580, 741894816, 793097232, 417698328, 258524998, 649464364, 375945182, 311060359, 406508178, 954803508, 619018236, 296427474, 269710041, 30501269, 570102791, 210375862, 302082492, 574780808, 173975181, 472334998, 28942551, 984195213, 161853795, 831483579, 221920641, 109977589, 702058424, 174411089, 128827548, 789837512, 375120260, 413241082, 567470001, 304998304, 320734351, 318633376, 731305850, 160137804, 868018015, 765738958, 741753847, 803794131, 133797182, 466579134, 339549015, 609612095, 956596358, 647034370, 580669127, 920440489, 826931134, 598813719, 183457646, 509255987, 476024676, 300576722, 466456056, 325069564, 862338800, 315114886, 757911634, 845276726, 960986799, 896058008, 662862477, 825149990, 88481152, 376930138, 718400439, 898992816, 105268843, 947679959, 592654934, 165796903, 444951888, 196690548, 775181734, 794517924, 337391605, 347551587, 757013287, 861921337, 776271821, 494029462, 42715250, 768490002, 164486353, 818318162, 453956191, 277639886, 818373611, 28978154, 168069102, 71722770, 761885729, 68161779, 584541940, 457844970, 779461685, 245894470, 551361999, 472165826, 892135874, 46979102, 989097519, 918195393, 531440010, 889178970, 233894267, 105411490, 557532964, 944475503, 112412588, 451794403, 981580368, 769680952, 154713865, 75224331, 50284558, 849876240, 717682888, 537900712, 291837346, 867781677, 534507495, 453860107, 349813936, 762289525, 342065168, 313756921, 319201357, 968554905, 635754486, 765545184, 783717681, 238825992, 625690441, 159361982, 715852723, 601592795, 326948880, 952289191, 674878583, 67355948, 321144043, 9936221, 580490255, 818489650, 391836916, 979544037, 213208289, 33951904, 277958276, 609853875, 434822608, 404856557, 21601325, 483582949, 919693768, 701564212, 210157547, 174381896, 612389734, 205121927, 203720636, 853245521, 948045410, 545371629, 721234825, 887059697, 480681120, 207730081, 289037493, 149395535, 534086548, 130958388, 636980011, 333502630, 618462554, 386238441, 873850259, 647412661, 662068861, 667670376, 743391487, 85828842, 268098833, 800878494, 98573479, 902505563, 524152884, 556060348, 472546043, 117578773, 915773206, 8555030, 737673538, 30244433, 171666314, 640122062, 24423426, 472991661, 581217350, 868494291, 567023143, 600965503, 683701715, 211404615, 365942840, 199098416, 817193507, 660776678, 323156226, 796062709, 142353573, 486646916, 865666700, 640090457, 384798734, 347537822, 905839951, 993142021, 106480410, 25296711, 505098034, 911677609, 667831823, 123235749, 565498799, 825407999, 902158133, 636442840, 142866107, 494151391, 549852349, 189070258, 679892935, 722305453, 551494510, 487215855, 131801618, 292234966, 220034291, 748848409, 724290421, 594843650, 787943224, 667595084, 784894615, 968075740, 930168039, 980773346, 92167655, 257361651, 324873234, 987669240, 47617470, 759947825, 440448856, 767156798, 361916814, 177800884, 189604022, 423544098, 693663371, 890366692, 930173043, 830535563, 536282282, 842465026, 343678125, 829854422, 160323270, 96022391, 478426562, 978496738, 379037804, 185935994, 695532848, 484364274, 448181091, 889629770, 558111319, 545003977, 955067283, 314738226, 328065816, 618732281, 441638445, 269496552, 462019346, 352226698, 896218658, 897653854, 329596019, 471841760, 457629249, 137822287, 927848639, 546545773, 110848430, 780863664, 268982599, 552677624, 266216467, 457107380, 748232602, 968590703, 678588137, 720381924, 290493803, 704497957, 935813201, 847324213, 992708790, 103040611, 678808499, 660143173, 700592283, 441239217, 553754414, 832407718, 750942746, 578892009, 502935668, 778606553, 918382193, 685394886, 438571867, 516820459, 840969406, 863895459, 879151230, 224170300, 350795422, 741192125, 648700340, 983376217, 609869586, 124321095, 264170742, 612338647, 875376010, 273104598, 55469953, 21310456, 63275679, 84295111, 497532948, 53499514, 277590663, 339320499, 752064798, 999585609, 752899672, 580277162, 141656967, 252294374, 377530023, 512120666, 656466646, 907522652, 566777593, 650573552, 557346807, 515608530, 178937673, 502623202, 277323611, 84607385, 997029522, 229552075, 915080767, 526775168, 66255853, 65014126, 616026555, 614087484, 807772040, 844040435, 335848688, 738442708, 749264525, 651537639, 119584462, 501973050, 847204192, 467030377, 896541033, 232450752, 116343004, 263881077, 428175706, 878574352, 110761895, 717004533, 504761031, 309475093, 572191966, 69183634, 733235884, 615058715, 519868840, 557775964, 287085427, 210730684, 471562795, 447170604, 860982372, 995540584, 819962002, 265992196, 300105269, 972892972, 332522689, 870951354, 531904469, 622923672, 513010038, 572444061, 740686290, 571108905, 58291933, 465133906, 467259103, 731008374, 979987240, 36438480, 188664775, 494522612, 753598047, 620740733, 768411919, 335205688, 701699997, 790020474, 508623558, 921533586, 522150636, 41857457, 526617665, 913392228, 864632768, 153685883, 292614187, 18986731, 688479330, 177014293, 830498920, 482889229, 503500942, 505867971, 910278109, 438834476, 167173459, 665204976, 42237748, 485387415, 220831468, 338903369, 588418937, 30961685, 326481409, 240642078, 877067029, 434014034, 724065998, 619920727, 780044785, 698189275, 878481530, 702225458, 287624002, 471253142, 818059799, 297188677, 161291664, 306435471, 566912987, 253311258, 71457220, 835702091, 347401503, 572896298, 292926076, 218397318, 452049578, 73320953, 992702335, 691524291, 857036978, 933660122, 497794194, 717129134, 813691244, 285952473, 995264232, 391554424, 696159076, 479560480, 769944023, 230794430, 725777449, 587612929, 901254839, 369082330, 464209121, 655798949, 318185087, 890189610, 289346903, 776610939, 967639160, 785361405, 878758230, 345456882, 6093387, 132944636, 427168083, 641378858, 693761019, 368131791, 844617147, 477914254, 556233469, 636941104, 196964278, 155596067, 875822115, 375228013, 984787188, 989784883, 226221989, 760208878, 424456308, 676617333, 977234816, 564304024, 679076100, 652006578, 697578632, 313674732, 849749714, 65557754, 594429022, 806412244, 710877855, 259733352, 755069648, 5277325, 930128962, 655219464, 319770783, 209452798, 699074050, 448707029, 773818901, 904579381, 779181345, 645242447, 794808570, 982796513, 871325512, 568303944, 567315196, 972093624, 346378613, 786802427, 909682846, 388367411, 284577980, 992416232, 642526398, 814628054, 949031496, 987973933, 409303230, 144255513, 754427299, 878533894, 763920283, 61095963, 794043034, 518633983, 736318935, 694593537, 607249969, 1271247, 882715382, 80304485, 478492014, 117757178, 247838470, 205877633, 505390633, 389839486, 411112323, 304299930, 179254695, 196098447, 799195422, 361144692, 725736892, 147774128, 130589577, 457177302, 714741813, 763897760, 321654602, 298100798, 337977052, 257357393, 897413694, 366993999, 155103024, 15258190, 762598697, 54997736, 453491171, 407417400, 906048473, 708606338, 692658014, 293904962, 775670308, 707729863, 805725591, 419436661, 968829389, 483360002, 732386186, 607098718, 570882192, 313131750, 631302622, 427414251, 132062469, 795950052, 98547364, 994920237, 499844070, 764842890, 795204780, 450664424, 694903676, 903642934, 284031782, 977861733, 299998851, 569283937, 726681526, 496707598, 984314538, 793242284, 995971396, 166579315, 902787910, 951842526, 434055251, 892231770, 582579108, 83581085, 347956689, 860999320, 671773164, 491476234, 734682256, 676937856, 901046134, 653517894, 739057599, 59658027, 861815162, 195672917, 824794507, 90875796, 291462604, 916025392, 169370666, 643797238, 66780642, 658242365, 133250696, 23825063, 359165262, 576547351, 45912378, 623727067, 570730876, 183685105, 884373251, 571958123, 788044057, 2680890, 3070028, 145965328, 273229439, 176293222, 970903491, 776188672, 179216860, 105537985, 866338524, 886790454, 505677907, 926192207, 228941840, 567509910, 612110366, 266425996, 494798659, 818069063, 705536643, 42748009, 998500268, 189531764, 564649762, 479886835, 771222749, 929247156, 716644657, 712124746, 843192698, 801793941, 801475626, 111825321, 804367251, 452944764, 500194708, 262189289, 813548096, 914341953, 335496653, 717103655, 436111796, 443585642, 678431559, 611136861, 373071016, 391231650, 981091484, 594912070, 737337302, 87162128, 544972234, 305468137, 747728665, 679772905, 148288668, 310220689, 60297795, 396602078, 792350915, 875709448, 311997068, 846704297, 57149446, 258839941, 937899439, 930554090, 573009559, 398544864, 10050845, 412253436, 902526869, 673890562, 555300862, 490903134, 110621368, 319581203, 715032450, 620505756, 421470962, 241062075, 504431927, 214288513, 665081715, 653648325, 741507325, 355241793, 25759565, 520549527, 630713436, 754920658, 186885459, 637690277, 221764616, 754474771, 380741349, 896174987, 45177104, 382101513, 691999147, 653146504, 831658771, 622252475, 859718133, 430013823, 103698667, 735284122, 850895488, 932875160, 336581064, 78487463, 574323020, 341034898, 215138568, 107496130, 912392956, 926313541, 653145079, 893689622, 340335917, 185649751, 998136694, 589680291, 469739273, 616029938, 725713241, 739672944, 101318080, 635284397, 602403562, 940545552, 638758720, 555827852, 448249907, 927071018, 822265606, 197373369, 471954425, 551078915, 876772729, 469054824, 828308954, 811180982, 886662211, 283062891, 827918806, 169464777, 551298984, 950292521, 805150079, 918539117, 291771299, 770958556, 743706983, 848063333, 482833928, 35728510, 461053347, 571059803, 602684727, 193036830, 184621126, 24666953, 753954932, 14224950, 888748067, 998158070, 253552256, 185335919, 838662911, 113404379, 40284411, 773761877, 733963562, 773549164, 614504827, 776460785, 141704955, 267981608, 761903232, 327374516, 11330856, 811485921, 88898305, 749793651, 900924322, 573719106, 125296467, 682770712, 400405580, 362676768, 50953117, 342388622, 726036155, 376910752, 912176386, 828714871, 122833583, 368987390, 106514874, 503123914, 788066321, 105113445, 377647593, 742625317, 649671568, 896213779, 576115577, 46067107, 479030747, 165433004, 289816627, 925767884, 268803925, 544412991, 927878449, 177243323, 722114015, 677537804, 623902546, 242397283, 194692662, 86008206, 620092641, 887194408, 849278251, 283205046, 229145691, 96896353, 44516211, 464601228, 427876043, 41426318, 513539191, 882570642, 822570179, 655903783, 972926188, 476103312, 484847365, 985024823, 253990032, 211772454, 715982760, 991240993, 46986042, 410103078, 344371320, 452890703, 713099151, 76576262, 278466043, 206212847, 665216699, 896146751, 874333428, 742150518, 302210184, 652834669, 860796055, 887515468, 376144853, 175445437, 952213381, 658958345, 590702620, 643186069, 354414481, 266949514, 584873411, 117105688, 65713067, 452994669, 53679, 455106984, 138218568, 812920764, 745269901, 589856538, 493770319, 669615895, 373280721, 177685069, 691178922, 182653948, 439321596, 59867403, 787952248, 334041625, 591233035, 350916093, 536876422, 734060502, 4211162, 670311631, 181251941, 736086484, 77224255, 876573273, 452877524, 284082997, 660973246, 318396497, 168958041, 389556127, 541589573, 205511137, 549483164, 146148431, 281932693, 646709951, 826053333, 721697803, 296070907, 410560904, 431390746, 407432130, 164915777, 585577737, 491239779, 819046152, 335665184, 837447130, 763543207, 436002401, 705158149, 792295200, 182341974, 166967906, 212930681, 58410046, 740609478, 366313945, 182177429, 957104833, 171705573, 148129519, 159055207, 514786695, 943665081, 239227067, 100506423, 853928606, 473684019, 864766403, 795470231, 594630915, 962196519, 637826696, 649248043, 167439512, 208142841, 542691442, 346039149, 761230490, 26898055, 190033614, 776648294, 86970289, 868597812, 66639564, 934019227, 892018911, 220131971, 945714197, 769812612, 169455256, 485415371, 565031152, 805898803, 158187456, 962936974, 15853578, 144793015, 723598672, 943741511, 842567337, 196485038, 907548386, 113392127, 796876345, 302944116, 79752413, 592027769, 957949462, 108503217, 766518043, 698139510, 775504746, 160281013, 691942067, 848775337, 484403958, 126880566, 611713254, 972915279, 709014776, 401884021, 951895380, 110478626, 847786266, 213952236, 467269652, 717479912, 471412382, 419321005, 366810721, 779089534, 64914746, 186445091, 529615278, 914506580, 855204894, 393029752, 699948300, 721873083, 102293909, 236772272, 739417176, 812195641, 642530335, 78782118, 801626464, 685821963, 527299527, 593599558, 570125711, 2653453, 189979468, 912069478, 726969084, 972659275, 807477263, 645761604, 333523306, 801984700, 339952175, 994152832, 747780270, 761507954, 547190333, 662978006, 567510828, 573661445, 414151418, 503559728, 811969299, 952091197, 868795974, 394922786, 465410541, 989469663, 402142908, 159142970, 774825721, 840502385, 311390149, 462907874, 493100017, 422805829, 306961184, 740250980, 120890767, 19106612, 700362487, 604174148, 7506198, 381874734, 105578558, 840037108, 485472957, 146148128, 661492535, 341195893, 477174863, 59464885, 977754338, 732873151, 974157214, 961241404, 292609110, 851777330, 390178547, 831899799, 959087197, 268402630, 847362771, 583491851, 443763810, 267404795, 498875669, 732515132, 709802434, 760137428, 595054103, 71927525, 414732908, 46950745, 456280563, 936196843, 136365610, 200788395, 937570602, 457293959, 879647112, 288697091, 356961859, 593910129, 249461301, 990405248, 672771650, 62852216, 157980548, 563096531, 406762033, 186089415, 749736347, 16009610, 494564073, 714995306, 658973320, 884789123, 744367417, 474606454, 604771830, 374742159, 494829014, 709821981, 464755258, 782656124, 819643035, 686143508, 984251819, 636051509, 218445110, 558637240, 648582135, 147228284, 25323628, 931605647, 472194706, 861576313, 790150595, 104549897, 39458183, 820812127, 657219438, 213044598, 284877192, 148395261, 99225910, 718865311, 672628968, 687046513, 90709667, 926059656, 572249180, 744960414, 55099427, 237351901, 449645960, 712433600, 915669555, 752567560, 442244610, 299434120, 792753217, 692210385, 827695004, 23913731, 986408396, 417429258, 170097551, 428473981, 733528182, 661360843, 908795473, 315812758, 355261487, 193721255, 905669129, 666331780, 744975596, 498165769, 478144980, 468502167, 960982535, 228771734, 523539212, 578217251, 178110371, 593528730, 950934799, 460448041, 45150977, 298075393, 859973307, 15503901, 779445355, 280409033, 905760541, 238981913, 610041531, 992487550, 926963088, 450795553, 617306191, 984303791, 380793333, 674698485, 516330620, 643893716, 949394482, 207372270, 778731506, 268330873, 595237237, 432619123, 890174599, 435174640, 674402656, 641149228, 21613916, 411404993, 751601714, 240295885, 727173243, 237651434, 187805758, 933659211, 401574245, 977624560, 906875753, 82757334, 675098405, 501306633, 17428134, 389758934, 34076391, 36837551, 531122744, 211962428, 297051217, 904808326, 354548428, 553629340, 355075038, 293972337, 452312386, 605055035, 370809409, 463041340, 119621750, 787225007, 836330818, 772616387, 499000835, 239957944, 9812012, 56731767, 359194976, 117283830, 950416114, 272291447, 990226846, 395281006, 907833250, 889323778, 574080818, 979999778, 39460057, 837626861, 954735096, 829566910, 903055362, 936625452, 667717457, 770960621, 599286523, 109083636, 232349308, 464070087, 131480569, 791476700, 474812138, 693736583, 808335082, 438000284, 591623626, 212756597, 646434137, 769601750, 848431856, 674705700, 739596515, 6948533, 205664169, 80897877, 971828432, 70049486, 646279027, 21103455, 332543453, 321964913, 728024241, 878937128, 378347811, 933599640, 4182155, 429241141, 204978255, 599786456, 888122884, 221528750, 560720420, 620656832, 476211656, 799448569, 365297764, 118990317, 249595256, 301621777, 486401336, 315078488, 18130280, 616246780, 857020572, 34352609, 495460534, 769176726, 935219068, 99924617, 110548405, 576656707, 530193443, 201836478, 3101160, 310938411, 86771508, 745430877, 3394048, 918937654, 54598597, 155994831, 914554147, 651459496, 732594078, 39636927, 776732410, 856681086, 137376088, 907983438, 203969735, 425629108, 445364956, 425943659, 763432141, 747278175, 238057915, 499339142, 818229856, 945452772, 809316337, 50086403, 485485004, 644136459, 824884308, 798077648, 984616129, 970565812, 229676494, 972539516, 656874767, 533133748, 132039529, 77225170, 523935940, 646153814, 489012052, 836791961, 482405359, 445540909, 207495986, 49190739, 657367870, 16383303, 447493480, 68146397, 807583118, 911401677, 820039001, 820136353, 417895819, 60294119, 115874475, 856642328, 39287955, 414406680, 166878415, 450534430, 377348741, 994235314, 251003020, 39584227, 983204520, 289837856, 166848445, 292261610, 223699859, 270227962, 733145937, 387347639, 720815342, 316653051, 269538555, 411303967, 411997422, 895550275, 411474902, 509496011, 534546505, 168000885, 3984887, 503362386, 779788844, 95897269, 17000062, 918203573, 337544448, 955415918, 476834938, 864424068, 82078580, 499164303, 771795884, 228339568, 789738251, 608229084, 749047971, 389496945, 977699058, 80889384, 403020954, 260836961, 632059505, 255699681, 407722513, 894628690, 983531391, 432787051, 18591328, 315061487, 994177310, 61460056, 195103149, 20293248, 514826914, 941600627, 940392190, 836940654, 613346428, 962583834, 935504500, 970615883, 692303611, 650315631, 439047488, 483350350, 989687017, 386649121, 506671037, 497383833, 798433202, 717689056, 279301103, 223341110, 555107866, 228947595, 419159980, 501751093, 936536927, 26571232, 478855213, 249385324, 679142845, 461862401, 632598405, 132594859, 294068472, 26035590, 243747682, 776107656, 256103734, 765484076, 777973936, 395374318, 659413687, 87136976, 426290453, 961858887, 23364496, 412090147, 54021212, 385167232, 885467003, 864443912, 67259056, 697888545, 754265805, 591657785, 354909268, 554521367, 826163416, 994735244, 955512580, 740672088, 127318542, 43310528, 612637534, 69732749, 37230000, 276180277, 56623089, 765235422, 82553225, 481672050, 24198031, 977896518, 113389523, 491454170, 717149700, 451778500, 229633204, 206755465, 946243619, 850622300, 230347037, 652934379, 908805079, 501995077, 923862771, 740429973, 442322721, 595008835, 511409158, 134319136, 556544542, 850802033, 953725032, 299787663, 711814138, 617616138, 67122274, 838745274, 577298901, 396198553, 211039392, 703216753, 92842409, 329200582, 195568760, 944297660, 865953743, 562319499, 768185960, 241198618, 40965140, 13913889, 201871112, 481448062, 262049161, 603272931, 214336030, 154231470, 826497754, 480134919, 122526251, 804143696, 721769557, 128092637, 143217467, 320869435, 418173564, 319873710, 660136357, 7169900, 656518641, 914983157, 727707508, 60991683, 63852993, 433793150, 638860510, 581013005, 764744843, 812735988, 623965512, 667660249, 108392049, 807111623, 989019715, 115771606, 646013316, 863906765, 506947823, 86203375, 416689636, 463914537, 952004180, 246796338, 292630576, 513090144, 521730329, 648539285, 153265481, 532590999, 887943189, 351057430, 116565190, 86070812, 994711196, 530731134, 567684244, 48087224, 510014736, 67901396, 283891011, 371762650, 925895584, 638737709, 665136144, 149498008, 287883131, 280904265, 647399103, 862454503, 124333520, 675212239, 267525215, 966274790, 831234407, 499985566, 209156376, 404972868, 49948392, 120832540, 254788212, 439283170, 846092120, 26969693, 25844012, 203086775, 589391788, 100866582, 806827983, 676444851, 180230374, 846841252, 161232423, 560851217, 609964441, 437358314, 481653379, 629649214, 819821716, 158644049, 216655960, 823306681, 353115758, 852439939, 736311970, 685158445, 991237831, 652584945, 861383505, 769052992, 730477882, 393218227, 640800707, 713778160, 5552684, 556466041, 356469590, 399091405, 927374984, 424070164, 692550676, 13227574, 644259740, 934334967, 922174415, 961503373, 22024400, 898430086, 423108783, 604478137, 76580624, 793285391, 226799164, 445730559, 6294901, 702642278, 257231718, 699679426, 184751461, 617569570, 837255358, 803344297, 604498291, 502902443, 600688365, 639881229, 669868820, 241305005, 456556173, 302289881, 855678463, 501467613, 518292358, 990506389, 485485332, 873066079, 255065841, 745864632, 168995233, 321909498, 581251669, 488160985, 764708341, 292785782, 544696824, 149619874, 957016037, 717284535, 788808178, 74212381, 925315889, 253659983, 43509695, 130266263, 363518685, 877887363, 666263963, 222414090, 757257805, 572919394, 493706190, 146518349, 815628967, 853677535, 601954338, 506358994, 424283051, 246724586, 138734608, 622976103, 838555993, 241986125, 581453811, 440706213, 946007036, 564867991, 772371103, 260094941, 547539677, 43996176, 295111046, 548042698, 13962546, 180486749, 957502195, 127669467, 294460849, 272730713, 489685971, 591400085, 735563726, 779720617, 358478579, 624358205, 780132323, 686612103, 873542935, 720515698, 185064070, 300087047, 839011944, 149572550, 295815496, 603885672, 917021606, 414082388, 521738803, 203300703, 348215925, 116099581, 352629246, 353304501, 369216719, 946088514, 184640974, 643905704, 437912962, 798665912, 398183591, 449151843, 87946862, 448506432, 817697753, 177067442, 313913735, 110783374, 295267326, 971813259, 609856722, 32164854, 871986681, 980347146, 639324921, 694047628, 988716139, 915332739, 514596768, 871867612, 565852235, 628392365, 657646223, 937808209, 375465550, 301109488, 783535206, 199251614, 388463637, 3865366, 310403211, 877522588, 631547565, 5018972, 459922951, 655107514, 705308011, 964830916, 546640101, 786021234, 532813113, 634846117, 31129823, 902943133, 429974110, 828588628, 300381263, 182893946, 363419269, 484875056, 146650511, 533887161, 911616556, 341065797, 644119757, 768778729, 408593662, 49199417, 184690575, 561725593, 273633026, 310723415, 900099750, 366593905, 480529231, 922739507, 73132761, 137076018, 14708892, 617667628, 889328840, 606225980, 404342534, 859675108, 268274085, 302213796, 44158247, 912298945, 219171767, 278151498, 702466333, 409419218, 542825783, 456365145, 973910623, 992233859, 654995197, 352500085, 592390880, 642648819, 731271784, 319297078, 749845716, 122108465, 679222202, 132933464, 376718582, 621940373, 511285732, 544758082, 617434462, 405983337, 923942527, 646073233, 266579699, 440621222, 96004245, 907807522, 620049590, 624075338, 299456245, 47957838, 308236532, 157222307, 10343310, 250308047, 260802725, 95793170, 647939016, 97568977, 701331229, 655088502, 617317111, 506997225, 763337808, 717582220, 992670633, 499241059, 469826038, 17077860, 560407681, 351902232, 308881280, 649732920, 440776218, 766780710, 551853280, 381121564, 507885306, 458825772, 204975624, 855299456, 189003106, 622467510, 609057646, 65728776, 123306720, 449293907, 612154490, 280466121, 761038812, 208918815, 629134572, 108525612, 745049727, 592778672, 753611024, 107520382, 871048152, 414412344, 192617658, 921581582, 999869645, 247557928, 773535624, 563020333, 553150466, 593658260, 850903300, 525537637, 340942201, 228008220, 125527053, 994306249, 763468305, 85560615, 423560567, 442549253, 382930794, 831994303, 165167457, 359493328, 329662991, 733819026, 908234088, 666081217, 342367152, 15132885, 702317012, 648481368, 520164515, 97180115, 260221092, 559568062, 871089952, 925937437, 154303280, 701334732, 404659632, 636891150, 951267357, 629333650, 944246952, 580597673, 78055241, 856810488, 477805699, 731969315, 204682893, 109992108, 778151915, 115770976, 689171401, 120906154, 123996606, 147716327, 136680864, 173937892, 569832116, 151709189, 246212236, 397487906, 973989188, 553612009, 494226101, 573877720, 486269350, 459241148, 86477203, 812943643, 572014844, 555282393, 503018292, 321650419, 410206773, 167190645, 108899801, 753415461, 118701214, 179866417, 280804700, 662224560, 501341299, 261019242, 801773188, 74612897, 670960423, 459363167, 738231747, 349795684, 838020994, 185251762, 26617359, 593113799, 794463024, 965467550, 583568705, 446543618, 281210830, 408230189, 3539388, 35128258, 285369269, 961146219, 469712485, 742184870, 476576928, 143182740, 915881935, 378307583, 533362693, 392477192, 490985950, 756250671, 535513278, 319226503, 18906907, 700371670, 789903475, 643305906, 526375300, 2673856, 536850485, 342794545, 370630932, 884337475, 513955333, 80292123, 1726500, 27862116, 742117197, 855824058, 295093008, 675051482, 363945524, 880648382, 723705005, 11010698, 444221518, 719316066, 893207102, 960134020, 679735490, 205117700, 208388042, 834210329, 609232129, 829590829, 774970727, 7089602, 756330325, 410357501, 135487423, 588135627, 408897585, 621271474, 472429713, 26230876, 313276069, 989711135, 36873105, 122715109, 605960128, 138394012, 426263249, 355183138, 263895978, 268353025, 200655032, 520007609, 884842087, 42208253, 180620594, 319702508, 161110077, 301586865, 809243863, 32390174, 289396281, 429067186, 356747720, 81239289, 303022055, 715083606, 293975056, 317736876, 234032830, 576039051, 803878934, 791129708, 397060449, 849256412, 80718481, 793659981, 942300393, 504252934, 932351010, 606945720, 378877054, 26600683, 711518376, 353813975, 835803117, 55293950, 595335948, 893020965, 425625646, 705303072, 749401167, 471615068, 964862255, 952795470, 682232938, 970371526, 546443476, 732913427, 711241381, 504130959, 49852693, 699977618, 887246086, 973663198, 633969403, 473122641, 901028311, 937050049, 8326036, 84987475, 271173046, 619985133, 702217448, 712138702, 653162252, 279055351, 555298182, 528117855, 302437404, 502683603, 693845295, 227463507, 855783874, 503168930, 626104974, 667165114, 328818166, 795346169, 769823362, 151226163, 939215598, 198558276, 228308197, 286976351, 465101389, 991390690, 170509010, 572136638, 840039170, 422078079, 526097325, 204929178, 737621111, 497962645, 334136768, 291158505, 135338225, 841977554, 16142890, 317783291, 546419130, 113575715, 572076053, 584649112, 995762349, 665477245, 888331730, 524354589, 345161853, 216620589, 584595309, 866402245, 294764903, 739016492, 855556364, 124831363, 33510444, 870328035, 407456339, 29177427, 699712217, 741780225, 503635200, 858709846, 512878558, 274172794, 587342928, 302182443, 542557362, 899057048, 355671723, 611086949, 736775992, 805568240, 146847863, 527338367, 393092656, 584371487, 279525574, 390456815, 55347954, 919011172, 526113948, 504193727, 920066906, 790612622, 445700100, 465058779, 465043720, 81488934, 279226864, 352371777, 370826423, 869907934, 648382569, 871994111, 232639009, 535928928, 300708931, 113571516, 528085011, 438106083, 206375462, 309863234, 931094543, 163034087, 259061012, 584218221, 69707548, 415525766, 645448776, 888511450, 198464904, 945576069, 504918839, 344469732, 931484126, 646962145, 398644178, 254723908, 473781894, 551784666, 566471220, 286776158, 774945905, 921653875, 459678440, 532091399, 493195183, 373385401, 568089804, 798626585, 964619051, 73311730, 375931729, 783434309, 757908169, 272232474, 159065052, 952780695, 942336954, 958990293, 760364668, 969135731, 202800662, 267005750, 731044339, 106887442, 370557802, 64887556, 743869826, 731563002, 709838394, 880015870, 120473736, 727379347, 957699336, 629044422, 866880228, 352986104, 370169954, 543757962, 201567437, 253830842, 410818738, 908650543, 432716644, 452779944, 725409325, 89148888, 843972870, 415564788, 404481706, 340245348, 265238602, 817760903, 744267823, 327974198, 495139924, 149722661, 274375398, 59866767, 698652677, 725485741, 592492095, 267038273, 799649266, 29336147, 864962427, 326503959, 373039426, 527140300, 959942995, 236366025, 303549300, 936894780, 403412789, 278617058, 656242276, 950086998, 584008393, 915477969, 601799002, 30375215, 59569688, 241662237, 522336655, 881195838, 351715411, 927346939, 334636799, 14351265, 735572486, 337092342, 142789283, 282439964, 848326510, 144257343, 101091580, 387780639, 413564761, 80196493, 837436920, 457146393, 88662920, 131747522, 517794435, 544825673, 806763809, 271650888, 501191296, 513685466, 414583246, 18221477, 937109853, 136216074, 710111483, 178137733, 118109682, 686138300, 906550707, 118994330, 894015818, 554427071, 409303424, 190999274, 368678275, 665854874, 447742775, 988032277, 511143892, 693186812, 826233869, 312932993, 246086169, 367130917, 473511358, 700374251, 141375099, 287709068, 180583141, 361280501, 908885541, 301656885, 171838714, 283364689, 186288593, 578238765, 254938013, 132171662, 413788027, 265873276, 816510956, 492061927, 90033168, 687939009, 790483706, 429376578, 97378474, 581361790, 559487365, 886980552, 964689924, 964193638, 437159848, 322904202, 794714094, 812432139, 199641430, 624795231, 524064438, 636984610, 352568137, 417586671, 53057488, 151351828, 458338710, 122223881, 615833855, 560583564, 594973747, 931910677, 152916692, 2198747, 99155309, 859653827, 60556257, 404796065, 256250827, 903774458, 659241091, 971301285, 523699417, 836328309, 204851858, 721198813, 873223765, 872991811, 42985039, 820672257, 521097349, 983705168, 696412394, 24634413, 429173059, 962401625, 296250796, 333115263, 654472391, 889977841, 302057090, 709283223, 349729640, 455283332, 288419362, 618526346, 919886037, 831767972, 797791122, 683192894, 640914350, 765161421, 236941945, 431797163, 679169594, 830275485, 102787781, 599112548, 991400317, 771435364, 481875131, 138681778, 297507758, 32859383, 343094000, 372403952, 495860823, 6063850, 426374325, 595954892, 699126103, 913527277, 450584240, 892113233, 961002987, 404797432, 872378472, 484858896, 863376203, 559136619, 850869233, 112915045, 354522032, 89770019, 220365496, 138448608, 646563684, 236695916, 164087081, 657220420, 654689802, 306459676, 693306306, 110466307, 112607541, 881408403, 349787490, 18273441, 180397794, 187207626, 67488736, 611245625, 978288457, 934115642, 434398675, 122216171, 608494099, 179140053, 651920066, 23497077, 325024647, 39108916, 213161562, 601764182, 798573900, 845670490, 302580948, 961037859, 48256379, 996481812, 501141409, 841317546, 761317275, 568382470, 884250101, 946701970, 159625159, 367316430, 993047680, 573058492, 874884044, 61417725, 315067218, 978061346, 280791810, 981802774, 76354613, 533724355, 602835786, 94349633, 664358977, 100468465, 167900764, 206315591, 825094072, 395399318, 544710705, 497159488, 625104774, 930212978, 712947216, 575802511, 368512119, 283716525, 250805005, 125434817, 416131896, 425081619, 121271719, 806852465, 403034946, 480038054, 146003310, 300375818, 700313172, 453914927, 873167245, 631673837, 180985237, 338810196, 239682360, 196314312, 721682480, 426067295, 798103825, 146997810, 325606398, 308733150, 352740276, 599030834, 268654615, 82576267, 846118717, 59921668, 565982863, 443074524, 159304258, 91227999, 230764164, 744308286, 146808886, 984409828, 192673578, 707198450, 42879151, 435883214, 898891403, 502249300, 272225018, 283904662, 378041610, 764365459, 222830183, 488472223, 189075088, 809181247, 490360297, 321960291, 799823552, 308365238, 383174172, 759228085, 565090296, 80242367, 118083118, 367220048, 790671741, 720302899, 295244137, 130045031, 633828752, 610388779, 823690797, 378996360, 131342854, 558302228, 567410341, 119478802, 896930406, 211636129, 702946770, 207065762, 373265197, 318592848, 768966995, 991646083, 741223567, 182959366, 856092244, 361397457, 512671247, 499024618, 597652550, 119370568, 158778817, 486913496, 328762661, 355851774, 526360066, 591682830, 42173534, 238255549, 126601710, 375274982, 140428215, 84667916, 840841327, 205362832, 892959092, 914949086, 176520755, 209737749, 954446673, 660068782, 606770781, 435236472, 186661056, 857587336, 964986007, 936673888, 740825188, 78543334, 418857300, 420535386, 79530435, 714237435, 812034856, 407993167, 151494414, 311950554, 588895778, 14869345, 978574616, 101265122, 956507429, 998344941, 788538900, 495457688, 694669083, 671016583, 343807866, 295277754, 962397987, 744201206, 52876295, 739771753, 241299494, 318332665, 915375556, 201796456, 511716771, 27078927, 975616478, 243157317, 984498639, 647157261, 829491353, 213781822, 561877089, 229833463, 498490359, 470800166, 211155613, 711994595, 100760127, 493458346, 998103155, 216605636, 886372080, 392776061, 106522695, 900253775, 159310900, 559171977, 671807980, 456591680, 363886509, 371409079, 849192731, 877119078, 298062836, 776633319, 92520987, 930933947, 155418880, 637148930, 69699242, 666470878, 795887486, 343567233, 246963352, 878960146, 245241705, 260804408, 676070549, 244812935, 92474248, 416837623, 836959310, 822806217, 574194202, 498031533, 507931558, 287614896, 406109749, 991061210, 16993934, 513421742, 737374153, 94059331, 238699841, 629537022, 800464783, 218802069, 899304638, 137865237, 596242226, 879620874, 102956676, 199443016, 41798972, 863938838, 967793340, 759759571, 322388270, 602765425, 180164320, 491235317, 267123708, 25053695, 769684258, 582351567, 96813800, 798265439, 307706074, 582465356, 802975338, 126747309, 858202170, 506871869, 560374069, 840240316, 142327749, 752929483, 124991468, 294931113, 83169768, 880416227, 722931361, 103677953, 504039475, 568420970, 285399245, 787321242, 886974870, 686941056, 300765171, 217242329, 272595247, 819260995, 243164774, 468884805, 166806807, 714645489, 977259272, 670312618, 743583981, 800060240, 972641031, 551288245, 373713622, 402027449, 321510002, 278599421, 572709446, 635579207, 45164374, 478507365, 660583244, 21577246, 331477857, 419404351, 486672326, 163146961, 905796223, 919366597, 658579851, 798048065, 260227731, 674940560, 313836161, 778836250, 931475874, 411843895, 470963126, 23715129, 511530997, 383608675, 602075422, 852642105, 15877414, 608343244, 728947328, 820386715, 913881049, 535735149, 416027923, 621034933, 724012622, 464562056, 454903330, 515964498, 661760794, 905396227, 205850389, 245462905, 579669209, 129374630, 737517786, 314662802, 113230534, 590416899, 278477834, 26306853, 844558225, 373985838, 873577869, 495812491, 222849042, 82846800, 919355180, 183449150, 695661154, 990106156, 704399455, 246574663, 978019813, 351694013, 657786656, 867307467, 91944344, 458911521, 850231494, 570642517, 489745623, 48683575, 859079564, 997765309, 408147356, 472620093, 950499859, 898139797, 364777884, 239931188, 703101004, 253125118, 679598026, 413072909, 585419369, 377252952, 56581638, 816893625, 189948382, 72254800, 39269695, 27528279, 449738624, 208543034, 403170805, 959053014, 818754818, 654937978, 32743293, 409436887, 621035385, 950632447, 408918714, 757340161, 860791817, 893466801, 891123938, 488104136, 59650041, 792931199, 691684104, 201159600, 388326056, 311053621, 240369669, 823339435, 262779201, 489508489, 80690852, 495517355, 397971646, 584837958, 994719377, 573616960, 264435450, 263725323, 796084932, 107393340, 956110583, 411549381, 347056262, 767127785, 680936669, 569642269, 522799171, 326818466, 332887342, 946857957, 39334699, 965530261, 167967704, 333876549, 810527244, 691450277, 682984368, 860020574, 667212088, 847972605, 686521540, 825277185, 493264583, 84474482, 768446423, 982980244, 562741899, 652442335, 602178961, 417508255, 162074572, 244901151, 52009984, 719616590, 740936589, 585796772, 583154116, 106460112, 465341424, 221132482, 282973328, 324764078, 496211785, 741019781, 119949340, 98453009, 865806373, 444834782, 68790096, 332424810, 867042990, 202319559, 413750249, 14940457, 894893613, 798826956, 572435525, 40951998, 166696774, 108473807, 569001743, 603883743, 475061605, 90550102, 198012968, 537134305, 93623875, 171937613, 31015258, 967632941, 393999077, 416460052, 340342618, 619937967, 972329299, 382913511, 570902693, 24461553, 606812820, 335522214, 429455477, 676665385, 233136942, 599490549, 375866552, 757366306, 593813034, 907002989, 480751123, 199644336, 151144094, 276360240, 470508311, 667728830, 915504026, 634024908, 223064395, 248380672, 444205002, 603413377, 366440769, 501353189, 399822011, 660546944, 349610826, 59325545, 643361154, 924070634, 359648088, 196994735, 202897297, 545293181, 540175107, 856492404, 59424381, 422002708, 752141918, 718744392, 331857734, 720997095, 261768532, 291907083, 112765911, 856308768, 393285502, 425955678, 26573608, 974803418, 534867948, 398736786, 720696785, 531595248, 71823181, 274285795, 342981679, 788195390, 719118424, 388564065, 557154289, 458056468, 652780224, 259849222, 965606091, 402444661, 835122475, 748407465, 709060558, 771947366, 997390405, 160423841, 608546222, 252985875, 359945960, 635060797, 159559231, 936843296, 32027086, 653139179, 59240317, 765178937, 488839024, 27353250, 263663117, 722279105, 325328280, 100889666, 940899966, 405495355, 604281355, 273177590, 548811702, 862046244, 920152435, 854470973, 225254474, 115282960, 612010240, 554581514, 994776902, 707538462, 441355136, 31817971, 169061790, 621740274, 523510285, 109071984, 168992929, 618025991, 478218288, 618056724, 15641368, 272935098, 125848401, 374231910, 991053583, 643804197, 460725960, 295899014, 388904313, 600863192, 228806144, 182881163, 117105449, 241588463, 350424292, 314022264, 925807462, 734170000, 594191306, 958058352, 150305783, 486674653, 805208880, 822176902, 965982427, 723398431, 659775813, 228115008, 851697838, 140557923, 821031788, 735135532, 66985602, 943613934, 391861274, 402668383, 643196300, 815053007, 719428440, 346385297, 661169416, 658604216, 221178850, 556495935, 997295028, 490607860, 426758990, 985853178, 359009437, 946055949, 720906959, 505869927, 20222559, 168384677, 391004469, 560693760, 724648995, 148557277, 241502392, 427841392, 132950892, 147113489, 873556918, 817642983, 212159355, 868561693, 109792804, 6308825, 303436535, 585493997, 646271187, 150704647, 539035516, 226832563, 624941667, 149756128, 442992011, 909163860, 599941272, 600170762, 329886043, 662126414, 715089543, 133535378, 111422098, 651996272, 529347928, 903700685, 2325875, 8637151, 945734852, 939013112, 391515287, 992271743, 297297467, 843180659, 187461403, 899358455, 742543244, 43731000, 866281231, 52516796, 548580327, 532863338, 794857779, 54768160, 392974807, 979800045, 572901764, 51990062, 628450692, 998995491, 881485497, 89840097, 15126116, 558684234, 7351245, 342842976, 694884608, 157324788, 886500390, 993709305, 557906767, 801673340, 826091635, 454328444, 711514083, 162655239, 845189114, 860305629, 891583943, 549690035, 574523792, 6004479, 572241986, 451952907, 372862318, 836728461, 705897884, 929303406, 937422149, 377121323, 917102247, 941026831, 597068965, 52733151, 26267212, 852814801, 591264251, 226166392, 3023178, 693112987, 416112239, 981329332, 201836954, 184445134, 497780772, 276423462, 156775602, 578430067, 189535703, 747297757, 876593176, 934557737, 328613357, 351818244, 111352528, 353759224, 252537646, 390712609, 83921431, 856680694, 368549026, 979152360, 131495170, 471516207, 805450106, 281374666, 641170235, 388636599, 86558298, 319110126, 121657656, 586698950, 418197663, 589974307, 363931195, 993105063, 131907687, 673301293, 584447897, 500457295, 182948852, 452618868, 613546608, 90712736, 261657965, 650753346, 330089149, 899420936, 439824492, 991070442, 249882081, 565149357, 287217084, 802683013, 12882903, 271156363, 896567990, 714971796, 99264923, 652392717, 523562858, 279005230, 798078785, 530246521, 87840739, 432344551, 834720921, 391388167, 922125398, 897356189, 362930649, 854939974, 561262630, 909507819, 960930341, 256337274, 108273168, 729764858, 711029092, 400481434, 614271188, 348519381, 180067482, 606151378, 414937008, 767180266, 615925646, 813593250, 662377338, 193905634, 400701574, 778933021, 23918040, 970263131, 232340232, 541212829, 476573116, 707674013, 600731048, 769109013, 404183322, 938740730, 5891335, 189199690, 912954707, 123235487, 183035707, 171530396, 368490314, 588515721, 60560136, 232006513, 31340813, 45612197, 209786294, 915465287, 758984532, 931313139, 516650927, 431221508, 222455022, 220156389, 516125209, 982957378, 791466187, 184306140, 362964186, 695623695, 324453957, 656052630, 635027868, 824561249, 49376774, 157308322, 21496736, 724616349, 322508356, 910579842, 471904797, 197011591, 211394552, 651743568, 112307294, 298918257, 868672684, 206786908, 892304335, 505986036, 523401877, 500484407, 506269246, 836067703, 420010829, 334348633, 676512033, 423331165, 531162365, 103249453, 499018178, 867964301, 519101625, 976215400, 903971205, 627295400, 631876048, 268000481, 291759055, 399119324, 315449051, 229688316, 671803415, 550602123, 655646193, 995864726, 315954872, 60968769, 773114103, 922966994, 550211105, 210843739, 954189703, 841693374, 662598276, 366213350, 917097815, 663157632, 112047479, 129300019, 399485699, 983375668, 24274858, 408572254, 225573215, 384790028, 140769458, 711920876, 467386646, 530646532, 947129029, 127507863, 822900516, 915392686, 56938487, 387524289, 486873271, 395979263, 100570498, 160631377, 491820245, 742555898, 958366567, 374849074, 144896166, 789532424, 477399642, 498898935, 410418796, 388540294, 990232602, 536148721, 579037268, 136796057, 593331044, 389708610, 188259530, 153696722, 47135937, 309304342, 58165808, 980974810, 510688264, 79526395, 958682345, 576654603, 24843911, 413689345, 905924419, 675296084, 721952441, 533147511, 513706556, 769213189, 909865638, 814558234, 57967642, 380744243, 672808666, 342712919, 520440946, 490990709, 990745155, 678390060, 596226116, 127954604, 235449846, 323462089, 193666184, 839405301, 866595813, 98076489, 904990303, 804748094, 320925966, 676207317, 516945621, 451327438, 267622297, 557917497, 427905237, 795192120, 744705315, 527581041, 637838568, 853887252, 178020243, 768389779, 582831529, 596689859, 327795952, 433125884, 710206147, 776754279, 750975880, 439684669, 222363893, 227878210, 852890258, 814210666, 416673706, 906769877, 901625111, 118383181, 782307223, 246132706, 30897415, 306818121, 712610925, 801566209, 902892319, 194217502, 318193116, 680256920, 124503219, 669870257, 731990872, 773883205, 669167417, 594092053, 95151030, 197484136, 355476302, 186150239, 754132358, 566099267, 451970638, 718361766, 992829447, 523672823, 54087868, 613114370, 684564990, 767158756, 954145034, 822423682, 43470241, 844235798, 999735495, 639320617, 383943105, 232938658, 740206456, 20675911, 50710488, 125578888, 822694048, 777791748, 418037050, 944786626, 657973809, 734270863, 200237713, 230080531, 864529254, 454274880, 557649513, 446171417, 123126153, 176960671, 392796004, 34759813, 694702768, 527534163, 699403776, 618702266, 142036628, 814606824, 356919671, 546135229, 168212994, 46807739, 268849627, 614313527, 330189193, 701102688, 394575420, 140978715, 555276187, 427421309, 743979214, 381777644, 300750352, 856369892, 876011138, 101961180, 850565009, 715560127, 639907029, 998057569, 463807658, 166994382, 447659680, 121867020, 797212240, 35793395, 723234229, 904813971, 580482687, 637575543, 246411368, 572887874, 4275760, 782719659, 975844922, 383981291, 545438731, 870063717, 91456117, 373729936, 497057682, 712593286, 454554392, 778473938, 81572430, 298198454, 997402583, 784344267, 936678366, 73996605, 366042423, 703674549, 841607232, 234375723, 131095914, 751525812, 915295978, 83365399, 959313078, 405091367, 181279104, 422026469, 531838489, 44869458, 915802851, 576923891, 417403860, 781334362, 633237703, 268161871, 94381262, 639053829, 397417424, 151176782, 527613961, 611935537, 756982580, 806079637, 673281350, 580902384, 131456781, 764209493, 69191821, 657069923, 427825941, 678456165, 339580984, 633726255, 342091250, 339774173, 630684632, 623279142, 904296472, 738534180, 392968727, 62027530, 351592186, 708895814, 350812118, 144986931, 81122546, 572611771, 713975334, 85016025, 249268949, 34226, 395892677, 727196383, 816884506, 725486739, 988899247, 994013018, 276192936, 44585060, 354655055, 15082635, 55753608, 534216902, 167285952, 521142626, 872477067, 176592882, 350034908, 22734133, 525501021, 955806275, 287287442, 623155639, 578633753, 259553226, 724091138, 316744014, 473855948, 85802487, 475478487, 223817870, 251030200, 393202071, 808815835, 341475978, 586488103, 360185254, 277986901, 475540156, 659726127, 276025260, 557888931, 716722816, 500082135, 639754363, 922047017, 79467045, 365075228, 914451350, 291639989, 396298329, 6437665, 654953806, 757453131, 329706426, 202005856, 895447159, 135633542, 517053876, 325551404, 21985924, 176174306, 894925477, 677188909, 205237654, 813693886, 622626599, 60428101, 158541297, 149465821, 47057506, 788579195, 881268745, 830841990, 814699725, 603120345, 290504531, 159785608, 660920765, 5902030, 418704595, 654251501, 610519634, 512605077, 771592549, 86862085, 894538417, 47433569, 992398823, 427886999, 761258648, 184280418, 139387249, 497312931, 118083734, 353100092, 467711649, 742991289, 129576287, 132711532, 955710915, 936619149, 979088229, 846190171, 510414803, 431727636, 930420794, 821692021, 750736306, 410216883, 936463832, 180322634, 75569957, 636819137, 158107835, 124087264, 504899409, 993444054, 409791272, 796729256, 357406056, 935430969, 777739535, 808322616, 558312857, 888213709, 340548077, 186726084, 356853292, 350873266, 111823383, 217319208, 936443688, 272037631, 959516106, 687884596, 796377802, 499090835, 314901737, 999897839, 290762394, 843798222, 295021746, 229322014, 542056375, 619323067, 538241346, 683151400, 668677524, 587368053, 398104369, 648170330, 493248665, 430881803, 506273186, 327870417, 259260330, 992042236, 18702365, 669728551, 265001534, 690722071, 579459514, 788334689, 580200271, 870784126, 66155026, 443871158, 43423939, 203215949, 68261002, 59674979, 100788057, 148735354, 502075191, 8344688, 342994424, 232194492, 379441292, 48826567, 204783306, 590385348, 572918452, 851859062, 897514029, 943361823, 453416525, 902413822, 422001094, 666673150, 586502175, 652875278, 603662018, 629635226, 161657619, 608166838, 555374320, 443244967, 820110627, 255939266, 868319200, 633068948, 940856662, 837316417, 145926799, 886309074, 769441267, 447832083, 49361330, 440611393, 487475331, 162423694, 807609919, 108600679, 660326109, 518804404, 417672899, 63208750, 980230948, 692598526, 443466276, 524230845, 16608929, 561909070, 188749259, 146995758, 927532165, 722964898, 394600750, 818826428, 39400451, 150911860, 359142875, 198664162, 494989409, 370536953, 247066426, 583351932, 411793822, 62022436, 313648604, 988631639, 41576021, 172913448, 666579058, 394868018, 57993484, 452934117, 746204966, 170959559, 815136662, 896254367, 958086581, 884812708, 361113035, 64973588, 90428872, 569593514, 392881399, 28801037, 365841140, 234865311, 672967511, 801935144, 132825884, 181318420, 320815500, 317287632, 762962907, 898213426, 385799965, 877532896, 61899438, 439095773, 696083422, 805804891, 817310363, 70705806, 514579364, 480330958, 214914666, 809666811, 48580263, 153443282, 582759690, 735698122, 84108730, 263021530, 812620295, 671149817, 191534650, 238413316, 248714983, 595486275, 599720210, 786369463, 388768414, 283995155, 508717273, 789048008, 491937615, 409837602, 264508225, 472126006, 807264995, 241991236, 652713154, 430526913, 445933351, 25712305, 954390904, 595548495, 933874882, 306923409, 567025643, 938140827, 758550946, 976250208, 989379077, 24061260, 259653361, 176164612, 212181678, 302110452, 343274233, 480098148, 658479891, 877711152, 731685676, 887622339, 557021925, 295476944, 555222052, 487256263, 884527899, 426713668, 36130830, 250992121, 476009964, 333728505, 402940800, 790602567, 606548761, 940441187, 688716920, 180684783, 516458081, 293119249, 267466579, 959676219, 697790331, 113088084, 868354631, 532623296, 192964708, 621625786, 893194558, 673938370, 797331585, 23920721, 183578869, 587235354, 485634450, 617618254, 651501612, 552154282, 531110951, 812339984, 270634989, 441200221, 486855843, 618535471, 736885981, 46856256, 801408575, 369861537, 937783589, 657180320, 320388947, 986397959, 186466908, 63134905, 957162956, 992099126, 106677942, 866959794, 522069225, 179282694, 661494034, 885260353, 999498412, 856565880, 765973355, 353152978, 777114681, 950859225, 492924316, 130320574, 366514264, 982385324, 284300012, 827755988, 447533349, 638990046, 810456510, 151889685, 382693110, 224110833, 51967719, 669492260, 134069335, 265489758, 756490250, 836589206, 171377998, 708330323, 620821065, 753027392, 584223672, 49990920, 753583365, 180228596, 74686053, 753490373, 738089245, 278379146, 145593808, 608050936, 118898295, 877771249, 329642666, 580740753, 27398338, 823178900, 261862933, 936920244, 155453577, 664742754, 300373443, 612207902, 505995592, 555133123, 489985767, 693064492, 701022420, 696392364, 729145707, 809492082, 146480418, 939280559, 558594812, 411364284, 437955992, 152325838, 684285555, 621552928, 36557641, 879331336, 230915855, 512250103, 229365648, 145118842, 753889969, 285159790, 413759832, 29980131, 783111919, 628784318, 415674721, 753935040, 427219517, 421469639, 332286884, 251914159, 903148085, 716086947, 560968897, 459329735, 500995025, 621371203, 56094541, 692347521, 319070582, 984396420, 911866381, 574132216, 123709685, 498361507, 45295875, 329002661, 276575322, 300770330, 323660057, 605462860, 403338358, 561482492, 413687776, 222205952, 823236402, 88629997, 478758896, 242702907, 608009868, 753905657, 470478787, 720336325, 988646986, 249902289, 619521333, 517151755, 309426714, 428899578, 549391501, 649855412, 160191982, 439311455, 424890429, 807662367, 201252273, 896800567, 207954634, 702579233, 740440550, 490664776, 353687077, 438334389, 28609988, 962715167, 986464142, 629689902, 590915480, 780627383, 60381040, 722809086, 82222845, 723393056, 797961280, 241636874, 271021382, 260532308, 149698132, 511320618, 4995319, 245957051, 647243286, 758062011, 251552131, 644595214, 629011528, 995864644, 157393737, 836756976, 286167240, 943880966, 294723074, 521672980, 534205914, 503404297, 768288266, 291978785, 685489279, 400375337, 892013757, 327917564, 461437027, 248607419, 663749207, 162828101, 853147086, 211508313, 677729949, 421231950, 818899414, 588059177, 22617740, 867868932, 482884878, 678473444, 561158108, 410923237, 372195459, 860212439, 271001186, 448677564, 457051041, 75823803, 619216159, 527325734, 754478724, 230373210, 10741419, 352695754, 725745774, 992327056, 432641409, 36484372, 118562594, 254646835, 759231417, 153935740, 609799739, 470203875, 195340831, 803204064, 883094461, 600034, 77350047, 581160646, 382493213, 715864088, 3580829, 140043210, 799417440, 540678759, 315935749, 990616678, 205472032, 354327244, 855160096, 268204898, 118501166, 556324008, 800337170, 371955419, 952451875, 36907726, 666569152, 579498125, 293915607, 124942407, 986896191, 264255848, 211014336, 553069114, 492249812, 503689752, 806660108, 842491517, 61558632, 530990277, 671300769, 660823096, 61427922, 46513981, 830108485, 219880904, 645362487, 584529316, 993111001, 235302244, 368395703, 97084752, 593381816, 591654009, 221096589, 680704591, 14637069, 494275037, 730609224, 865975318, 726797044, 599665717, 160423002, 105085013, 554238624, 556531931, 159237504, 283638415, 612450184, 186580631, 932710345, 502803379, 999266569, 201856256, 52618669, 877820930, 696964998, 60914583, 661165745, 852747133, 529112080, 666292866, 562642421, 930776341, 997528143, 750821686, 282125498, 177087332, 114266011, 52059385, 97821116, 339258535, 910592845, 112094333, 467692326, 801226977, 764093867, 372677958, 81574094, 210252775, 799893582, 659430092, 507609195, 619554783, 7827656, 948237389, 481738070, 909463594, 351943181, 961290833, 20431758, 15293146, 310357942, 111586957, 154717832, 450204757, 661192727, 758529132, 149109739, 293647452, 132055644, 962570085, 393942297, 110431689, 18439703, 451335262, 650166285, 933087403, 664309430, 706439977, 521445136, 699558570, 742233918, 559491376, 376645580, 473566136, 709930549, 446526633, 753023247, 107239148, 736017648, 194077896, 744129255, 540100558, 214671313, 862512473, 883296670, 976015484, 836226233, 882592171, 91584138, 354856021, 477520248, 614852988, 940249651, 145474686, 222945405, 196571164, 506825641, 840944659, 741934860, 476187466, 82381886, 646247407, 760494846, 283307033, 178641558, 249004229, 483369576, 550604263, 609177578, 137007471, 16595717, 67646731, 597422085, 383131345, 570122256, 893370199, 837084174, 325249565, 887177385, 569052168, 424830902, 617314301, 809363056, 222029380, 124372301, 660746320, 577375620, 936020238, 473013903, 56104062, 723329105, 184590230, 300553059, 618309991, 327199226, 73942776, 528323246, 78967605, 391323990, 54630118, 757653292, 441500261, 395631316, 151799420, 643359118, 916928701, 875545019, 403844298, 769407302, 557137044, 696805549, 392470985, 947410253, 212193484, 235969685, 423449264, 659810470, 773221518, 838751803, 419292958, 352086664, 715947982, 884381237, 997244300, 707823657, 342354551, 49463538, 184129331, 530223709, 142835437, 360805330, 407102283, 919679778, 220777852, 894248922, 276290725, 528969927, 48335033, 639076198, 835424246, 960530220, 927150665, 667048111, 659632219, 764374461, 90057287, 502580398, 912250061, 482158625, 705096443, 996153989, 452574747, 462137297, 70668097, 432657709, 801533379, 321745306, 955663020, 207742916, 428104227, 570619744, 900982604, 47477596, 274557241, 236061473, 323675263, 915847602, 682745356, 928278329, 642068277, 529118086, 908827445, 955983754, 282935795, 82489519, 773943949, 2819006, 397187856, 105844392, 711466529, 541895008, 863259388, 517266326, 681622498, 639645370, 125676670, 774853568, 754435867, 925508216, 833357628, 793169820, 359427603, 667543736, 795720688, 237140924, 990349249, 281019669, 444851044, 150804787, 848524527, 606911152, 520142296, 855006513, 155724303, 889816264, 325463686, 300163200, 152373702, 238965264, 232607550, 88044616, 718163581, 547951039, 57781938, 475560559, 422877382, 560029854, 484129064, 491068509, 278577910, 189203938, 315884497, 444972238, 670584210, 866799282, 820926217, 980128468, 485865404, 94348104, 389096101, 627610021, 295153911, 964055135, 710645630, 259368219, 607291118, 630085579, 223571417, 253987908, 637750709, 55313317, 913516111, 342149646, 389616956, 709715064, 554375192, 868742715, 337203628, 402457471, 676890516, 281709944, 867713824, 220861363, 799871620, 167446791, 150148269, 994231553, 977188967, 468725017, 115524140, 162361047, 689234872, 52219245, 773800558, 334289288, 844148869, 45623860, 806036481, 739748630, 300952897, 922852170, 116018016, 174285557, 2287585, 794410716, 637984119, 741888489, 503613048, 916690266, 709307749, 185840065, 547100919, 998004363, 297256190, 782445206, 559533730, 345989111, 40670455, 850101106, 259184241, 479080994, 11634115, 633724607, 161969137, 594336326, 498239134, 460981570, 276348321, 875071337, 350410544, 744870459, 868713622, 731013472, 179992321, 778679295, 894642518, 284870849, 966380065, 278078567, 579747731, 22513351, 137537139, 529766518, 76618, 600661751, 607172567, 21292702, 44205533, 515065372, 145232634, 77824840, 923372569, 345825687, 167458169, 981538412, 216836109, 277992318, 81481048, 191091398, 645824908, 417734431, 116660000, 608900511, 127140975, 871562096, 687641917, 328350817, 259714496, 133031704, 932162015, 400017682, 533579269, 656752382, 726512797, 292925831, 110880572, 454509452, 703440021, 378792368, 603791574, 557535013, 769156454, 793508201, 679617812, 592100614, 149437316, 653430205, 583222668, 166095222, 246760206, 119997050, 284046968, 644991328, 378081825, 178851478, 521524755, 679052041, 72937081, 710544099, 584435320, 598560378, 516947282, 256862533, 361311074, 463808340, 918728099, 945269930, 921609050, 643399875, 784354136, 421683757, 949092619, 841301287, 759439874, 558947832, 538617009, 86682903, 850370187, 781372513, 536096620, 969855300, 111205372, 242081965, 618277691, 272647515, 824633147, 519683434, 433349874, 195775257, 954951647, 209114353, 591231024, 749536914, 215256206, 480734254, 354242939, 911040929, 412684243, 520535839, 915485745, 527696537, 823171861, 527558539, 4379960, 225666571, 191577787, 82107162, 253534973, 281361997, 947309920, 911349134, 840017937, 445215841, 185741470, 575557944, 797238643, 4179304, 513560177, 478179391, 774404560, 660045698, 753435434, 470180411, 796578440, 893271945, 330876324, 913785296, 141064854, 103389786, 744254322, 573545345, 382669039, 309413656, 333908546, 921508830, 439457290, 284559657, 493924372, 482300736, 758654259, 212280328, 947006753, 871114184, 289251116, 277313774, 32698387, 222566853, 397651149, 110894404, 630927139, 614656290, 642246938, 407103064, 313579989, 940708876, 202962665, 65539408, 302031904, 815038172, 198962579, 197173654, 594532308, 279104510, 442019648, 656291183, 997179003, 72510906, 976909549, 775107305, 26036256, 51675531, 410707130, 579588957, 270515645, 891375587, 6536685, 341027098, 237016075, 23310506, 349804289, 860052940, 547892442, 192474720, 761943114, 644031251, 425013163, 327053897, 304641256, 222938098, 10484049, 966984826, 450054358, 459824267, 191055912, 358346237, 563591434, 67555672, 136787728, 656817425, 791721275, 36990448, 496440385, 946359240, 988396153, 136171933, 809601772, 977473210, 73343617, 691009575, 343840847, 555370765, 787459455, 367694974, 864175789, 623651814, 594052165, 113766822, 621038547, 469827672, 191649366, 141296905, 240243129, 194017610, 8755186, 570939614, 543650775, 672249848, 303775367, 111975652, 348646452, 83244090, 59995880, 34681530, 546456650, 756177681, 417815719, 951775434, 663111118, 323683604, 78902994, 493599497, 904475821, 821678951, 665241724, 608379921, 358161343, 165421785, 156615253, 430169975, 328491829, 247629193, 267482962, 922891133, 850282534, 95555063, 875650178, 95087713, 946133727, 884936609, 76314786, 369772014, 221268352, 780401942, 540977194, 296397337, 233676820, 206669947, 47093847, 844025873, 139517271, 718710567, 278072627, 510069963, 373867677, 528589056, 856582215, 515542993, 887973414, 353763340, 388287937, 365101191, 441306664, 751748529, 42429472, 372176243, 867418623, 255315151, 419249488, 926169875, 726798365, 973548139, 573824927, 279935084, 811142769, 822808700, 903144307, 740472745, 684199885, 97582391, 320851317, 327099424, 441429327, 102504599, 686736371, 54412650, 692641691, 11800911, 829279358, 267901048, 530109215, 615333880, 940732265, 33452731, 347050429, 949983274, 209009686, 240885731, 245888679, 945953456, 568963399, 349747434, 114489695, 631375179, 564079477, 714801172, 68162918, 743977202, 48814783, 527547084, 859749982, 533608958, 223529178, 72137367, 264231756, 576368619, 990420712, 202678815, 605041066, 650842613, 968210352, 859380582, 331992695, 34240640, 407311433, 662840008, 804368831, 137065469, 828636242, 570685125, 215366510, 561323865, 891007771, 733289060, 839910736, 951315610, 22323306, 681789418, 552006549, 478633926, 617832196, 368107615, 470938120, 750223434, 875444320, 669536648, 743829118, 411519695, 437041348, 898766274, 953072981, 619793135, 928730321, 828921174, 893336847, 835393590, 913545355, 980434974, 445053938, 453719482, 674005302, 540293853, 818271394, 694889588, 697336737, 994880221, 968577900, 614082176, 886918369, 850842119, 751522884, 627700519, 919322046, 688907832, 596459079, 864971832, 861737595, 813558695, 776066126, 700959782, 60765245, 306342813, 878613143, 942828073, 659204178, 259378308, 203857822, 997887748, 315287313, 406846151, 944099144, 551117428, 164020406, 888977792, 66272007, 185885174, 302729276, 293646531, 502272869, 745524988, 121802932, 414762221, 702894998, 922699273, 288852168, 876108732, 670036109, 396024391, 524252941, 913227638, 897325644, 906374264, 984531100, 337319531, 490060150, 881302391, 845716640, 194353033, 125028051, 439253230, 857797888, 560666416, 86964844, 318165775, 497551216, 883048534, 753299786, 116097444, 298278578, 51173894, 379308215, 265072057, 921628202, 542672193, 435368861, 269507235, 527559402, 407062666, 493179202, 247443160, 594517433, 369579399, 676727065, 671159776, 56877591, 630967811, 911952040, 769454119, 770607290, 678806605, 900326803, 527539256, 881502562, 155080468, 309180940, 572195921, 955917758, 269583454, 768875775, 10086631, 187368319, 916426254, 694205625, 89863231, 743253529, 546227346, 476202041, 740324502, 834809898, 219627644, 784025357, 886081041, 67417974, 188663523, 516673717, 371228263, 175573608, 268269744, 478447528, 346285449, 604594208, 514127090, 569413517, 155337138, 393771175, 355200593, 348986438, 62913819, 655893684, 556071389, 153601924, 465010498, 886917465, 588068786, 188890060, 367859310, 556207754, 379587336, 635118559, 661400504, 871723435, 296658395, 186292412, 823246950, 455537442, 774101615, 582237107, 392889088, 741860963, 330652998, 425969381, 68096326, 947321500, 402496583, 751761880, 674841357, 468227704, 712744484, 402460150, 726523560, 254805643, 73553239, 276312962, 589163815, 753518377, 354235374, 602187768, 75963482, 769137985, 476787045, 800488955, 578635900, 603710725, 682070459, 216278470, 205083008, 42083539, 877223710, 147545173, 640392356, 791176479, 150449779, 657972594, 44118810, 132313251, 517953586, 832166472, 793727432, 842714729, 572265670, 148885979, 962503967, 192845918, 109106403, 586426351, 749205811, 298529524, 32095520, 82808479, 356457069, 156827333, 679536359, 997137879, 427965995, 247826703, 521580214, 529664322, 668608847, 431250608, 75150387, 644774841, 83321876, 195127749, 475068182, 755931871, 223548131, 571754703, 364307403, 900189688, 717630524, 491186789, 958718926, 406072862, 111705903, 566215935, 982214143, 923725084, 598834514, 471573116, 633487941, 497111166, 831017676, 864588613, 480334157, 890164970, 172310617, 140181378, 477048035, 821977836, 729034735, 338705051, 159449562, 569481924, 822871970, 597635261, 164891734, 840329758, 932457873, 328129449, 600834563, 190082078, 789144875, 665175879, 540015099, 752345535, 595274791, 422645046, 534464480, 595603784, 678770380, 841330523, 253676866, 908927305, 289824566, 845789366, 436910907, 503766127, 210666463, 317543316, 376176790, 823636855, 732612583, 40319495, 320975995, 846422356, 646682072, 7579772, 477136233, 640417310, 373878894, 495330345, 29006963, 13158780, 477711137, 734168629, 888346665, 924565339, 635632226, 456010053, 799700633, 941682121, 618155847, 437007220, 338530460, 962798210, 733906343, 243355045, 247112158, 83039330, 246571139, 210158333, 340304048, 712886985, 214299047, 243263798, 590183867, 307732230, 581707078, 886613905, 268069269, 530833912, 910919605, 230842836, 232571086, 449839350, 645870304, 624289363, 839032284, 48412052, 491938989, 536306262, 233753369, 171943468, 520354223, 787513536, 685330014, 157186422, 282051913, 92954136, 265440024, 36942864, 191120823, 146407147, 750936660, 276759948, 692953354, 35578238, 850090443, 457596296, 119609213, 645860426, 743420838, 436251506, 990003331, 323302751, 806884701, 652371783, 892909122, 24513900, 941344122, 284669545, 357921578, 959368868, 9811513, 758290409, 373133974, 921764419, 467994437, 396737625, 596665819, 866114607, 231058691, 248875961, 865675353, 801678772, 674581033, 798984114, 96589446, 288615808, 177604295, 254592458, 74671818, 604108290, 401001302, 422891382, 762252019, 631001011, 272453800, 844901993, 446395910, 551983368, 119734090, 750060143, 874745100, 85821413, 140604450, 912974634, 413595389, 550204302, 544643190, 574107074, 933109756, 508946564, 688023428, 444372005, 619732458, 573546650, 753368228, 310567866, 628137106, 635702444, 708371771, 171853990, 310327260, 908258853, 775419886, 212248206, 759658459, 415579078, 546560074, 224778819, 311655959, 361135509, 197071920, 710690868, 279089116, 614049319, 841954442, 499071844, 874718223, 527796171, 137544529, 348999598, 993766027, 428510064, 884929493, 229119934, 553475663, 423393201, 540099903, 182302334, 121959653, 892384948, 845711645, 699492174, 884921778, 26495563, 182529918, 74836107, 514784064, 560567231, 225794819, 275090891, 123306188, 450418761, 298853234, 45874114, 57359741, 833064149, 193587324, 826022520, 365835361, 515922203, 116140253, 558062331, 255122546, 694119896, 82187312, 755088093, 429077320, 54253876, 221242014, 452155379, 720575586, 501170, 567329486, 502661034, 444579035, 562345070, 676982490, 112063828, 829401994, 23940390, 796946128, 381892775, 305256150, 814919304, 385222119, 981376805, 781349314, 685426767, 705515865, 406976936, 302290533, 148528208, 541759310, 159806708, 244221174, 562914589, 920885318, 812935286, 381170237, 354787104, 71201061, 893196229, 781070220, 892504383, 370229028, 13912898, 750169183, 789233815, 943203976, 49452623, 403862285, 634083109, 212667378, 569465954, 672999646, 597469153, 975684416, 716478159, 231643490, 111875716, 860601392, 873407917, 556103158, 433235432, 54895197, 951753626, 388149249, 241265364, 188147521, 874782663, 774911518, 618562191, 778629647, 401882405, 768956670, 573273057, 463846311, 732649235, 342316033, 583137428, 951883833, 667884794, 852704264, 33072629, 457120095, 947891975, 319994697, 844577231, 808144845, 335752444, 850426663, 884260539, 747014304, 343519360, 422772256, 703553762, 460126974, 410633846, 773610737, 304009281, 798899126, 83968913, 448812096, 337444038, 569733629, 728919476, 512740011, 618756992, 206220377, 967429880, 57082907, 519582179, 304830316, 70922465, 351157186, 326209371, 31257379, 603797347, 327051239, 7542758, 782638475, 579415940, 651013599, 205612507, 378530870, 517937477, 663100997, 533658989, 810888792, 689305247, 396163528, 605815931, 477577860, 131925445, 846203053, 517608246, 346888875, 466561871, 645958608, 131489810, 535458103, 747406617, 52611144, 31096303, 737681785, 655100931, 843873661, 914253358, 431857371, 828451809, 833736215, 31850621, 146627638, 625726409, 741387028, 998973186, 286681584, 669048895, 974982144, 521984973, 120554664, 799899319, 428778142, 691298298, 17643445, 511098184, 117831017, 569891436, 271604219, 781399328, 987350510, 703238910, 564801918, 872730769, 964457143, 31515737, 782281872, 281968258, 361228486, 22319132, 153789328, 901584255, 478516351, 117084688, 235921623, 690601133, 813059459, 120208711, 452092324, 975085664, 688038071, 543417823, 871821204, 369248896, 100329581, 30077079, 218597450, 966860599, 101442070, 959536481, 531600638, 320926495, 831601080, 530713178, 879325917, 509893523, 618317610, 744407779, 711265351, 600635514, 502525311, 761743099, 13103321, 959683826, 485768364, 378994470, 115650182, 668925300, 707386518, 647353798, 351056979, 202163577, 775197361, 140790130, 581183885, 66423281, 665868173, 136313166, 547683796, 690211631, 859964729, 574890967, 987120474, 288335650, 176088066, 800212288, 445349490, 744574800, 956609008, 493787814, 390644678, 454141956, 461778065, 326478243, 435211218, 906841688, 642736021, 844214336, 609350318, 473907595, 446540649, 895763398, 893174118, 715055181, 768728243, 725324899, 655902273, 631862248, 887209426, 196572349, 919088601, 929922208, 354517158, 291508411, 552535253, 906405704, 972060268, 285758109, 597876239, 433761121, 311587985, 652962248, 45765545, 81510484, 944105924, 375443410, 153457504, 896886363, 907691485, 707051187, 359194502, 360573576, 329813518, 150124634, 851558251, 214255643, 687723226, 673174796, 201853964, 325159293, 118149262, 421573798, 189496280, 844478901, 1752693, 499818908, 352658282, 190011463, 158829707, 239317775, 151220177, 712940703, 980109089, 255101571, 777969960, 880670513, 655141856, 844508741, 499481037, 349878324, 552710067, 547717910, 777400145, 119565286, 744315990, 101731756, 864558260, 997618108, 287575347, 215361788, 889507431, 328091706, 875598765, 713834957, 282137803, 192345657, 513728306, 458193509, 909589667, 824034861, 909778159, 508065577, 404991904, 800448396, 622132641, 301831625, 789665673, 47175779, 969734857, 129088337, 928611875, 622066093, 994293286, 936984126, 326463764, 425652393, 762410998, 588670516, 6574330, 752113948, 22217051, 456748464, 908948343, 879876797, 774900405, 672306380, 749146120, 236008364, 413288299, 361684848, 723242033, 290821408, 337773027, 614420206, 120417053, 616716066, 191913445, 537547347, 651261445, 575852344, 11032506, 554646885, 912852307, 960770988, 163988373, 235626893, 955652989, 676419975, 809067058, 561560974, 93787238, 559318063, 427773364, 258189024, 192468168, 97265678, 455475514, 844349786, 716887379, 945874675, 319458461, 147303140, 770006175, 564668396, 898902957, 275239674, 742371559, 776624528, 809844228, 725239894, 155204984, 20357638, 185750123, 348361725, 386466714, 868431079, 164355366, 426456353, 823093754, 239194553, 642069986, 775067489, 284188368, 57673155, 927338389, 519209758, 868489620, 904274224, 135390781, 469018262, 451233267, 428178251, 361978636, 854303594, 400272293, 208677581, 973808888, 251011816, 38967631, 712368468, 776340741, 836042022, 321260524, 569654673, 463697428, 992568872, 600013145, 281965427, 189899738, 487247560, 343509068, 261361279, 682834885, 81748730, 120541796, 147149360, 901746748, 436309617, 503252671, 800750948, 449532639, 698151823, 699643129, 969975173, 370044722, 70916765, 583941681, 866271365, 997729481, 915074441, 181507711, 336640855, 723238170, 483732841, 458639110, 427121226, 666546390, 724578017, 940834741, 689506362, 624063900, 921362379, 158791266, 721911321, 811438957, 91313918, 458124482, 140415040, 970150508, 487869886, 233677998, 664793872, 677762412, 247763626, 131802842, 449845280, 375968785, 50208996, 665936326, 394130986, 460633414, 80271394, 82629818, 968242212, 292498752, 945970104, 547884705, 164778889, 287934646, 627048215, 595949578, 356800522, 67394680, 884978858, 117687388, 811372712, 440319325, 449804027, 399805179, 279112736, 496271995, 84236218, 203773993, 300717412, 589270661, 46403112, 595871293, 294838763, 612312104, 933532700, 559385316, 158247489, 92149751, 371742869, 957832736, 302783648, 570017557, 965402327, 270163764, 5041226, 590226041, 390349606, 505568591, 138681833, 332407286, 538315229, 53531125, 225388141, 482635924, 695417437, 620905321, 100047466, 918964739, 305892280, 650136655, 441492436, 215405087, 853523862, 463859659, 309725161, 557727753, 429025208, 954534414, 163524123, 936400858, 936606811, 619552390, 356781342, 229118611, 300651993, 842464074, 874668299, 216388874, 777168152, 525374877, 621955386, 170416724, 611932291, 200106155, 149458749, 666193393, 318007975, 634942245, 212743253, 989755794, 571768385, 343623598, 427016018, 111080460, 185735096, 483718367, 62273688, 622212324, 861363519, 363014936, 910757444, 583207672, 633851489, 751908807, 244634027, 555576373, 454738217, 405089358, 26079049, 614660948, 738619783, 45964092, 641533460, 166414320, 275387110, 327610524, 658803145, 816965509, 692321059, 312014050, 844051684, 927905977, 818908436, 638081756, 405768233, 772227538, 826029501, 377221447, 894228782, 175770350, 69348752, 923948540, 785350564, 16238, 200837087, 870339416, 435286975, 427958154, 434522715, 81726038, 697751881, 329273576, 269173949, 790259848, 686022838, 639341740, 723770367, 533054757, 466727745, 94271882, 782338770, 644012421, 242512352, 390348417, 611809924, 433555657, 933446393, 367408186, 259109908, 471707193, 177716663, 849462583, 609500703, 286612615, 906713819, 62356533, 205530472, 845396565, 85351524, 51895229, 783712656, 830096010, 760248399, 176724384, 125570823, 203388791, 91394027, 12822245, 712843056, 124358401, 994393697, 472217026, 125436565, 355632410, 850350294, 177801945, 757252903, 485011791, 126607022, 437417256, 496986583, 283018709, 428473099, 441420669, 577159413, 414583850, 5015517, 404215921, 479852811, 827853177, 531887606, 374655388, 154630820, 786399081, 500526298, 513409391, 410015824, 693468643, 469951036, 133559175, 878222525, 598992187, 201296459, 322859562, 703112345, 245984296, 286849745, 110387986, 663773680, 167743178, 130036056, 8995959, 460161605, 755294449, 601330730, 638350682, 879036187, 452136042, 495105104, 817018161, 156536575, 167182137, 142223705, 9344262, 530425933, 775635752, 351287109, 363016374, 956577785, 603527063, 251362453, 288883292, 579080421, 544188768, 313604807, 255993005, 891635462, 464370967, 582671832, 688295370, 518232275, 904867632, 724541539, 572685500, 560055870, 721543274, 332785845, 396543613, 907967810, 274986941, 906717107, 160974861, 626110113, 534837346, 461824503, 825912352, 837544626, 579991102, 646912647, 91793832, 71584642, 402795953, 650615686, 971820809, 926372741, 505139478, 217163301, 31918509, 435625230, 875326843, 595315891, 144455854, 843176758, 7737186, 882361243, 347209808, 449560433, 931265597, 554920839, 625022748, 459911929, 230639344, 742075215, 302694687, 257568308, 455939139, 418599094, 472754410, 474830792, 605715171, 48655407, 803555048, 783420344, 756847770, 743226896, 208090155, 759262998, 264223055, 995371552, 353029533, 115085333, 197438099, 4207726, 495279643, 696440910, 379238764, 921650278, 465701068, 490675829, 517907955, 874911363, 733871056, 588640997, 911583278, 550176734, 480596898, 160653778, 699307714, 736477963, 727861004, 516920415, 594489392, 219397468, 357970670, 957607928, 364952803, 167378949, 168950517, 398911508, 671426527, 142840599, 917009356, 492072161, 374179053, 694469445, 492259165, 879128333, 817568206, 673987623, 49991064, 627950149, 268534457, 141965334, 975132721, 316045157, 641161177, 793516165, 21171881, 203884661, 247358731, 837825833, 302964416, 287303231, 652041415, 623579216, 285115074, 782053026, 496110601, 734605632, 871865648, 285119653, 334352546, 121806422, 632279135, 885333350, 46359742, 763579594, 813127928, 137700446, 411078569, 362125137, 219097698, 32141136, 366415958, 892928698, 232018231, 516830193, 548989134, 772273893, 67024374, 381403202, 13828728, 827698634, 166749585, 290113105, 759913851, 219681827, 242178386, 997494566, 826299101, 66171455, 520356175, 636001977, 811276742, 915634948, 358540614, 315742661, 700115705, 692206914, 154517086, 878595995, 196230286, 912469287, 367788200, 663252017, 142612705, 465747876, 175809317, 514931082, 994141634, 901786935, 591089222, 619747431, 662396984, 512509478, 682361692, 443321413, 921375657, 797347736, 431992778, 675040704, 782208224, 394630989, 827557701, 115869082, 674149695, 643873606, 212037961, 911077058, 63725009, 163504157, 212771176, 868047473, 236898837, 598144528, 265404266, 502830958, 573372501, 224005185, 54470817, 464877102, 605582500, 760952687, 847684682, 73913756, 347614760, 498348300, 640735811, 615424183, 633560026, 107493531, 736766843, 479812803, 404432197, 861390642, 351537701, 417698116, 717867885, 943471362, 697033642, 757511783, 249571299, 93728002, 297998025, 660858186, 639751509, 692804474, 31538837, 33826166, 194751463, 798130574, 812320494, 433159564, 842570404, 203332505, 773477614, 955934620, 781720651, 293373171, 959242791, 585028926, 223968145, 379094795, 755211468, 842521724, 884529178, 92862323, 702830967, 118119101, 520060026, 762906698, 340300025, 3902933, 668041815, 91968580, 861595888, 43126869, 403759260, 962915156, 343343438, 902980184, 867151923, 303807371, 222899905, 259613873, 953370762, 12293043, 548322081, 397088239, 569581851, 5849043, 185604279, 137956348, 393116168, 673735286, 849863953, 465277685, 963068814, 181022150, 374085770, 360728575, 266292159, 696827163, 960951827, 68859919, 856531881, 846981037, 500839700, 8106293, 570784901, 640782652, 614385229, 884630773, 359801589, 841150909, 602823744, 846923734, 484822118, 46518910, 174454606, 44623845, 339512643, 908440531, 350283883, 323107877, 623577357, 44645455, 639402199, 574403312, 975989468, 34847117, 963287520, 310203217, 10044735, 990995208, 571149222, 59239961, 341641588, 721540892, 998982205, 203839562, 400143564, 219440357, 108817080, 807094706, 640834822, 791669153, 260645016, 420603574, 411639678, 143718245, 173003961, 192549277, 960232427, 494297723, 148276053, 24640177, 483454402, 7553210, 235477121, 262480152, 367160290, 1825236, 442696670, 130674784, 608579388, 941963687, 255089158, 796589197, 229225071, 314432695, 442740094, 664271392, 930154433, 115527459, 575295867, 185796968, 692432100, 16135787, 308176839, 955726933, 694029103, 339818461, 774898866, 632429881, 953694798, 276461649, 86292088, 997528677, 715531599, 675357146, 238895933, 552457439, 577229618, 924933658, 396913926, 162333796, 789419577, 63107104, 904329941, 58329287, 292550122, 245285036, 99065883, 491803690, 286854395, 963922960, 688775905, 763866563, 181634754, 600636291, 402528100, 324461437, 444960653, 735401551, 404886010, 958881485, 501408743, 917243293, 777472632, 876965390, 251273456, 73151667, 437902628, 861599367, 358756004, 133899668, 443125475, 485586416, 988606018, 320683714, 133639674, 21472407, 781547055, 704570794, 366906295, 836028636, 602552589, 874657046, 538329332, 809204568, 551945499, 439474834, 387963377, 367621502, 147310836, 492725145, 955978985, 91500424, 810922748, 948805688, 904209543, 767088219, 124858002, 816953987, 371797318, 949123014, 416138612, 875614067, 473866042, 145671975, 798001090, 193036276, 507127438, 383230588, 313862707, 802842749, 748130338, 13266802, 181448685, 416197581, 350727983, 252353106, 936796630, 815559863, 764617858, 701033378, 205007534, 374729944, 21032886, 856113246, 526712642, 853862437, 410099241, 217940821, 2041628, 74784411, 551040586, 547176857, 361160527, 669424896, 538836594, 473161245, 524926732, 537947849, 604036515, 394181122, 274713209, 10123810, 828219685, 226406523, 869124622, 423615212, 606701704, 958411319, 810214953, 553754808, 855197439, 825984014, 874633097, 204826987, 645864741, 46127285, 375562342, 587575537, 476201175, 781634866, 485718396, 613939502, 703401624, 40276902, 376095400, 711387573, 508334470, 173979462, 115869031, 496855543, 165787301, 36942537, 816208971, 82392311, 398594343, 677394042, 896950985, 571507723, 122237380, 986711606, 458305511, 120034345, 580058725, 581433529, 873386679, 338404979, 184207281, 800745631, 798647110, 334877105, 246035549, 518196351, 637914690, 641579091, 523612283, 828953812, 382010816, 991596086, 361482704, 211353775, 449631948, 977293652, 235136089, 939565846, 496274545, 566159454, 407850099, 551577670, 432023840, 399704507, 223475326, 659349283, 803815517, 832215533, 913136617, 517961060, 874580997, 374895296, 498535966, 640164536, 818107356, 591111184, 3141411, 868675079, 391751557, 609644095, 640883740, 701761151, 946331720, 410766566, 690815676, 198085339, 61799216, 672700044, 144833024, 311046510, 510238082, 249168018, 654508673, 893303328, 519390626, 690096167, 960703454, 856780850, 283624203, 225141435, 375280867, 157673134, 830660392, 304460606, 353195612, 857587602, 334995241, 593570294, 538689689, 56852069, 250456261, 831982339, 701406008, 396361454, 337781793, 228251810, 956913757, 47722332, 721188294, 942340221, 928026166, 733121938, 65465300, 266435014, 765888162, 804763027, 987117314, 200846579, 31427262, 886844658, 671948392, 407532961, 820629802, 478329535, 358648806, 297403431, 382014093, 409424916, 706311093, 437928871, 940029016, 359987384, 420912647, 854946583, 95952127, 200124908, 504483858, 899110816, 460965092, 929352943, 985566144, 532008583, 5273382, 427793332, 38557452, 841537694, 986509162, 642277363, 907253653, 444002231, 844569704, 61289990, 724614929, 187711963, 114478887, 222232884, 254159869, 373403004, 443521198, 563899018, 560259573, 387348497, 36840607, 238728735, 966277534, 261413774, 155727516, 258600039, 977943598, 475627525, 539569380, 23885997, 237706470, 369811186, 988141008, 421202096, 873720667, 629241170, 626588892, 815842298, 840637966, 307128308, 732470682, 563151463, 896297029, 797196154, 996960170, 108948894, 60588566, 288323446, 793885547, 232413808, 300646344, 161565990, 533959614, 528037881, 575464632, 147580271, 310465339, 447064614, 514149879, 168733770, 103244689, 424316799, 7429167, 756774625, 680721770, 150215299, 525421338, 723886679, 591484776, 861278019, 263501068, 824353600, 700681966, 92638876, 732522143, 76261896, 210266496, 324849612, 983360877, 933894139, 654269943, 811345492, 988354118, 844471374, 747502471, 325351974, 784463480, 283960333, 823395377, 996652323, 273509087, 436361014, 332883079, 127115633, 862442667, 524016645, 731033459, 695915808, 796408937, 330950568, 745649256, 406125627, 289216763, 987576148, 984964643, 910731682, 949641787, 192565000, 277247067, 608079708, 134678089, 135475945, 953445529, 659552938, 961149533, 154432506, 728460326, 884832003, 930628775, 702168321, 925433687, 532044042, 816098445, 856958273, 206828633, 657776167, 740963010, 43447408, 450897573, 698477979, 271359705, 138906726, 282619050, 395524169, 869714790, 387447812, 250334613, 913937295, 676868239, 953917063, 457927176, 500367259, 229485516, 680687901, 144775710, 80592020, 666290593, 323233303, 610591478, 312214936, 785895607, 858982562, 232777142, 189690884, 25280192, 9630468, 472496692, 139226624, 842832545, 730417665, 395855768, 73846714, 297552565, 742610747, 658849978, 574041485, 900869944, 396460609, 552379567, 572823241, 452807500, 344822832, 558526818, 283126010, 923257907, 244296103, 906885824, 338379886, 548178166, 590443093, 306016118, 408805593, 108163256, 600387371, 156263378, 796826328, 582910961, 65983559, 875052694, 209094552, 17448871, 406844493, 804345057, 977058870, 997161295, 875220124, 792326965, 4919035, 182190921, 131510268, 543603871, 998054780, 932768854, 742515042, 275110472, 713063634, 45861022, 621079516, 688303993, 139774444, 466115661, 23266090, 328275100, 399417804, 69185884, 205013294, 69759923, 711739169, 347845891, 720396096, 655429301, 721187031, 598767029, 617464213, 725597549, 395726602, 649124361, 237048644, 984577892, 796412836, 322857583, 693180692, 600582461, 767187277, 904872569, 980893776, 278417317, 375482422, 524884423, 889352985, 492811041, 261636853, 947866773, 953003271, 945549495, 768187178, 854902119, 35402567, 473044660, 862579706, 119218015, 172819223, 77046422, 917073154, 316113488, 366108456, 162452228, 162286755, 398504923, 981802837, 802502186, 25717762, 735497339, 746942402, 212452642, 117194702, 761787772, 144957076, 717706279, 990912073, 691362454, 933251244, 396178494, 503060526, 112897552, 763573699, 970216071, 991468873, 25881360, 2963222, 138628926, 759611103, 318362734, 378465806, 273957489, 925135240, 738232998, 562339114, 158907362, 398471979, 100225912, 911062736, 621926627, 80693138, 325580576, 689750379, 452539419, 513407922, 801839844, 534447486, 36374977, 882820853, 61066838, 683662338, 943980798, 646994655, 784839600, 572038034, 34101761, 799609958, 103948577, 8759094, 772116942, 666163752, 943544713, 73018995, 465604035, 245743424, 490937442, 337703811, 267926464, 84088381, 201173083, 177609821, 246469025, 42172635, 743310465, 829876134, 906525006, 147950959, 850977072, 162934796, 174916225, 635361363, 639604996, 338755089, 957451065, 456040705, 890915727, 113451246, 637777806, 326373387, 839517765, 291965578, 228912342, 130731758, 282994972, 269482580, 191955077, 272281179, 609938331, 949716061, 788396731, 593580319, 998617145, 911697201, 563624938, 225480998, 321289869, 578079613, 743948944, 363018279, 776636957, 891852880, 897047446, 839823075, 487054560, 241076378, 47631847, 225058044, 186985053, 828046161, 130749296, 822127020, 542670985, 267710634, 934175764, 166490702, 532035678, 980681492, 209941147, 748360803, 953726368, 586282629, 30235370, 670116837, 530279413, 560633349, 438530745, 750586984, 620252648, 267842427, 610573173, 442840222, 322530972, 861139553, 179340877, 685728204, 355381194, 604515846, 524373780, 652533368, 402144723, 674868418, 487641151, 914058839, 857834696, 714841559, 688164857, 727572347, 225140802, 894796360, 852638754, 532226044, 219634096, 258022168, 236837132, 186976952, 89098750, 773549052, 857182112, 919596226, 417541512, 995383184, 401455519, 128007927, 952732799, 972421489, 23031727, 416008363, 141379864, 395866402, 907239237, 643810600, 584551834, 897618435, 49512082, 242948742, 440406895, 422621064, 249006871, 496748122, 802205124, 959181771, 366156134, 334211937, 93831682, 641171473, 965611822, 559741220, 779395084, 286022831, 860134022, 102352634, 723811320, 132327375, 424774769, 927760290, 586248806, 208454225, 360490230, 127089328, 868524828, 653365377, 20936423, 450478439, 294453705, 479173080, 370532250, 466556242, 271553710, 223275500, 699626112, 683559607, 781955659, 975901506, 956432798, 955449935, 789916472, 268563864, 777275253, 169796323, 357775179, 570367455, 851792431, 85999682, 151601513, 357357820, 431089811, 810057076, 592114492, 270282112, 260835001, 195519779, 939799583, 947587247, 678034512, 408988632, 450171004, 848162809, 568251411, 294905953, 928000617, 683425604, 329443483, 572252736, 152193482, 84330188, 633471246, 847528322, 194345932, 193868614, 609512822, 611170304, 534590061, 118698809, 988082403, 696282092, 946516755, 85086091, 613467574, 913156391, 644754326, 775370386, 292842722, 376355322, 269201598, 460750239, 238039697, 980309779, 902959363, 410347767, 588774998, 607770118, 777146746, 14613609, 154388076, 483498388, 55547940, 948876661, 927405152, 527900954, 739865911, 108011880, 617169012, 537216451, 450750827, 109416774, 3982072, 249090566, 37469245, 963322961, 409187212, 14041518, 623971935, 441090921, 330802076, 194714752, 806432676, 555834432, 576978514, 208745067, 895395649, 877211042, 728784725, 742316760, 508339039, 514599921, 955981445, 277129655, 201565098, 359006626, 903573540, 998435772, 860982657, 172599776, 542156974, 377256668, 214064087, 199231909, 929824934, 187939699, 717004852, 20442425, 303705673, 684193605, 294280950, 946379652, 66266967, 859911663, 509279122, 199265879, 850023953, 611380061, 614995068, 863681833, 771057186, 740306034, 473245952, 262402558, 597874889, 473293236, 694537561, 913767531, 864279968, 700304257, 774424050, 6628322, 373282772, 891093310, 396167822, 354222126, 21680055, 805139729, 712320495, 671813589, 842871706, 494331628, 693839284, 796678515, 458280733, 176912659, 83447258, 105570591, 968973426, 341503047, 169367492, 711480567, 121678466, 210490608, 817027984, 772686561, 321924905, 386611252, 520836587, 602151815, 535988212, 631925112, 421550381, 953064865, 645944676, 532140593, 928510291, 316210919, 140800304, 511952826, 872400130, 77337742, 495533479, 770196138, 802077370, 376704738, 182726262, 823822763, 729632564, 366867590, 109944611, 764483743, 746587956, 296362238, 954820667, 15483719, 284054345, 595711030, 810717953, 646045369, 10494140, 477513904, 331899266, 816819773, 623402520, 310066077, 439324333, 736030366, 781268999, 562253080, 487104625, 233168656, 403554199, 537576743, 711169012, 644955646, 881209424, 722269955, 441866362, 592422743, 58270764, 512265634, 737437923, 957795918, 55499277, 42310661, 744985961, 409519651, 189364810, 662901790, 879581122, 143297428, 855319468, 665081702, 998496931, 724759847, 532089435, 515468759, 595532935, 973195676, 145862136, 696010793, 244532759, 282315183, 453900866, 639268967, 619201639, 397168312, 712201792, 444947322, 60356159, 598411137, 917100403, 261189048, 688096057, 22701841, 624272127, 618707225, 929041585, 636553424, 931389949, 708391650, 162376660, 893345458, 524436903, 807398744, 129727526, 909122628, 883970898, 876101513, 351552515, 940706542, 549140205, 810591717, 381709508, 235413611, 297708135, 169661863, 632177045, 733084413, 859675056, 253286024, 724055846, 326801436, 847696483, 238719485, 222719596, 640762726, 568916706, 522617229, 464294368, 986457366, 666956961, 877056924, 394109171, 86330393, 218071833, 668236393, 555248148, 904145517, 596771466, 256734147, 785573268, 243770615, 72792748, 40647522, 786239805, 958402889, 834557773, 270697892, 367001965, 802268058, 463931550, 869624566, 348848987, 100050777, 537502065, 890761890, 65115949, 709264241, 203223327, 704883110, 584175111, 357375202, 948025364, 391187736, 504936236, 365557988, 897754138, 963548147, 551518638, 763782870, 82920314, 563571086, 482914450, 777577898, 874233207, 802817779, 128390461, 203322875, 596731034, 178850749, 917633116, 480795644, 832593493, 68111923, 5815884, 796488219, 70736348, 186825799, 952433848, 812017572, 523305151, 181412727, 276199294, 872515106, 698668281, 400840184, 248257060, 978566673, 397403466, 21555423, 519583403, 73172221, 556061231, 82959064, 86667016, 715757195, 340757639, 124262513, 17183804, 353526319, 418534476, 261634980, 746947567, 199761963, 138727202, 187856656, 916426964, 325671254, 851986035, 720695449, 939537971, 820056911, 941714756, 953752173, 611259660, 158803202, 228723346, 557805378, 977911906, 653922379, 722656685, 583906133, 519339144, 818548772, 232849168, 267508959, 563586388, 210896472, 87361957, 355870338, 878028287, 164906524, 126506455, 896888215, 659719371, 434984502, 86815397, 691548777, 265309830, 998625294, 655095928, 174638638, 238497731, 671214739, 437085462, 661901548, 69719508, 356749178, 890778141, 25600822, 401158769, 396478448, 490256424, 476780070, 900723275, 753963998, 892359374, 767845774, 324062122, 598620718, 394047345, 367310168, 331362473, 422282222, 761586949, 49424511, 41733869, 40662555, 509334461, 197853442, 347632526, 588005536, 220841481, 601573015, 150536558, 330708785, 505488087, 738925192, 566830016, 488969575, 751421432, 348952006, 465252940, 546945995, 811462635, 282493357, 195777327, 589861484, 152920727, 421433790, 383758390, 734860339, 538528052, 144892893, 679229470, 293416162, 716821762, 648358763, 119944563, 504601789, 586851166, 354512880, 295003940, 248602121, 942070940, 584110570, 206237258, 820069805, 748777055, 770245284, 445604668, 690291223, 782790728, 207214294, 950782540, 925889648, 726156530, 940346688, 341433146, 189012710, 162055332, 484085864, 857816210, 100921963, 173287266, 795838714, 513967600, 688671493, 886512426, 962609216, 754101180, 455691849, 486648921, 181948813, 171469411, 97247034, 436592529, 582448368, 381032413, 281844479, 984412631, 166223654, 756065498, 117125865, 210665128, 837043143, 908728103, 680847529, 943360940, 607318691, 798183545, 869948758, 736142619, 658378803, 176375618, 510386185, 839159141, 848324775, 906856117, 634807338, 322803047, 669997417, 959419799, 468034414, 914708119, 790178895, 903113787, 244635081, 917621184, 441183274, 657404415, 35403057, 454823761, 676286558, 124549855, 752776483, 857925485, 985830420, 951484240, 351668080, 908656548, 32858774, 1506246, 14349081, 91997450, 518305385, 183729850, 970052368, 275173648, 768491076, 974284950, 14349141, 587276860, 944459991, 666217656, 591743582, 241296039, 721030454, 88274423, 951760600, 162431468, 260963665, 236248220, 638738789, 210167902, 573285754, 269846718, 541522081, 436704642, 752418794, 744473414, 494846565, 991867402, 713505998, 30317490, 258049603, 191302900, 91514439, 542875252, 225812823, 959262154, 74410834, 692404020, 268647796, 271880341, 724259351, 407590333, 620261935, 620300418, 710401431, 181213671, 239700514, 926373423, 298331279, 867305590, 524064364, 632344715, 32076714, 11320481, 479507989, 668944066, 404012138, 383363787, 691084127, 484685122, 763973998, 519928259, 954152574, 607916368, 715350068, 15534805, 74165598, 809405241, 309070591, 117875256, 381012444, 510654673, 871582164, 580479848, 295702343, 730280391, 382309120, 16383915, 308464264, 611933373, 481458963, 372070145, 274285433, 525753640, 149117125, 772513055, 437030364, 249866578, 856092536, 69825776, 166464077, 519941920, 303858022, 888561772, 585412675, 541996247, 449382276, 936339121, 982390405, 83370289, 861127480, 434830403, 547279072, 622781498, 721786423, 91940653, 500594766, 392206545, 466629321, 708107261, 497529962, 849763769, 999567917, 983053093, 826952134, 109906470, 303892113, 632862316, 658337428, 636805844, 301274566, 124709870, 453177483, 498125013, 331235156, 794283057, 443797259, 917412230, 314208015, 30730963, 488889083, 665014548, 897752994, 549018358, 707055334, 119597845, 907552365, 53798165, 289143928, 416117719, 126024144, 850970348, 843085639, 606560158, 611594439, 908217526, 921513090, 973034331, 632600828, 919930029, 848508709, 313764126, 342992073, 991380941, 72539747, 654091490, 112285215, 223332828, 435994616, 345530337, 738547235, 166769255, 834475189, 544363047, 740124302, 543531328, 678489699, 833585858, 442711447, 605394947, 130040040, 27775316, 444535486, 728630371, 910085113, 873276940, 711423088, 206296603, 362020150, 42463696, 990710449, 339860276, 427021558, 530241257, 847151287, 465696042, 534199454, 547370061, 488846347, 55591438, 41304795, 847827830, 864386120, 746010853, 467024471, 58682017, 344152640, 944820122, 660045355, 466838922, 323392117, 834300661, 782270658, 955071833, 851143951, 86064444, 507965367, 404963002, 850315340, 344937568, 405419051, 388943156, 164556509, 630415863, 233240533, 637430360, 870272456, 331345771, 322417439, 226833155, 512977917, 731964953, 916270575, 387473663, 193936613, 350643302, 139725739, 129291296, 203351947, 592109987, 451714835, 887629405, 580008958, 630674901, 68363024, 330063149, 70436774, 453313862, 894150249, 917652099, 165512893, 604220702, 54701883, 529945474, 980617958, 891919608, 927131801, 912141198, 714954201, 247304314, 515729277, 446988372, 650028985, 239497413, 881398037, 91514124, 410228293, 637796978, 165532339, 811249776, 179250419, 891608455, 723331760, 46311845, 648955644, 139619795, 334728991, 341315829, 167966084, 502599113, 160057412, 15098866, 747003153, 547553755, 152492583, 945750228, 762798210, 287986192, 900427813, 669148856, 851233942, 450085835, 761684473, 382294173, 784286169, 20942582, 312518796, 368390925, 4927666, 612833985, 598213206, 350859384, 552200019, 499903411, 406581340, 528349714, 819147673, 66472108, 171377736, 553584979, 891849241, 741522463, 352639219, 820552660, 697072854, 483993197, 592392364, 821882139, 846421733, 60734140, 502140419, 34301546, 829637455, 551846356, 535204997, 418804615, 634196400, 864262035, 803162150, 449588139, 643580763, 193557631, 35831741, 273408931, 343801220, 631977488, 684518485, 282458566, 585649656, 620829705, 79229083, 763701754, 815267592, 499401983, 834086107, 253187930, 846400465, 749874071, 579007085, 100401723, 415327439, 54619750, 363106171, 589905273, 295586019, 389219628, 648544776, 523322750, 255751399, 949746318, 115540225, 553795677, 718154854, 771463250, 374680156, 719944881, 51570151, 119844381, 614397240, 203107027, 826020923, 191917789, 643216319, 963246355, 689056987, 295496017, 306950173, 294444082, 717551858, 687246477, 531304446, 3492311, 786912327, 835207454, 444640817, 479269424, 5437719, 588622092, 85996613, 275482516, 123711742, 686984834, 607097121, 117123610, 831783987, 509193525, 168653457, 950872653, 663244855, 15928634, 435927582, 395555203, 157982922, 833700521, 513363443, 784196888, 179291296, 603764728, 687031478, 760777821, 56089051, 867946582, 675274306, 195635699, 189311600, 422933062, 688887381, 295826703, 312825296, 626440947, 260359851, 798764662, 866763211, 56770677, 534664998, 709597771, 184401164, 482362568, 812357451, 196607498, 49605496, 201868586, 250902563, 141462695, 935090704, 815209315, 537400543, 891939321, 185977538, 592273149, 275420355, 898756721, 964500831, 735717312, 885138, 984586239, 699516510, 660922665, 224082706, 665530512, 159921151, 329408605, 687186202, 330097984, 878958388, 325733034, 10291982, 199323008, 212816774, 791916046, 312845248, 826228097, 959569820, 448179906, 449190419, 712551883, 833699083, 966398000, 186143355, 877177285, 999938686, 26017365, 442342465, 883896521, 440424658, 267619975, 465951978, 664624989, 299042692, 595591966, 386136182, 89792616, 848139562, 19672176, 494838808, 634537502, 101164497, 832549880, 432086186, 383089923, 855122806, 712445207, 915594702, 133331185, 863652247, 917038040, 48027556, 236561162, 263102318, 247717590, 875517013, 128287081, 906815039, 462850964, 773412785, 283633873, 635008650, 768272543, 656474622, 473349924, 175634675, 112782919, 289471108, 752995986, 46059815, 190695732, 284493886, 255630062, 671103044, 776728374, 767446726, 392008182, 959431860, 886639172, 615851130, 299942484, 743116391, 228778633, 504144248, 598850612, 869632977, 512582092, 909234637, 901068834, 476295116, 324700189, 412598508, 676318573, 694259549, 968864729, 299876212, 138895729, 182295366, 106615855, 587369289, 708541072, 718215717, 90899054, 899965675, 136607697, 489851689, 640677228, 295647282, 336346167, 847471118, 589953600, 592839122, 559254864, 112930240, 903486638, 167332361, 393869011, 639799904, 344873831, 707526218, 74207976, 5175062, 307388942, 936431621, 835891525, 599048961, 483721499, 799267277, 738637640, 15062430, 179205394, 768306018, 958168162, 945580534, 697050016, 497792333, 748903620, 645739942, 578365894, 478565742, 748965486, 121384656, 346536663, 639688883, 904652456, 980856847, 37664498, 227411250, 422877328, 301584762, 203832437, 787544148, 710928709, 318399702, 148222233, 822382037, 483230348, 534163538, 344738125, 50547162, 334248065, 287349101, 658584762, 215913886, 339346551, 581981220, 696633690, 264507267, 206558282, 234048911, 551327635, 93115989, 661864384, 642663255, 896620984, 80697637, 269864560, 910829229, 82168999, 315621530, 661531592, 414235342, 842372231, 434326609, 15240906, 661914579, 4650920, 926853121, 684360249, 280447397, 372717697, 608764776, 276895983, 265236380, 267168071, 524471479, 828772307, 764275587, 606931836, 563057026, 68301430, 270980977, 97915247, 564097741, 936411433, 46380004, 367180294, 717626391, 568564763, 786259288, 913724030, 796435598, 890572176, 196144229, 37216350, 552478188, 191737766, 476966169, 258341903, 342619193, 714299144, 192734452, 909747286, 837374659, 789924871, 335124886, 15624242, 768672032, 734205899, 243970583, 796545948, 34214135, 694832835, 399427135, 204317913, 877861763, 280302719, 550375894, 503736582, 719593552, 311173752, 119575915, 752322610, 396537229, 513731810, 630890093, 57841950, 56900484, 950152751, 839618881, 161761630, 809732804, 444386411, 452389022, 907443093, 1391751, 332251276, 424213221, 285708103, 686821521, 511665754, 969075625, 485250804, 121283641, 570376055, 824078606, 316359454, 631152633, 554343547, 60251934, 604341, 586358220, 509084087, 772050516, 201027587, 631226448, 522840730, 144021355, 803658167, 263031165, 405717315, 96995508, 910734833, 982988669, 36825560, 185096635, 808726090, 774885514, 617305448, 828117395, 976587617, 183453311, 65392466, 387958993, 685116280, 697355083, 930378969, 117251101, 800746064, 145790964, 244507716, 374554482, 429361614, 410151781, 638234432, 431636266, 740382815, 131984591, 9392136, 851524031, 734867445, 282788910, 232648129, 463587071, 798290088, 140606911, 344264554, 718901731, 919187911, 744050255, 136885732, 112516910, 419306866, 534871188, 178446380, 39539686, 509676793, 318554883, 650584689, 354516615, 33581666, 12198623, 807377652, 966100808, 279182475, 95305434, 554266475, 162015383, 843824260, 426934857, 898806281, 138371782, 649978841, 680115658, 455077057, 728218655, 619714486, 656344625, 905268842, 834971552, 603721621, 874366233, 307984766, 339829210, 422667052, 620132635, 340397913, 30985706, 151628181, 674001127, 232378282, 504068506, 735687902, 307651127, 117805605, 531054023, 146468469, 864901516, 367256332, 114630411, 636402678, 642548364, 941746551, 65760878, 396063267, 628165892, 299496053, 868601493, 282692062, 923034561, 724683053, 178523404, 371632126, 726573067, 815865501, 215585858, 637434040, 774084973, 261411126, 889965768, 450401141, 217450280, 343428974, 557042755, 245155688, 107377082, 280520421, 872995441, 420585212, 311494534, 491939271, 249501157, 884237251, 306009106, 618911855, 2484201, 414578285, 758940369, 576996529, 9258122, 439302539, 824906065, 205905908, 538798224, 465000157, 579247995, 804072660, 397306706, 146700580, 526937547, 216956026, 82801974, 35826971, 84147959, 234614628, 268469398, 466806490, 9162947, 42205273, 660691617, 179261351, 87116431, 252881569, 394949657, 186781121, 753239912, 734034393, 381247094, 684123566, 872385092, 952948561, 121872674, 382240258, 748239274, 761237575, 766697993, 898423399, 311731305, 960339366, 946775088, 751902447, 179105362, 176044436, 782572795, 83392402, 770369993, 900936162, 92731948, 702277387, 309746124, 144405434, 344281161, 415216070, 473944369, 654521652, 330138840, 73089882, 594497082, 497874402, 346092601, 402119148, 569961999, 269840240, 817493325, 579757508, 681591997, 86384733, 252370557, 124868848, 386131734, 28739189, 67603269, 580668524, 479349374, 863843369, 332321231, 178388321, 554693607, 531230268, 90462722, 766459692, 489630827, 610068621, 574482193, 460798033, 57884403, 339010201, 751397939, 648783224, 729076029, 520220152, 607399914, 464753076, 944830946, 252457919, 920818507, 998768808, 325740480, 129850392, 190124766, 525738414, 739462817, 850598937, 673837504, 827503002, 971029978, 710893617, 931341953, 2535884, 559614825, 400660351, 292841935, 805457312, 464792942, 584007230, 73599852, 850446127, 689644434, 295078816, 404695231, 133687563, 827395483, 490203648, 719880540, 89594641, 538398032, 525036726, 506933230, 151636498, 100097018, 286136769, 921585248, 987752537, 324028447, 741129530, 98504756, 54475209, 648319437, 477937707, 456597573, 655598154, 643064782, 692192553, 665722633, 131727875, 133559032, 763460037, 633704276, 484789877, 145682024, 198813507, 172848986, 571583380, 3210347, 381246316, 195805580, 954111980, 516086638, 527624933, 772415993, 974212136, 568882555, 858830192, 933901684, 636752120, 213926105, 778214259, 879260654, 802705839, 782875037, 646926868, 155823554, 51883981, 920288210, 644750154, 486885960, 600488752, 992853085, 360719200, 666505856, 3816485, 732914031, 866575593, 824953234, 405933580, 562680998, 827246449, 700993252, 411952807, 265497736, 699231489, 602375787, 99998399, 397657981, 966293156, 116670334, 381729918, 577517585, 202841368, 291535506, 104409298, 601778804, 351100947, 231375815, 521635954, 248646312, 571978379, 675054083, 243662114, 832505939, 667811674, 367043666, 411871899, 47073226, 172139738, 588038695, 943756643, 631672388, 830423020, 720197364, 81810279, 789998953, 568284314, 438398679, 141723922, 252337765, 970279300, 592368772, 809193271, 388129130, 973400100, 288410523, 972926195, 370749066, 824609937, 331077979, 771030749, 923475607, 202576257, 529021772, 46805907, 746925193, 263076130, 712547943, 276506990, 346291832, 950649603, 323685359, 684957702, 381149646, 802310423, 12352738, 82792382, 738712855, 999579615, 870578944, 524292741, 367214536, 790874901, 799135277, 551388206, 975174642, 996499928, 847938990, 515558409, 736640262, 378896218, 178192071, 907079999, 870286846, 987805279, 231957286, 985307710, 575659599, 967913645, 653798305, 475741801, 247791508, 976675539, 446779714, 402156648, 716545860, 866363355, 478549672, 317994635, 794711411, 861139312, 408393975, 461481156, 219707892, 604012914, 875587440, 799893454, 287473959, 524250322, 188554573, 587072645, 997290273, 431087615, 643399992, 846195563, 757548829, 33352468, 163744505, 891574266, 976423327, 525722636, 618316920, 912764690, 267922450, 595467782, 68382715, 9855068, 195011060, 37809955, 994454887, 56977910, 485723225, 676753476, 364512039, 934331021, 68773212, 642316349, 906500016, 38196009, 953560841, 254554815, 546789419, 996009456, 533918880, 206938797, 355210751, 159501385, 18345311, 713580475, 478174431, 723778838, 122134860, 989610196, 96543495, 959139055, 800435578, 230690081, 133682979, 743132367, 746744921, 580115168, 840588, 525221880, 93436947, 750587045, 89934712, 500046657, 90165532, 225420180, 165971328, 22355917, 428805992, 889977193, 758589326, 344887379, 137017034, 643135821, 95861974, 246131172, 468038300, 767317554, 482016324, 138845811, 782029127, 126461440, 676491132, 969335900, 459781796, 838876131, 6856313, 116856132, 348228214, 183279631, 620284082, 675136444, 987985335, 978419346, 787270139, 775259006, 373714075, 852058348, 632955776, 265009162, 349854682, 843896103, 477234760, 292834660, 109505604, 599743081, 73807077, 271809493, 409467811, 704950788, 772594632, 1041619, 56616132, 478824025, 630012270, 827773404, 852726767, 70651035, 845009472, 32873981, 249394409, 257748767, 908951628, 734136981, 972452123, 406052184, 624755073, 330168392, 22018815, 40841463, 290644758, 318163214, 124330540, 274222286, 900080206, 493977557, 54996806, 251144961, 717191814, 663304317, 426740739, 752701480, 818243773, 625351191, 68663706, 869889291, 821680679, 634669906, 215356693, 937667289, 767441625, 267315076, 744843220, 149669558, 742811640, 40528603, 383955195, 244845835, 473353745, 389111982, 915474604, 724276687, 595786629, 492467083, 732778872, 639636219, 488103132, 753058923, 271370896, 307448401, 875865949, 827239911, 938752291, 435137364, 774537432, 963681016, 822702018, 860231214, 702396588, 955366699, 626207509, 411033153, 634377543, 889042075, 737819494, 746748448, 552218070, 872664564, 1159741, 491580017, 948167236, 734265765, 114294859, 413109705, 107793664, 521247423, 904831042, 798013512, 787659386, 615213623, 64226434, 822892454, 955633082, 988019489, 984581179, 156616882, 391259235, 620341928, 516586751, 833656488, 736994761, 992362695, 39069031, 882644608, 693905745, 974599661, 546734660, 477052396, 792420539, 590390668, 619235984, 375338018, 320892738, 689167099, 741676088, 378125490, 937016033, 911319838, 577469036, 208357368, 681565718, 932131635, 676951436, 181008518, 399908309, 280046588, 359169956, 82673171, 469847954, 577019564, 550291152, 525003806, 162938236, 890220701, 660452505, 684878849, 483335695, 504939785, 238454155, 687523857, 385574489, 527773853, 722175781, 337088350, 934091852, 123536285, 243976006, 610833726, 898563172, 887379781, 287584551, 642080690, 74853262, 703386103, 258251868, 150123893, 926593120, 819170954, 173546634, 337780929, 513708188, 890178688, 68682794, 280434961, 157095380, 271838639, 518769869, 429147456, 5705362, 151245315, 652862004, 744879985, 831852115, 851635897, 307838891, 316154845, 994017635, 584265930, 187556703, 760209230, 956261499, 174574348, 326209271, 79122, 706436789, 360589342, 991113686, 549135386, 326252350, 538211165, 910697172, 556587112, 565778125, 120230534, 966028253, 340187527, 560301132, 35240009, 962359542, 562036837, 527786140, 147487358, 296768858, 26316042, 248572665, 952332740, 830325988, 124737148, 8505585, 355688943, 378563084, 288481917, 920613116, 201292563, 922655223, 209773712, 323519013, 620477341, 103274570, 532871668, 133456014, 606628010, 172810088, 108941706, 362204432, 885385430, 729992869, 308500640, 72228269, 135308259, 492674149, 378011988, 966988412, 873511425, 936686447, 921480542, 529898215, 413919386, 290394807, 714050838, 185365842, 826672503, 54064953, 903966247, 964501660, 532838753, 479187371, 192214022, 795464917, 629810312, 227943178, 823780627, 769003202, 155041286, 111407999, 199720556, 136621070, 484933851, 288465394, 811225326, 701773021, 476041904, 960601095, 258996685, 264737704, 724509703, 400444300, 736655871, 932677177, 795681769, 937603203, 911987357, 634687367, 873958935, 698965830, 305366456, 19803735, 161441774, 562359752, 457286091, 309006622, 375249973, 679289355, 460479420, 787018627, 906458364, 267809902, 787050023, 114575006, 610279886, 679448511, 213778236, 338253575, 821115196, 211923936, 890427304, 331313682, 885864819, 5453562, 23707825, 173659010, 582273714, 33178110, 570179403, 729187234, 9405674, 413843857, 369630823, 142699832, 241230258, 360031061, 434986408, 568888627, 814404512, 779159263, 851507145, 67732688, 302280429, 991260520, 390526778, 374113960, 66038503, 625689442, 896620200, 151317150, 417847853, 289565885, 511377907, 708547031, 481548721, 124212876, 22542903, 478620515, 103563217, 432629456, 890459373, 959059379, 740603843, 491300401, 767412050, 239417051, 350639363, 156801608, 965455077, 920057493, 235944770, 350298446, 672635335, 441380877, 205876914, 889652762, 241868250, 72036784, 877053651, 670442574, 329311358, 109842371, 133450088, 677386667, 348881005, 145156907, 273936515, 527312627, 369864371, 561043138, 113227528, 134103938, 120683196, 325534756, 926553523, 827327215, 551704339, 385487755, 17174452, 545511232, 978285992, 402737373, 791330151, 388077377, 989286544, 797174223, 581699019, 211512093, 921175231, 612340823, 464989853, 81026366, 546329967, 582791599, 984581706, 805193238, 448641139, 799613458, 719188063, 970527002, 599053738, 82283392, 167997659, 547929358, 552276369, 588013446, 106971161, 546019779, 271552856, 298928239, 135366773, 869570252, 974406296, 85335516, 158952795, 716952456, 941005223, 19274901, 981158, 174825051, 122985613, 387571853, 336516150, 696870527, 593065522, 34475140, 906968269, 266052111, 122469322, 224445101, 31541696, 358525024, 486902975, 850396610, 32662413, 533943081, 165820472, 397579280, 813776624, 762836359, 873713950, 500164954, 979946550, 661182530, 545599927, 221752234, 546633839, 898515261, 701661394, 280669097, 95850756, 728407933, 341333662, 31980350, 563578525, 360242750, 913689113, 231266584, 754791317, 433896817, 61075676, 963392839, 382980220, 330052816, 782432992, 226144269, 704250136, 38380484, 503493888, 567219349, 585448038, 496353483, 326679769, 554227850, 812965999, 589114934, 315388004, 413973113, 984531656, 801628120, 700374975, 917586041, 210424748, 446684643, 332512242, 272457682, 825908513, 441386807, 689343974, 804091094, 748310390, 189235880, 96907350, 107417257, 610569627, 433902871, 79610949, 137438381, 396704648, 988753184, 262788807, 207345187, 951015223, 695095555, 84136551, 695429333, 60023457, 740530933, 997686854, 266575748, 575234223, 397716176, 72803130, 425163261, 162832811, 269030348, 534424572, 320618898, 20933226, 395107369, 601127253, 745605462, 339713536, 357753424, 531618530, 26372339, 731646418, 894698095, 360038327, 408968069, 598403575, 314897183, 287260491, 439886564, 623926712, 61582451, 402618477, 13518162, 187509961, 336897993, 24524719, 981678879, 50249795, 776462820, 264868286, 576206011, 15684554, 361881470, 45534309, 874166596, 753457623, 572032048, 573807774, 449581554, 278316921, 805342646, 337904743, 545189146, 228089866, 617865894, 904088819, 69334192, 453534887, 349985210, 137923618, 368325430, 85890214, 124526915, 535143560, 878616998, 875650179, 591372313, 369151321, 254594925, 378480339, 387356793, 381370421, 851845805, 648817490, 990443714, 136869651, 503018039, 491992242, 567004945, 793980805, 410634244, 932341106, 333286533, 755146682, 487614603, 35924468, 620573307, 944424425, 806130366, 844098135, 379695948, 90548238, 55645865, 757290482, 589653527, 766264590, 72478911, 348212807, 776923655, 848256488, 568913003, 649532535, 124529826, 283783202, 776958666, 316663530, 74580147, 482332436, 465600777, 426191612, 55234424, 913978023, 161421171, 826323402, 250710728, 520870593, 454189886, 371891853, 38802115, 454536881, 270204093, 772473481, 385726016, 669129701, 852727578, 128771419, 547246663, 60729838, 181073189, 305680451, 13017407, 45839352, 204787150, 430300033, 295895077, 101930350, 695858306, 775976754, 344008060, 138633062, 919836980, 582789107, 752165487, 906834355, 338888216, 882588540, 480425669, 528745174, 511627831, 971806493, 160673578, 372289627, 738442948, 477973356, 501009055, 909350355, 668227671, 460778664, 852330108, 744541473, 488555325, 419857369, 692512089, 617642937, 110112783, 307363068, 863751151, 1447608, 959334389, 531501603, 44139339, 474272631, 571679581, 925304341, 221361482, 534955563, 805463351, 655185011, 505002670, 86044079, 328499405, 463462121, 677894247, 528740682, 124268113, 840488457, 951978875, 312065423, 837445832, 58226297, 53044416, 82246449, 249887554, 518159238, 883407627, 7849526, 716847828, 886619562, 432160187, 462291703, 148317326, 733180248, 421349849, 520607604, 219716361, 400141489, 118357155, 20639412, 285371294, 578570566, 879570664, 496533416, 214847314, 747858419, 963494974, 912153714, 434324674, 234891888, 754514670, 42289592, 334799094, 445913903, 338516523, 809534789, 842668065, 707096712, 139412831, 534997929, 960781460, 265967200, 802438533, 614873287, 966516549, 14752526, 4553697, 954971002, 609674689, 937688596, 444036390, 490681480, 802673031, 25859832, 813669079, 206800383, 69568688, 248266765, 132497283, 680975176, 625881759, 508097747, 345502820, 72169190, 133923783, 632764471, 350818248, 107320963, 98488265, 29724274, 958310493, 745673391, 467129737, 20868356, 175497480, 570702526, 618436497, 212645650, 813529173, 436104158, 440203768, 90033519, 453889964, 444252672, 841197546, 653078115, 177340232, 523284249, 513389141, 961124927, 118743836, 227956376, 707680575, 588683884, 8755296, 822573650, 975878983, 912853716, 267555969, 348417031, 79020878, 189614065, 189013407, 581605596, 753662522, 893929475, 228861199, 699304566, 276885846, 633992863, 411756166, 455425746, 401822381, 938161422, 628854130, 237250690, 11939637, 124410959, 225988139, 891132505, 13940280, 262353710, 79407917, 925341747, 552742799, 273919668, 8053763, 275270543, 166401585, 634810056, 153111134, 773751713, 931644558, 486472593, 624343855, 21469817, 315507227, 86475231, 384741390, 828914098, 506745114, 937222146, 901704405, 624700169, 991250500, 674669195, 54061698, 330374485, 571543775, 815696003, 851567923, 886304427, 449159739, 625922420, 189469244, 552768445, 691555397, 786166000, 165818026, 442334066, 82941899, 611763274, 307065493, 799495490, 835537519, 428298934, 530543377, 421331558, 230074366, 192179005, 481105149, 822456149, 137860590, 679959447, 605853313, 513325575, 839133663, 5012960, 594531748, 810562457, 7222375, 355637679, 831427223, 209552520, 571270673, 567547129, 683286461, 45372272, 621503756, 736819250, 781185613, 438402858, 344748808, 261854859, 178565024, 686059580, 607129871, 744980032, 653329935, 216601686, 226451531, 432079645, 462321448, 782117269, 78489638, 752038950, 487856526, 275360437, 447467971, 873385689, 525289458, 51879292, 510108697, 453410219, 844897504, 743053358, 865999154, 841137710, 860328702, 232668189, 351867913, 54278853, 308547240, 823141600, 114362676, 725377682, 772630751, 366599782, 228513379, 218422279, 69414101, 595890512, 359241876, 395180852, 140131713, 482222932, 356415641, 131575781, 29763142, 803288994, 808057998, 232145592, 326097652, 960019834, 530753656, 535230202, 911511482, 553048979, 864027039, 767905353, 663379639, 95811887, 973869658, 74719863, 665035376, 947391820, 600846923, 903316650, 616115287, 728138541, 143859896, 131569039, 638842588, 939376144, 609199266, 712474870, 976378214, 80410996, 679284008, 68814635, 292604630, 798429976, 600410497, 738393739, 664836611, 22932340, 80220205, 148284049, 129450424, 316785994, 188515381, 349946981, 212143611, 767741442, 382503238, 506881210, 129542149, 640652572, 698438683, 613783707, 103298355, 392851256, 210484362, 757293917, 556694565, 272880179, 498007795, 805953854, 411190882, 961686384, 871879934, 971670183, 540059325, 319119826, 245194742, 137016364, 689834430, 669699112, 582551303, 48483185, 909868583, 937463919, 275178739, 804037067, 952260631, 717810465, 534838750, 65212307, 844442872, 657252666, 640330635, 992297569, 41497591, 21699716, 706580614, 865827450, 231449865, 587444198, 909420183, 948864341, 64736037, 76298314, 345962695, 732572905, 997310541, 257197859, 734096866, 283734366, 289431307, 934687473, 862059054, 956442874, 796683351, 335003696, 813113650, 691500456, 295329745, 123739235, 190112610, 655846702, 369065685, 661545385, 631149790, 764469756, 56019207, 724033446, 399166225, 779765787, 593766765, 722425284, 885199999, 616291439, 280298548, 86991438, 800791868, 700912518, 460739753, 511754930, 737335757, 345345301, 584172521, 947939222, 636911050, 927841860, 77509006, 777435858, 950309721, 929698561, 461878526, 60005082, 239431894, 547657817, 366473912, 467170798, 340578699, 242539315, 164784456, 958702629, 97435162, 377359355, 986044673, 375187076, 410767411, 715766715, 852098860, 387786482, 712387373, 942120461, 777185840, 272803232, 426258414, 574659989, 537544574, 914350395, 638819825, 559634184, 804300147, 443451807, 834335621, 293815848, 675856122, 972432447, 798307309, 495259127, 407733525, 40227695, 106716353, 632525450, 203709622, 650389576, 984533309, 826067313, 39485975, 435180393, 438079250, 400051783, 238641530, 307606039, 907249920, 345819271, 806400662, 30674637, 487651260, 903182771, 350481639, 90532022, 397702209, 830225250, 268582192, 818792105, 597241211, 975929546, 858820611, 454558133, 311864639, 19927239, 176999836, 917611889, 969899867, 922186649, 278144840, 616878938, 231189100, 790499486, 727272140, 1961273, 636547689, 857923506, 215080597, 113918948, 72269748, 650214060, 262126426, 6176448, 298721374, 597372298, 443260441, 615952960, 70077411, 159098349, 134580593, 222980809, 365726266, 244259854, 122666939, 746945654, 450981277, 472592896, 53898738, 788877193, 741540536, 946734412, 624482677, 559074070, 671237673, 904718522, 623322881, 788777540, 908242305, 420223573, 376148869, 839586101, 640533263, 320200969, 205588544, 467774129, 976488091, 836766497, 644346344, 247306792, 420187986, 163377792, 69881889, 93190282, 878688893, 155218612, 620706564, 854872642, 146113486, 862583675, 804563916, 929128161, 287221110, 198244310, 148245469, 572593352, 698396269, 264341305, 251650000, 838237617, 272588331, 487390330, 422064790, 350583903, 372562957, 472652903, 735189453, 501360236, 405878538, 966653939, 998885500, 642176095, 476627082, 708830996, 360274068, 838892110, 798334322, 142427196, 978095457, 17992263, 41574629, 799275501, 492896473, 198273533, 800523512, 537706086, 476510492, 206762318, 569273941, 224124570, 945607428, 425641197, 963806478, 219407941, 378524029, 255753723, 381043168, 898288954, 886873035, 423181353, 367096716, 148407387, 778251759, 270411613, 708551440, 139453167, 445656934, 734007270, 263718896, 604101657, 68241842, 714007771, 669332774, 508001, 862082528, 332356135, 168839930, 339249674, 177686172, 199357320, 417521206, 419630802, 552292856, 700891213, 244975303, 415212072, 931796605, 792032697, 918049756, 781643325, 202103348, 725920338, 303341798, 322230233, 75513096, 563932694, 306355232, 696914750, 306481613, 31446844, 428780994, 512436264, 60209654, 491457704, 843542864, 186189162, 983928500, 441594824, 4891933, 895199735, 283527807, 843281881, 462681375, 311162304, 155782901, 181157064, 430934853, 746522898, 137833858, 692268971, 264583830, 974428361, 436603720, 484573174, 350059510, 557797637, 845211974, 210387632, 520496793, 37367338, 870998384, 712469909, 66828114, 647633889, 832209170, 468492115, 563148428, 393943235, 244381293, 819328393, 309312399, 633421683, 203280541, 548529200, 420491974, 82984834, 995732646, 585183599, 204999194, 582680039, 106562907, 264303683, 793346692, 128251008, 553973951, 714475023, 936070275, 364781945, 455766826, 666063539, 348347577, 700948950, 816048805, 594972918, 507564341, 27992697, 31524973, 737352936, 775245829, 517705268, 1922386, 633081293, 633921596, 802603496, 731930499, 770278750, 691266134, 897434542, 315598532, 253445888, 413884076, 543501812, 756735826, 697543230, 755762954, 845674663, 321139894, 927884991, 593243914, 827460046, 462013796, 285875788, 352808098, 950980589, 444042564, 847410176, 838832483, 712275798, 122796785, 185211204, 831952987, 170128834, 403724282, 119800220, 195559355, 197714644, 111237079, 136581880, 231599060, 637783205, 512682161, 387632277, 8336665, 209466589, 144473361, 605505327, 822802006, 580477647, 323642351, 243792953, 668474395, 999366990, 848894028, 21450052, 598498913, 287363025, 923100538, 195317859, 897477525, 935805091, 768453817, 608979558, 578103615, 239686680, 339765174, 865456432, 144611561, 362677971, 302900125, 817050466, 485597313, 594137322, 928803423, 574875210, 105751880, 600449685, 989028387, 439156132, 949331543, 745433945, 568470460, 940246830, 972318833, 882145227, 341662167, 784481036, 424683063, 190114049, 376665321, 216448882, 561697268, 596501268, 37973918, 686546910, 203133026, 4466524, 633336662, 103306881, 920698259, 186933187, 543405525, 598356321, 177847163, 428608711, 994363723, 574284092, 543694813, 983888165, 967979200, 903027071, 836236007, 985068847, 31215914, 212978243, 773250206, 776536611, 777332350, 831907444, 597727070, 629540101, 642115575, 686761728, 84713709, 198306627, 419618362, 538211073, 816359523, 108501702, 198366424, 462533973, 524966452, 570570775, 982080880, 382703983, 583279326, 327653858, 927344742, 881105135, 133686985, 301134736, 374479736, 305323990, 914110124, 273978812, 476049492, 41180147, 176706403, 670034118, 565864320, 209021600, 371481263, 856343139, 834233824, 114724709, 111580425, 830191851, 835028877, 129024282, 75496351, 68908731, 642264541, 672032898, 583249325, 377761045, 36652410, 568572077, 511323917, 198440481, 408000570, 172900494, 986039263, 636537369, 688750587, 413671302, 312046722, 535813113, 227245945, 957702822, 409844186, 423418460, 368963695, 618496940, 636436006, 966342252, 740271180, 996265305, 786866557, 489404689, 375505437, 567752620, 203210946, 804618442, 158900769, 258946233, 539923776, 534384833, 943918848, 54249270, 480078670, 218387459, 135665424, 272600663, 195085515, 69687380, 900347260, 91221115, 245810552, 719008211, 798036912, 430982285, 536575114, 627189432, 786593572, 527110278, 729333143, 308395652, 925245500, 528564804, 470517389, 399652296, 69839608, 300929562, 69056538, 635776036, 438664137, 752453612, 576537063, 767792442, 491746052, 166415417, 266659529, 175144647, 466232653, 313134543, 65115237, 121559649, 365898740, 728853153, 559795947, 861956452, 860878978, 691247107, 705378607, 46846056, 108483622, 690414214, 297676780, 326745205, 286477879, 218724074, 828932739, 65014987, 849251248, 747046902, 9621090, 206930772, 684333466, 159928478, 287066560, 371586922, 886083689, 591794896, 980243312, 598664882, 80410288, 206167430, 851852132, 88388196, 699643248, 552278988, 56282823, 817221015, 431462141, 700587231, 625638021, 257038838, 188883400, 662294237, 514395161, 810919165, 415766050, 883552184, 932034104, 138320460, 284179340, 101483105, 636295128, 262036150, 298091674, 75092247, 659523097, 252340810, 928234324, 171038508, 411675346, 578460601, 953212709, 489280202, 194841826, 255446378, 422206581, 927991677, 332519653, 350661818, 268583286, 810590780, 206062643, 781623870, 63313711, 689821789, 983742120, 652504242, 180393067, 417664077, 708773387, 201129452, 277870372, 385245874, 853323431, 890451581, 93341336, 604448528, 511262046, 831948740, 899744315, 370502948, 63681474, 154987933, 267563754, 653748455, 598164464, 331733831, 286428234, 676194268, 100108238, 405802122, 75220939, 591800689, 567419625, 944638405, 17205638, 856921194, 424396398, 466801746, 927200777, 528019913, 272812452, 376228276, 201367764, 350741931, 203328151, 700016751, 195702440, 772022107, 8320863, 386426, 313503887, 92410942, 995879457, 754069172, 825643889, 733145539, 79322273, 21957047, 578703471, 935244424, 757139453, 138009701, 119600131, 814055303, 226841689, 610027666, 534307053, 224159347, 619560249, 108997754, 42652397, 644086053, 30175842, 556988850, 420082450, 343867334, 946763397, 264229086, 890909272, 654253990, 866541835, 252861435, 900267562, 533923841, 279872989, 784772261, 851390523, 18690832, 207994765, 379317468, 919336491, 975078385, 399349361, 189204659, 366305102, 618799244, 682626847, 272750762, 143343994, 309703469, 152766168, 158221771, 904053575, 543755378, 307098326, 614087474, 663099156, 471936419, 547712260, 318124867, 349020021, 552583734, 936841634, 25974905, 453127862, 720434456, 635930619, 511906650, 813266692, 878463427, 825817979, 255457328, 398296242, 214435157, 864500621, 260254662, 631248332, 136058945, 12453428, 693866224, 668368501, 620130529, 691363401, 691985005, 668705511, 737401128, 108977358, 787968296, 436114486, 54525754, 294889309, 69589804, 754640814, 105557736, 657901278, 185516396, 810361182, 31550195, 134728225, 618878495, 798940353, 839246903, 444470298, 564862424, 208629951, 490181115, 121312554, 751599500, 519639838, 242605994, 996837354, 713212314, 151206251, 268952982, 840874019, 938412010, 986467170, 833912254, 745472722, 779005612, 284469094, 170825974, 646731853, 828423607, 694894476, 559343372, 792508370, 949808978, 591918081, 993990044, 392359153, 72800446, 285279474, 66321408, 943541203, 461871708, 927358803, 405744261, 307384034, 50719574, 535888765, 485543633, 16212170, 208824311, 93908400, 113186290, 701813075, 589804077, 303190377, 597534624, 583024554, 388031480, 657095094, 34011360, 640670219, 159639616, 440964585, 896577440, 440528646, 778482391, 121361008, 202173089, 901677020, 911985628, 554373052, 277808590, 826683761, 237808235, 205695375, 961328252, 82211032, 239135974, 979465230, 60626259, 831541315, 166180727, 906096658, 710994408, 127541073, 861284513, 815555814, 753264634, 911935705, 196182329, 312308903, 371250139, 421458544, 789137682, 658192881, 653803109, 34882213, 487144690, 79953411, 226257853, 309058801, 849179651, 821527279, 669973354, 781191483, 233505654, 567859489, 834579685, 83413742, 34802854, 253728892, 620739400, 153661969, 916252607, 928272224, 165667176, 581259271, 751925005, 478298238, 866690906, 427400049, 893190015, 342363992, 652414230, 230926326, 359348744, 185192250, 904160346, 790536721, 660896822, 581677596, 438800389, 186583773, 612311920, 174210524, 604846351, 801082202, 601037012, 682345864, 151627841, 421367743, 14525815, 995992565, 303237336, 839900005, 729544337, 749649494, 369954468, 988379436, 612288922, 631132124, 550890517, 53140728, 55988090, 116074028, 245839468, 905783369, 499553354, 451291245, 24518000, 236284679, 149675383, 10497216, 345658134, 635897414, 48072218, 311963419, 336628427, 615771035, 145650780, 677214509, 341801980, 703982818, 880031556, 914614858, 849218851, 730167645, 607971564, 566182921, 43246000, 33464255, 572873236, 426847329, 439479175, 445634058, 250301016, 443123242, 30725035, 72625472, 172357470, 22549591, 327767722, 14268429, 259726091, 254516980, 921950886, 291815902, 18555383, 918180053, 663828049, 328949865, 398358853, 714044598, 901584856, 998460996, 762158820, 459971104, 185662779, 712601901, 926538843, 144079199, 958090997, 666031046, 752711923, 14124367, 313791363, 229631279, 479583564, 930766798, 483586160, 73537236, 415407325, 491397461, 386360130, 526526192, 159467929, 539095006, 150648586, 396635797, 727395624, 261934581, 288102668, 231041829, 62875481, 782985017, 247088010, 907234694, 388699689, 128683523, 950127101, 573720545, 193478133, 317300974, 507943708, 751909568, 9907918, 844863057, 883605908, 778041390, 1093562, 439382128, 962327399, 253886607, 292753351, 605839560, 127642105, 579962237, 754683846, 880091043, 130069306, 166385596, 275367505, 163466372, 671688377, 579145090, 211716816, 895208301, 35009133, 778353337, 750099602, 781766091, 752041478, 195244873, 229122565, 208140929, 704838518, 832529824, 754792682, 836792433, 51759322, 975644224, 875219458, 698441065, 390409087, 152973090, 63845751, 19905348, 412410137, 246272475, 93990719, 513064975, 774875958, 100822227, 2714459, 641194947, 736251214, 627792918, 918676545, 465051356, 392385538, 359616750, 151441822, 118800524, 272463606, 643885343, 239752610, 668713608, 42130227, 249301780, 228733330, 362167983, 793806923, 530589947, 713802976, 134951934, 145976104, 590221035, 391998822, 312029344, 971262361, 249410506, 984154759, 744075650, 60244093, 134823896, 938890682, 118685150, 918968426, 359018048, 600464016, 653753166, 943977685, 308898406, 283637438, 289742161, 138285298, 209051768, 171074970, 8226407, 680566652, 180837031, 344939513, 371920508, 517360807, 102145048, 953936082, 644789176, 54155301, 284830998, 295706794, 879874541, 862725577, 162486402, 213241018, 989529389, 826572479, 377774515, 250042914, 307054518, 160887601, 744522832, 671671866, 314904943, 130864883, 237237892, 445153305, 575673934, 468011023, 424512739, 411984974, 241008703, 691963185, 94668731, 608461239, 815042878, 452057377, 334244662, 108467681, 467266809, 677038014, 34196708, 871681575, 968956805, 323804203, 806125782, 640734383, 254794983, 43690638, 979585099, 123244794, 941567815, 84027861, 229116254, 385186252, 466210049, 789590174, 579743991, 820555819, 83023023, 786996092, 931133353, 191182651, 36582587, 444755354, 898526031, 855418226, 800282335, 41082954, 323107, 402535947, 166602441, 481319094, 609178058, 404193924, 189292129, 102881452, 382720973, 599804845, 361615965, 825649687, 297991492, 460667973, 866461792, 943136280, 609336653, 109569063, 939204154, 944573452, 452161609, 364754423, 175586826, 369040599, 874084647, 858369120, 959962885, 702890970, 905899939, 932512600, 474202131, 567873543, 811112591, 264933853, 980438195, 585177618, 302643886, 16285793, 296238229, 11872393, 701935453, 595031254, 593219237, 11670212, 181607755, 527517887, 726527067, 129875931, 751167505, 847985546, 56212787, 810914387, 753810240, 643647851, 396637389, 11175177, 232158458, 724872544, 404205256, 387965732, 585830428, 923244457, 531090589, 135843768, 370043854, 367636182, 428029098, 568527776, 443741709, 387747895, 838997412, 70682355, 494011171, 172659233, 208443454, 15793373, 137873455, 522013826, 389641218, 652239865, 239702755, 495260323, 720500782, 112895383, 568513704, 513336827, 567377225, 335996170, 178477375, 458074773, 790744123, 86294914, 525377176, 778204754, 850770078, 782610430, 745920540, 783041815, 215581692, 396761602, 370613198, 434236088, 600561103, 522242646, 909540871, 540240114, 953162344, 892156814, 870677339, 60906764, 91353584, 661899591, 955818182, 816017064, 517105630, 779455065, 956437775, 416863415, 660623273, 632349796, 980210938, 183167141, 5442015, 799734659, 379616047, 653901485, 934275222, 176701990, 960074882, 734846257, 983097126, 169439060, 603425147, 77724952, 241357833, 654394135, 471172650, 138753074, 507054713, 889427340, 198583212, 421996500, 999773608, 944260686, 688157670, 164188568, 612979418, 983051517, 465830499, 454596952, 869714957, 819397474, 864349014, 791201366, 74634990, 174395487, 108598786, 316902872, 46529151, 349685531, 154623868, 149148477, 170253399, 845824907, 233201818, 191334901, 552330327, 878304891, 960700260, 639155602, 983508290, 726579804, 166664110, 162816621, 375692369, 145423389, 375935561, 45885463, 809416613, 657490386, 820932541, 441424558, 116579167, 282018889, 886845984, 844357663, 212019857, 430578851, 753703318, 510515825, 520123186, 625587405, 554416987, 609580651, 996735949, 9493740, 438188666, 982821706, 829400313, 305506578, 322640710, 336526043, 585604085, 396866872, 981888407, 605116270, 720310340, 756051897, 170305090, 374195331, 465222637, 265398398, 237829681, 597006434, 296294658, 209266001, 702535828, 138481351, 750822628, 509728051, 316736139, 811924978, 913113520, 94244431, 194958469, 963348709, 731146413, 443757372, 205030778, 724436708, 872587590, 867183290, 348681945, 22950433, 717414294, 852250777, 306132248, 666666226, 741416291, 54025551, 55416008, 990813827, 274235571, 357975927, 575378920, 115775612, 45081500, 667903114, 132494539, 241669907, 145013371, 352417304, 863803041, 658372236, 11056610, 965340322, 724034261, 338031467, 276139286, 648165143, 971639463, 401223246, 2404939, 515590604, 650436812, 873838425, 20463058, 183170721, 656354371, 857678050, 389736937, 454342940, 759226980, 631987147, 307238666, 329292295, 811816215, 437994795, 436874341, 920858430, 421502683, 889227270, 767182758, 515589234, 801901200, 213297507, 633196696, 807144768, 507374807, 131324985, 678063555, 849581204, 910860844, 528044507, 676399175, 630890778, 308233900, 458790479, 614539535, 616546998, 3564554, 579278302, 93023724, 14855544, 604637474, 501146012, 604086363, 69419217, 242116224, 407895895, 649379158, 575458271, 788997872, 393585196, 166318692, 964949280, 378894549, 536581998, 227098158, 215484166, 107546677, 652690631, 363039231, 860836383, 557969782, 872981034, 225569, 467955048, 756428349, 196892441, 706963577, 258047533, 770021860, 912290130, 76567936, 576515367, 72902226, 759467716, 790195268, 275478940, 280974208, 340264026, 225600875, 190672550, 199114040, 96333038, 946039660, 308929204, 621631642, 118784596, 367611243, 257987378, 298651653, 964197617, 499854537, 305897758, 559607228, 378907790, 526936795, 150426601, 506384968, 731603534, 46328496, 364385594, 115839086, 795774454, 387712424, 152327352, 618108894, 231490886, 764803815, 841995208, 861691984, 199347455, 319304435, 303198814, 345735965, 227253985, 5881154, 777882334, 112359454, 41866552, 105439924, 981821754, 165177768, 814580076, 60896461, 967367820, 31621597, 590694182, 84049114, 785438275, 370253982, 517032051, 735001225, 435909050, 366117047, 68209503, 958400681, 810751348, 958554571, 250360766, 592174144, 543534612, 386427725, 967859149, 921022349, 14029152, 815805969, 812263150, 340765632, 586950100, 137139235, 441325421, 75186726, 468441661, 614825502, 858619477, 66803343, 970545109, 166740434, 852724686, 670028318, 538623293, 23461048, 768366648, 577875431, 806151240, 372281134, 65513993, 451499665, 780292967, 915432484, 629355315, 580394864, 349856506, 141527490, 465416831, 258387647, 380600444, 426881273, 612857229, 228094606, 141262140, 782239196, 815583103, 75313470, 698257931, 938255222, 844610452, 485391639, 194060417, 769663684, 339301623, 102510619, 641821645, 388563377, 432817699, 55083719, 413034153, 40869442, 780986734, 415282591, 227757760, 767472124, 525797225, 540608500, 248114948, 880838110, 853000316, 191070580, 500879315, 701023287, 963320089, 538692113, 397618950, 136060588, 498043044, 602193323, 214133231, 221088334, 554165514, 914053153, 32307067, 771886360, 67567548, 696004137, 513607653, 81307829, 663050561, 154416634, 66937569, 663674984, 904474767, 861723176, 361058290, 425761970, 538735386, 952003959, 367643922, 664496178, 660100932, 670737357, 81888384, 633718813, 479936708, 689883802, 668796961, 676452647, 198144222, 981280233, 766125746, 814417616, 75170535, 101673854, 214506718, 214169385, 766437142, 890030208, 297996935, 529334328, 490534141, 42541721, 357475858, 168716144, 905075059, 871052719, 106822399, 880579162, 610821005, 967188956, 401222596, 914154940, 477329030, 70247587, 945325977, 490028993, 31751989, 673631934, 629903017, 547953231, 91945538, 684904560, 319155437, 761736637, 943381052, 693561127, 306034987, 714309191, 491036861, 70622707, 131769292, 498945872, 526306783, 599306127, 202911692, 42760171, 386296766, 803122504, 548545756, 742480212, 601660363, 41053970, 181396178, 312488833, 180936844, 775403673, 352644391, 334674271, 541447630, 421180732, 804413909, 459875651, 866043081, 27714607, 923021745, 333082619, 724648991, 942989482, 569062124, 459201568, 817404383, 473025465, 60076239, 435401112, 516352870, 222540358, 486916207, 189920164, 518716565, 204579136, 619592167, 239868337, 229159284, 890340004, 596575806, 792148201, 171171377, 953746844, 372621403, 554624458, 902230087, 688495003, 864506190, 457383135, 433389317, 216620615, 937844747, 641297844, 624647585, 169871470, 415111757, 528707507, 560773965, 271660380, 603324185, 490055477, 402837211, 550618110, 664686927, 783040410, 372179787, 322082422, 106906794, 683710519, 562149067, 622169723, 189060190, 378791123, 860202921, 520339561, 515132908, 614575631, 888816123, 571326628, 977358978, 795118468, 694064685, 481181072, 606710926, 606610477, 560211819, 249279396, 427106705, 120368078, 246410745, 94511466, 653314913, 10709566, 390412508, 542892953, 637905530, 880464729, 201687561, 60858709, 377958462, 379939474, 489644540, 819091622, 175188164, 399244063, 520893848, 621142161, 711195199, 272523069, 696787124, 812309465, 930058292, 980874889, 792848869, 134090756, 457634031, 275766066, 747269540, 826660629, 997317868, 616391181, 597880588, 443649146, 898306124, 591976729, 42720077, 547433961, 45470915, 626047165, 431479958, 778212262, 782638777, 406566826, 55323098, 858085695, 109288792, 688636767, 494828001, 95307471, 372797332, 514180354, 92443314, 582051311, 918415160, 179528834, 696385299, 286283770, 684355153, 639344840, 470683449, 198663459, 718968202, 550270741, 157829324, 57431117, 419252712, 89045804, 693082840, 6780245, 3621366, 75291048, 414859778, 35549069, 606583451, 247868559, 339289203, 34251548, 754517335, 399130638, 846315122, 816556369, 448599703, 574984077, 635036806, 555752112, 832804880, 280441708, 384239152, 180042089, 649477845, 869840011, 132106452, 846483140, 339980526, 367570006, 78461503, 367442166, 95024484, 27110901, 33213355, 375677434, 934463353, 116578324, 850892590, 305260007, 416536063, 686182430, 781447676, 856894359, 249334565, 732844565, 347120656, 132858917, 723064056, 84795158, 982642397, 881925399, 917103853, 584143661, 679999825, 877475931, 877754882, 710179866, 958216782, 437384071, 87105978, 928708136, 873976863, 81990291, 736924313, 234174590, 25868228, 931713705, 566481101, 822598774, 343100115, 128149930, 272521140, 760806357, 454166720, 380947278, 902592603, 772088385, 100594174, 27206995, 161851220, 823311246, 258322543, 256338038, 58414151, 723756764, 235970522, 206197170, 311117523, 668215705, 317033771, 888566100, 238699461, 132782513, 362378471, 970565825, 854781914, 581124242, 701114280, 776824580, 568306771, 386177561, 230681992, 876211754, 964481470, 172366469, 286842093, 637880367, 473594761, 893626561, 706226787, 680642395, 931133196, 269522916, 924217960, 255060645, 198839936, 441242250, 143810034, 583434462, 783179318, 631992814, 198149226, 812840635, 879598502, 175470633, 101474661, 904404526, 199636820, 462807928, 158588575, 963068915, 527379918, 938536101, 95212575, 215603972, 819955741, 779882005, 502080173, 221880901, 584707643, 398586331, 150048399, 623736457, 860093544, 214646645, 51085086, 888396103, 229334911, 685720359, 654281063, 527376042, 859069644, 695143092, 440176403, 5980806, 319948728, 124652688, 548550756, 997979106, 497282222, 177587949, 782353528, 986465548, 620611376, 262621910, 636413324, 448599070, 163682015, 561837454, 658462425, 274789795, 283914410, 379556132, 697283171, 303002149, 162031972, 860823653, 322074249, 195743461, 674776106, 914030220, 890451059, 844976141, 357425594, 257098024, 270167509, 460664262, 798871159, 514485793, 834025774, 621506281, 913277254, 775041679, 431164694, 320660484, 713103379, 712323751, 219206714, 58820189, 45683455, 140288921, 916855353, 71308357, 996087832, 130132852, 821479149, 645986801, 21222439, 38086862, 114935016, 162485584, 548180187, 393173355, 184440366, 732918459, 935950285, 497884687, 866354310, 176384850, 783278640, 382925732, 604171709, 659168328, 105392023, 626683728, 649367330, 915483454, 601786131, 326430749, 571460660, 425203655, 24981064, 296248920, 737268865, 126881624, 194498799, 770900015, 500789564, 616043241, 35133721, 971701226, 153026863, 56873832, 536831183, 843729934, 407865579, 405033451, 515329731, 443648151, 513299444, 143852563, 449880909, 942546304, 21150685, 229060019, 311867606, 80987638, 549973103, 947604661, 352923324, 366159466, 561129752, 780617045, 477218181, 680326974, 872522522, 863088187, 997866210, 178663329, 332089591, 449610258, 31636157, 317981205, 126350196, 951300063, 668828418, 879207686, 883585681, 606828373, 650724859, 615338212, 157184175, 716693453, 99849823, 7169342, 327647869, 458410726, 206727462, 7182229, 325436855, 392197201, 850412786, 362217309, 717785307, 770311677, 632825237, 831419178, 484732703, 817034379, 355370779, 887139749, 268539782, 358393859, 757164772, 124613356, 326668256, 911048848, 618417523, 487870233, 745912608, 399238097, 637077800, 164687104, 798620013, 609435745, 981797079, 211553642, 834177296, 943922482, 760468445, 881028518, 11129700, 673278385, 680956102, 299970033, 977269800, 525594973, 47306885, 754680291, 647597250, 944391891, 825535381, 99724416, 846153062, 213540514, 933839983, 373576412, 677041091, 787704655, 999746406, 11349512, 502710368, 401101373, 436525883, 32298080, 681837955, 852671979, 581004028, 844664300, 633252979, 760405289, 203715871, 922496657, 481826689, 443994771, 244462326, 677693944, 795526850, 488466224, 31971580, 101252102, 710126470, 981724658, 939705123, 3183071, 255075652, 694823768, 675205718, 834662780, 340300118, 164514027, 314037039, 523717816, 543362663, 947658845, 522986227, 729184044, 694366663, 260477039, 142028887, 461766599, 721107002, 600839977, 795851501, 121006922, 783845607, 929013642, 89474726, 195477526, 225652358, 657975237, 109422626, 454188697, 218764240, 826524144, 609490278, 869136133, 489863506, 287337861, 672940596, 568263257, 76853373, 573722307, 816703433, 649254494, 17558056, 536995935, 540704326, 835512170, 494314860, 556695432, 550570112, 34316203, 554794367, 577761474, 835385012, 642819600, 950230760, 153100174, 197296660, 60107438, 53281543, 271687279, 72033219, 773784138, 660849448, 432997300, 168399653, 509227199, 503448148, 466934725, 505329951, 268141357, 865703265, 13347065, 211381468, 30448540, 271732324, 290337995, 148969330, 433003235, 425901148, 857286259, 601023496, 509112015, 951721826, 344812601, 113321366, 618748951, 230118976, 983475176, 635559630, 691074272, 224416042, 900342194, 129550662, 472755439, 762812370, 647539363, 158279807, 68087714, 904360412, 490297794, 414558241, 318111683, 212400041, 389681959, 203150665, 94962263, 809098932, 501862796, 531026267, 681213844, 71624252, 610911134, 732327763, 340630500, 39569349, 124254379, 201938083, 19726039, 689155766, 983571024, 354259425, 449435006, 95716820, 242616367, 674877622, 76588488, 541717676, 282073658, 139825841, 131508656, 519310046, 314063532, 366253692, 573235462, 238536902, 938656207, 809180007, 218551554, 623966253, 541182487, 246377898, 842280341, 202140362, 214270984, 373217605, 877609738, 576597295, 419444629, 744963714, 648014040, 236306638, 687203047, 127527592, 132068073, 894732628, 662962259, 324689864, 167071773, 65035715, 463808216, 393497237, 602523072, 31141618, 799827533, 961495511, 675814075, 937066747, 643174807, 385756232, 885076732, 85799026, 717482474, 19026215, 903670249, 995327254, 629400400, 436433300, 622746272, 709176715, 520760751, 561126485, 861734740, 720345123, 650704174, 736872631, 92044404, 944669334, 671402791, 463600180, 23736559, 716591793, 201385078, 780756408, 647387180, 538410609, 165812043, 182690896, 375446227, 911389110, 609080477, 796689004, 819294916, 820236141, 394644850, 423589142, 206314674, 755126988, 420583002, 832483889, 369735715, 273804984, 18926370, 164434299, 41321390, 952212692, 330240753, 258387385, 615392184, 161258923, 543965705, 510670343, 782195965, 689736125, 249249268, 180554357, 401039868, 627854928, 729539022, 73845980, 152217454, 932922501, 754779917, 195221702, 791250755, 803484505, 354934329, 457870556, 884173687, 103716580, 312787245, 743349457, 591844074, 772925815, 144025415, 423521950, 147280259, 796055188, 577741509, 60520096, 296201652, 266628088, 264444703, 598909544, 479064957, 910348648, 489757766, 246481696, 553713422, 118090275, 453618269, 897603289, 482889650, 731052976, 402366856, 302926983, 131232616, 802424533, 767724223, 333270752, 519315424, 110209612, 892862390, 339460475, 549119638, 550270963, 94832758, 257807012, 514521332, 793349531, 519974528, 833018608, 317243684, 167655381, 748650431, 445048712, 32194054, 431531911, 164526904, 275660610, 400450302, 456482752, 289187183, 68231670, 304797767, 778505739, 649076066, 998156665, 398538831, 535337411, 770416532, 415738763, 97801474, 944273829, 893965525, 11715331, 429311013, 253621739, 536983219, 664808800, 355578587, 604853718, 171383685, 475818301, 392192355, 463948676, 425938392, 949044557, 134231555, 124042254, 410295211, 21478145, 287290565, 259581912, 145428238, 632304713, 650840398, 1266550, 291060934, 927055338, 231526341, 104144056, 903192312, 846843538, 657811803, 429773174, 641000826, 985898369, 95708184, 159205417, 478235344, 87264783, 461017492, 421460284, 519448371, 774695530, 799905957, 445275955, 540622630, 255822723, 208816414, 290791919, 896849823, 191524676, 571220650, 372738243, 322804707, 863551114, 766933662, 259147584, 297567265, 488971925, 327246112, 223154232, 749211439, 940240310, 451726653, 835549090, 529808460, 221685042, 57842189, 968328538, 920627751, 827433584, 773314183, 412480300, 245862494, 547719878, 266569067, 933921770, 537085138, 919791543, 26795929, 233856529, 950988475, 130575613, 217079768, 173388938, 328775800, 862905763, 161812350, 612387956, 982491200, 905319221, 690388153, 263495617, 540664923, 141746379, 541395216, 510668942, 320599740, 508982472, 981590479, 885433515, 115233797, 497269047, 626021100, 268696463, 822821044, 959603999, 630278496, 442318046, 866253660, 526428278, 628587115, 576829418, 822374408, 671288772, 612569344, 38771227, 875009913, 696220848, 931182563, 212371677, 265671237, 652344210, 245567487, 310441268, 904397274, 399351172, 140348870, 936784819, 811633514, 450603679, 984077055, 177313640, 413913819, 359053323, 522297963, 106320417, 49392580, 292921004, 490830630, 771040824, 758930309, 871105201, 432897839, 824403118, 760356335, 194236202, 759164219, 119201508, 268831132, 121418904, 191421526, 308600222, 911644522, 880186934, 321043006, 743421036, 111167972, 123232071, 441642031, 257643698, 33197131, 240353090, 480689362, 840692722, 613943111, 997718822, 317871900, 240441426, 319838552, 70776849, 578654221, 867233943, 960092046, 29251925, 589755524, 916164976, 115420488, 322538247, 767305496, 744337274, 363068882, 975508943, 520274380, 890270204, 953053460, 952921257, 839236715, 79710743, 793077441, 665851652, 481644582, 604536552, 427966806, 497031005, 482089163, 291059402, 884514385, 149048331, 310879216, 791371026, 620094394, 671180145, 423531058, 743183728, 980007381, 125193392, 974844968, 626300670, 406461973, 306558402, 171180480, 149808255, 632829642, 466565696, 893301332, 405136113, 359439849, 407124420, 362840313, 136196363, 417359232, 139054955, 528555608, 675549654, 478110259, 853346610, 140156251, 43358118, 516195088, 885412790, 376389552, 798676200, 737737528, 671555811, 849223134, 377641109, 561302312, 77684324, 54004413, 15395951, 583819199, 971828377, 821159376, 595482289, 21858242, 463648951, 874750568, 605029023, 328071314, 951612915, 764546962, 888270258, 832563776, 387164142, 755249367, 185233849, 440951594, 83384767, 48559255, 3440624, 546816809, 181922576, 62957200, 720202345, 733270073, 759096522, 122506122, 910695810, 569388336, 729305332, 742573827, 674999380, 637086643, 174853876, 998540595, 863847723, 352992812, 649890413, 182404216, 66035981, 228983035, 170405571, 798581599, 449313456, 137870663, 523373552, 982173475, 729710929, 259903716, 430339961, 284648150, 60348900, 185526943, 615857902, 376235827, 921881177, 962270958, 337664993, 110691686, 723027516, 571712371, 184143877, 9016447, 77085170, 343443475, 509074694, 239362605, 670468239, 145461067, 391255406, 765023560, 674709989, 366354531, 701896698, 411117004, 491187900, 29946439, 429370065, 657765799, 707870466, 695629788, 570918648, 453667052, 811870010, 304680815, 877574831, 612032586, 218830940, 457092879, 318282161, 387671698, 516893174, 506497018, 306770445, 121868792, 214008423, 747335420, 261272962, 881424173, 461779364, 67082890, 381405720, 86428983, 570866920, 894194367, 715511996, 11462630, 459189186, 163327987, 469587679, 207324807, 188339951, 17739416, 660140767, 661737766, 736885192, 994395124, 300600486, 391099562, 349148236, 341828828, 875698248, 394288265, 540247188, 787094391, 269436692, 318097541, 795040025, 45370022, 963692832, 54386222, 432517084, 408967053, 402824904, 793328199, 24449125, 163663183, 320539657, 441491177, 767771613, 655031824, 440636882, 266295461, 71821923, 794043358, 317237090, 537832885, 812779081, 625965826, 372818712, 920353760, 794337424, 777961159, 823077856, 433588008, 125349009, 290930369, 884374608, 31308803, 279194743, 740284847, 476500260, 355255762, 493117181, 111398911, 644996351, 582290838, 326443255, 161825250, 81437950, 996115652, 163972371, 311710377, 208256729, 939811561, 415824058, 357971620, 412631, 875738313, 250298947, 75129731, 559284873, 901459775, 476877442, 949676649, 69132501, 140071071, 544067168, 626385645, 782115040, 585566508, 907275111, 841218273, 497237973, 806024381, 907460436, 929209598, 416609462, 880861147, 862773163, 839810980, 300687179, 846242580, 259264099, 44354248, 80680942, 557767017, 88144990, 542760423, 71322093, 365158368, 786761175, 603283429, 399762422, 44494407, 994481364, 488504036, 101731137, 895859939, 482813891, 938943343, 791810644, 556501914, 434786041, 804859600, 271573258, 629412978, 860134018, 30387083, 675673834, 597466136, 715624770, 232170294, 139227974, 654895306, 822490877, 184402613, 854100944, 759521746, 591576990, 733822536, 471511337, 922279115, 45613537, 780521355, 351940890, 50924228, 382335860, 61248060, 216721329, 735214422, 118704785, 564329559, 72673553, 617062568, 582711649, 79585059, 647810123, 543116874, 502020362, 554090548, 584048768, 949923166, 822084094, 526498102, 550933146, 374573573, 899823700, 175832182, 958496210, 928597835, 271340048, 944957592, 4048066, 211679890, 722993477, 418030340, 569998687, 273772515, 433106817, 913189695, 193861724, 493825489, 889172372, 68453033, 225369056, 707400890, 214142465, 686383652, 903224580, 522868980, 614259413, 698350894, 752157377, 857901937, 569976804, 180284340, 382512441, 446497220, 389890696, 143165447, 626008802, 96714041, 785413340, 400272787, 934161634, 578645594, 678868097, 160900310, 622225172, 749560048, 590998841, 843848421, 196633415, 612708743, 56353287, 813459900, 971032517, 279217342, 764650853, 725161513, 848412789, 384014871, 138023637, 384489365, 747872571, 634273356, 815687414, 902529389, 261890609, 674016330, 711613870, 780565560, 465777244, 12676649, 532915805, 764775762, 498492752, 88340986, 619896990, 644052369, 615661528, 557685364, 894216579, 156341673, 471400350, 129310789, 359273828, 842227223, 313436997, 177205479, 509211585, 149515714, 675888179, 947134585, 210300138, 964839244, 289836688, 860509148, 258890543, 989177502, 408563187, 79756673, 743444176, 41681336, 960679096, 712661842, 443363906, 180888833, 303642107, 830460296, 256211868, 387954266, 711450608, 381683491, 215461251, 768920769, 365286884, 953922346, 453885343, 432011702, 176340842, 525380640, 939084543, 958059942, 878367396, 220918389, 921305048, 704006275, 425683321, 531480897, 509641522, 974464965, 913241190, 724531967, 111539574, 233446634, 578414222, 269325239, 553370239, 659668076, 520995424, 256654426, 264353587, 300297038, 684909544, 54465737, 892375197, 294037095, 721969015, 555062759, 892251146, 458196956, 205516064, 832611947, 951372615, 99754502, 941402934, 607281591, 311760595, 998048930, 298045223, 334517721, 222079005, 719209980, 864371075, 933424832, 803571955, 27232015, 199530486, 371503423, 778169033, 282309907, 323995056, 883330894, 595839789, 569136949, 523414377, 173271261, 362265053, 480477800, 681464730, 593871769, 627637375, 33036832, 609528462, 511793622, 710914062, 829493293, 501923910, 249719000, 425574142, 782789111, 859562811, 338224939, 123676560, 21452658, 197528192, 254234602, 720425272, 902377740, 717131065, 992245148, 452482634, 309551684, 274090817, 146700444, 491761104, 343309851, 513575756, 872031642, 99040709, 356750698, 999944227, 448468104, 996962517, 789057748, 950097352, 552673246, 503264602, 698095927, 637776721, 183439731, 162842728, 956399001, 806967337, 994782507, 660590066, 909760464, 643885386, 874115833, 618013120, 300704801, 828006174, 411371260, 357879235, 849098554, 461697377, 544326055, 626463590, 353596644, 429981342, 176113196, 106107563, 876692145, 798809680, 887117051, 758233274, 203152370, 938994685, 351124123, 170033104, 963388625, 112221335, 136702517, 929639507, 321467624, 810042865, 458519735, 92289794, 61845488, 693686777, 905169756, 957857093, 414542852, 883234963, 541809761, 426096522, 781452508, 792055469, 311432951, 647327891, 229630435, 858305454, 451732842, 474980534, 582283276, 292795830, 702803118, 9268622, 198063400, 817104929, 228487011, 657234318, 892793747, 508342914, 889274388, 272184077, 365556765, 284366636, 234801166, 668064836, 765620267, 352131626, 57015191, 830993548, 80502376, 334601118, 633352895, 169582433, 126064622, 176374290, 641530701, 745844599, 515438249, 273862911, 459316285, 938736918, 748391462, 288547166, 838650981, 252630266, 434178381, 14649737, 258321782, 193664840, 849322523, 135081676, 520869650, 370063161, 691507395, 104514340, 100687491, 459031216, 991217949, 751443140, 122283446, 135904169, 484958173, 995773212, 190015502, 674138936, 66529490, 393006802, 684399215, 823572719, 164640222, 256619589, 783259210, 680093196, 927466192, 828327808, 360071339, 869162426, 643759116, 719176890, 413446641, 981475963, 464167130, 531778197, 152012660, 995240372, 341172237, 902914795, 447195740, 699191543, 47424924, 632849796, 525032146, 524667156, 604747693, 40594737, 287221397, 927233222, 660423872, 515454648, 521730875, 235107299, 264330613, 171480707, 998569178, 899531598, 130794967, 205906585, 664652328, 34465960, 88557940, 229766849, 475747987, 794743738, 57456170, 33579904, 145626984, 492641829, 526435357, 884436788, 892812083, 815126162, 298165628, 743601795, 884580048, 917503824, 927160947, 488390475, 151405037, 436287013, 86576325, 481282878, 99196531, 278104230, 364049995, 762215910, 688719329, 762438339, 123140266, 186381876, 550460322, 235178502, 270704451, 610643346, 794564874, 305423154, 177365503, 164814825, 383301093, 524748973, 888301926, 547481724, 874008851, 365923395, 860706298, 286806196, 134211500, 107147871, 525531843, 89903873, 107225459, 568149805, 681095977, 573732577, 795293059, 643285338, 969962195, 166501834, 276005190, 971506738, 403304333, 526904778, 832702288, 935371516, 170650055, 96528405, 621394990, 840311272, 65248626, 699203718, 331327785, 7961190, 171403261, 784510195, 213134161, 790644851, 839703874, 61767490, 754362991, 21728316, 88088015, 555190250, 524573256, 316610549, 37434572, 416193020, 992647315, 169239031, 67459414, 536326159, 872319403, 704908849, 569794591, 419486597, 246615906, 388416531, 383778513, 558365614, 837134469, 16679836, 129696204, 61337257, 975946644, 163326735, 931541855, 231780892, 805559230, 470456509, 882094687, 850465070, 10858615, 126080699, 237740777, 417976136, 845328193, 631403840, 94039237, 419133719, 877687432, 91235462, 30623274, 369296469, 572382227, 280027077, 819086470, 495426848, 274091119, 919243584, 727216110, 423945800, 377869132, 349823758, 581824582, 118397469, 515859172, 78649409, 978650195, 255093388, 907556774, 690245371, 141949666, 554296468, 913132846, 122677668, 188805586, 505889726, 602173902, 85647535, 651844118, 325045064, 521762946, 488688057, 616431563, 300096644, 736185309, 30259865, 562001084, 62687784, 510367654, 893552382, 88004227, 216605838, 737609998, 845760579, 1157117, 214653544, 476251871, 835938820, 281637573, 142507552, 545642196, 725232009, 136100162, 819859979, 311786301, 899716950, 594696858, 13352454, 377528521, 166144746, 547824856, 514288331, 869653549, 833309341, 347973954, 149589670, 715588268, 636470924, 684697369, 782243094, 95034949, 893227320, 364470207, 955607811, 133192923, 109969272, 552523742, 5995117, 219503329, 417061567, 613219677, 308302837, 635530205, 340160661, 132074331, 546858367, 60934613, 70611374, 7169425, 679328754, 305548724, 334659839, 895195737, 283399048, 357099512, 333915617, 505462244, 254613688, 425831868, 2760296, 879107127, 353000587, 328009631, 811377912, 695854716, 681339076, 159213010, 939783509, 347896169, 263176484, 563810548, 546669364, 685440188, 278244445, 627886820, 420159571, 642547917, 979110991, 34728795, 52836571, 306088640, 866553842, 394039057, 442405456, 460389350, 508641900, 842380414, 537112379, 274049380, 470853625, 250845215, 8517273, 222001670, 6627550, 17460521, 991054843, 21174576, 830321689, 402063537, 448810738, 437921673, 887592923, 954722084, 195380896, 965540390, 537439288, 869084659, 639558780, 655888439, 704627797, 633133368, 236676368, 670524054, 52154637, 679132885, 767780710, 708129169, 677076777, 668081659, 839507894, 193257720, 56172140, 776485510, 536509466, 686999578, 566150911, 147258473, 161186529, 936049067, 364553717, 476744643, 474044171, 108973914, 20825021, 142409683, 333994993, 449845940, 570418261, 682620574, 108950771, 98613996, 530817043, 813371633, 486602580, 344164713, 600293141, 434364390, 973282371, 797778902, 897458073, 302754260, 429080622, 599959973, 181748753, 288840372, 751479683, 643216068, 74294191, 665409994, 143272675, 555747413, 159840397, 822100337, 643727847, 991812779, 991493148, 986334728, 517165339, 285769638, 408318755, 809766245, 479384700, 319498737, 614819697, 940023347, 885558882, 278923732, 171890721, 408921590, 220541629, 441044743, 582995572, 267690382, 537828921, 16155411, 482825764, 984255641, 897226279, 28192348, 883985584, 322640874, 705478980, 877743912, 882337020, 81302222, 895458654, 241900450, 786569657, 235500687, 182300363, 212448496, 974877434, 683505303, 716453317, 855259419, 941498663, 444876950, 681347216, 883895945, 481759071, 486358587, 964686084, 272703417, 504162917, 263324580, 875442318, 30228077, 390573477, 585883902, 120785093, 78195974, 257428066, 262289646, 987144264, 840790790, 907453503, 872005358, 812273311, 429436709, 692299104, 210177125, 307781597, 572745950, 712994809, 843069526, 699309341, 4433931, 643705217, 375127981, 247005626, 891129848, 490917276, 476093369, 634188216, 723570309, 749871821, 943265132, 37962537, 394468880, 284453860, 798843749, 751775228, 306508487, 744083053, 848115036, 758072979, 658689162, 549549437, 757988133, 324220949, 729106723, 931252936, 387139280, 272698219, 372521513, 321322066, 690866597, 657771764, 835712121, 804659874, 679943049, 59471246, 798279133, 995082799, 120993866, 749617131, 277455032, 531467527, 884409550, 346746018, 779761031, 362618738, 649166311, 323896546, 710975025, 660922105, 133540166, 855590297, 437340372, 462171291, 720927726, 789493979, 148335156, 254372825, 596779159, 478980813, 851543224, 491059009, 909727399, 281931667, 945074163, 824964990, 741090303, 270389678, 103957332, 103623074, 985586631, 12955417, 41037068, 302949717, 441608574, 443798975, 7675545, 8813655, 980473184, 841023186, 836457550, 328689326, 462519548, 904700498, 561526741, 182467774, 610433850, 80460404, 335639221, 417781412, 326442249, 657723657, 524839372, 256329309, 454213097, 628306625, 807489817, 78041100, 825430200, 735179208, 763242709, 217800369, 249654121, 683806314, 404930748, 20533069, 34369626, 899778097, 48907212, 493950453, 102417385, 694440298, 374253780, 270890719, 293356744, 688533972, 68069713, 109616503, 305711726, 538566447, 272160224, 858163479, 971188330, 664451336, 422244809, 506691066, 797696601, 139161198, 823331996, 803568799, 753528845, 64642334, 768396011, 604446349, 116585185, 35561358, 872620637, 345268228, 464719110, 710192788, 128161693, 578049846, 642129818, 85762119, 646184559, 441761832, 918514956, 658113457, 977214209, 995204215, 583669732, 828966502, 258017456, 828017429, 795239429, 517910184, 809577762, 859453802, 46899095, 308972610, 637032480, 348442822, 899458726, 461143399, 477614712, 945572625, 392230029, 816891165, 983840916, 116219643, 984359210, 965608980, 405465779, 726071853, 552172772, 786393467, 788115179, 813729102, 423139100, 754921787, 564276609, 195609374, 994851523, 898587269, 49906996, 424225275, 912007387, 845031602, 755673166, 320827906, 836587013, 969674896, 426554167, 4511808, 206048430, 679136619, 423305702, 599179040, 444402951, 448979012, 358984940, 664209624, 486430089, 106701090, 198188231, 468074987, 827692816, 730469911, 45906520, 220358095, 264062402, 134227245, 291051642, 657851476, 530864997, 419406453, 463388418, 960197738, 555587931, 817157374, 235158913, 912431279, 325353660, 123016574, 7427866, 896773309, 839345630, 434536157, 217837845, 93306839, 173943805, 978264490, 601702067, 73939966, 938277742, 543959976, 251355763, 728060159, 671579007, 443599843, 808535447, 440852686, 696560783, 92109724, 231119047, 464747566, 658153400, 394245278, 46928340, 680227157, 828811337, 583141440, 369666256, 94311605, 624183995, 835077644, 528117627, 649508220, 955202804, 405936031, 499367101, 586851442, 956588593, 139327526, 116191849, 906126224, 127246893, 630239480, 964837581, 338612393, 248789751, 499413802, 786268935, 11950655, 488999892, 353566951, 118754703, 830530680, 506261916, 750118296, 996321693, 55912228, 148238116, 765649972, 153886358, 527004213, 539822766, 254286032, 696517554, 746528697, 478089530, 718398786, 915604917, 115261946, 34035357, 860499149, 438254298, 772928519, 549280011, 89815303, 667720032, 583264927, 418941853, 24335416, 905206045, 842266667, 320134468, 881859859, 63043328, 137932063, 713619929, 256015998, 52097886, 294380390, 227862797, 65695051, 717933945, 629346426, 470035492, 986731056, 584923476, 411913455, 448907321, 977793000, 777515902, 442943057, 365197923, 685158799, 748722444, 438294171, 837126041, 197678799, 627427917, 207860063, 11655585, 820572233, 188603101, 92977460, 729053491, 467364900, 776195443, 234916823, 103952475, 447146747, 687906716, 352525310, 162836230, 206998579, 776917130, 284989292, 65031468, 797417488, 260493291, 430423287, 945780017, 262410364, 798081668, 342302948, 902074209, 496112104, 747950543, 470770876, 150522200, 29673855, 109807053, 43718912, 214289226, 392740174, 867441455, 814044914, 655100505, 617563972, 218584255, 585064034, 747532032, 238649084, 914324012, 294310527, 948787574, 669390720, 843493503, 324494918, 386990196, 781506985, 758197613, 63423324, 200682577, 188375652, 523182199, 719422563, 193196443, 933596675, 105818262, 768073291, 569646589, 791455964, 298902807, 644395732, 18975837, 988254951, 630690354, 845695644, 240573471, 952858526, 959200561, 784418523, 789328314, 972243305, 583764643, 948413399, 140486492, 977790835, 815266074, 137003479, 535693808, 315252170, 629905630, 125669086, 65627198, 509579171, 64679676, 416132534, 60320173, 945465577, 425336294, 136179377, 880041549, 779897809, 813683302, 383324511, 660551728, 169829176, 744050070, 692933602, 266396703, 430227137, 637250450, 987849250, 666446463, 369174214, 911646475, 494704220, 244817398, 544780161, 521271810, 417531091, 505701516, 988039841, 904408150, 57107188, 811319857, 956058263, 497735188, 176292572, 758652151, 948745581, 647081870, 231799466, 535798916, 809854548, 845084124, 747944685, 141792714, 74712399, 969822359, 20115744, 986066772, 249352495, 63367605, 973026968, 295824338, 985806714, 494263813, 485843974, 756941374, 910108302, 95926861, 51251324, 690881939, 274544232, 973342638, 938558326, 767276793, 898270349, 527952571, 181872257, 646808449, 906035552, 975450429, 96474500, 625185841, 36188319, 14846339, 296281733, 120865850, 486658618, 762818671, 241112671, 116833949, 184052555, 854058623, 838275897, 974454876, 39694855, 543505560, 557907966, 427936117, 289237552, 886622020, 427691559, 964184140, 367451878, 333523299, 495047778, 569869753, 45540436, 545074560, 615956662, 388604354, 828202369, 556125839, 368003970, 888572458, 5858775, 145476153, 970773606, 983188985, 553167279, 733944680, 771068895, 184770250, 447566375, 837423115, 968008236, 281683794, 427701467, 107396387, 434812094, 738116985, 158101417, 105762118, 533341246, 486847654, 198616790, 818479010, 929373212, 18142870, 210996336, 798854545, 710335882, 851395426, 333715434, 607196343, 305778639, 816901860, 772358597, 698413898, 970657545, 858262688, 892730947, 983666100, 622924937, 119904638, 955575401, 733958313, 482639662, 53502327, 607389655, 938568938, 935814331, 51944993, 266712811, 559044583, 382614067, 788954857, 590316186, 172654078, 819360165, 88684421, 220411007, 386166177, 959696375, 573135619, 931327803, 580629545, 407963173, 848221775, 773644864, 333739389, 189650120, 420741864, 459389221, 945666885, 649401774, 741632207, 852854084, 7199555, 725125782, 517421187, 885478419, 734947249, 429779029, 625879600, 761043653, 397922340, 95235614, 226975128, 793457825, 239353351, 901576113, 93755885, 53414898, 749555874, 635502516, 776779452, 688801757, 710614938, 783836805, 808280959, 29098314, 260975724, 599264763, 418779912, 141472251, 90409258, 699976184, 249108839, 172423629, 388694503, 89475458, 483409169, 234895862, 205738362, 699926929, 372711683, 26007319, 721166120, 124699613, 950501991, 349874641, 586738631, 684900097, 511385858, 738761354, 915227544, 235216320, 906979746, 994042043, 267482829, 836571857, 140931864, 186767224, 59225474, 648129476, 455772731, 459391764, 320251633, 418913888, 330880173, 214159617, 49716276, 344962331, 555840894, 92990529, 181977363, 249164313, 110190937, 902609423, 726444331, 688690303, 635353715, 886678010, 246719724, 134509704, 110353197, 538140258, 437700283, 919298401, 523391007, 192995021, 995628766, 476644871, 398084477, 382049586, 836848368, 240936966, 708441207, 322783643, 836346835, 142922972, 540034316, 967505142, 483699061, 959908842, 705381647, 2632377, 488663489, 442803118, 993599107, 94666263, 176865987, 496148318, 421137740, 354236990, 65457568, 654085783, 541131495, 593434837, 364704332, 953707333, 953271713, 531515572, 190207463, 427030424, 683460981, 744770438, 752536165, 351155272, 301031823, 249154440, 303130026, 27875478, 3816014, 605550503, 342836019, 745783792, 663315346, 441572023, 655458936, 64100706, 570810664, 805299862, 304111028, 841690918, 846036322, 261232102, 248031846, 203707187, 997466244, 254522083, 710306903, 185638469, 987584485, 504157924, 609327669, 934456813, 339726689, 46509969, 595321884, 819710883, 81088509, 771809156, 404348063, 967527264, 396818412, 414394289, 914185757, 766601925, 367807864, 791392983, 321948235, 940906320, 609840378, 413308326, 278229530, 787235986, 147399850, 236535925, 824554907, 876177016, 96163549, 329403774, 555946502, 716401997, 896914482, 671612020, 841391612, 872988702, 586187297, 939826426, 319982195, 836550955, 896020779, 794634607, 345162615, 496519530, 216616408, 555211631, 532599910, 305354443, 494234935, 361696328, 523343269, 733256437, 249221769, 731695595, 792687111, 714966123, 123042746, 229407379, 20772035, 665363220, 55399020, 587422186, 675022794, 951214023, 668958800, 506462263, 761051157, 718727459, 944571752, 5288336, 946292403, 772773691, 707997358, 84370919, 624255258, 680248839, 227942722, 15151369, 223110728, 891328430, 490025767, 109469579, 11382337, 474744460, 497804224, 678045712, 141450798, 934519193, 785003353, 215598906, 114495816, 987624166, 961191703, 743326870, 236731201, 277744026, 90870273, 906132447, 97765923, 151503903, 431437639, 306514760, 476398923, 150960026, 124811428, 222013629, 418530101, 673522610, 562871679, 237594154, 170943795, 789087897, 178826697, 251202846, 308157942, 179565521, 55083755, 953323855, 671587368, 140603922, 344927004, 466027635, 219234711, 518961853, 226417851, 348111107, 586113091, 510816486, 361219700, 584777245, 889195826, 935756472, 899249380, 421190694, 44259573, 156082819, 59227880, 836441622, 110223531, 535135022, 934996840, 403809169, 1137941, 793258261, 274421474, 186593328, 906160682, 629221716, 405127997, 335794880, 660811214, 404736010, 748683818, 469936300, 287970676, 84752259, 220993705, 302921144, 467000475, 392856797, 603458739, 117528701, 382368304, 488132888, 136630976, 455303433, 30901926, 451860770, 748370270, 466252621, 567697960, 356640486, 350872009, 54770820, 752732435, 264639821, 806362904, 482732072, 853798181, 571945726, 769202965, 494829592, 732827178, 717616606, 634046328, 942410612, 42905703, 536667375, 840326766, 589698234, 377641362, 954298903, 94470595, 627173962, 231614720, 814395814, 120248063, 381520986, 324007952, 721039153, 323153699, 444686172, 727989434, 644977861, 892507345, 555888132, 720991502, 611215572, 443304126, 800413547, 492407143, 622392896, 389310138, 567188669, 719876724, 445744247, 978120332, 877875626, 432774507, 643060744, 399272444, 981871312, 115248343, 539979293, 737100522, 412467536, 5437906, 716929063, 811675586, 959548224, 881996397, 889266715, 195215262, 451413193, 557677878, 778622280, 984739180, 967928424, 199466131, 911481979, 468414209, 586471496, 879669951, 907466243, 858047416, 495475862, 788298151, 461614350, 314671177, 265244388, 12829631, 540952314, 59443303, 594375586, 354143177, 493502160, 265576433, 394203193, 993622757, 612135940, 117758606, 71290310, 381846330, 881647804, 421641167, 471710978, 499286850, 83260326, 308926319, 450378009, 251581515, 826556462, 889045655, 8290881, 267904802, 702629471, 425584815, 747312575, 47184379, 553242299, 246621126, 469599413, 740378115, 795294046, 906438579, 204170750, 807838743, 602619402, 501490128, 660732901, 594293703, 431307034, 129151861, 654924666, 900737744, 980045513, 364936662, 605869804, 925511249, 842772158, 527173846, 736528170, 625859607, 318585308, 483858642, 934658406, 920628558, 688820401, 368118733, 875933837, 582058572, 97707289, 985235785, 115749565, 474589103, 458653367, 807310520, 843667541, 478324075, 888144922, 554010982, 164047597, 407641572, 13483378, 865889011, 987934623, 165609174, 712993712, 140878389, 695703382, 586161231, 162364808, 921126203, 516457743, 295037735, 988667519, 584783921, 130264270, 991230134, 568135370, 411481760, 8758064, 180845784, 650270729, 480449573, 454375951, 982915932, 884083297, 364233186, 161470258, 283789650, 306266028, 999141699, 303803597, 770397782, 800045121, 755148874, 701503093, 255810048, 644669428, 573835058, 236397487, 788937765, 45948419, 71030683, 431759177, 611861706, 100977844, 82441970, 86991564, 374844529, 946242974, 660288002, 808358132, 107686930, 426311153, 908763159, 838958816, 170695792, 128271289, 456644664, 400045241, 682415650, 660724250, 420131653, 749690671, 886572054, 635337879, 923825637, 857152963, 970005010, 490199205, 791820884, 490484243, 704407956, 624438823, 879706577, 804727711, 3153664, 420818632, 513203828, 41428176, 232661009, 469165506, 624698612, 917409090, 593917189, 554622285, 187332479, 121883211, 690588822, 445727068, 561950942, 820847908, 938493639, 601539447, 399900780, 362856527, 954726172, 215321529, 737085207, 179888361, 279337070, 67302184, 143029930, 129963728, 484809559, 466821545, 121393019, 133782547, 878437998, 63476215, 397761258, 201316590, 192269536, 740610177, 507563279, 566322310, 181369762, 30173666, 187652931, 138354237, 935476796, 8780681, 239741591, 991437369, 373711364, 161269671, 482281521, 129832469, 294755138, 231934266, 448010302, 213219693, 138629540, 655847048, 737428562, 244368052, 62950844, 973052427, 666351142, 460374480, 503040025, 995801962, 327488146, 372731056, 44266612, 632459816, 266349369, 280748370, 274821280, 995837893, 887422516, 645052798, 708386676, 853459367, 586342905, 464589626, 98489205, 760576020, 910978607, 411950660, 706579837, 674905894, 14310684, 549360428, 226832822, 492999689, 356689254, 560899934, 418511228, 682876787, 622282517, 366726142, 508414563, 299813884, 919196915, 756116913, 502737979, 210048456, 636339325, 838041561, 443826950, 151385814, 642038395, 692595920, 737723998, 176185277, 884452977, 780876047, 710552819, 794536896, 779290817, 871895174, 26750433, 485963529, 870873495, 621849580, 120616641, 661687154, 178810985, 415861968, 195700127, 127381840, 642135556, 18951825, 25508720, 754615839, 282168651, 327720040, 35738954, 487133427, 650239582, 511169352, 66069776, 178710455, 263741792, 46432135, 496209827, 713971519, 712055978, 285321019, 58866341, 809131226, 229075925, 914348562, 97706203, 790431567, 120800020, 789927788, 532841133, 554270739, 899776583, 951261078, 72131865, 309986254, 364282158, 843976269, 639784895, 560875725, 44329305, 494539829, 746321758, 277344399, 234023212, 15784258, 204771330, 861971417, 270491032, 526013272, 849538400, 381533862, 291195883, 246384677, 981306201, 615239159, 792450829, 450387743, 63442147, 815789602, 306188088, 863514934, 745699606, 37300911, 931201368, 300139498, 255777419, 967132457, 353537003, 433692831, 820466728, 154471048, 767143670, 720361491, 586111850, 477581269, 545087755, 837656156, 413247448, 665901922, 902054802, 295365364, 119473206, 532704322, 855175002, 793417689, 900044876, 974890434, 423810070, 366344126, 951324535, 26326404, 90049046, 440740082, 44613281, 384400610, 152813044, 516623330, 849694254, 93236163, 118759501, 182719243, 665553685, 483157736, 64922448, 949340850, 985395474, 134849278, 490146189, 851340917, 536078522, 154624270, 244186366, 333452937, 709010876, 376242538, 99267675, 414177835, 919868306, 943445339, 224848233, 150929984, 133277070, 51625914, 609800377, 267036001, 319035858, 939479553, 190101621, 13079154, 504814338, 469404687, 579142910, 456149069, 125351160, 612294135, 924673613, 561008666, 88400542, 997439025, 191846495, 138879654, 865013386, 705371030, 438092779, 716823706, 552583395, 260813466, 450078209, 980237805, 414605819, 173416892, 475872690, 903023310, 402637346, 793909845, 330080115, 433148714, 80304735, 712275568, 981752633, 272978622, 556524113, 640586826, 338184844, 3040573, 199853516, 186003289, 516415799, 188252257, 939806645, 475782889, 282670470, 28794889, 834865958, 825144902, 7029396, 130845815, 764174936, 337658212, 759950662, 289132129, 529018942, 222819235, 309865284, 122314406, 588392674, 658163217, 33556503, 439425179, 158175104, 584334686, 94945531, 254779725, 813163192, 832449552, 795414548, 774593067, 301434524, 987689521, 832747192, 876589544, 136961641, 407630665, 775479490, 641384893, 88110687, 881662378, 740512845, 258917716, 594688817, 264576234, 781241065, 410268339, 949420451, 321148044, 348325062, 893689705, 308141038, 563401674, 290357458, 666922526, 865939280, 72844973, 38730927, 860381789, 296650746, 361118734, 62892734, 269114205, 782620088, 830912542, 284770953, 424503150, 936808174, 388561809, 344286558, 850927273, 485959518, 644750972, 727345965, 75272773, 42094192, 513940225, 270082597, 256633123, 148604443, 921129395, 307714827, 534620476, 452271079, 541727609, 212581587, 810061890, 793873370, 691994635, 745667256, 44492595, 863379850, 194629560, 850885397, 930433797, 442652872, 972701494, 841353504, 693406909, 27659534, 392289018, 558113670, 248765754, 142408251, 46647966, 203445969, 851186381, 414868398, 559046871, 317456543, 66598531, 256134395, 497688417, 936566966, 655670978, 205755247, 991155800, 661117898, 104138753, 931001648, 248488128, 974256343, 661087363, 999137777, 484583367, 160866319, 968602706, 844043439, 627413395, 250425814, 674191827, 4735450, 64000194, 620951347, 151108482, 237208187, 70275338, 159877126, 116711339, 745712862, 566830032, 457618723, 753430608, 903758135, 148101676, 812054400, 304811172, 153203829, 750998923, 731705402, 883445604, 789570353, 700013408, 574592434, 705798972, 844183132, 168943575, 75574957, 318056197, 996501070, 841355139, 398877656, 781134087, 483580934, 672785158, 833415526, 420242012, 266968338, 549515178, 965442900, 739178282, 189625155, 859536116, 119333128, 89895451, 212717906, 2060904, 246803264, 54082469, 724457263, 664730283, 96510988, 621312401, 249497128, 948454697, 535012142, 327426647, 99956734, 163655591, 74835939, 447290508, 625231130, 872737596, 141461354, 403637993, 856877447, 396876290, 360362793, 625788927, 735986079, 790781129, 992014210, 931576637, 667173804, 361646735, 917096715, 93759940, 165379837, 841775113, 249963791, 146328761, 485490862, 9429346, 816498822, 615292168, 974193656, 883277870, 905566470, 285373739, 653823764, 725471035, 673105248, 777693014, 409177581, 830100870, 633323595, 596573835, 431063267, 551707732, 624037513, 129726259, 500134901, 212045009, 705915049, 301151708, 616393363, 789771253, 516280073, 569575129, 616108146, 146511772, 743727439, 58036639, 619888430, 19223981, 584185472, 651866405, 693032402, 499139338, 275119477, 354792699, 696342333, 337260795, 500576614, 98316592, 118769863, 530240053, 208048618, 51399992, 995037123, 675844284, 273570119, 672469357, 970868784, 792063192, 447410628, 203043818, 118217382, 245638454, 86633604, 229334766, 456525918, 928860373, 268001777, 155138466, 674894430, 627280344, 336107390, 94809544, 73643520, 509988028, 570273325, 974450830, 149202259, 186158587, 548420245, 809375658, 168411086, 578630704, 977989728, 948555802, 94033005, 78343580, 825190587, 74447964, 935854439, 674018165, 43987440, 35646673, 93694902, 949245881, 806589037, 315856996, 301840436, 916136179, 973374203, 436458553, 134913483, 867208451, 106680227, 327145358, 245634754, 410411226, 62114564, 312222476, 665927500, 690331820, 796738252, 479523936, 926331941, 962956053, 623042696, 555644755, 723716155, 280840927, 255890146, 1638871, 53239888, 731146359, 277806554, 715516871, 575222744, 926826967, 470392694, 294188752, 190271003, 906987688, 973416524, 154423409, 564568275, 580957106, 353455569, 746246141, 588247534, 201466430, 895921917, 365669744, 512045123, 924861421, 456420350, 627583756, 627140835, 306301003, 56782053, 83737009, 590027040, 433532525, 289467186, 115365066, 394285475, 415581808, 73531010, 384411750, 540778271, 658386879, 52001458, 59518350, 172988246, 687070346, 624867540, 14372642, 83554520, 441599703, 37999163, 41870958, 562523420, 506360208, 379881447, 178371900, 88602882, 633294853, 332567973, 642594, 76593846, 572828060, 756046882, 316187599, 391330493, 95467632, 757987781, 408651048, 347746592, 510127385, 945677023, 766274079, 386527948, 419550642, 12994663, 862438456, 609776023, 881944771, 569829546, 617061, 368281494, 677971554, 64273348, 30205561, 869260686, 638897712, 984444005, 280306012, 476440768, 373332926, 533205119, 959357806, 556741759, 809638630, 471646523, 804553578, 616000282, 337023073, 955063091, 330325518, 287635833, 28476771, 887431568, 251575345, 609454764, 244504882, 824783975, 724160777, 705495365, 559026321, 81775089, 691518566, 471260894, 902858957, 991969237, 128037691, 522340123, 812085566, 430974390, 713149992, 846538292, 808065737, 253054856, 847427829, 687843360, 315944786, 845783078, 686590766, 636222568, 542377098, 818136641, 692592063, 506466775, 601330605, 615267687, 9535327, 578629335, 972435450, 304355294, 2588060, 132441386, 634757823, 813911312, 573909775, 395489761, 439066572, 899216158, 578350613, 809525397, 4760205, 822758429, 742127925, 735233013, 115285729, 352720567, 949461853, 474769993, 890999975, 535316527, 447342759, 725879785, 432906497, 476396639, 90523982, 628450583, 786867120, 229635773, 849722695, 55577762, 523912887, 886184054, 597236004, 169134502, 569619290, 351865111, 648020700, 406780930, 761809171, 286856128, 382516222, 656751526, 56957658, 132355164, 612108956, 32739669, 610652861, 842398289, 683217328, 855913775, 654822686, 616245914, 250331411, 715353709, 334234725, 641249116, 782224168, 781406626, 389348943, 936416449, 87569682, 536228984, 517389748, 671916404, 808894138, 338996864, 994107516, 876937234, 738136266, 547583345, 572443109, 93569076, 992645752, 403896138, 690945302, 994695831, 453593743, 882775309, 117113712, 474853338, 181237437, 559065378, 573150716, 456782582, 465589054, 411953404, 9672149, 187820401, 358621377, 463330095, 114208031, 149581979, 140069321, 297379973, 109503419, 565254649, 13081187, 583989979, 752750855, 308592024, 959356214, 862115922, 941307839, 299628396, 715133144, 876249108, 304940267, 396714228, 981231449, 148508902, 450154585, 252206909, 790200397, 496622215, 320747767, 948091207, 962899576, 510141197, 889139844, 841618406, 715772872, 884532525, 31885344, 657480667, 21397271, 416854327, 301470068, 250196570, 672360497, 548379332, 388738289, 998300232, 75693811, 938108220, 910222273, 959011876, 366759954, 618493466, 9498750, 167588245, 104818298, 118825516, 244205692, 498314386, 115700328, 343617637, 982525392, 550791573, 140274837, 827996919, 348046720, 834669263, 368207717, 311678149, 605240482, 259052572, 628351238, 247314513, 309564844, 88284357, 357623272, 858620666, 710252063, 921157429, 36656343, 653706688, 823879943, 77635226, 168072186, 463961184, 898900914, 394652437, 934019588, 239396203, 219186598, 287855363, 935927366, 540117135, 457502316, 348456650, 236998127, 265737927, 263030557, 731807511, 696824224, 123255390, 443889715, 779777239, 778156863, 825927226, 672625908, 866712596, 842942690, 819552826, 418374867, 743909818, 704593919, 336249296, 882413567, 899970400, 567660362, 634338319, 66741627, 133719384, 43145183, 151669207, 361820743, 819351561, 745359441, 574390115, 870182372, 537801873, 358406581, 886094264, 138154018, 547587886, 256612817, 870486732, 686038663, 861281538, 534784786, 21970482, 212475964, 350054463, 923166837, 733771484, 234222603, 574568315, 631779458, 155391078, 120430341, 64290476, 728641071, 588791732, 532394008, 657896001, 279459816, 280149606, 336370065, 864234462, 777946898, 584891225, 45879126, 17193600, 144942174, 205184258, 874759200, 736544353, 851218273, 848106933, 674707848, 907228151, 608556590, 752575817, 512445068, 318893986, 277699866, 423751588, 448937424, 426603413, 494124931, 283221868, 474609818, 797402690, 34734703, 302656582, 125854515, 662197259, 78398247, 67698016, 891105696, 893630677, 712663316, 98904529, 447586288, 756874602, 531274286, 821164506, 701826136, 819284855, 108507245, 839035379, 658503763, 763428400, 940563042, 19752261, 186535447, 376014621, 514371564, 434222781, 60127188, 788726524, 385389150, 106947548, 392365771, 58357194, 519872470, 465567789, 997841396, 867197108, 944256166, 88713747, 72315760, 476566013, 948723675, 208554484, 175989584, 114936176, 530176230, 728681623, 32040823, 915939140, 404834132, 406078808, 278432566, 548441830, 531288991, 561195352, 401838310, 688953499, 449772400, 363350380, 290262297, 335749251, 342832525, 940650323, 497080602, 127866545, 816899382, 849367584, 873196710, 233046848, 926700130, 201337995, 783919842, 248361253, 47817653, 609874791, 766683654, 885955436, 781284209, 987420002, 658717651, 636750366, 161906912, 403296602, 544887911, 979631687, 445904470, 861904174, 27868043, 831361673, 288173015, 871052774, 25469620, 833634136, 376717706, 296345702, 222212958, 671158798, 60948533, 269371559, 287658932, 245486913, 669535949, 180324707, 783822650, 195979391, 301386159, 383235424, 548037066, 732815917, 722594542, 731628083, 290622651, 716478290, 128384019, 862100381, 280622340, 157284828, 516133885, 685490487, 428500878, 906038762, 873461998, 262669490, 926641141, 456514266, 562734064, 740899842, 985652376, 658143354, 21796422, 844626445, 664819909, 905807060, 261017322, 329722841, 745748670, 514115268, 766976253, 960263574, 366072298, 64628382, 807297615, 941681675, 550526876, 974800521, 506661044, 251335827, 580479917, 417403417, 906139425, 442957768, 383239689, 451300010, 340893729, 778567634, 840345142, 897109122, 20914588, 387815976, 6127759, 396642295, 326626683, 759615298, 871345838, 896669942, 948701938, 493842932, 84277341, 552103312, 278771807, 395711846, 402359726, 100475468, 114671686, 733128160, 841314114, 306299815, 752605321, 521973090, 474835945, 812045115, 615281918, 968561871, 593020266, 99920862, 156317588, 166468669, 279250567, 463343100, 89356493, 552845385, 862202409, 716464511, 950265345, 983859693, 123560961, 935667690, 854298743, 774057457, 301966969, 38852420, 943585667, 595433212, 364262435, 405967603, 624079777, 634821354, 882365283, 629252529, 223540349, 451815603, 495651848, 761349068, 44930390, 559265888, 622079154, 469597355, 13623660, 494669600, 228668364, 425805422, 148571513, 951996110, 346593738, 440260097, 64835193, 819310127, 853187870, 2726080, 110659687, 38520502, 472912345, 852712823, 583233249, 806579636, 695852249, 382833836, 256163579, 194361751, 430825701, 585738364, 16824531, 342458111, 85677790, 655129429, 769808031, 717867343, 804487320, 221604571, 464820033, 148149350, 101572556, 623032936, 371221926, 409457969, 721275999, 371457007, 241353061, 515763453, 125866269, 815758100, 133874283, 357804650, 951681726, 699815220, 352279422, 778069690, 748169409, 979404583, 411137128, 844940040, 657815987, 254060190, 565875257, 668995239, 15332660, 617301834, 492722807, 48917032, 755500118, 633651668, 252402703, 461762242, 453373466, 817638900, 673892558, 992612184, 194907013, 990643190, 467737705, 809411082, 697328886, 636368639, 372404354, 261113117, 166777275, 45464720, 823976729, 496508821, 638495761, 979340022, 626951658, 697443645, 723699210, 371160528, 998341707, 108289916, 605869910, 274509395, 112072212, 481132982, 237474427, 422113799, 346943296, 616377340, 573912740, 425844738, 67585530, 57897350, 563900849, 926741479, 50838990, 396078150, 871888167, 491412285, 451856863, 254296593, 558722723, 700676472, 978998105, 305114166, 328462603, 545298224, 322791720, 370421269, 845136258, 121641192, 964214491, 898826593, 749988029, 28420075, 542513488, 356206473, 905199935, 676931373, 918930162, 496813493, 38562674, 588260828, 336364252, 809818209, 363223636, 365724929, 976003901, 868234557, 20788192, 420694314, 58042740, 906202796, 816300797, 490314340, 958553151, 546361097, 515586792, 585577585, 222710386, 109981207, 908821603, 959748876, 977278624, 312084861, 559405590, 734198283, 981930569, 206082986, 258278094, 802511220, 458914157, 829779912, 291082538, 939468938, 24969471, 784555600, 136190386, 923275160, 245697474, 997163233, 538815079, 645172957, 70997041, 17653677, 30589988, 160818584, 116604148, 605231755, 401271700, 239750542, 696435878, 514436300, 207419926, 211961811, 809429766, 771933914, 95977906, 618410492, 607995989, 537450381, 644179286, 785313163, 132075419, 578572362, 904951871, 120483398, 901495408, 138844629, 290636087, 830823985, 461010319, 882434401, 144812446, 845201683, 429386793, 986642885, 174859021, 117114804, 191194659, 639628364, 513499145, 711698714, 139639497, 372177999, 653607387, 983913656, 535405511, 254106996, 597801488, 764923159, 459139545, 349505430, 460368920, 627273752, 915469503, 576128159, 770037108, 760270845, 781566554, 638819318, 7921884, 895310454, 191540675, 947797245, 937298397, 80561742, 557799102, 183164394, 80802274, 384292397, 957642759, 290097368, 506871488, 983533801, 714473049, 444302333, 372928810, 17714988, 296283193, 595130169, 526836535, 341757577, 898013774, 361516299, 280314775, 133009025, 492867531, 186390949, 4866941, 521325172, 138243016, 818631907, 940112393, 516084485, 847287194, 303702719, 338911166, 990603273, 307953938, 227286806, 110978184, 456919115, 774573361, 878232458, 190985726, 432639060, 321806475, 644297743, 610218966, 214524488, 77178868, 471553760, 642754401, 767874635, 589805384, 186592638, 333553350, 824995940, 908263935, 721468824, 918315725, 521426666, 238863677, 550869532, 268249334, 747044401, 101199125, 169782770, 337989161, 284908081, 85451386, 798756971, 44676268, 147985457, 784636058, 516759410, 738665491, 355510736, 58342350, 340181371, 658769437, 913079188, 995055603, 21965722, 433316054, 519955501, 949400592, 616406956, 658341314, 409933772, 439122954, 626320759, 945214635, 543944839, 67739009, 200888264, 82022124, 910829559, 475226611, 883764077, 329985070, 708782563, 900956544, 460536155, 974793664, 223787932, 771686836, 342105477, 983946316, 527068823, 556602558, 469510110, 560233296, 332925185, 18526356, 230580901, 29675013, 653588897, 672157593, 347011087, 800374791, 281585632, 669555794, 259298048, 841212463, 925140076, 231600030, 120612061, 508276247, 477449903, 651019671, 472931036, 594209151, 617325783, 261881026, 4382264, 431371139, 263248189, 60941462, 954655301, 734614212, 43828713, 79124071, 341378793, 266325245, 151540590, 734762701, 140089307, 275624846, 60757477, 967045373, 757596208, 72515502, 68041302, 338952063, 529993775, 30789823, 965498466, 316600344, 374417777, 970844756, 816218081, 209402163, 604957515, 794926986, 898304783, 502189567, 530998731, 197379418, 546993012, 939422069, 775379345, 403289176, 168487087, 103629436, 549957978, 123556131, 763089199, 544767378, 556383417, 496140086, 289348677, 330107876, 375330289, 805884843, 632529493, 975861693, 948837625, 761209891, 216978530, 878951609, 379183797, 881237132, 876800215, 292388976, 803916473, 697511407, 129966183, 585315527, 595363685, 463419391, 529229871, 548650663, 47620513, 70490651, 405880401, 36391003, 635714808, 923932832, 837243384, 419120578, 143699994, 565782732, 29586688, 68395441, 397800657, 457766387, 60258288, 816257332, 835594192, 476080372, 949806250, 742006360, 905122712, 462987243, 500701520, 929500009, 655366986, 828084170, 664409453, 325245221, 995271069, 451052714, 21351085, 655973487, 539596685, 131291583, 157449375, 6807949, 750752571, 206377410, 701768908, 545376089, 451634583, 761301365, 566890394, 637409841, 461022961, 36618065, 368904080, 29630894, 877661356, 802703576, 800772261, 366488637, 73534485, 105874753, 533459734, 289061130, 347626778, 341400692, 78794592, 746809012, 693858655, 357851554, 64144200, 449104791, 287929799, 132590618, 812690272, 895897984, 336247141, 284556898, 530760809, 545531570, 635093168, 856357165, 577740991, 979683865, 652511118, 904476943, 818922946, 688633939, 890158059, 249548701, 527278556, 282704050, 854971519, 58333687, 657904768, 326810913, 501386582, 789123802, 470490356, 496754832, 513253574, 540382162, 781168052, 843073716, 422013927, 542202946, 505621664, 252127956, 625387993, 63109787, 645128792, 127287960, 501027134, 6697023, 285963908, 204239208, 588787484, 685984853, 889256092, 89071290, 987979730, 966001246, 30647766, 384084133, 635225924, 277395892, 521548594, 123593543, 86137168, 264586257, 236776020, 346089038, 859140165, 880634636, 290496578, 825162249, 949050142, 477711209, 842366809, 920108180, 872638852, 651189202, 355640761, 376119167, 795279774, 348101750, 811376519, 751294746, 343381691, 999476458, 101574969, 779652541, 149718984, 821558540, 69711320, 677843642, 454459098, 768870258, 465346991, 571981607, 795830973, 418484193, 129724026, 123014399, 524162207, 586244715, 242399287, 884222043, 650096041, 906724141, 777505812, 187344160, 37059848, 707361471, 738575703, 905568478, 55672369, 907286674, 788534291, 447412377, 767724228, 691723311, 117991945, 156827819, 926223323, 34743367, 528642320, 35986689, 62241730, 697639657, 80826729, 462209398, 627946250, 30269147, 949712928, 491199978, 488490658, 26056301, 286774748, 731457922, 33208806, 583966904, 398303347, 419222000, 434493291, 416533932, 644271630, 228276448, 887402439, 991845647, 440494325, 531628828, 403732940, 104087672, 27009716, 809933208, 966100405, 969032950, 685121569, 399383587, 461956266, 60011051, 595064745, 490310423, 410218309, 56342314, 139055116, 506821743, 534197493, 78839852, 778631437, 599325335, 757312066, 547745340, 944551755, 580686816, 789272214, 162456676, 584301260, 105792040, 350426097, 685568882, 357194973, 43645469, 565222640, 860037653, 720389072, 51537966, 307750685, 361567211, 891327654, 285661258, 643567568, 483830528, 1180825, 745959658, 858610288, 870791818, 489977959, 738108848, 61885962, 433197563, 860390213, 942927365, 979472776, 859271151, 505136733, 66125902, 36176538, 277524593, 38812111, 634942602, 260067207, 863972216, 460433199, 931395698, 188128588, 600028396, 885235076, 371927190, 801610001, 142196042, 259783385, 485983581, 454801209, 599418028, 903835575, 778483626, 276471688, 469263063, 740392436, 953279454, 481071025, 704180408, 303879789, 24584289, 146331736, 133007415, 463055167, 205470755, 854712867, 553690518, 809339539, 176185270, 709057218, 395655378, 407668316, 38618811, 522205780, 659015071, 192869933, 887170242, 94716615, 619497851, 909716392, 7849832, 145683737, 375790003, 48524976, 495183960, 988499230, 135519779, 506473540, 840198167, 562491511, 47608506, 213041337, 875643288, 520861074, 59574555, 70676550, 826541510, 226002580, 293364680, 702333092, 482086093, 573101520, 613095912, 395781133, 383427672, 356667528, 348657431, 418351318, 756608630, 78655432, 529425494, 218653185, 201900795, 676640662, 376876027, 916527280, 724357050, 91995795, 441739361, 440293859, 5341718, 495108504, 994322935, 790141241, 151299470, 548111138, 421809607, 146164399, 726762943, 784490032, 348809022, 792303271, 290076866, 553428337, 710192170, 9283808, 193990386, 470581024, 704800814, 102153470, 242317074, 79275155, 352081587, 639672189, 869387546, 371929689, 582886264, 10896083, 291789705, 755141909, 422549078, 522526159, 462143713, 966603041, 233714354, 263968030, 775569548, 517621721, 190321342, 256760769, 255580491, 96919231, 638895655, 932375054, 678207919, 924371055, 299568215, 262086337, 463720330, 780429501, 110553816, 544085401, 798867085, 993351797, 73115373, 295256749, 549672213, 599596513, 205355892, 878076019, 422707623, 587427244, 315980650, 903958245, 126562582, 226962455, 528783197, 602448675, 527413397, 102671893, 749039120, 891855789, 962365692, 642638618, 766964619, 61335851, 991268591, 965441064, 901861310, 880011970, 841198265, 179671198, 101073123, 128943039, 386456803, 639150059, 154101150, 820911314, 380892517, 691717139, 428641849, 131867546, 639740499, 934168680, 733999282, 835636751, 141887272, 701211426, 361639268, 713154702, 149330205, 261592240, 623594637, 577327313, 259753004, 934870888, 138974972, 481701715, 88212701, 390824452, 725095080, 216495931, 677954434, 464674029, 333454891, 158109672, 372611550, 178682310, 61720641, 261110643, 993419251, 524209645, 778373393, 454766807, 820252369, 885414638, 921760994, 446398936, 937483391, 894644323, 456457797, 936975126, 990755221, 459992648, 570840892, 100348020, 98080381, 688550824, 150801157, 921730218, 685354962, 328347218, 789741361, 431787394, 561051381, 24533749, 612199167, 813367972, 29281487, 188569300, 55460469, 174445999, 451734419, 219649278, 480991174, 921182130, 868830605, 385265774, 998919078, 400461057, 450118464, 473653307, 565577437, 130627130, 582284021, 336725967, 460231046, 356863320, 710793735, 337977003, 974983915, 848413382, 500103647, 496137457, 922945285, 760790504, 352209916, 408625167, 412576023, 703430085, 805298914, 81652381, 377281593, 892962383, 487569679, 892417842, 306057650, 417528605, 672083964, 650704841, 260732999, 777160714, 467042236, 305756132, 599122027, 676428806, 769623515, 251447075, 978977606, 547772878, 975620220, 820865600, 445409992, 530561569, 342510670, 554078268, 22790875, 357467436, 628429827, 782125760, 361548601, 138112163, 531590062, 117498778, 924650854, 546710167, 932164365, 310003367, 500457459, 501855707, 142238848, 468818243, 577253031, 43416147, 889552959, 696131578, 85251817, 741583135, 523333034, 719331816, 25999707, 756276710, 879426570, 193257954, 949052801, 874031168, 367516718, 958654477, 846272855, 363301295, 268839477, 206864755, 525527273, 651174091, 556836066, 330868459, 500562289, 182051223, 71755532, 606372241, 262991038, 838716376, 886902156, 338176863, 15827671, 167348812, 421768348, 629955793, 872583666, 139772211, 526907087, 548442504, 658765912, 783292588, 884613409, 655360754, 112901338, 972750311, 316466236, 549647612, 208801087, 385866178, 90766415, 402067597, 423105174, 795986883, 30191407, 287268717, 514410047, 54532003, 258771674, 327189336, 297893064, 396514461, 700125149, 834292286, 317559185, 645047710, 745440035, 685643898, 168988937, 904220570, 140608961, 414048856, 528829853, 9693683, 73946532, 112816024, 83764932, 487848328, 466686847, 77520914, 736060607, 812396179, 645494180, 917072898, 166938121, 105604535, 418371347, 481320764, 153856024, 709284074, 802449597, 462183596, 552595390, 319884616, 777838438, 688456480, 544330970, 575574124, 77716627, 78828198, 303546540, 304517815, 535279928, 787977151, 863930938, 899241013, 614566231, 487970242, 735966439, 270830275, 392677195, 31219739, 69649383, 377791082, 323873053, 126106650, 976743282, 640058515, 782321533, 758224153, 958757871, 878966573, 690761921, 342056872, 697096207, 373872902, 519150695, 587593130, 696930911, 690828155, 737606182, 493916726, 885726050, 852390135, 194134218, 42478926, 714361690, 63511326, 101511057, 96066870, 25163527, 920562649, 712782347, 700028187, 977484736, 525420941, 924155554, 607854489, 675355313, 654391067, 656165415, 156454887, 455478997, 384866586, 393239621, 31803571, 610105197, 26236060, 860029769, 328948009, 785459675, 317980312, 863691309, 273397566, 720641578, 532612290, 438400070, 775140933, 116130926, 745422411, 830560518, 949664460, 250283695, 32037076, 9713223, 987625308, 874797517, 739441331, 745559889, 776229593, 456694026, 392670908, 981186932, 670708243, 260458342, 60606233, 211050027, 621747005, 307356029, 252281653, 266847182, 755630324, 162462843, 171061107, 489039655, 694849806, 653175082, 53249337, 961033677, 762309540, 46451382, 43028157, 604547111, 853775831, 569656841, 377514097, 925852989, 192748758, 764147446, 84881742, 874581575, 744269521, 529140296, 803377778, 19346239, 988809776, 54564094, 130864897, 848980574, 14494783, 11891024, 448017364, 499708341, 711204744, 618561837, 373337428, 131630777, 337490287, 730848019, 579242334, 586856686, 523675027, 858797839, 739774426, 135800792, 895081908, 228298979, 884783056, 480892290, 96042413, 833871449, 944075684, 216155852, 464339778, 72813382, 949550079, 654803217, 80247501, 662015880, 759893340, 327106585, 892733806, 194319176, 611089924, 295346173, 449709061, 255279608, 883083516, 409926233, 670308514, 770279379, 319656039, 753224143, 296201462, 258618618, 734599442, 922562629, 693855908, 445426603, 39307751, 180608794, 924548817, 368082775, 160959249, 567171877, 371393446, 499085383, 508338820, 810282523, 724401422, 132215338, 473456356, 232411219, 536693983, 102038825, 763953878, 688705557, 540525786, 366683340, 587614838, 67422896, 519114487, 509077421, 233574000, 122705185, 295548127, 797884503, 724356579, 28064745, 236663069, 984830621, 632274272, 196015721, 405558074, 71726190, 997643954, 122911105, 669952116, 891776559, 603944452, 300380432, 440107743, 645475252, 307258657, 904313610, 205060034, 136341857, 415171623, 71034702, 358468501, 766555389, 731427542, 25939476, 724227430, 230077524, 940188917, 41448311, 669586442, 648075272, 480247820, 320833929, 93743950, 783450592, 760616539, 841530661, 81084712, 404150341, 353040517, 941738267, 680799914, 855459274, 419748286, 297491897, 322315339, 353517681, 360538205, 27116438, 233652477, 75536912, 245635505, 384610710, 398287244, 302159812, 687896367, 605405318, 2465282, 203389452, 375896685, 925760658, 767649936, 543833444, 156416724, 835932211, 57334827, 894218837, 674101667, 328455691, 300989429, 883712296, 229641315, 645691410, 833899368, 835612635, 692553095, 513838338, 225864124, 120842284, 162489809, 950844885, 587626056, 103894817, 415692077, 804674029, 205947991, 526991906, 284369333, 532817390, 313928476, 168956054, 140375161, 248914296, 806988403, 509242314, 172295748, 119367697, 846923040, 158793673, 254783238, 704977230, 285598138, 737202206, 551850352, 401867677, 91117728, 440291576, 19643573, 283545826, 930860139, 188466993, 799462141, 160014663, 426537782, 374652644, 207992753, 656612397, 385638960, 883842966, 592337582, 541863494, 101683513, 845251642, 790545551, 784844772, 607418480, 772603386, 444946770, 155196229, 61193259, 815401290, 82532233, 734751777, 634094680, 643511271, 987561970, 28642079, 524518728, 664744544, 870410857, 71088966, 442904776, 390913517, 803090930, 498878547, 818236902, 135930456, 278593894, 48428371, 962635275, 587872544, 428273562, 450210902, 893871113, 127442801, 407708682, 901144493, 700866032, 266418488, 588951562, 234826244, 724035608, 601017685, 272830168, 805735138, 75738246, 954255661, 858678522, 636672676, 343718286, 19103871, 196347570, 683202554, 557924879, 356914668, 868836001, 957074612, 3753467, 446040171, 270269657, 70998551, 896925639, 921858474, 621955820, 732822583, 624518681, 325268841, 660876273, 26066756, 777996265, 329112063, 144556529, 850163496, 429723366, 355081072, 527147899, 588300979, 743150433, 661447866, 664351290, 567802460, 620945466, 11431171, 669907857, 446079114, 77611006, 666278959, 544829859, 909534989, 650701187, 574738336, 659283318, 713467098, 43457724, 687828314, 591569968, 52773035, 212643311, 556983493, 969262732, 825513699, 616014654, 45760614, 682309042, 215059740, 388653344, 928259971, 952458297, 644550287, 521484515, 655383783, 430094519, 304919783, 939900851, 964225345, 433463680, 90171294, 599848275, 486531419, 415821566, 824184641, 899455868, 648252244, 950329669, 27591566, 202563794, 844202011, 41539415, 535663591, 426312649, 639315700, 847625002, 376948497, 390094559, 137940885, 999038598, 855419575, 764515494, 24383385, 938111772, 367707384, 535258515, 299814451, 958668189, 826322069, 808411154, 275333959, 121696083, 720432742, 241765246, 780725883, 139343809, 324587919, 768253769, 11514827, 987175746, 17963105, 918881938, 850229076, 770307584, 541504399, 784973971, 775462098, 700066449, 578310551, 165226769, 50225694, 100534069, 149165392, 276510274, 669782640, 194417949, 775330484, 863267000, 708285028, 874496724, 888888318, 329234243, 641814712, 361569061, 115812205, 529772852, 490685807, 980585359, 881402168, 804537375, 24292325, 987141144, 920381745, 188398396, 531378185, 286370038, 951525358, 438074324, 985318295, 662768657, 596443484, 920005782, 409256325, 58214417, 552941977, 247378964, 195476454, 771743475, 276561858, 879116872, 280995945, 824288028, 415123847, 247360634, 272882912, 27499546, 190769435, 844059990, 707740356, 102043550, 401428290, 791957814, 913396378, 363415784, 22778269, 225890428, 756001767, 784452284, 345373690, 792643765, 704824941, 376864792, 143423486, 669282586, 119650767, 138236693, 946523517, 504568714, 511286535, 548953952, 570962729, 182400608, 252745706, 846747613, 976017334, 707051419, 851457836, 373108667, 91035034, 652583988, 299089045, 286468675, 984239376, 387096800, 242514731, 889063155, 794129680, 900501199, 290010831, 331022456, 170157966, 932517717, 667634008, 303258950, 882385889, 771336221, 923312093, 618251121, 599611104, 449065900, 483335052, 626683078, 451772927, 858868323, 28508624, 777879850, 247256177, 385216029, 941370260, 164566533, 5404916, 121149285, 332381183, 624537323, 871735812, 988485670, 221504682, 881543570, 725665654, 350174032, 571358472, 640703237, 907810148, 449326955, 18750725, 112458690, 627223311, 107605037, 686317244, 274201771, 457686453, 480039111, 521136815, 688307354, 277179790, 558691027, 347562477, 251543461, 381857198, 600195893, 508069511, 856986974, 527984358, 855361441, 872416824, 723389520, 791249291, 490416041, 829100353, 837572768, 511236237, 492979919, 862831329, 501000613, 490615842, 887464291, 76829759, 586338359, 718683862, 409483894, 940587144, 364528062, 686821960, 410575668, 174324346, 436529653, 731180027, 947722518, 2842901, 696211608, 610962474, 271267196, 578917552, 106053062, 528021615, 144991863, 782914659, 514267937, 38899230, 912482071, 775719218, 544229688, 838453716, 478119701, 576208626, 403138020, 346849345, 937830072, 887973642, 554032542, 973593275, 919255731, 22425403, 349053501, 777839946, 207709918, 479919712, 23429955, 728742476, 537204336, 388461263, 340233476, 879372698, 124917129, 980273956, 483563057, 177346006, 381472754, 914814127, 244250853, 819448935, 34709933, 378061106, 376755521, 422205595, 599613252, 750426578, 605705463, 65104701, 748731003, 188477622, 687479160, 983872941, 404722786, 252344506, 929129980, 750203879, 900816783, 513680279, 873812617, 940408633, 622115788, 488489770, 435424943, 602113169, 310396285, 782303953, 558161004, 546201016, 897451704, 115704795, 940724050, 979100331, 387740215, 531133588, 995338154, 871811952, 278938069, 932779662, 677744523, 714491403, 179614093, 210732977, 627479656, 202301503, 477982620, 244275933, 320402025, 922319668, 896655288, 84356808, 579878104, 768474665, 560229584, 389050760, 467470404, 208958320, 58886003, 767111631, 724299733, 116232567, 400497456, 373995786, 478945410, 351550731, 964215715, 494204422, 234494954, 559740610, 6121377, 459722553, 400444518, 498185188, 490603894, 620981000, 22411861, 66618478, 871130029, 441614921, 279487149, 573484422, 460362422, 350577292, 291297258, 755658941, 458419366, 242191956, 881235898, 592337989, 795322890, 68663458, 287368512, 71226747, 941890588, 332808765, 85201701, 979813098, 651424383, 4125093, 717405173, 385129886, 134242763, 904266298, 935437243, 85899394, 540614912, 712904534, 812110746, 978387010, 609424553, 323093173, 522779031, 130087069, 749291670, 506972371, 496015781, 876159698, 236914366, 9686035, 504155106, 838237790, 593208807, 468021992, 503161747, 869800874, 779962525, 1407143, 700470578, 47813945, 730253071, 917305676, 128586163, 714080129, 446368825, 251359279, 431503868, 412465007, 976425706, 108893070, 712840652, 853347987, 223605327, 290448517, 720050784, 206812972, 726309109, 962210394, 388987236, 958659240, 26678563, 109897053, 960208679, 649789832, 155888106, 313627088, 905655937, 535846709, 650417951, 696912537, 259008643, 10712502, 170782472, 338446511, 364836758, 443247839, 381306796, 126689053, 273585021, 348144767, 493793132, 397699656, 37788275, 566307016, 29822733, 298196361, 636201008, 873494474, 934182029, 700886260, 516295853, 85065168, 579242296, 681421197, 607709231, 161591729, 981397507, 38602675, 42576977, 65675845, 961502276, 566148767, 172551324, 592416086, 937770186, 790798258, 619453171, 326564083, 382591549, 748640502, 885105083, 442475427, 146107629, 443463319, 586366745, 911483425, 261578515, 205918844, 780183705, 592230910, 589531596, 303992530, 307429710, 838746658, 616294573, 350219450, 722658168, 405218526, 661682110, 513389880, 398547350, 983476128, 53221453, 588455172, 94710026, 104938881, 672492554, 195923867, 647504693, 733441782, 712911257, 248344074, 717315030, 213164804, 310354577, 584340194, 497671817, 888556871, 141607469, 426270774, 949457659, 993879967, 19392306, 345992228, 772551107, 989441288, 780464995, 51019065, 184683652, 336694262, 206230709, 223023451, 389232684, 556481387, 417690414, 225964430, 845525004, 470440418, 278242498, 561540396, 335022417, 206491133, 245419248, 85449266, 656440435, 329412109, 625883297, 773092166, 89782405, 950002172, 913472376, 270850104, 779186456, 876303082, 740870130, 673707108, 278028562, 381950768, 82757295, 764938084, 876596212, 244291855, 786987913, 527931328, 383369286, 318089949, 607487625, 128081232, 548606862, 478910183, 784962156, 243411785, 89751889, 65690600, 999876664, 559329245, 649520883, 573670255, 43424468, 282821327, 686490787, 562748463, 747449758, 945684930, 355744426, 209004023, 225082700, 661933077, 380936841, 504457667, 338822153, 53895416, 74022312, 833727611, 551567482, 140050559, 959427051, 44536320, 701519847, 845158144, 969603441, 337985023, 266676862, 735471084, 15144009, 613573544, 249324013, 903121657, 886346155, 396038365, 617880642, 330373760, 721703096, 320809647, 202388532, 574871111, 772193860, 847764502, 863135079, 735077488, 124571543, 535683859, 799133587, 447550497, 453858485, 398622038, 621600194, 871362096, 365307237, 685740221, 69535519, 221885179, 685407800, 720519610, 833868975, 536173355, 863415350, 4421076, 636852585, 51251441, 737961887, 919386364, 233154864, 68557204, 202619491, 773610703, 6672183, 928752083, 935439689, 733518322, 945564946, 286057550, 462953607, 365197360, 965205772, 335873479, 700925570, 144000132, 246561718, 832645735, 179147425, 302463531, 452450843, 74914598, 272059632, 526086645, 868091081, 455406062, 194855302, 511435105, 997769587, 572020805, 882667558, 67042751, 632791279, 968751666, 740762247, 671061295, 470673939, 98950944, 817520846, 362958226, 305557693, 157805134, 63044662, 955681597, 684427700, 289174512, 163820625, 881800297, 614072494, 106844162, 276207809, 47836157, 355104122, 152829704, 587217936, 426912280, 514578430, 863544631, 374659904, 77214808, 340748257, 179890775, 43605192, 892055459, 314249556, 655163499, 311770315, 689253237, 275071129, 480412040, 820480221, 767982743, 915504366, 335326517, 974201352, 830993527, 384080573, 557728185, 782837348, 143179419, 827161944, 171459678, 40328742, 808283756, 211343471, 952313085, 550455384, 458842576, 179250134, 150338946, 853144840, 382091851, 993171846, 633942187, 829283648, 736358395, 313040780, 541049685, 18062870, 848291811, 7268117, 382662678, 46851101, 64851260, 671311682, 508651764, 388580365, 581146958, 420245741, 477197585, 856098202, 640244672, 309353007, 658473669, 608456173, 269149987, 818856873, 120962968, 164651368, 849005219, 332436466, 680010818, 642590867, 291109139, 264579401, 186700172, 446004565, 990522643, 794928171, 664481448, 754760928, 260256350, 432819891, 139123602, 322260281, 469558001, 176361611, 265568534, 373641300, 925248393, 346812205, 242412479, 867767184, 586552469, 391139182, 654031459, 858053660, 968278216, 5183962, 161250101, 121975842, 744162609, 906136205, 989763531, 75892109, 258910383, 552998052, 704350061, 990311637, 428597592, 460898779, 497978585, 389587451, 46691516, 329699202, 726893116, 633785312, 203164655, 986264950, 168368854, 563629890, 968093115, 885893101, 527563745, 139936794, 933798910, 800602360, 722524914, 930197149, 987828744, 373991274, 520626742, 820555240, 281863859, 988263658, 410163859, 183349716, 756858525, 357966970, 233200805, 23513873, 459980443, 18728698, 176423093, 442203849, 577373961, 405084393, 553045812, 886177542, 364555213, 401450602, 173078862, 327555385, 962876587, 268005727, 450430628, 611497381, 61652708, 765436219, 688023755, 251013765, 894021839, 632559360, 603750621, 406389532, 864943630, 971812500, 787996709, 711072352, 260415625, 348940047, 208128408, 511940864, 584298282, 442943054, 47425154, 390012634, 365999820, 53975482, 813159605, 833029801, 92272354, 204612333, 167515066, 667815601, 544177076, 874845556, 877274002, 515757471, 585730778, 32305849, 933770999, 637024288, 296718031, 756838961, 90128294, 403587139, 87290257, 879506051, 872432803, 262436476, 672121411, 726544433, 360245522, 285938325, 674817026, 501245318, 211094395, 804625333, 816411271, 791449640, 678447016, 584255396, 425058660, 98535211, 406928207, 57785682, 34168774, 107328352, 180250444, 998840921, 965618439, 100676053, 555741169, 860824141, 600263268, 336600312, 902973735, 618936316, 535077538, 82846280, 136274624, 15119374, 517019539, 660175037, 315091025, 726245270, 490190476, 834779907, 774677224, 607921765, 940008180, 672746710, 227670410, 125996754, 224294163, 820838959, 585886295, 927383243, 994384222, 947305763, 353465797, 370181351, 825238833, 732047627, 688513373, 984648114, 205145540, 177362370, 710324235, 384909270, 770184390, 506616450, 709653404, 597087809, 312880350, 900320272, 818564039, 838984953, 617179668, 956143290, 532210631, 940330651, 619230339, 981145788, 274533395, 664411518, 634912927, 570510091, 116643815, 931407854, 153410500, 971587428, 727429199, 958266931, 877936139, 540654540, 827498416, 504105889, 106029759, 279252520, 736936497, 556543195, 621242947, 42373308, 619611562, 24526057, 345046315, 788061929, 324528522, 503455513, 297433628, 593270225, 174568411, 947583541, 614508202, 630515978, 414636719, 358639658, 587807180, 793243924, 419202493, 316144280, 292835859, 708334753, 989069976, 823838937, 154078508, 698722996, 50125289, 974958693, 380885687, 409875387, 989549096, 671084032, 285256348, 419674464, 483308815, 299670262, 835105043, 347147562, 60109735, 102006353, 610509139, 342930116, 359442809, 676060362, 170549881, 973902033, 209296269, 493449548, 764592881, 4620809, 382196965, 507180620, 142070191, 840873499, 468222479, 52427852, 930507067, 425347631, 308066127, 553711581, 354299134, 381992843, 542164697, 267008595, 31751590, 192446440, 692754242, 515442204, 945912382, 781234482, 22034647, 391674310, 467954869, 54998391, 600968543, 701351247, 521428442, 7221346, 967734612, 418899152, 995444867, 424180007, 676360713, 983647721, 18210480, 507594949, 623632955, 81711878, 982625419, 665204459, 918459140, 18945829, 967594677, 794136490, 835201946, 863871457, 574534163, 69792634, 198142552, 511928234, 239127146, 184932352, 47661469, 105561993, 793757903, 7922574, 760414294, 984354905, 341824271, 205884027, 164843285, 659910946, 41278361, 212472502, 612294587, 745856068, 708898807, 977886360, 689110613, 938130713, 408954040, 39982683, 59259171, 3093743, 983233410, 443451062, 238160072, 72133548, 296643448, 605105507, 735500101, 256890510, 334096800, 750529413, 418312728, 433640482, 932946485, 511641935, 947398764, 820976153, 174009057, 521834194, 835882476, 124400383, 755160191, 599783450, 580704409, 285230504, 439672183, 557704828, 408944377, 345584555, 808492150, 919196227, 444590007, 952744387, 725646538, 266721330, 509070398, 190803528, 879664108, 580105624, 495817358, 250887247, 678630312, 65001249, 695956031, 252032703, 871313191, 854827072, 160704656, 485681817, 31683754, 567443064, 197971077, 695588909, 108573550, 261777728, 973292955, 199764655, 495799979, 310532635, 260801408, 565314132, 275458536, 470308835, 699715220, 719577007, 502346822, 4775649, 132354285, 291887498, 48816351, 912887865, 158136889, 804918348, 166644556, 524407172, 792473093, 352446024, 866958786, 397048127, 264739396, 310377642, 766566175, 8637954, 182161491, 508126268, 768535977, 257928149, 230472059, 928152858, 825357879, 930406856, 643313168, 291739843, 103348897, 90179708, 665542859, 639797746, 423791625, 90776075, 563904848, 761476059, 202517991, 460109347, 211303230, 983813607, 548487672, 908240532, 956530513, 844353896, 279917336, 109946072, 889644122, 427302296, 783333131, 315733760, 806400620, 586482617, 162305355, 456405528, 406178946, 184572640, 19974332, 456473152, 400094902, 136957039, 926128362, 347611075, 222853953, 400718994, 948145903, 544447873, 306051825, 289852094, 795622880, 917189164, 904760581, 187444945, 691227705, 413952358, 222224700, 706431859, 708171471, 288059925, 100607309, 110132456, 800557735, 611021105, 986044414, 785007580, 174712468, 198595624, 796573255, 920451867, 953844274, 570489560, 771321585, 590453144, 969472406, 825664219, 556562079, 725858806, 738756673, 741923152, 18635150, 659452642, 45883615, 107356921, 523355960, 378320115, 105634907, 323411956, 950664249, 344771393, 405979996, 698945535, 45141570, 213907426, 647449738, 872765824, 18183219, 272917244, 948524711, 916141328, 649253351, 329523688, 252944344, 438071795, 62029684, 652424087, 563151724, 792327085, 904448209, 646820646, 761539695, 733228074, 797656068, 780214041, 734396917, 156606991, 536750112, 878475014, 614063190, 545564829, 293296758, 934305086, 607939046, 659024717, 576519289, 310717832, 123382198, 919538728, 458571252, 833909947, 413288586, 109908385, 397771398, 547676099, 495017190, 6508941, 542376094, 498207946, 701975614, 88652288, 283398093, 876588937, 804897356, 430682772, 785613968, 132743877, 736592940, 476705676, 796038472, 177850419, 885226388, 139049930, 7087566, 588076645, 88923509, 630381578, 704587268, 502608219, 527002108, 477636557, 707887630, 824429315, 538326502, 540053509, 192741366, 794540233, 580577879, 289576387, 483945315, 669323102, 870050587, 829174713, 342140854, 965682100, 7702646, 615538111, 714317146, 151141038, 162908220, 693708353, 213906510, 751055746, 252587413, 675837456, 331762578, 146916268, 191922234, 559097079, 752062798, 572091883, 958594762, 499779045, 547194612, 884843557, 82854657, 838986087, 422916098, 970560577, 682950608, 897358460, 56586070, 674841757, 810038905, 917736001, 296206205, 38826013, 268417644, 121085635, 414322099, 329445268, 871899865, 61123184, 376344896, 824909441, 266583620, 553204898, 524894675, 137276231, 608014401, 53765513, 329586968, 802353770, 477024752, 983056318, 250732368, 828684058, 227110954, 280954623, 625515395, 961069112, 640844830, 718542990, 305895962, 869667777, 58061643, 212435748, 773460568, 900008526, 515313608, 218743341, 497935279, 725421373, 438244211, 6930711, 444682286, 651328575, 423718372, 675584966, 925267957, 405836066, 5418964, 709563469, 818555803, 287564808, 163836853, 137596888, 630068168, 197177063, 774912037, 785077696, 707741131, 736368125, 843131720, 603656685, 712590456, 907233009, 799764462, 527284416, 243598823, 179232021, 624926221, 753392759, 950228322, 616645344, 946615209, 787381153, 295166167, 706380934, 6111214, 838444370, 201674736, 246782668, 875897380, 953597148, 55884673, 913486225, 865277461, 255356520, 514691764, 749856601, 692850951, 501319749, 574102306, 923168604, 923575660, 491663013, 412271545, 890914073, 201436882, 376485886, 669323531, 440091536, 701660880, 585532823, 867613712, 551348295, 120748236, 122103104, 873953295, 121022999, 629943046, 784361916, 510753836, 466975960, 962046569, 557790954, 45886649, 992078485, 535822692, 42159159, 907981412, 20577051, 797013156, 8016372, 375678047, 690918700, 346481743, 781524167, 748663764, 912530741, 229168880, 631884411, 195816626, 174585756, 363032125, 917865438, 933059918, 739660641, 307375785, 257685633, 561140792, 608714402, 7107400, 623280639, 606056684, 942770824, 700666112, 375317986, 922532814, 675472314, 822398652, 875859378, 73672393, 803100941, 988406448, 107070690, 128168647, 719896694, 85715716, 805782574, 206498727, 188601810, 83167078, 378273865, 779551389, 226034071, 595601518, 258519084, 341628538, 649404910, 514872572, 270959264, 255324835, 577759587, 491500630, 939606697, 650252920, 510976273, 227676445, 701294580, 130445423, 312556697, 719585558, 958512169, 623449975, 194736198, 33687768, 603527094, 794344804, 928407235, 310524106, 773102113, 773971353, 342370403, 143152037, 508061574, 277484464, 610050742, 32924410, 413534921, 195188108, 56056192, 228437279, 73189911, 893912362, 167796721, 471904030, 76679014, 121677541, 90757724, 484269646, 155450944, 696124948, 807549843, 817338247, 87592424, 485670011, 402955975, 438161640, 611691778, 535378405, 308531485, 862884174, 167052813, 679273041, 321753633, 298596145, 423834936, 567318632, 259688530, 736349050, 18719870, 273823892, 607833889, 873846907, 790003693, 410545042, 777812096, 394544062, 208620584, 932114607, 81748294, 603626657, 957552697, 786707893, 259884503, 163414965, 150400043, 460489134, 872800124, 858443471, 78246767, 458636287, 238498657, 453691844, 843269435, 734906916, 383506483, 304468890, 225467346, 296834379, 164627725, 28594361, 549597966, 781776978, 769752792, 190564363, 995151381, 260662222, 881815177, 421825060, 628297220, 114476647, 360590675, 852670153, 777282659, 323031781, 299989022, 826190517, 556760027, 391222992, 998581881, 749363517, 925424304, 768514557, 763331376, 335126336, 283553648, 519713912, 827307257, 641095215, 510429869, 412809322, 598076192, 357837369, 922809557, 60185044, 358875797, 348297521, 559859452, 118180941, 955242984, 675096365, 669394776, 397690641, 616612731, 527784277, 132908533, 586889610, 781620401, 237564323, 467039512, 366000591, 306311302, 715449490, 626911295, 295230208, 33818322, 367573147, 152864404, 814548795, 299467832, 747210372, 8952219, 907686226, 35672829, 768355434, 551478645, 576465238, 538208866, 787986909, 48319943, 100095587, 124411763, 109428133, 265963359, 241093544, 579430737, 12793962, 848012263, 67355157, 538816520, 62936090, 75965180, 187487842, 652219773, 888171805, 274948674, 878554453, 188913325, 666600255, 883914038, 804625361, 259798997, 738813633, 264055746, 913717712, 498019011, 219110915, 21807429, 698734697, 877622961, 65321119, 292068344, 919105018, 983149118, 19838479, 161100742, 295717215, 391644559, 654488146, 149381954, 925331059, 414314293, 612462757, 465022123, 988294885, 837599753, 913641428, 429009761, 229405619, 867115482, 819183927, 88700324, 979303465, 371781146, 542072204, 609186061, 553794085, 655693594, 61108179, 644090237, 229218991, 423583973, 804835239, 968209745, 573069229, 885170816, 218122445, 211965130, 78301633, 485334378, 248094656, 940318723, 958568214, 479951754, 76962576, 955029126, 387765624, 598219288, 404780443, 451116738, 544254603, 356082942, 430112926, 293442128, 949250222, 415030540, 228232280, 207769639, 678311416, 592769073, 709582995, 701716116, 238554542, 616115046, 519177833, 691154603, 812337502, 546608149, 118976013, 54469287, 499714133, 451758142, 603355171, 513407418, 609943170, 166821615, 790218200, 92705361, 492954839, 632633421, 605677950, 373182523, 572970354, 951313427, 829425975, 260616427, 922280129, 537809752, 4069905, 216284539, 388239542, 995805852, 646306664, 82500429, 381552280, 653609459, 674714396, 398384235, 146800788, 583312536, 867199232, 327968905, 963101854, 984337914, 820516344, 18707451, 541215567, 95679896, 437487733, 566310620, 780189423, 241687451, 484945829, 919430611, 271425088, 965158352, 215108873, 544294109, 690704019, 53454793, 64959766, 902832340, 451707236, 455053264, 235418655, 867642854, 963436337, 827867348, 208091796, 896087392, 46038257, 489952437, 535859405, 379970998, 639787851, 124522312, 295273935, 805872744, 335931455, 918746351, 183412939, 199239636, 904152083, 712837918, 341905697, 957322363, 652974769, 594517814, 261883616, 906807946, 524910580, 448107716, 478910292, 608089057, 507367404, 58903488, 691947128, 55196687, 697527497, 700323890, 800025463, 76520927, 959094572, 867711557, 598690318, 88187597, 654050577, 459474306, 845038661, 134917622, 362087129, 828505864, 76144272, 692567905, 947386932, 761718451, 178907140, 825444213, 402566435, 565228552, 514078924, 839719580, 608756017, 91278897, 344284744, 692269699, 817974857, 306542584, 826743063, 345203667, 127252140, 887455655, 58495974, 446473567, 609962507, 658680658, 903271937, 697538052, 510908534, 545669706, 697326480, 275291625, 583852728, 194110032, 816792189, 872197743, 987315064, 229009682, 507789963, 28938430, 382905505, 397218569, 4793893, 344751265, 194725581, 38800826, 665877228, 880324839, 594471622, 890859178, 119610488, 578254693, 842032914, 295740764, 847833782, 735549267, 487395549, 824369491, 459308738, 89227733, 803706521, 571283430, 955707272, 847640669, 840959957, 17343555, 752187046, 479425454, 248983785, 175431375, 519273616, 5356081, 961815937, 497312810, 246484883, 595437398, 954871017, 627598819, 294431721, 936440898, 443192556, 908873174, 669118560, 934754699, 728304866, 357228352, 352816693, 639687823, 806657713, 361357947, 656545804, 354326015, 380446338, 70022081, 928219740, 472332507, 675718704, 640619700, 88944311, 769056009, 562271230, 991084687, 342685537, 528338264, 758143128, 920619891, 899306701, 674752229, 481893356, 671780228, 642013303, 931722285, 153621684, 957710950, 177940567, 38073085, 311017774, 909489314, 925830275, 272482075, 406280437, 882827433, 244549974, 364724774, 752943953, 165659759, 867292678, 304313879, 581420311, 723172626, 808790293, 91248665, 249150101, 3127693, 485461425, 738788584, 796335171, 159937833, 728684467, 258189584, 782056949, 126071983, 640160014, 733915657, 150593155, 493873585, 179655679, 392955035, 965192959, 928399309, 179130847, 393836238, 507420743, 196813588, 328354287, 157577886, 336439283, 466111754, 262261836, 756158446, 694518051, 52379863, 996319801, 8222515, 633209835, 810267582, 200812002, 579051873, 893747640, 857811631, 113059468, 996014113, 126440158, 164936769, 494493213, 239953286, 697429054, 380277147, 52373079, 133074248, 943661282, 578780752, 829715128, 786545791, 109067835, 149812667, 896617066, 499226494, 854842461, 331703646, 587783850, 636565832, 188357296, 57005403, 777934363, 769897587, 372990830, 968849595, 628992006, 830510636, 36633412, 634779796, 752899409, 773388011, 344045756, 761587644, 930356908, 758004425, 985512274, 448063315, 953138531, 770856951, 734554953, 189951718, 917331620, 31157219, 638463843, 166451344, 999732021, 380430662, 993779595, 63356578, 248221747, 843652632, 131448780, 268130610, 782374732, 310091708, 282983001, 446235411, 877151792, 215945278, 925128360, 655153086, 572208212, 319107390, 40820118, 594654916, 354282133, 390307524, 735155214, 579551989, 681124557, 379269214, 100171507, 63097313, 440956948, 940813497, 261623890, 142095950, 695357420, 605777184, 106135876, 351509495, 345024839, 26872173, 782937574, 634942691, 63642624, 419806298, 877040369, 214713871, 68889747, 537896021, 833110386, 11648596, 376064696, 493331901, 995567306, 251239977, 8259748, 757603210, 944169920, 130103695, 835131919, 503916001, 135307947, 648834366, 120886902, 795104209, 437425144, 369869345, 675850404, 903920856, 31828875, 417636941, 813285415, 581209506, 350159054, 726003234, 23779991, 982827982, 756060021, 855404159, 634211893, 930152240, 33531597, 561679364, 70990823, 967575584, 931907672, 942760596, 231194311, 636406236, 775024266, 629592592, 174467131, 403191661, 163583792, 860106686, 67992693, 50294792, 11965115, 742383574, 199137045, 235529705, 37645237, 220280926, 53808721, 70814331, 568215606, 694935184, 877594523, 908812519, 609102933, 587057299, 426845704, 795125443, 682948847, 958158273, 748031063, 757834368, 901458905, 489710138, 409763398, 161847056, 872955924, 975338084, 301292676, 331567925, 812637221, 189169086, 386329469, 519160062, 896509627, 364986975, 999106576, 739348237, 29646453, 226854989, 356961848, 451914088, 579103296, 430456646, 787940494, 595113746, 799579416, 64914472, 345812621, 4006791, 510818610, 142742069, 499226356, 567321790, 411721913, 354879074, 647444671, 817475482, 551650066, 992668397, 44232533, 183243721, 533786136, 432045902, 925461618, 952697802, 491057391, 639048509, 195346943, 251095528, 677006734, 351997137, 541086820, 54382954, 677816206, 275476146, 906053228, 75739074, 866566293, 18246503, 88722795, 901521755, 182527353, 747289676, 630870507, 549674715, 711095190, 361632717, 62756765, 76386006, 446474500, 541887138, 469572837, 739063557, 472476902, 250027042, 979334636, 409833698, 21002853, 35050304, 122390748, 892488839, 466467002, 214415364, 859351125, 763944842, 891578116, 131236841, 147352788, 110150642, 578189220, 187503236, 256651737, 592184762, 620123205, 506456988, 107192315, 23677368, 946859892, 650875146, 315527920, 66578573, 689147542, 335134960, 296988854, 435344455, 105971338, 956150408, 56311739, 425461289, 172021228, 974867886, 813517167, 965224958, 901581251, 650079096, 354618721, 426086315, 69208269, 713558590, 434350516, 264741886, 936417023, 47502154, 301937000, 102481741, 158591340, 336282764, 45044020, 566744493, 209675428, 435368608, 390076741, 865892422, 613592939, 491641197, 462928, 809656495, 35677515, 715925765, 21507283, 330269980, 992734019, 398253323, 275832632, 766350513, 682584132, 586132043, 113161090, 832431763, 19403291, 259370623, 343024961, 576602362, 963596280, 948285085, 150450888, 165093862, 661975729, 232092839, 381941956, 803495504, 348678252, 899511236, 422976098, 500999488, 566120232, 919403464, 959906247, 530888840, 189869865, 985094902, 493519488, 998097686, 204308394, 37638089, 848573261, 231812482, 265697750, 348064884, 470814214, 369191481, 57228660, 689898468, 904333906, 121068897, 89518765, 832501319, 522938431, 142929318, 172088131, 768166595, 679662301, 49644662, 486495027, 202207633, 633059341, 700876600, 941546248, 401850786, 288570043, 61294398, 518682138, 666283934, 663322989, 94529330, 578438418, 635357966, 287793115, 159553682, 700031027, 242944696, 782684085, 115800076, 953790950, 128449314, 937050816, 552257159, 980212825, 263963765, 767611824, 71264179, 304162931, 974928866, 883818570, 546658232, 206451319, 36080707, 201245687, 419192697, 988029233, 574525656, 23638665, 329440872, 141313642, 841585810, 903731625, 985112919, 380987190, 117820326, 896075204, 680397208, 733036711, 615974478, 95287610, 733721616, 258248264, 467104996, 190245977, 513350215, 227468378, 140179418, 888774230, 471478955, 463709540, 79322361, 144016204, 906817993, 336262675, 89282373, 523094687, 238261025, 26749241, 800506695, 528758485, 771015509, 543122969, 258139938, 781875356, 916496820, 489411537, 847456376, 138058756, 914911995, 782784965, 982207159, 653942178, 632874438, 70064152, 339087188, 566519575, 564250943, 848993160, 417212948, 266230869, 963804290, 982047834, 115913562, 14401313, 905095252, 717011328, 492909695, 125139954, 330356066, 282199164, 35765113, 206353897, 805575606, 397401965, 909845126, 853347574, 781618304, 844593381, 734721104, 747228631, 713324609, 270631926, 579904851, 813786094, 653892969, 187854369, 812166237, 456713349, 176935010, 607087798, 444921731, 849206269, 867027011, 694127544, 636216719, 856467730, 695228452, 844338262, 455690392, 228133114, 467791485, 815893519, 781436989, 782240613, 995519538, 601590860, 742144989, 730778169, 104355421, 67848071, 279578142, 390858395, 237579215, 937492749, 952776280, 631896088, 102152557, 960439290, 419906133, 775649585, 77808050, 477153109, 58517877, 451053263, 184447040, 813065418, 914805482, 252628098, 755806184, 64805517, 593045209, 310952295, 248460886, 626143652, 463620972, 391249156, 212809647, 104841842, 473154146, 580729504, 411737767, 402790115, 989190884, 6800004, 992290319, 238444378, 472676426, 699287733, 490496258, 699494221, 284990433, 569156474, 249772300, 323642291, 897412985, 933352481, 988721337, 58433697, 974484561, 746265893, 358239043, 869612001, 100809527, 703925695, 520632009, 690259470, 834774082, 194550962, 690907651, 606605195, 61688002, 818260579, 156774390, 66018680, 952237018, 319588785, 289478964, 807064376, 177581529, 695359173, 815810815, 600094628, 272135807, 866879837, 618304755, 217422914, 382253247, 23628722, 898309149, 628327890, 975834806, 33624296, 197028308, 756954448, 38901951, 455860670, 800707359, 501666402, 27921373, 184811457, 867088988, 538014898, 567622445, 460684324, 70614625, 185738342, 104551572, 498123299, 318339857, 844655045, 711064218, 350899817, 145913295, 524965996, 9937613, 436656128, 246118588, 822334117, 327766791, 245883747, 522883167, 884383979, 150396894, 27471286, 227876730, 954717004, 704348396, 66256947, 429977399, 644010630, 347428152, 998033596, 324780548, 51503204, 182737682, 648132216, 990163586, 943497382, 917365553, 218757339, 874212810, 31961922, 342629552, 793048361, 861539802, 112604799, 904398355, 200426110, 97877657, 361404164, 5072924, 830838247, 238536080, 352581982, 581240007, 975747903, 7436389, 844404956, 170824782, 441443892, 669871386, 3831792, 162882932, 514397655, 734904424, 143341839, 387468191, 129784472, 502438505, 987221587, 101518171, 327588282, 428335528, 117299809, 29993746, 231967086, 487131811, 352715862, 299610475, 743122216, 292709480, 773574938, 408160565, 81087708, 94450764, 979306820, 745882201, 995563704, 360487512, 951517816, 893522711, 329182049, 436127477, 911252845, 154539275, 675465576, 935026787, 922260832, 574608555, 668887102, 498994699, 521953341, 521603851, 76785449, 680473816, 723809280, 952387601, 235218666, 843261076, 517865188, 793692722, 177530029, 426872932, 583900630, 712857242, 64572431, 709868098, 668759893, 500938566, 633093450, 475033908, 685686195, 635755384, 707913360, 168801551, 872760272, 338421398, 958363781, 188588776, 554392124, 489262282, 208471348, 458437616, 309416259, 354361807, 439424117, 235120819, 266656139, 616440633, 185508691, 183383236, 656075230, 576368752, 954931064, 319995905, 628593827, 262213377, 684756242, 196902852, 751580722, 335435743, 452360598, 232846078, 503136118, 861075714, 747005347, 979134148, 279934785, 815107081, 482286462, 883428112, 915210951, 929517853, 806182135, 717090169, 573500810, 376222189, 158865909, 617911029, 741853997, 629079006, 809946768, 52137300, 976753412, 700918362, 381499938, 844827039, 386743341, 233451832, 205456051, 279232048, 684390745, 12519873, 827886608, 607412622, 183655608, 290002504, 962372666, 793928894, 383275822, 80903145, 102814432, 62875396, 842147986, 809942341, 515055197, 830377439, 933650505, 498457178, 782816731, 280949222, 458158617, 367018298, 700813003, 245479222, 281715672, 916019818, 326040864, 788121553, 503757235, 694971265, 553066121, 12460460, 912819270, 973362359, 662010775, 891025790, 785448736, 423082485, 72920013, 74867184, 782807346, 134433503, 796343010, 167105248, 971798657, 760811979, 639892429, 804068012, 752509287, 460889612, 656569741, 499563123, 392159393, 703934462, 132892443, 450456034, 815391892, 573330636, 247786324, 770572122, 179623612, 432819077, 308277223, 667111677, 669648358, 777026082, 482234013, 122415089, 556823203, 273437843, 785937384, 851585325, 697058440, 50237507, 366775167, 484063051, 325256153, 846645510, 995634805, 967232305, 702440942, 901773762, 3075844, 715525351, 192924878, 241988284, 373241186, 532180326, 414435191, 349509886, 272098714, 508142841, 248219834, 476284106, 575294477, 452146501, 658731194, 227590194, 57630611, 227190833, 408475268, 40133866, 738245725, 38022447, 411081748, 213485438, 707984155, 261243947, 42348829, 327212931, 474702679, 433898385, 255471881, 334750301, 820186088, 741326648, 773455556, 777903595, 355416872, 871992100, 54764425, 855020380, 63318178, 4087999, 589893419, 269082193, 535852320, 102798764, 506043429, 872037551, 889836293, 157170166, 834039886, 320507915, 293735449, 129601835, 716978029, 764591643, 232680425, 34766759, 33449714, 48275040, 852648021, 489818527, 617863557, 826730829, 728107865, 179834709, 531672432, 520895925, 713806105, 542309476, 655462854, 457110882, 658096300, 238062494, 894620622, 461439521, 270882783, 55830443, 559085865, 607976614, 46333872, 422592598, 888033537, 94430658, 615425792, 45442581, 185332734, 788858535, 177416873, 262082790, 239183566, 653129759, 390351672, 319991896, 7316796, 524894778, 376331572, 699330422, 684527187, 166056494, 860244022, 571014831, 282679118, 248807488, 991690884, 892272350, 455699717, 596820542, 731399426, 411003443, 834958961, 194249138, 706923914, 169063867, 106139097, 431572658, 505852072, 981644416, 988802696, 211089144, 290380755, 734897666, 750191527, 990387307, 659957074, 429966952, 886943784, 991447435, 781740540, 781749025, 410144556, 713249315, 526234953, 233048794, 225535916, 53982228, 329416247, 405768560, 418659992, 754138779, 579977486, 957411770, 2146865, 976578740, 147723123, 954334553, 147761157, 907813124, 73922143, 275492213, 16017612, 584615523, 112339472, 545783411, 311603734, 786210194, 832252489, 644196662, 688220729, 121025095, 143484176, 24620994, 99943861, 199485938, 237181059, 793860708, 607599082, 476733635, 790817292, 237691803, 291719531, 286664139, 801874463, 337483773, 555048233, 687164375, 278940407, 492465754, 958406561, 651998546, 736437081, 950807322, 18337182, 260882492, 214730896, 460029647, 131829650, 696714025, 614654930, 635339456, 505585437, 880025304, 500416852, 967699239, 683212316, 818373604, 447382347, 216968629, 718691255, 494563135, 770723521, 259950152, 885889832, 575374920, 112380237, 914211757, 53326925, 163807341, 777548228, 467807835, 895420686, 431427132, 458908042, 375511790, 367333489, 512059890, 771684194, 365464808, 414649369, 65953689, 45599596, 285436754, 498816946, 296485561, 995239011, 943212259, 824260676, 86207988, 239360749, 253873700, 430689496, 330194677, 755063345, 566779866, 986229301, 515102453, 824598052, 707916835, 939649958, 639838047, 794389826, 979998752, 500790176, 707069261, 852439917, 14922855, 795690598, 373070585, 544298212, 296356921, 190583592, 630434458, 419111452, 710078235, 410052769, 365348675, 664302425, 897054244, 127115820, 993430137, 119456891, 373531938, 186202389, 973804297, 259110884, 965782088, 453773924, 553411343, 329601978, 970051905, 971544578, 384700555, 736535369, 930478897, 857959718, 242353399, 502632282, 771728414, 551559016, 245367628, 866035449, 953266824, 594437003, 191032524, 744513204, 722743708, 98865500, 478771785, 578837701, 122846470, 183025351, 489774585, 393481692, 652817154, 203122020, 212638695, 906456898, 290862810, 78572502, 82692779, 197577064, 695774634, 518490714, 180444263, 205063864, 167210094, 387896495, 114047031, 67116558, 140993492, 309522107, 55477644, 525190568, 999813195, 106121291, 636251834, 864586891, 834262355, 802616860, 250403548, 595585098, 655829733, 654720228, 137595872, 368668079, 899413665, 306339958, 950978406, 637078907, 644288433, 355918890, 172926099, 311879582, 192448676, 844657036, 483742629, 95511055, 315403806, 845994186, 602024912, 475024554, 586582370, 421069174, 257277457, 821400329, 333848329, 308859713, 586289059, 914823460, 691139023, 460280871, 51907852, 942111921, 74025715, 146404027, 977175215, 419680782, 559881501, 792566106, 370062847, 234927790, 234108671, 416333763, 111896330, 844510380, 750332063, 750585977, 902383057, 30061102, 855151115, 553632244, 129822805, 296859239, 140130842, 596488606, 115749376, 970860332, 871444885, 517448266, 180253634, 956194545, 2775959, 57077513, 461639587, 999715927, 891093350, 260179595, 723281190, 165065518, 483047395, 756348075, 223898159, 138768875, 323051424, 134080041, 803205774, 730513900, 379476529, 197420831, 544799910, 452200968, 739659114, 386486442, 226846036, 559189421, 45576202, 20238102, 489334052, 40519882, 816198963, 528499412, 321361592, 346495622, 778852757, 784219404, 650470090, 143518359, 806326807, 155676215, 234968773, 530547214, 571266229, 580868690, 174480279, 97543020, 944207176, 971202172, 721070023, 539711599, 726461901, 943589793, 91853167, 440876918, 412282535, 292541583, 319499215, 937483205, 377870188, 281653404, 827654316, 827455607, 416074320, 374025865, 77630648, 289789868, 502277848, 572281850, 589969843, 708406502, 286833350, 971999155, 831511666, 994987278, 113288679, 350367344, 32885854, 356486095, 456235912, 332629966, 882277926, 885820797, 582533718, 234399130, 957210204, 165343820, 373740289, 740805684, 429472249, 989281096, 550752711, 795570271, 398322025, 347971691, 654817019, 910570201, 829343492, 352699284, 94712971, 410145581, 437789849, 120122771, 215691437, 713675187, 640086032, 905167175, 159886684, 787774201, 986671164, 442826650, 313529928, 935452198, 357339048, 153655696, 754028817, 540602631, 2514838, 752049936, 828786379, 747808867, 232825209, 343605490, 467676304, 775558064, 644844089, 713337540, 299792089, 339959953, 381593321, 221374524, 634560445, 819420011, 600303756, 158050687, 552237828, 793798495, 562655682, 63711119, 447539903, 700451696, 764949544, 19855188, 747064665, 881562562, 744502551, 683993111, 740966443, 284853284, 20559722, 236676520, 419991817, 428737126, 357578235, 177199067, 485890282, 544555701, 670126394, 498394376, 120065002, 756425497, 708469497, 146034727, 359825475, 223185592, 604741229, 784437523, 898646443, 766222117, 360558824, 669415077, 139286677, 5854091, 278273496, 794630634, 242285340, 490563535, 780708559, 506243604, 402800353, 357233311, 752272727, 144311061, 905226078, 676902930, 438286205, 998766459, 137577371, 959421812, 520341108, 77538361, 785851267, 880793947, 416051361, 414537096, 360979397, 62537711, 893607993, 68815330, 82303014, 473083171, 187192785, 831157316, 489459565, 737475505, 576102283, 832557512, 778701590, 604058410, 822163042, 482542779, 954643378, 748014520, 219540749, 263159153, 225005102, 770672875, 582862583, 76121527, 838451342, 438350099, 952591364, 354644263, 686269562, 631307882, 523567598, 160033227, 446317502, 472189923, 52389092, 341108890, 387088222, 107064544, 919956406, 678231171, 732278264, 242450226, 99116401, 621442245, 988705298, 705774304, 306004365, 64484671, 626353193, 911470324, 954861014, 304193957, 493914702, 973184163, 52691742, 184377257, 753695743, 286063924, 98921438, 691078922, 770193005, 438637025, 147571238, 132258009, 837498352, 471197506, 280182600, 754288716, 684031592, 289561805, 836208724, 706938806, 681398260, 606004817, 316518775, 921568585, 20131990, 963639395, 646036787, 468894425, 218399064, 521397594, 270136166, 456348669, 392546155, 233990032, 200654355, 30550915, 358720470, 366334576, 992261815, 856654460, 315332477, 689547616, 668301851, 840280230, 101121727, 348688299, 654049812, 166512341, 161909636, 369735005, 742918571, 460719686, 259914507, 194621524, 20442548, 256980583, 457838881, 557678272, 806199114, 808804554, 123744928, 354071525, 9245118, 862358000, 568107061, 639148481, 704848045, 864192849, 968791558, 374767465, 617337025, 332928450, 626035131, 671385807, 549258776, 542742929, 667194889, 789662829, 64243917, 272034004, 715305772, 342236553, 392592838, 841493384, 85160227, 842193138, 272236060, 170179268, 568860268, 403532344, 126253718, 871041781, 646418147, 696825946, 729264780, 438643484, 401161961, 330648734, 248216343, 416662316, 772344082, 983104643, 600224112, 26262033, 940754733, 374574730, 423607745, 901976894, 754183149, 957989820, 714709223, 389526567, 230418658, 692990544, 33936554, 117726084, 961198902, 486116219, 345532392, 345181469, 522158705, 666401972, 129130141, 228000917, 582819334, 207772070, 40831080, 243605472, 139942988, 125492012, 866951458, 707890980, 124928423, 488732076, 219007245, 335044936, 89136257, 474512717, 614726418, 573629007, 575803376, 293950301, 432137077, 341871597, 522093018, 641178194, 30229400, 266767552, 993301563, 625441873, 398687764, 733665453, 694032642, 476514327, 716745709, 279186695, 180840299, 77279632, 601003876, 142483063, 553188950, 308036207, 77974814, 923906956, 235129000, 786896834, 245002063, 167625193, 844213806, 954205635, 390957346, 300401305, 452640564, 773895467, 319508124, 76059796, 609254899, 563636075, 518449442, 101244618, 5030548, 723372530, 890572638, 407993955, 593139027, 613646666, 375271476, 404310516, 566742538, 775485298, 247379611, 997628211, 475532494, 961082785, 226565441, 436887733, 692845193, 649384165, 192792870, 656421471, 428343444, 383983293, 115894766, 733911555, 788110991, 594101776, 513120725, 757103159, 908946939, 900578872, 814891239, 734935059, 307399459, 845061388, 865477264, 120375541, 3612176, 269969451, 107514926, 227341573, 215404524, 207954921, 515854417, 529495773, 411070814, 602342776, 397285031, 951414494, 177087835, 750617632, 870605846, 603534876, 712191517, 847714645, 920227309, 706162014, 19143713, 723352614, 789681529, 437532825, 937393329, 653646445, 927781965, 336293180, 675408717, 665777767, 401951077, 943407761, 308706419, 340540607, 119172524, 729488897, 204044956, 350778106, 51616753, 573298500, 923739197, 219101490, 958265825, 474027791, 965462029, 912109515, 610731472, 792531093, 245329698, 637337803, 905224529, 710268853, 778954451, 877212627, 73673891, 309630178, 727027707, 377002318, 514275159, 930953452, 354429089, 665780225, 474473389, 768366661, 465723800, 337187642, 618962034, 885102169, 705758996, 648298496, 551508821, 874331419, 887319277, 219650240, 831563940, 65550396, 342677442, 753563326, 108114717, 30656478, 521903632, 32440225, 482118465, 264242193, 532071401, 449650226, 993520100, 972571249, 547152578, 743753828, 819183891, 824705194, 996951482, 89691488, 887880454, 698534927, 257387597, 570888620, 847107843, 989441131, 339960724, 457319761, 291798676, 596033, 827671452, 118538120, 503585220, 42092555, 69232690, 350212695, 159510087, 578246643, 938361796, 315963189, 305577834, 963880913, 187531663, 939534391, 994937532, 131168832, 709997621, 815331809, 257650817, 139733328, 984493425, 824875361, 114105163, 486160790, 607154117, 438214575, 728251795, 62528814, 861046843, 269890831, 908858672, 949423023, 587925326, 937640634, 168007938, 503557021, 753159547, 22236522, 10651204, 23053317, 546302543, 338883996, 753816659, 719371874, 670119839, 45270824, 870077416, 491518736, 374570843, 413159810, 559978263, 40185381, 980020684, 722013638, 222221614, 474219229, 962731403, 384796180, 424543438, 816169304, 925213057, 656529931, 143789688, 661261947, 464719113, 555385331, 828268031, 977083859, 663070514, 670356002, 219650394, 667358619, 239103014, 200083163, 740631825, 874233375, 597670211, 1484368, 470611452, 403067084, 427359820, 352624631, 397640942, 228586486, 412739480, 563471874, 193407494, 982839831, 518681898, 847945340, 540746084, 845117315, 445512572, 518776491, 391158407, 342053432, 703340096, 830287137, 919414686, 323557615, 316842487, 836132975, 246597249, 967705048, 484832645, 82749633, 958039312, 137623826, 911477757, 347784415, 623974496, 570465651, 327379191, 744593653, 211473804, 581237974, 548664032, 812471324, 482309189, 840783833, 16248350, 645909933, 293266991, 32976294, 430067426, 328062331, 145082568, 835371415, 281563627, 292340086, 440262136, 125863171, 430706342, 185503452, 208435864, 634479197, 268476991, 637275472, 338734951, 648918682, 783570410, 702334342, 13113634, 25899183, 704364941, 213992624, 230892243, 99939418, 427279692, 133370458, 702801633, 348134293, 877606186, 462447511, 805679547, 623035829, 238995894, 892227645, 314721626, 703623443, 640711499, 480250151, 917002974, 97473348, 471588829, 511053842, 36717728, 921005758, 566502505, 537269731, 690541246, 813650240, 598637549, 727947695, 788521638, 779652613, 281627413, 506086324, 247243296, 642250118, 373586879, 312509244, 346081236, 467476955, 171570271, 58907716, 938801952, 955658440, 598871547, 970302329, 298498440, 380094222, 970413377, 744472015, 107236022, 410181798, 184013065, 230838727, 232921282, 405516521, 526930145, 103862347, 594510283, 484091784, 660621499, 448013730, 961104676, 945968923, 85693537, 53560914, 929088625, 586062244, 503732944, 668160603, 142996886, 992145379, 377232596, 944204001, 486782802, 755958602, 457402829, 521402869, 116459916, 226397024, 27479571, 60597503, 885284648, 875042621, 87693502, 23605098, 861159092, 949674555, 551510746, 97310154, 109352038, 49379687, 857337704, 71082396, 679820227, 861124714, 835100405, 864503279, 212460075, 836866917, 285805184, 416148180, 818446192, 854849739, 366467324, 998359603, 717443815, 644372403, 930930409, 26640279, 269671341, 605118255, 488613749, 487250206, 356980942, 797804843, 836048364, 130399922, 885670693, 217345657, 202714246, 609477078, 737505181, 602384114, 676503364, 178091877, 366362534, 288275136, 468276690, 242047543, 624206963, 459420912, 348400353, 305554844, 433300059, 78715941, 427271968, 107206094, 604849598, 112815774, 402842627, 42498263, 376807386, 342292618, 297982898, 363412922, 210797413, 575664014, 481205821, 890474588, 869079920, 34394892, 156311857, 754978699, 623397642, 40379930, 769181979, 688411592, 807314317, 324034279, 539403029, 91476546, 671868783, 812623883, 935049361, 813928883, 887391997, 234522969, 624047843, 435514372, 406074369, 234739682, 46081724, 642827639, 723308434, 134219791, 463949204, 388946446, 450384238, 816304079, 628068196, 672767074, 97630155, 348089599, 49477069, 245220806, 94285451, 846806430, 438467734, 885183875, 24926022, 249107777, 785016464, 866550018, 808849120, 399117631, 361096191, 122160005, 308833481, 866244083, 537790715, 79237790, 669519194, 263107693, 246671815, 851682144, 468981153, 532991332, 903237514, 857147714, 650947830, 234535758, 850604938, 626972021, 733955658, 776198589, 488722482, 899266815, 862556396, 197849390, 621382237, 7034278, 527629037, 756910351, 316250734, 596905342, 813731254, 178143362, 304860711, 741184828, 470202952, 639780063, 757642270, 829060565, 588919026, 937979144, 118461618, 744550304, 698879385, 204952325, 670003054, 145286786, 490239552, 175228796, 604486508, 897078102, 656752795, 419648575, 643226939, 993793604, 793420767, 646294710, 976388177, 793695088, 5781587, 493671444, 438285451, 668627941, 126066307, 457433526, 603542657, 398663381, 254823738, 660262543, 841341906, 500634212, 424636793, 629949565, 300565265, 576676570, 931045658, 562317392, 850036750, 48935291, 651860158, 204353609, 218291327, 663976068, 101882759, 859800284, 591816, 811205101, 908843949, 444152345, 524202218, 361020968, 503088289, 663874138, 267094829, 798983632, 509836933, 282698247, 930617413, 648915981, 475270669, 520591647, 673416276, 739498815, 195005276, 701563091, 637438198, 980250945, 794584185, 906138439, 627361732, 961321807, 319960863, 615972390, 56631957, 724546250, 56996258, 897266740, 656402463, 941922612, 707695890, 946141029, 248207857, 214303966, 389562304, 722309623, 154582553, 140078919, 727328510, 605535990, 569054277, 891722252, 139520973, 271321810, 44920053, 371505823, 411670339, 173894629, 64024164, 891858314, 345602356, 346271882, 252890469, 116309681, 574794099, 294565966, 798784647, 876908811, 415797955, 469529982, 690119265, 187635958, 436721263, 345517082, 725365053, 31064838, 440761468, 228738496, 186374411, 895424367, 562823851, 752818177, 587081802, 794404197, 715745852, 74124747, 223633224, 369257882, 450582956, 61397950, 491676108, 246513455, 755212843, 572023640, 919563196, 854236375, 820351996, 937857280, 454920848, 38225285, 683859296, 294166941, 242452426, 985745101, 32091656, 869000403, 742209562, 224686534, 169255819, 64879969, 358218260, 953493444, 533221169, 214192945, 463408622, 891878624, 366863857, 529783740, 680758772, 946978853, 645037780, 422593746, 101261905, 647493476, 22906291, 346888326, 900135987, 120548267, 974158497, 613782454, 807840033, 304093802, 134562430, 52017369, 64850583, 435927445, 437467008, 286369396, 249154058, 296531436, 870582039, 400289881, 339651603, 811385503, 598940194, 331938209, 51526303, 741279605, 694800656, 86903949, 91193347, 993744568, 738551405, 807066062, 871896921, 662390841, 243555192, 310651567, 242266081, 759550174, 322920204, 168316629, 800922897, 440085941, 241349006, 947449962, 929574448, 5323195, 308860048, 251084237, 860537455, 558300586, 943776631, 902378541, 26763099, 697670072, 187000724, 630846296, 466182543, 843734093, 659456140, 826264315, 717647252, 739293072, 560100104, 985470399, 403946656, 859146130, 68054051, 263865615, 74582953, 354137901, 517236520, 327424998, 945364442, 110137059, 92194004, 228343488, 546194304, 912394778, 802097415, 195787222, 829225668, 748290559, 162578242, 137177259, 595018425, 65056280, 782115002, 837492137, 457990504, 280709650, 74466362, 224420145, 356579631, 79190831, 339475395, 789339923, 655206125, 843023266, 782321601, 963587644, 643370345, 851871898, 169633318, 100864648, 528885836, 874820137, 412724038, 363856929, 50660189, 358991146, 661377802, 931117886, 227678433, 215809941, 878153700, 528025056, 662243473, 843761203, 956546985, 293170864, 652452691, 858510280, 631646032, 85428297, 819077851, 246189723, 7399100, 301169646, 518891807, 579148651, 181826973, 704616673, 161986951, 614531094, 955626874, 386952583, 28756591, 938656297, 109232663, 762010860, 777258952, 568479434, 293352689, 126331296, 627240348, 755740168, 396738574, 538697445, 792519931, 231837982, 678633212, 102364019, 350017594, 460564258, 632737815, 777150321, 970033296, 981459719, 355436486, 229556338, 179058431, 169150097, 942097221, 457132930, 840406638, 97135077, 368564290, 748400437, 779312108, 960168231, 679452515, 54732069, 112070900, 551315545, 254136123, 510321012, 229884954, 157466021, 715793553, 873168015, 338307635, 691665811, 690358311, 250215744, 854659325, 113278304, 454892905, 29819904, 413855161, 592934874, 761078463, 26054544, 464284560, 141927296, 856068422, 609265978, 674807107, 609158451, 458503642, 626331565, 551394505, 303181848, 993810235, 488365636, 798466426, 610710413, 722720227, 317816086, 89685172, 526351115, 845067599, 47500690, 585602167, 894000689, 162647202, 474734667, 255373891, 798135133, 530977658, 618108944, 777701102, 993378048, 432532924, 486946861, 447583692, 421239440, 69170860, 313650676, 380535510, 406687244, 955759417, 246873510, 85163118, 28576760, 955717831, 973848943, 670216061, 449988200, 862801841, 445269791, 28216248, 459545967, 178320433, 778994280, 490380617, 603770653, 479828493, 691756906, 226977351, 604345796, 787027050, 460241954, 139990842, 891460525, 986679411, 905026035, 49712044, 789074218, 721360247, 65191073, 562064852, 716859120, 927675625, 210105212, 751606927, 192292876, 996017138, 649760464, 832146686, 358917416, 186632962, 864386921, 693144375, 613199413, 151741253, 803201680, 544672686, 860562075, 232128814, 867952358, 682617623, 452745490, 657702170, 538867257, 720218412, 947259542, 346892018, 987123185, 593885560, 842226805, 354115378, 525275879, 969876543, 205659993, 801463358, 164320711, 824449795, 245476189, 819407763, 251325179, 863273881, 563510550, 224766460, 490900494, 986882027, 786342472, 182121582, 340762571, 476472005, 713067963, 790337447, 90762366, 453105092, 205339823, 97703974, 512240215, 39442589, 733014501, 774066814, 139388337, 611329443, 539098574, 370965160, 883111109, 597504449, 3305163, 369909351, 906030966, 91327695, 852205140, 147625689, 538980068, 313808084, 648834032, 883719967, 677834186, 432377149, 188369690, 497541999, 563668136, 363079630, 880668266, 351630582, 829503636, 245076465, 832075154, 248658761, 284921819, 770268928, 383481902, 764766391, 427674804, 494865755, 174408634, 559033572, 947258820, 930354262, 182845367, 153344280, 477626388, 184999521, 824239136, 912446567, 883001973, 281593493, 198081708, 866616580, 216676271, 96522062, 684498859, 836900505, 974373653, 677077526, 218131253, 66700175, 296005816, 598932162, 813368390, 28219993, 662654629, 731882051, 644840001, 424549633, 654104559, 297555756, 749951480, 761431597, 838442576, 196985464, 720593595, 291054815, 9676449, 588009682, 207791689, 845634523, 108310544, 500241535, 677930179, 503212245, 755390518, 568136437, 493894394, 882605815, 403560195, 902374046, 889589332, 8003335, 222899256, 244355075, 559442517, 809729961, 178123535, 176884786, 195684593, 64395106, 685945223, 927724544, 515740489, 719551819, 70141848, 289880842, 423914124, 619790041, 504515033, 725552279, 414482609, 589003412, 924384031, 373214261, 962051628, 278654527, 801951534, 47184616, 887997779, 406866268, 381729653, 281444120, 481771167, 519944430, 466605640, 575964906, 665684128, 73432209, 276183495, 316439845, 141823714, 582050554, 475908057, 128285741, 780141569, 116810226, 925257559, 762693730, 141237113, 111092582, 788897421, 747985955, 533889598, 725168149, 165302189, 645598891, 92403604, 616680513, 932991418, 310519903, 637471029, 344279085, 677953636, 488660278, 98493435, 268542024, 916396950, 936350208, 58589824, 56004178, 819335475, 496990783, 234713856, 477040223, 797063959, 552069408, 291066000, 208059024, 680809150, 895850533, 38752004, 497653473, 407981310, 868868429, 949651329, 941703103, 863580618, 750988764, 908065942, 112889221, 565819309, 267946881, 796050728, 529775849, 471764235, 703137357, 789665895, 307759388, 127383016, 636513530, 694586885, 273496412, 244805842, 954186479, 543113226, 343001531, 171989887, 749639299, 681972353, 824015482, 527734940, 442026117, 278456576, 9572137, 540201522, 614404400, 594180340, 31426104, 210576469, 459297922, 14216729, 274536547, 484465597, 356759967, 610847209, 967389735, 315249434, 592516718, 276315745, 235410307, 369944681, 754988674, 223766541, 902680673, 418617767, 20003469, 925687561, 415482919, 819219529, 823587167, 12997758, 446737634, 722452881, 274401011, 732288266, 57667793, 768532431, 808790830, 999086416, 961712137, 489433053, 56665404, 221305979, 498285696, 612361240, 503702881, 229561271, 607046554, 326826716, 269853933, 547986116, 909369544, 357894107, 630438547, 930737522, 497748431, 323670112, 826844235, 723987390, 196431410, 792628023, 307365627, 278940374, 757384303, 671978819, 838359527, 536092968, 765887901, 145364276, 219438581, 97248482, 955588291, 724668241, 984338358, 212123481, 62682971, 706111405, 242737493, 383296851, 580519606, 368547562, 650792707, 93510382, 201443826, 316794838, 338664699, 21546567, 534709368, 368310795, 695780744, 340993049, 315201806, 52193914, 8347198, 990497673, 979514979, 722481094, 765191724, 391321859, 715827623, 622856639, 75192984, 159246644, 89083523, 561307140, 962064166, 632251255, 570516417, 382613516, 738934870, 683156939, 928012691, 896510021, 231269208, 605986708, 629899313, 49403443, 770897449, 665868716, 434750378, 638243543, 226612633, 793852167, 269907543, 188205862, 448645790, 285902416, 688789825, 701964516, 945428120, 355143461, 135456934, 986503770, 144854396, 517600999, 639411260, 990787321, 340009534, 960366986, 341054833, 111283593, 361900238, 138976175, 700605552, 241115721, 445021183, 943364927, 222024350, 296693700, 711675593, 87867175, 684238024, 326303357, 988071256, 192988306, 590172767, 575970443, 468686688, 267869755, 691362673, 674694706, 81620283, 219928009, 971501026, 40217459, 275128415, 9270797, 721737418, 940034963, 983907741, 679709395, 449712505, 632556383, 966391033, 519585862, 636170439, 783473588, 980844837, 732821565, 313077139, 710431897, 856627001, 906354028, 156839531, 305542883, 685806509, 724881187, 429741818, 14651192, 308610693, 754489694, 224787912, 581402462, 164052920, 895457641, 264153482, 626133751, 413643933, 743985216, 538066362, 361436188, 687791147, 543470441, 532601553, 827117384, 166819983, 11012858, 216147474, 17062921, 294905976, 658109697, 767972653, 678338479, 301372892, 580665087, 544270654, 401808234, 997233467, 459856807, 158266978, 675013934, 932322104, 548428672, 773948465, 894894882, 708531586, 31040345, 642608298, 34995373, 390067449, 63053419, 197616018, 331926630, 488042564, 776058523, 80621631, 341641762, 494186001, 857183010, 952343014, 611165752, 2245705, 359940898, 478810360, 79695835, 154420178, 568720163, 677157222, 38186918, 818490078, 939863454, 830255721, 527036550, 959579248, 587023419, 760762650, 753786195, 699568742, 578949913, 430732252, 669536584, 38774149, 857078894, 435973253, 929492522, 964042399, 781556235, 12141830, 237655646, 558402416, 251559634, 804335515, 249815776, 921601958, 273258097, 768003783, 17902772, 745436793, 53947366, 58511241, 105285184, 763315224, 416704268, 635256712, 518272459, 435761626, 522729645, 950032642, 547871406, 596306830, 427059028, 423281887, 293055997, 594124927, 885722869, 310621687, 962039575, 14934386, 993806932, 745788486, 796112228, 522184082, 396085926, 657189969, 800265182, 679857689, 540473584, 144232148, 205515528, 514381106, 88845681, 36971793, 726714504, 548064493, 943151987, 103382502, 258054878, 880373590, 223481990, 302551120, 918594265, 590460238, 400565763, 328989470, 655445081, 374563406, 33506136, 715202754, 17409568, 586273272, 628533328, 975529394, 174377640, 295514237, 938848860, 483188112, 114585872, 855272170, 800556477, 336795829, 733210022, 703976324, 537645182, 248330469, 901388093, 525102670, 864506262, 221576389, 927037192, 887514886, 97394412, 647689541, 67622768, 236530759, 833873787, 485241875, 563970420, 971706942, 963706445, 825134603, 6487151, 345206613, 864988302, 357295516, 48957279, 716437776, 316030925, 244182015, 692521764, 25289219, 704178683, 581544219, 358801486, 107814293, 743309851, 899474619, 160053376, 663143061, 888784802, 639881130, 923248083, 910890751, 367285318, 858846392, 896514850, 167708596, 618930404, 81001012, 686649980, 308989278, 447752909, 130596905, 894515534, 827482046, 28143031, 960798481, 220786320, 77361393, 991851681, 766215053, 215309010, 935045570, 671039253, 199975213, 60094121, 5202475, 843955545, 817757831, 650747551, 200787934, 313036089, 527148970, 929632140, 244574773, 40075231, 300307875, 241730303, 57128942, 185777397, 677799056, 192687659, 676023050, 149103328, 412733230, 222263995, 362437625, 922661089, 262747865, 170505482, 209663656, 422107067, 82091282, 541461963, 87157711, 67145244, 100006766, 483113324, 176097806, 904205330, 215712549, 256411401, 612010679, 688649214, 50272754, 664552874, 300678321, 146885681, 182515796, 338623032, 837662249, 274802416, 615580814, 546174286, 368208150, 652014594, 911774961, 992061850, 552988649, 88926644, 591000403, 724029540, 16704043, 114396556, 275222342, 88994804, 165512660, 147423646, 995888289, 570391300, 956228978, 114221063, 958145755, 962209245, 229457347, 208920063, 541287374, 947179785, 67203556, 149211202, 455327550, 406737057, 169041079, 277050285, 302673321, 174017503, 475465990, 865458525, 996149427, 242661858, 165944179, 504598716, 567824141, 883628029, 149158677, 534813460, 818347156, 400940976, 312182675, 173019178, 545384899, 9224880, 905495390, 261798435, 447147218, 451571358, 220796466, 485323877, 220008892, 836968487, 229131951, 760982603, 688938009, 293966313, 654902668, 34122064, 925075858, 967915095, 440496053, 781692308, 549520879, 318430537, 584278282, 847392696, 751899421, 473052483, 899388517, 478709601, 792442365, 593195546, 708534082, 886139784, 840577637, 816497590, 147143600, 262692628, 994511371, 464778833, 178118223, 422901639, 927161548, 836135821, 966275653, 314796385, 306026870, 747719799, 922179296, 144223893, 666111451, 384242853, 360818651, 778724052, 530334292, 969481117, 790452385, 944270936, 589568393, 923188650, 683682809, 720753069, 682249013, 30771092, 457813718, 789097827, 281425942, 95990936, 925212479, 415953530, 548112893, 135546443, 112789492, 98195008, 37189837, 859991580, 27323398, 991279720, 619366071, 686428835, 161543295, 848746634, 109799239, 564290994, 434958568, 673957661, 147940686, 521618059, 523280520, 590107280, 547916468, 904150562, 760278586, 139278273, 837097593, 436693413, 424552236, 628026840, 779618699, 846691869, 155705034, 253108518, 508611607, 429599854, 725709084, 978814595, 275169315, 965100587, 63443538, 114845902, 70429004, 731277397, 972899922, 77305442, 315882403, 669980441, 169162340, 505655336, 180540590, 278282944, 23617119, 755985404, 525050353, 531147915, 572154687, 660609195, 735755339, 801654521, 327828884, 242180128, 86806620, 626127995, 523254222, 6948488, 133956621, 289740615, 210787116, 387291434, 338350654, 210626770, 799297548, 391190137, 465492304, 748534739, 855918380, 644042829, 846445832, 998033968, 674617921, 530871375, 45803227, 974368804, 746634768, 98796195, 913574130, 299391385, 91442420, 380821420, 837939611, 38345865, 459232153, 234931589, 436824902, 205210644, 970002574, 988869171, 586026618, 235950015, 656406134, 585639525, 813193605, 321766155, 154072081, 694559189, 432372889, 754773627, 568664176, 976576801, 435350104, 442670860, 710672980, 65083290, 276891950, 350726329, 754446406, 122431415, 746737756, 484894889, 661213230, 757242805, 54270114, 983692691, 507507733, 541483342, 922930795, 877736125, 177734746, 340712113, 667434963, 36961831, 908166909, 779211597, 752637999, 306360040, 698487030, 317815227, 387528105, 884790793, 384831930, 535568963, 171774297, 18771762, 942802976, 414454284, 345440352, 763653490, 931816687, 516873092, 337346784, 291516284, 616006297, 726411519, 402123876, 415004358, 906034889, 699880751, 521233254, 574672021, 464573950, 613764248, 214676748, 129486560, 555665206, 789660807, 195914734, 499670964, 201175162, 157042394, 531207787, 564862942, 11268018, 827466919, 550443056, 954249790, 714754499, 590077878, 483474109, 615509255, 11792310, 759270292, 365405336, 652646063, 249099992, 253570584, 350607699, 326411856, 388932430, 316800413, 180499720, 735950644, 737823283, 972834709, 262737053, 76093206, 429650940, 724851739, 601724383, 577360833, 608494146, 319771678, 826404508, 529814956, 87694424, 767102729, 802985900, 555158031, 229767453, 764770361, 494351555, 205717898, 557042255, 579392130, 782508984, 988391910, 329534953, 516990530, 288512855, 289346345, 461044016, 143874971, 129135328, 940362536, 502568837, 119250575, 393109800, 200586193, 501820044, 95642026, 723024706, 332508898, 297305236, 73329783, 296472603, 231222139, 553468618, 168008673, 791677407, 245052909, 685085353, 137962744, 174862794, 842433735, 518477579, 121882621, 814651822, 487157052, 343978654, 324296246, 895713261, 292166885, 818929917, 15392186, 387901582, 927820639, 320270945, 961968735, 332262666, 210413126, 755219771, 952777514, 661364842, 221339388, 116131099, 825200751, 461014356, 108545759, 452651148, 396421123, 598114542, 340292426, 461870243, 30115866, 973102466, 891088832, 121017305, 616314904, 685453892, 292782398, 516635774, 762772982, 197356971, 435993982, 558075767, 251554811, 518304943, 807574862, 315926666, 419148023, 56638239, 400888467, 303065614, 216875420, 578395791, 334695224, 200622388, 506055781, 378276336, 338527666, 751746414, 953693382, 50442021, 783449625, 91519529, 120159651, 948833530, 138805985, 560365815, 147137791, 557268629, 969075246, 399472897, 698585162, 72380525, 727806493, 468773033, 538263980, 401268931, 676975959, 627527307, 534136573, 581942703, 105272615, 680728636, 490194050, 829042686, 986167597, 900352077, 490854803, 21427093, 785236114, 862332675, 973111893, 363297909, 102921489, 925554737, 146894779, 636127327, 880627151, 39677636, 239314679, 617533707, 864469843, 152760467, 771307264, 976653029, 989567834, 480785201, 846512766, 298834677, 135581750, 269940300, 179751231, 199192251, 176113710, 799889857, 10205414, 248380587, 427252927, 515924011, 509526697, 414756949, 185807696, 46816770, 897155060, 600180749, 512029450, 984931336, 717798089, 844621320, 3729352, 669356841, 484980858, 852540792, 249342168, 131540413, 383234298, 928901972, 421664459, 706193820, 253144005, 724904949, 2470335, 175881926, 166153887, 571433582, 897585336, 131140698, 860014683, 75802717, 716218866, 913693739, 765691888, 675819008, 242624914, 662827555, 516836242, 584629395, 829454359, 110877440, 354847394, 214227522, 558910038, 122259865, 881045079, 409917678, 793243773, 746706553, 881768757, 527878761, 565254329, 973258705, 940720397, 771768591, 966079743, 338453751, 205812495, 106441693, 83906275, 664773392, 325734215, 516486941, 917871244, 974804636, 440312853, 681732882, 517534532, 994526645, 688264595, 288921441, 837430214, 952961339, 432702526, 263516946, 203451117, 558314353, 407355188, 314628664, 418251119, 612319042, 142589390, 971534407, 614227685, 509962983, 112787127, 740128616, 18772880, 827706293, 43270452, 928463852, 442356724, 617832332, 80396156, 450959321, 468670731, 100847341, 580716694, 534497762, 489201957, 811029923, 259965098, 114783693, 191711118, 162058046, 409487770, 112326520, 966275292, 583657509, 745574827, 188761357, 163625196, 942410327, 844380357, 168740643, 314349926, 803623121, 98147542, 506272771, 305274167, 812580626, 111057808, 210840797, 426769427, 779187203, 595882698, 96940134, 441552709, 820512937, 784276631, 359000736, 169700445, 713063980, 327090460, 275795862, 259371625, 693408577, 684684810, 944612559, 94488248, 422608655, 328434642, 346129175, 59044065, 495775485, 136933292, 947963095, 41471825, 39687754, 557416847, 503917925, 167524413, 208321276, 479750822, 637255141, 223618468, 445960481, 370343274, 74302742, 923908288, 301824736, 683237747, 281584010, 883050540, 249732426, 760259995, 51255222, 419267742, 424113566, 412485308, 147281553, 996660814, 446644016, 489612849, 972527088, 643852593, 57024262, 942163239, 917836600, 422389790, 938471487, 533952839, 958643328, 14080045, 337167893, 627351775, 378064821, 704352606, 413765281, 530056280, 486220227, 264954138, 613960236, 740156266, 304279860, 294377737, 744421986, 387825769, 641627080, 859720240, 412817715, 421695887, 929267954, 419944713, 216961618, 83431237, 277668251, 704784154, 974085111, 187794981, 415783156, 954918584, 483300380, 847147343, 994169495, 976188468, 57263674, 324418480, 736314117, 240065489, 73168940, 592041471, 994987114, 164891536, 272411480, 800843233, 273807303, 377272076, 932112236, 632044734, 753850039, 62237876, 115477546, 911292529, 322794881, 296074749, 637001579, 682240518, 313087990, 816586817, 111239803, 528811232, 682189388, 818819407, 639902002, 904204823, 712288597, 388559764, 374803375, 729617209, 68603334, 504559616, 117257740, 745833658, 622175099, 981006399, 879865197, 916584897, 317426954, 446457822, 882858245, 725981868, 906019363, 302817183, 737049275, 755618774, 862210821, 289355423, 360593144, 402550564, 572452183, 891906993, 436190241, 265883991, 554917256, 536071083, 360584781, 552464786, 135442062, 339688433, 76330665, 672441393, 827641549, 224972222, 874313007, 544521914, 764805401, 477533022, 510501654, 990805095, 493150205, 574119591, 580060383, 876939672, 191907862, 330986057, 447164679, 708562467, 5867998, 876175777, 842394329, 23778797, 38965967, 673651693, 133350210, 394403515, 338023742, 463452527, 912520849, 57288537, 792966973, 879253690, 241541104, 17978743, 758488272, 50940689, 998540673, 79563660, 980251567, 189669858, 136765887, 404523600, 187149802, 871963681, 736498073, 968761468, 398436206, 888908558, 67157973, 342437300, 539156478, 32654563, 693747589, 677507921, 672424264, 551267378, 785364283, 905085600, 819846452, 496640037, 634926401, 934579317, 294223211, 637447639, 349799009, 493009157, 620381823, 843702858, 154300685, 360647417, 713908882, 379557681, 191254729, 87731133, 800747842, 6679968, 775788996, 653619376, 446495327, 816454065, 60656920, 183973964, 7979391, 287510211, 453085689, 73239066, 790385026, 548619047, 272295444, 480760654, 925328055, 719922610, 79363586, 854884227, 112043070, 161511194, 689449102, 547111505, 710627490, 903073517, 417910051, 648464345, 916653865, 446377476, 788719316, 829756811, 565198891, 466755622, 133785597, 979639873, 473356179, 721423630, 464018007, 539512083, 478922611, 999086288, 362486041, 387926611, 918153149, 5796605, 770405623, 778017526, 710115511, 172489996, 101481006, 928216127, 145665323, 151428851, 498014400, 292796516, 910539273, 560983109, 92083139, 509612890, 294889383, 454386593, 975263925, 228918134, 488110867, 181153525, 589454861, 859674573, 689975309, 219901187, 246210078, 220956838, 422191610, 376215468, 983086002, 546756317, 337204464, 925348255, 125902420, 730963415, 739264873, 808628812, 241144289, 669911318, 220558669, 867171476, 282963732, 595423117, 412934711, 557972266, 750035510, 446489633, 180737096, 278608958, 936633088, 896631444, 994675644, 814675754, 659351733, 235452016, 19807004, 655042108, 89415898, 69482895, 94932846, 954432673, 971634982, 214518331, 153413027, 58990090, 722495667, 875093796, 291611848, 209379077, 573543327, 988649853, 85832924, 288155134, 371238154, 334347038, 513485730, 585866472, 740090810, 145079062, 37680893, 618507666, 664183848, 996922460, 421311990, 713206292, 494095549, 34813323, 331676553, 931643249, 465556516, 708914047, 519419163, 287842720, 211173769, 259067916, 132877127, 585262456, 752409026, 493219706, 322996708, 220518718, 867437002, 450655943, 920603487, 313252537, 664692356, 577949099, 510949719, 732149750, 586404003, 885549563, 805190041, 854758915, 198719596, 547105574, 703347336, 401170552, 440614593, 160466627, 302180908, 525666474, 454269440, 822368614, 818826410, 654146592, 879368079, 232068938, 789009774, 757428572, 383872702, 210784510, 7689338, 537457366, 211754263, 715521892, 863108703, 231020805, 724609905, 930908802, 209166437, 835439151, 252523755, 692320919, 668660948, 763298537, 382875241, 359131055, 132577074, 742511275, 977615564, 734378841, 961798979, 893731998, 650435335, 653982578, 601938987, 425795122, 622412986, 197799891, 109872317, 147260283, 137974028, 616083601, 966076840, 924968810, 489102080, 41476709, 304632332, 371339029, 704204067, 238427715, 894033538, 535781796, 358122300, 664604136, 420270943, 718105792, 542642381, 989061537, 931635000, 704305295, 254754972, 727462653, 399655772, 923468438, 912291934, 4837188, 598718874, 977371910, 794625414, 882796444, 935669723, 956186125, 445197975, 319564913, 53014871, 336147888, 82899160, 443025626, 145070160, 121625871, 752663034, 433878326, 850033776, 438118958, 393941345, 919077109, 170726635, 597838429, 195390294, 352708189, 243162229, 216137516, 928467986, 399778286, 985502215, 151768436, 76874843, 315243881, 98935874, 621762811, 788879379, 823071509, 722078757, 638345391, 919638074, 660080629, 429510257, 874802241, 952054898, 744757811, 478567515, 336693762, 865187728, 30892163, 28296680, 171587997, 806380829, 696596727, 312595089, 459379398, 181187228, 287295388, 967926675, 335436848, 649930909, 519357711, 909482108, 83192698, 116224576, 535808027, 950717401, 547463169, 453275940, 744429790, 127311099, 34436549, 470487945, 650274705, 410614524, 467894956, 156062398, 391042837, 429366900, 231744524, 928960957, 7343520, 102383896, 278139523, 599651470, 439808007, 287849498, 589876587, 568068103, 805637681, 647405401, 948123766, 778967337, 222065126, 631915057, 853820273, 244516420, 759227120, 436507434, 470079161, 957118251, 4969016, 203540759, 354948578, 154594953, 31240383, 599794564, 872387051, 201084659, 422488080, 669085823, 551832901, 574425977, 890804388, 3865283, 587721859, 323288065, 345292123, 578383754, 902109424, 161167445, 842993588, 707740724, 476813120, 160164290, 763349998, 318739490, 24415413, 37551724, 395156300, 445441071, 804240749, 128008055, 761971917, 837579877, 744284295, 414017794, 771998141, 333223885, 536964819, 127844363, 136030955, 919615813, 805369368, 299438687, 555261413, 40543557, 806897994, 74892635, 142952642, 732285927, 747446124, 663669922, 225515098, 483744404, 607584744, 907216120, 767748755, 761556784, 327402779, 373288411, 510480324, 523684137, 892442821, 447792523, 972450457, 387426214, 384872016, 49072949, 960161553, 221522087, 921368455, 420223083, 419547812, 132629761, 570356495, 941252043, 983793922, 188749296, 953425507, 82655024, 878246505, 827293796, 950132654, 517138225, 223696620, 276363296, 283331543, 114380739, 101976535, 617323062, 279302442, 128826150, 408295462, 744496361, 166518911, 146737545, 854089873, 714521583, 926103323, 916080450, 939092404, 49206912, 935057892, 62528438, 205727104, 682887122, 552566059, 626060198, 604783708, 625185823, 287986312, 805007756, 141162542, 548735759, 827704115, 699650290, 170610030, 248857435, 267013517, 889102462, 707601588, 914266269, 980823702, 130951313, 111906349, 627585066, 516436118, 636762082, 92570234, 831493952, 16320237, 693284520, 968382462, 829440516, 406914538, 674928452, 236419604, 411624668, 856067016, 355414845, 752128447, 115802067, 719318848, 793716560, 869153427, 392243595, 948794190, 838057440, 252822175, 403116661, 902306756, 269094062, 198727838, 469643896, 948231971, 687167174, 619923260, 609081099, 76766684, 910269319, 885483434, 216806070, 313773328, 503146559, 816640854, 532861552, 930576567, 639358035, 396223791, 267068972, 706952880, 851754985, 789418783, 269341317, 140205575, 486757349, 793701151, 554721989, 438984014, 10216447, 446281372, 123723157, 902726085, 54530290, 211842476, 649803711, 66952214, 82673162, 306612372, 575320441, 276207684, 972085496, 736352481, 983156525, 787557981, 92777639, 961042687, 466038396, 784275035, 45975625, 949943914, 736365705, 463439409, 274845089, 89040899, 209059525, 438595770, 865888691, 586520579, 376925184, 575591468, 455484309, 744455137, 704761852, 825389732, 535422579, 199048910, 572893829, 413753698, 869667852, 6116559, 5471987, 104993154, 817479977, 457939504, 44606502, 548203710, 326763132, 99956212, 328614944, 651534940, 383073882, 368104356, 267618701, 738611137, 440975094, 142266846, 903658721, 130530158, 174299333, 520826157, 180468711, 178559585, 2658353, 41876510, 231876734, 521721897, 934165898, 513444081, 541968843, 693242100, 169745371, 102179066, 696521851, 313524355, 41935742, 701631385, 998493689, 352808208, 495950746, 704094963, 277829039, 939571470, 44908328, 578894831, 864041550, 24577032, 839088236, 772732284, 810745653, 155204776, 94024895, 761002682, 108939684, 688428306, 843184541, 290261237, 521985465, 270765198, 526918778, 69000944, 199543037, 706077419, 625263676, 469300454, 445007898, 869723906, 721388137, 855733771, 182273224, 24959699, 110938295, 964341287, 291942249, 973012277, 703632592, 717074987, 723823368, 462331888, 416383120, 748328492, 231404804, 873065933, 762664077, 967832170, 684994925, 312309101, 697862468, 319286164, 381519193, 718860804, 867211267, 654616150, 240392195, 873319705, 282768888, 808228735, 70649491, 998024280, 867161665, 674845870, 927454450, 385786343, 688639249, 575851579, 351030728, 4541559, 853626301, 255866949, 873812358, 479824210, 119674213, 603608551, 813697155, 184202798, 841964211, 292946858, 892894898, 16630489, 97694495, 691802712, 703004929, 258894087, 259434130, 765605861, 20384841, 968128064, 950575998, 864960071, 685882688, 412515519, 575944122, 290787059, 603053402, 515397910, 294360210, 717472973, 744023760, 21328014, 518353485, 394489272, 486063204, 837938254, 279010296, 93601160, 916583949, 438057099, 819891218, 793885918, 965811028, 883976095, 824676291, 609232672, 321167760, 548704125, 114017712, 664713229, 536511972, 414640831, 687228408, 750525755, 357701738, 969152496, 153780993, 88541667, 444815672, 765673963, 939023335, 763417656, 110966023, 354813427, 190389293, 986019514, 929179154, 79999466, 661672179, 273803925, 771575219, 999312286, 143131380, 621394090, 8721820, 419282, 797443538, 258501808, 335155507, 473145532, 482035287, 857215503, 160884593, 84297795, 96820923, 769020190, 456828493, 991451233, 225040743, 641287382, 862381893, 586842533, 687794214, 467356128, 357626687, 46129381, 432820217, 706521247, 447981255, 755852464, 373789663, 68003615, 230818633, 132215434, 408850494, 658477319, 721918948, 439027260, 857162340, 829222412, 43984961, 947313774, 26095678, 74533177, 368435244, 114907413, 716937977, 537420411, 958388668, 895296976, 84585302, 173594648, 745559863, 485763706, 578557224, 116625107, 610212449, 377268246, 593868473, 926383220, 246295691, 664953436, 389973466, 924842891, 638962273, 752814359, 292950629, 554982465, 472961028, 576480498, 87205770, 495897641, 391399712, 851646550, 575588055, 284659830, 159783396, 385693394, 847824955, 577624575, 423612143, 603348283, 37589497, 903680334, 922627927, 510825292, 633295969, 391563062, 651250869, 38764002, 661795106, 20165100, 778347469, 743349472, 45013276, 43687258, 805512459, 190412119, 285015394, 877464651, 822631185, 375981099, 872840089, 625355642, 834037895, 65197892, 517742638, 648806392, 285607607, 877371812, 619138354, 55800908, 553676044, 123268867, 377122068, 267186264, 457056790, 490931720, 114342983, 548934967, 382293428, 357385602, 418642561, 294334465, 52382937, 545096069, 939559089, 131801799, 545263959, 967928731, 242648829, 988574000, 342525326, 899465240, 73788900, 475164809, 153140503, 470260407, 254916926, 481869861, 895488935, 368571712, 577874643, 380940592, 20714136, 701025722, 934208817, 774701128, 73236847, 550052685, 303155156, 833128467, 644693452, 882015078, 782358043, 383046758, 287645738, 375961104, 193334393, 482703696, 367537654, 329956311, 886069908, 859653872, 25376100, 609248633, 266728884, 242759605, 131944644, 866201903, 319677310, 200419109, 787326760, 665368684, 32030909, 851699052, 357247872, 358299794, 738185910, 61596753, 568750693, 976680416, 460004871, 52278127, 594540343, 471077956, 917484792, 656794791, 452982181, 608421482, 201117580, 593370811, 830030532, 213890442, 11038564, 70049494, 628435993, 288335030, 965648242, 66049339, 853546938, 544455150, 621470114, 594966254, 605694029, 301483573, 423856933, 977275204, 289503991, 939200364, 445398810, 467705638, 624954250, 142769905, 555110697, 156373414, 54921517, 51335726, 537557994, 428021805, 919303551, 552639454, 778509703, 957910986, 296120480, 678796680, 905195905, 246769649, 916581238, 562813787, 844956446, 378230451, 411175856, 754488821, 832944167, 562526745, 525036470, 508966918, 849222570, 1849915, 727739668, 111811816, 28071383, 584053824, 366320441, 485231763, 801944594, 233727157, 585784340, 887222707, 465416160, 935598209, 723830137, 350379637, 150730361, 292709502, 957855975, 941277306, 917592704, 210991074, 597241125, 462678825, 965996337, 928080730, 533204851, 959224266, 441371604, 468984537, 120118022, 853822102, 497172923, 948596797, 823889230, 82335562, 395561897, 587940807, 557040343, 204796612, 43080445, 970057181, 497203694, 546220290, 787554702, 205860605, 560354507, 233573026, 348607864, 494599455, 862283527, 457315610, 940192814, 453563983, 5955140, 117159945, 821436242, 428874709, 810121690, 418714756, 111816822, 555391144, 611576602, 50705912, 322921652, 765090770, 710243852, 241625646, 530425577, 409012421, 887369519, 237742344, 778361253, 261239614, 904903317, 469558265, 190142295, 570420890, 421737521, 582564457, 783704429, 265401805, 567625601, 804971513, 663905970, 63939601, 998550634, 159065808, 912820587, 599667257, 92607556, 693401359, 375372419, 388985680, 343265018, 663024233, 359962433, 11208765, 617394486, 235892306, 2946842, 271960604, 648949176, 183167482, 827600027, 123521004, 524179556, 503920775, 506296889, 689937029, 766177020, 49586554, 927588688, 545745762, 754227928, 625903839, 122645065, 68581404, 873602522, 720733565, 774677183, 628299069, 541825200, 454109368, 448517666, 47646513, 362367061, 241623806, 634859318, 942772543, 714891201, 114332709, 678042325, 31571639, 759639963, 303807567, 868970888, 451386165, 941801446, 770282800, 37029400, 251734414, 974605129, 593438681, 201679725, 716030402, 922362832, 209733415, 886345803, 127763562, 1325821, 222191989, 974738292, 929400630, 242610889, 419453919, 412533186, 387259638, 246864141, 904151348, 50956967, 894319078, 588566538, 765423726, 626424779, 521949701, 852564629, 78753942, 242583367, 348192635, 258326401, 316727138, 278360379, 539409923, 5715504, 81963193, 433276008, 928552064, 228194293, 168482624, 894360473, 450082222, 974439339, 762626879, 825574204, 932210211, 601245711, 534922155, 519123137, 732901178, 78688160, 915473269, 652185631, 807596025, 276711682, 616149818, 910306342, 538133623, 137005556, 405625954, 111220861, 318675765, 575550025, 897782250, 340258313, 321278709, 242465132, 716564410, 303112827, 329546094, 875589755, 687498514, 262601236, 998058383, 113846655, 306221150, 833490833, 526294881, 457454801, 503013175, 116559314, 14840034, 683718202, 230968587, 457781576, 287922901, 270407249, 940309630, 111147472, 163419175, 263410242, 272132137, 106066375, 511614307, 482188937, 689538725, 984316571, 751032802, 389261497, 290988339, 36027478, 665733097, 356049445, 507071746, 28393107, 684073884, 582792594, 598836363, 490029854, 710007437, 912499820, 934962861, 119288623, 307257630, 753677909, 673556676, 30257755, 121694573, 130281334, 434027781, 219743549, 501009954, 751476758, 731883638, 266943631, 873578456, 157251798, 204209711, 68317877, 662110091, 507217526, 739701449, 787974083, 943897362, 425007958, 297197917, 861677445, 713097702, 42988357, 426066546, 577759805, 232667800, 848936501, 543102689, 697169837, 705205381, 311393703, 112149520, 306913932, 811393329, 140883896, 56102571, 259640932, 759072290, 213573626, 613283461, 813280763, 880690266, 664395918, 9437757, 312860425, 497042352, 417651958, 503743761, 871880422, 273657268, 849683630, 644029174, 559848921, 43845364, 739058552, 814011275, 709660786, 596189092, 68738255, 975247841, 707430611, 334893733, 371474802, 203594605, 796495907, 223094222, 269241264, 257719680, 968525084, 700149306, 383930689, 95442528, 752406413, 830221501, 845023926, 526249209, 737249765, 379543042, 778590777, 541997483, 805950102, 452343265, 422205939, 949371073, 701736867, 848511053, 17629408, 713007159, 567872254, 166211855, 135029327, 818121296, 287502092, 388849648, 615929776, 410974328, 297808061, 926570788, 887081220, 748495451, 835132250, 747266406, 285387791, 416606838, 559861423, 402478746, 435120779, 534641375, 969538243, 923033121, 593548638, 157608628, 947350678, 706494398, 496384175, 963607659, 657146370, 62450352, 628278488, 412374956, 527451644, 768168800, 282843494, 459822314, 525448471, 106122698, 206003545, 922727754, 578290401, 609926820, 406067789, 333499126, 943315234, 399447724, 994754502, 97872992, 597676998, 262825818, 721729019, 669213213, 584035442, 735658767, 466346917, 252157437, 579287834, 106106189, 812569756, 163244829, 528684170, 74176025, 97599839, 329714406, 544094296, 49496774, 865067115, 103957442, 581570118, 109750506, 709451390, 290370463, 419368039, 593777937, 707931354, 581909957, 767177368, 985359913, 885350920, 675376762, 391660552, 456089086, 227094366, 524234242, 127884838, 284304984, 646382691, 158840901, 196281916, 730229139, 634593968, 133621002, 790035234, 358516537, 990832612, 45831745, 957925524, 342143304, 112920828, 570463759, 665128362, 48973350, 646823830, 633705983, 628426022, 104619691, 934092789, 726509584, 880055576, 99538310, 747887453, 950424173, 251276236, 998669565, 225635439, 416656647, 292344434, 265460373, 407755473, 323348446, 20388220, 910349814, 286797875, 651066874, 459697349, 800930558, 36080363, 283380140, 371125672, 927135320, 427297093, 984614123, 669234883, 253045739, 178524104, 628928005, 779195896, 182865991, 78943504, 284736978, 376406380, 526681229, 998636141, 8314241, 279681011, 625222605, 244251821, 325300822, 968232969, 613896319, 506373932, 685743333, 124834113, 321674988, 439540079, 683308957, 637408101, 446581149, 615521279, 649244808, 94321378, 274718988, 697642290, 476380848, 222190143, 243041115, 571850906, 265977583, 271109503, 138237745, 363000630, 207900704, 767756767, 73966601, 977861021, 449170949, 621611548, 449498054, 89295044, 460771074, 804628650, 824941173, 621072239, 495295497, 96525512, 681669666, 128946969, 157734586, 78358288, 563941572, 479369174, 625067724, 268132843, 102764063, 852228038, 810608714, 539920594, 598686595, 963579920, 87490697, 359840011, 21511287, 291499121, 750976771, 213446014, 463867887, 692100885, 871053801, 853267818, 270788844, 556399895, 304576955, 138850807, 148285074, 896675119, 879947377, 691293699, 163309449, 950330842, 819236851, 359418876, 921237840, 307150168, 886112994, 899646646, 224477795, 745424926, 335128262, 405728369, 553938728, 769382677, 813506241, 997291654, 213883564, 468918233, 951223483, 720266473, 673716965, 722653918, 860770016, 783043857, 764488883, 706241035, 184526712, 805638031, 364171318, 611384869, 716594237, 957426529, 995757904, 75436482, 674623971, 715248540, 144413546, 505873460, 175642174, 485631789, 12106398, 426124297, 355622698, 367420133, 791972769, 24396919, 172367582, 315240841, 439903929, 483847551, 223287201, 820749319, 57179076, 15669015, 374888039, 777542341, 326212688, 835170082, 70331292, 644517030, 453259044, 111044650, 874223234, 986292802, 446014937, 666803670, 56804437, 757375450, 856031172, 158224744, 317201390, 952684302, 533873830, 394168746, 298257712, 546673603, 12517469, 308161786, 9634996, 322097294, 47058115, 714213742, 672873979, 109356815, 826259412, 773520690, 947034284, 994072058, 1296661, 916529786, 184846890, 933834209, 988753793, 794845590, 249461869, 557752906, 469704679, 892936167, 601657849, 520061031, 485667234, 95497035, 780575462, 684341798, 995762664, 186671667, 669262492, 795623196, 856102817, 349557818, 566807913, 868666336, 432732718, 897774508, 436196896, 239439365, 565250829, 756418695, 98483026, 812685073, 967281032, 485709094, 347057573, 733199907, 607857022, 777598616, 74293669, 522485133, 590673653, 767265247, 241844477, 887350460, 893011410, 43243527, 819480982, 655360170, 993644516, 274946534, 322635046, 920602623, 727674672, 231058965, 354356003, 100054654, 459964868, 445726761, 300339544, 281634268, 989146491, 282911126, 799176857, 423869564, 225014614, 675978462, 407726016, 975507771, 904270534, 292012268, 473698103, 766357544, 514578551, 684624588, 701518549, 950395808, 114800878, 463026118, 256697326, 559987387, 702332395, 46536461, 964082935, 391141918, 148377366, 164547861, 862165322, 519862589, 301355932, 912101669, 964500501, 953382869, 873045795, 515261244, 81825443, 371707741, 258018949, 25066841, 832307571, 888831968, 109305894, 929552774, 470969471, 28684853, 99724302, 957417005, 470394833, 958429233, 665847392, 310745855, 349248905, 444437304, 549783133, 248437561, 809545777, 696617742, 589755885, 281137526, 392867962, 684168317, 620596357, 101486861, 275500079, 247392225, 791059379, 393220707, 369894586, 359071323, 731144842, 129593984, 986702961, 221481848, 442642364, 28023918, 210031306, 944792282, 859418068, 916188592, 253073715, 251243188, 494968277, 79670124, 96755455, 798477019, 362256597, 880429727, 74184637, 532142454, 598454357, 31166616, 155924013, 605469235, 558540703, 488475068, 200508626, 931905570, 882694114, 333842168, 346452595, 208463016, 232184505, 733016968, 41426980, 169064128, 418711424, 993127042, 757553645, 317305392, 242004321, 135801447, 656897305, 629900591, 266461703, 777311897, 89454839, 575923650, 633027635, 950345380, 413536840, 147444682, 389298400, 539794750, 665101961, 896022753, 425433476, 141133219, 327871500, 176525377, 896391854, 996708334, 264782728, 64342997, 244406414, 690529967, 60691130, 799799189, 630409430, 469945309, 913463276, 722858750, 757017731, 755546708, 389015295, 137441446, 382627486, 99698372, 640606128, 506055804, 296983061, 937377110, 52596499, 921100155, 308507768, 147514651, 276337586, 424729198, 874907442, 521526350, 521089519, 951853129, 990844895, 112198924, 238031151, 38325918, 196472576, 455447530, 695717958, 757941066, 94916651, 850045702, 574841326, 791324632, 674356220, 806918042, 712411352, 433020232, 488951702, 562822009, 686508440, 735870277, 697066434, 808523828, 56975611, 536673711, 974226422, 553508493, 225426757, 957160474, 998989726, 128099191, 711361321, 668286655, 618275017, 384320743, 839798416, 750673974, 811682432, 987588670, 597080255, 826737403, 141176389, 234063857, 641019721, 201438095, 967839898, 592237903, 377707596, 386615904, 994268438, 522456418, 894358559, 711288554, 459750856, 787592001, 443070025, 697173402, 621331607, 716731266, 177122232, 236186309, 189979610, 545398282, 188304224, 879647433, 31772215, 857996767, 856422401, 725267711, 398479643, 29602201, 346406503, 894514540, 37147748, 545144290, 301677114, 714264959, 119822846, 551224270, 457479858, 284363737, 765543949, 610678950, 961637014, 816869739, 250213878, 100636415, 568560589, 554695778, 377416945, 388020661, 101344251, 780212906, 263866714, 601066941, 441628748, 71345366, 977905587, 733800010, 254961190, 574432023, 842077772, 726935989, 611035239, 149135449, 646642180, 163244262, 371443691, 408635147, 735485030, 309894310, 38354957, 815917696, 781383289, 960158883, 325674274, 577779405, 366843509, 85665050, 118167897, 197727417, 664655762, 489347382, 260763176, 722501747, 235104758, 10175030, 757334677, 521213392, 373861649, 434661453, 320001403, 558429534, 622596683, 841450784, 247941195, 839861888, 204773033, 991719280, 947250370, 1214170, 295002557, 26207871, 555128177, 988141918, 980549392, 888034913, 790875232, 207131838, 827574721, 10434120, 640868600, 230118974, 626380589, 269818941, 821000955, 166960708, 799509249, 266827702, 658459693, 551792516, 735293580, 364556126, 100472272, 634404813, 703509503, 897427264, 599811748, 587233062, 743966276, 946589505, 44323033, 242265515, 757351588, 221745757, 145369895, 553067423, 680337205, 27716801, 449467310, 521100163, 945156564, 13206884, 361917696, 146725184, 499208492, 922936759, 875480280, 835098318, 974949114, 218253154, 773364758, 670951653, 81284059, 464685090, 533636978, 256388483, 669601672, 53415985, 581273254, 33003595, 484122377, 127983122, 482648286, 133535745, 22382381, 895497301, 346502740, 662166293, 582606891, 327781972, 289704832, 148232133, 58809347, 187089504, 601580262, 439143383, 261040398, 887749030, 500093661, 265785621, 515609354, 876252140, 869262187, 922014402, 385333785, 743096258, 120965437, 189387454, 580146193, 898692772, 342277996, 121287248, 683534388, 382113686, 980088623, 831394782, 169566766, 674588467, 763584314, 132161699, 12029929, 499686236, 935453337, 675086461, 968638445, 729428404, 660599512, 420265200, 880051775, 607341046, 979455563, 634126423, 293431390, 157881884, 359345589, 809850989, 195182739, 222818235, 65049078, 434568413, 499221213, 865204650, 557141275, 33996536, 105769928, 20507123, 445205932, 388232586, 424435630, 800668909, 900319024, 43558815, 495203239, 978786271, 70133000, 281022687, 961017208, 299974481, 223909818, 401293690, 742562393, 737478370, 918842190, 916330175, 227254720, 958326663, 230764220, 427630206, 198593059, 357627225, 387002642, 528721131, 555526425, 699646461, 681479293, 822267224, 240888024, 301763560, 771378660, 376516495, 262215835, 853500064, 223560405, 640534592, 814240441, 935904531, 754411916, 104792781, 578148793, 130627397, 744349654, 25492715, 435258480, 432967942, 258217568, 330382262, 800116444, 703290496, 300366465, 48098109, 797783360, 676310332, 170982506, 139233071, 626449078, 227573474, 283264267, 126308796, 828261345, 639550508, 632412826, 248014696, 473567232, 934752063, 945533913, 820870657, 750871973, 985173545, 988804776, 500116857, 595769369, 626243305, 318993693, 56671564, 391143098, 728341421, 747063672, 997129469, 668139404, 197351509, 57502230, 702602813, 833463087, 646614063, 326772458, 827696771, 147217842, 360237084, 256542000, 438025934, 385611348, 425245599, 127503368, 725566611, 605032579, 864306708, 39480842, 245850891, 25923971, 871339263, 459426466, 388474894, 87162993, 147105928, 167096316, 665066314, 525060489, 509715358, 676483997, 505248258, 232928545, 279904683, 880361663, 263334060, 837383645, 525943870, 786232378, 592790934, 28384502, 747232696, 382552179, 575547093, 352541715, 544100933, 957386116, 279723293, 250510571, 685638301, 939304569, 420992364, 988768254, 940045867, 271906702, 560217759, 172353475, 394501906, 413346667, 711918452, 672253893, 76623293, 230023902, 947975695, 924327981, 104843725, 929558561, 91516436, 656597267, 137649465, 192072223, 722856436, 904028403, 695639856, 57069735, 868005513, 23802548, 726412698, 741792421, 308059486, 186161614, 303027708, 984803256, 463693381, 586960953, 235641417, 439497910, 501151530, 452191711, 902291953, 211410369, 41615308, 429365357, 587194092, 46196637, 922732850, 288302887, 795277362, 937545105, 397442070, 320395263, 232533498, 883142162, 766199973, 431890598, 508073252, 731161703, 327185492, 760603138, 985317650, 456819801, 454368361, 460113504, 688340321, 666285681, 963081786, 188983060, 566091184, 971834602, 241677294, 653156670, 105605026, 721942715, 752367067, 167846449, 298922641, 345395214, 757413474, 252258659, 516272732, 86612229, 765830441, 568689186, 591199598, 562083411, 378345818, 910500856, 783743955, 112402022, 353967979, 296193772, 718062304, 8685541, 676155037, 255761566, 139671100, 48767630, 539242908, 378771714, 348697930, 759151311, 417377883, 177982936, 922194056, 374428670, 251783133, 349847809, 967858699, 134658403, 192049390, 899638889, 103617964, 432189147, 528433712, 1777246, 765320906, 167699911, 841891684, 963267478, 415889520, 591804935, 88113212, 497732857, 302750596, 686849185, 934058786, 747623506, 120235638, 161160171, 859466630, 978373869, 277586507, 62538292, 649505314, 951272029, 112621654, 972519955, 182323364, 233597333, 424972898, 229477286, 362184260, 879334959, 162337178, 109440310, 696096290, 989249290, 61678022, 880623362, 917282368, 432632397, 951239511, 581643217, 739014516, 662709761, 404775191, 476374084, 393478767, 738774625, 188254166, 841047813, 138853858, 492440859, 688517956, 299179092, 868580088, 71494063, 364994318, 369417002, 314194684, 51833288, 917993842, 469258839, 35100969, 942903264, 759127277, 641147925, 555589946, 486340724, 722797831, 24648485, 388318519, 264509742, 6425244, 440788989, 690119533, 57657221, 280969968, 788959468, 605489439, 475955807, 476523134, 734265104, 27319897, 842349967, 593640124, 793235520, 455510416, 774589101, 228581958, 457746335, 722510791, 721529753, 6644640, 799016246, 457261100, 382545059, 554434940, 826564561, 305494328, 709506777, 158297220, 172531838, 2393870, 564790935, 530043080, 318433090, 227794941, 739054016, 116213046, 126472523, 282674204, 203044988, 977791206, 633639047, 518018438, 860648429, 814738927, 765379930, 917061637, 151546916, 186637834, 144106065, 116191069, 354533655, 792769175, 663396184, 910510131, 264188025, 647383387, 838724018, 444041343, 707035613, 800108284, 267674543, 491293399, 301017869, 996656794, 762718359, 734322010, 459941069, 622792031, 145632117, 675105038, 949522631, 106184097, 478856805, 88210844, 682288036, 994966509, 653912044, 73659605, 1912407, 2661714, 833870096, 788137224, 858194208, 137697732, 459028192, 962778666, 571450177, 876721346, 277959461, 399035602, 130037902, 38220704, 353704108, 85398389, 170032296, 340191443, 183611449, 495403658, 497027645, 754551204, 612285162, 319505799, 196699492, 133009882, 970879717, 864683653, 920871549, 190024591, 499031168, 58851182, 852815307, 375194729, 644500619, 788069474, 626033537, 347651772, 360318276, 796223263, 890134453, 792072140, 485463616, 810227629, 328646267, 126970487, 670840700, 143666474, 70193831, 650767311, 169890657, 2030060, 442230084, 751963315, 565113929, 595230101, 697692289, 902652588, 677041134, 238250820, 478689983, 519589874, 824107191, 428169115, 658276226, 957075333, 954836823, 603007738, 639378098, 319057097, 473727103, 833505084, 319695208, 787828110, 632265369, 525482501, 678739938, 503069605, 517191943, 15246729, 869529871, 491608415, 53659670, 209997514, 387474783, 57025151, 696755815, 701880770, 471717436, 736072688, 158020374, 259154271, 874221096, 829027927, 326258148, 79424145, 21756769, 197446415, 655657721, 885790778, 821997229, 377448524, 245242203, 495427986, 848144391, 907437376, 788355864, 7491320, 961263631, 288923951, 983019745, 442277415, 906082858, 567922387, 454484752, 988554574, 38099645, 913538950, 588222938, 425635453, 91225583, 965207401, 208118153, 693942046, 924821532, 730024873, 389444815, 76455799, 329099676, 52030234, 153070346, 262473952, 178994333, 411501568, 345333117, 566570470, 877698020, 174376087, 501486882, 99210610, 501737890, 358328309, 99621190, 938581990, 68664785, 356724217, 638575327, 927604874, 214595702, 120026865, 208641745, 691813727, 997862595, 324956969, 29220119, 960181891, 677893398, 823749933, 476388726, 147812724, 224734496, 455084878, 943825406, 724513245, 632300421, 884305810, 172770490, 441520455, 234773739, 840141592, 926014904, 227582589, 66636853, 291256411, 23974830, 945293105, 381978221, 180660151, 228868319, 610738466, 189815845, 895536248, 285937804, 499999477, 439259926, 866069845, 131026659, 891145121, 692161648, 866258726, 938357671, 534685431, 821683330, 336911141, 852911286, 190166515, 210662297, 600366817, 634564456, 750384173, 268290219, 631748027, 414699281, 238172274, 10469425, 790123900, 103832720, 478865535, 311513481, 361744907, 119194827, 815456896, 821787921, 660062483, 577665327, 983454689, 821778048, 505186674, 285803813, 771725860, 584615446, 252701539, 777399143, 528707024, 905793697, 266552818, 155245291, 539661269, 776539893, 960740637, 811465531, 248457050, 999100613, 132454562, 312926949, 751077056, 254286048, 616002637, 349955198, 464216170, 175428775, 770684308, 233160197, 455601602, 577515510, 983841764, 160162628, 383540701, 738713620, 208007465, 722958834, 264909464, 449913345, 344310730, 644356099, 654503790, 578554160, 758918236, 535419504, 629009925, 764027003, 65967628, 145076887, 745598630, 430128286, 290760580, 784540048, 500387520, 485543241, 564626207, 558864427, 467046621, 871135408, 834534836, 732042787, 876685908, 558895267, 228686098, 708203403, 636955802, 517067546, 647125695, 889013861, 781089942, 192707390, 762774705, 427146745, 903579676, 943772529, 678748098, 696511765, 637940088, 568609011, 774091729, 323442263, 656353519, 967776830, 472240162, 577502368, 421150894, 72502346, 172124067, 552602357, 455061464, 231091011, 471859478, 141310648, 337715110, 333108938, 134534571, 680427511, 141049784, 608492584, 25789644, 157836365, 607444356, 70378040, 507203925, 373292439, 953154067, 351163755, 796455864, 583975955, 776331986, 545200662, 805204767, 39984275, 122021941, 337274408, 877007499, 226541806, 825422700, 539133472, 438332858, 844345445, 943248598, 636139910, 416316756, 198190650, 101631508, 695649645, 753792877, 233909026, 433879531, 323377047, 534339809, 128886845, 234215071, 141406436, 275040696, 679769502, 359569669, 948023117, 577165120, 267461252, 689516259, 208860530, 222312290, 234730618, 383967805, 784124599, 357492476, 33332645, 336013946, 142871541, 875178182, 146812650, 7045063, 618535998, 119784852, 977639252, 283636846, 659041594, 353495098, 978522160, 369280691, 901289994, 4011482, 388236082, 63423571, 793114373, 960890577, 342892112, 498273868, 825216350, 602419025, 313553639, 146107542, 450465861, 765310208, 220653556, 528371559, 227654518, 734850209, 479534495, 495051968, 27850451, 500991028, 859051617, 222332494, 151774674, 881235070, 275059086, 934270411, 583627933, 440667915, 160524792, 394611319, 540566047, 352678894, 450015622, 429670187, 472270448, 582716630, 310253486, 625344781, 733628657, 943657684, 626361748, 383723155, 996635906, 698950680, 494839057, 209258573, 47310880, 250550123, 595923978, 412363929, 91361585, 318939105, 973156295, 945078016, 135672510, 616271749, 771886869, 338157334, 371127129, 759200845, 262870638, 319997388, 651706411, 362977386, 897980508, 88130861, 911322191, 55894420, 646932474, 883478127, 209198128, 845071738, 573499056, 187298261, 949496887, 809660319, 176201830, 730713149, 986469534, 121814457, 835432258, 23578646, 643046789, 981856518, 105702393, 11557192, 457756328, 778807076, 305975827, 845276829, 371266902, 788763359, 600157503, 597141448, 214730907, 462987119, 130853730, 781914733, 264901211, 828286872, 307088342, 91059958, 398040654, 238263914, 531346115, 217459062, 146778360, 918109272, 145843775, 847919945, 541009670, 472491007, 606501905, 360439585, 763232133, 229483481, 526052460, 592891086, 652432211, 899109757, 987645010, 707911113, 256074021, 105808765, 187507520, 425070785, 371507917, 571634873, 558730100, 684423157, 268468587, 729346852, 575487707, 714285355, 542110191, 409561665, 83758484, 705330315, 652163453, 216366387, 402879206, 266420734, 948261061, 975372857, 668964850, 890735448, 227542196, 876419231, 971304662, 438439847, 928411267, 592871364, 340334163, 296533743, 8259975, 735114319, 407779640, 164563695, 990960510, 719863636, 288323282, 31172539, 246338766, 182971555, 545615404, 118456522, 318755134, 382222293, 43241898, 548441699, 971998410, 896448362, 594075016, 859765140, 717380879, 59614863, 103275303, 81494707, 824689021, 962799957, 707856610, 115602957, 131377766, 156924362, 626325843, 107044030, 520177369, 672532352, 35542220, 736982854, 973778429, 299449096, 194590119, 241698499, 716541375, 29762613, 783556767, 702662211, 972637245, 83824584, 432338877, 767298936, 257137411, 415254061, 536357543, 820646171, 95598200, 481172798, 249095243, 141426120, 610949882, 624637117, 141972313, 859208992, 445304769, 854555904, 363702073, 188463683, 191011658, 483051565, 535702369, 979053237, 723567178, 733689771, 850011870, 114410427, 828398978, 480657242, 332683811, 80235055, 627883312, 611678530, 874800917, 626943499, 198009460, 747998513, 147090143, 315626870, 249176214, 236849924, 251731602, 261503083, 239042180, 432682220, 889464970, 498024088, 360080897, 116831003, 954044830, 293816539, 339021781, 205678551, 173650573, 671344127, 837275603, 80470904, 328566368, 299296251, 246850154, 281118807, 835905239, 324977274, 324099815, 185319571, 1315700, 835055942, 814879265, 460721074, 650853233, 918332760, 136157250, 804121069, 872117539, 481523297, 862551139, 470349723, 708941111, 406962696, 284687621, 384805430, 732769542, 716050279, 677444617, 94755273, 487246922, 744169122, 540980596, 162599401, 288932722, 736156579, 563552913, 309712226, 975505233, 431136423, 840745133, 918513963, 556901601, 882724956, 161154342, 162402041, 525762292, 225323484, 857131726, 410408696, 17427327, 592786575, 333278816, 543907795, 990575615, 504198250, 825872252, 62670675, 658774058, 20912579, 891529027, 292597506, 823615590, 105944217, 228053735, 107421983, 644412303, 767334082, 37148962, 13957312, 74364030, 870829311, 542673451, 359145841, 250098300, 56969225, 971779985, 924688803, 114696668, 26588233, 897006269, 433057475, 771719887, 834309862, 198427127, 152145449, 591001107, 216076311, 297850708, 555777773, 559842423, 239668752, 44880848, 545187866, 693629523, 97025032, 620760416, 884138014, 21501345, 208655194, 636816496, 704283264, 319898802, 689565220, 378226872, 859341445, 958210231, 164574548, 632499714, 718236270, 991959554, 977141558, 537419560, 608734174, 215651367, 327186599, 708980697, 720347629, 112194118, 828412538, 397946895, 337848744, 58807700, 820884629, 861689306, 739257606, 481980552, 684328839, 991475320, 412110124, 41815925, 678212273, 678291384, 43772936, 567999546, 701689068, 900526287, 929114101, 439355778, 144564106, 859577130, 81561940, 440752860, 471361049, 968157991, 671796373, 394940679, 898998666, 552515469, 262996474, 221745036, 118983607, 603557231, 847773985, 909117847, 233594595, 709126704, 926516280, 637710608, 4409874, 391504725, 717208333, 641511650, 346452549, 645869121, 270191856, 888633699, 936791550, 165767518, 561989771, 945480771, 60888789, 84254008, 107754521, 676959710, 411280671, 220278829, 890443714, 308761396, 30250911, 924740786, 624379939, 464894304, 565729261, 130927449, 250879943, 666090124, 713609359, 383946055, 193280896, 616038668, 209971308, 819528217, 221895673, 531074341, 940830818, 423869468, 589041194, 733101541, 90784215, 665605275, 174000186, 323477777, 966855465, 772134309, 365575654, 249515227, 61143579, 513562170, 690621859, 486392612, 78071904, 873706995, 324149378, 292357914, 802832384, 230028186, 15123074, 959060638, 340629762, 970942928, 767493011, 50744351, 365076670, 188472076, 327267073, 829103541, 79358530, 178114284, 511959911, 247818555, 941315662, 409265294, 379486487, 864641822, 288117218, 632532297, 765318601, 169791329, 630542112, 29705117, 225772617, 893014388, 13107443, 962554804, 624146372, 143421121, 740652187, 816732454, 594083739, 543993295, 515752911, 533543351, 270784849, 238074613, 978674514, 866926879, 623685699, 698904533, 547653892, 479538056, 152555278, 984344980, 244682158, 665535641, 348259948, 969139401, 409941098, 787343749, 418975191, 183560946, 87267258, 113573979, 815276968, 944106501, 96676140, 480057531, 225558312, 346855339, 551107962, 654329119, 985442676, 679974029, 899733886, 265153672, 868861374, 986347980, 209199868, 880211684, 893419664, 682981914, 115197339, 432758997, 222844657, 424223620, 189774851, 408002265, 672943118, 172323513, 129183180, 962673656, 833924785, 775618726, 186695986, 944380619, 976706147, 127286584, 131840168, 607269089, 47565052, 773014467, 869842489, 772827828, 268802230, 695011180, 734211340, 571751484, 795414942, 804160111, 536237127, 717747903, 902313728, 284878956, 74013813, 408951612, 392202757, 349881930, 880248984, 668691914, 243267771, 467695894, 952669433, 636712115, 987882515, 33947812, 678614539, 91992556, 617728345, 318626683, 348910740, 831006727, 307798718, 800029097, 240682491, 701610111, 735864983, 330195621, 793372942, 548411437, 950706689, 876430340, 241279238, 904988428, 430469894, 259273581, 466545195, 564807472, 851992698, 650701129, 339455309, 701107455, 492909735, 383840574, 109651525, 991880803, 401676904, 855009680, 998110504, 426807926, 325747550, 666266177, 398414550, 812401573, 334930562, 971678245, 713867756, 902781704, 635821692, 904743621, 133859733, 741493886, 836462521, 655722745, 632987717, 441217849, 904521859, 105244823, 444226970, 382192477, 184882874, 251687217, 943793524, 171144244, 879640355, 572301630, 877884828, 962243502, 641239545, 716966285, 545498295, 866599802, 530422269, 558614306, 591689297, 648204098, 161684663, 481343236, 755480214, 979415585, 608837546, 152212286, 161126629, 414076869, 991942674, 747474708, 905048374, 63028500, 590498975, 36468205, 257157597, 340862664, 28332678, 844525956, 17914531, 839532344, 846738743, 877095512, 758738, 204135509, 474064405, 259765531, 315738559, 212094468, 978063421, 118278864, 371813996, 933216216, 349741074, 819812960, 377093740, 2125623, 327923013, 861936712, 709766222, 218311785, 330723826, 839206970, 535474870, 608861185, 486736702, 141374513, 252963628, 187739600, 992617983, 282214991, 935202647, 780080666, 498256803, 222654901, 532815529, 147617032, 991521031, 825638940, 991550338, 390508796, 158059825, 857662316, 866520864, 661916352, 695750125, 357980818, 225326295, 707283006, 612802209, 347288494, 139805352, 810945152, 434331003, 73749721, 405271693, 873755611, 799449969, 331668677, 233464928, 632154896, 268083656, 473740454, 528503135, 299305008, 615876439, 759214880, 936634889, 179931152, 322321311, 298689076, 770579184, 944371175, 829404483, 213754189, 646082892, 133999295, 694370904, 20241228, 528682219, 578096429, 790190611, 619678050, 67966320, 69532313, 512755466, 492071322, 793046841, 661679242, 977207177, 867253813, 513411651, 647167736, 420378760, 592661299, 559895384, 281890792, 148495650, 150778369, 275648572, 449920678, 67357339, 798276350, 441295941, 574558217, 17448204, 739150347, 993963671, 335780257, 530365554, 332853517, 502545134, 63958082, 391968177, 910377568, 411392371, 507781704, 6237344, 375614687, 409923174, 795408504, 436300977, 603216661, 970516906, 333461297, 581005915, 58976720, 308336139, 474236052, 445328398, 983038030, 581666385, 426585669, 622163288, 656890638, 707388250, 907074476, 546509268, 355634986, 415300267, 242986098, 496003970, 50245401, 976412859, 825447177, 6503390, 321014634, 192616634, 471596113, 578238717, 47860704, 539663290, 249125214, 383730801, 173487122, 543670720, 337769896, 464927241, 996035594, 377706264, 305519920, 195784296, 901379682, 705463999, 486712094, 50867150, 394823646, 450145456, 461037035, 13536946, 941570615, 125794184, 654931181, 927133319, 614801570, 284351904, 953203088, 860424482, 497383401, 203330642, 653836544, 434206483, 389726606, 493119896, 79453441, 649518567, 624010958, 377760216, 369994070, 824534853, 450007118, 176056612, 138543645, 282689432, 826480659, 650352242, 536910062, 73994706, 521808340, 261432099, 530854889, 848886275, 530222254, 831024508, 501255198, 953510984, 730775546, 623891496, 954604575, 503457992, 439065488, 935504239, 839168746, 897965435, 539424312, 572116376, 437689976, 197406515, 822243275, 899412370, 760442036, 196985502, 321057112, 56460525, 93240379, 486221693, 257888389, 664627919, 278445866, 313543324, 393439113, 850263945, 204104102, 792845180, 109789855, 716753265, 884147455, 166412174, 654574261, 161790309, 694443508, 264620875, 497040712, 45143118, 649663304, 645773653, 398771737, 673291401, 440863730, 637045546, 338794502, 552548127, 777779967, 23398753, 561440739, 43996679, 468105627, 144643467, 651855066, 983497976, 227913833, 897704321, 292635921, 735111261, 815263961, 265321096, 298356568, 918284916, 297818687, 771644387, 714817752, 53897312, 17805621, 423330261, 298721697, 14839751, 107830463, 22321188, 161784481, 539782823, 461198315, 999595417, 240691835, 512912524, 223878415, 441946111, 668935167, 483224160, 713443879, 642370948, 797568564, 850018390, 287696217, 504651322, 623777318, 254904580, 221249339, 321130998, 371014035, 217888573, 275652227, 215763530, 369115701, 425903113, 604686643, 217204006, 435424496, 338189086, 94421116, 282120962, 552430087, 601978161, 824356320, 394504718, 971400932, 619362670, 272901384, 346077451, 849113100, 145886579, 432056885, 348870224, 703120894, 757932269, 300394882, 533871625, 138166913, 410377747, 857633832, 572071683, 565745679, 101183903, 683038891, 987518459, 904655752, 397767621, 691633806, 600489492, 275511078, 864889554, 884900466, 421825191, 934492875, 911554793, 623826195, 282804953, 913895482, 952623277, 730125776, 50982239, 963035137, 760459579, 906052371, 192270080, 79397246, 792533882, 981779608, 351732445, 692015883, 437910858, 610729170, 191640753, 567556789, 29724301, 426025529, 816485712, 958311253, 551189908, 404806445, 340264583, 600958933, 207545443, 428474611, 181429421, 589211544, 123721774, 444155803, 305988692, 224923359, 148026481, 71338183, 867440799, 157208898, 488739935, 477567487, 641445326, 229975323, 161536219, 8504947, 426734011, 417601221, 289809147, 233714899, 358392802, 829206776, 590679079, 175472999, 381552389, 546510019, 466463916, 656007555, 865492409, 620255874, 439030404, 396473763, 796637001, 734892135, 468951841, 612728478, 722547897, 43671685, 889122302, 221813208, 424932136, 186488193, 601596494, 809802005, 634596478, 336360351, 285171050, 709358193, 536630747, 848123990, 899804777, 809376028, 219898051, 248411672, 469001208, 909880577, 50259655, 513039169, 302482583, 483409290, 442619889, 278798975, 620512105, 894629688, 796013895, 42610668, 756318155, 984107847, 813464908, 300752278, 959781129, 460868254, 368716170, 802557800, 818187194, 732602198, 855590182, 837326148, 17279411, 642393730, 681266061, 81357046, 505820848, 276654258, 686505212, 71831818, 44856688, 753669877, 926114421, 876800541, 807657925, 564248496, 540395653, 378700994, 996737194, 633568756, 576658877, 499166919, 744223781, 139386874, 592218740, 776045628, 888829306, 238407161, 824037284, 957813927, 190231656, 635780504, 682780981, 560940728, 968207596, 68927031, 645137386, 3818313, 175924689, 523354260, 523267295, 62371822, 111929953, 465117534, 49850575, 800302485, 193309356, 761917650, 300117013, 386955072, 830666665, 142826527, 25981664, 955834694, 758272261, 725973563, 371085101, 724833972, 776661661, 389881414, 103849101, 323107977, 766152985, 4216148, 269837125, 928664179, 653433689, 927901847, 628403911, 809188351, 622369870, 200430098, 991015352, 911373293, 35076638, 589327157, 871829844, 270119599, 297460537, 872433300, 42318974, 840714869, 760112365, 349388198, 264843588, 713971446, 475833644, 46339778, 976509952, 877456497, 932328460, 738518068, 41361700, 956891378, 94331046, 825688288, 406738889, 208545348, 165742318, 427830327, 619519689, 750216639, 714500377, 400446400, 338978891, 643471391, 220644587, 817814455, 395201762, 36055217, 877718550, 25531172, 934578977, 138961546, 45148023, 991004635, 317992947, 575523064, 100352714, 790413216, 540205237, 279562059, 165253396, 7993283, 221862161, 91913759, 548314186, 35974764, 526834818, 543472533, 682652541, 834501689, 209320750, 298543394, 995172297, 930014979, 904581863, 229507352, 719272433, 37564745, 989761982, 516905366, 937684712, 649711362, 682923207, 757021029, 136965164, 475672759, 923340440, 160340757, 861244635, 848202307, 139721414, 389936673, 851935918, 350945578, 467131358, 455161727, 641169948, 791148506, 892902, 383956179, 515875448, 652649297, 354452410, 777998028, 194977211, 871946956, 957357750, 312559995, 555502731, 334314674, 182542928, 498598024, 127225934, 567785183, 78268656, 422865584, 99166093, 271942852, 838138392, 615537151, 305700311, 200227902, 636399591, 518370476, 743805611, 500687344, 63899200, 400729178, 770605382, 79132794, 217151884, 82447254, 374718897, 912734669, 570464000, 106955050, 370844878, 553737961, 906474917, 607940488, 787228170, 517462597, 889032805, 153097410, 928940863, 330281195, 886785216, 563922176, 367747182, 912794843, 847442488, 277369299, 32291856, 464273380, 586778139, 203153060, 593204912, 56599056, 347375159, 488620402, 667162706, 623204477, 113760382, 743211920, 541082043, 360738754, 36786846, 340084966, 471481115, 403400238, 76236419, 260836392, 705312818, 997588632, 598586034, 350838041, 385313414, 700396409, 757930200, 727874503, 574500987, 891115055, 244491239, 381203651, 520733655, 794529884, 580171285, 893675881, 351834958, 679370753, 976968389, 405951702, 401853075, 985596743, 498049008, 908384084, 251938819, 498337538, 446225192, 315216546, 972985027, 725673856, 88577220, 379263903, 660567346, 74090851, 603173008, 414687608, 86946375, 22186550, 211506277, 315558972, 817015752, 48515874, 421210339, 627579425, 168993639, 816432292, 492067653, 638686183, 686711925, 875165388, 965582732, 74399350, 735356293, 265920635, 432073755, 598096857, 917072060, 58372831, 120825715, 622242390, 661249347, 395016770, 575041806, 220579399, 751677597, 72213061, 848652081, 172105728, 478791362, 271370413, 4018861, 241705831, 586054834, 482818449, 482508238, 341642596, 972207951, 934098501, 26322311, 81645336, 139070575, 425046991, 192186943, 426661869, 573322151, 466483970, 171082753, 750311994, 948770384, 275968702, 421882723, 725135915, 315038429, 16979696, 144053784, 414933710, 139213876, 714290324, 732505268, 745796629, 540117951, 776437425, 786114160, 165574434, 546194227, 356726289, 833545610, 540588498, 222182273, 169210004, 709089195, 490982349, 598467665, 721690732, 543431031, 928940138, 575106746, 536612431, 5452230, 182218123, 126094430, 698565709, 926052481, 20522353, 885023051, 106007863, 313184052, 166018180, 51344282, 675571401, 279317528, 290857536, 991921619, 223112796, 730097303, 49409126, 698597866, 557437406, 988666934, 349409664, 798809911, 208572459, 119049912, 378082726, 468050545, 124010988, 775621581, 273598831, 192000108, 136826319, 414385176, 485261636, 966326290, 524708114, 291384394, 36825302, 266709129, 474786110, 197159404, 641038391, 351280489, 630943884, 492754074, 213533208, 671503819, 884809040, 200229550, 158153467, 165443927, 500469068, 740782949, 875482689, 796584183, 54965374, 45845621, 883382278, 683850236, 603189774, 634277393, 196621765, 869380778, 686217397, 620292433, 101182247, 631907231, 791365331, 879550741, 188699159, 86884885, 82146196, 137326802, 728820709, 358508448, 857907544, 94594218, 49968980, 407279079, 688421857, 573741543, 543821105, 373740237, 410581458, 830482613, 926948359, 508057111, 333124189, 100100161, 749495456, 392927080, 957628365, 180962487, 880154451, 804140543, 679425403, 263566557, 11645160, 837861416, 124915102, 180649185, 302567421, 828991465, 636460830, 200276036, 191217694, 499002820, 423633258, 286418696, 115688231, 661606569, 518727102, 967850598, 758286705, 867392259, 340101813, 155038790, 112979543, 177857649, 591600056, 553933980, 342567068, 417582751, 232116198, 674997088, 142367661, 460774198, 689612872, 342285918, 270834777, 68515988, 648415399, 570024196, 826894661, 434609996, 248591854, 745110444, 677201384, 255256248, 398974632, 584649506, 134717397, 941559695, 262716072, 119526698, 375362811, 641986452, 58625999, 523417171, 458767176, 412734515, 355165667, 527995430, 422243332, 535428501, 895980846, 998465326, 511736459, 282256618, 400784263, 27332422, 656204708, 755111742, 171360772, 500889267, 994670281, 542743441, 549268896, 759337126, 430272089, 683718379, 140843893, 304108499, 997495737, 666140092, 234401031, 355231851, 646294424, 20138891, 135084422, 432376611, 665590060, 679017325, 978196040, 861865847, 386057832, 256484605, 579706463, 847254232, 864540561, 155525790, 11824353, 700779585, 330411977, 57825484, 972206920, 61632298, 821546924, 191529261, 957898978, 121453556, 259106504, 682502117, 548911323, 525889843, 127880119, 165015470, 196343187, 706731689, 990315103, 860231298, 482553827, 230027030, 97291690, 176089409, 234919450, 269733109, 434980183, 495856173, 492179233, 58440907, 268809903, 762426531, 183716832, 711494481, 919995828, 549966689, 629839375, 961537951, 902458383, 399649738, 399398869, 132664905, 719156404, 515867982, 677289158, 864246995, 18328686, 253296837, 879410808, 850663281, 583067553, 211746927, 317586999, 261513340, 891419021, 195741215, 52965639, 668361749, 798882800, 447828644, 527936564, 30820147, 449704420, 882414806, 4305038, 62071798, 228468494, 909467693, 899182053, 386524664, 89332703, 219810915, 534198888, 866076925, 44986050, 961656565, 611610507, 877700126, 493044272, 707748853, 987889015, 503163432, 747897983, 825700030, 79884320, 741113730, 534016607, 301337407, 549324125, 772013098, 839846536, 528594785, 85981390, 659785966, 108029042, 530280284, 470643957, 190652846, 323523509, 322975150, 216636130, 163864457, 584643641, 481142597, 335881325, 945080226, 150633596, 187546954, 413700769, 634262994, 924292274, 4875734, 537605329, 611518496, 155076000, 205393977, 918903762, 736505628, 198166525, 115570051, 734703961, 263863795, 484195271, 428601323, 695634636, 713169665, 435665054, 855574968, 444225815, 759674538, 794397061, 235242093, 566165547, 654258115, 704283000, 539853898, 870738715, 438572670, 451887174, 855976755, 491790650, 418236546, 788299276, 902884178, 701070348, 867369794, 584190484, 462696891, 705776579, 631612566, 695307878, 956620825, 647329147, 685574836, 901334651, 360889235, 3374240, 996250035, 210221507, 688950530, 848060869, 292652863, 788426962, 509922518, 418713424, 366533405, 699001346, 880658195, 36617150, 225847008, 685179574, 538080725, 404736014, 85438551, 422123581, 55793065, 258391093, 808433291, 408232913, 29112866, 322501312, 13511859, 19916117, 857544200, 372835740, 414462663, 252079962, 998044476, 555624745, 509542851, 528778103, 889478421, 724475833, 775914011, 639748888, 544571185, 340867545, 96033548, 148586393, 687366301, 412250080, 203424139, 850250111, 909360926, 800356807, 160796737, 247434172, 424822908, 458715653, 804262932, 632631588, 737808543, 933879822, 410678994, 473412350, 317970310, 913022201, 283293242, 311439129, 599419072, 527319769, 370248744, 498031468, 333778961, 61273948, 557324226, 940883622, 969934824, 825742568, 888081058, 387420609, 180087760, 847108349, 437200886, 85030528, 298972273, 415096722, 597515787, 344910992, 902718072, 637699387, 43445115, 98985094, 345728067, 336882155, 815330813, 523541040, 501793755, 654951905, 3257393, 288559691, 333545528, 136107842, 268037538, 489617652, 554300622, 173622840, 131971567, 682951642, 370495868, 876842807, 108232738, 984269681, 841460706, 155091570, 223730401, 760752448, 294158245, 869007922, 75002725, 684122774, 316782787, 733909458, 467018766, 337154538, 262647990, 628536938, 333067932, 134816858, 255654138, 143885242, 656046200, 658308297, 395122897, 523463532, 536794349, 157294390, 627704944, 773103793, 843260204, 171918854, 383090178, 852558597, 701161846, 838720871, 228270620, 541747588, 469825794, 213114806, 431446029, 240659488, 445470827, 128453970, 131950480, 82013400, 478185290, 751036724, 327831377, 711205605, 817567386, 844027091, 622187712, 461189655, 84348151, 36420687, 180437202, 651087029, 947490038, 585943719, 175680124, 239837979, 464910864, 724016042, 180953214, 704909172, 720213902, 858721943, 685938257, 394913478, 523390760, 404214525, 164592142, 69027246, 40870573, 536755967, 706287798, 406248151, 191050637, 592106200, 187245365, 711963991, 539193840, 147760471, 556294608, 579117993, 931478803, 479828887, 333171518, 164550734, 436011356, 792154869, 56410557, 712945809, 123551008, 181273615, 524508088, 58075424, 790548574, 135932243, 419479816, 365116095, 120684060, 406823925, 256354089, 551315396, 677232844, 717910401, 120415701, 576289777, 311997089, 397951566, 434752342, 681844358, 880115873, 631940440, 226158987, 385247702, 814152565, 718173323, 401948286, 812964959, 810288389, 495420036, 874702787, 521710704, 889469144, 818628376, 703949560, 573953936, 566719076, 640191960, 619930474, 305580754, 700035041, 36249892, 542566171, 474372491, 828589966, 393647299, 311229898, 374449453, 743651404, 147334298, 943084522, 764179839, 753493275, 930193771, 203271380, 514282114, 336205861, 263772240, 220330715, 693344327, 808329108, 255472159, 755400820, 542684577, 392896639, 360875289, 56600579, 94031934, 181386725, 126511461, 435878470, 832240719, 240298838, 10902700, 848766754, 13755811, 292076093, 77610118, 443587700, 689362339, 744343488, 866700332, 505477828, 457515285, 838786475, 830927916, 379487086, 119914834, 32167366, 619516712, 151328449, 24921313, 751534590, 348400980, 435531159, 561492775, 645747490, 651986427, 644034489, 898815139, 640362798, 457233782, 824387409, 769777340, 336505727, 762514908, 774787810, 745315041, 361104881, 897457077, 969706218, 74594908, 598000398, 26609916, 761110908, 307953191, 63244681, 187709417, 470936397, 322636260, 855187750, 777841054, 212174350, 520085497, 686466829, 990515920, 521156303, 786252169, 605534489, 712757559, 478308221, 925700710, 610680500, 396711424, 442321905, 810901760, 983440283, 591908922, 410322331, 893714980, 414993017, 819483428, 833958379, 983907060, 528993509, 359447895, 369345995, 42089189, 605723686, 154592293, 75817414, 694186862, 261167045, 89536550, 196684283, 237006606, 243748195, 816612022, 875678651, 26909066, 595237195, 654079457, 722802737, 55390094, 459816455, 207642652, 11353313, 878566757, 756524403, 363667403, 558507875, 654572383, 522362142, 434851345, 472359008, 400366494, 438835406, 906351919, 212914893, 635638342, 25298946, 420409693, 268336201, 102429537, 712886198, 624737805, 639099234, 227522434, 192014503, 791810122, 582636099, 353645327, 514457961, 449444781, 726431049, 888370142, 59175589, 226097153, 541304853, 476338242, 502824653, 159885588, 911029126, 403248794, 435180682, 762710772, 369241528, 724918970, 697694744, 949253789, 26489141, 285762297, 734296236, 703610964, 17422329, 146578326, 600319383, 656918778, 729714592, 820013230, 784653156, 569705586, 430812359, 377674107, 489812274, 642171449, 534568775, 766086668, 467851121, 932814263, 420052367, 605085413, 156927523, 94460691, 863840283, 922930713, 428850423, 979484459, 171411160, 601689949, 244289415, 332848663, 355990470, 681667346, 384881874, 61920602, 884308226, 958420422, 355197635, 519374230, 342874827, 194066184, 460521735, 958090733, 162012933, 806855449, 352325942, 314439005, 237825249, 94886658, 609430373, 857888026, 209032838, 489486394, 575705463, 535290911, 586678010, 712465205, 236522673, 163126913, 48353344, 402470249, 204622938, 184860064, 45518925, 67254012, 502824076, 192366814, 508989828, 432619387, 514826256, 457253267, 540671112, 309981332, 715153567, 830588903, 881186426, 423984905, 127784074, 460903676, 739267697, 150901256, 33671190, 262932610, 205794031, 283969056, 478100051, 510520705, 375027603, 324939648, 278338199, 610494598, 63799724, 446848341, 448578293, 867709676, 654540611, 922548493, 144075088, 770290001, 421351469, 381838448, 941010748, 644555937, 724750254, 582694975, 717630330, 613751445, 414300789, 257765963, 634993777, 182969766, 426405192, 518511263, 368391997, 330139725, 240024606, 486614980, 817967630, 727328141, 731400492, 967246942, 524254477, 574190032, 592414340, 23248004, 679086651, 269953584, 526199020, 354774802, 607022600, 165845635, 847451343, 898568014, 448082817, 708548105, 184059614, 534896268, 743025909, 690276481, 760452445, 367035519, 946802329, 598562253, 826871280, 298101328, 389296003, 658788774, 384009753, 880302143, 297980821, 380490107, 353818894, 460811, 635193706, 540421377, 705734851, 868580362, 586914718, 43671867, 606271261, 536506282, 486699639, 312441433, 137732025, 716433603, 861219722, 795632647, 596281271, 822641716, 76139321, 755942337, 78413798, 924956134, 855908783, 61197861, 749992480, 617128652, 450189997, 612817327, 995199123, 852995457, 573758586, 437632207, 730357769, 934717391, 182200106, 495448983, 584658883, 988946344, 186359718, 229310434, 256573732, 884576325, 837580677, 599728333, 458171252, 514151297, 29033887, 893963958, 739537156, 229201298, 712016452, 714369147, 865237433, 987301282, 165769892, 510664467, 74880801, 252817364, 382727117, 533652541, 642270389, 208902350, 807999296, 254434502, 254804369, 483339997, 623129237, 244927891, 742335142, 814973275, 737000744, 724500090, 214073819, 657932698, 89878530, 924522114, 828430429, 62713711, 795839643, 1192772, 669034582, 247122989, 344862090, 968094448, 299468407, 457439033, 734394273, 203689140, 29655736, 464629672, 15163177, 420985325, 224614880, 143621982, 392238550, 651844253, 415639693, 381519711, 828896694, 820873069, 924463271, 626273689, 683872827, 440905917, 126725443, 153451480, 765694575, 632731259, 956530897, 13734633, 22354370, 519486939, 248090061, 45060587, 105289859, 831353836, 779347284, 880308485, 977979363, 433148829, 290640045, 663014338, 817082230, 101191528, 636827186, 408465574, 590047511, 345742228, 179486978, 59917527, 681285788, 211728990, 254497097, 697191628, 627634152, 244573707, 18784257, 79117565, 848258227, 924956683, 67913077, 223138299, 860185740, 477639882, 942545563, 791754842, 406883173, 765450795, 189618999, 165116488, 553721137, 57919860, 306608059, 352426842, 175633982, 136961632, 895741541, 97781265, 568556320, 336690239, 574441246, 260676526, 662034993, 416978893, 193491229, 919889015, 480630171, 699579276, 715782916, 851704350, 447534008, 584059699, 2171245, 834547351, 796296228, 242029344, 959258481, 395522478, 937793173, 346913577, 440384495, 367576072, 659594047, 118768671, 846392890, 859465518, 265843161, 275518421, 240380604, 828341248, 632346825, 267628702, 423383383, 484781648, 704462668, 369701323, 900274503, 956750192, 787639560, 399907891, 804032108, 214569841, 361508853, 234195457, 768329691, 116582363, 824490839, 645880888, 173724870, 399981378, 693581964, 486351877, 392387012, 691561495, 608418397, 840142288, 386175660, 891085709, 144450571, 255525968, 86967224, 716829478, 880741007, 621723825, 809165782, 84447622, 917674858, 242325775, 549474950, 677992553, 803021421, 658728117, 561217493, 502675151, 995348408, 398513718, 740455727, 87524993, 208665049, 689554057, 86836324, 598184816, 596613544, 987208588, 703357682, 448234291, 887615396, 152259869, 542827275, 588430881, 214680881, 671904922, 791848887, 716054061, 869202253, 992214072, 728478502, 607821942, 364747148, 928800079, 364520382, 251735924, 104922878, 46107204, 220339161, 98215213, 274537508, 989880107, 933602695, 255753104, 629850152, 863807328, 737455580, 497877072, 514000448, 90378191, 372397609, 666648152, 543463217, 481765604, 886373508, 536177410, 405043659, 971422879, 371621217, 167957684, 801001105, 759394740, 499568406, 867955789, 987210271, 398894086, 212824262, 683752444, 742843461, 577485470, 602950246, 762843705, 76902788, 285148928, 921736896, 147837526, 413123190, 287167271, 445343550, 371807786, 717309368, 183159323, 115378548, 27380371, 802265940, 185031175, 499049430, 142176028, 127945052, 54719775, 976964469, 600352100, 214635795, 769122986, 359852359, 947850858, 988496878, 798529971, 427872405, 432487299, 784402681, 961458605, 501835893, 670128713, 466869271, 683127794, 623111461, 452205569, 37048530, 445658754, 108861894, 656070719, 91910205, 479700680, 356058454, 385312428, 163948871, 881731389, 137316766, 161617942, 52432091, 289440062, 921790124, 276499486, 214147517, 492154504, 349288382, 183510756, 709956593, 364902773, 544994690, 694530457, 879688304, 778174405, 464859346, 524146049, 894746110, 361140356, 851268723, 376661137, 358547401, 236428587, 538445343, 791165770, 701081345, 834094250, 384730071, 419835974, 332460331, 151089564, 778719137, 78710442, 442299562, 427866968, 525261244, 442050335, 999712411, 410504174, 151598575, 355431190, 223699986, 359899408, 716823205, 786482787, 781167560, 653205142, 282903705, 316001533, 17342522, 314623570, 466042211, 229053264, 813239635, 166487045, 825338732, 664623093, 400529552, 566051381, 120223367, 103800003, 838253921, 103390879, 393932165, 730062961, 515984067, 442451632, 35431867, 171157557, 660382499, 969667023, 794537715, 845048433, 668917485, 833829168, 699700411, 788757636, 858409387, 569513017, 807536383, 52478397, 333302211, 207419130, 633583587, 2930710, 180881389, 23191578, 769939033, 281429931, 960273918, 859246877, 602963278, 147251439, 569212545, 960944371, 606171750, 573880468, 995093436, 875648604, 89057643, 469634735, 225934330, 345383057, 912770120, 101495270, 243085512, 859990187, 175211491, 617693412, 37860360, 668877412, 88318544, 682607122, 700227857, 170379562, 284871091, 793724576, 952337873, 713314899, 671947019, 514421220, 707284244, 36674121, 307668867, 714388148, 696061770, 285750647, 711124284, 841144623, 764067314, 755365601, 383667477, 206231727, 439944775, 510916424, 201045926, 614922975, 254356606, 181079149, 812847710, 859177201, 248790452, 233415094, 973129161, 980486444, 11402806, 382642641, 633824931, 561348392, 605919557, 422311258, 416948020, 464616490, 156999687, 515481781, 509694177, 484033741, 555124953, 572564133, 670902858, 715376368, 329583106, 736136138, 608178634, 352927819, 169222905, 422344488, 205411369, 761098729, 306652833, 251504599, 195595219, 403688640, 532063724, 894710774, 787139501, 728019377, 673563017, 735200692, 314988647, 237885394, 636256998, 191223059, 619008550, 642390983, 373598059, 452672034, 325111527, 557861659, 495471684, 207913677, 980142431, 426696565, 586258445, 767987726, 861146201, 93792466, 716777187, 181277599, 277058001, 148800635, 6053585, 153016017, 680304285, 767737667, 600937445, 984132721, 305685120, 113671927, 480087871, 335400086, 55236587, 13281790, 954411269, 518001287, 970489327, 180978330, 382113561, 990110298, 998017958, 377138280, 771430701, 901704265, 681907307, 145034133, 6198287, 120134231, 115792093, 415623340, 462526553, 300758345, 153082905, 296532424, 179366755, 25615807, 15077050, 454957684, 279878292, 869810918, 404202956, 642712670, 582970147, 174241369, 875973673, 3062201, 788451234, 801335832, 626345254, 366203908, 187596435, 707623728, 714680565, 679465210, 982727409, 577382497, 872983794, 563792758, 479607825, 39544890, 345371850, 29878703, 400450568, 591779137, 853942652, 935102132, 588879909, 750047604, 405730625, 851232134, 139997265, 875319016, 470337588, 359773424, 340912780, 112381312, 54244885, 47679516, 14698553, 542559091, 294082255, 135568973, 736836904, 311760823, 731690362, 327077297, 516964508, 216575271, 935974711, 81878621, 704390180, 491029196, 41070340, 462881647, 339544581, 65597498, 817036298, 109789402, 559455138, 711224631, 684058075, 799484213, 21824729, 627774594, 4237181, 240450412, 745548841, 59263664, 798083858, 368504148, 405801265, 836751015, 73001924, 856517249, 194008040, 38333721, 572445059, 671302840, 559117835, 104332491, 509596254, 977576457, 588343135, 974085592, 915148133, 657200791, 236191570, 110804634, 146610129, 60440094, 839981567, 615723953, 35786246, 33103709, 511522004, 302027156, 38202977, 810144059, 544091176, 379058339, 597804438, 916865225, 746668790, 168311111, 170408398, 84363013, 19185748, 925687578, 664816646, 494676776, 774350460, 752449035, 357393227, 483902613, 168611203, 910961353, 857435643, 452715688, 835177440, 35579065, 261560775, 356616649, 455228574, 314864339, 64175534, 635898254, 546526583, 651859369, 327264837, 282239031, 231891584, 687138604, 470638078, 800274116, 322889186, 149507650, 530978927, 28541289, 615737737, 3573, 248841714, 388644542, 235551185, 219846001, 824049834, 366703971, 237159295, 454888856, 327945731, 819003253, 101590541, 83719840, 977152789, 709650042, 575362303, 307855704, 77357477, 610917725, 853784556, 409769763, 688425169, 694553403, 72220016, 797205908, 66788517, 260866595, 932401554, 203752872, 193139036, 467420496, 729749283, 584610378, 527671803, 727957205, 245633546, 632025342, 920735502, 557276843, 924969320, 340605677, 330847926, 47996667, 793064494, 736993687, 225611288, 244478557, 854779766, 362360085, 759418349, 733188251, 538221383, 448660762, 871173418, 240598910, 215786274, 760597042, 60700231, 806596044, 624922358, 630466360, 335813961, 711671448, 456689342, 645100696, 535803411, 879889379, 560686544, 259267108, 31372850, 796062813, 684016970, 377683193, 661230062, 830662721, 705732116, 62945837, 600536908, 597946894, 927950447, 876691937, 261805040, 189383874, 449922641, 483359279, 52253209, 738598627, 953911355, 168726638, 418327304, 328484284, 72834778, 114789762, 731443783, 408933507, 801373547, 974792662, 944106675, 108116044, 21450059, 489125130, 662554883, 957314483, 307265563, 941592268, 66519929, 5097001, 155694929, 394423296, 602258804, 358457416, 497241172, 762750975, 122869199, 144601009, 733833079, 338957413, 810309414, 343633542, 152493084, 840033664, 369424927, 258443383, 767739516, 609758912, 656485289, 349831908, 320666402, 488263963, 397645147, 674279528, 345786229, 497318741, 627642439, 326773516, 400075029, 290011542, 927647629, 807755675, 315575269, 185830758, 497852588, 76652244, 47280101, 296818780, 862797509, 877913079, 678171413, 180130241, 286072329, 657115572, 859761768, 293601414, 557954823, 163303488, 343212444, 187854364, 75643768, 402108432, 438217710, 783037278, 930894628, 352444555, 483693425, 218718226, 704546156, 700586403, 335647971, 891253120, 509855830, 245224334, 559884358, 37386998, 799354826, 296899766, 778286016, 531477857, 307671700, 803473098, 966546896, 172796612, 210671818, 835447509, 275952121, 33357674, 629719656, 408809501, 930889738, 911044490, 583332228, 771624519, 671295344, 520764485, 50031514, 378838793, 426748224, 676363325, 519993981, 3495139, 374476060, 113738001, 467866381, 545769012, 414795869, 69005829, 789772844, 900291806, 964666528, 691977970, 195224267, 574522310, 255272579, 938151519, 191479402, 176045687, 436813479, 449440601, 166534938, 725740864, 446687690, 300358066, 988097390, 412186975, 765007887, 346608247, 652592048, 841964769, 118949129, 150325214, 596566863, 342819611, 298315869, 266464827, 616993008, 447012690, 78698846, 662624366, 954395726, 304717441, 46967251, 175530886, 389041333, 247786195, 8039987, 782316139, 158947844, 452210371, 797924827, 521640907, 191806876, 99105091, 956832692, 132390522, 541298400, 355531725, 178333861, 899503216, 832326518, 171597925, 227154420, 99957257, 909552625, 500614465, 734842226, 216345759, 902319643, 389394043, 922757613, 575434061, 755583538, 251448903, 569011548, 128795961, 868330100, 130916092, 531897322, 973092814, 226948352, 705596911, 626101651, 84470257, 751557650, 162238137, 21614334, 709726021, 321535591, 666576958, 712593436, 53675442, 255238273, 999026273, 444600876, 855760867, 146486765, 507399200, 550168777, 820532155, 777776264, 433319026, 511187151, 317529502, 363720694, 940180814, 470639064, 750784357, 63631599, 577546480, 941222013, 398369449, 298655055, 555309987, 474650496, 86097465, 84142596, 62461141, 977847963, 261857490, 490846531, 929039952, 980417683, 169125842, 465221360, 487597527, 107217220, 442015862, 490637841, 414897159, 845777779, 788544174, 555605341, 28684835, 635372115, 224267866, 537846971, 375559117, 975023604, 792956204, 101407949, 10427133, 25621536, 293871820, 871814616, 363245648, 171999514, 79406076, 963030226, 208557307, 414507487, 364526575, 950170759, 579383609, 208870509, 761595343, 970335246, 949438400, 618255618, 115950665, 862842120, 236700832, 892368779, 14998805, 508894872, 607579070, 143942217, 239587828, 924022451, 844715805, 93756169, 123650356, 426375244, 80942001, 951427560, 322926419, 158169298, 661849585, 484974336, 892734765, 60193043, 987850653, 936400586, 863943729, 649271742, 318455983, 443045080, 257861780, 53137110, 358713019, 942322468, 48278806, 882784285, 390410716, 395742452, 139467825, 251658737, 190343495, 630912837, 477158305, 226777091, 863372534, 515084324, 343992339, 986580941, 679039279, 432890517, 911410222, 512128749, 80576528, 601173486, 990021342, 480485208, 447305155, 176052705, 248944936, 264300989, 138245512, 959141617, 911580987, 415924049, 430310037, 177416107, 925088821, 587272388, 598666021, 716908803, 548636475, 100784980, 1360642, 701772538, 91940096, 769623680, 808140042, 715576039, 287489602, 565872856, 491856660, 661741083, 792103600, 892788570, 913818859, 31939145, 869080704, 293627945, 311447201, 193045262, 511273038, 556197070, 827879882, 506757073, 794924379, 550915210, 204691644, 690853225, 680320770, 39263222, 519710790, 180180329, 525065133, 548735228, 240848482, 203926056, 378505017, 158753830, 899965844, 566139648, 75689811, 267006903, 860137262, 471146097, 728704923, 722668892, 613277159, 691674566, 358635614, 789551951, 196882476, 480643314, 98696420, 646212428, 774096064, 414021463, 876970663, 235968364, 134540986, 63409177, 944043711, 619743501, 176118317, 45636217, 945728036, 626554828, 741940503, 695000496, 746868513, 21410563, 521015298, 851426751, 921132461, 21233523, 616674449, 90052620, 742143095, 302839176, 261347983, 466590804, 487774901, 49507144, 29524878, 22576918, 658162149, 254176722, 28788889, 492712236, 690234074, 281839324, 252809125, 430264624, 987918618, 11759088, 647087817, 265665089, 553528192, 169623267, 726531699, 247522209, 113152055, 437113956, 840984215, 753516135, 33521160, 417339403, 198254239, 679398331, 161676816, 680082825, 798339002, 713502787, 27400223, 220506525, 765047266, 603333799, 439594319, 269504100, 437821176, 4744650, 458965340, 244066099, 349818570, 614198838, 694173416, 186291246, 446761876, 806004558, 285930304, 464445146, 5280583, 637358156, 325222713, 993153448, 486209402, 385718185, 412422969, 607684139, 398460432, 370593545, 652971311, 34087627, 321262702, 715008822, 305239873, 99943857, 764982473, 34512300, 942076793, 558572452, 672667703, 436067940, 259479618, 736694571, 354404164, 239225809, 42007999, 58994502, 895405824, 570386049, 429352869, 32337586, 242757997, 547916848, 745931601, 337707821, 208831078, 954974090, 540567764, 370939032, 489262867, 641504441, 339088240, 139570138, 39975788, 389628869, 125545867, 631754717, 890086554, 255747877, 650581271, 848559023, 452416215, 573960961, 98374328, 616815509, 570074633, 163432936, 942333497, 873839258, 590925840, 889240704, 663174950, 675030995, 912886134, 774390409, 991836496, 240524428, 976949668, 640347945, 228353721, 735764927, 906787542, 639435973, 292962323, 248110421, 996966944, 973948916, 797434391, 898396612, 117197721, 961021201, 109217385, 569560969, 744482972, 550397446, 767214476, 242987413, 545485642, 559573786, 149513145, 844308837, 508766101, 788799181, 184147523, 226810346, 906256594, 655942795, 660447554, 905784792, 143272613, 59383058, 927852109, 216128762, 992102683, 820241999, 658439964, 283003184, 472607579, 696248562, 192982615, 542982395, 333517594, 89064946, 205922804, 268482853, 536584227, 412311207, 844163669, 463127743, 810726504, 595979237, 936739912, 496692821, 820537859, 504124126, 112724907, 392919504, 493344137, 537437725, 830032626, 196794722, 325985940, 400169727, 963700162, 718161562, 945350947, 78243112, 358538046, 479942671, 844378066, 576482595, 348138220, 490269139, 291306234, 648977504, 614041752, 811861866, 276655926, 84683425, 9872728, 818869778, 654412484, 896457787, 993726563, 89172553, 109553905, 281594303, 675432339, 291770361, 823475788, 358402538, 564991594, 535404474, 66170677, 342135077, 921755468, 285196994, 964385554, 587531250, 103695727, 334205577, 653446002, 914069467, 399807887, 475615329, 869544699, 102427048, 578510078, 362535288, 916633854, 829786751, 553272719, 699124170, 971248204, 942527502, 138998869, 16697140, 274930311, 334162476, 821108767, 663073812, 548675721, 173279238, 414163860, 146782856, 683813539, 109802674, 466484008, 148103876, 822370652, 613895230, 372233656, 66006756, 776227153, 955198845, 945501511, 609374615, 578464074, 197110206, 282974132, 669559480, 201371970, 202771568, 835117429, 556162787, 280127469, 742675046, 987797007, 906426621, 114624814, 289255121, 717260982, 572312822, 213346284, 512857493, 101887994, 929776574, 417081284, 760604937, 25245704, 333903036, 534598389, 62349129, 997399282, 712748471, 107964553, 710673175, 633831352, 30991380, 562108843, 620391674, 318272909, 979299146, 638709396, 681824248, 107582055, 42690860, 796078757, 624944489, 137138067, 21429297, 65739453, 596675190, 938917765, 549074731, 322527878, 591409889, 530593627, 3233756, 993745468, 70658604, 47157338, 985268155, 809040126, 391865965, 711351994, 166543387, 850948374, 735251309, 212986498, 190214438, 427699196, 670020912, 773428060, 778892559, 441147728, 590741746, 789633575, 943957243, 226223189, 520449200, 94762146, 396224766, 611776090, 973656532, 896242924, 281474435, 411275503, 964910705, 135493990, 675451088, 475728430, 74324318, 734527035, 957258534, 837121771, 127232386, 864693233, 756765070, 95474702, 905858850, 908740332, 794651537, 557876024, 396954218, 516096802, 54294518, 314213414, 832577329, 821016050, 590929501, 707214626, 475951878, 649166863, 662434178, 946628182, 545753919, 395420340, 892541196, 843546720, 183214569, 844365892, 405269996, 586787735, 199832190, 339925140, 743754755, 175359978, 807411017, 472098930, 191783827, 139644589, 989233827, 423436247, 135553528, 67817095, 955539991, 142049747, 958280088, 892121313, 382874392, 843526040, 646204734, 838406095, 125886195, 835354160, 611056074, 20277058, 916900413, 95073607, 91706156, 56661273, 777205695, 57628648, 521472447, 89576783, 769504764, 479674237, 959125512, 582386946, 455134902, 475983185, 925046077, 570130399, 828138542, 673621312, 979008660, 245841334, 524285539, 63083853, 122972279, 517440461, 509045925, 607908327, 397355730, 435804121, 205209039, 788956944, 582125018, 68505287, 104458505, 796082491, 462165163, 635497168, 599015235, 658468061, 220023930, 527907350, 657493801, 951012477, 848379362, 694927138, 193561733, 207068396, 82841902, 431783232, 514744392, 482852030, 795903127, 483831377, 995268437, 932292539, 441045059, 627981010, 405270732, 969426093, 806676502, 681191977, 219260770, 146867010, 651522346, 918151466, 163459986, 209046723, 294167673, 20656886, 136024234, 248724041, 513954735, 18523425, 541208146, 138990551, 438394793, 740462818, 234090294, 67165148, 333986232, 169630604, 719507281, 141649031, 319504367, 429741624, 287495023, 682055468, 160080299, 446366391, 379436198, 550303749, 782220533, 449038322, 112590394, 377047262, 533287253, 178809306, 758480831, 857665363, 122572198, 258004556, 62600360, 570404798, 486793511, 430960042, 493609311, 576530434, 409298454, 506342044, 279683401, 432597028, 737583969, 292331899, 414874901, 17791373, 772342548, 271727273, 129588661, 231399211, 626911524, 752228090, 752142604, 855024380, 546064805, 46887099, 870826243, 652502861, 977278858, 861756603, 160505917, 61430665, 326133433, 333449822, 47729688, 35727176, 189129278, 681205228, 986865710, 429437026, 41511090, 701621983, 410134708, 236971117, 868487644, 370509166, 554213, 470400394, 350122292, 673596418, 667228045, 316663976, 41060166, 414393937, 145297422, 924297278, 581743819, 617214286, 303843368, 691486036, 757560471, 757896034, 734605914, 68857053, 108646450, 764269819, 595166708, 220201725, 429664839, 548992493, 129079339, 928102866, 329945971, 934133719, 761764028, 388349404, 181856361, 699211096, 658436823, 427540768, 547662599, 617189756, 409757696, 241400767, 813900709, 655699415, 232413167, 437200344, 51401860, 32418709, 962967503, 630104596, 668131824, 546693127, 664551074, 534313626, 797005093, 523130070, 399515167, 756805421, 34011328, 481448069, 218895618, 169381967, 46409704, 901221443, 58039177, 549038300, 850513822, 56412086, 153831963, 866557863, 931191310, 517396245, 181846737, 466416566, 338465356, 796007632, 106455364, 946888009, 209014308, 707168651, 792575330, 629032591, 47679025, 781050678, 785238256, 538227052, 879896701, 217738180, 253791662, 762480753, 245171464, 764389591, 581681047, 322774705, 532917132, 753105093, 523444661, 784550086, 514467220, 791403971, 748642117, 181365974, 285304377, 482293796, 485620001, 661613529, 38031373, 775544608, 400144092, 909646689, 350968829, 259695447, 982760545, 866241139, 195514397, 488483995, 187311896, 339711676, 407783899, 594241761, 124421259, 414434293, 64532841, 283930340, 259017000, 629345386, 429048613, 861396670, 52093281, 283315268, 566284094, 162693184, 894535913, 102572532, 412464548, 64340553, 444790164, 495934924, 291440732, 395190591, 362763309, 659084356, 496590537, 116168631, 499595410, 822786921, 776895452, 295659896, 711357438, 203034752, 210997314, 986996638, 835426215, 822546507, 607319635, 667217741, 134968777, 286085633, 85731221, 984038956, 497614036, 67271738, 778532607, 57587601, 325091295, 918229246, 254341073, 410106517, 221380912, 858897593, 396143816, 678019342, 532432907, 697726239, 814259538, 470748205, 472060620, 887644791, 465487578, 781513287, 861973178, 330667380, 968406761, 886167965, 655525741, 236767716, 841059139, 83460858, 574915894, 83215115, 285579099, 966143268, 349189915, 165809005, 686915461, 82616313, 535327480, 364181228, 568286123, 140516566, 405076261, 485975280, 478648035, 882490062, 458303931, 404344913, 918495967, 641734934, 416634675, 840697065, 770214117, 345266311, 27825129, 360051847, 844919370, 49329882, 152228674, 323900221, 812060857, 868689092, 648827261, 132048981, 617668731, 354941562, 262946086, 253013815, 985413146, 527325542, 977031523, 692392895, 716954394, 269682980, 29885737, 611226974, 362619996, 432470285, 832235890, 362850712, 735475653, 234553226, 385704178, 576721725, 327797236, 748477529, 828150335, 363237269, 922194458, 793222160, 25127531, 310015557, 170406870, 907068535, 691338751, 114443775, 243987125, 836803451, 380375131, 918071256, 381460544, 627092272, 692731270, 144704260, 424303728, 364116871, 91821839, 827560282, 736655586, 376119809, 101361319, 156129810, 738058943, 634014753, 334432797, 143231237, 949154115, 144982224, 461925839, 291519093, 207917570, 843812429, 140119881, 575138008, 203132566, 447498151, 813378965, 385959157, 930673607, 570660541, 911755371, 858516720, 50115346, 84141585, 573920561, 379888947, 354724023, 519370296, 29047331, 338621591, 29568153, 597735719, 517175593, 736507199, 658794388, 654712995, 991098528, 107006615, 17648380, 992503858, 217747928, 873691135, 293371553, 548146832, 171170996, 966365006, 630645616, 642730119, 143960617, 280548936, 422368953, 619863741, 781404210, 285788577, 247238699, 331708623, 781111623, 594465235, 753088368, 442274175, 532116405, 395470522, 175374821, 586200984, 152417, 368532033, 560180092, 471867437, 688304610, 311729665, 453489050, 224198859, 629715442, 640403913, 408572993, 23549672, 110443535, 159406232, 897534699, 566112520, 882466928, 377270395, 318711675, 532817937, 985651527, 36712644, 263540646, 231945293, 139947589, 956478600, 346047033, 489552446, 555117442, 182094002, 678024655, 905324864, 886784440, 615060709, 394122571, 970266596, 37807338, 746961967, 390762139, 658848670, 82730646, 202681303, 648282461, 528215612, 10834436, 58018821, 668585065, 581591138, 808447740, 741483838, 705164819, 346004504, 966425610, 853763212, 721332480, 786095311, 84525197, 577843076, 404270476, 131154127, 727873172, 140215663, 292131725, 871031024, 306607222, 579313905, 520919305, 391692432, 558066587, 554389086, 141922006, 996895268, 164874220, 28024679, 196794922, 252525066, 194179895, 138700553, 20889534, 379152171, 885551078, 477547057, 877285267, 379340455, 163351116, 508240221, 232990254, 786451117, 237222858, 856528542, 930702212, 695787935, 357386028, 822549455, 145329061, 45005207, 775593544, 753622910, 259410350, 589261453, 847316010, 620351598, 98719215, 147409713, 885845418, 92953141, 475839332, 159613629, 464766512, 141470204, 137312810, 667478440, 364945614, 287148673, 584287504, 588440736, 846393647, 9219100, 288807033, 878235360, 645610631, 47959639, 257850963, 740814617, 36772026, 848432008, 646822939, 21016696, 807562957, 809930489, 365855088, 701137265, 591909064, 19103895, 319259713, 833679767, 161838233, 865807068, 710691362, 793688657, 633677347, 381566054, 575291253, 71316601, 408850303, 98175469, 821963379, 755604397, 212685248, 587770765, 736087695, 580478, 107767146, 995989274, 823421982, 905422028, 746333621, 374948811, 579280526, 657012595, 102470687, 726643469, 430339080, 374557723, 620014453, 268453628, 205587738, 930967710, 327385548, 504767594, 419639950, 259849838, 963794464, 959140873, 48000450, 525636415, 729501724, 930113726, 728566788, 539562667, 381405949, 469020161, 864975000, 522822393, 288663983, 989832967, 95985815, 129702497, 456863339, 714200460, 968164439, 169125100, 244725327, 832881689, 17159390, 449904665, 45147252, 226795721, 211058741, 202407387, 204194050, 977905600, 79599177, 782783756, 384318079, 171985481, 139879128, 798527139, 880851700, 748586792, 267748183, 234003478, 749092732, 723206164, 951005948, 368285423, 559733911, 908684668, 216264560, 420237196, 812611456, 960054909, 527571108, 886143236, 7071774, 8693149, 556057369, 607272322, 64810080, 470068144, 999094416, 429556180, 375423988, 565508167, 249842334, 914225126, 998922392, 179382442, 651434100, 146257214, 476772787, 712319663, 543482020, 386083325, 769999020, 180390862, 547079712, 52090884, 347244102, 957962067, 71488402, 948646343, 140068618, 680621552, 263034404, 375439472, 245140382, 810911244, 195994597, 271140265, 82859249, 963829027, 315219347, 946948192, 864767856, 464604234, 532706650, 261106510, 258504307, 932444514, 477485250, 873354886, 496623653, 760225738, 202255800, 154389741, 165065744, 590914440, 258385392, 150884991, 388815091, 711215884, 518167916, 692415650, 226175509, 323976120, 991939798, 865078889, 35642452, 411940880, 821875692, 381212242, 290232459, 490904944, 1407450, 406040276, 44280683, 133159237, 823164318, 992564108, 732308872, 470326020, 339763872, 913821955, 548349723, 678154625, 268532189, 220015664, 725750823, 380111283, 511300692, 780426346, 557132367, 836001182, 258436698, 390620164, 698314426, 433911590, 980796204, 811639663, 904325998, 474866276, 193780677, 625592141, 133913770, 929976234, 806383656, 93143164, 640355342, 171092491, 965896329, 388447804, 162673613, 719270371, 717758441, 29596570, 38452581, 593670998, 964153563, 146746491, 100445421, 133455962, 504849557, 227981878, 874459098, 861932652, 541348621, 168298263, 259585208, 87622990, 142156701, 448313407, 819392568, 11015933, 445991876, 93719616, 207395266, 464616412, 506721764, 983172656, 957967010, 774377459, 873416260, 414455526, 149461371, 289135835, 969272078, 999153117, 33484815, 974147073, 708261260, 187645423, 183963679, 914787523, 182679185, 337239552, 884568484, 324686496, 74027437, 737626465, 201780011, 35992320, 390327235, 795430768, 477781806, 889359984, 158011524, 771965315, 297672083, 985076039, 516521494, 907085004, 681232237, 818780629, 64017726, 432834742, 699237263, 168658277, 165669909, 356349048, 519750621, 214959054, 919076869, 687944029, 616710851, 278979387, 149613383, 99793501, 755177718, 396901934, 100119662, 780561105, 797031113, 507049993, 495464558, 282454406, 152909509, 733514454, 985614474, 660762402, 27500159, 780364676, 768843061, 962895763, 649634485, 894881667, 592687037, 492516522, 257947425, 188608335, 15482077, 769985813, 628568831, 301845929, 105554984, 530965215, 25764774, 482114743, 503646604, 843289064, 548178385, 955893424, 193993778, 155860988, 749696062, 887276489, 821672800, 201541544, 669479234, 342706050, 647517849, 77012944, 933164138, 372028747, 782725787, 662102275, 312842957, 457045723, 433573021, 304935158, 676772342, 708042406, 655590214, 29853011, 32162283, 651767331, 998382698, 44443900, 24031345, 342412328, 611475445, 388103168, 469618966, 226620018, 653400068, 918372100, 161637964, 273339154, 142434231, 540371819, 377943543, 602150005, 920403289, 78714989, 721606356, 237103604, 960755316, 771875217, 91531079, 758207026, 978770602, 647351805, 715241347, 787980764, 997359648, 923257810, 292631362, 341535664, 488107851, 794616143, 728023909, 679711176, 780857726, 931302714, 473906615, 211181369, 754408236, 767462075, 647290531, 598340187, 616824632, 245769265, 845344735, 775669233, 374848171, 298297997, 423098154, 868845880, 856598761, 225584755, 8570440, 115955611, 201324294, 540093180, 742042471, 695013982, 968624021, 742365406, 322616198, 420163284, 214555766, 224202494, 921259815, 413504961, 665404002, 502136909, 13996735, 427311614, 920364096, 352518400, 589254396, 797690558, 177046280, 796621248, 260896726, 537538480, 497958290, 989434996, 355495362, 5340975, 871419512, 348688467, 426306852, 543898606, 651456475, 448477062, 993085100, 31518167, 190169837, 602200899, 343074105, 227197018, 744661193, 199005193, 766934459, 988287532, 31273888, 106016487, 244664570, 196387891, 160224405, 281702326, 770078002, 783476714, 642643109, 328678605, 759141258, 101318181, 87571847, 232063176, 182385447, 129002617, 979543059, 116496592, 128561, 482548962, 226534041, 438037963, 632226951, 24187818, 711401956, 474963112, 151054121, 984513973, 96193316, 438539945, 20162629, 43325507, 274399939, 242201168, 185404073, 856419802, 985479083, 649367315, 113903647, 143447188, 727474955, 922772425, 431293850, 803780420, 758082715, 589982827, 211962448, 996573593, 876140579, 129116860, 927773370, 723689262, 894529371, 270268935, 174924723, 981834088, 530356675, 726115753, 239491265, 944622696, 252493658, 752325157, 170041767, 685787489, 304713645, 890177555, 712490271, 617680751, 523191657, 154594845, 876802622, 906702277, 470015673, 696240949, 928184447, 865493930, 355182458, 949876846, 635076645, 236746189, 461056925, 927674547, 862304461, 649393501, 402433306, 661640704, 231525170, 69840319, 675435537, 428490294, 926838401, 118485557, 582973756, 251524547, 994846897, 565322655, 422368073, 913980181, 946253730, 37141569, 303728194, 475970097, 747563796, 172946131, 963519182, 816526251, 247891336, 781524009, 437478984, 96665565, 364420912, 233297432, 801352528, 244855289, 991160613, 356869442, 131022908, 241723606, 781182096, 556634802, 80995046, 604677312, 639095775, 757617301, 747860744, 753667841, 309525322, 933265133, 485064810, 945096549, 913767132, 904255918, 899731535, 355540663, 721242881, 538098432, 256116225, 955561262, 343537452, 601949399, 344562064, 911127107, 282282333, 950656441, 404189206, 613865780, 152494926, 616201849, 729539347, 520075874, 553833551, 197550917, 353354682, 519527221, 661564796, 487798375, 552228187, 498432002, 319224056, 932904021, 971564071, 492944704, 768020464, 31116079, 325113081, 151209112, 942045199, 133354522, 526240205, 228641343, 541211746, 883299384, 484408871, 248464256, 41403665, 5592738, 590693383, 747116270, 854609159, 318044830, 882937258, 106331281, 771758496, 110293201, 551411611, 387843995, 810586929, 525155659, 603450933, 33824165, 214189884, 402398660, 260691938, 986575425, 492864974, 93895333, 507148147, 927013965, 748358555, 426943766, 849982494, 809884284, 653242951, 210629373, 461991386, 716219801, 808479312, 159399692, 413422871, 820785810, 999644153, 22300008, 203057624, 584341278, 117474133, 952413699, 464112417, 232724431, 926832080, 237403522, 130622039, 440172749, 845626328, 842291708, 689762911, 878667469, 765010167, 856992353, 319997564, 193202303, 347966783, 412781083, 497760063, 840676384, 775522703, 129386558, 213058334, 290387644, 318626469, 767012993, 419674953, 904591856, 753563270, 990323755, 83915961, 560827309, 691331824, 677711252, 469174786, 892641208, 549513336, 528245776, 924472810, 324477857, 348530289, 326263792, 249750577, 713161089, 897443099, 348724675, 208501362, 820614770, 851851623, 67265263, 416226234, 990089476, 412698872, 115617605, 949706213, 429408820, 899850607, 893010431, 782878034, 873321419, 430624273, 575962955, 925804707, 945817735, 141151777, 490234108, 739029818, 592836938, 857398879, 945635573, 309492931, 253153513, 1547157, 229732008, 933931849, 40496034, 644163648, 4973039, 351139662, 579348848, 900665097, 752606202, 20005639, 596139061, 510909576, 698312956, 411000142, 946018577, 128361769, 597947667, 873272315, 742023170, 256000771, 898987967, 849958295, 479625204, 199255169, 62090864, 568259375, 805423645, 369587798, 765634156, 186518455, 588529472, 925595762, 296786227, 163959932, 846987714, 145199359, 615230932, 442785622, 505545881, 722615141, 111046529, 872615462, 735388462, 807640035, 80747728, 650899878, 576640043, 734117891, 191899654, 957687339, 637125769, 401648559, 835670338, 342383928, 126111708, 247344650, 613820530, 708265162, 674031201, 960845389, 895318125, 646712201, 67586599, 628534531, 653081507, 240569376, 278929289, 819015653, 441470893, 441022352, 205666890, 82758357, 239421893, 19470622, 771460950, 15221807, 150306519, 902483852, 212175181, 133050532, 915217063, 20256946, 151983242, 126342818, 247516029, 398222792, 107566022, 527301453, 388507665, 621112232, 838168846, 709634957, 782260177, 882391882, 390639657, 857485359, 819763177, 307810943, 674320302, 673812244, 720146515, 695310336, 963312041, 704950977, 976779264, 409419826, 72221616, 201244527, 636768114, 203260720, 181153571, 632581751, 214142639, 406926819, 356703939, 513658605, 921768691, 68596680, 867438491, 687455210, 49675410, 992451208, 924861807, 333603494, 152549153, 802464894, 898795947, 150012056, 17242861, 75869438, 872422976, 302754664, 625122900, 725118563, 239107644, 97948576, 324475840, 410532790, 318917498, 970568114, 970105842, 753033718, 746992037, 482247597, 77270570, 887076573, 921075296, 433717297, 106527411, 10739840, 206322890, 505429606, 478687641, 793624192, 263657991, 934916082, 186144654, 68748866, 241174410, 338108163, 446531893, 78204403, 720735355, 785197721, 153840116, 647606065, 786779061, 82975732, 723169747, 942251794, 979547998, 800490452, 882253173, 926368676, 464365593, 503529597, 269160289, 253072388, 933130720, 935042861, 669545896, 140679259, 840377112, 364820494, 948656047, 508778319, 112774137, 686515534, 220796696, 790569820, 742819023, 631107300, 427275150, 753084268, 874910684, 595237650, 528845997, 369040243, 706701018, 751469831, 913815395, 793231092, 924516957, 964955140, 665535247, 73659304, 873769471, 52205546, 75640183, 424002834, 461425154, 342850683, 116718400, 410867861, 672839199, 766571630, 70576832, 389510974, 259238905, 142675419, 153860144, 592851505, 474680094, 728299931, 445174852, 190353462, 464543665, 987730938, 614046575, 231549505, 583690380, 9933570, 323587044, 558456970, 332869583, 570122814, 22943496, 702554138, 652879872, 484456073, 272248327, 199514577, 376328825, 738015364, 675012177, 909870187, 103101547, 605173310, 89922384, 274455393, 405797628, 600324207, 594042935, 138425612, 43250873, 408608355, 694940097, 84849658, 812955840, 295189074, 517165671, 701419514, 564862251, 529848233, 941994112, 105831371, 475631044, 223834261, 105806408, 459662178, 825054625, 209773285, 786110437, 762702130, 759730817, 402679799, 48938152, 198137906, 465166348, 93632897, 430988921, 656003393, 128385429, 206770568, 428883109, 604144377, 220661456, 438792780, 158239216, 6580504, 510214094, 211246417, 573260222, 626631167, 281333966, 503436437, 460377082, 58413167, 12347819, 640293717, 109448781, 351537761, 306646746, 907837507, 695463339, 640571747, 310942116, 162238985, 30472074, 625689213, 335394722, 988168357, 682665352, 512115735, 403233154, 749249794, 900653479, 3452698, 868809752, 343551795, 346866168, 515619623, 604017427, 745066806, 251827794, 832820755, 472988113, 749031577, 371127861, 541630462, 477288269, 965760100, 912186871, 732125972, 185487848, 218191643, 574014185, 277054511, 704782816, 810713342, 379841468, 567781684, 674797674, 820247441, 476769668, 715044029, 629942873, 42125571, 60611504, 792220027, 58775095, 829918081, 973155802, 332491452, 40758347, 318741171, 118423475, 569989085, 898209374, 344165459, 844590039, 244395599, 25707788, 537775694, 155419256, 664987795, 467801088, 334918894, 592626070, 167521021, 730001938, 324181399, 966325909, 613296675, 346222016, 957914852, 935119884, 36949473, 236641462, 574148442, 804788011, 250692110, 377840536, 969264937, 283116909, 99131678, 82884640, 545029275, 142064796, 288458490, 924747178, 385944163, 647328030, 201253059, 686635351, 758264065, 111797593, 469154286, 576509221, 99840491, 479542317, 203878465, 484553666, 364287254, 628541923, 300604552, 431730287, 892288970, 69659510, 992028380, 851301748, 509394386, 956346697, 953565075, 769708515, 624929033, 345409752, 254977344, 336724172, 868498283, 9949625, 95371944, 408889855, 5678294, 191874068, 637841315, 985170412, 294958063, 830012695, 232134630, 218403841, 698315369, 484287884, 993677609, 145844921, 30948706, 587676842, 307585365, 580388270, 107603577, 968120836, 282099036, 655411329, 116515711, 93432414, 312083228, 161289008, 63585744, 470470743, 380849202, 930719100, 5489334, 94981390, 10561062, 964408361, 843769215, 439437375, 298495329, 87644648, 941229116, 852242870, 846146132, 740201867, 991242706, 141941567, 32155208, 245932014, 493872421, 184989284, 661013745, 834720531, 662501225, 483620847, 173537887, 379485512, 480507486, 147513230, 346989242, 651910831, 682397320, 594012708, 840583128, 163007017, 554507692, 713268846, 801216019, 904389442, 913850110, 346890608, 486114739, 155860142, 106550774, 752865584, 266251270, 199268053, 50992587, 293629146, 219199302, 879664935, 481944718, 298743266, 149110792, 447487771, 513434651, 257670968, 411163484, 815261264, 327151051, 756093827, 383743201, 406158065, 586942438, 598159376, 953338691, 534385885, 984086712, 802539839, 568774155, 375214762, 404939601, 838946562, 348242709, 462038913, 644611046, 938318505, 454134060, 954020577, 721514693, 57876470, 172585251, 511887472, 576346902, 433615102, 161247042, 887650034, 922475829, 194421916, 729192090, 813757337, 422989599, 420725900, 842670193, 147960985, 366360614, 610705331, 529068758, 245979387, 320885595, 113432889, 644312719, 598413453, 397574167, 796753825, 824571152, 108654452, 671993842, 991065482, 83046734, 552664952, 514121778, 752001883, 751575429, 323148925, 195724064, 720807705, 272309867, 984514618, 751692308, 644478119, 918230478, 175857942, 655001231, 16236467, 116756811, 500181354, 505899639, 449526135, 165662046, 569240875, 212718095, 105870719, 242486867, 67358583, 909526625, 99834335, 772116664, 877007375, 29735686, 203850780, 729698656, 88253009, 664537643, 316612469, 66000101, 945949989, 971566713, 465156126, 466327192, 293008335, 830341128, 134138518, 486217140, 377245794, 852696879, 129037433, 837158344, 525789105, 684739031, 177355016, 645971150, 442816701, 672543596, 292724116, 540194570, 11547074, 539373897, 150126100, 140293354, 568442966, 140991611, 75662899, 142206280, 481581217, 591692025, 995944168, 137897969, 509215222, 41020776, 897363613, 103798584, 753157608, 967665616, 802420193, 630521304, 652054498, 746858380, 711937227, 389664413, 187503112, 56452317, 204095613, 934426610, 641436816, 744694860, 585609891, 170572551, 317432791, 622152526, 621950688, 960131307, 826157660, 849118357, 443168948, 267902951, 486843495, 215589771, 763149365, 526585546, 935878217, 815856864, 672421276, 929804616, 809871772, 80043523, 428399960, 598818922, 325429706, 223608652, 9759013, 343303133, 368185047, 324406196, 390477761, 890632197, 203199553, 623062676, 368919943, 61045529, 454665470, 634225351, 78158588, 898248405, 358928066, 150259685, 578365864, 888694896, 563258611, 653822968, 947561908, 21135500, 592209238, 322371934, 853508245, 337978941, 90722259, 396667990, 257316267, 724580684, 30243925, 525344942, 714739789, 459974406, 443576615, 956230120, 436271009, 779304411, 152556296, 348240283, 973455293, 999413787, 11210592, 544646829, 362815541, 147816530, 178165657, 502823960, 543789165, 805195365, 111107490, 67078418, 979178596, 149354512, 460429726, 138259169, 416744287, 689474310, 309998352, 259790010, 953637081, 823828973, 988678409, 757594397, 497917581, 907411875, 948395353, 863635737, 823907791, 636187909, 695076900, 931292149, 531839905, 277979451, 334853349, 188186669, 905097663, 345988140, 935257656, 252588359, 226326749, 856077500, 596265602, 610283051, 865389404, 722733603, 797431808, 525623699, 957281328, 334656148, 615369721, 256426723, 288008514, 227513678, 538561824, 697841587, 575135146, 707275604, 537138449, 604493845, 724105167, 229802032, 813750412, 68269876, 900673652, 670263599, 155633094, 46838459, 883402568, 209404948, 881681136, 121145588, 739631731, 110822163, 271599669, 783006423, 911366472, 836143383, 392192247, 967352177, 625758740, 144768253, 934152605, 831644969, 908978540, 608272398, 432669543, 668315353, 469338027, 777219556, 187592946, 416372276, 710079331, 521957661, 795049265, 523076796, 796922353, 225123564, 739496730, 182723363, 980276893, 896389075, 306908631, 991836041, 949168778, 581264774, 28196686, 672574560, 984281287, 671102670, 85930263, 587975844, 438276274, 978444004, 830112239, 400827027, 375839379, 760099459, 707510358, 999921960, 565034772, 299034700, 984808781, 255682093, 898092530, 445794625, 330780069, 232416841, 946680679, 530353592, 248873953, 905537847, 911648469, 291383340, 568012674, 145028028, 200674859, 371982575, 481955440, 216242895, 331268259, 851546983, 200921198, 384209780, 16639040, 778598266, 844619259, 137976342, 753522419, 742755167, 797403476, 796044063, 970890315, 936954398, 717269069, 783431082, 288786960, 113290666, 40597570, 902518435, 863370083, 319260211, 343121870, 711229445, 62473178, 56750743, 783191352, 387590076, 472277087, 680974383, 168111970, 282422902, 748174994, 209602643, 383062316, 416082822, 136075006, 566065769, 14238990, 411475706, 856631008, 375177358, 412906921, 853588652, 758656110, 484546579, 471885963, 522734932, 30508481, 296086885, 966643845, 591831357, 986668911, 688092229, 650257349, 439473748, 79903910, 3383775, 397266767, 379292585, 692250305, 73969434, 460590391, 486381233, 365512890, 679538200, 786192934, 407269657, 56976890, 473135234, 405307531, 956613804, 339070052, 481321007, 849366262, 515836252, 980737501, 381164233, 927520607, 606039556, 807810287, 684031068, 780771359, 900522437, 14488558, 861806889, 618495260, 558208064, 550775679, 461889668, 210963444, 160136524, 267582451, 611178150, 644681440, 82541707, 736678950, 193691444, 346929459, 895742054, 97478023, 805688501, 616563045, 288186568, 434196948, 666624414, 69285982, 354760546, 892604100, 88636388, 971813263, 702577602, 481916444, 726328334, 195113551, 484483591, 18047906, 527834471, 535706315, 981551641, 767094355, 382574314, 866727221, 746880109, 970317088, 959274053, 607223014, 258228015, 308781943, 167072260, 916002421, 304563939, 950303943, 699472785, 926671262, 885607874, 146885986, 159894085, 644343615, 802467284, 970871865, 3830987, 474108768, 234076817, 224790923, 302706292, 369259016, 77160329, 43750306, 532826086, 321758865, 938156922, 517675134, 408891506, 746545810, 509988080, 964518252, 961223791, 795156390, 978549271, 613162120, 250441867, 498940954, 652120594, 474029164, 366646277, 454985608, 4927120, 513372127, 252506289, 908085742, 658232871, 883462664, 348903282, 280628660, 297054171, 195136370, 564032366, 679003884, 60246184, 447110921, 715841910, 166043546, 516101629, 554216535, 59074950, 573138386, 293032144, 796098780, 49510914, 970209917, 877131302, 468020549, 693778350, 281293615, 695155013, 254342913, 317870606, 545168751, 611777514, 880952105, 119653122, 225337995, 930213346, 407292240, 488502578, 250869921, 272543839, 782712648, 2539727, 767597735, 932719970, 61318529, 86197349, 357874217, 819074971, 692609906, 895672582, 872731152, 902821830, 468183863, 105556474, 788163177, 74040927, 584166410, 507186554, 586760479, 984317772, 848970391, 494991454, 103973691, 124459131, 542945782, 416349179, 57055850, 51435631, 821351089, 455916754, 97530894, 822904638, 837199972, 666554337, 534811072, 321872633, 890548518, 11863822, 372375609, 814615862, 363510693, 513612892, 105628682, 652519540, 905495481, 160849493, 815442645, 94521492, 688813315, 990169761, 897526458, 192702916, 545276715, 486499885, 126423804, 624529028, 323106268, 276749589, 962857882, 381780674, 698203794, 162175158, 159714067, 818405866, 668567189, 476524533, 202447466, 311107450, 156900763, 689950779, 20656092, 339691020, 113068666, 167502445, 695720155, 185850363, 789477515, 931162747, 303664693, 77025847, 344441308, 14877792, 385943945, 469748289, 683586939, 839374405, 876832150, 74569086, 893293476, 572614078, 793642020, 897575861, 370638568, 576605872, 25549689, 767026165, 565371158, 204487247, 536454481, 195101049, 468532037, 672111571, 678584331, 568417029, 46367774, 269547958, 754866196, 951341167, 274328187, 172351686, 150208757, 142041474, 339264452, 294374676, 875898254, 730125966, 190644337, 641319707, 627640261, 921575483, 859923718, 770291741, 907371322, 567569906, 580454954, 814781907, 581784593, 319064536, 833123845, 952284081, 956124100, 184313832, 504432849, 367679281, 237791530, 714215107, 821263811, 284889452, 407847974, 370287771, 979595281, 291874097, 33812799, 221816765, 197877247, 455971066, 161344765, 365895393, 428613799, 640143061, 950413162, 220976528, 440223551, 913196166, 347892614, 633273256, 333048562, 578708157, 290695892, 198193541, 571275802, 518739863, 88253040, 71801888, 521626454, 42914740, 888850468, 400510217, 786811386, 505265937, 665414124, 116699090, 470277048, 423127613, 503364274, 776163351, 533319336, 913964215, 866110575, 774646494, 16064348, 265413255, 808265649, 379190526, 320274251, 670565942, 396084515, 916068558, 726835715, 457006600, 735764585, 861261541, 320494234, 813814862, 677272000, 466981749, 262726316, 554292563, 775172137, 286155026, 814824205, 992637032, 823520839, 996863918, 389937061, 234112346, 667440617, 207657643, 730929816, 601066343, 8043049, 96776870, 535048600, 912949322, 66390809, 65708312, 624482061, 52164257, 321842970, 255484174, 703195203, 398561472, 163487784, 851549688, 864873121, 480656507, 582845302, 813752889, 357767936, 493924769, 353084239, 927202229, 952705477, 7853379, 112043541, 110606753, 400638346, 518274109, 528240095, 225432705, 774180833, 984780578, 240180588, 76630252, 389874718, 54548500, 780135211, 987547183, 243802733, 172254023, 763165411, 392533180, 857985665, 196588010, 471076833, 789666335, 221845544, 732550253, 351562812, 590119415, 640146665, 791588949, 769755945, 325742953, 934210620, 662458572, 114524747, 425022854, 364692970, 714124086, 731159034, 899655345, 292521457, 851972293, 417715961, 642114140, 639251887, 107132869, 711704332, 570289469, 461763970, 421554140, 346906711, 929858781, 110509316, 500620643, 836093027, 62468449, 985247871, 511144896, 445059516, 295208034, 781351980, 315449395, 695850883, 402604029, 370348843, 571957250, 989985850, 105765090, 999943481, 709179748, 888037139, 917558103, 755584065, 134672592, 507289272, 910302404, 924858728, 188942378, 204027363, 282215419, 792613802, 417863021, 121969847, 710279246, 4595801, 755546478, 194635665, 187952915, 477923366, 941362653, 601581443, 485140183, 954732979, 285060378, 66506243, 733238641, 177856708, 373405843, 56845826, 121887298, 564819833, 658346435, 633919404, 417508033, 92056398, 842781271, 640832819, 298273277, 634463180, 556589452, 176538960, 687817959, 224004893, 447513643, 513177950, 172406076, 331715239, 187371872, 969055207, 953700548, 291718649, 20007529, 330540310, 391890088, 436380265, 106618311, 998141293, 256173877, 396366450, 789594887, 47204550, 385254091, 668527107, 81179671, 521946650, 960137809, 776442597, 41926497, 513667614, 26901795, 705482055, 175170223, 283977813, 633207380, 794793607, 619889671, 200499146, 451008284, 697063230, 825695717, 336198777, 457308077, 606769822, 346987973, 875104643, 884912912, 826161877, 256859770, 543132074, 675171473, 4739853, 190257080, 157922704, 864728094, 44007573, 608360831, 7466474, 352718365, 943318553, 758534786, 48806909, 300430354, 173931995, 315730619, 305359694, 188789515, 939367072, 506551009, 188661179, 196267266, 957548666, 603516395, 214804842, 65823341, 838488430, 42422448, 746683808, 841657371, 938619448, 678237037, 331354703, 775990532, 361829042, 56790237, 357811161, 165511975, 298209833, 602092199, 32412939, 226304135, 661772890, 168017618, 713741860, 225667866, 610869548, 787916132, 380708460, 272196490, 519375613, 773882438, 564468199, 243380107, 545273073, 585088210, 559560448, 481530538, 985479790, 670297634, 636216263, 733320158, 630331372, 868287059, 979740184, 228039970, 412660602, 29318342, 866259411, 826872522, 673815948, 152994720, 647586182, 275597016, 223691333, 813004665, 33338985, 26336380, 196752943, 170710146, 651212992, 572898906, 728188377, 273206207, 229366571, 773786958, 608059578, 737469530, 573325586, 157967581, 325378149, 89657791, 306578902, 26267739, 59951323, 162264743, 811793158, 218955036, 234728613, 978350689, 502391283, 414627632, 581004719, 481964463, 503177588, 623273958, 515762524, 958665856, 745016337, 938670822, 929901708, 857841141, 991965995, 132872714, 967027058, 926329257, 882206291, 225518800, 632873974, 846108341, 734869866, 79216024, 884719299, 425766286, 880723767, 852565045, 959043655, 806086733, 747464827, 860269158, 761449231, 163169121, 397503104, 552652012, 427368098, 294532438, 398398092, 859757078, 552900516, 656727606, 715922442, 800253083, 289492800, 803788544, 513912199, 858627066, 66494801, 648416182, 744359800, 780975456, 377020429, 234406108, 566852064, 775085555, 463026963, 712124099, 230763957, 705501257, 200807935, 655174056, 753814679, 464359622, 139885151, 190679639, 13385808, 579300460, 703061798, 547006495, 951495570, 533412846, 563228293, 535679899, 527404995, 231868091, 565923086, 686133749, 846261167, 655369702, 801026081, 325968015, 698417864, 112445859, 437090146, 428342993, 17260156, 2971987, 417978290, 962727323, 541852805, 640816950, 788221788, 259687010, 435702330, 46993806, 73644058, 846028147, 325539428, 402789280, 374473337, 335926996, 649351598, 991195894, 556563497, 495539098, 946705386, 591216794, 792360437, 965922841, 125462351, 478017126, 366898250, 289006042, 510256219, 997580757, 396608416, 638652087, 214157267, 745554920, 539632808, 215323488, 312885434, 67668948, 339865541, 4500306, 731691405, 568522187, 438318442, 355647726, 722145727, 878529665, 398758702, 297061900, 770689330, 549189589, 335148876, 646465055, 616688517, 687558930, 760356756, 249862403, 668514803, 580974128, 15222471, 471664909, 221030172, 197614313, 755377547, 86150392, 514227100, 937597968, 579533181, 414063233, 460291113, 654362756, 36694296, 215273498, 306317561, 753566644, 946549440, 708319452, 509276613, 135562864, 470125082, 7472704, 947176561, 362226529, 960608361, 523138562, 297727255, 832324665, 612769676, 214301724, 561045355, 792678864, 497003699, 455799316, 248124467, 775673424, 84328618, 810892143, 999935026, 439472871, 939717016, 964542614, 714032840, 917296995, 842553071, 891524831, 249173163, 371758335, 294413015, 242725373, 619189341, 942485790, 243007252, 369008414, 180291185, 538824766, 389467506, 902846795, 60092237, 557920568, 41455747, 855351292, 630845215, 363346443, 153925651, 405883037, 279656354, 624887966, 680963241, 27929697, 550528366, 616917298, 226755816, 456337620, 337959828, 56679551, 383172059, 159790687, 73608942, 642019111, 126402141, 49215843, 546640287, 786910323, 298568746, 307060030, 484433164, 122366332, 88896028, 638870247, 291530446, 168119178, 415428349, 638741436, 813032275, 72587618, 337242669, 281591488, 579540078, 537940643, 38109535, 471862293, 798447785, 411712280, 916335421, 196739563, 588360368, 48941332, 617715658, 994540076, 724096278, 459275029, 622619546, 155992868, 289436276, 85379287, 411738582, 629206008, 286385121, 262528790, 770590393, 916417640, 501513207, 469276038, 34797943, 775425482, 862271702, 460271812, 593384320, 106966539, 786832195, 432236696, 700617179, 646016441, 487332995, 533740706, 207910533, 772560750, 677144286, 139750799, 906007288, 832211795, 971101085, 2342181, 611045620, 50547735, 398544312, 487965529, 842151292, 767813976, 393089368, 952260988, 997855882, 785621401, 902340912, 864229347, 254475970, 511966575, 561140959, 193877616, 906119679, 165806965, 349282787, 888243586, 185560745, 142955756, 151783209, 60741261, 127653416, 436601548, 312268055, 181285041, 725589799, 673375062, 484438283, 450808716, 511419403, 140193506, 569450614, 637070234, 356715799, 924374080, 543433185, 442515469, 829270536, 167795592, 657458182, 651917484, 701586993, 269008382, 660509368, 348023024, 307598919, 390451191, 789131603, 923357303, 806946627, 213713163, 269178489, 73876988, 211118255, 415994634, 525183039, 476115693, 590688183, 460946750, 325981126, 786909566, 709892613, 877676056, 206700541, 81555907, 950930945, 713422494, 11432052, 530029688, 924644212, 452858539, 747198123, 259179749, 69520704, 690258644, 151610410, 76277782, 558586364, 863574974, 576701821, 816275322, 480364551, 710873174, 803656051, 613576376, 404702594, 246627622, 269793279, 215212593, 876841038, 646332546, 733980083, 195368891, 682449154, 145883845, 121574315, 931471873, 425408065, 677797924, 887080872, 125918861, 597690077, 857344985, 603196594, 683424863, 139875589, 16576840, 891373630, 797430476, 690148049, 881804089, 781697486, 825857742, 185532518, 741221247, 75192306, 695587954, 478481936, 847661627, 649741252, 969746773, 744797913, 532842567, 395240301, 833413010, 702356679, 568577746, 333149948, 328379250, 618555334, 203943428, 548641185, 556167743, 74948239, 556786245, 172086189, 853849650, 319030934, 614444754, 729877116, 64331871, 16446676, 322589714, 800660598, 419817948, 901126116, 497522627, 226029018, 341449913, 444576809, 779192338, 80702753, 793261906, 142896651, 385945900, 448907871, 316653546, 104980344, 282372895, 456531023, 458989402, 520740530, 952920261, 881986034, 844327970, 959136912, 243346501, 391584946, 535016610, 78576272, 144282709, 36405422, 901196619, 105604352, 207247822, 797962041, 153116165, 387693738, 684474374, 649276134, 57941686, 794733722, 558401053, 198847922, 29234033, 237708665, 394173955, 167880739, 508821797, 677500976, 343668778, 291521594, 359207740, 971074481, 169940348, 492640329, 468732870, 211083919, 365128403, 560744977, 281123918, 696003793, 157596743, 119683067, 406461433, 471624045, 929164149, 990486528, 997837027, 453837576, 755271353, 498236118, 437427002, 417749385, 732537243, 453445579, 828101685, 647871408, 322447340, 155349120, 568842411, 848091077, 221222658, 323266337, 426776811, 886577296, 8908979, 262578272, 193329368, 937834553, 514693063, 941171407, 467885314, 950997545, 63535210, 81053498, 353951314, 575212455, 339437270, 275485965, 51881774, 357972323, 401942311, 830918529, 417068681, 498607328, 380403725, 951420952, 974858578, 742750700, 95070620, 2151249, 521896932, 404990990, 337746684, 317701230, 439063184, 102744971, 5044691, 112590599, 267959685, 252620620, 812510024, 296264512, 839360575, 662998337, 658716606, 648835129, 844823198, 332835207, 83384055, 854009963, 742123123, 486509515, 231796569, 433574803, 101291575, 534489122, 464463659, 957335034, 80217972, 489109475, 284372965, 43494317, 956493254, 771914224, 787984559, 298119481, 719280820, 575814798, 962507740, 486933665, 202615337, 515477513, 706899062, 475987853, 948025661, 917700346, 887689834, 188508434, 338958219, 258271006, 390638669, 949070380, 691830744, 124581915, 802469937, 481399615, 185124797, 816187624, 547983215, 53969052, 852286278, 99507300, 432130737, 9876997, 516083190, 500519772, 758552010, 885287773, 765512551, 709057090, 90612982, 791039851, 563564736, 337324510, 136301212, 144890509, 784269293, 323717799, 64348033, 816111569, 907791957, 504076286, 961983973, 704396913, 372929826, 201371499, 566089041, 844099713, 822100104, 695967955, 16094191, 134598222, 334666275, 252811092, 727821817, 729856376, 854197532, 478291594, 599790732, 253039406, 313472477, 46294618, 644534575, 209697269, 142774856, 234992444, 93829240, 116916564, 868604579, 546289357, 765166553, 997968665, 205521262, 804965852, 869394939, 898670695, 53924070, 516616743, 776551133, 479042331, 388415330, 944828430, 380512368, 972765404, 121734290, 483621572, 922536183, 618377658, 617639226, 948477473, 930710119, 431989338, 337702891, 929951140, 855724542, 149940187, 903455747, 350303441, 144075780, 715826, 995910945, 951926371, 455182826, 508621339, 535175209, 739531894, 557722610, 758831802, 875478135, 343816242, 694262423, 57906236, 328801042, 266655362, 932221640, 23782857, 471375687, 753275655, 703972514, 271823077, 991876501, 549559507, 467879982, 54031170, 239779398, 950888725, 938434403, 232050506, 370509351, 936519252, 816783572, 299270382, 35718661, 665451963, 112026289, 311687785, 117441301, 967270790, 523472030, 4534533, 61447221, 877893635, 652986316, 654991639, 246587108, 841715663, 300455933, 780801180, 467478888, 285993307, 538756223, 68990773, 43209821, 626895356, 703059328, 954515271, 297136425, 916353849, 993269732, 90241896, 374008208, 385663764, 817537239, 227908271, 907444319, 833054679, 990041244, 888468755, 321255954, 175900145, 834184047, 342057996, 789738360, 63361796, 472952614, 454438705, 677126997, 585449418, 223730334, 624099179, 925328535, 914686784, 166851552, 513621152, 329357042, 61421359, 909831026, 305280794, 554928906, 809576309, 217245219, 473370483, 603169662, 586458775, 527915350, 343917358, 90504895, 413745098, 411252526, 741146258, 220105613, 905955799, 916326746, 144166500, 375436894, 699599431, 602694718, 64992061, 509443165, 10946709, 405455656, 921642713, 946073804, 837310937, 410790806, 9102445, 937422273, 316682795, 863900986, 651928937, 582632872, 3646459, 847072932, 707516077, 822337789, 61917590, 168001939, 853579593, 127602156, 404271305, 726592436, 392297445, 5172780, 561730119, 117612072, 676886139, 85880854, 88761982, 576081072, 962147578, 417753534, 8411936, 706270832, 69551874, 345412619, 753087757, 361813781, 276445820, 491062370, 148700130, 411127359, 115023615, 785914522, 736089485, 720902258, 909153161, 294543649, 329003736, 317361028, 283034474, 826627144, 266477866, 88568515, 10242253, 98491771, 125188863, 28244412, 638257175, 278922524, 48952565, 291594595, 9265656, 203778892, 107405383, 424288942, 804211086, 488864180, 895810556, 226176218, 421525026, 726169844, 247254683, 669872365, 199574869, 679020093, 777892446, 605588482, 631735160, 397205738, 465061750, 156863067, 597694630, 55508462, 702594785, 565370904, 532203382, 122696661, 66907250, 900468607, 415182427, 640810639, 132899533, 523918409, 966729515, 813924769, 174941861, 771266811, 480098983, 582494119, 242209431, 457025322, 271721954, 488501066, 920145796, 678262461, 962050863, 31919195, 433200554, 122986674, 486348472, 992118765, 901804976, 896230450, 614215002, 233435531, 174206361, 582340467, 523479400, 221363160, 96288667, 551295580, 504549813, 496309462, 883170934, 718368207, 944818287, 667724605, 972150330, 125064651, 298573422, 184785447, 559464903, 702786361, 281499975, 526676630, 696622694, 315770956, 356977612, 43419541, 382059126, 3970778, 302737971, 957340451, 525794834, 860634029, 600593936, 508053940, 201640333, 771842637, 517317269, 198017416, 720109389, 953572390, 533663440, 708917054, 21292953, 271620004, 958223773, 81113010, 581711844, 771172300, 104833217, 273971678, 403168749, 292097976, 969170964, 83515087, 225455842, 387703285, 882516594, 243323655, 825297703, 94334629, 611418781, 572822551, 340042572, 123400626, 812105285, 612661431, 487088530, 65036242, 868324200, 738172306, 14524605, 51020903, 148671066, 601893623, 422271772, 729100212, 674788374, 753819155, 634027478, 723333701, 743933032, 112484496, 271787500, 957132138, 531583249, 795446403, 95779824, 336440709, 778780755, 922424602, 344619920, 854421412, 236063227, 209254594, 890064134, 38516880, 791899574, 28179593, 347187858, 432370827, 985244780, 494964587, 769261857, 786653359, 821871087, 222699325, 283305842, 398790194, 400871385, 297250534, 448944542, 814442194, 334943202, 63471474, 271659312, 550270853, 94085208, 838680986, 843907559, 471668467, 119323626, 619493379, 531957701, 197853995, 285409402, 733158445, 130331798, 663920788, 674260263, 554697945, 61799083, 733406824, 327579271, 222036173, 692357160, 943681314, 21877340, 140229924, 715258409, 140004853, 570173293, 997760134, 879248189, 5284687, 552749201, 384272186, 991838220, 300385168, 765683772, 977431425, 92231964, 808174870, 95800409, 819668124, 552200691, 64232100, 643122856, 855163715, 464256510, 574355227, 475711218, 549824380, 157771808, 891763228, 483464755, 144432186, 984395665, 33712105, 457859883, 769934286, 502607320, 646725604, 133227430, 73493457, 678598210, 97294224, 387605969, 451949996, 643753398, 125141587, 971301868, 329892047, 428928898, 742462555, 910853298, 1566932, 242036209, 313127567, 441284035, 305962393, 514208894, 973776756, 694901373, 483377923, 535643780, 614328922, 730579051, 812489454, 913916531, 271119551, 290292947, 56825565, 649657727, 751918064, 704025072, 275753989, 342711474, 281603608, 749875336, 66051321, 857326631, 605673953, 268095739, 521299785, 121046083, 653194004, 322518513, 810946408, 921495890, 805888773, 283125173, 317037692, 983171497, 154760878, 313128698, 629029549, 812682422, 402256156, 576348581, 454104567, 278869480, 802546773, 475053341, 443730866, 935154361, 157666850, 102297374, 58220707, 216827979, 453326998, 122211568, 884334462, 7514246, 416729001, 393583170, 379605680, 212826790, 206759505, 491670490, 689635436, 140115302, 343243597, 469476046, 271126387, 17217784, 572635431, 80862927, 399768565, 978274491, 221378950, 912586594, 60528411, 799604429, 436473966, 347645809, 495282990, 725478685, 405972754, 735569993, 931886306, 965655546, 747604688, 414615847, 606026509, 974389765, 269295919, 610333075, 868392535, 718460500, 282182570, 130894624, 376903362, 585254615, 463520750, 88296198, 596795029, 732117690, 532522798, 173222809, 566389775, 323738623, 159422764, 594514955, 128086675, 780649992, 855265145, 690918542, 528706535, 992757548, 788373317, 333530694, 921613503, 541449366, 894209959, 147875461, 602090613, 685579840, 32445718, 125715580, 795343098, 97438146, 650717495, 20390724, 667164175, 782461147, 814501546, 210421505, 988452779, 113332673, 93282266, 125622567, 893196003, 992438232, 699764726, 175383892, 174302704, 328119968, 137120303, 363330140, 808518811, 44704938, 691836558, 414662204, 772516879, 623977061, 344258670, 767809232, 115101473, 535654611, 506907334, 270536297, 220615013, 639777915, 188901616, 768566610, 968882064, 571769675, 27612524, 612094333, 791683941, 781194226, 15950461, 517245035, 521171187, 797658757, 895947406, 271279872, 851534690, 508211059, 619195850, 641847717, 537485226, 686089710, 385055361, 30605065, 172439542, 888942466, 391900467, 621496231, 49840149, 614302770, 117739900, 466472157, 771278168, 572018458, 943198414, 73922637, 279210449, 515676008, 710714892, 962845067, 412076090, 216411567, 454869856, 688840862, 330664805, 814598522, 782689850, 972122247, 68559966, 854587839, 804192146, 563231475, 515260173, 586156928, 134766223, 346555112, 846762316, 623832079, 652443767, 840495962, 545320909, 480422324, 569292098, 680330031, 719349076, 586512850, 33018300, 561835224, 914084690, 471207026, 957975385, 790017190, 152619695, 367467186, 39018383, 985848917, 559989587, 290483532, 312071779, 928346961, 384626287, 897002325, 160703723, 51811515, 779179466, 862115494, 128202547, 570823315, 673530266, 626276841, 136357641, 481705069, 509662059, 283568505, 769681702, 337259538, 553284587, 140113918, 943115019, 955222484, 708894937, 432891711, 182165814, 190130330, 277855450, 637508896, 306870798, 451814760, 834530887, 862851385, 80325727, 870832720, 872568153, 696972663, 673564058, 266770838, 539319093, 26178017, 214369875, 78248572, 150871012, 918087615, 313853166, 868020781, 86495281, 159756659, 157294866, 805164058, 810547882, 869869669, 300755233, 390755258, 213771484, 449224516, 479642717, 452733643, 366441952, 24463826, 187094122, 5379524, 66367949, 648588905, 12426566, 928920529, 594558594, 944348133, 342371401, 166437065, 510726941, 164013421, 57526092, 867624622, 592014737, 579492629, 251423997, 198537277, 739492771, 491424686, 253462928, 487293668, 25921220, 937302926, 753333899, 829143488, 588140689, 519150495, 975388167, 732002831, 679155442, 79298100, 476263764, 41988372, 224701024, 594092693, 609324839, 337943370, 916187747, 96723301, 410714341, 299586661, 260301672, 846941594, 635600039, 509879211, 10992899, 508099753, 492318763, 746192327, 14337879, 473004710, 156438306, 398597232, 521206965, 634882256, 575064530, 148057638, 619360473, 852236103, 311508909, 103660997, 407509141, 502808452, 534967513, 255701286, 981138438, 257386237, 393848893, 683221940, 369366335, 871365221, 620171402, 323943408, 485840444, 484715676, 190682668, 855461118, 628155287, 277205981, 551688920, 111552989, 333049261, 707455833, 761555086, 628299688, 233692454, 95377610, 991653891, 545909539, 190041138, 952207221, 103675611, 808767630, 37486315, 558543966, 846732634, 82019018, 946514521, 109665898, 821520906, 156303178, 944684939, 229907185, 214354970, 222691632, 278278612, 292386015, 550099355, 90292847, 276814747, 507872963, 181194602, 215972812, 160301239, 171317594, 339757285, 568994153, 981717182, 833528336, 411513873, 169248100, 510251737, 92235481, 542844669, 441235923, 753417765, 586210745, 41447964, 874141513, 488505893, 723877828, 994020704, 957192940, 430741925, 706020572, 662885655, 35791231, 401140932, 199173982, 641223193, 125196204, 197837761, 958345426, 448442739, 186809282, 778413649, 665283626, 812281119, 706180444, 34503636, 602190871, 716957023, 679179227, 384304074, 845268234, 385718496, 954528167, 277866873, 96455559, 201716294, 278621028, 891032624, 249793220, 872109313, 972077786, 260219491, 192451565, 733090785, 218016896, 879228960, 660632691, 193542654, 148908146, 356706350, 437533788, 511735806, 55631802, 980094797, 732478130, 291903085, 50449648, 776903677, 884153208, 165436041, 966313245, 311343020, 947283619, 585701280, 42040880, 53901223, 883269414, 778087574, 371932919, 320845811, 588053191, 34875110, 378110208, 748986823, 816399339, 89475424, 378490069, 585569708, 59323142, 953714846, 866855533, 64900395, 136689297, 945874619, 310397012, 514867325, 880460379, 584264576, 661686490, 439755076, 822496923, 75433253, 438943049, 724729824, 550004708, 644197223, 238057281, 95288708, 743470978, 245434853, 114453758, 594257125, 337784564, 218276431, 507858792, 446357254, 901418288, 372070590, 900035357, 478534291, 575190293, 887711510, 206866996, 135497293, 846801676, 238506040, 614112873, 675671743, 798041770, 601329024, 921989064, 634372731, 986926892, 634436707, 118445490, 771053884, 919012185, 597591450, 490893568, 330119526, 667061805, 318771730, 652445728, 650514512, 462705905, 774886377, 478879402, 51867873, 393373322, 675465460, 517721018, 154221342, 372180394, 328492002, 135982084, 591027983, 187582652, 571845899, 350647475, 501495935, 264601960, 884028912, 293197801, 71556788, 587798559, 807537926, 437306332, 498498339, 93302689, 508535707, 944997513, 612525297, 202570876, 500497602, 180132296, 939952684, 362506090, 627807068, 49881899, 269874341, 766979748, 253143852, 862889138, 8461171, 611493943, 965250381, 948843053, 911875684, 202761869, 613440380, 868653780, 852275614, 599637160, 567421603, 604814940, 485919014, 552217996, 338973809, 482685910, 276396171, 703778325, 241695738, 693166373, 256013816, 928076690, 726130784, 345796410, 580095608, 567953012, 103861787, 56950728, 737157184, 254422697, 757770710, 233402090, 130452522, 68582336, 698339219, 482652072, 964933128, 644706740, 480891614, 815238855, 50169242, 991839737, 563520748, 230093696, 154640281, 599513661, 157245132, 371670596, 220513775, 297953557, 142320508, 380562459, 805133342, 879368170, 319752252, 207203477, 809432804, 54049362, 452833483, 954388466, 250364955, 67307284, 628813933, 172873513, 137117598, 465149047, 380346998, 996360617, 763441905, 171423635, 784983795, 152179101, 151605754, 326330907, 238503465, 895309803, 687920764, 620895171, 448599136, 689879026, 243033335, 337930811, 266715597, 102409665, 661654678, 944650965, 993812358, 675606096, 719039876, 805815157, 938271677, 103298384, 139210207, 599212275, 616627658, 292714673, 984494399, 246255938, 636412077, 658340850, 137646218, 599699577, 957525885, 643748347, 169275484, 351854421, 837771096, 776266871, 928104695, 47323636, 173577730, 248002255, 567682536, 93864722, 291774426, 783630604, 933122718, 542009398, 507789289, 367075229, 496968375, 588935785, 184393053, 343778632, 87037087, 477960610, 470611576, 650363224, 473547114, 223303679, 100320964, 634322747, 673497839, 914589042, 743384520, 819810315, 69271577, 609353181, 624440626, 704497400, 161211200, 234305750, 20772812, 872804853, 274973759, 175189125, 326910759, 736731783, 565840925, 499967377, 586603287, 535614560, 171528001, 351288907, 721760813, 318325791, 620351358, 51063930, 50987088, 360401745, 216223838, 570503407, 153743131, 809703552, 985207856, 852680800, 541955431, 654340865, 682538330, 271386423, 614792815, 538475254, 82658111, 211163223, 867869299, 879539846, 545487812, 770393689, 483811475, 424947414, 783937023, 962701233, 896652172, 388648948, 820587524, 942460965, 127023757, 160579985, 237980764, 454849225, 19084961, 370084032, 413002982, 287461941, 953440034, 734978031, 687306080, 232557081, 827005543, 698368621, 331224393, 701958122, 179819421, 835992729, 431655091, 384506030, 455852299, 325867805, 965591107, 472798237, 998694492, 226978383, 651264621, 794519396, 158213534, 129563797, 323801163, 956615004, 666820951, 422921958, 276960416, 209992496, 900282947, 459731404, 405070986, 476325128, 817625529, 628600862, 475772123, 18992803, 876219516, 737555429, 602355476, 72015210, 223015638, 543412757, 267643626, 818588674, 158372882, 173299042, 135361488, 290499277, 713422282, 715930004, 328453570, 957901963, 816551255, 112797849, 393718606, 451479041, 907984867, 747499911, 572163897, 501090363, 539049373, 747507184, 437195552, 947101723, 327242963, 19665147, 63638377, 741364457, 768028706, 813791803, 680788777, 847907889, 133483310, 38557023, 621598878, 212072180, 352005197, 59804850, 860517954, 563783841, 928820793, 727142529, 439205220, 386673786, 935024658, 387151579, 569183069, 797026744, 290342176, 323176794, 160119616, 436033315, 823418988, 376704276, 473091054, 526984199, 313630223, 966050126, 784250505, 449941832, 778951261, 766576070, 347715786, 46291364, 64619459, 100017336, 15939766, 138987694, 922424013, 772841267, 952546583, 610091107, 603775581, 799138450, 198313074, 428501955, 737383211, 731147424, 13192920, 552358437, 503567326, 798810785, 622185681, 773216520, 324593820, 482313974, 980186149, 110196922, 55523793, 601419452, 745152293, 758149452, 295445962, 957915810, 288876774, 860117477, 349557841, 444084145, 378621013, 619172375, 978296304, 472591399, 837907769, 37088019, 882086955, 820883640, 411192886, 120928443, 234602699, 233795521, 664841506, 355191436, 357706275, 477459566, 683806694, 494426294, 667494738, 102660090, 56685042, 540775674, 176882513, 513081730, 161939684, 117132968, 485673651, 337917438, 320170855, 69191037, 80095255, 388919046, 927973391, 437490021, 354092992, 483623756, 633900093, 97614546, 780072268, 163273809, 914591475, 136902241, 83212142, 28183675, 85122577, 884473659, 194891111, 247327301, 695387732, 197349412, 964725641, 355846317, 492258899, 233474492, 583029269, 411766047, 869010162, 464221300, 734408375, 265256571, 469299093, 997514255, 381818468, 722714723, 806583457, 33430232, 129804036, 738212396, 293305314, 166992535, 813935033, 931596271, 543899093, 248681151, 694087013, 330200646, 9706129, 334612597, 182644134, 849281388, 776262227, 85157134, 768554768, 72988627, 139031656, 639556383, 524310726, 669249749, 168333291, 773930007, 647772852, 497425182, 520622090, 868755546, 646126389, 176643234, 865250845, 79763786, 356575910, 174279610, 478263278, 223568875, 809624674, 496348606, 34720247, 96310255, 542399855, 842104715, 112483268, 652658060, 744460739, 809623264, 101536231, 456136988, 703167990, 204975778, 931310182, 91252360, 677354172, 85169944, 697051480, 268198452, 582363978, 269107224, 154409263, 133624094, 828232880, 523126357, 761244555, 513818155, 556212044, 216276922, 597154327, 502431676, 162886874, 568448130, 231558617, 534857671, 590713893, 182433847, 591652759, 669090240, 519893978, 60442057, 119482415, 190659070, 520057041, 228486010, 780226376, 295464539, 512984334, 73332806, 774853939, 713410152, 281476829, 188768817, 583216299, 892351120, 538328231, 395746232, 483678475, 75746554, 960625096, 244392213, 56262936, 241650800, 394857857, 623042727, 409395629, 284821141, 592692920, 167998535, 538331510, 744117606, 777473354, 947393637, 342533463, 681704391, 908825742, 105940896, 169010339, 787449339, 36854368, 128344544, 236043896, 859039246, 661084525, 522845775, 184758392, 480805669, 536265034, 549115405, 933768208, 265006462, 243275531, 557677989, 808005756, 734261579, 708142530, 779712021, 879796795, 220284916, 798174288, 294705541, 592329734, 746811563, 710754102, 174108552, 399943161, 599048166, 522848009, 291246146, 721866819, 554641493, 233034091, 539572365, 521074467, 589071326, 932142664, 45525889, 150901928, 806856795, 164941948, 396270256, 101054808, 129928067, 76630887, 134194847, 851450543, 257520077, 782202208, 983636142, 748153341, 640341645, 45858860, 777611508, 905004798, 133338531, 159420807, 737502762, 431800136, 761255512, 309599786, 789437874, 775537553, 919643590, 60724392, 138025640, 6644874, 816502046, 107554379, 516787390, 252589482, 34587593, 660643495, 740405066, 916672517, 836352210, 25520828, 852015160, 585946339, 315476184, 125053025, 765000114, 559900120, 179304059, 536204446, 3586611, 996197534, 724487731, 288807840, 469572770, 28646054, 305690919, 885697110, 120651633, 884823627, 90162350, 42718606, 720617242, 394847402, 43268215, 213483460, 655721684, 582434987, 155050489, 386288951, 22256052, 127262927, 370123255, 694434367, 540476314, 219412798, 400820268, 624646614, 349459886, 679083470, 670320873, 280433592, 632517063, 914589782, 890798299, 994987602, 890437948, 998379920, 659060873, 265176058, 713243920, 411268058, 969694778, 936484233, 147459258, 872918446, 848283770, 339272749, 213281682, 797629779, 829155509, 59468993, 957538127, 372314054, 969356184, 264214090, 399129875, 505106764, 725464666, 136758839, 700198949, 979612724, 488741359, 195651630, 603589580, 105757329, 893873170, 648103965, 340796727, 142705795, 693757542, 802237167, 250089012, 217789543, 25589483, 513077339, 470128137, 452777059, 850203212, 453233455, 177080421, 467620297, 370745448, 80478468, 419854022, 881793086, 42044755, 985864144, 30452167, 811210272, 106478526, 241240296, 486240230, 133797889, 420857579, 701254032, 311291517, 750877014, 283895698, 412239887, 477348564, 630232308, 536212608, 916679121, 146059142, 197976748, 503436761, 589483010, 668679584, 638090575, 449062126, 718518230, 844486425, 479941797, 915798744, 792891619, 700117263, 117643885, 269333100, 552449847, 580003107, 732188964, 103111309, 960610091, 587225043, 426081785, 671124364, 935771552, 85932917, 110522528, 844413353, 985016163, 575126400, 38448486, 239508100, 470195904, 449609907, 660037501, 919346739, 718599910, 558339488, 70531273, 20526756, 308732302, 346656323, 949411951, 449644925, 112046440, 757044924, 819553982, 229380061, 883318616, 810275561, 681247072, 74048252, 656340572, 572370917, 862624041, 339228084, 934283042, 895663868, 241527037, 256376050, 370765711, 796475219, 794270591, 630216886, 702367282, 145671740, 647609793, 145383052, 187762438, 437385261, 955159203, 824612419, 122319549, 778045837, 701792023, 291375916, 891074305, 24343752, 59038993, 672817182, 86030585, 62766249, 912555675, 43171735, 615320684, 268609263, 305894699, 495456584, 332244539, 479814752, 110500503, 180548824, 567162395, 11753516, 860829792, 907752567, 441014730, 194762170, 259512296, 480281098, 238257388, 271682198, 285839150, 652244882, 645480229, 659483281, 358965763, 426833568, 494209726, 196270902, 157646039, 752913308, 80787641, 3441158, 607513427, 659599700, 117481253, 503407209, 411703776, 342567372, 828750963, 278810949, 660823785, 367773760, 754210395, 631119733, 318953831, 483594264, 965031545, 349033600, 802210172, 275195919, 227608370, 262157778, 123471556, 819951692, 992376791, 220737883, 952802550, 213176311, 365214123, 679291605, 372977933, 909149061, 859326915, 528792474, 168508353, 416241291, 214791713, 274118008, 908084098, 91229035, 540144876, 875042256, 874977529, 522384835, 538034342, 143174228, 53784120, 937406190, 325879671, 593875247, 795295552, 843941061, 848467322, 939394714, 272157326, 474152239, 906934368, 152478420, 280075608, 760910672, 667419347, 876901528, 924670881, 718807836, 884238661, 975593608, 765043314, 876632915, 692868579, 763560996, 506740881, 468155932, 614206575, 996181102, 366779204, 633706898, 617383889, 52744834, 185870524, 156547400, 683163625, 532402287, 623898910, 680521733, 971232695, 381108143, 565516535, 924216711, 800723759, 811692258, 398604955, 439620996, 933771369, 187924883, 434742381, 231238837, 439088159, 875841663, 562489690, 880367023, 544916946, 557216861, 928063307, 814100052, 501597906, 106161190, 389475568, 180382664, 241744013, 470169848, 403751422, 584415188, 901009159, 763421717, 143448899, 413699558, 671093139, 850570780, 556818063, 178901581, 381718331, 239206378, 812736389, 953646350, 382843901, 603504032, 905588230, 84864977, 706007589, 273623700, 150865796, 112337167, 403721211, 533937337, 631334818, 629121742, 381832258, 242551062, 105121201, 82762650, 162206302, 802030441, 940518305, 209407458, 936120865, 276020057, 101172705, 71806331, 259028107, 962195134, 886205806, 694633319, 616305205, 140717228, 41890507, 109966366, 13245514, 884362910, 231484890, 78359648, 517285223, 831752224, 301711871, 955956359, 837608133, 79209986, 205227224, 474470662, 720883982, 738918195, 318244001, 882872932, 530045496, 332788305, 121140612, 390817768, 378274384, 581275680, 956798086, 284603334, 916148674, 780491529, 330696969, 392856666, 662891862, 799333438, 13607179, 140295257, 242883526, 984573823, 969473566, 577758896, 102522603, 105369903, 332033708, 572786881, 234256347, 589056973, 951506809, 97692753, 251771055, 773244996, 47962900, 815754056, 978154535, 536747203, 517544465, 741126695, 775823089, 861221821, 525840823, 474976579, 789743068, 667074201, 610452147, 547951612, 190652977, 520779452, 412354147, 312112086, 846347164, 657080940, 915556374, 449085557, 453366822, 63371175, 830801778, 34622099, 479221762, 3356101, 39082075, 229924821, 209891387, 608035861, 203002592, 971932150, 694234272, 89441354, 276608882, 632075849, 269239559, 363000121, 356869230, 739676063, 727115880, 766533489, 698475146, 79872015, 494053488, 59044299, 8476837, 679492505, 633769276, 142916846, 383289636, 199561488, 20411806, 138943530, 222997047, 664161602, 635944317, 36516068, 392684198, 138039349, 280219678, 829600769, 849304812, 126839851, 36548079, 999619527, 833887039, 964345427, 409001402, 16065452, 915934597, 770763527, 649705403, 30716127, 523665470, 65163792, 194219193, 138760471, 319275067, 712754555, 254031852, 477479491, 27264923, 171351782, 118760259, 698553004, 939311347, 208841520, 42328903, 876644731, 682413108, 378438126, 430133006, 698547492, 924434598, 457122325, 101099219, 5861350, 404636198, 63785940, 476898767, 424736672, 146022158, 302657778, 449562202, 173058939, 907368885, 863886797, 368835261, 240080094, 13248720, 25726, 816738842, 223982037, 510961795, 445731447, 447285521, 112951371, 53100499, 509970334, 703213857, 795766155, 551134454, 302449891, 378015240, 20761390, 927053975, 257612900, 574104613, 913639454, 313073927, 319708220, 296535043, 160847400, 507883858, 927132476, 909603554, 906071155, 88784825, 357209017, 287858816, 912996655, 162538003, 729292922, 268602183, 377281417, 415006831, 859932375, 895913598, 397803876, 269552379, 538992086, 327849083, 819061990, 48161870, 711353044, 597957203, 878433353, 488137426, 387193885, 40382089, 223893854, 38541869, 47368489, 227873207, 998641119, 604734245, 185378459, 208120641, 95789631, 102990957, 634304678, 8481864, 185776131, 946876183, 208744997, 480960541, 402901694, 444877508, 169423298, 841686772, 627142914, 315190398, 670248046, 886221519, 227773058, 844609711, 990897829, 322468454, 8742195, 149190506, 164381826, 370824592, 842691439, 204606856, 638942316, 176647970, 701444110, 538758184, 412922283, 418040945, 156223004, 301962760, 967118225, 797862038, 944535276, 872950927, 408655338, 673928485, 549493255, 230648193, 169300226, 329655823, 46433647, 819216082, 175135838, 982206428, 959926712, 29152280, 295177974, 298187568, 260474864, 706455861, 355128286, 903646637, 94819472, 256350544, 243067996, 818580400, 926534621, 426122262, 583350951, 309117203, 701222855, 803206182, 275132025, 962330784, 281707701, 667208939, 716018095, 869419506, 18708260, 675843429, 42488737, 518323842, 524690863, 657652243, 489828224, 94580977, 713104452, 595127782, 528781722, 190027479, 921152115, 938191806, 670608669, 642777941, 684340694, 373486542, 412145079, 407699234, 936139368, 74773068, 773224496, 150294237, 92027888, 146343043, 306289756, 150370494, 958358307, 788147569, 354874553, 652650507, 856929151, 521676900, 609242543, 426712300, 933418039, 584836706, 113291170, 621095027, 171816137, 739172124, 793842124, 98535234, 548379174, 533063636, 306432028, 439528259, 796097229, 439779301, 471155990, 98783298, 561027844, 94519496, 808752731, 991667042, 761573855, 103353168, 543575708, 742534800, 932511900, 477647503, 369441762, 976075500, 113474285, 341028337, 98699398, 469547540, 343978148, 823545148, 201087305, 221104206, 180955384, 835214633, 864300897, 5905220, 60714580, 595402983, 380740748, 936056297, 35942681, 915157503, 563444412, 591023554, 183688558, 331239150, 391381334, 3095623, 186253373, 670106997, 122963967, 593457865, 914119461, 693108227, 157614399, 159959067, 48353649, 328427412, 747667829, 954018479, 428169382, 123308849, 254224270, 205300047, 39533491, 66915422, 699244094, 958579133, 502927711, 547444456, 912852805, 718573775, 871233528, 5300588, 739794904, 628328212, 551753150, 940903121, 503022971, 815527274, 679407961, 201271739, 245408976, 301179669, 857686415, 143259129, 4472500, 937896074, 469460138, 871726839, 521832810, 452967474, 628985269, 160953416, 929756683, 225805736, 455764846, 662304585, 15213468, 245335652, 992462589, 750876046, 856736301, 732229786, 225998800, 144613370, 649242744, 940163538, 595638524, 618000692, 798023463, 566492497, 583681536, 606842320, 691251217, 364020114, 902576800, 151682315, 111109896, 81686301, 424161063, 891209636, 381774058, 41772216, 28331165, 767493826, 56308435, 20478207, 290450417, 821255823, 95291849, 581496169, 884137545, 70506956, 36607723, 824224272, 258723245, 897287947, 664400190, 973321376, 494950440, 903210693, 954141355, 269539173, 475682433, 180875871, 662757712, 178809724, 203817037, 927560467, 367202249, 884369673, 891120103, 562396236, 347942581, 465211973, 674392623, 663911949, 267772855, 972526965, 635808990, 900704772, 947690349, 976772386, 468483869, 666387860, 822976156, 838780716, 313261, 278112131, 597137791, 312891063, 512874977, 423653373, 476608625, 992441064, 421910902, 122830865, 321063880, 962287790, 177368787, 731325157, 310152810, 156544799, 119081801, 993968143, 539292858, 799650855, 866892612, 486547051, 571354833, 8980020, 941281839, 23339794, 359731019, 20382028, 432923641, 161564918, 717132336, 387392438, 678692188, 956541702, 907184699, 534647432, 686608972, 317422985, 485197325, 726450755, 538135805, 240787935, 312075893, 850135022, 586883518, 752402752, 134504281, 121527440, 42032232, 582626272, 974412136, 14044957, 954792282, 445631629, 958463660, 946730908, 810535975, 879683557, 547428748, 341426522, 17644150, 858224565, 953529385, 512954086, 107821363, 942085378, 464457923, 512307786, 470101993, 687991785, 790428871, 970295044, 418596101, 632176470, 742277922, 403121357, 990869479, 34538847, 615916259, 114802826, 71258624, 37433722, 549969402, 573215294, 364029857, 569007584, 639105966, 176353800, 700097799, 236866072, 243286942, 583713342, 709656539, 536779855, 667219873, 809601451, 605857725, 804844202, 329788003, 503952195, 604888152, 465821528, 133130707, 886025446, 727511216, 269089755, 419608722, 489078359, 706496673, 291280444, 409508757, 837226843, 792464390, 779991214, 318916112, 484694804, 113415840, 77368196, 342959939, 656426869, 143658968, 200565707, 336628882, 55697701, 610968564, 451844627, 913646726, 54702891, 863247906, 757928878, 677878423, 415409681, 655701965, 914440494, 182152296, 614236681, 84150499, 232057395, 244459909, 430989211, 492530287, 24476336, 685006873, 865148435, 388590470, 173384422, 822251841, 960563860, 114702993, 796173215, 226941505, 923344339, 675071268, 674680144, 152074129, 906021561, 156777422, 669745498, 811587637, 658218845, 961289267, 884935511, 635911203, 310513599, 282566810, 282938530, 568569013, 345186962, 134760154, 166996718, 123366033, 453108894, 394169316, 528139910, 93860641, 983350086, 863420790, 831748549, 641434391, 761632291, 900228549, 272977721, 279856177, 224923216, 219095615, 357748792, 541167392, 74405834, 25200667, 209368657, 209316408, 643210139, 741584239, 299443609, 620681644, 68703077, 587692080, 522152824, 764088662, 400454727, 17923002, 308301329, 968639305, 112527158, 494791605, 725343045, 774407417, 828738511, 896975148, 669164703, 203103088, 951955863, 85650258, 207481197, 972900579, 791851749, 189660588, 638764991, 886556893, 503261159, 396794215, 484139027, 779994531, 199061106, 465274695, 208159453, 143480579, 623337425, 503105161, 418726869, 448821989, 234232246, 69671485, 304798947, 662052961, 290167918, 773482714, 971747822, 438448839, 42683462, 666803455, 600372860, 78914748, 645038596, 485548388, 720159668, 940929585, 858358957, 177949067, 91939248, 778246220, 834265079, 806513702, 95437614, 52897974, 811657567, 652597520, 506937051, 291597836, 342793030, 62491732, 69690874, 772146408, 361965037, 932520165, 108526018, 634444892, 647684185, 858478147, 415460593, 695958466, 287371662, 183558421, 828509589, 450805623, 811435280, 948969476, 575594196, 31993631, 730204216, 984344094, 40659242, 842176186, 482194656, 204148200, 522269431, 598218529, 250314974, 851280201, 488748649, 704468893, 645632529, 888645627, 288665882, 988135990, 694224680, 768295192, 583118812, 153430331, 82954216, 411660206, 530896115, 318047845, 651750545, 419238304, 203387608, 801605549, 291272652, 175382252, 871092043, 670955498, 713116838, 383147464, 179775537, 307295660, 552713258, 835099423, 95421037, 324137932, 42340024, 465910157, 271689538, 547945850, 262358411, 604888151, 861862784, 522937682, 480307760, 971855518, 203550599, 611523083, 155448344, 769626047, 659332601, 591334951, 619414430, 94136980, 803750448, 298206680, 163771920, 196320296, 124312079, 570917559, 36805423, 568578456, 476903212, 242279068, 717886186, 265283574, 369874421, 949123882, 125766632, 453880387, 340911104, 716012596, 373491028, 209000685, 519926369, 575603163, 419740646, 459138559, 385263668, 412312376, 259542972, 280799263, 683598287, 73547723, 450881012, 193589113, 323085265, 488559384, 556424104, 700362689, 561575121, 609462871, 266032420, 817604964, 839881971, 698495225, 360211364, 682613098, 464184036, 974274605, 49046107, 882052673, 457498494, 987078230, 629248296, 989253939, 919388409, 671519499, 999670523, 493001074, 954410445, 785292858, 130143485, 656012446, 186703920, 929803489, 879228115, 617650867, 402655520, 585935618, 489279300, 748865014, 360368298, 365587304, 922337831, 669996027, 651757132, 421868050, 915909027, 768446691, 490369366, 512803097, 269826548, 398855503, 421234935, 859825646, 712031378, 381657279, 673234295, 143742269, 796499912, 163430523, 493696243, 974222667, 396484473, 993164105, 222723386, 11857719, 831806449, 625303285, 668604326, 281244907, 941483167, 156023907, 783706973, 759045305, 658845774, 761638237, 470465671, 106774912, 826685052, 765885327, 828803712, 923439084, 627755555, 492815529, 590766800, 967639241, 195298086, 599386229, 386412633, 865057096, 720499288, 124735499, 139449078, 713854084, 402253149, 728578797, 203210044, 191970535, 703481451, 812655852, 84729123, 241537663, 215085443, 795500400, 221417025, 818552186, 637240500, 385607335, 633396801, 302949470, 458997134, 552449852, 828946102, 350234001, 443539818, 466711985, 867905765, 99066410, 211035251, 900604607, 221864337, 605259002, 555388320, 391616032, 194800316, 899604023, 435369160, 505865773, 379216591, 559565443, 385660830, 929377869, 679071360, 314816156, 142265333, 143947827, 492376897, 924714665, 325196479, 335925061, 986517787, 712506942, 890756423, 994621792, 165761807, 70735827, 520353255, 656586073, 749320982, 447607553, 884757471, 808032531, 991816708, 280859880, 894437972, 233351065, 980823555, 428863493, 168348597, 434264553, 819024720, 413955127, 879755846, 181939260, 528592423, 867690221, 296848045, 254501954, 232615481, 811011108, 277631269, 86562230, 314050405, 738429304, 577347820, 28009173, 911249808, 460386443, 214942989, 303874016, 927615443, 412334511, 491253560, 218852695, 650179959, 622064822, 297755489, 7907559, 525868613, 837191592, 935385273, 186232438, 397030169, 34405123, 347657634, 507588504, 464198477, 888979117, 349441531, 736438706, 476956487, 166867736, 901172759, 781277805, 943458197, 672700360, 169111561, 171884466, 846899993, 780143412, 807479923, 910750875, 869778356, 161382647, 813454121, 420860717, 77499383, 741994834, 465662258, 105884862, 369885459, 864134312, 723952564, 208400572, 847323531, 298367523, 661712816, 749927193, 541274128, 200071426, 171396116, 355758761, 991790304, 406464569, 676563232, 158010768, 393458735, 984071144, 19059475, 868578312, 723281907, 340448860, 439595260, 873453565, 562311714, 59808716, 326886346, 460999072, 215220741, 172285533, 247635568, 497950554, 969604101, 684842336, 32864466, 695578271, 988977892, 594652294, 147988725, 75243603, 195026110, 895925962, 185918578, 181568319, 840071806, 507505751, 553549199, 572694295, 925962138, 530003222, 807300496, 530551200, 857869110, 771326743, 637627113, 751079219, 536090447, 157134603, 93860841, 894297035, 862756890, 94899912, 558414911, 238831255, 917003971, 322187528, 759205006, 228837456, 671355132, 701847207, 5634758, 823100463, 791087750, 100940904, 771534224, 66256578, 294367963, 991298927, 165333519, 684419641, 104021985, 669628342, 94004729, 438417522, 729551514, 81808503, 881691708, 847480824, 657838877, 374298177, 513482663, 559569942, 15279927, 8572570, 5365326, 685798296, 290192726, 685853305, 288503232, 90086360, 633787976, 908079049, 704691636, 527729406, 414728326, 626369945, 927429825, 915291710, 795058530, 734773997, 767186502, 262211348, 174551300, 105264256, 787204067, 493643306, 280283446, 759732056, 414454214, 348721356, 188987995, 913038040, 581378065, 511851168, 933349383, 644933944, 695936248, 508063698, 241795264, 724612813, 609301132, 441009280, 854859036, 745584696, 77516048, 472584958, 473070625, 982018437, 768711454, 670625937, 827823364, 590870083, 739816671, 736287079, 565914469, 785458129, 424474835, 999119635, 720044438, 403134453, 511317376, 164661117, 302926599, 232399831, 20941624, 114265424, 298393504, 955828238, 24435666, 484921662, 337240791, 944494419, 627888306, 124944667, 897790607, 996812646, 788471053, 940013313, 426224079, 617683992, 701133093, 127105818, 225692088, 119407368, 710493345, 322746963, 277874341, 700904696, 226414825, 32184627, 230616119, 536803012, 634372100, 897438984, 53747636, 959495334, 715847823, 879495671, 255696468, 558022409, 664501133, 201242418, 8178160, 908901650, 537804422, 998128457, 212926026, 253087964, 229413909, 91649330, 492218337, 189708637, 201731494, 903065783, 755955922, 794529725, 818835478, 141610813, 11109939, 241573541, 462742412, 635994990, 699883649, 590902129, 871312982, 979563653, 774325034, 401082308, 915623454, 628863356, 322655227, 74083614, 708951566, 916206482, 246070822, 831303344, 192956869, 651447545, 815359174, 445907877, 932062449, 924162017, 44909808, 29147391, 460548741, 743399392, 729539607, 615195043, 801086578, 871427925, 569881214, 308621676, 843382277, 542036766, 502650872, 203878867, 440029582, 883425739, 690874336, 591298906, 257314594, 216647931, 76420856, 109183749, 502984519, 827586469, 140462912, 48037457, 844533001, 604859664, 769516554, 632703416, 386294493, 658818520, 491011218, 437064538, 739456400, 199861446, 538389515, 712093815, 772693373, 400601029, 979539821, 208527539, 800490083, 694251932, 771758875, 445657568, 746130234, 570341786, 711797229, 704752330, 591018988, 241743862, 804031834, 513547280, 221775641, 72268921, 360693074, 326710760, 98163589, 922954665, 208804849, 697581580, 487304128, 374964408, 610501318, 89182365, 836731307, 199612412, 375985755, 573310291, 299388791, 96635974, 230439369, 545481365, 712126680, 271352039, 137428613, 977222500, 463466031, 505552192, 938131278, 321507100, 445661706, 590576439, 645921920, 36223366, 846836733, 468683408, 841637880, 118666952, 506499079, 685421487, 925381776, 152178958, 929428640, 57460135, 320856671, 543637577, 177682120, 91228849, 203491039, 300317057, 411885257, 394586355, 756362680, 933090600, 355940816, 371246465, 959967588, 326638719, 169549154, 581288005, 901135471, 534290102, 825657616, 635762784, 780778191, 974602198, 956541288, 166549533, 801160771, 237435826, 28148162, 763293118, 201022699, 281718555, 375026124, 508342621, 30783253, 488291977, 104143206, 156319871, 996649100, 612561985, 539134753, 343082855, 179155408, 538210155, 278735914, 272329225, 369342955, 735362822, 204231900, 996091990, 47143070, 268697245, 530401619, 876059965, 630475571, 727609395, 393827227, 356982702, 323774436, 422332057, 977475955, 482967783, 966850613, 157093884, 701555919, 344670793, 769184166, 29386630, 671213562, 263312462, 826383399, 920541656, 457882146, 762293629, 348763507, 163910104, 260690813, 714839033, 173261665, 827022534, 369872112, 520288939, 312882138, 967121646, 459157941, 124608000, 512304204, 96699728, 81863269, 86309950, 62085249, 687303148, 654221665, 914676510, 372955088, 79803930, 927647650, 668154035, 377118835, 903650975, 255087356, 184104021, 583522417, 159125252, 249837750, 853230425, 481044601, 554773505, 964008547, 366862510, 781331192, 133419249, 573855520, 74289007, 82062069, 54635643, 78573647, 889683844, 129007219, 724410491, 111276942, 495580201, 73871539, 287499787, 575452819, 745408700, 698089636, 107939839, 296612238, 595140171, 545046583, 736539201, 262548832, 867432754, 996945190, 491225384, 834617727, 615082843, 236872018, 273225819, 716244204, 656276686, 139098763, 311477312, 213160149, 278879183, 829964497, 959023204, 593164503, 357303248, 360913136, 727988863, 700862503, 459358490, 600471353, 792191227, 492827239, 765332317, 643685309, 233046953, 9430067, 646956555, 518730564, 346616300, 200647459, 769508920, 609277865, 938460854, 587560985, 228408132, 772426871, 991163231, 590400390, 826379154, 508342638, 236727535, 193960803, 124140421, 823589954, 256188923, 782492249, 136342342, 418286989, 75831440, 418351324, 595777390, 510889568, 207600146, 671715207, 761615385, 978794552, 525737966, 282190195, 293690161, 505105288, 669728708, 452762989, 417461577, 636582066, 452517703, 244675251, 350792833, 528020868, 241882908, 139804624, 550460970, 41162592, 533364790, 882150310, 380356575, 154586566, 930617282, 88698069, 489486740, 644709329, 126376644, 338317629, 520392627, 964573659, 433136421, 919616089, 610314797, 866471441, 619885288, 268405510, 24260862, 71536949, 88516952, 547055123, 610351925, 871121483, 630033128, 613414796, 113225753, 1907049, 312487540, 96453869, 93001728, 108208397, 668128352, 751502653, 47238674, 217472696, 306966731, 121206093, 119564686, 900609484, 545661127, 907359688, 163280950, 323941691, 394482464, 830360983, 982933210, 236525702, 732744194, 965903068, 369217792, 310869217, 130945518, 420673216, 119078559, 998027792, 433052527, 39883302, 462039260, 495752851, 574210806, 723496759, 13241944, 101639529, 830883017, 120091303, 689577972, 162055248, 77391136, 508490084, 167647433, 450132176, 101246035, 651478894, 384192873, 785782242, 56374806, 903755041, 225467170, 951086261, 455637303, 992609104, 586303529, 31057494, 898842695, 324611173, 609208362, 906604178, 222889736, 263312403, 146400537, 178199508, 631144465, 373547355, 358065454, 360677806, 905294016, 158892342, 413631856, 26570627, 796610658, 144822789, 77559329, 862037411, 578694931, 831376588, 423463491, 518560174, 387839245, 202398165, 232037675, 3587076, 63581166, 276035916, 739411195, 281065158, 175330030, 650165712, 758999584, 318348735, 807421188, 660478862, 578215710, 454006454, 885225580, 123059705, 426458104, 679310372, 384825926, 138600614, 545113760, 129683431, 593299129, 734067698, 280114255, 496521379, 956962315, 860414362, 533826871, 71941641, 942391775, 880816082, 858578494, 416430513, 324645707, 971492178, 346120810, 938629346, 828107774, 657441244, 281935728, 399163867, 804763058, 498121438, 933788419, 468509629, 665497491, 367180114, 505783112, 746515779, 617329034, 475978718, 640415101, 212340352, 381416205, 815293548, 423275842, 274862352, 641147690, 769759826, 675140502, 746218196, 444730010, 458857957, 176567942, 278690861, 68981330, 315417739, 187336007, 797034875, 807152528, 891617482, 860040184, 255165220, 631740028, 209435585, 278446352, 895853938, 942518547, 629155035, 985622161, 906477994, 493878985, 681638237, 833653283, 829218992, 62404261, 319174812, 793554254, 558833560, 81372070, 939199258, 285056233, 995211564, 347037104, 187028558, 405221688, 197569719, 21941762, 481888724, 696343911, 416628505, 387513618, 808183973, 267111189, 793473459, 54538344, 250150494, 29912930, 959872637, 143284386, 597878300, 109256650, 50297270, 206294795, 481162075, 993447708, 116552966, 695444277, 75777942, 372448220, 856505797, 525435589, 826679925, 761766744, 88021584, 784445127, 371604124, 80302652, 708508991, 601264132, 760197480, 321782486, 157786781, 746771879, 870251278, 651545163, 390939016, 929145319, 439431464, 437701583, 100613261, 829843879, 42362553, 673883806, 763386919, 211396693, 206019465, 512396141, 36040200, 824014326, 147534540, 994445462, 956676393, 667017454, 996633172, 616057582, 264940528, 50365869, 655415190, 670466503, 699476915, 422034462, 770406691, 897586286, 511916740, 232042745, 960841650, 396868639, 775932866, 826525888, 433023051, 543139852, 451569741, 105017378, 296873787, 187722871, 609407789, 824026634, 728311790, 714395784, 736758009, 632913944, 4691184, 802682299, 730880127, 84314748, 702242199, 17115905, 216751660, 921148743, 375619985, 920798350, 302942292, 292176843, 685629764, 315708998, 956417751, 183033848, 173294306, 293305319, 266729088, 261348780, 335590532, 933650114, 915302140, 953451387, 144730817, 226703352, 672899448, 468107557, 439103639, 580886659, 724704665, 467591017, 766366588, 211603168, 447954978, 318573308, 920590642, 379312052, 839540768, 586047629, 966969512, 178641389, 481869070, 84828071, 644231616, 511456039, 822369685, 567238970, 690897811, 179724567, 464339612, 59582744, 384205889, 794452810, 240460821, 337624658, 806110408, 55948669, 411668235, 352478842, 852362880, 508544272, 471407254, 225259002, 198851677, 924496987, 431043196, 659120535, 428701140, 942539458, 219844909, 112596779, 547902615, 359160431, 4508570, 204909036, 933525660, 965589463, 747779084, 502519175, 26012165, 841137597, 755363075, 825666701, 370121633, 389160434, 819812833, 68290252, 982498705, 868020461, 187887313, 12074751, 100769276, 456836795, 649992856, 801045150, 136486551, 708801554, 608408874, 186480063, 236513174, 648967198, 42140816, 875013376, 716846793, 164911127, 597837650, 161559649, 775390621, 859562912, 751368382, 492036325, 862529735, 515071607, 4884889, 797196543, 509227021, 77143342, 748522136, 12288441, 288771508, 949680210, 792622981, 348932795, 158558505, 296539059, 898972694, 556469626, 739166716, 746121091, 977120286, 797039855, 888298221, 858941279, 867758807, 817509777, 620763270, 95395399, 627545422, 601990866, 29773344, 892010602, 109257484, 687644821, 128899394, 897001598, 520102751, 805126501, 772526339, 593788342, 507875674, 915897935, 788629615, 428948750, 906454918, 110840061, 741487773, 669880831, 784522770, 697477690, 746702320, 389039569, 470897949, 738145362, 542626348, 606799907, 559545812, 335976433, 739760137, 572689539, 643623650, 616102740, 597544923, 757143131, 941128958, 600152952, 513605625, 876477118, 474430082, 606786918, 603405832, 726284124, 331613854, 100361991, 156327535, 106145370, 724276793, 925451534, 617788905, 835328792, 99758139, 139135096, 145198834, 415884348, 906974061, 983402866, 882008297, 609083584, 924379257, 445304949, 569356672, 671700103, 611064608, 48764393, 815664737, 216857330, 128668163, 900976131, 997360860, 460666685, 133361911, 640265896, 187920765, 590516667, 184295468, 127077283, 135592579, 256182441, 736184963, 742853961, 709627564, 254210641, 868951036, 625389810, 322286194, 24482995, 534285901, 889201206, 147397266, 37934250, 367183999, 802964727, 958892756, 576002910, 828892410, 794208423, 598349859, 648749361, 746857937, 728305319, 796257079, 509971994, 234626568, 31195417, 151888768, 545653065, 958143100, 349642640, 801456002, 64582428, 828775182, 536854759, 750380103, 410158129, 744805721, 132917529, 557411680, 231644047, 774421527, 963044217, 952226021, 721156729, 760782664, 224336896, 703954073, 212331747, 393799578, 126825886, 167634017, 654502341, 833313103, 972494650, 918479326, 868754923, 590129459, 276145351, 72188238, 372431986, 111681030, 378093042, 808057979, 524505149, 764285903, 143508058, 231205193, 818780196, 648771703, 660762020, 718954164, 72216969, 92759208, 506824524, 592996539, 975094958, 630648342, 625950793, 114061672, 223313286, 291231255, 68004777, 14679795, 194865226, 538907879, 172130478, 953054588, 22261844, 500707219, 678799720, 135553186, 698630462, 761640667, 476493906, 324690210, 829368149, 122988261, 252980588, 386748665, 473757967, 724330785, 440308846, 514451646, 248015205, 913998953, 914546678, 667866098, 74498599, 243509029, 586624242, 976443283, 412591500, 915191240, 890342730, 628657380, 572790999, 608364318, 575731892, 781924456, 101783571, 113682766, 932757171, 27198816, 408756980, 122928455, 781538594, 262124866, 50016916, 401045379, 626300813, 673864934, 507407695, 847099696, 699634612, 46500969, 693771715, 705661960, 19583846, 857716693, 237796982, 364143980, 775801722, 70266688, 410256564, 143930313, 661875559, 1602441, 798309731, 457980716, 489113421, 9093766, 294185988, 555317925, 576041143, 638190831, 880037414, 86837579, 942718849, 870113021, 434762720, 550935063, 268209881, 591136804, 810950619, 364629808, 932984643, 409423, 230433153, 310384605, 187213645, 344452564, 770634199, 119739377, 38930838, 212910152, 922436823, 264438708, 354113737, 555050007, 505761975, 531942855, 715003726, 6769665, 777712819, 957424109, 416645642, 330816538, 673133793, 383125881, 892130459, 45761245, 882566848, 952739725, 835965962, 992216620, 937810927, 858266268, 261640263, 540892210, 782332188, 895929646, 374694299, 861357023, 512130482, 487247799, 474466038, 615332381, 653620938, 502196797, 569975290, 746958445, 670406193, 168483957, 141377164, 625813457, 428780454, 648588813, 383792028, 936378614, 124358496, 224352884, 570021139, 965607251, 421806869, 125292193, 764703065, 867059093, 153518922, 901140693, 604164493, 651704766, 48748616, 117686008, 732046886, 544620932, 806846831, 728169500, 244393101, 110063515, 291103283, 195075431, 939021866, 712964358, 392709645, 375755946, 701919896, 142448393, 448877815, 161662764, 601467683, 388055313, 498816190, 718829053, 317946787, 713276904, 129851630, 84415380, 19481106, 702634665, 364336254, 106814926, 251600694, 186437567, 507442776, 657148964, 463215007, 635894894, 644900176, 227362305, 68055552, 242949609, 803232545, 221452835, 582752080, 367311583, 783958305, 400665052, 781774097, 501169702, 369759789, 422737577, 75815800, 327021088, 753124275, 822432631, 450826464, 287775126, 920767444, 668617961, 555971226, 293232537, 574523333, 917468610, 521469852, 562435736, 494470125, 404017732, 537208382, 35915292, 723370544, 863435950, 43230877, 593289998, 415792817, 141038020, 17504260, 256098245, 941878176, 674394992, 974976783, 430416817, 199149088, 98097085, 500828010, 669292946, 322550403, 385860114, 306969658, 977821126, 144556821, 858333758, 125998028, 211905837, 714309592, 30014042, 90408394, 201080940, 430314028, 37451274, 158133321, 303583889, 712321656, 482389046, 703259440, 444514950, 973644736, 335782130, 734987929, 236285552, 468396623, 434817218, 718091845, 679290020, 376873684, 962754552, 455685074, 146355648, 880733621, 510391172, 490405760, 685243943, 264959752, 365447984, 52558441, 483750692, 963073156, 410463201, 458805039, 945844850, 602528584, 410717389, 408416141, 985569581, 495991754, 771562947, 631996801, 171064386, 352474704, 190869354, 972559901, 870500648, 972834473, 491180762, 206749009, 64059742, 342010522, 408560391, 144476054, 430971118, 62098172, 496250785, 692312329, 199441367, 899856371, 699179645, 720140330, 355889509, 814951941, 328830219, 802540527, 690122251, 63477603, 473469237, 511256695, 515261618, 768545173, 768076163, 46336381, 656977824, 797301606, 355557671, 761339044, 442460747, 175130088, 822579407, 908725788, 397005993, 965457434, 871952253, 867869897, 440417420, 647244556, 392912864, 234998856, 617136943, 563763544, 271846858, 278659084, 901269782, 250635440, 874942914, 975587119, 957977702, 673860530, 297569463, 56448505, 969719219, 345367032, 755641156, 668689098, 894040547, 278247955, 857892747, 366911600, 592466273, 80847916, 961462764, 31486035, 620894849, 970652111, 821188624, 383808830, 11721493, 949375616, 517175691, 105796800, 568986140, 936786574, 894501983, 742391846, 911563099, 894238748, 281742058, 520479245, 169232327, 541238137, 306257780, 587905225, 45639336, 659155994, 134284802, 158503182, 415269594, 66080368, 125440182, 217065297, 608151430, 427415397, 310305634, 203755464, 710663037, 44661019, 34106456, 59215899, 295755216, 447855952, 10011094, 152746152, 89712400, 132174262, 770978879, 204364697, 915688129, 16217873, 852372715, 378459836, 580811484, 535721611, 448330117, 746484927, 905828794, 352439079, 825570424, 18636426, 995345344, 708427803, 564742988, 213353221, 141526779, 466350630, 774462361, 576804625, 18047411, 967323555, 681439761, 544870975, 976208180, 801161955, 542664576, 246137818, 314141202, 364405308, 37406932, 414283591, 361982090, 173306434, 566130015, 913741872, 171030096, 814670728, 106057609, 358093322, 64026639, 391637348, 328318535, 280039309, 161074187, 491932006, 732243329, 798993069, 624620619, 168738725, 27823948, 239410382, 663122287, 615792143, 168154382, 583679537, 284364453, 790754225, 128186543, 6675704, 190842017, 13400473, 848199588, 643444461, 394220915, 879376737, 157695214, 105225377, 846284117, 393289997, 793666644, 931193523, 683460798, 14998417, 943393519, 743333393, 631471605, 919236322, 615999667, 515683760, 154872964, 977958309, 565121288, 43284073, 714253543, 178126351, 293522727, 950648796, 175488515, 593428708, 257336895, 202092137, 812552579, 870135068, 776544003, 112272413, 292795159, 256725971, 27324312, 543614459, 971552217, 823845128, 45145827, 584753211, 823778766, 232620092, 626364890, 463331380, 616509456, 979225531, 48479820, 140120438, 800543504, 695488680, 151814594, 307800586, 456619602, 261694765, 488520945, 260600701, 155566246, 66506437, 237667418, 650269785, 153417837, 491769116, 142971637, 820853523, 373236451, 347943773, 252807905, 712624481, 451428785, 337141832, 678596586, 115176137, 410735766, 780015990, 785524261, 546867200, 822273100, 113475946, 792216594, 123592931, 836184045, 487825929, 374604796, 339615822, 897218451, 428764882, 463564810, 561247986, 660772722, 167358150, 582326274, 771349818, 173509647, 231893176, 427887984, 128498090, 124976693, 549663261, 712003470, 96427572, 445952031, 253892313, 874446484, 866129596, 738443325, 180568991, 384751043, 172679124, 408991219, 501673370, 309127310, 602718301, 129041723, 165321855, 445033358, 314571402, 268505730, 611601219, 411145075, 61498284, 369673959, 586967151, 738219852, 283482352, 982565838, 293111026, 168934406, 197492998, 479562322, 731109767, 162929139, 505666063, 359860746, 843658958, 480991898, 471945511, 333299990, 271743965, 825973216, 995413762, 281411091, 866818346, 319795525, 169993909, 390286381, 101817548, 587971832, 42903757, 912320721, 279695218, 924261616, 385770086, 285603783, 19804757, 714815783, 281807469, 237478240, 931140064, 343413607, 748024555, 998810380, 408467796, 229093472, 63019196, 343267381, 380723909, 104448401, 84660225, 184603655, 162617517, 420152716, 367846157, 281408529, 216633641, 758323319, 825826773, 599394272, 652980960, 456338597, 215034340, 336359679, 924157016, 953890961, 893097842, 55739355, 293409858, 592803352, 842115481, 566455674, 779223886, 567366463, 347952854, 52042711, 682271099, 753743144, 948875868, 980024223, 136069910, 989291515, 891935650, 887468472, 800650379, 512190603, 888293555, 554589388, 882976446, 458017777, 868877293, 364646374, 805120849, 104079928, 109928977, 575318525, 238006710, 9784497, 357525196, 854151306, 56713759, 641559953, 724657229, 924629676, 732590437, 296993711, 605060663, 663204712, 687501159, 448496036, 633379425, 908636634, 133589701, 322119414, 292210967, 140716911, 257946387, 32602403, 170492774, 568371635, 283757913, 302246533, 350669609, 550694968, 533344639, 681688046, 719513147, 238913895, 428925688, 681008582, 459472648, 620105000, 494245895, 717782001, 756709019, 362887255, 614079077, 95189474, 317671739, 130183824, 450228121, 195766760, 418256968, 408894093, 656463460, 972435131, 247875093, 421178787, 50861196, 558979737, 402694081, 238662273, 294230217, 193901048, 957021366, 59568958, 837226304, 272424080, 898402284, 390938752, 273736604, 621973865, 979073424, 166975565, 616807973, 948582808, 146531562, 617913109, 547391550, 700235034, 968418487, 317628029, 62677958, 191075626, 567388484, 930722477, 498665761, 726626805, 15804286, 36626825, 924699494, 167338036, 197789370, 10982554, 454405641, 744484169, 149054001, 672310972, 604837656, 123483561, 559592933, 938763575, 824410218, 228312326, 854734748, 74503697, 685734090, 562448258, 984206032, 766779754, 381994041, 827611273, 868407084, 423842274, 852374501, 556696951, 467377703, 525508824, 186063055, 326722698, 515005875, 515297075, 537180072, 91118735, 561255081, 792418050, 132946195, 879704389, 375319603, 981866038, 512596113, 325230891, 246150587, 997293053, 401015375, 771887529, 125327770, 880947608, 864857514, 740582949, 448220152, 435384492, 560466592, 893875193, 962717790, 288756787, 857456265, 111320772, 705726405, 756855911, 172027712, 842768058, 844227108, 5267370, 679155120, 100128866, 306983308, 113722975, 94596078, 943967555, 670789405, 592861885, 448230717, 570692144, 864569862, 239755591, 507571432, 331968089, 614396833, 272831980, 877339122, 695134481, 863472045, 506060738, 57925114, 183904252, 105030382, 725456121, 193421945, 612224893, 188182469, 935595760, 10202523, 876015087, 175068291, 475162318, 605519134, 270975194, 32729776, 521169438, 821563405, 466000775, 219649582, 490102626, 351567072, 356106393, 930231809, 419798900, 921095821, 125439479, 88557528, 328020590, 35786507, 718409475, 14200308, 845528039, 10893450, 928805853, 954362147, 272826054, 964298731, 895169032, 545261391, 913673117, 463106416, 687357079, 113524182, 131189338, 295891077, 855738169, 957325234, 170269805, 7243694, 223903866, 183743058, 163873923, 5289490, 954211155, 427094304, 441287796, 350585919, 466992471, 925590746, 699125297, 417420052, 783223976, 877930512, 6546517, 362894498, 313961283, 912914819, 170313486, 904336526, 256161006, 742872238, 575424788, 813932074, 148802517, 454952286, 461962420, 909224176, 182099633, 528507720, 338457517, 184437241, 56356091, 800770877, 511958202, 606923451, 850642286, 853906539, 285024366, 238349806, 818725518, 365281886, 852705474, 901751092, 973858496, 593898977, 431748280, 465587806, 941499963, 703897964, 492037100, 610455480, 529155475, 322823988, 531726781, 444179806, 174056726, 197203377, 655842414, 983299907, 737656837, 347372323, 62354171, 921221331, 865000940, 25648037, 920288089, 554934242, 760234089, 620047624, 227716716, 625646627, 62708526, 215943823, 966248403, 998697923, 66416495, 182806402, 946960539, 878898051, 921083097, 925652193, 420294796, 578221093, 940987435, 915435104, 768041674, 442924112, 691664286, 276592356, 327495770, 261143733, 176841817, 729744816, 954829147, 214209963, 141693065, 410414633, 819092676, 461481649, 201637879, 456103212, 826733702, 978390490, 470766199, 812104984, 193744343, 104208431, 744092496, 71058409, 207179799, 608691212, 993374746, 51311395, 511567823, 618707292, 785855547, 877125189, 604777042, 953006206, 972822793, 324878640, 531907602, 258524246, 900136995, 885990771, 480707967, 533107902, 121128836, 821395517, 946677157, 330556178, 323022461, 151189080, 533331702, 181080266, 266927895, 537839782, 8876201, 725821181, 494728712, 701004093, 769237786, 648808840, 907517880, 102666095, 585247137, 173363703, 759846852, 951167702, 71460761, 59944111, 982785998, 79359380, 970925272, 415330181, 919748448, 220628213, 836594849, 35683251, 13996441, 908394106, 957385161, 799602628, 105276881, 918722638, 491404202, 598376156, 301376486, 702580078, 983980381, 239432006, 986661673, 634920035, 46830095, 509776784, 851115841, 29772522, 275771409, 821482788, 78873882, 274741712, 593983061, 976396960, 472584527, 305937943, 544617244, 79723489, 2877801, 222836421, 127311740, 341130337, 514201857, 117884731, 6052544, 11653960, 410273702, 40451486, 835557000, 722043598, 883424865, 771708406, 805841002, 547390640, 318197360, 157573652, 288539457, 238875847, 962638725, 378597705, 61344819, 860898278, 552023731, 510261279, 481512558, 214658827, 687212563, 897757632, 810904806, 902533129, 124719986, 136261572, 62590939, 91038364, 80594357, 893664281, 474330120, 444338813, 457906052, 15073593, 187613736, 411390851, 44438477, 505814772, 339897062, 163569054, 908043145, 908524605, 801542263, 514408078, 654928769, 453090284, 669223167, 984168155, 167229498, 520357386, 870917981, 221230763, 147674848, 40015588, 926820374, 877121355, 499211795, 338649505, 551402782, 978674120, 408231324, 508918566, 71208798, 882455446, 832337796, 232453568, 190441539, 573990929, 857852329, 418623219, 369672652, 476775625, 820945154, 457862733, 44152341, 15836537, 997375358, 891994947, 90831656, 16756076, 136768558, 421431253, 65025604, 622529474, 3659555, 771176983, 50735472, 515203718, 163602480, 558566346, 776594586, 507947707, 39948798, 408582960, 353722667, 856826279, 243650430, 617504244, 576785957, 706621485, 648106415, 753212759, 511826108, 72404565, 912304444, 122039466, 834704958, 408277463, 559959624, 978467461, 899165586, 305961683, 607642240, 8788885, 74450257, 443991499, 541462547, 140882046, 342692593, 611382001, 57206174, 94149504, 532384641, 235738883, 853916514, 341787919, 69732085, 321889541, 569941756, 580466832, 388751722, 578535386, 449283192, 174407969, 277271878, 866041395, 180257749, 97862118, 799739083, 331536670, 291412670, 322365403, 359156637, 855139020, 962193216, 428764968, 862075976, 378010279, 169457255, 962016626, 209625710, 906244925, 261276586, 178672067, 718385436, 29210938, 540089002, 647189497, 920847589, 814352348, 950372668, 188338906, 352265892, 330021206, 498844044, 529951509, 409905442, 847809888, 484214202, 551090244, 917354463, 720918579, 609609718, 37878511, 420828023, 293390771, 467474906, 738966074, 469248810, 546935268, 324031634, 178271259, 349046950, 720567371, 673327228, 913833699, 178787138, 908818386, 861304581, 986767086, 378509432, 404130810, 73539003, 603900038, 888781109, 179666782, 313194207, 702756974, 292589752, 286561872, 92155100, 846339467, 393738006, 516852765, 641418173, 152290216, 773144099, 387819999, 207422505, 810486564, 438436804, 29744440, 256108175, 408450762, 245061940, 643277997, 209209816, 872603129, 622048063, 164780921, 643711443, 30104159, 750087556, 151725725, 596146556, 876359034, 84715937, 499101346, 289220144, 467229742, 122237187, 225252543, 558552302, 483803661, 724814848, 554697117, 105527521, 565774250, 437026198, 423615880, 465775032, 416164035, 742034431, 168271990, 30206889, 307246884, 849742626, 301566689, 410932429, 469663856, 569007674, 626923995, 115065027, 95615371, 106846935, 93310471, 646948771, 463861148, 871305445, 528105297, 366791674, 153537971, 899237888, 59481763, 202507538, 686100246, 700819948, 451082115, 488538021, 401770962, 175479257, 444279679, 513187673, 115831672, 236480016, 975482336, 558230948, 33504657, 873211493, 156613158, 268882189, 395994262, 641604792, 593638392, 527724980, 82514674, 562164280, 821317565, 26370092, 812789649, 683056325, 584263131, 557924195, 373712950, 264313309, 380798951, 87257375, 450203209, 944597933, 282688487, 686578116, 142339880, 754437900, 275203368, 556458175, 449806927, 551413320, 187783867, 328992601, 320030848, 491017550, 314507132, 227510989, 66262787, 456181224, 26766253, 312590687, 838065594, 369019969, 524967234, 718257015, 609506769, 367781567, 530239446, 984971082, 920434166, 806974042, 212749181, 933645115, 960798757, 441310699, 858235753, 993582159, 241966999, 422258154, 362331390, 897518403, 385705452, 26015865, 863516317, 296752868, 682462734, 640781021, 121539895, 522187296, 313074096, 780673386, 891822064, 732365576, 219698137, 490445830, 4633921, 323708260, 680071101, 834301823, 905788956, 919619345, 736684401, 802092006, 463033660, 629886165, 76606738, 811711774, 84127757, 405195200, 367483297, 934498271, 500915971, 160689541, 131930965, 219699011, 865727368, 900310040, 925461336, 186695108, 847400766, 548943696, 859948357, 384290470, 878476971, 864118597, 246949920, 928636614, 231722009, 53137893, 557608646, 653870741, 575116426, 105197460, 992941789, 195933535, 184975076, 971327712, 465568463, 240128932, 257882251, 659021744, 616230903, 592178382, 904828672, 883780255, 578150147, 995551973, 895253640, 282229589, 249800555, 564685023, 37527780, 473770202, 93335558, 827488589, 982063942, 616596973, 204258091, 578764224, 214944675, 545727748, 680383395, 338542468, 574377015, 881936460, 966878512, 185821274, 307279455, 917058920, 214741665, 866260239, 38073544, 249761401, 376805367, 772706729, 630095092, 743639623, 843532279, 993421935, 439820866, 69704808, 940719436, 863375194, 516610354, 177089434, 815452709, 344936273, 58079665, 538410545, 223855428, 221744061, 574721013, 715741533, 819497474, 913594494, 732936594, 427308377, 436217275, 569333583, 156032599, 68690734, 32723726, 653871268, 318757000, 164376688, 37654990, 499247777, 337042610, 361944950, 548782284, 336710454, 588551897, 512944116, 764677558, 863665119, 977771815, 626322696, 222501606, 957156432, 859095409, 74494255, 282439314, 57007817, 402911827, 201921550, 418688998, 414641132, 788414524, 276654782, 773454113, 349931919, 299264893, 365155792, 721283370, 979931184, 815608785, 307962197, 954906975, 911490012, 134194004, 683873333, 986958556, 656414364, 282118180, 442903925, 209897839, 152469654, 628643020, 818838327, 614840903, 310533939, 322121801, 841012302, 714495646, 105078030, 81732285, 609056032, 159900285, 40585981, 419831233, 327370690, 541910004, 161593823, 389393213, 216536409, 393359597, 912693877, 942672630, 14932390, 156251893, 457400212, 250083364, 616439288, 667256820, 936251008, 30069545, 372658412, 149707887, 227350838, 844287024, 151657138, 880631693, 257481042, 505011786, 711695197, 661044356, 711594114, 972634482, 986876160, 587278479, 849201032, 330635474, 277391447, 522124851, 787551676, 264862576, 820483367, 111246451, 921681294, 820887842, 286408294, 297496997, 440135667, 343577641, 755427285, 324920444, 837554705, 34473508, 772003277, 970905786, 594416769, 422546608, 191289121, 754233646, 800545585, 778440474, 52967533, 844862786, 452987144, 74916312, 186976862, 899904451, 637183962, 628880326, 319724001, 76249927, 32826677, 526468957, 903401811, 582906456, 436329313, 905245787, 255663992, 222928782, 941268381, 99384928, 784545862, 575468231, 941907858, 299397655, 835227176, 418734499, 379359460, 890884674, 189411381, 491439697, 267642018, 82384531, 155165936, 925456532, 257783334, 34310350, 731635737, 435401012, 137168193, 630363810, 549129372, 233692374, 402604069, 879076323, 741852211, 736674333, 806750067, 464888381, 208667019, 62744653, 140020597, 384270209, 729529675, 439332855, 643158514, 668318726, 350775565, 648193494, 185905204, 283426886, 422494727, 110087369, 736088227, 377378495, 625273957, 260570655, 296298811, 859936265, 458642230, 398199685, 137153252, 102997453, 769903734, 66739046, 814485285, 901537117, 189126625, 382021813, 325904888, 42874241, 177697296, 607314953, 824556891, 413993550, 218895000, 146414417, 986198028, 129623635, 817494863, 870592147, 519303547, 449440386, 261846448, 99375217, 301341879, 267332772, 487415323, 116300479, 269847107, 632646128, 901212849, 235847342, 873071523, 665315365, 247257109, 72545495, 343840820, 162189260, 929026424, 773075470, 997259918, 616274766, 747320401, 155298180, 40032942, 811974260, 697178546, 757267871, 120324972, 973383721, 155938017, 435595123, 542460396, 41849750, 167276099, 400716671, 375361944, 369750387, 860294909, 931802914, 740902109, 689318443, 589853800, 45944498, 685187760, 289127055, 39712097, 195075989, 75716633, 198027331, 935406844, 408588817, 472260981, 219099911, 258309584, 202891082, 180023235, 94707244, 772012134, 181117333, 244394367, 582082488, 126645631, 986797256, 993633410, 966847784, 754800437, 428126166, 47772836, 753831604, 698724928, 819752770, 676068333, 273818758, 797768836, 594247416, 189446097, 344060386, 479065496, 162223551, 233498216, 484168310, 754004095, 470957703, 57163791, 841974386, 150597297, 463649222, 782687709, 16417091, 750425854, 428324607, 960230271, 739675470, 874694376, 163287663, 428809251, 482515578, 55108058, 188891298, 103600401, 564537828, 179937918, 708799928, 339237061, 351007958, 154923909, 19867397, 79970903, 464928520, 670493003, 362627255, 273039041, 374420326, 916788157, 879700657, 442417300, 886590084, 880848242, 204077204, 737457247, 168520829, 144475013, 126310023, 943351957, 620097326, 676345642, 13431425, 332957063, 396362796, 922795494, 934977784, 95013620, 546092632, 276882345, 334078418, 740183391, 887496684, 376421862, 866910124, 581361500, 282152315, 906531042, 362286651, 440955165, 417381726, 776211628, 975987, 687107873, 374088664, 993588192, 500483928, 466197155, 152148389, 958596889, 139494177, 203024235, 606875070, 109441412, 917645715, 583796562, 454938498, 915883210, 173318880, 881800125, 312868301, 391745865, 898873132, 332257999, 439936986, 72730649, 250575306, 568752294, 678014325, 90937865, 534204352, 670301692, 793467472, 952991574, 562942800, 4152506, 192743164, 551380579, 153338169, 960002913, 915521740, 732018926, 16821431, 737030845, 609296986, 937518979, 256588559, 102726756, 463097628, 531214894, 506865406, 136173539, 501751505, 165007802, 962515691, 216813260, 404144840, 782183216, 43644191, 524206285, 874922259, 726571710, 355549130, 842065679, 838953089, 500010759, 461722832, 161755421, 664553302, 760489053, 79025410, 886405644, 250559656, 447999640, 634648327, 625426972, 833646675, 628729386, 195079144, 481902750, 435002358, 856887171, 179555956, 794715757, 772195390, 571445152, 466313949, 963857766, 320756054, 801350998, 347911481, 826800443, 71297879, 306921952, 492878381, 676184688, 710405806, 706874951, 701715596, 319896797, 75649027, 501398567, 703118741, 479118589, 124789737, 603848201, 119413651, 474684501, 20929662, 1368529, 346040433, 214041530, 175073279, 55231661, 671880756, 531610288, 111719836, 209198194, 95340255, 853122443, 540406322, 365293355, 209161916, 771363796, 659415961, 483845200, 789346000, 517124671, 380495885, 579510274, 568383810, 594326533, 713394092, 79624549, 724922125, 717324870, 406365556, 735074944, 915743078, 451885533, 729870318, 809328310, 887868687, 298622313, 749316843, 906200162, 977571862, 878160944, 240938200, 851038110, 203178152, 980312410, 335516530, 560820414, 79956815, 559235070, 897613252, 636496097, 613146039, 755603455, 505544422, 31299051, 749379500, 949955516, 321833766, 523706679, 675774414, 21805946, 350520555, 638041787, 759642784, 233037030, 97485550, 186898480, 111151789, 79952205, 359425591, 341746263, 124426881, 712819789, 745407437, 944661031, 910478563, 320313949, 852643024, 25512574, 760592649, 356673710, 65507439, 42081540, 768529573, 335043015, 487450870, 25937326, 217823426, 501670981, 905364646, 203175761, 74635404, 582215493, 36668159, 593120622, 217111731, 242055424, 383044680, 786613071, 603448299, 808269536, 327907818, 242828871, 677481098, 186816666, 182357067, 308834396, 970536407, 69494350, 990067248, 659659917, 724530792, 317768424, 542787356, 233658805, 765393483, 754887819, 752812085, 99604975, 292430934, 249754499, 877498797, 560869001, 752446491, 770183419, 830929823, 500335533, 813672467, 615294438, 484223100, 240233877, 554400176, 845520886, 405722079, 913951318, 343678473, 249362961, 908244380, 393877494, 385004274, 515140596, 797603022, 870532603, 46607111, 81280006, 369097501, 564752539, 743576787, 54795106, 739251279, 799245625, 503194332, 295947171, 739214667, 622681725, 656359150, 858439309, 930747268, 415142004, 534149446, 740307828, 837265136, 287928841, 837716798, 632857796, 897666147, 661988356, 935691623, 52828648, 922350275, 996198112, 329585590, 200818309, 418878225, 347106059, 13888366, 752666211, 825822209, 878662362, 760646933, 859194952, 649291631, 663299409, 182547655, 351750056, 262459621, 967657937, 723191939, 116729659, 557053945, 475800480, 635388675, 645375219, 229185610, 102546839, 754687932, 751368687, 909935137, 226659202, 188271111, 900199947, 319355171, 98600650, 305554208, 825518206, 143557032, 60629162, 91333540, 163574768, 149900498, 38814615, 129756997, 581278041, 535640995, 939085880, 374641031, 629699378, 727355605, 429031813, 745649308, 98751589, 830753852, 986719508, 244585113, 562676528, 100010564, 921750529, 325521690, 558499327, 306874874, 599815650, 53520781, 907542419, 960742990, 946239132, 466558910, 247299682, 619172808, 89640297, 529931857, 716284873, 383788763, 465853099, 229631854, 488158890, 225181371, 123679808, 202940831, 39148071, 534559227, 370007853, 878030139, 59237473, 750132963, 813811383, 894084635, 508517263, 498522816, 452347323, 401417963, 866713304, 690970285, 233767429, 401856640, 551411261, 114922650, 296847114, 144333456, 325092482, 471786969, 846851726, 438600651, 921281986, 104456173, 60394054, 316670963, 611174870, 671296686, 653754362, 80209464, 959817856, 405455330, 823112141, 980179111, 413854162, 874824715, 217411694, 787824848, 684296551, 106012774, 243247866, 463968478, 56019181, 496231303, 317588206, 621345608, 52236952, 501769936, 301244122, 722991958, 702024555, 552912278, 100379614, 44281503, 461565152, 744024426, 255433143, 31265636, 908085810, 25801299, 490331623, 537122675, 467483806, 63278586, 614458328, 496139710, 306878929, 570380481, 265750291, 579904967, 272803842, 556192315, 181398074, 742515868, 343418103, 276014766, 740664601, 801898515, 687352186, 390893365, 354296201, 841706607, 366794921, 993040985, 245252094, 938592599, 296438022, 734502912, 281462144, 767293725, 857322458, 782191840, 897546506, 256985560, 806906802, 918914397, 380207445, 815300491, 156623084, 257675224, 236882105, 118722001, 940803312, 96453024, 871927418, 135130569, 84112227, 800208800, 234829604, 496448996, 787590637, 565352259, 882867899, 36192786, 497253025, 765714393, 425855182, 464610825, 597768467, 628153364, 385545352, 17190974, 210721924, 117382915, 556212188, 699969619, 873632215, 392655029, 474320108, 537794, 470906933, 995409820, 803334050, 942424402, 512024463, 255277673, 669339814, 641082839, 624269128, 9475225, 184156521, 39871818, 311443033, 662322590, 780431474, 387188674, 531723181, 443080826, 804322967, 412939425, 723794112, 364327634, 681932765, 655277794, 684012425, 263345144, 310188627, 584355498, 956669649, 23232558, 147498678, 2460469, 563753750, 21866692, 730230007, 215591716, 888826165, 225357555, 279107501, 774033285, 101746394, 695783936, 360267892, 789608641, 103249160, 419865436, 81630194, 85214734, 568562081, 316325677, 645661811, 463573391, 171012575, 177376757, 166267944, 906878215, 250362421, 396017715, 836446763, 50631245, 616255833, 652246073, 690541018, 322027253, 53625500, 124704198, 103305376, 953579817, 258004616, 31785233, 684820717, 516286186, 688893032, 438554912, 624312695, 296708463, 767094164, 203251445, 388529802, 816769839, 589961075, 483262482, 519019255, 431858486, 217389187, 930949235, 321628648, 980588210, 890786698, 834761856, 985306580, 768253791, 943912154, 134728617, 977122639, 787426925, 300520268, 214781138, 803097121, 980325374, 267641119, 179320954, 507504098, 137858161, 748183619, 476054154, 646241322, 869170643, 53164753, 880245687, 246062909, 84047924, 802705913, 348152041, 827397955, 18234661, 287595992, 327930712, 533169367, 892326526, 695274337, 427537408, 460271341, 34192164, 91480844, 498027922, 823865017, 458150165, 507493005, 847260496, 850429663, 490237205, 253374362, 290071016, 789572965, 338646247, 33788990, 61052025, 833215270, 403543342, 185871291, 259385828, 739305579, 160179770, 104464836, 498402550, 919754098, 254970964, 895476188, 434450855, 307376102, 925667147, 26441490, 713311623, 863058835, 87412727, 993214071, 624081897, 897429357, 108269632, 894645190, 87900746, 603699715, 327996264, 791129699, 447687173, 81218137, 611503775, 9158296, 655594829, 852686700, 132694698, 270072096, 816405341, 156001790, 916231731, 630946420, 16751002, 952536738, 271005707, 86474739, 498535745, 155406686, 567405036, 803208175, 308155064, 78832770, 12728736, 254522064, 508931171, 843995836, 647441207, 34011532, 629799482, 576968475, 514877480, 368454184, 874336294, 347816075, 410240486, 837042798, 983396515, 314946711, 831594763, 858010042, 699220135, 760237225, 864042351, 423763431, 962238156, 441420412, 878441936, 110244073, 493424692, 290778252, 69871731, 416208662, 929402520, 372275976, 53770392, 391774771, 791129216, 743263299, 915525062, 57488186, 392562193, 474154454, 420596034, 533569830, 21433566, 521755085, 267916125, 205578755, 971308931, 451234504, 565216649, 406515847, 687522445, 256397969, 28992700, 189943523, 530703549, 138327525, 251229629, 347511977, 433088092, 45045426, 881669996, 611419234, 500939852, 441004220, 49816765, 632522370, 80709469, 619010957, 628942339, 285777735, 393103050, 357148200, 504076293, 631699434, 751571715, 241157287, 119162572, 934209217, 400977359, 761317599, 598662838, 314066408, 823516923, 269926465, 871720117, 609889797, 775669336, 464104088, 610848229, 355754634, 878125110, 876064618, 983001157, 569974750, 773336061, 661659174, 301966842, 777484254, 613557183, 56681246, 790055439, 132641447, 560671723, 770436815, 62248189, 158673162, 492036066, 761289393, 493751813, 207806764, 648978741, 38396582, 900401183, 737647993, 35544653, 636471551, 872756503, 132676222, 146237957, 453850051, 411893800, 270882430, 691626870, 458865534, 380962082, 947417096, 325892554, 716204171, 948942679, 274663154, 130852568, 408267302, 363133419, 742061504, 977062474, 733909715, 491168615, 428546748, 589044725, 446164874, 875987086, 896585385, 277249384, 779556388, 758609950, 623709720, 572295481, 229397554, 108659237, 988366671, 971214135, 943006119, 713306627, 998444511, 366523820, 126701325, 680641803, 576396799, 498421160, 944454439, 343685011, 913924244, 430089830, 178750843, 637144792, 442704890, 177200406, 494920915, 415431184, 393702902, 699918082, 307092434, 783611144, 299223674, 871279343, 449048076, 846441127, 366275459, 802691658, 614094134, 488148981, 892883431, 799709915, 233912073, 880579439, 814171868, 615349890, 783900493, 548531359, 900811752, 75917464, 116923281, 327164919, 840628519, 477491309, 27489982, 850931097, 979505335, 900218928, 495127257, 127552849, 427716721, 673225642, 601060715, 723196888, 257239326, 146339730, 978615707, 752665989, 690191464, 712851947, 260700237, 701327820, 173321010, 199228883, 280758181, 165339266, 982171785, 997894564, 293615785, 369330249, 702496027, 674120263, 877892201, 443516672, 69402535, 701551814, 868800212, 255881762, 476832280, 939741801, 202004492, 663550695, 395717622, 530566704, 336067536, 532688236, 534815639, 872408239, 992969186, 719525623, 826420416, 846300262, 769721745, 943519143, 648018199, 85703446, 30745398, 799737411, 17693812, 349185266, 296350920, 792233879, 983332621, 559117601, 814472143, 776675834, 270220259, 160651322, 518937137, 53528221, 445203437, 413330759, 495539926, 418924017, 220921790, 853770650, 18466521, 266674983, 707192007, 219542190, 856250976, 792144226, 754611453, 793363711, 448188974, 445232549, 269829202, 62549503, 323689878, 902450018, 983353638, 180196109, 722686257, 120206330, 326124605, 945954333, 102191900, 134154542, 741265842, 234652127, 718827295, 21178048, 583212064, 769086134, 445349163, 968820829, 602351677, 382857660, 654299396, 902826505, 601374948, 918816810, 423058687, 629290003, 72712827, 677892515, 810359493, 674661022, 416996977, 824607609, 825761619, 732107065, 797000417, 744918727, 399096651, 299818221, 69978051, 514165285, 715427086, 32182319, 713923579, 654669789, 480187422, 702106305, 86566591, 822642599, 850338625, 715480425, 27056408, 719576318, 300085679, 76869784, 621654878, 288787277, 474126954, 14892310, 744745235, 884930859, 339925233, 700275191, 949423433, 276429704, 727789902, 58934406, 863503803, 234763338, 464433579, 473304956, 623228338, 738189033, 227101225, 532657834, 627816751, 294289932, 276517069, 91860344, 232610126, 200148933, 189224608, 78119547, 734041777, 799728152, 476663797, 78512711, 375326602, 108459342, 515619756, 115198263, 957044975, 374344148, 666226063, 1600590, 98728568, 408889062, 912575601, 220155139, 667108378, 629260584, 19246054, 259330271, 815978657, 238626749, 48153479, 120418191, 800380586, 510061869, 59829262, 825524567, 334753491, 34182484, 936602892, 833706499, 591983559, 242723254, 760662256, 199325244, 45036472, 183441007, 640146560, 740127319, 864933869, 332039403, 178310561, 973970750, 240387920, 808401160, 414292993, 439582441, 865751640, 939498012, 49361673, 51927210, 404617638, 414163173, 505731489, 573480594, 233247500, 194760546, 183060041, 256795561, 13582226, 550014114, 8849244, 149791837, 310529261, 44801821, 736798497, 432697711, 562192691, 408872067, 153984389, 194021824, 138961305, 514372676, 935823804, 666266126, 849681544, 606657201, 424387001, 761474620, 812879676, 393448783, 538203230, 452054396, 466878369, 759825436, 672422854, 223326172, 911764386, 443436390, 995311906, 137106033, 300285165, 265400458, 364215853, 922428125, 779123225, 719147698, 223836003, 705021157, 352726029, 760720521, 814960860, 257198022, 737860752, 209414194, 763781059, 632059819, 343799235, 789747647, 106445651, 318427386, 236234803, 616775720, 639775602, 313354496, 806715643, 31497345, 167084440, 386618116, 702789042, 761591212, 216197526, 362938183, 54550875, 850858497, 524995796, 945250129, 664736955, 988934536, 120613890, 762316011, 344119144, 572751285, 183890153, 567999518, 692447457, 687567994, 950936643, 209137710, 33077232, 398415411, 110061699, 332748872, 73220783, 165170504, 940909220, 731925389, 127914722, 318352260, 32988496, 857932297, 429342231, 481137088, 799646091, 581722118, 174889926, 351278357, 351632326, 700117284, 950564425, 410218293, 868970903, 233915228, 923531760, 589440245, 199907514, 899105056, 323127938, 269322009, 95761148, 124327690, 784269523, 315149225, 412054353, 886541951, 206889028, 674010802, 571678612, 305960702, 254982613, 285715206, 952392165, 812666898, 433624205, 818383314, 618668175, 482909059, 757440184, 320018661, 653950442, 754047514, 841955649, 829334098, 382190621, 342711529, 473701402, 482938138, 265152614, 24009387, 300574237, 617904038, 590108627, 453624048, 37974221, 567996126, 51048494, 370101877, 325346993, 893917581, 392615754, 93160917, 44199000, 307010650, 196093831, 908867305, 407800066, 44865603, 612845302, 530307382, 685885, 210691028, 187925900, 444204554, 488491466, 923332400, 435269648, 27427247, 474377908, 901890259, 989815948, 671432298, 845335609, 374615957, 491933573, 360941401, 942284181, 365596956, 141300253, 701674290, 847812323, 848620229, 780293441, 243568056, 787350731, 74358681, 57443058, 606749178, 579993075, 405224296, 871158959, 797882869, 774403105, 914433945, 286594200, 559581679, 154287699, 125280598, 981058556, 65305596, 251028739, 813664571, 401337839, 378737585, 184514652, 987133982, 322119671, 147135969, 877842058, 996307569, 515760622, 582979985, 394237985, 899370039, 533032850, 210341471, 671034634, 705830040, 854157060, 278951559, 742332715, 23607953, 827662033, 759065017, 468964291, 453956896, 15174206, 482152279, 617856661, 162527246, 213196735, 408037515, 230783611, 954209428, 838454668, 481932851, 922671197, 23678015, 772793789, 390852589, 601511578, 169100334, 771121651, 251712859, 192907985, 757228352, 763318007, 708329173, 609824029, 238682037, 232026099, 258860069, 444187652, 349517767, 427893583, 169788331, 496628112, 5672294, 692965543, 495819154, 391983424, 95656280, 935648866, 302942668, 65033240, 104254655, 830981710, 136613469, 187842319, 410665587, 276758834, 962989290, 264826416, 612508309, 280979884, 700423206, 370507484, 244466154, 241626258, 694546640, 66251027, 307099839, 390890845, 875223133, 375529616, 834293097, 267324276, 440821328, 105408598, 993686696, 904297914, 293477102, 445840469, 311287477, 675974675, 200767904, 387997964, 173379272, 350056444, 879282800, 653908423, 180075225, 782261450, 107319619, 758818558, 159922406, 775106187, 803755345, 615533570, 944510643, 971322362, 627704043, 545048001, 385160763, 578077716, 703009002, 675523481, 874937653, 776446480, 88099381, 239727093, 935258708, 230741586, 338525743, 537315676, 59354417, 855548875, 807435254, 431986243, 632989971, 892219945, 754755280, 70067371, 284514624, 719351018, 44198882, 640623656, 965733499, 415728704, 907305052, 923008914, 631168405, 42203159, 588690831, 688621625, 531349905, 372801927, 283546586, 13232552, 97165959, 731716462, 12074829, 387169830, 645293362, 380421139, 441754349, 667043510, 150531927, 658951368, 500897328, 142288957, 644577107, 213964381, 240718608, 97925700, 932004908, 503619214, 495644587, 597288911, 790254371, 486860485, 825569836, 315719269, 771743532, 600474623, 397139070, 739685607, 789114040, 286886373, 297450027, 45978806, 740702015, 627621993, 931921539, 680550136, 400266646, 949560244, 506156072, 999180920, 796110279, 978251197, 551271934, 428764677, 45641402, 741456680, 986359182, 496355408, 835203971, 958512414, 713592504, 340998093, 195811602, 979310463, 949931422, 690309930, 836789619, 176054265, 312206492, 11067409, 742552586, 112409401, 60281045, 672976514, 648294606, 707172414, 246353787, 561121694, 235588415, 264068908, 26300437, 541403850, 632837896, 118270223, 901624101, 338474561, 303249274, 673702538, 786688202, 671572183, 542963937, 835873956, 647143318, 450086639, 541904793, 888374805, 495188646, 208587510, 345770005, 313975958, 724859485, 126909212, 184925580, 479129432, 621826479, 497938580, 870134092, 436586450, 11780588, 876582885, 948212796, 668863915, 766275375, 150672080, 669954560, 23084395, 126062278, 351778864, 746769545, 965631001, 603362929, 632337703, 822857926, 143756572, 453937299, 769912401, 887636088, 440568138, 318364336, 436635685, 750268478, 828235678, 969071365, 427827274, 150114450, 607264688, 733001213, 270809860, 943577766, 800082605, 485530452, 404418072, 472125259, 674385707, 64996111, 518075655, 946302178, 719029478, 145645571, 340653788, 829872729, 325167216, 403518970, 541409873, 724734131, 783910684, 798931227, 747982043, 485206967, 954523715, 554075946, 57312683, 199052213, 868675792, 252723287, 768122383, 150894509, 804997937, 612360070, 171480336, 382167316, 705954721, 616910229, 549306701, 542996526, 912195824, 187901075, 449604276, 826866656, 436779729, 897242120, 444478740, 458981018, 609407574, 316370429, 362376156, 589481380, 592147260, 376292830, 185358343, 473370953, 828041987, 63296194, 917922558, 729750960, 736084025, 938044773, 625420926, 112870648, 564391432, 16381208, 760761527, 602832826, 351800187, 64187541, 219166243, 796455831, 287689417, 532038708, 986015353, 741526619, 502810261, 610012890, 798271794, 46308333, 985884126, 130322935, 889179612, 341314415, 228870813, 317914827, 168354507, 538882416, 959480345, 649728931, 791680252, 889283558, 802949932, 396000078, 78056494, 461522951, 261780409, 47774504, 489004000, 265399221, 550758000, 108041910, 380887700, 593687913, 715206161, 603543508, 789062628, 682661236, 188608399, 76336998, 301748211, 211739260, 594161930, 129596254, 215578391, 228600044, 3767509, 410913980, 326024948, 743749140, 246612003, 204707149, 925769905, 702389991, 993956600, 467270767, 544561708, 644666700, 665344095, 359904661, 349660756, 707660032, 591463332, 588425034, 939217984, 133758613, 309390143, 153385741, 329697890, 832292420, 781676865, 637434004, 732445294, 329573238, 145239713, 622603824, 647611498, 163114030, 396852204, 546818190, 299342493, 269532080, 608193276, 878005805, 458884356, 102513655, 65550449, 904786989, 436304859, 185162967, 888600853, 974377868, 575761795, 118558543, 680567456, 3396895, 704046297, 191028410, 601204473, 687717284, 92911792, 390109227, 304775491, 124542043, 114036826, 27828518, 512509074, 118674233, 707616789, 201986773, 430643726, 356256934, 70560034, 969075432, 968056852, 45310630, 121104709, 510829573, 204252851, 549940169, 273478206, 333206802, 442317733, 852745329, 411670308, 319413458, 764215381, 739325104, 637460490, 39467442, 609060584, 221676077, 122682937, 957126850, 872511946, 825658066, 801154102, 774940083, 890105512, 230848774, 123319111, 719436104, 575960404, 629061208, 603083346, 291678404, 614343736, 205704106, 216765601, 938679900, 634509557, 231526641, 125897962, 581463998, 278259744, 231275204, 916495375, 768370372, 243220479, 374572699, 7157882, 508911371, 353159729, 366175092, 589436875, 710631172, 382815710, 970269987, 751940468, 183917709, 58906645, 510652065, 768085550, 271968412, 303658670, 171601419, 29874238, 996965066, 338699628, 690542305, 870528340, 654374694, 531250879, 160311798, 17236584, 401687281, 464178344, 933664420, 708231420, 503202854, 634257391, 553012445, 692247438, 451542590, 56382237, 882066975, 67655277, 595449847, 34763700, 311400761, 978623521, 591693693, 15240385, 844689755, 305413325, 264188266, 241636540, 388703149, 285102120, 283999842, 710904163, 214902933, 301396867, 872898619, 347466250, 743631263, 991706112, 42931496, 363287599, 314774407, 530985634, 825087607, 576621417, 972521187, 482186305, 773742107, 516466151, 733614788, 875125243, 323316249, 259162405, 135911599, 259538918, 637956185, 694603417, 230603275, 991461030, 786888200, 73357438, 403564147, 163309652, 814876870, 244247205, 79102002, 830119843, 953209727, 433791271, 656845136, 316316006, 755277949, 167904410, 69081264, 261899895, 526493218, 603048164, 178007485, 137344230, 872495411, 766412584, 117020219, 143635626, 76788561, 681311891, 124339292, 517040476, 474032056, 973614596, 442842779, 826325690, 813992305, 240096674, 649510024, 748043494, 757112534, 113542292, 944086176, 569980029, 238525494, 938931047, 23744919, 349637182, 694017955, 211763481, 346503420, 649881022, 143429102, 930421929, 466271766, 60960711, 966796474, 834179558, 536153966, 207639669, 87196843, 465417404, 421553033, 430705884, 41447667, 935659366, 757923948, 630450663, 971005297, 30828392, 665196309, 87948961, 886127588, 164426112, 923996271, 464932059, 637633389, 313763002, 422877887, 716489750, 232116879, 462076337, 576940926, 682597786, 240335037, 880503073, 652603192, 592021663, 181571625, 296938380, 337005346, 929825568, 926793478, 182220158, 424510097, 133857092, 992947883, 578549199, 463509046, 903201687, 793199929, 289802322, 816472557, 166566022, 389645647, 158639515, 990482284, 731172018, 738207844, 763228036, 22513586, 998994916, 379901146, 579287179, 834521737, 965663969, 55396291, 196716715, 965943909, 689857558, 621979295, 528690120, 703268180, 654759374, 20619702, 451276171, 588550591, 944820115, 815329799, 935795605, 317980894, 536599868, 968367089, 768168039, 461744106, 803707832, 979101903, 867804859, 441483474, 703532795, 88467165, 103597692, 71094464, 666885276, 525456314, 243784977, 389670181, 94138621, 879889677, 516007263, 333263282, 456393298, 221004615, 743296681, 155624335, 161128245, 647215463, 766498658, 960803225, 84933272, 630241664, 991571026, 770357410, 904130418, 733521569, 727832211, 852694071, 669704084, 694098864, 227723963, 392674809, 119860635, 4168820, 572505022, 373905928, 164967344, 431440542, 770780122, 185390140, 469527278, 136541539, 931202489, 31595800, 788036418, 494753275, 9342305, 345233340, 207768118, 631642390, 807455599, 555171652, 216658674, 579375603, 19775605, 110470256, 327945593, 213672889, 827089806, 555753125, 367205789, 478770215, 709740658, 676041298, 589617968, 785481680, 566097335, 330919812, 926229823, 586902317, 392238723, 663707051, 665107935, 848080829, 782703569, 219549043, 965702710, 134391210, 845085164, 699249776, 787993705, 629622315, 972655588, 305628998, 84097541, 8811571, 106161666, 981868860, 797763528, 143726876, 493655429, 752987783, 599651577, 162210054, 58933483, 230856786, 598747040, 877144049, 661811360, 225284628, 458543787, 654339814, 13157109, 740560214, 727430559, 863954136, 485501526, 962368825, 322219573, 200833413, 142947389, 283591638, 570100692, 7737307, 749487495, 4149207, 450999279, 250042974, 37380780, 322672803, 759674701, 511045076, 11473666, 518935233, 110082079, 282229697, 729257649, 822497840, 167019330, 161025906, 547021508, 637910048, 687204509, 630077980, 779239966, 472285107, 543502036, 55872763, 880884866, 741533579, 554900134, 914159750, 547190394, 982521668, 198596704, 228794250, 43127828, 595492274, 441361445, 39608589, 395735026, 157398301, 30305780, 243374928, 281175796, 315695378, 465511354, 324684766, 858993746, 849691769, 132439679, 876363694, 785171903, 329726665, 688475108, 850253610, 966239609, 439791882, 27180544, 329925951, 803459414, 361482984, 631552790, 32619919, 712872121, 63558317, 242763911, 920162015, 583040632, 281971969, 530280887, 698011835, 156950362, 727104879, 936435250, 230296227, 373871041, 777138156, 35960294, 486255272, 341779018, 229348049, 967424907, 388696724, 340494794, 312067732, 859793850, 770912778, 742472588, 685955861, 20566600, 768032193, 611514814, 54193724, 382875433, 911436284, 528237018, 292878066, 156269892, 87583106, 790404577, 372460379, 388197227, 6255139, 790584177, 95169355, 957022700, 495654957, 846050076, 257107641, 545489718, 485951687, 808086329, 761231173, 854681129, 807234, 437425964, 608870847, 248346072, 403860, 906846780, 743582380, 446460017, 515297756, 511921018, 584800972, 348930016, 880838527, 354445035, 7771535, 489551117, 462323639, 345271463, 648202410, 950753477, 358331229, 418193393, 997240525, 939026213, 827454764, 414511976, 728209187, 391030888, 133810220, 543665691, 403797045, 11219120, 489272770, 508917140, 181801933, 920419220, 69411298, 361488783, 593223512, 443152644, 392365043, 948304564, 632019300, 762415829, 896636296, 745780512, 826751661, 186640630, 491583121, 660077398, 420971635, 37568430, 823924211, 289761053, 115925352, 35916548, 949607777, 710610633, 708718622, 662071711, 792550656, 444002604, 149420553, 159949668, 428987584, 160794615, 495305290, 110434903, 415262303, 250393848, 853831260, 856392101, 879789312, 143282888, 482819310, 143342073, 999909182, 805518193, 48695426, 915250997, 171852131, 362427391, 811933799, 286479546, 83385632, 588562770, 251348667, 104999545, 832098390, 581479555, 329439349, 341620977, 292562458, 928268637, 923840140, 766062098, 634816803, 987652450, 670191742, 713888841, 365982540, 961928994, 276626091, 899599147, 591270430, 704313300, 627915045, 600468724, 341167275, 593423889, 810745483, 105499216, 650682265, 550590862, 155839984, 113217487, 544611474, 697834058, 782975334, 939834625, 43435512, 634251184, 675589527, 657864128, 855922905, 538226438, 98964628, 576444250, 845686828, 432660815, 443753174, 959402816, 29573725, 423138834, 723627300, 425602757, 647513525, 753978652, 786793767, 968568153, 559146423, 625126245, 602027863, 335328641, 51542195, 258264700, 399716668, 920291511, 546993452, 48995161, 3356725, 996329855, 556788924, 404795218, 787316597, 861141024, 182702668, 983955428, 853252196, 148718756, 71670279, 338538699, 195380491, 190354365, 999002704, 160746435, 395265851, 906626020, 171750964, 323183376, 266627758, 223305730, 344710249, 273034377, 241996050, 171202491, 880358597, 695842229, 147589228, 828589900, 23659793, 268784037, 656795842, 579503133, 499344055, 985787891, 477182505, 211541801, 391718876, 240223670, 459271332, 771451275, 865124133, 643514966, 33512727, 783087084, 545155336, 787661795, 37563336, 756765885, 35206598, 431209500, 348708312, 26774799, 272439509, 7618023, 124231292, 573630893, 725935305, 742124762, 158742427, 359735862, 752389136, 449437709, 585019951, 62293537, 538031699, 170548067, 433296452, 364979097, 388708495, 124443368, 983335647, 488699240, 737686982, 287999626, 53965822, 693852334, 911745175, 490070907, 386412679, 951391017, 125213674, 71475581, 154981751, 943853492, 892761585, 477670182, 191205994, 732013321, 153853057, 486070395, 821608743, 906951348, 381760434, 566668165, 98600557, 736068589, 910558742, 548291451, 217616705, 817293015, 141897321, 371589768, 852819181, 692525190, 916016128, 224422646, 509087593, 616500277, 558641268, 714424657, 812179941, 32420585, 16846505, 993012935, 630148708, 268037846, 54136216, 532608583, 279634453, 324266560, 675833805, 161172828, 359086414, 716344093, 888813554, 6005930, 618755419, 484602576, 129447364, 110685353, 309472998, 801791421, 924516170, 41102128, 816665545, 518370731, 673550540, 915810177, 491164789, 164378337, 713718190, 819685252, 213277228, 635208476, 983556376, 388243086, 924021954, 419703289, 986913789, 511342179, 258206925, 745839846, 956590819, 208339500, 909599933, 407363685, 383941468, 784797233, 388818044, 729075892, 531299775, 462945995, 801483078, 308654792, 915243228, 592562242, 41919015, 412138180, 640213203, 584194538, 651426654, 540133062, 663541422, 964499684, 993448501, 435259181, 39493032, 314785064, 844708428, 689436635, 648842666, 240320528, 397425876, 469610339, 233844560, 815283287, 555347923, 429807, 849587326, 152663166, 930658265, 300719915, 307320204, 178216402, 898299914, 797670056, 677609563, 603844815, 540404244, 471357353, 106525386, 824134824, 333796591, 468481090, 600425642, 898807231, 857333420, 443856775, 52499779, 660750500, 308004685, 581206002, 283957687, 471899429, 406239861, 704168945, 813532366, 896883706, 120711249, 552963915, 950325748, 329936763, 801604110, 507540795, 140650705, 89466553, 621667399, 417540477, 795624558, 715334153, 805839595, 758951670, 178117947, 336423896, 375616190, 677027767, 939439822, 96860510, 555233373, 494304960, 173056010, 100844376, 779330693, 993391781, 364166781, 74748382, 585354468, 349350902, 722766462, 935150781, 371021000, 897976304, 763187414, 919849924, 775419493, 361271750, 496199579, 931951467, 958212467, 816191773, 683867658, 631343031, 410014075, 937691198, 416455508, 454755009, 12462359, 770953389, 156889629, 953433813, 460833694, 152233697, 947243918, 980257580, 495541495, 220610336, 457097931, 168632034, 792480607, 477319616, 268707551, 235604062, 436817802, 558440414, 968633239, 123692569, 838960075, 158867352, 920739493, 739527219, 403096403, 804836129, 828643466, 46362913, 681279964, 646402349, 700103616, 69805598, 955337096, 462950303, 7607087, 712242077, 246531684, 365400083, 567590921, 976341566, 232669329, 726586668, 45265492, 425475939, 161699174, 300883035, 738708565, 14621275, 332495989, 897207180, 395066636, 747008840, 816699584, 778238104, 186224002, 796587175, 4158894, 286987188, 675195035, 490880177, 897603788, 907792974, 550363730, 136585637, 975325362, 869041207, 649018900, 99516455, 85262965, 239391237, 249774860, 586095740, 475595980, 369055926, 535753321, 143452058, 587832135, 842336885, 543448194, 476436853, 582503603, 498256788, 312120741, 855967026, 222933830, 233001639, 394172599, 134872196, 257010160, 420927957, 772847744, 19390675, 801800390, 435633620, 493144521, 839127155, 152243845, 271970455, 168208001, 805544992, 83416421, 547293502, 947464123, 764790807, 401431337, 328480530, 689631522, 11363123, 335168038, 705979847, 725680572, 33483946, 51567878, 739852194, 272825994, 442535306, 960064022, 297376489, 406526037, 892050960, 522681420, 832616530, 60612924, 708251066, 485100939, 910453602, 107026954, 579559727, 205359605, 987866142, 790297067, 582074190, 872333920, 266451943, 406634997, 447050396, 534403304, 956452662, 247256710, 729401516, 298915123, 651877914, 575401353, 162375727, 339469317, 581747241, 785719028, 104549478, 726681512, 352737441, 915079840, 25165009, 330630641, 392160831, 33863568, 225673661, 659391956, 857942366, 180436436, 442791913, 346616870, 144542051, 31523259, 944162208, 557079862, 249937203, 334199294, 979007056, 278040242, 913339001, 126899555, 466704942, 644497057, 433483171, 847689965, 109048847, 473284400, 851420085, 276724744, 776879171, 881960101, 333368688, 427124959, 57088053, 508846671, 201827255, 988473568, 686698208, 182218214, 295623279, 544955769, 221023238, 773311930, 483031404, 713123398, 679974289, 280009107, 737872230, 647081064, 316329706, 395314047, 377406846, 25221571, 895811504, 738236984, 142806801, 360125346, 911958661, 814724715, 373191487, 605509792, 157858264, 862558364, 129194333, 712368246, 312221417, 216039137, 353672351, 60467646, 406792128, 194732553, 993800619, 974287810, 380897054, 97672881, 406313554, 481516240, 374420894, 201517876, 235985091, 430863996, 782466585, 48259648, 905291545, 80856342, 97662594, 384385033, 81122443, 439516481, 736511130, 746448531, 581450238, 785314612, 98385747, 129956292, 945360693, 622143377, 785843583, 463743227, 679240266, 940591405, 755063535, 224056913, 343186950, 182678840, 255311995, 67600959, 790621325, 660043232, 6819772, 848193051, 711114104, 897923541, 764123158, 522395856, 898292476, 73517226, 425019400, 147463159, 503882238, 525266204, 695995115, 672573927, 845449581, 688005629, 763208031, 405186396, 981896382, 935586146, 77516672, 240815087, 731080090, 464782553, 981314444, 88340727, 855290677, 639268550, 385493711, 11190448, 700731042, 903355601, 926002596, 889621302, 69234478, 719414277, 606048315, 765007390, 946318782, 959939498, 93063390, 512163584, 654134670, 770865585, 30365499, 858591081, 500798540, 153968359, 363531817, 425136544, 899676977, 776911832, 823133263, 92705873, 877940426, 267052772, 557602408, 912658141, 86750286, 811378118, 296097589, 383485626, 59817847, 982547156, 900153072, 505180795, 21275948, 506888083, 732585268, 89278647, 618293526, 262255325, 941400918, 584575407, 749060240, 444064267, 820987627, 704903414, 626461180, 817201960, 171834279, 74604646, 121283758, 992263563, 460910495, 400597706, 455725101, 411008931, 516527768, 829358381, 344018243, 977604535, 59689102, 108797905, 800365431, 423208382, 495386972, 977143763, 626616080, 716926807, 64719283, 852788024, 221809651, 696578134, 817286529, 400991539, 351524281, 24266602, 46968621, 725075569, 586836731, 201147661, 554253614, 65874494, 727596868, 754628187, 67425605, 804662875, 792848082, 54473278, 287853946, 501642487, 828789132, 19541620, 338989290, 50695689, 915743194, 202646071, 705783158, 36958679, 870548563, 14292437, 614717936, 242604067, 607690470, 978544302, 648426801, 45309653, 361620169, 437126801, 941981638, 39824920, 79661263, 880489100, 228004676, 419452748, 801694196, 59608971, 234905532, 422687825, 487625557, 357447154, 233898433, 407051755, 824740817, 748809658, 826402654, 402892481, 678886820, 876343285, 468394047, 497550208, 38323218, 198752885, 754418217, 580484974, 483820475, 290272685, 781724781, 995698548, 404604673, 142055923, 956182259, 416433152, 398531419, 264511067, 645623111, 841424790, 148312175, 532399891, 268724076, 369459068, 684343396, 314373195, 828983269, 111619676, 7662910, 355111139, 642533848, 21016026, 62315891, 567074648, 919317966, 876046871, 253448015, 51915289, 588153842, 173321514, 865187699, 978626178, 169783745, 710528156, 717591518, 137111521, 340658680, 555778796, 782890577, 443650834, 188798393, 774738071, 330695673, 321675361, 620473603, 340977282, 347521535, 632730748, 964876436, 160393703, 565216333, 842083199, 318596065, 336168331, 555906511, 73443752, 907332517, 372935160, 813711032, 715770699, 36149539, 497813432, 894288948, 674556282, 459362753, 214123451, 348489507, 17852355, 925213529, 17529544, 338048677, 792093039, 419933027, 370286567, 257357855, 266021184, 944006371, 46674915, 309451841, 488924557, 800713723, 609896379, 836444277, 211707341, 98230700, 768840796, 979798564, 129121064, 280712443, 619990217, 11130082, 837948508, 739559321, 57465800, 608004873, 666459075, 845898813, 223457370, 472528872, 531621764, 29279944, 522792421, 336543131, 905187333, 46024672, 107072353, 328457427, 832874142, 882336075, 402419655, 529320923, 585525267, 815893680, 877678443, 532643905, 466082580, 978742697, 376222406, 458068290, 138116417, 829811254, 654930891, 457265162, 342691287, 872223390, 344463176, 32571698, 256148951, 615157529, 564457184, 860606876, 516872054, 392089963, 179060158, 229689762, 269642496, 787463870, 379200860, 295991778, 656123161, 633961048, 512779842, 811956641, 535037742, 2997335, 100935598, 987817936, 337110345, 257314643, 290992584, 93817220, 60209748, 427701104, 830196610, 176888976, 179778069, 175521926, 980396837, 804046857, 251772036, 300943356, 532396667, 871714905, 474049176, 59819795, 281400886, 585547379, 845570055, 830855551, 212268480, 235394616, 393276334, 595928035, 352587069, 351393386, 697714266, 681855036, 987297632, 963518829, 309589742, 86773862, 557526376, 195157768, 247703052, 892690172, 4199833, 410295355, 383064466, 854878223, 134333279, 240964078, 856522833, 15263575, 423219678, 233297551, 400816991, 316032860, 274141414, 733684335, 816719134, 477834456, 943850566, 700147931, 125002458, 685325385, 522960717, 681079623, 109986127, 64993603, 872152981, 942241349, 416511376, 825374260, 497323758, 23201383, 648278894, 402641614, 136554555, 395335423, 768364903, 492361353, 674991665, 17389976, 587226756, 91895288, 343271527, 856040514, 68977382, 773196804, 925855252, 903018444, 709828547, 141286526, 45957244, 683172582, 47100953, 138063688, 491068724, 732213179, 816132407, 909105039, 118249937, 448002243, 73602325, 254256855, 938880446, 805208308, 855601217, 544924206, 587841746, 854857580, 818618490, 673193472, 128931712, 552997707, 848715157, 828503375, 248027317, 386215663, 354500765, 324716201, 819355518, 829261690, 805388202, 620326294, 653490684, 741054021, 591605760, 953806258, 117585406, 286280957, 399586056, 980660298, 546521693, 716820708, 334756795, 111694327, 271404802, 836998218, 782042529, 147276262, 7677169, 658485749, 923950845, 244359184, 920636486, 290502322, 577436351, 564276948, 660969888, 253452486, 867809988, 174413202, 908595500, 396348657, 541350548, 209178731, 687710872, 324817927, 659051407, 319418047, 285997237, 362841790, 608237364, 12217535, 409440149, 479989024, 656554869, 325847936, 109985851, 333110893, 309557552, 210285231, 129805917, 595945604, 443716533, 318894336, 720404283, 844016489, 589155194, 852779580, 908955149, 674396047, 534470644, 278810778, 730443250, 572828061, 429600453, 634386910, 816385743, 993132877, 390866823, 117381883, 119024025, 908203457, 805294719, 517669194, 953791817, 785172839, 817527398, 39772327, 989106939, 186472009, 192813716, 519609129, 414865443, 254126120, 963540698, 40441423, 866073811, 445102080, 859346952, 950647758, 287603368, 261742732, 721815079, 635693217, 32076525, 828976387, 397087670, 889998324, 36317146, 733567102, 848569404, 881203989, 974512535, 26492291, 394058394, 488941429, 632281004, 679803308, 328529079, 640691296, 391347834, 674559034, 674126547, 755011671, 945953691, 53797537, 776684027, 916365427, 187798618, 206114232, 300886222, 916053968, 274715122, 850919399, 756202985, 72451314, 269110830, 874669004, 967766783, 132039368, 278027982, 313762256, 31623163, 353282822, 947944973, 944698824, 965967783, 426243148, 159269235, 507051579, 867837477, 318121670, 942260196, 613567996, 982501419, 135946625, 615312943, 451937063, 7683623, 147900879, 146195221, 272861848, 291408387, 503885184, 393259268, 850431754, 677949500, 341028741, 247150581, 360986992, 444028385, 61827456, 6406558, 952520439, 20255952, 462210094, 417443627, 398324581, 106787292, 680630559, 214142897, 742960325, 138081144, 260805984, 304537301, 90530715, 990238195, 59823318, 380701978, 461037411, 982790439, 856188688, 220131520, 889907207, 275730017, 720519355, 337985166, 756848041, 302271897, 976485628, 214978560, 737515882, 560767941, 717487728, 710456909, 130289659, 100057940, 534429544, 480479358, 103634381, 352410046, 928313611, 623165340, 220072637, 520784855, 962019007, 331065947, 17113759, 593627624, 143473152, 738554815, 200344486, 304826602, 896685771, 933840764, 203142557, 923875131, 80732131, 50088772, 575493136, 132336862, 546544037, 367376638, 71957059, 752618234, 473255647, 381226364, 638638122, 739168732, 323419739, 190873261, 3780677, 827284511, 211981755, 177924516, 754520422, 389769127, 971094158, 105419347, 972097288, 971886604, 551118864, 260258590, 868099821, 369032844, 144753468, 132575822, 945220236, 652597175, 554404733, 527738956, 48318165, 8064169, 13657214, 5647071, 918925011, 288350769, 292963352, 933563299, 18228484, 732054239, 503178888, 610217752, 953157977, 659969646, 777587518, 554201086, 408237442, 619976901, 39902127, 105465376, 977717283, 5892007, 576968647, 453764491, 815600361, 180334733, 451123853, 223504564, 51101736, 374020752, 265271317, 650564093, 503840841, 952995028, 997711072, 239910582, 275462993, 370997937, 261319384, 128917697, 451902011, 518339639, 376319334, 304772644, 365025749, 473460980, 786709977, 506662703, 988269922, 648673918, 18891032, 14109288, 702705711, 839611545, 174702095, 464987669, 559692211, 938414285, 505933585, 336670255, 443307951, 191470378, 363624042, 118892527, 176440251, 386060550, 160835230, 518165549, 251651019, 784694533, 669169475, 469528140, 423202130, 77531492, 60713394, 621880312, 128252228, 162721979, 942828133, 502577515, 222907649, 920302045, 38667760, 752002129, 749900194, 894113013, 711419715, 596426577, 971683072, 76925511, 657788748, 98820988, 850448161, 830302576, 835331420, 608242898, 669165886, 701028293, 351434082, 491097542, 609410349, 892109353, 728986047, 361770674, 830405764, 194877855, 583765695, 298454744, 823327748, 603946263, 27667454, 604586863, 360461779, 578192581, 776225551, 853464656, 970556118, 557957662, 853833156, 912520340, 961580344, 861686892, 152248074, 533107951, 168167849, 87490543, 809209417, 696907786, 231592595, 51579575, 354347921, 159819287, 358659029, 874507739, 310139292, 429897440, 843445291, 275936780, 104137487, 195308176, 237129086, 844035535, 209929269, 804729916, 887415938, 542434593, 100769645, 666856663, 814576711, 770240165, 228913962, 872538046, 226616662, 860731029, 853535633, 233943694, 337694649, 261043822, 479594507, 126081538, 986496655, 314487724, 220270148, 308802609, 444009265, 710928118, 283024651, 123028796, 646551151, 164358424, 107741359, 463327183, 859630171, 662843898, 710000080, 439017299, 58811514, 305142755, 47410106, 327159691, 52363453, 473315210, 489447282, 841416206, 92484295, 146848385, 923831415, 62930929, 426776320, 980940885, 452984169, 899813158, 764885614, 334852044, 56424105, 870225753, 550485522, 220740447, 781808016, 981501748, 917818265, 274122137, 296676465, 321617989, 789486395, 246462004, 544038688, 169188993, 449241355, 80471745, 698174352, 664457629, 920971148, 370818785, 159889570, 873075935, 221900362, 109163358, 434469268, 695777842, 822616892, 418446858, 301951329, 697623126, 75639094, 480417821, 735697831, 492239645, 310468166, 168620180, 791443621, 228463984, 279634686, 130836679, 618997945, 852615622, 657579292, 677999619, 871853670, 493238584, 345388287, 588998681, 112537252, 15270907, 997370782, 493059525, 222472147, 618670924, 576550074, 808611971, 922534957, 640523257, 996354618, 957366479, 958691696, 538777119, 135370590, 318497467, 389351649, 398428053, 628339583, 587368273, 826913204, 680136283, 117523185, 417451588, 258357823, 530224971, 447899892, 962227303, 384679760, 639608440, 921144859, 144918545, 684439535, 637479531, 567976751, 566893076, 220476081, 303571215, 530383679, 990725286, 287545148, 979102106, 326881730, 455090929, 1280656, 422664216, 157314346, 460926297, 363925166, 644759359, 515007176, 984879633, 5663881, 480653791, 629063997, 238200833, 28469649, 40257804, 494974225, 517964623, 700083229, 443563771, 180165459, 158973656, 808701318, 48039979, 358544177, 788056049, 267520714, 666708222, 327364902, 879331053, 507226520, 114756798, 50128822, 962402611, 40874168, 529089723, 369753455, 714299260, 706157662, 508692015, 483475191, 17992634, 457648437, 958531523, 63874900, 899784400, 532153822, 370863614, 335399548, 321108258, 312723, 59635638, 974513640, 518598402, 350110608, 587683989, 216171562, 602610627, 82775390, 116740889, 478796119, 397476280, 583362852, 807511005, 944481407, 243236170, 205440467, 578163722, 365282719, 544477167, 75425486, 814676440, 758828746, 181236212, 961192906, 974282107, 589346580, 32181524, 970812150, 634583316, 482087652, 877845772, 884472818, 812082864, 562517763, 335528557, 627701420, 466118042, 891184379, 617626321, 918762744, 223020617, 388079552, 591860500, 904093998, 718098849, 898608647, 679856458, 152903336, 160137082, 696616359, 359225246, 144451475, 772218766, 995790956, 396287064, 921334852, 184559342, 151494721, 353381883, 672321536, 456095344, 544383766, 600695951, 645140169, 851577320, 986689044, 419734157, 99230116, 360381782, 70020020, 430769884, 381009939, 861736168, 982333816, 841878698, 919308346, 617618311, 934255763, 529676131, 370225166, 644294346, 763235273, 918024902, 429366943, 825396100, 772669446, 847726374, 55962069, 966399894, 801986294, 708970036, 190132318, 901807702, 909428196, 848653621, 292377569, 167058430, 852484433, 496236629, 722785210, 889141615, 477310090, 444851446, 363862191, 94945747, 888532568, 514839716, 228206212, 82039690, 977672405, 242494985, 72875443, 574464764, 274357384, 496410389, 916692664, 826650271, 256103257, 837234478, 545444991, 874890656, 764987862, 747755691, 906573095, 803495276, 854958215, 269321606, 531086889, 500667661, 4035473, 261550429, 121271830, 63252087, 696241669, 552062892, 917326333, 871093384, 424637393, 688632278, 315188240, 292369122, 348589541, 309345874, 476613095, 234951419, 136467996, 769372877, 499794857, 68494044, 348135569, 593511316, 56882790, 188052132, 560435680, 212749735, 520113118, 867773833, 155116628, 75870331, 737101666, 263039769, 963329380, 374235441, 333799469, 747080776, 70384293, 916073679, 227776067, 65231239, 568007382, 812079501, 815434374, 739516900, 272287, 585914304, 646519178, 293783614, 895740393, 950624952, 120183820, 533293338, 386685441, 858760100, 41310982, 958250447, 404658254, 207343980, 439673341, 1943394, 261518238, 227699466, 862654782, 883074916, 414473459, 950280552, 562579873, 577205517, 803637049, 127066502, 208600445, 693944973, 124928871, 753993535, 517996580, 780979056, 913302824, 669080272, 771420149, 506930894, 279984489, 527744461, 942837432, 736628159, 585739673, 637744925, 699474887, 851176656, 608667970, 252456036, 961019404, 624169019, 828445010, 426406241, 596241276, 769480536, 212628254, 910542406, 719688443, 831770467, 189676096, 492247375, 169080332, 469063227, 93062866, 286028072, 959145129, 394731456, 53156127, 57028277, 252469628, 87547289, 377173966, 247291371, 415167470, 292778813, 628565765, 234497285, 83454926, 256513809, 5314440, 375475859, 520472464, 673375815, 9473777, 181578213, 602834628, 745075304, 194725716, 635273216, 403679472, 372362399, 37172903, 395444107, 22737680, 508201613, 804996465, 469884851, 665892616, 122913461, 120248809, 657321148, 998050512, 249587024, 93817838, 644573050, 945091251, 699250632, 141879759, 912387155, 644951909, 674936579, 843902846, 348258956, 988572189, 735405170, 259091200, 205202533, 1951491, 4232445, 816547400, 267203530, 28507642, 418645449, 540892307, 835742339, 141915879, 405938091, 575451034, 592895943, 464285196, 909890103, 669983172, 25576711, 158941299, 266103683, 243626547, 511234051, 21057860, 938031362, 467570918, 580179508, 431653329, 902650979, 933436438, 325419359, 730780486, 256057831, 505639510, 278044848, 379994068, 840898665, 51053545, 237319408, 215511581, 793559692, 914874588, 1094627, 197982832, 506510996, 160473442, 632188895, 198357953, 956795112, 756953126, 954763680, 45463056, 972892237, 787311015, 481584647, 845340547, 910887930, 135111774, 425719438, 892814312, 930083408, 892111140, 922477136, 396948086, 204770031, 227595033, 54518472, 325964159, 904814558, 837655424, 957290800, 412940544, 956358545, 92786543, 185097719, 478677999, 448784740, 354550172, 509455465, 744396851, 949861694, 197314625, 780181556, 398645153, 134817131, 930899411, 251825390, 726363590, 470019157, 860377929, 423385608, 411481973, 872813130, 24884623, 32491395, 535580979, 874508889, 767220651, 463621824, 140398558, 440751216, 517034338, 702975874, 708512388, 693338925, 29120300, 715405984, 329805173, 944955929, 622173589, 203786855, 139099811, 524440236, 383632595, 939764657, 172194298, 345826281, 42748552, 489353120, 107872727, 351388584, 551187996, 491541546, 512708920, 519352104, 252451540, 313937036, 811213958, 574482823, 316703432, 897586580, 847629622, 257562399, 575327105, 935846695, 176733929, 740390094, 400841212, 938431025, 791870134, 273556359, 973994345, 869847865, 455749913, 562380847, 89888754, 856363816, 613284095, 659941598, 805395310, 157084499, 127652618, 446086791, 10370021, 185764784, 713878481, 153705337, 501619045, 121814664, 11091284, 846093218, 719182150, 337141223, 347593582, 742164161, 690284948, 622551822, 286606612, 446210, 719001239, 918203986, 909980213, 331883327, 789626667, 101259172, 190087648, 950600571, 18050755, 525906712, 659039416, 33384097, 236449072, 33534545, 138962206, 718107344, 806422215, 824261968, 218256205, 996768238, 993100676, 699022060, 620711394, 582464030, 619535913, 762070836, 276652927, 378191893, 801377329, 190557085, 126132416, 251393177, 901937994, 787178051, 938746896, 568146203, 866110519, 418686081, 396742147, 757019357, 130306558, 382908004, 206818314, 541764847, 745021287, 250230400, 864339782, 134241472, 913124558, 124326888, 832970424, 137135039, 5785692, 717513349, 260327061, 611825756, 555288335, 721613180, 742934040, 101419921, 904549121, 74010659, 473054009, 464229208, 698481194, 54142265, 620401141, 517445194, 311694797, 325422729, 72457912, 90403756, 67055338, 939221538, 271530437, 259115256, 959263356, 516684217, 389801724, 376794260, 117993942, 161158465, 139211377, 397799625, 160030113, 524453476, 349593459, 279401592, 40343255, 12334782, 333241887, 804570072, 877464065, 380217772, 469474179, 917501460, 978168247, 691402587, 857638327, 884084341, 246123305, 556306887, 155772525, 342161189, 711649486, 589702851, 297888757, 267337949, 927327722, 965612958, 978667781, 644558866, 267395245, 706384198, 369997136, 384687400, 743630169, 441834143, 642819904, 729875747, 962004092, 630119184, 70123681, 337118701, 179450780, 899711082, 861414232, 81781527, 889671442, 31320345, 137292185, 708586790, 790204344, 646132596, 250402640, 290534484, 684464784, 775500094, 877144418, 670101792, 4474871, 491202341, 505493593, 529238338, 480896279, 393885599, 430524530, 420632630, 163635483, 705575376, 619716523, 134790166, 609551057, 401080035, 16670594, 857688338, 878277277, 973789166, 628926163, 323986736, 183892895, 263595232, 345354225, 651635999, 799491325, 171608801, 797329583, 984060262, 582497577, 742520811, 391326015, 191392077, 467864571, 235723808, 31426597, 631947915, 506041066, 281816586, 868841145, 423707874, 147914994, 772142739, 332890569, 144485789, 718889192, 772424611, 344628981, 884497426, 260476474, 592434890, 401387527, 423630, 218559811, 338115303, 875268143, 34826472, 990300487, 317705213, 575266709, 558372703, 164324678, 56564559, 157061810, 104671184, 372452807, 415588049, 835956724, 669643807, 104759804, 93959915, 552372737, 546669764, 122368049, 42446782, 157897736, 894866794, 528371789, 367012778, 117005840, 863642714, 460237183, 584591460, 254535521, 531818653, 437375255, 249618504, 37298994, 183399378, 679626906, 489001246, 558575568, 603739273, 966797369, 563292887, 4184379, 986030545, 387656251, 230427539, 376534779, 504309115, 85493565, 296130574, 88368811, 166029350, 396583850, 593061874, 641411660, 829538328, 996223017, 593957815, 673132470, 226691880, 257697670, 283949351, 697906169, 487240776, 649503798, 992150704, 932061855, 128597969, 872550803, 270248437, 781097690, 776397998, 510537394, 763568621, 445758956, 512646239, 386993488, 200075740, 544479270, 483278971, 234724401, 157904969, 162488344, 803860401, 641008318, 609577568, 525602237, 281913525, 473263453, 558138728, 922951199, 15187543, 863751465, 340606331, 292657850, 325039822, 134289711, 852215124, 42943814, 317285670, 876442413, 925844577, 262191607, 379839430, 287474054, 766910954, 419307687, 591510038, 978127969, 697290014, 794224082, 820137615, 77719845, 203796953, 273875555, 969105609, 772768124, 991741401, 98150014, 684169986, 879539554, 358494758, 42137445, 608030187, 980179790, 221932843, 942847944, 490581977, 839232630, 878508099, 573371708, 214278038, 43912760, 150050488, 834058578, 123998793, 274176319, 735882268, 567558251, 938673211, 178361260, 635205095, 337756860, 357194011, 437431536, 342821886, 356036033, 403836435, 960304831, 73410403, 532340925, 94335047, 250279570, 940677676, 511467228, 14975456, 120658082, 640514982, 855975230, 69501899, 118642111, 17418043, 44166202, 805733997, 216117768, 870908850, 631096037, 485832784, 880447192, 177062860, 193813785, 473434159, 244253720, 523008478, 95867147, 521440262, 251500155, 55274824, 383403316, 445277530, 51191396, 662622643, 347425798, 761180006, 564183117, 515990137, 308939666, 25431609, 150401565, 615132013, 826706429, 518490325, 974397609, 817308500, 752456616, 964373589, 663689176, 138825282, 520157279, 825930436, 142424798, 287917893, 979435616, 676207886, 198747809, 377155205, 860687525, 456052856, 514092015, 337087481, 922037446, 992358388, 764757053, 194531764, 634326214, 343088421, 298745049, 139126824, 155737347, 580186023, 989814866, 527486846, 963646525, 543082485, 375321850, 882987124, 253384358, 192012695, 869815685, 252486114, 314891160, 924841345, 196813849, 994604935, 123557703, 169044080, 101496769, 574184193, 451787377, 143128051, 670810850, 712920439, 415573814, 148700551, 289442177, 806947257, 709697961, 54202368, 708720828, 454867841, 660177991, 207126314, 904973678, 202939295, 85117949, 9305408, 950949022, 225296890, 402470425, 49280263, 120561412, 598356487, 910887126, 185840374, 814702670, 275310558, 442064512, 907469835, 723220495, 70588266, 762467962, 520280149, 82922093, 148118019, 198669022, 458144134, 150230669, 149239191, 304537830, 601873170, 78475706, 373174318, 535862738, 199840344, 154121383, 159140643, 218684991, 784575779, 456096836, 164534933, 980884104, 51354846, 348349965, 605545935, 637613725, 453888802, 59805517, 717817749, 439520279, 351488546, 86660316, 622506120, 32568234, 792079761, 788522925, 582303265, 482974058, 88264802, 370082528, 955102332, 262335537, 836454276, 576831913, 976284843, 570629690, 876091419, 646937324, 97512181, 172027820, 146936591, 396697293, 551898089, 153954392, 621110339, 363714491, 153652162, 417275209, 814465283, 889633094, 421907314, 858400669, 971842604, 811118314, 259704467, 489989640, 733702862, 822932175, 262919261, 217092478, 810044661, 77467106, 871422116, 926637659, 259934005, 79098876, 617649224, 140546399, 860076159, 583376179, 779844868, 7448778, 354875267, 405786402, 258841249, 437047621, 115060808, 689867288, 524764435, 471976245, 446160337, 183368852, 488139299, 310049115, 737398391, 568940751, 318828623, 876471228, 364751693, 396791309, 983350331, 347547088, 877780573, 347076383, 463508003, 689500839, 628536308, 497505762, 666593548, 968905937, 9369277, 855486775, 852081366, 529768020, 524212416, 647876534, 518160141, 918908465, 623496083, 938676480, 842595887, 451226582, 363702879, 968747941, 395671912, 94290106, 966006371, 305958876, 265921948, 676293331, 962972418, 266531274, 673148804, 13769973, 347931238, 816825604, 891214575, 15217574, 369630851, 180814907, 899233909, 956352938, 517086300, 463765015, 711454142, 533032656, 257023405, 192333132, 74936463, 226089146, 772599497, 369032039, 838834155, 415128983, 436683239, 773719901, 661718164, 701288862, 156515237, 910389644, 493119389, 464703025, 487211659, 563458350, 903596699, 821787634, 609622072, 569041890, 556118489, 269491515, 897991705, 599730454, 405045529, 887728101, 43191867, 871130780, 350203317, 171737219, 582946130, 128956319, 248174780, 565265518, 340377247, 117531732, 525708869, 394242390, 560095114, 78347876, 396733281, 198049335, 191244866, 559781334, 891900984, 312313527, 937204431, 589451427, 395276851, 599040731, 377959739, 860720323, 549696417, 350370094, 917659397, 824996947, 514622559, 33239111, 254711909, 61560335, 81848836, 472947059, 752975900, 358346578, 178577572, 159525692, 291855913, 248585642, 799534564, 810135006, 498316302, 675519873, 896350478, 264060389, 163369592, 895024566, 548233638, 809437287, 361284723, 89746037, 258536530, 674278866, 763514904, 519601518, 354804608, 972226048, 241895215, 245353612, 783528217, 437627813, 637226417, 192485877, 594568801, 184281591, 998454071, 988116973, 250015678, 536337126, 885199670, 189369241, 564818183, 167476183, 242025000, 422090441, 567049887, 967338158, 243882014, 101549792, 945456507, 957627413, 909599779, 577844437, 782964187, 619662136, 335610041, 437581291, 109800273, 485454949, 142880363, 814975647, 924588222, 621635167, 62544338, 979418295, 516086912, 199535386, 160474752, 560281822, 63148351, 7878033, 416337387, 934831693, 668722086, 95113647, 337629544, 306132628, 834301121, 223427116, 681397991, 449820445, 8455778, 757531043, 915587542, 486885657, 280347993, 64986332, 29670828, 141192507, 512412635, 696236215, 841582702, 435467426, 339981396, 245766425, 866506040, 96343301, 244861066, 51818224, 436106854, 698170268, 307968730, 370880793, 684052793, 828908217, 351545426, 689666425, 951562796, 200462978, 241483815, 310841361, 424810090, 522546067, 223345736, 555100946, 866944176, 574946997, 178185620, 456742828, 816920095, 750886470, 524716947, 598370923, 535443043, 611054006, 679903116, 846671094, 852112939, 107211797, 156949257, 285887649, 959817751, 512058237, 860134599, 246352067, 377986507, 614622636, 670966082, 205787863, 839182436, 300965888, 330785278, 899334530, 644554064, 338191907, 336290616, 563616085, 108881963, 682583966, 547402677, 219375019, 326903564, 705981264, 205236061, 763010950, 112865769, 127049984, 238027132, 620853120, 877755572, 165293666, 38832079, 695682961, 6713313, 534282835, 449218737, 950912380, 750476588, 795567668, 123096039, 397616813, 608103712, 246055547, 102609601, 334094649, 426298834, 555894189, 507974855, 900566764, 808816153, 901877694, 574572951, 158265330, 903571922, 485531716, 142717787, 271449190, 783173281, 947596484, 672561619, 48281208, 792379161, 181162740, 825328987, 242767570, 38388827, 108814705, 822909459, 732855541, 545957963, 783059204, 120477879, 631590658, 994991890, 18383966, 780351571, 98784032, 582496574, 427678928, 184188780, 391665082, 280849215, 812230753, 94064582, 553886677, 914930593, 470043400, 123467371, 178840526, 885539652, 310066268, 648294089, 394132378, 101205320, 159272760, 724333827, 607267316, 29801359, 497297139, 63925210, 389663463, 105775952, 122956303, 242938248, 121294414, 137855531, 757082840, 468169545, 529113055, 229142781, 265708582, 709064125, 439734844, 122124316, 589925877, 919406705, 920224567, 779987899, 713292565, 573664243, 840564264, 508680408, 851705822, 626159180, 605564890, 104007948, 278106254, 840499045, 56165957, 653161912, 120018917, 277658523, 821626374, 572191240, 606063658, 771630873, 4112846, 523606853, 702820426, 136385863, 759548455, 836453162, 443015855, 496352010, 113062728, 118914428, 393036095, 698302989, 501850493, 196028976, 588268163, 137372289, 786042732, 931917503, 118883512, 151316219, 628280809, 659305007, 19084581, 834085445, 942587954, 966420737, 289921233, 591848665, 456183129, 632412892, 390855156, 166607220, 759155645, 327386171, 68255510, 29692428, 774572866, 237592357, 275219173, 348620262, 258622023, 736588077, 35692614, 48022314, 955063080, 538976926, 193357590, 116097582, 906064015, 125031519, 110409289, 276376192, 939936098, 51694914, 621914921, 89009592, 746061801, 667170796, 563580643, 719433138, 212902097, 689521275, 778708477, 223559747, 162086288, 899193045, 308930050, 879826969, 41628287, 889653227, 549632279, 195990906, 214008074, 552427923, 174455934, 907848934, 307186644, 960136392, 675786077, 542206514, 902748752, 921073212, 382619488, 637721925, 442527608, 128450986, 662084332, 475415579, 925276599, 269616219, 327009092, 511714544, 650451911, 952583293, 388257416, 882673631, 867526072, 576712211, 786105386, 182752397, 672585314, 246222800, 125571923, 710460056, 963946894, 345691051, 396722779, 876355216, 829447457, 913463892, 803602097, 95970833, 706693229, 940344329, 470868758, 298210914, 705027049, 855801624, 14912024, 87629051, 86783886, 152086158, 143926846, 431343056, 609029153, 957976049, 35980321, 72943384, 412345639, 333700647, 619875835, 377562096, 104477930, 898579459, 502892938, 618432480, 897757275, 345734483, 827359104, 742733925, 492202267, 820517025, 184105306, 80559114, 583678390, 929931911, 643578004, 811463802, 571172374, 640777242, 973515030, 28545219, 717246445, 509546085, 718002665, 115957437, 798001706, 559994195, 973516163, 962830279, 240951562, 919053893, 191222998, 497178135, 219068805, 618468756, 283979015, 755875542, 869996706, 263817249, 429423142, 824504258, 647022043, 691270539, 782914276, 312538563, 419291126, 211999765, 857271394, 165653281, 944936361, 44767795, 580844279, 362761566, 79170684, 882294946, 961316711, 799119784, 808042187, 955663421, 46638811, 519133580, 593956158, 22933778, 561426092, 119321323, 59359113, 236972533, 222034686, 764261908, 332160809, 660167650, 764733450, 537312131, 373634525, 694556327, 378788341, 135293728, 464322799, 770952611, 610765867, 898047460, 547443125, 238266299, 44088047, 435180494, 133406444, 95374009, 675959384, 348623914, 564449067, 968664660, 129395480, 812172444, 601499078, 640270065, 682152182, 156029216, 136172043, 746433858, 592335344, 116947520, 526525046, 348980292, 889622847, 87040577, 934059652, 59006076, 928409840, 647048082, 705297356, 581573000, 142529770, 594620392, 501986146, 942575314, 703013273, 345871449, 349384676, 918079820, 769553231, 876471767, 136516205, 892023851, 686041314, 453092275, 111528556, 39369147, 498949279, 605399007, 910128115, 374895257, 255869534, 397282799, 37024591, 509944573, 551438302, 704982154, 444343107, 781549405, 810034449, 934819938, 642259505, 238714181, 483049786, 501014486, 253655840, 988486443, 681139557, 40474010, 60971471, 792492834, 501290017, 907979972, 227652094, 46405774, 683277225, 235660756, 159299269, 320120297, 172891522, 961873595, 498385054, 153576983, 635009471, 569023881, 878767201, 414963970, 548862331, 715904669, 697790156, 255514712, 561609848, 963061452, 773178910, 553397785, 367421313, 498699845, 475582083, 978643270, 788053226, 371759654, 906213258, 9190029, 424246335, 236673509, 712270461, 706119929, 502618433, 222831126, 7552115, 378129934, 534619705, 353737612, 990576831, 265303483, 110494116, 413465979, 878468107, 488311276, 740991831, 329025321, 121133987, 26720649, 210958985, 827962161, 819466984, 906149717, 912894747, 90217532, 186043400, 347908827, 380741279, 614170714, 793786865, 986531280, 702186135, 470093501, 279506533, 140450342, 711322654, 246991315, 814009780, 472897803, 873235296, 622085132, 896588173, 907037570, 650492691, 985561594, 283694996, 962154344, 881643107, 191570593, 383918102, 273819653, 685317810, 789590702, 837038561, 143794710, 917898786, 845389746, 508466425, 71182214, 658197570, 522200976, 908943180, 473852372, 342982504, 267742854, 151850971, 118292746, 856752791, 638402021, 187322845, 837179719, 490770383, 237132678, 743336856, 318670386, 709553153, 111752438, 38326276, 342207806, 426341127, 399517451, 191698738, 671934045, 418383124, 304384679, 504482095, 330157630, 171961696, 645382275, 911547683, 444823290, 894685796, 222617757, 888262127, 768848608, 753632865, 466417421, 292997948, 109502711, 649436768, 723024345, 451946725, 834838368, 425795292, 296884953, 211888353, 905722344, 596934994, 795368584, 919113547, 142330135, 101042390, 53508212, 482378811, 396492554, 544169178, 526089854, 385910627, 34755984, 883091525, 234252371, 5647154, 389817058, 715313199, 114627240, 499017615, 204103946, 580370819, 403252381, 621920353, 828519885, 664618651, 670157582, 960022638, 89112325, 506617429, 736910978, 623965211, 48015852, 723131460, 610348609, 287567214, 56549844, 557154672, 304004570, 233881959, 614821839, 212962317, 266079660, 92249765, 795580583, 960459795, 843953916, 930006891, 156259559, 655930271, 794963354, 643541053, 392396274, 146969729, 326598476, 267081555, 778678958, 303911224, 302641367, 958406197, 870645144, 312425235, 615308977, 189561974, 547203444, 352791704, 82714699, 925542649, 245239680, 119227192, 615859888, 125410691, 432730796, 376949424, 571071643, 20921575, 401647964, 509646232, 601994262, 404000900, 501342523, 378906892, 906164301, 41877915, 814000933, 786572051, 287629385, 683219304, 957363525, 393163582, 376547598, 80081313, 879907365, 215004473, 47965313, 632857724, 795106550, 932082893, 27411137, 845316869, 485824301, 518790797, 500582922, 625096409, 438688153, 687911275, 605580851, 303575999, 831153781, 191032479, 206358410, 496180467, 946930380, 72509031, 847165372, 746239771, 556538455, 880483537, 635840795, 228768838, 303368860, 322984293, 782979864, 466263072, 769158105, 948840480, 741132272, 920753794, 803610283, 433405224, 563652456, 670599438, 399475685, 904013321, 798569273, 172121183, 838107282, 554893329, 758570063, 541120225, 241455736, 895782188, 389334165, 892770989, 649771371, 778905376, 497327763, 403373950, 108213731, 493760006, 38021548, 871928119, 988775705, 567524738, 19591446, 39471147, 665514951, 12980283, 978430734, 342409420, 800397348, 634122336, 768453599, 788546306, 237097188, 584945450, 802086839, 362869463, 746237675, 717610054, 933141029, 905933621, 316225125, 727258946, 311410258, 121029650, 846918859, 511115208, 278155790, 520955855, 501624477, 649471801, 710801236, 533950390, 857912040, 749780370, 176899060, 650527766, 278582099, 30958992, 330912422, 356425536, 620664949, 870028611, 931605272, 279826621, 231850539, 769865764, 939279741, 23551886, 655499132, 766047358, 818808676, 838134432, 281207858, 565937027, 364469849, 24507562, 663422742, 22551540, 157157231, 117614503, 338815407, 375740070, 299475699, 172441071, 314140549, 947368178, 168325589, 214842719, 902700266, 756724642, 744183959, 127000406, 837296070, 608505558, 25880334, 907772448, 762308242, 50302096, 481406684, 161269949, 215537672, 555494590, 904695541, 435965163, 362819255, 164529251, 360222171, 120572999, 557696395, 726454999, 491263516, 662478712, 826695438, 663804639, 100933587, 205720501, 576599604, 215637955, 921981648, 261353893, 952590601, 825468449, 118189062, 522327292, 738227879, 248842566, 36477833, 697027444, 796980965, 793441402, 509558524, 418616011, 352139194, 52941438, 585453898, 827930448, 449468348, 625683145, 702011683, 837063632, 975844007, 520473638, 145085947, 102966505, 263522762, 697262540, 680142386, 834762888, 601585420, 906509637, 738294523, 401195485, 446019067, 33500151, 75881295, 937996938, 159329452, 130325451, 773084695, 631569967, 156181209, 927013080, 55194939, 616778582, 931407400, 988828778, 531151033, 345482074, 650932545, 210166551, 629597843, 567940759, 49744356, 868834650, 132995173, 23196303, 483064322, 445163515, 349118109, 458168884, 192504373, 218674295, 597218017, 986618715, 312382448, 807149545, 747333095, 243335710, 97971179, 816767425, 120524897, 80121300, 587560801, 524330970, 127260061, 427089094, 319187754, 527732948, 869805447, 461493809, 752328393, 778195436, 830824611, 23714080, 358413127, 675779042, 483326896, 884381304, 478848356, 911018526, 675509499, 381120027, 946036720, 702918352, 282223738, 806702692, 758295016, 928907208, 790058584, 618976736, 232229420, 676629066, 565866535, 473678929, 493455075, 313568331, 66594096, 902863747, 528478341, 269294800, 996161906, 546875039, 159093720, 840497592, 795139019, 350176285, 705081772, 199910061, 54679465, 765631896, 419962990, 398326138, 122893854, 447641626, 554492573, 915223844, 632830501, 544625432, 157930313, 471960341, 538714275, 864120104, 897749097, 535691274, 106476389, 106877581, 893972788, 181378162, 145971510, 73456963, 476904919, 910418760, 85957784, 695936392, 656965180, 527527239, 902047322, 119608068, 948841495, 426204776, 268819204, 218495684, 183349870, 717512776, 460094377, 445005507, 880984851, 687774286, 361681662, 238786366, 346728989, 973085893, 578128350, 431545957, 939411109, 310761842, 764175485, 368960372, 55897978, 888724105, 23758481, 185219039, 679242860, 508777788, 190914677, 904011158, 560935722, 980029626, 592947535, 444539096, 273879930, 919224421, 388730435, 259257905, 526362, 626245353, 771735888, 452936856, 685273410, 202066217, 165291195, 904627426, 601578489, 377627296, 424722792, 804329007, 977231319, 163795231, 746758017, 997314557, 542063347, 620787292, 448034918, 583546061, 44577233, 905381827, 954918506, 786274873, 3476481, 210049017, 494540760, 651913253, 435353860, 593768712, 705833314, 887884636, 329153944, 351082017, 552783480, 718203381, 927976858, 65968707, 209599289, 787293405, 738138729, 227412441, 325777879, 965486192, 550873385, 887696704, 315872700, 925661080, 224263066, 823583284, 560531135, 527315955, 251570848, 405847169, 649614524, 727509737, 166162958, 811163904, 166299, 365392832, 661821668, 462286214, 981438112, 177868726, 175383470, 275401939, 77266226, 702963290, 641655875, 124710794, 874258761, 310648083, 232475938, 363320067, 819676241, 631873575, 71968192, 115884005, 933711781, 745949753, 292476261, 850525276, 382086761, 147368356, 995334380, 99474233, 399147479, 372498167, 367301252, 607161253, 625507840, 502385732, 494697680, 496980027, 657252611, 255897226, 641729654, 736012888, 950314295, 358789406, 149445766, 546852779, 826456784, 344753021, 109980301, 192933822, 793515486, 287362202, 657442232, 125769471, 175983008, 451866, 770156201, 301572412, 504033560, 233447223, 677945265, 31240894, 617241985, 551246843, 714972861, 677624640, 846685852, 569047614, 672498489, 112722246, 547767217, 652805554, 594274486, 581652174, 736957898, 631934202, 12404390, 438254280, 455282155, 991302788, 431651388, 886740863, 993189399, 314739563, 216859134, 188102860, 330360398, 686199137, 295966973, 996661857, 777773949, 160923957, 901599501, 563565770, 12316576, 455189679, 793495827, 364850523, 136242659, 767795837, 59666278, 344944436, 773550780, 452593154, 372088510, 590367962, 193443867, 838114778, 431848703, 143611028, 72810444, 405912195, 125383134, 657471563, 418275611, 477006090, 528571431, 389129510, 453359468, 140631829, 799926501, 133602245, 935261864, 245277556, 203148188, 886279047, 315428914, 966387756, 266196220, 368201032, 262043451, 542220435, 670688723, 407517944, 89252308, 137644274, 549051752, 604486488, 274875614, 809102807, 271889654, 665852744, 775450333, 939222348, 579146471, 241095154, 954687598, 860517977, 590410446, 755417604, 695074651, 392111015, 989061023, 614900763, 941378862, 626232849, 241518691, 414973325, 446486076, 666917799, 528394618, 828613155, 412517430, 618201606, 302096443, 160560059, 208700530, 542917739, 663822100, 24530044, 583208273, 230681096, 189114892, 947660113, 193309002, 97787312, 818992680, 303550159, 273705180, 459133702, 636753802, 633170607, 697668193, 376995945, 98929425, 577492733, 34474083, 960009714, 800398676, 415288000, 379143865, 202383190, 583525295, 72767594, 634111798, 924017981, 797834582, 921008914, 78944131, 811021105, 860953098, 356683596, 289734461, 301078061, 158790039, 830580616, 750184084, 275619665, 528698855, 897559842, 491250644, 876769066, 499748584, 761943647, 552235532, 231127047, 547002668, 486190095, 620871479, 742369746, 48472180, 263816354, 219029880, 95523176, 482162502, 824611608, 489549594, 398772422, 465854223, 389479735, 140017136, 422228408, 953663377, 697100581, 107308605, 250000038, 553666803, 57059721, 200410088, 518922797, 554994963, 676143374, 880912053, 82906954, 221780733, 577742136, 572019888, 212360421, 604387525, 962971767, 200426970, 681844465, 652553979, 639249468, 51219877, 923951247, 387253895, 883129752, 454320657, 714566912, 33847405, 1156529, 69598096, 113924043, 399586091, 530808489, 622148588, 224820007, 857494391, 492756925, 940881292, 245172654, 861571695, 271535448, 336297996, 224451403, 47773343, 568259515, 39605035, 180143121, 48337294, 808337112, 26924358, 963050724, 255689811, 826990682, 611901125, 90500461, 957615891, 245734881, 161411520, 799526085, 67534750, 149069069, 581984231, 528847747, 118957500, 619697224, 498647029, 19180241, 127226253, 720431445, 115676931, 521101135, 946470940, 54845921, 422959706, 379459302, 711299489, 160034306, 990780042, 194925499, 891767568, 475577197, 977751154, 835655199, 466433331, 591179797, 394812381, 568808390, 507573435, 525344556, 797502243, 809305071, 317731462, 837230899, 441204905, 299635053, 827190522, 221898905, 919013599, 620627752, 885063741, 744241970, 158279729, 237490797, 333058100, 824082411, 276898817, 894478026, 506835526, 713578732, 140472377, 403373026, 329697389, 750008823, 132953021, 89249220, 61669008, 75632046, 788579566, 915176451, 351979723, 180751012, 298279488, 48523067, 597753667, 590476455, 7613731, 715475747, 429802376, 918520133, 41270175, 626707695, 890612422, 147724119, 701738422, 250746950, 877060065, 586986230, 137447391, 459808617, 889054453, 439893079, 161850765, 233112559, 391865574, 872155428, 189205646, 520699146, 506725178, 744506640, 996828691, 128724853, 688009486, 486436708, 232218154, 638606010, 896128836, 785912357, 61741378, 58560187, 459276831, 81665261, 722583434, 615450857, 897126085, 27366010, 497523694, 472038710, 551963130, 441562556, 9755918, 730133828, 848277609, 864349111, 710105292, 415957736, 309081633, 787772709, 151118454, 101232341, 645836869, 626720550, 303281839, 788696519, 249733016, 636054632, 8561534, 284104800, 959458455, 467032019, 816772043, 273588238, 220842592, 891875079, 744693970, 651890057, 285907451, 104012274, 923512326, 737188320, 696526199, 81747032, 600417717, 706253724, 214896933, 35128233, 624903214, 940363463, 354456154, 304869188, 835259060, 390591505, 113938407, 187945541, 670440580, 285478776, 365626599, 133082149, 329432359, 983929465, 659805729, 557157835, 879697967, 707898768, 555304588, 120126464, 541307924, 745746367, 847523897, 666365088, 266390511, 616271512, 272776173, 592480128, 875321601, 82028185, 33517666, 436256606, 921630236, 730740079, 707008514, 189838182, 259271760, 996117410, 381898334, 282250560, 33176084, 672466522, 624712741, 678137665, 214196927, 72347390, 458312824, 205249864, 241273713, 396562396, 244450533, 677911275, 395005270, 203019759, 691658934, 842172332, 147466337, 482095876, 453131423, 646686879, 662203932, 368622229, 786675044, 22179025, 734900962, 161362275, 340881209, 132569654, 97742332, 157114814, 854135560, 201808279, 224031590, 66426948, 977820774, 795022048, 801224, 503186295, 294870067, 509152038, 331531261, 367264134, 975748726, 929715407, 702955084, 902001373, 159571793, 44583727, 970172039, 510070600, 727325127, 504946797, 901524864, 102785101, 154464492, 874900640, 606850262, 491641793, 510561251, 570697589, 809677575, 507611340, 160927499, 560722359, 153720836, 691755432, 113944828, 668276899, 361676436, 509873114, 948352536, 792922194, 662469591, 54785969, 668575463, 605540535, 381376366, 833821481, 810216568, 124213344, 352827373, 269721494, 133819876, 800162697, 77004614, 934972617, 529069794, 604997299, 258775430, 788613302, 57179808, 472566308, 767515487, 584970225, 600577310, 177577044, 197918352, 595585700, 821171841, 881564637, 860837340, 71313305, 171244906, 313962523, 621687059, 506740561, 101429386, 250247448, 192760582, 959772401, 318855440, 320987910, 2315370, 597686539, 143615509, 686535207, 740675216, 927603413, 1995748, 947120490, 787244947, 74641171, 845540421, 395403866, 630735339, 35910545, 421951706, 65697012, 274439861, 770003684, 100338901, 580800811, 924775866, 693584198, 601063688, 715917285, 692212120, 888003079, 678461226, 158476550, 704368935, 764313649, 898495095, 272613919, 119755569, 977789129, 530601130, 510406511, 113209738, 280596709, 530200075, 262634378, 695854506, 572810635, 264421777, 636307887, 549914503, 335341548, 697440439, 461986730, 171818324, 676075696, 421686731, 474567442, 843744095, 434384348, 784535276, 592569303, 597708943, 145687414, 580293218, 78981143, 521013022, 756862994, 292903523, 804990977, 126851181, 537999459, 479197717, 252460070, 458445939, 888341594, 522048759, 418572458, 445974103, 526703211, 840031637, 99958436, 300586267, 666570827, 825967106, 362381316, 116537645, 425515262, 535995277, 340148467, 187469683, 285708174, 89511811, 318384214, 126379716, 561687077, 594741771, 979894104, 643724838, 822536887, 130593241, 283746160, 222204431, 8698992, 733761471, 834893607, 437746772, 260595941, 428691478, 714814317, 782757453, 588431443, 959682362, 925842382, 509847366, 873977704, 768810440, 291106679, 389643043, 582686712, 710371963, 279423146, 633222138, 66324509, 900136657, 52710586, 103436083, 12179412, 163879340, 329968750, 155396542, 104805373, 955981150, 588778093, 206680710, 916781435, 24724390, 585296436, 733421433, 190827512, 805821332, 482678865, 879537282, 676143178, 978603201, 382047971, 916139917, 919326407, 885432573, 740787526, 642484982, 641059682, 725638660, 585300445, 919543628, 955993401, 653651689, 947864521, 782451587, 32745140, 122393611, 423908349, 647423868, 397110567, 80037953, 271739409, 259025064, 521376259, 166191795, 912879691, 975124360, 710768206, 894487456, 192871709, 62276404, 577554103, 733180990, 595896823, 862294992, 95330817, 504455860, 774377111, 510095742, 684757602, 697823579, 401233218, 91099580, 3988556, 757432231, 26290580, 3014694, 446606386, 295376204, 847835702, 722377188, 538068288, 416846050, 256266546, 759070518, 360971392, 15579432, 940915128, 108736170, 646154719, 688613519, 228248295, 689458021, 551399114, 305127209, 5327045, 457523241, 72419062, 582429067, 570540272, 335427330, 809510345, 320555030, 885999496, 343307454, 834988612, 494359269, 551129992, 422277141, 594999629, 464348076, 727496258, 225439807, 857699059, 842928286, 185534856, 981017338, 442135016, 445684514, 151839006, 905954648, 925062644, 168352992, 677466283, 20746837, 627801348, 648197977, 979369882, 900937929, 179673856, 303267224, 171956527, 90809006, 419067129, 933161952, 213465187, 981516036, 982222618, 11651449, 513039593, 799127007, 356739647, 825292653, 393751058, 190195824, 687572493, 989709240, 623960623, 563156445, 916338632, 892714604, 865932551, 705116138, 63293527, 305028073, 586861709, 769777489, 32724162, 325816688, 379968154, 460846661, 104409533, 249152373, 580826412, 173242846, 622520596, 886089968, 80481497, 736301295, 300553987, 581420627, 579499433, 634400883, 82127978, 303480116, 223466414, 257054573, 704674584, 232079254, 562866867, 778282352, 513769027, 68869859, 292099243, 864321772, 125749647, 802718706, 520710889, 978503113, 64642361, 102601867, 174211599, 673865544, 526953641, 476775980, 974353062, 866984396, 341361459, 693081611, 493947992, 356573959, 243591316, 301047766, 936244423, 883518637, 22904263, 377232185, 132774453, 340023183, 724403779, 393053996, 597443758, 639116299, 739095604, 569788916, 65734731, 972418710, 859888842, 634651280, 46827514, 505670834, 537408616, 420573025, 925997952, 96585709, 26689168, 499826593, 554761156, 901544972, 7895931, 663186945, 836446897, 283092357, 150012018, 874203553, 641035020, 915551962, 428171689, 282474, 352024371, 214307177, 657762302, 181663942, 549150667, 12446742, 48011326, 658267043, 867012122, 982254867, 738829573, 402147885, 285470905, 29366623, 843924602, 105476721, 332691377, 301870031, 977476708, 291279837, 748688461, 671395525, 484857404, 288767353, 810968278, 40206921, 21327149, 322141126, 468345976, 389523556, 92566069, 370254404, 346754256, 771257079, 615559018, 706570366, 511048155, 545221285, 178028570, 669428449, 695454944, 888594469, 155197717, 651658655, 157353494, 36454264, 373146505, 116617082, 185464891, 383704768, 992577899, 579706058, 786618790, 598031334, 243231316, 202062328, 434446787, 663199526, 334503359, 439249446, 444952226, 890449447, 897597167, 781101584, 954279708, 426829590, 711161656, 517923876, 205471917, 963342159, 247412019, 178928830, 816555890, 769743867, 934977525, 350657911, 135213063, 591188799, 264014353, 20206061, 845040566, 553254500, 269511748, 949058429, 447778828, 48934971, 35562578, 328689694, 163955404, 523824960, 795281778, 384144866, 874386091, 606057928, 660724883, 343979695, 356312622, 375621142, 746997328, 92994313, 934053860, 692949496, 277366666, 366140563, 214880633, 526748466, 507328568, 922854238, 919433395, 920352353, 303066190, 785974913, 285977901, 938782491, 902237728, 771717412, 805353307, 566724159, 128479222, 342863599, 180868279, 791949161, 762060086, 515539164, 644853727, 486818923, 310762747, 962616919, 859604542, 676928353, 709778587, 952157897, 770060894, 248725834, 103443369, 721776233, 794942251, 837440991, 976997554, 627622625, 356450513, 557547249, 260520595, 949551284, 340394361, 27413993, 277797281, 24137687, 712557126, 260805011, 982198409, 538344451, 606469393, 175345922, 293217238, 614568183, 857199067, 989894012, 785995610, 682391849, 597751619, 926235276, 707776023, 958940960, 430191814, 289095471, 662541727, 138823815, 549000456, 791259980, 41997796, 574670398, 292105613, 393323743, 947651944, 745592823, 225135177, 367920201, 453874869, 207096550, 510166993, 487150394, 770158410, 608848411, 657347490, 992901741, 725154895, 215489763, 113565422, 883774996, 552973583, 259544997, 696825235, 629554809, 973955656, 35879835, 271592386, 928508730, 498783909, 164302418, 67843879, 42433150, 720217057, 3794552, 563426740, 962628400, 927405703, 112040589, 286562322, 621266919, 974792641, 945813110, 502940025, 358467640, 895105587, 789438995, 548451762, 1530134, 618517156, 828900371, 295371908, 714269470, 568363511, 681967157, 34212792, 841758427, 717068411, 615728869, 14678935, 342582830, 577862106, 917119661, 758748877, 740872001, 792022220, 208874992, 315451399, 946716020, 893752332, 275438654, 580984492, 223182026, 830072228, 322646024, 651560222, 349115999, 320364630, 681637583, 715499968, 17876615, 692413560, 283631858, 340595503, 173699330, 199229160, 341263837, 159446397, 81971484, 165936697, 850574449, 145965657, 559744047, 871654025, 82543366, 565202104, 257243895, 887129732, 172668638, 20606958, 781345625, 756247341, 11364851, 194364898, 297875638, 898770369, 712007258, 945871497, 514012240, 289695388, 628883595, 527407279, 204341933, 287854347, 936293262, 832900990, 13418918, 409892794, 103205672, 773198077, 957800316, 713623730, 746913424, 265611680, 812265642, 186086401, 283062201, 966937544, 799158777, 860207918, 920105146, 161506944, 697078362, 370998035, 540666930, 665685397, 944594890, 484523832, 787221360, 55021875, 937266935, 845111027, 779206560, 71773155, 915060186, 16573335, 747057252, 334378764, 514053112, 780919733, 509094351, 761490464, 213882210, 312246781, 544622605, 978442499, 217021446, 830547814, 691960397, 582563922, 254950401, 723995925, 813316745, 950443850, 727576708, 141104661, 109590282, 395112959, 773521191, 825331916, 214120773, 144624742, 228027120, 467957028, 64712708, 31703847, 190162833, 119734984, 619157757, 147750461, 133205643, 711484836, 998798683, 986321399, 993728917, 224298766, 464930001, 666534901, 678348363, 833673598, 243309740, 823075967, 217353881, 308250352, 399377793, 834828151, 348572894, 16508283, 861787247, 57231023, 318702663, 945133704, 640841987, 223562300, 40480134, 407197753, 295179850, 477633205, 410295430, 689956566, 848882891, 598110011, 265489020, 778939569, 817379574, 661589952, 955713776, 555902125, 396441300, 690465152, 580883909, 754964075, 176285695, 752221671, 721616648, 821426690, 140173532, 687991084, 782805928, 406147749, 370236422, 273616100, 39686916, 203405690, 70696631, 671011583, 345026126, 624681236, 157074135, 263704271, 226136737, 582824035, 563400158, 29701491, 876763846, 678048411, 861926398, 84751920, 479928452, 702088431, 888541494, 819780690, 317395779, 466053403, 870699608, 144025257, 688023722, 966979076, 212221389, 467843325, 543964668, 17822567, 892042480, 891608563, 861292811, 155096779, 710072475, 659085695, 473021311, 988215580, 626264270, 857835179, 599305396, 152247699, 499947659, 184213291, 711279672, 264177924, 819745819, 745609941, 936683580, 878856659, 331439072, 208575858, 613860032, 228718624, 514552250, 572731293, 15081416, 792916689, 468701751, 768136942, 372167859, 482694926, 493031432, 244815822, 405258286, 55446587, 408393279, 442499166, 305311214, 86817274, 725858625, 746135527, 69865617, 128371582, 866929865, 83442618, 430313371, 486269291, 886853156, 830380292, 959752867, 353828850, 248778377, 91892814, 327890086, 411240705, 375820587, 455194100, 174985268, 94416253, 971589056, 222982932, 411974279, 278339449, 202050182, 332245853, 810772721, 744971171, 341440767, 241587135, 722355173, 834795027, 809718059, 252803517, 307398397, 152193009, 314332226, 536381760, 992847976, 155539373, 35317306, 172439091, 240012059, 74669945, 492266404, 808776545, 318232704, 697615636, 266397343, 382767362, 708671341, 317421097, 123661046, 249131696, 681502607, 395423981, 114928601, 760201920, 938735258, 317697137, 459724860, 646578164, 611522494, 468638195, 1854662, 680234748, 744103915, 466931667, 474392785, 536202586, 816584681, 825553531, 984058365, 107061027, 954189571, 635730849, 292058212, 176335737, 554325395, 675294643, 832269567, 793504083, 830187794, 652540165, 369044566, 88181370, 602039641, 59241876, 586764142, 354801635, 6405127, 649861603, 365921046, 485520194, 906820278, 127873919, 790881804, 257653318, 826800363, 731438555, 389879028, 612836478, 207398936, 906053350, 486275423, 194409304, 597725320, 698054165, 612180953, 743191924, 736711743, 188587915, 532385812, 405774368, 302403804, 218765773, 266257463, 800510886, 132235176, 174795715, 319233089, 197595883, 229950836, 908533646, 457460677, 500676651, 790424437, 534573529, 342864930, 271053467, 836162051, 270977527, 519986645, 750113467, 338232842, 498427009, 848320192, 277450077, 706394110, 909903869, 928074691, 651720831, 346342835, 377554095, 795243410, 390503042, 563672043, 814326688, 570574654, 575191291, 805483863, 421757148, 28162102, 844237657, 1991790, 647553173, 439432176, 821119317, 764333935, 673086775, 594131293, 252477087, 454391710, 931260792, 650165162, 549314362, 788889057, 511084126, 217517276, 737208751, 382764778, 154440564, 379143862, 111549619, 517986271, 845912326, 317851637, 363955606, 719843864, 940442430, 432024959, 594837244, 406327814, 25938617, 250827382, 576094867, 163933286, 685951206, 315339530, 538815470, 569643756, 366308884, 906633840, 904224013, 715042908, 771965114, 737310318, 921730799, 288481206, 155430187, 397491054, 297106266, 776018875, 851678734, 572249298, 632525436, 53607565, 674803562, 910725628, 645666672, 161766311, 533996909, 604962353, 48534799, 407867535, 961218649, 283432496, 322058720, 36597976, 323367766, 804984216, 864697662, 37975319, 157960479, 746459406, 875725676, 549840261, 326624428, 489336102, 616359267, 387311544, 640359497, 101167905, 576877609, 273649955, 848869767, 554686283, 22653362, 757171973, 460528566, 539196835, 995664911, 515391802, 675779753, 991250581, 771199391, 161571391, 636768395, 572248419, 228551983, 636716252, 737135561, 971819820, 557415671, 286642727, 277049176, 755883769, 211906630, 517776545, 942227144, 660855103, 990223768, 835039533, 646402591, 824102205, 355923116, 725154378, 549476955, 615223376, 325720028, 756268928, 193551194, 809283905, 944063126, 257806473, 470376980, 274798126, 357076254, 949990165, 659659030, 641863217, 378062367, 17730179, 136212170, 305276017, 238235510, 284795408, 373488287, 679862501, 716417872, 83598023, 517046973, 827958502, 328936070, 781602101, 571755220, 247901674, 314242700, 132289496, 354393972, 820965162, 83172049, 562027669, 643297206, 82639602, 636565548, 84615658, 334220104, 348662152, 844847186, 173406497, 500467633, 484681964, 410673146, 742565483, 267017340, 284332481, 901081197, 564166127, 589439469, 175292980, 257590678, 702811382, 818884772, 503715275, 217633532, 791022228, 312246341, 989357090, 521756492, 262134535, 105642935, 432801918, 596675992, 496859091, 297256906, 408877621, 386166142, 4290524, 319813688, 15627152, 315207156, 673288236, 906806111, 54384962, 385698610, 923800751, 499532433, 945715388, 385197137, 207629934, 675169938, 893632928, 467445870, 781578391, 410252848, 103261855, 229859217, 553089460, 54664648, 347952700, 639371758, 235108761, 713801127, 730729082, 211185300, 302238196, 498137113, 778000793, 477342131, 730233284, 361433096, 161009475, 852182298, 573712444, 31153418, 790158705, 197661435, 883454361, 785169071, 257520377, 353617928, 740456572, 394029160, 502711542, 845720363, 203320423, 967554920, 199144058, 884284287, 110265979, 67931554, 63639436, 454658030, 932216927, 900613313, 111193378, 467781896, 534193305, 869783302, 900212883, 733669213, 470404843, 508578694, 335789014, 652483891, 104086534, 369335088, 746127589, 67866016, 625260345, 415464056, 200946066, 65909552, 340978146, 516875894, 49387393, 374115609, 45901489, 200848961, 388604384, 572719567, 752270925, 438020493, 935731773, 669298344, 199779505, 123934747, 414897597, 913865634, 228260899, 701905294, 297984966, 642496509, 852271626, 68698566, 112760731, 598038006, 679261908, 116099892, 104173047, 279483103, 67571355, 728201480, 647672145, 530200770, 464428772, 71512664, 618913015, 607701472, 685371798, 972508285, 819621323, 764475421, 596599190, 516200742, 434436130, 318940088, 625883690, 494943377, 310790292, 348538879, 566560178, 787117666, 497877634, 191934393, 954511863, 546697167, 104840297, 209560810, 719400460, 847524091, 674401279, 754463139, 95889631, 96197138, 361007834, 453859022, 853831673, 653975595, 493684790, 403703830, 463955874, 811189835, 964320605, 722345272, 31293217, 362503143, 518401187, 757683478, 294708719, 794392339, 30316327, 838400316, 913412795, 916297687, 250640324, 569615684, 92053113, 251351665, 970459404, 588211848, 510210991, 745505316, 294464909, 435777016, 231013847, 322718081, 968792066, 404442754, 448908388, 80226986, 547161788, 177150871, 621241066, 962252028, 94837914, 272478498, 718062637, 455836051, 518601575, 118840399, 517210302, 967363120, 780997120, 198440919, 559084376, 212413456, 545347028, 953537117, 218581277, 494273111, 783158014, 799414844, 712563737, 311627750, 115476262, 72372582, 801700595, 711269427, 723847236, 702052020, 956527860, 549942732, 746731724, 42264380, 347730330, 657885183, 573097179, 967929862, 419063242, 926809267, 350980656, 696127819, 178120684, 766013081, 588200855, 964361164, 18450253, 281865689, 768876845, 924444100, 268070505, 254252681, 163873640, 890348067, 311993813, 181653679, 547665791, 443735841, 348145564, 862662457, 45238597, 549287502, 263219637, 893160597, 347530798, 848137837, 106056563, 498216350, 15817316, 9645260, 429407608, 691186192, 395535327, 666147212, 422287214, 794744452, 288128277, 307563637, 997577085, 193402850, 56571292, 395187014, 194230954, 241090885, 627930114, 113084073, 641250353, 238029429, 711792969, 328390058, 733812770, 343624100, 328615609, 169710227, 748048973, 790914288, 208508728, 629531668, 568249790, 405646392, 602321864, 192573860, 263846915, 929777583, 950276528, 788763862, 887805252, 537167236, 132809330, 789933628, 409888027, 31736559, 539909784, 73745245, 517381026, 447997149, 950725101, 591207299, 694222536, 706708791, 647066729, 183926329, 697673364, 110624288, 725582627, 520783167, 293245143, 238438694, 876385001, 790834988, 193221511, 700299788, 208824403, 252369415, 911202964, 282243231, 866100249, 923683655, 945365465, 178005836, 566056792, 598239938, 333024230, 413840347, 304256207, 348191900, 742088882, 691374140, 184407203, 559963833, 423724110, 720975544, 260771129, 376895937, 677572567, 420642028, 746168357, 373228943, 754645651, 368284876, 515496542, 591283351, 454666223, 807243936, 891048513, 686829045, 222716902, 177157841, 447870149, 420605045, 580514831, 679826543, 949924851, 962877964, 130333438, 979219815, 128118383, 225512458, 565236301, 363828910, 647639227, 939365437, 636783066, 827483505, 973643554, 904084718, 425864941, 525128150, 289855619, 802629248, 766425539, 788825594, 282721114, 76350971, 427064014, 464022191, 774188234, 133729950, 402836263, 704127796, 94566802, 45976497, 685080324, 143976541, 959923322, 190238815, 829452672, 314925820, 495923216, 920581958, 63427845, 480594605, 213565255, 471348435, 961516968, 652133517, 383294033, 352100637, 861568083, 3468001, 874102504, 911197936, 215297797, 694437, 191561424, 40403745, 578820119, 43707344, 107314477, 339598317, 649946996, 125791547, 642732860, 972969413, 102677275, 655988188, 175806411, 484694396, 745185989, 846916478, 772015586, 294612294, 975910353, 354228766, 954320494, 260539007, 763781461, 8415028, 698607398, 459131011, 118881446, 220444021, 369506212, 550332540, 844348680, 293133100, 373115443, 178538750, 112647834, 904179786, 513436102, 770794106, 118894519, 928929025, 20944598, 193834414, 613654395, 930957660, 452343473, 924494018, 479485120, 776581783, 229535811, 423070060, 375115532, 116798662, 391267304, 50883048, 458589733, 260976166, 653397832, 505292190, 714192620, 771238979, 142615926, 356932216, 935464417, 864034404, 18433614, 491017449, 743561708, 440040432, 523503162, 454410270, 771076583, 845474746, 737578666, 133657028, 12699306, 384615245, 522243646, 808546038, 796830631, 555627538, 71065813, 373004584, 577515472, 621544376, 774325201, 789667499, 657724170, 427538845, 693769995, 841362183, 825532184, 151627212, 9419337, 76077832, 165731987, 928806090, 561238298, 52361742, 471979166, 682725266, 908577668, 276089460, 300636759, 421968705, 87149723, 573099286, 299215534, 659235295, 208969562, 515318930, 929296289, 36956355, 417096136, 313196338, 116334992, 436669844, 603127532, 206138712, 432942377, 827957891, 115054145, 330221647, 903511267, 871894704, 726677950, 973807896, 530650145, 256153058, 734182078, 892551096, 540371356, 561528834, 73665706, 933293994, 802633206, 27952049, 823170494, 432586201, 715884451, 177332712, 890220938, 358315005, 752185373, 126245651, 752737040, 277538485, 371647137, 213957590, 461266517, 488808380, 785856730, 437785319, 610637147, 396129005, 45093629, 468406803, 814385988, 474811386, 741747553, 428160914, 5991945, 55530004, 519225336, 151544968, 879908026, 14328480, 705902970, 814544736, 655819220, 409715516, 483790803, 623765673, 255531267, 858373663, 29945558, 60093827, 933933695, 76545127, 631322450, 290403623, 421603509, 50907775, 975762770, 520158699, 878449092, 209908452, 831918104, 793160839, 817108996, 622926589, 182678680, 640366288, 127159751, 771946782, 903127665, 998941442, 407506333, 981702741, 826022022, 995392670, 886144081, 911566537, 287512311, 473300880, 986554101, 562560799, 600188797, 120640013, 318494533, 984605726, 161334379, 435011613, 292180205, 876934514, 60457736, 422340067, 502710420, 165727850, 471614674, 808783343, 207899360, 894749357, 566149381, 113418443, 275272329, 674546275, 823469018, 862500366, 319351046, 75904297, 925333575, 521231150, 878715029, 623882281, 118458387, 820070802, 905840627, 785688389, 352004496, 690509058, 558590594, 224103000, 857196564, 510868699, 987535648, 84137275, 342730282, 112846342, 718085401, 110530863, 137856365, 676016104, 725975266, 108332155, 958818188, 481943654, 93422543, 280410621, 621816453, 467525565, 886355196, 929744391, 729028153, 553278630, 238482515, 879599482, 226654175, 209812378, 873380539, 234440336, 639466303, 110040835, 62549558, 439922604, 554072898, 821011438, 802343660, 791020583, 287357703, 485652626, 817328108, 221158491, 132468095, 399756767, 546488746, 482892185, 582806115, 871638938, 716534090, 277054576, 863707922, 44538445, 619382604, 571440323, 738812878, 202479926, 269671079, 85184165, 900282380, 51012882, 219130592, 542593891, 258803296, 208337015, 33161348, 681751072, 457855272, 590174991, 304001565, 380237618, 945535510, 347282549, 4920154, 228256630, 169345474, 141088276, 290487218, 248368679, 962440747, 330681289, 528387277, 975957065, 704870416, 42045233, 555016311, 174322603, 584510830, 781545090, 193390000, 173763117, 734462940, 441817185, 576775294, 412544121, 976726669, 552618617, 59702142, 212200116, 12089939, 11164344, 607716376, 5101408, 787309824, 548514615, 116555222, 642938835, 473779009, 648493554, 13444888, 758055765, 729941350, 625025361, 444450634, 129909799, 13986871, 951560491, 489712485, 295144142, 107721005, 844092328, 92491405, 718395844, 305203844, 846600577, 162356961, 346915946, 579250417, 775208824, 346956654, 70321756, 515159308, 316526052, 43929488, 917537415, 319064342, 282204505, 42533067, 75566318, 141592065, 481068164, 771264898, 800856331, 268268379, 331414098, 14284327, 977557403, 760939136, 669512382, 232698629, 575380269, 821915099, 385416520, 464062052, 81126052, 836359945, 591566666, 592507154, 511864171, 254757103, 12273620, 245043301, 921839163, 482202973, 315764828, 741102980, 28199219, 57737973, 710297287, 444349105, 849791269, 517793009, 662036636, 711654689, 2942711, 43552678, 958363642, 980910163, 675373444, 631666390, 398033665, 645585445, 508914426, 758236389, 725082805, 493017858, 219562958, 873875024, 259270358, 750913023, 426677037, 759075179, 314788942, 999881342, 135786717, 127723560, 611938686, 856864613, 14866455, 241655021, 797594839, 2056771, 381931045, 770392142, 928094538, 179572471, 887439994, 581348166, 979449932, 963040671, 226349909, 547746125, 291243353, 261995677, 856207301, 158698136, 623785665, 343398269, 259682081, 948707671, 475874103, 644204099, 228163156, 21199372, 387066834, 706670676, 522343519, 539820896, 398522064, 494652847, 788096823, 733095623, 901971898, 870471219, 313772793, 221914220, 108375387, 288468988, 795296607, 528157088, 87551215, 735092310, 591602600, 670894579, 378842350, 160481513, 759622159, 60673591, 93692170, 446804875, 185123647, 609282358, 908809496, 1252419, 993433124, 247669112, 420853936, 68891124, 581537293, 880589749, 53624976, 322536372, 93208731, 839028717, 749799827, 652761856, 515362028, 362649978, 584785944, 796711579, 202381225, 846623078, 800315255, 120011787, 328624981, 973986947, 854362412, 687238849, 463550144, 672752215, 701763593, 980243717, 496947445, 174739801, 784846733, 406018179, 109730233, 366337197, 306116112, 571922364, 22387836, 818442417, 421969418, 427482645, 42735953, 140316859, 653769902, 898301252, 786636228, 556880339, 840268950, 293765228, 662346114, 813656449, 85448221, 95632635, 496652131, 415532781, 605483727, 421218028, 448066313, 172027517, 738680133, 578778167, 820316816, 315277410, 345303094, 719420380, 501646550, 464265308, 489083582, 857200953, 211876204, 773311640, 973452103, 997120902, 451410330, 743708220, 511511829, 259092402, 803880863, 623299447, 689944925, 271887429, 357269533, 766553365, 9401042, 322235735, 153089306, 93918245, 817512017, 376337811, 918970296, 81763988, 981132668, 700473586, 633270640, 35837115, 575297631, 533965725, 454977399, 833401499, 169564209, 829794559, 182765729, 960069865, 450033865, 772817967, 572631590, 868658470, 538926323, 874638884, 11184608, 508851475, 919898542, 416484629, 958443558, 85265154, 581630870, 430724703, 443331220, 944988692, 216845162, 917742501, 159903258, 57479589, 530431858, 508892241, 273736157, 428872499, 590044403, 247322656, 70538894, 346198763, 847189169, 944316034, 839602075, 704364855, 154143753, 698158068, 992741737, 165180953, 832746231, 303042904, 132775682, 844450690, 251354475, 68905022, 772926383, 702032828, 694986414, 697363458, 289619011, 929489808, 74783845, 438994851, 565593667, 241522043, 35246457, 492152041, 373248241, 703132324, 583786775, 39765389, 587291049, 156853033, 453092298, 247280079, 221780298, 995911605, 196526018, 367472924, 340445183, 981154182, 153459210, 551615197, 68149747, 348847659, 25290284, 848476146, 809859851, 651772403, 404346449, 977651728, 661999839, 365928079, 146790370, 150723910, 813856425, 458142122, 113010103, 828543387, 495091749, 545699446, 886435210, 610202646, 545228981, 689879113, 84105597, 595008770, 729862013, 564176770, 121818043, 221056799, 798722725, 301731096, 258819421, 778841085, 935142332, 309875415, 31393595, 765425473, 145332597, 791850204, 868203002, 560100053, 624096375, 60183026, 710929848, 354174822, 743349370, 162165551, 474003721, 155913400, 432885353, 981255361, 137972496, 305533179, 522068549, 293712689, 885849333, 696941853, 774358276, 872567745, 384134832, 701312590, 254175629, 679479124, 493087728, 125316726, 596920633, 746410817, 904996466, 243162742, 759207539, 296531563, 842784359, 266478972, 264230011, 802550064, 284393687, 53063594, 544697342, 384253282, 447816125, 505757066, 929287600, 710873190, 659204240, 739365046, 557078926, 385785842, 244177272, 905680759, 549378756, 966342408, 236721841, 940135456, 459929023, 926288500, 397524218, 808940702, 383561642, 44221951, 204748025, 934797881, 257511912, 680664280, 987892815, 616374684, 885114520, 937660011, 168790959, 193174094, 468466421, 696565398, 873380989, 827928749, 75756108, 399764247, 920273290, 719984002, 926382536, 889157472, 877519998, 438750260, 163452138, 436107561, 416755845, 102874976, 76401873, 233241858, 86948292, 369549868, 372437602, 731251434, 818534691, 97594745, 973623772, 206956625, 821735775, 612358191, 470676389, 576900112, 678949674, 344303121, 10834079, 216932743, 17302022, 564618910, 52998117, 29268359, 488156299, 975470693, 1502106, 718523993, 297666427, 283672442, 50788865, 59313130, 291067827, 192963441, 376421866, 476916394, 801489335, 874728867, 474128950, 79323692, 941373700, 752169595, 195187932, 575168051, 248423554, 768153446, 645888458, 887383910, 939239417, 559657393, 754543143, 462384315, 991452832, 668049957, 636366033, 553483040, 231354725, 71728189, 75037728, 114243980, 839248936, 653229296, 636200355, 201582381, 167044209, 949929886, 914232441, 536662109, 335026276, 255500806, 307349828, 107122695, 48903752, 992067075, 297893562, 76962954, 250365978, 802469679, 107970932, 102371038, 357724610, 652771903, 658638822, 445041145, 424455294, 105590678, 701316246, 42309363, 851987562, 975657994, 528010561, 560034627, 315464852, 401551487, 508648799, 717541221, 320890888, 632712056, 761177915, 115779723, 984568590, 494717526, 751095584, 130044019, 79316658, 876723606, 399406995, 546324893, 828422655, 191720254, 68247787, 207732045, 221678708, 87906885, 303249251, 569915700, 330261249, 581592456, 996995871, 925326986, 697674964, 881936258, 85182234, 136565960, 842346990, 796471732, 683541370, 494603835, 655976890, 20368489, 325357595, 930850151, 554035772, 458580742, 863648025, 548590797, 412562134, 470806511, 235277822, 58375924, 641196406, 4231159, 489165630, 276460041, 600437086, 433183606, 541545767, 685030999, 333388466, 605307504, 877954812, 335578796, 510332439, 196273991, 704684397, 374033543, 954751538, 79217313, 76034277, 504074109, 834395722, 161867453, 513282232, 591794522, 393736725, 897575338, 225935483, 159313198, 778347146, 691168851, 17219653, 674161592, 65678853, 50073330, 354720022, 599342783, 225670172, 681537502, 749520052, 3808716, 226084374, 766419604, 575125208, 484874601, 756317471, 83133378, 1311203, 561417535, 969851506, 573754167, 359070838, 57438742, 921528217, 572370627, 233936936, 794934635, 33634211, 175402970, 969912837, 725746045, 12161898, 815020382, 896978407, 324357736, 272745001, 893173557, 830478608, 932558373, 298802990, 245615821, 874504668, 592632691, 707957526, 484013546, 984370140, 500714030, 832612626, 872913716, 587774601, 95489894, 671836917, 658826503, 526446501, 896445833, 947994177, 592902066, 258565394, 639480585, 865711684, 480126513, 304466516, 861702513, 410766534, 399624414, 621901884, 65454589, 566415005, 259382395, 573114714, 210820849, 939771922, 515846468, 23258736, 851218377, 473545663, 907258767, 270287093, 374464752, 247640801, 600436646, 74677031, 23140960, 114852327, 573475100, 904594298, 166560842, 772161620, 3732233, 858594556, 984715846, 497597339, 630757354, 553065107, 623372033, 196524764, 461980847, 415963920, 987466359, 308074546, 850317529, 401805913, 48445735, 969351944, 993627054, 296487757, 53882671, 449360282, 617415805, 205694452, 357963549, 334503843, 335719383, 293927888, 43669494, 569688283, 485845149, 499041216, 863939350, 238893514, 333268559, 726056052, 73850249, 213313698, 653409286, 189119886, 112151911, 584304996, 132737961, 158877749, 997830687, 982930991, 58855923, 664050170, 852247033, 186590437, 353832645, 968354759, 7619598, 702680624, 231758057, 818812025, 88837601, 674997910, 712288315, 972975397, 847999061, 142424439, 118653731, 638437470, 401051406, 44098904, 893451844, 532354833, 689270711, 304800744, 765778807, 745213953, 57320356, 842825098, 287016221, 134990352, 674920457, 723017631, 97960658, 336075331, 240833334, 211489067, 600219576, 196210508, 484513014, 4167025, 826501281, 491734912, 877265940, 794131702, 520500860, 100291892, 445169796, 164613404, 756316604, 887908923, 232928431, 285082494, 647791629, 898003312, 423678018, 87220126, 800521908, 541914278, 97992920, 415981798, 502244753, 659510754, 931924168, 700438918, 568367550, 157796831, 901123186, 458390923, 931480393, 410842018, 342009335, 57010099, 564707055, 766458836, 118284707, 738376625, 811155994, 858967361, 585901368, 580554909, 329608753, 485294875, 638338755, 447013244, 741579440, 166304704, 3402179, 522361550, 159688028, 973914312, 406376685, 751566224, 430563497, 38738435, 914847544, 391026311, 39579438, 575233787, 122013448, 942891618, 412040280, 555961277, 883605667, 756056115, 283080404, 874777832, 733872406, 341280375, 821632133, 739967094, 124514125, 950519385, 358750262, 463409879, 230823347, 900971687, 5249398, 870028528, 391325587, 383308822, 415556869, 66223196, 341382456, 135231439, 515175133, 254616383, 424933999, 776739053, 370336090, 950519428, 364938171, 624995001, 472428560, 804284906, 685420485, 329205037, 937310921, 814407189, 599431607, 507366875, 464892480, 404610790, 446963301, 586476506, 97663798, 465250387, 959033427, 976652302, 13511419, 903102055, 909113345, 730596273, 726268924, 515335101, 765099446, 954516543, 394496082, 256390220, 207089427, 614884980, 637383445, 340296956, 328942399, 19290898, 165738542, 187508372, 473134369, 389506528, 188237407, 165219471, 534758555, 845747565, 261402312, 309224982, 346337697, 442365000, 536612068, 644609390, 937051160, 320372584, 650290138, 309311621, 102670686, 880381837, 258225070, 525990995, 511387861, 98504648, 297632094, 369405958, 429267553, 506961725, 215268298, 92421904, 625044464, 778956753, 360088996, 954302971, 473377917, 408115030, 161599977, 365575883, 839127664, 316717059, 526633710, 357296151, 634901599, 27522561, 612215208, 815483171, 143628518, 45236162, 116825130, 667373397, 27288481, 50230790, 505313555, 571423696, 1659491, 883123239, 375382759, 526890250, 622127751, 243810382, 904430120, 790279955, 235872007, 47965728, 528113793, 624427609, 821453308, 553083326, 469907182, 152234846, 126552555, 37546830, 638603540, 150985559, 49993359, 797343229, 925354557, 672584832, 714394287, 118656056, 757731586, 164247789, 475706301, 798865053, 345555502, 93521497, 149806453, 770769649, 442429399, 213533340, 433672823, 210083083, 286031995, 916338084, 330747698, 660904261, 450725742, 526997423, 397470403, 225239222, 962614583, 915163132, 108700537, 237373453, 286203097, 724015158, 612547226, 173200802, 320889894, 167585766, 72633202, 190517415, 94624413, 788626593, 220557479, 297019297, 120862920, 397026731, 536804573, 417699015, 837892272, 423222715, 715721756, 670427432, 356343459, 687070266, 949189761, 478055746, 314954561, 839350791, 402105051, 101206613, 41661097, 819752897, 644579032, 604405242, 64596965, 917615724, 786033213, 516648207, 387541032, 12201179, 166794533, 238617832, 451636294, 117198069, 977942907, 235765682, 291905081, 409436547, 141229705, 902937711, 950942422, 329141116, 916560574, 978299470, 193992236, 927449416, 348663115, 359712678, 619327398, 765635763, 383048138, 725041628, 980814454, 253993441, 418845437, 557578136, 706932506, 269693663, 916041890, 487610681, 397991557, 19517597, 313225341, 964610773, 746093054, 263830809, 346111817, 155225334, 520942062, 374284486, 840661950, 727472807, 596301526, 486920281, 746267368, 355602262, 685068258, 688808680, 405047644, 74550114, 460430132, 983280893, 9620915, 18180097, 308021251, 538069659, 821226641, 866932973, 483273261, 71784690, 366605379, 2667991, 990507626, 650572295, 241088799, 877428277, 158715152, 989709013, 138983979, 720935951, 4010491, 923044524, 501015088, 16050875, 104447907, 113133406, 265713665, 942262843, 748072272, 689527296, 726435319, 460070322, 741632043, 494234951, 819845154, 757554022, 232120791, 367160544, 289954110, 131632113, 767480351, 183659114, 182955945, 878731369, 58576577, 301461163, 843756022, 544430032, 976551850, 714262463, 413723270, 770942258, 701806678, 481813458, 183378624, 609989275, 736423166, 19409658, 822776197, 845403130, 960983152, 979983712, 585504701, 816707103, 7758891, 119213959, 32458381, 134147402, 503989238, 101727031, 305801080, 183972152, 962068655, 372270121, 782390957, 382101943, 195817094, 644931382, 138757009, 570777205, 168425449, 431209105, 398627983, 942274586, 253675910, 332698764, 580839456, 268924867, 354442011, 176409227, 981707371, 14481036, 648279298, 238143076, 621905139, 911504375, 779096677, 646089788, 354478906, 136065831, 602355060, 875470356, 92518082, 1728567, 410656227, 301073914, 867511361, 655954162, 984885725, 959989409, 574270976, 103028623, 575792194, 433268722, 784648636, 76524128, 51959984, 135247333, 915700169, 98713786, 780811869, 181731845, 33846902, 579596058, 194541238, 794890843, 731041345, 396670933, 766354875, 658034045, 759299202, 410362403, 712418650, 18461654, 767508587, 665153615, 564855692, 372352782, 515511970, 110222346, 229585021, 539095368, 852787777, 795133910, 663038674, 334742621, 295343483, 348107967, 414632216, 661685797, 125675794, 466042811, 780367073, 996743280, 673551335, 451812183, 432710552, 947408654, 18804421, 785018337, 6667190, 313713723, 629849918, 633553200, 607055107, 715677524, 11310323, 390114580, 723713565, 992598619, 891563185, 985668319, 619773054, 229774941, 808022391, 239273236, 750522298, 525009267, 341941677, 242335082, 584401709, 596252850, 433149455, 523894263, 552231300, 478304397, 820771670, 63582188, 767518561, 404028328, 913982303, 89525265, 747430898, 20019634, 611632382, 109668609, 153096007, 76517535, 388436783, 388057105, 430652077, 444534128, 155603953, 645835608, 920509643, 379135936, 447915092, 576156465, 294358165, 382027792, 132374362, 761835853, 793632941, 954744329, 396897899, 740419464, 376163284, 117179028, 752977331, 880347853, 201062548, 932185573, 572457227, 389660321, 904175306, 728420089, 299268390, 620012356, 821839341, 704895759, 839469491, 746070616, 590915519, 160175099, 142201638, 280584986, 436822658, 102315841, 110440915, 906532905, 732740331, 154129355, 919975886, 687483336, 340324391, 40290198, 677959269, 554484340, 148137611, 416053173, 724276919, 81886725, 386362125, 320845895, 110307203, 888237767, 405013503, 336526470, 362542186, 154483633, 990092498, 365696748, 650050361, 582356115, 159889140, 11354630, 408600795, 381453483, 820131527, 425160241, 505480769, 894596646, 419780389, 344908227, 243573679, 709343127, 261515657, 460837132, 389166060, 270002106, 788947570, 474858721, 577515350, 748932850, 153544776, 164382414, 510345835, 342340304, 253690458, 711393588, 823315326, 623148280, 518905116, 307282281, 156353992, 32731283, 197657807, 205775688, 418781857, 10324990, 200054602, 940036809, 87385513, 200076075, 712515340, 765396858, 925894343, 653504196, 944501241, 753690580, 577589476, 867822704, 308904645, 597463157, 825829504, 875618050, 978073436, 500555319, 510915818, 584026402, 145830223, 912830814, 379444890, 674664289, 113110246, 424216623, 334179520, 937245523, 881899184, 145326880, 932284154, 510727958, 870138012, 815424934, 660787876, 966877303, 510959083, 493840030, 340598922, 596285018, 614105225, 699078868, 658006376, 484135158, 262289133, 594181665, 820652666, 746890471, 236818566, 428543200, 255782970, 266324071, 242829498, 525348868, 24503737, 169295086, 62902846, 938651192, 873277291, 625210134, 839187128, 71761822, 976205331, 152993479, 756581194, 998734529, 772418449, 439576405, 701229810, 375905829, 702079947, 794696839, 935410292, 22392785, 697762917, 654156462, 740885694, 125310509, 986393957, 16942186, 579100790, 177561130, 373162176, 905847619, 964644470, 478605520, 408535246, 182685491, 485057333, 304231152, 994485741, 520872150, 671389852, 404632905, 276804374, 337722109, 774141032, 251633934, 58065426, 550465011, 835579919, 807834616, 366359166, 730403452, 261483663, 444316046, 637593346, 311710221, 853771071, 967884077, 133332624, 224137450, 776753279, 763181004, 400570481, 176690883, 393539637, 148467106, 66463170, 918415064, 693144739, 27167664, 302978653, 1940475, 747198755, 412583034, 736425850, 457553886, 145500239, 291375106, 841558575, 172590964, 96491640, 515667043, 107564800, 948361865, 62760727, 455283733, 364108995, 392385544, 33923473, 218351148, 619835817, 847967489, 593782576, 480883734, 546129561, 378394268, 19496987, 453076301, 835226467, 52554433, 792148601, 600171488, 635026898, 19716453, 360338238, 935725588, 657694005, 285544769, 329999995, 539727930, 826408367, 407838487, 634223172, 473966046, 890260804, 973697639, 516393991, 408323053, 833901546, 760515941, 917195059, 106650349, 909371169, 961190395, 796966849, 376612552, 776383212, 331988435, 199150658, 985654492, 572228432, 721719972, 905913036, 180722448, 203782716, 245400510, 95948555, 566590479, 736068944, 794079069, 921655572, 834952098, 109977660, 955605720, 863344977, 845135078, 526871755, 614280199, 109768817, 569728994, 635795486, 801353343, 772030972, 822987168, 268992081, 373185792, 325249466, 831706953, 913740937, 753152698, 129661474, 245028480, 772271233, 300349984, 822464213, 97727785, 96393323, 316514116, 898245997, 232919860, 969680675, 982841237, 4457500, 586552152, 78137528, 96302296, 174237797, 161399131, 925363957, 545843334, 437619822, 391981882, 678225689, 388871371, 717033046, 233411239, 560480622, 523306940, 666619829, 997864063, 106764998, 533944949, 399566193, 792848211, 275651088, 169459918, 467108492, 714697069, 715941248, 870338173, 928298213, 795502686, 133319167, 651148103, 149969845, 432605630, 874277131, 577334168, 16555378, 869841517, 353291318, 250300597, 404664812, 754835489, 129029568, 578535191, 286628102, 85065266, 21483363, 673875927, 67651981, 369296329, 599915795, 288556086, 526681489, 579030149, 134468958, 950933243, 897117491, 100606148, 751972058, 234210350, 733103041, 753940152, 58647099, 726881853, 49444936, 148831561, 788990071, 186315464, 274743467, 435412444, 339622736, 748571750, 133790497, 923848120, 414776581, 925120064, 572313620, 650908761, 730576890, 730093332, 381809478, 694196614, 457222363, 149277173, 977596454, 723763054, 459508660, 897772152, 785339753, 320992726, 185308754, 138450012, 386564191, 485509325, 225484433, 644367691, 437051234, 237535724, 368308975, 523594133, 973181295, 146404129, 244733720, 244548877, 835115825, 842513976, 913574059, 74311073, 260834303, 931400442, 850425551, 716743797, 88823573, 420175167, 784997229, 775662465, 663584771, 997197307, 664338095, 183011008, 385043184, 931240379, 521733274, 836339138, 459402065, 82406364, 393123135, 154062054, 921231165, 286121514, 587032931, 510969042, 418549582, 407708737, 389142128, 250257378, 238528471, 343858539, 602291988, 436968529, 942314041, 856151538, 577708780, 979638516, 610343437, 742893684, 826629261, 183047549, 998082318, 705177162, 592608963, 185323036, 517399263, 343460395, 205939978, 917866098, 514298925, 180774553, 166036270, 651230569, 549900365, 630155464, 38018833, 185280789, 906755495, 652274265, 71112357, 157844821, 98335149, 334885058, 361590334, 736818126, 647197176, 680536075, 744430483, 109064997, 439507791, 948493190, 541246140, 131411436, 78776939, 441991705, 329425651, 808729076, 981054272, 308062446, 190094995, 990393503, 235965169, 714435048, 318453806, 614528044, 732424414, 183839877, 140206304, 436041308, 359209594, 893994358, 890334761, 234247343, 567303650, 787205768, 14736057, 918534334, 307189576, 875787191, 402311185, 665444400, 338184344, 359793320, 435228747, 460030930, 493135774, 692925148, 403655708, 666375126, 29107108, 522646635, 870808133, 21675809, 845837718, 600972496, 411271058, 456437684, 742873528, 506703571, 591575565, 674024077, 720342978, 660117903, 359714113, 550371207, 569857192, 545374426, 826347532, 930336680, 5657600, 43780320, 466820601, 940771089, 292200949, 670401250, 873319558, 466272802, 363189756, 217983973, 604280045, 307121041, 991320395, 575584250, 322295189, 588528317, 70325244, 474123954, 778161220, 794512142, 980273113, 334276788, 477300657, 527453812, 78927766, 759553169, 232553898, 841248847, 620982835, 819493168, 990983335, 469413832, 286474571, 845906817, 734239090, 917250320, 435547911, 766223430, 369971138, 856140627, 57101810, 959380206, 767529139, 902340109, 559814822, 699384402, 734050132, 903550272, 224741666, 781596007, 137326733, 61616616, 14151026, 5393223, 287420705, 602637871, 556807839, 962112228, 224134202, 747099334, 263439951, 707968154, 689789467, 567334238, 875267070, 152164172, 936381376, 391566114, 809394322, 323201099, 425917735, 695314135, 765012107, 424765131, 891234022, 669417448, 243165545, 109802078, 719293943, 263419428, 578585892, 493924683, 701640415, 995091590, 711210158, 231167208, 284922808, 567022943, 494965433, 747219013, 224356664, 569043262, 881445309, 104737187, 740305686, 352816225, 419971268, 683729272, 971366517, 950593596, 470549348, 280401679, 555334308, 280241319, 358893597, 219496298, 338703526, 217299075, 366915830, 939987436, 797593783, 672747627, 435291653, 247586746, 931259216, 23778976, 136088988, 898685828, 396267234, 24322979, 663862614, 921040152, 655523909, 277466729, 933597918, 125785888, 674006138, 646546601, 81286945, 926491796, 398267836, 173996293, 385363864, 183709137, 161628835, 843625521, 604983757, 421161155, 981032904, 956108965, 779469391, 766827368, 644251527, 697219021, 455130143, 137183222, 782203510, 752428572, 715399676, 926989480, 950125490, 224391645, 138310676, 854943037, 418760538, 475767779, 249361534, 408422018, 41692471, 818750346, 387254151, 210178623, 865743654, 89089611, 847556880, 63658169, 736975575, 30663775, 446786831, 820857608, 874679935, 679405505, 194911414, 104457032, 911418435, 61733860, 860413188, 944467504, 486330904, 207995892, 418442515, 249140373, 548014788, 149561748, 852683930, 9473052, 353189804, 560708481, 911586745, 707783377, 341914366, 941307353, 91316723, 597732991, 387672612, 90744580, 447676711, 180766358, 485157125, 988090511, 96892432, 696053135, 561157376, 22792207, 665264757, 107804728, 909326000, 91329617, 657767121, 755029130, 692932355, 838364068, 515053167, 591558665, 917698437, 639049323, 427615332, 56900052, 483953584, 23992014, 287898575, 9949292, 705182044, 34970515, 716715461, 949510671, 172789143, 603155907, 231886, 70421054, 135649023, 383326832, 952616766, 563980802, 873846131, 261873652, 456780651, 802712566, 147546977, 121656446, 438586945, 403092135, 206493940, 844736646, 74335615, 275414658, 174525487, 828145419, 350558550, 804925424, 622551691, 218941174, 107379742, 744423832, 7559847, 558114164, 332985914, 314667964, 375659009, 786357613, 978379038, 479798783, 722079568, 517571963, 875606622, 994901472, 553880495, 621435040, 315413787, 50037996, 872289859, 522798758, 581402585, 165216964, 804687460, 254327632, 744928515, 172206090, 826053027, 353402259, 242096086, 856314117, 26973726, 915065296, 52774488, 759850465, 112352304, 393732628, 764158817, 648209347, 673473371, 971189511, 136328055, 107930563, 956492838, 889536173, 316558534, 675166917, 610956309, 104769390, 654327961, 108838353, 647036557, 873800542, 700612189, 659438373, 558516925, 138774350, 218556455, 798918295, 125561074, 188886366, 489443545, 79459459, 54983277, 206055891, 233792486, 274023298, 209406649, 788490370, 404068681, 865575082, 722363258, 81340125, 26284238, 856490343, 320192139, 582658808, 292923205, 789341754, 386848990, 765796380, 682762532, 276093524, 422994252, 355611551, 157973709, 792572809, 443695409, 296137396, 396015076, 296512612, 889400900, 590969358, 871183537, 749006053, 672599854, 332697985, 650877522, 605865884, 465206236, 720992146, 74455881, 558946470, 990605522, 287732447, 3053524, 289639560, 614920072, 37035814, 83277331, 544381896, 693642631, 384534314, 597545003, 776074455, 9146011, 334565225, 464895963, 43667525, 541639767, 457427697, 705435270, 937901433, 447943505, 730376431, 358720930, 265322441, 697821814, 287464679, 431266504, 944531449, 889492616, 303386266, 356618228, 408618003, 962574993, 858123366, 567478036, 242820012, 553335739, 599841962, 643105015, 682376382, 855977043, 358095066, 474960064, 236147017, 435828826, 659163886, 37293999, 363871691, 20696559, 696256282, 697574683, 616646412, 864960336, 464439140, 543604698, 582689457, 571300615, 48759655, 403924660, 662400761, 952832857, 829025485, 337780517, 47906121, 980490631, 771156206, 755387640, 760746259, 280988150, 885775374, 141204894, 346740047, 942524974, 950378942, 591681918, 546889029, 887178997, 917526483, 192620307, 823083573, 700720342, 642577886, 416442357, 978660966, 397623242, 646457896, 44164668, 487369310, 648620360, 959728181, 935557233, 516637129, 238691257, 761270344, 469429305, 155741600, 423565393, 485019332, 160901278, 524866627, 391790249, 381269334, 384041437, 946381932, 649854223, 659038338, 883096616, 766923280, 403553075, 856691622, 246618520, 709882187, 600166208, 897909436, 550984841, 256611299, 165327588, 798744595, 144745379, 558260061, 824883353, 192503563, 726549183, 983537104, 276687212, 829279298, 296152181, 860192888, 883153403, 929450555, 694851068, 848731107, 267833163, 602401881, 363490050, 163476246, 807188744, 922625327, 435183921, 680807327, 540036653, 877031966, 586546401, 789859149, 340498193, 120248562, 842676230, 60151523, 426069769, 621401334, 113353229, 589960100, 270727150, 131191657, 425053837, 359574405, 186336917, 927524063, 629311919, 313066097, 122784603, 230985314, 696936048, 44277528, 802279527, 266477047, 24268073, 908828424, 971643899, 772964417, 118853387, 882068690, 617220591, 557101590, 586975489, 743597062, 620082074, 767133139, 799196600, 381856323, 641786629, 385440726, 185840772, 353470209, 144827024, 777310422, 9921363, 312362956, 666312840, 644592862, 775443026, 615381518, 529571726, 104248597, 931467721, 15707428, 988200931, 479805007, 970946195, 791455587, 641268013, 952089476, 778877811, 365671306, 730617530, 480950201, 303795539, 939684568, 649779051, 23338504, 486469763, 996394983, 74302768, 442483815, 512494370, 953485624, 831826773, 763162823, 154121035, 696126801, 672454447, 245147871, 821681276, 69009113, 834355604, 419253858, 71809209, 201151540, 299855576, 895602138, 730517924, 763809596, 921785478, 337595493, 46806044, 233095258, 909058194, 714209896, 56661569, 80638217, 625538053, 498301819, 1730151, 761192731, 935372030, 674621410, 597685181, 752311159, 615309365, 392536069, 352330034, 326964768, 536710181, 414397269, 55039154, 79752006, 592888039, 890978403, 323473786, 765242767, 725394121, 588755243, 272804457, 899872345, 336924154, 282244386, 86385590, 169297422, 446773014, 583208399, 798496412, 645944112, 20744284, 401749637, 13006388, 883705501, 616895171, 937647284, 498622630, 316973198, 681110488, 916811474, 326579589, 348661002, 682529904, 551720888, 140946151, 533148086, 149466581, 860437806, 572540318, 523190682, 516468042, 116904214, 774834542, 820641533, 583005875, 187206382, 437938308, 864554072, 934201422, 69452118, 641198310, 560499303, 248258066, 905549438, 886500906, 254251730, 139966061, 147825763, 208928292, 895713371, 633026128, 97296846, 135724335, 239072141, 39097168, 644282979, 776181356, 461865916, 286079451, 794758623, 768065967, 860745400, 145067540, 31082860, 91298698, 375088013, 802919751, 230249792, 533380001, 871959954, 574861278, 471578125, 893088589, 73210259, 406564087, 397280405, 379663961, 158947150, 1005415, 269890271, 252925648, 806659687, 573123761, 7674647, 261889515, 123604676, 471334712, 966565668, 992900418, 305393631, 348523224, 549781034, 893582268, 167940759, 915897590, 715586476, 649931736, 561291754, 70393025, 367252042, 229676279, 691024274, 482955298, 623685421, 689098615, 922746543, 863604428, 807033093, 889687166, 909046468, 864635191, 580152433, 277595946, 565549888, 666533472, 934849097, 74902765, 68766723, 369864232, 84450435, 390755113, 27754510, 93507685, 196843888, 465350352, 977377041, 194839969, 147635161, 518220193, 570812442, 749549013, 507166415, 350850236, 93476641, 502200910, 834057391, 977434251, 834568339, 402707837, 950334644, 499135644, 982670320, 480501236, 10177905, 771154138, 306189056, 689661255, 574007814, 532025111, 309125253, 677586139, 587154733, 217320654, 489362703, 298516385, 618283768, 7442103, 904910417, 666478797, 856339008, 619732460, 691536615, 630739869, 332557183, 930002158, 933362723, 128139896, 84186988, 959540292, 199362482, 166951603, 519219114, 110481222, 32836349, 933086818, 118538089, 213862802, 556821032, 980620460, 879016660, 542212775, 133297441, 109666288, 314335467, 910711200, 307464425, 890973622, 309315036, 751151232, 771323353, 201502855, 442252159, 538341040, 601072582, 776996160, 246016586, 325789692, 925952653, 931914245, 400674664, 549741959, 222974734, 407655553, 424284307, 565120360, 286089209, 427825245, 580155147, 218190670, 487122598, 506318738, 238185577, 410730532, 777500398, 805616217, 296904503, 669770359, 675786853, 723451152, 590334718, 358611022, 848234108, 446063120, 400250007, 576014812, 427836243, 513047471, 510879408, 328586132, 763121452, 973307437, 851080427, 199482198, 960164461, 601788309, 940659467, 165956266, 369819619, 448759071, 508260471, 764992929, 418324655, 441776144, 607374324, 500602937, 493749825, 233501385, 750965002, 791761198, 412822166, 748342985, 889192453, 677808210, 618968327, 886972954, 60777458, 760999053, 490247631, 837043279, 312108692, 192333468, 677068100, 669793965, 615285114, 996001585, 676729477, 278312596, 94916103, 778051547, 908926085, 611763004, 869548415, 613565697, 97774686, 494322644, 321312835, 986025058, 208664651, 284143416, 505195515, 394744438, 95126373, 286621622, 537790252, 851825139, 588885537, 371308247, 987306300, 813359169, 357205040, 423695529, 177025047, 561770479, 792407681, 798585349, 305583318, 600178455, 876670072, 730923198, 231886491, 122200082, 573421102, 513834393, 145104522, 786427086, 609783207, 217914802, 558588251, 692001808, 639118890, 362353620, 184942637, 221382142, 231981207, 302997021, 619687988, 185533215, 351271761, 478579493, 842054033, 74571546, 416208601, 253370907, 435311789, 595678882, 571274611, 994886737, 619291072, 532830347, 124025303, 771973617, 323692924, 929276167, 201043422, 237147870, 994357508, 408471700, 709844523, 910734877, 645708486, 716260149, 399338474, 161651842, 890954470, 537025788, 82857883, 210452283, 389258429, 918429357, 455499294, 396025739, 771751825, 257521085, 683189357, 94470850, 526576637, 16318017, 340359553, 452916444, 854574224, 987987641, 534005380, 549181980, 297650256, 118422763, 358587960, 291122188, 378792973, 631851078, 441637295, 535799400, 239169645, 641191883, 35626979, 107957574, 398416607, 449501456, 553469673, 509228821, 130514762, 606795173, 667896550, 988322433, 542648658, 171686842, 253153765, 214595451, 165008457, 913382244, 191051176, 148276817, 639512073, 236412038, 277839016, 458687707, 842886072, 806508409, 736000694, 597502039, 347020221, 904507495, 577376533, 588458953, 155888880, 418248974, 584223326, 255206628, 824962680, 499276735, 280303009, 184149651, 875397316, 556923237, 957384204, 631557983, 967235628, 285237420, 505496075, 508327558, 965827278, 326916651, 862360058, 86292246, 508571700, 637520411, 490243098, 657278388, 560871090, 57694492, 52709127, 690057583, 738316743, 825384514, 351310367, 110596439, 12393956, 718648135, 147335201, 3415784, 147565723, 880842535, 639196124, 313518589, 111691510, 320828057, 433495671, 42836989, 683961553, 80391499, 589372037, 799070436, 688320308, 811442098, 81154157, 616790811, 274296884, 704926018, 178494900, 709950277, 839865339, 238140363, 578548605, 802112756, 588939564, 260484156, 466963073, 462401095, 69824659, 121357385, 359727154, 125800962, 267407278, 695060006, 476440687, 922109215, 79141052, 120038833, 934445224, 908463557, 510102822, 511350220, 447014745, 933781468, 622503458, 25121785, 851096527, 476034914, 482166045, 860850196, 764693469, 125617815, 477402928, 626772414, 509324941, 401580871, 827093608, 432181338, 805538411, 927590615, 179508420, 538485088, 356533703, 906994068, 985544622, 385036850, 626627492, 217895249, 145894381, 207920897, 239765023, 974501499, 330864643, 635289299, 73519707, 565346037, 810562571, 753688236, 547396455, 781788705, 821282473, 434532711, 851601897, 678926027, 820867352, 507732354, 237303281, 884665566, 989923601, 169066843, 922718845, 196453905, 394121643, 575072280, 376083448, 168198104, 105129144, 24564504, 69383997, 70687, 65717852, 487704369, 646912696, 709173753, 777905568, 309733728, 540042881, 496200881, 371603412, 956742886, 562467363, 98579470, 544408095, 979256753, 427342916, 406720532, 932073642, 759231976, 616708073, 931923207, 171785271, 556868315, 188295108, 209351008, 550489858, 512916666, 183443676, 859856037, 659642344, 378320358, 8950987, 636137805, 652486531, 458550770, 820238210, 115017801, 655995537, 254704037, 957208016, 391762055, 917778551, 795870220, 351334888, 624046775, 461351834, 581246314, 64368171, 525932270, 940775405, 102464604, 347229983, 891023150, 169464852, 585908026, 675629420, 214119145, 540070470, 512872025, 530715141, 971187901, 28141797, 674592345, 688599078, 822536673, 170213393, 336300451, 990018225, 382728577, 59048386, 804557750, 879781878, 130827133, 865882045, 785241984, 103364524, 879359713, 136095660, 916213497, 394882676, 461569206, 551633579, 888200273, 871248855, 139961559, 899412624, 832211401, 664257599, 944969435, 181133862, 543834849, 66403703, 263285927, 419756599, 938723252, 872082362, 576224131, 128343412, 832379617, 826431318, 889421835, 536778909, 168573154, 34070649, 998295998, 725328004, 475791737, 86227437, 656573719, 185295769, 520922096, 35348177, 188802642, 358827146, 548843461, 590989935, 621264630, 628079944, 126394770, 151068434, 232272505, 362458343, 448532345, 428694233, 177285852, 642022083, 134010312, 853011091, 790600802, 40820809, 32178580, 375393108, 901645021, 646616042, 724818720, 873492982, 479660523, 777187694, 686550933, 79221807, 932622531, 767494415, 375443357, 669536350, 547808176, 966339805, 92438064, 329385926, 428091468, 251010350, 641186122, 678416679, 501632415, 646910223, 254427000, 543802465, 413197553, 114719486, 536972636, 698930215, 820452137, 95550119, 718123165, 746335212, 927253448, 749296707, 730034743, 214571230, 4261916, 481468486, 468810898, 555944954, 463326211, 32235592, 465058414, 343876280, 424382606, 772234116, 929704930, 277444047, 46693486, 594053641, 485195691, 849628563, 573101560, 946947700, 348737018, 248341823, 900737355, 21502610, 348174574, 397652977, 707937008, 782212998, 727520824, 721975514, 104131374, 32366399, 887331386, 844511136, 881885721, 116293782, 395006346, 614415918, 877061092, 395040161, 496270281, 430555784, 892655079, 866900450, 707509837, 543332489, 659439827, 319894264, 404513326, 76442082, 203360585, 972863982, 504621780, 109676832, 429686594, 698454192, 135741549, 309428194, 632159848, 82404209, 538863114, 380661036, 634561417, 399168554, 723974250, 524755110, 874930836, 308458969, 730209641, 41130089, 30477299, 521784735, 779951123, 786296051, 362220787, 366084086, 615052082, 511677879, 46488834, 174731076, 429105811, 308155699, 670835162, 263911432, 810660902, 350334229, 466661414, 292275495, 480633753, 647355614, 461823767, 452473557, 131934698, 347909773, 657015327, 670602147, 616073676, 146907591, 18622032, 330246166, 348814878, 468092818, 488466106, 725096698, 312501522, 625794415, 655892419, 170245285, 443448057, 754136814, 579344608, 476454347, 693392338, 815828019, 982868453, 534354666, 64373904, 556108480, 345913130, 321533054, 494943755, 366542215, 596123547, 304783554, 936691462, 950732160, 769580699, 889221304, 89565466, 532717612, 56006394, 656324835, 784507815, 941105899, 693335755, 996585578, 68729565, 285287873, 458932505, 752193908, 83581899, 652557986, 741778515, 605951082, 729482841, 984783528, 534841709, 734535555, 319314160, 895388480, 454712786, 216715603, 839096807, 786351871, 201929222, 660738289, 450135671, 248451035, 656738322, 225130357, 755958269, 608424449, 308148494, 153320536, 482094946, 55544958, 987559579, 511701269, 984953900, 469724756, 867935936, 954531443, 75824428, 108070793, 709770218, 999330638, 823813925, 829638080, 853743668, 154455998, 734592052, 243656611, 83696541, 976951556, 928628997, 586748015, 445092412, 700417052, 914838123, 857763944, 894243601, 547204158, 672359128, 993931219, 687269895, 914373488, 993200245, 668481297, 502324438, 400724049, 796285502, 287494465, 488409040, 784426050, 985242555, 255119680, 632842214, 536143431, 719550335, 707021313, 322266098, 231922499, 616389189, 100185946, 117222662, 386020543, 615683192, 708957105, 898737396, 93577426, 553003332, 997842836, 102466047, 571531589, 991453156, 637583346, 225395330, 193180768, 655895230, 237068903, 71016611, 990260609, 588490371, 209973741, 443154703, 689482011, 871246652, 758908495, 716874552, 489502690, 825790534, 146155788, 351176671, 298965036, 711672841, 482309832, 512923664, 549275820, 657462379, 668351644, 651302616, 342109739, 111332459, 148590674, 395935890, 885828005, 319923497, 120468910, 61938245, 967170829, 667866497, 731452469, 888719438, 902736257, 418391367, 442671842, 74951400, 778299834, 321051016, 631353257, 593943249, 434605205, 883998104, 827257482, 532697503, 528876271, 756217581, 57115783, 414818833, 435519832, 837670241, 623066521, 768094822, 358985642, 903619465, 614896855, 780907560, 798460008, 140662240, 933133416, 159287449, 910281683, 375431392, 514959593, 291503143, 329383113, 942263675, 743698095, 715736983, 589493603, 796805027, 840281163, 840475377, 520874446, 592944917, 145135421, 788664714, 445756795, 182955775, 547416607, 549952379, 319551578, 123384824, 255960699, 602300393, 425021145, 475510918, 387836074, 100721217, 417458908, 459714602, 725740644, 659828312, 664855084, 552042359, 223900371, 8354468, 42676713, 719617752, 506189282, 501337843, 226761572, 774446264, 963191022, 823466451, 506326090, 166350419, 288443319, 301405910, 438118828, 800467789, 454447233, 476063964, 147031412, 583225407, 511171719, 551828572, 795155316, 202134804, 300380877, 753171519, 983693034, 574139976, 141528897, 225341525, 353944913, 874629063, 216654199, 463395021, 115935568, 561020007, 464074247, 43083988, 439456497, 398772085, 298170461, 415723885, 112076938, 495390045, 639037316, 596121325, 217185501, 959163223, 680628596, 922591159, 925593847, 377030814, 184197207, 896867213, 902623829, 180653867, 530349972, 504369808, 985403678, 383863463, 52358534, 333705875, 624445713, 263966380, 364665733, 534295028, 598250418, 926830451, 86230847, 23057278, 111317750, 876575607, 142439376, 424682202, 598475801, 832087392, 961660471, 921233737, 382945726, 19581435, 851243411, 680075165, 886482642, 594097731, 167882363, 360109296, 128503479, 265754913, 500997299, 643076676, 644368348, 609129176, 117681237, 737419880, 718414403, 187293694, 810411694, 449598584, 899466994, 156942119, 251813725, 614063248, 281981061, 301759534, 9124967, 122181757, 860942615, 598788883, 452808319, 740462571, 604456305, 726592156, 218914696, 502149373, 34510756, 81267287, 816994986, 202300907, 641818223, 667852590, 567929157, 556392120, 713945183, 417913733, 977467215, 225600221, 258171524, 750608091, 532606668, 236996912, 177417684, 709928251, 723572133, 222490303, 635523663, 741230001, 49011079, 475295979, 402470883, 326234726, 608133130, 576414360, 794480954, 357464644, 580021879, 926236570, 429867503, 45965814, 626071727, 111907187, 388363118, 713273227, 381179970, 687602379, 42743215, 436627068, 213714020, 59814012, 47885629, 886636525, 359271417, 113804707, 494722585, 104624523, 285543840, 667925314, 824447278, 882456369, 94028924, 611877098, 818920553, 681181463, 509329900, 533251907, 795030066, 88551660, 364058556, 558069201, 440697503, 894813028, 692366833, 319582193, 263346909, 839881873, 716946728, 524243491, 210209322, 852180262, 510590414, 23611514, 895624776, 58889140, 637943534, 96899760, 515246024, 831305147, 450938102, 627061419, 237130411, 367799981, 686891986, 493350452, 584530166, 256129786, 257227906, 988799441, 510558282, 924721196, 348994091, 232092137, 920434138, 653368186, 34549981, 155457299, 27161108, 448966604, 458222164, 563500731, 581805105, 604209116, 277920349, 590777719, 41055373, 97540784, 242490664, 691205335, 76005069, 214490945, 195804801, 504050165, 634209479, 665071921, 962223654, 222683266, 907813320, 644652762, 198880224, 763278207, 848318634, 523653386, 731095628, 264462840, 298236729, 383521742, 441213475, 803171560, 700880255, 370161683, 672565354, 986469946, 279548551, 741040529, 366364944, 18327684, 242902982, 262821175, 978246142, 72660186, 910032515, 891915101, 453848765, 83569667, 184093617, 554179086, 558120636, 834975357, 773225156, 594394255, 387612584, 266789112, 742878358, 886440706, 679607410, 318036613, 205830020, 972841559, 392473176, 807388756, 835540282, 49883442, 657406177, 528932042, 157657047, 981367575, 575203048, 223484438, 981712055, 599873933, 285019029, 278966305, 502627592, 638166171, 311642272, 189451292, 100990947, 879887782, 373778631, 200425499, 824917146, 422090723, 384447878, 244174972, 569972088, 777177652, 909812734, 448887683, 808168383, 854760154, 404156095, 541531674, 18934510, 989624776, 898466914, 548354774, 326375917, 668974262, 665817169, 79330414, 371800792, 822857449, 225667938, 606733198, 27343945, 210191967, 68329896, 839091684, 89123684, 325595808, 340471581, 300087386, 102991284, 650601237, 367726563, 586646314, 455905510, 426912846, 775706501, 614540486, 698978941, 732767658, 587251988, 217953425, 642899073, 679256277, 382561591, 779996946, 924915282, 842776541, 86441030, 367410908, 399556619, 872081209, 356381074, 473477585, 458048488, 237785173, 886964781, 633415537, 917346689, 882256569, 229147539, 259926519, 485117058, 810442495, 71950392, 405389338, 754837500, 941242764, 718427168, 243204771, 223744730, 857876649, 348030019, 467970752, 694395164, 72470693, 435137189, 388985475, 547621956, 732467190, 830991330, 921724809, 920665405, 90207405, 679930084, 565193749, 143257443, 466252315, 124481198, 121019911, 970296729, 629199040, 257658451, 965818015, 698451909, 512586653, 204355815, 285663424, 997403546, 489611907, 818236999, 714003717, 598655164, 11137909, 512989373, 76870067, 124517308, 463059508, 588938566, 609299528, 166671240, 712755955, 891573928, 105732160, 147168478, 409406890, 187014622, 276884652, 20051298, 938103958, 645585264, 147443304, 684340533, 94375738, 491632615, 242673944, 518477804, 402542739, 419175952, 864884507, 806581551, 588634579, 552991672, 309264659, 948740857, 44256882, 657327043, 735194336, 221565470, 99547969, 370730844, 321210790, 51195320, 395463720, 545060931, 518748354, 30996130, 187150722, 68584530, 764629510, 869258357, 490011909, 899557285, 778627042, 499041907, 989657987, 328828007, 610511380, 684354826, 756179279, 883815267, 491509664, 240007486, 731949291, 285799042, 977549583, 142593529, 600033717, 257308933, 132879887, 328348622, 784502810, 53153449, 998020708, 112103285, 951369632, 476253145, 413557585, 97685423, 534475163, 457489243, 269370676, 237517101, 132362635, 135183981, 849753794, 229135504, 679269156, 515145292, 236961044, 217690325, 147606969, 281986285, 882128018, 144325193, 508410919, 862335819, 122354141, 251778549, 507972014, 505994324, 621985887, 464082905, 700393389, 585034312, 332976881, 251772306, 246586622, 119576811, 248022624, 723090128, 622887818, 953810355, 96152062, 967460961, 615228214, 891116449, 487417030, 335851140, 41591670, 455429880, 214895299, 56676257, 405117239, 346085036, 315256079, 773321651, 311474764, 406263297, 255519683, 912331449, 31264032, 759784214, 790434033, 118706857, 143952448, 558460993, 255769316, 872256303, 415715459, 450544193, 236853626, 903714872, 905441880, 76310598, 613958941, 665330215, 10119689, 905553846, 732015135, 624723245, 74389675, 354243452, 411482504, 308513919, 850996395, 580040172, 776095642, 983078060, 113119830, 286544148, 591446436, 910612613, 201031438, 899776463, 941414239, 983129985, 547398155, 173284732, 375116232, 39878658, 550531768, 869614245, 729369951, 400501185, 806323684, 376358072, 839302520, 195058031, 467327969, 136850279, 337984799, 279101112, 882561726, 527615354, 194736841, 575770707, 748847236, 768056696, 306650634, 443200073, 476113917, 667716132, 253531666, 513635668, 312202392, 34914895, 796740089, 438740175, 276601868, 660877, 111335488, 289494776, 794755611, 451464340, 446637932, 317321602, 730325754, 35686906, 133966608, 809862340, 886421669, 164587367, 548919068, 650797046, 805664753, 806871678, 946497522, 135126963, 524599269, 713383844, 22882777, 509497691, 172750259, 515378145, 395041789, 959018232, 79135405, 708991926, 210450655, 833124853, 851144818, 105156169, 784305228, 324266405, 789837947, 788699728, 798973179, 103143987, 223968901, 951879149, 579760720, 57260942, 77370017, 444921165, 308241983, 458998963, 340152485, 458388199, 791130406, 828873519, 132102833, 705699551, 503412990, 251154594, 132648375, 175971214, 225909215, 817439469, 769059127, 830366913, 196586184, 261342490, 686414703, 33400220, 494395384, 829961176, 591902466, 350261315, 122213932, 562099750, 282712456, 378449627, 884166693, 386222082, 702051812, 857591851, 163767546, 500176108, 114187841, 779927966, 397660301, 238266941, 5772478, 851586326, 126812877, 318538190, 730613602, 145334762, 156133377, 300274391, 844503262, 64324157, 997367168, 552995946, 533013028, 25187886, 793478287, 894529135, 200560336, 56667490, 382108262, 280236910, 467983840, 18000725, 688977475, 70508464, 149533528, 826258189, 935795149, 220883672, 165599405, 598513557, 900871755, 218232867, 127476162, 707899441, 96551572, 861995688, 455839363, 791574005, 731916331, 814211140, 695979255, 368363245, 459484017, 702477818, 754205227, 818376546, 993731420, 539629272, 587863348, 807261649, 323963539, 506471676, 936883719, 273672362, 260975744, 923676544, 999720678, 573802491, 693828058, 24439366, 814268639, 435376250, 80093581, 98987820, 559847121, 209848246, 36812458, 226272924, 607884774, 114740151, 912790500, 577804068, 51814524, 48878817, 343543444, 181034226, 846453531, 384349606, 208358110, 510593864, 113946563, 971017783, 121436328, 775812857, 964187319, 765948492, 738811504, 75290674, 182282532, 457897029, 770611224, 742819993, 341169748, 958068928, 535430835, 341348674, 248771149, 148937638, 513630772, 297331421, 223633866, 701722564, 418866499, 280258887, 379092707, 374968962, 26575956, 112421951, 407909519, 246357787, 530988960, 53002855, 290224095, 733847283, 636804581, 957335980, 737667839, 539560084, 123853324, 543584846, 645177091, 967300491, 671074595, 692527065, 269450792, 26668955, 16694991, 971777300, 900410380, 244381390, 961665099, 216200949, 992602167, 421792848, 126504338, 718583113, 199744673, 21382380, 721729787, 233403510, 725550736, 155164522, 941116081, 12003474, 484108618, 810738859, 874045367, 440692412, 216481608, 31497664, 152928560, 924032410, 274210217, 958959334, 141106668, 507838471, 730380857, 919072247, 742835852, 880042550, 536893185, 601092862, 831348650, 826671040, 270800284, 738314212, 550008039, 637044980, 416525215, 505944994, 670692903, 557524653, 582348180, 175566191, 742054263, 913514272, 473660368, 572883596, 930242122, 62565077, 898489195, 326311550, 892199189, 143179755, 356068873, 357034433, 133905442, 535471664, 269174406, 758576065, 269077424, 370702343, 727179914, 881628378, 169308935, 885432381, 58191510, 273234794, 228232365, 357463691, 930819875, 810121671, 668302639, 482796311, 819498749, 155132237, 609223488, 147812512, 302808055, 49643797, 58547737, 129665693, 993692513, 140808779, 735975428, 760924905, 614958254, 947374355, 252656532, 829610932, 255450406, 514685079, 900297982, 191913293, 743664675, 423504657, 40849096, 417340806, 324017911, 12219149, 875119591, 681806632, 768537993, 79850051, 554031132, 608887497, 71122239, 48493074, 33958108, 213678571, 648467648, 529338612, 825592758, 619435431, 992691799, 598495916, 580798234, 167335305, 761480860, 913913150, 982650142, 477121870, 8556990, 531572129, 192076113, 274798782, 763407879, 173031519, 255500660, 905364155, 888366823, 805933364, 599587061, 881911884, 986577537, 213668706, 521331755, 676959337, 686557183, 204904734, 12757667, 336389868, 344203496, 942443836, 802905638, 4530861, 682066672, 651677746, 320025644, 661853428, 408734848, 459522793, 932346953, 283364341, 528835145, 416885156, 368903054, 641078836, 538204795, 500119158, 597397694, 434334308, 750275227, 910669425, 702005646, 511015064, 619735921, 534216443, 511469831, 910665922, 715777333, 752893961, 234196401, 989870912, 623114954, 97208778, 384285421, 603083397, 116204964, 820845431, 236224749, 88495670, 12446326, 761798367, 40774067, 163235872, 735406084, 259865283, 791116118, 692789918, 683514258, 344738419, 852021495, 166690189, 798451892, 330490323, 521713090, 574738603, 709153808, 149453276, 469997302, 670889021, 143423247, 242208603, 357512760, 239315352, 518119870, 744502923, 814899346, 567065892, 995937584, 855063447, 898132022, 568233753, 969625278, 976725628, 955221831, 262094632, 3315382, 318380933, 231604857, 390693938, 693484096, 97918574, 428858921, 58310070, 919282626, 852983294, 598480230, 440049274, 277459999, 515211478, 685581997, 67913206, 579917248, 272619121, 772507598, 15768167, 261304378, 240033581, 351582016, 897305024, 247512573, 249304650, 23641354, 189184903, 452971851, 191866317, 88442500, 544431442, 781297214, 967006882, 229527335, 503628385, 232756639, 436430355, 777725972, 620434528, 327960648, 670711471, 69917412, 923676999, 664395725, 885672638, 950538831, 856292060, 515108069, 656254134, 411107072, 538942386, 591418166, 728063569, 838803821, 913112933, 206340705, 457097081, 240997597, 45005544, 403013080, 207124119, 788825434, 374709242, 532249346, 288245446, 841743583, 254104138, 378577240, 591060596, 338084120, 870112561, 279966183, 743918740, 896052289, 681615376, 451345266, 937718252, 882875820, 169823361, 570841107, 794852126, 55181682, 95225139, 775900362, 415815246, 93012766, 203514901, 155831885, 198679170, 573923482, 769847249, 162005600, 601393296, 389679512, 448615729, 29459247, 423970945, 750874173, 155219205, 139725532, 426240841, 729649930, 200206856, 237193611, 544197081, 388847441, 651932027, 514373508, 968674570, 839266332, 706428928, 806980381, 604175401, 61199737, 837183939, 678394144, 453896634, 801956516, 161791840, 737571467, 464282620, 630142746, 616263826, 163746533, 594372844, 667323043, 95209413, 236245392, 190023291, 295470128, 994041179, 717071290, 260769548, 199230378, 296230215, 79298786, 97914971, 461440989, 260407679, 150682064, 603978059, 143821430, 430795156, 620592135, 971060311, 781260719, 219774882, 20316101, 827063840, 823452259, 461885724, 656428877, 302848188, 715676624, 648354178, 730097864, 34641979, 714891961, 238999646, 566172706, 620747074, 449909325, 344309988, 879127791, 902710698, 216045666, 552569654, 472078638, 51184777, 560933452, 403786499, 871511869, 166181392, 864714027, 340775313, 888192625, 342504012, 14864556, 292801354, 830545636, 728608105, 283470662, 789827638, 962048304, 784566746, 398880098, 778753501, 310184730, 567753216, 530363800, 346267703, 589773766, 880960835, 856350618, 858833143, 939870373, 885258436, 651074739, 659011876, 959319381, 93617999, 964531491, 828801095, 114323993, 692879872, 405974941, 34026988, 841324122, 139056823, 890116964, 421964081, 100399703, 329898283, 69585533, 322684388, 537068927, 758713156, 972574368, 524477042, 260024278, 440270165, 879043864, 832284608, 993446584, 385285472, 822881642, 183005660, 748566864, 79332804, 861471671, 630071735, 399491529, 637348402, 231670596, 606168591, 635985530, 155149532, 716857158, 743372948, 678403928, 493454989, 650934963, 206225159, 126520429, 398179442, 569661237, 161657707, 842237312, 527032738, 216739244, 832031668, 226699693, 934964052, 58205987, 544296146, 673912120, 907362352, 891310903, 751552223, 368739413, 466010809, 347070206, 712113571, 951144661, 469750743, 111996432, 372458755, 353605243, 45010630, 347085752, 568534691, 620086666, 199791601, 255263327, 130454539, 860943325, 322166156, 368979576, 82382250, 321634804, 91064369, 98169140, 694165081, 709329375, 262388445, 810011014, 552693198, 810704, 164688532, 983420324, 715450598, 66919540, 387379186, 612595596, 939950991, 661822086, 74247218, 858224560, 110218745, 166429100, 227117175, 250249613, 914254695, 405489636, 358951283, 392105218, 609638932, 524866079, 955409992, 889685037, 278470709, 507800157, 255124984, 954609838, 501528944, 641988339, 259175834, 586154137, 194740967, 167160097, 828243318, 894314384, 945421755, 411619044, 122555774, 652051485, 14448811, 183627336, 271161545, 188807890, 114757178, 149140641, 222575007, 612139276, 46630582, 779681254, 149344395, 322032289, 431246809, 399064932, 187347825, 765749368, 673122246, 28972588, 585375298, 472284891, 768095462, 367713593, 554634859, 950963596, 272315288, 659599389, 365283988, 878900271, 563034095, 386519356, 530594164, 709741773, 971915476, 932073746, 463549115, 196682613, 241405772, 150634042, 796523869, 808581357, 614067467, 772824958, 673224393, 229433962, 212349888, 391845111, 297152454, 747659044, 845239400, 286217557, 767544853, 451960827, 638758314, 181559225, 380892460, 663828670, 126760574, 627654425, 124066900, 800071948, 397331496, 153080276, 483367839, 487892475, 460165599, 828535432, 421855386, 679868627, 969579846, 611159412, 892563505, 735427402, 370479043, 797778959, 450346771, 212736492, 961489691, 534942784, 390599148, 911518264, 704735549, 684187180, 13447575, 715985606, 571735834, 596650407, 766746861, 888782451, 583755602, 371437755, 529705616, 687158450, 728965152, 861464995, 641742970, 704520840, 219081531, 566238171, 543477620, 13356045, 44108989, 34734148, 729751757, 44652346, 387647513, 564288880, 43927939, 516897760, 173652145, 581634052, 465942519, 96026137, 238856646, 687656713, 516537043, 693300058, 99603544, 50055324, 7871166, 394797860, 628859045, 88116819, 544859258, 808220612, 507148297, 325680680, 286838216, 404753432, 128803063, 417289402, 874753082, 109049967, 550061564, 383725973, 531603754, 41936664, 382450411, 822632101, 981001588, 572518574, 305505121, 215097707, 116595223, 897698411, 108838848, 391322758, 185901751, 409066828, 590764960, 998767005, 234150567, 139715691, 520434355, 343634899, 811276617, 344133699, 765496411, 234505459, 327779039, 978800004, 725752514, 675688453, 935610571, 775142092, 318507303, 270704254, 635157804, 343880383, 19011841, 15446601, 176256253, 783346060, 747078761, 475731480, 505535505, 788751900, 811197269, 711082517, 665641278, 322093338, 284427774, 153715265, 595478729, 463299336, 217730409, 318134267, 663298125, 55622993, 137972942, 691961726, 498567101, 818463686, 97435919, 787863347, 791171511, 761753332, 13582325, 559355268, 883132265, 902974888, 943883784, 571891750, 39786177, 60223210, 744861888, 193105519, 497381868, 482585907, 407538856, 578835186, 823409616, 794207381, 729108682, 549704952, 516343790, 538994575, 968329577, 435662025, 538378444, 17192405, 110518416, 847841417, 792833873, 516056938, 861655591, 4442655, 942091345, 436134547, 245458506, 92752975, 145697865, 194492467, 701270342, 573882140, 922459036, 320333174, 585572450, 611922212, 238805016, 500177247, 406656776, 758265345, 908298537, 963971772, 885075695, 960946395, 160321109, 984906553, 607237, 186714080, 76394457, 325956999, 631540704, 41371780, 481719742, 214800210, 223486787, 513137025, 706771756, 614529929, 775630336, 883597904, 185655535, 767502080, 451143805, 782042471, 984401432, 613654712, 985503443, 889699381, 841211492, 743608964, 402451037, 110624239, 391067781, 481957785, 273478545, 356074430, 826335330, 489003332, 992258360, 199540282, 532663369, 249329694, 153455849, 861832451, 780241591, 559881452, 142249833, 756858485, 244875739, 402335186, 619851654, 488094148, 899209908, 339901643, 943275475, 215798761, 706847843, 348920072, 418638451, 610996221, 375933586, 659227171, 614578446, 130143072, 393158430, 781086641, 970256349, 589621273, 30304851, 738005539, 8891066, 757255555, 863166409, 627181393, 772577427, 592797964, 383317609, 52203264, 389831009, 177755799, 229217868, 944130418, 170422142, 268678210, 305023435, 333774160, 719537408, 449052657, 758510619, 134671411, 115556766, 245873509, 930498837, 208097722, 803696112, 839115758, 766869041, 375114781, 248985706, 40947273, 501346952, 85572586, 452800526, 983852309, 902817456, 394945290, 266552283, 695710669, 343573087, 756202192, 607870410, 595028661, 626254550, 829135822, 929826130, 820700209, 245142999, 89011927, 954246472, 434021289, 701986827, 193314792, 481011617, 425561483, 663245466, 507391489, 657094227, 448972366, 396814181, 325877902, 806135493, 461907553, 336768848, 456440141, 139579678, 728545134, 705959134, 642759883, 35948365, 71939262, 191098155, 345063761, 388941845, 892621988, 624147515, 323309107, 444700568, 766587839, 57896068, 613349928, 419438752, 72090356, 285533712, 385792181, 363651783, 554013782, 337534394, 643339212, 470845131, 840211044, 361778855, 317775505, 206824000, 993425128, 650959451, 938887144, 488852879, 307821497, 918079998, 896397867, 640441508, 757359481, 476952631, 843845899, 291603910, 21152621, 732590783, 424920301, 329449776, 944150729, 257308512, 786456715, 293156143, 927079914, 212372695, 45754425, 180364774, 728533225, 142985515, 26005200, 238439156, 196978127, 998048069, 318378297, 303380186, 343711972, 832249021, 904379717, 231878, 285300221, 928094073, 259612480, 738608446, 179323690, 640115758, 333871037, 817292539, 175246028, 928201699, 702154475, 607551231, 813047267, 276327147, 456488665, 27531617, 358346094, 960328166, 795378475, 563631759, 48301249, 330436850, 27688931, 756273451, 720423432, 465908422, 106718472, 117446323, 42226698, 710716183, 218270756, 168675578, 972717756, 161496227, 969615119, 945642392, 247669431, 573383454, 240967815, 303810417, 41078229, 918076213, 1477400, 90829388, 37587619, 329178565, 288357952, 461549642, 946138248, 196364267, 801939081, 853652982, 883267601, 482081508, 166261800, 556618129, 830567494, 141731823, 184237708, 301434266, 808918903, 295648927, 479179924, 389669866, 980192738, 765603160, 626586591, 321594921, 417456529, 735365662, 88221058, 4991544, 394403201, 860773634, 493727081, 16453863, 298140639, 499664440, 793999096, 257318084, 721523180, 517626570, 817974606, 890570778, 320582147, 230172641, 738880110, 559850427, 433976563, 619589137, 415636994, 548351198, 732654721, 678873145, 185831506, 233480818, 942731248, 270272163, 716214214, 467940001, 58402147, 79031677, 303711176, 42015396, 870737495, 800122885, 126423054, 962636128, 984461084, 789326693, 43536990, 968369098, 15280815, 337613628, 739341871, 584195901, 987306342, 329574085, 595509880, 330362028, 578353836, 179828773, 887652042, 646850926, 946104117, 216033854, 785329018, 658908723, 771867598, 246792310, 656442324, 481688414, 18018068, 191958416, 424705029, 720810934, 598517150, 152559131, 844847706, 434465687, 819461253, 102321202, 559996911, 804587429, 16543557, 356049640, 852784715, 606189603, 678455022, 773859268, 940410824, 933751914, 276474516, 436202627, 240774123, 514407588, 841918092, 154796136, 457059432, 173770379, 52148080, 716132016, 481972118, 137870154, 987622106, 990373774, 257830016, 128493546, 175748228, 554013532, 612153900, 934403256, 492179017, 70729176, 470554986, 306503966, 971443071, 348833635, 735772763, 663486354, 48900789, 904218893, 216497573, 92107053, 796774193, 285894066, 386445051, 583631025, 446844953, 4090955, 896517707, 435701128, 920517804, 26975825, 207025120, 925126594, 137007146, 32377012, 795460736, 517045296, 203067052, 524869435, 261526896, 980680415, 833657387, 364970602, 285339631, 677003119, 623397636, 734648886, 41328271, 786469657, 821667025, 337889477, 241679129, 664602214, 466981842, 544012360, 15498434, 774426075, 770867268, 147658861, 222360322, 64751011, 96475688, 634986822, 654404711, 542805807, 501294408, 822803160, 424829161, 299355145, 294652118, 111194194, 596763711, 623424690, 902677822, 4974420, 118258913, 678297557, 893715723, 20662489, 536178849, 925774756, 843626253, 702112692, 824794166, 45281672, 418408472, 641520994, 775181023, 821051870, 602459132, 746670069, 118466420, 52708026, 683013822, 637864884, 575287860, 548373719, 102081901, 240698182, 228216800, 806632577, 859790314, 711861046, 4165590, 801788185, 661718551, 713877881, 405089748, 739022065, 927127326, 220762351, 269257673, 192639018, 162224086, 496283990, 251179102, 84423294, 790846429, 788265217, 191718745, 878135279, 197622744, 803084907, 460310166, 50552701, 717804082, 310741015, 941981114, 503741771, 251993921, 563576372, 427165684, 967923634, 290220537, 199004514, 206608206, 121344302, 787995291, 768925763, 17120395, 9837205, 850909860, 678075452, 682541634, 849785297, 976753750, 732921105, 635107068, 611200367, 146294064, 288941358, 528759540, 530508515, 438398518, 138490500, 322910687, 771980508, 811544368, 472479002, 164149403, 745262348, 123123013, 731611706, 489993956, 140831318, 275876593, 932597673, 70941694, 275924094, 121828247, 601363001, 918245570, 287423486, 924284340, 383464645, 365292187, 476471343, 983281032, 943309341, 806395633, 342202912, 915234209, 918936251, 909865094, 474147117, 435041625, 959360392, 267423147, 774366803, 447681497, 212603240, 772674357, 326563927, 922788053, 74176524, 278473021, 891763748, 163050239, 965737721, 805986866, 743164466, 932256632, 521303213, 767844876, 631464881, 940782649, 181428146, 113234152, 358454316, 921391594, 759480370, 140665286, 532811719, 925542354, 754800573, 806660665, 224123288, 173184367, 654285836, 543581220, 261640434, 214676290, 64013064, 350332513, 123355899, 255714642, 312270378, 760255777, 99077591, 633650921, 661518722, 318131673, 178663783, 575744105, 318550824, 804010828, 667019214, 57108379, 661072613, 151453032, 776143233, 827672436, 187181443, 814571961, 221935538, 330001293, 519720319, 221590262, 755001959, 117857653, 699325363, 986979637, 639546517, 782306909, 176521002, 241720236, 596315745, 407722525, 855803235, 729383641, 123167396, 573759895, 102932796, 55207703, 308441380, 603029953, 684869362, 830882809, 762414581, 605105037, 419514581, 832073222, 790715713, 487713163, 434490113, 17960515, 102119843, 821124649, 830828574, 548487220, 51728474, 153156950, 985499722, 435660787, 552616880, 915089660, 515111583, 192321613, 536797864, 903864759, 157458865, 471044296, 884118369, 479375976, 262107733, 338725914, 941732855, 549246809, 429732625, 648597876, 173623854, 830983317, 149927719, 584223721, 995191346, 96544091, 181489560, 778289560, 821245469, 918959115, 481344556, 171584580, 481689493, 417579831, 276388942, 22813831, 429857360, 50855739, 522739285, 898766818, 239601006, 672573371, 833437102, 49062873, 168513442, 792505961, 133316076, 381012452, 90812940, 736238158, 862491112, 102572419, 842490365, 228963062, 736983942, 220842333, 671708583, 31573224, 648876069, 78108011, 828408280, 866919220, 956234973, 52768096, 606661922, 990408445, 174604465, 814401013, 528148817, 555417690, 911922472, 833144317, 536051275, 275680845, 286565545, 935972929, 415402221, 927057063, 589837773, 79424155, 637420244, 684590817, 171525012, 692166406, 564964574, 935596404, 45773044, 827395583, 252393217, 466091656, 206032773, 175242990, 166625640, 26840597, 709945752, 511463564, 247850243, 307780525, 307139287, 249929556, 49094594, 706190659, 240241535, 430888126, 439334639, 505835887, 360209630, 826989987, 216568361, 693903868, 758166877, 793036342, 295862418, 882211632, 64160649, 330497506, 126704669, 417099448, 681242471, 964149891, 753373407, 544010889, 174114803, 320523683, 63681793, 822784702, 52832909, 733708485, 768997839, 629714548, 479787320, 79936222, 580554249, 383190039, 554548165, 836919808, 485594548, 698639449, 283262005, 927653524, 755864841, 507261659, 126732515, 683949292, 590487030, 876421599, 420362632, 697371425, 94821042, 464234997, 732721352, 884466726, 822947034, 195581359, 322047452, 718240449, 60604828, 732312381, 59963834, 769933695, 395152386, 261856516, 483498669, 751052934, 176523822, 363913579, 666069473, 340839487, 157277897, 997592562, 792495015, 187045030, 351464454, 883809180, 921680247, 2149803, 650395090, 194159790, 197736041, 435853827, 67764255, 700019281, 142817386, 41063434, 311710901, 896407590, 366283350, 848094885, 420360258, 265320702, 451175727, 190708080, 887996470, 754377327, 891952080, 812742714, 955118389, 513100799, 246779096, 887439705, 596472821, 307536394, 591986677, 578520344, 558082132, 793788878, 350076278, 725820313, 342130801, 816303319, 790405431, 31988171, 358736180, 827916444, 493909970, 44604842, 912958946, 725563272, 332045644, 17119648, 664699490, 343086164, 605211252, 438477314, 348734657, 493898192, 895095024, 225102760, 958906488, 498012693, 182415524, 752647480, 504166011, 213218127, 480520369, 588218000, 497898923, 158372256, 659471447, 865835577, 315687483, 142137783, 984649049, 309362685, 203044485, 267472999, 301507310, 883471743, 999756311, 297107743, 971886763, 319486684, 444997809, 237182968, 859102783, 35551236, 688263415, 132987080, 5493416, 928691002, 290093347, 777059999, 745978270, 447086717, 965179594, 688444421, 483994814, 659197731, 532521913, 120826363, 550697046, 426476516, 188877217, 580594380, 574815624, 546819100, 620203118, 893215637, 319370070, 177314676, 523590868, 493371085, 332353682, 185622026, 720374327, 578939291, 764684261, 788433351, 137231737, 759668668, 317653438, 443401434, 510645113, 595279956, 881386912, 667953139, 286889111, 792681484, 844304842, 574436717, 725245713, 602254636, 726293246, 174385344, 417140752, 625671632, 443967490, 952543096, 248526439, 802742087, 221866289, 794843252, 496196553, 65612032, 217291763, 61076560, 581314, 787109550, 334534033, 386934900, 505041048, 551261993, 302732972, 679959018, 151048146, 616657619, 505686502, 488644093, 407520053, 336774592, 988287225, 506097042, 757605331, 208464343, 30229089, 416840653, 559844346, 407637176, 838724274, 923545167, 720350174, 8572395, 664094373, 671191947, 934279949, 121068193, 794290209, 247654834, 500978700, 797612828, 823992684, 709725874, 903377588, 401955563, 747089033, 583593381, 320802269, 491347955, 594233570, 897071922, 197822903, 575684590, 836231192, 968339846, 971607550, 136530560, 842011288, 357535585, 683102445, 92336384, 272124276, 171286050, 938928358, 922544905, 232771353, 419428957, 448813293, 252651355, 461904543, 424322486, 681954878, 544434535, 796882340, 309686150, 357441059, 836384759, 571958435, 922737044, 992221852, 67089059, 882596041, 981208235, 363264265, 422459799, 232305587, 977310750, 210645566, 146639136, 94852429, 754551959, 516512324, 162352095, 579319741, 765880112, 401496430, 690661211, 783273548, 588948783, 248455967, 473931874, 206572977, 445259859, 489897593, 304808300, 254635294, 559971895, 473766494, 58140968, 804923287, 182058123, 18858635, 415737334, 275738542, 65100574, 191542902, 917179393, 418188909, 981897596, 189170608, 417438175, 601547223, 710379363, 435519975, 332893226, 390392462, 390445866, 750633554, 230495869, 851082349, 619461324, 3403640, 112866463, 80524784, 905882801, 83735480, 855669766, 710823602, 632919904, 233058880, 601180580, 934996567, 527450719, 964834285, 15865598, 134498965, 397374175, 768133341, 599105366, 700762578, 703687203, 154268140, 998989217, 142256407, 942384730, 177611391, 888866410, 794286321, 151515643, 706343643, 748341433, 554833168, 578067401, 764412967, 762345609, 734853127, 655365596, 532151926, 929579085, 471374027, 293746065, 482878997, 956016772, 225737719, 768956375, 107089518, 307027538, 947218899, 12267907, 397263264, 965273368, 290674, 419393745, 528387341, 215999730, 100304823, 111796128, 724131630, 552595524, 899376157, 849484403, 258227667, 81022604, 405165528, 295095284, 758755591, 582178847, 901416776, 964045241, 158331640, 526816406, 258063086, 238430743, 523968299, 84629947, 716815889, 339707358, 799962707, 33649645, 721984024, 99859731, 529563350, 263755469, 380146839, 385668718, 105638071, 163236706, 407662953, 984416471, 395685789, 121252287, 384609527, 679722992, 676898870, 417815752, 666111663, 352942585, 154723559, 133933042, 942913808, 855012363, 134819523, 466056982, 913694720, 585335089, 204920307, 453002801, 124752185, 515823018, 129186008, 769964167, 817111555, 613979478, 492621202, 885276949, 966883318, 348836124, 333607024, 791722302, 181773349, 921897372, 21723477, 31820964, 204272178, 188670635, 894616158, 777924546, 929825380, 136694582, 213474906, 152351163, 10990171, 917609630, 148281934, 696483222, 214916435, 140920179, 860403229, 148662343, 606007177, 847578419, 222771483, 643129162, 436815369, 242620727, 940485138, 417533636, 511021103, 132392765, 134833836, 850714567, 399233411, 83856307, 723919842, 802947140, 342308229, 338154908, 368572768, 783862802, 61035256, 264535777, 424765175, 862516994, 163708395, 59498984, 444492908, 883060239, 850002863, 40339524, 72552779, 627393236, 643860567, 40021489, 426626504, 569830859, 710036898, 828393402, 38256997, 825946846, 439540503, 235953265, 448677154, 848372635, 752294255, 3230807, 901334636, 762266853, 459636575, 878842385, 857372868, 19516596, 282690041, 596946599, 309057188, 372283374, 556453179, 979623827, 775045280, 938001516, 334273553, 315718949, 206613457, 795051376, 839712451, 597945264, 642871006, 837478389, 952120244, 425397197, 660554503, 459652706, 995877263, 970718609, 380917980, 645143505, 306899646, 658269438, 828465373, 809314591, 111205059, 529296047, 994589780, 103986248, 919808782, 790007247, 556454165, 215511418, 265042626, 653330536, 997210702, 974409490, 359475866, 599214611, 882293903, 991733124, 425906937, 523925658, 433534788, 112425051, 979666847, 16929155, 993719840, 452252376, 173734883, 481681909, 849728722, 155237704, 365284160, 579879424, 687337744, 880408675, 287083657, 201926869, 433493579, 564256369, 813036615, 947598878, 33701087, 49830500, 314289972, 683639269, 419561596, 117672496, 286731552, 4157527, 503860535, 144298036, 255224021, 713533476, 838405983, 903120492, 710299870, 690084981, 299043857, 640877553, 721174613, 975892511, 986736989, 945291149, 561755658, 652085992, 477966735, 687211807, 838982544, 86478785, 495774986, 418631446, 518941482, 121892929, 63363503, 840986235, 451384284, 709118835, 24736291, 374860762, 384593990, 512297420, 285599534, 465145539, 608815979, 826187530, 237552723, 757014456, 714725218, 712291158, 97348421, 239486424, 779581200, 524473788, 375079410, 622728978, 892079262, 602877468, 207032056, 725399971, 590729340, 302196884, 718272893, 151476716, 367366817, 495212402, 233528890, 203337048, 108516721, 834851123, 711110190, 917764573, 439989809, 699992096, 313444456, 140861016, 292844703, 665738281, 576452933, 606154924, 482302715, 243537317, 278787136, 939258102, 804015732, 570636501, 998137453, 670819114, 497757205, 348457120, 528205573, 304208834, 926793519, 460972344, 268848677, 605970941, 177666230, 185613027, 916660867, 63982291, 585734623, 232940458, 791208140, 526534283, 332301125, 100674364, 751619808, 948950869, 707360533, 231203856, 146793596, 46809510, 631710321, 840368179, 472289754, 810016448, 888285907, 285140871, 547129197, 469764866, 57949351, 509697391, 880472804, 273222388, 315542038, 710732321, 971658256, 78936857, 473954542, 783404145, 329481146, 168384456, 147826805, 20215957, 546014666, 293918921, 463339377, 899121344, 866848528, 814159470, 64820323, 669918938, 311481169, 215849082, 972410310, 986996155, 573728562, 365799479, 113185645, 322522391, 153309721, 95029870, 286389352, 635659984, 907645676, 311695567, 689636959, 342739589, 528832457, 170055686, 464436691, 412283554, 505692787, 326915281, 349869659, 922455668, 332352622, 352915155, 523749069, 62465191, 682671512, 670550873, 343427762, 497753760, 698328978, 335557209, 607372763, 742866268, 276371406, 337842334, 925274874, 528207585, 821776990, 806901223, 514459510, 943358216, 421006404, 254524979, 414879422, 856050546, 897905307, 758684817, 167234272, 24530118, 300357302, 90443435, 665756791, 153399474, 793029612, 529424014, 114521388, 293741987, 940181362, 747532994, 469986402, 121504499, 707545341, 34820461, 764536774, 565928154, 7887824, 150974851, 584541152, 157137261, 379122075, 31765912, 517316826, 193377032, 989729091, 606896298, 251445874, 689276850, 505156593, 619303298, 484708738, 329193960, 522612097, 657253500, 97510937, 697615253, 268273290, 145735849, 510130243, 119417968, 981931609, 854927051, 345279710, 685218103, 805614216, 349315377, 347007679, 880923524, 390120610, 57615755, 56321311, 524629001, 909833389, 268903607, 225409324, 124016719, 108188125, 856286516, 241070647, 120136751, 165983852, 398490534, 33085982, 639010881, 787973559, 79224302, 898302451, 112723585, 853024271, 930577423, 283094449, 660967214, 450301764, 563263104, 363636546, 250083257, 140719962, 46602026, 14363563, 288870648, 240981756, 831204635, 538781355, 488098369, 389682539, 217361340, 312550023, 576953571, 756971621, 593599349, 154179540, 899656967, 261151782, 428478720, 15600720, 352588081, 951456602, 26402989, 427782519, 380744166, 908324005, 916123237, 151129374, 168434438, 174387616, 36381621, 546682282, 983420238, 11976997, 975132456, 942853761, 92834316, 593205186, 845204413, 86878622, 457619461, 889286598, 472547082, 424098265, 561595627, 230869056, 842807567, 430816007, 739359241, 879800723, 130738994, 832042851, 354896140, 911527413, 678731550, 411035287, 154499266, 998504683, 706839496, 714835217, 924779463, 364114030, 334773147, 185730419, 789025213, 619177562, 177304418, 34141240, 902297426, 741796741, 856851132, 60059714, 511205486, 352330115, 953308121, 639637460, 503110051, 95796384, 142997232, 565877096, 192815116, 232839793, 987942829, 456345574, 257764085, 177956290, 415784123, 13795326, 822539096, 708617821, 992072493, 439006059, 695808279, 266831548, 32446476, 159714122, 406892811, 71828781, 635529586, 593316116, 466323354, 681260084, 239208073, 25545584, 457397382, 123305509, 257335328, 857963328, 225286181, 431691879, 105110265, 773130878, 820056498, 31355590, 388572949, 619338423, 291492954, 330615933, 893484991, 412863198, 917015301, 187318121, 634730155, 840977731, 864675685, 678014653, 868301078, 98089611, 451435680, 719464865, 651406547, 771492340, 469710089, 859143091, 36457855, 995067007, 344905154, 35251772, 18597430, 241902292, 334431561, 268808023, 612662016, 384130811, 139739951, 151542675, 173972180, 436601366, 192124433, 917990866, 116666329, 538766429, 743186471, 751743392, 719962239, 16337764, 41480222, 324992704, 808664568, 226763615, 666948600, 117280551, 861144245, 956282540, 89036607, 520369358, 965814447, 290686980, 129292376, 18885421, 21901551, 308849829, 583659809, 884241509, 988969834, 215705588, 477903080, 264265405, 199813850, 774146845, 464219194, 816821775, 911283993, 709941721, 410193826, 82651911, 189194175, 608319440, 977843552, 264235447, 440816646, 5983730, 541962290, 483802175, 511822593, 671529442, 311806266, 440181733, 334485831, 135931357, 843424846, 414035857, 570625792, 235105209, 268631368, 842432364, 771563438, 196399638, 850710196, 650731895, 208010576, 857420609, 207672045, 435318743, 893205708, 877084299, 528393820, 402185594, 251737553, 107819435, 118167779, 444656226, 894275515, 696080660, 176062586, 312754136, 554598953, 569689921, 322838562, 663946348, 732070203, 456468471, 729396217, 518976887, 450975704, 47663291, 247480436, 181405139, 574843326, 909664080, 69773617, 909249346, 178095989, 700966395, 547618721, 133088831, 393205244, 485570522, 972938455, 122707267, 58810091, 295114126, 366449664, 184111934, 101894722, 622220013, 425240180, 850344835, 329245158, 849743218, 402289374, 336874079, 993694198, 76217107, 475001627, 437414921, 802717997, 287823199, 563442684, 32440021, 704062737, 317807224, 982016472, 671523816, 556384303, 975191673, 827376249, 277722148, 585381609, 877234587, 925793623, 712551211, 21158214, 556335243, 621385309, 277782866, 181687585, 523627435, 603306540, 468684662, 148638600, 194563076, 912216849, 608516602, 399544567, 988701751, 291961565, 180913104, 173690872, 714994765, 707205919, 809763845, 148995059, 373609720, 912244196, 886283250, 457566126, 265500878, 99943646, 674185036, 298965013, 254341996, 87437439, 587383532, 964177588, 239110474, 779056452, 720869039, 340724118, 476892151, 858714808, 894039422, 332348724, 8390325, 648345038, 802606539, 439920012, 220501700, 616836716, 289888810, 125093174, 330473491, 393455410, 661218326, 459611942, 65075449, 24069065, 999502187, 142027850, 928516348, 589435252, 187729790, 769328335, 56401197, 524217076, 710634200, 219825745, 507015605, 318299689, 526577914, 634413611, 805378336, 997804946, 754833954, 528540619, 653615275, 617494293, 907243958, 489311940, 327879423, 725624235, 505799373, 138450535, 714273411, 154445858, 814916667, 910474384, 574249612, 968438425, 337674800, 148694119, 663426867, 799542139, 177219278, 800960761, 10135554, 289834572, 564505953, 331456430, 43859718, 109097733, 810913628, 765047808, 416224011, 304848138, 882308016, 534014876, 484294484, 308665266, 944677062, 659218146, 967431894, 1940713, 703202475, 832910882, 604919622, 855925094, 638524285, 442697407, 658521489, 134267209, 315072180, 383992192, 711093885, 204024114, 443112774, 11105262, 521197550, 944574300, 81131625, 90260139, 941549130, 310207696, 318271801, 626631835, 191882824, 360203731, 8562646, 336999966, 458411772, 884522670, 892016966, 25393963, 724282549, 603778876, 364077301, 135068866, 25559052, 558086655, 784650584, 666350835, 571755067, 967522317, 932413382, 255745650, 986013362, 770283600, 853769353, 194958062, 157260435, 140472229, 68994286, 109746380, 329643698, 319694395, 673894136, 394750658, 584159689, 711804662, 518232029, 714286983, 119873864, 493793405, 483750368, 857401997, 662116030, 518268865, 651088395, 633290061, 800287007, 201075721, 847873049, 23937872, 723144440, 989710380, 745802260, 229236415, 607130338, 704641904, 546335601, 990302602, 319070337, 491265028, 842846755, 267466101, 879463036, 675501021, 474753866, 530003195, 836451732, 841654032, 223051001, 380372225, 726230502, 263123318, 584933554, 713157694, 336503985, 459721308, 979917129, 110514573, 622588172, 482691788, 23958305, 588877916, 592630875, 236973881, 239752132, 631326306, 881199064, 914411152, 268701596, 879915491, 462887790, 923721706, 335774758, 245444626, 594185548, 78028794, 519811473, 445456101, 398051168, 965666832, 855907877, 523779362, 47678763, 311591187, 349933468, 222641450, 241149410, 798610197, 16222735, 294327158, 895325834, 300306473, 409172812, 669207531, 878568696, 237072455, 818275292, 130980463, 240432359, 275188339, 580679523, 148645706, 129990462, 115008273, 708755679, 944484637, 200224791, 896796951, 37427218, 754782596, 507623136, 615200326, 540308229, 197059597, 443492871, 988326335, 804543674, 235178529, 920402113, 649658092, 721948591, 526846430, 412035419, 207808616, 430589353, 431093010, 599283869, 862478872, 702867205, 774159625, 388123276, 144654434, 21586143, 163599057, 201547155, 470528347, 367700761, 403449953, 267891424, 463209790, 9216131, 18447927, 555741220, 766921148, 285339314, 143423685, 742382357, 542953865, 916982645, 728673142, 4971797, 356153892, 615584810, 128220952, 3579846, 975853360, 45149011, 630751087, 889886707, 689971781, 936349572, 888679259, 335629486, 690131804, 662261423, 846940116, 225219914, 366695329, 692765650, 578549289, 954881396, 397132568, 803138148, 190032365, 263513304, 646584031, 21551344, 818503627, 760709773, 33591525, 298695019, 708102125, 424562487, 886707964, 142204627, 187566388, 104302901, 917699625, 968125085, 222118211, 449881119, 936159175, 932578405, 101445197, 187878231, 500461545, 978293503, 193688869, 451570347, 593528445, 627691452, 146068000, 922124301, 575926979, 573545732, 208952515, 951413756, 994655151, 887365579, 771983169, 637770662, 559527093, 158271701, 38169122, 812267862, 764547945, 63298440, 311570867, 141850310, 505508681, 848251605, 151809510, 800222223, 397858694, 687938467, 571780335, 630229605, 181167670, 368898236, 494937237, 406076681, 53605468, 779942793, 894017929, 417868169, 665922928, 600450418, 855644125, 73428705, 534773701, 294100631, 594986999, 634970878, 821463706, 492108542, 337647333, 612175928, 226563695, 882536830, 938334277, 412461405, 371092611, 555961193, 375533431, 87661928, 748372739, 446694944, 795790209, 928375875, 177485692, 290482547, 986909109, 726690443, 153728562, 227908055, 906726348, 852630922, 634396798, 863788594, 586245575, 139493989, 91962721, 967717609, 289406414, 875279941, 48798941, 199441932, 347883096, 172697298, 115465066, 939251527, 338738695, 455938246, 310861788, 506309933, 786658944, 336402959, 349236114, 665042393, 94120099, 220480474, 213363408, 104485882, 717321498, 328484592, 589356113, 786293621, 429891123, 958603905, 460273449, 884342032, 792557457, 88416052, 693842637, 82698884, 185368512, 435118530, 888790133, 910647560, 114399997, 647733323, 630139040, 70143457, 511063302, 428597177, 330214623, 151516964, 699234959, 442246063, 551213994, 956614831, 905521227, 560913925, 128616904, 245517469, 233768130, 501070827, 615716983, 366109296, 412308993, 85030221, 986177033, 95037967, 394256215, 460007447, 60084018, 63926098, 243072093, 750927912, 3889886, 406705041, 553809809, 293269121, 366999799, 358742040, 290494132, 608682335, 168769849, 968940541, 768714338, 737346271, 782354386, 575420468, 583254603, 290098086, 550083131, 233305158, 875091947, 135323476, 811809410, 376835737, 611582565, 642042651, 614647859, 375944312, 782870898, 205769221, 731523112, 197848003, 862633908, 49331184, 607424118, 296696327, 950478678, 291988783, 801950889, 430538156, 120211568, 300138004, 443180682, 26023199, 998402250, 691535749, 745905437, 587353590, 130726069, 738215212, 983823366, 942619098, 431656462, 690407495, 856260939, 440899434, 400991435, 347584069, 271399249, 677677244, 595022325, 743467716, 615365344, 154726926, 915548810, 221575545, 789973650, 939906134, 762921631, 762380802, 961283963, 277771717, 937031499, 907230923, 443457569, 191591141, 558489769, 905938571, 301676156, 882218008, 721676113, 404974763, 676402390, 559492093, 223604321, 895287947, 443243605, 706104309, 702577742, 230821765, 76284885, 477918443, 316274928, 984362297, 235894951, 599586779, 460206821, 393584362, 707641343, 157596940, 846084851, 324107453, 546378039, 37683841, 973591241, 447079337, 780019291, 916647376, 547502327, 285065356, 625354905, 818717513, 743076310, 470819199, 519757341, 513992298, 421692017, 883800419, 511237651, 782800328, 188397894, 104811742, 316511550, 544848829, 748437261, 192220238, 307191711, 604728751, 673973609, 20531090, 368583839, 401356325, 955967631, 122102392, 941892126, 288535341, 480593734, 44724948, 474500813, 764475066, 200598649, 586312425, 320403788, 585835975, 19892411, 631577017, 666357020, 309711504, 615608677, 111891236, 203836015, 521501450, 435558293, 878442699, 599313222, 358937702, 993282337, 426767369, 600132129, 449562352, 739981928, 388198418, 120842372, 63412876, 779870479, 986937435, 520892993, 218075546, 571198045, 192352038, 875063172, 575261156, 641812877, 300050025, 588855292, 384055818, 376743114, 292679703, 420040789, 30137698, 935719707, 523913422, 653656962, 529217845, 568294145, 734248073, 494076246, 739919237, 730172103, 259408039, 785240687, 405962349, 909885629, 849811961, 801563796, 804553466, 727620214, 368920639, 578599163, 820151042, 862731428, 446828905, 200044513, 987125864, 186217981, 469069368, 781988449, 471469825, 900697280, 437148369, 861535319, 284423792, 664218933, 613092718, 634642739, 567528129, 415443131, 921446901, 160313909, 599720175, 811223238, 852624687, 960414018, 639827437, 577186583, 738681294, 256253374, 289623149, 967925016, 24886189, 32589988, 161760265, 145570314, 67592331, 968049042, 861656329, 393401631, 9733845, 983513216, 910318966, 180906003, 874401966, 51294360, 140247338, 206552930, 640007707, 132578273, 562687280, 549609006, 322906697, 185015108, 917886003, 264445742, 570003144, 198020503, 565309910, 872012658, 125940856, 37226172, 650652309, 890016117, 20586593, 78997844, 615574266, 706751046, 871089983, 140128339, 780699043, 741741376, 899239408, 390671538, 378444526, 638630358, 107716070, 493555098, 809409354, 903155155, 410801919, 65897641, 407896971, 887484336, 94178267, 954269777, 235485106, 673498436, 926037876, 514665354, 893904706, 597024436, 481333444, 606204043, 36379158, 861572348, 715560280, 480284928, 926464193, 171905839, 873376591, 684104016, 954809036, 534970308, 275029596, 401996663, 855080192, 276241924, 877275346, 26991150, 739481499, 505849307, 88308425, 714649300, 271279279, 389093781, 91053265, 860412638, 697383292, 354128094, 758636659, 405014498, 664501976, 56323910, 761003295, 795024478, 418146918, 221722061, 493597974, 247030174, 937881722, 499759738, 217018043, 510522051, 479229949, 767641591, 983546449, 677702027, 365141275, 172057716, 341011700, 513971297, 911204041, 755429727, 41830333, 442520289, 385421670, 517748729, 793199317, 443458356, 980953893, 359319670, 283550371, 960217673, 929293038, 522454566, 276814735, 938290129, 735414643, 244215093, 281974679, 703093876, 91484161, 377979346, 551988870, 305877702, 869874608, 73137496, 841552554, 156363387, 825985185, 278036139, 43845088, 468411000, 242404126, 288296194, 149301712, 99054885, 431095471, 219292325, 116910852, 137768109, 345451185, 213279310, 865108938, 231822200, 32185774, 615376427, 356004856, 447094658, 821279017, 138693752, 379621811, 845273932, 16624400, 584819960, 292021331, 17755980, 337911253, 182709011, 711961787, 33460733, 281837017, 724405772, 333422932, 378558583, 198112622, 222582072, 992525301, 56916544, 786613438, 750478258, 217190321, 440926563, 581932272, 496848936, 986078658, 495154452, 7401488, 969970027, 442762081, 751468239, 540465782, 787784292, 945122860, 293133572, 129069016, 880483892, 837119945, 600786166, 913645032, 626153690, 477166156, 639642598, 521566498, 269791440, 871461897, 193507896, 539622883, 43830703, 792779703, 367925937, 916465616, 54738352, 827610228, 582661813, 80510151, 429181958, 253550646, 557664493, 275000299, 896678305, 603701310, 961448866, 116652558, 549185254, 255101209, 507693703, 212042582, 1519313, 873190130, 282563486, 899110275, 880919167, 19297657, 146311981, 694930031, 637560074, 16165961, 810570090, 379529060, 526156770, 959326212, 673839798, 309138010, 171289164, 505222186, 797925048, 921456232, 268217472, 955458422, 118849826, 930811204, 287307574, 462565962, 197210144, 281418235, 327538054, 504659613, 197910356, 49692475, 564535021, 749111332, 934307550, 683253165, 902089093, 225390984, 891600850, 53416933, 631920222, 475539854, 644045723, 181915177, 389666571, 972341651, 741124112, 58357839, 365531430, 752849159, 725379682, 672749601, 979862676, 968392740, 354770661, 366290257, 243881365, 233910023, 382439092, 292717277, 195964018, 123610781, 355334172, 161919993, 722344219, 329603951, 695281437, 197014569, 410162791, 363605522, 949620357, 861632573, 80283055, 94454871, 808530046, 335328581, 17480601, 71356352, 195059494, 857953212, 543901215, 178136321, 490879749, 804349811, 612964377, 675542764, 647464411, 131555067, 759920346, 64269581, 585608032, 822340567, 149139512, 549560649, 538683865, 85598694, 344240118, 535239509, 245596956, 16829957, 950286464, 639166385, 496753410, 871411577, 970768320, 199460605, 754462922, 989234888, 921487833, 404652829, 839473815, 4641374, 418951468, 597564926, 474898700, 953040005, 362356250, 366978918, 668498405, 196115332, 466665658, 955252888, 170516027, 616648384, 374303111, 385547132, 328292706, 230039521, 203068734, 893118060, 291608895, 570085829, 571839783, 707879242, 738283330, 265337298, 950224646, 734128002, 162151724, 232868636, 844470110, 297103864, 778011513, 295650340, 178029145, 296722855, 214598110, 226847892, 394823438, 317935491, 245135201, 386365083, 434773392, 42908235, 418076346, 831194370, 626783009, 463153804, 826374509, 917062433, 482661082, 37465370, 263636183, 500797406, 350049011, 545888907, 481198765, 559141483, 715812795, 822017004, 317432297, 876144086, 56180773, 913146547, 881213167, 540444491, 968113415, 73662420, 867280919, 121046653, 446856283, 498590407, 172905646, 762475338, 716879395, 270763180, 571793553, 175321439, 417060582, 183395839, 423204947, 816171258, 632827913, 24472439, 991280586, 489643652, 563847791, 412872233, 758234167, 680487501, 16130638, 471970503, 83433989, 715962312, 870238494, 712649056, 260250692, 807022609, 211628292, 379598111, 263061534, 920253597, 181534486, 147341646, 534733225, 300258386, 585848191, 446570760, 806201123, 92154910, 784838928, 191992014, 238239288, 427359701, 264305952, 944004751, 310897501, 771686947, 777417256, 565571969, 843159038, 734938665, 248883128, 310895574, 691878051, 324949268, 960954735, 30394666, 750711717, 828216698, 116838992, 833191116, 56248096, 499875152, 25802771, 175278050, 247217518, 213180732, 397173678, 523235173, 212933523, 820303471, 857949372, 730577561, 85720792, 652129248, 651353125, 732406455, 353226346, 349813117, 562819614, 23186102, 626952445, 412794653, 891242041, 832139480, 201054698, 66010849, 1660223, 607115908, 145352043, 624843531, 585126157, 279492165, 638187937, 621263726, 540019629, 982700049, 727676666, 102417204, 357129128, 3264020, 776988877, 992872179, 974577439, 328526248, 841650335, 783131371, 680836672, 295103574, 371593763, 700081443, 560580778, 540318609, 817587555, 144709511, 660657559, 867116914, 216344265, 589070428, 798015589, 262582252, 744009476, 310830661, 38801922, 578316387, 665983338, 394493280, 940758308, 25412292, 293360018, 715278017, 467134782, 444442165, 532553790, 265990548, 873974975, 314223733, 236125172, 124958116, 812162681, 842426137, 212301133, 179554952, 993163208, 260072016, 197096172, 418063072, 764312952, 955390186, 553810141, 641937219, 134935336, 441266963, 463461561, 704947717, 70402155, 3604215, 699333523, 407337431, 450536636, 857595432, 256357192, 509902719, 219575658, 153572682, 200004344, 138472121, 719262832, 162504210, 404511620, 465906357, 694098414, 149830783, 357740036, 4449334, 233717513, 486771155, 661298973, 937415059, 411399292, 181283507, 500594246, 276817631, 623005499, 50589768, 874889987, 194953382, 43321861, 803003868, 824783427, 756192342, 399322220, 505958429, 204570022, 540813658, 980326270, 124735615, 655973168, 995132079, 428093787, 402197030, 776335627, 137226996, 640130456, 249142087, 747053261, 946245858, 695777204, 276028469, 457673059, 236107335, 130176950, 657367695, 594057980, 880283763, 361054500, 952356849, 753058273, 517160287, 793053338, 317405910, 770952097, 446896176, 884167255, 881996667, 929808988, 617960353, 4655112, 596129703, 950232496, 199091289, 346186348, 186142990, 802597999, 715101774, 444188944, 528002430, 742210107, 729303864, 24645473, 327885973, 446721459, 331290120, 564745192, 742190644, 579894974, 222096104, 824926277, 484377127, 685797602, 714225829, 400503396, 169327535, 897174773, 818897074, 966496673, 458636373, 782139438, 323137854, 254474234, 64010969, 557036046, 537631043, 675075242, 892628583, 618657496, 480147441, 983255320, 330274149, 846059304, 860618256, 681565381, 18105820, 723478754, 344311865, 152831129, 684152149, 371911775, 669434740, 753640539, 357447363, 944943594, 320493963, 983303696, 710173931, 78286919, 354752332, 280747633, 83036025, 209830, 536413772, 385026986, 236971900, 105903987, 607149243, 263190919, 526275625, 941367891, 898878095, 771265676, 266358094, 204535326, 898209984, 275467881, 951162827, 951822170, 874299273, 408486640, 473932908, 988517313, 509092542, 697623879, 556232466, 548203695, 845914836, 779706423, 447277470, 490197674, 221911641, 112933398, 614206893, 689783376, 911835276, 152887932, 620406592, 367458756, 495226201, 57695635, 168996993, 156126721, 798722363, 752692033, 798540896, 328505344, 204522548, 588067598, 892639816, 417336897, 244447873, 314793173, 463214376, 970702763, 395292368, 514669354, 264614150, 939940990, 24086436, 145349870, 100304889, 747492006, 47590240, 790731475, 754551153, 269954751, 854682447, 358647113, 563891200, 686427296, 91730316, 605101250, 872619948, 469156406, 142041905, 401470059, 342972086, 565884105, 915550946, 896335540, 343469558, 503031847, 328396308, 585285154, 414639645, 616349916, 883655534, 789692568, 992683815, 658687627, 964563887, 291468331, 36210474, 802593180, 461752852, 647628005, 762638976, 25141781, 387777012, 157591855, 253672719, 885486660, 863172279, 571017271, 522549089, 380366964, 658939736, 192184781, 4873339, 111153999, 557837857, 746544868, 416871536, 666812063, 422788087, 520144418, 324081212, 129618413, 45982746, 364654394, 953547944, 84772748, 194385239, 508528909, 712323194, 429385112, 189618291, 577639826, 166208902, 130204687, 331568988, 37336997, 667063057, 885375263, 772041092, 833945978, 725127230, 649904031, 402707571, 66988341, 806067413, 519074354, 382181021, 258537777, 196532877, 577878685, 205173546, 954626691, 681996543, 594085226, 755066627, 71277009, 190757955, 446362479, 284870859, 831349179, 665139227, 994956838, 385305040, 351302571, 762230433, 97819321, 712937262, 764645952, 787270048, 17217667, 12716292, 545002432, 197238601, 308163819, 231160446, 27427045, 118748703, 132308380, 593406328, 719146473, 833473358, 159352151, 803907230, 272796733, 406528040, 878268705, 878606229, 858547895, 546432022, 645085249, 859531454, 724570604, 254125285, 692500735, 882203690, 503338483, 423726266, 421300541, 693415792, 532920182, 672674136, 400048925, 671996908, 448743287, 858890844, 207077523, 734279848, 562872067, 29223091, 703637812, 260697637, 606112276, 683137700, 816506090, 933778336, 45022069, 771111597, 413888885, 636097429, 621181372, 118466143, 275297351, 592284655, 586914654, 813893833, 951231505, 123852409, 678328048, 157812469, 585838286, 259944344, 421252250, 637779891, 346078446, 771260740, 476758160, 56455414, 818196726, 833781113, 465307201, 788832865, 623932879, 957188580, 398937787, 636203135, 917258238, 434133625, 951797147, 473053030, 338915270, 135077390, 16452531, 311394366, 613001250, 458791757, 906911837, 174259487, 255626074, 61087924, 924817742, 571103277, 101286638, 580899125, 456912129, 495675504, 345364473, 892915518, 765314379, 409938327, 958127486, 841185087, 455688255, 103177053, 569930626, 1315509, 253825146, 289325574, 715407714, 181511159, 433539943, 350473358, 279513170, 501066285, 229563056, 879195113, 980015728, 1494379, 921129862, 219571874, 222347755, 424489486, 286153404, 692415236, 608014692, 474863070, 216501921, 430081000, 12538559, 883335190, 198511027, 445735020, 438769701, 531237415, 654275420, 661621716, 377603743, 634942305, 986637611, 602112117, 489261902, 207144724, 395328973, 796281619, 168945028, 74832669, 95603872, 812994982, 257691099, 980939385, 730149164, 127026914, 693146757, 628286632, 265390138, 757066192, 763797917, 941926092, 202813113, 951539821, 410947626, 229432, 959476087, 750560365, 761332808, 82387660, 355464067, 747884889, 352180819, 438271883, 919059990, 892923135, 789780895, 355626960, 80555899, 368506987, 287540901, 729718896, 715646981, 461686451, 353436971, 871308232, 360446116, 554010131, 117094712, 941942447, 277491011, 389714011, 43877519, 146008960, 400176917, 899860728, 536922148, 846902737, 171955208, 184566229, 709865480, 255913198, 525324854, 777340234, 986236982, 764256369, 716108925, 436517040, 715113883, 412753702, 327778415, 55788581, 584901697, 638352327, 347918058, 302598412, 202000858, 357049483, 608257006, 36095216, 734700570, 825188056, 980055637, 133095404, 941944128, 419238775, 301810330, 795384828, 759110606, 271446053, 587068042, 215090547, 656574052, 227263772, 483606492, 205869042, 957772168, 197228583, 11804125, 360764109, 216833383, 95315956, 852499134, 364387626, 247670480, 495157725, 188707487, 164792604, 588285322, 929083091, 750161093, 874360519, 101123845, 285865646, 553587992, 484903977, 877323171, 46403358, 341686268, 556023550, 525067329, 225667342, 821006849, 516772150, 668926979, 509777173, 864038854, 765402054, 167809960, 760657126, 57674237, 644923891, 263554907, 158812418, 689472896, 6968811, 719902689, 463336871, 415043571, 118424044, 767398339, 983972616, 662519872, 379559554, 361385530, 228005065, 339907875, 833015305, 989327247, 31466552, 372304562, 45534413, 712505648, 50392700, 891407560, 999253162, 312601387, 811052517, 876050111, 591441739, 351233834, 778948366, 386789597, 26119509, 392468162, 968806573, 216864973, 768511140, 230607377, 846548562, 98589422, 416049842, 531860379, 230921727, 544208502, 727482465, 409535983, 339064831, 796157207, 20753579, 109012101, 899785869, 330426880, 90972256, 414563304, 45716729, 55829806, 476851207, 678071268, 195406278, 215451246, 63766178, 838123945, 464798958, 702987174, 746189392, 454723687, 276900805, 284577038, 911268589, 599024481, 516715752, 266212248, 355837794, 227309973, 904796071, 2225778, 150875469, 993784771, 704154567, 702773848, 950523556, 670971839, 494006010, 114438762, 400250127, 14481790, 460853290, 75452734, 792709602, 16202940, 760257843, 608938180, 353323362, 91778274, 738455293, 661458620, 73880093, 493327370, 13548908, 105874476, 252599765, 260859550, 480324987, 827579616, 299504247, 207900221, 346749092, 75857462, 371534173, 670938088, 325260468, 842458171, 419841310, 210616997, 942072306, 326410479, 568763115, 931839034, 367415193, 882959525, 611384750, 97566162, 604576224, 788544402, 150133491, 31389961, 818085707, 224191173, 319551095, 251201566, 260601082, 673576982, 772515096, 616603879, 494788112, 234393937, 263131740, 559498214, 541511862, 895207914, 217248475, 160534539, 29334175, 295126254, 108078933, 402376097, 233591836, 77953204, 905879924, 70017991, 884595096, 224511423, 377108252, 39671050, 125374733, 322549705, 738921124, 645486980, 275851530, 955633671, 382123043, 992778222, 300424281, 320201709, 611631771, 733292502, 932157210, 961994455, 643120345, 820403586, 614659060, 873021928, 597448627, 56035565, 256521802, 954955071, 560450881, 748624100, 957088483, 960616301, 76637089, 471123795, 192520577, 675496226, 732509456, 532239918, 361300355, 538330969, 272239667, 491780611, 650791947, 749178212, 4453809, 744619672, 625819632, 672048163, 445764610, 960930224, 194374275, 157992020, 619520675, 190167274, 302681877, 461895044, 81023449, 914346232, 867108092, 565601980, 184117960, 472364822, 513039860, 952846900, 455912421, 865200136, 329823748, 260131291, 786574063, 744719460, 41458125, 227629034, 917910273, 782225141, 439525064, 816671435, 639645725, 415529683, 82126710, 664313045, 190160442, 386071110, 2755153, 856591660, 409711727, 623726647, 76074697, 686005594, 723527767, 785821045, 257332980, 709907161, 881992720, 356271500, 175829016, 352743685, 582317604, 466112995, 370959575, 454310902, 848731778, 554405080, 359613215, 671251542, 296040164, 950272088, 647828864, 548412551, 552042060, 937020055, 952946509, 159649055, 761383371, 405386725, 944379658, 241054883, 956835951, 716863297, 410512092, 49486356, 3685005, 975807901, 148833254, 245632180, 280081344, 227341615, 191766988, 988821974, 36624897, 820585909, 891880925, 828984902, 44738532, 401527357, 210464926, 570941075, 164801286, 414855097, 355264182, 290881985, 413857833, 660432946, 219882274, 101446061, 540638936, 705873978, 496831863, 745913241, 706598252, 191638063, 159783697, 507958256, 668205749, 629233778, 347448226, 413659292, 629920746, 455235333, 766290558, 152706802, 85638176, 44109957, 495411711, 670095201, 737035058, 938270808, 505988587, 466791808, 721865221, 170212070, 481771705, 991564599, 105344547, 19606238, 859684009, 599342974, 825534298, 153742423, 190003582, 686860109, 665911892, 114878290, 982991891, 994275773, 64142355, 478577107, 960709790, 728448110, 431712635, 869610317, 796652220, 961395861, 649307629, 625101481, 495218511, 842043936, 684193850, 672337608, 669206923, 28990377, 65559918, 765573664, 323953388, 699063519, 871897772, 926607758, 292704051, 407291007, 86850819, 436122783, 151303767, 145335028, 164667745, 163758627, 661349530, 528475527, 954518659, 538765742, 855066046, 828527525, 167985723, 523887245, 316851426, 578423528, 341591455, 903307983, 99640416, 552313602, 438750613, 725093889, 986386822, 471605779, 230910283, 812819380, 606498717, 199958034, 587185447, 784954094, 790568870, 491185803, 24964609, 699090720, 962429119, 864787890, 227988039, 859810955, 804603738, 22077674, 131145149, 222310246, 110841383, 407326997, 543044827, 483993065, 217336797, 503421823, 893435420, 265211075, 170177748, 107737625, 834734044, 685150068, 829140878, 966542861, 461000225, 186425898, 136664391, 94074935, 786619549, 895482959, 480048515, 877578427, 590174312, 654478103, 727939021, 454826282, 844449012, 990634364, 198651560, 367435788, 371641536, 75756442, 542765661, 879434752, 213909579, 994449119, 893304567, 27363797, 123089928, 891007454, 37540132, 661442962, 134458234, 531164951, 944139833, 712533330, 664150413, 166252586, 630647117, 555851052, 758614475, 122294031, 222817925, 499646890, 422700556, 103312992, 681537736, 470585236, 637536229, 817650164, 931286245, 283459082, 543706654, 333947967, 537240053, 812223877, 359846870, 242812977, 729588628, 321184391, 672727341, 856186011, 210169085, 805821401, 975401652, 105204030, 639996427, 280253248, 61120497, 903804010, 9526818, 747975205, 294743908, 362043190, 102046228, 527182754, 202128952, 801181311, 71441204, 354717693, 112278962, 693253471, 636838881, 719917264, 799319148, 730162389, 218063651, 811397018, 505212720, 250758334, 349926044, 297186918, 374261588, 422946846, 873705219, 254385135, 70739601, 429425535, 969723988, 601407081, 86978262, 688888488, 702124558, 276216047, 291654898, 301563193, 362002172, 221926623, 833447916, 636900861, 597918112, 842775034, 72352314, 134887361, 7118253, 758931347, 990991488, 66413101, 153161623, 440006829, 735039830, 781111639, 340612375, 713706780, 426553463, 937871226, 196985892, 975090450, 397200453, 250096746, 82981755, 674500617, 537006911, 223131820, 267446954, 589986687, 310611207, 262849737, 52970203, 304643964, 931249218, 95606045, 802790435, 380199302, 473003405, 138456536, 258099170, 811825052, 151848499, 959922570, 619095290, 249216066, 391439695, 698604798, 435454080, 855649332, 896084675, 171744778, 776992994, 200043897, 434088909, 294799633, 811122638, 205387056, 289669557, 449127645, 367057017, 223362123, 250363863, 492718184, 626864309, 322307105, 598396145, 280022398, 725524883, 914940796, 576047966, 810991837, 881757488, 816432057, 503142987, 553970831, 181573480, 211242456, 7983219, 181454398, 627200812, 328441243, 871998857, 674264415, 229269012, 830212104, 866743051, 863546745, 899391637, 182626518, 732010697, 153341243, 336668787, 2412202, 147198651, 992051551, 44015092, 40216045, 938705487, 553674966, 492491457, 310490358, 319184791, 241735303, 421223140, 474253486, 521843320, 899204155, 965429131, 702161642, 860589504, 403671254, 868887465, 546727888, 236335851, 738329503, 104198353, 427706964, 159082927, 267959103, 277235800, 941565379, 263349280, 835354229, 537794163, 107383838, 164407922, 972567439, 473275337, 199507571, 592018312, 288169277, 313303160, 861354991, 277800033, 319877572, 569606240, 960046835, 45844465, 905899135, 57207637, 540663447, 916557360, 603365707, 379119263, 374881384, 99813519, 701743655, 533596095, 342039, 602907412, 851671970, 822627427, 663937589, 957094848, 775150026, 365308501, 272347201, 118014573, 227830677, 52267793, 807923005, 663835092, 742074137, 131171955, 416820044, 54909453, 387689201, 387574663, 68454297, 111780475, 561049035, 156969320, 766559117, 590762362, 827936196, 957338226, 59635737, 80278847, 584816470, 75495367, 477844050, 695729764, 842601079, 510338328, 942316751, 199859790, 25497970, 235800538, 449374333, 319436371, 47071180, 480123485, 30462300, 885934306, 947339877, 235522761, 148024787, 743412368, 405498745, 534213671, 45106725, 221258757, 19261391, 580335226, 759073675, 855885844, 772941085, 247104086, 703200024, 197523433, 659940732, 349950255, 654301085, 374559298, 923093772, 204653305, 734418709, 156797277, 741167018, 80243143, 725056845, 585924, 281945340, 883145228, 119817817, 730768099, 598510575, 65202128, 176375962, 424437587, 517694869, 694802516, 996505813, 773277553, 727941545, 24947366, 662905332, 305974950, 318423796, 112032678, 93177595, 490985466, 936276856, 142656171, 226391666, 323167149, 39745767, 423660463, 254833081, 35053513, 284990770, 557747312, 335922512, 430074818, 401738923, 53108124, 231752666, 58871770, 265611345, 618367018, 349805193, 702687246, 484712521, 961899785, 169445983, 60789160, 587943748, 408642387, 805170169, 196797700, 801482318, 836326334, 743840962, 526534188, 304302209, 438947444, 184037605, 151886284, 924213409, 27513709, 384822951, 861070049, 68088025, 137417764, 3696375, 991686845, 312991783, 189538009, 43981954, 514619080, 97066810, 376583399, 383524121, 314187079, 710506752, 411711783, 885922992, 109362289, 534989130, 622663847, 834846484, 241477214, 23400944, 15877963, 451576345, 582173574, 92904743, 6400460, 569015331, 273979895, 546259909, 249556793, 882906080, 817588074, 840529544, 723193701, 668096729, 206103732, 642332369, 274877058, 355211075, 547007875, 278093685, 458038061, 245299363, 345902274, 420661061, 495746013, 264973337, 889760882, 917764134, 45427628, 992489799, 617064525, 917859731, 876751904, 128234365, 611635580, 968570502, 821480615, 238360128, 634332851, 462541831, 679988747, 14288320, 120493, 611807730, 351807616, 121689121, 466260784, 779007775, 28275329, 147198633, 291150207, 121141598, 680547689, 525650852, 969092155, 669246191, 223376468, 575727072, 332521276, 549586920, 635124531, 660993665, 585649051, 755715368, 590574419, 291457736, 889167411, 606682305, 791644528, 836320368, 659816237, 842974521, 853176519, 659620970, 501357346, 858060405, 929013901, 281037683, 604570778, 630467529, 483325866, 116137072, 794184594, 145849323, 35764270, 946450108, 208516591, 524144183, 463437262, 614599940, 888858912, 185478198, 163425899, 669611862, 441886060, 187355048, 379210140, 186619532, 839035421, 639020532, 505973496, 372401590, 277641588, 164694704, 735316085, 776281177, 282439461, 274016392, 138491575, 891004497, 633683344, 414854510, 761180335, 285601082, 57255396, 78099921, 186620567, 64228967, 633203440, 90324033, 881182205, 457148172, 367455613, 534442081, 121367573, 608438617, 278952333, 999687115, 572362311, 119312455, 133234357, 4842717, 141181735, 874778242, 923068036, 5834675, 819784012, 382613752, 891357690, 501096593, 235199372, 281151895, 123961584, 227166318, 265483905, 323135317, 653850657, 973494698, 49304074, 227109896, 309400064, 255332284, 121876057, 415268679, 894823340, 811971919, 480744003, 34951711, 387230469, 525631687, 994215244, 828729794, 668998152, 2490294, 984605590, 630703345, 201344349, 749690706, 705901640, 44903966, 446314758, 937822275, 486978390, 330339162, 41179374, 869339328, 97154462, 937226172, 2879429, 446053547, 362951418, 778223041, 525016260, 731894208, 910401835, 906416363, 360515439, 105471890, 356975304, 237080114, 895950760, 662029394, 615672864, 939983231, 136359934, 128666883, 530715962, 108793885, 825969152, 738428309, 338983054, 729546845, 801983876, 886992480, 506626207, 393195031, 688986820, 490541067, 840096811, 895999325, 939433818, 611835332, 413588548, 757171443, 684932871, 72020722, 854926320, 984945160, 302336654, 114031603, 214349240, 70088155, 877350158, 626769709, 228404600, 534844835, 851086753, 215964093, 363157852, 331186057, 543147775, 911819849, 234966978, 87449812, 501121179, 530303472, 686387299, 891749422, 94835812, 604282420, 768041715, 629369937, 808159812, 869710834, 625328, 329793696, 876823415, 477789423, 410231420, 612216704, 706569550, 991889748, 857145736, 317051417, 752194834, 327919685, 155774898, 887014681, 156845782, 408626999, 390858007, 713602852, 607538133, 117244791, 377706737, 769837228, 360405345, 997981003, 792817119, 978608117, 9507872, 854824060, 530602045, 496501538, 303970013, 670711377, 693304784, 329016620, 749692055, 697597142, 5151269, 601641507, 728140389, 834905904, 891575811, 96021269, 651039365, 380746095, 403280110, 545624995, 369058720, 519488165, 504668224, 507166214, 648514671, 576961627, 883140995, 934119542, 55038331, 501808384, 186524628, 687138757, 489661887, 51894755, 678108197, 302387353, 385513652, 152155987, 540156914, 772354294, 981801043, 759590450, 334656531, 753808061, 401300835, 483683511, 454271784, 354622260, 887325298, 865414319, 377798753, 346974784, 198883484, 697386316, 471086096, 351979341, 561093512, 934245554, 955896740, 554415306, 378790615, 57603686, 334433345, 369379335, 452759261, 322763544, 502915688, 359911052, 775749538, 615834509, 289188568, 16524527, 376878642, 911259709, 216383501, 795560147, 99178516, 827273275, 631942244, 741243454, 475560309, 33340765, 970849053, 147939836, 687164004, 797170554, 464304697, 54565999, 243229327, 841822685, 723022133, 709416313, 162109756, 893706159, 900689468, 936356025, 826426282, 636485490, 889022728, 443806364, 800637286, 371975882, 99588416, 936058175, 731426302, 131169241, 169699844, 743253474, 276986155, 253076764, 963095364, 273386692, 144066283, 747646078, 959492399, 504871829, 241301357, 666934657, 420055690, 975413061, 171845394, 702962877, 322564340, 553956582, 397688809, 8979646, 536685952, 213733949, 682712227, 66977369, 917908541, 365882758, 460187264, 940355465, 121178853, 932034162, 950132754, 626187256, 983550931, 200315336, 291989153, 771112830, 67289800, 635791598, 256612613, 229817829, 65017285, 921576266, 81198848, 275981620, 406373888, 76511510, 291409056, 831298076, 716889542, 138111020, 956873687, 868208018, 655401080, 192455434, 38841089, 312546011, 869646430, 759019029, 174502630, 459879121, 784359517, 815696487, 531190286, 479449215, 220126553, 377894609, 34143382, 406011044, 863825094, 591508738, 242185140, 112083742, 767663300, 243808283, 824252828, 783331845, 702131338, 33791335, 987422927, 490327373, 300977432, 591486792, 142973173, 12379062, 589079282, 578883156, 666755491, 354231626, 94369930, 498392696, 950477457, 460893061, 772511189, 873560373, 857273940, 898915315, 36308411, 122869383, 118145787, 568668605, 510737237, 881440862, 647163302, 284072991, 903610719, 750176380, 71351745, 506301418, 122574170, 483210947, 541126186, 633899483, 944652625, 798263982, 984000284, 890908453, 624178456, 147068479, 848908417, 220121799, 477651047, 821267181, 448775301, 982491973, 52213314, 3230262, 156931347, 875219170, 457084357, 631004612, 782391435, 852572288, 554327240, 964023297, 364700031, 378502903, 793926466, 18672842, 423554816, 784128714, 347986270, 244950324, 669558768, 748923705, 841064204, 73667218, 140905472, 105801894, 221572331, 424601955, 494898106, 885117795, 55149752, 783360816, 44678262, 914617822, 791137221, 285888503, 920619000, 249329189, 399817159, 324243594, 175164587, 939696542, 432684183, 206113032, 21981931, 224437994, 330272900, 313046884, 657619817, 596794445, 112540355, 821157236, 767703843, 861639, 455968287, 394921059, 431111370, 561148384, 532333400, 338099933, 484462652, 290806767, 217044255, 195173032, 924150978, 565828231, 168103611, 938911510, 216896623, 542457021, 347447268, 772305347, 50237660, 967103321, 709059433, 884767477, 988031332, 385843474, 893940083, 563434534, 404554950, 729335057, 311436087, 101427905, 40797133, 306534097, 566282350, 491680695, 549467308, 994704196, 467665451, 408006268, 539312010, 681130215, 433500983, 296464716, 817850418, 733697624, 526959822, 848002291, 465787077, 861100508, 581205883, 369759679, 167985557, 240998181, 404073318, 128737613, 637653620, 698382493, 403207860, 537965536, 173364246, 568821712, 566589683, 710539772, 495829709, 917867072, 487504493, 613565230, 759992036, 628062190, 114096241, 560203200, 501569234, 905622353, 420847892, 321270128, 922815822, 411209840, 351069362, 534429020, 395579756, 981886645, 583756438, 109221353, 914842960, 849945098, 724472276, 827095534, 141106831, 971096937, 322384212, 394199220, 435071394, 240896190, 687800158, 567993014, 748083747, 29395138, 75459065, 833031690, 868892950, 354784762, 444142083, 33103917, 339530893, 517006990, 832387769, 547843736, 212490223, 111342608, 710136803, 716945846, 978441049, 992349039, 775446882, 171414295, 933151665, 753764873, 954335009, 626564984, 632932732, 955502813, 246580319, 929384883, 454577845, 110843846, 125287361, 540895749, 912089927, 908149857, 750187045, 256916776, 585109046, 925368580, 869953938, 818503485, 942203808, 471152472, 825891688, 379808805, 611315392, 865343909, 411620730, 657033964, 416177392, 338089478, 838048269, 462317943, 681190749, 366603404, 437237506, 629219751, 101392207, 830031234, 361805905, 228215393, 870984542, 229677963, 141689344, 760234749, 537418980, 374060179, 88783617, 466413901, 169372715, 82257595, 123093033, 969903152, 479083875, 595969362, 975997316, 512163009, 502037896, 485147462, 940566794, 68917904, 322890490, 195008460, 444112721, 137807686, 596245870, 334164066, 963914292, 993322219, 995510967, 16710089, 64917709, 187979166, 72221936, 355284870, 217455051, 106102715, 325605146, 450817701, 439616560, 540688787, 256543898, 980705226, 143519795, 449384347, 597848432, 166328467, 670458009, 936170934, 190364961, 576292537, 188972735, 929684547, 624926011, 551135064, 267689916, 44434869, 945696719, 66655812, 233701447, 914335748, 967601084, 472301697, 340421372, 186931175, 130258639, 960088679, 926003206, 870617644, 653884420, 664264788, 27032311, 129043300, 585527209, 536325558, 855995176, 53357895, 336840792, 429003200, 465352751, 473651520, 952151544, 496795668, 805312294, 219819380, 173632607, 210465429, 136307903, 490200655, 105402059, 249129026, 91749408, 33241489, 513969848, 464894093, 619545574, 143133689, 761761735, 762289120, 459625878, 664313438, 126599504, 860612535, 787246689, 179930628, 876883790, 880743015, 654786712, 87724838, 278358709, 528438789, 988010434, 882654640, 538016610, 469471139, 955981167, 232294652, 683760322, 435904659, 219309595, 868720147, 926226058, 172644146, 204336432, 522148866, 880278961, 854394910, 339877888, 857826580, 385224617, 558783306, 728590052, 640256537, 460290597, 129377857, 518112175, 187737228, 533596857, 723477644, 81026956, 703416113, 438225716, 987034038, 804265528, 350089283, 602055728, 328528472, 128962491, 623244190, 848464800, 934040805, 139837248, 593748304, 378218117, 126461522, 725300086, 966716379, 184714405, 383733821, 238545095, 325117946, 555180738, 347801948, 282916240, 980903654, 416034412, 305638584, 452667514, 949597011, 334321615, 150538143, 841534787, 357564997, 24163627, 723675677, 955484147, 410093870, 332057129, 676533052, 704625803, 53571749, 780549093, 277183153, 309734837, 205243553, 196452132, 242572202, 859307882, 868606712, 517522878, 455435511, 787565701, 26907019, 906069645, 664405988, 385422918, 456286026, 717678214, 778628921, 802049407, 349585366, 114349691, 333948582, 903130747, 905007522, 275619710, 936642878, 878721938, 498984970, 268855899, 176877411, 586452996, 72944934, 613052193, 77738958, 27042922, 513539567, 251856195, 289776545, 992340269, 689755400, 504408647, 354171046, 902766842, 145291259, 942436528, 925106434, 453862043, 193170784, 123923298, 868629873, 855644262, 978348380, 676824455, 722884816, 119351193, 722744367, 736093807, 27973030, 192516162, 338774510, 560472346, 679998257, 934119377, 817902625, 985651964, 86868631, 362516627, 221333654, 189079721, 266065297, 598225972, 663424668, 769370815, 931975291, 538943977, 932690957, 156386017, 65665985, 768591755, 354869425, 720552410, 785977267, 429882527, 874277644, 45525756, 488567967, 140705558, 362821141, 471788382, 485599419, 564816361, 718482442, 988853047, 624397405, 386721224, 304137210, 511803373, 204227658, 676517882, 157499246, 223591066, 705187862, 80610867, 707140484, 143767756, 984197820, 895128948, 417369859, 297447556, 197457960, 825653763, 412782311, 371156949, 730003927, 67811504, 585987895, 515480000, 938168773, 981860130, 112276732, 971817471, 828188847, 862754015, 931096454, 557606122, 964394211, 12271265, 844574245, 957071969, 671921624, 396610380, 623322169, 198451175, 967881746, 341285430, 597615317, 575730786, 992262695, 521755212, 975673582, 170636249, 199275056, 78784747, 887741579, 153735542, 59013554, 659658698, 930427845, 850165422, 543894754, 418590905, 438598385, 589827850, 83213969, 791305236, 176693149, 668710346, 330805513, 993059906, 861868209, 336555572, 320725327, 259235173, 789570480, 651823084, 44677960, 324916059, 117541251, 486254769, 10788141, 707843051, 292837121, 202450280, 501188277, 585860401, 747288135, 970056783, 189923019, 601766874, 169954394, 83063482, 44804898, 46201908, 833428332, 509005128, 74294687, 641365087, 447306846, 175620289, 39602965, 761321751, 105067756, 705344849, 516313187, 521838068, 71551687, 316557993, 438169030, 880395743, 776028270, 542717304, 592346305, 903757447, 505329549, 667522233, 97083405, 105013494, 548470613, 229139707, 615446139, 593189401, 289278307, 639870612, 381139892, 602609740, 817906354, 397463055, 403176820, 267212966, 924497601, 98388136, 893353226, 889917691, 754184941, 749969258, 608658153, 267282705, 36760594, 600956956, 610823143, 812622205, 369092508, 769499760, 731573691, 295012159, 167514214, 781573751, 251333472, 60688559, 466123967, 190016624, 285619620, 831905899, 385452481, 167331937, 226192452, 981354849, 768370133, 969747076, 440532519, 717334918, 199056306, 76020648, 111205386, 778740323, 704299608, 885147196, 390997032, 374727345, 575016833, 333129316, 587078358, 478673577, 15123608, 24536582, 199350769, 949185271, 328556816, 759041383, 748742965, 573459104, 1301493, 785588425, 141284527, 625903472, 592195350, 589847052, 884457124, 765649572, 26978511, 840815568, 102617035, 147132104, 423995130, 21605074, 440821313, 676122097, 233559211, 286517210, 286749107, 29704826, 591533879, 989435675, 965249952, 510102456, 791294799, 839818482, 469032853, 810258838, 795674119, 268366991, 259687309, 670863980, 842609420, 662983846, 962499955, 453446032, 290033951, 350308461, 200322874, 141098455, 402332199, 202146022, 496021563, 511303239, 267089548, 646782089, 864257368, 458692045, 799047822, 201188183, 103668066, 544498049, 822062289, 210264788, 88573690, 85076986, 768453708, 62897537, 701438173, 652578307, 343253095, 596615417, 117809341, 867268159, 790750778, 310235560, 862569074, 582890928, 780734338, 409335410, 6059523, 448404721, 208430354, 915221638, 407466340, 711751743, 690278403, 312243433, 529756436, 387323809, 307943936, 235589457, 89099766, 782331517, 273464472, 728971220, 528767666, 484323934, 690623882, 879395226, 819732193, 64935181, 921421646, 291588099, 681976493, 570768232, 126291041, 690526251, 633049040, 732504759, 350037710, 861353188, 320763709, 224951730, 557705183, 747349390, 9543738, 473275829, 724198958, 355928389, 304491225, 262980831, 455258717, 410345050, 267563978, 210149400, 320894116, 27283338, 907744652, 474655863, 720381045, 812980619, 450705594, 609011005, 86444821, 648042956, 651921875, 811494232, 156565232, 332532255, 311607671, 286231313, 822433646, 614487727, 193852484, 577874651, 686122027, 415551281, 638151422, 283645766, 953509261, 102565505, 891086335, 8142636, 443985871, 447422043, 873330543, 857865457, 953198989, 289353379, 64751471, 844356971, 687606643, 273154995, 502680493, 528624692, 66157082, 355602007, 152266733, 868619039, 915876991, 146631278, 603112690, 442146253, 274764021, 31607163, 869122340, 844422124, 806513927, 825519510, 923398939, 688620143, 393854432, 469398333, 186105960, 688862217, 995504140, 205839392, 770928682, 848591482, 775627134, 402584063, 353294985, 911481594, 370352365, 980719637, 479295659, 300925025, 785768934, 392473133, 602510564, 977419014, 530197163, 750391391, 198102805, 566287953, 791341484, 519763953, 465577407, 690312971, 277161412, 5601063, 711090026, 718809779, 425078463, 736601408, 248229868, 547202815, 864371708, 140288816, 515056414, 201077386, 671640947, 987796962, 964431920, 182554048, 238957616, 591573760, 985381599, 717962956, 991599118, 814242312, 784344795, 219977558, 214378167, 220765674, 720722139, 319665136, 74877098, 958430214, 327870715, 917229099, 773405395, 440450553, 275459126, 909710103, 52756464, 354825747, 829626668, 161535381, 511783424, 871683853, 223582986, 908225841, 199648439, 432203265, 756533481, 631420177, 240153424, 138774566, 705304911, 354613894, 617626227, 671333305, 395648269, 435172050, 850759845, 314078107, 685536371, 817771537, 140289960, 697341887, 969788909, 205689373, 323905306, 497645096, 988824328, 161322126, 549551235, 582100844, 340076044, 829407418, 758729122, 125256648, 224124534, 752966763, 324363155, 591130373, 254770196, 428758711, 541676573, 253040403, 520335945, 684990381, 898906309, 59136886, 267516105, 202729860, 320819592, 977506410, 984594373, 850418756, 107714626, 119895709, 71774894, 303850105, 529310094, 360719453, 254815353, 390734841, 733069781, 776354861, 245626087, 618282316, 271626508, 363272058, 671009138, 879648717, 214246770, 475274213, 40809827, 337055339, 520577968, 245368978, 385156454, 609269891, 974912993, 105412564, 54922841, 733160322, 774152493, 814047110, 572374535, 819938667, 374685187, 560350570, 99402061, 167421134, 293485067, 242474651, 461574802, 807669437, 218904032, 236963621, 779113234, 364978211, 994730608, 202567035, 75057956, 264032947, 978233826, 852776027, 688035565, 736377113, 431651816, 28340723, 718842545, 460963504, 948852727, 238617659, 228415949, 677175099, 24774470, 235637880, 939588859, 870014836, 60856895, 223878214, 437976818, 330730837, 404725849, 269168216, 39610891, 808230619, 510409126, 187375738, 646515614, 178667977, 475656976, 817376417, 679525636, 747708065, 702441013, 840081250, 972077139, 110154483, 962296365, 503342607, 918991509, 189704828, 666125750, 288495146, 487999890, 472427435, 158928542, 375391787, 466399070, 409695510, 264653127, 624565119, 505430453, 700722788, 931015989, 427590116, 953975275, 425610436, 551859413, 371068943, 756992449, 847456252, 873613256, 83401325, 563746924, 354409277, 538615516, 111816525, 263722436, 210915987, 515704310, 981804875, 766223693, 277368555, 500266262, 832032822, 286117108, 459489626, 488830818, 357224131, 90684121, 972992706, 945708561, 826451041, 383805857, 17314357, 787550287, 486781663, 900379737, 43903666, 970171853, 983721700, 863092916, 135544414, 6096240, 722145534, 563460568, 461728557, 160697075, 478440003, 925763723, 245211168, 947356087, 856825515, 505918951, 847723611, 43076655, 910082883, 277399345, 63366456, 505004529, 115207286, 26807934, 570385711, 496254610, 411708701, 913779137, 773268180, 106080991, 479891861, 233707626, 772276355, 847289049, 494315923, 292887234, 473211549, 15282937, 198784480, 416995632, 700678861, 206988572, 779558375, 172079872, 710426012, 897552019, 530629283, 903059475, 504967286, 474325867, 700402855, 329780462, 31132988, 443365293, 865676040, 919447487, 390068240, 531602202, 334036675, 622246728, 131556315, 753066302, 355106452, 262847283, 935304536, 662497833, 136669179, 605777386, 847139264, 449726566, 116597852, 472770092, 637166343, 103897010, 932928080, 406002254, 557445045, 405327773, 347740785, 647807163, 697323179, 418879465, 812931683, 507437104, 566264790, 236787033, 847174027, 763135528, 109136523, 693143898, 242209635] 147356))
+
+test6 :: Test
+test6 = TestCase (assertEqual "for (countComponents [733269546, 524802987, 72086815, 103722653, 313657156, 58069999, 353091422, 554813822, 114770023, 918192658, 168879343, 882206127, 944978310, 388146622, 737703634, 407620826, 38430349, 40847830, 789453838, 282500835, 232652237, 504082080, 438264572, 499427643, 957046787, 27397753, 390803213, 888316253, 373463662, 432190458, 178158376, 168094295, 766781132, 588739468, 608546107, 385942320, 885831047, 124476698, 183120413, 554797456, 161069591, 876608970, 299057686, 944374054, 315312289, 609231440, 396369581, 634760015, 341344906, 712544888, 687073029, 495279022, 677254848, 716347008, 718279054, 244683404, 476859014, 524422602, 728345668, 951231738, 714584282, 327512115, 188853582, 384399541, 849079791, 98203480, 842348399, 809856880, 353161950, 454290616, 833386321, 383897031, 863354795, 331271257, 799173196, 817067438, 615877316, 715733783, 549916832, 417766600, 718287497, 984946705, 849643153, 104818376, 845750196, 347700448, 586867495, 178328058, 43243588, 167210945, 714900993, 752722505, 333142961, 383644272, 164858469, 211727096, 923679216, 559596876, 759342359, 393916237, 405676219, 166384021, 766389524, 394950629, 795445051, 468026022, 222962690, 284600960, 197536830, 657125062, 693918890, 106934004, 284860109, 516701792, 553059996, 254084527, 941626562, 930928633, 904792640, 825342608, 120711584, 725593408, 451675515, 777885457, 432176398, 619396751, 401702906, 721161431, 995440483, 285003748, 411292600, 392217874, 922880894, 429414047, 873476225, 966589670, 950571426, 899007550, 717981213, 410383921, 588082262, 832114638, 176349496, 307027402, 186712430, 564418657, 258165090, 760928668, 934396822, 331093756, 902483497, 99103652, 56006105, 374580017, 498977776, 435506969, 935798888, 610996414, 467636053, 46396415, 258790060, 340630250, 119842464, 12870426, 201109326, 262903464, 658733348, 766660852, 210011909, 754107622, 112949017, 534490058, 394459859, 645091865, 330969669, 830981702, 593448962, 54654675, 945123220, 295688323, 895958637, 723228239, 373996317, 391048512, 107540529, 724393957, 47971974, 919451427, 547098896, 72477289, 842342494, 969067412, 595655620, 753387391, 459489665, 66411873, 303368903, 501864767, 691180353, 100650825, 564671711, 534656361, 897312174, 961243755, 751283944, 439154406, 827176881, 150938906, 445833817, 177417984, 413761535, 34222511, 192567131, 427442476, 985823506, 862133020, 267069889, 639882279, 947789587, 745499656, 587428878, 714061232, 934560200, 937702883, 790014590, 680309760, 846136799, 4609765, 513104864, 179036053, 715866038, 901117692, 932361771, 604820788, 607089795, 227621000, 178176170, 560442687, 389387129, 562457364, 595010230, 9752681, 676592417, 254404491, 959457087, 955803558, 156611482, 80933089, 13053047, 588033253, 197085839, 860566748, 532322424, 318248351, 471361942, 725712347, 183159328, 93439973, 17141246, 576178030, 721602028, 250522505, 467397151, 370056295, 812107933, 437191892, 452082031, 9411020, 833025018, 598549312, 652668946, 662948316, 335791329, 700085771, 472301495, 563038858, 267820162, 337255850, 520604316, 876450081, 957236221, 694517631, 497658040, 305577577, 470403202, 926427079, 974704126, 677358417, 57009345, 415384936, 184768106, 520274515, 862380741, 600746131, 708646319, 496776260, 45735535, 59801042, 972949532, 784680107, 821676182, 272485198, 217573668, 60346659, 107690186, 657267259, 385333883, 624555551, 760358323, 388472275, 113851455, 539131152, 799267445, 315873418, 718626069, 249458499, 872177219, 846022976, 920800202, 3883783, 464055934, 680485861, 689213227, 133182260, 830573988, 611308820, 924208320, 759261982, 191048603, 905410986, 288522849, 153910433, 704527360, 452614043, 287774332, 255508502, 775345284, 337473057, 736074932, 808127024, 424732577, 403474745, 597237576, 818490992, 975449574, 632443688, 463892436, 649821594, 839376263, 937793595, 901236790, 7310914, 263453115, 870101467, 648016599, 349451953, 437491844, 684934445, 360643067, 429506597, 317742387, 660629743, 58180706, 458362635, 81988017, 863390005, 146050111, 652849467, 383826566, 931094766, 521584183, 68190445, 182490553, 7950723, 168375075, 375566344, 139629702, 404399720, 245625959, 675130531, 167766222, 534190889, 1743666, 241138490, 762704334, 527017187, 450824499, 913874059, 396107659, 110645520, 620635976, 422508686, 448106462, 268995533, 292526977, 836153530, 121642748, 359146690, 5818843, 912191030, 249784235, 446851357, 372387767, 124999257, 34067061, 91878807, 242918175, 625456018, 720333915, 25693822, 790124804, 362015273, 408400371, 121321966, 414062550, 407054931, 161502641, 475685441, 22796009, 84772415, 513518854, 212675523, 978075226, 790307262, 579125858, 590946601, 768212738, 682665365, 357187866, 815763674, 512897997, 75537048, 826070176, 41787024, 419396051, 858785395, 954430139, 398054602, 908265395, 506657218, 690245614, 562256212, 30356521, 424922910, 561838303, 88905391, 426791944, 806092767, 338326091, 995218336, 870235480, 590655981, 137191589, 869428493, 481202701, 977224016, 762896902, 467429088, 778314421, 540689207, 333958043, 514375113, 231209023, 305754323, 640697666, 466260069, 906196053, 760877801, 868172875, 84459796, 497267282, 684552202, 449037894, 491747183, 342807599, 744893541, 423470477, 305082410, 366705818, 67274730, 696858752, 906357651, 218244635, 757781222, 159632085, 205787704, 660475309, 699159282, 50711976, 569177483, 205655281, 245211770, 747217473, 186550094, 519475979, 109880674, 393313219, 254952173, 938961436, 134190427, 430547252, 923647354, 978026485, 552180819, 542954947, 103128613, 774085702, 285004170, 303113673, 557749429, 632715517, 710339051, 626964742, 220990349, 75899991, 919228871, 517192265, 276058573, 383709186, 108345950, 330632850, 83243364, 706319341, 639724993, 783882589, 281667457, 655197081, 985834705, 786546703, 662280550, 885217101, 681568174, 519573144, 843351648, 814263638, 342751675, 391644941, 732662196, 678055915, 176606516, 588031615, 931628436, 95968231, 986074455, 308896905, 435627579, 850204254, 810930237, 433826573, 406234244, 47187914, 230135812, 572507349, 714633187, 785817951, 514470111, 205962131, 789427475, 111353151, 461630840, 307666729, 789701143, 632659871, 512804259, 765749506, 918466904, 768609506, 387340302, 587589978, 225444431, 603866749, 867977878, 102479445, 231254814, 229007126, 974916002, 503575385, 817771811, 517156778, 911071180, 303946446, 460433650, 232217021, 252133411, 115106730, 731726818, 606226541, 326569255, 638120072, 872291910, 234384085, 818490377, 720031821, 852768071, 677427822, 173984827, 86141829, 83011878, 677413788, 779160394, 781407724, 554050806, 92536395, 309494030, 797124458, 43920598, 235734061, 821066146, 84164267, 117272792, 506427341, 744886181, 469463391, 286987463, 493528250, 7840671, 130284965, 136629295, 865944116, 893726402, 277469031, 695843936, 260534505, 951150460, 939131257, 535837518, 388103033, 716065663, 674290298, 887651797, 302897103, 514711411, 43901582, 531247119, 121999271, 716146109, 81615144, 29301916, 702515572, 762151816, 70369603, 512107575, 310209669, 125610293, 611077637, 529815033, 29511743, 546895109, 861415334, 929431626, 283004927, 679455366, 132047350, 710062973, 609153089, 282868848, 353678319, 561145930, 857305473, 23257243, 535772310, 132995053, 492410739, 69797566, 775129500, 677668208, 671009057, 738069839, 415504117, 513562648, 211913682, 471095529, 555124574, 511788374, 638097851, 169719105, 308137025, 149853575, 133549594, 168019944, 118606798, 580853299, 619532619, 661056088, 947770406, 550343060, 53626235, 660850913, 546361281, 531926577, 69730663, 593944877, 285334076, 692352240, 977342769, 21347605, 198140281, 700996074, 498164340, 32655144, 114371239, 462430250, 555965840, 746328922, 637459552, 388518181, 115164316, 204515427, 780440172, 80015291, 457485906, 76719326, 344694817, 263887774, 47099772, 163013806, 10262049, 405461333, 476657523, 2450618, 183502623, 651794040, 658196390, 496477335, 999923389, 174706223, 503599248, 625067673, 922695594, 299735850, 496012605, 616776241, 245424932, 448529645, 355864317, 697233919, 150993521, 476893527, 281609400, 210536974, 427695646, 336094564, 700433244, 907473479, 863126217, 506706591, 128113992, 543634451, 304252632, 629007659, 189019244, 845741575, 179215565, 75310525, 802397314, 990724304, 103422424, 633696381, 113555702, 409443169, 550900989, 517038795, 2126282, 634510051, 8961010, 159265696, 136804575, 656524882, 2453820, 390310040, 642864481, 895593306, 546962697, 57655658, 508015526, 709170779, 538031462, 376283690, 520168249, 336589043, 113486183, 816368372, 674026222, 275400690, 756306807, 872756563, 358715738, 998613038, 20058737, 993126770, 414701819, 460074772, 962559695, 952154881, 861554363, 100092602, 174072657, 246904342, 306774761, 106828870, 737357619, 690399522, 658589079, 880881477, 598605076, 16919693, 26642860, 849979443, 397929454, 10940237, 438803734, 181985566, 353043538, 101519950, 239677540, 371229732, 560365185, 549882114, 137832828, 163957739, 809330385, 527027691, 284095117, 66892655, 86269967, 176751137, 549425551, 520678195, 220365742, 435712935, 719403374, 420199360, 363665263, 869792436, 789700230, 343875541, 699790827, 606941420, 359471509, 660087890, 263610247, 892709977, 507611558, 862675213, 685486033, 898894713, 216260834, 587451613, 834500513, 468252426, 513213627, 703929132, 596351762, 699068786, 620819034, 1757769, 290282550, 684443739, 391788101, 718560379, 424677035, 607432317, 623367691, 496688012, 813229612, 276664493, 121237769, 747238345, 186658807, 417715836, 700371461, 257720050, 713865649, 477066134, 844578659, 939531271, 525438684, 212998556, 452041265, 763077826, 253825710, 973878512, 935450788, 505675103, 204347412, 651692575, 510026263, 438580771, 745498709, 780937871, 242699562, 687401613, 534624596, 641150059, 513650797, 336148212, 372076670, 409849710, 211827051, 699289064, 752686282, 857474891, 569926657, 677188525, 965946807, 589588242, 891801879, 719400462, 133289671, 687901982, 693486675, 266810853, 384076943, 428271229, 586323796, 816038054, 7926099, 319739772, 762869070, 845950407, 526456004, 680973663, 225587792, 891578875, 881480359, 290936333, 473943038, 992724674, 748196219, 944750890, 127710867, 161013185, 836337779, 353970445, 853391031, 107396308, 853504907, 513959492, 684068086, 523903938, 31003948, 329124699, 403473896, 832801002, 781195209, 356109576, 87752510, 87126298, 353621927, 799872245, 436138038, 859352456, 696201633, 296913086, 438854542, 242444928, 522424483, 279014458, 311799111, 582739788, 416203821, 428436079, 221489739, 924357485, 758104834, 770154302, 412529180, 322166578, 283967199, 379981227, 890565484, 793794340, 734302721, 43217187, 587616607, 511420214, 938465238, 734570163, 632602142, 312770083, 296862818, 757749759, 839604051, 494640644, 496352198, 400751498, 495105823, 616521456, 816155905, 367254688, 916693178, 991755887, 284699370, 94080770, 662504417, 666510955, 414722909, 843490263, 98326717, 21933153, 531947619, 866934736, 428833921, 209035881, 464896921, 493354833, 790785042, 101375293, 854525179, 871856896, 410494374, 658161093, 333043689, 250519487, 840430584, 533300514, 159315940, 926728238, 586877747, 72242915, 957829915, 94187621, 284393007, 812850367, 456950397, 972782217, 433659099, 794785434, 34295234, 690391301, 749743622, 855067022, 925588302, 566960686, 231186661, 562712119, 316070559, 689131304, 573392161, 492498711, 896395515, 941646108, 103861460, 939428887, 655954131, 479652051, 922448128, 334371394, 320803013, 669428417, 149445800, 79584582, 406692457, 322332148, 388955368, 771511928, 594683214, 966769880, 702204787, 990766683, 922453520, 590445142, 552863688, 583160471, 555413606, 542595763, 254416489, 8671522, 45586846, 135065985, 448080259, 854649405, 575693295, 434826069, 465817603, 492752831, 445568762, 918159154, 776396295, 433936479, 263985536, 90680788, 619312150, 430641371, 610504866, 849703366, 538883974, 12818608, 8052682, 177636054, 867414514, 986699731, 338705807, 226735585, 500044901, 666521279, 988454264, 240988309, 427209397, 217958523, 420934756, 278459350, 506806052, 549327899, 18071041, 675086849, 320853741, 545653266, 898686834, 124282236, 284573071, 51089482, 78599749, 461831013, 122964677, 737467174, 532197823, 827280813, 31330859, 865480711, 373531306, 298364485, 408905589, 189930779, 497396920, 472535643, 787571526, 875640062, 985403217, 947411362, 636193763, 754671423, 835188889, 409986446, 531440568, 931405320, 591603010, 805816115, 173806497, 188876852, 727201582, 305017845, 502240343, 827407712, 636535204, 47311753, 891302410, 789163172, 661571242, 223400344, 539431374, 343141761, 75090582, 952288601, 730332377, 396341872, 634854251, 531959378, 422144618, 338129669, 58738862, 439467798, 877528338, 579547569, 701298600, 321025943, 101897124, 143569428, 481514998, 869610495, 726950949, 419794611, 226269961, 984694479, 795602129, 896978141, 650049484, 300428322, 481211469, 532092876, 510865151, 81368928, 127575141, 615294928, 480309045, 360062022, 780807967, 203086650, 487248751, 866248753, 975262040, 981061421, 619806461, 115367206, 84033737, 848831453, 566484724, 760074093, 753216473, 12392101, 1220682, 572741036, 201299970, 636940660, 347918297, 921458020, 686264357, 157060506, 198861138, 62365741, 481548912, 530186232, 738807151, 832847494, 33072398, 37024815, 918851982, 205051938, 215649828, 891908682, 446187730, 177463216, 796076331, 768640094, 16674612, 96176270, 242696328, 226363722, 285425191, 308226904, 571347721, 977672028, 514228966, 803045969, 53150818, 175952347, 563114634, 978223299, 719851952, 116224169, 762300078, 76910232, 542019423, 278697257, 529500637, 603837112, 95097269, 131051703, 393691483, 166163229, 841246098, 997611539, 43606064, 463441326, 579905676, 892050274, 73038461, 837828509, 678809218, 13982269, 325952233, 469017272, 332254935, 975529487, 544360154, 65478522, 711743508, 546127373, 663791699, 736827159, 341057940, 851982205, 228161072, 563639613, 952816324, 326900578, 933322707, 249568918, 396772705, 738570102, 732561321, 373833615, 69698842, 263761554, 190400079, 401216912, 637181811, 914380318, 430941414, 853430499, 905725925, 370653853, 498228995, 556128934, 596512267, 810132766, 616933984, 561932389, 824722296, 965796254, 128608374, 944670710, 467979906, 786749298, 643807800, 775696684, 219575386, 130945240, 829745527, 802041075, 408487249, 699914560, 766714424, 113386909, 939385663, 816362629, 619151642, 348115449, 653266000, 226961712, 314722255, 52519024, 853978675, 180452586, 761520705, 779917562, 544356199, 713561927, 978635410, 900919651, 810419536, 168654461, 553813574, 978470595, 37452265, 792670395, 392251814, 587610833, 11611107, 129434897, 752457600, 506948282, 489283205, 829391589, 31786069, 765493681, 995530754, 87275766, 558116603, 425737715, 608404375, 479717669, 811984258, 757687975, 686975653, 7921266, 968790744, 951705797, 999856954, 787597025, 184592882, 589876185, 833314315, 203448924, 14422843, 974863666, 10786701, 717392546, 48622399, 408357291, 950416106, 48746870, 228684741, 286726607, 947371030, 450165789, 559344805, 798945687, 366453469, 668215153, 568091617, 411708517, 106057136, 165918809, 819807696, 752126027, 862994750, 910957636, 492329893, 523948364, 336825140, 250617845, 643259033, 927185412, 251744370, 466567233, 128850487, 427660570, 261769795, 703237986, 606010086, 304554661, 938234692, 757982864, 49702346, 935500659, 982691052, 857376940, 754008543, 533202393, 455579660, 218949664, 29697369, 673261576, 212712874, 606613867, 206138904, 695215706, 413356831, 246179589, 15528645, 47767788, 243936074, 657856393, 114499403, 491611724, 5940609, 950287838, 580176656, 590396573, 413820451, 908743785, 995156343, 581067490, 290363120, 405684156, 523028335, 525661672, 663001369, 231451308, 664276573, 916912647, 22309333, 372099640, 69212349, 475862370, 247843270, 818872434, 708949492, 313886089, 884849322, 328766245, 812693908, 358922715, 168403871, 615897108, 444677370, 903873180, 925321343, 447601826, 319793566, 583204749, 970512123, 874680174, 857990811, 806566143, 394827043, 872088562, 384259638, 40624914, 358019991, 37894975, 887286572, 670561265, 883005735, 906489844, 926314215, 704254556, 591136472, 883384954, 881736776, 357102540, 652901258, 340684636, 546802135, 719229216, 623050210, 958530331, 633400486, 526303008, 543943045, 519009369, 279218332, 592667537, 169665431, 13493569, 344595961, 238870704, 709215106, 975048534, 738096032, 118945058, 174130051, 422682850, 327154799, 380598874, 680031134, 757944848, 811434030, 6999939, 591273819, 733092085, 677134688, 844914236, 795842784, 549818711, 989509809, 353722739, 692281150, 14956050, 449074860, 175414061, 470678950, 993608151, 249770006, 716143772, 797520000, 364451750, 170496582, 254398643, 20928693, 274801241, 818212569, 372954384, 675333492, 399741574, 82521639, 469658385, 792282528, 311766675, 599983336, 300055568, 334313002, 81545594, 717053659, 592743224, 725923827, 908029454, 886437708, 802872737, 960340937, 48442948, 593743956, 944692247, 137869582, 202901005, 598252130, 316113255, 585597311, 297355339, 824038937, 770169623, 869924487, 139914863, 208997180, 751708147, 93474494, 411029936, 989156612, 120896844, 664977508, 763767473, 954106749, 911639534, 195928418, 588553153, 396621693, 371001453, 987998120, 277394906, 457845453, 831501537, 565531108, 118610477, 416095926, 699638001, 450727114, 125851366, 604479979, 770917805, 167968733, 329895640, 711839293, 412336886, 177386745, 437817092, 669693381, 77250568, 887974081, 254858788, 5822635, 147641918, 447932897, 894755412, 85238838, 935055788, 482479519, 278016725, 364896884, 128771780, 328679483, 945473988, 843911508, 253487506, 977891874, 963774861, 712501041, 288851612, 35550139, 755414415, 747079826, 483212123, 820170690, 6071110, 607155712, 834513876, 502172225, 709292004, 228252964, 903894633, 913276289, 697775055, 631146071, 334412437, 413699109, 607932532, 463620657, 358066801, 557408419, 469531581, 769524573, 12008014, 681729436, 264494496, 135565873, 314324811, 933942598, 202565243, 887172827, 213567459, 898073828, 130460478, 71415885, 155721512, 561217999, 342123366, 832829969, 649052455, 781441606, 39372800, 78921646, 754715928, 399450117, 236646826, 62307696, 582579062, 303293045, 617357269, 234545358, 243407223, 485859318, 270104586, 177765814, 340731586, 923548761, 89220207, 693086203, 660418660, 537060778, 938502483, 499993899, 281250878, 421184210, 582377723, 490345651, 220715405, 902226562, 626847162, 505349258, 98408866, 259009292, 532729521, 393908009, 876714334, 194800266, 69546163, 41791414, 301760382, 291828378, 923026425, 419833903, 391348094, 449816831, 938625696, 882884090, 200195685, 621657257, 461930547, 30489896, 71577386, 50407028, 396936244, 757801664, 450788032, 157665181, 969824075, 172959960, 941771494, 644939728, 131359236, 443515250, 250689438, 350522052, 396015057, 109081738, 225603533, 381069751, 602559221, 14139525, 695144826, 720514107, 516003075, 588743222, 508281487, 786212551, 387199562, 816648608, 351361867, 543979630, 941849584, 101445915, 356523552, 355228680, 901861151, 82038772, 955797845, 161383502, 900964930, 587522554, 781684743, 832451857, 871318178, 395640162, 942652907, 543280360, 368920687, 368565327, 644315881, 946216606, 567217620, 512541852, 267077216, 800521004, 231322368, 720780501, 744992554, 846758986, 422684768, 872476138, 496604357, 7466325, 345963626, 687421519, 157067018, 30475045, 496112371, 410887833, 555379255, 175174484, 290650036, 205922495, 852579609, 756648192, 405393619, 417259170, 128237160, 478556893, 460336566, 462600679, 530717128, 977338142, 8845161, 711600075, 344156760, 307732769, 220474819, 635021147, 255251329, 986182888, 56844566, 224465803, 376618099, 887238841, 665742239, 526156063, 922735228, 43988219, 634432587, 893851113, 179737348, 87883814, 971269694, 708892687, 534749997, 35050058, 709050633, 478252924, 243525472, 110014530, 570601586, 566130563, 520504709, 512162728, 134059183, 283652455, 534450781, 364094024, 959412737, 531361409, 589000004, 127941877, 740737829, 184399333, 473085027, 410904811, 788509563, 208324149, 353356900, 228775277, 900291899, 546078665, 114320938, 604624453, 208674251, 101848685, 553073945, 591517564, 177558508, 215059629, 717464855, 937293916, 365308488, 622598019, 617065496, 298030314, 933837061, 702215456, 584056159, 679730001, 542751863, 465208613, 830602729, 306178251, 40678796, 920261632, 414476291, 11311095, 274892523, 813553788, 367959413, 588491501, 8821592, 520111031, 501262246, 18784108, 249722400, 76640529, 159920215, 760035776, 720178437, 491145822, 206032978, 174176460, 820672461, 618514871, 426930382, 366775778, 667544908, 169708125, 756966937, 741052733, 71617465, 155487273, 825176926, 253715596, 262825387, 879189305, 110483234, 841516302, 757501692, 415692724, 820883725, 869117322, 792338447, 299112660, 628499843, 265380612, 676688002, 622824455, 703744248, 50566898, 929384756, 54393695, 298722833, 555395000, 728719124, 778473925, 428942031, 892340810, 211015532, 439058334, 599310529, 802953676, 848563241, 507897185, 878922516, 299588650, 434546956, 428348169, 211673922, 240863478, 254234749, 436381289, 978176125, 110523897, 982304115, 826694677, 61763871, 747961966, 67387524, 844379433, 462718061, 549671470, 520716462, 251270047, 711293252, 862259253, 202183584, 469418609, 865736695, 594865614, 165167745, 868801251, 314560109, 842477392, 298339096, 511135606, 264334047, 831795718, 805380668, 980148430, 490930224, 850681674, 600049054, 598363950, 963420588, 368234370, 186251866, 772498784, 521095354, 120467855, 444260940, 482152499, 469146536, 338012457, 509504975, 340545589, 666527956, 307415891, 852246883, 527226715, 369416848, 896826734, 686624017, 969297708, 262155730, 181241081, 318477707, 981005550, 305649917, 715883216, 204510814, 896358024, 670239578, 136959592, 6686440, 476370538, 448700785, 864645708, 686267082, 344028921, 842856869, 899983909, 584884277, 682001657, 623458974, 39503166, 113647487, 829100278, 67277774, 2893736, 258599835, 127687447, 240252621, 603876722, 208585619, 516062186, 849477698, 529007815, 764372017, 87640452, 12247442, 72322071, 942249583, 711977657, 227077727, 664502152, 749222385, 309669091, 474298426, 933289809, 858150305, 641793241, 465611060, 627926565, 625115752, 349593006, 239910122, 847332929, 844309250, 91190245, 732729614, 629961973, 181797409, 651124151, 85766262, 220064893, 204409313, 691944207, 822571604, 828153659, 420390135, 333591253, 501540945, 405252244, 284997217, 116124842, 350508932, 876329224, 537852977, 164977306, 736622415, 162325908, 144441266, 991851432, 274365225, 114715512, 176777247, 631113102, 488237735, 722786467, 849700592, 601181051, 44965779, 322842987, 520057622, 957265604, 18123078, 113272782, 982749629, 880527238, 116992449, 241381422, 602617704, 625495031, 808069903, 639754685, 934155339, 333144408, 914174162, 875487653, 670023131, 755846205, 183859919, 859294484, 932742270, 970328014, 387575179, 700211369, 609731189, 643731316, 413030039, 838200062, 675317328, 849284495, 943605591, 557785158, 101859869, 340598615, 214454799, 132082808, 384542893, 744964040, 432861206, 806862021, 11993941, 772833610, 12346848, 542227988, 686357815, 882312918, 368663404, 816004928, 588942798, 810477171, 548537192, 266005621, 767599433, 27605422, 880420166, 104563421, 204163076, 288599541, 541047753, 400097691, 639779413, 675268456, 462200203, 154750307, 461416112, 331224042, 268943680, 377799528, 329530905, 857454271, 697898706, 530740933, 248124931, 483969751, 662759283, 407008932, 820924561, 873806375, 462118393, 225812839, 364208747, 22008488, 550448476, 944201109, 367723667, 14021371, 80106269, 823062321, 951396079, 860911240, 235846663, 979356872, 138107262, 316644379, 656439302, 643408898, 324454937, 176924039, 699030917, 844756402, 979780590, 795783837, 667874384, 824709795, 254136540, 533410713, 615381483, 262022587, 465514319, 639343598, 781129568, 316331861, 195618012, 134290285, 861132476, 190715717, 618676075, 447826721, 257408858, 587935619, 735399109, 48776202, 305316372, 196098770, 749866898, 607038512, 190236489, 402808598, 59252912, 903876021, 872860039, 841983907, 321179722, 898011253, 559703910, 732819951, 514885449, 898479685, 966066968, 16281923, 717710284, 361899997, 740584324, 485865857, 864212152, 159475902, 568488039, 460040547, 803922710, 289461183, 958398898, 991322180, 860029361, 970219068, 183963762, 755886056, 170261236, 726764997, 367963882, 579105657, 559341319, 927278717, 2732406, 940563750, 538334489, 801725493, 225472840, 676690160, 559388268, 362043085, 695573784, 307615505, 18458803, 408668677, 645203957, 158280687, 11152803, 691992554, 270582559, 794819881, 262493545, 340951838, 103045238, 937762597, 404766469, 320884733, 754758903, 752950509, 103875388, 18639637, 125629415, 193369781, 994754586, 754743261, 216717343, 134909086, 585601876, 190160818, 840521454, 547890407, 852206162, 760840802, 925457796, 280839670, 308611496, 224194734, 437593433, 228405291, 385449791, 676715987, 674125751, 47254452, 822906520, 100959296, 468536763, 150700047, 780198272, 217770912, 781967650, 934566439, 364733900, 178097134, 165076598, 902715923, 8516144, 133615044, 731212335, 466032680, 439232270, 562896366, 118796135, 824910158, 889474421, 183111834, 938671334, 642280042, 274403283, 325209697, 524258818, 770964186, 165599566, 403306954, 766750155, 322637003, 267396385, 441452642, 340223418, 981474105, 460026492, 732710031, 349342902, 257281743, 486551942, 691672221, 442829258, 89222652, 198141789, 806685392, 727098541, 591553720, 926273350, 879512889, 562919915, 189841528, 157819346, 362294168, 404203232, 881867812, 353283390, 933077469, 665121861, 734231704, 969211151, 935488472, 518443543, 84285845, 146403736, 141299547, 10873841, 289219440, 402865035, 752068666, 215740401, 312286501, 38119076, 304437244, 30867048, 807832966, 244855105, 760807000, 274693068, 583180796, 668826980, 232493283, 415910910, 505537866, 107260958, 536558381, 612361644, 637449705, 756475991, 108183877, 18664590, 112262106, 430244507, 494729925, 177325468, 242436759, 88906080, 212883946, 263294271, 215618987, 491091424, 190315288, 713220495, 785801825, 508706170, 277716204, 253513138, 291549970, 858721067, 472556984, 844370147, 758397406, 721469345, 633850950, 590440148, 246676356, 178557417, 259960472, 892716830, 85369957, 476588690, 715177688, 155534396, 8989147, 588913021, 980070522, 565693217, 509429517, 763490570, 191970701, 434975091, 263854082, 254488050, 801719192, 123241762, 862749180, 523059399, 408394247, 619737854, 534113475, 84996603, 556333345, 268191425, 13146538, 991247084, 520064600, 984532683, 389231394, 662834574, 129466425, 424141233, 385570905, 258279252, 893969175, 297872101, 702319330, 51119108, 196991741, 553583113, 965661098, 221395502, 917791148, 586929641, 201609564, 91367279, 19898923, 547266867, 518958719, 797397006, 189945777, 880939247, 284008786, 683673104, 90675474, 851411130, 919287488, 775642539, 516252901, 576202384, 31523885, 708777857, 123709236, 34042052, 623584514, 658300922, 462246157, 142052113, 712192922, 213732321, 55053820, 950480668, 108682716, 483560035, 474389677, 254480161, 962155525, 179099911, 462693456, 391663508, 362769674, 353110421, 640263123, 15267230, 816386414, 434753003, 172836573, 868557308, 686525368, 19206388, 862010968, 181318741, 376229043, 289267057, 311373804, 679589777, 283795347, 994304761, 43743317, 968108779, 417344939, 194750101, 286886814, 639359932, 985143655, 420291439, 930093303, 987984235, 719607308, 183835437, 969899652, 321262579, 724476909, 21511747, 808088484, 412129162, 84427385, 243867963, 553315451, 161936834, 688101788, 733464865, 516975320, 349909020, 63165312, 307482687, 446785532, 133803691, 602244567, 31736535, 635466635, 848089465, 597968189, 788971895, 246708530, 96421353, 359547637, 246228641, 705611698, 526047900, 282061374, 767009478, 480468438, 86340080, 835321679, 528948823, 941356313, 156472832, 700053192, 443357134, 26960381, 221283231, 644432521, 38222348, 945647911, 968721319, 613740681, 843503567, 980519949, 876370960, 253413075, 626728970, 51777292, 792455509, 934962256, 698489630, 138708728, 278328893, 436586181, 294306179, 691029117, 852067093, 832782352, 834802322, 937351189, 169480160, 967710090, 373658647, 878196042, 95117658, 500609906, 326104159, 848460297, 188581517, 567143437, 628218461, 128294261, 687235483, 683634499, 418306151, 32747615, 917343322, 96456538, 621055171, 854529896, 437339165, 122616784, 192769447, 954787649, 333295584, 2441285, 661933112, 530184690, 856017415, 769943545, 618933466, 768090425, 573201047, 167331053, 329187103, 166557126, 365297392, 374463814, 257879004, 632393907, 708057687, 906029942, 941833822, 290915357, 75590450, 803117980, 224948336, 660365133, 679322832, 747439519, 504861436, 742648689, 900407980, 856287566, 198975426, 672796062, 620618090, 41085739, 111277063, 495476381, 38382132, 987590538, 210598006, 79578642, 992989626, 616222240, 914497076, 706315493, 459384789, 424100025, 267846924, 121683258, 962867533, 466204580, 888543773, 567245832, 235033843, 267491033, 627548749, 278096413, 190392157, 33883033, 662556859, 272791225, 153580489, 391516103, 155464151, 111977479, 382604032, 603563787, 731279327, 210473840, 441553132, 580850035, 879945068, 893908393, 954285993, 493725378, 76902437, 128726676, 130272519, 284937044, 590034773, 239403188, 972698491, 815721864, 875027833, 536219846, 815361966, 398058514, 372320012, 329606730, 50819662, 352191783, 411140015, 517638989, 750386163, 332745055, 387798466, 463692627, 400365801, 365039843, 545887105, 873766576, 34790000, 100806261, 127996747, 763147315, 34341244, 194092645, 98021018, 415368660, 89972735, 195176047, 976023550, 883039637, 364243564, 263259086, 760947588, 46214722, 830643031, 879633782, 725264973, 564308463, 661197487, 110482028, 288983095, 505816524, 641340933, 682200719, 56661673, 237255626, 511992433, 371107026, 845903673, 713636732, 872897508, 318545182, 792158614, 916575, 329444643, 525882700, 108254952, 114517241, 610300012, 643193270, 418168165, 51059584, 482921976, 471358956, 528802886, 974398890, 377456237, 16113010, 936510695, 88084079, 280293327, 762656463, 993199733, 839883588, 14336393, 902632463, 728162949, 689671230, 834518521, 524076542, 927483626, 650833503, 627540322, 877303114, 663035928, 353567130, 269730031, 389337750, 245453903, 959374655, 587640596, 919294605, 854017008, 579821089, 787659353, 587082785, 27770877, 640904990, 332040146, 85656267, 863623769, 599942628, 861495783, 478486823, 799416003, 675516697, 936691997, 33210285, 526549645, 538749666, 198460793, 990176523, 720792917, 183089938, 45183888, 531022473, 31608057, 967220180, 404881866, 893580884, 245826507, 417896960, 649437497, 988106352, 243615812, 718535953, 675290866, 495065532, 518139229, 884505847, 779726315, 754714177, 301133326, 642720247, 877393946, 961407235, 653239438, 239116749, 544364289, 319671142, 793262395, 147800602, 894780706, 972753474, 896441438, 571921996, 161295874, 694222396, 806821166, 193829753, 205745766, 321847656, 942924406, 575288695, 515756309, 874707891, 987338815, 271383856, 528917916, 224373623, 612203003, 581900728, 923476322, 115540367, 152210226, 123514132, 214943243, 31644237, 404041093, 331041285, 30468484, 750861232, 158064572, 787374078, 843428268, 316866603, 294877328, 339280025, 829434306, 754754976, 46049410, 46611156, 186307118, 741613739, 371818511, 122851812, 193294391, 652097215, 105639125, 866027499, 858571833, 976173114, 7717761, 180493135, 677604058, 379843791, 980322722, 31093968, 406781852, 555120988, 952871076, 107050978, 103671971, 323220186, 504429999, 474687459, 733404404, 739860027, 393288270, 498575934, 83114722, 502528670, 546207425, 460734422, 285963399, 226356462, 345443974, 254684315, 635088737, 140378950, 775207943, 465958130, 181427747, 690997037, 890557033, 827021098, 619007680, 173938545, 802069653, 827231933, 838511292, 113357926, 64303058, 108957247, 409355217, 378447195, 555266610, 694852605, 803046542, 572240043, 854152098, 838564350, 366008277, 424332453, 264942647, 733052801, 5607443, 349436320, 346881188, 233529363, 702367716, 528088973, 110519104, 185221384, 190444249, 264934760, 673994987, 374579120, 751590268, 694857064, 734606007, 289455595, 766677565, 870104508, 195007257, 236697060, 913877183, 963389762, 291502653, 964280755, 310771596, 708664472, 358174801, 496718961, 527715879, 866647663, 222018390, 385680857, 386419695, 972360381, 692998295, 549537801, 659477092, 569035212, 515547422, 389488228, 630327248, 656663105, 40890235, 21200834, 161357362, 376308170, 318923513, 821878712, 303824770, 901946564, 233851521, 406276209, 605629031, 245859445, 519169169, 252986702, 112204543, 243571165, 280738061, 85391293, 206717230, 711157039, 500681024, 356067085, 128072045, 933271127, 513380139, 783855578, 379515106, 874805018, 194031953, 270020684, 723068098, 644285322, 434906770, 953524779, 859884602, 393707231, 422070541, 98530866, 811494882, 595985838, 785047527, 581926857, 706460964, 873009749, 201312583, 416284664, 148847498, 345939805, 712255309, 973296452, 420972132, 674462684, 719715454, 828541729, 122679581, 959490733, 255808531, 131442718, 675977573, 415189189, 397889539, 880588638, 22773007, 532672630, 694875650, 59638571, 850502713, 749429443, 139488955, 369874884, 168751343, 140903293, 908289691, 168490185, 371565303, 267029443, 883881486, 496869343, 73515357, 824967899, 619470076, 109230893, 900483348, 635833755, 706490904, 272466467, 151329568, 955244464, 695118453, 727821200, 959434658, 231933124, 288575180, 416524330, 810509603, 233353991, 7539311, 506899604, 455923168, 116160624, 545002975, 728410130, 40105703, 27000615, 305936658, 809614608, 918053084, 458931281, 789475474, 500126178, 286783699, 796402116, 302948744, 278105213, 986937831, 586564163, 12244270, 227526735, 999572475, 973856413, 777018047, 233235589, 264316144, 980819469, 299117383, 558355892, 93095661, 283202425, 906177640, 966143570, 868380573, 898985696, 769821708, 641202003, 701632139, 961773850, 527355578, 568014425, 591455894, 418726291, 573439156, 944610596, 513845406, 835054221, 92600185, 81900913, 157788400, 808796205, 977899862, 583912495, 686989096, 570722572, 410972819, 832144910, 575421614, 5394107, 187921827, 904090284, 351602344, 72841509, 18597806, 134968067, 902769224, 291485606, 467018568, 138826245, 381667659, 894833763, 613445627, 853104797, 452088063, 604009489, 814757622, 979360761, 375595546, 286466079, 594737485, 669880241, 508597860, 416345730, 843133926, 630564002, 647220339, 329265042, 362602254, 478532349, 780767439, 88838692, 534027468, 599348963, 942874072, 556218521, 693787054, 858436095, 593911204, 921035428, 116658624, 259409984, 123523710, 36513769, 808032046, 705444759, 254020208, 95640565, 434352840, 755466678, 79533567, 467223056, 458011295, 589089128, 763169449, 147022643, 128420077, 673428078, 129069146, 862464122, 394184357, 318068887, 882157710, 860358776, 907800163, 432944045, 541072690, 389480901, 185347763, 930424653, 507432603, 726228187, 288693317, 726688810, 74275998, 914758849, 646731294, 943200817, 124213988, 861379078, 869622674, 681513051, 341162062, 464999457, 566938331, 180380424, 240826402, 140058952, 727212869, 53662813, 108890744, 359550649, 54938713, 927756566, 56512359, 608697855, 602528567, 804704194, 680592155, 466250372, 775668309, 429544930, 68610846, 437262474, 123091536, 685632975, 773880553, 567847772, 114067166, 257249134, 763188379, 339285592, 35482027, 451431115, 120380394, 612183126, 940562462, 731049366, 646511441, 932921001, 541194825, 686869069, 468140714, 87819636, 255643882, 514282616, 816604449, 196157383, 255834440, 139779365, 726924006, 997582704, 699410312, 861320304, 778499684, 134979143, 502091851, 678541976, 87289728, 318194942, 735597958, 104264544, 78704761, 995625775, 644399386, 603582792, 59511066, 141544982, 87431913, 666457673, 20017772, 839793913, 168943259, 206780597, 412633781, 596444169, 822113328, 804745480, 103558842, 898514240, 806761510, 300330713, 693926407, 678678763, 987033464, 544102867, 676310766, 55423100, 182467514, 119880278, 704737267, 883682479, 834108208, 230796183, 617298185, 515011987, 523195008, 480228335, 950660445, 909722777, 54039095, 423290806, 861257650, 53948867, 762886142, 580128725, 517963113, 683919226, 69136327, 8819421, 364279924, 499411148, 804340888, 653193700, 322294501, 363607037, 667557017, 94695771, 489890309, 757976243, 64318781, 602727094, 387586433, 883134392, 644861835, 12792531, 850547770, 959765443, 794928849, 650452608, 470935108, 863585430, 494868048, 751768267, 935867054, 818194813, 459618048, 3043185, 586971424, 813237814, 176445033, 9011552, 249379241, 452402244, 647202528, 606019559, 693951321, 643413351, 635700990, 864593318, 879980407, 553629506, 383091408, 413753838, 535536979, 488710791, 184369252, 237038126, 965918456, 457494516, 685365742, 565711351, 468135223, 928451504, 48888234, 446135251, 581316297, 736693624, 442370090, 287607503, 767345854, 273874537, 924930891, 332254723, 704055689, 768025784, 86895197, 856006317, 801098153, 174581569, 782328435, 278745510, 637130640, 990423867, 623853718, 780053007, 929693214, 708580777, 81961361, 307145827, 940119752, 274326390, 881069109, 770724852, 635228852, 166097442, 105528140, 551804859, 910421984, 118064094, 779505946, 178006714, 827897435, 943184331, 607937685, 675566292, 840127040, 692087872, 439449560, 834004332, 599125253, 191920630, 736128002, 789177253, 822563151, 150662556, 40509867, 110635382, 350995216, 163376644, 646239899, 969456593, 388207185, 23095187, 929385223, 593788890, 31447348, 204645105, 701322056, 926346669, 166039250, 75409606, 832710983, 525526212, 314467648, 131623362, 576772397, 659172929, 880307077, 785845064, 797449643, 877374313, 526622476, 586869789, 549398591, 855949029, 455294046, 789978805, 369511788, 438057397, 477387101, 844182998, 308255500, 412097016, 851918776, 57690084, 75782358, 846174416, 358788020, 151242191, 338621314, 444192788, 32273656, 383256426, 149821976, 167885215, 145102621, 252683897, 536047719, 452310551, 297350701, 523125484, 372513962, 24795241, 755268977, 800835214, 58839012, 400081448, 218968500, 362263453, 840076933, 605706363, 647066495, 929332514, 571325885, 179266795, 348694313, 283972582, 737143319, 228152117, 371214141, 855450142, 504420328, 629224350, 878206860, 789488579, 489535342, 25660347, 530805761, 14298114, 213267968, 146002129, 867570075, 134811474, 177446674, 307865366, 474943126, 120750751, 878876409, 136650617, 72497446, 66956762, 940198397, 923702766, 903235634, 208509583, 224994792, 397231269, 624750370, 502091955, 11256866, 218408182, 555028901, 900544613, 722397761, 177029245, 972305873, 224169147, 88078923, 278948975, 99730944, 46303775, 861987719, 717293671, 537869087, 905068655, 630149613, 942029791, 172786637, 720024959, 321234727, 932634383, 920228152, 851721007, 483247314, 694575161, 611702812, 815906669, 354453619, 699698899, 338498083, 987853746, 625918686, 382817546, 383929840, 784398444, 219519007, 773354932, 924577154, 886255655, 622949708, 304766743, 83899456, 472000041, 470063369, 69444405, 742280843, 207705002, 722732132, 314363043, 648283439, 372270992, 728551449, 9313247, 841137689, 592395438, 623866108, 372765742, 428026903, 775810518, 435615729, 706239432, 552134885, 276056069, 386460832, 948324471, 248365464, 80837085, 734396084, 430601176, 650243979, 50700297, 530561023, 742749046, 723904561, 636690432, 764487670, 761388376, 490765083, 154855929, 993345468, 93714775, 660361917, 11360319, 8002578, 742786538, 16103893, 15122290, 701718913, 107645907, 678486483, 65597093, 479300491, 212031286, 258859567, 270964438, 554040103, 460594906, 468002825, 75514090, 793426814, 628500566, 845090345, 199041922, 790476988, 273339024, 643369952, 161306808, 398901205, 229650206, 310860174, 127109891, 265489138, 858461616, 108353873, 873188767, 761822735, 846398233, 84711254, 599122043, 272514872, 668254279, 558724268, 553058936, 944421447, 142570035, 520030037, 220385781, 160130604, 771096230, 904770263, 444477655, 401484424, 859413563, 637198432, 118193485, 50813543, 956044186, 710083850, 953128656, 39134836, 821608485, 876576394, 166574982, 676734485, 932031016, 978556362, 333334777, 937285444, 269113407, 926650359, 61227422, 624666800, 695997952, 979763796, 441370893, 711195668, 859970510, 372552777, 263681080, 985279511, 561200455, 689593977, 639448969, 833947915, 501640516, 44946537, 161737982, 899386268, 689728014, 364341459, 612721879, 260894682, 586783648, 166697855, 927460050, 980594327, 734681219, 986421341, 848644531, 121690358, 855708565, 236079167, 297280609, 556088449, 272709156, 287372688, 561486561, 618101725, 678973739, 915509389, 152946205, 354735210, 918882529, 172525354, 713031785, 809726952, 702808756, 104791527, 316599148, 990804878, 467689774, 860363426, 947608696, 917121393, 270571037, 314559270, 636504942, 996933728, 419151121, 876808534, 549394210, 755822453, 184750270, 657701549, 293632955, 848848114, 683703123, 96624668, 88526, 979959204, 945312043, 5519052, 390030258, 173786903, 740924390, 964294780, 999152808, 227313974, 987871259, 328585211, 572531881, 863288961, 330910319, 208641217, 666007434, 904108406, 761997908, 680681008, 702355389, 489061172, 905088019, 390029381, 803602887, 801330242, 925876043, 784094351, 205726980, 654911901, 17879941, 552012614, 382701588, 944166733, 665646272, 24419897, 878881388, 95488916, 389359253, 966084327, 882055853, 936882912, 178937024, 63998622, 776316118, 34263989, 111067793, 604413062, 870052994, 679400651, 623674540, 337756847, 384798351, 203309808, 856106599, 486764999, 363599450, 965725686, 60847588, 565434354, 326852811, 406677271, 198883068, 951615122, 601811757, 594331304, 845346888, 978975276, 942718737, 574741696, 110621490, 913820809, 519644052, 238388895, 184007278, 31896719, 745841045, 116433366, 659142889, 742730840, 518580224, 799593892, 438890188, 420393337, 70403857, 256331151, 48677277, 692276638, 171635786, 614138499, 942285695, 558701106, 534758912, 265640015, 234097454, 110751255, 858416548, 393614526, 50257147, 351494955, 759529502, 290765963, 254490868, 113831690, 436367381, 457163778, 535881954, 68397009, 182605070, 124227595, 598953717, 384197029, 509175568, 815823390, 259973824, 216243762, 124729777, 35763081, 770367850, 309939759, 674710159, 545285713, 911917095, 768560415, 782375141, 48458151, 252552159, 544206753, 48188177, 966666677, 494325705, 551611538, 370880818, 896254274, 360493937, 424368903, 200183889, 557244687, 963559981, 361358044, 551424097, 682518839, 188988926, 26496315, 53336659, 70731625, 250570173, 214123472, 150126925, 745068647, 678331847, 212342467, 866934143, 823910256, 439184611, 608734039, 676494702, 60988939, 145928409, 530433158, 620455469, 626975441, 170346362, 596458312, 617724362, 592654165, 860052920, 396761024, 213818517, 539824594, 476701931, 37212693, 580533304, 731706695, 813058196, 643590643, 824979324, 683540714, 254582272, 897631760, 47573356, 199893284, 820959335, 245349897, 400719491, 716181093, 773208607, 101071937, 719337665, 105086321, 582615476, 28550482, 979348206, 616748586, 10214389, 905329781, 27292741, 6555843, 445901487, 905292443, 594932340, 100980909, 571804275, 960489516, 246379949, 854757219, 530632170, 940177623, 853264858, 894850001, 625025989, 958682024, 112218886, 183930711, 78875815, 271813632, 789596730, 738379483, 713712911, 280527950, 171757329, 858092197, 603443575, 339587780, 94922154, 59428541, 30728541, 142257419, 446645494, 211810336, 757738243, 575870552, 247285650, 421724960, 65477157, 122858154, 981676478, 363398278, 383689661, 417007346, 165295240, 906777877, 253092903, 709071921, 242050975, 773481280, 831630606, 355641280, 186618776, 366163544, 297283547, 238785893, 823455224, 230309664, 679490417, 127008818, 203741919, 849714351, 806455605, 926841046, 238250549, 831382177, 38943984, 641326416, 42949145, 436012148, 294193203, 573487837, 494076372, 932538513, 886632535, 250600417, 226049757, 241861931, 862435541, 636690940, 841508934, 12116233, 343112362, 762262217, 973460941, 492258999, 760088112, 875192917, 518996164, 366166515, 144325124, 492877578, 624462380, 383996586, 168725010, 761193231, 533945864, 973092774, 64254923, 274699301, 909861154, 325026112, 966332404, 225487767, 628519774, 206805669, 44502910, 578806318, 188342782, 86266057, 346932587, 160899527, 876733547, 137375272, 396976031, 471688003, 41120448, 884940124, 945632131, 101849022, 392604776, 696895233, 223677061, 985213797, 795664794, 65638085, 490297255, 315646024, 97568798, 637994704, 645889461, 116202930, 607476947, 362295748, 314774908, 90359475, 348514382, 39362302, 495514719, 841272621, 323087957, 216682469, 206266731, 249863608, 402000573, 280499828, 687358894, 901965397, 124875033, 739701294, 703579215, 713612893, 342636237, 73342729, 874041301, 799280216, 37382478, 407487851, 448161659, 240556667, 46530190, 803963133, 15472644, 165503309, 436644918, 169552144, 250869220, 831771883, 633810829, 218121993, 41918849, 187402651, 224733826, 139371186, 944865940, 192872353, 325987077, 432903440, 454687407, 817598253, 969525764, 628905358, 857437277, 632054477, 159026680, 850851045, 120676301, 215978244, 723439148, 896500418, 11535210, 454620671, 248992943, 350125839, 482191415, 517298061, 542150126, 131674356, 74924465, 977525231, 592123812, 531968345, 780329643, 661044535, 486644222, 383361311, 677543204, 694620687, 794503112, 327015333, 605553676, 306079102, 781787414, 299072815, 675065022, 288236715, 20144490, 956820525, 612371293, 418197479, 224857559, 617649037, 198978152, 822281050, 973333131, 533654642, 46011427, 25097619, 823173434, 418184939, 755878903, 945279800, 106185261, 321677827, 846582543, 445093155, 751663436, 739093531, 919346490, 209234997, 135006235, 277037864, 152182399, 627210080, 861400924, 486228289, 972097882, 968986967, 867215889, 297373749, 17351434, 425680960, 52618073, 873267844, 604410442, 338045497, 771534651, 932440753, 286031834, 692187848, 414088163, 578674639, 652478528, 484868910, 54190157, 367930350, 859446738, 719897239, 728722109, 359045581, 802433542, 78229629, 353004913, 154072778, 72932610, 601135804, 467558855, 910463630, 243620114, 63953389, 982819079, 350769859, 27810528, 900591892, 618530435, 158722583, 228769105, 63980022, 882978001, 665564014, 11672371, 837408005, 390043626, 958893635, 575776910, 90026211, 301713037, 538224872, 459925144, 725455149, 416259231, 606406167, 377618306, 438207615, 397637608, 84843093, 781971750, 280272295, 156842033, 988680994, 468007629, 432399821, 618137018, 952104321, 210559379, 550138105, 212572918, 354764534, 152972592, 320561437, 22969945, 419282964, 440727062, 510891917, 283738629, 879072412, 764370235, 318631917, 166506852, 896824884, 897755157, 241298036, 683616596, 346448702, 763844222, 425309273, 131625912, 334396197, 668048991, 931590173, 322728614, 443293523, 43392370, 24041374, 350093161, 927493484, 290166989, 648950244, 605778493, 488295622, 521784589, 681342944, 659322550, 744132865, 10787743, 543295843, 968335062, 271187313, 608527607, 282333152, 134915588, 464195961, 878766359, 890920863, 887175843, 732745967, 53944244, 800756952, 125865324, 688634379, 82127128, 444415126, 512153534, 17379122, 426167935, 69853759, 532778405, 634612499, 34999785, 174474882, 38255488, 749411818, 584592201, 398499912, 429032170, 941254738, 72836974, 182785797, 656087019, 91759886, 328739288, 611512195, 685240104, 854476394, 550436552, 451037824, 487482390, 783949222, 946408398, 233366859, 307294175, 820438007, 224385123, 41087315, 450724924, 829461625, 959331787, 30173657, 928764724, 822612887, 934790881, 220123324, 34012205, 900526399, 252104998, 650484727, 474681192, 135018698, 584322358, 585384674, 144391448, 643963346, 554189476, 435194784, 626272803, 58579267, 386514025, 977189163, 473835673, 992544829, 189094181, 837456680, 682206687, 905480512, 488042290, 310004976, 143410604, 296977726, 575138181, 281949801, 533132992, 739720422, 435043678, 506110580, 44416677, 922909387, 380137118, 587146287, 309053512, 803642309, 634020766, 651300052, 853150755, 177596946, 439649449, 315734932, 537126396, 658260465, 604244813, 503925207, 55615453, 408915916, 893538863, 923097429, 293275425, 170765496, 156235101, 605935659, 617244044, 475722760, 447859679, 254104042, 120610359, 392456340, 217373435, 921847785, 959405960, 480314882, 953365015, 922330877, 861571592, 215870377, 886914036, 221417337, 666859576, 165742627, 999017065, 417741286, 328010262, 29104416, 781639905, 549802295, 687394556, 646419843, 150997773, 440179696, 268429125, 438689397, 178907378, 420330578, 752295801, 466849653, 73033569, 621396048, 492034193, 428694762, 178515949, 844800348, 545152422, 289252719, 868901198, 483249079, 316444736, 973456540, 774926038, 548340095, 421998412, 550146148, 558026701, 379264671, 197610034, 260223438, 182044690, 43627381, 323788537, 636849313, 270371714, 950359615, 964371555, 576922657, 741887609, 163611423, 444271663, 976847784, 109823652, 734310864, 205366120, 973270092, 162827086, 416270582, 342315291, 53372518, 51045153, 344750376, 285030891, 80551998, 555112028, 14464462, 975949171, 489821497, 587210614, 84120248, 58653457, 997033947, 111108917, 4457907, 309362935, 47791922, 770023390, 780011803, 654215836, 310801550, 323091515, 690707312, 378804524, 988474804, 503899954, 538044175, 225159172, 468100371, 241417339, 470825976, 801015621, 789536745, 119553533, 702222170, 746171548, 201946802, 707046045, 336981893, 179990339, 330609634, 12720439, 927836088, 864348060, 77905836, 518179947, 277482499, 318301731, 631248993, 472683119, 358820178, 667179238, 116005658, 605214556, 33357852, 110193022, 643416736, 457086605, 799952155, 958656331, 837707477, 707097765, 587879262, 869273360, 121503285, 351115979, 912780414, 984745722, 452026707, 314360819, 209695840, 342994153, 307671839, 497644824, 68378373, 239840613, 921663891, 112716608, 280040523, 228133626, 257833587, 950466314, 5138258, 527894444, 654885342, 734499779, 150318702, 996057733, 768661957, 544758701, 916583401, 204722795, 756286406, 201813931, 573545521, 271679792, 800986535, 101790042, 645919691, 897428258, 469895686, 394729673, 857942952, 151877880, 779725136, 773509577, 93724931, 257317356, 153541523, 408038058, 326798831, 702857142, 366925021, 647069988, 754767201, 300839879, 50366967, 506970442, 994751226, 968300078, 657791940, 648452222, 870592479, 171635748, 530306917, 757086663, 686327435, 560179757, 497886250, 790323949, 104058460, 641585996, 963007060, 533877577, 836337754, 519981392, 26230407, 78275431, 667029469, 643960734, 567915740, 906689410, 387730398, 318069575, 923202204, 545889192, 308500775, 536522910, 946767652, 421083032, 916200390, 563695216, 805746560, 755574653, 324928713, 5456934, 258433316, 465647612, 342063047, 646207191, 373227091, 147502371, 196685146, 769200983, 44523966, 954908067, 361353720, 74811952, 527885894, 403032568, 161100754, 892399964, 969049400, 515079165, 833002652, 898679990, 334878574, 454866878, 131310652, 878649364, 898902370, 180832484, 689717312, 761512779, 610237490, 604462719, 42439495, 470167543, 210479921, 558849040, 695329501, 703277080, 298804786, 228159270, 719562887, 280802862, 155138327, 461179093, 267672388, 924723360, 973846722, 882938426, 703475433, 332804159, 387049500, 435385201, 423618302, 95827760, 101584955, 877336760, 288032710, 549002899, 700576950, 408945326, 651937007, 492571809, 432953660, 642747464, 551365032, 554298842, 539247843, 189647899, 487269675, 870238623, 237101330, 398511441, 169880338, 869564778, 136098869, 620591528, 145123903, 914913250, 724456154, 34714693, 361311538, 500519431, 787150951, 238150252, 335836478, 277474567, 386776951, 39208195, 181820554, 295048199, 475553932, 852065977, 292048082, 561405579, 185927209, 959450459, 821208335, 187623541, 279097777, 352798609, 694471189, 78541080, 704062889, 311959248, 691514887, 302597252, 691658508, 975054367, 776774856, 198954493, 209069907, 914379164, 847649171, 538775612, 807915631, 435173745, 929390700, 273809074, 963865167, 934090838, 772256869, 710594962, 672773929, 62291838, 428721055, 354254107, 973930290, 769512906, 769757286, 587518626, 815504475, 558611547, 323306622, 907302720, 527462339, 410795865, 934050272, 221045449, 233923038, 699348956, 488407363, 966544567, 308782998, 858400196, 757103478, 956735966, 895957183, 306549363, 976586796, 195594276, 699412173, 336212027, 448744211, 472674119, 533685208, 664623781, 831297852, 232898898, 466444524, 72347968, 294787240, 241002901, 773978083, 937016552, 369849373, 579184297, 760406484, 879812657, 269277503, 902433457, 774766708, 781303869, 839563343, 806315478, 383313907, 775971158, 304151973, 535816392, 226879804, 703316013, 878021718, 275092488, 574447767, 62945886, 183169326, 916795778, 105073163, 403212033, 982862202, 255955270, 875709490, 504729021, 490406210, 64894160, 401058840, 815589485, 24544907, 315834257, 96486923, 744616249, 263013693, 478493542, 136340302, 471746601, 92426497, 217194233, 549556503, 526046993, 885266860, 436289085, 381221589, 837341155, 615085228, 508364458, 227813235, 407625961, 907606166, 608946866, 354511773, 835354546, 214734315, 546616997, 12024928, 656059151, 993511805, 657767676, 960680335, 850900787, 403775366, 37410906, 796912150, 553072606, 375123286, 574665165, 246128157, 21335398, 181884330, 955249715, 922985131, 149191783, 356860174, 394878628, 33967627, 596182879, 872147037, 357174618, 623773675, 390437255, 103388372, 674349967, 461284034, 220824997, 936396874, 850647288, 301600141, 623845619, 668308418, 412244217, 377962179, 86654295, 794184625, 402789049, 555267951, 50170473, 565823454, 206723673, 223678829, 671700063, 626053851, 196711851, 287793141, 75525091, 40131035, 516625317, 690993706, 167243473, 985063756, 418198071, 860069905, 277947569, 276920070, 972882198, 833089088, 51435037, 54815973, 79661449, 318983961, 320588561, 529268263, 18807042, 765706854, 215224575, 644177850, 689894881, 436834950, 324129072, 75771713, 950008641, 285257199, 917063310, 502370800, 39703155, 131658387, 242465502, 384942860, 630048461, 16336928, 30440198, 888481514, 398618690, 290912084, 725611382, 531601962, 224730533, 613280966, 254477467, 763738735, 693323943, 910247012, 534843674, 97259025, 688948737, 575759119, 826867001, 497595752, 279927335, 78741270, 354070884, 633095900, 415022990, 200053888, 664042926, 359626912, 656171223, 14010625, 187681125, 562187377, 693718723, 720752742, 292385447, 175007252, 718071995, 147375238, 608283882, 980680329, 500587151, 438760648, 290208726, 504408341, 163050992, 363528283, 623000702, 751893919, 645611200, 475453741, 43127949, 892074267, 752109534, 282995338, 912854360, 521472687, 651041783, 328360897, 851684173, 665207804, 725442669, 273921851, 333157358, 793379304, 232443636, 324754069, 417062958, 383317309, 767872191, 245267960, 54012987, 220373076, 102509641, 744077293, 945569301, 850123187, 457300095, 908616446, 858706420, 640311409, 760093459, 877565620, 930451542, 81284563, 345709082, 158573093, 82655841, 356827655, 195877290, 583733019, 599126342, 186412086, 848652561, 263053330, 240771252, 286842017, 923226850, 823042315, 911481109, 609621555, 5502950, 417236513, 755182924, 300387416, 52436426, 639612588, 151228361, 842225492, 679274010, 759965600, 605383690, 426775825, 500750290, 235014669, 546627250, 387495215, 900180592, 416282603, 204059405, 130668259, 114928899, 125216853, 771448350, 872096249, 151446613, 128795877, 668999909, 8212809, 655810976, 651662549, 381659250, 999665071, 296838042, 197872081, 903708522, 767907558, 485537737, 705860355, 376586664, 758454407, 809196370, 175211726, 939462454, 535783604, 342244888, 598995439, 496997651, 421218749, 385239302, 215313974, 244417499, 984931334, 216089967, 710199131, 263202761, 203092538, 837000176, 304278277, 854842435, 795942356, 656428311, 159182726, 991589368, 377541106, 623477827, 127818096, 315591208, 186573115, 281510817, 901256159, 765589689, 861094602, 978664808, 48455114, 636553056, 650359483, 561368808, 109515548, 462431601, 115345603, 661114097, 431285904, 238961078, 377064263, 14514682, 983277607, 15943387, 543741273, 846866227, 982860281, 691076422, 364028620, 392231226, 413807033, 916027498, 885876039, 836367239, 209339720, 926013999, 3626012, 555547706, 360332435, 285775374, 996858067, 340599925, 471899075, 746244594, 525050942, 624568926, 576897759, 447756338, 266027665, 769130857, 475113010, 610950318, 957823614, 825089436, 787534418, 777433033, 589421737, 716501216, 614450000, 438456270, 978865922, 327088446, 594954578, 982328988, 382253127, 98688825, 665209864, 468920449, 97204839, 567608907, 990299394, 346918891, 10477696, 127956492, 39548663, 32421657, 644274319, 515518155, 926486906, 572251842, 371654168, 90412987, 961842268, 22292267, 714549062, 828487342, 25654528, 758260549, 663214446, 738281991, 712332352, 280185258, 899156449, 27820701, 927842962, 306029709, 586108257, 105147104, 398014644, 404068067, 571481418, 109228217, 81331213, 326003828, 912432361, 565169183, 248740200, 784170922, 374211540, 576810460, 26872907, 417203035, 205126300, 601509129, 691889061, 947929607, 774401186, 827753872, 660375506, 574990993, 852734474, 479644896, 958920034, 238220032, 191839680, 690176145, 822017948, 983469286, 196397629, 336711840, 511898089, 195568830, 455000981, 131759130, 420954222, 675940465, 934380790, 35571343, 718685165, 358511939, 764905575, 138424804, 208657136, 299297890, 271024242, 296158204, 410106439, 405874909, 989739047, 692884608, 810112491, 636784080, 771549294, 119324754, 515824687, 856823599, 820557026, 257778640, 456957883, 198969763, 430743728, 236536999, 711727022, 509148618, 308719602, 497364417, 46643446, 754096935, 693132893, 275585455, 977138788, 951630794, 354134717, 703019892, 131328191, 761244791, 793380098, 582541257, 990771139, 305527808, 400093028, 319552607, 97255792, 567610113, 965326472, 588410204, 225368315, 290990775, 803755839, 491559615, 423669034, 945529651, 74593011, 371528180, 617744793, 378412854, 743893663, 69376167, 858767233, 795951636, 78680815, 40455649, 407583150, 315331045, 17999459, 536642166, 44986831, 64051528, 871423103, 874537503, 27499613, 832739283, 803902232, 686448223, 395978039, 711814425, 205182011, 662070958, 817948450, 248206459, 879370117, 805609755, 704019092, 256643056, 879796809, 750904489, 980171931, 332922021, 943474011, 725032678, 304707264, 737946481, 920810362, 891987301, 38427829, 918160126, 316544311, 402347203, 95965179, 920520684, 696255659, 165614383, 404072196, 509057806, 293977428, 561578183, 7816564, 496296787, 184130277, 109430171, 633285542, 923336193, 730048603, 569200378, 861256487, 676206489, 707184030, 770520422, 498334161, 422895315, 919253714, 664354314, 107850908, 506951505, 893597176, 612999923, 790462871, 445673008, 365784345, 562111519, 252132261, 226726057, 404190115, 117287117, 75041225, 183599849, 466448018, 784901550, 461579675, 527068607, 129689036, 499766602, 852836266, 311246693, 770726552, 698100007, 511725189, 281938703, 652972669, 536591556, 584509611, 583875210, 556401134, 522067151, 565848128, 46593846, 455323452, 578916925, 402514356, 561165972, 249294557, 649349724, 126103396, 115278071, 598458167, 618890075, 773446200, 263329586, 109063971, 561178785, 692897787, 449123301, 648461303, 992805517, 40662242, 421598337, 816032004, 290481190, 952125045, 492211338, 223023481, 243732783, 410225796, 463669511, 829591485, 481206726, 796436911, 239691302, 691873210, 620131014, 920906813, 977920759, 549451094, 203849457, 209981970, 310334831, 929464990, 348952971, 316219742, 415790393, 669664545, 439550381, 781449153, 12374815, 397117110, 586749647, 636142075, 225503874, 37009237, 207751334, 252714140, 935342568, 936951312, 652234903, 489707, 894202882, 110337598, 765196166, 373211376, 246201298, 989190107, 986599799, 555145602, 236352806, 933655120, 695176367, 916358868, 849461297, 910273423, 406748971, 931607085, 856003388, 29772197, 638863708, 917603539, 451423847, 889494580, 792658852, 871047667, 248846126, 271452324, 723304371, 339406170, 221582037, 280026928, 674638198, 495437571, 337470910, 847715918, 872870585, 950971715, 448218960, 652336654, 24318299, 722344601, 646470384, 231248255, 325402961, 112400250, 45067132, 504871475, 87317831, 836976669, 688590687, 868482350, 380072713, 947512195, 874358751, 514675907, 818029292, 98450187, 335028675, 102719535, 558465097, 928176874, 279570671, 672369162, 449163149, 796900229, 621926669, 483858060, 405234367, 262969327, 235619759, 963704645, 955239721, 548665262, 252196365, 440012668, 418619774, 481541057, 852460316, 55127855, 403110372, 773941876, 35682552, 298951716, 858942890, 282315600, 447413427, 281178479, 913813775, 519737221, 143723683, 200282715, 849597316, 276508155, 999167184, 990369609, 458305079, 613894757, 981084567, 999914195, 98808469, 496963921, 527800837, 616260687, 901036492, 352699837, 176870980, 86914339, 901670344, 116444591, 902927992, 706910839, 145946, 177907707, 333673740, 766134624, 768815058, 706452435, 140310486, 234174659, 852076680, 547832118, 183220900, 894724196, 170901898, 698987271, 759208461, 192758146, 275446271, 880804791, 819197038, 957040237, 462897462, 327182493, 98728596, 101233646, 71489650, 970678230, 570262382, 962552452, 83391023, 261118735, 256610190, 399693414, 209830355, 660578032, 954581583, 677849223, 998954876, 514354965, 85359903, 315313578, 335933260, 651467739, 303491358, 106449326, 331827923, 498842371, 18201721, 541079988, 729756947, 208187113, 204920409, 179022086, 260033676, 323404836, 747259683, 449196180, 956346763, 390475054, 568533815, 545118108, 481355053, 189706932, 69389857, 370503756, 456378419, 754026086, 413067172, 392086596, 914420222, 318800592, 576753322, 722274541, 93784204, 291594549, 202772593, 892042910, 831610772, 458933590, 275777962, 791000309, 326796068, 706661470, 311408152, 997856839, 25855336, 454230530, 872115027, 42335778, 790279863, 559857134, 462452317, 683562571, 438599244, 493546279, 254440633, 724172736, 850629314, 904609698, 594838696, 991794846, 209014828, 702358443, 673811609, 905781181, 897600962, 418973902, 580000314, 192590988, 668389535, 822308038, 970018718, 318780322, 518949346, 33191925, 994354277, 917885384, 387840171, 774696974, 12446714, 440512005, 542366575, 76061491, 503859415, 444138895, 85868379, 751994556, 238980891, 852286074, 737066099, 129341623, 697081238, 141490863, 43783479, 790061207, 431311596, 503203322, 91535223, 154891536, 157694693, 450705139, 692594591, 429260782, 867973545, 576038821, 163920643, 547383038, 551042695, 763714545, 989496, 109812632, 29256561, 664077320, 742332574, 781803322, 181814140, 981150674, 987081831, 912994391, 352508139, 346831879, 750029426, 373453956, 550359512, 857850879, 897563016, 472873279, 58519637, 939366481, 373847081, 828831776, 377417302, 969716188, 597395860, 451495964, 562902162, 680369434, 357174062, 718255940, 351554648, 499313882, 857454621, 382567722, 946442772, 104717935, 322410713, 27103448, 688160686, 387294279, 795513023, 851698056, 130759253, 997609992, 178060267, 275246822, 708046173, 329979468, 992853846, 977848690, 565229752, 183386024, 479072559, 968437497, 463440114, 221356527, 595880352, 651104114, 984798552, 897881081, 144249456, 455089945, 414315458, 71709384, 598016803, 256331455, 45625035, 183208652, 511100998, 750812235, 115982909, 601461380, 501552135, 10607968, 143917410, 43327815, 175879877, 136497827, 896217092, 731441862, 897134407, 175814197, 925126287, 122632019, 561886616, 287001626, 761381254, 517520215, 199470126, 270692691, 660583974, 107703293, 919517342, 283887363, 674519327, 485527268, 120521564, 182191424, 511128633, 709634001, 421337058, 409067897, 856949229, 420961051, 191943383, 613979379, 496683280, 81292049, 32264090, 456378751, 546606308, 305510123, 462699937, 297717928, 74251553, 798839508, 926297522, 250597256, 860286030, 896825386, 510255306, 627149890, 163989523, 54478281, 317292311, 961262418, 942204456, 898629214, 447096090, 540668385, 443000929, 753262903, 818233337, 440721323, 316519111, 788942804, 4139510, 103104246, 734932815, 369104914, 833379376, 406160484, 295670648, 317740309, 620207361, 96279693, 788284329, 293642265, 735516956, 622247307, 540043693, 863171955, 360312005, 701419402, 223612531, 575671300, 401346847, 236349626, 920208807, 830544370, 556510437, 331921520, 887375976, 595204266, 643459033, 210775308, 876208901, 702006049, 641101118, 251566848, 618116940, 786844060, 962459774, 193538707, 294726736, 423832811, 614806449, 904083866, 13024434, 46098888, 184533460, 460189990, 988177341, 605205081, 447247993, 858247748, 351107996, 946632215, 64476008, 83537895, 849378386, 613358948, 212913242, 909035336, 638647450, 762209181, 92282474, 111668219, 393543306, 563748296, 379493520, 298147228, 506102502, 677011632, 891391291, 810897046, 166894532, 470017180, 736132219, 146605667, 408203370, 169034507, 973085381, 34855818, 458706654, 170009897, 260575892, 272217476, 263814145, 321632208, 796433427, 288110301, 150646995, 747064964, 227010306, 341139311, 67538378, 63679085, 595762926, 427360922, 408518905, 784576033, 688453409, 967435751, 1805874, 489124385, 49547695, 322716084, 541344811, 123925783, 89183887, 363928039, 618186576, 204499023, 210922950, 700494278, 864138778, 986949972, 229604527, 503407025, 380900976, 128495065, 242003640, 344887581, 40685357, 104467254, 519896613, 147999220, 223395771, 857724062, 158062445, 576432910, 563692778, 176716108, 634958719, 903086066, 217962262, 950626659, 718486486, 306986607, 63750243, 580668492, 914404095, 428637676, 725732756, 719499918, 202138835, 651697861, 8573954, 581944220, 875557901, 707398957, 352773813, 325295541, 454579590, 991307961, 334039908, 368111650, 615888189, 189735232, 910579839, 651226557, 596709150, 374612159, 183446091, 648527849, 671736458, 48511641, 306532658, 585411305, 194294414, 598061031, 275034066, 581190198, 655469368, 360516425, 86331867, 18722592, 468590477, 203740871, 991512518, 871809060, 157450974, 183080316, 719257361, 76954361, 159531910, 995538455, 727196881, 654601867, 914175716, 936039016, 799358589, 730302156, 942106467, 381635688, 205106313, 20950148, 571572891, 722754699, 796811442, 743390443, 532212977, 136393438, 143835229, 698607255, 778792800, 683853426, 701756028, 458727616, 526802941, 680838825, 142180824, 450237521, 32230038, 508175378, 348101126, 996052058, 618819650, 38459982, 975589883, 197808705, 959766645, 122580138, 349036254, 63167149, 539108549, 351551077, 256297558, 713422512, 340438505, 560898264, 609274780, 207947874, 945805530, 824977686, 993632418, 195645318, 48724614, 786171135, 31588171, 971268901, 428142628, 161074668, 42352964, 903618093, 503220965, 352167303, 902179431, 424605707, 955980745, 657193217, 212164830, 366049544, 36892225, 681670517, 740904439, 187642570, 80129495, 561921425, 755218559, 995509599, 810446394, 434498852, 138693537, 995961267, 948001926, 570050440, 245902051, 469457947, 78412876, 400901601, 755930406, 392715935, 438463683, 313264933, 190208942, 429703992, 933408503, 646040945, 893490860, 181324853, 9029599, 583441599, 899125775, 569790661, 76652959, 897652586, 631173730, 447802025, 553640116, 601529006, 765858062, 172525279, 852168181, 534837699, 497262630, 174634090, 55371372, 94074262, 73605903, 854665166, 975763300, 433175213, 346414102, 920950677, 33594451, 692518672, 803210002, 981353949, 321409809, 856067752, 922171156, 723292596, 89595991, 281294572, 948457711, 414218221, 391465276, 847558223, 175330338, 124817262, 851849033, 757429725, 182487677, 531479623, 145884928, 962675733, 466776771, 145142987, 210594387, 440798063, 38575029, 192504041, 714943775, 677859268, 674883319, 164586601, 69186238, 843689737, 815158869, 381714803, 593556466, 756614372, 978482612, 792398103, 157192868, 449325665, 206333814, 86430805, 607493294, 291154081, 442174372, 629036912, 672573097, 586683604, 941686225, 307772920, 132903268, 943761555, 698606194, 9528128, 886439733, 476327351, 407792646, 103890622, 35971091, 407736809, 934464784, 172426653, 369454077, 102163337, 416460765, 787757730, 787631599, 814210399, 368669167, 934732659, 335902670, 295218742, 708077580, 786506255, 209340980, 195093540, 961006915, 468832918, 451609963, 330563391, 361018001, 471057697, 665471834, 745012625, 864880677, 68881620, 611943072, 588622733, 676736864, 21191584, 191595465, 642751439, 834202866, 71769561, 416140074, 582230843, 289907889, 274204299, 42890905, 765150067, 959177984, 511382422, 139950298, 848495838, 982335178, 935778652, 160300749, 330524207, 48298383, 405052370, 111451110, 410635124, 738438534, 622078030, 542317759, 417430918, 256346744, 706452087, 856594487, 695994020, 652267322, 582844897, 426919999, 821867437, 91632505, 764080304, 973103456, 391606564, 520450704, 844449631, 519911284, 606572353, 171168781, 245283201, 672956169, 621062509, 280584791, 662283358, 654745104, 266145090, 903570601, 152192037, 861536873, 394208710, 28927684, 621824418, 419200732, 625566775, 157717113, 7672584, 639438899, 88803849, 717707195, 650164926, 54095911, 959811136, 2114959, 745150459, 498323170, 970576472, 731382376, 953147394, 805951326, 888959605, 113692876, 281814770, 259507339, 564577674, 914896573, 288093690, 327665062, 363037109, 297278098, 822467031, 313121627, 298377262, 746896962, 243177907, 67810737, 783467323, 754777111, 259717945, 890615359, 981049107, 876061873, 171553462, 962827134, 21627760, 306435753, 455212441, 209193442, 493882339, 592806876, 132436028, 250851989, 794388084, 720779107, 699573201, 678643625, 391714128, 358860776, 643494832, 557519545, 957649981, 245028173, 191014508, 845228331, 625078700, 415249937, 978275576, 660812861, 664469453, 123896638, 294379786, 38840960, 659092701, 6540666, 67386322, 819822526, 355755805, 908985199, 396739043, 896493919, 569765211, 32306751, 249356284, 704545340, 597723993, 129748085, 81686517, 883942943, 910079530, 946171060, 873729096, 249436876, 34451550, 319444910, 623624072, 27356184, 34059097, 200774640, 889545865, 422048429, 536167067, 254192035, 944633432, 385702743, 222607224, 269389866, 316201111, 256958170, 112720541, 15236000, 16916645, 252110423, 975521101, 722922277, 234987395, 194513019, 162851586, 506935448, 747028343, 973617973, 351600456, 61034407, 732890077, 355134590, 276746629, 119536084, 966713534, 586102682, 966654062, 864726947, 291517492, 774968143, 496072850, 108655557, 836491966, 298235486, 993598629, 308152442, 684282420, 148986466, 289717693, 117089014, 938034282, 385305499, 918651948, 799205028, 20688124, 384388227, 650469879, 672353631, 877618292, 7299756, 182370111, 473763902, 303800128, 430811573, 820138057, 248974121, 346436998, 859944814, 580888257, 938961120, 976853612, 682691999, 740209353, 16332590, 47963829, 504108755, 752891339, 856518094, 14402305, 865876711, 965301683, 631927827, 941770699, 268252495, 987373886, 257759849, 791810441, 764732704, 190268016, 478120042, 870634100, 531505687, 989844720, 115205058, 683430912, 295211272, 648627596, 384482106, 711616658, 245225794, 793593521, 557081388, 186929433, 724626805, 262476230, 63374483, 327733836, 348618031, 842273539, 142363871, 79528863, 435205050, 611069396, 454880721, 610934834, 27695772, 794829831, 376251935, 56992908, 342423215, 802445062, 395617424, 972699049, 6424577, 78853728, 245671656, 892417750, 451209980, 804464637, 5247953, 914921890, 29756516, 743171900, 678952774, 481507498, 982794871, 34210949, 779456099, 74890079, 783212571, 623914520, 216509661, 82511443, 788523594, 322785034, 99497552, 887398816, 539262390, 363135596, 90644975, 143641147, 999653628, 611074226, 581364530, 163809727, 529908609, 994688502, 875220505, 96469231, 95307908, 755249740, 282490904, 619687056, 314196593, 878316776, 687855305, 888217588, 292915145, 69310511, 46102536, 504666531, 942184208, 542526311, 295393672, 684588351, 74521736, 228376925, 214828179, 49237557, 428928317, 990341197, 772208506, 227721930, 792329074, 519180143, 612692599, 332327828, 728107805, 850603899, 226064829, 858754113, 44143647, 317229435, 439176171, 71032383, 392869934, 599195594, 158330358, 45588711, 134590139, 29348821, 763250028, 796881968, 819787265, 15578518, 805392025, 550259689, 759359492, 819113655, 202066216, 593312154, 281745527, 736301287, 381101817, 333581636, 775914086, 779782898, 341033787, 770664348, 706968315, 650690365, 932560800, 124014138, 311619396, 216507063, 313237159, 400317729, 866103943, 92335126, 123395285, 109367069, 680017891, 350046559, 124366303, 670438714, 389096809, 254539453, 960141539, 724524976, 379112995, 223148141, 11695661, 723671860, 334658439, 813021768, 395766232, 465222471, 704512848, 665401638, 324026325, 598254474, 711477398, 798939311, 6434459, 90322073, 857784216, 852773471, 227172635, 308990071, 333802152, 147947207, 894441609, 401179411, 366740410, 335460610, 301506957, 592991442, 16740710, 407225501, 998577305, 840650395, 402368371, 369033774, 647017577, 729440130, 211279606, 984861265, 855881860, 706335732, 36303099, 47789182, 712974911, 60918124, 196180336, 676651469, 507703964, 953936566, 583266849, 486734798, 68622538, 986403647, 443660650, 8675916, 813346245, 697517716, 48016504, 793419882, 563075765, 463180898, 945898316, 933833681, 410434759, 708327726, 153450271, 68535134, 141401661, 477131702, 697709374, 714350693, 727852780, 292468247, 134716365, 64756498, 212054696, 662676209, 470465144, 879154051, 997603363, 568500330, 52058885, 337973645, 707024854, 483186420, 334092593, 753186716, 76935234, 832047063, 507163132, 335296658, 861219858, 854302515, 448047908, 16768237, 118474687, 106142545, 769850317, 383792466, 641385318, 379323722, 882262030, 130524322, 392111414, 177795840, 557357253, 652358873, 482061876, 340271085, 71461712, 19736734, 827681210, 558508303, 207851810, 773195553, 926990418, 879406517, 377052409, 920469133, 91927255, 29615778, 7971294, 697358890, 664778949, 113295673, 593952334, 204682961, 938368887, 973041223, 416375775, 12774082, 196223489, 602518576, 854870986, 804169079, 894476234, 912099579, 172518933, 30815705, 640989448, 76757672, 529704091, 496400654, 516362613, 48615790, 644032331, 371735425, 338192335, 251949259, 198317310, 445031500, 850057349, 259313387, 618656959, 52801874, 566128729, 242435053, 19410388, 379263275, 40342595, 308473498, 432818802, 783201171, 301059376, 562780991, 950625011, 88666400, 142326774, 999572549, 533869072, 480317858, 130279630, 807707716, 294767442, 602559169, 874693918, 541387695, 921735412, 941578126, 387239229, 226606043, 107675407, 518124816, 427072147, 906334970, 542317302, 317357530, 906548500, 245603284, 797850239, 901798521, 787990643, 600270980, 28111708, 21553440, 30777540, 356997955, 111251935, 312062845, 994460374, 711453164, 328586238, 706718017, 11031896, 75640361, 984551342, 341956203, 887597119, 555521158, 765057569, 681283757, 977741323, 34644363, 545957525, 345018390, 932124004, 602461436, 618933453, 890039909, 223473545, 653481864, 939607965, 247487449, 47906187, 792860883, 29174293, 960514152, 812132486, 356745183, 343605808, 306853179, 920706149, 296098823, 171694040, 903113329, 564090837, 604618559, 794569938, 818803057, 528639969, 322205095, 617297851, 459127410, 242544756, 886052623, 396273228, 792748159, 436841147, 184973348, 552440313, 126063034, 577544942, 469070035, 416386219, 733298370, 918178535, 56918160, 701384619, 427822004, 283629403, 531526697, 464183999, 159856369, 589792296, 617242997, 21913227, 581029214, 177896682, 391685220, 924401017, 887093248, 977866326, 199218479, 631008578, 794741160, 489100802, 916993227, 249762634, 681238305, 949455601, 973399286, 849327598, 600167412, 935967249, 925564679, 92563443, 789433003, 962906590, 792953904, 514527170, 262393269, 96815788, 481156829, 399628008, 920274289, 356039764, 646606702, 939602687, 725385905, 57710993, 602606390, 590401914, 221268980, 55490321, 521958583, 951333012, 241656547, 146352572, 86185090, 898730570, 586900762, 277652890, 549377669, 279678864, 384474649, 29772127, 353678877, 971880529, 206474170, 668470405, 634204045, 763368922, 623707717, 169814565, 624086086, 90397284, 405334453, 273530455, 129740918, 58418904, 488261163, 303557037, 798496780, 699816234, 269375778, 740593380, 498520985, 217674532, 271808728, 548085856, 296806588, 306383255, 246064517, 809336700, 153947466, 786941322, 779950491, 847018439, 5480717, 90009247, 347053164, 324633548, 61887922, 277796619, 947246538, 31953113, 697682338, 97548686, 952199907, 261997172, 840130419, 820996403, 644354296, 157205564, 67399993, 3046006, 468981338, 751907506, 385614871, 418151787, 908790032, 843998324, 814673852, 637835108, 747171952, 50728496, 265403904, 284009418, 949932348, 723346733, 936795557, 984403726, 599037372, 425901508, 823534994, 540406872, 617768047, 239248368, 505150530, 42864861, 958943759, 740851550, 562104129, 402941583, 565702593, 215195820, 352904866, 231869352, 190214747, 285252663, 761654141, 497941966, 575655402, 117702617, 184372430, 122195806, 272540089, 332020591, 670360269, 981588545, 190607395, 125213716, 41962024, 299001546, 597492277, 124077650, 15668885, 872079855, 951281398, 18024194, 530476549, 612384566, 406675559, 8247023, 898250084, 676220298, 318961927, 510143094, 45931356, 76119338, 176286704, 15480531, 982570682, 137952864, 990188694, 67597889, 749679108, 848555512, 374621609, 376143179, 647146183, 28074363, 217473064, 564655196, 473381188, 87752546, 32657010, 762777660, 453004904, 719615071, 705495641, 998909920, 115908303, 516924570, 477599906, 94586530, 726190330, 523168466, 921348895, 922172330, 516466713, 912906705, 759509168, 289011153, 329032594, 96921050, 708528960, 755045531, 115194507, 822850914, 586168120, 208299919, 190642688, 892868181, 170624145, 35799892, 941742411, 485749786, 240795166, 905817355, 607681793, 670673475, 920553806, 975048916, 690923885, 441690997, 780847858, 788736630, 171943505, 701983400, 348282236, 211503586, 810780244, 190712918, 544514511, 975903754, 921513188, 362306988, 923883162, 196621653, 483661243, 174468907, 942783243, 978314795, 939178489, 218659073, 265787095, 892119101, 859481385, 909733039, 444461512, 886269581, 744203340, 952903509, 719165968, 841016814, 999950879, 471936607, 763991660, 112726002, 383332316, 27043250, 781325232, 718236871, 289641789, 864293592, 903684544, 163650401, 711524430, 256201745, 696959246, 955854108, 402158621, 501299438, 718596829, 76905028, 454293486, 966611147, 851369350, 57349617, 593964166, 458565153, 220729998, 987018413, 357042388, 640359970, 317429443, 979380972, 797784975, 354701901, 896632514, 642929218, 771280879, 784926563, 630536109, 967965944, 677958864, 752386364, 841836315, 959933758, 104877080, 914128379, 55342998, 604237043, 972432154, 925873949, 747345865, 106154381, 110660014, 670072354, 949728179, 303723822, 101661641, 85474390, 138891267, 39249944, 225569293, 128836686, 97195995, 663870373, 321658544, 428879278, 814112803, 316105761, 31292031, 668852076, 905827710, 270867335, 630306166, 141583373, 821563597, 928099398, 12794677, 360847389, 262292758, 552066708, 498996579, 181853852, 273665581, 523564824, 296757731, 992485211, 595877433, 79052667, 42303031, 966490876, 667378970, 136727225, 619567043, 620794854, 850321022, 540640679, 67913009, 365187653, 730047168, 580761409, 955584151, 631627958, 888730455, 266278494, 219104877, 464259400, 746093596, 96662340, 562946660, 481754887, 4438727, 615426212, 225773240, 156176909, 22037506, 421822928, 928827289, 508365124, 533538538, 615992073, 558055690, 552759937, 74028649, 357074300, 470952761, 945674506, 767247059, 694609264, 238975799, 135479685, 422523716, 112006141, 28804550, 145781585, 37997441, 375497962, 755976139, 941653936, 426633240, 314902398, 121109156, 886677873, 346868049, 977748602, 856984385, 435082620, 208360737, 205944349, 603182773, 400147422, 651741854, 62952088, 18417421, 985594565, 403320789, 991505889, 3525341, 637339095, 22980792, 750632636, 906426665, 962256145, 949070169, 10361954, 341747957, 174556667, 934548943, 429242823, 557833150, 57363672, 948630318, 49064502, 337149208, 78357340, 588635549, 9929370, 763930040, 271259289, 618019063, 868458264, 498230578, 921893392, 830449170, 983948127, 615479849, 118687442, 441060425, 599859412, 315367232, 950169798, 754841195, 445555709, 754384595, 869650678, 130162694, 253841156, 703319442, 156847473, 760415920, 998121587, 335471695, 694793882, 195476890, 815005005, 861262399, 358014976, 978914051, 717883577, 202220187, 431093928, 170817946, 620312902, 687593623, 446148474, 812812827, 51142657, 214238744, 880037640, 754252796, 54072915, 96225198, 353981733, 142211702, 719503928, 608735599, 806237886, 62057238, 397763405, 777277605, 937172315, 103711599, 726741503, 474454906, 561954030, 427332368, 111309039, 233848081, 142123256, 80069861, 739466847, 545714989, 56278714, 570554625, 8112158, 839138757, 249691108, 658209375, 705606932, 191770548, 627337361, 713954399, 648415810, 649592350, 804973683, 367097684, 907364094, 959306114, 679860393, 217896398, 798743732, 942045735, 725268676, 715606248, 867957437, 979674796, 917562475, 560359655, 512345735, 664594893, 813474264, 219726268, 344002660, 934661554, 994731282, 102922683, 160404841, 410541190, 150244251, 395155012, 939382662, 404543524, 273501162, 991679003, 858718253, 672126202, 744514572, 889269499, 249276312, 867678529, 376723413, 870574540, 219933673, 390306594, 122986793, 670072301, 882578344, 979203639, 417455294, 984817598, 321314105, 935464106, 714547584, 859995845, 426379126, 189542121, 773851111, 475689925, 782808766, 938684086, 942507363, 730820055, 292172691, 970021254, 285866524, 453931911, 636603921, 34145849, 853070647, 900232683, 478876101, 946168391, 220078461, 344556879, 653855814, 200995429, 589371589, 679533531, 246647721, 298545623, 728329422, 824353070, 483579853, 71287626, 437227970, 920427696, 210077826, 636736743, 436759245, 178966127, 192004064, 500250946, 784774087, 730493522, 610847035, 628785582, 31951218, 479264538, 246600301, 938321273, 248771748, 262262876, 859836310, 888555342, 291271401, 241221352, 251324357, 629496351, 663924703, 165322061, 162596618, 59715272, 701610471, 465149040, 837032698, 742590507, 678923173, 433429717, 992968077, 927851208, 59997829, 747147250, 873784943, 277102858, 518803472, 533424949, 534433600, 920979214, 813315487, 563894273, 697135796, 152063147, 281537494, 903566714, 22362252, 442840723, 467471433, 379341762, 291207911, 550030572, 900381959, 487086576, 503253731, 472982911, 975941863, 30400277, 473379837, 857088494, 842169310, 676816640, 997253164, 942778741, 560025008, 509899014, 933013710, 313913272, 334877271, 286479857, 189724977, 904825704, 603570268, 688848122, 879214851, 815284791, 419156567, 371899553, 812758572, 115467878, 927158205, 536534763, 729215356, 417804093, 823325439, 368360743, 277915247, 978073618, 110764490, 211055455, 730936074, 484029897, 444355806, 291381168, 446284651, 227537215, 806941984, 836824104, 262721827, 798174689, 70498723, 84266745, 748589659, 962559830, 4213546, 907144821, 543609621, 718657829, 205938446, 689375220, 400097513, 877613757, 567408903, 317697938, 143089314, 655749048, 216896970, 91228882, 464133929, 965501002, 224445442, 509614948, 66145695, 639981543, 613308493, 96334976, 269921917, 765109488, 177903166, 882648584, 37642945, 213479470, 103367486, 816273342, 355591405, 218061275, 74697203, 440082206, 967839114, 772387757, 929163971, 202310565, 180812295, 351104713, 303535273, 86689974, 518199078, 511197850, 93781531, 88106817, 633383607, 328997501, 992228963, 46189561, 502225063, 579074629, 679341934, 89490226, 671017977, 314985197, 600326547, 95299420, 963404242, 138589908, 996837512, 401432815, 517902661, 198210278, 316318092, 152597581, 773178608, 537646203, 835792407, 925039844, 702267026, 341925575, 596903324, 888707949, 981823195, 219926173, 735616762, 949718523, 819681043, 885391672, 24762586, 9483692, 996762248, 869733355, 675128420, 782279655, 735113855, 366011689, 738136656, 462947508, 105915335, 998891522, 378956582, 958015169, 415743413, 521768764, 473635629, 927134052, 276443721, 187820876, 815427096, 691115008, 899274445, 360867272, 238698070, 625873091, 36918325, 919678948, 350901723, 913092001, 711430324, 876810509, 110313493, 761507263, 103320144, 684719867, 437888702, 465896167, 937777566, 103898959, 477703323, 963407886, 419021263, 820873280, 638694960, 389598979, 534527013, 505910502, 414962398, 314120895, 122458253, 656029976, 344118231, 612067413, 477502207, 321338202, 573021401, 655749207, 70004740, 204397689, 328132459, 389318146, 814624850, 662709496, 170442173, 451739425, 163462063, 570240622, 245861671, 408306555, 879850186, 928773620, 594353778, 139237244, 941384665, 183849354, 449588055, 34970883, 21447659, 10990658, 996348029, 692496723, 630350438, 426024002, 775193826, 890679821, 700692839, 118414619, 240625974, 946750087, 360441165, 382785061, 81000083, 928723145, 561442764, 721218675, 293402409, 58917727, 32882088, 693063084, 412821544, 788187441, 888693910, 327889561, 863766038, 167679228, 134312701, 763346653, 110324285, 161001870, 506733208, 231611352, 627176751, 826229138, 666316193, 664743461, 875847240, 136646686, 692216306, 595338563, 967869178, 728597776, 299297814, 222709454, 950839600, 666624502, 687263398, 684751916, 502699829, 635787199, 750394979, 188329930, 168249110, 393721089, 752221703, 253782938, 807468741, 714114639, 595879109, 258064945, 830655717, 84221394, 768714982, 536570556, 843354272, 892783033, 342766677, 965607117, 633791082, 513404911, 415195228, 956825106, 459892795, 852904332, 437583023, 715441837, 804507633, 801954043, 806081984, 860852594, 922544748, 408158033, 179399224, 99761607, 288205887, 415706501, 150423125, 785961759, 670920188, 708765870, 621952445, 225422236, 191690911, 87470530, 118953735, 993962136, 113341815, 753753363, 885028741, 826510780, 328374344, 421529939, 686721623, 189613687, 273587513, 361659666, 229929958, 769764980, 436870983, 769015922, 604228461, 419887111, 568584712, 97353944, 458484896, 14961257, 489296542, 569246848, 862896047, 621329346, 200218478, 4676425, 357260771, 361153320, 633979206, 891207684, 499895801, 739626826, 5873326, 81765628, 745885761, 964614753, 552617829, 315453741, 63265651, 585575036, 3837039, 323359420, 36764803, 564839840, 350468818, 504336281, 826083437, 680393437, 426037892, 629750370, 310809372, 278046360, 486556505, 202174180, 585938656, 122761414, 916915865, 387708901, 126275845, 396601407, 185875939, 627345647, 1055532, 695749101, 623789289, 906945545, 125312217, 176331740, 98576097, 968600333, 299294415, 191427384, 959468785, 262137803, 534722392, 110521753, 239109801, 815798204, 827682398, 246709995, 420929106, 886718439, 432678589, 812921665, 737652559, 45655128, 75199291, 218050988, 697130457, 889148893, 468697867, 936032595, 166127279, 786162009, 29364826, 567793167, 162472462, 440423079, 117616481, 102245034, 435465143, 424448910, 644464269, 238112776, 1150448, 98375520, 191485577, 350997022, 462749766, 136528924, 752798048, 383066506, 645429798, 665239536, 887860130, 244205948, 525202092, 509715674, 436004457, 452968920, 111414152, 403708788, 341510984, 705204000, 200888759, 333049287, 248358526, 134412123, 930622329, 614516402, 868984361, 100309778, 751482657, 952352618, 448390331, 63354672, 351518634, 117200175, 239566530, 942840333, 102362295, 739293892, 222817412, 737540227, 652492844, 15399479, 601442592, 959856550, 621891953, 410960930, 784600480, 941214907, 852149610, 209076341, 901443065, 738961171, 852882069, 746616040, 522328903, 164875884, 193639427, 332151474, 865251305, 354510712, 60990897, 947593019, 612161838, 953404282, 719022791, 616720809, 834334236, 85692998, 827871060, 30179673, 847990050, 181084323, 478077778, 740464146, 824511460, 695882183, 742021661, 858788847, 607740157, 212069171, 985767043, 528250252, 465435899, 510084469, 823914029, 199963619, 428169616, 137022163, 982136495, 342146729, 82726699, 226193887, 817259823, 431242498, 198115446, 534084831, 894004, 737930351, 374533784, 831369518, 575397712, 661205283, 222914152, 291588721, 481039242, 762635299, 825829941, 503606884, 37819877, 506243883, 596298061, 330468561, 97115237, 108224540, 634384489, 809482672, 889313092, 266241145, 186527807, 294719535, 709549076, 182176225, 591273335, 676590350, 347641424, 340020606, 297111994, 272853812, 562114253, 877129234, 710329776, 724991771, 717168275, 526484998, 604400712, 965460251, 299721261, 4121553, 437250821, 398424484, 206817524, 215019923, 318057165, 639281877, 671419156, 15422262, 898058481, 74677816, 292780127, 132086598, 479781812, 610630540, 444384843, 999173276, 723846411, 267397376, 355197853, 394103683, 578120645, 793821840, 500729154, 271574762, 382972502, 37191934, 119391727, 202382566, 616396605, 790524779, 637791604, 224399419, 565818796, 61578057, 162634301, 388560677, 686467281, 879941137, 527783913, 959553457, 977777288, 365947669, 562233799, 520493388, 360961951, 3476472, 763984876, 219507094, 28199632, 262495023, 614345514, 564095166, 203382548, 683810872, 120485771, 805178268, 28912249, 106866645, 591241090, 673908035, 315387149, 971925177, 507590045, 23129233, 877152178, 743225907, 827335228, 298613425, 126700991, 516785550, 3414293, 909820416, 627154216, 652383759, 256169781, 329092356, 410971945, 557376092, 854896042, 12263521, 122094640, 302277453, 759982861, 59369622, 700233982, 572814639, 712248157, 61116477, 360252243, 247157621, 359173167, 777044512, 800596539, 713273376, 576652159, 341929602, 483009626, 840208136, 717825192, 90798496, 27639611, 192555487, 578486420, 140430203, 347266616, 609087252, 821286349, 281390895, 76092686, 690695960, 234345647, 6513694, 943405421, 745738839, 714898357, 409085773, 418645327, 448952034, 837571256, 255216581, 778814200, 731845986, 461964671, 226269329, 16053310, 381971257, 191245879, 795527579, 411451630, 940604212, 86068770, 189102845, 635110777, 122303568, 450743368, 46930676, 305585499, 319152285, 674524200, 6135764, 965075750, 685410354, 606112241, 457905622, 924335279, 851424627, 982836600, 704606474, 742119041, 879980591, 138699944, 298297380, 600456108, 443781285, 30443803, 988181923, 15783530, 320602935, 785914527, 485881927, 275561110, 877603071, 581286531, 598221136, 579807505, 760263804, 982868704, 263821060, 319472540, 378580143, 296178657, 968863101, 954617275, 133430121, 726772663, 199597548, 432437904, 24257103, 969984876, 426343879, 474048568, 496306232, 53799975, 560149022, 841946987, 693687948, 435854033, 133419004, 595439259, 571846218, 644710028, 643594930, 336705711, 236848483, 527037955, 224204384, 344737530, 838182377, 745248020, 471492653, 406629024, 180012024, 158107512, 856621979, 265363247, 30852015, 197488143, 587696658, 463892972, 833569716, 769405321, 326869948, 289202166, 670604778, 320481860, 584280446, 967717867, 193067945, 634082337, 238249639, 811686145, 979758375, 950455525, 621222664, 336735423, 324769391, 654905435, 10070377, 761044484, 626227801, 227960812, 412184972, 152828804, 876143058, 440739430, 434195193, 667482661, 489569423, 907671662, 530628591, 413169422, 40615269, 831947853, 695451934, 973845206, 480345590, 844013021, 510469850, 981995842, 121370501, 529349898, 935373161, 25117315, 712290153, 916874554, 901279438, 749382486, 797233158, 823692249, 756113809, 621514363, 926039436, 447885975, 204417677, 933965909, 973405823, 275635586, 979816036, 520115213, 219935302, 568425842, 26309050, 511350399, 904530007, 255279180, 745287244, 346847877, 110844207, 389651155, 483703625, 468423310, 185556840, 699273069, 200594692, 350601250, 57381625, 784300852, 883614960, 195709988, 631922215, 859694721, 743815722, 492100104, 792573585, 853235652, 181120507, 80749209, 616794329, 857530897, 817108874, 898951102, 581576213, 772949266, 30499388, 68934610, 389475443, 457519422, 616210534, 961445686, 403548000, 62696297, 36696583, 784620585, 368655599, 588230828, 935921384, 414997257, 768463998, 7816471, 912052576, 653717915, 364442114, 131201977, 896412506, 509089687, 22941034, 965270662, 237597715, 40881418, 292974501, 136266780, 266383853, 669199787, 803902743, 223257880, 13329290, 21584846, 658982596, 214589913, 590466660, 641327362, 624258944, 746510412, 418869563, 177941643, 470193946, 992712101, 830240502, 250888846, 151827540, 749136230, 722540562, 372405325, 937164499, 43093095, 965762008, 258039608, 279945269, 94221174, 971174491, 773025914, 459756949, 33184361, 766999865, 88946193, 880818674, 599033506, 421591434, 106710740, 275680290, 224042177, 378426033, 320356444, 51545155, 647873567, 846663386, 653534285, 158259112, 55604750, 186378545, 359511274, 152493942, 511784538, 112960021, 522363035, 399011444, 923870420, 691559349, 151485228, 820400389, 779352497, 413741020, 19197538, 78160588, 701440870, 176729583, 967341, 570208835, 49240616, 682683826, 211872950, 493672631, 495143251, 86421893, 872314624, 495181671, 723713724, 441113982, 210442324, 623429215, 353676778, 770008001, 85047098, 883404015, 305444435, 264808359, 592461705, 933271872, 315501657, 647751237, 281333086, 61315511, 922139431, 31415644, 802409868, 814701266, 201144475, 655316283, 81113354, 413887456, 804515583, 771018449, 610624833, 872345424, 521618265, 128902190, 859583167, 176959220, 671423223, 715069725, 131451397, 627998566, 777210888, 141852871, 812042267, 232530532, 264737202, 816808228, 302436404, 854703638, 368125244, 248497781, 291413702, 838597242, 343398560, 178227298, 685413266, 115702004, 867356014, 663647233, 478548243, 742047808, 710427097, 491385328, 409447478, 359639822, 847342330, 768907152, 627818004, 68610491, 774359234, 268551118, 155917102, 446206379, 924600916, 400185468, 668077528, 93527409, 703493620, 860575941, 474680001, 10347446, 973885746, 475575840, 401469706, 249155220, 162809374, 484778174, 940552325, 459664561, 333119165, 902627147, 616143686, 936377137, 972511675, 848960407, 132552695, 348594150, 398355634, 357787691, 291989444, 545368878, 195942413, 19674745, 729771464, 192556847, 752234221, 401467075, 533124473, 648422867, 113618822, 657094334, 417876121, 455088890, 686243711, 668423178, 212195748, 750816982, 303685091, 673534046, 682471328, 608340220, 417328952, 669072761, 278548947, 989866450, 579029450, 315547445, 266737317, 627211858, 281219388, 643679438, 667475441, 801864222, 346465291, 730559786, 81808942, 662746162, 879477005, 594612010, 301903374, 104738216, 4101215, 809797625, 148850533, 476199040, 821940126, 970604379, 821758181, 498203029, 920731722, 293812346, 63265251, 90474377, 404110113, 949453759, 518471143, 596969347, 352121977, 486554473, 486073996, 684063923, 85414078, 651684997, 173926711, 755949044, 752599059, 857300388, 169655686, 144306338, 778903576, 735205791, 564282235, 684916879, 205401736, 352670619, 42081257, 287847989, 34414580, 683319236, 505753935, 774314763, 463678296, 958389595, 231525131, 950525665, 937732251, 923851414, 306633455, 931969972, 381183704, 18524608, 483059263, 998570168, 268696559, 556978884, 375570289, 681052451, 883504198, 310581068, 919414453, 620602082, 934526066, 397114925, 710034782, 717604815, 251569948, 419762342, 855054959, 965192888, 136164262, 400690704, 450633631, 126692513, 855020039, 876317490, 47296242, 418876743, 336171445, 718962866, 629849054, 16968833, 334912074, 525073374, 316553216, 423083611, 7215827, 618301642, 163065864, 1075207, 165808851, 573707257, 164806142, 345395530, 253786185, 915058696, 920907565, 617713286, 86923233, 310868066, 832905836, 899490966, 306187641, 577883970, 314884563, 784928510, 905201853, 963335959, 296164069, 788225983, 43798654, 776922843, 646318915, 992244501, 227485389, 53472301, 331097921, 540415677, 948614384, 921314872, 374881488, 714992804, 266019341, 577120625, 118653284, 745297419, 445202716, 485810842, 515553401, 641544480, 168510497, 115838137, 78093747, 424110535, 699256044, 135420016, 932125672, 206722525, 652935426, 668544864, 15023353, 724945676, 576431556, 74391421, 619457924, 878923034, 329491357, 739380600, 51742849, 202909774, 364989586, 523033523, 597120235, 271714665, 746078927, 992176060, 295979376, 347529659, 283155864, 721017476, 466230220, 21034694, 702341290, 937140868, 333861004, 853549762, 639998705, 669684665, 542744079, 503978634, 728549774, 618126193, 365008114, 343282436, 769942887, 282472267, 6386475, 902705771, 216515063, 994556837, 949051677, 393422935, 704342403, 22177374, 549260428, 679440516, 441522290, 493756409, 57623235, 697212428, 282350173, 569297561, 463026255, 447008256, 59145465, 362804770, 888638931, 862897194, 629237446, 655673448, 859768511, 303129060, 860796038, 579687410, 157737925, 388834454, 699606254, 411837317, 564492247, 867553484, 569172369, 221903692, 700380758, 995731649, 559972310, 336938130, 603445495, 478668667, 552777207, 237807812, 989622865, 453476272, 667776644, 150177424, 279717521, 34207614, 546160730, 669533326, 824304694, 870182237, 839941464, 576812560, 777948891, 944831940, 966453788, 550783551, 288805169, 44198653, 325806945, 574764267, 627732266, 487413215, 848584916, 971961468, 398983188, 371444621, 382067255, 180005846, 262337358, 223194541, 473031270, 335077882, 708610197, 458068983, 985271788, 71472647, 461665960, 376142348, 646578021, 867343186, 652046478, 123812825, 689557189, 151911264, 509154146, 796618129, 4568744, 412438596, 649149392, 389906373, 828870151, 8623064, 979994837, 193568238, 413275392, 332599200, 782034714, 98434610, 592613075, 288409416, 620075098, 72937373, 638347599, 833386631, 207075845, 294701062, 539808846, 236883690, 490393627, 724353053, 185987829, 325933159, 521643582, 784510831, 17071048, 848118802, 312009207, 577269636, 358144276, 937073256, 850199619, 599675734, 240358999, 228910212, 896729588, 557241003, 285280444, 668937175, 551434878, 941081973, 305414637, 972435963, 628538170, 841975964, 465588734, 558716017, 582671687, 89899346, 345016963, 650687927, 773402728, 631001968, 924998152, 776204497, 369492707, 515117725, 146348233, 774947688, 679867863, 167981706, 459932979, 367285328, 503552207, 485147934, 404840498, 359771844, 93599110, 617445249, 37769434, 798201198, 295435412, 23732959, 791546950, 316995937, 265716619, 494237641, 143036528, 33864696, 694443843, 23703356, 839883197, 113242648, 676802920, 203081146, 230190366, 167874479, 781275348, 753876892, 365104668, 611541808, 435271817, 473200145, 135937636, 495844451, 853904708, 678793574, 191792005, 831049649, 231686547, 36579778, 315288521, 579562673, 90034865, 410000717, 378326594, 706828137, 700301463, 207220247, 313419761, 65003266, 98472935, 441378355, 387287004, 160345127, 10992913, 145440335, 575311004, 801864840, 492022229, 168183067, 119627628, 676017352, 247929786, 92443145, 962528798, 67652271, 2782948, 471008973, 743494005, 590881866, 488573949, 555779404, 918843669, 498861779, 274883227, 355821144, 536713972, 235438440, 392859820, 120537286, 164357392, 827126974, 735866473, 479183788, 709550917, 582739837, 909085062, 541885754, 595730333, 151879789, 51640444, 464181725, 581721644, 29398405, 163962466, 603042909, 752177839, 157905803, 821723137, 891679061, 527819101, 289448451, 467480652, 838847793, 457338304, 680974052, 215610178, 953486188, 740869321, 93111848, 481175621, 319592023, 15707291, 732437660, 56275954, 324816938, 262417274, 931545208, 177326779, 997124202, 612919534, 168792252, 274941450, 144269937, 767413396, 680990203, 432662102, 692241708, 605656534, 527838492, 410910700, 319142498, 525167260, 331838411, 838265544, 658309364, 757482586, 353157162, 110368781, 78596857, 362356794, 785242595, 35504621, 122578531, 344402701, 345485077, 149191505, 386451140, 970412644, 342571611, 667736864, 57555101, 710503010, 438079984, 115607637, 703536129, 339949083, 309503396, 459615244, 986073848, 64415369, 374002807, 430349049, 862421963, 238621854, 511209246, 630322859, 858464078, 306844265, 673125097, 238396138, 902584257, 393063133, 2502222, 236294330, 473811270, 468285893, 935611184, 423695165, 224728791, 888314602, 22896725, 814983423, 621820397, 343578945, 452109837, 846161603, 828508614, 565745464, 40252130, 978911081, 511483435, 191720650, 859512025, 925088769, 931080397, 161554475, 917927973, 801296497, 795447660, 994197801, 541465311, 580972157, 970368003, 966462147, 76106435, 991668931, 477498444, 76827912, 928420839, 959262804, 849069004, 584296898, 706367848, 519660888, 399156517, 665635812, 940465324, 226046988, 438976703, 949342456, 313972879, 859654743, 943565247, 715042723, 440131487, 682614431, 422232328, 982842039, 845564688, 568167641, 301253146, 624319448, 574014003, 243813507, 835827117, 341442218, 117491001, 893149486, 841390999, 140866787, 248519229, 738377228, 118044386, 140719131, 23450971, 209017701, 96784003, 770636562, 644995529, 54970505, 790125981, 730204438, 199491774, 3258039, 577005729, 122763546, 853632592, 796641250, 908985127, 812988144, 669630749, 412388323, 525548769, 71966853, 813006349, 942778610, 517088913, 551545067, 988997316, 305894653, 615545100, 839329871, 86016129, 299198160, 438956336, 44733576, 439923975, 110748635, 454335043, 500989708, 111145748, 279025120, 749207540, 333964389, 50892035, 289073747, 691567511, 317864233, 172925570, 22965653, 633514871, 550839160, 791781502, 319522573, 66786956, 332879056, 641154525, 450081221, 749668058, 504722037, 327053989, 51743938, 559397071, 894075432, 243568307, 215859800, 589652984, 695216154, 669000824, 882069141, 390427855, 997159193, 959872750, 859423154, 196525804, 724097989, 518301928, 14201938, 44425977, 482469294, 419009256, 82028559, 59496493, 853286538, 106776229, 119396278, 324752744, 383966770, 81257296, 694990874, 50951612, 99520816, 959119103, 801880425, 329222465, 159091500, 830385499, 521455197, 80971362, 265059921, 548604676, 664057066, 294642230, 144442633, 699459133, 50819187, 760803740, 965321474, 334832318, 498378553, 722475798, 994569826, 786107215, 465715306, 589519407, 640538447, 487159326, 12214561, 388736403, 370650923, 437357334, 888039483, 815984930, 640285414, 659821143, 850806132, 72501798, 965372444, 906579256, 508683312, 640866096, 962863352, 948733411, 956802136, 31828834, 261284334, 549570833, 566893428, 767918577, 32805892, 549711747, 110238278, 533748161, 975301984, 47874007, 29056339, 732020756, 908851535, 346182537, 522107291, 173521838, 128122186, 520187990, 658188120, 227569880, 366761456, 592424459, 16492909, 634739521, 203103919, 764245707, 133035546, 710482850, 351124238, 426289714, 920114903, 173734835, 548707109, 458984696, 478012087, 368880625, 44055093, 296267699, 554036948, 932902362, 614278564, 341475952, 688892926, 888994813, 587590419, 320160974, 344402847, 926967710, 635060506, 720320153, 124852345, 209559764, 64569748, 261783453, 620852435, 785357714, 294530471, 608499365, 148563570, 549246234, 100035834, 222503964, 510855957, 429573343, 752753274, 857756060, 7021290, 133412306, 439874602, 209989451, 184374539, 700241927, 777507743, 30194789, 151033894, 279944650, 963791042, 528889298, 280067726, 752061252, 497320215, 966708203, 306983547, 560988466, 250455587, 248821831, 231438973, 550047005, 558210844, 103069061, 406602762, 106769766, 892464708, 78038689, 160956713, 890333309, 469801988, 478473452, 207149009, 635056549, 373967301, 218809956, 945848398, 765572084, 454658612, 692302438, 931240470, 646451551, 91494328, 581819678, 421999213, 67360447, 774608685, 890067814, 237961423, 182997236, 414641840, 896936042, 570957840, 713358389, 277368599, 98667755, 981424262, 365923927, 788026181, 806143458, 572455558, 733238088, 969717276, 118349796, 187321877, 859384678, 726704737, 513596102, 588431076, 987922655, 907844750, 974088810, 128804351, 805331946, 283892184, 437322355, 371200510, 32245820, 178126591, 337565251, 230301572, 269725702, 781599984, 805713692, 655043934, 526526140, 219243449, 992492231, 531130176, 824617488, 359815480, 44206408, 184914429, 626191415, 354255846, 496269030, 77968342, 328615631, 224730246, 799419738, 346808608, 210132056, 490511022, 164261473, 10648979, 267037153, 131693136, 208514071, 541377371, 884891316, 424223421, 969791300, 114510414, 734719372, 572015004, 986525255, 92114509, 329166391, 435026189, 840585464, 620542954, 132779256, 39396256, 858237472, 540019993, 459983936, 92832078, 249302052, 616265392, 643463550, 737811644, 869448139, 965729986, 659140107, 203337976, 907265125, 338731473, 381838266, 186436618, 222586861, 323999573, 845905485, 130412289, 529868069, 75490879, 199149683, 482859375, 213640502, 445948786, 669294687, 574063603, 751602207, 50949007, 714424035, 478452521, 33724444, 1601155, 532607961, 306460360, 194703765, 196315540, 686905001, 212298467, 92030781, 570724085, 735704964, 104312386, 701600687, 131103481, 969920519, 529071945, 916587928, 641310055, 79073863, 790761278, 258616884, 755038306, 606634202, 8779576, 391982322, 475148123, 438635542, 759424648, 507473744, 355395573, 517945320, 875215171, 91878504, 40809635, 734671093, 494773981, 439612833, 863380236, 39077680, 700185201, 948619484, 363284779, 803164266, 759834299, 131165800, 488760616, 804988377, 369652917, 494029072, 849474432, 296370813, 514790049, 422023247, 998747115, 582110107, 27010693, 574347699, 744942685, 219688794, 336532494, 780305517, 460307446, 745844234, 830950020, 210951929, 751373215, 727365082, 820981658, 170332118, 696993417, 873296239, 461644371, 699345045, 498101052, 34161695, 358016493, 396029463, 605356149, 677840312, 61128842, 91802163, 307977414, 335434207, 868550723, 87713905, 174671568, 541568517, 921629981, 640096498, 330031514, 85737678, 558748198, 35001053, 592175879, 735479602, 260680640, 53496209, 517165910, 453184974, 852636222, 470233376, 722862294, 627313042, 402972092, 538562107, 458184176, 422370703, 186208170, 595616246, 436574194, 244947561, 288934682, 355232004, 787412884, 557000686, 711514848, 995570299, 282033584, 869401509, 774030150, 476865262, 817445194, 108587979, 33987950, 219092864, 446827099, 788625983, 979026891, 608091881, 249954965, 78284886, 164124926, 571415399, 191101167, 61317513, 193457890, 835929888, 815599674, 300898437, 897307866, 871702812, 734140593, 646565137, 394376525, 678320016, 662659796, 904717525, 45342133, 70523240, 945955029, 156012335, 2796798, 371298171, 173570521, 426419529, 883690501, 198793015, 708795735, 753410378, 17542464, 968744483, 618523916, 287745302, 726615472, 591447062, 995606702, 592156436, 370379639, 974617429, 922912905, 407493590, 534468676, 353446104, 548319171, 119597317, 380130212, 859059682, 443604174, 12700352, 285721481, 535493163, 822632136, 626164151, 729490892, 302417303, 799128993, 917003647, 46556003, 253924807, 532822461, 442766986, 832081359, 277207609, 379052629, 889642935, 570262057, 142145591, 745662605, 920694408, 699958585, 781744946, 521887853, 972881705, 958438140, 23367885, 376524222, 522901848, 644250382, 840572824, 40015390, 928435382, 879118414, 258314089, 226841716, 101042852, 534167953, 562081369, 759522923, 900836557, 689541408, 538908033, 998743026, 847639402, 96049415, 100025463, 258613570, 439125941, 345255417, 370619812, 983325901, 871435262, 398776259, 203959237, 48143237, 134400476, 30551141, 545932847, 800464613, 319919779, 555973668, 356623889, 209007574, 390430048, 414042037, 383243871, 179518390, 113556985, 686104018, 107040874, 622189547, 660329790, 574292719, 45730729, 325390656, 472374377, 255791376, 747621202, 534093133, 147423325, 38315311, 245837367, 261301413, 452504653, 984538037, 860187130, 181890005, 880540657, 214677303, 849387596, 717210697, 464025290, 534587110, 309380390, 368589468, 869288404, 811855206, 65119105, 880755938, 240575203, 65176399, 765153462, 738433609, 960734211, 764897064, 928097220, 134721712, 477821874, 974697906, 368566327, 845012441, 852965573, 653242097, 444064534, 912704601, 297155504, 629038404, 451641347, 50872048, 891936763, 674863591, 468843785, 342733268, 192556441, 631601159, 593402103, 26007601, 46555526, 70803737, 707846274, 745452044, 283920639, 505538881, 400045627, 473706610, 112275084, 281374502, 706183358, 637099724, 769106495, 484137169, 652165978, 554892606, 114514482, 939779287, 70529017, 787007427, 99480054, 117834675, 170606182, 693456877, 158281240, 136801763, 776294419, 252147475, 619790228, 890821306, 30161007, 927157855, 692413430, 825132556, 361096336, 423219191, 495304144, 986786824, 718780867, 80021704, 28981806, 603155175, 260517557, 919835092, 344769522, 108232521, 170599180, 777242601, 210851014, 868775073, 43074612, 922754729, 919768948, 256274597, 235579331, 997058157, 154272837, 350018944, 794296217, 664016174, 257027053, 645100144, 854338482, 715415036, 838851900, 270825155, 473377109, 350420857, 17435464, 996664054, 669077448, 574448862, 785286450, 448296915, 854683307, 59204266, 13391360, 537686223, 181620550, 866074633, 11478569, 237121534, 464044755, 975625949, 840889816, 240239552, 541332164, 309728374, 837125904, 987260071, 978682680, 999318536, 301001775, 319261801, 224351803, 49091759, 509474791, 31334807, 708372791, 266581328, 592345504, 142867035, 847567633, 530494242, 687272254, 652645884, 933888555, 426295218, 842827113, 859167385, 676684627, 958687774, 833468159, 808658996, 81307578, 39952996, 263423017, 782971821, 91937305, 654563565, 24827277, 728633847, 550510200, 467532443, 591277136, 582157643, 886637960, 422420649, 288213581, 161490900, 825266032, 646758282, 686717702, 89461817, 914225540, 754835256, 960246911, 553925886, 144223510, 829340143, 470875435, 794498298, 832889198, 992812818, 984256304, 408755673, 266876245, 280766153, 10838389, 15229395, 208493226, 893519503, 358813862, 556305670, 221729844, 739558746, 225737295, 697090365, 773902344, 798552680, 635141295, 267475332, 456394575, 582807274, 61977547, 458083681, 697519998, 676067630, 865869404, 591333657, 469407, 47967297, 974410003, 532367419, 580151069, 57772939, 827030482, 651322250, 25331599, 523872325, 273183619, 570635712, 22472034, 32679200, 90892752, 572987119, 259284665, 162843774, 223277148, 596832086, 215927330, 833659230, 805688288, 531058356, 339534624, 359274332, 622540222, 528380779, 837432395, 348865171, 857943116, 117519714, 408482423, 637892835, 885545998, 306290376, 998503416, 350017167, 968820485, 380077490, 319787465, 293164593, 79805546, 872065018, 266922716, 187367971, 611732402, 169944317, 877109401, 918287345, 358577272, 509791195, 72714174, 874636587, 408938185, 588190484, 230492761, 767659766, 814072214, 836264015, 522111111, 92041971, 208100730, 5188531, 633162118, 711744201, 212705674, 746927221, 369084481, 571687968, 4019929, 73079793, 54931752, 255155009, 778647935, 287422051, 995461431, 731430867, 958107880, 601441669, 944339053, 240696120, 479987465, 756941107, 938096993, 435497167, 251342999, 47246590, 380400, 378921561, 678923068, 683457248, 679514373, 901206652, 916039659, 810320748, 369906007, 993868584, 434341713, 854865358, 680713924, 43342374, 499225667, 956961644, 547433701, 289242508, 500016522, 44796830, 784669690, 36113360, 74383380, 834075697, 998787717, 898032937, 990154921, 379217430, 809625720, 246056730, 698456930, 531876987, 372384730, 177578537, 306449710, 513119607, 787938784, 161829180, 763801983, 512158397, 656241652, 581992132, 722595766, 700630403, 580595237, 797076394, 840625597, 970685368, 49383171, 515297114, 576192084, 321698959, 57626294, 449469962, 479440025, 977210597, 528390046, 981426903, 387858787, 708356026, 68012653, 180640861, 563241786, 336836569, 413878657, 464869512, 454087798, 834989022, 287882084, 851018684, 920614860, 594521346, 890768355, 289010105, 117675677, 382959620, 477319870, 949587082, 770300500, 915793429, 833572249, 388980124, 572480195, 807805052, 827816163, 958302306, 797533982, 759109030, 509277516, 705741451, 550443145, 928381964, 882808312, 380659138, 659301351, 884584130, 758714167, 998176086, 540304443, 691657079, 664994969, 569135367, 975378833, 935863538, 515599337, 755959900, 524853352, 705271236, 700041070, 94838429, 850696089, 113103298, 955477193, 736798537, 892350421, 811929810, 377335308, 997512563, 743511607, 901712099, 866292899, 27096478, 426655705, 813695378, 841389237, 514858479, 868720486, 941432213, 224705509, 470005716, 771211542, 140634430, 315431649, 336548574, 203858814, 751709864, 82463757, 481361671, 433670277, 639114445, 576564016, 358298526, 415947170, 94003859, 930161607, 376482643, 434737576, 752341099, 832707648, 227701622, 554616294, 895762186, 73491673, 133267170, 281043819, 497820687, 593945226, 692103083, 456176270, 809562899, 831301673, 599139760, 756716925, 52254788, 696429417, 55273092, 639351466, 510165885, 838305699, 14442966, 117118820, 571131481, 210618876, 681682091, 728552829, 802875248, 727371674, 397320828, 678914573, 399387193, 250115586, 667927139, 554580202, 651272305, 362806533, 830279391, 586301773, 842953832, 223303780, 402454635, 1957989, 961849065, 609805299, 269565002, 95923760, 255571054, 341964075, 951811059, 43092861, 838728270, 585814105, 117466642, 111030447, 638106714, 219203917, 86669764, 913432587, 823999304, 955335667, 47391280, 138053297, 268514424, 8186490, 121459210, 360223796, 634764260, 679535853, 391199104, 567774705, 635040566, 675376897, 741874494, 109940387, 189975501, 284572843, 157415623, 923457481, 851696722, 448814349, 689952576, 829107027, 213533426, 54423502, 748083865, 93338, 183922555, 758026802, 640028942, 790343742, 57834125, 600312380, 472269866, 320101221, 377116351, 436664033, 767214359, 884418428, 690553882, 644951348, 508403073, 668228769, 284097989, 167753562, 351372558, 146800885, 119824166, 864429130, 10193587, 913887298, 377339015, 795831102, 786315516, 787856480, 586738231, 343568630, 784957942, 550481868, 659888747, 385902891, 747261261, 436991539, 549302297, 582002497, 729534417, 731425066, 186165595, 803556665, 551771519, 767065771, 911458263, 433296785, 113864806, 221398332, 402550953, 40548491, 683569572, 237638425, 810057684, 522945349, 753799508, 973577586, 880307509, 456878498, 595893812, 179845945, 961902732, 832621090, 868877873, 222024783, 274806570, 120963754, 84521158, 914482996, 757211155, 539294915, 586097104, 244025255, 996851551, 147543102, 479409372, 906962161, 713479530, 796684339, 380549933, 920097425, 504095758, 610683394, 105454610, 583865943, 318824357, 809508039, 509815016, 610266369, 329810726, 95894751, 423707543, 515616031, 795729321, 518508231, 465692459, 342780805, 104062168, 159337719, 259265016, 184608525, 181252567, 783972339, 306170482, 391063340, 676800496, 234782279, 363016993, 229870973, 928563760, 818336433, 648249217, 32991436, 702097261, 991285271, 739472824, 72055906, 172234248, 104188538, 309100839, 591253223, 241533998, 913541312, 785436237, 850720035, 604049965, 69842566, 439762486, 781242529, 295133609, 176748170, 212906353, 163622726, 487922345, 397834479, 117550594, 278305327, 457102352, 173727070, 968750663, 367429947, 249837036, 517617342, 870288661, 297663274, 546369669, 512231212, 833565086, 109648972, 235278883, 771075087, 596226665, 836320098, 614786262, 608426600, 619969523, 417038902, 322258542, 84168929, 627371488, 513614140, 304964475, 952171318, 171930008, 455213495, 813680632, 171794508, 7126136, 484822638, 359333654, 763161418, 133959538, 544955635, 610183221, 689988899, 539828851, 743877649, 898230760, 396401733, 259791890, 385320421, 294072315, 491331815, 290771070, 205333424, 335104243, 248120206, 747968326, 412943120, 700441562, 336302668, 811958826, 179362179, 49626176, 190364478, 177469636, 299822140, 566544731, 308355711, 183081548, 251881558, 813235453, 713246378, 777441853, 173017390, 827927713, 616971844, 348771420, 528448639, 829144136, 2020721, 667032270, 483854423, 605824058, 40732549, 20519761, 175357414, 983060023, 713599754, 923079969, 375075366, 585612747, 434468748, 619187864, 201691076, 25158769, 498528215, 927519352, 514250265, 921864954, 253530107, 743969478, 219227564, 525076051, 113513371, 651078652, 865802432, 991744699, 799478070, 666436638, 771881200, 710911994, 589194115, 873936611, 234038077, 502208452, 825456155, 506463733, 697447995, 341737431, 240385641, 643678554, 777199240, 636196770, 299855467, 199344949, 943657945, 243034395, 807122556, 630620258, 774873345, 260816137, 998370121, 216164020, 744087290, 513852598, 371417201, 168780032, 959659758, 113515888, 530423322, 659876021, 800392972, 675584446, 864373946, 473893313, 538524914, 126320973, 870993273, 169911107, 555622277, 808638157, 847495791, 425909832, 279267551, 667006867, 568103850, 952359827, 17414912, 118653469, 518778758, 164168856, 990733836, 277594312, 579777016, 83297385, 289430044, 583499276, 685269217, 231441707, 97643295, 399084790, 642521549, 476560354, 831597276, 442687724, 476151997, 400944227, 57625914, 600537531, 928918496, 645837153, 469538850, 74832071, 836576052, 369483636, 720391512, 762415508, 633526306, 481002549, 821608297, 537581429, 791731313, 411898499, 732965328, 789171429, 539254999, 127155137, 123507524, 938131560, 927983478, 472448003, 866178388, 652411071, 778767043, 463253787, 485986803, 160623439, 601782572, 456420353, 639274405, 225301328, 482124132, 945820985, 494024602, 983396298, 456784391, 198902017, 541571961, 195295662, 260623354, 961412244, 996665372, 135870594, 943518691, 186613738, 291273764, 145767780, 192332498, 10146719, 743978966, 23978642, 322113505, 670122736, 692109117, 468871061, 819721732, 847057593, 131113606, 661773050, 898593085, 698823924, 789585532, 477477867, 475233480, 546459996, 21155250, 454684391, 735499859, 377812990, 625829899, 820978298, 734332818, 771965315, 219260118, 753159774, 573480545, 864211056, 902726107, 554875251, 277578465, 630206879, 43140437, 457026683, 389626525, 516551220, 163478315, 88307572, 246811592, 928503925, 137428841, 529521438, 787973079, 438015832, 101230944, 253915104, 453249045, 332240828, 298765357, 297811259, 100543107, 345523047, 544598333, 306390480, 252010735, 265557618, 705367556, 426093790, 481199811, 11887082, 956767985, 914939898, 342304995, 904977065, 289789012, 311407154, 325714209, 58906922, 592712222, 946982581, 544375311, 60985398, 303620877, 433530042, 588284925, 266282306, 426296131, 206275292, 900587865, 383691923, 30653064, 247570093, 921539313, 442447378, 739282390, 742805953, 69475946, 762035486, 397386310, 193790143, 690787313, 214214253, 418827472, 557206375, 618323129, 310873620, 425079903, 495428745, 276125259, 346859500, 673547135, 98513445, 978897453, 473723837, 449377163, 414461438, 929743929, 587316159, 997255169, 654131058, 154296012, 73850801, 341025863, 62531789, 987676791, 548321886, 451941473, 815881952, 723801484, 555271202, 207947624, 803492398, 886210115, 883702861, 671688048, 241113965, 957382680, 644028355, 283189088, 264249541, 816037102, 61736396, 273547168, 364059628, 527769840, 132965132, 120787025, 865126143, 934343154, 59288859, 88269936, 627438160, 590655534, 360265228, 323126529, 154366562, 363578336, 61191023, 347880708, 553539122, 48465362, 452568422, 556258818, 539537605, 825787608, 844402385, 714058909, 46953840, 259716867, 737827018, 142944309, 914059328, 359615623, 445866473, 895820641, 329569940, 166434152, 338527689, 574009253, 58588095, 148891667, 811846205, 26302066, 464531611, 869044022, 358973023, 758997138, 23735332, 51312855, 136766648, 88254328, 205339132, 437856190, 271749049, 991492432, 201240569, 801237850, 604361170, 569877638, 740467967, 976698140, 970922428, 488914391, 694366818, 459312760, 61262524, 394535148, 929557763, 628105754, 131145744, 471510212, 882755064, 401421829, 896247667, 509294963, 630183502, 513643480, 652351247, 696174059, 471315985, 789521966, 307638898, 531351174, 155202288, 451652619, 655062564, 857784087, 58325092, 203246922, 91821522, 529842008, 477659777, 139560895, 710499923, 102925640, 104538792, 545842861, 345182187, 837501801, 650134856, 364998317, 87348119, 682788968, 86939737, 340591252, 86340719, 36821649, 716050927, 116338675, 691314967, 425421799, 608518731, 441002908, 326255013, 624272601, 935912556, 117111197, 33254811, 569274604, 810383453, 256558842, 496867703, 801802648, 495044743, 897780493, 235490261, 437394130, 811375926, 362888943, 829965481, 49409333, 241200774, 804885617, 382185342, 273950174, 647253803, 84539474, 183254988, 252343687, 286342134, 506958482, 7390900, 298830821, 138916273, 307039102, 171720097, 292841969, 155062612, 117130804, 860458719, 448654521, 719463856, 582690640, 698629914, 622936016, 163937198, 34805736, 664356567, 69931922, 618731192, 653739801, 19245446, 698050560, 802790548, 653085486, 300277502, 948220979, 207382921, 62185198, 300684474, 814766104, 986458949, 583003191, 300044312, 978805693, 880953429, 193102062, 883356026, 884686904, 452830167, 753240818, 58389120, 205088257, 392565975, 568105616, 648117105, 405028614, 56520106, 464958847, 200260991, 277425145, 648540072, 162076059, 133550200, 299357569, 122541343, 526819942, 210095317, 592968108, 705252281, 752096525, 355859776, 333052326, 11877383, 522040027, 676379929, 859359595, 472518811, 598996598, 643821314, 751695843, 516909694, 890620436, 635254831, 453632946, 388615982, 536213330, 340942560, 120399732, 304484611, 60328274, 812699975, 132237731, 205935962, 982193444, 359796512, 554661887, 794050566, 141407647, 994942633, 550901469, 393005957, 81480175, 662482413, 521137625, 828972115, 41143426, 915224670, 346424486, 29275832, 732615479, 523111481, 236309480, 650427112, 571393529, 813007246, 815902671, 538451937, 634313066, 878455381, 280412050, 229005131, 313045486, 960908331, 473063139, 135153576, 365934874, 652996131, 166661697, 681557781, 322168, 63945311, 223754680, 432269577, 265944615, 113724324, 441981293, 366994760, 699358809, 594770959, 133210546, 897919269, 709013504, 848027968, 747596872, 680105254, 558138361, 962637226, 858379499, 68044369, 420709805, 882430047, 378223100, 196397055, 530838694, 433978674, 49609431, 140556671, 996916679, 71720302, 811738530, 585872600, 514376782, 437811587, 528872300, 603036818, 795726182, 473778217, 130596837, 527041760, 458778341, 189386855, 803213980, 346672636, 157566088, 228090858, 73889857, 636094370, 902549649, 528158757, 62499720, 204424153, 288421236, 75849298, 960633381, 283838932, 990229180, 601739599, 600429032, 840446709, 59439328, 354178094, 399462825, 716426394, 893605603, 854696049, 544754960, 447425694, 937249152, 312149720, 232392822, 567231165, 876399978, 420112666, 545960236, 292661495, 501763732, 480508643, 338332138, 316826722, 284346796, 737164862, 267518927, 416167368, 176465791, 838256623, 195111176, 997801822, 607226666, 977795764, 209111414, 821514105, 636778007, 834241271, 870462154, 655991146, 892074968, 30060285, 684303873, 491110421, 719634820, 6224906, 322443631, 434548654, 210679850, 806464844, 626370064, 558712312, 56125666, 838966558, 326616786, 364835918, 146567267, 174494305, 38672100, 991943211, 418148348, 822316095, 766655025, 867579554, 172418542, 210141607, 619924418, 190254364, 201136337, 388964713, 405576870, 681983591, 872226000, 671944501, 888007639, 439185866, 267109626, 521282534, 90454733, 54630792, 767439718, 309104443, 578177831, 196803327, 315892476, 848524473, 108235765, 435748636, 647505522, 94243038, 325361612, 143761691, 255263543, 834690894, 545336018, 680901865, 555235743, 176468062, 29544598, 741771603, 841586438, 566470504, 198216458, 284628024, 501334223, 246220961, 413672984, 572332347, 668228261, 900577714, 148737195, 732017124, 703193842, 602746246, 492504625, 508823931, 240794995, 737673156, 211758526, 580431704, 798644049, 385588856, 241708893, 694834295, 770663863, 94357023, 873179363, 871327311, 944977430, 91323765, 957988656, 259856151, 335644010, 774428287, 281707344, 873808526, 129898675, 871465648, 529457121, 935148369, 947789605, 827389543, 895386630, 585226871, 621701753, 308632401, 134376509, 175030232, 487743005, 940902850, 254400800, 941174731, 764093412, 443257598, 296824535, 413535041, 608069230, 338626884, 662770239, 507989872, 894189200, 518249244, 582432679, 787210691, 138058330, 550186616, 637287299, 679669301, 32832696, 484693498, 687515663, 292676484, 645774587, 14411267, 907399234, 956172681, 312998994, 860588833, 563402183, 826837944, 165626203, 812950749, 294371968, 105544951, 61463797, 648192088, 207805736, 838681823, 959019299, 502728546, 10186795, 19828995, 400798578, 809290390, 701278953, 393381320, 159184168, 128341925, 292586161, 820227322, 173872500, 260452783, 233443652, 259908695, 943664896, 686352128, 341085206, 624014292, 288712849, 666813212, 339816098, 41699771, 1814833, 557906730, 83336674, 600700815, 835491957, 88223631, 572038677, 731106820, 998497643, 798358226, 136996749, 10450722, 947242205, 973681991, 463188688, 482363350, 772535272, 585869784, 967839683, 756433989, 241094651, 160141021, 846140427, 268332082, 509014476, 919993662, 710276972, 375552133, 721661759, 412978543, 915292892, 444867255, 884585085, 273836389, 932914538, 511872483, 598501049, 839818942, 448885807, 962498640, 103089890, 19150473, 403929569, 90957064, 842702832, 710780352, 546568949, 355489274, 549018702, 309715360, 403214968, 540752425, 85279297, 887381029, 228061953, 642335421, 275904415, 396427604, 775293557, 859539536, 636790573, 345411529, 346008008, 502646736, 410124944, 636437421, 459102362, 497404197, 424799492, 722335324, 136629119, 319172818, 465729067, 256432270, 876587429, 533392686, 372143529, 194423664, 102071516, 897689412, 194974909, 784857017, 32450937, 671229114, 280513640, 914225988, 221717038, 984256190, 614402559, 883864286, 180643726, 38750980, 289167901, 638615081, 866870788, 481085215, 35616489, 786964468, 402637777, 363203074, 268682804, 421681616, 48583634, 577103446, 902817874, 57219506, 399363603, 451633730, 247263396, 559577075, 637624284, 57230525, 714136375, 755104558, 459126532, 666950282, 84945030, 707972622, 408211325, 560852417, 470060983, 803825898, 676816221, 422372419, 921904225, 147790465, 803063661, 354929779, 990130933, 502810258, 195672241, 529933350, 360391150, 670669009, 300879473, 48731081, 413016888, 308801292, 815435658, 199997205, 618700616, 29491083, 888283251, 341529152, 35928391, 138732873, 382740640, 649509378, 632211954, 926331317, 965362046, 253219579, 174591, 632790722, 838863779, 425974122, 230029495, 917084428, 604008295, 210095150, 380502018, 494843759, 840461022, 401652809, 545601182, 121407952, 52013442, 853334544, 718831376, 382302370, 840985523, 461108517, 729899555, 286397563, 573354080, 921864635, 144751586, 203054007, 732920145, 314523322, 711303206, 823500256, 405586337, 300091635, 917544310, 662498935, 124201041, 412570562, 825245328, 879108678, 596852552, 446395826, 236755065, 567050868, 117296142, 495525494, 590696241, 137913688, 215581299, 6449771, 885884829, 927443283, 998669439, 654222369, 295310590, 581419990, 280639469, 997702347, 408798652, 295868433, 151286290, 422808327, 754738372, 693349772, 251733316, 107919954, 556726895, 537402457, 749377607, 541251126, 898699256, 241527742, 172277709, 374611593, 495068848, 726216468, 515580940, 67752787, 786763000, 898697922, 426045291, 485892726, 911208650, 969832185, 366722576, 519364908, 330090892, 645241337, 830386518, 901562196, 357846123, 515827170, 452385134, 487846333, 695760287, 578985072, 242640251, 725634605, 653762654, 273309888, 168079196, 14589326, 630075112, 345165501, 510472464, 165347701, 664671315, 202993193, 438677506, 493944443, 594295140, 594620455, 936061816, 400834033, 467629905, 627538636, 251587921, 527618001, 74820491, 528415947, 417944473, 487835556, 320656540, 2375437, 519930607, 710883198, 698383808, 192589417, 783769983, 156952084, 500485725, 664502443, 18761216, 296545074, 146896048, 746075401, 87584811, 870085705, 856238689, 500754914, 15533633, 641602940, 569596160, 107376580, 734815559, 444068328, 510589317, 55592968, 23008747, 190303987, 966614155, 346689353, 765247264, 448017611, 299421490, 160244733, 19417185, 162342783, 525798597, 100370736, 764579802, 814682575, 154377733, 788739209, 849254315, 221293476, 800707491, 428163281, 877199110, 636370280, 793948328, 579987892, 673842301, 50091115, 827570103, 717096905, 520743765, 78020204, 589500642, 442547943, 743126218, 402894199, 882554789, 199815076, 759178071, 856586733, 740627889, 575204315, 350879580, 580655951, 61703075, 271391228, 859993801, 961940131, 699928783, 963383481, 71881021, 610737159, 917418370, 608769105, 515027937, 199450190, 930634468, 363688696, 413837979, 194645008, 666106356, 621862108, 187630965, 165789249, 596917684, 258170101, 261830277, 421585842, 117404489, 755126979, 607851765, 622791475, 287467785, 188358259, 63568178, 671140093, 947523396, 881692874, 877175242, 971771790, 129937306, 65281010, 188049626, 756544815, 472898527, 469655632, 153015761, 864789076, 749885383, 184964592, 846359773, 595671130, 17515851, 797539469, 446048906, 107774162, 696897928, 507463782, 800493964, 728224618, 301691544, 293200705, 684794235, 976087363, 174721326, 125729694, 625669667, 83171018, 353844160, 679639341, 74372779, 292122419, 264094510, 61361029, 501117048, 358207400, 567993926, 972866563, 903120874, 3522598, 643845585, 450227824, 736729672, 677160192, 909668889, 908011503, 768268018, 525187181, 73511904, 322206698, 551502843, 116641116, 184797919, 423286987, 813081905, 996595510, 832730047, 486831972, 362721561, 370468251, 540028029, 205036212, 701388962, 985331823, 655043486, 749708969, 240074110, 657619956, 63999006, 580842836, 569810449, 432548106, 385071969, 546969284, 676026530, 467381275, 113087668, 90214614, 331834912, 808563731, 859766504, 530945433, 592223301, 594144488, 491226684, 790970126, 970643942, 498467026, 757091907, 285259536, 162452081, 933362348, 944139787, 278221650, 185188683, 135361719, 358874857, 563476838, 937019345, 760411601, 832892557, 838819676, 454790293, 449352378, 673547031, 157047267, 568847676, 998924284, 824140570, 805260106, 68276723, 81588832, 775065300, 694624359, 267174410, 984406769, 151384322, 87836165, 422569407, 583448727, 859566842, 310375817, 567142493, 735091031, 16941791, 635800558, 797012996, 161100242, 810275367, 738403226, 949335056, 277160675, 974748425, 523359398, 705375576, 510945771, 223171499, 724861095, 786846214, 429171029, 580327044, 846358199, 623728973, 604098967, 969073570, 95180330, 450163322, 337946657, 1790897, 565958823, 700031354, 331405964, 716441314, 866921564, 854790309, 201631962, 859857424, 781657299, 738392265, 998290426, 145894726, 470553313, 423188173, 989557847, 819954932, 224147016, 3877708, 842743449, 651776537, 341926461, 571959088, 320352371, 750542234, 527563164, 334434547, 856675427, 97390943, 898747037, 74767758, 118438563, 943330247, 467471391, 793903924, 38286925, 298595635, 798674822, 358936204, 503703191, 5901319, 92629468, 476981715, 693965631, 688678684, 156385971, 883222158, 970839446, 16116271, 107040247, 933896779, 769249691, 682595542, 398404018, 851870397, 796737982, 261070235, 930936335, 194094412, 920582493, 657756810, 582041854, 521669826, 492120736, 163919888, 971218157, 201336106, 558816275, 642898100, 78945428, 739648107, 25274450, 413068084, 292541227, 18584815, 680090111, 442496644, 249151312, 790808240, 222962717, 699619525, 199854152, 132366496, 321746552, 301572630, 965261167, 925807473, 862336731, 252635933, 393874191, 809921231, 175555684, 256365035, 133769441, 174555748, 584657016, 250124228, 932731542, 598791175, 442904214, 46660788, 925676346, 613760353, 936357230, 916399726, 650529453, 238155113, 762974283, 531793220, 429673455, 575590935, 923054102, 553873592, 139832305, 963374559, 33205340, 314801125, 894417946, 198052493, 521007289, 954468367, 834876994, 292185013, 909646384, 184510609, 831608351, 748291262, 122970134, 645665575, 208957276, 431894166, 914747947, 323308185, 488658473, 309723430, 403546502, 121974947, 626825703, 185577210, 474034389, 188932536, 822796016, 464072770, 795964484, 475941189, 310662791, 797095637, 61619659, 462420446, 555068846, 885829220, 394615491, 203553982, 809211673, 602175854, 905844105, 951266774, 425499942, 660268645, 215527307, 241020174, 645570977, 501194257, 964111869, 884568704, 295798648, 285829252, 747721178, 102196673, 133200451, 57050506, 892196282, 946715408, 948790970, 429258770, 961784800, 751292171, 489475190, 569293792, 800627737, 17646848, 544175338, 353593408, 788132439, 124847011, 918913408, 980192081, 933766429, 397675662, 822888159, 206296301, 143683133, 863859908, 464672195, 834270554, 45132572, 702814856, 252286497, 722242575, 699251017, 222825891, 413343826, 878076900, 442273007, 199231760, 532326173, 84102481, 423385468, 89327241, 855286952, 449109233, 749624093, 769241120, 895083951, 514150508, 871478549, 830560772, 551275157, 747730452, 660148300, 253983727, 642149262, 195838550, 280837951, 973667853, 432274027, 898210487, 342213070, 553910509, 789097813, 312092351, 991222966, 70934914, 219271508, 767886533, 746821811, 506468614, 907340326, 89002192, 831013055, 781972232, 449525227, 364996442, 984595344, 258134408, 665473949, 535703625, 30064561, 463624722, 128922812, 897606134, 841139988, 659568122, 540443749, 747560260, 615433555, 335928252, 852609335, 412288761, 358810567, 347897589, 632138809, 602365977, 790414181, 676971047, 311637081, 525209708, 383620192, 378978509, 151147462, 767212547, 686078500, 740221849, 174846033, 722172986, 996871732, 941042884, 534774064, 170428574, 406642361, 754292593, 673098745, 912759120, 868657052, 131400364, 644582551, 82939642, 612900486, 726028494, 868455331, 491305009, 82212970, 430462539, 250924050, 868819778, 47716315, 803205115, 709391569, 345958897, 88841286, 978953477, 539457011, 735918799, 28387584, 805257994, 888478831, 45521874, 41997365, 320803690, 979666676, 667764336, 278942179, 631913615, 749035543, 535696787, 393774730, 524812811, 60293141, 66459495, 775065422, 251285466, 360204401, 889913473, 954649867, 83914304, 892271018, 371500824, 413878371, 173765568, 153686988, 14743823, 211128434, 557090042, 365495380, 430478747, 552976334, 993540772, 543079400, 354221092, 954000708, 454282672, 762916725, 346083762, 615964270, 556324755, 714475169, 332734540, 629733239, 84182964, 722126580, 60661819, 466498674, 564149795, 342921862, 110067080, 661105130, 768625941, 566781434, 864099156, 764099711, 988554882, 645379247, 359375653, 275030085, 397065836, 303787945, 88093541, 867398725, 167203858, 57924455, 2135641, 806644082, 210285306, 127219630, 88803202, 887323864, 943661146, 777203529, 241754656, 152825901, 214133602, 401469245, 964782324, 945655455, 604506937, 549191444, 114982118, 363858456, 785175775, 605734343, 861967851, 604266737, 863167779, 145858098, 656612277, 144103498, 620012342, 482174035, 375568295, 620645890, 77493377, 704834521, 719345880, 374915326, 613367260, 439745964, 295947293, 781605486, 187005954, 930965469, 188971088, 88038904, 380958417, 998713867, 361125862, 405291331, 631082236, 260196428, 825193541, 944719132, 864520077, 765081327, 988683483, 838884664, 752762491, 238245137, 32114683, 178536022, 775629160, 696267387, 600608187, 880376554, 222439488, 825373958, 517326931, 809667325, 188307539, 598416410, 206917073, 772073278, 167998322, 384290034, 697006275, 73691729, 6302948, 544625090, 267551595, 47156792, 727169948, 694802793, 522772178, 947691233, 985931481, 1230038, 993899611, 810653177, 808873440, 508042615, 272109084, 86627650, 230531656, 576495714, 120948268, 996948149, 732107686, 35207609, 787298662, 590308652, 143327794, 886726886, 687177908, 102286101, 612754828, 809482899, 37104337, 570972230, 354252560, 425101570, 33562334, 823855938, 666199381, 675901946, 424664115, 22643594, 154012156, 179495783, 295005513, 744846391, 65830277, 374979327, 780650550, 20279880, 88729243, 164130118, 456762512, 389376557, 485983690, 608113017, 364804471, 895506298, 9727639, 427061793, 113296363, 305222148, 505213068, 633688898, 16042087, 391384456, 881157365, 846716496, 652811124, 551395681, 319735370, 118725270, 823152589, 425167304, 305757340, 321453789, 462501907, 190429352, 225261455, 235951071, 175950039, 544014277, 719164965, 986985099, 802891858, 855574482, 991591285, 281718023, 979144805, 427395292, 390947849, 919401252, 668055166, 584099032, 761810450, 781665807, 445384669, 965027289, 250452374, 222526500, 318249712, 939035053, 420610308, 949807855, 906561694, 408602137, 43530056, 614911138, 317496306, 874179874, 631691351, 72053758, 276267380, 572397615, 931403560, 458252461, 472563556, 938418200, 351977177, 62991593, 531291678, 338001740, 29092903, 971638589, 861501701, 356940316, 248688258, 546931673, 475737085, 123626112, 101407831, 193518750, 491374116, 850170641, 170858341, 363184195, 40241018, 622053690, 677391561, 977446802, 803951265, 39242693, 568864600, 466321073, 844933381, 791592352, 890649865, 981428782, 112553233, 893045351, 126154921, 153208965, 616220349, 191973451, 878426532, 18632443, 495609403, 790681367, 284811714, 398589142, 753763668, 71812748, 933743221, 993241080, 625960220, 352639622, 774179501, 566493950, 768779741, 83959501, 947529355, 454991491, 833350568, 374867919, 161620492, 646727535, 975778213, 930419483, 802076720, 739882994, 409772395, 415851482, 78836706, 587024543, 923148965, 958807795, 159078861, 956168, 429651094, 921777248, 784060605, 637092012, 794519684, 787902252, 738251348, 113948344, 644296237, 242624818, 613337442, 986926879, 998115488, 568402217, 720402320, 53668670, 319357680, 353914987, 26804565, 179732090, 854787832, 466158881, 434017018, 209566244, 345210390, 998023737, 649960179, 519697118, 480993161, 446610904, 917598078, 975051905, 658728201, 73745113, 822618059, 511331076, 16367490, 639008076, 571797168, 362338369, 427196457, 437045417, 304944984, 276161568, 932306106, 367318875, 755292306, 107975571, 120288653, 997225514, 269061616, 892079265, 3527352, 130063681, 221330062, 663146023, 585495164, 159773297, 377063990, 928886467, 555364118, 932338200, 483654682, 863509638, 845666514, 864738032, 145438793, 640724541, 640829419, 831201073, 188180911, 518372916, 769417038, 972320178, 948128018, 346337684, 65784573, 411198689, 640138600, 677761039, 639131574, 584151094, 179018276, 606498318, 463009267, 368086882, 870303327, 784378674, 324678264, 273709746, 884569789, 933813299, 824393132, 264927441, 449288052, 264951910, 325972730, 81955732, 628578938, 942894317, 33980996, 145896828, 331887641, 479165617, 33031987, 543355040, 325113175, 580841727, 143050702, 162339134, 995085132, 89543432, 336712006, 946318502, 214562941, 658323083, 289514154, 225556717, 480610139, 819102946, 973452872, 546293022, 320303295, 542042551, 124280755, 841417440, 584510511, 558575301, 660603223, 375214778, 447322915, 135844370, 879479267, 227935639, 48642764, 708399205, 892573864, 733668943, 166852937, 489715305, 24562924, 940238513, 471797728, 874804981, 316107930, 505411064, 273709304, 105191321, 538094134, 10162305, 794007566, 705413550, 576638518, 535923070, 12941373, 537028453, 825856598, 444412847, 153419275, 971428143, 829865710, 812511746, 497769678, 755157569, 554445135, 595074051, 40911721, 592895544, 800840924, 687617260, 697478473, 304207159, 175474410, 465053099, 532834711, 231847842, 322745941, 547708923, 404138180, 185888610, 489426014, 499394184, 144204205, 331141538, 240575987, 421230117, 505990155, 994433324, 592055862, 403941193, 251539356, 186059791, 294731687, 208476548, 899252868, 364304136, 343598608, 851103140, 240695186, 232615534, 903375201, 82246119, 211523760, 216449840, 158544100, 518583861, 753023878, 547757011, 750958594, 643361758, 121640621, 727395807, 988269174, 418946406, 835714372, 962059097, 3949160, 507233759, 538537411, 901413730, 159179192, 293427441, 444017534, 71143135, 423802150, 113431563, 216692636, 417267721, 741201047, 982159550, 353600855, 891458587, 943090875, 129535897, 234714985, 738238277, 626817597, 865736884, 284960197, 282504103, 964053385, 216923449, 71661997, 34064916, 595201793, 789439275, 470048516, 458408218, 624472277, 438259949, 384229540, 887548118, 85224613, 232558489, 14905057, 422583836, 133810748, 270835763, 385417275, 384954484, 712095271, 984454246, 172154258, 939744268, 275716386, 825898305, 175496166, 131072872, 414562548, 623713981, 390327295, 480646660, 604392232, 762491482, 35366341, 371017619, 387302616, 272022089, 101073218, 64209186, 24755251, 522526359, 283221693, 643806502, 536355183, 984751205, 497753865, 860935714, 308449347, 553206633, 704446437, 883554503, 847377933, 857667288, 314200267, 173228908, 300508557, 198844161, 141446141, 520854343, 685635006, 698167915, 638690097, 114077291, 298258636, 33512595, 616104129, 265634653, 501856141, 137693666, 368367328, 222449060, 731579770, 789565225, 818122392, 883641009, 448719863, 762474517, 786482015, 27323980, 723925795, 805527710, 175817410, 474065170, 436090708, 670244541, 233594789, 276046907, 774179663, 791485187, 938029205, 914676581, 357397028, 877585990, 281711086, 616390809, 797030856, 466614461, 903242734, 17982179, 134377136, 285487416, 309816224, 904431303, 555805358, 363591755, 423935418, 993911649, 937506031, 285897967, 292484959, 639937393, 343984532, 922399388, 908297111, 291831543, 970305568, 82122780, 977501474, 83528920, 421274267, 338263822, 523888137, 49256107, 929260949, 805552071, 755522549, 188104247, 356100053, 776439678, 372870527, 429783074, 479346121, 509057714, 637659501, 379365291, 419859639, 410802167, 258499362, 432522146, 302447158, 603411952, 693144263, 658327981, 200655752, 548347831, 602987821, 433226755, 661807922, 338021641, 365916652, 825087120, 102031406, 66840417, 760601731, 138943343, 28050937, 466144256, 154339185, 74082010, 254522942, 153111542, 813115452, 47590505, 657634387, 985055089, 656817900, 322514986, 92269708, 448079577, 536913233, 231289444, 209574935, 876666819, 950297023, 334957400, 636233524, 149791002, 161159139, 254597292, 561214906, 960524064, 830001338, 591108755, 88871184, 171487058, 307198424, 222905668, 230207693, 457269016, 615332510, 865267659, 150722531, 449441527, 509444531, 689949043, 24292075, 104166153, 68727919, 799315811, 351111833, 327225440, 539679997, 853671864, 677200391, 125246527, 501311976, 173772288, 471960000, 990873105, 18844200, 271099382, 573783846, 196535549, 708738138, 556574600, 733934093, 131105051, 743724788, 683207932, 907506433, 592493509, 181205826, 242666971, 482303155, 127307921, 129255440, 9996654, 830874475, 664525206, 239343583, 90687430, 816423547, 819133851, 297518058, 419983784, 248697693, 903706314, 594290060, 929545471, 126117965, 930103138, 46057896, 636610089, 437155616, 665166214, 124586329, 191995933, 401519280, 121647366, 660260421, 476174334, 859563365, 15984131, 822809673, 987040173, 5849595, 501487793, 810616102, 466631689, 284013229, 717690284, 352913358, 39827763, 360069991, 123376895, 728029347, 383204277, 59013963, 834088870, 285195391, 785339506, 911395167, 307169344, 328877168, 770347120, 913715817, 393160939, 722767484, 713617273, 157505363, 200907361, 362960160, 551386657, 193877963, 314333664, 68662522, 53359017, 287994515, 164033941, 541838360, 315779153, 561556114, 805856258, 41715727, 843219462, 57832391, 295403189, 814355404, 975915146, 480098308, 671673376, 847688275, 263671872, 610717002, 38849176, 647015763, 608723281, 135694674, 885277902, 860695023, 643758600, 709195164, 826642138, 846117851, 97562672, 695907728, 718235405, 64758511, 870046758, 709521807, 62337579, 563985583, 227314077, 253769456, 293166916, 523002342, 26137179, 758718985, 591768817, 869303124, 725586834, 703819939, 928049961, 490245273, 863384566, 555832319, 677155956, 189804574, 721352201, 898454821, 409883875, 1632898, 992827231, 280530252, 117876533, 295758454, 377198159, 180332512, 662812315, 344484165, 149093619, 309470748, 765992383, 959682722, 519142980, 187068371, 770396466, 521722235, 289949324, 111115411, 987388825, 586112231, 80916976, 348533497, 566861523, 631652074, 581056501, 290987941, 956642834, 206694369, 453726452, 224538606, 583801269, 656177205, 908386148, 523317956, 209497034, 689133470, 32833920, 543973018, 188566413, 31031956, 822249548, 608669864, 227998805, 292152327, 68294562, 2388075, 831391689, 641107952, 997985965, 370302897, 643466794, 556551390, 389937486, 44095100, 972024821, 502870350, 556008144, 107877263, 661741130, 731411307, 818016740, 571274313, 602964606, 951851794, 19110355, 336026955, 453092477, 658360481, 51080015, 425954288, 65451834, 894164384, 416225823, 590077045, 328196753, 169277289, 151518352, 886453790, 263101013, 572412796, 640451119, 465420786, 752113436, 964728762, 576826492, 984305881, 926232352, 514509454, 940478742, 585426721, 112427216, 82656706, 289665979, 200488628, 227719057, 132494644, 150855551, 76513177, 430838829, 496062946, 913769477, 436974552, 308159363, 217629601, 447348610, 262009148, 566908928, 573913320, 499645002, 405334598, 185949631, 658170941, 763028053, 15510300, 468048673, 816299084, 832273938, 341246982, 919157419, 436822250, 659598406, 374593214, 387859617, 453387783, 148469215, 370997669, 99222675, 302999748, 15011717, 788809425, 823711508, 884414792, 349569766, 80011487, 427676618, 958672892, 852579561, 602538209, 213424540, 728578620, 799083138, 875941991, 308440062, 448786234, 477267160, 792797071, 934542713, 507980792, 473984652, 677802472, 487080978, 66998114, 335824596, 118851708, 637685976, 682870629, 138328084, 974553612, 267985989, 43034656, 817827558, 443612055, 273542873, 672918807, 531019397, 156435347, 778765330, 247184042, 400240740, 537182715, 990743992, 15259336, 61139091, 664087954, 355386171, 613877068, 291934433, 662532245, 149273425, 114867405, 601803376, 99857869, 293106951, 845395508, 920653867, 230848983, 985113612, 267454749, 31173521, 538153289, 956066270, 498615045, 522882634, 813093627, 111059392, 602528573, 583470141, 728641775, 565646578, 835862923, 78885758, 127149398, 71088605, 400691234, 661463106, 423620347, 185807305, 142328414, 210262072, 610801996, 546152739, 681846501, 215896101, 56735468, 222958722, 806875241, 99938585, 634511981, 630621236, 899304738, 15479186, 992375080, 871187090, 202345069, 874858041, 646443042, 159421459, 778526858, 142443563, 284381101, 208317445, 433588522, 620634153, 126805603, 165643842, 347999537, 122968255, 330986334, 53217511, 574482548, 165827442, 854424737, 752748097, 87425498, 197909663, 401976915, 420067971, 226165886, 27428951, 917805329, 581820609, 647349795, 477056175, 868248784, 170077269, 506468665, 349170230, 568634302, 543242298, 948220850, 500444581, 133040676, 137855276, 493919882, 203230379, 854444908, 391178940, 595867733, 12933048, 670230263, 877030996, 974646420, 904669342, 878560139, 909547673, 841318169, 966771437, 48220879, 960504603, 44319485, 180625033, 313493773, 235492774, 413600676, 634913668, 865453083, 606200454, 106241202, 570088845, 792447957, 166498911, 845480029, 752076489, 996199024, 662227145, 93041672, 225375846, 628610549, 280410049, 14218432, 504376617, 474655150, 18757719, 827133075, 191101464, 20374309, 250425776, 330239475, 231344030, 887216203, 295953721, 20791254, 466331827, 406182411, 140371365, 465917064, 713979245, 107917878, 409270442, 821788239, 955056431, 273409659, 667722419, 47707995, 270803550, 811877883, 84905254, 286914004, 767845531, 294884255, 595825165, 754379457, 68210568, 59476889, 80642294, 381917880, 127332546, 693526454, 79529007, 695058938, 364918565, 818492707, 692386637, 693534865, 193768223, 179018994, 499441113, 631467053, 693772139, 278146600, 490745156, 20055068, 17528990, 176375997, 404253451, 35578724, 354326858, 991063258, 870557915, 191661597, 851850759, 550532383, 546343361, 494068522, 395709065, 805083141, 33502367, 886570606, 727476372, 320215851, 281301136, 440560026, 829362326, 878142042, 301168301, 387869954, 667082385, 6359637, 691538686, 255989839, 353671775, 332038481, 26049351, 287297862, 188961624, 677512983, 860214453, 959300575, 420886205, 173459347, 271039841, 717566078, 838455160, 766985375, 570119194, 978692301, 439751592, 363269940, 546195765, 600018364, 409937010, 814413537, 519112240, 795868142, 232315691, 405217811, 604977803, 392566029, 306319038, 129933978, 785082343, 236609906, 161120838, 719049918, 235781782, 125792725, 595631846, 565316426, 993314397, 334542940, 523405593, 910857089, 8342563, 998420813, 335626292, 982802643, 907944964, 156756397, 446718568, 217100797, 787664873, 302670605, 557150240, 736664857, 441563692, 798554764, 722010440, 389148746, 985229840, 607825714, 221513586, 843679896, 754994183, 222268106, 675577876, 191577610, 502393575, 502797154, 3711092, 807490253, 949411185, 547338051, 304002931, 757754840, 433082975, 911956887, 742734935, 959646152, 593340570, 354644816, 179973094, 726812407, 13180897, 709135351, 992598641, 691002138, 925014953, 822355270, 527797509, 231464838, 561750193, 400843883, 751471190, 901177311, 209072540, 785515205, 470868100, 387061462, 838000128, 897842378, 205432438, 768269300, 277090001, 532834582, 968680190, 846713854, 236660491, 643996695, 207868719, 821764138, 966558500, 337920208, 587051394, 272438457, 218520013, 482255487, 702441963, 688557479, 198647356, 859096496, 267428423, 515404379, 829881729, 691964610, 385098470, 363047856, 528563626, 800181440, 995014392, 839742294, 639964246, 984712136, 94938600, 852240425, 754811407, 436004442, 740198963, 645627089, 510878609, 100117622, 104697561, 979524080, 320182760, 983979130, 952682738, 771962836, 50421810, 676180830, 596404394, 616495440, 75108138, 366502083, 832252530, 246037023, 562832132, 149824584, 225954276, 77349052, 271017462, 402423884, 915404831, 490422589, 402700208, 381386610, 986629146, 431808239, 341591737, 882785393, 217996716, 984387560, 884713373, 2311963, 867706781, 213876948, 508873917, 581519217, 915533909, 419056036, 945240605, 952177653, 621270404, 327782808, 42389669, 15504660, 980401799, 892633568, 926457398, 186171919, 690808588, 531241496, 374240280, 533667167, 429738664, 828669815, 859633015, 192104394, 868048321, 857699607, 652158498, 364726455, 37356042, 341427574, 706286218, 832025986, 182064904, 969020304, 51611208, 864816640, 125967861, 124597784, 959890946, 660139341, 473768096, 975834372, 109556732, 710744400, 647985796, 109661945, 410008707, 136589859, 619628241, 780847266, 751899367, 547795277, 62140971, 391120746, 56160568, 416363746, 937148065, 389976188, 530999577, 519123938, 244083091, 669142219, 738942889, 351514671, 470970090, 13883008, 679805584, 517897542, 456124067, 333785571, 111969080, 636996243, 728745471, 706963917, 567253075, 487138415, 60522622, 348180180, 701840913, 259604560, 838421824, 242829998, 611067778, 255453178, 908447721, 694654276, 330341611, 419207331, 725134803, 310918917, 250952975, 875950178, 669140573, 295027789, 983196543, 665026760, 814613018, 264018220, 244317155, 137773221, 750586353, 876021537, 81610950, 221873308, 315171919, 792785537, 916030115, 648579995, 50453828, 713379738, 32168458, 312091005, 207892887, 592963560, 693573491, 275700535, 826165618, 818535763, 871261979, 652093853, 99206372, 259896023, 432147624, 39130533, 387827813, 34018356, 290776874, 986899289, 996914764, 320470269, 505701664, 513090910, 218729371, 149073901, 45105668, 305467795, 789959145, 48179355, 419819754, 915323716, 266038220, 698138591, 534273488, 7489539, 753733542, 265185803, 399031766, 62794083, 564379821, 568690722, 534545272, 688934514, 201879798, 95282792, 862009182, 331166150, 24707632, 775833524, 861282884, 993676016, 774826478, 138174720, 862073355, 890854790, 833677465, 191012934, 417295657, 683497904, 185896324, 638133542, 791586577, 676768931, 751591393, 88839128, 816479742, 331943450, 845398494, 529366511, 90254415, 575412831, 950471525, 743976973, 72114414, 498345736, 357141122, 41542750, 251727637, 832231552, 800334607, 606419668, 546937007, 985080957, 26665614, 896180717, 631387507, 740348744, 729144311, 312087778, 555276036, 259164738, 899161362, 328546151, 385805689, 529706270, 789973617, 231386931, 578767611, 943759819, 579366716, 977087226, 10418923, 461649854, 663200008, 488284920, 715402200, 656893069, 661612946, 69273997, 824863018, 157368476, 376993403, 913219751, 950618069, 219401368, 233321472, 639482269, 941367906, 82653695, 426052578, 242819309, 248102745, 610295435, 326165310, 642263569, 12051703, 47920551, 848626800, 817753715, 964399734, 126120013, 300877308, 293601659, 354677389, 605529470, 173497246, 107528607, 262060742, 386569750, 258171732, 728849385, 733972905, 190727445, 826114849, 183286330, 814880166, 514302838, 572963604, 860988975, 563266376, 396629673, 119793463, 332524607, 282815901, 455577752, 285395399, 231913963, 347160845, 665041014, 503457841, 886017181, 297248663, 24417314, 139468030, 948262898, 297355118, 63839497, 652817461, 895366908, 405487418, 547771950, 297128235, 945302256, 242031510, 536108289, 186903426, 326263234, 963002916, 662568557, 350104195, 310180557, 556507426, 781752394, 779327271, 348839264, 187235915, 113353852, 568943207, 985760985, 995380751, 936364877, 300269910, 594430456, 836281230, 557161083, 630670302, 580056588, 864802955, 256527245, 539771129, 827673461, 685112777, 402900243, 198234237, 6389755, 298375659, 825347865, 932765460, 980501197, 440634551, 132775136, 811132442, 349917221, 64598889, 165345535, 197808996, 781834352, 655735688, 655639236, 307916406, 824894324, 314845868, 717833166, 318324520, 680200012, 559194026, 592741932, 71907170, 513430488, 203161424, 798491818, 638234966, 814354936, 928709105, 594525505, 765656266, 203578466, 955931394, 119401031, 928342427, 191266299, 282282146, 635318625, 325358639, 411023429, 731026564, 590812073, 66020005, 942359117, 144276233, 569372082, 147226091, 316546704, 184473733, 845534085, 320213268, 775652297, 485780674, 198314914, 715540498, 755145123, 631651342, 298798864, 161970599, 190286324, 336378452, 338085176, 213664434, 840675877, 7864610, 996892796, 117294911, 438021596, 922125092, 36980570, 858881320, 122644631, 203780463, 922207264, 104333386, 269739523, 202505770, 880028518, 4349104, 385346752, 635354192, 978799665, 910671121, 573342661, 640457148, 374246603, 127076579, 512235832, 299340908, 755481848, 609062691, 475149815, 834178444, 563755695, 637915097, 497392220, 564828883, 890611344, 475803914, 383738131, 881533267, 954987037, 955294051, 531816768, 244781736, 824905960, 182053745, 324421824, 425241829, 736491107, 937516111, 75003775, 847895227, 192096660, 11320631, 267677230, 539760059, 735769110, 583232916, 827023909, 245146678, 761243172, 645149566, 220849559, 626431783, 330033628, 362940090, 831112530, 567773230, 601182229, 786606394, 457715989, 181405664, 796919152, 479710161, 887468771, 861534501, 362469591, 831849546, 436291778, 371214975, 326696861, 507713207, 729885171, 698171607, 566054479, 98247107, 213148898, 327415345, 292007315, 599729858, 329727834, 333374254, 600877321, 41363745, 711930061, 414641732, 929362100, 293120471, 4352572, 898091869, 518100924, 101163151, 751358826, 937273677, 489530975, 339146283, 597589373, 117159039, 547292529, 777639847, 169356050, 952416889, 309014868, 492822807, 927068693, 162745778, 509571823, 545120864, 44281880, 131020854, 960576423, 358408689, 314470401, 530122320, 7894544, 103741147, 494223290, 762597442, 409004425, 475923318, 101578606, 489878089, 613168309, 823738982, 826251567, 390312512, 544618706, 649004494, 724375863, 710470625, 843621261, 704176125, 160502418, 651549276, 902085146, 958712393, 739861826, 744939803, 849542791, 733700915, 443886211, 663097289, 70502609, 783386613, 474861896, 692655061, 935573265, 388417643, 300821987, 129424179, 822051047, 797005819, 692188377, 620057149, 328462351, 787448697, 287738466, 787463391, 532730886, 343498559, 158743732, 143366306, 813475413, 559591826, 954045498, 474762767, 864578998, 334611573, 279484139, 304854266, 904610919, 849642326, 240712268, 333627932, 901932941, 233728393, 3629166, 554787490, 403422185, 848795407, 837955612, 968548679, 116777015, 728081182, 602000436, 200693347, 919892228, 953441265, 985213128, 236044895, 743467819, 853037942, 80515200, 729580235, 432192835, 630640715, 632126678, 702800717, 141856926, 148861111, 789549813, 846817047, 956129564, 101801593, 514475320, 236183439, 873211231, 187901162, 865511497, 896920698, 78627306, 255250021, 840779523, 356153273, 623032032, 161485498, 30910118, 295380727, 924369989, 322193128, 687996569, 594063114, 578703333, 39415829, 260951456, 838090999, 887505544, 362135358, 355243637, 141643591, 766016276, 231525414, 60227095, 988527950, 134198831, 624133047, 378475575, 586555728, 278353923, 843590082, 854182178, 38057021, 757369496, 710099444, 490227546, 596584723, 53258140, 201444059, 776430929, 520483178, 574067371, 244125528, 744610897, 219809934, 241328802, 441561898, 152374675, 954505920, 969133203, 826995382, 779119144, 671924348, 753776909, 972629325, 707803714, 356123545, 745298132, 812286220, 827907062, 258528201, 758874169, 100017746, 415856471, 20163572, 988821565, 626166656, 539583919, 285757330, 1091372, 5268012, 608918030, 302834564, 701366624, 981863828, 115430465, 248623319, 652710649, 46920273, 434581668, 182822777, 401755349, 609615872, 45351405, 628058121, 411209856, 853704721, 123222784, 795202435, 217156086, 548995661, 340433712, 320792008, 630243036, 480284164, 940577592, 731183528, 109625033, 718063543, 141389963, 773742445, 234252018, 15091152, 518069509, 572874788, 198363010, 352548731, 230726769, 300315843, 703590602, 277409481, 106667229, 252159172, 562096554, 686513101, 158975280, 961074931, 998410939, 555690832, 188363813, 172506571, 337090896, 724635168, 258842549, 591799065, 386027529, 88869123, 413784393, 696633035, 693724983, 561996818, 802301225, 617410617, 39110006, 244933268, 499205663, 133041457, 73922138, 977362507, 246964851, 275119659, 487021734, 572809291, 645022857, 990717079, 35874082, 944763895, 875935964, 493806035, 990005132, 639455848, 536683238, 807209181, 319661817, 386068096, 696317576, 353658531, 73991245, 561939837, 698927596, 251858761, 124725468, 159205065, 248902705, 616948316, 405931973, 977738129, 266972604, 309115184, 926510172, 770188458, 247573412, 133500792, 236004285, 692112062, 765202333, 710430379, 764358072, 459424174, 44843068, 591843923, 315867770, 263254755, 100683267, 404800050, 587243076, 759205933, 452592467, 580663218, 627812932, 86954155, 321878788, 158549111, 119258739, 970335186, 789910055, 39525627, 298039547, 343654099, 596598520, 732044778, 660763593, 621880628, 767976221, 5545038, 643266369, 910723294, 485570400, 695414145, 634311790, 474242921, 193251401, 600514481, 557655937, 337204154, 351658024, 295502029, 894843775, 115706789, 113348353, 330518183, 237829050, 487735624, 434987973, 518443716, 533938442, 520014743, 705769161, 893279108, 76172076, 871768125, 392180946, 274899546, 546235451, 159618379, 491800231, 171830695, 53241745, 894871513, 189397699, 240094051, 367911087, 415308656, 902831923, 212666794, 570917325, 126947841, 616662171, 242078386, 459944989, 425009137, 22175988, 59312317, 922475028, 938663034, 923975826, 463705523, 104090942, 762674772, 767701345, 264424086, 807756977, 152155516, 718996148, 284728914, 632384077, 319355808, 188673341, 885974133, 397500496, 470449108, 337218808, 275402911, 807590560, 832573750, 157529768, 776535573, 669658774, 272094262, 563323972, 131154851, 776119313, 478269394, 619434963, 816403468, 914686347, 265512876, 72754695, 959320478, 585072330, 548325255, 254896517, 555407817, 2652054, 182214515, 657952393, 666399312, 291941742, 640145402, 17936604, 107477600, 425696474, 61190271, 610994748, 92845835, 706073539, 692234084, 195229656, 584805376, 431247452, 54445888, 267852335, 922641176, 250383983, 471331518, 20378636, 520911250, 464824339, 680344393, 947727948, 678478331, 615386935, 120225757, 1024286, 364168706, 151798728, 414682147, 918902340, 101702480, 708678857, 190411462, 81754518, 628378789, 760326274, 313928536, 669579486, 998842947, 887095876, 994607051, 905302374, 448706654, 116021425, 893727355, 318192698, 352103795, 186380524, 249924806, 658402059, 273146808, 990051529, 636748403, 704793759, 312077890, 314226154, 473567389, 243773374, 777865129, 633160158, 672073264, 557834724, 934376872, 62605653, 571080422, 268333526, 660900296, 767559353, 507667115, 855985877, 515363276, 46465162, 90285337, 747664786, 225165056, 175962182, 792086146, 384004340, 454813948, 540031373, 648818000, 907155185, 974044283, 468945526, 124072605, 772935732, 34879518, 972487590, 288347946, 718758974, 299809872, 750823497, 571850005, 922658350, 961783092, 802452473, 166102519, 640058834, 955923178, 851216771, 969975047, 832652086, 993436947, 37638523, 155697378, 938243369, 124371855, 807918521, 194708069, 111392898, 409699396, 422939873, 684626786, 680778607, 990011322, 968848597, 236160250, 174894520, 71858952, 557343727, 151507370, 974943860, 58763664, 650167896, 157150024, 598941876, 253692289, 318862899, 438631339, 711849675, 18245414, 867545663, 523818135, 145548893, 209267259, 545968434, 698916009, 935961746, 919636567, 608098934, 20088816, 825627324, 481865383, 961568821, 433668375, 643030535, 82200462, 247192181, 499109749, 994600363, 98622961, 354664572, 364167685, 285045204, 781551493, 415481972, 535360937, 275398160, 370279369, 444428317, 765639019, 563396524, 262230184, 747744907, 511669752, 622098311, 982615519, 729625958, 244778575, 508293756, 563056124, 369010256, 574940839, 681739478, 929777020, 905094101, 739338416, 782027399, 902737231, 176461535, 31691758, 854582915, 209391793, 333913945, 606634970, 388527011, 190573207, 516076915, 476324523, 814869830, 202266135, 595480377, 404240268, 414669094, 362226833, 391565277, 192204430, 928170355, 921175284, 157700268, 800964278, 230559090, 627606966, 937787285, 726049809, 77769845, 338868863, 504343755, 866826946, 945655025, 509798047, 590728734, 640135113, 774209064, 118986088, 7877293, 939692595, 663014694, 850446882, 373853041, 712508645, 401406526, 28180469, 551307048, 971049040, 980480168, 235359304, 780763058, 473199763, 836262339, 509844292, 264182187, 437053323, 869376232, 878984845, 842567159, 325026321, 548870743, 444704291, 365729219, 68883361, 697047118, 438413666, 717771151, 11140835, 886372829, 148358359, 25469973, 276843683, 216153573, 501593537, 718461226, 496434885, 375673974, 864258431, 964875775, 179793699, 868962043, 408939637, 403134400, 624860540, 117189674, 817514086, 177850935, 187111156, 678852872, 258410786, 34512134, 255627753, 94440277, 543972473, 371297354, 676518224, 123027187, 901708552, 31328643, 40123062, 20796408, 589401970, 662498771, 432872480, 143273686, 188111645, 271779685, 54598311, 470057484, 165393839, 335878166, 109100165, 579518398, 595973602, 781592167, 923108527, 804714561, 827172217, 553017025, 73450325, 294942548, 561156890, 403316743, 179643263, 115555198, 925699700, 766654542, 827002147, 549044618, 453615932, 477984906, 715061183, 934757900, 602385551, 684656812, 201111431, 813120499, 4509106, 157631507, 844426356, 660434923, 712321726, 420419249, 306788497, 398113790, 359222688, 97410227, 747851406, 697452085, 556396509, 567421598, 160619200, 793711506, 62011459, 848319000, 885297865, 610915330, 305378029, 997362653, 33735156, 435829587, 919610833, 42470893, 13056157, 842558442, 489496061, 517440192, 406748917, 240194909, 292796260, 565300225, 966876040, 609663142, 376815693, 106926830, 580699208, 200538468, 937109266, 79471969, 863555360, 690863831, 438370014, 420006862, 494695904, 764940679, 167729468, 892931680, 675677041, 893751784, 534305118, 223278479, 862026639, 685990396, 969218480, 860349314, 813402602, 167701971, 381768285, 85292243, 767489608, 116626749, 890223388, 580719629, 513802303, 282349406, 261067203, 383704616, 89728287, 540475112, 179806415, 581425138, 262516615, 707581872, 938579219, 244188492, 795570054, 761776847, 49370486, 397055373, 750743094, 243651881, 865482129, 201124984, 54321029, 771337016, 653203368, 812129908, 795726340, 1167748, 75353739, 200508753, 182427560, 344021558, 77694406, 395455791, 640559125, 457701446, 27381785, 296388094, 378262556, 964868308, 335923492, 687096413, 758033964, 438363111, 912545770, 525836815, 749057174, 211463111, 484222931, 303435098, 239557516, 566407955, 36638698, 434023209, 569213073, 151732228, 481724522, 165287867, 724477258, 285848522, 536141020, 64199928, 931823629, 702539184, 432209586, 539475929, 55907598, 820405734, 921838918, 161886237, 175273372, 489182749, 958418397, 614179891, 634382056, 199924681, 430718672, 549694252, 74801642, 317472279, 71801840, 948206089, 769150383, 513591170, 685556657, 835137067, 471401879, 513141052, 849085009, 669335439, 704937004, 956734653, 536407628, 866959194, 413767553, 642790679, 286366635, 520732283, 329045896, 695778916, 462500427, 907405567, 766265810, 656694013, 255286157, 480682334, 81371052, 236115246, 160661812, 437692945, 779315392, 633374705, 733251887, 109267937, 566604541, 220193451, 835052917, 455913677, 863249599, 682454603, 796806109, 200960453, 136124610, 784730038, 360650148, 899394689, 360394543, 26392103, 318023358, 386198225, 36876452, 666516957, 223374488, 931041437, 739303782, 246755433, 805602850, 563881768, 719625485, 502033503, 531086150, 323187696, 981099120, 484840767, 864422580, 708200445, 353984452, 778607859, 965775841, 798527074, 39807964, 790905198, 106564008, 882462214, 979379582, 950390028, 504007382, 461496177, 71620536, 141794217, 987875485, 694021639, 487802374, 184873027, 426684335, 255481659, 726294948, 152334257, 117751830, 269188881, 203495536, 321283194, 444566899, 741859011, 338311765, 797113294, 813132111, 775735097, 801559971, 733605980, 347584362, 558287620, 207307260, 677463178, 949738888, 978255690, 51399791, 790071888, 739211947, 643273950, 356505268, 92640942, 427891331, 440719496, 440124969, 159464148, 470224334, 965250548, 617380358, 995110368, 156894777, 995291689, 170822853, 582767835, 856341843, 370548058, 525836681, 224761218, 732875440, 852237873, 290827579, 409523111, 653870717, 358085932, 800952351, 640691946, 641350871, 571549011, 673500710, 842553694, 24108886, 511119873, 854053007, 168613415, 761991995, 570237611, 488691248, 231380396, 651236484, 692672989, 993219122, 285808399, 300731570, 971706062, 408981601, 918116926, 709448468, 160915671, 862529361, 359221955, 433910640, 300156931, 196498613, 10645913, 871506087, 302072923, 617492644, 980321910, 298686629, 904682324, 508424213, 273882409, 555775050, 614797527, 460313411, 159348363, 5395289, 344504832, 279966166, 21662889, 865883754, 813846808, 750241154, 394001875, 558994543, 182731795, 209618892, 696967140, 152096418, 615387182, 743447054, 663816774, 185230434, 289658431, 295495938, 322469428, 233241396, 530673015, 280409215, 517190366, 544076553, 302191877, 992249303, 873181803, 891689129, 497285018, 163065991, 980089740, 152499010, 390176785, 883143282, 902580066, 96920150, 683921875, 779650307, 942024101, 159257820, 49252248, 800548861, 588705226, 773887302, 828330506, 51710550, 384579382, 938404374, 249394407, 901751202, 951674049, 559976722, 428130614, 453488301, 989418288, 653335783, 66637881, 188985393, 99280816, 579498735, 618229007, 324889806, 311914453, 349654334, 853079105, 319864797, 455521961, 501076927, 301535485, 777144179, 426186777, 182504695, 275174127, 158662582, 510283241, 674935510, 338485345, 566655639, 477755405, 995456630, 44813636, 202096428, 743262658, 870477782, 757255960, 866844142, 715254561, 497905446, 202884484, 607356827, 524295734, 954949231, 818456774, 775924971, 553935208, 241052055, 925285941, 85477509, 396128066, 399461192, 193338345, 664803349, 190617922, 680352753, 510946364, 312258655, 38045078, 695419893, 533575310, 787904483, 784370334, 561950015, 750571947, 145675953, 165684522, 467894562, 370812000, 382433819, 829566056, 211485809, 962407288, 23007908, 27299817, 470769220, 159343876, 788036926, 993762226, 857911662, 48262463, 757438819, 204356807, 186193522, 8759737, 320379504, 871765652, 513658423, 776618981, 649624978, 460013103, 920870476, 809597508, 107279364, 391026178, 513762654, 201590799, 52153060, 896571078, 318663280, 731121745, 359158074, 199470816, 802010715, 844287868, 202772484, 828565319, 686409929, 337395904, 718107584, 804319564, 510861612, 670116833, 995817844, 290852793, 965853418, 14063824, 724030244, 702355702, 546749951, 194989635, 892895309, 228950054, 224975202, 246629859, 961999657, 276479873, 454214513, 764835886, 10634929, 833282104, 773541996, 65635813, 891373462, 199036917, 227221142, 474952694, 108449305, 202472082, 881220756, 211300327, 282759822, 223841106, 50849477, 676609610, 333407807, 204387392, 152234962, 96493112, 243936671, 866050818, 33574990, 301124103, 298456417, 123232171, 135267047, 292156703, 910032260, 757157977, 189012548, 761371060, 790418341, 41612193, 741182421, 422870508, 191242807, 792936230, 324199365, 737486417, 983443728, 797682293, 209843279, 323326165, 358838611, 296140150, 252966488, 754121071, 902061924, 998931964, 990477286, 423281724, 251571805, 746142736, 850493261, 6670408, 114959675, 972510613, 427340765, 421231944, 93964726, 455028555, 587825863, 566368966, 744339984, 122549773, 850560642, 664823532, 501335944, 456779581, 162247376, 677405865, 598441831, 992114842, 483951639, 373757144, 858314737, 768361951, 776347050, 986061188, 14040753, 338731725, 684242248, 6575192, 185244794, 789714407, 344120705, 952808977, 446833380, 389831867, 508021208, 177121809, 631349233, 879572330, 864846908, 386113007, 187034233, 967974173, 651404020, 443347585, 170820592, 665999280, 258185201, 873602802, 772534500, 169715350, 696916242, 315624806, 936964000, 19660814, 82150849, 465730757, 775397334, 721285626, 531301402, 549155916, 103848094, 125238799, 822874429, 397665748, 127337080, 588692930, 84076960, 678548467, 258758740, 188700754, 243581570, 414847609, 155728838, 818386935, 252659615, 716126062, 902949951, 70440158, 928285114, 796812252, 732376731, 990809593, 686936659, 205734437, 69373808, 863100591, 365271319, 559311147, 871484594, 291324676, 586152270, 658145736, 202509539, 331599676, 101819830, 679789583, 106716441, 824878088, 26716834, 166295969, 341354514, 800649506, 417903810, 604627804, 37687227, 359101372, 771647402, 878347954, 965243255, 555021669, 163502479, 591110684, 559030676, 504869415, 117124256, 879215078, 412045049, 316468605, 533364862, 652841150, 308133739, 371397586, 446303767, 314028555, 624448321, 408470724, 996641726, 688608566, 998403441, 128061261, 897684652, 606140651, 300380619, 173113652, 545186719, 454216517, 357874672, 322592451, 238209133, 237215917, 704305504, 77676047, 540553513, 660808220, 67526786, 275192813, 738928339, 914942160, 597261481, 764153209, 729871510, 912435587, 542799227, 116591344, 112863848, 462176375, 754737490, 969804277, 87151469, 895161967, 804860587, 814969733, 196077848, 239756757, 303943682, 148954052, 108736954, 7715062, 584583172, 836884994, 540710804, 371501579, 256770079, 946089455, 318039467, 499518255, 671478634, 244579278, 864005043, 999992824, 258386245, 753169566, 938506400, 711546784, 622142961, 819685289, 253807415, 231417512, 298554760, 873856677, 77935208, 516946047, 141161959, 790666858, 812639947, 367752235, 549088965, 767096263, 128899383, 993716093, 585325667, 510941656, 255552223, 828936698, 419472455, 910783619, 324387990, 862032556, 928146456, 367336825, 885303412, 273628035, 927128205, 454211452, 313069965, 379825258, 770275162, 16736179, 955641412, 244807116, 109454712, 810380300, 43168194, 417948163, 728813793, 89459509, 710992416, 128395228, 232241610, 875887837, 198379375, 781061632, 161465720, 885820498, 504835495, 571713849, 647244288, 562655483, 900029713, 708244652, 763909615, 902430795, 503693130, 98145426, 661368366, 486897938, 685059447, 225294140, 526185964, 276120309, 989717824, 148432163, 988347180, 322613969, 23087746, 760023428, 657079811, 524621937, 353277210, 252577335, 32413512, 617381982, 387705722, 758602222, 377830389, 85507643, 747514019, 624058542, 719879865, 726639980, 717152433, 248623910, 983327452, 225038131, 733994312, 429887841, 862506484, 760458357, 353636118, 608961372, 376022938, 833354248, 467217265, 620972687, 876128840, 180113300, 461745747, 469893429, 426697342, 597457365, 188565475, 462283982, 884385306, 326768899, 380278964, 475147339, 743948815, 319941116, 271906836, 868402292, 332752272, 87376840, 940238588, 153210892, 854169388, 18074328, 99101549, 25413900, 55172272, 524228739, 136473234, 107237406, 593521764, 677542978, 240798890, 570967972, 710413887, 764067453, 426728345, 298190959, 327823576, 262021686, 733931012, 946367138, 503448288, 233807919, 183477985, 348625364, 437347229, 224113550, 43599507, 577840136, 212355298, 140286388, 373738459, 233310923, 952104784, 140261089, 593730904, 814533023, 293073070, 84523809, 933432818, 970024664, 543104537, 675632975, 740533089, 750260019, 175287549, 760229244, 863829943, 741302247, 63488731, 611156208, 785904434, 378671110, 428469168, 139850544, 168896913, 763176933, 607504491, 863020358, 172213315, 176338194, 411708313, 90556602, 820442247, 866524195, 856509829, 628610393, 855362802, 856224695, 804508122, 213848522, 286893950, 408263291, 571538629, 945709033, 262975309, 422711958, 895451755, 60069506, 272554823, 128300166, 994114078, 960462773, 849052563, 71641071, 704527405, 388360755, 380412321, 878781266, 179573886, 414955041, 4235552, 444119133, 118194860, 493051149, 663362595, 158681230, 168947682, 678866157, 399112648, 900235443, 329020383, 379881128, 216400699, 856217147, 974234485, 123334449, 346442382, 316271697, 324460675, 871678505, 842805905, 294542270, 124832221, 889422758, 976339701, 288774192, 709020002, 170976955, 167767109, 627355487, 619276160, 245614695, 545251911, 526807968, 621516115, 518474749, 159802581, 595872407, 493787102, 787668737, 952163956, 76240996, 12222081, 915464920, 419247550, 517479926, 215580514, 278667675, 559787310, 475420556, 412813170, 908183675, 841920243, 960762322, 66483202, 802682808, 575853563, 283769405, 919510138, 82092268, 340578640, 526194624, 739580372, 438204069, 781804265, 466621889, 168082918, 219430584, 545488118, 371163947, 24941373, 765309707, 309781966, 46315237, 670575905, 614029102, 721950095, 109171810, 456260033, 482832005, 963312147, 114685470, 336100916, 588774157, 472640696, 427403524, 942835041, 6800750, 935077709, 380254602, 924537797, 35883710, 856778699, 154873675, 836424490, 467606222, 95333959, 255230400, 465227476, 581113779, 663241090, 576268142, 855531927, 806517378, 769491440, 722937512, 534701223, 649424386, 258354973, 797566391, 211185597, 30114118, 707557839, 146608859, 716176642, 303671376, 141583002, 18566370, 259626759, 833323065, 634905414, 177893512, 328819437, 374706618, 326223876, 337675575, 48732336, 454703191, 524888442, 395387838, 563111883, 242989832, 831470278, 836804815, 747499431, 644635950, 601186760, 204617695, 829483306, 756764811, 148250633, 371374745, 413173781, 958729151, 205281007, 602490260, 583230457, 865612081, 492242215, 312834288, 408891097, 230182513, 499905537, 335986940, 878899194, 894124708, 496082565, 784188092, 503729024, 140484645, 206247884, 330735481, 64960321, 699490139, 499663182, 468700149, 575251776, 247746548, 919650173, 368232032, 274309106, 581615689, 859985939, 576217559, 231554684, 143356443, 993102327, 70160923, 18052946, 9861084, 799362906, 933457444, 531544773, 716841398, 323751872, 906248867, 166762394, 869785278, 976759510, 202798740, 804458751, 303384445, 53181132, 475165295, 595630720, 599956265, 344341812, 999131453, 613306217, 105975713, 289357079, 625435281, 227364344, 499139951, 567336347, 369886831, 990553875, 152226455, 821592755, 207036609, 943617161, 216323693, 795177562, 209137587, 345158721, 55450374, 780106515, 573140891, 544570742, 232748674, 36659805, 941272459, 671098223, 829955354, 151837274, 158312004, 92982677, 90437444, 729380041, 734390050, 881461609, 485327127, 864456379, 353178444, 5717303, 304238442, 124257466, 35488420, 470328707, 399857513, 868665518, 427257805, 482304533, 162985274, 48396141, 594223613, 348128671, 969199489, 473567479, 148726312, 973326991, 695827613, 821595768, 126130197, 304595284, 987384116, 641969199, 539089226, 535449838, 222129775, 185819600, 676281772, 54888106, 290047847, 330214955, 285005651, 504177865, 277105826, 549160108, 309064915, 257357305, 296515713, 715719123, 450076555, 790268959, 43548591, 244245731, 682931879, 9143233, 81454622, 859058301, 91436589, 140750450, 362813059, 583063429, 106149079, 10202415, 899843905, 706195137, 793875034, 498257091, 846214273, 962226503, 948138929, 880375366, 166028857, 807072502, 772299883, 565011665, 503734081, 716561796, 645515772, 521994975, 655486881, 238511391, 470107337, 600305806, 604674201, 718301080, 225445656, 715371503, 719316777, 693593680, 145738751, 814813586, 763440336, 161340824, 408093948, 92509190, 765387313, 258490051, 521887814, 406235307, 129023568, 304295993, 689446019, 92597369, 744827409, 120935591, 419981259, 915568387, 952044993, 523844010, 578582403, 280961522, 800207115, 121947208, 293393013, 598371830, 959538459, 873788332, 256346760, 197011501, 456494195, 430776161, 996147601, 711635451, 156077835, 612549457, 36334104, 852861471, 825228583, 47202109, 715446979, 574017421, 67927761, 439488677, 665247956, 440090321, 885983574, 590114837, 517669848, 716829088, 41933612, 995779433, 135502065, 271295832, 803495047, 690789280, 179432246, 752796261, 373931571, 643404359, 31158238, 389530158, 570572039, 221408417, 859344300, 480758293, 158350815, 43995876, 804045998, 174833179, 453296292, 911920655, 339853361, 400823523, 251315347, 361498850, 711733637, 907357044, 289552309, 637927313, 857604244, 114200789, 478900391, 988503871, 94268497, 953823024, 148229657, 3699847, 654692913, 495730134, 608295725, 322819665, 860192698, 477621075, 326199244, 91573797, 558053212, 122042422, 499273345, 905013562, 469273131, 114556166, 469635572, 209617839, 925236311, 579155209, 188869760, 863532576, 762348454, 894321114, 598924671, 548072245, 758969888, 248730187, 22865214, 416755901, 849326930, 405460131, 307650108, 325968695, 584937633, 770587794, 930225118, 37227256, 696651535, 880047586, 795227943, 970207074, 219235015, 477627330, 27058500, 816955418, 417575988, 253593608, 750585854, 805092351, 362941668, 113062297, 741322876, 840354079, 970608171, 155168218, 331156776, 414559769, 578125118, 994482529, 950801796, 4315185, 411297828, 835057651, 667691035, 440164701, 303154060, 444067084, 681499861, 912110667, 223481109, 238045005, 95422806, 158746835, 693023783, 939416008, 875953869, 808080725, 777555968, 259689564, 744183783, 965987185, 685343322, 772528570, 146617773, 710892650, 310042225, 408636894, 534673736, 877016604, 879547594, 818005110, 226712838, 152018775, 543706471, 275086545, 217160090, 932891373, 785818491, 75879488, 722096893, 84465382, 951473386, 652333403, 675373975, 728972858, 917506027, 115727143, 750986064, 387092232, 144383817, 541534372, 182805897, 418576153, 323820716, 601748092, 175232377, 791288382, 495122909, 801761885, 567550903, 507831094, 43983203, 853257931, 818194024, 685949631, 33248653, 446113160, 553521612, 583317104, 638241870, 470400867, 913683021, 799771315, 542217874, 849196119, 578125559, 739491000, 331452307, 386670152, 484718267, 546145622, 599773333, 606573682, 692685735, 421179322, 73044869, 494261828, 696776395, 975035253, 106116546, 287601969, 124968885, 953583578, 365090717, 183791307, 241288181, 220468901, 568138970, 372604953, 612259903, 44980239, 118331091, 761772723, 955775028, 336199950, 236511065, 770324004, 157721901, 961882119, 558948662, 559256445, 928851410, 858178715, 905619642, 995132893, 447851587, 542854858, 166697231, 971164957, 574305869, 528590930, 832268476, 107002551, 222057001, 702273791, 659111279, 424608880, 441381503, 471745807, 525506177, 877662769, 296017110, 625925036, 705593481, 976777480, 21376420, 831072625, 53361520, 758187296, 42619204, 965195351, 545338576, 390224383, 298824118, 323466401, 722526138, 247716230, 540889921, 136938189, 955097510, 896557395, 142977875, 539772099, 177481109, 359104203, 134909590, 521129118, 910140327, 699938024, 306215558, 343542731, 891154079, 271281476, 250244181, 479790255, 50497220, 890519320, 12412592, 698549585, 37336695, 193485182, 575251189, 693825788, 680745702, 634147283, 122204218, 655063097, 771973551, 78978045, 687353568, 967553467, 952497772, 563568028, 366031683, 233251503, 787865713, 101538888, 753160599, 221610491, 211727359, 134252172, 239373000, 511660869, 260725523, 418177720, 389869769, 942261419, 437383184, 954645757, 434985758, 552931859, 180364834, 157159798, 583717755, 317491533, 804629655, 380829790, 250335572, 118461662, 188056244, 834056178, 276066164, 892494502, 646737261, 500918500, 151061442, 613444514, 346287339, 303326819, 906963858, 364287133, 967237039, 243758558, 419219253, 209710069, 316906254, 502909151, 784083346, 861238049, 774690470, 491285513, 867587893, 685927141, 731050884, 3397142, 892013549, 361665196, 124215817, 445904643, 876169176, 948416100, 211716033, 464549544, 830020511, 509216928, 142497041, 252185515, 367790766, 990485124, 146010163, 203004025, 348294952, 710383818, 169476948, 983617556, 897431138, 107547578, 532227749, 143395589, 897379647, 92888075, 35483514, 810165543, 545272227, 767550003, 287820628, 784160137, 782517844, 158006306, 882803724, 668499654, 112047192, 914185701, 273008904, 260388605, 238054878, 83279067, 153449524, 828263516, 919668430, 424968909, 120850725, 756158558, 253391078, 887191982, 904539588, 959672617, 310588787, 931152331, 764570918, 422972196, 149838867, 129124598, 220728757, 54561063, 731827350, 895949435, 364556663, 605898873, 6977075, 528377315, 137413997, 540136074, 444819960, 939933767, 553708920, 684080709, 190762811, 307021011, 91961868, 623804736, 557512876, 361197790, 430397748, 328103673, 697337181, 133338249, 933643640, 734330582, 981349679, 966017610, 898164516, 187889349, 989307996, 714392017, 765602866, 698253927, 916132789, 376509631, 94859475, 626634225, 743793524, 773197049, 308330393, 808154015, 556555025, 678778555, 398842187, 904432109, 56117274, 364083057, 792172715, 229937193, 61482690, 406337011, 815673827, 338849830, 922419471, 96689570, 301221482, 292076699, 334444196, 121950018, 544695410, 471750611, 167591523, 916323883, 829094303, 327979137, 207504679, 597711538, 132734832, 172196842, 964342313, 244817358, 480430505, 792692291, 438099892, 940358779, 685316942, 59673320, 186469866, 834786664, 864377935, 663655199, 383385520, 587265274, 983060291, 848223118, 458104515, 971606988, 442808941, 638089983, 372201360, 580071301, 118499882, 435809213, 288573527, 341064601, 237624410, 277329541, 993393155, 171500052, 678370175, 477038199, 781783451, 462207229, 859371093, 972721773, 678591725, 416807374, 715394717, 512633423, 261243384, 745731762, 582872911, 992635338, 424279931, 547299765, 613682322, 759466955, 864863475, 881833635, 108393935, 825728885, 752662047, 718629782, 24335325, 264531015, 735970998, 955234847, 899470018, 137958995, 729997850, 97969914, 923752212, 512428618, 946790592, 637329437, 576053594, 795955634, 186246067, 501446976, 373789324, 513853898, 712738654, 560866059, 509033942, 899266863, 107318519, 957669078, 179550467, 945402326, 800044541, 164233833, 167447012, 876179418, 73353392, 299852252, 139792288, 362632795, 226041885, 94081985, 258197023, 775301442, 10639756, 532279306, 831466450, 935627227, 856281600, 354508308, 170022231, 401238978, 94032153, 837097412, 945795496, 446172811, 457708576, 14248424, 68737462, 945669044, 213030379, 277927695, 446179842, 231686601, 749773969, 302211267, 612244072, 519164351, 789348831, 53345131, 843905184, 418524989, 980734031, 251491575, 623159805, 390646788, 128809138, 553854545, 313705327, 890965923, 308665835, 333464309, 440692258, 700305887, 289985646, 963945988, 337900751, 434950441, 905648369, 608543197, 861405891, 766466698, 138281471, 895499141, 763590670, 164043332, 719985643, 150295018, 718645579, 399079948, 798308103, 806093914, 772012789, 97653684, 767324753, 622524268, 208524240, 886938103, 146980829, 820783058, 128801913, 993179239, 481072268, 308943769, 908728783, 582504120, 110521008, 734155652, 604849786, 227918792, 585348909, 864351532, 373252804, 758328172, 763066238, 825543447, 706845725, 128660157, 390954450, 363752054, 296988000, 234154241, 851923184, 133015401, 310718724, 624842262, 435271808, 891539537, 139733262, 445636368, 38043307, 784846575, 379361309, 725410527, 580611160, 163381959, 872885576, 705266647, 370119502, 728197479, 714400175, 370245498, 363956697, 288555275, 552912551, 389397761, 823896564, 650121796, 186827596, 252710678, 668679317, 529445957, 477183395, 33985775, 781265175, 486414401, 491324605, 31990399, 486948994, 95627856, 578967114, 760678122, 362007999, 497707157, 671393134, 119424057, 831789046, 375481500, 91053021, 530472382, 196871361, 42937207, 321368232, 735768557, 189049703, 455946840, 855992700, 255196046, 3786634, 835270774, 559042276, 822477671, 697268532, 934532799, 900379030, 96077236, 713424183, 761805697, 22470790, 261457109, 932594129, 846303653, 244091229, 176951595, 62810364, 886378410, 372875946, 637257926, 985807585, 747108386, 790445191, 710930672, 182295970, 244735145, 736702778, 706809291, 333341119, 105298848, 915919667, 91002782, 364804304, 175102800, 690847777, 883211783, 709759887, 450617346, 257128889, 791832899, 806002197, 820100046, 352824254, 243074534, 745137051, 798725711, 48114551, 955231114, 605010258, 41083308, 198031001, 303590462, 180817066, 41186939, 139921800, 461614516, 165725960, 873182316, 107686680, 928478775, 964139705, 963522177, 77470798, 611057181, 461089185, 276939757, 788582061, 280981388, 54146079, 103232543, 55965088, 994275296, 637816775, 605887706, 797386501, 75845804, 35068845, 61716617, 930742491, 268105755, 453324626, 632968702, 843629741, 548724663, 945105713, 176251016, 629839757, 358220210, 251544086, 95694305, 595463472, 534146851, 123372570, 868194401, 200568676, 273335889, 501725608, 161191764, 751614207, 376892130, 206233522, 654491088, 141641060, 593981462, 700319594, 186622732, 767543414, 71462297, 46586365, 240697981, 833206946, 158442673, 656778096, 508563036, 485508056, 583239290, 445112633, 565481365, 992070095, 294515958, 92619013, 344727252, 199429727, 972040962, 190527586, 377854767, 960413645, 306240200, 697784597, 424987244, 722892669, 140176737, 813444104, 93698160, 487680480, 869145533, 634009077, 254377349, 737818551, 865050302, 525322314, 180277780, 940649729, 735278655, 877887973, 916943471, 563299439, 335864831, 640952312, 944228794, 398904830, 611026076, 779153053, 262952881, 396201904, 902276753, 57629050, 510415429, 533981785, 991793806, 80963107, 43685009, 262573580, 361790359, 678943430, 343521836, 190660831, 534592741, 31158380, 348743811, 27696786, 200688928, 487552194, 721075811, 861767094, 631245155, 763336688, 131635768, 863539133, 154616060, 260218345, 269271912, 232207230, 399330618, 731659231, 768993422, 18279480, 907377321, 990182110, 570523078, 259827941, 80227405, 403853845, 668734628, 326473300, 775832369, 139165297, 597143578, 877444788, 889145026, 293402327, 605973247, 936462076, 409060742, 144912702, 152694837, 197957429, 638674367, 107468291, 250489811, 226797697, 447548920, 720419857, 426289309, 478506565, 318702300, 199508272, 974967605, 529819302, 847520482, 324764207, 655583752, 622171712, 328204650, 23842271, 84416346, 142389622, 244549988, 683143973, 4219252, 128619656, 217012183, 617909832, 397314149, 383984144, 202142847, 576950272, 4819380, 767000101, 598215380, 332002267, 532040321, 758966408, 875177533, 586484071, 546771860, 759465430, 920828475, 607477917, 689535996, 15624705, 398916806, 428846861, 789370311, 519190857, 583547797, 670290788, 793382199, 600863563, 287182040, 769164602, 693353592, 251608361, 952708777, 79428385, 443470959, 32717170, 48079978, 795162979, 277484830, 214954732, 461671060, 886577720, 20007386, 427966036, 310130622, 491626328, 791080538, 295336013, 436175444, 885196330, 480268781, 373420544, 178072272, 798168898, 238492398, 294766293, 537448284, 187238248, 662254920, 149555476, 922426254, 610379170, 833417415, 902054465, 354432727, 516591108, 911734079, 666134729, 242469809, 66089849, 859760052, 361917206, 476111692, 569351624, 337919280, 238918095, 422329512, 241635459, 671369684, 368138355, 907681830, 261665994, 905237383, 709364421, 1411373, 575321184, 185277054, 67378494, 821190347, 849727798, 301332379, 493492986, 988426610, 746122172, 936697034, 876785107, 506122136, 174670444, 534043150, 579934048, 257118882, 421298124, 871016276, 473968156, 282314814, 376225068, 689603940, 871574626, 74252606, 487673943, 528464774, 595668243, 468053823, 137020345, 165351297, 694964371, 666738029, 977434570, 180527703, 813492208, 683086182, 10598515, 597465539, 824559237, 714981382, 257526, 509710205, 641986059, 111139340, 34846402, 473042142, 739248641, 298430303, 545418523, 705643316, 442495616, 485545391, 832886998, 304262685, 669868766, 985162230, 79544533, 519034402, 23414562, 437595423, 134612803, 823960964, 814561721, 92309914, 816621414, 749441579, 889127056, 163622976, 784346722, 759746838, 690983127, 791588963, 280355011, 512125704, 643464269, 139566685, 159107581, 970788605, 281952808, 38207299, 969469026, 991983114, 427531294, 178521649, 477188157, 283494623, 488667665, 849101470, 125533580, 680748703, 850383397, 401245284, 691930157, 510768904, 548669448, 799574302, 846544707, 632555311, 334181263, 649174919, 694337913, 845730155, 242429801, 3250090, 675530235, 685681560, 486274311, 350739049, 519568757, 111737646, 336662725, 52258934, 944153112, 526848227, 632832047, 731286087, 44824577, 121709669, 941961305, 222199408, 629225305, 141033232, 209065314, 808544255, 710277331, 892762220, 911823376, 443175423, 598804577, 34381798, 821168259, 62777338, 983572798, 315642270, 476457115, 201553548, 494558037, 470574484, 648125341, 231600827, 457508517, 225873005, 998018221, 626180329, 398919188, 69874014, 250600894, 693015912, 393194250, 302947310, 916310078, 310992424, 473522977, 774405667, 133123085, 276846371, 425314660, 582962923, 496245627, 162546196, 821966315, 146044812, 191172896, 465720270, 575812191, 942198229, 855166408, 546986681, 352803701, 22219404, 592405554, 392068370, 669589051, 287567920, 296324927, 202345911, 247507541, 108088570, 122170403, 835870605, 407239513, 295924227, 378932186, 250015229, 851094809, 938288362, 827667496, 573616077, 568879391, 390537160, 798707443, 25019201, 186110864, 566443439, 335020991, 665820772, 30955525, 993338351, 855134468, 832844871, 335247968, 527508398, 5970392, 421409926, 432700058, 337694270, 605644735, 784166209, 40520971, 954752553, 594922792, 991418340, 340411583, 934746726, 318600828, 478963872, 12411768, 23955742, 14269221, 803692610, 976641316, 9444507, 562474990, 434865724, 607750595, 746410547, 658834691, 331198326, 506944280, 867193682, 561290784, 385560683, 655216939, 21606614, 32889176, 72654648, 89997332, 278691150, 287463871, 546219483, 371272013, 369979055, 243821633, 446385726, 116126861, 962560726, 23853054, 945400698, 6601913, 987851006, 588813337, 592621339, 393974626, 727625773, 408250757, 947854589, 65936539, 340396373, 538958651, 358442847, 64734247, 645020634, 690290764, 943074489, 778051737, 527903631, 770807816, 760111628, 173647183, 290122711, 575855285, 738230390, 579089477, 329983862, 680935396, 122669234, 871515168, 870127320, 246787235, 423558312, 452616936, 306617774, 603967783, 632150393, 499019537, 452291549, 955833287, 955171642, 740173156, 408728901, 2843556, 14556124, 117621816, 4556601, 220050807, 343526189, 671375299, 239937221, 540652370, 750015482, 83555701, 539931499, 845219718, 558902717, 710695941, 141954201, 329257589, 447914338, 982920014, 331187212, 923483812, 307253648, 132302384, 881220757, 301751747, 71534563, 904930244, 218203479, 780850456, 604546037, 357512390, 632529562, 427855725, 867098880, 218351116, 399818681, 526930114, 88936323, 913564052, 924651145, 576142833, 205726098, 769035167, 522789294, 269116166, 439085797, 785777724, 863988313, 4421996, 393050786, 824082431, 591438403, 996037194, 790236416, 106962727, 140197265, 867269987, 818571651, 899486854, 629671749, 710652187, 97726970, 749029871, 831931367, 856084236, 312756447, 575544945, 106075659, 294867315, 988306433, 557115179, 931693234, 239086184, 55849912, 822474529, 945028713, 309781972, 546401863, 825490622, 521270357, 821646313, 275825806, 17083739, 911422242, 472201486, 416162344, 658263759, 313864293, 708535034, 855288102, 365392317, 103910135, 559607773, 813312005, 608984000, 643417913, 868801757, 127326044, 96533334, 577820184, 92081468, 89422263, 389666091, 148017468, 63976236, 839649946, 276296684, 294880639, 231513152, 190077468, 65634504, 879006969, 417497174, 773912021, 159923511, 886266870, 812526391, 690376236, 378874913, 707398425, 65631497, 27943941, 438383871, 444034042, 954532645, 330808929, 975003364, 997062931, 356215774, 989846664, 709972467, 674792321, 334418581, 330907546, 765143921, 411481094, 573427535, 337998505, 503501861, 118846361, 865079936, 935391905, 708593815, 765662757, 754680723, 545595546, 759011460, 620712534, 353487086, 631728706, 457554389, 966998023, 112807936, 466214967, 796014487, 250535136, 421597614, 825535863, 781680741, 862965480, 686435342, 836701254, 108045064, 363521009, 878757395, 572216789, 762196850, 532210920, 136927496, 972813215, 582895502, 285931351, 836696756, 694735515, 186231612, 116522521, 447687183, 230569010, 445209736, 576549892, 895272181, 364953408, 468971838, 133289564, 163650161, 149971217, 126093433, 587264322, 511515605, 525024231, 67815260, 555696909, 314890432, 300535610, 144067630, 973928932, 999504249, 285506066, 439201545, 396994990, 323361430, 415532022, 659436306, 511933027, 831664685, 264507528, 481687977, 401289463, 803473800, 365451939, 619475989, 276789771, 123725792, 377061568, 350861048, 74997282, 631188016, 729178321, 233751202, 418743680, 511365391, 8331534, 725267797, 985485086, 660035359, 261776455, 752679817, 597756013, 91927292, 320731653, 519470501, 953229494, 175370208, 994546204, 613156740, 694145695, 334205351, 902459845, 933838909, 359976753, 560092381, 155741070, 908436979, 900210120, 184361866, 655968008, 375944865, 701850183, 435111867, 457686748, 428182331, 575142599, 187779520, 617575488, 939904629, 549786291, 224217359, 876032685, 534449669, 207631627, 444549121, 869249276, 398839729, 903285445, 633887900, 974538994, 393714534, 999266417, 632989807, 437362271, 701649553, 285938343, 410285357, 611342041, 901859565, 362171220, 834287652, 49859952, 849156723, 785510905, 589006446, 120684252, 83435173, 191002412, 473630724, 830913845, 292745663, 899433351, 309938061, 324915089, 432119287, 655718613, 751157685, 344619991, 576003041, 910935967, 705584748, 899280521, 457557955, 781490474, 436931620, 772995291, 368648326, 328346293, 388785316, 794620148, 473967070, 169206691, 81727781, 929538285, 327899973, 547205702, 665608983, 9663122, 452241707, 418250745, 197292141, 233904589, 814422323, 869055111, 656042555, 148989121, 97510416, 144062543, 127578028, 787318843, 762862317, 332702997, 850786857, 179916671, 675577123, 35309820, 211233662, 544705576, 108912289, 775562124, 941978966, 51907637, 171513003, 922896589, 315193775, 987765887, 579928144, 449323200, 98540235, 323100233, 760267821, 720205321, 548866071, 667637794, 444246899, 819702088, 291811897, 974802594, 922188328, 752868595, 7897490, 722228015, 106582438, 56038596, 777715590, 206698688, 764314418, 51484817, 984802117, 890328826, 593838153, 511184155, 432348677, 338929006, 69497911, 192154695, 656954776, 61193291, 265592913, 440723885, 321417695, 386705850, 551094684, 586404236, 866712725, 33516793, 425083417, 455430309, 754141819, 2076131, 697436934, 8753523, 842675344, 481346358, 219612837, 311252435, 344656285, 951009962, 228943931, 834094886, 35813698, 416349406, 69747313, 27599363, 886970577, 828474436, 194233109, 138486961, 774468404, 938704979, 511783304, 137185599, 622027462, 702288979, 980271564, 875870014, 351821917, 836711996, 662829627, 827215861, 102351841, 565647706, 661752919, 469916929, 446352987, 917029459, 673265266, 827385952, 810872822, 471475860, 213534830, 114556198, 611462230, 508600735, 169750989, 543114743, 729945099, 417592028, 679583494, 899564084, 787412332, 484750292, 95500589, 46330011, 357828895, 688810017, 468657709, 364546548, 154901278, 588814786, 436868404, 356212656, 83111871, 818570865, 635936735, 700533201, 569854738, 886107289, 417321805, 395359719, 110842776, 616752956, 704044957, 256771805, 854721070, 766020021, 102875926, 147937850, 70524858, 751407823, 434868434, 449935724, 560348062, 890444774, 362217358, 743828042, 96277956, 547926110, 656698864, 725886495, 814545436, 537193588, 51305309, 684284561, 429209632, 428406437, 361480861, 895057312, 468435663, 567963571, 631878759, 996692557, 851529726, 310260446, 747038126, 145072821, 292080268, 674897363, 563832728, 898501640, 987534679, 20185483, 147616139, 950292322, 61036825, 215453722, 969848378, 611339725, 63490978, 464554739, 463331777, 289573961, 826004711, 885093845, 798346524, 26298224, 86675876, 522092516, 220989584, 49373865, 769715565, 884982448, 825376805, 568279306, 682645590, 413431977, 215140436, 299917375, 384320026, 714430190, 113941958, 862626932, 881449710, 984564645, 70325694, 68485577, 837259294, 858957626, 745515477, 194068917, 87382686, 227836443, 15472435, 926676552, 967899927, 841089889, 536749276, 510112487, 322064537, 245140722, 333200664, 79775044, 921153424, 638072841, 63942797, 642378744, 392052046, 488951393, 19915430, 197261599, 502706896, 638958852, 174191730, 765209825, 14259551, 642138747, 79379778, 449403147, 919030559, 950229451, 981921197, 169773378, 435593034, 632801588, 285882292, 886296284, 459896779, 125273967, 693869981, 529106508, 636347851, 575444659, 946983351, 966863375, 684384167, 340364733, 982051591, 589838824, 81008733, 122664931, 620635583, 291987146, 642091584, 733907073, 595879, 185979919, 110081396, 20739321, 355907743, 468710262, 81754864, 905749741, 256088302, 58652045, 684087799, 493315767, 401858007, 699932287, 628649597, 829665999, 284531891, 569495009, 254931843, 336144004, 257788686, 540989255, 309981548, 199688457, 704312109, 163350349, 34585859, 426736477, 252985357, 893809131, 131618271, 532546517, 645122357, 70015165, 408394234, 663796774, 803940228, 240349561, 26619877, 187795616, 970170867, 613147078, 82915004, 790057938, 298179145, 192293718, 256460965, 20615310, 803278609, 28198528, 881888960, 454533869, 213642716, 11101132, 130403365, 296775584, 408394807, 686460913, 179062073, 673697249, 7268146, 548516447, 345704370, 783083333, 612556057, 898926335, 873345902, 527710134, 372553782, 819616133, 236672993, 865996460, 913237399, 339321110, 666614305, 500170013, 570855118, 172750425, 739318185, 138762634, 21640057, 341111462, 445927682, 24562151, 892966270, 196087061, 749110661, 884651022, 997933724, 789680249, 770400828, 45756272, 15888991, 297395975, 620348436, 895415386, 623029552, 68671462, 83355570, 273794804, 130016994, 757957130, 26831548, 872396671, 862631374, 858063504, 510821664, 671752775, 333620741, 127565198, 903251823, 594243595, 618637096, 423933313, 614588413, 623722600, 129831472, 456616694, 714107367, 106291466, 152545216, 843373390, 900067958, 35230307, 844142679, 97666619, 346771439, 859704313, 972048702, 952146233, 788991595, 674057570, 799116756, 355434523, 66091089, 681180931, 563341894, 932235701, 453567835, 873637830, 268089702, 420473791, 254809809, 713155328, 308859925, 224354081, 838828768, 174397578, 248067867, 658180535, 118216570, 935133071, 106079993, 789275453, 282388928, 431018458, 791011323, 275629260, 823164405, 222712518, 308011452, 295280662, 811214413, 493450360, 937896338, 409669566, 326156482, 682103227, 325923940, 136905051, 652403758, 179428854, 12050950, 376749713, 224058895, 967966093, 349044825, 270439753, 81330249, 337109510, 924706320, 647550148, 982286090, 737065839, 881511305, 500698844, 143964988, 623183187, 728972342, 444151974, 530304469, 164252405, 374080802, 474634612, 103711107, 591960142, 75231372, 24379847, 256697662, 211732109, 814651169, 195191582, 155787821, 789628782, 924703704, 144343437, 952000549, 2109974, 304112677, 965605443, 525324314, 258739158, 563348335, 238615846, 758201060, 246931061, 364228487, 541533284, 770551184, 168903740, 676889251, 343600146, 480461936, 838303575, 659903314, 86403721, 383408803, 716674142, 948374157, 919679340, 882713549, 368575307, 233681384, 932530711, 803715170, 717163811, 530524549, 634412972, 444576890, 204591747, 233938419, 533576069, 704857753, 808268124, 125842000, 985911638, 651440072, 332686165, 107135658, 428440354, 817648107, 253892482, 458989428, 817157194, 584792210, 379216536, 558117874, 992159345, 316746554, 494500518, 566765734, 978243077, 628731043, 119118944, 572009822, 702093741, 863401307, 523834657, 737079013, 609668057, 946761161, 534820616, 233574077, 95603101, 461214994, 924837541, 45089786, 23607068, 974419485, 251966450, 340189006, 434232949, 807559586, 878080599, 779674753, 769825099, 411166547, 652988285, 741579341, 288449768, 912112690, 954758076, 783344296, 975000551, 327602002, 690418288, 335222675, 629872799, 770369842, 280490879, 77961234, 25850166, 822048232, 732461288, 486438094, 887427392, 406974161, 653397734, 591685480, 491331034, 809477557, 82077678, 730224128, 60102544, 212799224, 997552930, 98164519, 661163144, 783083039, 187452854, 786137417, 721970809, 967053802, 778228810, 420678847, 605244644, 674791686, 256288877, 579488556, 995006487, 473966089, 702464040, 411034740, 812934991, 635457658, 984866064, 181773989, 609129242, 650016876, 521206358, 873445166, 454589227, 837963056, 303464791, 219619422, 341567592, 708983139, 165903000, 815192600, 48736657, 605887872, 923701834, 784397532, 509933098, 262049039, 218575275, 930701487, 781901720, 76714006, 555501257, 619133103, 915130047, 445689452, 547815382, 144850395, 241068132, 325682166, 661873959, 994822104, 309691929, 517091123, 539514894, 733541963, 371781006, 386044478, 326042939, 156227661, 261688275, 941564019, 544878828, 960850381, 404132335, 244982998, 363639959, 478721869, 805134513, 832852313, 499941494, 389537013, 988738334, 973082547, 320530101, 306886864, 441194520, 889299729, 164331136, 881231648, 504794469, 84930211, 147920543, 904012292, 876943475, 574047504, 752483133, 460975770, 334839198, 413508227, 873426386, 732313279, 577349272, 684043988, 916599157, 906140820, 264380418, 87739839, 655044414, 992144849, 522300546, 871105643, 538331803, 976989346, 169377550, 914865347, 926867257, 638607707, 741680631, 953064965, 306783522, 669037377, 441582862, 114900431, 337713244, 507455860, 635045116, 696888408, 608721418, 600517319, 635264394, 80429055, 180549866, 228079573, 419508809, 182521045, 173520476, 538795932, 459032061, 715922500, 739210776, 180851417, 14310801, 321807588, 723806448, 431300874, 188286288, 747003567, 662440194, 54940099, 98319890, 312470570, 492100163, 666574948, 634313719, 179882221, 714003739, 255727819, 434582675, 53057327, 123570481, 814462879, 551130973, 783350612, 421818272, 210940639, 869310100, 799239482, 730071624, 651710316, 24977205, 562905308, 797295081, 847017788, 27014338, 469728652, 457125402, 241022081, 55271980, 967268993, 41522408, 599119904, 917140264, 300340908, 636507762, 317210196, 229549780, 796514282, 355457634, 9994876, 621728029, 630472073, 71532312, 787937665, 926504774, 479239317, 179598215, 148354463, 518310121, 278000319, 611769957, 324506135, 502748942, 715552903, 209853753, 119452349, 77384043, 762898893, 336808957, 743226085, 582089143, 237444647, 779908609, 179353333, 69978650, 489072302, 309332820, 114046742, 339387333, 963048042, 736844868, 394264632, 543485884, 800141192, 176246323, 420382789, 478337365, 398714246, 85627492, 746532463, 421912707, 81910281, 562199796, 122996384, 325485175, 886610782, 800453445, 612700288, 711031788, 559204780, 855608907, 916258969, 155129213, 359776084, 328390501, 128870292, 377378739, 233083583, 255424937, 804786420, 662976559, 467509361, 843823855, 165379997, 863806560, 727870030, 844444385, 941479286, 239962740, 6187834, 908957425, 123606967, 994586009, 731333908, 340500933, 406754502, 930116737, 545047888, 20458744, 407339218, 774413504, 256286733, 161439799, 223133972, 258073462, 435502783, 615698978, 550496502, 507509142, 401885866, 321713465, 286856396, 236269359, 179248296, 12158995, 96956560, 125296085, 701263704, 17170125, 78966102, 495013638, 343052935, 948188208, 283587371, 321229396, 450186946, 129090722, 951127958, 738439711, 338665052, 470277079, 429124836, 439649950, 483756855, 152094903, 513233140, 739427090, 792070707, 244062718, 533941047, 4083909, 872417296, 778922490, 546567200, 685084287, 552044058, 16371914, 598815327, 218593490, 823760406, 567381938, 49988315, 143077900, 694769909, 398142238, 366792444, 81835770, 419319020, 291980051, 861876075, 847498395, 42224155, 650468046, 262679882, 370766254, 296935595, 700859352, 271484730, 631584383, 34626656, 32518361, 138848666, 608213603, 727067448, 682586313, 757050698, 41761206, 645483186, 266336090, 822854048, 74032185, 845051068, 63919924, 892711382, 396446844, 960760699, 169869448, 672849192, 501274131, 425634046, 487628479, 283758077, 980559106, 645632502, 405067242, 975760370, 395669726, 872978153, 211712793, 329793273, 668153592, 701482585, 800823240, 550890728, 491882126, 735384952, 480659516, 927033177, 34929480, 485207252, 179287234, 46236501, 394854203, 692316212, 888579751, 397837962, 563167160, 235990792, 614416216, 699264379, 448437703, 105424439, 541464828, 49163120, 803338556, 638350589, 73164684, 528582859, 555039593, 750281567, 488065721, 450654618, 152898018, 826275753, 707966592, 615426239, 880587539, 659395762, 919059573, 292374807, 431128108, 591247026, 807028545, 798417952, 558985068, 179310875, 169526588, 891503947, 213429532, 350567106, 750705856, 247947542, 567513947, 499361134, 979163546, 847534751, 184268312, 219377849, 798680600, 707226578, 267766095, 759534924, 464381721, 619663661, 766039361, 877594144, 505745313, 848799938, 795388486, 483846569, 184556270, 116549620, 731538213, 875489531, 116101250, 318871011, 968857503, 249948140, 630171805, 94654159, 600325411, 449400321, 352777444, 871424896, 438430106, 571278671, 31368605, 788571946, 566125289, 783430460, 899038240, 670603893, 421773590, 351173377, 737463709, 108782167, 322931303, 525098741, 790718475, 46151213, 743004734, 303461887, 160191225, 763360618, 49275441, 168883602, 735025890, 957114972, 431347994, 812048557, 969879958, 103851499, 672965820, 703369295, 684000450, 576007361, 612913366, 208071976, 51026784, 37425448, 775246514, 590965187, 232748533, 505070729, 403650953, 298359445, 79341684, 444937645, 96321676, 656783661, 808217829, 231221261, 257428676, 249314006, 167463813, 345744046, 338896579, 474107324, 789992786, 355719352, 526104400, 404512660, 645828913, 493676646, 56660055, 885266840, 89860430, 602110182, 991018454, 144443861, 881254873, 109568176, 363099981, 515645635, 948686300, 776975596, 680017946, 554060442, 600109554, 397355565, 490265906, 770956819, 825563090, 454328176, 754494469, 315145228, 109684518, 253845150, 956097314, 958105018, 556003874, 191345923, 758291863, 666317329, 236369982, 605591665, 345355253, 764691742, 752236157, 220032471, 948143290, 835999685, 149247241, 353458560, 484503522, 572573798, 581498775, 597152131, 490480173, 277482522, 957136456, 465083935, 877651901, 362177312, 184077594, 436966437, 111053081, 870240906, 430245163, 543629025, 420664961, 678955278, 46932516, 266431056, 286859879, 903493156, 836868967, 253058978, 978790452, 667505688, 248528452, 611189967, 390099240, 893688167, 966926945, 884996739, 304760371, 497873692, 332451708, 944299850, 838601134, 101749038, 470681193, 877565400, 940687940, 665280826, 575139315, 714606952, 524712257, 41726140, 175647422, 268652631, 747572732, 776797244, 558791445, 331385411, 139072402, 453388435, 537337382, 711745216, 351486928, 306139954, 680114357, 636712680, 473528563, 794619091, 198053191, 125429120, 776609629, 59955122, 105499002, 569339501, 127919966, 727313277, 421491967, 661861039, 787800602, 276654338, 349573974, 704476166, 292501285, 240866296, 117720821, 646464362, 430225993, 64124815, 222270591, 721304013, 481754513, 427043892, 463621509, 10035375, 227858135, 316040053, 226208264, 12362593, 337934535, 904727625, 894972825, 66900435, 914713764, 410078251, 1602706, 577845733, 576911177, 304440064, 221635167, 596682381, 37592555, 852590288, 109815625, 323209805, 292481305, 49782214, 322458373, 751438410, 522605083, 533974562, 556874695, 247543397, 998666511, 301293792, 568472874, 995189169, 981855319, 403347287, 34573258, 957495153, 678740128, 646288809, 519302629, 534818243, 343007087, 872054997, 994118669, 469584440, 112438440, 72615764, 117058282, 293061724, 124890844, 407107539, 884626160, 428898676, 172119334, 174436198, 245201098, 959876549, 109663726, 641364924, 88978777, 599703988, 601510366, 884981766, 876856486, 353803959, 918770096, 845657758, 663719699, 707747891, 216348848, 197883205, 51865400, 70965561, 493051545, 214478786, 865030202, 301137583, 57601068, 869311683, 993262781, 965096367, 942080944, 655746414, 603326216, 75822170, 297526297, 641056242, 312650575, 527119016, 87484932, 741205537, 750499932, 779435504, 493777457, 120355222, 286256045, 585446091, 557164418, 598267232, 671894848, 275748157, 787223589, 183352647, 854244127, 827007262, 321590811, 98968887, 418775884, 136276105, 53062881, 480595904, 812287112, 132094193, 870933677, 825320572, 510150726, 576981568, 692569558, 302533421, 234527252, 631919486, 773882565, 588422180, 539572355, 257757594, 559429836, 395667868, 619309398, 128672291, 977438985, 202852480, 200315590, 161551080, 765877472, 782559062, 780664959, 429412646, 89881614, 986412334, 813339054, 196015659, 527783503, 634271047, 411864606, 679751597, 358140524, 280811127, 312501985, 386774947, 116282885, 336299818, 318945832, 587524102, 39784437, 363645662, 694548172, 419131876, 980824164, 740744433, 396315075, 485920241, 678321187, 574730287, 289659508, 551555188, 293063631, 251875156, 888692100, 540548856, 924091956, 845741666, 119281145, 312035491, 513284263, 868913542, 533455314, 522674228, 203957781, 661034274, 107082906, 55688465, 954263032, 57426018, 205346169, 34319993, 680704831, 299083991, 216720335, 466508559, 368165763, 927761170, 953916046, 390403821, 361145027, 509914234, 426708332, 622200301, 98405507, 115048363, 489718990, 707250090, 232126139, 852291686, 859672736, 714645138, 721396893, 240651893, 320091787, 811243864, 701199894, 606645755, 16262341, 257254721, 998723668, 845608517, 434127989, 73857210, 574929705, 958128452, 707860664, 312064402, 93631016, 815650439, 574681847, 346400853, 327075582, 482399618, 436887967, 283441956, 652252100, 493583650, 833985033, 672813742, 300303234, 329523599, 646834036, 206849755, 520315374, 226431238, 647392184, 852918057, 73979107, 422491468, 83470112, 696706238, 496281787, 199727409, 322133106, 702141805, 135096109, 982652988, 235008196, 387135924, 303013419, 481428693, 678826510, 150702399, 167561380, 950255989, 230609356, 836021811, 998711280, 301842876, 678902129, 440541442, 141446699, 995941850, 1193571, 133170915, 497354153, 115368163, 25255799, 734393652, 865766141, 178470904, 560310976, 298312412, 466256493, 268750860, 751234296, 965616776, 841308586, 454014121, 874270051, 20247785, 729166012, 820523528, 467940554, 319084915, 641205112, 901788455, 403102120, 793124353, 138519172, 304118436, 869337331, 695551366, 976957574, 567129000, 647490938, 784864719, 307531068, 846841757, 255493814, 22654169, 836222364, 924379226, 209963777, 560623348, 627146851, 463047597, 85122408, 191186943, 246422899, 130477737, 508269295, 829634705, 923204162, 95038161, 21301708, 445361481, 942649320, 411962538, 186983800, 325545429, 865218676, 409529737, 793571660, 832674318, 494116818, 219239853, 199406000, 115856919, 392666990, 448796445, 205915809, 515878637, 343932822, 743390301, 412751771, 730940638, 939210058, 79778427, 419213095, 914292707, 662094052, 86337945, 589778934, 102432018, 62139054, 937044102, 648790106, 521988747, 82668730, 485982690, 292866732, 711706963, 562625364, 867817351, 892150215, 534059920, 912583987, 668532275, 509851022, 437686853, 230095362, 505290853, 572043818, 781412720, 121106777, 728919594, 447069181, 421468833, 571782248, 950457780, 469741434, 207248702, 911417420, 761517229, 641597377, 397926554, 739028755, 605424200, 284752762, 952745909, 72170747, 734169254, 109817562, 756030041, 417527579, 925521838, 539537062, 612656450, 916693922, 133166135, 584209861, 32248073, 463786667, 44718080, 416521556, 255070358, 794135939, 265842220, 26339163, 328659550, 877550861, 362035411, 738313750, 831098249, 198823723, 763762247, 554745953, 486593096, 159121676, 605322899, 956288530, 313757224, 571277786, 681499887, 86592615, 352676096, 822106319, 601481829, 325522936, 152810409, 331115472, 830043557, 874207398, 970838859, 523157410, 240373515, 635048292, 800108375, 543432403, 981224191, 108802442, 778486867, 747167498, 129068332, 194238252, 461793655, 231616441, 614542808, 425044398, 878715139, 74072133, 316725321, 763098564, 199415283, 732268242, 380132370, 802379089, 567536733, 494529697, 625176977, 555320900, 994334389, 15098704, 408414350, 743907855, 750707423, 521540653, 367269318, 619492287, 230954610, 796278812, 891553100, 640059242, 208943845, 974328768, 492399353, 820348751, 987137944, 254879913, 357063737, 228033764, 521273704, 108253365, 621943855, 288219612, 864316212, 940583054, 822221936, 394811855, 525976183, 855346808, 272258377, 145055100, 245030083, 836818779, 39081568, 719100358, 270606881, 662352010, 760729995, 800333590, 571469196, 57733254, 141898438, 537257241, 232173343, 738025728, 992429662, 860395205, 97968357, 548291990, 252052978, 777926096, 801307020, 319180373, 531587090, 83160024, 342347712, 883633216, 592541331, 557281353, 41612989, 432170718, 748308152, 33101070, 129497716, 719519045, 623394505, 441525159, 24520592, 365763185, 846996150, 445491939, 143475207, 899156849, 285961068, 728186615, 740410154, 400887416, 164952923, 222167010, 179418998, 978327081, 428310141, 365576350, 651705212, 39208792, 932664943, 429314634, 564301242, 635720488, 105796152, 180035193, 126276565, 793628935, 484180149, 606434827, 358385877, 303898376, 612676005, 145110430, 717481900, 162864776, 700738003, 176666511, 45559223, 182315272, 162258079, 538915169, 680951486, 940385269, 602976194, 469831126, 561114265, 260304595, 810824567, 910252135, 398509881, 129923483, 460260763, 147180258, 771741928, 234945785, 396932527, 124516823, 188448881, 253349996, 185433481, 597781760, 394798394, 799231899, 926699035, 771125557, 146151774, 836444615, 440411133, 210161351, 280590895, 85220226, 757641057, 96856453, 284217172, 213523431, 247337595, 316757565, 627294841, 543998629, 197320205, 939725025, 134738500, 625155002, 893197021, 934929383, 738187366, 926742572, 584607397, 322094830, 47457803, 363411235, 958134499, 238021937, 677816769, 927276026, 964430815, 298485180, 76742432, 61371579, 719909666, 565326686, 971268717, 633422671, 23010223, 221042087, 322725542, 302445148, 463741904, 687652345, 424233221, 363582293, 460208467, 399134044, 440757434, 653518852, 667081392, 567889629, 962300276, 813045214, 383102401, 354355552, 29028583, 479006417, 174931431, 80028157, 132187563, 104985171, 877844978, 357706594, 910828401, 301111503, 403718326, 166022188, 869722579, 241979170, 518501540, 812145908, 619217941, 534499233, 941015376, 210433908, 237228043, 442021920, 432358866, 834853860, 780932244, 884681533, 684580229, 578275940, 106283914, 578266139, 74187291, 962518612, 490551750, 840832670, 472680171, 366037772, 722297386, 453478531, 295463256, 650161528, 944903975, 842800975, 680407425, 655879616, 631746151, 738539309, 23050703, 77699223, 702327086, 275625280, 2512925, 418921218, 167245190, 698337458, 412944577, 963591052, 143115323, 549778464, 665618827, 709381021, 679717233, 248496086, 504919143, 375731720, 228933325, 160955475, 769924447, 486629421, 18100733, 259381094, 50003253, 493287403, 547099224, 87708016, 666402146, 766036714, 948579100, 824008458, 484260776, 577264670, 504193506, 518948449, 300533073, 29086592, 796852688, 699174522, 475184275, 798920988, 562538621, 628238664, 979227085, 413511704, 681713968, 502357084, 929436677, 164154233, 689298503, 40362964, 822917158, 833363734, 652255538, 447488336, 717100041, 947200441, 983643771, 736487816, 962225713, 452947502, 654510974, 657260593, 85875436, 548967989, 566531133, 300163780, 988561297, 501890467, 88114122, 721467268, 786740041, 319891409, 986762780, 232113564, 467961203, 234010843, 546442990, 738701112, 735919671, 483238041, 967209457, 415372380, 693758546, 610818814, 312852267, 88310605, 604981923, 177818771, 411264352, 45552564, 635454397, 950736099, 264820498, 940566043, 99308174, 425707871, 976527044, 786090555, 420135428, 512847459, 564250451, 195519046, 395124951, 179457705, 558782756, 102846011, 402849896, 538329703, 845904677, 82594809, 729054490, 941142910, 41183623, 390386430, 548582909, 300318370, 761556756, 181894528, 463850099, 294966568, 474523171, 165709914, 31482374, 223906733, 744062850, 533163343, 108393538, 752463222, 273360935, 373185919, 717363279, 144257898, 229944777, 540925715, 12035646, 675903138, 869985735, 215938001, 618839279, 105950953, 940299302, 766890592, 651184935, 515899009, 689444025, 14812378, 57507435, 543790658, 296040138, 66974565, 946690198, 633937406, 137294402, 749312393, 932275644, 886311808, 400020906, 663996480, 400732243, 19095299, 50154555, 214121847, 214611869, 268913356, 221467360, 878911835, 446255090, 329905551, 257466179, 900847811, 927441263, 27153400, 44494879, 363878179, 527878748, 793439160, 652654616, 402860268, 168945093, 202635037, 923823064, 891514207, 126997271, 797564797, 785569908, 520252225, 177365725, 192993622, 793261779, 602965946, 145220015, 221930325, 46227323, 389821410, 970175648, 689997634, 934827794, 479021778, 957288864, 525273761, 695596833, 258811007, 572821547, 504581518, 62281673, 703420558, 360664639, 415939669, 959214165, 110249692, 967074488, 679260363, 375385984, 593900588, 596003652, 484248602, 72702798, 378349965, 602827623, 594758679, 757153012, 794055285, 612839983, 343016934, 160835016, 350176315, 994102171, 315096394, 675441578, 319547369, 329298761, 522269313, 269631339, 277198233, 947424815, 306445658, 379031469, 66958985, 555087628, 939932968, 965845219, 563179019, 883535909, 803388402, 3430461, 386573820, 772270933, 746814044, 519165728, 263509593, 813317984, 879000235, 845970816, 705313609, 344144961, 87407210, 585105205, 777492878, 535940358, 485765471, 843011556, 14175368, 452894266, 827165578, 746085460, 766657495, 253941941, 505569919, 560222949, 933961297, 225327617, 432456882, 305399939, 889035964, 850087084, 341868403, 487517941, 430349876, 972949075, 935376716, 699816613, 282280855, 877606342, 114344337, 701886574, 177097652, 978792052, 802229953, 321771825, 55537564, 690374201, 167450708, 233637604, 833945917, 47852983, 290144233, 570829324, 421475633, 892271392, 133164765, 974683277, 182518469, 618008925, 512535065, 351807965, 967585134, 70465191, 116507684, 530569610, 101652611, 644498255, 192871572, 359902445, 511354745, 395259050, 193292012, 924416105, 46546961, 958813063, 640594005, 872703168, 262399275, 790433058, 985858144, 663050625, 1353629, 710927072, 110770238, 406935759, 388615735, 750053932, 31802646, 491214704, 541565147, 63978204, 441207453, 698574804, 374307008, 769269936, 730904745, 343418544, 388013376, 706524382, 236524370, 300403116, 496648337, 31583329, 766916914, 178667030, 428134171, 443271889, 119185813, 242614893, 767313605, 184450647, 427070517, 251894360, 406915566, 29491077, 814660798, 76648828, 384944496, 757463147, 342241834, 700158005, 325653609, 669271453, 569155113, 435203845, 498200542, 875142326, 96352641, 905813985, 933491281, 10573623, 30651114, 175171054, 898884103, 188022855, 133148539, 569659654, 400407075, 731834965, 766020807, 79229835, 170100432, 747464649, 867467418, 496520643, 694221621, 107393148, 2815876, 942212978, 738941288, 306540066, 401714540, 996759927, 531432165, 350508587, 955502433, 86503107, 901530416, 354686837, 632273223, 637410142, 91313126, 311140064, 897947485, 907493054, 350388808, 20762261, 478637708, 200309416, 313632115, 726583654, 887457088, 243934539, 635597705, 560843553, 713817267, 817748160, 62270788, 98112626, 525588881, 594485098, 371041211, 342618064, 432815121, 872103794, 498033340, 723732382, 256130825, 879403542, 924604439, 75275455, 348932054, 624734770, 449079381, 414092998, 38572686, 276054698, 506351663, 95647258, 833180993, 361559938, 849431513, 431456728, 886963167, 349850026, 309217010, 308447561, 666692869, 285677715, 949482974, 450194863, 659635714, 754269309, 283625728, 848219889, 523934221, 925775438, 952013024, 45976055, 169094117, 4157263, 61988741, 135927891, 804551190, 643859808, 765467607, 277385595, 143903501, 239938106, 766451061, 674025778, 729971405, 632675692, 136670661, 541313512, 704648871, 955101740, 523419353, 941011348, 395049677, 779398629, 127738569, 332391654, 570881378, 461092532, 682112746, 229171778, 697318316, 826536884, 561094504, 207359843, 624892685, 356873675, 366882662, 818015079, 745053284, 890998321, 211115366, 48810078, 73946939, 442864844, 263788963, 270326394, 820480165, 956938452, 710329947, 436130224, 406494453, 821951131, 793852856, 849837566, 354341758, 671243189, 901677744, 13624365, 381084295, 714918308, 921614485, 384043192, 95095886, 492824163, 57060862, 816987923, 984792501, 74386319, 123779362, 816827265, 113569593, 780757833, 908425108, 524010333, 316708242, 750205057, 324830258, 169395767, 364792158, 90577542, 548572913, 106687261, 445699758, 343748570, 157434297, 219835362, 777250327, 365925341, 83972101, 335948032, 383041508, 940640982, 89418514, 144838528, 84490394, 974564684, 228686724, 207958916, 686723157, 311542805, 198137359, 778879197, 152030043, 240916967, 641423704, 982680626, 407518053, 673963850, 578806446, 207682634, 449871543, 935284610, 471892985, 443245091, 654976624, 676376314, 365843921, 507909270, 209698563, 462785600, 273310928, 306254803, 146437743, 649650749, 75375320, 197179278, 829192221, 530322499, 320817935, 178622481, 335842703, 584851493, 534196027, 318037909, 206191036, 139135670, 747821374, 244410943, 336341455, 417367863, 764715616, 773462603, 491297607, 971859833, 691948538, 196508685, 215195712, 264829096, 784577129, 918599843, 427715010, 764583580, 50974778, 49022261, 931190179, 134308925, 687437912, 377844727, 45666516, 140155970, 761693220, 402470445, 654464451, 523245299, 49210738, 707133409, 551125786, 159995890, 9347318, 315194480, 105949236, 104632423, 306663589, 527347639, 726932203, 470122161, 847627638, 645315387, 400662323, 717915848, 750811951, 847736996, 675117936, 243751892, 895134534, 569787157, 403413613, 395770837, 622992513, 300602690, 851745501, 859167346, 320028503, 473974660, 194451414, 551906292, 719741067, 570306891, 942450189, 658701333, 514981797, 731795057, 333229942, 779595131, 119433226, 491884563, 652923844, 674048157, 342564490, 521366504, 457544236, 499190151, 103622416, 640902643, 843572323, 369942339, 933333313, 713935634, 808004982, 511800389, 464606479, 995561872, 791549403, 386847116, 735368330, 267840789, 509697674, 791763216, 11931703, 266936514, 216393320, 554757667, 927019693, 871966473, 554533019, 436013354, 202805402, 610886877, 33635909, 923368737, 534739390, 313339784, 950655684, 96992451, 647762697, 147078672, 156014982, 477768454, 154189656, 80229750, 730477925, 117845046, 450208085, 125063010, 810937215, 85954862, 868681965, 426558694, 256782317, 446489289, 575256709, 393408890, 132194583, 682817623, 759646852, 981710997, 137191141, 876755481, 660470138, 295898628, 707652023, 553661775, 626265800, 249980373, 788531481, 250975997, 930197402, 238075862, 651417273, 970530948, 843554783, 932285215, 417462264, 412907106, 332824283, 390345056, 244110907, 203630763, 768062633, 23589717, 361681597, 261830487, 989159225, 950645810, 224557449, 338088855, 2100318, 441254196, 101252367, 656415006, 234678226, 557523114, 579284275, 150344764, 75999956, 427790292, 598132904, 133263466, 813157359, 561260346, 237485681, 891111832, 825261961, 345307741, 823343114, 570620132, 604594294, 677403887, 850188421, 980947962, 354568228, 337868895, 498768378, 174547616, 164935271, 376670199, 430721524, 544019415, 911898160, 401669896, 660075606, 915754431, 775688430, 837559291, 60073729, 488881049, 987145952, 535415007, 608809457, 811321885, 154242149, 678566308, 303102221, 819866017, 23429798, 858303635, 758300102, 974860748, 194678102, 205197794, 37634660, 342464786, 761101712, 734926205, 460112283, 490166047, 296669831, 676757448, 467066052, 930154901, 9452637, 283743906, 763418065, 908630497, 194136598, 312620248, 998155536, 544588293, 66782100, 731809716, 172631854, 406193054, 172470399, 429911155, 950815697, 718592071, 512473136, 19636833, 530477970, 86085171, 963040829, 51629456, 928650960, 959223083, 951637329, 717341848, 499538432, 677969391, 87148124, 176327506, 636792445, 370496845, 910659152, 818601465, 751151872, 363788718, 136278289, 59836326, 894216367, 711400017, 710114490, 864386409, 374797007, 591851278, 351756156, 622200049, 641667465, 952964328, 296081480, 588547630, 902244500, 17903843, 952817481, 560917332, 42383802, 460005047, 187394968, 305815448, 813157751, 426931440, 597725136, 578773087, 99969843, 911596470, 892178894, 478811269, 140339380, 364694016, 816956906, 552993626, 944453666, 211420570, 737393011, 689790795, 790043002, 93738967, 565427548, 897484645, 139437626, 505848344, 110930335, 817669853, 866669463, 529313009, 809792006, 665728339, 84771749, 3105529, 305426798, 387715908, 972999496, 622817874, 355911842, 539453529, 712199986, 987027848, 21267302, 747904072, 198954494, 828532790, 980608010, 769795606, 869315701, 520742807, 609092225, 492962591, 232160083, 830055321, 224443937, 366314141, 202688488, 698010354, 879838634, 946559697, 610146786, 374641512, 64986349, 189689005, 712602312, 215205330, 253664022, 211117646, 684352216, 126407641, 790652191, 337117364, 757600637, 763058236, 607146172, 469828375, 435253777, 11889354, 678640733, 379286174, 368948104, 806711917, 118945621, 29823041, 235136725, 250973327, 119777910, 588044290, 479198176, 522131097, 911021459, 586796007, 214724240, 194015274, 198934629, 925218136, 426044970, 605661407, 974083662, 85231477, 949509900, 96770051, 587857821, 937978799, 161714371, 658119034, 540677589, 681884284, 599054246, 434746337, 404201305, 107134165, 388405895, 994478235, 408007559, 251426871, 380110190, 208926867, 152247664, 359442802, 660502633, 286618998, 324268681, 848159332, 506799038, 176616291, 475798421, 459807696, 91914903, 438330345, 372752478, 561621059, 994007860, 701401636, 934214397, 380840907, 818287132, 739983047, 865979108, 801864153, 737924252, 153994631, 764633492, 967272004, 764232432, 391819604, 844190089, 958921865, 907531769, 942338293, 571673920, 228977590, 425002239, 148759481, 810324051, 929061753, 708452068, 629031374, 592199886, 260760646, 322241175, 597501746, 950817433, 327578530, 100946974, 968092298, 192543754, 976055462, 73006890, 379095156, 105527790, 646857563, 82943046, 157988724, 722563550, 485632393, 552780720, 470196718, 603254874, 810135471, 502196004, 133597855, 546064605, 669356700, 708540467, 863926096, 48070877, 162988831, 356688136, 693304345, 10319238, 159535396, 64063209, 907516263, 872557484, 820859636, 383171648, 236204444, 171323174, 992156092, 91749668, 256726792, 615518821, 398102036, 219892914, 781529960, 474030130, 135862501, 288357517, 993293480, 36484763, 776842382, 785050610, 512366228, 152325701, 707524343, 274232368, 505697611, 793747918, 72427259, 885508991, 36942305, 395721954, 362817506, 837061743, 286141733, 72871637, 240766305, 952422222, 965410133, 296549287, 566854722, 306039953, 261515647, 704460093, 324774609, 44010669, 422702628, 444075529, 412532270, 681082615, 342909732, 855158017, 487331519, 353349836, 742845456, 646395402, 588924922, 658812402, 425254904, 85451780, 504278403, 101107659, 744642747, 184633913, 494884915, 50505180, 313310975, 145797594, 769161564, 515450174, 380181887, 232692093, 497751161, 726616430, 47726785, 385336262, 703687763, 333978918, 864898857, 290574517, 13029729, 228791097, 830783943, 358304031, 23333338, 800507256, 392353021, 725422618, 894921895, 855657402, 88141589, 56398877, 561430869, 810822196, 339625507, 651268794, 117748838, 432831623, 805622171, 896677124, 329566105, 694784654, 954854483, 394563062, 748684751, 500950498, 319379419, 996853938, 73653275, 114716066, 505073864, 363646947, 650823848, 269084162, 139003095, 824908795, 83078452, 851748700, 857060073, 694451630, 688152038, 502770662, 446445543, 244229084, 120190158, 848036573, 33660496, 105688425, 58606064, 166435535, 216191194, 660645884, 626643732, 205211133, 893729746, 712780673, 814792202, 913512145, 718185137, 258277041, 98569657, 239135442, 214197443, 818569394, 54925692, 798470731, 459813059, 445837314, 784289908, 355262679, 443058651, 473758317, 430290240, 185624632, 941673756, 267408476, 679255121, 94240869, 524244997, 137114604, 911368188, 748895089, 710750581, 313847214, 219740616, 777226006, 15674815, 348731152, 738163767, 684851629, 335121786, 426119303, 157777176, 45712305, 725877549, 466061382, 556514441, 682253962, 124271201, 598940382, 670044125, 960607693, 846444093, 298549661, 68285120, 185680941, 775855072, 218693570, 328449387, 504187973, 898084652, 641012604, 295521918, 506217198, 250516723, 717509484, 755476422, 930433279, 358657707, 122081039, 515701030, 892549861, 847999078, 233905120, 751613079, 992960520, 931418752, 349478602, 363301501, 722002783, 492554476, 763169004, 417991527, 11600298, 438281027, 130239494, 938161091, 191091153, 542367897, 988394560, 248736454, 190092789, 801388165, 890917239, 483530692, 486655304, 178395691, 56789158, 567876270, 813623419, 602340846, 755640717, 67627772, 643948512, 643490257, 893877883, 652396979, 775148782, 921158368, 267775471, 47724837, 851639171, 522081634, 772132170, 208480961, 593007085, 515077501, 490799010, 586102710, 980415496, 612971858, 420574970, 784845456, 907277557, 539953881, 774248063, 381849510, 350584888, 195051220, 670552454, 399873265, 897995539, 418728816, 692826496, 139760321, 941225671, 580552085, 57209237, 41397560, 145627596, 157090966, 946520353, 316396010, 525807692, 818787664, 764409888, 385078898, 645585433, 907286616, 618123886, 389779621, 569861250, 67093612, 406013590, 691709593, 153817703, 928159845, 78170649, 109248399, 151228825, 786285686, 591056968, 712532245, 828752945, 825515018, 305282822, 179947260, 151205991, 965601435, 86866959, 663458194, 380216296, 279204031, 770081202, 4396141, 415252873, 868758478, 484067460, 121136075, 17022135, 54212088, 312420170, 503006148, 807192164, 707901970, 145386695, 481907140, 364063774, 87327233, 824492410, 28785991, 962225496, 319354116, 709259239, 149709944, 28570973, 666464012, 787005433, 471374901, 929997021, 72977304, 430347156, 943186774, 119425972, 416989685, 684099119, 982562678, 852711588, 477452860, 387713696, 615965739, 544853749, 436851266, 301599234, 292405370, 588572559, 206271264, 472879017, 452126391, 159554606, 968355026, 934031076, 158761019, 342846203, 294129993, 967383768, 806443986, 284112644, 321534629, 166178555, 315120816, 188105984, 791677819, 746481771, 266117797, 908314183, 204068192, 768142762, 652000730, 5153774, 597757082, 877248888, 563477632, 929032709, 547320770, 517433052, 486955491, 822223557, 15295363, 526006684, 734083541, 42303237, 60765173, 517220058, 612513050, 173470154, 391693768, 662518391, 839816543, 749211025, 586792333, 944330825, 33978080, 266214449, 86167336, 114316226, 498506554, 903446594, 354229740, 554326067, 40239309, 89490673, 458314095, 473828443, 943895923, 44445510, 867076176, 735782992, 545793719, 535111612, 656542847, 366741149, 973274434, 960587484, 325131069, 20793932, 702756780, 192484190, 593209478, 398264104, 745980860, 547807844, 432501474, 402185034, 80423537, 442437756, 163751093, 288607873, 102207424, 213378537, 909733356, 607726172, 281422743, 371448196, 983233912, 610556550, 892992713, 464944472, 850045556, 72561966, 276643533, 325582294, 817829520, 787435313, 410063430, 120217178, 412002209, 110583172, 667300696, 112600047, 514998155, 423847464, 580009325, 695501564, 770819514, 151238488, 317471442, 674224772, 845235184, 769372650, 462626662, 58807333, 877232438, 860331134, 580043352, 590453466, 465742235, 637587428, 29342549, 811231060, 280055685, 411269515, 439721691, 1174411, 658896535, 87580930, 580848096, 253284769, 727508512, 827203437, 4775239, 700321387, 903523498, 635508275, 605587422, 183440394, 287714529, 513602826, 689974700, 876464014, 396672352, 331536745, 599848134, 322055424, 164777204, 592317365, 457938770, 661953352, 589384997, 229084875, 798622630, 501715094, 350194816, 54851602, 777407197, 51731649, 998417285, 146605908, 850171072, 65765632, 476624238, 438786710, 278228073, 828968550, 895638597, 834738898, 146553098, 338237351, 319831077, 974698845, 283838361, 635362530, 365824602, 980013265, 584544456, 630971597, 91579978, 359128111, 638780411, 234153345, 857673130, 657805035, 131929262, 150407039, 693947890, 281404424, 875111001, 713218820, 728828770, 308827883, 413398389, 670480552, 384382844, 969322195, 376832987, 68674427, 476633083, 97447862, 968850190, 824638867, 74623630, 97023379, 746618502, 68279684, 146254616, 436829992, 697646542, 313744992, 700185866, 878772553, 24455037, 182464979, 497714802, 517667671, 844838718, 660809512, 101407150, 801915084, 72463731, 256321081, 543626079, 252680767, 271506888, 260173303, 934906288, 84954742, 350834127, 321082767, 489425506, 833526785, 514473497, 964393883, 847065397, 454148508, 282306394, 88257051, 608469810, 396157588, 901803575, 901767346, 243010989, 463014164, 462184055, 453760350, 625452548, 928737149, 946537170, 835578636, 229049626, 338153788, 691755537, 117096805, 843671411, 886841205, 554338908, 21123360, 529134068, 492801573, 554353764, 224195520, 155609455, 935674456, 389964934, 19842407, 667825243, 635787598, 685006418, 721025352, 637329362, 383802994, 366455166, 252963134, 283622986, 856243146, 731184998, 904276049, 552880201, 107796659, 736523794, 169483652, 748150907, 951262717, 839667292, 373473101, 506177975, 698173295, 763586728, 971937063, 818621112, 251778093, 821315856, 730707834, 414678004, 120308236, 44903437, 916277647, 961722102, 243671306, 800509181, 941019044, 228108984, 390799177, 822879288, 834254031, 374334298, 662786905, 250908402, 935761652, 188565904, 537751110, 496260868, 41773535, 859054775, 368116080, 715084166, 785540124, 528892299, 349851416, 794422660, 314945805, 327908497, 436117241, 155167059, 964709926, 901612480, 89400381, 339030180, 339956727, 925770068, 3329568, 251235717, 22857408, 975133088, 323550677, 124995356, 412451667, 919382861, 248907459, 385985789, 518948147, 492959109, 212830896, 847891027, 210460780, 771797630, 309903625, 445812633, 779863120, 867337262, 385999905, 255404991, 690590973, 809117742, 249789783, 911692517, 72453851, 864474399, 620487967, 350310894, 913503330, 789818346, 330276868, 576070605, 635592332, 116542989, 562676219, 455325733, 166721778, 382632426, 879998064, 402325680, 27243756, 970111610, 760280530, 831664748, 910009571, 60803316, 978996475, 256677090, 629051589, 380989478, 581709550, 572806769, 746529882, 839725624, 684990944, 665894112, 288912122, 440580560, 173657040, 308946159, 180216119, 832556790, 899139915, 115777566, 457550451, 449585084, 970692972, 590348922, 101927924, 227252753, 792229879, 778719531, 810077735, 858951375, 957558582, 511591532, 220683706, 147047959, 511302113, 334913857, 720953250, 607128894, 831606973, 290062625, 272176858, 62008008, 568030597, 772446993, 748721743, 704014515, 103836614, 376522933, 729818216, 771697396, 94753037, 379912624, 481119824, 182220913, 375481271, 96378273, 277007574, 575380237, 800196801, 855750193, 214963226, 353794728, 29246338, 533422820, 516793783, 346529207, 672744050, 40866008, 548743260, 286286818, 205260760, 817209507, 703232036, 868544535, 844588306, 9665949, 52663379, 703291134, 188469151, 977994860, 250551777, 771988136, 885959818, 489454846, 703096070, 369827245, 164228467, 998781481, 409853350, 958367096, 40743970, 904808996, 796893622, 852840892, 60024220, 124114856, 255007198, 347174701, 106881280, 369351834, 410998023, 315576816, 59552734, 937705449, 777166195, 138002400, 201775412, 736094680, 555537459, 225636599, 737271681, 867600520, 458600114, 194078911, 456975503, 208163918, 993297618, 51827601, 55492860, 343081173, 981337465, 768610824, 318098266, 458986544, 330886345, 497118194, 688289613, 342974250, 232269764, 246088036, 210479215, 372010320, 827141091, 473930836, 726017376, 736063140, 800735733, 959269655, 517679156, 335758669, 983981199, 575390060, 773555659, 76053525, 626878794, 886996727, 618785169, 620917970, 358758438, 462371457, 885802480, 687985623, 197971903, 50948433, 594990762, 422775201, 136319840, 721749331, 619727566, 713758331, 801832436, 883208908, 815926152, 297759706, 58933782, 98435316, 843632674, 455208442, 850903572, 621424978, 265233826, 220059823, 330902598, 822773537, 561180578, 737086555, 774203871, 958642161, 241206263, 299047863, 397108037, 161179873, 508042462, 598639757, 529366782, 896079489, 859939210, 995798945, 476320570, 86047995, 226101090, 842038780, 132871407, 304858268, 830092500, 370534546, 480640203, 793683781, 714671224, 405820950, 5617127, 410718973, 50976859, 15881889, 980492416, 481551122, 278041185, 40549172, 204852028, 686311465, 7955678, 997172630, 49437661, 781199081, 193638628, 272033138, 778439063, 897979849, 663699510, 732716184, 500504672, 245612277, 487638609, 783958825, 24716109, 206118604, 577826185, 505332646, 236242716, 37613552, 812363904, 749795674, 774603049, 158065354, 81224522, 81186390, 748039003, 527631415, 493328358, 310489394, 392507189, 334608766, 469265654, 420153033, 114446289, 818397637, 762123591, 620339483, 632776806, 29176000, 550354101, 751994256, 281662904, 137702565, 753717684, 839483381, 588404440, 599008265, 514104296, 501343947, 447139064, 547035818, 115176818, 415473798, 34159044, 167287734, 657546884, 14853032, 605807710, 843938375, 899992060, 806905907, 368656304, 121367627, 930259356, 535173318, 255880583, 744800207, 777352234, 114381162, 17256749, 912030071, 400134432, 74039267, 55954661, 470241742, 720137903, 295920023, 238902600, 828429276, 969572880, 296430738, 864344333, 336430014, 947454946, 412079166, 227134180, 204401367, 901877690, 844598163, 985946132, 592947964, 589296981, 68371609, 279749378, 444679914, 173592312, 300954012, 741211386, 247475138, 934181105, 163584553, 544689720, 517753571, 441431386, 295795467, 378119527, 706029728, 795890908, 874510594, 878947223, 727901022, 710534713, 831704623, 686545024, 600811984, 601709472, 271979539, 613955660, 819461199, 115858045, 34988464, 565978221, 574787311, 400060573, 76855303, 154356485, 688981252, 52790760, 273862424, 692524378, 45644270, 499377999, 764383579, 308071378, 319884982, 208219118, 192040900, 512259117, 202683556, 523640523, 600670016, 253666003, 561987612, 41343153, 641044369, 216626697, 215873656, 609904257, 430593797, 172623073, 225141335, 49713515, 14128766, 210722052, 940909627, 544941583, 753223924, 349324275, 573687909, 480612902, 484465864, 491148981, 309265708, 232416537, 605127047, 733524234, 335464599, 804511391, 707626594, 275757651, 105794710, 855330630, 552891374, 903791882, 526556538, 997335754, 650267545, 441748368, 338172093, 765561644, 403116633, 784775119, 599752169, 277604967, 291799976, 439375668, 580836580, 540872815, 145933765, 173321547, 308066326, 181988299, 992563357, 547530258, 177227672, 377695805, 963361982, 368651635, 412039965, 776655426, 13031113, 276698880, 862704771, 272517976, 682934639, 217774685, 569410316, 790180641, 808044917, 790837362, 120160288, 781710421, 178588449, 633602193, 305099968, 564868868, 655486268, 4253788, 620156328, 805722846, 201228761, 530500758, 756098820, 72251660, 844279651, 716012246, 188675019, 967256575, 323091983, 997746991, 827774939, 504513638, 564281728, 740632203, 610962925, 671649972, 903166360, 953667255, 951110683, 180543020, 62059005, 664732318, 303389132, 245488915, 722262363, 927585101, 845260187, 955308102, 758430456, 211666335, 564591894, 374198327, 651706603, 261622544, 400735493, 574587143, 799898380, 734327268, 78332353, 250441419, 327005478, 851834334, 36006840, 512208105, 34310588, 737748667, 742942062, 361067353, 164015760, 984662236, 848051055, 113863096, 986441013, 999843028, 862937448, 133858142, 562248473, 159949559, 427257096, 91594761, 36977936, 806067842, 993331135, 366255425, 944239212, 91041150, 874276455, 536588337, 519718896, 176160137, 904926734, 19834456, 889860272, 641723063, 26431230, 346301568, 604990736, 751709400, 768425198, 153742014, 729766983, 774838428, 908952888, 446232863, 821938560, 797932512, 435522373, 697334591, 982111090, 534449695, 541143452, 585166859, 893128961, 970108191, 956201311, 46699795, 171237442, 215929110, 636845581, 285105676, 355197827, 511782159, 820357188, 520836192, 362944541, 123817419, 920976793, 119689435, 961190039, 437459558, 781092476, 389828972, 74612686, 559361203, 886348507, 739141098, 40503552, 411594524, 655444265, 702000766, 799894428, 38858594, 870639466, 224857050, 1669533, 957101979, 346541197, 756884630, 705377000, 997539593, 895475841, 570832370, 442234833, 518162738, 58664643, 228689694, 980637713, 807702866, 589626410, 859725960, 121226353, 439577980, 29700719, 552828089, 660433342, 547609664, 949121079, 115388242, 921529836, 717578308, 809509069, 935582653, 388399730, 60564407, 14334892, 387477104, 969028892, 280272317, 788607895, 66138377, 984888281, 119001637, 589862523, 556059816, 217539620, 409120377, 835482859, 979745659, 917122552, 623279310, 75229518, 276778397, 766616236, 199349082, 33915610, 444942617, 818553437, 75828215, 895059009, 515055255, 140723812, 188529737, 13926613, 859100172, 10501149, 979757353, 85686062, 954743784, 604585641, 251665153, 545088215, 810445463, 422772552, 266310052, 815923990, 577902720, 937850770, 241588251, 965764885, 139422682, 374281596, 337321734, 78137274, 256209978, 877375858, 484219649, 807272622, 623431724, 573739722, 923064764, 99434055, 312015441, 429688258, 488164794, 250435238, 718774268, 192644535, 714418476, 780216953, 698320836, 202402613, 646183094, 263275861, 96445907, 834369845, 560398815, 102719931, 38750217, 963280841, 42808252, 659386127, 840277999, 754736712, 210638182, 176709430, 329323584, 946786058, 104550420, 474262297, 79811532, 792510483, 886414021, 830840021, 66475217, 809536909, 352233655, 587238873, 824364138, 949440421, 394599359, 458125168, 756592777, 247949076, 938660754, 275779801, 959202332, 928314701, 150855748, 7629030, 797214791, 910165050, 576517777, 876471438, 120572047, 937808789, 488531692, 891641754, 45597607, 85741596, 508803150, 192393246, 948331387, 307814648, 968103987, 828249108, 426702672, 116478077, 622524176, 678727264, 840041060, 182507726, 126156148, 61252052, 218976097, 503256970, 576243579, 789487362, 522595687, 465936873, 866007909, 288134131, 308160632, 121606512, 567577195, 296547036, 960469619, 420004332, 36047469, 822626303, 65235120, 728310612, 939385631, 96111622, 609781841, 699037922, 252756591, 953065904, 749368719, 331309172, 233733736, 840473898, 799185885, 885887296, 791196489, 792646088, 2594210, 813234838, 37192269, 237544271, 445613803, 66738376, 933759805, 837400701, 959534351, 630620896, 626232122, 686189349, 489378682, 40319420, 499841954, 129938113, 931096473, 147110661, 309166214, 867379487, 678250648, 261586768, 596934890, 641502070, 105012791, 391054976, 201299362, 471662562, 514784400, 230584599, 212467794, 233361899, 958384607, 925070547, 119091780, 460577737, 807338515, 880155130, 267696462, 125272351, 923430794, 963011990, 611822979, 619371200, 256169087, 168728549, 366849249, 145861769, 159222128, 137724435, 364481542, 806367011, 648520662, 397038045, 55490525, 780580457, 354375697, 164186175, 213469039, 272231273, 956863538, 392371572, 222881733, 843945050, 357325928, 597078237, 568934125, 696961676, 392707362, 357887882, 364359428, 767698170, 432733187, 689490887, 678706399, 835296278, 730429503, 408068604, 361803326, 30175833, 808207036, 173984807, 123888984, 551306481, 57553567, 791193542, 553156701, 768925074, 317718322, 328912127, 560133023, 870569281, 722149802, 481006848, 694463989, 13452322, 18725744, 709337192, 126084401, 304177196, 806114615, 319142811, 347276355, 756932616, 967607581, 676066933, 232296324, 756268104, 4259638, 473653258, 885098630, 406330703, 151595495, 817986131, 85849606, 783587311, 632622730, 99160000, 581520807, 163152354, 780022576, 568754405, 952706388, 591604391, 490430205, 919523919, 36737297, 813127205, 815428941, 135754990, 751333025, 966229111, 940170811, 761765560, 707539488, 798086315, 665382970, 596749744, 786278681, 53692103, 724071483, 895691553, 158678668, 713844754, 119356582, 621591705, 525564937, 48629217, 215302183, 626857561, 329254658, 216008851, 850638504, 140485136, 665619034, 867825219, 169397460, 887882393, 205494846, 391627899, 885776727, 189766344, 938317144, 23740366, 670176535, 611936226, 701564807, 739529105, 891464611, 887386510, 69170255, 367067635, 45884645, 58609624, 161960658, 112237824, 563750861, 867338408, 906991247, 543628567, 477440847, 770374754, 979874907, 482064516, 984351047, 159829231, 349056036, 789334692, 547039822, 903787760, 891591043, 552653542, 765666329, 877175698, 478003839, 918307529, 388136463, 868938012, 438087738, 330446794, 693283835, 51362799, 694761808, 779148675, 780106666, 558867930, 570552693, 844480608, 893365321, 783555331, 494502825, 727637773, 722029360, 669383175, 589272751, 246483875, 159989193, 489217202, 817629649, 851171262, 442894551, 289912665, 621890508, 708870767, 174332227, 691382543, 676437765, 763342016, 27219800, 466036478, 843982178, 932339874, 786333262, 169912310, 44766328, 478014794, 591508200, 428589304, 227427868, 357789813, 720148002, 918504255, 159137619, 461813180, 669917089, 520336597, 960177907, 231765346, 66597192, 19245632, 957383971, 584706526, 460712914, 122397812, 867916488, 10003690, 708823170, 515871199, 377192239, 14070552, 955726486, 267589927, 480971994, 777157155, 411624043, 632252413, 374866894, 939166500, 791221755, 819344158, 273521287, 404219554, 723864329, 276468400, 172756982, 769297964, 426030449, 680658044, 407487058, 109163848, 4679914, 144432855, 174210348, 935645960, 643118482, 994263320, 300920488, 739164603, 980410715, 55079869, 915676081, 789041750, 8984318, 194504097, 850720821, 232328240, 471677290, 621718642, 745494738, 217171968, 507465261, 922012592, 44306526, 596797589, 704887845, 454155426, 717110934, 776320091, 507614749, 447947585, 735845612, 153714918, 354218348, 184714432, 95243492, 288158974, 666941808, 681467179, 309050739, 640023717, 340391362, 351154063, 182735169, 367988226, 898794569, 537041128, 94759501, 988859775, 272022952, 86291264, 528348503, 279575139, 212408095, 400813546, 702023589, 508536132, 601145498, 62389496, 252915103, 916073174, 910108014, 749445353, 35045886, 169420633, 330973716, 788997719, 528383632, 332658776, 19406093, 226232001, 425804488, 395522940, 435262220, 495826361, 454515411, 663683022, 28380374, 179611378, 405088280, 508411247, 67919956, 653599009, 782789358, 822724292, 382422348, 637606526, 673828125, 616088055, 113854255, 79440083, 158650955, 491102910, 248439561, 280325179, 894039439, 979719800, 365047050, 665771929, 607483860, 599862543, 65481337, 64749800, 679368567, 223937474, 163387484, 876333246, 880794655, 484462130, 830231273, 700860808, 198433102, 392162846, 617790384, 512739417, 599502352, 512664357, 928248257, 707269479, 431836741, 478048210, 604467254, 436945331, 79398244, 83369200, 954506256, 291169371, 348403901, 533493519, 360835765, 999560378, 373970993, 80595497, 621213609, 15995852, 129148545, 368196446, 362558552, 773858181, 814717303, 59849355, 734534636, 885289703, 876442326, 227300552, 740443943, 368263419, 386902524, 561138414, 945325771, 561507952, 68768379, 495386447, 519746790, 327416000, 398111177, 939513593, 289569896, 442589235, 220830307, 795007866, 857918165, 72282301, 280323691, 958343802, 650290753, 779551564, 161913855, 309083865, 791238940, 651711424, 862733716, 136127114, 731125734, 529587363, 233466038, 385638617, 233063640, 136082800, 780329793, 215631717, 775589558, 992887429, 355475363, 347798195, 498758028, 130904948, 849060941, 280797083, 293446193, 92956638, 5998286, 255808905, 894226028, 77671335, 721280487, 791283518, 931093689, 950786999, 597207243, 536175473, 258209078, 933910868, 281786799, 371176595, 414706304, 573632519, 5219177, 964561594, 63715973, 51645387, 202395618, 373576255, 756324778, 583627215, 822530749, 333962246, 699780014, 574750990, 731620123, 346848501, 446322584, 809965989, 153592225, 782098271, 183965751, 947482543, 212732709, 548972034, 174459127, 351727755, 566733509, 456836828, 219712807, 24310403, 188919175, 670669898, 864938175, 369714891, 108942467, 308000827, 576629587, 622507216, 271416540, 715531449, 241140887, 122957707, 888978780, 170966722, 242314945, 734394231, 840597075, 391322557, 773521153, 344709208, 846575551, 321690937, 41108761, 218599851, 699205704, 900430518, 395674053, 973753372, 157086054, 915368009, 127294651, 379765825, 945072239, 994073833, 14627762, 196505683, 658867821, 718899096, 105494581, 664002313, 191658293, 147630572, 73043775, 137722833, 701677191, 496051116, 631826220, 510251119, 825012987, 255504339, 928612640, 770121044, 403241516, 418446918, 699010207, 888022262, 446030534, 879552490, 227100491, 366419373, 551798877, 710005332, 103186837, 10508211, 924707510, 397418871, 288295446, 347115730, 344832850, 677395857, 614102660, 544669266, 119791478, 497639942, 926017113, 333385160, 552156912, 558939733, 518443235, 12008162, 118265974, 870052427, 264110964, 933384721, 912429990, 19262092, 792397583, 499578600, 487708395, 342495603, 154850766, 589453726, 263521928, 111974637, 968826452, 194267317, 438331271, 528980000, 345491080, 132727946, 454920746, 325409790, 751163565, 205564550, 360007071, 188382658, 443567402, 487759852, 515086617, 943931447, 166086775, 82526424, 463708531, 742822178, 353735044, 202499149, 49521672, 39026991, 344182188, 203903961, 111360922, 902647290, 945702185, 21632823, 807570926, 459967732, 945389907, 130781615, 370879794, 441914632, 514218135, 565386254, 590363351, 462685379, 441132608, 957631194, 96914859, 221860065, 391758363, 257754546, 124287996, 219523037, 568337509, 986693919, 681078288, 863162953, 972237639, 807499857, 852608032, 433698170, 553905923, 254693915, 783349534, 504278168, 445298180, 209866773, 962322825, 224808369, 181198264, 956486880, 57148655, 228327393, 960103412, 713222382, 227970427, 828325675, 918228730, 706380603, 781751880, 392803647, 371028046, 511008721, 670456111, 410163020, 552489040, 679380236, 208289894, 254981554, 998606285, 958618614, 160172607, 275036963, 974344876, 703063334, 272806219, 555244133, 57255142, 778140692, 20794559, 244636015, 882620079, 913654281, 522467299, 852734950, 62835582, 143189832, 476768944, 381079799, 454449076, 107927680, 971633803, 226394548, 476745178, 515903496, 885583866, 23021668, 588766490, 664538886, 928737193, 279337009, 793653742, 904035529, 129476956, 380081165, 15689624, 534137509, 705281100, 393555034, 641853949, 503570648, 416448448, 800159986, 509122985, 252450302, 705194035, 885462889, 963099485, 41483387, 147826211, 510535356, 775836437, 934505139, 494277918, 744719190, 164962042, 148906176, 736331245, 945532080, 431268638, 652679992, 454865373, 314889931, 537535088, 236039847, 899847934, 329283927, 992105826, 200437471, 346955693, 320221779, 763205637, 711828723, 866046100, 229026376, 851318690, 39925779, 587854279, 834391744, 570931148, 984238103, 41440304, 775826073, 363077388, 494503911, 502421499, 871847522, 91558577, 354724358, 406076998, 616732102, 926662698, 305855221, 86393943, 947234994, 735307946, 85781822, 559580816, 663913860, 126813848, 653107767, 397090402, 222156910, 906817135, 550049364, 44999546, 860754986, 569947365, 172214739, 89048200, 985021512, 13994051, 154166919, 584862923, 894580594, 170702726, 942563880, 100869570, 486759799, 945966380, 222524636, 13361612, 790829085, 593622861, 865521988, 650210436, 589435377, 794398935, 26856696, 635904923, 602965893, 305928773, 107543531, 169894717, 585866629, 70119714, 412016818, 357994227, 891253776, 968140589, 469968930, 375985106, 410040797, 99046984, 931373517, 391083701, 824611878, 212584839, 335250852, 933150905, 604634600, 680400608, 109818643, 671846335, 590194421, 583224067, 424684974, 223286830, 219118933, 18822812, 868593504, 356188272, 383356749, 523397173, 339409861, 239336297, 248750664, 190851975, 325275576, 347486222, 245879320, 640886329, 382085982, 329430657, 532482044, 966819481, 864378106, 517123944, 168950249, 392043236, 771168565, 389848982, 415026044, 523476377, 505609523, 635614303, 932997603, 402700553, 440748569, 878276403, 360596480, 329204579, 850093097, 810000891, 875020583, 749024686, 376824901, 167502137, 193842242, 993005422, 399389332, 758550311, 571120516, 852260346, 527582648, 453972463, 874074768, 368698869, 603236151, 856134126, 203855265, 68413490, 853134475, 25132404, 947358680, 895527161, 927396891, 206072927, 743727739, 392495368, 273597629, 466219339, 508594635, 416664642, 660611790, 359318202, 934586024, 990878033, 176950416, 619332272, 89892102, 717670134, 329153632, 445666163, 392140543, 427991865, 784858269, 534699456, 866596917, 599498127, 554217225, 626717649, 164304490, 527808665, 49361315, 197339009, 506044909, 54843829, 639010819, 821047177, 679522044, 267042684, 337839464, 920036196, 292564967, 525189912, 914738315, 434955090, 447915492, 650418370, 968274832, 745080594, 94280705, 925198801, 941865299, 513050352, 473950186, 832085939, 979669149, 734000066, 351129460, 237395274, 246311736, 825535287, 641347289, 182057719, 287120114, 296470406, 872354752, 787010752, 926027352, 527252671, 395555911, 935937093, 629584814, 293173533, 216029121, 293032954, 488818720, 669406158, 480576450, 489804180, 872143502, 552216510, 873536784, 596431806, 786948832, 480483203, 676941267, 657005375, 297714514, 173386514, 445412063, 133642702, 855047080, 945838074, 999942480, 227741190, 260514524, 167269338, 99245720, 291946622, 340715850, 433019304, 948084513, 79865019, 934773608, 147173962, 861407225, 343737339, 794932102, 219934979, 26570647, 576354273, 416681811, 358830079, 503420538, 379247050, 251386107, 11028516, 899403027, 915510758, 39357646, 318069592, 1838151, 653639574, 463502941, 929294163, 757919424, 816415458, 583385504, 101300254, 912613634, 715991937, 695998726, 287516606, 382802420, 853743800, 963081215, 777885345, 529628270, 816978247, 352744771, 378664811, 416492234, 794818161, 725859540, 777003975, 612989840, 274779490, 587243841, 357014581, 695819777, 515900266, 256510470, 650232969, 951656611, 986115962, 399795051, 466705401, 934767429, 314993153, 640476273, 871866293, 452583988, 160328921, 373531211, 179906458, 529719603, 210454647, 743333924, 563603431, 58731013, 622931948, 951100275, 861932770, 153883955, 170152496, 583941003, 962029180, 675241208, 659695893, 483269208, 545105601, 851382036, 402413894, 13621669, 261361523, 232413113, 365777038, 914881680, 845543618, 565257037, 929697323, 560135925, 939984161, 292643306, 874381420, 278046336, 959464160, 282324401, 569094114, 110298526, 5667662, 188902813, 515680369, 495258845, 844844561, 808360727, 643407418, 71059987, 276266064, 283394028, 204758639, 200004930, 464710288, 138308526, 312657448, 708125486, 519455324, 296783573, 541139445, 767263395, 932123061, 899835446, 999495436, 247259069, 92215005, 205700695, 646983888, 960743801, 275861492, 26732074, 853721665, 439420356, 72820977, 13797028, 194752762, 201381927, 400444190, 225631965, 121061923, 39664743, 280684065, 804576415, 125906844, 502043717, 492851887, 483812821, 385952158, 557932625, 521780899, 397500382, 493150841, 963596515, 451459957, 625337244, 257210548, 791551191, 854361894, 757259331, 876486201, 351670582, 87627571, 432500014, 786830215, 62166574, 112950775, 670528988, 203473244, 759659108, 335571063, 53638896, 956684146, 665330278, 285551212, 844974930, 111596329, 961900314, 338615082, 281849721, 997049203, 506833989, 857779076, 125308220, 583499595, 621449831, 332146019, 789634051, 582562508, 879455982, 552122757, 192742297, 581379401, 710364483, 917605979, 350336918, 79747914, 497097545, 61554751, 664555035, 60497770, 337753496, 121012285, 111910291, 655374060, 483873367, 125801769, 261569731, 396576251, 473796000, 590214669, 504071688, 293759422, 166884225, 172402450, 915635684, 450402208, 284373786, 744489605, 576903478, 717268294, 438738742, 558309143, 144452592, 494086862, 905777339, 169252990, 896053246, 936404255, 178960139, 114568530, 252888382, 864578554, 916280063, 343122013, 985420275, 434795759, 723334828, 69639655, 230492958, 103220323, 862707997, 520022027, 755838466, 989629058, 257735872, 27111469, 931416762, 172333236, 929982409, 419371715, 63616034, 802866695, 768442070, 349246137, 484151122, 287859809, 54283257, 603339648, 882973739, 859076971, 337001232, 954809642, 177329846, 417877006, 995382250, 325238060, 45652159, 573767637, 171331603, 953545677, 469572728, 801443476, 607018539, 897898021, 2527342, 404285315, 572349674, 753157092, 899405808, 972914043, 855144162, 234910049, 247041857, 517806005, 667608690, 622553684, 413650714, 419724485, 859498273, 336742963, 90954855, 46895809, 335003796, 980540115, 1651841, 912315315, 408261183, 231403242, 705781540, 238264665, 586020453, 93719284, 661792416, 475385123, 670749796, 747554495, 166623534, 456680642, 450856245, 426277911, 641202964, 553469127, 694890269, 601604520, 978852360, 577350233, 2346795, 36029860, 941923302, 117754699, 210420850, 754338543, 530843209, 282129130, 964891939, 760790007, 915997257, 632223933, 419284298, 680657248, 848358015, 246267672, 134504350, 473008479, 496836064, 424852645, 936870584, 525075980, 834216995, 88994203, 701771852, 793902139, 304701619, 26984238, 667376816, 653136087, 671851592, 278649261, 730150641, 709260059, 161079310, 410676721, 652621561, 73912214, 573950678, 142100017, 849500055, 833721468, 854077485, 196817092, 141294440, 874807572, 208016006, 613984619, 236759850, 467424568, 590276283, 104713762, 145178969, 800340364, 274892604, 707464633, 399508121, 536645510, 944869817, 442645804, 328283876, 81826976, 934882189, 788114226, 696353582, 115124972, 866189765, 709573279, 424190677, 277019704, 591987688, 170906815, 691070662, 830407540, 958831653, 757319150, 739073252, 285511647, 822574348, 630905500, 525593532, 249222652, 19663528, 54142884, 392961946, 818814111, 981778535, 141293605, 407111276, 513380347, 996637162, 556527041, 190336305, 929970008, 39063324, 11967889, 335608917, 12278554, 386621808, 278879154, 772366992, 286500262, 249818188, 126546914, 240667542, 379489583, 770756634, 421753710, 783783059, 13132093, 127987018, 618526052, 782788596, 405667675, 35398946, 551976800, 26159669, 411094934, 764474734, 123831384, 442410042, 883445782, 585879021, 172484128, 343388599, 507424867, 136597407, 41878304, 717157848, 981150373, 691249548, 793580399, 79790084, 57650964, 622057023, 816212585, 529278215, 646883514, 561988683, 237637889, 133611670, 781105496, 403474453, 54537232, 915203923, 100843592, 592485374, 793828247, 828471809, 155785884, 886285176, 931754930, 783300284, 128040051, 507773625, 850215723, 864553781, 409724563, 617291784, 745539122, 977609962, 478857792, 999613293, 964930835, 459739624, 744690894, 873139859, 830944168, 325334683, 542576016, 649810819, 325461007, 693629916, 371917684, 391749818, 936688564, 610465425, 326703448, 395431898, 732945742, 204335890, 942873678, 212148508, 999797967, 398854231, 810952934, 942136352, 309522044, 759861989, 931444892, 456096620, 59906367, 76597895, 526379410, 618811300, 607149483, 475031950, 969605934, 675703643, 277182824, 715789479, 411345429, 936669871, 987984568, 65318240, 807094596, 253584053, 681265408, 932285000, 459259684, 733650105, 897846858, 848987510, 144899622, 446921206, 23970815, 509707607, 821815835, 104797216, 492359716, 600872421, 506871963, 24855971, 752039152, 978667567, 716667424, 214614728, 776070946, 892761605, 201146564, 204745646, 18144593, 852758486, 710009658, 808836389, 784761367, 918996557, 183541268, 748568008, 28226548, 771970719, 989285001, 454113510, 350545053, 486933530, 638538746, 570501279, 631083063, 823471078, 185206316, 553959881, 558333630, 69120770, 905350280, 262021058, 870035192, 777020146, 535918188, 457862095, 678730710, 221939795, 168675311, 749369771, 900672825, 869835776, 268875225, 746437072, 894130908, 96977212, 611898328, 994510349, 109529156, 667274837, 332747932, 803749430, 838531794, 776809165, 514304266, 40466766, 563963159, 607969123, 666602582, 757406777, 10703555, 738879126, 99807963, 963125548, 951195789, 957955565, 689570223, 373470513, 905398944, 603782520, 132610421, 167486252, 72279526, 805807688, 971962021, 37615179, 104007961, 883619894, 464833545, 305305308, 501287305, 501957126, 526841525, 930135416, 578903746, 764870002, 516289375, 506336086, 445889884, 667768602, 692101888, 654855458, 339903547, 255706149, 444798603, 623174579, 604645562, 504347303, 512278652, 919009310, 434121127, 477314286, 439470074, 592339103, 197120899, 347052877, 88297732, 994966581, 31482474, 860394853, 559602699, 438549382, 135123929, 451925908, 848827445, 547648183, 57176622, 518163500, 574170613, 511961457, 407168935, 194622837, 382142070, 70178276, 609672028, 969699347, 416245565, 745610872, 580303458, 264288281, 455016408, 989491975, 819362526, 487645189, 667597357, 414009703, 114792207, 961486720, 571633729, 141690660, 787753993, 797756206, 285937936, 488976849, 323630152, 671647447, 754801540, 322580921, 563968039, 724976206, 753297692, 656608734, 887423317, 262570930, 538996881, 86309622, 619374345, 610916437, 257194370, 446563843, 244097067, 124607929, 299863148, 218281334, 647573419, 736027164, 262849536, 126657337, 503827417, 114888643, 472722393, 839769866, 8326937, 935840023, 85677250, 979632512, 430810299, 14510939, 609778670, 623065148, 715972577, 766273299, 569434417, 790223433, 705684338, 557442339, 491604670, 53635509, 890785302, 167728306, 84500301, 354464611, 834057646, 134772025, 525980451, 176504192, 791663045, 557242157, 463769406, 166346967, 768430127, 572039584, 78252183, 122644355, 858619881, 537701769, 638450138, 234284279, 636694331, 635776958, 747333735, 558443230, 367967650, 118914689, 667325007, 627601818, 534284753, 113015667, 540214651, 557620227, 926194405, 39839, 531548184, 715153507, 285608593, 422398766, 167892699, 428184374, 496659098, 328167397, 119904784, 405000986, 207438006, 361312777, 553342212, 56496963, 803159790, 837797568, 151071389, 533059272, 364835387, 47689147, 181975868, 852615929, 888869337, 521504821, 814236281, 146977086, 773988057, 206106699, 853856030, 978780857, 217283642, 455673031, 715497472, 933539346, 179179679, 902637669, 744420286, 259067095, 73861148, 732064042, 503892858, 635856056, 107261497, 821838613, 656349979, 705686548, 911729941, 590289673, 42150477, 937685517, 354355559, 153386540, 682982951, 147980172, 352324392, 590669386, 271673598, 757624266, 546381823, 554125518, 959870896, 119142970, 175869274, 602178750, 433036483, 117468930, 279933810, 24669786, 521367401, 691286600, 867709003, 722780546, 874546212, 619292717, 966180036, 308827967, 811437570, 648303822, 771596849, 853304211, 255288475, 458822305, 636424615, 282151501, 327773646, 456920889, 365247793, 904172410, 320696842, 283229498, 641733636, 613031416, 148981454, 210533476, 878628707, 241077133, 934158940, 245277128, 488823854, 886877602, 391501741, 817118591, 503701498, 152615008, 484403557, 434577848, 191233549, 872274067, 79291276, 652379679, 488679566, 516391969, 53601418, 467978823, 283917841, 468957839, 337276389, 9734243, 415428101, 673470000, 419540037, 727691343, 526337615, 288508577, 356005348, 907583400, 92372187, 894208976, 855479283, 288522939, 133341315, 189422587, 124834253, 319040658, 309986934, 423166556, 69514629, 618972347, 237732972, 110404055, 527971725, 470546869, 198436637, 303999349, 112659871, 963978797, 64927381, 839465122, 910447562, 347787528, 507962548, 78860573, 854853472, 620468175, 730018756, 701728349, 613451398, 726949702, 165156002, 999764540, 614221759, 617970177, 320218208, 338760605, 779094583, 454640071, 395742790, 500870776, 455450251, 550178570, 468714252, 567283729, 846625610, 80079924, 483128630, 276503267, 24095109, 9429634, 765325534, 418041208, 564196092, 984419936, 351158227, 468399898, 882242511, 329327304, 414493046, 126647476, 715233584, 682929955, 793701503, 23309797, 155872668, 416689123, 477839208, 204124808, 280287587, 938960514, 529026633, 913108981, 819880458, 344243550, 491709611, 794343307, 955268384, 120082590, 922310804, 830681857, 710356503, 624898175, 632269131, 545642857, 973014785, 416046444, 693775795, 122062124, 483906541, 621120307, 306759306, 435930154, 197020838, 841570030, 329293579, 965747554, 230017222, 796926807, 495143312, 614028710, 82017064, 467491591, 157689538, 704515297, 218880928, 31429220, 706586841, 707823482, 595364155, 950008992, 976599809, 756291291, 208126919, 943130348, 541255464, 739174697, 994157589, 939835481, 402505205, 760571418, 632803406, 888021890, 762349042, 375006130, 3738113, 192922830, 300718323, 166673904, 328516425, 485460784, 553849459, 268174067, 215756829, 580469526, 486669368, 207042937, 208599985, 850146645, 128353756, 117557142, 51099884, 468220948, 295574772, 904371542, 464783383, 348364455, 530098276, 657803593, 36367550, 953684199, 967090542, 96160784, 705848650, 9020980, 94989846, 844882558, 27997384, 546847715, 977740525, 735929481, 597919225, 25201871, 424539988, 384375906, 483106378, 290669262, 772595204, 382226647, 10008484, 137968028, 202177103, 333265510, 274619239, 899741532, 176187590, 78141875, 472586571, 270929917, 304648194, 238340431, 347097476, 585955336, 353581206, 713958380, 803213133, 927187633, 453716213, 478963099, 751327177, 484123735, 533056898, 832478977, 341985315, 865966889, 220263217, 958503278, 546544619, 606933705, 212331750, 982304133, 410192924, 996734283, 105788820, 718562968, 417717658, 577811955, 639281073, 87145907, 933303496, 299945736, 982544509, 516689190, 842224188, 256400144, 912251456, 542291176, 180163228, 844907578, 661857158, 795628986, 234538482, 79252086, 804795094, 426580435, 676406256, 864598638, 825316475, 320478683, 107386310, 622815246, 194150702, 818514458, 421677719, 860880629, 619252523, 465274951, 787738846, 990529493, 648595661, 339264717, 301780908, 966949277, 778554003, 909141408, 120430402, 996381368, 111903507, 626250533, 447060128, 724364039, 125188133, 574456621, 929539973, 376691630, 382845157, 787962153, 199314534, 303341102, 845513462, 61841870, 59780779, 530994150, 446041959, 157239555, 404797325, 830525512, 268564218, 359506301, 314111210, 286298690, 958545383, 207588419, 577315866, 215250197, 847732718, 688746544, 190113465, 593702551, 239335289, 574156653, 796934093, 87335198, 90503168, 164923060, 442828452, 580819586, 592634705, 33095689, 777507884, 950950084, 569507045, 752966074, 868668264, 903464914, 167938954, 979252266, 381277025, 332734838, 862320828, 246566237, 124374939, 485561163, 784247141, 311255244, 879091205, 539710278, 822110246, 824747724, 844087872, 762163324, 795995545, 222605259, 344410822, 932444940, 773693710, 768144328, 428167864, 585642091, 292658408, 686919887, 846927949, 382829870, 181209306, 742644329, 540689141, 430987478, 178669138, 606181262, 939705925, 242756903, 125701350, 699458469, 835345838, 150116461, 177549779, 420331452, 986832630, 751528915, 229252302, 2767616, 78038263, 445606320, 439576358, 148861684, 528525016, 773813155, 451461613, 423038202, 909651209, 141627320, 316705665, 7253303, 702056437, 768224851, 760870515, 257878944, 688687569, 842078278, 674194011, 991530197, 627873445, 456622525, 236822281, 528929968, 867891181, 400272184, 971987500, 928569138, 556689978, 522281606, 465245970, 157253935, 550309799, 182182637, 661740811, 956880849, 139875198, 359641769, 771190148, 156291184, 257734372, 903183480, 882239363, 787172295, 597684512, 350588719, 692299376, 816816481, 123317137, 617287946, 578546385, 821187202, 550185194, 546427027, 694389004, 877028922, 915730388, 337734309, 790964718, 356729873, 963135882, 346216176, 440046979, 614650227, 101732587, 142879951, 895605845, 498273014, 526984157, 796533132, 331221491, 316084815, 668631293, 389292520, 638626001, 4272883, 504324382, 389718843, 63468134, 815268128, 73703933, 604766267, 546293459, 359414734, 388645750, 462104676, 97277276, 4332120, 401413626, 691656671, 702133883, 198915254, 212464741, 34765592, 553058636, 655211923, 555309506, 943076553, 258444907, 225989804, 978242030, 21842113, 286461496, 982832703, 440231367, 533623563, 124447314, 902083868, 805307371, 334324882, 303595579, 105224553, 618748190, 927790961, 184492902, 408996255, 790675046, 497045703, 639965962, 432759492, 398775647, 724956872, 379310450, 366178343, 144260194, 525183736, 924190712, 973533200, 756317085, 253106711, 64007831, 24531549, 9880794, 124850154, 565705332, 567662432, 785369175, 529857796, 214079237, 505043782, 826418353, 735427812, 656533658, 893194358, 763597972, 672498313, 257895080, 510762362, 470673111, 674366160, 280338486, 778051594, 880668428, 118205790, 498948676, 632473051, 62972568, 523351906, 378188033, 386581322, 276604191, 642482996, 905659799, 666924799, 203660741, 868289998, 107501829, 337680858, 815478517, 879282383, 637101465, 857998421, 892788400, 44637905, 370756870, 207999157, 212972573, 860256170, 606932476, 199577398, 208119937, 899862967, 356738736, 913826041, 1577964, 315972933, 922685793, 879121170, 270727769, 693668620, 94837945, 121488581, 549367136, 633384602, 235015407, 239141499, 889305844, 580769127, 942896890, 73763216, 625450322, 48393254, 896864968, 805759410, 965662301, 649886856, 657330846, 981546681, 28230711, 457907522, 169375932, 337943617, 20158356, 748188188, 825625339, 541882655, 119419825, 830779335, 718093967, 383624143, 364401707, 530209757, 168848218, 579084497, 279880363, 156680538, 472934242, 202784885, 137865632, 237833814, 739816799, 17146622, 684181934, 373641884, 734176436, 879784691, 146171485, 390981751, 415890016, 590762656, 56276252, 262620264, 456889646, 246624969, 787618516, 652107208, 537675525, 571741175, 391827078, 819784253, 806487665, 953957224, 977552393, 500820567, 680484550, 559824393, 248418311, 535719242, 856168319, 367539534, 851999348, 105618996, 153658573, 474717539, 202677338, 648112049, 625527872, 404821228, 255722305, 346544493, 844355230, 167836123, 284864302, 701870924, 214387999, 378607351, 82036729, 838045718, 619248021, 273279748, 867055038, 224318386, 122761543, 308029330, 351731476, 164952210, 686299342, 625927677, 546403222, 651182225, 867668198, 275016005, 60123905, 946855483, 901388314, 315218587, 700592290, 104231770, 923631077, 546604971, 631757469, 465366875, 650128466, 892592043, 852570548, 892110989, 417954715, 992145218, 599458418, 44524270, 52932874, 601714025, 463837058, 660463271, 291520275, 10774755, 417651426, 48528894, 751492782, 865661625, 221039222, 917686651, 754380459, 649678266, 879888683, 141349905, 532552303, 319593708, 936484989, 160671892, 953734119, 855834753, 638678444, 348418132, 887332361, 486990676, 888823871, 438422295, 844064769, 936111266, 582520423, 418298433, 209155358, 52634878, 978267155, 795891683, 651682763, 324851331, 698302887, 659027325, 823937082, 938264222, 310443561, 671601280, 671209561, 482351066, 976691235, 401647729, 813762978, 24120890, 301936688, 48078537, 157746640, 371762119, 364006329, 933946785, 387848573, 121027594, 174303789, 966572028, 636658166, 377709538, 440310052, 298170101, 634890488, 784246411, 998212894, 423134524, 798633085, 929969357, 175327592, 748607921, 701613543, 10121596, 510818564, 585587616, 337825454, 650593336, 725487300, 393944438, 53059028, 421876095, 304515863, 37449631, 43100631, 574566329, 411279059, 357385565, 249827373, 442167774, 808274563, 911049970, 421036042, 773050769, 510194504, 616945039, 167946181, 484382399, 664136147, 954260444, 648769520, 455791734, 825211755, 726288806, 88478534, 818331804, 91799368, 223807367, 627382018, 309226974, 793626540, 86496004, 67212234, 548812359, 125465543, 470690636, 637996556, 293273424, 491142717, 280137448, 155634223, 890884466, 597632738, 838641753, 69309764, 667199754, 164369079, 912702732, 920398687, 553911809, 505199431, 927672050, 136358004, 811395039, 331888603, 574384097, 858019600, 28895855, 319649720, 529365427, 256912643, 931370110, 324986449, 837184416, 523074649, 206938708, 618495951, 469155583, 663496875, 211763711, 543392803, 770292520, 283932311, 744031068, 904413299, 529833802, 845718231, 632548028, 542304333, 23314782, 682382372, 920980082, 554963954, 441989165, 557231478, 268188132, 864500009, 790296155, 423807593, 234037489, 402273571, 633722893, 60121803, 763109544, 684408814, 890160896, 865005404, 333538531, 330954813, 105414066, 879869440, 743133469, 417185315, 512976544, 356856865, 840401823, 58576471, 771703202, 157814555, 353435656, 379263716, 763674467, 658441829, 377731927, 93466067, 959115536, 554946227, 180485424, 985026345, 325327022, 325252640, 904520238, 280819565, 783690322, 287022435, 961966146, 940264287, 269493793, 55286531, 146756683, 142789599, 620325594, 875314385, 815743780, 783102183, 167615624, 853115043, 487787251, 839731092, 575373503, 771746530, 167992364, 985182799, 507767052, 817211716, 854032160, 49869988, 532650907, 394202958, 344383485, 855451143, 812281628, 762898384, 596326301, 963893369, 293731306, 898193717, 200359329, 947483834, 361246227, 777474138, 864800446, 957587296, 119053766, 175127677, 448815526, 13669057, 281639116, 541524407, 851353432, 46853369, 360442189, 497077685, 450374533, 37777363, 774946345, 9084235, 167257835, 687909450, 716806194, 263112185, 946831291, 61855492, 640881587, 721719275, 298653090, 985202346, 606257034, 697244957, 576567003, 107134556, 204919266, 62686728, 793585424, 93078185, 199175932, 893502089, 568892727, 408335424, 542797807, 227876933, 711914639, 702225659, 790148494, 788036898, 881401251, 947882269, 21664456, 125097607, 390054241, 725600115, 580773921, 577289628, 791459430, 975247934, 703283994, 875362210, 401595587, 821073656, 870775825, 820899595, 397711337, 787529128, 342139884, 87780532, 663103194, 279986538, 932379445, 496689769, 717561437, 515286281, 668863549, 309719241, 524885152, 249697692, 50264215, 750353944, 956296027, 700971712, 582238683, 927743363, 938732238, 756895683, 352145803, 442634068, 146619241, 15507134, 427794596, 708731122, 116091763, 406291721, 456241590, 381171108, 169591900, 788715841, 212723779, 190389298, 654032731, 658732142, 104958889, 19983187, 164161828, 821476981, 405658855, 517068502, 501081331, 256069063, 655412730, 825136662, 996338299, 644636040, 116687495, 13932459, 836807028, 360748342, 368911719, 693832736, 606728466, 491564501, 56920056, 828107013, 518847251, 639960207, 630597799, 296026218, 213850471, 357377667, 484827739, 839080590, 996777803, 925487359, 117342023, 745061073, 937676275, 946640352, 920788269, 96936079, 748320172, 971858719, 39802410, 839902145, 461353041, 535285029, 784616827, 117745739, 895114768, 941818119, 834877073, 636848910, 478249940, 940834840, 676802764, 582357707, 612164925, 820634892, 607802402, 1128267, 28926529, 845707165, 305942109, 805147906, 851867784, 708543706, 915707225, 495624568, 338740277, 863829617, 799968121, 462577964, 637038699, 90650895, 644918197, 257118270, 779589466, 747068688, 27980698, 196517961, 431803900, 716972011, 187526610, 764309845, 250228166, 658671861, 661976699, 635054191, 310147088, 339555005, 484643154, 44915490, 692726801, 474086975, 721506735, 161292415, 273348450, 54081133, 826554268, 392250480, 496284765, 45536602, 207448823, 716892959, 32803457, 186674716, 706406982, 313322962, 626429400, 840207856, 111883086, 80657494, 469450698, 789173787, 250119700, 357431434, 147440978, 95037746, 614445947, 59369421, 73895079, 6456206, 901828662, 6724540, 504952133, 509760756, 659983156, 31648831, 713854650, 964206913, 731479235, 54943641, 513387597, 15854514, 675932341, 15050493, 172850679, 198766723, 274131102, 124634245, 329110932, 433405629, 358321053, 786611366, 67984006, 520302193, 945848580, 567805032, 34285797, 248436684, 553684255, 339456060, 917309015, 379305858, 9383816, 791234844, 322849330, 246147672, 775600303, 387621039, 578838761, 180444216, 508186808, 82385246, 159447942, 756343589, 341829149, 844409181, 618872135, 511820146, 223212532, 196233473, 435093930, 394391318, 278192564, 315584471, 634466355, 51070582, 619297260, 641212656, 459595880, 504594578, 636837122, 200800929, 642198508, 424364758, 502749097, 463723154, 677983857, 913930121, 16646784, 39663009, 614837810, 646525341, 831697180, 458122064, 654495821, 622334451, 787589474, 40985600, 206703649, 623957807, 973975086, 130496812, 604846050, 37765091, 556588746, 910628538, 146023995, 230559166, 778317944, 759355768, 536619323, 705244026, 726107423, 343310054, 959477152, 377129617, 33002825, 187654615, 305699274, 3513834, 177190915, 791994099, 950349348, 694740470, 433354946, 904687329, 99759506, 807908926, 872583062, 520701997, 966519786, 717368478, 881246861, 314352378, 631019009, 217669948, 170921728, 293068164, 227806730, 257805080, 291772369, 666889025, 394300353, 547980427, 47181135, 439255090, 753345468, 191286938, 400480578, 938867915, 707719631, 427120887, 236600071, 218434837, 230638298, 472597738, 577220542, 328902151, 195430460, 606066542, 72496026, 493962063, 91402152, 991732872, 77064071, 671882922, 947494438, 785940704, 684895229, 178560569, 190783421, 754187280, 188834064, 768640775, 72214770, 623519577, 734146019, 181651392, 447455102, 782930908, 143468271, 202048906, 655586917, 928902254, 967983661, 500068397, 937282011, 806625266, 660067012, 215450706, 450709181, 29376900, 467904061, 901210951, 962000449, 315313724, 382049591, 559194225, 274472823, 17918762, 432229318, 764944250, 627481188, 293757317, 936770133, 156256256, 736280866, 577178009, 76056510, 618760116, 28988671, 335400378, 734432628, 678703561, 497155410, 338797830, 385589942, 744873843, 322492633, 812533220, 324950285, 112916210, 726972336, 673636325, 13658580, 880105744, 422949824, 242330396, 137604028, 982901835, 995357841, 678749606, 448327498, 988706242, 700678691, 722729408, 461558162, 393092635, 305164679, 305356432, 410731871, 658810645, 994866774, 469016698, 11757047, 652998697, 507145263, 447530723, 239465954, 848423418, 380214041, 873134, 486652614, 810883188, 572212516, 646593378, 927210128, 305902514, 875032654, 633773328, 841763058, 840630636, 199812397, 664424574, 418243407, 436788169, 999816894, 915076916, 280908904, 277170388, 925814135, 710419131, 181375323, 716553770, 399620613, 631445830, 264907115, 774685519, 468854484, 634228039, 353403625, 26769126, 517304908, 823650789, 123520630, 455690508, 550666934, 675913289, 928049755, 335920928, 756492645, 646005801, 157579238, 628651961, 22621086, 704156176, 599152681, 802269937, 464163705, 545918237, 444020289, 64243590, 897242345, 502330399, 199782923, 69635660, 638636727, 549542860, 297347550, 756924701, 92864849, 848368007, 637238042, 978426529, 82007547, 156418636, 44495668, 146655205, 604892837, 237503130, 936542281, 357043444, 166786633, 451917368, 624698625, 642279436, 694498320, 996884174, 741464755, 674460267, 249939279, 808838385, 509359680, 17569922, 284773799, 375786623, 603794203, 930563262, 975269575, 771473077, 327020828, 914031494, 210014371, 65970711, 554173071, 335355033, 876682459, 546137332, 79533693, 38415197, 654346231, 132506001, 795717657, 891991347, 514785489, 719179507, 468151493, 708065555, 822457795, 465194188, 457193931, 697867611, 388500890, 289024993, 754431190, 712434406, 618071484, 324007922, 162274140, 231092580, 880223022, 623472456, 812442643, 910368480, 802848684, 975512615, 999425261, 15979791, 907587538, 115269602, 613192176, 640551578, 29314890, 764581966, 717093112, 339949421, 860549433, 461637624, 431957498, 873270421, 985230232, 53835404, 749671865, 542429659, 864512267, 347390274, 150837024, 770065790, 923795414, 848447638, 865918424, 593587453, 163379904, 983180709, 348213639, 69901248, 248184649, 450695601, 331027793, 479612341, 875350129, 364440153, 985698530, 90532815, 895994989, 689071482, 443210911, 13950501, 54124454, 7792376, 149473419, 256853969, 791113829, 393655881, 172951050, 760533509, 779424092, 158761572, 426479249, 708577031, 668225231, 732464601, 55255551, 968646572, 442090910, 689454100, 954241519, 288461108, 229629917, 540479874, 548458713, 205597244, 851184266, 676190708, 5664611, 727424741, 767690744, 666641331, 169588920, 400997328, 310642805, 547583356, 285842676, 358691922, 736778403, 69848867, 799346973, 102835513, 496649111, 73287278, 83439306, 592863763, 892307842, 727226794, 633413427, 825303228, 878610114, 783646787, 603357245, 537190484, 223269188, 944736189, 124426345, 964368755, 182493618, 750468687, 600371753, 965106709, 912118834, 867846889, 590938321, 203750042, 831704051, 575778599, 645847013, 837847163, 772039433, 170377913, 358547635, 384810784, 552663168, 179239986, 946665563, 933336813, 644487660, 74512856, 174988134, 212328655, 982174464, 325775147, 333948247, 510718954, 68582617, 538983139, 854270794, 644861150, 568380214, 43616685, 350944574, 113598719, 176797039, 19895718, 772705530, 648303007, 135197190, 831976046, 153831512, 722783096, 934376057, 868355731, 511584418, 852440736, 235049723, 87979872, 898134706, 989886358, 715608797, 992070536, 442802188, 133476190, 52730150, 332140432, 605183322, 884942256, 324431554, 406506572, 385418747, 543834499, 557751316, 435817008, 729117468, 916246611, 858795238, 877786313, 376046159, 690956542, 310738812, 156050776, 895239158, 963368181, 112568427, 458904252, 817310414, 518897193, 887394244, 432191523, 161005465, 283739603, 922844345, 922720459, 27690296, 762003860, 874348220, 867235127, 752010671, 838044633, 128099211, 54614166, 938238446, 156047303, 848272402, 402239990, 547658646, 630064118, 800652049, 752848536, 819063656, 775747735, 744389935, 550888415, 8554205, 327126590, 892774886, 676561034, 941909947, 543388700, 741597211, 868486768, 562404743, 640456393, 922678622, 232430900, 359253622, 852736226, 57476712, 974812483, 842384677, 516847491, 924518177, 654887437, 54361365, 71979869, 566769160, 395401327, 604345863, 713484264, 628489652, 390003270, 355816189, 481367024, 394745762, 847624018, 45331840, 459442478, 753688379, 439118014, 673868107, 238172647, 977675892, 971835196, 485479977, 653544807, 842870691, 114562618, 1908969, 119638991, 145167702, 940725583, 621182878, 275034603, 411846454, 191965518, 144529623, 132252163, 793268613, 783092603, 318745488, 488594464, 905518790, 192090310, 25978746, 497975378, 924102312, 961188146, 15480551, 785337740, 218407856, 670262468, 330133147, 421920127, 400028988, 214280324, 711826734, 245213335, 906759376, 391323119, 902450470, 263043272, 48470677, 3625701, 854411284, 494833908, 350629490, 246778028, 830839442, 483400592, 557178302, 450154982, 36190162, 701491445, 22245271, 885969918, 872762897, 843679295, 626858461, 463964167, 727306389, 69645017, 823982593, 351117003, 179230350, 908008202, 67876860, 962456223, 773759749, 893946800, 920004025, 520653100, 891136487, 540477850, 124034469, 17003992, 197497373, 498816547, 848737805, 771132709, 898670644, 780217362, 743039129, 649865076, 618200438, 74165725, 481631245, 323986979, 454975758, 599561624, 109202531, 319546298, 915087756, 358984163, 56643988, 264216861, 465148370, 509332071, 265066352, 311688626, 179675255, 386301289, 597733205, 388813532, 572141171, 487428618, 307535249, 504860558, 121448618, 601764651, 870638379, 928455624, 524980213, 145647807, 578297112, 789174787, 631748571, 687216468, 123085990, 147135865, 323619962, 218049683, 550524121, 507953839, 519677669, 532740641, 829394123, 163509570, 83648817, 261117204, 699700674, 466671690, 107058084, 25639372, 935882552, 972194880, 759436355, 152551532, 700548565, 554395324, 227108872, 752966891, 492027189, 185963797, 446990656, 168422392, 848306399, 629613692, 753785058, 299895932, 865844477, 220641102, 639249532, 754226733, 100751648, 834529512, 716315095, 712567773, 972942856, 929408627, 867092447, 768712807, 34462782, 449720712, 509180792, 500797412, 749680483, 564458106, 437620016, 335553819, 208096624, 313409624, 734016525, 668242574, 925555773, 144579904, 650063160, 598309578, 954677010, 21308142, 611398971, 793699376, 801547630, 349891097, 274056273, 40161801, 523691443, 421444480, 954685488, 295658148, 861028055, 21415829, 48463718, 185492074, 198348632, 267039505, 262266869, 740044357, 525917061, 122649123, 171074878, 364193382, 664165488, 921818699, 500061816, 470918933, 232961028, 228651053, 816327186, 415058804, 321587953, 243744781, 205815105, 299156792, 315580728, 254802125, 576342632, 558158321, 467442296, 631950337, 974272233, 296920372, 360741440, 954839633, 201417543, 953542405, 684015237, 603715764, 231962619, 641638566, 742020239, 542175562, 603649604, 870388152, 698035683, 321082452, 645900854, 9025311, 248597480, 63706520, 295010314, 334642602, 593889658, 819258663, 155708398, 334707253, 856020594, 996772575, 796315505, 444754510, 959792182, 684592454, 328354727, 432187713, 411708224, 741743428, 910671736, 503075328, 884144969, 286440077, 754649666, 210916575, 642779624, 599015326, 260398475, 893896020, 17261352, 989974440, 617310038, 877737158, 215203667, 244622012, 427791440, 531445950, 219308696, 312790721, 871135862, 536756421, 280823573, 305043070, 144733038, 218407798, 140368928, 228429868, 273511935, 400948392, 382716525, 695358692, 782372784, 95552368, 752004230, 703985386, 323792164, 645432488, 846950965, 383710331, 24733333, 193701086, 514209125, 67470618, 689517137, 858075583, 944906608, 628495127, 893140546, 884411827, 6914145, 783293311, 917866305, 882929101, 358858733, 881005370, 135287972, 120736106, 66658820, 393415780, 29827885, 707965334, 590110505, 858845855, 621194351, 749030840, 31011763, 503354910, 757980146, 699170876, 935390002, 727474272, 145135074, 749613678, 735905664, 451576109, 388916196, 470512744, 255105514, 327522129, 442907442, 709056949, 74823078, 764626025, 960103336, 288725535, 538047099, 683094219, 501506421, 965518610, 595697530, 445089331, 257358477, 519002816, 290887173, 492965475, 561470770, 84012779, 890042231, 622105213, 478008222, 974609848, 29545517, 40652166, 77149053, 342875583, 942189266, 446668121, 889302433, 573579644, 841722057, 765308489, 538781293, 6587408, 106439707, 831053669, 7744247, 495472465, 69655558, 833494788, 749757128, 286413513, 631364533, 733493054, 737933721, 92830524, 25075383, 773571292, 184981392, 912684095, 540008719, 18329574, 347088481, 968457814, 974860227, 263711794, 452246674, 692994856, 91735762, 464903364, 798770853, 615924815, 223917380, 904555791, 949725366, 559103927, 994114998, 874076577, 18388223, 786446673, 940812061, 645944824, 237252167, 238858482, 376241514, 590431571, 128750550, 631643381, 382517797, 752464757, 24418818, 159552138, 512242345, 110197410, 70639613, 44455300, 571173572, 101539211, 848858139, 129373492, 477410516, 452480234, 618285892, 707676549, 782584916, 911005347, 389566700, 404069546, 347544389, 77282289, 831318416, 672069788, 347904818, 672922487, 769735642, 85073440, 443639121, 24250103, 226745582, 984523845, 608225613, 694606977, 744228287, 248839256, 156996448, 858480503, 643549444, 135909924, 80112806, 530623803, 359886837, 791233872, 718701081, 192003906, 371627169, 526290227, 138445066, 746105159, 338522673, 738595539, 365754278, 801734728, 488516866, 898613425, 459874326, 53858829, 288682608, 889379287, 566972207, 460602879, 400272312, 272946303, 878921062, 943233154, 642993061, 723296875, 700947805, 291671151, 575630253, 529297854, 46189895, 632771048, 464252710, 277262203, 586032321, 522270791, 402007703, 533162728, 78817868, 314952736, 137374713, 617768921, 827557929, 533493602, 522065299, 713429703, 214648640, 663005864, 243717346, 920681785, 120452612, 786925532, 613550598, 239434484, 511571532, 311114760, 228059576, 768763342, 40191323, 812105408, 657373364, 687117641, 314787655, 260075984, 612131520, 844354545, 614827983, 467985795, 598568264, 710963414, 402843797, 302407722, 223157171, 641845169, 70307027, 354628075, 221609194, 155581220, 260255755, 975783409, 571540577, 878325606, 217038223, 796810763, 499113997, 19436706, 287999934, 998833948, 428216662, 210762248, 105334274, 746083429, 581205314, 465823039, 333359019, 593958817, 728102973, 983567874, 244327581, 753082945, 809067815, 368626513, 5602104, 553555654, 239420033, 651598660, 784699490, 918391507, 217129157, 75283187, 634639695, 357041362, 244301154, 571793805, 739866347, 901919274, 108672934, 658231495, 371974286, 553320493, 129230351, 331156364, 409847548, 245592680, 791815718, 917968308, 530592400, 402667315, 959881101, 482249147, 776752425, 463732336, 538725096, 619715072, 933493760, 944653075, 832405904, 922561234, 41341967, 139745811, 763916529, 302654435, 791731422, 253605886, 847717382, 593689628, 590199895, 923056581, 626128975, 183980869, 397130588, 129305561, 417677121, 859563287, 854263555, 897931231, 694060264, 429514667, 551897745, 166278575, 157488921, 214088508, 157478315, 45879890, 63738496, 851668335, 136064167, 647830188, 67546764, 128119050, 148662002, 321580800, 553145887, 600274255, 459102683, 164775967, 611136805, 824633335, 76377319, 507080148, 393533848, 549515383, 968248723, 562648919, 861311095, 532927429, 534098400, 431208905, 155028521, 695778857, 475922822, 938652034, 342991615, 356878320, 837914237, 537031219, 840805395, 737002962, 949979739, 209703750, 456765806, 45767897, 362060418, 750559748, 746223804, 84473586, 910832916, 53541078, 885976622, 810205600, 299379074, 443692944, 861206204, 208691030, 670799845, 927158554, 845818563, 698757204, 723099335, 109020054, 547523724, 757720189, 581841673, 688253406, 48787755, 642622363, 292211077, 645401239, 119352215, 385401035, 219765348, 166432649, 329382907, 563434608, 966433579, 517491348, 380055281, 630575274, 81940498, 530401184, 24812012, 347153805, 839111929, 356637419, 740422537, 576489617, 996878729, 698176577, 772911222, 342146752, 145695878, 911730327, 852927676, 508690111, 540510712, 874144920, 489152659, 485859262, 289501139, 434080626, 24457095, 386588299, 89910499, 962395742, 918926852, 775965898, 656585505, 301704281, 14961227, 699652743, 724434102, 582818851, 880184442, 990724540, 371698459, 411452392, 455489315, 753541117, 9896322, 10445033, 634823085, 52464276, 278531402, 95439836, 139348803, 502008349, 828017454, 650828550, 998420990, 851411305, 362447256, 971462340, 460181592, 79475408, 592379356, 275869716, 205562662, 122473039, 34871225, 567162553, 293243432, 491101658, 990965442, 619454953, 578910068, 498960201, 686614180, 358717699, 27938368, 370417360, 190132072, 536429152, 183759230, 913623486, 831529346, 204761032, 935628892, 25905541, 525312477, 309314565, 812105757, 269897171, 225487684, 653379304, 651617872, 315372638, 985489263, 837430094, 204068347, 186126530, 495360375, 976380429, 669605301, 481616973, 81399778, 941740018, 633967851, 878778619, 927124014, 52868628, 87345329, 981155150, 304702470, 700412329, 761898405, 416981765, 928740972, 845388770, 368950153, 813744936, 164358374, 563474830, 817126578, 936201279, 76365579, 576487526, 85743806, 346913888, 929142525, 566697885, 901561648, 120150762, 899639143, 757987875, 36973649, 604026714, 396208154, 164553989, 351821039, 94605774, 133491999, 347203669, 673580322, 947476889, 382230727, 341405318, 308399855, 90647745, 210782402, 722856020, 79007690, 279619783, 183940920, 619560927, 489609770, 182359700, 762244659, 613432365, 216070683, 756672600, 593372011, 501330520, 67533678, 144695784, 105949861, 323668013, 127289284, 200059877, 660662494, 73558645, 465031343, 41889248, 498561536, 292125934, 398010709, 376569027, 544403800, 286534084, 853349378, 50108490, 590202847, 584477193, 829429013, 23693470, 178475695, 883078289, 551369170, 59778818, 49347375, 710181782, 617789142, 778715297, 455074874, 550007761, 75184231, 550993028, 885732294, 73165833, 694301592, 766495809, 530872375, 705672701, 81871279, 820045943, 165084260, 693747414, 605768809, 723896313, 423470956, 192598816, 63396399, 887377452, 822859675, 159410332, 486167629, 432827743, 669984429, 322882971, 749157784, 159856333, 111664760, 995177585, 237475895, 787262904, 558183120, 572566530, 151761111, 626163341, 665849111, 540615178, 284604060, 878616967, 231789768, 992336923, 779125717, 629601970, 806926137, 696373284, 691840986, 507977534, 733763270, 22068666, 502252583, 626339844, 219583535, 903210486, 923781395, 808825348, 923822259, 139136439, 307812050, 114247260, 659251371, 493834321, 267443138, 145447136, 552670335, 842818888, 517069566, 688874882, 386373785, 400951484, 70469073, 547570505, 793590878, 210396008, 75544842, 536210199, 706177623, 476224711, 55371564, 708706207, 621562307, 772824609, 921020084, 836082739, 303301418, 314149049, 689524359, 988220618, 552644380, 548741769, 805135810, 255814089, 257636692, 274397059, 642219451, 208375838, 750887192, 909878233, 462479806, 588581638, 450795322, 467225235, 12391162, 674300642, 686056978, 274771871, 48189040, 493449574, 273589518, 777217410, 6621958, 255837873, 145190171, 695379092, 842551681, 610733266, 486949080, 413010370, 334046913, 223360047, 461435958, 753023173, 333602428, 148534176, 583810059, 710036568, 813473449, 916752000, 83140429, 121572984, 580338635, 280191861, 461445147, 857346160, 104458395, 144107749, 267883049, 569469139, 550980370, 342570585, 362649570, 683355403, 467449123, 265125006, 993350975, 222861003, 89940388, 311775191, 561781263, 770228552, 284902493, 968990731, 982608617, 216031216, 921741785, 487643306, 966181851, 256274650, 289111309, 719310620, 327271381, 579372042, 359312838, 18468044, 673385243, 179785413, 521620591, 426814811, 736237670, 511620340, 130279830, 310238178, 593462085, 495751314, 188816648, 130776212, 61319163, 718889909, 705294921, 184873387, 365180680, 958024118, 830290919, 127600559, 425030547, 97089190, 790145467, 376999840, 201420074, 257678190, 617033618, 781080506, 296309708, 151195205, 351973984, 647906472, 927229236, 558297771, 727371022, 541040680, 986508306, 396667666, 848884317, 622086007, 229828685, 894924562, 873920241, 467667476, 350251041, 472512312, 962353900, 641567315, 969269831, 445053560, 46408582, 608005502, 298040478, 749452518, 57122204, 295627728, 57625585, 710447569, 859291049, 23555682, 565698903, 819413333, 876295325, 854233612, 944185651, 291227795, 67503593, 726468910, 543989966, 796595421, 880357716, 13239375, 573958358, 51403483, 684950302, 772137740, 101695537, 920218853, 373920982, 302468472, 767075180, 227364140, 792766068, 222637936, 788543045, 571527720, 685957694, 9364901, 152475501, 954312595, 575780653, 404105011, 142073195, 191101035, 403440837, 215316849, 678449206, 410912173, 91242534, 472640615, 541916706, 957910522, 121262793, 67146487, 306756363, 170702238, 68590010, 791014160, 702862734, 182570663, 703207152, 587548461, 762439700, 497975123, 18403038, 331900420, 197937934, 985374804, 77956397, 416840284, 209552050, 549167288, 877356020, 899448300, 712403449, 86387704, 409383409, 681849890, 77126150, 855865587, 626565884, 596426430, 190618987, 425458867, 601104032, 620372530, 518141438, 372706272, 25325830, 256495595, 964066824, 984608296, 495282269, 545990158, 668374141, 583552025, 693640114, 698248121, 29011947, 314917442, 980332242, 619962483, 673803671, 423497960, 515931396, 9488528, 704215987, 513005141, 153323797, 314285440, 971180845, 796598390, 877322318, 831932422, 613425042, 724239751, 76807492, 747560242, 913290617, 251331978, 533034839, 204270399, 810983622, 564161316, 957352953, 316711009, 487634697, 548648962, 131494225, 166228770, 467733470, 760306191, 331588799, 996945593, 365959300, 48531577, 340700883, 836227580, 296944795, 771676333, 234508321, 949119680, 833416377, 867607706, 576406740, 243435154, 438981242, 562272281, 467348698, 810298399, 982632293, 736980800, 410575872, 465816360, 918114181, 819471510, 458888926, 964111765, 711805465, 730196693, 452214958, 857831204, 933808384, 829028939, 421430796, 939868465, 307610945, 616614389, 69869854, 289395120, 987078691, 9318840, 958922429, 259521528, 230072702, 697020833, 496424657, 6763931, 412361980, 45223857, 964401138, 836141088, 859813829, 633494492, 670365082, 328011994, 900171487, 718512540, 831621629, 528615307, 895999083, 318049165, 540913921, 673621081, 476071629, 35155482, 952442444, 730341575, 642779712, 180459370, 25570641, 458680705, 148698684, 149899953, 257255331, 507980845, 399769280, 229651890, 847988172, 834644615, 425255317, 693774200, 925980139, 593367680, 301172342, 341020219, 679278454, 684035121, 247309204, 708601528, 705896637, 475450297, 475394888, 63160348, 975543739, 776928654, 152799583, 417552899, 761097552, 890236360, 209912220, 685606914, 5451979, 161441786, 68310832, 944935544, 215236866, 796523458, 683060811, 793370050, 629245063, 663019982, 680022665, 762001411, 185787708, 274837744, 167728627, 510015378, 416495225, 538079751, 741999871, 945860673, 848447396, 337340546, 253866121, 530130252, 585561504, 313434203, 811401575, 301416161, 745575437, 906712516, 246390160, 42704004, 421608261, 824138937, 736531751, 205529047, 455184020, 274809872, 825795792, 170648829, 616987445, 38951515, 813268575, 941421351, 369013345, 149680055, 412037809, 245560713, 349367354, 102196438, 861837564, 551579928, 771654830, 111073660, 773157236, 873264091, 466544853, 661870560, 181948889, 92188358, 469925018, 470054229, 320314579, 886147941, 273883864, 477986652, 924777698, 913693069, 946221726, 870781455, 359272914, 197421131, 886376717, 189918912, 750882424, 127951027, 605608166, 272536923, 81873739, 901640038, 51442527, 149003506, 288279972, 990023654, 862225816, 685838347, 941967440, 360582705, 660186982, 869554178, 9857586, 892127886, 995024217, 584664932, 2024369, 638348917, 227385933, 122906093, 33102056, 764222737, 838441317, 838079144, 733969602, 950530109, 426664081, 661011350, 718495624, 129680576, 964676996, 375277460, 722798818, 10548465, 433196327, 889031717, 500093330, 596319905, 669601547, 35456953, 65355439, 317888767, 881629848, 749487078, 858601513, 966010965, 33862052, 199970075, 505521434, 584616816, 385539876, 824864023, 28279356, 630350524, 412085174, 429293768, 719727422, 24307457, 909632600, 497712073, 734441070, 353925832, 215658898, 881892363, 534006192, 601833152, 796761845, 7753821, 67602189, 479186445, 805431467, 894488891, 220540133, 850701070, 349121372, 385673259, 226309087, 705962180, 675382204, 752561733, 172627030, 855097130, 347392319, 895110448, 122335045, 886225924, 241489131, 600948966, 233409630, 755394786, 113923748, 375655794, 27184854, 815548046, 399380544, 23849443, 208765197, 111188198, 847484033, 222860250, 359248258, 246600180, 454134845, 577672636, 315547832, 798011710, 422064385, 528999434, 956312853, 941391049, 805912282, 394822622, 841133536, 153090420, 740662545, 524791557, 993075457, 247951647, 522862464, 494187914, 591671200, 310758685, 914962676, 164286814, 438392793, 113686298, 255633211, 238056772, 98598365, 762648451, 581098474, 290229484, 717564654, 437105123, 879971210, 262416723, 31711023, 584787514, 271253497, 850963535, 110647124, 112815159, 90103587, 549513963, 539482892, 190543819, 329966656, 802319447, 766625181, 165350415, 896972323, 577856278, 50812854, 872227700, 757367041, 202923205, 840265216, 437069506, 285934556, 395591742, 344761055, 504944098, 220655763, 921652857, 452358065, 600498858, 407358912, 713246183, 840916638, 879781152, 524508044, 92737410, 626012199, 371637753, 467222196, 657408359, 107448513, 625449260, 72297235, 769859681, 884897489, 607037000, 214369928, 891830665, 547671964, 796953770, 411486870, 119669427, 47894588, 318078047, 954141249, 22019364, 172748691, 800311373, 951193255, 580837977, 576917210, 240890770, 76813439, 337545760, 721383576, 121453562, 694713742, 583008875, 835188592, 839446574, 202068917, 408183691, 267185992, 743741802, 676317911, 713509868, 198551460, 854056331, 812488359, 792568104, 308403968, 612696054, 688636408, 553207857, 893136210, 710678603, 721123992, 470741853, 285151758, 224162260, 190421175, 759276497, 586479727, 774707439, 115337569, 530743258, 36551485, 208593186, 124869657, 843038543, 917093099, 351328247, 8516841, 472437732, 636290215, 378523737, 148142140, 519673597, 684484052, 994031515, 750309519, 97690644, 984844935, 660180627, 521499436, 172469247, 32244695, 628392398, 253247319, 985104145, 940565383, 117619140, 314363205, 687868514, 803544173, 510993856, 336525211, 376331733, 955884216, 78228314, 863937317, 254250141, 471977748, 197636110, 972151502, 161935148, 185664703, 535089011, 727334938, 383090292, 897864920, 355558321, 690457407, 260344217, 776513417, 743499299, 323054325, 609387313, 227766932, 586784296, 720488965, 330038430, 961242607, 686353569, 628783191, 651966662, 886707872, 825503141, 906569058, 229694338, 83019111, 684599704, 987669778, 22224309, 954852422, 14049440, 998354728, 566837000, 795473509, 280245071, 235009670, 298747096, 496728869, 284098092, 261079852, 897142119, 539128066, 156035594, 352896862, 141548008, 167560906, 457548859, 892686810, 702235375, 752552428, 39304873, 105159024, 308978002, 608923273, 276901134, 733923997, 808610124, 876313500, 565685850, 991339300, 76604174, 160818513, 296640681, 461655836, 709979763, 281676332, 636031753, 408178943, 120285563, 513286830, 276161790, 283945000, 113844689, 313450079, 594339329, 760365414, 423919763, 674384672, 86656999, 420232096, 599447699, 11716398, 302990927, 92369912, 677157522, 820470094, 308583717, 427304296, 986222073, 651606947, 204896467, 996341376, 651182521, 591139867, 103319620, 107228177, 264212398, 709026398, 237223946, 627261095, 38556532, 694352116, 626119311, 924466620, 337883825, 753996839, 451264104, 994092224, 497443113, 954902620, 54919700, 88697989, 122931984, 752412920, 90280041, 993841458, 446447222, 254722320, 313427038, 609369573, 535170532, 387275841, 143810641, 418993385, 401997958, 240134376, 455661001, 28914154, 477119398, 225572439, 164886425, 387285346, 438833846, 511621658, 45715580, 130214910, 293484356, 371474364, 505038806, 722403820, 134386236, 49288247, 493394195, 45779840, 880892113, 910198193, 652658251, 137772009, 480788770, 628467682, 228572614, 238880708, 862058176, 977281072, 49003306, 308720719, 380608303, 903007268, 925429571, 33452796, 135568896, 469483335, 622329789, 19752252, 445009588, 489630944, 5152100, 417316095, 866728446, 351732269, 59200203, 409172947, 80676409, 748039424, 404824745, 756634557, 717941512, 910791980, 81467308, 239621970, 670605840, 571240011, 859243295, 580977307, 975035789, 281717751, 820347211, 610325058, 464090416, 724928025, 138748213, 108156466, 191803176, 166152642, 748580333, 861538673, 979949338, 477785639, 414571248, 752107968, 565686617, 478681769, 837691990, 253537149, 84098983, 636584550, 201175023, 20952994, 129350024, 377163194, 822301107, 780530423, 58440101, 146823377, 392697055, 454419295, 407736393, 419042433, 288813264, 139286722, 844157358, 846981469, 350452052, 620424873, 694761587, 704291077, 74646253, 385310670, 689020299, 236988181, 361480196, 218559084, 972433006, 67456951, 175094782, 848376279, 902257126, 152083173, 992074812, 387078743, 679579336, 553271230, 948810709, 173098557, 316646614, 64591438, 128739159, 237956838, 327298750, 736409599, 698077447, 795226067, 529462411, 448096634, 77781957, 471219824, 656110197, 183631070, 298719892, 134602519, 677816868, 212175136, 231929663, 856972319, 459185697, 174135432, 197024847, 250054372, 292812714, 225141862, 654092113, 301502092, 878439697, 259813049, 273233011, 865475060, 148601271, 531029087, 300058070, 506405636, 351993375, 471188152, 208777571, 286366855, 86284806, 803487612, 82011831, 236568364, 583832742, 343023106, 655990271, 242579023, 905212857, 964683372, 629831081, 365882586, 166802416, 587649849, 595701806, 138031909, 943073732, 389461208, 304236960, 18281912, 898652693, 260634012, 118074773, 354772390, 66248254, 839213610, 904517961, 186607356, 840739492, 725494607, 183015966, 328131173, 396751134, 761601280, 949391918, 442639044, 905655530, 880903504, 937250593, 597186463, 651091192, 23264600, 12092815, 777865931, 358672252, 397460348, 235199847, 249233784, 235542402, 284334052, 44237571, 357909032, 347383420, 805686721, 613689690, 886750406, 754070455, 416237303, 295198571, 73259436, 589117847, 653857880, 68276351, 423064820, 137594511, 163080790, 571465063, 896464116, 486814205, 449990909, 867328440, 842893580, 218303650, 509739669, 502226105, 627470091, 892141731, 199458803, 197713, 644804887, 453215195, 590887878, 625537190, 574450814, 279242324, 429754689, 194217338, 351252131, 498225131, 474066809, 900421214, 90042930, 768712176, 953579525, 652660366, 849993731, 273472679, 541697381, 815528499, 6463639, 737079517, 19104259, 136601668, 359165334, 987472427, 139223892, 970357180, 612211153, 595870938, 500915859, 756689091, 481869876, 463461077, 390070999, 894232003, 641496668, 727974794, 815801764, 958094215, 212754336, 785393354, 939197571, 425775852, 382177109, 511868405, 198968309, 665008666, 599851910, 97126792, 278800782, 115318844, 266446055, 927774493, 431998150, 450583778, 622555817, 696688287, 262685283, 235860200, 991348837, 99285566, 486187320, 857218997, 419066122, 692900135, 613250004, 318345438, 65896902, 743273455, 708269493, 871016810, 843836429, 962072645, 970522981, 556189652, 276507548, 177851301, 336138805, 13068168, 15839485, 728101822, 430852039, 457943794, 769127464, 201099093, 347155549, 390042961, 395976729, 221742203, 586261592, 735800349, 149997902, 978978738, 769491288, 694540791, 53416848, 344102786, 900991521, 860174573, 15204275, 925983036, 744676732, 855453161, 673011165, 752335958, 887069420, 56527164, 107899104, 588243823, 162679763, 298914103, 541737882, 507518823, 527459714, 904395232, 315772707, 443759453, 737943748, 990706657, 479218784, 973336659, 813629359, 702361709, 59831934, 594267166, 297498649, 495594403, 333265574, 676931715, 411294705, 680414445, 188627378, 671819069, 211448646, 124875240, 495444479, 983031484, 16088061, 45998179, 81819314, 736471144, 945076446, 306066047, 18930516, 468244162, 978528988, 513196473, 29918644, 772006379, 981938088, 129850787, 365719278, 307245228, 786645640, 243959254, 991185786, 565111071, 773382804, 236309235, 373957452, 113945664, 581783075, 372103086, 452019019, 244800453, 753968590, 12552382, 753283249, 145607937, 889486310, 148577, 684133038, 465218997, 830606077, 580671174, 364430338, 127743237, 511505464, 820511219, 936926422, 712164452, 644472433, 300325489, 456914251, 837196226, 717312645, 731666158, 843068998, 824507231, 512272461, 644462994, 674288824, 490818920, 624361497, 232574737, 350906574, 300103076, 795828201, 319341354, 115955078, 341709184, 370817257, 949251355, 43827741, 244701717, 647070083, 360149398, 676633409, 317205138, 859378528, 534409249, 839116877, 907168618, 61895592, 595623485, 345051281, 776001631, 625382509, 580852661, 184709479, 903882605, 473278484, 489128950, 555223084, 588352371, 96751942, 215495174, 856476809, 440530927, 534999939, 613586874, 82691980, 211986691, 108984431, 673360659, 55207987, 623551880, 765640494, 95785060, 14902505, 93272264, 872777382, 194094718, 824107062, 9749378, 917249597, 391923814, 5909639, 248335186, 939227284, 546486622, 955544189, 575521496, 560001561, 695583799, 218846803, 412190144, 11745197, 998210447, 537539543, 648396125, 200832040, 824034918, 142103031, 958462505, 809748540, 888384956, 325775603, 371519964, 10749680, 810531821, 365254000, 519271391, 223047360, 16048917, 648541424, 689127599, 308207880, 124643064, 827006322, 80352794, 26728274, 24734991, 76598089, 161476123, 890347070, 852790795, 52678501, 611695741, 165246584, 751233113, 799129622, 855799991, 578784440, 507147531, 916263180, 85162018, 103877978, 64161259, 463739092, 267001153, 124666995, 301284501, 136369019, 650643098, 888728737, 861425407, 261573522, 946808722, 275438620, 870462739, 827344225, 977365237, 767808963, 831665071, 368017411, 904579020, 127203289, 403881501, 592418998, 688947173, 887860551, 289248439, 175200482, 847252298, 193817709, 356780453, 137079217, 651158955, 861150654, 595072777, 851692631, 753226475, 273780164, 902286208, 674700693, 91147876, 535753192, 846908351, 332658558, 768794067, 299973510, 793705657, 728907501, 40134532, 827453386, 927281632, 151484454, 757804264, 277237621, 325998698, 98885661, 884270694, 302855500, 346245338, 297359461, 528068833, 184098391, 764796482, 138192328, 256399859, 131212090, 741089578, 532654681, 581858122, 973836653, 85386315, 462673604, 407402400, 833858567, 305278968, 69002937, 728068795, 65548511, 933239969, 331690898, 526503930, 887178939, 99232301, 567053597, 442259649, 491786696, 411654014, 92006412, 92463976, 457365245, 763588362, 703524704, 43198158, 103457021, 981246620, 96526999, 341281629, 826696143, 38117789, 90773901, 469807473, 800804421, 451947241, 426623094, 424774897, 262810769, 89517076, 655602771, 67734240, 935349035, 582150927, 579805764, 816410073, 957232263, 404117676, 657088028, 790858192, 830719364, 200760877, 106827099, 36371557, 539855306, 352487692, 308538880, 827486948, 9872655, 685661341, 84072763, 745688715, 633410111, 654292617, 250838888, 829968559, 467825633, 174689001, 622345896, 311707832, 795168814, 969492100, 231793716, 767041178, 135176686, 772387042, 506507922, 80059733, 146095367, 942781992, 161169529, 895238672, 764687873, 206613201, 506629763, 984340766, 678844157, 307818068, 996053283, 88637753, 762209245, 511448672, 289177648, 106878856, 600925707, 280877213, 461945408, 174061112, 687992492, 608234044, 529719723, 14904001, 143302001, 834223680, 266715328, 665542023, 877044874, 429739907, 305933549, 592321692, 30205156, 223336031, 827253916, 794907397, 742486903, 286967545, 101132204, 187210923, 237130696, 125311452, 301076524, 771952721, 113557129, 272955623, 727935454, 442577633, 960260351, 908551664, 902793811, 3593065, 495060420, 350242645, 310767464, 522696327, 445924505, 845717200, 379342371, 102032865, 587673062, 887933441, 13979757, 207185666, 755262341, 167828410, 710744999, 747745721, 646855474, 14755677, 306773170, 694705332, 60701815, 194511508, 638191240, 458063678, 319435206, 463599453, 809159517, 646172638, 829969593, 95589210, 102880822, 632818132, 393517478, 864381750, 971214483, 322839249, 259487309, 909196200, 291000936, 882319486, 292398042, 190515065, 666145848, 213523971, 495194753, 47681964, 874428549, 291706606, 864603139, 609616543, 913008890, 788049349, 849365679, 455828223, 252722594, 302891058, 917742405, 948397875, 46612639, 120875664, 523453255, 352203032, 237945674, 825360822, 497495442, 935271439, 476693232, 673176745, 168814417, 445609568, 469956730, 260375362, 433845095, 948279109, 203008434, 69699705, 527445791, 542282692, 719100276, 856261373, 214853049, 422134966, 601163120, 104002444, 228358404, 614276667, 552399355, 612645196, 111810008, 188686846, 979873056, 68658130, 843237682, 922511845, 428155230, 99987807, 100675161, 70673085, 493062431, 781332554, 273969402, 879262461, 786355895, 420438049, 476056711, 481678625, 531730353, 433755292, 253795877, 631231562, 377674829, 68224639, 928400245, 509168468, 256254301, 316862867, 625209311, 213328239, 94878981, 546293066, 151451464, 142533731, 795863536, 888582533, 422225466, 993484568, 56463609, 454407586, 839119031, 878690435, 374990656, 465301124, 359567913, 493147551, 734161475, 656024984, 584821025, 739472905, 864868301, 567869750, 860309136, 635811789, 451975421, 283001831, 483509111, 200530726, 152675548, 885364845, 861673939, 528962344, 389504147, 865399858, 196350894, 417762681, 439914193, 586569113, 997044612, 484376467, 780252862, 267156576, 373632271, 187672222, 312520004, 400407195, 884896623, 445410328, 610066176, 899022254, 861966469, 734830119, 493601854, 62193919, 114327054, 777723424, 618362662, 763791422, 76721153, 882621079, 735780931, 520795051, 139558445, 530356562, 191435085, 357767348, 732949511, 296407750, 345516957, 7897823, 456229035, 432062331, 842450041, 461636391, 349842892, 459725415, 591464284, 771067972, 113058973, 591079840, 939202336, 98989318, 854771997, 218462878, 587641636, 111252020, 118017008, 967014847, 762318301, 783740350, 400420495, 579646139, 817174197, 511992454, 387682646, 821825821, 758844517, 145604556, 138797052, 323524683, 707523919, 689325997, 529586016, 97508712, 600891499, 226106394, 248310546, 236179337, 728418892, 859068898, 467670275, 853901730, 526901430, 963042261, 731332642, 803166069, 884391945, 849784770, 56411799, 61295438, 412839359, 883675892, 287050339, 823694104, 395293384, 461062337, 749207267, 841930575, 209596853, 185164232, 986101494, 812799060, 107278107, 492475904, 169907724, 562324192, 632742920, 938932500, 928346315, 877812301, 905286994, 462827631, 77126603, 756081011, 164485488, 586259687, 85114925, 342712289, 898023291, 768438497, 604019744, 426397755, 403553737, 987860061, 238344853, 482280012, 262161974, 244235096, 407608645, 50509836, 645814487, 380921338, 358469906, 598089523, 204887418, 442209040, 967106498, 985646996, 494517697, 350889849, 993488999, 699088401, 972322967, 848796866, 92019152, 821403968, 946130032, 542912358, 614856365, 870046678, 391465695, 568628985, 192575830, 919795856, 963632496, 36915440, 991692910, 300071746, 55339806, 722150449, 434046688, 204562790, 773451790, 394320650, 504067559, 377158430, 970269168, 190356418, 34497580, 131315712, 65905407, 862065107, 145122811, 51168066, 740171462, 249842830, 384238433, 338550668, 512549582, 7104671, 402268758, 104661638, 380117140, 422543139, 354886887, 68392317, 388396272, 813560716, 915441893, 234583223, 773210120, 75683853, 52080439, 868067115, 769168878, 449902220, 196911354, 33849741, 631718053, 302109247, 221201504, 719753550, 533879810, 149849171, 306601602, 564276895, 855648613, 887759052, 289955958, 475225004, 307507524, 495978571, 863172406, 609153662, 712120303, 440312876, 605580773, 359808809, 897371392, 199197413, 918059091, 809475555, 965353293, 361134629, 303847128, 773458740, 586786880, 827066752, 473039215, 461657082, 520288315, 131517248, 512906382, 524151716, 577028255, 101517756, 822845834, 939461625, 827091710, 343707236, 214221949, 370257422, 114608579, 567273870, 638037058, 68644411, 838225232, 533015754, 51008721, 592279568, 274580144, 465431343, 861055758, 443920755, 632296770, 621861844, 307318577, 914530745, 172692025, 123466599, 699696743, 699886129, 180898416, 318436303, 656427609, 197251661, 288821499, 855908185, 610836947, 23478487, 608326150, 747014896, 975502279, 910029377, 770872271, 446227213, 655845911, 322687258, 830038395, 336687105, 486863354, 519066808, 625360535, 577097476, 883724706, 231164475, 544275490, 55814314, 237175913, 417769198, 319260862, 936491995, 742556593, 426022265, 270975656, 881814533, 229399555, 841828774, 68286899, 581129403, 383584458, 656524215, 820849097, 610434619, 851722076, 70836628, 18649940, 935029676, 149368487, 145991616, 218435977, 887110759, 466517094, 72697913, 894785832, 283109624, 969936023, 601193361, 821454100, 316649728, 274800742, 51120166, 676285581, 665514057, 651898038, 744732055, 976448996, 279230495, 703626819, 469191030, 571993721, 390270723, 695063481, 888573364, 575715059, 776223896, 178918281, 286606360, 962448396, 166850421, 711518933, 435758089, 408106851, 433190214, 184384880, 764899728, 884696086, 308273806, 603411450, 218968628, 885646827, 236063222, 662321019, 608061089, 670049477, 700241073, 567455327, 586583229, 232735591, 37376600, 737923042, 821113756, 200665376, 423013188, 403217297, 743932676, 216162937, 395373953, 318249137, 670007383, 303223336, 554271130, 394443512, 110560623, 138792706, 495817987, 444310197, 112965918, 95356796, 576130785, 246663044, 476653381, 524320409, 345942434, 249356021, 892894813, 189900260, 334133849, 275613342, 570710570, 805380091, 931689164, 947165277, 539111127, 67739862, 586780374, 90255110, 339246022, 401181109, 765890258, 151327877, 588671517, 905622, 775175424, 991739560, 917720474, 169354562, 697184873, 784208015, 446943463, 482139921, 48448330, 447805102, 562363320, 321733722, 955617528, 384727084, 98401918, 936522352, 445924112, 911636989, 713724241, 771508391, 433542947, 31526099, 659770763, 162073143, 714532537, 120122907, 229356453, 612597308, 598267958, 996104794, 248100327, 624025867, 480602960, 298135320, 794814614, 609642096, 656128125, 731652878, 144601945, 986893856, 769046439, 376424099, 429722727, 469815274, 496719987, 940137495, 618091885, 858064286, 488708003, 918616681, 905298555, 557221806, 398949485, 507643970, 209227273, 701613576, 157429382, 623221732, 23119552, 353975766, 634623198, 633541353, 610241494, 444646480, 685714665, 316965737, 132856035, 169564274, 340319668, 178302474, 757283918, 534412022, 720092866, 583088557, 834554709, 359529645, 520999413, 371113647, 313585217, 79873681, 94712777, 13521556, 561600686, 53792274, 506712751, 124352886, 642769199, 213977305, 777622533, 526624263, 188976751, 572535171, 248926807, 255286703, 958716218, 118156255, 151150860, 40840851, 274187577, 651652808, 951325225, 590979360, 613470665, 317647911, 491309961, 680195696, 831300597, 868551843, 599752395, 806128309, 331554137, 208016241, 591914602, 198415913, 549061024, 40739807, 401157312, 723886494, 292600343, 27711275, 848636483, 646115562, 188720541, 782907690, 560833757, 617876551, 640244799, 933870055, 116620741, 389368729, 881471831, 557654405, 569646747, 702059951, 420792314, 995780948, 136387944, 886097988, 601569584, 100454548, 427771323, 953799551, 380001913, 823900613, 854067254, 702983436, 646302126, 288149048, 684538939, 162830933, 58352618, 552973326, 658378332, 194053816, 852087351, 87626832, 253862376, 86342567, 542008221, 546092947, 249349657, 876942407, 640436390, 421744495, 66163360, 225824037, 715102062, 930671250, 823553934, 520742069, 193057566, 736605678, 244597016, 633965487, 547188277, 316637838, 567434149, 191586876, 959887427, 698663009, 902170886, 725483674, 647321774, 804680815, 576572464, 835527517, 541710196, 69289605, 741999737, 257515824, 423166701, 433885436, 450384276, 335647728, 667889496, 561084329, 189811364, 376056078, 490173187, 299538561, 182002781, 977327705, 30304777, 159129791, 280265385, 838947096, 692024583, 111775102, 510104699, 566807577, 310365274, 48553016, 7562815, 97032503, 390988050, 113940184, 786552824, 183473135, 919158310, 721662471, 891559776, 893888758, 507810993, 832478172, 156549058, 50575802, 585602771, 649485248, 741136090, 60469153, 260396715, 811328083, 162191424, 585530190, 297847959, 274046038, 874390131, 12778419, 605908662, 738693122, 861580264, 868888035, 335950807, 630638062, 727459536, 467817458, 484967521, 797803864, 716309210, 394248321, 861178022, 596427303, 917830277, 428475261, 180104979, 986945104, 365763263, 542402700, 179566476, 842265905, 833537676, 405325819, 566009111, 919134968, 964666618, 774165412, 297926852, 742766, 951373651, 624707720, 320081653, 111758302, 508807053, 744960895, 810872300, 684043957, 556420918, 355505140, 264048140, 683962715, 282645958, 722412802, 282390442, 68049556, 653387947, 172024431, 631635453, 15797109, 324691883, 157025767, 959850578, 142223084, 521030392, 809099986, 251808726, 211017724, 227591371, 507069834, 735498777, 43436859, 77721121, 471749790, 642927033, 927124191, 906032305, 65244635, 843129247, 509806945, 158869098, 638389072, 152269799, 524363689, 296086972, 295706739, 953838574, 568735279, 174069645, 794560725, 580623924, 985212565, 768004278, 657164799, 844958718, 837968879, 132368739, 248124324, 210842382, 676225781, 169118878, 386306103, 633992885, 667797347, 415351337, 102181188, 790501886, 688822193, 816338697, 574405482, 382584203, 242067520, 21603294, 632015473, 115008457, 494177232, 713260707, 144373406, 390484342, 813203980, 744213362, 24029945, 724962504, 975843054, 588237022, 83935832, 661413518, 943013111, 975831716, 822011042, 560829671, 905066188, 730415759, 99805128, 548454627, 458438468, 96046238, 804742251, 278966307, 912317912, 421519681, 221801638, 903568547, 290623392, 616355362, 381846700, 32888790, 496232404, 717340578, 457612253, 257561693, 988900186, 154096912, 824984154, 886294500, 45128655, 137463117, 123892030, 974308010, 481602336, 61784256, 494539279, 146015250, 450933848, 671640857, 880099222, 52013847, 850059372, 266747977, 43560792, 965206153, 657698506, 567996984, 530655381, 549484158, 194266563, 768449640, 712469205, 105458262, 763272580, 343007961, 148682373, 802834691, 116611456, 676891232, 950215366, 168196271, 464453962, 953939966, 571942840, 60613234, 448740596, 646955201, 209091097, 189792195, 328914574, 429856810, 36247112, 519943011, 848031423, 17545519, 555252552, 837417060, 752472163, 775635160, 449754867, 812079994, 466219552, 173426709, 366362504, 852280833, 906676660, 5870121, 302073007, 519590945, 609724317, 104810031, 774813014, 237319827, 216315895, 512755967, 625099953, 857970844, 234972776, 231635322, 314018396, 37293370, 118978380, 413971031, 413971193, 232463699, 532287544, 917093731, 761065537, 171652363, 998923043, 299184419, 242040764, 826134041, 30707254, 235980972, 322446398, 557172367, 33080742, 76238120, 542805273, 478160312, 913194409, 755074343, 580043065, 23141959, 579597648, 308721743, 193788107, 858319381, 401062418, 514753600, 276677285, 33368171, 881516920, 28531665, 904217298, 94553770, 977867204, 699416864, 447285935, 7085139, 923734838, 847715306, 681892960, 701607991, 175822518, 707423341, 69203131, 500753834, 792712880, 919569083, 498090335, 429436252, 34790245, 91974800, 111802748, 536205611, 520094757, 468281347, 321584149, 154763960, 641118197, 835645511, 712918750, 992343568, 198520931, 833470241, 961283233, 81878487, 309511931, 708881817, 340419623, 874174372, 308022288, 985340576, 215687792, 167918527, 976655341, 490506304, 986538191, 278477373, 619826278, 490469418, 236470356, 202325164, 535034802, 650692280, 354893076, 892984822, 681507378, 278813493, 25983354, 167512634, 44275821, 615830922, 296411632, 807897842, 812199305, 244780522, 838686937, 379280496, 778530620, 646402622, 225372158, 116103064, 414972057, 614988457, 269379085, 658309452, 535620869, 559927590, 924476812, 865177183, 177875275, 220295341, 927783136, 338313414, 769337608, 493239929, 276107951, 619440851, 112119113, 258392788, 842048470, 42565423, 457146207, 824951630, 580679898, 627075340, 122043283, 464295096, 266958508, 225879637, 55664475, 863156306, 460369626, 650040223, 889855875, 535228018, 743435722, 199379115, 672898617, 505778864, 464058302, 499514830, 578411786, 584308486, 116825000, 448627159, 47075952, 752027131, 362194044, 339745835, 958319028, 545777550, 85097604, 686188801, 980031460, 736820265, 624259430, 694938211, 919194765, 915405423, 998033452, 849264699, 717231244, 770668552, 149123559, 53300186, 65135780, 629502328, 151508830, 856010859, 582947258, 603207070, 977724198, 906953949, 313070738, 399477931, 722232921, 76957964, 37095038, 246428579, 497360636, 954175874, 233883269, 856473570, 784493705, 586218963, 374542311, 199460226, 534280112, 570735807, 706437398, 363388905, 934946396, 743279035, 174894713, 220315073, 307389257, 518158798, 483272736, 157709288, 739297097, 8235615, 26110196, 446111105, 96806640, 688987978, 907562349, 565372423, 707265153, 101338734, 347852265, 615706064, 233930546, 518917826, 118677028, 463254530, 128978352, 426261198, 810604282, 100286694, 851894270, 429124216, 640539186, 78185493, 691371309, 5260221, 118411698, 73370808, 688692211, 935651783, 158084124, 912429349, 148780005, 336660597, 190557918, 705835920, 828383101, 209601606, 898568033, 148220061, 899118674, 123256356, 784771226, 980565679, 426776318, 366673748, 994845587, 226325712, 886192475, 506198741, 85305767, 894363540, 531302731, 226228608, 618963615, 50669838, 283925925, 577272528, 987734496, 528701316, 195457424, 753373558, 631832621, 774743234, 437990667, 402413562, 534643984, 196698414, 30388549, 340985455, 276400873, 641617156, 537817459, 453837222, 642126309, 891120572, 40399517, 259251219, 463776848, 302402838, 194598014, 572635153, 699467985, 242967397, 904175211, 489660606, 806102208, 14512086, 820287368, 895136087, 160608415, 259388215, 634180897, 840851419, 510163126, 636760953, 657445286, 577816955, 582977584, 644614458, 627910415, 950606042, 205552981, 945880030, 331332629, 699010901, 83448397, 586841780, 342100315, 363426190, 587219364, 227940871, 805233772, 233848364, 579556810, 860211926, 715166760, 809470427, 263097385, 80259675, 644504171, 781456791, 559788917, 731617070, 106820759, 415082281, 768434967, 156712456, 200380804, 111347773, 104018937, 873009212, 297347337, 378717624, 77670667, 288490691, 657375710, 700829649, 100072738, 516941702, 242064288, 85762576, 367737147, 236951230, 335359692, 550694111, 776988708, 883723609, 365339726, 120947097, 868016794, 152511762, 811659265, 480824684, 150926362, 91850674, 936278270, 378330740, 812958587, 787099294, 721473526, 53212220, 818874627, 518052091, 629500278, 648376879, 554523868, 484348422, 389313570, 47694755, 252883434, 162699236, 148128279, 964639860, 947796296, 856211230, 658027532, 81062719, 181500963, 843425365, 297613236, 745479168, 622949600, 476527913, 136945552, 363215427, 82436118, 936928548, 800620716, 413823848, 363848991, 804826008, 206111069, 182219006, 541792114, 604958484, 365313827, 923605000, 625107088, 549521196, 815991260, 847805884, 538510360, 508466632, 994718630, 521004462, 310807034, 929911799, 877706627, 123060101, 397604894, 352205059, 53753926, 363409209, 349565876, 609369098, 714228127, 526400723, 591744518, 377201069, 885816921, 802802089, 760421207, 442781322, 431574337, 507990251, 179799384, 80376001, 241887167, 243718563, 985589491, 99761318, 172101305, 462838692, 418475012, 114635495, 606597048, 589967662, 862273788, 722593302, 916819492, 79956670, 525604657, 35853985, 370444477, 338528018, 963845124, 913346178, 6708242, 17355371, 44148028, 419455665, 354843035, 731223518, 441201718, 32821563, 126430042, 54441440, 425931935, 695303220, 233711674, 68759552, 288975824, 232345019, 816009684, 828707887, 391632055, 102290730, 470259647, 133154134, 593623977, 892870184, 237689577, 1507808, 637652094, 546840582, 505694892, 851433659, 293181293, 440799445, 761523801, 798342193, 975564672, 818714078, 831547590, 217580066, 78897352, 643517313, 214617046, 343475597, 184691877, 639667427, 221405328, 786332317, 755391081, 918695361, 147068116, 467700179, 77488146, 636314728, 48175682, 379696271, 713766613, 113213257, 920081021, 555856694, 307435095, 478486972, 786574184, 712150231, 954869838, 74880457, 325434067, 57563811, 717851564, 397042541, 850673750, 684418448, 895860969, 746428612, 818707039, 259746644, 512364671, 787150217, 390430246, 564651754, 199085545, 175481227, 917627943, 632146595, 748144062, 609266628, 1395544, 826311549, 217748675, 102130535, 840940321, 26171165, 793465656, 638393442, 655889489, 197168275, 20578565, 315511513, 352473936, 95979998, 517202234, 432621677, 208762704, 840255881, 525029871, 903954227, 408930980, 972851921, 708808314, 980639749, 445016860, 838506809, 323324298, 169958584, 495602354, 215169967, 743192622, 929886883, 190590062, 640545498, 167790165, 172768981, 213259682, 231866648, 948102145, 191185208, 272318904, 80007320, 833905470, 605329299, 740839667, 836551390, 864491175, 651518752, 966565145, 382169141, 335973398, 459561360, 226343911, 902067854, 981640784, 141798772, 75791260, 36458982, 11730558, 767094063, 907979670, 588824142, 89736030, 868303224, 368541495, 833667252, 231744171, 629828961, 58067941, 779536876, 248205116, 588671772, 850115498, 154530566, 247195156, 812237487, 278418242, 182008270, 692138601, 8392862, 356565027, 5648185, 543511803, 600834477, 859572119, 814260502, 581137862, 785900195, 867250680, 152797565, 325313408, 371106858, 209696307, 477163192, 305547699, 879526247, 489686875, 59196084, 161359570, 25544332, 320165356, 693175919, 155542806, 127003230, 255584461, 915966890, 85251946, 907501973, 424961927, 938363031, 464052029, 184824710, 952970715, 458438221, 566173874, 916481349, 92391294, 335753085, 473489700, 277076389, 168555930, 397628002, 154335310, 527477437, 982945846, 910558298, 507358556, 913223234, 574718819, 861402653, 532577053, 643900536, 693641522, 579830261, 993403688, 810255148, 342908134, 532993287, 309796141, 430829971, 391108498, 790930623, 169998839, 582253321, 721809802, 881022955, 317146932, 541767494, 860137160, 451763222, 15232434, 257277233, 666666560, 869477934, 648161950, 988774258, 365062803, 305013108, 344316472, 680499548, 809952424, 894778339, 863010939, 642297101, 306855135, 566615708, 471371920, 388837188, 238804608, 950552322, 329527438, 686041512, 222341322, 858605592, 341656799, 82588764, 609882486, 885010575, 226074591, 137922191, 941863570, 441388404, 840392116, 205035057, 15396750, 169749419, 575218641, 25646809, 7880, 527307238, 692822516, 159951626, 929775253, 103978032, 319712597, 398403702, 875538679, 710723544, 244040863, 347643227, 940177916, 372968113, 18987207, 57549284, 155028016, 636309968, 128566716, 161070013, 511456226, 41563454, 15722398, 51777851, 758299989, 623527740, 25997602, 839890398, 746481732, 368315182, 649532706, 905704755, 302872691, 194907423, 525336591, 172762931, 110396518, 834910157, 206993269, 56010452, 433098755, 170880237, 681552424, 976104733, 868387124, 440028069, 810178829, 69846275, 675936384, 49708179, 171904248, 28479580, 183774508, 409932860, 260278568, 524309949, 999953615, 258146475, 168169350, 795325519, 846941648, 85023372, 306568170, 928872322, 315250017, 739801232, 973116792, 225929422, 463111311, 599395927, 596419520, 368005396, 572351846, 685724853, 917943558, 535385624, 135312096, 840049085, 688430904, 772334672, 31012421, 246269000, 356759580, 267052717, 380755355, 836484300, 171242868, 733669915, 880624752, 349982506, 343762610, 579248253, 967724375, 260604348, 723491028, 238715879, 524793755, 842642601, 555657540, 62739652, 324551311, 416981273, 27366344, 391669948, 324962635, 172319950, 940357799, 45993024, 484935403, 329085541, 944269127, 680041364, 171869239, 758757277, 625602499, 999668615, 980470467, 60356992, 738019505, 975595601, 847957175, 944155212, 961465320, 438088925, 30007169, 885660057, 496488234, 504928388, 618708849, 693783041, 785324064, 667905833, 812754642, 891717373, 733420326, 818533789, 919319790, 979708017, 925597995, 492379833, 379566292, 970490188, 800035997, 353110866, 266841137, 339503257, 694451400, 593985094, 808638408, 149602936, 870035785, 8720264, 50725993, 337632839, 572771746, 762579320, 756718010, 782376787, 186310050, 567929586, 726869977, 791443453, 689655828, 752013399, 38978888, 830801056, 512404532, 347393050, 132862895, 254365613, 194632473, 577525218, 77492304, 145309440, 868660746, 30894729, 902450842, 182296672, 538457069, 478565096, 398918563, 198341853, 893384680, 643463125, 711141026, 703058789, 903735131, 380400264, 967223152, 266354891, 999260172, 631006865, 186898952, 800737682, 803090095, 544163363, 371080469, 889964113, 915462766, 71786024, 290366401, 131494024, 378981376, 133359016, 784038575, 949893327, 782104077, 154149965, 491792306, 750258344, 46439558, 876702888, 448391967, 456408454, 134888655, 726665348, 715787208, 83309869, 406137387, 43216624, 59512026, 641654121, 684990671, 298405067, 172297013, 700398732, 917054270, 874271872, 881862097, 419413366, 297633612, 582802983, 270123046, 995433994, 841006187, 524882533, 416844180, 887167854, 401983153, 371806024, 514710730, 637886376, 709739268, 180610932, 326610709, 641224469, 402851308, 210962993, 731335525, 527625529, 278266533, 988223518, 983623212, 263322785, 319880770, 148229108, 261784860, 858357280, 736665734, 571149308, 256151593, 136449918, 362657842, 414781641, 274164163, 814011884, 51119295, 917987682, 100318340, 747790914, 340043260, 105437812, 622583823, 906511667, 65567118, 268281754, 787890132, 997490897, 930929453, 742010202, 978729408, 136759861, 850532722, 689910406, 892634443, 452776531, 776632552, 441319310, 787928368, 339173584, 861549747, 228817854, 253380409, 842886403, 540580718, 285087216, 959800467, 881436905, 67820817, 918784671, 119506007, 741301109, 39678045, 504089730, 514664871, 766379416, 258545566, 892257512, 993530381, 738974329, 249344745, 403551962, 166653027, 886114136, 94181207, 630270117, 698697889, 429225311, 773189108, 156713538, 264494941, 217742177, 290461173, 876066592, 32231282, 361512745, 312824208, 861135403, 536071166, 552882916, 613534696, 750650966, 484768592, 974695340, 901402527, 344683976, 285375568, 173258062, 576825031, 635981395, 865780649, 806686206, 933819215, 99868730, 369438861, 852635768, 728084061, 805631029, 483116566, 366142445, 496543486, 699610130, 966082653, 48339432, 779570370, 220523782, 569079065, 254775294, 904459380, 173794221, 80862936, 604002877, 419788395, 294467167, 675137830, 930475062, 279350537, 545453309, 580092525, 682680683, 608449142, 845418018, 922314686, 956718642, 71985279, 183186337, 842604907, 427359709, 152842043, 804026525, 152868142, 777731919, 616788551, 281475784, 355046517, 125452128, 224514077, 942893707, 132735724, 445625111, 223656590, 858424450, 890642398, 641106257, 284047462, 454091913, 407982949, 96463356, 592408898, 215823829, 42363887, 989806681, 199215193, 953581726, 520418040, 391979938, 618959960, 34029422, 238240163, 120398958, 688534572, 593564278, 398954395, 324909184, 467264457, 898427282, 440339203, 587554304, 530985526, 308089447, 623978108, 585299751, 447269166, 982202071, 450715873, 358561620, 191578087, 273588807, 4108553, 139660853, 242718550, 652039269, 788026273, 106646569, 857843852, 391422959, 135660766, 175945496, 487311731, 500113482, 355746362, 537719508, 917352309, 640876827, 634950230, 195001696, 547486575, 102068981, 591249102, 734700429, 946549509, 935168423, 601392233, 131117725, 64918955, 525101683, 355823828, 660988732, 283346331, 804770657, 205593147, 221668637, 246971185, 639599954, 771740571, 276283761, 943985149, 773261091, 815879596, 831264886, 636512247, 759796314, 654427820, 692074264, 955845319, 671011276, 854943399, 695272775, 843223486, 36551099, 188359974, 510663038, 224018709, 148876290, 733060127, 353660902, 801561456, 764705619, 11508808, 938353507, 770709564, 503648835, 496132342, 664818778, 55075572, 9447087, 395251955, 289476196, 11375074, 93100567, 562038875, 435291490, 59882880, 188386898, 844267857, 892638934, 850146294, 485583552, 216935261, 80941440, 270134959, 390258881, 661050833, 980958505, 692739360, 433804028, 84584002, 588461356, 253549157, 123889539, 917461455, 555913077, 145107138, 597373467, 666340233, 78690029, 434495069, 681804643, 941681264, 423197959, 653991520, 461222486, 438009287, 458755093, 621391098, 701919456, 119532401, 477671687, 548724555, 150365721, 310553119, 360425251, 677912, 907856587, 727851034, 127149620, 498441607, 580561005, 678414664, 340613166, 880239776, 610894169, 449418216, 544121607, 503098185, 862251377, 109554550, 572300987, 65246968, 690556295, 689462048, 523007382, 769335179, 336778731, 383496784, 506244005, 679748071, 352003208, 663153277, 140680075, 601607405, 212991476, 28044273, 126318354, 440241, 759938314, 528909039, 912645617, 874852018, 935769313, 804272641, 609242964, 873191485, 762908908, 907891680, 225826807, 995483882, 883211660, 567253689, 321309191, 736876750, 938526070, 298997891, 834529238, 174241171, 722133097, 388213285, 230443664, 60801932, 727963887, 244234339, 541883823, 611279039, 780081966, 186399973, 158519866, 667649041, 93548460, 699594210, 551173519, 479626704, 264667346, 680351618, 35383536, 914225924, 832824075, 406730516, 642955317, 581935787, 243733296, 968978727, 4746406, 669617254, 322773152, 167678359, 648925149, 838695869, 445436703, 313290861, 237446389, 903934627, 9707456, 112192603, 930730901, 310034876, 288305398, 842154490, 173338565, 910022196, 224186753, 674542281, 819545611, 293319303, 297754253, 879224405, 662919960, 582109763, 514721979, 310738717, 652085444, 319174310, 716295825, 248297175, 948499671, 933874001, 177157301, 430382779, 832126244, 284273474, 734320877, 603951819, 757760458, 866635263, 200507984, 7335986, 310010554, 39721949, 256259125, 961480437, 64752637, 140520674, 673389929, 697158657, 38596993, 746874265, 682287842, 554613508, 931129649, 743815760, 469920956, 474323809, 179440160, 233805494, 385587729, 265852774, 589521030, 122532875, 897254534, 411816138, 283103489, 816793106, 41838264, 97697954, 365956398, 20488986, 400970809, 41653537, 843425023, 12505788, 899121785, 626505624, 535145352, 459238159, 698110541, 117579442, 792172766, 504301006, 187200120, 228294634, 402086399, 98049230, 495347614, 222475445, 275446638, 895621393, 946901530, 147149688, 59443884, 181249747, 266639119, 529999716, 401949612, 503851929, 284150051, 274703888, 298341975, 992155755, 844449166, 467206308, 612646191, 918766020, 699222157, 559619955, 560377372, 505605552, 352382769, 901016169, 986796680, 965420895, 325712276, 141790711, 214719274, 395919862, 869561646, 314649361, 887246472, 179548114, 900655509, 37596239, 398694443, 960752522, 846982518, 118875504, 997985113, 735096010, 474015567, 693549967, 115042124, 901790636, 736478974, 660661226, 133101702, 313427347, 230797430, 571280520, 627201090, 157557985, 377706448, 955577054, 474425404, 400126742, 939369989, 156509429, 285803046, 981978099, 260721635, 492371008, 21044626, 636091371, 268616257, 758581668, 248780219, 788230024, 940053341, 664402910, 212103482, 972275121, 429992367, 439325339, 65021877, 521358114, 8141385, 853217969, 508411491, 59304989, 610975305, 360366555, 255224873, 760685507, 22327550, 641369701, 770905847, 580583444, 725250451, 558940739, 208838288, 407502900, 752863460, 948210126, 980973821, 175677555, 701235476, 115889826, 128478761, 13192125, 119081984, 591156383, 57295091, 821279671, 223921665, 32436548, 640257175, 847340980, 163321145, 547433396, 3736947, 912781612, 455177088, 341032682, 651472510, 198748200, 355152874, 534827765, 11214210, 394902472, 341685517, 751731510, 815157117, 837255044, 208913897, 226413549, 634303124, 696719137, 345565674, 742325211, 81155618, 74109966, 119212448, 941952322, 602751439, 996787680, 391899425, 961189815, 144196064, 351768171, 942028800, 239781006, 96082815, 663713639, 987154269, 709365140, 365033818, 680706287, 673035090, 863013235, 294399009, 998670673, 616778735, 252987728, 274056151, 651235527, 740496057, 599461063, 539022215, 673667046, 290913796, 212108567, 300354912, 736089479, 881921581, 189510791, 749119575, 375181990, 833094966, 804582728, 42250255, 349772645, 518879405, 381299212, 493211210, 350488264, 713389953, 280619733, 307501493, 867302997, 550489445, 331570288, 182265972, 193603996, 976913041, 471702955, 103850194, 210594166, 890922353, 369423813, 287969927, 575371476, 877710929, 61224650, 708038044, 658988562, 834264952, 175873962, 5312545, 913872748, 920840306, 106762933, 338464727, 553118986, 406488012, 401170001, 737738929, 658034795, 689368021, 308729050, 618026875, 628187158, 15159267, 620148313, 699281925, 739440991, 135064426, 70997517, 978874736, 242830465, 593717708, 857972100, 677403620, 934618319, 767498668, 651163012, 777087462, 857028085, 743123537, 588641590, 56394687, 634931457, 524780664, 52615274, 201370559, 901730579, 986133139, 174348216, 262653279, 443625504, 318209479, 516579821, 624318276, 33780857, 692808402, 934182132, 370244102, 838346281, 218404698, 206127237, 170449264, 65175341, 166136893, 730695482, 313278591, 626646637, 56288201, 638391004, 543047607, 633519694, 103202117, 786046383, 581615845, 558968818, 898627946, 144790171, 259556795, 723060856, 66460396, 885449997, 242119598, 493231494, 507651234, 473290099, 280566035, 551394543, 938870701, 498897347, 623159790, 488457124, 464753195, 164121822, 59341780, 807593266, 485511601, 759414073, 150280311, 221628561, 667367015, 17176353, 422046423, 945984727, 565857648, 894580840, 232805010, 585110159, 663663673, 720574371, 226748339, 442760174, 38321806, 972384540, 24888408, 191632916, 479759591, 271573343, 292857627, 187241869, 615241996, 595388829, 777348153, 659073332, 939051230, 312549942, 292845846, 214244567, 346804890, 400093554, 166723594, 239032011, 43437087, 434311595, 992491942, 312565785, 157337228, 908999593, 417145311, 849857549, 621087563, 942472384, 455982554, 984233731, 989884074, 503867823, 348552100, 531691541, 214515529, 364450097, 740703006, 799835391, 644727434, 740186973, 376603292, 561466352, 582526191, 800409708, 431576241, 851252154, 718228906, 950111817, 481043496, 953589277, 336991972, 981386635, 13200991, 358994283, 530876557, 225881039, 869860610, 105243434, 328723559, 765650200, 595409530, 801322846, 730897203, 130629478, 820650472, 190784970, 467854680, 283833943, 221757187, 948042892, 455873374, 600611752, 632972919, 665723272, 461980040, 549561643, 325627724, 783913446, 860790309, 608637944, 734449675, 674178488, 439940495, 81014086, 658951217, 977437213, 7161753, 697278956, 621766167, 313335213, 594046121, 70658325, 89498198, 421018235, 762221956, 230861417, 854254811, 199330438, 410106298, 295651058, 165097775, 809524181, 348226596, 794502690, 552999802, 190851779, 261598790, 933413910, 346342799, 456067264, 818299321, 615918718, 996545389, 917694394, 368699096, 72959472, 528238892, 636711808, 915899513, 225957582, 324454763, 800661865, 526978500, 614085911, 146368514, 318337730, 310051574, 846597609, 413583304, 244075529, 559621503, 824523680, 500255924, 729074619, 515768409, 461993647, 210025062, 416885777, 550894381, 249464556, 19989604, 551775151, 550079336, 795789352, 742977035, 929474726, 746027544, 39014448, 209111090, 780867438, 512757520, 414460511, 836986939, 937642980, 866159371, 753867236, 737828860, 218640002, 24437976, 953204515, 85823275, 756467025, 312078179, 72331293, 92081183, 994522550, 908744356, 943159578, 669089415, 412439711, 614433219, 144049151, 533364972, 579726759, 155939896, 228482533, 804690232, 845426292, 180459902, 173967536, 161859664, 368471584, 321429330, 909462178, 150066313, 911470360, 243363732, 198980884, 722143744, 596667126, 934501800, 705150489, 305388202, 300808964, 129948531, 161873896, 653577051, 288366843, 987212685, 894364987, 945692499, 72562293, 327930378, 349411471, 212054800, 820044822, 523729507, 666998317, 644781047, 106133996, 877714591, 633095209, 214603638, 199272752, 627195862, 705283588, 505708600, 595201099, 63668465, 361365582, 842643175, 161825653, 905708920, 782001349, 981136708, 690183335, 384577578, 509310447, 815625370, 105907335, 404905037, 639428508, 394514561, 331958272, 381573503, 280885852, 319268532, 817488604, 823075381, 865913088, 819412779, 289838519, 621843572, 409338692, 698008377, 757685914, 532775680, 159147984, 646581601, 960961217, 740242840, 767703866, 391557833, 336327628, 426598935, 387291313, 828631078, 615542992, 502486029, 923891525, 785240496, 220748240, 805312972, 42312687, 745145809, 679157368, 971819873, 184555601, 832095391, 372510634, 605953444, 104750907, 633283071, 407913912, 776367985, 672252297, 55089716, 537511391, 318957367, 333805, 415175198, 769105780, 745503748, 499007241, 475837735, 102616616, 899767371, 44138257, 41109493, 79793352, 33176390, 213298558, 917299145, 447244760, 386671208, 943975831, 45476490, 154987689, 182824411, 219191087, 582042261, 647612281, 630093283, 886358366, 737964338, 740896692, 380694477, 858612849, 344971266, 529633215, 456628271, 738473260, 7729259, 275195786, 223255067, 344415363, 585006127, 48860577, 707456959, 221717403, 972538197, 928799044, 211172637, 590747614, 618307165, 238864078, 34688570, 697059370, 413250830, 616757294, 347968392, 736139985, 249166861, 327019348, 977607498, 657101356, 838402988, 986832897, 943454637, 930657994, 274026821, 351120344, 938032261, 555378098, 729551641, 241374673, 639410807, 197230748, 806234899, 158521386, 969925494, 405880257, 97410876, 698790480, 666148245, 73862115, 515251928, 441019604, 280218304, 287580039, 256060372, 280049682, 933281360, 628932482, 544697551, 276172422, 7912471, 267759516, 589694738, 321844480, 315726097, 375302720, 647761248, 660848154, 747465259, 776157987, 676001705, 17029621, 532641724, 574694517, 459822697, 259963415, 601611052, 275689863, 159705806, 48193187, 243119227, 161216348, 981356260, 200478260, 835437024, 614397330, 353136093, 658292696, 67412847, 992518788, 55070348, 996950001, 252958578, 638928429, 472352354, 558542137, 551818227, 63457214, 123911569, 80281569, 309698966, 156196062, 142971301, 89375855, 93519739, 319927508, 907456759, 868577083, 802080498, 128231414, 905001404, 896946439, 215734291, 552480820, 707011049, 214587488, 778405351, 612142532, 855014163, 583614877, 666051451, 573154931, 228477968, 832360754, 283767446, 750405334, 337820084, 291246355, 524187512, 109063827, 529330795, 377262172, 216814944, 641980703, 551980685, 450273040, 282072072, 184642190, 81376948, 49553770, 566479449, 158309220, 675353678, 612443702, 101983886, 659380863, 689926718, 854038181, 134962632, 947485667, 218924642, 203403585, 209847287, 652142868, 220831272, 20294535, 134983489, 747863234, 526755350, 143282362, 446961901, 461731079, 634686665, 980003646, 773984353, 668902079, 867476878, 184735459, 719383949, 916489304, 684850363, 684358198, 433451811, 523373999, 740685303, 525370569, 163304049, 192331754, 892249446, 528885198, 630351530, 795877068, 815888091, 995712179, 524419913, 313422764, 543905063, 216771104, 962300344, 506436911, 402160833, 610117866, 241306891, 879917572, 987395387, 859604439, 739795332, 736492421, 12973572, 893782784, 177239464, 666065262, 396860143, 46888769, 861730320, 861785873, 130579124, 33345506, 655310614, 895094049, 572516570, 650156643, 127591879, 295207684, 852292964, 655341210, 203670308, 561044223, 894219830, 549582891, 984659600, 866006527, 606158045, 570685775, 235057673, 807248090, 254754897, 597048002, 641313165, 195635995, 181951564, 69427813, 899245420, 372681501, 52019211, 482564065, 694674642, 507067158, 16789182, 83532161, 2124599, 142093677, 502637088, 908308760, 981569168, 352165269, 692211067, 511502943, 822648889, 483668306, 950314405, 83681014, 423585960, 986649040, 923331234, 471704049, 593449112, 393203570, 692202621, 210822819, 620722209, 329939505, 24034177, 703251621, 814215253, 514313643, 884124799, 104360861, 997354774, 873460852, 339079156, 212982683, 513589388, 180976878, 780777146, 339061142, 605186935, 395701513, 836189384, 593158078, 449610554, 739205092, 818645800, 771129621, 905545637, 263210372, 109067348, 175666605, 907759316, 445484469, 239542606, 705067979, 907390292, 659040793, 433800213, 135197635, 576259619, 466110750, 233558534, 867140055, 560623511, 991581666, 484766527, 286602257, 509213718, 343525516, 86037690, 948274831, 771566741, 707686893, 953560771, 391831568, 456760695, 227145720, 364026087, 411932211, 111005394, 633894082, 291110851, 454041142, 315165667, 852997122, 581642396, 190312496, 936981266, 360915777, 537236639, 418599384, 860089672, 807171211, 770972010, 778719326, 148910472, 806892359, 871006785, 799639655, 804370573, 777767530, 647640561, 735453922, 15102465, 908347617, 194326620, 200002866, 863510129, 46042471, 44719815, 363890878, 431573068, 380359461, 257618815, 416032528, 118655307, 40530012, 867023996, 411867246, 432711012, 98746650, 530254212, 249010710, 434679623, 734325275, 618959022, 821461654, 909413987, 684769, 404560331, 417514256, 696701479, 379755657, 311067238, 519923286, 293297972, 755080554, 25901738, 490588291, 804498437, 681404622, 712220833, 754889029, 600862922, 951814042, 417369647, 640640310, 14499612, 445211495, 265029393, 997435276, 295461056, 309575307, 428560938, 227081603, 512181204, 848636846, 452142880, 527831340, 542639102, 361846777, 919667637, 19878607, 358265883, 433203503, 588323291, 840286394, 848026466, 464252788, 971262255, 105670931, 893425964, 803966476, 89502410, 309703079, 303196377, 372545637, 897720625, 955567861, 330652725, 980066305, 645764335, 583133075, 629318957, 836163834, 315181586, 628662770, 93915165, 883440819, 249462328, 638719271, 269999720, 718262319, 827661600, 332293705, 726111687, 412180865, 377700587, 495958062, 210054554, 192265281, 284335299, 429081176, 805101860, 417674456, 737882482, 415100320, 35025905, 788355164, 984945229, 395490206, 51929286, 769235907, 333312998, 696120846, 58734973, 715710810, 149848052, 26072490, 579686643, 32600418, 406615412, 928749315, 174128110, 341978129, 939545086, 337566343, 685030424, 348833733, 581933808, 535247077, 404941792, 869382541, 327294668, 329475088, 179755908, 27667063, 471762050, 607639630, 509669596, 753633085, 281856002, 585082754, 679611631, 485891979, 805472972, 46189738, 648785438, 961391840, 914380124, 727385563, 732327352, 330235064, 968312531, 817317381, 276859929, 161889229, 151260016, 844301228, 544589249, 584170457, 865800451, 893795389, 535226085, 673342958, 174674396, 55044701, 951075291, 578622515, 108205213, 94899238, 327852739, 460345727, 85757842, 294133548, 646549792, 423763317, 531146334, 438160975, 309908036, 265264231, 5444694, 351534754, 508796310, 237351077, 25706710, 159383596, 576535785, 220636068, 612042356, 228269578, 746086800, 54823640, 501768604, 586530841, 492776651, 883021481, 863612312, 881227974, 27871182, 347135184, 591512795, 907299075, 710951313, 158499276, 422791571, 24021484, 631555999, 61013014, 122434080, 451779001, 143731837, 94778369, 688064653, 776608490, 461052791, 801882587, 298787089, 898671961, 2451300, 479975735, 975155915, 217173724, 811293227, 758872866, 885484271, 7922987, 907916874, 189723311, 413400892, 827771080, 964742000, 754801310, 33214582, 275312118, 220320885, 87122162, 94686073, 278945421, 162372071, 61832551, 534055932, 463346126, 97663825, 870497329, 74824395, 450491031, 688402030, 684123396, 209228511, 446221936, 365686503, 455568505, 33108206, 110508879, 806789865, 635348304, 400745199, 11344833, 274799438, 680715525, 819380078, 511880549, 223701233, 335065947, 466159781, 774678573, 994551543, 478048991, 655067781, 78076009, 913952779, 361574992, 111298109, 867340963, 853709322, 633316875, 11300035, 800656898, 792885285, 772358178, 925708401, 79214708, 878753478, 277923055, 302095707, 894338909, 341191172, 439144001, 390301796, 508408088, 607472692, 777532907, 4243886, 512248337, 74153653, 441270278, 641957605, 768090855, 735041891, 133414657, 78396076, 80616573, 994832359, 884098866, 765883713, 755576292, 12478478, 408732085, 868890307, 786632736, 807464695, 701144907, 15708220, 899995964, 939467424, 957891216, 652506402, 128877951, 94396328, 536492875, 421402041, 364123702, 386328155, 228870912, 97714268, 928545780, 70008020, 345776683, 33518224, 848114039, 59286364, 986234890, 907591046, 855838019, 382639614, 651081016, 408420644, 92499576, 70894411, 471565502, 897370284, 197400362, 954215996, 173598503, 864880562, 775009316, 883380830, 578988667, 141946125, 756649081, 498853835, 648534976, 697002149, 904462075, 495401209, 535499994, 735941700, 284846108, 467098054, 107694059, 648272723, 797157084, 933874573, 646155997, 926593191, 404450418, 774556059, 897948136, 86903153, 551348362, 480684288, 694707582, 798153663, 358290031, 89172323, 764025398, 740264018, 6408188, 992737429, 395113978, 485483788, 37058931, 772157698, 171173557, 999105701, 121868710, 782590616, 789471608, 317782229, 396986118, 573181806, 536235576, 531071488, 576610399, 439684215, 242435148, 930796770, 389645649, 43948779, 977344310, 547485982, 290909430, 686579818, 958740580, 942831665, 941860707, 374665366, 362456519, 512554070, 549972846, 282208096, 394372681, 699636098, 616338499, 823106335, 361340108, 821758220, 178402613, 21852866, 917558108, 795550340, 972679897, 869692750, 817201345, 629552288, 185699181, 92310154, 657699252, 961583000, 971789018, 871424123, 654175527, 692012949, 709736811, 171445252, 791856671, 430215659, 299818895, 623649442, 609686991, 562676269, 934320097, 528738825, 821083605, 306270973, 494355044, 231348207, 283766548, 506208291, 688227363, 269438963, 9886128, 423287510, 88121902, 677607369, 942864165, 978746020, 944880264, 777847542, 4768981, 397102179, 164757062, 160637335, 190713351, 41959824, 191048113, 982386164, 582845136, 960862299, 370552746, 995450909, 762222154, 704316957, 827145437, 397301435, 67269951, 614457808, 111135356, 369908377, 219546381, 253500929, 95311180, 729889931, 700966368, 19923978, 540498230, 498799204, 604489627, 221561581, 380853188, 38910287, 484205773, 100152811, 665871064, 394041871, 25346846, 965561889, 466114096, 466947576, 17349756, 276488318, 64339221, 478166723, 10427294, 124628551, 948861611, 742772159, 377927830, 311964629, 691941719, 614126998, 972958183, 349832606, 491223897, 650697539, 744574992, 898666189, 262289823, 744441454, 878539602, 813534089, 547924462, 736290525, 72024943, 944771132, 578348806, 371140579, 758116426, 395795801, 872822334, 402418286, 649241307, 324285984, 4421931, 530719914, 311398800, 680751796, 47830140, 930970033, 659933339, 547575851, 421699724, 689295460, 671996694, 680891104, 641269550, 619411931, 491302251, 4283285, 230111439, 138918340, 606371728, 319130527, 380196816, 743212332, 997041162, 298541189, 543842755, 625680895, 67554342, 943117971, 338829951, 703051121, 306734455, 556928531, 324274527, 810791320, 379216282, 729110120, 732656173, 358604926, 366206596, 78295467, 77906926, 501559394, 20372295, 658738967, 987413011, 74166874, 642993830, 250016634, 170404385, 79609893, 986873419, 387971745, 427256678, 775535160, 214164624, 903473175, 830193809, 737287600, 891567744, 851213744, 260108995, 901062755, 838223895, 707105428, 771147848, 298887613, 806333276, 628677927, 918706454, 700566947, 682475513, 193219074, 597275152, 628067, 953293774, 406772896, 125285310, 546389949, 646841077, 959164453, 778230962, 95217089, 770249612, 408336640, 553095363, 990174238, 94966822, 857331095, 940108169, 318668499, 334846953, 947216732, 83307408, 472791974, 338170269, 114145939, 57555996, 505087893, 394712334, 537316539, 356726594, 311883118, 727983324, 853601132, 77768451, 474682531, 425358781, 805627867, 892728965, 198778027, 951560161, 614789588, 600367099, 612562552, 481970733, 990147693, 788453889, 780859372, 556403359, 276237395, 492569291, 735604625, 570051467, 801670372, 218245573, 314632531, 165440430, 678925809, 835576647, 554095076, 5228175, 562415125, 351455052, 780559183, 59999752, 247957401, 559668518, 640049767, 513349348, 253692155, 514407670, 17889718, 361286578, 636577642, 988956379, 242591373, 566609526, 29336835, 762998632, 294142996, 226609955, 258240360, 889009129, 344291468, 11542828, 207448229, 381177407, 43264168, 245106584, 787375713, 109711109, 995237283, 923169314, 571144061, 585340748, 574540742, 326305087, 758620702, 955093869, 344297447, 366565195, 665085903, 433933072, 305555240, 216305751, 325391461, 791836859, 610438967, 705426049, 544723532, 483321007, 464772502, 479483913, 631579508, 372308323, 633023282, 481664919, 718886043, 225286300, 75339906, 755324677, 595117238, 415171305, 313378586, 221257708, 529854448, 758736871, 989579326, 906535851, 687765188, 556119719, 550410236, 31474405, 90828324, 497243877, 365437223, 341533901, 908274867, 410324696, 497949245, 383525489, 549800179, 548560466, 242885175, 988026055, 160954791, 647855408, 816905405, 612740732, 954003230, 413152703, 824371005, 765898550, 444535311, 757233527, 101353223, 462775855, 247049090, 979606648, 344710868, 401589672, 480115293, 644887985, 170989057, 968048461, 634644014, 409875826, 326151569, 985890649, 8398442, 349884935, 959978244, 16160085, 422156938, 362903092, 495357505, 143772526, 182390239, 418017739, 802908903, 246918214, 337982332, 827082148, 503529918, 615756041, 698336730, 913600314, 130322851, 633791479, 255209606, 85029487, 162313906, 212067064, 460570820, 507041744, 740551638, 228167135, 442865684, 869805094, 54111662, 574781950, 577310516, 240410086, 9925416, 771401779, 947012690, 691071989, 135273632, 570105188, 541286328, 472135885, 86878962, 61648456, 38210042, 851109469, 282596725, 180753683, 243000570, 397589982, 274215292, 659363962, 186557104, 277672510, 625418751, 164615236, 775358597, 772796905, 288986548, 89592973, 802152044, 228728125, 903510492, 390264163, 897811603, 79492676, 704915780, 407065073, 420897487, 48410985, 957395205, 943150280, 102167024, 69264641, 81921848, 454078134, 476145439, 528110996, 340878473, 937103319, 628282111, 401005487, 344398, 622341507, 439124035, 436144320, 511381181, 365655913, 149478763, 583590820, 794604483, 430804729, 415138716, 234143299, 53993786, 511492093, 81801607, 785587076, 815602052, 931403885, 174692945, 703296352, 29795115, 17550374, 182894425, 437530798, 989599539, 774250425, 605633104, 855682562, 923926279, 224221809, 953620625, 910178746, 994998567, 153859099, 187771514, 68262262, 654590665, 539663991, 125256511, 491306967, 526769303, 545658560, 184139066, 122275785, 843000659, 803273136, 760429002, 342012208, 502465249, 298368531, 429801585, 212537479, 45732167, 405693650, 395019760, 297086984, 174814819, 748028164, 787020740, 501074801, 871649572, 343068670, 322628133, 546544871, 334916539, 886465200, 248799529, 492372675, 355998104, 775630910, 833036333, 282857524, 45584683, 526488592, 160040927, 546917955, 260853322, 977837791, 501293068, 95212192, 157080579, 338567051, 264194684, 952222751, 557255046, 353988285, 591695221, 714087456, 126196733, 392097696, 360438779, 893519957, 26782096, 909970783, 970154801, 710775265, 164223713, 115908276, 730357222, 451280542, 328710246, 629241757, 937749908, 684460230, 202761343, 666471149, 990803568, 51965580, 200265140, 238100123, 129323989, 275688168, 845239364, 14016850, 595887367, 462119116, 606316638, 614050427, 479231570, 546885182, 263307823, 852647085, 387586824, 556153454, 862540787, 980364024, 347567270, 533632219, 773458900, 655452474, 896494207, 675866310, 470392254, 607926645, 310215110, 423913903, 693653093, 591166474, 957461843, 220183442, 877491804, 867836752, 502036325, 251164172, 680241771, 853540493, 171941921, 562350029, 300096083, 920718663, 155053778, 674742507, 336325473, 52047659, 823325285, 218587566, 389597705, 57435853, 292710630, 662119206, 724760625, 670610908, 599141136, 844553521, 724478421, 149561892, 568298525, 403768153, 58434004, 306685810, 475905974, 258961878, 930300260, 115241288, 774011598, 830252410, 672710907, 581722387, 25096165, 175194438, 319217459, 508690811, 31328406, 319787823, 486694029, 291009699, 506312443, 515179854, 388051824, 536710308, 728857889, 979255960, 399789698, 529162583, 964698101, 376289407, 367376555, 904429982, 738302580, 535894169, 962176159, 113416984, 237837750, 200598800, 831389255, 582812077, 270119747, 603609991, 935661723, 888645902, 52657655, 765910292, 335802955, 664887317, 247441007, 739095158, 44176552, 19915634, 647202932, 85178623, 338407453, 636420997, 893974538, 935292246, 497913894, 204432496, 618217719, 777047430, 500699136, 384275836, 468370979, 523123146, 67598775, 910091218, 259167988, 271022101, 740299684, 658172072, 669538921, 422733674, 164720814, 872344934, 950417040, 135213186, 490769509, 443140073, 126564170, 34667009, 119158421, 754560455, 614809849, 804431532, 813789965, 953073167, 50896307, 911133527, 967740309, 671336871, 771559007, 92215511, 777325091, 917858419, 550286841, 445483507, 836412261, 699168835, 511256133, 947200614, 424268538, 325281821, 93249575, 769167015, 503057449, 216996554, 834447925, 101923121, 895756834, 788364643, 729896690, 761070606, 566729693, 342313583, 428775364, 295840610, 292554052, 33014899, 216208234, 223446139, 12944325, 755618859, 407115718, 482723856, 952965736, 151337789, 648227645, 592203035, 401302389, 393054332, 639392176, 380620107, 846799696, 495154325, 38219396, 705503770, 178327364, 433054335, 635600066, 581001147, 332110554, 573775786, 527990154, 558904025, 915338965, 465220688, 178252987, 634170347, 653751852, 201627498, 632772949, 176211807, 477437984, 455960839, 669863231, 905012306, 308838958, 701169905, 517630698, 513116351, 860106174, 429035144, 257795140, 385717840, 366832219, 192152540, 15228897, 48276407, 233567602, 155368267, 187721780, 322055068, 798135789, 874795103, 348483086, 378565260, 557816171, 451105732, 215905031, 401888890, 739590354, 40176267, 527937113, 632725534, 868428862, 643511881, 457217721, 642972129, 415428075, 743182562, 972773384, 679562532, 916592042, 375102094, 779304031, 599030108, 688062372, 599533246, 495371150, 936030873, 276294589, 937492640, 745023713, 882364507, 554332832, 121090417, 859016679, 331830860, 479164066, 929883519, 719642564, 428941973, 657667557, 611704500, 197824825, 67340808, 95493470, 58958074, 479433849, 407402630, 977010738, 701363914, 954912136, 35819713, 332721293, 417342027, 985278192, 789385937, 744423808, 938967094, 553976822, 294317221, 681972712, 871680300, 492621086, 360053136, 720579176, 988742680, 856748209, 802038694, 728754722, 570180581, 587242624, 831681272, 832956831, 115574660, 22959523, 339218865, 505244294, 340965560, 997314432, 921126238, 113018767, 988913504, 472679713, 790147637, 376827842, 858994088, 220084510, 292913928, 224503085, 722114375, 28808769, 448849054, 943847791, 286655707, 894429501, 888768226, 54032548, 366178790, 653548845, 213384971, 961885161, 994317403, 770233959, 289807569, 927681159, 140042357, 36677123, 523484190, 594967370, 184440777, 163242859, 886529301, 668722894, 168584910, 1056594, 833379189, 363910302, 997119242, 297142121, 358389882, 248071407, 543243168, 492307324, 843321293, 725539112, 862900077, 95540456, 337588695, 867421729, 205575864, 849085755, 78689294, 53623149, 94474446, 238570509, 212394601, 609451729, 81082394, 96875910, 100534388, 610326895, 304099275, 26850340, 679904302, 108003269, 247309873, 557892787, 834285371, 976647683, 651115707, 306696821, 659404055, 26253215, 759622632, 435993121, 627102449, 49852351, 590516791, 804960339, 932541795, 619287337, 472889498, 484879390, 795994627, 574000536, 587964653, 372467582, 119297428, 980270948, 146378950, 330058456, 941167994, 644084199, 152287265, 874326643, 234457545, 160184665, 168983934, 554300038, 598412049, 504666636, 494849088, 842278638, 283120204, 615778353, 416292595, 969250811, 817968650, 284140604, 871452020, 192269698, 505546853, 813676757, 874805145, 538091988, 539375898, 699499928, 725780527, 29245371, 774272657, 305810075, 127335418, 291669461, 966635942, 138076040, 578694806, 890485002, 474529824, 130820396, 183849704, 130549610, 494369611, 73503943, 751671279, 75360425, 152707285, 71448238, 448602424, 835603793, 145236620, 961142830, 817739431, 613275012, 243777816, 826025395, 52787471, 895669864, 340031272, 212725265, 849200535, 259750014, 728726602, 73878309, 433793317, 925030792, 206972795, 411477690, 263240974, 871048307, 837240883, 317024549, 339199044, 530362833, 116810433, 762060156, 892965109, 623615109, 365445896, 432050201, 446289460, 271237917, 446075167, 193293260, 97769503, 512107627, 209134726, 583706721, 496825404, 480348462, 158698466, 601123680, 463107996, 915238504, 530932193, 613243861, 537564778, 651190704, 954290063, 984399402, 274794031, 156860569, 380693407, 453470796, 764382049, 791413357, 27032555, 436840341, 236789031, 831426949, 944591711, 272507530, 178728923, 416013531, 218331227, 225715723, 925481527, 859269328, 479964949, 236738672, 43323872, 678741033, 822012839, 322567404, 523966009, 620349838, 742306332, 2078795, 298476384, 586319064, 523757784, 718675933, 906325049, 993617253, 401334224, 574213824, 404340131, 350931013, 130744094, 607481074, 990604517, 41835965, 712982737, 988717966, 666504787, 766815341, 140734557, 973555130, 916434279, 47100361, 742662739, 439780218, 828475709, 68895768, 244531328, 45918917, 64813974, 240818792, 147143763, 234614728, 919142637, 15156526, 953354635, 517948804, 279203853, 622513446, 505674128, 810465808, 187275435, 660691035, 151021429, 547345398, 573663112, 333251941, 974246872, 443061774, 575883919, 977885327, 426483146, 524519374, 664062537, 759067513, 471091001, 453748733, 418591031, 259938642, 690610455, 867799184, 797385938, 722008279, 742477091, 345401751, 971112819, 494685141, 18884132, 939262008, 414349315, 48994092, 955072961, 834208963, 691057847, 50146395, 726415097, 470115581, 285270971, 745320903, 876657108, 741509321, 792743973, 965528827, 220889314, 402224141, 352203586, 731771027, 56942414, 454993427, 725559988, 3274959, 22459577, 848149473, 913908451, 584005138, 625159240, 944526258, 579876927, 369654115, 154435735, 163069968, 79536110, 369500849, 950129179, 998221183, 307482136, 824098736, 792196946, 750604747, 168608824, 432534381, 863573972, 439643543, 125573102, 928531793, 604484748, 231282203, 582872727, 822858512, 308950084, 626260868, 572913425, 204246716, 535480974, 840389, 498744277, 720565574, 885395973, 868002016, 319076538, 1823710, 922140497, 106846347, 111276725, 334590074, 794418375, 278907559, 249866642, 482672206, 857790411, 897240925, 802642778, 978946573, 260962286, 723427097, 886755456, 711258684, 239612596, 635355210, 187328849, 671455908, 568079417, 270604552, 684238891, 300250332, 401809703, 316062279, 316682005, 22917624, 457466215, 696338514, 991019318, 515084375, 822813784, 699304522, 984146735, 398339749, 459262102, 480874613, 155318747, 196105017, 726089011, 403730557, 800554180, 283152618, 783652019, 936674791, 307308886, 874398203, 247990783, 563128555, 652272189, 945205155, 80764294, 882719466, 620134969, 94879343, 571818773, 551258390, 131202960, 958397028, 687084294, 195826081, 87648785, 597582109, 6145182, 438003325, 822910869, 488131267, 799574949, 493574287, 932156713, 810755576, 166921180, 644795180, 605877607, 22927034, 629937796, 231497356, 505721413, 253095831, 455360519, 464049242, 608142512, 284287209, 242891176, 331481955, 481209793, 421484460, 296035833, 127073726, 785290920, 324329803, 605154286, 308587123, 447774888, 813941666, 191473691, 198461382, 209940153, 249188934, 382420079, 688328896, 35107694, 876958811, 680969241, 397765300, 556910733, 165591443, 140356903, 572072195, 8937008, 712000774, 312072094, 485493005, 550707358, 473504151, 340360704, 618809140, 538846696, 148953254, 215596001, 536229200, 72836325, 634657067, 728892792, 552956109, 735377840, 592021632, 905640109, 584525308, 344386787, 672285818, 867586566, 402308304, 677338569, 186351686, 389178659, 463194438, 922993540, 86923480, 420683167, 926742037, 799738847, 812642504, 166440663, 84718459, 52743638, 986013192, 453652936, 706453739, 445316438, 584618925, 887384882, 233326900, 325848614, 670901406, 218272890, 665041578, 664744301, 43734569, 31503030, 813605926, 154859270, 697741922, 182447307, 779628171, 950677499, 715942296, 685479061, 571195556, 502917873, 347697678, 543508201, 710146673, 114473881, 470847368, 826688881, 269963660, 24285428, 102844472, 681224922, 439047166, 204299412, 976037929, 415570296, 386528853, 410546925, 343380073, 836636187, 11239136, 260937905, 359904294, 182048135, 783779483, 367363227, 82198202, 701921486, 156694756, 956813326, 852335553, 518193730, 783453187, 381931491, 271207037, 145268677, 649570494, 330805846, 617263078, 417551715, 632494090, 459924871, 875435047, 81017985, 727696358, 499843688, 924110313, 374504802, 928814795, 489653691, 668837649, 539127241, 72308355, 420611836, 410612941, 656812805, 660304762, 760369808, 579653634, 489334843, 506418744, 891840115, 495261891, 614842325, 837962409, 933666737, 734665418, 584475499, 727980802, 300609157, 740652929, 589442451, 158377629, 207129459, 45963102, 7294928, 196116212, 898418201, 508489367, 881837377, 712615754, 11632717, 16706668, 806891397, 158314937, 866801884, 381817351, 123544709, 508476574, 10526269, 751035925, 166333833, 258059208, 429202301, 237585344, 984940889, 541714848, 50812515, 868662336, 358344937, 460533406, 892092723, 333696346, 365918129, 433956439, 803980236, 28592695, 972936785, 306992825, 642836962, 565146628, 31432219, 265914031, 632968511, 104400167, 811893279, 162726468, 644128934, 439765414, 127688121, 489185948, 263465951, 26730047, 361205106, 512467137, 728466683, 146786879, 397938155, 180365331, 594006550, 834330353, 377612328, 645867740, 278854127, 46099988, 696490794, 800123745, 743402121, 953743966, 242553298, 985256198, 23116118, 846756753, 944670817, 997102667, 632042546, 619164321, 860951687, 870945055, 1068715, 950411543, 505671921, 459168660, 125253287, 409140303, 96342064, 475955959, 88677510, 199486128, 862679344, 868857320, 785356882, 257819103, 822306667, 267753772, 903130806, 294195908, 466386176, 690839524, 430914096, 453080788, 121473752, 251832695, 280346114, 74201351, 561091193, 836768122, 362444525, 364161706, 536337903, 994381989, 112582999, 191938822, 459653410, 582176185, 94571296, 676737374, 547210293, 59082108, 181228562, 851378195, 179666227, 476607257, 532521456, 996798723, 821491079, 472001072, 178738431, 601403877, 506106444, 687708624, 986015499, 547813148, 157456582, 41472188, 268947245, 28631713, 749519525, 893208340, 639889378, 102443164, 619139513, 560316655, 363454302, 823892398, 952819172, 524864715, 861976921, 834087897, 498526067, 258192323, 766886607, 371002271, 752494780, 651899638, 352926667, 869320681, 171198138, 760327912, 701507758, 924375798, 483495357, 242459884, 632972355, 73930693, 388170261, 654977128, 435831037, 199715765, 818580122, 477469452, 622984621, 41019469, 866461792, 319724423, 326167520, 560920226, 837635921, 799779126, 194369991, 816649947, 463464511, 93738732, 967217433, 303801558, 450013017, 418658381, 188998412, 760824164, 893178562, 973240050, 91878755, 100245013, 616759800, 352622620, 969352299, 91755058, 361218000, 394309388, 249863825, 697951861, 940701110, 738813453, 56040184, 800837546, 459457795, 488643918, 974573352, 185886827, 274663514, 950473852, 42287502, 472521593, 32875164, 853402475, 471695104, 542988890, 934804384, 164806990, 594989302, 474177974, 690824736, 491345027, 673700323, 786013775, 858307721, 5608389, 196574561, 828478431, 888947164, 595144522, 979876968, 864038355, 171590762, 547250836, 902285826, 74441584, 450688931, 840359990, 980351788, 958369557, 913342262, 57030507, 863124689, 101362186, 25348868, 890961703, 654149846, 112397726, 307494606, 212533499, 135530405, 378531340, 260224836, 233310938, 655335626, 51782901, 522301262, 685063954, 982387993, 597774246, 178326365, 932405556, 123662561, 747715515, 603778542, 192340, 360650436, 699258068, 596376888, 68572353, 928354438, 540457023, 62507313, 704021848, 972548426, 204717567, 695146997, 802540434, 720185992, 870871671, 7853967, 903649157, 480443912, 766680061, 178129381, 225555475, 5248614, 979179939, 846025450, 167321615, 826166964, 979814843, 769621463, 608528942, 165518982, 643885116, 75557558, 426018080, 7649703, 228725695, 513426982, 538950673, 686113479, 707102962, 605058507, 703298677, 562365065, 367716071, 676228460, 942706869, 554595966, 294123417, 109275867, 377526754, 408053383, 522720737, 738157385, 851960106, 42299220, 950541763, 534387948, 45752413, 426689539, 542243561, 941060441, 172206882, 926588903, 650305721, 504415665, 369281549, 912615911, 411030225, 148087923, 796052413, 713993473, 36018369, 100597581, 907179642, 338741350, 510860907, 946406528, 98404572, 282291644, 392215126, 778758072, 19938742, 452699328, 982491503, 153879812, 595394364, 131594755, 191694386, 946065515, 541357352, 396763023, 129846261, 452138655, 44518564, 378315556, 925430091, 701568614, 939485958, 961345752, 703976183, 878625850, 633873490, 267949851, 407216220, 96449453, 304799794, 316092083, 395472302, 239920358, 627371766, 505293823, 888044999, 381644982, 605275410, 722447127, 832225311, 420230979, 614858706, 195810290, 305229555, 707122777, 483187247, 96404870, 401212009, 288547440, 33561025, 477072379, 968141895, 35645047, 697450887, 783470341, 469594941, 507066288, 463594896, 452721600, 328799755, 265478880, 169615042, 853191213, 857933098, 22807999, 199049888, 419591031, 576928855, 871014433, 209659583, 499782044, 564609816, 403089621, 976816347, 835275565, 369407486, 649369388, 279079923, 16798806, 32845030, 455996900, 597586286, 110730465, 64949081, 529582054, 115426333, 485092810, 403177078, 270718054, 953934496, 830173278, 125350259, 597686281, 969873087, 457193464, 613500968, 875380727, 923122912, 483788384, 38354059, 225340993, 429677445, 956312, 539970924, 363777970, 493166053, 696324165, 803572525, 220825562, 541135659, 813690333, 568827559, 302961309, 950544010, 740221715, 991098313, 110915564, 687150652, 944437916, 257299518, 18968342, 381927755, 786595194, 401432545, 906643767, 449432245, 93631766, 334705187, 451816761, 937534312, 442070521, 283953523, 541082226, 750043070, 685536793, 932543808, 38653039, 548587114, 537148818, 76033520, 515764954, 122089450, 689009562, 717537551, 297415032, 653338925, 980440273, 313114265, 376929862, 208530881, 511720352, 243983642, 357655407, 423568667, 505341660, 519185532, 294650432, 998078777, 65438988, 398051903, 831186594, 356071725, 325546733, 466705361, 2795039, 53452246, 201771118, 897692125, 122814446, 898187428, 822769295, 769061171, 805351126, 339036504, 410535721, 557202170, 720028704, 238902278, 522616981, 286234409, 752896372, 756969257, 277382232, 154631899, 488777744, 301123926, 990935381, 714007433, 577094057, 547097353, 475055497, 905117175, 572394167, 77619596, 516666795, 825997455, 136879382, 59708717, 971774087, 940022017, 734096013, 858596453, 135849061, 226475530, 296676642, 887435045, 147520155, 54343716, 542714526, 946677931, 780738399, 727201551, 351051816, 123209416, 811270432, 151109112, 981608099, 919562329, 539528338, 161840996, 904260042, 939306860, 758287314, 391708049, 227622416, 123239081, 853988415, 860733187, 179531536, 361836464, 630603060, 101600444, 780774824, 352314331, 587759274, 576958495, 593891399, 966533358, 272096087, 209470522, 88548471, 403566019, 837750266, 29871799, 648940831, 534909517, 354962380, 700325384, 712879591, 431186294, 408759296, 928773251, 852448954, 240011951, 737278997, 10405624, 912981387, 645433639, 92900174, 508999371, 427508000, 642563529, 914098362, 511418408, 376461398, 49217961, 311323339, 184958882, 500603718, 751651409, 105311931, 935129409, 462285912, 930142222, 614774831, 856806871, 211889025, 902922353, 151120028, 556362646, 85014828, 978495399, 834014325, 726225985, 90688059, 243873856, 965695701, 612393088, 425883642, 259406547, 386352284, 90270799, 520645727, 522407166, 211527886, 975417019, 930446364, 144170723, 107813407, 76532442, 343854344, 307435447, 99478892, 84911909, 29286998, 879211765, 289449778, 981999556, 968205890, 686191444, 815257949, 908400786, 251051368, 994372505, 973454753, 328183639, 85686892, 196883235, 231881309, 342920405, 65011243, 656108289, 689124858, 900411211, 942422102, 916562710, 452860506, 648952955, 316741112, 376617979, 728531660, 402328389, 965672667, 332648887, 939101366, 562557347, 433517667, 208517591, 925477148, 425158065, 921669762, 458130640, 951427679, 914401807, 147502162, 392622977, 507274826, 217649065, 293346949, 544181349, 179925379, 223608162, 943073174, 351562243, 365888182, 355734694, 399422317, 734241295, 822368932, 212582589, 4008481, 974420443, 935866812, 566911120, 11279644, 769217462, 929100507, 732722715, 95465053, 566135310, 197530180, 825515250, 39477125, 246705720, 87943959, 15905410, 284274712, 931849787, 210889211, 933363010, 459609682, 690632884, 260104261, 304196626, 102703728, 248490479, 710467424, 341008460, 546622028, 168649209, 882307131, 442476646, 511920767, 398345006, 353138293, 602661479, 254491392, 891994199, 799776165, 446138299, 157278702, 645391231, 638611838, 31941090, 116905052, 379030946, 485406976, 795638636, 847054377, 698942078, 662486358, 618856336, 765475602, 751869827, 722305288, 134743456, 775217177, 344162119, 957479385, 454164236, 992392533, 414151381, 985169252, 300548572, 956393021, 892534325, 753435407, 63029268, 117997887, 367002068, 204514325, 567892774, 390351598, 749044178, 847523392, 616726060, 295641346, 334897976, 811433553, 278640356, 126285866, 385277977, 244519954, 138654507, 740856123, 432660529, 688371127, 712987236, 65729469, 603682138, 733252271, 15223317, 512641967, 954176740, 80889988, 727813480, 87933112, 366420617, 326858588, 234016383, 313517329, 823107244, 700999532, 280539714, 686464556, 673018380, 33291306, 459071159, 118017117, 658953233, 140583194, 844897395, 330433466, 763746422, 56557105, 812530551, 890591333, 454741332, 623457745, 846339767, 695707299, 647338536, 242461059, 77677861, 295117628, 348056518, 416280954, 326921383, 97595671, 775819090, 34679656, 426621011, 538234713, 493189248, 320716256, 708289758, 531940717, 974812302, 893778676, 17425630, 100784634, 382372475, 507486067, 791413966, 686062235, 90456396, 681354993, 625729843, 411683370, 3189507, 209092399, 591882518, 787570310, 393075996, 748313296, 291595461, 415353921, 80212226, 19526025, 974721958, 961743644, 982519489, 60586560, 530431767, 742987205, 338817480, 964608592, 130557853, 46362860, 9773780, 45571651, 743321226, 7971023, 518240545, 216850178, 496940068, 83485884, 766228309, 848225828, 957894337, 391991908, 717361234, 750964619, 836673375, 97012468, 516036217, 379544347, 599416444, 834336820, 694784622, 614071629, 2894999, 798295165, 149514367, 731309381, 572930365, 15261235, 653140758, 359368655, 340234057, 423243446, 488248562, 409683733, 54395632, 839759704, 638377965, 105509390, 254710946, 754418332, 57446429, 341395435, 57371980, 763057563, 208410830, 387973016, 469158315, 89055923, 201010799, 781946891, 677257236, 550018714, 301053894, 755572924, 696869245, 85085694, 179839859, 856457496, 488554082, 582059539, 226691465, 974219114, 935930639, 31478616, 772009064, 900876692, 669550200, 630051670, 143489930, 388682309, 232573952, 422762591, 616831555, 26761058, 506116946, 167706413, 585134288, 127183936, 635031704, 559290448, 817684581, 792156499, 998882942, 52191426, 822255585, 183648351, 897264266, 715677837, 138777485, 39614568, 554674256, 581569739, 22504192, 793418956, 552840275, 853649464, 923063118, 283241735, 349588151, 858596954, 216210085, 22107145, 871607682, 513927143, 513764224, 886650416, 34158454, 904787286, 871344853, 573631032, 513162576, 452985824, 991311569, 650224412, 535748110, 925886575, 893524457, 910029474, 2611205, 891404556, 105485018, 87349467, 779013594, 4761634, 945822359, 570983967, 735937861, 99105490, 98686790, 582130211, 102266895, 21605586, 826178197, 84793843, 832229259, 252853713, 129732695, 450162996, 286581972, 851233906, 12562311, 340971417, 320340941, 51345957, 313927069, 974870067, 215197119, 949563035, 114276840, 252386894, 405277375, 139110645, 216920143, 364925878, 268539289, 744572831, 665091910, 813221952, 844917625, 737787571, 206632813, 915182504, 515950542, 929388650, 348652406, 8377601, 820305699, 787802585, 413317140, 635738237, 544997134, 503113049, 652875493, 263031371, 589664617, 187160918, 999023514, 911085585, 180369784, 959895161, 198783926, 437818841, 968468747, 835857871, 658596367, 827958811, 163187381, 78140504, 24246651, 61140750, 232132857, 550889555, 881834379, 989251422, 690439497, 319882213, 906960600, 85695334, 299594360, 78150609, 816363196, 447340032, 293679306, 494150943, 108087260, 432880810, 738999271, 920242757, 293897338, 772265914, 325757495, 392037191, 318081708, 714126197, 871563807, 518087685, 456473519, 672811715, 563917739, 975274587, 440709062, 483076039, 202027168, 730844077, 488143879, 723866275, 18282703, 411591281, 203907559, 143095655, 552258701, 738713474, 27072252, 989138741, 274543131, 644738066, 140193756, 78033996, 380426149, 981818229, 165495415, 103288107, 740489511, 861254777, 287477211, 747309745, 100628121, 692344991, 704400078, 853086881, 307608365, 260449628, 195613818, 19225403, 172118579, 498057084, 933203868, 343125668, 629965912, 494910337, 97601410, 724020574, 400833767, 668256688, 676269964, 799514460, 666549148, 420631611, 33154091, 766308596, 816095182, 575519420, 554275802, 438078537, 654181836, 365321064, 325275598, 320161311, 321552858, 68486620, 695515176, 403651720, 905186414, 239684834, 947015260, 264145825, 201202101, 789248065, 302017105, 339579258, 877988743, 707855736, 605119266, 23216373, 449174205, 437740404, 398746991, 990864396, 46028566, 197135251, 644429681, 710581888, 252929942, 763731204, 48303017, 165219718, 768244821, 903057062, 756858158, 750833427, 40132944, 129537674, 243126871, 931257477, 742941078, 420282351, 389384589, 89893932, 965860696, 395784248, 247015011, 55140994, 97339921, 316703503, 954922653, 326257647, 690063863, 257651874, 990546285, 72847056, 78674915, 956729171, 138319218, 789875260, 466011705, 201125047, 104837267, 780851632, 615042053, 989889113, 21402335, 227273266, 688986609, 51206276, 857901084, 635184856, 499437267, 852301179, 914297762, 296847193, 625914118, 556364805, 316898025, 578504279, 157086427, 808618271, 240142733, 628699513, 938160290, 109809997, 476947521, 661712543, 499446596, 608031349, 631603854, 763470741, 792693615, 722274350, 809250131, 776570445, 127990541, 110547801, 555544473, 994967726, 927256448, 558648893, 112375050, 780982092, 968783584, 947708392, 169881543, 695663449, 590451106, 843084653, 466074304, 600089101, 784947832, 92157140, 901410559, 809005048, 893649366, 699576405, 975324924, 404015469, 523821457, 468494894, 670909454, 216008304, 397464262, 306308966, 436537076, 805997489, 388422564, 438762516, 517382831, 443162621, 362213035, 586504110, 142474003, 652573233, 51490951, 132755624, 851045264, 68284999, 519024856, 122428536, 864316112, 618526265, 262316221, 411649077, 8504316, 888660049, 930421991, 355892362, 260528644, 940624822, 821092053, 969887813, 551896297, 681462564, 242370328, 706291000, 946548537, 253627958, 962016893, 332664852, 158905559, 10457231, 493821899, 525708121, 726446028, 934381916, 885156114, 311136133, 160698730, 417825168, 626224952, 365411971, 122201680, 152725476, 960596132, 980828667, 144934541, 871683387, 602554898, 145439650, 385150284, 409921338, 464201985, 521663893, 271973351, 772059361, 817092340, 55577252, 174511478, 567240481, 248627152, 140758413, 159404308, 387842585, 962520193, 801105482, 443257231, 652561413, 23510022, 867253811, 662696768, 884363112, 384917596, 90007375, 497468337, 449569199, 358488762, 127665586, 960183965, 655131687, 599983234, 730770496, 743360646, 253390981, 219501265, 144048527, 459829543, 220615148, 520925208, 906010047, 763870782, 217016510, 374878989, 638317648, 682360165, 44890373, 255457967, 769020601, 832860196, 643368857, 148667433, 198910962, 173787194, 98477572, 611377275, 136026248, 670509049, 712164040, 12208387, 447506616, 21842390, 994882735, 275044059, 431967650, 9080866, 855789883, 853360161, 782655504, 240755559, 455969860, 136482346, 807093552, 534518584, 360871379, 464141833, 154796127, 783783820, 883130976, 17248541, 568800659, 583404376, 441768649, 738724998, 503521084, 406326430, 925864920, 130561699, 202096549, 847010190, 63254850, 12265091, 968263002, 396970011, 876936991, 434729917, 269504546, 152933357, 288968692, 723751650, 734207261, 208391777, 153814071, 94351231, 258302763, 604602246, 183967130, 279211930, 401267279, 718252892, 930091831, 444336198, 933837207, 491604210, 978709404, 716589423, 251564113, 279717152, 519672234, 462744402, 968573485, 625102376, 452748760, 189682112, 343514614, 77934871, 286223139, 261620227, 558097202, 835525653, 187900685, 413040017, 27179704, 397290167, 222682642, 542601514, 135094274, 487280280, 410269984, 242756299, 984524212, 651506558, 990266444, 686792532, 404802914, 784465801, 729111332, 503335644, 136632961, 953493714, 972010968, 193074449, 345707766, 686425168, 606006585, 259011795, 222763016, 887823683, 877072433, 591413679, 717333824, 916581349, 997342738, 537388963, 662851806, 539021650, 517299722, 562736825, 671850224, 703848359, 182865538, 336040650, 321290950, 118768145, 781439688, 783575093, 769578260, 645437476, 870242355, 462180477, 963183243, 742826379, 723033085, 690685182, 889567340, 772715963, 36949009, 575783676, 518290394, 290340026, 941168485, 126680555, 934106677, 318061049, 581556405, 290854419, 313726519, 753115044, 935905967, 604787222, 14896227, 722911658, 186543450, 571163673, 217161660, 902621969, 717312670, 997457395, 612362065, 893424523, 834689941, 157786621, 277861484, 911435964, 151396344, 70416214, 452686615, 58896062, 336373073, 122510582, 54121192, 542713084, 826861033, 839353099, 419887158, 56268323, 879410205, 755952561, 175136547, 97786986, 815202188, 739863887, 16917099, 458764760, 682534963, 19962607, 842944738, 289471940, 813788035, 376342168, 236744788, 354914419, 883862121, 188934401, 722114089, 43553399, 88700137, 710664843, 181547021, 66260762, 894439142, 906446090, 884893959, 300714529, 531543661, 217415209, 879931656, 28466241, 134742437, 212729902, 644666403, 492185575, 37659476, 784188444, 801686559, 883010319, 971539108, 859589249, 291501383, 120103200, 614752375, 79284477, 894795571, 882784295, 962575052, 980165541, 984561409, 334154685, 763227903, 89597015, 527178803, 8465674, 783002477, 95331002, 148896980, 483570987, 418927869, 729330681, 597745385, 496651041, 751675302, 582201101, 454418081, 355452526, 128973266, 388346351, 828246597, 658007984, 547869117, 832918356, 934520638, 198053267, 27213558, 15302200, 579866776, 839012590, 190317891, 110833289, 177253669, 344473190, 988388877, 12562687, 774600491, 699621949, 517791037, 561774927, 664202817, 269465884, 665720023, 855674869, 626194595, 664447217, 677851126, 759909603, 470342203, 838172008, 577635810, 740087460, 348260238, 79574510, 790671610, 109630330, 504079512, 138083103, 442393635, 159731071, 181603522, 996678268, 272372048, 848591939, 845672689, 753967990, 328419116, 220440786, 40765374, 54927312, 193380264, 160858568, 878136067, 675783862, 83339849, 478553226, 43921787, 121328913, 818935754, 147441312, 106201193, 526496922, 206004014, 118300185, 47471309, 366750931, 24767503, 804066644, 412016951, 268033948, 762098414, 903394941, 433813306, 517527785, 662235531, 324789946, 715030705, 975243040, 773071076, 926579812, 128434740, 245977245, 204260319, 2177420, 65798425, 818145541, 282038308, 985805333, 122513459, 508099248, 512991716, 378608225, 892314918, 541378423, 207719443, 941874153, 435600318, 747030937, 778031141, 397268893, 404429514, 681226643, 806789005, 219439504, 372624512, 500952338, 337501078, 970475598, 545874324, 777443846, 672281001, 775177933, 367600979, 146736360, 824153157, 740933077, 408587614, 985911736, 393915314, 978249561, 406034500, 868608788, 700727758, 137667400, 404812523, 601788128, 33172853, 811184734, 383440960, 62829465, 118816474, 238237197, 49864372, 42823807, 453490857, 57324468, 920059585, 823045887, 796913976, 143500361, 578404546, 124979888, 633155722, 390178660, 653449884, 676737616, 972462716, 893247443, 13014079, 331730958, 573559556, 4339297, 967601847, 72091074, 418829230, 177414952, 708133063, 689894097, 345898790, 403102900, 874457101, 622389488, 708393976, 607333139, 682929359, 62545086, 620376911, 356035153, 508748156, 644648986, 896508622, 56225423, 395818903, 536092323, 519385390, 85810646, 94412428, 628058605, 921129600, 491979874, 572208827, 247172353, 272925536, 898579590, 248600207, 994012007, 546180224, 335158756, 634246214, 193471399, 369043294, 192647108, 459465698, 294384542, 210076383, 23638091, 129249196, 461107377, 174304644, 195838649, 366708124, 227637238, 898040658, 987936949, 965941551, 201049737, 605470661, 632348947, 360844491, 850384542, 363511357, 379709539, 551851574, 654602390, 210641602, 623571876, 82254489, 588920455, 250386739, 825433988, 181973036, 476285150, 333707372, 651134010, 757784039, 942977148, 160402637, 127306686, 917325659, 427433544, 967598373, 6024457, 587836429, 635237333, 270919591, 129583190, 724850722, 149658248, 386963018, 921509889, 735134556, 77578467, 959356849, 430788853, 54725567, 221530981, 43658994, 661208094, 9039755, 42085500, 13945542, 428787191, 62513040, 396212313, 914668516, 737878713, 763417243, 597993848, 123748175, 806384757, 668784646, 854470224, 565860084, 874553047, 867404105, 964241939, 239379072, 975073571, 778780680, 967020896, 768576282, 881319374, 63515247, 580276285, 368560459, 908499358, 570128338, 996633825, 93464933, 196958475, 283138458, 997235411, 856859915, 605206017, 796767217, 361833201, 213977550, 859124201, 342488282, 83563923, 707150813, 378127589, 837670953, 91467349, 804216121, 566445642, 480926154, 918166898, 642719126, 271547739, 292412257, 86846620, 211118020, 738583198, 467439889, 875789227, 675930128, 833712270, 259101171, 111709202, 867671960, 743396190, 799636768, 863708257, 336021365, 608609365, 77785038, 694508736, 696237876, 695827679, 965136361, 847613937, 492763630, 917043801, 707177268, 88700314, 861213382, 89021174, 458101972, 551739233, 76408221, 10886188, 742511160, 850940753, 719810583, 723325376, 554224064, 614612784, 596120295, 151440380, 864172160, 468838075, 763637646, 391991024, 139975065, 643229521, 983744790, 629557150, 745009154, 589252301, 700125704, 19411969, 185215032, 317998700, 354024333, 135247169, 768756821, 666044110, 206656645, 672013484, 222730851, 370266164, 141892857, 300865256, 131058158, 876358960, 28925147, 576520229, 195646067, 191095881, 765025271, 165791844, 291229588, 218275508, 496888972, 213717494, 437595426, 892768816, 456907480, 163281981, 564652483, 943571100, 29166501, 467558400, 499181421, 490756992, 685764294, 855078577, 23087424, 149697137, 579078319, 865133080, 705643956, 382531116, 120643245, 377448256, 704014619, 64111394, 865512000, 909758944, 809758707, 686092799, 232397957, 237813643, 79803008, 553030443, 652049126, 498675941, 665844418, 184520612, 183772118, 264218230, 732900071, 154628796, 699013985, 394312521, 240007383, 805409830, 85366085, 27362737, 96001259, 899705660, 174771942, 751274572, 452404257, 858293175, 177920721, 682650273, 929425513, 603718557, 99776543, 414790133, 209108811, 415570619, 818124881, 927164394, 693434281, 946525903, 255591371, 20907430, 492682052, 142092070, 917302634, 124952501, 925790238, 420619011, 537855037, 914257959, 643317890, 368533971, 654039476, 351502955, 34255772, 169275919, 496183998, 25825865, 161423367, 675016968, 497862669, 47487864, 523867559, 214844070, 483456014, 527146668, 696069602, 264887172, 136674345, 688668283, 604558628, 220939306, 694776425, 817807479, 778547368, 935476775, 275620241, 272218703, 787072148, 47838340, 179850341, 979715097, 687103196, 87676454, 760233516, 559396599, 911067604, 445800034, 704586032, 599961020, 539568842, 839690803, 60138691, 857758248, 11744388, 404277669, 605396411, 604279279, 438893827, 632935389, 865193690, 193902858, 378782279, 926011205, 913765133, 99624863, 472741311, 189667041, 299428607, 262884907, 209073395, 423247730, 595454562, 703736228, 566051360, 755235361, 597177182, 588721304, 244715702, 221884057, 23846238, 726836477, 655998082, 975519152, 923482979, 584611274, 472683137, 498904017, 160692042, 557812706, 159443946, 81781993, 60725157, 683842725, 527575984, 347537154, 705755094, 902505732, 280271403, 387884701, 771508489, 684325789, 136002769, 278453006, 352723900, 470678242, 791977180, 287459918, 523762418, 422974680, 915457247, 443479272, 65826387, 318827922, 913218248, 64823648, 30561863, 891959394, 139223142, 850621012, 203990365, 334090835, 850570228, 848152085, 826203167, 34407235, 74590069, 787409584, 919164185, 183110569, 834056233, 233880133, 823762103, 683448988, 279044078, 321753657, 784739715, 396292759, 466947406, 319453001, 349058208, 409209975, 482478394, 509867439, 556578219, 72431904, 429005562, 641647229, 642516162, 940909185, 914867387, 637218495, 355808811, 83067563, 199691972, 557757856, 984140251, 838204188, 901229760, 881869717, 994528496, 941871595, 578748775, 21198590, 219292486, 742177898, 359937345, 839811051, 193047288, 838578379, 709342922, 449380735, 559555029, 882891501, 212831301, 300759609, 43745645, 662869639, 157275753, 759267661, 738065698, 960409006, 818147542, 711178229, 403689147, 805082192, 654914500, 410896112, 616112463, 569699258, 659262735, 589204593, 443738751, 335319285, 291623120, 630911057, 381763030, 114587484, 252924326, 34569581, 6405015, 410453977, 511350755, 105467696, 163660080, 899010298, 162973774, 744650110, 663337054, 585054665, 331786690, 63971869, 115949942, 912751366, 366571200, 105014734, 405886735, 881495005, 311099372, 116892808, 247376098, 129475224, 273076298, 248437453, 826472116, 92008119, 280332604, 173745820, 95111043, 959750986, 918664752, 85492348, 930003407, 691890073, 866383697, 630114113, 605284257, 298398292, 253401959, 227118892, 831490641, 629918301, 250289992, 730166948, 692134028, 272506634, 226822068, 42780775, 459459876, 162856868, 693922816, 220164648, 530935953, 658828942, 603005956, 851823072, 516297496, 333751516, 225997276, 24265021, 598137084, 356600668, 493181572, 401555099, 829512157, 592954073, 642238293, 395369063, 979955395, 187764913, 143018469, 56275661, 594185331, 775723991, 448236420, 81032416, 282798336, 110364484, 538105402, 607582970, 343905725, 350376730, 364289462, 704173423, 227185624, 335572284, 63303684, 936065333, 671963018, 232587912, 745910610, 924676500, 889825730, 476209473, 244449544, 350603472, 807590822, 332554836, 529967638, 973306644, 727931306, 378233901, 554738904, 531010833, 710675970, 257789297, 865600019, 62516247, 502969839, 749279162, 462822286, 572879559, 775431021, 672852813, 726334071, 489643707, 214984372, 378514586, 355563460, 293882063, 612500024, 631548399, 81209217, 459936293, 487745047, 755700882, 798518274, 697200612, 936616116, 177535934, 134734650, 852274493, 258827930, 81415947, 538868076, 912935450, 265292203, 603584344, 262286837, 660031207, 199330738, 821162814, 793722043, 517804962, 563453422, 499804981, 653252949, 107927316, 35707287, 395430205, 986506599, 516573491, 669157111, 535013569, 187667439, 828771484, 63089773, 185770329, 30615646, 679805464, 129467621, 997157553, 225270604, 282928500, 105131656, 836617524, 699134504, 739019768, 443387183, 522193759, 96499517, 560000816, 444458056, 962042496, 780159363, 139327147, 689036047, 659025845, 706879078, 517949044, 800598009, 848652528, 321801711, 489860308, 144512303, 940679974, 68420145, 308967846, 473764923, 946785808, 627424309, 695468306, 658881369, 17548937, 577321781, 201779827, 479870394, 823923576, 835985936, 729480559, 251046605, 293159852, 959165783, 858513020, 130016694, 301881192, 104050518, 805187759, 615024146, 927152645, 660479359, 442056758, 14448667, 431148038, 58471550, 953155410, 648711166, 637686546, 428863394, 272382464, 341168897, 288937130, 546180324, 919464683, 452148753, 299853072, 778050168, 837992215, 504672852, 836742098, 865979226, 445064974, 731364796, 929200490, 782770258, 769379411, 317848950, 654181687, 178480855, 849570096, 983641348, 158811715, 426177947, 748461414, 517018601, 222547683, 814315327, 877349684, 744102836, 389478620, 792741158, 973159339, 326528458, 782742563, 440073343, 70773523, 84473604, 667099994, 191441384, 869310187, 612996565, 938195326, 496198785, 624336975, 679781521, 931047785, 430581649, 229768516, 844944382, 795594264, 429883509, 481205026, 784088858, 24599149, 288537803, 920064621, 403228456, 681372746, 581410316, 348699157, 951061973, 545360629, 569095339, 984260722, 356154623, 782458096, 797094037, 176342851, 623538265, 346438947, 999087783, 31359770, 160317870, 760146370, 633691391, 939041935, 94860096, 32819299, 352046329, 621767915, 646993350, 462778770, 94173475, 119531061, 124279170, 697378063, 796273917, 789856553, 217084651, 266854974, 359257574, 756625642, 236502097, 365311484, 646335529, 705214766, 281491035, 843478624, 381741658, 581322139, 374956697, 54031958, 938287723, 74520793, 229468695, 179893645, 438961804, 940609687, 265089669, 485559285, 611193019, 921116155, 795602169, 176666847, 130989729, 762739753, 871603779, 430749688, 85113867, 606294795, 264831077, 455721325, 223256344, 220322025, 2764241, 917852381, 827977016, 558120400, 260284222, 968209997, 72917613, 930353868, 813507320, 424799028, 23315882, 660704372, 971147607, 232573542, 381238525, 137307094, 654988653, 711194206, 426273183, 944412961, 842226057, 726637081, 674167160, 974457374, 550742908, 766779287, 787712397, 116020368, 391424722, 646182330, 453014488, 94754650, 901892331, 693311585, 656318366, 826595671, 664820875, 340568581, 320964849, 515467315, 392267858, 564857922, 728271535, 107667523, 488467242, 638092138, 723706735, 620579558, 268585250, 234132931, 570796661, 823560990, 901919715, 109588543, 205948092, 71830873, 503140608, 409410566, 905053902, 602161318, 387893565, 431466550, 281919973, 171551991, 660989866, 697409305, 404460990, 647717663, 484779614, 698218115, 332082929, 131450413, 207517511, 619883476, 656755400, 220037623, 651791726, 579394190, 698992677, 417401079, 666750060, 704699458, 648483345, 306855847, 564721793, 286423957, 673618615, 955435926, 945847434, 540394987, 286065474, 244069542, 876580081, 66877, 419026225, 585278496, 346013524, 8771132, 203458418, 516478877, 667180785, 198035719, 872096289, 874066562, 739981821, 117479085, 565934008, 294510192, 209149610, 672724720, 362033383, 104339686, 310710878, 294475523, 796153822, 880063258, 449145981, 132064288, 855349876, 616912982, 158137549, 730437164, 981579187, 982114294, 763309792, 7340051, 475188065, 409420186, 487797766, 10177549, 911744404, 730738631, 528604980, 678484362, 905471588, 622286732, 509157623, 203631189, 723081787, 307766218, 784466583, 42962799, 981222928, 490696638, 933405196, 351985659, 463449449, 532623365, 734040823, 563513510, 525862823, 621109976, 465659005, 753327232, 834212943, 683664533, 837548613, 808985800, 985477576, 502859714, 112127226, 950135350, 930949700, 470083647, 25763912, 817100380, 17986204, 865387433, 648254195, 198633133, 477381884, 133230241, 376978741, 47445800, 887300543, 819572454, 457681561, 276584157, 37760001, 691777259, 698008076, 799695434, 665683262, 471986953, 987092812, 604333286, 34637033, 9414410, 381553752, 428940294, 607961103, 737421207, 658241930, 555015513, 657441791, 490958977, 265337529, 31292533, 552972899, 23057922, 878812276, 732261497, 440163358, 871258324, 499276686, 663251526, 400759482, 486901687, 557272797, 469431952, 331123787, 271586148, 553351379, 897317154, 738670847, 921794588, 171300099, 660103493, 759938167, 104846144, 811167074, 314694850, 36160383, 604210097, 246278869, 467743486, 406622327, 781278146, 135163534, 362697190, 214886614, 592999012, 627575434, 992036754, 430481929, 856661288, 510974510, 761503621, 998637339, 302080195, 101436217, 951609046, 635525804, 211355704, 532685512, 704379835, 595886100, 505738398, 491549414, 853050764, 767753938, 492677809, 927966441, 986002702, 933475085, 418311735, 457392138, 735622014, 192365486, 440415841, 604344046, 447157307, 49120444, 11747959, 793966337, 952643531, 565718796, 884341084, 815902516, 759638708, 268651853, 571148487, 669346639, 151487255, 698730988, 54410571, 826731979, 544671813, 900355430, 894109857, 870166064, 316236590, 113023134, 138604421, 372238693, 283865962, 969309512, 157781474, 790268393, 543805237, 527813858, 237590342, 65452910, 85172753, 573404784, 433083471, 101210165, 521229356, 10365520, 536744771, 892070149, 831178711, 129785630, 604785756, 357941256, 590845120, 464886893, 388374504, 930290663, 447512268, 68896688, 988526653, 392246549, 424908494, 39660430, 570979399, 15488313, 396473366, 640722017, 207569078, 623426757, 486070616, 753600036, 167255996, 983171003, 201621863, 747409958, 86022373, 52960087, 309396643, 884007966, 541917383, 22951548, 929514024, 750451002, 925121245, 105982237, 990521534, 478844481, 613077807, 125619501, 527123485, 193536069, 764087019, 664873827, 789862699, 965563196, 566977620, 376378470, 914976908, 911930464, 717786533, 91776269, 84900839, 199904665, 883785675, 776269786, 145921549, 636210620, 539250635, 606649054, 869540896, 363477873, 5680467, 90261908, 634533373, 834245211, 162429438, 293209392, 586381025, 561733723, 807660794, 707668670, 88289098, 224726767, 356863229, 820821435, 541451400, 925249027, 758999642, 657029020, 171164458, 538180506, 775599351, 660178602, 833085314, 718033814, 648917033, 979330843, 48970868, 497942350, 790390141, 501097276, 97796077, 938349299, 732814286, 940876214, 667876867, 136004884, 464216337, 936491666, 815513911, 56261851, 830437959, 844094074, 771009470, 209526296, 209013951, 437484980, 14164682, 733962741, 873829016, 892272563, 80174633, 770692453, 584209051, 340989220, 925758981, 616278075, 418509424, 896475183, 485680218, 92016078, 536149800, 169497220, 336254481, 21346343, 968492967, 659545303, 119839970, 787270166, 641327092, 576090645, 812477654, 436967372, 818410344, 344115560, 691089207, 60242225, 512863120, 936028289, 716150722, 464807127, 803337108, 866515175, 610061909, 628158415, 969368742, 417563786, 21634715, 798346985, 669486018, 868905419, 227790029, 26179447, 112212194, 511972005, 683244903, 681060891, 915977314, 446668283, 53159382, 935314165, 501561653, 382692850, 107944379, 65539350, 24202766, 594090826, 213779436, 505603244, 747009847, 49821044, 128303354, 706855076, 539997748, 842567040, 520045248, 876803655, 93180707, 965024921, 27651411, 133087966, 694070596, 202266048, 738842632, 570400309, 675278449, 417950847, 806817456, 264845712, 30319409, 102075651, 950733559, 80324951, 670219010, 385477050, 274213276, 839496124, 951835760, 896619546, 522279878, 414182870, 352301156, 844115001, 854216120, 235505386, 955211847, 17474642, 567667229, 361813256, 686600130, 247605355, 1871106, 903573204, 625020463, 498295767, 656134642, 839701409, 585122955, 279349708, 52803564, 120959942, 552650633, 82085704, 770918724, 407022418, 96970217, 988854196, 140390050, 546137155, 79948618, 115819041, 277049268, 303593544, 141829212, 33758709, 769526512, 796197545, 283266775, 398501373, 310134777, 844821584, 422730502, 933680861, 747490058, 360026651, 800035794, 395998186, 445257589, 210007365, 703090097, 175640616, 82783529, 179987294, 993241364, 361992029, 139296814, 65472026, 623553259, 798396394, 218930597, 827159362, 450739999, 1044900, 650748752, 608629048, 94779245, 220173381, 914228464, 970777837, 322360229, 294777003, 264499146, 992240565, 801828252, 986075728, 496641407, 594646581, 604107493, 265323982, 922418712, 584205691, 361522897, 612107640, 893027502, 438416063, 591791749, 291462536, 820705676, 853076681, 815199823, 790451660, 726687288, 95491973, 410470178, 245331958, 289499918, 305453491, 972000772, 190865702, 835119875, 208604626, 851192731, 960530281, 489526902, 74367918, 475426194, 495886337, 905203412, 618098696, 784382288, 745000614, 878768281, 815964899, 478952284, 348150132, 857451615, 132124882, 962513167, 815255810, 153286520, 614973967, 525253794, 261139324, 27278938, 513058058, 652096762, 904496880, 376074875, 347952452, 539743384, 446085290, 924453936, 384024800, 110292316, 229298759, 850296184, 740834825, 554504971, 288258476, 611215598, 510147640, 566951655, 824854718, 621085913, 159121463, 999467549, 690656398, 436947675, 990944827, 109640369, 534583946, 545139909, 367265113, 268266478, 982685427, 108159068, 818120690, 793272978, 430484371, 500990407, 555804585, 48601500, 969968429, 616883627, 442440649, 43829373, 299380700, 175559820, 77396136, 619882894, 196388690, 711402488, 920285530, 546827871, 443094504, 647725584, 679404706, 727493075, 107605461, 407656433, 715740876, 670127001, 645045552, 722571497, 153669899, 748348850, 601157659, 150419809, 670603158, 551755811, 332718532, 287014257, 191969911, 893233078, 223594616, 350345140, 682777705, 486018109, 423449981, 596210231, 573518137, 752447941, 562858696, 392133410, 837285701, 177979383, 341087369, 39710285, 887921202, 62715137, 546744039, 6412162, 591642125, 210280481, 691928093, 431900620, 969237904, 175684124, 704626799, 314233768, 560538241, 188389712, 113388465, 659833737, 219822604, 273802189, 235763176, 996569513, 318818961, 489257230, 711373107, 577028340, 969008754, 907246517, 576800392, 545598573, 331510597, 503279843, 759361559, 373983450, 169786430, 398420548, 256872788, 328316784, 757046661, 69215266, 658764798, 970149591, 260069075, 300853090, 889298841, 277324068, 417326330, 343391282, 878535506, 60293500, 895791956, 105624970, 338468159, 107193527, 33996140, 77208867, 274808725, 654036912, 59178537, 540072866, 793291824, 764725552, 314988350, 742998312, 798755125, 589059160, 621101727, 726681084, 979669225, 40848336, 901730788, 154131986, 626568113, 465266401, 867701462, 968660564, 887324677, 210329254, 917162424, 411769049, 523570372, 480489532, 82376923, 391961164, 632521320, 484364572, 836575150, 16959149, 101692983, 440630497, 8217069, 185977260, 703134811, 357145996, 247657816, 996697770, 144708957, 513019340, 487508714, 614737980, 732787370, 682536308, 386533327, 12084924, 398836314, 423623274, 489266973, 387688575, 673055908, 303818269, 881013868, 470155844, 328150065, 543103801, 752038193, 563638641, 862084050, 220482642, 597187966, 828075592, 554758098, 797701660, 336484277, 666332736, 376774919, 832375846, 520054021, 137673827, 96408551, 538884030, 639137043, 959031775, 241224688, 795395447, 402436128, 352821059, 814239368, 919816215, 825504293, 59384479, 580847336, 298426299, 340465839, 688866171, 554466212, 820101341, 764140659, 530927763, 806742485, 752390886, 121275750, 296263451, 563720226, 95866905, 816656152, 540199677, 218790505, 867604362, 972206141, 614940882, 519054931, 229923133, 329977275, 792781504, 97095991, 740324875, 23904865, 707117884, 295615544, 244272649, 363202549, 516647950, 329997484, 514529602, 482816250, 667825952, 501519173, 515398828, 382009031, 301519957, 652480497, 84839908, 382062571, 971799555, 781413981, 613755965, 596637473, 390560593, 201466252, 157737991, 867097394, 276696061, 4979777, 274684561, 566069894, 38858623, 179758057, 734035962, 357724722, 861762897, 243642007, 847762939, 673563794, 242842822, 661777199, 97583161, 655897118, 742874960, 739776231, 752271638, 758181566, 776175994, 918299696, 320645951, 218895262, 162583338, 878259449, 908022915, 790721313, 138345224, 796038723, 717368795, 285160171, 85662149, 487328669, 437034528, 195036914, 382876668, 881095449, 553495841, 776703055, 259930028, 793787336, 875021707, 238355508, 155760525, 597208276, 275596404, 701062753, 431028762, 736245443, 850260560, 581201981, 834855115, 170434684, 732974265, 789241796, 652828490, 138734116, 47396363, 797673121, 569669945, 920243550, 123340945, 351105903, 781312782, 803392443, 293027608, 496001419, 974646870, 355674451, 555625165, 498683076, 176641681, 184572622, 882524642, 645536941, 63300210, 449709431, 653074130, 57277918, 409795357, 14122565, 339065017, 756293197, 521769731, 506867999, 446511358, 565239406, 429929675, 828503488, 577654307, 299147861, 747412376, 484518320, 178640332, 473445314, 789411388, 804101284, 315998651, 364261020, 366143837, 60701422, 804751842, 601590149, 897533037, 80835517, 570873527, 253246777, 144336547, 910018495, 464093441, 878077361, 660295716, 60094049, 454685810, 60393548, 278250603, 489929498, 472311714, 945952590, 864555090, 391128640, 541355702, 436638372, 998467342, 200522496, 487903633, 212509850, 232793479, 125244222, 72699977, 832069009, 702779606, 395170595, 906080035, 113512030, 629335294, 913508711, 225855209, 96685014, 569274362, 440993420, 739582772, 612403001, 427808922, 663259513, 276088896, 47584816, 14815900, 713182607, 204787712, 257935289, 309443195, 443845242, 771014331, 279448895, 900166595, 499619812, 684188622, 765842683, 655391851, 186913105, 27773502, 110349681, 772430738, 829706422, 216750867, 883778962, 423280188, 61049348, 421460692, 871512177, 834774250, 419143212, 796848615, 218061756, 438392806, 372527668, 26066028, 783342488, 535241679, 150084777, 482727430, 990582349, 500148433, 340597864, 534938697, 903698574, 621768472, 389765490, 207771899, 770583171, 947607025, 700389060, 282366212, 465338005, 221400323, 129195931, 521720549, 153024538, 762861529, 626064216, 299848928, 92200559, 458386122, 642671683, 584584564, 67305462, 327577391, 424963844, 927713601, 594813819, 224248486, 502004701, 532191988, 99139627, 477913120, 141352640, 426843933, 366165484, 865024768, 244918214, 474575669, 889731488, 864221064, 9389870, 366074582, 171769659, 145745095, 221119148, 69034519, 919136310, 784653403, 573640464, 867385329, 357491680, 7568781, 865562755, 977460091, 17407939, 42518170, 772577076, 583648008, 443554183, 672222827, 959340600, 490776471, 694624611, 958622018, 878481450, 720794504, 299558988, 57505060, 694474096, 411663418, 630488561, 894837890, 758430912, 408670759, 161025832, 894661748, 144137815, 216049331, 681479406, 767543423, 273491997, 937972371, 865228453, 819476933, 147753964, 825245221, 581865166, 460933207, 210266923, 749327530, 777497765, 693267855, 797388710, 2255263, 509884973, 34161439, 762347043, 697842875, 516211986, 920355013, 21649035, 562596538, 690063617, 56818098, 622240486, 915306710, 46090305, 345131163, 608006680, 32750673, 206111652, 947618749, 620226907, 180217867, 549970143, 373460045, 334325559, 145828479, 377864618, 659579839, 77785055, 230703917, 54509154, 462636029, 362545252, 337392768, 742276138, 714210142, 622341527, 236034074, 218130115, 278937871, 498786659, 46605692, 447793504, 255943677, 676493984, 75281583, 661775791, 978481330, 395994466, 900204186, 963032415, 457014002, 827380006, 128521941, 66484228, 752949268, 442300095, 950240722, 302403771, 244133044, 478285178, 457581485, 181982810, 128122033, 664761164, 333368056, 238368996, 193688772, 436398708, 496947610, 931494045, 251919518, 464234745, 942223065, 845142419, 242188658, 283075959, 106989618, 976058947, 594133431, 334354206, 869225875, 89266234, 8295203, 116945428, 368758739, 749673180, 206817379, 995179221, 572794510, 474518420, 680314726, 830539383, 660715060, 143037579, 617829293, 182505978, 350536381, 615464326, 334657797, 367045004, 258064871, 878236456, 543547819, 405013893, 995423726, 424891421, 406660333, 567114656, 118280634, 322695475, 321117868, 584021501, 245925613, 749496742, 960783729, 407968148, 492903574, 820712721, 26472542, 283281933, 93151861, 373382879, 905372092, 407598533, 483096472, 290193028, 199576618, 481363870, 335345376, 806664526, 163486725, 325454945, 402216101, 79967960, 337164463, 348897595, 82062443, 355251740, 196729766, 339538436, 21887544, 218263713, 974492158, 793653155, 739169421, 720019847, 129805603, 358486741, 685670494, 247103173, 949193417, 498970160, 200468356, 77615855, 712611659, 22348433, 490798440, 331443372, 865930382, 603882702, 937863701, 811604539, 671177562, 954506167, 719604254, 133442559, 500746137, 89436746, 388386448, 574714203, 182329685, 606199565, 116884231, 169942613, 793272469, 130570974, 359232901, 181390040, 91797178, 627467981, 779838174, 970553655, 551393649, 127119523, 673590579, 15020680, 226273020, 985068800, 47546755, 93205231, 513569614, 523265703, 154158236, 201234596, 71472045, 426607667, 858361385, 140891903, 258264585, 689486433, 327579821, 648880797, 57094972, 632640274, 36981848, 197716827, 318005725, 801197856, 151751255, 597303553, 843761322, 873885004, 206421210, 543046077, 218362526, 139050962, 271087926, 884907196, 765625705, 656471681, 195767987, 163788539, 419947208, 80174489, 44653435, 666908400, 272956506, 61109136, 788173754, 795644239, 275907430, 788042215, 776305477, 271115600, 247277490, 170951489, 691242101, 519215676, 565262107, 500091923, 549438567, 454485285, 617038341, 264863864, 143798478, 669645477, 287824033, 387647461, 221681620, 541640833, 339856791, 117319089, 801281634, 864574613, 964607937, 622584297, 184663664, 554598224, 468975528, 496572514, 581472373, 714970703, 15547439, 201458420, 640821362, 17102017, 112489061, 639038305, 774276641, 837129697, 690446676, 381599837, 669031616, 972402479, 901281800, 88530937, 707058771, 483650922, 96561012, 792461347, 956534149, 761833649, 138798075, 724129932, 360524400, 176454403, 648911936, 836062835, 456356137, 452842169, 894511050, 321152093, 276296865, 973310318, 563556614, 537850266, 652578692, 441994496, 861354297, 416221825, 999946347, 626707872, 651071856, 696321531, 48739210, 70761340, 690824715, 939230647, 387464979, 756373827, 912716828, 657031624, 180503897, 5794438, 29048829, 123048079, 15845035, 127941836, 970618144, 327936091, 768037321, 904872242, 168376002, 228148995, 206282500, 88752955, 46340876, 347753446, 629855940, 215022004, 543112547, 391511722, 576723252, 632508892, 154243896, 911581747, 628677064, 868848130, 882420308, 732703292, 452722831, 673205349, 525420912, 66287246, 106161652, 507391977, 802793427, 709729666, 959213077, 516342028, 47784162, 662334539, 862575570, 551350047, 51936685, 552598521, 437563695, 22597737, 472681844, 861146467, 544097865, 348770190, 9662094, 192808379, 365622561, 302528069, 236748936, 754803740, 618670840, 492275407, 318975431, 623088302, 554818059, 526719521, 663872397, 323493164, 30579510, 182869094, 555663566, 171496521, 136436217, 294573464, 896784958, 867406992, 260447374, 214159036, 380026092, 309197108, 794038673, 475625962, 240476927, 256917026, 570821259, 129033495, 911596551, 544107024, 86112603, 619000491, 214391809, 522178129, 638755608, 892100961, 210007116, 321345863, 175586110, 17775411, 630733857, 328868592, 870711272, 550092282, 821235254, 400625299, 684174022, 305084936, 831587555, 621801797, 153994975, 706402397, 913421528, 818474059, 808843564, 745329512, 318731431, 945381724, 965177571, 66043495, 399356444, 523843960, 364443480, 456733651, 186203054, 179946274, 829384468, 633239493, 973540770, 580304990, 121955372, 419584933, 395480210, 209938695, 915628638, 383276987, 883459067, 907426253, 206246516, 503889890, 251981208, 235480533, 257293040, 636528229, 220920702, 761173750, 440465067, 447485534, 855684861, 920126253, 420913391, 785493285, 657084414, 349840042, 390961684, 180537766, 522920528, 158472091, 92037123, 794797285, 412758132, 760776207, 234835630, 51872133, 52814997, 57275470, 741319575, 174550507, 224742790, 933113153, 782884927, 354547898, 518450187, 680388805, 844818712, 340731944, 220438188, 582968847, 985923183, 856860074, 457507656, 592841030, 131898499, 945587647, 193821484, 831688722, 244529605, 250204908, 275521510, 225903192, 178349943, 620068530, 3393454, 422263070, 995764311, 828991697, 114863494, 458386387, 52953603, 149898914, 716458538, 340829096, 38065595, 887215058, 895693348, 139335501, 344234757, 561741204, 817141770, 422680888, 59623240, 870525520, 549148042, 626039450, 772488393, 443655990, 876295778, 249975744, 129500401, 831612586, 498583920, 337453431, 934436125, 548212161, 309516577, 482535693, 950377533, 206775806, 585427204, 776337336, 928538629, 573085980, 1946551, 449088034, 67162096, 523194593, 612153904, 312102805, 613777394, 850400317, 924391770, 348319584, 242840983, 220801387, 233662801, 78852771, 282390814, 140603623, 454427901, 315649008, 129758069, 302393646, 190750533, 954395152, 81222137, 300178809, 445092246, 7526746, 585207736, 719826672, 807377973, 615415196, 952185403, 810638760, 995115517, 859952224, 347343778, 969272710, 221649080, 32394011, 527575229, 73811168, 262435150, 906196252, 296237443, 235755019, 28269508, 146738798, 389711351, 532889017, 327743843, 400049281, 276554048, 336566135, 278424133, 691794519, 810218110, 272409848, 779957679, 301090471, 15968781, 151039413, 239838639, 711115644, 484005475, 707160472, 150053127, 855654923, 148564726, 58246910, 414264360, 218725283, 110188467, 988893610, 416584491, 758005485, 928599129, 59881266, 330642050, 322870347, 631333832, 977350757, 906243349, 408810000, 160276158, 290849874, 944065559, 398013735, 595623667, 907128663, 549158596, 42266271, 978553158, 277080736, 226676911, 776329836, 687065701, 968084208, 197092155, 180524722, 922570591, 692478340, 78470392, 777079483, 828897349, 689241067, 349695121, 508011427, 851454918, 147541829, 907949763, 59781844, 233546543, 839833408, 690900462, 293371632, 424025896, 408008327, 104378350, 722375872, 481039293, 791323762, 711959388, 427155599, 894416977, 651165196, 70311069, 76457184, 59012424, 566662226, 683888831, 63792042, 339428789, 802087728, 707579275, 236988626, 83437692, 377863213, 863921278, 904245712, 412997340, 235007666, 815262830, 221415220, 911026778, 1976817, 376349735, 194255316, 219636880, 585960303, 281290410, 801296636, 990174834, 249446950, 117557382, 283613428, 437648281, 679866119, 502827545, 210255393, 574209862, 123054123, 730447030, 222603574, 570746420, 251084361, 426458079, 330280903, 20560824, 982182213, 987465594, 684542743, 343307986, 715067773, 200211383, 643621680, 306209913, 693705620, 807664748, 781405025, 767832389, 735771888, 563269991, 259686914, 299354107, 249134629, 229823372, 626777285, 338392324, 872546421, 164872638, 62496455, 619156645, 27261272, 711179914, 308952775, 350164032, 969443236, 758983270, 763893214, 182228502, 89947968, 842376231, 583178294, 840695222, 927398068, 500329381, 879911953, 140410979, 764319870, 552901359, 522477113, 328315229, 30506420, 270013149, 198188834, 24998093, 971589799, 780573535, 143689580, 960523292, 76105038, 273552309, 668265807, 582134929, 47944573, 941793473, 356395561, 243582257, 98617298, 683787609, 386978003, 537317424, 37271631, 232589062, 706632320, 8278627, 313832403, 916411536, 665456381, 519745564, 535149758, 111771765, 845037011, 924533316, 609977033, 434038928, 161534396, 67273611, 333991428, 72683371, 559177550, 74753428, 894015473, 763819955, 502530530, 300855125, 674007285, 133541577, 782558546, 988898621, 846010948, 106288976, 53463682, 765595796, 757148573, 815879999, 326846470, 4998664, 341220122, 433107211, 702005838, 479236919, 877671124, 556737608, 980755252, 184579095, 556076417, 600174385, 695254377, 86254208, 598876119, 147498999, 719874125, 327447029, 148963267, 922360780, 444114283, 120688720, 452669493, 187781486, 422316668, 378370578, 49339467, 90834064, 952626007, 718130578, 408269689, 974160095, 604124189, 780152461, 45833649, 771784260, 358826135, 325837451, 830119029, 267300347, 226077244, 463158389, 890655774, 575128372, 364432111, 943178044, 619906585, 589356385, 923700252, 203979818, 49936630, 729804471, 789561288, 289305278, 649759425, 859603101, 375201985, 819094579, 577612674, 556587658, 563913876, 775193148, 562524251, 92935838, 81080355, 176798305, 625808157, 593983242, 199911541, 238094853, 875876644, 81665858, 883944391, 769596645, 623615349, 649143130, 660584113, 288954116, 898138668, 749880863, 789367740, 445379104, 409136583, 193475016, 600072436, 729671396, 870714112, 649767203, 145986096, 216772301, 169149019, 891157617, 636906724, 259097288, 489329031, 854009855, 800849530, 20512265, 938969067, 434087175, 921057533, 580262143, 449129288, 821033774, 330983761, 456687537, 520712371, 806890972, 949957624, 694331139, 87375350, 449289320, 747411891, 699445860, 610353375, 860008254, 124364021, 415141275, 856620578, 600289896, 343521295, 79258555, 28541091, 866410718, 401525959, 10177667, 620229961, 212771375, 856526979, 874774861, 431380438, 580870453, 573995818, 181339879, 387924839, 468365938, 307383293, 332589526, 50405325, 145473985, 325196899, 951103350, 771658209, 702882405, 817058330, 325192016, 638503370, 175670954, 183798186, 505141003, 364383899, 468305977, 307305218, 95298092, 586482621, 595500302, 750771813, 248133251, 659836883, 416971264, 703299196, 715531424, 145270576, 927077356, 312694076, 869140834, 389835382, 872127495, 54623456, 626434091, 382806619, 990692995, 717438404, 351005323, 220408165, 682401028, 221928286, 983863967, 343365933, 794063471, 856532167, 8875458, 480832329, 452679537, 823170878, 93510676, 849417597, 248659949, 739165601, 465617995, 568601303, 183501555, 590698718, 382795579, 156017042, 789301578, 84929681, 980221866, 329303659, 398561700, 963642367, 754596246, 850786660, 589936610, 851533567, 239577638, 111394735, 137563796, 752466779, 530188423, 189487524, 71809337, 915065993, 142932193, 802063184, 360720833, 764715877, 673753348, 453411020, 969275560, 949041319, 661138460, 803002111, 294570565, 738373750, 982108080, 975329334, 972201528, 465002295, 236111670, 658332012, 438249021, 252408425, 482025209, 468461942, 68656145, 106899790, 921321240, 802137237, 243938867, 957622231, 490349450, 288055181, 117524017, 562749093, 787188864, 759974862, 433258021, 372781573, 60675624, 884833733, 639271837, 688381115, 12516993, 22840189, 497382947, 240448136, 978211514, 77090962, 648835472, 257934451, 982613481, 221775557, 616889731, 186320920, 282802071, 630533170, 64655587, 200377232, 256744045, 300940931, 13642172, 290885179, 846960781, 504737172, 550187731, 600731919, 868905187, 671197340, 254354967, 362028164, 740148677, 805186310, 303018695, 187812158, 978591759, 801004962, 15348906, 703204613, 31864441, 976155391, 818874004, 23193028, 220589347, 432677306, 267751557, 487460971, 167204495, 638463815, 669659528, 938411587, 248002683, 799736235, 310549101, 284544505, 138617731, 686165626, 358972541, 668572513, 855612351, 635318613, 196872316, 911923498, 425078054, 795762983, 812416760, 340568162, 310020211, 529397694, 959994098, 73187202, 483492721, 906412015, 729643064, 784273244, 373377209, 352798381, 921858288, 58372163, 709443436, 347183064, 840996204, 588991526, 403698428, 850335438, 386448846, 52233417, 9087168, 151614875, 870576495, 397768489, 338854201, 611515807, 40265368, 766120819, 734447007, 601539916, 215274774, 988502187, 936779640, 433245180, 263511358, 402034260, 758704563, 48347537, 965748030, 513873572, 334586991, 344251579, 222316676, 296562185, 206003531, 188029866, 843434394, 786488353, 985824165, 467334576, 363421038, 976340181, 781736645, 110716489, 800684755, 100539409, 9582051, 126081420, 502275795, 929356669, 390219766, 383360455, 194988938, 163598107, 565369194, 343130698, 796145606, 811889718, 695630737, 238903754, 654545620, 618973315, 558778518, 641047387, 617215969, 308360447, 266497064, 513519316, 732911599, 456879677, 405640287, 517624835, 144428118, 360042869, 359872646, 124238966, 129930362, 781340292, 283033956, 890046155, 356078981, 351685686, 54524540, 14475890, 155447502, 197733636, 369004719, 66225240, 226063266, 94863530, 29727492, 758400846, 337514908, 546441504, 105584053, 538041642, 429299710, 895454852, 700926937, 168531218, 347470960, 802811532, 516302335, 426283923, 650724731, 371749595, 356066183, 813856170, 989482913, 421690287, 255920440, 15950115, 83907213, 852025396, 948451944, 32513977, 410183532, 529922200, 457434391, 950995176, 714123730, 974865520, 991149895, 525782131, 909251529, 888803108, 233634102, 631544448, 907451252, 588134256, 451321283, 665598587, 231556587, 234018286, 48422796, 135278873, 412579583, 763043122, 400519920, 520349784, 584588871, 937107514, 129743742, 269997684, 674184419, 174108567, 581257286, 992993571, 531297453, 428318087, 658491376, 270335221, 406255807, 495140834, 96472105, 519945482, 839614211, 410546596, 800028840, 304570824, 725289567, 569992148, 572324157, 337702253, 800160832, 929715119, 896433779, 529304191, 271276541, 977014807, 166698990, 808771322, 845928661, 436074274, 402201644, 351927773, 130293013, 270284033, 570890781, 956708678, 395554172, 438395214, 213388864, 417501968, 605550898, 43014552, 210622133, 15044918, 523643817, 955565123, 50650205, 470770627, 212864591, 197068699, 17480988, 935982854, 710633771, 965730594, 348055413, 998442071, 60004694, 812078956, 784286031, 274732474, 578202458, 585455392, 915583907, 928764672, 364004123, 470567318, 34675552, 536630017, 539730067, 378434806, 897024529, 879032768, 694958333, 456901865, 351571083, 134426684, 699023959, 562436443, 384860486, 704652179, 31592508, 18715383, 763444694, 115599064, 778422600, 305488304, 100034761, 140678818, 596134853, 412544208, 764254706, 312378713, 937582249, 639097641, 664350182, 941952442, 402721458, 622072844, 893000252, 940588794, 644382094, 87486092, 678520079, 140086023, 213738344, 62301809, 885605558, 941189593, 793636021, 829070592, 131345915, 64611664, 556398189, 427637644, 186135136, 367031050, 185412106, 338239233, 460576950, 447381832, 883894310, 549370272, 519595665, 870749793, 370626640, 513515674, 843271455, 303432462, 598951131, 572782319, 215367098, 616002904, 795300723, 188789574, 155611087, 842655424, 699249482, 196936638, 19107894, 89022751, 361281643, 378099817, 223832327, 149241860, 921557895, 35197006, 552087946, 796268440, 998517000, 210024200, 104290564, 167938632, 675302138, 675012075, 231484477, 374544218, 105771204, 57114529, 807309306, 47282682, 287378569, 332634663, 671802821, 252461929, 406045049, 819689492, 749736371, 686016702, 265372151, 37639813, 983352352, 621661208, 854109132, 642549003, 82979314, 297732376, 593729545, 661076396, 994031005, 570204423, 268641919, 193572798, 704057319, 510904550, 267422191, 826187136, 897812737, 517250991, 850901131, 881434139, 281712303, 526977841, 588041640, 151567267, 452551702, 894968004, 479781437, 647356192, 153168506, 680965539, 612652452, 83920134, 364866807, 473650601, 289712070, 29138024, 271499918, 367354950, 971697712, 60741678, 730147380, 473909161, 102708895, 13249878, 60253691, 785157578, 649626023, 984150679, 258134512, 527814752, 167573368, 656210080, 729858227, 130424708, 438272784, 954830723, 378500055, 123370204, 489033043, 687753305, 257416646, 358242900, 458199566, 148978325, 876520340, 779680389, 644307902, 757764267, 920077875, 880732071, 678894972, 224035473, 915836691, 521535075, 978271400, 33179018, 984296557, 718350381, 400514816, 318562541, 264418568, 987550912, 681101189, 467731650, 189861795, 876735252, 319629649, 241728383, 577118608, 579235444, 225794469, 558781501, 477900412, 872696060, 135703208, 667153910, 226404282, 35898646, 474765206, 477239657, 97933033, 987982839, 430316380, 878897195, 648968048, 565412958, 814249459, 887094615, 23722976, 179927604, 68423177, 151334477, 858093572, 678987327, 434963259, 388835251, 270666610, 57008342, 922529385, 911323514, 24271330, 946480526, 813760090, 105948919, 924702476, 148247970, 766785231, 643930713, 229930857, 255380085, 23075859, 952043623, 544404940, 708326061, 602226307, 512078430, 417576719, 837638170, 499122664, 489027091, 502499586, 476615874, 299727312, 70953343, 610043519, 885859618, 363684138, 301266930, 309231240, 868556888, 192897865, 169711204, 988921811, 636246725, 74246318, 529954686, 700755576, 271992599, 731367645, 284419400, 144240158, 572907363, 594440853, 125510822, 820184437, 865087731, 489924355, 9161738, 226040103, 694101647, 786266131, 350326474, 581231885, 911195666, 79188443, 289460716, 349608081, 476768768, 192932048, 523004150, 32501399, 104172521, 639477784, 774473007, 827021227, 373164240, 769381767, 406925000, 46301010, 697420822, 263450541, 847983769, 782018940, 241505656, 987882235, 931911537, 540493147, 483526379, 770940678, 377555029, 534258452, 150406199, 930619993, 111779522, 493152940, 766544639, 221521883, 32281559, 54024973, 805972178, 401831709, 734745472, 986898217, 379300356, 869628848, 667918937, 589796851, 29933170, 160219285, 38397351, 583419826, 991523794, 175298583, 951930463, 227908617, 513703128, 594977103, 731966840, 208473884, 201536340, 169872524, 465754475, 917300102, 424824711, 962713727, 374396026, 24261737, 702488305, 178340443, 786220598, 853866577, 461312450, 229507291, 773544122, 872750936, 653213415, 297509324, 415983609, 588226398, 182262355, 249101924, 827281516, 912238383, 762687778, 392728758, 101609038, 546779245, 278171667, 572035556, 431693882, 600636597, 594845803, 178154662, 401238829, 778801693, 515353892, 957996209, 405452381, 841573875, 892758722, 984010076, 342236717, 468865161, 314492409, 267544813, 715230585, 578754032, 936617410, 312369406, 944585270, 69607773, 28946543, 811229369, 168770759, 25940866, 517893490, 575819866, 610957789, 242278750, 828854149, 81563990, 788207955, 664537320, 198435713, 375696879, 942401884, 602618695, 291785496, 503541098, 320071991, 987951110, 418452486, 911878141, 26491251, 748675996, 123956145, 74612983, 859860841, 16049010, 185664244, 299894477, 629216196, 444777675, 126350166, 580714114, 332563282, 631362450, 320744817, 456867693, 763870766, 414345060, 717180026, 971873709, 179231022, 10234248, 776137661, 987391576, 937747073, 938048763, 124794457, 683241936, 981385249, 367806831, 843585543, 64310547, 535395814, 480757306, 926021529, 181265794, 304058606, 665274320, 36294167, 101670537, 404461717, 565133719, 578570014, 149219790, 687782221, 307384684, 468419027, 926871416, 866967975, 43058345, 609116242, 910904970, 960832113, 730296772, 333542318, 64858648, 666510162, 754945779, 154936552, 596615132, 267466370, 84249156, 159691959, 408197419, 874250241, 42851814, 280240115, 462208355, 7690355, 614719368, 220399492, 594607963, 613242847, 658481619, 180845691, 490989707, 82052689, 848404733, 475088974, 657500913, 667806124, 930646185, 320712500, 169072283, 167009665, 417680238, 240891027, 620789809, 932444285, 824618099, 579951787, 365637653, 727848866, 81104726, 762287718, 408188878, 404262153, 446876625, 532071528, 784477149, 876853560, 301112380, 550994324, 816894140, 363513554, 122892457, 266780242, 976932689, 339298015, 38335618, 363339409, 259245484, 655159689, 403360714, 898447353, 983174004, 8035366, 164120893, 730035801, 980307340, 512843750, 524093832, 663947207, 564065094, 810738094, 281460260, 729439259, 467148950, 187257591, 798269866, 673429245, 880701831, 340498738, 710311563, 40151422, 964397413, 684173256, 583333364, 157275766, 48189879, 478129678, 950451795, 966878235, 694358287, 866677255, 150135827, 292179185, 182235117, 580342760, 29958569, 369210402, 189457283, 941189030, 68537931, 864963254, 689379906, 9873489, 523671712, 811820390, 114454163, 731450610, 248750423, 692334742, 137386905, 896068311, 700021384, 214194149, 824292351, 803999438, 517856789, 53747314, 264730567, 38810940, 130882107, 833075906, 605844321, 226739569, 594527215, 118274185, 930346802, 807650882, 227848816, 824280051, 268930672, 250189028, 16365646, 264395696, 971948378, 150660014, 113419001, 394719795, 330568186, 998700446, 553083786, 676447217, 242756610, 820005739, 559664425, 147245783, 656153057, 995421316, 256295162, 597228582, 53900881, 630281322, 941735838, 207006393, 572346678, 304181488, 612616670, 437289499, 765783318, 993277980, 495519708, 420230743, 530019466, 771080481, 401094829, 760472128, 497184630, 22511355, 139832288, 184681082, 77481225, 618791420, 937658164, 455784936, 938559663, 767845900, 487421179, 177216918, 914818785, 175143143, 230655565, 800198191, 528054280, 347243316, 828179891, 933019618, 38182837, 181327328, 48297909, 485557674, 213741306, 964855406, 924328494, 442819235, 518809454, 231782536, 236943551, 564245280, 566992745, 641535502, 735280434, 544787249, 625548788, 920632407, 878430804, 596882811, 578702665, 556230072, 974035213, 273232268, 133182137, 989962612, 247837455, 941728710, 108227678, 287259368, 908426368, 485921090, 96581824, 463215160, 753676407, 503053170, 737981634, 76014948, 563661583, 410804903, 965175045, 970655620, 801584737, 199624735, 68454888, 117702576, 58108319, 553365021, 956894245, 846674457, 250254250, 309727101, 562657631, 937824959, 267190840, 5555665, 855482174, 123902044, 922233294, 318160924, 85014967, 507305435, 959488079, 135716484, 151438945, 195697319, 74180116, 731580796, 767710410, 434815429, 512017398, 439481314, 12555697, 516056519, 141910473, 60855988, 577039977, 107856515, 88853136, 994293254, 725196846, 243747523, 87770969, 818384262, 778826573, 289543335, 534023737, 661353730, 81803609, 377890063, 525798394, 234478513, 326608294, 616862817, 990692601, 695548332, 467545507, 17882125, 96162863, 169800631, 186475749, 585126552, 515690612, 650725631, 600973008, 330530821, 51121191, 230718122, 570348848, 542773045, 70385919, 274123990, 156909332, 684243074, 397800717, 14038118, 643106554, 160957234, 693957418, 369021222, 275078260, 763664323, 541813622, 719853633, 577890957, 849849624, 105117177, 973305950, 172659095, 948551324, 751980332, 203111559, 29326709, 893113036, 861849316, 762996264, 42449789, 571751021, 848171814, 770894855, 873275767, 204161156, 473499775, 622600598, 533674198, 606968106, 847831323, 347862322, 165276847, 99641882, 554927518, 862192939, 637142994, 986540768, 9511034, 129220679, 623071719, 340271190, 713528941, 280515126, 741949576, 596676868, 605936398, 531974344, 264226385, 804250444, 290373152, 796029683, 289664913, 137972033, 531015156, 123465911, 752938286, 850077426, 960151505, 153240666, 880046330, 156830179, 789745969, 53737396, 440573948, 732209356, 113128942, 683563306, 139751368, 368142859, 144930497, 246974096, 111826686, 273870215, 191120629, 531449778, 699024704, 862224586, 133992143, 517644565, 972710777, 926322785, 142021582, 63536606, 975154955, 226651085, 733720004, 660674887, 624861048, 479644145, 121054996, 808545374, 915353881, 90557438, 354059228, 481159142, 472752599, 540295107, 164806254, 609257132, 426343106, 997301232, 888001875, 497118704, 61463153, 840397745, 442539126, 793849823, 616291098, 52697596, 805437582, 727905728, 525392589, 844998533, 899285002, 92647310, 882782144, 956343761, 635932322, 126079609, 662087299, 422489954, 510372059, 780259188, 7011858, 960988834, 423480255, 266534406, 593254832, 164396107, 222459109, 742303804, 67035599, 275122119, 667462554, 116779926, 979273129, 392104781, 407594722, 997010084, 833888481, 527897232, 193527696, 827155822, 672079708, 918313992, 94196212, 867949683, 717958705, 434793010, 167843240, 855823445, 44238679, 159432468, 722580580, 174087508, 256223330, 531219045, 253049685, 449838043, 870823104, 618349095, 524211445, 560410181, 953204865, 189822575, 896457633, 37376953, 849500509, 137931616, 255152590, 534832783, 57683168, 961219285, 953322977, 589861817, 946549738, 500699518, 169667265, 228323038, 825537955, 890899980, 148086952, 433924885, 627718137, 828477512, 897529840, 382397428, 947571433, 453502249, 1020591, 806160129, 192261902, 203252282, 615889907, 950298712, 616855510, 997976953, 391312511, 779424475, 925178541, 26533589, 932113974, 538210789, 127721752, 188538742, 792728649, 927426730, 822008622, 837537214, 23963412, 224888077, 568822652, 410169309, 711739870, 810747861, 179207491, 167335540, 28128022, 128930066, 787065391, 99901944, 124800324, 2040979, 148876411, 121533988, 896087593, 435511364, 69034050, 418109507, 214696357, 753780770, 755524922, 976565645, 488133962, 13465602, 473461479, 785021232, 898792387, 489404922, 212313341, 748492649, 459056027, 156285951, 71011581, 549842590, 117794685, 831649238, 136586776, 446586926, 861262919, 675711118, 932323718, 135523642, 425660702, 701086590, 713812653, 650098219, 281933183, 856491926, 937305365, 51407660, 396675055, 229987758, 208507955, 465940427, 183253515, 966274391, 633353214, 344015468, 300683745, 876243747, 170835979, 871444652, 552847089, 472724348, 834072758, 666793863, 598586658, 584568171, 769452406, 784166201, 898222251, 327691377, 941510173, 739777307, 617078807, 174517521, 947593811, 177342777, 452410815, 797847868, 295582407, 120359996, 330019955, 906250091, 581954220, 333152439, 754483559, 422021076, 865186926, 306064769, 561307471, 537101281, 288623107, 197764603, 397936551, 873964905, 615990363, 345905422, 219440117, 477018191, 201516344, 700261886, 257341953, 265339524, 559469358, 903596270, 324831206, 438396306, 223924098, 333241046, 419567375, 215974580, 95343095, 671210804, 267175770, 161761984, 241700340, 816891106, 875253388, 688962862, 18550152, 339540144, 877929378, 361696134, 315245309, 879150811, 781171995, 459364565, 26916761, 55321723, 542575066, 372892867, 512211658, 315432597, 381140864, 678620354, 953838053, 487906973, 423170656, 739193387, 383795864, 192959998, 7685898, 790600778, 678007269, 404661928, 224482522, 19653661, 992190832, 334914727, 80754756, 163392736, 267460805, 720877384, 787103963, 198363630, 880377461, 273555908, 365081468, 89088891, 402127447, 742095972, 462302620, 926934303, 754027066, 5248557, 922166565, 416598882, 949239455, 712938786, 3859881, 616189682, 440833178, 48957880, 833898260, 893759224, 834099936, 281181806, 760907840, 59168085, 761583600, 654729543, 947962053, 442746594, 245123416, 328119578, 509680443, 726086826, 869838116, 765921968, 523597779, 518203166, 866107138, 431912527, 282342104, 418647860, 382061850, 73966273, 913870105, 275451731, 602606625, 839608960, 552024595, 206089695, 446991201, 93403772, 200194640, 866928407, 895781205, 389612660, 985790704, 119380617, 55231275, 401646460, 598532031, 343064147, 130908759, 657626473, 644587764, 72435050, 317868070, 211364178, 360633679, 451816138, 14561906, 441027151, 440467141, 966836252, 947593146, 918646226, 392590945, 833083221, 546441720, 672958244, 4098134, 744359706, 684043439, 876385807, 545294137, 752496241, 976344977, 86135499, 347690287, 256497410, 993333333, 62835486, 553677716, 194407555, 733505140, 904216687, 937465447, 178343356, 877923535, 736380294, 762341366, 949744871, 188836779, 957906382, 642133422, 567613939, 157005819, 65448218, 404757615, 319569328, 391566687, 776602093, 702765879, 856863640, 360516587, 800123326, 332877631, 472275519, 72040088, 375740959, 120179137, 620898917, 160137040, 155640161, 392156142, 598917725, 429517751, 689466599, 294192338, 435635669, 7741321, 452450878, 36843851, 976706791, 640063235, 644568129, 821338544, 746105846, 184018502, 879754498, 506584143, 806278339, 654152471, 28288356, 344236294, 928421155, 700208266, 695647296, 824168931, 296051259, 363875675, 259689713, 377309398, 99793373, 722783488, 553761913, 85153667, 326629568, 501478515, 556436802, 249610108, 652255148, 814467024, 565638521, 90259476, 594987588, 478132016, 561214535, 404789618, 867426064, 803967815, 199905379, 996668148, 272551222, 51695490, 714785861, 391530414, 831424775, 50983933, 983393716, 308588077, 527363643, 300815446, 545940050, 635156914, 52972668, 648476093, 525547034, 913954957, 373173303, 396708085, 226490049, 396270401, 606682496, 500195429, 840027660, 121955831, 686808675, 363171801, 829444213, 801418089, 919914440, 98864563, 748556311, 155679444, 16928050, 300225047, 949082609, 752926398, 657626369, 776942772, 654660736, 77898927, 455435973, 869079816, 275499826, 836656847, 504390013, 454186111, 760978552, 767014960, 721724190, 706538301, 959849764, 940872819, 231740804, 242013329, 296358905, 968941605, 98118208, 59244209, 658429386, 604679025, 788587098, 415290266, 297891195, 668192405, 697743055, 890742564, 443683652, 713920939, 975370548, 384848087, 163579303, 422359591, 930488893, 50612331, 165649324, 692289985, 828987862, 870333035, 591150570, 116333110, 152116479, 834659335, 503988566, 936200312, 67941050, 731225067, 10272992, 609464357, 866570980, 206366349, 554563428, 987366376, 906634395, 769882242, 543575183, 128411769, 500497552, 589415965, 135852902, 350563090, 723873103, 378095365, 218442927, 95949045, 978274835, 825321214, 715296715, 314661399, 776871765, 640201991, 966611189, 747372019, 855888816, 585601430, 160341237, 242948223, 531357516, 198286163, 430098976, 969762453, 609071086, 820323055, 245860116, 750810285, 768772428, 249055845, 793499638, 79684574, 847207850, 569312671, 230848970, 914318266, 518253503, 797111408, 541190036, 160616364, 367566904, 636713863, 80203384, 722389112, 15472705, 739261738, 224514016, 22588636, 662255661, 257207632, 189705460, 494163001, 298483870, 61841393, 473416245, 950748912, 804617821, 495072734, 901011542, 297953056, 770268179, 477700033, 949986170, 338556133, 623269162, 210473986, 741446358, 631594685, 292679759, 719971519, 93420519, 613273846, 645055149, 75810848, 432686568, 636636691, 23660334, 533809553, 633355834, 738866722, 572510884, 85473003, 644391688, 518988226, 853593919, 193433896, 681043594, 515806245, 521037812, 326307993, 310112998, 670997616, 898291023, 301749866, 757689356, 867793171, 424466464, 110716609, 577423974, 904586981, 511888789, 363468362, 334759655, 725238142, 95223412, 693146636, 561671470, 188664515, 182314751, 91059875, 852637828, 799761943, 749626886, 627127448, 76087334, 855514079, 243708370, 803472947, 838316804, 918920326, 19874189, 627555241, 410650463, 786447734, 978878661, 240965771, 440958551, 270864933, 291834390, 669260010, 465817881, 551398430, 821609663, 104163339, 152041438, 921156945, 223208859, 53389870, 224186705, 716312427, 76369428, 334763102, 149983374, 479810983, 610385929, 748814027, 932304495, 443195778, 118895494, 377269263, 378832105, 42502391, 173859641, 477640389, 725010982, 470136884, 220999868, 827627394, 563201840, 560780960, 968381781, 915811353, 293881025, 874164574, 921134013, 884558544, 600774009, 529635279, 821884407, 445586224, 420935804, 489098669, 197489985, 10126832, 74739121, 58086409, 206232159, 951687018, 548766539, 263184956, 315711629, 664189277, 98642244, 834352762, 473609860, 649750750, 818608086, 579392613, 334910165, 594921382, 151032172, 518251333, 678025776, 139173736, 203939984, 436002504, 7341758, 939936035, 352893742, 475801153, 21246997, 504386293, 821715737, 10659800, 491606820, 350402429, 792309680, 922478558, 806287100, 941880314, 245815841, 209465608, 779935844, 577304522, 121916718, 965880880, 93580715, 624802606, 438879343, 289572598, 793921644, 896651823, 869189992, 10605465, 801545721, 658380225, 288492941, 924093527, 471228032, 376136580, 650515285, 450938697, 714538091, 584151442, 508753253, 700540083, 611464049, 987952567, 944572866, 81535356, 182251024, 311293065, 465389989, 746401360, 243425321, 518670663, 482635362, 642685806, 327303299, 331070099, 191158377, 194454147, 620309840, 475343839, 707675696, 128065284, 874463762, 306629214, 224190800, 575117153, 589593534, 723084982, 172660981, 189525902, 351334050, 66984823, 622147409, 171776039, 373019683, 728177333, 519447586, 414053518, 142314531, 409475231, 410627821, 360105280, 9571425, 248836611, 725776576, 660931672, 315931119, 730094912, 235451595, 400873651, 739515662, 300757640, 226552823, 996880148, 91773816, 745052093, 959495327, 276439450, 937449730, 372694918, 157927150, 313351547, 432139543, 68209013, 422129443, 843865993, 262123418, 523712395, 702824909, 543038140, 59873929, 5107448, 965209065, 259900885, 8378806, 83571462, 528942734, 523916463, 638536124, 747917059, 668669529, 288758347, 556005330, 723957, 698798490, 771700564, 199646049, 564506663, 625905332, 993742615, 989353487, 991134055, 768084219, 162458989, 216503320, 763728994, 481905421, 827522817, 735520847, 857751085, 384256823, 507054965, 824224583, 115046556, 273926482, 426270728, 171604674, 334265976, 16701505, 317111222, 946997570, 955133680, 344920684, 857986351, 710901825, 934905402, 685260485, 318594860, 543375960, 356459138, 315265536, 897122757, 30487905, 610284357, 472925075, 645806434, 968701406, 498194088, 386026027, 96698807, 778874215, 557694802, 984723880, 427447241, 741935414, 70325925, 784494352, 649044495, 226461964, 683196412, 256443753, 676046427, 296050835, 767651408, 870428809, 599606839, 159140167, 269929080, 467558295, 855438896, 759718141, 122942656, 877701158, 912764830, 287522491, 532299609, 605740820, 661656653, 611331664, 616238586, 747950840, 56776471, 155772798, 171645603, 207297808, 643839081, 647731300, 271527871, 497441116, 593779099, 807076210, 872762411, 82584103, 71439008, 667709954, 366373613, 481075167, 869693557, 161071878, 769300149, 461079317, 961822073, 211028679, 557832838, 207530847, 656255766, 824933213, 801850579, 912364657, 497973063, 770699088, 522399461, 548612836, 140881518, 410835313, 437855531, 544366690, 95297790, 244093684, 739248826, 89704219, 924251769, 282904414, 957311361, 257749128, 368575887, 160293502, 863343406, 609447946, 968056601, 330992285, 298785536, 349869562, 807291819, 65157781, 387381417, 554575628, 72532043, 216965139, 209542512, 958228503, 163338117, 512824707, 563929386, 543814482, 492551348, 375525571, 666562874, 693312795, 614917187, 104069716, 611744448, 44907456, 259019801, 757081927, 755217576, 577933615, 586643742, 747965298, 394138883, 73234602, 119641954, 635100752, 13095438, 351720923, 689139312, 624619459, 820726346, 187636039, 139347866, 850816050, 463433437, 655535327, 717637578, 23209998, 769232733, 659307498, 493486312, 396477667, 826000603, 687244864, 277224157, 614136216, 467954362, 931202201, 810444072, 129575047, 713729037, 688447021, 179218873, 849409611, 825322455, 320249796, 932560971, 50599133, 61727059, 620828775, 315803315, 853453309, 231562757, 152492870, 885289487, 862036502, 236514051, 184745905, 370101536, 111232044, 731913237, 327418669, 505692479, 17738406, 169012813, 336043217, 226301791, 354991406, 554373627, 323847950, 147549234, 695687205, 261288459, 686149176, 576752320, 140888334, 430850957, 336064427, 178004583, 353089267, 672694045, 835651478, 798974659, 700782738, 604672588, 421212326, 744232637, 45872994, 417785202, 253392867, 504509543, 417233325, 49033929, 130869562, 597873758, 112597916, 476351255, 831454010, 547218802, 930147377, 581358219, 122379410, 548883216, 136673010, 642278117, 7856853, 563720654, 811167966, 894067767, 397290819, 601095052, 529899967, 433647111, 360145872, 578757984, 407100945, 980659107, 836114658, 37195838, 397164966, 959674638, 500378369, 223829009, 570290462, 820441405, 786983217, 29613329, 121490136, 675918909, 917510046, 100930079, 717092491, 582832279, 62078710, 829904184, 926382782, 216120298, 190581972, 735054001, 38404246, 70313043, 621146579, 655400875, 456635716, 746526369, 272208445, 428026532, 326162731, 814761482, 83130990, 156670527, 431308843, 126671179, 88631620, 784248304, 256919415, 678988231, 524425595, 968679749, 192108100, 743447103, 980295800, 368435483, 944452820, 458520540, 794109423, 529233851, 739177959, 20744789, 197764481, 488789838, 905358873, 233137711, 559666344, 721099689, 314188369, 51382616, 364350854, 330026001, 329044615, 271556737, 741491880, 805065521, 522431955, 499515166, 985335217, 659398033, 363547173, 980279937, 877529179, 197824983, 813002580, 65249898, 622032113, 489314863, 7958469, 653685919, 366707810, 358420288, 599298364, 491008381, 701381571, 432012200, 99536492, 837095309, 608582567, 294905374, 139002768, 415870347, 903263877, 421238938, 783140693, 942377591, 484194932, 670872793, 62906634, 301408413, 604631758, 228309467, 347071057, 19361262, 375106520, 588232361, 140180051, 279345675, 218988017, 388530451, 84143223, 707041188, 148561109, 642301049, 206304387, 906019931, 435939418, 310999732, 814379751, 46720247, 850418072, 379625525, 500867984, 763398361, 930448830, 156749553, 517208101, 710738380, 806565237, 26398817, 860700904, 262878077, 64051852, 922530304, 833337383, 483037011, 323821876, 516151531, 384955558, 83150463, 926223037, 848008920, 553720163, 129898551, 364268728, 322761561, 84470013, 237938321, 905608585, 721575625, 892184183, 555959854, 256769269, 210595029, 103098795, 484756379, 740348313, 461273340, 57471124, 617652914, 981431200, 172577772, 980481, 682682762, 42944284, 703477701, 809815364, 216511747, 923571603, 556265918, 643737576, 463363980, 237403282, 1732375, 290471906, 425878066, 754837372, 511276572, 482017969, 650118940, 566938784, 418191527, 446689682, 616002644, 545331506, 984843989, 403367215, 903416535, 607437110, 989408065, 538794164, 903846414, 695922947, 170636007, 27547556, 640979355, 940345558, 634631405, 814547996, 520795687, 511460983, 19211770, 391174601, 375803652, 777489171, 803807478, 8695604, 221704581, 13322850, 147498501, 648758494, 640455329, 671323459, 568476210, 889227407, 683372581, 422899914, 3803927, 270060078, 429224806, 374426867, 19382635, 219080806, 782759932, 757628510, 75200634, 110602093, 171039099, 94476846, 650665819, 229696410, 507597585, 837812441, 930993292, 280779312, 1585534, 909683630, 853018211, 203821861, 975094953, 391810594, 499804044, 58085865, 319558251, 359918387, 533883921, 256857731, 667103272, 318358587, 96994671, 713946267, 308758454, 975932600, 74091260, 52639357, 838199638, 200944370, 547147903, 654095209, 189456396, 377079452, 553838485, 629693128, 487707914, 802131112, 716577427, 729621599, 141603446, 480214644, 920253055, 334811941, 334632874, 427576580, 260806491, 591863767, 375958359, 169565363, 832067383, 463085346, 642105449, 893739174, 47525853, 498605395, 706884654, 175076528, 882427824, 15688932, 183368270, 363354867, 969174376, 485363434, 284074052, 686942704, 856273734, 505058488, 538201359, 950965915, 178230728, 79134922, 259124339, 701538094, 351665761, 105996209, 984061129, 723488255, 969850709, 94211820, 288925313, 243279846, 768148809, 36398025, 150983019, 539468810, 304808239, 857477598, 145942526, 688161759, 214248024, 319163565, 873125947, 591986996, 353060929, 395818889, 762200427, 677117948, 119500054, 382186248, 689711204, 486900437, 701044825, 361867486, 988631251, 579491430, 439428386, 281550686, 735243963, 844183007, 890558039, 637493565, 461579984, 409513640, 346911560, 394702277, 958643060, 349400278, 974637542, 287311835, 946973549, 212799839, 754096267, 844488881, 955853714, 109974031, 469725277, 851435631, 809629825, 374636194, 59464084, 120786273, 217170505, 617271935, 322860287, 714549702, 864212256, 287603057, 34546512, 828109929, 783891761, 901434936, 867646751, 929251430, 280200073, 582810034, 664402259, 254470189, 964507460, 167313354, 811189552, 811907141, 688310212, 845973625, 874142107, 673948609, 460739309, 17344205, 6575696, 378722845, 111177037, 754527603, 738653931, 775496516, 36244320, 346521459, 392938782, 944549466, 613834471, 864719399, 892123435, 778682085, 20814157, 641841589, 676393487, 120976255, 428868036, 814141711, 741995156, 729398296, 711756593, 737502591, 572661741, 700706675, 257337589, 334417375, 558853924, 532529339, 415824307, 282364953, 454089465, 795421724, 416173418, 81101293, 865731367, 164724408, 455786833, 300474494, 702631494, 927412277, 132468073, 164485960, 284040592, 526940037, 242621562, 450039254, 947129365, 20884173, 61402751, 976612775, 978755420, 5506871, 399317982, 628892304, 338282857, 145026640, 332917480, 462961144, 758180417, 250059096, 546449024, 364380327, 744174834, 614996660, 842913107, 224520802, 429055869, 236742903, 921365334, 411013023, 675647757, 656303445, 215085861, 82669411, 348609423, 997179115, 339645602, 277423797, 602883958, 544041962, 275600292, 333789303, 110257465, 625066388, 666039484, 564134613, 347618779, 617719354, 808710010, 187543775, 534894515, 841634313, 107270991, 925705266, 569507016, 19706285, 173137297, 383556620, 897475874, 343731526, 88214764, 734956549, 895233007, 730741064, 921315714, 111178365, 72559493, 742099332, 856444833, 632050912, 933517518, 563024433, 46281556, 689366671, 376392690, 688994223, 915705854, 273188880, 547126089, 950267632, 483746604, 383178061, 333773044, 436040783, 97798207, 729601201, 564473992, 490949666, 431494573, 434543650, 744469222, 98011217, 699543921, 180366185, 292944660, 596121331, 88273757, 553250588, 430957479, 235769477, 119348263, 326305903, 346693183, 874113328, 418145199, 603905398, 524978862, 756894742, 160464198, 81670939, 283954653, 429792616, 756611180, 269230570, 282840968, 495781607, 788359758, 750951888, 659339815, 189702246, 336005367, 851364688, 845966357, 456344164, 978029644, 720450894, 927534731, 706140852, 496375233, 179790571, 305935408, 877518049, 541909996, 406171041, 710508759, 926219787, 47558456, 923633652, 680363142, 712113827, 637313611, 92564621, 18232003, 633905296, 273693570, 451543318, 208199496, 32761098, 404221146, 19924950, 122219135, 261765502, 710683210, 214933228, 352654742, 34026560, 582692108, 49632301, 301875019, 418936923, 636292766, 415244274, 865269258, 111676620, 304242569, 943072372, 944029193, 78146266, 653399144, 71849127, 297580668, 532988481, 854451136, 671428982, 487889147, 673062605, 82846252, 766745466, 828303339, 640016904, 935542676, 703844931, 541708403, 67445241, 6274375, 128177695, 367417370, 201581267, 51481967, 425930979, 889751796, 557216188, 598437326, 639254499, 56305406, 164300888, 925450476, 985850700, 351502282, 814337161, 765997642, 858313949, 658453411, 689240969, 273129635, 545702952, 176402583, 415154420, 67278325, 488392019, 475493738, 46192642, 888580522, 755496255, 756823108, 123911491, 757633218, 236929152, 106963112, 728936273, 646601815, 596278221, 24545653, 575309253, 690114396, 525876835, 212323813, 380924811, 673544216, 979981543, 725810031, 408347560, 615675988, 11676696, 526122951, 385574677, 736731996, 523795356, 781712625, 146646715, 831993491, 890806003, 736370206, 644648059, 599395052, 620531832, 228861979, 385515927, 172177909, 170296343, 981526552, 840043260, 378683066, 767329603, 96303443, 173014275, 181262708, 208252587, 58923056, 194452403, 289977139, 837269762, 963225514, 243490605, 858720299, 554684979, 663597534, 461326458, 1152998, 745328619, 999233745, 191913154, 906193889, 226448885, 580119890, 459031700, 308634324, 330509516, 646886828, 898104258, 811749776, 608888164, 878237193, 529088617, 172535858, 666360525, 437763139, 417414931, 82985992, 534961622, 499475799, 794041975, 525623761, 221138049, 659476809, 631787644, 467685431, 444230861, 224737072, 944447782, 572237296, 816978138, 638802394, 829136901, 967253330, 611531291, 13270093, 122628369, 809642622, 935342487, 987695651, 360003161, 95718347, 132159977, 75387354, 987829342, 483643857, 418815576, 656561194, 923594333, 611581911, 536796654, 122474589, 174044726, 869389533, 793562985, 851810536, 882668831, 32692564, 812511440, 443580948, 119062244, 141326384, 854487538, 410251692, 806461648, 921473145, 832255555, 447928457, 861143727, 102425824, 30499828, 832067323, 582243490, 647710501, 311889896, 639199561, 449199697, 235216375, 904300083, 356615571, 223357202, 677153981, 381359918, 396656301, 214641946, 922789022, 256940040, 105739956, 317548798, 320687535, 242033402, 162349764, 371934793, 336094782, 525978918, 734652910, 218778956, 970620003, 424848786, 328035858, 21544050, 403241863, 658966810, 946768441, 591224202, 259208247, 847768083, 830186311, 104147491, 573264539, 73471233, 360513558, 984308283, 582514420, 120700055, 271385248, 305761967, 517490770, 854110738, 736963032, 856757988, 998365612, 972661550, 332290228, 475811652, 398956280, 873625305, 477681575, 704071366, 903818642, 856940152, 111880387, 166589346, 406717565, 389059694, 115168749, 520756774, 786892549, 40961256, 183554606, 953218454, 897635298, 271294237, 181725440, 233615678, 668817159, 24738158, 954738887, 121613834, 833621397, 960545823, 244057834, 558523745, 349009212, 81033247, 721764052, 798574646, 530768903, 915342264, 380677898, 903803167, 151655018, 356612021, 413341495, 67381149, 1033957, 346762135, 191515683, 366403817, 268452926, 4884722, 844387383, 506989501, 634804504, 949660238, 212115454, 124086735, 989474406, 956594777, 886433016, 558023081, 183980867, 435578667, 237783502, 369453535, 822027509, 241846707, 727659733, 182299674, 886795680, 277841604, 270712211, 885762280, 12193613, 301525937, 492128497, 667199437, 647067128, 840030202, 118391532, 441052503, 174104565, 37663741, 659566427, 789277211, 15470410, 106867232, 22474221, 407076312, 940317765, 334437415, 737144955, 791590387, 806413377, 248311238, 937649009, 391451960, 246107734, 187122682, 999147805, 254500004, 330451017, 755512437, 334246314, 318611010, 951353765, 314456018, 341091941, 864463937, 150872418, 862435339, 765427079, 62688953, 747873737, 178935098, 599766878, 799049398, 886273108, 312531931, 767816623, 185035706, 596280351, 21026704, 478075459, 473427555, 892753637, 836053298, 155790494, 387697187, 14960617, 265901050, 694169227, 475976262, 753981016, 281233932, 211618298, 190736863, 928721584, 73612048, 464580731, 917464050, 560970843, 224331154, 918441023, 58770287, 54759693, 325052281, 82813945, 50220191, 353252868, 32951773, 472702110, 237271651, 808433962, 365878754, 259692341, 580326766, 627520959, 478547800, 560335939, 445328981, 211652093, 648100026, 621877471, 466066471, 834957213, 33988263, 618836453, 983132013, 705179847, 717385819, 835985953, 660864700, 188303196, 226981740, 222394738, 651930228, 214695908, 921670189, 618423605, 738882421, 472188369, 615345847, 461514039, 772088546, 550325303, 19606697, 126184823, 54240027, 272975175, 174803986, 318349775, 769239072, 756227947, 388387752, 796334473, 422990376, 359970351, 428042813, 269531787, 471947809, 697904572, 296178421, 973707732, 194476208, 107266154, 170921852, 933830060, 38485085, 810259508, 34843158, 929396899, 274801201, 49951300, 538045429, 149513349, 170319394, 911796629, 538317289, 698334830, 728749442, 79866299, 738732849, 766874692, 668137856, 787985931, 664331017, 186710583, 316987826, 819788123, 408509357, 497263981, 795284805, 739884678, 770156657, 696215201, 649359813, 327732123, 890734154, 848238850, 705051339, 325591218, 453871135, 583070583, 595359123, 115887051, 415075172, 135862231, 105256329, 917953244, 293307147, 474510710, 55119362, 92886872, 649956893, 812668244, 231300291, 377152038, 992561733, 43230094, 922094896, 31519937, 920371254, 286426450, 47211657, 658379215, 231661445, 341810122, 644910295, 472929234, 732039279, 74132705, 749595255, 480366298, 168764294, 750970921, 600988104, 407131357, 2513578, 442399526, 31939916, 286853973, 86254206, 378691584, 761042417, 458200936, 330671736, 9198601, 651970311, 152864255, 573246562, 386742456, 865714798, 785768614, 836854784, 881899332, 671797299, 367819839, 352691670, 512149851, 65622617, 438910349, 968506611, 927424410, 541046545, 79591601, 938263743, 117727721, 738664278, 29184421, 360630175, 886537952, 995980888, 4768820, 221237996, 640995304, 671244964, 773405898, 210225482, 527327825, 331005093, 236321877, 8918836, 405855409, 903397452, 774531050, 239603316, 152763381, 533327529, 258339144, 314301022, 72364786, 223252590, 82174034, 754218827, 666477669, 372148215, 615209618, 799274040, 389013447, 392233088, 993337599, 557474462, 987151887, 468973936, 217399969, 198844947, 375870158, 791688915, 481420750, 419481577, 427680383, 397020188, 131666438, 912395546, 962007786, 606410116, 419666172, 718736074, 611257923, 701326380, 883674566, 671187624, 86555690, 948726772, 728524724, 772554641, 502886880, 484753170, 628768758, 158764517, 886179692, 870802170, 855629972, 260744142, 531463462, 64358595, 127818171, 29928061, 882991808, 576314634, 448385079, 298602344, 770574354, 462427186, 278339125, 931050182, 218364460, 838243951, 552576193, 542401480, 430387123, 411237123, 823440141, 215932244, 700092406, 78354932, 87294130, 398155154, 495291425, 258389488, 567091503, 222574336, 647610077, 380840754, 695439044, 502414576, 792007160, 994742611, 393113076, 210871856, 601869358, 854060409, 927218705, 686219292, 487458909, 480334965, 556425232, 860507064, 697609953, 229068654, 478905134, 426129563, 751304066, 538699756, 444566400, 631331651, 38914770, 179186108, 4352548, 414409293, 777440648, 44726255, 110797737, 816666455, 731022281, 323167120, 284406999, 56960034, 707112757, 605601587, 727417604, 908555588, 635662018, 714493017, 501782508, 53025254, 26609155, 577758599, 645705259, 477637743, 933366894, 247258240, 231569181, 340669168, 563981862, 658479295, 464022885, 25502618, 913875901, 392997280, 827938619, 115792997, 368540286, 332440439, 439025316, 388639019, 194940664, 893283210, 926660907, 677782399, 119828872, 316289007, 336991490, 364333234, 519696095, 473507505, 332024251, 116835416, 49545447, 837937011, 290714801, 157995574, 350171910, 348150124, 712940527, 332839815, 778556802, 10881088, 987617476, 859822886, 690987016, 546817593, 625922202, 440776972, 736051262, 861952334, 710880749, 620404036, 702068391, 44451883, 672945711, 165627459, 716351732, 687207910, 359674583, 60845305, 223463333, 313408815, 295919816, 26799365, 256827322, 486735068, 604666824, 774364709, 748060905, 476898103, 912674170, 826767855, 718644131, 583042427, 303518499, 333567212, 69059765, 728851901, 56249891, 809853275, 837393145, 509341625, 563017024, 988270551, 463583412, 187319591, 945028508, 793568398, 349354653, 86092932, 782738030, 684502081, 661225790, 448702726, 230211405, 926532718, 851413339, 989025190, 98429530, 749303279, 670644726, 868353640, 927194921, 530177171, 904486437, 61603669, 991298169, 476234007, 170796634, 28652740, 35515690, 986346584, 90443209, 258653107, 778296659, 805613248, 859124896, 914174689, 624842814, 862831799, 417931361, 891070585, 690205311, 474274795, 7879179, 250447795, 814039938, 294679218, 265567831, 760929613, 796901618, 55909736, 239305940, 947876186, 69935138, 18741444, 572131773, 347373128, 936575590, 652527284, 102146357, 617675819, 131745191, 79601855, 318114403, 213067283, 623520498, 87275758, 747981978, 575152352, 411984677, 145800550, 110600719, 236269648, 652031903, 809310535, 215367223, 52957641, 354776285, 49998167, 961639741, 900350715, 14593872, 174931106, 945714545, 219283918, 639417376, 888732663, 307153068, 692058108, 476589862, 155410085, 25371228, 585648313, 280576980, 204383169, 674986969, 755249450, 507374275, 916568479, 801794473, 228581316, 445747889, 87289970, 117279988, 331423695, 858541632, 838597961, 305902769, 379949374, 130005245, 945630257, 726517116, 4539903, 445093153, 369567397, 283622115, 813386230, 518989431, 207092128, 355654976, 554513921, 555851364, 550960221, 852502428, 981434598, 611040903, 378304556, 418055209, 438815350, 806228600, 24157298, 115604930, 209968548, 120091427, 431872205, 969817827, 984662321, 753974152, 165095434, 619335536, 460300723, 771076727, 641292104, 560766809, 389437091, 18511480, 497856631, 105292398, 115520317, 282052356, 397246275, 221201717, 405037106, 507393988, 708172144, 286947212, 255524263, 403817139, 438788030, 258563547, 756679258, 538030698, 63344284, 582942760, 336634068, 183462454, 375891240, 337472233, 872898517, 403906637, 346730474, 245122971, 313788443, 619356696, 683161326, 236334343, 446387207, 807564855, 991367963, 847872981, 269895119, 594678325, 126974426, 442088989, 607145124, 188192529, 616709387, 457067888, 193388210, 547744462, 527135422, 252256797, 318851751, 881542066, 867869323, 376128205, 506888329, 443271092, 738708729, 824515794, 359201686, 877072243, 220483290, 753212022, 99569939, 107603633, 386893632, 834566993, 20693311, 488743174, 533836635, 773122283, 776609254, 466750567, 632117748, 2506525, 660614843, 631275828, 697697570, 742420988, 281573382, 31182869, 801073533, 361969976, 645011307, 608760249, 970574544, 184542235, 856895142, 934928159, 549230766, 432563428, 189913488, 777112359, 568384852, 623386533, 112383329, 947731632, 163679221, 380633886, 617101209, 803142360, 845189017, 445888873, 185320787, 830555118, 29630197, 611071797, 382074060, 388640214, 844818855, 171816557, 190214400, 656538003, 227477082, 332812805, 791147195, 741839391, 531204856, 77365984, 52517009, 64768413, 858480243, 359396963, 518306963, 160338866, 182621428, 969645530, 934070455, 531968360, 378641461, 430357535, 210933283, 291219225, 685035670, 408557041, 281769367, 178486731, 212496498, 896416490, 471425064, 481430584, 282664527, 440725550, 21846366, 997377593, 803434581, 204298595, 838865792, 356820791, 292598886, 12943471, 440236159, 318402304, 158449331, 399626579, 628514714, 123042122, 822476232, 452768530, 835010566, 364600921, 960883317, 391071803, 912910455, 478741966, 595927898, 621544147, 952782963, 193914909, 696911741, 812785266, 297073936, 204068904, 296344709, 844908058, 766398428, 182988466, 44697681, 539016136, 858620338, 257957208, 940152653, 182680536, 652317326, 629654744, 15631294, 376320824, 938117897, 897500859, 79547576, 826846547, 786017201, 950639540, 338455741, 159119327, 773124249, 537495166, 629412949, 91456064, 937019142, 831364117, 555459812, 643981263, 540690347, 708797966, 301638164, 89383393, 141772331, 415822890, 332698590, 110897701, 704196741, 316069408, 92501884, 860828255, 316189606, 121459181, 775781658, 197063733, 544336510, 761292099, 573558939, 808756324, 285200863, 162636338, 273629757, 673875463, 299196394, 862562172, 914825188, 723986452, 187527831, 220215667, 908273505, 58281450, 527196947, 168242045, 450634176, 20004315, 276585828, 181786868, 848884685, 61069974, 58485771, 89458185, 208521881, 698099418, 80318807, 729193061, 835664872, 702600956, 937377835, 239435173, 621892398, 849574, 360918605, 707995282, 271513797, 320879897, 217222378, 279401989, 528637807, 53715694, 895454411, 932431264, 430307083, 376702107, 229843394, 746417049, 195707695, 692914068, 57367187, 59421076, 961345555, 714914545, 788091277, 544547726, 419710353, 60964772, 60769329, 906287131, 675560390, 252575500, 816143797, 654288369, 161087184, 837746237, 139483749, 614095081, 692566670, 30408307, 761850043, 107801207, 155508896, 190557481, 411733808, 818475109, 840391053, 763413280, 957611228, 41055070, 631919214, 858244622, 259890780, 577561511, 611724893, 274626190, 935218731, 50090103, 398017604, 131387040, 471578965, 272924123, 575329314, 293670470, 976122470, 835428383, 354370704, 643891635, 580026282, 42112560, 185188150, 787033367, 787600901, 92031923, 405386231, 600396182, 3998782, 882186014, 128847843, 275150830, 147826048, 534579613, 391895994, 716675846, 686232271, 95191376, 146923599, 980781430, 3471680, 579977669, 945870079, 357756265, 386277833, 359126499, 905390372, 831808708, 757117539, 61936958, 10024918, 263324015, 293549819, 376030320, 37602865, 359471880, 631305356, 356355985, 94083662, 780310608, 731451535, 906683285, 124482005, 512560846, 567034510, 835497724, 354068559, 914395194, 618199709, 632128798, 754010695, 768683793, 590555423, 416393034, 555324763, 43919773, 668876104, 426406303, 921712189, 534442617, 539694019, 667632925, 66515768, 860848090, 903268094, 977336477, 37968816, 457677811, 588353721, 584988005, 759726518, 411980907, 60536805, 323532778, 961861339, 184401918, 812982520, 330392522, 66109428, 792859853, 358182057, 236255668, 861600932, 701641297, 180113837, 806072080, 545253491, 270557765, 438477211, 121433879, 600682348, 644425537, 434536444, 239184093, 898406069, 382989884, 158721717, 990787364, 652243911, 667329680, 797169911, 764733660, 801136695, 57909988, 952859350, 921129670, 898950421, 714104646, 2640913, 598998101, 211496875, 116138463, 517345267, 854621696, 380387031, 116368949, 20216103, 873080256, 288415128, 537338446, 68080866, 498427378, 242594399, 435813567, 882084746, 19587768, 951905668, 845394517, 85667517, 854617709, 3047461, 377031233, 678201149, 437937261, 687882541, 344598552, 577603224, 708061632, 177513493, 688296481, 9169305, 209665191, 899230454, 837452571, 673202518, 303293249, 16978184, 825033186, 4851820, 136672116, 524807304, 68365192, 150275491, 852578448, 591929724, 355821321, 751361836, 256538104, 467756062, 333270446, 291338583, 665443245, 678089993, 748003590, 966973712, 375139007, 403798047, 76175392, 874664139, 918099543, 729762791, 704292507, 558662606, 276945401, 580765445, 521483653, 599302973, 77818319, 936672307, 672036953, 345998460, 223673681, 422753197, 455755029, 233947774, 453363234, 81827899, 193660950, 880748885, 309219296, 530688684, 835968280, 223832008, 990181088, 650927039, 752837502, 26419188, 280320757, 959355874, 491178802, 734021025, 219568161, 5189911, 353881272, 362571220, 532273943, 237492835, 16087135, 589503971, 440147191, 5139141, 76446, 474760293, 616987263, 232692290, 300788126, 976608563, 645825943, 260315384, 263325055, 767445100, 192811995, 375650732, 85608915, 948248212, 220559444, 546526343, 369806816, 683878468, 475910640, 619711777, 6755402, 362311631, 223169442, 391866908, 930367746, 344368653, 335166137, 23970470, 906050876, 316755998, 41819030, 238376451, 447698440, 544132359, 132768236, 620349178, 957444252, 884145212, 886250607, 248090087, 4062680, 898552169, 912731992, 247320597, 522690006, 303106151, 322167079, 556107758, 986315397, 844742047, 278254189, 912265658, 416977458, 267110719, 420686369, 917706023, 548209147, 891688272, 64148495, 263505499, 448712949, 469446360, 978115819, 570236802, 322181104, 219201549, 53758047, 904380230, 473245242, 870540503, 105825576, 655622339, 359216828, 559954750, 637039808, 766338171, 776716489, 445218455, 852280842, 260535859, 546796101, 536507799, 776638496, 560488906, 268057478, 507068448, 987837360, 35674118, 42503342, 824724072, 62063761, 477887289, 855495415, 780665584, 925892945, 419595035, 896113881, 86235875, 232991202, 933122839, 767383257, 886205724, 858499064, 528744565, 359095825, 428431546, 592888987, 748066172, 611133416, 420717781, 333652936, 68919790, 509912925, 592680335, 268842726, 147499405, 6272153, 639916495, 146252002, 662948453, 69693091, 48980497, 501094835, 373382417, 619586878, 628391865, 2129835, 548568033, 866720694, 142168509, 79312143, 939501700, 627942489, 544063101, 166245963, 429234544, 818348409, 994921724, 75992914, 74641750, 884195485, 294385418, 18936486, 577310146, 737106328, 551751150, 844432678, 994204355, 900797318, 986705925, 679882751, 957623247, 263980816, 81592194, 894490731, 294477020, 884622826, 397734693, 801157249, 878763207, 426003886, 723405504, 32518801, 281205162, 783462022, 88980886, 816924984, 622770867, 305074652, 928700491, 900516899, 882699108, 495826282, 576560259, 82807132, 88386994, 269955574, 508195515, 813546059, 445388541, 760670023, 345184656, 254587088, 206036512, 403066371, 934707950, 611049549, 60065573, 561662499, 177086131, 507734908, 397391594, 874307829, 414246178, 587461843, 935878482, 394843426, 118264359, 299400991, 601546965, 330405718, 257133164, 903892784, 555347699, 901430752, 403354957, 398499124, 411858794, 528576813, 313032211, 191077565, 202270657, 186569945, 859731647, 425707766, 372697884, 398675391, 251523303, 445194443, 702553175, 451639332, 651064685, 518638902, 79791977, 924963048, 636775652, 310262293, 245937896, 983186343, 76090973, 604210129, 794247884, 166336480, 118018856, 602993173, 344261812, 237582087, 783774456, 310896406, 131599067, 594506680, 163880805, 87503825, 269756580, 694164078, 565990187, 576671592, 450417582, 498520076, 992134980, 604328582, 237646019, 560228881, 168229497, 180702781, 705277692, 725850809, 389769915, 848541902, 451837680, 85622144, 449495012, 8871342, 132374438, 890631570, 877775072, 276418293, 19933933, 572371108, 543019561, 781284072, 575752076, 691920416, 437290019, 850150498, 640519188, 328186793, 626961506, 729992936, 423944056, 658250543, 861433060, 750708278, 541138834, 585186786, 70752085, 245973659, 434189469, 35256203, 544948387, 269582055, 445103479, 235684209, 907036977, 464962000, 588911711, 897505911, 132326464, 49746638, 51988748, 394646130, 305432558, 63962276, 374843689, 43431281, 169112489, 580388283, 824832230, 365212138, 632222540, 891755702, 109193170, 651359286, 244283166, 904748031, 567265844, 243179755, 112233227, 479701367, 379469593, 311018045, 816296020, 545906443, 771782766, 270767745, 920445982, 31888031, 387477298, 120621061, 609700093, 227800837, 952129970, 482135753, 782128964, 591177993, 882335560, 671805461, 125228353, 686532397, 565950842, 466632395, 948610609, 455348305, 791074590, 115374190, 543361481, 238900055, 71490140, 950865448, 253155697, 931087775, 748731709, 581648952, 263763258, 546112399, 183602469, 544963469, 580382641, 766765998, 803610584, 59120349, 586620177, 44027581, 849312573, 177527960, 383314348, 737981569, 728032461, 481587359, 898527886, 590290511, 673082335, 437661906, 362326655, 287688759, 953631363, 696993353, 833698246, 169120441, 853570563, 942693635, 695809388, 653483449, 277598952, 301826918, 250583491, 60819940, 214429031, 15751308, 782484405, 755366551, 119184484, 465226192, 856077894, 234418167, 355632080, 687478101, 613001497, 513088718, 426365335, 676582356, 911517532, 296369172, 250067943, 142017014, 608950569, 299239790, 214919145, 363731213, 546291041, 726331163, 726075232, 712500669, 945219362, 138058227, 29259580, 658937049, 793068285, 424379057, 633707941, 625426676, 855770387, 455075354, 516608976, 826929438, 976909128, 743798661, 338713763, 917195431, 593933122, 739966877, 197508732, 946306336, 133306810, 743063234, 932343386, 428280919, 849191726, 588163502, 800244736, 707418901, 358132979, 783621627, 626709228, 868397835, 620912529, 396790427, 354747612, 504891899, 850957309, 537888755, 668582409, 107512208, 682068549, 733335916, 304023721, 527760999, 816479950, 788465066, 397075861, 693352547, 269648430, 356735643, 293443663, 41396542, 891005022, 90953760, 509746007, 964587540, 998534023, 577503376, 764003352, 49554191, 828930058, 250169413, 684673851, 591832641, 851556441, 458492376, 406651687, 988553715, 237938332, 188978572, 612049663, 19289823, 723831463, 717959854, 693167146, 112068326, 12333750, 665656779, 486446751, 970344400, 263133374, 579878513, 764224798, 873789172, 270621340, 752238607, 935226916, 548388441, 66390085, 178576817, 955679726, 530421706, 380283806, 245605420, 393411247, 231217861, 390684144, 740380235, 654680135, 596157511, 157414696, 27660187, 626407989, 607482713, 863843164, 258687799, 46718773, 149888668, 519235784, 830213807, 309318448, 70639454, 618969432, 944929331, 541003610, 264035963, 690509569, 212176752, 63986894, 156277119, 974500742, 981951916, 838623452, 208355834, 976242776, 378960861, 250680031, 386023493, 249009334, 979831680, 787658634, 291868069, 150607692, 562730344, 115824369, 709644423, 528304821, 462637736, 825958285, 750758732, 2694931, 148147192, 969077209, 276152681, 533191994, 864563605, 272369737, 970963201, 619174743, 645366719, 914603531, 825432838, 10247780, 815594617, 204106961, 763771107, 733293774, 592721365, 332800103, 477598322, 536121126, 760418982, 736866714, 387761762, 874420506, 649839278, 287849616, 901067411, 105966597, 422442081, 410216444, 147297630, 96502732, 859704765, 295783566, 804886270, 338681132, 200454515, 745229304, 334372341, 355448617, 96647957, 509705683, 572430512, 695635176, 423483412, 237927930, 26311799, 160668514, 762729406, 153989740, 498954283, 51931238, 541948069, 371886205, 807744819, 442990643, 307639964, 820405898, 686047708, 758497593, 140175660, 853971570, 529921527, 984106408, 190962330, 422706512, 677843393, 405179032, 116994831, 952324847, 800889325, 512602550, 584814468, 401871340, 88316549, 321422526, 988715374, 626080409, 500256983, 539015369, 502245350, 831143509, 788284149, 926778107, 525323047, 692651652, 93655458, 299330902, 185922571, 486216531, 46093626, 804028345, 803449016, 836853984, 729031662, 334373739, 595209105, 66437099, 607400076, 850349211, 76438569, 210579763, 539470621, 582498531, 347116398, 674602652, 880194791, 967382016, 222064551, 902662178, 726507403, 271794837, 731116025, 234825311, 830144145, 680284345, 136850070, 101394724, 945565249, 332439607, 332021960, 252949662, 286664524, 788633948, 106949419, 200554696, 769458928, 974265087, 987669590, 379578442, 484706426, 591072785, 8028530, 175890763, 107682925, 382524502, 468274771, 308140841, 937326063, 881788408, 562807080, 171381240, 54170667, 224641120, 827060859, 133029670, 845901603, 370345639, 14670630, 557902605, 951599496, 551124702, 485425317, 592177734, 165524407, 854554493, 112260226, 391728277, 94722009, 464218421, 190274530, 671501402, 930481585, 989951574, 96814518, 947138521, 187873337, 116313281, 455568483, 674391463, 819122186, 400325177, 693361549, 635948062, 799949240, 659608964, 632675615, 483359312, 294495003, 116398468, 459356968, 265259060, 645911720, 605447412, 782257378, 575609946, 697851505, 941725419, 286168564, 643169663, 574036604, 396745236, 222994092, 295894185, 596365341, 954423287, 427324827, 391451652, 400308533, 436972764, 603152383, 519584161, 560244734, 947127698, 769910787, 330348393, 731522757, 603407723, 132365111, 976145822, 852788863, 27110832, 410709303, 784966561, 383030545, 676223305, 222040514, 384200088, 729807150, 613547883, 841177807, 201988532, 817565697, 496603517, 268063255, 127433255, 476026039, 522928644, 947503429, 474678727, 417580009, 861818461, 751948792, 235420198, 752680523, 335040456, 675392440, 850670845, 615347156, 919428244, 272315331, 729055048, 444777693, 115083211, 798560469, 451603759, 524101772, 911664431, 678938556, 682807618, 3012685, 270122575, 540826195, 851898436, 20649528, 670963749, 891373126, 336514940, 243662001, 878032750, 25025681, 4521404, 421796331, 344408480, 960094305, 384986539, 891627681, 905280619, 61753272, 295232739, 396395651, 302443849, 734443986, 331074745, 737859230, 343917583, 609710844, 350450536, 970220095, 400425567, 304710304, 985366974, 134043914, 838225554, 941251089, 699020688, 536771798, 790335692, 552117434, 153359259, 793895842, 902951391, 287065277, 933373880, 663340014, 525091084, 519936513, 35390677, 538084037, 503813360, 853204551, 627804544, 295979308, 988739125, 158438953, 263050147, 979253605, 692878265, 996836195, 646786657, 790743875, 848856215, 705324439, 604909599, 350781336, 763669332, 975826564, 862433584, 488032792, 357615540, 753705293, 875582654, 929230844, 541983491, 453947220, 426083435, 886845428, 561247483, 137768627, 978928000, 183761162, 934030599, 911719131, 878436922, 328308407, 21669424, 709034151, 425372235, 569833717, 253661259, 665368379, 662889362, 196579139, 849178709, 201573454, 753176850, 814256794, 419126237, 280342715, 702849787, 258048660, 281390642, 706748926, 864418860, 959994492, 389789204, 948206028, 221967574, 830139266, 219797332, 223393969, 583915547, 800193181, 947176977, 16041222, 448062544, 168538486, 668693764, 480545845, 497016621, 506563192, 715212881, 994886808, 955387366, 291728021, 918565482, 385014370, 435955051, 734206044, 690405511, 814521875, 81332077, 622721526, 863284703, 748958194, 954148464, 382121985, 599975421, 803803794, 431152719, 678153977, 545742014, 755190510, 293292047, 609114922, 185727752, 663095919, 218208609, 485745825, 684543890, 596359392, 590341006, 841022167, 382212649, 148973440, 655272539, 618709148, 790049306, 312607920, 43253531, 457041021, 141655409, 466887381, 385633924, 879006409, 5006651, 209523121, 833036556, 751247155, 676058760, 116489888, 62226789, 694205760, 937815446, 980935868, 229968017, 237382977, 670176284, 573556941, 772652086, 130146724, 703926776, 691920551, 371664876, 771919456, 228526151, 587727093, 282525918, 45222259, 57010442, 785745089, 826408858, 468973534, 272824182, 371865799, 527499111, 993427152, 83869014, 84763749, 140544308, 991902597, 845649378, 349584281, 674130938, 99511147, 100515585, 858020657, 237914976, 748381342, 895083485, 469039686, 733551374, 14216169, 660887951, 409006810, 663048273, 994622076, 12500690, 982146303, 608707854, 908324746, 828481978, 692016623, 676916774, 160336193, 531023613, 995515245, 41476058, 337892076, 788297152, 145312984, 649972381, 241172545, 304826045, 673348075, 831513067, 956574432, 27165147, 760012405, 248863613, 650234539, 265478744, 925706144, 513153001, 471779354, 175441617, 383232789, 92092471, 527646452, 712711689, 377346656, 152884588, 243858285, 857403603, 143725310, 168504688, 398011630, 912663308, 748362631, 62662661, 540158127, 810198188, 673614332, 600329602, 371868351, 881407399, 144426284, 577073215, 135746591, 856147722, 144264478, 49705147, 515855754, 572389450, 83183573, 328933274, 334225100, 848619219, 957126345, 236794502, 754344986, 803550641, 602666621, 611522061, 657572808, 987101997, 325972499, 92209719, 53927068, 554656876, 488748394, 860079550, 273315639, 723301414, 208550281, 711592593, 735732929, 826899454, 441161154, 632897501, 57146582, 876400378, 209598988, 440920283, 6417327, 617144185, 29058144, 584964504, 801791852, 675043035, 703141401, 982375200, 799185020, 373985952, 764895746, 338153302, 771503803, 443614748, 764986394, 64056244, 767738269, 178028641, 464984091, 990411181, 414846140, 706738916, 40190964, 494527829, 497900745, 704682051, 577050844, 620284734, 120364357, 917997320, 525476335, 613122761, 508218475, 334257140, 708081645, 964844460, 426585798, 495602331, 976145072, 901075050, 733738136, 238985449, 595324954, 673084320, 626785076, 384625814, 446893284, 891518681, 936154889, 225868598, 776802403, 168468043, 350793620, 597734911, 319822571, 896389733, 253217569, 92339296, 87073446, 883196336, 179056197, 231722920, 172290495, 742682165, 95155312, 383745273, 814260047, 45172181, 888610922, 36398323, 82827143, 448918279, 209493439, 569553459, 243848805, 570677107, 914617757, 536649508, 707119175, 342298291, 793135814, 212748695, 289257464, 533740498, 508765963, 540167436, 401847053, 42517917, 448286155, 70507911, 69514179, 605537734, 141664966, 83591296, 973663089, 172018654, 571948431, 473052177, 447122249, 739755072, 581389001, 604538162, 982530359, 200848888, 283679120, 265918025, 816443090, 750873034, 375389752, 391308459, 542054674, 9736139, 40889556, 256676732, 144450130, 138364554, 587100792, 437849161, 372812683, 615074465, 196172265, 797080391, 34637552, 631674030, 838253400, 659406564, 919932399, 313269776, 519738324, 158878494, 977130207, 405583851, 165001999, 4305203, 563084697, 474584477, 577608709, 743643513, 296169935, 868331427, 995905336, 451217775, 24530834, 638003591, 356272770, 759892037, 46571750, 151684878, 84501094, 340876060, 399397760, 520305107, 972368102, 637619534, 439638910, 474606562, 634728449, 972813137, 555631961, 142032722, 555073635, 646807018, 671529218, 297490736, 886570635, 995514571, 674184485, 875486038, 774866670, 494740126, 255928358, 788397513, 866006729, 592639439, 730545298, 848248564, 278248976, 692054310, 215174639, 132839506, 101350574, 580156829, 859795827, 295545371, 594785798, 366321473, 490460395, 60388957, 339503853, 384162736, 188636543, 484533875, 181253339, 133371378, 491223789, 101009326, 170947042, 134789863, 843072574, 110644943, 797666729, 75523216, 178374585, 431933753, 654147923, 458135114, 497411295, 972250072, 106051824, 641236823, 107775287, 419691708, 31370523, 882887064, 836225647, 498142898, 187310292, 522572373, 421301538, 507322167, 61518669, 139322471, 731077474, 319422219, 152255620, 501962862, 178964093, 245241389, 733435395, 434661795, 40489839, 398408962, 172978791, 881364580, 859340160, 118094396, 954370637, 935297210, 8330641, 508629017, 408767005, 90669142, 151263665, 757945682, 451319583, 750648362, 338716609, 53757371, 698274523, 21826343, 20390078, 852872855, 533454017, 23218417, 585843671, 768300248, 63839520, 679295845, 626954228, 246583589, 819697500, 265929374, 204835963, 194403392, 596739914, 623875629, 902948558, 167327712, 186714740, 492924207, 431589813, 503228276, 148175028, 302335880, 845189758, 542587504, 162212215, 277006158, 848379909, 375079907, 173258988, 42714325, 39099382, 635911186, 34064373, 856196469, 112550438, 689856643, 191134563, 777365947, 47022493, 832627971, 364611457, 297187122, 696683506, 443434144, 890044168, 739291954, 679180294, 51995494, 404035153, 750434696, 941489481, 147855595, 108924593, 736868925, 39849295, 280005122, 25509818, 5022468, 730741466, 438849855, 344779638, 850526840, 711490370, 556280884, 113435163, 978660349, 928697874, 386609557, 61101828, 452502620, 145169454, 121002327, 199420982, 263636912, 377411784, 978313970, 656663873, 463343633, 598045545, 932076884, 512248395, 291722610, 727566466, 376099320, 314318664, 85604978, 624061763, 752148170, 527701570, 804453778, 303974923, 35006093, 142377112, 392257107, 187630346, 839269762, 568468641, 2732483, 857320179, 664737523, 654359558, 711631866, 6445117, 782982467, 703843671, 660148572, 66784311, 504302707, 86730908, 621227110, 450488784, 71128860, 785385395, 557603092, 959416799, 39948424, 847006005, 573815887, 43311857, 523792936, 503315720, 650690027, 905498566, 45400685, 91960935, 39839498, 89572752, 213947470, 598359973, 670583907, 917651274, 886456731, 827490673, 337555400, 398295662, 729263627, 29715483, 359728781, 247262916, 294978456, 132014172, 615291965, 574719089, 60842766, 263858030, 395054448, 475199743, 937943330, 635077631, 144983845, 73003895, 61301639, 811346098, 990701912, 242546370, 432385100, 661254464, 993615344, 797740280, 635349315, 433638824, 404241937, 461342592, 911875488, 409526414, 902588406, 521193361, 648382456, 157178841, 702478530, 391341405, 92060945, 225918851, 241201872, 287312837, 672967868, 976200740, 991486725, 737105022, 861674154, 971446948, 170344114, 308005293, 6268706, 264055462, 501598617, 980463585, 946802401, 761814037, 873043248, 415502554, 254405268, 801107769, 701392118, 21164551, 654766821, 87786759, 778136811, 927336903, 269465185, 222110870, 182379630, 474036064, 224480883, 99089163, 482908529, 626740805, 49638241, 793008938, 862481606, 733216241, 830649541, 682675381, 830647137, 401829125, 886235714, 204424024, 869715275, 521466653, 334603846, 866212237, 643588410, 563685492, 620623848, 457194473, 610955311, 17608331, 266909781, 140111254, 920662135, 928517524, 295110513, 189495287, 809032008, 593452003, 377768328, 524880987, 949831691, 441397795, 307513298, 589262440, 886416330, 945836290, 518065026, 813156194, 549044738, 283768161, 451328527, 814475829, 786344741, 96738056, 674605887, 466042145, 392546168, 554251693, 409849210, 699575862, 915067003, 350692869, 9509313, 591842927, 490762653, 443881815, 175217655, 169278141, 132483545, 275854243, 955430593, 347757487, 623876748, 382410367, 379866364, 423824893, 766735950, 304246182, 842562966, 990615456, 420878184, 935307247, 408433569, 811034059, 463083985, 204909571, 261237053, 896727201, 438680638, 78777605, 573075627, 443376638, 862742020, 737626856, 707905033, 992469537, 49448517, 823134226, 43528700, 822726044, 96503097, 40378780, 218670636, 935087337, 317121429, 348897656, 665113137, 727844471, 381778400, 100252916, 182847809, 84431129, 82867551, 356364338, 405531485, 82215784, 960613508, 469625230, 256060342, 803861660, 52173079, 709402072, 599224927, 52770981, 321236592, 892308599, 309061585, 260081691, 199009285, 93889466, 426383475, 689908533, 905651418, 154694499, 864456842, 552973295, 389370272, 333941377, 226949361, 204773943, 668118273, 187218091, 60527683, 77482892, 811645783, 687708481, 12914705, 256865040, 820411893, 125206166, 894883932, 133009356, 306234130, 940191466, 549712179, 913988798, 755886466, 484519076, 342002862, 350485576, 573419952, 552988977, 717150797, 399600407, 673879183, 195403625, 464734314, 896353077, 647198929, 699471800, 260649503, 933164347, 804956864, 916552020, 490455807, 560578883, 786584816, 33159195, 769651323, 377492981, 148572532, 304753469, 242203226, 645180290, 761026623, 920777582, 371730223, 602737969, 73165974, 855390109, 192623255, 144302917, 419208321, 975802842, 21440894, 479744198, 812128156, 317267149, 844453883, 850757402, 786122765, 685042596, 283654118, 850196535, 174027102, 775584825, 595178650, 92217578, 735983351, 966409361, 560864970, 970130267, 128785680, 883412027, 380814505, 795837192, 557746764, 951859748, 80054023, 477663051, 273706108, 10061774, 105048344, 250193071, 612258275, 354667609, 308158873, 681244491, 845058224, 648357631, 868049727, 655820228, 559138976, 19030765, 894252116, 139061728, 430774095, 132894651, 66888915, 574842819, 769826312, 857901434, 193524931, 603078250, 482174265, 691974982, 848590841, 544982141, 902550139, 286318702, 671485779, 793369065, 194066117, 582847289, 632614549, 975744545, 371015512, 65557915, 839996732, 527563790, 397809138, 545166283, 286871910, 614485610, 414220019, 638571611, 676463978, 104507271, 404266615, 563984842, 92373741, 443660026, 782021062, 740984511, 425208144, 132137898, 920314680, 207812239, 231709949, 630650854, 883027319, 301415119, 636372389, 904746010, 628918823, 597901806, 542240509, 148602930, 301521930, 938845736, 147558761, 125010176, 434865768, 893017002, 176337292, 159803835, 221593103, 614271272, 458973493, 251724221, 241794054, 171498401, 387691713, 646825575, 590832065, 522924636, 955870620, 217606630, 934459132, 246635166, 587967343, 918084339, 499312715, 519785369, 905196335, 454352799, 756354124, 978529303, 116140730, 340328435, 652521384, 473595741, 616462749, 613725383, 65208846, 995972840, 239083313, 456178189, 77812728, 388663976, 86468800, 12846974, 855975377, 747151573, 264042595, 344011976, 587691331, 849724955, 455285195, 629496876, 457795934, 690120475, 315251013, 36225058, 599349420, 530311021, 841562363, 703644912, 718551986, 148456834, 422413765, 78058721, 841855198, 721324184, 754150913, 721302454, 195458972, 151601647, 627558977, 91647346, 667557836, 240075416, 615608132, 502577048, 808882450, 94564416, 493028038, 404974931, 968860292, 94607542, 677418966, 749979281, 627191436, 694455697, 564903220, 363176729, 873109574, 505960505, 412907149, 710650459, 97829074, 11502198, 369687528, 761659514, 318512980, 66284669, 437135567, 368157459, 800943490, 972238143, 478428633, 855538266, 321983088, 656874977, 43681349, 541679947, 937934651, 244457206, 315193894, 319702720, 707622371, 246514147, 151533229, 568852457, 147783131, 969033312, 186736567, 320865792, 43514826, 677033573, 923317185, 612412973, 174104992, 918151958, 109287585, 938927103, 518114981, 973941256, 476999701, 213068022, 622903875, 310474359, 854886680, 957426811, 376010753, 292746941, 364603825, 894105052, 25691539, 82514570, 41302710, 581779951, 808558692, 320060428, 942222083, 193766884, 133525587, 75843652, 344895825, 114181286, 902391418, 560401494, 150645242, 473837029, 602564434, 717678379, 346232561, 466370994, 866990082, 3834409, 155888557, 129581803, 574303958, 550156176, 939048536, 960794611, 258125498, 164255663, 912945696, 467031278, 692140131, 293004792, 881572784, 254026801, 975419815, 509495733, 40545634, 595775609, 533700414, 406303121, 272983543, 855441483, 374977887, 506247381, 15507237, 989800636, 626362399, 847726484, 800361614, 286496808, 551783517, 469648486, 98477765, 262270214, 278412117, 645054522, 381066485, 678249268, 454880540, 337197715, 324727694, 294254312, 32320770, 716401083, 189210077, 539629752, 991692968, 97928103, 138748467, 122118363, 56445737, 935953238, 842913032, 49339139, 817341832, 580293005, 431004603, 412224203, 323570307, 640667962, 923952619, 210850509, 510149075, 567926853, 739333898, 606464540, 908244944, 834436987, 943114090, 957211262, 855416901, 726545549, 95757850, 784254781, 776838250, 115526066, 76943826, 7075090, 767893226, 492000293, 655912102, 162928894, 361102737, 586811697, 807176898, 828391266, 674294882, 395508648, 157516832, 831260856, 780420911, 187633507, 693019071, 201546504, 672613503, 309318515, 304158474, 961019147, 700749772, 560211331, 412756014, 697195225, 602351670, 330297457, 688652858, 149390597, 568442948, 413437837, 204524062, 148404701, 187373647, 578422728, 861457778, 135061794, 680453851, 543602229, 326917305, 568068662, 567285833, 277393172, 918263837, 848761695, 377760905, 670300677, 837317536, 249837952, 668141962, 385673896, 237739756, 499015005, 827443254, 560260997, 93880803, 644443431, 490962463, 884477836, 9480277, 415888417, 483301306, 367902629, 608235548, 183589386, 997954070, 826816799, 397448238, 196407170, 679717571, 764905576, 291437702, 791255920, 265628348, 519546385, 328385073, 371763061, 168918225, 645529856, 519775673, 348694272, 155986276, 691704010, 746828005, 316718435, 714200737, 705217259, 762138292, 61471141, 41405878, 864679537, 965049846, 857917199, 914065851, 297494779, 876089636, 635899262, 926204037, 94995863, 354545615, 822396515, 366071634, 279704079, 50397337, 202370647, 999266471, 975620863, 231932118, 552724166, 802354962, 56911018, 260990001, 300193469, 227265902, 694533559, 837236910, 887443561, 628653749, 21240579, 933805329, 202377276, 362730687, 760799956, 817861548, 675577882, 4321148, 529014530, 153152242, 462716461, 751777097, 9635372, 111223546, 568345069, 37012152, 263910959, 757934347, 823267112, 22658690, 838713863, 463842960, 485466704, 514191812, 301187225, 575397411, 871503496, 415562034, 143014952, 95163494, 552434141, 914352623, 782827288, 957547441, 675335589, 213978674, 209725738, 423364269, 207659632, 529804332, 870081464, 846733508, 443313762, 135166798, 230774888, 772453887, 960147441, 603084785, 821581610, 873550226, 532906198, 969327554, 106693597, 769481754, 777410479, 875624821, 703281941, 858168968, 96377221, 992311336, 361437725, 729139451, 657166634, 543388465, 6348198, 298291966, 522774037, 329746938, 388669662, 408857542, 337014284, 954682987, 558009821, 878125665, 833426425, 695891818, 624613443, 80999014, 436537260, 148578229, 589603734, 452165700, 741318503, 745351065, 416012420, 474829443, 69748165, 61468181, 209961471, 636597180, 272933332, 971687898, 390119116, 59385932, 190160119, 103957391, 995152439, 957384056, 254487904, 109149274, 313907860, 497607887, 882992268, 172434063, 746682614, 567861392, 214326277, 192671228, 314334650, 220102757, 476067300, 388342175, 842080160, 62572951, 843400948, 577532749, 697815406, 458566967, 667916796, 822303737, 733086053, 667704760, 796179867, 632461880, 95013406, 882537747, 739058720, 173938160, 203702024, 649819404, 914530325, 364874164, 88008999, 978004629, 131000503, 875636820, 801191869, 341948558, 125410393, 800739301, 436984809, 269791410, 912162923, 209266548, 420809580, 856139458, 803681309, 333725918, 751236985, 141033795, 285345536, 215591021, 89813724, 269198260, 153095567, 958591561, 17299741, 847021230, 303964896, 82246950, 465428827, 115525547, 780224754, 869198976, 388291413, 476587483, 691967127, 164826558, 199218146, 401373213, 778742148, 785368994, 496260720, 105954110, 398900290, 219614748, 228453637, 139747621, 595548136, 71518080, 343975805, 540199555, 840531664, 44840239, 589231776, 510546553, 923702957, 286713970, 353758234, 565240608, 794314111, 567420321, 988426956, 457651339, 899769446, 942464606, 302424207, 947012026, 756814600, 676683142, 307811738, 359602841, 242398282, 502432905, 606677937, 620526147, 280242919, 162443412, 476834571, 574493117, 785859248, 739430314, 475070834, 12145637, 409826423, 221112197, 482556169, 304419577, 599005896, 944896304, 378563938, 767391327, 764957484, 698420843, 86518889, 848548899, 940875217, 356832632, 82389492, 141351138, 253057193, 505710376, 768858246, 69215061, 494390492, 486671878, 158779046, 205068140, 927517611, 405213144, 533823405, 636174259, 671652233, 823607725, 970246585, 581237369, 748502857, 603996296, 248077030, 938336152, 487801580, 935653494, 705099190, 609508419, 321068590, 171648803, 123104655, 864070529, 627623587, 153973723, 532757332, 334067313, 301162418, 763531369, 118185494, 277343915, 297058812, 956116570, 27916952, 50987701, 555953984, 374975108, 254105485, 756982147, 946280062, 432006454, 615619859, 41044323, 51176565, 93025987, 464457540, 568995841, 547436389, 234332994, 873705678, 793910941, 718626690, 618801266, 588992054, 317919234, 114701380, 631830284, 965866910, 462662021, 288222047, 940667246, 889946910, 686356074, 651975611, 751283629, 438254259, 930832394, 663817812, 648690183, 830808762, 559113671, 503740336, 564984518, 728178610, 274625284, 917683332, 307702865, 280453477, 894841285, 41921673, 620010590, 784197179, 211836271, 474035307, 279274307, 946489897, 291470157, 270173729, 935838009, 623979862, 556609329, 464487059, 340990566, 434770623, 631662358, 38075281, 842380206, 500850392, 613391011, 18080374, 285250260, 529845193, 631271575, 374291512, 262739384, 985094109, 303903201, 16259429, 810359256, 363767310, 439533694, 865903562, 239947506, 617332994, 12008655, 687928866, 948278772, 502425279, 65739255, 81068619, 232652789, 803273676, 221975694, 952453329, 954101455, 419276262, 385219432, 912933418, 753984171, 879530618, 201860243, 425718240, 278382069, 591339775, 284643345, 41778741, 441409569, 857060151, 654989304, 641813047, 910548369, 326618557, 403218292, 529860296, 934915671, 278218756, 690631372, 789621732, 297657116, 292201877, 300172876, 960938884, 6494442, 408434538, 631194439, 495729658, 906370223, 334719880, 36067661, 265056536, 375085696, 502127399, 559431996, 219055310, 952137127, 981975430, 41298331, 592853985, 429247851, 277759472, 598943926, 621676538, 437256746, 910929529, 391158258, 732923131, 635407846, 946781382, 781366059, 538891546, 630564488, 525489062, 367680406, 315439237, 994056845, 591395668, 663549817, 846533929, 802030127, 788951116, 628933255, 647739058, 409694710, 592117609, 553457158, 673045219, 919656333, 983067109, 468448263, 16864831, 575662694, 249444633, 418119785, 778411705, 525105517, 491573168, 939331936, 108707336, 910388406, 674647760, 726347222, 370136626, 493648808, 699500868, 594882768, 901552603, 716526019, 285354664, 110951687, 416039799, 58969569, 630345142, 744166147, 908464451, 266658899, 135696016, 615828551, 274701707, 302399839, 380580879, 341987509, 326369586, 256745490, 655147334, 405872875, 113280123, 933482227, 802469607, 381541662, 498865114, 495779685, 967570007, 821541556, 290582034, 664037255, 210085915, 483137595, 207842196, 138524769, 164615489, 942077022, 136029720, 110227423, 125519767, 32594694, 580669389, 110083398, 159966298, 278586564, 651514556, 206429803, 241778484, 408295766, 538231054, 40159268, 314474695, 847619050, 392249356, 818770268, 919066645, 294828896, 309466180, 611441273, 586321901, 817309867, 899109802, 759462533, 574660273, 468504471, 521462233, 942808544, 723622267, 56447073, 5157631, 750144953, 763817451, 978331972, 680097812, 105756140, 247015460, 175517670, 420429163, 786786754, 357218723, 613180909, 136172357, 756075206, 552831291, 659432456, 2679440, 330672781, 400354207, 832423875, 829560244, 964790095, 49545740, 110490325, 949908909, 546020473, 972646140, 940082015, 840888057, 725398813, 958007018, 451000364, 238151178, 737105967, 805008075, 870502660, 876656816, 726783282, 129128717, 953151559, 771271007, 328571096, 309301886, 515073405, 387913337, 183620066, 32759920, 92011287, 415965918, 289056564, 409397259, 98324621, 86039657, 335724611, 37673345, 760097979, 321461057, 127630198, 207972784, 975999880, 785590053, 249756361, 163767303, 534889206, 183447255, 616173844, 431146841, 545584195, 147154115, 411197564, 328772347, 533020004, 573015415, 268027550, 972295303, 592287894, 361397434, 651709520, 757591399, 156156700, 790433458, 378147201, 668181497, 517614797, 35349612, 839385479, 682152248, 888691415, 345294522, 225523954, 374725032, 1657739, 771600563, 809896448, 314099086, 851956157, 724387074, 588238065, 822330246, 350784184, 160586399, 849465966, 753220757, 643305190, 204884894, 553687438, 607977918, 592906946, 828887047, 127047889, 916362002, 646657819, 379640414, 204894069, 37048682, 618445676, 762372526, 854408436, 553553708, 812291857, 245342896, 818643249, 15500611, 62794820, 517081109, 731718478, 693874711, 723222312, 106275511, 463569536, 773710985, 823082227, 74109380, 913000930, 115385232, 601861096, 851806615, 458866271, 790228285, 225582710, 725226169, 549874551, 985873222, 244807331, 312336424, 237392741, 425100621, 410471626, 565457102, 599695524, 505945249, 65898405, 459141754, 611642336, 465408530, 718916847, 999608263, 184154573, 147043989, 42648971, 526225092, 532929887, 670305970, 708711188, 904743600, 393293020, 627857070, 200848627, 716941864, 588437201, 338790662, 285806616, 386784331, 804780404, 705101006, 998293510, 512042853, 181595844, 433426612, 597547510, 394286849, 881860372, 507478255, 340942820, 612963310, 273101543, 785931568, 300451863, 720925724, 822463727, 666616362, 514973587, 908630781, 360136153, 14157790, 202800300, 352175084, 120615576, 601098518, 400010156, 366526131, 139368683, 675687028, 206462322, 857533824, 808120159, 378303355, 639957738, 887842752, 902271815, 599082431, 509531551, 680945956, 1887878, 295497473, 33844237, 735616326, 308706703, 51327328, 355290038, 506187518, 955001122, 664316989, 73014639, 942020888, 499917702, 534270874, 671292900, 151783178, 699601203, 803142442, 842302694, 338390010, 108151870, 5831947, 416375860, 878549545, 759617565, 955548319, 425328977, 65073051, 626723105, 177562274, 325545489, 253171965, 884961558, 382824481, 372274227, 399765892, 328686480, 450658389, 980157974, 230376620, 283288592, 226019867, 668782184, 347965320, 662432974, 909215941, 601858225, 698875047, 573615696, 864841739, 475967377, 707452908, 338579752, 48520135, 409099122, 853222866, 577751637, 835862414, 186961866, 6792256, 159530824, 116003389, 188873387, 439410850, 888735143, 654374027, 988354762, 469232873, 852783163, 206219439, 810598036, 799096786, 899769812, 339845271, 671228513, 282484818, 387257891, 281527088, 510461992, 842369532, 390165392, 725760353, 494110751, 493579292, 311932937, 95473478, 618983775, 156591731, 245883891, 315601869, 333238460, 21921227, 714469859, 407290788, 892719716, 140880728, 945368778, 483567174, 929570571, 980074786, 265020147, 285410277, 595536429, 48236931, 605024997, 490602362, 522728224, 203790845, 193341270, 73394742, 398036878, 888647974, 324020636, 988735580, 505347892, 941052184, 932938660, 590982554, 349718931, 286497777, 870624316, 303868647, 325144471, 567433823, 13645123, 902387268, 672441160, 693576365, 146595045, 317477733, 165494128, 524100704, 83348306, 466275586, 859809111, 806868317, 894945488, 429890827, 187808789, 571308643, 117283443, 328930974, 296656633, 785375609, 795146827, 51710388, 598082269, 574605651, 218219488, 861642484, 36671644, 825058457, 551843296, 595286817, 196687555, 333916870, 39910427, 948609734, 649730018, 535323734, 27471623, 991009743, 639565908, 550954211, 220933760, 968393989, 338774917, 601266988, 984115804, 883733555, 962972471, 434136775, 607808435, 967786190, 543759522, 190978211, 12035162, 542603873, 911386396, 830876821, 157766137, 943213452, 217020403, 431668303, 183505198, 21874401, 529890544, 861287235, 678306014, 891917776, 243362578, 183462546, 671587911, 956306215, 408346556, 446847445, 189250926, 749543863, 125916578, 322871964, 183403385, 420509830, 920375206, 667187876, 317314919, 564865133, 775265480, 640910154, 890349344, 858257387, 166129216, 777561566, 336680179, 339757062, 477887943, 942511687, 618288193, 405908363, 195179449, 59376326, 814316148, 696963220, 139983, 635087606, 923041707, 255032623, 194416990, 192125619, 875822010, 778466295, 762417754, 178452992, 851724946, 663165283, 603451583, 466820675, 387444564, 489932704, 951226129, 894312627, 237444605, 532444006, 448051295, 941125333, 457751312, 837401179, 517862439, 774809144, 110399635, 397328303, 891532765, 564153122, 535222861, 575627654, 577614480, 404603044, 830685664, 992220790, 753430054, 200737936, 181493750, 676755736, 357506711, 622489173, 100520830, 190245833, 187407675, 290405517, 998427396, 558691913, 475568142, 204630365, 126252025, 215499216, 999399090, 196346657, 778120602, 953943371, 164992655, 86691065, 789093511, 563418127, 562788045, 763555483, 96397832, 352570026, 347079136, 67299099, 458503557, 126402413, 959719122, 948521022, 842599317, 306189761, 54162026, 146893675, 43740914, 332199296, 473701977, 905250809, 432966620, 848260737, 821391712, 307878893, 208679509, 747475074, 208629517, 225313492, 975690138, 610696544, 31376389, 507343022, 500203756, 123426984, 575633586, 202344116, 386115553, 501963795, 683567585, 302557730, 248092269, 577059873, 875995709, 29909224, 842674029, 193775658, 258309173, 191079778, 93613830, 561137503, 969278493, 694347311, 763606833, 84102846, 36099334, 23063507, 524427058, 776456252, 674603900, 629369067, 977668389, 256627112, 669047847, 779537915, 24990802, 108199772, 58153775, 323093024, 387373991, 156905804, 409140842, 381844654, 180261234, 602282492, 30033908, 212781342, 523463640, 970405843, 821164164, 761711064, 281213975, 852587905, 685643883, 228256863, 174035872, 920887054, 628433109, 864317658, 660828091, 304984427, 240562939, 961739483, 995908791, 378770855, 575471407, 240429987, 771627767, 843941093, 646145836, 201234368, 68077834, 787016003, 318397006, 65896359, 572492012, 733629547, 852449461, 266102355, 364817645, 146072269, 674866984, 730936970, 233866138, 688102811, 579870366, 835094751, 50732570, 860871464, 506278883, 596523904, 667937361, 971384940, 344103519, 927530647, 765467001, 273871306, 721138022, 533349842, 468889904, 52289711, 251223215, 807985294, 801408231, 568230456, 500573171, 947829269, 55842552, 196515563, 411183938, 597155107, 948918818, 938215126, 205887306, 752194869, 879906757, 139745061, 923842816, 24066568, 411487316, 314370183, 972833125, 905395435, 718866644, 43076332, 150290338, 180552145, 242632913, 606595592, 476045726, 591634610, 399216015, 647652191, 523818798, 900111429, 874985964, 75273202, 202545741, 367253434, 87105484, 821352128, 191318699, 912394206, 223193589, 618457975, 726079201, 418335823, 766950782, 367029696, 380996546, 236085862, 972077135, 349853625, 899810226, 776177314, 211769285, 460449764, 344457303, 609820486, 134249923, 223686108, 631816578, 157185903, 978492275, 686712006, 487692575, 786079162, 349917358, 579477794, 683244920, 559965022, 507171846, 999446489, 939467661, 678609634, 471683577, 722612735, 475200418, 42716543, 379291026, 138620823, 210300645, 410810852, 632191566, 328313887, 514270304, 862969025, 922228877, 219336923, 453267418, 644842451, 692143425, 194308408, 654857508, 475979092, 986685764, 505865921, 45431500, 784604252, 910417277, 172981760, 674508436, 197771671, 341775058, 693500545, 150014449, 922031409, 120547578, 596141549, 552517351, 663522975, 628266045, 232726237, 385088146, 476638105, 429188493, 922070051, 582234457, 688305146, 268822503, 422065389, 948837095, 578917876, 65947863, 415793233, 260475285, 568980188, 220247092, 301422250, 335473726, 799603508, 409011091, 587812686, 640408057, 939230175, 753909039, 93786140, 139351094, 585716936, 249764480, 433652594, 383064094, 502493060, 450357753, 564888813, 329952028, 494021420, 368742086, 136131774, 500262906, 514506248, 648367112, 769533506, 21362275, 261037114, 130922504, 754439133, 356583134, 915386257, 173450005, 145829401, 662110683, 320839175, 629525455, 861847203, 391839613, 68485761, 159647814, 567205572, 264930580, 396047779, 40830458, 971528309, 992960135, 644141981, 980610134, 790660511, 843001054, 463767695, 872856874, 348117584, 362155417, 700223161, 251530266, 703123479, 843609253, 287153400, 684695921, 24294327, 64619053, 430509216, 5535408, 364855221, 216252366, 494269991, 565374934, 569438153, 875021843, 35908900, 191059888, 248128777, 976003117, 391798600, 441012117, 35603765, 979182069, 667183120, 437502496, 660160992, 954481444, 507457398, 279789936, 236927893, 44828876, 961794453, 355864099, 891339068, 357380555, 890833944, 672124442, 387191492, 904114560, 342241456, 95842192, 770976086, 400071999, 200993347, 532632606, 420896044, 550880999, 327312089, 644574214, 826391444, 799542735, 178520247, 172865881, 641165134, 355276926, 529987410, 292581900, 571827285, 913885755, 593604134, 854705427, 831695228, 255149343, 546881209, 157735061, 727301779, 444353680, 183378589, 677468284, 444169241, 403793734, 146228770, 115401781, 655478758, 697156832, 905229372, 327916754, 340328987, 629658581, 180459418, 377734215, 338524545, 157612136, 540442921, 44060964, 770117833, 873232404, 143234248, 530657517, 723910594, 499154449, 467393563, 959536385, 756774981, 466533196, 397934900, 248544900, 179789119, 696026537, 328416502, 677556317, 879654039, 908491866, 499694503, 612153280, 50690817, 754982016, 864031461, 276547308, 510551083, 92808679, 230421139, 881118072, 314850224, 398134822, 912751832, 700455216, 683522842, 848340098, 357988891, 231482227, 736121406, 650307042, 439406754, 5269883, 852243048, 917264347, 944841639, 179266524, 986206935, 34100607, 453158224, 768772074, 77863769, 417757491, 779077976, 202659886, 311676037, 633237603, 632033527, 75184980, 351621068, 534885094, 370241061, 883757060, 24940775, 647072145, 797577787, 295667845, 209731541, 366515138, 967280381, 827198637, 662050518, 165197128, 93064991, 12480738, 803654448, 960674346, 644662980, 317775004, 508046065, 605598627, 381932889, 966613067, 479208615, 237942, 132807274, 348879056, 342228696, 398745278, 332848111, 953586590, 712266003, 416695282, 164315623, 457716430, 265500375, 497292935, 615740213, 941487998, 803623220, 111777967, 191291008, 340419451, 289078666, 779501034, 692034059, 406451188, 168319487, 988789698, 157806189, 546853679, 530019528, 70923557, 170433599, 49346601, 245239973, 736775424, 659778704, 494464610, 406390591, 847422678, 63150509, 873437124, 965923778, 189732724, 407546164, 79818682, 224072676, 983054273, 446221821, 605247048, 391687658, 306914395, 665981289, 629504354, 524324867, 550458303, 466846322, 958879745, 440990974, 519040055, 628347281, 715882785, 351385847, 189338738, 146730375, 904936781, 788502408, 207205255, 585712817, 834928065, 102253173, 899589233, 232792243, 667851483, 548098912, 419932273, 635347437, 432137871, 612550229, 240205903, 100990189, 637058796, 257979054, 783535295, 140744602, 720165370, 301991051, 429438343, 655269231, 451445847, 747168984, 750309274, 192528164, 840760752, 322858697, 864087230, 537446363, 625372665, 959244184, 954380412, 215175471, 994902083, 337787818, 627946849, 153506054, 32594167, 163944421, 68792836, 951804385, 689809320, 988796, 617140490, 462533660, 989461326, 239553883, 5275636, 351913683, 354493200, 306106263, 896093664, 777163988, 388892110, 969200263, 432699436, 399333230, 865649213, 315735264, 339510899, 48841240, 959154535, 196390113, 936800733, 987910316, 587767903, 628688348, 214929399, 635016922, 402484538, 54274782, 964016141, 96419567, 719312253, 796513005, 212395401, 436868416, 913955398, 839824756, 144816732, 932550646, 363261294, 8150038, 131862794, 47651253, 271163838, 71333157, 959437416, 251116023, 334350377, 441978082, 482208332, 119886200, 919314482, 259782012, 805173857, 853947531, 341491009, 348613538, 811627937, 680532518, 364248586, 936652587, 887138913, 606014123, 422482389, 444199743, 91709587, 40752608, 459622866, 38196607, 536235645, 984619670, 148194293, 935319667, 688448790, 846749294, 579461984, 480885430, 378858015, 94953553, 191995067, 207937545, 736953365, 975604258, 937269344, 455751814, 504270149, 283014861, 38821673, 82903279, 275591785, 888087294, 520058947, 136143289, 926955376, 387321583, 403353800, 924789613, 392738961, 982101939, 232164345, 227372861, 43706433, 523906916, 338394518, 856587020, 978050942, 443366569, 529420988, 911303814, 793189343, 983198322, 804089434, 834536396, 153815203, 116734980, 719023293, 123420261, 79355230, 886206001, 41561521, 21245922, 882598128, 802153839, 835570763, 581025419, 353269670, 637518139, 175035423, 289620543, 484969222, 906376781, 326275251, 416055608, 83525663, 290686771, 206000117, 5414489, 232258026, 920013199, 421357416, 638770384, 259399235, 633440765, 254069496, 990306919, 60820729, 789819202, 121607634, 405772954, 175784667, 478551926, 549390659, 363765094, 664199082, 300776641, 162775216, 950937760, 112220685, 793459334, 705609734, 578401175, 861996799, 271109784, 874564088, 608584611, 737482328, 17113577, 929523529, 535041412, 839587191, 762589128, 338613969, 307302500, 423136008, 547907, 54172853, 814028266, 492486382, 204797184, 844712890, 440541410, 231508943, 734350035, 140786739, 531768651, 398682782, 289289602, 857372009, 38391524, 737013357, 991291813, 140442455, 640977650, 313606365, 190519486, 164035814, 602873588, 52394808, 167969803, 137247806, 579148818, 528906751, 98556152, 312148785, 949596197, 341635564, 627685819, 939789923, 585542633, 684928267, 633716329, 581654938, 842970524, 672621182, 774099668, 342032766, 230741096, 259636341, 814292819, 159696778, 974589013, 777527475, 220347264, 497713903, 158181224, 850380443, 776097726, 117189742, 344816497, 298617280, 92404578, 517134792, 632871155, 986801197, 86752488, 638367832, 828714983, 810787638, 266157015, 840453364, 831146850, 698869563, 669536753, 521100728, 941076562, 492976844, 235369733, 79684549, 759531250, 822289697, 828261642, 696541825, 272445587, 12980645, 614574700, 789162046, 613313390, 197966883, 637070437, 190199657, 842849148, 626405347, 184932012, 564481782, 489411882, 747191807, 417614033, 478611791, 548477044, 227121878, 496374065, 670306430, 247365078, 601535510, 704465934, 790108567, 804443516, 491371393, 812767752, 736124257, 435729866, 83458191, 696845148, 282825379, 516334373, 706930649, 888348494, 9725931, 67773913, 119998380, 239860647, 273783638, 946958097, 753062630, 674142600, 559574794, 526200373, 327409529, 374340434, 816827877, 276275850, 464368219, 134908857, 877948404, 844633225, 684705435, 809943892, 442338665, 64327905, 641746026, 161977855, 227074529, 232142609, 721920521, 230252751, 333678045, 230646920, 966868506, 775321550, 797772980, 327120684, 940771083, 611747586, 117592551, 86884416, 435401596, 992730768, 664018630, 222178792, 508854385, 5289468, 990682193, 55030701, 60146826, 694724425, 629912141, 683136730, 680648591, 463923051, 733324705, 823418284, 550746033, 640696395, 968185801, 606184055, 781016585, 764359708, 496302912, 368687512, 71427394, 769173012, 225556895, 156978817, 760572357, 708487350, 645932835, 566129205, 748034106, 461030046, 514070705, 326793871, 902729332, 327225515, 471650901, 329790797, 594725926, 837325917, 692810988, 301225441, 719351862, 605785704, 678100717, 706154662, 234267995, 743485689, 359661731, 620800772, 469349219, 493857367, 608649409, 245201316, 543574484, 175280898, 122039552, 920059477, 106798501, 32604565, 312564112, 649816044, 107950056, 995080378, 828541086, 926759341, 683044161, 93865092, 842130278, 233856957, 575561081, 417264443, 828599397, 507915860, 958353279, 776909261, 503619046, 985531211, 135123129, 141522842, 282405594, 79826741, 776430144, 646995613, 662288733, 48170781, 972830926, 17570797, 778431397, 86799906, 692890527, 466294228, 198854234, 386212263, 959195598, 380758846, 928115291, 743917777, 771383689, 916249690, 657310607, 200639965, 541063097, 378454077, 771447280, 193767848, 645469154, 721345088, 480342242, 377507308, 318721193, 977451452, 520805658, 152456650, 79519384, 468326406, 926399365, 153051586, 546478516, 233129817, 105341693, 812786730, 535774792, 191421323, 431176792, 686357462, 783701467, 340487508, 950220017, 269455288, 717833928, 664962068, 717077079, 37993833, 881880849, 317764558, 817410905, 737546614, 665341777, 997055871, 738408248, 998749394, 485058559, 114912422, 585157644, 400414430, 449119574, 737269784, 357474190, 506736555, 886592397, 603292505, 400483346, 148861622, 860201928, 384029232, 933890240, 803611260, 42374429, 725120069, 538172198, 117214244, 210366484, 995015671, 806029505, 542686213, 264725932, 949734597, 467477514, 660946009, 226031044, 493635496, 116812476, 239416381, 816364087, 501064377, 94123502, 223433347, 814291496, 966061640, 396440579, 902554128, 818219844, 26662668, 8145063, 891182964, 301150699, 942289319, 597144559, 615949534, 991148080, 209759054, 176076728, 676032041, 728001273, 387787518, 980952084, 414488836, 591105209, 75506603, 968092101, 912517677, 674396973, 595462784, 956628968, 633945835, 222067206, 243327282, 199162421, 142658059, 526124917, 399753642, 463613079, 963310731, 58973763, 367309117, 750506295, 217426364, 501958884, 340186774, 594951756, 246495555, 833830554, 427098258, 336154838, 642618099, 936862422, 917625537, 186764230, 85511602, 543894100, 483131693, 617743616, 579357485, 620307632, 752057352, 954458915, 316381722, 733549732, 932633931, 134666465, 754363211, 617979699, 435132556, 318393788, 436959830, 506409734, 893107690, 573350394, 799046286, 610037459, 258173258, 466980807, 863968084, 878417424, 882424188, 452122664, 655089840, 814346751, 789852255, 189786543, 374723889, 126288717, 823263878, 831740406, 840034404, 336705680, 392939913, 634397065, 61959603, 429456570, 493171187, 225704558, 884518081, 610186030, 656854008, 396402455, 378561162, 586046855, 688707749, 578405131, 659727570, 120584564, 870946237, 929391278, 664171898, 41527067, 234250825, 627098116, 944103720, 178241433, 23357054, 102202027, 436919143, 195324733, 778574703, 441840888, 774604687, 284370538, 14837947, 959018598, 134746567, 933129655, 803403596, 619978688, 525907217, 976491274, 132339946, 564610036, 68528049, 389578068, 989832168, 852794652, 752963774, 817344610, 2175492, 31769154, 30207239, 508011170, 577661754, 572533465, 895501268, 930462615, 52583075, 446568982, 324027072, 699345576, 222155152, 988261700, 193585184, 899817097, 807040602, 685622895, 221944175, 653622261, 375808257, 546116059, 987504566, 939132701, 402263877, 78495990, 185167756, 500442747, 745618586, 501682375, 285500964, 628769051, 61112643, 592508407, 536386652, 505469622, 969104685, 718855729, 246466021, 639499015, 742659544, 764508186, 887760828, 598519622, 172825867, 529721202, 591832295, 92126069, 128730325, 209738459, 499212820, 545723452, 148651818, 22156209, 831119326, 93907249, 378571177, 521931488, 673485766, 886997435, 173173253, 8855849, 856663311, 639863810, 855169942, 195032029, 91940470, 802746786, 12390419, 989698005, 901360539, 611728989, 291595095, 817343737, 933406536, 613401575, 107779947, 318738241, 407292649, 193003606, 603995044, 332905943, 410242493, 447706464, 167943623, 753367650, 900631866, 49724267, 457139923, 259468341, 795317177, 453161880, 295912923, 319075308, 833711198, 526362514, 415762150, 644266175, 396161806, 960393978, 483401147, 448954954, 470329633, 782231159, 915641341, 241237251, 891944204, 41644296, 394296124, 172054401, 629023021, 398337426, 790859938, 148727291, 975268774, 428635233, 293668442, 637227057, 570337407, 288171478, 220450755, 677002406, 720765819, 299043334, 41869068, 614508726, 903127830, 378222859, 694368989, 777944907, 554866455, 209260534, 828689205, 293808509, 68438572, 509317278, 397658561, 90224766, 68564642, 82634355, 592209934, 151321972, 958498011, 467018262, 315535932, 476758554, 550857828, 542659378, 785149422, 649202188, 195930157, 979265943, 373754188, 851859159, 391540209, 50758448, 626238561, 711993530, 714930627, 965676441, 278379328, 988034508, 481070718, 130440810, 169596339, 140852140, 928297547, 756569584, 238789676, 425689665, 168655364, 612992760, 88027537, 196565643, 537543813, 936370302, 101399103, 116046068, 309905550, 181893451, 387172781, 519505265, 900352881, 532825690, 918400436, 679048648, 725189293, 374281068, 212404153, 195052723, 838832869, 812243937, 669719104, 755865052, 10330155, 848017965, 67894241, 852647477, 650790487, 45654714, 443421691, 275975248, 471103353, 702200183, 679557860, 148615974, 612735399, 922149625, 536411152, 861586923, 927589553, 19878211, 111640500, 734578966, 173981915, 726737212, 607826374, 40429104, 840534701, 482848616, 92257741, 394851888, 60587561, 980470590, 901243323, 841551715, 812230245, 72238684, 148412157, 740624302, 85271181, 215138774, 949274441, 812658657, 136587012, 546301872, 784079050, 472075136, 417121487, 303596227, 154445833, 866652278, 423463350, 743183358, 330425525, 938377700, 325554406, 951848840, 62057060, 532771872, 947984754, 349859423, 773076066, 39870106, 760227438, 985777641, 806906099, 343957858, 476955034, 936778342, 886410244, 169689349, 831622769, 779937363, 180246177, 1864975, 798052484, 860058396, 811820357, 848400894, 37642362, 188605529, 382427835, 624139622, 572864427, 116508282, 387760183, 949818762, 682698986, 219390863, 152172167, 171729470, 845788080, 975624748, 174651179, 124028005, 696012657, 63286532, 893568093, 944196508, 7870538, 924483817, 611245146, 995764475, 996002315, 526452867, 862674175, 288582555, 619141754, 951214007, 473069720, 121350279, 515732870, 271806590, 969514067, 962538498, 269196741, 422849656, 149771522, 202280026, 123301201, 394749690, 189012553, 157496805, 83876881, 603548086, 104432710, 217905133, 203086298, 159477087, 689296098, 584639901, 752913887, 588302293, 194386109, 172854974, 422899882, 325122776, 858293656, 403930416, 921376938, 148356228, 593533321, 979032008, 42356643, 310228148, 883927150, 771603459, 507250036, 903691242, 361576332, 383422081, 805140676, 981225537, 187472457, 462810224, 842807203, 373338162, 814232926, 175485488, 963209488, 356359572, 916162665, 560411381, 90680011, 394636855, 145278336, 197129757, 43447567, 109623440, 400799273, 943410775, 135727611, 786375041, 359361152, 392350381, 978299347, 421737277, 963813499, 259712316, 445055621, 129621700, 82182904, 41952078, 388717787, 542654401, 350831712, 804436293, 72767780, 545602998, 146910197, 124237493, 19498315, 410618652, 901438685, 228866006, 111927177, 332735159, 251635502, 434709091, 569425895, 727446718, 311138708, 250607238, 546621198, 535768892, 185290278, 788333312, 819706302, 391838647, 805031376, 456925491, 37617435, 460717650, 676316300, 267935791, 841420225, 916231290, 67453678, 773031427, 456014449, 278987176, 551660904, 50060068, 156402227, 59723882, 510124985, 474833491, 405908489, 29992137, 695097794, 74704573, 876610930, 276981263, 597418172, 593938193, 181904189, 540398735, 407525303, 67156597, 561695106, 667726948, 670265327, 905651785, 667270199, 101270320, 113836583, 257318426, 818169186, 595877591, 75639531, 169700260, 424356478, 379424773, 537966365, 229715291, 946822746, 477273277, 908800845, 72542458, 814116834, 701778880, 565385458, 65268207, 786876292, 72233639, 110506726, 701758044, 14972909, 671017633, 590328672, 470666051, 963289684, 114781700, 335219636, 217879039, 430405734, 713517926, 138010599, 909081787, 951103468, 445072073, 353341378, 396315505, 733495942, 378934368, 343031716, 913222453, 368990102, 678288818, 997471553, 197247341, 361095419, 152720452, 412107103, 25090718, 378475051, 424379828, 842239826, 962310887, 428054252, 801588166, 621973799, 424646024, 214376988, 600492402, 333958466, 176356066, 26119317, 964518356, 605227459, 146184450, 483711666, 71093929, 775099119, 242858655, 266557804, 867084957, 565052140, 455703953, 603029522, 295730989, 276293444, 114645502, 704000847, 832581784, 335552594, 855789701, 5842676, 470367434, 963066997, 673030727, 351896632, 871762656, 131567234, 752505123, 200415132, 298926229, 159758453, 36998404, 625465084, 708495206, 888429604, 983832571, 943990071, 524867871, 40597223, 947276784, 97390584, 667819622, 497898761, 599406046, 903406565, 474594333, 264548024, 708852662, 649626804, 956509499, 304402295, 441372491, 317283299, 116583550, 267276167, 867174900, 853305162, 177627319, 139358880, 631321982, 570893703, 58080033, 930414265, 144179682, 119495694, 646996958, 831874712, 748687984, 203718163, 496494626, 411185168, 93578425, 144984454, 343774265, 341750089, 287209666, 469067422, 628093006, 12857439, 530730777, 201151740, 445533652, 113956597, 64902286, 543564291, 480831556, 402495426, 839959847, 26352747, 271318749, 234900094, 890557626, 55366060, 135261500, 352169035, 654453741, 595480233, 735972539, 537686762, 98027874, 430085186, 802112014, 391350951, 357768319, 175852260, 755205019, 607774208, 826462337, 475333570, 451038508, 766358286, 309250490, 686434787, 166978624, 767051814, 204618713, 314450975, 669724539, 165470522, 328333526, 463175624, 493971516, 787201805, 983951356, 487013117, 407173940, 969022032, 834923695, 442242889, 376061726, 449338563, 410355556, 924675522, 688947172, 230738108, 516269140, 187168330, 926029362, 875378489, 978194160, 990708989, 805467238, 29748058, 641483213, 515346041, 516280837, 106762413, 533555764, 490405735, 9864996, 467384782, 93064584, 834468345, 473777184, 378464598, 758052874, 175524708, 937680017, 894703796, 2951116, 719767255, 631945485, 160938715, 649928753, 591967553, 217278567, 637815832, 587407452, 739716280, 249168782, 705661322, 573401971, 240009214, 673061644, 809591872, 769886894, 191652211, 85173834, 673767379, 628194447, 718240244, 491011642, 907632157, 925785719, 240958695, 578073000, 661236255, 582842566, 54509105, 854573623, 140502660, 553489937, 359052203, 415415040, 434722447, 7609856, 772571215, 834548950, 208463047, 449807018, 453381687, 164326574, 331964190, 5054600, 84233475, 88977912, 746099065, 758041399, 547068180, 805438509, 773563029, 770198108, 149171205, 701009037, 629139216, 547647580, 214633087, 66237099, 589914642, 564777435, 490815990, 241281060, 794748059, 246458405, 111738445, 86978922, 953402790, 321724290, 391969597, 117149113, 927039158, 273952307, 468609900, 772343597, 9109651, 339825306, 32911062, 779632385, 543999369, 552961494, 823240097, 792437594, 406717659, 415013032, 536358382, 575890392, 560260186, 730859169, 137745509, 257727000, 463253652, 151398077, 527596230, 769303810, 535008688, 242267394, 873077554, 998621103, 65499778, 795928034, 86579386, 128188036, 312203782, 59514853, 5904825, 855885859, 223762137, 276442813, 971482993, 316412432, 681535046, 182471375, 734632048, 74297839, 795712600, 36964232, 875595291, 70824870, 497776980, 378952797, 980079774, 934843263, 525706500, 232231657, 964358814, 777830705, 399775779, 666887094, 834827732, 817635326, 928976038, 675809044, 926869232, 324206051, 136418282, 179916994, 160721703, 635348796, 773105107, 254059825, 389004116, 886695590, 489134407, 41054844, 158807444, 743353909, 346917425, 226770711, 461225589, 529517610, 60880683, 192375707, 156750730, 891944655, 248616794, 919332852, 667921994, 15439340, 144922386, 379146611, 117920319, 653980117, 154866841, 860198540, 927821069, 819586504, 487430164, 72503814, 285984179, 305997496, 355312007, 241845160, 311439121, 363509536, 546519230, 121473300, 782806911, 494716501, 41179982, 879745790, 946597404, 565121475, 384288274, 109779356, 942216665, 337784102, 299813188, 249587028, 654271582, 604322816, 614252739, 890190706, 180676447, 273609009, 464631823, 475450804, 1387848, 919237257, 536111351, 682036902, 284123433, 503197698, 731697972, 724387577, 96576362, 994515704, 644406022, 511605503, 56983986, 385341632, 195754827, 888576413, 991778731, 85705535, 547921744, 738854245, 595646176, 305777186, 9812011, 90604793, 59801019, 72083800, 164776667, 553327335, 474104069, 196115549, 305828712, 766394630, 226216332, 476930214, 134258336, 175750098, 915916926, 560344990, 250780832, 700519324, 849888384, 535666997, 226081487, 117696605, 473366546, 425232577, 692018403, 383836476, 567346777, 467668915, 577504171, 591480837, 989473615, 19449096, 730631150, 3634615, 582216604, 207504315, 127856782, 732703644, 811604508, 47708590, 457494135, 921717233, 453256414, 479354105, 284057677, 481276346, 880906897, 308919164, 509320444, 455344012, 39062108, 245216294, 689666091, 583879851, 753776939, 76019325, 185502780, 764386186, 127281691, 390063331, 487666649, 180040374, 495222730, 576833538, 496666713, 130415580, 777667990, 172939946, 138197276, 819325672, 800662533, 389714475, 350845994, 47880373, 884562193, 565807830, 410182581, 947449535, 975166896, 568590954, 156435551, 873823892, 865347823, 490277152, 436856422, 592960178, 273616719, 947536904, 82923811, 90752721, 940533061, 542968666, 616655846, 604266893, 180034542, 798152673, 963239864, 712431389, 859015158, 894925376, 535365232, 278552083, 235714167, 383088338, 894207757, 773690912, 917988348, 359228694, 19255502, 121282436, 987110210, 183223336, 915697365, 968877952, 682810434, 327849815, 480660954, 55420300, 429875271, 168772948, 522858392, 183347272, 624398734, 912957677, 635773584, 664400120, 868341768, 444124933, 481129811, 232553846, 622993447, 981453433, 919685243, 763023738, 580068865, 404061395, 73302775, 261093153, 454921925, 602265643, 625904679, 470855250, 241320699, 128144006, 452776406, 673879859, 313704661, 633674090, 164618379, 406609439, 388918054, 808416901, 99091899, 378208174, 785828139, 255204944, 3025348, 311390035, 62639590, 909752812, 367892553, 760686451, 729530198, 207578121, 941654441, 299439868, 535030884, 482375111, 450725000, 365749011, 281116466, 304638100, 207322911, 662393283, 214682507, 318746380, 471768465, 644189076, 269262526, 48551405, 959827068, 429553890, 207646003, 963893965, 204018865, 941950525, 10757157, 274586764, 226460246, 564477529, 464674806, 811065511, 188278643, 391339986, 358800233, 299879396, 81023401, 66393041, 60618578, 575201808, 386219738, 297821220, 105663972, 682834596, 895189028, 998240133, 211084501, 217176470, 30913701, 543152230, 410259144, 584852164, 162115585, 229227241, 439291641, 363877115, 244507485, 994597777, 378468091, 452453755, 487249800, 306379784, 416614293, 812865581, 441876356, 580858934, 27138144, 682275310, 65400244, 255910189, 512233766, 600709240, 652574957, 7723021, 655097138, 200604350, 263635160, 597331428, 831078148, 740381950, 141977296, 940405956, 857439862, 523641078, 31555623, 540375807, 441549207, 963633461, 633266135, 426087812, 670096855, 304073694, 638890865, 447041499, 831418753, 487633396, 555411193, 179689553, 556999303, 772362026, 16636541, 423370159, 930490347, 204104625, 123977414, 545690675, 971987782, 187953982, 957627883, 585900380, 100155912, 715432742, 908239856, 619310499, 1062811, 887594183, 550803003, 567101647, 361971240, 714192958, 848607691, 609009942, 695449798, 400518495, 884180732, 250786514, 581995430, 1314688, 654767632, 548462864, 146060279, 366727570, 526111228, 275693975, 313490491, 231894329, 88967342, 165707215, 137299238, 443631044, 923661818, 872591762, 295519190, 635122185, 754221877, 196311156, 213190554, 120717948, 57854339, 96267422, 212859676, 460502597, 290405253, 295541263, 994036730, 236669782, 14924641, 346679684, 12619386, 242520815, 406744538, 177275990, 817072341, 807375046, 333433820, 550420736, 52395854, 331258706, 758604241, 791640285, 507059801, 661207397, 930391346, 865546109, 536783425, 713229574, 454052245, 775159109, 234518078, 976498527, 648271694, 967940624, 724453194, 999767328, 340339353, 669723387, 818124927, 234578032, 919230806, 294993472, 833600374, 354078748, 777761769, 605070918, 867234524, 102568952, 528237739, 80050153, 799898927, 585712090, 497321603, 31916733, 971708837, 294586412, 549342191, 731724108, 439577650, 527096617, 86992000, 336935691, 266268823, 52063550, 858788811, 299685690, 377855858, 172500456, 20802168, 230592378, 308378250, 498109967, 827157437, 686938053, 759170104, 94657778, 770613410, 463609056, 464735207, 992843021, 213846766, 997538749, 659450135, 977966036, 342913941, 411645609, 763367077, 22681045, 530842556, 860084556, 99991680, 568776156, 140654806, 499841437, 30409863, 726455809, 153809927, 929646232, 594588160, 104580186, 550315752, 449523757, 522783645, 339814732, 24824277, 925448804, 408661689, 908226898, 847302222, 129500985, 317974024, 828517548, 298403011, 751732753, 172109134, 354687121, 789395048, 333775583, 43970852, 658386259, 578948501, 235621223, 892873012, 19983163, 637137004, 825181965, 235905666, 401538183, 493956493, 110543432, 611999805, 33586722, 844145784, 168464905, 700065317, 10358394, 399355134, 778722587, 562617590, 487227841, 824922063, 287760233, 210627090, 79706371, 448593541, 643567554, 813254282, 828922074, 431793377, 971957790, 251458663, 683627066, 209741813, 78098750, 47309273, 399976681, 605110957, 686181519, 740456683, 955232969, 497620959, 110882281, 423471992, 630826789, 940584388, 550876817, 524981127, 508770315, 604987429, 815282501, 354250178, 150125149, 4245727, 72329495, 792719996, 25935008, 414247427, 115841541, 410462924, 39447037, 407563631, 274781359, 448085543, 919079435, 718046439, 595428415, 161440760, 842060199, 654107709, 74077565, 144198296, 45951806, 213469719, 999528862, 26233010, 387611038, 724985497, 294037038, 120279002, 280876010, 463455203, 923936810, 129673111, 783573412, 648972173, 374513855, 181682038, 183423300, 297931864, 526296745, 170064941, 408988075, 171077825, 686999827, 234806803, 608306865, 496862661, 345455146, 976082000, 76357024, 833298443, 210252091, 321005069, 648230285, 656579597, 297999081, 345713078, 556851544, 128092373, 609054012, 946620350, 181829896, 869075287, 328330770, 594476644, 323780011, 929419383, 30557906, 717798904, 438038350, 150308744, 128850704, 205683665, 744926748, 546190335, 102854396, 337140646, 296532696, 649588499, 382886978, 221251186, 689584985, 458231047, 230452540, 754318078, 179456627, 355467038, 64096236, 759586074, 753440142, 702398056, 192176995, 92973846, 254860192, 545161491, 331796941, 49408932, 557438637, 133862173, 460980883, 171310501, 337344882, 497613308, 188478888, 173404785, 325246032, 664649507, 994302663, 914176577, 688417568, 274080622, 868407309, 347011905, 11232230, 919352031, 742877815, 61366142, 436495908, 29314268, 495092386, 885100033, 361972391, 646138499, 731768461, 846950914, 525199266, 803929585, 961683321, 855476047, 700082962, 744639464, 13504115, 740700144, 821288215, 922994581, 195277649, 757586243, 532561160, 47974494, 172536431, 206015852, 837556052, 181906429, 709689104, 686941495, 517652963, 510170793, 30229949, 318547247, 272021558, 391596038, 880756128, 446326190, 593317848, 224304819, 696093028, 169838874, 146760811, 894229521, 790225741, 953270932, 22797567, 929078337, 74449479, 981083976, 556840942, 332343209, 669746120, 67713914, 805338527, 678562162, 610932494, 520003317, 149613525, 790124164, 993765097, 276649084, 75025984, 181639094, 992437939, 190337432, 871834282, 479374308, 356116585, 9292448, 291364436, 469446246, 653628601, 470308454, 430871932, 138958854, 233779695, 818414160, 828813244, 774045121, 755797519, 257722567, 585705943, 493579347, 111871237, 516609643, 864816273, 613065011, 291421033, 90686731, 68146566, 893323390, 414885831, 485875366, 406082214, 124838156, 123396271, 829066655, 285876293, 571444409, 831843708, 700075532, 734124893, 213767834, 198958450, 314174677, 556232450, 659152215, 147680394, 48525901, 246534245, 881467657, 32334427, 26704474, 509195138, 871226997, 919443713, 552158886, 11718917, 684459636, 109760955, 643796675, 468726266, 69674858, 56695209, 454384979, 469271217, 453784805, 448550000, 720153943, 951422898, 677347544, 405882833, 276407433, 347260758, 232865566, 513955164, 666685515, 541485118, 354316351, 741765232, 421625678, 251111500, 65506187, 334535475, 339893980, 117772745, 657963933, 410301333, 41789386, 932946971, 437522860, 97602581, 434555470, 307219404, 118766996, 600505101, 640333884, 46581678, 880891441, 224719404, 973235545, 972917382, 171865955, 449541681, 112687637, 942363802, 205021397, 647713852, 424017127, 299857209, 394498519, 744431538, 635269239, 249550940, 392835764, 694243574, 355399824, 906912956, 593951986, 134396167, 65686414, 342246738, 768221138, 502748801, 313433839, 126158535, 162200451, 789270666, 675764501, 63431350, 527711777, 301394936, 813958712, 714265098, 715793899, 499439054, 14127353, 709609339, 835429898, 768675331, 462320743, 655353055, 173800922, 662294172, 60156741, 758558859, 11246237, 629041325, 51594841, 675050128, 365840857, 787502192, 756155305, 398554162, 300149697, 98297549, 609059145, 674983551, 612769732, 506245234, 659122757, 372858213, 337099849, 37305689, 322200131, 408291487, 246267817, 963744532, 933597069, 216821295, 988781319, 514180857, 201096170, 44991323, 58553719, 58210205, 893515202, 790963120, 286901592, 243069201, 610313580, 132615522, 274828910, 818893118, 358665181, 154591702, 980595901, 163084497, 591099037, 553277199, 297067978, 888512536, 791983529, 975105595, 762057326, 175990440, 694638487, 702010812, 103607990, 43918801, 101348171, 300542719, 269608104, 172365855, 820540538, 202459125, 379874333, 148663402, 612056545, 321314714, 253017755, 90147729, 706148260, 30354286, 193197924, 345548124, 548531230, 706715451, 732113637, 171906056, 159994955, 110332061, 308181354, 47528112, 285475913, 611504370, 438665148, 790077321, 266403945, 365779824, 149909795, 226129007, 151464947, 810096089, 191557022, 52367982, 251745258, 312870249, 944864836, 296399067, 869064827, 968625997, 826101763, 569635067, 363363026, 766807869, 210670878, 560259994, 573291748, 571104939, 768433663, 360714369, 73278471, 397943719, 441358442, 483227756, 339854089, 264525948, 7197948, 150912992, 23592503, 49475067, 501717001, 726731899, 847898540, 323948057, 176494882, 302674292, 142759553, 254096821, 849035539, 9190229, 52079310, 416940412, 586745183, 911221565, 727582765, 2253787, 139009677, 692809303, 191172065, 248096153, 647285589, 483072479, 679512388, 13893432, 14096892, 64861375, 648372181, 249508657, 58703273, 662162111, 577759196, 869729222, 650328091, 962354018, 321442864, 397330049, 947391471, 217077192, 455760613, 291980585, 742815643, 142247100, 803478263, 716062449, 135240504, 829889965, 682072663, 103720549, 297219494, 81056091, 553423171, 791972316, 834664043, 869923808, 388415106, 506588674, 392926971, 594556740, 743081545, 108420818, 220161532, 276505759, 543126705, 247626200, 562448917, 169557278, 660700978, 278773437, 93160050, 299137437, 560971435, 127968811, 714165130, 283749744, 710774048, 578226100, 170671524, 647577398, 941610584, 295069924, 933742597, 316066198, 218689004, 124594673, 397837660, 301576959, 593333041, 408939335, 60656202, 940917596, 852044655, 439335602, 988284094, 974720123, 745746842, 101097923, 767683031, 199067915, 21337860, 983131617, 65646979, 410885095, 106122156, 147277345, 114855291, 220375980, 115762609, 401359102, 331343687, 374647630, 821188113, 837645688, 734266317, 872034554, 854123891, 283789480, 371944276, 764779227, 401694873, 810719763, 79948497, 177310099, 985943124, 451801278, 905515603, 523107774, 50857817, 580014485, 384618754, 390810414, 639884603, 8449387, 813508997, 949563541, 286188015, 647908304, 764162814, 201849043, 333053580, 211851646, 938834235, 145039667, 204449546, 967453663, 854365509, 734056113, 879120569, 588687729, 343395360, 994081552, 797106989, 583918982, 401215602, 912830276, 82111674, 496147258, 271253553, 75943324, 263397413, 591856183, 199086194, 990600874, 671421091, 367821576, 269477629, 105742386, 434564631, 662056409, 65307798, 765987056, 983426238, 117778940, 977941444, 134941852, 616899200, 803768117, 915944898, 87125639, 333312242, 200087782, 730836133, 440229444, 920684926, 97926919, 335470546, 671750393, 335294562, 812272085, 341986005, 192034540, 580717155, 789364339, 730528494, 169441272, 329699787, 684034518, 446108513, 316405240, 44692725, 569065486, 334001546, 655005937, 222931039, 65470001, 533808717, 623570809, 188140557, 859319667, 148821308, 678975991, 761526655, 726395412, 425897572, 350036708, 359818920, 179268088, 424684210, 318562193, 44902816, 455965855, 702691643, 234265962, 471470691, 676770959, 419201218, 122712514, 315409086, 627566257, 658871461, 802772063, 92415490, 223399010, 915173564, 382847587, 999372881, 937832126, 272041172, 904249305, 913100853, 228946745, 679535308, 365900933, 58771732, 898823116, 542446557, 159324895, 497061825, 656217319, 563109349, 848003078, 351337241, 710767204, 690031057, 366613766, 409663971, 943674705, 879827334, 735867498, 468805202, 972014624, 248405869, 955316574, 808733695, 790396429, 162316888, 372426684, 436224273, 543501543, 788887471, 794187536, 570884547, 965958124, 80568199, 594957696, 118405889, 184153443, 882006169, 246926129, 719147052, 505166941, 609211377, 685174900, 446877611, 959820732, 609590765, 686921502, 955635529, 357870695, 891778129, 272796162, 633707602, 637165674, 561733348, 309579006, 550709033, 84483712, 79609379, 78619712, 854529906, 544701557, 353226704, 54613417, 302181824, 474948351, 483616269, 691927147, 925937659, 604138652, 314941065, 665241294, 443225442, 692359781, 123229038, 422834743, 189278029, 292331291, 517800795, 789630500, 109767265, 250592600, 539190305, 971961787, 681657908, 729389999, 603522922, 301040391, 977934544, 447131870, 891802116, 699152739, 651709649, 900423860, 399353769, 187426857, 503289504, 760917324, 86114415, 911239551, 538861283, 513928396, 281186533, 523016598, 636074029, 169826782, 194177899, 333680228, 487898330, 520748865, 783007567, 592028207, 595785912, 913504166, 355780709, 770702058, 2463579, 288124782, 863498929, 700363312, 455888481, 652797635, 626999425, 830921092, 37523189, 922133209, 261440832, 910871346, 4772940, 855167858, 927523256, 399140629, 944708301, 35944209, 160575554, 673455404, 680118201, 151134571, 756503551, 989304270, 176131493, 65887335, 758216490, 856757979, 685912545, 264483277, 740408382, 131275685, 650292557, 620199939, 837477749, 379131019, 902331323, 275722028, 207513572, 894649640, 92320165, 681941988, 509145873, 324373991, 41034336, 200081107, 18356687, 245762147, 47416094, 712897356, 732053389, 61467748, 422968224, 947408561, 282305639, 353044023, 378657466, 64617873, 354074308, 204995354, 233209709, 815471741, 221356663, 69168201, 912247674, 677227571, 400329226, 579350619, 610275942, 909773291, 139773352, 99017384, 808627855, 929780637, 810297821, 593829000, 400996867, 494552087, 642724586, 890148272, 770205431, 56893117, 381456138, 240428372, 582846859, 403000194, 201657540, 328285395, 286346428, 549308035, 113450175, 561178266, 714701722, 326960139, 551912367, 108887540, 742252562, 314848233, 363234463, 924729902, 336548145, 673171008, 964596400, 407157139, 559300500, 206229160, 57389399, 678425554, 951239332, 315246364, 821948093, 852676602, 565245225, 175309624, 570926522, 73001151, 899630988, 345129461, 562992385, 389460941, 65506893, 774316736, 393172492, 742208911, 18492176, 761183228, 685420866, 540350693, 71596605, 788160666, 868642711, 467717560, 208491130, 414955811, 140836274, 877291721, 69495516, 373090633, 720638885, 720539643, 439616058, 378903676, 965176835, 144022924, 563364113, 200566918, 191657319, 797524534, 751947212, 38962264, 722640749, 786251969, 578210715, 356248619, 144971410, 869488095, 460365660, 62242100, 946802554, 642594793, 829902932, 523196909, 112176169, 395832411, 270404562, 353203271, 815408451, 766568161, 396555446, 234883054, 22700833, 188893034, 530484000, 840576730, 966057381, 600196408, 505819180, 709242617, 204840484, 983431003, 450820985, 351274226, 54243150, 878626764, 798158329, 212933274, 87281860, 792792254, 833030462, 460383963, 933000024, 22950892, 324554972, 15598890, 827249146, 280858512, 505251113, 543669141, 191821479, 382054158, 159814081, 191919727, 80905286, 135046221, 954228326, 136753, 715472481, 134813027, 384313995, 734040877, 72962668, 61006637, 223694045, 230140646, 271357162, 817056576, 351639711, 489051402, 75331602, 706244211, 750331846, 837401918, 765865999, 791310879, 508087983, 706746135, 387914311, 490042334, 669873299, 389816153, 575306534, 396030085, 995368171, 521223166, 770892672, 277928983, 881876817, 480127146, 113060419, 278229428, 205229738, 257304446, 742192751, 647770523, 31286384, 41671986, 428748508, 254410204, 783803849, 182029958, 309923760, 565475870, 697302667, 211658548, 67753770, 363886627, 349085370, 755190637, 653998873, 280414514, 402391944, 89041785, 146177324, 702055662, 496415978, 194066650, 332405450, 475742451, 670898379, 16761328, 794485274, 456275982, 69709186, 219577041, 369826987, 467155733, 523337125, 306928585, 324058981, 299391389, 332327070, 82386000, 114965119, 798379221, 565069572, 862506699, 911068692, 745975737, 822925069, 385827312, 473036680, 1667869, 47583634, 763812488, 514187306, 820515593, 829884625, 972128804, 144870842, 604785158, 952391864, 63491836, 176447834, 381319995, 807450405, 989747859, 3228722, 396218334, 491864957, 481262849, 987540215, 870198171, 97722468, 831574418, 54833721, 951705389, 902353861, 831850308, 719958730, 844398011, 1222495, 1790623, 88626839, 185948956, 527446545, 796968304, 978898871, 361498857, 115490225, 442782839, 303033184, 185685473, 783881778, 166583566, 704312852, 616551987, 319163884, 22045926, 769468357, 144473134, 561420902, 620566792, 244204236, 531618984, 9788337, 920652499, 983427230, 360504604, 928462899, 394880628, 526327381, 167532036, 396087201, 277881265, 363196994, 800902670, 507095207, 153380340, 310767688, 728140202, 12205376, 671771701, 626331440, 184513353, 120456279, 916859615, 567029365, 489290005, 663711963, 318889851, 790540199, 544084693, 663180797, 481963099, 84611912, 280070982, 540337524, 826577814, 410896159, 672175311, 852320183, 382225757, 984913019, 522678764, 958862927, 347455216, 977456388, 331050752, 329505409, 661533184, 370872602, 948783690, 985554942, 685768706, 967677795, 391577904, 683331162, 434145813, 906700990, 122674636, 467990634, 28334303, 212894693, 231863915, 324982284, 979448209, 251621070, 607249478, 706009925, 133743513, 211131041, 528810991, 886969998, 24569489, 886086959, 111192519, 638263232, 787754067, 122686393, 685672956, 513791575, 154039890, 85931684, 388686941, 975747951, 113322321, 430000479, 947208405, 407227476, 525948625, 921216061, 667703717, 967790406, 953034006, 108213949, 907660616, 368526705, 783911177, 186891793, 673929845, 812391907, 429207716, 782930228, 84886734, 457014060, 527866318, 767410690, 507530642, 168425158, 426512804, 634688339, 399692251, 31835599, 83672998, 466846727, 213391891, 516781047, 830258184, 76612395, 614151109, 797081140, 530669033, 991919088, 279253187, 700040180, 171452377, 508896348, 107068707, 287591966, 990520119, 826393036, 350611306, 83517089, 362013840, 806269454, 297102068, 934465293, 226227914, 802687175, 677154806, 476840691, 296898252, 378697782, 389858501, 18375274, 108740438, 913553258, 832341278, 147676157, 470093795, 477178900, 968413802, 652204339, 803978382, 852188466, 912433068, 333827319, 28544569, 983905678, 243983354, 598330059, 835506840, 277552815, 368274915, 148386113, 277705278, 489133110, 876880104, 109689142, 436937400, 868364598, 572099537, 509180966, 818727750, 454222822, 455217066, 899678108, 430728194, 111487548, 89757795, 251524724, 491661990, 914564500, 357069593, 662872101, 514997626, 358596787, 767755990, 334901824, 583583858, 324495740, 931732954, 490877107, 426245621, 501134201, 379227030, 779342028, 637669186, 870143606, 100476740, 106718696, 793232284, 564980462, 903599428, 175670769, 570653681, 531089453, 169822207, 578708391, 18590941, 101477351, 715223831, 907670958, 127649185, 646804372, 449751147, 866861579, 447112880, 727453780, 607395081, 88138824, 122680845, 104260848, 606177380, 727268019, 10750029, 496571036, 577792576, 449619943, 816023322, 181386268, 395103918, 670020868, 575410123, 720260461, 984564041, 694722350, 567410299, 832218314, 217831696, 793724170, 551310122, 554399770, 64843668, 607147082, 478803441, 461016454, 568689508, 464164303, 107038491, 540280715, 216279997, 777156152, 633157802, 3623524, 736931452, 625593105, 222106271, 994760773, 937618847, 578920367, 773719498, 812204264, 158700498, 899517202, 931156147, 478134918, 594710781, 811807544, 529584596, 455117801, 822565262, 612583241, 936350772, 790775515, 278551814, 24070389, 477839838, 361076445, 571049302, 367666119, 632852528, 676992152, 816471784, 473189843, 390472623, 826044362, 323346976, 545406473, 895710499, 600311479, 919504752, 432590957, 724860059, 165626228, 450651922, 209956560, 873883836, 512754176, 756386350, 933381967, 531422712, 970296651, 450248797, 421211445, 70557781, 932014762, 372462724, 460269251, 627116772, 91429432, 392860976, 818374180, 923571800, 660049231, 351478414, 206726423, 818819878, 160519196, 242925501, 663032444, 607088258, 729861355, 459741768, 531542240, 892645243, 949582366, 287390024, 892911199, 4248324, 232176615, 123135463, 907280690, 138293422, 586541132, 569335241, 192311030, 154212565, 500844448, 207746039, 567594358, 421151009, 747344949, 869439127, 271315019, 269160426, 118324343, 55650857, 508516060, 47452871, 184119511, 858547655, 472197352, 707151282, 726720396, 174426478, 692351885, 617487034, 485004353, 166124055, 230414006, 167700511, 468800009, 675201229, 748645965, 239511416, 455426088, 127118481, 95109972, 993928047, 204781494, 570955158, 604563521, 777877054, 116038504, 28493130, 805302494, 606180797, 570660002, 469404959, 799298712, 805377263, 264090198, 240330183, 275100730, 529646464, 638832655, 908216164, 538829033, 254329828, 464039845, 172535418, 695263035, 838160680, 568705832, 393152884, 523234590, 762609674, 209695512, 811502890, 755922462, 298129447, 739272466, 413074780, 168725042, 909448000, 178097733, 851818064, 947253673, 369277102, 964821460, 461932662, 69366118, 982658900, 14727145, 881182769, 467396318, 815142971, 913391437, 746798677, 7156227, 203799769, 953268006, 120486313, 147124808, 371961696, 507395580, 192899474, 204935986, 481444542, 472991263, 331548533, 644002690, 978445040, 192924121, 890129335, 280961233, 962308537, 703691531, 746133557, 340816742, 459212067, 928667465, 73079681, 236455341, 419024728, 309701364, 769401153, 437839470, 287651705, 363944705, 966059668, 517851859, 492711413, 246570630, 434273765, 586399057, 799793162, 973617705, 939732364, 892671854, 465627152, 4216319, 114023836, 537160919, 834943752, 494764325, 18272357, 752898924, 965239566, 284645524, 893267797, 689902992, 460358187, 458449860, 321052720, 472224789, 419753702, 722821337, 752349105, 938075123, 24183950, 309269225, 128887280, 394758001, 948168852, 342360744, 489737253, 236841375, 50431336, 920866778, 858482033, 681449763, 582676346, 729253031, 514737750, 272221110, 562109408, 931614477, 506681261, 793076781, 169295944, 177267200, 602876361, 906156298, 457512350, 981014384, 548721841, 974920054, 261207937, 1341538, 879367501, 808790762, 25668810, 121832357, 739714693, 247786112, 715956280, 903020300, 907948647, 281845812, 910361254, 203768664, 795082887, 544393318, 884941412, 328285004, 659903368, 285531604, 194087866, 369417169, 897402524, 767370162, 879307200, 517213558, 58591621, 343355219, 91576791, 301394240, 993481328, 755592063, 427252930, 355302157, 749861681, 989133148, 944754838, 328555584, 953697057, 221731998, 966112415, 981152775, 922384388, 96624951, 909064271, 429004400, 572510631, 555652258, 73053908, 243710115, 43837793, 235889361, 201805296, 562334796, 969281624, 106995128, 416069283, 741274739, 9492153, 789419910, 808418698, 368384531, 38167392, 979214146, 940259061, 33257236, 207094089, 874003085, 808147702, 684224845, 266810051, 528618209, 293865258, 557794598, 266505705, 840520610, 449439500, 113725153, 980457887, 437163789, 614686447, 793231649, 756836155, 77030739, 434526900, 83085578, 405410144, 303969403, 828576909, 999486980, 690430449, 49510168, 519534118, 272921150, 739859758, 105116810, 990700157, 668953060, 292261398, 492723527, 816884349, 127900878, 359098937, 783659646, 259790556, 468904313, 81233637, 721452883, 37904078, 572550821, 308275346, 492608287, 141611181, 993919943, 244481275, 605781805, 947747955, 471789985, 435251800, 389704995, 494233648, 952782290, 80020580, 259345906, 983056783, 417388680, 764341039, 833874123, 394710507, 523523245, 813137722, 71109174, 712554011, 657255107, 84722642, 394930644, 908610169, 394282488, 80383869, 595321583, 743997594, 699001790, 68611026, 735960621, 549965719, 347232869, 461574188, 442696743, 81748771, 858943306, 475811501, 373065656, 589019720, 116625929, 649003681, 833641403, 524631323, 983449506, 278623974, 644972202, 768999942, 605046580, 556767752, 283901864, 470638608, 476259817, 814531797, 961705696, 773296682, 307833604, 303958287, 572905786, 382986121, 959937181, 95290034, 295862130, 62243548, 633343003, 846679633, 467005412, 723890093, 296424721, 42224331, 601876185, 554022021, 483155577, 401699491, 344999299, 798902099, 685482282, 757011001, 760535266, 809754037, 617220952, 206062849, 897115431, 823101525, 770025898, 421967340, 2599308, 927574378, 986743021, 651736861, 253363031, 200781049, 735562417, 790515173, 373607827, 482732592, 996967363, 235145431, 106985463, 419048714, 449151158, 812368552, 430050791, 952564406, 781562174, 705497573, 992695286, 742761152, 630890544, 12856822, 192490437, 35466045, 287072344, 999259310, 570380038, 823684491, 465658285, 999587532, 95318531, 892730030, 685251242, 702544767, 707753158, 818158631, 674975574, 99442080, 406929465, 366454374, 534246403, 177657929, 272795362, 997004228, 358908485, 875103949, 61760988, 667141417, 58657383, 898835621, 281281276, 470673589, 512264756, 27183530, 818581499, 107531792, 615859488, 745165275, 378360564, 89647479, 789197740, 771667185, 736663471, 672017793, 813802524, 98066113, 787252934, 976822096, 660976203, 942509774, 760121419, 871772296, 629202223, 133330510, 794011193, 463228066, 408295883, 959316001, 220846636, 961313820, 305531542, 480764834, 331508797, 655740132, 856413249, 348782806, 254933231, 776175303, 552725010, 490117650, 753506246, 85546069, 305568237, 556636528, 765077790, 147482121, 326656956, 357294687, 942824851, 90289900, 617572253, 919009069, 830783091, 64160019, 377217929, 239219920, 431083475, 669191350, 568594940, 743053983, 851285776, 64715971, 294019017, 802079891, 339317210, 278647192, 40577196, 396875320, 418388226, 556846481, 660239301, 826491522, 539932920, 127724191, 766950135, 839537005, 250041628, 823162136, 996419004, 599269339, 311513824, 341773724, 552534936, 193731627, 144653995, 107005880, 687974043, 396971215, 862321696, 308095929, 178028017, 859908049, 524425636, 599571756, 629914491, 829312619, 511597901, 578456154, 214636938, 364884952, 17205702, 693961971, 982527293, 993378255, 443494611, 964413522, 571216468, 444356806, 201629688, 615047087, 746414891, 94290915, 725481458, 973585226, 795331232, 775801774, 886341216, 197622585, 16637369, 265308149, 362262886, 301612184, 576375311, 154399619, 428229459, 95021498, 978946048, 123355216, 554977290, 918192395, 57313116, 796006272, 201215964, 934609658, 796991309, 163177499, 38431954, 959166715, 997967726, 851932285, 665566538, 642964015, 753566283, 393944554, 523099950, 387166709, 179004992, 331315326, 731008318, 295249936, 303756991, 420134727, 989106393, 684701584, 168663473, 268633689, 167060670, 9417200, 289456904, 982248960, 169323767, 562127021, 723812574, 185650775, 829431426, 689960860, 89699507, 851569160, 650280049, 219111411, 408416040, 129512280, 241592421, 777302999, 459752712, 158044319, 780056314, 96967004, 969445669, 125977519, 36616737, 552371726, 81822013, 102052829, 425938275, 260255304, 354018615, 748071522, 31734403, 308653600, 924785082, 858936417, 182829392, 908748078, 145146988, 566034000, 752504891, 931744939, 128016133, 837988270, 677017121, 695778863, 779298839, 143913831, 339105259, 38928501, 945062296, 894697503, 893048260, 721879998, 729819652, 865540360, 182057872, 13906064, 239780118, 505944692, 684358299, 481849783, 951348246, 94130793, 654841808, 752324129, 502907265, 610515772, 45201958, 956427140, 441922519, 96395429, 243389467, 116687133, 290936246, 593513878, 668397102, 64510019, 164020254, 496223103, 956073803, 198658127, 786507788, 181404799, 626885570, 115261735, 97247384, 954258883, 673267635, 128799154, 340417420, 481393152, 716110477, 177261395, 668024677, 125000838, 338827625, 153014486, 821204739, 806634775, 128391385, 660194826, 264054152, 274730074, 910248829, 387423117, 370014253, 240830482, 318778331, 369006421, 996607669, 973527977, 235393442, 502475343, 718755838, 312258592, 51964206, 977616702, 723059302, 921608322, 632471414, 137446661, 200991850, 181252077, 254080666, 519817116, 679869597, 411181886, 647120869, 912814968, 410364708, 898825272, 738180135, 594921505, 838871190, 936099405, 943028406, 619891150, 88315879, 960454689, 276211200, 37587921, 536071016, 146077710, 33233950, 544015463, 636710593, 169848246, 583509040, 688228902, 80537827, 741169272, 827431947, 421437742, 301049147, 760363673, 465907526, 484023408, 843652684, 526838870, 313072457, 936305625, 314510570, 901349103, 55459930, 371739880, 426201149, 185066839, 66853257, 974960942, 676732728, 888055520, 947544399, 607343416, 771141918, 714924233, 270716603, 991036624, 999726718, 942557310, 724829588, 453784784, 828160867, 939246142, 199342929, 907419877, 428128458, 504038677, 118105104, 659981703, 519456404, 180232930, 499750716, 741323883, 403908085, 136539141, 680970702, 377706295, 298170747, 721072367, 234405177, 542874269, 881618464, 282459026, 942504134, 181251978, 995968238, 216120864, 969126671, 477908900, 954299663, 345008217, 488775293, 438872215, 724406257, 972458322, 863532223, 601731609, 448791251, 440657151, 359458781, 541267519, 690937683, 673981570, 750106357, 345099154, 247794492, 264724758, 215110339, 588250586, 944610647, 594047532, 693538936, 654242465, 955446951, 121803824, 29692209, 86177497, 554574177, 126738384, 329318082, 656725553, 873606253, 747020023, 71706167, 733908074, 673639099, 108261504, 865416643, 37379903, 408364354, 684261160, 249061559, 476192138, 277691827, 427071788, 159525463, 836518019, 561924123, 401250727, 69050096, 521566800, 11422518, 299027930, 508157732, 701619787, 793412191, 521818123, 754647449, 933419906, 652514499, 838757683, 356637920, 622777082, 880050366, 582560029, 809629858, 13191889, 201268583, 260603188, 941969804, 227716764, 849942792, 524118065, 268829013, 135348346, 125174627, 127081237, 812306512, 653788446, 837317816, 779389419, 545010618, 107676567, 109832046, 2038913, 333038624, 538843100, 826646447, 257325185, 162028030, 881875351, 554946277, 976497816, 353175644, 897277578, 860685625, 785108662, 946719855, 75618542, 128424020, 492443797, 473005604, 6033075, 267528261, 666539641, 378901172, 567135826, 315722349, 995086660, 427622486, 968178772, 591398467, 732806834, 216024768, 61581456, 351660339, 635827247, 884238996, 577345844, 305828812, 587334482, 710295293, 380882943, 226357773, 922035001, 680308213, 707958057, 170495014, 428231698, 445587628, 544589818, 466510374, 946823516, 94729983, 957942931, 448227787, 769843538, 590225904, 810402417, 555960439, 724960399, 932015071, 290109062, 738616365, 13430207, 20919202, 76231208, 564487755, 282031788, 459649161, 815434312, 899140290, 680761520, 265828857, 46744135, 111969622, 121011926, 339938160, 509107271, 793794634, 17159777, 501168187, 547258027, 410371193, 945170005, 900887221, 807295696, 43390240, 127579809, 425735908, 16578223, 733300757, 695474805, 257780940, 905442357, 501443384, 650189428, 54897909, 485372467, 436687963, 993515093, 256919009, 320942476, 718350722, 655096540, 424209272, 431488246, 380681415, 80967064, 791609428, 448182907, 347375996, 472201808, 566030530, 799772478, 34005188, 446406555, 627048013, 108086024, 150089717, 53958564, 385917672, 517663177, 463523362, 294008290, 303869355, 775177780, 555903035, 305570808, 255664388, 280601486, 656534260, 849027868, 924807410, 337904612, 897290472, 629092365, 302166037, 183008667, 818649065, 131102424, 362706820, 502775026, 220537832, 419613490, 449620004, 742802374, 512421663, 268749195, 600989479, 672142520, 814422116, 871712866, 178610551, 555483116, 10005825, 589441357, 551535243, 359362177, 556724653, 512577314, 102721283, 718286599, 904752357, 416942002, 777971861, 165097507, 258385264, 862763783, 227304532, 673422387, 943563552, 506101283, 235394652, 477676370, 687645161, 674275985, 163601110, 318943270, 735726218, 365012312, 972851693, 565799738, 882498496, 57784421, 408569095, 27523491, 847898279, 209395279, 643482774, 247750648, 196924159, 65142672, 275928542, 890475554, 711274291, 522132184, 499072396, 513289546, 270191970, 171977456, 41994593, 414081318, 576417259, 971932803, 173684022, 608708778, 192729735, 176341002, 565235187, 849976733, 358238998, 413768186, 163346381, 764377219, 204832748, 138383771, 282067930, 144341213, 343255015, 681727749, 741071269, 457709434, 25966973, 531476587, 900682076, 147729441, 26615547, 911482507, 254026273, 895302256, 595430176, 880068040, 835666992, 175925543, 933856227, 70243005, 140171863, 380667781, 580720236, 708820475, 498986841, 324753828, 438988266, 221751139, 589009731, 713233475, 303654409, 45996316, 505565513, 951229196, 894664178, 562251253, 578239813, 8015937, 214223417, 245874219, 623549382, 325580872, 405424812, 838418905, 711257711, 541889843, 87243190, 922458447, 20394471, 373083352, 902522140, 843182479, 273554687, 392300404, 810461566, 691297438, 93195872, 361666052, 757510090, 485049922, 407712300, 808436578, 364553940, 547605771, 918613893, 185263421, 574008924, 245297508, 585937206, 948151200, 207688439, 332401691, 794462817, 912676299, 717043426, 406226556, 812346143, 868129448, 514925989, 850962341, 698188603, 968681815, 926355797, 658027439, 363430089, 118882752, 354855580, 569685647, 570052063, 729908537, 897150179, 626261557, 447023049, 271177629, 953748525, 956460152, 245350387, 833997526, 541713184, 694099192, 58133832, 856704569, 350376660, 831641807, 448179598, 918047764, 485132952, 869036854, 389947022, 523317367, 434683560, 26971114, 809523507, 756454452, 314382579, 319423548, 802341126, 752923363, 154217373, 411330798, 718937086, 739542061, 453543599, 292470683, 106088668, 435897969, 663864847, 864951381, 594099537, 845639015, 416445831, 140066105, 221585896, 686003278, 79116712, 775707333, 381885451, 640530019, 813181860, 781668897, 48171598, 193826956, 139618934, 934492619, 678221369, 954295768, 734769358, 906636353, 506708933, 974723108, 476419830, 384888101, 441210828, 313393412, 876972153, 496367552, 20364484, 623262513, 816374986, 740149902, 962606084, 237767260, 595168979, 470651729, 489618011, 370356504, 48054577, 547926174, 872849164, 552544582, 662076425, 298967799, 79584623, 417844649, 758694172, 572843591, 552334990, 587655234, 43339267, 904366485, 143344741, 391469482, 933467833, 530566304, 738400085, 460155527, 409268011, 872267223, 405405215, 192186222, 201632496, 561651434, 73084242, 834856962, 183197962, 314118444, 20919637, 662007461, 80141005, 43966917, 304297803, 501783361, 513799931, 201406172, 347688825, 739360394, 71847660, 315540333, 273813125, 904226157, 792199433, 39339811, 434401351, 464659338, 99838923, 250045816, 500468296, 740423922, 764093252, 350208280, 382959531, 980674247, 461320722, 994974970, 850190270, 107552507, 696345166, 891655313, 678323450, 852707903, 500942526, 277035506, 389309163, 891776648, 146720246, 68123850, 308977072, 825369375, 594332158, 637189032, 104831600, 227497930, 631055080, 596595021, 435090632, 260249027, 257717478, 404608618, 56032559, 332881982, 962148396, 10448641, 509081986, 442878585, 739154554, 515735281, 958824673, 529604089, 399112192, 241498456, 427222587, 119142981, 995360700, 223248999, 408629570, 433213785, 407881517, 192292763, 260367550, 581187345, 926016706, 24715162, 148669064, 887379961, 51784575, 998915873, 287600455, 854600325, 492877693, 717980274, 24012827, 776127481, 391470386, 149902416, 615832065, 571207091, 879755177, 905933917, 56118047, 185070751, 774919259, 930773405, 853343982, 55103418, 10933290, 513981480, 234609802, 318545256, 890486848, 400953541, 306307137, 753482952, 308254401, 433045264, 817368247, 233985789, 5552054, 66696593, 744170976, 396370330, 654260290, 377629698, 25442803, 590880738, 352877113, 997428445, 966173168, 888238924, 517749691, 663505504, 708102472, 531950301, 963291021, 802752002, 838202661, 772608198, 985321112, 529352315, 283823445, 11640097, 404188460, 970617581, 627474377, 785145119, 627950583, 26048815, 843384325, 207540886, 197380669, 449778777, 504553444, 991580322, 540123488, 682874364, 669665050, 966406839, 582590728, 779556071, 831673489, 301672705, 543217535, 586840298, 8663019, 474887845, 191591577, 214978592, 655586260, 376526790, 887965012, 827367851, 584307467, 453759093, 890888506, 690924797, 408136187, 571916564, 813113131, 67146178, 765890975, 993305239, 348388194, 915364645, 62306843, 533099179, 199667507, 694244521, 512143273, 782939232, 573568439, 218715475, 610746892, 64978531, 8062095, 643087144, 984567032, 687776311, 571371325, 454840841, 74126259, 953398728, 836598202, 122671133, 342127054, 412891202, 24720906, 143324598, 153394264, 125505547, 281323754, 743890682, 601236733, 964414298, 618808531, 20781575, 703824306, 909228957, 519021155, 862566690, 55573877, 358640298, 309640488, 187811228, 436582468, 879394346, 217006920, 109539292, 201683702, 365785514, 670448276, 901407481, 8478806, 249640714, 744963482, 329202674, 250537714, 614731649, 308413626, 196470986, 542243897, 799752023, 923390622, 902231176, 630656330, 955877386, 164655019, 157455128, 629459700, 203404067, 756516452, 131559, 848755908, 221444025, 207693780, 606562519, 56402710, 570883265, 242553242, 597789990, 101381743, 962802430, 817823994, 507364489, 314523350, 329290931, 328028044, 981140338, 447303847, 488437018, 543672063, 497880950, 547131580, 182169875, 61668743, 350517068, 939829395, 684072732, 48628072, 148358299, 552792896, 626990746, 38404738, 841824758, 659233982, 664681751, 863763945, 407480264, 399021941, 788888151, 371680206, 185867956, 241043997, 120624752, 34888694, 154842949, 550629993, 908559158, 372636262, 419532820, 740661903, 240857326, 424851911, 561545366, 267220029, 645107487, 882182099, 27850083, 653388916, 582501079, 491545312, 301714295, 188818586, 726600650, 771796515, 407806501, 792930963, 557537713, 281761855, 537784044, 151578869, 550509705, 203139571, 868557609, 972743620, 745550902, 651353720, 352337279, 141092172, 258955516, 227305826, 513933981, 393387711, 802862409, 679199747, 614574839, 915391257, 429070536, 351642930, 388120634, 406783818, 483361253, 686145747, 987260135, 164433420, 858705126, 667587136, 193829253, 658626570, 795686102, 807539482, 487666047, 691542742, 10030205, 201712801, 903325285, 638278622, 850605036, 454130646, 83364555, 321742256, 694974995, 529729451, 703090473, 600530099, 865695211, 29007246, 274223265, 990320891, 748754176, 606783313, 989091255, 11861393, 965754356, 420021686, 378201226, 122193963, 531293262, 310252608, 345474534, 35946794, 449416026, 353410609, 771642353, 218178606, 316548839, 606006104, 311915893, 169787970, 470591443, 450090274, 560400626, 243023888, 588871114, 557631915, 334292600, 455336691, 961667322, 646116761, 531589859, 922172065, 565119156, 989152891, 864655121, 348133587, 976808304, 26599746, 808581836, 953330668, 829769424, 129763238, 841235462, 279017063, 845018521, 872711053, 768415276, 770585733, 2286373, 847107361, 649197367, 144645022, 118192958, 159574745, 85876771, 623537337, 649697970, 53502955, 56028468, 276018678, 420398362, 515449391, 2761097, 673026067, 604989882, 600750876, 796480575, 577628513, 587341291, 354845529, 309250470, 829200576, 266552809, 605638794, 720024412, 683300847, 489645522, 58467652, 419455133, 384117804, 716468088, 500138921, 567613677, 767132690, 826546515, 762416015, 439747445, 53303469, 437048419, 918642844, 572169830, 271848141, 162622301, 744746957, 748367348, 32382073, 320189346, 81123780, 782419703, 675999668, 443488586, 258664987, 141939689, 597850653, 122334455, 281313052, 61189061, 634887609, 365685042, 494665475, 257064354, 516835518, 658498456, 726091843, 902359523, 665682683, 427985652, 944244930, 860960289, 988789100, 990941356, 390474986, 759758660, 950226666, 915057316, 986986132, 781916870, 155421544, 20578325, 642481572, 30064838, 364673499, 662707623, 138961886, 999927380, 400358312, 766351785, 167964952, 134848675, 505107201, 431217782, 129751685, 663728737, 640584682, 879616093, 147031526, 778317079, 951254108, 448643035, 406410053, 952127504, 569533717, 394395634, 374670751, 687398908, 654698783, 117131804, 439831939, 815875678, 803547379, 872883843, 136962423, 930497735, 140571766, 512492347, 766266564, 487931012, 210616266, 262192202, 99989546, 532009199, 732294490, 36921051, 631187784, 167632046, 414639924, 922046020, 498484342, 930523746, 373551930, 525078069, 920789532, 614072339, 886926951, 395816383, 740444745, 764264976, 676814520, 646605988, 882697843, 764445785, 725518500, 140644565, 546025636, 672297648, 799192050, 828730035, 587190304, 196378850, 398085753, 605942844, 378365384, 765076698, 747366166, 399100248, 297426377, 12336187, 498949627, 824894915, 886015472, 673170766, 401907136, 524206892, 956983870, 923371790, 736825670, 495942276, 490137316, 647248436, 354613645, 556545446, 810273618, 637271328, 916925885, 611811636, 834454356, 875452697, 789612511, 876159766, 944435524, 717102094, 452127141, 761038292, 844921273, 425622063, 32842181, 448598822, 995032850, 191048514, 61479123, 746226287, 209239451, 420565625, 966384152, 393200386, 429175013, 481079549, 750228662, 307700955, 393415968, 296283824, 31601803, 8906117, 362021215, 60223637, 106393055, 461568229, 397222832, 484338913, 360167843, 121240523, 187335272, 536575135, 334487008, 980739918, 426621486, 74417045, 451825705, 973254139, 437817758, 45311600, 673373181, 230059583, 29110391, 199616007, 362182452, 734340805, 946221071, 708487132, 605346770, 855841400, 301769523, 737918618, 711401969, 632468732, 520305682, 596222549, 723954671, 44632803, 247401388, 649186522, 900439624, 624919310, 138807166, 955263315, 372695030, 136749995, 371753608, 550489790, 331968932, 28048197, 688244491, 874088166, 402980620, 136835211, 960327339, 499309331, 69038199, 395964238, 627144296, 118083752, 779062372, 582011219, 895526978, 858667609, 872730300, 579418850, 321766352, 646781309, 906387814, 716845566, 939415906, 899004632, 211482069, 627572555, 524652269, 437316681, 810984917, 224154661, 983970992, 625445860, 670287983, 196652074, 294233332, 472850244, 847995717, 139500432, 394417540, 842158175, 102198165, 354408771, 737319416, 598047484, 972955874, 573953516, 342523445, 130964832, 342393707, 628216984, 180141026, 965029185, 364504964, 398595456, 874216379, 331837868, 852623814, 871979136, 301845815, 782650535, 868427831, 104571811, 38596828, 523346582, 187890653, 711164523, 468128982, 207054757, 371237749, 858670391, 658252087, 994450794, 882303543, 441211342, 742532977, 480100766, 335306190, 625176042, 272771442, 283786714, 789367599, 564613704, 363394530, 360728015, 80314586, 718604, 666744821, 603152244, 811422893, 220910606, 314706788, 385042275, 298813713, 698969305, 554431675, 772471324, 79533899, 663887869, 933808509, 858343696, 236324052, 828646170, 384489814, 439039910, 258319741, 726463126, 834301369, 93676686, 560051088, 216245590, 193856770, 441376719, 21499404, 975485706, 629210582, 385401870, 370473011, 193732017, 897601511, 83553170, 307269147, 913673390, 186922812, 482100434, 26330227, 925262591, 167948153, 487841008, 252769184, 445176105, 639144423, 244137826, 664959394, 144626591, 673295541, 586146600, 836753168, 57901130, 135428663, 195657669, 46473570, 12681831, 412585618, 905619768, 718339461, 375105657, 534158569, 532171475, 150288656, 622885992, 743453635, 935879692, 349399311, 638749857, 391764863, 281517457, 900615572, 619267831, 421678017, 993553797, 591144348, 346211267, 153492018, 744984013, 96926225, 310119868, 789549994, 733912517, 43985795, 248481880, 386284069, 461376197, 442721614, 870702307, 475995622, 877548189, 460895008, 621171427, 620417519, 511567171, 509339086, 231639160, 64324506, 616868740, 486757997, 732853178, 634790003, 872100608, 502400557, 326578646, 252882117, 239792105, 545624283, 914785160, 591909072, 688036757, 59516436, 658019457, 942976021, 700171551, 204726906, 449100304, 213560782, 737507130, 548352820, 823495874, 871743170, 966495684, 877956235, 254958492, 268117068, 1273703, 399403716, 766198197, 458534960, 881787790, 682001227, 65964290, 489433005, 876776740, 98593261, 219702718, 282019988, 84921584, 960015017, 491420684, 699715841, 170792977, 84304915, 147325768, 541235984, 799455676, 219526488, 899908688, 212442224, 772777460, 742103148, 866891410, 606746465, 889718265, 600253491, 290507545, 621486774, 716948817, 778438457, 244188571, 946961632, 258770125, 585372811, 890999114, 408973489, 178440485, 448014261, 652851485, 254068137, 699865535, 917586378, 25471693, 452594727, 120024545, 303134923, 309793534, 731919716, 937418836, 996067312, 922225245, 642368327, 642504166, 504236546, 306525233, 271455279, 346821531, 531423051, 326120845, 431624093, 833483706, 708297309, 38527525, 968591190, 326194917, 783133279, 556664533, 320366316, 188938940, 988006097, 447013353, 674319705, 132240518, 215144234, 967089032, 169130648, 51999037, 266143986, 822255170, 350493415, 154485428, 981550092, 636691395, 612795941, 181452923, 697198737, 346513342, 233674723, 13836246, 891680154, 559338855, 289804401, 873938964, 946180646, 826195070, 639973230, 840321368, 888417075, 165800594, 165563253, 577395420, 108312438, 914214374, 232167850, 608557513, 565030488, 975198356, 877869003, 168251931, 616085599, 887608208, 152228029, 271384695, 469686818, 625116935, 103720234, 255866379, 944059241, 628695011, 469241869, 294037824, 216628538, 734316852, 881999055, 405066397, 585477294, 625384214, 461089593, 305203293, 216786036, 932934497, 589642248, 853136893, 184413181, 994922364, 203386418, 482047831, 824130119, 994110709, 971224047, 431019288, 721705840, 211060272, 884227119, 776981485, 710764692, 767360879, 193883418, 578895063, 103195619, 665561040, 2201843, 291576, 606010670, 782919568, 789392737, 437816627, 891125443, 758911453, 262227725, 685739204, 279465596, 773781095, 574491621, 886160478, 682779892, 570909744, 811829398, 864203752, 516828869, 59235524, 483299629, 720935636, 973973692, 129549296, 523987589, 904743901, 904807873, 432475360, 188454685, 693966862, 84477330, 350636618, 682921918, 871214229, 982868717, 455820715, 485663173, 222826596, 388448780, 218789965, 784034059, 708249375, 412178529, 595614817, 914946533, 245404326, 310630123, 178232381, 780088238, 110863402, 65446470, 905244032, 617408725, 489731124, 201247002, 211428766, 939408320, 842523937, 403203831, 646940107, 764123025, 334801269, 327319175, 730109033, 486427391, 13973448, 785595309, 822178170, 175160168, 949396619, 326236154, 370676927, 701685280, 745255019, 896457199, 416860287, 60674582, 342149070, 462240592, 851899658, 779751828, 679243866, 757468704, 717336367, 242730909, 772405381, 811215735, 324763766, 521974350, 254148827, 653498195, 623420331, 751560979, 418951689, 20385857, 931457253, 860951845, 720834805, 745856979, 415292323, 467321261, 187417356, 529112609, 329672395, 794680256, 681176155, 11102461, 353414919, 38988313, 134391543, 397144512, 261344287, 156445516, 190214118, 400715696, 298131567, 771275398, 688625908, 821260638, 937618634, 433857196, 757692882, 59913945, 46366412, 646339045, 160658467, 203359981, 326139746, 314485574, 695272282, 8989201, 116097254, 539936025, 217893291, 821212396, 951157222, 350372176, 695456765, 371156773, 878784051, 433057762, 627611021, 783487873, 257786121, 968545633, 270366952, 525165836, 162305148, 769070738, 962064026, 399676804, 968006649, 619371290, 229911254, 238551497, 373997118, 952995771, 185117368, 780332602, 57051961, 450727735, 929051755, 406992084, 207089689, 696923704, 584714208, 924702056, 242103656, 58828005, 873608761, 561181453, 277004711, 115034589, 397881723, 804642095, 437329293, 595108678, 237763283, 815097101, 756779612, 793342681, 117768176, 429940352, 9758740, 411728456, 708530151, 44287364, 77319141, 850088699, 907416766, 48425287, 269370880, 206269201, 191625698, 3310490, 692464078, 373052568, 97354281, 652271513, 657335955, 19918071, 172988576, 203876006, 978444823, 426302454, 827263555, 283899547, 901055573, 764754199, 685688165, 258974058, 172194967, 851787468, 42921280, 508166107, 329030129, 874346600, 229464804, 106797366, 89639607, 795613452, 328578578, 690298706, 327648855, 955320779, 743254299, 725033519, 822756241, 707603579, 103769441, 9135383, 527208513, 143091830, 6090641, 962112369, 711434482, 986390313, 746576079, 945240163, 626358859, 475060871, 964378948, 495726670, 769967941, 889222964, 497937928, 46850210, 331159167, 145776655, 753260594, 179500692, 721434644, 90500011, 209212527, 325805954, 179400129, 661161328, 876757008, 737495088, 700042529, 545499293, 344523815, 870788200, 487163578, 452261289, 136323184, 538592832, 61681653, 652925510, 919721606, 106070538, 991634906, 152454926, 613835522, 730559380, 510957845, 429044403, 861900975, 616659804, 471431391, 737670470, 233800026, 460038472, 424015628, 702395821, 598038925, 534735918, 332143528, 781205478, 812840314, 479662372, 340982793, 812054322, 272339673, 888573069, 253500373, 238023797, 936518906, 831837169, 479646996, 536152757, 362153327, 852142100, 801524811, 168769148, 369232037, 379065853, 133477071, 288382444, 255244842, 745635074, 389759204, 902762002, 945398992, 957803680, 779667964, 908706354, 306508857, 120558834, 699800697, 598601135, 784079884, 974098916, 780942728, 44468833, 296148816, 310343918, 360701049, 594833728, 8842699, 265660277, 293414858, 956731402, 781906045, 29067019, 239354856, 341773822, 328550861, 729822458, 13434787, 86734117, 790654960, 204989767, 22381095, 934913411, 19864784, 836449676, 611342366, 252603460, 18787111, 696699111, 828345487, 110820529, 485545044, 44719857, 290813174, 208376373, 481188979, 826516787, 609747636, 581632343, 70579030, 896815517, 895062758, 999300014, 605942818, 71068768, 515609854, 752423981, 405606247, 17280461, 574575818, 459225693, 770253908, 136731104, 465184002, 984581508, 277211050, 127692513, 125715237, 634842743, 224638869, 412061060, 811949768, 120569098, 146661090, 185326059, 392816493, 566477012, 291978192, 843911388, 316005361, 820968002, 254730085, 112000852, 151295010, 608061445, 452907024, 522051888, 310343694, 676287782, 65861902, 869038310, 314100205, 710120159, 453172150, 585087067, 90821572, 315824885, 613933651, 648316343, 433862937, 190032013, 415833217, 920037008, 854915994, 619778624, 153639327, 560039499, 463876242, 61304436, 409886835, 485004033, 987188811, 912763735, 570945144, 147543082, 270086883, 766022112, 557255493, 270231374, 927818911, 627016697, 205605122, 818738726, 563353922, 954047077, 203120001, 463963255, 409166015, 191013326, 914658271, 702862805, 762876951, 667948977, 340762470, 555650495, 434920306, 994181450, 442155683, 100555195, 874247024, 992663315, 686844707, 561369521, 790812979, 946905411, 57950246, 755702756, 366499123, 436441208, 384125566, 653179050, 564248199, 389869284, 120718397, 439346366, 533803698, 533594921, 351061141, 435519202, 746799943, 366616499, 953555640, 414000253, 713174112, 853200989, 957203656, 64270580, 295672333, 936956753, 148094751, 939174941, 103836649, 757195975, 883441959, 935026978, 122002243, 518361255, 265037579, 922895539, 207338531, 117857280, 15139618, 328489157, 114497683, 472625071, 606979777, 998192423, 803556836, 121333431, 534680063, 307162581, 34377272, 357560410, 398050016, 159517496, 800564503, 205681637, 128588170, 134806214, 741032290, 871890598, 50957912, 180592436, 521342099, 527750205, 665229280, 93520774, 314453209, 288309090, 152716341, 74458483, 187493213, 360325703, 634375336, 267575355, 978444055, 842823906, 370296356, 341980436, 724724792, 286998846, 893085166, 969001468, 114312114, 76011114, 222923038, 225756099, 10176449, 119069779, 896497261, 621819624, 231502073, 269355718, 772561433, 995389272, 817979363, 910455717, 160827609, 113589327, 558198666, 930353512, 744450729, 927353308, 606526332, 687917158, 896668422, 381329781, 444525693, 441568438, 550630535, 378723692, 249754448, 639403100, 615119803, 431976493, 949011258, 974555827, 198628911, 87498005, 494414662, 34730712, 118241231, 403835386, 92013388, 219006289, 536864893, 70137265, 765985526, 409566554, 596997944, 585070763, 906548981, 171467249, 954625222, 210768417, 241388734, 857453587, 346962261, 571739760, 755272175, 621663165, 506367537, 931200425, 366660079, 34188132, 254452482, 435753563, 728656471, 977509511, 24094071, 74387418, 13299970, 83819462, 666095709, 554888401, 398660736, 671138564, 474158191, 680545979, 99102897, 719839339, 76130481, 679247295, 701925901, 1531263, 757140150, 786055699, 191402284, 894196410, 871747165, 86664403, 651267083, 470936935, 685779777, 478568296, 893485857, 525034675, 95108451, 694136918, 330378990, 396708808, 209710712, 695312063, 125370011, 498221598, 807294264, 233796491, 175608071, 363573163, 447268446, 626080263, 742895285, 570182185, 13597199, 4320591, 936248391, 676348154, 894930845, 45806124, 669359342, 318462166, 274550664, 85625338, 2495153, 689859298, 500045589, 804839123, 792454470, 776325618, 123640229, 397372701, 552005972, 375019581, 587021979, 444209861, 589416973, 581495413, 476306413, 941778328, 647474253, 413365655, 565723094, 338757419, 119303189, 316399853, 645698820, 205765936, 270229897, 97467852, 210618761, 857027379, 413786375, 530817477, 385179859, 143260587, 524229513, 539376793, 482731449, 880494280, 112237280, 873731401, 84568363, 199268481, 477994893, 697857496, 559222490, 772937884, 476705923, 372402474, 280248760, 637245094, 59428361, 421903892, 816086947, 848567385, 494416512, 672372872, 192755774, 37531252, 310449332, 574392117, 965842435, 30998150, 585549525, 380894478, 166898947, 830920911, 707694867, 969078965, 751289350, 737535687, 652203156, 781107021, 940415144, 697330563, 26461618, 764902731, 73054544, 265451441, 108208235, 638835613, 539759437, 940152916, 641775167, 461397669, 83521129, 279301475, 603193873, 595076432, 985570865, 432900769, 900157117, 107712702, 83407259, 68969185, 886484586, 374014244, 240781626, 936424617, 194917057, 392763583, 460841656, 344107632, 171764948, 284944714, 684096850, 293693335, 701084629, 137820118, 196454084, 101006778, 71879996, 967979960, 418544555, 556047198, 248601943, 849070450, 657476442, 128678355, 732258199, 935790701, 432876923, 11497321, 639834153, 334936931, 314934753, 656619148, 872901156, 683055825, 922673142, 760927395, 620022457, 202555108, 857375457, 638125422, 392275731, 583037601, 485184477, 987460329, 251584658, 695452269, 311911425, 238601187, 572606987, 711295470, 458918820, 222866038, 198751541, 264244724, 621945539, 136289624, 2796311, 39682091, 183011514, 103422002, 714851562, 432869169, 306917080, 64427903, 58749110, 500908630, 598892335, 41134756, 859449489, 481293552, 389442222, 919250537, 979140710, 220654808, 450585415, 417016808, 345484411, 893141884, 608221083, 571262451, 894296362, 810586944, 574720298, 255961179, 73990828, 631671075, 382799826, 144797612, 64540179, 692571803, 828000782, 661920283, 767171915, 226084253, 952742781, 423109552, 649009028, 766187205, 968942080, 331046392, 1894481, 370766917, 502136693, 129858507, 68389012, 424730095, 245945962, 409861718, 993729006, 608205434, 421475655, 436154566, 741532984, 904492740, 818586775, 672965012, 318270660, 280960555, 518281073, 564637824, 575804113, 180967779, 450486988, 213753637, 244029258, 544415891, 227729074, 76545598, 368141458, 139064483, 91700370, 942124755, 328487181, 513225780, 669807292, 132502815, 606829879, 793536895, 921630906, 610009979, 745019019, 690135236, 372275636, 89865955, 775693930, 767722726, 919847686, 389388742, 114206802, 539280042, 996712121, 681286998, 543661361, 217571863, 156587380, 831551104, 290551278, 568725939, 669240849, 80132185, 302165201, 514663895, 235063641, 14587102, 132416726, 207908566, 607748219, 720148180, 778927017, 238293778, 260226859, 193904584, 199747944, 671345159, 420593521, 33422504, 231950102, 615194579, 218038055, 775979314, 141287007, 611007479, 73361993, 865578833, 322769292, 74166150, 40563697, 980014178, 450570819, 683211039, 557019390, 562447814, 392647476, 70172096, 433779230, 214878203, 106667119, 994929965, 895176247, 924195602, 778333759, 25435889, 697261976, 957194910, 505030640, 276872216, 808463233, 922375513, 282646697, 547650091, 778381291, 204135331, 221056124, 921563194, 537985690, 809694546, 322152731, 866460607, 110796235, 349380160, 391548727, 362221151, 667602438, 974149820, 239495758, 418946291, 712191708, 280028419, 457508584, 97054650, 538501672, 724924050, 964506074, 64774394, 799545882, 716021150, 293568372, 158663172, 630283758, 621569688, 692285330, 565876288, 329836033, 671453455, 627877924, 511547130, 807330126, 531545549, 304531311, 820858189, 160700149, 710936791, 323458057, 235344478, 426822510, 420092532, 283971040, 127379375, 2098641, 630210089, 353159164, 273625538, 235924788, 497371561, 876560777, 374841261, 685625771, 223255986, 937832605, 684474670, 392589615, 317731685, 974009234, 288962399, 438717813, 826182588, 975841068, 286498020, 616447374, 588648531, 692108532, 388755540, 281558635, 699664920, 274094786, 496341528, 150755441, 906532838, 395290244, 901612501, 779520876, 341114949, 514855165, 748574845, 589979455, 414825408, 84687905, 798763624, 267405775, 22977363, 352200770, 716089729, 826799659, 198110696, 678115931, 763257, 461408356, 668128699, 196139039, 341907682, 620979373, 539517528, 42496351, 123879943, 882526555, 484245796, 460414666, 21319118, 550841169, 523633684, 444218987, 531496637, 219934169, 421850108, 462778223, 183866905, 186372756, 293108393, 895972593, 394059534, 257890483, 336826384, 172965244, 885186469, 948424608, 517861424, 987779082, 995559851, 941465811, 718957143, 718154796, 477914771, 209679238, 342676166, 491936719, 418155044, 363880235, 943757254, 205612661, 42425718, 468170926, 83358894, 882966502, 666309744, 231569020, 556009079, 815045332, 27597393, 517291759, 38175033, 449073027, 636084942, 516655634, 693451266, 510556096, 536222252, 100009440, 349272968, 412770622, 1178956, 311885436, 429724627, 853637745, 11520930, 721069403, 185472923, 486776158, 73800263, 840299175, 578700409, 57496585, 353142571, 881140434, 610630781, 555915409, 209157432, 838657309, 577816768, 833241192, 9589935, 270492777, 245998670, 443637637, 541108210, 616141136, 548522170, 441886656, 511936831, 841334098, 960497936, 284737985, 461757526, 882759848, 886052350, 743494971, 610456759, 422402043, 678980239, 21182671, 497605753, 89911839, 916114548, 578409901, 88806990, 180980950, 415348029, 992127880, 681704764, 51344279, 703090334, 524137460, 119314524, 391467676, 165171086, 481952345, 881464175, 167126299, 189884385, 90778829, 16490430, 509801322, 231648385, 884038700, 486872426, 797136081, 489808140, 861267454, 183108807, 451430059, 114587124, 786230818, 945179288, 292934583, 60086641, 512950963, 703563342, 430593866, 417779225, 104030012, 564312208, 735674079, 218007791, 28235676, 568422660, 181467353, 451793552, 409516364, 581295792, 147870917, 782709427, 707551236, 811790263, 967918941, 37514875, 926765613, 672131896, 703051499, 108867527, 557812065, 924175977, 28386272, 58498901, 331993293, 605404677, 645858251, 85766200, 912402481, 183549111, 676210805, 423258173, 943433678, 81100377, 917081096, 380483732, 225669605, 557451157, 400474803, 522675165, 867260307, 692594925, 593123150, 829817261, 883838208, 453366229, 105824560, 986992126, 408087382, 121750354, 977354466, 544258492, 574027235, 910045797, 56669094, 574292774, 874472367, 579597978, 54455585, 640799332, 30579979, 561956990, 243250661, 522276920, 943621238, 416323447, 323963622, 585414232, 392073198, 432216358, 80015073, 215091300, 740593490, 693057879, 937160428, 270515865, 371667453, 318223160, 5058626, 721344267, 98169688, 576822883, 241333986, 277676312, 232097875, 892799295, 412427893, 446413694, 503932993, 708358843, 15502644, 826151102, 177722722, 409131163, 697884397, 777593072, 741352862, 991356324, 56600785, 978690255, 88467615, 472164059, 727520595, 314794156, 572123991, 81096560, 768065525, 464102351, 851931693, 268493667, 565340144, 969192794, 158300711, 948770328, 877509942, 269164946, 665366453, 898994212, 768307994, 93297827, 125908436, 308282335, 865080708, 555043429, 230098558, 320994772, 839111393, 932646770, 242516853, 340914973, 222763106, 459025516, 251257878, 504589390, 463927715, 86053587, 382511535, 665382646, 740284445, 808272266, 196669954, 663230683, 622964737, 324664364, 534251999, 578386507, 446409296, 739641712, 931975545, 864161772, 404267292, 488344428, 930015645, 499208042, 455274430, 589080082, 432563504, 583364329, 403303195, 746687740, 873025992, 940102632, 837541169, 933047949, 623672247, 664644085, 429213722, 401959663, 176628186, 129157341, 909716230, 272644417, 719293281, 81134283, 260370583, 924300761, 739346060, 991991260, 849580162, 783230196, 28228739, 210227431, 511134411, 816644651, 742130541, 968778714, 957423521, 229604464, 654461806, 882412349, 930036383, 270044842, 81624569, 621431723, 372811559, 420145619, 847925181, 138503367, 306544984, 26125180, 823125941, 751795581, 213254357, 53984593, 370637089, 950900065, 941418127, 630837365, 253595375, 818749052, 79047185, 511965308, 685049997, 282448254, 80146111, 457849301, 376783710, 81500041, 285844278, 103546494, 512664123, 247831102, 601597379, 233143392, 12148030, 606258802, 283285244, 762403064, 245153275, 917653145, 730735169, 55677570, 881819990, 326590485, 32263941, 749580622, 248371287, 397678466, 211184557, 478827264, 999042542, 654973028, 35507563, 478847915, 446583976, 49567099, 872289338, 724667322, 525932727, 546597375, 849008773, 179234388, 91588226, 627652590, 619677760, 926638732, 560021958, 208391769, 856711737, 548285845, 171649815, 567633304, 538522234, 933853359, 284645868, 892931750, 686634594, 774561810, 11159738, 714095664, 621839587, 3940254, 824424790, 844075294, 55124406, 350973719, 758041630, 534197870, 927370313, 157338931, 79783929, 98750588, 473942207, 829725870, 188477227, 63989152, 646128096, 97403168, 728465533, 279251557, 886435756, 866638392, 496747851, 681803214, 339632276, 236961225, 495783472, 329947599, 769218761, 244118093, 912915209, 450212315, 155395104, 119336042, 383899295, 378771543, 616341728, 782704677, 584723497, 816157927, 137066194, 349941582, 503879228, 913659034, 476194084, 852705972, 626255754, 620477842, 589945426, 757997315, 148578021, 526478325, 496118893, 326901287, 395219639, 243173902, 555182840, 730638837, 275292147, 776392080, 810888004, 182659666, 889983155, 585085492, 268546173, 910019333, 915151334, 749026380, 760726223, 602285128, 270781915, 543335900, 580241706, 292305785, 517852563, 996040628, 491309512, 479825194, 724915288, 885501690, 229405103, 598331647, 153403159, 929170423, 310597527, 952942712, 31767017, 790440998, 487004432, 756521999, 487561238, 100710444, 289133445, 251886268, 615468662, 552626863, 675887683, 854083835, 533848353, 92914466, 847743322, 282284524, 451067015, 1825653, 36969172, 120644272, 995508385, 889703967, 518512575, 729041007, 513748946, 740586030, 105372029, 621116320, 615317012, 608364797, 956474088, 371789839, 837334839, 115014249, 250347741, 528870684, 617019317, 740818345, 613003878, 810827816, 621735629, 144211874, 348424188, 832138794, 592852297, 420638574, 130662586, 339977490, 385045313, 735050396, 324603106, 963546817, 252653652, 538604666, 700944928, 272653719, 594097640, 928526106, 766865606, 193679469, 159171236, 320664064, 360141177, 807116595, 782111194, 719939216, 814895927, 777779049, 115042879, 666277142, 163421521, 757755409, 316776801, 761741941, 378917609, 823900579, 974639275, 482487172, 146487723, 319916369, 338017453, 283654765, 445126639, 60219620, 194223973, 758342110, 24059868, 664156287, 484915868, 58299744, 760271667, 901775594, 594306265, 466624509, 652861340, 474823034, 600969577, 961160909, 750345590, 736668690, 525066494, 181795610, 510558400, 65428858, 125183649, 444274731, 977256460, 295343060, 381649297, 562209038, 291888220, 510854412, 188582115, 602583596, 346058263, 514488362, 601579507, 107725481, 332646208, 655612972, 521189308, 243582233, 89844629, 568642261, 314838211, 208651925, 253461017, 704977995, 162479275, 114476357, 854247525, 713596947, 261453009, 735620924, 207499417, 311960242, 292679423, 510965784, 752884758, 672514450, 37460436, 41266716, 44694405, 798715897, 153653446, 280084843, 434702266, 380289084, 312229941, 889797432, 34723683, 837572068, 468224566, 37911092, 579672626, 652276996, 920539719, 508481873, 273988331, 377243653, 604907078, 359893812, 422433183, 731209978, 841174179, 142642744, 671461407, 307784389, 729346615, 784905647, 247559064, 190609176, 970772290, 14643627, 688431200, 639183855, 159532319, 159596880, 918433286, 201586867, 384683075, 800889830, 622768428, 74911015, 570265220, 139266797, 856903937, 208336614, 909529452, 674233867, 416494930, 711359191, 383091158, 664275922, 679608971, 438682928, 493353638, 616578191, 82295984, 457680003, 120316397, 956917872, 263189714, 951431609, 940359524, 200114214, 192611869, 712796729, 792308284, 671632609, 589253915, 977229518, 245684798, 182206274, 22366240, 702584569, 725866045, 678860735, 705232476, 10746827, 309564658, 731229361, 395569485, 992265491, 557764851, 388190761, 938430754, 431408348, 485837155, 698778881, 579379913, 589203311, 583195745, 100284288, 466507273, 776052767, 381084633, 753102014, 704339760, 863388850, 375907265, 886210588, 299306650, 169556778, 364776252, 26240073, 548643771, 578190136, 241557403, 807492610, 246380720, 48387947, 630408132, 731369113, 101827946, 507147558, 264657235, 195239731, 261316605, 54944404, 408147943, 364757560, 888176339, 947641990, 581828921, 246550385, 599136286, 23648149, 755672495, 139458788, 172639073, 764320103, 631110676, 664338835, 118370116, 821772118, 278785454, 320780548, 61460199, 496871195, 583462902, 740794895, 512954590, 496849729, 68081857, 797216959, 40776516, 17406879, 651605706, 124994616, 390334254, 749953050, 575198974, 432033684, 17926031, 815423659, 123718777, 798251979, 171954142, 517383849, 658436387, 703662576, 466722770, 731533466, 61847281, 731483079, 50869276, 914737598, 342705934, 368919281, 55621909, 651236588, 148894929, 679480, 133114496, 254839543, 371213795, 622485850, 12311087, 746048274, 264731953, 170029699, 485080774, 782669400, 907164059, 37425070, 813757113, 867574120, 674318647, 34284863, 988837905, 771570068, 961277006, 819942655, 554169199, 751384114, 186789825, 864620962, 811066447, 1384027, 921440568, 487829367, 733323513, 577557072, 693560072, 613474036, 16295715, 17895585, 500823881, 51751019, 335325683, 798615012, 422718095, 126622937, 201150628, 525758102, 949312415, 154924870, 762943120, 319356863, 745004999, 335019154, 6429089, 966229859, 408124604, 620983874, 563036423, 150032115, 441876235, 105293349, 256323116, 952920966, 578294128, 41891091, 303114356, 784533505, 449620456, 412525333, 207335885, 696044959, 157373115, 974974655, 540384795, 506727884, 190391072, 881623997, 562061470, 46848128, 731647581, 809806113, 307149633, 693289449, 107759306, 887722669, 850767685, 172551164, 863375593, 72453441, 750150412, 894466942, 17387847, 742835338, 657689913, 264391695, 796396184, 934116726, 593034152, 597831922, 143342176, 111522598, 924948838, 642544317, 363187083, 701768068, 509053839, 20447308, 590036910, 704727125, 775111950, 224502808, 600498320, 724336971, 45022178, 295562345, 192490212, 82004533, 179392479, 975149429, 102572010, 184796983, 254578270, 510078265, 845542182, 639626705, 725320178, 806164438, 371182280, 572000013, 758771671, 624070727, 162479344, 146360379, 422899751, 134684845, 343566146, 553289033, 750003882, 472744568, 698686343, 396876981, 885060884, 896817754, 136081322, 823321401, 702496819, 349456056, 504204503, 744713803, 323984683, 959115081, 271896884, 597828245, 115944681, 121598065, 770863656, 779539505, 860880753, 597321360, 758989317, 381695617, 992585488, 684137455, 848083029, 10670427, 75411508, 323531987, 167895837, 624505735, 365849308, 997453564, 713529116, 77010788, 769821678, 828900033, 906522423, 64472786, 153338188, 28593306, 756405388, 71547008, 814111418, 257683918, 55203963, 71810453, 627255054, 400533964, 595266262, 947826973, 451808632, 407146777, 664001143, 787646691, 700110928, 657390186, 794531230, 702909305, 469891692, 707625994, 776043645, 77986347, 687591314, 669615262, 110994169, 593264140, 349071851, 880778358, 3093457, 256487515, 669059739, 55962614, 378819543, 454562318, 926192708, 508209061, 627412432, 635840841, 966848431, 252207752, 274154470, 767518080, 536581715, 973922046, 792367926, 740558478, 835592989, 74384283, 14757617, 26386674, 513388030, 961331519, 955098563, 167339952, 242472693, 412979174, 745160692, 421268599, 742983364, 79778508, 546595893, 812944450, 77941084, 970385871, 825718583, 863936104, 528684214, 16230365, 668841750, 319282664, 699873557, 179570559, 320274423, 100189542, 994667805, 295028544, 592718322, 546644803, 933555142, 703066308, 946332222, 941432401, 514241843, 351138692, 522917257, 809714575, 512386742, 746751513, 127316552, 512478976, 352964366, 473713703, 596321227, 752460615, 559341865, 425855738, 319677373, 317599107, 699378657, 224565130, 856081783, 317119713, 671854337, 614153593, 420073896, 626773585, 150997523, 620647398, 549042156, 222856417, 757541882, 14645476, 729683499, 55018081, 523345052, 48620382, 360203224, 941417519, 195301379, 160003378, 183678440, 56235034, 879349116, 622789501, 781653498, 171663287, 270575757, 496187837, 810822867, 587053375, 618481302, 686861628, 417308915, 662741265, 117474875, 314964245, 289279639, 879778203, 335032086, 57612196, 723288910, 337024867, 94169547, 413363451, 878914461, 949306166, 274162207, 639013237, 428600382, 463314424, 798399720, 880419117, 141466920, 876544183, 411024281, 666936637, 336754335, 424548351, 118025037, 127359837, 187150640, 667027476, 386716343, 839039704, 659403448, 489120457, 18601306, 425685088, 453340621, 431153354, 214858500, 330236885, 180772884, 853459956, 468485211, 834128346, 751647265, 556792340, 554619227, 791815806, 922642148, 48674639, 558752901, 74300303, 160443279, 268934348, 425626200, 229419489, 915249623, 702810282, 496398984, 625692283, 5609317, 981638389, 475639970, 606051372, 780573744, 42034751, 298526384, 197176874, 991724674, 806365245, 971547984, 220245788, 761756907, 662253761, 860863066, 33707128, 412775391, 24897913, 15920004, 676157840, 291423835, 869176012, 204700749, 866196135, 977171197, 349778489, 880616170, 121116016, 292627259, 960518058, 921635314, 217482719, 576539450, 569226447, 498768624, 47390153, 934531330, 404846335, 405503643, 28046587, 483035535, 345679889, 904393468, 99145291, 602520705, 54237579, 821432845, 238267877, 688793222, 32261819, 181742221, 990765801, 209497534, 678625214, 749559029, 545684992, 235352791, 97926711, 730738962, 681155733, 592574342, 697586049, 748980589, 831048579, 895207624, 576823366, 779990049, 314711736, 69908857, 528531326, 996491582, 386137089, 480914478, 331435250, 809758063, 777568833, 309184563, 564087315, 636669977, 128055241, 82431866, 790689181, 687013135, 370080632, 199987483, 660148584, 402086777, 99799420, 657958847, 758146496, 629336433, 65296704, 138260806, 101525834, 531985669, 957372950, 916858350, 509993804, 531216276, 28800806, 687764339, 475089946, 778820418, 652316101, 200642130, 229809340, 391059845, 448910302, 658034636, 747342232, 803843324, 91713672, 499089581, 787373808, 859190332, 483402228, 961495788, 787195241, 705606606, 620898097, 234150601, 619112460, 198924501, 795903441, 944254418, 697721256, 563477960, 5334845, 215296757, 138662160, 3653488, 750045116, 618130766, 891681179, 579432495, 252618367, 457086390, 796939681, 281993246, 725310800, 434691476, 111166657, 83234977, 324083462, 97562569, 757192738, 820841997, 403515333, 590604584, 681307902, 795809147, 381967491, 991488348, 331917578, 965750230, 430575507, 117999998, 919274867, 683951255, 40968550, 197397333, 59873448, 465966145, 120136672, 21320325, 837843411, 285580348, 847134791, 740010129, 455186086, 542118964, 427978068, 890128498, 681154610, 934158339, 742571866, 923700583, 121437838, 83218137, 796836570, 16389430, 282416343, 69483218, 613446037, 995389727, 634055890, 962311809, 777843079, 972370343, 903065830, 615212186, 38108591, 120581088, 687865662, 270354706, 128752290, 913716748, 631329192, 142096135, 683812102, 519235733, 442932760, 298838874, 363632602, 301557737, 285911351, 750981868, 215355408, 831693943, 859147205, 431685245, 322420921, 756204583, 626580075, 151087721, 236804545, 817147948, 959452370, 450982381, 858533421, 951500645, 96362422, 281076551, 509048270, 988180559, 484456579, 502208954, 597510974, 459899690, 413980275, 468934852, 314023865, 845762588, 567174850, 811293096, 407561426, 381002890, 594121944, 899434787, 579770852, 841867729, 491577990, 175383076, 506020388, 375791545, 343893131, 568008424, 444459235, 458073289, 642705787, 176760764, 524636776, 512434433, 688270967, 481336297, 543780893, 756728720, 515989454, 196682614, 130905453, 29697380, 865285145, 720985905, 954860399, 263736929, 492822053, 570450490, 721838801, 300789037, 142501572, 801877005, 924846797, 717486830, 675810581, 428734147, 4388394, 817875722, 441774705, 304139304, 350023361, 495372988, 954911938, 223301005, 516002600, 66798054, 120216369, 64201805, 125524337, 736528441, 830733128, 929883038, 477797321, 925409349, 34331599, 258922451, 775577487, 463609342, 621196559, 412750519, 911529, 312223507, 356938319, 305267312, 289841574, 537398086, 558499709, 200233904, 112831256, 9826738, 598424283, 706777812, 780045723, 457562830, 770790286, 730358717, 548521847, 893146564, 251764612, 925040842, 148951722, 490432317, 631287521, 237276530, 336717934, 361132296, 960639371, 600133403, 749155620, 882343884, 755934123, 335175951, 25188292, 886812533, 422289880, 597441739, 525277521, 436720334, 643675685, 240609171, 675974753, 331998340, 572139270, 12587492, 731816761, 31357927, 617484151, 549446264, 498968388, 844046010, 435711060, 844352243, 619553427, 454810495, 993927172, 798090900, 927885898, 997298583, 290066136, 377535006, 220076646, 4729104, 28968691, 614121776, 224488186, 367282569, 169237100, 972895654, 773195563, 629335357, 896892843, 468359350, 707046325, 715751913, 465138030, 829870893, 202695150, 812795942, 601924037, 419860598, 344848713, 741670875, 163444068, 935129034, 25977304, 750077213, 255960896, 377568071, 837219803, 681721156, 685469668, 778026932, 822740616, 784834955, 81212312, 35023788, 194731688, 383058600, 834898659, 491536682, 78866753, 698968204, 495096372, 991116089, 684206102, 144364044, 856505297, 203324456, 387558682, 1937649, 371737322, 178170397, 725205107, 428427194, 236441396, 534915532, 788605939, 390678072, 464169387, 712487059, 680884109, 15321534, 562332933, 684668264, 84186951, 939036441, 391244184, 281392582, 4652552, 386399405, 298628024, 637237327, 383346720, 392819153, 692594485, 348048370, 756579348, 153122632, 474778502, 68824430, 32887685, 209916638, 715934309, 152794321, 639100843, 355937346, 502386728, 349273337, 748929821, 564125423, 867251677, 974171666, 373400864, 34247863, 136143172, 154136062, 323619958, 150023627, 505571542, 791626164, 864815940, 480918763, 642899557, 95789353, 306644236, 926947019, 526917392, 842917908, 785854519, 44717175, 919905072, 672168368, 118720549, 919502565, 948982165, 714686580, 912938147, 819521540, 984254018, 141176337, 57025103, 658295306, 890851595, 129980869, 49018731, 489668150, 856150897, 437867161, 161167322, 70490204, 293511684, 565947382, 956041341, 398514750, 663983572, 76722230, 975307900, 40532485, 185724489, 150132345, 783806358, 991370986, 24570568, 702603208, 931279151, 560732689, 397101841, 417476847, 293445790, 938385285, 258623332, 797734915, 609385857, 979455416, 376066371, 498283035, 837121215, 257018730, 425471739, 881751783, 56935452, 761111129, 526630483, 348250493, 396454976, 769915677, 555631656, 634426628, 315322935, 217298616, 536983140, 492405125, 986412427, 231617423, 36903042, 96399007, 203295109, 771484081, 925973722, 663245424, 893224799, 3582394, 8714844, 75154699, 297427282, 701764644, 184493054, 257664758, 684126415, 716925270, 45135638, 2418709, 371187311, 171861855, 128583465, 685349012, 29363507, 374273883, 638417590, 337469605, 608534886, 779163410, 428035043, 616101583, 681549495, 887020396, 719433701, 312343097, 773232156, 878346775, 970197992, 979825130, 761454191, 549166632, 205125767, 768281368, 702747216, 475919307, 296767609, 301498169, 949709464, 59864494, 70597372, 847915341, 271386890, 331682719, 706833357, 367411736, 639682121, 116841355, 516354684, 201852398, 539879987, 236521555, 30773176, 71841121, 200881078, 948624842, 405136106, 685809486, 331088653, 871460772, 622000136, 783986147, 740209200, 33777959, 115451347, 414990654, 568627483, 850443833, 758681622, 175447441, 450745842, 595679148, 864859769, 718881883, 670438461, 396093242, 161842993, 122837163, 526129916, 27008692, 722398437, 262566399, 754028094, 917074888, 405761485, 758475537, 797698687, 246881905, 948075852, 931182058, 32375720, 162403057, 431562955, 502045337, 411287733, 344378020, 704636977, 316327777, 313175997, 539911677, 286267168, 817602082, 797614849, 207249692, 505822669, 56052948, 344085673, 121916948, 724771350, 492516115, 305933823, 936444763, 952967771, 379256187, 377200934, 324304702, 826315744, 306084658, 205744895, 989454971, 408956941, 522025999, 118106216, 639383268, 970515878, 718101890, 925462863, 588994147, 312708824, 426119478, 967516510, 245907593, 802971431, 477889383, 86227908, 75919610, 47016548, 102486901, 557665860, 913801836, 789920124, 239043055, 705988832, 667192416, 254902847, 550595545, 913237148, 825319112, 574865954, 282854568, 182535256, 824331905, 935899769, 397698022, 25695203, 671995022, 610207987, 923132882, 134462072, 318387929, 250020081, 2743776, 910738308, 430133085, 807890516, 187733413, 958633823, 573607875, 900369888, 749023273, 520726210, 880562019, 143259461, 48866724, 88622562, 811244430, 826032831, 622979596, 159164165, 196033815, 600352967, 952164357, 102194717, 150494119, 737838952, 432217812, 933168241, 140169317, 614493577, 307402316, 246419585, 380668035, 124278043, 257462967, 985597262, 22964912, 547545437, 435550436, 3870022, 626581031, 325076787, 226046316, 367659641, 283575604, 497825834, 514223399, 601598973, 128288004, 804356345, 249405892, 910384235, 663596093, 142267732, 559167848, 503604125, 256184165, 331092784, 807418363, 158054481, 746209148, 645845499, 789233901, 839427761, 590139251, 325117643, 109098411, 492388721, 764209870, 860396537, 904035524, 863671596, 194716093, 456727990, 433352052, 352011835, 978411386, 128636372, 215462646, 496688738, 826225003, 383090099, 597308112, 234102723, 575110599, 666782864, 673131950, 697736704, 416947224, 215818345, 354639934, 246679262, 373391645, 351200952, 116006046, 533141421, 895284700, 1763000, 482202720, 397948529, 894365119, 988823661, 339726019, 856675851, 581209179, 750647241, 863434565, 914360617, 212397819, 323792132, 683511976, 474652467, 117934933, 857402478, 513780488, 434983468, 230155397, 104925310, 845115733, 828196650, 123648719, 227302756, 878192912, 828366811, 948692237, 678120053, 54822342, 812346239, 471645918, 665309590, 575608480, 374755801, 455824532, 470310973, 102604973, 9097109, 725290338, 610661947, 627167291, 206180620, 374848331, 528931340, 783173878, 861522480, 401497329, 546620883, 875232564, 965120291, 292205904, 902460176, 277111264, 481581518, 75327501, 607136965, 470279400, 352588379, 91552999, 32777766, 768142303, 136770738, 673212340, 825978901, 730349841, 920264747, 934545028, 88430855, 250292879, 824166579, 246473789, 996933200, 68778872, 247832907, 617487930, 455858773, 973979191, 791545437, 938538367, 849409412, 794174103, 319738292, 11575832, 242956003, 781850890, 323242645, 774939720, 627787333, 287151909, 664760707, 226445293, 18584927, 950964469, 778892697, 186020020, 308439224, 146240942, 723543837, 677801157, 230432676, 254346181, 320743312, 972240118, 491857004, 158910559, 119445788, 804006417, 566646268, 852374300, 575251867, 535254888, 248129127, 869975769, 132048919, 257812433, 747089730, 131193585, 27041367, 680554107, 343494579, 41444418, 343812825, 167943820, 105485960, 554844969, 36313589, 716786872, 777250140, 518956212, 382482017, 925471899, 615795622, 274639604, 399082231, 900038738, 639463531, 669845994, 547345449, 674898358, 278489930, 772083389, 609846472, 396721217, 478928480, 362727998, 199434405, 201531025, 909073883, 241680664, 471959717, 623332806, 786436022, 678583639, 979554460, 584565531, 863241421, 879709544, 285429629, 145674377, 624939158, 584326770, 596404785, 487975690, 118364450, 402562836, 88532490, 722271034, 932734821, 37786584, 589413630, 982825588, 134232960, 74347924, 723762718, 695907848, 176115895, 578667011, 658732844, 29784402, 776990043, 544731507, 530470863, 784595762, 588324667, 299157494, 583019609, 857178250, 760906880, 426865588, 159529465, 68384249, 435096663, 311157404, 325099326, 730797189, 797483997, 804156752, 957403955, 676426950, 731935825, 224068296, 688130547, 133628364, 454769663, 640391276, 583030018, 924410827, 409349039, 930279107, 697685056, 448111795, 479381275, 541744848, 473878807, 177410520, 858836298, 355093058, 242192282, 268598102, 439820529, 490634170, 686361629, 447344671, 977396979, 860251557, 62527256, 292999841, 749556166, 998857690, 789420112, 148869341, 909414649, 552824932, 746373726, 577688207, 214324232, 639998901, 269929118, 290373683, 995511904, 439460489, 15491320, 52756263, 260383111, 838417661, 125295024, 619523013, 447140129, 294395062, 959981112, 715378221, 285848876, 917220974, 874902039, 229364096, 403138996, 295293293, 692123145, 465609046, 359437577, 546495592, 464380305, 510904544, 890927459, 674648672, 107258848, 514429592, 234612905, 790198755, 618444390, 630512751, 52218151, 877177045, 859504394, 133329068, 803223887, 798323156, 259412357, 798749827, 642192904, 444168883, 173382143, 326647166, 40408121, 7729623, 474742358, 367503790, 869480050, 370263365, 260161075, 51043841, 794310476, 273185635, 172417444, 575818652, 815647281, 838719668, 881382611, 69365742, 192952104, 108167165, 519645576, 851842869, 605386928, 33352898, 810324102, 776633306, 737975541, 454524786, 854021205, 590284637, 208063496, 870600962, 791716337, 687919981, 110453135, 403605499, 847847126, 374863480, 14379212, 348930721, 338225085, 861471650, 289612381, 895961605, 553566384, 195497601, 276691833, 478725440, 904000343, 119370110, 873461382, 539717673, 654913305, 253351430, 708018769, 294539820, 624364887, 278107364, 402434069, 10306941, 780629072, 242680063, 981093982, 348640139, 448237697, 133748436, 958454270, 11753360, 128335068, 589546727, 199933140, 112580138, 779934240, 531581469, 323612005, 204263933, 349902587, 147801333, 525409029, 69804606, 347210664, 611002626, 441920975, 480970705, 517520208, 998753149, 388266720, 852585978, 992143357, 728317217, 271285698, 321272159, 802946149, 352625499, 796422006, 150993118, 620436265, 634102351, 445561951, 17867415, 515280413, 676847833, 267073136, 966878077, 885019961, 785681364, 935901276, 190352085, 841126882, 42861342, 790887439, 187265203, 119778188, 586683228, 655576981, 521454762, 434091562, 300684655, 99321354, 376519764, 103387233, 596631354, 972577908, 536058514, 393976466, 714557212, 708319451, 348664673, 994877652, 837783306, 197557512, 183460550, 25764989, 548130542, 608416994, 969712778, 808447675, 643016781, 985162133, 382081511, 41420106, 749016692, 288006797, 394606600, 933748706, 441994559, 19691550, 873483787, 543335690, 149768412, 465826811, 76206223, 813644052, 177638849, 983228612, 400383572, 921338414, 524034874, 406898887, 111863948, 590646957, 271337267, 464849878, 975481758, 501189762, 870988978, 980983555, 386004114, 584906343, 63739919, 695442484, 778525182, 112021103, 512700306, 427703834, 25054508, 134521740, 799891925, 838762401, 78078049, 942645888, 885763168, 598676062, 893072653, 51586053, 613666582, 348867006, 248474408, 713490176, 105499338, 32398676, 931852013, 704271074, 258528008, 302834795, 645114415, 381853283, 479450502, 886939233, 889907901, 93378043, 636027633, 97799330, 857697804, 552900853, 814335744, 653870069, 928464414, 897423741, 376122056, 759138831, 370094074, 55777757, 243061855, 838598649, 364254950, 359137075, 460466931, 637294330, 199820261, 324172512, 127459582, 558403065, 431030307, 676965152, 404617765, 377396600, 856897956, 363022331, 27677238, 257781227, 933156914, 289463430, 503876618, 608317333, 867948305, 377759089, 80306615, 634886485, 290093854, 194580276, 877540940, 187995452, 197155239, 270905911, 258975036, 422356457, 158022591, 497448736, 318562606, 19960290, 848703689, 226646718, 103281007, 460577810, 310619348, 717833050, 312390838, 412234508, 859373589, 500900375, 973252082, 857428185, 550848436, 469378449, 916616197, 120717488, 72412848, 508345760, 362252340, 298067712, 532586856, 379265342, 425328048, 186128904, 203843322, 95840407, 507913575, 971309214, 495717292, 502595841, 401599901, 823397965, 783450247, 222872690, 824909696, 35962256, 260716914, 394342404, 148455145, 498827729, 708710862, 225424955, 222707729, 672565976, 541658194, 451257794, 106465057, 567325165, 548968596, 954162601, 831541654, 849172576, 260810907, 628281674, 792532152, 373744591, 590335323, 720496748, 897896639, 332459794, 874652503, 599149428, 102265675, 769748368, 373129898, 870691866, 352180080, 251838710, 714482622, 707952320, 705894960, 391787682, 837093621, 69876041, 732749900, 357972288, 527933346, 382621052, 165864093, 584283046, 927701680, 647598361, 376398936, 486633540, 713973922, 43975374, 833920927, 421039788, 376005621, 207416993, 563228204, 652694583, 300840493, 829511038, 991925356, 973309799, 541799803, 886889907, 289004263, 737261887, 272900966, 631885582, 271309890, 326697836, 470872288, 816003007, 795444759, 611987255, 431049853, 623521551, 148739167, 834973048, 497121875, 46961186, 298601435, 398125586, 650875790, 299024116, 850339374, 726908997, 868538534, 225080991, 686056747, 25921669, 182105945, 143178530, 914283322, 876536911, 124588308, 222534449, 971845446, 440927648, 685715638, 467277061, 441901148, 795994415, 529737066, 191556418, 27841012, 921683840, 877836579, 267776463, 161045110, 572398593, 923091384, 158133645, 52174406, 763402589, 818945614, 503505004, 180593086, 639025371, 977949960, 696895413, 901154666, 251117098, 861975367, 248163077, 424546475, 563599906, 262782663, 314552247, 541134737, 893662015, 828291689, 952878003, 564650762, 453382845, 252916976, 41917718, 754700955, 764462674, 269317005, 427511236, 785112887, 105821241, 623350562, 606180015, 995528315, 948340581, 158267242, 633331693, 447700022, 7891721, 532796367, 567516278, 55706369, 738975964, 72272000, 196939005, 468073085, 921566436, 373718911, 289105855, 527734181, 233441562, 461542551, 89988343, 61135507, 522473050, 42972746, 552873358, 202042850, 616381024, 624906916, 74019527, 97493947, 29604420, 802258039, 171533080, 603490930, 376758029, 597871616, 61451323, 110334873, 475180613, 268422888, 55577729, 77073825, 954085502, 754516475, 900674251, 663326014, 354097320, 377689886, 370384861, 817890435, 16630535, 522662590, 627078624, 305246468, 29600352, 116420782, 53097290, 117521173, 695376626, 671381343, 245078309, 113658835, 143352028, 560842475, 59620147, 427604963, 711665409, 466770310, 662525589, 981334790, 341430276, 219136648, 153197894, 912174778, 794024681, 41064355, 637347010, 612216280, 141129107, 838376064, 81100429, 198413810, 544662159, 297358253, 754592189, 769641759, 258164550, 19710624, 8542834, 831718081, 69799729, 411198572, 341838011, 766561163, 350705819, 507513326, 101071439, 331687277, 853324298, 957627738, 178254803, 232324474, 340466282, 19969137, 492797524, 809236443, 79502263, 157773837, 946195124, 208451579, 362561390, 61075774, 198336633, 426815006, 891841893, 64573710, 997452836, 932907900, 791471319, 330923754, 449192982, 273903013, 580215127, 477530049, 48950159, 224958151, 492304589, 93110556, 578316734, 281892119, 118117812, 468387619, 154168425, 507153640, 444877037, 941034764, 309845753, 94541086, 758802774, 702598776, 613691904, 807258249, 106897207, 725851064, 518966822, 796785241, 554322801, 405325979, 666025494, 767962696, 668965340, 653779493, 108514263, 83234521, 233566566, 493323212, 490867229, 145728694, 262540300, 721515335, 98649144, 677240430, 144314865, 855183556, 364670779, 838108811, 313939019, 11626490, 596533208, 57598030, 314764108, 411552820, 892674425, 417528014, 536043485, 933118853, 309927236, 616036360, 211130321, 991088493, 553808693, 621216160, 717458008, 224652667, 810828920, 995731404, 326090689, 209477499, 535983440, 258239503, 317562973, 852762496, 996263282, 450107519, 982749677, 182814755, 489293384, 634802772, 551305317, 587796658, 341377566, 863498307, 474932402, 261888369, 967164834, 301097623, 220535729, 90242498, 725955297, 511812330, 566826604, 780240093, 501883955, 934317326, 741902574, 854647846, 592263397, 707922966, 699018499, 100724486, 57913074, 421068158, 958442502, 851453517, 465626292, 449727342, 497090953, 387695646, 726620678, 969917992, 647225928, 99780018, 720079922, 449277017, 38204310, 541815937, 684258300, 906806433, 132727926, 72444577, 844097145, 286642091, 608270056, 472777247, 180799487, 274970324, 591857925, 896446346, 848396287, 186262353, 618831702, 572124059, 482824823, 568975643, 563131380, 704077163, 249754875, 549489249, 909428047, 242128051, 550642023, 494203725, 164939144, 360151022, 49064039, 679687932, 245444595, 680724998, 853034719, 696450945, 746817191, 122084965, 662149386, 10867296, 946397527, 482749538, 304202607, 713164137, 308869905, 706606904, 775464026, 923028988, 185336919, 862329213, 638345713, 256053943, 545565826, 968069760, 601487190, 101853624, 354285194, 173951552, 185860644, 780501543, 740739086, 575769376, 902063754, 358326070, 645858045, 666987533, 926665942, 44524032, 571498113, 592048916, 578110604, 101592902, 399065368, 769723557, 744264801, 840934079, 495929279, 662594427, 833229471, 91805172, 612546706, 600958746, 354071280, 36184950, 793155858, 453268557, 510097023, 475538780, 495699622, 489874961, 598159490, 852388239, 378119213, 72914486, 20466999, 465143631, 872411152, 100754466, 93527465, 398978952, 50948459, 494076817, 523200144, 330976089, 998304029, 201559921, 402126004, 78419634, 735219524, 751825876, 843749378, 453308088, 896604426, 523266950, 970872977, 884344498, 301220971, 303073079, 185508389, 557826870, 924046814, 793098449, 814458843, 688264369, 6912279, 187106847, 353745241, 852667348, 440673026, 228487215, 353011522, 440383251, 725401259, 449474829, 116920041, 756016763, 921041031, 138512990, 19301515, 697502134, 748187854, 808953860, 368821403, 419626386, 722097031, 463174796, 48212830, 190734337, 951825384, 540024084, 608204913, 850277308, 313405480, 321083678, 683259653, 998513253, 767438385, 429631113, 517317884, 732014900, 779687058, 342678260, 105483679, 247722649, 343315487, 974525047, 143682113, 826633980, 232268732, 834924084, 822702205, 959227422, 484314567, 183840754, 453208386, 633243549, 89825685, 174573561, 893610019, 197659597, 490827532, 855170010, 197865824, 498064652, 329819789, 346452229, 314129353, 512336755, 400772140, 915219473, 730485420, 936276630, 309065879, 225834139, 535172389, 41586395, 868501304, 786086147, 414290663, 722491951, 866970205, 884963409, 160248122, 104561556, 810978219, 621703574, 326630240, 687186571, 407922488, 874810711, 29046598, 244041841, 88333688, 328153070, 930008860, 971860167, 547113655, 88668428, 515969798, 452346537, 323342171, 426554801, 140305923, 719561216, 22660239, 827973004, 913691938, 592024496, 832232351, 666197287, 582498317, 692732681, 986826891, 982426977, 290748219, 258553896, 933890886, 555096314, 60421360, 931555647, 281848910, 194876173, 736543405, 985544735, 741503105, 286028519, 834566029, 541324270, 124996837, 954887021, 304953100, 918491604, 341292719, 631797018, 741206063, 147689495, 276822103, 629228284, 345038293, 314629678, 445792216, 314961655, 335616558, 22008126, 678375852, 966855465, 551715857, 679606814, 30915912, 310499030, 821241469, 275983235, 889071860, 136558158, 165676358, 879767763, 423936223, 777203876, 845171223, 844200823, 688389221, 532098471, 37229059, 241818566, 984366719, 769058269, 873411484, 747226122, 255463958, 455202580, 46015788, 115939862, 475396395, 2833924, 173555010, 474236503, 340058141, 875032998, 228389634, 257428921, 730486537, 663422670, 512094824, 837242422, 589997326, 397389866, 301600592, 982643386, 836020693, 367148286, 847039200, 886697739, 299190843, 899538748, 702738122, 117094188, 149563496, 678854287, 430232583, 294657036, 681075388, 413682757, 787536093, 656095178, 978105755, 940829715, 697240920, 189475866, 312741125, 224682394, 181890355, 304405712, 860643674, 799351923, 882773386, 65067070, 354161564, 711246157, 827476456, 137330168, 13460158, 587200881, 711121718, 974851492, 751465421, 533933433, 126306072, 92842096, 326657572, 102172301, 829791464, 792325985, 516878864, 526165469, 163106545, 584153603, 503276119, 793802413, 830644681, 637563540, 518884247, 72161230, 623914811, 197267734, 963896944, 698873066, 528095720, 679945984, 499067063, 512721661, 703408190, 491533254, 350554432, 233792806, 705835676, 809996184, 587655792, 945507572, 659077581, 647308968, 273422246, 729063472, 873133855, 897027336, 59890325, 618881667, 93905356, 958757583, 859128406, 943173724, 256590268, 972999568, 113014069, 772044612, 866722094, 472591212, 842515246, 851415199, 429308079, 93416800, 686187193, 563466861, 292323794, 836827104, 659835281, 428461640, 524594456, 677161535, 2389172, 107381704, 58458053, 78159651, 189750608, 557090363, 119855218, 735089529, 738091728, 84146871, 447869318, 285401587, 396046391, 811660963, 284396093, 206691385, 210963781, 449096401, 333231956, 896953021, 940443878, 859939776, 990059188, 470874269, 241453626, 243342482, 493207145, 373544405, 183401808, 252945485, 160071088, 304085247, 294802266, 215496343, 616178676, 826269135, 906263946, 493934150, 102879603, 450222263, 196449258, 910757180, 288847905, 858675850, 504192947, 988176161, 359073842, 879310905, 921170170, 644558276, 797626489, 804928351, 353757913, 414490028, 7474308, 217093497, 773524664, 842035173, 127774686, 962612434, 350140162, 653420600, 151559065, 104324044, 402585353, 206216831, 913462785, 202727271, 724064342, 66980362, 13749861, 478135350, 681591431, 809911544, 457997697, 789459811, 345621492, 667525305, 100126309, 128620663, 25932363, 709326090, 835062393, 727052582, 845548854, 244918018, 516213708, 393306646, 929203494, 901665406, 714502127, 18314857, 821934000, 839544999, 611235658, 166713244, 235388005, 252183987, 595912559, 978118106, 848179731, 783237044, 696902378, 367522228, 242514386, 366823205, 792076198, 463776465, 127373403, 925110435, 217775607, 880872668, 933065055, 280514951, 252208539, 539244097, 429766636, 404264122, 964593019, 991468532, 1929282, 29573362, 372065376, 412483527, 816609136, 94163331, 732057362, 383991824, 597226261, 821221202, 237481977, 629082978, 59580469, 366802077, 264484413, 595480935, 450621971, 762871400, 796976965, 746173920, 670152353, 393873923, 415574156, 454710269, 780168439, 64602239, 394350405, 121847786, 669787913, 130938000, 312139875, 87974280, 461015749, 270103182, 108552199, 319067617, 422396317, 780955949, 170929705, 349485350, 409303090, 766161234, 663508189, 503795500, 7292188, 255018570, 573066685, 680734265, 645778623, 827935267, 694613412, 202022554, 564030647, 146868281, 571258020, 53490370, 758517285, 623273205, 210005975, 153869466, 104243540, 679660595, 953103249, 674468957, 637952528, 278559539, 338449772, 566965088, 170828266, 350324205, 511179497, 599600607, 806732877, 681359346, 130436399, 963193438, 428313372, 617094311, 477387603, 747599233, 715365236, 564727468, 893509488, 292047431, 608863819, 67982995, 475837406, 68788302, 150240670, 58876724, 506064640, 59846423, 225357994, 806616361, 585538739, 705102479, 431641285, 545349637, 14485987, 819938314, 694156960, 287203707, 40643671, 5108148, 248124232, 44856038, 533498410, 243760104, 160809537, 506327724, 799674282, 350304289, 334160698, 305867266, 182123765, 323857720, 806083671, 228007939, 922862056, 339266014, 894644334, 515822527, 407304513, 21592592, 909694990, 61704679, 179166303, 949585911, 970951150, 626782950, 487141065, 215307718, 145747990, 898738213, 308953206, 943114962, 217628298, 802163921, 362136646, 944413771, 812386677, 360858678, 175112387, 901239086, 207008930, 967041218, 180649303, 226412041, 617929727, 689452705, 318228497, 859718594, 780802490, 800450872, 351126111, 660900784, 235100159, 171849433, 320717570, 615167289, 715352097, 525668595, 807773555, 855452396, 552405812, 511597613, 157688065, 418091440, 569957214, 874338472, 272789070, 93650421, 324893432, 773177116, 83232943, 341142181, 288714994, 66769188, 517881315, 490511857, 725420002, 828530183, 424475131, 987225453, 247498532, 205453929, 98501114, 952089072, 808904693, 461588214, 782900752, 18702019, 474194837, 40964459, 660992611, 275183154, 943468448, 501318557, 709328093, 524653806, 36266563, 266874733, 605550477, 312101153, 221448296, 218990774, 23655050, 123743345, 77243523, 594486945, 365338754, 500368670, 47230822, 855140892, 320998639, 327911971, 477874157, 65247507, 1811403, 955641214, 685218664, 706999254, 306597560, 310245374, 397635621, 561007524, 730173129, 574140711, 483364395, 795173167, 14084423, 691518484, 651016656, 666878394, 50679988, 146760846, 797199454, 411613486, 706778286, 719928209, 230542628, 701108994, 491686040, 459929714, 849007556, 292060675, 347567855, 760162313, 527690214, 775271308, 507876854, 230386981, 704513316, 179930687, 809604623, 330290695, 719935511, 836512736, 764404917, 128010040, 235124354, 119963664, 341818532, 971169837, 323337852, 173726362, 972152578, 845649310, 941692100, 656067884, 590714893, 433869350, 354008888, 221398279, 878336717, 306722510, 400732882, 636490723, 589941740, 365262581, 913778026, 642742422, 386246636, 589805529, 353528122, 572758526, 79825575, 273532510, 765294583, 734650790, 970516200, 789662673, 448884717, 558206414, 841277199, 24458585, 455912594, 893668725, 549358264, 347723369, 119548710, 649248341, 218849098, 358443251, 846243857, 552243343, 759394753, 426524896, 475869992, 721885799, 22273509, 834278814, 924650760, 579130106, 129989746, 51586294, 216839685, 648083021, 536204928, 945522232, 99642328, 323795134, 137724947, 895213255, 386872586, 239521148, 248527656, 645783550, 145031015, 758414562, 516390424, 944020256, 846298373, 301028219, 884300978, 498802174, 742782265, 29124086, 99694821, 577095526, 718725211, 203622232, 983253558, 826389187, 574950090, 222823076, 366219509, 853786904, 752305845, 314812207, 917047522, 806146344, 123049901, 261789224, 4165785, 416666283, 253331137, 713360664, 217255968, 705329753, 465293524, 258444160, 811721687, 905384197, 922261867, 646968828, 308386701, 336548381, 514263570, 333172478, 598025041, 509269866, 147210818, 35839887, 419158507, 4153185, 884130124, 839146452, 889219342, 540175193, 888660602, 263110887, 657884128, 453638276, 726169580, 595089649, 784691064, 795886179, 755022738, 230194404, 115078545, 948902156, 208040346, 842938125, 278419513, 838469956, 64275589, 205335622, 767368616, 94472436, 11842670, 47910210, 599520350, 789259609, 926198336, 536990027, 919892549, 642685784, 919192530, 967060080, 835709452, 300896907, 528956764, 86344046, 84220846, 320683023, 764179394, 790795997, 580690902, 16921552, 755232645, 523610362, 154278739, 430281168, 291135191, 94537189, 98595648, 117993230, 873734495, 194815551, 845308569, 470731135, 373962286, 293643509, 320927959, 573350783, 304464701, 707813313, 409778469, 622245517, 445851257, 720042888, 311216554, 666482054, 182025350, 997240830, 532907533, 314301538, 968290131, 881070866, 395588081, 635915896, 196359419, 708524238, 797555897, 230008187, 367273762, 504055121, 393508124, 27845151, 938819036, 885172003, 314488698, 250504143, 144043098, 942222977, 410325419, 531286272, 966791173, 484401996, 697644833, 662785949, 667824728, 997926575, 78903417, 830976172, 150011828, 990526496, 475986179, 511054210, 49321204, 955547280, 492962708, 205988050, 909046027, 891078171, 441848647, 158512197, 638899057, 781788478, 418497031, 454203505, 428959329, 190324056, 446583007, 524005480, 23203862, 161791851, 731307733, 235933252, 87494411, 551358708, 882056055, 122504913, 986161462, 774983543, 481002308, 563372209, 150851559, 452903233, 324154150, 270299600, 303334061, 273165920, 44566403, 591708521, 999647497, 349943538, 215397406, 127819031, 90354817, 347383050, 409630381, 238501058, 622341139, 81359001, 279098928, 618748701, 66215244, 43329529, 664787908, 598139071, 289674616, 395672964, 237463599, 131524172, 454682049, 578646784, 772752799, 516619110, 703775165, 868044414, 376485031, 988324725, 929593080, 703346218, 510853383, 852229398, 955179895, 546376426, 407017830, 703920762, 159034908, 368257375, 41050148, 219897217, 186636880, 815984528, 954082723, 749346422, 167694104, 37032300, 507825846, 498891453, 626032365, 172559709, 935404211, 781732092, 333887925, 888348246, 144052369, 862309764, 6647566, 154014302, 399526991, 773347022, 754157899, 633924520, 863918261, 988257603, 499260924, 604220756, 177166395, 7981972, 351841461, 43539771, 5043262, 465145452, 808279267, 613877966, 504541270, 157549164, 691537518, 287257041, 723859276, 747775479, 391533879, 373789150, 314776291, 96483851, 776284238, 697940951, 196841956, 854859739, 466066661, 369060531, 554811140, 128532489, 353007119, 586416666, 689322894, 323423322, 797973035, 71825947, 912422525, 596706575, 933264563, 35674735, 424071624, 940695457, 564997150, 511670161, 551811861, 73966941, 201429966, 484812223, 856076498, 386160363, 69651767, 894686606, 966543037, 90220056, 377409971, 823979310, 809182506, 906893817, 954924054, 735161670, 210704405, 583579895, 893444120, 108797792, 27673295, 373236280, 3926459, 620261790, 203273171, 15714950, 793200867, 470372462, 618929967, 936285740, 316251172, 464928557, 787795205, 388249859, 329821107, 363439832, 543688402, 51933304, 966858223, 313405814, 909965846, 500219611, 941662299, 862251463, 415209963, 507920184, 739455211, 607777167, 377777974, 429214756, 406243334, 450944650, 163910894, 876834993, 434581456, 871719392, 814071779, 897827872, 839083510, 694269573, 314805828, 888043307, 892244434, 267381219, 135616240, 451552773, 883608512, 941024564, 208137479, 2138072, 969917249, 779769205, 365199394, 549768874, 860314917, 334530086, 369714023, 192675412, 812874814, 610053972, 256852661, 908418356, 659451095, 408067894, 953172801, 926491691, 632824457, 56683426, 924158848, 588500020, 164588873, 742560745, 155056869, 15517115, 869753458, 156555228, 4594959, 64379684, 415101636, 13806391, 698993082, 672276403, 114770139, 371865091, 75546865, 587425668, 368504672, 210989906, 532429908, 322538469, 950628918, 734476843, 15322287, 197676926, 841053142, 73972903, 637370413, 798661586, 911397615, 188866278, 644730924, 941035484, 514578769, 491878793, 468042944, 687886095, 517874865, 946593573, 49592480, 874474280, 677887608, 575189243, 323423840, 849311554, 325819453, 542917777, 653411452, 104356216, 668742807, 40068263, 277533142, 813853667, 651876172, 977063440, 377007548, 440877863, 767766576, 150775759, 812985927, 430227772, 649881733, 427450343, 483431919, 867025422, 601676761, 161584900, 877241141, 468047351, 967822960, 934579059, 453914925, 687948302, 577787331, 216008066, 783962866, 440204483, 929373579, 99477971, 90856809, 920515901, 888683243, 564128352, 822817955, 270850525, 844443615, 788657979, 237998272, 673284032, 487657538, 745930947, 957516846, 817347071, 865575164, 58901883, 533248840, 772904638, 611525891, 898183746, 444228618, 408143344, 948179824, 788001062, 882743347, 287306032, 947703135, 355590438, 328451640, 269973102, 103393823, 857044057, 96055819, 146716410, 259696631, 331590184, 67788027, 263542675, 446614768, 625995264, 339777164, 364096088, 677341408, 903970504, 68480504, 288080208, 123015525, 407536868, 19539568, 338986270, 848294670, 723514819, 438594661, 632064628, 69018650, 393363882, 243001449, 740601300, 994346409, 32670126, 897817072, 447582399, 676617536, 64143829, 846980959, 894882868, 651083690, 983051582, 818687686, 721722276, 258578265, 829505905, 846597445, 126029079, 384459722, 594041825, 760763736, 589964564, 805387479, 30030910, 727095284, 145116860, 207096607, 201512076, 57801357, 94425033, 645855218, 168689140, 951091470, 288064719, 31306997, 473353284, 384841736, 642589217, 394314466, 242493046, 873435846, 954295399, 484416469, 894798941, 652105531, 951804824, 927059755, 575441266, 718107687, 688579259, 804374233, 675939522, 990179473, 981198306, 270069046, 511981724, 812637755, 522760410, 684609682, 65338402, 803733238, 258141277, 502245993, 516072013, 451858036, 417565148, 162200804, 901557892, 777938741, 257528953, 442316710, 861386479, 805671270, 828286452, 921354372, 94632258, 461206627, 551662561, 121694125, 281493708, 659313067, 108160881, 802070747, 129819585, 465826589, 852552756, 297866381, 312192679, 696807926, 463644386, 810720689, 960187175, 906009012, 141004091, 572415407, 498884440, 557772400, 445138349, 710728507, 127502881, 801612461, 109861271, 923848204, 691626798, 793384009, 884435906, 500180121, 911177985, 837935370, 282631013, 235855886, 204544040, 631253018, 975403367, 415997745, 94830139, 605681074, 644372200, 269910178, 473724817, 674713708, 108997776, 795461871, 223550298, 76687318, 544376808, 20033845, 443516134, 499400650, 284276520, 237105538, 312279527, 438793378, 523973451, 239068750, 596584475, 363272005, 272140084, 119499254, 779609332, 339375043, 517488769, 504816350, 581423527, 471382331, 61261202, 507092496, 451042425, 154552242, 739030545, 682516135, 631261260, 598998649, 844114486, 157498699, 903749170, 979667274, 753767379, 169391314, 419877223, 720712098, 738196230, 256991498, 323559832, 93041342, 596758667, 99411882, 246204527, 537150182, 649688984, 86505686, 475061900, 668225506, 465575695, 617468441, 428788932, 850050120, 335696521, 393279115, 148676614, 994019746, 817129519, 431284104, 935741494, 679044460, 943500162, 531681206, 763727620, 813069727, 40133968, 49983421, 699698896, 432801678, 195320355, 623964624, 551879558, 298441460, 714416550, 761721443, 944928566, 865270640, 78199768, 307972324, 179123697, 653446598, 368498171, 683672839, 966278378, 723000542, 662855649, 242687194, 264136312, 571133016, 127653519, 71970606, 98826814, 218206132, 68679470, 885891716, 495840488, 626999810, 772984058, 800454901, 964770055, 223709463, 42101749, 76063275, 759352275, 37797103, 44000322, 425099886, 538587342, 740816569, 814298553, 743723738, 644968494, 312594532, 552236611, 516348680, 961786797, 531353263, 27805567, 768027378, 95038508, 576199252, 322669770, 574776760, 48347631, 200111021, 435223607, 78892802, 665479145, 718508595, 464660953, 932110844, 225884229, 580581389, 478873857, 656503455, 632217740, 178809502, 688814116, 450628618, 207475381, 159226864, 11407890, 377470913, 46510036, 332079106, 841854779, 703438905, 84433576, 156979394, 175703837, 61764001, 246262159, 726817562, 723457879, 71932367, 69669502, 101888716, 789417916, 133855983, 265035329, 749973227, 445642217, 494022008, 248086605, 919809016, 389055126, 224918141, 959651473, 493746460, 465377005, 649347766, 71004535, 338584315, 847286288, 572483379, 978251350, 735456448, 184941555, 194331314, 622115747, 124575117, 364399262, 546743622, 770965944, 867169198, 382975869, 302178546, 260236927, 65915, 743331495, 305725334, 587981247, 664328390, 556661938, 432235345, 315839957, 477473270, 550662015, 505812642, 653379347, 406254661, 196029388, 582637779, 922192519, 863204156, 2019344, 875452412, 454420842, 820387894, 225278591, 331550538, 792720024, 787601980, 818631101, 996723463, 361283667, 978835536, 367897899, 630341482, 940874384, 263583548, 147415294, 393942950, 190446575, 881133877, 341932871, 490391123, 235150040, 638440045, 138656479, 200275228, 352688215, 208298586, 692646177, 699951410, 918114782, 758946616, 451010187, 399637122, 970849940, 839887104, 936278755, 746728158, 28690340, 13082632, 23497973, 413999248, 830155588, 828637880, 5652435, 734462131, 838481459, 795773087, 748916508, 166939499, 760227096, 32713493, 550233880, 979354649, 883495993, 739714815, 984177875, 587064507, 556684046, 195988928, 777215424, 802568157, 370686367, 388921468, 895905992, 503989759, 55888342, 174912981, 111373511, 714786738, 500000588, 759107005, 359369353, 171018440, 330269638, 205967400, 334857987, 458818570, 770257830, 600161284, 775151850, 775242338, 571178277, 568602887, 254852843, 728011851, 741305665, 672661780, 502641871, 262734850, 530685871, 830455452, 755085302, 343093502, 165198051, 84545507, 23412116, 316219282, 433554607, 483409910, 902545950, 243262647, 14272719, 805261660, 442737560, 691018320, 20855896, 750765009, 428224009, 129299897, 652315130, 870322457, 978104945, 327857815, 769282816, 697792338, 617843025, 350842918, 157950435, 782942747, 896108213, 35468513, 346302543, 295505859, 16450853, 136410355, 401968223, 370679551, 747570097, 455012713, 223292942, 938740950, 256523954, 399152597, 841920913, 739836246, 915355291, 658180271, 385184675, 128337891, 207653480, 279335191, 944238424, 924637698, 461796594, 444035518, 300046943, 26329251, 668431333, 685561921, 244852478, 698343449, 106202541, 968305752, 325842638, 379843500, 987754107, 23195227, 899875118, 91552582, 110880416, 989203981, 70488361, 700282409, 88825285, 364134215, 49043632, 879589168, 323175338, 921453452, 792027683, 596275881, 116590762, 280535881, 206661886, 182738100, 728901383, 662281107, 881428431, 843390946, 788764685, 578314958, 316473364, 504682862, 335714928, 35130826, 553548602, 585533916, 401777225, 540411359, 351820355, 570836027, 966866332, 595282586, 392804183, 867160235, 354924919, 508678012, 487935974, 61007711, 934508698, 250059495, 480508969, 38658909, 245281599, 815984736, 727511787, 666565362, 810792561, 709448927, 213613077, 684182619, 458999077, 369909834, 37182574, 371205938, 530584293, 460159263, 865178049, 458873400, 779524865, 40910477, 708405537, 962661353, 878438501, 826808043, 200937227, 309255912, 864518922, 895381418, 174569741, 756115929, 25601100, 550079238, 171244354, 837172790, 624253895, 373818381, 426672756, 389217613, 594606192, 159181395, 422485921, 931193277, 501950978, 719710313, 133881675, 727749522, 837985059, 121685031, 77920312, 492893410, 874381526, 943092219, 589009635, 165003896, 624714744, 733743422, 316996174, 35405169, 209888592, 818772144, 455753601, 375871347, 331965204, 589733041, 599615604, 123398496, 133091256, 807743871, 186024870, 216069287, 390222034, 764880208, 298211509, 177872015, 263585318, 209764317, 317471517, 801628189, 470723030, 589574966, 32096869, 281895606, 122926738, 600401235, 93649154, 328691694, 551494558, 421136263, 950313334, 268992907, 88890337, 702786683, 678862871, 909111664, 274868356, 222839284, 335672499, 519416314, 20569010, 43385739, 381421539, 802159647, 20969318, 321144653, 880170331, 908441118, 477693297, 934308059, 193382622, 159722851, 688872755, 672456200, 202521488, 904946965, 808613445, 42561200, 754218234, 300425372, 748586271, 36363728, 499283975, 244744062, 534401748, 773816513, 836122577, 416535363, 93221309, 128031698, 987468223, 468416479, 36075629, 809514919, 271796640, 251418731, 336518984, 684625898, 604362584, 924661034, 352743713, 770384396, 606953802, 121664343, 424704644, 256059878, 529875801, 614664996, 377149532, 913215546, 466122075, 18008248, 372266574, 182358458, 291875805, 503791939, 834145524, 727328986, 568901969, 479254736, 641623943, 712731293, 218282843, 543510010, 326146642, 514950430, 369159814, 851848053, 373393246, 717996140, 918333865, 375260577, 812651329, 960122973, 472359327, 156790229, 894523728, 165654675, 358302765, 134809358, 71638073, 457575867, 501151582, 259730609, 461810016, 2083806, 447070856, 537759240, 884270740, 388643447, 594598673, 860387478, 495581558, 158560402, 790269003, 140374718, 172651271, 777085755, 412702651, 241966334, 163654544, 488548424, 290085693, 277102819, 872733399, 944567811, 794119982, 429540350, 88526604, 143000205, 459224860, 997191618, 660185727, 351127341, 918491171, 315867279, 991342159, 21034786, 724348481, 136110290, 415142913, 555762622, 254148964, 654680024, 247435483, 194518398, 515297499, 340792432, 59733798, 741199996, 776884618, 899017034, 689640350, 601702843, 424085935, 709783087, 884591018, 950150121, 500281261, 769460977, 758820384, 267278120, 318768849, 927214964, 249012616, 627454706, 490749859, 617473807, 878236935, 445373756, 758894774, 928040023, 547574681, 266268103, 138270463, 59289124, 418616293, 440117702, 482688448, 455146639, 536474109, 392156046, 697341035, 108951858, 865914838, 426557256, 742411052, 646484246, 286118145, 328416165, 402972264, 184836407, 75513930, 595976851, 624543366, 230955129, 251789037, 505390121, 175403004, 573331496, 15372841, 905752994, 53076435, 870755451, 28671424, 944521045, 234137304, 149936820, 54145378, 370106224, 8522575, 706736580, 674275481, 896588166, 523902165, 262481693, 784594107, 559578493, 877007700, 380116184, 147072683, 435214950, 996161543, 486691975, 170334311, 382152603, 508008158, 748265152, 616824521, 425379625, 495866248, 244992873, 184335106, 248520452, 946859696, 941883702, 914493184, 651530901, 442720297, 800006828, 361185653, 722453218, 518520526, 864004978, 191164106, 254592273, 522290892, 959982542, 370685256, 19976405, 274574519, 955479043, 385689529, 445929896, 140621780, 381106780, 913251200, 291883791, 868304871, 912037279, 481955293, 432132276, 23499383, 903279546, 913970233, 914377330, 613809280, 441589050, 187912332, 146686429, 134381845, 72993394, 92204798, 46997206, 671569379, 302189138, 682019466, 566276014, 615596038, 835301611, 137309469, 202488515, 632146531, 259605456, 822754164, 85055673, 825233488, 528426082, 181278001, 743903506, 245696945, 90880593, 613378894, 244795631, 418012942, 491364320, 460247107, 5777347, 12529659, 791216352, 332072852, 665179087, 717145055, 359535973, 133741096, 790910768, 788707708, 774709368, 827968618, 947660559, 620273376, 109247982, 99279663, 936347568, 747429349, 815017110, 676666515, 879325176, 255469336, 429148625, 263566322, 383017992, 546695311, 158664218, 257169883, 97062978, 255617527, 372662841, 520944930, 305198052, 817754713, 866303993, 640586700, 365535030, 413738534, 791628087, 830169485, 47107024, 510058501, 563860824, 207793828, 510317922, 947714247, 650986915, 594585847, 44081443, 267246609, 824802643, 359789839, 557592057, 55940479, 407080566, 83371444, 676664459, 287465377, 742794167, 386175143, 799909560, 265990628, 277149486, 613739196, 137253669, 758895936, 86741427, 61437637, 926695789, 309588436, 957246958, 782138323, 8457568, 693728421, 763528651, 157883849, 439779477, 713966263, 147747117, 652945554, 150800368, 397904851, 767181248, 936516865, 62388805, 495548433, 848911682, 699229562, 93067568, 917058212, 881515571, 212839859, 895273658, 685120733, 331460659, 101426192, 640473824, 345668336, 849038460, 97934151, 759019723, 934779241, 389975160, 133179555, 146549194, 461144612, 59099849, 498767560, 734390544, 886082861, 595533327, 321638589, 391672977, 811589068, 22413230, 42431840, 953581701, 736690056, 397032375, 910465986, 933042233, 72833909, 845256715, 434150901, 771489598, 426578386, 344630426, 887254352, 116588312, 522199262, 681505725, 758477762, 292543792, 561812580, 150971084, 537146476, 792783798, 76402344, 447364046, 964506969, 825335367, 300792139, 560614026, 616780306, 524365540, 628820233, 735318147, 112175621, 270086331, 861492441, 402921978, 343838741, 764871598, 948967692, 542244959, 217363391, 974859152, 83870006, 321066862, 561685319, 746452238, 673773804, 610190075, 30270728, 474154705, 143562451, 160916043, 795770870, 946434848, 746756034, 218107053, 810706733, 557931397, 226222929, 73567205, 499406805, 22995469, 580763558, 846136403, 941074623, 548332595, 866708608, 837724024, 399242886, 456874295, 577995151, 762989420, 196734315, 853902889, 667814888, 308392683, 355308907, 416839458, 122547970, 711320145, 826238645, 124331380, 472304186, 557092969, 598896465, 86341960, 903572670, 950618300, 438428248, 733865741, 537908613, 225842340, 142581410, 747455497, 56381044, 893392342, 20617590, 665020992, 439338219, 278181338, 238739709, 324551949, 657471799, 414780328, 451297511, 36810881, 558625438, 750890960, 324523961, 180351781, 493761716, 2333175, 158702555, 937155245, 820822311, 21680861, 888813599, 162341582, 755170302, 115939009, 601721583, 531174750, 213327006, 405715693, 910620312, 346908599, 92967778, 656479273, 752245251, 862902629, 772216933, 433506447, 703010794, 241708263, 340484000, 714587611, 807025410, 87645528, 650050848, 172117762, 495299075, 382780029, 593474182, 107569698, 699405477, 438305976, 102615335, 738243987, 45128925, 246841753, 557215223, 506421704, 361300817, 237613526, 482998404, 135273457, 392490537, 540384287, 718365848, 597228843, 278970273, 830630127, 294515417, 257437180, 262688960, 120096933, 492582968, 529565044, 689318330, 810041611, 931613326, 675317170, 74181814, 96056760, 231533378, 954330594, 105898649, 28283499, 967751603, 903232444, 955519774, 480885994, 457175449, 91156631, 965300889, 921867074, 429664203, 880605746, 508586129, 393231869, 361322291, 448690690, 355805484, 470239786, 97413112, 165644141, 685114787, 280064313, 500011049, 742441981, 191694899, 978890517, 9000575, 117596743, 637967323, 158293214, 334999625, 921019812, 722509869, 985680077, 672961936, 391435854, 430485466, 712907260, 552466450, 542907212, 103111915, 65513530, 758454194, 672459004, 92692619, 981955698, 144615033, 498654809, 720623089, 401448091, 567185187, 411389220, 441032304, 847644185, 817332214, 676101330, 951775702, 669708630, 744095753, 601516235, 381378728, 964386377, 610154977, 72178216, 112040405, 467217838, 590795187, 560038652, 109113553, 105124903, 697689614, 926282780, 566044126, 741522994, 643581467, 322039487, 875511933, 85469673, 670107923, 109073373, 739025959, 515766447, 809805087, 680382242, 92099403, 299263456, 778629023, 342609096, 176148994, 968730209, 732219508, 74153775, 855192116, 794980291, 192173409, 825201500, 813158053, 558763513, 556424297, 119129601, 69670310, 663033899, 343886687, 147918959, 629919699, 520490609, 619340489, 523736877, 240509058, 781486935, 344253843, 13612905, 585348604, 853401722, 957483223, 512379001, 532168349, 929606887, 522117728, 592091841, 136689874, 779323315, 457175672, 923168291, 368918104, 683805959, 595472603, 79565694, 732147952, 657261942, 610851699, 180988623, 112006550, 236975686, 982479828, 551689419, 970050030, 749259970, 987474912, 438983611, 66779530, 939279360, 682828394, 944347133, 487573240, 483369892, 36918659, 920378000, 679597173, 225718818, 362144524, 656946577, 367896336, 557093634, 370397675, 156172398, 987031457, 77725518, 773530003, 112915438, 787018767, 405687443, 954017029, 565377828, 501194967, 780597691, 15188744, 696688058, 786184587, 458717397, 105908055, 404726830, 61776356, 456860151, 960789167, 735960266, 537759656, 164804605, 240885745, 755378749, 633496513, 478192426, 928316713, 255937329, 907370381, 447202248, 248450561, 61952433, 578528739, 225852609, 186138179, 442386799, 858120704, 645873657, 969683879, 138653273, 690797877, 547208373, 46943640, 429617898, 416240210, 822122221, 127399720, 87778917, 648124446, 252491523, 650687706, 299620527, 953508946, 392905510, 356621841, 205156574, 779301125, 936077053, 227618201, 344719380, 626398753, 585919065, 338442360, 540265203, 951929228, 733392152, 901517025, 875841623, 481337886, 57515345, 859604063, 962384674, 274464260, 188218881, 160251383, 129541961, 763496728, 892844644, 12588012, 626009811, 961732765, 587054582, 423952619, 212463559, 337106722, 224874662, 54352349, 425012879, 574814442, 208132935, 927715473, 706393602, 203312272, 554998778, 192593052, 25338506, 669216580, 12277671, 804801551, 594009922, 890255652, 237705795, 575928343, 446123877, 404043388, 855878372, 728185300, 714839573, 21526716, 551921543, 12539509, 509113677, 258114986, 25773945, 292540260, 148303898, 108338353, 747707562, 136167797, 372361401, 300959096, 634109107, 629453841, 565347471, 839101912, 165405213, 573716354, 147185862, 209566905, 230897678, 207058362, 215203322, 727078554, 521363557, 25842441, 450457524, 569387109, 150533446, 510362388, 590421548, 798918208, 537134021, 553602535, 865718299, 45120381, 627220021, 398391007, 518575826, 552496306, 149144473, 627702620, 282040325, 484327292, 507471366, 440119607, 443961032, 175211170, 195005452, 704795704, 269987269, 834818583, 404234781, 195419239, 309702357, 24696809, 380272013, 455821407, 199087088, 914573720, 92977098, 684261104, 571366325, 68196856, 254808645, 446526124, 95030756, 27704415, 557698218, 130075459, 19899209, 892168533, 968067579, 316038202, 772821898, 307425022, 188223835, 983006107, 212982825, 390567993, 687317136, 2944179, 676604159, 718496690, 86552276, 82338470, 831855682, 702668957, 473650745, 336810216, 216558524, 701869944, 104636692, 821451292, 148987036, 587314239, 226695999, 456922302, 613605246, 818651932, 636291801, 647353725, 552354894, 188034175, 866963128, 80491012, 527379991, 19784615, 464683351, 208152778, 456383265, 678876918, 969329259, 69661566, 626640387, 852849526, 654209688, 107605373, 463375080, 820950242, 297759884, 705583510, 636274682, 878163202, 3548159, 969829932, 768663605, 551455367, 313420920, 858013011, 501837751, 200757150, 7727171, 612090605, 127841200, 583868495, 190777376, 712468575, 761534634, 28003592, 638809904, 67273754, 80391988, 442077307, 844189690, 838063575, 174926004, 807107291, 570144877, 693089052, 598327628, 670009276, 995759353, 698433344, 798969038, 650606911, 151524603, 604992477, 364334588, 924183783, 291354162, 440343859, 676910250, 171373196, 997703687, 202217640, 741838307, 712809089, 62261878, 47315303, 77736645, 94367325, 752670235, 832738190, 86352840, 145096237, 376411200, 601781172, 219611893, 264350879, 786223144, 991894986, 501200518, 278340139, 305353394, 15133682, 367859254, 133729090, 8760331, 454071648, 147732700, 501820222, 595024254, 451515188, 479887429, 183197618, 875399379, 391590890, 958531415, 206889048, 117624497, 240401762, 759075536, 84996073, 968320403, 291927167, 457039275, 617044110, 76984709, 610043261, 868327890, 778286118, 984972397, 191650268, 92436685, 9496948, 595619350, 342653972, 484131427, 301387248, 260169050, 83748649, 276818929, 426887925, 250278983, 49316479, 621884220, 905750024, 165675737, 361966031, 634122195, 892141495, 967034476, 111096673, 582380508, 74512527, 498367606, 174867841, 621579870, 377309573, 83092286, 541821182, 729259388, 13242237, 835983144, 788857312, 931926277, 306578070, 824069332, 925372970, 173171453, 91636193, 294118693, 50108138, 29447968, 68981643, 360441748, 278370559, 657038025, 419059186, 459221286, 586425428, 567192524, 421638113, 511443851, 845536462, 207186607, 194176222, 227100307, 928518701, 974578141, 175269577, 159968539, 824701294, 406085850, 760402573, 755911372, 899192940, 531627071, 970133252, 460280530, 687762367, 737291597, 40733397, 529934157, 89400633, 280556850, 890519511, 482814410, 122875214, 363374175, 41598160, 941797001, 859083888, 776022029, 785583561, 73270524, 956833979, 903999483, 772878899, 372740008, 142370175, 576021260, 954178542, 881254822, 695251692, 350903524, 161622347, 604270863, 553650552, 412192647, 390617492, 688619772, 576367665, 132369802, 374883516, 398381615, 449499635, 891528358, 573884935, 984286222, 36430134, 500126486, 52741037, 812611828, 660069956, 988506746, 830830913, 752620482, 385163886, 278104329, 724049007, 51605964, 18203834, 481009928, 20617874, 780515066, 906768296, 582102251, 888279735, 243199146, 405255848, 622660554, 506111885, 890164501, 594823801, 336437381, 946703037, 229969757, 830193458, 224291235, 181498081, 51104516, 875207842, 646654212, 679423349, 163979122, 236852382, 196204979, 814834134, 528143722, 144087606, 429507225, 499705994, 85223406, 378163576, 874436054, 970019659, 602961929, 379668778, 692162665, 18399063, 27532195, 993995350, 199646954, 116208578, 725991837, 329464440, 787100941, 416396978, 376334639, 492191785, 953292328, 990593574, 836754490, 814231921, 951562267, 928814666, 165968738, 656643627, 771713992, 408902291, 752335692, 359003235, 412864962, 949919255, 575848572, 218552170, 26402554, 135996885, 903246450, 240628736, 657052793, 233890236, 495738815, 760115332, 889303998, 939415343, 702033009, 540122185, 461864841, 124760864, 978840326, 14786787, 597695991, 882544150, 38162003, 610166811, 513889633, 747310882, 627771579, 16393955, 77288425, 565701471, 187707621, 310639899, 739386506, 76020233, 150583398, 966804430, 833363364, 61838485, 954282312, 948208429, 203414792, 919290218, 670918543, 779354669, 165759899, 408269987, 258919929, 871976504, 92937831, 970739973, 557008043, 598969896, 395633484, 287158346, 970983117, 868666160, 48106435, 736645715, 830630006, 173829842, 867566626, 392744989, 955958936, 325474480, 390673781, 451776668, 945824756, 395904573, 212542015, 395622550, 512175210, 963460310, 244521978, 141230710, 179194428, 81177675, 916502555, 938584965, 107257132, 482270265, 121980475, 876580392, 856421997, 610868480, 163527652, 561612860, 369750464, 402571256, 296110660, 83476470, 13394221, 113890048, 889899096, 957760591, 419260038, 612416731, 97187432, 635811077, 711454279, 308136164, 461056602, 154666511, 623330573, 210915976, 603687912, 569126453, 500537758, 756388207, 883750879, 498898787, 92759641, 342672944, 845851392, 843291513, 708809523, 269766326, 919823547, 223555074, 781761244, 168079782, 694296007, 611684899, 502638803, 21671387, 722166231, 120377429, 305551106, 899447096, 807402861, 281760977, 219405945, 305669862, 553341628, 880653014, 813171611, 380811694, 903029120, 364644582, 944852681, 789986691, 21724347, 551499273, 470117353, 891356542, 985253825, 600448471, 60588189, 61380294, 251075624, 834853161, 200623844, 526227839, 248502118, 434842649, 332745802, 642345138, 105088594, 870384226, 5343582, 757924154, 543258660, 559069830, 396181640, 439006944, 602581639, 521332831, 503876714, 855323511, 663160340, 916302300, 864374042, 475611830, 909044311, 582898964, 387315209, 725835099, 648971824, 64710042, 433124674, 347774157, 875672464, 781058636, 889026595, 385848084, 506376542, 49789055, 382268778, 254671850, 43553324, 204305277, 83894975, 503684712, 528711775, 87293897, 644293119, 762684029, 418087230, 487088416, 944827003, 981036698, 534289750, 157505993, 489354881, 709843900, 419341996, 664743366, 466110381, 618030996, 844454172, 158699611, 873991886, 789215839, 211407954, 827948826, 958032741, 63132925, 759533552, 230916413, 788768855, 570180746, 497932006, 351686195, 54087233, 105155035, 544591366, 837768264, 812936202, 409407579, 280522891, 867744150, 601188886, 889563822, 144813508, 305885297, 587851410, 420601981, 380499223, 655205264, 423632848, 957421660, 715131157, 730975107, 994599826, 247244983, 245922444, 382026147, 720228640, 424109608, 94773504, 636291573, 934815676, 240128335, 827506374, 809151139, 789961784, 876955606, 321158349, 583480451, 380298264, 728544884, 928396594, 682148677, 590123936, 327901081, 972466468, 304474993, 681902068, 332264097, 981031531, 851290197, 997390130, 291030626, 540022639, 421851444, 488220321, 251557355, 797781185, 934473580, 849376415, 836153687, 92099644, 501030652, 841741383, 611148043, 228536735, 816763969, 683812098, 542330043, 531290067, 900276257, 958792511, 597392726, 37322118, 955093087, 125261456, 633813107, 747223200, 742628028, 648992448, 872220901, 860347205, 801104422, 158182552, 186035372, 69829331, 837692718, 847369852, 53868325, 519428755, 571759619, 280374725, 37069019, 783315823, 131843355, 470015706, 370714959, 108650587, 686016842, 248449956, 613252776, 955158200, 316603404, 323954394, 408918752, 104705182, 254391900, 426348181, 727004367, 483842685, 2799158, 887583757, 77516717, 986178543, 58742314, 410540854, 529276213, 998602242, 617947888, 344885038, 95904551, 454359677, 980757172, 926405141, 447994714, 245671287, 313392410, 775525093, 490487916, 701686440, 634762052, 782482192, 610431958, 325548088, 983828501, 280661848, 318319914, 284123788, 578714838, 403593115, 112845446, 744631028, 361044054, 770339065, 958494479, 837803182, 267948182, 262866933, 807289272, 808408639, 818343207, 442456979, 409095352, 200477777, 388037789, 798938839, 261347720, 679089553, 499496725, 638680161, 845311880, 166751678, 999671706, 993958094, 348982796, 763051821, 621288420, 369185190, 319657893, 848785201, 313359829, 174101087, 271308839, 684427260, 399264781, 374553847, 969386168, 447062592, 850928549, 487813705, 674095768, 114096671, 7874748, 341186830, 782606192, 949734919, 158230725, 293127559, 296771350, 688872054, 900673761, 723287031, 477987873, 87657408, 475414995, 139563153, 689220274, 811813134, 84466198, 857020724, 202575319, 431344970, 12301957, 877713444, 517709881, 285094303, 292456062, 332902839, 488087568, 300747910, 98508028, 409525779, 325910679, 288597614, 990336079, 536988054, 135435598, 167660352, 922685004, 42165732, 783934865, 291221953, 998390641, 649657030, 610929135, 363985960, 264477416, 972216247, 391745170, 6009147, 318067799, 463619354, 817565100, 313401284, 596650471, 551755675, 364678208, 859726309, 365746442, 608155699, 680642154, 534508846, 224215359, 117783834, 565443459, 476048901, 751754981, 218216433, 275396886, 672953134, 197732789, 151688543, 407142918, 631514124, 321273931, 825077429, 681273559, 59212026, 111824964, 722308273, 185707751, 701061867, 773077223, 464756052, 733762104, 741194026, 240404928, 812532141, 272688172, 792444360, 69179991, 732785739, 198908280, 184424308, 276640358, 611330718, 871982548, 672542953, 120244544, 696413324, 448874230, 168535619, 967787219, 538434387, 421530782, 277421056, 540109405, 288079765, 70142655, 742223951, 910817088, 759510546, 601681621, 40994321, 452136451, 797958105, 643792616, 469799091, 160156341, 941154383, 868791110, 541547734, 297580356, 444618951, 488690439, 961545412, 455491315, 707576868, 730393480, 216283997, 322205469, 506744453, 462368146, 715947301, 27714507, 959209820, 155005717, 535355, 831485001, 657576660, 390108046, 887181652, 838510477, 231102919, 836065775, 9956039, 575323629, 2897046, 441519070, 578028038, 638746130, 822562664, 107517515, 857649303, 886352537, 655854499, 374748928, 784657331, 954958555, 571772213, 425524437, 36911962, 48177838, 802863180, 680406041, 405259475, 208780856, 971646089, 171053436, 120034919, 790557589, 967323250, 205792761, 345514245, 247642665, 210860316, 496393334, 138941557, 995677229, 620963092, 495501401, 252916769, 949069619, 404636055, 522161559, 466245792, 990040289, 315739384, 376248953, 521532355, 520372248, 345446946, 480851841, 321502056, 443675925, 420332709, 180579696, 370133142, 896070714, 610217668, 875930269, 585588487, 930391446, 456365493, 904465551, 776105942, 500362309, 585885635, 782124048, 117581246, 399787420, 925852151, 853850296, 467104887, 963588674, 128830867, 960715212, 185703019, 768650074, 769597720, 824718647, 187354066, 89873456, 328843310, 127219228, 559244270, 232778434, 580785254, 60939245, 566071562, 831518195, 393935692, 522444954, 504754389, 490328852, 684257114, 921916998, 937821858, 143507467, 684031787, 662134081, 104624787, 982269244, 152363367, 407673630, 485352971, 130343610, 447622546, 581826347, 270922388, 486798883, 460091888, 260228035, 373595683, 837215428, 319226680, 501111115, 986206104, 62795508, 931822820, 654575186, 885850842, 679685309, 779775632, 151808339, 877425260, 980652753, 962643679, 340974644, 881823856, 669098574, 348748700, 789847297, 452062817, 486934072, 25201944, 616385564, 150708002, 2036212, 750446580, 530070706, 748638333, 314783207, 266968807, 987097617, 845882901, 620656778, 282537765, 535320323, 171884646, 47939259, 871178447, 919889757, 703696391, 738841033, 782068017, 995563221, 872215920, 241759086, 714176055, 956384266, 94581186, 590006111, 843619597, 419793158, 912768959, 647537834, 29149007, 386032703, 947438176, 417910158, 300267446, 21831586, 71426292, 82727263, 458907650, 820844012, 385570163, 939157373, 833977306, 875972863, 39057304, 101496487, 687352256, 115322944, 649544438, 728851162, 434226477, 764085814, 330644238, 424388154, 653903423, 392039405, 362863651, 522391383, 941046544, 303032422, 407951524, 465714238, 256452942, 21443131, 935033199, 893427354, 94316966, 454507221, 359141393, 798998003, 755114419, 407630521, 638736396, 281299289, 226333943, 799440283, 674147175, 307865116, 249915132, 565500313, 30482507, 700621139, 296061374, 287409966, 939593404, 651491575, 196306225, 793419634, 273694659, 505762479, 938916389, 913633664, 326577458, 833611980, 602185926, 39542369, 67742151, 211295295, 461113962, 822279284, 80408196, 179675090, 190125817, 209013266, 173285486, 48977148, 5399831, 819585423, 105647462, 468082594, 999522996, 56496321, 709520833, 445816108, 173948177, 280789983, 128419029, 388936018, 455684673, 947525582, 432314967, 930535250, 273787430, 469376468, 43375033, 643355388, 24159349, 953397621, 330555650, 10771105, 854181964, 654902445, 67742513, 15330147, 475060576, 870091156, 169833593, 250617409, 1416937, 204916629, 692898634, 79217000, 684521168, 3422890, 14480174, 178967941, 472129412, 498728720, 433781260, 984168002, 134915951, 69712227, 477634263, 31594837, 177322371, 168971287, 220815968, 178445913, 398367666, 953585821, 523590764, 862149453, 405388789, 974808476, 228253333, 134894548, 511425012, 63452048, 838512272, 607655504, 177962803, 22938769, 304189735, 615241101, 436756490, 166186513, 335224073, 801670517, 719860640, 660032307, 78592253, 862548587, 23332493, 589698883, 572892611, 474004244, 592967843, 906359945, 662469088, 252795085, 514492299, 724876215, 924140011, 174416778, 78859849, 103929317, 190470410, 880428431, 782690846, 407256780, 59869478, 398757931, 547105682, 767421890, 742634464, 203899745, 225905172, 144766584, 67839364, 212326792, 963735007, 889715010, 910382217, 414009380, 773120724, 707265217, 20148884, 900949168, 640245466, 660578675, 458609843, 321786846, 773621018, 487231677, 673324006, 24242878, 799980900, 732180679, 592128260, 406491156, 95690411, 968174287, 935863378, 961378989, 95361465, 111987065, 577719914, 182639011, 482104267, 199269823, 887631984, 929618777, 312981160, 298819303, 239449009, 447730511, 895578813, 602379715, 220629581, 677729635, 8118717, 487625388, 3822954, 301942059, 834741253, 489908871, 988634322, 266064019, 335593656, 112639283, 603031561, 154347419, 941703893, 137560899, 363447830, 669786725, 297567282, 771402355, 709085741, 264476736, 706704626, 677939906, 814138453, 981394001, 297092846, 911871474, 693852264, 84772891, 278019988, 38061445, 38239314, 63662430, 714530901, 794915734, 268819661, 3937271, 962763373, 361010323, 495541682, 290558139, 128625509, 572516778, 60637352, 819630386, 778304632, 937499599, 596947696, 951362579, 568033933, 510589663, 140425005, 983359250, 491456411, 112121665, 472103778, 297730636, 712106033, 853742099, 821039097, 530624305, 186379314, 1824756, 524414749, 687143911, 577653984, 529493801, 165303383, 897008, 625311802, 751888878, 601050209, 443084795, 812738466, 483129244, 299601041, 445423845, 716450172, 89480914, 758837044, 659976144, 730267678, 183479278, 933713333, 53669721, 469528965, 416919847, 669276003, 162950252, 606798054, 89505962, 609706238, 567370677, 9306034, 195740451, 465571546, 799692717, 730789046, 558678042, 17355186, 675180001, 393104506, 821459831, 896213822, 341749937, 339608577, 117757494, 539810100, 246836313, 585961782, 355582773, 242140934, 696681592, 727690926, 623129760, 743710479, 646758293, 758066669, 541370676, 82868625, 61405148, 736462739, 193108013, 567274622, 145418676, 840747449, 135865097, 480949437, 655074573, 469187797, 406371735, 721908899, 922384908, 332500852, 126563432, 930945945, 655174455, 984166343, 902627244, 91890016, 930322407, 270957037, 988717555, 777762604, 438876037, 194305649, 857732955, 229817675, 134179019, 3587415, 886799932, 752449385, 500692550, 288158281, 366712237, 734570906, 817701166, 808457552, 517055578, 148942607, 575709242, 661326898, 835962691, 113072623, 881448662, 637540251, 290664370, 436699144, 750808492, 873765260, 156196119, 140473211, 380193309, 668321562, 577365668, 15567817, 243799160, 171621090, 315340802, 305076773, 516127162, 159198257, 734748134, 259338210, 617601382, 248920766, 10881816, 493421850, 981012575, 434823985, 735661255, 847330525, 760719338, 827106414, 292016614, 246572233, 253254545, 476753238, 926857787, 245240911, 451724501, 668289399, 663737898, 207395854, 706107302, 320972747, 768260502, 257668560, 287407768, 138812714, 411021112, 906774416, 162315620, 33021863, 480317252, 172249191, 625226381, 650161966, 610485751, 480274205, 122946683, 925702011, 501625442, 774099687, 989889234, 739249240, 223671956, 791883745, 335416612, 168658873, 333530699, 159262616, 801181888, 71590043, 183019411, 466938553, 306881258, 591478265, 275539998, 233272640, 426981638, 884381539, 357984655, 911516922, 229272408, 688498246, 699069223, 966543966, 546418700, 229835704, 991732356, 571213672, 817178835, 81711653, 58152413, 601656108, 848242858, 940353751, 203087969, 878225654, 192876489, 422178028, 778988499, 678047136, 12379458, 496662596, 486115582, 854351648, 659393012, 356359787, 8031093, 866786409, 444466635, 210572174, 140900461, 620081187, 755613691, 515444837, 327227288, 219193448, 92257244, 436739489, 931111545, 756778677, 690734905, 51148189, 445199439, 9467098, 817102161, 791584367, 776097104, 844202119, 424162457, 122647259, 559815439, 363162191, 429412249, 761971230, 837389014, 325396345, 60571779, 33085301, 670568027, 219717725, 822800286, 129636094, 877492834, 928553117, 990064222, 923632121, 370332438, 178797336, 206251997, 246221825, 948721375, 276081744, 576722410, 697589260, 190175064, 722877248, 996322788, 739454530, 351265090, 123171927, 569570143, 93486909, 979360649, 525270338, 155117217, 695446821, 565428695, 798120535, 190496879, 83687322, 593486547, 316549432, 901078471, 105195452, 220534685, 811331177, 308385307, 141637171, 82410439, 664839394, 910335266, 201675964, 283032486, 424384893, 285866903, 376659663, 359528424, 607901718, 499079512, 419091361, 733560152, 110307604, 673240094, 522143136, 955114285, 779949251, 14379958, 403498215, 658341434, 996909608, 668284431, 842278767, 961061073, 880288753, 648219797, 48162019, 696567998, 33228909, 919986411, 595160576, 274521853, 540354620, 100952629, 20396595, 123721149, 699412792, 632849404, 73602082, 360179222, 431336529, 625171518, 355438931, 360945726, 778765719, 846762679, 638072858, 635939427, 603149006, 660170087, 959336152, 403732574, 607186817, 359638468, 468006851, 674966539, 219480164, 747519667, 605189666, 524877975, 385910262, 796957263, 424233447, 299970080, 726685933, 744206607, 245200059, 299062923, 775781490, 960272179, 353564478, 813041760, 325491146, 409620944, 691883226, 751655987, 580133741, 852841874, 837798541, 189326111, 992517669, 288682637, 716944099, 870194612, 866391100, 451753713, 223270953, 681917072, 214108421, 74442701, 699030424, 159661051, 104903832, 749552670, 838873007, 566641588, 337181322, 322691684, 864198248, 122698967, 768271994, 394309264, 130038143, 693305654, 551671229, 935312848, 930952190, 940967302, 214841689, 126975719, 359489622, 575928620, 630010067, 671597652, 444190516, 782241799, 201638571, 3847776, 815119876, 344052894, 385082507, 610886270, 451890764, 524272899, 230705784, 483415447, 634997714, 962031543, 489997199, 121170003, 89843993, 185631259, 548151756, 531872657, 49783717, 613987747, 343534207, 646806462, 192373282, 836113266, 700536199, 858079853, 473434290, 121192412, 4231654, 446521644, 73909200, 840993138, 578365571, 405473843, 465489969, 33847705, 978813035, 966179234, 424193360, 624249836, 316753972, 153133897, 257652434, 295325824, 759483421, 615025545, 802641892, 960055881, 823311875, 754320336, 873038718, 705495988, 838454896, 530478665, 186803667, 550894630, 621273006, 698817221, 749884914, 845047653, 819082101, 683991404, 708025035, 685559421, 676290489, 207507947, 659019064, 899231692, 845962819, 19124350, 968702400, 77441352, 477326434, 314539563, 913151053, 774854845, 855202986, 289688156, 917292761, 919802716, 118754354, 250865459, 466011035, 361550335, 269050314, 967570845, 716217164, 694365451, 316582920, 485330685, 263136405, 47639023, 734985907, 804673693, 345968331, 507150689, 118319111, 764915074, 510751751, 662756400, 555418368, 292209034, 190517285, 35054970, 149560885, 777955955, 985305228, 346868934, 469916457, 778543799, 932733988, 668071711, 437467494, 878755484, 37873875, 81463563, 424638145, 433003175, 580480609, 113034977, 597168452, 990089325, 349281744, 627921595, 287475852, 203007685, 719800389, 361040868, 892590699, 2009739, 796234016, 280253996, 557529573, 240751943, 427144602, 747320355, 489378545, 789680097, 611913794, 723632095, 960010328, 179879500, 864328774, 617240108, 105037392, 912048232, 700434866, 72035846, 28826052, 854693742, 593569152, 414832676, 152377126, 542262807, 166133670, 375905275, 424307998, 917224554, 12291240, 760035246, 62377764, 487679145, 350431925, 644806273, 783529180, 196098613, 235531036, 492142519, 410008292, 162245564, 833051825, 24043956, 963836608, 570637257, 158668397, 415003486, 842302441, 798035927, 370477994, 257925137, 129569247, 468567730, 718311748, 42816386, 851383804, 765236770, 53191948, 464958041, 768766293, 85466126, 831191575, 331961342, 89290601, 201870526, 578848555, 290387734, 78930194, 575439773, 21500301, 506659087, 278364266, 801005930, 637440549, 300952568, 502442706, 295309931, 149900213, 546948927, 55542489, 934294649, 778497638, 334849817, 430249084, 474779043, 954258349, 663107268, 428446988, 124149404, 87573581, 556690343, 132478476, 121964221, 874730452, 48985791, 588664746, 261791827, 724032342, 70961287, 582847494, 440298918, 133885326, 565206986, 516936875, 933777994, 216680021, 133281629, 166680408, 840091491, 248460447, 514658122, 245746923, 611555521, 911200076, 202780509, 849430127, 518783450, 587590224, 765111329, 797672484, 392585714, 327406169, 456762375, 548513076, 676570258, 863175303, 348018353, 110518673, 63312126, 378355522, 195930804, 611624158, 466404258, 388537915, 432256216, 329508950, 427618428, 950837693, 547161175, 472247148, 970571993, 979272699, 137444754, 322213234, 348533865, 961168877, 756475922, 27568697, 100286497, 557059686, 952836580, 639602879, 942752825, 361554448, 794912352, 458893983, 173573015, 487332308, 973510939, 889759932, 301119430, 476196980, 564247067, 525956389, 783459128, 879309778, 369330961, 424494696, 680175471, 226918199, 294196069, 404395635, 326795036, 961094186, 949036272, 939955377, 481812572, 749695967, 665064805, 405650069, 930871439, 376486705, 553752767, 791681983, 527810012, 153123463, 563996286, 560236974, 893877037, 581567397, 952133218, 179286873, 96367651, 855612419, 61178722, 684789805, 418848711, 639418366, 577590416, 186020356, 3835285, 65038245, 885599892, 430816687, 859902911, 317533621, 44248736, 344583039, 132501918, 48720335, 178263812, 393143724, 245562444, 575629997, 362781993, 17407664, 480776283, 249371893, 76418719, 872914857, 365609714, 295548807, 169625719, 565787777, 936828905, 60797736, 677777392, 24801500, 570832334, 239823118, 361013612, 955776100, 8520059, 299210442, 480983540, 24773264, 595147706, 641916200, 954194952, 595084159, 271911960, 276033780, 931448437, 895452957, 952469071, 24644224, 580725839, 281718994, 816214733, 455551005, 991168649, 203519014, 507601286, 701437730, 372306119, 459353424, 723828077, 28724675, 168557724, 203342372, 870887117, 213933708, 839261730, 878303433, 538278992, 982096885, 211090832, 472879608, 527069419, 834434267, 949683453, 199510770, 758016491, 813542588, 753478823, 432761133, 126114954, 859586870, 769303443, 725180584, 538894193, 211991063, 886616820, 570709311, 643585135, 273181051, 41628988, 921435200, 614936623, 20327990, 755890910, 587286453, 357285668, 906799135, 284087131, 287223665, 679036231, 250318014, 88809361, 402632700, 617247496, 808204611, 492116615, 307215881, 335903035, 62419911, 294331633, 246296465, 694297176, 227120576, 527961127, 309671445, 307384582, 429398322, 628214203, 509003517, 749703976, 61914105, 57262727, 44346954, 82414041, 17855753, 767508899, 16986374, 611012743, 978413767, 204180378, 751704318, 632538348, 941556522, 160439822, 122370137, 939488535, 536762506, 946101650, 520740309, 813607005, 525154361, 381597518, 977352499, 50222904, 143138701, 327749946, 14595297, 674993065, 770369445, 247798884, 937335769, 952168669, 93371083, 934720737, 709146748, 511417216, 92078373, 871954994, 124506170, 921640277, 64901878, 232475835, 297041036, 275748584, 34730900, 244012848, 17007552, 701769979, 181932844, 813014097, 414351326, 635392020, 843541358, 286083412, 223566989, 134766796, 428639254, 216411958, 842213826, 321449995, 36056947, 813809980, 462185563, 444794224, 195899942, 999963233, 192105536, 277815027, 313167125, 535263833, 575644090, 945475562, 784376393, 863774240, 189860766, 324023019, 402815910, 247911319, 613810119, 624787257, 900604119, 367504384, 523822977, 848015520, 640828982, 896499167, 670215733, 945338154, 877480691, 445189, 411436381, 925791777, 734247216, 998981528, 51817255, 470716156, 851900719, 83819457, 804321341, 254807986, 211965767, 458490011, 6853225, 844133189, 277915823, 352064774, 128382109, 490216052, 708462648, 655567877, 994326737, 125406299, 235730319, 771865849, 537748332, 68386796, 797058154, 730989013, 777906493, 998971000, 422312516, 566908291, 125632605, 472185159, 388725700, 220199122, 549960329, 541395281, 824943862, 204898012, 89869864, 417749067, 154228354, 37926322, 946044012, 270636947, 869950847, 78279364, 998066079, 389748740, 223055244, 804595197, 253389031, 705347387, 73105598, 539656422, 791393119, 510522111, 643355724, 884056589, 552484359, 870550428, 104975623, 741597626, 456652376, 204169072, 456836773, 85974257, 83668913, 368974155, 247085854, 337886081, 29052244, 952810248, 944105981, 429244442, 448585492, 72540352, 114209728, 573404337, 173458192, 756166367, 622413244, 872160803, 803465117, 831620648, 919130195, 501247947, 947202093, 221566106, 472898311, 895719219, 510707760, 639147840, 401694026, 15174905, 290373239, 187111666, 160426616, 960370755, 386392473, 199340963, 372562299, 65452202, 309333606, 427091858, 765692962, 106866025, 519207319, 920657204, 834311149, 545143697, 562304688, 985915011, 115454303, 981921954, 798152347, 690971322, 762064893, 553970142, 731968172, 573997976, 986473905, 466888176, 787657202, 253209571, 142045930, 830412145, 734479840, 696600726, 581803090, 818364700, 208578301, 424646302, 207943381, 307689312, 195539136, 627463821, 191722872, 206263249, 953616506, 501082739, 314340665, 197708574, 149254979, 469576362, 492380986, 311882392, 33305564, 364882517, 881012678, 401444540, 771018053, 595784048, 539727568, 340177070, 381205089, 15715975, 10081180, 108706565, 217176046, 772327232, 950512323, 980985293, 512850370, 877464048, 153073960, 515537958, 196548673, 875264636, 307159093, 578875585, 424129535, 603584943, 359046445, 493598175, 892289525, 476873883, 725840307, 10891461, 761591748, 662642889, 893634561, 110537752, 982828415, 483182229, 975753388, 912306034, 790156328, 588861803, 482517875, 102292471, 187202393, 956696358, 71368752, 961478599, 48225681, 385003653, 140216617, 973224087, 149831407, 609253070, 916165360, 339548126, 197230063, 719756122, 913956595, 638380708, 279783313, 922443799, 668305319, 344089777, 734303608, 949822055, 182696679, 17106747, 592023257, 240596051, 786417896, 449918461, 472361805, 869849305, 709074072, 396305082, 849303402, 468462936, 530574289, 541534052, 339727209, 50606591, 268609557, 356456582, 865766289, 431422436, 192249691, 336637460, 722787914, 847478568, 612621146, 265617615, 860086457, 90639551, 623131474, 274791989, 150989308, 131427161, 208665642, 318137435, 246982762, 579724729, 87333613, 928125824, 663615341, 355386281, 420506832, 526108059, 670669471, 955971295, 269323652, 985681290, 633562827, 660480883, 407050710, 104225336, 63520512, 559966386, 989594079, 425911926, 2497312, 515253867, 8626114, 818833179, 947757325, 700753943, 987772697, 532118547, 262731791, 870108682, 707010687, 431924187, 563600642, 65873824, 549421114, 647555139, 924203100, 872639299, 618591016, 644961735, 902297588, 424181250, 591301215, 387087807, 509167574, 382846657, 781846083, 27763081, 577833438, 791855441, 52909063, 337464460, 275851664, 846573066, 126221612, 461764508, 248612472, 80188943, 189583944, 38976997, 292671661, 941489402, 524468210, 269739281, 729290040, 92560552, 753970661, 3874368, 781725612, 561499459, 977813403, 821675035, 431253126, 415943364, 556346954, 752003191, 880264602, 960005177, 191249304, 287923473, 391193777, 19321179, 356339390, 460694970, 312404457, 148382238, 780760467, 329302077, 389494413, 361217610, 685847360, 643886056, 778203571, 177413274, 767108051, 565225896, 836446228, 621824260, 26984839, 773561276, 244206279, 184117852, 326224927, 29668543, 704496724, 945977322, 7793753, 308002175, 36812453, 73692436, 768237856, 637869065, 861446883, 555642892, 155835144, 358238208, 178714745, 87115768, 731705971, 680307795, 762543739, 183500201, 74698493, 668794318, 446709340, 535332657, 462799554, 994212168, 412252640, 584639833, 16717132, 542445530, 256956772, 924978599, 980853067, 885498238, 998530042, 922714735, 295139189, 804204765, 668397245, 166941469, 508876817, 66137146, 798514472, 595914444, 910419148, 782874896, 870990405, 194851135, 152479789, 865414227, 665239764, 987308628, 595589515, 886203134, 38377300, 679928630, 241448445, 532457789, 867607974, 992661656, 211847550, 840820345, 230089159, 176442833, 730053226, 746264573, 103587034, 713241664, 60910134, 764192765, 672607615, 79096092, 565065649, 543828818, 429119425, 334463600, 225577596, 838122634, 732716866, 786255313, 438341756, 723440633, 79574591, 274598706, 558817103, 191433061, 232372138, 925651987, 145838578, 274395337, 121194323, 415628674, 680649061, 901726004, 513908765, 107693670, 576037601, 186291184, 42583139, 403835398, 403332396, 284908772, 913960984, 15258754, 374662265, 994340559, 786303275, 977089274, 968174451, 17831229, 302853461, 374464348, 725225855, 94880769, 57492202, 705705073, 842421432, 325116494, 495029568, 354803042, 300302686, 137334629, 351382129, 965208373, 115218974, 588728344, 920669403, 876697972, 864669400, 879271280, 627106854, 335598749, 86203307, 96851889, 994575362, 357713064, 835615894, 128702003, 882237268, 493260746, 367699794, 327095071, 40572610, 884739751, 651587824, 801654799, 881460633, 693925143, 86626131, 172929607, 917119995, 319979259, 762190157, 504797365, 64733203, 56088919, 627391742, 114056201, 162528965, 161789284, 750019182, 427131134, 209283902, 76655500, 361812387, 268163206, 337610536, 851762897, 602299654, 774661173, 618633123, 111488030, 850296780, 975382566, 100775554, 344429637, 787755011, 828778682, 789167697, 844533215, 969364209, 53508590, 806653498, 875182815, 263540406, 751427149, 68425703, 281441040, 625608407, 534727303, 977374958, 70672783, 53686844, 412017771, 536021702, 806151396, 781497000, 589588041, 106433007, 249180017, 896088342, 301294803, 811104458, 980409256, 398034730, 584501006, 765933963, 352292620, 231638220, 559278239, 148416838, 333453572, 616722762, 611939536, 24313788, 826798189, 414585360, 855457168, 844485298, 699362634, 776839433, 10560795, 23341532, 463531458, 201230093, 619646700, 880659198, 263151615, 832007547, 975738135, 873908607, 842080281, 679574067, 892052472, 478123661, 203513848, 597202147, 611136574, 241996510, 896572163, 489309071, 745156427, 247938740, 216293669, 519843443, 699075999, 685881415, 283910216, 644893386, 654270937, 282916504, 374079790, 568264733, 65712439, 573796619, 738699512, 8666099, 580013252, 687670624, 326839658, 650324234, 610011059, 231536890, 126312497, 827308011, 41436554, 349863974, 97130434, 179252689, 879400824, 203155764, 130758596, 71642213, 884988536, 187558382, 111068283, 998861548, 181302720, 854713060, 410137659, 909759194, 745463578, 375316982, 279650610, 126437361, 700604748, 851265934, 930473839, 857620708, 727878373, 511681927, 636695950, 239169296, 766418389, 576556325, 783338391, 696375477, 339339090, 839031206, 535494374, 769644182, 330717601, 343400581, 1582639, 616378445, 862540845, 194950589, 267262686, 942787869, 91149097, 17208505, 169387698, 696826038, 507199642, 944711247, 395027832, 791906784, 129530092, 589352355, 303044519, 924200438, 39680819, 217697111, 755116178, 696373247, 588568525, 459582665, 879472749, 656776441, 769309356, 292450511, 474313312, 529328273, 666707722, 26419749, 420871497, 752846494, 392178747, 595282593, 526147549, 569573198, 447795160, 564123382, 56746592, 936370780, 606407877, 455433935, 679901177, 15046535, 975279868, 915360467, 303766601, 84593245, 855837291, 146595096, 163683747, 566200092, 292691982, 473765873, 412124211, 316823449, 16780790, 892747882, 15247427, 32021548, 464127145, 414409619, 599976935, 409526892, 321034316, 331686932, 106762809, 684826038, 532692598, 224088371, 852324888, 831004597, 867177412, 833087610, 988516547, 467036594, 368350637, 426976828, 453157787, 881360921, 928295771, 993282489, 625791224, 538670573, 369331056, 606659767, 92066229, 307457680, 241368982, 852605267, 900615877, 163996040, 813301616, 389896311, 309940879, 363563756, 533433131, 96277011, 420116790, 192733778, 810427322, 843622997, 638911122, 70061566, 767551977, 29271395, 761393745, 952499323, 208114671, 14910839, 772313682, 972752138, 921712230, 205242941, 11600540, 155502084, 151740346, 818760466, 176763957, 786847692, 808430079, 588531461, 550595137, 462391380, 344095987, 782148983, 866715721, 479906517, 720247221, 556457706, 473572655, 137777474, 834373892, 982792650, 359188606, 868408423, 583678435, 952853354, 418705505, 902765317, 308240939, 850464719, 76733591, 191179927, 478709178, 767384795, 937448951, 709195801, 488080267, 477083180, 463006770, 616289798, 65043725, 190131423, 288105061, 83744600, 172720707, 49089353, 285716697, 344651624, 161400078, 78649884, 821308021, 347993588, 832152385, 283416278, 703499663, 366533491, 935411905, 802593093, 819234573, 23047065, 635307794, 950906101, 256020837, 25170544, 287840654, 509129038, 613672304, 458006400, 132603612, 212904699, 174102640, 785083701, 823632186, 224907077, 148970307, 981356192, 888583739, 923278593, 324268585, 942534544, 644193162, 366200224, 364571554, 822784648, 255602160, 482758862, 376280261, 759639646, 426146325, 208566621, 108319311, 29776599, 637274755, 801048872, 226288625, 279564998, 360869205, 169736357, 328936511, 962477479, 799182051, 811044664, 872906198, 792862846, 388234379, 328689973, 780264169, 438320205, 24171105, 774022910, 203127141, 644416534, 5318639, 546334405, 711651931, 511992585, 830291249, 462742689, 495291427, 109725655, 750691735, 324597301, 308497657, 215934859, 999570258, 757488577, 776744528, 855130258, 352379438, 599357663, 573768073, 6258889, 374118645, 963272100, 782469532, 234715642, 904741380, 241563318, 17241597, 243484914, 712532114, 432808156, 724983028, 377319615, 61511569, 962926897, 532253472, 8294184, 292162282, 364271125, 453325910, 105908275, 143083692, 794213084, 74859, 302465269, 214374818, 254109688, 216859933, 97200663, 201083092, 295372773, 290918581, 424814968, 47060994, 689464310, 10478149, 8115370, 986030245, 532836468, 426544362, 431262857, 34055504, 804928927, 327724087, 5361158, 602380390, 222780514, 43547310, 528587458, 581866920, 970965681, 637741073, 426774781, 460370901, 556505037, 418748456, 306994514, 375492182, 435043043, 22602334, 849878337, 985824023, 368246229, 920828301, 954349056, 185408217, 499213837, 112900825, 691147237, 388695413, 633721276, 998903237, 872921168, 728192170, 171880382, 457025947, 38860378, 224905218, 159315543, 429092775, 283133920, 127792657, 893606313, 469963, 26165773, 578389505, 256411170, 51976624, 800208027, 423981828, 810393440, 189119240, 212448624, 376323057, 553735429, 972620776, 593837984, 300117096, 3749510, 493345943, 97682146, 325250096, 353349907, 678952603, 503328657, 39466750, 213230645, 979120749, 253400767, 820397139, 344238568, 639177956, 809769919, 288137477, 941283339, 190560685, 782959520, 988917747, 438440715, 862619091, 693137617, 792724121, 986787494, 810520506, 244042480, 228102974, 451192637, 564531427, 524815768, 763124873, 78148279, 983194512, 927170121, 509730, 463790697, 401812632, 782415109, 21651873, 297285392, 410192248, 711954784, 266056580, 529257564, 389919629, 829334023, 281880604, 516452064, 578537965, 765650413, 604473693, 376377944, 56917268, 397905264, 666968747, 439041554, 387280957, 556712586, 588077439, 208631296, 347533231, 742052265, 951382724, 410301924, 418818329, 484695175, 837516494, 70060913, 855825096, 652194220, 702567264, 416728947, 735465494, 682050224, 801961879, 436948995, 636469588, 602942456, 446231253, 472502721, 621998379, 843724489, 183261271, 616071983, 307104906, 941212926, 542448290, 759462364, 169317927, 478825212, 685222708, 576369192, 644080777, 521906618, 88954754, 186258251, 990601522, 618666686, 786999756, 494385156, 181974365, 807513966, 224819428, 814937293, 985868409, 207308348, 757308329, 463226271, 332613033, 790913068, 279044358, 848405086, 656734089, 463561121, 234582074, 96486734, 690091573, 779353177, 487584387, 798082393, 367131319, 185132608, 947769168, 505018325, 47523495, 224182123, 523091621, 166401089, 877287217, 424367994, 279260290, 21101544, 784107587, 404402558, 565862607, 524409817, 109684836, 626705375, 369036867, 182272288, 251602881, 356941928, 808675382, 190481002, 484243883, 618329232, 298091304, 212920598, 425889449, 374479807, 420487138, 285411826, 980176139, 541004988, 487071953, 952312153, 332809597, 200894254, 491252146, 549224042, 127611647, 639950391, 696703346, 326575987, 102281180, 502154888, 89125734, 213048819, 784797846, 541417194, 451144894, 400943564, 42995826, 419291608, 203106432, 776835494, 962909901, 576141688, 766838992, 706044092, 550508009, 95752031, 590458577, 981700598, 398941226, 39142036, 569113238, 26791506, 26160704, 635120499, 206768227, 535542999, 134846276, 412178109, 567845116, 718364050, 635086828, 595384245, 520015645, 519924520, 498264439, 851486459, 198237035, 174535212, 838637059, 867806687, 963554125, 283010533, 749203023, 892072820, 782262959, 576488685, 924890272, 385531118, 338751538, 442935538, 545655484, 405078042, 45032178, 284721528, 950583605, 789584597, 149818822, 476257632, 274436223, 228674676, 491211794, 976888951, 97614164, 856624923, 231769222, 30716700, 76352434, 451733946, 875861653, 777874592, 667949805, 773332400, 274914231, 390418399, 733079183, 811154824, 207126608, 899568270, 756590589, 577749183, 125328716, 363448708, 657978295, 182915029, 567251507, 991334473, 533424797, 305251453, 674707663, 774323243, 308259261, 210821781, 950764169, 848144217, 782586756, 9558090, 717814086, 188420765, 335412094, 604514312, 168984390, 581187186, 82151555, 540541289, 181141892, 117396708, 683194280, 952795845, 716664804, 62077854, 434101953, 146380089, 815966787, 361322770, 397476664, 933678032, 548611551, 768395806, 116994412, 713533625, 472911711, 725333443, 218077391, 446068517, 291030386, 89155549, 835119189, 588075028, 268570533, 461140843, 850721044, 648421233, 720035461, 284641310, 98728789, 749715356, 311650806, 668667981, 774941629, 845496504, 938561861, 581275608, 114182374, 504881524, 840108388, 602200977, 377178646, 116780629, 246332399, 903003036, 875119504, 757790313, 172006812, 66918421, 995784996, 672737539, 446113009, 113324199, 935467510, 861323191, 622465247, 780699998, 952690108, 898061951, 991418093, 518313180, 552215967, 678037031, 96378610, 595443627, 695350263, 36584100, 239065688, 971035186, 578104307, 6401276, 246986862, 475410916, 99444227, 155470767, 288509850, 38617489, 718220299, 770423315, 510935379, 694154770, 728987866, 510437547, 869241286, 705100191, 943806557, 801235735, 199738730, 639633749, 335026536, 579445881, 822649939, 809418754, 20488829, 290047212, 224632238, 215661265, 307174581, 947815015, 867705094, 143925299, 860260006, 261226567, 709238347, 551716382, 886149425, 433988782, 422131819, 13218934, 711583529, 405754298, 784662805, 969393939, 631025430, 990342639, 484475942, 452539188, 319857132, 285092818, 2560034, 483566782, 127191730, 167158858, 254836136, 901903650, 671254449, 14477035, 403019047, 306914858, 426888303, 516709314, 866438956, 658077251, 73648750, 503005980, 720373418, 769303640, 969783423, 236492028, 175605735, 368812300, 279700621, 531035405, 641584242, 986266298, 239996663, 155456963, 802468054, 966877079, 950034443, 648652734, 159223765, 662543150, 333283984, 445290121, 802188390, 982116795, 875774745, 201815947, 588873603, 863263419, 329994834, 438147795, 353830414, 428473736, 384117877, 800259795, 211294150, 27356920, 636250874, 684328182, 125300605, 216713205, 519802724, 948195903, 954126459, 762322997, 619797711, 845534253, 103386361, 135670839, 458980073, 126270649, 385361668, 734179554, 970177454, 250933369, 458179590, 493767062, 242133843, 961137520, 963638541, 611667611, 133197569, 299792728, 926669933, 658227173, 764284978, 160413249, 551677933, 482386755, 403978716, 966072705, 253311185, 820319672, 375366664, 742571033, 521282153, 909127483, 412194066, 318466863, 229623810, 39786754, 255962491, 164929756, 123047945, 398952369, 93401350, 151107271, 765028961, 209833469, 943822929, 323184114, 498417485, 861288554, 110261650, 400268426, 791581555, 863585894, 170601483, 370710327, 653464148, 102503145, 937742174, 17936540, 407121581, 464872896, 442215260, 219594653, 185798573, 211853162, 396199095, 888268298, 195970090, 70669920, 882818627, 916387604, 948884561, 431655050, 580622982, 15933628, 129394515, 414298821, 111557807, 189444695, 940060219, 572818571, 858714239, 455641113, 501441535, 628001827, 28321961, 314620007, 355453364, 132189687, 674458353, 651995115, 696482667, 740499326, 603662815, 684302753, 734420421, 773443158, 612153307, 258656152, 675718713, 802954810, 530266920, 181658575, 323014031, 597375708, 962642298, 355958509, 800791423, 562244361, 810587128, 253360486, 571652984, 912852425, 983818743, 445877532, 452189750, 644226983, 460193343, 342180364, 761002064, 492766714, 216802966, 475927632, 414344865, 576994151, 653370788, 514483061, 41964929, 424688441, 960416258, 838827223, 927182452, 471242274, 65890246, 478818440, 344324437, 9358908, 542417353, 419462916, 228483315, 477353820, 622636270, 608548518, 924601584, 91812918, 81489108, 37906783, 107463713, 496799401, 9653998, 936759949, 856069529, 573723169, 552386032, 231516265, 18056502, 758675181, 331137732, 111835842, 230433955, 453861243, 970308157, 12920221, 104855595, 469536476, 353826511, 671068121, 820711056, 186258279, 508928529, 126526894, 786613646, 591493239, 126395174, 378120887, 785554991, 831548070, 971723009, 80605392, 494595744, 411424526, 825536520, 956281275, 91725402, 927786300, 516402550, 725814068, 206466193, 483543725, 652381023, 811878907, 685483374, 67216216, 531502648, 515195749, 770493407, 42125735, 359571501, 364600569, 718408966, 69049827, 984053642, 297751332, 517593461, 529050695, 353843653, 994841616, 192310309, 575109674, 979416781, 825504674, 836557497, 632325568, 166388398, 257854601, 233840227, 843940230, 96341828, 694704021, 201705917, 909417606, 356091924, 213713475, 498157046, 97736458, 838499631, 387803212, 621647699, 224774567, 949271265, 60742040, 119348215, 457027137, 954625404, 932875367, 959423310, 527749590, 11333301, 512878510, 647262288, 141801060, 468588206, 580600801, 41583203, 603849694, 908195423, 750957925, 147237910, 792263511, 14009470, 362606636, 781649781, 493690000, 531894947, 986791963, 967124109, 788367011, 672579044, 360264928, 237884048, 443708711, 789575773, 748391493, 353286470, 899748374, 706465884, 786101470, 305188651, 406666245, 888846587, 876146181, 81137223, 838990524, 114143135, 699407721, 141082590, 602994634, 841165000, 786515736, 371601448, 876415510, 674837615, 306071276, 819334921, 425708799, 869137421, 965849785, 767023901, 995689214, 476094476, 159558998, 857282146, 125354761, 807887502, 957048073, 976799182, 86702368, 298589018, 489956322, 497959923, 484130405, 685550588, 948851320, 861415623, 650936641, 771123634, 547692259, 493913122, 45106575, 206389590, 456388783, 549434841, 912045197, 639131120, 209082508, 398060692, 624878632, 144011120, 308054603, 921628748, 827507446, 219466257, 407411508, 573300808, 280499019, 449086254, 62318111, 878930037, 877054558, 250396257, 503624127, 781662090, 952528737, 189512470, 969901894, 197280414, 416213365, 145734144, 671679078, 410185952, 40307882, 749075173, 968844988, 782195886, 808476852, 776231250, 793637219, 936541949, 833171465, 886509860, 620516030, 491415238, 534540704, 704372386, 69724911, 761816869, 854495246, 257928897, 102624038, 749717124, 252695953, 572533900, 436867965, 800417424, 843797742, 632539767, 271388375, 946698919, 259569465, 414798157, 367677540, 163878668, 382400200, 207761424, 52818952, 144605878, 23289024, 116398049, 520731952, 957514543, 450089448, 452919086, 280571310, 392954932, 479475049, 314667517, 709747030, 30080216, 737869556, 368844647, 472212305, 704421640, 263233880, 593188450, 702775982, 67092636, 945503635, 692945932, 477942246, 321551047, 405703002, 267961343, 276811270, 923950260, 400819372, 602340988, 206743139, 912386155, 465930496, 700774177, 330670075, 776406698, 879117279, 204370690, 130663602, 982925799, 702541038, 374754320, 971691905, 557315848, 43706360, 185701857, 385391985, 658402885, 166903278, 70932882, 823136202, 955030014, 217512949, 138402112, 298043860, 909142306, 951571538, 800695706, 682156448, 441763538, 193321517, 443086305, 509269691, 174657622, 446743591, 842067948, 167908729, 870130460, 766244044, 817256587, 695286325, 504216584, 810646933, 542167128, 913683880, 358454602, 746811101, 121721678, 185292856, 728435215, 835257215, 674687033, 54246893, 820792818, 521063067, 816988961, 567191050, 662571486, 875232383, 455354020, 357349298, 472601180, 697291535, 581640725, 930695397, 918487147, 373724755, 977471050, 594507462, 42398923, 704568198, 6477614, 273540828, 30512847, 917437701, 390283316, 171706039, 248744424, 416508888, 901337592, 408948216, 575784856, 996200437, 136585567, 506930510, 351973389, 333594350, 775198888, 333829833, 698522544, 326376283, 791416711, 997379528, 395784331, 660648965, 245592305, 67078803, 609784433, 54289271, 688396279, 875523922, 877599863, 876532093, 677476655, 803937148, 906251995, 603024317, 260083316, 236034084, 511433856, 300700664, 633908598, 344555034, 264395980, 817886936, 66047966, 123523126, 349041583, 539473975, 73891063, 829662529, 294975589, 603778276, 943604573, 442104206, 467637805, 43920422, 222082618, 494971081, 732887480, 699297436, 321573090, 234257812, 315205916, 509544538, 487182425, 638396599, 237032489, 557729404, 883072283, 307945506, 560757939, 44603523, 6338750, 193953455, 428200839, 531582664, 369249220, 245164082, 583416270, 470146207, 609798231, 305813106, 88655166, 791166307, 621712812, 349536736, 276193518, 149857172, 603839266, 644436467, 803835430, 183729479, 455623565, 779378957, 648386197, 925471316, 548625187, 511272719, 350801656, 948480837, 645921392, 925219699, 694450554, 856702887, 72999086, 44775826, 269039699, 409348070, 946597445, 891860442, 115575271, 938310257, 921275039, 420100116, 310652977, 357857925, 582823941, 715678237, 174261621, 651927094, 230468507, 651957924, 689072417, 436415018, 51414093, 261476281, 83309120, 380289405, 756879403, 799761841, 416920576, 374703997, 926491735, 362559061, 492697245, 99439346, 472979097, 787732593, 798609147, 486607577, 458760568, 687641461, 974249472, 62837404, 712771127, 201463625, 358577795, 362314135, 534607151, 901246045, 455077344, 248422010, 658556277, 109432260, 961681305, 154995308, 72316942, 471502675, 356232587, 193477583, 960665157, 210200250, 950274899, 652310029, 24217364, 42753165, 686986418, 169066211, 878094238, 562734602, 402485983, 850580137, 832484657, 27378681, 847996672, 215307026, 211437931, 139873542, 372415258, 896440764, 984002094, 402472216, 174678062, 815499658, 265021064, 317449028, 617988202, 923237938, 347165169, 36397398, 526113916, 245612488, 338424788, 332351970, 892200710, 441643352, 130204072, 822805932, 509159843, 151143846, 660069002, 633097432, 250025409, 721533260, 781488404, 989506083, 842803169, 887643237, 964825715, 953499136, 785827197, 596731174, 17134232, 968306734, 869161765, 608333729, 218537584, 671780771, 629244113, 233117956, 770641448, 479632751, 605228780, 401291049, 620784482, 758454459, 51831101, 686576525, 932948096, 116566497, 645390418, 615335521, 499037128, 61486542, 598144081, 446217387, 629748572, 406168161, 724616549, 81704934, 896383438, 806077682, 699137731, 721160874, 156899502, 937606475, 643068748, 391141733, 887887542, 821181863, 985309283, 811377010, 152734482, 629404999, 892862030, 198198311, 619969090, 916952637, 67821879, 86597643, 128213668, 311912902, 465578040, 821255633, 3121095, 840696494, 7973529, 250593605, 959744345, 907977074, 697134772, 105899724, 458114560, 303684564, 807717442, 242064766, 306218957, 680279065, 188936476, 797275778, 640324093, 468362284, 441782844, 106563074, 894519297, 701624605, 398503930, 983457371, 901264176, 67039397, 432035474, 528655093, 398480105, 922249010, 398456280, 148338711, 616032372, 986729150, 36331726, 472420284, 288784244, 182475525, 357251258, 995770214, 793055791, 920935875, 734135040, 101703673, 265983293, 626060264, 677280520, 368263479, 878496188, 672729302, 545917575, 26696124, 604000445, 746924036, 270983185, 586856846, 792783410, 327975610, 912589282, 211700044, 442848994, 739347076, 173953723, 83122297, 341092305, 624100227, 691309742, 453986491, 525266835, 570037299, 494838631, 187137891, 30528142, 29624612, 381058555, 507947909, 306538967, 309614369, 254035827, 414492547, 152028664, 859726402, 420746116, 105215270, 166638009, 764203831, 87360720, 39828841, 183136250, 195754233, 931072303, 483977218, 430755911, 568048565, 533867560, 843460276, 763459885, 82002294, 478820810, 76789668, 926257770, 124933846, 73671898, 383960674, 997729346, 829479692, 416482157, 696382497, 238603038, 948269593, 124017608, 713476998, 543588754, 971997630, 847423313, 275863919, 527096467, 450078589, 56675636, 61349770, 533112548, 71706149, 545873292, 370163913, 50157267, 206927754, 430424025, 381632065, 97434453, 843766398, 547011743, 216433912, 892695889, 616133624, 254765382, 733206230, 680590909, 37549124, 193191284, 136563344, 707983765, 387290667, 654517346, 119819132, 922464964, 780738205, 964930272, 922235786, 809309876, 49760242, 515908342, 789625796, 890999274, 64045211, 939842757, 499256356, 298891978, 974927600, 138157166, 223505636, 430980344, 369166841, 964086034, 78031520, 691108943, 281991112, 417760962, 914305246, 767578236, 363843344, 280597473, 506953064, 497913575, 666520962, 569676078, 243980473, 505200123, 863043120, 142646922, 689727748, 919565091, 773252942, 84513314, 538802350, 760103079, 532414542, 586779921, 733772217, 469335160, 782726599, 647185405, 347028817, 351196898, 388829447, 142059308, 573958343, 551520245, 393682579, 347728609, 996047571, 708436009, 322270567, 730355357, 300777986, 138693813, 171075010, 856623141, 684778860, 735280654, 832789961, 221105027, 688627703, 536568284, 958160298, 880981492, 976496165, 223355157, 958343783, 641831790, 650204670, 276040411, 114223930, 762112597, 697351491, 473222080, 87150415, 128374568, 441196105, 476105668, 762171, 599274987, 535575854, 153791778, 837694554, 471025585, 709887121, 385389181, 599764281, 185536753, 166363178, 10603705, 741966499, 434339257, 861521170, 567495268, 537283465, 201659395, 482657036, 475856811, 518250581, 168727968, 563393196, 735380303, 322082982, 434531558, 739756966, 232065193, 594869237, 172148660, 412966495, 244233928, 774502498, 587571417, 397623301, 491486519, 565495358, 803187610, 142056112, 754326163, 240900027, 54920763, 172010901, 71819471, 902551206, 244627022, 774560552, 412762387, 305008595, 620552521, 330093269, 982699301, 456531370, 680515937, 468205424, 704965069, 342652370, 640449082, 237239906, 724353420, 91814067, 699126178, 139209619, 754861974, 994285821, 665225987, 883898559, 4731952, 761380268, 825019502, 53184344, 906679043, 772235930, 587606247, 832848407, 94420974, 538027261, 933049092, 853915849, 639532427, 52228866, 332334634, 452437816, 523905264, 457793129, 1269410, 27446367, 308779235, 327993893, 953628324, 368001083, 890574503, 709348008, 418281797, 453710251, 898796740, 274426368, 398795653, 23350635, 311589910, 722958703, 110530547, 827755825, 783439613, 469824109, 75503161, 706500536, 104503178, 370629754, 425096803, 985034698, 988347839, 341431727, 88852456, 437257732, 452310227, 134452525, 118272542, 817617395, 883165537, 90647566, 196832144, 898542547, 447432868, 421189875, 12421406, 335787497, 368370570, 257423741, 67204240, 50116780, 297095823, 449698943, 730723146, 1235341, 828357335, 29498057, 2863201, 66474168, 654708499, 129571274, 90247376, 695968665, 230444196, 207334608, 359548800, 930900360, 486223034, 280424746, 639442923, 138867558, 477139459, 842552980, 703075792, 601805472, 805488835, 383419511, 592505238, 558655965, 460084431, 861290417, 231024615, 440580547, 490597555, 960352551, 174353879, 690086186, 631867477, 10296086, 399597241, 218355439, 142139835, 699891351, 707534068, 45702051, 207298163, 284048600, 207353987, 566689169, 321536911, 199785744, 227712995, 243160705, 319066072, 425216304, 724399849, 824264140, 980987461, 820443072, 64842042, 840524917, 163636490, 121387097, 884325097, 671821715, 417865882, 340983022, 731625026, 575524124, 683389925, 997095608, 860489978, 916657528, 453382896, 942282913, 246340205, 509102636, 296351208, 810868809, 72624243, 556836511, 67278297, 75609674, 79234637, 79169915, 936811037, 657912185, 523885475, 743112465, 775229899, 15509916, 759401079, 739646831, 88437790, 678959046, 836795005, 242391893, 963210127, 433141, 185410163, 21174593, 93625633, 676226733, 798887664, 745200080, 678047266, 791013408, 765912888, 467220592, 442977349, 25620962, 433244413, 473505911, 224789138, 200079151, 895184286, 173075658, 11807969, 462477816, 725455057, 562118930, 474352565, 786477420, 77208131, 353584474, 621134686, 345329371, 653371596, 152804231, 391008246, 571515122, 671698861, 593781252, 852043473, 837767766, 529399031, 614210302, 473743754, 518396411, 28964100, 892905897, 115512685, 581319693, 390981936, 773548241, 685378369, 289050124, 423816593, 598040637, 656088657, 868614187, 744296469, 443111113, 22366516, 81923549, 51014568, 356662282, 816563622, 418530507, 260424425, 336023275, 991786613, 956116511, 59659169, 987042315, 88899811, 313755788, 835455312, 157012666, 801731095, 530868795, 325092285, 326899590, 767940222, 71810855, 887040400, 263317442, 634466754, 618763740, 408353446, 191820446, 568787178, 534198620, 695579516, 97093681, 55526758, 259742385, 731810929, 217826081, 424933452, 491560336, 642074839, 998363486, 650347395, 630499182, 324862848, 21321527, 568271529, 20086984, 772772287, 970372249, 737979605, 288277003, 494240812, 830557068, 289821012, 515904750, 564397474, 163708307, 844621928, 292977470, 871013930, 524359450, 921208829, 693309577, 870278744, 108068476, 89502308, 371640993, 294421915, 194384863, 801382356, 737762669, 971222235, 867294219, 749422053, 908916498, 455394209, 707551745, 478015350, 892605105, 815482800, 323960195, 967333659, 547480558, 785065052, 398852914, 933518629, 737309720, 999072368, 511135792, 48456294, 11327389, 604973183, 231710840, 313264811, 415669241, 781662234, 549531446, 484476274, 231844634, 945320454, 357381950, 797953988, 608695873, 828971770, 936297597, 827941941, 389473070, 515398165, 189682716, 545669231, 717651844, 889231650, 966292354, 664560206, 904256424, 350000832, 915953512, 602748815, 8083663, 705939203, 110351968, 892417494, 927001657, 55946250, 147232100, 895481338, 435626415, 61211759, 975731068, 584081321, 517740725, 427504783, 480983617, 176562719, 268130823, 97433980, 575962131, 840326981, 2781807, 573003131, 308778587, 264685455, 514006212, 293479728, 353721040, 656719149, 198011956, 66458251, 168445215, 476736715, 727886171, 683356349, 591897186, 944277202, 759077289, 338035426, 478816279, 114059095, 690079476, 563652498, 140812317, 270346699, 67033447, 979748160, 607875340, 775291011, 771530842, 301903181, 804280121, 297096229, 731193091, 100118504, 87810891, 573171761, 654386942, 959464985, 613481157, 489522051, 702986276, 291961561, 91604417, 52439790, 967712739, 315898004, 379981171, 440059243, 841876349, 577914579, 625869113, 777810754, 140835529, 292833025, 399213732, 574500990, 106149626, 882154628, 660442469, 44575295, 671470688, 549000771, 644803778, 77901845, 694339462, 275054575, 808920969, 45215359, 121002489, 407277539, 72231940, 991066830, 946856752, 772567584, 489399056, 3532302, 365082664, 237771100, 784849212, 248024029, 54423839, 724010685, 668997471, 960906294, 63107383, 11806386, 543099393, 784761272, 126417557, 851789581, 36245378, 927058180, 934973485, 598060507, 432689062, 957687856, 647503628, 813408486, 756217639, 356977533, 913334087, 59353110, 289750855, 907431404, 797715471, 636271482, 850010208, 240392436, 739299072, 549365213, 33601051, 500302320, 542989759, 492964288, 714846992, 172084339, 234576628, 919468412, 856122442, 350193398, 331809446, 484626986, 981766260, 708600614, 901937024, 913599001, 424410033, 704089390, 309543475, 88084450, 477770988, 820365727, 258912357, 88758602, 201483679, 833044988, 853023790, 149965933, 823989582, 795248696, 48946949, 235087129, 891126567, 874097348, 151255760, 888401368, 558803953, 150196424, 407105217, 149920487, 548730548, 512233547, 41687823, 797264369, 459441258, 24156513, 546917280, 166055918, 726701656, 716408371, 496309883, 931054437, 329551265, 57447614, 756370966, 962814721, 837446318, 463626176, 180552202, 364374230, 628253220, 837754441, 537682211, 1547688, 878743455, 598769114, 149537932, 537450145, 969067302, 829505257, 939007617, 874537334, 860753244, 396074990, 409161131, 386772529, 234594082, 112408133, 390246928, 549817411, 460693032, 944675611, 217859673, 204008920, 970213688, 750092656, 533124645, 865636171, 347872523, 643637127, 656543735, 889781911, 202394548, 684021095, 947751223, 250572568, 342153271, 889818629, 921841409, 122732421, 607784528, 455648666, 807201921, 305918011, 702175987, 334567599, 45137342, 402958424, 188830054, 35987848, 428193848, 568609529, 393217373, 903460578, 778306582, 77372392, 744916563, 434477789, 134313699, 272606992, 268406234, 622929869, 929859004, 363557008, 597062184, 450448496, 436542380, 542911245, 54827686, 833501322, 861493030, 992219021, 203180808, 542244975, 821605137, 808327935, 242479857, 585525759, 334222118, 692816267, 592513787, 967824153, 837872432, 439283887, 724874285, 729866935, 205741746, 45387211, 675293808, 756669260, 511393522, 329170771, 364120289, 205050478, 686406134, 705654159, 926161702, 825405896, 585641326, 970569543, 390236933, 395341767, 719579007, 133619877, 34098902, 590692627, 601060881, 32984897, 427847357, 623701219, 919883419, 390460398, 2276307, 448158544, 283292451, 332977523, 906288269, 485616039, 605855381, 463342063, 264492884, 794726085, 351721121, 368305812, 801363053, 75379610, 937112343, 331219800, 328079919, 673764448, 818307332, 569056105, 220659229, 964679489, 443521069, 543164858, 979869115, 865275811, 624325922, 653449127, 609586814, 975360486, 474575613, 997719580, 280503598, 487724395, 106480957, 139483355, 868165060, 185238210, 407669349, 563065834, 610096440, 367451423, 980715923, 344831404, 262028744, 380680253, 964784053, 250460376, 741941119, 512029682, 893476298, 501370441, 635381518, 651586627, 234872556, 659362811, 53092104, 887586415, 80425413, 981693094, 996487136, 421932973, 807684934, 195818759, 219729282, 992079527, 832392520, 892777694, 685865113, 647254363, 440403665, 63851579, 279352764, 902543525, 257882439, 897496502, 572863310, 430140016, 326294377, 298052393, 961639033, 719836289, 874765001, 125262823, 794612496, 746842144, 268601158, 878017259, 325126443, 405610869, 837553560, 171272985, 419098786, 518764421, 798584064, 105427412, 769333955, 196919881, 206690258, 403240004, 311254675, 396802751, 724266292, 435648527, 264245824, 429551895, 224029437, 21438762, 993352134, 622892306, 728153874, 25719834, 374473137, 942180070, 225688652, 845510051, 367758963, 818112213, 411565289, 50909755, 260870487, 328117043, 37781609, 876875605, 147034295, 459612252, 776508397, 261579509, 57040610, 350680621, 627194096, 798950532, 724870589, 983502864, 809935670, 93478195, 857584488, 831885347, 647101514, 617540568, 382945703, 117243271, 567981012, 182315568, 792691363, 861243520, 717127678, 352277983, 36848913, 594355999, 638917277, 456127690, 720587640, 267126272, 458125506, 342376448, 297810332, 700249834, 543971627, 541297964, 411282358, 264472804, 765033955, 466856658, 274484195, 874208301, 205233365, 726655544, 923115879, 95934119, 188493158, 332407896, 797445588, 839914226, 358854264, 709902648, 259406164, 197733541, 802338277, 660234656, 586586044, 146658700, 179530419, 905792698, 774177302, 612664198, 150892934, 255968013, 987697480, 806492664, 177108066, 368296427, 998458025, 301402391, 825766499, 763447589, 724610281, 619553660, 919970429, 50981775, 347359493, 851470580, 385473797, 842189113, 721939478, 738990699, 286692541, 440683011, 984666674, 538141953, 785891282, 541104645, 567621513, 776636510, 85428101, 376981546, 173920654, 318622291, 981484434, 391808395, 305952456, 749851205, 988384230, 959592842, 244702112, 252106646, 669928225, 374321843, 669448382, 987633342, 902914207, 778684350, 570953927, 951590464, 845391963, 647405741, 616240257, 950984946, 788065404, 940943900, 42384884, 857716405, 880056696, 488976071, 834998378, 224666168, 73782365, 824946645, 712105769, 909309720, 662825772, 588196413, 565086930, 585684829, 702501996, 659541912, 113827017, 296132432, 861965010, 134589934, 569138698, 197529428, 537514919, 709496292, 190073264, 527435316, 644004596, 821737166, 33931088, 692662581, 84587095, 561707256, 873296474, 934955573, 12266405, 238306000, 499252251, 538888928, 607698467, 115686485, 372205117, 381089532, 160333516, 874455088, 919715660, 791120583, 161688909, 79051010, 226449859, 699197138, 230255144, 356428881, 295718171, 196555605, 523227987, 587232802, 658582094, 386619775, 36344759, 490332353, 256903918, 930318510, 176173645, 212253242, 780572198, 645665578, 903275171, 312806408, 301574020, 628423317, 684895944, 859155156, 831508353, 515075583, 341871829, 382400163, 567623262, 339480425, 659502294, 553454645, 754696063, 904194228, 906296568, 233536171, 388671571, 232951946, 596355095, 908916821, 342423828, 657209170, 194584696, 190155043, 843273740, 416066992, 451425435, 682361426, 736973206, 230681160, 296311362, 764681155, 280370267, 126222848, 290985855, 444567107, 216601604, 132052615, 39543568, 388648168, 560597850, 902527871, 169627341, 702742152, 551030531, 987193463, 345879683, 146811362, 54876804, 518986225, 674710734, 88057808, 417389017, 696151298, 575078647, 131110925, 947471504, 181914174, 583732888, 908729942, 660624131, 79095853, 444647521, 695151406, 137227638, 45825986, 503722854, 921165954, 520359067, 584458115, 882977192, 23849143, 284368869, 558483300, 783237559, 228808279, 176095748, 359904060, 816897598, 960723047, 158342987, 900467007, 196240477, 739125676, 200409398, 769315466, 860771733, 910343172, 602911704, 640607525, 279487923, 161975066, 40554478, 768645215, 215534906, 498835036, 939183515, 724572786, 18276475, 17639890, 981157055, 237098682, 731968643, 568069977, 73348246, 439237994, 996533670, 737492849, 180628782, 585077596, 70631197, 198850683, 419852065, 697282094, 286102573, 584942945, 587409581, 522466501, 847173528, 692225409, 592701229, 217367933, 129364164, 126027872, 135068895, 179791662, 826742594, 545470039, 796440262, 985725909, 347823712, 124301444, 986513628, 131201529, 287870838, 473409219, 562573504, 902027607, 883386357, 37165680, 635415618, 15038362, 617405424, 503984040, 415670758, 683415702, 94240439, 397425631, 541611241, 533683073, 685208869, 600204369, 357916680, 868470539, 217070762, 445372670, 895811473, 546806907, 885550706, 739803854, 381856239, 143796814, 390681756, 136459310, 568215448, 203477935, 108780068, 85147949, 283127836, 55994203, 690687545, 878845536, 695682116, 177230036, 526331327, 56808622, 657342134, 594771643, 392674982, 416730557, 130957605, 788913963, 35724854, 430208095, 673428612, 359034640, 179144878, 641868369, 511279648, 614077077, 743464324, 464119794, 964651755, 165047168, 153402877, 653607191, 380438709, 816045390, 533442014, 851778662, 716055265, 638251370, 357128934, 603414136, 196695410, 535200952, 365787428, 320753267, 787397653, 75171814, 477251111, 945936787, 386196993, 214139078, 88931072, 477281948, 461349968, 175280086, 347279674, 383832232, 756534314, 943422691, 918261056, 944862004, 167859753, 934914584, 419621913, 138088027, 657903651, 867964858, 166060101, 116787317, 27092999, 443235779, 821784160, 75197667, 401404613, 452806751, 602806753, 938119806, 565077125, 712638764, 213064898, 992697006, 479210672, 871768434, 192179495, 28693249, 335380578, 131529988, 241233921, 577315064, 42066155, 877965545, 323730090, 852110559, 346378651, 876597330, 442605333, 414922591, 243300143, 670887408, 435158843, 145776436, 664729670, 428605940, 109980331, 248862636, 749297183, 869707876, 308457712, 435404863, 862567417, 38434084, 614984752, 232566287, 389453913, 698675427, 107635262, 104784463, 943281818, 510644042, 700625764, 307983418, 874125759, 83867265, 110650096, 632156406, 276849560, 491258456, 967640458, 946805668, 333392288, 47893315, 615192046, 244836914, 120078925, 343657449, 86306009, 108878785, 440316658, 890231711, 71703927, 474445314, 935854415, 415221858, 484740424, 276123635, 523839473, 372724123, 902929681, 269071218, 396943888, 590001170, 228172029, 449991519, 950203931, 523104141, 509137990, 633471046, 590042370, 599687302, 336522042, 312341632, 98427735, 964498300, 944864386, 523941410, 571835241, 62481265, 21682676, 526304071, 760347370, 90468265, 859263066, 585183352, 700218096, 824476812, 936006512, 541172396, 996803078, 109770964, 235909299, 76784582, 646165209, 478419345, 891394015, 213536309, 903980860, 615851633, 377443856, 466591914, 728892818, 382366688, 776388877, 715887503, 622404097, 826972249, 988777171, 466433541, 878413580, 305075984, 15837637, 258726516, 217470240, 488309581, 774209251, 624642371, 459956761, 630406111, 166736886, 910313453, 377541137, 447740421, 460047142, 110505965, 953354513, 742721530, 860374625, 805616154, 464750283, 547223193, 571517206, 548443907, 971602714, 461383320, 166506327, 914862440, 501950289, 438409413, 147229132, 604221413, 5017560, 495261767, 165531997, 875104124, 706986040, 998909064, 79151406, 65779531, 436957990, 727502840, 336273130, 833871469, 643248865, 77464093, 942468427, 687319781, 124869561, 961417737, 670220852, 860350042, 130856559, 529413982, 905939252, 893430763, 374036065, 567658454, 741471032, 394380159, 45416834, 341848947, 916270060, 857384317, 757484719, 276106366, 483971798, 448591643, 109672832, 468260468, 257261527, 33021084, 879168854, 949231322, 142445927, 123002472, 100273212, 734811208, 477492550, 345546354, 61349347, 338856896, 274316827, 384615179, 618314558, 910108673, 937003543, 787219779, 83099996, 679686288, 927739239, 673710638, 755218695, 72829236, 208196756, 647893821, 814587491, 419849143, 974987747, 797660230, 997951837, 26491410, 880957775, 315646398, 261069840, 53625317, 298191662, 322687091, 216741839, 86580083, 938896320, 375831260, 419664617, 917864739, 935703218, 238001668, 646418058, 659260374, 277084955, 392123909, 26525721, 881102803, 751192075, 585499638, 31287316, 616521391, 803506897, 220398786, 939662360, 72907376, 477920043, 987460257, 589984573, 919627901, 435088877, 684758327, 373429822, 762747529, 993529612, 299477403, 639731792, 364303096, 26355664, 505497756, 351747381, 708975175, 257408707, 38635100, 661405530, 837023077, 579402460, 938113111, 690955145, 441644631, 890570319, 399827616, 574248856, 994463602, 844153696, 381363261, 405979739, 146839676, 856143878, 468755649, 217306671, 929914941, 384924398, 244070469, 335130996, 579282671, 802974212, 480547621, 666517389, 827177264, 669734574, 121000040, 906425758, 900759923, 100080232, 775577039, 372588205, 211602597, 777364404, 412304193, 982002821, 2442810, 204157842, 300981500, 974304187, 849423759, 903325856, 116258175, 34205755, 338569281, 894949212, 571880527, 100906507, 884977835, 676759522, 419160016, 822618946, 353642697, 265342717, 425072368, 94247145, 769377764, 94982664, 648902067, 526627255, 245635314, 415913969, 195360321, 331766790, 796850031, 642623038, 19561241, 442110646, 705854869, 955861974, 881879129, 619204306, 612256666, 501036194, 992486951, 792809901, 564484385, 485700775, 281161288, 837015500, 386099634, 297323814, 773214658, 582200611, 395844054, 259014573, 893641887, 253480486, 418448912, 176074458, 646366008, 107045140, 748281845, 762717891, 800548042, 377713487, 780711462, 28676407, 854309894, 165151032, 982929564, 248946881, 328827981, 812794086, 412115706, 957293812, 950690696, 741027132, 964412009, 633816085, 560236017, 853517713, 675035947, 476560403, 737099220, 5094778, 621319884, 561025706, 144388128, 529887098, 194906458, 784636245, 161870183, 222885941, 985257220, 345982742, 410811679, 523903205, 162122219, 833609041, 150176080, 99788116, 764830615, 675130231, 536576998, 684139792, 596338144, 940429343, 987525799, 556444930, 378131953, 753501228, 806622114, 633840545, 470878516, 117569593, 802858745, 139523011, 62333892, 283479244, 531740804, 991531623, 836930180, 461941897, 904984109, 46777414, 492984201, 993562792, 747047343, 50587069, 647805155, 518546668, 26552468, 17833056, 740086774, 192872120, 566288207, 919041990, 188798633, 450492860, 265243505, 996280106, 821114512, 839391476, 648287566, 49229039, 823487154, 772206510, 183177504, 583846893, 385142026, 846113344, 684985281, 906861647, 699264644, 107636742, 964330024, 922611035, 421154798, 150465578, 569975941, 570699429, 226215324, 886756982, 945393371, 179993412, 320502162, 504619343, 83484990, 603438815, 505187175, 715783258, 314695362, 75828082, 644716517, 519584552, 816256770, 844944633, 438313953, 437832172, 232264718, 330150356, 365574349, 927227086, 732416809, 86702988, 216988691, 742973521, 53004358, 603912606, 850628623, 886645808, 535376046, 108421360, 512074925, 296019960, 391598724, 88899322, 651089227, 949634540, 622445282, 181850912, 656262561, 928854455, 412654748, 690000872, 663944242, 92750465, 333346276, 391780266, 861512487, 856176132, 539369671, 878223656, 814814744, 891740432, 847836588, 621298303, 479754306, 875624373, 545492355, 925942710, 327650400, 543805572, 467710688, 827996262, 662373424, 6207682, 548120910, 809279988, 460607134, 211658693, 985859577, 966623724, 636294014, 726286890, 368101061, 946995278, 250509138, 267907155, 228096706, 225801936, 594118865, 760223223, 794596605, 967801245, 798916755, 346112149, 958947949, 538513352, 317500439, 35157329, 149871804, 251963379, 626367232, 923509465, 242947185, 418632829, 469833173, 586284209, 192397959, 291112008, 223892734, 848915047, 348554684, 83711907, 609692515, 427637316, 532780490, 113345833, 765790536, 663569404, 992006714, 969674237, 193056711, 485385332, 814032152, 692654690, 729829472, 135668685, 197522093, 532619790, 79909090, 604772473, 563254274, 322342833, 963271323, 923091979, 678596718, 253808826, 243429943, 949508454, 836817749, 553304009, 235472399, 332545319, 674517410, 193141584, 444766330, 364900687, 509994983, 968630933, 385918716, 783318956, 911625541, 625229712, 195589761, 538091886, 793538209, 205345247, 79334589, 629889236, 689937485, 189076670, 433683167, 388008823, 30591670, 732916446, 939706581, 968981525, 257032557, 606122221, 398248764, 453014079, 820121702, 96539938, 556328655, 374967777, 536214404, 836111643, 869367293, 543004004, 686980890, 52753530, 369188865, 741707719, 966963409, 280882307, 20928347, 359225527, 911229150, 595059434, 47772256, 394000589, 779068879, 215343742, 854857647, 651366297, 86080710, 485587447, 313934852, 636987940, 519303353, 823820458, 940437087, 682712727, 805284788, 844046594, 773254103, 425718703, 231332317, 622458471, 848262795, 8990568, 895699016, 820096634, 696754297, 661564233, 789363664, 20258547, 678551852, 3829705, 98420585, 765431991, 16766368, 469064481, 403608559, 904456881, 2711256, 316574927, 829276386, 690148359, 485240154, 350597862, 517256195, 166818777, 215936148, 968098501, 404013884, 500064801, 111297953, 187074322, 949958427, 901048599, 629908902, 768805746, 85458549, 119889456, 299250679, 281738177, 893649002, 225438237, 25250729, 401493332, 358989918, 296966568, 307349249, 484974180, 475433935, 594427530, 936280530, 996309589, 191063224, 803760748, 154134772, 491787883, 783117641, 688977385, 699515738, 331310202, 82964943, 143939179, 567141533, 821332035, 662561950, 958553477, 644852359, 908424417, 163992638, 592538621, 467704091, 391145664, 153540838, 763331258, 760847887, 40695301, 34450335, 527705358, 230879239, 471701518, 648138479, 346740962, 831721518, 5550324, 877084515, 289199531, 907479927, 668538297, 835219062, 987416835, 332023461, 371401077, 550521851, 534527639, 698876138, 537856123, 823951409, 281947532, 191793738, 800355027, 68706183, 869301922, 450808032, 860804335, 302965594, 50919737, 986787997, 776420796, 231962084, 839457742, 520076443, 881819659, 119350270, 826341560, 794999746, 177514067, 648178296, 233833710, 672508752, 615780720, 918730567, 919394188, 970428564, 694635856, 612484168, 672463059, 679617717, 688570237, 831731920, 876130631, 808823034, 801027100, 893821571, 476119477, 976466737, 566219264, 284332036, 26986764, 215866166, 917409087, 251646390, 525081188, 779140357, 345743605, 241454901, 744699585, 458140801, 856171770, 356623549, 217783000, 216714563, 403994483, 61570977, 902531082, 637545495, 25617914, 920150042, 836115679, 725961216, 598409304, 248333744, 729947593, 360352037, 964063339, 595404361, 50332240, 658083943, 450791992, 266360866, 99320280, 220670511, 136694755, 665475139, 400958717, 212945357, 72856771, 232527826, 528392801, 14335177, 118589404, 868132676, 277847244, 215931745, 913768071, 621042655, 209018285, 665678526, 960299055, 38260237, 401647495, 217377033, 966254008, 232207646, 829915386, 891108866, 431559917, 755521040, 358232956, 813610842, 826815432, 814138729, 827556317, 718778491, 664158135, 502969726, 368820212, 773370047, 952241921, 637761606, 753029077, 477878492, 400966586, 481536994, 166448535, 482021373, 911867911, 896323081, 785178830, 344545749, 691344383, 481499043, 13351213, 861915058, 991897586, 61711238, 346049700, 257291547, 240100896, 275038316, 960198664, 232089664, 325507777, 742179996, 122578459, 884099434, 154132490, 22406724, 394282164, 795528798, 945369347, 89855353, 577648604, 722031693, 677673367, 120043960, 91751542, 137319663, 260534125, 377905831, 193196070, 529873952, 937112279, 906970450, 798556480, 496074891, 633449487, 311356074, 580053065, 617339113, 660419407, 894010935, 617303937, 164280935, 148268029, 869233296, 854119228, 453934609, 354552701, 201093273, 158627497, 287968969, 541075911, 505861103, 395449331, 88478437, 838758376, 880649135, 927371877, 230682434, 626104391, 81745981, 813105, 666186451, 993457207, 334852059, 428013704, 370119026, 656442168, 30046191, 91182117, 699746390, 685655969, 388103612, 78854447, 340158491, 758002102, 278726257, 251055403, 310498498, 113201774, 488894226, 982988222, 758667112, 988896084, 875121520, 200012065, 284442838, 896813659, 597923141, 242971577, 853411942, 843704276, 42981437, 755072320, 888707349, 260664902, 566504339, 33460958, 824133895, 485596816, 420990048, 454585875, 560146864, 365297753, 410282809, 393270132, 9265758, 882707060, 332834005, 499640746, 656851136, 496227397, 126147949, 587310395, 732063579, 246011192, 398399710, 309921570, 942127089, 765231998, 73389702, 56959405, 575103857, 865839065, 186194463, 603311996, 684796621, 373334248, 234473897, 726323857, 902460598, 74539538, 266368939, 404378432, 83936329, 750009785, 311411820, 619408717, 453095021, 317297833, 228223488, 229458556, 837612734, 157810845, 632688583, 88476772, 875341685, 562628143, 334652152, 887127193, 454734108, 546355320, 221699046, 96212213, 595771410, 781255921, 652291313, 404155366, 599610451, 88831683, 752727440, 30457591, 255583703, 900748952, 921387852, 408930599, 464829424, 737409134, 511267947, 158206190, 259750971, 522417965, 759534679, 113395490, 542784929, 674637997, 260193007, 337008447, 69277246, 525312361, 757867749, 659956710, 368342476, 190548311, 669218567, 762145391, 408678198, 821874107, 639353305, 497491200, 319087384, 872689962, 283833305, 32847905, 732510078, 748658088, 887805251, 933824898, 588067522, 523303976, 632209251, 68811130, 967389595, 374840515, 768285426, 570736346, 278318214, 245663742, 894762068, 657383735, 408909992, 753588243, 923803237, 51651905, 81908547, 650536991, 390135064, 54342992, 462227780, 946328428, 389329952, 975213035, 301208128, 455794881, 621479162, 37302806, 426152809, 372309039, 707131954, 582438382, 954426075, 124265394, 645994655, 340378652, 544214492, 884464467, 205964904, 142771514, 721386904, 101459938, 964756599, 662766416, 42016102, 34381496, 314438127, 999364023, 63700358, 348923954, 807768566, 454183058, 712593972, 390611394, 823801914, 847400730, 633902701, 626573043, 324338365, 353850368, 530859209, 230920362, 146707290, 568599854, 285160478, 908912691, 132362836, 578739077, 127062975, 158918335, 755875494, 542219438, 873899334, 232506547, 151833316, 185032698, 577556892, 884924689, 356312250, 875892579, 543440709, 404094364, 924410630, 471989367, 705644687, 416798404, 132025187, 949026193, 869617918, 610095637, 14061364, 415029004, 278084537, 939035329, 459198901, 66642743, 561568347, 218295265, 929129797, 442799384, 458277384, 445051573, 719364022, 777262449, 241168848, 557119327, 668596194, 393313591, 796026051, 773847870, 698322831, 847322128, 384658594, 838300248, 896942426, 13273496, 219709515, 606448003, 510301006, 923975143, 288451154, 497159320, 360636494, 735749600, 444646680, 591567081, 11865446, 181329167, 8549602, 660470457, 859948561, 647581540, 442087358, 453822087, 527081753, 436494212, 827413354, 143514371, 951401735, 120113231, 164526820, 986398849, 429450166, 160889194, 13982178, 972801624, 74942423, 110124744, 63828305, 534131047, 962842229, 444275758, 650234940, 847613819, 503310855, 553429371, 421700771, 992651378, 407180605, 694954095, 224108354, 461557064, 857648791, 244699696, 900252314, 953310347, 5678655, 345101657, 249365940, 152924831, 799404337, 538851225, 648379033, 777262037, 93666929, 75021840, 50113695, 200909809, 64367393, 130918471, 108299027, 295284909, 457380170, 460877936, 284296364, 413064671, 504356250, 828475453, 230217486, 22312272, 451098941, 237866774, 840792005, 829098199, 468428660, 700045305, 323381270, 895466204, 407337070, 21442521, 737675124, 648605389, 955242751, 229565748, 798509524, 451306944, 166402103, 629727329, 487536362, 261613005, 939169736, 284391364, 994398641, 992365732, 715327949, 893673912, 602483687, 568689807, 404243115, 203670092, 982115837, 679794537, 65615037, 445852459, 177622745, 80212184, 980810777, 739147855, 725023089, 564477472, 185769739, 687835149, 109451171, 731746130, 352764968, 874051749, 948551590, 267233598, 664947546, 579548991, 570730487, 730980580, 63682306, 615807112, 190363378, 431457003, 352361243, 700687222, 829226177, 350651472, 176861090, 794462719, 343512317, 619615075, 56783555, 340475929, 483173189, 97276535, 323082912, 96730172, 537729787, 254448612, 314370701, 450553764, 961329845, 14659873, 111404028, 261640385, 767229630, 562388900, 363205174, 119389993, 665139078, 14978446, 27469672, 424162699, 954162835, 749291964, 873582019, 649600093, 299641379, 68657363, 839997511, 289124945, 66168945, 84809055, 74808959, 207258959, 751533594, 105449897, 426194843, 22180670, 81381553, 865097136, 784104265, 815810132, 772732906, 421758429, 533130779, 318421071, 904834662, 644572856, 328100370, 729689105, 260866520, 672530363, 725647200, 552807859, 693518266, 748769296, 359403186, 833437781, 64322284, 291169601, 748796643, 144454554, 666033450, 742526012, 723118742, 813647509, 98670670, 929522330, 249922967, 438987699, 904780599, 677024, 516519419, 624667862, 933425683, 375717136, 434607496, 318236341, 235231978, 416729887, 238528720, 698961411, 215363387, 319947409, 166208712, 752865754, 807830103, 56736796, 265254664, 776421185, 173234671, 703858540, 835073338, 200642492, 137332078, 256732598, 237606917, 473223738, 171793730, 381902268, 595520720, 144625643, 662554781, 166532776, 847083708, 740767591, 9483488, 442543163, 960173158, 234734032, 265372509, 613534674, 633536633, 282699798, 763947804, 312485158, 258649241, 734578795, 944054505, 313266959, 160511122, 159535700, 297471018, 772468642, 782325525, 549537368, 454806562, 14438791, 195203632, 630121977, 809863535, 926826734, 802983740, 348578050, 895552203, 109545794, 770364143, 212567821, 497514370, 447587862, 584894567, 837243954, 846849131, 154072889, 948799621, 31229273, 215436637, 957415754, 126252557, 510130953, 85920838, 678143272, 297637979, 884733819, 816149112, 146704338, 388224908, 381902650, 403440665, 634062109, 98556889, 19199800, 551629359, 787877640, 46010290, 41500563, 44517834, 331070764, 251464409, 279382021, 319911061, 142018129, 261631996, 170904102, 623885730, 799169124, 379381436, 442800832, 820853042, 676354409, 294823068, 265205512, 36404261, 770065583, 439533472, 707473365, 267117005, 738554918, 951919064, 893490002, 266424214, 758405443, 748183287, 569636054, 211498325, 977955456, 6716787, 852876348, 230374233, 48384369, 418469466, 673047836, 945692393, 616629084, 825807279, 795506975, 111935757, 40490376, 756405435, 572642794, 893723892, 299260560, 361485621, 136207522, 48971260, 624798718, 183065574, 776769798, 275328696, 9663183, 822095782, 659924146, 527805796, 476341917, 591479181, 208324898, 220154852, 4366418, 400762456, 112988789, 759860153, 815928303, 160599067, 408015874, 581755422, 453175322, 223804752, 680737826, 753610324, 99427208, 137722566, 923739250, 978828894, 767404298, 589234038, 904184018, 842960410, 442465642, 316994047, 238138672, 443458190, 890108902, 475076814, 713744249, 296908379, 332627434, 349936823, 700041920, 519825176, 257604744, 767630340, 68446589, 301224635, 527773046, 415055145, 288105894, 290491719, 712880740, 715707940, 706633257, 441642551, 448463661, 59348877, 187454551, 79127147, 975326470, 40442959, 813441866, 505071630, 777338177, 424842216, 323491009, 224295782, 828967959, 676459618, 68915925, 176985829, 224622460, 926925290, 70331341, 91978771, 447213855, 796594107, 564473286, 446134829, 231377833, 791850905, 782682481, 448816335, 802265962, 998683048, 545550699, 557003318, 188095482, 807646301, 483181303, 452287097, 636813320, 516148023, 943124320, 794212231, 457895396, 474772306, 888290982, 844444955, 719370122, 413128556, 50735188, 913064159, 215941312, 453108756, 152512470, 556711524, 33715227, 95267037, 132933772, 735311139, 386687442, 269367303, 556097044, 995027241, 212586094, 738422949, 895550116, 455817996, 694169816, 785356476, 796110222, 10914594, 164848909, 991060757, 821448734, 440725623, 539358063, 387189777, 38595336, 961449002, 284067710, 410173703, 263512607, 903033362, 675439715, 328834965, 18987809, 840881798, 593119320, 198870089, 533951256, 57165532, 930915997, 971675473, 283252643, 568110502, 58316914, 250324563, 911526729, 82475816, 685430915, 363576324, 519365162, 607120252, 284253973, 387978080, 899179716, 883470218, 783675553, 145228611, 108172955, 635386969, 912975468, 667626232, 669123142, 714969934, 946378686, 731729919, 526250872, 686623625, 580997330, 74868430, 33666027, 369854065, 556952869, 198476119, 778031987, 360937393, 978100374, 543209899, 48323971, 117439455, 733802031, 344442605, 397437252, 570490163, 501374194, 933938691, 845628444, 218301669, 689979526, 628731574, 930229859, 463578071, 808492633, 48491694, 527149478, 267603616, 161658416, 170774361, 356523553, 44066345, 155306039, 506350642, 454778803, 878383043, 432039834, 554135125, 112003175, 797404848, 712335601, 619641011, 23538738, 40681371, 98442673, 666804172, 471701030, 100409545, 268069076, 733589914, 71553134, 5500858, 829557938, 652990454, 626174768, 113480145, 955032889, 4152973, 638882040, 819305011, 609372703, 580529587, 994200899, 724397447, 237755581, 759271137, 601598698, 146295961, 769047515, 966842287, 33873613, 854980874, 227651080, 207911171, 893525377, 949573386, 283202493, 475962708, 262377378, 764703952, 534492266, 627660965, 221101722, 642880844, 96915882, 867334241, 926925890, 267226296, 327826098, 103327139, 105455741, 648984742, 884795282, 530461496, 87148609, 316009961, 537993439, 402420347, 724717192, 239848551, 612628258, 163015649, 189636214, 292380330, 492922358, 825564798, 374994030, 564007798, 37346792, 354111004, 736029545, 811281510, 99260343, 155340315, 917728913, 348509300, 934459883, 480049546, 19494212, 192874124, 403803285, 532485059, 287604863, 547686731, 901493684, 771980246, 41176428, 359191732, 304226738, 499465003, 825186606, 946509285, 144473020, 861411921, 581349662, 96952447, 427143385, 792015386, 891300129, 327225182, 937123324, 858375343, 819683702, 470309970, 745634838, 455312285, 282979746, 555665506, 168814037, 758392937, 393467802, 473701642, 761181509, 760665229, 218023503, 937280379, 213484491, 931783100, 140593561, 858172306, 596241557, 355814144, 579880685, 624029891, 426562822, 175462567, 974999798, 956501261, 787758204, 901720321, 17239771, 236122676, 278616768, 61844844, 243084417, 331188002, 2092237, 588285904, 965465082, 902987521, 631661031, 964893560, 991347672, 281283452, 553368908, 124422019, 371651389, 924916881, 163885401, 666049950, 541072957, 989718495, 296739014, 672241690, 175093994, 548785143, 588488740, 950589793, 458636609, 224987410, 730199391, 869525953, 177913015, 729681764, 340901947, 29159514, 402546580, 938755268, 656210290, 480527729, 482560085, 163127041, 613721664, 324659773, 395287001, 971073121, 358343324, 951578983, 54718114, 29160039, 922182490, 148041507, 899835307, 750962624, 594949110, 606442520, 884898481, 845963986, 802528666, 392893168, 439892631, 803523874, 599707661, 928040176, 797365616, 751910119, 171241099, 152595673, 210946998, 875248165, 490403833, 718807231, 554425182, 916276005, 888873490, 580997131, 417165903, 7445790, 976122704, 10509363, 535303252, 782041535, 83842884, 108617573, 301835502, 801292378, 525698985, 927013185, 814241737, 995798947, 585909283, 739525405, 825874119, 908082473, 393892845, 874192208, 658368595, 259333890, 830547140, 274865952, 17499063, 559679248, 222802955, 309576884, 203375375, 626967781, 386780645, 911613100, 354859861, 483873748, 256197604, 968530961, 811110244, 182973128, 220417386, 705903904, 218937566, 673707165, 504897682, 193554641, 583412229, 171175658, 240661069, 601716272, 188962580, 908815658, 387502557, 660871198, 415055916, 329703109, 133389469, 776899032, 296848199, 344229629, 908721973, 429841900, 890735990, 666705606, 488718024, 42915268, 160633060, 319706029, 959177943, 482062220, 414893351, 175539282, 766104630, 526491311, 407843729, 935556238, 140132164, 738924551, 139673753, 86235563, 609200429, 843085719, 162402795, 150505985, 708528677, 552768592, 630989819, 619749038, 422962482, 288721294, 317033981, 799207892, 707946254, 914884383, 525510095, 857747728, 248594936, 503236466, 406521585, 687419774, 559857113, 203847137, 109709513, 316039542, 622121999, 774554268, 314185414, 768584290, 432452601, 326792508, 328330008, 667963732, 964130487, 279313420, 165626169, 719916460, 709309675, 550286858, 267541129, 376771074, 795452463, 878430296, 869810118, 913789830, 231495052, 839317936, 698470, 23746053, 482441044, 505481670, 441910657, 631098081, 449455205, 999107723, 470823675, 336186987, 102555643, 405732823, 697110932, 474443601, 631640286, 645147052, 580643407, 377075836, 971500952, 834679485, 968822883, 24552309, 959638058, 84033983, 496083572, 333845404, 628765428, 297382873, 32554219, 202536417, 224373223, 233996722, 540648769, 999396935, 796646052, 602169139, 7498191, 954758164, 243572333, 252477538, 43775106, 202483267, 607946547, 171070487, 142808942, 2053548, 500875833, 2709482, 705024661, 71824286, 449668646, 923668675, 83728195, 988298906, 347765565, 112727872, 266769133, 616481699, 374658627, 378941528, 409372325, 775969893, 492598970, 885901811, 419430374, 874595231, 758493835, 735623002, 46482869, 369539294, 527348979, 376006573, 135112238, 926909854, 129248414, 737084572, 523086519, 205032682, 926237919, 871069573, 384858190, 874793257, 644005177, 952317532, 220333834, 886413194, 615815148, 407389120, 584966487, 933616927, 830479887, 264857821, 75617904, 830678282, 376506620, 491759649, 666381792, 810937516, 338953802, 38419825, 550426287, 636624131, 469293808, 125026328, 691941946, 755380547, 642125327, 965157346, 960690789, 582546297, 163096737, 318080382, 582135508, 918364419, 986527541, 502588486, 731170751, 463727257, 619778753, 846263187, 628934749, 366149920, 949827787, 202169990, 378435925, 748466468, 870893096, 157095651, 229809773, 370360527, 902825985, 741023986, 261745894, 707895381, 818489356, 99811144, 372393406, 759549187, 97482850, 755220179, 334352032, 947247614, 310409315, 971788555, 927011030, 106701374, 257156118, 230813578, 870172444, 604539298, 342821534, 122889807, 204692022, 828051865, 489281797, 173536174, 460393301, 701323945, 865854048, 133341155, 98108964, 968381088, 125758257, 76203629, 469867582, 36602324, 897996165, 282697774, 956220686, 767728514, 423008061, 94295031, 766216943, 786643171, 35103854, 87923917, 937225347, 114803364, 684295587, 962269945, 343269253, 572032647, 788738845, 206401671, 263103491, 211869058, 897090904, 553658810, 166707389, 272039738, 796360470, 168078445, 394113813, 789279890, 590055037, 199658506, 345043986, 987654393, 867527341, 817587778, 321467980, 278031359, 864640810, 145581187, 400585085, 605324933, 683544593, 234045557, 564576795, 297202680, 619183447, 88255973, 509957504, 419098061, 360779464, 635195809, 467896629, 50575048, 779423777, 576984973, 992284658, 820484173, 74932985, 535767925, 728312733, 89789441, 658534062, 533184596, 697428507, 846850137, 625483053, 520472348, 326179669, 117426492, 54735163, 922587500, 739974524, 797436319, 303626174, 603309394, 215302474, 803925127, 767629970, 917500790, 881063666, 189082602, 474238890, 994560999, 216001022, 858969648, 421572930, 884173840, 590722739, 619408315, 367981089, 38747292, 470327002, 662894110, 878444345, 883713820, 439255846, 622343489, 583864247, 229777783, 985127497, 886816862, 132908432, 864028926, 143678739, 651041239, 29232300, 209136882, 987534468, 885501826, 22424126, 165728863, 216580443, 604104504, 186973571, 21631654, 814504850, 150848084, 490141215, 113030764, 617846880, 597249475, 476604608, 879034362, 554968934, 857617887, 324232259, 781936525, 245167484, 970178532, 493480885, 955331666, 530612799, 173549673, 561205420, 138897227, 544822690, 299756701, 576430035, 287280952, 357308433, 346920256, 439843193, 468156868, 654072911, 519527386, 92038746, 957334088, 909182751, 315106714, 309059464, 31405854, 250501375, 928398453, 409798234, 114707721, 57708076, 952811657, 199608252, 630003673, 651570680, 751420642, 784427699, 632385550, 528596570, 747599006, 495402980, 646967070, 569137691, 490362645, 272966650, 305660330, 153490348, 159445864, 628748068, 171424157, 839770700, 514324572, 962044260, 894248226, 522505218, 456219159, 155933550, 759969097, 353535976, 278938686, 792296034, 541224727, 461260400, 881600951, 365092364, 974517954, 3110323, 624103665, 135116249, 520631195, 623495188, 534776117, 388035595, 317624437, 614591753, 265257903, 270960490, 334813640, 984650700, 763101902, 318850134, 73551372, 671850789, 710601637, 579753723, 72940882, 941068207, 491326666, 660510790, 831316294, 160890061, 179963442, 339263454, 953839883, 151310595, 826446656, 438229737, 206452286, 750893838, 114144675, 42811641, 503680213, 950056039, 954406587, 246016657, 704505551, 373799159, 544871364, 134627537, 966632642, 438796168, 133324375, 855022714, 617409779, 621054394, 926007814, 171492407, 660468263, 890857439, 300959734, 214644265, 101319581, 86862954, 135886760, 28219007, 477469231, 589951569, 479109947, 702914477, 98287231, 999422817, 195573110, 185286355, 713240724, 419337632, 263574392, 668677175, 455503147, 393465575, 185972922, 800867515, 904074535, 466538928, 841305898, 50322503, 504536183, 216885645, 868660362, 10429507, 745822650, 749872809, 249946446, 376112238, 688198007, 146704367, 566039036, 753063477, 303908852, 286974451, 421702114, 722046149, 475952976, 448082356, 723751704, 589191828, 671846236, 551246225, 160252325, 531619845, 701089974, 851437755, 680995803, 164552063, 568751979, 476270935, 975810676, 289213891, 64131913, 645722713, 988184333, 136624817, 590622568, 637211039, 958768498, 150301309, 112606168, 947416157, 452996483, 107067964, 677001533, 689884676, 556743967, 474794344, 103942677, 369285578, 839765152, 993129556, 796299677, 435286005, 998087817, 219897761, 871138631, 361344135, 49422049, 656527709, 96821541, 914116140, 841186231, 987515580, 368496293, 143723613, 306409402, 285515593, 376127741, 681114394, 105267208, 439644957, 704171472, 237265632, 725816353, 916294193, 501102905, 326701748, 2936241, 435803296, 60462777, 713520244, 111675402, 808378895, 225807843, 30439265, 664547108, 966476899, 649065455, 804409482, 374418457, 665223915, 46333101, 549661884, 811493226, 536190887, 199062230, 686018537, 72606131, 662573020, 994557954, 98830967, 454609717, 781480845, 372100169, 926245465, 608108683, 662407570, 839331346, 692958840, 340057799, 195397322, 778127843, 745886569, 885234802, 582378674, 885042300, 362777557, 234633789, 584957883, 52176850, 289612622, 159391538, 781164861, 341199536, 958995106, 414620595, 366695135, 732709927, 556813676, 995691367, 958872691, 732948228, 960171174, 412466681, 316246584, 587286386, 969266157, 666849753, 341165848, 277043097, 120964611, 446409931, 269675486, 606294232, 633639254, 225002422, 256175575, 842261313, 351590208, 416055880, 642810074, 950872056, 785627503, 88796708, 944193611, 110403297, 784877272, 733802353, 364596885, 81022224, 839643354, 638856785, 128150242, 266656559, 747013991, 628147107, 122991504, 399961034, 335890909, 999221323, 482290331, 161454101, 795233221, 429312345, 872535929, 137238112, 165915226, 965031677, 65002474, 172281300, 862353342, 196939640, 693045689, 709784994, 532567787, 637157022, 291380626, 340029785, 476645962, 586843787, 233845601, 92029329, 680169024, 410770211, 933457851, 712537739, 936750144, 633444859, 906837386, 950736592, 476878694, 564002244, 842391769, 985089794, 795546795, 420911746, 916707990, 772802407, 136036705, 88584441, 835642200, 818651614, 504184135, 978851229, 308656842, 34004559, 158281706, 547305068, 172229686, 825667054, 96135985, 380519164, 725593719, 983964746, 445427392, 646264669, 450521030, 379245216, 14851517, 682717480, 851534536, 425637280, 141550466, 14987936, 719493651, 990801898, 855510732, 328780067, 477168517, 848171223, 592953006, 371229213, 939195716, 355463882, 169522686, 960073378, 223218171, 521509343, 706475190, 991562558, 964620779, 668193377, 522931606, 632238037, 845429797, 840828991, 948469481, 354805026, 752851865, 273667399, 359630951, 189511298, 998593264, 133066859, 418466826, 106236620, 478045676, 45141421, 647526387, 514619297, 297619425, 457561670, 392001361, 798704856, 651387149, 64500041, 802971005, 325081848, 741911896, 924996791, 623294071, 334457207, 420550909, 308598979, 863775634, 808847767, 268720500, 757768902, 759852788, 438011961, 691041196, 813701784, 439402759, 360272101, 67333811, 260517028, 329992476, 302800026, 353121554, 857727044, 481508025, 805444386, 315871890, 724516401, 8578388, 937751618, 812815457, 998999438, 184266324, 54761841, 80947646, 732254983, 725364707, 182166195, 894392780, 192619536, 638904171, 691686783, 543223976, 585283588, 704394471, 656706508, 603512054, 942909588, 34443792, 422097275, 419123172, 906966980, 885482698, 816301339, 517341988, 448693700, 308840710, 476783068, 383789735, 85235884, 4515738, 223746406, 651031720, 859912790, 371778422, 770976137, 362089737, 58355939, 995651649, 980937254, 242023891, 637580596, 476681173, 560333862, 524869150, 104025664, 643429386, 278336734, 725619183, 593762268, 843017075, 963993744, 697172038, 891334638, 45746553, 807906900, 246222152, 845260592, 240469121, 907411801, 856475205, 280434852, 5271381, 653561125, 88716615, 747488748, 125118166, 724930234, 46717876, 36068745, 355613542, 891469249, 510049395, 547825659, 306113023, 548047068, 283560830, 269581563, 76854926, 237685116, 790329550, 112814133, 178534451, 988327860, 743194780, 794336396, 3513999, 709150689, 336021942, 591368681, 52594533, 901765774, 663471024, 638162218, 905807174, 245024703, 422703184, 18494669, 937746404, 76619048, 351231312, 784539631, 273762396, 268251190, 348622369, 749704094, 836165940, 706436852, 850861041, 942370861, 363049176, 41528070, 98558474, 807774583, 222777196, 418283548, 123550828, 252940432, 128806286, 385879007, 615359309, 435603808, 186624474, 173985528, 446951696, 418504775, 763862806, 385214114, 724184265, 824701805, 89488719, 877143375, 350801070, 317131824, 205319719, 981458766, 153885809, 980219068, 236615531, 210470039, 359091713, 843647656, 86321499, 886907447, 419887207, 590236483, 413215542, 142252183, 476311614, 596141307, 601089107, 339478588, 877631419, 554584110, 993858538, 604932416, 556078403, 420417864, 764421810, 104220563, 375264294, 926994584, 928662027, 947632052, 947043117, 811178095, 16674373, 853679663, 776340530, 882091006, 91345090, 152760901, 589931375, 695434362, 560764369, 873821831, 353393913, 360692923, 642270288, 465487949, 496376752, 939621127, 47715810, 781658296, 273875677, 297215163, 86812124, 442107569, 27152666, 737143035, 158202797, 860100557, 595694947, 456200528, 478163627, 383662626, 863695729, 459862025, 622417400, 798896993, 787835233, 408273885, 671087924, 556081991, 482587073, 984308085, 918079498, 165134422, 450065850, 343357386, 894227998, 561786076, 963286671, 120910730, 579856835, 678427240, 637879610, 762689305, 21547909, 804500326, 767562707, 644085815, 368081178, 874808470, 574976339, 939785892, 990904386, 668243179, 752510115, 118874775, 232130638, 232352178, 456049444, 712630574, 223325388, 28658632, 196974463, 854655990, 927329474, 745839476, 100598813, 299265475, 132206604, 431027339, 34314695, 143152011, 130801842, 927866632, 883479387, 130422460, 741417435, 668675950, 643510628, 39039799, 928396588, 613665781, 540359693, 626792794, 897705459, 428239534, 961316993, 13494728, 169766984, 792796463, 321851553, 342573593, 985287159, 406093860, 269186512, 836822031, 696660670, 238419259, 824355278, 274766334, 142860399, 100425003, 154761119, 939198622, 195962396, 564727627, 224222086, 272768497, 909876413, 682658932, 463807568, 486812743, 95159979, 836848134, 686406651, 498859789, 56925053, 323358437, 269631171, 709391014, 212626701, 608400513, 366566652, 243415080, 259648486, 503212185, 81782301, 780999735, 706769734, 466377320, 959633033, 79183608, 665165656, 183524948, 238143419, 640496674, 56690036, 802740832, 129601835, 942817717, 387835254, 142285158, 487924160, 711205540, 986014256, 187247469, 663831993, 255982437, 181408007, 316781029, 716286595, 178017817, 668811909, 927753099, 323125955, 638333186, 688671319, 437457719, 581876277, 926666828, 931430762, 629070223, 776632084, 663971944, 976152321, 354518104, 542553222, 787433223, 190771892, 923217225, 192335102, 516284047, 19138745, 446368596, 457634066, 947372634, 326563447, 43099997, 522567386, 954458051, 482331978, 481165248, 428155991, 6525820, 20065784, 238374092, 895577258, 486028325, 485446441, 412175530, 751656634, 711002528, 53435485, 725610804, 685806721, 433142107, 262825365, 350833650, 182753290, 433547014, 840394900, 637976663, 750070384, 402374285, 898520666, 278500601, 439923960, 693203418, 814646831, 465200077, 969541004, 957864080, 768476727, 523545118, 124152312, 912791613, 991940235, 494850279, 932788200, 800322462, 552036858, 222066156, 958872632, 825062742, 757339896, 588042045, 749635822, 777411358, 781343250, 338902110, 508169542, 114941149, 100227759, 713167588, 599943134, 708950020, 894923149, 897285085, 694871375, 387250071, 901495018, 590693724, 33095012, 805883691, 799679510, 854211157, 952491271, 186215161, 182571151, 962398292, 770975740, 210024570, 160310885, 303941777, 785074123, 961124978, 531597496, 307414542, 224425220, 335775682, 286295035, 177573569, 272725755, 826040468, 368273128, 597849852, 203252850, 154808351, 21280862, 717984772, 429299899, 355747959, 457289791, 472447718, 415365564, 809948537, 323006687, 790950356, 972317228, 785005786, 119884384, 239602250, 776876140, 664364033, 732296664, 722776614, 56485128, 582462266, 441459193, 523078655, 433022982, 355304312, 525760001, 18203884, 803128608, 142290819, 690972183, 172436778, 288112141, 971368184, 701986736, 600244293, 799909328, 860275198, 311977691, 740894340, 525025745, 184721147, 919122301, 888586443, 431841085, 652099149, 71491801, 297432660, 934567965, 421100169, 547322134, 722145566, 836884713, 673610415, 270510391, 451932485, 153448475, 43220101, 802025181, 336929085, 289514025, 519305201, 220927078, 695961237, 131427053, 498372920, 115268322, 981448992, 457383891, 393438643, 258279780, 890267885, 438523434, 12981242, 910492820, 335447437, 347531387, 587243254, 283424133, 86848939, 91156098, 618969204, 598732539, 255968265, 293335615, 970144436, 766232779, 680232727, 290640761, 895473512, 810391263, 216745055, 427918039, 31810656, 458047529, 760856789, 291189254, 305431117, 764454205, 60737848, 605625296, 783559738, 210429303, 685024750, 510506564, 94879690, 766618765, 91363986, 563660992, 356057581, 290850335, 419648920, 741171338, 935221371, 997546870, 764117801, 341515825, 701781163, 897262056, 162530290, 545046758, 12618294, 917146996, 866829513, 922598881, 210946197, 92770517, 960847047, 675793373, 875915937, 874613699, 412570622, 857658256, 84492783, 966870421, 753925317, 915843326, 407916170, 592301732, 210452152, 650228194, 865421608, 92916033, 113463693, 904665822, 606820825, 657503183, 562838674, 379894765, 522647624, 547335459, 614047504, 875748046, 630733058, 319014374, 516914724, 265450135, 437123393, 526487816, 465604018, 584762397, 413732727, 753990897, 306894815, 405395619, 526701939, 161706461, 767873671, 992731502, 112727288, 717911450, 158144996, 879608882, 852067830, 329996747, 673633238, 960438742, 211411152, 836422700, 22143931, 964474509, 172840454, 301277494, 179784374, 903330253, 711713401, 35579796, 312155882, 344271866, 916790396, 140118402, 382049115, 753040002, 877939374, 300146864, 757444050, 478026206, 166447540, 726137469, 265269223, 831013577, 303557325, 666529687, 595443837, 592353473, 764829973, 805766712, 602878591, 389163695, 927330289, 651861063, 464080793, 521160288, 83288727, 848580667, 632578234, 882878587, 264540827, 599454082, 324802528, 439843619, 284894194, 266542668, 124494599, 476200396, 214615641, 595641946, 858445683, 423604974, 57032351, 992783493, 500075193, 262738578, 49520206, 742378126, 113632802, 588876657, 388763376, 531994382, 785228797, 722925088, 539878102, 226815982, 286700072, 202824917, 675027914, 493145620, 220456683, 491565833, 848168927, 585238064, 988606921, 624239826, 12948948, 548437418, 742478903, 595306232, 708025596, 445960575, 654121840, 40926913, 515170447, 406414202, 587819921, 209423074, 529285431, 163824638, 873652543, 172173955, 640090325, 40823272, 987024686, 20313243, 837976577, 625491972, 525605476, 684292787, 770500352, 930920257, 919595742, 861384787, 924288565, 195136976, 221146969, 270428346, 780201305, 420663215, 659641492, 201284657, 834134437, 275515071, 103538674, 825445996, 966440541, 717491625, 500168597, 600317637, 427934215, 702607664, 494269650, 987200755, 368059561, 432880615, 311179866, 968907762, 861620384, 110920096, 877911849, 423991243, 760632369, 857591617, 434604762, 406733415, 196971390, 229722028, 396635755, 788542921, 850645392, 896275526, 147248609, 54740944, 568092166, 954941221, 601787543, 784673285, 138011969, 653788745, 338072495, 159424096, 904541291, 487266204, 648678508, 525281021, 91846135, 738688845, 523409590, 650618777, 238264315, 874087755, 291693852, 951999059, 285228146, 217996522, 42394381, 614242551, 678029973, 316059007, 238249578, 164133024, 252649378, 489890688, 527513817, 644642842, 402086316, 544860464, 563758055, 380692197, 626665669, 516782519, 382183865, 141319642, 678101171, 327210681, 35234526, 403453478, 603617260, 882435669, 872501876, 690932609, 54910393, 733824721, 389755905, 22139624, 177172162, 595918756, 402529294, 9836435, 775547897, 909711539, 42027930, 79311763, 323420161, 411622515, 677023176, 792418028, 12833540, 575143514, 638735638, 562219855, 782303902, 715147001, 134854947, 335928688, 235607658, 104575896, 273314572, 691678962, 994994794, 389620076, 356161683, 907578455, 59531806, 692227325, 11683711, 76603059, 619568274, 453868582, 481558890, 17290062, 576882023, 645701688, 900950900, 663678262, 893367641, 749378130, 161231184, 116092764, 460766285, 279899153, 59314535, 698909245, 110861569, 623840368, 447604632, 820002434, 512122109, 126245457, 669768842, 682996099, 10109734, 556139898, 545540860, 400271142, 920631845, 889817550, 42157434, 638738401, 915371506, 422664741, 671409682, 276748564, 128719164, 98525333, 708817451, 338519937, 118554386, 246928489, 906882966, 728381865, 703131425, 240368313, 189249426, 358525062, 640287345, 348067092, 433887909, 500113942, 276420001, 401049879, 792058115, 978817137, 301970558, 917520939, 207314992, 814258979, 892413303, 584092865, 336331548, 147583095, 398534745, 476068771, 869251610, 923696135, 23506947, 886189363, 894193066, 661783963, 824986097, 110845624, 527481924, 164058957, 158041021, 766727307, 898431622, 941825913, 635847518, 383083145, 427660061, 964525643, 789717393, 348508418, 612251504, 33475099, 577184254, 272933781, 617130639, 560861922, 29462250, 294984343, 732689078, 763057245, 337751001, 639848342, 544631860, 595312263, 132899009, 160254541, 822975946, 313280325, 880207341, 420100418, 831525554, 439677255, 794612710, 624471393, 775652245, 239383097, 257094099, 596558589, 966082565, 583752277, 41314648, 546676703, 515757301, 582866110, 429770170, 530224859, 973154045, 82608343, 628391929, 626239803, 520745802, 118280586, 292318410, 54144124, 852694993, 334138620, 628870248, 678294288, 378435805, 910609349, 154392323, 372611937, 456933534, 317949365, 711036779, 476659127, 631216782, 212561187, 511446919, 569355352, 404580095, 474843684, 178838641, 837873609, 625101145, 286915126, 423238788, 887004211, 727044141, 970580011, 418988667, 217237492, 209216524, 216296448, 660195655, 766380650, 762980489, 9590964, 694265369, 200468756, 50859966, 320188594, 274487389, 235779040, 602448333, 431449618, 257712752, 220399412, 576513217, 936392882, 279838805, 928726848, 870267193, 108837709, 55915891, 225549844, 147295006, 568874249, 950831804, 695845781, 832250400, 610478586, 439113427, 769010405, 899342476, 624078841, 841124523, 487917175, 448844575, 586197659, 393920925, 556039716, 227398164, 472502511, 158694199, 695831948, 196278967, 25031553, 506478143, 61714338, 836803930, 617674396, 782787642, 165155110, 801210832, 811583487, 438220624, 46894689, 354469465, 487930224, 394599489, 786087424, 267700403, 275498255, 80939704, 556393120, 757268721, 762251259, 317283655, 90583492, 547303472, 285834195, 853756268, 521521103, 941863488, 191399051, 334959527, 498150037, 883223879, 353253284, 497638416, 492417940, 692279369, 205622392, 662018065, 513986950, 704981531, 463647032, 261795086, 744062220, 56902464, 690512865, 587465871, 350409533, 147228109, 145300830, 221932506, 466948612, 197456394, 177205822, 558946417, 223387651, 515150062, 326251792, 536697251, 725019428, 867348778, 472605888, 750709155, 171240493, 966595897, 711451040, 649187521, 793934742, 728444500, 727305637, 916638819, 669380488, 226715819, 480637444, 779134208, 179838101, 794607997, 745154908, 586037692, 584280661, 925684175, 244583183, 76306145, 12800886, 121697116, 103482385, 773265126, 341565766, 935040694, 825180703, 630217260, 332389228, 786542902, 934657521, 402705004, 958335437, 131762115, 228858166, 119417913, 21505120, 204163296, 821904831, 736478088, 724294435, 991456820, 814222903, 838821485, 105289090, 499250607, 189827646, 570483810, 160885006, 954686114, 371137224, 461510269, 262492628, 175463678, 53718360, 87617477, 958707365, 759120586, 987634775, 917580320, 390171334, 832193054, 549751798, 663271980, 529484487, 698325219, 654975739, 620730360, 713997034, 893899468, 702204030, 489713307, 938065193, 933370188, 346926665, 92320965, 461251326, 676261866, 242642202, 649877878, 854874922, 562688914, 548545271, 695075284, 544188841, 334962761, 389383389, 6746174, 511319275, 560113385, 236483630, 905865376, 501502248, 756177783, 341381982, 934863222, 874901019, 15398556, 781502564, 964253154, 712030043, 23120898, 30390442, 472394119, 126233846, 543590510, 143791736, 905056662, 450247151, 527745803, 537576700, 218373738, 824584101, 702413713, 927718226, 359061447, 15639807, 402666743, 854061571, 712229526, 116410395, 444525274, 747432192, 762364125, 554257378, 622265840, 40858326, 161226381, 879135723, 191267954, 392805819, 377408655, 19557019, 156732791, 394544931, 751847594, 630993852, 154795075, 645481200, 14431254, 659942315, 835255201, 555099237, 153923009, 556808022, 771990974, 343310607, 708463272, 586310213, 821479979, 489097352, 66497231, 117602075, 25812901, 894921341, 905591787, 456822478, 599773412, 267067356, 51431495, 985258765, 492964638, 716413207, 593796742, 65899793, 792658136, 353541813, 533178948, 82460181, 29599830, 181833822, 121202462, 917361349, 818858756, 804052142, 345991031, 295283673, 775405668, 296197252, 488912597, 546934158, 476992867, 678318114, 293897060, 840849137, 397134237, 796569268, 721180277, 86835464, 25974164, 109460209, 749385285, 780346415, 98510525, 146347332, 67674643, 869668622, 773072252, 978753498, 499358949, 893387027, 518168356, 828050545, 969388536, 232810220, 638403946, 478628590, 932788540, 240982542, 234032616, 252506939, 628204750, 807431173, 338647518, 840112449, 449642365, 175786494, 268066564, 597536914, 814100577, 980675004, 930765089, 697584331, 500406900, 940945910, 322255412, 347736984, 273843586, 959325171, 846726712, 773584279, 361101925, 730823962, 251699215, 813677355, 614439104, 864034887, 670749289, 71323345, 819906274, 519360977, 87493333, 248428987, 549080667, 897931259, 582260458, 146358284, 680518621, 921163666, 362739214, 891440989, 910649288, 995978543, 72703577, 81968127, 172279210, 168589603, 247276223, 761593676, 343454230, 533141200, 757644131, 293100421, 986470660, 833482896, 22081908, 963237745, 223163414, 372695686, 179229993, 363745201, 363611828, 232026647, 907871846, 942812696, 608003988, 860893527, 244561244, 902721918, 876739794, 716136199, 573291372, 31135294, 405617185, 72833803, 888384920, 885416303, 829541572, 515625223, 388762276, 735106833, 44232942, 916106309, 638203101, 528410301, 478737732, 351760354, 406336879, 736038814, 239132221, 653244990, 8498959, 175015286, 246899978, 491675616, 595674037, 541969777, 54831023, 717133202, 381218927, 874350038, 507214975, 76481674, 31865213, 460144233, 428891906, 713657556, 527533282, 378301208, 541945683, 382491605, 956973765, 957891268, 770657412, 140496486, 793233875, 554409678, 719608870, 828456397, 12827802, 611642611, 540663386, 197157519, 972345106, 353922236, 673581376, 812949484, 643404259, 1743374, 223560959, 176984089, 21401820, 840053283, 686964816, 418378554, 692892448, 771823035, 139258369, 691392815, 985963734, 517354461, 502578470, 502091827, 348901435, 511912378, 903116767, 437981286, 248594491, 582706126, 249413614, 971728392, 3366776, 416409124, 301342929, 407768468, 765998266, 344092997, 485356959, 794331792, 603721069, 271523104, 560177367, 911271713, 880433469, 222434717, 109693987, 425373085, 822362444, 896541572, 788724180, 130100625, 266919386, 87235862, 641763761, 838220333, 493659998, 9568004, 731436694, 129280200, 343435653, 193706540, 167437463, 379777998, 616940528, 975723098, 267223966, 152222109, 643581101, 970266940, 114078896, 437994219, 623878404, 828700386, 804551724, 885827392, 141803408, 453385818, 396053682, 244384148, 72769802, 529311312, 189419481, 581156034, 815690642, 362577451, 953989453, 47196230, 845398137, 970926720, 540204990, 66322633, 150469311, 272161784, 56446710, 780729633, 192819340, 308138948, 934054563, 934301935, 141271281, 106471710, 699037298, 638022136, 674679815, 696100073, 740626951, 643297510, 287886651, 921959256, 709687823, 385783353, 798895917, 976501102, 887504190, 839790104, 620882557, 823476026, 753185948, 710033974, 448569760, 153752219, 537567633, 44421211, 480691550, 832967894, 906630653, 461578002, 327963522, 589847601, 413007367, 746700808, 530871777, 219938899, 381626295, 572547494, 707323685, 893159020, 420728034, 232881489, 995018436, 112055082, 507898071, 872286128, 480890889, 313210873, 363210667, 864992161, 944218965, 606728655, 744972254, 271338973, 155813602, 754886787, 660058546, 330728750, 795513665, 227257274, 814913571, 138845128, 857353689, 336946202, 902307423, 469874974, 632734116, 223943034, 475312409, 911700360, 831466785, 773490572, 880819013, 758061077, 401677749, 676411662, 272347078, 639920685, 421908622, 437185223, 743297195, 840799884, 174139591, 386422018, 77369114, 878912436, 249939676, 276805039, 769846882, 246793963, 944013412, 289455486, 909954836, 170138258, 991911422, 641549625, 458671901, 513618507, 699105428, 894740711, 674902671, 509608121, 152591735, 661447619, 740780857, 900227221, 536441031, 339650540, 107180612, 221636291, 968071356, 868902892, 908001876, 375708088, 306956938, 114895689, 6863626, 672020828, 81529132, 406827913, 112751286, 929586569, 963320126, 299162137, 768568623, 754949955, 352872147, 553312705, 924931084, 629499984, 944781442, 107445001, 65055385, 120974366, 408543206, 791075658, 250768083, 641668409, 964529133, 553010851, 754183581, 515416056, 591117047, 455871194, 883576388, 143997190, 437732129, 181524739, 184649347, 61579417, 84834794, 907801237, 94232495, 572005843, 186204386, 88983207, 748382714, 900146802, 43545941, 764706302, 799694053, 780553632, 906672561, 621750163, 613779556, 579937700, 789354886, 130131466, 129622213, 227739801, 213223857, 142904812, 100741001, 567700723, 964772223, 274465610, 494844707, 186330658, 658372086, 997826925, 653607707, 936542400, 516146753, 74835158, 694085251, 68575528, 330639133, 309918830, 216986496, 196006432, 969723731, 939854115, 514253571, 606834962, 433941103, 333068002, 913674356, 662163256, 191158791, 609167899, 155336006, 767716207, 898508768, 720234231, 225844687, 558128424, 181266920, 337314418, 702207993, 156928273, 237340250, 972476994, 15055379, 854689224, 30860224, 256665087, 518463050, 846623856, 942385502, 847113237, 859518573, 526532647, 64790178, 852135642, 919412803, 8432012, 207579780, 842933389, 993563481, 183591366, 698498279, 613928304, 741030068, 765802946, 484844116, 583159665, 302203541, 925372669, 801409794, 237331314, 790715609, 657312248, 100530050, 286406688, 407111814, 838842764, 867881261, 971460369, 997827920, 531327561, 772027072, 540861667, 791648208, 502915444, 244896731, 31508071, 673698224, 351140096, 593131205, 334130667, 468119746, 574885398, 680103964, 397396040, 528174899, 741701055, 759792957, 77059667, 3052120, 139576191, 237430457, 347651792, 121604519, 285801064, 809033039, 984165573, 596155912, 39623748, 355198407, 528632061, 481935000, 863307748, 957197925, 178061857, 782095025, 160723922, 831115048, 235788100, 810238776, 153143637, 920696818, 632306325, 104981421, 938295669, 613797160, 900301152, 583812264, 175431817, 963151245, 826326978, 158886882, 406233187, 573409929, 490010356, 57248210, 384578063, 543710015, 401103646, 713702325, 483366521, 185739856, 668942131, 174464521, 14339114, 196519591, 569544925, 306752912, 755359921, 605731911, 625207649, 261508060, 2206993, 387207519, 641085675, 941522598, 643820168, 298006882, 710151008, 117555315, 600577421, 310613849, 400610152, 194942432, 943031100, 701591775, 47895919, 586691573, 647644637, 59643000, 620737962, 695350425, 410668455, 959636695, 45355691, 154783133, 87153602, 106095082, 865516484, 222687340, 38340363, 685857119, 538880035, 345322945, 419777407, 966419204, 801221193, 303854085, 475097066, 718871847, 789674356, 834371820, 251267627, 997601525, 62951546, 560190094, 250574052, 282765557, 509747191, 448437053, 695503523, 923908721, 422636989, 845120228, 322851127, 399331078, 423750211, 262686996, 409889558, 378668839, 302986434, 841257336, 979134871, 289827052, 630889867, 631571316, 678736814, 62969532, 547197643, 943558953, 810843558, 227661028, 791946538, 176845082, 691544124, 480333563, 745193619, 281113132, 229318543, 267379834, 119732216, 873198997, 85848106, 411089193, 302488136, 302630590, 694542254, 493261495, 957087812, 902178042, 83112436, 582956330, 496135101, 457732766, 942545244, 852971705, 626901427, 983298100, 228156340, 162035416, 341763117, 665525090, 515430523, 176027058, 652832264, 400442691, 477406091, 293703301, 936857633, 492315112, 474035802, 690610502, 50835621, 98574948, 511883797, 26697880, 91395430, 749224099, 557146834, 945322172, 843860730, 277199359, 167564572, 923753636, 885579256, 438385607, 937317873, 686643362, 924022195, 934593963, 820133248, 694373992, 789953378, 690408563, 905447068, 780272329, 10173673, 859179005, 213404616, 223694778, 895943599, 330210818, 206283304, 697519275, 904425326, 384554286, 448519178, 148050741, 891331783, 652543417, 447927324, 447582780, 263531434, 513860928, 378970749, 520023684, 983546869, 191169590, 628711113, 60396559, 387527216, 786375817, 498115628, 215613630, 25378436, 437379088, 525160537, 17748253, 4868291, 898433439, 490018223, 482805388, 735306667, 214020648, 800373571, 177473144, 597821370, 237241242, 68471481, 171039217, 657412074, 86003585, 728197273, 422794717, 155396998, 35948238, 143504523, 534227529, 601533434, 867031088, 795544034, 578812463, 690132939, 5318603, 766423635, 273141787, 955510468, 374330521, 887260345, 803354599, 314226677, 438078172, 877198355, 520471192, 408483653, 803947738, 663104427, 95305371, 129009104, 632053721, 152864014, 437172113, 413888760, 672503109, 909772705, 384170434, 961481109, 196111945, 352142462, 784557310, 810776482, 633583308, 680773241, 549825896, 92323619, 246516788, 574581839, 599380617, 673815431, 437779404, 517519537, 259766690, 754215358, 600988108, 301811084, 9900755, 826925650, 103241702, 841744678, 802587327, 808831222, 629197665, 584770025, 336209612, 677569062, 209664249, 556064099, 250462551, 912734441, 786091278, 731045417, 823680793, 421191429, 208426494, 486997413, 171396589, 422108415, 577285350, 475916732, 660831946, 909205144, 852063832, 114033732, 44491605, 800853373, 485490369, 576211206, 217560701, 56834727, 803000001, 497250976, 747967467, 495144440, 494027197, 602632549, 822540091, 978379219, 303406792, 802564989, 517067285, 329096931, 237063918, 495810927, 520805338, 407671040, 11218871, 476545679, 356632937, 682400594, 690532897, 398715617, 338026183, 313506695, 10041755, 772866119, 72365233, 81258866, 733290160, 635302537, 935853064, 388323409, 486003863, 617909670, 322604523, 762423202, 115348206, 655231474, 440790062, 254372789, 564151133, 854624394, 61191298, 633036749, 603972836, 621217464, 50581705, 590843081, 483516561, 27349749, 70921471, 959696085, 981406810, 189168743, 802266800, 445703408, 961824608, 402437633, 488833372, 506185913, 604202077, 803656522, 351631959, 239281553, 502631477, 538800078, 249010882, 531487484, 751117838, 119661532, 65889493, 6838016, 229430879, 729826813, 949130630, 290488272, 981368055, 802506450, 480643876, 708308710, 365774711, 385570590, 687019191, 566175581, 79552358, 568989768, 865973089, 137862191, 970397404, 573810931, 480541608, 32917738, 848248599, 574460480, 718534097, 256172572, 418017234, 482109770, 572211388, 973006550, 183485152, 309897560, 587357947, 869200324, 99026389, 184306889, 878857917, 808129042, 932547027, 155962094, 419859996, 19813744, 367847470, 338042635, 328905822, 42905020, 271542736, 195621736, 681389078, 235994072, 879866347, 540659883, 79882726, 37312393, 682197273, 620187728, 886055599, 79153056, 367854394, 614616152, 155109182, 621722036, 630446348, 164781892, 277481945, 545821495, 319766206, 829054706, 259211903, 728810817, 153753417, 612359944, 623099534, 898845396, 99709505, 262301037, 535931381, 164744687, 394503834, 758521058, 517247758, 319986660, 108568313, 938354152, 863828232, 579323124, 636707325, 53628863, 989727022, 455933253, 145680961, 953770173, 355099808, 292326209, 449248118, 700882262, 237919065, 860465371, 998801300, 958362086, 857387652, 42299547, 789369132, 792805407, 271406721, 727787684, 359760412, 35682638, 845110249, 675205635, 309031664, 947284626, 529337985, 122296457, 65893481, 993949500, 619407914, 498785500, 221366873, 928980646, 634671226, 104396877, 452826489, 538515080, 252365539, 647329186, 985764736, 139999803, 408935567, 167546369, 978793056, 945867126, 355490296, 804338138, 274426279, 682190918, 13958480, 594283389, 173040520, 135306893, 347882488, 249791476, 522593022, 739099180, 877580248, 108735775, 91715672, 452629704, 752334071, 993149114, 558443658, 20858635, 772492918, 224420169, 612757179, 342660385, 572139899, 801823661, 439158542, 86233624, 990820780, 458217409, 240902355, 650363161, 616070608, 658657748, 210786008, 836876966, 647383834, 584656681, 383902920, 471962201, 342232067, 552736001, 534834305, 796762714, 486128763, 371497267, 556044641, 894034272, 579763119, 196804550, 530109618, 702378444, 307267808, 761514017, 272978384, 257100335, 516180564, 527192505, 887040072, 802566137, 32930206, 61801911, 436519887, 619567224, 528282825, 908199592, 113886539, 670937112, 440233933, 909414886, 818835276, 517049081, 821697708, 134339566, 727838129, 818193097, 647744588, 234285976, 50718798, 39904682, 206899657, 362789149, 379038375, 647809368, 841225301, 422942962, 998966574, 996147898, 246443395, 510115834, 774125339, 973592861, 848636792, 510581948, 275832251, 111319849, 26949893, 823149790, 422231671, 762719133, 775314703, 515794571, 312858361, 182660844, 564247823, 282219189, 894336363, 171721448, 366163024, 542892523, 921575329, 390309859, 80271134, 742286238, 759000032, 381029898, 47630116, 51154549, 186618935, 614181532, 548919880, 589273399, 112652293, 422986118, 383010540, 564753790, 538481608, 480291052, 129627217, 767551523, 401674152, 404133067, 794647858, 369406971, 973575576, 463170230, 52404695, 225520193, 165453228, 584009535, 372029608, 943255283, 342612689, 570059066, 909253852, 398520599, 571335730, 910907771, 346904278, 765119283, 694510417, 172317596, 642365358, 559771591, 816280882, 321933939, 119442004, 248545888, 783983546, 800095498, 247448131, 327343438, 856999218, 49850189, 612413935, 742894933, 153662981, 343947062, 172393758, 472344388, 959854857, 501126467, 219134998, 87207391, 448961194, 523505607, 807986230, 350841454, 768444241, 290129795, 437677826, 820840193, 407579496, 766344622, 970854744, 635962883, 349579708, 965501490, 16069757, 971861727, 762496947, 180280622, 485827787, 354661703, 326443171, 73149639, 128737516, 896595563, 551327912, 63405570, 754958465, 348319373, 240813678, 270106905, 454957847, 622177216, 265344194, 768661412, 128453939, 679336409, 260217670, 1017343, 127762143, 44043394, 236791649, 428792411, 314388292, 274799161, 648020361, 238152890, 210891597, 999703394, 53601478, 23978616, 626665938, 78440891, 338399186, 666831423, 600828461, 804773778, 938976687, 955832705, 946124608, 871556770, 640732674, 125869345, 827942374, 293948916, 294341021, 327705454, 453645410, 951408883, 668220457, 718894113, 790661029, 951177977, 53515649, 918911172, 402912702, 503606193, 147060228, 146582338, 58977749, 517790130, 562747723, 630368226, 807805043, 950311993, 710029381, 935447809, 579986141, 248471054, 378665662, 445782928, 721281340, 401144193, 517745541, 816467618, 643501377, 705410044, 975407496, 28061242, 777299705, 362412778, 547469996, 134011969, 521932581, 654592747, 102683858, 560782188, 865633414, 252511547, 390923226, 190918336, 277724241, 440923775, 637483700, 14885873, 112485139, 92086519, 414292285, 457321304, 630802246, 918665350, 386557656, 440826302, 659952320, 328569763, 944869468, 124265077, 36969748, 289926705, 44991254, 392676623, 675734801, 61965733, 835064238, 977959936, 595947826, 1585283, 91332728, 733228737, 710338624, 354970153, 155632762, 263516267, 766162322, 377927569, 757301593, 169482612, 347268741, 397842633, 192040572, 583326644, 418761079, 264076994, 808057344, 594380953, 890205263, 212042707, 870875210, 43111237, 694798689, 108567042, 16530930, 480839455, 993406307, 427636583, 86313705, 621006462, 618771317, 293689350, 858130379, 635142905, 354365111, 997270933, 995761937, 964830085, 696241840, 747226579, 863645317, 329053475, 937742900, 503544156, 718871694, 599462596, 33418605, 845899963, 216486121, 982774135, 617087556, 620898194, 761120627, 217947761, 799578620, 333322836, 878014061, 975255682, 86165013, 621389509, 376795490, 315466293, 165275509, 997268522, 450287008, 67072280, 332318810, 565030109, 659355713, 915814091, 614786003, 618663944, 229809114, 880866646, 170535192, 801747489, 564599725, 635151241, 752115870, 125190257, 19380139, 462964668, 994471565, 253027487, 206145269, 83404450, 639365281, 812920258, 937705547, 745434143, 604597986, 598851961, 177784796, 856341286, 703663085, 7424987, 3335361, 682804635, 392617921, 682643431, 80553960, 716560972, 811278014, 318804829, 640353700, 904125970, 860744208, 329294144, 551150194, 142564607, 746880737, 672883044, 104701568, 707779672, 356928918, 592412795, 990723703, 863603282, 602318998, 115907148, 719289237, 609322718, 846673675, 367327789, 114055120, 571221899, 659487975, 742805204, 414740039, 54451029, 285953911, 430587584, 479499637, 847700132, 611630003, 382849809, 271615740, 87222125, 21948661, 331832410, 642448142, 363429609, 564768435, 905305409, 906558700, 91910055, 429100460, 882931516, 231770877, 436951279, 694123288, 272267561, 975101685, 724762033, 449610498, 279110630, 625718986, 498741153, 875693307, 913655062, 176214799, 132727358, 135846151, 382970153, 162507823, 76045063, 484613626, 3321992, 739780669, 811575326, 663115944, 131922388, 762838636, 11701586, 604244772, 170011592, 81585340, 565253779, 675865848, 633371589, 487682440, 845397886, 680598517, 406790237, 64557737, 433825302, 554686855, 541287856, 728141263, 521180342, 644286346, 988787994, 829077744, 901375922, 721593501, 213385574, 655553253, 701964240, 979636847, 853083954, 428977404, 128213244, 6700481, 446713510, 286002893, 215775051, 653042753, 108981293, 67116962, 607857245, 223792235, 727131650, 831675694, 25472663, 141733592, 481778842, 24574146, 664421734, 591060457, 472944728, 143838930, 144638093, 79174107, 77609138, 291870822, 304104075, 558264724, 861583999, 516209766, 551825498, 353650620, 608795053, 604021766, 762242045, 433800240, 938634650, 14769563, 354207059, 973365835, 545090367, 21130371, 269867710, 889951780, 500318661, 861770190, 478593117, 888443070, 742992307, 16043985, 470978530, 823429450, 184920492, 510818621, 378798236, 484521846, 965012776, 442388949, 408076688, 273264568, 734881660, 507387381, 834296743, 688685568, 813957435, 860174253, 259686018, 440848694, 619688798, 884710145, 913275689, 86407061, 100464232, 133683179, 639833609, 867730386, 809270848, 904646140, 299145826, 36913328, 338355481, 279016912, 349609449, 552396480, 813314680, 82794439, 575914057, 359215510, 43638933, 264067723, 495886956, 760937839, 235002530, 142096770, 847471557, 923430018, 966894677, 973779095, 724963784, 27140505, 13272410, 960423881, 47918291, 156077644, 960015461, 617822248, 219550812, 304693318, 651411871, 104714797, 106111158, 454294723, 189591059, 870929783, 570258064, 206165664, 714046397, 27564631, 709812380, 145158550, 608050286, 791627600, 904378800, 748095147, 342036630, 480004469, 967280955, 370320812, 217602493, 675049082, 389836761, 644444908, 510554270, 413155252, 526731171, 820396165, 494482906, 385697322, 618879184, 775799165, 219711352, 225482174, 584767447, 674012341, 734106001, 531477872, 380924251, 661963445, 725276857, 100069205, 395424457, 474217970, 242251470, 480980736, 509126868, 899230178, 245955690, 869869462, 60238998, 311549305, 378260814, 970562253, 678295560, 907010255, 569432795, 685610679, 58210703, 412380513, 988109403, 585316351, 957658333, 783932579, 229537652, 612731536, 586799457, 812107712, 682695925, 715684979, 188936816, 235619521, 366505071, 954140971, 792670586, 742424193, 889760443, 690402795, 590205847, 478142484, 37232245, 590742520, 634413709, 474553578, 862415894, 790013349, 734597766, 320894862, 540865803, 963415368, 74899806, 586496940, 504722076, 953449231, 748383333, 556621044, 690169709, 435223016, 543198323, 18125486, 329198541, 144715834, 158515383, 336157392, 20550705, 61971906, 113538198, 865161913, 900018680, 839950336, 758018997, 873369236, 928483075, 890729119, 340264557, 79297731, 321154529, 674534388, 324233093, 320476571, 643333518, 995146597, 372814905, 544585302, 840933468, 922639662, 364742398, 935630791, 613803746, 326797603, 843954616, 350905746, 356245866, 195251371, 449461361, 990448368, 682661208, 470104523, 398747354, 568751944, 680906302, 712149572, 968263046, 339826548, 127279248, 75436285, 59946228, 822916614, 732242860, 568611775, 954223722, 338952193, 768698327, 200201171, 58806073, 81435505, 974008935, 193499118, 318654979, 647478114, 547288489, 657007115, 719476787, 632125387, 682263288, 318420732, 637956060, 238857882, 97359475, 26099110, 409703070, 414433629, 218123956, 611851667, 169912254, 498819506, 687817794, 553710203, 40868572, 530339199, 517644593, 805396488, 831801381, 160492170, 656978876, 517021413, 137083974, 511475063, 85146993, 882805563, 560735377, 363959460, 414515113, 853672054, 153580605, 141162583, 692345642, 219818357, 742799831, 749286758, 552206307, 433003334, 704039093, 738758322, 937915258, 152577989, 611325659, 967208577, 806779051, 981897465, 860635632, 449096052, 414942665, 702580531, 854079467, 252084693, 686890372, 545488975, 45657925, 578020326, 980187780, 269631403, 886565837, 187036599, 261073319, 336265753, 253662174, 667411348, 396477717, 381550859, 589857578, 995127575, 398504906, 494027938, 747761631, 791487884, 717096661, 160838188, 762650179, 460474570, 480293607, 907884354, 239452547, 812617321, 14368977, 960161027, 969594451, 443317136, 361189593, 988970396, 918583268, 641066518, 174827630, 330582556, 950382668, 703290159, 501332659, 71102491, 546862619, 265416886, 971477328, 409299223, 778264219, 870269142, 457106767, 441439770, 322999545, 94350160, 131560175, 117880335, 830314967, 398780740, 425067714, 831955802, 744061456, 23603630, 106532290, 145152452, 227967428, 490431013, 394861754, 135624688, 91109817, 849478510, 532209288, 705499945, 142540255, 871855737, 111839115, 960322788, 902220956, 912501077, 814916955, 183846799, 737821683, 379387513, 288370548, 643780574, 630052621, 25774418, 736361078, 217952219, 866304723, 223905716, 77009127, 644703061, 384945728, 153685789, 174938214, 922205188, 437314287, 591328344, 364494052, 475824510, 84532466, 917693461, 978792013, 52267380, 143365185, 117841829, 587963161, 660571402, 361002920, 870404511, 32291552, 184871894, 361557674, 900435728, 392842218, 335132533, 952443044, 200463457, 983701569, 429687185, 797926534, 479705095, 3205037, 877974583, 778096075, 63368599, 598066170, 518391424, 871927473, 160185286, 545145478, 727948568, 52383571, 427607965, 333444632, 950870016, 365255671, 503223386, 584799751, 665612509, 585342319, 620437978, 320109282, 190902155, 286892902, 271559827, 343334504, 838656274, 305041926, 703106382, 712228123, 315080970, 574536642, 669321874, 585996554, 2107786, 543412705, 884362508, 737341972, 38222789, 357098477, 668053172, 113603562, 789154205, 612871706, 68773744, 926476124, 279600083, 145469415, 953666356, 372412496, 50685177, 410897067, 890950373, 382862875, 377385323, 917711605, 80238531, 1177576, 83342731, 261610909, 385686942, 626143598, 286445290, 873709658, 663955754, 720759082, 409690466, 43784657, 735578846, 73460298, 416568792, 985695519, 224672311, 845559968, 832350843, 944193825, 252391322, 109491549, 654885232, 540903938, 748784280, 298720815, 81226662, 66350059, 22586875, 575661923, 877979583, 720624671, 867575337, 750401762, 171523453, 431575205, 968232494, 417450170, 462151449, 173188379, 679841854, 597516600, 207649632, 639544751, 423380854, 293533256, 856436076, 949571176, 201119200, 821580109, 186342160, 376652583, 622395692, 993741561, 490688791, 53248416, 183736766, 876915630, 386613484, 753921269, 581010465, 285197609, 669575839, 313089548, 474011343, 255670473, 498615612, 14343789, 922270687, 782618142, 179714861, 542795727, 729561043, 632744111, 840296898, 945916316, 959411468, 379524476, 380413969, 861783975, 770520811, 325605700, 737491437, 634938764, 471633730, 535125036, 223641132, 6533211, 328178144, 111174574, 568388380, 154949177, 658490061, 706798596, 796289738, 959279216, 326182044, 411405814, 225850013, 694927417, 234655658, 573643747, 136361006, 449848758, 448034078, 99616929, 349006610, 762417122, 547087694, 171161077, 65118103, 816885970, 384321133, 523135530, 764364771, 76899529, 90496673, 867952428, 579387275, 873358596, 789119229, 897259380, 848980003, 519848844, 555081476, 145505939, 608532541, 648448094, 328498259, 611462317, 361630108, 262101048, 221608542, 494026185, 897645993, 241658533, 681206755, 346479326, 208687853, 365286538, 24869982, 689458853, 959268573, 80167029, 524072501, 392218458, 154062735, 184796196, 110331242, 736885150, 963011126, 983909513, 164301579, 278579139, 236771749, 619888935, 306969167, 711447413, 562835333, 853069723, 957824968, 395543790, 51495649, 864654693, 686000777, 451311880, 72599531, 682304075, 515119922, 733406572, 573479753, 361947741, 520593968, 791955104, 545874414, 502192751, 46715761, 724245141, 627376795, 85750610, 755172331, 470972362, 181128707, 843958739, 393114271, 285822755, 729422196, 934042793, 83419885, 189208095, 855571201, 357929387, 528380864, 868271779, 361172795, 931546260, 833050513, 36523918, 417039549, 690407133, 549061971, 199392063, 168062498, 190420377, 871295678, 775174189, 679811903, 747316696, 475927111, 456614089, 550816563, 177739368, 586864877, 289932170, 186617985, 568987823, 184958936, 51690643, 787130368, 838152588, 202707326, 649095338, 95440765, 360411736, 313291407, 33556711, 418758914, 75088194, 954549227, 145009230, 401545717, 47473929, 369827429, 965649403, 695237745, 461186154, 322619934, 97223119, 273576057, 56110072, 889692260, 762837644, 468152262, 388268729, 376030632, 29791215, 26009209, 278010827, 62726189, 860438713, 800115911, 685308087, 792605672, 744862074, 719660649, 36518808, 55692538, 144279027, 305546808, 699828530, 181851955, 483438948, 127129743, 213362468, 615803203, 650808134, 959598640, 812357882, 535954786, 846940362, 375100140, 178855945, 552987422, 356077296, 29023095, 811291106, 401108658, 879717055, 749855637, 906488264, 673325404, 384231979, 731540782, 347036939, 692642467, 513487104, 640910129, 412105437, 544758589, 592932386, 435868552, 768250635, 11375377, 304419387, 560251752, 505271815, 199823130, 634266261, 2881618, 557454566, 43169455, 785756380, 448669510, 724347141, 700913721, 262075744, 120766766, 312702039, 408806712, 195078073, 900405014, 433596754, 316096872, 370526553, 515095925, 616056619, 352142155, 598674590, 391495114, 356048153, 969688402, 598226511, 670736846, 347316883, 931747691, 609738453, 721167483, 457068455, 240209344, 352082373, 577297538, 500346717, 655232739, 12326449, 486442439, 7964389, 379758992, 565602178, 39837973, 458526349, 508515763, 168003305, 744391992, 430908282, 558617215, 379671914, 527519610, 227897042, 457528007, 844152865, 185546371, 362645841, 884404030, 819541952, 774790491, 929187612, 10707153, 157327105, 796160387, 173146995, 524623325, 215236285, 757239260, 52937340, 880058633, 13513635, 190130182, 520844598, 274847067, 492968444, 36277155, 123713924, 583353156, 291877378, 751345687, 851910791, 300747394, 308118858, 235017230, 282942025, 503066919, 527860352, 941607629, 244222897, 781680784, 904578392, 766514482, 949500894, 362623486, 187979460, 600779544, 450130129, 932346889, 753956621, 898234749, 260295777, 999846515, 907896960, 753701019, 963164940, 386089780, 960981379, 78029494, 470495915, 877779608, 934930423, 997114079, 872792173, 637721171, 29902233, 899350306, 730904711, 207309504, 762300907, 712715872, 225989757, 547113924, 911479497, 259939658, 34555586, 191383541, 355136544, 599836612, 951348793, 431342895, 528488392, 359829893, 413129148, 660694175, 283535185, 329281177, 342832912, 24571550, 673012858, 48301616, 527149600, 727049159, 892741689, 668639356, 10426318, 537322392, 779905506, 585370256, 449662648, 191247359, 479987175, 665590577, 579503524, 123944712, 708110132, 109812990, 29652747, 511764189, 385705896, 839820140, 968083053, 102241827, 575369490, 862858689, 977086698, 580488534, 973275021, 465920965, 28189667, 599101804, 793142069, 132509288, 440364037, 182832503, 312411921, 296381532, 106513010, 947486311, 20022622, 138683314, 65810915, 490616476, 703272471, 914553142, 17142258, 727635567, 590775152, 73653660, 12085125, 728369058, 602214540, 648231370, 699272259, 798853700, 645942251, 378221387, 508170730, 724682914, 189397787, 287292961, 781588144, 781510265, 770903958, 423107143, 750475949, 842215909, 349976725, 505868822, 34820215, 143813411, 765450797, 446732012, 743749548, 717538447, 500481225, 108853392, 137318965, 999216508, 356358656, 404668748, 532181606, 932392034, 20356109, 981679429, 341713580, 48060162, 433139048, 21276079, 286752639, 351873620, 56742963, 597936540, 372260857, 724055634, 825552494, 539947237, 690830058, 814194146, 590832744, 51812287, 278449800, 509612921, 897126783, 129625213, 335462193, 343615459, 611466260, 334906916, 796966680, 693715704, 106189976, 605324758, 111664140, 34898966, 628844269, 642032090, 40907658, 138734639, 114110170, 609358320, 263880859, 784105485, 783543426, 669875133, 947750229, 346716066, 682646963, 759497696, 104120004, 657265921, 115656328, 723684636, 428507639, 605334928, 808591281, 578813562, 409696327, 440269806, 653974003, 808521127, 308443423, 850841152, 49386408, 787221543, 653750272, 83909409, 54081778, 895472686, 489166547, 269625727, 827530681, 824222588, 505590453, 78428574, 362370057, 326656111, 34413157, 119562161, 57055486, 112120485, 197995873, 606121535, 896058960, 630101533, 403901863, 72922886, 264728033, 935809624, 405121865, 969238451, 497850966, 346453619, 209220745, 684946768, 524714155, 700832801, 619059116, 680262751, 453429208, 281196971, 725216876, 791055123, 42254237, 440343602, 313196350, 753223836, 782165881, 56582855, 878938312, 414274907, 713314826, 897657313, 524415430, 938262582, 57190594, 66692750, 661458726, 355855995, 484213833, 124692915, 864649593, 203397314, 53523107, 791283811, 206864067, 830372084, 437010677, 939211840, 347780902, 971945852, 554380897, 321664502, 852362818, 67133151, 296101204, 70160478, 522990836, 231157782, 833008684, 786037960, 139705146, 318706650, 883515313, 698650246, 8855974, 252745273, 208229684, 384561833, 914523409, 760308194, 917983915, 504259720, 430721089, 320729954, 966211199, 172758276, 222909839, 912742334, 100249578, 692862721, 831129466, 871060395, 268719495, 239953290, 930353013, 182114951, 688588829, 397627303, 821342190, 482459793, 980507464, 665047467, 829742187, 808668169, 208803560, 15696167, 116420156, 316253453, 119219112, 214634576, 296646204, 173426300, 989031871, 324232085, 453827191, 61150224, 524584063, 424979432, 248613698, 762321477, 837126008, 400429215, 653882831, 792344895, 529360333, 763562126, 837983166, 438596551, 688838537, 360672996, 924525127, 930213428, 978520652, 70877571, 693267059, 95121799, 943648946, 567280887, 27350441, 4028453, 42083843, 69899212, 60637469, 4972216, 390265992, 681866677, 132926453, 869346517, 686833966, 790979574, 43827189, 161193461, 723757646, 687310889, 584791514, 877838724, 959340036, 136123820, 580661648, 767622154, 197686422, 113687444, 31693713, 463098697, 942127675, 611887414, 388001344, 142052934, 333667680, 179065443, 973435917, 68885466, 897348146, 22250344, 544785725, 721599020, 229660316, 166683511, 950461157, 919879704, 784999080, 459409584, 103571819, 188743285, 49194600, 70210785, 138412482, 333620799, 90063135, 658693823, 643797206, 721192066, 7202203, 198217528, 754802159, 746088379, 764478392, 870504174, 952826025, 337551329, 527225315, 830539242, 963909151, 884685163, 607292052, 550056065, 951837613, 913839376, 270539673, 482018053, 134759418, 49010385, 760410766, 291680495, 49894224, 996388385, 996279205, 424571779, 416798600, 466320430, 859077775, 566493018, 392160170, 488344362, 748721773, 264497966, 96718372, 405136799, 690963382, 976362936, 225052360, 352848330, 682747767, 293280931, 438908262, 627044245, 463435429, 948885705, 3415764, 29925189, 35061651, 747308063, 875177835, 325255441, 137550308, 881484294, 796058838, 810696769, 923315323, 131044576, 94843720, 923459993, 639862689, 627342971, 903216159, 678245323, 683093135, 820616557, 802422838, 443788479, 652981000, 376248853, 198993187, 89712522, 548253969, 363700218, 412594107, 743609402, 977124320, 496166864, 981001297, 324158692, 484625075, 924598426, 514643952, 203644228, 206686104, 909948584, 426007996, 682406008, 917639229, 525196248, 532660859, 716563102, 539095731, 778955254, 64228668, 707879366, 578790992, 304107037, 560230657, 341200235, 481201379, 133574007, 480020524, 786870797, 489191534, 793319059, 31977833, 563374928, 742031448, 510173714, 391144421, 227602003, 610992482, 722891410, 9467629, 912637885, 899422556, 605814404, 545908017, 138057645, 823723881, 617973523, 190690307, 722338979, 300263658, 426396633, 824868262, 14055412, 633872264, 990284008, 451112376, 898623804, 93031574, 467040897, 185653834, 380013422, 633072659, 531753742, 106132982, 912798591, 19831086, 738785499, 256515184, 566064634, 982794577, 218921361, 49016227, 30993696, 176985026, 102135278, 972559629, 915014872, 341363900, 167845435, 311387327, 437048099, 271502674, 239917868, 954592678, 339781540, 839789026, 402100117, 685728521, 277855468, 94525791, 733425015, 910170339, 595301065, 455970673, 607165808, 659041118, 472213288, 748719157, 994542576, 628844235, 304516739, 230207434, 448201121, 38180818, 889424918, 890723356, 701551365, 860561307, 365783280, 481192137, 160238438, 588625262, 902970949, 812758616, 674153792, 74158672, 96765047, 177197228, 234940136, 671715281, 686796611, 992648742, 394676376, 205159731, 976113948, 963932303, 306905340, 575803724, 195879151, 34288186, 674581634, 343877877, 716739031, 769802265, 736786448, 230558690, 658758950, 485729487, 709886431, 821912447, 421335856, 784209345, 859601690, 88497974, 689710583, 104979089, 896068426, 321045508, 885685581, 832160238, 895596089, 360121293, 887074632, 866347506, 619325993, 12921842, 992986168, 778148405, 366182457, 498924866, 681161238, 966582682, 764339073, 561264496, 43064894, 178358834, 14556670, 268586423, 507284818, 787648054, 961767232, 895927583, 164991203, 65082231, 700508600, 2501194, 636282183, 265794377, 440087578, 612079582, 693444527, 865093959, 70945030, 547910748, 527969455, 673471237, 88992733, 452299075, 768615047, 200765916, 894924929, 35778537, 203434156, 910009289, 584854554, 778631685, 158165943, 839428019, 927351626, 668794379, 554400889, 86833053, 505612175, 81867175, 769166159, 887118804, 723315475, 755838906, 114928620, 806833479, 301570868, 475234566, 104945611, 143821736, 779178321, 957070454, 96663720, 352302426, 42365511, 661028045, 501810053, 780956238, 181113986, 273000045, 105901328, 714965962, 776256943, 210298694, 363393233, 624682315, 969626921, 387037754, 180254392, 690801394, 302988355, 185349562, 804767486, 121795613, 307445129, 427020245, 15999789, 38680172, 754441318, 175601714, 743471072, 119311747, 725524233, 807168981, 714543703, 684072085, 490105914, 769986270, 93364387, 455829107, 209996981, 8876626, 477586519, 918081112, 831178794, 570162110, 957938605, 352520754, 328397537, 115443140, 387054768, 921039965, 514839843, 220390558, 257382295, 818020893, 797690393, 46900094, 84929564, 569430282, 856503149, 627178735, 155544259, 502359323, 133133301, 874144310, 847627297, 903067010, 871177326, 704407228, 668834258, 487840398, 473430423, 929345225, 946056340, 101378975, 466365999, 980189708, 120787172, 323996594, 918162598, 406122100, 410745012, 933017778, 742513992, 638386340, 87965409, 581329243, 389545556, 759042017, 499909341, 179091593, 38063240, 428780035, 553452147, 748465158, 390763328, 451042, 68418713, 860135350, 341763956, 188117139, 515610285, 946156397, 753625434, 186490539, 960499692, 124202920, 910514235, 742780117, 999135421, 694987752, 403161491, 542068271, 267483302, 366498094, 623262972, 11205351, 832780893, 393536080, 751300286, 678893981, 994879937, 374675790, 364280445, 366593849, 317037887, 171977161, 387713765, 260519094, 539676924, 988729717, 894836544, 669791790, 781427019, 741749124, 614492106, 477114513, 591748074, 218035744, 204216674, 859153829, 449930493, 734922049, 838549041, 637744609, 495169383, 912212291, 346750926, 740057922, 298610113, 317156850, 185978585, 75026678, 418721277, 8655779, 189266518, 813846837, 622452989, 718921723, 61840985, 792649554, 114032542, 514816507, 229407660, 758611945, 442937155, 564569610, 580830865, 680656858, 303167693, 461129861, 885828788, 4498978, 222677099, 662678773, 339371582, 352031287, 217704381, 513017047, 180066623, 223212093, 251592343, 358055481, 64412405, 609205496, 695795546, 336344654, 752743339, 336361923, 483092802, 56016550, 26518347, 850079594, 714859700, 410302936, 993034735, 748991006, 433764786, 298434878, 318008601, 128598743, 462736757, 200081524, 638610976, 438167446, 62143523, 411848352, 590321382, 402477680, 302032843, 884870950, 584823105, 296345123, 803404511, 30005546, 233191008, 89973756, 639641661, 113094348, 643131180, 585942920, 925151118, 737354906, 365509083, 344757474, 453107872, 264020317, 824179340, 699209647, 318111214, 261003653, 641709692, 518231863, 14396405, 111091085, 395443488, 233702784, 255257297, 249235922, 313477140, 967723924, 313515723, 765959076, 679583425, 405821822, 526051111, 113249528, 212953851, 276014630, 431309032, 368680547, 823037582, 226791038, 236345453, 27272652, 210484910, 821588542, 235518585, 701206583, 616270112, 947729028, 110636603, 814553581, 766764128, 641381916, 501209501, 302543453, 802599258, 678884032, 59333735, 134877316, 524322777, 955209725, 639600195, 506400641, 520167110, 425694426, 31986729, 362674769, 345596520, 612410195, 112783762, 800944283, 819298384, 534200642, 251492849, 901066942, 360376815, 968708672, 408356106, 469328096, 812795137, 972146425, 906380830, 406309168, 668675895, 287515804, 717557615, 636519540, 118197187, 896431280, 397853555, 699476633, 657331091, 908642692, 230568718, 311449304, 960336556, 504576091, 221486301, 64509596, 133043249, 893286243, 352886365, 338556315, 424086165, 543691022, 581649267, 610671216, 631027639, 303454838, 380939066, 344233671, 218101077, 690418367, 740209409, 932730153, 277815888, 246434082, 179818396, 831956097, 685616986, 246126257, 484563828, 765013812, 275358837, 536515171, 759344965, 315867875, 302830387, 109120378, 832870629, 914021599, 628171548, 349662418, 483573207, 885436686, 120847522, 506795945, 14536550, 811855850, 755215401, 417590152, 244315443, 333338140, 138046752, 960808888, 670511787, 317269220, 360601907, 674164538, 611169824, 180838174, 729074990, 607567343, 453805054, 175990498, 404568209, 287096521, 478392461, 622237263, 790894501, 307137493, 624733576, 141334436, 970595441, 964086344, 766153597, 642259978, 27660298, 182623390, 159765177, 410377481, 822110279, 897263368, 437957214, 3563032, 948389652, 987535189, 860967368, 192671699, 70857444, 627539653, 685274163, 579029180, 752731552, 274833340, 61438943, 6743233, 676491619, 501380635, 27070857, 640168310, 974034397, 840969277, 690694103, 23809715, 46039559, 490775344, 293223758, 354244649, 870353972, 363861277, 770202030, 37567933, 809787159, 517342686, 383583323, 826392935, 989727317, 372412800, 242598078, 890183303, 913007560, 595459415, 235536082, 197097408, 494980954, 7102097, 39638590, 265767479, 289106801, 970001756, 871570155, 590788981, 513461165, 579930577, 405703398, 205174531, 310183483, 589152607, 764676658, 814706508, 523173360, 278047610, 976533132, 477027936, 511575122, 23195239, 653440645, 729076753, 218359814, 708565238, 478901164, 893955758, 830184382, 746348836, 921322404, 159338692, 165994118, 356492932, 454933293, 706936949, 269813535, 431603297, 882763357, 825377127, 705599039, 810146124, 973651377, 377721282, 193308728, 691185873, 144850158, 306736857, 136908197, 990037037, 12536844, 573387908, 715304618, 232915963, 829240942, 984117679, 15745888, 779063107, 870430480, 782189530, 445192161, 505799830, 118138253, 78286318, 460915965, 794601757, 115353154, 49720813, 816676932, 785288424, 838030015, 607467337, 256795938, 552944550, 202761562, 871800992, 907654605, 694093373, 738602857, 368642476, 39411640, 15871041, 971067855, 798749026, 597853937, 598719239, 522167299, 34205459, 47659867, 960502914, 675136028, 969041645, 580747288, 774577906, 373498175, 874169909, 483919136, 161765845, 142053611, 862174516, 848580142, 846593866, 942379671, 68679902, 606968753, 289967246, 634584746, 134685632, 202094916, 684636192, 292805947, 721025758, 353545973, 642409536, 662840200, 167856859, 693867154, 83548554, 556491049, 237207083, 746229283, 646007694, 88752212, 183857435, 957037316, 648552524, 837980560, 106566836, 148653524, 453636081, 22313279, 327071429, 172550915, 691811012, 821298913, 835211731, 265601240, 382032345, 402197621, 829913154, 422163201, 961990416, 193458142, 826506726, 109044224, 880889354, 348964439, 405683253, 825549472, 672939235, 252025529, 146458367, 760747528, 927478028, 10459041, 39298781, 951147069, 44983691, 576070118, 776107269, 396386821, 943420048, 927217245, 294386698, 905606524, 499486787, 550210846, 400667707, 20523693, 259184312, 770663282, 454751017, 296480994, 946989893, 78676248, 780583741, 106810664, 389261294, 897396397, 840316871, 178526945, 989560808, 569146729, 120949737, 489582508, 74537205, 192583246, 469189551, 699445110, 795979745, 781923393, 72695611, 676093457, 175984656, 149447768, 420569760, 129425249, 214419978, 818173776, 625888349, 687739445, 858209292, 510833273, 155963065, 693169860, 347315313, 296733505, 972212765, 407208346, 306302009, 474718844, 880726873, 936629823, 589902467, 32583556, 70635247, 895822887, 347778114, 868986741, 472231380, 214374319, 959296154, 346563710, 815992820, 103106157, 961390807, 362237383, 759593485, 719333552, 919252938, 82227948, 259495342, 302596963, 914075310, 3661366, 693643713, 707615450, 442825706, 331867306, 896230637, 354459111, 329115379, 287820970, 903879648, 231419606, 270041351, 156149832, 790006253, 646763746, 249859817, 409383256, 579268873, 50036405, 23146074, 643329578, 844468549, 962801600, 881001700, 928426944, 947485745, 720163933, 284004343, 679437016, 983947081, 775980838, 911800949, 514865055, 942040768, 95715509, 183470307, 896490464, 24292888, 487146252, 561308773, 284713946, 765687413, 518025771, 52432530, 919582485, 437677109, 557390935, 486387552, 821615138, 686429098, 744699245, 852824194, 736791301, 417191825, 987938175, 778984289, 373990562, 119321000, 706554258, 251782744, 236969387, 402748883, 817655298, 25137902, 560874761, 789036924, 896043059, 845511117, 474078812, 603404566, 925265970, 632999581, 811909718, 655833129, 978103089, 758027260, 75137813, 727920645, 840325809, 644898965, 973593047, 121741852, 947220551, 27856605, 459033764, 389875403, 654415760, 239498550, 3052170, 127985988, 553069639, 269916746, 478728213, 972250785, 536368002, 686794887, 375819702, 789257061, 899321048, 894706864, 633785746, 426105670, 47098767, 242294358, 28134126, 925464071, 556544617, 343553869, 49872023, 984229844, 108544543, 403797269, 255296570, 485109364, 430735283, 4073231, 522304980, 132233244, 234335015, 705338820, 698575944, 301742579, 969771380, 364326865, 573860701, 111421879, 2977513, 634715036, 791786812, 900063765, 177061806, 547790693, 728209621, 481965684, 165355261, 970111678, 521804027, 526942529, 302164501, 488221972, 531725943, 794921606, 360036392, 539116690, 430865122, 387529325, 624982147, 33978345, 846243989, 385324192, 211412483, 651654244, 947205090, 532919610, 873118680, 923099392, 780342798, 494718230, 365776583, 639897643, 486627644, 911901069, 876689060, 658404608, 550159747, 684891284, 536662694, 975105142, 237398284, 945594747, 946004555, 713880245, 225839596, 530768803, 887128924, 872962361, 807550737, 583041669, 963456334, 669879971, 243600385, 147767408, 71725150, 371675114, 66610136, 379159029, 552768324, 521994786, 226979410, 391508808, 805677206, 182204209, 266016408, 14393589, 941301076, 874971120, 224099125, 722960559, 84277660, 330509314, 388889374, 929481853, 672546257, 571813978, 526552576, 732388452, 496775175, 183166757, 784152407, 177240176, 977842110, 115463121, 657421030, 317981070, 450410022, 960486630, 552570676, 667638707, 543332963, 669851512, 26358926, 456663933, 522501041, 45632137, 21920594, 254284288, 665679441, 705267069, 958161784, 318201157, 457042125, 859473248, 741254782, 618986015, 870749750, 381912709, 771996770, 814012524, 480229487, 366257724, 972806552, 129245517, 821803023, 447098668, 500631959, 85080441, 663268716, 766973330, 792775684, 98457957, 154614041, 737906161, 15691130, 890303535, 812080298, 642941405, 811098817, 409411258, 337883806, 159276060, 298376424, 947459964, 234871244, 29195206, 115165834, 744684750, 842103476, 807724276, 51992892, 979772025, 712900285, 361789123, 533606150, 358318710, 190458289, 885936910, 306321642, 117006678, 606270471, 311020840, 303580908, 168600041, 303500486, 408185592, 811203507, 58722383, 668842157, 467166059, 869202839, 63043032, 577529828, 453215996, 538867573, 169947564, 828809013, 232930997, 101134125, 505903545, 435350541, 168714776, 413388852, 424426524, 55474440, 501520204, 342284281, 886555172, 528208241, 902620929, 343052140, 247445665, 163467686, 484343802, 443700870, 895049916, 789547797, 14204827, 105512611, 768360706, 377735593, 171290995, 843677923, 43105240, 138690972, 990728282, 885296340, 512448251, 770310125, 879819817, 928327402, 809728838, 40287625, 811988981, 138126360, 566998780, 388856551, 641029612, 10673987, 862335199, 425368719, 811084802, 578836133, 758483575, 118463034, 759136170, 802472398, 662229977, 249134749, 343855362, 625682600, 801940572, 633349380, 572849608, 912491938, 103178309, 502754518, 561470563, 653149394, 517191412, 715683816, 550472329, 616392923, 719045292, 600963375, 22433141, 411984550, 563180193, 502774934, 752230345, 407784600, 849989970, 164974278, 201531642, 100016033, 279438, 296853745, 798325364, 359579439, 346025777, 546640596, 67508351, 859587938, 513600431, 346375894, 19493779, 412393610, 686816688, 763643142, 210285497, 801501151, 545169895, 37359374, 476345357, 125194227, 693756146, 125432875, 180039629, 247802052, 190492073, 996823960, 229091739, 794716721, 194574145, 59181896, 590699565, 885266578, 954735387, 923746393, 587508999, 222560375, 294447150, 409951290, 1169225, 360102875, 317961457, 884174887, 170419439, 65566249, 447949172, 565222122, 395550419, 14237072, 256217977, 948168446, 638627318, 642017982, 787781560, 162999042, 173385949, 562259582, 10270372, 576766338, 701391685, 239160736, 583901978, 104590974, 479874389, 434851424, 251751230, 904809083, 504224907, 802911996, 146640212, 117959244, 743119981, 604075438, 13130940, 500515610, 925708513, 207989968, 888778662, 539176623, 345034118, 518961962, 488518120, 639869837, 599843559, 422658853, 614846085, 835857399, 786940059, 435047584, 194137589, 230708077, 477321856, 838998178, 316181354, 370292214, 298373555, 625159271, 87537717, 309929256, 961052292, 842373636, 433717746, 11480527, 656236098, 64661872, 872628353, 59251625, 432130192, 320521362, 510997795, 614986571, 364846913, 417490298, 494468791, 199890826, 989611079, 290976703, 214908676, 837255242, 932823614, 808029505, 465566440, 809547299, 928581576, 605396874, 581431624, 152705188, 985465986, 676063917, 135387276, 475126395, 552194147, 653467635, 881087802, 612176873, 997527543, 595697939, 36210376, 258959224, 785435263, 373059705, 727713290, 267263058, 434427064, 245792101, 656131487, 826130553, 834657279, 731976427, 426693476, 523809886, 968167427, 280172157, 99741973, 156381290, 816172259, 914836551, 727487494, 418227683, 572153203, 851517347, 757204148, 352715945, 249018236, 965729368, 406783989, 605765123, 884721845, 427915396, 725504024, 460348957, 578547507, 75960013, 109907567, 615595757, 627001288, 361276105, 952746571, 138570932, 512528601, 94482708, 514689446, 244084122, 230584502, 464453077, 165058902, 916315075, 269368201, 756180220, 225188574, 675413444, 186516990, 410688469, 892483488, 851107457, 625515363, 679314707, 12377104, 196387719, 634821254, 911625993, 927720551, 223622502, 549144507, 345353882, 911721817, 753746505, 232975527, 267277738, 586715697, 207555122, 789839311, 416243183, 386255927, 551230875, 120711144, 532259830, 101168663, 425750829, 901058443, 87543642, 313486964, 90961799, 518007077, 501094187, 392590119, 567966956, 965552546, 887334651, 549769404, 989756137, 843337790, 590448036, 50538282, 63935504, 537155795, 846886503, 411139616, 383463874, 348848532, 36935126, 714349722, 827802963, 194916375, 498486860, 792591874, 616412720, 214827691, 564800546, 711023008, 525711727, 40903146, 539794499, 792598974, 873025831, 24971710, 740116709, 855552936, 90021621, 147530120, 787216835, 884626364, 317312642, 828930411, 362966704, 203223226, 555723229, 885938803, 136397291, 506276263, 860598014, 963284363, 955009867, 755720373, 462561098, 517691503, 360529381, 412958335, 204625574, 690580472, 1761849, 404925990, 568499667, 101995973, 378426274, 772846591, 947253409, 167920278, 47245896, 698159751, 498650514, 307129271, 977833141, 6290703, 209691279, 380929751, 50967220, 526617886, 847565814, 566037948, 105093868, 379491482, 556437318, 16752769, 378617485, 951971953, 708861705, 243827370, 803891948, 385970184, 166381106, 204223282, 536971376, 386950168, 906309662, 710349116, 314132977, 405487778, 367181272, 477118866, 156738047, 22589301, 781539379, 178660093, 984733670, 672585771, 942739102, 514409043, 201066953, 493589953, 836029969, 204233869, 407362350, 941946747, 703570364, 704186450, 967202569, 960134276, 130953532, 958211169, 138219500, 985217062, 698794664, 182249333, 530792766, 709745271, 865281391, 724332116, 352341029, 329044557, 232332439, 941069141, 499520305, 522385008, 12495925, 890706932, 107545694, 880866546, 133911450, 722645470, 778230106, 151536467, 564176538, 369642244, 58639105, 400038191, 653007854, 950496058, 333308097, 39413720, 357058587, 398343455, 373727161, 740815832, 31893260, 693501590, 806477572, 41697397, 938891041, 592085978, 224891872, 352848874, 632225609, 854442593, 470242345, 783004743, 300798827, 89775092, 187843833, 838172381, 92041050, 97732794, 390488304, 405928912, 75563964, 848260507, 363032015, 296257316, 828480827, 909002076, 808382121, 508291628, 126713983, 224554026, 689852989, 632180280, 672626574, 103267796, 38324786, 968186774, 738767517, 578344132, 866618444, 500904916, 449702909, 590974776, 347171245, 953362808, 984456422, 488192685, 6345577, 599456872, 264846804, 428605481, 485200422, 22966202, 859982014, 661023413, 205941428, 441941112, 41657877, 29613300, 185051112, 45837863, 864289382, 13663912, 749610744, 622533199, 577967687, 683945229, 690850367, 675658173, 969170180, 116803314, 915023768, 207887996, 628663793, 691630935, 934311492, 49237194, 3672428, 454897176, 325232678, 385595121, 732352924, 917958377, 110369336, 463294713, 176045755, 393603396, 209378813, 559258793, 280023267, 174584605, 83331257, 5573948, 331460165, 379132269, 686260993, 939552502, 739978519, 799645246, 783149313, 219931519, 693000776, 942062084, 886331410, 978071592, 381312052, 94632393, 822111583, 449741833, 321602171, 756291955, 820950442, 281542376, 260428144, 387125610, 763980764, 63330909, 26995215, 919411579, 382040992, 266110348, 770434067, 254717360, 265999146, 180517495, 113418398, 180746600, 841388550, 790157362, 262574405, 975200190, 219226476, 902536190, 970153055, 932580015, 224427227, 663044785, 989445136, 185786324, 755404565, 272437185, 608901945, 143455880, 993155310, 757066752, 932963228, 94329466, 702246758, 721397438, 352589056, 473303449, 39396671, 337116, 20583792, 661100176, 154207063, 252631555, 291392308, 909999795, 641529788, 604269243, 979904665, 631090931, 757720120, 135340327, 272820398, 230697244, 712065072, 290500031, 444904836, 303323889, 571982322, 964425023, 859854868, 110006643, 521964531, 329808530, 558263560, 850028344, 847247123, 285823991, 92444755, 879672525, 159079951, 169962363, 882833349, 550652507, 310417677, 473826459, 271525807, 104065079, 486645759, 501640543, 748839722, 59504175, 779269218, 623633520, 69350709, 196947216, 366296616, 801540623, 48763424, 351786981, 99038676, 389109887, 527878802, 212814703, 36953921, 249371078, 263812260, 486032698, 588968563, 481550319, 363272129, 998341211, 563353196, 4892145, 43646167, 908743733, 895244446, 745159142, 507654704, 233957980, 834397926, 802893318, 948302526, 803504104, 907568741, 227193513, 407457393, 589590360, 627287251, 270226716, 100408167, 198872797, 118002689, 933124237, 441884367, 970207031, 775055263, 913707414, 342658005, 960468637, 888430567, 68711856, 784619896, 659061052, 900058194, 711739590, 211205620, 68714775, 206906294, 631317832, 717819844, 622980711, 335176743, 673703776, 388783296, 682860746, 701810511, 5915050, 927080889, 551621923, 124895160, 420077620, 583419412, 343318610, 600694675, 874954206, 969163601, 175020363, 969686468, 822807001, 611634514, 224448948, 97177994, 683198071, 95045288, 142624009, 675825992, 29201229, 994390549, 362159699, 346909503, 578185538, 983133925, 43192887, 163132916, 650634990, 279354992, 550606513, 826918786, 443911887, 437288299, 573134856, 199597429, 136527099, 586866128, 424335568, 343884159, 788315747, 504629667, 465854775, 60413421, 493077775, 515594495, 799619063, 329114998, 583092967, 998045385, 877284299, 162216074, 932871346, 859595921, 125836382, 743370165, 447222129, 554572084, 822872970, 739029605, 818512072, 912548493, 612662397, 746025096, 377081542, 546501966, 153543409, 993542669, 226843694, 42101772, 622744346, 49080821, 750408230, 907415072, 440634338, 905161536, 525867366, 594948921, 227010723, 922437152, 602134130, 280768464, 139347848, 832970516, 397498580, 780986591, 480935383, 774302628, 513894356, 124104078, 497816273, 305950636, 910967807, 708961085, 332271508, 571935274, 978633701, 896525409, 406457763, 997346789, 757442808, 729951397, 34868106, 139787809, 379352058, 242931657, 696906031, 522246256, 747423841, 34889311, 357734234, 989120205, 562479654, 605559420, 104233754, 855444191, 408690633, 184401196, 676083877, 277375484, 595537915, 669466938, 714066903, 206684954, 538371846, 5730429, 168536910, 775351698, 171483838, 679459913, 595877454, 920426575, 977234687, 51181198, 734100222, 472180469, 219290405, 998022023, 113345126, 72498928, 646294108, 247228296, 181036856, 598793471, 361090130, 525894661, 305176386, 58526389, 954476382, 336193554, 240561381, 32455117, 878955016, 740460388, 305968758, 410739787, 220419575, 621891441, 537453628, 73219595, 641351040, 925862885, 351312297, 990636672, 537633430, 69748353, 637415595, 968680426, 456106800, 133671668, 110672936, 404478865, 901886321, 637127251, 762228622, 411860880, 695158996, 496577503, 80865502, 722413750, 100822309, 146590471, 149828524, 934925349, 603938800, 994360730, 518377299, 209044139, 546273955, 367554771, 225317459, 866405737, 960754608, 187510503, 585837448, 754653601, 776654001, 880908133, 263535263, 491106450, 870660116, 33923571, 479467292, 428333317, 636421545, 723358743, 957817189, 114520354, 664693675, 794837086, 750003634, 736642421, 141378638, 391039814, 687041933, 383183744, 9206524, 815445506, 763793048, 288597446, 809986429, 130399381, 294424045, 997024588, 570441256, 334039157, 220961575, 420661477, 473620590, 912665454, 480977271, 615974438, 213633813, 700192586, 98839814, 584584318, 490177651, 753255430, 121850207, 477943123, 476179321, 103564868, 383745973, 967147728, 803601201, 729125154, 887085783, 858608203, 9466931, 811823496, 231330624, 509384058, 357950809, 726146628, 838847512, 326985862, 682331948, 908652784, 793240908, 666806585, 627424496, 692240072, 654529980, 150377488, 239064205, 163929119, 343702160, 138817204, 300453297, 737873437, 519048483, 81069025, 856874160, 429118377, 835507635, 891474515, 121222765, 393706059, 100089088, 568438717, 456915567, 63701224, 632680361, 752560750, 565776472, 615619716, 149467416, 419237826, 197076672, 447758142, 55068517, 838201116, 71822632, 148084686, 896110916, 126691830, 880797659, 185000418, 694086853, 769143123, 969147116, 852149078, 47727818, 593382313, 194509459, 317155978, 854822410, 466762696, 495719461, 522428983, 608708347, 523472505, 43262661, 616606663, 735449382, 456481714, 13776818, 898211215, 108939403, 726886468, 909660021, 154637828, 549614633, 482900840, 965991179, 326265053, 397641940, 319546449, 427079213, 925295771, 169216647, 292146041, 616881628, 129757258, 408685982, 191650919, 316128519, 176361143, 444210546, 424733276, 659964160, 856226026, 262937608, 749334499, 919246895, 516757334, 570429746, 913871850, 676210276, 36465938, 368988306, 531748474, 296427936, 375783875, 245749675, 255906392, 965553080, 487398269, 312434855, 594264759, 22790229, 877906788, 631234627, 831835911, 161024241, 727393998, 928287193, 219270383, 50978832, 990653663, 51130315, 284707537, 798531306, 492509073, 641374091, 478356969, 251335439, 627902257, 300456493, 130378523, 780836465, 528172122, 900499023, 405933781, 745680449, 376324916, 686172932, 686506237, 44509099, 561548597, 48491615, 600679856, 460562398, 200891282, 326178817, 916538389, 625139417, 117870693, 50293706, 523284092, 259264550, 814002673, 434489057, 35600546, 245636732, 170204809, 990739190, 999666662, 729312894, 508904058, 804178149, 210920962, 32812081, 485278125, 313231843, 386607364, 25321644, 996242598, 363961835, 436510669, 689743755, 199485990, 646544584, 660118394, 482375553, 939401278, 944270487, 814748280, 932060582, 617759614, 226763727, 11241107, 440503065, 90715788, 130878233, 823885814, 272674103, 352132562, 93644978, 685508049, 499314882, 547523345, 50178364, 637354603, 247927123, 279770714, 574986096, 618204959, 95431542, 293337124, 872946224, 900525712, 605473181, 110260287, 995272628, 451387380, 279708171, 525599395, 908652231, 405578886, 979520195, 442093921, 446198531, 141056652, 210271109, 604434469, 154153548, 993443833, 919996305, 847433726, 102504096, 762377480, 570964789, 169178528, 703791502, 889240141, 40432159, 561882762, 858544372, 300332749, 63822578, 16334175, 387349469, 603328427, 762039931, 746895166, 599234872, 297424810, 95734318, 835044834, 62612177, 211718260, 643233884, 469301309, 55522087, 934046935, 741740121, 415707462, 144496919, 107879803, 404292460, 447737376, 353118826, 902244576, 125934784, 410853320, 23474060, 234835231, 373608706, 208067527, 104047636, 839143273, 480595132, 999914408, 37306867, 87422819, 249175932, 812889503, 893009527, 882926122, 909704028, 681552417, 409165972, 409901339, 562449908, 705045162, 226984797, 624935364, 182230290, 176760415, 384908776, 6383623, 464918262, 191413934, 813634127, 851028544, 644150578, 992842417, 126974106, 332126384, 907730929, 398772706, 535270959, 982516087, 71038728, 242212118, 203686301, 158339210, 181251772, 580928436, 175674981, 295538224, 748618526, 350674588, 944654302, 503121073, 557205608, 312970154, 502652120, 463646223, 112801915, 525032280, 173654249, 789025414, 419571586, 675704608, 892974135, 538827760, 761407749, 624834201, 347247718, 946788938, 407479899, 331407165, 96568443, 981020113, 722434267, 316740706, 230076230, 403628580, 575469969, 262459244, 870415293, 11806017, 78594460, 532248760, 497573929, 435530809, 418175595, 931609831, 12788558, 920038328, 726991897, 327986944, 217682021, 36186804, 286797333, 659733783, 318556821, 42574838, 12831534, 349907616, 353774952, 256024358, 183890503, 478340903, 229817940, 958327696, 684741499, 161747782, 506952871, 205374550, 306898754, 412571420, 133344295, 129818090, 502879439, 988228354, 78778402, 658106220, 545815238, 471090784, 581945582, 136449660, 20890091, 243043178, 364581519, 629113608, 876374662, 543681701, 492807603, 615956621, 67814230, 158043111, 217951660, 294995343, 146567124, 167696521, 323977163, 675214475, 547844056, 83977747, 718348010, 389726879, 208889792, 996444081, 321666370, 220978476, 860542700, 925312763, 835727500, 280346847, 894128873, 448699294, 315344129, 652710430, 622312571, 945337872, 282354921, 950641631, 824337150, 59446415, 540925313, 557234119, 159301448, 661622062, 18555713, 961244628, 940912199, 176658800, 20674665, 13491787, 159531564, 175664008, 803864792, 991876128, 392662746, 150131831, 284128805, 457982076, 947455433, 684247132, 721164068, 703988943, 54591920, 692059748, 630246548, 697596465, 468784765, 328181913, 599839095, 73913256, 32473493, 230524961, 311735197, 821973146, 857305144, 708555486, 955979171, 190813195, 877584104, 435622868, 791736695, 824284825, 694666939, 970966986, 777179908, 733254788, 767596326, 540942353, 145313784, 193633985, 543087077, 347342555, 419854826, 485243418, 862192983, 467543991, 81691888, 332893495, 744211668, 585318654, 416680010, 74829267, 548256073, 74490670, 303597210, 948881918, 610496625, 511344498, 484474349, 543730803, 168106291, 114290741, 855593070, 365911445, 478031424, 657921285, 785869551, 54658056, 734880714, 310838081, 659115805, 525404024, 108011470, 720809870, 404180692, 662172563, 476921774, 242800522, 693671539, 551255487, 486446292, 761641147, 556836668, 824873543, 243818095, 825899315, 10150217, 718224133, 671794349, 828374374, 356101747, 71213108, 584679619, 596397335, 652001401, 140874150, 283723396, 214877644, 500742575, 200829325, 433091816, 74255720, 808796706, 620006153, 35073608, 975631714, 747930476, 882917379, 64612209, 364239083, 281555134, 567108535, 711236924, 387895465, 306292472, 750946598, 313715795, 821603343, 543751850, 219094443, 479616536, 119146401, 651946765, 412804854, 42377488, 438509690, 516365544, 913422448, 117474314, 596097700, 17449898, 932466136, 217821298, 375032931, 880987381, 791012547, 616223155, 687694753, 776377153, 247072430, 596034599, 19262471, 332119464, 425694186, 20816317, 559688812, 194616216, 211032548, 547623647, 224543244, 607433969, 973319236, 97027491, 253222826, 174358438, 473694144, 868738108, 430316126, 492823807, 748715275, 718143152, 749999382, 67603039, 339401905, 662292947, 932023170, 526873378, 115848861, 572426027, 543066040, 542638255, 732741570, 388536363, 570402690, 606150499, 955592196, 863391161, 424914416, 114798390, 356989044, 171616975, 491191039, 70753228, 928629709, 790769089, 596655683, 968702994, 219011957, 618689019, 396318744, 936816664, 420311119, 709376050, 965585298, 910832993, 757786875, 539467795, 822311716, 727844242, 751451418, 447866402, 784944999, 378961650, 38661532, 248097017, 632751750, 330366448, 468739203, 330091493, 553011815, 622872911, 212915335, 200837583, 260821688, 271373107, 456398590, 984447135, 603266221, 614281025, 412846175, 83829807, 92701191, 571751779, 557268226, 133625140, 632021240, 591101464, 813240031, 55557016, 498995178, 221855565, 791571910, 648533097, 220514792, 317295069, 614371141, 229403755, 829451977, 427109524, 71158059, 233813425, 13240338, 577354781, 978300068, 544770829, 531166821, 100444780, 186225085, 31432995, 297401097, 586665550, 336195197, 315808243, 523518893, 59000226, 997408463, 96867034, 923007049, 470284298, 877098116, 726424696, 985245737, 671777194, 612630397, 525193936, 610933254, 206504148, 773769105, 854310690, 745100579, 873425063, 209053674, 228496541, 342220845, 211590119, 966520743, 558189622, 603912221, 617173176, 909338751, 479976018, 629646168, 603724667, 237652652, 818505519, 36047712, 615469532, 211302573, 488862569, 53261207, 56551209, 885899287, 406464557, 329964046, 540380286, 918445534, 291661107, 756679112, 726465142, 933651957, 389959979, 609794092, 758213599, 49146192, 138313133, 853923859, 970286165, 254046626, 591873003, 995169734, 294797334, 647178220, 472846040, 579702267, 98326086, 641454770, 793891705, 639811810, 910411099, 570769381, 606171121, 933466240, 217291280, 345677687, 968024858, 797878856, 966183583, 437844528, 490577515, 877260067, 922978113, 948136772, 38660551, 640555733, 507445490, 738977447, 267097638, 888066433, 679893021, 679045600, 564671768, 422557060, 99204752, 992093509, 436279851, 115543856, 952404712, 278360307, 175297630, 73940998, 568767218, 675018538, 288442911, 747128028, 368073340, 145480860, 184130428, 26282099, 260371204, 496581378, 803213339, 420819645, 163504707, 803829490, 865188760, 776231968, 236251445, 766147494, 853717558, 237243031, 791173854, 787966831, 585846134, 465127995, 335215026, 807176497, 762257673, 461150912, 544638489, 275731168, 223072111, 518047916, 802620061, 892866826, 633274485, 380344314, 423641523, 138219494, 112963770, 898032818, 407545053, 341301043, 804273456, 878201799, 348810341, 609384352, 557378084, 947597461, 588377410, 268098902, 164581237, 733360210, 326758702, 187615095, 962444761, 733318072, 44377055, 553413650, 526224557, 720054245, 802581758, 360389943, 532085597, 932960744, 711518947, 959945697, 442449077, 639857841, 529018804, 911348334, 442676783, 374456415, 538668845, 575524242, 12634550, 664038746, 562916556, 230221241, 725702426, 818941647, 199224635, 674703690, 336199847, 866837259, 327649732, 936620005, 869008732, 107741796, 395808935, 765281421, 738078088, 436519407, 546281875, 401710078, 229719001, 554955259, 262058953, 764893356, 870262750, 505945569, 230603650, 488428406, 433770269, 280788584, 961412633, 503645693, 415219465, 691996237, 319302461, 464273329, 849844584, 396252333, 876263842, 439144933, 148153536, 851258791, 583171612, 908827417, 855941377, 495130312, 646056566, 857767835, 893585058, 338940620, 952204098, 821191469, 550694877, 592478676, 581234692, 488206627, 617717432, 45102790, 284935110, 153163209, 108631048, 448658802, 545302896, 507127712, 298034162, 988159132, 301968964, 873523863, 278841002, 155663139, 914596184, 370703194, 325671370, 430685533, 545161372, 439573728, 733472645, 968552925, 359441693, 384719114, 547753625, 753033639, 750428720, 86893102, 588346049, 437322334, 482335955, 327061458, 83288415, 113985891, 285757826, 62822764, 962170160, 856954175, 199197495, 843186957, 871814468, 980383078, 504831290, 48202074, 272493051, 913230702, 6071960, 285564263, 693053590, 989158133, 405575114, 274679499, 7412224, 753948475, 779911791, 631134622, 30769332, 59660816, 502033417, 648705233, 399898169, 664213999, 191519307, 200048703, 879051624, 404045121, 996285166, 142131348, 370130599, 497991903, 705286607, 468484187, 296476545, 932145612, 360891765, 51970354, 193329393, 597842503, 645748760, 734622928, 432123114, 246196167, 852593006, 551835235, 258348115, 698549423, 414653042, 868545438, 583980016, 793700141, 293424430, 109073787, 543501994, 119965784, 125897650, 459006340, 123856374, 54269452, 599932826, 883968612, 10790830, 622576308, 593777396, 612652746, 950331918, 717293216, 215477442, 860566498, 730040547, 162593038, 957990594, 236006833, 348319504, 681323895, 545279536, 459443411, 169725003, 975488234, 70268903, 356777310, 565139650, 387131261, 187068978, 493865796, 58950900, 949144246, 648590697, 642591144, 980866434, 497920267, 451305314, 734525383, 887010277, 274908862, 656559480, 216483089, 559351500, 288321005, 225966994, 676765139, 82641752, 714715792, 171667422, 254506476, 754082041, 47208158, 264386203, 687470583, 355029223, 187987076, 29130220, 954320563, 859928702, 531397058, 976269481, 785381628, 993631399, 109008020, 855410000, 836107670, 310862873, 596792497, 145075832, 706970227, 607090552, 688803812, 387772842, 636641088, 605199873, 443070491, 874786296, 789178056, 306709655, 530807553, 7733030, 237591083, 755846699, 340631166, 532462185, 695822709, 841270797, 387213453, 585542729, 911241028, 426606534, 228417196, 127922206, 421493652, 434800138, 837565887, 899032870, 213363876, 366300433, 614773782, 362067986, 791704432, 652152258, 710124838, 660018576, 789420470, 462049724, 399086682, 715883653, 557498203, 313727496, 194784126, 772184505, 774733134, 375543260, 324695508, 598898876, 876386580, 843059885, 50698433, 512767375, 228120480, 258304472, 213552810, 463529257, 428240214, 790827418, 620310361, 438138633, 452479066, 319320406, 608855382, 756057867, 868162898, 778211805, 818576665, 44569882, 664845923, 436268237, 578915562, 275597755, 896986557, 60555394, 734303683, 576743618, 610246588, 402473487, 166684157, 751577938, 927622039, 938452810, 771454126, 438433293, 696641390, 493796512, 906978692, 435591843, 562606302, 622230743, 163573819, 521003396, 120752404, 426491368, 529282084, 887722549, 878385516, 981780995, 128671402, 419453765, 932052016, 760943354, 827794494, 344626701, 80465750, 638476884, 32129120, 628606078, 209596236, 351375794, 154115356, 681417664, 885344532, 766863502, 317608002, 399760525, 324185647, 811980834, 723260682, 50848303, 710507359, 815467502, 860354459, 698894254, 435174537, 450627707, 511914623, 520545216, 516302191, 882465354, 429329252, 536718952, 146805714, 720329666, 789415954, 35795112, 793069063, 244067797, 775756457, 290905931, 971031570, 968408842, 138630747, 801451448, 847007997, 978607603, 780880047, 286373945, 334125051, 412320357, 708134212, 424035421, 601309191, 616100461, 556219389, 20829882, 547796674, 782479426, 308767171, 723574183, 176660197, 867630565, 999099024, 540421706, 885677986, 936936942, 320897042, 362727929, 88051802, 255121913, 417290818, 958162551, 638355841, 813908180, 861518580, 753690673, 25825412, 994818430, 573300605, 537581779, 467736132, 235107664, 616778697, 581246641, 619445204, 674355849, 679356849, 361983430, 13607430, 52723756, 546446993, 126704171, 663764366, 602091018, 678121972, 849905163, 753518956, 101580061, 404356241, 547484163, 314775911, 470285056, 469548382, 148339084, 975558987, 328266683, 987485478, 847155766, 766484118, 627407149, 908498691, 145050310, 108683102, 344035748, 294755739, 662303601, 431865719, 745734582, 774818913, 146232832, 353881452, 854610620, 301524488, 249966577, 77688065, 516533042, 216000845, 984290265, 895901334, 238279404, 245475199, 187715763, 926168794, 948295415, 23336328, 490743588, 25229903, 412246272, 365966322, 857494157, 74122439, 6752509, 306942847, 814103848, 788317646, 220409933, 457140659, 928626138, 325120922, 961044067, 236697594, 239344102, 80409984, 763825238, 430324942, 491533150, 513891653, 317408141, 874515422, 352067859, 523337731, 206005702, 313754271, 329002828, 301451904, 583067225, 491894152, 546502840, 169427827, 776919031, 53879379, 755738913, 122068595, 414045286, 842543186, 984195725, 393036290, 921135131, 592047759, 419691722, 888318298, 337704678, 190817484, 535951769, 465547096, 401047145, 25308790, 980050463, 798735610, 832604939, 854935367, 445319812, 24547545, 958336903, 259036270, 571626986, 576104186, 733439648, 430670775, 958479512, 387643590, 154753507, 206904584, 678381271, 41301245, 986322393, 927298140, 272633180, 966886416, 743714058, 100677560, 256974112, 920424881, 544093693, 370359480, 608336942, 882393858, 356169683, 453935771, 31033201, 47146959, 21341871, 720467139, 434684282, 426941611, 476590986, 663859447, 149602012, 213751301, 683888574, 808920311, 206817689, 658355983, 465980209, 561631903, 421377702, 287284470, 730653738, 456589343, 23160290, 962727398, 802730856, 94033037, 210586975, 868008884, 75111584, 823610307, 879111900, 227029625, 498964669, 54319013, 503328575, 999131303, 53079720, 114255442, 960516772, 574057001, 917804591, 971269142, 112755616, 652820506, 344151803, 776866902, 761680580, 199880843, 655706830, 798903983, 475235158, 841009525, 145309811, 872334902, 427666010, 33283517, 47484765, 924962219, 904727976, 581891261, 607354213, 377886752, 416886306, 358954296, 43345418, 998465783, 288263966, 390551828, 678624803, 924296978, 53334398, 346729578, 59408183, 452705345, 28169625, 3987528, 32143981, 405380196, 470351179, 906893304, 262385898, 154717978, 241252620, 973967295, 164772427, 512124458, 635480436, 600159889, 83828725, 546787588, 562517550, 771503797, 467011754, 845502208, 680633251, 675797540, 778198103, 294345044, 718570579, 125312970, 829127673, 575356095, 839476901, 671141799, 18291770, 200787864, 445555527, 848182402, 865495994, 660135678, 802659612, 162242139, 47593906, 400302170, 334185105, 813283039, 839950823, 801080095, 911889034, 141381895, 688195660, 512364269, 434889658, 663266884, 587254018, 249663750, 875866775, 137172433, 552365279, 903230317, 989343275, 687746460, 885409431, 598965807, 362208496, 567068882, 283236838, 94733237, 357054110, 873359769, 983578116, 257752565, 719596345, 125595012, 701808641, 712475410, 643128835, 107606655, 298111017, 547791701, 827563781, 153706026, 748435476, 62981614, 911149335, 750907161, 36309772, 285205750, 82246603, 836967276, 454855609, 663284721, 82549294, 697373435, 829456464, 420745295, 19485818, 801626371, 741897204, 106114336, 257274104, 591877050, 249160090, 630405878, 894968319, 522808679, 633863758, 171916879, 651632297, 338717070, 27287672, 51537449, 512910911, 490911568, 246415080, 224212094, 446598312, 474278308, 404471519, 892168875, 200344471, 280074192, 488304530, 533850174, 386224961, 164962050, 278694731, 516696393, 33929805, 298678329, 483029963, 391884522, 848688166, 970544560, 195743449, 811937846, 277158565, 547416774, 849766329, 29278325, 401102894, 774092899, 717571737, 54916085, 722234630, 735906980, 942872745, 338986859, 659972661, 46277376, 820985507, 888796832, 300515480, 209311128, 951800868, 142247985, 341517936, 433939381, 531377358, 849099855, 481845661, 684590825, 884985893, 551526717, 506483316, 990972244, 62509374, 63321257, 974998734, 93272659, 424510823, 439949903, 759924672, 695694545, 944422822, 510330129, 727457181, 705419350, 983289042, 996919694, 655738388, 247684526, 40085964, 623989241, 968345588, 563974355, 208920132, 755198071, 503537706, 76486968, 685585579, 172329548, 938465761, 867268507, 706424138, 925578690, 543406975, 129716638, 808255984, 853458378, 34986103, 86665108, 830701598, 519002633, 450568691, 762365449, 964821301, 755480797, 116286672, 330361635, 808729422, 655775175, 458919358, 480429163, 893754556, 619312653, 672908457, 849278720, 994619467, 402196520, 702591807, 405954247, 808373252, 310039147, 95285471, 926811294, 297816046, 246912996, 487386929, 474380982, 594245653, 449057297, 720125684, 959084160, 426707032, 380036319, 163557058, 600292761, 696182222, 651241978, 311556930, 302349554, 144654746, 151516441, 867264858, 230436666, 908219405, 837195884, 251812197, 271203070, 172125870, 102913099, 965345934, 550816019, 210812384, 627804408, 49542358, 725997743, 165676107, 148006132, 526960770, 126071902, 990520537, 137948946, 588420029, 489737858, 305062744, 955372776, 989012974, 61247684, 182085203, 632199521, 620458196, 686734197, 579487526, 77234787, 989589157, 688094947, 180892467, 590240901, 442028853, 617421618, 988931904, 383086053, 629683197, 996700185, 351908858, 676412014, 747664528, 274868416, 613576890, 474020877, 265595505, 180670695, 970130070, 777597145, 71606131, 850618732, 314045272, 899387976, 743025808, 997617442, 187442716, 860369150, 521777909, 711416645, 467396851, 435248197, 462690055, 115441464, 698343170, 349454409, 31346244, 810442490, 984056055, 735766642, 630645283, 863231318, 289903447, 429726867, 514379921, 511172863, 998662577, 265548043, 259973326, 715305036, 13615902, 794306948, 248589526, 555162195, 948972532, 467404367, 403058152, 850783818, 674599830, 112373743, 520433668, 421781675, 283585830, 759855452, 53108792, 79017156, 834441954, 213115650, 427420673, 625402163, 726336914, 626637584, 343212296, 233052777, 823856711, 20866732, 990400924, 816488012, 815780746, 907527055, 994357407, 156925420, 63785531, 678369380, 691587256, 708423697, 461518858, 478505752, 224741785, 406716590, 721518919, 255959561, 156274661, 437084505, 553951362, 662442101, 795022226, 662021186, 819418620, 80111819, 741005704, 448823423, 948722351, 329294343, 776178211, 626176872, 955958915, 440761813, 380160392, 846286114, 982954035, 79575226, 973748797, 578322500, 618945, 60606142, 22224835, 44238113, 603259598, 403451388, 983492857, 541236073, 781942555, 206878444, 170373441, 444868979, 894971657, 49670571, 720551627, 251107501, 887857532, 281491086, 871865362, 51231007, 747519642, 333787092, 752804480, 832784883, 203037204, 216111326, 845308906, 105661386, 592108766, 906152301, 21797177, 501849485, 745824642, 844364609, 948663962, 216094206, 477510409, 175392498, 33509655, 26985252, 848492003, 875747931, 940019834, 780200028, 171946621, 180413114, 46998650, 788805951, 986157100, 845220615, 479425487, 970299166, 267098383, 596407523, 948737987, 102909713, 90979138, 874125879, 476240666, 616016517, 186306028, 177395099, 954662010, 870544781, 676875643, 589752123, 945980932, 992770381, 667173715, 278569908, 85788285, 474159014, 276764605, 505753403, 241074462, 271040280, 235609725, 427308877, 806798018, 663477000, 607637414, 939948477, 237217814, 163808258, 422407804, 180896748, 531645550, 111111777, 168288956, 842727453, 438407871, 962337804, 597466263, 476047055, 729491134, 49236002, 982312400, 85924313, 554846414, 998303989, 842816006, 663835300, 402188283, 617633363, 708369068, 621417221, 964253904, 614324231, 703653259, 671189299, 733178993, 806130330, 8632458, 585334826, 668848142, 468584439, 87353164, 73204666, 854653802, 779046204, 487685957, 896551864, 723588157, 782707562, 321507242, 444765698, 848363612, 28011255, 19697745, 311364440, 378193502, 135506815, 658728357, 852726686, 178515616, 883103199, 259160760, 795329080, 865570203, 473666346, 566190891, 47124844, 47426185, 953419000, 908518181, 820686294, 689432740, 508848902, 250113344, 533215278, 903888601, 13015479, 233344032, 500574384, 318168754, 960800962, 800282135, 645705956, 954665934, 193601935, 924873407, 270932027, 817190709, 188263578, 222429564, 173469674, 907155069, 26876801, 953092768, 583739508, 878150376, 907924812, 863841090, 152870593, 484925996, 109384364, 98197780, 164010520, 884863217, 214449097, 250991925, 4289231, 231416760, 215296519, 921792338, 557300509, 563155512, 749498797, 444712828, 716396946, 314191148, 272839849, 421956730, 253252262, 980596174, 788224409, 740104211, 712077992, 14410428, 415523976, 944363614, 344955292, 985844232, 671829290, 372829829, 42291188, 350130192, 642779680, 414024313, 645968400, 227286420, 98173407, 813514006, 503454511, 330837868, 12576242, 783491342, 464899913, 486739255, 443688212, 369138645, 497474007, 948860802, 500229685, 176768153, 580329700, 87698362, 908043314, 20001139, 175409777, 993849055, 616392755, 140603734, 383179672, 494053943, 680720293, 124345961, 801232004, 94506372, 776509565, 932228211, 415134777, 325712720, 924737863, 971010916, 664558771, 320478864, 876833654, 690827329, 658954289, 890828017, 485402461, 699869800, 812792691, 749275057, 49024980, 598381433, 483949705, 971159474, 714310134, 52461645, 635227263, 200277887, 910281470, 354431583, 93268201, 367823894, 352408018, 19696332, 335878191, 671163224, 46638244, 413109426, 676330321, 231414735, 460031065, 180074721, 42355641, 395149091, 787662147, 39545524, 273607006, 240462184, 732739698, 545548140, 76310325, 665643437, 302009264, 65616166, 884403184, 948755329, 85804004, 177026915, 331850712, 877707720, 881901016, 178818046, 563107301, 726710087, 730929699, 329297577, 144598246, 862495706, 42094806, 132993929, 502640918, 488251653, 693917074, 755760531, 498055096, 696359371, 867586482, 629377392, 370621749, 29176970, 652884680, 683243804, 195014871, 827420697, 928685358, 983964030, 684828054, 775262978, 952805309, 118662426, 496225362, 683002033, 565569402, 807761196, 843946320, 629854949, 754042989, 921050151, 918421105, 170479393, 368170537, 236590720, 816338533, 33867564, 636548460, 352944810, 324870840, 74298260, 747221644, 175790679, 439112627, 742394932, 738893165, 625598126, 67038512, 145154683, 875696557, 207311598, 580248386, 634629971, 387305366, 411674409, 607342356, 615394150, 118897178, 738760151, 437514733, 705275585, 370526564, 459366295, 30983469, 609442065, 397745587, 350825764, 983083030, 457322201, 377711347, 890899300, 987971219, 755423431, 122197412, 760974765, 613976254, 597201322, 765046771] 18775)," 76464 (countComponents [733269546, 524802987, 72086815, 103722653, 313657156, 58069999, 353091422, 554813822, 114770023, 918192658, 168879343, 882206127, 944978310, 388146622, 737703634, 407620826, 38430349, 40847830, 789453838, 282500835, 232652237, 504082080, 438264572, 499427643, 957046787, 27397753, 390803213, 888316253, 373463662, 432190458, 178158376, 168094295, 766781132, 588739468, 608546107, 385942320, 885831047, 124476698, 183120413, 554797456, 161069591, 876608970, 299057686, 944374054, 315312289, 609231440, 396369581, 634760015, 341344906, 712544888, 687073029, 495279022, 677254848, 716347008, 718279054, 244683404, 476859014, 524422602, 728345668, 951231738, 714584282, 327512115, 188853582, 384399541, 849079791, 98203480, 842348399, 809856880, 353161950, 454290616, 833386321, 383897031, 863354795, 331271257, 799173196, 817067438, 615877316, 715733783, 549916832, 417766600, 718287497, 984946705, 849643153, 104818376, 845750196, 347700448, 586867495, 178328058, 43243588, 167210945, 714900993, 752722505, 333142961, 383644272, 164858469, 211727096, 923679216, 559596876, 759342359, 393916237, 405676219, 166384021, 766389524, 394950629, 795445051, 468026022, 222962690, 284600960, 197536830, 657125062, 693918890, 106934004, 284860109, 516701792, 553059996, 254084527, 941626562, 930928633, 904792640, 825342608, 120711584, 725593408, 451675515, 777885457, 432176398, 619396751, 401702906, 721161431, 995440483, 285003748, 411292600, 392217874, 922880894, 429414047, 873476225, 966589670, 950571426, 899007550, 717981213, 410383921, 588082262, 832114638, 176349496, 307027402, 186712430, 564418657, 258165090, 760928668, 934396822, 331093756, 902483497, 99103652, 56006105, 374580017, 498977776, 435506969, 935798888, 610996414, 467636053, 46396415, 258790060, 340630250, 119842464, 12870426, 201109326, 262903464, 658733348, 766660852, 210011909, 754107622, 112949017, 534490058, 394459859, 645091865, 330969669, 830981702, 593448962, 54654675, 945123220, 295688323, 895958637, 723228239, 373996317, 391048512, 107540529, 724393957, 47971974, 919451427, 547098896, 72477289, 842342494, 969067412, 595655620, 753387391, 459489665, 66411873, 303368903, 501864767, 691180353, 100650825, 564671711, 534656361, 897312174, 961243755, 751283944, 439154406, 827176881, 150938906, 445833817, 177417984, 413761535, 34222511, 192567131, 427442476, 985823506, 862133020, 267069889, 639882279, 947789587, 745499656, 587428878, 714061232, 934560200, 937702883, 790014590, 680309760, 846136799, 4609765, 513104864, 179036053, 715866038, 901117692, 932361771, 604820788, 607089795, 227621000, 178176170, 560442687, 389387129, 562457364, 595010230, 9752681, 676592417, 254404491, 959457087, 955803558, 156611482, 80933089, 13053047, 588033253, 197085839, 860566748, 532322424, 318248351, 471361942, 725712347, 183159328, 93439973, 17141246, 576178030, 721602028, 250522505, 467397151, 370056295, 812107933, 437191892, 452082031, 9411020, 833025018, 598549312, 652668946, 662948316, 335791329, 700085771, 472301495, 563038858, 267820162, 337255850, 520604316, 876450081, 957236221, 694517631, 497658040, 305577577, 470403202, 926427079, 974704126, 677358417, 57009345, 415384936, 184768106, 520274515, 862380741, 600746131, 708646319, 496776260, 45735535, 59801042, 972949532, 784680107, 821676182, 272485198, 217573668, 60346659, 107690186, 657267259, 385333883, 624555551, 760358323, 388472275, 113851455, 539131152, 799267445, 315873418, 718626069, 249458499, 872177219, 846022976, 920800202, 3883783, 464055934, 680485861, 689213227, 133182260, 830573988, 611308820, 924208320, 759261982, 191048603, 905410986, 288522849, 153910433, 704527360, 452614043, 287774332, 255508502, 775345284, 337473057, 736074932, 808127024, 424732577, 403474745, 597237576, 818490992, 975449574, 632443688, 463892436, 649821594, 839376263, 937793595, 901236790, 7310914, 263453115, 870101467, 648016599, 349451953, 437491844, 684934445, 360643067, 429506597, 317742387, 660629743, 58180706, 458362635, 81988017, 863390005, 146050111, 652849467, 383826566, 931094766, 521584183, 68190445, 182490553, 7950723, 168375075, 375566344, 139629702, 404399720, 245625959, 675130531, 167766222, 534190889, 1743666, 241138490, 762704334, 527017187, 450824499, 913874059, 396107659, 110645520, 620635976, 422508686, 448106462, 268995533, 292526977, 836153530, 121642748, 359146690, 5818843, 912191030, 249784235, 446851357, 372387767, 124999257, 34067061, 91878807, 242918175, 625456018, 720333915, 25693822, 790124804, 362015273, 408400371, 121321966, 414062550, 407054931, 161502641, 475685441, 22796009, 84772415, 513518854, 212675523, 978075226, 790307262, 579125858, 590946601, 768212738, 682665365, 357187866, 815763674, 512897997, 75537048, 826070176, 41787024, 419396051, 858785395, 954430139, 398054602, 908265395, 506657218, 690245614, 562256212, 30356521, 424922910, 561838303, 88905391, 426791944, 806092767, 338326091, 995218336, 870235480, 590655981, 137191589, 869428493, 481202701, 977224016, 762896902, 467429088, 778314421, 540689207, 333958043, 514375113, 231209023, 305754323, 640697666, 466260069, 906196053, 760877801, 868172875, 84459796, 497267282, 684552202, 449037894, 491747183, 342807599, 744893541, 423470477, 305082410, 366705818, 67274730, 696858752, 906357651, 218244635, 757781222, 159632085, 205787704, 660475309, 699159282, 50711976, 569177483, 205655281, 245211770, 747217473, 186550094, 519475979, 109880674, 393313219, 254952173, 938961436, 134190427, 430547252, 923647354, 978026485, 552180819, 542954947, 103128613, 774085702, 285004170, 303113673, 557749429, 632715517, 710339051, 626964742, 220990349, 75899991, 919228871, 517192265, 276058573, 383709186, 108345950, 330632850, 83243364, 706319341, 639724993, 783882589, 281667457, 655197081, 985834705, 786546703, 662280550, 885217101, 681568174, 519573144, 843351648, 814263638, 342751675, 391644941, 732662196, 678055915, 176606516, 588031615, 931628436, 95968231, 986074455, 308896905, 435627579, 850204254, 810930237, 433826573, 406234244, 47187914, 230135812, 572507349, 714633187, 785817951, 514470111, 205962131, 789427475, 111353151, 461630840, 307666729, 789701143, 632659871, 512804259, 765749506, 918466904, 768609506, 387340302, 587589978, 225444431, 603866749, 867977878, 102479445, 231254814, 229007126, 974916002, 503575385, 817771811, 517156778, 911071180, 303946446, 460433650, 232217021, 252133411, 115106730, 731726818, 606226541, 326569255, 638120072, 872291910, 234384085, 818490377, 720031821, 852768071, 677427822, 173984827, 86141829, 83011878, 677413788, 779160394, 781407724, 554050806, 92536395, 309494030, 797124458, 43920598, 235734061, 821066146, 84164267, 117272792, 506427341, 744886181, 469463391, 286987463, 493528250, 7840671, 130284965, 136629295, 865944116, 893726402, 277469031, 695843936, 260534505, 951150460, 939131257, 535837518, 388103033, 716065663, 674290298, 887651797, 302897103, 514711411, 43901582, 531247119, 121999271, 716146109, 81615144, 29301916, 702515572, 762151816, 70369603, 512107575, 310209669, 125610293, 611077637, 529815033, 29511743, 546895109, 861415334, 929431626, 283004927, 679455366, 132047350, 710062973, 609153089, 282868848, 353678319, 561145930, 857305473, 23257243, 535772310, 132995053, 492410739, 69797566, 775129500, 677668208, 671009057, 738069839, 415504117, 513562648, 211913682, 471095529, 555124574, 511788374, 638097851, 169719105, 308137025, 149853575, 133549594, 168019944, 118606798, 580853299, 619532619, 661056088, 947770406, 550343060, 53626235, 660850913, 546361281, 531926577, 69730663, 593944877, 285334076, 692352240, 977342769, 21347605, 198140281, 700996074, 498164340, 32655144, 114371239, 462430250, 555965840, 746328922, 637459552, 388518181, 115164316, 204515427, 780440172, 80015291, 457485906, 76719326, 344694817, 263887774, 47099772, 163013806, 10262049, 405461333, 476657523, 2450618, 183502623, 651794040, 658196390, 496477335, 999923389, 174706223, 503599248, 625067673, 922695594, 299735850, 496012605, 616776241, 245424932, 448529645, 355864317, 697233919, 150993521, 476893527, 281609400, 210536974, 427695646, 336094564, 700433244, 907473479, 863126217, 506706591, 128113992, 543634451, 304252632, 629007659, 189019244, 845741575, 179215565, 75310525, 802397314, 990724304, 103422424, 633696381, 113555702, 409443169, 550900989, 517038795, 2126282, 634510051, 8961010, 159265696, 136804575, 656524882, 2453820, 390310040, 642864481, 895593306, 546962697, 57655658, 508015526, 709170779, 538031462, 376283690, 520168249, 336589043, 113486183, 816368372, 674026222, 275400690, 756306807, 872756563, 358715738, 998613038, 20058737, 993126770, 414701819, 460074772, 962559695, 952154881, 861554363, 100092602, 174072657, 246904342, 306774761, 106828870, 737357619, 690399522, 658589079, 880881477, 598605076, 16919693, 26642860, 849979443, 397929454, 10940237, 438803734, 181985566, 353043538, 101519950, 239677540, 371229732, 560365185, 549882114, 137832828, 163957739, 809330385, 527027691, 284095117, 66892655, 86269967, 176751137, 549425551, 520678195, 220365742, 435712935, 719403374, 420199360, 363665263, 869792436, 789700230, 343875541, 699790827, 606941420, 359471509, 660087890, 263610247, 892709977, 507611558, 862675213, 685486033, 898894713, 216260834, 587451613, 834500513, 468252426, 513213627, 703929132, 596351762, 699068786, 620819034, 1757769, 290282550, 684443739, 391788101, 718560379, 424677035, 607432317, 623367691, 496688012, 813229612, 276664493, 121237769, 747238345, 186658807, 417715836, 700371461, 257720050, 713865649, 477066134, 844578659, 939531271, 525438684, 212998556, 452041265, 763077826, 253825710, 973878512, 935450788, 505675103, 204347412, 651692575, 510026263, 438580771, 745498709, 780937871, 242699562, 687401613, 534624596, 641150059, 513650797, 336148212, 372076670, 409849710, 211827051, 699289064, 752686282, 857474891, 569926657, 677188525, 965946807, 589588242, 891801879, 719400462, 133289671, 687901982, 693486675, 266810853, 384076943, 428271229, 586323796, 816038054, 7926099, 319739772, 762869070, 845950407, 526456004, 680973663, 225587792, 891578875, 881480359, 290936333, 473943038, 992724674, 748196219, 944750890, 127710867, 161013185, 836337779, 353970445, 853391031, 107396308, 853504907, 513959492, 684068086, 523903938, 31003948, 329124699, 403473896, 832801002, 781195209, 356109576, 87752510, 87126298, 353621927, 799872245, 436138038, 859352456, 696201633, 296913086, 438854542, 242444928, 522424483, 279014458, 311799111, 582739788, 416203821, 428436079, 221489739, 924357485, 758104834, 770154302, 412529180, 322166578, 283967199, 379981227, 890565484, 793794340, 734302721, 43217187, 587616607, 511420214, 938465238, 734570163, 632602142, 312770083, 296862818, 757749759, 839604051, 494640644, 496352198, 400751498, 495105823, 616521456, 816155905, 367254688, 916693178, 991755887, 284699370, 94080770, 662504417, 666510955, 414722909, 843490263, 98326717, 21933153, 531947619, 866934736, 428833921, 209035881, 464896921, 493354833, 790785042, 101375293, 854525179, 871856896, 410494374, 658161093, 333043689, 250519487, 840430584, 533300514, 159315940, 926728238, 586877747, 72242915, 957829915, 94187621, 284393007, 812850367, 456950397, 972782217, 433659099, 794785434, 34295234, 690391301, 749743622, 855067022, 925588302, 566960686, 231186661, 562712119, 316070559, 689131304, 573392161, 492498711, 896395515, 941646108, 103861460, 939428887, 655954131, 479652051, 922448128, 334371394, 320803013, 669428417, 149445800, 79584582, 406692457, 322332148, 388955368, 771511928, 594683214, 966769880, 702204787, 990766683, 922453520, 590445142, 552863688, 583160471, 555413606, 542595763, 254416489, 8671522, 45586846, 135065985, 448080259, 854649405, 575693295, 434826069, 465817603, 492752831, 445568762, 918159154, 776396295, 433936479, 263985536, 90680788, 619312150, 430641371, 610504866, 849703366, 538883974, 12818608, 8052682, 177636054, 867414514, 986699731, 338705807, 226735585, 500044901, 666521279, 988454264, 240988309, 427209397, 217958523, 420934756, 278459350, 506806052, 549327899, 18071041, 675086849, 320853741, 545653266, 898686834, 124282236, 284573071, 51089482, 78599749, 461831013, 122964677, 737467174, 532197823, 827280813, 31330859, 865480711, 373531306, 298364485, 408905589, 189930779, 497396920, 472535643, 787571526, 875640062, 985403217, 947411362, 636193763, 754671423, 835188889, 409986446, 531440568, 931405320, 591603010, 805816115, 173806497, 188876852, 727201582, 305017845, 502240343, 827407712, 636535204, 47311753, 891302410, 789163172, 661571242, 223400344, 539431374, 343141761, 75090582, 952288601, 730332377, 396341872, 634854251, 531959378, 422144618, 338129669, 58738862, 439467798, 877528338, 579547569, 701298600, 321025943, 101897124, 143569428, 481514998, 869610495, 726950949, 419794611, 226269961, 984694479, 795602129, 896978141, 650049484, 300428322, 481211469, 532092876, 510865151, 81368928, 127575141, 615294928, 480309045, 360062022, 780807967, 203086650, 487248751, 866248753, 975262040, 981061421, 619806461, 115367206, 84033737, 848831453, 566484724, 760074093, 753216473, 12392101, 1220682, 572741036, 201299970, 636940660, 347918297, 921458020, 686264357, 157060506, 198861138, 62365741, 481548912, 530186232, 738807151, 832847494, 33072398, 37024815, 918851982, 205051938, 215649828, 891908682, 446187730, 177463216, 796076331, 768640094, 16674612, 96176270, 242696328, 226363722, 285425191, 308226904, 571347721, 977672028, 514228966, 803045969, 53150818, 175952347, 563114634, 978223299, 719851952, 116224169, 762300078, 76910232, 542019423, 278697257, 529500637, 603837112, 95097269, 131051703, 393691483, 166163229, 841246098, 997611539, 43606064, 463441326, 579905676, 892050274, 73038461, 837828509, 678809218, 13982269, 325952233, 469017272, 332254935, 975529487, 544360154, 65478522, 711743508, 546127373, 663791699, 736827159, 341057940, 851982205, 228161072, 563639613, 952816324, 326900578, 933322707, 249568918, 396772705, 738570102, 732561321, 373833615, 69698842, 263761554, 190400079, 401216912, 637181811, 914380318, 430941414, 853430499, 905725925, 370653853, 498228995, 556128934, 596512267, 810132766, 616933984, 561932389, 824722296, 965796254, 128608374, 944670710, 467979906, 786749298, 643807800, 775696684, 219575386, 130945240, 829745527, 802041075, 408487249, 699914560, 766714424, 113386909, 939385663, 816362629, 619151642, 348115449, 653266000, 226961712, 314722255, 52519024, 853978675, 180452586, 761520705, 779917562, 544356199, 713561927, 978635410, 900919651, 810419536, 168654461, 553813574, 978470595, 37452265, 792670395, 392251814, 587610833, 11611107, 129434897, 752457600, 506948282, 489283205, 829391589, 31786069, 765493681, 995530754, 87275766, 558116603, 425737715, 608404375, 479717669, 811984258, 757687975, 686975653, 7921266, 968790744, 951705797, 999856954, 787597025, 184592882, 589876185, 833314315, 203448924, 14422843, 974863666, 10786701, 717392546, 48622399, 408357291, 950416106, 48746870, 228684741, 286726607, 947371030, 450165789, 559344805, 798945687, 366453469, 668215153, 568091617, 411708517, 106057136, 165918809, 819807696, 752126027, 862994750, 910957636, 492329893, 523948364, 336825140, 250617845, 643259033, 927185412, 251744370, 466567233, 128850487, 427660570, 261769795, 703237986, 606010086, 304554661, 938234692, 757982864, 49702346, 935500659, 982691052, 857376940, 754008543, 533202393, 455579660, 218949664, 29697369, 673261576, 212712874, 606613867, 206138904, 695215706, 413356831, 246179589, 15528645, 47767788, 243936074, 657856393, 114499403, 491611724, 5940609, 950287838, 580176656, 590396573, 413820451, 908743785, 995156343, 581067490, 290363120, 405684156, 523028335, 525661672, 663001369, 231451308, 664276573, 916912647, 22309333, 372099640, 69212349, 475862370, 247843270, 818872434, 708949492, 313886089, 884849322, 328766245, 812693908, 358922715, 168403871, 615897108, 444677370, 903873180, 925321343, 447601826, 319793566, 583204749, 970512123, 874680174, 857990811, 806566143, 394827043, 872088562, 384259638, 40624914, 358019991, 37894975, 887286572, 670561265, 883005735, 906489844, 926314215, 704254556, 591136472, 883384954, 881736776, 357102540, 652901258, 340684636, 546802135, 719229216, 623050210, 958530331, 633400486, 526303008, 543943045, 519009369, 279218332, 592667537, 169665431, 13493569, 344595961, 238870704, 709215106, 975048534, 738096032, 118945058, 174130051, 422682850, 327154799, 380598874, 680031134, 757944848, 811434030, 6999939, 591273819, 733092085, 677134688, 844914236, 795842784, 549818711, 989509809, 353722739, 692281150, 14956050, 449074860, 175414061, 470678950, 993608151, 249770006, 716143772, 797520000, 364451750, 170496582, 254398643, 20928693, 274801241, 818212569, 372954384, 675333492, 399741574, 82521639, 469658385, 792282528, 311766675, 599983336, 300055568, 334313002, 81545594, 717053659, 592743224, 725923827, 908029454, 886437708, 802872737, 960340937, 48442948, 593743956, 944692247, 137869582, 202901005, 598252130, 316113255, 585597311, 297355339, 824038937, 770169623, 869924487, 139914863, 208997180, 751708147, 93474494, 411029936, 989156612, 120896844, 664977508, 763767473, 954106749, 911639534, 195928418, 588553153, 396621693, 371001453, 987998120, 277394906, 457845453, 831501537, 565531108, 118610477, 416095926, 699638001, 450727114, 125851366, 604479979, 770917805, 167968733, 329895640, 711839293, 412336886, 177386745, 437817092, 669693381, 77250568, 887974081, 254858788, 5822635, 147641918, 447932897, 894755412, 85238838, 935055788, 482479519, 278016725, 364896884, 128771780, 328679483, 945473988, 843911508, 253487506, 977891874, 963774861, 712501041, 288851612, 35550139, 755414415, 747079826, 483212123, 820170690, 6071110, 607155712, 834513876, 502172225, 709292004, 228252964, 903894633, 913276289, 697775055, 631146071, 334412437, 413699109, 607932532, 463620657, 358066801, 557408419, 469531581, 769524573, 12008014, 681729436, 264494496, 135565873, 314324811, 933942598, 202565243, 887172827, 213567459, 898073828, 130460478, 71415885, 155721512, 561217999, 342123366, 832829969, 649052455, 781441606, 39372800, 78921646, 754715928, 399450117, 236646826, 62307696, 582579062, 303293045, 617357269, 234545358, 243407223, 485859318, 270104586, 177765814, 340731586, 923548761, 89220207, 693086203, 660418660, 537060778, 938502483, 499993899, 281250878, 421184210, 582377723, 490345651, 220715405, 902226562, 626847162, 505349258, 98408866, 259009292, 532729521, 393908009, 876714334, 194800266, 69546163, 41791414, 301760382, 291828378, 923026425, 419833903, 391348094, 449816831, 938625696, 882884090, 200195685, 621657257, 461930547, 30489896, 71577386, 50407028, 396936244, 757801664, 450788032, 157665181, 969824075, 172959960, 941771494, 644939728, 131359236, 443515250, 250689438, 350522052, 396015057, 109081738, 225603533, 381069751, 602559221, 14139525, 695144826, 720514107, 516003075, 588743222, 508281487, 786212551, 387199562, 816648608, 351361867, 543979630, 941849584, 101445915, 356523552, 355228680, 901861151, 82038772, 955797845, 161383502, 900964930, 587522554, 781684743, 832451857, 871318178, 395640162, 942652907, 543280360, 368920687, 368565327, 644315881, 946216606, 567217620, 512541852, 267077216, 800521004, 231322368, 720780501, 744992554, 846758986, 422684768, 872476138, 496604357, 7466325, 345963626, 687421519, 157067018, 30475045, 496112371, 410887833, 555379255, 175174484, 290650036, 205922495, 852579609, 756648192, 405393619, 417259170, 128237160, 478556893, 460336566, 462600679, 530717128, 977338142, 8845161, 711600075, 344156760, 307732769, 220474819, 635021147, 255251329, 986182888, 56844566, 224465803, 376618099, 887238841, 665742239, 526156063, 922735228, 43988219, 634432587, 893851113, 179737348, 87883814, 971269694, 708892687, 534749997, 35050058, 709050633, 478252924, 243525472, 110014530, 570601586, 566130563, 520504709, 512162728, 134059183, 283652455, 534450781, 364094024, 959412737, 531361409, 589000004, 127941877, 740737829, 184399333, 473085027, 410904811, 788509563, 208324149, 353356900, 228775277, 900291899, 546078665, 114320938, 604624453, 208674251, 101848685, 553073945, 591517564, 177558508, 215059629, 717464855, 937293916, 365308488, 622598019, 617065496, 298030314, 933837061, 702215456, 584056159, 679730001, 542751863, 465208613, 830602729, 306178251, 40678796, 920261632, 414476291, 11311095, 274892523, 813553788, 367959413, 588491501, 8821592, 520111031, 501262246, 18784108, 249722400, 76640529, 159920215, 760035776, 720178437, 491145822, 206032978, 174176460, 820672461, 618514871, 426930382, 366775778, 667544908, 169708125, 756966937, 741052733, 71617465, 155487273, 825176926, 253715596, 262825387, 879189305, 110483234, 841516302, 757501692, 415692724, 820883725, 869117322, 792338447, 299112660, 628499843, 265380612, 676688002, 622824455, 703744248, 50566898, 929384756, 54393695, 298722833, 555395000, 728719124, 778473925, 428942031, 892340810, 211015532, 439058334, 599310529, 802953676, 848563241, 507897185, 878922516, 299588650, 434546956, 428348169, 211673922, 240863478, 254234749, 436381289, 978176125, 110523897, 982304115, 826694677, 61763871, 747961966, 67387524, 844379433, 462718061, 549671470, 520716462, 251270047, 711293252, 862259253, 202183584, 469418609, 865736695, 594865614, 165167745, 868801251, 314560109, 842477392, 298339096, 511135606, 264334047, 831795718, 805380668, 980148430, 490930224, 850681674, 600049054, 598363950, 963420588, 368234370, 186251866, 772498784, 521095354, 120467855, 444260940, 482152499, 469146536, 338012457, 509504975, 340545589, 666527956, 307415891, 852246883, 527226715, 369416848, 896826734, 686624017, 969297708, 262155730, 181241081, 318477707, 981005550, 305649917, 715883216, 204510814, 896358024, 670239578, 136959592, 6686440, 476370538, 448700785, 864645708, 686267082, 344028921, 842856869, 899983909, 584884277, 682001657, 623458974, 39503166, 113647487, 829100278, 67277774, 2893736, 258599835, 127687447, 240252621, 603876722, 208585619, 516062186, 849477698, 529007815, 764372017, 87640452, 12247442, 72322071, 942249583, 711977657, 227077727, 664502152, 749222385, 309669091, 474298426, 933289809, 858150305, 641793241, 465611060, 627926565, 625115752, 349593006, 239910122, 847332929, 844309250, 91190245, 732729614, 629961973, 181797409, 651124151, 85766262, 220064893, 204409313, 691944207, 822571604, 828153659, 420390135, 333591253, 501540945, 405252244, 284997217, 116124842, 350508932, 876329224, 537852977, 164977306, 736622415, 162325908, 144441266, 991851432, 274365225, 114715512, 176777247, 631113102, 488237735, 722786467, 849700592, 601181051, 44965779, 322842987, 520057622, 957265604, 18123078, 113272782, 982749629, 880527238, 116992449, 241381422, 602617704, 625495031, 808069903, 639754685, 934155339, 333144408, 914174162, 875487653, 670023131, 755846205, 183859919, 859294484, 932742270, 970328014, 387575179, 700211369, 609731189, 643731316, 413030039, 838200062, 675317328, 849284495, 943605591, 557785158, 101859869, 340598615, 214454799, 132082808, 384542893, 744964040, 432861206, 806862021, 11993941, 772833610, 12346848, 542227988, 686357815, 882312918, 368663404, 816004928, 588942798, 810477171, 548537192, 266005621, 767599433, 27605422, 880420166, 104563421, 204163076, 288599541, 541047753, 400097691, 639779413, 675268456, 462200203, 154750307, 461416112, 331224042, 268943680, 377799528, 329530905, 857454271, 697898706, 530740933, 248124931, 483969751, 662759283, 407008932, 820924561, 873806375, 462118393, 225812839, 364208747, 22008488, 550448476, 944201109, 367723667, 14021371, 80106269, 823062321, 951396079, 860911240, 235846663, 979356872, 138107262, 316644379, 656439302, 643408898, 324454937, 176924039, 699030917, 844756402, 979780590, 795783837, 667874384, 824709795, 254136540, 533410713, 615381483, 262022587, 465514319, 639343598, 781129568, 316331861, 195618012, 134290285, 861132476, 190715717, 618676075, 447826721, 257408858, 587935619, 735399109, 48776202, 305316372, 196098770, 749866898, 607038512, 190236489, 402808598, 59252912, 903876021, 872860039, 841983907, 321179722, 898011253, 559703910, 732819951, 514885449, 898479685, 966066968, 16281923, 717710284, 361899997, 740584324, 485865857, 864212152, 159475902, 568488039, 460040547, 803922710, 289461183, 958398898, 991322180, 860029361, 970219068, 183963762, 755886056, 170261236, 726764997, 367963882, 579105657, 559341319, 927278717, 2732406, 940563750, 538334489, 801725493, 225472840, 676690160, 559388268, 362043085, 695573784, 307615505, 18458803, 408668677, 645203957, 158280687, 11152803, 691992554, 270582559, 794819881, 262493545, 340951838, 103045238, 937762597, 404766469, 320884733, 754758903, 752950509, 103875388, 18639637, 125629415, 193369781, 994754586, 754743261, 216717343, 134909086, 585601876, 190160818, 840521454, 547890407, 852206162, 760840802, 925457796, 280839670, 308611496, 224194734, 437593433, 228405291, 385449791, 676715987, 674125751, 47254452, 822906520, 100959296, 468536763, 150700047, 780198272, 217770912, 781967650, 934566439, 364733900, 178097134, 165076598, 902715923, 8516144, 133615044, 731212335, 466032680, 439232270, 562896366, 118796135, 824910158, 889474421, 183111834, 938671334, 642280042, 274403283, 325209697, 524258818, 770964186, 165599566, 403306954, 766750155, 322637003, 267396385, 441452642, 340223418, 981474105, 460026492, 732710031, 349342902, 257281743, 486551942, 691672221, 442829258, 89222652, 198141789, 806685392, 727098541, 591553720, 926273350, 879512889, 562919915, 189841528, 157819346, 362294168, 404203232, 881867812, 353283390, 933077469, 665121861, 734231704, 969211151, 935488472, 518443543, 84285845, 146403736, 141299547, 10873841, 289219440, 402865035, 752068666, 215740401, 312286501, 38119076, 304437244, 30867048, 807832966, 244855105, 760807000, 274693068, 583180796, 668826980, 232493283, 415910910, 505537866, 107260958, 536558381, 612361644, 637449705, 756475991, 108183877, 18664590, 112262106, 430244507, 494729925, 177325468, 242436759, 88906080, 212883946, 263294271, 215618987, 491091424, 190315288, 713220495, 785801825, 508706170, 277716204, 253513138, 291549970, 858721067, 472556984, 844370147, 758397406, 721469345, 633850950, 590440148, 246676356, 178557417, 259960472, 892716830, 85369957, 476588690, 715177688, 155534396, 8989147, 588913021, 980070522, 565693217, 509429517, 763490570, 191970701, 434975091, 263854082, 254488050, 801719192, 123241762, 862749180, 523059399, 408394247, 619737854, 534113475, 84996603, 556333345, 268191425, 13146538, 991247084, 520064600, 984532683, 389231394, 662834574, 129466425, 424141233, 385570905, 258279252, 893969175, 297872101, 702319330, 51119108, 196991741, 553583113, 965661098, 221395502, 917791148, 586929641, 201609564, 91367279, 19898923, 547266867, 518958719, 797397006, 189945777, 880939247, 284008786, 683673104, 90675474, 851411130, 919287488, 775642539, 516252901, 576202384, 31523885, 708777857, 123709236, 34042052, 623584514, 658300922, 462246157, 142052113, 712192922, 213732321, 55053820, 950480668, 108682716, 483560035, 474389677, 254480161, 962155525, 179099911, 462693456, 391663508, 362769674, 353110421, 640263123, 15267230, 816386414, 434753003, 172836573, 868557308, 686525368, 19206388, 862010968, 181318741, 376229043, 289267057, 311373804, 679589777, 283795347, 994304761, 43743317, 968108779, 417344939, 194750101, 286886814, 639359932, 985143655, 420291439, 930093303, 987984235, 719607308, 183835437, 969899652, 321262579, 724476909, 21511747, 808088484, 412129162, 84427385, 243867963, 553315451, 161936834, 688101788, 733464865, 516975320, 349909020, 63165312, 307482687, 446785532, 133803691, 602244567, 31736535, 635466635, 848089465, 597968189, 788971895, 246708530, 96421353, 359547637, 246228641, 705611698, 526047900, 282061374, 767009478, 480468438, 86340080, 835321679, 528948823, 941356313, 156472832, 700053192, 443357134, 26960381, 221283231, 644432521, 38222348, 945647911, 968721319, 613740681, 843503567, 980519949, 876370960, 253413075, 626728970, 51777292, 792455509, 934962256, 698489630, 138708728, 278328893, 436586181, 294306179, 691029117, 852067093, 832782352, 834802322, 937351189, 169480160, 967710090, 373658647, 878196042, 95117658, 500609906, 326104159, 848460297, 188581517, 567143437, 628218461, 128294261, 687235483, 683634499, 418306151, 32747615, 917343322, 96456538, 621055171, 854529896, 437339165, 122616784, 192769447, 954787649, 333295584, 2441285, 661933112, 530184690, 856017415, 769943545, 618933466, 768090425, 573201047, 167331053, 329187103, 166557126, 365297392, 374463814, 257879004, 632393907, 708057687, 906029942, 941833822, 290915357, 75590450, 803117980, 224948336, 660365133, 679322832, 747439519, 504861436, 742648689, 900407980, 856287566, 198975426, 672796062, 620618090, 41085739, 111277063, 495476381, 38382132, 987590538, 210598006, 79578642, 992989626, 616222240, 914497076, 706315493, 459384789, 424100025, 267846924, 121683258, 962867533, 466204580, 888543773, 567245832, 235033843, 267491033, 627548749, 278096413, 190392157, 33883033, 662556859, 272791225, 153580489, 391516103, 155464151, 111977479, 382604032, 603563787, 731279327, 210473840, 441553132, 580850035, 879945068, 893908393, 954285993, 493725378, 76902437, 128726676, 130272519, 284937044, 590034773, 239403188, 972698491, 815721864, 875027833, 536219846, 815361966, 398058514, 372320012, 329606730, 50819662, 352191783, 411140015, 517638989, 750386163, 332745055, 387798466, 463692627, 400365801, 365039843, 545887105, 873766576, 34790000, 100806261, 127996747, 763147315, 34341244, 194092645, 98021018, 415368660, 89972735, 195176047, 976023550, 883039637, 364243564, 263259086, 760947588, 46214722, 830643031, 879633782, 725264973, 564308463, 661197487, 110482028, 288983095, 505816524, 641340933, 682200719, 56661673, 237255626, 511992433, 371107026, 845903673, 713636732, 872897508, 318545182, 792158614, 916575, 329444643, 525882700, 108254952, 114517241, 610300012, 643193270, 418168165, 51059584, 482921976, 471358956, 528802886, 974398890, 377456237, 16113010, 936510695, 88084079, 280293327, 762656463, 993199733, 839883588, 14336393, 902632463, 728162949, 689671230, 834518521, 524076542, 927483626, 650833503, 627540322, 877303114, 663035928, 353567130, 269730031, 389337750, 245453903, 959374655, 587640596, 919294605, 854017008, 579821089, 787659353, 587082785, 27770877, 640904990, 332040146, 85656267, 863623769, 599942628, 861495783, 478486823, 799416003, 675516697, 936691997, 33210285, 526549645, 538749666, 198460793, 990176523, 720792917, 183089938, 45183888, 531022473, 31608057, 967220180, 404881866, 893580884, 245826507, 417896960, 649437497, 988106352, 243615812, 718535953, 675290866, 495065532, 518139229, 884505847, 779726315, 754714177, 301133326, 642720247, 877393946, 961407235, 653239438, 239116749, 544364289, 319671142, 793262395, 147800602, 894780706, 972753474, 896441438, 571921996, 161295874, 694222396, 806821166, 193829753, 205745766, 321847656, 942924406, 575288695, 515756309, 874707891, 987338815, 271383856, 528917916, 224373623, 612203003, 581900728, 923476322, 115540367, 152210226, 123514132, 214943243, 31644237, 404041093, 331041285, 30468484, 750861232, 158064572, 787374078, 843428268, 316866603, 294877328, 339280025, 829434306, 754754976, 46049410, 46611156, 186307118, 741613739, 371818511, 122851812, 193294391, 652097215, 105639125, 866027499, 858571833, 976173114, 7717761, 180493135, 677604058, 379843791, 980322722, 31093968, 406781852, 555120988, 952871076, 107050978, 103671971, 323220186, 504429999, 474687459, 733404404, 739860027, 393288270, 498575934, 83114722, 502528670, 546207425, 460734422, 285963399, 226356462, 345443974, 254684315, 635088737, 140378950, 775207943, 465958130, 181427747, 690997037, 890557033, 827021098, 619007680, 173938545, 802069653, 827231933, 838511292, 113357926, 64303058, 108957247, 409355217, 378447195, 555266610, 694852605, 803046542, 572240043, 854152098, 838564350, 366008277, 424332453, 264942647, 733052801, 5607443, 349436320, 346881188, 233529363, 702367716, 528088973, 110519104, 185221384, 190444249, 264934760, 673994987, 374579120, 751590268, 694857064, 734606007, 289455595, 766677565, 870104508, 195007257, 236697060, 913877183, 963389762, 291502653, 964280755, 310771596, 708664472, 358174801, 496718961, 527715879, 866647663, 222018390, 385680857, 386419695, 972360381, 692998295, 549537801, 659477092, 569035212, 515547422, 389488228, 630327248, 656663105, 40890235, 21200834, 161357362, 376308170, 318923513, 821878712, 303824770, 901946564, 233851521, 406276209, 605629031, 245859445, 519169169, 252986702, 112204543, 243571165, 280738061, 85391293, 206717230, 711157039, 500681024, 356067085, 128072045, 933271127, 513380139, 783855578, 379515106, 874805018, 194031953, 270020684, 723068098, 644285322, 434906770, 953524779, 859884602, 393707231, 422070541, 98530866, 811494882, 595985838, 785047527, 581926857, 706460964, 873009749, 201312583, 416284664, 148847498, 345939805, 712255309, 973296452, 420972132, 674462684, 719715454, 828541729, 122679581, 959490733, 255808531, 131442718, 675977573, 415189189, 397889539, 880588638, 22773007, 532672630, 694875650, 59638571, 850502713, 749429443, 139488955, 369874884, 168751343, 140903293, 908289691, 168490185, 371565303, 267029443, 883881486, 496869343, 73515357, 824967899, 619470076, 109230893, 900483348, 635833755, 706490904, 272466467, 151329568, 955244464, 695118453, 727821200, 959434658, 231933124, 288575180, 416524330, 810509603, 233353991, 7539311, 506899604, 455923168, 116160624, 545002975, 728410130, 40105703, 27000615, 305936658, 809614608, 918053084, 458931281, 789475474, 500126178, 286783699, 796402116, 302948744, 278105213, 986937831, 586564163, 12244270, 227526735, 999572475, 973856413, 777018047, 233235589, 264316144, 980819469, 299117383, 558355892, 93095661, 283202425, 906177640, 966143570, 868380573, 898985696, 769821708, 641202003, 701632139, 961773850, 527355578, 568014425, 591455894, 418726291, 573439156, 944610596, 513845406, 835054221, 92600185, 81900913, 157788400, 808796205, 977899862, 583912495, 686989096, 570722572, 410972819, 832144910, 575421614, 5394107, 187921827, 904090284, 351602344, 72841509, 18597806, 134968067, 902769224, 291485606, 467018568, 138826245, 381667659, 894833763, 613445627, 853104797, 452088063, 604009489, 814757622, 979360761, 375595546, 286466079, 594737485, 669880241, 508597860, 416345730, 843133926, 630564002, 647220339, 329265042, 362602254, 478532349, 780767439, 88838692, 534027468, 599348963, 942874072, 556218521, 693787054, 858436095, 593911204, 921035428, 116658624, 259409984, 123523710, 36513769, 808032046, 705444759, 254020208, 95640565, 434352840, 755466678, 79533567, 467223056, 458011295, 589089128, 763169449, 147022643, 128420077, 673428078, 129069146, 862464122, 394184357, 318068887, 882157710, 860358776, 907800163, 432944045, 541072690, 389480901, 185347763, 930424653, 507432603, 726228187, 288693317, 726688810, 74275998, 914758849, 646731294, 943200817, 124213988, 861379078, 869622674, 681513051, 341162062, 464999457, 566938331, 180380424, 240826402, 140058952, 727212869, 53662813, 108890744, 359550649, 54938713, 927756566, 56512359, 608697855, 602528567, 804704194, 680592155, 466250372, 775668309, 429544930, 68610846, 437262474, 123091536, 685632975, 773880553, 567847772, 114067166, 257249134, 763188379, 339285592, 35482027, 451431115, 120380394, 612183126, 940562462, 731049366, 646511441, 932921001, 541194825, 686869069, 468140714, 87819636, 255643882, 514282616, 816604449, 196157383, 255834440, 139779365, 726924006, 997582704, 699410312, 861320304, 778499684, 134979143, 502091851, 678541976, 87289728, 318194942, 735597958, 104264544, 78704761, 995625775, 644399386, 603582792, 59511066, 141544982, 87431913, 666457673, 20017772, 839793913, 168943259, 206780597, 412633781, 596444169, 822113328, 804745480, 103558842, 898514240, 806761510, 300330713, 693926407, 678678763, 987033464, 544102867, 676310766, 55423100, 182467514, 119880278, 704737267, 883682479, 834108208, 230796183, 617298185, 515011987, 523195008, 480228335, 950660445, 909722777, 54039095, 423290806, 861257650, 53948867, 762886142, 580128725, 517963113, 683919226, 69136327, 8819421, 364279924, 499411148, 804340888, 653193700, 322294501, 363607037, 667557017, 94695771, 489890309, 757976243, 64318781, 602727094, 387586433, 883134392, 644861835, 12792531, 850547770, 959765443, 794928849, 650452608, 470935108, 863585430, 494868048, 751768267, 935867054, 818194813, 459618048, 3043185, 586971424, 813237814, 176445033, 9011552, 249379241, 452402244, 647202528, 606019559, 693951321, 643413351, 635700990, 864593318, 879980407, 553629506, 383091408, 413753838, 535536979, 488710791, 184369252, 237038126, 965918456, 457494516, 685365742, 565711351, 468135223, 928451504, 48888234, 446135251, 581316297, 736693624, 442370090, 287607503, 767345854, 273874537, 924930891, 332254723, 704055689, 768025784, 86895197, 856006317, 801098153, 174581569, 782328435, 278745510, 637130640, 990423867, 623853718, 780053007, 929693214, 708580777, 81961361, 307145827, 940119752, 274326390, 881069109, 770724852, 635228852, 166097442, 105528140, 551804859, 910421984, 118064094, 779505946, 178006714, 827897435, 943184331, 607937685, 675566292, 840127040, 692087872, 439449560, 834004332, 599125253, 191920630, 736128002, 789177253, 822563151, 150662556, 40509867, 110635382, 350995216, 163376644, 646239899, 969456593, 388207185, 23095187, 929385223, 593788890, 31447348, 204645105, 701322056, 926346669, 166039250, 75409606, 832710983, 525526212, 314467648, 131623362, 576772397, 659172929, 880307077, 785845064, 797449643, 877374313, 526622476, 586869789, 549398591, 855949029, 455294046, 789978805, 369511788, 438057397, 477387101, 844182998, 308255500, 412097016, 851918776, 57690084, 75782358, 846174416, 358788020, 151242191, 338621314, 444192788, 32273656, 383256426, 149821976, 167885215, 145102621, 252683897, 536047719, 452310551, 297350701, 523125484, 372513962, 24795241, 755268977, 800835214, 58839012, 400081448, 218968500, 362263453, 840076933, 605706363, 647066495, 929332514, 571325885, 179266795, 348694313, 283972582, 737143319, 228152117, 371214141, 855450142, 504420328, 629224350, 878206860, 789488579, 489535342, 25660347, 530805761, 14298114, 213267968, 146002129, 867570075, 134811474, 177446674, 307865366, 474943126, 120750751, 878876409, 136650617, 72497446, 66956762, 940198397, 923702766, 903235634, 208509583, 224994792, 397231269, 624750370, 502091955, 11256866, 218408182, 555028901, 900544613, 722397761, 177029245, 972305873, 224169147, 88078923, 278948975, 99730944, 46303775, 861987719, 717293671, 537869087, 905068655, 630149613, 942029791, 172786637, 720024959, 321234727, 932634383, 920228152, 851721007, 483247314, 694575161, 611702812, 815906669, 354453619, 699698899, 338498083, 987853746, 625918686, 382817546, 383929840, 784398444, 219519007, 773354932, 924577154, 886255655, 622949708, 304766743, 83899456, 472000041, 470063369, 69444405, 742280843, 207705002, 722732132, 314363043, 648283439, 372270992, 728551449, 9313247, 841137689, 592395438, 623866108, 372765742, 428026903, 775810518, 435615729, 706239432, 552134885, 276056069, 386460832, 948324471, 248365464, 80837085, 734396084, 430601176, 650243979, 50700297, 530561023, 742749046, 723904561, 636690432, 764487670, 761388376, 490765083, 154855929, 993345468, 93714775, 660361917, 11360319, 8002578, 742786538, 16103893, 15122290, 701718913, 107645907, 678486483, 65597093, 479300491, 212031286, 258859567, 270964438, 554040103, 460594906, 468002825, 75514090, 793426814, 628500566, 845090345, 199041922, 790476988, 273339024, 643369952, 161306808, 398901205, 229650206, 310860174, 127109891, 265489138, 858461616, 108353873, 873188767, 761822735, 846398233, 84711254, 599122043, 272514872, 668254279, 558724268, 553058936, 944421447, 142570035, 520030037, 220385781, 160130604, 771096230, 904770263, 444477655, 401484424, 859413563, 637198432, 118193485, 50813543, 956044186, 710083850, 953128656, 39134836, 821608485, 876576394, 166574982, 676734485, 932031016, 978556362, 333334777, 937285444, 269113407, 926650359, 61227422, 624666800, 695997952, 979763796, 441370893, 711195668, 859970510, 372552777, 263681080, 985279511, 561200455, 689593977, 639448969, 833947915, 501640516, 44946537, 161737982, 899386268, 689728014, 364341459, 612721879, 260894682, 586783648, 166697855, 927460050, 980594327, 734681219, 986421341, 848644531, 121690358, 855708565, 236079167, 297280609, 556088449, 272709156, 287372688, 561486561, 618101725, 678973739, 915509389, 152946205, 354735210, 918882529, 172525354, 713031785, 809726952, 702808756, 104791527, 316599148, 990804878, 467689774, 860363426, 947608696, 917121393, 270571037, 314559270, 636504942, 996933728, 419151121, 876808534, 549394210, 755822453, 184750270, 657701549, 293632955, 848848114, 683703123, 96624668, 88526, 979959204, 945312043, 5519052, 390030258, 173786903, 740924390, 964294780, 999152808, 227313974, 987871259, 328585211, 572531881, 863288961, 330910319, 208641217, 666007434, 904108406, 761997908, 680681008, 702355389, 489061172, 905088019, 390029381, 803602887, 801330242, 925876043, 784094351, 205726980, 654911901, 17879941, 552012614, 382701588, 944166733, 665646272, 24419897, 878881388, 95488916, 389359253, 966084327, 882055853, 936882912, 178937024, 63998622, 776316118, 34263989, 111067793, 604413062, 870052994, 679400651, 623674540, 337756847, 384798351, 203309808, 856106599, 486764999, 363599450, 965725686, 60847588, 565434354, 326852811, 406677271, 198883068, 951615122, 601811757, 594331304, 845346888, 978975276, 942718737, 574741696, 110621490, 913820809, 519644052, 238388895, 184007278, 31896719, 745841045, 116433366, 659142889, 742730840, 518580224, 799593892, 438890188, 420393337, 70403857, 256331151, 48677277, 692276638, 171635786, 614138499, 942285695, 558701106, 534758912, 265640015, 234097454, 110751255, 858416548, 393614526, 50257147, 351494955, 759529502, 290765963, 254490868, 113831690, 436367381, 457163778, 535881954, 68397009, 182605070, 124227595, 598953717, 384197029, 509175568, 815823390, 259973824, 216243762, 124729777, 35763081, 770367850, 309939759, 674710159, 545285713, 911917095, 768560415, 782375141, 48458151, 252552159, 544206753, 48188177, 966666677, 494325705, 551611538, 370880818, 896254274, 360493937, 424368903, 200183889, 557244687, 963559981, 361358044, 551424097, 682518839, 188988926, 26496315, 53336659, 70731625, 250570173, 214123472, 150126925, 745068647, 678331847, 212342467, 866934143, 823910256, 439184611, 608734039, 676494702, 60988939, 145928409, 530433158, 620455469, 626975441, 170346362, 596458312, 617724362, 592654165, 860052920, 396761024, 213818517, 539824594, 476701931, 37212693, 580533304, 731706695, 813058196, 643590643, 824979324, 683540714, 254582272, 897631760, 47573356, 199893284, 820959335, 245349897, 400719491, 716181093, 773208607, 101071937, 719337665, 105086321, 582615476, 28550482, 979348206, 616748586, 10214389, 905329781, 27292741, 6555843, 445901487, 905292443, 594932340, 100980909, 571804275, 960489516, 246379949, 854757219, 530632170, 940177623, 853264858, 894850001, 625025989, 958682024, 112218886, 183930711, 78875815, 271813632, 789596730, 738379483, 713712911, 280527950, 171757329, 858092197, 603443575, 339587780, 94922154, 59428541, 30728541, 142257419, 446645494, 211810336, 757738243, 575870552, 247285650, 421724960, 65477157, 122858154, 981676478, 363398278, 383689661, 417007346, 165295240, 906777877, 253092903, 709071921, 242050975, 773481280, 831630606, 355641280, 186618776, 366163544, 297283547, 238785893, 823455224, 230309664, 679490417, 127008818, 203741919, 849714351, 806455605, 926841046, 238250549, 831382177, 38943984, 641326416, 42949145, 436012148, 294193203, 573487837, 494076372, 932538513, 886632535, 250600417, 226049757, 241861931, 862435541, 636690940, 841508934, 12116233, 343112362, 762262217, 973460941, 492258999, 760088112, 875192917, 518996164, 366166515, 144325124, 492877578, 624462380, 383996586, 168725010, 761193231, 533945864, 973092774, 64254923, 274699301, 909861154, 325026112, 966332404, 225487767, 628519774, 206805669, 44502910, 578806318, 188342782, 86266057, 346932587, 160899527, 876733547, 137375272, 396976031, 471688003, 41120448, 884940124, 945632131, 101849022, 392604776, 696895233, 223677061, 985213797, 795664794, 65638085, 490297255, 315646024, 97568798, 637994704, 645889461, 116202930, 607476947, 362295748, 314774908, 90359475, 348514382, 39362302, 495514719, 841272621, 323087957, 216682469, 206266731, 249863608, 402000573, 280499828, 687358894, 901965397, 124875033, 739701294, 703579215, 713612893, 342636237, 73342729, 874041301, 799280216, 37382478, 407487851, 448161659, 240556667, 46530190, 803963133, 15472644, 165503309, 436644918, 169552144, 250869220, 831771883, 633810829, 218121993, 41918849, 187402651, 224733826, 139371186, 944865940, 192872353, 325987077, 432903440, 454687407, 817598253, 969525764, 628905358, 857437277, 632054477, 159026680, 850851045, 120676301, 215978244, 723439148, 896500418, 11535210, 454620671, 248992943, 350125839, 482191415, 517298061, 542150126, 131674356, 74924465, 977525231, 592123812, 531968345, 780329643, 661044535, 486644222, 383361311, 677543204, 694620687, 794503112, 327015333, 605553676, 306079102, 781787414, 299072815, 675065022, 288236715, 20144490, 956820525, 612371293, 418197479, 224857559, 617649037, 198978152, 822281050, 973333131, 533654642, 46011427, 25097619, 823173434, 418184939, 755878903, 945279800, 106185261, 321677827, 846582543, 445093155, 751663436, 739093531, 919346490, 209234997, 135006235, 277037864, 152182399, 627210080, 861400924, 486228289, 972097882, 968986967, 867215889, 297373749, 17351434, 425680960, 52618073, 873267844, 604410442, 338045497, 771534651, 932440753, 286031834, 692187848, 414088163, 578674639, 652478528, 484868910, 54190157, 367930350, 859446738, 719897239, 728722109, 359045581, 802433542, 78229629, 353004913, 154072778, 72932610, 601135804, 467558855, 910463630, 243620114, 63953389, 982819079, 350769859, 27810528, 900591892, 618530435, 158722583, 228769105, 63980022, 882978001, 665564014, 11672371, 837408005, 390043626, 958893635, 575776910, 90026211, 301713037, 538224872, 459925144, 725455149, 416259231, 606406167, 377618306, 438207615, 397637608, 84843093, 781971750, 280272295, 156842033, 988680994, 468007629, 432399821, 618137018, 952104321, 210559379, 550138105, 212572918, 354764534, 152972592, 320561437, 22969945, 419282964, 440727062, 510891917, 283738629, 879072412, 764370235, 318631917, 166506852, 896824884, 897755157, 241298036, 683616596, 346448702, 763844222, 425309273, 131625912, 334396197, 668048991, 931590173, 322728614, 443293523, 43392370, 24041374, 350093161, 927493484, 290166989, 648950244, 605778493, 488295622, 521784589, 681342944, 659322550, 744132865, 10787743, 543295843, 968335062, 271187313, 608527607, 282333152, 134915588, 464195961, 878766359, 890920863, 887175843, 732745967, 53944244, 800756952, 125865324, 688634379, 82127128, 444415126, 512153534, 17379122, 426167935, 69853759, 532778405, 634612499, 34999785, 174474882, 38255488, 749411818, 584592201, 398499912, 429032170, 941254738, 72836974, 182785797, 656087019, 91759886, 328739288, 611512195, 685240104, 854476394, 550436552, 451037824, 487482390, 783949222, 946408398, 233366859, 307294175, 820438007, 224385123, 41087315, 450724924, 829461625, 959331787, 30173657, 928764724, 822612887, 934790881, 220123324, 34012205, 900526399, 252104998, 650484727, 474681192, 135018698, 584322358, 585384674, 144391448, 643963346, 554189476, 435194784, 626272803, 58579267, 386514025, 977189163, 473835673, 992544829, 189094181, 837456680, 682206687, 905480512, 488042290, 310004976, 143410604, 296977726, 575138181, 281949801, 533132992, 739720422, 435043678, 506110580, 44416677, 922909387, 380137118, 587146287, 309053512, 803642309, 634020766, 651300052, 853150755, 177596946, 439649449, 315734932, 537126396, 658260465, 604244813, 503925207, 55615453, 408915916, 893538863, 923097429, 293275425, 170765496, 156235101, 605935659, 617244044, 475722760, 447859679, 254104042, 120610359, 392456340, 217373435, 921847785, 959405960, 480314882, 953365015, 922330877, 861571592, 215870377, 886914036, 221417337, 666859576, 165742627, 999017065, 417741286, 328010262, 29104416, 781639905, 549802295, 687394556, 646419843, 150997773, 440179696, 268429125, 438689397, 178907378, 420330578, 752295801, 466849653, 73033569, 621396048, 492034193, 428694762, 178515949, 844800348, 545152422, 289252719, 868901198, 483249079, 316444736, 973456540, 774926038, 548340095, 421998412, 550146148, 558026701, 379264671, 197610034, 260223438, 182044690, 43627381, 323788537, 636849313, 270371714, 950359615, 964371555, 576922657, 741887609, 163611423, 444271663, 976847784, 109823652, 734310864, 205366120, 973270092, 162827086, 416270582, 342315291, 53372518, 51045153, 344750376, 285030891, 80551998, 555112028, 14464462, 975949171, 489821497, 587210614, 84120248, 58653457, 997033947, 111108917, 4457907, 309362935, 47791922, 770023390, 780011803, 654215836, 310801550, 323091515, 690707312, 378804524, 988474804, 503899954, 538044175, 225159172, 468100371, 241417339, 470825976, 801015621, 789536745, 119553533, 702222170, 746171548, 201946802, 707046045, 336981893, 179990339, 330609634, 12720439, 927836088, 864348060, 77905836, 518179947, 277482499, 318301731, 631248993, 472683119, 358820178, 667179238, 116005658, 605214556, 33357852, 110193022, 643416736, 457086605, 799952155, 958656331, 837707477, 707097765, 587879262, 869273360, 121503285, 351115979, 912780414, 984745722, 452026707, 314360819, 209695840, 342994153, 307671839, 497644824, 68378373, 239840613, 921663891, 112716608, 280040523, 228133626, 257833587, 950466314, 5138258, 527894444, 654885342, 734499779, 150318702, 996057733, 768661957, 544758701, 916583401, 204722795, 756286406, 201813931, 573545521, 271679792, 800986535, 101790042, 645919691, 897428258, 469895686, 394729673, 857942952, 151877880, 779725136, 773509577, 93724931, 257317356, 153541523, 408038058, 326798831, 702857142, 366925021, 647069988, 754767201, 300839879, 50366967, 506970442, 994751226, 968300078, 657791940, 648452222, 870592479, 171635748, 530306917, 757086663, 686327435, 560179757, 497886250, 790323949, 104058460, 641585996, 963007060, 533877577, 836337754, 519981392, 26230407, 78275431, 667029469, 643960734, 567915740, 906689410, 387730398, 318069575, 923202204, 545889192, 308500775, 536522910, 946767652, 421083032, 916200390, 563695216, 805746560, 755574653, 324928713, 5456934, 258433316, 465647612, 342063047, 646207191, 373227091, 147502371, 196685146, 769200983, 44523966, 954908067, 361353720, 74811952, 527885894, 403032568, 161100754, 892399964, 969049400, 515079165, 833002652, 898679990, 334878574, 454866878, 131310652, 878649364, 898902370, 180832484, 689717312, 761512779, 610237490, 604462719, 42439495, 470167543, 210479921, 558849040, 695329501, 703277080, 298804786, 228159270, 719562887, 280802862, 155138327, 461179093, 267672388, 924723360, 973846722, 882938426, 703475433, 332804159, 387049500, 435385201, 423618302, 95827760, 101584955, 877336760, 288032710, 549002899, 700576950, 408945326, 651937007, 492571809, 432953660, 642747464, 551365032, 554298842, 539247843, 189647899, 487269675, 870238623, 237101330, 398511441, 169880338, 869564778, 136098869, 620591528, 145123903, 914913250, 724456154, 34714693, 361311538, 500519431, 787150951, 238150252, 335836478, 277474567, 386776951, 39208195, 181820554, 295048199, 475553932, 852065977, 292048082, 561405579, 185927209, 959450459, 821208335, 187623541, 279097777, 352798609, 694471189, 78541080, 704062889, 311959248, 691514887, 302597252, 691658508, 975054367, 776774856, 198954493, 209069907, 914379164, 847649171, 538775612, 807915631, 435173745, 929390700, 273809074, 963865167, 934090838, 772256869, 710594962, 672773929, 62291838, 428721055, 354254107, 973930290, 769512906, 769757286, 587518626, 815504475, 558611547, 323306622, 907302720, 527462339, 410795865, 934050272, 221045449, 233923038, 699348956, 488407363, 966544567, 308782998, 858400196, 757103478, 956735966, 895957183, 306549363, 976586796, 195594276, 699412173, 336212027, 448744211, 472674119, 533685208, 664623781, 831297852, 232898898, 466444524, 72347968, 294787240, 241002901, 773978083, 937016552, 369849373, 579184297, 760406484, 879812657, 269277503, 902433457, 774766708, 781303869, 839563343, 806315478, 383313907, 775971158, 304151973, 535816392, 226879804, 703316013, 878021718, 275092488, 574447767, 62945886, 183169326, 916795778, 105073163, 403212033, 982862202, 255955270, 875709490, 504729021, 490406210, 64894160, 401058840, 815589485, 24544907, 315834257, 96486923, 744616249, 263013693, 478493542, 136340302, 471746601, 92426497, 217194233, 549556503, 526046993, 885266860, 436289085, 381221589, 837341155, 615085228, 508364458, 227813235, 407625961, 907606166, 608946866, 354511773, 835354546, 214734315, 546616997, 12024928, 656059151, 993511805, 657767676, 960680335, 850900787, 403775366, 37410906, 796912150, 553072606, 375123286, 574665165, 246128157, 21335398, 181884330, 955249715, 922985131, 149191783, 356860174, 394878628, 33967627, 596182879, 872147037, 357174618, 623773675, 390437255, 103388372, 674349967, 461284034, 220824997, 936396874, 850647288, 301600141, 623845619, 668308418, 412244217, 377962179, 86654295, 794184625, 402789049, 555267951, 50170473, 565823454, 206723673, 223678829, 671700063, 626053851, 196711851, 287793141, 75525091, 40131035, 516625317, 690993706, 167243473, 985063756, 418198071, 860069905, 277947569, 276920070, 972882198, 833089088, 51435037, 54815973, 79661449, 318983961, 320588561, 529268263, 18807042, 765706854, 215224575, 644177850, 689894881, 436834950, 324129072, 75771713, 950008641, 285257199, 917063310, 502370800, 39703155, 131658387, 242465502, 384942860, 630048461, 16336928, 30440198, 888481514, 398618690, 290912084, 725611382, 531601962, 224730533, 613280966, 254477467, 763738735, 693323943, 910247012, 534843674, 97259025, 688948737, 575759119, 826867001, 497595752, 279927335, 78741270, 354070884, 633095900, 415022990, 200053888, 664042926, 359626912, 656171223, 14010625, 187681125, 562187377, 693718723, 720752742, 292385447, 175007252, 718071995, 147375238, 608283882, 980680329, 500587151, 438760648, 290208726, 504408341, 163050992, 363528283, 623000702, 751893919, 645611200, 475453741, 43127949, 892074267, 752109534, 282995338, 912854360, 521472687, 651041783, 328360897, 851684173, 665207804, 725442669, 273921851, 333157358, 793379304, 232443636, 324754069, 417062958, 383317309, 767872191, 245267960, 54012987, 220373076, 102509641, 744077293, 945569301, 850123187, 457300095, 908616446, 858706420, 640311409, 760093459, 877565620, 930451542, 81284563, 345709082, 158573093, 82655841, 356827655, 195877290, 583733019, 599126342, 186412086, 848652561, 263053330, 240771252, 286842017, 923226850, 823042315, 911481109, 609621555, 5502950, 417236513, 755182924, 300387416, 52436426, 639612588, 151228361, 842225492, 679274010, 759965600, 605383690, 426775825, 500750290, 235014669, 546627250, 387495215, 900180592, 416282603, 204059405, 130668259, 114928899, 125216853, 771448350, 872096249, 151446613, 128795877, 668999909, 8212809, 655810976, 651662549, 381659250, 999665071, 296838042, 197872081, 903708522, 767907558, 485537737, 705860355, 376586664, 758454407, 809196370, 175211726, 939462454, 535783604, 342244888, 598995439, 496997651, 421218749, 385239302, 215313974, 244417499, 984931334, 216089967, 710199131, 263202761, 203092538, 837000176, 304278277, 854842435, 795942356, 656428311, 159182726, 991589368, 377541106, 623477827, 127818096, 315591208, 186573115, 281510817, 901256159, 765589689, 861094602, 978664808, 48455114, 636553056, 650359483, 561368808, 109515548, 462431601, 115345603, 661114097, 431285904, 238961078, 377064263, 14514682, 983277607, 15943387, 543741273, 846866227, 982860281, 691076422, 364028620, 392231226, 413807033, 916027498, 885876039, 836367239, 209339720, 926013999, 3626012, 555547706, 360332435, 285775374, 996858067, 340599925, 471899075, 746244594, 525050942, 624568926, 576897759, 447756338, 266027665, 769130857, 475113010, 610950318, 957823614, 825089436, 787534418, 777433033, 589421737, 716501216, 614450000, 438456270, 978865922, 327088446, 594954578, 982328988, 382253127, 98688825, 665209864, 468920449, 97204839, 567608907, 990299394, 346918891, 10477696, 127956492, 39548663, 32421657, 644274319, 515518155, 926486906, 572251842, 371654168, 90412987, 961842268, 22292267, 714549062, 828487342, 25654528, 758260549, 663214446, 738281991, 712332352, 280185258, 899156449, 27820701, 927842962, 306029709, 586108257, 105147104, 398014644, 404068067, 571481418, 109228217, 81331213, 326003828, 912432361, 565169183, 248740200, 784170922, 374211540, 576810460, 26872907, 417203035, 205126300, 601509129, 691889061, 947929607, 774401186, 827753872, 660375506, 574990993, 852734474, 479644896, 958920034, 238220032, 191839680, 690176145, 822017948, 983469286, 196397629, 336711840, 511898089, 195568830, 455000981, 131759130, 420954222, 675940465, 934380790, 35571343, 718685165, 358511939, 764905575, 138424804, 208657136, 299297890, 271024242, 296158204, 410106439, 405874909, 989739047, 692884608, 810112491, 636784080, 771549294, 119324754, 515824687, 856823599, 820557026, 257778640, 456957883, 198969763, 430743728, 236536999, 711727022, 509148618, 308719602, 497364417, 46643446, 754096935, 693132893, 275585455, 977138788, 951630794, 354134717, 703019892, 131328191, 761244791, 793380098, 582541257, 990771139, 305527808, 400093028, 319552607, 97255792, 567610113, 965326472, 588410204, 225368315, 290990775, 803755839, 491559615, 423669034, 945529651, 74593011, 371528180, 617744793, 378412854, 743893663, 69376167, 858767233, 795951636, 78680815, 40455649, 407583150, 315331045, 17999459, 536642166, 44986831, 64051528, 871423103, 874537503, 27499613, 832739283, 803902232, 686448223, 395978039, 711814425, 205182011, 662070958, 817948450, 248206459, 879370117, 805609755, 704019092, 256643056, 879796809, 750904489, 980171931, 332922021, 943474011, 725032678, 304707264, 737946481, 920810362, 891987301, 38427829, 918160126, 316544311, 402347203, 95965179, 920520684, 696255659, 165614383, 404072196, 509057806, 293977428, 561578183, 7816564, 496296787, 184130277, 109430171, 633285542, 923336193, 730048603, 569200378, 861256487, 676206489, 707184030, 770520422, 498334161, 422895315, 919253714, 664354314, 107850908, 506951505, 893597176, 612999923, 790462871, 445673008, 365784345, 562111519, 252132261, 226726057, 404190115, 117287117, 75041225, 183599849, 466448018, 784901550, 461579675, 527068607, 129689036, 499766602, 852836266, 311246693, 770726552, 698100007, 511725189, 281938703, 652972669, 536591556, 584509611, 583875210, 556401134, 522067151, 565848128, 46593846, 455323452, 578916925, 402514356, 561165972, 249294557, 649349724, 126103396, 115278071, 598458167, 618890075, 773446200, 263329586, 109063971, 561178785, 692897787, 449123301, 648461303, 992805517, 40662242, 421598337, 816032004, 290481190, 952125045, 492211338, 223023481, 243732783, 410225796, 463669511, 829591485, 481206726, 796436911, 239691302, 691873210, 620131014, 920906813, 977920759, 549451094, 203849457, 209981970, 310334831, 929464990, 348952971, 316219742, 415790393, 669664545, 439550381, 781449153, 12374815, 397117110, 586749647, 636142075, 225503874, 37009237, 207751334, 252714140, 935342568, 936951312, 652234903, 489707, 894202882, 110337598, 765196166, 373211376, 246201298, 989190107, 986599799, 555145602, 236352806, 933655120, 695176367, 916358868, 849461297, 910273423, 406748971, 931607085, 856003388, 29772197, 638863708, 917603539, 451423847, 889494580, 792658852, 871047667, 248846126, 271452324, 723304371, 339406170, 221582037, 280026928, 674638198, 495437571, 337470910, 847715918, 872870585, 950971715, 448218960, 652336654, 24318299, 722344601, 646470384, 231248255, 325402961, 112400250, 45067132, 504871475, 87317831, 836976669, 688590687, 868482350, 380072713, 947512195, 874358751, 514675907, 818029292, 98450187, 335028675, 102719535, 558465097, 928176874, 279570671, 672369162, 449163149, 796900229, 621926669, 483858060, 405234367, 262969327, 235619759, 963704645, 955239721, 548665262, 252196365, 440012668, 418619774, 481541057, 852460316, 55127855, 403110372, 773941876, 35682552, 298951716, 858942890, 282315600, 447413427, 281178479, 913813775, 519737221, 143723683, 200282715, 849597316, 276508155, 999167184, 990369609, 458305079, 613894757, 981084567, 999914195, 98808469, 496963921, 527800837, 616260687, 901036492, 352699837, 176870980, 86914339, 901670344, 116444591, 902927992, 706910839, 145946, 177907707, 333673740, 766134624, 768815058, 706452435, 140310486, 234174659, 852076680, 547832118, 183220900, 894724196, 170901898, 698987271, 759208461, 192758146, 275446271, 880804791, 819197038, 957040237, 462897462, 327182493, 98728596, 101233646, 71489650, 970678230, 570262382, 962552452, 83391023, 261118735, 256610190, 399693414, 209830355, 660578032, 954581583, 677849223, 998954876, 514354965, 85359903, 315313578, 335933260, 651467739, 303491358, 106449326, 331827923, 498842371, 18201721, 541079988, 729756947, 208187113, 204920409, 179022086, 260033676, 323404836, 747259683, 449196180, 956346763, 390475054, 568533815, 545118108, 481355053, 189706932, 69389857, 370503756, 456378419, 754026086, 413067172, 392086596, 914420222, 318800592, 576753322, 722274541, 93784204, 291594549, 202772593, 892042910, 831610772, 458933590, 275777962, 791000309, 326796068, 706661470, 311408152, 997856839, 25855336, 454230530, 872115027, 42335778, 790279863, 559857134, 462452317, 683562571, 438599244, 493546279, 254440633, 724172736, 850629314, 904609698, 594838696, 991794846, 209014828, 702358443, 673811609, 905781181, 897600962, 418973902, 580000314, 192590988, 668389535, 822308038, 970018718, 318780322, 518949346, 33191925, 994354277, 917885384, 387840171, 774696974, 12446714, 440512005, 542366575, 76061491, 503859415, 444138895, 85868379, 751994556, 238980891, 852286074, 737066099, 129341623, 697081238, 141490863, 43783479, 790061207, 431311596, 503203322, 91535223, 154891536, 157694693, 450705139, 692594591, 429260782, 867973545, 576038821, 163920643, 547383038, 551042695, 763714545, 989496, 109812632, 29256561, 664077320, 742332574, 781803322, 181814140, 981150674, 987081831, 912994391, 352508139, 346831879, 750029426, 373453956, 550359512, 857850879, 897563016, 472873279, 58519637, 939366481, 373847081, 828831776, 377417302, 969716188, 597395860, 451495964, 562902162, 680369434, 357174062, 718255940, 351554648, 499313882, 857454621, 382567722, 946442772, 104717935, 322410713, 27103448, 688160686, 387294279, 795513023, 851698056, 130759253, 997609992, 178060267, 275246822, 708046173, 329979468, 992853846, 977848690, 565229752, 183386024, 479072559, 968437497, 463440114, 221356527, 595880352, 651104114, 984798552, 897881081, 144249456, 455089945, 414315458, 71709384, 598016803, 256331455, 45625035, 183208652, 511100998, 750812235, 115982909, 601461380, 501552135, 10607968, 143917410, 43327815, 175879877, 136497827, 896217092, 731441862, 897134407, 175814197, 925126287, 122632019, 561886616, 287001626, 761381254, 517520215, 199470126, 270692691, 660583974, 107703293, 919517342, 283887363, 674519327, 485527268, 120521564, 182191424, 511128633, 709634001, 421337058, 409067897, 856949229, 420961051, 191943383, 613979379, 496683280, 81292049, 32264090, 456378751, 546606308, 305510123, 462699937, 297717928, 74251553, 798839508, 926297522, 250597256, 860286030, 896825386, 510255306, 627149890, 163989523, 54478281, 317292311, 961262418, 942204456, 898629214, 447096090, 540668385, 443000929, 753262903, 818233337, 440721323, 316519111, 788942804, 4139510, 103104246, 734932815, 369104914, 833379376, 406160484, 295670648, 317740309, 620207361, 96279693, 788284329, 293642265, 735516956, 622247307, 540043693, 863171955, 360312005, 701419402, 223612531, 575671300, 401346847, 236349626, 920208807, 830544370, 556510437, 331921520, 887375976, 595204266, 643459033, 210775308, 876208901, 702006049, 641101118, 251566848, 618116940, 786844060, 962459774, 193538707, 294726736, 423832811, 614806449, 904083866, 13024434, 46098888, 184533460, 460189990, 988177341, 605205081, 447247993, 858247748, 351107996, 946632215, 64476008, 83537895, 849378386, 613358948, 212913242, 909035336, 638647450, 762209181, 92282474, 111668219, 393543306, 563748296, 379493520, 298147228, 506102502, 677011632, 891391291, 810897046, 166894532, 470017180, 736132219, 146605667, 408203370, 169034507, 973085381, 34855818, 458706654, 170009897, 260575892, 272217476, 263814145, 321632208, 796433427, 288110301, 150646995, 747064964, 227010306, 341139311, 67538378, 63679085, 595762926, 427360922, 408518905, 784576033, 688453409, 967435751, 1805874, 489124385, 49547695, 322716084, 541344811, 123925783, 89183887, 363928039, 618186576, 204499023, 210922950, 700494278, 864138778, 986949972, 229604527, 503407025, 380900976, 128495065, 242003640, 344887581, 40685357, 104467254, 519896613, 147999220, 223395771, 857724062, 158062445, 576432910, 563692778, 176716108, 634958719, 903086066, 217962262, 950626659, 718486486, 306986607, 63750243, 580668492, 914404095, 428637676, 725732756, 719499918, 202138835, 651697861, 8573954, 581944220, 875557901, 707398957, 352773813, 325295541, 454579590, 991307961, 334039908, 368111650, 615888189, 189735232, 910579839, 651226557, 596709150, 374612159, 183446091, 648527849, 671736458, 48511641, 306532658, 585411305, 194294414, 598061031, 275034066, 581190198, 655469368, 360516425, 86331867, 18722592, 468590477, 203740871, 991512518, 871809060, 157450974, 183080316, 719257361, 76954361, 159531910, 995538455, 727196881, 654601867, 914175716, 936039016, 799358589, 730302156, 942106467, 381635688, 205106313, 20950148, 571572891, 722754699, 796811442, 743390443, 532212977, 136393438, 143835229, 698607255, 778792800, 683853426, 701756028, 458727616, 526802941, 680838825, 142180824, 450237521, 32230038, 508175378, 348101126, 996052058, 618819650, 38459982, 975589883, 197808705, 959766645, 122580138, 349036254, 63167149, 539108549, 351551077, 256297558, 713422512, 340438505, 560898264, 609274780, 207947874, 945805530, 824977686, 993632418, 195645318, 48724614, 786171135, 31588171, 971268901, 428142628, 161074668, 42352964, 903618093, 503220965, 352167303, 902179431, 424605707, 955980745, 657193217, 212164830, 366049544, 36892225, 681670517, 740904439, 187642570, 80129495, 561921425, 755218559, 995509599, 810446394, 434498852, 138693537, 995961267, 948001926, 570050440, 245902051, 469457947, 78412876, 400901601, 755930406, 392715935, 438463683, 313264933, 190208942, 429703992, 933408503, 646040945, 893490860, 181324853, 9029599, 583441599, 899125775, 569790661, 76652959, 897652586, 631173730, 447802025, 553640116, 601529006, 765858062, 172525279, 852168181, 534837699, 497262630, 174634090, 55371372, 94074262, 73605903, 854665166, 975763300, 433175213, 346414102, 920950677, 33594451, 692518672, 803210002, 981353949, 321409809, 856067752, 922171156, 723292596, 89595991, 281294572, 948457711, 414218221, 391465276, 847558223, 175330338, 124817262, 851849033, 757429725, 182487677, 531479623, 145884928, 962675733, 466776771, 145142987, 210594387, 440798063, 38575029, 192504041, 714943775, 677859268, 674883319, 164586601, 69186238, 843689737, 815158869, 381714803, 593556466, 756614372, 978482612, 792398103, 157192868, 449325665, 206333814, 86430805, 607493294, 291154081, 442174372, 629036912, 672573097, 586683604, 941686225, 307772920, 132903268, 943761555, 698606194, 9528128, 886439733, 476327351, 407792646, 103890622, 35971091, 407736809, 934464784, 172426653, 369454077, 102163337, 416460765, 787757730, 787631599, 814210399, 368669167, 934732659, 335902670, 295218742, 708077580, 786506255, 209340980, 195093540, 961006915, 468832918, 451609963, 330563391, 361018001, 471057697, 665471834, 745012625, 864880677, 68881620, 611943072, 588622733, 676736864, 21191584, 191595465, 642751439, 834202866, 71769561, 416140074, 582230843, 289907889, 274204299, 42890905, 765150067, 959177984, 511382422, 139950298, 848495838, 982335178, 935778652, 160300749, 330524207, 48298383, 405052370, 111451110, 410635124, 738438534, 622078030, 542317759, 417430918, 256346744, 706452087, 856594487, 695994020, 652267322, 582844897, 426919999, 821867437, 91632505, 764080304, 973103456, 391606564, 520450704, 844449631, 519911284, 606572353, 171168781, 245283201, 672956169, 621062509, 280584791, 662283358, 654745104, 266145090, 903570601, 152192037, 861536873, 394208710, 28927684, 621824418, 419200732, 625566775, 157717113, 7672584, 639438899, 88803849, 717707195, 650164926, 54095911, 959811136, 2114959, 745150459, 498323170, 970576472, 731382376, 953147394, 805951326, 888959605, 113692876, 281814770, 259507339, 564577674, 914896573, 288093690, 327665062, 363037109, 297278098, 822467031, 313121627, 298377262, 746896962, 243177907, 67810737, 783467323, 754777111, 259717945, 890615359, 981049107, 876061873, 171553462, 962827134, 21627760, 306435753, 455212441, 209193442, 493882339, 592806876, 132436028, 250851989, 794388084, 720779107, 699573201, 678643625, 391714128, 358860776, 643494832, 557519545, 957649981, 245028173, 191014508, 845228331, 625078700, 415249937, 978275576, 660812861, 664469453, 123896638, 294379786, 38840960, 659092701, 6540666, 67386322, 819822526, 355755805, 908985199, 396739043, 896493919, 569765211, 32306751, 249356284, 704545340, 597723993, 129748085, 81686517, 883942943, 910079530, 946171060, 873729096, 249436876, 34451550, 319444910, 623624072, 27356184, 34059097, 200774640, 889545865, 422048429, 536167067, 254192035, 944633432, 385702743, 222607224, 269389866, 316201111, 256958170, 112720541, 15236000, 16916645, 252110423, 975521101, 722922277, 234987395, 194513019, 162851586, 506935448, 747028343, 973617973, 351600456, 61034407, 732890077, 355134590, 276746629, 119536084, 966713534, 586102682, 966654062, 864726947, 291517492, 774968143, 496072850, 108655557, 836491966, 298235486, 993598629, 308152442, 684282420, 148986466, 289717693, 117089014, 938034282, 385305499, 918651948, 799205028, 20688124, 384388227, 650469879, 672353631, 877618292, 7299756, 182370111, 473763902, 303800128, 430811573, 820138057, 248974121, 346436998, 859944814, 580888257, 938961120, 976853612, 682691999, 740209353, 16332590, 47963829, 504108755, 752891339, 856518094, 14402305, 865876711, 965301683, 631927827, 941770699, 268252495, 987373886, 257759849, 791810441, 764732704, 190268016, 478120042, 870634100, 531505687, 989844720, 115205058, 683430912, 295211272, 648627596, 384482106, 711616658, 245225794, 793593521, 557081388, 186929433, 724626805, 262476230, 63374483, 327733836, 348618031, 842273539, 142363871, 79528863, 435205050, 611069396, 454880721, 610934834, 27695772, 794829831, 376251935, 56992908, 342423215, 802445062, 395617424, 972699049, 6424577, 78853728, 245671656, 892417750, 451209980, 804464637, 5247953, 914921890, 29756516, 743171900, 678952774, 481507498, 982794871, 34210949, 779456099, 74890079, 783212571, 623914520, 216509661, 82511443, 788523594, 322785034, 99497552, 887398816, 539262390, 363135596, 90644975, 143641147, 999653628, 611074226, 581364530, 163809727, 529908609, 994688502, 875220505, 96469231, 95307908, 755249740, 282490904, 619687056, 314196593, 878316776, 687855305, 888217588, 292915145, 69310511, 46102536, 504666531, 942184208, 542526311, 295393672, 684588351, 74521736, 228376925, 214828179, 49237557, 428928317, 990341197, 772208506, 227721930, 792329074, 519180143, 612692599, 332327828, 728107805, 850603899, 226064829, 858754113, 44143647, 317229435, 439176171, 71032383, 392869934, 599195594, 158330358, 45588711, 134590139, 29348821, 763250028, 796881968, 819787265, 15578518, 805392025, 550259689, 759359492, 819113655, 202066216, 593312154, 281745527, 736301287, 381101817, 333581636, 775914086, 779782898, 341033787, 770664348, 706968315, 650690365, 932560800, 124014138, 311619396, 216507063, 313237159, 400317729, 866103943, 92335126, 123395285, 109367069, 680017891, 350046559, 124366303, 670438714, 389096809, 254539453, 960141539, 724524976, 379112995, 223148141, 11695661, 723671860, 334658439, 813021768, 395766232, 465222471, 704512848, 665401638, 324026325, 598254474, 711477398, 798939311, 6434459, 90322073, 857784216, 852773471, 227172635, 308990071, 333802152, 147947207, 894441609, 401179411, 366740410, 335460610, 301506957, 592991442, 16740710, 407225501, 998577305, 840650395, 402368371, 369033774, 647017577, 729440130, 211279606, 984861265, 855881860, 706335732, 36303099, 47789182, 712974911, 60918124, 196180336, 676651469, 507703964, 953936566, 583266849, 486734798, 68622538, 986403647, 443660650, 8675916, 813346245, 697517716, 48016504, 793419882, 563075765, 463180898, 945898316, 933833681, 410434759, 708327726, 153450271, 68535134, 141401661, 477131702, 697709374, 714350693, 727852780, 292468247, 134716365, 64756498, 212054696, 662676209, 470465144, 879154051, 997603363, 568500330, 52058885, 337973645, 707024854, 483186420, 334092593, 753186716, 76935234, 832047063, 507163132, 335296658, 861219858, 854302515, 448047908, 16768237, 118474687, 106142545, 769850317, 383792466, 641385318, 379323722, 882262030, 130524322, 392111414, 177795840, 557357253, 652358873, 482061876, 340271085, 71461712, 19736734, 827681210, 558508303, 207851810, 773195553, 926990418, 879406517, 377052409, 920469133, 91927255, 29615778, 7971294, 697358890, 664778949, 113295673, 593952334, 204682961, 938368887, 973041223, 416375775, 12774082, 196223489, 602518576, 854870986, 804169079, 894476234, 912099579, 172518933, 30815705, 640989448, 76757672, 529704091, 496400654, 516362613, 48615790, 644032331, 371735425, 338192335, 251949259, 198317310, 445031500, 850057349, 259313387, 618656959, 52801874, 566128729, 242435053, 19410388, 379263275, 40342595, 308473498, 432818802, 783201171, 301059376, 562780991, 950625011, 88666400, 142326774, 999572549, 533869072, 480317858, 130279630, 807707716, 294767442, 602559169, 874693918, 541387695, 921735412, 941578126, 387239229, 226606043, 107675407, 518124816, 427072147, 906334970, 542317302, 317357530, 906548500, 245603284, 797850239, 901798521, 787990643, 600270980, 28111708, 21553440, 30777540, 356997955, 111251935, 312062845, 994460374, 711453164, 328586238, 706718017, 11031896, 75640361, 984551342, 341956203, 887597119, 555521158, 765057569, 681283757, 977741323, 34644363, 545957525, 345018390, 932124004, 602461436, 618933453, 890039909, 223473545, 653481864, 939607965, 247487449, 47906187, 792860883, 29174293, 960514152, 812132486, 356745183, 343605808, 306853179, 920706149, 296098823, 171694040, 903113329, 564090837, 604618559, 794569938, 818803057, 528639969, 322205095, 617297851, 459127410, 242544756, 886052623, 396273228, 792748159, 436841147, 184973348, 552440313, 126063034, 577544942, 469070035, 416386219, 733298370, 918178535, 56918160, 701384619, 427822004, 283629403, 531526697, 464183999, 159856369, 589792296, 617242997, 21913227, 581029214, 177896682, 391685220, 924401017, 887093248, 977866326, 199218479, 631008578, 794741160, 489100802, 916993227, 249762634, 681238305, 949455601, 973399286, 849327598, 600167412, 935967249, 925564679, 92563443, 789433003, 962906590, 792953904, 514527170, 262393269, 96815788, 481156829, 399628008, 920274289, 356039764, 646606702, 939602687, 725385905, 57710993, 602606390, 590401914, 221268980, 55490321, 521958583, 951333012, 241656547, 146352572, 86185090, 898730570, 586900762, 277652890, 549377669, 279678864, 384474649, 29772127, 353678877, 971880529, 206474170, 668470405, 634204045, 763368922, 623707717, 169814565, 624086086, 90397284, 405334453, 273530455, 129740918, 58418904, 488261163, 303557037, 798496780, 699816234, 269375778, 740593380, 498520985, 217674532, 271808728, 548085856, 296806588, 306383255, 246064517, 809336700, 153947466, 786941322, 779950491, 847018439, 5480717, 90009247, 347053164, 324633548, 61887922, 277796619, 947246538, 31953113, 697682338, 97548686, 952199907, 261997172, 840130419, 820996403, 644354296, 157205564, 67399993, 3046006, 468981338, 751907506, 385614871, 418151787, 908790032, 843998324, 814673852, 637835108, 747171952, 50728496, 265403904, 284009418, 949932348, 723346733, 936795557, 984403726, 599037372, 425901508, 823534994, 540406872, 617768047, 239248368, 505150530, 42864861, 958943759, 740851550, 562104129, 402941583, 565702593, 215195820, 352904866, 231869352, 190214747, 285252663, 761654141, 497941966, 575655402, 117702617, 184372430, 122195806, 272540089, 332020591, 670360269, 981588545, 190607395, 125213716, 41962024, 299001546, 597492277, 124077650, 15668885, 872079855, 951281398, 18024194, 530476549, 612384566, 406675559, 8247023, 898250084, 676220298, 318961927, 510143094, 45931356, 76119338, 176286704, 15480531, 982570682, 137952864, 990188694, 67597889, 749679108, 848555512, 374621609, 376143179, 647146183, 28074363, 217473064, 564655196, 473381188, 87752546, 32657010, 762777660, 453004904, 719615071, 705495641, 998909920, 115908303, 516924570, 477599906, 94586530, 726190330, 523168466, 921348895, 922172330, 516466713, 912906705, 759509168, 289011153, 329032594, 96921050, 708528960, 755045531, 115194507, 822850914, 586168120, 208299919, 190642688, 892868181, 170624145, 35799892, 941742411, 485749786, 240795166, 905817355, 607681793, 670673475, 920553806, 975048916, 690923885, 441690997, 780847858, 788736630, 171943505, 701983400, 348282236, 211503586, 810780244, 190712918, 544514511, 975903754, 921513188, 362306988, 923883162, 196621653, 483661243, 174468907, 942783243, 978314795, 939178489, 218659073, 265787095, 892119101, 859481385, 909733039, 444461512, 886269581, 744203340, 952903509, 719165968, 841016814, 999950879, 471936607, 763991660, 112726002, 383332316, 27043250, 781325232, 718236871, 289641789, 864293592, 903684544, 163650401, 711524430, 256201745, 696959246, 955854108, 402158621, 501299438, 718596829, 76905028, 454293486, 966611147, 851369350, 57349617, 593964166, 458565153, 220729998, 987018413, 357042388, 640359970, 317429443, 979380972, 797784975, 354701901, 896632514, 642929218, 771280879, 784926563, 630536109, 967965944, 677958864, 752386364, 841836315, 959933758, 104877080, 914128379, 55342998, 604237043, 972432154, 925873949, 747345865, 106154381, 110660014, 670072354, 949728179, 303723822, 101661641, 85474390, 138891267, 39249944, 225569293, 128836686, 97195995, 663870373, 321658544, 428879278, 814112803, 316105761, 31292031, 668852076, 905827710, 270867335, 630306166, 141583373, 821563597, 928099398, 12794677, 360847389, 262292758, 552066708, 498996579, 181853852, 273665581, 523564824, 296757731, 992485211, 595877433, 79052667, 42303031, 966490876, 667378970, 136727225, 619567043, 620794854, 850321022, 540640679, 67913009, 365187653, 730047168, 580761409, 955584151, 631627958, 888730455, 266278494, 219104877, 464259400, 746093596, 96662340, 562946660, 481754887, 4438727, 615426212, 225773240, 156176909, 22037506, 421822928, 928827289, 508365124, 533538538, 615992073, 558055690, 552759937, 74028649, 357074300, 470952761, 945674506, 767247059, 694609264, 238975799, 135479685, 422523716, 112006141, 28804550, 145781585, 37997441, 375497962, 755976139, 941653936, 426633240, 314902398, 121109156, 886677873, 346868049, 977748602, 856984385, 435082620, 208360737, 205944349, 603182773, 400147422, 651741854, 62952088, 18417421, 985594565, 403320789, 991505889, 3525341, 637339095, 22980792, 750632636, 906426665, 962256145, 949070169, 10361954, 341747957, 174556667, 934548943, 429242823, 557833150, 57363672, 948630318, 49064502, 337149208, 78357340, 588635549, 9929370, 763930040, 271259289, 618019063, 868458264, 498230578, 921893392, 830449170, 983948127, 615479849, 118687442, 441060425, 599859412, 315367232, 950169798, 754841195, 445555709, 754384595, 869650678, 130162694, 253841156, 703319442, 156847473, 760415920, 998121587, 335471695, 694793882, 195476890, 815005005, 861262399, 358014976, 978914051, 717883577, 202220187, 431093928, 170817946, 620312902, 687593623, 446148474, 812812827, 51142657, 214238744, 880037640, 754252796, 54072915, 96225198, 353981733, 142211702, 719503928, 608735599, 806237886, 62057238, 397763405, 777277605, 937172315, 103711599, 726741503, 474454906, 561954030, 427332368, 111309039, 233848081, 142123256, 80069861, 739466847, 545714989, 56278714, 570554625, 8112158, 839138757, 249691108, 658209375, 705606932, 191770548, 627337361, 713954399, 648415810, 649592350, 804973683, 367097684, 907364094, 959306114, 679860393, 217896398, 798743732, 942045735, 725268676, 715606248, 867957437, 979674796, 917562475, 560359655, 512345735, 664594893, 813474264, 219726268, 344002660, 934661554, 994731282, 102922683, 160404841, 410541190, 150244251, 395155012, 939382662, 404543524, 273501162, 991679003, 858718253, 672126202, 744514572, 889269499, 249276312, 867678529, 376723413, 870574540, 219933673, 390306594, 122986793, 670072301, 882578344, 979203639, 417455294, 984817598, 321314105, 935464106, 714547584, 859995845, 426379126, 189542121, 773851111, 475689925, 782808766, 938684086, 942507363, 730820055, 292172691, 970021254, 285866524, 453931911, 636603921, 34145849, 853070647, 900232683, 478876101, 946168391, 220078461, 344556879, 653855814, 200995429, 589371589, 679533531, 246647721, 298545623, 728329422, 824353070, 483579853, 71287626, 437227970, 920427696, 210077826, 636736743, 436759245, 178966127, 192004064, 500250946, 784774087, 730493522, 610847035, 628785582, 31951218, 479264538, 246600301, 938321273, 248771748, 262262876, 859836310, 888555342, 291271401, 241221352, 251324357, 629496351, 663924703, 165322061, 162596618, 59715272, 701610471, 465149040, 837032698, 742590507, 678923173, 433429717, 992968077, 927851208, 59997829, 747147250, 873784943, 277102858, 518803472, 533424949, 534433600, 920979214, 813315487, 563894273, 697135796, 152063147, 281537494, 903566714, 22362252, 442840723, 467471433, 379341762, 291207911, 550030572, 900381959, 487086576, 503253731, 472982911, 975941863, 30400277, 473379837, 857088494, 842169310, 676816640, 997253164, 942778741, 560025008, 509899014, 933013710, 313913272, 334877271, 286479857, 189724977, 904825704, 603570268, 688848122, 879214851, 815284791, 419156567, 371899553, 812758572, 115467878, 927158205, 536534763, 729215356, 417804093, 823325439, 368360743, 277915247, 978073618, 110764490, 211055455, 730936074, 484029897, 444355806, 291381168, 446284651, 227537215, 806941984, 836824104, 262721827, 798174689, 70498723, 84266745, 748589659, 962559830, 4213546, 907144821, 543609621, 718657829, 205938446, 689375220, 400097513, 877613757, 567408903, 317697938, 143089314, 655749048, 216896970, 91228882, 464133929, 965501002, 224445442, 509614948, 66145695, 639981543, 613308493, 96334976, 269921917, 765109488, 177903166, 882648584, 37642945, 213479470, 103367486, 816273342, 355591405, 218061275, 74697203, 440082206, 967839114, 772387757, 929163971, 202310565, 180812295, 351104713, 303535273, 86689974, 518199078, 511197850, 93781531, 88106817, 633383607, 328997501, 992228963, 46189561, 502225063, 579074629, 679341934, 89490226, 671017977, 314985197, 600326547, 95299420, 963404242, 138589908, 996837512, 401432815, 517902661, 198210278, 316318092, 152597581, 773178608, 537646203, 835792407, 925039844, 702267026, 341925575, 596903324, 888707949, 981823195, 219926173, 735616762, 949718523, 819681043, 885391672, 24762586, 9483692, 996762248, 869733355, 675128420, 782279655, 735113855, 366011689, 738136656, 462947508, 105915335, 998891522, 378956582, 958015169, 415743413, 521768764, 473635629, 927134052, 276443721, 187820876, 815427096, 691115008, 899274445, 360867272, 238698070, 625873091, 36918325, 919678948, 350901723, 913092001, 711430324, 876810509, 110313493, 761507263, 103320144, 684719867, 437888702, 465896167, 937777566, 103898959, 477703323, 963407886, 419021263, 820873280, 638694960, 389598979, 534527013, 505910502, 414962398, 314120895, 122458253, 656029976, 344118231, 612067413, 477502207, 321338202, 573021401, 655749207, 70004740, 204397689, 328132459, 389318146, 814624850, 662709496, 170442173, 451739425, 163462063, 570240622, 245861671, 408306555, 879850186, 928773620, 594353778, 139237244, 941384665, 183849354, 449588055, 34970883, 21447659, 10990658, 996348029, 692496723, 630350438, 426024002, 775193826, 890679821, 700692839, 118414619, 240625974, 946750087, 360441165, 382785061, 81000083, 928723145, 561442764, 721218675, 293402409, 58917727, 32882088, 693063084, 412821544, 788187441, 888693910, 327889561, 863766038, 167679228, 134312701, 763346653, 110324285, 161001870, 506733208, 231611352, 627176751, 826229138, 666316193, 664743461, 875847240, 136646686, 692216306, 595338563, 967869178, 728597776, 299297814, 222709454, 950839600, 666624502, 687263398, 684751916, 502699829, 635787199, 750394979, 188329930, 168249110, 393721089, 752221703, 253782938, 807468741, 714114639, 595879109, 258064945, 830655717, 84221394, 768714982, 536570556, 843354272, 892783033, 342766677, 965607117, 633791082, 513404911, 415195228, 956825106, 459892795, 852904332, 437583023, 715441837, 804507633, 801954043, 806081984, 860852594, 922544748, 408158033, 179399224, 99761607, 288205887, 415706501, 150423125, 785961759, 670920188, 708765870, 621952445, 225422236, 191690911, 87470530, 118953735, 993962136, 113341815, 753753363, 885028741, 826510780, 328374344, 421529939, 686721623, 189613687, 273587513, 361659666, 229929958, 769764980, 436870983, 769015922, 604228461, 419887111, 568584712, 97353944, 458484896, 14961257, 489296542, 569246848, 862896047, 621329346, 200218478, 4676425, 357260771, 361153320, 633979206, 891207684, 499895801, 739626826, 5873326, 81765628, 745885761, 964614753, 552617829, 315453741, 63265651, 585575036, 3837039, 323359420, 36764803, 564839840, 350468818, 504336281, 826083437, 680393437, 426037892, 629750370, 310809372, 278046360, 486556505, 202174180, 585938656, 122761414, 916915865, 387708901, 126275845, 396601407, 185875939, 627345647, 1055532, 695749101, 623789289, 906945545, 125312217, 176331740, 98576097, 968600333, 299294415, 191427384, 959468785, 262137803, 534722392, 110521753, 239109801, 815798204, 827682398, 246709995, 420929106, 886718439, 432678589, 812921665, 737652559, 45655128, 75199291, 218050988, 697130457, 889148893, 468697867, 936032595, 166127279, 786162009, 29364826, 567793167, 162472462, 440423079, 117616481, 102245034, 435465143, 424448910, 644464269, 238112776, 1150448, 98375520, 191485577, 350997022, 462749766, 136528924, 752798048, 383066506, 645429798, 665239536, 887860130, 244205948, 525202092, 509715674, 436004457, 452968920, 111414152, 403708788, 341510984, 705204000, 200888759, 333049287, 248358526, 134412123, 930622329, 614516402, 868984361, 100309778, 751482657, 952352618, 448390331, 63354672, 351518634, 117200175, 239566530, 942840333, 102362295, 739293892, 222817412, 737540227, 652492844, 15399479, 601442592, 959856550, 621891953, 410960930, 784600480, 941214907, 852149610, 209076341, 901443065, 738961171, 852882069, 746616040, 522328903, 164875884, 193639427, 332151474, 865251305, 354510712, 60990897, 947593019, 612161838, 953404282, 719022791, 616720809, 834334236, 85692998, 827871060, 30179673, 847990050, 181084323, 478077778, 740464146, 824511460, 695882183, 742021661, 858788847, 607740157, 212069171, 985767043, 528250252, 465435899, 510084469, 823914029, 199963619, 428169616, 137022163, 982136495, 342146729, 82726699, 226193887, 817259823, 431242498, 198115446, 534084831, 894004, 737930351, 374533784, 831369518, 575397712, 661205283, 222914152, 291588721, 481039242, 762635299, 825829941, 503606884, 37819877, 506243883, 596298061, 330468561, 97115237, 108224540, 634384489, 809482672, 889313092, 266241145, 186527807, 294719535, 709549076, 182176225, 591273335, 676590350, 347641424, 340020606, 297111994, 272853812, 562114253, 877129234, 710329776, 724991771, 717168275, 526484998, 604400712, 965460251, 299721261, 4121553, 437250821, 398424484, 206817524, 215019923, 318057165, 639281877, 671419156, 15422262, 898058481, 74677816, 292780127, 132086598, 479781812, 610630540, 444384843, 999173276, 723846411, 267397376, 355197853, 394103683, 578120645, 793821840, 500729154, 271574762, 382972502, 37191934, 119391727, 202382566, 616396605, 790524779, 637791604, 224399419, 565818796, 61578057, 162634301, 388560677, 686467281, 879941137, 527783913, 959553457, 977777288, 365947669, 562233799, 520493388, 360961951, 3476472, 763984876, 219507094, 28199632, 262495023, 614345514, 564095166, 203382548, 683810872, 120485771, 805178268, 28912249, 106866645, 591241090, 673908035, 315387149, 971925177, 507590045, 23129233, 877152178, 743225907, 827335228, 298613425, 126700991, 516785550, 3414293, 909820416, 627154216, 652383759, 256169781, 329092356, 410971945, 557376092, 854896042, 12263521, 122094640, 302277453, 759982861, 59369622, 700233982, 572814639, 712248157, 61116477, 360252243, 247157621, 359173167, 777044512, 800596539, 713273376, 576652159, 341929602, 483009626, 840208136, 717825192, 90798496, 27639611, 192555487, 578486420, 140430203, 347266616, 609087252, 821286349, 281390895, 76092686, 690695960, 234345647, 6513694, 943405421, 745738839, 714898357, 409085773, 418645327, 448952034, 837571256, 255216581, 778814200, 731845986, 461964671, 226269329, 16053310, 381971257, 191245879, 795527579, 411451630, 940604212, 86068770, 189102845, 635110777, 122303568, 450743368, 46930676, 305585499, 319152285, 674524200, 6135764, 965075750, 685410354, 606112241, 457905622, 924335279, 851424627, 982836600, 704606474, 742119041, 879980591, 138699944, 298297380, 600456108, 443781285, 30443803, 988181923, 15783530, 320602935, 785914527, 485881927, 275561110, 877603071, 581286531, 598221136, 579807505, 760263804, 982868704, 263821060, 319472540, 378580143, 296178657, 968863101, 954617275, 133430121, 726772663, 199597548, 432437904, 24257103, 969984876, 426343879, 474048568, 496306232, 53799975, 560149022, 841946987, 693687948, 435854033, 133419004, 595439259, 571846218, 644710028, 643594930, 336705711, 236848483, 527037955, 224204384, 344737530, 838182377, 745248020, 471492653, 406629024, 180012024, 158107512, 856621979, 265363247, 30852015, 197488143, 587696658, 463892972, 833569716, 769405321, 326869948, 289202166, 670604778, 320481860, 584280446, 967717867, 193067945, 634082337, 238249639, 811686145, 979758375, 950455525, 621222664, 336735423, 324769391, 654905435, 10070377, 761044484, 626227801, 227960812, 412184972, 152828804, 876143058, 440739430, 434195193, 667482661, 489569423, 907671662, 530628591, 413169422, 40615269, 831947853, 695451934, 973845206, 480345590, 844013021, 510469850, 981995842, 121370501, 529349898, 935373161, 25117315, 712290153, 916874554, 901279438, 749382486, 797233158, 823692249, 756113809, 621514363, 926039436, 447885975, 204417677, 933965909, 973405823, 275635586, 979816036, 520115213, 219935302, 568425842, 26309050, 511350399, 904530007, 255279180, 745287244, 346847877, 110844207, 389651155, 483703625, 468423310, 185556840, 699273069, 200594692, 350601250, 57381625, 784300852, 883614960, 195709988, 631922215, 859694721, 743815722, 492100104, 792573585, 853235652, 181120507, 80749209, 616794329, 857530897, 817108874, 898951102, 581576213, 772949266, 30499388, 68934610, 389475443, 457519422, 616210534, 961445686, 403548000, 62696297, 36696583, 784620585, 368655599, 588230828, 935921384, 414997257, 768463998, 7816471, 912052576, 653717915, 364442114, 131201977, 896412506, 509089687, 22941034, 965270662, 237597715, 40881418, 292974501, 136266780, 266383853, 669199787, 803902743, 223257880, 13329290, 21584846, 658982596, 214589913, 590466660, 641327362, 624258944, 746510412, 418869563, 177941643, 470193946, 992712101, 830240502, 250888846, 151827540, 749136230, 722540562, 372405325, 937164499, 43093095, 965762008, 258039608, 279945269, 94221174, 971174491, 773025914, 459756949, 33184361, 766999865, 88946193, 880818674, 599033506, 421591434, 106710740, 275680290, 224042177, 378426033, 320356444, 51545155, 647873567, 846663386, 653534285, 158259112, 55604750, 186378545, 359511274, 152493942, 511784538, 112960021, 522363035, 399011444, 923870420, 691559349, 151485228, 820400389, 779352497, 413741020, 19197538, 78160588, 701440870, 176729583, 967341, 570208835, 49240616, 682683826, 211872950, 493672631, 495143251, 86421893, 872314624, 495181671, 723713724, 441113982, 210442324, 623429215, 353676778, 770008001, 85047098, 883404015, 305444435, 264808359, 592461705, 933271872, 315501657, 647751237, 281333086, 61315511, 922139431, 31415644, 802409868, 814701266, 201144475, 655316283, 81113354, 413887456, 804515583, 771018449, 610624833, 872345424, 521618265, 128902190, 859583167, 176959220, 671423223, 715069725, 131451397, 627998566, 777210888, 141852871, 812042267, 232530532, 264737202, 816808228, 302436404, 854703638, 368125244, 248497781, 291413702, 838597242, 343398560, 178227298, 685413266, 115702004, 867356014, 663647233, 478548243, 742047808, 710427097, 491385328, 409447478, 359639822, 847342330, 768907152, 627818004, 68610491, 774359234, 268551118, 155917102, 446206379, 924600916, 400185468, 668077528, 93527409, 703493620, 860575941, 474680001, 10347446, 973885746, 475575840, 401469706, 249155220, 162809374, 484778174, 940552325, 459664561, 333119165, 902627147, 616143686, 936377137, 972511675, 848960407, 132552695, 348594150, 398355634, 357787691, 291989444, 545368878, 195942413, 19674745, 729771464, 192556847, 752234221, 401467075, 533124473, 648422867, 113618822, 657094334, 417876121, 455088890, 686243711, 668423178, 212195748, 750816982, 303685091, 673534046, 682471328, 608340220, 417328952, 669072761, 278548947, 989866450, 579029450, 315547445, 266737317, 627211858, 281219388, 643679438, 667475441, 801864222, 346465291, 730559786, 81808942, 662746162, 879477005, 594612010, 301903374, 104738216, 4101215, 809797625, 148850533, 476199040, 821940126, 970604379, 821758181, 498203029, 920731722, 293812346, 63265251, 90474377, 404110113, 949453759, 518471143, 596969347, 352121977, 486554473, 486073996, 684063923, 85414078, 651684997, 173926711, 755949044, 752599059, 857300388, 169655686, 144306338, 778903576, 735205791, 564282235, 684916879, 205401736, 352670619, 42081257, 287847989, 34414580, 683319236, 505753935, 774314763, 463678296, 958389595, 231525131, 950525665, 937732251, 923851414, 306633455, 931969972, 381183704, 18524608, 483059263, 998570168, 268696559, 556978884, 375570289, 681052451, 883504198, 310581068, 919414453, 620602082, 934526066, 397114925, 710034782, 717604815, 251569948, 419762342, 855054959, 965192888, 136164262, 400690704, 450633631, 126692513, 855020039, 876317490, 47296242, 418876743, 336171445, 718962866, 629849054, 16968833, 334912074, 525073374, 316553216, 423083611, 7215827, 618301642, 163065864, 1075207, 165808851, 573707257, 164806142, 345395530, 253786185, 915058696, 920907565, 617713286, 86923233, 310868066, 832905836, 899490966, 306187641, 577883970, 314884563, 784928510, 905201853, 963335959, 296164069, 788225983, 43798654, 776922843, 646318915, 992244501, 227485389, 53472301, 331097921, 540415677, 948614384, 921314872, 374881488, 714992804, 266019341, 577120625, 118653284, 745297419, 445202716, 485810842, 515553401, 641544480, 168510497, 115838137, 78093747, 424110535, 699256044, 135420016, 932125672, 206722525, 652935426, 668544864, 15023353, 724945676, 576431556, 74391421, 619457924, 878923034, 329491357, 739380600, 51742849, 202909774, 364989586, 523033523, 597120235, 271714665, 746078927, 992176060, 295979376, 347529659, 283155864, 721017476, 466230220, 21034694, 702341290, 937140868, 333861004, 853549762, 639998705, 669684665, 542744079, 503978634, 728549774, 618126193, 365008114, 343282436, 769942887, 282472267, 6386475, 902705771, 216515063, 994556837, 949051677, 393422935, 704342403, 22177374, 549260428, 679440516, 441522290, 493756409, 57623235, 697212428, 282350173, 569297561, 463026255, 447008256, 59145465, 362804770, 888638931, 862897194, 629237446, 655673448, 859768511, 303129060, 860796038, 579687410, 157737925, 388834454, 699606254, 411837317, 564492247, 867553484, 569172369, 221903692, 700380758, 995731649, 559972310, 336938130, 603445495, 478668667, 552777207, 237807812, 989622865, 453476272, 667776644, 150177424, 279717521, 34207614, 546160730, 669533326, 824304694, 870182237, 839941464, 576812560, 777948891, 944831940, 966453788, 550783551, 288805169, 44198653, 325806945, 574764267, 627732266, 487413215, 848584916, 971961468, 398983188, 371444621, 382067255, 180005846, 262337358, 223194541, 473031270, 335077882, 708610197, 458068983, 985271788, 71472647, 461665960, 376142348, 646578021, 867343186, 652046478, 123812825, 689557189, 151911264, 509154146, 796618129, 4568744, 412438596, 649149392, 389906373, 828870151, 8623064, 979994837, 193568238, 413275392, 332599200, 782034714, 98434610, 592613075, 288409416, 620075098, 72937373, 638347599, 833386631, 207075845, 294701062, 539808846, 236883690, 490393627, 724353053, 185987829, 325933159, 521643582, 784510831, 17071048, 848118802, 312009207, 577269636, 358144276, 937073256, 850199619, 599675734, 240358999, 228910212, 896729588, 557241003, 285280444, 668937175, 551434878, 941081973, 305414637, 972435963, 628538170, 841975964, 465588734, 558716017, 582671687, 89899346, 345016963, 650687927, 773402728, 631001968, 924998152, 776204497, 369492707, 515117725, 146348233, 774947688, 679867863, 167981706, 459932979, 367285328, 503552207, 485147934, 404840498, 359771844, 93599110, 617445249, 37769434, 798201198, 295435412, 23732959, 791546950, 316995937, 265716619, 494237641, 143036528, 33864696, 694443843, 23703356, 839883197, 113242648, 676802920, 203081146, 230190366, 167874479, 781275348, 753876892, 365104668, 611541808, 435271817, 473200145, 135937636, 495844451, 853904708, 678793574, 191792005, 831049649, 231686547, 36579778, 315288521, 579562673, 90034865, 410000717, 378326594, 706828137, 700301463, 207220247, 313419761, 65003266, 98472935, 441378355, 387287004, 160345127, 10992913, 145440335, 575311004, 801864840, 492022229, 168183067, 119627628, 676017352, 247929786, 92443145, 962528798, 67652271, 2782948, 471008973, 743494005, 590881866, 488573949, 555779404, 918843669, 498861779, 274883227, 355821144, 536713972, 235438440, 392859820, 120537286, 164357392, 827126974, 735866473, 479183788, 709550917, 582739837, 909085062, 541885754, 595730333, 151879789, 51640444, 464181725, 581721644, 29398405, 163962466, 603042909, 752177839, 157905803, 821723137, 891679061, 527819101, 289448451, 467480652, 838847793, 457338304, 680974052, 215610178, 953486188, 740869321, 93111848, 481175621, 319592023, 15707291, 732437660, 56275954, 324816938, 262417274, 931545208, 177326779, 997124202, 612919534, 168792252, 274941450, 144269937, 767413396, 680990203, 432662102, 692241708, 605656534, 527838492, 410910700, 319142498, 525167260, 331838411, 838265544, 658309364, 757482586, 353157162, 110368781, 78596857, 362356794, 785242595, 35504621, 122578531, 344402701, 345485077, 149191505, 386451140, 970412644, 342571611, 667736864, 57555101, 710503010, 438079984, 115607637, 703536129, 339949083, 309503396, 459615244, 986073848, 64415369, 374002807, 430349049, 862421963, 238621854, 511209246, 630322859, 858464078, 306844265, 673125097, 238396138, 902584257, 393063133, 2502222, 236294330, 473811270, 468285893, 935611184, 423695165, 224728791, 888314602, 22896725, 814983423, 621820397, 343578945, 452109837, 846161603, 828508614, 565745464, 40252130, 978911081, 511483435, 191720650, 859512025, 925088769, 931080397, 161554475, 917927973, 801296497, 795447660, 994197801, 541465311, 580972157, 970368003, 966462147, 76106435, 991668931, 477498444, 76827912, 928420839, 959262804, 849069004, 584296898, 706367848, 519660888, 399156517, 665635812, 940465324, 226046988, 438976703, 949342456, 313972879, 859654743, 943565247, 715042723, 440131487, 682614431, 422232328, 982842039, 845564688, 568167641, 301253146, 624319448, 574014003, 243813507, 835827117, 341442218, 117491001, 893149486, 841390999, 140866787, 248519229, 738377228, 118044386, 140719131, 23450971, 209017701, 96784003, 770636562, 644995529, 54970505, 790125981, 730204438, 199491774, 3258039, 577005729, 122763546, 853632592, 796641250, 908985127, 812988144, 669630749, 412388323, 525548769, 71966853, 813006349, 942778610, 517088913, 551545067, 988997316, 305894653, 615545100, 839329871, 86016129, 299198160, 438956336, 44733576, 439923975, 110748635, 454335043, 500989708, 111145748, 279025120, 749207540, 333964389, 50892035, 289073747, 691567511, 317864233, 172925570, 22965653, 633514871, 550839160, 791781502, 319522573, 66786956, 332879056, 641154525, 450081221, 749668058, 504722037, 327053989, 51743938, 559397071, 894075432, 243568307, 215859800, 589652984, 695216154, 669000824, 882069141, 390427855, 997159193, 959872750, 859423154, 196525804, 724097989, 518301928, 14201938, 44425977, 482469294, 419009256, 82028559, 59496493, 853286538, 106776229, 119396278, 324752744, 383966770, 81257296, 694990874, 50951612, 99520816, 959119103, 801880425, 329222465, 159091500, 830385499, 521455197, 80971362, 265059921, 548604676, 664057066, 294642230, 144442633, 699459133, 50819187, 760803740, 965321474, 334832318, 498378553, 722475798, 994569826, 786107215, 465715306, 589519407, 640538447, 487159326, 12214561, 388736403, 370650923, 437357334, 888039483, 815984930, 640285414, 659821143, 850806132, 72501798, 965372444, 906579256, 508683312, 640866096, 962863352, 948733411, 956802136, 31828834, 261284334, 549570833, 566893428, 767918577, 32805892, 549711747, 110238278, 533748161, 975301984, 47874007, 29056339, 732020756, 908851535, 346182537, 522107291, 173521838, 128122186, 520187990, 658188120, 227569880, 366761456, 592424459, 16492909, 634739521, 203103919, 764245707, 133035546, 710482850, 351124238, 426289714, 920114903, 173734835, 548707109, 458984696, 478012087, 368880625, 44055093, 296267699, 554036948, 932902362, 614278564, 341475952, 688892926, 888994813, 587590419, 320160974, 344402847, 926967710, 635060506, 720320153, 124852345, 209559764, 64569748, 261783453, 620852435, 785357714, 294530471, 608499365, 148563570, 549246234, 100035834, 222503964, 510855957, 429573343, 752753274, 857756060, 7021290, 133412306, 439874602, 209989451, 184374539, 700241927, 777507743, 30194789, 151033894, 279944650, 963791042, 528889298, 280067726, 752061252, 497320215, 966708203, 306983547, 560988466, 250455587, 248821831, 231438973, 550047005, 558210844, 103069061, 406602762, 106769766, 892464708, 78038689, 160956713, 890333309, 469801988, 478473452, 207149009, 635056549, 373967301, 218809956, 945848398, 765572084, 454658612, 692302438, 931240470, 646451551, 91494328, 581819678, 421999213, 67360447, 774608685, 890067814, 237961423, 182997236, 414641840, 896936042, 570957840, 713358389, 277368599, 98667755, 981424262, 365923927, 788026181, 806143458, 572455558, 733238088, 969717276, 118349796, 187321877, 859384678, 726704737, 513596102, 588431076, 987922655, 907844750, 974088810, 128804351, 805331946, 283892184, 437322355, 371200510, 32245820, 178126591, 337565251, 230301572, 269725702, 781599984, 805713692, 655043934, 526526140, 219243449, 992492231, 531130176, 824617488, 359815480, 44206408, 184914429, 626191415, 354255846, 496269030, 77968342, 328615631, 224730246, 799419738, 346808608, 210132056, 490511022, 164261473, 10648979, 267037153, 131693136, 208514071, 541377371, 884891316, 424223421, 969791300, 114510414, 734719372, 572015004, 986525255, 92114509, 329166391, 435026189, 840585464, 620542954, 132779256, 39396256, 858237472, 540019993, 459983936, 92832078, 249302052, 616265392, 643463550, 737811644, 869448139, 965729986, 659140107, 203337976, 907265125, 338731473, 381838266, 186436618, 222586861, 323999573, 845905485, 130412289, 529868069, 75490879, 199149683, 482859375, 213640502, 445948786, 669294687, 574063603, 751602207, 50949007, 714424035, 478452521, 33724444, 1601155, 532607961, 306460360, 194703765, 196315540, 686905001, 212298467, 92030781, 570724085, 735704964, 104312386, 701600687, 131103481, 969920519, 529071945, 916587928, 641310055, 79073863, 790761278, 258616884, 755038306, 606634202, 8779576, 391982322, 475148123, 438635542, 759424648, 507473744, 355395573, 517945320, 875215171, 91878504, 40809635, 734671093, 494773981, 439612833, 863380236, 39077680, 700185201, 948619484, 363284779, 803164266, 759834299, 131165800, 488760616, 804988377, 369652917, 494029072, 849474432, 296370813, 514790049, 422023247, 998747115, 582110107, 27010693, 574347699, 744942685, 219688794, 336532494, 780305517, 460307446, 745844234, 830950020, 210951929, 751373215, 727365082, 820981658, 170332118, 696993417, 873296239, 461644371, 699345045, 498101052, 34161695, 358016493, 396029463, 605356149, 677840312, 61128842, 91802163, 307977414, 335434207, 868550723, 87713905, 174671568, 541568517, 921629981, 640096498, 330031514, 85737678, 558748198, 35001053, 592175879, 735479602, 260680640, 53496209, 517165910, 453184974, 852636222, 470233376, 722862294, 627313042, 402972092, 538562107, 458184176, 422370703, 186208170, 595616246, 436574194, 244947561, 288934682, 355232004, 787412884, 557000686, 711514848, 995570299, 282033584, 869401509, 774030150, 476865262, 817445194, 108587979, 33987950, 219092864, 446827099, 788625983, 979026891, 608091881, 249954965, 78284886, 164124926, 571415399, 191101167, 61317513, 193457890, 835929888, 815599674, 300898437, 897307866, 871702812, 734140593, 646565137, 394376525, 678320016, 662659796, 904717525, 45342133, 70523240, 945955029, 156012335, 2796798, 371298171, 173570521, 426419529, 883690501, 198793015, 708795735, 753410378, 17542464, 968744483, 618523916, 287745302, 726615472, 591447062, 995606702, 592156436, 370379639, 974617429, 922912905, 407493590, 534468676, 353446104, 548319171, 119597317, 380130212, 859059682, 443604174, 12700352, 285721481, 535493163, 822632136, 626164151, 729490892, 302417303, 799128993, 917003647, 46556003, 253924807, 532822461, 442766986, 832081359, 277207609, 379052629, 889642935, 570262057, 142145591, 745662605, 920694408, 699958585, 781744946, 521887853, 972881705, 958438140, 23367885, 376524222, 522901848, 644250382, 840572824, 40015390, 928435382, 879118414, 258314089, 226841716, 101042852, 534167953, 562081369, 759522923, 900836557, 689541408, 538908033, 998743026, 847639402, 96049415, 100025463, 258613570, 439125941, 345255417, 370619812, 983325901, 871435262, 398776259, 203959237, 48143237, 134400476, 30551141, 545932847, 800464613, 319919779, 555973668, 356623889, 209007574, 390430048, 414042037, 383243871, 179518390, 113556985, 686104018, 107040874, 622189547, 660329790, 574292719, 45730729, 325390656, 472374377, 255791376, 747621202, 534093133, 147423325, 38315311, 245837367, 261301413, 452504653, 984538037, 860187130, 181890005, 880540657, 214677303, 849387596, 717210697, 464025290, 534587110, 309380390, 368589468, 869288404, 811855206, 65119105, 880755938, 240575203, 65176399, 765153462, 738433609, 960734211, 764897064, 928097220, 134721712, 477821874, 974697906, 368566327, 845012441, 852965573, 653242097, 444064534, 912704601, 297155504, 629038404, 451641347, 50872048, 891936763, 674863591, 468843785, 342733268, 192556441, 631601159, 593402103, 26007601, 46555526, 70803737, 707846274, 745452044, 283920639, 505538881, 400045627, 473706610, 112275084, 281374502, 706183358, 637099724, 769106495, 484137169, 652165978, 554892606, 114514482, 939779287, 70529017, 787007427, 99480054, 117834675, 170606182, 693456877, 158281240, 136801763, 776294419, 252147475, 619790228, 890821306, 30161007, 927157855, 692413430, 825132556, 361096336, 423219191, 495304144, 986786824, 718780867, 80021704, 28981806, 603155175, 260517557, 919835092, 344769522, 108232521, 170599180, 777242601, 210851014, 868775073, 43074612, 922754729, 919768948, 256274597, 235579331, 997058157, 154272837, 350018944, 794296217, 664016174, 257027053, 645100144, 854338482, 715415036, 838851900, 270825155, 473377109, 350420857, 17435464, 996664054, 669077448, 574448862, 785286450, 448296915, 854683307, 59204266, 13391360, 537686223, 181620550, 866074633, 11478569, 237121534, 464044755, 975625949, 840889816, 240239552, 541332164, 309728374, 837125904, 987260071, 978682680, 999318536, 301001775, 319261801, 224351803, 49091759, 509474791, 31334807, 708372791, 266581328, 592345504, 142867035, 847567633, 530494242, 687272254, 652645884, 933888555, 426295218, 842827113, 859167385, 676684627, 958687774, 833468159, 808658996, 81307578, 39952996, 263423017, 782971821, 91937305, 654563565, 24827277, 728633847, 550510200, 467532443, 591277136, 582157643, 886637960, 422420649, 288213581, 161490900, 825266032, 646758282, 686717702, 89461817, 914225540, 754835256, 960246911, 553925886, 144223510, 829340143, 470875435, 794498298, 832889198, 992812818, 984256304, 408755673, 266876245, 280766153, 10838389, 15229395, 208493226, 893519503, 358813862, 556305670, 221729844, 739558746, 225737295, 697090365, 773902344, 798552680, 635141295, 267475332, 456394575, 582807274, 61977547, 458083681, 697519998, 676067630, 865869404, 591333657, 469407, 47967297, 974410003, 532367419, 580151069, 57772939, 827030482, 651322250, 25331599, 523872325, 273183619, 570635712, 22472034, 32679200, 90892752, 572987119, 259284665, 162843774, 223277148, 596832086, 215927330, 833659230, 805688288, 531058356, 339534624, 359274332, 622540222, 528380779, 837432395, 348865171, 857943116, 117519714, 408482423, 637892835, 885545998, 306290376, 998503416, 350017167, 968820485, 380077490, 319787465, 293164593, 79805546, 872065018, 266922716, 187367971, 611732402, 169944317, 877109401, 918287345, 358577272, 509791195, 72714174, 874636587, 408938185, 588190484, 230492761, 767659766, 814072214, 836264015, 522111111, 92041971, 208100730, 5188531, 633162118, 711744201, 212705674, 746927221, 369084481, 571687968, 4019929, 73079793, 54931752, 255155009, 778647935, 287422051, 995461431, 731430867, 958107880, 601441669, 944339053, 240696120, 479987465, 756941107, 938096993, 435497167, 251342999, 47246590, 380400, 378921561, 678923068, 683457248, 679514373, 901206652, 916039659, 810320748, 369906007, 993868584, 434341713, 854865358, 680713924, 43342374, 499225667, 956961644, 547433701, 289242508, 500016522, 44796830, 784669690, 36113360, 74383380, 834075697, 998787717, 898032937, 990154921, 379217430, 809625720, 246056730, 698456930, 531876987, 372384730, 177578537, 306449710, 513119607, 787938784, 161829180, 763801983, 512158397, 656241652, 581992132, 722595766, 700630403, 580595237, 797076394, 840625597, 970685368, 49383171, 515297114, 576192084, 321698959, 57626294, 449469962, 479440025, 977210597, 528390046, 981426903, 387858787, 708356026, 68012653, 180640861, 563241786, 336836569, 413878657, 464869512, 454087798, 834989022, 287882084, 851018684, 920614860, 594521346, 890768355, 289010105, 117675677, 382959620, 477319870, 949587082, 770300500, 915793429, 833572249, 388980124, 572480195, 807805052, 827816163, 958302306, 797533982, 759109030, 509277516, 705741451, 550443145, 928381964, 882808312, 380659138, 659301351, 884584130, 758714167, 998176086, 540304443, 691657079, 664994969, 569135367, 975378833, 935863538, 515599337, 755959900, 524853352, 705271236, 700041070, 94838429, 850696089, 113103298, 955477193, 736798537, 892350421, 811929810, 377335308, 997512563, 743511607, 901712099, 866292899, 27096478, 426655705, 813695378, 841389237, 514858479, 868720486, 941432213, 224705509, 470005716, 771211542, 140634430, 315431649, 336548574, 203858814, 751709864, 82463757, 481361671, 433670277, 639114445, 576564016, 358298526, 415947170, 94003859, 930161607, 376482643, 434737576, 752341099, 832707648, 227701622, 554616294, 895762186, 73491673, 133267170, 281043819, 497820687, 593945226, 692103083, 456176270, 809562899, 831301673, 599139760, 756716925, 52254788, 696429417, 55273092, 639351466, 510165885, 838305699, 14442966, 117118820, 571131481, 210618876, 681682091, 728552829, 802875248, 727371674, 397320828, 678914573, 399387193, 250115586, 667927139, 554580202, 651272305, 362806533, 830279391, 586301773, 842953832, 223303780, 402454635, 1957989, 961849065, 609805299, 269565002, 95923760, 255571054, 341964075, 951811059, 43092861, 838728270, 585814105, 117466642, 111030447, 638106714, 219203917, 86669764, 913432587, 823999304, 955335667, 47391280, 138053297, 268514424, 8186490, 121459210, 360223796, 634764260, 679535853, 391199104, 567774705, 635040566, 675376897, 741874494, 109940387, 189975501, 284572843, 157415623, 923457481, 851696722, 448814349, 689952576, 829107027, 213533426, 54423502, 748083865, 93338, 183922555, 758026802, 640028942, 790343742, 57834125, 600312380, 472269866, 320101221, 377116351, 436664033, 767214359, 884418428, 690553882, 644951348, 508403073, 668228769, 284097989, 167753562, 351372558, 146800885, 119824166, 864429130, 10193587, 913887298, 377339015, 795831102, 786315516, 787856480, 586738231, 343568630, 784957942, 550481868, 659888747, 385902891, 747261261, 436991539, 549302297, 582002497, 729534417, 731425066, 186165595, 803556665, 551771519, 767065771, 911458263, 433296785, 113864806, 221398332, 402550953, 40548491, 683569572, 237638425, 810057684, 522945349, 753799508, 973577586, 880307509, 456878498, 595893812, 179845945, 961902732, 832621090, 868877873, 222024783, 274806570, 120963754, 84521158, 914482996, 757211155, 539294915, 586097104, 244025255, 996851551, 147543102, 479409372, 906962161, 713479530, 796684339, 380549933, 920097425, 504095758, 610683394, 105454610, 583865943, 318824357, 809508039, 509815016, 610266369, 329810726, 95894751, 423707543, 515616031, 795729321, 518508231, 465692459, 342780805, 104062168, 159337719, 259265016, 184608525, 181252567, 783972339, 306170482, 391063340, 676800496, 234782279, 363016993, 229870973, 928563760, 818336433, 648249217, 32991436, 702097261, 991285271, 739472824, 72055906, 172234248, 104188538, 309100839, 591253223, 241533998, 913541312, 785436237, 850720035, 604049965, 69842566, 439762486, 781242529, 295133609, 176748170, 212906353, 163622726, 487922345, 397834479, 117550594, 278305327, 457102352, 173727070, 968750663, 367429947, 249837036, 517617342, 870288661, 297663274, 546369669, 512231212, 833565086, 109648972, 235278883, 771075087, 596226665, 836320098, 614786262, 608426600, 619969523, 417038902, 322258542, 84168929, 627371488, 513614140, 304964475, 952171318, 171930008, 455213495, 813680632, 171794508, 7126136, 484822638, 359333654, 763161418, 133959538, 544955635, 610183221, 689988899, 539828851, 743877649, 898230760, 396401733, 259791890, 385320421, 294072315, 491331815, 290771070, 205333424, 335104243, 248120206, 747968326, 412943120, 700441562, 336302668, 811958826, 179362179, 49626176, 190364478, 177469636, 299822140, 566544731, 308355711, 183081548, 251881558, 813235453, 713246378, 777441853, 173017390, 827927713, 616971844, 348771420, 528448639, 829144136, 2020721, 667032270, 483854423, 605824058, 40732549, 20519761, 175357414, 983060023, 713599754, 923079969, 375075366, 585612747, 434468748, 619187864, 201691076, 25158769, 498528215, 927519352, 514250265, 921864954, 253530107, 743969478, 219227564, 525076051, 113513371, 651078652, 865802432, 991744699, 799478070, 666436638, 771881200, 710911994, 589194115, 873936611, 234038077, 502208452, 825456155, 506463733, 697447995, 341737431, 240385641, 643678554, 777199240, 636196770, 299855467, 199344949, 943657945, 243034395, 807122556, 630620258, 774873345, 260816137, 998370121, 216164020, 744087290, 513852598, 371417201, 168780032, 959659758, 113515888, 530423322, 659876021, 800392972, 675584446, 864373946, 473893313, 538524914, 126320973, 870993273, 169911107, 555622277, 808638157, 847495791, 425909832, 279267551, 667006867, 568103850, 952359827, 17414912, 118653469, 518778758, 164168856, 990733836, 277594312, 579777016, 83297385, 289430044, 583499276, 685269217, 231441707, 97643295, 399084790, 642521549, 476560354, 831597276, 442687724, 476151997, 400944227, 57625914, 600537531, 928918496, 645837153, 469538850, 74832071, 836576052, 369483636, 720391512, 762415508, 633526306, 481002549, 821608297, 537581429, 791731313, 411898499, 732965328, 789171429, 539254999, 127155137, 123507524, 938131560, 927983478, 472448003, 866178388, 652411071, 778767043, 463253787, 485986803, 160623439, 601782572, 456420353, 639274405, 225301328, 482124132, 945820985, 494024602, 983396298, 456784391, 198902017, 541571961, 195295662, 260623354, 961412244, 996665372, 135870594, 943518691, 186613738, 291273764, 145767780, 192332498, 10146719, 743978966, 23978642, 322113505, 670122736, 692109117, 468871061, 819721732, 847057593, 131113606, 661773050, 898593085, 698823924, 789585532, 477477867, 475233480, 546459996, 21155250, 454684391, 735499859, 377812990, 625829899, 820978298, 734332818, 771965315, 219260118, 753159774, 573480545, 864211056, 902726107, 554875251, 277578465, 630206879, 43140437, 457026683, 389626525, 516551220, 163478315, 88307572, 246811592, 928503925, 137428841, 529521438, 787973079, 438015832, 101230944, 253915104, 453249045, 332240828, 298765357, 297811259, 100543107, 345523047, 544598333, 306390480, 252010735, 265557618, 705367556, 426093790, 481199811, 11887082, 956767985, 914939898, 342304995, 904977065, 289789012, 311407154, 325714209, 58906922, 592712222, 946982581, 544375311, 60985398, 303620877, 433530042, 588284925, 266282306, 426296131, 206275292, 900587865, 383691923, 30653064, 247570093, 921539313, 442447378, 739282390, 742805953, 69475946, 762035486, 397386310, 193790143, 690787313, 214214253, 418827472, 557206375, 618323129, 310873620, 425079903, 495428745, 276125259, 346859500, 673547135, 98513445, 978897453, 473723837, 449377163, 414461438, 929743929, 587316159, 997255169, 654131058, 154296012, 73850801, 341025863, 62531789, 987676791, 548321886, 451941473, 815881952, 723801484, 555271202, 207947624, 803492398, 886210115, 883702861, 671688048, 241113965, 957382680, 644028355, 283189088, 264249541, 816037102, 61736396, 273547168, 364059628, 527769840, 132965132, 120787025, 865126143, 934343154, 59288859, 88269936, 627438160, 590655534, 360265228, 323126529, 154366562, 363578336, 61191023, 347880708, 553539122, 48465362, 452568422, 556258818, 539537605, 825787608, 844402385, 714058909, 46953840, 259716867, 737827018, 142944309, 914059328, 359615623, 445866473, 895820641, 329569940, 166434152, 338527689, 574009253, 58588095, 148891667, 811846205, 26302066, 464531611, 869044022, 358973023, 758997138, 23735332, 51312855, 136766648, 88254328, 205339132, 437856190, 271749049, 991492432, 201240569, 801237850, 604361170, 569877638, 740467967, 976698140, 970922428, 488914391, 694366818, 459312760, 61262524, 394535148, 929557763, 628105754, 131145744, 471510212, 882755064, 401421829, 896247667, 509294963, 630183502, 513643480, 652351247, 696174059, 471315985, 789521966, 307638898, 531351174, 155202288, 451652619, 655062564, 857784087, 58325092, 203246922, 91821522, 529842008, 477659777, 139560895, 710499923, 102925640, 104538792, 545842861, 345182187, 837501801, 650134856, 364998317, 87348119, 682788968, 86939737, 340591252, 86340719, 36821649, 716050927, 116338675, 691314967, 425421799, 608518731, 441002908, 326255013, 624272601, 935912556, 117111197, 33254811, 569274604, 810383453, 256558842, 496867703, 801802648, 495044743, 897780493, 235490261, 437394130, 811375926, 362888943, 829965481, 49409333, 241200774, 804885617, 382185342, 273950174, 647253803, 84539474, 183254988, 252343687, 286342134, 506958482, 7390900, 298830821, 138916273, 307039102, 171720097, 292841969, 155062612, 117130804, 860458719, 448654521, 719463856, 582690640, 698629914, 622936016, 163937198, 34805736, 664356567, 69931922, 618731192, 653739801, 19245446, 698050560, 802790548, 653085486, 300277502, 948220979, 207382921, 62185198, 300684474, 814766104, 986458949, 583003191, 300044312, 978805693, 880953429, 193102062, 883356026, 884686904, 452830167, 753240818, 58389120, 205088257, 392565975, 568105616, 648117105, 405028614, 56520106, 464958847, 200260991, 277425145, 648540072, 162076059, 133550200, 299357569, 122541343, 526819942, 210095317, 592968108, 705252281, 752096525, 355859776, 333052326, 11877383, 522040027, 676379929, 859359595, 472518811, 598996598, 643821314, 751695843, 516909694, 890620436, 635254831, 453632946, 388615982, 536213330, 340942560, 120399732, 304484611, 60328274, 812699975, 132237731, 205935962, 982193444, 359796512, 554661887, 794050566, 141407647, 994942633, 550901469, 393005957, 81480175, 662482413, 521137625, 828972115, 41143426, 915224670, 346424486, 29275832, 732615479, 523111481, 236309480, 650427112, 571393529, 813007246, 815902671, 538451937, 634313066, 878455381, 280412050, 229005131, 313045486, 960908331, 473063139, 135153576, 365934874, 652996131, 166661697, 681557781, 322168, 63945311, 223754680, 432269577, 265944615, 113724324, 441981293, 366994760, 699358809, 594770959, 133210546, 897919269, 709013504, 848027968, 747596872, 680105254, 558138361, 962637226, 858379499, 68044369, 420709805, 882430047, 378223100, 196397055, 530838694, 433978674, 49609431, 140556671, 996916679, 71720302, 811738530, 585872600, 514376782, 437811587, 528872300, 603036818, 795726182, 473778217, 130596837, 527041760, 458778341, 189386855, 803213980, 346672636, 157566088, 228090858, 73889857, 636094370, 902549649, 528158757, 62499720, 204424153, 288421236, 75849298, 960633381, 283838932, 990229180, 601739599, 600429032, 840446709, 59439328, 354178094, 399462825, 716426394, 893605603, 854696049, 544754960, 447425694, 937249152, 312149720, 232392822, 567231165, 876399978, 420112666, 545960236, 292661495, 501763732, 480508643, 338332138, 316826722, 284346796, 737164862, 267518927, 416167368, 176465791, 838256623, 195111176, 997801822, 607226666, 977795764, 209111414, 821514105, 636778007, 834241271, 870462154, 655991146, 892074968, 30060285, 684303873, 491110421, 719634820, 6224906, 322443631, 434548654, 210679850, 806464844, 626370064, 558712312, 56125666, 838966558, 326616786, 364835918, 146567267, 174494305, 38672100, 991943211, 418148348, 822316095, 766655025, 867579554, 172418542, 210141607, 619924418, 190254364, 201136337, 388964713, 405576870, 681983591, 872226000, 671944501, 888007639, 439185866, 267109626, 521282534, 90454733, 54630792, 767439718, 309104443, 578177831, 196803327, 315892476, 848524473, 108235765, 435748636, 647505522, 94243038, 325361612, 143761691, 255263543, 834690894, 545336018, 680901865, 555235743, 176468062, 29544598, 741771603, 841586438, 566470504, 198216458, 284628024, 501334223, 246220961, 413672984, 572332347, 668228261, 900577714, 148737195, 732017124, 703193842, 602746246, 492504625, 508823931, 240794995, 737673156, 211758526, 580431704, 798644049, 385588856, 241708893, 694834295, 770663863, 94357023, 873179363, 871327311, 944977430, 91323765, 957988656, 259856151, 335644010, 774428287, 281707344, 873808526, 129898675, 871465648, 529457121, 935148369, 947789605, 827389543, 895386630, 585226871, 621701753, 308632401, 134376509, 175030232, 487743005, 940902850, 254400800, 941174731, 764093412, 443257598, 296824535, 413535041, 608069230, 338626884, 662770239, 507989872, 894189200, 518249244, 582432679, 787210691, 138058330, 550186616, 637287299, 679669301, 32832696, 484693498, 687515663, 292676484, 645774587, 14411267, 907399234, 956172681, 312998994, 860588833, 563402183, 826837944, 165626203, 812950749, 294371968, 105544951, 61463797, 648192088, 207805736, 838681823, 959019299, 502728546, 10186795, 19828995, 400798578, 809290390, 701278953, 393381320, 159184168, 128341925, 292586161, 820227322, 173872500, 260452783, 233443652, 259908695, 943664896, 686352128, 341085206, 624014292, 288712849, 666813212, 339816098, 41699771, 1814833, 557906730, 83336674, 600700815, 835491957, 88223631, 572038677, 731106820, 998497643, 798358226, 136996749, 10450722, 947242205, 973681991, 463188688, 482363350, 772535272, 585869784, 967839683, 756433989, 241094651, 160141021, 846140427, 268332082, 509014476, 919993662, 710276972, 375552133, 721661759, 412978543, 915292892, 444867255, 884585085, 273836389, 932914538, 511872483, 598501049, 839818942, 448885807, 962498640, 103089890, 19150473, 403929569, 90957064, 842702832, 710780352, 546568949, 355489274, 549018702, 309715360, 403214968, 540752425, 85279297, 887381029, 228061953, 642335421, 275904415, 396427604, 775293557, 859539536, 636790573, 345411529, 346008008, 502646736, 410124944, 636437421, 459102362, 497404197, 424799492, 722335324, 136629119, 319172818, 465729067, 256432270, 876587429, 533392686, 372143529, 194423664, 102071516, 897689412, 194974909, 784857017, 32450937, 671229114, 280513640, 914225988, 221717038, 984256190, 614402559, 883864286, 180643726, 38750980, 289167901, 638615081, 866870788, 481085215, 35616489, 786964468, 402637777, 363203074, 268682804, 421681616, 48583634, 577103446, 902817874, 57219506, 399363603, 451633730, 247263396, 559577075, 637624284, 57230525, 714136375, 755104558, 459126532, 666950282, 84945030, 707972622, 408211325, 560852417, 470060983, 803825898, 676816221, 422372419, 921904225, 147790465, 803063661, 354929779, 990130933, 502810258, 195672241, 529933350, 360391150, 670669009, 300879473, 48731081, 413016888, 308801292, 815435658, 199997205, 618700616, 29491083, 888283251, 341529152, 35928391, 138732873, 382740640, 649509378, 632211954, 926331317, 965362046, 253219579, 174591, 632790722, 838863779, 425974122, 230029495, 917084428, 604008295, 210095150, 380502018, 494843759, 840461022, 401652809, 545601182, 121407952, 52013442, 853334544, 718831376, 382302370, 840985523, 461108517, 729899555, 286397563, 573354080, 921864635, 144751586, 203054007, 732920145, 314523322, 711303206, 823500256, 405586337, 300091635, 917544310, 662498935, 124201041, 412570562, 825245328, 879108678, 596852552, 446395826, 236755065, 567050868, 117296142, 495525494, 590696241, 137913688, 215581299, 6449771, 885884829, 927443283, 998669439, 654222369, 295310590, 581419990, 280639469, 997702347, 408798652, 295868433, 151286290, 422808327, 754738372, 693349772, 251733316, 107919954, 556726895, 537402457, 749377607, 541251126, 898699256, 241527742, 172277709, 374611593, 495068848, 726216468, 515580940, 67752787, 786763000, 898697922, 426045291, 485892726, 911208650, 969832185, 366722576, 519364908, 330090892, 645241337, 830386518, 901562196, 357846123, 515827170, 452385134, 487846333, 695760287, 578985072, 242640251, 725634605, 653762654, 273309888, 168079196, 14589326, 630075112, 345165501, 510472464, 165347701, 664671315, 202993193, 438677506, 493944443, 594295140, 594620455, 936061816, 400834033, 467629905, 627538636, 251587921, 527618001, 74820491, 528415947, 417944473, 487835556, 320656540, 2375437, 519930607, 710883198, 698383808, 192589417, 783769983, 156952084, 500485725, 664502443, 18761216, 296545074, 146896048, 746075401, 87584811, 870085705, 856238689, 500754914, 15533633, 641602940, 569596160, 107376580, 734815559, 444068328, 510589317, 55592968, 23008747, 190303987, 966614155, 346689353, 765247264, 448017611, 299421490, 160244733, 19417185, 162342783, 525798597, 100370736, 764579802, 814682575, 154377733, 788739209, 849254315, 221293476, 800707491, 428163281, 877199110, 636370280, 793948328, 579987892, 673842301, 50091115, 827570103, 717096905, 520743765, 78020204, 589500642, 442547943, 743126218, 402894199, 882554789, 199815076, 759178071, 856586733, 740627889, 575204315, 350879580, 580655951, 61703075, 271391228, 859993801, 961940131, 699928783, 963383481, 71881021, 610737159, 917418370, 608769105, 515027937, 199450190, 930634468, 363688696, 413837979, 194645008, 666106356, 621862108, 187630965, 165789249, 596917684, 258170101, 261830277, 421585842, 117404489, 755126979, 607851765, 622791475, 287467785, 188358259, 63568178, 671140093, 947523396, 881692874, 877175242, 971771790, 129937306, 65281010, 188049626, 756544815, 472898527, 469655632, 153015761, 864789076, 749885383, 184964592, 846359773, 595671130, 17515851, 797539469, 446048906, 107774162, 696897928, 507463782, 800493964, 728224618, 301691544, 293200705, 684794235, 976087363, 174721326, 125729694, 625669667, 83171018, 353844160, 679639341, 74372779, 292122419, 264094510, 61361029, 501117048, 358207400, 567993926, 972866563, 903120874, 3522598, 643845585, 450227824, 736729672, 677160192, 909668889, 908011503, 768268018, 525187181, 73511904, 322206698, 551502843, 116641116, 184797919, 423286987, 813081905, 996595510, 832730047, 486831972, 362721561, 370468251, 540028029, 205036212, 701388962, 985331823, 655043486, 749708969, 240074110, 657619956, 63999006, 580842836, 569810449, 432548106, 385071969, 546969284, 676026530, 467381275, 113087668, 90214614, 331834912, 808563731, 859766504, 530945433, 592223301, 594144488, 491226684, 790970126, 970643942, 498467026, 757091907, 285259536, 162452081, 933362348, 944139787, 278221650, 185188683, 135361719, 358874857, 563476838, 937019345, 760411601, 832892557, 838819676, 454790293, 449352378, 673547031, 157047267, 568847676, 998924284, 824140570, 805260106, 68276723, 81588832, 775065300, 694624359, 267174410, 984406769, 151384322, 87836165, 422569407, 583448727, 859566842, 310375817, 567142493, 735091031, 16941791, 635800558, 797012996, 161100242, 810275367, 738403226, 949335056, 277160675, 974748425, 523359398, 705375576, 510945771, 223171499, 724861095, 786846214, 429171029, 580327044, 846358199, 623728973, 604098967, 969073570, 95180330, 450163322, 337946657, 1790897, 565958823, 700031354, 331405964, 716441314, 866921564, 854790309, 201631962, 859857424, 781657299, 738392265, 998290426, 145894726, 470553313, 423188173, 989557847, 819954932, 224147016, 3877708, 842743449, 651776537, 341926461, 571959088, 320352371, 750542234, 527563164, 334434547, 856675427, 97390943, 898747037, 74767758, 118438563, 943330247, 467471391, 793903924, 38286925, 298595635, 798674822, 358936204, 503703191, 5901319, 92629468, 476981715, 693965631, 688678684, 156385971, 883222158, 970839446, 16116271, 107040247, 933896779, 769249691, 682595542, 398404018, 851870397, 796737982, 261070235, 930936335, 194094412, 920582493, 657756810, 582041854, 521669826, 492120736, 163919888, 971218157, 201336106, 558816275, 642898100, 78945428, 739648107, 25274450, 413068084, 292541227, 18584815, 680090111, 442496644, 249151312, 790808240, 222962717, 699619525, 199854152, 132366496, 321746552, 301572630, 965261167, 925807473, 862336731, 252635933, 393874191, 809921231, 175555684, 256365035, 133769441, 174555748, 584657016, 250124228, 932731542, 598791175, 442904214, 46660788, 925676346, 613760353, 936357230, 916399726, 650529453, 238155113, 762974283, 531793220, 429673455, 575590935, 923054102, 553873592, 139832305, 963374559, 33205340, 314801125, 894417946, 198052493, 521007289, 954468367, 834876994, 292185013, 909646384, 184510609, 831608351, 748291262, 122970134, 645665575, 208957276, 431894166, 914747947, 323308185, 488658473, 309723430, 403546502, 121974947, 626825703, 185577210, 474034389, 188932536, 822796016, 464072770, 795964484, 475941189, 310662791, 797095637, 61619659, 462420446, 555068846, 885829220, 394615491, 203553982, 809211673, 602175854, 905844105, 951266774, 425499942, 660268645, 215527307, 241020174, 645570977, 501194257, 964111869, 884568704, 295798648, 285829252, 747721178, 102196673, 133200451, 57050506, 892196282, 946715408, 948790970, 429258770, 961784800, 751292171, 489475190, 569293792, 800627737, 17646848, 544175338, 353593408, 788132439, 124847011, 918913408, 980192081, 933766429, 397675662, 822888159, 206296301, 143683133, 863859908, 464672195, 834270554, 45132572, 702814856, 252286497, 722242575, 699251017, 222825891, 413343826, 878076900, 442273007, 199231760, 532326173, 84102481, 423385468, 89327241, 855286952, 449109233, 749624093, 769241120, 895083951, 514150508, 871478549, 830560772, 551275157, 747730452, 660148300, 253983727, 642149262, 195838550, 280837951, 973667853, 432274027, 898210487, 342213070, 553910509, 789097813, 312092351, 991222966, 70934914, 219271508, 767886533, 746821811, 506468614, 907340326, 89002192, 831013055, 781972232, 449525227, 364996442, 984595344, 258134408, 665473949, 535703625, 30064561, 463624722, 128922812, 897606134, 841139988, 659568122, 540443749, 747560260, 615433555, 335928252, 852609335, 412288761, 358810567, 347897589, 632138809, 602365977, 790414181, 676971047, 311637081, 525209708, 383620192, 378978509, 151147462, 767212547, 686078500, 740221849, 174846033, 722172986, 996871732, 941042884, 534774064, 170428574, 406642361, 754292593, 673098745, 912759120, 868657052, 131400364, 644582551, 82939642, 612900486, 726028494, 868455331, 491305009, 82212970, 430462539, 250924050, 868819778, 47716315, 803205115, 709391569, 345958897, 88841286, 978953477, 539457011, 735918799, 28387584, 805257994, 888478831, 45521874, 41997365, 320803690, 979666676, 667764336, 278942179, 631913615, 749035543, 535696787, 393774730, 524812811, 60293141, 66459495, 775065422, 251285466, 360204401, 889913473, 954649867, 83914304, 892271018, 371500824, 413878371, 173765568, 153686988, 14743823, 211128434, 557090042, 365495380, 430478747, 552976334, 993540772, 543079400, 354221092, 954000708, 454282672, 762916725, 346083762, 615964270, 556324755, 714475169, 332734540, 629733239, 84182964, 722126580, 60661819, 466498674, 564149795, 342921862, 110067080, 661105130, 768625941, 566781434, 864099156, 764099711, 988554882, 645379247, 359375653, 275030085, 397065836, 303787945, 88093541, 867398725, 167203858, 57924455, 2135641, 806644082, 210285306, 127219630, 88803202, 887323864, 943661146, 777203529, 241754656, 152825901, 214133602, 401469245, 964782324, 945655455, 604506937, 549191444, 114982118, 363858456, 785175775, 605734343, 861967851, 604266737, 863167779, 145858098, 656612277, 144103498, 620012342, 482174035, 375568295, 620645890, 77493377, 704834521, 719345880, 374915326, 613367260, 439745964, 295947293, 781605486, 187005954, 930965469, 188971088, 88038904, 380958417, 998713867, 361125862, 405291331, 631082236, 260196428, 825193541, 944719132, 864520077, 765081327, 988683483, 838884664, 752762491, 238245137, 32114683, 178536022, 775629160, 696267387, 600608187, 880376554, 222439488, 825373958, 517326931, 809667325, 188307539, 598416410, 206917073, 772073278, 167998322, 384290034, 697006275, 73691729, 6302948, 544625090, 267551595, 47156792, 727169948, 694802793, 522772178, 947691233, 985931481, 1230038, 993899611, 810653177, 808873440, 508042615, 272109084, 86627650, 230531656, 576495714, 120948268, 996948149, 732107686, 35207609, 787298662, 590308652, 143327794, 886726886, 687177908, 102286101, 612754828, 809482899, 37104337, 570972230, 354252560, 425101570, 33562334, 823855938, 666199381, 675901946, 424664115, 22643594, 154012156, 179495783, 295005513, 744846391, 65830277, 374979327, 780650550, 20279880, 88729243, 164130118, 456762512, 389376557, 485983690, 608113017, 364804471, 895506298, 9727639, 427061793, 113296363, 305222148, 505213068, 633688898, 16042087, 391384456, 881157365, 846716496, 652811124, 551395681, 319735370, 118725270, 823152589, 425167304, 305757340, 321453789, 462501907, 190429352, 225261455, 235951071, 175950039, 544014277, 719164965, 986985099, 802891858, 855574482, 991591285, 281718023, 979144805, 427395292, 390947849, 919401252, 668055166, 584099032, 761810450, 781665807, 445384669, 965027289, 250452374, 222526500, 318249712, 939035053, 420610308, 949807855, 906561694, 408602137, 43530056, 614911138, 317496306, 874179874, 631691351, 72053758, 276267380, 572397615, 931403560, 458252461, 472563556, 938418200, 351977177, 62991593, 531291678, 338001740, 29092903, 971638589, 861501701, 356940316, 248688258, 546931673, 475737085, 123626112, 101407831, 193518750, 491374116, 850170641, 170858341, 363184195, 40241018, 622053690, 677391561, 977446802, 803951265, 39242693, 568864600, 466321073, 844933381, 791592352, 890649865, 981428782, 112553233, 893045351, 126154921, 153208965, 616220349, 191973451, 878426532, 18632443, 495609403, 790681367, 284811714, 398589142, 753763668, 71812748, 933743221, 993241080, 625960220, 352639622, 774179501, 566493950, 768779741, 83959501, 947529355, 454991491, 833350568, 374867919, 161620492, 646727535, 975778213, 930419483, 802076720, 739882994, 409772395, 415851482, 78836706, 587024543, 923148965, 958807795, 159078861, 956168, 429651094, 921777248, 784060605, 637092012, 794519684, 787902252, 738251348, 113948344, 644296237, 242624818, 613337442, 986926879, 998115488, 568402217, 720402320, 53668670, 319357680, 353914987, 26804565, 179732090, 854787832, 466158881, 434017018, 209566244, 345210390, 998023737, 649960179, 519697118, 480993161, 446610904, 917598078, 975051905, 658728201, 73745113, 822618059, 511331076, 16367490, 639008076, 571797168, 362338369, 427196457, 437045417, 304944984, 276161568, 932306106, 367318875, 755292306, 107975571, 120288653, 997225514, 269061616, 892079265, 3527352, 130063681, 221330062, 663146023, 585495164, 159773297, 377063990, 928886467, 555364118, 932338200, 483654682, 863509638, 845666514, 864738032, 145438793, 640724541, 640829419, 831201073, 188180911, 518372916, 769417038, 972320178, 948128018, 346337684, 65784573, 411198689, 640138600, 677761039, 639131574, 584151094, 179018276, 606498318, 463009267, 368086882, 870303327, 784378674, 324678264, 273709746, 884569789, 933813299, 824393132, 264927441, 449288052, 264951910, 325972730, 81955732, 628578938, 942894317, 33980996, 145896828, 331887641, 479165617, 33031987, 543355040, 325113175, 580841727, 143050702, 162339134, 995085132, 89543432, 336712006, 946318502, 214562941, 658323083, 289514154, 225556717, 480610139, 819102946, 973452872, 546293022, 320303295, 542042551, 124280755, 841417440, 584510511, 558575301, 660603223, 375214778, 447322915, 135844370, 879479267, 227935639, 48642764, 708399205, 892573864, 733668943, 166852937, 489715305, 24562924, 940238513, 471797728, 874804981, 316107930, 505411064, 273709304, 105191321, 538094134, 10162305, 794007566, 705413550, 576638518, 535923070, 12941373, 537028453, 825856598, 444412847, 153419275, 971428143, 829865710, 812511746, 497769678, 755157569, 554445135, 595074051, 40911721, 592895544, 800840924, 687617260, 697478473, 304207159, 175474410, 465053099, 532834711, 231847842, 322745941, 547708923, 404138180, 185888610, 489426014, 499394184, 144204205, 331141538, 240575987, 421230117, 505990155, 994433324, 592055862, 403941193, 251539356, 186059791, 294731687, 208476548, 899252868, 364304136, 343598608, 851103140, 240695186, 232615534, 903375201, 82246119, 211523760, 216449840, 158544100, 518583861, 753023878, 547757011, 750958594, 643361758, 121640621, 727395807, 988269174, 418946406, 835714372, 962059097, 3949160, 507233759, 538537411, 901413730, 159179192, 293427441, 444017534, 71143135, 423802150, 113431563, 216692636, 417267721, 741201047, 982159550, 353600855, 891458587, 943090875, 129535897, 234714985, 738238277, 626817597, 865736884, 284960197, 282504103, 964053385, 216923449, 71661997, 34064916, 595201793, 789439275, 470048516, 458408218, 624472277, 438259949, 384229540, 887548118, 85224613, 232558489, 14905057, 422583836, 133810748, 270835763, 385417275, 384954484, 712095271, 984454246, 172154258, 939744268, 275716386, 825898305, 175496166, 131072872, 414562548, 623713981, 390327295, 480646660, 604392232, 762491482, 35366341, 371017619, 387302616, 272022089, 101073218, 64209186, 24755251, 522526359, 283221693, 643806502, 536355183, 984751205, 497753865, 860935714, 308449347, 553206633, 704446437, 883554503, 847377933, 857667288, 314200267, 173228908, 300508557, 198844161, 141446141, 520854343, 685635006, 698167915, 638690097, 114077291, 298258636, 33512595, 616104129, 265634653, 501856141, 137693666, 368367328, 222449060, 731579770, 789565225, 818122392, 883641009, 448719863, 762474517, 786482015, 27323980, 723925795, 805527710, 175817410, 474065170, 436090708, 670244541, 233594789, 276046907, 774179663, 791485187, 938029205, 914676581, 357397028, 877585990, 281711086, 616390809, 797030856, 466614461, 903242734, 17982179, 134377136, 285487416, 309816224, 904431303, 555805358, 363591755, 423935418, 993911649, 937506031, 285897967, 292484959, 639937393, 343984532, 922399388, 908297111, 291831543, 970305568, 82122780, 977501474, 83528920, 421274267, 338263822, 523888137, 49256107, 929260949, 805552071, 755522549, 188104247, 356100053, 776439678, 372870527, 429783074, 479346121, 509057714, 637659501, 379365291, 419859639, 410802167, 258499362, 432522146, 302447158, 603411952, 693144263, 658327981, 200655752, 548347831, 602987821, 433226755, 661807922, 338021641, 365916652, 825087120, 102031406, 66840417, 760601731, 138943343, 28050937, 466144256, 154339185, 74082010, 254522942, 153111542, 813115452, 47590505, 657634387, 985055089, 656817900, 322514986, 92269708, 448079577, 536913233, 231289444, 209574935, 876666819, 950297023, 334957400, 636233524, 149791002, 161159139, 254597292, 561214906, 960524064, 830001338, 591108755, 88871184, 171487058, 307198424, 222905668, 230207693, 457269016, 615332510, 865267659, 150722531, 449441527, 509444531, 689949043, 24292075, 104166153, 68727919, 799315811, 351111833, 327225440, 539679997, 853671864, 677200391, 125246527, 501311976, 173772288, 471960000, 990873105, 18844200, 271099382, 573783846, 196535549, 708738138, 556574600, 733934093, 131105051, 743724788, 683207932, 907506433, 592493509, 181205826, 242666971, 482303155, 127307921, 129255440, 9996654, 830874475, 664525206, 239343583, 90687430, 816423547, 819133851, 297518058, 419983784, 248697693, 903706314, 594290060, 929545471, 126117965, 930103138, 46057896, 636610089, 437155616, 665166214, 124586329, 191995933, 401519280, 121647366, 660260421, 476174334, 859563365, 15984131, 822809673, 987040173, 5849595, 501487793, 810616102, 466631689, 284013229, 717690284, 352913358, 39827763, 360069991, 123376895, 728029347, 383204277, 59013963, 834088870, 285195391, 785339506, 911395167, 307169344, 328877168, 770347120, 913715817, 393160939, 722767484, 713617273, 157505363, 200907361, 362960160, 551386657, 193877963, 314333664, 68662522, 53359017, 287994515, 164033941, 541838360, 315779153, 561556114, 805856258, 41715727, 843219462, 57832391, 295403189, 814355404, 975915146, 480098308, 671673376, 847688275, 263671872, 610717002, 38849176, 647015763, 608723281, 135694674, 885277902, 860695023, 643758600, 709195164, 826642138, 846117851, 97562672, 695907728, 718235405, 64758511, 870046758, 709521807, 62337579, 563985583, 227314077, 253769456, 293166916, 523002342, 26137179, 758718985, 591768817, 869303124, 725586834, 703819939, 928049961, 490245273, 863384566, 555832319, 677155956, 189804574, 721352201, 898454821, 409883875, 1632898, 992827231, 280530252, 117876533, 295758454, 377198159, 180332512, 662812315, 344484165, 149093619, 309470748, 765992383, 959682722, 519142980, 187068371, 770396466, 521722235, 289949324, 111115411, 987388825, 586112231, 80916976, 348533497, 566861523, 631652074, 581056501, 290987941, 956642834, 206694369, 453726452, 224538606, 583801269, 656177205, 908386148, 523317956, 209497034, 689133470, 32833920, 543973018, 188566413, 31031956, 822249548, 608669864, 227998805, 292152327, 68294562, 2388075, 831391689, 641107952, 997985965, 370302897, 643466794, 556551390, 389937486, 44095100, 972024821, 502870350, 556008144, 107877263, 661741130, 731411307, 818016740, 571274313, 602964606, 951851794, 19110355, 336026955, 453092477, 658360481, 51080015, 425954288, 65451834, 894164384, 416225823, 590077045, 328196753, 169277289, 151518352, 886453790, 263101013, 572412796, 640451119, 465420786, 752113436, 964728762, 576826492, 984305881, 926232352, 514509454, 940478742, 585426721, 112427216, 82656706, 289665979, 200488628, 227719057, 132494644, 150855551, 76513177, 430838829, 496062946, 913769477, 436974552, 308159363, 217629601, 447348610, 262009148, 566908928, 573913320, 499645002, 405334598, 185949631, 658170941, 763028053, 15510300, 468048673, 816299084, 832273938, 341246982, 919157419, 436822250, 659598406, 374593214, 387859617, 453387783, 148469215, 370997669, 99222675, 302999748, 15011717, 788809425, 823711508, 884414792, 349569766, 80011487, 427676618, 958672892, 852579561, 602538209, 213424540, 728578620, 799083138, 875941991, 308440062, 448786234, 477267160, 792797071, 934542713, 507980792, 473984652, 677802472, 487080978, 66998114, 335824596, 118851708, 637685976, 682870629, 138328084, 974553612, 267985989, 43034656, 817827558, 443612055, 273542873, 672918807, 531019397, 156435347, 778765330, 247184042, 400240740, 537182715, 990743992, 15259336, 61139091, 664087954, 355386171, 613877068, 291934433, 662532245, 149273425, 114867405, 601803376, 99857869, 293106951, 845395508, 920653867, 230848983, 985113612, 267454749, 31173521, 538153289, 956066270, 498615045, 522882634, 813093627, 111059392, 602528573, 583470141, 728641775, 565646578, 835862923, 78885758, 127149398, 71088605, 400691234, 661463106, 423620347, 185807305, 142328414, 210262072, 610801996, 546152739, 681846501, 215896101, 56735468, 222958722, 806875241, 99938585, 634511981, 630621236, 899304738, 15479186, 992375080, 871187090, 202345069, 874858041, 646443042, 159421459, 778526858, 142443563, 284381101, 208317445, 433588522, 620634153, 126805603, 165643842, 347999537, 122968255, 330986334, 53217511, 574482548, 165827442, 854424737, 752748097, 87425498, 197909663, 401976915, 420067971, 226165886, 27428951, 917805329, 581820609, 647349795, 477056175, 868248784, 170077269, 506468665, 349170230, 568634302, 543242298, 948220850, 500444581, 133040676, 137855276, 493919882, 203230379, 854444908, 391178940, 595867733, 12933048, 670230263, 877030996, 974646420, 904669342, 878560139, 909547673, 841318169, 966771437, 48220879, 960504603, 44319485, 180625033, 313493773, 235492774, 413600676, 634913668, 865453083, 606200454, 106241202, 570088845, 792447957, 166498911, 845480029, 752076489, 996199024, 662227145, 93041672, 225375846, 628610549, 280410049, 14218432, 504376617, 474655150, 18757719, 827133075, 191101464, 20374309, 250425776, 330239475, 231344030, 887216203, 295953721, 20791254, 466331827, 406182411, 140371365, 465917064, 713979245, 107917878, 409270442, 821788239, 955056431, 273409659, 667722419, 47707995, 270803550, 811877883, 84905254, 286914004, 767845531, 294884255, 595825165, 754379457, 68210568, 59476889, 80642294, 381917880, 127332546, 693526454, 79529007, 695058938, 364918565, 818492707, 692386637, 693534865, 193768223, 179018994, 499441113, 631467053, 693772139, 278146600, 490745156, 20055068, 17528990, 176375997, 404253451, 35578724, 354326858, 991063258, 870557915, 191661597, 851850759, 550532383, 546343361, 494068522, 395709065, 805083141, 33502367, 886570606, 727476372, 320215851, 281301136, 440560026, 829362326, 878142042, 301168301, 387869954, 667082385, 6359637, 691538686, 255989839, 353671775, 332038481, 26049351, 287297862, 188961624, 677512983, 860214453, 959300575, 420886205, 173459347, 271039841, 717566078, 838455160, 766985375, 570119194, 978692301, 439751592, 363269940, 546195765, 600018364, 409937010, 814413537, 519112240, 795868142, 232315691, 405217811, 604977803, 392566029, 306319038, 129933978, 785082343, 236609906, 161120838, 719049918, 235781782, 125792725, 595631846, 565316426, 993314397, 334542940, 523405593, 910857089, 8342563, 998420813, 335626292, 982802643, 907944964, 156756397, 446718568, 217100797, 787664873, 302670605, 557150240, 736664857, 441563692, 798554764, 722010440, 389148746, 985229840, 607825714, 221513586, 843679896, 754994183, 222268106, 675577876, 191577610, 502393575, 502797154, 3711092, 807490253, 949411185, 547338051, 304002931, 757754840, 433082975, 911956887, 742734935, 959646152, 593340570, 354644816, 179973094, 726812407, 13180897, 709135351, 992598641, 691002138, 925014953, 822355270, 527797509, 231464838, 561750193, 400843883, 751471190, 901177311, 209072540, 785515205, 470868100, 387061462, 838000128, 897842378, 205432438, 768269300, 277090001, 532834582, 968680190, 846713854, 236660491, 643996695, 207868719, 821764138, 966558500, 337920208, 587051394, 272438457, 218520013, 482255487, 702441963, 688557479, 198647356, 859096496, 267428423, 515404379, 829881729, 691964610, 385098470, 363047856, 528563626, 800181440, 995014392, 839742294, 639964246, 984712136, 94938600, 852240425, 754811407, 436004442, 740198963, 645627089, 510878609, 100117622, 104697561, 979524080, 320182760, 983979130, 952682738, 771962836, 50421810, 676180830, 596404394, 616495440, 75108138, 366502083, 832252530, 246037023, 562832132, 149824584, 225954276, 77349052, 271017462, 402423884, 915404831, 490422589, 402700208, 381386610, 986629146, 431808239, 341591737, 882785393, 217996716, 984387560, 884713373, 2311963, 867706781, 213876948, 508873917, 581519217, 915533909, 419056036, 945240605, 952177653, 621270404, 327782808, 42389669, 15504660, 980401799, 892633568, 926457398, 186171919, 690808588, 531241496, 374240280, 533667167, 429738664, 828669815, 859633015, 192104394, 868048321, 857699607, 652158498, 364726455, 37356042, 341427574, 706286218, 832025986, 182064904, 969020304, 51611208, 864816640, 125967861, 124597784, 959890946, 660139341, 473768096, 975834372, 109556732, 710744400, 647985796, 109661945, 410008707, 136589859, 619628241, 780847266, 751899367, 547795277, 62140971, 391120746, 56160568, 416363746, 937148065, 389976188, 530999577, 519123938, 244083091, 669142219, 738942889, 351514671, 470970090, 13883008, 679805584, 517897542, 456124067, 333785571, 111969080, 636996243, 728745471, 706963917, 567253075, 487138415, 60522622, 348180180, 701840913, 259604560, 838421824, 242829998, 611067778, 255453178, 908447721, 694654276, 330341611, 419207331, 725134803, 310918917, 250952975, 875950178, 669140573, 295027789, 983196543, 665026760, 814613018, 264018220, 244317155, 137773221, 750586353, 876021537, 81610950, 221873308, 315171919, 792785537, 916030115, 648579995, 50453828, 713379738, 32168458, 312091005, 207892887, 592963560, 693573491, 275700535, 826165618, 818535763, 871261979, 652093853, 99206372, 259896023, 432147624, 39130533, 387827813, 34018356, 290776874, 986899289, 996914764, 320470269, 505701664, 513090910, 218729371, 149073901, 45105668, 305467795, 789959145, 48179355, 419819754, 915323716, 266038220, 698138591, 534273488, 7489539, 753733542, 265185803, 399031766, 62794083, 564379821, 568690722, 534545272, 688934514, 201879798, 95282792, 862009182, 331166150, 24707632, 775833524, 861282884, 993676016, 774826478, 138174720, 862073355, 890854790, 833677465, 191012934, 417295657, 683497904, 185896324, 638133542, 791586577, 676768931, 751591393, 88839128, 816479742, 331943450, 845398494, 529366511, 90254415, 575412831, 950471525, 743976973, 72114414, 498345736, 357141122, 41542750, 251727637, 832231552, 800334607, 606419668, 546937007, 985080957, 26665614, 896180717, 631387507, 740348744, 729144311, 312087778, 555276036, 259164738, 899161362, 328546151, 385805689, 529706270, 789973617, 231386931, 578767611, 943759819, 579366716, 977087226, 10418923, 461649854, 663200008, 488284920, 715402200, 656893069, 661612946, 69273997, 824863018, 157368476, 376993403, 913219751, 950618069, 219401368, 233321472, 639482269, 941367906, 82653695, 426052578, 242819309, 248102745, 610295435, 326165310, 642263569, 12051703, 47920551, 848626800, 817753715, 964399734, 126120013, 300877308, 293601659, 354677389, 605529470, 173497246, 107528607, 262060742, 386569750, 258171732, 728849385, 733972905, 190727445, 826114849, 183286330, 814880166, 514302838, 572963604, 860988975, 563266376, 396629673, 119793463, 332524607, 282815901, 455577752, 285395399, 231913963, 347160845, 665041014, 503457841, 886017181, 297248663, 24417314, 139468030, 948262898, 297355118, 63839497, 652817461, 895366908, 405487418, 547771950, 297128235, 945302256, 242031510, 536108289, 186903426, 326263234, 963002916, 662568557, 350104195, 310180557, 556507426, 781752394, 779327271, 348839264, 187235915, 113353852, 568943207, 985760985, 995380751, 936364877, 300269910, 594430456, 836281230, 557161083, 630670302, 580056588, 864802955, 256527245, 539771129, 827673461, 685112777, 402900243, 198234237, 6389755, 298375659, 825347865, 932765460, 980501197, 440634551, 132775136, 811132442, 349917221, 64598889, 165345535, 197808996, 781834352, 655735688, 655639236, 307916406, 824894324, 314845868, 717833166, 318324520, 680200012, 559194026, 592741932, 71907170, 513430488, 203161424, 798491818, 638234966, 814354936, 928709105, 594525505, 765656266, 203578466, 955931394, 119401031, 928342427, 191266299, 282282146, 635318625, 325358639, 411023429, 731026564, 590812073, 66020005, 942359117, 144276233, 569372082, 147226091, 316546704, 184473733, 845534085, 320213268, 775652297, 485780674, 198314914, 715540498, 755145123, 631651342, 298798864, 161970599, 190286324, 336378452, 338085176, 213664434, 840675877, 7864610, 996892796, 117294911, 438021596, 922125092, 36980570, 858881320, 122644631, 203780463, 922207264, 104333386, 269739523, 202505770, 880028518, 4349104, 385346752, 635354192, 978799665, 910671121, 573342661, 640457148, 374246603, 127076579, 512235832, 299340908, 755481848, 609062691, 475149815, 834178444, 563755695, 637915097, 497392220, 564828883, 890611344, 475803914, 383738131, 881533267, 954987037, 955294051, 531816768, 244781736, 824905960, 182053745, 324421824, 425241829, 736491107, 937516111, 75003775, 847895227, 192096660, 11320631, 267677230, 539760059, 735769110, 583232916, 827023909, 245146678, 761243172, 645149566, 220849559, 626431783, 330033628, 362940090, 831112530, 567773230, 601182229, 786606394, 457715989, 181405664, 796919152, 479710161, 887468771, 861534501, 362469591, 831849546, 436291778, 371214975, 326696861, 507713207, 729885171, 698171607, 566054479, 98247107, 213148898, 327415345, 292007315, 599729858, 329727834, 333374254, 600877321, 41363745, 711930061, 414641732, 929362100, 293120471, 4352572, 898091869, 518100924, 101163151, 751358826, 937273677, 489530975, 339146283, 597589373, 117159039, 547292529, 777639847, 169356050, 952416889, 309014868, 492822807, 927068693, 162745778, 509571823, 545120864, 44281880, 131020854, 960576423, 358408689, 314470401, 530122320, 7894544, 103741147, 494223290, 762597442, 409004425, 475923318, 101578606, 489878089, 613168309, 823738982, 826251567, 390312512, 544618706, 649004494, 724375863, 710470625, 843621261, 704176125, 160502418, 651549276, 902085146, 958712393, 739861826, 744939803, 849542791, 733700915, 443886211, 663097289, 70502609, 783386613, 474861896, 692655061, 935573265, 388417643, 300821987, 129424179, 822051047, 797005819, 692188377, 620057149, 328462351, 787448697, 287738466, 787463391, 532730886, 343498559, 158743732, 143366306, 813475413, 559591826, 954045498, 474762767, 864578998, 334611573, 279484139, 304854266, 904610919, 849642326, 240712268, 333627932, 901932941, 233728393, 3629166, 554787490, 403422185, 848795407, 837955612, 968548679, 116777015, 728081182, 602000436, 200693347, 919892228, 953441265, 985213128, 236044895, 743467819, 853037942, 80515200, 729580235, 432192835, 630640715, 632126678, 702800717, 141856926, 148861111, 789549813, 846817047, 956129564, 101801593, 514475320, 236183439, 873211231, 187901162, 865511497, 896920698, 78627306, 255250021, 840779523, 356153273, 623032032, 161485498, 30910118, 295380727, 924369989, 322193128, 687996569, 594063114, 578703333, 39415829, 260951456, 838090999, 887505544, 362135358, 355243637, 141643591, 766016276, 231525414, 60227095, 988527950, 134198831, 624133047, 378475575, 586555728, 278353923, 843590082, 854182178, 38057021, 757369496, 710099444, 490227546, 596584723, 53258140, 201444059, 776430929, 520483178, 574067371, 244125528, 744610897, 219809934, 241328802, 441561898, 152374675, 954505920, 969133203, 826995382, 779119144, 671924348, 753776909, 972629325, 707803714, 356123545, 745298132, 812286220, 827907062, 258528201, 758874169, 100017746, 415856471, 20163572, 988821565, 626166656, 539583919, 285757330, 1091372, 5268012, 608918030, 302834564, 701366624, 981863828, 115430465, 248623319, 652710649, 46920273, 434581668, 182822777, 401755349, 609615872, 45351405, 628058121, 411209856, 853704721, 123222784, 795202435, 217156086, 548995661, 340433712, 320792008, 630243036, 480284164, 940577592, 731183528, 109625033, 718063543, 141389963, 773742445, 234252018, 15091152, 518069509, 572874788, 198363010, 352548731, 230726769, 300315843, 703590602, 277409481, 106667229, 252159172, 562096554, 686513101, 158975280, 961074931, 998410939, 555690832, 188363813, 172506571, 337090896, 724635168, 258842549, 591799065, 386027529, 88869123, 413784393, 696633035, 693724983, 561996818, 802301225, 617410617, 39110006, 244933268, 499205663, 133041457, 73922138, 977362507, 246964851, 275119659, 487021734, 572809291, 645022857, 990717079, 35874082, 944763895, 875935964, 493806035, 990005132, 639455848, 536683238, 807209181, 319661817, 386068096, 696317576, 353658531, 73991245, 561939837, 698927596, 251858761, 124725468, 159205065, 248902705, 616948316, 405931973, 977738129, 266972604, 309115184, 926510172, 770188458, 247573412, 133500792, 236004285, 692112062, 765202333, 710430379, 764358072, 459424174, 44843068, 591843923, 315867770, 263254755, 100683267, 404800050, 587243076, 759205933, 452592467, 580663218, 627812932, 86954155, 321878788, 158549111, 119258739, 970335186, 789910055, 39525627, 298039547, 343654099, 596598520, 732044778, 660763593, 621880628, 767976221, 5545038, 643266369, 910723294, 485570400, 695414145, 634311790, 474242921, 193251401, 600514481, 557655937, 337204154, 351658024, 295502029, 894843775, 115706789, 113348353, 330518183, 237829050, 487735624, 434987973, 518443716, 533938442, 520014743, 705769161, 893279108, 76172076, 871768125, 392180946, 274899546, 546235451, 159618379, 491800231, 171830695, 53241745, 894871513, 189397699, 240094051, 367911087, 415308656, 902831923, 212666794, 570917325, 126947841, 616662171, 242078386, 459944989, 425009137, 22175988, 59312317, 922475028, 938663034, 923975826, 463705523, 104090942, 762674772, 767701345, 264424086, 807756977, 152155516, 718996148, 284728914, 632384077, 319355808, 188673341, 885974133, 397500496, 470449108, 337218808, 275402911, 807590560, 832573750, 157529768, 776535573, 669658774, 272094262, 563323972, 131154851, 776119313, 478269394, 619434963, 816403468, 914686347, 265512876, 72754695, 959320478, 585072330, 548325255, 254896517, 555407817, 2652054, 182214515, 657952393, 666399312, 291941742, 640145402, 17936604, 107477600, 425696474, 61190271, 610994748, 92845835, 706073539, 692234084, 195229656, 584805376, 431247452, 54445888, 267852335, 922641176, 250383983, 471331518, 20378636, 520911250, 464824339, 680344393, 947727948, 678478331, 615386935, 120225757, 1024286, 364168706, 151798728, 414682147, 918902340, 101702480, 708678857, 190411462, 81754518, 628378789, 760326274, 313928536, 669579486, 998842947, 887095876, 994607051, 905302374, 448706654, 116021425, 893727355, 318192698, 352103795, 186380524, 249924806, 658402059, 273146808, 990051529, 636748403, 704793759, 312077890, 314226154, 473567389, 243773374, 777865129, 633160158, 672073264, 557834724, 934376872, 62605653, 571080422, 268333526, 660900296, 767559353, 507667115, 855985877, 515363276, 46465162, 90285337, 747664786, 225165056, 175962182, 792086146, 384004340, 454813948, 540031373, 648818000, 907155185, 974044283, 468945526, 124072605, 772935732, 34879518, 972487590, 288347946, 718758974, 299809872, 750823497, 571850005, 922658350, 961783092, 802452473, 166102519, 640058834, 955923178, 851216771, 969975047, 832652086, 993436947, 37638523, 155697378, 938243369, 124371855, 807918521, 194708069, 111392898, 409699396, 422939873, 684626786, 680778607, 990011322, 968848597, 236160250, 174894520, 71858952, 557343727, 151507370, 974943860, 58763664, 650167896, 157150024, 598941876, 253692289, 318862899, 438631339, 711849675, 18245414, 867545663, 523818135, 145548893, 209267259, 545968434, 698916009, 935961746, 919636567, 608098934, 20088816, 825627324, 481865383, 961568821, 433668375, 643030535, 82200462, 247192181, 499109749, 994600363, 98622961, 354664572, 364167685, 285045204, 781551493, 415481972, 535360937, 275398160, 370279369, 444428317, 765639019, 563396524, 262230184, 747744907, 511669752, 622098311, 982615519, 729625958, 244778575, 508293756, 563056124, 369010256, 574940839, 681739478, 929777020, 905094101, 739338416, 782027399, 902737231, 176461535, 31691758, 854582915, 209391793, 333913945, 606634970, 388527011, 190573207, 516076915, 476324523, 814869830, 202266135, 595480377, 404240268, 414669094, 362226833, 391565277, 192204430, 928170355, 921175284, 157700268, 800964278, 230559090, 627606966, 937787285, 726049809, 77769845, 338868863, 504343755, 866826946, 945655025, 509798047, 590728734, 640135113, 774209064, 118986088, 7877293, 939692595, 663014694, 850446882, 373853041, 712508645, 401406526, 28180469, 551307048, 971049040, 980480168, 235359304, 780763058, 473199763, 836262339, 509844292, 264182187, 437053323, 869376232, 878984845, 842567159, 325026321, 548870743, 444704291, 365729219, 68883361, 697047118, 438413666, 717771151, 11140835, 886372829, 148358359, 25469973, 276843683, 216153573, 501593537, 718461226, 496434885, 375673974, 864258431, 964875775, 179793699, 868962043, 408939637, 403134400, 624860540, 117189674, 817514086, 177850935, 187111156, 678852872, 258410786, 34512134, 255627753, 94440277, 543972473, 371297354, 676518224, 123027187, 901708552, 31328643, 40123062, 20796408, 589401970, 662498771, 432872480, 143273686, 188111645, 271779685, 54598311, 470057484, 165393839, 335878166, 109100165, 579518398, 595973602, 781592167, 923108527, 804714561, 827172217, 553017025, 73450325, 294942548, 561156890, 403316743, 179643263, 115555198, 925699700, 766654542, 827002147, 549044618, 453615932, 477984906, 715061183, 934757900, 602385551, 684656812, 201111431, 813120499, 4509106, 157631507, 844426356, 660434923, 712321726, 420419249, 306788497, 398113790, 359222688, 97410227, 747851406, 697452085, 556396509, 567421598, 160619200, 793711506, 62011459, 848319000, 885297865, 610915330, 305378029, 997362653, 33735156, 435829587, 919610833, 42470893, 13056157, 842558442, 489496061, 517440192, 406748917, 240194909, 292796260, 565300225, 966876040, 609663142, 376815693, 106926830, 580699208, 200538468, 937109266, 79471969, 863555360, 690863831, 438370014, 420006862, 494695904, 764940679, 167729468, 892931680, 675677041, 893751784, 534305118, 223278479, 862026639, 685990396, 969218480, 860349314, 813402602, 167701971, 381768285, 85292243, 767489608, 116626749, 890223388, 580719629, 513802303, 282349406, 261067203, 383704616, 89728287, 540475112, 179806415, 581425138, 262516615, 707581872, 938579219, 244188492, 795570054, 761776847, 49370486, 397055373, 750743094, 243651881, 865482129, 201124984, 54321029, 771337016, 653203368, 812129908, 795726340, 1167748, 75353739, 200508753, 182427560, 344021558, 77694406, 395455791, 640559125, 457701446, 27381785, 296388094, 378262556, 964868308, 335923492, 687096413, 758033964, 438363111, 912545770, 525836815, 749057174, 211463111, 484222931, 303435098, 239557516, 566407955, 36638698, 434023209, 569213073, 151732228, 481724522, 165287867, 724477258, 285848522, 536141020, 64199928, 931823629, 702539184, 432209586, 539475929, 55907598, 820405734, 921838918, 161886237, 175273372, 489182749, 958418397, 614179891, 634382056, 199924681, 430718672, 549694252, 74801642, 317472279, 71801840, 948206089, 769150383, 513591170, 685556657, 835137067, 471401879, 513141052, 849085009, 669335439, 704937004, 956734653, 536407628, 866959194, 413767553, 642790679, 286366635, 520732283, 329045896, 695778916, 462500427, 907405567, 766265810, 656694013, 255286157, 480682334, 81371052, 236115246, 160661812, 437692945, 779315392, 633374705, 733251887, 109267937, 566604541, 220193451, 835052917, 455913677, 863249599, 682454603, 796806109, 200960453, 136124610, 784730038, 360650148, 899394689, 360394543, 26392103, 318023358, 386198225, 36876452, 666516957, 223374488, 931041437, 739303782, 246755433, 805602850, 563881768, 719625485, 502033503, 531086150, 323187696, 981099120, 484840767, 864422580, 708200445, 353984452, 778607859, 965775841, 798527074, 39807964, 790905198, 106564008, 882462214, 979379582, 950390028, 504007382, 461496177, 71620536, 141794217, 987875485, 694021639, 487802374, 184873027, 426684335, 255481659, 726294948, 152334257, 117751830, 269188881, 203495536, 321283194, 444566899, 741859011, 338311765, 797113294, 813132111, 775735097, 801559971, 733605980, 347584362, 558287620, 207307260, 677463178, 949738888, 978255690, 51399791, 790071888, 739211947, 643273950, 356505268, 92640942, 427891331, 440719496, 440124969, 159464148, 470224334, 965250548, 617380358, 995110368, 156894777, 995291689, 170822853, 582767835, 856341843, 370548058, 525836681, 224761218, 732875440, 852237873, 290827579, 409523111, 653870717, 358085932, 800952351, 640691946, 641350871, 571549011, 673500710, 842553694, 24108886, 511119873, 854053007, 168613415, 761991995, 570237611, 488691248, 231380396, 651236484, 692672989, 993219122, 285808399, 300731570, 971706062, 408981601, 918116926, 709448468, 160915671, 862529361, 359221955, 433910640, 300156931, 196498613, 10645913, 871506087, 302072923, 617492644, 980321910, 298686629, 904682324, 508424213, 273882409, 555775050, 614797527, 460313411, 159348363, 5395289, 344504832, 279966166, 21662889, 865883754, 813846808, 750241154, 394001875, 558994543, 182731795, 209618892, 696967140, 152096418, 615387182, 743447054, 663816774, 185230434, 289658431, 295495938, 322469428, 233241396, 530673015, 280409215, 517190366, 544076553, 302191877, 992249303, 873181803, 891689129, 497285018, 163065991, 980089740, 152499010, 390176785, 883143282, 902580066, 96920150, 683921875, 779650307, 942024101, 159257820, 49252248, 800548861, 588705226, 773887302, 828330506, 51710550, 384579382, 938404374, 249394407, 901751202, 951674049, 559976722, 428130614, 453488301, 989418288, 653335783, 66637881, 188985393, 99280816, 579498735, 618229007, 324889806, 311914453, 349654334, 853079105, 319864797, 455521961, 501076927, 301535485, 777144179, 426186777, 182504695, 275174127, 158662582, 510283241, 674935510, 338485345, 566655639, 477755405, 995456630, 44813636, 202096428, 743262658, 870477782, 757255960, 866844142, 715254561, 497905446, 202884484, 607356827, 524295734, 954949231, 818456774, 775924971, 553935208, 241052055, 925285941, 85477509, 396128066, 399461192, 193338345, 664803349, 190617922, 680352753, 510946364, 312258655, 38045078, 695419893, 533575310, 787904483, 784370334, 561950015, 750571947, 145675953, 165684522, 467894562, 370812000, 382433819, 829566056, 211485809, 962407288, 23007908, 27299817, 470769220, 159343876, 788036926, 993762226, 857911662, 48262463, 757438819, 204356807, 186193522, 8759737, 320379504, 871765652, 513658423, 776618981, 649624978, 460013103, 920870476, 809597508, 107279364, 391026178, 513762654, 201590799, 52153060, 896571078, 318663280, 731121745, 359158074, 199470816, 802010715, 844287868, 202772484, 828565319, 686409929, 337395904, 718107584, 804319564, 510861612, 670116833, 995817844, 290852793, 965853418, 14063824, 724030244, 702355702, 546749951, 194989635, 892895309, 228950054, 224975202, 246629859, 961999657, 276479873, 454214513, 764835886, 10634929, 833282104, 773541996, 65635813, 891373462, 199036917, 227221142, 474952694, 108449305, 202472082, 881220756, 211300327, 282759822, 223841106, 50849477, 676609610, 333407807, 204387392, 152234962, 96493112, 243936671, 866050818, 33574990, 301124103, 298456417, 123232171, 135267047, 292156703, 910032260, 757157977, 189012548, 761371060, 790418341, 41612193, 741182421, 422870508, 191242807, 792936230, 324199365, 737486417, 983443728, 797682293, 209843279, 323326165, 358838611, 296140150, 252966488, 754121071, 902061924, 998931964, 990477286, 423281724, 251571805, 746142736, 850493261, 6670408, 114959675, 972510613, 427340765, 421231944, 93964726, 455028555, 587825863, 566368966, 744339984, 122549773, 850560642, 664823532, 501335944, 456779581, 162247376, 677405865, 598441831, 992114842, 483951639, 373757144, 858314737, 768361951, 776347050, 986061188, 14040753, 338731725, 684242248, 6575192, 185244794, 789714407, 344120705, 952808977, 446833380, 389831867, 508021208, 177121809, 631349233, 879572330, 864846908, 386113007, 187034233, 967974173, 651404020, 443347585, 170820592, 665999280, 258185201, 873602802, 772534500, 169715350, 696916242, 315624806, 936964000, 19660814, 82150849, 465730757, 775397334, 721285626, 531301402, 549155916, 103848094, 125238799, 822874429, 397665748, 127337080, 588692930, 84076960, 678548467, 258758740, 188700754, 243581570, 414847609, 155728838, 818386935, 252659615, 716126062, 902949951, 70440158, 928285114, 796812252, 732376731, 990809593, 686936659, 205734437, 69373808, 863100591, 365271319, 559311147, 871484594, 291324676, 586152270, 658145736, 202509539, 331599676, 101819830, 679789583, 106716441, 824878088, 26716834, 166295969, 341354514, 800649506, 417903810, 604627804, 37687227, 359101372, 771647402, 878347954, 965243255, 555021669, 163502479, 591110684, 559030676, 504869415, 117124256, 879215078, 412045049, 316468605, 533364862, 652841150, 308133739, 371397586, 446303767, 314028555, 624448321, 408470724, 996641726, 688608566, 998403441, 128061261, 897684652, 606140651, 300380619, 173113652, 545186719, 454216517, 357874672, 322592451, 238209133, 237215917, 704305504, 77676047, 540553513, 660808220, 67526786, 275192813, 738928339, 914942160, 597261481, 764153209, 729871510, 912435587, 542799227, 116591344, 112863848, 462176375, 754737490, 969804277, 87151469, 895161967, 804860587, 814969733, 196077848, 239756757, 303943682, 148954052, 108736954, 7715062, 584583172, 836884994, 540710804, 371501579, 256770079, 946089455, 318039467, 499518255, 671478634, 244579278, 864005043, 999992824, 258386245, 753169566, 938506400, 711546784, 622142961, 819685289, 253807415, 231417512, 298554760, 873856677, 77935208, 516946047, 141161959, 790666858, 812639947, 367752235, 549088965, 767096263, 128899383, 993716093, 585325667, 510941656, 255552223, 828936698, 419472455, 910783619, 324387990, 862032556, 928146456, 367336825, 885303412, 273628035, 927128205, 454211452, 313069965, 379825258, 770275162, 16736179, 955641412, 244807116, 109454712, 810380300, 43168194, 417948163, 728813793, 89459509, 710992416, 128395228, 232241610, 875887837, 198379375, 781061632, 161465720, 885820498, 504835495, 571713849, 647244288, 562655483, 900029713, 708244652, 763909615, 902430795, 503693130, 98145426, 661368366, 486897938, 685059447, 225294140, 526185964, 276120309, 989717824, 148432163, 988347180, 322613969, 23087746, 760023428, 657079811, 524621937, 353277210, 252577335, 32413512, 617381982, 387705722, 758602222, 377830389, 85507643, 747514019, 624058542, 719879865, 726639980, 717152433, 248623910, 983327452, 225038131, 733994312, 429887841, 862506484, 760458357, 353636118, 608961372, 376022938, 833354248, 467217265, 620972687, 876128840, 180113300, 461745747, 469893429, 426697342, 597457365, 188565475, 462283982, 884385306, 326768899, 380278964, 475147339, 743948815, 319941116, 271906836, 868402292, 332752272, 87376840, 940238588, 153210892, 854169388, 18074328, 99101549, 25413900, 55172272, 524228739, 136473234, 107237406, 593521764, 677542978, 240798890, 570967972, 710413887, 764067453, 426728345, 298190959, 327823576, 262021686, 733931012, 946367138, 503448288, 233807919, 183477985, 348625364, 437347229, 224113550, 43599507, 577840136, 212355298, 140286388, 373738459, 233310923, 952104784, 140261089, 593730904, 814533023, 293073070, 84523809, 933432818, 970024664, 543104537, 675632975, 740533089, 750260019, 175287549, 760229244, 863829943, 741302247, 63488731, 611156208, 785904434, 378671110, 428469168, 139850544, 168896913, 763176933, 607504491, 863020358, 172213315, 176338194, 411708313, 90556602, 820442247, 866524195, 856509829, 628610393, 855362802, 856224695, 804508122, 213848522, 286893950, 408263291, 571538629, 945709033, 262975309, 422711958, 895451755, 60069506, 272554823, 128300166, 994114078, 960462773, 849052563, 71641071, 704527405, 388360755, 380412321, 878781266, 179573886, 414955041, 4235552, 444119133, 118194860, 493051149, 663362595, 158681230, 168947682, 678866157, 399112648, 900235443, 329020383, 379881128, 216400699, 856217147, 974234485, 123334449, 346442382, 316271697, 324460675, 871678505, 842805905, 294542270, 124832221, 889422758, 976339701, 288774192, 709020002, 170976955, 167767109, 627355487, 619276160, 245614695, 545251911, 526807968, 621516115, 518474749, 159802581, 595872407, 493787102, 787668737, 952163956, 76240996, 12222081, 915464920, 419247550, 517479926, 215580514, 278667675, 559787310, 475420556, 412813170, 908183675, 841920243, 960762322, 66483202, 802682808, 575853563, 283769405, 919510138, 82092268, 340578640, 526194624, 739580372, 438204069, 781804265, 466621889, 168082918, 219430584, 545488118, 371163947, 24941373, 765309707, 309781966, 46315237, 670575905, 614029102, 721950095, 109171810, 456260033, 482832005, 963312147, 114685470, 336100916, 588774157, 472640696, 427403524, 942835041, 6800750, 935077709, 380254602, 924537797, 35883710, 856778699, 154873675, 836424490, 467606222, 95333959, 255230400, 465227476, 581113779, 663241090, 576268142, 855531927, 806517378, 769491440, 722937512, 534701223, 649424386, 258354973, 797566391, 211185597, 30114118, 707557839, 146608859, 716176642, 303671376, 141583002, 18566370, 259626759, 833323065, 634905414, 177893512, 328819437, 374706618, 326223876, 337675575, 48732336, 454703191, 524888442, 395387838, 563111883, 242989832, 831470278, 836804815, 747499431, 644635950, 601186760, 204617695, 829483306, 756764811, 148250633, 371374745, 413173781, 958729151, 205281007, 602490260, 583230457, 865612081, 492242215, 312834288, 408891097, 230182513, 499905537, 335986940, 878899194, 894124708, 496082565, 784188092, 503729024, 140484645, 206247884, 330735481, 64960321, 699490139, 499663182, 468700149, 575251776, 247746548, 919650173, 368232032, 274309106, 581615689, 859985939, 576217559, 231554684, 143356443, 993102327, 70160923, 18052946, 9861084, 799362906, 933457444, 531544773, 716841398, 323751872, 906248867, 166762394, 869785278, 976759510, 202798740, 804458751, 303384445, 53181132, 475165295, 595630720, 599956265, 344341812, 999131453, 613306217, 105975713, 289357079, 625435281, 227364344, 499139951, 567336347, 369886831, 990553875, 152226455, 821592755, 207036609, 943617161, 216323693, 795177562, 209137587, 345158721, 55450374, 780106515, 573140891, 544570742, 232748674, 36659805, 941272459, 671098223, 829955354, 151837274, 158312004, 92982677, 90437444, 729380041, 734390050, 881461609, 485327127, 864456379, 353178444, 5717303, 304238442, 124257466, 35488420, 470328707, 399857513, 868665518, 427257805, 482304533, 162985274, 48396141, 594223613, 348128671, 969199489, 473567479, 148726312, 973326991, 695827613, 821595768, 126130197, 304595284, 987384116, 641969199, 539089226, 535449838, 222129775, 185819600, 676281772, 54888106, 290047847, 330214955, 285005651, 504177865, 277105826, 549160108, 309064915, 257357305, 296515713, 715719123, 450076555, 790268959, 43548591, 244245731, 682931879, 9143233, 81454622, 859058301, 91436589, 140750450, 362813059, 583063429, 106149079, 10202415, 899843905, 706195137, 793875034, 498257091, 846214273, 962226503, 948138929, 880375366, 166028857, 807072502, 772299883, 565011665, 503734081, 716561796, 645515772, 521994975, 655486881, 238511391, 470107337, 600305806, 604674201, 718301080, 225445656, 715371503, 719316777, 693593680, 145738751, 814813586, 763440336, 161340824, 408093948, 92509190, 765387313, 258490051, 521887814, 406235307, 129023568, 304295993, 689446019, 92597369, 744827409, 120935591, 419981259, 915568387, 952044993, 523844010, 578582403, 280961522, 800207115, 121947208, 293393013, 598371830, 959538459, 873788332, 256346760, 197011501, 456494195, 430776161, 996147601, 711635451, 156077835, 612549457, 36334104, 852861471, 825228583, 47202109, 715446979, 574017421, 67927761, 439488677, 665247956, 440090321, 885983574, 590114837, 517669848, 716829088, 41933612, 995779433, 135502065, 271295832, 803495047, 690789280, 179432246, 752796261, 373931571, 643404359, 31158238, 389530158, 570572039, 221408417, 859344300, 480758293, 158350815, 43995876, 804045998, 174833179, 453296292, 911920655, 339853361, 400823523, 251315347, 361498850, 711733637, 907357044, 289552309, 637927313, 857604244, 114200789, 478900391, 988503871, 94268497, 953823024, 148229657, 3699847, 654692913, 495730134, 608295725, 322819665, 860192698, 477621075, 326199244, 91573797, 558053212, 122042422, 499273345, 905013562, 469273131, 114556166, 469635572, 209617839, 925236311, 579155209, 188869760, 863532576, 762348454, 894321114, 598924671, 548072245, 758969888, 248730187, 22865214, 416755901, 849326930, 405460131, 307650108, 325968695, 584937633, 770587794, 930225118, 37227256, 696651535, 880047586, 795227943, 970207074, 219235015, 477627330, 27058500, 816955418, 417575988, 253593608, 750585854, 805092351, 362941668, 113062297, 741322876, 840354079, 970608171, 155168218, 331156776, 414559769, 578125118, 994482529, 950801796, 4315185, 411297828, 835057651, 667691035, 440164701, 303154060, 444067084, 681499861, 912110667, 223481109, 238045005, 95422806, 158746835, 693023783, 939416008, 875953869, 808080725, 777555968, 259689564, 744183783, 965987185, 685343322, 772528570, 146617773, 710892650, 310042225, 408636894, 534673736, 877016604, 879547594, 818005110, 226712838, 152018775, 543706471, 275086545, 217160090, 932891373, 785818491, 75879488, 722096893, 84465382, 951473386, 652333403, 675373975, 728972858, 917506027, 115727143, 750986064, 387092232, 144383817, 541534372, 182805897, 418576153, 323820716, 601748092, 175232377, 791288382, 495122909, 801761885, 567550903, 507831094, 43983203, 853257931, 818194024, 685949631, 33248653, 446113160, 553521612, 583317104, 638241870, 470400867, 913683021, 799771315, 542217874, 849196119, 578125559, 739491000, 331452307, 386670152, 484718267, 546145622, 599773333, 606573682, 692685735, 421179322, 73044869, 494261828, 696776395, 975035253, 106116546, 287601969, 124968885, 953583578, 365090717, 183791307, 241288181, 220468901, 568138970, 372604953, 612259903, 44980239, 118331091, 761772723, 955775028, 336199950, 236511065, 770324004, 157721901, 961882119, 558948662, 559256445, 928851410, 858178715, 905619642, 995132893, 447851587, 542854858, 166697231, 971164957, 574305869, 528590930, 832268476, 107002551, 222057001, 702273791, 659111279, 424608880, 441381503, 471745807, 525506177, 877662769, 296017110, 625925036, 705593481, 976777480, 21376420, 831072625, 53361520, 758187296, 42619204, 965195351, 545338576, 390224383, 298824118, 323466401, 722526138, 247716230, 540889921, 136938189, 955097510, 896557395, 142977875, 539772099, 177481109, 359104203, 134909590, 521129118, 910140327, 699938024, 306215558, 343542731, 891154079, 271281476, 250244181, 479790255, 50497220, 890519320, 12412592, 698549585, 37336695, 193485182, 575251189, 693825788, 680745702, 634147283, 122204218, 655063097, 771973551, 78978045, 687353568, 967553467, 952497772, 563568028, 366031683, 233251503, 787865713, 101538888, 753160599, 221610491, 211727359, 134252172, 239373000, 511660869, 260725523, 418177720, 389869769, 942261419, 437383184, 954645757, 434985758, 552931859, 180364834, 157159798, 583717755, 317491533, 804629655, 380829790, 250335572, 118461662, 188056244, 834056178, 276066164, 892494502, 646737261, 500918500, 151061442, 613444514, 346287339, 303326819, 906963858, 364287133, 967237039, 243758558, 419219253, 209710069, 316906254, 502909151, 784083346, 861238049, 774690470, 491285513, 867587893, 685927141, 731050884, 3397142, 892013549, 361665196, 124215817, 445904643, 876169176, 948416100, 211716033, 464549544, 830020511, 509216928, 142497041, 252185515, 367790766, 990485124, 146010163, 203004025, 348294952, 710383818, 169476948, 983617556, 897431138, 107547578, 532227749, 143395589, 897379647, 92888075, 35483514, 810165543, 545272227, 767550003, 287820628, 784160137, 782517844, 158006306, 882803724, 668499654, 112047192, 914185701, 273008904, 260388605, 238054878, 83279067, 153449524, 828263516, 919668430, 424968909, 120850725, 756158558, 253391078, 887191982, 904539588, 959672617, 310588787, 931152331, 764570918, 422972196, 149838867, 129124598, 220728757, 54561063, 731827350, 895949435, 364556663, 605898873, 6977075, 528377315, 137413997, 540136074, 444819960, 939933767, 553708920, 684080709, 190762811, 307021011, 91961868, 623804736, 557512876, 361197790, 430397748, 328103673, 697337181, 133338249, 933643640, 734330582, 981349679, 966017610, 898164516, 187889349, 989307996, 714392017, 765602866, 698253927, 916132789, 376509631, 94859475, 626634225, 743793524, 773197049, 308330393, 808154015, 556555025, 678778555, 398842187, 904432109, 56117274, 364083057, 792172715, 229937193, 61482690, 406337011, 815673827, 338849830, 922419471, 96689570, 301221482, 292076699, 334444196, 121950018, 544695410, 471750611, 167591523, 916323883, 829094303, 327979137, 207504679, 597711538, 132734832, 172196842, 964342313, 244817358, 480430505, 792692291, 438099892, 940358779, 685316942, 59673320, 186469866, 834786664, 864377935, 663655199, 383385520, 587265274, 983060291, 848223118, 458104515, 971606988, 442808941, 638089983, 372201360, 580071301, 118499882, 435809213, 288573527, 341064601, 237624410, 277329541, 993393155, 171500052, 678370175, 477038199, 781783451, 462207229, 859371093, 972721773, 678591725, 416807374, 715394717, 512633423, 261243384, 745731762, 582872911, 992635338, 424279931, 547299765, 613682322, 759466955, 864863475, 881833635, 108393935, 825728885, 752662047, 718629782, 24335325, 264531015, 735970998, 955234847, 899470018, 137958995, 729997850, 97969914, 923752212, 512428618, 946790592, 637329437, 576053594, 795955634, 186246067, 501446976, 373789324, 513853898, 712738654, 560866059, 509033942, 899266863, 107318519, 957669078, 179550467, 945402326, 800044541, 164233833, 167447012, 876179418, 73353392, 299852252, 139792288, 362632795, 226041885, 94081985, 258197023, 775301442, 10639756, 532279306, 831466450, 935627227, 856281600, 354508308, 170022231, 401238978, 94032153, 837097412, 945795496, 446172811, 457708576, 14248424, 68737462, 945669044, 213030379, 277927695, 446179842, 231686601, 749773969, 302211267, 612244072, 519164351, 789348831, 53345131, 843905184, 418524989, 980734031, 251491575, 623159805, 390646788, 128809138, 553854545, 313705327, 890965923, 308665835, 333464309, 440692258, 700305887, 289985646, 963945988, 337900751, 434950441, 905648369, 608543197, 861405891, 766466698, 138281471, 895499141, 763590670, 164043332, 719985643, 150295018, 718645579, 399079948, 798308103, 806093914, 772012789, 97653684, 767324753, 622524268, 208524240, 886938103, 146980829, 820783058, 128801913, 993179239, 481072268, 308943769, 908728783, 582504120, 110521008, 734155652, 604849786, 227918792, 585348909, 864351532, 373252804, 758328172, 763066238, 825543447, 706845725, 128660157, 390954450, 363752054, 296988000, 234154241, 851923184, 133015401, 310718724, 624842262, 435271808, 891539537, 139733262, 445636368, 38043307, 784846575, 379361309, 725410527, 580611160, 163381959, 872885576, 705266647, 370119502, 728197479, 714400175, 370245498, 363956697, 288555275, 552912551, 389397761, 823896564, 650121796, 186827596, 252710678, 668679317, 529445957, 477183395, 33985775, 781265175, 486414401, 491324605, 31990399, 486948994, 95627856, 578967114, 760678122, 362007999, 497707157, 671393134, 119424057, 831789046, 375481500, 91053021, 530472382, 196871361, 42937207, 321368232, 735768557, 189049703, 455946840, 855992700, 255196046, 3786634, 835270774, 559042276, 822477671, 697268532, 934532799, 900379030, 96077236, 713424183, 761805697, 22470790, 261457109, 932594129, 846303653, 244091229, 176951595, 62810364, 886378410, 372875946, 637257926, 985807585, 747108386, 790445191, 710930672, 182295970, 244735145, 736702778, 706809291, 333341119, 105298848, 915919667, 91002782, 364804304, 175102800, 690847777, 883211783, 709759887, 450617346, 257128889, 791832899, 806002197, 820100046, 352824254, 243074534, 745137051, 798725711, 48114551, 955231114, 605010258, 41083308, 198031001, 303590462, 180817066, 41186939, 139921800, 461614516, 165725960, 873182316, 107686680, 928478775, 964139705, 963522177, 77470798, 611057181, 461089185, 276939757, 788582061, 280981388, 54146079, 103232543, 55965088, 994275296, 637816775, 605887706, 797386501, 75845804, 35068845, 61716617, 930742491, 268105755, 453324626, 632968702, 843629741, 548724663, 945105713, 176251016, 629839757, 358220210, 251544086, 95694305, 595463472, 534146851, 123372570, 868194401, 200568676, 273335889, 501725608, 161191764, 751614207, 376892130, 206233522, 654491088, 141641060, 593981462, 700319594, 186622732, 767543414, 71462297, 46586365, 240697981, 833206946, 158442673, 656778096, 508563036, 485508056, 583239290, 445112633, 565481365, 992070095, 294515958, 92619013, 344727252, 199429727, 972040962, 190527586, 377854767, 960413645, 306240200, 697784597, 424987244, 722892669, 140176737, 813444104, 93698160, 487680480, 869145533, 634009077, 254377349, 737818551, 865050302, 525322314, 180277780, 940649729, 735278655, 877887973, 916943471, 563299439, 335864831, 640952312, 944228794, 398904830, 611026076, 779153053, 262952881, 396201904, 902276753, 57629050, 510415429, 533981785, 991793806, 80963107, 43685009, 262573580, 361790359, 678943430, 343521836, 190660831, 534592741, 31158380, 348743811, 27696786, 200688928, 487552194, 721075811, 861767094, 631245155, 763336688, 131635768, 863539133, 154616060, 260218345, 269271912, 232207230, 399330618, 731659231, 768993422, 18279480, 907377321, 990182110, 570523078, 259827941, 80227405, 403853845, 668734628, 326473300, 775832369, 139165297, 597143578, 877444788, 889145026, 293402327, 605973247, 936462076, 409060742, 144912702, 152694837, 197957429, 638674367, 107468291, 250489811, 226797697, 447548920, 720419857, 426289309, 478506565, 318702300, 199508272, 974967605, 529819302, 847520482, 324764207, 655583752, 622171712, 328204650, 23842271, 84416346, 142389622, 244549988, 683143973, 4219252, 128619656, 217012183, 617909832, 397314149, 383984144, 202142847, 576950272, 4819380, 767000101, 598215380, 332002267, 532040321, 758966408, 875177533, 586484071, 546771860, 759465430, 920828475, 607477917, 689535996, 15624705, 398916806, 428846861, 789370311, 519190857, 583547797, 670290788, 793382199, 600863563, 287182040, 769164602, 693353592, 251608361, 952708777, 79428385, 443470959, 32717170, 48079978, 795162979, 277484830, 214954732, 461671060, 886577720, 20007386, 427966036, 310130622, 491626328, 791080538, 295336013, 436175444, 885196330, 480268781, 373420544, 178072272, 798168898, 238492398, 294766293, 537448284, 187238248, 662254920, 149555476, 922426254, 610379170, 833417415, 902054465, 354432727, 516591108, 911734079, 666134729, 242469809, 66089849, 859760052, 361917206, 476111692, 569351624, 337919280, 238918095, 422329512, 241635459, 671369684, 368138355, 907681830, 261665994, 905237383, 709364421, 1411373, 575321184, 185277054, 67378494, 821190347, 849727798, 301332379, 493492986, 988426610, 746122172, 936697034, 876785107, 506122136, 174670444, 534043150, 579934048, 257118882, 421298124, 871016276, 473968156, 282314814, 376225068, 689603940, 871574626, 74252606, 487673943, 528464774, 595668243, 468053823, 137020345, 165351297, 694964371, 666738029, 977434570, 180527703, 813492208, 683086182, 10598515, 597465539, 824559237, 714981382, 257526, 509710205, 641986059, 111139340, 34846402, 473042142, 739248641, 298430303, 545418523, 705643316, 442495616, 485545391, 832886998, 304262685, 669868766, 985162230, 79544533, 519034402, 23414562, 437595423, 134612803, 823960964, 814561721, 92309914, 816621414, 749441579, 889127056, 163622976, 784346722, 759746838, 690983127, 791588963, 280355011, 512125704, 643464269, 139566685, 159107581, 970788605, 281952808, 38207299, 969469026, 991983114, 427531294, 178521649, 477188157, 283494623, 488667665, 849101470, 125533580, 680748703, 850383397, 401245284, 691930157, 510768904, 548669448, 799574302, 846544707, 632555311, 334181263, 649174919, 694337913, 845730155, 242429801, 3250090, 675530235, 685681560, 486274311, 350739049, 519568757, 111737646, 336662725, 52258934, 944153112, 526848227, 632832047, 731286087, 44824577, 121709669, 941961305, 222199408, 629225305, 141033232, 209065314, 808544255, 710277331, 892762220, 911823376, 443175423, 598804577, 34381798, 821168259, 62777338, 983572798, 315642270, 476457115, 201553548, 494558037, 470574484, 648125341, 231600827, 457508517, 225873005, 998018221, 626180329, 398919188, 69874014, 250600894, 693015912, 393194250, 302947310, 916310078, 310992424, 473522977, 774405667, 133123085, 276846371, 425314660, 582962923, 496245627, 162546196, 821966315, 146044812, 191172896, 465720270, 575812191, 942198229, 855166408, 546986681, 352803701, 22219404, 592405554, 392068370, 669589051, 287567920, 296324927, 202345911, 247507541, 108088570, 122170403, 835870605, 407239513, 295924227, 378932186, 250015229, 851094809, 938288362, 827667496, 573616077, 568879391, 390537160, 798707443, 25019201, 186110864, 566443439, 335020991, 665820772, 30955525, 993338351, 855134468, 832844871, 335247968, 527508398, 5970392, 421409926, 432700058, 337694270, 605644735, 784166209, 40520971, 954752553, 594922792, 991418340, 340411583, 934746726, 318600828, 478963872, 12411768, 23955742, 14269221, 803692610, 976641316, 9444507, 562474990, 434865724, 607750595, 746410547, 658834691, 331198326, 506944280, 867193682, 561290784, 385560683, 655216939, 21606614, 32889176, 72654648, 89997332, 278691150, 287463871, 546219483, 371272013, 369979055, 243821633, 446385726, 116126861, 962560726, 23853054, 945400698, 6601913, 987851006, 588813337, 592621339, 393974626, 727625773, 408250757, 947854589, 65936539, 340396373, 538958651, 358442847, 64734247, 645020634, 690290764, 943074489, 778051737, 527903631, 770807816, 760111628, 173647183, 290122711, 575855285, 738230390, 579089477, 329983862, 680935396, 122669234, 871515168, 870127320, 246787235, 423558312, 452616936, 306617774, 603967783, 632150393, 499019537, 452291549, 955833287, 955171642, 740173156, 408728901, 2843556, 14556124, 117621816, 4556601, 220050807, 343526189, 671375299, 239937221, 540652370, 750015482, 83555701, 539931499, 845219718, 558902717, 710695941, 141954201, 329257589, 447914338, 982920014, 331187212, 923483812, 307253648, 132302384, 881220757, 301751747, 71534563, 904930244, 218203479, 780850456, 604546037, 357512390, 632529562, 427855725, 867098880, 218351116, 399818681, 526930114, 88936323, 913564052, 924651145, 576142833, 205726098, 769035167, 522789294, 269116166, 439085797, 785777724, 863988313, 4421996, 393050786, 824082431, 591438403, 996037194, 790236416, 106962727, 140197265, 867269987, 818571651, 899486854, 629671749, 710652187, 97726970, 749029871, 831931367, 856084236, 312756447, 575544945, 106075659, 294867315, 988306433, 557115179, 931693234, 239086184, 55849912, 822474529, 945028713, 309781972, 546401863, 825490622, 521270357, 821646313, 275825806, 17083739, 911422242, 472201486, 416162344, 658263759, 313864293, 708535034, 855288102, 365392317, 103910135, 559607773, 813312005, 608984000, 643417913, 868801757, 127326044, 96533334, 577820184, 92081468, 89422263, 389666091, 148017468, 63976236, 839649946, 276296684, 294880639, 231513152, 190077468, 65634504, 879006969, 417497174, 773912021, 159923511, 886266870, 812526391, 690376236, 378874913, 707398425, 65631497, 27943941, 438383871, 444034042, 954532645, 330808929, 975003364, 997062931, 356215774, 989846664, 709972467, 674792321, 334418581, 330907546, 765143921, 411481094, 573427535, 337998505, 503501861, 118846361, 865079936, 935391905, 708593815, 765662757, 754680723, 545595546, 759011460, 620712534, 353487086, 631728706, 457554389, 966998023, 112807936, 466214967, 796014487, 250535136, 421597614, 825535863, 781680741, 862965480, 686435342, 836701254, 108045064, 363521009, 878757395, 572216789, 762196850, 532210920, 136927496, 972813215, 582895502, 285931351, 836696756, 694735515, 186231612, 116522521, 447687183, 230569010, 445209736, 576549892, 895272181, 364953408, 468971838, 133289564, 163650161, 149971217, 126093433, 587264322, 511515605, 525024231, 67815260, 555696909, 314890432, 300535610, 144067630, 973928932, 999504249, 285506066, 439201545, 396994990, 323361430, 415532022, 659436306, 511933027, 831664685, 264507528, 481687977, 401289463, 803473800, 365451939, 619475989, 276789771, 123725792, 377061568, 350861048, 74997282, 631188016, 729178321, 233751202, 418743680, 511365391, 8331534, 725267797, 985485086, 660035359, 261776455, 752679817, 597756013, 91927292, 320731653, 519470501, 953229494, 175370208, 994546204, 613156740, 694145695, 334205351, 902459845, 933838909, 359976753, 560092381, 155741070, 908436979, 900210120, 184361866, 655968008, 375944865, 701850183, 435111867, 457686748, 428182331, 575142599, 187779520, 617575488, 939904629, 549786291, 224217359, 876032685, 534449669, 207631627, 444549121, 869249276, 398839729, 903285445, 633887900, 974538994, 393714534, 999266417, 632989807, 437362271, 701649553, 285938343, 410285357, 611342041, 901859565, 362171220, 834287652, 49859952, 849156723, 785510905, 589006446, 120684252, 83435173, 191002412, 473630724, 830913845, 292745663, 899433351, 309938061, 324915089, 432119287, 655718613, 751157685, 344619991, 576003041, 910935967, 705584748, 899280521, 457557955, 781490474, 436931620, 772995291, 368648326, 328346293, 388785316, 794620148, 473967070, 169206691, 81727781, 929538285, 327899973, 547205702, 665608983, 9663122, 452241707, 418250745, 197292141, 233904589, 814422323, 869055111, 656042555, 148989121, 97510416, 144062543, 127578028, 787318843, 762862317, 332702997, 850786857, 179916671, 675577123, 35309820, 211233662, 544705576, 108912289, 775562124, 941978966, 51907637, 171513003, 922896589, 315193775, 987765887, 579928144, 449323200, 98540235, 323100233, 760267821, 720205321, 548866071, 667637794, 444246899, 819702088, 291811897, 974802594, 922188328, 752868595, 7897490, 722228015, 106582438, 56038596, 777715590, 206698688, 764314418, 51484817, 984802117, 890328826, 593838153, 511184155, 432348677, 338929006, 69497911, 192154695, 656954776, 61193291, 265592913, 440723885, 321417695, 386705850, 551094684, 586404236, 866712725, 33516793, 425083417, 455430309, 754141819, 2076131, 697436934, 8753523, 842675344, 481346358, 219612837, 311252435, 344656285, 951009962, 228943931, 834094886, 35813698, 416349406, 69747313, 27599363, 886970577, 828474436, 194233109, 138486961, 774468404, 938704979, 511783304, 137185599, 622027462, 702288979, 980271564, 875870014, 351821917, 836711996, 662829627, 827215861, 102351841, 565647706, 661752919, 469916929, 446352987, 917029459, 673265266, 827385952, 810872822, 471475860, 213534830, 114556198, 611462230, 508600735, 169750989, 543114743, 729945099, 417592028, 679583494, 899564084, 787412332, 484750292, 95500589, 46330011, 357828895, 688810017, 468657709, 364546548, 154901278, 588814786, 436868404, 356212656, 83111871, 818570865, 635936735, 700533201, 569854738, 886107289, 417321805, 395359719, 110842776, 616752956, 704044957, 256771805, 854721070, 766020021, 102875926, 147937850, 70524858, 751407823, 434868434, 449935724, 560348062, 890444774, 362217358, 743828042, 96277956, 547926110, 656698864, 725886495, 814545436, 537193588, 51305309, 684284561, 429209632, 428406437, 361480861, 895057312, 468435663, 567963571, 631878759, 996692557, 851529726, 310260446, 747038126, 145072821, 292080268, 674897363, 563832728, 898501640, 987534679, 20185483, 147616139, 950292322, 61036825, 215453722, 969848378, 611339725, 63490978, 464554739, 463331777, 289573961, 826004711, 885093845, 798346524, 26298224, 86675876, 522092516, 220989584, 49373865, 769715565, 884982448, 825376805, 568279306, 682645590, 413431977, 215140436, 299917375, 384320026, 714430190, 113941958, 862626932, 881449710, 984564645, 70325694, 68485577, 837259294, 858957626, 745515477, 194068917, 87382686, 227836443, 15472435, 926676552, 967899927, 841089889, 536749276, 510112487, 322064537, 245140722, 333200664, 79775044, 921153424, 638072841, 63942797, 642378744, 392052046, 488951393, 19915430, 197261599, 502706896, 638958852, 174191730, 765209825, 14259551, 642138747, 79379778, 449403147, 919030559, 950229451, 981921197, 169773378, 435593034, 632801588, 285882292, 886296284, 459896779, 125273967, 693869981, 529106508, 636347851, 575444659, 946983351, 966863375, 684384167, 340364733, 982051591, 589838824, 81008733, 122664931, 620635583, 291987146, 642091584, 733907073, 595879, 185979919, 110081396, 20739321, 355907743, 468710262, 81754864, 905749741, 256088302, 58652045, 684087799, 493315767, 401858007, 699932287, 628649597, 829665999, 284531891, 569495009, 254931843, 336144004, 257788686, 540989255, 309981548, 199688457, 704312109, 163350349, 34585859, 426736477, 252985357, 893809131, 131618271, 532546517, 645122357, 70015165, 408394234, 663796774, 803940228, 240349561, 26619877, 187795616, 970170867, 613147078, 82915004, 790057938, 298179145, 192293718, 256460965, 20615310, 803278609, 28198528, 881888960, 454533869, 213642716, 11101132, 130403365, 296775584, 408394807, 686460913, 179062073, 673697249, 7268146, 548516447, 345704370, 783083333, 612556057, 898926335, 873345902, 527710134, 372553782, 819616133, 236672993, 865996460, 913237399, 339321110, 666614305, 500170013, 570855118, 172750425, 739318185, 138762634, 21640057, 341111462, 445927682, 24562151, 892966270, 196087061, 749110661, 884651022, 997933724, 789680249, 770400828, 45756272, 15888991, 297395975, 620348436, 895415386, 623029552, 68671462, 83355570, 273794804, 130016994, 757957130, 26831548, 872396671, 862631374, 858063504, 510821664, 671752775, 333620741, 127565198, 903251823, 594243595, 618637096, 423933313, 614588413, 623722600, 129831472, 456616694, 714107367, 106291466, 152545216, 843373390, 900067958, 35230307, 844142679, 97666619, 346771439, 859704313, 972048702, 952146233, 788991595, 674057570, 799116756, 355434523, 66091089, 681180931, 563341894, 932235701, 453567835, 873637830, 268089702, 420473791, 254809809, 713155328, 308859925, 224354081, 838828768, 174397578, 248067867, 658180535, 118216570, 935133071, 106079993, 789275453, 282388928, 431018458, 791011323, 275629260, 823164405, 222712518, 308011452, 295280662, 811214413, 493450360, 937896338, 409669566, 326156482, 682103227, 325923940, 136905051, 652403758, 179428854, 12050950, 376749713, 224058895, 967966093, 349044825, 270439753, 81330249, 337109510, 924706320, 647550148, 982286090, 737065839, 881511305, 500698844, 143964988, 623183187, 728972342, 444151974, 530304469, 164252405, 374080802, 474634612, 103711107, 591960142, 75231372, 24379847, 256697662, 211732109, 814651169, 195191582, 155787821, 789628782, 924703704, 144343437, 952000549, 2109974, 304112677, 965605443, 525324314, 258739158, 563348335, 238615846, 758201060, 246931061, 364228487, 541533284, 770551184, 168903740, 676889251, 343600146, 480461936, 838303575, 659903314, 86403721, 383408803, 716674142, 948374157, 919679340, 882713549, 368575307, 233681384, 932530711, 803715170, 717163811, 530524549, 634412972, 444576890, 204591747, 233938419, 533576069, 704857753, 808268124, 125842000, 985911638, 651440072, 332686165, 107135658, 428440354, 817648107, 253892482, 458989428, 817157194, 584792210, 379216536, 558117874, 992159345, 316746554, 494500518, 566765734, 978243077, 628731043, 119118944, 572009822, 702093741, 863401307, 523834657, 737079013, 609668057, 946761161, 534820616, 233574077, 95603101, 461214994, 924837541, 45089786, 23607068, 974419485, 251966450, 340189006, 434232949, 807559586, 878080599, 779674753, 769825099, 411166547, 652988285, 741579341, 288449768, 912112690, 954758076, 783344296, 975000551, 327602002, 690418288, 335222675, 629872799, 770369842, 280490879, 77961234, 25850166, 822048232, 732461288, 486438094, 887427392, 406974161, 653397734, 591685480, 491331034, 809477557, 82077678, 730224128, 60102544, 212799224, 997552930, 98164519, 661163144, 783083039, 187452854, 786137417, 721970809, 967053802, 778228810, 420678847, 605244644, 674791686, 256288877, 579488556, 995006487, 473966089, 702464040, 411034740, 812934991, 635457658, 984866064, 181773989, 609129242, 650016876, 521206358, 873445166, 454589227, 837963056, 303464791, 219619422, 341567592, 708983139, 165903000, 815192600, 48736657, 605887872, 923701834, 784397532, 509933098, 262049039, 218575275, 930701487, 781901720, 76714006, 555501257, 619133103, 915130047, 445689452, 547815382, 144850395, 241068132, 325682166, 661873959, 994822104, 309691929, 517091123, 539514894, 733541963, 371781006, 386044478, 326042939, 156227661, 261688275, 941564019, 544878828, 960850381, 404132335, 244982998, 363639959, 478721869, 805134513, 832852313, 499941494, 389537013, 988738334, 973082547, 320530101, 306886864, 441194520, 889299729, 164331136, 881231648, 504794469, 84930211, 147920543, 904012292, 876943475, 574047504, 752483133, 460975770, 334839198, 413508227, 873426386, 732313279, 577349272, 684043988, 916599157, 906140820, 264380418, 87739839, 655044414, 992144849, 522300546, 871105643, 538331803, 976989346, 169377550, 914865347, 926867257, 638607707, 741680631, 953064965, 306783522, 669037377, 441582862, 114900431, 337713244, 507455860, 635045116, 696888408, 608721418, 600517319, 635264394, 80429055, 180549866, 228079573, 419508809, 182521045, 173520476, 538795932, 459032061, 715922500, 739210776, 180851417, 14310801, 321807588, 723806448, 431300874, 188286288, 747003567, 662440194, 54940099, 98319890, 312470570, 492100163, 666574948, 634313719, 179882221, 714003739, 255727819, 434582675, 53057327, 123570481, 814462879, 551130973, 783350612, 421818272, 210940639, 869310100, 799239482, 730071624, 651710316, 24977205, 562905308, 797295081, 847017788, 27014338, 469728652, 457125402, 241022081, 55271980, 967268993, 41522408, 599119904, 917140264, 300340908, 636507762, 317210196, 229549780, 796514282, 355457634, 9994876, 621728029, 630472073, 71532312, 787937665, 926504774, 479239317, 179598215, 148354463, 518310121, 278000319, 611769957, 324506135, 502748942, 715552903, 209853753, 119452349, 77384043, 762898893, 336808957, 743226085, 582089143, 237444647, 779908609, 179353333, 69978650, 489072302, 309332820, 114046742, 339387333, 963048042, 736844868, 394264632, 543485884, 800141192, 176246323, 420382789, 478337365, 398714246, 85627492, 746532463, 421912707, 81910281, 562199796, 122996384, 325485175, 886610782, 800453445, 612700288, 711031788, 559204780, 855608907, 916258969, 155129213, 359776084, 328390501, 128870292, 377378739, 233083583, 255424937, 804786420, 662976559, 467509361, 843823855, 165379997, 863806560, 727870030, 844444385, 941479286, 239962740, 6187834, 908957425, 123606967, 994586009, 731333908, 340500933, 406754502, 930116737, 545047888, 20458744, 407339218, 774413504, 256286733, 161439799, 223133972, 258073462, 435502783, 615698978, 550496502, 507509142, 401885866, 321713465, 286856396, 236269359, 179248296, 12158995, 96956560, 125296085, 701263704, 17170125, 78966102, 495013638, 343052935, 948188208, 283587371, 321229396, 450186946, 129090722, 951127958, 738439711, 338665052, 470277079, 429124836, 439649950, 483756855, 152094903, 513233140, 739427090, 792070707, 244062718, 533941047, 4083909, 872417296, 778922490, 546567200, 685084287, 552044058, 16371914, 598815327, 218593490, 823760406, 567381938, 49988315, 143077900, 694769909, 398142238, 366792444, 81835770, 419319020, 291980051, 861876075, 847498395, 42224155, 650468046, 262679882, 370766254, 296935595, 700859352, 271484730, 631584383, 34626656, 32518361, 138848666, 608213603, 727067448, 682586313, 757050698, 41761206, 645483186, 266336090, 822854048, 74032185, 845051068, 63919924, 892711382, 396446844, 960760699, 169869448, 672849192, 501274131, 425634046, 487628479, 283758077, 980559106, 645632502, 405067242, 975760370, 395669726, 872978153, 211712793, 329793273, 668153592, 701482585, 800823240, 550890728, 491882126, 735384952, 480659516, 927033177, 34929480, 485207252, 179287234, 46236501, 394854203, 692316212, 888579751, 397837962, 563167160, 235990792, 614416216, 699264379, 448437703, 105424439, 541464828, 49163120, 803338556, 638350589, 73164684, 528582859, 555039593, 750281567, 488065721, 450654618, 152898018, 826275753, 707966592, 615426239, 880587539, 659395762, 919059573, 292374807, 431128108, 591247026, 807028545, 798417952, 558985068, 179310875, 169526588, 891503947, 213429532, 350567106, 750705856, 247947542, 567513947, 499361134, 979163546, 847534751, 184268312, 219377849, 798680600, 707226578, 267766095, 759534924, 464381721, 619663661, 766039361, 877594144, 505745313, 848799938, 795388486, 483846569, 184556270, 116549620, 731538213, 875489531, 116101250, 318871011, 968857503, 249948140, 630171805, 94654159, 600325411, 449400321, 352777444, 871424896, 438430106, 571278671, 31368605, 788571946, 566125289, 783430460, 899038240, 670603893, 421773590, 351173377, 737463709, 108782167, 322931303, 525098741, 790718475, 46151213, 743004734, 303461887, 160191225, 763360618, 49275441, 168883602, 735025890, 957114972, 431347994, 812048557, 969879958, 103851499, 672965820, 703369295, 684000450, 576007361, 612913366, 208071976, 51026784, 37425448, 775246514, 590965187, 232748533, 505070729, 403650953, 298359445, 79341684, 444937645, 96321676, 656783661, 808217829, 231221261, 257428676, 249314006, 167463813, 345744046, 338896579, 474107324, 789992786, 355719352, 526104400, 404512660, 645828913, 493676646, 56660055, 885266840, 89860430, 602110182, 991018454, 144443861, 881254873, 109568176, 363099981, 515645635, 948686300, 776975596, 680017946, 554060442, 600109554, 397355565, 490265906, 770956819, 825563090, 454328176, 754494469, 315145228, 109684518, 253845150, 956097314, 958105018, 556003874, 191345923, 758291863, 666317329, 236369982, 605591665, 345355253, 764691742, 752236157, 220032471, 948143290, 835999685, 149247241, 353458560, 484503522, 572573798, 581498775, 597152131, 490480173, 277482522, 957136456, 465083935, 877651901, 362177312, 184077594, 436966437, 111053081, 870240906, 430245163, 543629025, 420664961, 678955278, 46932516, 266431056, 286859879, 903493156, 836868967, 253058978, 978790452, 667505688, 248528452, 611189967, 390099240, 893688167, 966926945, 884996739, 304760371, 497873692, 332451708, 944299850, 838601134, 101749038, 470681193, 877565400, 940687940, 665280826, 575139315, 714606952, 524712257, 41726140, 175647422, 268652631, 747572732, 776797244, 558791445, 331385411, 139072402, 453388435, 537337382, 711745216, 351486928, 306139954, 680114357, 636712680, 473528563, 794619091, 198053191, 125429120, 776609629, 59955122, 105499002, 569339501, 127919966, 727313277, 421491967, 661861039, 787800602, 276654338, 349573974, 704476166, 292501285, 240866296, 117720821, 646464362, 430225993, 64124815, 222270591, 721304013, 481754513, 427043892, 463621509, 10035375, 227858135, 316040053, 226208264, 12362593, 337934535, 904727625, 894972825, 66900435, 914713764, 410078251, 1602706, 577845733, 576911177, 304440064, 221635167, 596682381, 37592555, 852590288, 109815625, 323209805, 292481305, 49782214, 322458373, 751438410, 522605083, 533974562, 556874695, 247543397, 998666511, 301293792, 568472874, 995189169, 981855319, 403347287, 34573258, 957495153, 678740128, 646288809, 519302629, 534818243, 343007087, 872054997, 994118669, 469584440, 112438440, 72615764, 117058282, 293061724, 124890844, 407107539, 884626160, 428898676, 172119334, 174436198, 245201098, 959876549, 109663726, 641364924, 88978777, 599703988, 601510366, 884981766, 876856486, 353803959, 918770096, 845657758, 663719699, 707747891, 216348848, 197883205, 51865400, 70965561, 493051545, 214478786, 865030202, 301137583, 57601068, 869311683, 993262781, 965096367, 942080944, 655746414, 603326216, 75822170, 297526297, 641056242, 312650575, 527119016, 87484932, 741205537, 750499932, 779435504, 493777457, 120355222, 286256045, 585446091, 557164418, 598267232, 671894848, 275748157, 787223589, 183352647, 854244127, 827007262, 321590811, 98968887, 418775884, 136276105, 53062881, 480595904, 812287112, 132094193, 870933677, 825320572, 510150726, 576981568, 692569558, 302533421, 234527252, 631919486, 773882565, 588422180, 539572355, 257757594, 559429836, 395667868, 619309398, 128672291, 977438985, 202852480, 200315590, 161551080, 765877472, 782559062, 780664959, 429412646, 89881614, 986412334, 813339054, 196015659, 527783503, 634271047, 411864606, 679751597, 358140524, 280811127, 312501985, 386774947, 116282885, 336299818, 318945832, 587524102, 39784437, 363645662, 694548172, 419131876, 980824164, 740744433, 396315075, 485920241, 678321187, 574730287, 289659508, 551555188, 293063631, 251875156, 888692100, 540548856, 924091956, 845741666, 119281145, 312035491, 513284263, 868913542, 533455314, 522674228, 203957781, 661034274, 107082906, 55688465, 954263032, 57426018, 205346169, 34319993, 680704831, 299083991, 216720335, 466508559, 368165763, 927761170, 953916046, 390403821, 361145027, 509914234, 426708332, 622200301, 98405507, 115048363, 489718990, 707250090, 232126139, 852291686, 859672736, 714645138, 721396893, 240651893, 320091787, 811243864, 701199894, 606645755, 16262341, 257254721, 998723668, 845608517, 434127989, 73857210, 574929705, 958128452, 707860664, 312064402, 93631016, 815650439, 574681847, 346400853, 327075582, 482399618, 436887967, 283441956, 652252100, 493583650, 833985033, 672813742, 300303234, 329523599, 646834036, 206849755, 520315374, 226431238, 647392184, 852918057, 73979107, 422491468, 83470112, 696706238, 496281787, 199727409, 322133106, 702141805, 135096109, 982652988, 235008196, 387135924, 303013419, 481428693, 678826510, 150702399, 167561380, 950255989, 230609356, 836021811, 998711280, 301842876, 678902129, 440541442, 141446699, 995941850, 1193571, 133170915, 497354153, 115368163, 25255799, 734393652, 865766141, 178470904, 560310976, 298312412, 466256493, 268750860, 751234296, 965616776, 841308586, 454014121, 874270051, 20247785, 729166012, 820523528, 467940554, 319084915, 641205112, 901788455, 403102120, 793124353, 138519172, 304118436, 869337331, 695551366, 976957574, 567129000, 647490938, 784864719, 307531068, 846841757, 255493814, 22654169, 836222364, 924379226, 209963777, 560623348, 627146851, 463047597, 85122408, 191186943, 246422899, 130477737, 508269295, 829634705, 923204162, 95038161, 21301708, 445361481, 942649320, 411962538, 186983800, 325545429, 865218676, 409529737, 793571660, 832674318, 494116818, 219239853, 199406000, 115856919, 392666990, 448796445, 205915809, 515878637, 343932822, 743390301, 412751771, 730940638, 939210058, 79778427, 419213095, 914292707, 662094052, 86337945, 589778934, 102432018, 62139054, 937044102, 648790106, 521988747, 82668730, 485982690, 292866732, 711706963, 562625364, 867817351, 892150215, 534059920, 912583987, 668532275, 509851022, 437686853, 230095362, 505290853, 572043818, 781412720, 121106777, 728919594, 447069181, 421468833, 571782248, 950457780, 469741434, 207248702, 911417420, 761517229, 641597377, 397926554, 739028755, 605424200, 284752762, 952745909, 72170747, 734169254, 109817562, 756030041, 417527579, 925521838, 539537062, 612656450, 916693922, 133166135, 584209861, 32248073, 463786667, 44718080, 416521556, 255070358, 794135939, 265842220, 26339163, 328659550, 877550861, 362035411, 738313750, 831098249, 198823723, 763762247, 554745953, 486593096, 159121676, 605322899, 956288530, 313757224, 571277786, 681499887, 86592615, 352676096, 822106319, 601481829, 325522936, 152810409, 331115472, 830043557, 874207398, 970838859, 523157410, 240373515, 635048292, 800108375, 543432403, 981224191, 108802442, 778486867, 747167498, 129068332, 194238252, 461793655, 231616441, 614542808, 425044398, 878715139, 74072133, 316725321, 763098564, 199415283, 732268242, 380132370, 802379089, 567536733, 494529697, 625176977, 555320900, 994334389, 15098704, 408414350, 743907855, 750707423, 521540653, 367269318, 619492287, 230954610, 796278812, 891553100, 640059242, 208943845, 974328768, 492399353, 820348751, 987137944, 254879913, 357063737, 228033764, 521273704, 108253365, 621943855, 288219612, 864316212, 940583054, 822221936, 394811855, 525976183, 855346808, 272258377, 145055100, 245030083, 836818779, 39081568, 719100358, 270606881, 662352010, 760729995, 800333590, 571469196, 57733254, 141898438, 537257241, 232173343, 738025728, 992429662, 860395205, 97968357, 548291990, 252052978, 777926096, 801307020, 319180373, 531587090, 83160024, 342347712, 883633216, 592541331, 557281353, 41612989, 432170718, 748308152, 33101070, 129497716, 719519045, 623394505, 441525159, 24520592, 365763185, 846996150, 445491939, 143475207, 899156849, 285961068, 728186615, 740410154, 400887416, 164952923, 222167010, 179418998, 978327081, 428310141, 365576350, 651705212, 39208792, 932664943, 429314634, 564301242, 635720488, 105796152, 180035193, 126276565, 793628935, 484180149, 606434827, 358385877, 303898376, 612676005, 145110430, 717481900, 162864776, 700738003, 176666511, 45559223, 182315272, 162258079, 538915169, 680951486, 940385269, 602976194, 469831126, 561114265, 260304595, 810824567, 910252135, 398509881, 129923483, 460260763, 147180258, 771741928, 234945785, 396932527, 124516823, 188448881, 253349996, 185433481, 597781760, 394798394, 799231899, 926699035, 771125557, 146151774, 836444615, 440411133, 210161351, 280590895, 85220226, 757641057, 96856453, 284217172, 213523431, 247337595, 316757565, 627294841, 543998629, 197320205, 939725025, 134738500, 625155002, 893197021, 934929383, 738187366, 926742572, 584607397, 322094830, 47457803, 363411235, 958134499, 238021937, 677816769, 927276026, 964430815, 298485180, 76742432, 61371579, 719909666, 565326686, 971268717, 633422671, 23010223, 221042087, 322725542, 302445148, 463741904, 687652345, 424233221, 363582293, 460208467, 399134044, 440757434, 653518852, 667081392, 567889629, 962300276, 813045214, 383102401, 354355552, 29028583, 479006417, 174931431, 80028157, 132187563, 104985171, 877844978, 357706594, 910828401, 301111503, 403718326, 166022188, 869722579, 241979170, 518501540, 812145908, 619217941, 534499233, 941015376, 210433908, 237228043, 442021920, 432358866, 834853860, 780932244, 884681533, 684580229, 578275940, 106283914, 578266139, 74187291, 962518612, 490551750, 840832670, 472680171, 366037772, 722297386, 453478531, 295463256, 650161528, 944903975, 842800975, 680407425, 655879616, 631746151, 738539309, 23050703, 77699223, 702327086, 275625280, 2512925, 418921218, 167245190, 698337458, 412944577, 963591052, 143115323, 549778464, 665618827, 709381021, 679717233, 248496086, 504919143, 375731720, 228933325, 160955475, 769924447, 486629421, 18100733, 259381094, 50003253, 493287403, 547099224, 87708016, 666402146, 766036714, 948579100, 824008458, 484260776, 577264670, 504193506, 518948449, 300533073, 29086592, 796852688, 699174522, 475184275, 798920988, 562538621, 628238664, 979227085, 413511704, 681713968, 502357084, 929436677, 164154233, 689298503, 40362964, 822917158, 833363734, 652255538, 447488336, 717100041, 947200441, 983643771, 736487816, 962225713, 452947502, 654510974, 657260593, 85875436, 548967989, 566531133, 300163780, 988561297, 501890467, 88114122, 721467268, 786740041, 319891409, 986762780, 232113564, 467961203, 234010843, 546442990, 738701112, 735919671, 483238041, 967209457, 415372380, 693758546, 610818814, 312852267, 88310605, 604981923, 177818771, 411264352, 45552564, 635454397, 950736099, 264820498, 940566043, 99308174, 425707871, 976527044, 786090555, 420135428, 512847459, 564250451, 195519046, 395124951, 179457705, 558782756, 102846011, 402849896, 538329703, 845904677, 82594809, 729054490, 941142910, 41183623, 390386430, 548582909, 300318370, 761556756, 181894528, 463850099, 294966568, 474523171, 165709914, 31482374, 223906733, 744062850, 533163343, 108393538, 752463222, 273360935, 373185919, 717363279, 144257898, 229944777, 540925715, 12035646, 675903138, 869985735, 215938001, 618839279, 105950953, 940299302, 766890592, 651184935, 515899009, 689444025, 14812378, 57507435, 543790658, 296040138, 66974565, 946690198, 633937406, 137294402, 749312393, 932275644, 886311808, 400020906, 663996480, 400732243, 19095299, 50154555, 214121847, 214611869, 268913356, 221467360, 878911835, 446255090, 329905551, 257466179, 900847811, 927441263, 27153400, 44494879, 363878179, 527878748, 793439160, 652654616, 402860268, 168945093, 202635037, 923823064, 891514207, 126997271, 797564797, 785569908, 520252225, 177365725, 192993622, 793261779, 602965946, 145220015, 221930325, 46227323, 389821410, 970175648, 689997634, 934827794, 479021778, 957288864, 525273761, 695596833, 258811007, 572821547, 504581518, 62281673, 703420558, 360664639, 415939669, 959214165, 110249692, 967074488, 679260363, 375385984, 593900588, 596003652, 484248602, 72702798, 378349965, 602827623, 594758679, 757153012, 794055285, 612839983, 343016934, 160835016, 350176315, 994102171, 315096394, 675441578, 319547369, 329298761, 522269313, 269631339, 277198233, 947424815, 306445658, 379031469, 66958985, 555087628, 939932968, 965845219, 563179019, 883535909, 803388402, 3430461, 386573820, 772270933, 746814044, 519165728, 263509593, 813317984, 879000235, 845970816, 705313609, 344144961, 87407210, 585105205, 777492878, 535940358, 485765471, 843011556, 14175368, 452894266, 827165578, 746085460, 766657495, 253941941, 505569919, 560222949, 933961297, 225327617, 432456882, 305399939, 889035964, 850087084, 341868403, 487517941, 430349876, 972949075, 935376716, 699816613, 282280855, 877606342, 114344337, 701886574, 177097652, 978792052, 802229953, 321771825, 55537564, 690374201, 167450708, 233637604, 833945917, 47852983, 290144233, 570829324, 421475633, 892271392, 133164765, 974683277, 182518469, 618008925, 512535065, 351807965, 967585134, 70465191, 116507684, 530569610, 101652611, 644498255, 192871572, 359902445, 511354745, 395259050, 193292012, 924416105, 46546961, 958813063, 640594005, 872703168, 262399275, 790433058, 985858144, 663050625, 1353629, 710927072, 110770238, 406935759, 388615735, 750053932, 31802646, 491214704, 541565147, 63978204, 441207453, 698574804, 374307008, 769269936, 730904745, 343418544, 388013376, 706524382, 236524370, 300403116, 496648337, 31583329, 766916914, 178667030, 428134171, 443271889, 119185813, 242614893, 767313605, 184450647, 427070517, 251894360, 406915566, 29491077, 814660798, 76648828, 384944496, 757463147, 342241834, 700158005, 325653609, 669271453, 569155113, 435203845, 498200542, 875142326, 96352641, 905813985, 933491281, 10573623, 30651114, 175171054, 898884103, 188022855, 133148539, 569659654, 400407075, 731834965, 766020807, 79229835, 170100432, 747464649, 867467418, 496520643, 694221621, 107393148, 2815876, 942212978, 738941288, 306540066, 401714540, 996759927, 531432165, 350508587, 955502433, 86503107, 901530416, 354686837, 632273223, 637410142, 91313126, 311140064, 897947485, 907493054, 350388808, 20762261, 478637708, 200309416, 313632115, 726583654, 887457088, 243934539, 635597705, 560843553, 713817267, 817748160, 62270788, 98112626, 525588881, 594485098, 371041211, 342618064, 432815121, 872103794, 498033340, 723732382, 256130825, 879403542, 924604439, 75275455, 348932054, 624734770, 449079381, 414092998, 38572686, 276054698, 506351663, 95647258, 833180993, 361559938, 849431513, 431456728, 886963167, 349850026, 309217010, 308447561, 666692869, 285677715, 949482974, 450194863, 659635714, 754269309, 283625728, 848219889, 523934221, 925775438, 952013024, 45976055, 169094117, 4157263, 61988741, 135927891, 804551190, 643859808, 765467607, 277385595, 143903501, 239938106, 766451061, 674025778, 729971405, 632675692, 136670661, 541313512, 704648871, 955101740, 523419353, 941011348, 395049677, 779398629, 127738569, 332391654, 570881378, 461092532, 682112746, 229171778, 697318316, 826536884, 561094504, 207359843, 624892685, 356873675, 366882662, 818015079, 745053284, 890998321, 211115366, 48810078, 73946939, 442864844, 263788963, 270326394, 820480165, 956938452, 710329947, 436130224, 406494453, 821951131, 793852856, 849837566, 354341758, 671243189, 901677744, 13624365, 381084295, 714918308, 921614485, 384043192, 95095886, 492824163, 57060862, 816987923, 984792501, 74386319, 123779362, 816827265, 113569593, 780757833, 908425108, 524010333, 316708242, 750205057, 324830258, 169395767, 364792158, 90577542, 548572913, 106687261, 445699758, 343748570, 157434297, 219835362, 777250327, 365925341, 83972101, 335948032, 383041508, 940640982, 89418514, 144838528, 84490394, 974564684, 228686724, 207958916, 686723157, 311542805, 198137359, 778879197, 152030043, 240916967, 641423704, 982680626, 407518053, 673963850, 578806446, 207682634, 449871543, 935284610, 471892985, 443245091, 654976624, 676376314, 365843921, 507909270, 209698563, 462785600, 273310928, 306254803, 146437743, 649650749, 75375320, 197179278, 829192221, 530322499, 320817935, 178622481, 335842703, 584851493, 534196027, 318037909, 206191036, 139135670, 747821374, 244410943, 336341455, 417367863, 764715616, 773462603, 491297607, 971859833, 691948538, 196508685, 215195712, 264829096, 784577129, 918599843, 427715010, 764583580, 50974778, 49022261, 931190179, 134308925, 687437912, 377844727, 45666516, 140155970, 761693220, 402470445, 654464451, 523245299, 49210738, 707133409, 551125786, 159995890, 9347318, 315194480, 105949236, 104632423, 306663589, 527347639, 726932203, 470122161, 847627638, 645315387, 400662323, 717915848, 750811951, 847736996, 675117936, 243751892, 895134534, 569787157, 403413613, 395770837, 622992513, 300602690, 851745501, 859167346, 320028503, 473974660, 194451414, 551906292, 719741067, 570306891, 942450189, 658701333, 514981797, 731795057, 333229942, 779595131, 119433226, 491884563, 652923844, 674048157, 342564490, 521366504, 457544236, 499190151, 103622416, 640902643, 843572323, 369942339, 933333313, 713935634, 808004982, 511800389, 464606479, 995561872, 791549403, 386847116, 735368330, 267840789, 509697674, 791763216, 11931703, 266936514, 216393320, 554757667, 927019693, 871966473, 554533019, 436013354, 202805402, 610886877, 33635909, 923368737, 534739390, 313339784, 950655684, 96992451, 647762697, 147078672, 156014982, 477768454, 154189656, 80229750, 730477925, 117845046, 450208085, 125063010, 810937215, 85954862, 868681965, 426558694, 256782317, 446489289, 575256709, 393408890, 132194583, 682817623, 759646852, 981710997, 137191141, 876755481, 660470138, 295898628, 707652023, 553661775, 626265800, 249980373, 788531481, 250975997, 930197402, 238075862, 651417273, 970530948, 843554783, 932285215, 417462264, 412907106, 332824283, 390345056, 244110907, 203630763, 768062633, 23589717, 361681597, 261830487, 989159225, 950645810, 224557449, 338088855, 2100318, 441254196, 101252367, 656415006, 234678226, 557523114, 579284275, 150344764, 75999956, 427790292, 598132904, 133263466, 813157359, 561260346, 237485681, 891111832, 825261961, 345307741, 823343114, 570620132, 604594294, 677403887, 850188421, 980947962, 354568228, 337868895, 498768378, 174547616, 164935271, 376670199, 430721524, 544019415, 911898160, 401669896, 660075606, 915754431, 775688430, 837559291, 60073729, 488881049, 987145952, 535415007, 608809457, 811321885, 154242149, 678566308, 303102221, 819866017, 23429798, 858303635, 758300102, 974860748, 194678102, 205197794, 37634660, 342464786, 761101712, 734926205, 460112283, 490166047, 296669831, 676757448, 467066052, 930154901, 9452637, 283743906, 763418065, 908630497, 194136598, 312620248, 998155536, 544588293, 66782100, 731809716, 172631854, 406193054, 172470399, 429911155, 950815697, 718592071, 512473136, 19636833, 530477970, 86085171, 963040829, 51629456, 928650960, 959223083, 951637329, 717341848, 499538432, 677969391, 87148124, 176327506, 636792445, 370496845, 910659152, 818601465, 751151872, 363788718, 136278289, 59836326, 894216367, 711400017, 710114490, 864386409, 374797007, 591851278, 351756156, 622200049, 641667465, 952964328, 296081480, 588547630, 902244500, 17903843, 952817481, 560917332, 42383802, 460005047, 187394968, 305815448, 813157751, 426931440, 597725136, 578773087, 99969843, 911596470, 892178894, 478811269, 140339380, 364694016, 816956906, 552993626, 944453666, 211420570, 737393011, 689790795, 790043002, 93738967, 565427548, 897484645, 139437626, 505848344, 110930335, 817669853, 866669463, 529313009, 809792006, 665728339, 84771749, 3105529, 305426798, 387715908, 972999496, 622817874, 355911842, 539453529, 712199986, 987027848, 21267302, 747904072, 198954494, 828532790, 980608010, 769795606, 869315701, 520742807, 609092225, 492962591, 232160083, 830055321, 224443937, 366314141, 202688488, 698010354, 879838634, 946559697, 610146786, 374641512, 64986349, 189689005, 712602312, 215205330, 253664022, 211117646, 684352216, 126407641, 790652191, 337117364, 757600637, 763058236, 607146172, 469828375, 435253777, 11889354, 678640733, 379286174, 368948104, 806711917, 118945621, 29823041, 235136725, 250973327, 119777910, 588044290, 479198176, 522131097, 911021459, 586796007, 214724240, 194015274, 198934629, 925218136, 426044970, 605661407, 974083662, 85231477, 949509900, 96770051, 587857821, 937978799, 161714371, 658119034, 540677589, 681884284, 599054246, 434746337, 404201305, 107134165, 388405895, 994478235, 408007559, 251426871, 380110190, 208926867, 152247664, 359442802, 660502633, 286618998, 324268681, 848159332, 506799038, 176616291, 475798421, 459807696, 91914903, 438330345, 372752478, 561621059, 994007860, 701401636, 934214397, 380840907, 818287132, 739983047, 865979108, 801864153, 737924252, 153994631, 764633492, 967272004, 764232432, 391819604, 844190089, 958921865, 907531769, 942338293, 571673920, 228977590, 425002239, 148759481, 810324051, 929061753, 708452068, 629031374, 592199886, 260760646, 322241175, 597501746, 950817433, 327578530, 100946974, 968092298, 192543754, 976055462, 73006890, 379095156, 105527790, 646857563, 82943046, 157988724, 722563550, 485632393, 552780720, 470196718, 603254874, 810135471, 502196004, 133597855, 546064605, 669356700, 708540467, 863926096, 48070877, 162988831, 356688136, 693304345, 10319238, 159535396, 64063209, 907516263, 872557484, 820859636, 383171648, 236204444, 171323174, 992156092, 91749668, 256726792, 615518821, 398102036, 219892914, 781529960, 474030130, 135862501, 288357517, 993293480, 36484763, 776842382, 785050610, 512366228, 152325701, 707524343, 274232368, 505697611, 793747918, 72427259, 885508991, 36942305, 395721954, 362817506, 837061743, 286141733, 72871637, 240766305, 952422222, 965410133, 296549287, 566854722, 306039953, 261515647, 704460093, 324774609, 44010669, 422702628, 444075529, 412532270, 681082615, 342909732, 855158017, 487331519, 353349836, 742845456, 646395402, 588924922, 658812402, 425254904, 85451780, 504278403, 101107659, 744642747, 184633913, 494884915, 50505180, 313310975, 145797594, 769161564, 515450174, 380181887, 232692093, 497751161, 726616430, 47726785, 385336262, 703687763, 333978918, 864898857, 290574517, 13029729, 228791097, 830783943, 358304031, 23333338, 800507256, 392353021, 725422618, 894921895, 855657402, 88141589, 56398877, 561430869, 810822196, 339625507, 651268794, 117748838, 432831623, 805622171, 896677124, 329566105, 694784654, 954854483, 394563062, 748684751, 500950498, 319379419, 996853938, 73653275, 114716066, 505073864, 363646947, 650823848, 269084162, 139003095, 824908795, 83078452, 851748700, 857060073, 694451630, 688152038, 502770662, 446445543, 244229084, 120190158, 848036573, 33660496, 105688425, 58606064, 166435535, 216191194, 660645884, 626643732, 205211133, 893729746, 712780673, 814792202, 913512145, 718185137, 258277041, 98569657, 239135442, 214197443, 818569394, 54925692, 798470731, 459813059, 445837314, 784289908, 355262679, 443058651, 473758317, 430290240, 185624632, 941673756, 267408476, 679255121, 94240869, 524244997, 137114604, 911368188, 748895089, 710750581, 313847214, 219740616, 777226006, 15674815, 348731152, 738163767, 684851629, 335121786, 426119303, 157777176, 45712305, 725877549, 466061382, 556514441, 682253962, 124271201, 598940382, 670044125, 960607693, 846444093, 298549661, 68285120, 185680941, 775855072, 218693570, 328449387, 504187973, 898084652, 641012604, 295521918, 506217198, 250516723, 717509484, 755476422, 930433279, 358657707, 122081039, 515701030, 892549861, 847999078, 233905120, 751613079, 992960520, 931418752, 349478602, 363301501, 722002783, 492554476, 763169004, 417991527, 11600298, 438281027, 130239494, 938161091, 191091153, 542367897, 988394560, 248736454, 190092789, 801388165, 890917239, 483530692, 486655304, 178395691, 56789158, 567876270, 813623419, 602340846, 755640717, 67627772, 643948512, 643490257, 893877883, 652396979, 775148782, 921158368, 267775471, 47724837, 851639171, 522081634, 772132170, 208480961, 593007085, 515077501, 490799010, 586102710, 980415496, 612971858, 420574970, 784845456, 907277557, 539953881, 774248063, 381849510, 350584888, 195051220, 670552454, 399873265, 897995539, 418728816, 692826496, 139760321, 941225671, 580552085, 57209237, 41397560, 145627596, 157090966, 946520353, 316396010, 525807692, 818787664, 764409888, 385078898, 645585433, 907286616, 618123886, 389779621, 569861250, 67093612, 406013590, 691709593, 153817703, 928159845, 78170649, 109248399, 151228825, 786285686, 591056968, 712532245, 828752945, 825515018, 305282822, 179947260, 151205991, 965601435, 86866959, 663458194, 380216296, 279204031, 770081202, 4396141, 415252873, 868758478, 484067460, 121136075, 17022135, 54212088, 312420170, 503006148, 807192164, 707901970, 145386695, 481907140, 364063774, 87327233, 824492410, 28785991, 962225496, 319354116, 709259239, 149709944, 28570973, 666464012, 787005433, 471374901, 929997021, 72977304, 430347156, 943186774, 119425972, 416989685, 684099119, 982562678, 852711588, 477452860, 387713696, 615965739, 544853749, 436851266, 301599234, 292405370, 588572559, 206271264, 472879017, 452126391, 159554606, 968355026, 934031076, 158761019, 342846203, 294129993, 967383768, 806443986, 284112644, 321534629, 166178555, 315120816, 188105984, 791677819, 746481771, 266117797, 908314183, 204068192, 768142762, 652000730, 5153774, 597757082, 877248888, 563477632, 929032709, 547320770, 517433052, 486955491, 822223557, 15295363, 526006684, 734083541, 42303237, 60765173, 517220058, 612513050, 173470154, 391693768, 662518391, 839816543, 749211025, 586792333, 944330825, 33978080, 266214449, 86167336, 114316226, 498506554, 903446594, 354229740, 554326067, 40239309, 89490673, 458314095, 473828443, 943895923, 44445510, 867076176, 735782992, 545793719, 535111612, 656542847, 366741149, 973274434, 960587484, 325131069, 20793932, 702756780, 192484190, 593209478, 398264104, 745980860, 547807844, 432501474, 402185034, 80423537, 442437756, 163751093, 288607873, 102207424, 213378537, 909733356, 607726172, 281422743, 371448196, 983233912, 610556550, 892992713, 464944472, 850045556, 72561966, 276643533, 325582294, 817829520, 787435313, 410063430, 120217178, 412002209, 110583172, 667300696, 112600047, 514998155, 423847464, 580009325, 695501564, 770819514, 151238488, 317471442, 674224772, 845235184, 769372650, 462626662, 58807333, 877232438, 860331134, 580043352, 590453466, 465742235, 637587428, 29342549, 811231060, 280055685, 411269515, 439721691, 1174411, 658896535, 87580930, 580848096, 253284769, 727508512, 827203437, 4775239, 700321387, 903523498, 635508275, 605587422, 183440394, 287714529, 513602826, 689974700, 876464014, 396672352, 331536745, 599848134, 322055424, 164777204, 592317365, 457938770, 661953352, 589384997, 229084875, 798622630, 501715094, 350194816, 54851602, 777407197, 51731649, 998417285, 146605908, 850171072, 65765632, 476624238, 438786710, 278228073, 828968550, 895638597, 834738898, 146553098, 338237351, 319831077, 974698845, 283838361, 635362530, 365824602, 980013265, 584544456, 630971597, 91579978, 359128111, 638780411, 234153345, 857673130, 657805035, 131929262, 150407039, 693947890, 281404424, 875111001, 713218820, 728828770, 308827883, 413398389, 670480552, 384382844, 969322195, 376832987, 68674427, 476633083, 97447862, 968850190, 824638867, 74623630, 97023379, 746618502, 68279684, 146254616, 436829992, 697646542, 313744992, 700185866, 878772553, 24455037, 182464979, 497714802, 517667671, 844838718, 660809512, 101407150, 801915084, 72463731, 256321081, 543626079, 252680767, 271506888, 260173303, 934906288, 84954742, 350834127, 321082767, 489425506, 833526785, 514473497, 964393883, 847065397, 454148508, 282306394, 88257051, 608469810, 396157588, 901803575, 901767346, 243010989, 463014164, 462184055, 453760350, 625452548, 928737149, 946537170, 835578636, 229049626, 338153788, 691755537, 117096805, 843671411, 886841205, 554338908, 21123360, 529134068, 492801573, 554353764, 224195520, 155609455, 935674456, 389964934, 19842407, 667825243, 635787598, 685006418, 721025352, 637329362, 383802994, 366455166, 252963134, 283622986, 856243146, 731184998, 904276049, 552880201, 107796659, 736523794, 169483652, 748150907, 951262717, 839667292, 373473101, 506177975, 698173295, 763586728, 971937063, 818621112, 251778093, 821315856, 730707834, 414678004, 120308236, 44903437, 916277647, 961722102, 243671306, 800509181, 941019044, 228108984, 390799177, 822879288, 834254031, 374334298, 662786905, 250908402, 935761652, 188565904, 537751110, 496260868, 41773535, 859054775, 368116080, 715084166, 785540124, 528892299, 349851416, 794422660, 314945805, 327908497, 436117241, 155167059, 964709926, 901612480, 89400381, 339030180, 339956727, 925770068, 3329568, 251235717, 22857408, 975133088, 323550677, 124995356, 412451667, 919382861, 248907459, 385985789, 518948147, 492959109, 212830896, 847891027, 210460780, 771797630, 309903625, 445812633, 779863120, 867337262, 385999905, 255404991, 690590973, 809117742, 249789783, 911692517, 72453851, 864474399, 620487967, 350310894, 913503330, 789818346, 330276868, 576070605, 635592332, 116542989, 562676219, 455325733, 166721778, 382632426, 879998064, 402325680, 27243756, 970111610, 760280530, 831664748, 910009571, 60803316, 978996475, 256677090, 629051589, 380989478, 581709550, 572806769, 746529882, 839725624, 684990944, 665894112, 288912122, 440580560, 173657040, 308946159, 180216119, 832556790, 899139915, 115777566, 457550451, 449585084, 970692972, 590348922, 101927924, 227252753, 792229879, 778719531, 810077735, 858951375, 957558582, 511591532, 220683706, 147047959, 511302113, 334913857, 720953250, 607128894, 831606973, 290062625, 272176858, 62008008, 568030597, 772446993, 748721743, 704014515, 103836614, 376522933, 729818216, 771697396, 94753037, 379912624, 481119824, 182220913, 375481271, 96378273, 277007574, 575380237, 800196801, 855750193, 214963226, 353794728, 29246338, 533422820, 516793783, 346529207, 672744050, 40866008, 548743260, 286286818, 205260760, 817209507, 703232036, 868544535, 844588306, 9665949, 52663379, 703291134, 188469151, 977994860, 250551777, 771988136, 885959818, 489454846, 703096070, 369827245, 164228467, 998781481, 409853350, 958367096, 40743970, 904808996, 796893622, 852840892, 60024220, 124114856, 255007198, 347174701, 106881280, 369351834, 410998023, 315576816, 59552734, 937705449, 777166195, 138002400, 201775412, 736094680, 555537459, 225636599, 737271681, 867600520, 458600114, 194078911, 456975503, 208163918, 993297618, 51827601, 55492860, 343081173, 981337465, 768610824, 318098266, 458986544, 330886345, 497118194, 688289613, 342974250, 232269764, 246088036, 210479215, 372010320, 827141091, 473930836, 726017376, 736063140, 800735733, 959269655, 517679156, 335758669, 983981199, 575390060, 773555659, 76053525, 626878794, 886996727, 618785169, 620917970, 358758438, 462371457, 885802480, 687985623, 197971903, 50948433, 594990762, 422775201, 136319840, 721749331, 619727566, 713758331, 801832436, 883208908, 815926152, 297759706, 58933782, 98435316, 843632674, 455208442, 850903572, 621424978, 265233826, 220059823, 330902598, 822773537, 561180578, 737086555, 774203871, 958642161, 241206263, 299047863, 397108037, 161179873, 508042462, 598639757, 529366782, 896079489, 859939210, 995798945, 476320570, 86047995, 226101090, 842038780, 132871407, 304858268, 830092500, 370534546, 480640203, 793683781, 714671224, 405820950, 5617127, 410718973, 50976859, 15881889, 980492416, 481551122, 278041185, 40549172, 204852028, 686311465, 7955678, 997172630, 49437661, 781199081, 193638628, 272033138, 778439063, 897979849, 663699510, 732716184, 500504672, 245612277, 487638609, 783958825, 24716109, 206118604, 577826185, 505332646, 236242716, 37613552, 812363904, 749795674, 774603049, 158065354, 81224522, 81186390, 748039003, 527631415, 493328358, 310489394, 392507189, 334608766, 469265654, 420153033, 114446289, 818397637, 762123591, 620339483, 632776806, 29176000, 550354101, 751994256, 281662904, 137702565, 753717684, 839483381, 588404440, 599008265, 514104296, 501343947, 447139064, 547035818, 115176818, 415473798, 34159044, 167287734, 657546884, 14853032, 605807710, 843938375, 899992060, 806905907, 368656304, 121367627, 930259356, 535173318, 255880583, 744800207, 777352234, 114381162, 17256749, 912030071, 400134432, 74039267, 55954661, 470241742, 720137903, 295920023, 238902600, 828429276, 969572880, 296430738, 864344333, 336430014, 947454946, 412079166, 227134180, 204401367, 901877690, 844598163, 985946132, 592947964, 589296981, 68371609, 279749378, 444679914, 173592312, 300954012, 741211386, 247475138, 934181105, 163584553, 544689720, 517753571, 441431386, 295795467, 378119527, 706029728, 795890908, 874510594, 878947223, 727901022, 710534713, 831704623, 686545024, 600811984, 601709472, 271979539, 613955660, 819461199, 115858045, 34988464, 565978221, 574787311, 400060573, 76855303, 154356485, 688981252, 52790760, 273862424, 692524378, 45644270, 499377999, 764383579, 308071378, 319884982, 208219118, 192040900, 512259117, 202683556, 523640523, 600670016, 253666003, 561987612, 41343153, 641044369, 216626697, 215873656, 609904257, 430593797, 172623073, 225141335, 49713515, 14128766, 210722052, 940909627, 544941583, 753223924, 349324275, 573687909, 480612902, 484465864, 491148981, 309265708, 232416537, 605127047, 733524234, 335464599, 804511391, 707626594, 275757651, 105794710, 855330630, 552891374, 903791882, 526556538, 997335754, 650267545, 441748368, 338172093, 765561644, 403116633, 784775119, 599752169, 277604967, 291799976, 439375668, 580836580, 540872815, 145933765, 173321547, 308066326, 181988299, 992563357, 547530258, 177227672, 377695805, 963361982, 368651635, 412039965, 776655426, 13031113, 276698880, 862704771, 272517976, 682934639, 217774685, 569410316, 790180641, 808044917, 790837362, 120160288, 781710421, 178588449, 633602193, 305099968, 564868868, 655486268, 4253788, 620156328, 805722846, 201228761, 530500758, 756098820, 72251660, 844279651, 716012246, 188675019, 967256575, 323091983, 997746991, 827774939, 504513638, 564281728, 740632203, 610962925, 671649972, 903166360, 953667255, 951110683, 180543020, 62059005, 664732318, 303389132, 245488915, 722262363, 927585101, 845260187, 955308102, 758430456, 211666335, 564591894, 374198327, 651706603, 261622544, 400735493, 574587143, 799898380, 734327268, 78332353, 250441419, 327005478, 851834334, 36006840, 512208105, 34310588, 737748667, 742942062, 361067353, 164015760, 984662236, 848051055, 113863096, 986441013, 999843028, 862937448, 133858142, 562248473, 159949559, 427257096, 91594761, 36977936, 806067842, 993331135, 366255425, 944239212, 91041150, 874276455, 536588337, 519718896, 176160137, 904926734, 19834456, 889860272, 641723063, 26431230, 346301568, 604990736, 751709400, 768425198, 153742014, 729766983, 774838428, 908952888, 446232863, 821938560, 797932512, 435522373, 697334591, 982111090, 534449695, 541143452, 585166859, 893128961, 970108191, 956201311, 46699795, 171237442, 215929110, 636845581, 285105676, 355197827, 511782159, 820357188, 520836192, 362944541, 123817419, 920976793, 119689435, 961190039, 437459558, 781092476, 389828972, 74612686, 559361203, 886348507, 739141098, 40503552, 411594524, 655444265, 702000766, 799894428, 38858594, 870639466, 224857050, 1669533, 957101979, 346541197, 756884630, 705377000, 997539593, 895475841, 570832370, 442234833, 518162738, 58664643, 228689694, 980637713, 807702866, 589626410, 859725960, 121226353, 439577980, 29700719, 552828089, 660433342, 547609664, 949121079, 115388242, 921529836, 717578308, 809509069, 935582653, 388399730, 60564407, 14334892, 387477104, 969028892, 280272317, 788607895, 66138377, 984888281, 119001637, 589862523, 556059816, 217539620, 409120377, 835482859, 979745659, 917122552, 623279310, 75229518, 276778397, 766616236, 199349082, 33915610, 444942617, 818553437, 75828215, 895059009, 515055255, 140723812, 188529737, 13926613, 859100172, 10501149, 979757353, 85686062, 954743784, 604585641, 251665153, 545088215, 810445463, 422772552, 266310052, 815923990, 577902720, 937850770, 241588251, 965764885, 139422682, 374281596, 337321734, 78137274, 256209978, 877375858, 484219649, 807272622, 623431724, 573739722, 923064764, 99434055, 312015441, 429688258, 488164794, 250435238, 718774268, 192644535, 714418476, 780216953, 698320836, 202402613, 646183094, 263275861, 96445907, 834369845, 560398815, 102719931, 38750217, 963280841, 42808252, 659386127, 840277999, 754736712, 210638182, 176709430, 329323584, 946786058, 104550420, 474262297, 79811532, 792510483, 886414021, 830840021, 66475217, 809536909, 352233655, 587238873, 824364138, 949440421, 394599359, 458125168, 756592777, 247949076, 938660754, 275779801, 959202332, 928314701, 150855748, 7629030, 797214791, 910165050, 576517777, 876471438, 120572047, 937808789, 488531692, 891641754, 45597607, 85741596, 508803150, 192393246, 948331387, 307814648, 968103987, 828249108, 426702672, 116478077, 622524176, 678727264, 840041060, 182507726, 126156148, 61252052, 218976097, 503256970, 576243579, 789487362, 522595687, 465936873, 866007909, 288134131, 308160632, 121606512, 567577195, 296547036, 960469619, 420004332, 36047469, 822626303, 65235120, 728310612, 939385631, 96111622, 609781841, 699037922, 252756591, 953065904, 749368719, 331309172, 233733736, 840473898, 799185885, 885887296, 791196489, 792646088, 2594210, 813234838, 37192269, 237544271, 445613803, 66738376, 933759805, 837400701, 959534351, 630620896, 626232122, 686189349, 489378682, 40319420, 499841954, 129938113, 931096473, 147110661, 309166214, 867379487, 678250648, 261586768, 596934890, 641502070, 105012791, 391054976, 201299362, 471662562, 514784400, 230584599, 212467794, 233361899, 958384607, 925070547, 119091780, 460577737, 807338515, 880155130, 267696462, 125272351, 923430794, 963011990, 611822979, 619371200, 256169087, 168728549, 366849249, 145861769, 159222128, 137724435, 364481542, 806367011, 648520662, 397038045, 55490525, 780580457, 354375697, 164186175, 213469039, 272231273, 956863538, 392371572, 222881733, 843945050, 357325928, 597078237, 568934125, 696961676, 392707362, 357887882, 364359428, 767698170, 432733187, 689490887, 678706399, 835296278, 730429503, 408068604, 361803326, 30175833, 808207036, 173984807, 123888984, 551306481, 57553567, 791193542, 553156701, 768925074, 317718322, 328912127, 560133023, 870569281, 722149802, 481006848, 694463989, 13452322, 18725744, 709337192, 126084401, 304177196, 806114615, 319142811, 347276355, 756932616, 967607581, 676066933, 232296324, 756268104, 4259638, 473653258, 885098630, 406330703, 151595495, 817986131, 85849606, 783587311, 632622730, 99160000, 581520807, 163152354, 780022576, 568754405, 952706388, 591604391, 490430205, 919523919, 36737297, 813127205, 815428941, 135754990, 751333025, 966229111, 940170811, 761765560, 707539488, 798086315, 665382970, 596749744, 786278681, 53692103, 724071483, 895691553, 158678668, 713844754, 119356582, 621591705, 525564937, 48629217, 215302183, 626857561, 329254658, 216008851, 850638504, 140485136, 665619034, 867825219, 169397460, 887882393, 205494846, 391627899, 885776727, 189766344, 938317144, 23740366, 670176535, 611936226, 701564807, 739529105, 891464611, 887386510, 69170255, 367067635, 45884645, 58609624, 161960658, 112237824, 563750861, 867338408, 906991247, 543628567, 477440847, 770374754, 979874907, 482064516, 984351047, 159829231, 349056036, 789334692, 547039822, 903787760, 891591043, 552653542, 765666329, 877175698, 478003839, 918307529, 388136463, 868938012, 438087738, 330446794, 693283835, 51362799, 694761808, 779148675, 780106666, 558867930, 570552693, 844480608, 893365321, 783555331, 494502825, 727637773, 722029360, 669383175, 589272751, 246483875, 159989193, 489217202, 817629649, 851171262, 442894551, 289912665, 621890508, 708870767, 174332227, 691382543, 676437765, 763342016, 27219800, 466036478, 843982178, 932339874, 786333262, 169912310, 44766328, 478014794, 591508200, 428589304, 227427868, 357789813, 720148002, 918504255, 159137619, 461813180, 669917089, 520336597, 960177907, 231765346, 66597192, 19245632, 957383971, 584706526, 460712914, 122397812, 867916488, 10003690, 708823170, 515871199, 377192239, 14070552, 955726486, 267589927, 480971994, 777157155, 411624043, 632252413, 374866894, 939166500, 791221755, 819344158, 273521287, 404219554, 723864329, 276468400, 172756982, 769297964, 426030449, 680658044, 407487058, 109163848, 4679914, 144432855, 174210348, 935645960, 643118482, 994263320, 300920488, 739164603, 980410715, 55079869, 915676081, 789041750, 8984318, 194504097, 850720821, 232328240, 471677290, 621718642, 745494738, 217171968, 507465261, 922012592, 44306526, 596797589, 704887845, 454155426, 717110934, 776320091, 507614749, 447947585, 735845612, 153714918, 354218348, 184714432, 95243492, 288158974, 666941808, 681467179, 309050739, 640023717, 340391362, 351154063, 182735169, 367988226, 898794569, 537041128, 94759501, 988859775, 272022952, 86291264, 528348503, 279575139, 212408095, 400813546, 702023589, 508536132, 601145498, 62389496, 252915103, 916073174, 910108014, 749445353, 35045886, 169420633, 330973716, 788997719, 528383632, 332658776, 19406093, 226232001, 425804488, 395522940, 435262220, 495826361, 454515411, 663683022, 28380374, 179611378, 405088280, 508411247, 67919956, 653599009, 782789358, 822724292, 382422348, 637606526, 673828125, 616088055, 113854255, 79440083, 158650955, 491102910, 248439561, 280325179, 894039439, 979719800, 365047050, 665771929, 607483860, 599862543, 65481337, 64749800, 679368567, 223937474, 163387484, 876333246, 880794655, 484462130, 830231273, 700860808, 198433102, 392162846, 617790384, 512739417, 599502352, 512664357, 928248257, 707269479, 431836741, 478048210, 604467254, 436945331, 79398244, 83369200, 954506256, 291169371, 348403901, 533493519, 360835765, 999560378, 373970993, 80595497, 621213609, 15995852, 129148545, 368196446, 362558552, 773858181, 814717303, 59849355, 734534636, 885289703, 876442326, 227300552, 740443943, 368263419, 386902524, 561138414, 945325771, 561507952, 68768379, 495386447, 519746790, 327416000, 398111177, 939513593, 289569896, 442589235, 220830307, 795007866, 857918165, 72282301, 280323691, 958343802, 650290753, 779551564, 161913855, 309083865, 791238940, 651711424, 862733716, 136127114, 731125734, 529587363, 233466038, 385638617, 233063640, 136082800, 780329793, 215631717, 775589558, 992887429, 355475363, 347798195, 498758028, 130904948, 849060941, 280797083, 293446193, 92956638, 5998286, 255808905, 894226028, 77671335, 721280487, 791283518, 931093689, 950786999, 597207243, 536175473, 258209078, 933910868, 281786799, 371176595, 414706304, 573632519, 5219177, 964561594, 63715973, 51645387, 202395618, 373576255, 756324778, 583627215, 822530749, 333962246, 699780014, 574750990, 731620123, 346848501, 446322584, 809965989, 153592225, 782098271, 183965751, 947482543, 212732709, 548972034, 174459127, 351727755, 566733509, 456836828, 219712807, 24310403, 188919175, 670669898, 864938175, 369714891, 108942467, 308000827, 576629587, 622507216, 271416540, 715531449, 241140887, 122957707, 888978780, 170966722, 242314945, 734394231, 840597075, 391322557, 773521153, 344709208, 846575551, 321690937, 41108761, 218599851, 699205704, 900430518, 395674053, 973753372, 157086054, 915368009, 127294651, 379765825, 945072239, 994073833, 14627762, 196505683, 658867821, 718899096, 105494581, 664002313, 191658293, 147630572, 73043775, 137722833, 701677191, 496051116, 631826220, 510251119, 825012987, 255504339, 928612640, 770121044, 403241516, 418446918, 699010207, 888022262, 446030534, 879552490, 227100491, 366419373, 551798877, 710005332, 103186837, 10508211, 924707510, 397418871, 288295446, 347115730, 344832850, 677395857, 614102660, 544669266, 119791478, 497639942, 926017113, 333385160, 552156912, 558939733, 518443235, 12008162, 118265974, 870052427, 264110964, 933384721, 912429990, 19262092, 792397583, 499578600, 487708395, 342495603, 154850766, 589453726, 263521928, 111974637, 968826452, 194267317, 438331271, 528980000, 345491080, 132727946, 454920746, 325409790, 751163565, 205564550, 360007071, 188382658, 443567402, 487759852, 515086617, 943931447, 166086775, 82526424, 463708531, 742822178, 353735044, 202499149, 49521672, 39026991, 344182188, 203903961, 111360922, 902647290, 945702185, 21632823, 807570926, 459967732, 945389907, 130781615, 370879794, 441914632, 514218135, 565386254, 590363351, 462685379, 441132608, 957631194, 96914859, 221860065, 391758363, 257754546, 124287996, 219523037, 568337509, 986693919, 681078288, 863162953, 972237639, 807499857, 852608032, 433698170, 553905923, 254693915, 783349534, 504278168, 445298180, 209866773, 962322825, 224808369, 181198264, 956486880, 57148655, 228327393, 960103412, 713222382, 227970427, 828325675, 918228730, 706380603, 781751880, 392803647, 371028046, 511008721, 670456111, 410163020, 552489040, 679380236, 208289894, 254981554, 998606285, 958618614, 160172607, 275036963, 974344876, 703063334, 272806219, 555244133, 57255142, 778140692, 20794559, 244636015, 882620079, 913654281, 522467299, 852734950, 62835582, 143189832, 476768944, 381079799, 454449076, 107927680, 971633803, 226394548, 476745178, 515903496, 885583866, 23021668, 588766490, 664538886, 928737193, 279337009, 793653742, 904035529, 129476956, 380081165, 15689624, 534137509, 705281100, 393555034, 641853949, 503570648, 416448448, 800159986, 509122985, 252450302, 705194035, 885462889, 963099485, 41483387, 147826211, 510535356, 775836437, 934505139, 494277918, 744719190, 164962042, 148906176, 736331245, 945532080, 431268638, 652679992, 454865373, 314889931, 537535088, 236039847, 899847934, 329283927, 992105826, 200437471, 346955693, 320221779, 763205637, 711828723, 866046100, 229026376, 851318690, 39925779, 587854279, 834391744, 570931148, 984238103, 41440304, 775826073, 363077388, 494503911, 502421499, 871847522, 91558577, 354724358, 406076998, 616732102, 926662698, 305855221, 86393943, 947234994, 735307946, 85781822, 559580816, 663913860, 126813848, 653107767, 397090402, 222156910, 906817135, 550049364, 44999546, 860754986, 569947365, 172214739, 89048200, 985021512, 13994051, 154166919, 584862923, 894580594, 170702726, 942563880, 100869570, 486759799, 945966380, 222524636, 13361612, 790829085, 593622861, 865521988, 650210436, 589435377, 794398935, 26856696, 635904923, 602965893, 305928773, 107543531, 169894717, 585866629, 70119714, 412016818, 357994227, 891253776, 968140589, 469968930, 375985106, 410040797, 99046984, 931373517, 391083701, 824611878, 212584839, 335250852, 933150905, 604634600, 680400608, 109818643, 671846335, 590194421, 583224067, 424684974, 223286830, 219118933, 18822812, 868593504, 356188272, 383356749, 523397173, 339409861, 239336297, 248750664, 190851975, 325275576, 347486222, 245879320, 640886329, 382085982, 329430657, 532482044, 966819481, 864378106, 517123944, 168950249, 392043236, 771168565, 389848982, 415026044, 523476377, 505609523, 635614303, 932997603, 402700553, 440748569, 878276403, 360596480, 329204579, 850093097, 810000891, 875020583, 749024686, 376824901, 167502137, 193842242, 993005422, 399389332, 758550311, 571120516, 852260346, 527582648, 453972463, 874074768, 368698869, 603236151, 856134126, 203855265, 68413490, 853134475, 25132404, 947358680, 895527161, 927396891, 206072927, 743727739, 392495368, 273597629, 466219339, 508594635, 416664642, 660611790, 359318202, 934586024, 990878033, 176950416, 619332272, 89892102, 717670134, 329153632, 445666163, 392140543, 427991865, 784858269, 534699456, 866596917, 599498127, 554217225, 626717649, 164304490, 527808665, 49361315, 197339009, 506044909, 54843829, 639010819, 821047177, 679522044, 267042684, 337839464, 920036196, 292564967, 525189912, 914738315, 434955090, 447915492, 650418370, 968274832, 745080594, 94280705, 925198801, 941865299, 513050352, 473950186, 832085939, 979669149, 734000066, 351129460, 237395274, 246311736, 825535287, 641347289, 182057719, 287120114, 296470406, 872354752, 787010752, 926027352, 527252671, 395555911, 935937093, 629584814, 293173533, 216029121, 293032954, 488818720, 669406158, 480576450, 489804180, 872143502, 552216510, 873536784, 596431806, 786948832, 480483203, 676941267, 657005375, 297714514, 173386514, 445412063, 133642702, 855047080, 945838074, 999942480, 227741190, 260514524, 167269338, 99245720, 291946622, 340715850, 433019304, 948084513, 79865019, 934773608, 147173962, 861407225, 343737339, 794932102, 219934979, 26570647, 576354273, 416681811, 358830079, 503420538, 379247050, 251386107, 11028516, 899403027, 915510758, 39357646, 318069592, 1838151, 653639574, 463502941, 929294163, 757919424, 816415458, 583385504, 101300254, 912613634, 715991937, 695998726, 287516606, 382802420, 853743800, 963081215, 777885345, 529628270, 816978247, 352744771, 378664811, 416492234, 794818161, 725859540, 777003975, 612989840, 274779490, 587243841, 357014581, 695819777, 515900266, 256510470, 650232969, 951656611, 986115962, 399795051, 466705401, 934767429, 314993153, 640476273, 871866293, 452583988, 160328921, 373531211, 179906458, 529719603, 210454647, 743333924, 563603431, 58731013, 622931948, 951100275, 861932770, 153883955, 170152496, 583941003, 962029180, 675241208, 659695893, 483269208, 545105601, 851382036, 402413894, 13621669, 261361523, 232413113, 365777038, 914881680, 845543618, 565257037, 929697323, 560135925, 939984161, 292643306, 874381420, 278046336, 959464160, 282324401, 569094114, 110298526, 5667662, 188902813, 515680369, 495258845, 844844561, 808360727, 643407418, 71059987, 276266064, 283394028, 204758639, 200004930, 464710288, 138308526, 312657448, 708125486, 519455324, 296783573, 541139445, 767263395, 932123061, 899835446, 999495436, 247259069, 92215005, 205700695, 646983888, 960743801, 275861492, 26732074, 853721665, 439420356, 72820977, 13797028, 194752762, 201381927, 400444190, 225631965, 121061923, 39664743, 280684065, 804576415, 125906844, 502043717, 492851887, 483812821, 385952158, 557932625, 521780899, 397500382, 493150841, 963596515, 451459957, 625337244, 257210548, 791551191, 854361894, 757259331, 876486201, 351670582, 87627571, 432500014, 786830215, 62166574, 112950775, 670528988, 203473244, 759659108, 335571063, 53638896, 956684146, 665330278, 285551212, 844974930, 111596329, 961900314, 338615082, 281849721, 997049203, 506833989, 857779076, 125308220, 583499595, 621449831, 332146019, 789634051, 582562508, 879455982, 552122757, 192742297, 581379401, 710364483, 917605979, 350336918, 79747914, 497097545, 61554751, 664555035, 60497770, 337753496, 121012285, 111910291, 655374060, 483873367, 125801769, 261569731, 396576251, 473796000, 590214669, 504071688, 293759422, 166884225, 172402450, 915635684, 450402208, 284373786, 744489605, 576903478, 717268294, 438738742, 558309143, 144452592, 494086862, 905777339, 169252990, 896053246, 936404255, 178960139, 114568530, 252888382, 864578554, 916280063, 343122013, 985420275, 434795759, 723334828, 69639655, 230492958, 103220323, 862707997, 520022027, 755838466, 989629058, 257735872, 27111469, 931416762, 172333236, 929982409, 419371715, 63616034, 802866695, 768442070, 349246137, 484151122, 287859809, 54283257, 603339648, 882973739, 859076971, 337001232, 954809642, 177329846, 417877006, 995382250, 325238060, 45652159, 573767637, 171331603, 953545677, 469572728, 801443476, 607018539, 897898021, 2527342, 404285315, 572349674, 753157092, 899405808, 972914043, 855144162, 234910049, 247041857, 517806005, 667608690, 622553684, 413650714, 419724485, 859498273, 336742963, 90954855, 46895809, 335003796, 980540115, 1651841, 912315315, 408261183, 231403242, 705781540, 238264665, 586020453, 93719284, 661792416, 475385123, 670749796, 747554495, 166623534, 456680642, 450856245, 426277911, 641202964, 553469127, 694890269, 601604520, 978852360, 577350233, 2346795, 36029860, 941923302, 117754699, 210420850, 754338543, 530843209, 282129130, 964891939, 760790007, 915997257, 632223933, 419284298, 680657248, 848358015, 246267672, 134504350, 473008479, 496836064, 424852645, 936870584, 525075980, 834216995, 88994203, 701771852, 793902139, 304701619, 26984238, 667376816, 653136087, 671851592, 278649261, 730150641, 709260059, 161079310, 410676721, 652621561, 73912214, 573950678, 142100017, 849500055, 833721468, 854077485, 196817092, 141294440, 874807572, 208016006, 613984619, 236759850, 467424568, 590276283, 104713762, 145178969, 800340364, 274892604, 707464633, 399508121, 536645510, 944869817, 442645804, 328283876, 81826976, 934882189, 788114226, 696353582, 115124972, 866189765, 709573279, 424190677, 277019704, 591987688, 170906815, 691070662, 830407540, 958831653, 757319150, 739073252, 285511647, 822574348, 630905500, 525593532, 249222652, 19663528, 54142884, 392961946, 818814111, 981778535, 141293605, 407111276, 513380347, 996637162, 556527041, 190336305, 929970008, 39063324, 11967889, 335608917, 12278554, 386621808, 278879154, 772366992, 286500262, 249818188, 126546914, 240667542, 379489583, 770756634, 421753710, 783783059, 13132093, 127987018, 618526052, 782788596, 405667675, 35398946, 551976800, 26159669, 411094934, 764474734, 123831384, 442410042, 883445782, 585879021, 172484128, 343388599, 507424867, 136597407, 41878304, 717157848, 981150373, 691249548, 793580399, 79790084, 57650964, 622057023, 816212585, 529278215, 646883514, 561988683, 237637889, 133611670, 781105496, 403474453, 54537232, 915203923, 100843592, 592485374, 793828247, 828471809, 155785884, 886285176, 931754930, 783300284, 128040051, 507773625, 850215723, 864553781, 409724563, 617291784, 745539122, 977609962, 478857792, 999613293, 964930835, 459739624, 744690894, 873139859, 830944168, 325334683, 542576016, 649810819, 325461007, 693629916, 371917684, 391749818, 936688564, 610465425, 326703448, 395431898, 732945742, 204335890, 942873678, 212148508, 999797967, 398854231, 810952934, 942136352, 309522044, 759861989, 931444892, 456096620, 59906367, 76597895, 526379410, 618811300, 607149483, 475031950, 969605934, 675703643, 277182824, 715789479, 411345429, 936669871, 987984568, 65318240, 807094596, 253584053, 681265408, 932285000, 459259684, 733650105, 897846858, 848987510, 144899622, 446921206, 23970815, 509707607, 821815835, 104797216, 492359716, 600872421, 506871963, 24855971, 752039152, 978667567, 716667424, 214614728, 776070946, 892761605, 201146564, 204745646, 18144593, 852758486, 710009658, 808836389, 784761367, 918996557, 183541268, 748568008, 28226548, 771970719, 989285001, 454113510, 350545053, 486933530, 638538746, 570501279, 631083063, 823471078, 185206316, 553959881, 558333630, 69120770, 905350280, 262021058, 870035192, 777020146, 535918188, 457862095, 678730710, 221939795, 168675311, 749369771, 900672825, 869835776, 268875225, 746437072, 894130908, 96977212, 611898328, 994510349, 109529156, 667274837, 332747932, 803749430, 838531794, 776809165, 514304266, 40466766, 563963159, 607969123, 666602582, 757406777, 10703555, 738879126, 99807963, 963125548, 951195789, 957955565, 689570223, 373470513, 905398944, 603782520, 132610421, 167486252, 72279526, 805807688, 971962021, 37615179, 104007961, 883619894, 464833545, 305305308, 501287305, 501957126, 526841525, 930135416, 578903746, 764870002, 516289375, 506336086, 445889884, 667768602, 692101888, 654855458, 339903547, 255706149, 444798603, 623174579, 604645562, 504347303, 512278652, 919009310, 434121127, 477314286, 439470074, 592339103, 197120899, 347052877, 88297732, 994966581, 31482474, 860394853, 559602699, 438549382, 135123929, 451925908, 848827445, 547648183, 57176622, 518163500, 574170613, 511961457, 407168935, 194622837, 382142070, 70178276, 609672028, 969699347, 416245565, 745610872, 580303458, 264288281, 455016408, 989491975, 819362526, 487645189, 667597357, 414009703, 114792207, 961486720, 571633729, 141690660, 787753993, 797756206, 285937936, 488976849, 323630152, 671647447, 754801540, 322580921, 563968039, 724976206, 753297692, 656608734, 887423317, 262570930, 538996881, 86309622, 619374345, 610916437, 257194370, 446563843, 244097067, 124607929, 299863148, 218281334, 647573419, 736027164, 262849536, 126657337, 503827417, 114888643, 472722393, 839769866, 8326937, 935840023, 85677250, 979632512, 430810299, 14510939, 609778670, 623065148, 715972577, 766273299, 569434417, 790223433, 705684338, 557442339, 491604670, 53635509, 890785302, 167728306, 84500301, 354464611, 834057646, 134772025, 525980451, 176504192, 791663045, 557242157, 463769406, 166346967, 768430127, 572039584, 78252183, 122644355, 858619881, 537701769, 638450138, 234284279, 636694331, 635776958, 747333735, 558443230, 367967650, 118914689, 667325007, 627601818, 534284753, 113015667, 540214651, 557620227, 926194405, 39839, 531548184, 715153507, 285608593, 422398766, 167892699, 428184374, 496659098, 328167397, 119904784, 405000986, 207438006, 361312777, 553342212, 56496963, 803159790, 837797568, 151071389, 533059272, 364835387, 47689147, 181975868, 852615929, 888869337, 521504821, 814236281, 146977086, 773988057, 206106699, 853856030, 978780857, 217283642, 455673031, 715497472, 933539346, 179179679, 902637669, 744420286, 259067095, 73861148, 732064042, 503892858, 635856056, 107261497, 821838613, 656349979, 705686548, 911729941, 590289673, 42150477, 937685517, 354355559, 153386540, 682982951, 147980172, 352324392, 590669386, 271673598, 757624266, 546381823, 554125518, 959870896, 119142970, 175869274, 602178750, 433036483, 117468930, 279933810, 24669786, 521367401, 691286600, 867709003, 722780546, 874546212, 619292717, 966180036, 308827967, 811437570, 648303822, 771596849, 853304211, 255288475, 458822305, 636424615, 282151501, 327773646, 456920889, 365247793, 904172410, 320696842, 283229498, 641733636, 613031416, 148981454, 210533476, 878628707, 241077133, 934158940, 245277128, 488823854, 886877602, 391501741, 817118591, 503701498, 152615008, 484403557, 434577848, 191233549, 872274067, 79291276, 652379679, 488679566, 516391969, 53601418, 467978823, 283917841, 468957839, 337276389, 9734243, 415428101, 673470000, 419540037, 727691343, 526337615, 288508577, 356005348, 907583400, 92372187, 894208976, 855479283, 288522939, 133341315, 189422587, 124834253, 319040658, 309986934, 423166556, 69514629, 618972347, 237732972, 110404055, 527971725, 470546869, 198436637, 303999349, 112659871, 963978797, 64927381, 839465122, 910447562, 347787528, 507962548, 78860573, 854853472, 620468175, 730018756, 701728349, 613451398, 726949702, 165156002, 999764540, 614221759, 617970177, 320218208, 338760605, 779094583, 454640071, 395742790, 500870776, 455450251, 550178570, 468714252, 567283729, 846625610, 80079924, 483128630, 276503267, 24095109, 9429634, 765325534, 418041208, 564196092, 984419936, 351158227, 468399898, 882242511, 329327304, 414493046, 126647476, 715233584, 682929955, 793701503, 23309797, 155872668, 416689123, 477839208, 204124808, 280287587, 938960514, 529026633, 913108981, 819880458, 344243550, 491709611, 794343307, 955268384, 120082590, 922310804, 830681857, 710356503, 624898175, 632269131, 545642857, 973014785, 416046444, 693775795, 122062124, 483906541, 621120307, 306759306, 435930154, 197020838, 841570030, 329293579, 965747554, 230017222, 796926807, 495143312, 614028710, 82017064, 467491591, 157689538, 704515297, 218880928, 31429220, 706586841, 707823482, 595364155, 950008992, 976599809, 756291291, 208126919, 943130348, 541255464, 739174697, 994157589, 939835481, 402505205, 760571418, 632803406, 888021890, 762349042, 375006130, 3738113, 192922830, 300718323, 166673904, 328516425, 485460784, 553849459, 268174067, 215756829, 580469526, 486669368, 207042937, 208599985, 850146645, 128353756, 117557142, 51099884, 468220948, 295574772, 904371542, 464783383, 348364455, 530098276, 657803593, 36367550, 953684199, 967090542, 96160784, 705848650, 9020980, 94989846, 844882558, 27997384, 546847715, 977740525, 735929481, 597919225, 25201871, 424539988, 384375906, 483106378, 290669262, 772595204, 382226647, 10008484, 137968028, 202177103, 333265510, 274619239, 899741532, 176187590, 78141875, 472586571, 270929917, 304648194, 238340431, 347097476, 585955336, 353581206, 713958380, 803213133, 927187633, 453716213, 478963099, 751327177, 484123735, 533056898, 832478977, 341985315, 865966889, 220263217, 958503278, 546544619, 606933705, 212331750, 982304133, 410192924, 996734283, 105788820, 718562968, 417717658, 577811955, 639281073, 87145907, 933303496, 299945736, 982544509, 516689190, 842224188, 256400144, 912251456, 542291176, 180163228, 844907578, 661857158, 795628986, 234538482, 79252086, 804795094, 426580435, 676406256, 864598638, 825316475, 320478683, 107386310, 622815246, 194150702, 818514458, 421677719, 860880629, 619252523, 465274951, 787738846, 990529493, 648595661, 339264717, 301780908, 966949277, 778554003, 909141408, 120430402, 996381368, 111903507, 626250533, 447060128, 724364039, 125188133, 574456621, 929539973, 376691630, 382845157, 787962153, 199314534, 303341102, 845513462, 61841870, 59780779, 530994150, 446041959, 157239555, 404797325, 830525512, 268564218, 359506301, 314111210, 286298690, 958545383, 207588419, 577315866, 215250197, 847732718, 688746544, 190113465, 593702551, 239335289, 574156653, 796934093, 87335198, 90503168, 164923060, 442828452, 580819586, 592634705, 33095689, 777507884, 950950084, 569507045, 752966074, 868668264, 903464914, 167938954, 979252266, 381277025, 332734838, 862320828, 246566237, 124374939, 485561163, 784247141, 311255244, 879091205, 539710278, 822110246, 824747724, 844087872, 762163324, 795995545, 222605259, 344410822, 932444940, 773693710, 768144328, 428167864, 585642091, 292658408, 686919887, 846927949, 382829870, 181209306, 742644329, 540689141, 430987478, 178669138, 606181262, 939705925, 242756903, 125701350, 699458469, 835345838, 150116461, 177549779, 420331452, 986832630, 751528915, 229252302, 2767616, 78038263, 445606320, 439576358, 148861684, 528525016, 773813155, 451461613, 423038202, 909651209, 141627320, 316705665, 7253303, 702056437, 768224851, 760870515, 257878944, 688687569, 842078278, 674194011, 991530197, 627873445, 456622525, 236822281, 528929968, 867891181, 400272184, 971987500, 928569138, 556689978, 522281606, 465245970, 157253935, 550309799, 182182637, 661740811, 956880849, 139875198, 359641769, 771190148, 156291184, 257734372, 903183480, 882239363, 787172295, 597684512, 350588719, 692299376, 816816481, 123317137, 617287946, 578546385, 821187202, 550185194, 546427027, 694389004, 877028922, 915730388, 337734309, 790964718, 356729873, 963135882, 346216176, 440046979, 614650227, 101732587, 142879951, 895605845, 498273014, 526984157, 796533132, 331221491, 316084815, 668631293, 389292520, 638626001, 4272883, 504324382, 389718843, 63468134, 815268128, 73703933, 604766267, 546293459, 359414734, 388645750, 462104676, 97277276, 4332120, 401413626, 691656671, 702133883, 198915254, 212464741, 34765592, 553058636, 655211923, 555309506, 943076553, 258444907, 225989804, 978242030, 21842113, 286461496, 982832703, 440231367, 533623563, 124447314, 902083868, 805307371, 334324882, 303595579, 105224553, 618748190, 927790961, 184492902, 408996255, 790675046, 497045703, 639965962, 432759492, 398775647, 724956872, 379310450, 366178343, 144260194, 525183736, 924190712, 973533200, 756317085, 253106711, 64007831, 24531549, 9880794, 124850154, 565705332, 567662432, 785369175, 529857796, 214079237, 505043782, 826418353, 735427812, 656533658, 893194358, 763597972, 672498313, 257895080, 510762362, 470673111, 674366160, 280338486, 778051594, 880668428, 118205790, 498948676, 632473051, 62972568, 523351906, 378188033, 386581322, 276604191, 642482996, 905659799, 666924799, 203660741, 868289998, 107501829, 337680858, 815478517, 879282383, 637101465, 857998421, 892788400, 44637905, 370756870, 207999157, 212972573, 860256170, 606932476, 199577398, 208119937, 899862967, 356738736, 913826041, 1577964, 315972933, 922685793, 879121170, 270727769, 693668620, 94837945, 121488581, 549367136, 633384602, 235015407, 239141499, 889305844, 580769127, 942896890, 73763216, 625450322, 48393254, 896864968, 805759410, 965662301, 649886856, 657330846, 981546681, 28230711, 457907522, 169375932, 337943617, 20158356, 748188188, 825625339, 541882655, 119419825, 830779335, 718093967, 383624143, 364401707, 530209757, 168848218, 579084497, 279880363, 156680538, 472934242, 202784885, 137865632, 237833814, 739816799, 17146622, 684181934, 373641884, 734176436, 879784691, 146171485, 390981751, 415890016, 590762656, 56276252, 262620264, 456889646, 246624969, 787618516, 652107208, 537675525, 571741175, 391827078, 819784253, 806487665, 953957224, 977552393, 500820567, 680484550, 559824393, 248418311, 535719242, 856168319, 367539534, 851999348, 105618996, 153658573, 474717539, 202677338, 648112049, 625527872, 404821228, 255722305, 346544493, 844355230, 167836123, 284864302, 701870924, 214387999, 378607351, 82036729, 838045718, 619248021, 273279748, 867055038, 224318386, 122761543, 308029330, 351731476, 164952210, 686299342, 625927677, 546403222, 651182225, 867668198, 275016005, 60123905, 946855483, 901388314, 315218587, 700592290, 104231770, 923631077, 546604971, 631757469, 465366875, 650128466, 892592043, 852570548, 892110989, 417954715, 992145218, 599458418, 44524270, 52932874, 601714025, 463837058, 660463271, 291520275, 10774755, 417651426, 48528894, 751492782, 865661625, 221039222, 917686651, 754380459, 649678266, 879888683, 141349905, 532552303, 319593708, 936484989, 160671892, 953734119, 855834753, 638678444, 348418132, 887332361, 486990676, 888823871, 438422295, 844064769, 936111266, 582520423, 418298433, 209155358, 52634878, 978267155, 795891683, 651682763, 324851331, 698302887, 659027325, 823937082, 938264222, 310443561, 671601280, 671209561, 482351066, 976691235, 401647729, 813762978, 24120890, 301936688, 48078537, 157746640, 371762119, 364006329, 933946785, 387848573, 121027594, 174303789, 966572028, 636658166, 377709538, 440310052, 298170101, 634890488, 784246411, 998212894, 423134524, 798633085, 929969357, 175327592, 748607921, 701613543, 10121596, 510818564, 585587616, 337825454, 650593336, 725487300, 393944438, 53059028, 421876095, 304515863, 37449631, 43100631, 574566329, 411279059, 357385565, 249827373, 442167774, 808274563, 911049970, 421036042, 773050769, 510194504, 616945039, 167946181, 484382399, 664136147, 954260444, 648769520, 455791734, 825211755, 726288806, 88478534, 818331804, 91799368, 223807367, 627382018, 309226974, 793626540, 86496004, 67212234, 548812359, 125465543, 470690636, 637996556, 293273424, 491142717, 280137448, 155634223, 890884466, 597632738, 838641753, 69309764, 667199754, 164369079, 912702732, 920398687, 553911809, 505199431, 927672050, 136358004, 811395039, 331888603, 574384097, 858019600, 28895855, 319649720, 529365427, 256912643, 931370110, 324986449, 837184416, 523074649, 206938708, 618495951, 469155583, 663496875, 211763711, 543392803, 770292520, 283932311, 744031068, 904413299, 529833802, 845718231, 632548028, 542304333, 23314782, 682382372, 920980082, 554963954, 441989165, 557231478, 268188132, 864500009, 790296155, 423807593, 234037489, 402273571, 633722893, 60121803, 763109544, 684408814, 890160896, 865005404, 333538531, 330954813, 105414066, 879869440, 743133469, 417185315, 512976544, 356856865, 840401823, 58576471, 771703202, 157814555, 353435656, 379263716, 763674467, 658441829, 377731927, 93466067, 959115536, 554946227, 180485424, 985026345, 325327022, 325252640, 904520238, 280819565, 783690322, 287022435, 961966146, 940264287, 269493793, 55286531, 146756683, 142789599, 620325594, 875314385, 815743780, 783102183, 167615624, 853115043, 487787251, 839731092, 575373503, 771746530, 167992364, 985182799, 507767052, 817211716, 854032160, 49869988, 532650907, 394202958, 344383485, 855451143, 812281628, 762898384, 596326301, 963893369, 293731306, 898193717, 200359329, 947483834, 361246227, 777474138, 864800446, 957587296, 119053766, 175127677, 448815526, 13669057, 281639116, 541524407, 851353432, 46853369, 360442189, 497077685, 450374533, 37777363, 774946345, 9084235, 167257835, 687909450, 716806194, 263112185, 946831291, 61855492, 640881587, 721719275, 298653090, 985202346, 606257034, 697244957, 576567003, 107134556, 204919266, 62686728, 793585424, 93078185, 199175932, 893502089, 568892727, 408335424, 542797807, 227876933, 711914639, 702225659, 790148494, 788036898, 881401251, 947882269, 21664456, 125097607, 390054241, 725600115, 580773921, 577289628, 791459430, 975247934, 703283994, 875362210, 401595587, 821073656, 870775825, 820899595, 397711337, 787529128, 342139884, 87780532, 663103194, 279986538, 932379445, 496689769, 717561437, 515286281, 668863549, 309719241, 524885152, 249697692, 50264215, 750353944, 956296027, 700971712, 582238683, 927743363, 938732238, 756895683, 352145803, 442634068, 146619241, 15507134, 427794596, 708731122, 116091763, 406291721, 456241590, 381171108, 169591900, 788715841, 212723779, 190389298, 654032731, 658732142, 104958889, 19983187, 164161828, 821476981, 405658855, 517068502, 501081331, 256069063, 655412730, 825136662, 996338299, 644636040, 116687495, 13932459, 836807028, 360748342, 368911719, 693832736, 606728466, 491564501, 56920056, 828107013, 518847251, 639960207, 630597799, 296026218, 213850471, 357377667, 484827739, 839080590, 996777803, 925487359, 117342023, 745061073, 937676275, 946640352, 920788269, 96936079, 748320172, 971858719, 39802410, 839902145, 461353041, 535285029, 784616827, 117745739, 895114768, 941818119, 834877073, 636848910, 478249940, 940834840, 676802764, 582357707, 612164925, 820634892, 607802402, 1128267, 28926529, 845707165, 305942109, 805147906, 851867784, 708543706, 915707225, 495624568, 338740277, 863829617, 799968121, 462577964, 637038699, 90650895, 644918197, 257118270, 779589466, 747068688, 27980698, 196517961, 431803900, 716972011, 187526610, 764309845, 250228166, 658671861, 661976699, 635054191, 310147088, 339555005, 484643154, 44915490, 692726801, 474086975, 721506735, 161292415, 273348450, 54081133, 826554268, 392250480, 496284765, 45536602, 207448823, 716892959, 32803457, 186674716, 706406982, 313322962, 626429400, 840207856, 111883086, 80657494, 469450698, 789173787, 250119700, 357431434, 147440978, 95037746, 614445947, 59369421, 73895079, 6456206, 901828662, 6724540, 504952133, 509760756, 659983156, 31648831, 713854650, 964206913, 731479235, 54943641, 513387597, 15854514, 675932341, 15050493, 172850679, 198766723, 274131102, 124634245, 329110932, 433405629, 358321053, 786611366, 67984006, 520302193, 945848580, 567805032, 34285797, 248436684, 553684255, 339456060, 917309015, 379305858, 9383816, 791234844, 322849330, 246147672, 775600303, 387621039, 578838761, 180444216, 508186808, 82385246, 159447942, 756343589, 341829149, 844409181, 618872135, 511820146, 223212532, 196233473, 435093930, 394391318, 278192564, 315584471, 634466355, 51070582, 619297260, 641212656, 459595880, 504594578, 636837122, 200800929, 642198508, 424364758, 502749097, 463723154, 677983857, 913930121, 16646784, 39663009, 614837810, 646525341, 831697180, 458122064, 654495821, 622334451, 787589474, 40985600, 206703649, 623957807, 973975086, 130496812, 604846050, 37765091, 556588746, 910628538, 146023995, 230559166, 778317944, 759355768, 536619323, 705244026, 726107423, 343310054, 959477152, 377129617, 33002825, 187654615, 305699274, 3513834, 177190915, 791994099, 950349348, 694740470, 433354946, 904687329, 99759506, 807908926, 872583062, 520701997, 966519786, 717368478, 881246861, 314352378, 631019009, 217669948, 170921728, 293068164, 227806730, 257805080, 291772369, 666889025, 394300353, 547980427, 47181135, 439255090, 753345468, 191286938, 400480578, 938867915, 707719631, 427120887, 236600071, 218434837, 230638298, 472597738, 577220542, 328902151, 195430460, 606066542, 72496026, 493962063, 91402152, 991732872, 77064071, 671882922, 947494438, 785940704, 684895229, 178560569, 190783421, 754187280, 188834064, 768640775, 72214770, 623519577, 734146019, 181651392, 447455102, 782930908, 143468271, 202048906, 655586917, 928902254, 967983661, 500068397, 937282011, 806625266, 660067012, 215450706, 450709181, 29376900, 467904061, 901210951, 962000449, 315313724, 382049591, 559194225, 274472823, 17918762, 432229318, 764944250, 627481188, 293757317, 936770133, 156256256, 736280866, 577178009, 76056510, 618760116, 28988671, 335400378, 734432628, 678703561, 497155410, 338797830, 385589942, 744873843, 322492633, 812533220, 324950285, 112916210, 726972336, 673636325, 13658580, 880105744, 422949824, 242330396, 137604028, 982901835, 995357841, 678749606, 448327498, 988706242, 700678691, 722729408, 461558162, 393092635, 305164679, 305356432, 410731871, 658810645, 994866774, 469016698, 11757047, 652998697, 507145263, 447530723, 239465954, 848423418, 380214041, 873134, 486652614, 810883188, 572212516, 646593378, 927210128, 305902514, 875032654, 633773328, 841763058, 840630636, 199812397, 664424574, 418243407, 436788169, 999816894, 915076916, 280908904, 277170388, 925814135, 710419131, 181375323, 716553770, 399620613, 631445830, 264907115, 774685519, 468854484, 634228039, 353403625, 26769126, 517304908, 823650789, 123520630, 455690508, 550666934, 675913289, 928049755, 335920928, 756492645, 646005801, 157579238, 628651961, 22621086, 704156176, 599152681, 802269937, 464163705, 545918237, 444020289, 64243590, 897242345, 502330399, 199782923, 69635660, 638636727, 549542860, 297347550, 756924701, 92864849, 848368007, 637238042, 978426529, 82007547, 156418636, 44495668, 146655205, 604892837, 237503130, 936542281, 357043444, 166786633, 451917368, 624698625, 642279436, 694498320, 996884174, 741464755, 674460267, 249939279, 808838385, 509359680, 17569922, 284773799, 375786623, 603794203, 930563262, 975269575, 771473077, 327020828, 914031494, 210014371, 65970711, 554173071, 335355033, 876682459, 546137332, 79533693, 38415197, 654346231, 132506001, 795717657, 891991347, 514785489, 719179507, 468151493, 708065555, 822457795, 465194188, 457193931, 697867611, 388500890, 289024993, 754431190, 712434406, 618071484, 324007922, 162274140, 231092580, 880223022, 623472456, 812442643, 910368480, 802848684, 975512615, 999425261, 15979791, 907587538, 115269602, 613192176, 640551578, 29314890, 764581966, 717093112, 339949421, 860549433, 461637624, 431957498, 873270421, 985230232, 53835404, 749671865, 542429659, 864512267, 347390274, 150837024, 770065790, 923795414, 848447638, 865918424, 593587453, 163379904, 983180709, 348213639, 69901248, 248184649, 450695601, 331027793, 479612341, 875350129, 364440153, 985698530, 90532815, 895994989, 689071482, 443210911, 13950501, 54124454, 7792376, 149473419, 256853969, 791113829, 393655881, 172951050, 760533509, 779424092, 158761572, 426479249, 708577031, 668225231, 732464601, 55255551, 968646572, 442090910, 689454100, 954241519, 288461108, 229629917, 540479874, 548458713, 205597244, 851184266, 676190708, 5664611, 727424741, 767690744, 666641331, 169588920, 400997328, 310642805, 547583356, 285842676, 358691922, 736778403, 69848867, 799346973, 102835513, 496649111, 73287278, 83439306, 592863763, 892307842, 727226794, 633413427, 825303228, 878610114, 783646787, 603357245, 537190484, 223269188, 944736189, 124426345, 964368755, 182493618, 750468687, 600371753, 965106709, 912118834, 867846889, 590938321, 203750042, 831704051, 575778599, 645847013, 837847163, 772039433, 170377913, 358547635, 384810784, 552663168, 179239986, 946665563, 933336813, 644487660, 74512856, 174988134, 212328655, 982174464, 325775147, 333948247, 510718954, 68582617, 538983139, 854270794, 644861150, 568380214, 43616685, 350944574, 113598719, 176797039, 19895718, 772705530, 648303007, 135197190, 831976046, 153831512, 722783096, 934376057, 868355731, 511584418, 852440736, 235049723, 87979872, 898134706, 989886358, 715608797, 992070536, 442802188, 133476190, 52730150, 332140432, 605183322, 884942256, 324431554, 406506572, 385418747, 543834499, 557751316, 435817008, 729117468, 916246611, 858795238, 877786313, 376046159, 690956542, 310738812, 156050776, 895239158, 963368181, 112568427, 458904252, 817310414, 518897193, 887394244, 432191523, 161005465, 283739603, 922844345, 922720459, 27690296, 762003860, 874348220, 867235127, 752010671, 838044633, 128099211, 54614166, 938238446, 156047303, 848272402, 402239990, 547658646, 630064118, 800652049, 752848536, 819063656, 775747735, 744389935, 550888415, 8554205, 327126590, 892774886, 676561034, 941909947, 543388700, 741597211, 868486768, 562404743, 640456393, 922678622, 232430900, 359253622, 852736226, 57476712, 974812483, 842384677, 516847491, 924518177, 654887437, 54361365, 71979869, 566769160, 395401327, 604345863, 713484264, 628489652, 390003270, 355816189, 481367024, 394745762, 847624018, 45331840, 459442478, 753688379, 439118014, 673868107, 238172647, 977675892, 971835196, 485479977, 653544807, 842870691, 114562618, 1908969, 119638991, 145167702, 940725583, 621182878, 275034603, 411846454, 191965518, 144529623, 132252163, 793268613, 783092603, 318745488, 488594464, 905518790, 192090310, 25978746, 497975378, 924102312, 961188146, 15480551, 785337740, 218407856, 670262468, 330133147, 421920127, 400028988, 214280324, 711826734, 245213335, 906759376, 391323119, 902450470, 263043272, 48470677, 3625701, 854411284, 494833908, 350629490, 246778028, 830839442, 483400592, 557178302, 450154982, 36190162, 701491445, 22245271, 885969918, 872762897, 843679295, 626858461, 463964167, 727306389, 69645017, 823982593, 351117003, 179230350, 908008202, 67876860, 962456223, 773759749, 893946800, 920004025, 520653100, 891136487, 540477850, 124034469, 17003992, 197497373, 498816547, 848737805, 771132709, 898670644, 780217362, 743039129, 649865076, 618200438, 74165725, 481631245, 323986979, 454975758, 599561624, 109202531, 319546298, 915087756, 358984163, 56643988, 264216861, 465148370, 509332071, 265066352, 311688626, 179675255, 386301289, 597733205, 388813532, 572141171, 487428618, 307535249, 504860558, 121448618, 601764651, 870638379, 928455624, 524980213, 145647807, 578297112, 789174787, 631748571, 687216468, 123085990, 147135865, 323619962, 218049683, 550524121, 507953839, 519677669, 532740641, 829394123, 163509570, 83648817, 261117204, 699700674, 466671690, 107058084, 25639372, 935882552, 972194880, 759436355, 152551532, 700548565, 554395324, 227108872, 752966891, 492027189, 185963797, 446990656, 168422392, 848306399, 629613692, 753785058, 299895932, 865844477, 220641102, 639249532, 754226733, 100751648, 834529512, 716315095, 712567773, 972942856, 929408627, 867092447, 768712807, 34462782, 449720712, 509180792, 500797412, 749680483, 564458106, 437620016, 335553819, 208096624, 313409624, 734016525, 668242574, 925555773, 144579904, 650063160, 598309578, 954677010, 21308142, 611398971, 793699376, 801547630, 349891097, 274056273, 40161801, 523691443, 421444480, 954685488, 295658148, 861028055, 21415829, 48463718, 185492074, 198348632, 267039505, 262266869, 740044357, 525917061, 122649123, 171074878, 364193382, 664165488, 921818699, 500061816, 470918933, 232961028, 228651053, 816327186, 415058804, 321587953, 243744781, 205815105, 299156792, 315580728, 254802125, 576342632, 558158321, 467442296, 631950337, 974272233, 296920372, 360741440, 954839633, 201417543, 953542405, 684015237, 603715764, 231962619, 641638566, 742020239, 542175562, 603649604, 870388152, 698035683, 321082452, 645900854, 9025311, 248597480, 63706520, 295010314, 334642602, 593889658, 819258663, 155708398, 334707253, 856020594, 996772575, 796315505, 444754510, 959792182, 684592454, 328354727, 432187713, 411708224, 741743428, 910671736, 503075328, 884144969, 286440077, 754649666, 210916575, 642779624, 599015326, 260398475, 893896020, 17261352, 989974440, 617310038, 877737158, 215203667, 244622012, 427791440, 531445950, 219308696, 312790721, 871135862, 536756421, 280823573, 305043070, 144733038, 218407798, 140368928, 228429868, 273511935, 400948392, 382716525, 695358692, 782372784, 95552368, 752004230, 703985386, 323792164, 645432488, 846950965, 383710331, 24733333, 193701086, 514209125, 67470618, 689517137, 858075583, 944906608, 628495127, 893140546, 884411827, 6914145, 783293311, 917866305, 882929101, 358858733, 881005370, 135287972, 120736106, 66658820, 393415780, 29827885, 707965334, 590110505, 858845855, 621194351, 749030840, 31011763, 503354910, 757980146, 699170876, 935390002, 727474272, 145135074, 749613678, 735905664, 451576109, 388916196, 470512744, 255105514, 327522129, 442907442, 709056949, 74823078, 764626025, 960103336, 288725535, 538047099, 683094219, 501506421, 965518610, 595697530, 445089331, 257358477, 519002816, 290887173, 492965475, 561470770, 84012779, 890042231, 622105213, 478008222, 974609848, 29545517, 40652166, 77149053, 342875583, 942189266, 446668121, 889302433, 573579644, 841722057, 765308489, 538781293, 6587408, 106439707, 831053669, 7744247, 495472465, 69655558, 833494788, 749757128, 286413513, 631364533, 733493054, 737933721, 92830524, 25075383, 773571292, 184981392, 912684095, 540008719, 18329574, 347088481, 968457814, 974860227, 263711794, 452246674, 692994856, 91735762, 464903364, 798770853, 615924815, 223917380, 904555791, 949725366, 559103927, 994114998, 874076577, 18388223, 786446673, 940812061, 645944824, 237252167, 238858482, 376241514, 590431571, 128750550, 631643381, 382517797, 752464757, 24418818, 159552138, 512242345, 110197410, 70639613, 44455300, 571173572, 101539211, 848858139, 129373492, 477410516, 452480234, 618285892, 707676549, 782584916, 911005347, 389566700, 404069546, 347544389, 77282289, 831318416, 672069788, 347904818, 672922487, 769735642, 85073440, 443639121, 24250103, 226745582, 984523845, 608225613, 694606977, 744228287, 248839256, 156996448, 858480503, 643549444, 135909924, 80112806, 530623803, 359886837, 791233872, 718701081, 192003906, 371627169, 526290227, 138445066, 746105159, 338522673, 738595539, 365754278, 801734728, 488516866, 898613425, 459874326, 53858829, 288682608, 889379287, 566972207, 460602879, 400272312, 272946303, 878921062, 943233154, 642993061, 723296875, 700947805, 291671151, 575630253, 529297854, 46189895, 632771048, 464252710, 277262203, 586032321, 522270791, 402007703, 533162728, 78817868, 314952736, 137374713, 617768921, 827557929, 533493602, 522065299, 713429703, 214648640, 663005864, 243717346, 920681785, 120452612, 786925532, 613550598, 239434484, 511571532, 311114760, 228059576, 768763342, 40191323, 812105408, 657373364, 687117641, 314787655, 260075984, 612131520, 844354545, 614827983, 467985795, 598568264, 710963414, 402843797, 302407722, 223157171, 641845169, 70307027, 354628075, 221609194, 155581220, 260255755, 975783409, 571540577, 878325606, 217038223, 796810763, 499113997, 19436706, 287999934, 998833948, 428216662, 210762248, 105334274, 746083429, 581205314, 465823039, 333359019, 593958817, 728102973, 983567874, 244327581, 753082945, 809067815, 368626513, 5602104, 553555654, 239420033, 651598660, 784699490, 918391507, 217129157, 75283187, 634639695, 357041362, 244301154, 571793805, 739866347, 901919274, 108672934, 658231495, 371974286, 553320493, 129230351, 331156364, 409847548, 245592680, 791815718, 917968308, 530592400, 402667315, 959881101, 482249147, 776752425, 463732336, 538725096, 619715072, 933493760, 944653075, 832405904, 922561234, 41341967, 139745811, 763916529, 302654435, 791731422, 253605886, 847717382, 593689628, 590199895, 923056581, 626128975, 183980869, 397130588, 129305561, 417677121, 859563287, 854263555, 897931231, 694060264, 429514667, 551897745, 166278575, 157488921, 214088508, 157478315, 45879890, 63738496, 851668335, 136064167, 647830188, 67546764, 128119050, 148662002, 321580800, 553145887, 600274255, 459102683, 164775967, 611136805, 824633335, 76377319, 507080148, 393533848, 549515383, 968248723, 562648919, 861311095, 532927429, 534098400, 431208905, 155028521, 695778857, 475922822, 938652034, 342991615, 356878320, 837914237, 537031219, 840805395, 737002962, 949979739, 209703750, 456765806, 45767897, 362060418, 750559748, 746223804, 84473586, 910832916, 53541078, 885976622, 810205600, 299379074, 443692944, 861206204, 208691030, 670799845, 927158554, 845818563, 698757204, 723099335, 109020054, 547523724, 757720189, 581841673, 688253406, 48787755, 642622363, 292211077, 645401239, 119352215, 385401035, 219765348, 166432649, 329382907, 563434608, 966433579, 517491348, 380055281, 630575274, 81940498, 530401184, 24812012, 347153805, 839111929, 356637419, 740422537, 576489617, 996878729, 698176577, 772911222, 342146752, 145695878, 911730327, 852927676, 508690111, 540510712, 874144920, 489152659, 485859262, 289501139, 434080626, 24457095, 386588299, 89910499, 962395742, 918926852, 775965898, 656585505, 301704281, 14961227, 699652743, 724434102, 582818851, 880184442, 990724540, 371698459, 411452392, 455489315, 753541117, 9896322, 10445033, 634823085, 52464276, 278531402, 95439836, 139348803, 502008349, 828017454, 650828550, 998420990, 851411305, 362447256, 971462340, 460181592, 79475408, 592379356, 275869716, 205562662, 122473039, 34871225, 567162553, 293243432, 491101658, 990965442, 619454953, 578910068, 498960201, 686614180, 358717699, 27938368, 370417360, 190132072, 536429152, 183759230, 913623486, 831529346, 204761032, 935628892, 25905541, 525312477, 309314565, 812105757, 269897171, 225487684, 653379304, 651617872, 315372638, 985489263, 837430094, 204068347, 186126530, 495360375, 976380429, 669605301, 481616973, 81399778, 941740018, 633967851, 878778619, 927124014, 52868628, 87345329, 981155150, 304702470, 700412329, 761898405, 416981765, 928740972, 845388770, 368950153, 813744936, 164358374, 563474830, 817126578, 936201279, 76365579, 576487526, 85743806, 346913888, 929142525, 566697885, 901561648, 120150762, 899639143, 757987875, 36973649, 604026714, 396208154, 164553989, 351821039, 94605774, 133491999, 347203669, 673580322, 947476889, 382230727, 341405318, 308399855, 90647745, 210782402, 722856020, 79007690, 279619783, 183940920, 619560927, 489609770, 182359700, 762244659, 613432365, 216070683, 756672600, 593372011, 501330520, 67533678, 144695784, 105949861, 323668013, 127289284, 200059877, 660662494, 73558645, 465031343, 41889248, 498561536, 292125934, 398010709, 376569027, 544403800, 286534084, 853349378, 50108490, 590202847, 584477193, 829429013, 23693470, 178475695, 883078289, 551369170, 59778818, 49347375, 710181782, 617789142, 778715297, 455074874, 550007761, 75184231, 550993028, 885732294, 73165833, 694301592, 766495809, 530872375, 705672701, 81871279, 820045943, 165084260, 693747414, 605768809, 723896313, 423470956, 192598816, 63396399, 887377452, 822859675, 159410332, 486167629, 432827743, 669984429, 322882971, 749157784, 159856333, 111664760, 995177585, 237475895, 787262904, 558183120, 572566530, 151761111, 626163341, 665849111, 540615178, 284604060, 878616967, 231789768, 992336923, 779125717, 629601970, 806926137, 696373284, 691840986, 507977534, 733763270, 22068666, 502252583, 626339844, 219583535, 903210486, 923781395, 808825348, 923822259, 139136439, 307812050, 114247260, 659251371, 493834321, 267443138, 145447136, 552670335, 842818888, 517069566, 688874882, 386373785, 400951484, 70469073, 547570505, 793590878, 210396008, 75544842, 536210199, 706177623, 476224711, 55371564, 708706207, 621562307, 772824609, 921020084, 836082739, 303301418, 314149049, 689524359, 988220618, 552644380, 548741769, 805135810, 255814089, 257636692, 274397059, 642219451, 208375838, 750887192, 909878233, 462479806, 588581638, 450795322, 467225235, 12391162, 674300642, 686056978, 274771871, 48189040, 493449574, 273589518, 777217410, 6621958, 255837873, 145190171, 695379092, 842551681, 610733266, 486949080, 413010370, 334046913, 223360047, 461435958, 753023173, 333602428, 148534176, 583810059, 710036568, 813473449, 916752000, 83140429, 121572984, 580338635, 280191861, 461445147, 857346160, 104458395, 144107749, 267883049, 569469139, 550980370, 342570585, 362649570, 683355403, 467449123, 265125006, 993350975, 222861003, 89940388, 311775191, 561781263, 770228552, 284902493, 968990731, 982608617, 216031216, 921741785, 487643306, 966181851, 256274650, 289111309, 719310620, 327271381, 579372042, 359312838, 18468044, 673385243, 179785413, 521620591, 426814811, 736237670, 511620340, 130279830, 310238178, 593462085, 495751314, 188816648, 130776212, 61319163, 718889909, 705294921, 184873387, 365180680, 958024118, 830290919, 127600559, 425030547, 97089190, 790145467, 376999840, 201420074, 257678190, 617033618, 781080506, 296309708, 151195205, 351973984, 647906472, 927229236, 558297771, 727371022, 541040680, 986508306, 396667666, 848884317, 622086007, 229828685, 894924562, 873920241, 467667476, 350251041, 472512312, 962353900, 641567315, 969269831, 445053560, 46408582, 608005502, 298040478, 749452518, 57122204, 295627728, 57625585, 710447569, 859291049, 23555682, 565698903, 819413333, 876295325, 854233612, 944185651, 291227795, 67503593, 726468910, 543989966, 796595421, 880357716, 13239375, 573958358, 51403483, 684950302, 772137740, 101695537, 920218853, 373920982, 302468472, 767075180, 227364140, 792766068, 222637936, 788543045, 571527720, 685957694, 9364901, 152475501, 954312595, 575780653, 404105011, 142073195, 191101035, 403440837, 215316849, 678449206, 410912173, 91242534, 472640615, 541916706, 957910522, 121262793, 67146487, 306756363, 170702238, 68590010, 791014160, 702862734, 182570663, 703207152, 587548461, 762439700, 497975123, 18403038, 331900420, 197937934, 985374804, 77956397, 416840284, 209552050, 549167288, 877356020, 899448300, 712403449, 86387704, 409383409, 681849890, 77126150, 855865587, 626565884, 596426430, 190618987, 425458867, 601104032, 620372530, 518141438, 372706272, 25325830, 256495595, 964066824, 984608296, 495282269, 545990158, 668374141, 583552025, 693640114, 698248121, 29011947, 314917442, 980332242, 619962483, 673803671, 423497960, 515931396, 9488528, 704215987, 513005141, 153323797, 314285440, 971180845, 796598390, 877322318, 831932422, 613425042, 724239751, 76807492, 747560242, 913290617, 251331978, 533034839, 204270399, 810983622, 564161316, 957352953, 316711009, 487634697, 548648962, 131494225, 166228770, 467733470, 760306191, 331588799, 996945593, 365959300, 48531577, 340700883, 836227580, 296944795, 771676333, 234508321, 949119680, 833416377, 867607706, 576406740, 243435154, 438981242, 562272281, 467348698, 810298399, 982632293, 736980800, 410575872, 465816360, 918114181, 819471510, 458888926, 964111765, 711805465, 730196693, 452214958, 857831204, 933808384, 829028939, 421430796, 939868465, 307610945, 616614389, 69869854, 289395120, 987078691, 9318840, 958922429, 259521528, 230072702, 697020833, 496424657, 6763931, 412361980, 45223857, 964401138, 836141088, 859813829, 633494492, 670365082, 328011994, 900171487, 718512540, 831621629, 528615307, 895999083, 318049165, 540913921, 673621081, 476071629, 35155482, 952442444, 730341575, 642779712, 180459370, 25570641, 458680705, 148698684, 149899953, 257255331, 507980845, 399769280, 229651890, 847988172, 834644615, 425255317, 693774200, 925980139, 593367680, 301172342, 341020219, 679278454, 684035121, 247309204, 708601528, 705896637, 475450297, 475394888, 63160348, 975543739, 776928654, 152799583, 417552899, 761097552, 890236360, 209912220, 685606914, 5451979, 161441786, 68310832, 944935544, 215236866, 796523458, 683060811, 793370050, 629245063, 663019982, 680022665, 762001411, 185787708, 274837744, 167728627, 510015378, 416495225, 538079751, 741999871, 945860673, 848447396, 337340546, 253866121, 530130252, 585561504, 313434203, 811401575, 301416161, 745575437, 906712516, 246390160, 42704004, 421608261, 824138937, 736531751, 205529047, 455184020, 274809872, 825795792, 170648829, 616987445, 38951515, 813268575, 941421351, 369013345, 149680055, 412037809, 245560713, 349367354, 102196438, 861837564, 551579928, 771654830, 111073660, 773157236, 873264091, 466544853, 661870560, 181948889, 92188358, 469925018, 470054229, 320314579, 886147941, 273883864, 477986652, 924777698, 913693069, 946221726, 870781455, 359272914, 197421131, 886376717, 189918912, 750882424, 127951027, 605608166, 272536923, 81873739, 901640038, 51442527, 149003506, 288279972, 990023654, 862225816, 685838347, 941967440, 360582705, 660186982, 869554178, 9857586, 892127886, 995024217, 584664932, 2024369, 638348917, 227385933, 122906093, 33102056, 764222737, 838441317, 838079144, 733969602, 950530109, 426664081, 661011350, 718495624, 129680576, 964676996, 375277460, 722798818, 10548465, 433196327, 889031717, 500093330, 596319905, 669601547, 35456953, 65355439, 317888767, 881629848, 749487078, 858601513, 966010965, 33862052, 199970075, 505521434, 584616816, 385539876, 824864023, 28279356, 630350524, 412085174, 429293768, 719727422, 24307457, 909632600, 497712073, 734441070, 353925832, 215658898, 881892363, 534006192, 601833152, 796761845, 7753821, 67602189, 479186445, 805431467, 894488891, 220540133, 850701070, 349121372, 385673259, 226309087, 705962180, 675382204, 752561733, 172627030, 855097130, 347392319, 895110448, 122335045, 886225924, 241489131, 600948966, 233409630, 755394786, 113923748, 375655794, 27184854, 815548046, 399380544, 23849443, 208765197, 111188198, 847484033, 222860250, 359248258, 246600180, 454134845, 577672636, 315547832, 798011710, 422064385, 528999434, 956312853, 941391049, 805912282, 394822622, 841133536, 153090420, 740662545, 524791557, 993075457, 247951647, 522862464, 494187914, 591671200, 310758685, 914962676, 164286814, 438392793, 113686298, 255633211, 238056772, 98598365, 762648451, 581098474, 290229484, 717564654, 437105123, 879971210, 262416723, 31711023, 584787514, 271253497, 850963535, 110647124, 112815159, 90103587, 549513963, 539482892, 190543819, 329966656, 802319447, 766625181, 165350415, 896972323, 577856278, 50812854, 872227700, 757367041, 202923205, 840265216, 437069506, 285934556, 395591742, 344761055, 504944098, 220655763, 921652857, 452358065, 600498858, 407358912, 713246183, 840916638, 879781152, 524508044, 92737410, 626012199, 371637753, 467222196, 657408359, 107448513, 625449260, 72297235, 769859681, 884897489, 607037000, 214369928, 891830665, 547671964, 796953770, 411486870, 119669427, 47894588, 318078047, 954141249, 22019364, 172748691, 800311373, 951193255, 580837977, 576917210, 240890770, 76813439, 337545760, 721383576, 121453562, 694713742, 583008875, 835188592, 839446574, 202068917, 408183691, 267185992, 743741802, 676317911, 713509868, 198551460, 854056331, 812488359, 792568104, 308403968, 612696054, 688636408, 553207857, 893136210, 710678603, 721123992, 470741853, 285151758, 224162260, 190421175, 759276497, 586479727, 774707439, 115337569, 530743258, 36551485, 208593186, 124869657, 843038543, 917093099, 351328247, 8516841, 472437732, 636290215, 378523737, 148142140, 519673597, 684484052, 994031515, 750309519, 97690644, 984844935, 660180627, 521499436, 172469247, 32244695, 628392398, 253247319, 985104145, 940565383, 117619140, 314363205, 687868514, 803544173, 510993856, 336525211, 376331733, 955884216, 78228314, 863937317, 254250141, 471977748, 197636110, 972151502, 161935148, 185664703, 535089011, 727334938, 383090292, 897864920, 355558321, 690457407, 260344217, 776513417, 743499299, 323054325, 609387313, 227766932, 586784296, 720488965, 330038430, 961242607, 686353569, 628783191, 651966662, 886707872, 825503141, 906569058, 229694338, 83019111, 684599704, 987669778, 22224309, 954852422, 14049440, 998354728, 566837000, 795473509, 280245071, 235009670, 298747096, 496728869, 284098092, 261079852, 897142119, 539128066, 156035594, 352896862, 141548008, 167560906, 457548859, 892686810, 702235375, 752552428, 39304873, 105159024, 308978002, 608923273, 276901134, 733923997, 808610124, 876313500, 565685850, 991339300, 76604174, 160818513, 296640681, 461655836, 709979763, 281676332, 636031753, 408178943, 120285563, 513286830, 276161790, 283945000, 113844689, 313450079, 594339329, 760365414, 423919763, 674384672, 86656999, 420232096, 599447699, 11716398, 302990927, 92369912, 677157522, 820470094, 308583717, 427304296, 986222073, 651606947, 204896467, 996341376, 651182521, 591139867, 103319620, 107228177, 264212398, 709026398, 237223946, 627261095, 38556532, 694352116, 626119311, 924466620, 337883825, 753996839, 451264104, 994092224, 497443113, 954902620, 54919700, 88697989, 122931984, 752412920, 90280041, 993841458, 446447222, 254722320, 313427038, 609369573, 535170532, 387275841, 143810641, 418993385, 401997958, 240134376, 455661001, 28914154, 477119398, 225572439, 164886425, 387285346, 438833846, 511621658, 45715580, 130214910, 293484356, 371474364, 505038806, 722403820, 134386236, 49288247, 493394195, 45779840, 880892113, 910198193, 652658251, 137772009, 480788770, 628467682, 228572614, 238880708, 862058176, 977281072, 49003306, 308720719, 380608303, 903007268, 925429571, 33452796, 135568896, 469483335, 622329789, 19752252, 445009588, 489630944, 5152100, 417316095, 866728446, 351732269, 59200203, 409172947, 80676409, 748039424, 404824745, 756634557, 717941512, 910791980, 81467308, 239621970, 670605840, 571240011, 859243295, 580977307, 975035789, 281717751, 820347211, 610325058, 464090416, 724928025, 138748213, 108156466, 191803176, 166152642, 748580333, 861538673, 979949338, 477785639, 414571248, 752107968, 565686617, 478681769, 837691990, 253537149, 84098983, 636584550, 201175023, 20952994, 129350024, 377163194, 822301107, 780530423, 58440101, 146823377, 392697055, 454419295, 407736393, 419042433, 288813264, 139286722, 844157358, 846981469, 350452052, 620424873, 694761587, 704291077, 74646253, 385310670, 689020299, 236988181, 361480196, 218559084, 972433006, 67456951, 175094782, 848376279, 902257126, 152083173, 992074812, 387078743, 679579336, 553271230, 948810709, 173098557, 316646614, 64591438, 128739159, 237956838, 327298750, 736409599, 698077447, 795226067, 529462411, 448096634, 77781957, 471219824, 656110197, 183631070, 298719892, 134602519, 677816868, 212175136, 231929663, 856972319, 459185697, 174135432, 197024847, 250054372, 292812714, 225141862, 654092113, 301502092, 878439697, 259813049, 273233011, 865475060, 148601271, 531029087, 300058070, 506405636, 351993375, 471188152, 208777571, 286366855, 86284806, 803487612, 82011831, 236568364, 583832742, 343023106, 655990271, 242579023, 905212857, 964683372, 629831081, 365882586, 166802416, 587649849, 595701806, 138031909, 943073732, 389461208, 304236960, 18281912, 898652693, 260634012, 118074773, 354772390, 66248254, 839213610, 904517961, 186607356, 840739492, 725494607, 183015966, 328131173, 396751134, 761601280, 949391918, 442639044, 905655530, 880903504, 937250593, 597186463, 651091192, 23264600, 12092815, 777865931, 358672252, 397460348, 235199847, 249233784, 235542402, 284334052, 44237571, 357909032, 347383420, 805686721, 613689690, 886750406, 754070455, 416237303, 295198571, 73259436, 589117847, 653857880, 68276351, 423064820, 137594511, 163080790, 571465063, 896464116, 486814205, 449990909, 867328440, 842893580, 218303650, 509739669, 502226105, 627470091, 892141731, 199458803, 197713, 644804887, 453215195, 590887878, 625537190, 574450814, 279242324, 429754689, 194217338, 351252131, 498225131, 474066809, 900421214, 90042930, 768712176, 953579525, 652660366, 849993731, 273472679, 541697381, 815528499, 6463639, 737079517, 19104259, 136601668, 359165334, 987472427, 139223892, 970357180, 612211153, 595870938, 500915859, 756689091, 481869876, 463461077, 390070999, 894232003, 641496668, 727974794, 815801764, 958094215, 212754336, 785393354, 939197571, 425775852, 382177109, 511868405, 198968309, 665008666, 599851910, 97126792, 278800782, 115318844, 266446055, 927774493, 431998150, 450583778, 622555817, 696688287, 262685283, 235860200, 991348837, 99285566, 486187320, 857218997, 419066122, 692900135, 613250004, 318345438, 65896902, 743273455, 708269493, 871016810, 843836429, 962072645, 970522981, 556189652, 276507548, 177851301, 336138805, 13068168, 15839485, 728101822, 430852039, 457943794, 769127464, 201099093, 347155549, 390042961, 395976729, 221742203, 586261592, 735800349, 149997902, 978978738, 769491288, 694540791, 53416848, 344102786, 900991521, 860174573, 15204275, 925983036, 744676732, 855453161, 673011165, 752335958, 887069420, 56527164, 107899104, 588243823, 162679763, 298914103, 541737882, 507518823, 527459714, 904395232, 315772707, 443759453, 737943748, 990706657, 479218784, 973336659, 813629359, 702361709, 59831934, 594267166, 297498649, 495594403, 333265574, 676931715, 411294705, 680414445, 188627378, 671819069, 211448646, 124875240, 495444479, 983031484, 16088061, 45998179, 81819314, 736471144, 945076446, 306066047, 18930516, 468244162, 978528988, 513196473, 29918644, 772006379, 981938088, 129850787, 365719278, 307245228, 786645640, 243959254, 991185786, 565111071, 773382804, 236309235, 373957452, 113945664, 581783075, 372103086, 452019019, 244800453, 753968590, 12552382, 753283249, 145607937, 889486310, 148577, 684133038, 465218997, 830606077, 580671174, 364430338, 127743237, 511505464, 820511219, 936926422, 712164452, 644472433, 300325489, 456914251, 837196226, 717312645, 731666158, 843068998, 824507231, 512272461, 644462994, 674288824, 490818920, 624361497, 232574737, 350906574, 300103076, 795828201, 319341354, 115955078, 341709184, 370817257, 949251355, 43827741, 244701717, 647070083, 360149398, 676633409, 317205138, 859378528, 534409249, 839116877, 907168618, 61895592, 595623485, 345051281, 776001631, 625382509, 580852661, 184709479, 903882605, 473278484, 489128950, 555223084, 588352371, 96751942, 215495174, 856476809, 440530927, 534999939, 613586874, 82691980, 211986691, 108984431, 673360659, 55207987, 623551880, 765640494, 95785060, 14902505, 93272264, 872777382, 194094718, 824107062, 9749378, 917249597, 391923814, 5909639, 248335186, 939227284, 546486622, 955544189, 575521496, 560001561, 695583799, 218846803, 412190144, 11745197, 998210447, 537539543, 648396125, 200832040, 824034918, 142103031, 958462505, 809748540, 888384956, 325775603, 371519964, 10749680, 810531821, 365254000, 519271391, 223047360, 16048917, 648541424, 689127599, 308207880, 124643064, 827006322, 80352794, 26728274, 24734991, 76598089, 161476123, 890347070, 852790795, 52678501, 611695741, 165246584, 751233113, 799129622, 855799991, 578784440, 507147531, 916263180, 85162018, 103877978, 64161259, 463739092, 267001153, 124666995, 301284501, 136369019, 650643098, 888728737, 861425407, 261573522, 946808722, 275438620, 870462739, 827344225, 977365237, 767808963, 831665071, 368017411, 904579020, 127203289, 403881501, 592418998, 688947173, 887860551, 289248439, 175200482, 847252298, 193817709, 356780453, 137079217, 651158955, 861150654, 595072777, 851692631, 753226475, 273780164, 902286208, 674700693, 91147876, 535753192, 846908351, 332658558, 768794067, 299973510, 793705657, 728907501, 40134532, 827453386, 927281632, 151484454, 757804264, 277237621, 325998698, 98885661, 884270694, 302855500, 346245338, 297359461, 528068833, 184098391, 764796482, 138192328, 256399859, 131212090, 741089578, 532654681, 581858122, 973836653, 85386315, 462673604, 407402400, 833858567, 305278968, 69002937, 728068795, 65548511, 933239969, 331690898, 526503930, 887178939, 99232301, 567053597, 442259649, 491786696, 411654014, 92006412, 92463976, 457365245, 763588362, 703524704, 43198158, 103457021, 981246620, 96526999, 341281629, 826696143, 38117789, 90773901, 469807473, 800804421, 451947241, 426623094, 424774897, 262810769, 89517076, 655602771, 67734240, 935349035, 582150927, 579805764, 816410073, 957232263, 404117676, 657088028, 790858192, 830719364, 200760877, 106827099, 36371557, 539855306, 352487692, 308538880, 827486948, 9872655, 685661341, 84072763, 745688715, 633410111, 654292617, 250838888, 829968559, 467825633, 174689001, 622345896, 311707832, 795168814, 969492100, 231793716, 767041178, 135176686, 772387042, 506507922, 80059733, 146095367, 942781992, 161169529, 895238672, 764687873, 206613201, 506629763, 984340766, 678844157, 307818068, 996053283, 88637753, 762209245, 511448672, 289177648, 106878856, 600925707, 280877213, 461945408, 174061112, 687992492, 608234044, 529719723, 14904001, 143302001, 834223680, 266715328, 665542023, 877044874, 429739907, 305933549, 592321692, 30205156, 223336031, 827253916, 794907397, 742486903, 286967545, 101132204, 187210923, 237130696, 125311452, 301076524, 771952721, 113557129, 272955623, 727935454, 442577633, 960260351, 908551664, 902793811, 3593065, 495060420, 350242645, 310767464, 522696327, 445924505, 845717200, 379342371, 102032865, 587673062, 887933441, 13979757, 207185666, 755262341, 167828410, 710744999, 747745721, 646855474, 14755677, 306773170, 694705332, 60701815, 194511508, 638191240, 458063678, 319435206, 463599453, 809159517, 646172638, 829969593, 95589210, 102880822, 632818132, 393517478, 864381750, 971214483, 322839249, 259487309, 909196200, 291000936, 882319486, 292398042, 190515065, 666145848, 213523971, 495194753, 47681964, 874428549, 291706606, 864603139, 609616543, 913008890, 788049349, 849365679, 455828223, 252722594, 302891058, 917742405, 948397875, 46612639, 120875664, 523453255, 352203032, 237945674, 825360822, 497495442, 935271439, 476693232, 673176745, 168814417, 445609568, 469956730, 260375362, 433845095, 948279109, 203008434, 69699705, 527445791, 542282692, 719100276, 856261373, 214853049, 422134966, 601163120, 104002444, 228358404, 614276667, 552399355, 612645196, 111810008, 188686846, 979873056, 68658130, 843237682, 922511845, 428155230, 99987807, 100675161, 70673085, 493062431, 781332554, 273969402, 879262461, 786355895, 420438049, 476056711, 481678625, 531730353, 433755292, 253795877, 631231562, 377674829, 68224639, 928400245, 509168468, 256254301, 316862867, 625209311, 213328239, 94878981, 546293066, 151451464, 142533731, 795863536, 888582533, 422225466, 993484568, 56463609, 454407586, 839119031, 878690435, 374990656, 465301124, 359567913, 493147551, 734161475, 656024984, 584821025, 739472905, 864868301, 567869750, 860309136, 635811789, 451975421, 283001831, 483509111, 200530726, 152675548, 885364845, 861673939, 528962344, 389504147, 865399858, 196350894, 417762681, 439914193, 586569113, 997044612, 484376467, 780252862, 267156576, 373632271, 187672222, 312520004, 400407195, 884896623, 445410328, 610066176, 899022254, 861966469, 734830119, 493601854, 62193919, 114327054, 777723424, 618362662, 763791422, 76721153, 882621079, 735780931, 520795051, 139558445, 530356562, 191435085, 357767348, 732949511, 296407750, 345516957, 7897823, 456229035, 432062331, 842450041, 461636391, 349842892, 459725415, 591464284, 771067972, 113058973, 591079840, 939202336, 98989318, 854771997, 218462878, 587641636, 111252020, 118017008, 967014847, 762318301, 783740350, 400420495, 579646139, 817174197, 511992454, 387682646, 821825821, 758844517, 145604556, 138797052, 323524683, 707523919, 689325997, 529586016, 97508712, 600891499, 226106394, 248310546, 236179337, 728418892, 859068898, 467670275, 853901730, 526901430, 963042261, 731332642, 803166069, 884391945, 849784770, 56411799, 61295438, 412839359, 883675892, 287050339, 823694104, 395293384, 461062337, 749207267, 841930575, 209596853, 185164232, 986101494, 812799060, 107278107, 492475904, 169907724, 562324192, 632742920, 938932500, 928346315, 877812301, 905286994, 462827631, 77126603, 756081011, 164485488, 586259687, 85114925, 342712289, 898023291, 768438497, 604019744, 426397755, 403553737, 987860061, 238344853, 482280012, 262161974, 244235096, 407608645, 50509836, 645814487, 380921338, 358469906, 598089523, 204887418, 442209040, 967106498, 985646996, 494517697, 350889849, 993488999, 699088401, 972322967, 848796866, 92019152, 821403968, 946130032, 542912358, 614856365, 870046678, 391465695, 568628985, 192575830, 919795856, 963632496, 36915440, 991692910, 300071746, 55339806, 722150449, 434046688, 204562790, 773451790, 394320650, 504067559, 377158430, 970269168, 190356418, 34497580, 131315712, 65905407, 862065107, 145122811, 51168066, 740171462, 249842830, 384238433, 338550668, 512549582, 7104671, 402268758, 104661638, 380117140, 422543139, 354886887, 68392317, 388396272, 813560716, 915441893, 234583223, 773210120, 75683853, 52080439, 868067115, 769168878, 449902220, 196911354, 33849741, 631718053, 302109247, 221201504, 719753550, 533879810, 149849171, 306601602, 564276895, 855648613, 887759052, 289955958, 475225004, 307507524, 495978571, 863172406, 609153662, 712120303, 440312876, 605580773, 359808809, 897371392, 199197413, 918059091, 809475555, 965353293, 361134629, 303847128, 773458740, 586786880, 827066752, 473039215, 461657082, 520288315, 131517248, 512906382, 524151716, 577028255, 101517756, 822845834, 939461625, 827091710, 343707236, 214221949, 370257422, 114608579, 567273870, 638037058, 68644411, 838225232, 533015754, 51008721, 592279568, 274580144, 465431343, 861055758, 443920755, 632296770, 621861844, 307318577, 914530745, 172692025, 123466599, 699696743, 699886129, 180898416, 318436303, 656427609, 197251661, 288821499, 855908185, 610836947, 23478487, 608326150, 747014896, 975502279, 910029377, 770872271, 446227213, 655845911, 322687258, 830038395, 336687105, 486863354, 519066808, 625360535, 577097476, 883724706, 231164475, 544275490, 55814314, 237175913, 417769198, 319260862, 936491995, 742556593, 426022265, 270975656, 881814533, 229399555, 841828774, 68286899, 581129403, 383584458, 656524215, 820849097, 610434619, 851722076, 70836628, 18649940, 935029676, 149368487, 145991616, 218435977, 887110759, 466517094, 72697913, 894785832, 283109624, 969936023, 601193361, 821454100, 316649728, 274800742, 51120166, 676285581, 665514057, 651898038, 744732055, 976448996, 279230495, 703626819, 469191030, 571993721, 390270723, 695063481, 888573364, 575715059, 776223896, 178918281, 286606360, 962448396, 166850421, 711518933, 435758089, 408106851, 433190214, 184384880, 764899728, 884696086, 308273806, 603411450, 218968628, 885646827, 236063222, 662321019, 608061089, 670049477, 700241073, 567455327, 586583229, 232735591, 37376600, 737923042, 821113756, 200665376, 423013188, 403217297, 743932676, 216162937, 395373953, 318249137, 670007383, 303223336, 554271130, 394443512, 110560623, 138792706, 495817987, 444310197, 112965918, 95356796, 576130785, 246663044, 476653381, 524320409, 345942434, 249356021, 892894813, 189900260, 334133849, 275613342, 570710570, 805380091, 931689164, 947165277, 539111127, 67739862, 586780374, 90255110, 339246022, 401181109, 765890258, 151327877, 588671517, 905622, 775175424, 991739560, 917720474, 169354562, 697184873, 784208015, 446943463, 482139921, 48448330, 447805102, 562363320, 321733722, 955617528, 384727084, 98401918, 936522352, 445924112, 911636989, 713724241, 771508391, 433542947, 31526099, 659770763, 162073143, 714532537, 120122907, 229356453, 612597308, 598267958, 996104794, 248100327, 624025867, 480602960, 298135320, 794814614, 609642096, 656128125, 731652878, 144601945, 986893856, 769046439, 376424099, 429722727, 469815274, 496719987, 940137495, 618091885, 858064286, 488708003, 918616681, 905298555, 557221806, 398949485, 507643970, 209227273, 701613576, 157429382, 623221732, 23119552, 353975766, 634623198, 633541353, 610241494, 444646480, 685714665, 316965737, 132856035, 169564274, 340319668, 178302474, 757283918, 534412022, 720092866, 583088557, 834554709, 359529645, 520999413, 371113647, 313585217, 79873681, 94712777, 13521556, 561600686, 53792274, 506712751, 124352886, 642769199, 213977305, 777622533, 526624263, 188976751, 572535171, 248926807, 255286703, 958716218, 118156255, 151150860, 40840851, 274187577, 651652808, 951325225, 590979360, 613470665, 317647911, 491309961, 680195696, 831300597, 868551843, 599752395, 806128309, 331554137, 208016241, 591914602, 198415913, 549061024, 40739807, 401157312, 723886494, 292600343, 27711275, 848636483, 646115562, 188720541, 782907690, 560833757, 617876551, 640244799, 933870055, 116620741, 389368729, 881471831, 557654405, 569646747, 702059951, 420792314, 995780948, 136387944, 886097988, 601569584, 100454548, 427771323, 953799551, 380001913, 823900613, 854067254, 702983436, 646302126, 288149048, 684538939, 162830933, 58352618, 552973326, 658378332, 194053816, 852087351, 87626832, 253862376, 86342567, 542008221, 546092947, 249349657, 876942407, 640436390, 421744495, 66163360, 225824037, 715102062, 930671250, 823553934, 520742069, 193057566, 736605678, 244597016, 633965487, 547188277, 316637838, 567434149, 191586876, 959887427, 698663009, 902170886, 725483674, 647321774, 804680815, 576572464, 835527517, 541710196, 69289605, 741999737, 257515824, 423166701, 433885436, 450384276, 335647728, 667889496, 561084329, 189811364, 376056078, 490173187, 299538561, 182002781, 977327705, 30304777, 159129791, 280265385, 838947096, 692024583, 111775102, 510104699, 566807577, 310365274, 48553016, 7562815, 97032503, 390988050, 113940184, 786552824, 183473135, 919158310, 721662471, 891559776, 893888758, 507810993, 832478172, 156549058, 50575802, 585602771, 649485248, 741136090, 60469153, 260396715, 811328083, 162191424, 585530190, 297847959, 274046038, 874390131, 12778419, 605908662, 738693122, 861580264, 868888035, 335950807, 630638062, 727459536, 467817458, 484967521, 797803864, 716309210, 394248321, 861178022, 596427303, 917830277, 428475261, 180104979, 986945104, 365763263, 542402700, 179566476, 842265905, 833537676, 405325819, 566009111, 919134968, 964666618, 774165412, 297926852, 742766, 951373651, 624707720, 320081653, 111758302, 508807053, 744960895, 810872300, 684043957, 556420918, 355505140, 264048140, 683962715, 282645958, 722412802, 282390442, 68049556, 653387947, 172024431, 631635453, 15797109, 324691883, 157025767, 959850578, 142223084, 521030392, 809099986, 251808726, 211017724, 227591371, 507069834, 735498777, 43436859, 77721121, 471749790, 642927033, 927124191, 906032305, 65244635, 843129247, 509806945, 158869098, 638389072, 152269799, 524363689, 296086972, 295706739, 953838574, 568735279, 174069645, 794560725, 580623924, 985212565, 768004278, 657164799, 844958718, 837968879, 132368739, 248124324, 210842382, 676225781, 169118878, 386306103, 633992885, 667797347, 415351337, 102181188, 790501886, 688822193, 816338697, 574405482, 382584203, 242067520, 21603294, 632015473, 115008457, 494177232, 713260707, 144373406, 390484342, 813203980, 744213362, 24029945, 724962504, 975843054, 588237022, 83935832, 661413518, 943013111, 975831716, 822011042, 560829671, 905066188, 730415759, 99805128, 548454627, 458438468, 96046238, 804742251, 278966307, 912317912, 421519681, 221801638, 903568547, 290623392, 616355362, 381846700, 32888790, 496232404, 717340578, 457612253, 257561693, 988900186, 154096912, 824984154, 886294500, 45128655, 137463117, 123892030, 974308010, 481602336, 61784256, 494539279, 146015250, 450933848, 671640857, 880099222, 52013847, 850059372, 266747977, 43560792, 965206153, 657698506, 567996984, 530655381, 549484158, 194266563, 768449640, 712469205, 105458262, 763272580, 343007961, 148682373, 802834691, 116611456, 676891232, 950215366, 168196271, 464453962, 953939966, 571942840, 60613234, 448740596, 646955201, 209091097, 189792195, 328914574, 429856810, 36247112, 519943011, 848031423, 17545519, 555252552, 837417060, 752472163, 775635160, 449754867, 812079994, 466219552, 173426709, 366362504, 852280833, 906676660, 5870121, 302073007, 519590945, 609724317, 104810031, 774813014, 237319827, 216315895, 512755967, 625099953, 857970844, 234972776, 231635322, 314018396, 37293370, 118978380, 413971031, 413971193, 232463699, 532287544, 917093731, 761065537, 171652363, 998923043, 299184419, 242040764, 826134041, 30707254, 235980972, 322446398, 557172367, 33080742, 76238120, 542805273, 478160312, 913194409, 755074343, 580043065, 23141959, 579597648, 308721743, 193788107, 858319381, 401062418, 514753600, 276677285, 33368171, 881516920, 28531665, 904217298, 94553770, 977867204, 699416864, 447285935, 7085139, 923734838, 847715306, 681892960, 701607991, 175822518, 707423341, 69203131, 500753834, 792712880, 919569083, 498090335, 429436252, 34790245, 91974800, 111802748, 536205611, 520094757, 468281347, 321584149, 154763960, 641118197, 835645511, 712918750, 992343568, 198520931, 833470241, 961283233, 81878487, 309511931, 708881817, 340419623, 874174372, 308022288, 985340576, 215687792, 167918527, 976655341, 490506304, 986538191, 278477373, 619826278, 490469418, 236470356, 202325164, 535034802, 650692280, 354893076, 892984822, 681507378, 278813493, 25983354, 167512634, 44275821, 615830922, 296411632, 807897842, 812199305, 244780522, 838686937, 379280496, 778530620, 646402622, 225372158, 116103064, 414972057, 614988457, 269379085, 658309452, 535620869, 559927590, 924476812, 865177183, 177875275, 220295341, 927783136, 338313414, 769337608, 493239929, 276107951, 619440851, 112119113, 258392788, 842048470, 42565423, 457146207, 824951630, 580679898, 627075340, 122043283, 464295096, 266958508, 225879637, 55664475, 863156306, 460369626, 650040223, 889855875, 535228018, 743435722, 199379115, 672898617, 505778864, 464058302, 499514830, 578411786, 584308486, 116825000, 448627159, 47075952, 752027131, 362194044, 339745835, 958319028, 545777550, 85097604, 686188801, 980031460, 736820265, 624259430, 694938211, 919194765, 915405423, 998033452, 849264699, 717231244, 770668552, 149123559, 53300186, 65135780, 629502328, 151508830, 856010859, 582947258, 603207070, 977724198, 906953949, 313070738, 399477931, 722232921, 76957964, 37095038, 246428579, 497360636, 954175874, 233883269, 856473570, 784493705, 586218963, 374542311, 199460226, 534280112, 570735807, 706437398, 363388905, 934946396, 743279035, 174894713, 220315073, 307389257, 518158798, 483272736, 157709288, 739297097, 8235615, 26110196, 446111105, 96806640, 688987978, 907562349, 565372423, 707265153, 101338734, 347852265, 615706064, 233930546, 518917826, 118677028, 463254530, 128978352, 426261198, 810604282, 100286694, 851894270, 429124216, 640539186, 78185493, 691371309, 5260221, 118411698, 73370808, 688692211, 935651783, 158084124, 912429349, 148780005, 336660597, 190557918, 705835920, 828383101, 209601606, 898568033, 148220061, 899118674, 123256356, 784771226, 980565679, 426776318, 366673748, 994845587, 226325712, 886192475, 506198741, 85305767, 894363540, 531302731, 226228608, 618963615, 50669838, 283925925, 577272528, 987734496, 528701316, 195457424, 753373558, 631832621, 774743234, 437990667, 402413562, 534643984, 196698414, 30388549, 340985455, 276400873, 641617156, 537817459, 453837222, 642126309, 891120572, 40399517, 259251219, 463776848, 302402838, 194598014, 572635153, 699467985, 242967397, 904175211, 489660606, 806102208, 14512086, 820287368, 895136087, 160608415, 259388215, 634180897, 840851419, 510163126, 636760953, 657445286, 577816955, 582977584, 644614458, 627910415, 950606042, 205552981, 945880030, 331332629, 699010901, 83448397, 586841780, 342100315, 363426190, 587219364, 227940871, 805233772, 233848364, 579556810, 860211926, 715166760, 809470427, 263097385, 80259675, 644504171, 781456791, 559788917, 731617070, 106820759, 415082281, 768434967, 156712456, 200380804, 111347773, 104018937, 873009212, 297347337, 378717624, 77670667, 288490691, 657375710, 700829649, 100072738, 516941702, 242064288, 85762576, 367737147, 236951230, 335359692, 550694111, 776988708, 883723609, 365339726, 120947097, 868016794, 152511762, 811659265, 480824684, 150926362, 91850674, 936278270, 378330740, 812958587, 787099294, 721473526, 53212220, 818874627, 518052091, 629500278, 648376879, 554523868, 484348422, 389313570, 47694755, 252883434, 162699236, 148128279, 964639860, 947796296, 856211230, 658027532, 81062719, 181500963, 843425365, 297613236, 745479168, 622949600, 476527913, 136945552, 363215427, 82436118, 936928548, 800620716, 413823848, 363848991, 804826008, 206111069, 182219006, 541792114, 604958484, 365313827, 923605000, 625107088, 549521196, 815991260, 847805884, 538510360, 508466632, 994718630, 521004462, 310807034, 929911799, 877706627, 123060101, 397604894, 352205059, 53753926, 363409209, 349565876, 609369098, 714228127, 526400723, 591744518, 377201069, 885816921, 802802089, 760421207, 442781322, 431574337, 507990251, 179799384, 80376001, 241887167, 243718563, 985589491, 99761318, 172101305, 462838692, 418475012, 114635495, 606597048, 589967662, 862273788, 722593302, 916819492, 79956670, 525604657, 35853985, 370444477, 338528018, 963845124, 913346178, 6708242, 17355371, 44148028, 419455665, 354843035, 731223518, 441201718, 32821563, 126430042, 54441440, 425931935, 695303220, 233711674, 68759552, 288975824, 232345019, 816009684, 828707887, 391632055, 102290730, 470259647, 133154134, 593623977, 892870184, 237689577, 1507808, 637652094, 546840582, 505694892, 851433659, 293181293, 440799445, 761523801, 798342193, 975564672, 818714078, 831547590, 217580066, 78897352, 643517313, 214617046, 343475597, 184691877, 639667427, 221405328, 786332317, 755391081, 918695361, 147068116, 467700179, 77488146, 636314728, 48175682, 379696271, 713766613, 113213257, 920081021, 555856694, 307435095, 478486972, 786574184, 712150231, 954869838, 74880457, 325434067, 57563811, 717851564, 397042541, 850673750, 684418448, 895860969, 746428612, 818707039, 259746644, 512364671, 787150217, 390430246, 564651754, 199085545, 175481227, 917627943, 632146595, 748144062, 609266628, 1395544, 826311549, 217748675, 102130535, 840940321, 26171165, 793465656, 638393442, 655889489, 197168275, 20578565, 315511513, 352473936, 95979998, 517202234, 432621677, 208762704, 840255881, 525029871, 903954227, 408930980, 972851921, 708808314, 980639749, 445016860, 838506809, 323324298, 169958584, 495602354, 215169967, 743192622, 929886883, 190590062, 640545498, 167790165, 172768981, 213259682, 231866648, 948102145, 191185208, 272318904, 80007320, 833905470, 605329299, 740839667, 836551390, 864491175, 651518752, 966565145, 382169141, 335973398, 459561360, 226343911, 902067854, 981640784, 141798772, 75791260, 36458982, 11730558, 767094063, 907979670, 588824142, 89736030, 868303224, 368541495, 833667252, 231744171, 629828961, 58067941, 779536876, 248205116, 588671772, 850115498, 154530566, 247195156, 812237487, 278418242, 182008270, 692138601, 8392862, 356565027, 5648185, 543511803, 600834477, 859572119, 814260502, 581137862, 785900195, 867250680, 152797565, 325313408, 371106858, 209696307, 477163192, 305547699, 879526247, 489686875, 59196084, 161359570, 25544332, 320165356, 693175919, 155542806, 127003230, 255584461, 915966890, 85251946, 907501973, 424961927, 938363031, 464052029, 184824710, 952970715, 458438221, 566173874, 916481349, 92391294, 335753085, 473489700, 277076389, 168555930, 397628002, 154335310, 527477437, 982945846, 910558298, 507358556, 913223234, 574718819, 861402653, 532577053, 643900536, 693641522, 579830261, 993403688, 810255148, 342908134, 532993287, 309796141, 430829971, 391108498, 790930623, 169998839, 582253321, 721809802, 881022955, 317146932, 541767494, 860137160, 451763222, 15232434, 257277233, 666666560, 869477934, 648161950, 988774258, 365062803, 305013108, 344316472, 680499548, 809952424, 894778339, 863010939, 642297101, 306855135, 566615708, 471371920, 388837188, 238804608, 950552322, 329527438, 686041512, 222341322, 858605592, 341656799, 82588764, 609882486, 885010575, 226074591, 137922191, 941863570, 441388404, 840392116, 205035057, 15396750, 169749419, 575218641, 25646809, 7880, 527307238, 692822516, 159951626, 929775253, 103978032, 319712597, 398403702, 875538679, 710723544, 244040863, 347643227, 940177916, 372968113, 18987207, 57549284, 155028016, 636309968, 128566716, 161070013, 511456226, 41563454, 15722398, 51777851, 758299989, 623527740, 25997602, 839890398, 746481732, 368315182, 649532706, 905704755, 302872691, 194907423, 525336591, 172762931, 110396518, 834910157, 206993269, 56010452, 433098755, 170880237, 681552424, 976104733, 868387124, 440028069, 810178829, 69846275, 675936384, 49708179, 171904248, 28479580, 183774508, 409932860, 260278568, 524309949, 999953615, 258146475, 168169350, 795325519, 846941648, 85023372, 306568170, 928872322, 315250017, 739801232, 973116792, 225929422, 463111311, 599395927, 596419520, 368005396, 572351846, 685724853, 917943558, 535385624, 135312096, 840049085, 688430904, 772334672, 31012421, 246269000, 356759580, 267052717, 380755355, 836484300, 171242868, 733669915, 880624752, 349982506, 343762610, 579248253, 967724375, 260604348, 723491028, 238715879, 524793755, 842642601, 555657540, 62739652, 324551311, 416981273, 27366344, 391669948, 324962635, 172319950, 940357799, 45993024, 484935403, 329085541, 944269127, 680041364, 171869239, 758757277, 625602499, 999668615, 980470467, 60356992, 738019505, 975595601, 847957175, 944155212, 961465320, 438088925, 30007169, 885660057, 496488234, 504928388, 618708849, 693783041, 785324064, 667905833, 812754642, 891717373, 733420326, 818533789, 919319790, 979708017, 925597995, 492379833, 379566292, 970490188, 800035997, 353110866, 266841137, 339503257, 694451400, 593985094, 808638408, 149602936, 870035785, 8720264, 50725993, 337632839, 572771746, 762579320, 756718010, 782376787, 186310050, 567929586, 726869977, 791443453, 689655828, 752013399, 38978888, 830801056, 512404532, 347393050, 132862895, 254365613, 194632473, 577525218, 77492304, 145309440, 868660746, 30894729, 902450842, 182296672, 538457069, 478565096, 398918563, 198341853, 893384680, 643463125, 711141026, 703058789, 903735131, 380400264, 967223152, 266354891, 999260172, 631006865, 186898952, 800737682, 803090095, 544163363, 371080469, 889964113, 915462766, 71786024, 290366401, 131494024, 378981376, 133359016, 784038575, 949893327, 782104077, 154149965, 491792306, 750258344, 46439558, 876702888, 448391967, 456408454, 134888655, 726665348, 715787208, 83309869, 406137387, 43216624, 59512026, 641654121, 684990671, 298405067, 172297013, 700398732, 917054270, 874271872, 881862097, 419413366, 297633612, 582802983, 270123046, 995433994, 841006187, 524882533, 416844180, 887167854, 401983153, 371806024, 514710730, 637886376, 709739268, 180610932, 326610709, 641224469, 402851308, 210962993, 731335525, 527625529, 278266533, 988223518, 983623212, 263322785, 319880770, 148229108, 261784860, 858357280, 736665734, 571149308, 256151593, 136449918, 362657842, 414781641, 274164163, 814011884, 51119295, 917987682, 100318340, 747790914, 340043260, 105437812, 622583823, 906511667, 65567118, 268281754, 787890132, 997490897, 930929453, 742010202, 978729408, 136759861, 850532722, 689910406, 892634443, 452776531, 776632552, 441319310, 787928368, 339173584, 861549747, 228817854, 253380409, 842886403, 540580718, 285087216, 959800467, 881436905, 67820817, 918784671, 119506007, 741301109, 39678045, 504089730, 514664871, 766379416, 258545566, 892257512, 993530381, 738974329, 249344745, 403551962, 166653027, 886114136, 94181207, 630270117, 698697889, 429225311, 773189108, 156713538, 264494941, 217742177, 290461173, 876066592, 32231282, 361512745, 312824208, 861135403, 536071166, 552882916, 613534696, 750650966, 484768592, 974695340, 901402527, 344683976, 285375568, 173258062, 576825031, 635981395, 865780649, 806686206, 933819215, 99868730, 369438861, 852635768, 728084061, 805631029, 483116566, 366142445, 496543486, 699610130, 966082653, 48339432, 779570370, 220523782, 569079065, 254775294, 904459380, 173794221, 80862936, 604002877, 419788395, 294467167, 675137830, 930475062, 279350537, 545453309, 580092525, 682680683, 608449142, 845418018, 922314686, 956718642, 71985279, 183186337, 842604907, 427359709, 152842043, 804026525, 152868142, 777731919, 616788551, 281475784, 355046517, 125452128, 224514077, 942893707, 132735724, 445625111, 223656590, 858424450, 890642398, 641106257, 284047462, 454091913, 407982949, 96463356, 592408898, 215823829, 42363887, 989806681, 199215193, 953581726, 520418040, 391979938, 618959960, 34029422, 238240163, 120398958, 688534572, 593564278, 398954395, 324909184, 467264457, 898427282, 440339203, 587554304, 530985526, 308089447, 623978108, 585299751, 447269166, 982202071, 450715873, 358561620, 191578087, 273588807, 4108553, 139660853, 242718550, 652039269, 788026273, 106646569, 857843852, 391422959, 135660766, 175945496, 487311731, 500113482, 355746362, 537719508, 917352309, 640876827, 634950230, 195001696, 547486575, 102068981, 591249102, 734700429, 946549509, 935168423, 601392233, 131117725, 64918955, 525101683, 355823828, 660988732, 283346331, 804770657, 205593147, 221668637, 246971185, 639599954, 771740571, 276283761, 943985149, 773261091, 815879596, 831264886, 636512247, 759796314, 654427820, 692074264, 955845319, 671011276, 854943399, 695272775, 843223486, 36551099, 188359974, 510663038, 224018709, 148876290, 733060127, 353660902, 801561456, 764705619, 11508808, 938353507, 770709564, 503648835, 496132342, 664818778, 55075572, 9447087, 395251955, 289476196, 11375074, 93100567, 562038875, 435291490, 59882880, 188386898, 844267857, 892638934, 850146294, 485583552, 216935261, 80941440, 270134959, 390258881, 661050833, 980958505, 692739360, 433804028, 84584002, 588461356, 253549157, 123889539, 917461455, 555913077, 145107138, 597373467, 666340233, 78690029, 434495069, 681804643, 941681264, 423197959, 653991520, 461222486, 438009287, 458755093, 621391098, 701919456, 119532401, 477671687, 548724555, 150365721, 310553119, 360425251, 677912, 907856587, 727851034, 127149620, 498441607, 580561005, 678414664, 340613166, 880239776, 610894169, 449418216, 544121607, 503098185, 862251377, 109554550, 572300987, 65246968, 690556295, 689462048, 523007382, 769335179, 336778731, 383496784, 506244005, 679748071, 352003208, 663153277, 140680075, 601607405, 212991476, 28044273, 126318354, 440241, 759938314, 528909039, 912645617, 874852018, 935769313, 804272641, 609242964, 873191485, 762908908, 907891680, 225826807, 995483882, 883211660, 567253689, 321309191, 736876750, 938526070, 298997891, 834529238, 174241171, 722133097, 388213285, 230443664, 60801932, 727963887, 244234339, 541883823, 611279039, 780081966, 186399973, 158519866, 667649041, 93548460, 699594210, 551173519, 479626704, 264667346, 680351618, 35383536, 914225924, 832824075, 406730516, 642955317, 581935787, 243733296, 968978727, 4746406, 669617254, 322773152, 167678359, 648925149, 838695869, 445436703, 313290861, 237446389, 903934627, 9707456, 112192603, 930730901, 310034876, 288305398, 842154490, 173338565, 910022196, 224186753, 674542281, 819545611, 293319303, 297754253, 879224405, 662919960, 582109763, 514721979, 310738717, 652085444, 319174310, 716295825, 248297175, 948499671, 933874001, 177157301, 430382779, 832126244, 284273474, 734320877, 603951819, 757760458, 866635263, 200507984, 7335986, 310010554, 39721949, 256259125, 961480437, 64752637, 140520674, 673389929, 697158657, 38596993, 746874265, 682287842, 554613508, 931129649, 743815760, 469920956, 474323809, 179440160, 233805494, 385587729, 265852774, 589521030, 122532875, 897254534, 411816138, 283103489, 816793106, 41838264, 97697954, 365956398, 20488986, 400970809, 41653537, 843425023, 12505788, 899121785, 626505624, 535145352, 459238159, 698110541, 117579442, 792172766, 504301006, 187200120, 228294634, 402086399, 98049230, 495347614, 222475445, 275446638, 895621393, 946901530, 147149688, 59443884, 181249747, 266639119, 529999716, 401949612, 503851929, 284150051, 274703888, 298341975, 992155755, 844449166, 467206308, 612646191, 918766020, 699222157, 559619955, 560377372, 505605552, 352382769, 901016169, 986796680, 965420895, 325712276, 141790711, 214719274, 395919862, 869561646, 314649361, 887246472, 179548114, 900655509, 37596239, 398694443, 960752522, 846982518, 118875504, 997985113, 735096010, 474015567, 693549967, 115042124, 901790636, 736478974, 660661226, 133101702, 313427347, 230797430, 571280520, 627201090, 157557985, 377706448, 955577054, 474425404, 400126742, 939369989, 156509429, 285803046, 981978099, 260721635, 492371008, 21044626, 636091371, 268616257, 758581668, 248780219, 788230024, 940053341, 664402910, 212103482, 972275121, 429992367, 439325339, 65021877, 521358114, 8141385, 853217969, 508411491, 59304989, 610975305, 360366555, 255224873, 760685507, 22327550, 641369701, 770905847, 580583444, 725250451, 558940739, 208838288, 407502900, 752863460, 948210126, 980973821, 175677555, 701235476, 115889826, 128478761, 13192125, 119081984, 591156383, 57295091, 821279671, 223921665, 32436548, 640257175, 847340980, 163321145, 547433396, 3736947, 912781612, 455177088, 341032682, 651472510, 198748200, 355152874, 534827765, 11214210, 394902472, 341685517, 751731510, 815157117, 837255044, 208913897, 226413549, 634303124, 696719137, 345565674, 742325211, 81155618, 74109966, 119212448, 941952322, 602751439, 996787680, 391899425, 961189815, 144196064, 351768171, 942028800, 239781006, 96082815, 663713639, 987154269, 709365140, 365033818, 680706287, 673035090, 863013235, 294399009, 998670673, 616778735, 252987728, 274056151, 651235527, 740496057, 599461063, 539022215, 673667046, 290913796, 212108567, 300354912, 736089479, 881921581, 189510791, 749119575, 375181990, 833094966, 804582728, 42250255, 349772645, 518879405, 381299212, 493211210, 350488264, 713389953, 280619733, 307501493, 867302997, 550489445, 331570288, 182265972, 193603996, 976913041, 471702955, 103850194, 210594166, 890922353, 369423813, 287969927, 575371476, 877710929, 61224650, 708038044, 658988562, 834264952, 175873962, 5312545, 913872748, 920840306, 106762933, 338464727, 553118986, 406488012, 401170001, 737738929, 658034795, 689368021, 308729050, 618026875, 628187158, 15159267, 620148313, 699281925, 739440991, 135064426, 70997517, 978874736, 242830465, 593717708, 857972100, 677403620, 934618319, 767498668, 651163012, 777087462, 857028085, 743123537, 588641590, 56394687, 634931457, 524780664, 52615274, 201370559, 901730579, 986133139, 174348216, 262653279, 443625504, 318209479, 516579821, 624318276, 33780857, 692808402, 934182132, 370244102, 838346281, 218404698, 206127237, 170449264, 65175341, 166136893, 730695482, 313278591, 626646637, 56288201, 638391004, 543047607, 633519694, 103202117, 786046383, 581615845, 558968818, 898627946, 144790171, 259556795, 723060856, 66460396, 885449997, 242119598, 493231494, 507651234, 473290099, 280566035, 551394543, 938870701, 498897347, 623159790, 488457124, 464753195, 164121822, 59341780, 807593266, 485511601, 759414073, 150280311, 221628561, 667367015, 17176353, 422046423, 945984727, 565857648, 894580840, 232805010, 585110159, 663663673, 720574371, 226748339, 442760174, 38321806, 972384540, 24888408, 191632916, 479759591, 271573343, 292857627, 187241869, 615241996, 595388829, 777348153, 659073332, 939051230, 312549942, 292845846, 214244567, 346804890, 400093554, 166723594, 239032011, 43437087, 434311595, 992491942, 312565785, 157337228, 908999593, 417145311, 849857549, 621087563, 942472384, 455982554, 984233731, 989884074, 503867823, 348552100, 531691541, 214515529, 364450097, 740703006, 799835391, 644727434, 740186973, 376603292, 561466352, 582526191, 800409708, 431576241, 851252154, 718228906, 950111817, 481043496, 953589277, 336991972, 981386635, 13200991, 358994283, 530876557, 225881039, 869860610, 105243434, 328723559, 765650200, 595409530, 801322846, 730897203, 130629478, 820650472, 190784970, 467854680, 283833943, 221757187, 948042892, 455873374, 600611752, 632972919, 665723272, 461980040, 549561643, 325627724, 783913446, 860790309, 608637944, 734449675, 674178488, 439940495, 81014086, 658951217, 977437213, 7161753, 697278956, 621766167, 313335213, 594046121, 70658325, 89498198, 421018235, 762221956, 230861417, 854254811, 199330438, 410106298, 295651058, 165097775, 809524181, 348226596, 794502690, 552999802, 190851779, 261598790, 933413910, 346342799, 456067264, 818299321, 615918718, 996545389, 917694394, 368699096, 72959472, 528238892, 636711808, 915899513, 225957582, 324454763, 800661865, 526978500, 614085911, 146368514, 318337730, 310051574, 846597609, 413583304, 244075529, 559621503, 824523680, 500255924, 729074619, 515768409, 461993647, 210025062, 416885777, 550894381, 249464556, 19989604, 551775151, 550079336, 795789352, 742977035, 929474726, 746027544, 39014448, 209111090, 780867438, 512757520, 414460511, 836986939, 937642980, 866159371, 753867236, 737828860, 218640002, 24437976, 953204515, 85823275, 756467025, 312078179, 72331293, 92081183, 994522550, 908744356, 943159578, 669089415, 412439711, 614433219, 144049151, 533364972, 579726759, 155939896, 228482533, 804690232, 845426292, 180459902, 173967536, 161859664, 368471584, 321429330, 909462178, 150066313, 911470360, 243363732, 198980884, 722143744, 596667126, 934501800, 705150489, 305388202, 300808964, 129948531, 161873896, 653577051, 288366843, 987212685, 894364987, 945692499, 72562293, 327930378, 349411471, 212054800, 820044822, 523729507, 666998317, 644781047, 106133996, 877714591, 633095209, 214603638, 199272752, 627195862, 705283588, 505708600, 595201099, 63668465, 361365582, 842643175, 161825653, 905708920, 782001349, 981136708, 690183335, 384577578, 509310447, 815625370, 105907335, 404905037, 639428508, 394514561, 331958272, 381573503, 280885852, 319268532, 817488604, 823075381, 865913088, 819412779, 289838519, 621843572, 409338692, 698008377, 757685914, 532775680, 159147984, 646581601, 960961217, 740242840, 767703866, 391557833, 336327628, 426598935, 387291313, 828631078, 615542992, 502486029, 923891525, 785240496, 220748240, 805312972, 42312687, 745145809, 679157368, 971819873, 184555601, 832095391, 372510634, 605953444, 104750907, 633283071, 407913912, 776367985, 672252297, 55089716, 537511391, 318957367, 333805, 415175198, 769105780, 745503748, 499007241, 475837735, 102616616, 899767371, 44138257, 41109493, 79793352, 33176390, 213298558, 917299145, 447244760, 386671208, 943975831, 45476490, 154987689, 182824411, 219191087, 582042261, 647612281, 630093283, 886358366, 737964338, 740896692, 380694477, 858612849, 344971266, 529633215, 456628271, 738473260, 7729259, 275195786, 223255067, 344415363, 585006127, 48860577, 707456959, 221717403, 972538197, 928799044, 211172637, 590747614, 618307165, 238864078, 34688570, 697059370, 413250830, 616757294, 347968392, 736139985, 249166861, 327019348, 977607498, 657101356, 838402988, 986832897, 943454637, 930657994, 274026821, 351120344, 938032261, 555378098, 729551641, 241374673, 639410807, 197230748, 806234899, 158521386, 969925494, 405880257, 97410876, 698790480, 666148245, 73862115, 515251928, 441019604, 280218304, 287580039, 256060372, 280049682, 933281360, 628932482, 544697551, 276172422, 7912471, 267759516, 589694738, 321844480, 315726097, 375302720, 647761248, 660848154, 747465259, 776157987, 676001705, 17029621, 532641724, 574694517, 459822697, 259963415, 601611052, 275689863, 159705806, 48193187, 243119227, 161216348, 981356260, 200478260, 835437024, 614397330, 353136093, 658292696, 67412847, 992518788, 55070348, 996950001, 252958578, 638928429, 472352354, 558542137, 551818227, 63457214, 123911569, 80281569, 309698966, 156196062, 142971301, 89375855, 93519739, 319927508, 907456759, 868577083, 802080498, 128231414, 905001404, 896946439, 215734291, 552480820, 707011049, 214587488, 778405351, 612142532, 855014163, 583614877, 666051451, 573154931, 228477968, 832360754, 283767446, 750405334, 337820084, 291246355, 524187512, 109063827, 529330795, 377262172, 216814944, 641980703, 551980685, 450273040, 282072072, 184642190, 81376948, 49553770, 566479449, 158309220, 675353678, 612443702, 101983886, 659380863, 689926718, 854038181, 134962632, 947485667, 218924642, 203403585, 209847287, 652142868, 220831272, 20294535, 134983489, 747863234, 526755350, 143282362, 446961901, 461731079, 634686665, 980003646, 773984353, 668902079, 867476878, 184735459, 719383949, 916489304, 684850363, 684358198, 433451811, 523373999, 740685303, 525370569, 163304049, 192331754, 892249446, 528885198, 630351530, 795877068, 815888091, 995712179, 524419913, 313422764, 543905063, 216771104, 962300344, 506436911, 402160833, 610117866, 241306891, 879917572, 987395387, 859604439, 739795332, 736492421, 12973572, 893782784, 177239464, 666065262, 396860143, 46888769, 861730320, 861785873, 130579124, 33345506, 655310614, 895094049, 572516570, 650156643, 127591879, 295207684, 852292964, 655341210, 203670308, 561044223, 894219830, 549582891, 984659600, 866006527, 606158045, 570685775, 235057673, 807248090, 254754897, 597048002, 641313165, 195635995, 181951564, 69427813, 899245420, 372681501, 52019211, 482564065, 694674642, 507067158, 16789182, 83532161, 2124599, 142093677, 502637088, 908308760, 981569168, 352165269, 692211067, 511502943, 822648889, 483668306, 950314405, 83681014, 423585960, 986649040, 923331234, 471704049, 593449112, 393203570, 692202621, 210822819, 620722209, 329939505, 24034177, 703251621, 814215253, 514313643, 884124799, 104360861, 997354774, 873460852, 339079156, 212982683, 513589388, 180976878, 780777146, 339061142, 605186935, 395701513, 836189384, 593158078, 449610554, 739205092, 818645800, 771129621, 905545637, 263210372, 109067348, 175666605, 907759316, 445484469, 239542606, 705067979, 907390292, 659040793, 433800213, 135197635, 576259619, 466110750, 233558534, 867140055, 560623511, 991581666, 484766527, 286602257, 509213718, 343525516, 86037690, 948274831, 771566741, 707686893, 953560771, 391831568, 456760695, 227145720, 364026087, 411932211, 111005394, 633894082, 291110851, 454041142, 315165667, 852997122, 581642396, 190312496, 936981266, 360915777, 537236639, 418599384, 860089672, 807171211, 770972010, 778719326, 148910472, 806892359, 871006785, 799639655, 804370573, 777767530, 647640561, 735453922, 15102465, 908347617, 194326620, 200002866, 863510129, 46042471, 44719815, 363890878, 431573068, 380359461, 257618815, 416032528, 118655307, 40530012, 867023996, 411867246, 432711012, 98746650, 530254212, 249010710, 434679623, 734325275, 618959022, 821461654, 909413987, 684769, 404560331, 417514256, 696701479, 379755657, 311067238, 519923286, 293297972, 755080554, 25901738, 490588291, 804498437, 681404622, 712220833, 754889029, 600862922, 951814042, 417369647, 640640310, 14499612, 445211495, 265029393, 997435276, 295461056, 309575307, 428560938, 227081603, 512181204, 848636846, 452142880, 527831340, 542639102, 361846777, 919667637, 19878607, 358265883, 433203503, 588323291, 840286394, 848026466, 464252788, 971262255, 105670931, 893425964, 803966476, 89502410, 309703079, 303196377, 372545637, 897720625, 955567861, 330652725, 980066305, 645764335, 583133075, 629318957, 836163834, 315181586, 628662770, 93915165, 883440819, 249462328, 638719271, 269999720, 718262319, 827661600, 332293705, 726111687, 412180865, 377700587, 495958062, 210054554, 192265281, 284335299, 429081176, 805101860, 417674456, 737882482, 415100320, 35025905, 788355164, 984945229, 395490206, 51929286, 769235907, 333312998, 696120846, 58734973, 715710810, 149848052, 26072490, 579686643, 32600418, 406615412, 928749315, 174128110, 341978129, 939545086, 337566343, 685030424, 348833733, 581933808, 535247077, 404941792, 869382541, 327294668, 329475088, 179755908, 27667063, 471762050, 607639630, 509669596, 753633085, 281856002, 585082754, 679611631, 485891979, 805472972, 46189738, 648785438, 961391840, 914380124, 727385563, 732327352, 330235064, 968312531, 817317381, 276859929, 161889229, 151260016, 844301228, 544589249, 584170457, 865800451, 893795389, 535226085, 673342958, 174674396, 55044701, 951075291, 578622515, 108205213, 94899238, 327852739, 460345727, 85757842, 294133548, 646549792, 423763317, 531146334, 438160975, 309908036, 265264231, 5444694, 351534754, 508796310, 237351077, 25706710, 159383596, 576535785, 220636068, 612042356, 228269578, 746086800, 54823640, 501768604, 586530841, 492776651, 883021481, 863612312, 881227974, 27871182, 347135184, 591512795, 907299075, 710951313, 158499276, 422791571, 24021484, 631555999, 61013014, 122434080, 451779001, 143731837, 94778369, 688064653, 776608490, 461052791, 801882587, 298787089, 898671961, 2451300, 479975735, 975155915, 217173724, 811293227, 758872866, 885484271, 7922987, 907916874, 189723311, 413400892, 827771080, 964742000, 754801310, 33214582, 275312118, 220320885, 87122162, 94686073, 278945421, 162372071, 61832551, 534055932, 463346126, 97663825, 870497329, 74824395, 450491031, 688402030, 684123396, 209228511, 446221936, 365686503, 455568505, 33108206, 110508879, 806789865, 635348304, 400745199, 11344833, 274799438, 680715525, 819380078, 511880549, 223701233, 335065947, 466159781, 774678573, 994551543, 478048991, 655067781, 78076009, 913952779, 361574992, 111298109, 867340963, 853709322, 633316875, 11300035, 800656898, 792885285, 772358178, 925708401, 79214708, 878753478, 277923055, 302095707, 894338909, 341191172, 439144001, 390301796, 508408088, 607472692, 777532907, 4243886, 512248337, 74153653, 441270278, 641957605, 768090855, 735041891, 133414657, 78396076, 80616573, 994832359, 884098866, 765883713, 755576292, 12478478, 408732085, 868890307, 786632736, 807464695, 701144907, 15708220, 899995964, 939467424, 957891216, 652506402, 128877951, 94396328, 536492875, 421402041, 364123702, 386328155, 228870912, 97714268, 928545780, 70008020, 345776683, 33518224, 848114039, 59286364, 986234890, 907591046, 855838019, 382639614, 651081016, 408420644, 92499576, 70894411, 471565502, 897370284, 197400362, 954215996, 173598503, 864880562, 775009316, 883380830, 578988667, 141946125, 756649081, 498853835, 648534976, 697002149, 904462075, 495401209, 535499994, 735941700, 284846108, 467098054, 107694059, 648272723, 797157084, 933874573, 646155997, 926593191, 404450418, 774556059, 897948136, 86903153, 551348362, 480684288, 694707582, 798153663, 358290031, 89172323, 764025398, 740264018, 6408188, 992737429, 395113978, 485483788, 37058931, 772157698, 171173557, 999105701, 121868710, 782590616, 789471608, 317782229, 396986118, 573181806, 536235576, 531071488, 576610399, 439684215, 242435148, 930796770, 389645649, 43948779, 977344310, 547485982, 290909430, 686579818, 958740580, 942831665, 941860707, 374665366, 362456519, 512554070, 549972846, 282208096, 394372681, 699636098, 616338499, 823106335, 361340108, 821758220, 178402613, 21852866, 917558108, 795550340, 972679897, 869692750, 817201345, 629552288, 185699181, 92310154, 657699252, 961583000, 971789018, 871424123, 654175527, 692012949, 709736811, 171445252, 791856671, 430215659, 299818895, 623649442, 609686991, 562676269, 934320097, 528738825, 821083605, 306270973, 494355044, 231348207, 283766548, 506208291, 688227363, 269438963, 9886128, 423287510, 88121902, 677607369, 942864165, 978746020, 944880264, 777847542, 4768981, 397102179, 164757062, 160637335, 190713351, 41959824, 191048113, 982386164, 582845136, 960862299, 370552746, 995450909, 762222154, 704316957, 827145437, 397301435, 67269951, 614457808, 111135356, 369908377, 219546381, 253500929, 95311180, 729889931, 700966368, 19923978, 540498230, 498799204, 604489627, 221561581, 380853188, 38910287, 484205773, 100152811, 665871064, 394041871, 25346846, 965561889, 466114096, 466947576, 17349756, 276488318, 64339221, 478166723, 10427294, 124628551, 948861611, 742772159, 377927830, 311964629, 691941719, 614126998, 972958183, 349832606, 491223897, 650697539, 744574992, 898666189, 262289823, 744441454, 878539602, 813534089, 547924462, 736290525, 72024943, 944771132, 578348806, 371140579, 758116426, 395795801, 872822334, 402418286, 649241307, 324285984, 4421931, 530719914, 311398800, 680751796, 47830140, 930970033, 659933339, 547575851, 421699724, 689295460, 671996694, 680891104, 641269550, 619411931, 491302251, 4283285, 230111439, 138918340, 606371728, 319130527, 380196816, 743212332, 997041162, 298541189, 543842755, 625680895, 67554342, 943117971, 338829951, 703051121, 306734455, 556928531, 324274527, 810791320, 379216282, 729110120, 732656173, 358604926, 366206596, 78295467, 77906926, 501559394, 20372295, 658738967, 987413011, 74166874, 642993830, 250016634, 170404385, 79609893, 986873419, 387971745, 427256678, 775535160, 214164624, 903473175, 830193809, 737287600, 891567744, 851213744, 260108995, 901062755, 838223895, 707105428, 771147848, 298887613, 806333276, 628677927, 918706454, 700566947, 682475513, 193219074, 597275152, 628067, 953293774, 406772896, 125285310, 546389949, 646841077, 959164453, 778230962, 95217089, 770249612, 408336640, 553095363, 990174238, 94966822, 857331095, 940108169, 318668499, 334846953, 947216732, 83307408, 472791974, 338170269, 114145939, 57555996, 505087893, 394712334, 537316539, 356726594, 311883118, 727983324, 853601132, 77768451, 474682531, 425358781, 805627867, 892728965, 198778027, 951560161, 614789588, 600367099, 612562552, 481970733, 990147693, 788453889, 780859372, 556403359, 276237395, 492569291, 735604625, 570051467, 801670372, 218245573, 314632531, 165440430, 678925809, 835576647, 554095076, 5228175, 562415125, 351455052, 780559183, 59999752, 247957401, 559668518, 640049767, 513349348, 253692155, 514407670, 17889718, 361286578, 636577642, 988956379, 242591373, 566609526, 29336835, 762998632, 294142996, 226609955, 258240360, 889009129, 344291468, 11542828, 207448229, 381177407, 43264168, 245106584, 787375713, 109711109, 995237283, 923169314, 571144061, 585340748, 574540742, 326305087, 758620702, 955093869, 344297447, 366565195, 665085903, 433933072, 305555240, 216305751, 325391461, 791836859, 610438967, 705426049, 544723532, 483321007, 464772502, 479483913, 631579508, 372308323, 633023282, 481664919, 718886043, 225286300, 75339906, 755324677, 595117238, 415171305, 313378586, 221257708, 529854448, 758736871, 989579326, 906535851, 687765188, 556119719, 550410236, 31474405, 90828324, 497243877, 365437223, 341533901, 908274867, 410324696, 497949245, 383525489, 549800179, 548560466, 242885175, 988026055, 160954791, 647855408, 816905405, 612740732, 954003230, 413152703, 824371005, 765898550, 444535311, 757233527, 101353223, 462775855, 247049090, 979606648, 344710868, 401589672, 480115293, 644887985, 170989057, 968048461, 634644014, 409875826, 326151569, 985890649, 8398442, 349884935, 959978244, 16160085, 422156938, 362903092, 495357505, 143772526, 182390239, 418017739, 802908903, 246918214, 337982332, 827082148, 503529918, 615756041, 698336730, 913600314, 130322851, 633791479, 255209606, 85029487, 162313906, 212067064, 460570820, 507041744, 740551638, 228167135, 442865684, 869805094, 54111662, 574781950, 577310516, 240410086, 9925416, 771401779, 947012690, 691071989, 135273632, 570105188, 541286328, 472135885, 86878962, 61648456, 38210042, 851109469, 282596725, 180753683, 243000570, 397589982, 274215292, 659363962, 186557104, 277672510, 625418751, 164615236, 775358597, 772796905, 288986548, 89592973, 802152044, 228728125, 903510492, 390264163, 897811603, 79492676, 704915780, 407065073, 420897487, 48410985, 957395205, 943150280, 102167024, 69264641, 81921848, 454078134, 476145439, 528110996, 340878473, 937103319, 628282111, 401005487, 344398, 622341507, 439124035, 436144320, 511381181, 365655913, 149478763, 583590820, 794604483, 430804729, 415138716, 234143299, 53993786, 511492093, 81801607, 785587076, 815602052, 931403885, 174692945, 703296352, 29795115, 17550374, 182894425, 437530798, 989599539, 774250425, 605633104, 855682562, 923926279, 224221809, 953620625, 910178746, 994998567, 153859099, 187771514, 68262262, 654590665, 539663991, 125256511, 491306967, 526769303, 545658560, 184139066, 122275785, 843000659, 803273136, 760429002, 342012208, 502465249, 298368531, 429801585, 212537479, 45732167, 405693650, 395019760, 297086984, 174814819, 748028164, 787020740, 501074801, 871649572, 343068670, 322628133, 546544871, 334916539, 886465200, 248799529, 492372675, 355998104, 775630910, 833036333, 282857524, 45584683, 526488592, 160040927, 546917955, 260853322, 977837791, 501293068, 95212192, 157080579, 338567051, 264194684, 952222751, 557255046, 353988285, 591695221, 714087456, 126196733, 392097696, 360438779, 893519957, 26782096, 909970783, 970154801, 710775265, 164223713, 115908276, 730357222, 451280542, 328710246, 629241757, 937749908, 684460230, 202761343, 666471149, 990803568, 51965580, 200265140, 238100123, 129323989, 275688168, 845239364, 14016850, 595887367, 462119116, 606316638, 614050427, 479231570, 546885182, 263307823, 852647085, 387586824, 556153454, 862540787, 980364024, 347567270, 533632219, 773458900, 655452474, 896494207, 675866310, 470392254, 607926645, 310215110, 423913903, 693653093, 591166474, 957461843, 220183442, 877491804, 867836752, 502036325, 251164172, 680241771, 853540493, 171941921, 562350029, 300096083, 920718663, 155053778, 674742507, 336325473, 52047659, 823325285, 218587566, 389597705, 57435853, 292710630, 662119206, 724760625, 670610908, 599141136, 844553521, 724478421, 149561892, 568298525, 403768153, 58434004, 306685810, 475905974, 258961878, 930300260, 115241288, 774011598, 830252410, 672710907, 581722387, 25096165, 175194438, 319217459, 508690811, 31328406, 319787823, 486694029, 291009699, 506312443, 515179854, 388051824, 536710308, 728857889, 979255960, 399789698, 529162583, 964698101, 376289407, 367376555, 904429982, 738302580, 535894169, 962176159, 113416984, 237837750, 200598800, 831389255, 582812077, 270119747, 603609991, 935661723, 888645902, 52657655, 765910292, 335802955, 664887317, 247441007, 739095158, 44176552, 19915634, 647202932, 85178623, 338407453, 636420997, 893974538, 935292246, 497913894, 204432496, 618217719, 777047430, 500699136, 384275836, 468370979, 523123146, 67598775, 910091218, 259167988, 271022101, 740299684, 658172072, 669538921, 422733674, 164720814, 872344934, 950417040, 135213186, 490769509, 443140073, 126564170, 34667009, 119158421, 754560455, 614809849, 804431532, 813789965, 953073167, 50896307, 911133527, 967740309, 671336871, 771559007, 92215511, 777325091, 917858419, 550286841, 445483507, 836412261, 699168835, 511256133, 947200614, 424268538, 325281821, 93249575, 769167015, 503057449, 216996554, 834447925, 101923121, 895756834, 788364643, 729896690, 761070606, 566729693, 342313583, 428775364, 295840610, 292554052, 33014899, 216208234, 223446139, 12944325, 755618859, 407115718, 482723856, 952965736, 151337789, 648227645, 592203035, 401302389, 393054332, 639392176, 380620107, 846799696, 495154325, 38219396, 705503770, 178327364, 433054335, 635600066, 581001147, 332110554, 573775786, 527990154, 558904025, 915338965, 465220688, 178252987, 634170347, 653751852, 201627498, 632772949, 176211807, 477437984, 455960839, 669863231, 905012306, 308838958, 701169905, 517630698, 513116351, 860106174, 429035144, 257795140, 385717840, 366832219, 192152540, 15228897, 48276407, 233567602, 155368267, 187721780, 322055068, 798135789, 874795103, 348483086, 378565260, 557816171, 451105732, 215905031, 401888890, 739590354, 40176267, 527937113, 632725534, 868428862, 643511881, 457217721, 642972129, 415428075, 743182562, 972773384, 679562532, 916592042, 375102094, 779304031, 599030108, 688062372, 599533246, 495371150, 936030873, 276294589, 937492640, 745023713, 882364507, 554332832, 121090417, 859016679, 331830860, 479164066, 929883519, 719642564, 428941973, 657667557, 611704500, 197824825, 67340808, 95493470, 58958074, 479433849, 407402630, 977010738, 701363914, 954912136, 35819713, 332721293, 417342027, 985278192, 789385937, 744423808, 938967094, 553976822, 294317221, 681972712, 871680300, 492621086, 360053136, 720579176, 988742680, 856748209, 802038694, 728754722, 570180581, 587242624, 831681272, 832956831, 115574660, 22959523, 339218865, 505244294, 340965560, 997314432, 921126238, 113018767, 988913504, 472679713, 790147637, 376827842, 858994088, 220084510, 292913928, 224503085, 722114375, 28808769, 448849054, 943847791, 286655707, 894429501, 888768226, 54032548, 366178790, 653548845, 213384971, 961885161, 994317403, 770233959, 289807569, 927681159, 140042357, 36677123, 523484190, 594967370, 184440777, 163242859, 886529301, 668722894, 168584910, 1056594, 833379189, 363910302, 997119242, 297142121, 358389882, 248071407, 543243168, 492307324, 843321293, 725539112, 862900077, 95540456, 337588695, 867421729, 205575864, 849085755, 78689294, 53623149, 94474446, 238570509, 212394601, 609451729, 81082394, 96875910, 100534388, 610326895, 304099275, 26850340, 679904302, 108003269, 247309873, 557892787, 834285371, 976647683, 651115707, 306696821, 659404055, 26253215, 759622632, 435993121, 627102449, 49852351, 590516791, 804960339, 932541795, 619287337, 472889498, 484879390, 795994627, 574000536, 587964653, 372467582, 119297428, 980270948, 146378950, 330058456, 941167994, 644084199, 152287265, 874326643, 234457545, 160184665, 168983934, 554300038, 598412049, 504666636, 494849088, 842278638, 283120204, 615778353, 416292595, 969250811, 817968650, 284140604, 871452020, 192269698, 505546853, 813676757, 874805145, 538091988, 539375898, 699499928, 725780527, 29245371, 774272657, 305810075, 127335418, 291669461, 966635942, 138076040, 578694806, 890485002, 474529824, 130820396, 183849704, 130549610, 494369611, 73503943, 751671279, 75360425, 152707285, 71448238, 448602424, 835603793, 145236620, 961142830, 817739431, 613275012, 243777816, 826025395, 52787471, 895669864, 340031272, 212725265, 849200535, 259750014, 728726602, 73878309, 433793317, 925030792, 206972795, 411477690, 263240974, 871048307, 837240883, 317024549, 339199044, 530362833, 116810433, 762060156, 892965109, 623615109, 365445896, 432050201, 446289460, 271237917, 446075167, 193293260, 97769503, 512107627, 209134726, 583706721, 496825404, 480348462, 158698466, 601123680, 463107996, 915238504, 530932193, 613243861, 537564778, 651190704, 954290063, 984399402, 274794031, 156860569, 380693407, 453470796, 764382049, 791413357, 27032555, 436840341, 236789031, 831426949, 944591711, 272507530, 178728923, 416013531, 218331227, 225715723, 925481527, 859269328, 479964949, 236738672, 43323872, 678741033, 822012839, 322567404, 523966009, 620349838, 742306332, 2078795, 298476384, 586319064, 523757784, 718675933, 906325049, 993617253, 401334224, 574213824, 404340131, 350931013, 130744094, 607481074, 990604517, 41835965, 712982737, 988717966, 666504787, 766815341, 140734557, 973555130, 916434279, 47100361, 742662739, 439780218, 828475709, 68895768, 244531328, 45918917, 64813974, 240818792, 147143763, 234614728, 919142637, 15156526, 953354635, 517948804, 279203853, 622513446, 505674128, 810465808, 187275435, 660691035, 151021429, 547345398, 573663112, 333251941, 974246872, 443061774, 575883919, 977885327, 426483146, 524519374, 664062537, 759067513, 471091001, 453748733, 418591031, 259938642, 690610455, 867799184, 797385938, 722008279, 742477091, 345401751, 971112819, 494685141, 18884132, 939262008, 414349315, 48994092, 955072961, 834208963, 691057847, 50146395, 726415097, 470115581, 285270971, 745320903, 876657108, 741509321, 792743973, 965528827, 220889314, 402224141, 352203586, 731771027, 56942414, 454993427, 725559988, 3274959, 22459577, 848149473, 913908451, 584005138, 625159240, 944526258, 579876927, 369654115, 154435735, 163069968, 79536110, 369500849, 950129179, 998221183, 307482136, 824098736, 792196946, 750604747, 168608824, 432534381, 863573972, 439643543, 125573102, 928531793, 604484748, 231282203, 582872727, 822858512, 308950084, 626260868, 572913425, 204246716, 535480974, 840389, 498744277, 720565574, 885395973, 868002016, 319076538, 1823710, 922140497, 106846347, 111276725, 334590074, 794418375, 278907559, 249866642, 482672206, 857790411, 897240925, 802642778, 978946573, 260962286, 723427097, 886755456, 711258684, 239612596, 635355210, 187328849, 671455908, 568079417, 270604552, 684238891, 300250332, 401809703, 316062279, 316682005, 22917624, 457466215, 696338514, 991019318, 515084375, 822813784, 699304522, 984146735, 398339749, 459262102, 480874613, 155318747, 196105017, 726089011, 403730557, 800554180, 283152618, 783652019, 936674791, 307308886, 874398203, 247990783, 563128555, 652272189, 945205155, 80764294, 882719466, 620134969, 94879343, 571818773, 551258390, 131202960, 958397028, 687084294, 195826081, 87648785, 597582109, 6145182, 438003325, 822910869, 488131267, 799574949, 493574287, 932156713, 810755576, 166921180, 644795180, 605877607, 22927034, 629937796, 231497356, 505721413, 253095831, 455360519, 464049242, 608142512, 284287209, 242891176, 331481955, 481209793, 421484460, 296035833, 127073726, 785290920, 324329803, 605154286, 308587123, 447774888, 813941666, 191473691, 198461382, 209940153, 249188934, 382420079, 688328896, 35107694, 876958811, 680969241, 397765300, 556910733, 165591443, 140356903, 572072195, 8937008, 712000774, 312072094, 485493005, 550707358, 473504151, 340360704, 618809140, 538846696, 148953254, 215596001, 536229200, 72836325, 634657067, 728892792, 552956109, 735377840, 592021632, 905640109, 584525308, 344386787, 672285818, 867586566, 402308304, 677338569, 186351686, 389178659, 463194438, 922993540, 86923480, 420683167, 926742037, 799738847, 812642504, 166440663, 84718459, 52743638, 986013192, 453652936, 706453739, 445316438, 584618925, 887384882, 233326900, 325848614, 670901406, 218272890, 665041578, 664744301, 43734569, 31503030, 813605926, 154859270, 697741922, 182447307, 779628171, 950677499, 715942296, 685479061, 571195556, 502917873, 347697678, 543508201, 710146673, 114473881, 470847368, 826688881, 269963660, 24285428, 102844472, 681224922, 439047166, 204299412, 976037929, 415570296, 386528853, 410546925, 343380073, 836636187, 11239136, 260937905, 359904294, 182048135, 783779483, 367363227, 82198202, 701921486, 156694756, 956813326, 852335553, 518193730, 783453187, 381931491, 271207037, 145268677, 649570494, 330805846, 617263078, 417551715, 632494090, 459924871, 875435047, 81017985, 727696358, 499843688, 924110313, 374504802, 928814795, 489653691, 668837649, 539127241, 72308355, 420611836, 410612941, 656812805, 660304762, 760369808, 579653634, 489334843, 506418744, 891840115, 495261891, 614842325, 837962409, 933666737, 734665418, 584475499, 727980802, 300609157, 740652929, 589442451, 158377629, 207129459, 45963102, 7294928, 196116212, 898418201, 508489367, 881837377, 712615754, 11632717, 16706668, 806891397, 158314937, 866801884, 381817351, 123544709, 508476574, 10526269, 751035925, 166333833, 258059208, 429202301, 237585344, 984940889, 541714848, 50812515, 868662336, 358344937, 460533406, 892092723, 333696346, 365918129, 433956439, 803980236, 28592695, 972936785, 306992825, 642836962, 565146628, 31432219, 265914031, 632968511, 104400167, 811893279, 162726468, 644128934, 439765414, 127688121, 489185948, 263465951, 26730047, 361205106, 512467137, 728466683, 146786879, 397938155, 180365331, 594006550, 834330353, 377612328, 645867740, 278854127, 46099988, 696490794, 800123745, 743402121, 953743966, 242553298, 985256198, 23116118, 846756753, 944670817, 997102667, 632042546, 619164321, 860951687, 870945055, 1068715, 950411543, 505671921, 459168660, 125253287, 409140303, 96342064, 475955959, 88677510, 199486128, 862679344, 868857320, 785356882, 257819103, 822306667, 267753772, 903130806, 294195908, 466386176, 690839524, 430914096, 453080788, 121473752, 251832695, 280346114, 74201351, 561091193, 836768122, 362444525, 364161706, 536337903, 994381989, 112582999, 191938822, 459653410, 582176185, 94571296, 676737374, 547210293, 59082108, 181228562, 851378195, 179666227, 476607257, 532521456, 996798723, 821491079, 472001072, 178738431, 601403877, 506106444, 687708624, 986015499, 547813148, 157456582, 41472188, 268947245, 28631713, 749519525, 893208340, 639889378, 102443164, 619139513, 560316655, 363454302, 823892398, 952819172, 524864715, 861976921, 834087897, 498526067, 258192323, 766886607, 371002271, 752494780, 651899638, 352926667, 869320681, 171198138, 760327912, 701507758, 924375798, 483495357, 242459884, 632972355, 73930693, 388170261, 654977128, 435831037, 199715765, 818580122, 477469452, 622984621, 41019469, 866461792, 319724423, 326167520, 560920226, 837635921, 799779126, 194369991, 816649947, 463464511, 93738732, 967217433, 303801558, 450013017, 418658381, 188998412, 760824164, 893178562, 973240050, 91878755, 100245013, 616759800, 352622620, 969352299, 91755058, 361218000, 394309388, 249863825, 697951861, 940701110, 738813453, 56040184, 800837546, 459457795, 488643918, 974573352, 185886827, 274663514, 950473852, 42287502, 472521593, 32875164, 853402475, 471695104, 542988890, 934804384, 164806990, 594989302, 474177974, 690824736, 491345027, 673700323, 786013775, 858307721, 5608389, 196574561, 828478431, 888947164, 595144522, 979876968, 864038355, 171590762, 547250836, 902285826, 74441584, 450688931, 840359990, 980351788, 958369557, 913342262, 57030507, 863124689, 101362186, 25348868, 890961703, 654149846, 112397726, 307494606, 212533499, 135530405, 378531340, 260224836, 233310938, 655335626, 51782901, 522301262, 685063954, 982387993, 597774246, 178326365, 932405556, 123662561, 747715515, 603778542, 192340, 360650436, 699258068, 596376888, 68572353, 928354438, 540457023, 62507313, 704021848, 972548426, 204717567, 695146997, 802540434, 720185992, 870871671, 7853967, 903649157, 480443912, 766680061, 178129381, 225555475, 5248614, 979179939, 846025450, 167321615, 826166964, 979814843, 769621463, 608528942, 165518982, 643885116, 75557558, 426018080, 7649703, 228725695, 513426982, 538950673, 686113479, 707102962, 605058507, 703298677, 562365065, 367716071, 676228460, 942706869, 554595966, 294123417, 109275867, 377526754, 408053383, 522720737, 738157385, 851960106, 42299220, 950541763, 534387948, 45752413, 426689539, 542243561, 941060441, 172206882, 926588903, 650305721, 504415665, 369281549, 912615911, 411030225, 148087923, 796052413, 713993473, 36018369, 100597581, 907179642, 338741350, 510860907, 946406528, 98404572, 282291644, 392215126, 778758072, 19938742, 452699328, 982491503, 153879812, 595394364, 131594755, 191694386, 946065515, 541357352, 396763023, 129846261, 452138655, 44518564, 378315556, 925430091, 701568614, 939485958, 961345752, 703976183, 878625850, 633873490, 267949851, 407216220, 96449453, 304799794, 316092083, 395472302, 239920358, 627371766, 505293823, 888044999, 381644982, 605275410, 722447127, 832225311, 420230979, 614858706, 195810290, 305229555, 707122777, 483187247, 96404870, 401212009, 288547440, 33561025, 477072379, 968141895, 35645047, 697450887, 783470341, 469594941, 507066288, 463594896, 452721600, 328799755, 265478880, 169615042, 853191213, 857933098, 22807999, 199049888, 419591031, 576928855, 871014433, 209659583, 499782044, 564609816, 403089621, 976816347, 835275565, 369407486, 649369388, 279079923, 16798806, 32845030, 455996900, 597586286, 110730465, 64949081, 529582054, 115426333, 485092810, 403177078, 270718054, 953934496, 830173278, 125350259, 597686281, 969873087, 457193464, 613500968, 875380727, 923122912, 483788384, 38354059, 225340993, 429677445, 956312, 539970924, 363777970, 493166053, 696324165, 803572525, 220825562, 541135659, 813690333, 568827559, 302961309, 950544010, 740221715, 991098313, 110915564, 687150652, 944437916, 257299518, 18968342, 381927755, 786595194, 401432545, 906643767, 449432245, 93631766, 334705187, 451816761, 937534312, 442070521, 283953523, 541082226, 750043070, 685536793, 932543808, 38653039, 548587114, 537148818, 76033520, 515764954, 122089450, 689009562, 717537551, 297415032, 653338925, 980440273, 313114265, 376929862, 208530881, 511720352, 243983642, 357655407, 423568667, 505341660, 519185532, 294650432, 998078777, 65438988, 398051903, 831186594, 356071725, 325546733, 466705361, 2795039, 53452246, 201771118, 897692125, 122814446, 898187428, 822769295, 769061171, 805351126, 339036504, 410535721, 557202170, 720028704, 238902278, 522616981, 286234409, 752896372, 756969257, 277382232, 154631899, 488777744, 301123926, 990935381, 714007433, 577094057, 547097353, 475055497, 905117175, 572394167, 77619596, 516666795, 825997455, 136879382, 59708717, 971774087, 940022017, 734096013, 858596453, 135849061, 226475530, 296676642, 887435045, 147520155, 54343716, 542714526, 946677931, 780738399, 727201551, 351051816, 123209416, 811270432, 151109112, 981608099, 919562329, 539528338, 161840996, 904260042, 939306860, 758287314, 391708049, 227622416, 123239081, 853988415, 860733187, 179531536, 361836464, 630603060, 101600444, 780774824, 352314331, 587759274, 576958495, 593891399, 966533358, 272096087, 209470522, 88548471, 403566019, 837750266, 29871799, 648940831, 534909517, 354962380, 700325384, 712879591, 431186294, 408759296, 928773251, 852448954, 240011951, 737278997, 10405624, 912981387, 645433639, 92900174, 508999371, 427508000, 642563529, 914098362, 511418408, 376461398, 49217961, 311323339, 184958882, 500603718, 751651409, 105311931, 935129409, 462285912, 930142222, 614774831, 856806871, 211889025, 902922353, 151120028, 556362646, 85014828, 978495399, 834014325, 726225985, 90688059, 243873856, 965695701, 612393088, 425883642, 259406547, 386352284, 90270799, 520645727, 522407166, 211527886, 975417019, 930446364, 144170723, 107813407, 76532442, 343854344, 307435447, 99478892, 84911909, 29286998, 879211765, 289449778, 981999556, 968205890, 686191444, 815257949, 908400786, 251051368, 994372505, 973454753, 328183639, 85686892, 196883235, 231881309, 342920405, 65011243, 656108289, 689124858, 900411211, 942422102, 916562710, 452860506, 648952955, 316741112, 376617979, 728531660, 402328389, 965672667, 332648887, 939101366, 562557347, 433517667, 208517591, 925477148, 425158065, 921669762, 458130640, 951427679, 914401807, 147502162, 392622977, 507274826, 217649065, 293346949, 544181349, 179925379, 223608162, 943073174, 351562243, 365888182, 355734694, 399422317, 734241295, 822368932, 212582589, 4008481, 974420443, 935866812, 566911120, 11279644, 769217462, 929100507, 732722715, 95465053, 566135310, 197530180, 825515250, 39477125, 246705720, 87943959, 15905410, 284274712, 931849787, 210889211, 933363010, 459609682, 690632884, 260104261, 304196626, 102703728, 248490479, 710467424, 341008460, 546622028, 168649209, 882307131, 442476646, 511920767, 398345006, 353138293, 602661479, 254491392, 891994199, 799776165, 446138299, 157278702, 645391231, 638611838, 31941090, 116905052, 379030946, 485406976, 795638636, 847054377, 698942078, 662486358, 618856336, 765475602, 751869827, 722305288, 134743456, 775217177, 344162119, 957479385, 454164236, 992392533, 414151381, 985169252, 300548572, 956393021, 892534325, 753435407, 63029268, 117997887, 367002068, 204514325, 567892774, 390351598, 749044178, 847523392, 616726060, 295641346, 334897976, 811433553, 278640356, 126285866, 385277977, 244519954, 138654507, 740856123, 432660529, 688371127, 712987236, 65729469, 603682138, 733252271, 15223317, 512641967, 954176740, 80889988, 727813480, 87933112, 366420617, 326858588, 234016383, 313517329, 823107244, 700999532, 280539714, 686464556, 673018380, 33291306, 459071159, 118017117, 658953233, 140583194, 844897395, 330433466, 763746422, 56557105, 812530551, 890591333, 454741332, 623457745, 846339767, 695707299, 647338536, 242461059, 77677861, 295117628, 348056518, 416280954, 326921383, 97595671, 775819090, 34679656, 426621011, 538234713, 493189248, 320716256, 708289758, 531940717, 974812302, 893778676, 17425630, 100784634, 382372475, 507486067, 791413966, 686062235, 90456396, 681354993, 625729843, 411683370, 3189507, 209092399, 591882518, 787570310, 393075996, 748313296, 291595461, 415353921, 80212226, 19526025, 974721958, 961743644, 982519489, 60586560, 530431767, 742987205, 338817480, 964608592, 130557853, 46362860, 9773780, 45571651, 743321226, 7971023, 518240545, 216850178, 496940068, 83485884, 766228309, 848225828, 957894337, 391991908, 717361234, 750964619, 836673375, 97012468, 516036217, 379544347, 599416444, 834336820, 694784622, 614071629, 2894999, 798295165, 149514367, 731309381, 572930365, 15261235, 653140758, 359368655, 340234057, 423243446, 488248562, 409683733, 54395632, 839759704, 638377965, 105509390, 254710946, 754418332, 57446429, 341395435, 57371980, 763057563, 208410830, 387973016, 469158315, 89055923, 201010799, 781946891, 677257236, 550018714, 301053894, 755572924, 696869245, 85085694, 179839859, 856457496, 488554082, 582059539, 226691465, 974219114, 935930639, 31478616, 772009064, 900876692, 669550200, 630051670, 143489930, 388682309, 232573952, 422762591, 616831555, 26761058, 506116946, 167706413, 585134288, 127183936, 635031704, 559290448, 817684581, 792156499, 998882942, 52191426, 822255585, 183648351, 897264266, 715677837, 138777485, 39614568, 554674256, 581569739, 22504192, 793418956, 552840275, 853649464, 923063118, 283241735, 349588151, 858596954, 216210085, 22107145, 871607682, 513927143, 513764224, 886650416, 34158454, 904787286, 871344853, 573631032, 513162576, 452985824, 991311569, 650224412, 535748110, 925886575, 893524457, 910029474, 2611205, 891404556, 105485018, 87349467, 779013594, 4761634, 945822359, 570983967, 735937861, 99105490, 98686790, 582130211, 102266895, 21605586, 826178197, 84793843, 832229259, 252853713, 129732695, 450162996, 286581972, 851233906, 12562311, 340971417, 320340941, 51345957, 313927069, 974870067, 215197119, 949563035, 114276840, 252386894, 405277375, 139110645, 216920143, 364925878, 268539289, 744572831, 665091910, 813221952, 844917625, 737787571, 206632813, 915182504, 515950542, 929388650, 348652406, 8377601, 820305699, 787802585, 413317140, 635738237, 544997134, 503113049, 652875493, 263031371, 589664617, 187160918, 999023514, 911085585, 180369784, 959895161, 198783926, 437818841, 968468747, 835857871, 658596367, 827958811, 163187381, 78140504, 24246651, 61140750, 232132857, 550889555, 881834379, 989251422, 690439497, 319882213, 906960600, 85695334, 299594360, 78150609, 816363196, 447340032, 293679306, 494150943, 108087260, 432880810, 738999271, 920242757, 293897338, 772265914, 325757495, 392037191, 318081708, 714126197, 871563807, 518087685, 456473519, 672811715, 563917739, 975274587, 440709062, 483076039, 202027168, 730844077, 488143879, 723866275, 18282703, 411591281, 203907559, 143095655, 552258701, 738713474, 27072252, 989138741, 274543131, 644738066, 140193756, 78033996, 380426149, 981818229, 165495415, 103288107, 740489511, 861254777, 287477211, 747309745, 100628121, 692344991, 704400078, 853086881, 307608365, 260449628, 195613818, 19225403, 172118579, 498057084, 933203868, 343125668, 629965912, 494910337, 97601410, 724020574, 400833767, 668256688, 676269964, 799514460, 666549148, 420631611, 33154091, 766308596, 816095182, 575519420, 554275802, 438078537, 654181836, 365321064, 325275598, 320161311, 321552858, 68486620, 695515176, 403651720, 905186414, 239684834, 947015260, 264145825, 201202101, 789248065, 302017105, 339579258, 877988743, 707855736, 605119266, 23216373, 449174205, 437740404, 398746991, 990864396, 46028566, 197135251, 644429681, 710581888, 252929942, 763731204, 48303017, 165219718, 768244821, 903057062, 756858158, 750833427, 40132944, 129537674, 243126871, 931257477, 742941078, 420282351, 389384589, 89893932, 965860696, 395784248, 247015011, 55140994, 97339921, 316703503, 954922653, 326257647, 690063863, 257651874, 990546285, 72847056, 78674915, 956729171, 138319218, 789875260, 466011705, 201125047, 104837267, 780851632, 615042053, 989889113, 21402335, 227273266, 688986609, 51206276, 857901084, 635184856, 499437267, 852301179, 914297762, 296847193, 625914118, 556364805, 316898025, 578504279, 157086427, 808618271, 240142733, 628699513, 938160290, 109809997, 476947521, 661712543, 499446596, 608031349, 631603854, 763470741, 792693615, 722274350, 809250131, 776570445, 127990541, 110547801, 555544473, 994967726, 927256448, 558648893, 112375050, 780982092, 968783584, 947708392, 169881543, 695663449, 590451106, 843084653, 466074304, 600089101, 784947832, 92157140, 901410559, 809005048, 893649366, 699576405, 975324924, 404015469, 523821457, 468494894, 670909454, 216008304, 397464262, 306308966, 436537076, 805997489, 388422564, 438762516, 517382831, 443162621, 362213035, 586504110, 142474003, 652573233, 51490951, 132755624, 851045264, 68284999, 519024856, 122428536, 864316112, 618526265, 262316221, 411649077, 8504316, 888660049, 930421991, 355892362, 260528644, 940624822, 821092053, 969887813, 551896297, 681462564, 242370328, 706291000, 946548537, 253627958, 962016893, 332664852, 158905559, 10457231, 493821899, 525708121, 726446028, 934381916, 885156114, 311136133, 160698730, 417825168, 626224952, 365411971, 122201680, 152725476, 960596132, 980828667, 144934541, 871683387, 602554898, 145439650, 385150284, 409921338, 464201985, 521663893, 271973351, 772059361, 817092340, 55577252, 174511478, 567240481, 248627152, 140758413, 159404308, 387842585, 962520193, 801105482, 443257231, 652561413, 23510022, 867253811, 662696768, 884363112, 384917596, 90007375, 497468337, 449569199, 358488762, 127665586, 960183965, 655131687, 599983234, 730770496, 743360646, 253390981, 219501265, 144048527, 459829543, 220615148, 520925208, 906010047, 763870782, 217016510, 374878989, 638317648, 682360165, 44890373, 255457967, 769020601, 832860196, 643368857, 148667433, 198910962, 173787194, 98477572, 611377275, 136026248, 670509049, 712164040, 12208387, 447506616, 21842390, 994882735, 275044059, 431967650, 9080866, 855789883, 853360161, 782655504, 240755559, 455969860, 136482346, 807093552, 534518584, 360871379, 464141833, 154796127, 783783820, 883130976, 17248541, 568800659, 583404376, 441768649, 738724998, 503521084, 406326430, 925864920, 130561699, 202096549, 847010190, 63254850, 12265091, 968263002, 396970011, 876936991, 434729917, 269504546, 152933357, 288968692, 723751650, 734207261, 208391777, 153814071, 94351231, 258302763, 604602246, 183967130, 279211930, 401267279, 718252892, 930091831, 444336198, 933837207, 491604210, 978709404, 716589423, 251564113, 279717152, 519672234, 462744402, 968573485, 625102376, 452748760, 189682112, 343514614, 77934871, 286223139, 261620227, 558097202, 835525653, 187900685, 413040017, 27179704, 397290167, 222682642, 542601514, 135094274, 487280280, 410269984, 242756299, 984524212, 651506558, 990266444, 686792532, 404802914, 784465801, 729111332, 503335644, 136632961, 953493714, 972010968, 193074449, 345707766, 686425168, 606006585, 259011795, 222763016, 887823683, 877072433, 591413679, 717333824, 916581349, 997342738, 537388963, 662851806, 539021650, 517299722, 562736825, 671850224, 703848359, 182865538, 336040650, 321290950, 118768145, 781439688, 783575093, 769578260, 645437476, 870242355, 462180477, 963183243, 742826379, 723033085, 690685182, 889567340, 772715963, 36949009, 575783676, 518290394, 290340026, 941168485, 126680555, 934106677, 318061049, 581556405, 290854419, 313726519, 753115044, 935905967, 604787222, 14896227, 722911658, 186543450, 571163673, 217161660, 902621969, 717312670, 997457395, 612362065, 893424523, 834689941, 157786621, 277861484, 911435964, 151396344, 70416214, 452686615, 58896062, 336373073, 122510582, 54121192, 542713084, 826861033, 839353099, 419887158, 56268323, 879410205, 755952561, 175136547, 97786986, 815202188, 739863887, 16917099, 458764760, 682534963, 19962607, 842944738, 289471940, 813788035, 376342168, 236744788, 354914419, 883862121, 188934401, 722114089, 43553399, 88700137, 710664843, 181547021, 66260762, 894439142, 906446090, 884893959, 300714529, 531543661, 217415209, 879931656, 28466241, 134742437, 212729902, 644666403, 492185575, 37659476, 784188444, 801686559, 883010319, 971539108, 859589249, 291501383, 120103200, 614752375, 79284477, 894795571, 882784295, 962575052, 980165541, 984561409, 334154685, 763227903, 89597015, 527178803, 8465674, 783002477, 95331002, 148896980, 483570987, 418927869, 729330681, 597745385, 496651041, 751675302, 582201101, 454418081, 355452526, 128973266, 388346351, 828246597, 658007984, 547869117, 832918356, 934520638, 198053267, 27213558, 15302200, 579866776, 839012590, 190317891, 110833289, 177253669, 344473190, 988388877, 12562687, 774600491, 699621949, 517791037, 561774927, 664202817, 269465884, 665720023, 855674869, 626194595, 664447217, 677851126, 759909603, 470342203, 838172008, 577635810, 740087460, 348260238, 79574510, 790671610, 109630330, 504079512, 138083103, 442393635, 159731071, 181603522, 996678268, 272372048, 848591939, 845672689, 753967990, 328419116, 220440786, 40765374, 54927312, 193380264, 160858568, 878136067, 675783862, 83339849, 478553226, 43921787, 121328913, 818935754, 147441312, 106201193, 526496922, 206004014, 118300185, 47471309, 366750931, 24767503, 804066644, 412016951, 268033948, 762098414, 903394941, 433813306, 517527785, 662235531, 324789946, 715030705, 975243040, 773071076, 926579812, 128434740, 245977245, 204260319, 2177420, 65798425, 818145541, 282038308, 985805333, 122513459, 508099248, 512991716, 378608225, 892314918, 541378423, 207719443, 941874153, 435600318, 747030937, 778031141, 397268893, 404429514, 681226643, 806789005, 219439504, 372624512, 500952338, 337501078, 970475598, 545874324, 777443846, 672281001, 775177933, 367600979, 146736360, 824153157, 740933077, 408587614, 985911736, 393915314, 978249561, 406034500, 868608788, 700727758, 137667400, 404812523, 601788128, 33172853, 811184734, 383440960, 62829465, 118816474, 238237197, 49864372, 42823807, 453490857, 57324468, 920059585, 823045887, 796913976, 143500361, 578404546, 124979888, 633155722, 390178660, 653449884, 676737616, 972462716, 893247443, 13014079, 331730958, 573559556, 4339297, 967601847, 72091074, 418829230, 177414952, 708133063, 689894097, 345898790, 403102900, 874457101, 622389488, 708393976, 607333139, 682929359, 62545086, 620376911, 356035153, 508748156, 644648986, 896508622, 56225423, 395818903, 536092323, 519385390, 85810646, 94412428, 628058605, 921129600, 491979874, 572208827, 247172353, 272925536, 898579590, 248600207, 994012007, 546180224, 335158756, 634246214, 193471399, 369043294, 192647108, 459465698, 294384542, 210076383, 23638091, 129249196, 461107377, 174304644, 195838649, 366708124, 227637238, 898040658, 987936949, 965941551, 201049737, 605470661, 632348947, 360844491, 850384542, 363511357, 379709539, 551851574, 654602390, 210641602, 623571876, 82254489, 588920455, 250386739, 825433988, 181973036, 476285150, 333707372, 651134010, 757784039, 942977148, 160402637, 127306686, 917325659, 427433544, 967598373, 6024457, 587836429, 635237333, 270919591, 129583190, 724850722, 149658248, 386963018, 921509889, 735134556, 77578467, 959356849, 430788853, 54725567, 221530981, 43658994, 661208094, 9039755, 42085500, 13945542, 428787191, 62513040, 396212313, 914668516, 737878713, 763417243, 597993848, 123748175, 806384757, 668784646, 854470224, 565860084, 874553047, 867404105, 964241939, 239379072, 975073571, 778780680, 967020896, 768576282, 881319374, 63515247, 580276285, 368560459, 908499358, 570128338, 996633825, 93464933, 196958475, 283138458, 997235411, 856859915, 605206017, 796767217, 361833201, 213977550, 859124201, 342488282, 83563923, 707150813, 378127589, 837670953, 91467349, 804216121, 566445642, 480926154, 918166898, 642719126, 271547739, 292412257, 86846620, 211118020, 738583198, 467439889, 875789227, 675930128, 833712270, 259101171, 111709202, 867671960, 743396190, 799636768, 863708257, 336021365, 608609365, 77785038, 694508736, 696237876, 695827679, 965136361, 847613937, 492763630, 917043801, 707177268, 88700314, 861213382, 89021174, 458101972, 551739233, 76408221, 10886188, 742511160, 850940753, 719810583, 723325376, 554224064, 614612784, 596120295, 151440380, 864172160, 468838075, 763637646, 391991024, 139975065, 643229521, 983744790, 629557150, 745009154, 589252301, 700125704, 19411969, 185215032, 317998700, 354024333, 135247169, 768756821, 666044110, 206656645, 672013484, 222730851, 370266164, 141892857, 300865256, 131058158, 876358960, 28925147, 576520229, 195646067, 191095881, 765025271, 165791844, 291229588, 218275508, 496888972, 213717494, 437595426, 892768816, 456907480, 163281981, 564652483, 943571100, 29166501, 467558400, 499181421, 490756992, 685764294, 855078577, 23087424, 149697137, 579078319, 865133080, 705643956, 382531116, 120643245, 377448256, 704014619, 64111394, 865512000, 909758944, 809758707, 686092799, 232397957, 237813643, 79803008, 553030443, 652049126, 498675941, 665844418, 184520612, 183772118, 264218230, 732900071, 154628796, 699013985, 394312521, 240007383, 805409830, 85366085, 27362737, 96001259, 899705660, 174771942, 751274572, 452404257, 858293175, 177920721, 682650273, 929425513, 603718557, 99776543, 414790133, 209108811, 415570619, 818124881, 927164394, 693434281, 946525903, 255591371, 20907430, 492682052, 142092070, 917302634, 124952501, 925790238, 420619011, 537855037, 914257959, 643317890, 368533971, 654039476, 351502955, 34255772, 169275919, 496183998, 25825865, 161423367, 675016968, 497862669, 47487864, 523867559, 214844070, 483456014, 527146668, 696069602, 264887172, 136674345, 688668283, 604558628, 220939306, 694776425, 817807479, 778547368, 935476775, 275620241, 272218703, 787072148, 47838340, 179850341, 979715097, 687103196, 87676454, 760233516, 559396599, 911067604, 445800034, 704586032, 599961020, 539568842, 839690803, 60138691, 857758248, 11744388, 404277669, 605396411, 604279279, 438893827, 632935389, 865193690, 193902858, 378782279, 926011205, 913765133, 99624863, 472741311, 189667041, 299428607, 262884907, 209073395, 423247730, 595454562, 703736228, 566051360, 755235361, 597177182, 588721304, 244715702, 221884057, 23846238, 726836477, 655998082, 975519152, 923482979, 584611274, 472683137, 498904017, 160692042, 557812706, 159443946, 81781993, 60725157, 683842725, 527575984, 347537154, 705755094, 902505732, 280271403, 387884701, 771508489, 684325789, 136002769, 278453006, 352723900, 470678242, 791977180, 287459918, 523762418, 422974680, 915457247, 443479272, 65826387, 318827922, 913218248, 64823648, 30561863, 891959394, 139223142, 850621012, 203990365, 334090835, 850570228, 848152085, 826203167, 34407235, 74590069, 787409584, 919164185, 183110569, 834056233, 233880133, 823762103, 683448988, 279044078, 321753657, 784739715, 396292759, 466947406, 319453001, 349058208, 409209975, 482478394, 509867439, 556578219, 72431904, 429005562, 641647229, 642516162, 940909185, 914867387, 637218495, 355808811, 83067563, 199691972, 557757856, 984140251, 838204188, 901229760, 881869717, 994528496, 941871595, 578748775, 21198590, 219292486, 742177898, 359937345, 839811051, 193047288, 838578379, 709342922, 449380735, 559555029, 882891501, 212831301, 300759609, 43745645, 662869639, 157275753, 759267661, 738065698, 960409006, 818147542, 711178229, 403689147, 805082192, 654914500, 410896112, 616112463, 569699258, 659262735, 589204593, 443738751, 335319285, 291623120, 630911057, 381763030, 114587484, 252924326, 34569581, 6405015, 410453977, 511350755, 105467696, 163660080, 899010298, 162973774, 744650110, 663337054, 585054665, 331786690, 63971869, 115949942, 912751366, 366571200, 105014734, 405886735, 881495005, 311099372, 116892808, 247376098, 129475224, 273076298, 248437453, 826472116, 92008119, 280332604, 173745820, 95111043, 959750986, 918664752, 85492348, 930003407, 691890073, 866383697, 630114113, 605284257, 298398292, 253401959, 227118892, 831490641, 629918301, 250289992, 730166948, 692134028, 272506634, 226822068, 42780775, 459459876, 162856868, 693922816, 220164648, 530935953, 658828942, 603005956, 851823072, 516297496, 333751516, 225997276, 24265021, 598137084, 356600668, 493181572, 401555099, 829512157, 592954073, 642238293, 395369063, 979955395, 187764913, 143018469, 56275661, 594185331, 775723991, 448236420, 81032416, 282798336, 110364484, 538105402, 607582970, 343905725, 350376730, 364289462, 704173423, 227185624, 335572284, 63303684, 936065333, 671963018, 232587912, 745910610, 924676500, 889825730, 476209473, 244449544, 350603472, 807590822, 332554836, 529967638, 973306644, 727931306, 378233901, 554738904, 531010833, 710675970, 257789297, 865600019, 62516247, 502969839, 749279162, 462822286, 572879559, 775431021, 672852813, 726334071, 489643707, 214984372, 378514586, 355563460, 293882063, 612500024, 631548399, 81209217, 459936293, 487745047, 755700882, 798518274, 697200612, 936616116, 177535934, 134734650, 852274493, 258827930, 81415947, 538868076, 912935450, 265292203, 603584344, 262286837, 660031207, 199330738, 821162814, 793722043, 517804962, 563453422, 499804981, 653252949, 107927316, 35707287, 395430205, 986506599, 516573491, 669157111, 535013569, 187667439, 828771484, 63089773, 185770329, 30615646, 679805464, 129467621, 997157553, 225270604, 282928500, 105131656, 836617524, 699134504, 739019768, 443387183, 522193759, 96499517, 560000816, 444458056, 962042496, 780159363, 139327147, 689036047, 659025845, 706879078, 517949044, 800598009, 848652528, 321801711, 489860308, 144512303, 940679974, 68420145, 308967846, 473764923, 946785808, 627424309, 695468306, 658881369, 17548937, 577321781, 201779827, 479870394, 823923576, 835985936, 729480559, 251046605, 293159852, 959165783, 858513020, 130016694, 301881192, 104050518, 805187759, 615024146, 927152645, 660479359, 442056758, 14448667, 431148038, 58471550, 953155410, 648711166, 637686546, 428863394, 272382464, 341168897, 288937130, 546180324, 919464683, 452148753, 299853072, 778050168, 837992215, 504672852, 836742098, 865979226, 445064974, 731364796, 929200490, 782770258, 769379411, 317848950, 654181687, 178480855, 849570096, 983641348, 158811715, 426177947, 748461414, 517018601, 222547683, 814315327, 877349684, 744102836, 389478620, 792741158, 973159339, 326528458, 782742563, 440073343, 70773523, 84473604, 667099994, 191441384, 869310187, 612996565, 938195326, 496198785, 624336975, 679781521, 931047785, 430581649, 229768516, 844944382, 795594264, 429883509, 481205026, 784088858, 24599149, 288537803, 920064621, 403228456, 681372746, 581410316, 348699157, 951061973, 545360629, 569095339, 984260722, 356154623, 782458096, 797094037, 176342851, 623538265, 346438947, 999087783, 31359770, 160317870, 760146370, 633691391, 939041935, 94860096, 32819299, 352046329, 621767915, 646993350, 462778770, 94173475, 119531061, 124279170, 697378063, 796273917, 789856553, 217084651, 266854974, 359257574, 756625642, 236502097, 365311484, 646335529, 705214766, 281491035, 843478624, 381741658, 581322139, 374956697, 54031958, 938287723, 74520793, 229468695, 179893645, 438961804, 940609687, 265089669, 485559285, 611193019, 921116155, 795602169, 176666847, 130989729, 762739753, 871603779, 430749688, 85113867, 606294795, 264831077, 455721325, 223256344, 220322025, 2764241, 917852381, 827977016, 558120400, 260284222, 968209997, 72917613, 930353868, 813507320, 424799028, 23315882, 660704372, 971147607, 232573542, 381238525, 137307094, 654988653, 711194206, 426273183, 944412961, 842226057, 726637081, 674167160, 974457374, 550742908, 766779287, 787712397, 116020368, 391424722, 646182330, 453014488, 94754650, 901892331, 693311585, 656318366, 826595671, 664820875, 340568581, 320964849, 515467315, 392267858, 564857922, 728271535, 107667523, 488467242, 638092138, 723706735, 620579558, 268585250, 234132931, 570796661, 823560990, 901919715, 109588543, 205948092, 71830873, 503140608, 409410566, 905053902, 602161318, 387893565, 431466550, 281919973, 171551991, 660989866, 697409305, 404460990, 647717663, 484779614, 698218115, 332082929, 131450413, 207517511, 619883476, 656755400, 220037623, 651791726, 579394190, 698992677, 417401079, 666750060, 704699458, 648483345, 306855847, 564721793, 286423957, 673618615, 955435926, 945847434, 540394987, 286065474, 244069542, 876580081, 66877, 419026225, 585278496, 346013524, 8771132, 203458418, 516478877, 667180785, 198035719, 872096289, 874066562, 739981821, 117479085, 565934008, 294510192, 209149610, 672724720, 362033383, 104339686, 310710878, 294475523, 796153822, 880063258, 449145981, 132064288, 855349876, 616912982, 158137549, 730437164, 981579187, 982114294, 763309792, 7340051, 475188065, 409420186, 487797766, 10177549, 911744404, 730738631, 528604980, 678484362, 905471588, 622286732, 509157623, 203631189, 723081787, 307766218, 784466583, 42962799, 981222928, 490696638, 933405196, 351985659, 463449449, 532623365, 734040823, 563513510, 525862823, 621109976, 465659005, 753327232, 834212943, 683664533, 837548613, 808985800, 985477576, 502859714, 112127226, 950135350, 930949700, 470083647, 25763912, 817100380, 17986204, 865387433, 648254195, 198633133, 477381884, 133230241, 376978741, 47445800, 887300543, 819572454, 457681561, 276584157, 37760001, 691777259, 698008076, 799695434, 665683262, 471986953, 987092812, 604333286, 34637033, 9414410, 381553752, 428940294, 607961103, 737421207, 658241930, 555015513, 657441791, 490958977, 265337529, 31292533, 552972899, 23057922, 878812276, 732261497, 440163358, 871258324, 499276686, 663251526, 400759482, 486901687, 557272797, 469431952, 331123787, 271586148, 553351379, 897317154, 738670847, 921794588, 171300099, 660103493, 759938167, 104846144, 811167074, 314694850, 36160383, 604210097, 246278869, 467743486, 406622327, 781278146, 135163534, 362697190, 214886614, 592999012, 627575434, 992036754, 430481929, 856661288, 510974510, 761503621, 998637339, 302080195, 101436217, 951609046, 635525804, 211355704, 532685512, 704379835, 595886100, 505738398, 491549414, 853050764, 767753938, 492677809, 927966441, 986002702, 933475085, 418311735, 457392138, 735622014, 192365486, 440415841, 604344046, 447157307, 49120444, 11747959, 793966337, 952643531, 565718796, 884341084, 815902516, 759638708, 268651853, 571148487, 669346639, 151487255, 698730988, 54410571, 826731979, 544671813, 900355430, 894109857, 870166064, 316236590, 113023134, 138604421, 372238693, 283865962, 969309512, 157781474, 790268393, 543805237, 527813858, 237590342, 65452910, 85172753, 573404784, 433083471, 101210165, 521229356, 10365520, 536744771, 892070149, 831178711, 129785630, 604785756, 357941256, 590845120, 464886893, 388374504, 930290663, 447512268, 68896688, 988526653, 392246549, 424908494, 39660430, 570979399, 15488313, 396473366, 640722017, 207569078, 623426757, 486070616, 753600036, 167255996, 983171003, 201621863, 747409958, 86022373, 52960087, 309396643, 884007966, 541917383, 22951548, 929514024, 750451002, 925121245, 105982237, 990521534, 478844481, 613077807, 125619501, 527123485, 193536069, 764087019, 664873827, 789862699, 965563196, 566977620, 376378470, 914976908, 911930464, 717786533, 91776269, 84900839, 199904665, 883785675, 776269786, 145921549, 636210620, 539250635, 606649054, 869540896, 363477873, 5680467, 90261908, 634533373, 834245211, 162429438, 293209392, 586381025, 561733723, 807660794, 707668670, 88289098, 224726767, 356863229, 820821435, 541451400, 925249027, 758999642, 657029020, 171164458, 538180506, 775599351, 660178602, 833085314, 718033814, 648917033, 979330843, 48970868, 497942350, 790390141, 501097276, 97796077, 938349299, 732814286, 940876214, 667876867, 136004884, 464216337, 936491666, 815513911, 56261851, 830437959, 844094074, 771009470, 209526296, 209013951, 437484980, 14164682, 733962741, 873829016, 892272563, 80174633, 770692453, 584209051, 340989220, 925758981, 616278075, 418509424, 896475183, 485680218, 92016078, 536149800, 169497220, 336254481, 21346343, 968492967, 659545303, 119839970, 787270166, 641327092, 576090645, 812477654, 436967372, 818410344, 344115560, 691089207, 60242225, 512863120, 936028289, 716150722, 464807127, 803337108, 866515175, 610061909, 628158415, 969368742, 417563786, 21634715, 798346985, 669486018, 868905419, 227790029, 26179447, 112212194, 511972005, 683244903, 681060891, 915977314, 446668283, 53159382, 935314165, 501561653, 382692850, 107944379, 65539350, 24202766, 594090826, 213779436, 505603244, 747009847, 49821044, 128303354, 706855076, 539997748, 842567040, 520045248, 876803655, 93180707, 965024921, 27651411, 133087966, 694070596, 202266048, 738842632, 570400309, 675278449, 417950847, 806817456, 264845712, 30319409, 102075651, 950733559, 80324951, 670219010, 385477050, 274213276, 839496124, 951835760, 896619546, 522279878, 414182870, 352301156, 844115001, 854216120, 235505386, 955211847, 17474642, 567667229, 361813256, 686600130, 247605355, 1871106, 903573204, 625020463, 498295767, 656134642, 839701409, 585122955, 279349708, 52803564, 120959942, 552650633, 82085704, 770918724, 407022418, 96970217, 988854196, 140390050, 546137155, 79948618, 115819041, 277049268, 303593544, 141829212, 33758709, 769526512, 796197545, 283266775, 398501373, 310134777, 844821584, 422730502, 933680861, 747490058, 360026651, 800035794, 395998186, 445257589, 210007365, 703090097, 175640616, 82783529, 179987294, 993241364, 361992029, 139296814, 65472026, 623553259, 798396394, 218930597, 827159362, 450739999, 1044900, 650748752, 608629048, 94779245, 220173381, 914228464, 970777837, 322360229, 294777003, 264499146, 992240565, 801828252, 986075728, 496641407, 594646581, 604107493, 265323982, 922418712, 584205691, 361522897, 612107640, 893027502, 438416063, 591791749, 291462536, 820705676, 853076681, 815199823, 790451660, 726687288, 95491973, 410470178, 245331958, 289499918, 305453491, 972000772, 190865702, 835119875, 208604626, 851192731, 960530281, 489526902, 74367918, 475426194, 495886337, 905203412, 618098696, 784382288, 745000614, 878768281, 815964899, 478952284, 348150132, 857451615, 132124882, 962513167, 815255810, 153286520, 614973967, 525253794, 261139324, 27278938, 513058058, 652096762, 904496880, 376074875, 347952452, 539743384, 446085290, 924453936, 384024800, 110292316, 229298759, 850296184, 740834825, 554504971, 288258476, 611215598, 510147640, 566951655, 824854718, 621085913, 159121463, 999467549, 690656398, 436947675, 990944827, 109640369, 534583946, 545139909, 367265113, 268266478, 982685427, 108159068, 818120690, 793272978, 430484371, 500990407, 555804585, 48601500, 969968429, 616883627, 442440649, 43829373, 299380700, 175559820, 77396136, 619882894, 196388690, 711402488, 920285530, 546827871, 443094504, 647725584, 679404706, 727493075, 107605461, 407656433, 715740876, 670127001, 645045552, 722571497, 153669899, 748348850, 601157659, 150419809, 670603158, 551755811, 332718532, 287014257, 191969911, 893233078, 223594616, 350345140, 682777705, 486018109, 423449981, 596210231, 573518137, 752447941, 562858696, 392133410, 837285701, 177979383, 341087369, 39710285, 887921202, 62715137, 546744039, 6412162, 591642125, 210280481, 691928093, 431900620, 969237904, 175684124, 704626799, 314233768, 560538241, 188389712, 113388465, 659833737, 219822604, 273802189, 235763176, 996569513, 318818961, 489257230, 711373107, 577028340, 969008754, 907246517, 576800392, 545598573, 331510597, 503279843, 759361559, 373983450, 169786430, 398420548, 256872788, 328316784, 757046661, 69215266, 658764798, 970149591, 260069075, 300853090, 889298841, 277324068, 417326330, 343391282, 878535506, 60293500, 895791956, 105624970, 338468159, 107193527, 33996140, 77208867, 274808725, 654036912, 59178537, 540072866, 793291824, 764725552, 314988350, 742998312, 798755125, 589059160, 621101727, 726681084, 979669225, 40848336, 901730788, 154131986, 626568113, 465266401, 867701462, 968660564, 887324677, 210329254, 917162424, 411769049, 523570372, 480489532, 82376923, 391961164, 632521320, 484364572, 836575150, 16959149, 101692983, 440630497, 8217069, 185977260, 703134811, 357145996, 247657816, 996697770, 144708957, 513019340, 487508714, 614737980, 732787370, 682536308, 386533327, 12084924, 398836314, 423623274, 489266973, 387688575, 673055908, 303818269, 881013868, 470155844, 328150065, 543103801, 752038193, 563638641, 862084050, 220482642, 597187966, 828075592, 554758098, 797701660, 336484277, 666332736, 376774919, 832375846, 520054021, 137673827, 96408551, 538884030, 639137043, 959031775, 241224688, 795395447, 402436128, 352821059, 814239368, 919816215, 825504293, 59384479, 580847336, 298426299, 340465839, 688866171, 554466212, 820101341, 764140659, 530927763, 806742485, 752390886, 121275750, 296263451, 563720226, 95866905, 816656152, 540199677, 218790505, 867604362, 972206141, 614940882, 519054931, 229923133, 329977275, 792781504, 97095991, 740324875, 23904865, 707117884, 295615544, 244272649, 363202549, 516647950, 329997484, 514529602, 482816250, 667825952, 501519173, 515398828, 382009031, 301519957, 652480497, 84839908, 382062571, 971799555, 781413981, 613755965, 596637473, 390560593, 201466252, 157737991, 867097394, 276696061, 4979777, 274684561, 566069894, 38858623, 179758057, 734035962, 357724722, 861762897, 243642007, 847762939, 673563794, 242842822, 661777199, 97583161, 655897118, 742874960, 739776231, 752271638, 758181566, 776175994, 918299696, 320645951, 218895262, 162583338, 878259449, 908022915, 790721313, 138345224, 796038723, 717368795, 285160171, 85662149, 487328669, 437034528, 195036914, 382876668, 881095449, 553495841, 776703055, 259930028, 793787336, 875021707, 238355508, 155760525, 597208276, 275596404, 701062753, 431028762, 736245443, 850260560, 581201981, 834855115, 170434684, 732974265, 789241796, 652828490, 138734116, 47396363, 797673121, 569669945, 920243550, 123340945, 351105903, 781312782, 803392443, 293027608, 496001419, 974646870, 355674451, 555625165, 498683076, 176641681, 184572622, 882524642, 645536941, 63300210, 449709431, 653074130, 57277918, 409795357, 14122565, 339065017, 756293197, 521769731, 506867999, 446511358, 565239406, 429929675, 828503488, 577654307, 299147861, 747412376, 484518320, 178640332, 473445314, 789411388, 804101284, 315998651, 364261020, 366143837, 60701422, 804751842, 601590149, 897533037, 80835517, 570873527, 253246777, 144336547, 910018495, 464093441, 878077361, 660295716, 60094049, 454685810, 60393548, 278250603, 489929498, 472311714, 945952590, 864555090, 391128640, 541355702, 436638372, 998467342, 200522496, 487903633, 212509850, 232793479, 125244222, 72699977, 832069009, 702779606, 395170595, 906080035, 113512030, 629335294, 913508711, 225855209, 96685014, 569274362, 440993420, 739582772, 612403001, 427808922, 663259513, 276088896, 47584816, 14815900, 713182607, 204787712, 257935289, 309443195, 443845242, 771014331, 279448895, 900166595, 499619812, 684188622, 765842683, 655391851, 186913105, 27773502, 110349681, 772430738, 829706422, 216750867, 883778962, 423280188, 61049348, 421460692, 871512177, 834774250, 419143212, 796848615, 218061756, 438392806, 372527668, 26066028, 783342488, 535241679, 150084777, 482727430, 990582349, 500148433, 340597864, 534938697, 903698574, 621768472, 389765490, 207771899, 770583171, 947607025, 700389060, 282366212, 465338005, 221400323, 129195931, 521720549, 153024538, 762861529, 626064216, 299848928, 92200559, 458386122, 642671683, 584584564, 67305462, 327577391, 424963844, 927713601, 594813819, 224248486, 502004701, 532191988, 99139627, 477913120, 141352640, 426843933, 366165484, 865024768, 244918214, 474575669, 889731488, 864221064, 9389870, 366074582, 171769659, 145745095, 221119148, 69034519, 919136310, 784653403, 573640464, 867385329, 357491680, 7568781, 865562755, 977460091, 17407939, 42518170, 772577076, 583648008, 443554183, 672222827, 959340600, 490776471, 694624611, 958622018, 878481450, 720794504, 299558988, 57505060, 694474096, 411663418, 630488561, 894837890, 758430912, 408670759, 161025832, 894661748, 144137815, 216049331, 681479406, 767543423, 273491997, 937972371, 865228453, 819476933, 147753964, 825245221, 581865166, 460933207, 210266923, 749327530, 777497765, 693267855, 797388710, 2255263, 509884973, 34161439, 762347043, 697842875, 516211986, 920355013, 21649035, 562596538, 690063617, 56818098, 622240486, 915306710, 46090305, 345131163, 608006680, 32750673, 206111652, 947618749, 620226907, 180217867, 549970143, 373460045, 334325559, 145828479, 377864618, 659579839, 77785055, 230703917, 54509154, 462636029, 362545252, 337392768, 742276138, 714210142, 622341527, 236034074, 218130115, 278937871, 498786659, 46605692, 447793504, 255943677, 676493984, 75281583, 661775791, 978481330, 395994466, 900204186, 963032415, 457014002, 827380006, 128521941, 66484228, 752949268, 442300095, 950240722, 302403771, 244133044, 478285178, 457581485, 181982810, 128122033, 664761164, 333368056, 238368996, 193688772, 436398708, 496947610, 931494045, 251919518, 464234745, 942223065, 845142419, 242188658, 283075959, 106989618, 976058947, 594133431, 334354206, 869225875, 89266234, 8295203, 116945428, 368758739, 749673180, 206817379, 995179221, 572794510, 474518420, 680314726, 830539383, 660715060, 143037579, 617829293, 182505978, 350536381, 615464326, 334657797, 367045004, 258064871, 878236456, 543547819, 405013893, 995423726, 424891421, 406660333, 567114656, 118280634, 322695475, 321117868, 584021501, 245925613, 749496742, 960783729, 407968148, 492903574, 820712721, 26472542, 283281933, 93151861, 373382879, 905372092, 407598533, 483096472, 290193028, 199576618, 481363870, 335345376, 806664526, 163486725, 325454945, 402216101, 79967960, 337164463, 348897595, 82062443, 355251740, 196729766, 339538436, 21887544, 218263713, 974492158, 793653155, 739169421, 720019847, 129805603, 358486741, 685670494, 247103173, 949193417, 498970160, 200468356, 77615855, 712611659, 22348433, 490798440, 331443372, 865930382, 603882702, 937863701, 811604539, 671177562, 954506167, 719604254, 133442559, 500746137, 89436746, 388386448, 574714203, 182329685, 606199565, 116884231, 169942613, 793272469, 130570974, 359232901, 181390040, 91797178, 627467981, 779838174, 970553655, 551393649, 127119523, 673590579, 15020680, 226273020, 985068800, 47546755, 93205231, 513569614, 523265703, 154158236, 201234596, 71472045, 426607667, 858361385, 140891903, 258264585, 689486433, 327579821, 648880797, 57094972, 632640274, 36981848, 197716827, 318005725, 801197856, 151751255, 597303553, 843761322, 873885004, 206421210, 543046077, 218362526, 139050962, 271087926, 884907196, 765625705, 656471681, 195767987, 163788539, 419947208, 80174489, 44653435, 666908400, 272956506, 61109136, 788173754, 795644239, 275907430, 788042215, 776305477, 271115600, 247277490, 170951489, 691242101, 519215676, 565262107, 500091923, 549438567, 454485285, 617038341, 264863864, 143798478, 669645477, 287824033, 387647461, 221681620, 541640833, 339856791, 117319089, 801281634, 864574613, 964607937, 622584297, 184663664, 554598224, 468975528, 496572514, 581472373, 714970703, 15547439, 201458420, 640821362, 17102017, 112489061, 639038305, 774276641, 837129697, 690446676, 381599837, 669031616, 972402479, 901281800, 88530937, 707058771, 483650922, 96561012, 792461347, 956534149, 761833649, 138798075, 724129932, 360524400, 176454403, 648911936, 836062835, 456356137, 452842169, 894511050, 321152093, 276296865, 973310318, 563556614, 537850266, 652578692, 441994496, 861354297, 416221825, 999946347, 626707872, 651071856, 696321531, 48739210, 70761340, 690824715, 939230647, 387464979, 756373827, 912716828, 657031624, 180503897, 5794438, 29048829, 123048079, 15845035, 127941836, 970618144, 327936091, 768037321, 904872242, 168376002, 228148995, 206282500, 88752955, 46340876, 347753446, 629855940, 215022004, 543112547, 391511722, 576723252, 632508892, 154243896, 911581747, 628677064, 868848130, 882420308, 732703292, 452722831, 673205349, 525420912, 66287246, 106161652, 507391977, 802793427, 709729666, 959213077, 516342028, 47784162, 662334539, 862575570, 551350047, 51936685, 552598521, 437563695, 22597737, 472681844, 861146467, 544097865, 348770190, 9662094, 192808379, 365622561, 302528069, 236748936, 754803740, 618670840, 492275407, 318975431, 623088302, 554818059, 526719521, 663872397, 323493164, 30579510, 182869094, 555663566, 171496521, 136436217, 294573464, 896784958, 867406992, 260447374, 214159036, 380026092, 309197108, 794038673, 475625962, 240476927, 256917026, 570821259, 129033495, 911596551, 544107024, 86112603, 619000491, 214391809, 522178129, 638755608, 892100961, 210007116, 321345863, 175586110, 17775411, 630733857, 328868592, 870711272, 550092282, 821235254, 400625299, 684174022, 305084936, 831587555, 621801797, 153994975, 706402397, 913421528, 818474059, 808843564, 745329512, 318731431, 945381724, 965177571, 66043495, 399356444, 523843960, 364443480, 456733651, 186203054, 179946274, 829384468, 633239493, 973540770, 580304990, 121955372, 419584933, 395480210, 209938695, 915628638, 383276987, 883459067, 907426253, 206246516, 503889890, 251981208, 235480533, 257293040, 636528229, 220920702, 761173750, 440465067, 447485534, 855684861, 920126253, 420913391, 785493285, 657084414, 349840042, 390961684, 180537766, 522920528, 158472091, 92037123, 794797285, 412758132, 760776207, 234835630, 51872133, 52814997, 57275470, 741319575, 174550507, 224742790, 933113153, 782884927, 354547898, 518450187, 680388805, 844818712, 340731944, 220438188, 582968847, 985923183, 856860074, 457507656, 592841030, 131898499, 945587647, 193821484, 831688722, 244529605, 250204908, 275521510, 225903192, 178349943, 620068530, 3393454, 422263070, 995764311, 828991697, 114863494, 458386387, 52953603, 149898914, 716458538, 340829096, 38065595, 887215058, 895693348, 139335501, 344234757, 561741204, 817141770, 422680888, 59623240, 870525520, 549148042, 626039450, 772488393, 443655990, 876295778, 249975744, 129500401, 831612586, 498583920, 337453431, 934436125, 548212161, 309516577, 482535693, 950377533, 206775806, 585427204, 776337336, 928538629, 573085980, 1946551, 449088034, 67162096, 523194593, 612153904, 312102805, 613777394, 850400317, 924391770, 348319584, 242840983, 220801387, 233662801, 78852771, 282390814, 140603623, 454427901, 315649008, 129758069, 302393646, 190750533, 954395152, 81222137, 300178809, 445092246, 7526746, 585207736, 719826672, 807377973, 615415196, 952185403, 810638760, 995115517, 859952224, 347343778, 969272710, 221649080, 32394011, 527575229, 73811168, 262435150, 906196252, 296237443, 235755019, 28269508, 146738798, 389711351, 532889017, 327743843, 400049281, 276554048, 336566135, 278424133, 691794519, 810218110, 272409848, 779957679, 301090471, 15968781, 151039413, 239838639, 711115644, 484005475, 707160472, 150053127, 855654923, 148564726, 58246910, 414264360, 218725283, 110188467, 988893610, 416584491, 758005485, 928599129, 59881266, 330642050, 322870347, 631333832, 977350757, 906243349, 408810000, 160276158, 290849874, 944065559, 398013735, 595623667, 907128663, 549158596, 42266271, 978553158, 277080736, 226676911, 776329836, 687065701, 968084208, 197092155, 180524722, 922570591, 692478340, 78470392, 777079483, 828897349, 689241067, 349695121, 508011427, 851454918, 147541829, 907949763, 59781844, 233546543, 839833408, 690900462, 293371632, 424025896, 408008327, 104378350, 722375872, 481039293, 791323762, 711959388, 427155599, 894416977, 651165196, 70311069, 76457184, 59012424, 566662226, 683888831, 63792042, 339428789, 802087728, 707579275, 236988626, 83437692, 377863213, 863921278, 904245712, 412997340, 235007666, 815262830, 221415220, 911026778, 1976817, 376349735, 194255316, 219636880, 585960303, 281290410, 801296636, 990174834, 249446950, 117557382, 283613428, 437648281, 679866119, 502827545, 210255393, 574209862, 123054123, 730447030, 222603574, 570746420, 251084361, 426458079, 330280903, 20560824, 982182213, 987465594, 684542743, 343307986, 715067773, 200211383, 643621680, 306209913, 693705620, 807664748, 781405025, 767832389, 735771888, 563269991, 259686914, 299354107, 249134629, 229823372, 626777285, 338392324, 872546421, 164872638, 62496455, 619156645, 27261272, 711179914, 308952775, 350164032, 969443236, 758983270, 763893214, 182228502, 89947968, 842376231, 583178294, 840695222, 927398068, 500329381, 879911953, 140410979, 764319870, 552901359, 522477113, 328315229, 30506420, 270013149, 198188834, 24998093, 971589799, 780573535, 143689580, 960523292, 76105038, 273552309, 668265807, 582134929, 47944573, 941793473, 356395561, 243582257, 98617298, 683787609, 386978003, 537317424, 37271631, 232589062, 706632320, 8278627, 313832403, 916411536, 665456381, 519745564, 535149758, 111771765, 845037011, 924533316, 609977033, 434038928, 161534396, 67273611, 333991428, 72683371, 559177550, 74753428, 894015473, 763819955, 502530530, 300855125, 674007285, 133541577, 782558546, 988898621, 846010948, 106288976, 53463682, 765595796, 757148573, 815879999, 326846470, 4998664, 341220122, 433107211, 702005838, 479236919, 877671124, 556737608, 980755252, 184579095, 556076417, 600174385, 695254377, 86254208, 598876119, 147498999, 719874125, 327447029, 148963267, 922360780, 444114283, 120688720, 452669493, 187781486, 422316668, 378370578, 49339467, 90834064, 952626007, 718130578, 408269689, 974160095, 604124189, 780152461, 45833649, 771784260, 358826135, 325837451, 830119029, 267300347, 226077244, 463158389, 890655774, 575128372, 364432111, 943178044, 619906585, 589356385, 923700252, 203979818, 49936630, 729804471, 789561288, 289305278, 649759425, 859603101, 375201985, 819094579, 577612674, 556587658, 563913876, 775193148, 562524251, 92935838, 81080355, 176798305, 625808157, 593983242, 199911541, 238094853, 875876644, 81665858, 883944391, 769596645, 623615349, 649143130, 660584113, 288954116, 898138668, 749880863, 789367740, 445379104, 409136583, 193475016, 600072436, 729671396, 870714112, 649767203, 145986096, 216772301, 169149019, 891157617, 636906724, 259097288, 489329031, 854009855, 800849530, 20512265, 938969067, 434087175, 921057533, 580262143, 449129288, 821033774, 330983761, 456687537, 520712371, 806890972, 949957624, 694331139, 87375350, 449289320, 747411891, 699445860, 610353375, 860008254, 124364021, 415141275, 856620578, 600289896, 343521295, 79258555, 28541091, 866410718, 401525959, 10177667, 620229961, 212771375, 856526979, 874774861, 431380438, 580870453, 573995818, 181339879, 387924839, 468365938, 307383293, 332589526, 50405325, 145473985, 325196899, 951103350, 771658209, 702882405, 817058330, 325192016, 638503370, 175670954, 183798186, 505141003, 364383899, 468305977, 307305218, 95298092, 586482621, 595500302, 750771813, 248133251, 659836883, 416971264, 703299196, 715531424, 145270576, 927077356, 312694076, 869140834, 389835382, 872127495, 54623456, 626434091, 382806619, 990692995, 717438404, 351005323, 220408165, 682401028, 221928286, 983863967, 343365933, 794063471, 856532167, 8875458, 480832329, 452679537, 823170878, 93510676, 849417597, 248659949, 739165601, 465617995, 568601303, 183501555, 590698718, 382795579, 156017042, 789301578, 84929681, 980221866, 329303659, 398561700, 963642367, 754596246, 850786660, 589936610, 851533567, 239577638, 111394735, 137563796, 752466779, 530188423, 189487524, 71809337, 915065993, 142932193, 802063184, 360720833, 764715877, 673753348, 453411020, 969275560, 949041319, 661138460, 803002111, 294570565, 738373750, 982108080, 975329334, 972201528, 465002295, 236111670, 658332012, 438249021, 252408425, 482025209, 468461942, 68656145, 106899790, 921321240, 802137237, 243938867, 957622231, 490349450, 288055181, 117524017, 562749093, 787188864, 759974862, 433258021, 372781573, 60675624, 884833733, 639271837, 688381115, 12516993, 22840189, 497382947, 240448136, 978211514, 77090962, 648835472, 257934451, 982613481, 221775557, 616889731, 186320920, 282802071, 630533170, 64655587, 200377232, 256744045, 300940931, 13642172, 290885179, 846960781, 504737172, 550187731, 600731919, 868905187, 671197340, 254354967, 362028164, 740148677, 805186310, 303018695, 187812158, 978591759, 801004962, 15348906, 703204613, 31864441, 976155391, 818874004, 23193028, 220589347, 432677306, 267751557, 487460971, 167204495, 638463815, 669659528, 938411587, 248002683, 799736235, 310549101, 284544505, 138617731, 686165626, 358972541, 668572513, 855612351, 635318613, 196872316, 911923498, 425078054, 795762983, 812416760, 340568162, 310020211, 529397694, 959994098, 73187202, 483492721, 906412015, 729643064, 784273244, 373377209, 352798381, 921858288, 58372163, 709443436, 347183064, 840996204, 588991526, 403698428, 850335438, 386448846, 52233417, 9087168, 151614875, 870576495, 397768489, 338854201, 611515807, 40265368, 766120819, 734447007, 601539916, 215274774, 988502187, 936779640, 433245180, 263511358, 402034260, 758704563, 48347537, 965748030, 513873572, 334586991, 344251579, 222316676, 296562185, 206003531, 188029866, 843434394, 786488353, 985824165, 467334576, 363421038, 976340181, 781736645, 110716489, 800684755, 100539409, 9582051, 126081420, 502275795, 929356669, 390219766, 383360455, 194988938, 163598107, 565369194, 343130698, 796145606, 811889718, 695630737, 238903754, 654545620, 618973315, 558778518, 641047387, 617215969, 308360447, 266497064, 513519316, 732911599, 456879677, 405640287, 517624835, 144428118, 360042869, 359872646, 124238966, 129930362, 781340292, 283033956, 890046155, 356078981, 351685686, 54524540, 14475890, 155447502, 197733636, 369004719, 66225240, 226063266, 94863530, 29727492, 758400846, 337514908, 546441504, 105584053, 538041642, 429299710, 895454852, 700926937, 168531218, 347470960, 802811532, 516302335, 426283923, 650724731, 371749595, 356066183, 813856170, 989482913, 421690287, 255920440, 15950115, 83907213, 852025396, 948451944, 32513977, 410183532, 529922200, 457434391, 950995176, 714123730, 974865520, 991149895, 525782131, 909251529, 888803108, 233634102, 631544448, 907451252, 588134256, 451321283, 665598587, 231556587, 234018286, 48422796, 135278873, 412579583, 763043122, 400519920, 520349784, 584588871, 937107514, 129743742, 269997684, 674184419, 174108567, 581257286, 992993571, 531297453, 428318087, 658491376, 270335221, 406255807, 495140834, 96472105, 519945482, 839614211, 410546596, 800028840, 304570824, 725289567, 569992148, 572324157, 337702253, 800160832, 929715119, 896433779, 529304191, 271276541, 977014807, 166698990, 808771322, 845928661, 436074274, 402201644, 351927773, 130293013, 270284033, 570890781, 956708678, 395554172, 438395214, 213388864, 417501968, 605550898, 43014552, 210622133, 15044918, 523643817, 955565123, 50650205, 470770627, 212864591, 197068699, 17480988, 935982854, 710633771, 965730594, 348055413, 998442071, 60004694, 812078956, 784286031, 274732474, 578202458, 585455392, 915583907, 928764672, 364004123, 470567318, 34675552, 536630017, 539730067, 378434806, 897024529, 879032768, 694958333, 456901865, 351571083, 134426684, 699023959, 562436443, 384860486, 704652179, 31592508, 18715383, 763444694, 115599064, 778422600, 305488304, 100034761, 140678818, 596134853, 412544208, 764254706, 312378713, 937582249, 639097641, 664350182, 941952442, 402721458, 622072844, 893000252, 940588794, 644382094, 87486092, 678520079, 140086023, 213738344, 62301809, 885605558, 941189593, 793636021, 829070592, 131345915, 64611664, 556398189, 427637644, 186135136, 367031050, 185412106, 338239233, 460576950, 447381832, 883894310, 549370272, 519595665, 870749793, 370626640, 513515674, 843271455, 303432462, 598951131, 572782319, 215367098, 616002904, 795300723, 188789574, 155611087, 842655424, 699249482, 196936638, 19107894, 89022751, 361281643, 378099817, 223832327, 149241860, 921557895, 35197006, 552087946, 796268440, 998517000, 210024200, 104290564, 167938632, 675302138, 675012075, 231484477, 374544218, 105771204, 57114529, 807309306, 47282682, 287378569, 332634663, 671802821, 252461929, 406045049, 819689492, 749736371, 686016702, 265372151, 37639813, 983352352, 621661208, 854109132, 642549003, 82979314, 297732376, 593729545, 661076396, 994031005, 570204423, 268641919, 193572798, 704057319, 510904550, 267422191, 826187136, 897812737, 517250991, 850901131, 881434139, 281712303, 526977841, 588041640, 151567267, 452551702, 894968004, 479781437, 647356192, 153168506, 680965539, 612652452, 83920134, 364866807, 473650601, 289712070, 29138024, 271499918, 367354950, 971697712, 60741678, 730147380, 473909161, 102708895, 13249878, 60253691, 785157578, 649626023, 984150679, 258134512, 527814752, 167573368, 656210080, 729858227, 130424708, 438272784, 954830723, 378500055, 123370204, 489033043, 687753305, 257416646, 358242900, 458199566, 148978325, 876520340, 779680389, 644307902, 757764267, 920077875, 880732071, 678894972, 224035473, 915836691, 521535075, 978271400, 33179018, 984296557, 718350381, 400514816, 318562541, 264418568, 987550912, 681101189, 467731650, 189861795, 876735252, 319629649, 241728383, 577118608, 579235444, 225794469, 558781501, 477900412, 872696060, 135703208, 667153910, 226404282, 35898646, 474765206, 477239657, 97933033, 987982839, 430316380, 878897195, 648968048, 565412958, 814249459, 887094615, 23722976, 179927604, 68423177, 151334477, 858093572, 678987327, 434963259, 388835251, 270666610, 57008342, 922529385, 911323514, 24271330, 946480526, 813760090, 105948919, 924702476, 148247970, 766785231, 643930713, 229930857, 255380085, 23075859, 952043623, 544404940, 708326061, 602226307, 512078430, 417576719, 837638170, 499122664, 489027091, 502499586, 476615874, 299727312, 70953343, 610043519, 885859618, 363684138, 301266930, 309231240, 868556888, 192897865, 169711204, 988921811, 636246725, 74246318, 529954686, 700755576, 271992599, 731367645, 284419400, 144240158, 572907363, 594440853, 125510822, 820184437, 865087731, 489924355, 9161738, 226040103, 694101647, 786266131, 350326474, 581231885, 911195666, 79188443, 289460716, 349608081, 476768768, 192932048, 523004150, 32501399, 104172521, 639477784, 774473007, 827021227, 373164240, 769381767, 406925000, 46301010, 697420822, 263450541, 847983769, 782018940, 241505656, 987882235, 931911537, 540493147, 483526379, 770940678, 377555029, 534258452, 150406199, 930619993, 111779522, 493152940, 766544639, 221521883, 32281559, 54024973, 805972178, 401831709, 734745472, 986898217, 379300356, 869628848, 667918937, 589796851, 29933170, 160219285, 38397351, 583419826, 991523794, 175298583, 951930463, 227908617, 513703128, 594977103, 731966840, 208473884, 201536340, 169872524, 465754475, 917300102, 424824711, 962713727, 374396026, 24261737, 702488305, 178340443, 786220598, 853866577, 461312450, 229507291, 773544122, 872750936, 653213415, 297509324, 415983609, 588226398, 182262355, 249101924, 827281516, 912238383, 762687778, 392728758, 101609038, 546779245, 278171667, 572035556, 431693882, 600636597, 594845803, 178154662, 401238829, 778801693, 515353892, 957996209, 405452381, 841573875, 892758722, 984010076, 342236717, 468865161, 314492409, 267544813, 715230585, 578754032, 936617410, 312369406, 944585270, 69607773, 28946543, 811229369, 168770759, 25940866, 517893490, 575819866, 610957789, 242278750, 828854149, 81563990, 788207955, 664537320, 198435713, 375696879, 942401884, 602618695, 291785496, 503541098, 320071991, 987951110, 418452486, 911878141, 26491251, 748675996, 123956145, 74612983, 859860841, 16049010, 185664244, 299894477, 629216196, 444777675, 126350166, 580714114, 332563282, 631362450, 320744817, 456867693, 763870766, 414345060, 717180026, 971873709, 179231022, 10234248, 776137661, 987391576, 937747073, 938048763, 124794457, 683241936, 981385249, 367806831, 843585543, 64310547, 535395814, 480757306, 926021529, 181265794, 304058606, 665274320, 36294167, 101670537, 404461717, 565133719, 578570014, 149219790, 687782221, 307384684, 468419027, 926871416, 866967975, 43058345, 609116242, 910904970, 960832113, 730296772, 333542318, 64858648, 666510162, 754945779, 154936552, 596615132, 267466370, 84249156, 159691959, 408197419, 874250241, 42851814, 280240115, 462208355, 7690355, 614719368, 220399492, 594607963, 613242847, 658481619, 180845691, 490989707, 82052689, 848404733, 475088974, 657500913, 667806124, 930646185, 320712500, 169072283, 167009665, 417680238, 240891027, 620789809, 932444285, 824618099, 579951787, 365637653, 727848866, 81104726, 762287718, 408188878, 404262153, 446876625, 532071528, 784477149, 876853560, 301112380, 550994324, 816894140, 363513554, 122892457, 266780242, 976932689, 339298015, 38335618, 363339409, 259245484, 655159689, 403360714, 898447353, 983174004, 8035366, 164120893, 730035801, 980307340, 512843750, 524093832, 663947207, 564065094, 810738094, 281460260, 729439259, 467148950, 187257591, 798269866, 673429245, 880701831, 340498738, 710311563, 40151422, 964397413, 684173256, 583333364, 157275766, 48189879, 478129678, 950451795, 966878235, 694358287, 866677255, 150135827, 292179185, 182235117, 580342760, 29958569, 369210402, 189457283, 941189030, 68537931, 864963254, 689379906, 9873489, 523671712, 811820390, 114454163, 731450610, 248750423, 692334742, 137386905, 896068311, 700021384, 214194149, 824292351, 803999438, 517856789, 53747314, 264730567, 38810940, 130882107, 833075906, 605844321, 226739569, 594527215, 118274185, 930346802, 807650882, 227848816, 824280051, 268930672, 250189028, 16365646, 264395696, 971948378, 150660014, 113419001, 394719795, 330568186, 998700446, 553083786, 676447217, 242756610, 820005739, 559664425, 147245783, 656153057, 995421316, 256295162, 597228582, 53900881, 630281322, 941735838, 207006393, 572346678, 304181488, 612616670, 437289499, 765783318, 993277980, 495519708, 420230743, 530019466, 771080481, 401094829, 760472128, 497184630, 22511355, 139832288, 184681082, 77481225, 618791420, 937658164, 455784936, 938559663, 767845900, 487421179, 177216918, 914818785, 175143143, 230655565, 800198191, 528054280, 347243316, 828179891, 933019618, 38182837, 181327328, 48297909, 485557674, 213741306, 964855406, 924328494, 442819235, 518809454, 231782536, 236943551, 564245280, 566992745, 641535502, 735280434, 544787249, 625548788, 920632407, 878430804, 596882811, 578702665, 556230072, 974035213, 273232268, 133182137, 989962612, 247837455, 941728710, 108227678, 287259368, 908426368, 485921090, 96581824, 463215160, 753676407, 503053170, 737981634, 76014948, 563661583, 410804903, 965175045, 970655620, 801584737, 199624735, 68454888, 117702576, 58108319, 553365021, 956894245, 846674457, 250254250, 309727101, 562657631, 937824959, 267190840, 5555665, 855482174, 123902044, 922233294, 318160924, 85014967, 507305435, 959488079, 135716484, 151438945, 195697319, 74180116, 731580796, 767710410, 434815429, 512017398, 439481314, 12555697, 516056519, 141910473, 60855988, 577039977, 107856515, 88853136, 994293254, 725196846, 243747523, 87770969, 818384262, 778826573, 289543335, 534023737, 661353730, 81803609, 377890063, 525798394, 234478513, 326608294, 616862817, 990692601, 695548332, 467545507, 17882125, 96162863, 169800631, 186475749, 585126552, 515690612, 650725631, 600973008, 330530821, 51121191, 230718122, 570348848, 542773045, 70385919, 274123990, 156909332, 684243074, 397800717, 14038118, 643106554, 160957234, 693957418, 369021222, 275078260, 763664323, 541813622, 719853633, 577890957, 849849624, 105117177, 973305950, 172659095, 948551324, 751980332, 203111559, 29326709, 893113036, 861849316, 762996264, 42449789, 571751021, 848171814, 770894855, 873275767, 204161156, 473499775, 622600598, 533674198, 606968106, 847831323, 347862322, 165276847, 99641882, 554927518, 862192939, 637142994, 986540768, 9511034, 129220679, 623071719, 340271190, 713528941, 280515126, 741949576, 596676868, 605936398, 531974344, 264226385, 804250444, 290373152, 796029683, 289664913, 137972033, 531015156, 123465911, 752938286, 850077426, 960151505, 153240666, 880046330, 156830179, 789745969, 53737396, 440573948, 732209356, 113128942, 683563306, 139751368, 368142859, 144930497, 246974096, 111826686, 273870215, 191120629, 531449778, 699024704, 862224586, 133992143, 517644565, 972710777, 926322785, 142021582, 63536606, 975154955, 226651085, 733720004, 660674887, 624861048, 479644145, 121054996, 808545374, 915353881, 90557438, 354059228, 481159142, 472752599, 540295107, 164806254, 609257132, 426343106, 997301232, 888001875, 497118704, 61463153, 840397745, 442539126, 793849823, 616291098, 52697596, 805437582, 727905728, 525392589, 844998533, 899285002, 92647310, 882782144, 956343761, 635932322, 126079609, 662087299, 422489954, 510372059, 780259188, 7011858, 960988834, 423480255, 266534406, 593254832, 164396107, 222459109, 742303804, 67035599, 275122119, 667462554, 116779926, 979273129, 392104781, 407594722, 997010084, 833888481, 527897232, 193527696, 827155822, 672079708, 918313992, 94196212, 867949683, 717958705, 434793010, 167843240, 855823445, 44238679, 159432468, 722580580, 174087508, 256223330, 531219045, 253049685, 449838043, 870823104, 618349095, 524211445, 560410181, 953204865, 189822575, 896457633, 37376953, 849500509, 137931616, 255152590, 534832783, 57683168, 961219285, 953322977, 589861817, 946549738, 500699518, 169667265, 228323038, 825537955, 890899980, 148086952, 433924885, 627718137, 828477512, 897529840, 382397428, 947571433, 453502249, 1020591, 806160129, 192261902, 203252282, 615889907, 950298712, 616855510, 997976953, 391312511, 779424475, 925178541, 26533589, 932113974, 538210789, 127721752, 188538742, 792728649, 927426730, 822008622, 837537214, 23963412, 224888077, 568822652, 410169309, 711739870, 810747861, 179207491, 167335540, 28128022, 128930066, 787065391, 99901944, 124800324, 2040979, 148876411, 121533988, 896087593, 435511364, 69034050, 418109507, 214696357, 753780770, 755524922, 976565645, 488133962, 13465602, 473461479, 785021232, 898792387, 489404922, 212313341, 748492649, 459056027, 156285951, 71011581, 549842590, 117794685, 831649238, 136586776, 446586926, 861262919, 675711118, 932323718, 135523642, 425660702, 701086590, 713812653, 650098219, 281933183, 856491926, 937305365, 51407660, 396675055, 229987758, 208507955, 465940427, 183253515, 966274391, 633353214, 344015468, 300683745, 876243747, 170835979, 871444652, 552847089, 472724348, 834072758, 666793863, 598586658, 584568171, 769452406, 784166201, 898222251, 327691377, 941510173, 739777307, 617078807, 174517521, 947593811, 177342777, 452410815, 797847868, 295582407, 120359996, 330019955, 906250091, 581954220, 333152439, 754483559, 422021076, 865186926, 306064769, 561307471, 537101281, 288623107, 197764603, 397936551, 873964905, 615990363, 345905422, 219440117, 477018191, 201516344, 700261886, 257341953, 265339524, 559469358, 903596270, 324831206, 438396306, 223924098, 333241046, 419567375, 215974580, 95343095, 671210804, 267175770, 161761984, 241700340, 816891106, 875253388, 688962862, 18550152, 339540144, 877929378, 361696134, 315245309, 879150811, 781171995, 459364565, 26916761, 55321723, 542575066, 372892867, 512211658, 315432597, 381140864, 678620354, 953838053, 487906973, 423170656, 739193387, 383795864, 192959998, 7685898, 790600778, 678007269, 404661928, 224482522, 19653661, 992190832, 334914727, 80754756, 163392736, 267460805, 720877384, 787103963, 198363630, 880377461, 273555908, 365081468, 89088891, 402127447, 742095972, 462302620, 926934303, 754027066, 5248557, 922166565, 416598882, 949239455, 712938786, 3859881, 616189682, 440833178, 48957880, 833898260, 893759224, 834099936, 281181806, 760907840, 59168085, 761583600, 654729543, 947962053, 442746594, 245123416, 328119578, 509680443, 726086826, 869838116, 765921968, 523597779, 518203166, 866107138, 431912527, 282342104, 418647860, 382061850, 73966273, 913870105, 275451731, 602606625, 839608960, 552024595, 206089695, 446991201, 93403772, 200194640, 866928407, 895781205, 389612660, 985790704, 119380617, 55231275, 401646460, 598532031, 343064147, 130908759, 657626473, 644587764, 72435050, 317868070, 211364178, 360633679, 451816138, 14561906, 441027151, 440467141, 966836252, 947593146, 918646226, 392590945, 833083221, 546441720, 672958244, 4098134, 744359706, 684043439, 876385807, 545294137, 752496241, 976344977, 86135499, 347690287, 256497410, 993333333, 62835486, 553677716, 194407555, 733505140, 904216687, 937465447, 178343356, 877923535, 736380294, 762341366, 949744871, 188836779, 957906382, 642133422, 567613939, 157005819, 65448218, 404757615, 319569328, 391566687, 776602093, 702765879, 856863640, 360516587, 800123326, 332877631, 472275519, 72040088, 375740959, 120179137, 620898917, 160137040, 155640161, 392156142, 598917725, 429517751, 689466599, 294192338, 435635669, 7741321, 452450878, 36843851, 976706791, 640063235, 644568129, 821338544, 746105846, 184018502, 879754498, 506584143, 806278339, 654152471, 28288356, 344236294, 928421155, 700208266, 695647296, 824168931, 296051259, 363875675, 259689713, 377309398, 99793373, 722783488, 553761913, 85153667, 326629568, 501478515, 556436802, 249610108, 652255148, 814467024, 565638521, 90259476, 594987588, 478132016, 561214535, 404789618, 867426064, 803967815, 199905379, 996668148, 272551222, 51695490, 714785861, 391530414, 831424775, 50983933, 983393716, 308588077, 527363643, 300815446, 545940050, 635156914, 52972668, 648476093, 525547034, 913954957, 373173303, 396708085, 226490049, 396270401, 606682496, 500195429, 840027660, 121955831, 686808675, 363171801, 829444213, 801418089, 919914440, 98864563, 748556311, 155679444, 16928050, 300225047, 949082609, 752926398, 657626369, 776942772, 654660736, 77898927, 455435973, 869079816, 275499826, 836656847, 504390013, 454186111, 760978552, 767014960, 721724190, 706538301, 959849764, 940872819, 231740804, 242013329, 296358905, 968941605, 98118208, 59244209, 658429386, 604679025, 788587098, 415290266, 297891195, 668192405, 697743055, 890742564, 443683652, 713920939, 975370548, 384848087, 163579303, 422359591, 930488893, 50612331, 165649324, 692289985, 828987862, 870333035, 591150570, 116333110, 152116479, 834659335, 503988566, 936200312, 67941050, 731225067, 10272992, 609464357, 866570980, 206366349, 554563428, 987366376, 906634395, 769882242, 543575183, 128411769, 500497552, 589415965, 135852902, 350563090, 723873103, 378095365, 218442927, 95949045, 978274835, 825321214, 715296715, 314661399, 776871765, 640201991, 966611189, 747372019, 855888816, 585601430, 160341237, 242948223, 531357516, 198286163, 430098976, 969762453, 609071086, 820323055, 245860116, 750810285, 768772428, 249055845, 793499638, 79684574, 847207850, 569312671, 230848970, 914318266, 518253503, 797111408, 541190036, 160616364, 367566904, 636713863, 80203384, 722389112, 15472705, 739261738, 224514016, 22588636, 662255661, 257207632, 189705460, 494163001, 298483870, 61841393, 473416245, 950748912, 804617821, 495072734, 901011542, 297953056, 770268179, 477700033, 949986170, 338556133, 623269162, 210473986, 741446358, 631594685, 292679759, 719971519, 93420519, 613273846, 645055149, 75810848, 432686568, 636636691, 23660334, 533809553, 633355834, 738866722, 572510884, 85473003, 644391688, 518988226, 853593919, 193433896, 681043594, 515806245, 521037812, 326307993, 310112998, 670997616, 898291023, 301749866, 757689356, 867793171, 424466464, 110716609, 577423974, 904586981, 511888789, 363468362, 334759655, 725238142, 95223412, 693146636, 561671470, 188664515, 182314751, 91059875, 852637828, 799761943, 749626886, 627127448, 76087334, 855514079, 243708370, 803472947, 838316804, 918920326, 19874189, 627555241, 410650463, 786447734, 978878661, 240965771, 440958551, 270864933, 291834390, 669260010, 465817881, 551398430, 821609663, 104163339, 152041438, 921156945, 223208859, 53389870, 224186705, 716312427, 76369428, 334763102, 149983374, 479810983, 610385929, 748814027, 932304495, 443195778, 118895494, 377269263, 378832105, 42502391, 173859641, 477640389, 725010982, 470136884, 220999868, 827627394, 563201840, 560780960, 968381781, 915811353, 293881025, 874164574, 921134013, 884558544, 600774009, 529635279, 821884407, 445586224, 420935804, 489098669, 197489985, 10126832, 74739121, 58086409, 206232159, 951687018, 548766539, 263184956, 315711629, 664189277, 98642244, 834352762, 473609860, 649750750, 818608086, 579392613, 334910165, 594921382, 151032172, 518251333, 678025776, 139173736, 203939984, 436002504, 7341758, 939936035, 352893742, 475801153, 21246997, 504386293, 821715737, 10659800, 491606820, 350402429, 792309680, 922478558, 806287100, 941880314, 245815841, 209465608, 779935844, 577304522, 121916718, 965880880, 93580715, 624802606, 438879343, 289572598, 793921644, 896651823, 869189992, 10605465, 801545721, 658380225, 288492941, 924093527, 471228032, 376136580, 650515285, 450938697, 714538091, 584151442, 508753253, 700540083, 611464049, 987952567, 944572866, 81535356, 182251024, 311293065, 465389989, 746401360, 243425321, 518670663, 482635362, 642685806, 327303299, 331070099, 191158377, 194454147, 620309840, 475343839, 707675696, 128065284, 874463762, 306629214, 224190800, 575117153, 589593534, 723084982, 172660981, 189525902, 351334050, 66984823, 622147409, 171776039, 373019683, 728177333, 519447586, 414053518, 142314531, 409475231, 410627821, 360105280, 9571425, 248836611, 725776576, 660931672, 315931119, 730094912, 235451595, 400873651, 739515662, 300757640, 226552823, 996880148, 91773816, 745052093, 959495327, 276439450, 937449730, 372694918, 157927150, 313351547, 432139543, 68209013, 422129443, 843865993, 262123418, 523712395, 702824909, 543038140, 59873929, 5107448, 965209065, 259900885, 8378806, 83571462, 528942734, 523916463, 638536124, 747917059, 668669529, 288758347, 556005330, 723957, 698798490, 771700564, 199646049, 564506663, 625905332, 993742615, 989353487, 991134055, 768084219, 162458989, 216503320, 763728994, 481905421, 827522817, 735520847, 857751085, 384256823, 507054965, 824224583, 115046556, 273926482, 426270728, 171604674, 334265976, 16701505, 317111222, 946997570, 955133680, 344920684, 857986351, 710901825, 934905402, 685260485, 318594860, 543375960, 356459138, 315265536, 897122757, 30487905, 610284357, 472925075, 645806434, 968701406, 498194088, 386026027, 96698807, 778874215, 557694802, 984723880, 427447241, 741935414, 70325925, 784494352, 649044495, 226461964, 683196412, 256443753, 676046427, 296050835, 767651408, 870428809, 599606839, 159140167, 269929080, 467558295, 855438896, 759718141, 122942656, 877701158, 912764830, 287522491, 532299609, 605740820, 661656653, 611331664, 616238586, 747950840, 56776471, 155772798, 171645603, 207297808, 643839081, 647731300, 271527871, 497441116, 593779099, 807076210, 872762411, 82584103, 71439008, 667709954, 366373613, 481075167, 869693557, 161071878, 769300149, 461079317, 961822073, 211028679, 557832838, 207530847, 656255766, 824933213, 801850579, 912364657, 497973063, 770699088, 522399461, 548612836, 140881518, 410835313, 437855531, 544366690, 95297790, 244093684, 739248826, 89704219, 924251769, 282904414, 957311361, 257749128, 368575887, 160293502, 863343406, 609447946, 968056601, 330992285, 298785536, 349869562, 807291819, 65157781, 387381417, 554575628, 72532043, 216965139, 209542512, 958228503, 163338117, 512824707, 563929386, 543814482, 492551348, 375525571, 666562874, 693312795, 614917187, 104069716, 611744448, 44907456, 259019801, 757081927, 755217576, 577933615, 586643742, 747965298, 394138883, 73234602, 119641954, 635100752, 13095438, 351720923, 689139312, 624619459, 820726346, 187636039, 139347866, 850816050, 463433437, 655535327, 717637578, 23209998, 769232733, 659307498, 493486312, 396477667, 826000603, 687244864, 277224157, 614136216, 467954362, 931202201, 810444072, 129575047, 713729037, 688447021, 179218873, 849409611, 825322455, 320249796, 932560971, 50599133, 61727059, 620828775, 315803315, 853453309, 231562757, 152492870, 885289487, 862036502, 236514051, 184745905, 370101536, 111232044, 731913237, 327418669, 505692479, 17738406, 169012813, 336043217, 226301791, 354991406, 554373627, 323847950, 147549234, 695687205, 261288459, 686149176, 576752320, 140888334, 430850957, 336064427, 178004583, 353089267, 672694045, 835651478, 798974659, 700782738, 604672588, 421212326, 744232637, 45872994, 417785202, 253392867, 504509543, 417233325, 49033929, 130869562, 597873758, 112597916, 476351255, 831454010, 547218802, 930147377, 581358219, 122379410, 548883216, 136673010, 642278117, 7856853, 563720654, 811167966, 894067767, 397290819, 601095052, 529899967, 433647111, 360145872, 578757984, 407100945, 980659107, 836114658, 37195838, 397164966, 959674638, 500378369, 223829009, 570290462, 820441405, 786983217, 29613329, 121490136, 675918909, 917510046, 100930079, 717092491, 582832279, 62078710, 829904184, 926382782, 216120298, 190581972, 735054001, 38404246, 70313043, 621146579, 655400875, 456635716, 746526369, 272208445, 428026532, 326162731, 814761482, 83130990, 156670527, 431308843, 126671179, 88631620, 784248304, 256919415, 678988231, 524425595, 968679749, 192108100, 743447103, 980295800, 368435483, 944452820, 458520540, 794109423, 529233851, 739177959, 20744789, 197764481, 488789838, 905358873, 233137711, 559666344, 721099689, 314188369, 51382616, 364350854, 330026001, 329044615, 271556737, 741491880, 805065521, 522431955, 499515166, 985335217, 659398033, 363547173, 980279937, 877529179, 197824983, 813002580, 65249898, 622032113, 489314863, 7958469, 653685919, 366707810, 358420288, 599298364, 491008381, 701381571, 432012200, 99536492, 837095309, 608582567, 294905374, 139002768, 415870347, 903263877, 421238938, 783140693, 942377591, 484194932, 670872793, 62906634, 301408413, 604631758, 228309467, 347071057, 19361262, 375106520, 588232361, 140180051, 279345675, 218988017, 388530451, 84143223, 707041188, 148561109, 642301049, 206304387, 906019931, 435939418, 310999732, 814379751, 46720247, 850418072, 379625525, 500867984, 763398361, 930448830, 156749553, 517208101, 710738380, 806565237, 26398817, 860700904, 262878077, 64051852, 922530304, 833337383, 483037011, 323821876, 516151531, 384955558, 83150463, 926223037, 848008920, 553720163, 129898551, 364268728, 322761561, 84470013, 237938321, 905608585, 721575625, 892184183, 555959854, 256769269, 210595029, 103098795, 484756379, 740348313, 461273340, 57471124, 617652914, 981431200, 172577772, 980481, 682682762, 42944284, 703477701, 809815364, 216511747, 923571603, 556265918, 643737576, 463363980, 237403282, 1732375, 290471906, 425878066, 754837372, 511276572, 482017969, 650118940, 566938784, 418191527, 446689682, 616002644, 545331506, 984843989, 403367215, 903416535, 607437110, 989408065, 538794164, 903846414, 695922947, 170636007, 27547556, 640979355, 940345558, 634631405, 814547996, 520795687, 511460983, 19211770, 391174601, 375803652, 777489171, 803807478, 8695604, 221704581, 13322850, 147498501, 648758494, 640455329, 671323459, 568476210, 889227407, 683372581, 422899914, 3803927, 270060078, 429224806, 374426867, 19382635, 219080806, 782759932, 757628510, 75200634, 110602093, 171039099, 94476846, 650665819, 229696410, 507597585, 837812441, 930993292, 280779312, 1585534, 909683630, 853018211, 203821861, 975094953, 391810594, 499804044, 58085865, 319558251, 359918387, 533883921, 256857731, 667103272, 318358587, 96994671, 713946267, 308758454, 975932600, 74091260, 52639357, 838199638, 200944370, 547147903, 654095209, 189456396, 377079452, 553838485, 629693128, 487707914, 802131112, 716577427, 729621599, 141603446, 480214644, 920253055, 334811941, 334632874, 427576580, 260806491, 591863767, 375958359, 169565363, 832067383, 463085346, 642105449, 893739174, 47525853, 498605395, 706884654, 175076528, 882427824, 15688932, 183368270, 363354867, 969174376, 485363434, 284074052, 686942704, 856273734, 505058488, 538201359, 950965915, 178230728, 79134922, 259124339, 701538094, 351665761, 105996209, 984061129, 723488255, 969850709, 94211820, 288925313, 243279846, 768148809, 36398025, 150983019, 539468810, 304808239, 857477598, 145942526, 688161759, 214248024, 319163565, 873125947, 591986996, 353060929, 395818889, 762200427, 677117948, 119500054, 382186248, 689711204, 486900437, 701044825, 361867486, 988631251, 579491430, 439428386, 281550686, 735243963, 844183007, 890558039, 637493565, 461579984, 409513640, 346911560, 394702277, 958643060, 349400278, 974637542, 287311835, 946973549, 212799839, 754096267, 844488881, 955853714, 109974031, 469725277, 851435631, 809629825, 374636194, 59464084, 120786273, 217170505, 617271935, 322860287, 714549702, 864212256, 287603057, 34546512, 828109929, 783891761, 901434936, 867646751, 929251430, 280200073, 582810034, 664402259, 254470189, 964507460, 167313354, 811189552, 811907141, 688310212, 845973625, 874142107, 673948609, 460739309, 17344205, 6575696, 378722845, 111177037, 754527603, 738653931, 775496516, 36244320, 346521459, 392938782, 944549466, 613834471, 864719399, 892123435, 778682085, 20814157, 641841589, 676393487, 120976255, 428868036, 814141711, 741995156, 729398296, 711756593, 737502591, 572661741, 700706675, 257337589, 334417375, 558853924, 532529339, 415824307, 282364953, 454089465, 795421724, 416173418, 81101293, 865731367, 164724408, 455786833, 300474494, 702631494, 927412277, 132468073, 164485960, 284040592, 526940037, 242621562, 450039254, 947129365, 20884173, 61402751, 976612775, 978755420, 5506871, 399317982, 628892304, 338282857, 145026640, 332917480, 462961144, 758180417, 250059096, 546449024, 364380327, 744174834, 614996660, 842913107, 224520802, 429055869, 236742903, 921365334, 411013023, 675647757, 656303445, 215085861, 82669411, 348609423, 997179115, 339645602, 277423797, 602883958, 544041962, 275600292, 333789303, 110257465, 625066388, 666039484, 564134613, 347618779, 617719354, 808710010, 187543775, 534894515, 841634313, 107270991, 925705266, 569507016, 19706285, 173137297, 383556620, 897475874, 343731526, 88214764, 734956549, 895233007, 730741064, 921315714, 111178365, 72559493, 742099332, 856444833, 632050912, 933517518, 563024433, 46281556, 689366671, 376392690, 688994223, 915705854, 273188880, 547126089, 950267632, 483746604, 383178061, 333773044, 436040783, 97798207, 729601201, 564473992, 490949666, 431494573, 434543650, 744469222, 98011217, 699543921, 180366185, 292944660, 596121331, 88273757, 553250588, 430957479, 235769477, 119348263, 326305903, 346693183, 874113328, 418145199, 603905398, 524978862, 756894742, 160464198, 81670939, 283954653, 429792616, 756611180, 269230570, 282840968, 495781607, 788359758, 750951888, 659339815, 189702246, 336005367, 851364688, 845966357, 456344164, 978029644, 720450894, 927534731, 706140852, 496375233, 179790571, 305935408, 877518049, 541909996, 406171041, 710508759, 926219787, 47558456, 923633652, 680363142, 712113827, 637313611, 92564621, 18232003, 633905296, 273693570, 451543318, 208199496, 32761098, 404221146, 19924950, 122219135, 261765502, 710683210, 214933228, 352654742, 34026560, 582692108, 49632301, 301875019, 418936923, 636292766, 415244274, 865269258, 111676620, 304242569, 943072372, 944029193, 78146266, 653399144, 71849127, 297580668, 532988481, 854451136, 671428982, 487889147, 673062605, 82846252, 766745466, 828303339, 640016904, 935542676, 703844931, 541708403, 67445241, 6274375, 128177695, 367417370, 201581267, 51481967, 425930979, 889751796, 557216188, 598437326, 639254499, 56305406, 164300888, 925450476, 985850700, 351502282, 814337161, 765997642, 858313949, 658453411, 689240969, 273129635, 545702952, 176402583, 415154420, 67278325, 488392019, 475493738, 46192642, 888580522, 755496255, 756823108, 123911491, 757633218, 236929152, 106963112, 728936273, 646601815, 596278221, 24545653, 575309253, 690114396, 525876835, 212323813, 380924811, 673544216, 979981543, 725810031, 408347560, 615675988, 11676696, 526122951, 385574677, 736731996, 523795356, 781712625, 146646715, 831993491, 890806003, 736370206, 644648059, 599395052, 620531832, 228861979, 385515927, 172177909, 170296343, 981526552, 840043260, 378683066, 767329603, 96303443, 173014275, 181262708, 208252587, 58923056, 194452403, 289977139, 837269762, 963225514, 243490605, 858720299, 554684979, 663597534, 461326458, 1152998, 745328619, 999233745, 191913154, 906193889, 226448885, 580119890, 459031700, 308634324, 330509516, 646886828, 898104258, 811749776, 608888164, 878237193, 529088617, 172535858, 666360525, 437763139, 417414931, 82985992, 534961622, 499475799, 794041975, 525623761, 221138049, 659476809, 631787644, 467685431, 444230861, 224737072, 944447782, 572237296, 816978138, 638802394, 829136901, 967253330, 611531291, 13270093, 122628369, 809642622, 935342487, 987695651, 360003161, 95718347, 132159977, 75387354, 987829342, 483643857, 418815576, 656561194, 923594333, 611581911, 536796654, 122474589, 174044726, 869389533, 793562985, 851810536, 882668831, 32692564, 812511440, 443580948, 119062244, 141326384, 854487538, 410251692, 806461648, 921473145, 832255555, 447928457, 861143727, 102425824, 30499828, 832067323, 582243490, 647710501, 311889896, 639199561, 449199697, 235216375, 904300083, 356615571, 223357202, 677153981, 381359918, 396656301, 214641946, 922789022, 256940040, 105739956, 317548798, 320687535, 242033402, 162349764, 371934793, 336094782, 525978918, 734652910, 218778956, 970620003, 424848786, 328035858, 21544050, 403241863, 658966810, 946768441, 591224202, 259208247, 847768083, 830186311, 104147491, 573264539, 73471233, 360513558, 984308283, 582514420, 120700055, 271385248, 305761967, 517490770, 854110738, 736963032, 856757988, 998365612, 972661550, 332290228, 475811652, 398956280, 873625305, 477681575, 704071366, 903818642, 856940152, 111880387, 166589346, 406717565, 389059694, 115168749, 520756774, 786892549, 40961256, 183554606, 953218454, 897635298, 271294237, 181725440, 233615678, 668817159, 24738158, 954738887, 121613834, 833621397, 960545823, 244057834, 558523745, 349009212, 81033247, 721764052, 798574646, 530768903, 915342264, 380677898, 903803167, 151655018, 356612021, 413341495, 67381149, 1033957, 346762135, 191515683, 366403817, 268452926, 4884722, 844387383, 506989501, 634804504, 949660238, 212115454, 124086735, 989474406, 956594777, 886433016, 558023081, 183980867, 435578667, 237783502, 369453535, 822027509, 241846707, 727659733, 182299674, 886795680, 277841604, 270712211, 885762280, 12193613, 301525937, 492128497, 667199437, 647067128, 840030202, 118391532, 441052503, 174104565, 37663741, 659566427, 789277211, 15470410, 106867232, 22474221, 407076312, 940317765, 334437415, 737144955, 791590387, 806413377, 248311238, 937649009, 391451960, 246107734, 187122682, 999147805, 254500004, 330451017, 755512437, 334246314, 318611010, 951353765, 314456018, 341091941, 864463937, 150872418, 862435339, 765427079, 62688953, 747873737, 178935098, 599766878, 799049398, 886273108, 312531931, 767816623, 185035706, 596280351, 21026704, 478075459, 473427555, 892753637, 836053298, 155790494, 387697187, 14960617, 265901050, 694169227, 475976262, 753981016, 281233932, 211618298, 190736863, 928721584, 73612048, 464580731, 917464050, 560970843, 224331154, 918441023, 58770287, 54759693, 325052281, 82813945, 50220191, 353252868, 32951773, 472702110, 237271651, 808433962, 365878754, 259692341, 580326766, 627520959, 478547800, 560335939, 445328981, 211652093, 648100026, 621877471, 466066471, 834957213, 33988263, 618836453, 983132013, 705179847, 717385819, 835985953, 660864700, 188303196, 226981740, 222394738, 651930228, 214695908, 921670189, 618423605, 738882421, 472188369, 615345847, 461514039, 772088546, 550325303, 19606697, 126184823, 54240027, 272975175, 174803986, 318349775, 769239072, 756227947, 388387752, 796334473, 422990376, 359970351, 428042813, 269531787, 471947809, 697904572, 296178421, 973707732, 194476208, 107266154, 170921852, 933830060, 38485085, 810259508, 34843158, 929396899, 274801201, 49951300, 538045429, 149513349, 170319394, 911796629, 538317289, 698334830, 728749442, 79866299, 738732849, 766874692, 668137856, 787985931, 664331017, 186710583, 316987826, 819788123, 408509357, 497263981, 795284805, 739884678, 770156657, 696215201, 649359813, 327732123, 890734154, 848238850, 705051339, 325591218, 453871135, 583070583, 595359123, 115887051, 415075172, 135862231, 105256329, 917953244, 293307147, 474510710, 55119362, 92886872, 649956893, 812668244, 231300291, 377152038, 992561733, 43230094, 922094896, 31519937, 920371254, 286426450, 47211657, 658379215, 231661445, 341810122, 644910295, 472929234, 732039279, 74132705, 749595255, 480366298, 168764294, 750970921, 600988104, 407131357, 2513578, 442399526, 31939916, 286853973, 86254206, 378691584, 761042417, 458200936, 330671736, 9198601, 651970311, 152864255, 573246562, 386742456, 865714798, 785768614, 836854784, 881899332, 671797299, 367819839, 352691670, 512149851, 65622617, 438910349, 968506611, 927424410, 541046545, 79591601, 938263743, 117727721, 738664278, 29184421, 360630175, 886537952, 995980888, 4768820, 221237996, 640995304, 671244964, 773405898, 210225482, 527327825, 331005093, 236321877, 8918836, 405855409, 903397452, 774531050, 239603316, 152763381, 533327529, 258339144, 314301022, 72364786, 223252590, 82174034, 754218827, 666477669, 372148215, 615209618, 799274040, 389013447, 392233088, 993337599, 557474462, 987151887, 468973936, 217399969, 198844947, 375870158, 791688915, 481420750, 419481577, 427680383, 397020188, 131666438, 912395546, 962007786, 606410116, 419666172, 718736074, 611257923, 701326380, 883674566, 671187624, 86555690, 948726772, 728524724, 772554641, 502886880, 484753170, 628768758, 158764517, 886179692, 870802170, 855629972, 260744142, 531463462, 64358595, 127818171, 29928061, 882991808, 576314634, 448385079, 298602344, 770574354, 462427186, 278339125, 931050182, 218364460, 838243951, 552576193, 542401480, 430387123, 411237123, 823440141, 215932244, 700092406, 78354932, 87294130, 398155154, 495291425, 258389488, 567091503, 222574336, 647610077, 380840754, 695439044, 502414576, 792007160, 994742611, 393113076, 210871856, 601869358, 854060409, 927218705, 686219292, 487458909, 480334965, 556425232, 860507064, 697609953, 229068654, 478905134, 426129563, 751304066, 538699756, 444566400, 631331651, 38914770, 179186108, 4352548, 414409293, 777440648, 44726255, 110797737, 816666455, 731022281, 323167120, 284406999, 56960034, 707112757, 605601587, 727417604, 908555588, 635662018, 714493017, 501782508, 53025254, 26609155, 577758599, 645705259, 477637743, 933366894, 247258240, 231569181, 340669168, 563981862, 658479295, 464022885, 25502618, 913875901, 392997280, 827938619, 115792997, 368540286, 332440439, 439025316, 388639019, 194940664, 893283210, 926660907, 677782399, 119828872, 316289007, 336991490, 364333234, 519696095, 473507505, 332024251, 116835416, 49545447, 837937011, 290714801, 157995574, 350171910, 348150124, 712940527, 332839815, 778556802, 10881088, 987617476, 859822886, 690987016, 546817593, 625922202, 440776972, 736051262, 861952334, 710880749, 620404036, 702068391, 44451883, 672945711, 165627459, 716351732, 687207910, 359674583, 60845305, 223463333, 313408815, 295919816, 26799365, 256827322, 486735068, 604666824, 774364709, 748060905, 476898103, 912674170, 826767855, 718644131, 583042427, 303518499, 333567212, 69059765, 728851901, 56249891, 809853275, 837393145, 509341625, 563017024, 988270551, 463583412, 187319591, 945028508, 793568398, 349354653, 86092932, 782738030, 684502081, 661225790, 448702726, 230211405, 926532718, 851413339, 989025190, 98429530, 749303279, 670644726, 868353640, 927194921, 530177171, 904486437, 61603669, 991298169, 476234007, 170796634, 28652740, 35515690, 986346584, 90443209, 258653107, 778296659, 805613248, 859124896, 914174689, 624842814, 862831799, 417931361, 891070585, 690205311, 474274795, 7879179, 250447795, 814039938, 294679218, 265567831, 760929613, 796901618, 55909736, 239305940, 947876186, 69935138, 18741444, 572131773, 347373128, 936575590, 652527284, 102146357, 617675819, 131745191, 79601855, 318114403, 213067283, 623520498, 87275758, 747981978, 575152352, 411984677, 145800550, 110600719, 236269648, 652031903, 809310535, 215367223, 52957641, 354776285, 49998167, 961639741, 900350715, 14593872, 174931106, 945714545, 219283918, 639417376, 888732663, 307153068, 692058108, 476589862, 155410085, 25371228, 585648313, 280576980, 204383169, 674986969, 755249450, 507374275, 916568479, 801794473, 228581316, 445747889, 87289970, 117279988, 331423695, 858541632, 838597961, 305902769, 379949374, 130005245, 945630257, 726517116, 4539903, 445093153, 369567397, 283622115, 813386230, 518989431, 207092128, 355654976, 554513921, 555851364, 550960221, 852502428, 981434598, 611040903, 378304556, 418055209, 438815350, 806228600, 24157298, 115604930, 209968548, 120091427, 431872205, 969817827, 984662321, 753974152, 165095434, 619335536, 460300723, 771076727, 641292104, 560766809, 389437091, 18511480, 497856631, 105292398, 115520317, 282052356, 397246275, 221201717, 405037106, 507393988, 708172144, 286947212, 255524263, 403817139, 438788030, 258563547, 756679258, 538030698, 63344284, 582942760, 336634068, 183462454, 375891240, 337472233, 872898517, 403906637, 346730474, 245122971, 313788443, 619356696, 683161326, 236334343, 446387207, 807564855, 991367963, 847872981, 269895119, 594678325, 126974426, 442088989, 607145124, 188192529, 616709387, 457067888, 193388210, 547744462, 527135422, 252256797, 318851751, 881542066, 867869323, 376128205, 506888329, 443271092, 738708729, 824515794, 359201686, 877072243, 220483290, 753212022, 99569939, 107603633, 386893632, 834566993, 20693311, 488743174, 533836635, 773122283, 776609254, 466750567, 632117748, 2506525, 660614843, 631275828, 697697570, 742420988, 281573382, 31182869, 801073533, 361969976, 645011307, 608760249, 970574544, 184542235, 856895142, 934928159, 549230766, 432563428, 189913488, 777112359, 568384852, 623386533, 112383329, 947731632, 163679221, 380633886, 617101209, 803142360, 845189017, 445888873, 185320787, 830555118, 29630197, 611071797, 382074060, 388640214, 844818855, 171816557, 190214400, 656538003, 227477082, 332812805, 791147195, 741839391, 531204856, 77365984, 52517009, 64768413, 858480243, 359396963, 518306963, 160338866, 182621428, 969645530, 934070455, 531968360, 378641461, 430357535, 210933283, 291219225, 685035670, 408557041, 281769367, 178486731, 212496498, 896416490, 471425064, 481430584, 282664527, 440725550, 21846366, 997377593, 803434581, 204298595, 838865792, 356820791, 292598886, 12943471, 440236159, 318402304, 158449331, 399626579, 628514714, 123042122, 822476232, 452768530, 835010566, 364600921, 960883317, 391071803, 912910455, 478741966, 595927898, 621544147, 952782963, 193914909, 696911741, 812785266, 297073936, 204068904, 296344709, 844908058, 766398428, 182988466, 44697681, 539016136, 858620338, 257957208, 940152653, 182680536, 652317326, 629654744, 15631294, 376320824, 938117897, 897500859, 79547576, 826846547, 786017201, 950639540, 338455741, 159119327, 773124249, 537495166, 629412949, 91456064, 937019142, 831364117, 555459812, 643981263, 540690347, 708797966, 301638164, 89383393, 141772331, 415822890, 332698590, 110897701, 704196741, 316069408, 92501884, 860828255, 316189606, 121459181, 775781658, 197063733, 544336510, 761292099, 573558939, 808756324, 285200863, 162636338, 273629757, 673875463, 299196394, 862562172, 914825188, 723986452, 187527831, 220215667, 908273505, 58281450, 527196947, 168242045, 450634176, 20004315, 276585828, 181786868, 848884685, 61069974, 58485771, 89458185, 208521881, 698099418, 80318807, 729193061, 835664872, 702600956, 937377835, 239435173, 621892398, 849574, 360918605, 707995282, 271513797, 320879897, 217222378, 279401989, 528637807, 53715694, 895454411, 932431264, 430307083, 376702107, 229843394, 746417049, 195707695, 692914068, 57367187, 59421076, 961345555, 714914545, 788091277, 544547726, 419710353, 60964772, 60769329, 906287131, 675560390, 252575500, 816143797, 654288369, 161087184, 837746237, 139483749, 614095081, 692566670, 30408307, 761850043, 107801207, 155508896, 190557481, 411733808, 818475109, 840391053, 763413280, 957611228, 41055070, 631919214, 858244622, 259890780, 577561511, 611724893, 274626190, 935218731, 50090103, 398017604, 131387040, 471578965, 272924123, 575329314, 293670470, 976122470, 835428383, 354370704, 643891635, 580026282, 42112560, 185188150, 787033367, 787600901, 92031923, 405386231, 600396182, 3998782, 882186014, 128847843, 275150830, 147826048, 534579613, 391895994, 716675846, 686232271, 95191376, 146923599, 980781430, 3471680, 579977669, 945870079, 357756265, 386277833, 359126499, 905390372, 831808708, 757117539, 61936958, 10024918, 263324015, 293549819, 376030320, 37602865, 359471880, 631305356, 356355985, 94083662, 780310608, 731451535, 906683285, 124482005, 512560846, 567034510, 835497724, 354068559, 914395194, 618199709, 632128798, 754010695, 768683793, 590555423, 416393034, 555324763, 43919773, 668876104, 426406303, 921712189, 534442617, 539694019, 667632925, 66515768, 860848090, 903268094, 977336477, 37968816, 457677811, 588353721, 584988005, 759726518, 411980907, 60536805, 323532778, 961861339, 184401918, 812982520, 330392522, 66109428, 792859853, 358182057, 236255668, 861600932, 701641297, 180113837, 806072080, 545253491, 270557765, 438477211, 121433879, 600682348, 644425537, 434536444, 239184093, 898406069, 382989884, 158721717, 990787364, 652243911, 667329680, 797169911, 764733660, 801136695, 57909988, 952859350, 921129670, 898950421, 714104646, 2640913, 598998101, 211496875, 116138463, 517345267, 854621696, 380387031, 116368949, 20216103, 873080256, 288415128, 537338446, 68080866, 498427378, 242594399, 435813567, 882084746, 19587768, 951905668, 845394517, 85667517, 854617709, 3047461, 377031233, 678201149, 437937261, 687882541, 344598552, 577603224, 708061632, 177513493, 688296481, 9169305, 209665191, 899230454, 837452571, 673202518, 303293249, 16978184, 825033186, 4851820, 136672116, 524807304, 68365192, 150275491, 852578448, 591929724, 355821321, 751361836, 256538104, 467756062, 333270446, 291338583, 665443245, 678089993, 748003590, 966973712, 375139007, 403798047, 76175392, 874664139, 918099543, 729762791, 704292507, 558662606, 276945401, 580765445, 521483653, 599302973, 77818319, 936672307, 672036953, 345998460, 223673681, 422753197, 455755029, 233947774, 453363234, 81827899, 193660950, 880748885, 309219296, 530688684, 835968280, 223832008, 990181088, 650927039, 752837502, 26419188, 280320757, 959355874, 491178802, 734021025, 219568161, 5189911, 353881272, 362571220, 532273943, 237492835, 16087135, 589503971, 440147191, 5139141, 76446, 474760293, 616987263, 232692290, 300788126, 976608563, 645825943, 260315384, 263325055, 767445100, 192811995, 375650732, 85608915, 948248212, 220559444, 546526343, 369806816, 683878468, 475910640, 619711777, 6755402, 362311631, 223169442, 391866908, 930367746, 344368653, 335166137, 23970470, 906050876, 316755998, 41819030, 238376451, 447698440, 544132359, 132768236, 620349178, 957444252, 884145212, 886250607, 248090087, 4062680, 898552169, 912731992, 247320597, 522690006, 303106151, 322167079, 556107758, 986315397, 844742047, 278254189, 912265658, 416977458, 267110719, 420686369, 917706023, 548209147, 891688272, 64148495, 263505499, 448712949, 469446360, 978115819, 570236802, 322181104, 219201549, 53758047, 904380230, 473245242, 870540503, 105825576, 655622339, 359216828, 559954750, 637039808, 766338171, 776716489, 445218455, 852280842, 260535859, 546796101, 536507799, 776638496, 560488906, 268057478, 507068448, 987837360, 35674118, 42503342, 824724072, 62063761, 477887289, 855495415, 780665584, 925892945, 419595035, 896113881, 86235875, 232991202, 933122839, 767383257, 886205724, 858499064, 528744565, 359095825, 428431546, 592888987, 748066172, 611133416, 420717781, 333652936, 68919790, 509912925, 592680335, 268842726, 147499405, 6272153, 639916495, 146252002, 662948453, 69693091, 48980497, 501094835, 373382417, 619586878, 628391865, 2129835, 548568033, 866720694, 142168509, 79312143, 939501700, 627942489, 544063101, 166245963, 429234544, 818348409, 994921724, 75992914, 74641750, 884195485, 294385418, 18936486, 577310146, 737106328, 551751150, 844432678, 994204355, 900797318, 986705925, 679882751, 957623247, 263980816, 81592194, 894490731, 294477020, 884622826, 397734693, 801157249, 878763207, 426003886, 723405504, 32518801, 281205162, 783462022, 88980886, 816924984, 622770867, 305074652, 928700491, 900516899, 882699108, 495826282, 576560259, 82807132, 88386994, 269955574, 508195515, 813546059, 445388541, 760670023, 345184656, 254587088, 206036512, 403066371, 934707950, 611049549, 60065573, 561662499, 177086131, 507734908, 397391594, 874307829, 414246178, 587461843, 935878482, 394843426, 118264359, 299400991, 601546965, 330405718, 257133164, 903892784, 555347699, 901430752, 403354957, 398499124, 411858794, 528576813, 313032211, 191077565, 202270657, 186569945, 859731647, 425707766, 372697884, 398675391, 251523303, 445194443, 702553175, 451639332, 651064685, 518638902, 79791977, 924963048, 636775652, 310262293, 245937896, 983186343, 76090973, 604210129, 794247884, 166336480, 118018856, 602993173, 344261812, 237582087, 783774456, 310896406, 131599067, 594506680, 163880805, 87503825, 269756580, 694164078, 565990187, 576671592, 450417582, 498520076, 992134980, 604328582, 237646019, 560228881, 168229497, 180702781, 705277692, 725850809, 389769915, 848541902, 451837680, 85622144, 449495012, 8871342, 132374438, 890631570, 877775072, 276418293, 19933933, 572371108, 543019561, 781284072, 575752076, 691920416, 437290019, 850150498, 640519188, 328186793, 626961506, 729992936, 423944056, 658250543, 861433060, 750708278, 541138834, 585186786, 70752085, 245973659, 434189469, 35256203, 544948387, 269582055, 445103479, 235684209, 907036977, 464962000, 588911711, 897505911, 132326464, 49746638, 51988748, 394646130, 305432558, 63962276, 374843689, 43431281, 169112489, 580388283, 824832230, 365212138, 632222540, 891755702, 109193170, 651359286, 244283166, 904748031, 567265844, 243179755, 112233227, 479701367, 379469593, 311018045, 816296020, 545906443, 771782766, 270767745, 920445982, 31888031, 387477298, 120621061, 609700093, 227800837, 952129970, 482135753, 782128964, 591177993, 882335560, 671805461, 125228353, 686532397, 565950842, 466632395, 948610609, 455348305, 791074590, 115374190, 543361481, 238900055, 71490140, 950865448, 253155697, 931087775, 748731709, 581648952, 263763258, 546112399, 183602469, 544963469, 580382641, 766765998, 803610584, 59120349, 586620177, 44027581, 849312573, 177527960, 383314348, 737981569, 728032461, 481587359, 898527886, 590290511, 673082335, 437661906, 362326655, 287688759, 953631363, 696993353, 833698246, 169120441, 853570563, 942693635, 695809388, 653483449, 277598952, 301826918, 250583491, 60819940, 214429031, 15751308, 782484405, 755366551, 119184484, 465226192, 856077894, 234418167, 355632080, 687478101, 613001497, 513088718, 426365335, 676582356, 911517532, 296369172, 250067943, 142017014, 608950569, 299239790, 214919145, 363731213, 546291041, 726331163, 726075232, 712500669, 945219362, 138058227, 29259580, 658937049, 793068285, 424379057, 633707941, 625426676, 855770387, 455075354, 516608976, 826929438, 976909128, 743798661, 338713763, 917195431, 593933122, 739966877, 197508732, 946306336, 133306810, 743063234, 932343386, 428280919, 849191726, 588163502, 800244736, 707418901, 358132979, 783621627, 626709228, 868397835, 620912529, 396790427, 354747612, 504891899, 850957309, 537888755, 668582409, 107512208, 682068549, 733335916, 304023721, 527760999, 816479950, 788465066, 397075861, 693352547, 269648430, 356735643, 293443663, 41396542, 891005022, 90953760, 509746007, 964587540, 998534023, 577503376, 764003352, 49554191, 828930058, 250169413, 684673851, 591832641, 851556441, 458492376, 406651687, 988553715, 237938332, 188978572, 612049663, 19289823, 723831463, 717959854, 693167146, 112068326, 12333750, 665656779, 486446751, 970344400, 263133374, 579878513, 764224798, 873789172, 270621340, 752238607, 935226916, 548388441, 66390085, 178576817, 955679726, 530421706, 380283806, 245605420, 393411247, 231217861, 390684144, 740380235, 654680135, 596157511, 157414696, 27660187, 626407989, 607482713, 863843164, 258687799, 46718773, 149888668, 519235784, 830213807, 309318448, 70639454, 618969432, 944929331, 541003610, 264035963, 690509569, 212176752, 63986894, 156277119, 974500742, 981951916, 838623452, 208355834, 976242776, 378960861, 250680031, 386023493, 249009334, 979831680, 787658634, 291868069, 150607692, 562730344, 115824369, 709644423, 528304821, 462637736, 825958285, 750758732, 2694931, 148147192, 969077209, 276152681, 533191994, 864563605, 272369737, 970963201, 619174743, 645366719, 914603531, 825432838, 10247780, 815594617, 204106961, 763771107, 733293774, 592721365, 332800103, 477598322, 536121126, 760418982, 736866714, 387761762, 874420506, 649839278, 287849616, 901067411, 105966597, 422442081, 410216444, 147297630, 96502732, 859704765, 295783566, 804886270, 338681132, 200454515, 745229304, 334372341, 355448617, 96647957, 509705683, 572430512, 695635176, 423483412, 237927930, 26311799, 160668514, 762729406, 153989740, 498954283, 51931238, 541948069, 371886205, 807744819, 442990643, 307639964, 820405898, 686047708, 758497593, 140175660, 853971570, 529921527, 984106408, 190962330, 422706512, 677843393, 405179032, 116994831, 952324847, 800889325, 512602550, 584814468, 401871340, 88316549, 321422526, 988715374, 626080409, 500256983, 539015369, 502245350, 831143509, 788284149, 926778107, 525323047, 692651652, 93655458, 299330902, 185922571, 486216531, 46093626, 804028345, 803449016, 836853984, 729031662, 334373739, 595209105, 66437099, 607400076, 850349211, 76438569, 210579763, 539470621, 582498531, 347116398, 674602652, 880194791, 967382016, 222064551, 902662178, 726507403, 271794837, 731116025, 234825311, 830144145, 680284345, 136850070, 101394724, 945565249, 332439607, 332021960, 252949662, 286664524, 788633948, 106949419, 200554696, 769458928, 974265087, 987669590, 379578442, 484706426, 591072785, 8028530, 175890763, 107682925, 382524502, 468274771, 308140841, 937326063, 881788408, 562807080, 171381240, 54170667, 224641120, 827060859, 133029670, 845901603, 370345639, 14670630, 557902605, 951599496, 551124702, 485425317, 592177734, 165524407, 854554493, 112260226, 391728277, 94722009, 464218421, 190274530, 671501402, 930481585, 989951574, 96814518, 947138521, 187873337, 116313281, 455568483, 674391463, 819122186, 400325177, 693361549, 635948062, 799949240, 659608964, 632675615, 483359312, 294495003, 116398468, 459356968, 265259060, 645911720, 605447412, 782257378, 575609946, 697851505, 941725419, 286168564, 643169663, 574036604, 396745236, 222994092, 295894185, 596365341, 954423287, 427324827, 391451652, 400308533, 436972764, 603152383, 519584161, 560244734, 947127698, 769910787, 330348393, 731522757, 603407723, 132365111, 976145822, 852788863, 27110832, 410709303, 784966561, 383030545, 676223305, 222040514, 384200088, 729807150, 613547883, 841177807, 201988532, 817565697, 496603517, 268063255, 127433255, 476026039, 522928644, 947503429, 474678727, 417580009, 861818461, 751948792, 235420198, 752680523, 335040456, 675392440, 850670845, 615347156, 919428244, 272315331, 729055048, 444777693, 115083211, 798560469, 451603759, 524101772, 911664431, 678938556, 682807618, 3012685, 270122575, 540826195, 851898436, 20649528, 670963749, 891373126, 336514940, 243662001, 878032750, 25025681, 4521404, 421796331, 344408480, 960094305, 384986539, 891627681, 905280619, 61753272, 295232739, 396395651, 302443849, 734443986, 331074745, 737859230, 343917583, 609710844, 350450536, 970220095, 400425567, 304710304, 985366974, 134043914, 838225554, 941251089, 699020688, 536771798, 790335692, 552117434, 153359259, 793895842, 902951391, 287065277, 933373880, 663340014, 525091084, 519936513, 35390677, 538084037, 503813360, 853204551, 627804544, 295979308, 988739125, 158438953, 263050147, 979253605, 692878265, 996836195, 646786657, 790743875, 848856215, 705324439, 604909599, 350781336, 763669332, 975826564, 862433584, 488032792, 357615540, 753705293, 875582654, 929230844, 541983491, 453947220, 426083435, 886845428, 561247483, 137768627, 978928000, 183761162, 934030599, 911719131, 878436922, 328308407, 21669424, 709034151, 425372235, 569833717, 253661259, 665368379, 662889362, 196579139, 849178709, 201573454, 753176850, 814256794, 419126237, 280342715, 702849787, 258048660, 281390642, 706748926, 864418860, 959994492, 389789204, 948206028, 221967574, 830139266, 219797332, 223393969, 583915547, 800193181, 947176977, 16041222, 448062544, 168538486, 668693764, 480545845, 497016621, 506563192, 715212881, 994886808, 955387366, 291728021, 918565482, 385014370, 435955051, 734206044, 690405511, 814521875, 81332077, 622721526, 863284703, 748958194, 954148464, 382121985, 599975421, 803803794, 431152719, 678153977, 545742014, 755190510, 293292047, 609114922, 185727752, 663095919, 218208609, 485745825, 684543890, 596359392, 590341006, 841022167, 382212649, 148973440, 655272539, 618709148, 790049306, 312607920, 43253531, 457041021, 141655409, 466887381, 385633924, 879006409, 5006651, 209523121, 833036556, 751247155, 676058760, 116489888, 62226789, 694205760, 937815446, 980935868, 229968017, 237382977, 670176284, 573556941, 772652086, 130146724, 703926776, 691920551, 371664876, 771919456, 228526151, 587727093, 282525918, 45222259, 57010442, 785745089, 826408858, 468973534, 272824182, 371865799, 527499111, 993427152, 83869014, 84763749, 140544308, 991902597, 845649378, 349584281, 674130938, 99511147, 100515585, 858020657, 237914976, 748381342, 895083485, 469039686, 733551374, 14216169, 660887951, 409006810, 663048273, 994622076, 12500690, 982146303, 608707854, 908324746, 828481978, 692016623, 676916774, 160336193, 531023613, 995515245, 41476058, 337892076, 788297152, 145312984, 649972381, 241172545, 304826045, 673348075, 831513067, 956574432, 27165147, 760012405, 248863613, 650234539, 265478744, 925706144, 513153001, 471779354, 175441617, 383232789, 92092471, 527646452, 712711689, 377346656, 152884588, 243858285, 857403603, 143725310, 168504688, 398011630, 912663308, 748362631, 62662661, 540158127, 810198188, 673614332, 600329602, 371868351, 881407399, 144426284, 577073215, 135746591, 856147722, 144264478, 49705147, 515855754, 572389450, 83183573, 328933274, 334225100, 848619219, 957126345, 236794502, 754344986, 803550641, 602666621, 611522061, 657572808, 987101997, 325972499, 92209719, 53927068, 554656876, 488748394, 860079550, 273315639, 723301414, 208550281, 711592593, 735732929, 826899454, 441161154, 632897501, 57146582, 876400378, 209598988, 440920283, 6417327, 617144185, 29058144, 584964504, 801791852, 675043035, 703141401, 982375200, 799185020, 373985952, 764895746, 338153302, 771503803, 443614748, 764986394, 64056244, 767738269, 178028641, 464984091, 990411181, 414846140, 706738916, 40190964, 494527829, 497900745, 704682051, 577050844, 620284734, 120364357, 917997320, 525476335, 613122761, 508218475, 334257140, 708081645, 964844460, 426585798, 495602331, 976145072, 901075050, 733738136, 238985449, 595324954, 673084320, 626785076, 384625814, 446893284, 891518681, 936154889, 225868598, 776802403, 168468043, 350793620, 597734911, 319822571, 896389733, 253217569, 92339296, 87073446, 883196336, 179056197, 231722920, 172290495, 742682165, 95155312, 383745273, 814260047, 45172181, 888610922, 36398323, 82827143, 448918279, 209493439, 569553459, 243848805, 570677107, 914617757, 536649508, 707119175, 342298291, 793135814, 212748695, 289257464, 533740498, 508765963, 540167436, 401847053, 42517917, 448286155, 70507911, 69514179, 605537734, 141664966, 83591296, 973663089, 172018654, 571948431, 473052177, 447122249, 739755072, 581389001, 604538162, 982530359, 200848888, 283679120, 265918025, 816443090, 750873034, 375389752, 391308459, 542054674, 9736139, 40889556, 256676732, 144450130, 138364554, 587100792, 437849161, 372812683, 615074465, 196172265, 797080391, 34637552, 631674030, 838253400, 659406564, 919932399, 313269776, 519738324, 158878494, 977130207, 405583851, 165001999, 4305203, 563084697, 474584477, 577608709, 743643513, 296169935, 868331427, 995905336, 451217775, 24530834, 638003591, 356272770, 759892037, 46571750, 151684878, 84501094, 340876060, 399397760, 520305107, 972368102, 637619534, 439638910, 474606562, 634728449, 972813137, 555631961, 142032722, 555073635, 646807018, 671529218, 297490736, 886570635, 995514571, 674184485, 875486038, 774866670, 494740126, 255928358, 788397513, 866006729, 592639439, 730545298, 848248564, 278248976, 692054310, 215174639, 132839506, 101350574, 580156829, 859795827, 295545371, 594785798, 366321473, 490460395, 60388957, 339503853, 384162736, 188636543, 484533875, 181253339, 133371378, 491223789, 101009326, 170947042, 134789863, 843072574, 110644943, 797666729, 75523216, 178374585, 431933753, 654147923, 458135114, 497411295, 972250072, 106051824, 641236823, 107775287, 419691708, 31370523, 882887064, 836225647, 498142898, 187310292, 522572373, 421301538, 507322167, 61518669, 139322471, 731077474, 319422219, 152255620, 501962862, 178964093, 245241389, 733435395, 434661795, 40489839, 398408962, 172978791, 881364580, 859340160, 118094396, 954370637, 935297210, 8330641, 508629017, 408767005, 90669142, 151263665, 757945682, 451319583, 750648362, 338716609, 53757371, 698274523, 21826343, 20390078, 852872855, 533454017, 23218417, 585843671, 768300248, 63839520, 679295845, 626954228, 246583589, 819697500, 265929374, 204835963, 194403392, 596739914, 623875629, 902948558, 167327712, 186714740, 492924207, 431589813, 503228276, 148175028, 302335880, 845189758, 542587504, 162212215, 277006158, 848379909, 375079907, 173258988, 42714325, 39099382, 635911186, 34064373, 856196469, 112550438, 689856643, 191134563, 777365947, 47022493, 832627971, 364611457, 297187122, 696683506, 443434144, 890044168, 739291954, 679180294, 51995494, 404035153, 750434696, 941489481, 147855595, 108924593, 736868925, 39849295, 280005122, 25509818, 5022468, 730741466, 438849855, 344779638, 850526840, 711490370, 556280884, 113435163, 978660349, 928697874, 386609557, 61101828, 452502620, 145169454, 121002327, 199420982, 263636912, 377411784, 978313970, 656663873, 463343633, 598045545, 932076884, 512248395, 291722610, 727566466, 376099320, 314318664, 85604978, 624061763, 752148170, 527701570, 804453778, 303974923, 35006093, 142377112, 392257107, 187630346, 839269762, 568468641, 2732483, 857320179, 664737523, 654359558, 711631866, 6445117, 782982467, 703843671, 660148572, 66784311, 504302707, 86730908, 621227110, 450488784, 71128860, 785385395, 557603092, 959416799, 39948424, 847006005, 573815887, 43311857, 523792936, 503315720, 650690027, 905498566, 45400685, 91960935, 39839498, 89572752, 213947470, 598359973, 670583907, 917651274, 886456731, 827490673, 337555400, 398295662, 729263627, 29715483, 359728781, 247262916, 294978456, 132014172, 615291965, 574719089, 60842766, 263858030, 395054448, 475199743, 937943330, 635077631, 144983845, 73003895, 61301639, 811346098, 990701912, 242546370, 432385100, 661254464, 993615344, 797740280, 635349315, 433638824, 404241937, 461342592, 911875488, 409526414, 902588406, 521193361, 648382456, 157178841, 702478530, 391341405, 92060945, 225918851, 241201872, 287312837, 672967868, 976200740, 991486725, 737105022, 861674154, 971446948, 170344114, 308005293, 6268706, 264055462, 501598617, 980463585, 946802401, 761814037, 873043248, 415502554, 254405268, 801107769, 701392118, 21164551, 654766821, 87786759, 778136811, 927336903, 269465185, 222110870, 182379630, 474036064, 224480883, 99089163, 482908529, 626740805, 49638241, 793008938, 862481606, 733216241, 830649541, 682675381, 830647137, 401829125, 886235714, 204424024, 869715275, 521466653, 334603846, 866212237, 643588410, 563685492, 620623848, 457194473, 610955311, 17608331, 266909781, 140111254, 920662135, 928517524, 295110513, 189495287, 809032008, 593452003, 377768328, 524880987, 949831691, 441397795, 307513298, 589262440, 886416330, 945836290, 518065026, 813156194, 549044738, 283768161, 451328527, 814475829, 786344741, 96738056, 674605887, 466042145, 392546168, 554251693, 409849210, 699575862, 915067003, 350692869, 9509313, 591842927, 490762653, 443881815, 175217655, 169278141, 132483545, 275854243, 955430593, 347757487, 623876748, 382410367, 379866364, 423824893, 766735950, 304246182, 842562966, 990615456, 420878184, 935307247, 408433569, 811034059, 463083985, 204909571, 261237053, 896727201, 438680638, 78777605, 573075627, 443376638, 862742020, 737626856, 707905033, 992469537, 49448517, 823134226, 43528700, 822726044, 96503097, 40378780, 218670636, 935087337, 317121429, 348897656, 665113137, 727844471, 381778400, 100252916, 182847809, 84431129, 82867551, 356364338, 405531485, 82215784, 960613508, 469625230, 256060342, 803861660, 52173079, 709402072, 599224927, 52770981, 321236592, 892308599, 309061585, 260081691, 199009285, 93889466, 426383475, 689908533, 905651418, 154694499, 864456842, 552973295, 389370272, 333941377, 226949361, 204773943, 668118273, 187218091, 60527683, 77482892, 811645783, 687708481, 12914705, 256865040, 820411893, 125206166, 894883932, 133009356, 306234130, 940191466, 549712179, 913988798, 755886466, 484519076, 342002862, 350485576, 573419952, 552988977, 717150797, 399600407, 673879183, 195403625, 464734314, 896353077, 647198929, 699471800, 260649503, 933164347, 804956864, 916552020, 490455807, 560578883, 786584816, 33159195, 769651323, 377492981, 148572532, 304753469, 242203226, 645180290, 761026623, 920777582, 371730223, 602737969, 73165974, 855390109, 192623255, 144302917, 419208321, 975802842, 21440894, 479744198, 812128156, 317267149, 844453883, 850757402, 786122765, 685042596, 283654118, 850196535, 174027102, 775584825, 595178650, 92217578, 735983351, 966409361, 560864970, 970130267, 128785680, 883412027, 380814505, 795837192, 557746764, 951859748, 80054023, 477663051, 273706108, 10061774, 105048344, 250193071, 612258275, 354667609, 308158873, 681244491, 845058224, 648357631, 868049727, 655820228, 559138976, 19030765, 894252116, 139061728, 430774095, 132894651, 66888915, 574842819, 769826312, 857901434, 193524931, 603078250, 482174265, 691974982, 848590841, 544982141, 902550139, 286318702, 671485779, 793369065, 194066117, 582847289, 632614549, 975744545, 371015512, 65557915, 839996732, 527563790, 397809138, 545166283, 286871910, 614485610, 414220019, 638571611, 676463978, 104507271, 404266615, 563984842, 92373741, 443660026, 782021062, 740984511, 425208144, 132137898, 920314680, 207812239, 231709949, 630650854, 883027319, 301415119, 636372389, 904746010, 628918823, 597901806, 542240509, 148602930, 301521930, 938845736, 147558761, 125010176, 434865768, 893017002, 176337292, 159803835, 221593103, 614271272, 458973493, 251724221, 241794054, 171498401, 387691713, 646825575, 590832065, 522924636, 955870620, 217606630, 934459132, 246635166, 587967343, 918084339, 499312715, 519785369, 905196335, 454352799, 756354124, 978529303, 116140730, 340328435, 652521384, 473595741, 616462749, 613725383, 65208846, 995972840, 239083313, 456178189, 77812728, 388663976, 86468800, 12846974, 855975377, 747151573, 264042595, 344011976, 587691331, 849724955, 455285195, 629496876, 457795934, 690120475, 315251013, 36225058, 599349420, 530311021, 841562363, 703644912, 718551986, 148456834, 422413765, 78058721, 841855198, 721324184, 754150913, 721302454, 195458972, 151601647, 627558977, 91647346, 667557836, 240075416, 615608132, 502577048, 808882450, 94564416, 493028038, 404974931, 968860292, 94607542, 677418966, 749979281, 627191436, 694455697, 564903220, 363176729, 873109574, 505960505, 412907149, 710650459, 97829074, 11502198, 369687528, 761659514, 318512980, 66284669, 437135567, 368157459, 800943490, 972238143, 478428633, 855538266, 321983088, 656874977, 43681349, 541679947, 937934651, 244457206, 315193894, 319702720, 707622371, 246514147, 151533229, 568852457, 147783131, 969033312, 186736567, 320865792, 43514826, 677033573, 923317185, 612412973, 174104992, 918151958, 109287585, 938927103, 518114981, 973941256, 476999701, 213068022, 622903875, 310474359, 854886680, 957426811, 376010753, 292746941, 364603825, 894105052, 25691539, 82514570, 41302710, 581779951, 808558692, 320060428, 942222083, 193766884, 133525587, 75843652, 344895825, 114181286, 902391418, 560401494, 150645242, 473837029, 602564434, 717678379, 346232561, 466370994, 866990082, 3834409, 155888557, 129581803, 574303958, 550156176, 939048536, 960794611, 258125498, 164255663, 912945696, 467031278, 692140131, 293004792, 881572784, 254026801, 975419815, 509495733, 40545634, 595775609, 533700414, 406303121, 272983543, 855441483, 374977887, 506247381, 15507237, 989800636, 626362399, 847726484, 800361614, 286496808, 551783517, 469648486, 98477765, 262270214, 278412117, 645054522, 381066485, 678249268, 454880540, 337197715, 324727694, 294254312, 32320770, 716401083, 189210077, 539629752, 991692968, 97928103, 138748467, 122118363, 56445737, 935953238, 842913032, 49339139, 817341832, 580293005, 431004603, 412224203, 323570307, 640667962, 923952619, 210850509, 510149075, 567926853, 739333898, 606464540, 908244944, 834436987, 943114090, 957211262, 855416901, 726545549, 95757850, 784254781, 776838250, 115526066, 76943826, 7075090, 767893226, 492000293, 655912102, 162928894, 361102737, 586811697, 807176898, 828391266, 674294882, 395508648, 157516832, 831260856, 780420911, 187633507, 693019071, 201546504, 672613503, 309318515, 304158474, 961019147, 700749772, 560211331, 412756014, 697195225, 602351670, 330297457, 688652858, 149390597, 568442948, 413437837, 204524062, 148404701, 187373647, 578422728, 861457778, 135061794, 680453851, 543602229, 326917305, 568068662, 567285833, 277393172, 918263837, 848761695, 377760905, 670300677, 837317536, 249837952, 668141962, 385673896, 237739756, 499015005, 827443254, 560260997, 93880803, 644443431, 490962463, 884477836, 9480277, 415888417, 483301306, 367902629, 608235548, 183589386, 997954070, 826816799, 397448238, 196407170, 679717571, 764905576, 291437702, 791255920, 265628348, 519546385, 328385073, 371763061, 168918225, 645529856, 519775673, 348694272, 155986276, 691704010, 746828005, 316718435, 714200737, 705217259, 762138292, 61471141, 41405878, 864679537, 965049846, 857917199, 914065851, 297494779, 876089636, 635899262, 926204037, 94995863, 354545615, 822396515, 366071634, 279704079, 50397337, 202370647, 999266471, 975620863, 231932118, 552724166, 802354962, 56911018, 260990001, 300193469, 227265902, 694533559, 837236910, 887443561, 628653749, 21240579, 933805329, 202377276, 362730687, 760799956, 817861548, 675577882, 4321148, 529014530, 153152242, 462716461, 751777097, 9635372, 111223546, 568345069, 37012152, 263910959, 757934347, 823267112, 22658690, 838713863, 463842960, 485466704, 514191812, 301187225, 575397411, 871503496, 415562034, 143014952, 95163494, 552434141, 914352623, 782827288, 957547441, 675335589, 213978674, 209725738, 423364269, 207659632, 529804332, 870081464, 846733508, 443313762, 135166798, 230774888, 772453887, 960147441, 603084785, 821581610, 873550226, 532906198, 969327554, 106693597, 769481754, 777410479, 875624821, 703281941, 858168968, 96377221, 992311336, 361437725, 729139451, 657166634, 543388465, 6348198, 298291966, 522774037, 329746938, 388669662, 408857542, 337014284, 954682987, 558009821, 878125665, 833426425, 695891818, 624613443, 80999014, 436537260, 148578229, 589603734, 452165700, 741318503, 745351065, 416012420, 474829443, 69748165, 61468181, 209961471, 636597180, 272933332, 971687898, 390119116, 59385932, 190160119, 103957391, 995152439, 957384056, 254487904, 109149274, 313907860, 497607887, 882992268, 172434063, 746682614, 567861392, 214326277, 192671228, 314334650, 220102757, 476067300, 388342175, 842080160, 62572951, 843400948, 577532749, 697815406, 458566967, 667916796, 822303737, 733086053, 667704760, 796179867, 632461880, 95013406, 882537747, 739058720, 173938160, 203702024, 649819404, 914530325, 364874164, 88008999, 978004629, 131000503, 875636820, 801191869, 341948558, 125410393, 800739301, 436984809, 269791410, 912162923, 209266548, 420809580, 856139458, 803681309, 333725918, 751236985, 141033795, 285345536, 215591021, 89813724, 269198260, 153095567, 958591561, 17299741, 847021230, 303964896, 82246950, 465428827, 115525547, 780224754, 869198976, 388291413, 476587483, 691967127, 164826558, 199218146, 401373213, 778742148, 785368994, 496260720, 105954110, 398900290, 219614748, 228453637, 139747621, 595548136, 71518080, 343975805, 540199555, 840531664, 44840239, 589231776, 510546553, 923702957, 286713970, 353758234, 565240608, 794314111, 567420321, 988426956, 457651339, 899769446, 942464606, 302424207, 947012026, 756814600, 676683142, 307811738, 359602841, 242398282, 502432905, 606677937, 620526147, 280242919, 162443412, 476834571, 574493117, 785859248, 739430314, 475070834, 12145637, 409826423, 221112197, 482556169, 304419577, 599005896, 944896304, 378563938, 767391327, 764957484, 698420843, 86518889, 848548899, 940875217, 356832632, 82389492, 141351138, 253057193, 505710376, 768858246, 69215061, 494390492, 486671878, 158779046, 205068140, 927517611, 405213144, 533823405, 636174259, 671652233, 823607725, 970246585, 581237369, 748502857, 603996296, 248077030, 938336152, 487801580, 935653494, 705099190, 609508419, 321068590, 171648803, 123104655, 864070529, 627623587, 153973723, 532757332, 334067313, 301162418, 763531369, 118185494, 277343915, 297058812, 956116570, 27916952, 50987701, 555953984, 374975108, 254105485, 756982147, 946280062, 432006454, 615619859, 41044323, 51176565, 93025987, 464457540, 568995841, 547436389, 234332994, 873705678, 793910941, 718626690, 618801266, 588992054, 317919234, 114701380, 631830284, 965866910, 462662021, 288222047, 940667246, 889946910, 686356074, 651975611, 751283629, 438254259, 930832394, 663817812, 648690183, 830808762, 559113671, 503740336, 564984518, 728178610, 274625284, 917683332, 307702865, 280453477, 894841285, 41921673, 620010590, 784197179, 211836271, 474035307, 279274307, 946489897, 291470157, 270173729, 935838009, 623979862, 556609329, 464487059, 340990566, 434770623, 631662358, 38075281, 842380206, 500850392, 613391011, 18080374, 285250260, 529845193, 631271575, 374291512, 262739384, 985094109, 303903201, 16259429, 810359256, 363767310, 439533694, 865903562, 239947506, 617332994, 12008655, 687928866, 948278772, 502425279, 65739255, 81068619, 232652789, 803273676, 221975694, 952453329, 954101455, 419276262, 385219432, 912933418, 753984171, 879530618, 201860243, 425718240, 278382069, 591339775, 284643345, 41778741, 441409569, 857060151, 654989304, 641813047, 910548369, 326618557, 403218292, 529860296, 934915671, 278218756, 690631372, 789621732, 297657116, 292201877, 300172876, 960938884, 6494442, 408434538, 631194439, 495729658, 906370223, 334719880, 36067661, 265056536, 375085696, 502127399, 559431996, 219055310, 952137127, 981975430, 41298331, 592853985, 429247851, 277759472, 598943926, 621676538, 437256746, 910929529, 391158258, 732923131, 635407846, 946781382, 781366059, 538891546, 630564488, 525489062, 367680406, 315439237, 994056845, 591395668, 663549817, 846533929, 802030127, 788951116, 628933255, 647739058, 409694710, 592117609, 553457158, 673045219, 919656333, 983067109, 468448263, 16864831, 575662694, 249444633, 418119785, 778411705, 525105517, 491573168, 939331936, 108707336, 910388406, 674647760, 726347222, 370136626, 493648808, 699500868, 594882768, 901552603, 716526019, 285354664, 110951687, 416039799, 58969569, 630345142, 744166147, 908464451, 266658899, 135696016, 615828551, 274701707, 302399839, 380580879, 341987509, 326369586, 256745490, 655147334, 405872875, 113280123, 933482227, 802469607, 381541662, 498865114, 495779685, 967570007, 821541556, 290582034, 664037255, 210085915, 483137595, 207842196, 138524769, 164615489, 942077022, 136029720, 110227423, 125519767, 32594694, 580669389, 110083398, 159966298, 278586564, 651514556, 206429803, 241778484, 408295766, 538231054, 40159268, 314474695, 847619050, 392249356, 818770268, 919066645, 294828896, 309466180, 611441273, 586321901, 817309867, 899109802, 759462533, 574660273, 468504471, 521462233, 942808544, 723622267, 56447073, 5157631, 750144953, 763817451, 978331972, 680097812, 105756140, 247015460, 175517670, 420429163, 786786754, 357218723, 613180909, 136172357, 756075206, 552831291, 659432456, 2679440, 330672781, 400354207, 832423875, 829560244, 964790095, 49545740, 110490325, 949908909, 546020473, 972646140, 940082015, 840888057, 725398813, 958007018, 451000364, 238151178, 737105967, 805008075, 870502660, 876656816, 726783282, 129128717, 953151559, 771271007, 328571096, 309301886, 515073405, 387913337, 183620066, 32759920, 92011287, 415965918, 289056564, 409397259, 98324621, 86039657, 335724611, 37673345, 760097979, 321461057, 127630198, 207972784, 975999880, 785590053, 249756361, 163767303, 534889206, 183447255, 616173844, 431146841, 545584195, 147154115, 411197564, 328772347, 533020004, 573015415, 268027550, 972295303, 592287894, 361397434, 651709520, 757591399, 156156700, 790433458, 378147201, 668181497, 517614797, 35349612, 839385479, 682152248, 888691415, 345294522, 225523954, 374725032, 1657739, 771600563, 809896448, 314099086, 851956157, 724387074, 588238065, 822330246, 350784184, 160586399, 849465966, 753220757, 643305190, 204884894, 553687438, 607977918, 592906946, 828887047, 127047889, 916362002, 646657819, 379640414, 204894069, 37048682, 618445676, 762372526, 854408436, 553553708, 812291857, 245342896, 818643249, 15500611, 62794820, 517081109, 731718478, 693874711, 723222312, 106275511, 463569536, 773710985, 823082227, 74109380, 913000930, 115385232, 601861096, 851806615, 458866271, 790228285, 225582710, 725226169, 549874551, 985873222, 244807331, 312336424, 237392741, 425100621, 410471626, 565457102, 599695524, 505945249, 65898405, 459141754, 611642336, 465408530, 718916847, 999608263, 184154573, 147043989, 42648971, 526225092, 532929887, 670305970, 708711188, 904743600, 393293020, 627857070, 200848627, 716941864, 588437201, 338790662, 285806616, 386784331, 804780404, 705101006, 998293510, 512042853, 181595844, 433426612, 597547510, 394286849, 881860372, 507478255, 340942820, 612963310, 273101543, 785931568, 300451863, 720925724, 822463727, 666616362, 514973587, 908630781, 360136153, 14157790, 202800300, 352175084, 120615576, 601098518, 400010156, 366526131, 139368683, 675687028, 206462322, 857533824, 808120159, 378303355, 639957738, 887842752, 902271815, 599082431, 509531551, 680945956, 1887878, 295497473, 33844237, 735616326, 308706703, 51327328, 355290038, 506187518, 955001122, 664316989, 73014639, 942020888, 499917702, 534270874, 671292900, 151783178, 699601203, 803142442, 842302694, 338390010, 108151870, 5831947, 416375860, 878549545, 759617565, 955548319, 425328977, 65073051, 626723105, 177562274, 325545489, 253171965, 884961558, 382824481, 372274227, 399765892, 328686480, 450658389, 980157974, 230376620, 283288592, 226019867, 668782184, 347965320, 662432974, 909215941, 601858225, 698875047, 573615696, 864841739, 475967377, 707452908, 338579752, 48520135, 409099122, 853222866, 577751637, 835862414, 186961866, 6792256, 159530824, 116003389, 188873387, 439410850, 888735143, 654374027, 988354762, 469232873, 852783163, 206219439, 810598036, 799096786, 899769812, 339845271, 671228513, 282484818, 387257891, 281527088, 510461992, 842369532, 390165392, 725760353, 494110751, 493579292, 311932937, 95473478, 618983775, 156591731, 245883891, 315601869, 333238460, 21921227, 714469859, 407290788, 892719716, 140880728, 945368778, 483567174, 929570571, 980074786, 265020147, 285410277, 595536429, 48236931, 605024997, 490602362, 522728224, 203790845, 193341270, 73394742, 398036878, 888647974, 324020636, 988735580, 505347892, 941052184, 932938660, 590982554, 349718931, 286497777, 870624316, 303868647, 325144471, 567433823, 13645123, 902387268, 672441160, 693576365, 146595045, 317477733, 165494128, 524100704, 83348306, 466275586, 859809111, 806868317, 894945488, 429890827, 187808789, 571308643, 117283443, 328930974, 296656633, 785375609, 795146827, 51710388, 598082269, 574605651, 218219488, 861642484, 36671644, 825058457, 551843296, 595286817, 196687555, 333916870, 39910427, 948609734, 649730018, 535323734, 27471623, 991009743, 639565908, 550954211, 220933760, 968393989, 338774917, 601266988, 984115804, 883733555, 962972471, 434136775, 607808435, 967786190, 543759522, 190978211, 12035162, 542603873, 911386396, 830876821, 157766137, 943213452, 217020403, 431668303, 183505198, 21874401, 529890544, 861287235, 678306014, 891917776, 243362578, 183462546, 671587911, 956306215, 408346556, 446847445, 189250926, 749543863, 125916578, 322871964, 183403385, 420509830, 920375206, 667187876, 317314919, 564865133, 775265480, 640910154, 890349344, 858257387, 166129216, 777561566, 336680179, 339757062, 477887943, 942511687, 618288193, 405908363, 195179449, 59376326, 814316148, 696963220, 139983, 635087606, 923041707, 255032623, 194416990, 192125619, 875822010, 778466295, 762417754, 178452992, 851724946, 663165283, 603451583, 466820675, 387444564, 489932704, 951226129, 894312627, 237444605, 532444006, 448051295, 941125333, 457751312, 837401179, 517862439, 774809144, 110399635, 397328303, 891532765, 564153122, 535222861, 575627654, 577614480, 404603044, 830685664, 992220790, 753430054, 200737936, 181493750, 676755736, 357506711, 622489173, 100520830, 190245833, 187407675, 290405517, 998427396, 558691913, 475568142, 204630365, 126252025, 215499216, 999399090, 196346657, 778120602, 953943371, 164992655, 86691065, 789093511, 563418127, 562788045, 763555483, 96397832, 352570026, 347079136, 67299099, 458503557, 126402413, 959719122, 948521022, 842599317, 306189761, 54162026, 146893675, 43740914, 332199296, 473701977, 905250809, 432966620, 848260737, 821391712, 307878893, 208679509, 747475074, 208629517, 225313492, 975690138, 610696544, 31376389, 507343022, 500203756, 123426984, 575633586, 202344116, 386115553, 501963795, 683567585, 302557730, 248092269, 577059873, 875995709, 29909224, 842674029, 193775658, 258309173, 191079778, 93613830, 561137503, 969278493, 694347311, 763606833, 84102846, 36099334, 23063507, 524427058, 776456252, 674603900, 629369067, 977668389, 256627112, 669047847, 779537915, 24990802, 108199772, 58153775, 323093024, 387373991, 156905804, 409140842, 381844654, 180261234, 602282492, 30033908, 212781342, 523463640, 970405843, 821164164, 761711064, 281213975, 852587905, 685643883, 228256863, 174035872, 920887054, 628433109, 864317658, 660828091, 304984427, 240562939, 961739483, 995908791, 378770855, 575471407, 240429987, 771627767, 843941093, 646145836, 201234368, 68077834, 787016003, 318397006, 65896359, 572492012, 733629547, 852449461, 266102355, 364817645, 146072269, 674866984, 730936970, 233866138, 688102811, 579870366, 835094751, 50732570, 860871464, 506278883, 596523904, 667937361, 971384940, 344103519, 927530647, 765467001, 273871306, 721138022, 533349842, 468889904, 52289711, 251223215, 807985294, 801408231, 568230456, 500573171, 947829269, 55842552, 196515563, 411183938, 597155107, 948918818, 938215126, 205887306, 752194869, 879906757, 139745061, 923842816, 24066568, 411487316, 314370183, 972833125, 905395435, 718866644, 43076332, 150290338, 180552145, 242632913, 606595592, 476045726, 591634610, 399216015, 647652191, 523818798, 900111429, 874985964, 75273202, 202545741, 367253434, 87105484, 821352128, 191318699, 912394206, 223193589, 618457975, 726079201, 418335823, 766950782, 367029696, 380996546, 236085862, 972077135, 349853625, 899810226, 776177314, 211769285, 460449764, 344457303, 609820486, 134249923, 223686108, 631816578, 157185903, 978492275, 686712006, 487692575, 786079162, 349917358, 579477794, 683244920, 559965022, 507171846, 999446489, 939467661, 678609634, 471683577, 722612735, 475200418, 42716543, 379291026, 138620823, 210300645, 410810852, 632191566, 328313887, 514270304, 862969025, 922228877, 219336923, 453267418, 644842451, 692143425, 194308408, 654857508, 475979092, 986685764, 505865921, 45431500, 784604252, 910417277, 172981760, 674508436, 197771671, 341775058, 693500545, 150014449, 922031409, 120547578, 596141549, 552517351, 663522975, 628266045, 232726237, 385088146, 476638105, 429188493, 922070051, 582234457, 688305146, 268822503, 422065389, 948837095, 578917876, 65947863, 415793233, 260475285, 568980188, 220247092, 301422250, 335473726, 799603508, 409011091, 587812686, 640408057, 939230175, 753909039, 93786140, 139351094, 585716936, 249764480, 433652594, 383064094, 502493060, 450357753, 564888813, 329952028, 494021420, 368742086, 136131774, 500262906, 514506248, 648367112, 769533506, 21362275, 261037114, 130922504, 754439133, 356583134, 915386257, 173450005, 145829401, 662110683, 320839175, 629525455, 861847203, 391839613, 68485761, 159647814, 567205572, 264930580, 396047779, 40830458, 971528309, 992960135, 644141981, 980610134, 790660511, 843001054, 463767695, 872856874, 348117584, 362155417, 700223161, 251530266, 703123479, 843609253, 287153400, 684695921, 24294327, 64619053, 430509216, 5535408, 364855221, 216252366, 494269991, 565374934, 569438153, 875021843, 35908900, 191059888, 248128777, 976003117, 391798600, 441012117, 35603765, 979182069, 667183120, 437502496, 660160992, 954481444, 507457398, 279789936, 236927893, 44828876, 961794453, 355864099, 891339068, 357380555, 890833944, 672124442, 387191492, 904114560, 342241456, 95842192, 770976086, 400071999, 200993347, 532632606, 420896044, 550880999, 327312089, 644574214, 826391444, 799542735, 178520247, 172865881, 641165134, 355276926, 529987410, 292581900, 571827285, 913885755, 593604134, 854705427, 831695228, 255149343, 546881209, 157735061, 727301779, 444353680, 183378589, 677468284, 444169241, 403793734, 146228770, 115401781, 655478758, 697156832, 905229372, 327916754, 340328987, 629658581, 180459418, 377734215, 338524545, 157612136, 540442921, 44060964, 770117833, 873232404, 143234248, 530657517, 723910594, 499154449, 467393563, 959536385, 756774981, 466533196, 397934900, 248544900, 179789119, 696026537, 328416502, 677556317, 879654039, 908491866, 499694503, 612153280, 50690817, 754982016, 864031461, 276547308, 510551083, 92808679, 230421139, 881118072, 314850224, 398134822, 912751832, 700455216, 683522842, 848340098, 357988891, 231482227, 736121406, 650307042, 439406754, 5269883, 852243048, 917264347, 944841639, 179266524, 986206935, 34100607, 453158224, 768772074, 77863769, 417757491, 779077976, 202659886, 311676037, 633237603, 632033527, 75184980, 351621068, 534885094, 370241061, 883757060, 24940775, 647072145, 797577787, 295667845, 209731541, 366515138, 967280381, 827198637, 662050518, 165197128, 93064991, 12480738, 803654448, 960674346, 644662980, 317775004, 508046065, 605598627, 381932889, 966613067, 479208615, 237942, 132807274, 348879056, 342228696, 398745278, 332848111, 953586590, 712266003, 416695282, 164315623, 457716430, 265500375, 497292935, 615740213, 941487998, 803623220, 111777967, 191291008, 340419451, 289078666, 779501034, 692034059, 406451188, 168319487, 988789698, 157806189, 546853679, 530019528, 70923557, 170433599, 49346601, 245239973, 736775424, 659778704, 494464610, 406390591, 847422678, 63150509, 873437124, 965923778, 189732724, 407546164, 79818682, 224072676, 983054273, 446221821, 605247048, 391687658, 306914395, 665981289, 629504354, 524324867, 550458303, 466846322, 958879745, 440990974, 519040055, 628347281, 715882785, 351385847, 189338738, 146730375, 904936781, 788502408, 207205255, 585712817, 834928065, 102253173, 899589233, 232792243, 667851483, 548098912, 419932273, 635347437, 432137871, 612550229, 240205903, 100990189, 637058796, 257979054, 783535295, 140744602, 720165370, 301991051, 429438343, 655269231, 451445847, 747168984, 750309274, 192528164, 840760752, 322858697, 864087230, 537446363, 625372665, 959244184, 954380412, 215175471, 994902083, 337787818, 627946849, 153506054, 32594167, 163944421, 68792836, 951804385, 689809320, 988796, 617140490, 462533660, 989461326, 239553883, 5275636, 351913683, 354493200, 306106263, 896093664, 777163988, 388892110, 969200263, 432699436, 399333230, 865649213, 315735264, 339510899, 48841240, 959154535, 196390113, 936800733, 987910316, 587767903, 628688348, 214929399, 635016922, 402484538, 54274782, 964016141, 96419567, 719312253, 796513005, 212395401, 436868416, 913955398, 839824756, 144816732, 932550646, 363261294, 8150038, 131862794, 47651253, 271163838, 71333157, 959437416, 251116023, 334350377, 441978082, 482208332, 119886200, 919314482, 259782012, 805173857, 853947531, 341491009, 348613538, 811627937, 680532518, 364248586, 936652587, 887138913, 606014123, 422482389, 444199743, 91709587, 40752608, 459622866, 38196607, 536235645, 984619670, 148194293, 935319667, 688448790, 846749294, 579461984, 480885430, 378858015, 94953553, 191995067, 207937545, 736953365, 975604258, 937269344, 455751814, 504270149, 283014861, 38821673, 82903279, 275591785, 888087294, 520058947, 136143289, 926955376, 387321583, 403353800, 924789613, 392738961, 982101939, 232164345, 227372861, 43706433, 523906916, 338394518, 856587020, 978050942, 443366569, 529420988, 911303814, 793189343, 983198322, 804089434, 834536396, 153815203, 116734980, 719023293, 123420261, 79355230, 886206001, 41561521, 21245922, 882598128, 802153839, 835570763, 581025419, 353269670, 637518139, 175035423, 289620543, 484969222, 906376781, 326275251, 416055608, 83525663, 290686771, 206000117, 5414489, 232258026, 920013199, 421357416, 638770384, 259399235, 633440765, 254069496, 990306919, 60820729, 789819202, 121607634, 405772954, 175784667, 478551926, 549390659, 363765094, 664199082, 300776641, 162775216, 950937760, 112220685, 793459334, 705609734, 578401175, 861996799, 271109784, 874564088, 608584611, 737482328, 17113577, 929523529, 535041412, 839587191, 762589128, 338613969, 307302500, 423136008, 547907, 54172853, 814028266, 492486382, 204797184, 844712890, 440541410, 231508943, 734350035, 140786739, 531768651, 398682782, 289289602, 857372009, 38391524, 737013357, 991291813, 140442455, 640977650, 313606365, 190519486, 164035814, 602873588, 52394808, 167969803, 137247806, 579148818, 528906751, 98556152, 312148785, 949596197, 341635564, 627685819, 939789923, 585542633, 684928267, 633716329, 581654938, 842970524, 672621182, 774099668, 342032766, 230741096, 259636341, 814292819, 159696778, 974589013, 777527475, 220347264, 497713903, 158181224, 850380443, 776097726, 117189742, 344816497, 298617280, 92404578, 517134792, 632871155, 986801197, 86752488, 638367832, 828714983, 810787638, 266157015, 840453364, 831146850, 698869563, 669536753, 521100728, 941076562, 492976844, 235369733, 79684549, 759531250, 822289697, 828261642, 696541825, 272445587, 12980645, 614574700, 789162046, 613313390, 197966883, 637070437, 190199657, 842849148, 626405347, 184932012, 564481782, 489411882, 747191807, 417614033, 478611791, 548477044, 227121878, 496374065, 670306430, 247365078, 601535510, 704465934, 790108567, 804443516, 491371393, 812767752, 736124257, 435729866, 83458191, 696845148, 282825379, 516334373, 706930649, 888348494, 9725931, 67773913, 119998380, 239860647, 273783638, 946958097, 753062630, 674142600, 559574794, 526200373, 327409529, 374340434, 816827877, 276275850, 464368219, 134908857, 877948404, 844633225, 684705435, 809943892, 442338665, 64327905, 641746026, 161977855, 227074529, 232142609, 721920521, 230252751, 333678045, 230646920, 966868506, 775321550, 797772980, 327120684, 940771083, 611747586, 117592551, 86884416, 435401596, 992730768, 664018630, 222178792, 508854385, 5289468, 990682193, 55030701, 60146826, 694724425, 629912141, 683136730, 680648591, 463923051, 733324705, 823418284, 550746033, 640696395, 968185801, 606184055, 781016585, 764359708, 496302912, 368687512, 71427394, 769173012, 225556895, 156978817, 760572357, 708487350, 645932835, 566129205, 748034106, 461030046, 514070705, 326793871, 902729332, 327225515, 471650901, 329790797, 594725926, 837325917, 692810988, 301225441, 719351862, 605785704, 678100717, 706154662, 234267995, 743485689, 359661731, 620800772, 469349219, 493857367, 608649409, 245201316, 543574484, 175280898, 122039552, 920059477, 106798501, 32604565, 312564112, 649816044, 107950056, 995080378, 828541086, 926759341, 683044161, 93865092, 842130278, 233856957, 575561081, 417264443, 828599397, 507915860, 958353279, 776909261, 503619046, 985531211, 135123129, 141522842, 282405594, 79826741, 776430144, 646995613, 662288733, 48170781, 972830926, 17570797, 778431397, 86799906, 692890527, 466294228, 198854234, 386212263, 959195598, 380758846, 928115291, 743917777, 771383689, 916249690, 657310607, 200639965, 541063097, 378454077, 771447280, 193767848, 645469154, 721345088, 480342242, 377507308, 318721193, 977451452, 520805658, 152456650, 79519384, 468326406, 926399365, 153051586, 546478516, 233129817, 105341693, 812786730, 535774792, 191421323, 431176792, 686357462, 783701467, 340487508, 950220017, 269455288, 717833928, 664962068, 717077079, 37993833, 881880849, 317764558, 817410905, 737546614, 665341777, 997055871, 738408248, 998749394, 485058559, 114912422, 585157644, 400414430, 449119574, 737269784, 357474190, 506736555, 886592397, 603292505, 400483346, 148861622, 860201928, 384029232, 933890240, 803611260, 42374429, 725120069, 538172198, 117214244, 210366484, 995015671, 806029505, 542686213, 264725932, 949734597, 467477514, 660946009, 226031044, 493635496, 116812476, 239416381, 816364087, 501064377, 94123502, 223433347, 814291496, 966061640, 396440579, 902554128, 818219844, 26662668, 8145063, 891182964, 301150699, 942289319, 597144559, 615949534, 991148080, 209759054, 176076728, 676032041, 728001273, 387787518, 980952084, 414488836, 591105209, 75506603, 968092101, 912517677, 674396973, 595462784, 956628968, 633945835, 222067206, 243327282, 199162421, 142658059, 526124917, 399753642, 463613079, 963310731, 58973763, 367309117, 750506295, 217426364, 501958884, 340186774, 594951756, 246495555, 833830554, 427098258, 336154838, 642618099, 936862422, 917625537, 186764230, 85511602, 543894100, 483131693, 617743616, 579357485, 620307632, 752057352, 954458915, 316381722, 733549732, 932633931, 134666465, 754363211, 617979699, 435132556, 318393788, 436959830, 506409734, 893107690, 573350394, 799046286, 610037459, 258173258, 466980807, 863968084, 878417424, 882424188, 452122664, 655089840, 814346751, 789852255, 189786543, 374723889, 126288717, 823263878, 831740406, 840034404, 336705680, 392939913, 634397065, 61959603, 429456570, 493171187, 225704558, 884518081, 610186030, 656854008, 396402455, 378561162, 586046855, 688707749, 578405131, 659727570, 120584564, 870946237, 929391278, 664171898, 41527067, 234250825, 627098116, 944103720, 178241433, 23357054, 102202027, 436919143, 195324733, 778574703, 441840888, 774604687, 284370538, 14837947, 959018598, 134746567, 933129655, 803403596, 619978688, 525907217, 976491274, 132339946, 564610036, 68528049, 389578068, 989832168, 852794652, 752963774, 817344610, 2175492, 31769154, 30207239, 508011170, 577661754, 572533465, 895501268, 930462615, 52583075, 446568982, 324027072, 699345576, 222155152, 988261700, 193585184, 899817097, 807040602, 685622895, 221944175, 653622261, 375808257, 546116059, 987504566, 939132701, 402263877, 78495990, 185167756, 500442747, 745618586, 501682375, 285500964, 628769051, 61112643, 592508407, 536386652, 505469622, 969104685, 718855729, 246466021, 639499015, 742659544, 764508186, 887760828, 598519622, 172825867, 529721202, 591832295, 92126069, 128730325, 209738459, 499212820, 545723452, 148651818, 22156209, 831119326, 93907249, 378571177, 521931488, 673485766, 886997435, 173173253, 8855849, 856663311, 639863810, 855169942, 195032029, 91940470, 802746786, 12390419, 989698005, 901360539, 611728989, 291595095, 817343737, 933406536, 613401575, 107779947, 318738241, 407292649, 193003606, 603995044, 332905943, 410242493, 447706464, 167943623, 753367650, 900631866, 49724267, 457139923, 259468341, 795317177, 453161880, 295912923, 319075308, 833711198, 526362514, 415762150, 644266175, 396161806, 960393978, 483401147, 448954954, 470329633, 782231159, 915641341, 241237251, 891944204, 41644296, 394296124, 172054401, 629023021, 398337426, 790859938, 148727291, 975268774, 428635233, 293668442, 637227057, 570337407, 288171478, 220450755, 677002406, 720765819, 299043334, 41869068, 614508726, 903127830, 378222859, 694368989, 777944907, 554866455, 209260534, 828689205, 293808509, 68438572, 509317278, 397658561, 90224766, 68564642, 82634355, 592209934, 151321972, 958498011, 467018262, 315535932, 476758554, 550857828, 542659378, 785149422, 649202188, 195930157, 979265943, 373754188, 851859159, 391540209, 50758448, 626238561, 711993530, 714930627, 965676441, 278379328, 988034508, 481070718, 130440810, 169596339, 140852140, 928297547, 756569584, 238789676, 425689665, 168655364, 612992760, 88027537, 196565643, 537543813, 936370302, 101399103, 116046068, 309905550, 181893451, 387172781, 519505265, 900352881, 532825690, 918400436, 679048648, 725189293, 374281068, 212404153, 195052723, 838832869, 812243937, 669719104, 755865052, 10330155, 848017965, 67894241, 852647477, 650790487, 45654714, 443421691, 275975248, 471103353, 702200183, 679557860, 148615974, 612735399, 922149625, 536411152, 861586923, 927589553, 19878211, 111640500, 734578966, 173981915, 726737212, 607826374, 40429104, 840534701, 482848616, 92257741, 394851888, 60587561, 980470590, 901243323, 841551715, 812230245, 72238684, 148412157, 740624302, 85271181, 215138774, 949274441, 812658657, 136587012, 546301872, 784079050, 472075136, 417121487, 303596227, 154445833, 866652278, 423463350, 743183358, 330425525, 938377700, 325554406, 951848840, 62057060, 532771872, 947984754, 349859423, 773076066, 39870106, 760227438, 985777641, 806906099, 343957858, 476955034, 936778342, 886410244, 169689349, 831622769, 779937363, 180246177, 1864975, 798052484, 860058396, 811820357, 848400894, 37642362, 188605529, 382427835, 624139622, 572864427, 116508282, 387760183, 949818762, 682698986, 219390863, 152172167, 171729470, 845788080, 975624748, 174651179, 124028005, 696012657, 63286532, 893568093, 944196508, 7870538, 924483817, 611245146, 995764475, 996002315, 526452867, 862674175, 288582555, 619141754, 951214007, 473069720, 121350279, 515732870, 271806590, 969514067, 962538498, 269196741, 422849656, 149771522, 202280026, 123301201, 394749690, 189012553, 157496805, 83876881, 603548086, 104432710, 217905133, 203086298, 159477087, 689296098, 584639901, 752913887, 588302293, 194386109, 172854974, 422899882, 325122776, 858293656, 403930416, 921376938, 148356228, 593533321, 979032008, 42356643, 310228148, 883927150, 771603459, 507250036, 903691242, 361576332, 383422081, 805140676, 981225537, 187472457, 462810224, 842807203, 373338162, 814232926, 175485488, 963209488, 356359572, 916162665, 560411381, 90680011, 394636855, 145278336, 197129757, 43447567, 109623440, 400799273, 943410775, 135727611, 786375041, 359361152, 392350381, 978299347, 421737277, 963813499, 259712316, 445055621, 129621700, 82182904, 41952078, 388717787, 542654401, 350831712, 804436293, 72767780, 545602998, 146910197, 124237493, 19498315, 410618652, 901438685, 228866006, 111927177, 332735159, 251635502, 434709091, 569425895, 727446718, 311138708, 250607238, 546621198, 535768892, 185290278, 788333312, 819706302, 391838647, 805031376, 456925491, 37617435, 460717650, 676316300, 267935791, 841420225, 916231290, 67453678, 773031427, 456014449, 278987176, 551660904, 50060068, 156402227, 59723882, 510124985, 474833491, 405908489, 29992137, 695097794, 74704573, 876610930, 276981263, 597418172, 593938193, 181904189, 540398735, 407525303, 67156597, 561695106, 667726948, 670265327, 905651785, 667270199, 101270320, 113836583, 257318426, 818169186, 595877591, 75639531, 169700260, 424356478, 379424773, 537966365, 229715291, 946822746, 477273277, 908800845, 72542458, 814116834, 701778880, 565385458, 65268207, 786876292, 72233639, 110506726, 701758044, 14972909, 671017633, 590328672, 470666051, 963289684, 114781700, 335219636, 217879039, 430405734, 713517926, 138010599, 909081787, 951103468, 445072073, 353341378, 396315505, 733495942, 378934368, 343031716, 913222453, 368990102, 678288818, 997471553, 197247341, 361095419, 152720452, 412107103, 25090718, 378475051, 424379828, 842239826, 962310887, 428054252, 801588166, 621973799, 424646024, 214376988, 600492402, 333958466, 176356066, 26119317, 964518356, 605227459, 146184450, 483711666, 71093929, 775099119, 242858655, 266557804, 867084957, 565052140, 455703953, 603029522, 295730989, 276293444, 114645502, 704000847, 832581784, 335552594, 855789701, 5842676, 470367434, 963066997, 673030727, 351896632, 871762656, 131567234, 752505123, 200415132, 298926229, 159758453, 36998404, 625465084, 708495206, 888429604, 983832571, 943990071, 524867871, 40597223, 947276784, 97390584, 667819622, 497898761, 599406046, 903406565, 474594333, 264548024, 708852662, 649626804, 956509499, 304402295, 441372491, 317283299, 116583550, 267276167, 867174900, 853305162, 177627319, 139358880, 631321982, 570893703, 58080033, 930414265, 144179682, 119495694, 646996958, 831874712, 748687984, 203718163, 496494626, 411185168, 93578425, 144984454, 343774265, 341750089, 287209666, 469067422, 628093006, 12857439, 530730777, 201151740, 445533652, 113956597, 64902286, 543564291, 480831556, 402495426, 839959847, 26352747, 271318749, 234900094, 890557626, 55366060, 135261500, 352169035, 654453741, 595480233, 735972539, 537686762, 98027874, 430085186, 802112014, 391350951, 357768319, 175852260, 755205019, 607774208, 826462337, 475333570, 451038508, 766358286, 309250490, 686434787, 166978624, 767051814, 204618713, 314450975, 669724539, 165470522, 328333526, 463175624, 493971516, 787201805, 983951356, 487013117, 407173940, 969022032, 834923695, 442242889, 376061726, 449338563, 410355556, 924675522, 688947172, 230738108, 516269140, 187168330, 926029362, 875378489, 978194160, 990708989, 805467238, 29748058, 641483213, 515346041, 516280837, 106762413, 533555764, 490405735, 9864996, 467384782, 93064584, 834468345, 473777184, 378464598, 758052874, 175524708, 937680017, 894703796, 2951116, 719767255, 631945485, 160938715, 649928753, 591967553, 217278567, 637815832, 587407452, 739716280, 249168782, 705661322, 573401971, 240009214, 673061644, 809591872, 769886894, 191652211, 85173834, 673767379, 628194447, 718240244, 491011642, 907632157, 925785719, 240958695, 578073000, 661236255, 582842566, 54509105, 854573623, 140502660, 553489937, 359052203, 415415040, 434722447, 7609856, 772571215, 834548950, 208463047, 449807018, 453381687, 164326574, 331964190, 5054600, 84233475, 88977912, 746099065, 758041399, 547068180, 805438509, 773563029, 770198108, 149171205, 701009037, 629139216, 547647580, 214633087, 66237099, 589914642, 564777435, 490815990, 241281060, 794748059, 246458405, 111738445, 86978922, 953402790, 321724290, 391969597, 117149113, 927039158, 273952307, 468609900, 772343597, 9109651, 339825306, 32911062, 779632385, 543999369, 552961494, 823240097, 792437594, 406717659, 415013032, 536358382, 575890392, 560260186, 730859169, 137745509, 257727000, 463253652, 151398077, 527596230, 769303810, 535008688, 242267394, 873077554, 998621103, 65499778, 795928034, 86579386, 128188036, 312203782, 59514853, 5904825, 855885859, 223762137, 276442813, 971482993, 316412432, 681535046, 182471375, 734632048, 74297839, 795712600, 36964232, 875595291, 70824870, 497776980, 378952797, 980079774, 934843263, 525706500, 232231657, 964358814, 777830705, 399775779, 666887094, 834827732, 817635326, 928976038, 675809044, 926869232, 324206051, 136418282, 179916994, 160721703, 635348796, 773105107, 254059825, 389004116, 886695590, 489134407, 41054844, 158807444, 743353909, 346917425, 226770711, 461225589, 529517610, 60880683, 192375707, 156750730, 891944655, 248616794, 919332852, 667921994, 15439340, 144922386, 379146611, 117920319, 653980117, 154866841, 860198540, 927821069, 819586504, 487430164, 72503814, 285984179, 305997496, 355312007, 241845160, 311439121, 363509536, 546519230, 121473300, 782806911, 494716501, 41179982, 879745790, 946597404, 565121475, 384288274, 109779356, 942216665, 337784102, 299813188, 249587028, 654271582, 604322816, 614252739, 890190706, 180676447, 273609009, 464631823, 475450804, 1387848, 919237257, 536111351, 682036902, 284123433, 503197698, 731697972, 724387577, 96576362, 994515704, 644406022, 511605503, 56983986, 385341632, 195754827, 888576413, 991778731, 85705535, 547921744, 738854245, 595646176, 305777186, 9812011, 90604793, 59801019, 72083800, 164776667, 553327335, 474104069, 196115549, 305828712, 766394630, 226216332, 476930214, 134258336, 175750098, 915916926, 560344990, 250780832, 700519324, 849888384, 535666997, 226081487, 117696605, 473366546, 425232577, 692018403, 383836476, 567346777, 467668915, 577504171, 591480837, 989473615, 19449096, 730631150, 3634615, 582216604, 207504315, 127856782, 732703644, 811604508, 47708590, 457494135, 921717233, 453256414, 479354105, 284057677, 481276346, 880906897, 308919164, 509320444, 455344012, 39062108, 245216294, 689666091, 583879851, 753776939, 76019325, 185502780, 764386186, 127281691, 390063331, 487666649, 180040374, 495222730, 576833538, 496666713, 130415580, 777667990, 172939946, 138197276, 819325672, 800662533, 389714475, 350845994, 47880373, 884562193, 565807830, 410182581, 947449535, 975166896, 568590954, 156435551, 873823892, 865347823, 490277152, 436856422, 592960178, 273616719, 947536904, 82923811, 90752721, 940533061, 542968666, 616655846, 604266893, 180034542, 798152673, 963239864, 712431389, 859015158, 894925376, 535365232, 278552083, 235714167, 383088338, 894207757, 773690912, 917988348, 359228694, 19255502, 121282436, 987110210, 183223336, 915697365, 968877952, 682810434, 327849815, 480660954, 55420300, 429875271, 168772948, 522858392, 183347272, 624398734, 912957677, 635773584, 664400120, 868341768, 444124933, 481129811, 232553846, 622993447, 981453433, 919685243, 763023738, 580068865, 404061395, 73302775, 261093153, 454921925, 602265643, 625904679, 470855250, 241320699, 128144006, 452776406, 673879859, 313704661, 633674090, 164618379, 406609439, 388918054, 808416901, 99091899, 378208174, 785828139, 255204944, 3025348, 311390035, 62639590, 909752812, 367892553, 760686451, 729530198, 207578121, 941654441, 299439868, 535030884, 482375111, 450725000, 365749011, 281116466, 304638100, 207322911, 662393283, 214682507, 318746380, 471768465, 644189076, 269262526, 48551405, 959827068, 429553890, 207646003, 963893965, 204018865, 941950525, 10757157, 274586764, 226460246, 564477529, 464674806, 811065511, 188278643, 391339986, 358800233, 299879396, 81023401, 66393041, 60618578, 575201808, 386219738, 297821220, 105663972, 682834596, 895189028, 998240133, 211084501, 217176470, 30913701, 543152230, 410259144, 584852164, 162115585, 229227241, 439291641, 363877115, 244507485, 994597777, 378468091, 452453755, 487249800, 306379784, 416614293, 812865581, 441876356, 580858934, 27138144, 682275310, 65400244, 255910189, 512233766, 600709240, 652574957, 7723021, 655097138, 200604350, 263635160, 597331428, 831078148, 740381950, 141977296, 940405956, 857439862, 523641078, 31555623, 540375807, 441549207, 963633461, 633266135, 426087812, 670096855, 304073694, 638890865, 447041499, 831418753, 487633396, 555411193, 179689553, 556999303, 772362026, 16636541, 423370159, 930490347, 204104625, 123977414, 545690675, 971987782, 187953982, 957627883, 585900380, 100155912, 715432742, 908239856, 619310499, 1062811, 887594183, 550803003, 567101647, 361971240, 714192958, 848607691, 609009942, 695449798, 400518495, 884180732, 250786514, 581995430, 1314688, 654767632, 548462864, 146060279, 366727570, 526111228, 275693975, 313490491, 231894329, 88967342, 165707215, 137299238, 443631044, 923661818, 872591762, 295519190, 635122185, 754221877, 196311156, 213190554, 120717948, 57854339, 96267422, 212859676, 460502597, 290405253, 295541263, 994036730, 236669782, 14924641, 346679684, 12619386, 242520815, 406744538, 177275990, 817072341, 807375046, 333433820, 550420736, 52395854, 331258706, 758604241, 791640285, 507059801, 661207397, 930391346, 865546109, 536783425, 713229574, 454052245, 775159109, 234518078, 976498527, 648271694, 967940624, 724453194, 999767328, 340339353, 669723387, 818124927, 234578032, 919230806, 294993472, 833600374, 354078748, 777761769, 605070918, 867234524, 102568952, 528237739, 80050153, 799898927, 585712090, 497321603, 31916733, 971708837, 294586412, 549342191, 731724108, 439577650, 527096617, 86992000, 336935691, 266268823, 52063550, 858788811, 299685690, 377855858, 172500456, 20802168, 230592378, 308378250, 498109967, 827157437, 686938053, 759170104, 94657778, 770613410, 463609056, 464735207, 992843021, 213846766, 997538749, 659450135, 977966036, 342913941, 411645609, 763367077, 22681045, 530842556, 860084556, 99991680, 568776156, 140654806, 499841437, 30409863, 726455809, 153809927, 929646232, 594588160, 104580186, 550315752, 449523757, 522783645, 339814732, 24824277, 925448804, 408661689, 908226898, 847302222, 129500985, 317974024, 828517548, 298403011, 751732753, 172109134, 354687121, 789395048, 333775583, 43970852, 658386259, 578948501, 235621223, 892873012, 19983163, 637137004, 825181965, 235905666, 401538183, 493956493, 110543432, 611999805, 33586722, 844145784, 168464905, 700065317, 10358394, 399355134, 778722587, 562617590, 487227841, 824922063, 287760233, 210627090, 79706371, 448593541, 643567554, 813254282, 828922074, 431793377, 971957790, 251458663, 683627066, 209741813, 78098750, 47309273, 399976681, 605110957, 686181519, 740456683, 955232969, 497620959, 110882281, 423471992, 630826789, 940584388, 550876817, 524981127, 508770315, 604987429, 815282501, 354250178, 150125149, 4245727, 72329495, 792719996, 25935008, 414247427, 115841541, 410462924, 39447037, 407563631, 274781359, 448085543, 919079435, 718046439, 595428415, 161440760, 842060199, 654107709, 74077565, 144198296, 45951806, 213469719, 999528862, 26233010, 387611038, 724985497, 294037038, 120279002, 280876010, 463455203, 923936810, 129673111, 783573412, 648972173, 374513855, 181682038, 183423300, 297931864, 526296745, 170064941, 408988075, 171077825, 686999827, 234806803, 608306865, 496862661, 345455146, 976082000, 76357024, 833298443, 210252091, 321005069, 648230285, 656579597, 297999081, 345713078, 556851544, 128092373, 609054012, 946620350, 181829896, 869075287, 328330770, 594476644, 323780011, 929419383, 30557906, 717798904, 438038350, 150308744, 128850704, 205683665, 744926748, 546190335, 102854396, 337140646, 296532696, 649588499, 382886978, 221251186, 689584985, 458231047, 230452540, 754318078, 179456627, 355467038, 64096236, 759586074, 753440142, 702398056, 192176995, 92973846, 254860192, 545161491, 331796941, 49408932, 557438637, 133862173, 460980883, 171310501, 337344882, 497613308, 188478888, 173404785, 325246032, 664649507, 994302663, 914176577, 688417568, 274080622, 868407309, 347011905, 11232230, 919352031, 742877815, 61366142, 436495908, 29314268, 495092386, 885100033, 361972391, 646138499, 731768461, 846950914, 525199266, 803929585, 961683321, 855476047, 700082962, 744639464, 13504115, 740700144, 821288215, 922994581, 195277649, 757586243, 532561160, 47974494, 172536431, 206015852, 837556052, 181906429, 709689104, 686941495, 517652963, 510170793, 30229949, 318547247, 272021558, 391596038, 880756128, 446326190, 593317848, 224304819, 696093028, 169838874, 146760811, 894229521, 790225741, 953270932, 22797567, 929078337, 74449479, 981083976, 556840942, 332343209, 669746120, 67713914, 805338527, 678562162, 610932494, 520003317, 149613525, 790124164, 993765097, 276649084, 75025984, 181639094, 992437939, 190337432, 871834282, 479374308, 356116585, 9292448, 291364436, 469446246, 653628601, 470308454, 430871932, 138958854, 233779695, 818414160, 828813244, 774045121, 755797519, 257722567, 585705943, 493579347, 111871237, 516609643, 864816273, 613065011, 291421033, 90686731, 68146566, 893323390, 414885831, 485875366, 406082214, 124838156, 123396271, 829066655, 285876293, 571444409, 831843708, 700075532, 734124893, 213767834, 198958450, 314174677, 556232450, 659152215, 147680394, 48525901, 246534245, 881467657, 32334427, 26704474, 509195138, 871226997, 919443713, 552158886, 11718917, 684459636, 109760955, 643796675, 468726266, 69674858, 56695209, 454384979, 469271217, 453784805, 448550000, 720153943, 951422898, 677347544, 405882833, 276407433, 347260758, 232865566, 513955164, 666685515, 541485118, 354316351, 741765232, 421625678, 251111500, 65506187, 334535475, 339893980, 117772745, 657963933, 410301333, 41789386, 932946971, 437522860, 97602581, 434555470, 307219404, 118766996, 600505101, 640333884, 46581678, 880891441, 224719404, 973235545, 972917382, 171865955, 449541681, 112687637, 942363802, 205021397, 647713852, 424017127, 299857209, 394498519, 744431538, 635269239, 249550940, 392835764, 694243574, 355399824, 906912956, 593951986, 134396167, 65686414, 342246738, 768221138, 502748801, 313433839, 126158535, 162200451, 789270666, 675764501, 63431350, 527711777, 301394936, 813958712, 714265098, 715793899, 499439054, 14127353, 709609339, 835429898, 768675331, 462320743, 655353055, 173800922, 662294172, 60156741, 758558859, 11246237, 629041325, 51594841, 675050128, 365840857, 787502192, 756155305, 398554162, 300149697, 98297549, 609059145, 674983551, 612769732, 506245234, 659122757, 372858213, 337099849, 37305689, 322200131, 408291487, 246267817, 963744532, 933597069, 216821295, 988781319, 514180857, 201096170, 44991323, 58553719, 58210205, 893515202, 790963120, 286901592, 243069201, 610313580, 132615522, 274828910, 818893118, 358665181, 154591702, 980595901, 163084497, 591099037, 553277199, 297067978, 888512536, 791983529, 975105595, 762057326, 175990440, 694638487, 702010812, 103607990, 43918801, 101348171, 300542719, 269608104, 172365855, 820540538, 202459125, 379874333, 148663402, 612056545, 321314714, 253017755, 90147729, 706148260, 30354286, 193197924, 345548124, 548531230, 706715451, 732113637, 171906056, 159994955, 110332061, 308181354, 47528112, 285475913, 611504370, 438665148, 790077321, 266403945, 365779824, 149909795, 226129007, 151464947, 810096089, 191557022, 52367982, 251745258, 312870249, 944864836, 296399067, 869064827, 968625997, 826101763, 569635067, 363363026, 766807869, 210670878, 560259994, 573291748, 571104939, 768433663, 360714369, 73278471, 397943719, 441358442, 483227756, 339854089, 264525948, 7197948, 150912992, 23592503, 49475067, 501717001, 726731899, 847898540, 323948057, 176494882, 302674292, 142759553, 254096821, 849035539, 9190229, 52079310, 416940412, 586745183, 911221565, 727582765, 2253787, 139009677, 692809303, 191172065, 248096153, 647285589, 483072479, 679512388, 13893432, 14096892, 64861375, 648372181, 249508657, 58703273, 662162111, 577759196, 869729222, 650328091, 962354018, 321442864, 397330049, 947391471, 217077192, 455760613, 291980585, 742815643, 142247100, 803478263, 716062449, 135240504, 829889965, 682072663, 103720549, 297219494, 81056091, 553423171, 791972316, 834664043, 869923808, 388415106, 506588674, 392926971, 594556740, 743081545, 108420818, 220161532, 276505759, 543126705, 247626200, 562448917, 169557278, 660700978, 278773437, 93160050, 299137437, 560971435, 127968811, 714165130, 283749744, 710774048, 578226100, 170671524, 647577398, 941610584, 295069924, 933742597, 316066198, 218689004, 124594673, 397837660, 301576959, 593333041, 408939335, 60656202, 940917596, 852044655, 439335602, 988284094, 974720123, 745746842, 101097923, 767683031, 199067915, 21337860, 983131617, 65646979, 410885095, 106122156, 147277345, 114855291, 220375980, 115762609, 401359102, 331343687, 374647630, 821188113, 837645688, 734266317, 872034554, 854123891, 283789480, 371944276, 764779227, 401694873, 810719763, 79948497, 177310099, 985943124, 451801278, 905515603, 523107774, 50857817, 580014485, 384618754, 390810414, 639884603, 8449387, 813508997, 949563541, 286188015, 647908304, 764162814, 201849043, 333053580, 211851646, 938834235, 145039667, 204449546, 967453663, 854365509, 734056113, 879120569, 588687729, 343395360, 994081552, 797106989, 583918982, 401215602, 912830276, 82111674, 496147258, 271253553, 75943324, 263397413, 591856183, 199086194, 990600874, 671421091, 367821576, 269477629, 105742386, 434564631, 662056409, 65307798, 765987056, 983426238, 117778940, 977941444, 134941852, 616899200, 803768117, 915944898, 87125639, 333312242, 200087782, 730836133, 440229444, 920684926, 97926919, 335470546, 671750393, 335294562, 812272085, 341986005, 192034540, 580717155, 789364339, 730528494, 169441272, 329699787, 684034518, 446108513, 316405240, 44692725, 569065486, 334001546, 655005937, 222931039, 65470001, 533808717, 623570809, 188140557, 859319667, 148821308, 678975991, 761526655, 726395412, 425897572, 350036708, 359818920, 179268088, 424684210, 318562193, 44902816, 455965855, 702691643, 234265962, 471470691, 676770959, 419201218, 122712514, 315409086, 627566257, 658871461, 802772063, 92415490, 223399010, 915173564, 382847587, 999372881, 937832126, 272041172, 904249305, 913100853, 228946745, 679535308, 365900933, 58771732, 898823116, 542446557, 159324895, 497061825, 656217319, 563109349, 848003078, 351337241, 710767204, 690031057, 366613766, 409663971, 943674705, 879827334, 735867498, 468805202, 972014624, 248405869, 955316574, 808733695, 790396429, 162316888, 372426684, 436224273, 543501543, 788887471, 794187536, 570884547, 965958124, 80568199, 594957696, 118405889, 184153443, 882006169, 246926129, 719147052, 505166941, 609211377, 685174900, 446877611, 959820732, 609590765, 686921502, 955635529, 357870695, 891778129, 272796162, 633707602, 637165674, 561733348, 309579006, 550709033, 84483712, 79609379, 78619712, 854529906, 544701557, 353226704, 54613417, 302181824, 474948351, 483616269, 691927147, 925937659, 604138652, 314941065, 665241294, 443225442, 692359781, 123229038, 422834743, 189278029, 292331291, 517800795, 789630500, 109767265, 250592600, 539190305, 971961787, 681657908, 729389999, 603522922, 301040391, 977934544, 447131870, 891802116, 699152739, 651709649, 900423860, 399353769, 187426857, 503289504, 760917324, 86114415, 911239551, 538861283, 513928396, 281186533, 523016598, 636074029, 169826782, 194177899, 333680228, 487898330, 520748865, 783007567, 592028207, 595785912, 913504166, 355780709, 770702058, 2463579, 288124782, 863498929, 700363312, 455888481, 652797635, 626999425, 830921092, 37523189, 922133209, 261440832, 910871346, 4772940, 855167858, 927523256, 399140629, 944708301, 35944209, 160575554, 673455404, 680118201, 151134571, 756503551, 989304270, 176131493, 65887335, 758216490, 856757979, 685912545, 264483277, 740408382, 131275685, 650292557, 620199939, 837477749, 379131019, 902331323, 275722028, 207513572, 894649640, 92320165, 681941988, 509145873, 324373991, 41034336, 200081107, 18356687, 245762147, 47416094, 712897356, 732053389, 61467748, 422968224, 947408561, 282305639, 353044023, 378657466, 64617873, 354074308, 204995354, 233209709, 815471741, 221356663, 69168201, 912247674, 677227571, 400329226, 579350619, 610275942, 909773291, 139773352, 99017384, 808627855, 929780637, 810297821, 593829000, 400996867, 494552087, 642724586, 890148272, 770205431, 56893117, 381456138, 240428372, 582846859, 403000194, 201657540, 328285395, 286346428, 549308035, 113450175, 561178266, 714701722, 326960139, 551912367, 108887540, 742252562, 314848233, 363234463, 924729902, 336548145, 673171008, 964596400, 407157139, 559300500, 206229160, 57389399, 678425554, 951239332, 315246364, 821948093, 852676602, 565245225, 175309624, 570926522, 73001151, 899630988, 345129461, 562992385, 389460941, 65506893, 774316736, 393172492, 742208911, 18492176, 761183228, 685420866, 540350693, 71596605, 788160666, 868642711, 467717560, 208491130, 414955811, 140836274, 877291721, 69495516, 373090633, 720638885, 720539643, 439616058, 378903676, 965176835, 144022924, 563364113, 200566918, 191657319, 797524534, 751947212, 38962264, 722640749, 786251969, 578210715, 356248619, 144971410, 869488095, 460365660, 62242100, 946802554, 642594793, 829902932, 523196909, 112176169, 395832411, 270404562, 353203271, 815408451, 766568161, 396555446, 234883054, 22700833, 188893034, 530484000, 840576730, 966057381, 600196408, 505819180, 709242617, 204840484, 983431003, 450820985, 351274226, 54243150, 878626764, 798158329, 212933274, 87281860, 792792254, 833030462, 460383963, 933000024, 22950892, 324554972, 15598890, 827249146, 280858512, 505251113, 543669141, 191821479, 382054158, 159814081, 191919727, 80905286, 135046221, 954228326, 136753, 715472481, 134813027, 384313995, 734040877, 72962668, 61006637, 223694045, 230140646, 271357162, 817056576, 351639711, 489051402, 75331602, 706244211, 750331846, 837401918, 765865999, 791310879, 508087983, 706746135, 387914311, 490042334, 669873299, 389816153, 575306534, 396030085, 995368171, 521223166, 770892672, 277928983, 881876817, 480127146, 113060419, 278229428, 205229738, 257304446, 742192751, 647770523, 31286384, 41671986, 428748508, 254410204, 783803849, 182029958, 309923760, 565475870, 697302667, 211658548, 67753770, 363886627, 349085370, 755190637, 653998873, 280414514, 402391944, 89041785, 146177324, 702055662, 496415978, 194066650, 332405450, 475742451, 670898379, 16761328, 794485274, 456275982, 69709186, 219577041, 369826987, 467155733, 523337125, 306928585, 324058981, 299391389, 332327070, 82386000, 114965119, 798379221, 565069572, 862506699, 911068692, 745975737, 822925069, 385827312, 473036680, 1667869, 47583634, 763812488, 514187306, 820515593, 829884625, 972128804, 144870842, 604785158, 952391864, 63491836, 176447834, 381319995, 807450405, 989747859, 3228722, 396218334, 491864957, 481262849, 987540215, 870198171, 97722468, 831574418, 54833721, 951705389, 902353861, 831850308, 719958730, 844398011, 1222495, 1790623, 88626839, 185948956, 527446545, 796968304, 978898871, 361498857, 115490225, 442782839, 303033184, 185685473, 783881778, 166583566, 704312852, 616551987, 319163884, 22045926, 769468357, 144473134, 561420902, 620566792, 244204236, 531618984, 9788337, 920652499, 983427230, 360504604, 928462899, 394880628, 526327381, 167532036, 396087201, 277881265, 363196994, 800902670, 507095207, 153380340, 310767688, 728140202, 12205376, 671771701, 626331440, 184513353, 120456279, 916859615, 567029365, 489290005, 663711963, 318889851, 790540199, 544084693, 663180797, 481963099, 84611912, 280070982, 540337524, 826577814, 410896159, 672175311, 852320183, 382225757, 984913019, 522678764, 958862927, 347455216, 977456388, 331050752, 329505409, 661533184, 370872602, 948783690, 985554942, 685768706, 967677795, 391577904, 683331162, 434145813, 906700990, 122674636, 467990634, 28334303, 212894693, 231863915, 324982284, 979448209, 251621070, 607249478, 706009925, 133743513, 211131041, 528810991, 886969998, 24569489, 886086959, 111192519, 638263232, 787754067, 122686393, 685672956, 513791575, 154039890, 85931684, 388686941, 975747951, 113322321, 430000479, 947208405, 407227476, 525948625, 921216061, 667703717, 967790406, 953034006, 108213949, 907660616, 368526705, 783911177, 186891793, 673929845, 812391907, 429207716, 782930228, 84886734, 457014060, 527866318, 767410690, 507530642, 168425158, 426512804, 634688339, 399692251, 31835599, 83672998, 466846727, 213391891, 516781047, 830258184, 76612395, 614151109, 797081140, 530669033, 991919088, 279253187, 700040180, 171452377, 508896348, 107068707, 287591966, 990520119, 826393036, 350611306, 83517089, 362013840, 806269454, 297102068, 934465293, 226227914, 802687175, 677154806, 476840691, 296898252, 378697782, 389858501, 18375274, 108740438, 913553258, 832341278, 147676157, 470093795, 477178900, 968413802, 652204339, 803978382, 852188466, 912433068, 333827319, 28544569, 983905678, 243983354, 598330059, 835506840, 277552815, 368274915, 148386113, 277705278, 489133110, 876880104, 109689142, 436937400, 868364598, 572099537, 509180966, 818727750, 454222822, 455217066, 899678108, 430728194, 111487548, 89757795, 251524724, 491661990, 914564500, 357069593, 662872101, 514997626, 358596787, 767755990, 334901824, 583583858, 324495740, 931732954, 490877107, 426245621, 501134201, 379227030, 779342028, 637669186, 870143606, 100476740, 106718696, 793232284, 564980462, 903599428, 175670769, 570653681, 531089453, 169822207, 578708391, 18590941, 101477351, 715223831, 907670958, 127649185, 646804372, 449751147, 866861579, 447112880, 727453780, 607395081, 88138824, 122680845, 104260848, 606177380, 727268019, 10750029, 496571036, 577792576, 449619943, 816023322, 181386268, 395103918, 670020868, 575410123, 720260461, 984564041, 694722350, 567410299, 832218314, 217831696, 793724170, 551310122, 554399770, 64843668, 607147082, 478803441, 461016454, 568689508, 464164303, 107038491, 540280715, 216279997, 777156152, 633157802, 3623524, 736931452, 625593105, 222106271, 994760773, 937618847, 578920367, 773719498, 812204264, 158700498, 899517202, 931156147, 478134918, 594710781, 811807544, 529584596, 455117801, 822565262, 612583241, 936350772, 790775515, 278551814, 24070389, 477839838, 361076445, 571049302, 367666119, 632852528, 676992152, 816471784, 473189843, 390472623, 826044362, 323346976, 545406473, 895710499, 600311479, 919504752, 432590957, 724860059, 165626228, 450651922, 209956560, 873883836, 512754176, 756386350, 933381967, 531422712, 970296651, 450248797, 421211445, 70557781, 932014762, 372462724, 460269251, 627116772, 91429432, 392860976, 818374180, 923571800, 660049231, 351478414, 206726423, 818819878, 160519196, 242925501, 663032444, 607088258, 729861355, 459741768, 531542240, 892645243, 949582366, 287390024, 892911199, 4248324, 232176615, 123135463, 907280690, 138293422, 586541132, 569335241, 192311030, 154212565, 500844448, 207746039, 567594358, 421151009, 747344949, 869439127, 271315019, 269160426, 118324343, 55650857, 508516060, 47452871, 184119511, 858547655, 472197352, 707151282, 726720396, 174426478, 692351885, 617487034, 485004353, 166124055, 230414006, 167700511, 468800009, 675201229, 748645965, 239511416, 455426088, 127118481, 95109972, 993928047, 204781494, 570955158, 604563521, 777877054, 116038504, 28493130, 805302494, 606180797, 570660002, 469404959, 799298712, 805377263, 264090198, 240330183, 275100730, 529646464, 638832655, 908216164, 538829033, 254329828, 464039845, 172535418, 695263035, 838160680, 568705832, 393152884, 523234590, 762609674, 209695512, 811502890, 755922462, 298129447, 739272466, 413074780, 168725042, 909448000, 178097733, 851818064, 947253673, 369277102, 964821460, 461932662, 69366118, 982658900, 14727145, 881182769, 467396318, 815142971, 913391437, 746798677, 7156227, 203799769, 953268006, 120486313, 147124808, 371961696, 507395580, 192899474, 204935986, 481444542, 472991263, 331548533, 644002690, 978445040, 192924121, 890129335, 280961233, 962308537, 703691531, 746133557, 340816742, 459212067, 928667465, 73079681, 236455341, 419024728, 309701364, 769401153, 437839470, 287651705, 363944705, 966059668, 517851859, 492711413, 246570630, 434273765, 586399057, 799793162, 973617705, 939732364, 892671854, 465627152, 4216319, 114023836, 537160919, 834943752, 494764325, 18272357, 752898924, 965239566, 284645524, 893267797, 689902992, 460358187, 458449860, 321052720, 472224789, 419753702, 722821337, 752349105, 938075123, 24183950, 309269225, 128887280, 394758001, 948168852, 342360744, 489737253, 236841375, 50431336, 920866778, 858482033, 681449763, 582676346, 729253031, 514737750, 272221110, 562109408, 931614477, 506681261, 793076781, 169295944, 177267200, 602876361, 906156298, 457512350, 981014384, 548721841, 974920054, 261207937, 1341538, 879367501, 808790762, 25668810, 121832357, 739714693, 247786112, 715956280, 903020300, 907948647, 281845812, 910361254, 203768664, 795082887, 544393318, 884941412, 328285004, 659903368, 285531604, 194087866, 369417169, 897402524, 767370162, 879307200, 517213558, 58591621, 343355219, 91576791, 301394240, 993481328, 755592063, 427252930, 355302157, 749861681, 989133148, 944754838, 328555584, 953697057, 221731998, 966112415, 981152775, 922384388, 96624951, 909064271, 429004400, 572510631, 555652258, 73053908, 243710115, 43837793, 235889361, 201805296, 562334796, 969281624, 106995128, 416069283, 741274739, 9492153, 789419910, 808418698, 368384531, 38167392, 979214146, 940259061, 33257236, 207094089, 874003085, 808147702, 684224845, 266810051, 528618209, 293865258, 557794598, 266505705, 840520610, 449439500, 113725153, 980457887, 437163789, 614686447, 793231649, 756836155, 77030739, 434526900, 83085578, 405410144, 303969403, 828576909, 999486980, 690430449, 49510168, 519534118, 272921150, 739859758, 105116810, 990700157, 668953060, 292261398, 492723527, 816884349, 127900878, 359098937, 783659646, 259790556, 468904313, 81233637, 721452883, 37904078, 572550821, 308275346, 492608287, 141611181, 993919943, 244481275, 605781805, 947747955, 471789985, 435251800, 389704995, 494233648, 952782290, 80020580, 259345906, 983056783, 417388680, 764341039, 833874123, 394710507, 523523245, 813137722, 71109174, 712554011, 657255107, 84722642, 394930644, 908610169, 394282488, 80383869, 595321583, 743997594, 699001790, 68611026, 735960621, 549965719, 347232869, 461574188, 442696743, 81748771, 858943306, 475811501, 373065656, 589019720, 116625929, 649003681, 833641403, 524631323, 983449506, 278623974, 644972202, 768999942, 605046580, 556767752, 283901864, 470638608, 476259817, 814531797, 961705696, 773296682, 307833604, 303958287, 572905786, 382986121, 959937181, 95290034, 295862130, 62243548, 633343003, 846679633, 467005412, 723890093, 296424721, 42224331, 601876185, 554022021, 483155577, 401699491, 344999299, 798902099, 685482282, 757011001, 760535266, 809754037, 617220952, 206062849, 897115431, 823101525, 770025898, 421967340, 2599308, 927574378, 986743021, 651736861, 253363031, 200781049, 735562417, 790515173, 373607827, 482732592, 996967363, 235145431, 106985463, 419048714, 449151158, 812368552, 430050791, 952564406, 781562174, 705497573, 992695286, 742761152, 630890544, 12856822, 192490437, 35466045, 287072344, 999259310, 570380038, 823684491, 465658285, 999587532, 95318531, 892730030, 685251242, 702544767, 707753158, 818158631, 674975574, 99442080, 406929465, 366454374, 534246403, 177657929, 272795362, 997004228, 358908485, 875103949, 61760988, 667141417, 58657383, 898835621, 281281276, 470673589, 512264756, 27183530, 818581499, 107531792, 615859488, 745165275, 378360564, 89647479, 789197740, 771667185, 736663471, 672017793, 813802524, 98066113, 787252934, 976822096, 660976203, 942509774, 760121419, 871772296, 629202223, 133330510, 794011193, 463228066, 408295883, 959316001, 220846636, 961313820, 305531542, 480764834, 331508797, 655740132, 856413249, 348782806, 254933231, 776175303, 552725010, 490117650, 753506246, 85546069, 305568237, 556636528, 765077790, 147482121, 326656956, 357294687, 942824851, 90289900, 617572253, 919009069, 830783091, 64160019, 377217929, 239219920, 431083475, 669191350, 568594940, 743053983, 851285776, 64715971, 294019017, 802079891, 339317210, 278647192, 40577196, 396875320, 418388226, 556846481, 660239301, 826491522, 539932920, 127724191, 766950135, 839537005, 250041628, 823162136, 996419004, 599269339, 311513824, 341773724, 552534936, 193731627, 144653995, 107005880, 687974043, 396971215, 862321696, 308095929, 178028017, 859908049, 524425636, 599571756, 629914491, 829312619, 511597901, 578456154, 214636938, 364884952, 17205702, 693961971, 982527293, 993378255, 443494611, 964413522, 571216468, 444356806, 201629688, 615047087, 746414891, 94290915, 725481458, 973585226, 795331232, 775801774, 886341216, 197622585, 16637369, 265308149, 362262886, 301612184, 576375311, 154399619, 428229459, 95021498, 978946048, 123355216, 554977290, 918192395, 57313116, 796006272, 201215964, 934609658, 796991309, 163177499, 38431954, 959166715, 997967726, 851932285, 665566538, 642964015, 753566283, 393944554, 523099950, 387166709, 179004992, 331315326, 731008318, 295249936, 303756991, 420134727, 989106393, 684701584, 168663473, 268633689, 167060670, 9417200, 289456904, 982248960, 169323767, 562127021, 723812574, 185650775, 829431426, 689960860, 89699507, 851569160, 650280049, 219111411, 408416040, 129512280, 241592421, 777302999, 459752712, 158044319, 780056314, 96967004, 969445669, 125977519, 36616737, 552371726, 81822013, 102052829, 425938275, 260255304, 354018615, 748071522, 31734403, 308653600, 924785082, 858936417, 182829392, 908748078, 145146988, 566034000, 752504891, 931744939, 128016133, 837988270, 677017121, 695778863, 779298839, 143913831, 339105259, 38928501, 945062296, 894697503, 893048260, 721879998, 729819652, 865540360, 182057872, 13906064, 239780118, 505944692, 684358299, 481849783, 951348246, 94130793, 654841808, 752324129, 502907265, 610515772, 45201958, 956427140, 441922519, 96395429, 243389467, 116687133, 290936246, 593513878, 668397102, 64510019, 164020254, 496223103, 956073803, 198658127, 786507788, 181404799, 626885570, 115261735, 97247384, 954258883, 673267635, 128799154, 340417420, 481393152, 716110477, 177261395, 668024677, 125000838, 338827625, 153014486, 821204739, 806634775, 128391385, 660194826, 264054152, 274730074, 910248829, 387423117, 370014253, 240830482, 318778331, 369006421, 996607669, 973527977, 235393442, 502475343, 718755838, 312258592, 51964206, 977616702, 723059302, 921608322, 632471414, 137446661, 200991850, 181252077, 254080666, 519817116, 679869597, 411181886, 647120869, 912814968, 410364708, 898825272, 738180135, 594921505, 838871190, 936099405, 943028406, 619891150, 88315879, 960454689, 276211200, 37587921, 536071016, 146077710, 33233950, 544015463, 636710593, 169848246, 583509040, 688228902, 80537827, 741169272, 827431947, 421437742, 301049147, 760363673, 465907526, 484023408, 843652684, 526838870, 313072457, 936305625, 314510570, 901349103, 55459930, 371739880, 426201149, 185066839, 66853257, 974960942, 676732728, 888055520, 947544399, 607343416, 771141918, 714924233, 270716603, 991036624, 999726718, 942557310, 724829588, 453784784, 828160867, 939246142, 199342929, 907419877, 428128458, 504038677, 118105104, 659981703, 519456404, 180232930, 499750716, 741323883, 403908085, 136539141, 680970702, 377706295, 298170747, 721072367, 234405177, 542874269, 881618464, 282459026, 942504134, 181251978, 995968238, 216120864, 969126671, 477908900, 954299663, 345008217, 488775293, 438872215, 724406257, 972458322, 863532223, 601731609, 448791251, 440657151, 359458781, 541267519, 690937683, 673981570, 750106357, 345099154, 247794492, 264724758, 215110339, 588250586, 944610647, 594047532, 693538936, 654242465, 955446951, 121803824, 29692209, 86177497, 554574177, 126738384, 329318082, 656725553, 873606253, 747020023, 71706167, 733908074, 673639099, 108261504, 865416643, 37379903, 408364354, 684261160, 249061559, 476192138, 277691827, 427071788, 159525463, 836518019, 561924123, 401250727, 69050096, 521566800, 11422518, 299027930, 508157732, 701619787, 793412191, 521818123, 754647449, 933419906, 652514499, 838757683, 356637920, 622777082, 880050366, 582560029, 809629858, 13191889, 201268583, 260603188, 941969804, 227716764, 849942792, 524118065, 268829013, 135348346, 125174627, 127081237, 812306512, 653788446, 837317816, 779389419, 545010618, 107676567, 109832046, 2038913, 333038624, 538843100, 826646447, 257325185, 162028030, 881875351, 554946277, 976497816, 353175644, 897277578, 860685625, 785108662, 946719855, 75618542, 128424020, 492443797, 473005604, 6033075, 267528261, 666539641, 378901172, 567135826, 315722349, 995086660, 427622486, 968178772, 591398467, 732806834, 216024768, 61581456, 351660339, 635827247, 884238996, 577345844, 305828812, 587334482, 710295293, 380882943, 226357773, 922035001, 680308213, 707958057, 170495014, 428231698, 445587628, 544589818, 466510374, 946823516, 94729983, 957942931, 448227787, 769843538, 590225904, 810402417, 555960439, 724960399, 932015071, 290109062, 738616365, 13430207, 20919202, 76231208, 564487755, 282031788, 459649161, 815434312, 899140290, 680761520, 265828857, 46744135, 111969622, 121011926, 339938160, 509107271, 793794634, 17159777, 501168187, 547258027, 410371193, 945170005, 900887221, 807295696, 43390240, 127579809, 425735908, 16578223, 733300757, 695474805, 257780940, 905442357, 501443384, 650189428, 54897909, 485372467, 436687963, 993515093, 256919009, 320942476, 718350722, 655096540, 424209272, 431488246, 380681415, 80967064, 791609428, 448182907, 347375996, 472201808, 566030530, 799772478, 34005188, 446406555, 627048013, 108086024, 150089717, 53958564, 385917672, 517663177, 463523362, 294008290, 303869355, 775177780, 555903035, 305570808, 255664388, 280601486, 656534260, 849027868, 924807410, 337904612, 897290472, 629092365, 302166037, 183008667, 818649065, 131102424, 362706820, 502775026, 220537832, 419613490, 449620004, 742802374, 512421663, 268749195, 600989479, 672142520, 814422116, 871712866, 178610551, 555483116, 10005825, 589441357, 551535243, 359362177, 556724653, 512577314, 102721283, 718286599, 904752357, 416942002, 777971861, 165097507, 258385264, 862763783, 227304532, 673422387, 943563552, 506101283, 235394652, 477676370, 687645161, 674275985, 163601110, 318943270, 735726218, 365012312, 972851693, 565799738, 882498496, 57784421, 408569095, 27523491, 847898279, 209395279, 643482774, 247750648, 196924159, 65142672, 275928542, 890475554, 711274291, 522132184, 499072396, 513289546, 270191970, 171977456, 41994593, 414081318, 576417259, 971932803, 173684022, 608708778, 192729735, 176341002, 565235187, 849976733, 358238998, 413768186, 163346381, 764377219, 204832748, 138383771, 282067930, 144341213, 343255015, 681727749, 741071269, 457709434, 25966973, 531476587, 900682076, 147729441, 26615547, 911482507, 254026273, 895302256, 595430176, 880068040, 835666992, 175925543, 933856227, 70243005, 140171863, 380667781, 580720236, 708820475, 498986841, 324753828, 438988266, 221751139, 589009731, 713233475, 303654409, 45996316, 505565513, 951229196, 894664178, 562251253, 578239813, 8015937, 214223417, 245874219, 623549382, 325580872, 405424812, 838418905, 711257711, 541889843, 87243190, 922458447, 20394471, 373083352, 902522140, 843182479, 273554687, 392300404, 810461566, 691297438, 93195872, 361666052, 757510090, 485049922, 407712300, 808436578, 364553940, 547605771, 918613893, 185263421, 574008924, 245297508, 585937206, 948151200, 207688439, 332401691, 794462817, 912676299, 717043426, 406226556, 812346143, 868129448, 514925989, 850962341, 698188603, 968681815, 926355797, 658027439, 363430089, 118882752, 354855580, 569685647, 570052063, 729908537, 897150179, 626261557, 447023049, 271177629, 953748525, 956460152, 245350387, 833997526, 541713184, 694099192, 58133832, 856704569, 350376660, 831641807, 448179598, 918047764, 485132952, 869036854, 389947022, 523317367, 434683560, 26971114, 809523507, 756454452, 314382579, 319423548, 802341126, 752923363, 154217373, 411330798, 718937086, 739542061, 453543599, 292470683, 106088668, 435897969, 663864847, 864951381, 594099537, 845639015, 416445831, 140066105, 221585896, 686003278, 79116712, 775707333, 381885451, 640530019, 813181860, 781668897, 48171598, 193826956, 139618934, 934492619, 678221369, 954295768, 734769358, 906636353, 506708933, 974723108, 476419830, 384888101, 441210828, 313393412, 876972153, 496367552, 20364484, 623262513, 816374986, 740149902, 962606084, 237767260, 595168979, 470651729, 489618011, 370356504, 48054577, 547926174, 872849164, 552544582, 662076425, 298967799, 79584623, 417844649, 758694172, 572843591, 552334990, 587655234, 43339267, 904366485, 143344741, 391469482, 933467833, 530566304, 738400085, 460155527, 409268011, 872267223, 405405215, 192186222, 201632496, 561651434, 73084242, 834856962, 183197962, 314118444, 20919637, 662007461, 80141005, 43966917, 304297803, 501783361, 513799931, 201406172, 347688825, 739360394, 71847660, 315540333, 273813125, 904226157, 792199433, 39339811, 434401351, 464659338, 99838923, 250045816, 500468296, 740423922, 764093252, 350208280, 382959531, 980674247, 461320722, 994974970, 850190270, 107552507, 696345166, 891655313, 678323450, 852707903, 500942526, 277035506, 389309163, 891776648, 146720246, 68123850, 308977072, 825369375, 594332158, 637189032, 104831600, 227497930, 631055080, 596595021, 435090632, 260249027, 257717478, 404608618, 56032559, 332881982, 962148396, 10448641, 509081986, 442878585, 739154554, 515735281, 958824673, 529604089, 399112192, 241498456, 427222587, 119142981, 995360700, 223248999, 408629570, 433213785, 407881517, 192292763, 260367550, 581187345, 926016706, 24715162, 148669064, 887379961, 51784575, 998915873, 287600455, 854600325, 492877693, 717980274, 24012827, 776127481, 391470386, 149902416, 615832065, 571207091, 879755177, 905933917, 56118047, 185070751, 774919259, 930773405, 853343982, 55103418, 10933290, 513981480, 234609802, 318545256, 890486848, 400953541, 306307137, 753482952, 308254401, 433045264, 817368247, 233985789, 5552054, 66696593, 744170976, 396370330, 654260290, 377629698, 25442803, 590880738, 352877113, 997428445, 966173168, 888238924, 517749691, 663505504, 708102472, 531950301, 963291021, 802752002, 838202661, 772608198, 985321112, 529352315, 283823445, 11640097, 404188460, 970617581, 627474377, 785145119, 627950583, 26048815, 843384325, 207540886, 197380669, 449778777, 504553444, 991580322, 540123488, 682874364, 669665050, 966406839, 582590728, 779556071, 831673489, 301672705, 543217535, 586840298, 8663019, 474887845, 191591577, 214978592, 655586260, 376526790, 887965012, 827367851, 584307467, 453759093, 890888506, 690924797, 408136187, 571916564, 813113131, 67146178, 765890975, 993305239, 348388194, 915364645, 62306843, 533099179, 199667507, 694244521, 512143273, 782939232, 573568439, 218715475, 610746892, 64978531, 8062095, 643087144, 984567032, 687776311, 571371325, 454840841, 74126259, 953398728, 836598202, 122671133, 342127054, 412891202, 24720906, 143324598, 153394264, 125505547, 281323754, 743890682, 601236733, 964414298, 618808531, 20781575, 703824306, 909228957, 519021155, 862566690, 55573877, 358640298, 309640488, 187811228, 436582468, 879394346, 217006920, 109539292, 201683702, 365785514, 670448276, 901407481, 8478806, 249640714, 744963482, 329202674, 250537714, 614731649, 308413626, 196470986, 542243897, 799752023, 923390622, 902231176, 630656330, 955877386, 164655019, 157455128, 629459700, 203404067, 756516452, 131559, 848755908, 221444025, 207693780, 606562519, 56402710, 570883265, 242553242, 597789990, 101381743, 962802430, 817823994, 507364489, 314523350, 329290931, 328028044, 981140338, 447303847, 488437018, 543672063, 497880950, 547131580, 182169875, 61668743, 350517068, 939829395, 684072732, 48628072, 148358299, 552792896, 626990746, 38404738, 841824758, 659233982, 664681751, 863763945, 407480264, 399021941, 788888151, 371680206, 185867956, 241043997, 120624752, 34888694, 154842949, 550629993, 908559158, 372636262, 419532820, 740661903, 240857326, 424851911, 561545366, 267220029, 645107487, 882182099, 27850083, 653388916, 582501079, 491545312, 301714295, 188818586, 726600650, 771796515, 407806501, 792930963, 557537713, 281761855, 537784044, 151578869, 550509705, 203139571, 868557609, 972743620, 745550902, 651353720, 352337279, 141092172, 258955516, 227305826, 513933981, 393387711, 802862409, 679199747, 614574839, 915391257, 429070536, 351642930, 388120634, 406783818, 483361253, 686145747, 987260135, 164433420, 858705126, 667587136, 193829253, 658626570, 795686102, 807539482, 487666047, 691542742, 10030205, 201712801, 903325285, 638278622, 850605036, 454130646, 83364555, 321742256, 694974995, 529729451, 703090473, 600530099, 865695211, 29007246, 274223265, 990320891, 748754176, 606783313, 989091255, 11861393, 965754356, 420021686, 378201226, 122193963, 531293262, 310252608, 345474534, 35946794, 449416026, 353410609, 771642353, 218178606, 316548839, 606006104, 311915893, 169787970, 470591443, 450090274, 560400626, 243023888, 588871114, 557631915, 334292600, 455336691, 961667322, 646116761, 531589859, 922172065, 565119156, 989152891, 864655121, 348133587, 976808304, 26599746, 808581836, 953330668, 829769424, 129763238, 841235462, 279017063, 845018521, 872711053, 768415276, 770585733, 2286373, 847107361, 649197367, 144645022, 118192958, 159574745, 85876771, 623537337, 649697970, 53502955, 56028468, 276018678, 420398362, 515449391, 2761097, 673026067, 604989882, 600750876, 796480575, 577628513, 587341291, 354845529, 309250470, 829200576, 266552809, 605638794, 720024412, 683300847, 489645522, 58467652, 419455133, 384117804, 716468088, 500138921, 567613677, 767132690, 826546515, 762416015, 439747445, 53303469, 437048419, 918642844, 572169830, 271848141, 162622301, 744746957, 748367348, 32382073, 320189346, 81123780, 782419703, 675999668, 443488586, 258664987, 141939689, 597850653, 122334455, 281313052, 61189061, 634887609, 365685042, 494665475, 257064354, 516835518, 658498456, 726091843, 902359523, 665682683, 427985652, 944244930, 860960289, 988789100, 990941356, 390474986, 759758660, 950226666, 915057316, 986986132, 781916870, 155421544, 20578325, 642481572, 30064838, 364673499, 662707623, 138961886, 999927380, 400358312, 766351785, 167964952, 134848675, 505107201, 431217782, 129751685, 663728737, 640584682, 879616093, 147031526, 778317079, 951254108, 448643035, 406410053, 952127504, 569533717, 394395634, 374670751, 687398908, 654698783, 117131804, 439831939, 815875678, 803547379, 872883843, 136962423, 930497735, 140571766, 512492347, 766266564, 487931012, 210616266, 262192202, 99989546, 532009199, 732294490, 36921051, 631187784, 167632046, 414639924, 922046020, 498484342, 930523746, 373551930, 525078069, 920789532, 614072339, 886926951, 395816383, 740444745, 764264976, 676814520, 646605988, 882697843, 764445785, 725518500, 140644565, 546025636, 672297648, 799192050, 828730035, 587190304, 196378850, 398085753, 605942844, 378365384, 765076698, 747366166, 399100248, 297426377, 12336187, 498949627, 824894915, 886015472, 673170766, 401907136, 524206892, 956983870, 923371790, 736825670, 495942276, 490137316, 647248436, 354613645, 556545446, 810273618, 637271328, 916925885, 611811636, 834454356, 875452697, 789612511, 876159766, 944435524, 717102094, 452127141, 761038292, 844921273, 425622063, 32842181, 448598822, 995032850, 191048514, 61479123, 746226287, 209239451, 420565625, 966384152, 393200386, 429175013, 481079549, 750228662, 307700955, 393415968, 296283824, 31601803, 8906117, 362021215, 60223637, 106393055, 461568229, 397222832, 484338913, 360167843, 121240523, 187335272, 536575135, 334487008, 980739918, 426621486, 74417045, 451825705, 973254139, 437817758, 45311600, 673373181, 230059583, 29110391, 199616007, 362182452, 734340805, 946221071, 708487132, 605346770, 855841400, 301769523, 737918618, 711401969, 632468732, 520305682, 596222549, 723954671, 44632803, 247401388, 649186522, 900439624, 624919310, 138807166, 955263315, 372695030, 136749995, 371753608, 550489790, 331968932, 28048197, 688244491, 874088166, 402980620, 136835211, 960327339, 499309331, 69038199, 395964238, 627144296, 118083752, 779062372, 582011219, 895526978, 858667609, 872730300, 579418850, 321766352, 646781309, 906387814, 716845566, 939415906, 899004632, 211482069, 627572555, 524652269, 437316681, 810984917, 224154661, 983970992, 625445860, 670287983, 196652074, 294233332, 472850244, 847995717, 139500432, 394417540, 842158175, 102198165, 354408771, 737319416, 598047484, 972955874, 573953516, 342523445, 130964832, 342393707, 628216984, 180141026, 965029185, 364504964, 398595456, 874216379, 331837868, 852623814, 871979136, 301845815, 782650535, 868427831, 104571811, 38596828, 523346582, 187890653, 711164523, 468128982, 207054757, 371237749, 858670391, 658252087, 994450794, 882303543, 441211342, 742532977, 480100766, 335306190, 625176042, 272771442, 283786714, 789367599, 564613704, 363394530, 360728015, 80314586, 718604, 666744821, 603152244, 811422893, 220910606, 314706788, 385042275, 298813713, 698969305, 554431675, 772471324, 79533899, 663887869, 933808509, 858343696, 236324052, 828646170, 384489814, 439039910, 258319741, 726463126, 834301369, 93676686, 560051088, 216245590, 193856770, 441376719, 21499404, 975485706, 629210582, 385401870, 370473011, 193732017, 897601511, 83553170, 307269147, 913673390, 186922812, 482100434, 26330227, 925262591, 167948153, 487841008, 252769184, 445176105, 639144423, 244137826, 664959394, 144626591, 673295541, 586146600, 836753168, 57901130, 135428663, 195657669, 46473570, 12681831, 412585618, 905619768, 718339461, 375105657, 534158569, 532171475, 150288656, 622885992, 743453635, 935879692, 349399311, 638749857, 391764863, 281517457, 900615572, 619267831, 421678017, 993553797, 591144348, 346211267, 153492018, 744984013, 96926225, 310119868, 789549994, 733912517, 43985795, 248481880, 386284069, 461376197, 442721614, 870702307, 475995622, 877548189, 460895008, 621171427, 620417519, 511567171, 509339086, 231639160, 64324506, 616868740, 486757997, 732853178, 634790003, 872100608, 502400557, 326578646, 252882117, 239792105, 545624283, 914785160, 591909072, 688036757, 59516436, 658019457, 942976021, 700171551, 204726906, 449100304, 213560782, 737507130, 548352820, 823495874, 871743170, 966495684, 877956235, 254958492, 268117068, 1273703, 399403716, 766198197, 458534960, 881787790, 682001227, 65964290, 489433005, 876776740, 98593261, 219702718, 282019988, 84921584, 960015017, 491420684, 699715841, 170792977, 84304915, 147325768, 541235984, 799455676, 219526488, 899908688, 212442224, 772777460, 742103148, 866891410, 606746465, 889718265, 600253491, 290507545, 621486774, 716948817, 778438457, 244188571, 946961632, 258770125, 585372811, 890999114, 408973489, 178440485, 448014261, 652851485, 254068137, 699865535, 917586378, 25471693, 452594727, 120024545, 303134923, 309793534, 731919716, 937418836, 996067312, 922225245, 642368327, 642504166, 504236546, 306525233, 271455279, 346821531, 531423051, 326120845, 431624093, 833483706, 708297309, 38527525, 968591190, 326194917, 783133279, 556664533, 320366316, 188938940, 988006097, 447013353, 674319705, 132240518, 215144234, 967089032, 169130648, 51999037, 266143986, 822255170, 350493415, 154485428, 981550092, 636691395, 612795941, 181452923, 697198737, 346513342, 233674723, 13836246, 891680154, 559338855, 289804401, 873938964, 946180646, 826195070, 639973230, 840321368, 888417075, 165800594, 165563253, 577395420, 108312438, 914214374, 232167850, 608557513, 565030488, 975198356, 877869003, 168251931, 616085599, 887608208, 152228029, 271384695, 469686818, 625116935, 103720234, 255866379, 944059241, 628695011, 469241869, 294037824, 216628538, 734316852, 881999055, 405066397, 585477294, 625384214, 461089593, 305203293, 216786036, 932934497, 589642248, 853136893, 184413181, 994922364, 203386418, 482047831, 824130119, 994110709, 971224047, 431019288, 721705840, 211060272, 884227119, 776981485, 710764692, 767360879, 193883418, 578895063, 103195619, 665561040, 2201843, 291576, 606010670, 782919568, 789392737, 437816627, 891125443, 758911453, 262227725, 685739204, 279465596, 773781095, 574491621, 886160478, 682779892, 570909744, 811829398, 864203752, 516828869, 59235524, 483299629, 720935636, 973973692, 129549296, 523987589, 904743901, 904807873, 432475360, 188454685, 693966862, 84477330, 350636618, 682921918, 871214229, 982868717, 455820715, 485663173, 222826596, 388448780, 218789965, 784034059, 708249375, 412178529, 595614817, 914946533, 245404326, 310630123, 178232381, 780088238, 110863402, 65446470, 905244032, 617408725, 489731124, 201247002, 211428766, 939408320, 842523937, 403203831, 646940107, 764123025, 334801269, 327319175, 730109033, 486427391, 13973448, 785595309, 822178170, 175160168, 949396619, 326236154, 370676927, 701685280, 745255019, 896457199, 416860287, 60674582, 342149070, 462240592, 851899658, 779751828, 679243866, 757468704, 717336367, 242730909, 772405381, 811215735, 324763766, 521974350, 254148827, 653498195, 623420331, 751560979, 418951689, 20385857, 931457253, 860951845, 720834805, 745856979, 415292323, 467321261, 187417356, 529112609, 329672395, 794680256, 681176155, 11102461, 353414919, 38988313, 134391543, 397144512, 261344287, 156445516, 190214118, 400715696, 298131567, 771275398, 688625908, 821260638, 937618634, 433857196, 757692882, 59913945, 46366412, 646339045, 160658467, 203359981, 326139746, 314485574, 695272282, 8989201, 116097254, 539936025, 217893291, 821212396, 951157222, 350372176, 695456765, 371156773, 878784051, 433057762, 627611021, 783487873, 257786121, 968545633, 270366952, 525165836, 162305148, 769070738, 962064026, 399676804, 968006649, 619371290, 229911254, 238551497, 373997118, 952995771, 185117368, 780332602, 57051961, 450727735, 929051755, 406992084, 207089689, 696923704, 584714208, 924702056, 242103656, 58828005, 873608761, 561181453, 277004711, 115034589, 397881723, 804642095, 437329293, 595108678, 237763283, 815097101, 756779612, 793342681, 117768176, 429940352, 9758740, 411728456, 708530151, 44287364, 77319141, 850088699, 907416766, 48425287, 269370880, 206269201, 191625698, 3310490, 692464078, 373052568, 97354281, 652271513, 657335955, 19918071, 172988576, 203876006, 978444823, 426302454, 827263555, 283899547, 901055573, 764754199, 685688165, 258974058, 172194967, 851787468, 42921280, 508166107, 329030129, 874346600, 229464804, 106797366, 89639607, 795613452, 328578578, 690298706, 327648855, 955320779, 743254299, 725033519, 822756241, 707603579, 103769441, 9135383, 527208513, 143091830, 6090641, 962112369, 711434482, 986390313, 746576079, 945240163, 626358859, 475060871, 964378948, 495726670, 769967941, 889222964, 497937928, 46850210, 331159167, 145776655, 753260594, 179500692, 721434644, 90500011, 209212527, 325805954, 179400129, 661161328, 876757008, 737495088, 700042529, 545499293, 344523815, 870788200, 487163578, 452261289, 136323184, 538592832, 61681653, 652925510, 919721606, 106070538, 991634906, 152454926, 613835522, 730559380, 510957845, 429044403, 861900975, 616659804, 471431391, 737670470, 233800026, 460038472, 424015628, 702395821, 598038925, 534735918, 332143528, 781205478, 812840314, 479662372, 340982793, 812054322, 272339673, 888573069, 253500373, 238023797, 936518906, 831837169, 479646996, 536152757, 362153327, 852142100, 801524811, 168769148, 369232037, 379065853, 133477071, 288382444, 255244842, 745635074, 389759204, 902762002, 945398992, 957803680, 779667964, 908706354, 306508857, 120558834, 699800697, 598601135, 784079884, 974098916, 780942728, 44468833, 296148816, 310343918, 360701049, 594833728, 8842699, 265660277, 293414858, 956731402, 781906045, 29067019, 239354856, 341773822, 328550861, 729822458, 13434787, 86734117, 790654960, 204989767, 22381095, 934913411, 19864784, 836449676, 611342366, 252603460, 18787111, 696699111, 828345487, 110820529, 485545044, 44719857, 290813174, 208376373, 481188979, 826516787, 609747636, 581632343, 70579030, 896815517, 895062758, 999300014, 605942818, 71068768, 515609854, 752423981, 405606247, 17280461, 574575818, 459225693, 770253908, 136731104, 465184002, 984581508, 277211050, 127692513, 125715237, 634842743, 224638869, 412061060, 811949768, 120569098, 146661090, 185326059, 392816493, 566477012, 291978192, 843911388, 316005361, 820968002, 254730085, 112000852, 151295010, 608061445, 452907024, 522051888, 310343694, 676287782, 65861902, 869038310, 314100205, 710120159, 453172150, 585087067, 90821572, 315824885, 613933651, 648316343, 433862937, 190032013, 415833217, 920037008, 854915994, 619778624, 153639327, 560039499, 463876242, 61304436, 409886835, 485004033, 987188811, 912763735, 570945144, 147543082, 270086883, 766022112, 557255493, 270231374, 927818911, 627016697, 205605122, 818738726, 563353922, 954047077, 203120001, 463963255, 409166015, 191013326, 914658271, 702862805, 762876951, 667948977, 340762470, 555650495, 434920306, 994181450, 442155683, 100555195, 874247024, 992663315, 686844707, 561369521, 790812979, 946905411, 57950246, 755702756, 366499123, 436441208, 384125566, 653179050, 564248199, 389869284, 120718397, 439346366, 533803698, 533594921, 351061141, 435519202, 746799943, 366616499, 953555640, 414000253, 713174112, 853200989, 957203656, 64270580, 295672333, 936956753, 148094751, 939174941, 103836649, 757195975, 883441959, 935026978, 122002243, 518361255, 265037579, 922895539, 207338531, 117857280, 15139618, 328489157, 114497683, 472625071, 606979777, 998192423, 803556836, 121333431, 534680063, 307162581, 34377272, 357560410, 398050016, 159517496, 800564503, 205681637, 128588170, 134806214, 741032290, 871890598, 50957912, 180592436, 521342099, 527750205, 665229280, 93520774, 314453209, 288309090, 152716341, 74458483, 187493213, 360325703, 634375336, 267575355, 978444055, 842823906, 370296356, 341980436, 724724792, 286998846, 893085166, 969001468, 114312114, 76011114, 222923038, 225756099, 10176449, 119069779, 896497261, 621819624, 231502073, 269355718, 772561433, 995389272, 817979363, 910455717, 160827609, 113589327, 558198666, 930353512, 744450729, 927353308, 606526332, 687917158, 896668422, 381329781, 444525693, 441568438, 550630535, 378723692, 249754448, 639403100, 615119803, 431976493, 949011258, 974555827, 198628911, 87498005, 494414662, 34730712, 118241231, 403835386, 92013388, 219006289, 536864893, 70137265, 765985526, 409566554, 596997944, 585070763, 906548981, 171467249, 954625222, 210768417, 241388734, 857453587, 346962261, 571739760, 755272175, 621663165, 506367537, 931200425, 366660079, 34188132, 254452482, 435753563, 728656471, 977509511, 24094071, 74387418, 13299970, 83819462, 666095709, 554888401, 398660736, 671138564, 474158191, 680545979, 99102897, 719839339, 76130481, 679247295, 701925901, 1531263, 757140150, 786055699, 191402284, 894196410, 871747165, 86664403, 651267083, 470936935, 685779777, 478568296, 893485857, 525034675, 95108451, 694136918, 330378990, 396708808, 209710712, 695312063, 125370011, 498221598, 807294264, 233796491, 175608071, 363573163, 447268446, 626080263, 742895285, 570182185, 13597199, 4320591, 936248391, 676348154, 894930845, 45806124, 669359342, 318462166, 274550664, 85625338, 2495153, 689859298, 500045589, 804839123, 792454470, 776325618, 123640229, 397372701, 552005972, 375019581, 587021979, 444209861, 589416973, 581495413, 476306413, 941778328, 647474253, 413365655, 565723094, 338757419, 119303189, 316399853, 645698820, 205765936, 270229897, 97467852, 210618761, 857027379, 413786375, 530817477, 385179859, 143260587, 524229513, 539376793, 482731449, 880494280, 112237280, 873731401, 84568363, 199268481, 477994893, 697857496, 559222490, 772937884, 476705923, 372402474, 280248760, 637245094, 59428361, 421903892, 816086947, 848567385, 494416512, 672372872, 192755774, 37531252, 310449332, 574392117, 965842435, 30998150, 585549525, 380894478, 166898947, 830920911, 707694867, 969078965, 751289350, 737535687, 652203156, 781107021, 940415144, 697330563, 26461618, 764902731, 73054544, 265451441, 108208235, 638835613, 539759437, 940152916, 641775167, 461397669, 83521129, 279301475, 603193873, 595076432, 985570865, 432900769, 900157117, 107712702, 83407259, 68969185, 886484586, 374014244, 240781626, 936424617, 194917057, 392763583, 460841656, 344107632, 171764948, 284944714, 684096850, 293693335, 701084629, 137820118, 196454084, 101006778, 71879996, 967979960, 418544555, 556047198, 248601943, 849070450, 657476442, 128678355, 732258199, 935790701, 432876923, 11497321, 639834153, 334936931, 314934753, 656619148, 872901156, 683055825, 922673142, 760927395, 620022457, 202555108, 857375457, 638125422, 392275731, 583037601, 485184477, 987460329, 251584658, 695452269, 311911425, 238601187, 572606987, 711295470, 458918820, 222866038, 198751541, 264244724, 621945539, 136289624, 2796311, 39682091, 183011514, 103422002, 714851562, 432869169, 306917080, 64427903, 58749110, 500908630, 598892335, 41134756, 859449489, 481293552, 389442222, 919250537, 979140710, 220654808, 450585415, 417016808, 345484411, 893141884, 608221083, 571262451, 894296362, 810586944, 574720298, 255961179, 73990828, 631671075, 382799826, 144797612, 64540179, 692571803, 828000782, 661920283, 767171915, 226084253, 952742781, 423109552, 649009028, 766187205, 968942080, 331046392, 1894481, 370766917, 502136693, 129858507, 68389012, 424730095, 245945962, 409861718, 993729006, 608205434, 421475655, 436154566, 741532984, 904492740, 818586775, 672965012, 318270660, 280960555, 518281073, 564637824, 575804113, 180967779, 450486988, 213753637, 244029258, 544415891, 227729074, 76545598, 368141458, 139064483, 91700370, 942124755, 328487181, 513225780, 669807292, 132502815, 606829879, 793536895, 921630906, 610009979, 745019019, 690135236, 372275636, 89865955, 775693930, 767722726, 919847686, 389388742, 114206802, 539280042, 996712121, 681286998, 543661361, 217571863, 156587380, 831551104, 290551278, 568725939, 669240849, 80132185, 302165201, 514663895, 235063641, 14587102, 132416726, 207908566, 607748219, 720148180, 778927017, 238293778, 260226859, 193904584, 199747944, 671345159, 420593521, 33422504, 231950102, 615194579, 218038055, 775979314, 141287007, 611007479, 73361993, 865578833, 322769292, 74166150, 40563697, 980014178, 450570819, 683211039, 557019390, 562447814, 392647476, 70172096, 433779230, 214878203, 106667119, 994929965, 895176247, 924195602, 778333759, 25435889, 697261976, 957194910, 505030640, 276872216, 808463233, 922375513, 282646697, 547650091, 778381291, 204135331, 221056124, 921563194, 537985690, 809694546, 322152731, 866460607, 110796235, 349380160, 391548727, 362221151, 667602438, 974149820, 239495758, 418946291, 712191708, 280028419, 457508584, 97054650, 538501672, 724924050, 964506074, 64774394, 799545882, 716021150, 293568372, 158663172, 630283758, 621569688, 692285330, 565876288, 329836033, 671453455, 627877924, 511547130, 807330126, 531545549, 304531311, 820858189, 160700149, 710936791, 323458057, 235344478, 426822510, 420092532, 283971040, 127379375, 2098641, 630210089, 353159164, 273625538, 235924788, 497371561, 876560777, 374841261, 685625771, 223255986, 937832605, 684474670, 392589615, 317731685, 974009234, 288962399, 438717813, 826182588, 975841068, 286498020, 616447374, 588648531, 692108532, 388755540, 281558635, 699664920, 274094786, 496341528, 150755441, 906532838, 395290244, 901612501, 779520876, 341114949, 514855165, 748574845, 589979455, 414825408, 84687905, 798763624, 267405775, 22977363, 352200770, 716089729, 826799659, 198110696, 678115931, 763257, 461408356, 668128699, 196139039, 341907682, 620979373, 539517528, 42496351, 123879943, 882526555, 484245796, 460414666, 21319118, 550841169, 523633684, 444218987, 531496637, 219934169, 421850108, 462778223, 183866905, 186372756, 293108393, 895972593, 394059534, 257890483, 336826384, 172965244, 885186469, 948424608, 517861424, 987779082, 995559851, 941465811, 718957143, 718154796, 477914771, 209679238, 342676166, 491936719, 418155044, 363880235, 943757254, 205612661, 42425718, 468170926, 83358894, 882966502, 666309744, 231569020, 556009079, 815045332, 27597393, 517291759, 38175033, 449073027, 636084942, 516655634, 693451266, 510556096, 536222252, 100009440, 349272968, 412770622, 1178956, 311885436, 429724627, 853637745, 11520930, 721069403, 185472923, 486776158, 73800263, 840299175, 578700409, 57496585, 353142571, 881140434, 610630781, 555915409, 209157432, 838657309, 577816768, 833241192, 9589935, 270492777, 245998670, 443637637, 541108210, 616141136, 548522170, 441886656, 511936831, 841334098, 960497936, 284737985, 461757526, 882759848, 886052350, 743494971, 610456759, 422402043, 678980239, 21182671, 497605753, 89911839, 916114548, 578409901, 88806990, 180980950, 415348029, 992127880, 681704764, 51344279, 703090334, 524137460, 119314524, 391467676, 165171086, 481952345, 881464175, 167126299, 189884385, 90778829, 16490430, 509801322, 231648385, 884038700, 486872426, 797136081, 489808140, 861267454, 183108807, 451430059, 114587124, 786230818, 945179288, 292934583, 60086641, 512950963, 703563342, 430593866, 417779225, 104030012, 564312208, 735674079, 218007791, 28235676, 568422660, 181467353, 451793552, 409516364, 581295792, 147870917, 782709427, 707551236, 811790263, 967918941, 37514875, 926765613, 672131896, 703051499, 108867527, 557812065, 924175977, 28386272, 58498901, 331993293, 605404677, 645858251, 85766200, 912402481, 183549111, 676210805, 423258173, 943433678, 81100377, 917081096, 380483732, 225669605, 557451157, 400474803, 522675165, 867260307, 692594925, 593123150, 829817261, 883838208, 453366229, 105824560, 986992126, 408087382, 121750354, 977354466, 544258492, 574027235, 910045797, 56669094, 574292774, 874472367, 579597978, 54455585, 640799332, 30579979, 561956990, 243250661, 522276920, 943621238, 416323447, 323963622, 585414232, 392073198, 432216358, 80015073, 215091300, 740593490, 693057879, 937160428, 270515865, 371667453, 318223160, 5058626, 721344267, 98169688, 576822883, 241333986, 277676312, 232097875, 892799295, 412427893, 446413694, 503932993, 708358843, 15502644, 826151102, 177722722, 409131163, 697884397, 777593072, 741352862, 991356324, 56600785, 978690255, 88467615, 472164059, 727520595, 314794156, 572123991, 81096560, 768065525, 464102351, 851931693, 268493667, 565340144, 969192794, 158300711, 948770328, 877509942, 269164946, 665366453, 898994212, 768307994, 93297827, 125908436, 308282335, 865080708, 555043429, 230098558, 320994772, 839111393, 932646770, 242516853, 340914973, 222763106, 459025516, 251257878, 504589390, 463927715, 86053587, 382511535, 665382646, 740284445, 808272266, 196669954, 663230683, 622964737, 324664364, 534251999, 578386507, 446409296, 739641712, 931975545, 864161772, 404267292, 488344428, 930015645, 499208042, 455274430, 589080082, 432563504, 583364329, 403303195, 746687740, 873025992, 940102632, 837541169, 933047949, 623672247, 664644085, 429213722, 401959663, 176628186, 129157341, 909716230, 272644417, 719293281, 81134283, 260370583, 924300761, 739346060, 991991260, 849580162, 783230196, 28228739, 210227431, 511134411, 816644651, 742130541, 968778714, 957423521, 229604464, 654461806, 882412349, 930036383, 270044842, 81624569, 621431723, 372811559, 420145619, 847925181, 138503367, 306544984, 26125180, 823125941, 751795581, 213254357, 53984593, 370637089, 950900065, 941418127, 630837365, 253595375, 818749052, 79047185, 511965308, 685049997, 282448254, 80146111, 457849301, 376783710, 81500041, 285844278, 103546494, 512664123, 247831102, 601597379, 233143392, 12148030, 606258802, 283285244, 762403064, 245153275, 917653145, 730735169, 55677570, 881819990, 326590485, 32263941, 749580622, 248371287, 397678466, 211184557, 478827264, 999042542, 654973028, 35507563, 478847915, 446583976, 49567099, 872289338, 724667322, 525932727, 546597375, 849008773, 179234388, 91588226, 627652590, 619677760, 926638732, 560021958, 208391769, 856711737, 548285845, 171649815, 567633304, 538522234, 933853359, 284645868, 892931750, 686634594, 774561810, 11159738, 714095664, 621839587, 3940254, 824424790, 844075294, 55124406, 350973719, 758041630, 534197870, 927370313, 157338931, 79783929, 98750588, 473942207, 829725870, 188477227, 63989152, 646128096, 97403168, 728465533, 279251557, 886435756, 866638392, 496747851, 681803214, 339632276, 236961225, 495783472, 329947599, 769218761, 244118093, 912915209, 450212315, 155395104, 119336042, 383899295, 378771543, 616341728, 782704677, 584723497, 816157927, 137066194, 349941582, 503879228, 913659034, 476194084, 852705972, 626255754, 620477842, 589945426, 757997315, 148578021, 526478325, 496118893, 326901287, 395219639, 243173902, 555182840, 730638837, 275292147, 776392080, 810888004, 182659666, 889983155, 585085492, 268546173, 910019333, 915151334, 749026380, 760726223, 602285128, 270781915, 543335900, 580241706, 292305785, 517852563, 996040628, 491309512, 479825194, 724915288, 885501690, 229405103, 598331647, 153403159, 929170423, 310597527, 952942712, 31767017, 790440998, 487004432, 756521999, 487561238, 100710444, 289133445, 251886268, 615468662, 552626863, 675887683, 854083835, 533848353, 92914466, 847743322, 282284524, 451067015, 1825653, 36969172, 120644272, 995508385, 889703967, 518512575, 729041007, 513748946, 740586030, 105372029, 621116320, 615317012, 608364797, 956474088, 371789839, 837334839, 115014249, 250347741, 528870684, 617019317, 740818345, 613003878, 810827816, 621735629, 144211874, 348424188, 832138794, 592852297, 420638574, 130662586, 339977490, 385045313, 735050396, 324603106, 963546817, 252653652, 538604666, 700944928, 272653719, 594097640, 928526106, 766865606, 193679469, 159171236, 320664064, 360141177, 807116595, 782111194, 719939216, 814895927, 777779049, 115042879, 666277142, 163421521, 757755409, 316776801, 761741941, 378917609, 823900579, 974639275, 482487172, 146487723, 319916369, 338017453, 283654765, 445126639, 60219620, 194223973, 758342110, 24059868, 664156287, 484915868, 58299744, 760271667, 901775594, 594306265, 466624509, 652861340, 474823034, 600969577, 961160909, 750345590, 736668690, 525066494, 181795610, 510558400, 65428858, 125183649, 444274731, 977256460, 295343060, 381649297, 562209038, 291888220, 510854412, 188582115, 602583596, 346058263, 514488362, 601579507, 107725481, 332646208, 655612972, 521189308, 243582233, 89844629, 568642261, 314838211, 208651925, 253461017, 704977995, 162479275, 114476357, 854247525, 713596947, 261453009, 735620924, 207499417, 311960242, 292679423, 510965784, 752884758, 672514450, 37460436, 41266716, 44694405, 798715897, 153653446, 280084843, 434702266, 380289084, 312229941, 889797432, 34723683, 837572068, 468224566, 37911092, 579672626, 652276996, 920539719, 508481873, 273988331, 377243653, 604907078, 359893812, 422433183, 731209978, 841174179, 142642744, 671461407, 307784389, 729346615, 784905647, 247559064, 190609176, 970772290, 14643627, 688431200, 639183855, 159532319, 159596880, 918433286, 201586867, 384683075, 800889830, 622768428, 74911015, 570265220, 139266797, 856903937, 208336614, 909529452, 674233867, 416494930, 711359191, 383091158, 664275922, 679608971, 438682928, 493353638, 616578191, 82295984, 457680003, 120316397, 956917872, 263189714, 951431609, 940359524, 200114214, 192611869, 712796729, 792308284, 671632609, 589253915, 977229518, 245684798, 182206274, 22366240, 702584569, 725866045, 678860735, 705232476, 10746827, 309564658, 731229361, 395569485, 992265491, 557764851, 388190761, 938430754, 431408348, 485837155, 698778881, 579379913, 589203311, 583195745, 100284288, 466507273, 776052767, 381084633, 753102014, 704339760, 863388850, 375907265, 886210588, 299306650, 169556778, 364776252, 26240073, 548643771, 578190136, 241557403, 807492610, 246380720, 48387947, 630408132, 731369113, 101827946, 507147558, 264657235, 195239731, 261316605, 54944404, 408147943, 364757560, 888176339, 947641990, 581828921, 246550385, 599136286, 23648149, 755672495, 139458788, 172639073, 764320103, 631110676, 664338835, 118370116, 821772118, 278785454, 320780548, 61460199, 496871195, 583462902, 740794895, 512954590, 496849729, 68081857, 797216959, 40776516, 17406879, 651605706, 124994616, 390334254, 749953050, 575198974, 432033684, 17926031, 815423659, 123718777, 798251979, 171954142, 517383849, 658436387, 703662576, 466722770, 731533466, 61847281, 731483079, 50869276, 914737598, 342705934, 368919281, 55621909, 651236588, 148894929, 679480, 133114496, 254839543, 371213795, 622485850, 12311087, 746048274, 264731953, 170029699, 485080774, 782669400, 907164059, 37425070, 813757113, 867574120, 674318647, 34284863, 988837905, 771570068, 961277006, 819942655, 554169199, 751384114, 186789825, 864620962, 811066447, 1384027, 921440568, 487829367, 733323513, 577557072, 693560072, 613474036, 16295715, 17895585, 500823881, 51751019, 335325683, 798615012, 422718095, 126622937, 201150628, 525758102, 949312415, 154924870, 762943120, 319356863, 745004999, 335019154, 6429089, 966229859, 408124604, 620983874, 563036423, 150032115, 441876235, 105293349, 256323116, 952920966, 578294128, 41891091, 303114356, 784533505, 449620456, 412525333, 207335885, 696044959, 157373115, 974974655, 540384795, 506727884, 190391072, 881623997, 562061470, 46848128, 731647581, 809806113, 307149633, 693289449, 107759306, 887722669, 850767685, 172551164, 863375593, 72453441, 750150412, 894466942, 17387847, 742835338, 657689913, 264391695, 796396184, 934116726, 593034152, 597831922, 143342176, 111522598, 924948838, 642544317, 363187083, 701768068, 509053839, 20447308, 590036910, 704727125, 775111950, 224502808, 600498320, 724336971, 45022178, 295562345, 192490212, 82004533, 179392479, 975149429, 102572010, 184796983, 254578270, 510078265, 845542182, 639626705, 725320178, 806164438, 371182280, 572000013, 758771671, 624070727, 162479344, 146360379, 422899751, 134684845, 343566146, 553289033, 750003882, 472744568, 698686343, 396876981, 885060884, 896817754, 136081322, 823321401, 702496819, 349456056, 504204503, 744713803, 323984683, 959115081, 271896884, 597828245, 115944681, 121598065, 770863656, 779539505, 860880753, 597321360, 758989317, 381695617, 992585488, 684137455, 848083029, 10670427, 75411508, 323531987, 167895837, 624505735, 365849308, 997453564, 713529116, 77010788, 769821678, 828900033, 906522423, 64472786, 153338188, 28593306, 756405388, 71547008, 814111418, 257683918, 55203963, 71810453, 627255054, 400533964, 595266262, 947826973, 451808632, 407146777, 664001143, 787646691, 700110928, 657390186, 794531230, 702909305, 469891692, 707625994, 776043645, 77986347, 687591314, 669615262, 110994169, 593264140, 349071851, 880778358, 3093457, 256487515, 669059739, 55962614, 378819543, 454562318, 926192708, 508209061, 627412432, 635840841, 966848431, 252207752, 274154470, 767518080, 536581715, 973922046, 792367926, 740558478, 835592989, 74384283, 14757617, 26386674, 513388030, 961331519, 955098563, 167339952, 242472693, 412979174, 745160692, 421268599, 742983364, 79778508, 546595893, 812944450, 77941084, 970385871, 825718583, 863936104, 528684214, 16230365, 668841750, 319282664, 699873557, 179570559, 320274423, 100189542, 994667805, 295028544, 592718322, 546644803, 933555142, 703066308, 946332222, 941432401, 514241843, 351138692, 522917257, 809714575, 512386742, 746751513, 127316552, 512478976, 352964366, 473713703, 596321227, 752460615, 559341865, 425855738, 319677373, 317599107, 699378657, 224565130, 856081783, 317119713, 671854337, 614153593, 420073896, 626773585, 150997523, 620647398, 549042156, 222856417, 757541882, 14645476, 729683499, 55018081, 523345052, 48620382, 360203224, 941417519, 195301379, 160003378, 183678440, 56235034, 879349116, 622789501, 781653498, 171663287, 270575757, 496187837, 810822867, 587053375, 618481302, 686861628, 417308915, 662741265, 117474875, 314964245, 289279639, 879778203, 335032086, 57612196, 723288910, 337024867, 94169547, 413363451, 878914461, 949306166, 274162207, 639013237, 428600382, 463314424, 798399720, 880419117, 141466920, 876544183, 411024281, 666936637, 336754335, 424548351, 118025037, 127359837, 187150640, 667027476, 386716343, 839039704, 659403448, 489120457, 18601306, 425685088, 453340621, 431153354, 214858500, 330236885, 180772884, 853459956, 468485211, 834128346, 751647265, 556792340, 554619227, 791815806, 922642148, 48674639, 558752901, 74300303, 160443279, 268934348, 425626200, 229419489, 915249623, 702810282, 496398984, 625692283, 5609317, 981638389, 475639970, 606051372, 780573744, 42034751, 298526384, 197176874, 991724674, 806365245, 971547984, 220245788, 761756907, 662253761, 860863066, 33707128, 412775391, 24897913, 15920004, 676157840, 291423835, 869176012, 204700749, 866196135, 977171197, 349778489, 880616170, 121116016, 292627259, 960518058, 921635314, 217482719, 576539450, 569226447, 498768624, 47390153, 934531330, 404846335, 405503643, 28046587, 483035535, 345679889, 904393468, 99145291, 602520705, 54237579, 821432845, 238267877, 688793222, 32261819, 181742221, 990765801, 209497534, 678625214, 749559029, 545684992, 235352791, 97926711, 730738962, 681155733, 592574342, 697586049, 748980589, 831048579, 895207624, 576823366, 779990049, 314711736, 69908857, 528531326, 996491582, 386137089, 480914478, 331435250, 809758063, 777568833, 309184563, 564087315, 636669977, 128055241, 82431866, 790689181, 687013135, 370080632, 199987483, 660148584, 402086777, 99799420, 657958847, 758146496, 629336433, 65296704, 138260806, 101525834, 531985669, 957372950, 916858350, 509993804, 531216276, 28800806, 687764339, 475089946, 778820418, 652316101, 200642130, 229809340, 391059845, 448910302, 658034636, 747342232, 803843324, 91713672, 499089581, 787373808, 859190332, 483402228, 961495788, 787195241, 705606606, 620898097, 234150601, 619112460, 198924501, 795903441, 944254418, 697721256, 563477960, 5334845, 215296757, 138662160, 3653488, 750045116, 618130766, 891681179, 579432495, 252618367, 457086390, 796939681, 281993246, 725310800, 434691476, 111166657, 83234977, 324083462, 97562569, 757192738, 820841997, 403515333, 590604584, 681307902, 795809147, 381967491, 991488348, 331917578, 965750230, 430575507, 117999998, 919274867, 683951255, 40968550, 197397333, 59873448, 465966145, 120136672, 21320325, 837843411, 285580348, 847134791, 740010129, 455186086, 542118964, 427978068, 890128498, 681154610, 934158339, 742571866, 923700583, 121437838, 83218137, 796836570, 16389430, 282416343, 69483218, 613446037, 995389727, 634055890, 962311809, 777843079, 972370343, 903065830, 615212186, 38108591, 120581088, 687865662, 270354706, 128752290, 913716748, 631329192, 142096135, 683812102, 519235733, 442932760, 298838874, 363632602, 301557737, 285911351, 750981868, 215355408, 831693943, 859147205, 431685245, 322420921, 756204583, 626580075, 151087721, 236804545, 817147948, 959452370, 450982381, 858533421, 951500645, 96362422, 281076551, 509048270, 988180559, 484456579, 502208954, 597510974, 459899690, 413980275, 468934852, 314023865, 845762588, 567174850, 811293096, 407561426, 381002890, 594121944, 899434787, 579770852, 841867729, 491577990, 175383076, 506020388, 375791545, 343893131, 568008424, 444459235, 458073289, 642705787, 176760764, 524636776, 512434433, 688270967, 481336297, 543780893, 756728720, 515989454, 196682614, 130905453, 29697380, 865285145, 720985905, 954860399, 263736929, 492822053, 570450490, 721838801, 300789037, 142501572, 801877005, 924846797, 717486830, 675810581, 428734147, 4388394, 817875722, 441774705, 304139304, 350023361, 495372988, 954911938, 223301005, 516002600, 66798054, 120216369, 64201805, 125524337, 736528441, 830733128, 929883038, 477797321, 925409349, 34331599, 258922451, 775577487, 463609342, 621196559, 412750519, 911529, 312223507, 356938319, 305267312, 289841574, 537398086, 558499709, 200233904, 112831256, 9826738, 598424283, 706777812, 780045723, 457562830, 770790286, 730358717, 548521847, 893146564, 251764612, 925040842, 148951722, 490432317, 631287521, 237276530, 336717934, 361132296, 960639371, 600133403, 749155620, 882343884, 755934123, 335175951, 25188292, 886812533, 422289880, 597441739, 525277521, 436720334, 643675685, 240609171, 675974753, 331998340, 572139270, 12587492, 731816761, 31357927, 617484151, 549446264, 498968388, 844046010, 435711060, 844352243, 619553427, 454810495, 993927172, 798090900, 927885898, 997298583, 290066136, 377535006, 220076646, 4729104, 28968691, 614121776, 224488186, 367282569, 169237100, 972895654, 773195563, 629335357, 896892843, 468359350, 707046325, 715751913, 465138030, 829870893, 202695150, 812795942, 601924037, 419860598, 344848713, 741670875, 163444068, 935129034, 25977304, 750077213, 255960896, 377568071, 837219803, 681721156, 685469668, 778026932, 822740616, 784834955, 81212312, 35023788, 194731688, 383058600, 834898659, 491536682, 78866753, 698968204, 495096372, 991116089, 684206102, 144364044, 856505297, 203324456, 387558682, 1937649, 371737322, 178170397, 725205107, 428427194, 236441396, 534915532, 788605939, 390678072, 464169387, 712487059, 680884109, 15321534, 562332933, 684668264, 84186951, 939036441, 391244184, 281392582, 4652552, 386399405, 298628024, 637237327, 383346720, 392819153, 692594485, 348048370, 756579348, 153122632, 474778502, 68824430, 32887685, 209916638, 715934309, 152794321, 639100843, 355937346, 502386728, 349273337, 748929821, 564125423, 867251677, 974171666, 373400864, 34247863, 136143172, 154136062, 323619958, 150023627, 505571542, 791626164, 864815940, 480918763, 642899557, 95789353, 306644236, 926947019, 526917392, 842917908, 785854519, 44717175, 919905072, 672168368, 118720549, 919502565, 948982165, 714686580, 912938147, 819521540, 984254018, 141176337, 57025103, 658295306, 890851595, 129980869, 49018731, 489668150, 856150897, 437867161, 161167322, 70490204, 293511684, 565947382, 956041341, 398514750, 663983572, 76722230, 975307900, 40532485, 185724489, 150132345, 783806358, 991370986, 24570568, 702603208, 931279151, 560732689, 397101841, 417476847, 293445790, 938385285, 258623332, 797734915, 609385857, 979455416, 376066371, 498283035, 837121215, 257018730, 425471739, 881751783, 56935452, 761111129, 526630483, 348250493, 396454976, 769915677, 555631656, 634426628, 315322935, 217298616, 536983140, 492405125, 986412427, 231617423, 36903042, 96399007, 203295109, 771484081, 925973722, 663245424, 893224799, 3582394, 8714844, 75154699, 297427282, 701764644, 184493054, 257664758, 684126415, 716925270, 45135638, 2418709, 371187311, 171861855, 128583465, 685349012, 29363507, 374273883, 638417590, 337469605, 608534886, 779163410, 428035043, 616101583, 681549495, 887020396, 719433701, 312343097, 773232156, 878346775, 970197992, 979825130, 761454191, 549166632, 205125767, 768281368, 702747216, 475919307, 296767609, 301498169, 949709464, 59864494, 70597372, 847915341, 271386890, 331682719, 706833357, 367411736, 639682121, 116841355, 516354684, 201852398, 539879987, 236521555, 30773176, 71841121, 200881078, 948624842, 405136106, 685809486, 331088653, 871460772, 622000136, 783986147, 740209200, 33777959, 115451347, 414990654, 568627483, 850443833, 758681622, 175447441, 450745842, 595679148, 864859769, 718881883, 670438461, 396093242, 161842993, 122837163, 526129916, 27008692, 722398437, 262566399, 754028094, 917074888, 405761485, 758475537, 797698687, 246881905, 948075852, 931182058, 32375720, 162403057, 431562955, 502045337, 411287733, 344378020, 704636977, 316327777, 313175997, 539911677, 286267168, 817602082, 797614849, 207249692, 505822669, 56052948, 344085673, 121916948, 724771350, 492516115, 305933823, 936444763, 952967771, 379256187, 377200934, 324304702, 826315744, 306084658, 205744895, 989454971, 408956941, 522025999, 118106216, 639383268, 970515878, 718101890, 925462863, 588994147, 312708824, 426119478, 967516510, 245907593, 802971431, 477889383, 86227908, 75919610, 47016548, 102486901, 557665860, 913801836, 789920124, 239043055, 705988832, 667192416, 254902847, 550595545, 913237148, 825319112, 574865954, 282854568, 182535256, 824331905, 935899769, 397698022, 25695203, 671995022, 610207987, 923132882, 134462072, 318387929, 250020081, 2743776, 910738308, 430133085, 807890516, 187733413, 958633823, 573607875, 900369888, 749023273, 520726210, 880562019, 143259461, 48866724, 88622562, 811244430, 826032831, 622979596, 159164165, 196033815, 600352967, 952164357, 102194717, 150494119, 737838952, 432217812, 933168241, 140169317, 614493577, 307402316, 246419585, 380668035, 124278043, 257462967, 985597262, 22964912, 547545437, 435550436, 3870022, 626581031, 325076787, 226046316, 367659641, 283575604, 497825834, 514223399, 601598973, 128288004, 804356345, 249405892, 910384235, 663596093, 142267732, 559167848, 503604125, 256184165, 331092784, 807418363, 158054481, 746209148, 645845499, 789233901, 839427761, 590139251, 325117643, 109098411, 492388721, 764209870, 860396537, 904035524, 863671596, 194716093, 456727990, 433352052, 352011835, 978411386, 128636372, 215462646, 496688738, 826225003, 383090099, 597308112, 234102723, 575110599, 666782864, 673131950, 697736704, 416947224, 215818345, 354639934, 246679262, 373391645, 351200952, 116006046, 533141421, 895284700, 1763000, 482202720, 397948529, 894365119, 988823661, 339726019, 856675851, 581209179, 750647241, 863434565, 914360617, 212397819, 323792132, 683511976, 474652467, 117934933, 857402478, 513780488, 434983468, 230155397, 104925310, 845115733, 828196650, 123648719, 227302756, 878192912, 828366811, 948692237, 678120053, 54822342, 812346239, 471645918, 665309590, 575608480, 374755801, 455824532, 470310973, 102604973, 9097109, 725290338, 610661947, 627167291, 206180620, 374848331, 528931340, 783173878, 861522480, 401497329, 546620883, 875232564, 965120291, 292205904, 902460176, 277111264, 481581518, 75327501, 607136965, 470279400, 352588379, 91552999, 32777766, 768142303, 136770738, 673212340, 825978901, 730349841, 920264747, 934545028, 88430855, 250292879, 824166579, 246473789, 996933200, 68778872, 247832907, 617487930, 455858773, 973979191, 791545437, 938538367, 849409412, 794174103, 319738292, 11575832, 242956003, 781850890, 323242645, 774939720, 627787333, 287151909, 664760707, 226445293, 18584927, 950964469, 778892697, 186020020, 308439224, 146240942, 723543837, 677801157, 230432676, 254346181, 320743312, 972240118, 491857004, 158910559, 119445788, 804006417, 566646268, 852374300, 575251867, 535254888, 248129127, 869975769, 132048919, 257812433, 747089730, 131193585, 27041367, 680554107, 343494579, 41444418, 343812825, 167943820, 105485960, 554844969, 36313589, 716786872, 777250140, 518956212, 382482017, 925471899, 615795622, 274639604, 399082231, 900038738, 639463531, 669845994, 547345449, 674898358, 278489930, 772083389, 609846472, 396721217, 478928480, 362727998, 199434405, 201531025, 909073883, 241680664, 471959717, 623332806, 786436022, 678583639, 979554460, 584565531, 863241421, 879709544, 285429629, 145674377, 624939158, 584326770, 596404785, 487975690, 118364450, 402562836, 88532490, 722271034, 932734821, 37786584, 589413630, 982825588, 134232960, 74347924, 723762718, 695907848, 176115895, 578667011, 658732844, 29784402, 776990043, 544731507, 530470863, 784595762, 588324667, 299157494, 583019609, 857178250, 760906880, 426865588, 159529465, 68384249, 435096663, 311157404, 325099326, 730797189, 797483997, 804156752, 957403955, 676426950, 731935825, 224068296, 688130547, 133628364, 454769663, 640391276, 583030018, 924410827, 409349039, 930279107, 697685056, 448111795, 479381275, 541744848, 473878807, 177410520, 858836298, 355093058, 242192282, 268598102, 439820529, 490634170, 686361629, 447344671, 977396979, 860251557, 62527256, 292999841, 749556166, 998857690, 789420112, 148869341, 909414649, 552824932, 746373726, 577688207, 214324232, 639998901, 269929118, 290373683, 995511904, 439460489, 15491320, 52756263, 260383111, 838417661, 125295024, 619523013, 447140129, 294395062, 959981112, 715378221, 285848876, 917220974, 874902039, 229364096, 403138996, 295293293, 692123145, 465609046, 359437577, 546495592, 464380305, 510904544, 890927459, 674648672, 107258848, 514429592, 234612905, 790198755, 618444390, 630512751, 52218151, 877177045, 859504394, 133329068, 803223887, 798323156, 259412357, 798749827, 642192904, 444168883, 173382143, 326647166, 40408121, 7729623, 474742358, 367503790, 869480050, 370263365, 260161075, 51043841, 794310476, 273185635, 172417444, 575818652, 815647281, 838719668, 881382611, 69365742, 192952104, 108167165, 519645576, 851842869, 605386928, 33352898, 810324102, 776633306, 737975541, 454524786, 854021205, 590284637, 208063496, 870600962, 791716337, 687919981, 110453135, 403605499, 847847126, 374863480, 14379212, 348930721, 338225085, 861471650, 289612381, 895961605, 553566384, 195497601, 276691833, 478725440, 904000343, 119370110, 873461382, 539717673, 654913305, 253351430, 708018769, 294539820, 624364887, 278107364, 402434069, 10306941, 780629072, 242680063, 981093982, 348640139, 448237697, 133748436, 958454270, 11753360, 128335068, 589546727, 199933140, 112580138, 779934240, 531581469, 323612005, 204263933, 349902587, 147801333, 525409029, 69804606, 347210664, 611002626, 441920975, 480970705, 517520208, 998753149, 388266720, 852585978, 992143357, 728317217, 271285698, 321272159, 802946149, 352625499, 796422006, 150993118, 620436265, 634102351, 445561951, 17867415, 515280413, 676847833, 267073136, 966878077, 885019961, 785681364, 935901276, 190352085, 841126882, 42861342, 790887439, 187265203, 119778188, 586683228, 655576981, 521454762, 434091562, 300684655, 99321354, 376519764, 103387233, 596631354, 972577908, 536058514, 393976466, 714557212, 708319451, 348664673, 994877652, 837783306, 197557512, 183460550, 25764989, 548130542, 608416994, 969712778, 808447675, 643016781, 985162133, 382081511, 41420106, 749016692, 288006797, 394606600, 933748706, 441994559, 19691550, 873483787, 543335690, 149768412, 465826811, 76206223, 813644052, 177638849, 983228612, 400383572, 921338414, 524034874, 406898887, 111863948, 590646957, 271337267, 464849878, 975481758, 501189762, 870988978, 980983555, 386004114, 584906343, 63739919, 695442484, 778525182, 112021103, 512700306, 427703834, 25054508, 134521740, 799891925, 838762401, 78078049, 942645888, 885763168, 598676062, 893072653, 51586053, 613666582, 348867006, 248474408, 713490176, 105499338, 32398676, 931852013, 704271074, 258528008, 302834795, 645114415, 381853283, 479450502, 886939233, 889907901, 93378043, 636027633, 97799330, 857697804, 552900853, 814335744, 653870069, 928464414, 897423741, 376122056, 759138831, 370094074, 55777757, 243061855, 838598649, 364254950, 359137075, 460466931, 637294330, 199820261, 324172512, 127459582, 558403065, 431030307, 676965152, 404617765, 377396600, 856897956, 363022331, 27677238, 257781227, 933156914, 289463430, 503876618, 608317333, 867948305, 377759089, 80306615, 634886485, 290093854, 194580276, 877540940, 187995452, 197155239, 270905911, 258975036, 422356457, 158022591, 497448736, 318562606, 19960290, 848703689, 226646718, 103281007, 460577810, 310619348, 717833050, 312390838, 412234508, 859373589, 500900375, 973252082, 857428185, 550848436, 469378449, 916616197, 120717488, 72412848, 508345760, 362252340, 298067712, 532586856, 379265342, 425328048, 186128904, 203843322, 95840407, 507913575, 971309214, 495717292, 502595841, 401599901, 823397965, 783450247, 222872690, 824909696, 35962256, 260716914, 394342404, 148455145, 498827729, 708710862, 225424955, 222707729, 672565976, 541658194, 451257794, 106465057, 567325165, 548968596, 954162601, 831541654, 849172576, 260810907, 628281674, 792532152, 373744591, 590335323, 720496748, 897896639, 332459794, 874652503, 599149428, 102265675, 769748368, 373129898, 870691866, 352180080, 251838710, 714482622, 707952320, 705894960, 391787682, 837093621, 69876041, 732749900, 357972288, 527933346, 382621052, 165864093, 584283046, 927701680, 647598361, 376398936, 486633540, 713973922, 43975374, 833920927, 421039788, 376005621, 207416993, 563228204, 652694583, 300840493, 829511038, 991925356, 973309799, 541799803, 886889907, 289004263, 737261887, 272900966, 631885582, 271309890, 326697836, 470872288, 816003007, 795444759, 611987255, 431049853, 623521551, 148739167, 834973048, 497121875, 46961186, 298601435, 398125586, 650875790, 299024116, 850339374, 726908997, 868538534, 225080991, 686056747, 25921669, 182105945, 143178530, 914283322, 876536911, 124588308, 222534449, 971845446, 440927648, 685715638, 467277061, 441901148, 795994415, 529737066, 191556418, 27841012, 921683840, 877836579, 267776463, 161045110, 572398593, 923091384, 158133645, 52174406, 763402589, 818945614, 503505004, 180593086, 639025371, 977949960, 696895413, 901154666, 251117098, 861975367, 248163077, 424546475, 563599906, 262782663, 314552247, 541134737, 893662015, 828291689, 952878003, 564650762, 453382845, 252916976, 41917718, 754700955, 764462674, 269317005, 427511236, 785112887, 105821241, 623350562, 606180015, 995528315, 948340581, 158267242, 633331693, 447700022, 7891721, 532796367, 567516278, 55706369, 738975964, 72272000, 196939005, 468073085, 921566436, 373718911, 289105855, 527734181, 233441562, 461542551, 89988343, 61135507, 522473050, 42972746, 552873358, 202042850, 616381024, 624906916, 74019527, 97493947, 29604420, 802258039, 171533080, 603490930, 376758029, 597871616, 61451323, 110334873, 475180613, 268422888, 55577729, 77073825, 954085502, 754516475, 900674251, 663326014, 354097320, 377689886, 370384861, 817890435, 16630535, 522662590, 627078624, 305246468, 29600352, 116420782, 53097290, 117521173, 695376626, 671381343, 245078309, 113658835, 143352028, 560842475, 59620147, 427604963, 711665409, 466770310, 662525589, 981334790, 341430276, 219136648, 153197894, 912174778, 794024681, 41064355, 637347010, 612216280, 141129107, 838376064, 81100429, 198413810, 544662159, 297358253, 754592189, 769641759, 258164550, 19710624, 8542834, 831718081, 69799729, 411198572, 341838011, 766561163, 350705819, 507513326, 101071439, 331687277, 853324298, 957627738, 178254803, 232324474, 340466282, 19969137, 492797524, 809236443, 79502263, 157773837, 946195124, 208451579, 362561390, 61075774, 198336633, 426815006, 891841893, 64573710, 997452836, 932907900, 791471319, 330923754, 449192982, 273903013, 580215127, 477530049, 48950159, 224958151, 492304589, 93110556, 578316734, 281892119, 118117812, 468387619, 154168425, 507153640, 444877037, 941034764, 309845753, 94541086, 758802774, 702598776, 613691904, 807258249, 106897207, 725851064, 518966822, 796785241, 554322801, 405325979, 666025494, 767962696, 668965340, 653779493, 108514263, 83234521, 233566566, 493323212, 490867229, 145728694, 262540300, 721515335, 98649144, 677240430, 144314865, 855183556, 364670779, 838108811, 313939019, 11626490, 596533208, 57598030, 314764108, 411552820, 892674425, 417528014, 536043485, 933118853, 309927236, 616036360, 211130321, 991088493, 553808693, 621216160, 717458008, 224652667, 810828920, 995731404, 326090689, 209477499, 535983440, 258239503, 317562973, 852762496, 996263282, 450107519, 982749677, 182814755, 489293384, 634802772, 551305317, 587796658, 341377566, 863498307, 474932402, 261888369, 967164834, 301097623, 220535729, 90242498, 725955297, 511812330, 566826604, 780240093, 501883955, 934317326, 741902574, 854647846, 592263397, 707922966, 699018499, 100724486, 57913074, 421068158, 958442502, 851453517, 465626292, 449727342, 497090953, 387695646, 726620678, 969917992, 647225928, 99780018, 720079922, 449277017, 38204310, 541815937, 684258300, 906806433, 132727926, 72444577, 844097145, 286642091, 608270056, 472777247, 180799487, 274970324, 591857925, 896446346, 848396287, 186262353, 618831702, 572124059, 482824823, 568975643, 563131380, 704077163, 249754875, 549489249, 909428047, 242128051, 550642023, 494203725, 164939144, 360151022, 49064039, 679687932, 245444595, 680724998, 853034719, 696450945, 746817191, 122084965, 662149386, 10867296, 946397527, 482749538, 304202607, 713164137, 308869905, 706606904, 775464026, 923028988, 185336919, 862329213, 638345713, 256053943, 545565826, 968069760, 601487190, 101853624, 354285194, 173951552, 185860644, 780501543, 740739086, 575769376, 902063754, 358326070, 645858045, 666987533, 926665942, 44524032, 571498113, 592048916, 578110604, 101592902, 399065368, 769723557, 744264801, 840934079, 495929279, 662594427, 833229471, 91805172, 612546706, 600958746, 354071280, 36184950, 793155858, 453268557, 510097023, 475538780, 495699622, 489874961, 598159490, 852388239, 378119213, 72914486, 20466999, 465143631, 872411152, 100754466, 93527465, 398978952, 50948459, 494076817, 523200144, 330976089, 998304029, 201559921, 402126004, 78419634, 735219524, 751825876, 843749378, 453308088, 896604426, 523266950, 970872977, 884344498, 301220971, 303073079, 185508389, 557826870, 924046814, 793098449, 814458843, 688264369, 6912279, 187106847, 353745241, 852667348, 440673026, 228487215, 353011522, 440383251, 725401259, 449474829, 116920041, 756016763, 921041031, 138512990, 19301515, 697502134, 748187854, 808953860, 368821403, 419626386, 722097031, 463174796, 48212830, 190734337, 951825384, 540024084, 608204913, 850277308, 313405480, 321083678, 683259653, 998513253, 767438385, 429631113, 517317884, 732014900, 779687058, 342678260, 105483679, 247722649, 343315487, 974525047, 143682113, 826633980, 232268732, 834924084, 822702205, 959227422, 484314567, 183840754, 453208386, 633243549, 89825685, 174573561, 893610019, 197659597, 490827532, 855170010, 197865824, 498064652, 329819789, 346452229, 314129353, 512336755, 400772140, 915219473, 730485420, 936276630, 309065879, 225834139, 535172389, 41586395, 868501304, 786086147, 414290663, 722491951, 866970205, 884963409, 160248122, 104561556, 810978219, 621703574, 326630240, 687186571, 407922488, 874810711, 29046598, 244041841, 88333688, 328153070, 930008860, 971860167, 547113655, 88668428, 515969798, 452346537, 323342171, 426554801, 140305923, 719561216, 22660239, 827973004, 913691938, 592024496, 832232351, 666197287, 582498317, 692732681, 986826891, 982426977, 290748219, 258553896, 933890886, 555096314, 60421360, 931555647, 281848910, 194876173, 736543405, 985544735, 741503105, 286028519, 834566029, 541324270, 124996837, 954887021, 304953100, 918491604, 341292719, 631797018, 741206063, 147689495, 276822103, 629228284, 345038293, 314629678, 445792216, 314961655, 335616558, 22008126, 678375852, 966855465, 551715857, 679606814, 30915912, 310499030, 821241469, 275983235, 889071860, 136558158, 165676358, 879767763, 423936223, 777203876, 845171223, 844200823, 688389221, 532098471, 37229059, 241818566, 984366719, 769058269, 873411484, 747226122, 255463958, 455202580, 46015788, 115939862, 475396395, 2833924, 173555010, 474236503, 340058141, 875032998, 228389634, 257428921, 730486537, 663422670, 512094824, 837242422, 589997326, 397389866, 301600592, 982643386, 836020693, 367148286, 847039200, 886697739, 299190843, 899538748, 702738122, 117094188, 149563496, 678854287, 430232583, 294657036, 681075388, 413682757, 787536093, 656095178, 978105755, 940829715, 697240920, 189475866, 312741125, 224682394, 181890355, 304405712, 860643674, 799351923, 882773386, 65067070, 354161564, 711246157, 827476456, 137330168, 13460158, 587200881, 711121718, 974851492, 751465421, 533933433, 126306072, 92842096, 326657572, 102172301, 829791464, 792325985, 516878864, 526165469, 163106545, 584153603, 503276119, 793802413, 830644681, 637563540, 518884247, 72161230, 623914811, 197267734, 963896944, 698873066, 528095720, 679945984, 499067063, 512721661, 703408190, 491533254, 350554432, 233792806, 705835676, 809996184, 587655792, 945507572, 659077581, 647308968, 273422246, 729063472, 873133855, 897027336, 59890325, 618881667, 93905356, 958757583, 859128406, 943173724, 256590268, 972999568, 113014069, 772044612, 866722094, 472591212, 842515246, 851415199, 429308079, 93416800, 686187193, 563466861, 292323794, 836827104, 659835281, 428461640, 524594456, 677161535, 2389172, 107381704, 58458053, 78159651, 189750608, 557090363, 119855218, 735089529, 738091728, 84146871, 447869318, 285401587, 396046391, 811660963, 284396093, 206691385, 210963781, 449096401, 333231956, 896953021, 940443878, 859939776, 990059188, 470874269, 241453626, 243342482, 493207145, 373544405, 183401808, 252945485, 160071088, 304085247, 294802266, 215496343, 616178676, 826269135, 906263946, 493934150, 102879603, 450222263, 196449258, 910757180, 288847905, 858675850, 504192947, 988176161, 359073842, 879310905, 921170170, 644558276, 797626489, 804928351, 353757913, 414490028, 7474308, 217093497, 773524664, 842035173, 127774686, 962612434, 350140162, 653420600, 151559065, 104324044, 402585353, 206216831, 913462785, 202727271, 724064342, 66980362, 13749861, 478135350, 681591431, 809911544, 457997697, 789459811, 345621492, 667525305, 100126309, 128620663, 25932363, 709326090, 835062393, 727052582, 845548854, 244918018, 516213708, 393306646, 929203494, 901665406, 714502127, 18314857, 821934000, 839544999, 611235658, 166713244, 235388005, 252183987, 595912559, 978118106, 848179731, 783237044, 696902378, 367522228, 242514386, 366823205, 792076198, 463776465, 127373403, 925110435, 217775607, 880872668, 933065055, 280514951, 252208539, 539244097, 429766636, 404264122, 964593019, 991468532, 1929282, 29573362, 372065376, 412483527, 816609136, 94163331, 732057362, 383991824, 597226261, 821221202, 237481977, 629082978, 59580469, 366802077, 264484413, 595480935, 450621971, 762871400, 796976965, 746173920, 670152353, 393873923, 415574156, 454710269, 780168439, 64602239, 394350405, 121847786, 669787913, 130938000, 312139875, 87974280, 461015749, 270103182, 108552199, 319067617, 422396317, 780955949, 170929705, 349485350, 409303090, 766161234, 663508189, 503795500, 7292188, 255018570, 573066685, 680734265, 645778623, 827935267, 694613412, 202022554, 564030647, 146868281, 571258020, 53490370, 758517285, 623273205, 210005975, 153869466, 104243540, 679660595, 953103249, 674468957, 637952528, 278559539, 338449772, 566965088, 170828266, 350324205, 511179497, 599600607, 806732877, 681359346, 130436399, 963193438, 428313372, 617094311, 477387603, 747599233, 715365236, 564727468, 893509488, 292047431, 608863819, 67982995, 475837406, 68788302, 150240670, 58876724, 506064640, 59846423, 225357994, 806616361, 585538739, 705102479, 431641285, 545349637, 14485987, 819938314, 694156960, 287203707, 40643671, 5108148, 248124232, 44856038, 533498410, 243760104, 160809537, 506327724, 799674282, 350304289, 334160698, 305867266, 182123765, 323857720, 806083671, 228007939, 922862056, 339266014, 894644334, 515822527, 407304513, 21592592, 909694990, 61704679, 179166303, 949585911, 970951150, 626782950, 487141065, 215307718, 145747990, 898738213, 308953206, 943114962, 217628298, 802163921, 362136646, 944413771, 812386677, 360858678, 175112387, 901239086, 207008930, 967041218, 180649303, 226412041, 617929727, 689452705, 318228497, 859718594, 780802490, 800450872, 351126111, 660900784, 235100159, 171849433, 320717570, 615167289, 715352097, 525668595, 807773555, 855452396, 552405812, 511597613, 157688065, 418091440, 569957214, 874338472, 272789070, 93650421, 324893432, 773177116, 83232943, 341142181, 288714994, 66769188, 517881315, 490511857, 725420002, 828530183, 424475131, 987225453, 247498532, 205453929, 98501114, 952089072, 808904693, 461588214, 782900752, 18702019, 474194837, 40964459, 660992611, 275183154, 943468448, 501318557, 709328093, 524653806, 36266563, 266874733, 605550477, 312101153, 221448296, 218990774, 23655050, 123743345, 77243523, 594486945, 365338754, 500368670, 47230822, 855140892, 320998639, 327911971, 477874157, 65247507, 1811403, 955641214, 685218664, 706999254, 306597560, 310245374, 397635621, 561007524, 730173129, 574140711, 483364395, 795173167, 14084423, 691518484, 651016656, 666878394, 50679988, 146760846, 797199454, 411613486, 706778286, 719928209, 230542628, 701108994, 491686040, 459929714, 849007556, 292060675, 347567855, 760162313, 527690214, 775271308, 507876854, 230386981, 704513316, 179930687, 809604623, 330290695, 719935511, 836512736, 764404917, 128010040, 235124354, 119963664, 341818532, 971169837, 323337852, 173726362, 972152578, 845649310, 941692100, 656067884, 590714893, 433869350, 354008888, 221398279, 878336717, 306722510, 400732882, 636490723, 589941740, 365262581, 913778026, 642742422, 386246636, 589805529, 353528122, 572758526, 79825575, 273532510, 765294583, 734650790, 970516200, 789662673, 448884717, 558206414, 841277199, 24458585, 455912594, 893668725, 549358264, 347723369, 119548710, 649248341, 218849098, 358443251, 846243857, 552243343, 759394753, 426524896, 475869992, 721885799, 22273509, 834278814, 924650760, 579130106, 129989746, 51586294, 216839685, 648083021, 536204928, 945522232, 99642328, 323795134, 137724947, 895213255, 386872586, 239521148, 248527656, 645783550, 145031015, 758414562, 516390424, 944020256, 846298373, 301028219, 884300978, 498802174, 742782265, 29124086, 99694821, 577095526, 718725211, 203622232, 983253558, 826389187, 574950090, 222823076, 366219509, 853786904, 752305845, 314812207, 917047522, 806146344, 123049901, 261789224, 4165785, 416666283, 253331137, 713360664, 217255968, 705329753, 465293524, 258444160, 811721687, 905384197, 922261867, 646968828, 308386701, 336548381, 514263570, 333172478, 598025041, 509269866, 147210818, 35839887, 419158507, 4153185, 884130124, 839146452, 889219342, 540175193, 888660602, 263110887, 657884128, 453638276, 726169580, 595089649, 784691064, 795886179, 755022738, 230194404, 115078545, 948902156, 208040346, 842938125, 278419513, 838469956, 64275589, 205335622, 767368616, 94472436, 11842670, 47910210, 599520350, 789259609, 926198336, 536990027, 919892549, 642685784, 919192530, 967060080, 835709452, 300896907, 528956764, 86344046, 84220846, 320683023, 764179394, 790795997, 580690902, 16921552, 755232645, 523610362, 154278739, 430281168, 291135191, 94537189, 98595648, 117993230, 873734495, 194815551, 845308569, 470731135, 373962286, 293643509, 320927959, 573350783, 304464701, 707813313, 409778469, 622245517, 445851257, 720042888, 311216554, 666482054, 182025350, 997240830, 532907533, 314301538, 968290131, 881070866, 395588081, 635915896, 196359419, 708524238, 797555897, 230008187, 367273762, 504055121, 393508124, 27845151, 938819036, 885172003, 314488698, 250504143, 144043098, 942222977, 410325419, 531286272, 966791173, 484401996, 697644833, 662785949, 667824728, 997926575, 78903417, 830976172, 150011828, 990526496, 475986179, 511054210, 49321204, 955547280, 492962708, 205988050, 909046027, 891078171, 441848647, 158512197, 638899057, 781788478, 418497031, 454203505, 428959329, 190324056, 446583007, 524005480, 23203862, 161791851, 731307733, 235933252, 87494411, 551358708, 882056055, 122504913, 986161462, 774983543, 481002308, 563372209, 150851559, 452903233, 324154150, 270299600, 303334061, 273165920, 44566403, 591708521, 999647497, 349943538, 215397406, 127819031, 90354817, 347383050, 409630381, 238501058, 622341139, 81359001, 279098928, 618748701, 66215244, 43329529, 664787908, 598139071, 289674616, 395672964, 237463599, 131524172, 454682049, 578646784, 772752799, 516619110, 703775165, 868044414, 376485031, 988324725, 929593080, 703346218, 510853383, 852229398, 955179895, 546376426, 407017830, 703920762, 159034908, 368257375, 41050148, 219897217, 186636880, 815984528, 954082723, 749346422, 167694104, 37032300, 507825846, 498891453, 626032365, 172559709, 935404211, 781732092, 333887925, 888348246, 144052369, 862309764, 6647566, 154014302, 399526991, 773347022, 754157899, 633924520, 863918261, 988257603, 499260924, 604220756, 177166395, 7981972, 351841461, 43539771, 5043262, 465145452, 808279267, 613877966, 504541270, 157549164, 691537518, 287257041, 723859276, 747775479, 391533879, 373789150, 314776291, 96483851, 776284238, 697940951, 196841956, 854859739, 466066661, 369060531, 554811140, 128532489, 353007119, 586416666, 689322894, 323423322, 797973035, 71825947, 912422525, 596706575, 933264563, 35674735, 424071624, 940695457, 564997150, 511670161, 551811861, 73966941, 201429966, 484812223, 856076498, 386160363, 69651767, 894686606, 966543037, 90220056, 377409971, 823979310, 809182506, 906893817, 954924054, 735161670, 210704405, 583579895, 893444120, 108797792, 27673295, 373236280, 3926459, 620261790, 203273171, 15714950, 793200867, 470372462, 618929967, 936285740, 316251172, 464928557, 787795205, 388249859, 329821107, 363439832, 543688402, 51933304, 966858223, 313405814, 909965846, 500219611, 941662299, 862251463, 415209963, 507920184, 739455211, 607777167, 377777974, 429214756, 406243334, 450944650, 163910894, 876834993, 434581456, 871719392, 814071779, 897827872, 839083510, 694269573, 314805828, 888043307, 892244434, 267381219, 135616240, 451552773, 883608512, 941024564, 208137479, 2138072, 969917249, 779769205, 365199394, 549768874, 860314917, 334530086, 369714023, 192675412, 812874814, 610053972, 256852661, 908418356, 659451095, 408067894, 953172801, 926491691, 632824457, 56683426, 924158848, 588500020, 164588873, 742560745, 155056869, 15517115, 869753458, 156555228, 4594959, 64379684, 415101636, 13806391, 698993082, 672276403, 114770139, 371865091, 75546865, 587425668, 368504672, 210989906, 532429908, 322538469, 950628918, 734476843, 15322287, 197676926, 841053142, 73972903, 637370413, 798661586, 911397615, 188866278, 644730924, 941035484, 514578769, 491878793, 468042944, 687886095, 517874865, 946593573, 49592480, 874474280, 677887608, 575189243, 323423840, 849311554, 325819453, 542917777, 653411452, 104356216, 668742807, 40068263, 277533142, 813853667, 651876172, 977063440, 377007548, 440877863, 767766576, 150775759, 812985927, 430227772, 649881733, 427450343, 483431919, 867025422, 601676761, 161584900, 877241141, 468047351, 967822960, 934579059, 453914925, 687948302, 577787331, 216008066, 783962866, 440204483, 929373579, 99477971, 90856809, 920515901, 888683243, 564128352, 822817955, 270850525, 844443615, 788657979, 237998272, 673284032, 487657538, 745930947, 957516846, 817347071, 865575164, 58901883, 533248840, 772904638, 611525891, 898183746, 444228618, 408143344, 948179824, 788001062, 882743347, 287306032, 947703135, 355590438, 328451640, 269973102, 103393823, 857044057, 96055819, 146716410, 259696631, 331590184, 67788027, 263542675, 446614768, 625995264, 339777164, 364096088, 677341408, 903970504, 68480504, 288080208, 123015525, 407536868, 19539568, 338986270, 848294670, 723514819, 438594661, 632064628, 69018650, 393363882, 243001449, 740601300, 994346409, 32670126, 897817072, 447582399, 676617536, 64143829, 846980959, 894882868, 651083690, 983051582, 818687686, 721722276, 258578265, 829505905, 846597445, 126029079, 384459722, 594041825, 760763736, 589964564, 805387479, 30030910, 727095284, 145116860, 207096607, 201512076, 57801357, 94425033, 645855218, 168689140, 951091470, 288064719, 31306997, 473353284, 384841736, 642589217, 394314466, 242493046, 873435846, 954295399, 484416469, 894798941, 652105531, 951804824, 927059755, 575441266, 718107687, 688579259, 804374233, 675939522, 990179473, 981198306, 270069046, 511981724, 812637755, 522760410, 684609682, 65338402, 803733238, 258141277, 502245993, 516072013, 451858036, 417565148, 162200804, 901557892, 777938741, 257528953, 442316710, 861386479, 805671270, 828286452, 921354372, 94632258, 461206627, 551662561, 121694125, 281493708, 659313067, 108160881, 802070747, 129819585, 465826589, 852552756, 297866381, 312192679, 696807926, 463644386, 810720689, 960187175, 906009012, 141004091, 572415407, 498884440, 557772400, 445138349, 710728507, 127502881, 801612461, 109861271, 923848204, 691626798, 793384009, 884435906, 500180121, 911177985, 837935370, 282631013, 235855886, 204544040, 631253018, 975403367, 415997745, 94830139, 605681074, 644372200, 269910178, 473724817, 674713708, 108997776, 795461871, 223550298, 76687318, 544376808, 20033845, 443516134, 499400650, 284276520, 237105538, 312279527, 438793378, 523973451, 239068750, 596584475, 363272005, 272140084, 119499254, 779609332, 339375043, 517488769, 504816350, 581423527, 471382331, 61261202, 507092496, 451042425, 154552242, 739030545, 682516135, 631261260, 598998649, 844114486, 157498699, 903749170, 979667274, 753767379, 169391314, 419877223, 720712098, 738196230, 256991498, 323559832, 93041342, 596758667, 99411882, 246204527, 537150182, 649688984, 86505686, 475061900, 668225506, 465575695, 617468441, 428788932, 850050120, 335696521, 393279115, 148676614, 994019746, 817129519, 431284104, 935741494, 679044460, 943500162, 531681206, 763727620, 813069727, 40133968, 49983421, 699698896, 432801678, 195320355, 623964624, 551879558, 298441460, 714416550, 761721443, 944928566, 865270640, 78199768, 307972324, 179123697, 653446598, 368498171, 683672839, 966278378, 723000542, 662855649, 242687194, 264136312, 571133016, 127653519, 71970606, 98826814, 218206132, 68679470, 885891716, 495840488, 626999810, 772984058, 800454901, 964770055, 223709463, 42101749, 76063275, 759352275, 37797103, 44000322, 425099886, 538587342, 740816569, 814298553, 743723738, 644968494, 312594532, 552236611, 516348680, 961786797, 531353263, 27805567, 768027378, 95038508, 576199252, 322669770, 574776760, 48347631, 200111021, 435223607, 78892802, 665479145, 718508595, 464660953, 932110844, 225884229, 580581389, 478873857, 656503455, 632217740, 178809502, 688814116, 450628618, 207475381, 159226864, 11407890, 377470913, 46510036, 332079106, 841854779, 703438905, 84433576, 156979394, 175703837, 61764001, 246262159, 726817562, 723457879, 71932367, 69669502, 101888716, 789417916, 133855983, 265035329, 749973227, 445642217, 494022008, 248086605, 919809016, 389055126, 224918141, 959651473, 493746460, 465377005, 649347766, 71004535, 338584315, 847286288, 572483379, 978251350, 735456448, 184941555, 194331314, 622115747, 124575117, 364399262, 546743622, 770965944, 867169198, 382975869, 302178546, 260236927, 65915, 743331495, 305725334, 587981247, 664328390, 556661938, 432235345, 315839957, 477473270, 550662015, 505812642, 653379347, 406254661, 196029388, 582637779, 922192519, 863204156, 2019344, 875452412, 454420842, 820387894, 225278591, 331550538, 792720024, 787601980, 818631101, 996723463, 361283667, 978835536, 367897899, 630341482, 940874384, 263583548, 147415294, 393942950, 190446575, 881133877, 341932871, 490391123, 235150040, 638440045, 138656479, 200275228, 352688215, 208298586, 692646177, 699951410, 918114782, 758946616, 451010187, 399637122, 970849940, 839887104, 936278755, 746728158, 28690340, 13082632, 23497973, 413999248, 830155588, 828637880, 5652435, 734462131, 838481459, 795773087, 748916508, 166939499, 760227096, 32713493, 550233880, 979354649, 883495993, 739714815, 984177875, 587064507, 556684046, 195988928, 777215424, 802568157, 370686367, 388921468, 895905992, 503989759, 55888342, 174912981, 111373511, 714786738, 500000588, 759107005, 359369353, 171018440, 330269638, 205967400, 334857987, 458818570, 770257830, 600161284, 775151850, 775242338, 571178277, 568602887, 254852843, 728011851, 741305665, 672661780, 502641871, 262734850, 530685871, 830455452, 755085302, 343093502, 165198051, 84545507, 23412116, 316219282, 433554607, 483409910, 902545950, 243262647, 14272719, 805261660, 442737560, 691018320, 20855896, 750765009, 428224009, 129299897, 652315130, 870322457, 978104945, 327857815, 769282816, 697792338, 617843025, 350842918, 157950435, 782942747, 896108213, 35468513, 346302543, 295505859, 16450853, 136410355, 401968223, 370679551, 747570097, 455012713, 223292942, 938740950, 256523954, 399152597, 841920913, 739836246, 915355291, 658180271, 385184675, 128337891, 207653480, 279335191, 944238424, 924637698, 461796594, 444035518, 300046943, 26329251, 668431333, 685561921, 244852478, 698343449, 106202541, 968305752, 325842638, 379843500, 987754107, 23195227, 899875118, 91552582, 110880416, 989203981, 70488361, 700282409, 88825285, 364134215, 49043632, 879589168, 323175338, 921453452, 792027683, 596275881, 116590762, 280535881, 206661886, 182738100, 728901383, 662281107, 881428431, 843390946, 788764685, 578314958, 316473364, 504682862, 335714928, 35130826, 553548602, 585533916, 401777225, 540411359, 351820355, 570836027, 966866332, 595282586, 392804183, 867160235, 354924919, 508678012, 487935974, 61007711, 934508698, 250059495, 480508969, 38658909, 245281599, 815984736, 727511787, 666565362, 810792561, 709448927, 213613077, 684182619, 458999077, 369909834, 37182574, 371205938, 530584293, 460159263, 865178049, 458873400, 779524865, 40910477, 708405537, 962661353, 878438501, 826808043, 200937227, 309255912, 864518922, 895381418, 174569741, 756115929, 25601100, 550079238, 171244354, 837172790, 624253895, 373818381, 426672756, 389217613, 594606192, 159181395, 422485921, 931193277, 501950978, 719710313, 133881675, 727749522, 837985059, 121685031, 77920312, 492893410, 874381526, 943092219, 589009635, 165003896, 624714744, 733743422, 316996174, 35405169, 209888592, 818772144, 455753601, 375871347, 331965204, 589733041, 599615604, 123398496, 133091256, 807743871, 186024870, 216069287, 390222034, 764880208, 298211509, 177872015, 263585318, 209764317, 317471517, 801628189, 470723030, 589574966, 32096869, 281895606, 122926738, 600401235, 93649154, 328691694, 551494558, 421136263, 950313334, 268992907, 88890337, 702786683, 678862871, 909111664, 274868356, 222839284, 335672499, 519416314, 20569010, 43385739, 381421539, 802159647, 20969318, 321144653, 880170331, 908441118, 477693297, 934308059, 193382622, 159722851, 688872755, 672456200, 202521488, 904946965, 808613445, 42561200, 754218234, 300425372, 748586271, 36363728, 499283975, 244744062, 534401748, 773816513, 836122577, 416535363, 93221309, 128031698, 987468223, 468416479, 36075629, 809514919, 271796640, 251418731, 336518984, 684625898, 604362584, 924661034, 352743713, 770384396, 606953802, 121664343, 424704644, 256059878, 529875801, 614664996, 377149532, 913215546, 466122075, 18008248, 372266574, 182358458, 291875805, 503791939, 834145524, 727328986, 568901969, 479254736, 641623943, 712731293, 218282843, 543510010, 326146642, 514950430, 369159814, 851848053, 373393246, 717996140, 918333865, 375260577, 812651329, 960122973, 472359327, 156790229, 894523728, 165654675, 358302765, 134809358, 71638073, 457575867, 501151582, 259730609, 461810016, 2083806, 447070856, 537759240, 884270740, 388643447, 594598673, 860387478, 495581558, 158560402, 790269003, 140374718, 172651271, 777085755, 412702651, 241966334, 163654544, 488548424, 290085693, 277102819, 872733399, 944567811, 794119982, 429540350, 88526604, 143000205, 459224860, 997191618, 660185727, 351127341, 918491171, 315867279, 991342159, 21034786, 724348481, 136110290, 415142913, 555762622, 254148964, 654680024, 247435483, 194518398, 515297499, 340792432, 59733798, 741199996, 776884618, 899017034, 689640350, 601702843, 424085935, 709783087, 884591018, 950150121, 500281261, 769460977, 758820384, 267278120, 318768849, 927214964, 249012616, 627454706, 490749859, 617473807, 878236935, 445373756, 758894774, 928040023, 547574681, 266268103, 138270463, 59289124, 418616293, 440117702, 482688448, 455146639, 536474109, 392156046, 697341035, 108951858, 865914838, 426557256, 742411052, 646484246, 286118145, 328416165, 402972264, 184836407, 75513930, 595976851, 624543366, 230955129, 251789037, 505390121, 175403004, 573331496, 15372841, 905752994, 53076435, 870755451, 28671424, 944521045, 234137304, 149936820, 54145378, 370106224, 8522575, 706736580, 674275481, 896588166, 523902165, 262481693, 784594107, 559578493, 877007700, 380116184, 147072683, 435214950, 996161543, 486691975, 170334311, 382152603, 508008158, 748265152, 616824521, 425379625, 495866248, 244992873, 184335106, 248520452, 946859696, 941883702, 914493184, 651530901, 442720297, 800006828, 361185653, 722453218, 518520526, 864004978, 191164106, 254592273, 522290892, 959982542, 370685256, 19976405, 274574519, 955479043, 385689529, 445929896, 140621780, 381106780, 913251200, 291883791, 868304871, 912037279, 481955293, 432132276, 23499383, 903279546, 913970233, 914377330, 613809280, 441589050, 187912332, 146686429, 134381845, 72993394, 92204798, 46997206, 671569379, 302189138, 682019466, 566276014, 615596038, 835301611, 137309469, 202488515, 632146531, 259605456, 822754164, 85055673, 825233488, 528426082, 181278001, 743903506, 245696945, 90880593, 613378894, 244795631, 418012942, 491364320, 460247107, 5777347, 12529659, 791216352, 332072852, 665179087, 717145055, 359535973, 133741096, 790910768, 788707708, 774709368, 827968618, 947660559, 620273376, 109247982, 99279663, 936347568, 747429349, 815017110, 676666515, 879325176, 255469336, 429148625, 263566322, 383017992, 546695311, 158664218, 257169883, 97062978, 255617527, 372662841, 520944930, 305198052, 817754713, 866303993, 640586700, 365535030, 413738534, 791628087, 830169485, 47107024, 510058501, 563860824, 207793828, 510317922, 947714247, 650986915, 594585847, 44081443, 267246609, 824802643, 359789839, 557592057, 55940479, 407080566, 83371444, 676664459, 287465377, 742794167, 386175143, 799909560, 265990628, 277149486, 613739196, 137253669, 758895936, 86741427, 61437637, 926695789, 309588436, 957246958, 782138323, 8457568, 693728421, 763528651, 157883849, 439779477, 713966263, 147747117, 652945554, 150800368, 397904851, 767181248, 936516865, 62388805, 495548433, 848911682, 699229562, 93067568, 917058212, 881515571, 212839859, 895273658, 685120733, 331460659, 101426192, 640473824, 345668336, 849038460, 97934151, 759019723, 934779241, 389975160, 133179555, 146549194, 461144612, 59099849, 498767560, 734390544, 886082861, 595533327, 321638589, 391672977, 811589068, 22413230, 42431840, 953581701, 736690056, 397032375, 910465986, 933042233, 72833909, 845256715, 434150901, 771489598, 426578386, 344630426, 887254352, 116588312, 522199262, 681505725, 758477762, 292543792, 561812580, 150971084, 537146476, 792783798, 76402344, 447364046, 964506969, 825335367, 300792139, 560614026, 616780306, 524365540, 628820233, 735318147, 112175621, 270086331, 861492441, 402921978, 343838741, 764871598, 948967692, 542244959, 217363391, 974859152, 83870006, 321066862, 561685319, 746452238, 673773804, 610190075, 30270728, 474154705, 143562451, 160916043, 795770870, 946434848, 746756034, 218107053, 810706733, 557931397, 226222929, 73567205, 499406805, 22995469, 580763558, 846136403, 941074623, 548332595, 866708608, 837724024, 399242886, 456874295, 577995151, 762989420, 196734315, 853902889, 667814888, 308392683, 355308907, 416839458, 122547970, 711320145, 826238645, 124331380, 472304186, 557092969, 598896465, 86341960, 903572670, 950618300, 438428248, 733865741, 537908613, 225842340, 142581410, 747455497, 56381044, 893392342, 20617590, 665020992, 439338219, 278181338, 238739709, 324551949, 657471799, 414780328, 451297511, 36810881, 558625438, 750890960, 324523961, 180351781, 493761716, 2333175, 158702555, 937155245, 820822311, 21680861, 888813599, 162341582, 755170302, 115939009, 601721583, 531174750, 213327006, 405715693, 910620312, 346908599, 92967778, 656479273, 752245251, 862902629, 772216933, 433506447, 703010794, 241708263, 340484000, 714587611, 807025410, 87645528, 650050848, 172117762, 495299075, 382780029, 593474182, 107569698, 699405477, 438305976, 102615335, 738243987, 45128925, 246841753, 557215223, 506421704, 361300817, 237613526, 482998404, 135273457, 392490537, 540384287, 718365848, 597228843, 278970273, 830630127, 294515417, 257437180, 262688960, 120096933, 492582968, 529565044, 689318330, 810041611, 931613326, 675317170, 74181814, 96056760, 231533378, 954330594, 105898649, 28283499, 967751603, 903232444, 955519774, 480885994, 457175449, 91156631, 965300889, 921867074, 429664203, 880605746, 508586129, 393231869, 361322291, 448690690, 355805484, 470239786, 97413112, 165644141, 685114787, 280064313, 500011049, 742441981, 191694899, 978890517, 9000575, 117596743, 637967323, 158293214, 334999625, 921019812, 722509869, 985680077, 672961936, 391435854, 430485466, 712907260, 552466450, 542907212, 103111915, 65513530, 758454194, 672459004, 92692619, 981955698, 144615033, 498654809, 720623089, 401448091, 567185187, 411389220, 441032304, 847644185, 817332214, 676101330, 951775702, 669708630, 744095753, 601516235, 381378728, 964386377, 610154977, 72178216, 112040405, 467217838, 590795187, 560038652, 109113553, 105124903, 697689614, 926282780, 566044126, 741522994, 643581467, 322039487, 875511933, 85469673, 670107923, 109073373, 739025959, 515766447, 809805087, 680382242, 92099403, 299263456, 778629023, 342609096, 176148994, 968730209, 732219508, 74153775, 855192116, 794980291, 192173409, 825201500, 813158053, 558763513, 556424297, 119129601, 69670310, 663033899, 343886687, 147918959, 629919699, 520490609, 619340489, 523736877, 240509058, 781486935, 344253843, 13612905, 585348604, 853401722, 957483223, 512379001, 532168349, 929606887, 522117728, 592091841, 136689874, 779323315, 457175672, 923168291, 368918104, 683805959, 595472603, 79565694, 732147952, 657261942, 610851699, 180988623, 112006550, 236975686, 982479828, 551689419, 970050030, 749259970, 987474912, 438983611, 66779530, 939279360, 682828394, 944347133, 487573240, 483369892, 36918659, 920378000, 679597173, 225718818, 362144524, 656946577, 367896336, 557093634, 370397675, 156172398, 987031457, 77725518, 773530003, 112915438, 787018767, 405687443, 954017029, 565377828, 501194967, 780597691, 15188744, 696688058, 786184587, 458717397, 105908055, 404726830, 61776356, 456860151, 960789167, 735960266, 537759656, 164804605, 240885745, 755378749, 633496513, 478192426, 928316713, 255937329, 907370381, 447202248, 248450561, 61952433, 578528739, 225852609, 186138179, 442386799, 858120704, 645873657, 969683879, 138653273, 690797877, 547208373, 46943640, 429617898, 416240210, 822122221, 127399720, 87778917, 648124446, 252491523, 650687706, 299620527, 953508946, 392905510, 356621841, 205156574, 779301125, 936077053, 227618201, 344719380, 626398753, 585919065, 338442360, 540265203, 951929228, 733392152, 901517025, 875841623, 481337886, 57515345, 859604063, 962384674, 274464260, 188218881, 160251383, 129541961, 763496728, 892844644, 12588012, 626009811, 961732765, 587054582, 423952619, 212463559, 337106722, 224874662, 54352349, 425012879, 574814442, 208132935, 927715473, 706393602, 203312272, 554998778, 192593052, 25338506, 669216580, 12277671, 804801551, 594009922, 890255652, 237705795, 575928343, 446123877, 404043388, 855878372, 728185300, 714839573, 21526716, 551921543, 12539509, 509113677, 258114986, 25773945, 292540260, 148303898, 108338353, 747707562, 136167797, 372361401, 300959096, 634109107, 629453841, 565347471, 839101912, 165405213, 573716354, 147185862, 209566905, 230897678, 207058362, 215203322, 727078554, 521363557, 25842441, 450457524, 569387109, 150533446, 510362388, 590421548, 798918208, 537134021, 553602535, 865718299, 45120381, 627220021, 398391007, 518575826, 552496306, 149144473, 627702620, 282040325, 484327292, 507471366, 440119607, 443961032, 175211170, 195005452, 704795704, 269987269, 834818583, 404234781, 195419239, 309702357, 24696809, 380272013, 455821407, 199087088, 914573720, 92977098, 684261104, 571366325, 68196856, 254808645, 446526124, 95030756, 27704415, 557698218, 130075459, 19899209, 892168533, 968067579, 316038202, 772821898, 307425022, 188223835, 983006107, 212982825, 390567993, 687317136, 2944179, 676604159, 718496690, 86552276, 82338470, 831855682, 702668957, 473650745, 336810216, 216558524, 701869944, 104636692, 821451292, 148987036, 587314239, 226695999, 456922302, 613605246, 818651932, 636291801, 647353725, 552354894, 188034175, 866963128, 80491012, 527379991, 19784615, 464683351, 208152778, 456383265, 678876918, 969329259, 69661566, 626640387, 852849526, 654209688, 107605373, 463375080, 820950242, 297759884, 705583510, 636274682, 878163202, 3548159, 969829932, 768663605, 551455367, 313420920, 858013011, 501837751, 200757150, 7727171, 612090605, 127841200, 583868495, 190777376, 712468575, 761534634, 28003592, 638809904, 67273754, 80391988, 442077307, 844189690, 838063575, 174926004, 807107291, 570144877, 693089052, 598327628, 670009276, 995759353, 698433344, 798969038, 650606911, 151524603, 604992477, 364334588, 924183783, 291354162, 440343859, 676910250, 171373196, 997703687, 202217640, 741838307, 712809089, 62261878, 47315303, 77736645, 94367325, 752670235, 832738190, 86352840, 145096237, 376411200, 601781172, 219611893, 264350879, 786223144, 991894986, 501200518, 278340139, 305353394, 15133682, 367859254, 133729090, 8760331, 454071648, 147732700, 501820222, 595024254, 451515188, 479887429, 183197618, 875399379, 391590890, 958531415, 206889048, 117624497, 240401762, 759075536, 84996073, 968320403, 291927167, 457039275, 617044110, 76984709, 610043261, 868327890, 778286118, 984972397, 191650268, 92436685, 9496948, 595619350, 342653972, 484131427, 301387248, 260169050, 83748649, 276818929, 426887925, 250278983, 49316479, 621884220, 905750024, 165675737, 361966031, 634122195, 892141495, 967034476, 111096673, 582380508, 74512527, 498367606, 174867841, 621579870, 377309573, 83092286, 541821182, 729259388, 13242237, 835983144, 788857312, 931926277, 306578070, 824069332, 925372970, 173171453, 91636193, 294118693, 50108138, 29447968, 68981643, 360441748, 278370559, 657038025, 419059186, 459221286, 586425428, 567192524, 421638113, 511443851, 845536462, 207186607, 194176222, 227100307, 928518701, 974578141, 175269577, 159968539, 824701294, 406085850, 760402573, 755911372, 899192940, 531627071, 970133252, 460280530, 687762367, 737291597, 40733397, 529934157, 89400633, 280556850, 890519511, 482814410, 122875214, 363374175, 41598160, 941797001, 859083888, 776022029, 785583561, 73270524, 956833979, 903999483, 772878899, 372740008, 142370175, 576021260, 954178542, 881254822, 695251692, 350903524, 161622347, 604270863, 553650552, 412192647, 390617492, 688619772, 576367665, 132369802, 374883516, 398381615, 449499635, 891528358, 573884935, 984286222, 36430134, 500126486, 52741037, 812611828, 660069956, 988506746, 830830913, 752620482, 385163886, 278104329, 724049007, 51605964, 18203834, 481009928, 20617874, 780515066, 906768296, 582102251, 888279735, 243199146, 405255848, 622660554, 506111885, 890164501, 594823801, 336437381, 946703037, 229969757, 830193458, 224291235, 181498081, 51104516, 875207842, 646654212, 679423349, 163979122, 236852382, 196204979, 814834134, 528143722, 144087606, 429507225, 499705994, 85223406, 378163576, 874436054, 970019659, 602961929, 379668778, 692162665, 18399063, 27532195, 993995350, 199646954, 116208578, 725991837, 329464440, 787100941, 416396978, 376334639, 492191785, 953292328, 990593574, 836754490, 814231921, 951562267, 928814666, 165968738, 656643627, 771713992, 408902291, 752335692, 359003235, 412864962, 949919255, 575848572, 218552170, 26402554, 135996885, 903246450, 240628736, 657052793, 233890236, 495738815, 760115332, 889303998, 939415343, 702033009, 540122185, 461864841, 124760864, 978840326, 14786787, 597695991, 882544150, 38162003, 610166811, 513889633, 747310882, 627771579, 16393955, 77288425, 565701471, 187707621, 310639899, 739386506, 76020233, 150583398, 966804430, 833363364, 61838485, 954282312, 948208429, 203414792, 919290218, 670918543, 779354669, 165759899, 408269987, 258919929, 871976504, 92937831, 970739973, 557008043, 598969896, 395633484, 287158346, 970983117, 868666160, 48106435, 736645715, 830630006, 173829842, 867566626, 392744989, 955958936, 325474480, 390673781, 451776668, 945824756, 395904573, 212542015, 395622550, 512175210, 963460310, 244521978, 141230710, 179194428, 81177675, 916502555, 938584965, 107257132, 482270265, 121980475, 876580392, 856421997, 610868480, 163527652, 561612860, 369750464, 402571256, 296110660, 83476470, 13394221, 113890048, 889899096, 957760591, 419260038, 612416731, 97187432, 635811077, 711454279, 308136164, 461056602, 154666511, 623330573, 210915976, 603687912, 569126453, 500537758, 756388207, 883750879, 498898787, 92759641, 342672944, 845851392, 843291513, 708809523, 269766326, 919823547, 223555074, 781761244, 168079782, 694296007, 611684899, 502638803, 21671387, 722166231, 120377429, 305551106, 899447096, 807402861, 281760977, 219405945, 305669862, 553341628, 880653014, 813171611, 380811694, 903029120, 364644582, 944852681, 789986691, 21724347, 551499273, 470117353, 891356542, 985253825, 600448471, 60588189, 61380294, 251075624, 834853161, 200623844, 526227839, 248502118, 434842649, 332745802, 642345138, 105088594, 870384226, 5343582, 757924154, 543258660, 559069830, 396181640, 439006944, 602581639, 521332831, 503876714, 855323511, 663160340, 916302300, 864374042, 475611830, 909044311, 582898964, 387315209, 725835099, 648971824, 64710042, 433124674, 347774157, 875672464, 781058636, 889026595, 385848084, 506376542, 49789055, 382268778, 254671850, 43553324, 204305277, 83894975, 503684712, 528711775, 87293897, 644293119, 762684029, 418087230, 487088416, 944827003, 981036698, 534289750, 157505993, 489354881, 709843900, 419341996, 664743366, 466110381, 618030996, 844454172, 158699611, 873991886, 789215839, 211407954, 827948826, 958032741, 63132925, 759533552, 230916413, 788768855, 570180746, 497932006, 351686195, 54087233, 105155035, 544591366, 837768264, 812936202, 409407579, 280522891, 867744150, 601188886, 889563822, 144813508, 305885297, 587851410, 420601981, 380499223, 655205264, 423632848, 957421660, 715131157, 730975107, 994599826, 247244983, 245922444, 382026147, 720228640, 424109608, 94773504, 636291573, 934815676, 240128335, 827506374, 809151139, 789961784, 876955606, 321158349, 583480451, 380298264, 728544884, 928396594, 682148677, 590123936, 327901081, 972466468, 304474993, 681902068, 332264097, 981031531, 851290197, 997390130, 291030626, 540022639, 421851444, 488220321, 251557355, 797781185, 934473580, 849376415, 836153687, 92099644, 501030652, 841741383, 611148043, 228536735, 816763969, 683812098, 542330043, 531290067, 900276257, 958792511, 597392726, 37322118, 955093087, 125261456, 633813107, 747223200, 742628028, 648992448, 872220901, 860347205, 801104422, 158182552, 186035372, 69829331, 837692718, 847369852, 53868325, 519428755, 571759619, 280374725, 37069019, 783315823, 131843355, 470015706, 370714959, 108650587, 686016842, 248449956, 613252776, 955158200, 316603404, 323954394, 408918752, 104705182, 254391900, 426348181, 727004367, 483842685, 2799158, 887583757, 77516717, 986178543, 58742314, 410540854, 529276213, 998602242, 617947888, 344885038, 95904551, 454359677, 980757172, 926405141, 447994714, 245671287, 313392410, 775525093, 490487916, 701686440, 634762052, 782482192, 610431958, 325548088, 983828501, 280661848, 318319914, 284123788, 578714838, 403593115, 112845446, 744631028, 361044054, 770339065, 958494479, 837803182, 267948182, 262866933, 807289272, 808408639, 818343207, 442456979, 409095352, 200477777, 388037789, 798938839, 261347720, 679089553, 499496725, 638680161, 845311880, 166751678, 999671706, 993958094, 348982796, 763051821, 621288420, 369185190, 319657893, 848785201, 313359829, 174101087, 271308839, 684427260, 399264781, 374553847, 969386168, 447062592, 850928549, 487813705, 674095768, 114096671, 7874748, 341186830, 782606192, 949734919, 158230725, 293127559, 296771350, 688872054, 900673761, 723287031, 477987873, 87657408, 475414995, 139563153, 689220274, 811813134, 84466198, 857020724, 202575319, 431344970, 12301957, 877713444, 517709881, 285094303, 292456062, 332902839, 488087568, 300747910, 98508028, 409525779, 325910679, 288597614, 990336079, 536988054, 135435598, 167660352, 922685004, 42165732, 783934865, 291221953, 998390641, 649657030, 610929135, 363985960, 264477416, 972216247, 391745170, 6009147, 318067799, 463619354, 817565100, 313401284, 596650471, 551755675, 364678208, 859726309, 365746442, 608155699, 680642154, 534508846, 224215359, 117783834, 565443459, 476048901, 751754981, 218216433, 275396886, 672953134, 197732789, 151688543, 407142918, 631514124, 321273931, 825077429, 681273559, 59212026, 111824964, 722308273, 185707751, 701061867, 773077223, 464756052, 733762104, 741194026, 240404928, 812532141, 272688172, 792444360, 69179991, 732785739, 198908280, 184424308, 276640358, 611330718, 871982548, 672542953, 120244544, 696413324, 448874230, 168535619, 967787219, 538434387, 421530782, 277421056, 540109405, 288079765, 70142655, 742223951, 910817088, 759510546, 601681621, 40994321, 452136451, 797958105, 643792616, 469799091, 160156341, 941154383, 868791110, 541547734, 297580356, 444618951, 488690439, 961545412, 455491315, 707576868, 730393480, 216283997, 322205469, 506744453, 462368146, 715947301, 27714507, 959209820, 155005717, 535355, 831485001, 657576660, 390108046, 887181652, 838510477, 231102919, 836065775, 9956039, 575323629, 2897046, 441519070, 578028038, 638746130, 822562664, 107517515, 857649303, 886352537, 655854499, 374748928, 784657331, 954958555, 571772213, 425524437, 36911962, 48177838, 802863180, 680406041, 405259475, 208780856, 971646089, 171053436, 120034919, 790557589, 967323250, 205792761, 345514245, 247642665, 210860316, 496393334, 138941557, 995677229, 620963092, 495501401, 252916769, 949069619, 404636055, 522161559, 466245792, 990040289, 315739384, 376248953, 521532355, 520372248, 345446946, 480851841, 321502056, 443675925, 420332709, 180579696, 370133142, 896070714, 610217668, 875930269, 585588487, 930391446, 456365493, 904465551, 776105942, 500362309, 585885635, 782124048, 117581246, 399787420, 925852151, 853850296, 467104887, 963588674, 128830867, 960715212, 185703019, 768650074, 769597720, 824718647, 187354066, 89873456, 328843310, 127219228, 559244270, 232778434, 580785254, 60939245, 566071562, 831518195, 393935692, 522444954, 504754389, 490328852, 684257114, 921916998, 937821858, 143507467, 684031787, 662134081, 104624787, 982269244, 152363367, 407673630, 485352971, 130343610, 447622546, 581826347, 270922388, 486798883, 460091888, 260228035, 373595683, 837215428, 319226680, 501111115, 986206104, 62795508, 931822820, 654575186, 885850842, 679685309, 779775632, 151808339, 877425260, 980652753, 962643679, 340974644, 881823856, 669098574, 348748700, 789847297, 452062817, 486934072, 25201944, 616385564, 150708002, 2036212, 750446580, 530070706, 748638333, 314783207, 266968807, 987097617, 845882901, 620656778, 282537765, 535320323, 171884646, 47939259, 871178447, 919889757, 703696391, 738841033, 782068017, 995563221, 872215920, 241759086, 714176055, 956384266, 94581186, 590006111, 843619597, 419793158, 912768959, 647537834, 29149007, 386032703, 947438176, 417910158, 300267446, 21831586, 71426292, 82727263, 458907650, 820844012, 385570163, 939157373, 833977306, 875972863, 39057304, 101496487, 687352256, 115322944, 649544438, 728851162, 434226477, 764085814, 330644238, 424388154, 653903423, 392039405, 362863651, 522391383, 941046544, 303032422, 407951524, 465714238, 256452942, 21443131, 935033199, 893427354, 94316966, 454507221, 359141393, 798998003, 755114419, 407630521, 638736396, 281299289, 226333943, 799440283, 674147175, 307865116, 249915132, 565500313, 30482507, 700621139, 296061374, 287409966, 939593404, 651491575, 196306225, 793419634, 273694659, 505762479, 938916389, 913633664, 326577458, 833611980, 602185926, 39542369, 67742151, 211295295, 461113962, 822279284, 80408196, 179675090, 190125817, 209013266, 173285486, 48977148, 5399831, 819585423, 105647462, 468082594, 999522996, 56496321, 709520833, 445816108, 173948177, 280789983, 128419029, 388936018, 455684673, 947525582, 432314967, 930535250, 273787430, 469376468, 43375033, 643355388, 24159349, 953397621, 330555650, 10771105, 854181964, 654902445, 67742513, 15330147, 475060576, 870091156, 169833593, 250617409, 1416937, 204916629, 692898634, 79217000, 684521168, 3422890, 14480174, 178967941, 472129412, 498728720, 433781260, 984168002, 134915951, 69712227, 477634263, 31594837, 177322371, 168971287, 220815968, 178445913, 398367666, 953585821, 523590764, 862149453, 405388789, 974808476, 228253333, 134894548, 511425012, 63452048, 838512272, 607655504, 177962803, 22938769, 304189735, 615241101, 436756490, 166186513, 335224073, 801670517, 719860640, 660032307, 78592253, 862548587, 23332493, 589698883, 572892611, 474004244, 592967843, 906359945, 662469088, 252795085, 514492299, 724876215, 924140011, 174416778, 78859849, 103929317, 190470410, 880428431, 782690846, 407256780, 59869478, 398757931, 547105682, 767421890, 742634464, 203899745, 225905172, 144766584, 67839364, 212326792, 963735007, 889715010, 910382217, 414009380, 773120724, 707265217, 20148884, 900949168, 640245466, 660578675, 458609843, 321786846, 773621018, 487231677, 673324006, 24242878, 799980900, 732180679, 592128260, 406491156, 95690411, 968174287, 935863378, 961378989, 95361465, 111987065, 577719914, 182639011, 482104267, 199269823, 887631984, 929618777, 312981160, 298819303, 239449009, 447730511, 895578813, 602379715, 220629581, 677729635, 8118717, 487625388, 3822954, 301942059, 834741253, 489908871, 988634322, 266064019, 335593656, 112639283, 603031561, 154347419, 941703893, 137560899, 363447830, 669786725, 297567282, 771402355, 709085741, 264476736, 706704626, 677939906, 814138453, 981394001, 297092846, 911871474, 693852264, 84772891, 278019988, 38061445, 38239314, 63662430, 714530901, 794915734, 268819661, 3937271, 962763373, 361010323, 495541682, 290558139, 128625509, 572516778, 60637352, 819630386, 778304632, 937499599, 596947696, 951362579, 568033933, 510589663, 140425005, 983359250, 491456411, 112121665, 472103778, 297730636, 712106033, 853742099, 821039097, 530624305, 186379314, 1824756, 524414749, 687143911, 577653984, 529493801, 165303383, 897008, 625311802, 751888878, 601050209, 443084795, 812738466, 483129244, 299601041, 445423845, 716450172, 89480914, 758837044, 659976144, 730267678, 183479278, 933713333, 53669721, 469528965, 416919847, 669276003, 162950252, 606798054, 89505962, 609706238, 567370677, 9306034, 195740451, 465571546, 799692717, 730789046, 558678042, 17355186, 675180001, 393104506, 821459831, 896213822, 341749937, 339608577, 117757494, 539810100, 246836313, 585961782, 355582773, 242140934, 696681592, 727690926, 623129760, 743710479, 646758293, 758066669, 541370676, 82868625, 61405148, 736462739, 193108013, 567274622, 145418676, 840747449, 135865097, 480949437, 655074573, 469187797, 406371735, 721908899, 922384908, 332500852, 126563432, 930945945, 655174455, 984166343, 902627244, 91890016, 930322407, 270957037, 988717555, 777762604, 438876037, 194305649, 857732955, 229817675, 134179019, 3587415, 886799932, 752449385, 500692550, 288158281, 366712237, 734570906, 817701166, 808457552, 517055578, 148942607, 575709242, 661326898, 835962691, 113072623, 881448662, 637540251, 290664370, 436699144, 750808492, 873765260, 156196119, 140473211, 380193309, 668321562, 577365668, 15567817, 243799160, 171621090, 315340802, 305076773, 516127162, 159198257, 734748134, 259338210, 617601382, 248920766, 10881816, 493421850, 981012575, 434823985, 735661255, 847330525, 760719338, 827106414, 292016614, 246572233, 253254545, 476753238, 926857787, 245240911, 451724501, 668289399, 663737898, 207395854, 706107302, 320972747, 768260502, 257668560, 287407768, 138812714, 411021112, 906774416, 162315620, 33021863, 480317252, 172249191, 625226381, 650161966, 610485751, 480274205, 122946683, 925702011, 501625442, 774099687, 989889234, 739249240, 223671956, 791883745, 335416612, 168658873, 333530699, 159262616, 801181888, 71590043, 183019411, 466938553, 306881258, 591478265, 275539998, 233272640, 426981638, 884381539, 357984655, 911516922, 229272408, 688498246, 699069223, 966543966, 546418700, 229835704, 991732356, 571213672, 817178835, 81711653, 58152413, 601656108, 848242858, 940353751, 203087969, 878225654, 192876489, 422178028, 778988499, 678047136, 12379458, 496662596, 486115582, 854351648, 659393012, 356359787, 8031093, 866786409, 444466635, 210572174, 140900461, 620081187, 755613691, 515444837, 327227288, 219193448, 92257244, 436739489, 931111545, 756778677, 690734905, 51148189, 445199439, 9467098, 817102161, 791584367, 776097104, 844202119, 424162457, 122647259, 559815439, 363162191, 429412249, 761971230, 837389014, 325396345, 60571779, 33085301, 670568027, 219717725, 822800286, 129636094, 877492834, 928553117, 990064222, 923632121, 370332438, 178797336, 206251997, 246221825, 948721375, 276081744, 576722410, 697589260, 190175064, 722877248, 996322788, 739454530, 351265090, 123171927, 569570143, 93486909, 979360649, 525270338, 155117217, 695446821, 565428695, 798120535, 190496879, 83687322, 593486547, 316549432, 901078471, 105195452, 220534685, 811331177, 308385307, 141637171, 82410439, 664839394, 910335266, 201675964, 283032486, 424384893, 285866903, 376659663, 359528424, 607901718, 499079512, 419091361, 733560152, 110307604, 673240094, 522143136, 955114285, 779949251, 14379958, 403498215, 658341434, 996909608, 668284431, 842278767, 961061073, 880288753, 648219797, 48162019, 696567998, 33228909, 919986411, 595160576, 274521853, 540354620, 100952629, 20396595, 123721149, 699412792, 632849404, 73602082, 360179222, 431336529, 625171518, 355438931, 360945726, 778765719, 846762679, 638072858, 635939427, 603149006, 660170087, 959336152, 403732574, 607186817, 359638468, 468006851, 674966539, 219480164, 747519667, 605189666, 524877975, 385910262, 796957263, 424233447, 299970080, 726685933, 744206607, 245200059, 299062923, 775781490, 960272179, 353564478, 813041760, 325491146, 409620944, 691883226, 751655987, 580133741, 852841874, 837798541, 189326111, 992517669, 288682637, 716944099, 870194612, 866391100, 451753713, 223270953, 681917072, 214108421, 74442701, 699030424, 159661051, 104903832, 749552670, 838873007, 566641588, 337181322, 322691684, 864198248, 122698967, 768271994, 394309264, 130038143, 693305654, 551671229, 935312848, 930952190, 940967302, 214841689, 126975719, 359489622, 575928620, 630010067, 671597652, 444190516, 782241799, 201638571, 3847776, 815119876, 344052894, 385082507, 610886270, 451890764, 524272899, 230705784, 483415447, 634997714, 962031543, 489997199, 121170003, 89843993, 185631259, 548151756, 531872657, 49783717, 613987747, 343534207, 646806462, 192373282, 836113266, 700536199, 858079853, 473434290, 121192412, 4231654, 446521644, 73909200, 840993138, 578365571, 405473843, 465489969, 33847705, 978813035, 966179234, 424193360, 624249836, 316753972, 153133897, 257652434, 295325824, 759483421, 615025545, 802641892, 960055881, 823311875, 754320336, 873038718, 705495988, 838454896, 530478665, 186803667, 550894630, 621273006, 698817221, 749884914, 845047653, 819082101, 683991404, 708025035, 685559421, 676290489, 207507947, 659019064, 899231692, 845962819, 19124350, 968702400, 77441352, 477326434, 314539563, 913151053, 774854845, 855202986, 289688156, 917292761, 919802716, 118754354, 250865459, 466011035, 361550335, 269050314, 967570845, 716217164, 694365451, 316582920, 485330685, 263136405, 47639023, 734985907, 804673693, 345968331, 507150689, 118319111, 764915074, 510751751, 662756400, 555418368, 292209034, 190517285, 35054970, 149560885, 777955955, 985305228, 346868934, 469916457, 778543799, 932733988, 668071711, 437467494, 878755484, 37873875, 81463563, 424638145, 433003175, 580480609, 113034977, 597168452, 990089325, 349281744, 627921595, 287475852, 203007685, 719800389, 361040868, 892590699, 2009739, 796234016, 280253996, 557529573, 240751943, 427144602, 747320355, 489378545, 789680097, 611913794, 723632095, 960010328, 179879500, 864328774, 617240108, 105037392, 912048232, 700434866, 72035846, 28826052, 854693742, 593569152, 414832676, 152377126, 542262807, 166133670, 375905275, 424307998, 917224554, 12291240, 760035246, 62377764, 487679145, 350431925, 644806273, 783529180, 196098613, 235531036, 492142519, 410008292, 162245564, 833051825, 24043956, 963836608, 570637257, 158668397, 415003486, 842302441, 798035927, 370477994, 257925137, 129569247, 468567730, 718311748, 42816386, 851383804, 765236770, 53191948, 464958041, 768766293, 85466126, 831191575, 331961342, 89290601, 201870526, 578848555, 290387734, 78930194, 575439773, 21500301, 506659087, 278364266, 801005930, 637440549, 300952568, 502442706, 295309931, 149900213, 546948927, 55542489, 934294649, 778497638, 334849817, 430249084, 474779043, 954258349, 663107268, 428446988, 124149404, 87573581, 556690343, 132478476, 121964221, 874730452, 48985791, 588664746, 261791827, 724032342, 70961287, 582847494, 440298918, 133885326, 565206986, 516936875, 933777994, 216680021, 133281629, 166680408, 840091491, 248460447, 514658122, 245746923, 611555521, 911200076, 202780509, 849430127, 518783450, 587590224, 765111329, 797672484, 392585714, 327406169, 456762375, 548513076, 676570258, 863175303, 348018353, 110518673, 63312126, 378355522, 195930804, 611624158, 466404258, 388537915, 432256216, 329508950, 427618428, 950837693, 547161175, 472247148, 970571993, 979272699, 137444754, 322213234, 348533865, 961168877, 756475922, 27568697, 100286497, 557059686, 952836580, 639602879, 942752825, 361554448, 794912352, 458893983, 173573015, 487332308, 973510939, 889759932, 301119430, 476196980, 564247067, 525956389, 783459128, 879309778, 369330961, 424494696, 680175471, 226918199, 294196069, 404395635, 326795036, 961094186, 949036272, 939955377, 481812572, 749695967, 665064805, 405650069, 930871439, 376486705, 553752767, 791681983, 527810012, 153123463, 563996286, 560236974, 893877037, 581567397, 952133218, 179286873, 96367651, 855612419, 61178722, 684789805, 418848711, 639418366, 577590416, 186020356, 3835285, 65038245, 885599892, 430816687, 859902911, 317533621, 44248736, 344583039, 132501918, 48720335, 178263812, 393143724, 245562444, 575629997, 362781993, 17407664, 480776283, 249371893, 76418719, 872914857, 365609714, 295548807, 169625719, 565787777, 936828905, 60797736, 677777392, 24801500, 570832334, 239823118, 361013612, 955776100, 8520059, 299210442, 480983540, 24773264, 595147706, 641916200, 954194952, 595084159, 271911960, 276033780, 931448437, 895452957, 952469071, 24644224, 580725839, 281718994, 816214733, 455551005, 991168649, 203519014, 507601286, 701437730, 372306119, 459353424, 723828077, 28724675, 168557724, 203342372, 870887117, 213933708, 839261730, 878303433, 538278992, 982096885, 211090832, 472879608, 527069419, 834434267, 949683453, 199510770, 758016491, 813542588, 753478823, 432761133, 126114954, 859586870, 769303443, 725180584, 538894193, 211991063, 886616820, 570709311, 643585135, 273181051, 41628988, 921435200, 614936623, 20327990, 755890910, 587286453, 357285668, 906799135, 284087131, 287223665, 679036231, 250318014, 88809361, 402632700, 617247496, 808204611, 492116615, 307215881, 335903035, 62419911, 294331633, 246296465, 694297176, 227120576, 527961127, 309671445, 307384582, 429398322, 628214203, 509003517, 749703976, 61914105, 57262727, 44346954, 82414041, 17855753, 767508899, 16986374, 611012743, 978413767, 204180378, 751704318, 632538348, 941556522, 160439822, 122370137, 939488535, 536762506, 946101650, 520740309, 813607005, 525154361, 381597518, 977352499, 50222904, 143138701, 327749946, 14595297, 674993065, 770369445, 247798884, 937335769, 952168669, 93371083, 934720737, 709146748, 511417216, 92078373, 871954994, 124506170, 921640277, 64901878, 232475835, 297041036, 275748584, 34730900, 244012848, 17007552, 701769979, 181932844, 813014097, 414351326, 635392020, 843541358, 286083412, 223566989, 134766796, 428639254, 216411958, 842213826, 321449995, 36056947, 813809980, 462185563, 444794224, 195899942, 999963233, 192105536, 277815027, 313167125, 535263833, 575644090, 945475562, 784376393, 863774240, 189860766, 324023019, 402815910, 247911319, 613810119, 624787257, 900604119, 367504384, 523822977, 848015520, 640828982, 896499167, 670215733, 945338154, 877480691, 445189, 411436381, 925791777, 734247216, 998981528, 51817255, 470716156, 851900719, 83819457, 804321341, 254807986, 211965767, 458490011, 6853225, 844133189, 277915823, 352064774, 128382109, 490216052, 708462648, 655567877, 994326737, 125406299, 235730319, 771865849, 537748332, 68386796, 797058154, 730989013, 777906493, 998971000, 422312516, 566908291, 125632605, 472185159, 388725700, 220199122, 549960329, 541395281, 824943862, 204898012, 89869864, 417749067, 154228354, 37926322, 946044012, 270636947, 869950847, 78279364, 998066079, 389748740, 223055244, 804595197, 253389031, 705347387, 73105598, 539656422, 791393119, 510522111, 643355724, 884056589, 552484359, 870550428, 104975623, 741597626, 456652376, 204169072, 456836773, 85974257, 83668913, 368974155, 247085854, 337886081, 29052244, 952810248, 944105981, 429244442, 448585492, 72540352, 114209728, 573404337, 173458192, 756166367, 622413244, 872160803, 803465117, 831620648, 919130195, 501247947, 947202093, 221566106, 472898311, 895719219, 510707760, 639147840, 401694026, 15174905, 290373239, 187111666, 160426616, 960370755, 386392473, 199340963, 372562299, 65452202, 309333606, 427091858, 765692962, 106866025, 519207319, 920657204, 834311149, 545143697, 562304688, 985915011, 115454303, 981921954, 798152347, 690971322, 762064893, 553970142, 731968172, 573997976, 986473905, 466888176, 787657202, 253209571, 142045930, 830412145, 734479840, 696600726, 581803090, 818364700, 208578301, 424646302, 207943381, 307689312, 195539136, 627463821, 191722872, 206263249, 953616506, 501082739, 314340665, 197708574, 149254979, 469576362, 492380986, 311882392, 33305564, 364882517, 881012678, 401444540, 771018053, 595784048, 539727568, 340177070, 381205089, 15715975, 10081180, 108706565, 217176046, 772327232, 950512323, 980985293, 512850370, 877464048, 153073960, 515537958, 196548673, 875264636, 307159093, 578875585, 424129535, 603584943, 359046445, 493598175, 892289525, 476873883, 725840307, 10891461, 761591748, 662642889, 893634561, 110537752, 982828415, 483182229, 975753388, 912306034, 790156328, 588861803, 482517875, 102292471, 187202393, 956696358, 71368752, 961478599, 48225681, 385003653, 140216617, 973224087, 149831407, 609253070, 916165360, 339548126, 197230063, 719756122, 913956595, 638380708, 279783313, 922443799, 668305319, 344089777, 734303608, 949822055, 182696679, 17106747, 592023257, 240596051, 786417896, 449918461, 472361805, 869849305, 709074072, 396305082, 849303402, 468462936, 530574289, 541534052, 339727209, 50606591, 268609557, 356456582, 865766289, 431422436, 192249691, 336637460, 722787914, 847478568, 612621146, 265617615, 860086457, 90639551, 623131474, 274791989, 150989308, 131427161, 208665642, 318137435, 246982762, 579724729, 87333613, 928125824, 663615341, 355386281, 420506832, 526108059, 670669471, 955971295, 269323652, 985681290, 633562827, 660480883, 407050710, 104225336, 63520512, 559966386, 989594079, 425911926, 2497312, 515253867, 8626114, 818833179, 947757325, 700753943, 987772697, 532118547, 262731791, 870108682, 707010687, 431924187, 563600642, 65873824, 549421114, 647555139, 924203100, 872639299, 618591016, 644961735, 902297588, 424181250, 591301215, 387087807, 509167574, 382846657, 781846083, 27763081, 577833438, 791855441, 52909063, 337464460, 275851664, 846573066, 126221612, 461764508, 248612472, 80188943, 189583944, 38976997, 292671661, 941489402, 524468210, 269739281, 729290040, 92560552, 753970661, 3874368, 781725612, 561499459, 977813403, 821675035, 431253126, 415943364, 556346954, 752003191, 880264602, 960005177, 191249304, 287923473, 391193777, 19321179, 356339390, 460694970, 312404457, 148382238, 780760467, 329302077, 389494413, 361217610, 685847360, 643886056, 778203571, 177413274, 767108051, 565225896, 836446228, 621824260, 26984839, 773561276, 244206279, 184117852, 326224927, 29668543, 704496724, 945977322, 7793753, 308002175, 36812453, 73692436, 768237856, 637869065, 861446883, 555642892, 155835144, 358238208, 178714745, 87115768, 731705971, 680307795, 762543739, 183500201, 74698493, 668794318, 446709340, 535332657, 462799554, 994212168, 412252640, 584639833, 16717132, 542445530, 256956772, 924978599, 980853067, 885498238, 998530042, 922714735, 295139189, 804204765, 668397245, 166941469, 508876817, 66137146, 798514472, 595914444, 910419148, 782874896, 870990405, 194851135, 152479789, 865414227, 665239764, 987308628, 595589515, 886203134, 38377300, 679928630, 241448445, 532457789, 867607974, 992661656, 211847550, 840820345, 230089159, 176442833, 730053226, 746264573, 103587034, 713241664, 60910134, 764192765, 672607615, 79096092, 565065649, 543828818, 429119425, 334463600, 225577596, 838122634, 732716866, 786255313, 438341756, 723440633, 79574591, 274598706, 558817103, 191433061, 232372138, 925651987, 145838578, 274395337, 121194323, 415628674, 680649061, 901726004, 513908765, 107693670, 576037601, 186291184, 42583139, 403835398, 403332396, 284908772, 913960984, 15258754, 374662265, 994340559, 786303275, 977089274, 968174451, 17831229, 302853461, 374464348, 725225855, 94880769, 57492202, 705705073, 842421432, 325116494, 495029568, 354803042, 300302686, 137334629, 351382129, 965208373, 115218974, 588728344, 920669403, 876697972, 864669400, 879271280, 627106854, 335598749, 86203307, 96851889, 994575362, 357713064, 835615894, 128702003, 882237268, 493260746, 367699794, 327095071, 40572610, 884739751, 651587824, 801654799, 881460633, 693925143, 86626131, 172929607, 917119995, 319979259, 762190157, 504797365, 64733203, 56088919, 627391742, 114056201, 162528965, 161789284, 750019182, 427131134, 209283902, 76655500, 361812387, 268163206, 337610536, 851762897, 602299654, 774661173, 618633123, 111488030, 850296780, 975382566, 100775554, 344429637, 787755011, 828778682, 789167697, 844533215, 969364209, 53508590, 806653498, 875182815, 263540406, 751427149, 68425703, 281441040, 625608407, 534727303, 977374958, 70672783, 53686844, 412017771, 536021702, 806151396, 781497000, 589588041, 106433007, 249180017, 896088342, 301294803, 811104458, 980409256, 398034730, 584501006, 765933963, 352292620, 231638220, 559278239, 148416838, 333453572, 616722762, 611939536, 24313788, 826798189, 414585360, 855457168, 844485298, 699362634, 776839433, 10560795, 23341532, 463531458, 201230093, 619646700, 880659198, 263151615, 832007547, 975738135, 873908607, 842080281, 679574067, 892052472, 478123661, 203513848, 597202147, 611136574, 241996510, 896572163, 489309071, 745156427, 247938740, 216293669, 519843443, 699075999, 685881415, 283910216, 644893386, 654270937, 282916504, 374079790, 568264733, 65712439, 573796619, 738699512, 8666099, 580013252, 687670624, 326839658, 650324234, 610011059, 231536890, 126312497, 827308011, 41436554, 349863974, 97130434, 179252689, 879400824, 203155764, 130758596, 71642213, 884988536, 187558382, 111068283, 998861548, 181302720, 854713060, 410137659, 909759194, 745463578, 375316982, 279650610, 126437361, 700604748, 851265934, 930473839, 857620708, 727878373, 511681927, 636695950, 239169296, 766418389, 576556325, 783338391, 696375477, 339339090, 839031206, 535494374, 769644182, 330717601, 343400581, 1582639, 616378445, 862540845, 194950589, 267262686, 942787869, 91149097, 17208505, 169387698, 696826038, 507199642, 944711247, 395027832, 791906784, 129530092, 589352355, 303044519, 924200438, 39680819, 217697111, 755116178, 696373247, 588568525, 459582665, 879472749, 656776441, 769309356, 292450511, 474313312, 529328273, 666707722, 26419749, 420871497, 752846494, 392178747, 595282593, 526147549, 569573198, 447795160, 564123382, 56746592, 936370780, 606407877, 455433935, 679901177, 15046535, 975279868, 915360467, 303766601, 84593245, 855837291, 146595096, 163683747, 566200092, 292691982, 473765873, 412124211, 316823449, 16780790, 892747882, 15247427, 32021548, 464127145, 414409619, 599976935, 409526892, 321034316, 331686932, 106762809, 684826038, 532692598, 224088371, 852324888, 831004597, 867177412, 833087610, 988516547, 467036594, 368350637, 426976828, 453157787, 881360921, 928295771, 993282489, 625791224, 538670573, 369331056, 606659767, 92066229, 307457680, 241368982, 852605267, 900615877, 163996040, 813301616, 389896311, 309940879, 363563756, 533433131, 96277011, 420116790, 192733778, 810427322, 843622997, 638911122, 70061566, 767551977, 29271395, 761393745, 952499323, 208114671, 14910839, 772313682, 972752138, 921712230, 205242941, 11600540, 155502084, 151740346, 818760466, 176763957, 786847692, 808430079, 588531461, 550595137, 462391380, 344095987, 782148983, 866715721, 479906517, 720247221, 556457706, 473572655, 137777474, 834373892, 982792650, 359188606, 868408423, 583678435, 952853354, 418705505, 902765317, 308240939, 850464719, 76733591, 191179927, 478709178, 767384795, 937448951, 709195801, 488080267, 477083180, 463006770, 616289798, 65043725, 190131423, 288105061, 83744600, 172720707, 49089353, 285716697, 344651624, 161400078, 78649884, 821308021, 347993588, 832152385, 283416278, 703499663, 366533491, 935411905, 802593093, 819234573, 23047065, 635307794, 950906101, 256020837, 25170544, 287840654, 509129038, 613672304, 458006400, 132603612, 212904699, 174102640, 785083701, 823632186, 224907077, 148970307, 981356192, 888583739, 923278593, 324268585, 942534544, 644193162, 366200224, 364571554, 822784648, 255602160, 482758862, 376280261, 759639646, 426146325, 208566621, 108319311, 29776599, 637274755, 801048872, 226288625, 279564998, 360869205, 169736357, 328936511, 962477479, 799182051, 811044664, 872906198, 792862846, 388234379, 328689973, 780264169, 438320205, 24171105, 774022910, 203127141, 644416534, 5318639, 546334405, 711651931, 511992585, 830291249, 462742689, 495291427, 109725655, 750691735, 324597301, 308497657, 215934859, 999570258, 757488577, 776744528, 855130258, 352379438, 599357663, 573768073, 6258889, 374118645, 963272100, 782469532, 234715642, 904741380, 241563318, 17241597, 243484914, 712532114, 432808156, 724983028, 377319615, 61511569, 962926897, 532253472, 8294184, 292162282, 364271125, 453325910, 105908275, 143083692, 794213084, 74859, 302465269, 214374818, 254109688, 216859933, 97200663, 201083092, 295372773, 290918581, 424814968, 47060994, 689464310, 10478149, 8115370, 986030245, 532836468, 426544362, 431262857, 34055504, 804928927, 327724087, 5361158, 602380390, 222780514, 43547310, 528587458, 581866920, 970965681, 637741073, 426774781, 460370901, 556505037, 418748456, 306994514, 375492182, 435043043, 22602334, 849878337, 985824023, 368246229, 920828301, 954349056, 185408217, 499213837, 112900825, 691147237, 388695413, 633721276, 998903237, 872921168, 728192170, 171880382, 457025947, 38860378, 224905218, 159315543, 429092775, 283133920, 127792657, 893606313, 469963, 26165773, 578389505, 256411170, 51976624, 800208027, 423981828, 810393440, 189119240, 212448624, 376323057, 553735429, 972620776, 593837984, 300117096, 3749510, 493345943, 97682146, 325250096, 353349907, 678952603, 503328657, 39466750, 213230645, 979120749, 253400767, 820397139, 344238568, 639177956, 809769919, 288137477, 941283339, 190560685, 782959520, 988917747, 438440715, 862619091, 693137617, 792724121, 986787494, 810520506, 244042480, 228102974, 451192637, 564531427, 524815768, 763124873, 78148279, 983194512, 927170121, 509730, 463790697, 401812632, 782415109, 21651873, 297285392, 410192248, 711954784, 266056580, 529257564, 389919629, 829334023, 281880604, 516452064, 578537965, 765650413, 604473693, 376377944, 56917268, 397905264, 666968747, 439041554, 387280957, 556712586, 588077439, 208631296, 347533231, 742052265, 951382724, 410301924, 418818329, 484695175, 837516494, 70060913, 855825096, 652194220, 702567264, 416728947, 735465494, 682050224, 801961879, 436948995, 636469588, 602942456, 446231253, 472502721, 621998379, 843724489, 183261271, 616071983, 307104906, 941212926, 542448290, 759462364, 169317927, 478825212, 685222708, 576369192, 644080777, 521906618, 88954754, 186258251, 990601522, 618666686, 786999756, 494385156, 181974365, 807513966, 224819428, 814937293, 985868409, 207308348, 757308329, 463226271, 332613033, 790913068, 279044358, 848405086, 656734089, 463561121, 234582074, 96486734, 690091573, 779353177, 487584387, 798082393, 367131319, 185132608, 947769168, 505018325, 47523495, 224182123, 523091621, 166401089, 877287217, 424367994, 279260290, 21101544, 784107587, 404402558, 565862607, 524409817, 109684836, 626705375, 369036867, 182272288, 251602881, 356941928, 808675382, 190481002, 484243883, 618329232, 298091304, 212920598, 425889449, 374479807, 420487138, 285411826, 980176139, 541004988, 487071953, 952312153, 332809597, 200894254, 491252146, 549224042, 127611647, 639950391, 696703346, 326575987, 102281180, 502154888, 89125734, 213048819, 784797846, 541417194, 451144894, 400943564, 42995826, 419291608, 203106432, 776835494, 962909901, 576141688, 766838992, 706044092, 550508009, 95752031, 590458577, 981700598, 398941226, 39142036, 569113238, 26791506, 26160704, 635120499, 206768227, 535542999, 134846276, 412178109, 567845116, 718364050, 635086828, 595384245, 520015645, 519924520, 498264439, 851486459, 198237035, 174535212, 838637059, 867806687, 963554125, 283010533, 749203023, 892072820, 782262959, 576488685, 924890272, 385531118, 338751538, 442935538, 545655484, 405078042, 45032178, 284721528, 950583605, 789584597, 149818822, 476257632, 274436223, 228674676, 491211794, 976888951, 97614164, 856624923, 231769222, 30716700, 76352434, 451733946, 875861653, 777874592, 667949805, 773332400, 274914231, 390418399, 733079183, 811154824, 207126608, 899568270, 756590589, 577749183, 125328716, 363448708, 657978295, 182915029, 567251507, 991334473, 533424797, 305251453, 674707663, 774323243, 308259261, 210821781, 950764169, 848144217, 782586756, 9558090, 717814086, 188420765, 335412094, 604514312, 168984390, 581187186, 82151555, 540541289, 181141892, 117396708, 683194280, 952795845, 716664804, 62077854, 434101953, 146380089, 815966787, 361322770, 397476664, 933678032, 548611551, 768395806, 116994412, 713533625, 472911711, 725333443, 218077391, 446068517, 291030386, 89155549, 835119189, 588075028, 268570533, 461140843, 850721044, 648421233, 720035461, 284641310, 98728789, 749715356, 311650806, 668667981, 774941629, 845496504, 938561861, 581275608, 114182374, 504881524, 840108388, 602200977, 377178646, 116780629, 246332399, 903003036, 875119504, 757790313, 172006812, 66918421, 995784996, 672737539, 446113009, 113324199, 935467510, 861323191, 622465247, 780699998, 952690108, 898061951, 991418093, 518313180, 552215967, 678037031, 96378610, 595443627, 695350263, 36584100, 239065688, 971035186, 578104307, 6401276, 246986862, 475410916, 99444227, 155470767, 288509850, 38617489, 718220299, 770423315, 510935379, 694154770, 728987866, 510437547, 869241286, 705100191, 943806557, 801235735, 199738730, 639633749, 335026536, 579445881, 822649939, 809418754, 20488829, 290047212, 224632238, 215661265, 307174581, 947815015, 867705094, 143925299, 860260006, 261226567, 709238347, 551716382, 886149425, 433988782, 422131819, 13218934, 711583529, 405754298, 784662805, 969393939, 631025430, 990342639, 484475942, 452539188, 319857132, 285092818, 2560034, 483566782, 127191730, 167158858, 254836136, 901903650, 671254449, 14477035, 403019047, 306914858, 426888303, 516709314, 866438956, 658077251, 73648750, 503005980, 720373418, 769303640, 969783423, 236492028, 175605735, 368812300, 279700621, 531035405, 641584242, 986266298, 239996663, 155456963, 802468054, 966877079, 950034443, 648652734, 159223765, 662543150, 333283984, 445290121, 802188390, 982116795, 875774745, 201815947, 588873603, 863263419, 329994834, 438147795, 353830414, 428473736, 384117877, 800259795, 211294150, 27356920, 636250874, 684328182, 125300605, 216713205, 519802724, 948195903, 954126459, 762322997, 619797711, 845534253, 103386361, 135670839, 458980073, 126270649, 385361668, 734179554, 970177454, 250933369, 458179590, 493767062, 242133843, 961137520, 963638541, 611667611, 133197569, 299792728, 926669933, 658227173, 764284978, 160413249, 551677933, 482386755, 403978716, 966072705, 253311185, 820319672, 375366664, 742571033, 521282153, 909127483, 412194066, 318466863, 229623810, 39786754, 255962491, 164929756, 123047945, 398952369, 93401350, 151107271, 765028961, 209833469, 943822929, 323184114, 498417485, 861288554, 110261650, 400268426, 791581555, 863585894, 170601483, 370710327, 653464148, 102503145, 937742174, 17936540, 407121581, 464872896, 442215260, 219594653, 185798573, 211853162, 396199095, 888268298, 195970090, 70669920, 882818627, 916387604, 948884561, 431655050, 580622982, 15933628, 129394515, 414298821, 111557807, 189444695, 940060219, 572818571, 858714239, 455641113, 501441535, 628001827, 28321961, 314620007, 355453364, 132189687, 674458353, 651995115, 696482667, 740499326, 603662815, 684302753, 734420421, 773443158, 612153307, 258656152, 675718713, 802954810, 530266920, 181658575, 323014031, 597375708, 962642298, 355958509, 800791423, 562244361, 810587128, 253360486, 571652984, 912852425, 983818743, 445877532, 452189750, 644226983, 460193343, 342180364, 761002064, 492766714, 216802966, 475927632, 414344865, 576994151, 653370788, 514483061, 41964929, 424688441, 960416258, 838827223, 927182452, 471242274, 65890246, 478818440, 344324437, 9358908, 542417353, 419462916, 228483315, 477353820, 622636270, 608548518, 924601584, 91812918, 81489108, 37906783, 107463713, 496799401, 9653998, 936759949, 856069529, 573723169, 552386032, 231516265, 18056502, 758675181, 331137732, 111835842, 230433955, 453861243, 970308157, 12920221, 104855595, 469536476, 353826511, 671068121, 820711056, 186258279, 508928529, 126526894, 786613646, 591493239, 126395174, 378120887, 785554991, 831548070, 971723009, 80605392, 494595744, 411424526, 825536520, 956281275, 91725402, 927786300, 516402550, 725814068, 206466193, 483543725, 652381023, 811878907, 685483374, 67216216, 531502648, 515195749, 770493407, 42125735, 359571501, 364600569, 718408966, 69049827, 984053642, 297751332, 517593461, 529050695, 353843653, 994841616, 192310309, 575109674, 979416781, 825504674, 836557497, 632325568, 166388398, 257854601, 233840227, 843940230, 96341828, 694704021, 201705917, 909417606, 356091924, 213713475, 498157046, 97736458, 838499631, 387803212, 621647699, 224774567, 949271265, 60742040, 119348215, 457027137, 954625404, 932875367, 959423310, 527749590, 11333301, 512878510, 647262288, 141801060, 468588206, 580600801, 41583203, 603849694, 908195423, 750957925, 147237910, 792263511, 14009470, 362606636, 781649781, 493690000, 531894947, 986791963, 967124109, 788367011, 672579044, 360264928, 237884048, 443708711, 789575773, 748391493, 353286470, 899748374, 706465884, 786101470, 305188651, 406666245, 888846587, 876146181, 81137223, 838990524, 114143135, 699407721, 141082590, 602994634, 841165000, 786515736, 371601448, 876415510, 674837615, 306071276, 819334921, 425708799, 869137421, 965849785, 767023901, 995689214, 476094476, 159558998, 857282146, 125354761, 807887502, 957048073, 976799182, 86702368, 298589018, 489956322, 497959923, 484130405, 685550588, 948851320, 861415623, 650936641, 771123634, 547692259, 493913122, 45106575, 206389590, 456388783, 549434841, 912045197, 639131120, 209082508, 398060692, 624878632, 144011120, 308054603, 921628748, 827507446, 219466257, 407411508, 573300808, 280499019, 449086254, 62318111, 878930037, 877054558, 250396257, 503624127, 781662090, 952528737, 189512470, 969901894, 197280414, 416213365, 145734144, 671679078, 410185952, 40307882, 749075173, 968844988, 782195886, 808476852, 776231250, 793637219, 936541949, 833171465, 886509860, 620516030, 491415238, 534540704, 704372386, 69724911, 761816869, 854495246, 257928897, 102624038, 749717124, 252695953, 572533900, 436867965, 800417424, 843797742, 632539767, 271388375, 946698919, 259569465, 414798157, 367677540, 163878668, 382400200, 207761424, 52818952, 144605878, 23289024, 116398049, 520731952, 957514543, 450089448, 452919086, 280571310, 392954932, 479475049, 314667517, 709747030, 30080216, 737869556, 368844647, 472212305, 704421640, 263233880, 593188450, 702775982, 67092636, 945503635, 692945932, 477942246, 321551047, 405703002, 267961343, 276811270, 923950260, 400819372, 602340988, 206743139, 912386155, 465930496, 700774177, 330670075, 776406698, 879117279, 204370690, 130663602, 982925799, 702541038, 374754320, 971691905, 557315848, 43706360, 185701857, 385391985, 658402885, 166903278, 70932882, 823136202, 955030014, 217512949, 138402112, 298043860, 909142306, 951571538, 800695706, 682156448, 441763538, 193321517, 443086305, 509269691, 174657622, 446743591, 842067948, 167908729, 870130460, 766244044, 817256587, 695286325, 504216584, 810646933, 542167128, 913683880, 358454602, 746811101, 121721678, 185292856, 728435215, 835257215, 674687033, 54246893, 820792818, 521063067, 816988961, 567191050, 662571486, 875232383, 455354020, 357349298, 472601180, 697291535, 581640725, 930695397, 918487147, 373724755, 977471050, 594507462, 42398923, 704568198, 6477614, 273540828, 30512847, 917437701, 390283316, 171706039, 248744424, 416508888, 901337592, 408948216, 575784856, 996200437, 136585567, 506930510, 351973389, 333594350, 775198888, 333829833, 698522544, 326376283, 791416711, 997379528, 395784331, 660648965, 245592305, 67078803, 609784433, 54289271, 688396279, 875523922, 877599863, 876532093, 677476655, 803937148, 906251995, 603024317, 260083316, 236034084, 511433856, 300700664, 633908598, 344555034, 264395980, 817886936, 66047966, 123523126, 349041583, 539473975, 73891063, 829662529, 294975589, 603778276, 943604573, 442104206, 467637805, 43920422, 222082618, 494971081, 732887480, 699297436, 321573090, 234257812, 315205916, 509544538, 487182425, 638396599, 237032489, 557729404, 883072283, 307945506, 560757939, 44603523, 6338750, 193953455, 428200839, 531582664, 369249220, 245164082, 583416270, 470146207, 609798231, 305813106, 88655166, 791166307, 621712812, 349536736, 276193518, 149857172, 603839266, 644436467, 803835430, 183729479, 455623565, 779378957, 648386197, 925471316, 548625187, 511272719, 350801656, 948480837, 645921392, 925219699, 694450554, 856702887, 72999086, 44775826, 269039699, 409348070, 946597445, 891860442, 115575271, 938310257, 921275039, 420100116, 310652977, 357857925, 582823941, 715678237, 174261621, 651927094, 230468507, 651957924, 689072417, 436415018, 51414093, 261476281, 83309120, 380289405, 756879403, 799761841, 416920576, 374703997, 926491735, 362559061, 492697245, 99439346, 472979097, 787732593, 798609147, 486607577, 458760568, 687641461, 974249472, 62837404, 712771127, 201463625, 358577795, 362314135, 534607151, 901246045, 455077344, 248422010, 658556277, 109432260, 961681305, 154995308, 72316942, 471502675, 356232587, 193477583, 960665157, 210200250, 950274899, 652310029, 24217364, 42753165, 686986418, 169066211, 878094238, 562734602, 402485983, 850580137, 832484657, 27378681, 847996672, 215307026, 211437931, 139873542, 372415258, 896440764, 984002094, 402472216, 174678062, 815499658, 265021064, 317449028, 617988202, 923237938, 347165169, 36397398, 526113916, 245612488, 338424788, 332351970, 892200710, 441643352, 130204072, 822805932, 509159843, 151143846, 660069002, 633097432, 250025409, 721533260, 781488404, 989506083, 842803169, 887643237, 964825715, 953499136, 785827197, 596731174, 17134232, 968306734, 869161765, 608333729, 218537584, 671780771, 629244113, 233117956, 770641448, 479632751, 605228780, 401291049, 620784482, 758454459, 51831101, 686576525, 932948096, 116566497, 645390418, 615335521, 499037128, 61486542, 598144081, 446217387, 629748572, 406168161, 724616549, 81704934, 896383438, 806077682, 699137731, 721160874, 156899502, 937606475, 643068748, 391141733, 887887542, 821181863, 985309283, 811377010, 152734482, 629404999, 892862030, 198198311, 619969090, 916952637, 67821879, 86597643, 128213668, 311912902, 465578040, 821255633, 3121095, 840696494, 7973529, 250593605, 959744345, 907977074, 697134772, 105899724, 458114560, 303684564, 807717442, 242064766, 306218957, 680279065, 188936476, 797275778, 640324093, 468362284, 441782844, 106563074, 894519297, 701624605, 398503930, 983457371, 901264176, 67039397, 432035474, 528655093, 398480105, 922249010, 398456280, 148338711, 616032372, 986729150, 36331726, 472420284, 288784244, 182475525, 357251258, 995770214, 793055791, 920935875, 734135040, 101703673, 265983293, 626060264, 677280520, 368263479, 878496188, 672729302, 545917575, 26696124, 604000445, 746924036, 270983185, 586856846, 792783410, 327975610, 912589282, 211700044, 442848994, 739347076, 173953723, 83122297, 341092305, 624100227, 691309742, 453986491, 525266835, 570037299, 494838631, 187137891, 30528142, 29624612, 381058555, 507947909, 306538967, 309614369, 254035827, 414492547, 152028664, 859726402, 420746116, 105215270, 166638009, 764203831, 87360720, 39828841, 183136250, 195754233, 931072303, 483977218, 430755911, 568048565, 533867560, 843460276, 763459885, 82002294, 478820810, 76789668, 926257770, 124933846, 73671898, 383960674, 997729346, 829479692, 416482157, 696382497, 238603038, 948269593, 124017608, 713476998, 543588754, 971997630, 847423313, 275863919, 527096467, 450078589, 56675636, 61349770, 533112548, 71706149, 545873292, 370163913, 50157267, 206927754, 430424025, 381632065, 97434453, 843766398, 547011743, 216433912, 892695889, 616133624, 254765382, 733206230, 680590909, 37549124, 193191284, 136563344, 707983765, 387290667, 654517346, 119819132, 922464964, 780738205, 964930272, 922235786, 809309876, 49760242, 515908342, 789625796, 890999274, 64045211, 939842757, 499256356, 298891978, 974927600, 138157166, 223505636, 430980344, 369166841, 964086034, 78031520, 691108943, 281991112, 417760962, 914305246, 767578236, 363843344, 280597473, 506953064, 497913575, 666520962, 569676078, 243980473, 505200123, 863043120, 142646922, 689727748, 919565091, 773252942, 84513314, 538802350, 760103079, 532414542, 586779921, 733772217, 469335160, 782726599, 647185405, 347028817, 351196898, 388829447, 142059308, 573958343, 551520245, 393682579, 347728609, 996047571, 708436009, 322270567, 730355357, 300777986, 138693813, 171075010, 856623141, 684778860, 735280654, 832789961, 221105027, 688627703, 536568284, 958160298, 880981492, 976496165, 223355157, 958343783, 641831790, 650204670, 276040411, 114223930, 762112597, 697351491, 473222080, 87150415, 128374568, 441196105, 476105668, 762171, 599274987, 535575854, 153791778, 837694554, 471025585, 709887121, 385389181, 599764281, 185536753, 166363178, 10603705, 741966499, 434339257, 861521170, 567495268, 537283465, 201659395, 482657036, 475856811, 518250581, 168727968, 563393196, 735380303, 322082982, 434531558, 739756966, 232065193, 594869237, 172148660, 412966495, 244233928, 774502498, 587571417, 397623301, 491486519, 565495358, 803187610, 142056112, 754326163, 240900027, 54920763, 172010901, 71819471, 902551206, 244627022, 774560552, 412762387, 305008595, 620552521, 330093269, 982699301, 456531370, 680515937, 468205424, 704965069, 342652370, 640449082, 237239906, 724353420, 91814067, 699126178, 139209619, 754861974, 994285821, 665225987, 883898559, 4731952, 761380268, 825019502, 53184344, 906679043, 772235930, 587606247, 832848407, 94420974, 538027261, 933049092, 853915849, 639532427, 52228866, 332334634, 452437816, 523905264, 457793129, 1269410, 27446367, 308779235, 327993893, 953628324, 368001083, 890574503, 709348008, 418281797, 453710251, 898796740, 274426368, 398795653, 23350635, 311589910, 722958703, 110530547, 827755825, 783439613, 469824109, 75503161, 706500536, 104503178, 370629754, 425096803, 985034698, 988347839, 341431727, 88852456, 437257732, 452310227, 134452525, 118272542, 817617395, 883165537, 90647566, 196832144, 898542547, 447432868, 421189875, 12421406, 335787497, 368370570, 257423741, 67204240, 50116780, 297095823, 449698943, 730723146, 1235341, 828357335, 29498057, 2863201, 66474168, 654708499, 129571274, 90247376, 695968665, 230444196, 207334608, 359548800, 930900360, 486223034, 280424746, 639442923, 138867558, 477139459, 842552980, 703075792, 601805472, 805488835, 383419511, 592505238, 558655965, 460084431, 861290417, 231024615, 440580547, 490597555, 960352551, 174353879, 690086186, 631867477, 10296086, 399597241, 218355439, 142139835, 699891351, 707534068, 45702051, 207298163, 284048600, 207353987, 566689169, 321536911, 199785744, 227712995, 243160705, 319066072, 425216304, 724399849, 824264140, 980987461, 820443072, 64842042, 840524917, 163636490, 121387097, 884325097, 671821715, 417865882, 340983022, 731625026, 575524124, 683389925, 997095608, 860489978, 916657528, 453382896, 942282913, 246340205, 509102636, 296351208, 810868809, 72624243, 556836511, 67278297, 75609674, 79234637, 79169915, 936811037, 657912185, 523885475, 743112465, 775229899, 15509916, 759401079, 739646831, 88437790, 678959046, 836795005, 242391893, 963210127, 433141, 185410163, 21174593, 93625633, 676226733, 798887664, 745200080, 678047266, 791013408, 765912888, 467220592, 442977349, 25620962, 433244413, 473505911, 224789138, 200079151, 895184286, 173075658, 11807969, 462477816, 725455057, 562118930, 474352565, 786477420, 77208131, 353584474, 621134686, 345329371, 653371596, 152804231, 391008246, 571515122, 671698861, 593781252, 852043473, 837767766, 529399031, 614210302, 473743754, 518396411, 28964100, 892905897, 115512685, 581319693, 390981936, 773548241, 685378369, 289050124, 423816593, 598040637, 656088657, 868614187, 744296469, 443111113, 22366516, 81923549, 51014568, 356662282, 816563622, 418530507, 260424425, 336023275, 991786613, 956116511, 59659169, 987042315, 88899811, 313755788, 835455312, 157012666, 801731095, 530868795, 325092285, 326899590, 767940222, 71810855, 887040400, 263317442, 634466754, 618763740, 408353446, 191820446, 568787178, 534198620, 695579516, 97093681, 55526758, 259742385, 731810929, 217826081, 424933452, 491560336, 642074839, 998363486, 650347395, 630499182, 324862848, 21321527, 568271529, 20086984, 772772287, 970372249, 737979605, 288277003, 494240812, 830557068, 289821012, 515904750, 564397474, 163708307, 844621928, 292977470, 871013930, 524359450, 921208829, 693309577, 870278744, 108068476, 89502308, 371640993, 294421915, 194384863, 801382356, 737762669, 971222235, 867294219, 749422053, 908916498, 455394209, 707551745, 478015350, 892605105, 815482800, 323960195, 967333659, 547480558, 785065052, 398852914, 933518629, 737309720, 999072368, 511135792, 48456294, 11327389, 604973183, 231710840, 313264811, 415669241, 781662234, 549531446, 484476274, 231844634, 945320454, 357381950, 797953988, 608695873, 828971770, 936297597, 827941941, 389473070, 515398165, 189682716, 545669231, 717651844, 889231650, 966292354, 664560206, 904256424, 350000832, 915953512, 602748815, 8083663, 705939203, 110351968, 892417494, 927001657, 55946250, 147232100, 895481338, 435626415, 61211759, 975731068, 584081321, 517740725, 427504783, 480983617, 176562719, 268130823, 97433980, 575962131, 840326981, 2781807, 573003131, 308778587, 264685455, 514006212, 293479728, 353721040, 656719149, 198011956, 66458251, 168445215, 476736715, 727886171, 683356349, 591897186, 944277202, 759077289, 338035426, 478816279, 114059095, 690079476, 563652498, 140812317, 270346699, 67033447, 979748160, 607875340, 775291011, 771530842, 301903181, 804280121, 297096229, 731193091, 100118504, 87810891, 573171761, 654386942, 959464985, 613481157, 489522051, 702986276, 291961561, 91604417, 52439790, 967712739, 315898004, 379981171, 440059243, 841876349, 577914579, 625869113, 777810754, 140835529, 292833025, 399213732, 574500990, 106149626, 882154628, 660442469, 44575295, 671470688, 549000771, 644803778, 77901845, 694339462, 275054575, 808920969, 45215359, 121002489, 407277539, 72231940, 991066830, 946856752, 772567584, 489399056, 3532302, 365082664, 237771100, 784849212, 248024029, 54423839, 724010685, 668997471, 960906294, 63107383, 11806386, 543099393, 784761272, 126417557, 851789581, 36245378, 927058180, 934973485, 598060507, 432689062, 957687856, 647503628, 813408486, 756217639, 356977533, 913334087, 59353110, 289750855, 907431404, 797715471, 636271482, 850010208, 240392436, 739299072, 549365213, 33601051, 500302320, 542989759, 492964288, 714846992, 172084339, 234576628, 919468412, 856122442, 350193398, 331809446, 484626986, 981766260, 708600614, 901937024, 913599001, 424410033, 704089390, 309543475, 88084450, 477770988, 820365727, 258912357, 88758602, 201483679, 833044988, 853023790, 149965933, 823989582, 795248696, 48946949, 235087129, 891126567, 874097348, 151255760, 888401368, 558803953, 150196424, 407105217, 149920487, 548730548, 512233547, 41687823, 797264369, 459441258, 24156513, 546917280, 166055918, 726701656, 716408371, 496309883, 931054437, 329551265, 57447614, 756370966, 962814721, 837446318, 463626176, 180552202, 364374230, 628253220, 837754441, 537682211, 1547688, 878743455, 598769114, 149537932, 537450145, 969067302, 829505257, 939007617, 874537334, 860753244, 396074990, 409161131, 386772529, 234594082, 112408133, 390246928, 549817411, 460693032, 944675611, 217859673, 204008920, 970213688, 750092656, 533124645, 865636171, 347872523, 643637127, 656543735, 889781911, 202394548, 684021095, 947751223, 250572568, 342153271, 889818629, 921841409, 122732421, 607784528, 455648666, 807201921, 305918011, 702175987, 334567599, 45137342, 402958424, 188830054, 35987848, 428193848, 568609529, 393217373, 903460578, 778306582, 77372392, 744916563, 434477789, 134313699, 272606992, 268406234, 622929869, 929859004, 363557008, 597062184, 450448496, 436542380, 542911245, 54827686, 833501322, 861493030, 992219021, 203180808, 542244975, 821605137, 808327935, 242479857, 585525759, 334222118, 692816267, 592513787, 967824153, 837872432, 439283887, 724874285, 729866935, 205741746, 45387211, 675293808, 756669260, 511393522, 329170771, 364120289, 205050478, 686406134, 705654159, 926161702, 825405896, 585641326, 970569543, 390236933, 395341767, 719579007, 133619877, 34098902, 590692627, 601060881, 32984897, 427847357, 623701219, 919883419, 390460398, 2276307, 448158544, 283292451, 332977523, 906288269, 485616039, 605855381, 463342063, 264492884, 794726085, 351721121, 368305812, 801363053, 75379610, 937112343, 331219800, 328079919, 673764448, 818307332, 569056105, 220659229, 964679489, 443521069, 543164858, 979869115, 865275811, 624325922, 653449127, 609586814, 975360486, 474575613, 997719580, 280503598, 487724395, 106480957, 139483355, 868165060, 185238210, 407669349, 563065834, 610096440, 367451423, 980715923, 344831404, 262028744, 380680253, 964784053, 250460376, 741941119, 512029682, 893476298, 501370441, 635381518, 651586627, 234872556, 659362811, 53092104, 887586415, 80425413, 981693094, 996487136, 421932973, 807684934, 195818759, 219729282, 992079527, 832392520, 892777694, 685865113, 647254363, 440403665, 63851579, 279352764, 902543525, 257882439, 897496502, 572863310, 430140016, 326294377, 298052393, 961639033, 719836289, 874765001, 125262823, 794612496, 746842144, 268601158, 878017259, 325126443, 405610869, 837553560, 171272985, 419098786, 518764421, 798584064, 105427412, 769333955, 196919881, 206690258, 403240004, 311254675, 396802751, 724266292, 435648527, 264245824, 429551895, 224029437, 21438762, 993352134, 622892306, 728153874, 25719834, 374473137, 942180070, 225688652, 845510051, 367758963, 818112213, 411565289, 50909755, 260870487, 328117043, 37781609, 876875605, 147034295, 459612252, 776508397, 261579509, 57040610, 350680621, 627194096, 798950532, 724870589, 983502864, 809935670, 93478195, 857584488, 831885347, 647101514, 617540568, 382945703, 117243271, 567981012, 182315568, 792691363, 861243520, 717127678, 352277983, 36848913, 594355999, 638917277, 456127690, 720587640, 267126272, 458125506, 342376448, 297810332, 700249834, 543971627, 541297964, 411282358, 264472804, 765033955, 466856658, 274484195, 874208301, 205233365, 726655544, 923115879, 95934119, 188493158, 332407896, 797445588, 839914226, 358854264, 709902648, 259406164, 197733541, 802338277, 660234656, 586586044, 146658700, 179530419, 905792698, 774177302, 612664198, 150892934, 255968013, 987697480, 806492664, 177108066, 368296427, 998458025, 301402391, 825766499, 763447589, 724610281, 619553660, 919970429, 50981775, 347359493, 851470580, 385473797, 842189113, 721939478, 738990699, 286692541, 440683011, 984666674, 538141953, 785891282, 541104645, 567621513, 776636510, 85428101, 376981546, 173920654, 318622291, 981484434, 391808395, 305952456, 749851205, 988384230, 959592842, 244702112, 252106646, 669928225, 374321843, 669448382, 987633342, 902914207, 778684350, 570953927, 951590464, 845391963, 647405741, 616240257, 950984946, 788065404, 940943900, 42384884, 857716405, 880056696, 488976071, 834998378, 224666168, 73782365, 824946645, 712105769, 909309720, 662825772, 588196413, 565086930, 585684829, 702501996, 659541912, 113827017, 296132432, 861965010, 134589934, 569138698, 197529428, 537514919, 709496292, 190073264, 527435316, 644004596, 821737166, 33931088, 692662581, 84587095, 561707256, 873296474, 934955573, 12266405, 238306000, 499252251, 538888928, 607698467, 115686485, 372205117, 381089532, 160333516, 874455088, 919715660, 791120583, 161688909, 79051010, 226449859, 699197138, 230255144, 356428881, 295718171, 196555605, 523227987, 587232802, 658582094, 386619775, 36344759, 490332353, 256903918, 930318510, 176173645, 212253242, 780572198, 645665578, 903275171, 312806408, 301574020, 628423317, 684895944, 859155156, 831508353, 515075583, 341871829, 382400163, 567623262, 339480425, 659502294, 553454645, 754696063, 904194228, 906296568, 233536171, 388671571, 232951946, 596355095, 908916821, 342423828, 657209170, 194584696, 190155043, 843273740, 416066992, 451425435, 682361426, 736973206, 230681160, 296311362, 764681155, 280370267, 126222848, 290985855, 444567107, 216601604, 132052615, 39543568, 388648168, 560597850, 902527871, 169627341, 702742152, 551030531, 987193463, 345879683, 146811362, 54876804, 518986225, 674710734, 88057808, 417389017, 696151298, 575078647, 131110925, 947471504, 181914174, 583732888, 908729942, 660624131, 79095853, 444647521, 695151406, 137227638, 45825986, 503722854, 921165954, 520359067, 584458115, 882977192, 23849143, 284368869, 558483300, 783237559, 228808279, 176095748, 359904060, 816897598, 960723047, 158342987, 900467007, 196240477, 739125676, 200409398, 769315466, 860771733, 910343172, 602911704, 640607525, 279487923, 161975066, 40554478, 768645215, 215534906, 498835036, 939183515, 724572786, 18276475, 17639890, 981157055, 237098682, 731968643, 568069977, 73348246, 439237994, 996533670, 737492849, 180628782, 585077596, 70631197, 198850683, 419852065, 697282094, 286102573, 584942945, 587409581, 522466501, 847173528, 692225409, 592701229, 217367933, 129364164, 126027872, 135068895, 179791662, 826742594, 545470039, 796440262, 985725909, 347823712, 124301444, 986513628, 131201529, 287870838, 473409219, 562573504, 902027607, 883386357, 37165680, 635415618, 15038362, 617405424, 503984040, 415670758, 683415702, 94240439, 397425631, 541611241, 533683073, 685208869, 600204369, 357916680, 868470539, 217070762, 445372670, 895811473, 546806907, 885550706, 739803854, 381856239, 143796814, 390681756, 136459310, 568215448, 203477935, 108780068, 85147949, 283127836, 55994203, 690687545, 878845536, 695682116, 177230036, 526331327, 56808622, 657342134, 594771643, 392674982, 416730557, 130957605, 788913963, 35724854, 430208095, 673428612, 359034640, 179144878, 641868369, 511279648, 614077077, 743464324, 464119794, 964651755, 165047168, 153402877, 653607191, 380438709, 816045390, 533442014, 851778662, 716055265, 638251370, 357128934, 603414136, 196695410, 535200952, 365787428, 320753267, 787397653, 75171814, 477251111, 945936787, 386196993, 214139078, 88931072, 477281948, 461349968, 175280086, 347279674, 383832232, 756534314, 943422691, 918261056, 944862004, 167859753, 934914584, 419621913, 138088027, 657903651, 867964858, 166060101, 116787317, 27092999, 443235779, 821784160, 75197667, 401404613, 452806751, 602806753, 938119806, 565077125, 712638764, 213064898, 992697006, 479210672, 871768434, 192179495, 28693249, 335380578, 131529988, 241233921, 577315064, 42066155, 877965545, 323730090, 852110559, 346378651, 876597330, 442605333, 414922591, 243300143, 670887408, 435158843, 145776436, 664729670, 428605940, 109980331, 248862636, 749297183, 869707876, 308457712, 435404863, 862567417, 38434084, 614984752, 232566287, 389453913, 698675427, 107635262, 104784463, 943281818, 510644042, 700625764, 307983418, 874125759, 83867265, 110650096, 632156406, 276849560, 491258456, 967640458, 946805668, 333392288, 47893315, 615192046, 244836914, 120078925, 343657449, 86306009, 108878785, 440316658, 890231711, 71703927, 474445314, 935854415, 415221858, 484740424, 276123635, 523839473, 372724123, 902929681, 269071218, 396943888, 590001170, 228172029, 449991519, 950203931, 523104141, 509137990, 633471046, 590042370, 599687302, 336522042, 312341632, 98427735, 964498300, 944864386, 523941410, 571835241, 62481265, 21682676, 526304071, 760347370, 90468265, 859263066, 585183352, 700218096, 824476812, 936006512, 541172396, 996803078, 109770964, 235909299, 76784582, 646165209, 478419345, 891394015, 213536309, 903980860, 615851633, 377443856, 466591914, 728892818, 382366688, 776388877, 715887503, 622404097, 826972249, 988777171, 466433541, 878413580, 305075984, 15837637, 258726516, 217470240, 488309581, 774209251, 624642371, 459956761, 630406111, 166736886, 910313453, 377541137, 447740421, 460047142, 110505965, 953354513, 742721530, 860374625, 805616154, 464750283, 547223193, 571517206, 548443907, 971602714, 461383320, 166506327, 914862440, 501950289, 438409413, 147229132, 604221413, 5017560, 495261767, 165531997, 875104124, 706986040, 998909064, 79151406, 65779531, 436957990, 727502840, 336273130, 833871469, 643248865, 77464093, 942468427, 687319781, 124869561, 961417737, 670220852, 860350042, 130856559, 529413982, 905939252, 893430763, 374036065, 567658454, 741471032, 394380159, 45416834, 341848947, 916270060, 857384317, 757484719, 276106366, 483971798, 448591643, 109672832, 468260468, 257261527, 33021084, 879168854, 949231322, 142445927, 123002472, 100273212, 734811208, 477492550, 345546354, 61349347, 338856896, 274316827, 384615179, 618314558, 910108673, 937003543, 787219779, 83099996, 679686288, 927739239, 673710638, 755218695, 72829236, 208196756, 647893821, 814587491, 419849143, 974987747, 797660230, 997951837, 26491410, 880957775, 315646398, 261069840, 53625317, 298191662, 322687091, 216741839, 86580083, 938896320, 375831260, 419664617, 917864739, 935703218, 238001668, 646418058, 659260374, 277084955, 392123909, 26525721, 881102803, 751192075, 585499638, 31287316, 616521391, 803506897, 220398786, 939662360, 72907376, 477920043, 987460257, 589984573, 919627901, 435088877, 684758327, 373429822, 762747529, 993529612, 299477403, 639731792, 364303096, 26355664, 505497756, 351747381, 708975175, 257408707, 38635100, 661405530, 837023077, 579402460, 938113111, 690955145, 441644631, 890570319, 399827616, 574248856, 994463602, 844153696, 381363261, 405979739, 146839676, 856143878, 468755649, 217306671, 929914941, 384924398, 244070469, 335130996, 579282671, 802974212, 480547621, 666517389, 827177264, 669734574, 121000040, 906425758, 900759923, 100080232, 775577039, 372588205, 211602597, 777364404, 412304193, 982002821, 2442810, 204157842, 300981500, 974304187, 849423759, 903325856, 116258175, 34205755, 338569281, 894949212, 571880527, 100906507, 884977835, 676759522, 419160016, 822618946, 353642697, 265342717, 425072368, 94247145, 769377764, 94982664, 648902067, 526627255, 245635314, 415913969, 195360321, 331766790, 796850031, 642623038, 19561241, 442110646, 705854869, 955861974, 881879129, 619204306, 612256666, 501036194, 992486951, 792809901, 564484385, 485700775, 281161288, 837015500, 386099634, 297323814, 773214658, 582200611, 395844054, 259014573, 893641887, 253480486, 418448912, 176074458, 646366008, 107045140, 748281845, 762717891, 800548042, 377713487, 780711462, 28676407, 854309894, 165151032, 982929564, 248946881, 328827981, 812794086, 412115706, 957293812, 950690696, 741027132, 964412009, 633816085, 560236017, 853517713, 675035947, 476560403, 737099220, 5094778, 621319884, 561025706, 144388128, 529887098, 194906458, 784636245, 161870183, 222885941, 985257220, 345982742, 410811679, 523903205, 162122219, 833609041, 150176080, 99788116, 764830615, 675130231, 536576998, 684139792, 596338144, 940429343, 987525799, 556444930, 378131953, 753501228, 806622114, 633840545, 470878516, 117569593, 802858745, 139523011, 62333892, 283479244, 531740804, 991531623, 836930180, 461941897, 904984109, 46777414, 492984201, 993562792, 747047343, 50587069, 647805155, 518546668, 26552468, 17833056, 740086774, 192872120, 566288207, 919041990, 188798633, 450492860, 265243505, 996280106, 821114512, 839391476, 648287566, 49229039, 823487154, 772206510, 183177504, 583846893, 385142026, 846113344, 684985281, 906861647, 699264644, 107636742, 964330024, 922611035, 421154798, 150465578, 569975941, 570699429, 226215324, 886756982, 945393371, 179993412, 320502162, 504619343, 83484990, 603438815, 505187175, 715783258, 314695362, 75828082, 644716517, 519584552, 816256770, 844944633, 438313953, 437832172, 232264718, 330150356, 365574349, 927227086, 732416809, 86702988, 216988691, 742973521, 53004358, 603912606, 850628623, 886645808, 535376046, 108421360, 512074925, 296019960, 391598724, 88899322, 651089227, 949634540, 622445282, 181850912, 656262561, 928854455, 412654748, 690000872, 663944242, 92750465, 333346276, 391780266, 861512487, 856176132, 539369671, 878223656, 814814744, 891740432, 847836588, 621298303, 479754306, 875624373, 545492355, 925942710, 327650400, 543805572, 467710688, 827996262, 662373424, 6207682, 548120910, 809279988, 460607134, 211658693, 985859577, 966623724, 636294014, 726286890, 368101061, 946995278, 250509138, 267907155, 228096706, 225801936, 594118865, 760223223, 794596605, 967801245, 798916755, 346112149, 958947949, 538513352, 317500439, 35157329, 149871804, 251963379, 626367232, 923509465, 242947185, 418632829, 469833173, 586284209, 192397959, 291112008, 223892734, 848915047, 348554684, 83711907, 609692515, 427637316, 532780490, 113345833, 765790536, 663569404, 992006714, 969674237, 193056711, 485385332, 814032152, 692654690, 729829472, 135668685, 197522093, 532619790, 79909090, 604772473, 563254274, 322342833, 963271323, 923091979, 678596718, 253808826, 243429943, 949508454, 836817749, 553304009, 235472399, 332545319, 674517410, 193141584, 444766330, 364900687, 509994983, 968630933, 385918716, 783318956, 911625541, 625229712, 195589761, 538091886, 793538209, 205345247, 79334589, 629889236, 689937485, 189076670, 433683167, 388008823, 30591670, 732916446, 939706581, 968981525, 257032557, 606122221, 398248764, 453014079, 820121702, 96539938, 556328655, 374967777, 536214404, 836111643, 869367293, 543004004, 686980890, 52753530, 369188865, 741707719, 966963409, 280882307, 20928347, 359225527, 911229150, 595059434, 47772256, 394000589, 779068879, 215343742, 854857647, 651366297, 86080710, 485587447, 313934852, 636987940, 519303353, 823820458, 940437087, 682712727, 805284788, 844046594, 773254103, 425718703, 231332317, 622458471, 848262795, 8990568, 895699016, 820096634, 696754297, 661564233, 789363664, 20258547, 678551852, 3829705, 98420585, 765431991, 16766368, 469064481, 403608559, 904456881, 2711256, 316574927, 829276386, 690148359, 485240154, 350597862, 517256195, 166818777, 215936148, 968098501, 404013884, 500064801, 111297953, 187074322, 949958427, 901048599, 629908902, 768805746, 85458549, 119889456, 299250679, 281738177, 893649002, 225438237, 25250729, 401493332, 358989918, 296966568, 307349249, 484974180, 475433935, 594427530, 936280530, 996309589, 191063224, 803760748, 154134772, 491787883, 783117641, 688977385, 699515738, 331310202, 82964943, 143939179, 567141533, 821332035, 662561950, 958553477, 644852359, 908424417, 163992638, 592538621, 467704091, 391145664, 153540838, 763331258, 760847887, 40695301, 34450335, 527705358, 230879239, 471701518, 648138479, 346740962, 831721518, 5550324, 877084515, 289199531, 907479927, 668538297, 835219062, 987416835, 332023461, 371401077, 550521851, 534527639, 698876138, 537856123, 823951409, 281947532, 191793738, 800355027, 68706183, 869301922, 450808032, 860804335, 302965594, 50919737, 986787997, 776420796, 231962084, 839457742, 520076443, 881819659, 119350270, 826341560, 794999746, 177514067, 648178296, 233833710, 672508752, 615780720, 918730567, 919394188, 970428564, 694635856, 612484168, 672463059, 679617717, 688570237, 831731920, 876130631, 808823034, 801027100, 893821571, 476119477, 976466737, 566219264, 284332036, 26986764, 215866166, 917409087, 251646390, 525081188, 779140357, 345743605, 241454901, 744699585, 458140801, 856171770, 356623549, 217783000, 216714563, 403994483, 61570977, 902531082, 637545495, 25617914, 920150042, 836115679, 725961216, 598409304, 248333744, 729947593, 360352037, 964063339, 595404361, 50332240, 658083943, 450791992, 266360866, 99320280, 220670511, 136694755, 665475139, 400958717, 212945357, 72856771, 232527826, 528392801, 14335177, 118589404, 868132676, 277847244, 215931745, 913768071, 621042655, 209018285, 665678526, 960299055, 38260237, 401647495, 217377033, 966254008, 232207646, 829915386, 891108866, 431559917, 755521040, 358232956, 813610842, 826815432, 814138729, 827556317, 718778491, 664158135, 502969726, 368820212, 773370047, 952241921, 637761606, 753029077, 477878492, 400966586, 481536994, 166448535, 482021373, 911867911, 896323081, 785178830, 344545749, 691344383, 481499043, 13351213, 861915058, 991897586, 61711238, 346049700, 257291547, 240100896, 275038316, 960198664, 232089664, 325507777, 742179996, 122578459, 884099434, 154132490, 22406724, 394282164, 795528798, 945369347, 89855353, 577648604, 722031693, 677673367, 120043960, 91751542, 137319663, 260534125, 377905831, 193196070, 529873952, 937112279, 906970450, 798556480, 496074891, 633449487, 311356074, 580053065, 617339113, 660419407, 894010935, 617303937, 164280935, 148268029, 869233296, 854119228, 453934609, 354552701, 201093273, 158627497, 287968969, 541075911, 505861103, 395449331, 88478437, 838758376, 880649135, 927371877, 230682434, 626104391, 81745981, 813105, 666186451, 993457207, 334852059, 428013704, 370119026, 656442168, 30046191, 91182117, 699746390, 685655969, 388103612, 78854447, 340158491, 758002102, 278726257, 251055403, 310498498, 113201774, 488894226, 982988222, 758667112, 988896084, 875121520, 200012065, 284442838, 896813659, 597923141, 242971577, 853411942, 843704276, 42981437, 755072320, 888707349, 260664902, 566504339, 33460958, 824133895, 485596816, 420990048, 454585875, 560146864, 365297753, 410282809, 393270132, 9265758, 882707060, 332834005, 499640746, 656851136, 496227397, 126147949, 587310395, 732063579, 246011192, 398399710, 309921570, 942127089, 765231998, 73389702, 56959405, 575103857, 865839065, 186194463, 603311996, 684796621, 373334248, 234473897, 726323857, 902460598, 74539538, 266368939, 404378432, 83936329, 750009785, 311411820, 619408717, 453095021, 317297833, 228223488, 229458556, 837612734, 157810845, 632688583, 88476772, 875341685, 562628143, 334652152, 887127193, 454734108, 546355320, 221699046, 96212213, 595771410, 781255921, 652291313, 404155366, 599610451, 88831683, 752727440, 30457591, 255583703, 900748952, 921387852, 408930599, 464829424, 737409134, 511267947, 158206190, 259750971, 522417965, 759534679, 113395490, 542784929, 674637997, 260193007, 337008447, 69277246, 525312361, 757867749, 659956710, 368342476, 190548311, 669218567, 762145391, 408678198, 821874107, 639353305, 497491200, 319087384, 872689962, 283833305, 32847905, 732510078, 748658088, 887805251, 933824898, 588067522, 523303976, 632209251, 68811130, 967389595, 374840515, 768285426, 570736346, 278318214, 245663742, 894762068, 657383735, 408909992, 753588243, 923803237, 51651905, 81908547, 650536991, 390135064, 54342992, 462227780, 946328428, 389329952, 975213035, 301208128, 455794881, 621479162, 37302806, 426152809, 372309039, 707131954, 582438382, 954426075, 124265394, 645994655, 340378652, 544214492, 884464467, 205964904, 142771514, 721386904, 101459938, 964756599, 662766416, 42016102, 34381496, 314438127, 999364023, 63700358, 348923954, 807768566, 454183058, 712593972, 390611394, 823801914, 847400730, 633902701, 626573043, 324338365, 353850368, 530859209, 230920362, 146707290, 568599854, 285160478, 908912691, 132362836, 578739077, 127062975, 158918335, 755875494, 542219438, 873899334, 232506547, 151833316, 185032698, 577556892, 884924689, 356312250, 875892579, 543440709, 404094364, 924410630, 471989367, 705644687, 416798404, 132025187, 949026193, 869617918, 610095637, 14061364, 415029004, 278084537, 939035329, 459198901, 66642743, 561568347, 218295265, 929129797, 442799384, 458277384, 445051573, 719364022, 777262449, 241168848, 557119327, 668596194, 393313591, 796026051, 773847870, 698322831, 847322128, 384658594, 838300248, 896942426, 13273496, 219709515, 606448003, 510301006, 923975143, 288451154, 497159320, 360636494, 735749600, 444646680, 591567081, 11865446, 181329167, 8549602, 660470457, 859948561, 647581540, 442087358, 453822087, 527081753, 436494212, 827413354, 143514371, 951401735, 120113231, 164526820, 986398849, 429450166, 160889194, 13982178, 972801624, 74942423, 110124744, 63828305, 534131047, 962842229, 444275758, 650234940, 847613819, 503310855, 553429371, 421700771, 992651378, 407180605, 694954095, 224108354, 461557064, 857648791, 244699696, 900252314, 953310347, 5678655, 345101657, 249365940, 152924831, 799404337, 538851225, 648379033, 777262037, 93666929, 75021840, 50113695, 200909809, 64367393, 130918471, 108299027, 295284909, 457380170, 460877936, 284296364, 413064671, 504356250, 828475453, 230217486, 22312272, 451098941, 237866774, 840792005, 829098199, 468428660, 700045305, 323381270, 895466204, 407337070, 21442521, 737675124, 648605389, 955242751, 229565748, 798509524, 451306944, 166402103, 629727329, 487536362, 261613005, 939169736, 284391364, 994398641, 992365732, 715327949, 893673912, 602483687, 568689807, 404243115, 203670092, 982115837, 679794537, 65615037, 445852459, 177622745, 80212184, 980810777, 739147855, 725023089, 564477472, 185769739, 687835149, 109451171, 731746130, 352764968, 874051749, 948551590, 267233598, 664947546, 579548991, 570730487, 730980580, 63682306, 615807112, 190363378, 431457003, 352361243, 700687222, 829226177, 350651472, 176861090, 794462719, 343512317, 619615075, 56783555, 340475929, 483173189, 97276535, 323082912, 96730172, 537729787, 254448612, 314370701, 450553764, 961329845, 14659873, 111404028, 261640385, 767229630, 562388900, 363205174, 119389993, 665139078, 14978446, 27469672, 424162699, 954162835, 749291964, 873582019, 649600093, 299641379, 68657363, 839997511, 289124945, 66168945, 84809055, 74808959, 207258959, 751533594, 105449897, 426194843, 22180670, 81381553, 865097136, 784104265, 815810132, 772732906, 421758429, 533130779, 318421071, 904834662, 644572856, 328100370, 729689105, 260866520, 672530363, 725647200, 552807859, 693518266, 748769296, 359403186, 833437781, 64322284, 291169601, 748796643, 144454554, 666033450, 742526012, 723118742, 813647509, 98670670, 929522330, 249922967, 438987699, 904780599, 677024, 516519419, 624667862, 933425683, 375717136, 434607496, 318236341, 235231978, 416729887, 238528720, 698961411, 215363387, 319947409, 166208712, 752865754, 807830103, 56736796, 265254664, 776421185, 173234671, 703858540, 835073338, 200642492, 137332078, 256732598, 237606917, 473223738, 171793730, 381902268, 595520720, 144625643, 662554781, 166532776, 847083708, 740767591, 9483488, 442543163, 960173158, 234734032, 265372509, 613534674, 633536633, 282699798, 763947804, 312485158, 258649241, 734578795, 944054505, 313266959, 160511122, 159535700, 297471018, 772468642, 782325525, 549537368, 454806562, 14438791, 195203632, 630121977, 809863535, 926826734, 802983740, 348578050, 895552203, 109545794, 770364143, 212567821, 497514370, 447587862, 584894567, 837243954, 846849131, 154072889, 948799621, 31229273, 215436637, 957415754, 126252557, 510130953, 85920838, 678143272, 297637979, 884733819, 816149112, 146704338, 388224908, 381902650, 403440665, 634062109, 98556889, 19199800, 551629359, 787877640, 46010290, 41500563, 44517834, 331070764, 251464409, 279382021, 319911061, 142018129, 261631996, 170904102, 623885730, 799169124, 379381436, 442800832, 820853042, 676354409, 294823068, 265205512, 36404261, 770065583, 439533472, 707473365, 267117005, 738554918, 951919064, 893490002, 266424214, 758405443, 748183287, 569636054, 211498325, 977955456, 6716787, 852876348, 230374233, 48384369, 418469466, 673047836, 945692393, 616629084, 825807279, 795506975, 111935757, 40490376, 756405435, 572642794, 893723892, 299260560, 361485621, 136207522, 48971260, 624798718, 183065574, 776769798, 275328696, 9663183, 822095782, 659924146, 527805796, 476341917, 591479181, 208324898, 220154852, 4366418, 400762456, 112988789, 759860153, 815928303, 160599067, 408015874, 581755422, 453175322, 223804752, 680737826, 753610324, 99427208, 137722566, 923739250, 978828894, 767404298, 589234038, 904184018, 842960410, 442465642, 316994047, 238138672, 443458190, 890108902, 475076814, 713744249, 296908379, 332627434, 349936823, 700041920, 519825176, 257604744, 767630340, 68446589, 301224635, 527773046, 415055145, 288105894, 290491719, 712880740, 715707940, 706633257, 441642551, 448463661, 59348877, 187454551, 79127147, 975326470, 40442959, 813441866, 505071630, 777338177, 424842216, 323491009, 224295782, 828967959, 676459618, 68915925, 176985829, 224622460, 926925290, 70331341, 91978771, 447213855, 796594107, 564473286, 446134829, 231377833, 791850905, 782682481, 448816335, 802265962, 998683048, 545550699, 557003318, 188095482, 807646301, 483181303, 452287097, 636813320, 516148023, 943124320, 794212231, 457895396, 474772306, 888290982, 844444955, 719370122, 413128556, 50735188, 913064159, 215941312, 453108756, 152512470, 556711524, 33715227, 95267037, 132933772, 735311139, 386687442, 269367303, 556097044, 995027241, 212586094, 738422949, 895550116, 455817996, 694169816, 785356476, 796110222, 10914594, 164848909, 991060757, 821448734, 440725623, 539358063, 387189777, 38595336, 961449002, 284067710, 410173703, 263512607, 903033362, 675439715, 328834965, 18987809, 840881798, 593119320, 198870089, 533951256, 57165532, 930915997, 971675473, 283252643, 568110502, 58316914, 250324563, 911526729, 82475816, 685430915, 363576324, 519365162, 607120252, 284253973, 387978080, 899179716, 883470218, 783675553, 145228611, 108172955, 635386969, 912975468, 667626232, 669123142, 714969934, 946378686, 731729919, 526250872, 686623625, 580997330, 74868430, 33666027, 369854065, 556952869, 198476119, 778031987, 360937393, 978100374, 543209899, 48323971, 117439455, 733802031, 344442605, 397437252, 570490163, 501374194, 933938691, 845628444, 218301669, 689979526, 628731574, 930229859, 463578071, 808492633, 48491694, 527149478, 267603616, 161658416, 170774361, 356523553, 44066345, 155306039, 506350642, 454778803, 878383043, 432039834, 554135125, 112003175, 797404848, 712335601, 619641011, 23538738, 40681371, 98442673, 666804172, 471701030, 100409545, 268069076, 733589914, 71553134, 5500858, 829557938, 652990454, 626174768, 113480145, 955032889, 4152973, 638882040, 819305011, 609372703, 580529587, 994200899, 724397447, 237755581, 759271137, 601598698, 146295961, 769047515, 966842287, 33873613, 854980874, 227651080, 207911171, 893525377, 949573386, 283202493, 475962708, 262377378, 764703952, 534492266, 627660965, 221101722, 642880844, 96915882, 867334241, 926925890, 267226296, 327826098, 103327139, 105455741, 648984742, 884795282, 530461496, 87148609, 316009961, 537993439, 402420347, 724717192, 239848551, 612628258, 163015649, 189636214, 292380330, 492922358, 825564798, 374994030, 564007798, 37346792, 354111004, 736029545, 811281510, 99260343, 155340315, 917728913, 348509300, 934459883, 480049546, 19494212, 192874124, 403803285, 532485059, 287604863, 547686731, 901493684, 771980246, 41176428, 359191732, 304226738, 499465003, 825186606, 946509285, 144473020, 861411921, 581349662, 96952447, 427143385, 792015386, 891300129, 327225182, 937123324, 858375343, 819683702, 470309970, 745634838, 455312285, 282979746, 555665506, 168814037, 758392937, 393467802, 473701642, 761181509, 760665229, 218023503, 937280379, 213484491, 931783100, 140593561, 858172306, 596241557, 355814144, 579880685, 624029891, 426562822, 175462567, 974999798, 956501261, 787758204, 901720321, 17239771, 236122676, 278616768, 61844844, 243084417, 331188002, 2092237, 588285904, 965465082, 902987521, 631661031, 964893560, 991347672, 281283452, 553368908, 124422019, 371651389, 924916881, 163885401, 666049950, 541072957, 989718495, 296739014, 672241690, 175093994, 548785143, 588488740, 950589793, 458636609, 224987410, 730199391, 869525953, 177913015, 729681764, 340901947, 29159514, 402546580, 938755268, 656210290, 480527729, 482560085, 163127041, 613721664, 324659773, 395287001, 971073121, 358343324, 951578983, 54718114, 29160039, 922182490, 148041507, 899835307, 750962624, 594949110, 606442520, 884898481, 845963986, 802528666, 392893168, 439892631, 803523874, 599707661, 928040176, 797365616, 751910119, 171241099, 152595673, 210946998, 875248165, 490403833, 718807231, 554425182, 916276005, 888873490, 580997131, 417165903, 7445790, 976122704, 10509363, 535303252, 782041535, 83842884, 108617573, 301835502, 801292378, 525698985, 927013185, 814241737, 995798947, 585909283, 739525405, 825874119, 908082473, 393892845, 874192208, 658368595, 259333890, 830547140, 274865952, 17499063, 559679248, 222802955, 309576884, 203375375, 626967781, 386780645, 911613100, 354859861, 483873748, 256197604, 968530961, 811110244, 182973128, 220417386, 705903904, 218937566, 673707165, 504897682, 193554641, 583412229, 171175658, 240661069, 601716272, 188962580, 908815658, 387502557, 660871198, 415055916, 329703109, 133389469, 776899032, 296848199, 344229629, 908721973, 429841900, 890735990, 666705606, 488718024, 42915268, 160633060, 319706029, 959177943, 482062220, 414893351, 175539282, 766104630, 526491311, 407843729, 935556238, 140132164, 738924551, 139673753, 86235563, 609200429, 843085719, 162402795, 150505985, 708528677, 552768592, 630989819, 619749038, 422962482, 288721294, 317033981, 799207892, 707946254, 914884383, 525510095, 857747728, 248594936, 503236466, 406521585, 687419774, 559857113, 203847137, 109709513, 316039542, 622121999, 774554268, 314185414, 768584290, 432452601, 326792508, 328330008, 667963732, 964130487, 279313420, 165626169, 719916460, 709309675, 550286858, 267541129, 376771074, 795452463, 878430296, 869810118, 913789830, 231495052, 839317936, 698470, 23746053, 482441044, 505481670, 441910657, 631098081, 449455205, 999107723, 470823675, 336186987, 102555643, 405732823, 697110932, 474443601, 631640286, 645147052, 580643407, 377075836, 971500952, 834679485, 968822883, 24552309, 959638058, 84033983, 496083572, 333845404, 628765428, 297382873, 32554219, 202536417, 224373223, 233996722, 540648769, 999396935, 796646052, 602169139, 7498191, 954758164, 243572333, 252477538, 43775106, 202483267, 607946547, 171070487, 142808942, 2053548, 500875833, 2709482, 705024661, 71824286, 449668646, 923668675, 83728195, 988298906, 347765565, 112727872, 266769133, 616481699, 374658627, 378941528, 409372325, 775969893, 492598970, 885901811, 419430374, 874595231, 758493835, 735623002, 46482869, 369539294, 527348979, 376006573, 135112238, 926909854, 129248414, 737084572, 523086519, 205032682, 926237919, 871069573, 384858190, 874793257, 644005177, 952317532, 220333834, 886413194, 615815148, 407389120, 584966487, 933616927, 830479887, 264857821, 75617904, 830678282, 376506620, 491759649, 666381792, 810937516, 338953802, 38419825, 550426287, 636624131, 469293808, 125026328, 691941946, 755380547, 642125327, 965157346, 960690789, 582546297, 163096737, 318080382, 582135508, 918364419, 986527541, 502588486, 731170751, 463727257, 619778753, 846263187, 628934749, 366149920, 949827787, 202169990, 378435925, 748466468, 870893096, 157095651, 229809773, 370360527, 902825985, 741023986, 261745894, 707895381, 818489356, 99811144, 372393406, 759549187, 97482850, 755220179, 334352032, 947247614, 310409315, 971788555, 927011030, 106701374, 257156118, 230813578, 870172444, 604539298, 342821534, 122889807, 204692022, 828051865, 489281797, 173536174, 460393301, 701323945, 865854048, 133341155, 98108964, 968381088, 125758257, 76203629, 469867582, 36602324, 897996165, 282697774, 956220686, 767728514, 423008061, 94295031, 766216943, 786643171, 35103854, 87923917, 937225347, 114803364, 684295587, 962269945, 343269253, 572032647, 788738845, 206401671, 263103491, 211869058, 897090904, 553658810, 166707389, 272039738, 796360470, 168078445, 394113813, 789279890, 590055037, 199658506, 345043986, 987654393, 867527341, 817587778, 321467980, 278031359, 864640810, 145581187, 400585085, 605324933, 683544593, 234045557, 564576795, 297202680, 619183447, 88255973, 509957504, 419098061, 360779464, 635195809, 467896629, 50575048, 779423777, 576984973, 992284658, 820484173, 74932985, 535767925, 728312733, 89789441, 658534062, 533184596, 697428507, 846850137, 625483053, 520472348, 326179669, 117426492, 54735163, 922587500, 739974524, 797436319, 303626174, 603309394, 215302474, 803925127, 767629970, 917500790, 881063666, 189082602, 474238890, 994560999, 216001022, 858969648, 421572930, 884173840, 590722739, 619408315, 367981089, 38747292, 470327002, 662894110, 878444345, 883713820, 439255846, 622343489, 583864247, 229777783, 985127497, 886816862, 132908432, 864028926, 143678739, 651041239, 29232300, 209136882, 987534468, 885501826, 22424126, 165728863, 216580443, 604104504, 186973571, 21631654, 814504850, 150848084, 490141215, 113030764, 617846880, 597249475, 476604608, 879034362, 554968934, 857617887, 324232259, 781936525, 245167484, 970178532, 493480885, 955331666, 530612799, 173549673, 561205420, 138897227, 544822690, 299756701, 576430035, 287280952, 357308433, 346920256, 439843193, 468156868, 654072911, 519527386, 92038746, 957334088, 909182751, 315106714, 309059464, 31405854, 250501375, 928398453, 409798234, 114707721, 57708076, 952811657, 199608252, 630003673, 651570680, 751420642, 784427699, 632385550, 528596570, 747599006, 495402980, 646967070, 569137691, 490362645, 272966650, 305660330, 153490348, 159445864, 628748068, 171424157, 839770700, 514324572, 962044260, 894248226, 522505218, 456219159, 155933550, 759969097, 353535976, 278938686, 792296034, 541224727, 461260400, 881600951, 365092364, 974517954, 3110323, 624103665, 135116249, 520631195, 623495188, 534776117, 388035595, 317624437, 614591753, 265257903, 270960490, 334813640, 984650700, 763101902, 318850134, 73551372, 671850789, 710601637, 579753723, 72940882, 941068207, 491326666, 660510790, 831316294, 160890061, 179963442, 339263454, 953839883, 151310595, 826446656, 438229737, 206452286, 750893838, 114144675, 42811641, 503680213, 950056039, 954406587, 246016657, 704505551, 373799159, 544871364, 134627537, 966632642, 438796168, 133324375, 855022714, 617409779, 621054394, 926007814, 171492407, 660468263, 890857439, 300959734, 214644265, 101319581, 86862954, 135886760, 28219007, 477469231, 589951569, 479109947, 702914477, 98287231, 999422817, 195573110, 185286355, 713240724, 419337632, 263574392, 668677175, 455503147, 393465575, 185972922, 800867515, 904074535, 466538928, 841305898, 50322503, 504536183, 216885645, 868660362, 10429507, 745822650, 749872809, 249946446, 376112238, 688198007, 146704367, 566039036, 753063477, 303908852, 286974451, 421702114, 722046149, 475952976, 448082356, 723751704, 589191828, 671846236, 551246225, 160252325, 531619845, 701089974, 851437755, 680995803, 164552063, 568751979, 476270935, 975810676, 289213891, 64131913, 645722713, 988184333, 136624817, 590622568, 637211039, 958768498, 150301309, 112606168, 947416157, 452996483, 107067964, 677001533, 689884676, 556743967, 474794344, 103942677, 369285578, 839765152, 993129556, 796299677, 435286005, 998087817, 219897761, 871138631, 361344135, 49422049, 656527709, 96821541, 914116140, 841186231, 987515580, 368496293, 143723613, 306409402, 285515593, 376127741, 681114394, 105267208, 439644957, 704171472, 237265632, 725816353, 916294193, 501102905, 326701748, 2936241, 435803296, 60462777, 713520244, 111675402, 808378895, 225807843, 30439265, 664547108, 966476899, 649065455, 804409482, 374418457, 665223915, 46333101, 549661884, 811493226, 536190887, 199062230, 686018537, 72606131, 662573020, 994557954, 98830967, 454609717, 781480845, 372100169, 926245465, 608108683, 662407570, 839331346, 692958840, 340057799, 195397322, 778127843, 745886569, 885234802, 582378674, 885042300, 362777557, 234633789, 584957883, 52176850, 289612622, 159391538, 781164861, 341199536, 958995106, 414620595, 366695135, 732709927, 556813676, 995691367, 958872691, 732948228, 960171174, 412466681, 316246584, 587286386, 969266157, 666849753, 341165848, 277043097, 120964611, 446409931, 269675486, 606294232, 633639254, 225002422, 256175575, 842261313, 351590208, 416055880, 642810074, 950872056, 785627503, 88796708, 944193611, 110403297, 784877272, 733802353, 364596885, 81022224, 839643354, 638856785, 128150242, 266656559, 747013991, 628147107, 122991504, 399961034, 335890909, 999221323, 482290331, 161454101, 795233221, 429312345, 872535929, 137238112, 165915226, 965031677, 65002474, 172281300, 862353342, 196939640, 693045689, 709784994, 532567787, 637157022, 291380626, 340029785, 476645962, 586843787, 233845601, 92029329, 680169024, 410770211, 933457851, 712537739, 936750144, 633444859, 906837386, 950736592, 476878694, 564002244, 842391769, 985089794, 795546795, 420911746, 916707990, 772802407, 136036705, 88584441, 835642200, 818651614, 504184135, 978851229, 308656842, 34004559, 158281706, 547305068, 172229686, 825667054, 96135985, 380519164, 725593719, 983964746, 445427392, 646264669, 450521030, 379245216, 14851517, 682717480, 851534536, 425637280, 141550466, 14987936, 719493651, 990801898, 855510732, 328780067, 477168517, 848171223, 592953006, 371229213, 939195716, 355463882, 169522686, 960073378, 223218171, 521509343, 706475190, 991562558, 964620779, 668193377, 522931606, 632238037, 845429797, 840828991, 948469481, 354805026, 752851865, 273667399, 359630951, 189511298, 998593264, 133066859, 418466826, 106236620, 478045676, 45141421, 647526387, 514619297, 297619425, 457561670, 392001361, 798704856, 651387149, 64500041, 802971005, 325081848, 741911896, 924996791, 623294071, 334457207, 420550909, 308598979, 863775634, 808847767, 268720500, 757768902, 759852788, 438011961, 691041196, 813701784, 439402759, 360272101, 67333811, 260517028, 329992476, 302800026, 353121554, 857727044, 481508025, 805444386, 315871890, 724516401, 8578388, 937751618, 812815457, 998999438, 184266324, 54761841, 80947646, 732254983, 725364707, 182166195, 894392780, 192619536, 638904171, 691686783, 543223976, 585283588, 704394471, 656706508, 603512054, 942909588, 34443792, 422097275, 419123172, 906966980, 885482698, 816301339, 517341988, 448693700, 308840710, 476783068, 383789735, 85235884, 4515738, 223746406, 651031720, 859912790, 371778422, 770976137, 362089737, 58355939, 995651649, 980937254, 242023891, 637580596, 476681173, 560333862, 524869150, 104025664, 643429386, 278336734, 725619183, 593762268, 843017075, 963993744, 697172038, 891334638, 45746553, 807906900, 246222152, 845260592, 240469121, 907411801, 856475205, 280434852, 5271381, 653561125, 88716615, 747488748, 125118166, 724930234, 46717876, 36068745, 355613542, 891469249, 510049395, 547825659, 306113023, 548047068, 283560830, 269581563, 76854926, 237685116, 790329550, 112814133, 178534451, 988327860, 743194780, 794336396, 3513999, 709150689, 336021942, 591368681, 52594533, 901765774, 663471024, 638162218, 905807174, 245024703, 422703184, 18494669, 937746404, 76619048, 351231312, 784539631, 273762396, 268251190, 348622369, 749704094, 836165940, 706436852, 850861041, 942370861, 363049176, 41528070, 98558474, 807774583, 222777196, 418283548, 123550828, 252940432, 128806286, 385879007, 615359309, 435603808, 186624474, 173985528, 446951696, 418504775, 763862806, 385214114, 724184265, 824701805, 89488719, 877143375, 350801070, 317131824, 205319719, 981458766, 153885809, 980219068, 236615531, 210470039, 359091713, 843647656, 86321499, 886907447, 419887207, 590236483, 413215542, 142252183, 476311614, 596141307, 601089107, 339478588, 877631419, 554584110, 993858538, 604932416, 556078403, 420417864, 764421810, 104220563, 375264294, 926994584, 928662027, 947632052, 947043117, 811178095, 16674373, 853679663, 776340530, 882091006, 91345090, 152760901, 589931375, 695434362, 560764369, 873821831, 353393913, 360692923, 642270288, 465487949, 496376752, 939621127, 47715810, 781658296, 273875677, 297215163, 86812124, 442107569, 27152666, 737143035, 158202797, 860100557, 595694947, 456200528, 478163627, 383662626, 863695729, 459862025, 622417400, 798896993, 787835233, 408273885, 671087924, 556081991, 482587073, 984308085, 918079498, 165134422, 450065850, 343357386, 894227998, 561786076, 963286671, 120910730, 579856835, 678427240, 637879610, 762689305, 21547909, 804500326, 767562707, 644085815, 368081178, 874808470, 574976339, 939785892, 990904386, 668243179, 752510115, 118874775, 232130638, 232352178, 456049444, 712630574, 223325388, 28658632, 196974463, 854655990, 927329474, 745839476, 100598813, 299265475, 132206604, 431027339, 34314695, 143152011, 130801842, 927866632, 883479387, 130422460, 741417435, 668675950, 643510628, 39039799, 928396588, 613665781, 540359693, 626792794, 897705459, 428239534, 961316993, 13494728, 169766984, 792796463, 321851553, 342573593, 985287159, 406093860, 269186512, 836822031, 696660670, 238419259, 824355278, 274766334, 142860399, 100425003, 154761119, 939198622, 195962396, 564727627, 224222086, 272768497, 909876413, 682658932, 463807568, 486812743, 95159979, 836848134, 686406651, 498859789, 56925053, 323358437, 269631171, 709391014, 212626701, 608400513, 366566652, 243415080, 259648486, 503212185, 81782301, 780999735, 706769734, 466377320, 959633033, 79183608, 665165656, 183524948, 238143419, 640496674, 56690036, 802740832, 129601835, 942817717, 387835254, 142285158, 487924160, 711205540, 986014256, 187247469, 663831993, 255982437, 181408007, 316781029, 716286595, 178017817, 668811909, 927753099, 323125955, 638333186, 688671319, 437457719, 581876277, 926666828, 931430762, 629070223, 776632084, 663971944, 976152321, 354518104, 542553222, 787433223, 190771892, 923217225, 192335102, 516284047, 19138745, 446368596, 457634066, 947372634, 326563447, 43099997, 522567386, 954458051, 482331978, 481165248, 428155991, 6525820, 20065784, 238374092, 895577258, 486028325, 485446441, 412175530, 751656634, 711002528, 53435485, 725610804, 685806721, 433142107, 262825365, 350833650, 182753290, 433547014, 840394900, 637976663, 750070384, 402374285, 898520666, 278500601, 439923960, 693203418, 814646831, 465200077, 969541004, 957864080, 768476727, 523545118, 124152312, 912791613, 991940235, 494850279, 932788200, 800322462, 552036858, 222066156, 958872632, 825062742, 757339896, 588042045, 749635822, 777411358, 781343250, 338902110, 508169542, 114941149, 100227759, 713167588, 599943134, 708950020, 894923149, 897285085, 694871375, 387250071, 901495018, 590693724, 33095012, 805883691, 799679510, 854211157, 952491271, 186215161, 182571151, 962398292, 770975740, 210024570, 160310885, 303941777, 785074123, 961124978, 531597496, 307414542, 224425220, 335775682, 286295035, 177573569, 272725755, 826040468, 368273128, 597849852, 203252850, 154808351, 21280862, 717984772, 429299899, 355747959, 457289791, 472447718, 415365564, 809948537, 323006687, 790950356, 972317228, 785005786, 119884384, 239602250, 776876140, 664364033, 732296664, 722776614, 56485128, 582462266, 441459193, 523078655, 433022982, 355304312, 525760001, 18203884, 803128608, 142290819, 690972183, 172436778, 288112141, 971368184, 701986736, 600244293, 799909328, 860275198, 311977691, 740894340, 525025745, 184721147, 919122301, 888586443, 431841085, 652099149, 71491801, 297432660, 934567965, 421100169, 547322134, 722145566, 836884713, 673610415, 270510391, 451932485, 153448475, 43220101, 802025181, 336929085, 289514025, 519305201, 220927078, 695961237, 131427053, 498372920, 115268322, 981448992, 457383891, 393438643, 258279780, 890267885, 438523434, 12981242, 910492820, 335447437, 347531387, 587243254, 283424133, 86848939, 91156098, 618969204, 598732539, 255968265, 293335615, 970144436, 766232779, 680232727, 290640761, 895473512, 810391263, 216745055, 427918039, 31810656, 458047529, 760856789, 291189254, 305431117, 764454205, 60737848, 605625296, 783559738, 210429303, 685024750, 510506564, 94879690, 766618765, 91363986, 563660992, 356057581, 290850335, 419648920, 741171338, 935221371, 997546870, 764117801, 341515825, 701781163, 897262056, 162530290, 545046758, 12618294, 917146996, 866829513, 922598881, 210946197, 92770517, 960847047, 675793373, 875915937, 874613699, 412570622, 857658256, 84492783, 966870421, 753925317, 915843326, 407916170, 592301732, 210452152, 650228194, 865421608, 92916033, 113463693, 904665822, 606820825, 657503183, 562838674, 379894765, 522647624, 547335459, 614047504, 875748046, 630733058, 319014374, 516914724, 265450135, 437123393, 526487816, 465604018, 584762397, 413732727, 753990897, 306894815, 405395619, 526701939, 161706461, 767873671, 992731502, 112727288, 717911450, 158144996, 879608882, 852067830, 329996747, 673633238, 960438742, 211411152, 836422700, 22143931, 964474509, 172840454, 301277494, 179784374, 903330253, 711713401, 35579796, 312155882, 344271866, 916790396, 140118402, 382049115, 753040002, 877939374, 300146864, 757444050, 478026206, 166447540, 726137469, 265269223, 831013577, 303557325, 666529687, 595443837, 592353473, 764829973, 805766712, 602878591, 389163695, 927330289, 651861063, 464080793, 521160288, 83288727, 848580667, 632578234, 882878587, 264540827, 599454082, 324802528, 439843619, 284894194, 266542668, 124494599, 476200396, 214615641, 595641946, 858445683, 423604974, 57032351, 992783493, 500075193, 262738578, 49520206, 742378126, 113632802, 588876657, 388763376, 531994382, 785228797, 722925088, 539878102, 226815982, 286700072, 202824917, 675027914, 493145620, 220456683, 491565833, 848168927, 585238064, 988606921, 624239826, 12948948, 548437418, 742478903, 595306232, 708025596, 445960575, 654121840, 40926913, 515170447, 406414202, 587819921, 209423074, 529285431, 163824638, 873652543, 172173955, 640090325, 40823272, 987024686, 20313243, 837976577, 625491972, 525605476, 684292787, 770500352, 930920257, 919595742, 861384787, 924288565, 195136976, 221146969, 270428346, 780201305, 420663215, 659641492, 201284657, 834134437, 275515071, 103538674, 825445996, 966440541, 717491625, 500168597, 600317637, 427934215, 702607664, 494269650, 987200755, 368059561, 432880615, 311179866, 968907762, 861620384, 110920096, 877911849, 423991243, 760632369, 857591617, 434604762, 406733415, 196971390, 229722028, 396635755, 788542921, 850645392, 896275526, 147248609, 54740944, 568092166, 954941221, 601787543, 784673285, 138011969, 653788745, 338072495, 159424096, 904541291, 487266204, 648678508, 525281021, 91846135, 738688845, 523409590, 650618777, 238264315, 874087755, 291693852, 951999059, 285228146, 217996522, 42394381, 614242551, 678029973, 316059007, 238249578, 164133024, 252649378, 489890688, 527513817, 644642842, 402086316, 544860464, 563758055, 380692197, 626665669, 516782519, 382183865, 141319642, 678101171, 327210681, 35234526, 403453478, 603617260, 882435669, 872501876, 690932609, 54910393, 733824721, 389755905, 22139624, 177172162, 595918756, 402529294, 9836435, 775547897, 909711539, 42027930, 79311763, 323420161, 411622515, 677023176, 792418028, 12833540, 575143514, 638735638, 562219855, 782303902, 715147001, 134854947, 335928688, 235607658, 104575896, 273314572, 691678962, 994994794, 389620076, 356161683, 907578455, 59531806, 692227325, 11683711, 76603059, 619568274, 453868582, 481558890, 17290062, 576882023, 645701688, 900950900, 663678262, 893367641, 749378130, 161231184, 116092764, 460766285, 279899153, 59314535, 698909245, 110861569, 623840368, 447604632, 820002434, 512122109, 126245457, 669768842, 682996099, 10109734, 556139898, 545540860, 400271142, 920631845, 889817550, 42157434, 638738401, 915371506, 422664741, 671409682, 276748564, 128719164, 98525333, 708817451, 338519937, 118554386, 246928489, 906882966, 728381865, 703131425, 240368313, 189249426, 358525062, 640287345, 348067092, 433887909, 500113942, 276420001, 401049879, 792058115, 978817137, 301970558, 917520939, 207314992, 814258979, 892413303, 584092865, 336331548, 147583095, 398534745, 476068771, 869251610, 923696135, 23506947, 886189363, 894193066, 661783963, 824986097, 110845624, 527481924, 164058957, 158041021, 766727307, 898431622, 941825913, 635847518, 383083145, 427660061, 964525643, 789717393, 348508418, 612251504, 33475099, 577184254, 272933781, 617130639, 560861922, 29462250, 294984343, 732689078, 763057245, 337751001, 639848342, 544631860, 595312263, 132899009, 160254541, 822975946, 313280325, 880207341, 420100418, 831525554, 439677255, 794612710, 624471393, 775652245, 239383097, 257094099, 596558589, 966082565, 583752277, 41314648, 546676703, 515757301, 582866110, 429770170, 530224859, 973154045, 82608343, 628391929, 626239803, 520745802, 118280586, 292318410, 54144124, 852694993, 334138620, 628870248, 678294288, 378435805, 910609349, 154392323, 372611937, 456933534, 317949365, 711036779, 476659127, 631216782, 212561187, 511446919, 569355352, 404580095, 474843684, 178838641, 837873609, 625101145, 286915126, 423238788, 887004211, 727044141, 970580011, 418988667, 217237492, 209216524, 216296448, 660195655, 766380650, 762980489, 9590964, 694265369, 200468756, 50859966, 320188594, 274487389, 235779040, 602448333, 431449618, 257712752, 220399412, 576513217, 936392882, 279838805, 928726848, 870267193, 108837709, 55915891, 225549844, 147295006, 568874249, 950831804, 695845781, 832250400, 610478586, 439113427, 769010405, 899342476, 624078841, 841124523, 487917175, 448844575, 586197659, 393920925, 556039716, 227398164, 472502511, 158694199, 695831948, 196278967, 25031553, 506478143, 61714338, 836803930, 617674396, 782787642, 165155110, 801210832, 811583487, 438220624, 46894689, 354469465, 487930224, 394599489, 786087424, 267700403, 275498255, 80939704, 556393120, 757268721, 762251259, 317283655, 90583492, 547303472, 285834195, 853756268, 521521103, 941863488, 191399051, 334959527, 498150037, 883223879, 353253284, 497638416, 492417940, 692279369, 205622392, 662018065, 513986950, 704981531, 463647032, 261795086, 744062220, 56902464, 690512865, 587465871, 350409533, 147228109, 145300830, 221932506, 466948612, 197456394, 177205822, 558946417, 223387651, 515150062, 326251792, 536697251, 725019428, 867348778, 472605888, 750709155, 171240493, 966595897, 711451040, 649187521, 793934742, 728444500, 727305637, 916638819, 669380488, 226715819, 480637444, 779134208, 179838101, 794607997, 745154908, 586037692, 584280661, 925684175, 244583183, 76306145, 12800886, 121697116, 103482385, 773265126, 341565766, 935040694, 825180703, 630217260, 332389228, 786542902, 934657521, 402705004, 958335437, 131762115, 228858166, 119417913, 21505120, 204163296, 821904831, 736478088, 724294435, 991456820, 814222903, 838821485, 105289090, 499250607, 189827646, 570483810, 160885006, 954686114, 371137224, 461510269, 262492628, 175463678, 53718360, 87617477, 958707365, 759120586, 987634775, 917580320, 390171334, 832193054, 549751798, 663271980, 529484487, 698325219, 654975739, 620730360, 713997034, 893899468, 702204030, 489713307, 938065193, 933370188, 346926665, 92320965, 461251326, 676261866, 242642202, 649877878, 854874922, 562688914, 548545271, 695075284, 544188841, 334962761, 389383389, 6746174, 511319275, 560113385, 236483630, 905865376, 501502248, 756177783, 341381982, 934863222, 874901019, 15398556, 781502564, 964253154, 712030043, 23120898, 30390442, 472394119, 126233846, 543590510, 143791736, 905056662, 450247151, 527745803, 537576700, 218373738, 824584101, 702413713, 927718226, 359061447, 15639807, 402666743, 854061571, 712229526, 116410395, 444525274, 747432192, 762364125, 554257378, 622265840, 40858326, 161226381, 879135723, 191267954, 392805819, 377408655, 19557019, 156732791, 394544931, 751847594, 630993852, 154795075, 645481200, 14431254, 659942315, 835255201, 555099237, 153923009, 556808022, 771990974, 343310607, 708463272, 586310213, 821479979, 489097352, 66497231, 117602075, 25812901, 894921341, 905591787, 456822478, 599773412, 267067356, 51431495, 985258765, 492964638, 716413207, 593796742, 65899793, 792658136, 353541813, 533178948, 82460181, 29599830, 181833822, 121202462, 917361349, 818858756, 804052142, 345991031, 295283673, 775405668, 296197252, 488912597, 546934158, 476992867, 678318114, 293897060, 840849137, 397134237, 796569268, 721180277, 86835464, 25974164, 109460209, 749385285, 780346415, 98510525, 146347332, 67674643, 869668622, 773072252, 978753498, 499358949, 893387027, 518168356, 828050545, 969388536, 232810220, 638403946, 478628590, 932788540, 240982542, 234032616, 252506939, 628204750, 807431173, 338647518, 840112449, 449642365, 175786494, 268066564, 597536914, 814100577, 980675004, 930765089, 697584331, 500406900, 940945910, 322255412, 347736984, 273843586, 959325171, 846726712, 773584279, 361101925, 730823962, 251699215, 813677355, 614439104, 864034887, 670749289, 71323345, 819906274, 519360977, 87493333, 248428987, 549080667, 897931259, 582260458, 146358284, 680518621, 921163666, 362739214, 891440989, 910649288, 995978543, 72703577, 81968127, 172279210, 168589603, 247276223, 761593676, 343454230, 533141200, 757644131, 293100421, 986470660, 833482896, 22081908, 963237745, 223163414, 372695686, 179229993, 363745201, 363611828, 232026647, 907871846, 942812696, 608003988, 860893527, 244561244, 902721918, 876739794, 716136199, 573291372, 31135294, 405617185, 72833803, 888384920, 885416303, 829541572, 515625223, 388762276, 735106833, 44232942, 916106309, 638203101, 528410301, 478737732, 351760354, 406336879, 736038814, 239132221, 653244990, 8498959, 175015286, 246899978, 491675616, 595674037, 541969777, 54831023, 717133202, 381218927, 874350038, 507214975, 76481674, 31865213, 460144233, 428891906, 713657556, 527533282, 378301208, 541945683, 382491605, 956973765, 957891268, 770657412, 140496486, 793233875, 554409678, 719608870, 828456397, 12827802, 611642611, 540663386, 197157519, 972345106, 353922236, 673581376, 812949484, 643404259, 1743374, 223560959, 176984089, 21401820, 840053283, 686964816, 418378554, 692892448, 771823035, 139258369, 691392815, 985963734, 517354461, 502578470, 502091827, 348901435, 511912378, 903116767, 437981286, 248594491, 582706126, 249413614, 971728392, 3366776, 416409124, 301342929, 407768468, 765998266, 344092997, 485356959, 794331792, 603721069, 271523104, 560177367, 911271713, 880433469, 222434717, 109693987, 425373085, 822362444, 896541572, 788724180, 130100625, 266919386, 87235862, 641763761, 838220333, 493659998, 9568004, 731436694, 129280200, 343435653, 193706540, 167437463, 379777998, 616940528, 975723098, 267223966, 152222109, 643581101, 970266940, 114078896, 437994219, 623878404, 828700386, 804551724, 885827392, 141803408, 453385818, 396053682, 244384148, 72769802, 529311312, 189419481, 581156034, 815690642, 362577451, 953989453, 47196230, 845398137, 970926720, 540204990, 66322633, 150469311, 272161784, 56446710, 780729633, 192819340, 308138948, 934054563, 934301935, 141271281, 106471710, 699037298, 638022136, 674679815, 696100073, 740626951, 643297510, 287886651, 921959256, 709687823, 385783353, 798895917, 976501102, 887504190, 839790104, 620882557, 823476026, 753185948, 710033974, 448569760, 153752219, 537567633, 44421211, 480691550, 832967894, 906630653, 461578002, 327963522, 589847601, 413007367, 746700808, 530871777, 219938899, 381626295, 572547494, 707323685, 893159020, 420728034, 232881489, 995018436, 112055082, 507898071, 872286128, 480890889, 313210873, 363210667, 864992161, 944218965, 606728655, 744972254, 271338973, 155813602, 754886787, 660058546, 330728750, 795513665, 227257274, 814913571, 138845128, 857353689, 336946202, 902307423, 469874974, 632734116, 223943034, 475312409, 911700360, 831466785, 773490572, 880819013, 758061077, 401677749, 676411662, 272347078, 639920685, 421908622, 437185223, 743297195, 840799884, 174139591, 386422018, 77369114, 878912436, 249939676, 276805039, 769846882, 246793963, 944013412, 289455486, 909954836, 170138258, 991911422, 641549625, 458671901, 513618507, 699105428, 894740711, 674902671, 509608121, 152591735, 661447619, 740780857, 900227221, 536441031, 339650540, 107180612, 221636291, 968071356, 868902892, 908001876, 375708088, 306956938, 114895689, 6863626, 672020828, 81529132, 406827913, 112751286, 929586569, 963320126, 299162137, 768568623, 754949955, 352872147, 553312705, 924931084, 629499984, 944781442, 107445001, 65055385, 120974366, 408543206, 791075658, 250768083, 641668409, 964529133, 553010851, 754183581, 515416056, 591117047, 455871194, 883576388, 143997190, 437732129, 181524739, 184649347, 61579417, 84834794, 907801237, 94232495, 572005843, 186204386, 88983207, 748382714, 900146802, 43545941, 764706302, 799694053, 780553632, 906672561, 621750163, 613779556, 579937700, 789354886, 130131466, 129622213, 227739801, 213223857, 142904812, 100741001, 567700723, 964772223, 274465610, 494844707, 186330658, 658372086, 997826925, 653607707, 936542400, 516146753, 74835158, 694085251, 68575528, 330639133, 309918830, 216986496, 196006432, 969723731, 939854115, 514253571, 606834962, 433941103, 333068002, 913674356, 662163256, 191158791, 609167899, 155336006, 767716207, 898508768, 720234231, 225844687, 558128424, 181266920, 337314418, 702207993, 156928273, 237340250, 972476994, 15055379, 854689224, 30860224, 256665087, 518463050, 846623856, 942385502, 847113237, 859518573, 526532647, 64790178, 852135642, 919412803, 8432012, 207579780, 842933389, 993563481, 183591366, 698498279, 613928304, 741030068, 765802946, 484844116, 583159665, 302203541, 925372669, 801409794, 237331314, 790715609, 657312248, 100530050, 286406688, 407111814, 838842764, 867881261, 971460369, 997827920, 531327561, 772027072, 540861667, 791648208, 502915444, 244896731, 31508071, 673698224, 351140096, 593131205, 334130667, 468119746, 574885398, 680103964, 397396040, 528174899, 741701055, 759792957, 77059667, 3052120, 139576191, 237430457, 347651792, 121604519, 285801064, 809033039, 984165573, 596155912, 39623748, 355198407, 528632061, 481935000, 863307748, 957197925, 178061857, 782095025, 160723922, 831115048, 235788100, 810238776, 153143637, 920696818, 632306325, 104981421, 938295669, 613797160, 900301152, 583812264, 175431817, 963151245, 826326978, 158886882, 406233187, 573409929, 490010356, 57248210, 384578063, 543710015, 401103646, 713702325, 483366521, 185739856, 668942131, 174464521, 14339114, 196519591, 569544925, 306752912, 755359921, 605731911, 625207649, 261508060, 2206993, 387207519, 641085675, 941522598, 643820168, 298006882, 710151008, 117555315, 600577421, 310613849, 400610152, 194942432, 943031100, 701591775, 47895919, 586691573, 647644637, 59643000, 620737962, 695350425, 410668455, 959636695, 45355691, 154783133, 87153602, 106095082, 865516484, 222687340, 38340363, 685857119, 538880035, 345322945, 419777407, 966419204, 801221193, 303854085, 475097066, 718871847, 789674356, 834371820, 251267627, 997601525, 62951546, 560190094, 250574052, 282765557, 509747191, 448437053, 695503523, 923908721, 422636989, 845120228, 322851127, 399331078, 423750211, 262686996, 409889558, 378668839, 302986434, 841257336, 979134871, 289827052, 630889867, 631571316, 678736814, 62969532, 547197643, 943558953, 810843558, 227661028, 791946538, 176845082, 691544124, 480333563, 745193619, 281113132, 229318543, 267379834, 119732216, 873198997, 85848106, 411089193, 302488136, 302630590, 694542254, 493261495, 957087812, 902178042, 83112436, 582956330, 496135101, 457732766, 942545244, 852971705, 626901427, 983298100, 228156340, 162035416, 341763117, 665525090, 515430523, 176027058, 652832264, 400442691, 477406091, 293703301, 936857633, 492315112, 474035802, 690610502, 50835621, 98574948, 511883797, 26697880, 91395430, 749224099, 557146834, 945322172, 843860730, 277199359, 167564572, 923753636, 885579256, 438385607, 937317873, 686643362, 924022195, 934593963, 820133248, 694373992, 789953378, 690408563, 905447068, 780272329, 10173673, 859179005, 213404616, 223694778, 895943599, 330210818, 206283304, 697519275, 904425326, 384554286, 448519178, 148050741, 891331783, 652543417, 447927324, 447582780, 263531434, 513860928, 378970749, 520023684, 983546869, 191169590, 628711113, 60396559, 387527216, 786375817, 498115628, 215613630, 25378436, 437379088, 525160537, 17748253, 4868291, 898433439, 490018223, 482805388, 735306667, 214020648, 800373571, 177473144, 597821370, 237241242, 68471481, 171039217, 657412074, 86003585, 728197273, 422794717, 155396998, 35948238, 143504523, 534227529, 601533434, 867031088, 795544034, 578812463, 690132939, 5318603, 766423635, 273141787, 955510468, 374330521, 887260345, 803354599, 314226677, 438078172, 877198355, 520471192, 408483653, 803947738, 663104427, 95305371, 129009104, 632053721, 152864014, 437172113, 413888760, 672503109, 909772705, 384170434, 961481109, 196111945, 352142462, 784557310, 810776482, 633583308, 680773241, 549825896, 92323619, 246516788, 574581839, 599380617, 673815431, 437779404, 517519537, 259766690, 754215358, 600988108, 301811084, 9900755, 826925650, 103241702, 841744678, 802587327, 808831222, 629197665, 584770025, 336209612, 677569062, 209664249, 556064099, 250462551, 912734441, 786091278, 731045417, 823680793, 421191429, 208426494, 486997413, 171396589, 422108415, 577285350, 475916732, 660831946, 909205144, 852063832, 114033732, 44491605, 800853373, 485490369, 576211206, 217560701, 56834727, 803000001, 497250976, 747967467, 495144440, 494027197, 602632549, 822540091, 978379219, 303406792, 802564989, 517067285, 329096931, 237063918, 495810927, 520805338, 407671040, 11218871, 476545679, 356632937, 682400594, 690532897, 398715617, 338026183, 313506695, 10041755, 772866119, 72365233, 81258866, 733290160, 635302537, 935853064, 388323409, 486003863, 617909670, 322604523, 762423202, 115348206, 655231474, 440790062, 254372789, 564151133, 854624394, 61191298, 633036749, 603972836, 621217464, 50581705, 590843081, 483516561, 27349749, 70921471, 959696085, 981406810, 189168743, 802266800, 445703408, 961824608, 402437633, 488833372, 506185913, 604202077, 803656522, 351631959, 239281553, 502631477, 538800078, 249010882, 531487484, 751117838, 119661532, 65889493, 6838016, 229430879, 729826813, 949130630, 290488272, 981368055, 802506450, 480643876, 708308710, 365774711, 385570590, 687019191, 566175581, 79552358, 568989768, 865973089, 137862191, 970397404, 573810931, 480541608, 32917738, 848248599, 574460480, 718534097, 256172572, 418017234, 482109770, 572211388, 973006550, 183485152, 309897560, 587357947, 869200324, 99026389, 184306889, 878857917, 808129042, 932547027, 155962094, 419859996, 19813744, 367847470, 338042635, 328905822, 42905020, 271542736, 195621736, 681389078, 235994072, 879866347, 540659883, 79882726, 37312393, 682197273, 620187728, 886055599, 79153056, 367854394, 614616152, 155109182, 621722036, 630446348, 164781892, 277481945, 545821495, 319766206, 829054706, 259211903, 728810817, 153753417, 612359944, 623099534, 898845396, 99709505, 262301037, 535931381, 164744687, 394503834, 758521058, 517247758, 319986660, 108568313, 938354152, 863828232, 579323124, 636707325, 53628863, 989727022, 455933253, 145680961, 953770173, 355099808, 292326209, 449248118, 700882262, 237919065, 860465371, 998801300, 958362086, 857387652, 42299547, 789369132, 792805407, 271406721, 727787684, 359760412, 35682638, 845110249, 675205635, 309031664, 947284626, 529337985, 122296457, 65893481, 993949500, 619407914, 498785500, 221366873, 928980646, 634671226, 104396877, 452826489, 538515080, 252365539, 647329186, 985764736, 139999803, 408935567, 167546369, 978793056, 945867126, 355490296, 804338138, 274426279, 682190918, 13958480, 594283389, 173040520, 135306893, 347882488, 249791476, 522593022, 739099180, 877580248, 108735775, 91715672, 452629704, 752334071, 993149114, 558443658, 20858635, 772492918, 224420169, 612757179, 342660385, 572139899, 801823661, 439158542, 86233624, 990820780, 458217409, 240902355, 650363161, 616070608, 658657748, 210786008, 836876966, 647383834, 584656681, 383902920, 471962201, 342232067, 552736001, 534834305, 796762714, 486128763, 371497267, 556044641, 894034272, 579763119, 196804550, 530109618, 702378444, 307267808, 761514017, 272978384, 257100335, 516180564, 527192505, 887040072, 802566137, 32930206, 61801911, 436519887, 619567224, 528282825, 908199592, 113886539, 670937112, 440233933, 909414886, 818835276, 517049081, 821697708, 134339566, 727838129, 818193097, 647744588, 234285976, 50718798, 39904682, 206899657, 362789149, 379038375, 647809368, 841225301, 422942962, 998966574, 996147898, 246443395, 510115834, 774125339, 973592861, 848636792, 510581948, 275832251, 111319849, 26949893, 823149790, 422231671, 762719133, 775314703, 515794571, 312858361, 182660844, 564247823, 282219189, 894336363, 171721448, 366163024, 542892523, 921575329, 390309859, 80271134, 742286238, 759000032, 381029898, 47630116, 51154549, 186618935, 614181532, 548919880, 589273399, 112652293, 422986118, 383010540, 564753790, 538481608, 480291052, 129627217, 767551523, 401674152, 404133067, 794647858, 369406971, 973575576, 463170230, 52404695, 225520193, 165453228, 584009535, 372029608, 943255283, 342612689, 570059066, 909253852, 398520599, 571335730, 910907771, 346904278, 765119283, 694510417, 172317596, 642365358, 559771591, 816280882, 321933939, 119442004, 248545888, 783983546, 800095498, 247448131, 327343438, 856999218, 49850189, 612413935, 742894933, 153662981, 343947062, 172393758, 472344388, 959854857, 501126467, 219134998, 87207391, 448961194, 523505607, 807986230, 350841454, 768444241, 290129795, 437677826, 820840193, 407579496, 766344622, 970854744, 635962883, 349579708, 965501490, 16069757, 971861727, 762496947, 180280622, 485827787, 354661703, 326443171, 73149639, 128737516, 896595563, 551327912, 63405570, 754958465, 348319373, 240813678, 270106905, 454957847, 622177216, 265344194, 768661412, 128453939, 679336409, 260217670, 1017343, 127762143, 44043394, 236791649, 428792411, 314388292, 274799161, 648020361, 238152890, 210891597, 999703394, 53601478, 23978616, 626665938, 78440891, 338399186, 666831423, 600828461, 804773778, 938976687, 955832705, 946124608, 871556770, 640732674, 125869345, 827942374, 293948916, 294341021, 327705454, 453645410, 951408883, 668220457, 718894113, 790661029, 951177977, 53515649, 918911172, 402912702, 503606193, 147060228, 146582338, 58977749, 517790130, 562747723, 630368226, 807805043, 950311993, 710029381, 935447809, 579986141, 248471054, 378665662, 445782928, 721281340, 401144193, 517745541, 816467618, 643501377, 705410044, 975407496, 28061242, 777299705, 362412778, 547469996, 134011969, 521932581, 654592747, 102683858, 560782188, 865633414, 252511547, 390923226, 190918336, 277724241, 440923775, 637483700, 14885873, 112485139, 92086519, 414292285, 457321304, 630802246, 918665350, 386557656, 440826302, 659952320, 328569763, 944869468, 124265077, 36969748, 289926705, 44991254, 392676623, 675734801, 61965733, 835064238, 977959936, 595947826, 1585283, 91332728, 733228737, 710338624, 354970153, 155632762, 263516267, 766162322, 377927569, 757301593, 169482612, 347268741, 397842633, 192040572, 583326644, 418761079, 264076994, 808057344, 594380953, 890205263, 212042707, 870875210, 43111237, 694798689, 108567042, 16530930, 480839455, 993406307, 427636583, 86313705, 621006462, 618771317, 293689350, 858130379, 635142905, 354365111, 997270933, 995761937, 964830085, 696241840, 747226579, 863645317, 329053475, 937742900, 503544156, 718871694, 599462596, 33418605, 845899963, 216486121, 982774135, 617087556, 620898194, 761120627, 217947761, 799578620, 333322836, 878014061, 975255682, 86165013, 621389509, 376795490, 315466293, 165275509, 997268522, 450287008, 67072280, 332318810, 565030109, 659355713, 915814091, 614786003, 618663944, 229809114, 880866646, 170535192, 801747489, 564599725, 635151241, 752115870, 125190257, 19380139, 462964668, 994471565, 253027487, 206145269, 83404450, 639365281, 812920258, 937705547, 745434143, 604597986, 598851961, 177784796, 856341286, 703663085, 7424987, 3335361, 682804635, 392617921, 682643431, 80553960, 716560972, 811278014, 318804829, 640353700, 904125970, 860744208, 329294144, 551150194, 142564607, 746880737, 672883044, 104701568, 707779672, 356928918, 592412795, 990723703, 863603282, 602318998, 115907148, 719289237, 609322718, 846673675, 367327789, 114055120, 571221899, 659487975, 742805204, 414740039, 54451029, 285953911, 430587584, 479499637, 847700132, 611630003, 382849809, 271615740, 87222125, 21948661, 331832410, 642448142, 363429609, 564768435, 905305409, 906558700, 91910055, 429100460, 882931516, 231770877, 436951279, 694123288, 272267561, 975101685, 724762033, 449610498, 279110630, 625718986, 498741153, 875693307, 913655062, 176214799, 132727358, 135846151, 382970153, 162507823, 76045063, 484613626, 3321992, 739780669, 811575326, 663115944, 131922388, 762838636, 11701586, 604244772, 170011592, 81585340, 565253779, 675865848, 633371589, 487682440, 845397886, 680598517, 406790237, 64557737, 433825302, 554686855, 541287856, 728141263, 521180342, 644286346, 988787994, 829077744, 901375922, 721593501, 213385574, 655553253, 701964240, 979636847, 853083954, 428977404, 128213244, 6700481, 446713510, 286002893, 215775051, 653042753, 108981293, 67116962, 607857245, 223792235, 727131650, 831675694, 25472663, 141733592, 481778842, 24574146, 664421734, 591060457, 472944728, 143838930, 144638093, 79174107, 77609138, 291870822, 304104075, 558264724, 861583999, 516209766, 551825498, 353650620, 608795053, 604021766, 762242045, 433800240, 938634650, 14769563, 354207059, 973365835, 545090367, 21130371, 269867710, 889951780, 500318661, 861770190, 478593117, 888443070, 742992307, 16043985, 470978530, 823429450, 184920492, 510818621, 378798236, 484521846, 965012776, 442388949, 408076688, 273264568, 734881660, 507387381, 834296743, 688685568, 813957435, 860174253, 259686018, 440848694, 619688798, 884710145, 913275689, 86407061, 100464232, 133683179, 639833609, 867730386, 809270848, 904646140, 299145826, 36913328, 338355481, 279016912, 349609449, 552396480, 813314680, 82794439, 575914057, 359215510, 43638933, 264067723, 495886956, 760937839, 235002530, 142096770, 847471557, 923430018, 966894677, 973779095, 724963784, 27140505, 13272410, 960423881, 47918291, 156077644, 960015461, 617822248, 219550812, 304693318, 651411871, 104714797, 106111158, 454294723, 189591059, 870929783, 570258064, 206165664, 714046397, 27564631, 709812380, 145158550, 608050286, 791627600, 904378800, 748095147, 342036630, 480004469, 967280955, 370320812, 217602493, 675049082, 389836761, 644444908, 510554270, 413155252, 526731171, 820396165, 494482906, 385697322, 618879184, 775799165, 219711352, 225482174, 584767447, 674012341, 734106001, 531477872, 380924251, 661963445, 725276857, 100069205, 395424457, 474217970, 242251470, 480980736, 509126868, 899230178, 245955690, 869869462, 60238998, 311549305, 378260814, 970562253, 678295560, 907010255, 569432795, 685610679, 58210703, 412380513, 988109403, 585316351, 957658333, 783932579, 229537652, 612731536, 586799457, 812107712, 682695925, 715684979, 188936816, 235619521, 366505071, 954140971, 792670586, 742424193, 889760443, 690402795, 590205847, 478142484, 37232245, 590742520, 634413709, 474553578, 862415894, 790013349, 734597766, 320894862, 540865803, 963415368, 74899806, 586496940, 504722076, 953449231, 748383333, 556621044, 690169709, 435223016, 543198323, 18125486, 329198541, 144715834, 158515383, 336157392, 20550705, 61971906, 113538198, 865161913, 900018680, 839950336, 758018997, 873369236, 928483075, 890729119, 340264557, 79297731, 321154529, 674534388, 324233093, 320476571, 643333518, 995146597, 372814905, 544585302, 840933468, 922639662, 364742398, 935630791, 613803746, 326797603, 843954616, 350905746, 356245866, 195251371, 449461361, 990448368, 682661208, 470104523, 398747354, 568751944, 680906302, 712149572, 968263046, 339826548, 127279248, 75436285, 59946228, 822916614, 732242860, 568611775, 954223722, 338952193, 768698327, 200201171, 58806073, 81435505, 974008935, 193499118, 318654979, 647478114, 547288489, 657007115, 719476787, 632125387, 682263288, 318420732, 637956060, 238857882, 97359475, 26099110, 409703070, 414433629, 218123956, 611851667, 169912254, 498819506, 687817794, 553710203, 40868572, 530339199, 517644593, 805396488, 831801381, 160492170, 656978876, 517021413, 137083974, 511475063, 85146993, 882805563, 560735377, 363959460, 414515113, 853672054, 153580605, 141162583, 692345642, 219818357, 742799831, 749286758, 552206307, 433003334, 704039093, 738758322, 937915258, 152577989, 611325659, 967208577, 806779051, 981897465, 860635632, 449096052, 414942665, 702580531, 854079467, 252084693, 686890372, 545488975, 45657925, 578020326, 980187780, 269631403, 886565837, 187036599, 261073319, 336265753, 253662174, 667411348, 396477717, 381550859, 589857578, 995127575, 398504906, 494027938, 747761631, 791487884, 717096661, 160838188, 762650179, 460474570, 480293607, 907884354, 239452547, 812617321, 14368977, 960161027, 969594451, 443317136, 361189593, 988970396, 918583268, 641066518, 174827630, 330582556, 950382668, 703290159, 501332659, 71102491, 546862619, 265416886, 971477328, 409299223, 778264219, 870269142, 457106767, 441439770, 322999545, 94350160, 131560175, 117880335, 830314967, 398780740, 425067714, 831955802, 744061456, 23603630, 106532290, 145152452, 227967428, 490431013, 394861754, 135624688, 91109817, 849478510, 532209288, 705499945, 142540255, 871855737, 111839115, 960322788, 902220956, 912501077, 814916955, 183846799, 737821683, 379387513, 288370548, 643780574, 630052621, 25774418, 736361078, 217952219, 866304723, 223905716, 77009127, 644703061, 384945728, 153685789, 174938214, 922205188, 437314287, 591328344, 364494052, 475824510, 84532466, 917693461, 978792013, 52267380, 143365185, 117841829, 587963161, 660571402, 361002920, 870404511, 32291552, 184871894, 361557674, 900435728, 392842218, 335132533, 952443044, 200463457, 983701569, 429687185, 797926534, 479705095, 3205037, 877974583, 778096075, 63368599, 598066170, 518391424, 871927473, 160185286, 545145478, 727948568, 52383571, 427607965, 333444632, 950870016, 365255671, 503223386, 584799751, 665612509, 585342319, 620437978, 320109282, 190902155, 286892902, 271559827, 343334504, 838656274, 305041926, 703106382, 712228123, 315080970, 574536642, 669321874, 585996554, 2107786, 543412705, 884362508, 737341972, 38222789, 357098477, 668053172, 113603562, 789154205, 612871706, 68773744, 926476124, 279600083, 145469415, 953666356, 372412496, 50685177, 410897067, 890950373, 382862875, 377385323, 917711605, 80238531, 1177576, 83342731, 261610909, 385686942, 626143598, 286445290, 873709658, 663955754, 720759082, 409690466, 43784657, 735578846, 73460298, 416568792, 985695519, 224672311, 845559968, 832350843, 944193825, 252391322, 109491549, 654885232, 540903938, 748784280, 298720815, 81226662, 66350059, 22586875, 575661923, 877979583, 720624671, 867575337, 750401762, 171523453, 431575205, 968232494, 417450170, 462151449, 173188379, 679841854, 597516600, 207649632, 639544751, 423380854, 293533256, 856436076, 949571176, 201119200, 821580109, 186342160, 376652583, 622395692, 993741561, 490688791, 53248416, 183736766, 876915630, 386613484, 753921269, 581010465, 285197609, 669575839, 313089548, 474011343, 255670473, 498615612, 14343789, 922270687, 782618142, 179714861, 542795727, 729561043, 632744111, 840296898, 945916316, 959411468, 379524476, 380413969, 861783975, 770520811, 325605700, 737491437, 634938764, 471633730, 535125036, 223641132, 6533211, 328178144, 111174574, 568388380, 154949177, 658490061, 706798596, 796289738, 959279216, 326182044, 411405814, 225850013, 694927417, 234655658, 573643747, 136361006, 449848758, 448034078, 99616929, 349006610, 762417122, 547087694, 171161077, 65118103, 816885970, 384321133, 523135530, 764364771, 76899529, 90496673, 867952428, 579387275, 873358596, 789119229, 897259380, 848980003, 519848844, 555081476, 145505939, 608532541, 648448094, 328498259, 611462317, 361630108, 262101048, 221608542, 494026185, 897645993, 241658533, 681206755, 346479326, 208687853, 365286538, 24869982, 689458853, 959268573, 80167029, 524072501, 392218458, 154062735, 184796196, 110331242, 736885150, 963011126, 983909513, 164301579, 278579139, 236771749, 619888935, 306969167, 711447413, 562835333, 853069723, 957824968, 395543790, 51495649, 864654693, 686000777, 451311880, 72599531, 682304075, 515119922, 733406572, 573479753, 361947741, 520593968, 791955104, 545874414, 502192751, 46715761, 724245141, 627376795, 85750610, 755172331, 470972362, 181128707, 843958739, 393114271, 285822755, 729422196, 934042793, 83419885, 189208095, 855571201, 357929387, 528380864, 868271779, 361172795, 931546260, 833050513, 36523918, 417039549, 690407133, 549061971, 199392063, 168062498, 190420377, 871295678, 775174189, 679811903, 747316696, 475927111, 456614089, 550816563, 177739368, 586864877, 289932170, 186617985, 568987823, 184958936, 51690643, 787130368, 838152588, 202707326, 649095338, 95440765, 360411736, 313291407, 33556711, 418758914, 75088194, 954549227, 145009230, 401545717, 47473929, 369827429, 965649403, 695237745, 461186154, 322619934, 97223119, 273576057, 56110072, 889692260, 762837644, 468152262, 388268729, 376030632, 29791215, 26009209, 278010827, 62726189, 860438713, 800115911, 685308087, 792605672, 744862074, 719660649, 36518808, 55692538, 144279027, 305546808, 699828530, 181851955, 483438948, 127129743, 213362468, 615803203, 650808134, 959598640, 812357882, 535954786, 846940362, 375100140, 178855945, 552987422, 356077296, 29023095, 811291106, 401108658, 879717055, 749855637, 906488264, 673325404, 384231979, 731540782, 347036939, 692642467, 513487104, 640910129, 412105437, 544758589, 592932386, 435868552, 768250635, 11375377, 304419387, 560251752, 505271815, 199823130, 634266261, 2881618, 557454566, 43169455, 785756380, 448669510, 724347141, 700913721, 262075744, 120766766, 312702039, 408806712, 195078073, 900405014, 433596754, 316096872, 370526553, 515095925, 616056619, 352142155, 598674590, 391495114, 356048153, 969688402, 598226511, 670736846, 347316883, 931747691, 609738453, 721167483, 457068455, 240209344, 352082373, 577297538, 500346717, 655232739, 12326449, 486442439, 7964389, 379758992, 565602178, 39837973, 458526349, 508515763, 168003305, 744391992, 430908282, 558617215, 379671914, 527519610, 227897042, 457528007, 844152865, 185546371, 362645841, 884404030, 819541952, 774790491, 929187612, 10707153, 157327105, 796160387, 173146995, 524623325, 215236285, 757239260, 52937340, 880058633, 13513635, 190130182, 520844598, 274847067, 492968444, 36277155, 123713924, 583353156, 291877378, 751345687, 851910791, 300747394, 308118858, 235017230, 282942025, 503066919, 527860352, 941607629, 244222897, 781680784, 904578392, 766514482, 949500894, 362623486, 187979460, 600779544, 450130129, 932346889, 753956621, 898234749, 260295777, 999846515, 907896960, 753701019, 963164940, 386089780, 960981379, 78029494, 470495915, 877779608, 934930423, 997114079, 872792173, 637721171, 29902233, 899350306, 730904711, 207309504, 762300907, 712715872, 225989757, 547113924, 911479497, 259939658, 34555586, 191383541, 355136544, 599836612, 951348793, 431342895, 528488392, 359829893, 413129148, 660694175, 283535185, 329281177, 342832912, 24571550, 673012858, 48301616, 527149600, 727049159, 892741689, 668639356, 10426318, 537322392, 779905506, 585370256, 449662648, 191247359, 479987175, 665590577, 579503524, 123944712, 708110132, 109812990, 29652747, 511764189, 385705896, 839820140, 968083053, 102241827, 575369490, 862858689, 977086698, 580488534, 973275021, 465920965, 28189667, 599101804, 793142069, 132509288, 440364037, 182832503, 312411921, 296381532, 106513010, 947486311, 20022622, 138683314, 65810915, 490616476, 703272471, 914553142, 17142258, 727635567, 590775152, 73653660, 12085125, 728369058, 602214540, 648231370, 699272259, 798853700, 645942251, 378221387, 508170730, 724682914, 189397787, 287292961, 781588144, 781510265, 770903958, 423107143, 750475949, 842215909, 349976725, 505868822, 34820215, 143813411, 765450797, 446732012, 743749548, 717538447, 500481225, 108853392, 137318965, 999216508, 356358656, 404668748, 532181606, 932392034, 20356109, 981679429, 341713580, 48060162, 433139048, 21276079, 286752639, 351873620, 56742963, 597936540, 372260857, 724055634, 825552494, 539947237, 690830058, 814194146, 590832744, 51812287, 278449800, 509612921, 897126783, 129625213, 335462193, 343615459, 611466260, 334906916, 796966680, 693715704, 106189976, 605324758, 111664140, 34898966, 628844269, 642032090, 40907658, 138734639, 114110170, 609358320, 263880859, 784105485, 783543426, 669875133, 947750229, 346716066, 682646963, 759497696, 104120004, 657265921, 115656328, 723684636, 428507639, 605334928, 808591281, 578813562, 409696327, 440269806, 653974003, 808521127, 308443423, 850841152, 49386408, 787221543, 653750272, 83909409, 54081778, 895472686, 489166547, 269625727, 827530681, 824222588, 505590453, 78428574, 362370057, 326656111, 34413157, 119562161, 57055486, 112120485, 197995873, 606121535, 896058960, 630101533, 403901863, 72922886, 264728033, 935809624, 405121865, 969238451, 497850966, 346453619, 209220745, 684946768, 524714155, 700832801, 619059116, 680262751, 453429208, 281196971, 725216876, 791055123, 42254237, 440343602, 313196350, 753223836, 782165881, 56582855, 878938312, 414274907, 713314826, 897657313, 524415430, 938262582, 57190594, 66692750, 661458726, 355855995, 484213833, 124692915, 864649593, 203397314, 53523107, 791283811, 206864067, 830372084, 437010677, 939211840, 347780902, 971945852, 554380897, 321664502, 852362818, 67133151, 296101204, 70160478, 522990836, 231157782, 833008684, 786037960, 139705146, 318706650, 883515313, 698650246, 8855974, 252745273, 208229684, 384561833, 914523409, 760308194, 917983915, 504259720, 430721089, 320729954, 966211199, 172758276, 222909839, 912742334, 100249578, 692862721, 831129466, 871060395, 268719495, 239953290, 930353013, 182114951, 688588829, 397627303, 821342190, 482459793, 980507464, 665047467, 829742187, 808668169, 208803560, 15696167, 116420156, 316253453, 119219112, 214634576, 296646204, 173426300, 989031871, 324232085, 453827191, 61150224, 524584063, 424979432, 248613698, 762321477, 837126008, 400429215, 653882831, 792344895, 529360333, 763562126, 837983166, 438596551, 688838537, 360672996, 924525127, 930213428, 978520652, 70877571, 693267059, 95121799, 943648946, 567280887, 27350441, 4028453, 42083843, 69899212, 60637469, 4972216, 390265992, 681866677, 132926453, 869346517, 686833966, 790979574, 43827189, 161193461, 723757646, 687310889, 584791514, 877838724, 959340036, 136123820, 580661648, 767622154, 197686422, 113687444, 31693713, 463098697, 942127675, 611887414, 388001344, 142052934, 333667680, 179065443, 973435917, 68885466, 897348146, 22250344, 544785725, 721599020, 229660316, 166683511, 950461157, 919879704, 784999080, 459409584, 103571819, 188743285, 49194600, 70210785, 138412482, 333620799, 90063135, 658693823, 643797206, 721192066, 7202203, 198217528, 754802159, 746088379, 764478392, 870504174, 952826025, 337551329, 527225315, 830539242, 963909151, 884685163, 607292052, 550056065, 951837613, 913839376, 270539673, 482018053, 134759418, 49010385, 760410766, 291680495, 49894224, 996388385, 996279205, 424571779, 416798600, 466320430, 859077775, 566493018, 392160170, 488344362, 748721773, 264497966, 96718372, 405136799, 690963382, 976362936, 225052360, 352848330, 682747767, 293280931, 438908262, 627044245, 463435429, 948885705, 3415764, 29925189, 35061651, 747308063, 875177835, 325255441, 137550308, 881484294, 796058838, 810696769, 923315323, 131044576, 94843720, 923459993, 639862689, 627342971, 903216159, 678245323, 683093135, 820616557, 802422838, 443788479, 652981000, 376248853, 198993187, 89712522, 548253969, 363700218, 412594107, 743609402, 977124320, 496166864, 981001297, 324158692, 484625075, 924598426, 514643952, 203644228, 206686104, 909948584, 426007996, 682406008, 917639229, 525196248, 532660859, 716563102, 539095731, 778955254, 64228668, 707879366, 578790992, 304107037, 560230657, 341200235, 481201379, 133574007, 480020524, 786870797, 489191534, 793319059, 31977833, 563374928, 742031448, 510173714, 391144421, 227602003, 610992482, 722891410, 9467629, 912637885, 899422556, 605814404, 545908017, 138057645, 823723881, 617973523, 190690307, 722338979, 300263658, 426396633, 824868262, 14055412, 633872264, 990284008, 451112376, 898623804, 93031574, 467040897, 185653834, 380013422, 633072659, 531753742, 106132982, 912798591, 19831086, 738785499, 256515184, 566064634, 982794577, 218921361, 49016227, 30993696, 176985026, 102135278, 972559629, 915014872, 341363900, 167845435, 311387327, 437048099, 271502674, 239917868, 954592678, 339781540, 839789026, 402100117, 685728521, 277855468, 94525791, 733425015, 910170339, 595301065, 455970673, 607165808, 659041118, 472213288, 748719157, 994542576, 628844235, 304516739, 230207434, 448201121, 38180818, 889424918, 890723356, 701551365, 860561307, 365783280, 481192137, 160238438, 588625262, 902970949, 812758616, 674153792, 74158672, 96765047, 177197228, 234940136, 671715281, 686796611, 992648742, 394676376, 205159731, 976113948, 963932303, 306905340, 575803724, 195879151, 34288186, 674581634, 343877877, 716739031, 769802265, 736786448, 230558690, 658758950, 485729487, 709886431, 821912447, 421335856, 784209345, 859601690, 88497974, 689710583, 104979089, 896068426, 321045508, 885685581, 832160238, 895596089, 360121293, 887074632, 866347506, 619325993, 12921842, 992986168, 778148405, 366182457, 498924866, 681161238, 966582682, 764339073, 561264496, 43064894, 178358834, 14556670, 268586423, 507284818, 787648054, 961767232, 895927583, 164991203, 65082231, 700508600, 2501194, 636282183, 265794377, 440087578, 612079582, 693444527, 865093959, 70945030, 547910748, 527969455, 673471237, 88992733, 452299075, 768615047, 200765916, 894924929, 35778537, 203434156, 910009289, 584854554, 778631685, 158165943, 839428019, 927351626, 668794379, 554400889, 86833053, 505612175, 81867175, 769166159, 887118804, 723315475, 755838906, 114928620, 806833479, 301570868, 475234566, 104945611, 143821736, 779178321, 957070454, 96663720, 352302426, 42365511, 661028045, 501810053, 780956238, 181113986, 273000045, 105901328, 714965962, 776256943, 210298694, 363393233, 624682315, 969626921, 387037754, 180254392, 690801394, 302988355, 185349562, 804767486, 121795613, 307445129, 427020245, 15999789, 38680172, 754441318, 175601714, 743471072, 119311747, 725524233, 807168981, 714543703, 684072085, 490105914, 769986270, 93364387, 455829107, 209996981, 8876626, 477586519, 918081112, 831178794, 570162110, 957938605, 352520754, 328397537, 115443140, 387054768, 921039965, 514839843, 220390558, 257382295, 818020893, 797690393, 46900094, 84929564, 569430282, 856503149, 627178735, 155544259, 502359323, 133133301, 874144310, 847627297, 903067010, 871177326, 704407228, 668834258, 487840398, 473430423, 929345225, 946056340, 101378975, 466365999, 980189708, 120787172, 323996594, 918162598, 406122100, 410745012, 933017778, 742513992, 638386340, 87965409, 581329243, 389545556, 759042017, 499909341, 179091593, 38063240, 428780035, 553452147, 748465158, 390763328, 451042, 68418713, 860135350, 341763956, 188117139, 515610285, 946156397, 753625434, 186490539, 960499692, 124202920, 910514235, 742780117, 999135421, 694987752, 403161491, 542068271, 267483302, 366498094, 623262972, 11205351, 832780893, 393536080, 751300286, 678893981, 994879937, 374675790, 364280445, 366593849, 317037887, 171977161, 387713765, 260519094, 539676924, 988729717, 894836544, 669791790, 781427019, 741749124, 614492106, 477114513, 591748074, 218035744, 204216674, 859153829, 449930493, 734922049, 838549041, 637744609, 495169383, 912212291, 346750926, 740057922, 298610113, 317156850, 185978585, 75026678, 418721277, 8655779, 189266518, 813846837, 622452989, 718921723, 61840985, 792649554, 114032542, 514816507, 229407660, 758611945, 442937155, 564569610, 580830865, 680656858, 303167693, 461129861, 885828788, 4498978, 222677099, 662678773, 339371582, 352031287, 217704381, 513017047, 180066623, 223212093, 251592343, 358055481, 64412405, 609205496, 695795546, 336344654, 752743339, 336361923, 483092802, 56016550, 26518347, 850079594, 714859700, 410302936, 993034735, 748991006, 433764786, 298434878, 318008601, 128598743, 462736757, 200081524, 638610976, 438167446, 62143523, 411848352, 590321382, 402477680, 302032843, 884870950, 584823105, 296345123, 803404511, 30005546, 233191008, 89973756, 639641661, 113094348, 643131180, 585942920, 925151118, 737354906, 365509083, 344757474, 453107872, 264020317, 824179340, 699209647, 318111214, 261003653, 641709692, 518231863, 14396405, 111091085, 395443488, 233702784, 255257297, 249235922, 313477140, 967723924, 313515723, 765959076, 679583425, 405821822, 526051111, 113249528, 212953851, 276014630, 431309032, 368680547, 823037582, 226791038, 236345453, 27272652, 210484910, 821588542, 235518585, 701206583, 616270112, 947729028, 110636603, 814553581, 766764128, 641381916, 501209501, 302543453, 802599258, 678884032, 59333735, 134877316, 524322777, 955209725, 639600195, 506400641, 520167110, 425694426, 31986729, 362674769, 345596520, 612410195, 112783762, 800944283, 819298384, 534200642, 251492849, 901066942, 360376815, 968708672, 408356106, 469328096, 812795137, 972146425, 906380830, 406309168, 668675895, 287515804, 717557615, 636519540, 118197187, 896431280, 397853555, 699476633, 657331091, 908642692, 230568718, 311449304, 960336556, 504576091, 221486301, 64509596, 133043249, 893286243, 352886365, 338556315, 424086165, 543691022, 581649267, 610671216, 631027639, 303454838, 380939066, 344233671, 218101077, 690418367, 740209409, 932730153, 277815888, 246434082, 179818396, 831956097, 685616986, 246126257, 484563828, 765013812, 275358837, 536515171, 759344965, 315867875, 302830387, 109120378, 832870629, 914021599, 628171548, 349662418, 483573207, 885436686, 120847522, 506795945, 14536550, 811855850, 755215401, 417590152, 244315443, 333338140, 138046752, 960808888, 670511787, 317269220, 360601907, 674164538, 611169824, 180838174, 729074990, 607567343, 453805054, 175990498, 404568209, 287096521, 478392461, 622237263, 790894501, 307137493, 624733576, 141334436, 970595441, 964086344, 766153597, 642259978, 27660298, 182623390, 159765177, 410377481, 822110279, 897263368, 437957214, 3563032, 948389652, 987535189, 860967368, 192671699, 70857444, 627539653, 685274163, 579029180, 752731552, 274833340, 61438943, 6743233, 676491619, 501380635, 27070857, 640168310, 974034397, 840969277, 690694103, 23809715, 46039559, 490775344, 293223758, 354244649, 870353972, 363861277, 770202030, 37567933, 809787159, 517342686, 383583323, 826392935, 989727317, 372412800, 242598078, 890183303, 913007560, 595459415, 235536082, 197097408, 494980954, 7102097, 39638590, 265767479, 289106801, 970001756, 871570155, 590788981, 513461165, 579930577, 405703398, 205174531, 310183483, 589152607, 764676658, 814706508, 523173360, 278047610, 976533132, 477027936, 511575122, 23195239, 653440645, 729076753, 218359814, 708565238, 478901164, 893955758, 830184382, 746348836, 921322404, 159338692, 165994118, 356492932, 454933293, 706936949, 269813535, 431603297, 882763357, 825377127, 705599039, 810146124, 973651377, 377721282, 193308728, 691185873, 144850158, 306736857, 136908197, 990037037, 12536844, 573387908, 715304618, 232915963, 829240942, 984117679, 15745888, 779063107, 870430480, 782189530, 445192161, 505799830, 118138253, 78286318, 460915965, 794601757, 115353154, 49720813, 816676932, 785288424, 838030015, 607467337, 256795938, 552944550, 202761562, 871800992, 907654605, 694093373, 738602857, 368642476, 39411640, 15871041, 971067855, 798749026, 597853937, 598719239, 522167299, 34205459, 47659867, 960502914, 675136028, 969041645, 580747288, 774577906, 373498175, 874169909, 483919136, 161765845, 142053611, 862174516, 848580142, 846593866, 942379671, 68679902, 606968753, 289967246, 634584746, 134685632, 202094916, 684636192, 292805947, 721025758, 353545973, 642409536, 662840200, 167856859, 693867154, 83548554, 556491049, 237207083, 746229283, 646007694, 88752212, 183857435, 957037316, 648552524, 837980560, 106566836, 148653524, 453636081, 22313279, 327071429, 172550915, 691811012, 821298913, 835211731, 265601240, 382032345, 402197621, 829913154, 422163201, 961990416, 193458142, 826506726, 109044224, 880889354, 348964439, 405683253, 825549472, 672939235, 252025529, 146458367, 760747528, 927478028, 10459041, 39298781, 951147069, 44983691, 576070118, 776107269, 396386821, 943420048, 927217245, 294386698, 905606524, 499486787, 550210846, 400667707, 20523693, 259184312, 770663282, 454751017, 296480994, 946989893, 78676248, 780583741, 106810664, 389261294, 897396397, 840316871, 178526945, 989560808, 569146729, 120949737, 489582508, 74537205, 192583246, 469189551, 699445110, 795979745, 781923393, 72695611, 676093457, 175984656, 149447768, 420569760, 129425249, 214419978, 818173776, 625888349, 687739445, 858209292, 510833273, 155963065, 693169860, 347315313, 296733505, 972212765, 407208346, 306302009, 474718844, 880726873, 936629823, 589902467, 32583556, 70635247, 895822887, 347778114, 868986741, 472231380, 214374319, 959296154, 346563710, 815992820, 103106157, 961390807, 362237383, 759593485, 719333552, 919252938, 82227948, 259495342, 302596963, 914075310, 3661366, 693643713, 707615450, 442825706, 331867306, 896230637, 354459111, 329115379, 287820970, 903879648, 231419606, 270041351, 156149832, 790006253, 646763746, 249859817, 409383256, 579268873, 50036405, 23146074, 643329578, 844468549, 962801600, 881001700, 928426944, 947485745, 720163933, 284004343, 679437016, 983947081, 775980838, 911800949, 514865055, 942040768, 95715509, 183470307, 896490464, 24292888, 487146252, 561308773, 284713946, 765687413, 518025771, 52432530, 919582485, 437677109, 557390935, 486387552, 821615138, 686429098, 744699245, 852824194, 736791301, 417191825, 987938175, 778984289, 373990562, 119321000, 706554258, 251782744, 236969387, 402748883, 817655298, 25137902, 560874761, 789036924, 896043059, 845511117, 474078812, 603404566, 925265970, 632999581, 811909718, 655833129, 978103089, 758027260, 75137813, 727920645, 840325809, 644898965, 973593047, 121741852, 947220551, 27856605, 459033764, 389875403, 654415760, 239498550, 3052170, 127985988, 553069639, 269916746, 478728213, 972250785, 536368002, 686794887, 375819702, 789257061, 899321048, 894706864, 633785746, 426105670, 47098767, 242294358, 28134126, 925464071, 556544617, 343553869, 49872023, 984229844, 108544543, 403797269, 255296570, 485109364, 430735283, 4073231, 522304980, 132233244, 234335015, 705338820, 698575944, 301742579, 969771380, 364326865, 573860701, 111421879, 2977513, 634715036, 791786812, 900063765, 177061806, 547790693, 728209621, 481965684, 165355261, 970111678, 521804027, 526942529, 302164501, 488221972, 531725943, 794921606, 360036392, 539116690, 430865122, 387529325, 624982147, 33978345, 846243989, 385324192, 211412483, 651654244, 947205090, 532919610, 873118680, 923099392, 780342798, 494718230, 365776583, 639897643, 486627644, 911901069, 876689060, 658404608, 550159747, 684891284, 536662694, 975105142, 237398284, 945594747, 946004555, 713880245, 225839596, 530768803, 887128924, 872962361, 807550737, 583041669, 963456334, 669879971, 243600385, 147767408, 71725150, 371675114, 66610136, 379159029, 552768324, 521994786, 226979410, 391508808, 805677206, 182204209, 266016408, 14393589, 941301076, 874971120, 224099125, 722960559, 84277660, 330509314, 388889374, 929481853, 672546257, 571813978, 526552576, 732388452, 496775175, 183166757, 784152407, 177240176, 977842110, 115463121, 657421030, 317981070, 450410022, 960486630, 552570676, 667638707, 543332963, 669851512, 26358926, 456663933, 522501041, 45632137, 21920594, 254284288, 665679441, 705267069, 958161784, 318201157, 457042125, 859473248, 741254782, 618986015, 870749750, 381912709, 771996770, 814012524, 480229487, 366257724, 972806552, 129245517, 821803023, 447098668, 500631959, 85080441, 663268716, 766973330, 792775684, 98457957, 154614041, 737906161, 15691130, 890303535, 812080298, 642941405, 811098817, 409411258, 337883806, 159276060, 298376424, 947459964, 234871244, 29195206, 115165834, 744684750, 842103476, 807724276, 51992892, 979772025, 712900285, 361789123, 533606150, 358318710, 190458289, 885936910, 306321642, 117006678, 606270471, 311020840, 303580908, 168600041, 303500486, 408185592, 811203507, 58722383, 668842157, 467166059, 869202839, 63043032, 577529828, 453215996, 538867573, 169947564, 828809013, 232930997, 101134125, 505903545, 435350541, 168714776, 413388852, 424426524, 55474440, 501520204, 342284281, 886555172, 528208241, 902620929, 343052140, 247445665, 163467686, 484343802, 443700870, 895049916, 789547797, 14204827, 105512611, 768360706, 377735593, 171290995, 843677923, 43105240, 138690972, 990728282, 885296340, 512448251, 770310125, 879819817, 928327402, 809728838, 40287625, 811988981, 138126360, 566998780, 388856551, 641029612, 10673987, 862335199, 425368719, 811084802, 578836133, 758483575, 118463034, 759136170, 802472398, 662229977, 249134749, 343855362, 625682600, 801940572, 633349380, 572849608, 912491938, 103178309, 502754518, 561470563, 653149394, 517191412, 715683816, 550472329, 616392923, 719045292, 600963375, 22433141, 411984550, 563180193, 502774934, 752230345, 407784600, 849989970, 164974278, 201531642, 100016033, 279438, 296853745, 798325364, 359579439, 346025777, 546640596, 67508351, 859587938, 513600431, 346375894, 19493779, 412393610, 686816688, 763643142, 210285497, 801501151, 545169895, 37359374, 476345357, 125194227, 693756146, 125432875, 180039629, 247802052, 190492073, 996823960, 229091739, 794716721, 194574145, 59181896, 590699565, 885266578, 954735387, 923746393, 587508999, 222560375, 294447150, 409951290, 1169225, 360102875, 317961457, 884174887, 170419439, 65566249, 447949172, 565222122, 395550419, 14237072, 256217977, 948168446, 638627318, 642017982, 787781560, 162999042, 173385949, 562259582, 10270372, 576766338, 701391685, 239160736, 583901978, 104590974, 479874389, 434851424, 251751230, 904809083, 504224907, 802911996, 146640212, 117959244, 743119981, 604075438, 13130940, 500515610, 925708513, 207989968, 888778662, 539176623, 345034118, 518961962, 488518120, 639869837, 599843559, 422658853, 614846085, 835857399, 786940059, 435047584, 194137589, 230708077, 477321856, 838998178, 316181354, 370292214, 298373555, 625159271, 87537717, 309929256, 961052292, 842373636, 433717746, 11480527, 656236098, 64661872, 872628353, 59251625, 432130192, 320521362, 510997795, 614986571, 364846913, 417490298, 494468791, 199890826, 989611079, 290976703, 214908676, 837255242, 932823614, 808029505, 465566440, 809547299, 928581576, 605396874, 581431624, 152705188, 985465986, 676063917, 135387276, 475126395, 552194147, 653467635, 881087802, 612176873, 997527543, 595697939, 36210376, 258959224, 785435263, 373059705, 727713290, 267263058, 434427064, 245792101, 656131487, 826130553, 834657279, 731976427, 426693476, 523809886, 968167427, 280172157, 99741973, 156381290, 816172259, 914836551, 727487494, 418227683, 572153203, 851517347, 757204148, 352715945, 249018236, 965729368, 406783989, 605765123, 884721845, 427915396, 725504024, 460348957, 578547507, 75960013, 109907567, 615595757, 627001288, 361276105, 952746571, 138570932, 512528601, 94482708, 514689446, 244084122, 230584502, 464453077, 165058902, 916315075, 269368201, 756180220, 225188574, 675413444, 186516990, 410688469, 892483488, 851107457, 625515363, 679314707, 12377104, 196387719, 634821254, 911625993, 927720551, 223622502, 549144507, 345353882, 911721817, 753746505, 232975527, 267277738, 586715697, 207555122, 789839311, 416243183, 386255927, 551230875, 120711144, 532259830, 101168663, 425750829, 901058443, 87543642, 313486964, 90961799, 518007077, 501094187, 392590119, 567966956, 965552546, 887334651, 549769404, 989756137, 843337790, 590448036, 50538282, 63935504, 537155795, 846886503, 411139616, 383463874, 348848532, 36935126, 714349722, 827802963, 194916375, 498486860, 792591874, 616412720, 214827691, 564800546, 711023008, 525711727, 40903146, 539794499, 792598974, 873025831, 24971710, 740116709, 855552936, 90021621, 147530120, 787216835, 884626364, 317312642, 828930411, 362966704, 203223226, 555723229, 885938803, 136397291, 506276263, 860598014, 963284363, 955009867, 755720373, 462561098, 517691503, 360529381, 412958335, 204625574, 690580472, 1761849, 404925990, 568499667, 101995973, 378426274, 772846591, 947253409, 167920278, 47245896, 698159751, 498650514, 307129271, 977833141, 6290703, 209691279, 380929751, 50967220, 526617886, 847565814, 566037948, 105093868, 379491482, 556437318, 16752769, 378617485, 951971953, 708861705, 243827370, 803891948, 385970184, 166381106, 204223282, 536971376, 386950168, 906309662, 710349116, 314132977, 405487778, 367181272, 477118866, 156738047, 22589301, 781539379, 178660093, 984733670, 672585771, 942739102, 514409043, 201066953, 493589953, 836029969, 204233869, 407362350, 941946747, 703570364, 704186450, 967202569, 960134276, 130953532, 958211169, 138219500, 985217062, 698794664, 182249333, 530792766, 709745271, 865281391, 724332116, 352341029, 329044557, 232332439, 941069141, 499520305, 522385008, 12495925, 890706932, 107545694, 880866546, 133911450, 722645470, 778230106, 151536467, 564176538, 369642244, 58639105, 400038191, 653007854, 950496058, 333308097, 39413720, 357058587, 398343455, 373727161, 740815832, 31893260, 693501590, 806477572, 41697397, 938891041, 592085978, 224891872, 352848874, 632225609, 854442593, 470242345, 783004743, 300798827, 89775092, 187843833, 838172381, 92041050, 97732794, 390488304, 405928912, 75563964, 848260507, 363032015, 296257316, 828480827, 909002076, 808382121, 508291628, 126713983, 224554026, 689852989, 632180280, 672626574, 103267796, 38324786, 968186774, 738767517, 578344132, 866618444, 500904916, 449702909, 590974776, 347171245, 953362808, 984456422, 488192685, 6345577, 599456872, 264846804, 428605481, 485200422, 22966202, 859982014, 661023413, 205941428, 441941112, 41657877, 29613300, 185051112, 45837863, 864289382, 13663912, 749610744, 622533199, 577967687, 683945229, 690850367, 675658173, 969170180, 116803314, 915023768, 207887996, 628663793, 691630935, 934311492, 49237194, 3672428, 454897176, 325232678, 385595121, 732352924, 917958377, 110369336, 463294713, 176045755, 393603396, 209378813, 559258793, 280023267, 174584605, 83331257, 5573948, 331460165, 379132269, 686260993, 939552502, 739978519, 799645246, 783149313, 219931519, 693000776, 942062084, 886331410, 978071592, 381312052, 94632393, 822111583, 449741833, 321602171, 756291955, 820950442, 281542376, 260428144, 387125610, 763980764, 63330909, 26995215, 919411579, 382040992, 266110348, 770434067, 254717360, 265999146, 180517495, 113418398, 180746600, 841388550, 790157362, 262574405, 975200190, 219226476, 902536190, 970153055, 932580015, 224427227, 663044785, 989445136, 185786324, 755404565, 272437185, 608901945, 143455880, 993155310, 757066752, 932963228, 94329466, 702246758, 721397438, 352589056, 473303449, 39396671, 337116, 20583792, 661100176, 154207063, 252631555, 291392308, 909999795, 641529788, 604269243, 979904665, 631090931, 757720120, 135340327, 272820398, 230697244, 712065072, 290500031, 444904836, 303323889, 571982322, 964425023, 859854868, 110006643, 521964531, 329808530, 558263560, 850028344, 847247123, 285823991, 92444755, 879672525, 159079951, 169962363, 882833349, 550652507, 310417677, 473826459, 271525807, 104065079, 486645759, 501640543, 748839722, 59504175, 779269218, 623633520, 69350709, 196947216, 366296616, 801540623, 48763424, 351786981, 99038676, 389109887, 527878802, 212814703, 36953921, 249371078, 263812260, 486032698, 588968563, 481550319, 363272129, 998341211, 563353196, 4892145, 43646167, 908743733, 895244446, 745159142, 507654704, 233957980, 834397926, 802893318, 948302526, 803504104, 907568741, 227193513, 407457393, 589590360, 627287251, 270226716, 100408167, 198872797, 118002689, 933124237, 441884367, 970207031, 775055263, 913707414, 342658005, 960468637, 888430567, 68711856, 784619896, 659061052, 900058194, 711739590, 211205620, 68714775, 206906294, 631317832, 717819844, 622980711, 335176743, 673703776, 388783296, 682860746, 701810511, 5915050, 927080889, 551621923, 124895160, 420077620, 583419412, 343318610, 600694675, 874954206, 969163601, 175020363, 969686468, 822807001, 611634514, 224448948, 97177994, 683198071, 95045288, 142624009, 675825992, 29201229, 994390549, 362159699, 346909503, 578185538, 983133925, 43192887, 163132916, 650634990, 279354992, 550606513, 826918786, 443911887, 437288299, 573134856, 199597429, 136527099, 586866128, 424335568, 343884159, 788315747, 504629667, 465854775, 60413421, 493077775, 515594495, 799619063, 329114998, 583092967, 998045385, 877284299, 162216074, 932871346, 859595921, 125836382, 743370165, 447222129, 554572084, 822872970, 739029605, 818512072, 912548493, 612662397, 746025096, 377081542, 546501966, 153543409, 993542669, 226843694, 42101772, 622744346, 49080821, 750408230, 907415072, 440634338, 905161536, 525867366, 594948921, 227010723, 922437152, 602134130, 280768464, 139347848, 832970516, 397498580, 780986591, 480935383, 774302628, 513894356, 124104078, 497816273, 305950636, 910967807, 708961085, 332271508, 571935274, 978633701, 896525409, 406457763, 997346789, 757442808, 729951397, 34868106, 139787809, 379352058, 242931657, 696906031, 522246256, 747423841, 34889311, 357734234, 989120205, 562479654, 605559420, 104233754, 855444191, 408690633, 184401196, 676083877, 277375484, 595537915, 669466938, 714066903, 206684954, 538371846, 5730429, 168536910, 775351698, 171483838, 679459913, 595877454, 920426575, 977234687, 51181198, 734100222, 472180469, 219290405, 998022023, 113345126, 72498928, 646294108, 247228296, 181036856, 598793471, 361090130, 525894661, 305176386, 58526389, 954476382, 336193554, 240561381, 32455117, 878955016, 740460388, 305968758, 410739787, 220419575, 621891441, 537453628, 73219595, 641351040, 925862885, 351312297, 990636672, 537633430, 69748353, 637415595, 968680426, 456106800, 133671668, 110672936, 404478865, 901886321, 637127251, 762228622, 411860880, 695158996, 496577503, 80865502, 722413750, 100822309, 146590471, 149828524, 934925349, 603938800, 994360730, 518377299, 209044139, 546273955, 367554771, 225317459, 866405737, 960754608, 187510503, 585837448, 754653601, 776654001, 880908133, 263535263, 491106450, 870660116, 33923571, 479467292, 428333317, 636421545, 723358743, 957817189, 114520354, 664693675, 794837086, 750003634, 736642421, 141378638, 391039814, 687041933, 383183744, 9206524, 815445506, 763793048, 288597446, 809986429, 130399381, 294424045, 997024588, 570441256, 334039157, 220961575, 420661477, 473620590, 912665454, 480977271, 615974438, 213633813, 700192586, 98839814, 584584318, 490177651, 753255430, 121850207, 477943123, 476179321, 103564868, 383745973, 967147728, 803601201, 729125154, 887085783, 858608203, 9466931, 811823496, 231330624, 509384058, 357950809, 726146628, 838847512, 326985862, 682331948, 908652784, 793240908, 666806585, 627424496, 692240072, 654529980, 150377488, 239064205, 163929119, 343702160, 138817204, 300453297, 737873437, 519048483, 81069025, 856874160, 429118377, 835507635, 891474515, 121222765, 393706059, 100089088, 568438717, 456915567, 63701224, 632680361, 752560750, 565776472, 615619716, 149467416, 419237826, 197076672, 447758142, 55068517, 838201116, 71822632, 148084686, 896110916, 126691830, 880797659, 185000418, 694086853, 769143123, 969147116, 852149078, 47727818, 593382313, 194509459, 317155978, 854822410, 466762696, 495719461, 522428983, 608708347, 523472505, 43262661, 616606663, 735449382, 456481714, 13776818, 898211215, 108939403, 726886468, 909660021, 154637828, 549614633, 482900840, 965991179, 326265053, 397641940, 319546449, 427079213, 925295771, 169216647, 292146041, 616881628, 129757258, 408685982, 191650919, 316128519, 176361143, 444210546, 424733276, 659964160, 856226026, 262937608, 749334499, 919246895, 516757334, 570429746, 913871850, 676210276, 36465938, 368988306, 531748474, 296427936, 375783875, 245749675, 255906392, 965553080, 487398269, 312434855, 594264759, 22790229, 877906788, 631234627, 831835911, 161024241, 727393998, 928287193, 219270383, 50978832, 990653663, 51130315, 284707537, 798531306, 492509073, 641374091, 478356969, 251335439, 627902257, 300456493, 130378523, 780836465, 528172122, 900499023, 405933781, 745680449, 376324916, 686172932, 686506237, 44509099, 561548597, 48491615, 600679856, 460562398, 200891282, 326178817, 916538389, 625139417, 117870693, 50293706, 523284092, 259264550, 814002673, 434489057, 35600546, 245636732, 170204809, 990739190, 999666662, 729312894, 508904058, 804178149, 210920962, 32812081, 485278125, 313231843, 386607364, 25321644, 996242598, 363961835, 436510669, 689743755, 199485990, 646544584, 660118394, 482375553, 939401278, 944270487, 814748280, 932060582, 617759614, 226763727, 11241107, 440503065, 90715788, 130878233, 823885814, 272674103, 352132562, 93644978, 685508049, 499314882, 547523345, 50178364, 637354603, 247927123, 279770714, 574986096, 618204959, 95431542, 293337124, 872946224, 900525712, 605473181, 110260287, 995272628, 451387380, 279708171, 525599395, 908652231, 405578886, 979520195, 442093921, 446198531, 141056652, 210271109, 604434469, 154153548, 993443833, 919996305, 847433726, 102504096, 762377480, 570964789, 169178528, 703791502, 889240141, 40432159, 561882762, 858544372, 300332749, 63822578, 16334175, 387349469, 603328427, 762039931, 746895166, 599234872, 297424810, 95734318, 835044834, 62612177, 211718260, 643233884, 469301309, 55522087, 934046935, 741740121, 415707462, 144496919, 107879803, 404292460, 447737376, 353118826, 902244576, 125934784, 410853320, 23474060, 234835231, 373608706, 208067527, 104047636, 839143273, 480595132, 999914408, 37306867, 87422819, 249175932, 812889503, 893009527, 882926122, 909704028, 681552417, 409165972, 409901339, 562449908, 705045162, 226984797, 624935364, 182230290, 176760415, 384908776, 6383623, 464918262, 191413934, 813634127, 851028544, 644150578, 992842417, 126974106, 332126384, 907730929, 398772706, 535270959, 982516087, 71038728, 242212118, 203686301, 158339210, 181251772, 580928436, 175674981, 295538224, 748618526, 350674588, 944654302, 503121073, 557205608, 312970154, 502652120, 463646223, 112801915, 525032280, 173654249, 789025414, 419571586, 675704608, 892974135, 538827760, 761407749, 624834201, 347247718, 946788938, 407479899, 331407165, 96568443, 981020113, 722434267, 316740706, 230076230, 403628580, 575469969, 262459244, 870415293, 11806017, 78594460, 532248760, 497573929, 435530809, 418175595, 931609831, 12788558, 920038328, 726991897, 327986944, 217682021, 36186804, 286797333, 659733783, 318556821, 42574838, 12831534, 349907616, 353774952, 256024358, 183890503, 478340903, 229817940, 958327696, 684741499, 161747782, 506952871, 205374550, 306898754, 412571420, 133344295, 129818090, 502879439, 988228354, 78778402, 658106220, 545815238, 471090784, 581945582, 136449660, 20890091, 243043178, 364581519, 629113608, 876374662, 543681701, 492807603, 615956621, 67814230, 158043111, 217951660, 294995343, 146567124, 167696521, 323977163, 675214475, 547844056, 83977747, 718348010, 389726879, 208889792, 996444081, 321666370, 220978476, 860542700, 925312763, 835727500, 280346847, 894128873, 448699294, 315344129, 652710430, 622312571, 945337872, 282354921, 950641631, 824337150, 59446415, 540925313, 557234119, 159301448, 661622062, 18555713, 961244628, 940912199, 176658800, 20674665, 13491787, 159531564, 175664008, 803864792, 991876128, 392662746, 150131831, 284128805, 457982076, 947455433, 684247132, 721164068, 703988943, 54591920, 692059748, 630246548, 697596465, 468784765, 328181913, 599839095, 73913256, 32473493, 230524961, 311735197, 821973146, 857305144, 708555486, 955979171, 190813195, 877584104, 435622868, 791736695, 824284825, 694666939, 970966986, 777179908, 733254788, 767596326, 540942353, 145313784, 193633985, 543087077, 347342555, 419854826, 485243418, 862192983, 467543991, 81691888, 332893495, 744211668, 585318654, 416680010, 74829267, 548256073, 74490670, 303597210, 948881918, 610496625, 511344498, 484474349, 543730803, 168106291, 114290741, 855593070, 365911445, 478031424, 657921285, 785869551, 54658056, 734880714, 310838081, 659115805, 525404024, 108011470, 720809870, 404180692, 662172563, 476921774, 242800522, 693671539, 551255487, 486446292, 761641147, 556836668, 824873543, 243818095, 825899315, 10150217, 718224133, 671794349, 828374374, 356101747, 71213108, 584679619, 596397335, 652001401, 140874150, 283723396, 214877644, 500742575, 200829325, 433091816, 74255720, 808796706, 620006153, 35073608, 975631714, 747930476, 882917379, 64612209, 364239083, 281555134, 567108535, 711236924, 387895465, 306292472, 750946598, 313715795, 821603343, 543751850, 219094443, 479616536, 119146401, 651946765, 412804854, 42377488, 438509690, 516365544, 913422448, 117474314, 596097700, 17449898, 932466136, 217821298, 375032931, 880987381, 791012547, 616223155, 687694753, 776377153, 247072430, 596034599, 19262471, 332119464, 425694186, 20816317, 559688812, 194616216, 211032548, 547623647, 224543244, 607433969, 973319236, 97027491, 253222826, 174358438, 473694144, 868738108, 430316126, 492823807, 748715275, 718143152, 749999382, 67603039, 339401905, 662292947, 932023170, 526873378, 115848861, 572426027, 543066040, 542638255, 732741570, 388536363, 570402690, 606150499, 955592196, 863391161, 424914416, 114798390, 356989044, 171616975, 491191039, 70753228, 928629709, 790769089, 596655683, 968702994, 219011957, 618689019, 396318744, 936816664, 420311119, 709376050, 965585298, 910832993, 757786875, 539467795, 822311716, 727844242, 751451418, 447866402, 784944999, 378961650, 38661532, 248097017, 632751750, 330366448, 468739203, 330091493, 553011815, 622872911, 212915335, 200837583, 260821688, 271373107, 456398590, 984447135, 603266221, 614281025, 412846175, 83829807, 92701191, 571751779, 557268226, 133625140, 632021240, 591101464, 813240031, 55557016, 498995178, 221855565, 791571910, 648533097, 220514792, 317295069, 614371141, 229403755, 829451977, 427109524, 71158059, 233813425, 13240338, 577354781, 978300068, 544770829, 531166821, 100444780, 186225085, 31432995, 297401097, 586665550, 336195197, 315808243, 523518893, 59000226, 997408463, 96867034, 923007049, 470284298, 877098116, 726424696, 985245737, 671777194, 612630397, 525193936, 610933254, 206504148, 773769105, 854310690, 745100579, 873425063, 209053674, 228496541, 342220845, 211590119, 966520743, 558189622, 603912221, 617173176, 909338751, 479976018, 629646168, 603724667, 237652652, 818505519, 36047712, 615469532, 211302573, 488862569, 53261207, 56551209, 885899287, 406464557, 329964046, 540380286, 918445534, 291661107, 756679112, 726465142, 933651957, 389959979, 609794092, 758213599, 49146192, 138313133, 853923859, 970286165, 254046626, 591873003, 995169734, 294797334, 647178220, 472846040, 579702267, 98326086, 641454770, 793891705, 639811810, 910411099, 570769381, 606171121, 933466240, 217291280, 345677687, 968024858, 797878856, 966183583, 437844528, 490577515, 877260067, 922978113, 948136772, 38660551, 640555733, 507445490, 738977447, 267097638, 888066433, 679893021, 679045600, 564671768, 422557060, 99204752, 992093509, 436279851, 115543856, 952404712, 278360307, 175297630, 73940998, 568767218, 675018538, 288442911, 747128028, 368073340, 145480860, 184130428, 26282099, 260371204, 496581378, 803213339, 420819645, 163504707, 803829490, 865188760, 776231968, 236251445, 766147494, 853717558, 237243031, 791173854, 787966831, 585846134, 465127995, 335215026, 807176497, 762257673, 461150912, 544638489, 275731168, 223072111, 518047916, 802620061, 892866826, 633274485, 380344314, 423641523, 138219494, 112963770, 898032818, 407545053, 341301043, 804273456, 878201799, 348810341, 609384352, 557378084, 947597461, 588377410, 268098902, 164581237, 733360210, 326758702, 187615095, 962444761, 733318072, 44377055, 553413650, 526224557, 720054245, 802581758, 360389943, 532085597, 932960744, 711518947, 959945697, 442449077, 639857841, 529018804, 911348334, 442676783, 374456415, 538668845, 575524242, 12634550, 664038746, 562916556, 230221241, 725702426, 818941647, 199224635, 674703690, 336199847, 866837259, 327649732, 936620005, 869008732, 107741796, 395808935, 765281421, 738078088, 436519407, 546281875, 401710078, 229719001, 554955259, 262058953, 764893356, 870262750, 505945569, 230603650, 488428406, 433770269, 280788584, 961412633, 503645693, 415219465, 691996237, 319302461, 464273329, 849844584, 396252333, 876263842, 439144933, 148153536, 851258791, 583171612, 908827417, 855941377, 495130312, 646056566, 857767835, 893585058, 338940620, 952204098, 821191469, 550694877, 592478676, 581234692, 488206627, 617717432, 45102790, 284935110, 153163209, 108631048, 448658802, 545302896, 507127712, 298034162, 988159132, 301968964, 873523863, 278841002, 155663139, 914596184, 370703194, 325671370, 430685533, 545161372, 439573728, 733472645, 968552925, 359441693, 384719114, 547753625, 753033639, 750428720, 86893102, 588346049, 437322334, 482335955, 327061458, 83288415, 113985891, 285757826, 62822764, 962170160, 856954175, 199197495, 843186957, 871814468, 980383078, 504831290, 48202074, 272493051, 913230702, 6071960, 285564263, 693053590, 989158133, 405575114, 274679499, 7412224, 753948475, 779911791, 631134622, 30769332, 59660816, 502033417, 648705233, 399898169, 664213999, 191519307, 200048703, 879051624, 404045121, 996285166, 142131348, 370130599, 497991903, 705286607, 468484187, 296476545, 932145612, 360891765, 51970354, 193329393, 597842503, 645748760, 734622928, 432123114, 246196167, 852593006, 551835235, 258348115, 698549423, 414653042, 868545438, 583980016, 793700141, 293424430, 109073787, 543501994, 119965784, 125897650, 459006340, 123856374, 54269452, 599932826, 883968612, 10790830, 622576308, 593777396, 612652746, 950331918, 717293216, 215477442, 860566498, 730040547, 162593038, 957990594, 236006833, 348319504, 681323895, 545279536, 459443411, 169725003, 975488234, 70268903, 356777310, 565139650, 387131261, 187068978, 493865796, 58950900, 949144246, 648590697, 642591144, 980866434, 497920267, 451305314, 734525383, 887010277, 274908862, 656559480, 216483089, 559351500, 288321005, 225966994, 676765139, 82641752, 714715792, 171667422, 254506476, 754082041, 47208158, 264386203, 687470583, 355029223, 187987076, 29130220, 954320563, 859928702, 531397058, 976269481, 785381628, 993631399, 109008020, 855410000, 836107670, 310862873, 596792497, 145075832, 706970227, 607090552, 688803812, 387772842, 636641088, 605199873, 443070491, 874786296, 789178056, 306709655, 530807553, 7733030, 237591083, 755846699, 340631166, 532462185, 695822709, 841270797, 387213453, 585542729, 911241028, 426606534, 228417196, 127922206, 421493652, 434800138, 837565887, 899032870, 213363876, 366300433, 614773782, 362067986, 791704432, 652152258, 710124838, 660018576, 789420470, 462049724, 399086682, 715883653, 557498203, 313727496, 194784126, 772184505, 774733134, 375543260, 324695508, 598898876, 876386580, 843059885, 50698433, 512767375, 228120480, 258304472, 213552810, 463529257, 428240214, 790827418, 620310361, 438138633, 452479066, 319320406, 608855382, 756057867, 868162898, 778211805, 818576665, 44569882, 664845923, 436268237, 578915562, 275597755, 896986557, 60555394, 734303683, 576743618, 610246588, 402473487, 166684157, 751577938, 927622039, 938452810, 771454126, 438433293, 696641390, 493796512, 906978692, 435591843, 562606302, 622230743, 163573819, 521003396, 120752404, 426491368, 529282084, 887722549, 878385516, 981780995, 128671402, 419453765, 932052016, 760943354, 827794494, 344626701, 80465750, 638476884, 32129120, 628606078, 209596236, 351375794, 154115356, 681417664, 885344532, 766863502, 317608002, 399760525, 324185647, 811980834, 723260682, 50848303, 710507359, 815467502, 860354459, 698894254, 435174537, 450627707, 511914623, 520545216, 516302191, 882465354, 429329252, 536718952, 146805714, 720329666, 789415954, 35795112, 793069063, 244067797, 775756457, 290905931, 971031570, 968408842, 138630747, 801451448, 847007997, 978607603, 780880047, 286373945, 334125051, 412320357, 708134212, 424035421, 601309191, 616100461, 556219389, 20829882, 547796674, 782479426, 308767171, 723574183, 176660197, 867630565, 999099024, 540421706, 885677986, 936936942, 320897042, 362727929, 88051802, 255121913, 417290818, 958162551, 638355841, 813908180, 861518580, 753690673, 25825412, 994818430, 573300605, 537581779, 467736132, 235107664, 616778697, 581246641, 619445204, 674355849, 679356849, 361983430, 13607430, 52723756, 546446993, 126704171, 663764366, 602091018, 678121972, 849905163, 753518956, 101580061, 404356241, 547484163, 314775911, 470285056, 469548382, 148339084, 975558987, 328266683, 987485478, 847155766, 766484118, 627407149, 908498691, 145050310, 108683102, 344035748, 294755739, 662303601, 431865719, 745734582, 774818913, 146232832, 353881452, 854610620, 301524488, 249966577, 77688065, 516533042, 216000845, 984290265, 895901334, 238279404, 245475199, 187715763, 926168794, 948295415, 23336328, 490743588, 25229903, 412246272, 365966322, 857494157, 74122439, 6752509, 306942847, 814103848, 788317646, 220409933, 457140659, 928626138, 325120922, 961044067, 236697594, 239344102, 80409984, 763825238, 430324942, 491533150, 513891653, 317408141, 874515422, 352067859, 523337731, 206005702, 313754271, 329002828, 301451904, 583067225, 491894152, 546502840, 169427827, 776919031, 53879379, 755738913, 122068595, 414045286, 842543186, 984195725, 393036290, 921135131, 592047759, 419691722, 888318298, 337704678, 190817484, 535951769, 465547096, 401047145, 25308790, 980050463, 798735610, 832604939, 854935367, 445319812, 24547545, 958336903, 259036270, 571626986, 576104186, 733439648, 430670775, 958479512, 387643590, 154753507, 206904584, 678381271, 41301245, 986322393, 927298140, 272633180, 966886416, 743714058, 100677560, 256974112, 920424881, 544093693, 370359480, 608336942, 882393858, 356169683, 453935771, 31033201, 47146959, 21341871, 720467139, 434684282, 426941611, 476590986, 663859447, 149602012, 213751301, 683888574, 808920311, 206817689, 658355983, 465980209, 561631903, 421377702, 287284470, 730653738, 456589343, 23160290, 962727398, 802730856, 94033037, 210586975, 868008884, 75111584, 823610307, 879111900, 227029625, 498964669, 54319013, 503328575, 999131303, 53079720, 114255442, 960516772, 574057001, 917804591, 971269142, 112755616, 652820506, 344151803, 776866902, 761680580, 199880843, 655706830, 798903983, 475235158, 841009525, 145309811, 872334902, 427666010, 33283517, 47484765, 924962219, 904727976, 581891261, 607354213, 377886752, 416886306, 358954296, 43345418, 998465783, 288263966, 390551828, 678624803, 924296978, 53334398, 346729578, 59408183, 452705345, 28169625, 3987528, 32143981, 405380196, 470351179, 906893304, 262385898, 154717978, 241252620, 973967295, 164772427, 512124458, 635480436, 600159889, 83828725, 546787588, 562517550, 771503797, 467011754, 845502208, 680633251, 675797540, 778198103, 294345044, 718570579, 125312970, 829127673, 575356095, 839476901, 671141799, 18291770, 200787864, 445555527, 848182402, 865495994, 660135678, 802659612, 162242139, 47593906, 400302170, 334185105, 813283039, 839950823, 801080095, 911889034, 141381895, 688195660, 512364269, 434889658, 663266884, 587254018, 249663750, 875866775, 137172433, 552365279, 903230317, 989343275, 687746460, 885409431, 598965807, 362208496, 567068882, 283236838, 94733237, 357054110, 873359769, 983578116, 257752565, 719596345, 125595012, 701808641, 712475410, 643128835, 107606655, 298111017, 547791701, 827563781, 153706026, 748435476, 62981614, 911149335, 750907161, 36309772, 285205750, 82246603, 836967276, 454855609, 663284721, 82549294, 697373435, 829456464, 420745295, 19485818, 801626371, 741897204, 106114336, 257274104, 591877050, 249160090, 630405878, 894968319, 522808679, 633863758, 171916879, 651632297, 338717070, 27287672, 51537449, 512910911, 490911568, 246415080, 224212094, 446598312, 474278308, 404471519, 892168875, 200344471, 280074192, 488304530, 533850174, 386224961, 164962050, 278694731, 516696393, 33929805, 298678329, 483029963, 391884522, 848688166, 970544560, 195743449, 811937846, 277158565, 547416774, 849766329, 29278325, 401102894, 774092899, 717571737, 54916085, 722234630, 735906980, 942872745, 338986859, 659972661, 46277376, 820985507, 888796832, 300515480, 209311128, 951800868, 142247985, 341517936, 433939381, 531377358, 849099855, 481845661, 684590825, 884985893, 551526717, 506483316, 990972244, 62509374, 63321257, 974998734, 93272659, 424510823, 439949903, 759924672, 695694545, 944422822, 510330129, 727457181, 705419350, 983289042, 996919694, 655738388, 247684526, 40085964, 623989241, 968345588, 563974355, 208920132, 755198071, 503537706, 76486968, 685585579, 172329548, 938465761, 867268507, 706424138, 925578690, 543406975, 129716638, 808255984, 853458378, 34986103, 86665108, 830701598, 519002633, 450568691, 762365449, 964821301, 755480797, 116286672, 330361635, 808729422, 655775175, 458919358, 480429163, 893754556, 619312653, 672908457, 849278720, 994619467, 402196520, 702591807, 405954247, 808373252, 310039147, 95285471, 926811294, 297816046, 246912996, 487386929, 474380982, 594245653, 449057297, 720125684, 959084160, 426707032, 380036319, 163557058, 600292761, 696182222, 651241978, 311556930, 302349554, 144654746, 151516441, 867264858, 230436666, 908219405, 837195884, 251812197, 271203070, 172125870, 102913099, 965345934, 550816019, 210812384, 627804408, 49542358, 725997743, 165676107, 148006132, 526960770, 126071902, 990520537, 137948946, 588420029, 489737858, 305062744, 955372776, 989012974, 61247684, 182085203, 632199521, 620458196, 686734197, 579487526, 77234787, 989589157, 688094947, 180892467, 590240901, 442028853, 617421618, 988931904, 383086053, 629683197, 996700185, 351908858, 676412014, 747664528, 274868416, 613576890, 474020877, 265595505, 180670695, 970130070, 777597145, 71606131, 850618732, 314045272, 899387976, 743025808, 997617442, 187442716, 860369150, 521777909, 711416645, 467396851, 435248197, 462690055, 115441464, 698343170, 349454409, 31346244, 810442490, 984056055, 735766642, 630645283, 863231318, 289903447, 429726867, 514379921, 511172863, 998662577, 265548043, 259973326, 715305036, 13615902, 794306948, 248589526, 555162195, 948972532, 467404367, 403058152, 850783818, 674599830, 112373743, 520433668, 421781675, 283585830, 759855452, 53108792, 79017156, 834441954, 213115650, 427420673, 625402163, 726336914, 626637584, 343212296, 233052777, 823856711, 20866732, 990400924, 816488012, 815780746, 907527055, 994357407, 156925420, 63785531, 678369380, 691587256, 708423697, 461518858, 478505752, 224741785, 406716590, 721518919, 255959561, 156274661, 437084505, 553951362, 662442101, 795022226, 662021186, 819418620, 80111819, 741005704, 448823423, 948722351, 329294343, 776178211, 626176872, 955958915, 440761813, 380160392, 846286114, 982954035, 79575226, 973748797, 578322500, 618945, 60606142, 22224835, 44238113, 603259598, 403451388, 983492857, 541236073, 781942555, 206878444, 170373441, 444868979, 894971657, 49670571, 720551627, 251107501, 887857532, 281491086, 871865362, 51231007, 747519642, 333787092, 752804480, 832784883, 203037204, 216111326, 845308906, 105661386, 592108766, 906152301, 21797177, 501849485, 745824642, 844364609, 948663962, 216094206, 477510409, 175392498, 33509655, 26985252, 848492003, 875747931, 940019834, 780200028, 171946621, 180413114, 46998650, 788805951, 986157100, 845220615, 479425487, 970299166, 267098383, 596407523, 948737987, 102909713, 90979138, 874125879, 476240666, 616016517, 186306028, 177395099, 954662010, 870544781, 676875643, 589752123, 945980932, 992770381, 667173715, 278569908, 85788285, 474159014, 276764605, 505753403, 241074462, 271040280, 235609725, 427308877, 806798018, 663477000, 607637414, 939948477, 237217814, 163808258, 422407804, 180896748, 531645550, 111111777, 168288956, 842727453, 438407871, 962337804, 597466263, 476047055, 729491134, 49236002, 982312400, 85924313, 554846414, 998303989, 842816006, 663835300, 402188283, 617633363, 708369068, 621417221, 964253904, 614324231, 703653259, 671189299, 733178993, 806130330, 8632458, 585334826, 668848142, 468584439, 87353164, 73204666, 854653802, 779046204, 487685957, 896551864, 723588157, 782707562, 321507242, 444765698, 848363612, 28011255, 19697745, 311364440, 378193502, 135506815, 658728357, 852726686, 178515616, 883103199, 259160760, 795329080, 865570203, 473666346, 566190891, 47124844, 47426185, 953419000, 908518181, 820686294, 689432740, 508848902, 250113344, 533215278, 903888601, 13015479, 233344032, 500574384, 318168754, 960800962, 800282135, 645705956, 954665934, 193601935, 924873407, 270932027, 817190709, 188263578, 222429564, 173469674, 907155069, 26876801, 953092768, 583739508, 878150376, 907924812, 863841090, 152870593, 484925996, 109384364, 98197780, 164010520, 884863217, 214449097, 250991925, 4289231, 231416760, 215296519, 921792338, 557300509, 563155512, 749498797, 444712828, 716396946, 314191148, 272839849, 421956730, 253252262, 980596174, 788224409, 740104211, 712077992, 14410428, 415523976, 944363614, 344955292, 985844232, 671829290, 372829829, 42291188, 350130192, 642779680, 414024313, 645968400, 227286420, 98173407, 813514006, 503454511, 330837868, 12576242, 783491342, 464899913, 486739255, 443688212, 369138645, 497474007, 948860802, 500229685, 176768153, 580329700, 87698362, 908043314, 20001139, 175409777, 993849055, 616392755, 140603734, 383179672, 494053943, 680720293, 124345961, 801232004, 94506372, 776509565, 932228211, 415134777, 325712720, 924737863, 971010916, 664558771, 320478864, 876833654, 690827329, 658954289, 890828017, 485402461, 699869800, 812792691, 749275057, 49024980, 598381433, 483949705, 971159474, 714310134, 52461645, 635227263, 200277887, 910281470, 354431583, 93268201, 367823894, 352408018, 19696332, 335878191, 671163224, 46638244, 413109426, 676330321, 231414735, 460031065, 180074721, 42355641, 395149091, 787662147, 39545524, 273607006, 240462184, 732739698, 545548140, 76310325, 665643437, 302009264, 65616166, 884403184, 948755329, 85804004, 177026915, 331850712, 877707720, 881901016, 178818046, 563107301, 726710087, 730929699, 329297577, 144598246, 862495706, 42094806, 132993929, 502640918, 488251653, 693917074, 755760531, 498055096, 696359371, 867586482, 629377392, 370621749, 29176970, 652884680, 683243804, 195014871, 827420697, 928685358, 983964030, 684828054, 775262978, 952805309, 118662426, 496225362, 683002033, 565569402, 807761196, 843946320, 629854949, 754042989, 921050151, 918421105, 170479393, 368170537, 236590720, 816338533, 33867564, 636548460, 352944810, 324870840, 74298260, 747221644, 175790679, 439112627, 742394932, 738893165, 625598126, 67038512, 145154683, 875696557, 207311598, 580248386, 634629971, 387305366, 411674409, 607342356, 615394150, 118897178, 738760151, 437514733, 705275585, 370526564, 459366295, 30983469, 609442065, 397745587, 350825764, 983083030, 457322201, 377711347, 890899300, 987971219, 755423431, 122197412, 760974765, 613976254, 597201322, 765046771] 18775))
+
+test7 :: Test
+test7 = TestCase (assertEqual "for (countComponents [757732156, 737535686, 402213557, 630537551, 816896377, 976194453, 214824638, 917684868, 951791925, 8576363, 790430635, 958007275, 837854870, 644547512, 649535271, 887760457, 367307141, 265816775, 672089183, 543895101, 996236833, 946453407, 889569523, 254949308, 445284979, 841445442, 358803480, 815678286, 96237276, 644048411, 303304206, 275896644, 984622075, 229479804, 913552318, 22503934, 237327033, 48549727, 18398251, 695088402, 760193216, 43553395, 775444834, 548281506, 729875883, 224335750, 715486586, 199611072, 137713424, 466351856, 393816375, 619000789, 252812641, 934881105, 269146253, 389619476, 977823389, 720519243, 901603699, 183130439, 184362230, 702546156, 638332389, 512108280, 39485330, 443235343, 473177083, 30654084, 294466252, 762221571, 731250042, 664973391, 98071246, 581250391, 657163122, 839971041, 952297548, 436619377, 822511445, 564518757, 578626854, 875629170, 244260635, 209995794, 674919120, 331676220, 988388620, 314269237, 768210919, 312902200, 369609986, 474767129, 781449675, 664676944, 12038750, 895329380, 292365499, 169823309, 610446996, 411979952, 147363095, 742241110, 885864190, 145322830, 434199473, 540024609, 840027579, 936541008, 929222473, 778967301, 968406942, 241867268, 876265578, 264816794, 865211227, 391268381, 845407372, 650796206, 606857605, 463634525, 921809638, 345405942, 398584963, 231790070, 863088334, 974383933, 402518149, 619413692, 97992060, 896855847, 676941999, 19154928, 696112801, 467540382, 146153980, 668657268, 421493275, 51940257, 508304656, 123588020, 587058833, 141915313, 201868918, 638802588, 743684830, 385642640, 35356476, 673058032, 482311736, 899656913, 288619471, 104032758, 225012673, 94276711, 158507727, 771014665, 275242889, 367944330, 369602425, 548830936, 72936684, 876721437, 661195738, 87367894, 74597326, 317928449, 850514614, 744474962, 452931160, 843763292, 557900071, 774000787, 397372899, 377108325, 562836140, 581755347, 981431377, 515586820, 941413010, 587444867, 961980390, 576803645, 499631542, 615349325, 249340647, 452117048, 800352293, 465988205, 872253665, 753017858, 528093350, 111148723, 364314515, 559511364, 639330143, 962034196, 145260744, 440050, 418691713, 927397284, 641845206, 394398611, 973942501, 922576903, 882478056, 168899495, 845523361, 462277568, 414296617, 559429966, 48380351, 463707156, 425159033, 19980542, 377268066, 664819331, 60364917, 845791711, 61514909, 506863027, 491477385, 783192698, 557864106, 585667438, 690842522, 851710063, 333192130, 385084715, 201907499, 865068847, 784120216, 432496443, 365757443, 224179962, 925935386, 497630655, 605317807, 328534405, 429821186, 525772621, 366876308, 998567382, 602615186, 414291967, 980059224, 38921911, 478320202, 435905012, 347609979, 592822218, 811028348, 203988152, 971059511, 28696294, 764558422, 728838702, 411862991, 601165820, 600071744, 775549908, 977178736, 458325817, 442572383, 165651602, 881450694, 468677999, 689813108, 56617489, 879469317, 912161127, 675624084, 888196880, 874070006, 833293786, 485626698, 601549789, 29676986, 636906693, 547761606, 350267848, 792183767, 94645028, 146015165, 716781906, 340149476, 877442755, 921594939, 753050755, 953736063, 979624453, 322396495, 331026653, 675393757, 356450667, 960794629, 708646329, 20251760, 309794030, 458201091, 848776166, 302808908, 542990481, 288582717, 563458694, 220287214, 441685480, 214202446, 936941790, 503006458, 70070923, 899130738, 636099601, 794472908, 667458743, 461528312, 518102712, 98586872, 51968243, 573289623, 892222106, 277803399, 830986691, 24857219, 889287522, 834699145, 925282472, 708262844, 41122726, 330986942, 455531278, 254868592, 396784924, 760266364, 203034204, 427390600, 826509361, 966605809, 372536947, 396272841, 275980670, 744533939, 575246220, 208450423, 214438396, 20954444, 901341959, 85830439, 327356015, 205051829, 702136840, 824280313, 633064892, 183551106, 449719419, 725892902, 29519189, 696491489, 865888154, 829882313, 45741304, 298673378, 800428914, 537535718, 351252, 962768975, 911965312, 914402199, 852735758, 53647072, 448494102, 690230374, 334676848, 978060493, 589753553, 72607967, 86252378, 228226421, 733258078, 876074651, 831701095, 956708331, 148730673, 785084776, 844914399, 240689100, 214482059, 175927750, 203499308, 939991344, 273945489, 244696939, 30912028, 775224577, 89382599, 437475919, 692471331, 685506407, 926897657, 954688924, 665057745, 970935004, 450768116, 776871736, 6627455, 763443756, 618703109, 722863490, 810986888, 450758051, 781580987, 643515856, 183069061, 543920507, 423875384, 782403690, 696914978, 330916022, 999380413, 70450132, 590923107, 378132238, 472684651, 279166061, 943921808, 892419750, 798159760, 961057203, 447701128, 895711480, 330582648, 917887696, 525209810, 12074793, 594008437, 894127268, 34933883, 302760919, 58649116, 763393665, 182835361, 744714885, 170933659, 979011174, 974085670, 955893667, 389795150, 943720912, 577681585, 780218669, 507601298, 482501738, 326123842, 767974267, 929240980, 369392779, 604701611, 319826350, 253971634, 397452315, 97029817, 536554590, 521204641, 830080084, 934187072, 696656379, 847913453, 800242341, 32324605, 523139663, 431244090, 316148567, 909270044, 394128703, 362691965, 370496906, 706507840, 170117855, 579083886, 145131017, 900064698, 637895436, 918112925, 812519946, 354887184, 474139949, 461631989, 47314207, 870145709, 840011418, 36607566, 884882512, 933415724, 739453261, 591767292, 133210993, 385517949, 487137267, 574950308, 135212434, 534076071, 309249053, 794352148, 781148627, 384303510, 305371796, 947805989, 236412776, 15676840, 805674775, 541902060, 586113666, 659053290, 569794628, 486248261, 871633708, 643150192, 148047774, 186412572, 61952690, 483847736, 908775032, 997557764, 959496299, 623633318, 555434189, 796177722, 419960712, 385345280, 65007349, 570989074, 495392141, 74533477, 152675200, 963743883, 340239929, 255176612, 268814452, 368622982, 259099700, 13542633, 739028506, 572036999, 694293128, 211239971, 731858606, 859817472, 697870980, 337478808, 242915674, 426880911, 334723983, 547932961, 768416847, 723846280, 874586087, 611918335, 823567548, 377826530, 923964731, 997931317, 812600684, 803648662, 323535915, 715351753, 470093759, 272405105, 686965683, 860431729, 147056857, 273420387, 177422855, 459069510, 48055819, 978845267, 2935751, 679405539, 23026722, 735353241, 605587054, 253365530, 456496115, 455865407, 156380150, 572282542, 836697582, 111059506, 583031101, 442461954, 309705636, 412480926, 82164870, 929235166, 730950770, 559653171, 79078732, 372201785, 86541087, 730429549, 523042678, 908823316, 883709915, 485039740, 423273446, 597768349, 949780195, 689724058, 418550940, 370673581, 543464978, 881456984, 164031295, 40636225, 284968780, 390226487, 144446372, 949727908, 969556326, 178810871, 603103328, 554851159, 998784816, 869172012, 466609146, 781745206, 895400628, 333334805, 624698427, 602620871, 796551334, 274628001, 570398382, 25818846, 408191414, 219201431, 117581752, 997972435, 222543802, 62340432, 576518802, 198855752, 710676090, 660303721, 698360793, 223705056, 971076794, 434279002, 40807200, 346046374, 241619382, 315009145, 542398450, 27537493, 732623195, 398977486, 863425985, 777702158, 362498075, 307733101, 829513649, 888039654, 421395073, 623627514, 356639337, 871417354, 709392994, 23659660, 418805831, 709166466, 320603440, 925395423, 69819287, 555595409, 654886402, 156329272, 186167921, 491151867, 132263015, 869269235, 970792540, 986593213, 231824421, 925552666, 330436019, 384240783, 608193575, 639163914, 948664224, 476127953, 539597070, 105788617, 342157768, 957500539, 891020592, 68583684, 971672570, 673491951, 641752924, 382602810, 303580124, 457220757, 830278291, 121659540, 266761547, 813676674, 40817011, 296642985, 848378757, 321782459, 394202558, 54382787, 152406715, 549749581, 423661927, 912092494, 307039750, 857436481, 371666229, 229290768, 998472644, 607732655, 929537215, 38933161, 406680606, 153600768, 514321668, 799426634, 654077672, 981477151, 695549963, 318043643, 407120782, 137034807, 538343862, 781094286, 633759309, 724193520, 393011134, 440999076, 115362051, 920105246, 48051978, 301522877, 392197260, 371934873, 664878992, 772397193, 381541080, 5535604, 162257691, 47436197, 195147406, 186690805, 639703526, 108961301, 275997144, 477963603, 360899589, 367380200, 80165107, 40354471, 359363865, 86312554, 468266548, 188671081, 523368071, 120628577, 526197335, 875625873, 427867698, 697894727, 699407474, 16005370, 863768618, 780256500, 446523757, 727538641, 875809011, 69697163, 939055776, 66004483, 90891210, 924048056, 459236994, 298821137, 474684258, 174752255, 763648363, 789736177, 658136460, 976632343, 10132499, 865798911, 924390426, 407150067, 646556716, 376774441, 224929087, 318389325, 716478228, 984494486, 887946577, 937746039, 668619101, 267885024, 598275140, 870786996, 663965810, 106669475, 385103223, 460845730, 174149541, 412353757, 974425542, 883654247, 772165030, 971081325, 227187896, 206760868, 28848659, 405236935, 956119228, 570391216, 423873013, 799366683, 861671694, 497481112, 634124123, 998309061, 910627151, 997235635, 975471443, 597146687, 597053536, 977497421, 742245072, 602546438, 85908564, 537187571, 900699198, 108469089, 721669431, 114297763, 592111179, 497422144, 591405412, 814750379, 936576923, 936321996, 900955268, 958216165, 129810344, 135315808, 218277380, 694569009, 825711649, 947301813, 749235241, 514615244, 813636371, 667706116, 890242165, 600294422, 968415288, 27399427, 469038615, 683422990, 339188079, 734089017, 654439718, 69869250, 659620061, 965540680, 91480087, 971424084, 865774410, 898512654, 167024837, 398274541, 849355215, 781414599, 913342431, 48893741, 57765972, 57775362, 60963069, 570520726, 709977287, 941907101, 746630734, 283943218, 562947900, 693001858, 213348179, 257594804, 438719756, 553640065, 943051819, 330632954, 747252942, 112261504, 697020718, 77098517, 115985672, 893546578, 626461936, 576847020, 803405222, 863629663, 222724616, 948527325, 612319384, 922081741, 370747198, 948161985, 428837778, 157827158, 994087995, 945579404, 167369725, 517886146, 155906730, 325207378, 232105532, 36090412, 476289065, 504263204, 292639579, 459688386, 448693346, 109425192, 388789278, 424373953, 581436854, 212225245, 428575058, 224246948, 455136005, 563818097, 699045680, 561792262, 21718930, 252420285, 515567116, 870131327, 246252230, 23250813, 400124251, 893280395, 311500449, 196752228, 109377504, 929762563, 510420504, 93307215, 967887285, 580478719, 454886199, 438302398, 491972725, 728210584, 508881578, 295605713, 492489429, 805608960, 737962433, 486317501, 772466234, 403025036, 897902120, 655773904, 574503007, 940041745, 333801482, 787181069, 111360057, 847680843, 693987154, 342195611, 812687053, 674070932, 684845096, 783852417, 985641361, 411113103, 278313204, 766175005, 402022160, 980347182, 659786895, 707422266, 82683586, 453302008, 179881568, 466088056, 100405775, 162384221, 246852789, 239878984, 549943881, 790964587, 115138133, 469819680, 17415406, 665675556, 941329230, 849715340, 912281254, 263814304, 864173739, 90606415, 663326347, 447443182, 30512098, 245388974, 361672442, 320826490, 120792020, 699633880, 17910109, 430610473, 858056781, 382664603, 243752004, 192938603, 582849597, 741410586, 602486089, 740889102, 133208249, 526747082, 180867321, 659906367, 423335801, 914579143, 866205487, 811116339, 238571441, 476388632, 584958651, 623230732, 49741802, 957987313, 962377536, 450154130, 574864723, 558394547, 960053335, 819719880, 935298171, 811747488, 284889297, 628876153, 697865834, 43297698, 846528032, 466827205, 500912118, 826640296, 579815262, 327166048, 996377153, 349478854, 554944465, 973901958, 112937911, 828224738, 531279338, 265607222, 654284920, 651881990, 755181547, 112398141, 827655181, 199228219, 796917622, 526220994, 647498896, 534408787, 377353281, 678402846, 578159081, 715682632, 599148704, 95420446, 531973962, 685983635, 849026784, 170176864, 13805131, 406288374, 988152456, 406376464, 855265708, 281193329, 180880912, 738106547, 793512506, 387746623, 264855650, 57134570, 877448761, 189356634, 50278532, 69252061, 696334066, 271138412, 510842859, 194258744, 720627433, 33865700, 31865831, 984805620, 595973038, 400384655, 663338151, 136372656, 236123959, 20729314, 170003768, 442137222, 234422725, 654033073, 843937520, 130715672, 612541499, 894281562, 898441653, 402069380, 287863766, 286697397, 268746033, 804425412, 359279387, 958733036, 147563344, 638328111, 174269444, 793385739, 462296656, 586797338, 468875334, 279348058, 740185825, 146205900, 491506614, 267675862, 117729079, 605368898, 941535992, 363268568, 763870026, 889075929, 140311789, 421853608, 639217765, 156786179, 142769955, 449358875, 116490786, 169227911, 265425406, 555010992, 315159294, 71795046, 934323720, 309637685, 896894681, 423490497, 208147982, 46008419, 271110490, 93114620, 244844914, 274866013, 89780692, 60291609, 156375978, 898879908, 807228239, 246625427, 780568053, 909202017, 288421814, 155242034, 940739686, 798461423, 210221660, 901523695, 295252005, 144057478, 627484711, 848073621, 464326724, 778521316, 459315803, 607251193, 276196575, 356446733, 860568830, 624148052, 459445592, 935209402, 404996364, 966614990, 157797638, 374561191, 309752859, 677607176, 994443349, 881648121, 598465944, 55031456, 474058086, 513326323, 274123581, 276589482, 527177447, 307324138, 812815908, 134610911, 225190757, 396871260, 451181985, 308743627, 470855648, 10141103, 596711742, 967204254, 421243261, 700248318, 12042472, 883876539, 731845724, 364020120, 920602549, 821379031, 240461942, 484544389, 996360210, 687784312, 848884280, 260025778, 141730387, 527822472, 357824388, 82577159, 131747873, 247127270, 866413568, 915260076, 142523061, 301992008, 332695583, 267279135, 687372494, 375485414, 864448353, 130849843, 248729049, 103867785, 590033492, 310597599, 73853412, 863408892, 519681376, 881871223, 827663372, 564157616, 194376165, 457194424, 605278856, 184991373, 728579918, 128982581, 157961733, 89939216, 276127195, 309090702, 59681239, 410091257, 585561819, 110519884, 824887067, 39000621, 257178871, 994706438, 90472823, 472584314, 765482728, 118881414, 836452969, 280830892, 834501692, 637406166, 534530868, 458265483, 402535958, 629182012, 457949013, 18654559, 842305484, 588979409, 459543486, 338426335, 843960079, 787509588, 899575122, 261160901, 268442556, 506687437, 196551717, 639517334, 342100214, 58965369, 603406752, 224799654, 296195712, 531220714, 833436827, 520312161, 579370385, 668829403, 210173948, 729110010, 928730652, 502038733, 934269074, 409472759, 546565030, 33367399, 51140139, 41455475, 990839940, 23166752, 931501965, 325220534, 233710268, 869410213, 341242206, 566691676, 912377288, 945861682, 850543364, 683738127, 6032179, 835089287, 370551013, 968525396, 984773508, 294467961, 932258464, 75249830, 495980409, 632175034, 619065152, 94411588, 590307046, 468436315, 297886499, 643471067, 453264701, 944425861, 124538361, 240958931, 165947147, 675439240, 530238369, 217884379, 534921582, 915384134, 845368623, 84154426, 924144798, 633100977, 309577448, 80548363, 615609606, 355704152, 705180756, 862698347, 666035270, 337806471, 497357656, 30584229, 360460727, 543616986, 824501567, 836765234, 103584263, 334698104, 832288429, 91517533, 998429352, 341564798, 446477641, 462015083, 624894221, 927792789, 270337149, 316805186, 573696390, 497882811, 315194385, 761897694, 790193825, 100258660, 930259755, 116698547, 974894589, 104610399, 790895397, 772966316, 836998868, 636830692, 221325236, 723764792, 381768204, 149237628, 438549543, 243239871, 651271367, 472720867, 188616450, 136873546, 214179008, 829337610, 902278410, 482630171, 227634544, 701518520, 166212607, 893471510, 449563228, 885304290, 767191539, 570045532, 463315158, 894329641, 178690344, 909726640, 967988566, 189612903, 218365826, 723435480, 322445112, 548215762, 214942657, 833875580, 833613461, 644250026, 917751026, 294329378, 331423725, 707096294, 120519330, 958645826, 415947406, 662103996, 774751777, 576739022, 281189157, 644109134, 334431558, 257392547, 590185444, 592766233, 104611217, 495376183, 246853839, 654875684, 554326457, 113548949, 909716063, 231856410, 658389940, 231717203, 237269266, 469186859, 277934265, 778396553, 599645658, 575117882, 818231208, 828379431, 774887136, 913964857, 234002405, 168649660, 694143733, 114877320, 123470093, 647716643, 570362244, 391227406, 109924661, 230109082, 927296719, 220175694, 268965035, 811078101, 797930372, 345126977, 727980251, 836441544, 540670140, 242092563, 940448980, 823671322, 30302373, 358339505, 391967168, 494774920, 412085084, 31618823, 362796787, 373308526, 106538140, 704804459, 316311269, 360613163, 741826787, 67876841, 798265595, 648947560, 749812719, 173551148, 834134818, 299531282, 363715291, 577657470, 299736145, 905065274, 450722547, 650417714, 267792775, 160731406, 12210953, 319755417, 85943024, 964608796, 640576106, 792588652, 941405059, 591910949, 983278257, 573287439, 83850504, 709650303, 335664185, 314955033, 574517077, 471575202, 331150194, 529353510, 558577599, 456407135, 18065783, 246123066, 800894960, 200329164, 825306730, 785021953, 246237531, 390275824, 294801066, 143707896, 111868645, 38195993, 915345522, 557536511, 828599694, 660245258, 454496975, 890761378, 483351789, 532156391, 98451914, 367656117, 180459295, 205225944, 579977291, 531857924, 115953052, 349752242, 699846398, 429886087, 907005841, 248968357, 247232459, 970249776, 659739437, 709937817, 276165265, 881950091, 56316271, 331183431, 523271230, 546748398, 295151111, 974952209, 597715429, 236605532, 671155869, 772794593, 782082940, 597323743, 822706791, 708424269, 802516418, 274378791, 321249995, 569028908, 849724994, 442288236, 571252292, 577535714, 69401886, 925312889, 475033249, 129005416, 417023141, 992943862, 443458389, 142691575, 52801795, 349043433, 341543641, 300303371, 851311370, 14345332, 762334625, 91202475, 312485995, 88366457, 144498039, 27341128, 739910191, 732717464, 509709306, 552517855, 779671908, 562497218, 373736085, 552635916, 515684255, 135244821, 840020737, 212910726, 758541094, 264098584, 107293145, 158445812, 865214365, 650124184, 526364428, 817658550, 198201446, 117871177, 865395956, 39278449, 141897350, 466010186, 421816800, 930735521, 752672143, 356185309, 873984747, 24562522, 171835869, 364796830, 995969850, 398768053, 801029565, 296076348, 7109421, 435891110, 971420116, 639473915, 492105412, 44728816, 369098623, 346872491, 618512332, 382361381, 206843524, 574953830, 755275741, 65688946, 763050905, 282610510, 297505801, 51898199, 342019382, 106236564, 455926125, 51454174, 388482173, 173008992, 907040138, 946022316, 939111831, 383788358, 62663909, 687772188, 989342801, 965813758, 60788336, 472431391, 181537695, 334711220, 947180555, 105906173, 552859987, 307392906, 928521400, 255870974, 594747145, 534599424, 442910358, 504058258, 778222558, 423849795, 375660585, 791964386, 567781655, 849236664, 615317929, 176448696, 327689549, 19988771, 749765451, 563795819, 478967226, 898670775, 413388291, 930362922, 230127058, 52789854, 599875216, 425655250, 6267655, 865048014, 733440712, 563784969, 429434534, 668121593, 385109630, 111523339, 364970741, 639958856, 819171349, 200412351, 365535040, 563942036, 254821225, 862013811, 25321692, 821148812, 339475224, 208125655, 590660750, 232178376, 455615703, 268749356, 707575775, 913570643, 646534812, 235100152, 773737467, 820976763, 431250946, 187311654, 190919847, 248871425, 514108663, 444404815, 125434276, 772675632, 387401550, 848746309, 757812347, 421228988, 568215507, 104672979, 59193243, 748708352, 425725927, 398962752, 68025589, 607719666, 763676461, 449152150, 224128062, 957330093, 749112278, 567057667, 962661938, 594496731, 945777798, 402530057, 815270563, 842348941, 137958506, 264309663, 965740361, 185110579, 514426015, 719653913, 485142670, 375783280, 672601604, 21285767, 888896084, 166051213, 636277976, 507070131, 213058641, 317990352, 683308578, 930399938, 397716770, 435727452, 140739559, 105727172, 727409056, 160074986, 177356779, 479478459, 749227198, 7698293, 935632907, 789769683, 240311733, 292201381, 138368918, 158231747, 867159257, 700911871, 533363340, 987516058, 216725642, 111962687, 926709333, 925725238, 131885890, 758120243, 422308443, 206227072, 411439377, 297277776, 195759758, 121397652, 802936246, 638799364, 888100310, 980291905, 264151689, 983659464, 621260680, 817980798, 155505171, 390184985, 995394441, 387241021, 474267347, 851361815, 641163125, 619784320, 539629302, 756105768, 275907499, 558037648, 713074046, 976222018, 242170291, 238263670, 916727753, 928384688, 597353897, 235786638, 58215618, 2155964, 217402312, 274493288, 822652227, 965179468, 13612658, 158775512, 155091845, 547878536, 293614773, 123470022, 422879911, 808040441, 825175495, 348916375, 469267386, 517400108, 744373140, 62869891, 140879825, 215785389, 394782466, 449736636, 414764013, 342366587, 176849512, 943842028, 505866115, 204662167, 752322559, 281267698, 957534464, 639188782, 514571142, 931370277, 184568142, 704738560, 815332896, 732129749, 369119499, 432788571, 990628142, 983024988, 555219635, 170530998, 377515897, 220816105, 283857444, 126926676, 235451859, 229745749, 210512214, 942268526, 112854025, 109143218, 412012177, 547518882, 770039645, 139172539, 491536695, 610102809, 240187603, 447389520, 703859149, 900259756, 693712013, 367078869, 909429249, 314498739, 341608845, 775426608, 523565447, 767517298, 767568065, 75684690, 250977541, 942179357, 474477398, 121599495, 272780685, 777277649, 125689324, 147139726, 780215306, 676115017, 402300349, 675085517, 527691890, 27743777, 470263196, 441974038, 720601921, 46225724, 855660498, 818217459, 758483331, 597039251, 623614996, 899458982, 58713395, 287338998, 113992690, 437375835, 476494060, 400330424, 673246381, 290968127, 538822494, 175760522, 243797690, 236657665, 146093007, 974815506, 724459526, 68232074, 383907045, 564129016, 993445575, 955598933, 64892748, 562156770, 851056872, 169977096, 100432000, 939983969, 138940850, 232495449, 648528248, 41706724, 752359768, 895304825, 223507792, 939009089, 139832994, 313170881, 296420883, 758236662, 983668103, 579826112, 483680684, 229332650, 458090493, 763811674, 596181786, 948531677, 619231071, 469375513, 352036439, 632047788, 705956565, 877228964, 17078074, 815840788, 102436296, 880518608, 334687383, 851983533, 886456220, 637236624, 637597301, 58062105, 494352968, 100558896, 525277407, 783695184, 304379573, 242050125, 762522182, 576093325, 71184122, 749589004, 766504530, 342113416, 741838637, 590898356, 826979534, 980811598, 205029803, 324450995, 45898583, 940196724, 22878829, 660468558, 871217358, 967962547, 928085000, 891889828, 914083641, 504882806, 414756698, 180292570, 195939021, 936249419, 319375310, 768063919, 151736293, 89655122, 514662846, 943717098, 725011505, 238887425, 897911515, 539700956, 798326621, 743771530, 71778340, 848784163, 159474131, 545363138, 126794988, 101581357, 627370981, 676338817, 130790722, 692455832, 6096807, 920744414, 958549364, 255410935, 895294939, 344657752, 824754542, 807666101, 826707949, 193500779, 520986422, 529188443, 82207794, 73977910, 484489423, 883948832, 826400495, 728489229, 900175344, 189832437, 541161086, 926794934, 553923789, 943936733, 179351805, 358108550, 715257360, 700779611, 978955990, 508298140, 194422904, 808261289, 572432195, 34582253, 702850457, 610810131, 922848563, 75869986, 941101705, 451610701, 259315619, 51752412, 444396285, 92791638, 761282608, 862430271, 893834353, 856474694, 20498327, 669852355, 178335146, 443999478, 664909021, 604869667, 264450644, 852081668, 794323420, 754266423, 443952005, 776987298, 220298259, 290049483, 867604629, 30575413, 205244793, 443495495, 496843657, 765871889, 204201862, 397534992, 161187320, 399890152, 950589661, 915361090, 353771109, 995569641, 803929718, 633394819, 684772888, 85175999, 724668338, 741168734, 367105018, 167060075, 445240520, 171424027, 746465648, 636194721, 176463767, 548004479, 189614628, 81218713, 657090124, 203361839, 386453043, 812418621, 897213054, 300835149, 651791687, 179095727, 614933708, 874411592, 840703858, 333369996, 287550957, 966151324, 5837542, 493407304, 527776194, 276989461, 994513137, 438845583, 45568966, 29475612, 987268394, 586037820, 435586939, 456298718, 265101688, 260834998, 730710313, 956080839, 224062281, 913514873, 434021772, 310618301, 882483530, 327172800, 639893474, 204374088, 565858727, 346561820, 360149806, 720564222, 414542613, 66472966, 514417483, 725505075, 478600973, 334118824, 464482303, 727758198, 689537599, 723966733, 77454541, 657551495, 956107277, 6295325, 353281895, 981907516, 116408947, 606060770, 63610337, 303087506, 549983077, 419046963, 984910079, 243019387, 116876193, 323337563, 779448524, 533369055, 597761039, 597972072, 693875295, 408640400, 617348555, 741674964, 254991648, 289593634, 814737830, 152234064, 650450656, 23181074, 915226336, 935117294, 539747325, 201905642, 717059187, 607899575, 329939355, 574188215, 289216694, 855591142, 427899908, 866542314, 767422084, 224607672, 125306368, 82186962, 619642094, 938321792, 61581316, 164782343, 750213540, 684971629, 956866963, 382532184, 673250885, 148278326, 743630773, 830364254, 984222815, 605845071, 924053307, 622711981, 595619911, 486401452, 71432297, 636902452, 667956724, 18811314, 993771866, 131431310, 678884671, 700975385, 331180144, 429535911, 319629297, 359955375, 972375856, 463184611, 659526791, 360002753, 781619151, 279206919, 861877164, 249386135, 3070333, 167327109, 690894435, 861168495, 419604354, 246366603, 382211318, 969741646, 184129968, 39490442, 813511053, 99225008, 525174877, 354058876, 358353524, 847693741, 814807804, 100517671, 202038147, 585468873, 250303672, 431045354, 346386261, 85652230, 955824098, 780285507, 682184598, 539214504, 404336384, 885957687, 565379664, 967301944, 511179663, 729715650, 315177418, 132255592, 126227538, 181233041, 705329576, 634491239, 819250788, 462865472, 258152635, 513606195, 475280783, 525847644, 161050800, 911805114, 341241120, 711139408, 430192438, 441010440, 565931565, 977666241, 826261931, 576698811, 531547485, 261104656, 981782130, 842530280, 373162673, 636454622, 51589477, 823049044, 89054369, 493686037, 332879562, 520834668, 371909388, 850389966, 923640431, 757541760, 135679283, 392234944, 536827947, 190504329, 843090479, 845944560, 563376799, 573358862, 437298562, 9307981, 582526635, 625561967, 158970823, 927082850, 423083079, 952398206, 126540039, 55138091, 967012788, 633740314, 565322336, 229149106, 463146034, 883439486, 971555795, 361717520, 898707045, 502603990, 743756044, 992939379, 231132357, 927042323, 881659319, 832902784, 852421844, 770391256, 975075528, 416251245, 128679930, 525889119, 40354257, 514749085, 615769517, 581079872, 792549824, 983336057, 455111282, 30914513, 868771253, 882030438, 387257911, 202885532, 575424955, 995800549, 707723934, 812663760, 68478673, 478410914, 669363158, 215975086, 949403560, 554833097, 854895422, 263780891, 560662246, 303116133, 475252760, 704677356, 788694958, 240857356, 776373008, 578433274, 117224597, 442108102, 562438297, 833963086, 302033123, 824570021, 65190046, 377227499, 316336696, 713781686, 522678144, 508622027, 578657967, 891957411, 625457334, 121104903, 444447013, 443790216, 674385704, 553420392, 288209085, 304582613, 942719267, 903479842, 278898730, 243377127, 966164683, 536597033, 987608491, 620825198, 284430250, 915929529, 443955004, 909429503, 417351887, 936170901, 647112580, 913301031, 316864999, 932135605, 89843234, 592506694, 376973493, 657351493, 371380900, 415606255, 955988404, 966928312, 242661039, 810081577, 523056781, 881985887, 357046582, 514557568, 709299051, 294324329, 616274734, 143029664, 989146572, 465829681, 266810563, 187644780, 781372288, 335605867, 822970529, 259770664, 711195571, 233928893, 444085180, 426570345, 14296866, 359641851, 78391951, 892529329, 851281903, 288973898, 579990399, 569585281, 146419219, 576609368, 443071780, 546048894, 336816337, 305902204, 367137343, 525238186, 177776031, 725275296, 979826203, 344412003, 738277355, 232170222, 134428313, 221840273, 771886530, 245845888, 94714270, 546463098, 244292867, 842705232, 651934762, 76311951, 962611005, 729997532, 469092927, 974853696, 593163802, 921016953, 198673732, 360848035, 235408990, 730141831, 160406584, 125169243, 612740819, 368556106, 342804180, 123035813, 724429919, 948059007, 823315644, 680321175, 195772746, 862048414, 681684314, 903357387, 665755608, 96888696, 731874685, 631027528, 956737245, 915339214, 245743475, 848987093, 892398409, 877074470, 278850490, 139253974, 164129567, 981377497, 433871533, 659256456, 375229121, 540526621, 442646956, 405065909, 105659001, 754429583, 950748788, 864784065, 245810663, 824733474, 608184384, 282320981, 617422971, 682146148, 382432757, 576836819, 189354322, 878692539, 623991255, 432333702, 891673447, 10897034, 220360957, 489023188, 852598301, 641239053, 155979647, 604409269, 975739403, 353082345, 377373000, 874251501, 943316702, 884378788, 374509006, 281885384, 306188877, 503061046, 211389635, 494594683, 931871575, 95416770, 34408679, 402298938, 111363108, 32025397, 713884978, 525025664, 79553205, 960124263, 444061203, 570052480, 304622345, 75055383, 627860589, 444547414, 637831541, 584236382, 240560424, 117912673, 170695770, 364536846, 723172397, 624060754, 689019021, 381766254, 517513714, 541526102, 892958824, 147494932, 444915026, 899359037, 582586036, 189788537, 352616677, 20489823, 953090458, 558178434, 733275898, 762374626, 416515418, 431321869, 458875134, 690538068, 8648067, 37028738, 145043554, 436741631, 51245250, 14789642, 847252928, 156356007, 527862890, 707915394, 74316324, 470158843, 145177795, 202494917, 447354238, 493044052, 828264724, 245301569, 599343987, 203164598, 847557639, 616010461, 301283399, 136535169, 804930707, 757219436, 992108370, 538278151, 881083074, 477944783, 635771300, 841548978, 312713474, 358535469, 274498933, 951461747, 662193718, 521120156, 467882528, 263682188, 371515499, 763218957, 912424737, 967210194, 909521224, 329228538, 434244315, 572788548, 468711136, 252114318, 343559688, 342461465, 460513809, 971196458, 377214365, 675550211, 584271744, 357018694, 158373314, 741735871, 981033401, 384335804, 766056599, 14021661, 304567409, 337554110, 491117801, 919621072, 912604250, 593585361, 368362829, 528731991, 761799429, 408073755, 543616562, 891539665, 17785959, 12463808, 13300388, 356349463, 142759289, 282335667, 869098568, 777672230, 490007366, 294554609, 105943434, 453478901, 516755913, 719187933, 378234200, 18782494, 817187777, 483524465, 528463777, 628596702, 74724703, 732162916, 644626873, 378170574, 314405301, 305069446, 195062825, 30223453, 699001705, 30822599, 175167381, 896090378, 211334006, 365633175, 156253805, 944725794, 942780334, 684602018, 885294439, 811495525, 965301302, 134816728, 966604717, 749904645, 405027770, 379897130, 835928612, 226257727, 531746727, 391528288, 188865985, 285422771, 172274353, 237436520, 448204586, 793587462, 218149195, 538864460, 554479122, 289261052, 332053278, 750932963, 86972347, 190936595, 556408446, 664037552, 421352561, 564689419, 851646167, 350818562, 701582095, 125177861, 876347778, 981157855, 368080521, 254502687, 560175605, 496320217, 57461457, 804707584, 16887754, 803101902, 128065017, 551717624, 274830237, 322504587, 180639667, 171245864, 417203477, 460548904, 64720550, 570377700, 10508279, 155701433, 671601657, 865522912, 762154392, 743517454, 175816921, 447929738, 645606783, 964195544, 801242992, 129475563, 979200241, 379873116, 941396826, 704810924, 451104261, 649451312, 214029070, 438491334, 632250010, 246966622, 990882517, 3449075, 303536806, 422847702, 406541822, 459783042, 470718796, 834437445, 208221097, 280441453, 73324905, 212185978, 886709767, 340783865, 54495309, 428902720, 824730867, 221181047, 108858236, 94126211, 816166461, 379899925, 616985583, 49766810, 764488960, 117297407, 175990918, 327156531, 234846935, 972102773, 400076901, 760961268, 49486519, 893741275, 643266138, 654374380, 254149454, 373515215, 535202204, 852290759, 513441832, 784763054, 721245647, 503256135, 625051810, 435123393, 637982746, 906816053, 28177261, 169919786, 27690896, 599082772, 867113935, 575889677, 956485729, 219570552, 404083094, 209374498, 368832308, 267342673, 302361922, 467059712, 712311481, 144388676, 894861016, 828892075, 286552865, 208440526, 517094696, 503679020, 37256279, 362739566, 840216996, 480601805, 859553341, 51063888, 256563412, 110371306, 765814994, 87559534, 582337179, 562039020, 260052466, 16499979, 745223868, 920892494, 250885336, 545269244, 440266649, 893695868, 951883859, 147266684, 779782315, 397912711, 760459251, 697078058, 539893038, 515374968, 198259905, 47839861, 783966723, 94446139, 239965329, 190786887, 151064081, 817339115, 65338706, 592275633, 422747827, 232381656, 420160494, 231708459, 390649508, 383574248, 771749577, 424358621, 636937649, 968960394, 801233233, 475733934, 89617372, 758262130, 814510983, 39319404, 45979537, 679346942, 196921034, 734918173, 53944988, 724615428, 69548267, 828494252, 515149581, 126038013, 914694741, 499303710, 603277485, 26658685, 637852223, 674578927, 966158942, 983538432, 26955867, 900129594, 326654183, 186206052, 332091238, 607471278, 881678525, 321259812, 367975616, 656068913, 971288793, 885735878, 115525850, 42769539, 326949118, 177866981, 141326573, 789505129, 682992352, 386681065, 181746718, 313993679, 202031035, 925397187, 331354707, 178178719, 671627709, 390364568, 837380130, 633537322, 435070116, 539695768, 281382724, 52747764, 890377605, 814089749, 737646629, 557162069, 116483274, 706708210, 452959464, 836495551, 223943844, 619383489, 343377621, 592564338, 353396647, 273546855, 836624851, 676259226, 124711716, 186186819, 410118528, 255942419, 483761883, 908546312, 2724675, 799117495, 248187163, 62783072, 742417385, 470079985, 458855717, 798544054, 616308335, 48574972, 343570771, 505952433, 360823071, 273163265, 472798200, 340209615, 512696721, 345327477, 612930373, 874753406, 897716811, 743306736, 362858925, 639304060, 724243499, 713566172, 850079115, 698913146, 44084772, 466992474, 482743491, 26444216, 760324660, 784139066, 134468601, 722800509, 491599507, 716497796, 833119747, 884873413, 362461914, 630109627, 47885764, 98604090, 168579368, 517980212, 609513886, 153587888, 452836115, 192145221, 725743962, 946098605, 593127805, 266009304, 564223355, 148085103, 266979923, 980482473, 798847077, 309166579, 417447806, 208170218, 472333519, 342131880, 871904554, 608401809, 126764964, 455246243, 235969360, 644088121, 946959714, 480100177, 708734120, 588136923, 62687224, 142949600, 454444322, 768490829, 462895920, 909263154, 779591959, 806163192, 196817499, 998753993, 68609368, 805878485, 809945851, 705823810, 909930410, 774669347, 584932467, 508638445, 891706950, 920780414, 771188614, 777432078, 904574374, 409903515, 870771240, 728513469, 931928037, 359086704, 457720230, 849943289, 579039493, 965691734, 668749175, 255544773, 61120925, 567494906, 828386524, 364424300, 285637312, 61610016, 676389794, 758484480, 145100607, 559152899, 951474740, 861391596, 852179806, 773370830, 40895845, 968896858, 472489412, 182718757, 809089790, 522288056, 937010430, 123967769, 607540452, 285100782, 54755643, 916506133, 38289914, 347244656, 649657973, 854368642, 795075491, 161041242, 64148016, 327910306, 870613856, 915467279, 921242224, 231659150, 797398648, 68603334, 130982655, 202578549, 742855221, 601140100, 597193341, 269946797, 952109403, 592680272, 580216153, 671197166, 564248074, 331127303, 642287246, 589146255, 885580168, 823130767, 217941474, 796819834, 779011409, 561638626, 243966082, 744189237, 688094466, 428960960, 45011673, 478627505, 36129663, 158899647, 163701221, 219169053, 142154058, 768065091, 374124630, 88272778, 740793580, 284263064, 958346620, 870937357, 787291814, 635207812, 721343666, 390304655, 317603844, 256862508, 991229943, 912127497, 731688216, 808210838, 545167637, 692400085, 468107270, 597351794, 658947977, 775592111, 838278928, 460381893, 651908624, 517331936, 238150839, 776368632, 146897855, 952257335, 845198064, 327138002, 410451244, 774412219, 850780144, 534064120, 380965285, 645627345, 238011523, 702985337, 742021619, 299142231, 246007308, 749212682, 844246701, 387422121, 794447815, 667602389, 852387406, 163321670, 769893167, 795851546, 704372637, 278011014, 43955244, 294265123, 483215957, 46235550, 334725948, 22365999, 715578551, 338881964, 951262382, 96366964, 959845221, 844665941, 622119607, 283875773, 74875276, 608337449, 266623965, 422544853, 10952348, 764556013, 925744306, 619329417, 757032480, 699092424, 772900140, 966954666, 287833672, 868284344, 557555501, 976109080, 621221562, 905172146, 639424613, 319404840, 888159598, 418500758, 693775740, 639530484, 944979649, 563958570, 217386922, 39862842, 761330410, 503945272, 570161000, 695089673, 30740728, 278624871, 88270775, 483134928, 486857870, 884552920, 568494182, 248807789, 601487087, 582223622, 167941423, 9218579, 452894027, 817359050, 54591287, 316023414, 63083096, 381424510, 936851845, 419582262, 162404383, 318670106, 15534859, 926273729, 970305950, 548447825, 647586811, 179894291, 45055020, 339107947, 776280040, 107645675, 947781479, 442904169, 43306851, 942613031, 763953661, 296823121, 192194387, 245639039, 213514908, 254096747, 993376413, 952023783, 745936531, 221679087, 33647832, 467179473, 728077684, 581405692, 476457077, 59986855, 616379095, 376438648, 823064559, 703088427, 370077528, 442600886, 464032606, 382723310, 728896903, 252519780, 139329292, 376465932, 956551445, 784788137, 803292693, 279035038, 925273656, 559930240, 533960670, 663002657, 54584760, 883766910, 641780146, 51007038, 467107563, 458725069, 561949572, 524779948, 578031360, 957085129, 871802710, 127658864, 234328485, 922738752, 101951399, 651425087, 749720624, 424741601, 355723549, 431313903, 870455334, 633524731, 45057909, 217078659, 294059190, 297021478, 144021083, 696766307, 47447300, 231246448, 744118610, 949830900, 113138157, 940817900, 736084445, 153899645, 588353193, 527466035, 659593192, 518173168, 131599213, 704094381, 274511088, 186360583, 772690270, 734485421, 296136170, 96817284, 602659912, 588826692, 164674844, 186577083, 92344685, 255548587, 665189503, 758274205, 510505112, 944288702, 435241944, 432060107, 350508422, 360655281, 413544600, 240221017, 968648567, 203202308, 183998942, 937676053, 926208019, 254115414, 130798127, 528433206, 784444910, 42105414, 636174030, 168883551, 917103962, 148355802, 155482177, 416261069, 230409799, 749588782, 568599426, 568224799, 143614401, 607488503, 867416743, 375578064, 505290520, 925837691, 700122916, 625936267, 691955435, 746545602, 579294152, 554026971, 154732769, 218171458, 265359447, 937052389, 909089846, 240079828, 341009208, 18705302, 731072717, 873218417, 995140838, 267786750, 138364649, 574093734, 955509013, 317899042, 574720974, 78566825, 790259229, 570681092, 585889337, 948354931, 788206070, 81728845, 865220469, 368167574, 421123299, 512357736, 25156464, 194913820, 135975097, 620997533, 25202035, 7823296, 202547659, 820527438, 964501698, 373127769, 162564072, 890598272, 331729195, 861638166, 515497255, 21064547, 577982518, 627357212, 839076221, 674422585, 414318359, 738004189, 965629440, 831771012, 509605714, 826783985, 210958570, 696228377, 450123956, 419649402, 604032036, 822618128, 16048273, 335632450, 222330511, 769496371, 807302343, 702933791, 536849336, 803393574, 77673253, 457456916, 67152317, 573623030, 754515057, 198093248, 749605345, 336025800, 340129603, 301259640, 527712022, 938117093, 301376889, 219607024, 140170699, 752694261, 91476285, 41099637, 794954543, 61132478, 568086812, 370602087, 917008903, 817446106, 277485789, 176420045, 664204283, 541994719, 817715012, 938836326, 472562985, 56110483, 121150515, 48388444, 110888606, 957924675, 583672306, 3953360, 52409663, 564828429, 493686121, 606814030, 864514901, 435403154, 551160039, 245537754, 774052181, 276233480, 847092754, 146491055, 699822710, 975032935, 607086047, 385455330, 787484020, 630082845, 911658452, 378857330, 769141631, 331491189, 841461494, 262782023, 401716294, 687610648, 426297672, 370125003, 492253973, 334705960, 197665428, 858544281, 191466983, 465609791, 87546880, 348764462, 615878490, 811219565, 165618979, 432233219, 33386178, 817311665, 767873221, 388927113, 463024387, 354424341, 5343536, 588646859, 748822856, 135191078, 813213201, 748841733, 245424888, 86359644, 801119148, 764127659, 634027188, 97482455, 434043885, 637161813, 479533689, 948499653, 138506704, 893054344, 566767675, 949691256, 387972496, 601599056, 800737784, 390243708, 637126290, 670615860, 944559450, 746137708, 125385095, 325997204, 357483099, 193803387, 800850347, 777770905, 172536316, 89215787, 264255271, 563869065, 207896443, 149061203, 290576202, 656829102, 819678497, 464278310, 996207681, 821706210, 496316066, 915823070, 339878011, 627001148, 452643442, 561948732, 46097629, 605819100, 126911098, 250739737, 916262376, 583226449, 297219579, 909984474, 447233609, 48629995, 373758364, 375564011, 824724995, 95566012, 383012598, 348057436, 887067817, 491300429, 219053970, 468954693, 614738547, 395130808, 787140031, 879352958, 123748246, 657428075, 515156111, 918178724, 302731319, 136386259, 124283119, 598912821, 873325009, 404564932, 740005071, 717961351, 816358355, 377830074, 771954375, 761962158, 293856600, 175451516, 84199311, 741796213, 44938988, 120346283, 666330673, 119978350, 989698162, 759870062, 515988954, 830961131, 932542995, 376369967, 186316886, 138275978, 906197351, 319995116, 911393021, 217603608, 449204254, 356174298, 481066132, 515513288, 906082827, 199035144, 195320946, 505693405, 372955203, 521589233, 479510719, 848361304, 463456086, 355331607, 4918264, 78085349, 564271635, 486384050, 232879244, 502315245, 955018261, 491033925, 577068909, 302298654, 415219484, 989557456, 344571368, 136569182, 348876764, 702957439, 110250006, 354162607, 670788313, 44477905, 898767892, 982851535, 357177096, 935685590, 315180531, 530133803, 492821316, 430347782, 197239777, 784728877, 267882049, 194076459, 65867589, 946529068, 386070684, 796204419, 577333956, 489097831, 893159858, 736464890, 223413632, 910048532, 168293167, 568828770, 700364664, 461383889, 272289955, 590170724, 215706101, 327627900, 125426651, 258339148, 301585457, 373781727, 14046268, 941475522, 708303192, 502390643, 898616136, 469046159, 169795741, 182245817, 993926138, 781526030, 855039458, 753768564, 816613527, 823146974, 975469029, 695678936, 158761149, 675505393, 576146784, 361558506, 761669896, 521038342, 666669389, 2296348, 712139617, 537175971, 506211590, 259034198, 756666996, 900963421, 358037521, 936602207, 340500107, 972454560, 264408545, 274784526, 33955534, 233067628, 722620942, 433721464, 375431275, 324626910, 293879004, 413264736, 690831981, 523685832, 321775502, 333976971, 155450462, 179949993, 315130240, 427191266, 658024817, 879403618, 673897623, 201430399, 973837807, 224868928, 952222172, 700610781, 314285878, 652855298, 610043573, 116925152, 68612240, 81170759, 36951945, 989526446, 61240926, 956881682, 645223222, 476182932, 511107961, 892965606, 62594578, 848547604, 363842382, 77714101, 314673249, 682148268, 911591328, 769452875, 431843094, 718367817, 367760804, 852609279, 766419695, 590250124, 916426437, 63530489, 576658246, 49860500, 458923469, 303913539, 622923169, 784480903, 413038245, 921662847, 451086286, 111462804, 150043257, 648524574, 939283964, 687100965, 746062562, 112626287, 218753725, 971723074, 741128026, 70364300, 45320356, 945437286, 657153219, 667974892, 571938536, 242651863, 394717870, 641622287, 350986683, 812079549, 378752707, 329285367, 357523390, 688578972, 522414345, 668913893, 649123711, 915122629, 831758404, 461352739, 295669542, 687499045, 725837289, 918229296, 918873818, 127105740, 35834430, 839513863, 96594368, 214053365, 405607992, 892965748, 673263155, 162387739, 419291444, 145310181, 781388651, 865870574, 804389713, 445974059, 981136545, 180570515, 911763473, 121300284, 99391895, 913603832, 112704569, 808430776, 994996047, 833486015, 572953484, 42021352, 267467291, 300526133, 939683235, 587692180, 250181069, 896835144, 77140211, 911361074, 21920424, 856214790, 701491668, 406566966, 66187036, 729745642, 612707103, 211072417, 135139627, 974569467, 681252121, 402542375, 578084775, 833454064, 949682391, 583160919, 197310066, 538521064, 487864774, 888383773, 156082149, 150972051, 750793480, 937351356, 426387780, 314590634, 8216575, 683792237, 297699318, 568222863, 63345912, 118615737, 498830698, 292659062, 730806387, 119997324, 408831790, 207934941, 643071290, 184573265, 28475771, 555892892, 351253997, 677894590, 697526406, 124412467, 928057183, 753653135, 686178168, 500941478, 271290393, 700932740, 421368029, 475791530, 697203195, 974644715, 160436099, 206692272, 145259901, 622805838, 422510463, 12188627, 16198218, 988198882, 128362197, 145289505, 780903514, 475662035, 172600752, 104366472, 822275625, 326806150, 615365423, 773945646, 458540342, 514668415, 358522251, 508697152, 929811081, 626332364, 281962096, 904254487, 78166371, 746106397, 687335086, 890291517, 368573382, 967490470, 458904665, 573001193, 519868832, 911728281, 186573801, 386232071, 787321051, 462807058, 526651904, 41660034, 248031820, 112438846, 744144030, 986509928, 662075362, 79586584, 964499786, 864303325, 551292904, 963998107, 190029977, 772948292, 522228681, 813374733, 71719638, 308914921, 668916578, 653546910, 559276657, 632316841, 882901305, 270367716, 282951411, 826646455, 942535491, 476331610, 327754633, 729076391, 930984025, 555355974, 855975441, 475210104, 692217824, 892422824, 850786487, 557814008, 399609757, 64959409, 396649778, 136474560, 161332977, 754827589, 622609581, 276025941, 65466436, 138261133, 117215505, 607115202, 590363885, 653408346, 52802136, 957264966, 258040897, 566519023, 580304322, 10335991, 371945754, 365509434, 748790577, 684004718, 524412326, 598754374, 123818790, 935693380, 175679316, 215674127, 6738842, 842394487, 306252391, 363488791, 123066828, 147642685, 534866857, 428258996, 489459729, 521356539, 989744087, 726767421, 698238777, 852125210, 947129854, 425666625, 161922317, 858300424, 598720148, 118470507, 852841937, 468048568, 784375891, 175364940, 924251826, 29992293, 24910042, 990656184, 631067395, 99988101, 847957883, 902996089, 11764817, 615439038, 324402793, 990051505, 765438475, 629816571, 375643160, 805277225, 338426777, 606565969, 338138492, 502349743, 105225670, 676031620, 328684944, 417016894, 285602023, 923666815, 571572702, 330420314, 59476777, 839800992, 564836345, 485793866, 881642474, 679707185, 801177864, 408977869, 570913911, 917954196, 639330278, 572087971, 10333980, 938051024, 424380859, 833878560, 357829269, 251821921, 183770602, 529798001, 104379987, 226168597, 40411549, 432032002, 763416444, 707940726, 691374166, 820402200, 399541024, 962527762, 945653206, 818992948, 796868903, 426273017, 728939052, 414561213, 536572956, 953857079, 444165267, 205790863, 867390193, 774209570, 509221881, 375707712, 39643668, 622878614, 815830521, 598928038, 986435113, 974206125, 840773552, 864516329, 677586328, 465537121, 643829714, 230572623, 522685102, 519331144, 209818061, 459387757, 757438623, 966892423, 788425304, 895630100, 824311152, 995251369, 329779428, 617015717, 102654268, 417927875, 896802862, 641431017, 379294383, 335937826, 148374753, 436266820, 379287077, 510760350, 568686376, 118103574, 945708157, 805190400, 40309812, 898694155, 427978203, 93081523, 162466438, 54297035, 825251586, 423182996, 311713812, 533787664, 952021997, 579038926, 855681784, 770282832, 456025949, 172938049, 950526623, 442508772, 358107124, 605999501, 941494810, 127904897, 75392752, 246116887, 441711953, 467678019, 592806405, 27674535, 884838527, 886989877, 147442637, 351061720, 36889897, 67676779, 51272478, 453032560, 457644833, 299095311, 747737642, 573016029, 143377211, 700931155, 207818163, 660734266, 805560655, 555143462, 873883278, 452128706, 653154774, 821367259, 596657974, 135307882, 337361170, 666915952, 447622356, 374977428, 743321519, 970004528, 269634810, 935277706, 969318252, 642760626, 508064792, 949930788, 285238058, 770436512, 603541879, 149094351, 436236613, 379634108, 824078414, 624141856, 753148467, 354127677, 640885088, 171046933, 867542871, 308787920, 219946032, 688468327, 607961916, 790392766, 611131405, 428330178, 614857112, 242931402, 26836946, 722777570, 67853966, 223657821, 20740846, 38531329, 688686042, 838728628, 978534544, 792947738, 236975098, 28668997, 564237671, 90583692, 739961714, 619917399, 620680933, 307409430, 621631353, 102592029, 993460527, 508427584, 449607245, 827738640, 339847129, 605226611, 331677566, 33054163, 325080206, 834832849, 15682894, 639162835, 188617832, 727312662, 493406230, 390378574, 273368975, 871732281, 757670024, 759599604, 29200750, 551986959, 537325719, 122843660, 68074145, 680680316, 357141218, 449854643, 359341306, 333446533, 996180319, 170567794, 500722659, 445245499, 824778185, 374386641, 984788932, 86820374, 683338899, 566319515, 343835049, 830974111, 288812046, 218672356, 543509629, 809446764, 214026963, 82366259, 342779626, 232758894, 578414295, 870711989, 697995267, 209641959, 528880200, 803859590, 404116109, 201268756, 938923501, 719175799, 410341797, 114643743, 882321687, 165414789, 806550864, 466953754, 67481203, 440387475, 786640258, 27415676, 923406068, 753273185, 223742431, 411213840, 260760603, 471966390, 444599629, 466781690, 767300955, 355910668, 792716266, 179518929, 918282048, 192446855, 365872508, 93700544, 799453966, 283356288, 450687688, 782267910, 106305567, 860505301, 637399301, 188441210, 214065824, 353253006, 411945359, 985888357, 968772893, 652351261, 618953682, 64090842, 35844702, 902133683, 960912733, 139681347, 257863742, 27437014, 964534349, 849875472, 925536835, 310699357, 467146675, 457849487, 784711740, 240835612, 948131168, 926824594, 326467828, 855262527, 207057335, 286188711, 22086600, 810093320, 617866127, 964951771, 627238789, 367375100, 695389843, 775994963, 588620995, 279905415, 909799029, 167949841, 360390817, 333527163, 391055604, 232982181, 666108926, 806803851, 701722940, 481372161, 600380283, 533489459, 391402585, 225044508, 738626619, 606773630, 670949685, 631535462, 349227617, 629047813, 247484406, 133392409, 135215431, 566583155, 485214767, 484537115, 288918330, 41115344, 271088385, 151960450, 699362081, 577788816, 536526000, 111250629, 460387930, 505343533, 625275749, 667927464, 552176395, 833501802, 281986254, 340029015, 802070206, 747105334, 508847069, 276515256, 985736530, 874331458, 808672696, 818356458, 254191407, 673844138, 609234273, 670181379, 467876388, 327707934, 472040275, 665402656, 673321966, 325263443, 520865824, 268842549, 138655544, 149020479, 504791579, 125750048, 606530238, 100575623, 895551543, 52941724, 524346076, 932709431, 301681401, 969603905, 375027608, 525161648, 77915422, 182924312, 135296390, 85142810, 16366199, 114277848, 828424866, 85739994, 584365183, 207491335, 222460944, 932084581, 725732077, 506148608, 237055485, 589610937, 550943260, 749988162, 87269749, 874209793, 431799007, 753847401, 6975332, 466684927, 492994380, 46084529, 682166151, 459809803, 987776174, 383003067, 794535874, 447037141, 335752565, 203435223, 275986344, 149094188, 233775029, 752520933, 770783240, 127695622, 825204445, 947384976, 818140775, 281127390, 747391367, 942876091, 583879272, 574502384, 333214308, 198617479, 215065707, 269613306, 817559469, 767910962, 503420116, 83703152, 773271648, 290987571, 740727822, 234879448, 184668034, 20254837, 621480945, 466278384, 472613928, 271900277, 688538371, 914608786, 825082107, 427742920, 526438119, 766112088, 912519004, 742699609, 88917323, 126007890, 784064095, 876935439, 950442737, 364025045, 200652563, 507095265, 438130238, 405789262, 670217923, 904683373, 185232805, 139213367, 389017840, 53234832, 811676013, 771820178, 428468537, 188100373, 407803760, 243840967, 90284203, 679746942, 745024563, 332662252, 188904750, 213152660, 911794663, 710420947, 281902787, 63696994, 731063605, 800980286, 380124483, 177602181, 925134048, 303511680, 110275223, 545662874, 206293935, 197533931, 174727522, 916957476, 77126241, 916586814, 156294255, 879737498, 828688687, 786696730, 805089627, 850563220, 750952998, 438816223, 947401224, 894473977, 973574655, 1821882, 740727245, 927039898, 917036732, 285408621, 207544742, 271864416, 631969100, 976068915, 145161683, 842460960, 198982297, 390360167, 535853485, 783487362, 628960174, 573320222, 181961720, 700972885, 789897092, 757096405, 569775828, 363536568, 341919138, 735712358, 15763299, 600805432, 469065646, 502885563, 656347417, 654542793, 896709970, 196220779, 737330008, 832492018, 850459484, 131011066, 104098871, 857097471, 621982256, 815990167, 585388278, 731527529, 993706567, 81754584, 108856041, 350852164, 285265025, 313818850, 143266653, 89330941, 155599094, 792080222, 905695062, 875581756, 869805490, 322186971, 734231402, 555141035, 624032321, 291829966, 359304967, 578958028, 142811716, 484449197, 282878200, 90999390, 903277208, 255843378, 712442038, 94224367, 615059896, 386735401, 922505716, 694022020, 346738659, 428754274, 502300047, 807132905, 128118011, 843006865, 14170219, 644032106, 688238289, 416772751, 591587883, 702381014, 261988356, 918663401, 47261136, 992090640, 717056182, 337167319, 686164388, 612177093, 318537751, 269086366, 941598113, 543489540, 483164106, 726026505, 468359590, 560526753, 852311563, 887342796, 156932431, 58268134, 546077782, 21959294, 637297353, 246467320, 23374849, 259512393, 831867035, 88435783, 449833293, 922197669, 943007717, 833196230, 104145749, 286967691, 990405354, 160360704, 149246512, 681944234, 289423618, 565667894, 900077987, 846562897, 683220679, 978595184, 519465208, 943141150, 350202949, 648820927, 628741379, 345651752, 477797469, 321435399, 451534962, 545601021, 697236950, 748229736, 994351087, 63207022, 630595367, 569794795, 396587638, 520101306, 72471699, 768985017, 862184252, 237921561, 982446608, 723878013, 206625125, 221263950, 425642094, 798373680, 971675076, 669135419, 47412304, 980173909, 381268319, 105062702, 594608047, 572298830, 820305862, 995639309, 942771489, 562743505, 93546169, 782187283, 920168783, 686753160, 288615587, 607756904, 95182756, 259883842, 113569791, 861547199, 872948182, 116361044, 223843089, 714316951, 490894612, 335992403, 39310087, 777184195, 632443405, 49037710, 706276392, 821569156, 858631065, 628417077, 998790745, 303750443, 961325303, 54703623, 996779582, 186479054, 264089462, 392650176, 565394014, 183732583, 498292222, 447918554, 189461856, 672418501, 533076983, 368534227, 913768633, 888131061, 117970551, 432037347, 414222733, 491016211, 868820602, 187945649, 542382294, 560359943, 354677353, 878835567, 248509698, 624800168, 474982537, 461343969, 448341618, 541189664, 76142536, 271590613, 981782164, 715842392, 165551443, 299721544, 177461178, 533719354, 901943242, 836655122, 983476421, 170204453, 188221760, 688561941, 113873538, 260738727, 952846469, 7247506, 25911782, 776260810, 504445418, 210774563, 646624562, 784983497, 289940824, 347160435, 755739447, 559445612, 690149874, 233601073, 364574555, 416914957, 764755821, 631156002, 488276315, 508291912, 948451942, 776168546, 429790308, 898515210, 190950063, 811582993, 406983724, 191684693, 850115709, 141218979, 374790808, 893410758, 982194600, 770514969, 886148978, 441532174, 213661372, 240787570, 816124176, 715102862, 748580364, 324147094, 478884214, 246592737, 992818111, 124264814, 564051287, 80726820, 900514667, 341693090, 118731142, 75257581, 103678401, 756446712, 859964191, 852438443, 108240808, 147315310, 24639857, 546488546, 921749675, 883375449, 524735959, 166100887, 693771178, 709017720, 306289208, 83060713, 902554576, 587830595, 885705941, 409631255, 472464971, 958273769, 219400929, 327958661, 113904589, 768979708, 225103401, 341158312, 920018106, 944197557, 915817375, 311101718, 926851079, 491645059, 921556333, 537518761, 858662260, 687185469, 173283030, 567084637, 994174836, 716237467, 626974711, 758109537, 885874542, 964927887, 264732422, 68845730, 406532496, 65397079, 562710760, 563441859, 673410870, 765321137, 622899228, 158058287, 669352052, 976269632, 892294568, 508555186, 22759884, 408932722, 139313003, 227767516, 118589305, 929606438, 879051315, 410074092, 726280985, 920671171, 680047622, 335932464, 905513264, 305153839, 738853089, 8306526, 843652841, 399344083, 601611702, 458797884, 203721120, 10527418, 387063688, 797921802, 967750617, 453704250, 331999595, 172485543, 900672878, 48376961, 32616105, 829942312, 67143741, 227638853, 752251979, 518526114, 186644495, 875441304, 998613814, 782451946, 96753420, 306963561, 189032651, 806408307, 515808681, 184540869, 796691719, 108187869, 188935733, 263544061, 958251375, 700199824, 451939968, 342812545, 218936647, 18996645, 335411967, 530783917, 7953460, 915566086, 162277146, 734824212, 320076422, 405360168, 826348538, 802241018, 739291410, 349951687, 654024629, 71862895, 860136754, 269597298, 445613090, 320975855, 323466544, 751000726, 803218918, 744244251, 113959723, 675833747, 89931355, 283549153, 707561525, 303009284, 38924974, 38017772, 329966058, 184629398, 879005811, 652095698, 402642427, 383463653, 25028667, 571940285, 922024715, 709973843, 262414501, 839423684, 827556628, 716975880, 258414711, 288670785, 47718313, 585862143, 442265716, 118328844, 621751696, 933912078, 998928551, 912909771, 406050430, 303049832, 897831697, 199279363, 625753213, 543404577, 447432768, 859297103, 663549297, 7612463, 908310485, 853220290, 87136308, 294767797, 880056634, 302536591, 181019244, 186391746, 870409910, 955869386, 643684710, 933710487, 977537427, 946359425, 235459918, 226303626, 466476730, 440906620, 753932951, 59941605, 486251805, 613577598, 488731821, 396126133, 697179989, 348230648, 235986402, 492395956, 694627455, 592155741, 281906476, 686114258, 326068897, 317199846, 20862752, 457189676, 493120563, 451317616, 227027351, 17957470, 612822670, 789541097, 558074648, 27394851, 569128276, 985075207, 503287045, 988155325, 153796406, 640430102, 458657333, 952168480, 305133332, 315028144, 239569980, 229580392, 992971229, 106952404, 68832988, 437727637, 523280975, 547062665, 598726829, 211479536, 207755683, 999768736, 182856420, 978011905, 418167324, 80407929, 370730591, 427825612, 999212539, 376028780, 617849377, 969808956, 250841853, 957233388, 909028859, 3512424, 178276627, 731993970, 705719210, 837692871, 679425012, 820144878, 252593472, 82884108, 718502321, 262979531, 705199, 114591985, 181957481, 848668279, 553778458, 392733217, 786985350, 34150422, 708989429, 949853540, 936403306, 125951369, 133809031, 723208445, 56490004, 789977116, 818923800, 622110457, 231228758, 572449239, 481868620, 970842913, 681771643, 876567288, 77505646, 28797574, 294559853, 961195639, 869001666, 16428639, 525548307, 903121510, 20439296, 948694322, 375233505, 981112333, 112562223, 860218457, 530619011, 169530658, 64662830, 883595315, 753557270, 996492515, 437884715, 265010456, 821232505, 508152960, 258000335, 821632588, 932282627, 20032703, 7498294, 329415501, 371367855, 444082085, 54505381, 255163940, 550776408, 714748175, 856227446, 196247181, 210249548, 740857574, 983249612, 753223637, 251319135, 885050004, 915672179, 146194744, 349016120, 913472124, 270479893, 294755916, 426457831, 345262120, 792935883, 22817977, 856884646, 430863218, 253305120, 321741346, 816585079, 31806740, 435513092, 418378869, 717423312, 582356980, 990436782, 720542965, 92160562, 680590103, 489437333, 401133533, 849326098, 766999296, 435824914, 485999317, 220650446, 191863717, 796315395, 326584896, 345828022, 292703980, 588725105, 176343493, 538005313, 567287080, 677248914, 666877413, 59187162, 820358872, 933169372, 499241269, 312213348, 187704129, 393825020, 330866037, 41016290, 927621535, 161891000, 763765203, 942493249, 739202696, 737932513, 810703566, 299714178, 259584335, 885124164, 295476898, 234267158, 271281120, 387741062, 94127009, 497230445, 226309687, 669689181, 581100341, 529515117, 6444703, 676177816, 908977101, 564824142, 968706083, 706601855, 950683716, 762657022, 403295810, 627033063, 415726994, 650265835, 866792930, 41643853, 93141809, 665205369, 370546855, 674202300, 248115657, 640179574, 274553271, 806743936, 645332320, 140294780, 63074325, 377107112, 635317311, 878332198, 492627195, 825750153, 877103549, 613591787, 523338565, 746695793, 215548417, 491620750, 334232287, 890469351, 650654749, 697012539, 83693389, 144166469, 124564284, 796571428, 672760574, 145811794, 695743898, 279811349, 374089302, 71697581, 365820918, 684856971, 420138727, 369374052, 148525506, 72695697, 482383291, 275137903, 274532207, 89810238, 799033494, 489321969, 189888376, 686158621, 520031912, 411501203, 657148001, 245618525, 764475955, 37441626, 324281059, 655398898, 269352981, 223305500, 308628004, 385064375, 360667926, 75372312, 709245553, 503919777, 275379198, 105147184, 889958843, 301712565, 72292919, 24195891, 561564237, 879575322, 720812878, 628360884, 709986913, 924484430, 347891287, 127465043, 945942465, 756534169, 721175096, 588804932, 101473680, 713158916, 790037289, 868589502, 414626419, 325470883, 694852826, 842646262, 383329000, 858650234, 883846853, 869274476, 735586011, 992039307, 310073966, 175249708, 345701478, 50132119, 257531278, 292903856, 420697418, 948524835, 401260766, 983839534, 661144073, 328146567, 84973786, 821500818, 184015354, 713787436, 619160134, 214921303, 459694404, 314226263, 397385583, 91730753, 582443720, 270531744, 484918034, 971231840, 450051272, 335011654, 518933055, 121377587, 859970344, 950420718, 526706587, 758209127, 236792329, 284716818, 171597606, 739842348, 332919055, 36073955, 262991089, 647674609, 248953797, 700894709, 187861896, 478773110, 959650261, 266785333, 790948325, 411181442, 920722749, 462809164, 253683567, 732591860, 7026141, 601887622, 700939119, 212563771, 339374773, 164636366, 252000855, 562518515, 463834208, 389870172, 605506987, 265663135, 7880844, 334492966, 268005227, 646517178, 474334489, 371475586, 126526312, 680542163, 873540599, 349633259, 137063058, 689207005, 160777620, 8071042, 714826698, 47799409, 67179678, 289806847, 505971987, 918297115, 410503927, 77567109, 279767686, 192862760, 25437643, 280849080, 346142934, 951939476, 135188062, 451577891, 735099198, 566052413, 353957529, 733906574, 269015026, 830867540, 77904789, 418543201, 458507268, 515201248, 882623715, 399137605, 31264889, 402737766, 138545072, 336493814, 174809954, 716667071, 74508933, 433746361, 332712854, 904186631, 88626729, 381781450, 75826386, 393910245, 972277877, 535733926, 266535708, 864395890, 302124744, 724219200, 72505555, 90767624, 669948716, 49835725, 896420462, 442073419, 158180177, 49989738, 626509109, 668378130, 71869334, 495512594, 752482618, 729253529, 356545538, 22707911, 163728485, 913212544, 188159759, 102681306, 437287653, 544086724, 997149324, 291711505, 893827368, 27300496, 689142000, 306717017, 895911092, 714292319, 41713045, 594268547, 344986609, 766421214, 822173722, 336986884, 965852949, 430436729, 871452, 686482800, 303564299, 56111720, 852055078, 357909599, 878065037, 417157265, 219216404, 659711500, 222988189, 414796901, 349159689, 476374607, 394494363, 809222410, 878379381, 776903861, 816939973, 529550013, 469614781, 789792290, 332667132, 186984350, 6747342, 312480381, 865311553, 808651859, 880921263, 183876475, 1618771, 66000396, 548700578, 572461757, 380659300, 121030884, 167733249, 683769915, 210471403, 145705225, 634941934, 671825992, 929880333, 351448147, 412922342, 495167106, 980058649, 500491515, 835918469, 553037376, 838645435, 351107810, 163011351, 908831344, 742058712, 82528057, 859414436, 681927870, 158840354, 497284944, 562152498, 709551843, 161959288, 193754086, 210247966, 277402491, 400111933, 923434485, 22611703, 441593155, 378455207, 907865187, 768563023, 306573000, 192956864, 239820851, 887090311, 796925469, 506964525, 367021157, 968239637, 181934766, 746841179, 501838082, 825547789, 481416325, 22511981, 82350827, 276921457, 345205635, 492886618, 394912940, 342035839, 952805167, 756662665, 812283691, 766825489, 602351236, 974470537, 18049765, 754249974, 83764809, 796824208, 433094940, 978385593, 833798962, 304869883, 977348879, 968257704, 948304626, 934437778, 14268277, 503211253, 322183086, 196997455, 795836306, 316349086, 989410274, 591095246, 339606825, 263276369, 770450282, 786947039, 40190109, 14733293, 428028843, 1017496, 384753724, 631342669, 54186973, 862159675, 981316396, 91315701, 550018852, 801341494, 432054643, 150291313, 357458794, 456032968, 999414769, 511933892, 511477100, 230217332, 944835211, 814005825, 286183333, 961168117, 850993015, 467184393, 968909610, 428323256, 181607433, 981234072, 683288935, 318809929, 532928083, 255586449, 249134544, 955193810, 832478387, 984901413, 280721841, 903592633, 349839771, 887492142, 863305096, 41460899, 109818999, 927475128, 858856107, 741337308, 31538443, 587760825, 849927575, 35896357, 129478261, 308240223, 34402978, 9904018, 87883662, 464304401, 489754979, 68087715, 173811942, 401065172, 515371583, 805409764, 121477788, 971200466, 557150608, 403825612, 891087305, 286642441, 102530863, 819681043, 164626892, 760800103, 514236201, 300583503, 391737446, 623379018, 71263856, 537357411, 543905193, 934481854, 295944883, 666171925, 341899493, 825126784, 408436327, 35479003, 366318023, 187560845, 530536803, 330257219, 89065309, 608194928, 916831526, 880165803, 359744817, 561940469, 877406328, 383410708, 190106136, 870537264, 112465292, 851057795, 94894091, 261562101, 878117013, 792529479, 153870953, 417138630, 409428126, 761214819, 723495521, 693753624, 458721747, 689417937, 823298642, 876881591, 481956691, 619908832, 598558677, 703343403, 596914094, 981751900, 690176368, 833159270, 247181091, 813295352, 781346775, 380857724, 342587285, 462545804, 131771853, 263570930, 469213835, 746398919, 475168781, 923100011, 736787897, 467633596, 400076181, 229014767, 438161469, 934343545, 12290382, 740104471, 860294976, 932240637, 961759846, 562620085, 504461139, 253816344, 990150373, 633251281, 435194549, 745754647, 340768293, 199045875, 207111422, 467831373, 219019172, 843863550, 448937798, 25174740, 583106923, 812037953, 426151363, 257450979, 511448554, 7323466, 709352155, 911378328, 305945046, 344334632, 156278140, 733541265, 555157528, 433461056, 886598545, 859071782, 672110479, 12878336, 216236193, 911573437, 759885758, 802927176, 156956926, 491093307, 721592468, 408516654, 149876696, 137725044, 288149556, 436464013, 212119597, 951933305, 198659906, 507900299, 390352513, 834972835, 81907604, 603659178, 77700975, 465313891, 242414705, 901648102, 354026519, 856424777, 330690943, 697543626, 660508348, 907383906, 625647727, 768088744, 925677344, 377616269, 674772995, 455345789, 683436815, 670541878, 766197485, 295359236, 78015086, 626373191, 994275417, 285756227, 610840427, 568224319, 211784797, 886486112, 451003118, 154184025, 702950583, 434137727, 210250997, 424778650, 286164929, 628395232, 214638158, 359322394, 852916122, 893425244, 435518361, 354219308, 329965089, 731681280, 948777790, 273925157, 260301158, 57254188, 24769293, 777636370, 764889995, 844107737, 174416856, 692605836, 909341113, 29841461, 340848512, 324699488, 991095166, 44742545, 853925645, 944037176, 830420530, 957829802, 332000420, 486793674, 650514430, 516162001, 890408878, 91803624, 108244716, 432594391, 706478559, 142116436, 837997909, 437875068, 231177044, 841169188, 227487520, 760283440, 478623969, 67635377, 667346431, 831711927, 277789531, 460515893, 996570907, 142740214, 930962735, 287885043, 929292693, 535719841, 924068710, 888142742, 399315462, 263534779, 938232440, 988127598, 403699711, 180991427, 63694747, 348275832, 397154010, 941662520, 826427953, 109554811, 434752117, 18171367, 252243132, 633498796, 693776704, 478085266, 520443685, 397545381, 431042886, 41023170, 624866427, 186359845, 904824502, 445160849, 184895242, 778559800, 470359000, 798095077, 675751812, 689336648, 885948580, 154316861, 783898005, 866824085, 357162475, 752440712, 185358621, 469060071, 486799777, 27222522, 669567472, 356964305, 176657359, 165927462, 926748294, 891235359, 778457826, 172665399, 359240767, 624967033, 927216465, 781648538, 537416525, 334218155, 20728803, 465882818, 488544882, 659921202, 726505798, 200474040, 911747374, 185675998, 135928726, 537886686, 627483312, 845189978, 119203231, 920476115, 819842877, 357434270, 899670882, 892890670, 643975692, 647732583, 272396382, 247481537, 937626293, 815855713, 12164206, 139108187, 441193479, 186063230, 883378981, 791159421, 586082578, 624355150, 428395267, 711693820, 180909978, 305581623, 629333015, 794659889, 7597273, 280473371, 334396322, 745671750, 412623733, 73307506, 87992968, 989890490, 891639913, 349591523, 884523706, 210145605, 175391317, 743437444, 961954667, 333903873, 229247271, 650895775, 561729722, 110341550, 49628949, 365774963, 179615129, 325296489, 638375041, 259558640, 360462462, 785743893, 367569453, 74774497, 881641247, 140903050, 661092268, 629635053, 568703336, 693272477, 431857386, 82654338, 16161715, 139744676, 998590479, 71684382, 6361394, 33478232, 479435414, 986995275, 216513059, 743044696, 210825477, 914307517, 113711341, 294630080, 960436589, 753148939, 589905569, 70414977, 906165464, 258975188, 95569597, 127820077, 891650629, 822219315, 813015294, 969511777, 484011485, 745510555, 187728728, 859565014, 516346242, 396629819, 711156728, 179683195, 408633859, 167194415, 501781881, 120369808, 663858599, 972392715, 346705217, 718972595, 629502658, 202439829, 421226988, 508271441, 122884593, 476814172, 669621695, 953654831, 142002743, 760588210, 326450752, 698919200, 509492519, 848666545, 673997240, 284935629, 981767173, 414681170, 860402268, 249468610, 185692721, 667460215, 226060368, 172188097, 539062219, 738097136, 88956751, 529839592, 196184762, 429040343, 920400508, 409740938, 478266640, 308157869, 260700670, 597553655, 266134514, 932583471, 729717505, 552026218, 66270746, 891562452, 957557779, 705738810, 402346702, 783412122, 937743604, 765489999, 659751228, 273981418, 495056911, 266516587, 731321898, 254539979, 603648371, 25570606, 845666930, 95150740, 997911696, 367120471, 652104107, 220426841, 63359718, 695497188, 661312163, 613859334, 457594457, 724546999, 759411262, 319023102, 895922330, 868537670, 584000824, 807372740, 251039312, 674191783, 349140291, 778686062, 398646189, 918685154, 212453173, 619071074, 874064149, 199085024, 652246206, 298083694, 906064684, 829610318, 248628790, 77696396, 993511283, 477111245, 160441767, 656070395, 164800014, 470110054, 6498055, 118488238, 528662840, 92011691, 151934566, 812922799, 567969447, 297191356, 242885783, 849026838, 296183405, 783680024, 568474536, 75844534, 460678119, 954507239, 92085089, 874725762, 235976347, 419952781, 223789734, 791649187, 845888527, 128643649, 253169627, 866029607, 265224042, 756930083, 408060325, 517828724, 801293347, 242982160, 187980615, 326969601, 68578934, 25398514, 662545771, 682855074, 802240257, 159339851, 128488040, 254512196, 558243848, 432482356, 177251851, 747510234, 995735626, 522648292, 277986874, 150773341, 810605284, 842076903, 389579455, 670991085, 467605239, 32493099, 372160488, 857669321, 750927408, 906298008, 80609398, 104846539, 648649166, 131150221, 733037459, 445012293, 246422464, 378329710, 536051021, 114673294, 21758975, 250297872, 535237995, 887126045, 543291145, 68371808, 43136831, 855313708, 148342101, 143425825, 571245726, 339389798, 784695149, 526860806, 530573529, 512536185, 465059077, 346649201, 513294246, 466605461, 943351139, 335217236, 460114122, 77643638, 219140501, 314113119, 475248122, 364452089, 112909390, 204900820, 822534522, 122970526, 353803858, 213440053, 914995751, 451256704, 99627902, 836422351, 393648816, 484848932, 549379162, 623591340, 279225322, 282578253, 727589302, 484157442, 138640007, 74797645, 287528032, 52712092, 67886003, 506131062, 449466810, 95151994, 106744099, 741967645, 760304513, 220899010, 899398250, 834656388, 788807592, 766307785, 839322499, 308023366, 318389366, 622251539, 388803486, 902843953, 868174858, 726704320, 506978330, 660844452, 72203026, 985637192, 177995274, 419864770, 26301136, 111641099, 606480605, 860720090, 996299897, 162375412, 630559564, 338074903, 669333525, 176473592, 206651602, 834342618, 848773474, 964195766, 666026973, 894148368, 851616005, 294536051, 727515244, 870829610, 646770995, 843470472, 946102800, 620301304, 898642486, 774882403, 469755978, 572023713, 146583635, 793396582, 916491799, 16997254, 262670976, 31410828, 918804101, 306437301, 838685114, 745737370, 794646275, 327227898, 194484771, 323156104, 9449527, 895556691, 97265655, 24818853, 861334793, 312164827, 42314178, 332002679, 898288845, 733169099, 744471214, 683926261, 909528220, 775061002, 345613227, 958705092, 886621440, 722222189, 89623986, 837171465, 851824349, 938603554, 330399902, 879597314, 38282548, 922936147, 339135172, 270127039, 819663029, 179246986, 361074554, 827591963, 508164384, 209829660, 86584496, 510878598, 649532032, 543468415, 725158757, 469572067, 706022700, 179287805, 964106031, 267045111, 127834915, 273559314, 755721584, 173540723, 892025964, 937728843, 533252458, 839156607, 630768483, 376678650, 211552903, 140877646, 927001061, 963777604, 372301182, 906653478, 917371399, 598008437, 209801759, 955826743, 306111318, 657379521, 548970075, 90840066, 89881586, 17871686, 305639733, 443420510, 115688778, 555270211, 844573824, 815046896, 888292016, 124534966, 460913371, 111637418, 170956896, 757823998, 348846561, 399667919, 900124535, 411792054, 732333510, 555171236, 12869807, 517401224, 601828536, 133355140, 273060488, 154206483, 668625478, 713531370, 319787050, 129090858, 195217973, 693201488, 621373300, 327711721, 276174613, 443051657, 321474819, 874598166, 651832223, 634103468, 830797372, 26503754, 966618174, 185099998, 744349940, 686370038, 488228186, 877469906, 621966815, 263024171, 369610426, 494942232, 975653704, 571023921, 492162734, 804870143, 838578385, 475267055, 776288685, 232898820, 18712951, 345161332, 663785204, 485547928, 722219679, 516659376, 104611713, 431144062, 354038171, 486790433, 384024810, 546122066, 810782282, 162315461, 16445040, 259922046, 850346847, 844511444, 924510730, 880645468, 180153459, 665357835, 650723022, 361553964, 671850744, 518290847, 755895265, 919931439, 693631961, 531449791, 280919030, 521357511, 321790641, 247160680, 494413304, 682479840, 313650267, 298925001, 378666926, 461760349, 658718208, 204257673, 356555048, 965261134, 679576566, 531080228, 952519830, 744068069, 237710477, 193998462, 423894165, 607182440, 372573652, 810230454, 241301478, 972384649, 489933101, 280193785, 663359936, 18986768, 229369158, 958021165, 723991054, 358024544, 869203305, 689706708, 113875240, 546603715, 151608743, 198599505, 197614101, 451841452, 699744547, 582859712, 100275561, 644968575, 453549887, 592968159, 605765030, 511047182, 19076873, 933430944, 603737678, 221298640, 97501666, 160372410, 860779578, 133511151, 857735893, 287931797, 446911264, 651492550, 129257941, 47245749, 942755732, 42590732, 623257162, 499537934, 63526503, 285176020, 876999765, 101462652, 869745259, 940788564, 905975258, 11607410, 828681569, 595002887, 739605096, 142351755, 938325007, 953252961, 754983535, 35935740, 776810609, 868287745, 847898175, 883428198, 434407315, 810074742, 530965810, 981962464, 804486721, 103163636, 811554728, 79851541, 939887552, 204883591, 234651427, 109306739, 430586669, 509208919, 279530194, 182852728, 210065240, 637457409, 419940392, 284307697, 375688817, 192040708, 347486913, 565580648, 189242789, 131156484, 723272717, 4150308, 610366201, 839810063, 564797654, 807602534, 152382509, 330975619, 407063102, 826356178, 541831991, 889794922, 451716436, 174711526, 686148917, 12131814, 797540438, 773704689, 148549765, 737650526, 732458647, 551011011, 358631943, 957911232, 180815933, 510494917, 461963275, 799350029, 679810799, 792216428, 573003767, 788926378, 53126253, 830275331, 754574424, 829986301, 234868746, 611463425, 605767145, 310561240, 346935513, 881739315, 80890007, 446589219, 521408061, 529491905, 687893767, 566445632, 870496614, 693805152, 488503777, 657908102, 691692914, 688830949, 253484800, 67547947, 272275119, 889809595, 2720721, 925975970, 842642444, 254567712, 318134602, 385845213, 44571229, 545623670, 805808452, 655816387, 814525836, 53719883, 967222577, 925646601, 436189208, 131716625, 415977334, 333444988, 570699701, 490777883, 859548418, 760772798, 308604329, 94041523, 587828284, 901740340, 624708789, 716886297, 648747592, 553212744, 374517441, 613471910, 17798098, 146606053, 79615819, 585759098, 429900258, 229350721, 830506990, 140521043, 256868187, 8312333, 521225951, 934777271, 504094871, 364648416, 110525259, 354101163, 545704293, 354060409, 247979402, 888695240, 708316373, 764555689, 909645004, 141287871, 446889551, 753851310, 861828525, 235770014, 801526806, 790767798, 777415579, 948260570, 583215105, 198122212, 881574172, 972156092, 982272022, 795741706, 114163441, 74694048, 52562870, 961623703, 348060129, 378754007, 398703358, 619424040, 288501356, 714718479, 739092680, 690140227, 476820485, 858913661, 839004972, 915302373, 716384530, 575364368, 323993674, 519643144, 180401239, 589733738, 181791192, 786514560, 117637737, 872138161, 770351781, 303762921, 272533297, 148087527, 268344788, 871417041, 911230106, 81717673, 397110308, 623978402, 804406416, 452762841, 362553357, 130144920, 758224130, 368463012, 204156808, 859380161, 308957583, 747517896, 384415192, 28126824, 869104935, 662059503, 617300156, 377232341, 544655961, 520754415, 203376731, 132781112, 110536293, 821213121, 366673457, 11353285, 98679760, 836003646, 160653441, 315946425, 325254463, 481727840, 133754202, 512106, 420943715, 284547635, 655787, 475667286, 717960410, 419932570, 598351444, 233071557, 318291845, 51189497, 155227332, 101132344, 524113327, 904794705, 461405592, 331165505, 308811694, 756066317, 147942732, 683800903, 306112452, 606741355, 714582275, 480141440, 739013351, 186394442, 359127745, 525515060, 882113599, 995299482, 653312930, 372163562, 944893949, 521817577, 845151542, 441147587, 79260746, 527534742, 100415203, 154497854, 183087485, 702678446, 873457281, 825601938, 899386772, 279551966, 607457971, 466663551, 263141627, 12291507, 221487134, 578251966, 75646318, 374328835, 527905750, 360693713, 820017791, 596817969, 390317659, 134935109, 704312632, 496440381, 480761903, 23547282, 9955140, 832576965, 636266315, 629794023, 278791310, 94728209, 917136747, 255336310, 825239290, 242025708, 237529314, 110511978, 30153766, 989684233, 356495474, 937903694, 679526952, 991678812, 360376153, 711236126, 25951165, 881040651, 578028408, 495261599, 177888291, 516855011, 95252210, 361138179, 423068336, 90996407, 712295558, 772431581, 786371935, 674171243, 201936436, 820484204, 477887750, 462443294, 920655002, 932702171, 834886124, 693462577, 10312659, 670372937, 548418341, 303989945, 110152253, 774574782, 114100908, 634442557, 267638096, 650283596, 354306482, 994559275, 616785287, 266225341, 745874637, 530372729, 521420928, 629066838, 42684893, 795056860, 421941411, 169861676, 776749600, 310173112, 550797684, 769053957, 877375595, 103258742, 37262086, 652878434, 615539020, 73226071, 422951839, 731386363, 325923777, 386175792, 562149062, 807701474, 910920871, 379190313, 603132693, 390450404, 656574529, 354972999, 813559832, 183759084, 59297255, 634943891, 892389854, 655413800, 704956454, 328935262, 39334589, 821531694, 945023360, 517401324, 73501593, 401918208, 970183567, 867243852, 705442744, 376757902, 41955433, 325073430, 725599017, 902558725, 317347192, 624901883, 850837502, 718461767, 408649208, 370402126, 130050966, 196981438, 484503473, 827262235, 564470713, 178581777, 161556553, 377842657, 509299842, 47318304, 502347067, 482615705, 323935160, 189075206, 198650802, 467313060, 443015272, 78279159, 258641317, 280709465, 319104538, 530854438, 348219379, 362191015, 251511515, 695958313, 476677947, 365987067, 883854735, 971807031, 895655042, 717695988, 133475083, 494380124, 992076179, 670411947, 828720423, 69719695, 134541570, 309784292, 605850787, 24776326, 414299307, 107345056, 717826600, 605226944, 695217523, 398492540, 120271531, 495365177, 462762942, 571330633, 874753865, 980215344, 487690133, 65792098, 824501068, 931106461, 995659248, 873134767, 743004073, 295871245, 685335206, 464752762, 613829588, 761575091, 779235588, 645990593, 112856465, 359350832, 104663235, 536317899, 494320819, 663040828, 96286241, 13231308, 309885707, 595719447, 347736123, 448797344, 633803230, 744887573, 380491100, 324999970, 899082956, 10159267, 211832672, 179060042, 311004618, 401999806, 974337591, 153402038, 958634318, 818142200, 536425963, 783880610, 601556214, 859425855, 276433444, 309129404, 90209551, 776802861, 104805741, 10655124, 895975155, 791344597, 320881334, 393458716, 961338985, 608088638, 486384131, 641682505, 79229080, 226519787, 36481746, 368674033, 162483460, 164848195, 780341705, 381037582, 744930763, 432187206, 225904823, 251892389, 492953985, 455803325, 689917291, 32603372, 230757590, 412867155, 380645408, 972503807, 793469603, 240897400, 514513399, 708031336, 381282475, 502003249, 308268639, 247273422, 777599345, 241477837, 203500465, 169944847, 904290729, 350943103, 942218266, 808499052, 867240313, 408233958, 602550609, 533620680, 437093791, 480762297, 942098309, 701016414, 716857322, 931660541, 551327186, 601128258, 849248492, 665188802, 874499205, 508636130, 957772709, 326193098, 635996703, 938256386, 331795533, 404941438, 955427424, 905686800, 39142617, 170901040, 222985579, 815469902, 252408169, 331088586, 686345922, 6610212, 794048350, 149974256, 25184190, 405573598, 990703005, 932854193, 702029364, 485127824, 166929570, 777847412, 282086494, 921674176, 398737967, 471356858, 9645085, 616610623, 802294215, 744199521, 632582245, 109955403, 409008870, 621565929, 315694662, 248554805, 825971588, 5666887, 661584785, 373407409, 929176343, 158335399, 253641946, 136987744, 337252723, 617679316, 765871086, 328908646, 623377504, 563290137, 629413933, 23595082, 907106254, 824310318, 924166257, 357361964, 377144339, 253145333, 403447219, 536816110, 251486593, 144626331, 48826989, 507410583, 577232461, 138164015, 243799281, 390923924, 852284481, 600650592, 816139919, 830995633, 109956142, 261160720, 969106231, 565631617, 970907007, 185814320, 414121780, 463511066, 984401238, 357874845, 986115491, 20586910, 394289432, 815660018, 377629, 923938680, 396268313, 809075308, 701342583, 66470459, 89760642, 829378746, 427617944, 595824000, 918383593, 369009020, 92247078, 428056655, 405984075, 25637555, 151603755, 254810186, 279697556, 504047109, 250969942, 787441958, 831717029, 89167307, 620727728, 500038880, 5431707, 318670488, 524714926, 175460634, 703439813, 778386035, 236074651, 229426809, 492190492, 792738220, 754796215, 943704399, 148328407, 169992555, 265838408, 6565629, 638877917, 921875459, 532598614, 743739431, 838459410, 876836398, 560096557, 973463913, 956593134, 48235971, 412619131, 300362728, 640220059, 542736449, 585349655, 452421758, 430407375, 896430227, 471136001, 464157691, 9463577, 852166997, 685704999, 542989616, 75477695, 261955421, 292490133, 630534151, 7481451, 950825429, 203374464, 304928292, 63826975, 906810051, 924309039, 582591509, 558043725, 512805377, 351006498, 987140375, 25420879, 869026408, 344710934, 753344302, 23015460, 411585608, 918790343] 300)," 7625 (countComponents [757732156, 737535686, 402213557, 630537551, 816896377, 976194453, 214824638, 917684868, 951791925, 8576363, 790430635, 958007275, 837854870, 644547512, 649535271, 887760457, 367307141, 265816775, 672089183, 543895101, 996236833, 946453407, 889569523, 254949308, 445284979, 841445442, 358803480, 815678286, 96237276, 644048411, 303304206, 275896644, 984622075, 229479804, 913552318, 22503934, 237327033, 48549727, 18398251, 695088402, 760193216, 43553395, 775444834, 548281506, 729875883, 224335750, 715486586, 199611072, 137713424, 466351856, 393816375, 619000789, 252812641, 934881105, 269146253, 389619476, 977823389, 720519243, 901603699, 183130439, 184362230, 702546156, 638332389, 512108280, 39485330, 443235343, 473177083, 30654084, 294466252, 762221571, 731250042, 664973391, 98071246, 581250391, 657163122, 839971041, 952297548, 436619377, 822511445, 564518757, 578626854, 875629170, 244260635, 209995794, 674919120, 331676220, 988388620, 314269237, 768210919, 312902200, 369609986, 474767129, 781449675, 664676944, 12038750, 895329380, 292365499, 169823309, 610446996, 411979952, 147363095, 742241110, 885864190, 145322830, 434199473, 540024609, 840027579, 936541008, 929222473, 778967301, 968406942, 241867268, 876265578, 264816794, 865211227, 391268381, 845407372, 650796206, 606857605, 463634525, 921809638, 345405942, 398584963, 231790070, 863088334, 974383933, 402518149, 619413692, 97992060, 896855847, 676941999, 19154928, 696112801, 467540382, 146153980, 668657268, 421493275, 51940257, 508304656, 123588020, 587058833, 141915313, 201868918, 638802588, 743684830, 385642640, 35356476, 673058032, 482311736, 899656913, 288619471, 104032758, 225012673, 94276711, 158507727, 771014665, 275242889, 367944330, 369602425, 548830936, 72936684, 876721437, 661195738, 87367894, 74597326, 317928449, 850514614, 744474962, 452931160, 843763292, 557900071, 774000787, 397372899, 377108325, 562836140, 581755347, 981431377, 515586820, 941413010, 587444867, 961980390, 576803645, 499631542, 615349325, 249340647, 452117048, 800352293, 465988205, 872253665, 753017858, 528093350, 111148723, 364314515, 559511364, 639330143, 962034196, 145260744, 440050, 418691713, 927397284, 641845206, 394398611, 973942501, 922576903, 882478056, 168899495, 845523361, 462277568, 414296617, 559429966, 48380351, 463707156, 425159033, 19980542, 377268066, 664819331, 60364917, 845791711, 61514909, 506863027, 491477385, 783192698, 557864106, 585667438, 690842522, 851710063, 333192130, 385084715, 201907499, 865068847, 784120216, 432496443, 365757443, 224179962, 925935386, 497630655, 605317807, 328534405, 429821186, 525772621, 366876308, 998567382, 602615186, 414291967, 980059224, 38921911, 478320202, 435905012, 347609979, 592822218, 811028348, 203988152, 971059511, 28696294, 764558422, 728838702, 411862991, 601165820, 600071744, 775549908, 977178736, 458325817, 442572383, 165651602, 881450694, 468677999, 689813108, 56617489, 879469317, 912161127, 675624084, 888196880, 874070006, 833293786, 485626698, 601549789, 29676986, 636906693, 547761606, 350267848, 792183767, 94645028, 146015165, 716781906, 340149476, 877442755, 921594939, 753050755, 953736063, 979624453, 322396495, 331026653, 675393757, 356450667, 960794629, 708646329, 20251760, 309794030, 458201091, 848776166, 302808908, 542990481, 288582717, 563458694, 220287214, 441685480, 214202446, 936941790, 503006458, 70070923, 899130738, 636099601, 794472908, 667458743, 461528312, 518102712, 98586872, 51968243, 573289623, 892222106, 277803399, 830986691, 24857219, 889287522, 834699145, 925282472, 708262844, 41122726, 330986942, 455531278, 254868592, 396784924, 760266364, 203034204, 427390600, 826509361, 966605809, 372536947, 396272841, 275980670, 744533939, 575246220, 208450423, 214438396, 20954444, 901341959, 85830439, 327356015, 205051829, 702136840, 824280313, 633064892, 183551106, 449719419, 725892902, 29519189, 696491489, 865888154, 829882313, 45741304, 298673378, 800428914, 537535718, 351252, 962768975, 911965312, 914402199, 852735758, 53647072, 448494102, 690230374, 334676848, 978060493, 589753553, 72607967, 86252378, 228226421, 733258078, 876074651, 831701095, 956708331, 148730673, 785084776, 844914399, 240689100, 214482059, 175927750, 203499308, 939991344, 273945489, 244696939, 30912028, 775224577, 89382599, 437475919, 692471331, 685506407, 926897657, 954688924, 665057745, 970935004, 450768116, 776871736, 6627455, 763443756, 618703109, 722863490, 810986888, 450758051, 781580987, 643515856, 183069061, 543920507, 423875384, 782403690, 696914978, 330916022, 999380413, 70450132, 590923107, 378132238, 472684651, 279166061, 943921808, 892419750, 798159760, 961057203, 447701128, 895711480, 330582648, 917887696, 525209810, 12074793, 594008437, 894127268, 34933883, 302760919, 58649116, 763393665, 182835361, 744714885, 170933659, 979011174, 974085670, 955893667, 389795150, 943720912, 577681585, 780218669, 507601298, 482501738, 326123842, 767974267, 929240980, 369392779, 604701611, 319826350, 253971634, 397452315, 97029817, 536554590, 521204641, 830080084, 934187072, 696656379, 847913453, 800242341, 32324605, 523139663, 431244090, 316148567, 909270044, 394128703, 362691965, 370496906, 706507840, 170117855, 579083886, 145131017, 900064698, 637895436, 918112925, 812519946, 354887184, 474139949, 461631989, 47314207, 870145709, 840011418, 36607566, 884882512, 933415724, 739453261, 591767292, 133210993, 385517949, 487137267, 574950308, 135212434, 534076071, 309249053, 794352148, 781148627, 384303510, 305371796, 947805989, 236412776, 15676840, 805674775, 541902060, 586113666, 659053290, 569794628, 486248261, 871633708, 643150192, 148047774, 186412572, 61952690, 483847736, 908775032, 997557764, 959496299, 623633318, 555434189, 796177722, 419960712, 385345280, 65007349, 570989074, 495392141, 74533477, 152675200, 963743883, 340239929, 255176612, 268814452, 368622982, 259099700, 13542633, 739028506, 572036999, 694293128, 211239971, 731858606, 859817472, 697870980, 337478808, 242915674, 426880911, 334723983, 547932961, 768416847, 723846280, 874586087, 611918335, 823567548, 377826530, 923964731, 997931317, 812600684, 803648662, 323535915, 715351753, 470093759, 272405105, 686965683, 860431729, 147056857, 273420387, 177422855, 459069510, 48055819, 978845267, 2935751, 679405539, 23026722, 735353241, 605587054, 253365530, 456496115, 455865407, 156380150, 572282542, 836697582, 111059506, 583031101, 442461954, 309705636, 412480926, 82164870, 929235166, 730950770, 559653171, 79078732, 372201785, 86541087, 730429549, 523042678, 908823316, 883709915, 485039740, 423273446, 597768349, 949780195, 689724058, 418550940, 370673581, 543464978, 881456984, 164031295, 40636225, 284968780, 390226487, 144446372, 949727908, 969556326, 178810871, 603103328, 554851159, 998784816, 869172012, 466609146, 781745206, 895400628, 333334805, 624698427, 602620871, 796551334, 274628001, 570398382, 25818846, 408191414, 219201431, 117581752, 997972435, 222543802, 62340432, 576518802, 198855752, 710676090, 660303721, 698360793, 223705056, 971076794, 434279002, 40807200, 346046374, 241619382, 315009145, 542398450, 27537493, 732623195, 398977486, 863425985, 777702158, 362498075, 307733101, 829513649, 888039654, 421395073, 623627514, 356639337, 871417354, 709392994, 23659660, 418805831, 709166466, 320603440, 925395423, 69819287, 555595409, 654886402, 156329272, 186167921, 491151867, 132263015, 869269235, 970792540, 986593213, 231824421, 925552666, 330436019, 384240783, 608193575, 639163914, 948664224, 476127953, 539597070, 105788617, 342157768, 957500539, 891020592, 68583684, 971672570, 673491951, 641752924, 382602810, 303580124, 457220757, 830278291, 121659540, 266761547, 813676674, 40817011, 296642985, 848378757, 321782459, 394202558, 54382787, 152406715, 549749581, 423661927, 912092494, 307039750, 857436481, 371666229, 229290768, 998472644, 607732655, 929537215, 38933161, 406680606, 153600768, 514321668, 799426634, 654077672, 981477151, 695549963, 318043643, 407120782, 137034807, 538343862, 781094286, 633759309, 724193520, 393011134, 440999076, 115362051, 920105246, 48051978, 301522877, 392197260, 371934873, 664878992, 772397193, 381541080, 5535604, 162257691, 47436197, 195147406, 186690805, 639703526, 108961301, 275997144, 477963603, 360899589, 367380200, 80165107, 40354471, 359363865, 86312554, 468266548, 188671081, 523368071, 120628577, 526197335, 875625873, 427867698, 697894727, 699407474, 16005370, 863768618, 780256500, 446523757, 727538641, 875809011, 69697163, 939055776, 66004483, 90891210, 924048056, 459236994, 298821137, 474684258, 174752255, 763648363, 789736177, 658136460, 976632343, 10132499, 865798911, 924390426, 407150067, 646556716, 376774441, 224929087, 318389325, 716478228, 984494486, 887946577, 937746039, 668619101, 267885024, 598275140, 870786996, 663965810, 106669475, 385103223, 460845730, 174149541, 412353757, 974425542, 883654247, 772165030, 971081325, 227187896, 206760868, 28848659, 405236935, 956119228, 570391216, 423873013, 799366683, 861671694, 497481112, 634124123, 998309061, 910627151, 997235635, 975471443, 597146687, 597053536, 977497421, 742245072, 602546438, 85908564, 537187571, 900699198, 108469089, 721669431, 114297763, 592111179, 497422144, 591405412, 814750379, 936576923, 936321996, 900955268, 958216165, 129810344, 135315808, 218277380, 694569009, 825711649, 947301813, 749235241, 514615244, 813636371, 667706116, 890242165, 600294422, 968415288, 27399427, 469038615, 683422990, 339188079, 734089017, 654439718, 69869250, 659620061, 965540680, 91480087, 971424084, 865774410, 898512654, 167024837, 398274541, 849355215, 781414599, 913342431, 48893741, 57765972, 57775362, 60963069, 570520726, 709977287, 941907101, 746630734, 283943218, 562947900, 693001858, 213348179, 257594804, 438719756, 553640065, 943051819, 330632954, 747252942, 112261504, 697020718, 77098517, 115985672, 893546578, 626461936, 576847020, 803405222, 863629663, 222724616, 948527325, 612319384, 922081741, 370747198, 948161985, 428837778, 157827158, 994087995, 945579404, 167369725, 517886146, 155906730, 325207378, 232105532, 36090412, 476289065, 504263204, 292639579, 459688386, 448693346, 109425192, 388789278, 424373953, 581436854, 212225245, 428575058, 224246948, 455136005, 563818097, 699045680, 561792262, 21718930, 252420285, 515567116, 870131327, 246252230, 23250813, 400124251, 893280395, 311500449, 196752228, 109377504, 929762563, 510420504, 93307215, 967887285, 580478719, 454886199, 438302398, 491972725, 728210584, 508881578, 295605713, 492489429, 805608960, 737962433, 486317501, 772466234, 403025036, 897902120, 655773904, 574503007, 940041745, 333801482, 787181069, 111360057, 847680843, 693987154, 342195611, 812687053, 674070932, 684845096, 783852417, 985641361, 411113103, 278313204, 766175005, 402022160, 980347182, 659786895, 707422266, 82683586, 453302008, 179881568, 466088056, 100405775, 162384221, 246852789, 239878984, 549943881, 790964587, 115138133, 469819680, 17415406, 665675556, 941329230, 849715340, 912281254, 263814304, 864173739, 90606415, 663326347, 447443182, 30512098, 245388974, 361672442, 320826490, 120792020, 699633880, 17910109, 430610473, 858056781, 382664603, 243752004, 192938603, 582849597, 741410586, 602486089, 740889102, 133208249, 526747082, 180867321, 659906367, 423335801, 914579143, 866205487, 811116339, 238571441, 476388632, 584958651, 623230732, 49741802, 957987313, 962377536, 450154130, 574864723, 558394547, 960053335, 819719880, 935298171, 811747488, 284889297, 628876153, 697865834, 43297698, 846528032, 466827205, 500912118, 826640296, 579815262, 327166048, 996377153, 349478854, 554944465, 973901958, 112937911, 828224738, 531279338, 265607222, 654284920, 651881990, 755181547, 112398141, 827655181, 199228219, 796917622, 526220994, 647498896, 534408787, 377353281, 678402846, 578159081, 715682632, 599148704, 95420446, 531973962, 685983635, 849026784, 170176864, 13805131, 406288374, 988152456, 406376464, 855265708, 281193329, 180880912, 738106547, 793512506, 387746623, 264855650, 57134570, 877448761, 189356634, 50278532, 69252061, 696334066, 271138412, 510842859, 194258744, 720627433, 33865700, 31865831, 984805620, 595973038, 400384655, 663338151, 136372656, 236123959, 20729314, 170003768, 442137222, 234422725, 654033073, 843937520, 130715672, 612541499, 894281562, 898441653, 402069380, 287863766, 286697397, 268746033, 804425412, 359279387, 958733036, 147563344, 638328111, 174269444, 793385739, 462296656, 586797338, 468875334, 279348058, 740185825, 146205900, 491506614, 267675862, 117729079, 605368898, 941535992, 363268568, 763870026, 889075929, 140311789, 421853608, 639217765, 156786179, 142769955, 449358875, 116490786, 169227911, 265425406, 555010992, 315159294, 71795046, 934323720, 309637685, 896894681, 423490497, 208147982, 46008419, 271110490, 93114620, 244844914, 274866013, 89780692, 60291609, 156375978, 898879908, 807228239, 246625427, 780568053, 909202017, 288421814, 155242034, 940739686, 798461423, 210221660, 901523695, 295252005, 144057478, 627484711, 848073621, 464326724, 778521316, 459315803, 607251193, 276196575, 356446733, 860568830, 624148052, 459445592, 935209402, 404996364, 966614990, 157797638, 374561191, 309752859, 677607176, 994443349, 881648121, 598465944, 55031456, 474058086, 513326323, 274123581, 276589482, 527177447, 307324138, 812815908, 134610911, 225190757, 396871260, 451181985, 308743627, 470855648, 10141103, 596711742, 967204254, 421243261, 700248318, 12042472, 883876539, 731845724, 364020120, 920602549, 821379031, 240461942, 484544389, 996360210, 687784312, 848884280, 260025778, 141730387, 527822472, 357824388, 82577159, 131747873, 247127270, 866413568, 915260076, 142523061, 301992008, 332695583, 267279135, 687372494, 375485414, 864448353, 130849843, 248729049, 103867785, 590033492, 310597599, 73853412, 863408892, 519681376, 881871223, 827663372, 564157616, 194376165, 457194424, 605278856, 184991373, 728579918, 128982581, 157961733, 89939216, 276127195, 309090702, 59681239, 410091257, 585561819, 110519884, 824887067, 39000621, 257178871, 994706438, 90472823, 472584314, 765482728, 118881414, 836452969, 280830892, 834501692, 637406166, 534530868, 458265483, 402535958, 629182012, 457949013, 18654559, 842305484, 588979409, 459543486, 338426335, 843960079, 787509588, 899575122, 261160901, 268442556, 506687437, 196551717, 639517334, 342100214, 58965369, 603406752, 224799654, 296195712, 531220714, 833436827, 520312161, 579370385, 668829403, 210173948, 729110010, 928730652, 502038733, 934269074, 409472759, 546565030, 33367399, 51140139, 41455475, 990839940, 23166752, 931501965, 325220534, 233710268, 869410213, 341242206, 566691676, 912377288, 945861682, 850543364, 683738127, 6032179, 835089287, 370551013, 968525396, 984773508, 294467961, 932258464, 75249830, 495980409, 632175034, 619065152, 94411588, 590307046, 468436315, 297886499, 643471067, 453264701, 944425861, 124538361, 240958931, 165947147, 675439240, 530238369, 217884379, 534921582, 915384134, 845368623, 84154426, 924144798, 633100977, 309577448, 80548363, 615609606, 355704152, 705180756, 862698347, 666035270, 337806471, 497357656, 30584229, 360460727, 543616986, 824501567, 836765234, 103584263, 334698104, 832288429, 91517533, 998429352, 341564798, 446477641, 462015083, 624894221, 927792789, 270337149, 316805186, 573696390, 497882811, 315194385, 761897694, 790193825, 100258660, 930259755, 116698547, 974894589, 104610399, 790895397, 772966316, 836998868, 636830692, 221325236, 723764792, 381768204, 149237628, 438549543, 243239871, 651271367, 472720867, 188616450, 136873546, 214179008, 829337610, 902278410, 482630171, 227634544, 701518520, 166212607, 893471510, 449563228, 885304290, 767191539, 570045532, 463315158, 894329641, 178690344, 909726640, 967988566, 189612903, 218365826, 723435480, 322445112, 548215762, 214942657, 833875580, 833613461, 644250026, 917751026, 294329378, 331423725, 707096294, 120519330, 958645826, 415947406, 662103996, 774751777, 576739022, 281189157, 644109134, 334431558, 257392547, 590185444, 592766233, 104611217, 495376183, 246853839, 654875684, 554326457, 113548949, 909716063, 231856410, 658389940, 231717203, 237269266, 469186859, 277934265, 778396553, 599645658, 575117882, 818231208, 828379431, 774887136, 913964857, 234002405, 168649660, 694143733, 114877320, 123470093, 647716643, 570362244, 391227406, 109924661, 230109082, 927296719, 220175694, 268965035, 811078101, 797930372, 345126977, 727980251, 836441544, 540670140, 242092563, 940448980, 823671322, 30302373, 358339505, 391967168, 494774920, 412085084, 31618823, 362796787, 373308526, 106538140, 704804459, 316311269, 360613163, 741826787, 67876841, 798265595, 648947560, 749812719, 173551148, 834134818, 299531282, 363715291, 577657470, 299736145, 905065274, 450722547, 650417714, 267792775, 160731406, 12210953, 319755417, 85943024, 964608796, 640576106, 792588652, 941405059, 591910949, 983278257, 573287439, 83850504, 709650303, 335664185, 314955033, 574517077, 471575202, 331150194, 529353510, 558577599, 456407135, 18065783, 246123066, 800894960, 200329164, 825306730, 785021953, 246237531, 390275824, 294801066, 143707896, 111868645, 38195993, 915345522, 557536511, 828599694, 660245258, 454496975, 890761378, 483351789, 532156391, 98451914, 367656117, 180459295, 205225944, 579977291, 531857924, 115953052, 349752242, 699846398, 429886087, 907005841, 248968357, 247232459, 970249776, 659739437, 709937817, 276165265, 881950091, 56316271, 331183431, 523271230, 546748398, 295151111, 974952209, 597715429, 236605532, 671155869, 772794593, 782082940, 597323743, 822706791, 708424269, 802516418, 274378791, 321249995, 569028908, 849724994, 442288236, 571252292, 577535714, 69401886, 925312889, 475033249, 129005416, 417023141, 992943862, 443458389, 142691575, 52801795, 349043433, 341543641, 300303371, 851311370, 14345332, 762334625, 91202475, 312485995, 88366457, 144498039, 27341128, 739910191, 732717464, 509709306, 552517855, 779671908, 562497218, 373736085, 552635916, 515684255, 135244821, 840020737, 212910726, 758541094, 264098584, 107293145, 158445812, 865214365, 650124184, 526364428, 817658550, 198201446, 117871177, 865395956, 39278449, 141897350, 466010186, 421816800, 930735521, 752672143, 356185309, 873984747, 24562522, 171835869, 364796830, 995969850, 398768053, 801029565, 296076348, 7109421, 435891110, 971420116, 639473915, 492105412, 44728816, 369098623, 346872491, 618512332, 382361381, 206843524, 574953830, 755275741, 65688946, 763050905, 282610510, 297505801, 51898199, 342019382, 106236564, 455926125, 51454174, 388482173, 173008992, 907040138, 946022316, 939111831, 383788358, 62663909, 687772188, 989342801, 965813758, 60788336, 472431391, 181537695, 334711220, 947180555, 105906173, 552859987, 307392906, 928521400, 255870974, 594747145, 534599424, 442910358, 504058258, 778222558, 423849795, 375660585, 791964386, 567781655, 849236664, 615317929, 176448696, 327689549, 19988771, 749765451, 563795819, 478967226, 898670775, 413388291, 930362922, 230127058, 52789854, 599875216, 425655250, 6267655, 865048014, 733440712, 563784969, 429434534, 668121593, 385109630, 111523339, 364970741, 639958856, 819171349, 200412351, 365535040, 563942036, 254821225, 862013811, 25321692, 821148812, 339475224, 208125655, 590660750, 232178376, 455615703, 268749356, 707575775, 913570643, 646534812, 235100152, 773737467, 820976763, 431250946, 187311654, 190919847, 248871425, 514108663, 444404815, 125434276, 772675632, 387401550, 848746309, 757812347, 421228988, 568215507, 104672979, 59193243, 748708352, 425725927, 398962752, 68025589, 607719666, 763676461, 449152150, 224128062, 957330093, 749112278, 567057667, 962661938, 594496731, 945777798, 402530057, 815270563, 842348941, 137958506, 264309663, 965740361, 185110579, 514426015, 719653913, 485142670, 375783280, 672601604, 21285767, 888896084, 166051213, 636277976, 507070131, 213058641, 317990352, 683308578, 930399938, 397716770, 435727452, 140739559, 105727172, 727409056, 160074986, 177356779, 479478459, 749227198, 7698293, 935632907, 789769683, 240311733, 292201381, 138368918, 158231747, 867159257, 700911871, 533363340, 987516058, 216725642, 111962687, 926709333, 925725238, 131885890, 758120243, 422308443, 206227072, 411439377, 297277776, 195759758, 121397652, 802936246, 638799364, 888100310, 980291905, 264151689, 983659464, 621260680, 817980798, 155505171, 390184985, 995394441, 387241021, 474267347, 851361815, 641163125, 619784320, 539629302, 756105768, 275907499, 558037648, 713074046, 976222018, 242170291, 238263670, 916727753, 928384688, 597353897, 235786638, 58215618, 2155964, 217402312, 274493288, 822652227, 965179468, 13612658, 158775512, 155091845, 547878536, 293614773, 123470022, 422879911, 808040441, 825175495, 348916375, 469267386, 517400108, 744373140, 62869891, 140879825, 215785389, 394782466, 449736636, 414764013, 342366587, 176849512, 943842028, 505866115, 204662167, 752322559, 281267698, 957534464, 639188782, 514571142, 931370277, 184568142, 704738560, 815332896, 732129749, 369119499, 432788571, 990628142, 983024988, 555219635, 170530998, 377515897, 220816105, 283857444, 126926676, 235451859, 229745749, 210512214, 942268526, 112854025, 109143218, 412012177, 547518882, 770039645, 139172539, 491536695, 610102809, 240187603, 447389520, 703859149, 900259756, 693712013, 367078869, 909429249, 314498739, 341608845, 775426608, 523565447, 767517298, 767568065, 75684690, 250977541, 942179357, 474477398, 121599495, 272780685, 777277649, 125689324, 147139726, 780215306, 676115017, 402300349, 675085517, 527691890, 27743777, 470263196, 441974038, 720601921, 46225724, 855660498, 818217459, 758483331, 597039251, 623614996, 899458982, 58713395, 287338998, 113992690, 437375835, 476494060, 400330424, 673246381, 290968127, 538822494, 175760522, 243797690, 236657665, 146093007, 974815506, 724459526, 68232074, 383907045, 564129016, 993445575, 955598933, 64892748, 562156770, 851056872, 169977096, 100432000, 939983969, 138940850, 232495449, 648528248, 41706724, 752359768, 895304825, 223507792, 939009089, 139832994, 313170881, 296420883, 758236662, 983668103, 579826112, 483680684, 229332650, 458090493, 763811674, 596181786, 948531677, 619231071, 469375513, 352036439, 632047788, 705956565, 877228964, 17078074, 815840788, 102436296, 880518608, 334687383, 851983533, 886456220, 637236624, 637597301, 58062105, 494352968, 100558896, 525277407, 783695184, 304379573, 242050125, 762522182, 576093325, 71184122, 749589004, 766504530, 342113416, 741838637, 590898356, 826979534, 980811598, 205029803, 324450995, 45898583, 940196724, 22878829, 660468558, 871217358, 967962547, 928085000, 891889828, 914083641, 504882806, 414756698, 180292570, 195939021, 936249419, 319375310, 768063919, 151736293, 89655122, 514662846, 943717098, 725011505, 238887425, 897911515, 539700956, 798326621, 743771530, 71778340, 848784163, 159474131, 545363138, 126794988, 101581357, 627370981, 676338817, 130790722, 692455832, 6096807, 920744414, 958549364, 255410935, 895294939, 344657752, 824754542, 807666101, 826707949, 193500779, 520986422, 529188443, 82207794, 73977910, 484489423, 883948832, 826400495, 728489229, 900175344, 189832437, 541161086, 926794934, 553923789, 943936733, 179351805, 358108550, 715257360, 700779611, 978955990, 508298140, 194422904, 808261289, 572432195, 34582253, 702850457, 610810131, 922848563, 75869986, 941101705, 451610701, 259315619, 51752412, 444396285, 92791638, 761282608, 862430271, 893834353, 856474694, 20498327, 669852355, 178335146, 443999478, 664909021, 604869667, 264450644, 852081668, 794323420, 754266423, 443952005, 776987298, 220298259, 290049483, 867604629, 30575413, 205244793, 443495495, 496843657, 765871889, 204201862, 397534992, 161187320, 399890152, 950589661, 915361090, 353771109, 995569641, 803929718, 633394819, 684772888, 85175999, 724668338, 741168734, 367105018, 167060075, 445240520, 171424027, 746465648, 636194721, 176463767, 548004479, 189614628, 81218713, 657090124, 203361839, 386453043, 812418621, 897213054, 300835149, 651791687, 179095727, 614933708, 874411592, 840703858, 333369996, 287550957, 966151324, 5837542, 493407304, 527776194, 276989461, 994513137, 438845583, 45568966, 29475612, 987268394, 586037820, 435586939, 456298718, 265101688, 260834998, 730710313, 956080839, 224062281, 913514873, 434021772, 310618301, 882483530, 327172800, 639893474, 204374088, 565858727, 346561820, 360149806, 720564222, 414542613, 66472966, 514417483, 725505075, 478600973, 334118824, 464482303, 727758198, 689537599, 723966733, 77454541, 657551495, 956107277, 6295325, 353281895, 981907516, 116408947, 606060770, 63610337, 303087506, 549983077, 419046963, 984910079, 243019387, 116876193, 323337563, 779448524, 533369055, 597761039, 597972072, 693875295, 408640400, 617348555, 741674964, 254991648, 289593634, 814737830, 152234064, 650450656, 23181074, 915226336, 935117294, 539747325, 201905642, 717059187, 607899575, 329939355, 574188215, 289216694, 855591142, 427899908, 866542314, 767422084, 224607672, 125306368, 82186962, 619642094, 938321792, 61581316, 164782343, 750213540, 684971629, 956866963, 382532184, 673250885, 148278326, 743630773, 830364254, 984222815, 605845071, 924053307, 622711981, 595619911, 486401452, 71432297, 636902452, 667956724, 18811314, 993771866, 131431310, 678884671, 700975385, 331180144, 429535911, 319629297, 359955375, 972375856, 463184611, 659526791, 360002753, 781619151, 279206919, 861877164, 249386135, 3070333, 167327109, 690894435, 861168495, 419604354, 246366603, 382211318, 969741646, 184129968, 39490442, 813511053, 99225008, 525174877, 354058876, 358353524, 847693741, 814807804, 100517671, 202038147, 585468873, 250303672, 431045354, 346386261, 85652230, 955824098, 780285507, 682184598, 539214504, 404336384, 885957687, 565379664, 967301944, 511179663, 729715650, 315177418, 132255592, 126227538, 181233041, 705329576, 634491239, 819250788, 462865472, 258152635, 513606195, 475280783, 525847644, 161050800, 911805114, 341241120, 711139408, 430192438, 441010440, 565931565, 977666241, 826261931, 576698811, 531547485, 261104656, 981782130, 842530280, 373162673, 636454622, 51589477, 823049044, 89054369, 493686037, 332879562, 520834668, 371909388, 850389966, 923640431, 757541760, 135679283, 392234944, 536827947, 190504329, 843090479, 845944560, 563376799, 573358862, 437298562, 9307981, 582526635, 625561967, 158970823, 927082850, 423083079, 952398206, 126540039, 55138091, 967012788, 633740314, 565322336, 229149106, 463146034, 883439486, 971555795, 361717520, 898707045, 502603990, 743756044, 992939379, 231132357, 927042323, 881659319, 832902784, 852421844, 770391256, 975075528, 416251245, 128679930, 525889119, 40354257, 514749085, 615769517, 581079872, 792549824, 983336057, 455111282, 30914513, 868771253, 882030438, 387257911, 202885532, 575424955, 995800549, 707723934, 812663760, 68478673, 478410914, 669363158, 215975086, 949403560, 554833097, 854895422, 263780891, 560662246, 303116133, 475252760, 704677356, 788694958, 240857356, 776373008, 578433274, 117224597, 442108102, 562438297, 833963086, 302033123, 824570021, 65190046, 377227499, 316336696, 713781686, 522678144, 508622027, 578657967, 891957411, 625457334, 121104903, 444447013, 443790216, 674385704, 553420392, 288209085, 304582613, 942719267, 903479842, 278898730, 243377127, 966164683, 536597033, 987608491, 620825198, 284430250, 915929529, 443955004, 909429503, 417351887, 936170901, 647112580, 913301031, 316864999, 932135605, 89843234, 592506694, 376973493, 657351493, 371380900, 415606255, 955988404, 966928312, 242661039, 810081577, 523056781, 881985887, 357046582, 514557568, 709299051, 294324329, 616274734, 143029664, 989146572, 465829681, 266810563, 187644780, 781372288, 335605867, 822970529, 259770664, 711195571, 233928893, 444085180, 426570345, 14296866, 359641851, 78391951, 892529329, 851281903, 288973898, 579990399, 569585281, 146419219, 576609368, 443071780, 546048894, 336816337, 305902204, 367137343, 525238186, 177776031, 725275296, 979826203, 344412003, 738277355, 232170222, 134428313, 221840273, 771886530, 245845888, 94714270, 546463098, 244292867, 842705232, 651934762, 76311951, 962611005, 729997532, 469092927, 974853696, 593163802, 921016953, 198673732, 360848035, 235408990, 730141831, 160406584, 125169243, 612740819, 368556106, 342804180, 123035813, 724429919, 948059007, 823315644, 680321175, 195772746, 862048414, 681684314, 903357387, 665755608, 96888696, 731874685, 631027528, 956737245, 915339214, 245743475, 848987093, 892398409, 877074470, 278850490, 139253974, 164129567, 981377497, 433871533, 659256456, 375229121, 540526621, 442646956, 405065909, 105659001, 754429583, 950748788, 864784065, 245810663, 824733474, 608184384, 282320981, 617422971, 682146148, 382432757, 576836819, 189354322, 878692539, 623991255, 432333702, 891673447, 10897034, 220360957, 489023188, 852598301, 641239053, 155979647, 604409269, 975739403, 353082345, 377373000, 874251501, 943316702, 884378788, 374509006, 281885384, 306188877, 503061046, 211389635, 494594683, 931871575, 95416770, 34408679, 402298938, 111363108, 32025397, 713884978, 525025664, 79553205, 960124263, 444061203, 570052480, 304622345, 75055383, 627860589, 444547414, 637831541, 584236382, 240560424, 117912673, 170695770, 364536846, 723172397, 624060754, 689019021, 381766254, 517513714, 541526102, 892958824, 147494932, 444915026, 899359037, 582586036, 189788537, 352616677, 20489823, 953090458, 558178434, 733275898, 762374626, 416515418, 431321869, 458875134, 690538068, 8648067, 37028738, 145043554, 436741631, 51245250, 14789642, 847252928, 156356007, 527862890, 707915394, 74316324, 470158843, 145177795, 202494917, 447354238, 493044052, 828264724, 245301569, 599343987, 203164598, 847557639, 616010461, 301283399, 136535169, 804930707, 757219436, 992108370, 538278151, 881083074, 477944783, 635771300, 841548978, 312713474, 358535469, 274498933, 951461747, 662193718, 521120156, 467882528, 263682188, 371515499, 763218957, 912424737, 967210194, 909521224, 329228538, 434244315, 572788548, 468711136, 252114318, 343559688, 342461465, 460513809, 971196458, 377214365, 675550211, 584271744, 357018694, 158373314, 741735871, 981033401, 384335804, 766056599, 14021661, 304567409, 337554110, 491117801, 919621072, 912604250, 593585361, 368362829, 528731991, 761799429, 408073755, 543616562, 891539665, 17785959, 12463808, 13300388, 356349463, 142759289, 282335667, 869098568, 777672230, 490007366, 294554609, 105943434, 453478901, 516755913, 719187933, 378234200, 18782494, 817187777, 483524465, 528463777, 628596702, 74724703, 732162916, 644626873, 378170574, 314405301, 305069446, 195062825, 30223453, 699001705, 30822599, 175167381, 896090378, 211334006, 365633175, 156253805, 944725794, 942780334, 684602018, 885294439, 811495525, 965301302, 134816728, 966604717, 749904645, 405027770, 379897130, 835928612, 226257727, 531746727, 391528288, 188865985, 285422771, 172274353, 237436520, 448204586, 793587462, 218149195, 538864460, 554479122, 289261052, 332053278, 750932963, 86972347, 190936595, 556408446, 664037552, 421352561, 564689419, 851646167, 350818562, 701582095, 125177861, 876347778, 981157855, 368080521, 254502687, 560175605, 496320217, 57461457, 804707584, 16887754, 803101902, 128065017, 551717624, 274830237, 322504587, 180639667, 171245864, 417203477, 460548904, 64720550, 570377700, 10508279, 155701433, 671601657, 865522912, 762154392, 743517454, 175816921, 447929738, 645606783, 964195544, 801242992, 129475563, 979200241, 379873116, 941396826, 704810924, 451104261, 649451312, 214029070, 438491334, 632250010, 246966622, 990882517, 3449075, 303536806, 422847702, 406541822, 459783042, 470718796, 834437445, 208221097, 280441453, 73324905, 212185978, 886709767, 340783865, 54495309, 428902720, 824730867, 221181047, 108858236, 94126211, 816166461, 379899925, 616985583, 49766810, 764488960, 117297407, 175990918, 327156531, 234846935, 972102773, 400076901, 760961268, 49486519, 893741275, 643266138, 654374380, 254149454, 373515215, 535202204, 852290759, 513441832, 784763054, 721245647, 503256135, 625051810, 435123393, 637982746, 906816053, 28177261, 169919786, 27690896, 599082772, 867113935, 575889677, 956485729, 219570552, 404083094, 209374498, 368832308, 267342673, 302361922, 467059712, 712311481, 144388676, 894861016, 828892075, 286552865, 208440526, 517094696, 503679020, 37256279, 362739566, 840216996, 480601805, 859553341, 51063888, 256563412, 110371306, 765814994, 87559534, 582337179, 562039020, 260052466, 16499979, 745223868, 920892494, 250885336, 545269244, 440266649, 893695868, 951883859, 147266684, 779782315, 397912711, 760459251, 697078058, 539893038, 515374968, 198259905, 47839861, 783966723, 94446139, 239965329, 190786887, 151064081, 817339115, 65338706, 592275633, 422747827, 232381656, 420160494, 231708459, 390649508, 383574248, 771749577, 424358621, 636937649, 968960394, 801233233, 475733934, 89617372, 758262130, 814510983, 39319404, 45979537, 679346942, 196921034, 734918173, 53944988, 724615428, 69548267, 828494252, 515149581, 126038013, 914694741, 499303710, 603277485, 26658685, 637852223, 674578927, 966158942, 983538432, 26955867, 900129594, 326654183, 186206052, 332091238, 607471278, 881678525, 321259812, 367975616, 656068913, 971288793, 885735878, 115525850, 42769539, 326949118, 177866981, 141326573, 789505129, 682992352, 386681065, 181746718, 313993679, 202031035, 925397187, 331354707, 178178719, 671627709, 390364568, 837380130, 633537322, 435070116, 539695768, 281382724, 52747764, 890377605, 814089749, 737646629, 557162069, 116483274, 706708210, 452959464, 836495551, 223943844, 619383489, 343377621, 592564338, 353396647, 273546855, 836624851, 676259226, 124711716, 186186819, 410118528, 255942419, 483761883, 908546312, 2724675, 799117495, 248187163, 62783072, 742417385, 470079985, 458855717, 798544054, 616308335, 48574972, 343570771, 505952433, 360823071, 273163265, 472798200, 340209615, 512696721, 345327477, 612930373, 874753406, 897716811, 743306736, 362858925, 639304060, 724243499, 713566172, 850079115, 698913146, 44084772, 466992474, 482743491, 26444216, 760324660, 784139066, 134468601, 722800509, 491599507, 716497796, 833119747, 884873413, 362461914, 630109627, 47885764, 98604090, 168579368, 517980212, 609513886, 153587888, 452836115, 192145221, 725743962, 946098605, 593127805, 266009304, 564223355, 148085103, 266979923, 980482473, 798847077, 309166579, 417447806, 208170218, 472333519, 342131880, 871904554, 608401809, 126764964, 455246243, 235969360, 644088121, 946959714, 480100177, 708734120, 588136923, 62687224, 142949600, 454444322, 768490829, 462895920, 909263154, 779591959, 806163192, 196817499, 998753993, 68609368, 805878485, 809945851, 705823810, 909930410, 774669347, 584932467, 508638445, 891706950, 920780414, 771188614, 777432078, 904574374, 409903515, 870771240, 728513469, 931928037, 359086704, 457720230, 849943289, 579039493, 965691734, 668749175, 255544773, 61120925, 567494906, 828386524, 364424300, 285637312, 61610016, 676389794, 758484480, 145100607, 559152899, 951474740, 861391596, 852179806, 773370830, 40895845, 968896858, 472489412, 182718757, 809089790, 522288056, 937010430, 123967769, 607540452, 285100782, 54755643, 916506133, 38289914, 347244656, 649657973, 854368642, 795075491, 161041242, 64148016, 327910306, 870613856, 915467279, 921242224, 231659150, 797398648, 68603334, 130982655, 202578549, 742855221, 601140100, 597193341, 269946797, 952109403, 592680272, 580216153, 671197166, 564248074, 331127303, 642287246, 589146255, 885580168, 823130767, 217941474, 796819834, 779011409, 561638626, 243966082, 744189237, 688094466, 428960960, 45011673, 478627505, 36129663, 158899647, 163701221, 219169053, 142154058, 768065091, 374124630, 88272778, 740793580, 284263064, 958346620, 870937357, 787291814, 635207812, 721343666, 390304655, 317603844, 256862508, 991229943, 912127497, 731688216, 808210838, 545167637, 692400085, 468107270, 597351794, 658947977, 775592111, 838278928, 460381893, 651908624, 517331936, 238150839, 776368632, 146897855, 952257335, 845198064, 327138002, 410451244, 774412219, 850780144, 534064120, 380965285, 645627345, 238011523, 702985337, 742021619, 299142231, 246007308, 749212682, 844246701, 387422121, 794447815, 667602389, 852387406, 163321670, 769893167, 795851546, 704372637, 278011014, 43955244, 294265123, 483215957, 46235550, 334725948, 22365999, 715578551, 338881964, 951262382, 96366964, 959845221, 844665941, 622119607, 283875773, 74875276, 608337449, 266623965, 422544853, 10952348, 764556013, 925744306, 619329417, 757032480, 699092424, 772900140, 966954666, 287833672, 868284344, 557555501, 976109080, 621221562, 905172146, 639424613, 319404840, 888159598, 418500758, 693775740, 639530484, 944979649, 563958570, 217386922, 39862842, 761330410, 503945272, 570161000, 695089673, 30740728, 278624871, 88270775, 483134928, 486857870, 884552920, 568494182, 248807789, 601487087, 582223622, 167941423, 9218579, 452894027, 817359050, 54591287, 316023414, 63083096, 381424510, 936851845, 419582262, 162404383, 318670106, 15534859, 926273729, 970305950, 548447825, 647586811, 179894291, 45055020, 339107947, 776280040, 107645675, 947781479, 442904169, 43306851, 942613031, 763953661, 296823121, 192194387, 245639039, 213514908, 254096747, 993376413, 952023783, 745936531, 221679087, 33647832, 467179473, 728077684, 581405692, 476457077, 59986855, 616379095, 376438648, 823064559, 703088427, 370077528, 442600886, 464032606, 382723310, 728896903, 252519780, 139329292, 376465932, 956551445, 784788137, 803292693, 279035038, 925273656, 559930240, 533960670, 663002657, 54584760, 883766910, 641780146, 51007038, 467107563, 458725069, 561949572, 524779948, 578031360, 957085129, 871802710, 127658864, 234328485, 922738752, 101951399, 651425087, 749720624, 424741601, 355723549, 431313903, 870455334, 633524731, 45057909, 217078659, 294059190, 297021478, 144021083, 696766307, 47447300, 231246448, 744118610, 949830900, 113138157, 940817900, 736084445, 153899645, 588353193, 527466035, 659593192, 518173168, 131599213, 704094381, 274511088, 186360583, 772690270, 734485421, 296136170, 96817284, 602659912, 588826692, 164674844, 186577083, 92344685, 255548587, 665189503, 758274205, 510505112, 944288702, 435241944, 432060107, 350508422, 360655281, 413544600, 240221017, 968648567, 203202308, 183998942, 937676053, 926208019, 254115414, 130798127, 528433206, 784444910, 42105414, 636174030, 168883551, 917103962, 148355802, 155482177, 416261069, 230409799, 749588782, 568599426, 568224799, 143614401, 607488503, 867416743, 375578064, 505290520, 925837691, 700122916, 625936267, 691955435, 746545602, 579294152, 554026971, 154732769, 218171458, 265359447, 937052389, 909089846, 240079828, 341009208, 18705302, 731072717, 873218417, 995140838, 267786750, 138364649, 574093734, 955509013, 317899042, 574720974, 78566825, 790259229, 570681092, 585889337, 948354931, 788206070, 81728845, 865220469, 368167574, 421123299, 512357736, 25156464, 194913820, 135975097, 620997533, 25202035, 7823296, 202547659, 820527438, 964501698, 373127769, 162564072, 890598272, 331729195, 861638166, 515497255, 21064547, 577982518, 627357212, 839076221, 674422585, 414318359, 738004189, 965629440, 831771012, 509605714, 826783985, 210958570, 696228377, 450123956, 419649402, 604032036, 822618128, 16048273, 335632450, 222330511, 769496371, 807302343, 702933791, 536849336, 803393574, 77673253, 457456916, 67152317, 573623030, 754515057, 198093248, 749605345, 336025800, 340129603, 301259640, 527712022, 938117093, 301376889, 219607024, 140170699, 752694261, 91476285, 41099637, 794954543, 61132478, 568086812, 370602087, 917008903, 817446106, 277485789, 176420045, 664204283, 541994719, 817715012, 938836326, 472562985, 56110483, 121150515, 48388444, 110888606, 957924675, 583672306, 3953360, 52409663, 564828429, 493686121, 606814030, 864514901, 435403154, 551160039, 245537754, 774052181, 276233480, 847092754, 146491055, 699822710, 975032935, 607086047, 385455330, 787484020, 630082845, 911658452, 378857330, 769141631, 331491189, 841461494, 262782023, 401716294, 687610648, 426297672, 370125003, 492253973, 334705960, 197665428, 858544281, 191466983, 465609791, 87546880, 348764462, 615878490, 811219565, 165618979, 432233219, 33386178, 817311665, 767873221, 388927113, 463024387, 354424341, 5343536, 588646859, 748822856, 135191078, 813213201, 748841733, 245424888, 86359644, 801119148, 764127659, 634027188, 97482455, 434043885, 637161813, 479533689, 948499653, 138506704, 893054344, 566767675, 949691256, 387972496, 601599056, 800737784, 390243708, 637126290, 670615860, 944559450, 746137708, 125385095, 325997204, 357483099, 193803387, 800850347, 777770905, 172536316, 89215787, 264255271, 563869065, 207896443, 149061203, 290576202, 656829102, 819678497, 464278310, 996207681, 821706210, 496316066, 915823070, 339878011, 627001148, 452643442, 561948732, 46097629, 605819100, 126911098, 250739737, 916262376, 583226449, 297219579, 909984474, 447233609, 48629995, 373758364, 375564011, 824724995, 95566012, 383012598, 348057436, 887067817, 491300429, 219053970, 468954693, 614738547, 395130808, 787140031, 879352958, 123748246, 657428075, 515156111, 918178724, 302731319, 136386259, 124283119, 598912821, 873325009, 404564932, 740005071, 717961351, 816358355, 377830074, 771954375, 761962158, 293856600, 175451516, 84199311, 741796213, 44938988, 120346283, 666330673, 119978350, 989698162, 759870062, 515988954, 830961131, 932542995, 376369967, 186316886, 138275978, 906197351, 319995116, 911393021, 217603608, 449204254, 356174298, 481066132, 515513288, 906082827, 199035144, 195320946, 505693405, 372955203, 521589233, 479510719, 848361304, 463456086, 355331607, 4918264, 78085349, 564271635, 486384050, 232879244, 502315245, 955018261, 491033925, 577068909, 302298654, 415219484, 989557456, 344571368, 136569182, 348876764, 702957439, 110250006, 354162607, 670788313, 44477905, 898767892, 982851535, 357177096, 935685590, 315180531, 530133803, 492821316, 430347782, 197239777, 784728877, 267882049, 194076459, 65867589, 946529068, 386070684, 796204419, 577333956, 489097831, 893159858, 736464890, 223413632, 910048532, 168293167, 568828770, 700364664, 461383889, 272289955, 590170724, 215706101, 327627900, 125426651, 258339148, 301585457, 373781727, 14046268, 941475522, 708303192, 502390643, 898616136, 469046159, 169795741, 182245817, 993926138, 781526030, 855039458, 753768564, 816613527, 823146974, 975469029, 695678936, 158761149, 675505393, 576146784, 361558506, 761669896, 521038342, 666669389, 2296348, 712139617, 537175971, 506211590, 259034198, 756666996, 900963421, 358037521, 936602207, 340500107, 972454560, 264408545, 274784526, 33955534, 233067628, 722620942, 433721464, 375431275, 324626910, 293879004, 413264736, 690831981, 523685832, 321775502, 333976971, 155450462, 179949993, 315130240, 427191266, 658024817, 879403618, 673897623, 201430399, 973837807, 224868928, 952222172, 700610781, 314285878, 652855298, 610043573, 116925152, 68612240, 81170759, 36951945, 989526446, 61240926, 956881682, 645223222, 476182932, 511107961, 892965606, 62594578, 848547604, 363842382, 77714101, 314673249, 682148268, 911591328, 769452875, 431843094, 718367817, 367760804, 852609279, 766419695, 590250124, 916426437, 63530489, 576658246, 49860500, 458923469, 303913539, 622923169, 784480903, 413038245, 921662847, 451086286, 111462804, 150043257, 648524574, 939283964, 687100965, 746062562, 112626287, 218753725, 971723074, 741128026, 70364300, 45320356, 945437286, 657153219, 667974892, 571938536, 242651863, 394717870, 641622287, 350986683, 812079549, 378752707, 329285367, 357523390, 688578972, 522414345, 668913893, 649123711, 915122629, 831758404, 461352739, 295669542, 687499045, 725837289, 918229296, 918873818, 127105740, 35834430, 839513863, 96594368, 214053365, 405607992, 892965748, 673263155, 162387739, 419291444, 145310181, 781388651, 865870574, 804389713, 445974059, 981136545, 180570515, 911763473, 121300284, 99391895, 913603832, 112704569, 808430776, 994996047, 833486015, 572953484, 42021352, 267467291, 300526133, 939683235, 587692180, 250181069, 896835144, 77140211, 911361074, 21920424, 856214790, 701491668, 406566966, 66187036, 729745642, 612707103, 211072417, 135139627, 974569467, 681252121, 402542375, 578084775, 833454064, 949682391, 583160919, 197310066, 538521064, 487864774, 888383773, 156082149, 150972051, 750793480, 937351356, 426387780, 314590634, 8216575, 683792237, 297699318, 568222863, 63345912, 118615737, 498830698, 292659062, 730806387, 119997324, 408831790, 207934941, 643071290, 184573265, 28475771, 555892892, 351253997, 677894590, 697526406, 124412467, 928057183, 753653135, 686178168, 500941478, 271290393, 700932740, 421368029, 475791530, 697203195, 974644715, 160436099, 206692272, 145259901, 622805838, 422510463, 12188627, 16198218, 988198882, 128362197, 145289505, 780903514, 475662035, 172600752, 104366472, 822275625, 326806150, 615365423, 773945646, 458540342, 514668415, 358522251, 508697152, 929811081, 626332364, 281962096, 904254487, 78166371, 746106397, 687335086, 890291517, 368573382, 967490470, 458904665, 573001193, 519868832, 911728281, 186573801, 386232071, 787321051, 462807058, 526651904, 41660034, 248031820, 112438846, 744144030, 986509928, 662075362, 79586584, 964499786, 864303325, 551292904, 963998107, 190029977, 772948292, 522228681, 813374733, 71719638, 308914921, 668916578, 653546910, 559276657, 632316841, 882901305, 270367716, 282951411, 826646455, 942535491, 476331610, 327754633, 729076391, 930984025, 555355974, 855975441, 475210104, 692217824, 892422824, 850786487, 557814008, 399609757, 64959409, 396649778, 136474560, 161332977, 754827589, 622609581, 276025941, 65466436, 138261133, 117215505, 607115202, 590363885, 653408346, 52802136, 957264966, 258040897, 566519023, 580304322, 10335991, 371945754, 365509434, 748790577, 684004718, 524412326, 598754374, 123818790, 935693380, 175679316, 215674127, 6738842, 842394487, 306252391, 363488791, 123066828, 147642685, 534866857, 428258996, 489459729, 521356539, 989744087, 726767421, 698238777, 852125210, 947129854, 425666625, 161922317, 858300424, 598720148, 118470507, 852841937, 468048568, 784375891, 175364940, 924251826, 29992293, 24910042, 990656184, 631067395, 99988101, 847957883, 902996089, 11764817, 615439038, 324402793, 990051505, 765438475, 629816571, 375643160, 805277225, 338426777, 606565969, 338138492, 502349743, 105225670, 676031620, 328684944, 417016894, 285602023, 923666815, 571572702, 330420314, 59476777, 839800992, 564836345, 485793866, 881642474, 679707185, 801177864, 408977869, 570913911, 917954196, 639330278, 572087971, 10333980, 938051024, 424380859, 833878560, 357829269, 251821921, 183770602, 529798001, 104379987, 226168597, 40411549, 432032002, 763416444, 707940726, 691374166, 820402200, 399541024, 962527762, 945653206, 818992948, 796868903, 426273017, 728939052, 414561213, 536572956, 953857079, 444165267, 205790863, 867390193, 774209570, 509221881, 375707712, 39643668, 622878614, 815830521, 598928038, 986435113, 974206125, 840773552, 864516329, 677586328, 465537121, 643829714, 230572623, 522685102, 519331144, 209818061, 459387757, 757438623, 966892423, 788425304, 895630100, 824311152, 995251369, 329779428, 617015717, 102654268, 417927875, 896802862, 641431017, 379294383, 335937826, 148374753, 436266820, 379287077, 510760350, 568686376, 118103574, 945708157, 805190400, 40309812, 898694155, 427978203, 93081523, 162466438, 54297035, 825251586, 423182996, 311713812, 533787664, 952021997, 579038926, 855681784, 770282832, 456025949, 172938049, 950526623, 442508772, 358107124, 605999501, 941494810, 127904897, 75392752, 246116887, 441711953, 467678019, 592806405, 27674535, 884838527, 886989877, 147442637, 351061720, 36889897, 67676779, 51272478, 453032560, 457644833, 299095311, 747737642, 573016029, 143377211, 700931155, 207818163, 660734266, 805560655, 555143462, 873883278, 452128706, 653154774, 821367259, 596657974, 135307882, 337361170, 666915952, 447622356, 374977428, 743321519, 970004528, 269634810, 935277706, 969318252, 642760626, 508064792, 949930788, 285238058, 770436512, 603541879, 149094351, 436236613, 379634108, 824078414, 624141856, 753148467, 354127677, 640885088, 171046933, 867542871, 308787920, 219946032, 688468327, 607961916, 790392766, 611131405, 428330178, 614857112, 242931402, 26836946, 722777570, 67853966, 223657821, 20740846, 38531329, 688686042, 838728628, 978534544, 792947738, 236975098, 28668997, 564237671, 90583692, 739961714, 619917399, 620680933, 307409430, 621631353, 102592029, 993460527, 508427584, 449607245, 827738640, 339847129, 605226611, 331677566, 33054163, 325080206, 834832849, 15682894, 639162835, 188617832, 727312662, 493406230, 390378574, 273368975, 871732281, 757670024, 759599604, 29200750, 551986959, 537325719, 122843660, 68074145, 680680316, 357141218, 449854643, 359341306, 333446533, 996180319, 170567794, 500722659, 445245499, 824778185, 374386641, 984788932, 86820374, 683338899, 566319515, 343835049, 830974111, 288812046, 218672356, 543509629, 809446764, 214026963, 82366259, 342779626, 232758894, 578414295, 870711989, 697995267, 209641959, 528880200, 803859590, 404116109, 201268756, 938923501, 719175799, 410341797, 114643743, 882321687, 165414789, 806550864, 466953754, 67481203, 440387475, 786640258, 27415676, 923406068, 753273185, 223742431, 411213840, 260760603, 471966390, 444599629, 466781690, 767300955, 355910668, 792716266, 179518929, 918282048, 192446855, 365872508, 93700544, 799453966, 283356288, 450687688, 782267910, 106305567, 860505301, 637399301, 188441210, 214065824, 353253006, 411945359, 985888357, 968772893, 652351261, 618953682, 64090842, 35844702, 902133683, 960912733, 139681347, 257863742, 27437014, 964534349, 849875472, 925536835, 310699357, 467146675, 457849487, 784711740, 240835612, 948131168, 926824594, 326467828, 855262527, 207057335, 286188711, 22086600, 810093320, 617866127, 964951771, 627238789, 367375100, 695389843, 775994963, 588620995, 279905415, 909799029, 167949841, 360390817, 333527163, 391055604, 232982181, 666108926, 806803851, 701722940, 481372161, 600380283, 533489459, 391402585, 225044508, 738626619, 606773630, 670949685, 631535462, 349227617, 629047813, 247484406, 133392409, 135215431, 566583155, 485214767, 484537115, 288918330, 41115344, 271088385, 151960450, 699362081, 577788816, 536526000, 111250629, 460387930, 505343533, 625275749, 667927464, 552176395, 833501802, 281986254, 340029015, 802070206, 747105334, 508847069, 276515256, 985736530, 874331458, 808672696, 818356458, 254191407, 673844138, 609234273, 670181379, 467876388, 327707934, 472040275, 665402656, 673321966, 325263443, 520865824, 268842549, 138655544, 149020479, 504791579, 125750048, 606530238, 100575623, 895551543, 52941724, 524346076, 932709431, 301681401, 969603905, 375027608, 525161648, 77915422, 182924312, 135296390, 85142810, 16366199, 114277848, 828424866, 85739994, 584365183, 207491335, 222460944, 932084581, 725732077, 506148608, 237055485, 589610937, 550943260, 749988162, 87269749, 874209793, 431799007, 753847401, 6975332, 466684927, 492994380, 46084529, 682166151, 459809803, 987776174, 383003067, 794535874, 447037141, 335752565, 203435223, 275986344, 149094188, 233775029, 752520933, 770783240, 127695622, 825204445, 947384976, 818140775, 281127390, 747391367, 942876091, 583879272, 574502384, 333214308, 198617479, 215065707, 269613306, 817559469, 767910962, 503420116, 83703152, 773271648, 290987571, 740727822, 234879448, 184668034, 20254837, 621480945, 466278384, 472613928, 271900277, 688538371, 914608786, 825082107, 427742920, 526438119, 766112088, 912519004, 742699609, 88917323, 126007890, 784064095, 876935439, 950442737, 364025045, 200652563, 507095265, 438130238, 405789262, 670217923, 904683373, 185232805, 139213367, 389017840, 53234832, 811676013, 771820178, 428468537, 188100373, 407803760, 243840967, 90284203, 679746942, 745024563, 332662252, 188904750, 213152660, 911794663, 710420947, 281902787, 63696994, 731063605, 800980286, 380124483, 177602181, 925134048, 303511680, 110275223, 545662874, 206293935, 197533931, 174727522, 916957476, 77126241, 916586814, 156294255, 879737498, 828688687, 786696730, 805089627, 850563220, 750952998, 438816223, 947401224, 894473977, 973574655, 1821882, 740727245, 927039898, 917036732, 285408621, 207544742, 271864416, 631969100, 976068915, 145161683, 842460960, 198982297, 390360167, 535853485, 783487362, 628960174, 573320222, 181961720, 700972885, 789897092, 757096405, 569775828, 363536568, 341919138, 735712358, 15763299, 600805432, 469065646, 502885563, 656347417, 654542793, 896709970, 196220779, 737330008, 832492018, 850459484, 131011066, 104098871, 857097471, 621982256, 815990167, 585388278, 731527529, 993706567, 81754584, 108856041, 350852164, 285265025, 313818850, 143266653, 89330941, 155599094, 792080222, 905695062, 875581756, 869805490, 322186971, 734231402, 555141035, 624032321, 291829966, 359304967, 578958028, 142811716, 484449197, 282878200, 90999390, 903277208, 255843378, 712442038, 94224367, 615059896, 386735401, 922505716, 694022020, 346738659, 428754274, 502300047, 807132905, 128118011, 843006865, 14170219, 644032106, 688238289, 416772751, 591587883, 702381014, 261988356, 918663401, 47261136, 992090640, 717056182, 337167319, 686164388, 612177093, 318537751, 269086366, 941598113, 543489540, 483164106, 726026505, 468359590, 560526753, 852311563, 887342796, 156932431, 58268134, 546077782, 21959294, 637297353, 246467320, 23374849, 259512393, 831867035, 88435783, 449833293, 922197669, 943007717, 833196230, 104145749, 286967691, 990405354, 160360704, 149246512, 681944234, 289423618, 565667894, 900077987, 846562897, 683220679, 978595184, 519465208, 943141150, 350202949, 648820927, 628741379, 345651752, 477797469, 321435399, 451534962, 545601021, 697236950, 748229736, 994351087, 63207022, 630595367, 569794795, 396587638, 520101306, 72471699, 768985017, 862184252, 237921561, 982446608, 723878013, 206625125, 221263950, 425642094, 798373680, 971675076, 669135419, 47412304, 980173909, 381268319, 105062702, 594608047, 572298830, 820305862, 995639309, 942771489, 562743505, 93546169, 782187283, 920168783, 686753160, 288615587, 607756904, 95182756, 259883842, 113569791, 861547199, 872948182, 116361044, 223843089, 714316951, 490894612, 335992403, 39310087, 777184195, 632443405, 49037710, 706276392, 821569156, 858631065, 628417077, 998790745, 303750443, 961325303, 54703623, 996779582, 186479054, 264089462, 392650176, 565394014, 183732583, 498292222, 447918554, 189461856, 672418501, 533076983, 368534227, 913768633, 888131061, 117970551, 432037347, 414222733, 491016211, 868820602, 187945649, 542382294, 560359943, 354677353, 878835567, 248509698, 624800168, 474982537, 461343969, 448341618, 541189664, 76142536, 271590613, 981782164, 715842392, 165551443, 299721544, 177461178, 533719354, 901943242, 836655122, 983476421, 170204453, 188221760, 688561941, 113873538, 260738727, 952846469, 7247506, 25911782, 776260810, 504445418, 210774563, 646624562, 784983497, 289940824, 347160435, 755739447, 559445612, 690149874, 233601073, 364574555, 416914957, 764755821, 631156002, 488276315, 508291912, 948451942, 776168546, 429790308, 898515210, 190950063, 811582993, 406983724, 191684693, 850115709, 141218979, 374790808, 893410758, 982194600, 770514969, 886148978, 441532174, 213661372, 240787570, 816124176, 715102862, 748580364, 324147094, 478884214, 246592737, 992818111, 124264814, 564051287, 80726820, 900514667, 341693090, 118731142, 75257581, 103678401, 756446712, 859964191, 852438443, 108240808, 147315310, 24639857, 546488546, 921749675, 883375449, 524735959, 166100887, 693771178, 709017720, 306289208, 83060713, 902554576, 587830595, 885705941, 409631255, 472464971, 958273769, 219400929, 327958661, 113904589, 768979708, 225103401, 341158312, 920018106, 944197557, 915817375, 311101718, 926851079, 491645059, 921556333, 537518761, 858662260, 687185469, 173283030, 567084637, 994174836, 716237467, 626974711, 758109537, 885874542, 964927887, 264732422, 68845730, 406532496, 65397079, 562710760, 563441859, 673410870, 765321137, 622899228, 158058287, 669352052, 976269632, 892294568, 508555186, 22759884, 408932722, 139313003, 227767516, 118589305, 929606438, 879051315, 410074092, 726280985, 920671171, 680047622, 335932464, 905513264, 305153839, 738853089, 8306526, 843652841, 399344083, 601611702, 458797884, 203721120, 10527418, 387063688, 797921802, 967750617, 453704250, 331999595, 172485543, 900672878, 48376961, 32616105, 829942312, 67143741, 227638853, 752251979, 518526114, 186644495, 875441304, 998613814, 782451946, 96753420, 306963561, 189032651, 806408307, 515808681, 184540869, 796691719, 108187869, 188935733, 263544061, 958251375, 700199824, 451939968, 342812545, 218936647, 18996645, 335411967, 530783917, 7953460, 915566086, 162277146, 734824212, 320076422, 405360168, 826348538, 802241018, 739291410, 349951687, 654024629, 71862895, 860136754, 269597298, 445613090, 320975855, 323466544, 751000726, 803218918, 744244251, 113959723, 675833747, 89931355, 283549153, 707561525, 303009284, 38924974, 38017772, 329966058, 184629398, 879005811, 652095698, 402642427, 383463653, 25028667, 571940285, 922024715, 709973843, 262414501, 839423684, 827556628, 716975880, 258414711, 288670785, 47718313, 585862143, 442265716, 118328844, 621751696, 933912078, 998928551, 912909771, 406050430, 303049832, 897831697, 199279363, 625753213, 543404577, 447432768, 859297103, 663549297, 7612463, 908310485, 853220290, 87136308, 294767797, 880056634, 302536591, 181019244, 186391746, 870409910, 955869386, 643684710, 933710487, 977537427, 946359425, 235459918, 226303626, 466476730, 440906620, 753932951, 59941605, 486251805, 613577598, 488731821, 396126133, 697179989, 348230648, 235986402, 492395956, 694627455, 592155741, 281906476, 686114258, 326068897, 317199846, 20862752, 457189676, 493120563, 451317616, 227027351, 17957470, 612822670, 789541097, 558074648, 27394851, 569128276, 985075207, 503287045, 988155325, 153796406, 640430102, 458657333, 952168480, 305133332, 315028144, 239569980, 229580392, 992971229, 106952404, 68832988, 437727637, 523280975, 547062665, 598726829, 211479536, 207755683, 999768736, 182856420, 978011905, 418167324, 80407929, 370730591, 427825612, 999212539, 376028780, 617849377, 969808956, 250841853, 957233388, 909028859, 3512424, 178276627, 731993970, 705719210, 837692871, 679425012, 820144878, 252593472, 82884108, 718502321, 262979531, 705199, 114591985, 181957481, 848668279, 553778458, 392733217, 786985350, 34150422, 708989429, 949853540, 936403306, 125951369, 133809031, 723208445, 56490004, 789977116, 818923800, 622110457, 231228758, 572449239, 481868620, 970842913, 681771643, 876567288, 77505646, 28797574, 294559853, 961195639, 869001666, 16428639, 525548307, 903121510, 20439296, 948694322, 375233505, 981112333, 112562223, 860218457, 530619011, 169530658, 64662830, 883595315, 753557270, 996492515, 437884715, 265010456, 821232505, 508152960, 258000335, 821632588, 932282627, 20032703, 7498294, 329415501, 371367855, 444082085, 54505381, 255163940, 550776408, 714748175, 856227446, 196247181, 210249548, 740857574, 983249612, 753223637, 251319135, 885050004, 915672179, 146194744, 349016120, 913472124, 270479893, 294755916, 426457831, 345262120, 792935883, 22817977, 856884646, 430863218, 253305120, 321741346, 816585079, 31806740, 435513092, 418378869, 717423312, 582356980, 990436782, 720542965, 92160562, 680590103, 489437333, 401133533, 849326098, 766999296, 435824914, 485999317, 220650446, 191863717, 796315395, 326584896, 345828022, 292703980, 588725105, 176343493, 538005313, 567287080, 677248914, 666877413, 59187162, 820358872, 933169372, 499241269, 312213348, 187704129, 393825020, 330866037, 41016290, 927621535, 161891000, 763765203, 942493249, 739202696, 737932513, 810703566, 299714178, 259584335, 885124164, 295476898, 234267158, 271281120, 387741062, 94127009, 497230445, 226309687, 669689181, 581100341, 529515117, 6444703, 676177816, 908977101, 564824142, 968706083, 706601855, 950683716, 762657022, 403295810, 627033063, 415726994, 650265835, 866792930, 41643853, 93141809, 665205369, 370546855, 674202300, 248115657, 640179574, 274553271, 806743936, 645332320, 140294780, 63074325, 377107112, 635317311, 878332198, 492627195, 825750153, 877103549, 613591787, 523338565, 746695793, 215548417, 491620750, 334232287, 890469351, 650654749, 697012539, 83693389, 144166469, 124564284, 796571428, 672760574, 145811794, 695743898, 279811349, 374089302, 71697581, 365820918, 684856971, 420138727, 369374052, 148525506, 72695697, 482383291, 275137903, 274532207, 89810238, 799033494, 489321969, 189888376, 686158621, 520031912, 411501203, 657148001, 245618525, 764475955, 37441626, 324281059, 655398898, 269352981, 223305500, 308628004, 385064375, 360667926, 75372312, 709245553, 503919777, 275379198, 105147184, 889958843, 301712565, 72292919, 24195891, 561564237, 879575322, 720812878, 628360884, 709986913, 924484430, 347891287, 127465043, 945942465, 756534169, 721175096, 588804932, 101473680, 713158916, 790037289, 868589502, 414626419, 325470883, 694852826, 842646262, 383329000, 858650234, 883846853, 869274476, 735586011, 992039307, 310073966, 175249708, 345701478, 50132119, 257531278, 292903856, 420697418, 948524835, 401260766, 983839534, 661144073, 328146567, 84973786, 821500818, 184015354, 713787436, 619160134, 214921303, 459694404, 314226263, 397385583, 91730753, 582443720, 270531744, 484918034, 971231840, 450051272, 335011654, 518933055, 121377587, 859970344, 950420718, 526706587, 758209127, 236792329, 284716818, 171597606, 739842348, 332919055, 36073955, 262991089, 647674609, 248953797, 700894709, 187861896, 478773110, 959650261, 266785333, 790948325, 411181442, 920722749, 462809164, 253683567, 732591860, 7026141, 601887622, 700939119, 212563771, 339374773, 164636366, 252000855, 562518515, 463834208, 389870172, 605506987, 265663135, 7880844, 334492966, 268005227, 646517178, 474334489, 371475586, 126526312, 680542163, 873540599, 349633259, 137063058, 689207005, 160777620, 8071042, 714826698, 47799409, 67179678, 289806847, 505971987, 918297115, 410503927, 77567109, 279767686, 192862760, 25437643, 280849080, 346142934, 951939476, 135188062, 451577891, 735099198, 566052413, 353957529, 733906574, 269015026, 830867540, 77904789, 418543201, 458507268, 515201248, 882623715, 399137605, 31264889, 402737766, 138545072, 336493814, 174809954, 716667071, 74508933, 433746361, 332712854, 904186631, 88626729, 381781450, 75826386, 393910245, 972277877, 535733926, 266535708, 864395890, 302124744, 724219200, 72505555, 90767624, 669948716, 49835725, 896420462, 442073419, 158180177, 49989738, 626509109, 668378130, 71869334, 495512594, 752482618, 729253529, 356545538, 22707911, 163728485, 913212544, 188159759, 102681306, 437287653, 544086724, 997149324, 291711505, 893827368, 27300496, 689142000, 306717017, 895911092, 714292319, 41713045, 594268547, 344986609, 766421214, 822173722, 336986884, 965852949, 430436729, 871452, 686482800, 303564299, 56111720, 852055078, 357909599, 878065037, 417157265, 219216404, 659711500, 222988189, 414796901, 349159689, 476374607, 394494363, 809222410, 878379381, 776903861, 816939973, 529550013, 469614781, 789792290, 332667132, 186984350, 6747342, 312480381, 865311553, 808651859, 880921263, 183876475, 1618771, 66000396, 548700578, 572461757, 380659300, 121030884, 167733249, 683769915, 210471403, 145705225, 634941934, 671825992, 929880333, 351448147, 412922342, 495167106, 980058649, 500491515, 835918469, 553037376, 838645435, 351107810, 163011351, 908831344, 742058712, 82528057, 859414436, 681927870, 158840354, 497284944, 562152498, 709551843, 161959288, 193754086, 210247966, 277402491, 400111933, 923434485, 22611703, 441593155, 378455207, 907865187, 768563023, 306573000, 192956864, 239820851, 887090311, 796925469, 506964525, 367021157, 968239637, 181934766, 746841179, 501838082, 825547789, 481416325, 22511981, 82350827, 276921457, 345205635, 492886618, 394912940, 342035839, 952805167, 756662665, 812283691, 766825489, 602351236, 974470537, 18049765, 754249974, 83764809, 796824208, 433094940, 978385593, 833798962, 304869883, 977348879, 968257704, 948304626, 934437778, 14268277, 503211253, 322183086, 196997455, 795836306, 316349086, 989410274, 591095246, 339606825, 263276369, 770450282, 786947039, 40190109, 14733293, 428028843, 1017496, 384753724, 631342669, 54186973, 862159675, 981316396, 91315701, 550018852, 801341494, 432054643, 150291313, 357458794, 456032968, 999414769, 511933892, 511477100, 230217332, 944835211, 814005825, 286183333, 961168117, 850993015, 467184393, 968909610, 428323256, 181607433, 981234072, 683288935, 318809929, 532928083, 255586449, 249134544, 955193810, 832478387, 984901413, 280721841, 903592633, 349839771, 887492142, 863305096, 41460899, 109818999, 927475128, 858856107, 741337308, 31538443, 587760825, 849927575, 35896357, 129478261, 308240223, 34402978, 9904018, 87883662, 464304401, 489754979, 68087715, 173811942, 401065172, 515371583, 805409764, 121477788, 971200466, 557150608, 403825612, 891087305, 286642441, 102530863, 819681043, 164626892, 760800103, 514236201, 300583503, 391737446, 623379018, 71263856, 537357411, 543905193, 934481854, 295944883, 666171925, 341899493, 825126784, 408436327, 35479003, 366318023, 187560845, 530536803, 330257219, 89065309, 608194928, 916831526, 880165803, 359744817, 561940469, 877406328, 383410708, 190106136, 870537264, 112465292, 851057795, 94894091, 261562101, 878117013, 792529479, 153870953, 417138630, 409428126, 761214819, 723495521, 693753624, 458721747, 689417937, 823298642, 876881591, 481956691, 619908832, 598558677, 703343403, 596914094, 981751900, 690176368, 833159270, 247181091, 813295352, 781346775, 380857724, 342587285, 462545804, 131771853, 263570930, 469213835, 746398919, 475168781, 923100011, 736787897, 467633596, 400076181, 229014767, 438161469, 934343545, 12290382, 740104471, 860294976, 932240637, 961759846, 562620085, 504461139, 253816344, 990150373, 633251281, 435194549, 745754647, 340768293, 199045875, 207111422, 467831373, 219019172, 843863550, 448937798, 25174740, 583106923, 812037953, 426151363, 257450979, 511448554, 7323466, 709352155, 911378328, 305945046, 344334632, 156278140, 733541265, 555157528, 433461056, 886598545, 859071782, 672110479, 12878336, 216236193, 911573437, 759885758, 802927176, 156956926, 491093307, 721592468, 408516654, 149876696, 137725044, 288149556, 436464013, 212119597, 951933305, 198659906, 507900299, 390352513, 834972835, 81907604, 603659178, 77700975, 465313891, 242414705, 901648102, 354026519, 856424777, 330690943, 697543626, 660508348, 907383906, 625647727, 768088744, 925677344, 377616269, 674772995, 455345789, 683436815, 670541878, 766197485, 295359236, 78015086, 626373191, 994275417, 285756227, 610840427, 568224319, 211784797, 886486112, 451003118, 154184025, 702950583, 434137727, 210250997, 424778650, 286164929, 628395232, 214638158, 359322394, 852916122, 893425244, 435518361, 354219308, 329965089, 731681280, 948777790, 273925157, 260301158, 57254188, 24769293, 777636370, 764889995, 844107737, 174416856, 692605836, 909341113, 29841461, 340848512, 324699488, 991095166, 44742545, 853925645, 944037176, 830420530, 957829802, 332000420, 486793674, 650514430, 516162001, 890408878, 91803624, 108244716, 432594391, 706478559, 142116436, 837997909, 437875068, 231177044, 841169188, 227487520, 760283440, 478623969, 67635377, 667346431, 831711927, 277789531, 460515893, 996570907, 142740214, 930962735, 287885043, 929292693, 535719841, 924068710, 888142742, 399315462, 263534779, 938232440, 988127598, 403699711, 180991427, 63694747, 348275832, 397154010, 941662520, 826427953, 109554811, 434752117, 18171367, 252243132, 633498796, 693776704, 478085266, 520443685, 397545381, 431042886, 41023170, 624866427, 186359845, 904824502, 445160849, 184895242, 778559800, 470359000, 798095077, 675751812, 689336648, 885948580, 154316861, 783898005, 866824085, 357162475, 752440712, 185358621, 469060071, 486799777, 27222522, 669567472, 356964305, 176657359, 165927462, 926748294, 891235359, 778457826, 172665399, 359240767, 624967033, 927216465, 781648538, 537416525, 334218155, 20728803, 465882818, 488544882, 659921202, 726505798, 200474040, 911747374, 185675998, 135928726, 537886686, 627483312, 845189978, 119203231, 920476115, 819842877, 357434270, 899670882, 892890670, 643975692, 647732583, 272396382, 247481537, 937626293, 815855713, 12164206, 139108187, 441193479, 186063230, 883378981, 791159421, 586082578, 624355150, 428395267, 711693820, 180909978, 305581623, 629333015, 794659889, 7597273, 280473371, 334396322, 745671750, 412623733, 73307506, 87992968, 989890490, 891639913, 349591523, 884523706, 210145605, 175391317, 743437444, 961954667, 333903873, 229247271, 650895775, 561729722, 110341550, 49628949, 365774963, 179615129, 325296489, 638375041, 259558640, 360462462, 785743893, 367569453, 74774497, 881641247, 140903050, 661092268, 629635053, 568703336, 693272477, 431857386, 82654338, 16161715, 139744676, 998590479, 71684382, 6361394, 33478232, 479435414, 986995275, 216513059, 743044696, 210825477, 914307517, 113711341, 294630080, 960436589, 753148939, 589905569, 70414977, 906165464, 258975188, 95569597, 127820077, 891650629, 822219315, 813015294, 969511777, 484011485, 745510555, 187728728, 859565014, 516346242, 396629819, 711156728, 179683195, 408633859, 167194415, 501781881, 120369808, 663858599, 972392715, 346705217, 718972595, 629502658, 202439829, 421226988, 508271441, 122884593, 476814172, 669621695, 953654831, 142002743, 760588210, 326450752, 698919200, 509492519, 848666545, 673997240, 284935629, 981767173, 414681170, 860402268, 249468610, 185692721, 667460215, 226060368, 172188097, 539062219, 738097136, 88956751, 529839592, 196184762, 429040343, 920400508, 409740938, 478266640, 308157869, 260700670, 597553655, 266134514, 932583471, 729717505, 552026218, 66270746, 891562452, 957557779, 705738810, 402346702, 783412122, 937743604, 765489999, 659751228, 273981418, 495056911, 266516587, 731321898, 254539979, 603648371, 25570606, 845666930, 95150740, 997911696, 367120471, 652104107, 220426841, 63359718, 695497188, 661312163, 613859334, 457594457, 724546999, 759411262, 319023102, 895922330, 868537670, 584000824, 807372740, 251039312, 674191783, 349140291, 778686062, 398646189, 918685154, 212453173, 619071074, 874064149, 199085024, 652246206, 298083694, 906064684, 829610318, 248628790, 77696396, 993511283, 477111245, 160441767, 656070395, 164800014, 470110054, 6498055, 118488238, 528662840, 92011691, 151934566, 812922799, 567969447, 297191356, 242885783, 849026838, 296183405, 783680024, 568474536, 75844534, 460678119, 954507239, 92085089, 874725762, 235976347, 419952781, 223789734, 791649187, 845888527, 128643649, 253169627, 866029607, 265224042, 756930083, 408060325, 517828724, 801293347, 242982160, 187980615, 326969601, 68578934, 25398514, 662545771, 682855074, 802240257, 159339851, 128488040, 254512196, 558243848, 432482356, 177251851, 747510234, 995735626, 522648292, 277986874, 150773341, 810605284, 842076903, 389579455, 670991085, 467605239, 32493099, 372160488, 857669321, 750927408, 906298008, 80609398, 104846539, 648649166, 131150221, 733037459, 445012293, 246422464, 378329710, 536051021, 114673294, 21758975, 250297872, 535237995, 887126045, 543291145, 68371808, 43136831, 855313708, 148342101, 143425825, 571245726, 339389798, 784695149, 526860806, 530573529, 512536185, 465059077, 346649201, 513294246, 466605461, 943351139, 335217236, 460114122, 77643638, 219140501, 314113119, 475248122, 364452089, 112909390, 204900820, 822534522, 122970526, 353803858, 213440053, 914995751, 451256704, 99627902, 836422351, 393648816, 484848932, 549379162, 623591340, 279225322, 282578253, 727589302, 484157442, 138640007, 74797645, 287528032, 52712092, 67886003, 506131062, 449466810, 95151994, 106744099, 741967645, 760304513, 220899010, 899398250, 834656388, 788807592, 766307785, 839322499, 308023366, 318389366, 622251539, 388803486, 902843953, 868174858, 726704320, 506978330, 660844452, 72203026, 985637192, 177995274, 419864770, 26301136, 111641099, 606480605, 860720090, 996299897, 162375412, 630559564, 338074903, 669333525, 176473592, 206651602, 834342618, 848773474, 964195766, 666026973, 894148368, 851616005, 294536051, 727515244, 870829610, 646770995, 843470472, 946102800, 620301304, 898642486, 774882403, 469755978, 572023713, 146583635, 793396582, 916491799, 16997254, 262670976, 31410828, 918804101, 306437301, 838685114, 745737370, 794646275, 327227898, 194484771, 323156104, 9449527, 895556691, 97265655, 24818853, 861334793, 312164827, 42314178, 332002679, 898288845, 733169099, 744471214, 683926261, 909528220, 775061002, 345613227, 958705092, 886621440, 722222189, 89623986, 837171465, 851824349, 938603554, 330399902, 879597314, 38282548, 922936147, 339135172, 270127039, 819663029, 179246986, 361074554, 827591963, 508164384, 209829660, 86584496, 510878598, 649532032, 543468415, 725158757, 469572067, 706022700, 179287805, 964106031, 267045111, 127834915, 273559314, 755721584, 173540723, 892025964, 937728843, 533252458, 839156607, 630768483, 376678650, 211552903, 140877646, 927001061, 963777604, 372301182, 906653478, 917371399, 598008437, 209801759, 955826743, 306111318, 657379521, 548970075, 90840066, 89881586, 17871686, 305639733, 443420510, 115688778, 555270211, 844573824, 815046896, 888292016, 124534966, 460913371, 111637418, 170956896, 757823998, 348846561, 399667919, 900124535, 411792054, 732333510, 555171236, 12869807, 517401224, 601828536, 133355140, 273060488, 154206483, 668625478, 713531370, 319787050, 129090858, 195217973, 693201488, 621373300, 327711721, 276174613, 443051657, 321474819, 874598166, 651832223, 634103468, 830797372, 26503754, 966618174, 185099998, 744349940, 686370038, 488228186, 877469906, 621966815, 263024171, 369610426, 494942232, 975653704, 571023921, 492162734, 804870143, 838578385, 475267055, 776288685, 232898820, 18712951, 345161332, 663785204, 485547928, 722219679, 516659376, 104611713, 431144062, 354038171, 486790433, 384024810, 546122066, 810782282, 162315461, 16445040, 259922046, 850346847, 844511444, 924510730, 880645468, 180153459, 665357835, 650723022, 361553964, 671850744, 518290847, 755895265, 919931439, 693631961, 531449791, 280919030, 521357511, 321790641, 247160680, 494413304, 682479840, 313650267, 298925001, 378666926, 461760349, 658718208, 204257673, 356555048, 965261134, 679576566, 531080228, 952519830, 744068069, 237710477, 193998462, 423894165, 607182440, 372573652, 810230454, 241301478, 972384649, 489933101, 280193785, 663359936, 18986768, 229369158, 958021165, 723991054, 358024544, 869203305, 689706708, 113875240, 546603715, 151608743, 198599505, 197614101, 451841452, 699744547, 582859712, 100275561, 644968575, 453549887, 592968159, 605765030, 511047182, 19076873, 933430944, 603737678, 221298640, 97501666, 160372410, 860779578, 133511151, 857735893, 287931797, 446911264, 651492550, 129257941, 47245749, 942755732, 42590732, 623257162, 499537934, 63526503, 285176020, 876999765, 101462652, 869745259, 940788564, 905975258, 11607410, 828681569, 595002887, 739605096, 142351755, 938325007, 953252961, 754983535, 35935740, 776810609, 868287745, 847898175, 883428198, 434407315, 810074742, 530965810, 981962464, 804486721, 103163636, 811554728, 79851541, 939887552, 204883591, 234651427, 109306739, 430586669, 509208919, 279530194, 182852728, 210065240, 637457409, 419940392, 284307697, 375688817, 192040708, 347486913, 565580648, 189242789, 131156484, 723272717, 4150308, 610366201, 839810063, 564797654, 807602534, 152382509, 330975619, 407063102, 826356178, 541831991, 889794922, 451716436, 174711526, 686148917, 12131814, 797540438, 773704689, 148549765, 737650526, 732458647, 551011011, 358631943, 957911232, 180815933, 510494917, 461963275, 799350029, 679810799, 792216428, 573003767, 788926378, 53126253, 830275331, 754574424, 829986301, 234868746, 611463425, 605767145, 310561240, 346935513, 881739315, 80890007, 446589219, 521408061, 529491905, 687893767, 566445632, 870496614, 693805152, 488503777, 657908102, 691692914, 688830949, 253484800, 67547947, 272275119, 889809595, 2720721, 925975970, 842642444, 254567712, 318134602, 385845213, 44571229, 545623670, 805808452, 655816387, 814525836, 53719883, 967222577, 925646601, 436189208, 131716625, 415977334, 333444988, 570699701, 490777883, 859548418, 760772798, 308604329, 94041523, 587828284, 901740340, 624708789, 716886297, 648747592, 553212744, 374517441, 613471910, 17798098, 146606053, 79615819, 585759098, 429900258, 229350721, 830506990, 140521043, 256868187, 8312333, 521225951, 934777271, 504094871, 364648416, 110525259, 354101163, 545704293, 354060409, 247979402, 888695240, 708316373, 764555689, 909645004, 141287871, 446889551, 753851310, 861828525, 235770014, 801526806, 790767798, 777415579, 948260570, 583215105, 198122212, 881574172, 972156092, 982272022, 795741706, 114163441, 74694048, 52562870, 961623703, 348060129, 378754007, 398703358, 619424040, 288501356, 714718479, 739092680, 690140227, 476820485, 858913661, 839004972, 915302373, 716384530, 575364368, 323993674, 519643144, 180401239, 589733738, 181791192, 786514560, 117637737, 872138161, 770351781, 303762921, 272533297, 148087527, 268344788, 871417041, 911230106, 81717673, 397110308, 623978402, 804406416, 452762841, 362553357, 130144920, 758224130, 368463012, 204156808, 859380161, 308957583, 747517896, 384415192, 28126824, 869104935, 662059503, 617300156, 377232341, 544655961, 520754415, 203376731, 132781112, 110536293, 821213121, 366673457, 11353285, 98679760, 836003646, 160653441, 315946425, 325254463, 481727840, 133754202, 512106, 420943715, 284547635, 655787, 475667286, 717960410, 419932570, 598351444, 233071557, 318291845, 51189497, 155227332, 101132344, 524113327, 904794705, 461405592, 331165505, 308811694, 756066317, 147942732, 683800903, 306112452, 606741355, 714582275, 480141440, 739013351, 186394442, 359127745, 525515060, 882113599, 995299482, 653312930, 372163562, 944893949, 521817577, 845151542, 441147587, 79260746, 527534742, 100415203, 154497854, 183087485, 702678446, 873457281, 825601938, 899386772, 279551966, 607457971, 466663551, 263141627, 12291507, 221487134, 578251966, 75646318, 374328835, 527905750, 360693713, 820017791, 596817969, 390317659, 134935109, 704312632, 496440381, 480761903, 23547282, 9955140, 832576965, 636266315, 629794023, 278791310, 94728209, 917136747, 255336310, 825239290, 242025708, 237529314, 110511978, 30153766, 989684233, 356495474, 937903694, 679526952, 991678812, 360376153, 711236126, 25951165, 881040651, 578028408, 495261599, 177888291, 516855011, 95252210, 361138179, 423068336, 90996407, 712295558, 772431581, 786371935, 674171243, 201936436, 820484204, 477887750, 462443294, 920655002, 932702171, 834886124, 693462577, 10312659, 670372937, 548418341, 303989945, 110152253, 774574782, 114100908, 634442557, 267638096, 650283596, 354306482, 994559275, 616785287, 266225341, 745874637, 530372729, 521420928, 629066838, 42684893, 795056860, 421941411, 169861676, 776749600, 310173112, 550797684, 769053957, 877375595, 103258742, 37262086, 652878434, 615539020, 73226071, 422951839, 731386363, 325923777, 386175792, 562149062, 807701474, 910920871, 379190313, 603132693, 390450404, 656574529, 354972999, 813559832, 183759084, 59297255, 634943891, 892389854, 655413800, 704956454, 328935262, 39334589, 821531694, 945023360, 517401324, 73501593, 401918208, 970183567, 867243852, 705442744, 376757902, 41955433, 325073430, 725599017, 902558725, 317347192, 624901883, 850837502, 718461767, 408649208, 370402126, 130050966, 196981438, 484503473, 827262235, 564470713, 178581777, 161556553, 377842657, 509299842, 47318304, 502347067, 482615705, 323935160, 189075206, 198650802, 467313060, 443015272, 78279159, 258641317, 280709465, 319104538, 530854438, 348219379, 362191015, 251511515, 695958313, 476677947, 365987067, 883854735, 971807031, 895655042, 717695988, 133475083, 494380124, 992076179, 670411947, 828720423, 69719695, 134541570, 309784292, 605850787, 24776326, 414299307, 107345056, 717826600, 605226944, 695217523, 398492540, 120271531, 495365177, 462762942, 571330633, 874753865, 980215344, 487690133, 65792098, 824501068, 931106461, 995659248, 873134767, 743004073, 295871245, 685335206, 464752762, 613829588, 761575091, 779235588, 645990593, 112856465, 359350832, 104663235, 536317899, 494320819, 663040828, 96286241, 13231308, 309885707, 595719447, 347736123, 448797344, 633803230, 744887573, 380491100, 324999970, 899082956, 10159267, 211832672, 179060042, 311004618, 401999806, 974337591, 153402038, 958634318, 818142200, 536425963, 783880610, 601556214, 859425855, 276433444, 309129404, 90209551, 776802861, 104805741, 10655124, 895975155, 791344597, 320881334, 393458716, 961338985, 608088638, 486384131, 641682505, 79229080, 226519787, 36481746, 368674033, 162483460, 164848195, 780341705, 381037582, 744930763, 432187206, 225904823, 251892389, 492953985, 455803325, 689917291, 32603372, 230757590, 412867155, 380645408, 972503807, 793469603, 240897400, 514513399, 708031336, 381282475, 502003249, 308268639, 247273422, 777599345, 241477837, 203500465, 169944847, 904290729, 350943103, 942218266, 808499052, 867240313, 408233958, 602550609, 533620680, 437093791, 480762297, 942098309, 701016414, 716857322, 931660541, 551327186, 601128258, 849248492, 665188802, 874499205, 508636130, 957772709, 326193098, 635996703, 938256386, 331795533, 404941438, 955427424, 905686800, 39142617, 170901040, 222985579, 815469902, 252408169, 331088586, 686345922, 6610212, 794048350, 149974256, 25184190, 405573598, 990703005, 932854193, 702029364, 485127824, 166929570, 777847412, 282086494, 921674176, 398737967, 471356858, 9645085, 616610623, 802294215, 744199521, 632582245, 109955403, 409008870, 621565929, 315694662, 248554805, 825971588, 5666887, 661584785, 373407409, 929176343, 158335399, 253641946, 136987744, 337252723, 617679316, 765871086, 328908646, 623377504, 563290137, 629413933, 23595082, 907106254, 824310318, 924166257, 357361964, 377144339, 253145333, 403447219, 536816110, 251486593, 144626331, 48826989, 507410583, 577232461, 138164015, 243799281, 390923924, 852284481, 600650592, 816139919, 830995633, 109956142, 261160720, 969106231, 565631617, 970907007, 185814320, 414121780, 463511066, 984401238, 357874845, 986115491, 20586910, 394289432, 815660018, 377629, 923938680, 396268313, 809075308, 701342583, 66470459, 89760642, 829378746, 427617944, 595824000, 918383593, 369009020, 92247078, 428056655, 405984075, 25637555, 151603755, 254810186, 279697556, 504047109, 250969942, 787441958, 831717029, 89167307, 620727728, 500038880, 5431707, 318670488, 524714926, 175460634, 703439813, 778386035, 236074651, 229426809, 492190492, 792738220, 754796215, 943704399, 148328407, 169992555, 265838408, 6565629, 638877917, 921875459, 532598614, 743739431, 838459410, 876836398, 560096557, 973463913, 956593134, 48235971, 412619131, 300362728, 640220059, 542736449, 585349655, 452421758, 430407375, 896430227, 471136001, 464157691, 9463577, 852166997, 685704999, 542989616, 75477695, 261955421, 292490133, 630534151, 7481451, 950825429, 203374464, 304928292, 63826975, 906810051, 924309039, 582591509, 558043725, 512805377, 351006498, 987140375, 25420879, 869026408, 344710934, 753344302, 23015460, 411585608, 918790343] 300))
+
+test8 :: Test
+test8 = TestCase (assertEqual "for (countComponents [619553313, 311549588, 293974034, 719177211, 636097592, 934499673, 801255312, 606234653, 293695435, 443096204, 254559470, 88637959, 205638425, 519278337, 966044078, 450440117, 510296688, 480864064, 901175583, 718718378, 948343171, 889441683, 920129735, 195548372, 561877346, 638241467, 973864051, 4908819, 68990549, 120199015, 219449025, 251732255, 611587582, 668075345, 123783754, 5532799, 536597286, 522113102, 935337690, 301801900, 457804586, 780484783, 691813774, 957548488, 979380300, 849079301, 433201131, 579704986, 799754391, 751692397, 299099982, 119475090, 808573184, 106617188, 213526319, 532776618, 60238180, 925010710, 624543914, 697331153, 392113802, 759199886, 989650345, 139763368, 796449253, 916028761, 206550547, 430071998, 763468766, 572159404, 759622820, 754256182, 190856699, 521000185, 758245454, 438495828, 173493432, 386042938, 888378403, 115431161, 569033612, 247339865, 246903616, 671577839, 539564495, 649170716, 557674538, 259412214, 739916073, 836145568, 689773337, 880817317, 85008681, 79832287, 644192628, 957343725, 608352987, 784353316, 810152762, 439746705, 399254756, 809167973, 778662394, 290858492, 177094174, 707783931, 122499546, 478392418, 930263959, 776150854, 4186698, 188164913, 579138966, 876711665, 207626902, 995791574, 947758082, 379746238, 501232394, 120083519, 44834155, 368040062, 211069461, 759034373, 748520473, 514616218, 167988953, 709356675, 830146867, 127717839, 761738919, 396554649, 286299642, 298675076, 244602402, 1790997, 407650767, 204134757, 734293613, 734739043, 507536258, 629989259, 962337723, 193681842, 38666296, 464080090, 4413762, 211292102, 151376308, 105913034, 908450661, 588536099, 7338710, 3543243, 488028477, 113262164, 833405968, 866539185, 343383164, 261945018, 882178001, 304313111, 503710909, 909243258, 399616795, 637735197, 998305001, 648150736, 790691705, 134211499, 444269169, 401903566, 767912885, 112914644, 626309100, 974304659, 720783860, 545459654, 669318312, 559430312, 240755614, 832527059, 702152848, 81992444, 920841755, 245829512, 37448087, 449250602, 24101455, 451212396, 599113364, 964743535, 422280249, 667306625, 671589288, 14015979, 288051089, 933373777, 359898618, 168510857, 884363178, 419252716, 594606785, 783905374, 794228053, 235548511, 735078976, 538565365, 682712483, 466818053, 809139113, 865593670, 609776421, 516376423, 273247315, 938732682, 939348082, 686770112, 989757488, 507052286, 918117215, 758654456, 895402836, 558739179, 110357200, 284806645, 354838805, 534024423, 986153309, 457601242, 32750345, 868241163, 111404889, 956129063, 625114367, 185618751, 320547441, 601816808, 609978143, 877891775, 809673236, 141333536, 476401960, 983949920, 380412235, 629799073, 117231993, 270165596, 32840568, 896142585, 403012937, 309779545, 596292275, 738586598, 440886126, 128452728, 665898004, 135438338, 882415788, 19076500, 871351956, 397809931, 937748986, 802675919, 548243537, 739536439, 108117401, 840895353, 946413312, 495811775, 950801516, 640243047, 575445645, 641401926, 652445943, 41200370, 713254888, 29114880, 841776, 82501674, 979032469, 470603981, 16405210, 903436153, 966070711, 495935557, 84215636, 709101557, 453786473, 208989034, 891126368, 797347712, 76736099, 954888010, 971114522, 305868488, 751271281, 161885985, 709923631, 745062670, 247107695, 66186490, 859874603, 162584190, 776580581, 93172510, 63848140, 152134989, 172667430, 79759973, 525163733, 216285869, 8927132, 266196977, 19156999, 240645777, 540470742, 950038694, 721752313, 210687105, 662261369, 318255527, 625635021, 250177038, 484161583, 991731602, 326756870, 509906969, 308845132, 38692189, 985751696, 928549539, 535763745, 196422847, 583064273, 116671681, 58871279, 598906130, 372063311, 792971648, 928573081, 696585778, 464366132, 210693588, 1650176, 574159248, 391465444, 783243487, 374982452, 715167006, 240611896, 206761968, 546132267, 102704624, 148227017, 546373946, 740370945, 657449448, 971632271, 537818547, 397908241, 368850293, 762678661, 935602216, 995025093, 493301371, 25235882, 777296544, 50987717, 813868648, 632781479, 906425765, 524904332, 666550422, 860134744, 489333224, 434017810, 400787679, 329801839, 768187851, 32704060, 557664729, 266926188, 860546030, 526747455, 424958797, 759658544, 996458028, 452075586, 941890802, 546938881, 851959626, 734844154, 694987316, 319301852, 255541305, 572654529, 747686574, 320549191, 742871799, 964452614, 572365610, 201627843, 465609423, 935921750, 867914364, 546885810, 751221150, 21034379, 34875709, 318597155, 576944490, 824885662, 668807845, 72816259, 944454790, 299341825, 174030061, 504037076, 751251398, 519413688, 782906807, 479668067, 330240736, 298766151, 379102360, 284993429, 901965471, 668148179, 47895376, 735155786, 869902842, 659655863, 903381730, 524196508, 57219697, 398333205, 429263950, 853754603, 583520973, 591729613, 382787709, 245988338, 818179750, 32869045, 650707527, 119314197, 532974385, 224204228, 243791429, 389754562, 306761867, 78066384, 14861826, 319788334, 920079303, 828765165, 839396211, 534582621, 472517165, 253952370, 898126380, 851710394, 979673150, 965060687, 716353818, 723737103, 31696877, 438685965, 795912616, 522865256, 568622590, 341597261, 546065281, 48328102, 757473527, 863124844, 579710096, 751111028, 427364400, 671047431, 851064650, 25033868, 337520147, 536499098, 915815399, 950301997, 379834843, 575135229, 924718494, 391287254, 279791859, 600584351, 426033115, 277395353, 840085476, 270501780, 715558778, 372792287, 518109537, 372058426, 879726177, 965317056, 961504436, 95580724, 159337026, 429113966, 900345070, 963709460, 214833992, 725231984, 200682973, 598654575, 134054088, 668250890, 838688941, 510418233, 384441708, 592484266, 913996405, 440933425, 29464054, 847360901, 418273364, 840452060, 221798214, 716060969, 507718779, 102524375, 725401196, 322812210, 735984091, 547459144, 273411089, 868829904, 21917598, 336177587, 223475971, 927923135, 611676754, 160526322, 105559703, 427503136, 202588804, 780801817, 101813515, 984083659, 346689697, 148468835, 285867459, 911082414, 857950173, 551288100, 869619956, 542135739, 328551680, 240790876, 48984565, 534917673, 507069092, 925981087, 596388602, 516744569, 134901175, 502707171, 403615200, 491512318, 656338182, 884016688, 803584098, 221696061, 203395345, 619480462, 330681097, 291629419, 482414308, 468808824, 883058182, 38991155, 67507916, 667133323, 545070288, 10254836, 2021161, 581201095, 932232481, 408234009, 641052081, 945346115, 112262526, 333666282, 874310387, 351716011, 822190239, 661162843, 216966080, 267401502, 986698134, 801575333, 735493228, 692893669, 480186027, 888452293, 486814501, 772766791, 969558582, 418638618, 800406108, 813315181, 916177338, 509440460, 562970395, 813157025, 256291109, 933990529, 30095941, 415829191, 2944363, 259445623, 843069346, 464202440, 411676, 643836066, 66159494, 595389988, 642864347, 350075904, 393399609, 358006940, 470756907, 463957716, 615342065, 93548341, 162024739, 192076656, 529807618, 336154801, 188989285, 358386324, 800121174, 427692083, 62318989, 294336409, 850431741, 453105669, 315313841, 302917311, 942859802, 646154125, 166314582, 735353068, 522844393, 350220666, 862133740, 82267382, 814402977, 599976140, 688271484, 490189570, 148528461, 685541230, 976177118, 396017889, 453454251, 727788097, 948874479, 238216749, 72044222, 862576362, 448434300, 840261945, 293932937, 13898420, 21747035, 158260700, 319949742, 7404278, 996112955, 85566091, 670774226, 652925358, 312546561, 517761863, 561357620, 6645003, 32692903, 841081120, 94264236, 147865682, 705608506, 531155152, 450570607, 444300729, 279143530, 355850403, 211174346, 256962976, 187733968, 536940520, 742479472, 854750392, 113407489, 547671974, 543164603, 712390730, 384958976, 991700003, 139987059, 107541024, 855175755, 184312772, 526180504, 576934495, 926902099, 251974418, 121624450, 263083563, 981939885, 688661096, 261011300, 462211488, 584277022, 173578898, 561407554, 465795144, 621294461, 33500857, 738762522, 151154537, 943541149, 442678279, 370765496, 28053244, 627710512, 398627187, 828755529, 444162151, 325238556, 627256493, 750733232, 682239572, 455339647, 76809976, 383561317, 392480722, 599919275, 378200355, 915842916, 123918718, 422796107, 228718475, 846956497, 972241502, 15689283, 657731675, 881239111, 592402488, 673369121, 634655407, 5294559, 175991703, 64149641, 315482089, 566621317, 261466043, 584041903, 78276666, 496925142, 224402163, 852644227, 112190613, 435011831, 623523803, 824407054, 551108946, 123288269, 779545757, 908627799, 131232392, 629632559, 591166429, 208839618, 120288083, 391829481, 78926656, 745340645, 331684976, 610394655, 696003165, 912328507, 637067910, 147909685, 396674325, 74326848, 818596990, 415229556, 780893499, 253820278, 826611534, 160600928, 498900227, 228321440, 474959312, 508126541, 914963493, 946531965, 598135897, 216960623, 597400923, 127895691, 77684076, 367443393, 405469018, 191400259, 845681672, 684152265, 347483278, 705722782, 943072309, 303467935, 48017983, 337662051, 798093866, 314413638, 426476858, 657404414, 143793492, 83894385, 699415722, 266324482, 443012888, 43790186, 880417046, 545109789, 420414462, 714084167, 654898309, 838075461, 999663148, 937480990, 532315542, 722682642, 231069693, 9648488, 896546005, 904791086, 711834430, 294193779, 340147117, 39654203, 394653971, 447521600, 323307430, 748012619, 248018192, 596618762, 980103597, 201612187, 524456264, 393152804, 408645626, 237104992, 659294634, 262457379, 913829649, 411546607, 137620906, 679431408, 35012685, 492944430, 49350693, 145698455, 95428865, 915764334, 515337642, 76792640, 170640527, 808243098, 844891229, 129060302, 887217930, 601171862, 967135418, 31340148, 215751239, 274372999, 686662933, 354467181, 204820889, 696170039, 210820715, 926908792, 713079125, 917631247, 568980329, 527363081, 868236966, 60054587, 978496948, 580200182, 503687516, 326760614, 62975898, 743302870, 773639586, 986827086, 510094642, 989235935, 877192488, 623191918, 837819088, 443969281, 607590801, 189258420, 227823751, 498949314, 721573952, 168797418, 962612660, 499988982, 790065753, 103805836, 364387989, 521481829, 567964400, 811367808, 936220538, 331184201, 687730482, 906750749, 336329689, 59557943, 246671042, 339993170, 987908536, 987812266, 732818660, 556849190, 803126975, 63088747, 420908124, 65719128, 756803062, 610180284, 322321329, 253013529, 198819748, 615523589, 745306849, 91730458, 917343536, 189362656, 65024809, 102737953, 755790001, 35116370, 239804239, 583820512, 439586152, 691048449, 119452757, 612211001, 18749155, 128371889, 716896426, 464134068, 553071308, 359762339, 760676686, 70231331, 643136304, 708504386, 789055973, 212693711, 45814904, 959713465, 277833, 90727752, 424389356, 485649131, 161108176, 955756761, 610002293, 751241961, 762141154, 510437862, 25728704, 273014833, 254052622, 565355551, 534495725, 346814285, 702866505, 955243191, 109535891, 970691054, 739547220, 45501725, 988409666, 387097601, 157709568, 858354660, 181865055, 59366134, 206073764, 354037108, 884497870, 697900116, 176604373, 69683632, 670262173, 961519114, 84014252, 847919754, 691067290, 302965395, 796492979, 704145266, 565537362, 830800856, 510206237, 141154643, 203035071, 134958357, 331913102, 22542867, 941871638, 72598216, 355366179, 229395358, 297299159, 89679180, 159305183, 434680275, 435512325, 108510559, 876023464, 493114642, 51119944, 58295119, 28349703, 145278619, 731029984, 781251226, 397328008, 787901525, 81908792, 727100577, 727235940, 107546785, 30792678, 255715071, 167464711, 732510895, 282566386, 770060249, 52587408, 31282072, 648980525, 254606532, 414286054, 814000469, 539031543, 122873335, 588690322, 438479128, 565871007, 43396755, 822370565, 242446739, 847250008, 443695168, 765965431, 341539486, 782046104, 599823822, 838853572, 564219063, 583543815, 771681187, 448354599, 762533598, 330391230, 373518311, 501041958, 427786569, 107649759, 461292298, 19134470, 818598357, 189584490, 571336290, 185132263, 691539987, 214858071, 424245426, 925464336, 427937426, 652297193, 230899310, 176392571, 45652054, 379322123, 767782708, 797962147, 241482588, 26617113, 437243237, 842300334, 893083053, 393389690, 422329267, 660091261, 445608982, 742512600, 473316046, 868525017, 694081924, 851756788, 717401780, 273561548, 784199740, 196884659, 442515608, 858176045, 216185154, 77654544, 495521171, 273049281, 245608886, 478895505, 783311026, 148334768, 753909787, 645331520, 891511760, 976689169, 209952124, 932194605, 381505809, 176370232, 734769748, 447132995, 937878960, 897312529, 311720522, 307921829, 469698421, 591809305, 969014287, 732593963, 12183716, 829411909, 812665671, 596178821, 543375343, 691220681, 722904862, 135158864, 238472794, 113738152, 117426128, 405067000, 386398892, 762945630, 612730667, 743644649, 936416964, 178047560, 120450868, 66734165, 734422808, 648002226, 609281800, 921619520, 198447566, 719824532, 869061383, 213238121, 892629672, 655340, 243392261, 981719256, 570210302, 517978780, 752937036, 641645994, 964747382, 691966136, 403397224, 21997794, 25650278, 588357147, 490290822, 490305994, 334528486, 15217941, 858755515, 213704276, 215564728, 271863660, 26168637, 757542944, 373710478, 76907892, 512418710, 867497265, 755091138, 774692112, 389687924, 210824481, 725960792, 877558636, 851327921, 6483604, 90309348, 216555324, 89502763, 583725597, 551484800, 579013609, 768460461, 221406350, 793471189, 31054139, 906934494, 551496815, 514771776, 522087111, 981029282, 103330556, 161667912, 634070905, 637869131, 509539353, 748123577, 452468776, 686854331, 263252381, 297948319, 584890857, 989594247, 100912360, 559865282, 167205678, 621678173, 809239897, 226412777, 570978809, 420231325, 433202346, 885067915, 142569196, 274031220, 191701380, 986914574, 734571309, 302402543, 882805327, 873051940, 905967661, 55662506, 459541825, 671127736, 251733153, 516131890, 769432089, 272890431, 230510878, 664237336, 13674397, 145011657, 744282859, 411966769, 35844695, 781208586, 353168776, 197635203, 448836548, 304073457, 998517618, 833963286, 553285790, 676985715, 388831740, 451313918, 883843919, 732790849, 567038008, 664939838, 848846898, 710735917, 55010842, 204814317, 199038295, 323519727, 841095297, 261729301, 683557930, 946792306, 476791751, 359299155, 901404523, 843435901, 680606625, 934151056, 74497091, 861630276, 525829410, 978751894, 457354411, 256290004, 564704013, 591211382, 945423798, 797673290, 858595661, 979215759, 397348748, 800214178, 747047452, 308706756, 150465498, 738977474, 516286262, 748092451, 20142946, 60714518, 347084588, 301868737, 296723587, 723177995, 357196252, 630370035, 560794376, 609197949, 804889483, 206300059, 180618200, 190275203, 927875121, 265947360, 981491839, 4183032, 598857628, 96170039, 968393530, 651270632, 913664063, 151367656, 252021764, 606364947, 937900276, 533656084, 312009270, 377106698, 692272178, 11031117, 204640768, 344632234, 763492784, 147483776, 602559416, 677469181, 104741, 286843974, 934766367, 603046596, 236243806, 3827689, 180178831, 778595144, 363287987, 364623124, 150711380, 922200711, 806857336, 784934453, 7478435, 416718511, 815795982, 346620880, 921884217, 993659673, 107441890, 312642228, 920905047, 686729404, 731563825, 135532270, 505479793, 54550261, 981116447, 560732475, 941954932, 469808068, 179001545, 521914461, 232620528, 990926494, 711204032, 14041217, 943367187, 40716978, 276832336, 250990058, 566119412, 870998817, 431898426, 306593119, 524934233, 685939606, 195864191, 521210867, 119889517, 471034038, 787256874, 6743558, 127748490, 850051296, 878882917, 367304994, 101806360, 729167830, 533997286, 431755647, 148264427, 909874527, 248321493, 133679024, 144505976, 149016943, 972982535, 759612058, 3421378, 156703458, 732924755, 197865432, 328171779, 66983066, 769133691, 577491359, 588093783, 482491344, 526583811, 711657853, 410588499, 13418939, 623205142, 256421847, 294115706, 751772138, 349156503, 820082464, 951512839, 177462309, 410384826, 207499275, 352660348, 702327795, 942316170, 5610910, 148164249, 227228577, 766811516, 554130784, 996128686, 583396280, 9786270, 497802498, 278319631, 313973318, 575838372, 705302721, 466818187, 517191086, 512073182, 461141035, 68618157, 253707790, 147444870, 883829770, 273787673, 688760195, 262608083, 134417704, 323073507, 495093696, 187233258, 807456396, 294748437, 199135525, 926888835, 261710921, 617074590, 172656054, 566846197, 590261384, 532982155, 687206145, 647943880, 881232520, 62782601, 189393001, 175484338, 742304845, 511990542, 488772879, 708282316, 900203546, 419489116, 755108376, 56048557, 439546988, 934253978, 138630668, 832925520, 828069920, 254773386, 130490590, 393256403, 898905595, 829295703, 657558984, 446068460, 17089930, 104739217, 155327068, 170429201, 558739017, 561342411, 567730840, 326346171, 648946955, 567895879, 841776757, 554290909, 201886826, 627260531, 632627563, 897501627, 57868401, 583547546, 337003241, 90681463, 155811136, 1924171, 188442421, 674845382, 722817360, 930830787, 743057950, 138254659, 780032557, 107742359, 816339823, 725127701, 573002211, 117853113, 383308212, 395911245, 390076959, 762247521, 631606903, 87767655, 919017057, 863646857, 710666414, 60615834, 495476826, 497351879, 654043160, 6628430, 989147358, 727137027, 246865044, 112833994, 36706215, 273234627, 739828280, 654127010, 89906062, 302989202, 302194090, 10158633, 41802503, 388202917, 714174928, 853323356, 737824539, 544284117, 231781242, 773174075, 108432388, 824840109, 924330880, 750898414, 444029428, 910009482, 472180628, 933074104, 510979103, 50647027, 771373193, 266164009, 179457310, 72981122, 382037702, 123953859, 274083436, 970757570, 806796085, 427897950, 276374356, 103646753, 867706607, 520165129, 755302107, 161459072, 436836467, 183321315, 545838317, 115232626, 981176284, 491286800, 363794413, 553042440, 600427129, 431120958, 218722326, 674971228, 186490161, 582840346, 825476752, 751129551, 1704867, 433396370, 772469300, 960130853, 865370776, 35847019, 355887987, 604471379, 322613172, 286719557, 294962654, 4005505, 977184745, 515487040, 944202278, 413125849, 691465271, 864872100, 667250900, 380750834, 32236664, 527446854, 923119164, 18551276, 228537975, 403473526, 19576548, 790368194, 388830751, 646574428, 997159268, 620805815, 290168835, 67698338, 740964183, 743117233, 695663886, 187662997, 304257268, 137277073, 837924327, 947587215, 833907704, 69031845, 28302556, 180417464, 336081935, 915482730, 531368929, 413260855, 227046519, 831294966, 569202104, 766081309, 38033043, 538793864, 592128271, 208388511, 178196450, 228967308, 622584158, 412707793, 182670855, 154848570, 276819951, 173404324, 167337072, 88931123, 82394227, 849460981, 662401659, 659535277, 562621617, 529629402, 947949696, 36996884, 558598001, 467931403, 128970215, 877635398, 189860812, 862446273, 590993874, 607470845, 71820898, 937584034, 408366864, 10519154, 684274893, 798518171, 907104507, 319727393, 505111627, 115565673, 142200107, 400860284, 569808456, 577425138, 266982172, 445243421, 576747307, 849583591, 137596697, 853243358, 49177451, 797544749, 768346276, 969384824, 538313256, 17891144, 216289897, 3919268, 452950822, 47843297, 13256607, 193406457, 449927907, 951579934, 574706840, 184123071, 15850354, 685820378, 461942187, 466519494, 332426366, 243922382, 492795648, 275021800, 894560067, 711806488, 970159892, 522891039, 106169795, 674682320, 895840829, 528437159, 209648146, 932420429, 758991055, 114018399, 668274092, 314325290, 660999088, 11309999, 300976387, 772528187, 895616793, 847253745, 788957123, 849939080, 323030492, 338820942, 240647990, 493545696, 535039940, 623254134, 205254658, 364804745, 385752865, 713505393, 44021087, 708315966, 400979368, 390365749, 764203858, 690357270, 903239243, 564051307, 448131806, 499224837, 500298168, 707972043, 116489365, 721840586, 283052235, 922772412, 355001759, 577952574, 925873566, 721772728, 350227809, 692444067, 617679653, 380682223, 432505262, 3705945, 42218852, 581606138, 730282666, 838222247, 764106353, 746992230, 223802263, 764359993, 590176832, 25500817, 82610676, 553976298, 772877282, 728227648, 266258002, 660336803, 144628956, 454396230, 713994035, 321621582, 578475762, 251686338, 672166138, 224455023, 476843641, 850230807, 163903541, 352403178, 989840122, 353328597, 821908097, 112341330, 944967286, 780530514, 497897131, 797367347, 106866428, 274897800, 650775621, 931069293, 489269973, 846857646, 550492863, 889364008, 824750074, 847476041, 344587006, 17090312, 417219586, 115475845, 658918142, 456945186, 196262011, 501460215, 560562431, 243929393, 69616871, 219242349, 765954463, 557205935, 975413118, 553173070, 252051003, 978284766, 56322775, 705629802, 517738636, 437991498, 90473685, 562720005, 376246965, 774491325, 457710266, 420982497, 469451740, 550315659, 793416608, 846661517, 877360925, 73644438, 988131660, 120815521, 229726560, 379916515, 135484578, 207400078, 262078712, 210700727, 48564110, 185679643, 5475685, 744272018, 79917414, 945097403, 563864518, 135311079, 328503925, 692485941, 130488168, 681140731, 705272549, 131723466, 593434343, 727695188, 775533603, 925721417, 954900136, 332835703, 476909468, 460538811, 429791164, 932616152, 154385134, 990861205, 533536016, 520770525, 276616043, 519507449, 269359571, 342354674, 112131919, 476125050, 662681930, 248671065, 556173987, 201596515, 871460262, 656634686, 333535526, 404745494, 566044601, 88839914, 6355334, 709783121, 641953885, 395029667, 104784643, 594260177, 925382171, 737819503, 938898043, 777503794, 958590645, 771062922, 493636238, 183363185, 178706388, 545811976, 359139144, 299547725, 87820624, 529986919, 338161586, 780679260, 621454174, 727113472, 440998564, 666757593, 377736432, 123620770, 356895817, 387598046, 204254870, 559740194, 218703362, 630727239, 561754564, 371194404, 842222089, 758429091, 364027397, 431902887, 968249387, 955461501, 655695405, 359931938, 330591941, 3938269, 566446995, 648535768, 901471741, 79284029, 411279825, 754143236, 60357299, 580740085, 503972262, 995770315, 543321498, 293543514, 914019026, 879493302, 540949302, 313884235, 361926923, 385144101, 940423801, 189233116, 528357160, 22469655, 781146214, 73830977, 960097761, 942412343, 6020627, 592012685, 608605120, 510191623, 680786292, 960641663, 211686182, 618817129, 771984524, 429173254, 404349063, 916981528, 664480638, 421910780, 382017402, 43182459, 327147125, 979267171, 65001715, 478699455, 424575899, 484540242, 239142060, 85594914, 672377964, 863130067, 562194407, 23977692, 617556537, 693418276, 902355317, 489952708, 16058695, 539565606, 460708669, 732765349, 153322920, 14972075, 571504169, 298563343, 574857141, 427012090, 12449616, 118878364, 483949780, 877692293, 16491775, 789412070, 741580695, 6266621, 481188298, 416624819, 52163550, 934334017, 700091407, 79247144, 23968154, 903236764, 442718664, 468641373, 406923089, 632264761, 374902878, 807419218, 431662697, 940171851, 69021456, 894419414, 601488867, 62437082, 349318684, 413724302, 745069048, 348600041, 916859128, 934869807, 457633733, 675379028, 779794825, 540140496, 853949580, 425268126, 112080353, 882295611, 278922358, 83452432, 406990505, 486340406, 805192952, 870707487, 283685086, 56595163, 437546120, 510748016, 821367251, 307344119, 740834267, 982798536, 77989955, 311260360, 948321112, 116039488, 392158288, 132652092, 533152713, 586497478, 969484785, 631325887, 717577362, 456774858, 323935135, 17498367, 701563220, 185418172, 493013173, 672881841, 361344393, 351665416, 954928029, 295358985, 163069799, 421884584, 766974329, 619625516, 312523676, 320069497, 330812980, 60660298, 288734848, 29427967, 591206280, 391076727, 774232164, 984336433, 529705811, 515002570, 316505949, 638683977, 258460977, 910436157, 641069084, 153875819, 530376885, 641148990, 705263970, 354076176, 687267609, 478333862, 848234470, 124982596, 757706973, 696286737, 482710226, 42942561, 85697887, 862885867, 475282610, 285953526, 657336329, 840811887, 390126203, 696826945, 750333948, 45480990, 130424897, 743181714, 904638699, 364958917, 632244746, 859778871, 139476096, 429452274, 169242530, 683596996, 89713011, 924338199, 685442276, 860330237, 746391611, 45482450, 459205356, 817264120, 838155467, 432453557, 208772046, 198459337, 392617898, 524340158, 177749305, 972534522, 527094485, 461665671, 298894600, 879756567, 538153165, 756902217, 548115995, 760514827, 886012456, 390296053, 323334769, 569315083, 272678520, 744343335, 282727956, 489445663, 430396546, 707772361, 338531539, 145641890, 223380359, 766186938, 229894084, 52910695, 97401807, 343212272, 982263097, 681336382, 515192600, 638687026, 765467013, 501675480, 676251425, 386092094, 371853072, 969673443, 725549722, 828468198, 867998790, 99340198, 642161523, 80882684, 207199644, 701940953, 641704656, 528694995, 491524518, 605347371, 755872489, 358442745, 720396436, 949420027, 578629157, 554259054, 212827415, 412644847, 881662786, 106525242, 684457554, 163169236, 296549828, 747327146, 405351359, 512221867, 655614988, 36163596, 129935997, 577822107, 946223906, 429501983, 896460734, 110246160, 722847183, 474716437, 537464674, 623919591, 768839599, 907502591, 718996349, 394981317, 905108327, 438112843, 783276720, 858627835, 310683395, 441697503, 798982225, 17452149, 643512334, 236116399, 892013283, 821276323, 425638018, 362623557, 876837174, 281040196, 848135263, 585971575, 400512408, 130663602, 998414685, 771192277, 549182984, 655633143, 634172361, 202546818, 84953269, 895638948, 126366211, 294999061, 514176381, 817222404, 970377709, 744176841, 96021989, 918262956, 669104748, 615394299, 220392251, 535375960, 177326961, 538906536, 551235436, 304540905, 428762551, 544238707, 917206885, 418939716, 182468454, 26413633, 864538470, 26246449, 545720863, 962618254, 56575122, 413580915, 496546184, 724850400, 971389869, 559094496, 609718409, 658665281, 487570138, 689973050, 103516450, 614015239, 912566403, 960704208, 243040568, 907979951, 1152887, 506135575, 509978180, 112070037, 430187313, 180709361, 207224652, 75218538, 642198459, 33888538, 670122878, 118487762, 663123700, 326631773, 33186651, 511809674, 119033399, 360553556, 709829999, 368036645, 407608494, 976802700, 833526790, 397473709, 491767992, 484920296, 465064499, 624347168, 396965756, 938447158, 98448025, 496071205, 54081904, 485667895, 751690440, 895724855, 67929836, 242479774, 168700491, 317629034, 9583612, 821986640, 845172180, 59223084, 370491644, 832569485, 843009966, 21152613, 951530697, 794518553, 174942798, 583603479, 610825630, 141070379, 990196326, 399771736, 379520305, 797493680, 775502833, 742735688, 469134755, 597738099, 448957071, 757584633, 35143399, 876810612, 765655984, 259447695, 989705630, 593650384, 553727648, 933791408, 860649056, 593451066, 867790881, 593630503, 405495031, 972583454, 973982873, 707583796, 121126612, 236155026, 651510291, 210229915, 146872782, 343717477, 994936426, 946427200, 231861678, 939139584, 301942083, 667104114, 337382353, 95521652, 814981632, 295864463, 124300775, 944841334, 149269959, 75693198, 206192964, 782706736, 408997908, 273529118, 479753279, 167066309, 400203204, 756252099, 915786811, 964685513, 586058001, 434819296, 240388449, 744121840, 944543252, 546799450, 489474384, 340418217, 337213767, 128418824, 360504724, 435470921, 401388618, 357020451, 607823206, 946064618, 595737037, 521746959, 79339241, 250355295, 943425574, 867511198, 945458995, 469877907, 217125788, 551571230, 886357418, 965171530, 934166359, 43087456, 48830705, 343980506, 377066804, 830196753, 391265869, 759844971, 301806541, 650189870, 773814748, 155492700, 2679293, 384998431, 200453237, 188942213, 863642271, 327706802, 466594471, 666796285, 320559457, 521213792, 191023502, 169318664, 605352796, 1111939, 433094996, 945727928, 892506551, 706889965, 918098610, 273481339, 509593783, 623739964, 847703677, 652371253, 827637326, 675525628, 935412103, 177489420, 469018155, 884216890, 233824601, 452280254, 741654529, 883076663, 404821033, 413860540, 952068261, 456585248, 532453812, 329280184, 447438722, 860549828, 676064652, 179548380, 999001669, 801262418, 972420835, 130494545, 487431675, 662329903, 632096518, 205620632, 932830560, 752758377, 842416058, 420316498, 510149387, 100060275, 518888001, 555651253, 212350497, 649362777, 924092625, 807052113, 48213931, 869921729, 252250027, 708022869, 959049096, 111510907, 412876520, 50359255, 74487520, 962789879, 718005160, 130818576, 578690438, 415718159, 696614546, 863155610, 61250377, 373028969, 97851964, 790227012, 35013368, 47996486, 885160939, 418155225, 525341155, 733653588, 356687279, 772885478, 830343632, 395428473, 219767740, 656669967, 719127581, 411498783, 900086555, 61167971, 196886391, 172157814, 776863846, 855212708, 404732215, 487301514, 216362966, 733387646, 478604553, 887892391, 264513862, 223772827, 826221580, 748642292, 159148596, 468985872, 356986562, 615698758, 854209600, 956330657, 730760329, 170274411, 597864063, 905796361, 209768253, 531256295, 548713013, 346287012, 92985129, 301103191, 63429785, 97108053, 95699237, 472865389, 535081345, 268212543, 87107549, 540669180, 434790994, 389317345, 698388686, 490878341, 393994331, 17517503, 86453285, 52519692, 658204809, 837911637, 414741752, 634980775, 437348918, 712020540, 829714913, 374985355, 704217009, 707654383, 700373435, 658314114, 102273726, 339232901, 580999425, 535727861, 497963184, 493786115, 455361397, 386241319, 515277040, 522242270, 772410439, 105719500, 278278602, 320337059, 182347438, 937108241, 309285590, 553667251, 753541121, 868763853, 56710144, 864103477, 395735927, 928144619, 955547245, 31277768, 96351044, 16450219, 984362914, 896522647, 695149819, 841016548, 181152799, 660421351, 593359111, 244067740, 572423222, 730478471, 326925173, 682738480, 281955767, 784171568, 948982309, 579300218, 812749103, 997918584, 7945926, 971941143, 189838078, 476934948, 943166555, 266886467, 624928212, 763350411, 542825593, 617614213, 395231886, 877163356, 764988077, 604058327, 97142826, 396252401, 416572417, 302015782, 204781874, 507816835, 933523428, 157339106, 53428072, 982183264, 679663788, 922988159, 422406518, 122151031, 262071358, 837741935, 420818803, 338823626, 622596185, 339087987, 225181364, 391534612, 168222104, 86647746, 462795872, 491043281, 56047597, 437654649, 100148331, 957428321, 849096725, 146071918, 775347252, 67790628, 173949037, 939337575, 523484072, 760279270, 718096596, 340662263, 844548445, 292021890, 212162932, 676529880, 840133080, 733387134, 820394909, 40878915, 399455873, 835245300, 438620688, 195892453, 372445671, 793995528, 935005950, 672935865, 964332600, 863567428, 696029825, 270000613, 698352027, 935322204, 420198114, 826729316, 596735411, 724742346, 641744743, 107711724, 695246792, 594096659, 909863766, 131843677, 789215769, 416215742, 102596729, 442802779, 172188503, 612070396, 386375813, 280350512, 762982054, 530607170, 664328561, 449749847, 185881512, 758450792, 435161528, 534377007, 640764065, 914908542, 405180912, 467301828, 653687727, 576934313, 224182368, 723887014, 303126103, 754546969, 257868042, 658053900, 234998327, 663239579, 139603424, 455155337, 832259104, 848443418, 738617561, 452572648, 450633489, 246345477, 28470513, 980281646, 817437328, 587094221, 924065041, 281507040, 747866634, 166075219, 790696921, 110246296, 297000415, 451624130, 22789291, 162882186, 409878784, 166468303, 480174105, 92384632, 273247953, 428451961, 619041692, 582423702, 156186381, 116268524, 816839659, 433009084, 985122014, 121906727, 1995819, 714095430, 951605940, 620287748, 709909897, 850310923, 382284499, 93670134, 379214117, 438521244, 864217084, 652021218, 820196065, 309718732, 145447777, 958356152, 43520025, 198742277, 835295111, 102908403, 781280228, 260585538, 563763694, 593487301, 289249057, 955319578, 104981506, 49593718, 52686675, 371717964, 934188081, 325742178, 855396720, 215261569, 919112038, 622008139, 595458775, 224718474, 532139794, 728707224, 173235636, 360719369, 605562614, 788517191, 315222212, 450410975, 760520169, 815662172, 995015839, 626264090, 137862725, 856816793, 128770860, 130455653, 114314410, 532188591, 693628922, 623267538, 692750009, 221765298, 619123094, 294539155, 203294691, 799898578, 916829366, 771523674, 173164595, 390676788, 152187398, 683868700, 713881763, 536535924, 665063225, 913512335, 975105837, 318757475, 951882141, 703011297, 221780484, 115060606, 979838425, 704889649, 820502677, 847857803, 130625894, 73798403, 453257207, 676151252, 103064657, 186528851, 626416045, 895869936, 575751359, 102665153, 756928228, 869818140, 316904875, 157042527, 843710452, 815580041, 205056727, 17787870, 259851536, 174842101, 987435692, 286913547, 981585605, 434810274, 407154457, 384890331, 169856105, 134332860, 926005108, 177829209, 706136185, 584947819, 300046186, 461261439, 995277732, 190960792, 896470406, 161999087, 101280244, 193490179, 167041804, 290858963, 825346886, 520235463, 375369648, 213039203, 515213361, 375471291, 756310425, 698343314, 722486332, 897699652, 713844721, 170152881, 852463341, 371478912, 257917016, 463184677, 500729833, 8723592, 558349747, 566847014, 431626686, 834023904, 756745998, 344714181, 88516086, 35287459, 559877711, 124811655, 727090523, 914876540, 438815514, 494620001, 979849032, 748444585, 516906865, 230007951, 901317052, 983150477, 818680557, 512981785, 156941717, 607598977, 343866689, 779679015, 650250554, 911215880, 324788636, 279882096, 585754285, 705726078, 262277397, 636621846, 344974230, 874287572, 548392622, 484854270, 444353613, 151437970, 495005351, 423405417, 510579167, 520989417, 376677037, 296044716, 525249211, 805384834, 778544289, 909120990, 695543855, 838739941, 849573059, 723463315, 922195413, 642418811, 501215474, 939640666, 545194259, 317446042, 653196500, 454888835, 322596769, 932714468, 398655822, 373104263, 692384198, 635567851, 203644234, 105338398, 758873252, 929381758, 736254414, 538587588, 389892970, 117467790, 394351796, 529164253, 55265601, 879791433, 321362405, 36666368, 405773433, 480595784, 662509727, 502085824, 267580561, 50574006, 139520860, 687557281, 885476689, 433398757, 749984473, 496757122, 518701500, 901408638, 485461845, 785980349, 324133774, 792404586, 339784267, 267528837, 962348167, 754869798, 294397459, 774408094, 790110767, 761113932, 167164060, 514870569, 582150033, 621011333, 105778665, 190442427, 240972649, 300437511, 176398521, 16542531, 239310871, 82113950, 407866672, 349662604, 677130425, 451750009, 195354906, 163798478, 553044296, 380411329, 14663896, 611034846, 387016684, 777754737, 85179293, 995178033, 752098096, 312719473, 724670003, 851476651, 673301033, 435727758, 937714, 194341371, 301023625, 365063132, 18393427, 705702430, 854408063, 66552986, 557530089, 186485543, 506784857, 751737394, 8439534, 110801598, 975925764, 535859625, 577770174, 669088226, 569520671, 542697766, 685009502, 533734284, 784521914, 578750553, 540252565, 718162505, 264472676, 891430165, 708051121, 496738585, 996098157, 664490178, 635939017, 669449864, 639601283, 843722379, 923819166, 676066477, 644260761, 634922452, 420435872, 213725653, 912555932, 857496388, 420824724, 285861182, 872035357, 543423478, 240622481, 197858650, 774928406, 843224840, 536118928, 429694043, 665160919, 945719390, 181128627, 403296906, 983445974, 842740842, 416944163, 614961227, 948469830, 20977508, 375618836, 88761106, 811450492, 144492122, 737901842, 894373371, 869873017, 639279167, 825330599, 911964195, 17654372, 422629609, 195789597, 635771348, 627466410, 779070911, 405475089, 500538477, 40005515, 862141457, 578025335, 234251874, 573717387, 624407362, 294022705, 303929763, 74043209, 456893321, 254579128, 149753515, 573302895, 613698816, 139840234, 425168821, 423651589, 716549076, 370169112, 217275132, 936788949, 686462628, 686511957, 563959070, 106423898, 673882925, 348720667, 352672556, 252534581, 380002714, 423661881, 485640555, 262492689, 881141713, 621213788, 901944958, 831080132, 440048593, 271481522, 917425560, 671893668, 65383977, 711364091, 954135232, 237372123, 854571080, 144994922, 90476956, 567031811, 770904277, 964475060, 87865424, 720133538, 844029170, 278508383, 572673894, 876449563, 203243439, 454174163, 60400419, 730336478, 686744887, 392165796, 70939660, 995563757, 197103345, 417440706, 4252941, 228126127, 37837655, 939536985, 704148091, 612487977, 802113791, 892924115, 507560844, 971925265, 94649177, 982260892, 942392971, 423236281, 771736655, 474686121, 108843077, 511924917, 786841425, 558310422, 820991138, 299525518, 332941057, 227654251, 216959266, 677417668, 288074583, 38771903, 619963334, 842357090, 444887164, 780201540, 844339200, 205658227, 632357652, 443952306, 102000235, 678887120, 401900714, 84899237, 345508243, 849519288, 727723712, 38171854, 131803893, 750575261, 171109172, 939982803, 528269235, 466868854, 950532058, 698648799, 222143639, 500497360, 955127831, 26188265, 760667465, 469490445, 346199553, 271624047, 693244695, 563988728, 800651274, 598150786, 697445050, 702357782, 946866134, 24530627, 396194159, 255366326, 863638034, 344569231, 478789311, 957419727, 228810149, 186468934, 474555747, 419695704, 994153131, 191464289, 107907989, 667725797, 743878129, 429115835, 527295383, 372125634, 185083037, 317224017, 837066207, 307959533, 726127306, 44746661, 864495180, 364549963, 474850032, 59735754, 277731218, 369979832, 737926928, 541411623, 11394831, 229289690, 386923351, 691729798, 421999627, 50108102, 542177989, 530100485, 10973103, 805943964, 77808920, 266348468, 668368967, 709208660, 648970051, 738903436, 738760879, 508465731, 469813165, 651773850, 12323636, 38316771, 100597539, 290097912, 702453113, 908209048, 521619188, 221290222, 630520274, 848906467, 321323926, 314826341, 646780082, 654078829, 895981822, 597547806, 666093067, 359935608, 738170327, 943856814, 154977015, 125684817, 299252292, 749371917, 125654826, 790833315, 867425103, 431826776, 573214977, 392085536, 19647281, 899955597, 351544811, 179743202, 778947463, 682569786, 295786806, 120424926, 432258425, 808327262, 541632387, 77006761, 234611872, 996917587, 398172216, 791498968, 472513433, 471406992, 592110577, 810740872, 999255510, 28978126, 469366029, 770153666, 526487196, 764692925, 315544851, 993453518, 182957890, 732682798, 197725320, 441836087, 936710719, 733291717, 310186000, 723406393, 767060486, 828170845, 415886770, 542767137, 854426404, 129897288, 769891751, 88328822, 11962373, 277826826, 245397794, 131625949, 848524921, 577225595, 247839883, 628164928, 336485645, 65316901, 391134399, 931314199, 521371960, 960551495, 32804015, 632377324, 240330413, 33772712, 837576194, 696327473, 206733634, 683910296, 891154820, 168331053, 786509922, 141582949, 540110374, 387351271, 373697711, 665226620, 585639259, 190377918, 956817297, 77862662, 23762947, 146096144, 492857839, 768241889, 853257324, 685038429, 746607997, 220262915, 256103565, 964320401, 474044599, 618335876, 84208335, 484043076, 641009996, 5611438, 812989284, 275548955, 713606366, 268629242, 614592398, 299883139, 414301554, 596859058, 602349076, 625297258, 498474130, 886125663, 34331395, 819676247, 658293244, 61266203, 559585079, 691867707, 659828202, 346418608, 190567580, 418014177, 396660480, 48333228, 269452595, 950260738, 216244296, 269758505, 452595213, 699731462, 87987054, 380340215, 86507604, 459427532, 309157503, 305363415, 452347479, 366056098, 962595792, 816577362, 793270609, 425637203, 85127138, 856652639, 931342252, 466963018, 998644361, 705604019, 14046992, 69973764, 249939690, 707845819, 728816603, 797659942, 67617672, 621202609, 498204710, 122167116, 133612345, 149347508, 600402149, 164292450, 209846578, 657596272, 33930451, 536648478, 519697924, 548391889, 718178149, 95147481, 796739914, 696775453, 809532215, 318384693, 746698968, 688327330, 826165508, 580311339, 326219281, 332671319, 584322904, 265425760, 331323973, 409864434, 432161741, 840113490, 64150982, 521751159, 505792352, 542051060, 370640410, 116899484, 3965498, 369306132, 949479820, 932653599, 27375833, 17201535, 111059276, 493946450, 802217766, 523603583, 841657009, 49146909, 944915866, 53705873, 430027630, 546738660, 755325887, 305231495, 279045441, 746101897, 245640201, 526687566, 579464903, 725324425, 435476384, 965942646, 195741580, 377786221, 907798027, 512867858, 330151488, 628722898, 533325506, 920601471, 854161478, 550863891, 286896378, 727975186, 14186016, 173815983, 287647707, 218252883, 527887335, 130493876, 843573673, 660993856, 356588764, 13126900, 844269641, 222429411, 963820063, 166888328, 638291995, 768569763, 611521398, 825109344, 77258492, 603236174, 516767364, 600822438, 609758628, 220208019, 682587722, 992649978, 641459439, 443555466, 5022732, 674318840, 278286254, 484139367, 320526308, 300556637, 821516228, 962506372, 477473640, 604990580, 859145182, 227591966, 753484264, 290527847, 243173416, 776700044, 597012394, 639081421, 463799270, 643382952, 427258623, 208227119, 438938776, 155389589, 411396401, 620743, 122386681, 745303537, 597547071, 302694690, 211541248, 498919071, 406195876, 977298744, 342000094, 667516297, 107827087, 226136126, 840121561, 437484382, 592086124, 865271491, 255449335, 787160709, 7563588, 324024360, 939196593, 182324162, 548367080, 23140856, 732466845, 3806670, 990382086, 360659265, 303713353, 736114117, 970975981, 327929931, 650783212, 609311887, 245674318, 506112436, 380948746, 570098250, 834893474, 286775549, 369642155, 648697912, 17877171, 661434999, 127307823, 873560346, 733532411, 507429813, 599592457, 725229888, 318912651, 894571159, 261938624, 466647680, 340702285, 291942429, 332530291, 378530425, 574609003, 688237479, 357327144, 893270043, 632299890, 448646638, 585063026, 130583152, 402101030, 488885178, 902137040, 110947430, 932540012, 526106725, 956743660, 462721746, 738541046, 25847871, 265167406, 483301568, 73496970, 942642614, 96116188, 753017821, 542762319, 8351858, 399165154, 636573052, 764895392, 703026388, 919369893, 704475418, 48333142, 648196524, 804086470, 277453312, 91396242, 359639930, 347946145, 950484168, 857624734, 971972540, 890974588, 584600519, 80956428, 405791520, 624924663, 581627315, 901745095, 118422088, 689508128, 500218532, 494870349, 763115904, 562511797, 103777375, 733250532, 726115378, 620336263, 976939759, 349728986, 75854919, 339106147, 448330689, 996940471, 141290089, 875403813, 460505375, 580541882, 395237899, 909778925, 323759104, 546262288, 725781556, 97429582, 415635000, 97855898, 55812782, 500777081, 782648116, 855645718, 684615743, 765170695, 332500145, 932483530, 850311878, 417317171, 529247051, 72365658, 200530030, 691333369, 107783799, 798635939, 239913841, 774071237, 902809367, 544344398, 382898614, 22773081, 981076315, 649022097, 806333517, 167032411, 371536230, 53921980, 878856096, 242535103, 642420011, 84214249, 60709726, 187062432, 904239623, 105852238, 522395343, 11034628, 206540395, 143805959, 831723328, 146472449, 926876321, 57721881, 321767186, 724285421, 89525524, 292784964, 743156423, 960017191, 451837955, 526670824, 112047742, 658011623, 504411301, 335586096, 584534215, 841401995, 888831379, 548305723, 157713972, 904810846, 353897721, 510473384, 172727436, 290215090, 970485704, 710625589, 881455675, 912482780, 772198287, 222056893, 63536236, 347712106, 366467053, 979773266, 405762235, 106407147, 201649980, 759076045, 585155569, 883424739, 643005512, 610867329, 553921753, 199001012, 466014558, 869638896, 693081159, 873487832, 708302927, 284316835, 118674919, 463731581, 557125655, 967922534, 13144241, 158924651, 677934614, 86227882, 246344169, 967068915, 789277973, 236843702, 885033430, 886391238, 719724116, 637123166, 937180780, 194305999, 816526175, 93765364, 24487789, 253644746, 648538190, 261960061, 332811026, 993638319, 552207707, 585121350, 193428656, 242655386, 769116062, 355567151, 864917497, 978048738, 71971967, 190445710, 628629518, 242627418, 655729094, 848156856, 532348930, 19177077, 645300430, 401049990, 876651780, 700738568, 893522244, 419739919, 980085035, 351864110, 808696824, 150135578, 556624744, 322184540, 1050495, 606935430, 921752828, 950805415, 939955806, 630408911, 203360704, 112424005, 115784310, 123265828, 78563837, 942909185, 98761543, 763363409, 1103975, 262219919, 391994246, 492868799, 940067999, 348986552, 247966563, 321016312, 634055367, 424025834, 975256771, 505035284, 886494646, 600904663, 115563080, 296486401, 502984529, 493971873, 264398970, 447326132, 354128802, 526754508, 577030406, 724367783, 916153347, 371762110, 716226484, 376939559, 117253432, 255059022, 767470610, 593807601, 814083213, 592400672, 58804411, 250277657, 911444946, 347161062, 41359540, 37857189, 407983371, 108284201, 222575705, 278676894, 474492691, 697614202, 968796489, 492180937, 951141242, 576662254, 4473929, 828049513, 530011819, 775730178, 805068532, 90744971, 648789132, 727871012, 220219158, 567094297, 806799375, 987997350, 891354335, 791209636, 309726276, 767280041, 660889180, 199030280, 719378141, 733044195, 857960980, 828828686, 572693255, 731425453, 301482852, 151648131, 590025667, 74988254, 885344244, 387657684, 95700878, 601467087, 620658621, 958519518, 226950379, 804748161, 861864201, 707089591, 342686239, 454208930, 332829279, 784167039, 954961372, 777318077, 627838902, 887865292, 411915829, 710274146, 152492861, 518572240, 696867540, 693937885, 283506387, 874340100, 382104002, 809537558, 917653266, 683423095, 861966404, 654463950, 442636349, 554095315, 694877562, 425946676, 907654040, 324542271, 186064290, 272195661, 828024924, 951709389, 166225233, 930756509, 133769809, 708467936, 305179090, 659839025, 829446847, 237912998, 774791444, 242503906, 42219852, 917710434, 490132113, 262249696, 421403177, 113794895, 332078513, 192721381, 618044510, 55014835, 721912529, 164796993, 536630501, 658448473, 200190964, 42260873, 667037386, 939177811, 27832008, 328963225, 316502013, 254417887, 755481267, 429030142, 386068956, 692164054, 604922891, 846780096, 138999278, 962290413, 891842943, 780393512, 747785877, 332406082, 857997880, 275827588, 886005847, 235635918, 257071505, 329500796, 208145765, 156967933, 866145447, 885000149, 597164854, 350142369, 219825853, 885856535, 851204224, 414811878, 756371404, 42800631, 31713569, 95397717, 409164325, 247767140, 328628022, 756960442, 471274703, 710512299, 829460257, 863876036, 389437872, 658770143, 22172126, 385030990, 795414311, 943927869, 73056133, 401722348, 122340217, 223904193, 209236439, 221272141, 413298872, 112877390, 321707749, 700901233, 206455464, 390172356, 312636830, 895077187, 612655497, 507721886, 460730459, 376803479, 343702206, 116723433, 995276065, 779445882, 845719589, 443773984, 945861996, 452663978, 189135708, 134586156, 540112574, 344338728, 737083881, 637315148, 328080948, 568501933, 651586206, 736915574, 473740, 562215498, 218714571, 378421823, 841145166, 957772064, 772994453, 608082480, 166472474, 208424384, 866707832, 556271952, 595575578, 225441764, 376688139, 893634749, 316447175, 627683280, 212498538, 561098538, 259307305, 570383257, 464461715, 482525091, 49772610, 261135864, 840457529, 61030949, 119593645, 212791808, 928083336, 174926628, 878699517, 836571245, 674607081, 39010040, 434306302, 234005150, 653411823, 463736231, 818313260, 689020235, 362687562, 899415023, 944119294, 612516391, 684514184, 307346881, 270316628, 758176550, 297291058, 628547133, 479573148, 935410273, 331632011, 722554706, 481087886, 697803462, 629864470, 946794369, 52449181, 525762369, 345335975, 659555336, 409492837, 15055462, 800424998, 576020703, 298389581, 965736510, 490641512, 780164950, 39507803, 6466752, 319833158, 247873367, 201455205, 931332257, 213221646, 63750565, 337098386, 757510442, 246100407, 802934349, 111179302, 576695987, 312477188, 934549420, 564693685, 762671603, 649925744, 269453916, 698807477, 911407500, 681409762, 145073922, 161043254, 35910947, 84625942, 291279189, 448195724, 47622020, 865943132, 687776503, 276028330, 720782685, 92380665, 839835037, 271389789, 672210892, 605511036, 282501833, 839436966, 963635776, 975349268, 524719697, 843483114, 434431214, 392151725, 639324798, 485476276, 370009010, 858868113, 951713922, 426219627, 986918872, 263625328, 479505992, 71084262, 900832784, 63199771, 459387922, 508658446, 619964666, 190759720, 410736968, 579024339, 694297353, 526405176, 135463388, 900265583, 237512927, 148699810, 242238384, 97736518, 953008562, 666879706, 660494608, 358703146, 855140195, 99505929, 852326626, 457477591, 671552633, 824148336, 4685967, 49132321, 87300674, 529668722, 677806614, 86358815, 749788705, 356915351, 505688446, 128106539, 168330657, 395149659, 861344797, 188181075, 965491019, 438878750, 41769207, 701873142, 314435564, 272830064, 189618977, 90507872, 785621473, 959139959, 921031628, 995547759, 77067497, 238518644, 414702415, 475543539, 995978543, 366310992, 636726356, 240173717, 868665019, 654120675, 386365041, 699572787, 213016141, 828582444, 817332032, 630829289, 873668017, 437453268, 337951049, 739696242, 960277922, 130869114, 908233754, 185703222, 33017525, 785927028, 294634025, 831646486, 761880742, 540353840, 455837007, 964264722, 645467578, 236778530, 495597883, 405009583, 145958568, 544910592, 638175233, 426210089, 120532704, 742614618, 569406610, 688285811, 148815018, 861500865, 587878971, 304772534, 502328654, 825530409, 46108979, 432428994, 581947460, 647392304, 164469056, 640071673, 686356950, 754239008, 898701195, 63052740, 160714364, 286232230, 102877527, 27015580, 157677953, 219716295, 935051367, 15914961, 247072265, 916029868, 882391150, 602529558, 29814421, 556448577, 754703466, 356347478, 640007994, 53979037, 698797802, 638940652, 30365844, 431142661, 28089855, 626285558, 513920241, 791054692, 779028460, 419436514, 905756106, 304499080, 790497132, 935961619, 217590163, 19580008, 952717189, 397367391, 594311431, 98131242, 112294187, 6692661, 664885262, 800289138, 237387796, 525153419, 748503678, 697116071, 799491318, 439227279, 413686850, 737619754, 497429012, 271017983, 511522618, 481106043, 437885826, 489058586, 52502244, 867584423, 864696543, 254486995, 330113112, 338973185, 525945821, 615689395, 884570166, 221126155, 849958016, 818032566, 894104479, 259823503, 484921126, 697770707, 519864467, 812285322, 910856181, 911275064, 384195104, 372036899, 176511877, 796000675, 511897162, 298805337, 359944969, 471044520, 602308545, 428641464, 805157538, 914514857, 590519747, 648787127, 478255836, 799999529, 385629049, 391766628, 117128215, 134440716, 264926607, 407935499, 560783518, 419249487, 244321871, 306517158, 405208305, 526420083, 216270789, 8474067, 956979834, 96216400, 381028744, 810801464, 373862079, 397091242, 326590318, 40353157, 839157549, 285400708, 938744898, 5499326, 46495373, 683769013, 710535712, 795152260, 756502725, 323412897, 280619010, 654148924, 420971315, 24535245, 965289923, 972456317, 461392825, 817385431, 951637831, 881714418, 803842524, 392267455, 861420026, 674825653, 192869687, 579364172, 277694848, 205494563, 44141357, 633416873, 324350534, 198256247, 108088400, 212181236, 470729431, 692835001, 730634279, 827917301, 872938420, 614946180, 788342060, 949478086, 805090530, 740009161, 14424211, 492919961, 650335505, 858622714, 991168539, 452432837, 5207303, 571263437, 325842754, 489658914, 257881471, 734827598, 613778147, 577948939, 578868987, 355529409, 864521079, 79226262, 246634667, 661942372, 62816469, 649110410, 710481416, 951522219, 895200009, 901766786, 769181756, 627299140, 209653657, 681242407, 670675888, 791164286, 68761525, 362922455, 193543204, 786589783, 196733798, 840303664, 374738447, 151364976, 664982449, 745728606, 822177065, 393891600, 328396500, 199239512, 858595925, 731286067, 454314817, 53345079, 757024464, 119228865, 395332022, 231469042, 31720632, 132443737, 662762630, 394055604, 70003445, 471108718, 306121896, 770720629, 286951106, 330837869, 932333037, 632164944, 482008177, 671753792, 931213919, 270947162, 532202632, 743754406, 349662246, 740378917, 488034727, 322012784, 902386204, 127328858, 259453306, 171610591, 775414506, 94896879, 680364659, 212425262, 868199697, 219967010, 737551921, 582313647, 135986035, 90161435, 736801758, 688458479, 717732074, 189618168, 583824821, 533583028, 741984134, 327452889, 851159126, 397813540, 154789385, 899210908, 79485603, 59818866, 970888717, 349528884, 425993536, 229585377, 781085448, 859354881, 696373849, 940883486, 774031987, 138581218, 250181149, 713436386, 202601682, 658514680, 522275398, 708297064, 848796814, 586216010, 104102780, 70149850, 498066203, 793154606, 477911934, 328131421, 666229211, 117154363, 504405502, 365250879, 515026716, 25357287, 183817455, 155395130, 13385820, 489502432, 402388438, 479675141, 317333821, 54070591, 261513009, 362643307, 465622654, 472387059, 527375502, 82577807, 241856030, 172759680, 968936335, 812833506, 689744680, 806007099, 54512692, 362145023, 364822816, 724423038, 941150486, 615944063, 419660310, 62772854, 325835688, 227963796, 296034672, 750553073, 486239741, 674493387, 700717979, 296422763, 749921151, 370544594, 593357838, 637068808, 970774042, 660145380, 35546909, 996542514, 190205783, 491520329, 434277684, 907335347, 98863003, 171848829, 554962276, 7586700, 138878565, 641178340, 163097865, 491285641, 792442580, 428629835, 122670368, 676375517, 17023528, 865018089, 239286800, 399482577, 575282880, 856414461, 958453571, 458767471, 270356808, 640461980, 362137483, 971368137, 499254615, 246559811, 574642447, 41647430, 608276264, 128652553, 509469352, 919623409, 923579159, 530149614, 212630991, 775788371, 239078961, 734707247, 459709458, 358889789, 49427458, 760660728, 340507630, 524300311, 691488141, 583305625, 959161417, 601127453, 586781433, 485997683, 414997229, 993041117, 318703327, 608324746, 142021625, 309610180, 886900585, 785523270, 64814911, 358861224, 326110799, 209831017, 274684814, 155961658, 761214484, 633640985, 524258445, 832609694, 499290424, 567438577, 834167036, 254264791, 988490749, 6021067, 353439333, 586416614, 989211773, 238462618, 992361863, 202196607, 285309967, 185312758, 409380164, 492985015, 725751526, 293081843, 882496721, 946770496, 210573105, 442543619, 953578385, 179412053, 854778059, 950152338, 590184326, 6520878, 906805639, 764936349, 130341174, 640077523, 468068691, 920964130, 495964051, 145506515, 149170093, 625564922, 780393779, 237314945, 302692348, 203409047, 162051282, 876016657, 293664565, 23559987, 407588560, 950466118, 317160723, 605845680, 149652602, 901799245, 918497203, 724580152, 295244578, 821085135, 432586745, 110158255, 848847578, 779246670, 228537370, 265695054, 237234830, 896548747, 108486180, 419843335, 125103471, 427430194, 833636969, 963289574, 208476367, 320811440, 154853704, 635302121, 559005456, 149297797, 163595911, 472582143, 669351738, 285893986, 76854190, 543717592, 476394401, 487297699, 333302360, 682387392, 800953918, 512376139, 50865918, 8186243, 983499091, 941679034, 417753763, 707666402, 1686204, 987762302, 407595046, 57436207, 934689038, 54718152, 137072548, 20011749, 44629575, 184049561, 461888891, 699977831, 714633555, 515090437, 745759569, 345697308, 578981237, 982834397, 367550750, 665622980, 113658632, 692546460, 971894358, 119744079, 790934359, 680178653, 629074336, 772950221, 833514596, 147773290, 655860794, 882428647, 973844403, 516337935, 574694611, 828297889, 239178747, 6114549, 61342943, 88895314, 809968016, 205725171, 258224363, 796223570, 761721948, 471279485, 228904245, 410085982, 754952507, 459686926, 156504911, 832060701, 483494994, 352156160, 68442393, 177428226, 794157332, 770194295, 155943759, 431778733, 240436586, 712395669, 692575165, 329832850, 907480787, 5106536, 434829130, 928398667, 594379737, 252812846, 786636245, 508017330, 954116749, 668132835, 471643992, 742356602, 921793378, 207962298, 338584388, 981989203, 95393126, 309741252, 562249921, 968515486, 283853738, 111909021, 64873069, 392066491, 786224036, 384745153, 432159302, 707605887, 796079971, 408435009, 103613884, 929803431, 13785596, 201488001, 688783833, 92377753, 101474723, 125443091, 861708627, 472709796, 540805627, 377976947, 176913302, 158333076, 506165246, 541964132, 10392117, 346849909, 594031526, 148503443, 15402806, 874535504, 100583460, 668496956, 267379183, 354184703, 784871223, 206504443, 31907006, 369991762, 554085565, 584730131, 513761946, 569238526, 55699016, 77402009, 992491593, 456520058, 421044701, 696980228, 47919808, 17167158, 718171160, 11645337, 971141018, 477225934, 911017103, 542882020, 285122533, 436596854, 942607036, 116465193, 713413115, 608556252, 524828459, 178825971, 55910716, 833351394, 792379444, 340471697, 973120825, 145563327, 63685981, 597231883, 512872970, 877184191, 544907782, 960362070, 32733943, 726963446, 33594400, 537105434, 742101526, 548503137, 531570831, 37634932, 462883670, 383165509, 913852140, 517456257, 177860176, 278263703, 318594220, 743230198, 563153302, 266629564, 747406016, 413165041, 761726421, 535137531, 882459870, 223573856, 781169760, 277512849, 512736831, 346202255, 811260702, 898844042, 278800641, 69977398, 194559613, 121494405, 596540890, 633550886, 872337438, 843481844, 835112833, 486236612, 410711873, 579537970, 46136103, 232467619, 527392087, 409613329, 465730606, 387181738, 643465201, 3206321, 235376649, 767626858, 548906120, 366579560, 114641887, 567713518, 548174255, 257594088, 831278818, 878868588, 247716576, 779433362, 305089482, 442127831, 945854834, 554849953, 816605368, 6736003, 870161955, 958703754, 697648506, 321463796, 717151218, 769523459, 215520512, 269927561, 640235880, 176746727, 1886674, 140993066, 240976877, 205151135, 823232415, 294898189, 665097099, 638278335, 934512789, 495852701, 610732876, 203041353, 205725747, 945043229, 911510103, 647580644, 3272692, 67226326, 893476968, 602879623, 134942457, 709883698, 90414599, 205927767, 271284613, 646897452, 238102555, 72153076, 339872209, 242404795, 64453526, 94004915, 815096114, 680119845, 803100913, 224686580, 323586861, 497577206, 459381439, 30041021, 259402501, 926701834, 971361755, 910775044, 726873498, 428663048, 649004225, 928908682, 530297808, 420566638, 152169955, 552053017, 59708118, 954655103, 768862759, 257575941, 773381467, 445868825, 272939704, 665424551, 337220882, 576316151, 202388202, 876806173, 246133566, 76704042, 669862975, 214287948, 242577006, 307964704, 830259160, 251587686, 79967239, 62246358, 973287214, 681041823, 251552416, 405246804, 41180119, 292955491, 469472928, 657130830, 927556467, 495373005, 257608128, 172733391, 32872548, 530693010, 866272845, 998422937, 320914268, 721830743, 495250810, 470569528, 852778764, 190174841, 105260844, 885544424, 170711356, 566644050, 734639498, 621286817, 984282986, 974156196, 193328751, 976041603, 814681929, 739757013, 272725499, 27269795, 506129893, 765035982, 539933430, 491011253, 601555142, 813947718, 879553550, 909351072, 419947085, 433746839, 125390469, 70713663, 995000517, 935105, 819992348, 78585273, 458484882, 631086092, 265053202, 827576797, 191287887, 42227274, 401687216, 685128140, 380283279, 351861034, 331702074, 451947494, 590248865, 381459779, 939503715, 355227980, 350190526, 322421187, 414258782, 424899042, 482351483, 67115039, 387010276, 269084664, 39778905, 718946053, 337260111, 460697023, 638024669, 956168538, 498077056, 360451233, 17803851, 38988814, 912055811, 950746020, 779555083, 849910879, 669272608, 270738539, 976066417, 136134048, 245378104, 801422853, 428363298, 819542338, 605820784, 838327956, 683946083, 452821207, 544917368, 69734191, 571818824, 573686259, 782384036, 514828917, 896917356, 117214850, 853559478, 569765715, 14676139, 446375733, 491352243, 613295320, 379155469, 589711062, 387973775, 827846263, 978597893, 407548407, 321775064, 892004132, 774005256, 55006817, 935176115, 874202032, 420369813, 34676962, 696842763, 439778231, 733584352, 932278615, 732934862, 922800307, 500548770, 534942400, 231093280, 913910895, 414352494, 219930450, 738617066, 835563112, 101621025, 247871277, 981038997, 854057028, 258486015, 645563347, 160628076, 799252598, 694920123, 160838808, 149036397, 581759251, 529174581, 526686572, 448967583, 159430113, 733521453, 712051757, 337961693, 387108454, 520126054, 259890612, 545238586, 332970266, 839879276, 550375257, 989728992, 937407597, 37813092, 103442885, 575684295, 781542580, 21693693, 467629246, 616321428, 522226835, 624160937, 599973782, 525222365, 560639498, 665791515, 406790220, 638278484, 643220253, 971354845, 218261187, 539866601, 757352946, 393001729, 5823919, 647899249, 980683270, 409711134, 418324797, 889794557, 459526138, 76304238, 574598972, 32845616, 475490936, 802842962, 59987540, 746710737, 720148688, 632986130, 429748756, 670796994, 647808706, 536019876, 558724897, 167379049, 462388029, 39271560, 647570283, 571584072, 729822266, 30251466, 575318159, 912427509, 146449023, 909432313, 595979632, 287226712, 386134777, 885411822, 982485906, 127118830, 987620875, 886052590, 340570007, 322238073, 303473907, 118916009, 861036335, 674902458, 968206609, 312791991, 128670871, 301500647, 7514429, 355372418, 477384918, 867367411, 398654083, 539874216, 791647323, 123737552, 615824928, 729243688, 493763125, 586746368, 914373545, 412399739, 439019141, 865603074, 434043757, 930073223, 977204973, 80712974, 941385011, 966369600, 675572081, 732198539, 299903746, 607072696, 912838211, 329010645, 359441478, 992377994, 595616720, 832493505, 54736245, 38403509, 313098117, 311600072, 157725545, 994345641, 128066431, 281633394, 426910619, 316364121, 925094388, 54521614, 13261, 819620326, 719995225, 971588225, 267773901, 609365086, 967746415, 841901899, 648846768, 214092593, 182372269, 244538522, 246961691, 213645815, 430752672, 760301329, 290676321, 669929309, 334529266, 671735764, 136965716, 45709269, 138161392, 835207426, 469651515, 84584701, 146107690, 175753689, 510564103, 15641512, 943022680, 633869251, 153797579, 848081137, 970847288, 66633236, 964702551, 799655405, 456784253, 599419712, 678560127, 240662247, 39595078, 110448432, 638294939, 903273065, 635114807, 162716292, 921151708, 171621479, 769220134, 299017133, 117723698, 780688097, 682554676, 362756803, 990411939, 739879747, 92250652, 737263150, 383968711, 392406596, 86019141, 121906088, 756338318, 620084322, 606133528, 834432888, 865895871, 520152913, 625533185, 732877069, 962983248, 622453085, 189179064, 664814636, 726674498, 384284330, 547742560, 896830670, 225840873, 450695344, 294998934, 34881951, 472817272, 407618920, 176365444, 762949389, 569412526, 837479431, 482270126, 48174034, 85328993, 438481390, 92480864, 395414628, 999205997, 675664011, 119499333, 385465360, 917922759, 160291398, 877971804, 529980353, 414964726, 182598492, 379427294, 11973472, 515253518, 402415750, 565794813, 321212845, 558986705, 292117094, 337217174, 987129901, 554104290, 348325081, 68089841, 981519786, 136538176, 114728685, 3770099, 197573660, 24353988, 698109377, 902660566, 451130778, 982433787, 782923651, 218945078, 962736037, 43656479, 995536137, 533599826, 955934454, 242161409, 713920999, 770072443, 880660909, 7629113, 772756801, 138345218, 725610328, 377298041, 324773719, 942926200, 703813698, 622734581, 28744140, 416610253, 713779030, 911041348, 595920066, 519305168, 30781194, 90961383, 607488400, 605767491, 695762823, 978420952, 82265489, 721300720, 770769124, 150569321, 680687340, 770582568, 714401748, 285568329, 597696194, 506649923, 449469490, 409634742, 73162029, 978896515, 876691307, 40552384, 600412493, 539917575, 397685658, 125102813, 814684577, 777765892, 148533029, 999502049, 170980716, 176917622, 836404437, 195857216, 785590687, 264471640, 283338040, 303691528, 727295979, 988454504, 496212878, 328212114, 64380885, 44258916, 926952503, 586215034, 627441447, 446238137, 295922900, 71179877, 789520209, 184125662, 224771143, 34354515, 619871488, 281113270, 296619234, 973957569, 701479642, 91284183, 667180980, 625519435, 797888627, 118067800, 272427543, 971342835, 933434162, 610100814, 729131809, 748454479, 636196841, 285278543, 828467848, 394842147, 365516998, 527598519, 127993289, 118617337, 115766664, 502759711, 858988076, 561473775, 698276017, 476137647, 702810438, 254007351, 795720301, 527377874, 673760516, 80412798, 542270010, 959940028, 490268989, 322632108, 788694372, 843050796, 61270236, 242950287, 159200749, 928748479, 974076530, 375559294, 816640841, 283887989, 527887529, 746720961, 964821997, 237531708, 155387048, 778440515, 26839198, 953634599, 629506229, 74071077, 894956899, 149091767, 316165111, 736481288, 399009933, 829696482, 600054701, 206537886, 659192594, 153172185, 677101334, 431034993, 933261266, 768072567, 660425242, 66790372, 481177545, 535338940, 3460090, 13596271, 832631439, 936637380, 204872955, 30933021, 588439834, 490723478, 715409474, 578599220, 673340032, 840517704, 636882958, 263911695, 867655232, 535788604, 136832701, 176711439, 466886237, 744303487, 252813300, 721131679, 19789514, 570354216, 29141179, 198142497, 156184070, 303614472, 359061377, 719667306, 292358245, 363118859, 806408343, 997011708, 65600100, 479795344, 380100572, 238994216, 385821678, 739133983, 445851376, 626061314, 712122036, 932010290, 801799956, 809990512, 787447377, 6834474, 217506970, 565009469, 353393480, 152956319, 546489877, 386292904, 804967229, 915348670, 721605025, 834070638, 388474598, 758822328, 867976124, 402669941, 71579172, 15459156, 780510394, 637133686, 982734142, 557797708, 759214831, 637585625, 714534337, 618711705, 158062791, 842353673, 924063541, 288599934, 961761360, 265894390, 893338473, 604370036, 772477302, 506681338, 164459083, 101189456, 450958680, 987488317, 219759285, 738440837, 672985314, 247437339, 425448987, 676202601, 884065659, 145076097, 566916622, 977159559, 717899015, 745733252, 539021987, 38589098, 973042273, 911143281, 750994720, 865317867, 181796726, 144417393, 642771831, 10361056, 268625838, 476599153, 605427118, 796455897, 981214394, 631552487, 36006611, 891407316, 842388233, 542013124, 153826602, 485829744, 730124086, 497094730, 482020049, 457507394, 631725761, 352825655, 683987977, 552769778, 297439300, 734971628, 46112986, 951733722, 144228295, 94332522, 91435062, 585986533, 808382846, 8373417, 868318733, 631515401, 36077878, 991107551, 967045668, 463813202, 544834025, 207230496, 434912958, 27790349, 261227114, 236685806, 399465694, 369539947, 37197023, 174890817, 513321602, 192172480, 162170118, 477686860, 123106744, 322668732, 674283019, 271348307, 279448986, 102895097, 969758396, 8042980, 857196899, 176745369, 233221605, 376516256, 774542733, 946348295, 500908038, 426123487, 752117235, 890353564, 933059448, 498402358, 430856370, 961871827, 672742199, 908363585, 354600718, 68427880, 982209591, 11917511, 132195325, 207711762, 528222589, 187130700, 534885792, 644074054, 650576256, 966455651, 387003604, 865016223, 47783468, 556303019, 877305683, 653792143, 888917797, 750698658, 258134235, 605636586, 979464959, 86727932, 471261228, 414064549, 466382694, 205966779, 470077277, 441525019, 441659697, 809435708, 187855665, 711518265, 306103307, 650061979, 1148327, 996590031, 437993866, 969704284, 366796558, 967405140, 548548201, 556441042, 826516871, 303004771, 385464156, 441808891, 368104788, 945393640, 624007146, 930078100, 684563928, 807017134, 521229565, 316230103, 295734422, 919078088, 920827253, 899349437, 766703435, 543662943, 112550611, 979757075, 724699642, 251190627, 901924127, 558414964, 816165459, 927105512, 133400019, 266183028, 414990483, 960760287, 807840304, 627974235, 349540297, 361480455, 477997714, 794169929, 188628722, 807049350, 509312641, 648452630, 120336303, 577626843, 374116859, 841295010, 662247693, 577124874, 800096686, 473075871, 33299667, 747263990, 97707214, 157017107, 865191202, 235621481, 558023113, 575892040, 965782143, 876124248, 827643569, 173385700, 138096217, 172521901, 608739780, 941481833, 668203655, 812989872, 68869612, 703094497, 6753934, 709540592, 614748389, 791014955, 397500952, 997333220, 495083438, 789217641, 244346508, 160782988, 914201654, 334566850, 297036564, 636101388, 584657620, 185455183, 881537208, 928048786, 256605774, 873907666, 156141318, 890908111, 982217238, 873449283, 655111024, 664811941, 672231597, 435728869, 479421383, 730232047, 376547070, 601127294, 933265974, 986994136, 398777000, 976731031, 190780230, 455484891, 590856076, 148929105, 365508713, 390919847, 805335947, 983320619, 622236300, 544684987, 291471367, 346566123, 115430586, 725966230, 890985609, 616614359, 763292057, 499683011, 185148783, 349196040, 644683724, 165798068, 5144867, 290916337, 280601050, 859906388, 124991363, 142515302, 742840886, 78875161, 446851265, 507747252, 226600654, 553078187, 964198955, 942374493, 802920652, 280310054, 510113955, 403059489, 591383924, 385358373, 244109175, 498277496, 977539420, 780854283, 859194959, 922077936, 417609276, 103604057, 774416509, 671811290, 535880340, 489837536, 357151578, 622308331, 520234951, 924316990, 948114759, 346870319, 643217985, 629086791, 779168850, 19322557, 323319839, 411156585, 710366072, 309392836, 105451276, 583578385, 530707114, 969201698, 664591328, 632173182, 745862912, 591819576, 722974801, 98025138, 732477615, 511554263, 786367567, 6616824, 474958158, 41565011, 224325871, 542877514, 283027548, 918337195, 911850678, 243133022, 120002549, 778355453, 829171097, 672377125, 75120252, 571369603, 69222844, 238815422, 774528013, 127565737, 739184178, 322026699, 234828744, 732920640, 785054010, 454937181, 106496544, 234817001, 255527396, 438093560, 325519341, 750107270, 987785800, 188713207, 657707303, 208198962, 958324228, 809545416, 520392008, 294870118, 968530902, 502237447, 720899520, 547772187, 850433470, 318561285, 983172707, 809442401, 337328646, 994324075, 8802333, 143963524, 113500055, 534504188, 100893364, 909509073, 789996175, 213138551, 231312120, 98964160, 137355660, 166221680, 96010164, 841596711, 953696363, 664678371, 346693787, 211801786, 999413617, 623308206, 30363865, 147656392, 363399831, 323330678, 985095303, 70681630, 852270186, 194593313, 496223875, 804721269, 283230899, 327849678, 281084834, 674579989, 123831391, 60967676, 728505448, 212447376, 948107855, 248491272, 856827380, 345553182, 832861065, 182713388, 360451392, 161817433, 550388119, 177432885, 216181494, 140632423, 953610431, 627244492, 811593383, 343229192, 359801146, 892475473, 405969334, 951443669, 107393981, 280382040, 746430803, 549659501, 782517660, 676590988, 545207638, 113853578, 712295484, 581671455, 921257004, 371209201, 167150811, 846130031, 283801675, 147388200, 754655504, 41451338, 844571149, 36998474, 798978412, 234037513, 502841110, 568914175, 355189283, 767596387, 588384154, 655675051, 676816886, 129196928, 486429709, 429918922, 428890476, 937570760, 305382061, 445500932, 453414993, 459942877, 383823707, 777330778, 259460137, 645947402, 673485731, 959642897, 401153505, 382256884, 442039807, 965090693, 456870059, 228398829, 962086674, 220386497, 878969142, 761143544, 158119870, 77948313, 339710537, 170425755, 350615178, 490330816, 37766938, 605016407, 678933967, 906900787, 270562594, 18243165, 793129849, 743549655, 352976044, 813759167, 964965012, 395421978, 375534061, 528853429, 452774068, 566921495, 344877567, 404469294, 492297941, 536365555, 585521015, 130615806, 337942227, 424079031, 264704562, 953688647, 968664916, 855134237, 186623421, 169825852, 262353426, 25659639, 727699925, 662295320, 478957917, 789894823, 361837795, 992819467, 266697013, 389562285, 272412711, 386481577, 788758185, 459794590, 158046594, 746977602, 127942648, 385689537, 643561509, 978543319, 867923368, 400089731, 294106316, 614341411, 117190105, 719252346, 524286923, 112245133, 521018975, 832911944, 668021269, 772174960, 358340924, 63069523, 154089130, 318668803, 559000131, 191694470, 227058085, 559298562, 110409746, 470714690, 710232757, 675444754, 922458543, 385264463, 772340920, 26973630, 726268318, 422496007, 998810211, 311293975, 339378757, 997603623, 420131929, 227494023, 618728956, 640520934, 323864830, 61420915, 615113013, 542959040, 542767741, 760453726, 80488421, 716551448, 513560034, 695692158, 369766654, 919181493, 316263314, 497674990, 485395069, 219009092, 704223791, 528788543, 982293020, 514454409, 13982816, 921767698, 816598650, 25384122, 888494399, 729341349, 977991746, 571493392, 361243679, 67190341, 300273893, 813599205, 614078351, 961526586, 9939737, 248516310, 328704583, 102690229, 200037667, 145804251, 74257522, 519386827, 487998246, 794943774, 113523299, 675007577, 726738043, 179138334, 117802887, 90502132, 68135084, 94222480, 963425079, 440460352, 10171279, 227214060, 486186398, 167478847, 735665905, 254459019, 428052118, 977559298, 109171534, 823990883, 922069219, 499539418, 725558056, 686706177, 169211923, 556023628, 848252859, 49462771, 42950762, 584274372, 808148019, 511525539, 591472369, 798000804, 256897988, 544824276, 993077410, 304364560, 294183753, 320364419, 463849893, 299353674, 246795600, 33651123, 175535673, 108290312, 408523968, 208034105, 251237470, 755123877, 343519950, 812873199, 834316337, 508156218, 164121298, 956726882, 298913414, 107127011, 182455102, 144480084, 766290233, 370216467, 505692940, 82800801, 317691063, 68564345, 870360068, 259669423, 870238466, 276070592, 889830789, 344769876, 635979135, 799539597, 899500390, 330625566, 221516727, 154333735, 115741625, 904701070, 343272888, 427149763, 436122730, 573539040, 202327010, 10220331, 678887931, 368459113, 51650189, 956758774, 311304080, 405974723, 442113009, 19828391, 440926832, 577625671, 577894885, 851834943, 437724202, 726486994, 566700287, 236714567, 652703299, 422828223, 576875499, 464302118, 702662112, 390041477, 364561781, 515550968, 475896191, 313899102, 55309438, 633957676, 131381735, 418089620, 367862422, 561838276, 745946541, 674748652, 887550245, 684964759, 451636661, 793760433, 410617766, 212332565, 643418529, 731389165, 921537184, 688141922, 200092985, 774479382, 280551493, 383583645, 794896896, 503105029, 933515025, 108832897, 393420401, 824342208, 969412111, 332903786, 508819114, 298336693, 677270964, 189927985, 151767119, 851942832, 280455459, 656505995, 382869665, 109901003, 974811708, 5640215, 834938356, 678763180, 970342153, 455986990, 886446021, 510229238, 187079857, 633242532, 538787283, 812268522, 110034189, 814885449, 929278520, 665254717, 551029837, 806950356, 464263630, 786229618, 581793830, 392377969, 609503856, 73195721, 736348741, 295074869, 861662564, 769362271, 282280750, 855440432, 213505078, 857005168, 321789588, 263532190, 567604687, 353651288, 72068241, 13466565, 22800590, 832815016, 378951664, 35733737, 720093466, 584440425, 99014210, 638863190, 309063492, 264133626, 354728247, 926257805, 33003925, 860251213, 789033626, 199732100, 118260848, 39857883, 112006533, 598256194, 554899256, 335468563, 254037495, 953974802, 564538906, 484313661, 532755174, 802519026, 298720333, 176883979, 598428579, 741245042, 442501123, 348755711, 102735918, 925292419, 105603175, 565951778, 774724242, 440162318, 862627009, 562194254, 482698222, 326928964, 730964258, 739051141, 22139024, 383009483, 61053695, 482638722, 565107445, 464365949, 163431646, 567933963, 265986147, 685646589, 210910426, 562199018, 332503312, 86341813, 520906501, 706583110, 470386848, 851028543, 615261000, 468471341, 791776266, 406334864, 857095053, 31136446, 24856852, 439553887, 738966837, 590377067, 583685206, 489795490, 929783996, 3996642, 656366567, 668136410, 486853286, 874138800, 811548779, 539330043, 859647307, 542929146, 45900103, 962386179, 410960891, 521846649, 696871358, 257007990, 441112527, 446934664, 655169235, 538632530, 322623637, 857731908, 931645334, 761803503, 743681097, 103449868, 636869884, 476153047, 186459293, 983702599, 151329732, 482767706, 415933471, 380215834, 764874714, 688049327, 70824747, 290418151, 811540959, 908751933, 920023697, 774120143, 394086153, 374200860, 709331174, 425592218, 316433332, 676156247, 115961186, 205787981, 644442770, 506837095, 890248786, 13042675, 378378124, 420337027, 890902373, 689519626, 196349634, 157343219, 247468483, 157740174, 14534058, 6520148, 860900665, 975280768, 239092691, 901040475, 941031010, 15865009, 443533616, 785504669, 505615498, 562771298, 53496708, 940987774, 472879654, 768307891, 241506411, 793782477, 259173484, 57168977, 519613920, 528154609, 984641141, 194875493, 987855316, 729441298, 369882966, 276332356, 439618506, 736979090, 290302328, 543267400, 7589075, 850065907, 882679130, 91293254, 77079186, 252761482, 271213840, 176894817, 592408832, 905829321, 393328714, 1676008, 304118350, 90240483, 728968039, 660066504, 506237854, 871033792, 217736195, 623465881, 471570382, 412920056, 116228975, 670843696, 705159815, 282145656, 548998636, 690930054, 922843111, 501070676, 621330479, 28496076, 356164823, 375729223, 815901454, 224326239, 444003252, 895374305, 701302456, 779392993, 970192266, 486163091, 932645759, 909873381, 728298937, 874840448, 379736069, 100276047, 689416878, 110580060, 226854786, 700879820, 2282524, 138611535, 876981794, 104075677, 940101298, 883272359, 264138585, 505002156, 840771070, 19397746, 616837299, 641394337, 550454483, 134064188, 410409130, 473248330, 558383016, 393892283, 138652008, 905680187, 898395911, 172286937, 922583943, 732854838, 88104257, 823781679, 615145038, 802732433, 922067130, 72997171, 845370964, 448235302, 579575105, 95840707, 870915621, 246843046, 264734828, 828362513, 258980062, 97724296, 445490814, 862922102, 170260100, 332948690, 198788310, 678201506, 211746003, 878442123, 535406776, 40774473, 86453957, 433410944, 200681671, 834169736, 416877497, 839676247, 411165208, 746450421, 1554898, 837575361, 341435405, 17306493, 277776906, 699509092, 431564774, 568350174, 955238973, 51974464, 327246778, 767929090, 413758043, 163446192, 257059663, 658406313, 297650458, 125608398, 975507497, 170029948, 74296162, 230602924, 158368810, 692070811, 329389941, 637119334, 458750781, 647290072, 951546923, 737133853, 746558892, 567022201, 66355813, 125677337, 984406362, 953401381, 39688338, 59382157, 501625489, 883827114, 709807339, 519779080, 227207928, 915751576, 17028762, 433502642, 49164476, 881563070, 612851287, 367267200, 718656431, 261089374, 937146900, 892094285, 743305350, 177523002, 226395404, 580750349, 299326501, 274535357, 373921199, 900905046, 592704292, 397831167, 365278322, 353028622, 268902058, 657995054, 601817185, 638084931, 311703633, 922837932, 14509338, 443098873, 117414662, 223887329, 651123652, 534738248, 161208530, 93705226, 519933051, 6249048, 978679365, 325059161, 955671429, 696992974, 244658341, 876805219, 753158546, 16546705, 708061659, 9627146, 295175786, 979445528, 33345755, 145999999, 896376729, 502470651, 184058991, 915954330, 531697076, 83598100, 510933197, 205606157, 190037533, 918237300, 736724552, 77141234, 382698903, 291109718, 119705231, 911473518, 928677125, 938041333, 335207597, 255961481, 973387575, 920397950, 985142256, 229354580, 938897615, 202156784, 189283829, 7191545, 789145693, 502890347, 735137526, 15550222, 856710901, 92810694, 698298469, 32327317, 2710911, 691148156, 246005574, 11497498, 89640407, 778259418, 312647849, 866906586, 221544915, 912810428, 520789021, 863268555, 636794253, 354809545, 47431391, 453254251, 893650772, 314821269, 916004635, 497084749, 206562314, 223808151, 939371614, 221366808, 204336850, 55220562, 982881257, 231380610, 237385218, 10893398, 956712057, 454773847, 704833733, 789976129, 731531705, 922426042, 637797376, 188645015, 33021726, 546516395, 287131408, 216528711, 534123615, 585390926, 191721120, 161740856, 386475626, 751620535, 260196434, 900133740, 734300071, 194018486, 74586842, 153804364, 315814829, 537110095, 291578217, 500183504, 721660676, 140305999, 524213031, 660809208, 715265766, 594856503, 147967828, 589676786, 903687324, 234112618, 272082489, 754963876, 494642393, 986180832, 204451613, 887524214, 321192090, 539557750, 274731657, 76881177, 76463769, 283668061, 606061754, 228497444, 681912131, 850726107, 58326352, 64323947, 248429899, 291554402, 208366017, 370685666, 213499515, 686530279, 308598040, 378097622, 983689640, 880739650, 5159398, 411931715, 85397100, 384703631, 220857542, 385980713, 22139753, 432376103, 240356663, 466965090, 585090084, 973718581, 463969725, 714876832, 943646155, 990721352, 359482370, 121525448, 641597972, 943123065, 749257433, 923216225, 228092614, 214851280, 33364939, 931688107, 452660443, 428085481, 612426077, 196166457, 237029385, 94000335, 704572802, 585161404, 177314643, 906406726, 594919605, 119306510, 403668554, 461025551, 324097508, 107140543, 119320440, 194115410, 602363112, 634173570, 623107723, 320411969, 545130028, 373028141, 145629816, 422846309, 172023683, 195953908, 744408006, 100855655, 608189779, 448515328, 989820845, 463796018, 662825100, 396220723, 467507954, 824926577, 684126403, 591698201, 26068233, 706130532, 387911091, 494715115, 196942852, 422745420, 395323699, 266400496, 26727596, 851722286, 676051501, 473069380, 558340102, 783196201, 128988989, 873559947, 441438081, 887255690, 848172126, 30337501, 735929841, 460181292, 880173827, 631994188, 803600595, 178665255, 273855678, 266160523, 623022626, 647514818, 846429536, 366201026, 905958974, 210624065, 256717334, 436243941, 670434356, 742418267, 731624485, 525952265, 215731550, 719779614, 623117021, 335878326, 720176708, 66979076, 819368662, 583423395, 781247817, 695347300, 492882544, 879302008, 788492274, 701166564, 136529717, 46213103, 650521534, 185631870, 844323083, 550195586, 579045409, 995877323, 844437084, 320578830, 918432518, 965907419, 909404594, 311145453, 711893700, 246596454, 581902867, 730161745, 765408415, 859289460, 993049306, 756985503, 290298692, 368366528, 748080205, 807473236, 102765628, 673867248, 23713659, 673127767, 345547466, 994263021, 934535730, 32374072, 644509868, 962272903, 197400920, 433594818, 64197336, 74982666, 766317035, 317340004, 551561296, 844530668, 759927510, 91209587, 203435947, 714193108, 627409241, 392269281, 253006366, 423382354, 513973228, 688770913, 30578072, 103211687, 525898956, 874616085, 230061606, 385834993, 374057120, 722561013, 430407275, 969555215, 240348293, 171092879, 750561316, 560070849, 409518228, 360830810, 673966294, 156760078, 630658857, 940287561, 404962325, 412727691, 270748576, 429393430, 430663641, 669640814, 312778421, 821432019, 621604231, 608735657, 321837592, 494082561, 867054915, 877702146, 961764447, 764146537, 398744051, 189200588, 675934023, 557186184, 327675820, 917940884, 108809641, 112574204, 920955969, 720191294, 756300774, 472930851, 158593582, 532584038, 810992724, 630637575, 463012211, 152477419, 936881000, 401973947, 922059527, 195189170, 491058904, 936026696, 633739206, 296454793, 200731916, 756806842, 559932981, 576440135, 887164811, 102736516, 922807638, 950685393, 657144215, 766627601, 294941844, 152590838, 724521805, 747166134, 571918402, 68591389, 205449823, 818762934, 264709505, 911260262, 241594797, 833540962, 813529774, 40382795, 208576403, 945841076, 33243830, 906459726, 582703212, 357589552, 478384910, 39450223, 801241357, 468485106, 841125625, 636143339, 153015664, 369289087, 248441686, 169426084, 124840573, 724089730, 450256857, 110089987, 480373651, 330564138, 913551241, 237749322, 998589826, 631111041, 406257451, 784593825, 735188960, 786576125, 569009161, 496801445, 415261564, 149727447, 613947169, 363348379, 185411177, 100532378, 45739870, 646805456, 24727790, 387143640, 380224109, 701369274, 482182355, 365327804, 12032986, 973047376, 212784929, 242861257, 799717788, 895646848, 17745836, 134564004, 229311740, 819154280, 489119927, 46028928, 107485764, 410584299, 216366565, 796219100, 508829548, 29904605, 609305734, 200271545, 95283514, 267975321, 257742433, 401135281, 412621707, 689184499, 608854968, 962250522, 400532926, 735433150, 110514525, 668719912, 849688730, 659350815, 192569994, 680829532, 911295774, 361596574, 365548766, 637481902, 270224348, 569593291, 685074998, 122727626, 789046483, 380451266, 736022111, 700683026, 599228219, 692366656, 893161539, 105039644, 787543457, 592612361, 647801392, 916971317, 554054038, 930752539, 103449035, 960168956, 608406658, 944638656, 463739948, 987656661, 141376384, 388725499, 914542874, 327909673, 126492845, 437776339, 318254320, 195906134, 752789450, 790871542, 259655510, 860558252, 789796679, 127387465, 645653024, 148372654, 651427981, 984571011, 415522088, 503661967, 202871014, 835197061, 951190396, 397170917, 941463979, 814358218, 284508724, 258551541, 17476734, 616063506, 712162120, 715287541, 196767489, 725149461, 423212715, 739880933, 269149183, 227498951, 129459584, 284318647, 807590504, 635779949, 807051648, 526724291, 108533084, 952523841, 756202899, 812065476, 162385835, 695728709, 925188251, 218050219, 578884812, 994176593, 575299053, 795101313, 54433272, 329142702, 62086113, 350330024, 327046691, 915417756, 803009008, 719936470, 235509572, 857073965, 481449719, 146728669, 84389324, 999676890, 416777312, 194966112, 775031197, 372428387, 88810686, 57301095, 695648883, 944893062, 128589916, 243423974, 453211477, 646706929, 570473282, 30288076, 719209853, 440027447, 224939463, 118496306, 368375692, 102979905, 435709180, 647523550, 479679677, 457773454, 363587412, 661577580, 123239074, 904526694, 656775778, 241217241, 251679122, 818990329, 272421175, 190748300, 822987387, 23678501, 32754957, 9686381, 297245638, 692625569, 762072250, 22865306, 232237285, 306697900, 517759559, 816741153, 882404014, 136752168, 453898798, 447414311, 400243099, 128195024, 233038529, 612278458, 243417677, 679529059, 665530323, 654640302, 26868303, 534548213, 267561148, 713681683, 102501119, 900704713, 60693906, 23148854, 320928979, 119843206, 369124964, 143238003, 279495664, 187882372, 173218715, 467301192, 313025151, 907503324, 318947089, 132146013, 616793254, 834085892, 667215305, 474207334, 968309369, 479718202, 157504353, 154691672, 214019124, 941971102, 885871026, 808913567, 784447357, 207903086, 847755613, 123970241, 385419958, 213989345, 855254779, 444126184, 826354800, 207073229, 970420521, 35080784, 986757657, 465498742, 260951735, 496270305, 938404639, 387310771, 61426724, 959499629, 505799057, 671546716, 552036844, 108157926, 605166701, 630239122, 134795961, 228642538, 113559228, 700151351, 721949693, 104836717, 769117098, 760740859, 967700057, 983644252, 427665784, 431853568, 737677560, 722718048, 546656675, 382211235, 560616793, 808601991, 570902892, 689112286, 771931746, 119328745, 907844500, 861852950, 944931412, 182343923, 827699241, 474474720, 790762150, 425095054, 434888434, 249454153, 717821751, 351431813, 99106409, 719315320, 634455403, 550611942, 918813076, 944490410, 108517355, 479201660, 353542685, 483072762, 193586759, 144778185, 295058185, 952749780, 622348479, 877106285, 700590150, 96765832, 841226968, 4445784, 613681026, 207848835, 662614467, 649513584, 986252932, 544015419, 24605076, 844938480, 709230311, 63499270, 350777348, 223859642, 946476458, 827372530, 408085202, 718593372, 332841648, 756806454, 712004738, 848366233, 344129344, 891806985, 391953384, 651413230, 469751847, 323200509, 474815607, 826518053, 596391701, 668220147, 122950103, 25773626, 603759761, 605856241, 3694409, 978172419, 548294903, 424993825, 293321384, 206294224, 235034341, 543422684, 436929976, 513027025, 913008740, 959049801, 347513728, 659120097, 735242721, 730614223, 600712808, 56976783, 278768272, 422001273, 239129431, 660697556, 405870536, 157229072, 922428399, 701017475, 596212047, 151785553, 166216221, 915016473, 456512933, 375439343, 928290919, 599239452, 178021033, 330945795, 700676134, 904960350, 705597171, 491245099, 423150009, 616934276, 47780468, 294466028, 22560657, 268877754, 478410688, 539095575, 218857758, 461600118, 225375899, 27902956, 519267339, 456152695, 859331784, 183762526, 213185771, 331790082, 582606403, 797861799, 886122621, 507458725, 701190442, 304858935, 236716855, 8052010, 841859191, 232740488, 973759675, 970624017, 793805457, 775252488, 507735224, 482110324, 985851597, 132280458, 701592295, 447595408, 437821223, 76027425, 845876149, 271201224, 516450868, 697218273, 74146802, 356028997, 94557389, 288780681, 212928825, 491208955, 621791872, 729140258, 919241276, 510729599, 555591416, 114403888, 191352428, 645575937, 876143294, 873450299, 300885375, 371349725, 543761761, 590315747, 963730762, 133491548, 112584614, 570576680, 768706446, 491454684, 719999585, 535154673, 478526906, 331729532, 345666471, 394569640, 145985717, 765553037, 945928063, 607455114, 196872628, 978894395, 542123268, 911727228, 535749933, 26030783, 8169418, 815638338, 428129327, 173411190, 351262897, 646725498, 110013453, 523670376, 999171187, 911590298, 389306419, 28570403, 500429314, 15244104, 116445123, 707650401, 516819697, 337676752, 803236895, 481421858, 997535687, 956947133, 263724600, 264174157, 215130772, 12108998, 293084757, 853866411, 107898429, 379861641, 930918518, 410285069, 138062598, 301638966, 245560409, 833238137, 451551116, 9104431, 222064993, 843005990, 486481943, 22471196, 458301956, 850827724, 549041594, 500592117, 865949490, 879094840, 402296009, 644683927, 154816794, 302147231, 337135727, 116720854, 149595100, 939504762, 290554466, 163349621, 250417747, 870407355, 593939679, 988346539, 784696141, 464481091, 784730598, 60069567, 619494929, 824123569, 401864635, 91106098, 947174630, 40598357, 50480735, 261134462, 535614931, 350536681, 116173728, 210183290, 642469554, 962360121, 474621752, 510192497, 66155796, 201870047, 94216465, 716783983, 786657741, 215162574, 858966932, 415868114, 130538647, 995438480, 70888199, 987075447, 881157796, 339690793, 518138983, 535157562, 149004595, 455337395, 419350121, 38344829, 495150560, 590965613, 330362303, 702286177, 483083348, 93761059, 242796762, 15554855, 265775143, 242237821, 958608039, 50834490, 794446147, 700123540, 653799804, 515513979, 175134861, 681244270, 380744981, 987811289, 663455234, 430548598, 660652202, 294410011, 952731091, 325527515, 332179785, 429356930, 345659564, 511219359, 307963447, 176833830, 374680749, 227491831, 186988404, 723833236, 357694533, 934299305, 276469226, 200053421, 396042074, 911149552, 395780411, 259700351, 642200617, 358595339, 175521436, 929976640, 300948148, 132548054, 852634992, 170581292, 336883143, 459087231, 543897312, 200692402, 146327685, 515682406, 159512280, 788457136, 337051718, 3114177, 14479221, 98513805, 308218358, 921134543, 346746879, 65968703, 571870918, 40218113, 825167766, 499025782, 305122406, 281055981, 714624694, 774936551, 127030097, 179355941, 689711413, 908640757, 963534824, 530117192, 77722980, 418674415, 366270155, 319366417, 755044398, 926499848, 163425561, 619220243, 114320498, 277067487, 91551002, 634362474, 13920202, 939346794, 966870253, 930886020, 467388389, 541422178, 468924898, 104256157, 287551055, 397864089, 879041293, 474040257, 542452288, 536921249, 757340596, 517652644, 725172502, 237160920, 735658615, 196538579, 455474381, 128444327, 511492814, 337962474, 825568960, 331133971, 449296101, 612363088, 575189203, 92393064, 149567963, 523637114, 1227486, 427294279, 300065679, 980186692, 549902680, 902933320, 131346278, 873004805, 793274854, 98575519, 262778736, 717288405, 470606582, 174080118, 108091055, 350885054, 690568304, 297235761, 736140867, 563848996, 305308483, 71331009, 74923404, 722910049, 75619314, 212247166, 319200271, 409942479, 850736541, 146559141, 595531922, 21744118, 11305338, 503072401, 191400730, 14035314, 625592831, 286068214, 136747013, 849505030, 328136711, 399717487, 481422667, 213166604, 630975567, 948034826, 681321157, 622004613, 269948770, 81971296, 306810307, 660364067, 816321605, 857640758, 166822153, 478451009, 192656921, 37218944, 288445809, 390239221, 38196004, 481848525, 317433629, 645472528, 99141214, 898581168, 222401711, 249138637, 472513129, 118091347, 686828921, 115453273, 83868539, 214279539, 390138925, 258133202, 331800167, 849118866, 428732560, 610739150, 61385379, 944245319, 247353545, 699863535, 533702539, 34348730, 412766941, 158885891, 986200590, 160418146, 578222116, 294422809, 670487084, 364018775, 589783620, 328995301, 919458344, 23093424, 249877209, 245992448, 261732544, 374940309, 603068785, 528164493, 266923711, 611331187, 775908016, 465991054, 811699405, 299103315, 42056634, 398160556, 66440689, 643953742, 910067810, 693816295, 616099998, 198451219, 74639099, 945073970, 211980723, 146589735, 382235416, 564228377, 382846510, 738441913, 645995365, 72602122, 314981036, 631173247, 364225152, 524438554, 383486166, 662922168, 5740447, 628235003, 70205710, 501097669, 872189965, 959155065, 894380479, 337936413, 492267413, 690005891, 244741450, 73260907, 218687991, 742978603, 674373088, 581439479, 37173106, 976901541, 215047155, 569267639, 741594079, 562542378, 667868023, 779354454, 612796698, 592699038, 833961619, 590643472, 787978210, 704161117, 712823193, 426564225, 143073363, 577979837, 327402730, 740776973, 614966220, 961631356, 127839465, 791715652, 66555531, 543345077, 255713832, 816701650, 533835907, 773932462, 845398094, 486694616, 891591569, 326203031, 960369653, 444478672, 133432880, 745535681, 411670642, 690069171, 450464112, 936626076, 10395309, 158812459, 308479754, 220567538, 973964492, 126788645, 835270637, 475296416, 50055588, 839341396, 825863198, 786078926, 316437093, 460707674, 548570155, 889856918, 273331013, 208629036, 317181468, 246533442, 732578118, 889020297, 849670301, 77996276, 809499396, 594482383, 665644022, 804273557, 839564596, 22901092, 682616981, 750046609, 795555568, 121241105, 501296408, 21160387, 600848331, 716096854, 261878839, 760864542, 75039419, 21718159, 97974304, 992704944, 152989880, 958209708, 591081206, 661306041, 272003696, 163608515, 32367776, 819081062, 238413288, 373793686, 285661383, 756152425, 261012013, 444730418, 229526516, 809939870, 646582058, 565590784, 152099481, 579266340, 683464477, 772740332, 72721580, 822813114, 808527021, 913507521, 268657975, 703842248, 318481822, 994210501, 587166848, 63739344, 483149087, 679624938, 433721193, 181931127, 972509965, 711479239, 722933325, 57916183, 893439850, 283392459, 781352776, 872675265, 375133420, 248202, 206293760, 776975298, 308015877, 875290799, 292919941, 620987833, 748510767, 977379826, 969269123, 243891186, 933817275, 211690665, 406208348, 66672434, 685367766, 190687186, 587034917, 801554814, 585964950, 876014342, 420027364, 139438656, 303466674, 122166564, 33975087, 748523968, 672212095, 357077985, 517397705, 61576681, 195564318, 861401633, 314955164, 378123480, 692638300, 44480380, 267029805, 672715265, 658014778, 95875986, 902105668, 391378423, 471732789, 231592310, 69709220, 227685668, 440538911, 201730929, 944138587, 711201, 434452532, 875405033, 133474075, 210962027, 263203654, 944995182, 647993732, 583705506, 563232610, 452070232, 347488382, 837560641, 123541110, 382754749, 265874289, 936159774, 327412467, 413892195, 168500213, 591453372, 729966644, 755215149, 307405471, 623779169, 763362245, 737724532, 779792622, 285507077, 312867744, 433668480, 832380866, 672188523, 734000081, 457624051, 568150611, 60457613, 373020027, 314366792, 781413980, 522199414, 684029948, 813414462, 860328497, 603996080, 588928357, 208637863, 207037822, 134443782, 639361575, 612326829, 353501243, 639619464, 374268875, 4218351, 378908624, 441515887, 804626265, 576809047, 302242778, 197061075, 496766054, 601532330, 761917654, 514605883, 287857401, 285655984, 306043492, 761489408, 645847529, 876725722, 416261756, 595949492, 384303035, 48790084, 409537021, 244281008, 473883116, 972113015, 173301228, 170297673, 598863447, 796586391, 107146407, 456970067, 611481696, 984262804, 596109206, 47534497, 654430352, 439874667, 361595712, 995175053, 644518671, 785603853, 468625434, 687657030, 710307420, 825268315, 529851084, 648436261, 49494269, 590532461, 462140898, 685553620, 486937989, 819577371, 517616118, 940726465, 340041497, 936736505, 822380951, 538455022, 705170385, 406946266, 924183631, 346741751, 988330715, 500021173, 455833759, 250761714, 432842298, 64939154, 945755015, 721225481, 148598404, 954379071, 882543157, 5595623, 279548381, 363344878, 775649410, 37646014, 341334393, 4559923, 287534489, 440201770, 298269957, 281568716, 649440331, 436391825, 128293629, 468130301, 347583957, 9381982, 63589626, 218499316, 309412420, 446213821, 160850263, 199344531, 469478516, 137501313, 577260995, 267888827, 444307512, 683168364, 815544437, 580842313, 615796466, 34279938, 621596517, 662228996, 635105340, 719183279, 56072599, 959298412, 451944113, 172996608, 116648453, 610220012, 236727399, 265694609, 353751012, 589566348, 81278481, 414804787, 398163154, 772186670, 419733681, 194274494, 81947210, 809031963, 888396217, 544019802, 838813176, 576516931, 782338647, 252893644, 120091599, 891622104, 33372464, 398384619, 47896024, 541905316, 559243998, 888878758, 271596677, 481034228, 575986682, 729442792, 124143050, 696955708, 830573421, 307303260, 208348158, 598348132, 231308805, 97616195, 612614373, 865489423, 520400712, 840839484, 866579682, 845406048, 696502038, 255017214, 194032670, 230961590, 311807278, 836140144, 516365543, 163909285, 787325523, 108919039, 985219555, 640548428, 892779001, 194081203, 268521771, 594164153, 451087564, 367703890, 647560201, 188676364, 900539791, 983212275, 264724251, 657819758, 451048668, 751728607, 951776716, 957120712, 206765366, 675825756, 872011410, 763544843, 690817295, 219765119, 426119343, 971398827, 469185577, 388857620, 855488563, 471746604, 185747504, 727651587, 870898338, 673220439, 387649768, 12764034, 74880132, 147538108, 169184689, 102113039, 801611866, 484930659, 459069207, 494395079, 556654292, 639901764, 813183035, 862067592, 527404849, 66184871, 124967222, 293189666, 120275116, 522770789, 31666984, 336191444, 751936927, 468253399, 935270057, 33120481, 978139185, 654781868, 908230400, 281136521, 406493146, 316247468, 19032325, 123439106, 911247450, 748529731, 495636008, 965489702, 811208640, 297016925, 585124594, 185164925, 500715210, 929598356, 673085878, 209516194, 489050157, 913148381, 157808235, 119015127, 253287678, 264574260, 80667653, 348598927, 638610780, 325057487, 59990617, 654708233, 381590905, 295228498, 884237916, 840979612, 858492699, 728806968, 256241209, 361049487, 849401445, 697964406, 669636534, 432841122, 446117023, 447462538, 350877271, 51242418, 651365463, 444239174, 803072886, 994989628, 555028334, 311204304, 391905033, 496378781, 647557602, 576735585, 87334894, 122776176, 853620031, 691311637, 961271969, 30930462, 894409951, 244908596, 14552551, 684172315, 189080835, 775303270, 915675658, 909669674, 777564921, 911232252, 177126791, 367587280, 801625354, 807028361, 259045403, 90699211, 576559978, 453376677, 887337218, 467194389, 164207021, 950119873, 589476463, 769468331, 271603848, 781434475, 445496489, 953610175, 840764311, 616045908, 259338256, 120997834, 337504175, 520478810, 30530884, 168533937, 976340152, 370892743, 968139449, 796278578, 383510492, 372248312, 526906999, 3769242, 599831599, 676140390, 545834557, 616736622, 218553148, 795003156, 349121864, 603128486, 974249406, 54959775, 90192750, 628397608, 301281335, 124150027, 183339691, 370652692, 893133260, 306576141, 941524419, 55026906, 65929196, 393836224, 824745980, 235083323, 809612050, 930589226, 280852251, 185317648, 61620488, 785237719, 277157683, 615615832, 429242396, 651976037, 632151039, 160392400, 306500844, 783156754, 70001891, 219447980, 155296372, 446111458, 823312757, 25316361, 112187401, 437610542, 65431561, 960108438, 462974495, 449668202, 553741070, 277067848, 370376477, 837684907, 767938514, 764325812, 412370925, 520394430, 487379072, 298070970, 313206692, 890104900, 350874773, 287297526, 932260658, 894255396, 888240173, 467068772, 1181749, 151097655, 838492737, 724365964, 468109124, 864028032, 406010977, 737589438, 714981488, 29588628, 335878538, 938979265, 517298765, 846393651, 510970736, 538471432, 894597621, 621884773, 738106880, 733493738, 457076778, 665827299, 318467409, 311087833, 57372989, 502357486, 165120667, 731369989, 100932420, 527250339, 617580992, 53799566, 649925803, 868688303, 867832824, 812034600, 702234163, 754445416, 477818970, 426312868, 795078813, 113990482, 749991652, 349107440, 298910550, 592289359, 677272700, 466589355, 143461324, 407591824, 550720655, 257471989, 708855167, 413908972, 315685596, 727156003, 586077665, 173358250, 950947419, 946369898, 264494591, 848768423, 833718645, 351089627, 603700591, 159908560, 739022073, 205156646, 867591945, 383109192, 895295361, 922991484, 511850977, 329457380, 337196230, 594083641, 243596871, 359519461, 816048658, 96334873, 606249330, 648882753, 660466975, 558598230, 74755944, 777924743, 178825472, 447746705, 700055957, 47114987, 88878643, 897055454, 28260738, 29726078, 447252771, 879661648, 21434875, 38882323, 773696970, 255042193, 711184386, 782938695, 609705551, 60286988, 927736005, 947432675, 923151583, 868491384, 380785896, 929371576, 298592923, 169738572, 966004281, 108613307, 542833660, 269996392, 496968961, 502997419, 380832977, 663706289, 806320562, 996430560, 473539539, 274557355, 374362989, 319645548, 960598231, 551961169, 591209124, 196659144, 117524368, 101980244, 30831854, 44000665, 950654044, 542544246, 920207940, 460568568, 362375925, 112838725, 822103396, 350796010, 820026530, 883402617, 891254085, 341772621, 684895924, 996094720, 374584773, 740377273, 103948435, 36187451, 21784822, 889451097, 403890539, 498298760, 751664871, 82354802, 494532581, 914924441, 195225151, 812393245, 253733686, 483911881, 823085697, 426322189, 439971521, 75258384, 216161159, 788818905, 677912807, 874106457, 670836799, 73258743, 747010804, 943031761, 194664254, 578323948, 904076839, 778113341, 6095726, 237757210, 397653147, 564179748, 877141161, 628370580, 115977072, 461619681, 637621290, 93128835, 256665196, 449061702, 58276287, 60466096, 608675837, 938807373, 883421612, 882157407, 111755934, 410619269, 927072677, 51087862, 425653700, 892083462, 562508029, 421686211, 418722614, 106250958, 210263856, 476051769, 58779694, 427378907, 430815475, 584426754, 489163284, 497738374, 519224123, 983812662, 447557396, 933689113, 174530969, 679672309, 217465308, 152929005, 590805104, 612002642, 738742782, 310258343, 705548774, 380321357, 285813395, 433826948, 284579794, 574192295, 766095056, 585226458, 308548197, 569040321, 920289026, 381084522, 904728736, 100742422, 576520297, 347404001, 920192598, 294368336, 364062013, 566108473, 783865545, 304068388, 258028010, 713410006, 493938403, 916850288, 598928359, 855983860, 321180360, 47301061, 757154909, 870052838, 155748164, 395381053, 777883751, 425745410, 253368758, 525677452, 836250937, 638976961, 991631458, 82655967, 921315713, 654500142, 395344254, 258750495, 59194690, 438059124, 271674936, 331405405, 497252074, 603369594, 842888393, 114694180, 202018984, 55647452, 667981702, 743821617, 94710435, 875896347, 841933342, 139950541, 705211030, 97654878, 366271133, 951347920, 738574617, 294265811, 482424807, 747789285, 741993499, 672683579, 789156834, 803111323, 611445255, 874753563, 190674058, 622467184, 342280700, 121062831, 725258632, 706937506, 142480242, 730934753, 415089210, 229339492, 265345515, 642141263, 472219068, 116770350, 881587782, 344136363, 119658702, 604819846, 830277359, 564503300, 360901732, 225852292, 535780755, 767261524, 693580657, 538727381, 434860976, 371002595, 261376934, 806609632, 228825186, 882253830, 742453375, 887699262, 666197682, 734531210, 966433717, 890463556, 511744211, 764992303, 782543325, 579924746, 186790594, 533061794, 481379269, 338047971, 333423403, 688834550, 169497528, 457485833, 604201340, 382958801, 381403398, 310557717, 286037347, 898641233, 297409599, 200509746, 56988202, 42123776, 293412357, 11677718, 24945637, 851605985, 552565227, 560917100, 213697670, 402184851, 489196748, 562845589, 148725399, 770579512, 398387274, 588591186, 714598665, 924893985, 251903647, 854120911, 723909105, 948473174, 197480368, 152584965, 738591663, 555752332, 485730657, 334914553, 233847200, 5206513, 544117519, 84766958, 438092274, 95821174, 670577926, 953410079, 839124988, 587923503, 580585765, 871378306, 863943266, 314174408, 640712522, 886180989, 41540902, 789727810, 54115225, 341798459, 531487984, 901628910, 512204899, 110529246, 866399616, 565059898, 722697572, 760993981, 738327286, 277123840, 179571707, 105370677, 838415430, 276282042, 813845781, 621533659, 877797066, 627097641, 221366497, 413787457, 916267746, 158537480, 392473724, 487451254, 100584929, 604968591, 584281866, 895995932, 526556980, 927674982, 158573013, 84899517, 897999209, 617519026, 649893307, 127390147, 850193126, 602222764, 540245064, 275761739, 666598568, 412884721, 48040397, 434918771, 361325775, 348453153, 739511847, 547875537, 897442332, 25997234, 147368265, 484470677, 766755827, 503460250, 857505613, 954674417, 599183136, 832928556, 377512, 351695379, 373880276, 643951612, 796550278, 325981237, 489180741, 469480437, 302682118, 208650062, 161965496, 20548926, 808838655, 619533326, 615602028, 372850806, 639463284, 987860106, 185814541, 570201652, 352959312, 39578330, 140121718, 403263510, 943323952, 654132435, 869220546, 407468075, 357245308, 461516658, 856451416, 812259624, 766181974, 852985829, 759068353, 628430753, 889526323, 568106578, 728681216, 883949920, 860897597, 612230003, 437282745, 991940564, 622327757, 938276059, 192014783, 735465604, 225080563, 504344814, 898326129, 727833850, 551380006, 9023720, 535976675, 350389093, 549447088, 727293728, 435930453, 764649386, 169162777, 390428942, 651768699, 148258800, 531855537, 340956205, 794959928, 940093569, 954966102, 7210715, 675415708, 576939156, 541062982, 637118496, 511390830, 864086477, 207895591, 434917930, 779751884, 166303981, 373852213, 284439285, 238095884, 300711583, 94884830, 693428303, 240103402, 97326013, 41690710, 628610091, 680119841, 132527727, 39719523, 651516407, 563296450, 984142641, 873212010, 397886476, 777774232, 812160507, 679614869, 651947397, 191239654, 149922693, 563166347, 468521144, 694619135, 80367015, 857393304, 238334977, 223795730, 187556532, 66891999, 205626053, 45265973, 12095233, 934301353, 514735923, 214653095, 450879883, 332836226, 788311272, 493755624, 468778018, 599522178, 486891512, 981257069, 195933084, 822850295, 820883930, 429523543, 977729450, 116783797, 647551266, 883700480, 574367857, 248947195, 183357865, 462994959, 610753778, 863168719, 670162245, 655961023, 57576222, 329629701, 842845161, 395925495, 702466700, 519098439, 239274844, 380520618, 748481564, 315120865, 364134146, 656353859, 233622342, 530500549, 398101605, 186737379, 383579609, 663385054, 173602050, 426648287, 723590457, 271303303, 999455808, 772694156, 386326826, 290162510, 112404024, 678964903, 177091114, 769185703, 411969603, 101760845, 474428989, 140223360, 779437059, 793856610, 514930803, 537826085, 59282566, 855786983, 510641829, 44203842, 671876711, 70542497, 407827571, 752704635, 544522959, 993171446, 286103713, 878707864, 799959502, 816810122, 364094573, 414503877, 182995597, 318968321, 206800810, 473446355, 944478732, 945504889, 139433851, 32284022, 893620165, 650933464, 133277640, 671419103, 740254860, 429057163, 103376829, 22047854, 831182494, 835901723, 864120201, 251584609, 283478080, 426472350, 430235916, 215623149, 675303096, 393247745, 338605752, 712217303, 217933915, 82112663, 572115284, 861807256, 316858435, 977242877, 405252209, 991005956, 556080441, 731941516, 801825167, 150177237, 488554708, 188184394, 568726808, 224193122, 610463494, 237534473, 388666314, 684112137, 183032206, 802132917, 441346232, 584995, 599103664, 894084681, 362641201, 208136158, 531366589, 441149714, 449149479, 801937603, 336645184, 688514431, 989117533, 162037755, 742104015, 827680519, 88532587, 693776521, 981558275, 456112458, 772753267, 830932898, 470136321, 160926318, 528662143, 594298985, 238526427, 645945583, 133487376, 132047247, 25071906, 324727118, 98234201, 427631392, 996460907, 982722577, 662910207, 861281613, 151832613, 464045163, 26545143, 832020866, 331896363, 64561118, 27478315, 941202896, 743037391, 912977442, 958016849, 175326676, 595415956, 134442044, 735573609, 57397619, 14692662, 554759681, 106924503, 577468176, 577854387, 960589987, 3286332, 238866168, 324174634, 668782952, 737331019, 58862869, 614243771, 210933039, 447528640, 459809848, 794833685, 371190000, 982541681, 929104830, 193769584, 682762730, 449511083, 326673112, 101808049, 894897690, 867300604, 393781281, 292128270, 237472222, 202363736, 150144959, 348137597, 653156653, 194840038, 513525794, 605399348, 890968247, 168687972, 574684476, 343572175, 218750351, 538947015, 281683988, 475145552, 793425699, 734418775, 36312992, 435670104, 21173069, 478250689, 82780625, 458739926, 743895178, 824929267, 195830653, 460170500, 478894161, 108533953, 504999731, 598544230, 644790745, 882653170, 988959573, 594748118, 774487896, 631020056, 685320134, 740139773, 234696064, 61757608, 398728597, 854095959, 379213375, 308963435, 229493907, 98818426, 770751301, 519118396, 931707116, 394762060, 608794539, 8711556, 679232186, 846472837, 93901650, 709915551, 882387846, 655800276, 899968788, 301750969, 217844960, 677825359, 662316996, 399778748, 494033898, 787670313, 642856365, 362995083, 396023927, 994509169, 775180509, 322918043, 340585469, 498966957, 120220269, 396199352, 877931141, 809102745, 568066246, 699290426, 874969072, 449076629, 368869549, 579208025, 234254018, 688325881, 152523389, 548513722, 523397291, 466900541, 819867176, 786839013, 983275080, 270947838, 816268767, 603337681, 473638433, 515809531, 459381140, 428073392, 591309836, 592425478, 509125237, 347378178, 534303974, 447335596, 893647672, 505534698, 42975361, 297290588, 570817798, 176457574, 786773030, 19725225, 233927255, 238780490, 560494807, 533405314, 809078978, 319960918, 763817264, 953443281, 855736319, 249824196, 311786321, 732811526, 851040371, 546091258, 642164729, 239131780, 864399497, 880712993, 143485995, 576987240, 851174007, 102121173, 685538643, 220261057, 989066618, 112744297, 281583957, 436371101, 746422840, 362184443, 174855753, 759234084, 621251586, 94469366, 706047292, 72347371, 428890652, 451615649, 507483162, 599889009, 642025640, 303376857, 997969567, 381891523, 26715195, 561539562, 877537287, 807866640, 65027807, 753473430, 701144448, 963617008, 218968088, 784838912, 27940377, 905093065, 293422076, 374285726, 624974222, 841134368, 936962177, 903160119, 12471170, 648721619, 234180756, 790604476, 183772372, 29358276, 462313263, 777708263, 470328662, 306000468, 364899126, 628939488, 388189915, 926179367, 541896604, 377416011, 796796892, 434771850, 406208653, 797189252, 716737832, 834321666, 333237366, 772627523, 335278356, 813097941, 317732340, 567641969, 340489252, 213352291, 700785015, 216284027, 196899367, 743687726, 669866549, 443477163, 187683067, 832241004, 158081043, 872361411, 443814115, 451792526, 868608118, 650765955, 783222935, 432358025, 826605831, 992691412, 763531947, 243090460, 204193805, 506922884, 558669711, 311757937, 306653493, 691649223, 896098410, 538441570, 287388290, 206854627, 5210583, 346526450, 66628627, 367289481, 680824105, 563416988, 584824649, 565685589, 927403230, 392648548, 191646561, 221318908, 534471153, 222918242, 32266351, 884208766, 394631468, 513304987, 246310879, 670787009, 47975783, 385838004, 505159493, 131703751, 795624394, 825915677, 907875311, 87402500, 433287264, 496733883, 288216734, 469854027, 915730160, 344306507, 415566760, 117309965, 931692845, 724774492, 114121866, 680883709, 609713098, 911262628, 160072216, 746672533, 726915974, 702987331, 827041367, 408413125, 570518105, 188738292, 956844647, 958517560, 249461699, 246268164, 564033503, 672389252, 494342569, 775202117, 226442367, 218559201, 450837003, 729452419, 103312380, 49845818, 543491218, 132282499, 320206541, 342953445, 137759025, 320819848, 228702834, 757032156, 711857977, 523076029, 837159859, 71457524, 440566041, 647197480, 926154545, 253493392, 6384134, 229854194, 400279506, 6425539, 781238935, 534024910, 544346852, 544787456, 609013838, 238465370, 310661429, 124412327, 839862976, 624093819, 238494400, 659323702, 86741127, 42840993, 726410185, 501873458, 867793350, 894369787, 939109206, 583813828, 740811499, 637013435, 814504169, 745474232, 673122744, 455627462, 875177913, 427485225, 164262248, 700025289, 576998928, 168787472, 758128071, 123093005, 365412794, 533669473, 419967564, 571263295, 81513965, 692775405, 74318651, 540096767, 157665128, 127792340, 758720750, 815747898, 609630894, 361122455, 417284538, 311269282, 612114015, 378020616, 672169552, 832871202, 183868925, 287744977, 688966663, 640253586, 155415683, 782447518, 730416559, 158417621, 847121697, 251841439, 981949885, 569949726, 194734492, 994150142, 178280315, 291891069, 607289255, 559460787, 549368317, 684635106, 529909438, 3007973, 396843045, 879651999, 261068485, 684456456, 797189604, 477295511, 399836091, 687715088, 506329430, 745533999, 654621574, 777617283, 69854697, 454936952, 422523838, 366079206, 7206328, 589280947, 207994383, 311313845, 845695122, 525143051, 345879534, 908076308, 251075626, 735497988, 365023853, 584448456, 887487116, 917874190, 224147945, 927041262, 150564344, 523792041, 866086376, 986796206, 118358019, 200136740, 691290270, 927466171, 552555409, 811111203, 953490122, 257241936, 900534298, 634359263, 962754290, 904937195, 759086234, 269162560, 160873845, 754623796, 977738210, 686192510, 405579885, 463370545, 56264280, 89910703, 656623458, 620620967, 664438820, 646472, 372881054, 871706577, 935523021, 136555836, 644530224, 992563854, 492935657, 237718861, 491158350, 425657597, 703284660, 150124568, 293638162, 368595158, 800754670, 150707678, 787034278, 694017085, 563967082, 392432436, 819627763, 828992017, 690656459, 39812840, 342852508, 761636484, 163534443, 641221893, 970147829, 126677791, 327240394, 748882860, 22405872, 1454474, 551989423, 430537218, 784367164, 302213283, 48649621, 807450637, 56840097, 399489319, 737501203, 532956573, 99049479, 63305044, 811397567, 821935547, 50755083, 132907789, 657752980, 612558679, 23049498, 637584753, 797344248, 74282651, 680920163, 584763915, 637116255, 182163734, 371406131, 862609074, 181102742, 501793308, 781770747, 559056711, 226744408, 469413549, 731531120, 496900417, 329889544, 905651915, 289177187, 837777665, 140753222, 181667171, 642806441, 360732285, 348314966, 603609789, 329217443, 981064292, 112410065, 252842848, 413564564, 978741693, 984063654, 932550088, 535244946, 547971654, 789066170, 3170328, 906431025, 288087109, 221805535, 514058082, 480537365, 949576463, 575814696, 920164484, 792276617, 969647318, 81211066, 540332605, 910683917, 559076057, 311789574, 755074505, 751563053, 400024775, 544772773, 835912404, 230231688, 710390021, 665758008, 333849616, 682518303, 698930525, 805730373, 964119541, 807073345, 848772982, 368820313, 59562851, 467873918, 40094777, 159777950, 863245101, 797112665, 733195561, 229919769, 940694988, 342968815, 677260141, 678607748, 19952178, 398163188, 911785885, 631950864, 810121135, 875889896, 188968587, 208133723, 872308751, 340832486, 52231645, 702307309, 495763219, 613834269, 568759699, 394021273, 273599787, 586966300, 88369225, 332345875, 700837659, 75050148, 57599073, 868905702, 916659432, 113084314, 202221208, 312696254, 401972960, 165749955, 543993927, 814292153, 332728512, 567692677, 559255250, 757879771, 154599472, 558791941, 686782244, 751791593, 610471854, 354896885, 848626309, 253560827, 792911308, 469610015, 32025894, 933252701, 368916903, 953988928, 100458585, 301021536, 707724387, 478498278, 940128436, 480733850, 99739686, 772173150, 636263600, 611805427, 943385888, 747795210, 859911625, 250155383, 818834510, 822808775, 395661296, 442002769, 903217973, 703360688, 221557652, 914467308, 78036599, 878094578, 651000228, 681571489, 602512310, 872511175, 324126196, 586367964, 55165683, 981874083, 439443762, 405104517, 378050524, 689281606, 477961687, 419005024, 542813540, 316972678, 460524264, 760143706, 322050967, 800898569, 69284611, 278467178, 347868278, 69683960, 220876964, 653171960, 605459630, 6872650, 600919155, 124122448, 21206036, 980210221, 863559370, 225289542, 474120767, 656966883, 343211853, 156150986, 624767906, 59911538, 24052488, 838725214, 134916995, 806826860, 610080316, 139715744, 755952171, 823592907, 900305328, 904170810, 433347859, 389940673, 488560571, 559984293, 92451155, 94892807, 34967543, 178628861, 163270165, 297647483, 422091488, 277481599, 540983612, 704680295, 626674414, 502903617, 415803298, 892659033, 523495958, 15628591, 592649514, 205212345, 422685954, 160575364, 259782951, 70373633, 563888086, 668267040, 57418055, 902948036, 961726473, 671027561, 12051442, 364676852, 178452607, 957058979, 188677465, 223520838, 579888202, 172630130, 900533720, 491301080, 468615502, 699848824, 315357927, 101121233, 305987627, 510837284, 822081544, 55587121, 312248218, 199869234, 569032447, 145540129, 141627081, 899359238, 993127057, 824352681, 827725644, 173863590, 52650321, 835830870, 842010087, 176454290, 926867024, 795988489, 702907125, 375661045, 495526064, 680808947, 732525916, 145728826, 468355302, 893667652, 173157200, 341765360, 32519543, 566174089, 990633671, 404127119, 360426241, 238804546, 849427427, 142896517, 74037708, 9675187, 992484492, 268431121, 600963168, 584623937, 987233823, 358702894, 309168284, 544030778, 42273377, 960187786, 616936268, 588473920, 491132927, 411614011, 229724202, 906099852, 849286461, 614887429, 950925926, 100526209, 914346740, 980311646, 972374655, 940468543, 706958307, 936214034, 704242470, 697786708, 46622075, 226512049, 600641655, 880656833, 742963063, 380885590, 208594167, 589048250, 68296771, 378720471, 975784057, 939905904, 825696181, 26426513, 103841013, 494537372, 158847948, 477433306, 656033565, 558958993, 668808284, 884815853, 447274823, 422303641, 541988633, 90005099, 83968671, 534793419, 368604905, 305508644, 882845043, 835356541, 301997968, 415851321, 750696316, 99857181, 734007305, 817469541, 204733377, 812591828, 757836752, 45430547, 557352362, 692771083, 837646297, 484521686, 443487875, 131787342, 313053841, 467646456, 408151502, 740408651, 264022771, 72414731, 655240327, 426948894, 846607109, 533942373, 849982291, 749060473, 744093184, 534342533, 478855322, 586099267, 731415552, 806037939, 415578943, 381938307, 655916881, 785376915, 679739220, 910998362, 946645163, 836136895, 9484369, 565385955, 743974638, 505289179, 859358587, 291808890, 109272533, 980417796, 41078750, 216200524, 72422330, 980498512, 781498497, 902059013, 985826027, 265489918, 416850120, 732031868, 333971139, 179735622, 682647934, 562379330, 639397300, 396610173, 833092793, 125984245, 804045997, 848876277, 715506958, 800009099, 547409146, 917841504, 819048650, 797187878, 398919062, 604509886, 927181797, 960777686, 520550388, 176231605, 290026412, 964630846, 845002049, 887868395, 509957078, 381786087, 575387112, 448934123, 43188630, 906564835, 200386803, 267127569, 969700073, 908391984, 476367527, 413139361, 567332996, 837631291, 5552896, 524781401, 468678434, 915587180, 533389439, 161857319, 14121646, 963469910, 407389205, 8951360, 232175860, 822217931, 85307468, 203300073, 600141034, 987298379, 920629428, 994442063, 55214354, 722984499, 432950608, 239755010, 471382383, 685226060, 583051365, 821731983, 624010569, 619191146, 834073440, 130238011, 904163822, 991221552, 493634885, 65138111, 296860935, 621447282, 84274834, 508668493, 636418208, 402990734, 604685377, 768513363, 948465385, 303495022, 992422226, 593499896, 555912102, 36333046, 785339830, 597442057, 425268873, 828473072, 39941793, 2344780, 785042521, 273063814, 697972729, 636683355, 812369759, 626090525, 448296673, 496989300, 152373813, 703499231, 445875359, 115208840, 812250680, 837978296, 484219302, 897991702, 110424645, 63572863, 602699462, 536653002, 519556941, 615997467, 946941880, 658078551, 938408477, 108093108, 274873135, 6287736, 539806072, 521353476, 901745379, 206209480, 440561386, 898335727, 127789426, 383406556, 798867795, 989661508, 147177192, 103903962, 894431174, 361353430, 821500556, 774145016, 962707459, 944000982, 663606986, 414503712, 629234025, 736909539, 328095109, 351624407, 940614551, 847150679, 441959904, 276922825, 491438971, 198869868, 229085240, 770713494, 525876940, 858767540, 369621488, 169725651, 784260390, 693171810, 773429823, 737650578, 67544204, 285696771, 197461831, 890332989, 149872679, 695209346, 773435535, 124563630, 536328566, 591171806, 284636058, 943589368, 356656641, 264775610, 784441504, 733865590, 720971659, 241031636, 379768921, 865865310, 913471535, 497813128, 1832844, 221733645, 504568732, 567053638, 645488468, 863845781, 215722102, 489836519, 900589911, 70752887, 647236570, 181667539, 872043123, 193197320, 887327905, 985925246, 652294531, 969480352, 725849328, 653576847, 290520548, 264334928, 216876437, 769643399, 636839415, 686949384, 614914649, 847150190, 64448042, 458386125, 66788938, 579168168, 190349558, 263541475, 872054692, 412973434, 630025986, 847505832, 304232147, 682619321, 422844387, 429951141, 15203646, 333302146, 874751545, 771259057, 386007734, 60586711, 36568187, 189457400, 53504333, 460141592, 506171135, 929485201, 245689980, 371389382, 700951980, 428535241, 224047557, 649542636, 31779937, 851128192, 487001718, 172097859, 639625385, 23492233, 962823757, 23257927, 721519912, 352884163, 668946587, 654254987, 894267732, 925543516, 14145997, 147546374, 115518097, 363783207, 525153517, 536950020, 817649638, 685935657, 658044923, 220638066, 789622492, 316741889, 362986512, 680430968, 472776553, 35362929, 543669350, 585045733, 958677587, 373350864, 566723693, 540922833, 373408507, 372359762, 824994434, 273535847, 263389068, 813311966, 900805844, 924807753, 903835378, 551538130, 465212308, 558721687, 547428785, 631899696, 160134211, 258285737, 519492325, 672688184, 972749218, 919554646, 980602596, 493345726, 583966413, 320576711, 895189048, 176850353, 219632302, 254049016, 331198157, 874455668, 536291320, 346785193, 100902768, 930138298, 436635831, 296911869, 24663999, 98187702, 98393253, 671175076, 861789126, 678156574, 122258400, 685236346, 445023525, 23903269, 704418031, 224637592, 631945466, 595233588, 739778189, 207944453, 835283970, 749160095, 479243638, 541090014, 730056720, 661313867, 177545230, 448831225, 439331184, 350586212, 108940750, 57348164, 326884956, 41265366, 987823222, 49030970, 532140116, 500062565, 483104834, 203235037, 325347127, 471504529, 936768662, 267880602, 257252566, 235076756, 763446543, 927827412, 719325553, 592011835, 159282803, 373829759, 453621371, 557493883, 373754813, 285375483, 109990618, 366455100, 399099943, 283417061, 968147781, 791594587, 794286585, 92152761, 102409393, 63858221, 488715065, 111091044, 752351435, 89487876, 767637104, 943607758, 10104791, 415720373, 568568864, 79868288, 558552606, 863782906, 442834100, 604644998, 948382099, 889976297, 133074727, 993184942, 272564340, 410795039, 656892778, 214166250, 886837246, 593361710, 744018929, 862182977, 757392448, 255289782, 600974993, 917623326, 476019768, 156773769, 290932700, 790247873, 473976762, 971537563, 170568739, 741355129, 749500986, 479943534, 31207019, 136403400, 52991999, 277475661, 348741864, 98242240, 264443407, 383365401, 791858850, 623342023, 826460207, 91503070, 596879978, 548666878, 678487302, 289953722, 698782820, 409724701, 746099025, 515771218, 608977764, 178338801, 736097546, 919208988, 447043748, 932734109, 887341012, 51017908, 471917697, 140850088, 199090133, 651317708, 793682039, 60827127, 138457400, 78827001, 555585845, 349174554, 57812443, 931701544, 55923696, 674872853, 20462192, 844865523, 779534137, 36239798, 159557045, 7258725, 509855525, 286944251, 235980126, 369896236, 346268643, 906165283, 29704853, 251022387, 479909836, 495679667, 603284709, 897336882, 144827215, 85916616, 76110534, 100437850, 636143156, 442269443, 630524626, 412290214, 291581190, 166709820, 848127293, 773130242, 332437246, 199715725, 96816015, 580862150, 563074930, 9457443, 443857674, 846369470, 927504281, 323930526, 194037772, 427064322, 531234675, 984068226, 905372304, 457748598, 827812176, 660089533, 545961525, 707368019, 777992606, 837690196, 313915950, 110720220, 67950294, 822327510, 216709700, 675106031, 725137002, 23716120, 574691026, 804742360, 610399834, 502080836, 357726985, 89308560, 427439918, 234363980, 144450651, 339390528, 565066359, 31118679, 523540425, 706970553, 34086378, 724944432, 470349074, 136359008, 862951177, 766980016, 261270006, 892158040, 964087379, 880568856, 706926204, 310883929, 482413404, 206007675, 962218912, 591961415, 994549256, 604595925, 450478841, 947599830, 310274267, 219284966, 593479182, 915228764, 451957183, 55350904, 225347020, 756408462, 999377370, 71071023, 1263546, 422039960, 566113484, 29089137, 843273435, 196478630, 29083464, 677220670, 861853078, 948995055, 141684164, 531868979, 3100668, 173702656, 906613063, 793531479, 101911997, 698714611, 151086042, 134347528, 180329108, 132145096, 564199494, 345810735, 479910819, 680800913, 392134473, 921259226, 50027039, 640857951, 887706979, 486014305, 369549407, 596400104, 271403288, 164724163, 492605474, 992763318, 952522459, 156221118, 41933402, 317738296, 209026847, 737803304, 172394319, 37259414, 419213201, 365059566, 441539390, 73521714, 402639623, 570472820, 495427905, 18837111, 320410552, 477253148, 379168893, 723780953, 276142969, 680276496, 160386000, 985065537, 562267432, 186251179, 117210230, 648992914, 892434551, 614186968, 590432655, 699791269, 65938883, 461329357, 685647268, 860418598, 413766844, 703980954, 780926907, 559645628, 639234302, 339577257, 622211846, 33838466, 472014262, 718449484, 741270693, 27857332, 572516871, 260550163, 888676862, 23969929, 507670261, 912227186, 928147009, 491390923, 370792778, 191695884, 699362996, 262288656, 13566593, 99327315, 320878076, 574993667, 955685674, 334866668, 127970744, 186344542, 92509418, 583601964, 652184333, 772812947, 271862815, 28910488, 764907399, 213712379, 582422602, 967543953, 685141215, 962845713, 892539370, 324569309, 896763054, 253993184, 120861816, 55817326, 607081625, 710076507, 445863036, 120354238, 905897608, 67281648, 751599905, 939560527, 59812124, 847118870, 660341658, 818530111, 72454966, 606851094, 216270262, 917199528, 765473957, 711616234, 819969750, 697685642, 55835802, 782949815, 713771993, 323228503, 260271443, 133444143, 842063439, 205426855, 312679813, 559062632, 472086350, 721236183, 557537815, 534859848, 442388263, 437301059, 348100399, 899064689, 82002745, 84861668, 796091817, 189486418, 905635743, 671058649, 52206898, 205630159, 16871021, 468003676, 809320665, 132980942, 360947984, 258329826, 444592387, 261554113, 288233368, 615685052, 730249539, 536061195, 419414970, 294017082, 801049602, 940055118, 31810730, 42915651, 662014059, 577370715, 797892649, 385322089, 406179453, 54995043, 335974633, 555940901, 435372883, 510993641, 54505546, 789743878, 310495206, 419963113, 640970825, 976940647, 902028384, 668464964, 42128608, 481802420, 928557761, 910344580, 729476911, 36346432, 77630771, 282231728, 581421614, 650697182, 638251496, 989507817, 137700947, 684728856, 780136695, 722474133, 745496189, 436723974, 349812436, 537414501, 103519, 118654843, 105043109, 523321642, 220276987, 169788724, 831055998, 539604419, 741347470, 205195770, 249394564, 786893658, 659978544, 438968254, 555051714, 58173192, 43514882, 906120358, 60326232, 343119579, 223053197, 79445074, 890868377, 821138758, 911298127, 1248073, 384135255, 477947032, 763452880, 199899035, 125340499, 589146989, 817990117, 559373824, 616292940, 244938134, 433731120, 227788255, 867555596, 306383260, 235108048, 707044495, 943979969, 976598079, 333484298, 357798001, 978715740, 43643620, 35766834, 691635194, 207117355, 192089411, 393599867, 498373152, 838595322, 118676, 464790685, 393215879, 656066256, 366317069, 404724086, 955695650, 68723774, 585019236, 872203721, 218420400, 697581804, 461169843, 596958348, 469277615, 321855972, 159766849, 287423685, 934250316, 592306610, 800331938, 394268676, 391691954, 825450858, 487336172, 274051620, 411770157, 278268144, 711825325, 403772244, 179949168, 491771556, 132842518, 99614480, 880011139, 886998249, 713488219, 366630641, 802645400, 301228263, 275577008, 389837171, 749301506, 8603748, 651165818, 88344277, 914232778, 680027843, 464715986, 857844323, 162801009, 689426545, 878179847, 467290352, 232842990, 547521730, 675105808, 845493404, 247034796, 734361854, 363690828, 932699131, 899517980, 858388719, 966667296, 127630477, 456694467, 285347580, 601159864, 312832706, 692243879, 293043932, 857981346, 94110909, 259720166, 99647223, 281672034, 614400730, 226004009, 661638973, 267673146, 139226805, 869942726, 951579606, 347508109, 204239682, 374839212, 887573844, 372378087, 271168543, 115227255, 158011074, 755225816, 129346458, 677264163, 235060765, 89561796, 340561907, 762071234, 294422230, 311221148, 585536711, 695267639, 748296774, 430288047, 178312223, 934882401, 802367080, 405326397, 565028766, 315455128, 545150884, 463940152, 264285287, 649823804, 712759450, 442878746, 513779397, 444262336, 791031723, 882176660, 217578171, 531211541, 115199732, 193219596, 11354145, 771867121, 159582282, 214049635, 184848597, 8203656, 777171902, 78922719, 496658096, 786873975, 399503034, 318607653, 618873386, 315878876, 90733877, 851562727, 477176614, 542639336, 31671625, 321917174, 901665934, 309097893, 82388012, 676611740, 153950878, 44966304, 726278614, 827417748, 988020891, 619994483, 207951324, 503254767, 305282666, 161285669, 254181785, 942529183, 825818114, 836460165, 139463572, 613275776, 315114188, 250840638, 304561183, 977833964, 947044331, 219987909, 895988733, 860795950, 178146569, 632684307, 771354712, 807849044, 907131112, 316841717, 568450729, 519960328, 527503551, 255346328, 207716673, 666509297, 263669932, 356651096, 269014929, 665751318, 118227654, 319803980, 979503506, 897045580, 376066296, 9767907, 734652945, 99219995, 865313499, 711807334, 635223527, 98625842, 73305603, 827404496, 645771799, 209757543, 30141715, 26417733, 206832339, 159056856, 64684792, 398294114, 60266334, 696019054, 802704924, 712938694, 92202526, 15353334, 222810230, 486471156, 624350637, 219582681, 816064964, 546003016, 948000615, 806117158, 208549259, 692813292, 704626609, 892384824, 151860837, 338149178, 331270186, 60015478, 929734900, 91465625, 827681583, 132268476, 114545663, 30950326, 969848578, 255641097, 575352180, 39197450, 626670119, 176221889, 222890270, 138602888, 585655902, 312918697, 624891826, 445815076, 103299611, 540788437, 765671127, 93322195, 241496160, 349922969, 385102917, 720797065, 819986299, 403546583, 575394145, 334348490, 820199928, 524080197, 69893178, 638726404, 716855019, 299538068, 149716047, 448640416, 58663258, 56932227, 30754313, 286929744, 550926658, 960110078, 697310616, 230378450, 749648985, 163711744, 914452814, 17344594, 466393663, 516929707, 895330298, 299740643, 126247496, 889393291, 936701995, 200845798, 198882632, 123618184, 567541998, 60902807, 413791904, 424992724, 364936678, 890275949, 522442266, 250978006, 570378148, 340705937, 678657231, 999190644, 877535998, 118091462, 912317325, 193045489, 694003791, 15914381, 550819366, 360302061, 929296768, 40216703, 441923218, 466440708, 687155220, 241318179, 500888873, 245928481, 280401495, 156657614, 873575103, 304925776, 913494804, 18458703, 755578372, 399471763, 558703132, 925200101, 770909127, 53223810, 137102952, 85298590, 108196884, 632579151, 160631187, 942586463, 906218191, 423208766, 900395467, 903861919, 719740358, 651272003, 570401320, 923300037, 925794727, 359229888, 562352163, 377126687, 39628714, 443776334, 674654992, 176968228, 799837836, 392616569, 192474159, 802365552, 834767208, 841406405, 461898500, 885044697, 578431399, 743074470, 953763303, 99028161, 78757473, 54718361, 152609855, 609259102, 693454177, 899618509, 510130103, 23299789, 325847926, 463457695, 729130461, 38545273, 616859640, 652474780, 857632457, 510883164, 387891955, 546305280, 232381950, 409801057, 325071891, 524398151, 792871712, 197709236, 736263554, 763117993, 93990380, 731404412, 507950300, 366650834, 803049355, 109390629, 243088923, 317093495, 287030037, 448389950, 505542177, 603950581, 386296731, 416280482, 993735268, 610069199, 356615434, 115724754, 52109371, 507005873, 188579445, 217650192, 490704854, 897387397, 372108756, 506499610, 365620731, 295592653, 84666614, 548357427, 205890833, 711713558, 228429887, 629874571, 83548550, 713642759, 512576649, 165937681, 135517133, 966396047, 522639098, 256520195, 735462865, 271323644, 314901886, 295745288, 333419911, 83976015, 588418434, 432960368, 669422661, 637558289, 667726066, 454271593, 635779199, 859596095, 80120723, 684724474, 122333017, 918966625, 691109644, 578523324, 733333611, 171469020, 496821069, 444171956, 622368993, 446528609, 347881085, 310338813, 471532598, 732402317, 156181259, 280949291, 532105778, 963121396, 560741083, 962961119, 715962566, 315108382, 725739094, 274458773, 489260773, 440160517, 392719209, 996992173, 132545366, 554291167, 167311284, 824162038, 232395603, 902017367, 417199825, 640586676, 218672161, 87975207, 682412863, 863835011, 511172539, 414196424, 873974003, 683715623, 747868060, 6306870, 294918164, 877249928, 339616530, 574849406, 512974169, 87562237, 837591251, 499636757, 9778999, 86552252, 325601616, 203402648, 254745453, 54517750, 543064691, 596149815, 872625170, 256519554, 63527251, 199902959, 326339703, 340003897, 190003599, 259281906, 50716353, 439095872, 455499599, 562015139, 581524977, 146727430, 316236060, 118088040, 731918977, 524411311, 606522562, 451928564, 382197268, 709612891, 204751782, 466357768, 686302020, 67327379, 76189949, 877372266, 750660999, 49016858, 917748346, 123540689, 297324834, 379187349, 637883518, 767534782, 790777720, 715676933, 35466272, 850835945, 807185198, 122341932, 420259789, 281066245, 841647184, 856833878, 758508534, 253281647, 137687670, 212829822, 745125575, 404794238, 171510686, 610367940, 679192402, 731598724, 17625659, 601473723, 745046924, 889269089, 36272815, 155775708, 190494531, 874631625, 554380906, 599173094, 632826222, 107272270, 838436736, 251942763, 507670160, 166011182, 162630270, 926084813, 823777686, 844254400, 812426241, 616857111, 297329010, 833410236, 899917690, 41168487, 417738853, 109005087, 458868179, 124997998, 517049224, 1603318, 812629999, 164539015, 426741362, 444913534, 344847814, 356970935, 738640206, 434967470, 368050326, 807480280, 726815616, 890243248, 983345425, 5342650, 142107633, 787313171, 311058705, 893035774, 144691614, 353397907, 236310455, 683996782, 247379227, 451310097, 967468242, 188949556, 927632058, 507312242, 332086376, 583604283, 863327051, 845750674, 346429884, 570460343, 801609452, 115477511, 203884153, 712186542, 395476883, 105648684, 187442181, 531090486, 273025692, 287403432, 388460290, 391750242, 455126564, 990749869, 987157317, 559817967, 353090641, 867421370, 880873759, 826922703, 814115625, 933707182, 690900375, 423462805, 791760490, 261095759, 675955453, 115713465, 938878281, 908379586, 420721737, 32941599, 418133192, 767637883, 85318429, 306301517, 92953333, 948457422, 27264505, 624148017, 762455932, 167199309, 43874043, 62184539, 623594759, 955453182, 883777640, 863085760, 52577818, 901644761, 914015, 479262825, 496651689, 819179792, 657019200, 611384134, 966822811, 455310832, 233841682, 594524319, 11788352, 80900632, 811985424, 201744221, 631767743, 413873334, 759643024, 185716295, 916291744, 533655596, 456965760, 593722743, 758997474, 758836989, 322322631, 275503376, 814654705, 908135789, 586220865, 417657211, 234120967, 381432792, 798911910, 648726163, 34637247, 483537637, 170673371, 162226376, 444705254, 304402604, 510441319, 153588889, 136035138, 133807279, 572050830, 748698431, 410285847, 671058551, 466713605, 392076100, 559157437, 440198218, 725643108, 353791857, 958206567, 434076423, 539493394, 828783756, 616063212, 996322008, 139516878, 951064722, 661662564, 783561029, 760273597, 77532379, 570978876, 9354473, 445314375, 404926396, 991798506, 643784326, 868536431, 648706455, 176153489, 489410092, 777806478, 980395063, 198325070, 100231462, 619424504, 514919374, 211379221, 173211408, 410998886, 295478289, 818068410, 221096080, 265909670, 307655183, 483502035, 508774973, 615165578, 526466963, 854580534, 614232533, 332444741, 797080309, 294470430, 759034648, 596467979, 259677284, 546210629, 345914344, 777167848, 432017538, 159693965, 27024759, 57604903, 478353800, 397595680, 832041454, 928184383, 96051538, 690775979, 332112120, 927530840, 150422215, 815991364, 88887516, 996891171, 887172994, 383578679, 431071366, 491792293, 350024226, 307723910, 662821402, 744533768, 783487182, 990550486, 104005131, 922571244, 258970910, 646830586, 118773304, 421164210, 378469991, 57037603, 787690509, 857549392, 721322456, 934381274, 701505997, 126295428, 96251100, 896963592, 580622342, 270885408, 935107284, 561255371, 519042398, 948223264, 706307429, 628714241, 611026013, 621409473, 755759505, 927706470, 5181316, 136249401, 964184005, 993957793, 694418945, 915818844, 144189955, 697778144, 271043506, 282105214, 629825602, 598709346, 506601815, 280500942, 767549080, 865789192, 484998191, 798423574, 389100702, 325774117, 532760261, 860815862, 738123107, 513385786, 375345636, 355980718, 58469180, 786909487, 375369059, 149995914, 312069610, 507838109, 332029451, 310130428, 754586916, 908295043, 819489434, 955810530, 302299579, 31923024, 6608926, 217400031, 748067942, 717301782, 591204633, 146291617, 845243737, 429199708, 285909306, 726775183, 570711038, 826224888, 459454529, 387874168, 663572688, 387456489, 97318998, 451109696, 323435493, 841750071, 958071677, 35598528, 121382538, 509959658, 307108527, 374102046, 677462153, 771511012, 6053340, 767039862, 111544862, 131033917, 726979979, 813250639, 741790946, 594381980, 387356461, 977977479, 856147099, 512928339, 958882216, 328815146, 557939108, 197655483, 31722980, 446184096, 116799945, 738382815, 205216688, 178142255, 987814825, 414663151, 68787604, 147914950, 360938245, 510670495, 686242357, 619058523, 263992340, 253413009, 939153318, 773878340, 956241373, 840409380, 566901904, 318416237, 215290101, 590353453, 434228848, 662425968, 37901860, 448173535, 18262905, 413501087, 193735190, 614082536, 347684221, 866062298, 682733472, 595409555, 927482036, 573837326, 865716765, 246253996, 661468370, 901727841, 371217004, 929463590, 243756706, 922257758, 877958035, 891099290, 667895392, 860019975, 845816241, 591919795, 522194205, 996508595, 772716901, 805574505, 447419277, 737297767, 752774052, 548044839, 712162716, 316713317, 454976601, 509146781, 809111924, 415795854, 110702143, 791777818, 69621400, 781417511, 425074055, 202415804, 659492484, 913393286, 891861500, 749436782, 642101279, 950259627, 435431250, 85964865, 802504474, 752683864, 671496422, 168078137, 598034527, 749247019, 564036920, 221821170, 890602255, 49952638, 917077497, 250795968, 173137291, 131184365, 237148093, 751179846, 716376514, 62979236, 392791242, 690103337, 891989658, 469008506, 753584062, 176067824, 874857529, 552236352, 368476285, 134934253, 364759941, 786506843, 378710579, 850573419, 628649478, 316546751, 98648997, 142328312, 457334652, 296480109, 181012107, 371467456, 670279351, 976959852, 676039830, 635533394, 623653263, 111118793, 201442311, 615249852, 174102257, 981435480, 995182567, 258848563, 151955464, 652806965, 111937913, 891607176, 184491785, 97375528, 834791146, 604396494, 264163032, 385200003, 355380019, 875250597, 972998709, 747931156, 70889695, 851292125, 70862250, 647333712, 982958627, 336999501, 145122620, 937982564, 973651719, 123003246, 559121661, 358096249, 223488143, 966209847, 345309629, 673886543, 505485284, 695538214, 240751482, 758735754, 317534589, 423457458, 322444543, 407908206, 922169748, 531171111, 593396302, 26199682, 507552653, 88817552, 590216977, 292214301, 879759760, 313230056, 46294489, 44999168, 88780076, 534594180, 407683599, 218619163, 268441819, 755547685, 169251941, 856842223, 120362737, 214067135, 713318249, 480859577, 659588275, 210956562, 18473575, 316087567, 126834035, 723896791, 661109325, 388587920, 390784061, 542510483, 414333859, 770134890, 606166898, 427398033, 895731089, 685073962, 195396996, 512282094, 514961827, 755570016, 596239970, 97528836, 642059464, 400973383, 273200927, 893623609, 561094726, 391379374, 361477120, 209527123, 760630254, 658838275, 80384403, 13087586, 820926057, 261463133, 81384358, 242348040, 357731276, 146776320, 372617820, 84002853, 526489535, 122641867, 859677439, 315294375, 268229390, 114986428, 92363949, 989450720, 915768143, 625581404, 517754156, 784283252, 383420491, 410491800, 342838504, 201336691, 228034920, 201819401, 200100636, 81755494, 788000733, 271023767, 466196822, 155689685, 293481936, 895606914, 653656676, 794410491, 583678202, 115401511, 323331487, 929031912, 939777650, 831113473, 214317793, 387983673, 20247813, 255536277, 781619559, 777937471, 453139691, 495463229, 513234428, 301774395, 587460078, 399802963, 998115085, 552787039, 716862971, 268650823, 578685566, 605100501, 172994194, 543086037, 73333042, 834617133, 640178158, 920901918, 98436274, 558662399, 693332801, 678501059, 720149701, 525947535, 104867020, 57000409, 650097330, 171815633, 740226593, 410203545, 768173245, 687697714, 670010181, 799415961, 132379009, 58969612, 165750326, 431623654, 327424617, 824771554, 475043315, 447603928, 970393361, 455507831, 361990774, 752603950, 316148225, 527685198, 883368386, 525794876, 401413478, 728491752, 274446684, 42679422, 33536139, 946488485, 874783266, 240855979, 217132302, 14844374, 251026659, 454054437, 939003587, 636994389, 481963762, 854529497, 967895666, 896318562, 737289651, 954190677, 901400256, 320791961, 701902502, 571075832, 120884392, 20435058, 380026175, 373162411, 969696427, 658887593, 64811521, 521353295, 947388498, 118474505, 805626876, 782830096, 431498425, 791999001, 950635717, 507781233, 891156551, 740958392, 453577202, 688355899, 830508145, 646695867, 324833549, 506386516, 541607659, 174623710, 994120468, 384749182, 155188852, 9009529, 871334816, 324738813, 135418188, 546978555, 434541015, 660442180, 171889494, 561260947, 374594137, 646496676, 447938910, 892554652, 211117346, 814868188, 735073639, 615812125, 613778972, 434071869, 325086860, 963884563, 535013932, 718972374, 663845896, 771314399, 828912475, 731420392, 807062672, 624810500, 595380044, 164809476, 210707783, 780594243, 672184304, 104043663, 232783626, 413471528, 393931420, 14709032, 350317680, 704324680, 68058380, 898934439, 717437640, 68736352, 335092015, 499781233, 132126896, 803669437, 494455012, 210015554, 846443212, 969412495, 886072167, 196274643, 28437505, 807832940, 98967517, 738546615, 181312450, 615543462, 409520415, 93819045, 403226389, 997633256, 902473128, 282191441, 640917647, 196511399, 307985367, 637707879, 915858289, 415261217, 599044768, 511207268, 908515971, 569726877, 863967970, 265875581, 220612807, 186168584, 908889583, 67525798, 885901877, 968418769, 509591622, 616435977, 976782604, 580413867, 32545234, 670552207, 974442297, 481736469, 863075484, 787432277, 34032911, 254717635, 14738397, 997520517, 723662904, 822793018, 178536222, 293788624, 340273795, 69072203, 378663469, 972754831, 552766366, 366029434, 178360055, 112319057, 401165015, 333025333, 260112702, 735555331, 501640241, 988339196, 557442656, 252977650, 915425373, 929668502, 15472660, 513538527, 648551324, 184771682, 670476501, 531106311, 698812620, 673825000, 660782105, 258968003, 621658420, 74440288, 519388584, 1162777, 484519919, 556077901, 282405119, 40048704, 447376844, 427579636, 253797582, 983762479, 175916909, 907825967, 640622480, 825786220, 339507219, 212196925, 744081075, 980751363, 593868084, 176708370, 472653520, 791428723, 815993332, 819112039, 5617756, 518987816, 619783144, 543488934, 219444583, 927768808, 641776731, 964230783, 55505411, 43175521, 855152172, 139616312, 284766560, 248611098, 636819426, 656744881, 165460632, 423673347, 439268655, 548116865, 748028915, 386070348, 699274798, 343724480, 71995778, 293646342, 502982866, 674745046, 420327700, 827485229, 350832106, 381807567, 961290421, 257931814, 397002796, 105615563, 131848225, 741562551, 297658326, 493429895, 808488146, 801610166, 848766311, 444161868, 774659074, 576364984, 407257877, 458258931, 559470919, 739008280, 742064534, 430739043, 117870655, 32316187, 278266697, 660921901, 101430187, 887263062, 328724054, 79025843, 250589381, 175224349, 658952426, 869409779, 357003362, 31743723, 840496188, 311048680, 652649730, 159160159, 727974466, 136568103, 95828791, 416904017, 268768131, 855820314, 932817864, 414153198, 64596071, 253804041, 755900210, 378890819, 764007811, 11049768, 815471594, 58901332, 372640090, 722761496, 236712333, 323608705, 968870956, 635812158, 73372708, 19122765, 60797283, 170430591, 2970338, 313199408, 818094133, 665749675, 331021176, 746520975, 849255162, 550778810, 671137246, 217512400, 6914191, 87303409, 333521309, 943230769, 148187764, 109863949, 447816833, 945095836, 114470269, 839286283, 64115330, 259735140, 663272597, 596446292, 394606865, 523173781, 762047499, 146073965, 985948215, 493218440, 637359655, 62510578, 629045647, 421984369, 917058946, 382541688, 61892639, 475009693, 174194675, 274959414, 456230027, 222194458, 429929479, 757070186, 134091426, 258665101, 283107941, 528539999, 938828493, 328886540, 916899815, 237668908, 381734939, 271147333, 937761935, 92547540, 192597481, 843219129, 834179175, 101898718, 605742224, 749673190, 689491344, 426549111, 51770519, 207366432, 660770862, 506306906, 9455206, 968947357, 119119640, 765981521, 964500457, 605355292, 748532950, 373610649, 839546515, 725411122, 197999142, 552420807, 790028288, 319491504, 601221874, 950112729, 322696745, 32192965, 580352822, 820728618, 209298578, 421266723, 115611901, 622880586, 701660150, 140867838, 517810825, 927238430, 377409354, 163130332, 522446590, 596400731, 481012525, 728772980, 358324140, 718936966, 876085381, 252233813, 640090272, 503039909, 991371540, 10340996, 608173561, 534171135, 729489893, 49633686, 742205047, 964213413, 785325896, 815738635, 642849277, 924803315, 502007657, 117918828, 490941601, 297288478, 495967657, 547717467, 341348302, 787960093, 845364365, 697173059, 287647548, 934876655, 540502815, 689985512, 979600266, 280440510, 560679856, 558313873, 174283355, 691624033, 636318117, 410585018, 264433144, 329091038, 734520358, 799473132, 239223430, 435142698, 315353099, 358456967, 406428785, 434084862, 725417379, 903762107, 63732489, 502245935, 154820727, 217788419, 340045861, 682681034, 232301228, 983142824, 251979452, 924023977, 699383765, 867850202, 687262428, 794773763, 864102989, 99465952, 726358261, 230744414, 171346622, 527100164, 240292164, 809045209, 369771649, 989869289, 869963725, 94743715, 120550478, 935476708, 357755241, 604855969, 637004195, 267605175, 20473114, 132117840, 216313863, 748358443, 484147307, 777111485, 632969878, 235666244, 864692904, 961515465, 5393452, 314642625, 296216664, 122180452, 662774068, 372727976, 39890813, 481522066, 195467404, 107808505, 84961808, 543198224, 855916164, 382790423, 667284694, 898602126, 817663751, 973656560, 388632311, 527633572, 173981390, 646650219, 88737774, 172245353, 892838067, 161639305, 857972419, 303345217, 945081922, 111169974, 634890610, 182707378, 335551369, 623456806, 678879650, 500532371, 695371422, 421891644, 412284235, 945078022, 959382428, 62790941, 3190059, 505229361, 438357423, 928345207, 312987128, 222272420, 70736122, 121586650, 640754876, 270895484, 445661786, 467172743, 408758236, 721973755, 915211001, 539376450, 328215902, 33172509, 504867940, 147060290, 986793125, 283838442, 286266330, 915941031, 432356385, 261132537, 969900666, 4765187, 572187514, 492508210, 398879975, 686661415, 239478323, 976598301, 283283646, 368515535, 464813966, 715817178, 558061134, 8549426, 247759026, 936031336, 634459858, 877440602, 961469423, 116032279, 137543055, 726150768, 819750735, 557676299, 944852740, 410451417, 704384331, 225975151, 81327624, 535050719, 183167489, 275044815, 648334378, 98911021, 155274948, 319042809, 699383558, 426210718, 443392894, 409430721, 991946640, 698478306, 365641757, 607864724, 647496074, 834357871, 813339960, 141484432, 369170932, 867182731, 989596836, 275493115, 510370577, 231144328, 902886815, 775065449, 712232396, 313069712, 718209014, 295420434, 135429842, 136156746, 471224617, 225208849, 129868537, 883046726, 346366790, 486605843, 746218405, 167678900, 108611820, 984439089, 865844344, 295952601, 813918557, 435386207, 558993408, 425341249, 593611519, 992759157, 745287445, 557661212, 944591531, 954634745, 527402586, 361817993, 73848251, 118965313, 332393061, 30941715, 323307896, 399030677, 330911548, 78988476, 944526351, 772257641, 532346216, 929264254, 36607830, 319330577, 457533637, 135759198, 679131655, 497066291, 865921423, 452706811, 334556672, 815871305, 476778183, 89931070, 598514522, 894408213, 350387152, 868178492, 947291891, 230934064, 790880827, 215434246, 389303983, 330066415, 52205045, 930175809, 676484816, 399842203, 450734870, 87881531, 360145888, 89227038, 381275891, 246600792, 616843546, 9592862, 800451925, 469075347, 915836911, 876235546, 802383024, 912099843, 452290359, 671818741, 75219977, 950633779, 319077330, 449576284, 148728797, 746631627, 229948567, 270806601, 548028384, 526898036, 672201815, 72747098, 959356570, 978789472, 970102367, 129087003, 94913969, 764583051, 306735608, 333645201, 698579399, 720267019, 807414747, 358698345, 894173633, 147273995, 704896978, 887854554, 820017091, 40987931, 93760365, 530267963, 817528863, 711618760, 909449875, 953578182, 668277500, 544836311, 836663111, 129756810, 459737339, 338352088, 284160165, 364912953, 537722885, 311199352, 209959964, 21031605, 684275405, 729479061, 68953210, 942917253, 858352138, 744243592, 525346214, 725469369, 535847663, 429715728, 330356417, 701741131, 715477293, 288386930, 258842569, 761908941, 577292923, 507243128, 406237239, 337438637, 99902258, 628079153, 285823010, 32888067, 186836736, 65320378, 480443418, 461856931, 291069331, 853264485, 453741567, 984984631, 232253399, 818522081, 915978998, 388838212, 542206945, 808368018, 780503654, 212610184, 524341337, 129428385, 951618576, 606982387, 29158390, 128972937, 792252565, 131183458, 474648766, 283465267, 417148168, 861162634, 298992819, 153562779, 262056659, 356696840, 908917208, 873621108, 797472580, 755227062, 517253568, 805206960, 569966568, 269205474, 154183069, 19156502, 699682237, 264800109, 63065027, 636141637, 433098127, 97050962, 433680458, 775194090, 772487052, 547223720, 59423238, 866131592, 434620582, 658482951, 240586584, 390508080, 347861431, 973290184, 825034012, 490087005, 660287252, 618816828, 645701436, 993424954, 445521615, 665800654, 213619044, 784447273, 821924065, 883293092, 174672401, 257767546, 13760237, 565431572, 649642684, 338428979, 328358645, 583984565, 696866454, 461797968, 285039068, 249620972, 384269872, 797837111, 576415942, 888042392, 744058896, 823193289, 1565653, 198509794, 15522433, 85314852, 796564938, 323510509, 194316273, 159144417, 423967472, 594264900, 150132931, 519504781, 496317823, 360133943, 577405080, 625454289, 253348060, 270514455, 215182110, 83103612, 377968361, 519536591, 262428250, 579130664, 590609074, 142532416, 541391127, 557226777, 983491040, 628768220, 262740635, 366503963, 369798108, 887325458, 61943928, 128915323, 380887502, 62247174, 827483069, 663139910, 256373700, 162539675, 402224609, 934201280, 602797021, 600242737, 663547827, 318821684, 926832814, 991814421, 789112886, 521104362, 810969680, 62375348, 48320643, 387212589, 398239062, 992733111, 819396412, 757626612, 717186431, 489506055, 254854441, 12668386, 772706091, 492905844, 254047729, 887560879, 574471371, 821347796, 517454071, 560447123, 274976361, 570101605, 868147198, 860752156, 634402849, 22018635, 473997868, 810213931, 167608355, 822058363, 802333004, 720548017, 655360712, 531877269, 999826608, 360997994, 919834032, 56124845, 747416087, 54561819, 656088466, 478278480, 39930262, 557637708, 537823620, 796419168, 218834818, 821215891, 789555574, 394828592, 735525608, 185179062, 307426829, 272526252, 433843670, 161749762, 85571127, 83666406, 848603454, 185101106, 811978419, 116491223, 713365568, 608719014, 894506746, 30193715, 311564494, 517122973, 312165756, 278642453, 263636415, 44509806, 645094860, 485852254, 771358181, 830671676, 518130532, 525012309, 230067670, 721519124, 281624940, 611419936, 468035242, 563181000, 551740749, 207870848, 332010825, 117145933, 541890543, 510440386, 794845226, 207206039, 226921337, 7655675, 360494065, 469112510, 631916835, 613452794, 636924433, 773745602, 518102981, 364363413, 634968584, 20262316, 777110218, 679149180, 794496882, 480176225, 384496049, 352274192, 204919470, 792756468, 259290303, 327491409, 31941635, 149836680, 752401274, 663682179, 947876279, 603374731, 811957538, 964878385, 78976308, 525995761, 598832837, 857920556, 172090057, 222830329, 860628780, 254777492, 678439970, 656533144, 838920671, 527756610, 445694270, 907410193, 59809340, 388325840, 851841225, 325534273, 424114562, 682328742, 812349085, 584568159, 5804985, 581597001, 925785368, 773481691, 87938949, 53772261, 769023539, 598974907, 999223324, 384075339, 613272809, 141178044, 418663549, 916728235, 687365039, 449323374, 505870634, 163107838, 845434406, 274756654, 337121932, 260346667, 214282207, 183133969, 456948941, 288907936, 309243279, 949038955, 921568822, 844086470, 371542859, 317350850, 292013902, 614194262, 386117799, 264773319, 805303155, 424920940, 331004375, 632136095, 193312334, 588745376, 188536431, 475550400, 341507433, 972762333, 947920562, 494099667, 881938014, 912964456, 288421809, 73927537, 218209349, 11439357, 532431786, 575522689, 99834731, 988259858, 762242284, 208809653, 148056853, 745478330, 605552911, 795576154, 926352421, 886566776, 738325314, 471464863, 678512796, 196888295, 450852777, 848966198, 859518248, 610234241, 425638655, 839477657, 167750665, 308230814, 243679574, 399967347, 279200788, 249336263, 911493902, 6939748, 818740783, 377907541, 758391978, 655319171, 460449798, 619459495, 179173676, 549711314, 398070773, 323640946, 702617029, 917378262, 823689168, 193695661, 619724172, 943049296, 809577667, 482096076, 718875777, 946026971, 449880693, 22938195, 530013160, 390866073, 443000233, 179985256, 983823020, 138199877, 354285542, 1957313, 306833784, 137754849, 470145491, 825711906, 390290758, 439287210, 315072306, 515065559, 866779560, 543741428, 457494466, 475091840, 72732207, 354336859, 833327900, 276087654, 309137715, 720689022, 771086172, 375774849, 708939448, 609669500, 623333637, 24244866, 997855955, 734267370, 664130298, 263555818, 31192305, 918921841, 180321590, 259338031, 634356615, 27868655, 211460282, 455481908, 79766045, 610541867, 809343669, 949532904, 727617760, 332718027, 552710978, 779471665, 750740380, 904417418, 328588081, 339690972, 385052031, 387968862, 110172576, 269872544, 824169681, 805627815, 977617845, 397229410, 960093154, 896907042, 609860015, 449560070, 428930779, 923625628, 219975035, 35908612, 825133567, 167589557, 686249742, 242874400, 67259339, 673082007, 645678312, 336159700, 301939366, 668920331, 657732683, 493002881, 280148286, 829766436, 503538209, 462538278, 630826988, 521012114, 389576164, 49630140, 413456031, 219544876, 5248173, 960144794, 369372014, 823420348, 876865965, 824216343, 748299332, 794220736, 458682138, 835235016, 27612350, 618818609, 752314703, 570132250, 648758978, 412053047, 981949742, 197599761, 76337019, 736559812, 812523547, 861749722, 80665292, 484096290, 537700853, 426983594, 208100288, 13612886, 73709251, 838421101, 671971651, 140770128, 566122520, 407852631, 513250802, 106668262, 65946537, 891517778, 604013088, 399292582, 896868164, 539126862, 435414456, 233397254, 338209086, 523813279, 244328136, 858850014, 863461123, 701119441, 202696608, 345890814, 245744795, 243631611, 40038475, 951211349, 44233994, 483030638, 995860223, 425298663, 496238392, 45415464, 46735628, 159747970, 581481915, 904884258, 140624417, 801467888, 552783241, 400486888, 115233016, 893568036, 154967509, 489134168, 763779247, 675413855, 592297042, 882170039, 862256999, 306581667, 820541934, 656683004, 500609922, 504456622, 64116087, 559386869, 28812179, 965245923, 344761283, 945113543, 250271671, 827457080, 80436891, 575092516, 159363244, 215882544, 224419658, 757143138, 388325193, 489289427, 916099400, 655179719, 817291554, 725956464, 368986881, 849468963, 737564264, 216787042, 315460925, 980574067, 166752975, 751090356, 525345871, 192488596, 153980881, 816030484, 36840733, 23200421, 100454960, 384791207, 236372850, 480167833, 417660429, 915330347, 788181076, 318360411, 601730007, 831969134, 571406701, 658076597, 760957875, 301753333, 793530971, 425418487, 599702522, 710952766, 520401106, 522345551, 983724709, 126949254, 675123197, 308190840, 185991798, 171618074, 32254484, 685937522, 303592999, 491774172, 368134273, 424032688, 783329674, 525110215, 609745226, 282045458, 776794664, 595648081, 617961915, 446779942, 204147271, 754065305, 957219963, 983475207, 733535576, 621263590, 55741310, 833234322, 386021379, 868000200, 159914780, 937171500, 63365862, 746263811, 937855047, 861553181, 436680449, 21483223, 423956335, 500527651, 877700116, 649097682, 53039300, 189303338, 233720433, 922320898, 697319928, 609193188, 246891714, 652228860, 321305136, 494385373, 530411020, 818515120, 865600802, 84972357, 894867085, 940645636, 35611656, 727074599, 101329427, 973603262, 576764078, 204408724, 528510000, 682870558, 322219830, 674523332, 321939477, 573175549, 887222198, 542794207, 567495228, 646575355, 566897972, 82825103, 184137963, 58100611, 280842334, 194635856, 564690253, 360006757, 209114717, 239063028, 479436511, 319796845, 864383889, 619417709, 491268224, 145292279, 408168771, 423923887, 198564926, 784344827, 817314859, 764904570, 701355220, 545161146, 866447725, 535302934, 242105536, 67212918, 820842981, 760549398, 106761923, 801037732, 405733250, 754124844, 350405132, 128962019, 681489817, 725267259, 612698224, 865271672, 287844311, 516002232, 733290386, 620566451, 423427880, 526099456, 204177028, 192103904, 764760530, 429259480, 774658402, 853850434, 630854932, 290836069, 19081950, 74528292, 899810627, 312381890, 356587903, 761181567, 906455697, 709299020, 27321270, 184886421, 697159243, 187622853, 550964156, 521109750, 268875422, 178237857, 713866563, 554162208, 314399129, 888047653, 78061128, 43052746, 690423976, 594772766, 784611942, 43429730, 643926430, 958927559, 900616177, 404926675, 618520061, 483354385, 11041646, 211677041, 456901234, 721088676, 237164945, 426353392, 236955869, 365623585, 480636468, 464719530, 821841187, 549432625, 563257430, 550559455, 602984394, 403446901, 850828786, 24916814, 333903117, 800723333, 368856509, 936430644, 113068591, 662377231, 43134267, 326740020, 868236548, 507289437, 880475214, 848232137, 277028546, 263560200, 726916859, 172626142, 296092499, 351146468, 256040313, 914412149, 151688008, 481249838, 280200808, 63614682, 958109069, 336966448, 494722365, 68111490, 750779224, 498538866, 344156167, 475169155, 800290866, 774650365, 157712822, 380822579, 354894646, 907213029, 140669722, 869027324, 736804419, 101057544, 384147336, 911911061, 132422614, 379832339, 576201011, 566809099, 202211272, 9707422, 392748976, 27777851, 263953, 74654045, 942591763, 357865378, 398636255, 543667346, 650894070, 372174649, 282877113, 942084131, 329492162, 581795055, 969328440, 892495968, 840247019, 790705859, 928614876, 289444353, 89518269, 229660576, 103763450, 579624033, 165374735, 738273531, 421509702, 432778758, 82502181, 321701044, 501587963, 433490856, 730784397, 254667571, 886931279, 575879458, 474965230, 147217240, 557482217, 138376867, 543862783, 566457583, 330846348, 980763470, 251474502, 211076550, 350195577, 389766729, 157790298, 902122357, 581043965, 509074869, 531550077, 588964322, 988622120, 517466662, 199536414, 51250003, 441190359, 704942874, 612265018, 669196114, 433114236, 632326661, 721302450, 128619351, 766945729, 567983447, 617579366, 822402234, 287414756, 186740403, 124822458, 721738551, 307625383, 177696643, 13188973, 695057282, 105394245, 941461264, 66823454, 253384631, 194274084, 942099397, 263926261, 619249261, 244616045, 754981566, 521065408, 114355247, 57242138, 921442969, 291474060, 353384037, 846179842, 52823400, 903362762, 100315629, 268565748, 329856930, 888257549, 451980912, 559771480, 489806054, 342137969, 200369396, 340422963, 480119312, 621595861, 554962020, 355258277, 331036117, 203673492, 441899833, 939798847, 756661013, 485638917, 462297306, 403178635, 932182070, 365944246, 132674274, 23321176, 599609395, 869413958, 981705157, 460406286, 643702399, 65460718, 369046776, 904973035, 704043849, 140747394, 695213275, 962781796, 704913921, 35790977, 251231230, 77649787, 288392921, 5139720, 492544191, 261373743, 198497683, 370800470, 374871819, 308244509, 94616160, 670666392, 816306516, 672825668, 552803905, 271983175, 792743900, 468606475, 310232609, 300752644, 582368460, 661905786, 142890995, 792916732, 368872912, 758047365, 959548357, 596496714, 749966821, 258794834, 957028768, 639807255, 884108998, 750937168, 496803905, 975550683, 537236751, 305011851, 733799532, 503359638, 626237983, 974874932, 427825814, 76929359, 28717140, 839580952, 628724118, 780155887, 272514675, 472450637, 699532884, 694017791, 161839149, 63588129, 333900178, 826852228, 26047541, 583596753, 845928863, 867225811, 489881190, 991984339, 216119272, 324283078, 467254052, 504931471, 371640325, 480678550, 201221578, 517003479, 650709776, 649621385, 275015250, 694837913, 106748615, 59644661, 681364607, 376836002, 124472301, 120849057, 617982463, 187188900, 319844210, 98921673, 861440991, 70943852, 328235221, 311813285, 810961109, 905945973, 964558224, 939733645, 755611360, 98994525, 143701635, 600294491, 647029804, 936690571, 161677516, 669175096, 380660181, 856703803, 163237169, 990898295, 622640918, 207004787, 502933456, 767253713, 496408420, 199448457, 368879737, 182597072, 922837691, 273315319, 490811384, 642965484, 178291696, 309992065, 547346078, 216925537, 951307452, 88048059, 208582883, 129357815, 699618918, 991445674, 869672747, 818519235, 599163699, 265775392, 785133807, 139252891, 661132771, 365555876, 181936479, 914760105, 610254338, 570966010, 583316656, 381482746, 510183454, 271003572, 394159732, 541370854, 726629826, 954975839, 687439945, 486433800, 509373626, 494034386, 655965448, 180373762, 220991341, 330906350, 506565218, 652310075, 379746146, 537255769, 323489623, 120693024, 837706773, 561986223, 262534469, 790667041, 407073373, 17158369, 407699102, 402276728, 808437688, 945545148, 193392617, 882617966, 356142230, 210367551, 238987215, 530351986, 433272534, 395600204, 693421005, 206189932, 898045689, 809426953, 672101167, 288123447, 780407562, 29283031, 551073853, 485161142, 2622891, 384531893, 271887584, 87880028, 945080961, 965276904, 789387188, 703685077, 742862432, 339214219, 66249297, 540594412, 526520407, 972514578, 638721874, 410747193, 283191127, 582162912, 832146515, 941681314, 345432583, 918696923, 288693998, 213169701, 418705976, 269173673, 954033850, 863629431, 966797360, 95530045, 749472450, 808758880, 756482371, 665452782, 316539499, 535208459, 84984368, 800892770, 519811052, 600090484, 613724050, 167499320, 74144418, 85776773, 523815064, 875905186, 452523010, 452833372, 668408281, 691541369, 830282625, 336900876, 260999848, 28324661, 495866420, 743202351, 256392368, 297000340, 775537536, 839305771, 102413998, 161245733, 538437834, 320905804, 679379177, 907380957, 486628953, 331350717, 116472135, 519001340, 390602276, 757563792, 439832583, 646914909, 401116420, 141225869, 620890914, 692370897, 56095397, 511037893, 500029187, 353689285, 931038674, 493365873, 990540334, 276810101, 928784132, 781126398, 101160418, 120505992, 767766913, 806286356, 545422773, 254533809, 95342045, 474829333, 426860277, 140886551, 753814438, 26756207, 700525138, 398454083, 888113155, 945007791, 611842064, 221962598, 612406072, 675871540, 590598981, 786858106, 171056459, 346799053, 670018211, 52998985, 323281069, 746872960, 53100981, 146455716, 139550017, 324755681, 495408019, 820630387, 223735928, 563835351, 689486174, 976811499, 799022677, 893919621, 610148794, 738360990, 635490416, 859169689, 100912440, 459329010, 938180266, 244020071, 997192708, 904242459, 120138332, 582233043, 744916955, 908608347, 34390047, 154767352, 340499268, 144074723, 666373101, 701290839, 721818192, 344569230, 424230766, 986955392, 228505116, 312261694, 342852096, 496529624, 240532577, 795672921, 573471962, 488946397, 960560549, 14650671, 268982351, 195417562, 94680201, 591847265, 598911079, 256147311, 255489363, 494346565, 172973283, 841299201, 968027445, 308964174, 788076149, 534343350, 244598674, 189643632, 64376460, 69474746, 396452592, 108891686, 150497309, 821857919, 554099897, 791182447, 204648122, 675122558, 46593854, 107294296, 737276275, 590403548, 246906388, 768362900, 188373050, 832608426, 469767983, 803245210, 518956862, 500367272, 856918166, 838198038, 530819735, 669742381, 463588215, 266048326, 63355721, 873338054, 760364631, 115126602, 628278600, 200787170, 61102199, 867635556, 186626910, 289074566, 346862027, 440184964, 382923968, 914735027, 848525310, 692934791, 350701363, 789172051, 936822829, 672879062, 317918758, 327261169, 858300220, 489241375, 221743009, 691664187, 695855742, 739294375, 123649116, 715500970, 964062101, 918096977, 845853086, 86262497, 679709634, 362480487, 519978829, 240976485, 379857509, 377734423, 146554768, 303794980, 919153888, 256420860, 806226238, 83748564, 188979979, 553795801, 644334500, 390053546, 32974601, 595788156, 222547343, 551474909, 512769671, 654620231, 947876961, 890360498, 936221430, 525874918, 454977852, 968088590, 187247948, 432804910, 582703476, 322824327, 930168791, 546402829, 49758069, 226614706, 708134120, 611073452, 91673148, 26967056, 209399020, 831499471, 939317073, 352397890, 594297309, 174145636, 55900426, 357576695, 955655968, 259326027, 549349817, 992783122, 40013951, 421746198, 875448669, 621081065, 440733326, 944815034, 636844487, 840758909, 451029624, 46196611, 158565035, 624801091, 302396793, 294748147, 984087477, 761719566, 524329096, 610886853, 440081245, 662110925, 518551644, 311484893, 909521160, 926696261, 445066041, 890452661, 761377591, 660179292, 343456840, 806404167, 766402425, 409116286, 463723023, 154814914, 154520651, 555104120, 571882158, 12844874, 933434623, 752631967, 243589443, 558844809, 374834167, 632666826, 529649424, 51583973, 305552369, 188005387, 307497236, 644290411, 489892277, 412931832, 565483625, 319171500, 561410762, 66310243, 309596576, 681149558, 329781674, 599974944, 667207820, 889640264, 720190930, 907230505, 519206671, 455133084, 366215881, 615769306, 505182667, 837621985, 636246551, 229623377, 931530349, 553470906, 211342862, 333228432, 511783783, 735493698, 753134040, 892792216, 38983383, 474766070, 165741623, 373869613, 270902703, 130698932, 461670206, 978620405, 455542408, 762534738, 636836310, 916103754, 839157321, 99864993, 777641405, 39903287, 470438529, 401881240, 63046922, 718654400, 116793420, 662820615, 579357266, 878276150, 255067001, 671932840, 620510330, 115486824, 18048549, 392217254, 55825518, 916886592, 513935230, 446000483, 330474886, 125586318, 599059505, 673428095, 698775591, 182114273, 51357561, 181263538, 232811963, 29783714, 943901441, 281617202, 645815265, 523272135, 680338139, 821621896, 339730933, 909645289, 515362652, 917986025, 724894494, 302374936, 131849285, 813395999, 559491623, 348648985, 304073496, 654879652, 460056527, 476937001, 391037418, 264906359, 343986954, 856536453, 260478947, 326430682, 433617819, 819535930, 791930260, 682676210, 753954449, 388561527, 594882513, 164837390, 189852608, 941304455, 741088313, 874823354, 74972918, 85610050, 612163567, 71903979, 310262680, 428617494, 384312524, 299283309, 856459496, 610402430, 800619214, 38653964, 162170911, 464119097, 884769122, 323470395, 20361036, 23195658, 934997440, 596776797, 509335616, 740021776, 733160533, 853498124, 388894515, 836641982, 482955043, 274759396, 699313803, 371351208, 871126404, 522865099, 586214748, 698425568, 521472346, 27623140, 618659744, 108344325, 230702945, 579069081, 583409578, 910541072, 814158392, 418644670, 66239702, 943252003, 85984982, 388374482, 454440289, 244752310, 262818386, 578244712, 565202807, 746279581, 969047374, 75521196, 503816072, 894786773, 276234582, 101539067, 484100656, 83631135, 634734329, 360947163, 433080993, 843381534, 405914106, 585841720, 156495364, 46417150, 957012078, 613699459, 260931795, 683523644, 436803563, 422061359, 819957202, 170814117, 223329228, 466799937, 424098825, 591720857, 379883109, 334171250, 555405165, 223783944, 792726429, 207352498, 186221326, 317570848, 724217237, 424362341, 240350305, 692035458, 596551763, 64341454, 850748399, 295020165, 514502686, 262135531, 197970263, 387272552, 743277546, 61373454, 744556399, 230784520, 30112546, 564238279, 578675838, 835208804, 800210318, 592363352, 763901608, 178305233, 14761536, 934831774, 483228887, 947141316, 161366886, 393922026, 923840249, 378757933, 350297852, 632119092, 27976305, 800744076, 942152630, 858397896, 743431942, 762672850, 258816085, 185597947, 572569067, 187691236, 224893733, 82634846, 205424740, 820478111, 275984661, 592028754, 473450522, 711906823, 51562962, 697986973, 444951547, 147505982, 163165303, 612741245, 197972066, 791136170, 999399448, 240347283, 814296373, 256445042, 40033326, 879300519, 600823468, 412112912, 135887963, 536163201, 869768624, 831144411, 238224881, 548917264, 58981599, 879676980, 300564311, 688546943, 96060246, 638861869, 468948311, 109089581, 462698676, 339619987, 688489745, 962205538, 385736044, 771143734, 768989927, 391250800, 717785772, 720272815, 191126966, 407428543, 437167004, 124873510, 32917361, 869575962, 191133279, 130081814, 73970298, 377544894, 438391306, 79547944, 788887082, 143272416, 416982873, 260266364, 125298245, 239113774, 862110857, 123221510, 126173123, 73163234, 962391993, 229176695, 422958266, 929765308, 49839086, 203274927, 357658340, 712766571, 333765231, 856210200, 52141346, 414281324, 29648949, 797713829, 724049995, 524292461, 520833327, 669687273, 675112393, 280057440, 337127937, 938211854, 185151825, 495334458, 561623356, 298713435, 776204859, 514107904, 913554530, 125970105, 471904813, 268913551, 103215810, 475253868, 960216967, 957688148, 427138973, 108224042, 920847335, 382571602, 998192868, 229018242, 970478731, 961639773, 308872082, 991580651, 162306445, 656675780, 747359800, 832360063, 863764370, 175292686, 760682596, 658355443, 488329585, 159262446, 52446631, 884959695, 585406177, 76317101, 471777968, 441480323, 278247325, 41615377, 488938048, 925507991, 276076859, 329764756, 702223218, 903244230, 734614027, 357259117, 152611099, 670839380, 333194386, 6692529, 708432675, 846164739, 609238900, 755945693, 160953979, 435159865, 814394446, 913151763, 43368752, 495594285, 15841667, 68843299, 687326635, 928584282, 842430425, 902192151, 714863156, 847652813, 234768055, 156484954, 246607666, 380446325, 544845658, 78635230, 332010372, 49379871, 868495669, 850708471, 836948470, 126890038, 536273642, 358668490, 658223254, 21946478, 998581019, 479214901, 545274950, 533962691, 840424106, 796129892, 382447797, 893487149, 186425079, 290287033, 694254923, 207985592, 438939588, 918410489, 133059713, 26530374, 836308319, 618141734, 36774407, 945691712, 864840807, 122969046, 769546135, 455215805, 300004854, 463349521, 331233138, 662125452, 983464689, 197202689, 20856400, 996723969, 263183870, 294035948, 304845877, 351891082, 934689240, 379619040, 789717885, 284555001, 313560959, 296172915, 519291810, 614091918, 196714866, 755160812, 931677755, 408851183, 48500852, 882957538, 446647243, 16634781, 768429589, 675876055, 568710958, 233196228, 552727891, 100061048, 1361525, 173820493, 868185138, 375459682, 476085605, 247745415, 619605922, 691144836, 228508678, 172760758, 151301907, 770714084, 130386166, 891807421, 115397460, 312356449, 830975824, 418505474, 251600931, 694849598, 179902590, 649627026, 656881171, 309536344, 134996777, 525029987, 263877687, 24690244, 816798199, 362869380, 654665336, 713406050, 970000540, 184437120, 657257953, 707584451, 121151619, 744826261, 448643619, 897526010, 542601521, 438331250, 833397956, 923867813, 910482322, 133987160, 592188863, 888447555, 79876585, 112159874, 63718789, 803064851, 325682074, 783522597, 378416394, 934285621, 655681807, 539547689, 430009591, 286848891, 100418540, 308539479, 122105767, 87421552, 460388325, 565429938, 814198269, 492196174, 598265980, 27745377, 180318272, 97345447, 471045108, 422778610, 495563092, 626759014, 482267902, 817198639, 964638629, 900791513, 984464326, 101262146, 790311315, 505110789, 987515624, 196859826, 575668960, 276912763, 986078184, 146615355, 644466627, 747906143, 926517275, 402175218, 6438496, 827389596, 126471772, 412020929, 855975234, 874365254, 966767371, 513099415, 616879646, 111466764, 875021779, 468330260, 252544936, 673273527, 189216939, 492804971, 439620280, 306895962, 513741087, 182207433, 223387623, 585018874, 784456621, 763864699, 318413033, 541330680, 752569357, 398397229, 993604001, 60916804, 131280042, 797241999, 535340533, 708544792, 821076387, 466593175, 576989163, 986463684, 242377237, 653064179, 349359443, 189208347, 89546594, 519759810, 888476971, 387999310, 242564256, 501423292, 749557983, 456816991, 227590667, 872851547, 211088761, 262526825, 305777357, 256863233, 698038263, 122388422, 53209452, 862744143, 797950394, 770125793, 131787066, 863656543, 130201841, 612591006, 555980236, 835729397, 716651900, 847108903, 982449040, 898481505, 600266868, 498326383, 876140757, 984534793, 609478600, 496670013, 92608802, 165213760, 987402983, 433862145, 568624009, 313198597, 729893628, 489144501, 937872404, 986182884, 663813120, 399249938, 409884124, 373441500, 635128314, 977983716, 332422467, 693647141, 32899855, 190811603, 808266991, 330942655, 619339506, 177201693, 821210613, 522780806, 322842894, 21893871, 130624300, 617180252, 738344491, 958179226, 860956158, 190222746, 940358352, 151270085, 778037217, 600932654, 606721846, 972954591, 816071042, 538576070, 95933096, 612316041, 858253914, 589835659, 296555750, 775036567, 41938054, 560352147, 816581208, 127205316, 686459313, 4817401, 900326204, 550010704, 586940926, 538275694, 518604235, 966034680, 605952045, 828424869, 20025242, 471576858, 581897593, 555214713, 154106167, 743504755, 25030674, 695445145, 667662779, 530313748, 463728477, 810785985, 840914577, 682309226, 948705202, 276967131, 725203357, 489793103, 184490344, 698018260, 236204640, 849629292, 261378879, 676229603, 891246020, 537087077, 257338668, 64906835, 534517922, 122465954, 739003755, 349722043, 692672133, 220054829, 430105710, 353550400, 204271887, 605843091, 274613192, 511688636, 724992893, 646026721, 621582043, 411636349, 218712292, 243206226, 445947276, 712596872, 365663137, 320509159, 281202998, 646210339, 244819988, 578420819, 619752686, 993936232, 813409615, 453012042, 624490213, 734795575, 423540519, 367144224, 141148180, 616755648, 979605839, 607109025, 951566916, 297057171, 518286341, 970642217, 529176875, 252779686, 327949437, 544802725, 893161943, 881402901, 982635763, 90193105, 126427421, 566112130, 780094349, 959465468, 35159507, 926837159, 748286701, 456175016, 218222016, 135037033, 392432336, 443548688, 30688294, 302361518, 518346230, 685652689, 981222026, 553933148, 145332532, 396643150, 160254248, 812222493, 8805554, 167107803, 643230125, 799005242, 680228886, 584211876, 238133079, 21892070, 245373384, 377762991, 219935327, 109334278, 700483921, 223759864, 26697019, 79235502, 743471305, 846585084, 985809575, 739014349, 964647436, 861424284, 233256599, 539727157, 990496235, 646060270, 498099445, 689847620, 171950165, 815943069, 790874633, 121787482, 917536784, 793572070, 255633328, 811474110, 932066412, 9132998, 567808064, 381509857, 855546180, 31192972, 114690530, 666688611, 201454721, 601857761, 450819428, 66871809, 96196707, 703208769, 528979671, 993806757, 377913933, 837106444, 729834978, 70608445, 857978690, 447674505, 283354577, 765805905, 250374197, 154530940, 442321733, 604176508, 447007565, 201363536, 123323951, 575744067, 260748806, 983628463, 788400345, 700270575, 329423792, 592118350, 725431266, 492720543, 733934996, 618024992, 736738941, 13259000, 640470126, 934160736, 490090245, 769108691, 688712159, 33496482, 176604482, 223183831, 682448157, 147931846, 432448017, 301375019, 829379193, 485971937, 518406931, 366454448, 3701330, 771224373, 419729178, 477695034, 421340575, 359980484, 452951240, 945861093, 80400114, 159249674, 826961650, 246464286, 524942638, 310685259, 381482436, 172070474, 470780220, 730171028, 886541428, 875008629, 67204142, 774946580, 41621333, 589896473, 917491499, 764700022, 487104898, 401643996, 867463826, 767852249, 804680778, 835035917, 292899628, 556898553, 744300665, 230056106, 328029935, 754563408, 648335967, 897779476, 392223078, 73233237, 36501184, 227251247, 950239393, 252478139, 71607364, 371366370, 708885591, 515681755, 70655342, 447851268, 43732617, 719352450, 98881023, 427877872, 102331516, 415276420, 613793316, 247846134, 243404592, 682810048, 139336058, 238880328, 72688900, 904041114, 524464039, 739689621, 77260668, 253468498, 50466927, 342011457, 98544449, 941988087, 30807307, 525344535, 47619938, 747332614, 166978303, 319311241, 361772422, 803522286, 433055815, 270205848, 254869845, 439281889, 810734475, 195880620, 2108702, 591664468, 289997893, 316071160, 40265230, 343845604, 451284012, 749761085, 8167994, 807009283, 729363795, 511064358, 225002434, 931859938, 460146962, 794008807, 260331611, 688275350, 118302741, 506187928, 777236703, 981514860, 764374679, 576850555, 841038649, 222830290, 238098747, 303080193, 786839077, 341199553, 775267181, 11037812, 283017526, 164190463, 949186362, 793756995, 700177168, 169777151, 702931296, 22133, 738499476, 71684246, 23298536, 257961826, 683411382, 555157913, 116964622, 993648319, 528270213, 915387611, 121773447, 956751658, 145391197, 26744573, 965732934, 217334991, 765890686, 834175896, 945053332, 537079047, 998977019, 646566173, 434470924, 931187861, 706821575, 749710658, 70413216, 44010284, 495419853, 556138519, 600167517, 903355548, 931369719, 669765579, 72404981, 129651726, 735878827, 121989378, 465231372, 865834003, 481688571, 853110983, 271953371, 210398452, 67094886, 402786324, 956810902, 464051206, 315091351, 982751671, 576195862, 833992266, 788847762, 49629389, 635128675, 418947502, 671520619, 871430848, 519618699, 832670988, 116159430, 554447398, 91008890, 856880262, 769742105, 571625646, 456100114, 373355022, 900829318, 225440616, 12660550, 940660338, 901688870, 684357859, 706885954, 596093275, 611824744, 875337803, 825618790, 172613260, 486994742, 912907793, 523480890, 782021432, 181309499, 490907901, 430852240, 526145470, 841900418, 898219590, 328302102, 265015114, 899366246, 288309077, 532725392, 126881180, 612879962, 602074614, 745465797, 336079512, 345195404, 562021724, 722800965, 571272387, 778485144, 414421043, 850399657, 245234994, 462762586, 761602925, 551654227, 770571584, 964547645, 741955718, 570841734, 589875389, 788356653, 729180672, 314799182, 248855594, 122508161, 491739161, 392595471, 914140186, 24288773, 783996662, 430268288, 261828567, 337923613, 931530213, 505877812, 350709609, 19175653, 735788712, 353577729, 447083244, 451052174, 418583981, 939278286, 236028643, 756286598, 4304532, 958923881, 355672517, 51400726, 438543331, 146687367, 504256536, 634112675, 234569146, 629384396, 414045145, 553019798, 817097819, 173227775, 310862585, 751433919, 64100489, 163996401, 744151516, 184725196, 309021140, 553095311, 573405370, 185419780, 243616010, 404856160, 511440389, 616119465, 742128315, 539515435, 586972862, 65048192, 629906623, 790244856, 639320457, 497384735, 347762574, 823237258, 374427407, 896327385, 463612319, 773281860, 736527893, 121131441, 122922995, 238444674, 918896486, 736019694, 99172476, 787500129, 853814917, 676158149, 595102057, 47198649, 9319127, 495742540, 493862086, 647615562, 262645882, 814494165, 903723196, 20832945, 221469477, 279493841, 66342165, 114733660, 530950765, 660078099, 155335142, 927346404, 17341832, 72014042, 387970463, 867673037, 728527199, 960453313, 38997463, 298847064, 191157998, 457654723, 267260586, 458504343, 937015417, 615948885, 603090467, 811128278, 268364535, 183574693, 692059075, 58751761, 394236580, 369419163, 639768535, 455240887, 674592468, 953081465, 730747180, 684465411, 635025988, 909701319, 306468070, 409642448, 500569113, 173020870, 747844812, 549535438, 406373111, 499815897, 259983988, 552915866, 695968798, 271264281, 575651520, 37788948, 378433715, 705310709, 472125162, 776550795, 793936374, 273996743, 299697849, 423653488, 645581776, 467692150, 806295264, 541122526, 521282788, 534560306, 754164840, 516319008, 916488292, 169302244, 425088089, 505767915, 77794499, 161798005, 792240584, 188477120, 497996651, 235669505, 417655376, 874193743, 117095951, 532098318, 407468988, 748521984, 599481208, 490593757, 362784510, 885847054, 512034221, 722909369, 680388813, 866065505, 811103546, 136388852, 665234830, 291635223, 413367827, 683315967, 126783911, 465932199, 415823481, 45722713, 605246616, 684795853, 277655072, 323369804, 470569174, 644201454, 291219642, 433979905, 97499886, 106404955, 453836663, 7838408, 869379889, 473591311, 897905521, 264607118, 215624184, 467805588, 947770128, 217310809, 226350107, 647913037, 43783737, 551541077, 949724835, 105215633, 958251941, 224583159, 493391206, 526570992, 737140819, 515335515, 872730695, 375442694, 632510629, 456544983, 545808340, 635468625, 961175918, 451769810, 583140581, 332272441, 146389373, 911286020, 57278057, 628586800, 291081396, 491503612, 892946690, 41431399, 266793453, 441007783, 488465149, 461077813, 64386673, 921285774, 595851527, 982053313, 173998642, 724234523, 17113562, 946497649, 578740821, 586464719, 808258954, 662346106, 992888160, 770998070, 266688879, 662104807, 423439455, 476463461, 897480357, 451268163, 10885440, 288014592, 278648474, 391300914, 656466467, 976210517, 159547044, 959244011, 762177488, 63373867, 949296986, 746352465, 628780438, 185423495, 922374211, 662973830, 7655104, 941727448, 506835377, 100042104, 519660875, 405953002, 367801909, 373001382, 261929672, 86955268, 599517199, 541244877, 543571222, 723526671, 950356308, 366093295, 82006883, 105932503, 86788213, 712712836, 367440175, 698964032, 652183961, 669591036, 153196044, 195600554, 129685313, 555822901, 636520207, 499036086, 465982172, 275862851, 766455922, 628526258, 549877516, 340056711, 769378853, 254361370, 133114987, 817573748, 997528314, 7205203, 372319596, 166067869, 811726328, 106288698, 535823631, 934351890, 994246562, 111497636, 338730590, 58206557, 259658654, 15936424, 499348155, 886040724, 68726868, 867810395, 500669773, 133080722, 116828288, 575796875, 269524416, 905013518, 981234631, 560799776, 883320795, 791414274, 750282164, 920347000, 192485850, 539921790, 778137355, 628387413, 751635579, 717261926, 691297124, 622206793, 89025279, 163041932, 720577906, 422023939, 889062141, 145345571, 258459718, 623745438, 810609926, 82856745, 592801577, 331292939, 460910138, 617716940, 876753522, 293005657, 506243503, 453636460, 676165975, 904320049, 764582865, 34561135, 480742779, 502764004, 175422559, 449759617, 542867895, 156041565, 47880018, 748928639, 62341657, 507124200, 253780334, 3144703, 268796, 362217212, 501425203, 525392348, 340576191, 181699226, 450238282, 991269378, 736993331, 122233589, 246605435, 527044156, 268485836, 688696590, 138136292, 157276882, 597419299, 352608221, 686495179, 784918533, 147089711, 2563286, 304764397, 805193011, 181632940, 438742376, 899576329, 609548607, 80847343, 960113456, 405155, 622224243, 788447933, 986456663, 291729362, 964796841, 689776686, 710356388, 263379843, 17743086, 599796840, 397878394, 836396021, 580903716, 553093222, 361657221, 157183508, 668062871, 920283872, 92250997, 752772252, 959290228, 425396947, 27471627, 314357173, 367296277, 373718164, 203383735, 506427895, 24708877, 503195012, 771951113, 568943689, 623818776, 5365331, 834726236, 673403681, 372011203, 642154066, 669693293, 735107950, 791296566, 158353650, 918431510, 628582207, 232621869, 915064776, 151928148, 2288533, 520286300, 432024991, 87852593, 870170390, 993176202, 746181117, 843112863, 284359925, 329800858, 932522346, 490629988, 689707250, 211621555, 908717150, 465793273, 462171897, 752580111, 547215054, 971014180, 485814514, 540779079, 430077071, 152242489, 552391051, 450199811, 263217723, 701233834, 789219327, 648755250, 707786825, 839478396, 112736093, 635707908, 579692465, 985144123, 798291066, 544674079, 750786690, 185437324, 603901318, 879251715, 724019279, 806433703, 955478291, 206282798, 797032635, 126379875, 430776548, 239135555, 912685688, 960618133, 325422994, 116617263, 19902611, 861561328, 936547313, 194973823, 427671165, 977005901, 348916947, 845342136, 583503780, 354332148, 736796324, 491089697, 70322158, 991990719, 775026693, 21289482, 810509008, 942662323, 975850728, 166776422, 209899549, 590489641, 467588184, 469156370, 179554510, 922429921, 169155972, 636231372, 808960039, 719169450, 23562650, 811291161, 614680645, 692600303, 198844944, 525846262, 541880094, 293488168, 231865247, 782851807, 724192493, 423044861, 259201133, 779007272, 596136784, 232934070, 717163135, 511777090, 235525792, 503769218, 826567599, 987238901, 889032983, 787544409, 473114143, 36315420, 162937025, 742367653, 19395446, 33170465, 139800377, 673317538, 494477665, 444368100, 632198376, 93617342, 996981250, 481323837, 99623589, 315341584, 770649985, 731084, 371864587, 36043287, 11487002, 597913864, 881584140, 334601972, 636120246, 528578098, 535499753, 946628749, 754257063, 430682856, 378722361, 22809931, 976386631, 791420502, 83727890, 585026070, 466992316, 428379962, 204639717, 46976571, 561021819, 376939881, 854907790, 970671251, 232875520, 755336588, 87746022, 65335898, 391324819, 261556813, 856267003, 912437233, 435533630, 619735509, 166070381, 552941158, 112353317, 749425147, 715183032, 918610972, 611932166, 961808848, 80540536, 360978137, 175160115, 242931500, 569737178, 259203638, 729353153, 145992650, 582499721, 96382044, 602260696, 521067242, 214340212, 665131267, 476583931, 840287016, 614920607, 202002100, 225210461, 983189892, 423573402, 111309196, 585415815, 674742950, 470059469, 681215983, 464453251, 379628502, 949165410, 326758498, 160087878, 99800875, 718990324, 182724848, 648987090, 252594377, 238896180, 165450509, 760667848, 55517182, 530073585, 184366341, 721490735, 924615847, 230672385, 472862547, 729021308, 651443741, 105674102, 35609222, 226309759, 457318648, 602791673, 365687690, 749567883, 675883909, 100704086, 670177177, 802455228, 530381555, 730997824, 396478868, 134520196, 702802260, 48696771, 626690313, 263005181, 26154378, 605422997, 868650987, 288341589, 380737637, 843683342, 414096512, 723444971, 527628825, 813394751, 889577918, 877786570, 673974290, 845525629, 140226289, 999897184, 154345661, 32613745, 1649509, 384602348, 152577050, 504330097, 764854945, 155004411, 59596154, 957287564, 57949958, 286638810, 142189392, 179599808, 604980566, 759651418, 493922848, 447676568, 416726781, 872636230, 406521230, 404069122, 246692367, 942115820, 90717867, 429966636, 934694877, 798113239, 360842848, 911150116, 884366405, 258098512, 642832696, 548932764, 468082768, 931374420, 331780898, 445055558, 224134787, 80657574, 489647145, 987148276, 448789883, 492859775, 908259567, 874037988, 624632360, 825356428, 644888255, 325799207, 47988934, 334768667, 41399247, 103289061, 100874196, 548702886, 696075057, 392441555, 515466666, 81598133, 358852122, 136910566, 824987668, 45010473, 214705204, 85612219, 842800340, 598590028, 303227574, 148126848, 837424641, 453322928, 318106408, 811511721, 833832727, 105922208, 794099349, 378913073, 150257044, 796187437, 107392777, 518063983, 423758650, 983031541, 604539831, 213188513, 690105857, 692936268, 114731472, 924343301, 722394344, 723378452, 212503051, 900724217, 625937150, 430197115, 655908897, 229480285, 934839738, 231160107, 81357851, 381461413, 573659938, 795632946, 403833280, 688742558, 876559159, 861238001, 919396467, 40591557, 983760322, 531449962, 982712406, 86144407, 534041355, 824899658, 944432854, 897840247, 812903477, 977235836, 241164848, 329542891, 848785792, 716243167, 743214283, 71694894, 861792452, 235853382, 82372357, 520845915, 683093491, 994190954, 778327247, 630342107, 246238560, 158416623, 174705919, 746154679, 789929335, 596293510, 75074579, 520856159, 679952012, 818101553, 770362457, 462960833, 532272153, 707020405, 341155427, 519343632, 696421179, 597451075, 315278237, 992607200, 828708826, 706366738, 604918476, 213718065, 285182424, 221827534, 37048196, 263692770, 233148023, 357027607, 332575940, 189154299, 660428762, 825771885, 329139862, 12700250, 749862054, 936629425, 830819418, 671035652, 599679260, 896842142, 7945137, 254528673, 911158722, 253124963, 125703050, 477789760, 141534758, 674408277, 921440530, 813237109, 555072089, 20231181, 481881001, 946794464, 995003708, 864064311, 916592670, 715014474, 324077070, 592211990, 25359630, 977932341, 457688054, 55829957, 320540523, 147135125, 555248935, 427848301, 354385282, 421492029, 643828964, 410514349, 605879074, 956565583, 294681079, 516019333, 798095133, 908966765, 360125959, 191859903, 198690594, 711003274, 956110596, 406363172, 654959036, 108505654, 567033535, 406084887, 901415043, 183432602, 105498720, 716687140, 216629551, 979068393, 141973738, 503577780, 827725798, 107868862, 17802227, 483427972, 867180124, 986923852, 360785515, 662057085, 838892422, 470966323, 762877257, 857384412, 760469454, 481603804, 712856526, 722349959, 738241660, 910924863, 315249412, 396513883, 595050126, 47479436, 317922348, 617795596, 105964993, 265573133, 36598525, 517988840, 572848559, 816117781, 958519274, 510093104, 179545434, 152316152, 429492396, 471439452, 500125749, 743173667, 489384072, 912535550, 884466971, 662662429, 666325858, 94901468, 506064019, 921494115, 793803456, 368352722, 262926198, 111588542, 697382410, 436312495, 324819936, 436297680, 117508496, 403743288, 936017982, 587601767, 309339880, 931905846, 426011339, 238491128, 756849642, 649564474, 857593518, 136557009, 629788888, 503973834, 536992925, 471427153, 653340877, 792135962, 935825149, 965811262, 777583688, 950240859, 115840775, 892672395, 652073340, 491627583, 33444899, 678482258, 701972026, 859136416, 447521649, 71261732, 456883669, 794728114, 418763677, 306943551, 554352879, 11057712, 510129191, 785427341, 912554617, 652574781, 537189751, 242870645, 678427440, 667740470, 567546876, 992705746, 661533332, 541876333, 705763577, 200719403, 164737947, 231398546, 723033478, 896555169, 872625737, 766793304, 563741111, 416950175, 242481357, 300844803, 819322004, 983538748, 847059963, 109964529, 898486576, 149114422, 554882878, 617605566, 8044872, 141326842, 829459576, 173850646, 948060101, 974776680, 253699251, 758958399, 474429234, 666404614, 29770177, 601095783, 150769227, 447732396, 718145801, 7320188, 280482394, 294617355, 216762334, 22764685, 966361213, 260540788, 608643956, 804793168, 10377801, 515132239, 508035678, 89681598, 185451613, 759104854, 271147042, 206309744, 310120207, 542666617, 205258585, 737102706, 800942739, 72310170, 654831378, 32346718, 754795000, 51049450, 587352669, 565029735, 979345202, 357861711, 79375081, 774194099, 606003861, 304580862, 64069657, 200367433, 606355244, 120109008, 680651336, 571973979, 425246271, 535763652, 858272689, 264862454, 473676735, 275341956, 669580312, 906884193, 18394118, 918504480, 737579523, 824969358, 792642181, 215527856, 45855736, 864870613, 158573047, 988079121, 95771283, 534508413, 726176210, 512327841, 62603420, 328922684, 243915721, 441193863, 698570306, 571067078, 68076835, 797089468, 220504907, 592908977, 787446671, 589994606, 832740295, 672376366, 605261729, 102183580, 721841092, 177392490, 368126991, 668048130, 586291841, 693352347, 927789694, 386359179, 471068479, 55677261, 690287167, 407050479, 124915310, 276586063, 309113534, 807877006, 553152826, 957793583, 389065851, 599730284, 636649148, 101604365, 934973202, 85912300, 401170796, 112404657, 98392269, 837375863, 271920299, 589478718, 588487219, 751572879, 936190302, 848834374, 779440410, 261401511, 812210438, 504827336, 740178943, 415180595, 572084245, 269815035, 461731989, 913107679, 127187933, 790390462, 492611775, 357064085, 98801174, 175171127, 158134567, 828764243, 865153428, 132185334, 548953813, 29901637, 758919696, 572440244, 888063421, 293399249, 314117068, 747060205, 22087331, 990274778, 216000906, 264660472, 248400801, 3997320, 720904622, 631375352, 147755300, 21419709, 365587274, 823871972, 225408422, 426182715, 517084574, 494288170, 427642240, 723440823, 73653701, 321523361, 130649330, 72231776, 426250297, 238551255, 703964779, 133874677, 518759297, 195237395, 157855863, 564446215, 720605527, 529376913, 620351904, 213320102, 705940803, 931550698, 220496551, 299811648, 440641087, 25259240, 576768380, 222167845, 694434457, 358485600, 619607373, 585734007, 121647778, 684298988, 211442003, 244838789, 479243919, 717836636, 249738937, 681743888, 650024274, 687812440, 75704723, 365395753, 209992059, 263566019, 907622440, 41603326, 734105391, 105913136, 713421161, 243234675, 285008275, 680210831, 17859759, 356950688, 728419161, 953992346, 214663967, 914255895, 192837906, 419059454, 652275477, 299863815, 301181025, 265862100, 124275572, 647722376, 790679207, 702586177, 527925762, 856539872, 513554903, 249187430, 810011345, 126612850, 46833363, 976381579, 797361869, 492123148, 21676598, 841186470, 282582206, 703878114, 482542036, 271570776, 480929720, 730260440, 325630223, 203806704, 575448669, 137861100, 464746632, 607656416, 141764290, 595736223, 734336056, 758756716, 670322164, 64780316, 363181836, 246195051, 498491325, 170168863, 39693121, 679893211, 537527894, 896961595, 319295489, 975279175, 165898898, 468398971, 496959451, 686366103, 872750221, 330050516, 254280723, 163595070, 886927516, 355995252, 122904302, 174260873, 834536939, 573168942, 937899255, 114384746, 719344995, 465131394, 669066097, 488144486, 243190047, 457133739, 589367585, 126639692, 196973184, 163063987, 707391236, 770691925, 782984950, 825118556, 956913768, 760994331, 122841319, 870811108, 543381407, 542927498, 599839226, 112964744, 117214890, 111311682, 241314538, 615482904, 207236996, 912340506, 424258239, 189272464, 740461299, 832852909, 946527402, 718006752, 435918615, 281896262, 485128519, 751222239, 224906181, 214555122, 258411492, 156218412, 493804122, 156295691, 115515938, 237290546, 82615513, 761077482, 897621031, 88561234, 493239018, 792800517, 587801948, 77035461, 854351761, 362971859, 660142360, 185346561, 92262369, 225827020, 542386087, 913627369, 80590208, 955748797, 181397600, 740462207, 5483790, 938403636, 237305027, 623759528, 766641206, 871456519, 550670987, 372495848, 818268995, 154930536, 128466424, 609929557, 856210190, 939333352, 507082595, 488575285, 854188572, 424373547, 276743269, 296726733, 618059500, 432229213, 798507296, 891553245, 826229758, 29857323, 394452048, 4044681, 795072702, 688632542, 659995219, 698031852, 845292863, 682021762, 782651890, 336985018, 364946395, 193624505, 628143873, 464292003, 264048037, 78097165, 655299682, 839504655, 82904699, 221953458, 623667232, 629176709, 158938172, 174405660, 978186250, 579350286, 443102003, 217393532, 679720367, 837102705, 949415649, 232082390, 811553527, 851410355, 361701939, 872150358, 706495675, 203667386, 373879522, 607035299, 156002002, 1823497, 158033315, 155702653, 663577594, 372083541, 563625740, 672177214, 821232629, 473635832, 750596687, 431699286, 940849896, 203410322, 828070728, 990674778, 836487158, 982419412, 151299089, 990999208, 379727204, 604282531, 311540134, 484407134, 875895323, 67638030, 993185235, 441294975, 739871697, 63596926, 491161301, 437648246, 186454410, 809366123, 499191083, 336159765, 108275310, 602808567, 76197466, 30158816, 989090054, 998989587, 210800604, 877127985, 81602566, 864294259, 478057954, 585605909, 852603932, 215821107, 377892626, 141121821, 129254561, 781328775, 192111844, 358560881, 723113026, 760946101, 554307911, 569016956, 229796915, 394841075, 741014613, 388527933, 772092324, 503816451, 284772922, 421769447, 475360411, 460542435, 466073692, 587030327, 897049980, 964082050, 650785396, 34917966, 267274296, 93555553, 732636735, 496416977, 961289292, 191370347, 997722329, 341149769, 134669263, 718644315, 560708285, 955825158, 395358113, 470944678, 166794918, 459054141, 978902110, 218034088, 971147349, 222418436, 459948442, 972583987, 334516653, 335802275, 768697683, 21929631, 383022598, 603761488, 711019485, 388397836, 329045002, 191336825, 274553073, 915941477, 122626936, 234308171, 373993410, 28761292, 445910475, 111123804, 419152625, 817234421, 967455419, 885561964, 540300667, 840067058, 512339434, 563817424, 171775624, 213754389, 550477839, 155455612, 922926140, 917356306, 49632896, 574108847, 750591825, 887699853, 432154482, 393665368, 110721242, 628480969, 250072777, 82137284, 92284718, 664988930, 12907932, 800648052, 10216271, 560584789, 727288339, 955155204, 561317836, 758523068, 250651132, 818452032, 241346128, 158089267, 257535844, 959179986, 336239599, 13968538, 444508431, 640062356, 959008090, 953789421, 997402969, 56267320, 682428844, 73596415, 952111905, 787462735, 720379797, 23562322, 925934253, 726188597, 758962472, 985447224, 758981367, 887609405, 611220825, 293072972, 321892686, 772121627, 47985672, 194329005, 478973468, 364561809, 843600358, 720193323, 11149594, 58075759, 658962231, 799168347, 146728115, 246680542, 950409572, 777325509, 875814919, 685729725, 871785619, 496279712, 254311584, 69678393, 318464676, 136091437, 780490210, 917587789, 163750198, 976593346, 813694891, 536825336, 323206673, 862629396, 597651508, 411660772, 122884430, 324665665, 52877353, 629779826, 318167464, 901740661, 41075980, 242513627, 325904472, 254525275, 146311111, 187932434, 171219010, 793034753, 84766699, 312501269, 110694165, 765698137, 288472785, 754542397, 940866189, 528846955, 747424628, 194268987, 600474514, 917003752, 894905735, 918601496, 985957949, 914445487, 129548286, 435778328, 166326397, 143772083, 266213321, 769800600, 219059843, 470199015, 594552751, 946969306, 857405252, 115043981, 754482826, 871614349, 672381141, 19098665, 343858503, 371788447, 390276142, 934006605, 314983303, 958382959, 678118644, 649909670, 844368983, 495593915, 905770319, 381996609, 894135695, 817702696, 761688315, 550892077, 651429413, 679858462, 832887717, 533640274, 123073709, 486576979, 492555393, 728008441, 834088416, 330328003, 949989778, 837410185, 402789757, 410628145, 624853635, 570060783, 249911065, 574689756, 409163048, 1058862, 792145966, 364300352, 259870380, 121875344, 395536681, 15505156, 159849507, 794120631, 309320517, 422875865, 460494860, 826133779, 535556925, 594465428, 445153707, 579243065, 941643976, 569728642, 640145969, 431459457, 929344142, 640674525, 581058669, 275930361, 459296156, 907876171, 262292574, 118203816, 732838025, 855120699, 766462964, 15791631, 126853941, 415765933, 544071911, 259769061, 962873977, 46162148, 882833546, 545107808, 25840953, 290806601, 673566936, 170968001, 575297453, 739489145, 979733309, 525480374, 778535500, 96065973, 793714365, 854887786, 178018625, 593838203, 798163143, 677259199, 746921069, 644308677, 289804484, 645863091, 616517234, 221925671, 933568374, 514831805, 220311353, 423883619, 524229279, 423466984, 156177339, 582534237, 837714329, 540243989, 784892631, 131351155, 583126432, 14123694, 665708948, 857426116, 812856082, 37566711, 876006607, 779462457, 661228558, 109948133, 776347358, 48140501, 964184062, 984943214, 501438031, 39228866, 436722486, 938855908, 285260523, 103893662, 334935331, 734127330, 12025572, 73948457, 763034013, 260685733, 946288937, 515182692, 380606638, 974481139, 610215596, 251433344, 556921008, 437797123, 270199675, 585511097, 842703502, 27499775, 848002046, 360946114, 297481589, 433903761, 866865268, 705692805, 573968910, 14945090, 514014202, 966194949, 702949701, 219176920, 650660312, 470450522, 555950570, 786096880, 523284615, 353030043, 524047696, 910195070, 609123962, 665391917, 73999254, 551405671, 375240824, 379896563, 947769362, 929223466, 131984977, 397485853, 879053886, 401558454, 345299382, 672658488, 43406985, 390981087, 566108264, 207408972, 731170874, 963759531, 763418547, 647769040, 475574809, 660713895, 333904092, 319782008, 678803527, 54176143, 638524933, 470184671, 628637687, 388242991, 569787439, 517835422, 324829864, 714519038, 62706672, 821927518, 643107307, 559855670, 909077209, 6669094, 375228670, 556482980, 75382694, 551264502, 819698218, 375867198, 64047194, 248853353, 240305502, 755665197, 901644999, 621699603, 876811850, 83433555, 370290428, 368147786, 769587351, 140078335, 322483079, 998363369, 283312423, 963946549, 107815281, 431154353, 852934745, 116477116, 79952772, 916367695, 97185710, 527054583, 171605794, 414858312, 964655981, 285264367, 158159872, 371227998, 824490870, 11157420, 195950678, 891196326, 606469235, 15433692, 953228812, 932435258, 132872237, 596792307, 566537006, 963240700, 456576923, 623279200, 467398633, 431848879, 860502001, 969289931, 887105587, 894101720, 333303060, 166965705, 279059953, 661348608, 793813164, 558835379, 414177615, 456458646, 743957455, 821028778, 832768966, 899709212, 941605429, 333708150, 967682356, 778777821, 148807380, 754904984, 112984126, 721346090, 33127459, 410713504, 384843685, 562819551, 235824790, 693994439, 317259751, 700160514, 173054337, 22652302, 791223346, 239777705, 260082899, 592761544, 208050515, 851061399, 604370767, 433394388, 864451613, 629734718, 326962123, 339425856, 744378648, 193494190, 553076940, 145153196, 990065457, 544579633, 667376639, 77315142, 971736230, 895908452, 145574270, 16304416, 37273653, 796812599, 467458158, 617188974, 477283212, 794413429, 514114875, 228744644, 151364613, 535879648, 608331869, 644317182, 814307721, 420799401, 966724092, 304565586, 616806724, 83566870, 967642852, 262848248, 291801355, 797945261, 376419918, 690831013, 709397238, 916299382, 549585241, 573164368, 202387968, 90788877, 572388825, 813382559, 565487065, 946274807, 510718683, 345896007, 121541856, 739197806, 125000168, 544119674, 241886436, 666981620, 318683774, 635248405, 337555514, 691938163, 902955138, 385732185, 257604402, 518866347, 730857367, 572585558, 245873298, 863655285, 68333805, 409271148, 465847541, 656548857, 839428810, 263500597, 221236866, 560973544, 834884522, 107338261, 704425826, 849827265, 48888928, 854270904, 333203927, 462217510, 493248654, 234670892, 793522622, 947632289, 333656890, 346792542, 432025182, 399995985, 828802253, 945976507, 671039942, 29639166, 633485376, 742524195, 729805276, 760995715, 715953718, 144896773, 460144112, 661230129, 159120855, 789135042, 891738953, 13667950, 256878826, 893567678, 786583565, 899621660, 452743096, 776586195, 606889584, 789559941, 466932465, 171280333, 700477957, 545795291, 349584889, 240115102, 484476172, 965430698, 74489821, 296549153, 904531797, 101021280, 65542318, 218138986, 696332128, 531269207, 285699745, 41348312, 275968846, 307455220, 663480987, 610472940, 352900442, 164286572, 453440758, 463342775, 923556993, 57259470, 995123858, 864821445, 239132958, 248122167, 374469370, 278293231, 622943196, 269424513, 590564595, 925469495, 655715957, 526553216, 47393955, 667819632, 271535356, 476907187, 424584169, 954637502, 103410283, 914213888, 676700812, 948692957, 958927836, 499506917, 182851209, 957036403, 74345891, 676220621, 455433808, 871769092, 498727735, 496345709, 657769155, 921255142, 980522792, 532965472, 786750451, 210184780, 527883919, 844983704, 220015076, 9650145, 269261561, 484827363, 563083792, 864052183, 877566965, 972611257, 480334981, 508539831, 101650874, 572053145, 234484393, 917048318, 891416917, 525386891, 877862210, 36663871, 747545732, 21149666, 81146308, 293680793, 338290123, 242735458, 982069328, 339309696, 575511598, 541608340, 659857263, 871303150, 782229555, 441032717, 621995869, 469567375, 44345806, 556641446, 47445101, 669175651, 73617472, 420180536, 366040749, 662325289, 91494840, 791495775, 326282609, 525213981, 833397266, 815580628, 129783863, 731701566, 133493555, 264340418, 290716253, 26571137, 609054877, 279779933, 254365918, 231129928, 112923739, 6116503, 658531688, 85972289, 841332038, 478606804, 920547021, 615891319, 221161779, 998714538, 384403694, 147640530, 984237282, 732456724, 329733178, 876571079, 382262707, 369886252, 62701062, 163173989, 640588694, 915570407, 564671763, 770510425, 770685266, 171373874, 410900046, 843436729, 198749321, 460222931, 42939167, 981727637, 291811670, 899734528, 179175803, 198510868, 285571655, 320834946, 290926984, 483202002, 181474653, 635059003, 259438081, 574678287, 827871829, 486382404, 611796952, 240043326, 229146005, 810868022, 601529478, 99959809, 848659687, 582725482, 538765075, 82311048, 456613406, 808733857, 131237508, 736918622, 195654522, 17875627, 851113201, 80445619, 302066978, 665716611, 584818257, 824902644, 498428632, 992182106, 946993511, 504840546, 214159909, 685592345, 958556766, 479685715, 847784482, 914225504, 817765552, 29309088, 192345152, 377613889, 785311913, 112178315, 785099020, 939354428, 986587375, 507058373, 563753647, 868270924, 364001272, 594353986, 788631040, 935019345, 78012102, 523510361, 399162551, 191528825, 879406057, 332469418, 428389005, 687890483, 232672346, 175009700, 814662456, 864293511, 360569365, 988870256, 488857010, 335318505, 500828748, 127929561, 368577106, 550366555, 621132357, 735801713, 551973227, 611598515, 427907111, 331203537, 130915694, 990785868, 101001187, 490285266, 143321958, 859941206, 853740806, 33757188, 824467485, 352429170, 472687442, 526283091, 322628240, 550933186, 615093259, 937369104, 417829707, 117055777, 643750297, 514707479, 707704169, 840646748, 657923706, 747500689, 904497098, 14808226, 974185824, 852619095, 670731700, 669738718, 533108904, 933986620, 337937579, 662142973, 679055317, 472547326, 834470087, 985243653, 143808192, 520613815, 911031376, 668609145, 566321900, 340554309, 824983367, 103128463, 702372833, 729506681, 683536817, 266509939, 948799893, 373871564, 894079624, 43070948, 710248993, 975957775, 387809332, 399699027, 724210395, 242905249, 834549177, 184680463, 694533130, 95013713, 358064182, 721092921, 809715793, 125087045, 285711886, 772086540, 763287176, 918006629, 574402327, 772528205, 226601168, 473102835, 629706342, 231115411, 918188866, 901901695, 370290477, 198597101, 855227541, 861858301, 31586832, 314396077, 572917280, 741568154, 221074511, 90794145, 485413585, 820818068, 435203783, 719076071, 600113963, 593349244, 545081392, 495858986, 334324203, 765630351, 600351184, 2168016, 665801240, 594286842, 919927575, 49653500, 147542542, 674856940, 36481665, 788275404, 961835611, 272140421, 975915323, 749851786, 500066700, 749087476, 499681221, 194831203, 782434284, 669871114, 717526041, 127888252, 45361351, 312085754, 888910929, 229731876, 449302979, 830175680, 346428707, 20399341, 650580253, 726452268, 432940620, 39285367, 389587991, 959047432, 653160320, 380923946, 216392558, 325670371, 523418622, 683882436, 611882054, 577063295, 325140033, 409150062, 503019141, 810428646, 529565005, 82993158, 923515665, 7693088, 596900628, 21229595, 27448470, 328256386, 441548841, 242329469, 981923810, 64751755, 525918086, 542075650, 719064116, 46910081, 226736149, 184694809, 928952743, 62901811, 758470066, 239440523, 196762760, 440119000, 166753253, 193437684, 247307509, 599766609, 605848541, 754704620, 123282347, 269482105, 275574388, 863906665, 586964174, 4368927, 236870080, 741036051, 121869501, 796854065, 709518103, 469043144, 689180255, 16639305, 706195050, 107381522, 444210763, 915659273, 539273097, 452469780, 116819028, 635805278, 271865154, 26856459, 794730453, 16588473, 186496949, 365772527, 264542922, 639835855, 817466636, 907140960, 509842715, 840879157, 425914954, 646694601, 355122593, 839348459, 752819, 632387297, 272987069, 203244062, 413984241, 747899382, 605433795, 668401282, 848147624, 686968592, 937064328, 605814370, 796505174, 706829399, 85733768, 51186334, 363090621, 646716955, 403332356, 856921601, 701299151, 12253124, 298475939, 26524956, 128123582, 467609408, 8217770, 90931308, 301704646, 645944050, 975118397, 871434900, 402912044, 34373837, 348776844, 102531768, 252685317, 581482565, 117115376, 869672503, 575244061, 120482042, 53668035, 254152205, 363739092, 600156883, 826317445, 163673219, 345141560, 976356186, 316361519, 960212260, 269081964, 91520918, 952764729, 674791365, 138727936, 531662274, 560308535, 489037027, 539758639, 229733648, 633276405, 633015595, 984363612, 207833129, 449849743, 359019403, 740033397, 865427774, 882253582, 209069653, 808321356, 811524538, 14770570, 509353219, 637100070, 366072963, 960650479, 393338249, 372085053, 636540318, 851641694, 816888812, 392572223, 408704088, 954398752, 393692490, 515259888, 380086617, 760951274, 218696438, 238514253, 913770686, 683581382, 543573210, 337393224, 603792894, 569426886, 573276786, 11313738, 186855280, 887906748, 876343702, 307555261, 329044509, 69100633, 459340551, 973035760, 978102398, 248196201, 372495217, 13859151, 397486785, 71138638, 10976756, 6737673, 743831061, 465358256, 7083858, 350728598, 352013000, 804203183, 889998628, 853728164, 982760929, 153615090, 260347166, 686526972, 512378777, 355880355, 622136739, 258222162, 373697342, 633981107, 825479173, 564334845, 573605102, 808383228, 727534497, 239192730, 69358408, 529648551, 239559448, 69107485, 696750484, 502573040, 137208671, 396944844, 435615093, 121576765, 681258609, 675676615, 141502454, 392246273, 166942051, 377930413, 592772169, 532521682, 266445947, 813732580, 523498448, 118782880, 125794352, 251056267, 15565147, 540956225, 263269905, 793788849, 99434912, 891052690, 797964115, 530397208, 651562000, 671802710, 577388137, 772484123, 845418866, 465134178, 460633905, 369487322, 443469941, 931587707, 613968220, 198779434, 930984625, 75682207, 997332594, 814508870, 897081372, 331075627, 909801358, 650254312, 100274662, 566664341, 125372871, 786710395, 200388189, 188125562, 89030265, 8950326, 288581986, 6613010, 997551829, 159035548, 367035815, 589459957, 341037236, 62820176, 640241174, 927820108, 559842092, 802532006, 277656840, 780987090, 824704745, 149388592, 567968933, 644199966, 877003696, 313982643, 914637366, 806062084, 482368286, 422341670, 19296411, 11959561, 47410066, 937285153, 344745416, 170382428, 588158754, 231678102, 390781548, 962448724, 702291576, 706725233, 264095644, 320178167, 936693136, 989161679, 717694106, 772617122, 145342771, 405422602, 285485173, 687676709, 866527476, 211509751, 70394224, 651400408, 434810544, 663152254, 864772383, 370801719, 46775853, 654305926, 368183563, 675960356, 781801685, 638672934, 538254940, 473182741, 844108824, 753198487, 627820056, 287711911, 555431750, 278436572, 600650885, 72097819, 9755496, 768494496, 336323551, 587947332, 549146164, 697972495, 679549791, 129585882, 121844231, 157837365, 848376111, 569686145, 411202116, 736616883, 478996178, 223090937, 130078707, 121083165, 355288834, 944380599, 460218740, 332570042, 808753686, 777423859, 536574218, 342129660, 891886906, 462849896, 448231956, 291541096, 523609716, 794025678, 277952344, 467996448, 481495089, 467067274, 689319850, 940737764, 873361283, 108389560, 310555604, 443838431, 913722969, 346707286, 784931603, 1172096, 775052292, 221051723, 949720928, 975362806, 281540961, 17334983, 179926842, 2156868, 960811722, 491176277, 100791628, 905263570, 957249386, 84890454, 318860962, 885202203, 71135716, 988797640, 427575078, 298678434, 503490719, 74231595, 376639748, 992413440, 494383589, 425390738, 620937172, 525391266, 387783272, 976379301, 298667287, 965024521, 485759915, 415362509, 873633836, 958775269, 140892062, 9162367, 318746451, 479860861, 172724315, 714336000, 926936092, 324955531, 989739387, 785224426, 343175980, 518758219, 196887051, 213165897, 532149903, 774574912, 726307983, 404245632, 904006292, 403400556, 830071314, 639687601, 796685533, 156831544, 522766598, 643611279, 916395192, 983425952, 355168019, 782069989, 920384698, 314044732, 878019442, 821918726, 108109447, 708782593, 179034406, 636994229, 854474907, 636496569, 393352959, 703203042, 623076575, 152483027, 996587992, 938279541, 773580875, 680130663, 728488672, 736811750, 578721297, 966046199, 931850353, 672408932, 257684475, 500682650, 213088665, 120674987, 896411525, 252278446, 639785240, 495466470, 348067964, 435123120, 426618595, 283616254, 963506268, 460174315, 28587504, 74902204, 312733599, 343476133, 367414855, 917419722, 660668950, 826742860, 389653287, 186889959, 277694510, 381732480, 40889181, 478150564, 846096665, 802735644, 186234068, 813316640, 503770962, 246051321, 655634177, 795632882, 515443288, 74406860, 781134867, 224070525, 282304562, 598444448, 87610410, 627457712, 770711521, 291573675, 818351281, 734380257, 637395019, 325660493, 428363591, 43783803, 951970613, 960817332, 164714469, 839465510, 946574171, 482550227, 505153446, 974556204, 518610751, 61404252, 731561768, 323801110, 278813545, 860672012, 613238274, 413037607, 769088719, 849805497, 869562011, 866204888, 125437466, 488237735, 747348943, 677939029, 946682618, 676648581, 305136901, 744536038, 76326976, 273641031, 677681232, 734871504, 51625303, 545615907, 686826225, 52790494, 438670231, 466384504, 774788012, 112103191, 181343316, 760002728, 60950133, 875964005, 414449464, 415734359, 670070558, 992116423, 50522905, 522750765, 9309486, 873780674, 639161190, 609344946, 255282942, 385945084, 257806780, 783128592, 289871460, 859989992, 68011240, 864629617, 963438980, 143553854, 110615762, 106463206, 290813084, 724347663, 906663541, 662698486, 10855850, 393844723, 959951928, 999743018, 313544758, 279123914, 222415940, 459731745, 600934360, 118082795, 223363372, 870196385, 69667775, 95125817, 940011362, 977057429, 278852277, 151586497, 480819981, 170402580, 665936812, 269357447, 720178538, 396863895, 884731578, 105273607, 180656911, 772786931, 506104114, 544073673, 86465617, 85370283, 58073778, 463898212, 309196188, 405239486, 505780181, 576439418, 810864022, 804246982, 997594448, 878185861, 306085617, 770116692, 520723002, 924319368, 876607266, 937329503, 973094227, 692599545, 931431925, 812080024, 507874482, 422878413, 144116964, 154787217, 250174758, 651470575, 93883786, 11125634, 891172258, 939867298, 881185337, 740665675, 214995151, 694184808, 592078551, 135836976, 259912151, 291256987, 102217225, 64274195, 450302225, 581950814, 139811696, 595488724, 11064890, 948550652, 267337458, 8056815, 345812572, 767688438, 586411269, 434425727, 290943346, 516183603, 261293038, 436200598, 604119144, 322086592, 787241064, 987386984, 124949467, 696446310, 593439226, 887506149, 943026477, 586039411, 614962091, 476218011, 500545610, 100182506, 761228016, 771841014, 558079471, 553289997, 586687812, 19593196, 735840431, 130272267, 843585154, 224763527, 306164740, 411444600, 527151970, 720761434, 568748984, 698463031, 879484678, 147090313, 478460377, 130071836, 71760290, 872313733, 4611942, 9291441, 697364756, 712398814, 403288064, 251860931, 331753565, 499335651, 860378773, 666124243, 629478540, 229158492, 88411529, 941186361, 724391049, 826733360, 439971980, 401994229, 789519708, 974443308, 296491142, 871398488, 342900801, 463970112, 710681823, 543147058, 907358165, 385578555, 45275567, 554802422, 334670245, 248581148, 953865371, 242307137, 697663024, 845696159, 721149762, 608729182, 799961738, 986510643, 352727338, 471094747, 957460, 360371515, 441720920, 910038399, 53622887, 244288109, 889633808, 41904345, 311138104, 465476327, 559257248, 586357703, 404057319, 935336170, 624226189, 743103453, 414549274, 921124734, 120232984, 140058214, 176783015, 608957988, 432154649, 359758827, 477209694, 4219900, 334887625, 978303945, 328504023, 748593223, 576101499, 437169173, 173108493, 946883215, 496905573, 949736406, 984861431, 570745769, 294373429, 831414845, 438587198, 214080081, 718457860, 173932785, 31959969, 363624059, 337474761, 516826522, 286854145, 711681662, 86957084, 927715972, 349623021, 905886379, 268517278, 536500735, 985500636, 874924925, 240187834, 906962374, 262432883, 984669155, 315384824, 875485346, 263137429, 684406473, 97118433, 496132408, 571600994, 954885828, 909061101, 916175593, 855460872, 82814637, 604825194, 341772826, 15933179, 461691469, 416513623, 476357432, 881830523, 239025806, 247083796, 412109978, 218618036, 46579515, 728667714, 222584212, 192185452, 801472402, 466028628, 67926912, 839244241, 245684336, 256502675, 576026760, 761450449, 62722096, 67960834, 402818691, 744999853, 369358778, 49965002, 96240848, 542977470, 339383042, 985278541, 505152225, 176986615, 178452457, 608484024, 191555992, 75907158, 283552191, 605602787, 512698690, 956248133, 793246406, 892149214, 964434441, 856652717, 374930396, 779307938, 91990923, 974899193, 552583425, 289817354, 991730426, 395620992, 840079287, 47910631, 576422537, 671184287, 117427893, 38060390, 363539633, 399062260, 974383325, 322050421, 659943292, 540190760, 985638361, 360570098, 796459988, 192411885, 660452601, 450534589, 923982619, 705158025, 366215282, 555580300, 900050308, 163252290, 639158947, 159474419, 481144705, 886520134, 271943846, 913797184, 528906928, 150477693, 585805577, 350871491, 324232814, 877331431, 275238203, 675806893, 383936412, 669745560, 567330246, 479512137, 219161109, 305914009, 444087748, 652757731, 51343885, 880581106, 925734929, 370687677, 610481790, 919431500, 241512979, 173036273, 166436323, 650540618, 395433860, 573614263, 582178035, 974797978, 765379232, 275369815, 851887339, 770637640, 234566094, 974000159, 358866669, 183712548, 502476229, 636129360, 847830438, 303340468, 705743822, 336135631, 597745553, 186608495, 215744263, 413707261, 115873754, 72798800, 138659280, 753892100, 517292647, 948460549, 161473180, 683967442, 99055862, 210584138, 401371242, 950110174, 795594389, 73221008, 584838777, 572766898, 591656969, 351380237, 769831120, 371504746, 78514097, 351941478, 862679989, 918968824, 497404714, 949397901, 132784569, 537645399, 9101231, 97835962, 816006267, 317211218, 978899391, 407730389, 112450731, 273013522, 46213834, 882953986, 310421144, 927664732, 40549638, 384424383, 972532932, 232980210, 927483129, 217290376, 503306055, 633717606, 53964296, 531425399, 349553971, 514671483, 743598712, 394319311, 412741298, 98708025, 623015625, 597431829, 847877676, 886425061, 949455281, 181039518, 31081154, 547679619, 542770232, 541825349, 194418368, 885130927, 116382441, 351031134, 87075468, 994195445, 106087227, 814876567, 717702564, 384056057, 435765333, 680363813, 427099951, 503378936, 450791286, 404304570, 159791820, 541036012, 721857517, 35724119, 860342781, 282979985, 444729916, 917132226, 696325897, 564334147, 672288371, 612903898, 717111160, 284526835, 426511595, 650831543, 752188850, 215582272, 346424501, 273228374, 13204293, 636281616, 800767701, 781586125, 832034491, 437055079, 325522999, 644780078, 724473387, 297979118, 502927603, 377903439, 980026974, 352963636, 521598530, 934997537, 56029913, 629910906, 71094962, 203496683, 532751995, 111446570, 993655084, 321560471, 313766510, 566544695, 330490822, 348388797, 616052632, 376678058, 739801779, 498249339, 153251435, 781553408, 604888555, 545548040, 766877960, 865623343, 937953746, 345366986, 424893590, 749861164, 763995236, 581975284, 810422001, 606087635, 58581914, 98994219, 119008779, 313866427, 874782887, 794808459, 60750968, 343902503, 244027079, 753104225, 126343750, 764120766, 89543885, 464139233, 263941545, 737367143, 289975882, 18108247, 594376885, 438064249, 734664595, 763247619, 217717647, 95325590, 508107827, 329049033, 820335679, 942461922, 180598819, 650057625, 523227406, 230485624, 380932157, 113257107, 104684090, 593297848, 567717716, 957881064, 858640368, 840669771, 240395101, 831695519, 575494988, 816535124, 569132628, 787780378, 641551021, 866748442, 908386216, 5888560, 903836232, 872616641, 45586464, 956962137, 635086737, 381911343, 97899683, 345340008, 467688833, 403418404, 441066549, 812370027, 415104537, 386105233, 632481219, 469114773, 675999692, 90162215, 911316063, 281179531, 591945881, 547640697, 377801440, 106283636, 604650372, 418853890, 213258916, 157997632, 647764563, 860381927, 819719482, 158116261, 535822700, 447542568, 552768184, 449732043, 420225606, 732528239, 165413435, 719651293, 898263757, 537926325, 621208907, 155860426, 401169890, 581280148, 425545139, 73343384, 991612810, 76779829, 313314830, 756056535, 561555997, 844459155, 556279762, 944496663, 358057845, 760662863, 618595197, 368482119, 977612404, 90679799, 440292651, 678960633, 880233891, 727386049, 512278043, 932988087, 992142631, 766927146, 279436876, 635194573, 739147253, 452974351, 409885462, 570553941, 144265610, 423027857, 309159656, 448299313, 265166326, 66748251, 113796046, 514483426, 276370823, 641672962, 581496340, 642768570, 991519231, 793515687, 155089262, 145181707, 631094977, 426164096, 504770071, 36898109, 535301648, 493435644, 3169093, 205159414, 464853899, 786768301, 932191955, 389603844, 834595694, 65346934, 319201431, 565472344, 891656567, 755791215, 769738930, 725339122, 51276197, 28717536, 577457239, 223392536, 961644454, 185464527, 506100216, 630039651, 896168734, 353259669, 709106248, 143990392, 651369500, 32104283, 100521041, 761668453, 557282113, 383173974, 784897032, 85156241, 580198086, 88743711, 620847468, 553502150, 985238875, 697971313, 555140076, 161420545, 443722564, 467370912, 890771207, 345391748, 752897910, 667617079, 327857047, 700180109, 833485528, 304300941, 751116714, 605295173, 516303504, 923339569, 666096346, 955807804, 98906423, 171960623, 856717451, 384270544, 529228337, 573758573, 224361463, 515020579, 57337569, 520612678, 448596326, 513624454, 791340730, 823849875, 687354827, 139238492, 730448623, 153139633, 446645457, 340458392, 514910188, 999846821, 947884810, 431188062, 394935633, 480012559, 119373754, 259479120, 778646724, 122034733, 831507094, 746248289, 377393744, 375524744, 290861737, 372713625, 258124587, 555561971, 761864123, 701209528, 313364399, 134759962, 337078597, 488828035, 929741404, 659311827, 217633113, 895289031, 257411025, 931628033, 804592198, 756916101, 761935109, 531257416, 338511817, 828631538, 835014571, 722381123, 277785650, 131139175, 401667690, 530515791, 646569527, 775195411, 540386481, 973313165, 702117484, 62331172, 141384210, 177260638, 418440071, 879929740, 185434195, 93607477, 746581038, 415832002, 978258174, 519699974, 366440111, 324725623, 696293772, 682263995, 374819066, 940797500, 626824268, 337917568, 51895193, 668050504, 860284871, 378000985, 26455365, 994671091, 21470009, 876683303, 411838582, 986765916, 996711736, 680808985, 1992976, 441384564, 694267866, 949442540, 207187860, 392381305, 19315077, 462468293, 39207864, 1223287, 417058646, 114190193, 771329041, 360657325, 221825334, 42479734, 160653564, 219646772, 39600368, 577068266, 212707246, 994249824, 523282043, 841988468, 310639320, 739839874, 216507364, 884928616, 596803085, 731450801, 470982790, 916256032, 63759935, 865253122, 291614845, 385889241, 787033065, 138930187, 5568905, 160384919, 619453192, 1373593, 472495251, 774092007, 997660154, 109252089, 555341421, 453666476, 165840113, 990195916, 40951905, 637611284, 534217217, 920119164, 741963437, 457897113, 663055344, 502537420, 643642484, 217202389, 485693891, 609023088, 159382105, 920902283, 192953702, 478048090, 779800679, 521059098, 110555287, 286227091, 263860289, 100083574, 697540267, 220321070, 855537879, 586017280, 988268788, 825687016, 300690817, 710978572, 486101952, 40670986, 49523568, 886115495, 598136964, 238387208, 885019689, 287891572, 804153462, 817453701, 149476972, 411780719, 696050838, 405563208, 176868969, 935034139, 610169747, 725047520, 250683337, 763984100, 262727000, 634542993, 532170826, 320560217, 953691048, 630513950, 57250452, 531255481, 345593815, 774794089, 467132478, 360024512, 19807963, 340623420, 10667795, 728098010, 176123521, 332903394, 681305392, 670351047, 677606852, 423842557, 868602908, 652630282, 149062905, 988230019, 591596426, 249013178, 307305840, 319434680, 618658377, 507731567, 376415156, 597182115, 602360185, 702872487, 731752812, 173432108, 597002763, 681203406, 413905449, 961519356, 726110833, 44335583, 66508578, 457829511, 437679644, 175908780, 528985568, 223337673, 254281668, 267221479, 924043504, 863893179, 749392632, 395027497, 818204468, 867261327, 664922465, 940778463, 719838781, 427174265, 109973243, 367412165, 916246796, 438538576, 570981272, 878925539, 835608183, 52331390, 188562365, 852169375, 702809113, 677139191, 812290249, 122723023, 890750031, 638745739, 140563721, 744215359, 604206992, 440617205, 560417728, 641189121, 720195630, 605821867, 756136040, 206431465, 256000032, 259180556, 757389738, 444032174, 223029066, 173779790, 369275547, 834545963, 269968082, 567462390, 871469547, 24487227, 926351102, 537463934, 522061659, 268400608, 169859232, 426815434, 640170591, 937543219, 203091009, 50499079, 185946464, 670748700, 772155844, 791908060, 664778572, 424273218, 654437618, 846486650, 65029432, 195073840, 743660021, 264845812, 990065157, 755474685, 931476484, 971288256, 241097503, 761494161, 630313996, 875457794, 740643102, 847628591, 490352173, 894304840, 224086577, 185588638, 318131294, 723672672, 223685962, 605473087, 515212559, 676683257, 773755282, 868485503, 879978678, 813354431, 68712, 933774528, 103626157, 59437082, 804501862, 347187664, 129830171, 643328618, 335590058, 354582189, 949453710, 212332931, 905486629, 356262905, 434068143, 265289208, 212093810, 509432069, 625368447, 612945418, 872706841, 299589006, 889373385, 399752599, 894186264, 750602667, 359311390, 347290695, 992741901, 495768068, 416775818, 744400249, 535179545, 73511250, 986969801, 568470312, 592952081, 587766751, 557205084, 143139339, 94827725, 875115018, 1032462, 324532220, 183153133, 862246443, 959056400, 104667481, 835368612, 371914679, 744284846, 314223660, 370265942, 343640509, 623385243, 674350958, 611507910, 916898996, 785828743, 337145763, 836353050, 990590761, 948033819, 391138508, 108905617, 564852851, 836077056, 494975721, 84176809, 757123563, 614531999, 10343413, 561095841, 680093841, 985773455, 784513856, 871703746, 802190559, 110129960, 872966436, 186310298, 739507065, 594842795, 136952604, 333691623, 909382975, 242471058, 297682157, 866514590, 339299471, 833025975, 393850810, 102287938, 771711060, 673097170, 796925108, 519495093, 459119373, 385447029, 920454574, 174753003, 619169869, 397505201, 210782412, 127132590, 452624917, 664032153, 569927375, 576181013, 270504796, 568200039, 253823343, 49856321, 56715367, 147972557, 289518890, 547209913, 144123941, 904348403, 481608118, 653262698, 398500078, 284449262, 652872289, 150791980, 531984032, 395713617, 813648100, 113090667, 308300923, 174678075, 25576278, 236305461, 51026154, 663276003, 844352294, 107770345, 592269651, 832945895, 635189323, 146818167, 720159403, 228662308, 271596447, 342509522, 840196184, 366624236, 260381388, 794575585, 702135832, 591217443, 605011, 55342840, 583445830, 367487543, 775337111, 800998936, 711197199, 255558140, 476610816, 56528449, 298362629, 680275832, 765666487, 404434888, 665644900, 982532839, 282158, 601124160, 473025376, 672558525, 444579964, 523424762, 109341323, 131053069, 519371490, 440453678, 92768559, 846524512, 82656137, 863055152, 356109549, 743718814, 541206751, 997309690, 479665957, 277392588, 858701153, 938717046, 659601089, 517343405, 294304041, 365665538, 324441535, 72195115, 658650687, 854487155, 763358541, 303754221, 209050812, 294831628, 129382055, 258258792, 814723111, 597578813, 952454438, 616088626, 401261434, 777494551, 148300857, 219039730, 968719857, 842136740, 317169794, 709810161, 591383182, 717882005, 665260761, 930203249, 691191083, 691112625, 820627525, 828970560, 285420318, 978916657, 860300187, 324437785, 574179301, 638118320, 371636002, 722042363, 193174857, 698435464, 62485572, 799726927, 679448743, 474197154, 233480388, 89979131, 533690196, 858372303, 307206724, 815822565, 101545749, 306239651, 702467327, 459101574, 848219393, 376283160, 390584973, 185008984, 211068745, 356805334, 617705301, 546058832, 432418825, 479113482, 499347565, 821220930, 465766385, 883215064, 59381718, 542250219, 844132733, 866803939, 239455952, 15809585, 790214877, 39048321, 157215208, 318573323, 620893916, 773677075, 4749746, 700827158, 424195691, 812720612, 479121151, 384733679, 92300987, 153964567, 91750758, 789883784, 545416986, 841943814, 765525371, 71352721, 837693126, 944481810, 307011376, 460582925, 408670900, 111107848, 668704089, 359281735, 598887255, 199491662, 698734831, 78072221, 779139427, 843608025, 20640411, 456192304, 595773491, 991663719, 290315380, 681780322, 501740116, 920987595, 844197544, 773202549, 614689326, 891712063, 869020785, 608165966, 686705527, 894075341, 6992427, 960697594, 35177662, 222613790, 746039622, 690071515, 221341575, 648920023, 528305300, 440675228, 339399449, 614803745, 751741738, 90603494, 630252467, 574902326, 827573514, 169816246, 65514125, 127663375, 703740251, 522755165, 238732092, 617218800, 923667880, 75003320, 839462802, 452832923, 538109747, 135569750, 683571523, 751337865, 735048142, 70660344, 503540789, 779879583, 305986786, 36759197, 509915016, 491611419, 674920812, 329665121, 409078005, 316595185, 822664324, 97786993, 117547493, 97080545, 211945297, 328538000, 754895975, 949632416, 125540101, 649892869, 502725636, 154517206, 861778399, 413246787, 504372709, 297237073, 734963949, 288638126, 714593414, 713424653, 45241124, 193742059, 430917132, 745201182, 191273411, 986608896, 621437497, 300532368, 244888031, 548361033, 230739495, 259141404, 769985552, 45705784, 495871904, 216479244, 879272830, 814595889, 664243384, 751777761, 889727122, 699733073, 868457872, 616783444, 694567693, 27327750, 560737142, 645467235, 810554339, 909942889, 608744688, 506210293, 19067099, 333820367, 38849835, 343989917, 345831605, 99425163, 671024755, 378464694, 886358622, 426607076, 220971988, 637854090, 939035233, 304860418, 257339018, 947262541, 826075851, 895353210, 13138035, 265134581, 768000656, 860206089, 430405563, 916003094, 362720599, 400752842, 838515533, 267714871, 106156158, 83030303, 532549435, 571587656, 750558585, 974602402, 844139018, 788365889, 159246578, 27831167, 199170229, 429389948, 200400142, 800969947, 153348234, 375033237, 831414656, 862522345, 80938336, 245878915, 652712013, 417220477, 40885557, 522020032, 643402222, 749690274, 392060261, 285707483, 514921154, 499378454, 790870020, 914966900, 979658989, 21689350, 930050464, 128124379, 25557601, 427415723, 892200047, 554106345, 736514215, 896221868, 675966940, 899436423, 753930968, 728751022, 8330588, 756776339, 460970993, 706061703, 277108859, 614749267, 458126200, 511839457, 822749206, 185709602, 696969483, 906384662, 287061067, 807773289, 130357076, 625862490, 437419698, 793075591, 772161164, 680302314, 509709407, 592805242, 957902877, 746383991, 500775288, 150082152, 64431636, 239202056, 736944420, 925411477, 702807347, 731996096, 268165407, 954595096, 730174292, 264162356, 156690300, 450174632, 927300021, 276258031, 400080922, 887669263, 927498780, 610730110, 127628909, 801750825, 442064038, 505560615, 827294940, 568497788, 845049508, 663055848, 278679299, 682952735, 16983169, 198442752, 327546359, 158500012, 135338222, 322176321, 76724776, 853223705, 751982297, 965344768, 727726872, 441598276, 488426260, 66648211, 84919442, 788228026, 570208794, 189411009, 876321216, 756813117, 276120323, 287904645, 190660294, 212747456, 919747262, 279036451, 941947603, 671376602, 788855036, 5436792, 539618110, 754928056, 944176761, 124030881, 736714314, 984911634, 437133441, 998012228, 578143121, 268107221, 413617346, 74314974, 59434487, 18402438, 148213163, 856850852, 897834029, 196581656, 201967344, 556993678, 677759193, 571333318, 739611743, 647424354, 218893656, 540188264, 116840933, 612964714, 716160938, 165807628, 498488766, 435166674, 592677192, 489276931, 730322108, 581217310, 683592009, 971317169, 256967467, 766196124, 529584757, 737744781, 343247537, 688303094, 788846285, 330228371, 625720592, 126290285, 916187191, 231758306, 774241050, 609918804, 680976394, 261799999, 601849729, 369789293, 746162940, 815039740, 551588850, 236583478, 4495067, 195481748, 525709670, 607782855, 611551663, 917490056, 340233301, 128570689, 717327254, 834380414, 745099991, 426728499, 332236313, 131277044, 837274596, 478697538, 348918814, 257690633, 930491130, 398656811, 693653332, 200020986, 685000767, 711903388, 279831039, 937476260, 471638032, 278768612, 353568814, 737933664, 823423962, 976365600, 675300923, 387714272, 106732068, 953842875, 33529716, 784190377, 888279118, 256832408, 562061025, 280601307, 536400055, 904648047, 212890818, 628812665, 659537267, 441723275, 932329138, 78183277, 290257816, 173618594, 282551827, 53592538, 345325589, 500939637, 105609979, 398165327, 521712590, 356846408, 923121739, 388576684, 985225379, 161514839, 754572729, 620220787, 823617025, 239268074, 665003488, 784869383, 715884582, 552771492, 480161803, 574279407, 463880598, 626693893, 947500469, 692241200, 116309969, 391685893, 450174494, 531480149, 955016868, 245657595, 384954399, 167474191, 34785714, 794625591, 428957955, 536633445, 502607610, 913667752, 609968835, 264598818, 508897061, 623260390, 639910344, 535311934, 33518950, 243653939, 475273488, 688013693, 72867694, 11624038, 345253356, 62272900, 711109476, 898716186, 837042503, 285820721, 724173829, 420968721, 314278311, 150184316, 303955579, 404873173, 334974826, 508764860, 693046562, 373668633, 488863514, 647034749, 773130332, 453243753, 17832560, 351760022, 911265991, 525241895, 530114025, 62538847, 414688123, 754529433, 195841987, 143917960, 648847083, 108348088, 599342714, 609842114, 342851243, 922769068, 957786687, 131901941, 976964618, 672352474, 23881159, 684938150, 31923204, 14704804, 808471305, 443427946, 654961480, 117337781, 836374353, 195921793, 62674415, 528250768, 179137687, 41253847, 545533217, 412471041, 408174725, 850968821, 14815097, 633010161, 658485306, 577710985, 319611471, 624971221, 897040606, 971736134, 435083519, 745505820, 149669098, 162945539, 747962377, 302850389, 863306090, 851049851, 145334765, 533659149, 591430224, 649908576, 706104132, 373003917, 127761089, 984561923, 351775738, 178296336, 477606830, 823630447, 377515322, 879240084, 518822823, 201851853, 157365704, 46760978, 629672740, 963252130, 258234556, 411665142, 714178913, 845897604, 644035202, 953222193, 390842572, 803361224, 826805528, 734561170, 121572174, 446511059, 48546484, 490111194, 747568558, 622496723, 678552283, 476865017, 647849945, 48637404, 10414258, 711496396, 608820916, 492491124, 558263430, 579232544, 731650675, 742686102, 932838365, 531342236, 890567541, 558550733, 374085108, 423346511, 12532262, 177118124, 486919005, 395515185, 638495821, 509677164, 288715859, 993400956, 77413759, 893783750, 818852653, 386193807, 843850448, 21341923, 885082809, 814154101, 81371672, 540010766, 433676506, 68571958, 421153379, 224421183, 576306121, 544358915, 397719403, 46905799, 242040222, 512895521, 276791972, 11506804, 702559749, 81374668, 192592290, 333951138, 479108356, 498048864, 333206694, 641119284, 602215836, 194891310, 415072834, 231219824, 192017069, 74877383, 693844104, 271748795, 255039908, 913419581, 144830820, 158292015, 909993670, 877023984, 951869396, 845713225, 41455479, 828886640, 645946496, 560197047, 978174556, 274849297, 703262770, 327792411, 730343730, 383638601, 619219751, 903376078, 172597426, 487319815, 432392031, 25529428, 167918172, 971838432, 371052021, 790879569, 199830433, 315302479, 172624758, 262523972, 391640871, 663045201, 779659725, 663559941, 995840220, 326927391, 690079474, 664649714, 23302010, 613494190, 603944644, 876459319, 921834124, 259522236, 285787193, 904349416, 685835593, 529157573, 405450599, 581870564, 481422819, 521712665, 107094674, 831624627, 496461815, 97991715, 26993455, 132532001, 351396249, 247099210, 982883664, 18529163, 960316102, 340365848, 233938040, 866981370, 156849318, 551886198, 294734297, 998883456, 894224856, 461168407, 543057751, 481484615, 388890827, 485803080, 237890849, 711025582, 7798871, 120260415, 876745099, 767985, 139593230, 355716345, 783346681, 863339059, 706503259, 476211250, 375375937, 266799981, 90461695, 836867528, 448317301, 781753016, 950962970, 34845814, 883692010, 463909708, 760352743, 228743106, 597085057, 834356568, 477018703, 20761995, 41355138, 693064899, 593082101, 830546646, 850743595, 720372275, 198526031, 456498252, 641852415, 645731430, 599897213, 176130468, 344706277, 29609200, 692299732, 342050668, 367459235, 858250438, 366228502, 431538987, 153902750, 218161079, 533030595, 300865711, 981542865, 244297708, 341325073, 351674226, 380006293, 535316719, 494111894, 799922591, 18975423, 688524171, 831725589, 123053372, 779154020, 871512970, 911303259, 532162958, 689545728, 194303481, 717115355, 848460245, 704406319, 233538127, 505742441, 152420017, 318223202, 136872939, 155174233, 409731440, 373951452, 447466355, 882887045, 687425063, 374617164, 562570487, 263917743, 953913754, 164225879, 633781359, 437971010, 678899622, 416973822, 389249019, 418056234, 538744186, 522233294, 363269025, 42366404, 862319892, 658738490, 951260869, 2074222, 770943551, 909533089, 716766650, 113067266, 936704285, 198768744, 413026995, 852142709, 522695249, 217809971, 399946030, 873641976, 474699758, 847929693, 877855794, 740121483, 117036889, 447269506, 905978718, 31886821, 341201785, 635435051, 789202008, 485588167, 981953009, 299990169, 979646933, 928892969, 224638562, 229444081, 236619011, 838780481, 796981991, 576064084, 71219667, 908670845, 16125923, 60266384, 574844883, 338047007, 298876216, 90191366, 86716336, 18841566, 855258816, 277946752, 420531567, 970412775, 921675857, 83554543, 973203572, 9269616, 551339376, 657110071, 846337112, 907154914, 667934824, 184568667, 890961242, 95608076, 649200168, 462152104, 109368929, 605098409, 160131566, 526145838, 270526892, 175025811, 870418802, 748063620, 191820087, 104309019, 229508739, 989533191, 578188847, 373924473, 418084298, 44990262, 908867160, 992778124, 834341685, 86955052, 758089024, 418859999, 326843271, 443573833, 330247761, 758716988, 56444840, 259942594, 897864514, 759399216, 474845773, 148675669, 598141471, 400728739, 209586193, 404459529, 419171942, 10934811, 517306464, 289259558, 747674369, 379826641, 58995218, 447669745, 536173850, 335611648, 828154897, 562245363, 304858875, 82146801, 684391862, 765120117, 414199302, 687379833, 560943039, 645848924, 962814136, 923759823, 597850538, 306151488, 33568566, 12581475, 919211069, 281800066, 176504487, 212373427, 171131541, 796227595, 116993898, 833618793, 923509287, 754529102, 565432340, 926876623, 127622889, 101379883, 198433136, 473697261, 214422967, 44033279, 590168617, 828773842, 570496761, 376599774, 574012324, 874605094, 617568120, 564635532, 217790377, 913546076, 916742131, 730974623, 950138688, 977331224, 935002908, 431795366, 736589168, 440605709, 87808351, 804552327, 728841904, 420470545, 871352306, 234611640, 146877941, 904429079, 153463728, 565911599, 332309459, 918162042, 836132134, 632745115, 665204260, 806916011, 451988082, 35100691, 538230500, 880448422, 435029027, 929069425, 187359420, 348790055, 863414497, 838246050, 307507092, 190925121, 64553283, 592581318, 405108560, 235150380, 841031510, 296614713, 732765781, 196635321, 144309093, 446048400, 978246086, 876915514, 957097065, 572760684, 414621828, 24122606, 762071222, 179012109, 65144543, 889329811, 73783470, 655117254, 674680654, 947359504, 791448564, 970274797, 223886853, 206755623, 82689138, 163400772, 346003434, 13296248, 847049408, 574307409, 552033516, 727470464, 280204584, 547486435, 888920096, 359878424, 762510063, 697350351, 709038246, 105669161, 706834228, 858091936, 930040417, 829313071, 792649306, 83111061, 44016821, 673846464, 434137970, 747190778, 656919241, 316133636, 855015111, 188790750, 483124262, 570460689, 951491401, 654219080, 570515356, 126269800, 68301091, 583078895, 140496262, 255309127, 987817496, 82181860, 470600388, 654264920, 548708167, 774140019, 934530250, 755718062, 630033642, 842768264, 189883277, 18371623, 869702054, 951671079, 451653556, 440035507, 723392631, 802954650, 396545016, 518026631, 687616172, 622731347, 396759784, 491705622, 728279464, 310296131, 657951068, 551324960, 522681464, 227745582, 703874360, 787797177, 14974642, 697151586, 745857720, 691577029, 70616359, 960171991, 853977886, 952861625, 878793462, 430791560, 937010952, 337327311, 768181655, 646767123, 978431333, 862711513, 957029660, 468377087, 866787156, 677740022, 903793358, 865976254, 899406935, 422531772, 207277626, 642444187, 785081087, 675754384, 978977737, 285489447, 725340716, 511827248, 219152589, 472617994, 644248506, 375483977, 197267910, 72560826, 747767236, 400384042, 830159691, 377370234, 71479127, 573692714, 895310625, 142110021, 986364186, 21066904, 671021601, 33741887, 855514369, 862654073, 783002241, 774535378, 351597300, 518598918, 53226624, 474360690, 403335506, 999944692, 491278063, 429839323, 955993786, 239582465, 293449718, 825970531, 518085770, 296723160, 502135698, 336561562, 895705885, 180905730, 390212730, 732886498, 797887546, 136759899, 199932375, 595873928, 523679647, 849819075, 340026970, 862610966, 96275366, 129612792, 651970168, 90322285, 108382286, 801804043, 419413770, 214595434, 106711886, 58876300, 627895719, 573373953, 450672341, 734946425, 918887542, 672154759, 554783904, 229727484, 249215752, 732912231, 352997882, 767260825, 718429478, 83085887, 263969756, 787843632, 466494625, 20562286, 943194304, 187462704, 866828436, 739913884, 592675592, 171082586, 680907746, 881396799, 735195900, 17408865, 65587320, 701222421, 524827628, 611585393, 195918693, 102026857, 598464155, 466012142, 315853291, 289794383, 913073837, 949245034, 63729762, 595850972, 756279634, 797674817, 572493719, 500660761, 786069914, 937165576, 738997059, 659007575, 76620843, 825235912, 379640596, 779176250, 625949011, 685518172, 309089511, 683044033, 822004170, 785795086, 262230636, 325508649, 161139707, 913059182, 705963834, 820344148, 605058038, 716809139, 112372584, 162984492, 572553379, 972134674, 968123883, 940275441, 206807251, 787800755, 106828622, 444608304, 159691714, 152316303, 994962843, 128746828, 463405524, 704197154, 291457526, 502690110, 557410656, 593882136, 499238184, 317143740, 294818755, 921933443, 985307091, 545460421, 576998031, 991095584, 127946650, 436563195, 721053941, 587787775, 461068402, 849650925, 692759697, 935624366, 603653088, 576521927, 808129034, 863271002, 212413735, 753618710, 99025521, 201082598, 204251329, 173538994, 814173630, 52555492, 401274348, 278567921, 68444884, 355148790, 669398468, 643236669, 993919975, 30575111, 29856944, 978721268, 678042545, 976705676, 410162048, 634877058, 884891648, 624043468, 979091230, 799781580, 273082725, 18516849, 882350691, 810323168, 955389040, 583209581, 924449843, 995022691, 955120581, 90220437, 160614934, 69325233, 748685031, 820988623, 207298043, 561818012, 458427608, 131749022, 147129852, 181185864, 287770224, 905945813, 587529337, 937377746, 792843811, 722537849, 395054781, 263504557, 722086050, 702934844, 743285861, 996062024, 213373806, 606870400, 387920032, 926402575, 446149668, 956813781, 735611969, 755902296, 638146534, 598794707, 553222317, 301066294, 164606345, 73799782, 356715365, 841759140, 843296862, 285580007, 618156625, 457764816, 7999090, 551463253, 953728347, 634559109, 976910699, 14182691, 150349685, 59350106, 292203960, 617633744, 35126192, 232521082, 715180471, 729762450, 60941512, 641851088, 350084260, 306089213, 17592030, 512491615, 28844065, 187156198, 225250796, 190449800, 900080616, 887134814, 389220428, 355390207, 560500920, 498644676, 873820210, 712402331, 659900450, 470218551, 905351594, 651258982, 98063428, 467635560, 477432369, 487060634, 906698379, 963149898, 297928102, 422163813, 281678713, 632851979, 809961645, 615833044, 381550780, 169784931, 541864682, 436075099, 940121057, 42927975, 713419166, 178545767, 38511897, 128859195, 403623133, 927333330, 689572215, 746718914, 592617294, 856686216, 521802007, 787662955, 780904780, 780688960, 21600988, 463090921, 291951998, 124048549, 602240639, 311175359, 182055115, 444043370, 198084588, 32051111, 2186066, 743616412, 667469987, 670007448, 471146750, 808922453, 25857930, 678317930, 121763418, 740137143, 446155326, 691765276, 722899959, 749156797, 530420615, 228805486, 454570546, 688521215, 12435306, 876096398, 596550304, 764623177, 512126590, 657757829, 68135402, 297860268, 420530132, 630819688, 817107499, 246247955, 809991224, 411886127, 518939277, 967731022, 530676406, 602621248, 854776041, 316537413, 315299670, 825385984, 873649961, 78424378, 454138745, 465442376, 473125849, 141987149, 240793459, 320509630, 25557509, 50622734, 326359594, 764037924, 658613468, 414792324, 306209033, 551709051, 471259096, 656374340, 514545120, 15847895, 27667591, 2568251, 923558434, 158298773, 284425184, 276575576, 918749072, 900568222, 626178040, 225807608, 59258737, 392084386, 335426736, 804146913, 554966838, 997506885, 498616566, 906396919, 192205654, 633723859, 193274019, 502291082, 739955416, 978043907, 529396740, 409184078, 251251844, 850754760, 532478547, 869993056, 719280586, 246526683, 626978539, 468978122, 716707216, 945504218, 650708016, 994635523, 749909907, 474518703, 307325669, 390416305, 558876691, 732209884, 355686744, 833837668, 324865649, 915575241, 502343627, 231732907, 590611734, 186621747, 606758076, 343054932, 299439203, 625114615, 104314319, 185077059, 84163275, 800459525, 248332292, 929926296, 183214398, 499312485, 997563186, 317666973, 661401252, 327322936, 543632850, 746448414, 828521808, 249145660, 284267927, 701149154, 618826659, 86339995, 580605562, 321477142, 800884299, 640661992, 750002036, 768429789, 729316423, 725047592, 227625517, 624276576, 709502420, 856084176, 249449147, 554281864, 786299665, 183730323, 233873529, 923841613, 218907663, 742176558, 239729557, 508083368, 929891699, 76273399, 435312203, 796859831, 861523620, 687601818, 546023307, 548328398, 276424502, 46989841, 142603024, 132325279, 971868426, 901768515, 135021046, 256109534, 511669139, 539095771, 28431706, 681202262, 348358344, 670237128, 79456034, 116790086, 648773818, 6571368, 537691417, 188404585, 174959816, 909367324, 955444192, 890446942, 525873194, 980942420, 355973871, 715667392, 749835997, 569847508, 80156877, 116825095, 736566846, 937578533, 201822361, 179069628, 438701050, 586101656, 514542825, 626837327, 637585034, 865213734, 924983474, 260709840, 111368207, 373144288, 80941801, 229096604, 214132772, 769497344, 588819668, 470492690, 829857179, 362069079, 699998526, 420298437, 191166498, 399382717, 441925636, 841397958, 635774397, 66388152, 740669055, 972689053, 565473083, 449099401, 84303023, 735196678, 118419462, 833236580, 971722697, 856735691, 149117333, 347527538, 399196400, 75316451, 478333214, 65117228, 578377156, 658390157, 435998420, 509896680, 494613942, 54168955, 624735119, 256536258, 889635259, 509365132, 1017782, 716397154, 74466169, 105586827, 649198459, 720995806, 360182025, 535043311, 59783848, 416999816, 826285520, 97716099, 743846540, 268175761, 612462842, 565933780, 371445232, 465598745, 992761595, 344960898, 739880291, 83611715, 108432569, 869289197, 764989527, 793692863, 939726721, 283525384, 808186991, 587983632, 656450347, 337059806, 129708358, 818389465, 491032316, 110222832, 179144248, 692263407, 621439432, 348103944, 571363338, 263413616, 373873159, 891075896, 76837531, 508938676, 192308264, 659310729, 764236614, 975067720, 597178919, 793136083, 683155750, 148257216, 270380643, 754218127, 254600842, 499031267, 393025947, 396627374, 881515236, 81020459, 981397574, 491634264, 335921874, 973975913, 810540894, 308465080, 874124922, 118604409, 748976137, 969951397, 827219393, 257597422, 905398636, 821339080, 874319265, 771506463, 431368074, 230161956, 893424337, 58729388, 573168778, 881628426, 316283679, 119622782, 226520479, 744506366, 128145165, 507156444, 318968821, 357717550, 580764069, 391247181, 516539224, 923623423, 586383510, 113493870, 104178706, 209420495, 204015034, 966527439, 852788214, 813561272, 877226613, 563436033, 305063567, 763447218, 765064465, 592701119, 305657855, 510556925, 598925401, 434303288, 726363435, 834381936, 354824074, 195556487, 245640745, 125870057, 641521232, 1488252, 272797628, 793852865, 419743817, 273005473, 610498964, 322090497, 748638841, 357056918, 915222611, 337306102, 957045887, 753828294, 96961187, 576369482, 986513249, 858270497, 819782320, 506721350, 977939591, 429482977, 709059481, 735685536, 128125943, 486177455, 367388783, 979157840, 765638850, 610726083, 761559917, 871509691, 1770220, 915768697, 176163207, 644057095, 627655, 185873462, 909498332, 325910820, 601991449, 980283437, 177509787, 471999357, 994590045, 807967769, 291033890, 769420457, 725630898, 381985222, 893666040, 114907076, 358766973, 467372447, 609768915, 337087591, 292204825, 861076813, 275891453, 475915380, 94901004, 179790090, 811575571, 91502124, 989494766, 107948573, 113732138, 104746314, 968102864, 481487871, 270517608, 215966860, 987256830, 868600572, 342909270, 159431393, 199457070, 153075542, 106434517, 144597913, 61090149, 104798778, 510536769, 615947122, 446682314, 739875748, 232382352, 697234800, 614093747, 214914912, 484439384, 775250329, 714612292, 889603162, 167042265, 439594859, 44520150, 47251637, 295596824, 367078508, 897006258, 883200325, 910627170, 135030543, 604099144, 348758898, 629842175, 88443441, 265543390, 670026063, 117214520, 699687286, 114153234, 680254023, 97289331, 866037115, 927759759, 408315364, 977035564, 428952712, 537756108, 838155553, 835617258, 564382187, 959951323, 503484409, 375885438, 320408853, 786713922, 802758851, 935178591, 245796565, 87720528, 76912345, 320618762, 199305751, 357195747, 253402262, 507143098, 203389002, 33552830, 164643877, 234643071, 582840399, 324341078, 750996640, 653505372, 159198524, 282962826, 108057725, 82813569, 984537007, 717848481, 525836452, 208947037, 408675593, 283795358, 70130411, 552869020, 985500739, 446064081, 578760101, 580395152, 908205488, 298838982, 91811369, 142984643, 346571781, 458667497, 277084416, 724172852, 79830464, 559700738, 910655980, 623397821, 91004571, 24110317, 66314396, 41121993, 958677097, 791745322, 260185776, 440795843, 879686042, 682938300, 92891768, 9388318, 624560943, 375767631, 783932111, 919457675, 501917189, 350790539, 894490199, 10775503, 480563552, 955694687, 661929123, 258443586, 750720164, 74811647, 746138038, 931172312, 945347984, 996210952, 405857107, 585537125, 427326478, 809731010, 413215097, 234584273, 33462303, 43224590, 819320466, 793758958, 573911918, 303339034, 943110132, 195814952, 627028779, 228016209, 585816738, 116420203, 869300616, 940360505, 229969859, 504674450, 573472751, 362664623, 276704689, 776871715, 793024067, 689457243, 669121182, 293169386, 656260961, 146824261, 908479365, 889515318, 700588291, 240182370, 373457952, 172798075, 10013437, 969093113, 137214406, 618352112, 479692427, 770031429, 230130694, 243351473, 190730970, 670508813, 158472492, 441690289, 527904974, 382049109, 692673439, 949869349, 397879339, 870012563, 206843581, 122587988, 812532764, 363648174, 630133990, 626299972, 100323201, 882555328, 831985930, 144299496, 827909867, 227497108, 182743273, 426748226, 594513070, 788499201, 287532848, 288957479, 313857962, 437462540, 511637766, 302574519, 28057515, 601950432, 588126606, 462221788, 767233597, 324095892, 943522566, 899729183, 332302181, 348693990, 939785330, 446909848, 952818271, 863135785, 375730006, 76050385, 409856485, 760037241, 327805914, 306637908, 648452153, 76102108, 250821889, 392646142, 104092193, 205660438, 716942862, 849326889, 944899147, 953639256, 99461427, 114186377, 270109106, 704588701, 756972897, 508803442, 334401693, 500978743, 939325781, 455207919, 770378247, 556125537, 197703318, 850967128, 713050484, 527906715, 345281629, 778446008, 682381654, 988696817, 840127163, 425563763, 126934219, 702022892, 312393689, 604980662, 534487877, 387394379, 146239636, 603537808, 64153726, 950608661, 167741551, 287908605, 8249795, 807229262, 514915686, 817371280, 433264511, 720629928, 177630927, 310917041, 169941069, 645703260, 1706007, 484156944, 222983446, 219041399, 783673342, 635445447, 363751040, 498643600, 541531007, 879072903, 97269437, 301485839, 125639926, 585847804, 298148613, 733042798, 315984669, 550440830, 373558775, 303044687, 920145537, 920067288, 214709171, 247663427, 973627446, 329677894, 339755694, 894826555, 328968991, 326445832, 676702046, 661885668, 916156910, 106819983, 636445348, 924966248, 902590145, 341800893, 698515922, 207820531, 306020110, 365129584, 779341452, 323777550, 754422981, 382607500, 192589451, 77456213, 742463890, 731713923, 671118058, 548868831, 886707460, 628426744, 165043292, 515169459, 780588263, 529806555, 163869004, 515008529, 141016514, 28456431, 675008069, 33457337, 362301280, 610062416, 679987048, 708074530, 765240778, 903701448, 323504998, 261133772, 482121684, 390934296, 374309364, 355878985, 954287045, 301620057, 634321106, 678406954, 775783790, 160443628, 971362590, 803894201, 743172599, 147648837, 475872504, 732450951, 139984237, 163529311, 516153414, 424297823, 228957555, 676144106, 883453661, 40108573, 989264280, 409749699, 864457121, 334364279, 261641803, 115039365, 434950864, 27876501, 566429597, 427736369, 685733999, 929995602, 7673012, 755143685, 361390383, 504193951, 305686444, 706884067, 810903966, 525072209, 48793910, 419617426, 741622577, 649370703, 846195932, 613963084, 75283184, 158447085, 356124978, 833140705, 575260121, 86820252, 665183256, 160004095, 270004350, 376686665, 108822132, 985221229, 192194503, 682670204, 38210613, 238385118, 651781512, 31317627, 265999060, 117021715, 446514315, 482193735, 186515873, 138662511, 156274200, 711995580, 520182754, 257965420, 868297790, 711871123, 917473000, 268355140, 714244290, 465202816, 147209252, 265619311, 480537616, 415546877, 460691273, 255869853, 371086150, 555343771, 381872201, 220877813, 749329893, 785621477, 778956984, 944849154, 259382705, 44908356, 436866839, 927944655, 262467613, 719831900, 925504844, 322095560, 980217605, 412854965, 22776894, 517813076, 160957591, 271990550, 411015767, 431893944, 387398716, 789184693, 196749779, 212229181, 672862484, 78989192, 360691007, 162609450, 857856867, 752755186, 777066790, 541852845, 162360199, 173916119, 246648745, 339601814, 30843015, 558114130, 638370510, 714283902, 107171882, 381937331, 826973251, 567214366, 465888617, 811631710, 645979967, 779312666, 653952380, 525866628, 586298812, 35114115, 287996757, 269394436, 356667218, 295612374, 175642293, 253683172, 728061696, 547595548, 718165680, 244515437, 680448320, 218905016, 45180040, 23196130, 451756504, 862639556, 512286913, 262179337, 863461573, 93099381, 888923224, 464347864, 895429356, 91590750, 375371367, 842510910, 887430686, 148507012, 847117497, 722621155, 573834045, 372403464, 871300571, 766264016, 536422387, 420146098, 891506812, 53986584, 380426875, 823405792, 694853073, 389121870, 917076205, 195581655, 334804157, 235029604, 91645011, 590976291, 364316702, 674215928, 773906933, 429720728, 522560380, 323188602, 620857837, 236664676, 85598287, 380190415, 840634545, 779906514, 410052136, 169500059, 811285449, 561012287, 461837175, 603879181, 968021107, 112281987, 92695210, 419501070, 509202129, 39858009, 813318668, 65269832, 844424151, 879783174, 990358033, 974077353, 35679292, 283845998, 648859360, 596087621, 971576312, 988199204, 269405969, 107319622, 346767221, 765831364, 569735859, 597929169, 855597259, 78692, 96548399, 200383501, 871881184, 549883504, 978420388, 954135680, 679717930, 67310676, 945525485, 876368405, 475981195, 510446354, 380076376, 548222369, 665243591, 796425441, 811063858, 214274275, 501908934, 790593003, 107135704, 412033361, 294401356, 279270990, 323414578, 572137931, 539596925, 986873563, 312259928, 29973274, 237884523, 205953319, 708790336, 478490224, 439129961, 16682486, 17002247, 362140064, 830259883, 377841582, 58742023, 346005808, 721848287, 943720566, 240232837, 516174786, 142463646, 588528715, 215598368, 522083089, 784223997, 938592696, 849239513, 670161921, 872445710, 250756545, 750660808, 355999504, 231023327, 468678405, 579751892, 150744979, 482950126, 280093495, 606907893, 560100969, 999892748, 470156734, 93407315, 280097662, 44698061, 86094600, 477976516, 54473892, 794950449, 329660109, 154462681, 280580899, 754403314, 988485774, 283858401, 850402454, 935481751, 762674849, 885955700, 948141938, 252758941, 744086937, 373939191, 211650751, 986122190, 5655363, 508337422, 441476444, 309978556, 814469154, 687214564, 404037920, 568762406, 768530613, 2196581, 898260113, 197818574, 185013097, 857609386, 677417255, 843500346, 42438090, 465054243, 705484650, 129544195, 842688608, 920026643, 728995507, 690371118, 689519948, 177477737, 853151575, 66266602, 601453261, 560611163, 344597437, 532029644, 5759296, 486653185, 838273186, 537316784, 676724026, 436995351, 682192188, 76550510, 310046680, 191333377, 59361536, 799469169, 955409488, 57610355, 226438290, 690243235, 740647974, 855703435, 664199108, 833240771, 141161828, 232597743, 350474068, 146716546, 212465275, 140465183, 843141532, 193722510, 510104969, 284488771, 233520140, 148647121, 237604705, 338137009, 519865594, 147752130, 565965335, 512651548, 244696534, 713463721, 116548329, 843703113, 817619965, 726041250, 911959021, 203925319, 906349786, 616956225, 426669816, 612747134, 2066039, 903273319, 792315551, 275024313, 774202611, 38586598, 304721497, 380735917, 858977035, 38274514, 374407990, 569775595, 364043314, 569411675, 488050657, 813555364, 294939167, 78016207, 521239082, 924174393, 734246850, 101445410, 203970201, 191465402, 574746414, 34210657, 171683683, 965751130, 176636223, 682949477, 325769664, 989282795, 357153493, 344338730, 752287365, 288775710, 731941848, 855833405, 413902936, 236360158, 131392442, 44605083, 728459811, 623269380, 862831067, 579072778, 28163734, 576030054, 155707771, 270203871, 43276228, 540326108, 765479334, 603482222, 37970991, 906264367, 375327632, 53268508, 43670481, 267707169, 443187189, 676429567, 728973455, 702581784, 436717344, 372174460, 161779363, 168549542, 868912059, 766152344, 492126269, 482366137, 463219432, 809697996, 476757081, 889214257, 702228510, 227297115, 764028215, 629789023, 204603482, 759824718, 242144932, 348196748, 542695618, 113888491, 559067438, 378610391, 578554685, 983177662, 10933537, 251026307, 826223972, 346284367, 673143046, 722083024, 406991576, 589007939, 833730435, 577508706, 556780447, 195367867, 851051617, 457203010, 96554179, 7559132, 577246381, 423119830, 25462106, 467838822, 233472496, 893920711, 429607390, 917498215, 100859521, 420410131, 608274873, 186383299, 675091162, 232613901, 761058004, 919938689, 580215430, 851039016, 115033756, 842199678, 774003145, 539613579, 28919934, 913816286, 476653185, 959352307, 639326307, 270033948, 621240767, 138630859, 505205107, 934805261, 221337149, 282201138, 803800889, 802236083, 885723826, 235156156, 257461947, 362460809, 171960939, 490042041, 600467815, 730933255, 196987181, 567578307, 304676902, 282622437, 344895265, 98614823, 752075155, 860175019, 644889580, 372491620, 664160476, 70931605, 237940932, 871448896, 824221907, 897260696, 53200015, 939924046, 182250946, 99042895, 754061638, 606354264, 392948978, 764645334, 835995504, 876798657, 827001432, 348135067, 97092779, 531627501, 604745371, 941465832, 771042565, 711751399, 244474533, 622587149, 298624185, 207956250, 562168512, 395969431, 157347815, 339040682, 516825830, 960227484, 407211549, 558332917, 404462497, 638826849, 586994450, 166319708, 804216708, 746377788, 135167362, 21061966, 23821703, 732892760, 670915507, 909497816, 29813466, 369634518, 883132619, 279967918, 431122604, 337653818, 355701971, 317454053, 608094340, 557923704, 661552636, 732254495, 512587671, 135908720, 870993574, 644909471, 512643153, 698485515, 155821703, 21394056, 397400003, 687510512, 551237138, 372773978, 663213060, 171833030, 706271068, 812209315, 845062000, 673858099, 270504288, 191144641, 375173679, 607135911, 547969325, 425171155, 952816763, 183903286, 540415541, 524916741, 130063347, 915093438, 954472764, 135040565, 157511414, 998613509, 306321964, 310129637, 596098329, 313917715, 115150316, 989012810, 647025624, 720763716, 682049107, 359725640, 635940036, 350812043, 364725892, 531232807, 892279160, 661208213, 103700917, 70155479, 563303539, 799517505, 855757859, 958952147, 239266230, 863353805, 273488911, 96601544, 696380005, 937960800, 775994595, 229920165, 377661610, 157479377, 967019072, 288840501, 208336548, 610289338, 861842923, 146229534, 190369035, 347370501, 837168061, 373870070, 441431028, 185126483, 995095528, 75743400, 63672375, 879307925, 814718054, 472178037, 197089590, 71285262, 245945568, 516004871, 631170932, 422746025, 429546217, 895493093, 353099954, 495874170, 991346209, 893732208, 716642812, 145406379, 104410038, 808501787, 765108446, 283396892, 408530318, 386597778, 669420482, 670169531, 699844876, 182633227, 706594304, 277772684, 724373565, 288957879, 769118794, 221067998, 655334919, 568997404, 874033037, 866614084, 636599456, 753041809, 300323985, 72309500, 434662229, 67036054, 79628609, 799251089, 507638952, 398856695, 932234147, 825698018, 197466521, 508504939, 847093925, 240996111, 456176643, 869642962, 712921669, 302540103, 546099537, 449167679, 925954701, 872358117, 56616862, 660445049, 798449286, 631516102, 886313030, 24165630, 259652918, 585725909, 471512395, 810043019, 999752281, 984216701, 484965633, 224313270, 102571869, 164888163, 689382134, 417324993, 631568176, 230959320, 117053459, 286092956, 569932543, 259065097, 774676466, 915355477, 126787912, 145611728, 504598379, 555613042, 646180371, 53912757, 660008532, 888680319, 775529512, 892813214, 488154304, 55280436, 254636668, 259416029, 821007557, 786967184, 77285440, 67861639, 624443391, 631996718, 812211782, 549348844, 632189219, 585062113, 456839728, 747668938, 308476033, 759738200, 622158575, 563365997, 194509667, 596890895, 822731163, 114078841, 948862261, 956375524, 380060060, 225622012, 247234895, 867311247, 38822365, 799879796, 614607151, 119419670, 836949430, 963683457, 857960699, 525493543, 64471764, 499438509, 730881859, 452477183, 786698513, 396060099, 660150400, 484069090, 544360247, 963968877, 849917212, 497513525, 962495352, 789177951, 778064460, 742036948, 639362832, 865475137, 840066341, 38793182, 397886293, 647839368, 296909357, 456124629, 883510824, 26738226, 228967230, 835043826, 267861334, 435945094, 951355972, 465899049, 190323690, 660488156, 11348417, 17647655, 942353063, 853267223, 887029362, 234888087, 821459272, 924970703, 32565077, 539650755, 98287977, 811259213, 751767039, 669530550, 281991821, 213422781, 144610354, 464900263, 792676528, 748119124, 139531036, 6962624, 793049802, 972495738, 506486145, 449820849, 877527137, 402843065, 723302982, 169945681, 59048451, 487171350, 564329222, 932190501, 975838122, 864891145, 856694152, 624268920, 452746270, 345263139, 903065134, 483131682, 932434660, 610350891, 731069143, 279295830, 748842124, 9420080, 910182642, 200138208, 452544888, 438128866, 565165788, 501783866, 657340690, 59898124, 810462597, 388854592, 704046888, 402875913, 243922621, 803481065, 248924508, 746252365, 719413094, 475194015, 666250925, 543782365, 133349740, 519969827, 701433368, 397036822, 80733448, 341467415, 315628743, 568605398, 382501977, 57358502, 579729623, 163230826, 816233671, 654845605, 824044295, 956876201, 353826534, 3619449, 751276299, 330252155, 415741980, 992362448, 926748643, 143100795, 664474151, 381257452, 571462165, 498511952, 365845977, 611460163, 19974379, 219787648, 168445084, 255985402, 968825085, 241581469, 2098122, 936826311, 529413133, 949819923, 352562585, 669840954, 925323402, 605698957, 957509576, 448327434, 604267628, 220121517, 992803285, 786921878, 27250522, 608528496, 995075513, 233539985, 512864179, 531130003, 607537465, 314198112, 730283122, 581883241, 203921271, 261897404, 884131787, 732352412, 133307519, 538978313, 955935294, 476332423, 749814584, 509792033, 578727476, 392127897, 755682954, 440974008, 383212160, 336211191, 873809499, 499113791, 62251202, 908724320, 653793162, 633402032, 160844684, 525711086, 42145109, 531555344, 535177514, 280118130, 796012268, 461527634, 100292307, 436738382, 918701110, 388762261, 199387315, 714248581, 395585394, 734734778, 974124989, 806212181, 247042484, 16767798, 836975859, 297653179, 52602191, 940409886, 360167072, 380696982, 297947111, 79618833, 299509293, 84236654, 737564722, 58905123, 207830424, 477650553, 512614203, 976977923, 973495957, 34158787, 882878781, 733801150, 317284246, 765628989, 657270468, 491772956, 652691678, 126081148, 534227812, 593791238, 954428954, 272973518, 343770725, 544849258, 952960310, 107643614, 76435980, 625281860, 574434494, 814574201, 858605604, 756747940, 807835885, 920822675, 524465796, 174007879, 764527467, 804227558, 87885876, 777038818, 316199115, 217705163, 821486054, 143383085, 142436392, 921149855, 836062081, 649756364, 854022437, 344356375, 289627553, 334937936, 968997086, 86275040, 637336336, 954698128, 479985233, 41907867, 335176492, 303865408, 544662500, 885836911, 889134594, 432292288, 410213295, 492936955, 577869565, 486099120, 249350852, 116817922, 464999869, 559808156, 3120405, 343465659, 979188928, 882134368, 377125204, 670717573, 620843765, 169614504, 174383889, 769219416, 790630591, 973350141, 507520335, 42175654, 435655138, 93390816, 775256723, 46290214, 961512867, 789540810, 415974273, 575502005, 901915204, 403598454, 728330242, 171373127, 51844024, 317936144, 766234244, 448125644, 737894077, 839507595, 818052720, 813761264, 164973537, 375101662, 400794728, 874857506, 973680436, 370727171, 996901584, 583799493, 617227951, 260724791, 206393607, 870223182, 709551750, 874166883, 445510286, 776760245, 1813575, 581698707, 997997582, 433532838, 164442665, 287800983, 652291939, 233483814, 701353148, 450342231, 79360122, 447908535, 456777328, 551158718, 470183978, 81807692, 813287066, 256595913, 759164637, 684275111, 791819778, 928753839, 110651826, 164691143, 597490763, 724013830, 926000445, 645480155, 878030379, 38042123, 474845450, 44169647, 450473111, 299094080, 842559003, 389387441, 187419502, 44193059, 49416420, 488026629, 571824228, 327095237, 845074260, 768926250, 201327022, 249185110, 640146908, 910927771, 936062776, 523789324, 887194780, 916875146, 258191988, 201513568, 66977614, 128675339, 708560249, 969543337, 349629296, 562309497, 343355267, 945179951, 405763387, 195552968, 724359753, 973881252, 560284540, 428616658, 882105838, 658364290, 527015958, 454963883, 242714766, 595714064, 245832632, 520649186, 254669290, 293029315, 995806766, 86962838, 665513961, 363403246, 452833799, 901859254, 457661686, 313411801, 410510716, 236352064, 708404396, 58581255, 101245712, 59082432, 916657707, 630443943, 407550081, 585499425, 499529045, 804331773, 144707845, 925639095, 661671781, 743582676, 860597290, 346123138, 398103618, 641142772, 349056244, 814648235, 351008210, 884011192, 10046278, 178747197, 179227756, 180986909, 772247999, 343073663, 66584083, 955758723, 150447539, 440707092, 497223214, 690689354, 894876974, 547266001, 675874616, 550087350, 753889177, 697531865, 956440532, 611340948, 126267962, 229274894, 668455552, 84209897, 897263092, 358086343, 342894070, 79136607, 182789608, 28302123, 154496903, 234438152, 767730257, 343949151, 528724519, 637129994, 821344863, 309509614, 842363229, 360863055, 710137038, 218177945, 312358285, 611029081, 436441740, 771106047, 154769232, 115562608, 520447012, 620841201, 521394539, 484740985, 819797461, 186880897, 660129524, 155492893, 948206851, 702296425, 964850447, 966283841, 631349423, 496219984, 654427365, 993552794, 658499154, 752960850, 231748268, 425992569, 827861168, 444250388, 799150010, 406556067, 193084087, 824805143, 223255103, 616674595, 144359307, 767654324, 699704939, 51516212, 364158250, 574769849, 510888378, 595936790, 545320342, 374446176, 414667909, 25269824, 314680521, 630117827, 526185532, 391311006, 225125192, 951899356, 398638852, 208171659, 237266995, 134327541, 285127068, 625406533, 241355190, 753446828, 494264148, 313290716, 226864211, 952361389, 305694244, 604283278, 310236440, 716059791, 713606071, 392650428, 663242054, 491222231, 193554057, 363346589, 606448123, 162128868, 323753366, 526353042, 960603054, 328639943, 247943446, 947750081, 649383200, 322742923, 642940254, 605257738, 590110736, 577217640, 188476578, 337518841, 179940139, 602234974, 56830837, 34208674, 421293272, 373577467, 446298805, 127216430, 213771174, 774617387, 125306486, 996329964, 241853751, 715538122, 768325474, 373870341, 447587146, 864182414, 590642938, 912144175, 657063376, 878844994, 728153302, 525825136, 576369184, 540963933, 18798472, 21608419, 687028939, 72250344, 864586652, 637174272, 895125415, 859103898, 871686134, 821748067, 375188211, 532419236, 25547613, 665574609, 962071010, 219544843, 766754837, 773929697, 957299422, 734896500, 608572277, 133070331, 663446876, 24390098, 439606957, 361806305, 859220634, 74271055, 302851653, 785266014, 912229030, 65000616, 983294366, 567777425, 788356660, 76190141, 711035076, 477976311, 976190598, 309628364, 378382279, 137697481, 141291264, 491681330, 331585797, 11950536, 931542610, 926495137, 610968657, 124584758, 819320034, 411064434, 816402475, 199565311, 679502716, 197907199, 973450024, 571862514, 328233583, 943056434, 661903134, 97167784, 492779662, 703595644, 882149607, 254371373, 106107947, 551201782, 163874484, 967400329, 426578485, 424122624, 659747845, 690000066, 186511770, 770641289, 675756582, 974661738, 499844266, 742977716, 531623405, 557545223, 516377797, 670616723, 971276279, 585135804, 370501742, 462436831, 624156924, 379348133, 68445036, 24617326, 331108173, 796346083, 205496121, 98387046, 17858145, 688445330, 834262456, 16628108, 497052950, 557261706, 851570332, 219286393, 242126875, 966160671, 57517589, 244501702, 896946279, 787928806, 926670727, 234457462, 447173778, 482999089, 287374074, 821753309, 758019666, 437532909, 73512379, 936170101, 709870094, 838791990, 644060043, 997887840, 175859414, 264584022, 327883835, 188997236, 890434960, 567414930, 302086195, 138756153, 131296122, 550816557, 167120783, 642112579, 216629120, 217226726, 967987107, 788303296, 120594119, 935484261, 672519681, 695819760, 89852568, 865307457, 628928693, 985258176, 115596705, 60658932, 766550172, 999530526, 362454745, 447138111, 632904437, 760901655, 40634776, 608264892, 935498792, 274948962, 677911350, 395998269, 588758092, 748462713, 845565866, 511933679, 659478802, 317255759, 275037545, 134683458, 181945834, 178606706, 797306482, 876691317, 731391369, 456036253, 370729775, 559941564, 458073915, 644949052, 360084290, 298747675, 911020213, 842967350, 194347443, 474396448, 787080744, 674761474, 135575828, 469163333, 256912598, 496949171, 162313616, 985007370, 332370801, 513373152, 674409473, 98044900, 372236307, 141764701, 614016531, 826258346, 879217658, 61414507, 326244488, 778026950, 491076132, 288262634, 723273173, 956773263, 963059671, 813884965, 512082439, 722099105, 489230207, 394742234, 413145287, 461250794, 6962225, 202925410, 60529872, 8975160, 979677440, 28891389, 846835135, 379370563, 239851418, 708764110, 342499082, 291322460, 196397602, 39525931, 958439413, 284019625, 734494821, 358914562, 693211392, 149228698, 292024063, 147566869, 399221603, 222994053, 579572680, 647984423, 966836908, 346805039, 139218101, 916594531, 756084523, 265414819, 778743969, 980899570, 52147528, 950620035, 813099158, 387433441, 276372722, 703477671, 189206661, 420043087, 809264752, 565382473, 36183034, 919851701, 90736788, 996190778, 40139316, 864255989, 113489881, 562395774, 377418386, 659031541, 668408372, 647049075, 733214814, 703428867, 651970690, 243794772, 361900004, 607052100, 683962452, 730426360, 141641994, 707055023, 689812223, 84472324, 525228096, 224858467, 26444789, 945940192, 482219933, 304080930, 796581986, 17105003, 558581924, 924538721, 927691253, 725056099, 756884634, 729204694, 335457332, 572894685, 535478393, 1475339, 651176110, 58574981, 271053558, 499378573, 98810527, 952220410, 36596538, 754276750, 469441559, 731241025, 447238555, 260753863, 149897326, 604137547, 810775266, 82694444, 557576502, 414942506, 66701583, 897167583, 761471082, 397509159, 520484873, 670218387, 6349208, 138314648, 845030641, 50650769, 88476967, 815017545, 210075428, 87371783, 179138551, 869311610, 707108611, 768428888, 958768989, 995814083, 516002480, 759084564, 229169946, 640556657, 801070881, 638791804, 316243136, 624433097, 99860666, 176303315, 702332039, 352720993, 530089443, 536718303, 662368288, 454404151, 623545108, 94840617, 535362274, 358742447, 236618843, 884743724, 904253068, 184058952, 554898619, 13626622, 801538288, 217787154, 93481, 527467476, 43775327, 227010423, 316934555, 636081068, 622759075, 505356392, 957641836, 542630141, 200204427, 365888064, 549178603, 21062833, 989534441, 20226089, 211984962, 55609088, 759225564, 931296186, 700201768, 626666339, 359522512, 748150271, 490318339, 315654757, 170385987, 647682300, 166112496, 559852571, 693462043, 853509197, 476644496, 372166846, 89788633, 896881023, 879154690, 748531547, 554476578, 835453096, 641587822, 758820335, 15993603, 390949701, 243539402, 205038328, 66274545, 117852847, 574321339, 208203566, 360802736, 383438787, 395962201, 266847157, 573612425, 222331143, 261297307, 49099815, 415215463, 627448021, 413277425, 489551057, 122628894, 45380132, 607147290, 808958811, 274571188, 5741445, 924771430, 639849917, 318436487, 557959074, 980422339, 149248914, 954716282, 666907023, 488486794, 145441629, 353424422, 591193192, 940998630, 459084235, 134828989, 308573261, 3565943, 622975615, 444787617, 654934300, 200015390, 740345696, 163899697, 517392939, 96121779, 757121538, 149577370, 232624719, 965816425, 522566273, 178046949, 103619488, 96259396, 979212317, 324631672, 152680644, 455353567, 351282927, 865713394, 293693996, 955599928, 976484780, 358413942, 712047468, 122705243, 174539978, 152736487, 363314566, 378968280, 36567858, 401592671, 180771906, 56424538, 702761637, 214951203, 647858852, 693526698, 351169101, 187580787, 747441998, 472948729, 184952689, 254470542, 540314575, 490536642, 345976750, 556806322, 361292408, 767982556, 669683095, 140833712, 596043446, 703741130, 718006309, 810027000, 109284283, 31075600, 51263443, 289789536, 713468040, 249951901, 102645726, 217004130, 887626221, 499909286, 763760160, 329318238, 301780904, 273680068, 583127208, 21621962, 908340796, 371873602, 842449005, 405351228, 661745648, 658271210, 472952244, 371909267, 774596565, 288225228, 926621550, 900440944, 117850855, 88748958, 160245219, 398986085, 238557064, 136205176, 329086320, 98313250, 865704553, 528259626, 236199891, 583864116, 320100714, 897830499, 19379075, 885907695, 974264243, 187049432, 144577354, 931975905, 487293515, 555715053, 337508035, 675355954, 742462334, 466599916, 959301674, 521320198, 475602252, 57317554, 831597140, 898378002, 73843212, 487259006, 413868024, 155614423, 931522446, 789112643, 706738593, 77434227, 381285723, 344617088, 835594436, 894827243, 613090962, 404201435, 346323227, 485518862, 216400424, 427659485, 674773371, 94210246, 510609916, 466222942, 488852719, 676232741, 157015424, 71661335, 405659010, 689095838, 248444114, 515757266, 631547087, 970792433, 654214166, 942350927, 883666984, 838532733, 619635226, 405834333, 556364294, 78065804, 333678678, 581505399, 608826450, 800225239, 201100836, 17856493, 312327136, 472341822, 107057485, 647674719, 924157032, 522184950, 230183408, 47192027, 458391355, 553840124, 868873858, 856903339, 497361544, 355681769, 341303768, 936890497, 716020880, 406812690, 391374342, 24435090, 356592509, 591004229, 22451240, 360029701, 445908772, 904824983, 962411355, 151580653, 894167155, 806462313, 374112253, 780667024, 345794582, 196056977, 543044909, 362037890, 475301577, 42241360, 564626677, 581592153, 662609989, 936273328, 497411878, 133431766, 447410163, 391600178, 579393603, 880827270, 795953598, 654824669, 693624514, 834925453, 600030071, 779217564, 354252091, 987955227, 163900495, 116505662, 991222424, 236210029, 145424735, 797501355, 645612547, 899911533, 264765379, 272676515, 117806135, 444810672, 853619026, 573185478, 167462674, 735651760, 573044937, 92817412, 238085179, 351293556, 922318871, 464764094, 251289272, 578371413, 388254719, 670495013, 99879938, 955807054, 51124620, 786026316, 717012624, 605063109, 756617173, 596679357, 652286505, 573536181, 866106394, 211828323, 364071849, 245366224, 290598298, 464884032, 793190500, 238214609, 457611472, 1590929, 791905018, 674632557, 732073372, 400055783, 703476301, 280097800, 762826597, 619522967, 714014379, 11742352, 221122461, 689746955, 231090507, 32876676, 505677529, 733692898, 131472010, 450186781, 338731601, 934480004, 138116337, 412847594, 577279138, 413339055, 137501791, 449771198, 821162846, 586734299, 914038240, 996082508, 718409212, 482323393, 95896153, 900089412, 749139196, 286576606, 401156941, 312650420, 473603703, 144831025, 972333323, 352273814, 954473811, 125565496, 482183394, 7272488, 994705778, 712164459, 6942589, 321894664, 127833196, 974901813, 849776800, 8343955, 746702222, 555573391, 722426689, 802114218, 348335259, 158006393, 977694653, 188118912, 674258714, 734475171, 709264381, 398654874, 408294770, 288254590, 381238761, 664469604, 830468143, 680604837, 480854265, 842333482, 518246759, 858189211, 11242462, 168316256, 415089343, 483267094, 63897546, 547678289, 163810291, 433564740, 3570402, 221098393, 517024142, 931118762, 735958694, 335298136, 766456230, 603961713, 49915833, 894242622, 269654165, 310738942, 875911100, 789563897, 616205186, 880071500, 349993324, 82617227, 741719896, 40032004, 978804745, 78694079, 459424055, 550300612, 985502207, 574253030, 303883853, 349986750, 993763146, 516418196, 137755948, 280488308, 444790615, 645800217, 673810348, 905432325, 470403585, 889274820, 164420759, 810412894, 481536337, 865886425, 516017250, 353266726, 623787331, 429510958, 873752768, 580522165, 126553774, 364615200, 533300329, 647433801, 941640592, 680043922, 639120594, 755350090, 180746880, 933181902, 759542502, 826377206, 294820546, 883018442, 105105627, 261181826, 712699019, 119130544, 913164041, 947862057, 875676894, 273159379, 225743987, 404112304, 968698951, 697957991, 684274284, 567547857, 533025212, 48091937, 978479901, 600682343, 943049771, 735611568, 104197368, 594236321, 412938055, 943155442, 536170612, 139250389, 539400385, 710416007, 538490943, 374739700, 179999195, 239353596, 347629660, 849998712, 555768366, 569207310, 363326856, 812233102, 597685071, 682766405, 958194621, 103500444, 854849260, 72084137, 672248138, 161150668, 746593147, 280526303, 401597926, 425509291, 875216472, 440429773, 718695755, 751373677, 541899050, 791683976, 389884430, 292589861, 909319565, 277309245, 509912786, 311953541, 856164802, 479904888, 443529577, 18300307, 608513003, 313474151, 275602569, 772641072, 587406824, 346108405, 135215253, 212477740, 688647684, 7111162, 763637888, 921804682, 934838920, 796201406, 403249473, 147847775, 111642077, 841167487, 225526026, 869713975, 91809097, 685211783, 523316078, 832333564, 500296175, 770574148, 647402408, 537319320, 968087679, 639190210, 921969400, 820832136, 384629019, 399938773, 758560057, 6070484, 395568992, 782541175, 502529522, 213689172, 162253735, 310740853, 292141773, 896238202, 96161322, 23894936, 425681510, 556486904, 675444664, 697816249, 283322522, 293874059, 411224547, 27601140, 551044882, 782392412, 556432658, 262075058, 259455483, 651570067, 825723753, 546260849, 2638810, 566942713, 895070942, 504283739, 210568364, 466729381, 455582988, 819921823, 999895942, 953992347, 810144012, 199099466, 855497396, 960573012, 614330505, 812735726, 826164353, 201853653, 898867571, 223868115, 703061707, 588408662, 893368905, 609856245, 478058012, 148428243, 28018592, 372369568, 423709147, 791075425, 327604594, 597792888, 961628649, 219504261, 2265515, 616548430, 10682719, 562210513, 737607262, 162499160, 84175773, 177424366, 281679470, 163573893, 951127478, 99483646, 199569996, 870646152, 463134647, 192617212, 588909703, 711611602, 180014755, 353077725, 83702126, 760960887, 210783264, 466668727, 860841334, 865127326, 854054752, 504272549, 789748997, 633726082, 673272618, 253774299, 482425362, 224961391, 133740827, 412209588, 929887896, 598506189, 654237770, 376249251, 602690334, 766918927, 846331669, 966843841, 517949335, 240174996, 162411069, 170863817, 519916356, 11818362, 124111586, 59901014, 187796708, 689079806, 146768204, 649032198, 689911811, 860605820, 55782863, 405849086, 224050832, 773095925, 185165460, 172975051, 617058678, 152656407, 856594103, 811699283, 631050196, 601645690, 807552755, 243007908, 772424962, 72703754, 132889995, 300091878, 334094412, 194348193, 990939135, 330419274, 16267933, 822724718, 927580611, 276898909, 718612821, 732330026, 734491836, 494007202, 673778345, 486219479, 755059776, 337800300, 355915830, 823956226, 696669780, 942744977, 387880923, 66423870, 68974095, 143950004, 249869582, 79297416, 636796587, 168572253, 920367163, 727447965, 696608289, 108060376, 738498381, 533282549, 4281208, 635289054, 771601887, 924413387, 994676650, 294141700, 668013093, 3521445, 451031844, 281212646, 601987358, 253190459, 227426378, 915123435, 455683505, 218758145, 544887319, 330472319, 638719451, 840206497, 241436093, 791791716, 246744125, 983905672, 14207086, 63990939, 888029489, 80849760, 964795119, 38822926, 32387724, 791575690, 861539688, 777723893, 530970160, 920648502, 162816924, 158567959, 207347760, 514497026, 739256511, 261132417, 56556538, 892299818, 939379146, 338088998, 433116509, 628131284, 191578090, 85530669, 637335770, 623652203, 429234136, 294289758, 131065389, 439071959, 752464471, 96245554, 264478439, 703159762, 973709797, 927408425, 336181173, 253627917, 826597920, 585669744, 257917333, 359940599, 212806352, 59146128, 919792220, 85224236, 712410825, 638872480, 119434570, 695978279, 181907742, 284678899, 320715804, 370530703, 708646221, 587166908, 940776449, 426607442, 68552133, 121217905, 437959819, 508499158, 285592522, 514056189, 484268337, 277252805, 487836261, 177928062, 30504959, 786835693, 701784421, 189152821, 439762145, 552676150, 890637313, 247016182, 290297663, 311509585, 859395995, 543910116, 629012243, 398900946, 681614763, 336381820, 723766928, 752827138, 13571336, 449652261, 338342941, 475976836, 791736805, 12079804, 349275223, 812888166, 889892911, 378014548, 229140373, 437501439, 316921376, 794464584, 686610271, 662380588, 780143601, 331194119, 103227549, 342512531, 705692527, 218952630, 793011760, 478030123, 437513001, 886666070, 199896326, 270400325, 787825996, 896715627, 894269116, 498126576, 444281971, 377611480, 948195766, 299104381, 633558349, 221860321, 632188192, 953663297, 482634869, 368020457, 131568563, 118435075, 264929126, 45973382, 174714218, 601998875, 606624888, 258695796, 900391311, 219717920, 782541343, 911905911, 71022375, 46503492, 635972707, 101586097, 738922696, 751146259, 777514189, 924289411, 937115894, 776822740, 369333359, 755008440, 201299919, 557358665, 544870407, 389743965, 740791129, 442762622, 109140470, 705677380, 16780094, 209986483, 462717363, 299179396, 46810628, 258837221, 5824079, 382262050, 665545319, 559538910, 572914150, 837508175, 643179373, 488388943, 232069424, 62075000, 337965013, 652672081, 605848764, 796761784, 632345492, 556057006, 220344000, 802744268, 901223246, 2227963, 340289861, 765083170, 320826793, 367827302, 541098476, 962088963, 823049507, 952680938, 703616511, 969368798, 876482613, 700849011, 39615668, 385824248, 603430831, 527952218, 224758586, 762668876, 848379354, 920210282, 807098002, 602219273, 122939479, 156678304, 588540605, 240180535, 824949674, 872893076, 931638825, 640614348, 188075251, 729058734, 637919563, 973645346, 24378367, 308896144, 128486473, 852120115, 802515213, 302982276, 769611191, 366373899, 199916945, 797778097, 525614645, 285306933, 503921381, 949238862, 724667587, 488777023, 304298748, 375495313, 803516031, 817979793, 497904387, 72726551, 741807133, 467970906, 911048330, 323335441, 960198854, 120345824, 650472116, 966885399, 803418445, 80172289, 424096894, 152672462, 863389720, 737681584, 981057107, 383256657, 987160487, 449505130, 846891408, 553409519, 839472334, 472513769, 463551555, 764284868, 583090149, 952792226, 548679756, 868125748, 691372049, 872378890, 983251044, 415067298, 168420148, 171089173, 515404849, 438331966, 541597028, 325239278, 722830421, 613876120, 195339670, 291601903, 473826241, 283776891, 568635672, 102386434, 44938672, 220190226, 970575390, 400125641, 792366562, 605176879, 834676103, 508488915, 10425148, 179407363, 710736546, 952673859, 123626871, 286295221, 973473434, 418155242, 146695035, 810635791, 744651575, 404908718, 258046397, 400727746, 950780658, 896958290, 127147856, 288688315, 532739882, 265813769, 536137709, 261653004, 557293723, 647038622, 213160037, 909910484, 321938872, 267308778, 478185778, 634981043, 360521052, 761209673, 865858901, 239269757, 132717991, 660320129, 647348410, 982294220, 437172067, 17813646, 54750922, 529531456, 379131232, 791925252, 951023844, 68013248, 219816317, 71879952, 294523156, 181560745, 786685686, 436659381, 857776809, 422270817, 670098091, 669328850, 813480367, 895788371, 934255245, 8837653, 271316967, 468192100, 896113200, 971515717, 254140873, 211138778, 588319846, 98173480, 778465863, 905638090, 104822732, 44830499, 386553685, 464914291, 824379900, 149432684, 169932223, 259588128, 655572190, 618962145, 503757919, 244336571, 351812030, 157791204, 353461338, 875258405, 563609238, 406546491, 489965836, 506367379, 466605767, 769569268, 399584366, 999142421, 72790934, 291071737, 166082911, 501980390, 54085124, 824989568, 515817479, 95411249, 248179501, 222084097, 594464865, 388330436, 135319102, 590317310, 871806824, 647211667, 989186503, 402271828, 910606538, 776332595, 367853509, 593377349, 965969825, 648411785, 393299059, 345284006, 962890223, 867566564, 610265927, 12315919, 44680207, 77774085, 18072452, 593346875, 589337129, 829095008, 776380675, 6588751, 457253991, 872436044, 289527321, 542979097, 135113451, 129668948, 325676762, 372631439, 566962970, 364847856, 487897693, 96546709, 464365847, 153224128, 218148108, 653718215, 557322695, 634310028, 987676761, 117127493, 41465668, 122718807, 744077944, 956084092, 69815988, 653222318, 441040005, 961325965, 510385226, 296479514, 680384304, 870709161, 461073371, 369066288, 765824257, 37268079, 794926759, 808696346, 166608577, 713511621, 959500605, 728691383, 929912186, 454235071, 479549781, 828194861, 122355404, 170790592, 506257388, 510835469, 307224591, 739743521, 821150762, 413593359, 303812520, 389231276, 668519027, 272176485, 640879594, 344158921, 484925397, 772396863, 548450159, 902000924, 520045559, 580610985, 427028249, 386037778, 2453892, 456812897, 209775309, 110001652, 10223652, 835877799, 592293192, 813652410, 712038111, 539966168, 19074534, 478923069, 970902436, 67214383, 155744296, 154836456, 670383947, 773568740, 858454901, 320763842, 474844262, 406864245, 253973378, 272335908, 137992043, 606414320, 749541669, 447330664, 365041390, 953252324, 487343997, 157854246, 137420788, 884964752, 27259338, 932151964, 841151608, 778263324, 692122249, 671498067, 222761185, 398220438, 320284622, 624275229, 37018158, 867433639, 983772158, 486246993, 145839501, 612056912, 758887315, 114285560, 564446086, 368978882, 388439381, 267554439, 936657727, 559156815, 761326580, 334611621, 875202372, 204701172, 384260664, 180106089, 303760502, 908853765, 8521843, 22843330, 873380423, 201777224, 105605950, 281496437, 549771674, 937714919, 909136468, 69639937, 26245965, 550447712, 996579235, 331958236, 896067039, 265671542, 539748170, 362148076, 704037820, 911947433, 591938802, 909091019, 614823041, 863470654, 719268656, 274077680, 783966409, 440296391, 507834813, 81705993, 563871415, 785256061, 195046555, 506697536, 988113743, 442020957, 92332256, 601437032, 17487380, 767760832, 794205951, 22722529, 720356165, 353594013, 611281845, 285394439, 597034084, 64443160, 421386018, 13207957, 678514289, 989186919, 297858312, 197843104, 707770601, 721891283, 212154822, 587419888, 659776150, 547203918, 537171990, 555231142, 447849467, 811510690, 577528164, 771111912, 415746315, 74148262, 568770238, 503579233, 894792232, 406413725, 463908438, 308267350, 5894294, 545904411, 883028377, 953663408, 625232784, 578407836, 713503050, 822478063, 557674943, 924923413, 249357436, 389026773, 737635100, 695299016, 623707057, 847757414, 790035962, 942408156, 197522613, 897652264, 756898455, 240231505, 737907534, 650090073, 549566646, 92721967, 33022132, 648247677, 34834141, 592639504, 434185297, 998392382, 148931383, 419997634, 400555681, 686507133, 154571032, 926058425, 59734198, 779836903, 200596490, 171017541, 764779134, 972132795, 818366025, 657283605, 369110900, 97233971, 379724778, 588503360, 110967224, 272419983, 488538402, 903026163, 166458262, 673840492, 682021595, 205346935, 602842899, 88835400, 681643921, 49287354, 541606236, 470941131, 726945839, 780503262, 145890716, 739405592, 943966229, 491386602, 877106465, 431847505, 813828225, 474504189, 477706757, 719625493, 369052718, 980409029, 26659228, 272816644, 313576573, 146464120, 777188921, 725395940, 136049398, 701990515, 567372509, 403557690, 56857415, 427523654, 275148702, 797133997, 427292700, 406601499, 467149355, 105875739, 783694474, 742180443, 124565909, 344551819, 59602272, 545404750, 81459423, 354063896, 331767068, 444529175, 194127156, 99362366, 330870046, 661493085, 73460894, 718672250, 799702744, 382382405, 397790652, 465727863, 619108648, 704874393, 996404657, 687640606, 232901490, 530894335, 955200787, 908111529, 453575335, 702402367, 901976311, 708545354, 616069915, 257829, 109886018, 743051758, 974571132, 692466368, 60036642, 34329489, 957879169, 464578867, 126932325, 682942578, 486802208, 98812320, 331237813, 8321070, 40054755, 391197306, 423379847, 231712169, 300201445, 770915948, 661455075, 917724034, 380323755, 71335721, 897799996, 761087536, 92311267, 784206425, 817181982, 638764232, 136022507, 554745812, 364361053, 777540716, 383274185, 116261161, 655233813, 963958633, 182797972, 871400407, 27300490, 788968997, 879806494, 812380024, 847595008, 381649021, 711675775, 556188208, 71180506, 201491699, 622794339, 209184320, 362269479, 940526485, 678901042, 699008335, 447578687, 916172495, 255773515, 687964595, 77300041, 709173256, 591183497, 979466224, 139875129, 628728128, 700245189, 803630554, 249317041, 54833331, 340454984, 650954865, 15886442, 198608189, 128321070, 824383180, 640383310, 679190723, 261127042, 650209868, 751223745, 696408288, 958448447, 277598938, 61081140, 820151748, 784107361, 779680187, 759676178, 422317233, 763981399, 550946836, 370675863, 566374811, 243927207, 523985352, 152207656, 169349306, 218617652, 962130635, 648047319, 910612305, 882853188, 473916498, 68820052, 939908059, 65084865, 842570076, 670513442, 549123175, 32940767, 351413561, 280487900, 597746749, 271303771, 381249673, 385817004, 732184772, 645448166, 447485848, 9547480, 595217065, 752404621, 632854030, 685654655, 196518182, 887122614, 199157863, 612422118, 980591892, 342733540, 421155117, 582616465, 881073758, 766416640, 987440167, 689129140, 482162715, 514518633, 483890653, 386420676, 82395348, 824380866, 192618874, 202397356, 704733121, 170612681, 231556629, 913806922, 666939536, 617059525, 487803401, 956241526, 682522122, 589409592, 383064833, 338571744, 623269044, 8336855, 895168162, 176606988, 241851981, 713608057, 887995717, 788018506, 296410368, 366981050, 480626879, 260136759, 313300496, 42571084, 389025635, 895305803, 209939262, 58171271, 762510477, 437724003, 202813489, 497742304, 376384612, 241478610, 71911104, 540258313, 392660622, 722403372, 491419174, 733637016, 958586747, 193497893, 228047121, 703788524, 904604776, 363067795, 460094352, 980991038, 86464206, 257220775, 882422535, 69008234, 675681526, 207144931, 528417894, 95331500, 135234278, 845111935, 183583779, 835074403, 59874918, 374707323, 865216271, 490501563, 350238068, 590581622, 296341764, 596521404, 67347725, 113322400, 953029912, 282110226, 436135433, 966368486, 397942273, 649414798, 704555935, 161067373, 363554284, 290955613, 97211278, 177683232, 137165612, 47775843, 286872141, 958098784, 986766038, 191422997, 994096872, 207510091, 743373754, 704760924, 557475539, 348715740, 405345658, 639500015, 706879662, 875019520, 674943152, 867167806, 810097211, 108839531, 740727817, 711068324, 952109471, 11192641, 438301763, 13720657, 308426683, 570785337, 790323152, 317417345, 936869986, 522730858, 508942787, 313056534, 112039419, 216169707, 625901125, 765091501, 299261966, 271182813, 775118917, 549809965, 583466196, 711286715, 377220608, 569786684, 834997409, 201203422, 166363345, 874035086, 827497597, 104465729, 67856258, 943046939, 685314001, 980369043, 159390604, 4809114, 471047483, 310897688, 130522570, 615116595, 73669240, 973942637, 34090545, 955991897, 802678881, 23701232, 234934946, 973086375, 609485401, 319177740, 114930543, 364333551, 504637482, 248650356, 626078020, 124723706, 733829531, 34371196, 437700137, 30554926, 190135457, 330392045, 62969892, 656913422, 817458893, 472293946, 192991847, 331969855, 719981393, 23713247, 614523716, 455103136, 313513119, 535265370, 333278936, 522162342, 492987299, 565741222, 351386657, 639281072, 58501819, 958884199, 90123659, 67478997, 315385342, 4159962, 875241107, 665362341, 630928827, 119877934, 326944061, 814811224, 595781489, 454018051, 917827640, 698157191, 424204009, 479269023, 373511697, 708309619, 464981946, 300556053, 705485490, 678331205, 162346929, 540871219, 523651400, 575968789, 68553977, 532785048, 980913816, 39708699, 516464409, 917711784, 808977559, 287534548, 74078436, 187671249, 716334021, 284555236, 295826040, 746137973, 257154735, 113332139, 800341216, 433304551, 722055522, 685849773, 317401948, 160044456, 383462799, 224053559, 85072865, 146746837, 992161768, 254588706, 430894824, 53377150, 632120729, 98131732, 738215090, 21944309, 635476183, 572134024, 125360272, 370549357, 170468702, 999058656, 535361162, 681932799, 493877447, 86261542, 176233117, 23849507, 783367612, 982395520, 440335895, 520422003, 744237973, 694831566, 411650098, 93746719, 194806763, 372146533, 464103004, 789808210, 778722483, 829031797, 569494781, 610030166, 464530966, 818846565, 310654091, 590531664, 139330240, 276266936, 949088487, 265108734, 430747747, 894549498, 291527898, 165027609, 759419365, 183263108, 204787241, 631281639, 223327472, 17210039, 571317038, 585929347, 104923600, 877310953, 557909540, 346521106, 419855481, 342334476, 597559889, 13376150, 336817103, 622130192, 128192037, 212601144, 73105643, 204657559, 939564833, 301917715, 284531267, 199324396, 937201186, 638666480, 511231269, 574901273, 854322673, 137478326, 643168303, 738776074, 594716388, 476330700, 270316577, 294049949, 862050356, 126545498, 786394949, 998467588, 590782213, 526217711, 605848824, 786138356, 153226421, 324290631, 579083784, 8476124, 13321697, 798479088, 380631460, 560668758, 382749691, 972906315, 784650544, 282338623, 560318863, 305405817, 445643184, 783665604, 968187613, 16270451, 392869538, 142189104, 651461289, 566278282, 992429813, 212329825, 374912364, 700592847, 940829313, 144332665, 139017091, 325265026, 740278650, 416470524, 788349515, 263079890, 416844391, 773118186, 335954800, 720978095, 672012954, 645007951, 52410374, 764097116, 538834520, 321260567, 687517498, 535691237, 470296014, 179511554, 959480050, 129304666, 659665363, 23306251, 250398261, 257073617, 289295818, 898953627, 669787397, 818256567, 879084099, 612791786, 291292286, 535428166, 172255425, 985356598, 105755893, 971461870, 844465991, 563633881, 900409067, 388498000, 728131398, 728259787, 855986411, 479183064, 313926252, 519896760, 943129718, 863546918, 927874552, 827749383, 366576427, 578356628, 909203796, 287917590, 603783371, 817390984, 477398199, 972409819, 980527899, 548732831, 412722397, 596296894, 548732616, 775656818, 744393805, 689568367, 820242924, 574106470, 15391930, 451180188, 572466571, 158185506, 955239201, 537809387, 517328969, 38523128, 284316577, 360462275, 757175723, 520361422, 493071072, 120866519, 106229743, 378696410, 120204761, 14920573, 57524975, 719539617, 341376226, 773356756, 779154706, 400531726, 899799353, 327078160, 728272433, 900679513, 641994936, 225726519, 579625511, 522519266, 868444668, 860129705, 508478386, 976259500, 890619235, 694862297, 265917893, 290383147, 580280621, 589497050, 331484836, 860592338, 433781739, 975654976, 316226894, 875720723, 711754672, 347224378, 113660267, 366164764, 299162173, 953267347, 367475734, 209184667, 303189736, 804024767, 642242894, 640341692, 593571086, 439362042, 240494514, 30423812, 800024501, 465398111, 385490645, 280911772, 773264612, 631332477, 14157729, 870607671, 900205540, 257680519, 701162099, 234626326, 454159907, 349939959, 232165132, 577972008, 807396289, 274938807, 60421668, 389340678, 33065729, 113796152, 13160620, 97332676, 459950291, 406926334, 560694708, 344192181, 200805741, 799824125, 468215744, 288593698, 97322053, 505912069, 487897893, 844638603, 311861287, 163345207, 168170039, 347739908, 357898629, 28153405, 723017938, 924297054, 762976946, 564244692, 92034345, 992860171, 595976711, 423208163, 225428751, 47437515, 198414596, 178338061, 408904599, 841756740, 740447052, 767122988, 508301238, 223004839, 935510802, 345291206, 572359955, 855417693, 269375701, 767973507, 353835771, 599852901, 307733671, 846695973, 658757248, 716014252, 269555056, 990975891, 869192733, 263178362, 369585229, 34944531, 721568401, 324333995, 142680425, 206931899, 376597978, 445041950, 113975579, 775636218, 143798146, 570299168, 549930553, 374032558, 726346612, 354444180, 559594261, 527402425, 999857068, 409261037, 603611719, 806585687, 758757333, 668445754, 952864425, 638653708, 918730710, 299319933, 790214142, 18979122, 890540105, 366326304, 346900951, 850534047, 132125165, 453889853, 747736123, 342221638, 387900008, 688509493, 861320353, 855064589, 919246136, 464156404, 904276729, 893825508, 238262076, 191693048, 82652125, 221433613, 795847187, 997054522, 899366547, 839285035, 259901518, 904545331, 967097496, 535946628, 196138668, 837634596, 290859199, 885469760, 36789195, 447345596, 323405303, 532936656, 629093515, 251994031, 35446231, 244514726, 976384790, 457224448, 939340215, 889734074, 866916327, 655607783, 87092968, 883693219, 598877205, 882676272, 97274104, 930885063, 601018364, 84617670, 752579364, 28437060, 151726249, 603661963, 735056311, 65718383, 397795937, 955800935, 454193977, 98505112, 289487942, 212626883, 662715640, 525887073, 745331142, 440264525, 170661244, 250435683, 740080189, 539889146, 706675107, 347489943, 19404730, 732148026, 476785722, 553672029, 340736790, 708174933, 933381314, 238571108, 451938159, 719755341, 341625408, 882234522, 484105300, 943055338, 17566123, 888716755, 397271848, 750310357, 416765796, 94403221, 902247411, 156509357, 52334428, 561014241, 743132849, 429106882, 51348250, 401700933, 639683604, 453544052, 898091344, 448548271, 90660413, 702234453, 830270441, 800949573, 154565406, 296298582, 357994833, 370247578, 55165630, 773075766, 140991686, 453339720, 472755996, 203383036, 671504251, 456743560, 474079051, 420600810, 594438667, 996072553, 279756819, 227916575, 745194946, 137046448, 530796349, 255032007, 277156766, 848988517, 294593459, 187923225, 800214886, 852099013, 384745690, 79877316, 390248822, 635373407, 797076152, 107835834, 491074746, 668286557, 433975039, 7229373, 462697091, 883187395, 193111372, 762006167, 536493799, 545836629, 576159970, 582032755, 902464555, 835193706, 322505418, 605297086, 830406396, 406715240, 31838114, 634410859, 985018563, 728344146, 491315476, 446608126, 231204729, 338017228, 857103297, 481904224, 823155596, 706241993, 200611634, 960990380, 932711380, 215459632, 985324281, 729645472, 474682876, 473520896, 656800440, 580768862, 151578363, 73876208, 377939358, 141494952, 718081668, 505392736, 226263940, 475500626, 280388395, 626871328, 348857107, 475298664, 973029032, 619253786, 805204698, 296760903, 662767235, 263795330, 801868931, 526744746, 390339549, 699968479, 437261705, 2972159, 607900795, 523371402, 601407860, 289907026, 870098199, 635919503, 427257764, 180004245, 206875407, 439438392, 920042571, 518002724, 399272265, 390608323, 234352436, 793812870, 125612496, 921546753, 777196344, 569011583, 934292028, 838806654, 876429338, 672025065, 902618804, 458381215, 964599574, 562789745, 83348609, 321760160, 380366525, 258994339, 615642719, 144797991, 53725451, 160404085, 887743382, 887412535, 599563283, 158846111, 304407930, 273887177, 512472504, 78332044, 458368586, 200488295, 553386508, 398887758, 649615646, 894511494, 634966241, 502956221, 199634033, 469473379, 757824856, 75366495, 494887108, 429121968, 700777190, 985559833, 301415120, 928660006, 433134559, 398273524, 26891825, 784307004, 189852533, 50750583, 900901923, 624224812, 484555893, 564768960, 771706641, 437451983, 985225331, 566360261, 307341121, 670451356, 284985312, 990015628, 828204230, 661441331, 66632799, 7755508, 982944344, 64069223, 363018232, 307422104, 427595023, 60770919, 134972891, 402385979, 319581056, 959013901, 226652642, 57314877, 950243057, 373253574, 602922217, 596575357, 476159673, 610797782, 982452176, 478061100, 839268397, 276867116, 25417229, 283684154, 610676812, 731939678, 756181340, 945805659, 189309769, 415818118, 741136666, 857245289, 914432340, 662777279, 876796325, 80042347, 598643374, 134839125, 182519018, 949342652, 566137016, 688903826, 933392835, 199825134, 237551174, 289465034, 806523840, 368923855, 707967036, 894924803, 971049697, 302265489, 24896700, 65676798, 439457610, 453453116, 431572519, 425342812, 809778667, 76615505, 873515498, 379444600, 353567645, 432585954, 465056139, 952842592, 366499998, 947427654, 990813032, 694211861, 599697645, 100933282, 82734938, 991789923, 762574905, 378372400, 77205932, 334056496, 479547192, 532143555, 615069851, 994459893, 621862802, 990203813, 697779690, 337015454, 433991623, 211434673, 768079662, 481054453, 598237166, 274218212, 720823758, 956583735, 322258295, 615681339, 521188229, 705063320, 498073547, 992936307, 624743927, 960547780, 378730542, 938652752, 40138370, 991442553, 897255640, 999356049, 188653952, 629623209, 752630626, 123751706, 930048295, 603429193, 794035067, 202748646, 309273785, 232734888, 413276958, 942449864, 967464098, 632554729, 745346734, 458873256, 68789980, 420958380, 140487510, 590197457, 322420940, 886222484, 826759555, 254662297, 515859415, 328288881, 907659165, 320267054, 511092434, 827564453, 536522956, 514634862, 752922159, 774325890, 183318731, 881474566, 221824213, 352625401, 724365083, 926903219, 252340438, 5038878, 623588493, 265511218, 393155736, 206582624, 504102998, 968918429, 236823761, 260443302, 219869748, 115105086, 986315997, 661191530, 44315925, 411768007, 275620945, 486823464, 522604244, 374322793, 419321836, 489660734, 414420571, 293725924, 611597082, 569515019, 568667371, 570575927, 49755225, 703153001, 537501921, 615594848, 817450633, 872823500, 713744893, 565711326, 854720385, 797299734, 342981166, 378737884, 70731133, 264220670, 922885526, 522864381, 542641719, 368683279, 873426952, 278618170, 635317201, 359727810, 965530862, 361736049, 152076769, 752189724, 257558641, 198399876, 443989382, 898677098, 662183951, 206353051, 551608190, 488046265, 401063296, 326422735, 911848181, 8512934, 337231013, 497564975, 402202018, 429845869, 387214288, 973760981, 871736847, 837643204, 635949359, 442136169, 223188068, 35977480, 241900443, 396777480, 943225074, 685364003, 90935623, 897658874, 421086712, 259060067, 24745977, 647599717, 195930540, 56064796, 909105334, 314616490, 236197429, 822153646, 645445454, 5737116, 380964465, 346209820, 944584204, 993200035, 810881480, 196940664, 904758327, 97487792, 208576028, 96283793, 106819763, 949288601, 188293557, 503245403, 80155781, 364220868, 848896027, 330166799, 267081564, 651942321, 280049755, 240944037, 961779556, 285574882, 122060499, 2200992, 288150183, 755360436, 381217227, 440845861, 943813013, 732477917, 454274448, 948156389, 63746735, 804414516, 842214896, 382445756, 665560422, 435064089, 872888650, 503224326, 492990485, 681698223, 952285918, 990073225, 492055867, 281261743, 952342782, 515705547, 297803613, 959204306, 145176963, 264415540, 592950728, 144280844, 919057863, 80663540, 273398667, 277815367, 974378865, 787975350, 153065714, 665338830, 427501918, 32650087, 287677307, 362340631, 359119614, 37193703, 796631170, 312741584, 270022624, 161511363, 103625293, 176323456, 173329407, 270075311, 137417903, 678831656, 818980728, 370738550, 445417382, 838668756, 477805261, 162561412, 271405785, 387792422, 934158121, 590730679, 199702694, 929089343, 373070956, 170326621, 252452698, 527483488, 484701796, 112036071, 415230515, 174257530, 678328299, 211267871, 252430389, 622078572, 12016776, 508583930, 340072840, 701980083, 777132831, 37801326, 98278174, 848968092, 985759487, 121261046, 747081420, 698894907, 503150948, 986929474, 502881902, 522200685, 563504686, 631998073, 253104702, 488131282, 284507766, 871699392, 872519654, 134235617, 249668840, 669114037, 593822402, 206400028, 896104909, 661685242, 610500278, 244108513, 789712724, 180153994, 174112743, 121525031, 307846214, 391653778, 819147733, 770647301, 454872637, 815625662, 733786159, 916776890, 937244647, 801832609, 861727093, 685283358, 822136836, 180154782, 549549099, 684694170, 582250326, 53904195, 226797096, 960132102, 89865630, 532138067, 567303333, 943787441, 272947518, 378748702, 784850190, 891708525, 90849580, 658223963, 22803091, 224504317, 403038626, 409741121, 816894526, 974475069, 726911485, 158057524, 123024625, 492944322, 981455827, 787847886, 293320905, 645903807, 297467547, 436392568, 683781247, 82306246, 701628586, 343724464, 307702157, 27887661, 731786412, 589209860, 691533249, 551658267, 898357440, 400089882, 750287758, 352396311, 180003532, 939510739, 221900799, 666272400, 213238215, 902258389, 203504750, 974271008, 534152410, 360050522, 398220633, 873143675, 328400231, 666539233, 202770755, 975089778, 971257909, 198661722, 659399331, 462685285, 747315603, 194751189, 326236476, 400739705, 847278668, 992669718, 812096028, 971907103, 793285276, 885147112, 393761002, 769688498, 743823773, 661741008, 762380437, 651548377, 293485193, 308709785, 968804857, 762774252, 873570249, 651307314, 468382717, 68150691, 666150219, 568221932, 22734347, 628005535, 711494244, 416102245, 663530035, 721813599, 525432087, 233826276, 354764948, 532184115, 14620187, 575662820, 844069685, 243282867, 99675189, 731906635, 170330228, 732090490, 245601163, 171419262, 23320293, 746146504, 46262715, 108428764, 704714401, 920244443, 200088920, 123879486, 794810919, 268723491, 797789559, 648564514, 571967570, 106844937, 334798426, 9229707, 90538, 702583297, 37359919, 779260533, 487256312, 602453577, 193115712, 981375760, 173445943, 34538780, 448802874, 816005921, 595057484, 430750035, 505879225, 521741501, 730787758, 787049311, 408139581, 966739093, 731563375, 862583073, 78869013, 301468357, 499834907, 142578214, 894902686, 336295148, 968577988, 501237669, 668268697, 482400207, 472904271, 807506831, 427694006, 769112334, 953468314, 225972776, 635619099, 920480227, 761828959, 539415976, 668315563, 651745707, 897765822, 275345269, 761841425, 860319481, 256936164, 780301057, 724320055, 895776271, 281797225, 328744278, 327495571, 922466165, 271512060, 131229126, 491433532, 563015525, 916576719, 275325809, 162316341, 960660705, 692457690, 806149590, 589451342, 198870146, 460959489, 431824705, 379606601, 762267957, 621119603, 404993395, 469067170, 990983882, 811660820, 894098326, 872895305, 799091345, 258110188, 717730299, 112598483, 316081731, 771639124, 630932112, 325715041, 309285080, 425977201, 854948513, 140317032, 411734440, 85906978, 326303459, 992403760, 839229301, 554950359, 651188816, 228375568, 116399576, 717423105, 949954687, 108934402, 606906950, 41381491, 490949136, 151428304, 415467106, 593168231, 442720686, 230200855, 961911808, 471817971, 269961732, 459760033, 225590457, 757859347, 865951663, 52282118, 648007755, 402290916, 262892239, 920867893, 225825540, 496286949, 278338402, 483914093, 250143281, 297454051, 413375030, 795355403, 88167127, 272026859, 48888500, 826564246, 914454505, 939222797, 575834165, 489923810, 966315555, 339615466, 629836255, 650198287, 83277874, 180471559, 628450452, 254912855, 267601439, 772980188, 743644222, 883799456, 293784921, 416472046, 651618222, 38569769, 721668954, 580368260, 870833050, 821390277, 390939109, 462448795, 808095948, 829441880, 356107738, 614123761, 396977200, 816318096, 894188739, 24147205, 138885402, 375455008, 656545811, 596844435, 747936246, 775013145, 698891947, 581031613, 909321607, 404398005, 643624381, 474024963, 486630703, 880425160, 660116033, 506870978, 631149979, 510850390, 510646979, 650015129, 703439552, 668338170, 807773351, 249408971, 575884731, 90707295, 637711791, 350021693, 956890569, 124491932, 467237508, 906696094, 262515644, 376092348, 383294494, 675706608, 643174196, 348291985, 32160069, 756868488, 880618377, 30989660, 484820409, 575653080, 517521063, 373959571, 219544703, 274643382, 571882865, 730017532, 152016834, 231601595, 692445985, 545353889, 591245206, 42174334, 53408420, 567515316, 763568682, 247499092, 770116901, 30969942, 955689643, 446967684, 672049802, 702551034, 437397848, 649610439, 717183487, 394812096, 166243140, 675900340, 765221582, 814951743, 531189964, 754141099, 866099864, 601263979, 272375044, 767479163, 992198539, 975642429, 971915849, 490532007, 364550574, 191255031, 772920417, 14146983, 623607607, 357723301, 13944798, 944928772, 381219909, 928262620, 352411538, 188022415, 98057660, 6079026, 640479777, 227294870, 106615858, 723674382, 72564203, 508522659, 879896254, 12679078, 316785567, 55054224, 346123748, 925270359, 182297013, 922250823, 222493852, 108270528, 954974251, 38992564, 958862928, 406874125, 756550913, 408444217, 222295950, 210378682, 720551570, 241121594, 232102460, 30750473, 290952467, 671053756, 32904423, 887731549, 728586222, 767031188, 811504732, 618731888, 364918051, 910316899, 253318464, 745434625, 793958967, 186246052, 268256609, 181749088, 852392282, 715193225, 297484294, 818862357, 487272397, 213009722, 73513547, 332852020, 914658569, 61275660, 616779954, 562996253, 55476037, 685156527, 268035988, 755882884, 231378536, 558203225, 488509943, 408900540, 696763805, 936977408, 433704516, 453609009, 205593902, 431826245, 139807145, 666935257, 370296724, 254695184, 317298490, 365924638, 206284881, 180854998, 579512, 963573556, 666121705, 915712432, 385806824, 328353416, 758066604, 500493150, 822171360, 940463207, 316110844, 726378743, 132859678, 329904441, 261045375, 211360945, 808741952, 274061648, 404035191, 223613103, 664682817, 440878245, 433367082, 750241701, 255113633, 550391527, 529170807, 301087903, 78274614, 389325727, 370503278, 417176593, 113447958, 392875825, 587264181, 775375972, 878309395, 960021598, 925936193, 14565166, 343518040, 681334833, 13023046, 862038949, 783695873, 545634814, 158723290, 208467903, 634493924, 227822989, 97419651, 509470317, 887525877, 583872861, 327478540, 184998083, 817094336, 487600260, 39282513, 891330229, 498138601, 130369662, 591505205, 369360588, 804491831, 933683579, 597427467, 778183711, 183825559, 56310114, 660043354, 544907908, 166400272, 82769446, 188178514, 432843893, 987860024, 727419929, 184851998, 933995505, 438097507, 577721033, 705563747, 884862677, 858697581, 840642271, 425647058, 819662851, 887711876, 455414381, 624173623, 300039850, 967652850, 466368688, 225894791, 295261896, 755924765, 870262394, 45583469, 158579667, 750822940, 485686602, 538423690, 254091668, 108183449, 193991359, 480442735, 742848118, 948048360, 93266924, 56296142, 768759750, 865724039, 210407463, 815783804, 748628688, 353116164, 72945504, 4285685, 453297721, 624773380, 838639159, 75039785, 140070622, 837441665, 767003964, 965066023, 506586283, 903683548, 909361264, 972036059, 356036352, 278636269, 704300103, 209642957, 167094428, 498973310, 427895124, 414741352, 912943390, 376394430, 121218616, 983283171, 790062574, 329039979, 444978404, 793982301, 954711327, 865727638, 185593211, 438208790, 977982808, 750235838, 594088502, 549764635, 805720307, 365236224, 834736207, 903007631, 321241047, 362709768, 132650759, 356135017, 983322542, 793903704, 738365866, 830085220, 510478384, 59663765, 473651501, 663545633, 210398918, 58103815, 277166470, 235226320, 210619219, 608183940, 393395407, 960968601, 507563878, 955048628, 518951887, 570637735, 32797132, 468615528, 768418446, 731058015, 662729194, 767310451, 425916112, 344463815, 203480123, 411681751, 920885868, 412005561, 276695684, 444743331, 448544378, 190227685, 276654928, 177733267, 345664621, 637989174, 214445052, 329738840, 102369112, 89418738, 714109930, 563275658, 534440542, 785778401, 781402228, 406344626, 346589225, 848115572, 300789313, 194429821, 292114674, 340653278, 870855326, 735550646, 690149573, 301311451, 663943574, 317056942, 868211833, 937776920, 282877972, 979892017, 783693798, 941221440, 644405138, 949861048, 116570084, 468979750, 911852730, 989479104, 434603036, 838580317, 38545527, 885466818, 64357640, 177041810, 682607349, 158587868, 755449688, 778003710, 523957517, 611752195, 45459410, 434073530, 8525342, 713984754, 561644721, 313697122, 851590836, 119315566, 60867577, 513843175, 114753437, 64718072, 141259203, 131276225, 189513482, 35566525, 919094645, 217253972, 837424280, 138891728, 789829048, 809676233, 826741722, 5415430, 926159616, 859206192, 304838107, 302809256, 599443365, 376722080, 752413005, 421436304, 635771317, 460155281, 998805088, 638414685, 482933566, 986598222, 921239460, 175002034, 353181073, 572410406, 761641235, 903621131, 648782396, 75422632, 813222878, 611691259, 69030449, 195345624, 545277798, 442726118, 341659867, 202833344, 612872068, 161790649, 269435019, 932957691, 622162089, 520691259, 619270703, 50186912, 176349527, 5507969, 824390992, 895333020, 868270137, 611551782, 848192108, 45693376, 775462686, 198425360, 269886094, 374459686, 453481277, 99574193, 119185107, 344592555, 905618124, 932457465, 632258615, 685419799, 437301813, 868334510, 734022898, 630071821, 486439358, 627817803, 179501867, 892190972, 782298960, 929045050, 196402336, 442174347, 409223044, 763188793, 273811337, 787432544, 384684664, 258538373, 609880682, 913150160, 330746543, 294212181, 136936762, 143980646, 495598918, 780163675, 689347860, 533104962, 550437339, 98027760, 405398629, 53892587, 595028626, 764450574, 758828197, 51582692, 11049734, 847504701, 898932168, 14931112, 946233638, 270382438, 915139361, 339086708, 525132540, 866239078, 773558962, 730326117, 36791468, 128816079, 16275579, 720724972, 207528133, 943736004, 810136993, 246516539, 541023688, 891982015, 893082576, 594685198, 742094250, 783638072, 138328338, 303467098, 522624825, 472373425, 984141478, 838445520, 943080052, 41966722, 840577488, 750394277, 362523308, 165040969, 295068273, 832520007, 993657332, 177252887, 875930559, 839047105, 92724851, 493120679, 147793052, 577930831, 201940605, 899700083, 68114558, 148501250, 831288650, 879020938, 949189198, 612789992, 34459493, 42400019, 960492569, 718855815, 206124216, 924771219, 728265172, 44405448, 173094871, 314341908, 83539021, 680347521, 998405373, 29656252, 227010409, 238911432, 499264852, 166500396, 663465505, 821608846, 732314168, 184788591, 201850623, 513073420, 899199696, 12741038, 14974318, 164006795, 969007968, 724429484, 945472085, 132794569, 669296064, 213110685, 800151606, 577479485, 675944128, 598025837, 428280698, 976996417, 489678766, 243580419, 3267793, 273851731, 736294153, 125088116, 855053248, 101044863, 291014571, 365668884, 573134369, 797468891, 254794677, 55479833, 339235441, 241982522, 429695994, 312811051, 699936312, 155177276, 135670921, 263671228, 825484133, 55869458, 677481368, 583657667, 549835291, 333562869, 610419454, 746281899, 591901092, 662872524, 732551054, 314706323, 827708943, 940671913, 418519269, 855324547, 403876839, 48789391, 640694664, 169783746, 744536667, 970898642, 207574486, 44243740, 614119955, 721421132, 28359073, 436321792, 54296331, 80641862, 75746858, 910647803, 32683771, 421139737, 108576953, 875671614, 421514569, 177664179, 153788153, 578502260, 265769902, 617511353, 272955242, 30550977, 154577280, 68762387, 879122068, 907662402, 610172880, 394743776, 723015145, 647104324, 425726131, 659022576, 402146941, 476122036, 793486176, 787355283, 143942670, 781439361, 504578416, 977158919, 505887287, 793804770, 408183416, 272398758, 367124031, 168162359, 294423742, 663106925, 888503194, 854418691, 282349786, 654729943, 126476830, 856161497, 747532583, 643282536, 771933325, 363307461, 712565377, 663706326, 415840568, 700733506, 619046346, 145014484, 413904406, 865730689, 997082292, 293995903, 171695802, 119567682, 53631704, 557381884, 287789772, 234346100, 67979867, 593955177, 643540851, 147687840, 845190504, 540920110, 99841672, 41063899, 849307825, 473310046, 965081163, 989878594, 972320298, 795481913, 9171592, 373669553, 116706552, 842158279, 675156968, 587625537, 285761746, 758453697, 448466792, 865463825, 169307807, 672539123, 473384972, 513971668, 661544508, 372862736, 622035310, 502572866, 574268698, 335989078, 459498448, 47293656, 353206825, 182783309, 211153272, 224969092, 147158214, 181580706, 831614887, 50861347, 318434926, 536888199, 402109744, 271824390, 724212806, 260913441, 435219944, 525368666, 958211269, 208478922, 389336034, 898103787, 157323884, 939613622, 326990607, 506886421, 677810533, 708343594, 591433019, 847753773, 280508053, 682297341, 193245991, 964986523, 578490249, 989307072, 894138796, 806257781, 766626422, 635535515, 175565295, 187654828, 646781964, 846305764, 374177172, 61825886, 806127160, 936824993, 297700730, 516633768, 793579603, 324710627, 289808008, 631369949, 720912, 825428304, 665310550, 378186749, 554587266, 432078876, 657628957, 286205153, 862124288, 110735660, 106583454, 395365138, 842614466, 574045854, 847052373, 503481943, 174028426, 534098697, 158745041, 831554600, 594961636, 852414826, 507995302, 629097842, 877247454, 35812143, 315200789, 491588932, 176128401, 267892426, 34047115, 795346873, 851458595, 40121937, 229267317, 656479649, 451435924, 813487800, 156959260, 167142066, 745370581, 35760314, 941025466, 229018982, 520705417, 896867127, 600503420, 941331292, 199815812, 458131382, 944596612, 835149973, 935393471, 371170832, 645569496, 302910040, 32203593, 428071323, 61459705, 834896715, 798369329, 177179222, 331800585, 490956587, 342203194, 236333240, 320025130, 879741124, 420029048, 37972341, 13864210, 892504093, 629914650, 633122878, 148335138, 513018668, 958464265, 3241433, 925342120, 616242598, 262752116, 811630024, 830644382, 393647765, 80915542, 614025686, 443642180, 502173461, 682063531, 292244866, 445279742, 701560214, 369577457, 348319691, 777094063, 115017110, 225164498, 2105715, 377662577, 523153704, 521105968, 8659253, 780923156, 6491607, 216487473, 359488843, 164177586, 944636339, 572093295, 296513896, 137622307, 61981935, 763783757, 458256034, 795211777, 858464680, 254371173, 628449105, 77519469, 679561204, 52097117, 925437316, 332378431, 436698012, 828731345, 627800899, 819275949, 951534280, 532531594, 759984209, 342472922, 83678029, 347902976, 765127371, 992299603, 556846239, 294615315, 507592023, 208134616, 978120206, 259574491, 906155125, 884836064, 716056665, 879795941, 34213048, 285704258, 369798597, 515755238, 353402360, 486324, 199268222, 812642274, 221091823, 319946201, 138395616, 441562869, 979661776, 554451769, 266690173, 566358966, 375400262, 268170695, 997290058, 681140771, 815975113, 173535397, 467838705, 783752162, 246753351, 347556061, 225194623, 217158428, 435685661, 546783274, 40626538, 982947407, 168480184, 641314933, 580832657, 972320183, 55055712, 603323357, 890903723, 147874117, 360991670, 637226269, 322447285, 40568591, 88953839, 669314140, 703541519, 580587546, 872274636, 649109826, 60864246, 666041438, 278534160, 424721456, 770549641, 77881490, 190805872, 993118748, 471849682, 735973993, 465102309, 88794146, 168797340, 738860321, 387843359, 697150590, 165613437, 241188641, 446842857, 308560560, 19423632, 567655968, 307970358, 404102906, 309359772, 645365048, 689993018, 846057608, 525646052, 765011941, 994683413, 881476229, 48293086, 394345637, 69222781, 723220118, 656635278, 575835797, 148308250, 5037646, 4788468, 118238931, 378597467, 782045221, 539036976, 10908868, 698345979, 742994961, 11781423, 215604539, 462206368, 890867361, 351853044, 716344850, 255863319, 322752821, 353208605, 306979334, 203381196, 106115645, 372170288, 673390613, 228948125, 138114215, 336576124, 511850394, 516405801, 750641904, 102655041, 559330006, 533589239, 826750957, 454070185, 635673568, 709913574, 24031330, 862242702, 688427877, 448151301, 699875319, 671609820, 11010890, 22235204, 812278813, 971521223, 422507129, 486510556, 846811265, 65880202, 908905660, 988117790, 388205759, 345595669, 960573119, 384365362, 816044698, 366230579, 757398790, 38675888, 80450119, 272712292, 273555097, 119379305, 686277541, 451603803, 42810816, 514184803, 492261461, 84405350, 125978684, 608863515, 602295859, 562758810, 328838539, 2201072, 804452055, 682096357, 99217615, 60246461, 541927806, 335144366, 113752000, 866951245, 344405697, 200033839, 414317740, 737376716, 450465464, 633032805, 490738831, 513563041, 830829064, 687557168, 268953091, 92033968, 626523849, 452387144, 666367591, 592391799, 157693657, 983202210, 174827730, 403080988, 635183666, 217314266, 923371208, 232343800, 622737908, 639691484, 445221282, 666805062, 200198705, 751253689, 987347686, 791728078, 353090673, 265416268, 392255681, 590821556, 984401349, 156875653, 954296889, 182593934, 908270346, 868001388, 883443086, 961182258, 760815433, 856897745, 391490314, 266520944, 476140721, 86916152, 453643220, 756636701, 635483967, 932968992, 53898116, 215739285, 230305421, 218601863, 929562824, 142616288, 814767807, 323538058, 263690139, 875300568, 377465264, 947004085, 66409773, 448140159, 226209725, 677175900, 3858226, 30049052, 669183355, 90795143, 412414234, 852433661, 692422582, 78449038, 977947288, 372523072, 770666522, 134338545, 920132680, 873798938, 376183803, 386070683, 48048285, 122703533, 710588630, 939900087, 790951469, 986928179, 480957313, 43097937, 870271087, 730315099, 207767157, 36004229, 811021635, 592007232, 470258639, 427496100, 846995335, 40568000, 647746620, 343023780, 608530289, 611242371, 743112231, 546230740, 958885134, 13720002, 526096669, 42745409, 984204448, 247884178, 919352803, 28119761, 655056495, 53320557, 610170322, 411924375, 861936771, 336941898, 587786841, 273830673, 477992295, 369664324, 555107368, 46178818, 323140808, 578400645, 874928877, 558326133, 645336179, 497382691, 576581147, 208886461, 737941647, 203691155, 782093417, 863549732, 720140412, 87466011, 98549673, 855037944, 920643899, 378630401, 834677248, 856844669, 487696859, 404520519, 55195617, 394378971, 324401534, 430265467, 30478525, 379284966, 803645803, 254435110, 342920422, 605975540, 598674784, 617588218, 172109997, 872798837, 986091171, 215751267, 525509090, 468321751, 460866028, 746509058, 589645455, 281920516, 200825574, 684524647, 474254393, 2454401, 711370987, 794251544, 483240024, 796666208, 160455419, 181966242, 173970934, 289616239, 88438286, 863694427, 971981913, 901994061, 2365495, 625738503, 484851301, 896843225, 918667571, 676453438, 367321989, 343916268, 420028402, 111912525, 714356351, 168623518, 9102486, 556388909, 118164720, 551158520, 989704965, 569249794, 304567014, 246622173, 37436134, 775312700, 143487528, 764355171, 775679603, 93825652, 83970893, 50238427, 447619829, 729653587, 114093114, 200356469, 984567263, 74468221, 133245576, 580380253, 614160090, 248122675, 751061263, 408312125, 88969049, 916534590, 190444640, 379945833, 489299676, 645062807, 270392398, 310558934, 700122739, 47477888, 302777451, 714026565, 119201351, 989271059, 66719807, 679613148, 673561301, 499311127, 809481398, 785464983, 937334273, 817966181, 332547965, 727425144, 463433179, 670069796, 721440090, 777038708, 885821600, 383905493, 526346041, 660617034, 924436849, 575528275, 110478950, 1327988, 646479836, 117126501, 741983352, 606355140, 253625191, 357672145, 989621719, 366787776, 763369139, 604354334, 588349146, 901557655, 319814969, 776245767, 474950303, 197981607, 718780967, 387000822, 615231193, 703509897, 928007234, 756390861, 949373419, 631581608, 524730229, 429623622, 185868476, 89667701, 186568647, 550693280, 766908981, 880482779, 686410631, 325744033, 124978476, 952245263, 985136625, 56843709, 332716873, 273550777, 30698376, 559878827, 189486096, 633907875, 671228422, 81108195, 839771407, 509204212, 662034345, 162974032, 339664421, 746813948, 219117379, 89667819, 755194435, 335987384, 138948079, 522884330, 874785111, 399505456, 965004041, 402187898, 123991034, 637566790, 711734371, 872657003, 430873561, 321624484, 387219995, 91150319, 104766231, 190715326, 541706544, 683262626, 626977081, 571687257, 140199799, 223178803, 114763048, 659063526, 784612798, 709343936, 555561235, 263319046, 724876584, 46487088, 135527117, 969466297, 558594427, 870979803, 117985280, 837988782, 108777583, 352090848, 949991063, 466112371, 705671922, 783052140, 271130866, 541316467, 303658212, 350572986, 412139584, 716806668, 302720667, 201161669, 33138217, 747257241, 701588426, 757124021, 89362956, 736668872, 384088970, 587595459, 833833656, 128171345, 780880112, 745492951, 168484402, 219389191, 685072736, 50591793, 29240025, 796118693, 596318871, 819142860, 786645027, 359331272, 92816856, 440805010, 481368363, 339858612, 758281313, 944189429, 34458862, 275186868, 22666845, 201034887, 874701844, 566417319, 991920267, 213158911, 123067175, 939470602, 899998589, 389570164, 119928206, 565339942, 307071836, 789832368, 455825495, 174076812, 650207259, 541343112, 23608288, 22015815, 305691700, 141798971, 251329838, 320745885, 604277225, 773899580, 524266111, 296039130, 501563644, 591723653, 299817648, 624558913, 834626847, 974524458, 700014963, 913959125, 316144005, 656697876, 409622320, 301838392, 395528542, 326643017, 492773220, 81098630, 773131788, 889698242, 26433885, 711195618, 962162401, 944525954, 113367713, 526956790, 325827580, 725352585, 133935135, 489265177, 381716119, 622100375, 834404957, 613529280, 822780164, 966961536, 681387195, 643006310, 5947390, 329872334, 698866640, 93061019, 671733122, 567255883, 697748453, 797677456, 685954554, 468466014, 303910280, 998173992, 212364580, 707053325, 123191653, 249316182, 450327050, 441315557, 964929561, 234535142, 148281557, 891724691, 967471238, 121498624, 366196623, 749528148, 308612357, 817951291, 912762858, 388846656, 267062020, 576679710, 879274669, 25658176, 404028250, 109351505, 767514559, 110194239, 75062453, 665699970, 5996510, 231704477, 267837144, 224573057, 507686386, 623549823, 950210993, 800563988, 712727543, 950918322, 233586651, 983431606, 489135329, 555650526, 497942501, 298804811, 909267551, 782760813, 229250212, 910376369, 151230959, 864415390, 34381698, 425511307, 267255896, 797301771, 946128025, 356511327, 670540358, 722736585, 286640193, 788257938, 517449350, 354662555, 91993026, 378028526, 332183507, 383574105, 558783060, 26240986, 449910851, 156081291, 96676249, 992594090, 231280346, 870828031, 897205419, 547002455, 674497866, 579894119, 727754814, 361106494, 728526308, 877168226, 323063304, 603614607, 99799811, 674994838, 996467015, 491812825, 753887903, 253694876, 504391947, 986314000, 682392462, 109134330, 60886837, 394092890, 889565338, 257413108, 828804096, 769289651, 49902305, 417229126, 154071375, 900914943, 734960562, 732454077, 298097944, 634355042, 906720366, 362475914, 310644648, 212052168, 307467004, 514867665, 268945480, 995563918, 88182840, 875033226, 55803072, 816155572, 874499445, 76795418, 748877649, 733692035, 805013182, 440683497, 296358115, 407049687, 471892571, 51326522, 101238929, 519786580, 606410653, 932632327, 49943022, 186815975, 809891775, 56459265, 76496094, 238721991, 98028070, 852963093, 69278337, 529330707, 362462511, 434709950, 342488506, 58656739, 871062385, 952958211, 933004255, 493366183, 544782926, 61561730, 723487874, 466782646, 971289522, 219101735, 346381023, 72728496, 186481385, 606679546, 800395249, 559076660, 698103475, 777638560, 867664055, 205811312, 600638739, 429681770, 223629736, 336013225, 386071678, 693073714, 528524737, 859448062, 856079269, 740440375, 837223867, 992724258, 984899806, 423515779, 115418069, 98939575, 692892307, 67529626, 19337767, 471516619, 704284999, 304530898, 759191055, 922851394, 827489843, 351021820, 280450193, 127053797, 818098272, 97147866, 326746394, 32799309, 803062894, 712374870, 588264156, 846907223, 586913505, 716245483, 336997085, 916634191, 3956649, 81894004, 815955034, 527824032, 100523583, 434268694, 796076826, 986884705, 668705235, 295194363, 157373874, 552596477, 503261911, 534230841, 503786387, 867421775, 381795219, 167096385, 144952453, 154915871, 947119135, 289873358, 501696702, 949508331, 572051144, 839495435, 349700508, 259176319, 764368731, 776374117, 692425408, 992396221, 951573349, 275490854, 510969340, 516862028, 708076480, 879692745, 369253145, 776809676, 130737349, 696753671, 162572772, 794744832, 967759599, 306091705, 413856626, 439831927, 621070841, 579050274, 643134747, 730102492, 188793059, 368345850, 242265422, 497855062, 279724486, 395093998, 831944210, 943542399, 76138271, 86753314, 105397254, 938452441, 163769942, 97531296, 521217615, 421347132, 549017962, 894572524, 665896688, 908611179, 481343132, 37546991, 355052915, 807192291, 780435450, 738879004, 22074543, 756931349, 800951398, 61803839, 7273332, 831342232, 81460857, 632526241, 146578982, 965767356, 108572432, 353703754, 682572981, 883359241, 692135954, 342525151, 59829847, 640259686, 850704376, 177728444, 60345519, 426413263, 882533500, 433733697, 419531586, 523680803, 673845554, 75422383, 421260624, 276524488, 751482218, 376470529, 786926438, 972766685, 319715853, 454885398, 57414055, 806979375, 330939347, 489573147, 705221793, 14510357, 618004746, 19409675, 546989266, 386388689, 171512234, 639673110, 985446329, 646948876, 826542262, 475238949, 288596651, 163264916, 88470470, 672709532, 451411927, 808798462, 23268940, 435629194, 493211393, 263368167, 408735337, 282609502, 36148119, 210502268, 55421549, 738406654, 705736050, 587173527, 8899013, 45423933, 258105065, 372711532, 198087266, 889236583, 260226446, 648684403, 805360194, 151378594, 215849335, 723204259, 161458176, 326350488, 892028834, 869677341, 786276529, 925638532, 104337362, 797713680, 327903084, 224394477, 651677761, 735699532, 534385896, 846360483, 78405398, 806469002, 638102835, 975982448, 325872701, 396580135, 875205225, 888288682, 168150653, 71869751, 463335726, 819586146, 809295286, 16338333, 13582663, 427037118, 598431826, 400259493, 817911587, 102198952, 245482940, 587286306, 279473699, 710537803, 858629111, 650622197, 814409545, 376659445, 780582727, 49217266, 152335888, 6146950, 176011807, 485394732, 177270605, 982000924, 331919108, 689558040, 180069420, 465289065, 522252735, 618336640, 324190398, 419611397, 960559108, 892600206, 352343813, 908547308, 80020252, 448749243, 820657447, 142217366, 575273717, 925367819, 200704433, 140235755, 451865750, 970205395, 593356417, 289352238, 571488166, 575039691, 544219289, 324691101, 395242478, 249884856, 447569004, 976933117, 373650005, 414339032, 604912486, 964642019, 64281210, 263238106, 618151043, 393237242, 915258886, 252740706, 536871108, 141962463, 250240888, 649379994, 131999369, 267085110, 849455986, 472457612, 71374892, 562146955, 14765012, 169402560, 509187839, 887383404, 671368546, 567459656, 934941834, 545775565, 217761811, 261473062, 305221580, 296213076, 996001769, 38944682, 790360383, 134764198, 613094737, 527117388, 592943423, 601484797, 610592923, 319329009, 350944082, 83327247, 744045936, 71983473, 392690431, 822600477, 728820317, 504633969, 46270650, 891425408, 465025096, 633427007, 161519144, 883683761, 185678867, 138428721, 331612292, 166069156, 776376909, 456605073, 375152180, 804734737, 719844460, 315940542, 416977925, 646593836, 880272863, 25668895, 474669109, 193069252, 968183365, 231770070, 350024408, 650816288, 807107024, 973399830, 778128543, 266342985, 704356923, 750359021, 438700676, 14061691, 527135908, 556911605, 74259657, 962664102, 472513689, 992548496, 61871655, 682083948, 567332005, 448842980, 528709194, 450175306, 316996975, 920155862, 87287170, 549826177, 566304559, 239644891, 724935469, 201639071, 942995811, 502457859, 803223101, 844350848, 82491887, 845356887, 861300810, 566859767, 478885222, 596772510, 750894030, 576666288, 682533449, 234495102, 710289639, 617860234, 667485377, 813108027, 538611187, 970702944, 757667250, 871670267, 141506533, 660568113, 914076655, 380358375, 203164688, 967956636, 185260835, 631414146, 331057853, 894403395, 827319889, 325762804, 579330941, 287091744, 883710753, 643453232, 314430198, 488125028, 804323045, 139032782, 235427734, 879396052, 940853768, 819416782, 347444277, 189405713, 903636739, 247410023, 935604528, 427418620, 701308334, 399566759, 249805052, 123913784, 745508774, 125576226, 552441787, 911211663, 157663382, 221507507, 17306840, 107809372, 576891363, 569462240, 574281159, 978982033, 25698500, 461688359, 583300614, 757917540, 848631771, 778103495, 639817882, 276193148, 933934275, 359165617, 718034689, 682724846, 178947921, 41601118, 931912179, 131030142, 202223801, 22021789, 117631081, 635985603, 194433979, 647567047, 685361299, 849287968, 754278437, 151909531, 690260749, 901650550, 98368760, 45462398, 765839441, 998099095, 213801555, 367440558, 227560030, 90370939, 493350564, 304593533, 966044912, 810684981, 718965679, 444709063, 924698598, 385149123, 947152624, 648503499, 450030393, 971711494, 174831385, 427687758, 301167891, 168580617, 927972243, 390196185, 550460466, 509073433, 336713512, 895781549, 915534617, 179526815, 548424188, 171397276, 409271205, 353658503, 793262078, 699062055, 110046822, 309506802, 832243990, 819509690, 797173776, 858658194, 624601446, 850066104, 749793996, 858530470, 302941844, 370806508, 170170156, 370841653, 404451130, 884077351, 869421837, 997305865, 131899462, 815321991, 239433423, 717933256, 65150297, 142911664, 452572291, 253291525, 928255604, 226896916, 991461110, 734767069, 789477422, 602740253, 790564219, 208900935, 904087155, 398566359, 895378282, 321601609, 250125453, 390596557, 561153529, 236380832, 105959030, 478118215, 250157823, 776960070, 8241845, 141988013, 256590281, 573410498, 516573427, 633154391, 446876662, 963022304, 701488085, 310425028, 24262214, 451719951, 511863450, 543699356, 33344460, 65570009, 782861777, 258096370, 458159365, 988517377, 292372573, 508002669, 73147517, 427750281, 187056021, 763084229, 703932398, 226084539, 80987493, 785749569, 106069116, 139217775, 281867579, 702326251, 40948492, 786995501, 555079373, 867929960, 356655432, 405261607, 18771956, 1266318, 332065958, 709996763, 410476156, 52698741, 650036758, 584197035, 979047506, 850552772, 123633438, 790604912, 503107093, 733780009, 445601307, 570969366, 901774438, 691626415, 572991474, 356282871, 380808697, 524566428, 767942873, 876564874, 347358340, 868334311, 141804804, 165750250, 678340929, 266158175, 361245772, 174673861, 78104727, 940833958, 271202712, 879552011, 142562794, 814510963, 903203569, 83122307, 453286141, 73486828, 21751959, 491443569, 864998953, 403135606, 907253075, 654974336, 923563012, 215453993, 180004452, 561090376, 532580877, 502656823, 785629821, 253759280, 29004968, 77727622, 819345409, 98909363, 525435029, 763697260, 918892449, 346831140, 86619898, 179755716, 573316431, 106641555, 556811476, 445879356, 458104873, 743104750, 872757823, 352425513, 98165253, 918875465, 955394401, 57920956, 948959513, 959851979, 387461207, 330492581, 747516582, 844385144, 673114062, 266034479, 974697714, 528515574, 944178796, 688958248, 432097144, 983789267, 937568598, 523565567, 636271746, 207380918, 448531364, 446790779, 431534782, 998832248, 124045714, 144043426, 164021881, 790229551, 657545202, 946717345, 860148042, 999907869, 731518338, 303572889, 163225654, 3148513, 344138351, 592608585, 546459557, 886674323, 629653779, 7319080, 240498623, 347132317, 965564130, 650686896, 514991084, 35742730, 831282726, 260191862, 807028411, 631491606, 146306969, 262094150, 888923639, 566715475, 537387070, 85720525, 957637206, 720847014, 256495112, 367865817, 14756455, 739251810, 422040953, 500476923, 280178064, 36115497, 540562899, 278665178, 240710738, 424356516, 781840525, 855958149, 680416210, 197785360, 108379592, 207378350, 611222831, 904074741, 553989071, 41278691, 655480980, 290382521, 652218108, 145946026, 434957332, 110179097, 665574639, 682030168, 580609313, 674176594, 198241420, 571046141, 361864792, 171192784, 815001796, 242576555, 613416030, 414240667, 961931428, 721521510, 843893066, 995618777, 378273581, 487484424, 580857509, 976500189, 405427680, 901526059, 287809761, 878071914, 4104899, 537929649, 147449974, 736617954, 547324984, 394958569, 416716218, 52927929, 313940211, 412201077, 961702614, 117975968, 934804600, 867512450, 413839655, 293410853, 896062251, 410069876, 122261524, 489996603, 278197517, 479343077, 586647781, 286891412, 498023362, 487000580, 842101567, 790614081, 546453809, 847520871, 432186655, 441513495, 786143434, 777834625, 404330413, 300643842, 677193064, 472956670, 606706822, 908606400, 419736913, 723273768, 466052346, 899925361, 264199661, 56374548, 580696892, 839312203, 146739708, 418129592, 484981680, 583887021, 734735907, 763506565, 170299028, 319448353, 105328570, 229085688, 463537, 711516273, 747904004, 993438605, 316296856, 99892722, 47004575, 788655969, 511170430, 332297052, 516242390, 756199560, 584693883, 106401508, 589083084, 948115755, 128593440, 255499585, 672264218, 759820076, 73655062, 211521203, 813411778, 224133645, 277034684, 950877962, 63013075, 726222989, 146747940, 766519044, 447875948, 406316911, 672828388, 20474580, 659644100, 991423180, 48997044, 407234781, 852250448, 865666002, 279265206, 870218241, 840482204, 109685647, 403002817, 974406390, 853197236, 508109850, 111214392, 311551508, 921902601, 905942826, 876924984, 800376839, 413962135, 692532007, 385993539, 898723758, 715115310, 274731462, 271178544, 490401352, 517793272, 701859759, 952505171, 571544923, 626176074, 879782470, 228592161, 576944926, 666380939, 886652092, 978169939, 823496636, 810147421, 711101665, 865927152, 846297822, 251780638, 779535021, 528249933, 328923156, 679553064, 143153997, 953111001, 209957093, 56600497, 934565782, 79705510, 901416335, 173812281, 905992530, 765854831, 272709025, 657698118, 946445002, 404773340, 951802964, 997387121, 798462677, 741820175, 165245744, 191498354, 149548337, 823263848, 819870535, 343803627, 936968241, 114523060, 94457758, 824298551, 149673264, 857110679, 299066969, 73312014, 390429862, 445092405, 788785689, 422205628, 194766210, 993021722, 221532291, 66611483, 45730410, 157067211, 939844835, 778197226, 809026134, 88612539, 749223627, 495687175, 435606559, 293237190, 404521984, 276399500, 729490876, 221164970, 456536245, 500639287, 184976930, 67436525, 239481963, 126400046, 797252193, 979534625, 722992505, 913217454, 786394997, 155216322, 527765707, 845231622, 130678211, 851862834, 851975550, 886525803, 684541394, 328948160, 766390158, 195662604, 728870039, 832996370, 447121147, 9083543, 569854981, 335830148, 177019183, 645182690, 890086940, 237428591, 540486432, 460213460, 389271582, 493507968, 150346648, 467951647, 399249554, 278095193, 91846439, 241141613, 495920543, 359975439, 943294988, 318537401, 46275074, 121632684, 243706184, 608593958, 95755434, 687020841, 357006486, 466407236, 840282142, 767342126, 589306988, 818569892, 192026828, 625726256, 35166535, 497549604, 246688709, 522099507, 291923564, 656703655, 26124438, 155696416, 722791221, 314298078, 929831681, 73553410, 749232982, 850010034, 401905256, 399443028, 641193740, 32906350, 627213239, 311950005, 214306853, 845385741, 273738910, 734657113, 397062236, 900256339, 127026843, 551390863, 475453853, 303120416, 67805162, 421660191, 678382121, 291993171, 999617966, 620184233, 349314025, 860430620, 26501853, 213632230, 517177801, 29946289, 726165149, 167598969, 358385190, 315964384, 326984593, 28049571, 728224574, 324634222, 670560343, 244105078, 147728544, 383422289, 378722309, 75055767, 890924351, 202796333, 350598517, 409238539, 832904032, 405941288, 972706367, 963139753, 718358416, 926673490, 598565161, 617302017, 633006046, 592773607, 323301537, 347647807, 104181155, 678783893, 278857061, 422790593, 394360642, 744655748, 876875466, 716753405, 86978338, 164493890, 79959613, 265806877, 638634194, 473770425, 551744187, 646146528, 247337136, 868491458, 408356141, 929240875, 586717675, 797102638, 720857309, 492101167, 348337316, 470127919, 28330627, 403521363, 33941785, 243482984, 525698851, 672888553, 553110452, 398364054, 540245812, 301174650, 888459954, 524033711, 339043406, 115169874, 785698695, 926582424, 586360708, 191301568, 355083065, 638393534, 840652138, 972464206, 709188517, 146272110, 509858230, 159278280, 591015073, 793071610, 848309199, 888907572, 805787272, 949608324, 772374986, 422092293, 526332536, 439163465, 44623826, 476717381, 422430773, 671498734, 340164062, 540773256, 565616496, 718378809, 201553161, 424304252, 568118625, 279243578, 962887443, 761171443, 514401246, 967777303, 473853500, 486412361, 924045427, 654458113, 984541295, 219768060, 644148078, 644683129, 616359085, 202462037, 961967892, 960000142, 555277131, 115072555, 990106915, 968306745, 572341280, 126861896, 350828172, 124569250, 100526202, 891722503, 189070675, 329756627, 163540806, 670945019, 964027611, 642654789, 589510289, 448658223, 771879926, 700290450, 665463700, 503403945, 675036880, 70130010, 860870690, 393170694, 418751284, 180007537, 252085910, 851695092, 358844178, 350543724, 298309012, 874346274, 470363699, 74323997, 653898605, 234444575, 173885450, 353360115, 122497976, 432852055, 728492859, 301376796, 38142860, 80340471, 124993610, 731691115, 434375653, 229111406, 387720083, 382586298, 324810098, 897270892, 379796918, 322330830, 394632701, 370969958, 531996642, 730433434, 850526805, 643181039, 204369503, 654250776, 805069511, 432341702, 740268666, 556274607, 565413978, 211988687, 223623087, 838289311, 277544989, 490050647, 602455889, 916661191, 318572078, 177651046, 799482649, 374780794, 961908674, 169751639, 176663981, 602543463, 334636808, 483178979, 292469789, 451883294, 921375923, 259518061, 708672545, 515375301, 609396199, 670875476, 947875832, 237775527, 242713192, 803267701, 346449817, 773413643, 213743777, 505572163, 936365770, 962526159, 728982983, 692311147, 168300552, 989506432, 725182570, 737632583, 642956614, 275995186, 258600807, 687762833, 99398685, 749526945, 305016501, 134804740, 12278621, 829700647, 799420275, 557078231, 221071857, 214511925, 38445134, 362773709, 110872287, 612262328, 221792982, 621857370, 787700913, 496084775, 786505058, 422581799, 753116628, 464290063, 711280030, 991288405, 482560438, 420236519, 361077581, 954565485, 381173722, 205661284, 151250788, 466037518, 438554700, 894735436, 403980436, 232978285, 81879652, 387932539, 796265487, 920676939, 48570150, 765349827, 794268471, 952166144, 289020221, 499861621, 546233685, 590336244, 666365723, 76297503, 914489631, 616161727, 366837008, 714776502, 463591357, 615331735, 908905625, 707699995, 222801906, 214820073, 315329117, 176144190, 618910283, 938547315, 272412603, 348275974, 819552934, 944029320, 481310268, 162514960, 774168272, 556005027, 946282520, 59558201, 456773199, 744271554, 483660250, 213849626, 127284501, 591179008, 446071415, 973715811, 923228806, 860405886, 707157464, 331962900, 504339912, 2244148, 295278670, 498720285, 537916802, 610997509, 989130661, 766415406, 626298752, 293722307, 577663225, 723170775, 473458340, 629388590, 281879872, 664007083, 615212969, 66508270, 71511185, 539074002, 350459701, 653739026, 262603339, 911533732, 307868704, 575328932, 692430474, 562230316, 413390630, 927696819, 820026596, 631641181, 432966876, 535323786, 826253975, 735585726, 949293244, 582503951, 112879936, 995760499, 589229521, 635504259, 97268366, 942962607, 214110442, 242790611, 29614189, 916489573, 154320735, 585932324, 664729214, 373364030, 557219729, 184344850, 208160523, 728920269, 149273675, 469430796, 807148238, 126627486, 140583761, 535891477, 38736802, 661857957, 276893284, 776306728, 986414592, 451423322, 736984499, 303134246, 532147794, 97190001, 598632185, 895605687, 721045820, 575594882, 418077829, 714677477, 791387584, 863972901, 944051804, 44479510, 634705379, 884451249, 25993590, 372005948, 146492038, 904558951, 901104132, 880831086, 372161670, 894740584, 740650866, 122429863, 514709525, 688989327, 927880137, 654009562, 742476070, 152855343, 756915483, 454675242, 34573705, 29331720, 506794706, 292264495, 887066999, 995230948, 83432624, 275692135, 140351503, 802957717, 105206751, 337262792, 459093304, 666670758, 814111694, 809820226, 849797411, 533558525, 962900851, 963130803, 337275259, 394718583, 359609631, 796133681, 946565676, 150373646, 195472344, 700442418, 465260286, 613392524, 781210461, 274390486, 625388813, 250310652, 27896152, 360803068, 806920353, 174035208, 829101723, 796706457, 858506518, 324915972, 630862414, 933046671, 266383502, 144320723, 646886272, 774596727, 178005173, 399263127, 841960197, 637649111, 847036184, 885099518, 668623184, 709532911, 439873150, 698917723, 728859836, 698225450, 733128621, 155231415, 919803133, 484493388, 795421893, 251190735, 690189237, 461736274, 594847239, 837816677, 848176093, 375723044, 288769600, 740964422, 721940432, 6981188, 940206629, 967359229, 477984904, 584555403, 842811958, 852008203, 676064472, 781166989, 396034961, 729321491, 444245487, 846292329, 856906105, 163382338, 592370071, 463260247, 7520812, 481959432, 814159285, 672900090, 899174158, 859154782, 985114707, 251509821, 685593189, 882685359, 729819713, 30565922, 108591260, 850381864, 994191562, 340840401, 686576841, 954942062, 523134283, 742452247, 837408875, 135484511, 13184907, 682816185, 18074386, 816677855, 715525086, 43502349, 942125837, 796074442, 50005077, 636753301, 332365890, 521543568, 1079253, 307353398, 255932621, 548000148, 869646847, 329691324, 923754082, 435536223, 372436282, 445466538, 778347863, 859668801, 968396504, 444680678, 480862637, 197335363, 796254330, 683052706, 491026595, 192745346, 942370300, 432024742, 998046028, 356910191, 396438381, 207521288, 201307126, 613138015, 873258605, 649907002, 614949681, 154941414, 426103306, 815967869, 845357042, 934204543, 859186394, 372983328, 12383192, 733849299, 76849607, 606910500, 136705827, 221483319, 441633569, 408549905, 452527324, 139985607, 760378371, 609916815, 441583217, 850636952, 715010590, 162054434, 502277934, 279190761, 911329071, 675254955, 995001776, 271197041, 399478374, 993428985, 304165485, 609336051, 617935979, 489067346, 401061737, 730051818, 533420231, 500149105, 29062482, 716398389, 420148471, 627884416, 727850665, 451827931, 809255982, 732882740, 395843765, 209466315, 640835723, 613578011, 675143875, 23748278, 569704289, 675935521, 804280927, 78639965, 788521463, 716710590, 898980301, 448314902, 625908116, 307313659, 172376630, 726007746, 754431826, 976667854, 831554187, 554830681, 698594283, 10890244, 979063777, 998491579, 260549574, 606090684, 989612901, 743811316, 694200023, 251497694, 987539438, 224085891, 741078439, 974298020, 282619037, 419922063, 644153398, 321861133, 973377168, 106876005, 491499803, 432262063, 182795504, 702498791, 297291282, 368780823, 295963668, 659981215, 692064129, 142779940, 91615704, 783750993, 584742838, 411090931, 530870189, 126196134, 467814927, 278447714, 484145809, 811438912, 225872240, 87120235, 122255315, 442918856, 288275404, 319038526, 112616337, 287621927, 85463993, 684216966, 803214649, 658175490, 703085356, 107573155, 954067306, 367434910, 656469370, 202864388, 296795405, 252461871, 897036957, 69820241, 135221405, 577529982, 300949902, 30829412, 388910673, 374252406, 804924205, 784571157, 425503553, 664123245, 936206222, 619543034, 474193180, 288449519, 547416764, 338231637, 305016966, 380947000, 466500368, 895470489, 802954986, 639455417, 896883157, 609987147, 763721092, 43763838, 820836722, 739912262, 895606567, 476125338, 789084690, 667038309, 522016307, 286511669, 482722382, 418316062, 463782402, 318846463, 320575411, 876606332, 251843166, 885579088, 946431979, 695920540, 667211457, 933981058, 585373885, 992326452, 567654036, 505340626, 388303530, 179257800, 912615200, 918926984, 802480074, 388347115, 803399175, 960217631, 286681722, 752102465, 783093448, 945288930, 939478392, 63720131, 785849393, 290056896, 941799431, 391625231, 42088699, 594978519, 154278612, 280366301, 451482354, 204848965, 942648197, 126787947, 276003891, 92148546, 259565554, 858428132, 917075865, 950618838, 151548276, 303237523, 613378318, 615712291, 411806278, 20828129, 843915456, 833155502, 625340506, 379139408, 16883291, 697158274, 559917791, 605658383, 29134315, 118017653, 865022530, 423580673, 617144661, 752011854, 883704010, 130961649, 997736812, 427869029, 135548412, 440270917, 810216442, 855198607, 186525194, 423536758, 67459355, 553669335, 706338484, 790871522, 954937664, 756955058, 134911059, 384820712, 358549497, 577134525, 831533140, 695605362, 325452327, 956388602, 441753345, 780156122, 919049163, 180207484, 772859959, 660953392, 714386348, 580695358, 207477997, 957554162, 24524706, 667085869, 687971662, 263888236, 465618178, 432572662, 557448416, 850127697, 345956593, 323855963, 15968681, 968958735, 968917808, 659202145, 261887758, 551222252, 246038563, 733764864, 265202539, 768935130, 117948382, 249495341, 16949372, 288610159, 718555393, 825782132, 73144702, 636731988, 808429955, 73699701, 395013885, 829700865, 232502888, 596986583, 850490742, 497877682, 357300921, 632852276, 239471768, 915995988, 43276293, 905894795, 503904929, 622265682, 159078466, 613608464, 601376720, 983313913, 893454722, 128110523, 406399160, 582401660, 983728492, 493411968, 938690364, 74850082, 568491137, 496269719, 948578465, 275639240, 890231855, 24500468, 554075686, 985133915, 337507980, 351627874, 972398129, 647316227, 287034889, 736395535, 855652265, 912602844, 743963443, 800085547, 993192507, 912391598, 85826685, 936733585, 986033367, 473951732, 454974620, 368920938, 802442926, 610455180, 359801182, 767183711, 654258962, 128926570, 962502127, 417224947, 194579391, 114806925, 27831253, 921320845, 566898079, 505290464, 472506861, 381023875, 458720706, 214426576, 673430724, 473737442, 234753880, 928485621, 709147525, 965672610, 695405812, 194654102, 142439026, 352835881, 641170429, 244470005, 174740643, 185103124, 635251831, 267994855, 868914248, 384627107, 374852557, 543014792, 152823084, 15174824, 190685921, 696860566, 454795680, 599678847, 7872287, 83651908, 597640641, 53753239, 841064750, 308139148, 566142675, 295013913, 266756316, 225835045, 933038890, 621548638, 449601649, 723910895, 604329173, 599638803, 460589898, 618462210, 104523894, 54078880, 445920445, 873876609, 927123562, 668704558, 476875971, 960690342, 689364752, 654648845, 631814673, 488518060, 903605543, 825952269, 952409718, 319522915, 798588860, 742839200, 423634451, 183285256, 145927600, 622550684, 540560161, 45523991, 766703090, 359002810, 179499291, 273024777, 414913537, 895547116, 708831649, 775861044, 209738127, 328456339, 271318186, 624501180, 422894541, 711018727, 389269315, 841665597, 459997984, 35873816, 956607801, 270131034, 982227018, 518784655, 797395422, 36277354, 210092539, 398839563, 856594559, 567878236, 538603663, 420484270, 85014884, 337212092, 267439249, 150016964, 336626538, 139904478, 506787032, 823899803, 567541126, 694897948, 801118477, 769354997, 867510212, 512975751, 494536789, 608647304, 176442548, 292542607, 810302000, 703837667, 986238911, 694369280, 708067695, 127881530, 163799599, 357260642, 570472611, 805745246, 322965324, 549201194, 746201847, 896532537, 144016198, 332352384, 499326680, 376281220, 151206772, 820839899, 289443791, 87321420, 982290652, 125689110, 908071390, 495909828, 327167804, 305485338, 476248560, 247644285, 834911495, 769109077, 354744799, 795481812, 551734845, 872243701, 271050254, 370929244, 497063770, 318360688, 248962730, 723803822, 517467288, 495038794, 75702798, 960160398, 351277736, 426636581, 207172724, 157628568, 950750274, 618890630, 865754300, 832567956, 578903005, 914025616, 881428105, 372215617, 123632077, 263724298, 191653833, 397025925, 435128028, 134137437, 676981861, 956659557, 11250189, 448004564, 500508708, 760940815, 238201965, 858643771, 455692892, 669616443, 366766899, 9574580, 997026702, 649404363, 817160146, 76743749, 390553171, 855158737, 383863810, 388395170, 691850764, 611774771, 293833100, 165089833, 793694239, 799252048, 848762317, 587586717, 864375410, 802161242, 93011576, 634201298, 901227197, 772816001, 574942038, 882169460, 225023595, 955573677, 879688455, 636969993, 882890568, 590075269, 524273663, 648162321, 256789658, 652339221, 268180037, 967807136, 565115978, 171916121, 312307346, 87116328, 554132816, 2725785, 712363769, 917318999, 120179502, 996482050, 110922380, 961502560, 950368078, 16144463, 222827700, 535706656, 172349379, 952215569, 968875437, 554868509, 399206092, 941627119, 209851437, 775928864, 391868190, 655050415, 834240460, 9555266, 739949008, 243344935, 420351285, 807979557, 637793484, 220678188, 198855071, 626566901, 783689599, 956728147, 949469661, 866472173, 572483084, 292091755, 695730171, 105860568, 786859220, 663992496, 263138918, 898761764, 34983894, 91000668, 740930961, 865471820, 993970975, 333300266, 265355301, 808022889, 891111207, 307781382, 893080468, 725829277, 575100133, 168480361, 611471426, 126361252, 97378792, 174085458, 482601290, 306799715, 101843166, 315687362, 887758866, 860883755, 489387024, 108047817, 759639785, 244418403, 308646602, 11883738, 144925129, 593948287, 293564164, 32989882, 894636191, 713439241, 607847011, 821349348, 951028727, 541380810, 4402597, 836306413, 139093863, 282665117, 915058737, 536541476, 585566830, 538145315, 518587190, 146783561, 402655249, 175725650, 514816758, 228881480, 491340395, 294809531, 752059011, 940822095, 863846039, 539525248, 924471961, 110448839, 153927974, 787847933, 326693947, 379764409, 76430075, 609818576, 483343992, 558273227, 574183975, 332387882, 502245602, 644585705, 950796448, 941274714, 911923882, 706413010, 881210799, 155910123, 970182948, 100361166, 107779860, 468697257, 650402585, 966571057, 923880096, 228294528, 116851764, 626482883, 667063315, 122255674, 620264222, 968704665, 970431388, 974882164, 243408153, 92747043, 873126786, 680224289, 337273562, 492541637, 183200086, 276605370, 640457005, 346601210, 761202305, 876357932, 815529123, 264926933, 516896826, 199773940, 48803917, 798402084, 445516812, 629097681, 835972335, 250694149, 251787313, 384373147, 42215712, 823301084, 435467687, 207679012, 988114759, 413362450, 897876607, 792443182, 802654172, 804825690, 648410692, 178499013, 519548671, 793848427, 232638531, 949759939, 900836700, 776119165, 661100705, 495953337, 292163352, 303864464, 203173595, 104393751, 604017819, 798950892, 907072778, 367213045, 664326383, 644313337, 643624661, 952217448, 541573753, 194104787, 86679316, 398624189, 503867666, 229828219, 946499340, 695387983, 495373472, 237328802, 923054204, 558498598, 182120735, 216393611, 970544540, 688499669, 830186967, 28147170, 965080813, 231634508, 127313411, 187470554, 666243632, 249870549, 70420427, 599358571, 534153861, 40531111, 734984032, 895380363, 137523238, 995088613, 891899005, 231597485, 670419434, 783375155, 742204356, 286429804, 534932430, 831778295, 267889790, 16984683, 472949279, 876285118, 557287156, 693325890, 937204942, 853103847, 404452327, 295783723, 423383778, 75575174, 828351697, 865539436, 914034984, 974603553, 249716667, 871996694, 211104226, 809897012, 799344844, 207064233, 676887040, 580554783, 677536822, 614160864, 150830357, 303181010, 261730711, 738465669, 163794545, 146925932, 787545168, 294236376, 224833960, 749555439, 655433242, 457231229, 545732934, 998498491, 601955738, 39569688, 120327610, 952334818, 706429690, 76324484, 409971413, 744713793, 596050076, 62171241, 706349142, 27395962, 809622933, 112830314, 294617533, 354019235, 5119133, 88369028, 498160762, 971922270, 722637940, 893693363, 544197982, 729582785, 460777225, 740565688, 870799707, 834953395, 913473202, 169282553, 628165439, 144676402, 294131366, 371937405, 493967, 672700519, 291905485, 407963540, 840424035, 812520122, 886043207, 48862334, 568116577, 215064663, 370908396, 586643407, 968307353, 234870230, 268672026, 899789034, 982114577, 281875869, 351704202, 428717680, 301090888, 460166512, 790050724, 601414507, 685208145, 833241794, 477590161, 105845748, 201711141, 25672055, 684223445, 400121427, 802624337, 369143444, 282954570, 193719577, 359051520, 479523355, 538278533, 871532061, 882780731, 568602639, 631511648, 88796033, 931493845, 836420106, 449840411, 898425027, 178641144, 589620560, 430133029, 45592772, 931406010, 71651892, 516839274, 191600063, 774638290, 843452212, 136803275, 660264993, 208868717, 867162110, 128570534, 707674925, 365864035, 798517598, 714181377, 924221068, 39922557, 249129880, 539285415, 237411818, 53405120, 572006851, 622276920, 752922076, 633255520, 862723189, 740935416, 561716022, 851401249, 441309669, 488422532, 299854933, 470539343, 566728685, 295977872, 447138620, 257656977, 844117781, 871789125, 296512819, 305398527, 450996917, 482701099, 477529870, 396820703, 554432810, 691526984, 458164880, 53117096, 929743718, 532772200, 257024778, 451590500, 342271855, 95133934, 961364041, 165319183, 20637045, 598514939, 199826156, 183677108, 630874104, 696768783, 760586956, 295643253, 104481882, 633174841, 346642495, 953566383, 235868664, 738466391, 605250892, 825800978, 708480393, 859162888, 496715259, 250659999, 482739182, 384347854, 34959143, 455283994, 890989350, 487537969, 31994657, 30751428, 720269385, 858498861, 807624125, 462008206, 636988703, 773286748, 497311047, 857500649, 831590249, 689308946, 663855604, 484719073, 807413352, 721094217, 69761359, 92093941, 698142168, 147164128, 352480319, 897756144, 965865014, 985588611, 641616021, 148071675, 593760830, 40892130, 868522932, 578058442, 720468211, 622911057, 533877864, 173742716, 825141101, 541221471, 643653797, 468704390, 68289573, 630382826, 212679154, 728028520, 105544721, 765668197, 943955766, 532949867, 937966566, 902846794, 66093178, 867173123, 543321367, 715055167, 189187660, 9653234, 836188132, 945378341, 369100080, 470694444, 319023462, 827118234, 94297052, 153901725, 165664566, 556540188, 230350760, 640957196, 358146406, 579883527, 970854679, 162690328, 511634796, 23655034, 139164722, 498636325, 315008570, 33440051, 327394481, 972798464, 490930625, 818495602, 950771221, 197231546, 192324080, 962842779, 145335229, 757594280, 451148234, 518358788, 514445586, 491445890, 518083602, 538916822, 91944628, 979313531, 790633552, 558897701, 650492773, 293080443, 232236993, 42406299, 953051545, 885785485, 60237267, 460214108, 532638119, 123693703, 799334829, 836272423, 832612740, 709001948, 623430019, 830505376, 478747933, 927044429, 412050330, 464548551, 315209998, 395978754, 123333228, 268443771, 797294717, 763785537, 283176369, 554955614, 552030726, 764812101, 809701884, 208690845, 742127999, 448239201, 860269590, 753539422, 520602368, 288260723, 299973380, 252297033, 790277622, 5922468, 184181556, 609065549, 859975761, 442145892, 958378793, 755377992, 352647989, 471727988, 671151477, 184428854, 374570058, 900487113, 423706249, 542811085, 852109732, 273800964, 506337842, 690520195, 789710830, 488795298, 696968000, 458698451, 235130298, 209334343, 390759144, 353599315, 821341689, 944209833, 816221500, 340614631, 571481304, 485859160, 370251784, 48221783, 239317382, 930470978, 869685515, 261331584, 151462558, 718452612, 312232006, 814327458, 325833411, 205764480, 194734925, 132979074, 152178424, 450477772, 855891840, 732453536, 572277219, 511124842, 590325883, 22117947, 790835188, 569065820, 376069778, 48232940, 617291126, 603964091, 431242952, 698674590, 596867959, 485003531, 976023481, 995384626, 831288199, 743962594, 238398032, 526311557, 818129824, 712449662, 325609648, 350247442, 431374134, 656399077, 799457571, 604578672, 863889117, 161710768, 442825156, 537504934, 808801814, 592855515, 604632731, 434896838, 429685964, 986909400, 371691662, 292458047, 539698537, 331639718, 908061346, 893212261, 982605558, 598427032, 712992619, 762244096, 543024714, 194577511, 510421719, 561072542, 710722474, 555101921, 903078920, 493664367, 601577624, 364422386, 62572713, 169299784, 796972834, 710597628, 172920631, 191639996, 466965123, 781177150, 527275120, 481755451, 714131282, 208369731, 559847400, 808403007, 672932960, 425799921, 26619619, 124547072, 613640910, 343997411, 657731143, 792248927, 610009693, 739918684, 777412492, 310277482, 859181657, 67532476, 326213989, 380735445, 467686691, 696225236, 457093995, 772790343, 963885286, 911012706, 835231183, 990031566, 119259529, 378502254, 714746301, 260109245, 678727537, 637729782, 771484937, 279028127, 294307709, 160814419, 49098459, 252542162, 539241670, 356983428, 910755442, 266851578, 85311419, 420614950, 324180255, 869403107, 977909046, 782545383, 73090073, 587073146, 147918836, 603352210, 285048730, 599284585, 628858068, 257965936, 230245945, 424099362, 742724906, 13321467, 607384049, 359525000, 630170975, 688817254, 278030963, 833546792, 186952672, 491786572, 312524295, 530253799, 29435384, 210410122, 546078578, 681828173, 5490709, 274563403, 233958144, 785873027, 225183367, 131918696, 298345997, 125036105, 988147499, 244014724, 775232082, 845820761, 723364775, 201722073, 636502475, 908721910, 90360549, 697775197, 343834096, 234231816, 353380585, 911063781, 915423087, 950857195, 853868459, 828569653, 341586747, 349454995, 829098437, 488078954, 954461178, 160730159, 100291735, 998535463, 394439182, 945054712, 351009532, 421215359, 253684954, 502325285, 427411456, 777573655, 127790516, 368364828, 654521051, 429065973, 640990714, 521504911, 677756712, 964692062, 799456372, 871384024, 733233915, 499730327, 268452212, 173886326, 677595968, 118265224, 775373749, 690972864, 696783537, 361466199, 275646591, 358246052, 604826423, 974920865, 65604052, 989004197, 357767539, 763368519, 250525977, 527761497, 912747618, 309224509, 129390653, 450041394, 31353104, 586597959, 133932564, 33166421, 812278102, 193078276, 65612668, 14296644, 853810228, 613619105, 373423069, 308990292, 720625950, 10418654, 158122067, 784760783, 791771031, 109116717, 592013563, 242451291, 743570096, 498588360, 285564546, 356452427, 121241608, 870079790, 463739461, 893252555, 468797479, 893217610, 409342243, 890030123, 109297352, 126310701, 396351820, 300446976, 670080839, 952840859, 809690805, 800770449, 470708863, 565434486, 516412960, 93837139, 393324332, 538766777, 935497159, 799720402, 273954711, 739955009, 343079840, 167048968, 909838954, 994953862, 310108519, 343110311, 201733970, 736526718, 573959511, 539874543, 672587456, 184678874, 1045398, 564856818, 984738213, 780475735, 333647432, 984072334, 765566040, 47415711, 421660518, 89682718, 279471190, 919906288, 744819993, 365008365, 615285904, 553311081, 252571859, 540994374, 94670978, 676263689, 999143379, 10567159, 119181612, 133654668, 546248906, 450633695, 463007418, 962033481, 919001160, 406949989, 353261781, 418301491, 392543747, 596065429, 682957655, 196580332, 848192795, 640864874, 537817044, 171409904, 59605145, 674167498, 947741271, 560386796, 453785638, 477586480, 458800631, 612940402, 10750465, 216276978, 854777048, 671271776, 212910602, 120349845, 803797897, 417048685, 520607230, 860050063, 358945933, 859023709, 534322561, 545599014, 111357502, 182728772, 81044008, 790770837, 648853569, 524928866, 907376631, 809457798, 417879975, 358429667, 246417409, 934786365, 314531085, 103071255, 346944477, 477622215, 802905219, 581268859, 81785551, 739285425, 302068706, 651548496, 339876719, 14806281, 426695134, 519149869, 679124890, 974068975, 490911153, 812508670, 835711314, 959780179, 71516509, 59751990, 682477424, 484026963, 784863712, 245802770, 693763779, 818233779, 415393197, 6349607, 766064129, 951028560, 869579933, 89762388, 362947231, 927278007, 636820206, 767316388, 801461491, 889860525, 796953762, 888012928, 75837253, 178967768, 437937418, 729112445, 32481196, 983264718, 357508470, 954854273, 907768184, 306576937, 950442774, 233244830, 551114644, 611114279, 964642734, 569118707, 701630617, 673043513, 741279912, 339900584, 641644735, 863351750, 902464907, 91253269, 102391448, 561710439, 615866005, 367941767, 85250601, 239093656, 739750422, 944812236, 649341759, 340596888, 504659627, 727243448, 163951220, 484700818, 791850640, 614621071, 489699495, 6571911, 459023673, 772093247, 637959629, 533461751, 789831781, 185080802, 487426135, 350090245, 836429257, 922522693, 594258111, 170533314, 639781118, 754513914, 436778005, 322289669, 33633332, 6933622, 410433667, 363494950, 457590205, 170447199, 782535132, 565267109, 720506595, 785572502, 60005682, 407179685, 58464086, 631313532, 446100724, 263939957, 221430735, 899517448, 844628327, 73126074, 716725420, 513687404, 884525179, 453681919, 18029765, 299991827, 140555045, 283771878, 34960053, 390690528, 579848832, 39912359, 948044569, 173448425, 563701627, 842355239, 542656741, 93776502, 497032115, 388726297, 310213353, 925977760, 513786146, 690117123, 445718524, 679416501, 535311222, 860597225, 620441401, 634752161, 295296225, 184503308, 79577351, 942828473, 179889379, 268567688, 252516310, 931079628, 803326786, 751110838, 350445628, 555622980, 643584398, 846810626, 637415295, 168306999, 552485783, 311153622, 964750050, 296519615, 169580043, 542012277, 266220887, 981256451, 652337246, 786339089, 821172720, 112335564, 745607780, 829645907, 168539162, 882097898, 468347646, 168868252, 473035889, 461939240, 163046234, 496321272, 438032915, 502179552, 104110779, 27400240, 66430628, 611866562, 768420128, 763064979, 881138829, 745287353, 767735480, 779574697, 971750263, 553578706, 281291448, 774393101, 353092430, 426570750, 978500239, 211789544, 839524645, 81243811, 318757968, 142296974, 900757702, 908051396, 522440853, 691276365, 284685199, 348585680, 852486840, 532166201, 793496747, 422610444, 57081948, 504443384, 707675577, 529420372, 326272815, 43161867, 257264861, 770909571, 889731532, 138584526, 32724765, 822760487, 326576836, 996053537, 425064142, 8453684, 625993073, 699848095, 46464294, 384564787, 963260845, 265072471, 831716955, 115939756, 620988773, 385044012, 149696644, 819104936, 875592941, 101239829, 572802492, 620502185, 682540225, 773757829, 829226262, 99395959, 34354195, 353426549, 994277647, 498363703, 83554153, 720173369, 731485047, 306105624, 311447002, 962287212, 363343000, 316579552, 457235742, 383619303, 178999390, 611389653, 229650063, 105677914, 913474602, 145891375, 948311871, 650037238, 864064974, 661672836, 374450732, 840057499, 799133832, 200017341, 209044380, 863414865, 325273198, 850758150, 556605065, 912665047, 940591607, 460386102, 362151145, 537217131, 815049198, 584212523, 598553743, 545417854, 651583198, 495504266, 149236939, 616926035, 789155461, 788416453, 318111568, 568996331, 706068779, 983108046, 419110412, 793940234, 35224341, 149617764, 37197075, 264342894, 780417052, 847352042, 168833865, 797490449, 475594804, 274061710, 930079066, 672485163, 653689604, 326736295, 762235305, 695875581, 781144137, 468471889, 154722594, 739997179, 447322230, 660050188, 102184976, 736509239, 510721586, 868381665, 826113641, 417457653, 596281387, 965503486, 451297843, 469389622, 377265861, 260620111, 918992602, 514855680, 166434239, 709315937, 155845034, 55505706, 261550803, 264690508, 92980405, 59143571, 457560138, 362376865, 429067672, 660938483, 799430764, 86092989, 722769907, 775207012, 139410813, 797991256, 52364961, 700641911, 791115714, 860392672, 661111831, 663278223, 297661003, 416861954, 585875566, 794050135, 641971707, 113495501, 281061110, 409388135, 473583811, 97472067, 923835518, 824352456, 767814806, 646584134, 543097159, 512466911, 304519712, 742081724, 591111241, 300221778, 441554220, 826384509, 827123132, 592970848, 423253939, 718770456, 979265509, 350093299, 405917481, 604636064, 256309494, 986073436, 345009821, 243335978, 277149614, 27439576, 483341096, 64878955, 38666916, 375499876, 945701202, 221948749, 391344909, 603222416, 25636179, 76887845, 925268645, 515278019, 73402836, 229984079, 312647372, 341820142, 838103795, 349059273, 123176781, 424858105, 879860601, 10995788, 157863536, 472776026, 6200419, 886196020, 606971393, 740832398, 431447362, 595021710, 801425689, 607673603, 977479188, 902106115, 727877061, 798965983, 354092618, 637297976, 589277093, 492720986, 829819359, 749314641, 604098456, 282989351, 21652090, 755672829, 451783009, 291375312, 624692865, 750097177, 561461854, 308177682, 399998131, 145843787, 81438135, 282033074, 80130897, 87129145, 534915008, 684705120, 451371708, 232326629, 809750717, 582934908, 854687154, 10655094, 140380440, 58953003, 938536271, 57100437, 893363070, 772387540, 839626296, 329353254, 299175058, 958882418, 133403639, 106471448, 772604973, 819572000, 440955685, 10853675, 319584578, 181101322, 715430382, 168315236, 717134078, 336603244, 404696611, 331952646, 216044098, 972130467, 134807478, 596942662, 658729929, 124087340, 274739823, 107724393, 907690871, 340317706, 292889615, 30633770, 360305509, 143512868, 422903358, 941943737, 442108273, 32675998, 960512894, 459588734, 94679482, 502805527, 751685927, 802711520, 172113175, 989491970, 848109458, 597466370, 196756086, 432749143, 646585691, 208692851, 52475903, 676973462, 222935869, 752186364, 660505206, 674073859, 72377952, 11438377, 409949226, 728553116, 525007629, 88968294, 612342013, 803091660, 256102326, 984926195, 964403642, 749513192, 313650200, 420024181, 178858382, 158043377, 786697865, 295784897, 489792226, 787049989, 948871864, 409965382, 2761712, 555484679, 523719604, 174067201, 1477290, 580660149, 588961959, 929327802, 382451324, 667199756, 254584976, 905349240, 429486181, 640285310, 441789390, 544586437, 311421288, 475840191, 498331080, 49617000, 101129527, 144001536, 640620671, 722667293, 686890123, 171871901, 416140957, 195550262, 18029150, 536874156, 141689061, 899582165, 561327768, 163715400, 252757048, 518801249, 61311682, 6235283, 648941760, 365125240, 970479451, 721587416, 944325189, 290922367, 901005826, 685516466, 242636820, 298066925, 929756457, 487615421, 280923102, 616607818, 545637081, 107576001, 21747127, 557691060, 830829372, 504923358, 711166606, 199622776, 865126523, 301317861, 501063669, 672289787, 164178855, 484227256, 631622818, 232312411, 917647227, 977676099, 747299561, 792000460, 341401168, 881940794, 360870487, 112828082, 974010447, 513086205, 60100449, 62952168, 712157199, 321168272, 161211965, 622400507, 275733189, 51907332, 88379897, 459540244, 809279640, 212701927, 225894434, 292437468, 163271492, 880888824, 867311058, 131950357, 945322402, 5887537, 412083594, 995546722, 98067721, 520824611, 842931570, 536136604, 427704588, 558928513, 66031216, 387356607, 329057858, 15833217, 203881317, 680323063, 404653445, 307010734, 193580893, 253288766, 553128174, 682564883, 755742147, 661556526, 136907413, 223803748, 56761328, 834153755, 301736359, 275615923, 270239936, 941515936, 779065715, 61603601, 468669993, 874193843, 67781123, 401838515, 442359105, 346362084, 531707769, 736927718, 80175576, 862375535, 410310265, 187499987, 173639398, 823977075, 116011163, 973964449, 409567661, 782374282, 799092961, 661797136, 506514508, 319125025, 97257644, 902121167, 325052249, 229639823, 282462816, 99511094, 466168777, 481798362, 110165010, 899807782, 267104451, 724541717, 19269282, 428604043, 900204637, 284503775, 52671884, 776090760, 584893340, 399257923, 182043505, 982590241, 730228891, 839036532, 802445926, 419677253, 171723981, 135485399, 987083187, 77270897, 199022099, 170511675, 697979419, 690177503, 197256829, 384351536, 19703977, 262511003, 45620816, 18819835, 797466508, 171049056, 413637855, 466838046, 118812582, 853053841, 260223683, 445745198, 650527603, 224008071, 160732155, 430516143, 530051985, 642496871, 698237189, 669371010, 607940706, 819494469, 455423213, 203212837, 819581227, 851598917, 7509403, 410290946, 61084766, 477777273, 252158970, 152108354, 756577559, 62548420, 845967031, 86564986, 874577748, 833280674, 55277338, 109896874, 372674196, 805627991, 492202706, 206996543, 338977474, 525242869, 866115924, 647113216, 195385266, 375452591, 833923199, 202055662, 960163120, 389637069, 652101861, 344485581, 505291320, 772378123, 832146447, 400532420, 163512364, 830650001, 46031199, 214073422, 615368183, 149429529, 708671809, 920759347, 722039257, 130094499, 271084798, 692158109, 99085760, 352399394, 43141936, 639905363, 669696228, 9421457, 483048000, 485229561, 237845552, 666222336, 122797776, 358213065, 334589037, 470798245, 939366327, 555421261, 863603404, 373790397, 243974230, 486096838, 916477538, 702333574, 215905485, 538062026, 591036861, 223987848, 63300313, 876366112, 191633942, 826194818, 247774278, 909595037, 89264334, 464923159, 323686646, 999721958, 100380369, 295214937, 364156553, 371470529, 521536210, 548615427, 532935363, 446177735, 757654618, 194065539, 571909096, 569090913, 270092407, 617063528, 363571247, 225952075, 721323090, 710493019, 188591791, 376136735, 836350940, 764315235, 5180877, 955205402, 190594038, 731802362, 827914536, 898096394, 697485687, 482138331, 593155119, 344195577, 957307588, 541455570, 414924759, 203110586, 308472232, 854712745, 344335603, 163952098, 103750888, 554781426, 809345360, 697575297, 455535055, 647720500, 953719668, 58339596, 134885217, 652177581, 929375800, 327883276, 630664549, 126856145, 1159263, 729642322, 999934067, 428051343, 688296550, 229853599, 844228793, 852113359, 963256122, 390781797, 688520127, 359168884, 231361973, 927602150, 607045112, 58975354, 471095382, 453905487, 644151323, 822706557, 605052806, 289121787, 135143084, 537975876, 624831865, 302915479, 647656087, 78437926, 684048272, 939021690, 317696021, 516874935, 123584692, 807715482, 838528857, 321259979, 961803001, 360625542, 305961883, 453115987, 323091376, 597200481, 162902271, 885584683, 400362280, 299496455, 949047378, 593406183, 254358737, 132671279, 686427331, 471217330, 689741053, 710731341, 724281240, 975296011, 131606127, 403862356, 737591850, 508016274, 976695597, 718061239, 815926145, 478465102, 677600491, 7040926, 184890981, 588462162, 176008952, 937171298, 747468051, 324834315, 657142728, 832681453, 673224645, 517284990, 430618815, 828107002, 757840610, 730379927, 3303094, 518621051, 35881972, 16356951, 344720695, 60846143, 33841386, 211408319, 111790541, 607084527, 996459782, 261109025, 568799935, 384205444, 924841030, 460307787, 567722592, 401553585, 940994749, 342007887, 327294960, 256786502, 910565191, 460560660, 824244209, 817793859, 597663286, 934655533, 638656562, 91711594, 294206553, 698536078, 428021450, 658752244, 265659604, 573006270, 231480230, 389059889, 818273092, 989899611, 224946637, 643795750, 343021169, 743740360, 706221711, 231802246, 193840712, 254603018, 911736234, 251619466, 352596746, 700797225, 738155683, 838959556, 809660325, 504183545, 610562452, 334973052, 325446599, 535862004, 904038819, 234365986, 722898261, 753040299, 636435859, 820580849, 182044628, 211942608, 677525227, 807256077, 698401280, 617961119, 859432226, 362847402, 17612690, 242178795, 852031950, 414651948, 919355216, 148449573, 680013697, 825500085, 517819957, 127425375, 504442912, 369735419, 633344242, 553446596, 496180435, 133147212, 11766622, 796260121, 623805454, 967776343, 279697618, 122955319, 563840868, 790195304, 431509234, 533166627, 44969828, 309235552, 598213138, 136022093, 119064070, 676318810, 920010834, 71479056, 48841150, 842531180, 660283077, 572562099, 390874436, 998152186, 569694712, 804884520, 798309354, 293493241, 712977405, 96385794, 842731392, 347913142, 621050181, 551653028, 119913788, 379682074, 889013826, 901086359, 34668111, 935008980, 715640686, 339258365, 559898743, 276628882, 156478896, 549436201, 568352209, 495394913, 509249143, 729843455, 781947976, 505811050, 140580601, 837647606, 442774679, 711635741, 393577589, 845786860, 345698963, 299828549, 451525081, 338385538, 480815834, 838118576, 173835127, 579856678, 41480545, 294162950, 32297212, 219553968, 75426404, 747288873, 73130687, 557159699, 567387621, 351011389, 413558742, 820892672, 342938087, 153581178, 250133581, 831550612, 473819756, 291189103, 191895048, 708408087, 317797420, 529913024, 94929695, 224329743, 686448151, 649130969, 131679891, 165073552, 497172886, 505307880, 420288192, 516123191, 117534444, 752855009, 535641529, 548791978, 917915750, 581548884, 107925838, 82107462, 872527222, 333782115, 512501730, 632648749, 2109423, 291568566, 560923156, 112239396, 475763619, 712068992, 955194046, 97931136, 349086660, 244907698, 570806803, 698456703, 881187835, 123920940, 983499825, 598678414, 699238160, 943753749, 80854912, 523888237, 515568565, 738800545, 276709197, 254168159, 902334078, 343415204, 170299277, 20918672, 501042164, 510058381, 266811066, 947543750, 559374660, 405353660, 966069074, 799301672, 216739937, 611295526, 995301746, 279809879, 605853084, 909436156, 954884474, 621750995, 514097467, 35298723, 847334852, 815483926, 649594312, 373763397, 543239272, 869719902, 692292838, 203124082, 724912863, 764553290, 674987282, 626216670, 465172863, 471334645, 953412086, 918903378, 439297395, 879656584, 446264618, 568526182, 369619208, 650699027, 293265063, 755362674, 372467919, 844764993, 791262111, 609544760, 685738885, 491839729, 676167737, 454048491, 35012907, 941136881, 60585679, 757013207, 232640056, 479142845, 683082069, 525517423, 516578203, 373957254, 862896337, 157568607, 133259866, 670822141, 280596755, 782546954, 402027813, 987410925, 263873144, 851464156, 2665011, 190110748, 484117301, 822621073, 542402723, 951160813, 424688487, 309993151, 123979855, 804073100, 395102137, 365238564, 84388436, 952938039, 465730376, 887402189, 795616246, 709574910, 701176879, 254878129, 368129069, 813239019, 92324598, 702746069, 973320610, 322002131, 357782257, 343315080, 806780470, 724607626, 894419187, 716645006, 222314604, 705977224, 771945957, 653690992, 172447895, 975675475, 588031016, 398497740, 797828717, 823308974, 611354890, 689302764, 417796916, 394980933, 463099499, 735260071, 909088750, 674402931, 171676813, 384453475, 243020065, 414038992, 623103655, 121030648, 708357297, 84086297, 696888709, 904636841, 231055568, 655614486, 583212019, 694936343, 388003362, 94347728, 58603382, 447108873, 847883031, 477303792, 122809238, 818609015, 775084754, 301154442, 719575953, 749651759, 650280499, 386705041, 865399915, 318182104, 18155731, 394848145, 3999722, 195488054, 587173561, 793075429, 52989770, 325506902, 596444863, 241491312, 749258289, 454787148, 757800892, 635422550, 435404121, 983734263, 238861532, 803385421, 906850312, 102805468, 694407189, 623140755, 110660767, 486798247, 199674868, 881740337, 294516409, 3308509, 978014172, 769318738, 667499542, 742066833, 574212103, 988244469, 973110674, 847217890, 93964911, 577727401, 589778622, 406759706, 887578366, 132426820, 639908725, 390187719, 340845787, 965362160, 714194146, 911499992, 637488157, 884076121, 381701426, 787869987, 905888185, 312750920, 578851649, 282598215, 202983203, 235618926, 466284805, 21455566, 344441460, 256376407, 125539328, 900692840, 366397944, 675039656, 84598740, 634646862, 841028453, 611235644, 761154182, 842729617, 539666841, 16146629, 484854878, 863073511, 956192885, 145505707, 956303593, 254084516, 502196752, 16285661, 856974678, 742044531, 60052563, 721252040, 476515602, 306236506, 707511156, 510047370, 56419745, 741796365, 272662302, 796094951, 941855816, 966345463, 693951697, 706345287, 555919762, 441100795, 416240581, 269522025, 322714704, 616392663, 122584980, 312785668, 522435572, 751468492, 653454439, 139773712, 285676525, 379625711, 82218535, 678833436, 319893853, 912824292, 124487969, 667560909, 628297147, 983942629, 56039628, 336951047, 172550540, 670738520, 477589574, 523478477, 860048428, 134806689, 703941614, 34031342, 252502213, 23061346, 88339370, 559428804, 54190883, 952756654, 494569184, 606068154, 785848372, 176699215, 186865437, 445170625, 59451831, 808320317, 584248428, 659353481, 654966417, 811501470, 314133067, 722406160, 590012479, 326306394, 36701360, 872603444, 687273359, 600858898, 716680923, 541688500, 707327469, 332910971, 781058543, 817952241, 956015479, 455469651, 739055188, 19923048, 901806249, 235008289, 470888974, 55358197, 853128095, 718028916, 680398976, 649196053, 408830057, 625626999, 605484762, 746128474, 678594108, 470010247, 58807723, 83453535, 851703260, 747603980, 224015394, 212639810, 655816686, 58800229, 667580333, 940043414, 667400608, 268763592, 905327433, 440789204, 359821175, 766378857, 794681162, 141652611, 568934841, 845102934, 853325854, 80769306, 94462907, 625441423, 45496012, 13308399, 285808896, 714862641, 127863098, 37442477, 669490639, 146934911, 701934365, 362707589, 304294028, 641928162, 761436017, 514804496, 83284881, 648611840, 582742763, 825126250, 881682834, 88378013, 739205703, 270022763, 512090819, 152724392, 920796408, 625409126, 52215900, 432483764, 514342112, 296177440, 885041455, 444591125, 624760549, 661916, 34018578, 460110057, 299854743, 456316673, 146879681, 573605991, 267223776, 990033670, 761099221, 469891788, 88744507, 896762167, 642279633, 599820418, 838521130, 173516768, 794506064, 281581860, 569293747, 773961571, 180002607, 614149417, 99027911, 827763707, 122701779, 607133279, 503241973, 466176901, 22500294, 479924015, 827309110, 765219213, 469488011, 903358678, 133812412, 204631034, 448621961, 629383455, 502138302, 387243135, 18927723, 179535808, 468787334, 418590377, 258579718, 988466087, 470609087, 520426382, 681346640, 356849724, 8706293, 115993904, 48860922, 600400645, 364055534, 353258638, 648583907, 785761592, 609150669, 206181372, 614934591, 703479441, 70176513, 327435227, 117430705, 504558873, 665675039, 210263912, 671483987, 349905813, 591278442, 880671257, 553359324, 238354803, 61388602, 479870198, 202318623, 7746589, 220303744, 275870417, 949178832, 849441830, 932116584, 449474036, 684862914, 229965893, 604784122, 91002400, 27228562, 817758082, 40839120, 642138073, 519907920, 131205582, 375834135, 139192204, 88368018, 772702380, 230283228, 788297241, 230860331, 150393948, 966388069, 708307316, 439198852, 931990552, 588933584, 914851887, 730966911, 183544841, 659914889, 76650519, 842647897, 916039321, 509145936, 464295277, 753442745, 812968524, 819504661, 169602373, 99855443, 562735267, 483171141, 468819342, 63404663, 129066762, 319323751, 7327205, 982065701, 258794649, 720152449, 389729, 644384840, 724793908, 791550092, 610412377, 688158251, 358214384, 464512944, 257447946, 124156751, 415064340, 400934237, 669490980, 807616953, 316397097, 400665518, 270306788, 574662219, 363535391, 341495571, 152294120, 923240832, 123537893, 501511552, 627843346, 818662127, 410466598, 624555834, 892351593, 869285502, 65683151, 106366668, 467901228, 160444827, 146597979, 932165177, 251939176, 335301327, 73321106, 696607173, 936211970, 853782353, 529967170, 297926430, 888875520, 865580665, 504438730, 104167536, 182769037, 116024642, 953877996, 611441737, 295495622, 310567275, 267654742, 167963966, 693368036, 81817546, 269159862, 877628134, 640039612, 20623605, 267977364, 886304527, 883722493, 505563794, 111144925, 976195860, 621920896, 761516034, 613121631, 482227732, 159341467, 903476433, 405315291, 394723891, 246776721, 662541836, 577818640, 938170382, 889110169, 100411029, 731620745, 639502639, 6004744, 353043851, 647607869, 608905165, 507392289, 216638667, 71604440, 16106472, 368457144, 454638638, 893499317, 82548177, 382401148, 668258837, 89327723, 795617528, 353012444, 664214373, 164871844, 958868515, 324075039, 847754131, 409384072, 171949677, 666729400, 941748244, 44307797, 599235963, 108953997, 816799010, 189904819, 52142863, 10879510, 872678237, 120259893, 656425269, 184361286, 219861032, 674746258, 696115244, 814012647, 536108279, 587669410, 431533684, 214340769, 57376041, 498004786, 739632855, 490255576, 107470530, 314913227, 432126508, 612153175, 286565046, 264854870, 796018238, 779616289, 785123512, 249869309, 763594154, 982368837, 18330113, 148516783, 799652243, 374802911, 1183, 512066023, 383598246, 823057593, 847871336, 840075588, 418042858, 381120645, 725532560, 944981689, 284123689, 984380093, 345728894, 623946316, 513101075, 491721456, 338974520, 884200580, 381990793, 775835518, 864526782, 748165537, 355630717, 123951177, 639237253, 540037542, 436801233, 841542658, 710147248, 511661397, 123808721, 564456067, 111958540, 480405841, 353161985, 685218568, 574375315, 423549478, 547034282, 260518226, 993641399, 64730621, 751303927, 271037648, 653850795, 687570951, 973130472, 538049780, 456212006, 206000846, 194154809, 243948647, 189976828, 965797983, 586804614, 153100327, 564756338, 389186473, 504268122, 499888569, 539335826, 439475448, 831704894, 4288185, 114620817, 276961862, 448246457, 452398842, 710701600, 530882355, 419324575, 968285715, 851880551, 570317647, 326413940, 28513167, 372877942, 611919747, 584716873, 184127646, 303756804, 67011481, 533167529, 101474646, 385820705, 225055445, 620016955, 156731909, 883321611, 674118554, 183557108, 554720789, 396969098, 65131510, 720324744, 595369458, 528701057, 393395543, 173118410, 171076821, 128254915, 697448248, 100280016, 202724623, 232254489, 473179149, 881023190, 755733865, 154168604, 739359313, 406332098, 647680864, 237344471, 244958346, 44156236, 445119666, 303654316, 195818181, 532559279, 5653434, 476254497, 634470904, 234533796, 327712166, 558578336, 980243350, 903282865, 212601214, 786924697, 441761508, 984733988, 326040142, 491307723, 124323988, 302153508, 781667839, 860648398, 443509685, 963587231, 501100170, 343372713, 917417426, 614219691, 736468343, 418828527, 70349733, 403555194, 954222421, 648289371, 846057730, 458421791, 500542800, 32426848, 433778986, 528039265, 855579237, 764064176, 414099462, 984417585, 614261682, 81101531, 626448736, 979976301, 501106626, 78382029, 100404481, 650821837, 700192727, 333672000, 786002038, 183208645, 205145301, 212721734, 999933088, 864516660, 55607952, 676319419, 880588000, 936319259, 472896316, 218307229, 416577388, 84990283, 244396394, 359710355, 304682298, 954199536, 566848410, 271158028, 46283130, 631532320, 747912835, 102556901, 397389392, 235159325, 864489329, 825907390, 769799356, 733417975, 241995074, 156966793, 588539075, 819185878, 195640544, 221086697, 29695327, 948592334, 791674765, 957245835, 430173196, 968574159, 981297044, 560660807, 26790765, 977526467, 581637962, 989797083, 729355194, 453886952, 15478772, 152502429, 731954518, 859831531, 880427732, 874987134, 550444833, 710738811, 175667327, 421398023, 498162812, 852197168, 588492658, 659758054, 468867506, 786270753, 434554317, 211646744, 894195349, 770237478, 763375772, 661249927, 540346292, 491547659, 253758559, 676158530, 357683707, 152975207, 530522692, 817500016, 355729976, 579497420, 707202620, 923235661, 258770689, 715994050, 204930316, 847909236, 813928003, 23439129, 432626153, 595364714, 345088548, 447570748, 554770066, 510737990, 781447211, 165440295, 65350480, 417678627, 585720160, 621108731, 533139714, 356179411, 850358675, 118909115, 436220531, 480547631, 40293152, 660802469, 572563035, 922914955, 914910478, 168740068, 901756321, 210319185, 162235317, 18260560, 465751614, 343156425, 927215509, 750858623, 669921594, 627141021, 169293146, 482820991, 72675143, 345925380, 970989863, 715711868, 563879347, 678281652, 480737618, 319656722, 872890817, 910361827, 601716608, 67946636, 310070694, 189697617, 969898049, 745910200, 326387164, 902101201, 195838287, 52069082, 864513409, 709346734, 451650505, 632208078, 227084759, 75825283, 82428393, 753666533, 346353997, 555917768, 269788444, 963300147, 806546132, 965447953, 916791349, 884446266, 825314031, 254051179, 86012514, 463563991, 843270138, 951667723, 992114437, 346938044, 69810603, 937278752, 748690736, 208824562, 88856804, 686234111, 560154085, 427500022, 888787439, 517552918, 532903533, 576280959, 183830772, 325422756, 870678276, 623880758, 69997623, 194929758, 998803955, 396069121, 969376440, 690737529, 470210818, 501170410, 175428205, 339859671, 8732675, 639817568, 131832733, 954888599, 29041747, 806334902, 603207050, 283025107, 567290308, 364756362, 12355516, 173016987, 419181901, 74941787, 217325553, 426772905, 268197283, 589213456, 247289789, 697753219, 246465492, 638968914, 986970364, 623768898, 333149385, 738261807, 43008096, 222566646, 391839354, 957059778, 686047126, 49624497, 500265001, 359120278, 903150421, 974849586, 863419183, 801564673, 266528931, 319239145, 399624397, 412806215, 932066280, 431511377, 463309675, 186925308, 941973332, 130978913, 677577183, 989558, 46563045, 993301798, 269680836, 25287135, 905222937, 860610378, 633164452, 944189073, 987115819, 341570176, 12789504, 163513645, 482478929, 622853193, 300283684, 19695773, 40913545, 25935502, 579419096, 817735539, 764674544, 63094567, 358350831, 811943787, 928797032, 142616395, 310667920, 13478941, 561522194, 782444734, 212321207, 492792870, 742855469, 454810644, 840903653, 417634482, 524951765, 675970201, 295971187, 231116244, 458262852, 13182448, 55742185, 384514501, 272165420, 581578371, 475319133, 544182772, 542801090, 831927333, 639294841, 686526668, 268575980, 556676196, 636134401, 445716308, 189822703, 816818508, 313551292, 337525046, 918879241, 992534598, 561396405, 524306540, 111865182, 624788251, 454401730, 973981600, 203887886, 625764722, 490781985, 429950000, 699335249, 667893326, 491174957, 295456839, 857783439, 772530630, 918518444, 725373218, 833710221, 483372000, 289992368, 971237537, 32351516, 930694441, 663860829, 335663362, 698932670, 294439935, 382625082, 995609803, 462180170, 617208396, 390994775, 716126628, 615142434, 658056314, 826008452, 740490344, 482001044, 807195106, 904330745, 243187610, 465508478, 400121403, 541661381, 798323324, 799854403, 251725804, 701890788, 373814356, 480787494, 962377556, 293180341, 377298286, 127547904, 787776419, 671579794, 773682946, 181551335, 322191880, 406303947, 724527662, 282834025, 425288855, 476739338, 893063330, 593086928, 201166342, 919611739, 305704228, 773175264, 197000814, 589103704, 410730110, 647151130, 890502089, 521368450, 212732420, 293405381, 265221495, 813625006, 77331749, 417880119, 562705560, 887772755, 432631163, 536484432, 643698565, 931502116, 575999506, 9551636, 98773612, 883197167, 746397092, 434259457, 35973725, 628292395, 548252853, 179786784, 730567796, 893336724, 906084454, 429887969, 422661678, 410008950, 874392884, 475505901, 965432550, 700853933, 746869388, 89901380, 702158651, 877826356, 653447034, 148126961, 836176952, 461450706, 400385604, 801669648, 877316417, 999081131, 162178307, 843596036, 531174585, 928339128, 685724075, 959795479, 513296834, 497694443, 609862063, 839495311, 448860351, 726662800, 2754432, 769830654, 453706187, 153316585, 397049964, 756841250, 76999653, 503323463, 275365722, 46579638, 354517265, 620888258, 471041179, 367611756, 608526427, 786338659, 812076022, 158499764, 586498816, 640223287, 639077020, 73030509, 465487743, 592169506, 963995694, 182078014, 360488277, 901381350, 420228750, 120553420, 214728302, 166505484, 987749367, 374483948, 654359963, 422757401, 81525967, 672036091, 972289338, 210010989, 747989912, 508418070, 761019130, 324228491, 93641384, 68415060, 811133988, 407747223, 893519899, 218612952, 24656943, 603955911, 407419851, 278274704, 675233961, 352513525, 651754661, 581197749, 168631257, 851124917, 592679324, 537219398, 567205958, 292765374, 93510343, 394691032, 448427712, 132831554, 709037363, 51193544, 386899337, 280422390, 150956099, 463682669, 306361420, 587188915, 848238201, 900851447, 791244405, 423702908, 913866340, 16305534, 976159782, 507054483, 702301593, 985980803, 87847776, 897746604, 224050898, 177649737, 267880381, 914862266, 673999369, 761521307, 866313108, 844208002, 843485710, 891731942, 149977153, 728650616, 979240561, 38246390, 921818974, 357359267, 328595504, 558335736, 885045344, 390673815, 101199077, 750718643, 847125226, 572804845, 143126454, 313270682, 75736800, 956205239, 791510989, 658273598, 849152328, 441715650, 674302212, 489759419, 995515639, 842017789, 370877074, 134598078, 176137316, 303343278, 222665718, 570233626, 277174541, 335552842, 581282787, 745749690, 844699131, 689140241, 481664121, 499521987, 604540010, 287675067, 945789314, 163661881, 363927046, 806223042, 608500385, 541726113, 323368788, 450130530, 258939093, 45487920, 615614457, 806168341, 228776159, 481866797, 635507806, 625520038, 553031710, 647210781, 48534469, 523783028, 257637301, 712254599, 919508606, 902314188, 629917478, 461837102, 882690581, 839245058, 192400334, 619627652, 497884209, 799436131, 750913965, 993469091, 758528230, 432956891, 702229721, 731965003, 285160887, 663861274, 75366686, 866524460, 34333569, 848962362, 120261776, 838896186, 689542276, 911092217, 121515505, 609962588, 919484848, 63392269, 635717165, 41217738, 3792202, 90075524, 262898358, 301790070, 228050569, 540424442, 193907761, 146443438, 695767011, 673245914, 268677729, 407386044, 389097680, 186600215, 985599361, 77934894, 898779208, 948371608, 121164715, 795478838, 258059379, 756125727, 163417116, 686974036, 446430268, 834743531, 805564818, 777330533, 439415907, 455678273, 791424713, 674111743, 166531100, 311583608, 956431433, 955402016, 40393615, 201925712, 759585500, 884645032, 162203441, 761977707, 424291241, 519367775, 270371660, 553535530, 320365086, 846732830, 211667169, 717866772, 920571846, 48997273, 588163530, 692797733, 807692141, 293177773, 428238560, 521700393, 822019265, 126390668, 223748365, 628580638, 748194425, 188534018, 781024921, 576919746, 635037188, 973893375, 280114584, 345411054, 992356061, 51173195, 592765745, 974580480, 268466369, 192240070, 94354294, 907439840, 925768764, 453097805, 759866150, 631165926, 333875331, 410421610, 715854488, 88382838, 187616819, 29924921, 971274857, 122297559, 791515812, 119014410, 681815328, 27265843, 774309546, 94702986, 707613928, 850643382, 224905591, 108919755, 453929554, 162658366, 150313673, 72755236, 853818585, 489954188, 239377837, 689505849, 732752496, 840731976, 248495508, 836767992, 198484960, 982856425, 243514655, 965439051, 596659687, 724159965, 705469989, 846087819, 509403713, 682421996, 835644254, 766496776, 233891489, 486697897, 174554715, 293605064, 338769962, 363397508, 627136057, 104255451, 241959484, 360536394, 576664112, 402967168, 711018328, 895799222, 693360169, 459404398, 775632917, 457426577, 149183543, 23958176, 387012624, 648973325, 16536577, 219414894, 187077239, 19742271, 443553713, 471426843, 341409881, 527727772, 316622067, 86745496, 683786193, 936575282, 731506907, 534870842, 277344752, 941833310, 456589413, 711330345, 921781816, 17363128, 933245486, 17396372, 646799687, 869163099, 360591385, 796223718, 270738478, 630480663, 891871256, 652536200, 466441097, 10551296, 310399017, 465995785, 411631999, 329868270, 53388629, 364345436, 568404437, 484627171, 833847558, 607340569, 155873307, 950636381, 535540451, 387237287, 179292671, 398278547, 756777774, 206950631, 172265931, 837867342, 55311072, 170886794, 872348096, 534787196, 810067946, 91047730, 30871003, 815895875, 593880376, 111485846, 561247063, 743300762, 632294258, 996249304, 274435512, 897370331, 708444681, 40681298, 869204895, 622312699, 593953506, 910994008, 512826035, 275116845, 798863146, 671540070, 15788118, 257796056, 226094994, 326929075, 108498969, 628673766, 810105132, 766386501, 556259057, 127819164, 961143461, 808727359, 1171633, 326332515, 606776250, 285250297, 455550264, 611709691, 969310780, 81564369, 420290999, 290974652, 293357191, 222475134, 300810499, 212834730, 528843729, 434331279, 304954900, 275623889, 386349603, 102945992, 587600644, 166206329, 469994547, 906461094, 847233110, 61004614, 362810844, 985345875, 293315951, 190541504, 556433223, 340915715, 279202711, 293018496, 770512808, 708032051, 452115079, 691400693, 125607915, 90948459, 828282086, 375513278, 549857195, 921328565, 574737508, 507944011, 509819372, 212106977, 941747141, 689883118, 245972088, 930069414, 161505793, 364948727, 328534875, 614843235, 616178199, 739634963, 951742467, 92535529, 640270079, 661930773, 102765277, 95396778, 708748928, 950591230, 783754152, 185057956, 831837108, 107521190, 424902291, 531978502, 71739575, 741501656, 373945569, 166168434, 29965409, 714191868, 565849806, 592070539, 478097072, 19013982, 197846444, 722684420, 590589101, 951001878, 55942169, 664427954, 679942878, 502844835, 241057866, 95943966, 658816093, 756378118, 789926014, 296282252, 86943785, 548410910, 971068120, 314593677, 119549902, 210047181, 419705822, 52901665, 789466035, 637073038, 16628493, 805269173, 249686637, 458687768, 414572529, 359774624, 395309316, 817789002, 408741324, 232039873, 400889747, 689133428, 525112893, 890513412, 187389347, 985504435, 300183911, 333652459, 13085595, 656221850, 579903510, 911759227, 669413948, 879802040, 520573693, 585555568, 87977473, 241270078, 236162694, 392694973, 753287007, 15127641, 294576400, 619778372, 591469049, 931895081, 505752079, 212306542, 688418930, 203904334, 519047152, 378521094, 842315575, 66707711, 763770501, 410472470, 792353127, 606645111, 334265504, 895917922, 901021249, 182736610, 240360411, 368188464, 747220212, 413505562, 479575718, 219041935, 379522440, 323450884, 227134791, 398943819, 288340905, 285744937, 735193748, 917969625, 67178328, 724924058, 663070078, 15757639, 885904466, 951147647, 147431535, 898494257, 227521637, 553964676, 855848866, 996119367, 765355003, 581493198, 737864797, 142736626, 70882771, 132818867, 6143409, 262298062, 265470284, 452775153, 192398420, 885393843, 707096922, 750932043, 50790913, 677978445, 757429562, 551053348, 587374941, 682534516, 766487885, 264128048, 567885390, 212020503, 79203120, 765903446, 253701406, 910022168, 354963385, 1185315, 458043601, 900339608, 354809300, 540732466, 910352027, 410917321, 226960928, 148140456, 147490863, 329155350, 103311408, 8332617, 109490414, 143957992, 478408877, 327921922, 57573835, 954254077, 40162002, 448668406, 98066657, 280789656, 892668166, 725344002, 51089472, 292109975, 414280370, 425535611, 529994243, 98141614, 691734529, 676159808, 426980577, 542753526, 129397606, 13761003, 683019965, 304731052, 479452419, 68489293, 796217174, 224249420, 392658458, 548473646, 372026142, 925757855, 976343631, 388882223, 362438742, 552860640, 139961123, 353592349, 102149484, 144635724, 470705871, 764035298, 150219078, 450723274, 790252307, 889817455, 919600132, 227841659, 106980862, 491113400, 119231740, 676922482, 915263353, 808348368, 393687434, 582641893, 333273121, 299900065, 473323665, 236272941, 519727169, 186460105, 223680599, 102452616, 927754296, 495807494, 463717199, 558350998, 859798951, 50372314, 798287668, 600658235, 790471636, 326483005, 237088860, 207725290, 987389702, 677646197, 85619948, 676578024, 877535581, 923857549, 116537797, 256219012, 991233920, 288039072, 331194776, 41511391, 473593800, 514721480, 53190279, 861149654, 120429472, 60992010, 587168044, 647907488, 326232927, 509534878, 383471111, 366305632, 49747661, 223138631, 524175431, 790820589, 777404642, 492490663, 534831286, 195524021, 907098335, 512394894, 836249690, 886489640, 216900398, 846740974, 58155855, 439757279, 194696224, 205768779, 196374985, 89425327, 533526427, 565161528, 554902743, 105265790, 363401657, 168811183, 950712976, 924905054, 278295662, 860267160, 187542782, 391879590, 334043535, 834618152, 602853722, 195014483, 331902069, 239220642, 226903906, 993684199, 808607106, 665730599, 933571832, 275231449, 75379790, 177594143, 110860342, 169340581, 578666970, 795668283, 480929318, 567008863, 621903399, 179642920, 586005104, 900007349, 765076373, 28279245, 433418081, 861331957, 537685715, 458687018, 609885773, 672064694, 509244596, 895153135, 36408492, 399405831, 794371962, 237252544, 98127542, 305350083, 371163663, 710663371, 583507298, 803849426, 790957766, 736186919, 638414868, 514957154, 700680922, 401201341, 854704258, 401870294, 334957608, 635649569, 104695792, 998400173, 492541223, 369324370, 436366636, 982878700, 56239976, 988828782, 447282596, 825103745, 929242156, 296697760, 12036881, 645504028, 966002811, 370594332, 681729171, 363876821, 577121215, 818205988, 63519615, 561242096, 393143260, 319604570, 220600919, 764631393, 483401433, 538449254, 418117195, 65670421, 491904265, 30068395, 508422635, 313156979, 160019441, 124182599, 720410083, 217462961, 167316467, 454380642, 789142004, 298376539, 870246809, 917154259, 745443315, 959454955, 418852120, 543440955, 558967526, 941995592, 333677838, 30907868, 163697680, 423145918, 307834152, 235259973, 898196428, 620876614, 815150960, 634970586, 387786910, 179476084, 567893711, 535822028, 34428277, 416895609, 422353251, 324111177, 404542042, 167049755, 455643223, 795146114, 700874300, 439993704, 801766210, 420758613, 574787688, 153314835, 179427702, 803805569, 565222674, 664548161, 466925114, 485643326, 226096734, 845654368, 72753292, 832448006, 941133737, 592337137, 128819403, 405316548, 17336717, 283854228, 813355023, 1178423, 79198260, 260083250, 155013592, 172566066, 782824523, 532362225, 520641128, 97034692, 84405280, 794298009, 681726991, 898509421, 506758689, 768816453, 883843812, 471668965, 248543011, 500354553, 441388871, 824601792, 26597271, 322885920, 131551, 936839913, 695253111, 946180022, 663981434, 883347311, 825415915, 134342180, 712140365, 90132288, 351796721, 745952408, 292174033, 312104143, 558677443, 349731095, 21516069, 369432545, 652072662, 992338056, 915614350, 123380338, 253328352, 968801573, 792102238, 605906116, 365108728, 869773274, 384629445, 520807219, 449088545, 143552038, 270281684, 989694997, 580433756, 61588458, 562325046, 221965299, 347715251, 838287985, 34354347, 825981950, 405135153, 795039695, 752331046, 175184371, 832993619, 483439517, 759500393, 741086838, 211893269, 858929012, 821477731, 206972446, 209416812, 972526007, 692507158, 679120812, 886413133, 495684722, 872902000, 775565278, 618740805, 744796029, 81596484, 590661771, 366821795, 494101147, 575093408, 511862164, 775272642, 610075872, 272719564, 303711645, 178539156, 905155521, 873193748, 524468616, 404748499, 834029764, 62689214, 802504826, 169640933, 427548634, 271264463, 878961487, 814387774, 179282483, 750657412, 993499009, 255620138, 669633446, 761510483, 452017230, 280087825, 598105112, 24494578, 187249401, 793317448, 299922920, 689526072, 169469010, 315446944, 177004784, 905129956, 456474074, 843445052, 670980301, 813124939, 617910082, 363804077, 777844347, 296218303, 210701795, 622348015, 51261425, 109454681, 927611070, 819315320, 254392133, 516655141, 829461019, 409005073, 82204596, 596410633, 855565467, 231430900, 442957180, 613537500, 866906242, 859984392, 135547283, 95260082, 764253285, 723482642, 883643010, 356847895, 476178299, 353367839, 659133101, 302721668, 735742615, 794911090, 511981913, 581990359, 974754976, 450222280, 168988104, 75156187, 10673328, 644158230, 179310691, 862498851, 980669600, 788219334, 138182366, 456748984, 6824598, 440939012, 582228252, 599753148, 601804008, 18977394, 15109478, 606462566, 815967439, 850684312, 117342368, 561221794, 996548994, 884036973, 698984971, 954540176, 445142159, 367213242, 648987495, 169044168, 844876850, 615289546, 259610992, 563463017, 902792759, 599513406, 371938424, 722892398, 61825346, 442990180, 277910328, 498357661, 875255262, 103617499, 907752607, 54156199, 465794517, 586552813, 236619152, 112657298, 663047261, 142639017, 288014687, 396709637, 728930493, 957765031, 926371187, 95398621, 161453611, 365414631, 462586106, 208080916, 345781644, 7511218, 444041281, 79840778, 692697069, 199584301, 455016426, 634099348, 506688793, 244843186, 789951549, 545865361, 679136909, 763872912, 340225135, 485242619, 839000228, 315476422, 528414121, 854760270, 379918146, 740580369, 443821571, 122870360, 448299821, 105192927, 953083952, 640071690, 655340548, 910135206, 379472538, 962371996, 522855417, 122311976, 692069727, 302246514, 65230571, 639809730, 54596846, 40949993, 460901447, 100460405, 250974929, 415768665, 560829328, 300407099, 402971884, 895228548, 344368551, 615397622, 316058659, 889257904, 701676199, 937052057, 613950908, 573691215, 728140509, 340808082, 179388436, 549606912, 267792559, 435008466, 138435118, 20777715, 991384825, 390648809, 388964178, 56366842, 935538343, 370352349, 305247657, 879573636, 391723605, 907481003, 273859616, 804264557, 310869690, 429037401, 171082084, 948646918, 540553847, 752326316, 577648768, 968817748, 930401158, 952844076, 527801766, 46196544, 663225419, 836300029, 955879691, 336373677, 273215885, 53036583, 397679743, 138773600, 874893867, 802612402, 862423961, 72429759, 803013643, 116940272, 633333143, 360594158, 527411713, 609111484, 452453260, 927061425, 813104082, 91426422, 603607165, 95056352, 64259509, 401909311, 440998377, 290352476, 704783341, 784771796, 219138898, 162999573, 516078916, 843011621, 834516118, 164232432, 848275964, 606601134, 660548613, 514399901, 248553558, 398421918, 208708432, 979868725, 978741610, 770441288, 834521664, 861910069, 610035074, 864817631, 181422317, 665812786, 332518796, 745515057, 57008302, 57214060, 342438836, 750958455, 432970391, 736007462, 949669906, 938719753, 45280827, 925194144, 590060207, 444618273, 177981707, 135535820, 342963461, 543090872, 341717799, 802879826, 663906289, 862898248, 405759778, 174232381, 568590745, 3806664, 120063290, 502235625, 950086944, 633095354, 528055635, 732266173, 225563640, 422363298, 747802870, 360535286, 786322558, 711908937, 172964083, 795401515, 65060286, 967934678, 529201948, 405284656, 80172118, 210164321, 569917390, 776267479, 172317742, 251810076, 731260933, 954367777, 868104407, 845439435, 874935226, 478304449, 397710981, 186743545, 906951060, 713476243, 51494650, 547263728, 134842154, 273411638, 990318699, 713044455, 327074285, 989234602, 362924792, 71968523, 810218206, 881174088, 311014096, 368723565, 173991069, 227198604, 893953964, 515891033, 418667503, 75150141, 749025077, 600873436, 253901141, 833782232, 416672224, 656512339, 538226918, 988004553, 120667155, 72071135, 767647616, 845882916, 371848383, 295492123, 592481539, 953016120, 671750511, 53357565, 965917790, 400883185, 186690208, 806785485, 289102142, 803078110, 321138208, 128319976, 216813285, 299565765, 193488751, 769841045, 771624107, 829256226, 229854680, 135087996, 328513372, 208055752, 208172716, 640084476, 817400228, 250853764, 17682415, 978016203, 645404156, 701135307, 840678829, 824452694, 996486113, 825577718, 770503982, 660197991, 138191539, 567496303, 642055588, 118256655, 242113082, 677231248, 135368662, 212294923, 988351679, 91372843, 565494411, 959113202, 719124321, 405050602, 427115346, 494594590, 128309991, 814696736, 174880372, 108849250, 420003498, 543437465, 229102601, 964375894, 492662831, 84170181, 453419478, 499909203, 256748900, 503968589, 829334141, 509317875, 21178403, 620606542, 737104928, 913256291, 74174679, 25086263, 144497122, 784663875, 615398998, 915747568, 851807771, 257609176, 186825763, 254988612, 458321882, 410483042, 649959978, 450327392, 238781305, 533362603, 258798495, 712061847, 640801863, 696980364, 894769779, 398301349, 532200711, 720456874, 588490531, 104742879, 520375872, 408293925, 493120375, 812605193, 713564059, 808941365, 742386286, 779212424, 961983239, 120999008, 650018076, 721332699, 855362666, 827149957, 41480236, 369849538, 151066211, 597430612, 396749942, 334065209, 150505849, 553221471, 703124163, 309945965, 936951909, 850334224, 900968399, 359895856, 82690407, 523214982, 156578629, 95239291, 213510723, 5942503, 113524398, 782131022, 637124210, 364145253, 439664634, 869533141, 389712987, 290602962, 866518109, 650411546, 917066114, 368366395, 252617773, 161337645, 38255470, 585026389, 291941039, 613789962, 139664035, 654735128, 591783057, 738698558, 847593502, 683620772, 282622128, 54810602, 783487647, 498321300, 353700684, 911455399, 339256666, 805925424, 710005918, 57422114, 544373664, 497960573, 821070017, 788440871, 306340048, 41587780, 995614405, 682743467, 625733861, 596448524, 608842554, 34473294, 618727479, 140309785, 361814131, 970294765, 702128076, 3609884, 810403316, 847157012, 82668212, 535737415, 996864337, 319169824, 328622606, 656204182, 22421427, 975525924, 557639087, 705216722, 792536996, 258407694, 312083872, 446777978, 701732890, 43495332, 40782098, 208540652, 732348643, 173888803, 479709551, 916948884, 395367103, 915462133, 221251401, 847348147, 822407218, 486775119, 960237140, 758289248, 281094157, 167609540, 239879679, 65583131, 273765774, 467374466, 523843373, 669292872, 838193755, 324209645, 953845116, 342703282, 586198084, 484245637, 529093735, 396981882, 856863887, 20653222, 503809689, 65363777, 699986956, 75799830, 108209511, 490087159, 147517448, 885847199, 220854374, 777383441, 658700683, 673872667, 943059484, 749594386, 163085153, 586228628, 723029575, 123337198, 877826264, 998620928, 995086268, 36476548, 957079972, 742886357, 545029917, 646041227, 713427668, 488662826, 944570458, 430244918, 277267621, 111444620, 249865029, 65000732, 616857212, 990790791, 893674609, 591121472, 414169108, 799415556, 624606139, 534570912, 300838498, 617511783, 255492741, 118707835, 878116054, 55094317, 291034470, 155801131, 487425725, 384061158, 711667544, 870794404, 406135588, 141105459, 230678240, 460834192, 659708304, 117798632, 738763977, 15712088, 963528836, 431795941, 377966294, 865887238, 958904987, 561980350, 414876452, 845325659, 312348938, 750279741, 448276827, 695366638, 60677360, 721777143, 915668548, 792934153, 216025496, 893114311, 961457747, 365996412, 267451076, 308176589, 134374243, 624651912, 776467895, 306630913, 2040035, 274443754, 648310201, 869610574, 913840977, 506779440, 768716144, 964637619, 749204165, 249329310, 250094090, 30198460, 842968772, 718736270, 585929524, 116420303, 45693256, 681817716, 6052886, 50276707, 383976558, 249441181, 192727430, 749385571, 938004342, 840933323, 379819809, 495168586, 879107236, 339206318, 168860299, 136089309, 79000849, 910671791, 253146117, 704091437, 5693375, 186309511, 317281861, 942456901, 660214106, 244562658, 31335059, 5621375, 107650765, 826151896, 794016230, 375245698, 707548589, 267769862, 828516980, 360333558, 937285000, 888112082, 863395708, 45399429, 911069616, 856125081, 691481880, 422326842, 380759066, 950035325, 955588962, 709362004, 583250164, 624005174, 241685742, 6040932, 84814836, 179979386, 719917952, 383389327, 126581096, 114226316, 898494431, 369783828, 96706160, 624728275, 822867800, 833457479, 969406762, 543246700, 680573176, 327050651, 460094128, 736894771, 629527549, 183827756, 386046602, 840162073, 961813726, 781451628, 280526096, 521089685, 244949700, 92006792, 438329328, 506161326, 156620403, 582179580, 496898009, 702936726, 38719508, 11196495, 628328628, 679286830, 611394390, 376005652, 54125197, 849202566, 224209632, 593303815, 479845812, 138746377, 744122466, 336841673, 282856905, 982440171, 964222891, 879566905, 973304576, 143482747, 668602617, 925571341, 40384638, 489823218, 171851342, 293863085, 280501482, 620990117, 510282968, 217221996, 304514277, 536172141, 848456771, 869420991, 23031969, 2403360, 115933752, 869327245, 642606394, 852517504, 664163415, 379289784, 381517791, 318031937, 562177528, 388126727, 311160038, 677721920, 954885203, 181044309, 149488420, 729192681, 653219526, 648268479, 705219699, 496322801, 883342833, 19867934, 862365176, 382424050, 592072399, 702439745, 150058522, 7792554, 330196478, 844548458, 929076452, 691840621, 859228725, 137481513, 96440015, 864373503, 538689326, 279498098, 26505048, 267342133, 308405171, 223646938, 78468692, 173867283, 254431212, 391277549, 260518649, 513841803, 286842385, 721252440, 145368771, 652464904, 4996741, 907820676, 827606718, 895417574, 603678792, 269078120, 910638208, 998877642, 102097464, 293791174, 525259669, 291533628, 943163234, 598170264, 819464982, 99614222, 879384673, 805082667, 745196437, 100261338, 616597808, 178135071, 302583294, 842542016, 904090561, 433913451, 313075292, 458217045, 991827093, 897761584, 446559836, 89149555, 466945915, 410729534, 294724915, 547468817, 624856478, 925309014, 752980453, 908602923, 735779725, 541367426, 321740189, 889387093, 851551625, 922799365, 563438940, 790018415, 108761872, 542373716, 126568307, 373819911, 608107380, 281237818, 885188807, 702335635, 411777949, 544846278, 262588329, 506697893, 604640215, 365674032, 81255754, 937671589, 897428095, 216842081, 540668751, 650356782, 248431055, 718252458, 69039927, 582791498, 152285342, 501189710, 189988715, 147311914, 572342649, 868333231, 637551693, 152864102, 283067174, 697481431, 612574474, 857269989, 439821041, 646532192, 61150072, 280017938, 750261685, 914651943, 469723159, 903329042, 158643237, 722637597, 989068004, 453342508, 794520732, 707487132, 77224132, 946136339, 517211104, 30400901, 223038874, 736943273, 204255053, 145475994, 173791802, 295053703, 605032254, 617444456, 689777454, 529665365, 856014741, 501213152, 261768385, 315075845, 435978260, 686797767, 791499753, 988157712, 132942753, 747075937, 522926557, 868903912, 966534170, 146990149, 880359181, 635622960, 640944254, 107253002, 705779961, 40880445, 711820669, 189352736, 141724546, 887996957, 975696402, 50716579, 58361263, 167737259, 897382505, 886890532, 732971476, 412912407, 466697832, 349063970, 108417843, 95214620, 27411062, 907403164, 319315737, 572077766, 420665712, 174342107, 187540287, 189462699, 641497117, 554047759, 492877625, 67153768, 313281764, 786103646, 161600140, 685493773, 15727141, 686330885, 918451195, 937246568, 122941297, 316540687, 855328612, 586936050, 377215988, 874512045, 315172995, 218631554, 119301384, 741119379, 339991745, 398054156, 867407748, 402109908, 905122673, 796533267, 505549203, 271269422, 776164798, 242900827, 384525687, 167588974, 729498583, 760254135, 288988518, 226207255, 113486713, 480193474, 646742136, 366425919, 890162803, 456805225, 97889396, 180149685, 323848052, 318120083, 588491604, 32168281, 423536617, 194400977, 393054968, 934319613, 487035183, 558203519, 38343287, 747372738, 914247162, 983794261, 869563636, 502775301, 917737795, 556029032, 913027581, 361131744, 633796451, 289600105, 429707315, 686816806, 712254906, 589855459, 109113671, 757929480, 136084919, 145808013, 710498865, 15174143, 385352123, 146624841, 84179391, 825401692, 142279587, 10271328, 412781536, 417137753, 676028017, 616038675, 589108090, 199999795, 901402015, 9726313, 494441068, 451243457, 426910824, 209928988, 595663415, 216067957, 548787938, 576457028, 380280631, 669710027, 52430379, 196786419, 194013913, 22699638, 964239576, 142398217, 7324874, 93030744, 698011334, 859199233, 469821805, 742984593, 109560762, 752477259, 777376214, 256464859, 804831178, 786437670, 387482627, 786716393, 382488999, 173093090, 904979836, 806652664, 372345494, 244468787, 551647305, 324540551, 631280699, 528904621, 477451578, 460428467, 437993924, 464771599, 570046065, 93668164, 843117123, 779731212, 574363487, 405093568, 890620106, 765045494, 278294330, 344660501, 605612360, 234753586, 509129454, 174263819, 559264096, 970748628, 686047207, 972250215, 971578086, 879899974, 464873924, 333267359, 571128449, 668047677, 1315412, 575248346, 360552127, 398433169, 760957081, 819620651, 422835023, 404256286, 781852028, 767121210, 37616043, 627222224, 785603108, 915113563, 914523147, 842696998, 843023999, 615809434, 105672746, 465116443, 446729677, 424899913, 633323028, 806554152, 739234414, 573639612, 8681214, 379037232, 471297848, 839680597, 961203742, 311505698, 381249240, 987733529, 787421331, 87092745, 515191816, 385083828, 836212424, 186511111, 406291124, 78223012, 641669711, 446738742, 98103213, 492442596, 556094176, 683791756, 142005826, 486569480, 847063919, 79118346, 618766756, 169021337, 775438290, 244685567, 360328672, 611086753, 175806109, 443432469, 981771862, 753211342, 145256366, 423999772, 994900226, 109933282, 175545506, 949248007, 369505788, 840264969, 516307906, 515696986, 75847231, 454655763, 53675232, 842300706, 750186951, 332221722, 856303263, 680227590, 285959334, 823956377, 484521155, 382988359, 37289298, 114220943, 388396086, 837166654, 766795666, 317458489, 863020035, 947511551, 548081507, 860092752, 787770150, 169178358, 758656518, 920848849, 21935408, 477563899, 159974083, 417606807, 249955546, 581161184, 135188060, 181102451, 345737372, 874666236, 173403177, 854047106, 845256252, 472525942, 571488862, 922795640, 55229047, 16519677, 465246657, 692600669, 524250574, 925909928, 266131769, 198568499, 496362599, 749644697, 801731321, 741346089, 166912645, 807194391, 750803843, 479947672, 545805856, 880714384, 902669325, 115650326, 502439626, 350328138, 750364580, 695344374, 10898638, 149407600, 169525729, 987272183, 284826705, 212466082, 394205213, 558572020, 450027512, 677244651, 911293563, 730879909, 668398884, 164108577, 901263651, 7224810, 103008061, 597925226, 837244357, 979824041, 997237104, 495409998, 604145855, 133056594, 405260661, 969199540, 686432691, 779456802, 439012297, 167911948, 345717177, 902092201, 820855110, 671775931, 384241136, 788306214, 142073819, 723611588, 118060636, 740466141, 545729953, 204468346, 276824202, 936999399, 170988085, 253058249, 935450875, 776225555, 435570397, 428527838, 172368642, 968762406, 277014176, 68804476, 588844969, 824432129, 943561090, 951859344, 704179808, 910835750, 635782282, 561755844, 23927519, 34961530, 57873401, 135261584, 856183502, 289543179, 310710548, 589522679, 974783884, 138441568, 684162377, 206624516, 323365164, 48735853, 295776384, 726840673, 970200787, 84893370, 987346885, 453992478, 401267192, 104514580, 122467126, 960047374, 676286238, 328406004, 879612854, 330806280, 623119198, 287796978, 115681200, 434792424, 193214927, 396955648, 645136627, 612626178, 821833431, 588629284, 865773586, 358715628, 534929311, 754542026, 31266973, 434056109, 724676238, 129445261, 260137873, 309290115, 85959716, 644327922, 775238502, 544371785, 757518392, 733337223, 814356023, 522434840, 219910292, 704315631, 549337066, 324328208, 32412538, 864508285, 371906508, 884348460, 120517335, 861331369, 540673078, 399758154, 493272787, 125690745, 651214754, 89808244, 169313933, 366996503, 802839105, 266163863, 785603349, 892391138, 612459085, 633362332, 16002821, 457720408, 408246392, 36140619, 353949156, 104354845, 151231555, 272477312, 742501898, 327133701, 939717142, 373149202, 390795780, 416300004, 783608911, 504104304, 24790872, 901678889, 339747126, 328096093, 513405218, 974950604, 340372807, 471034700, 464522636, 747844381, 126361601, 735932726, 660950437, 442218269, 5169337, 176412258, 595414654, 628916348, 262804703, 650287156, 102070008, 190920062, 572742954, 77424605, 8080988, 675555805, 984042418, 811405737, 819112519, 771084530, 677667522, 354222790, 665374768, 642018561, 326979272, 993991889, 663038809, 24525989, 203747684, 147086375, 526862454, 902320037, 634626650, 991503149, 872616195, 672012880, 535402122, 89223873, 976912394, 919780616, 301767790, 451372875, 994840759, 121064439, 881777420, 759185788, 439522462, 110591184, 153304562, 856711434, 38897324, 851195622, 753228306, 192973733, 480811236, 881292283, 167369436, 928289705, 264432453, 196340777, 414719807, 343572055, 235141308, 673986631, 62031678, 113702595, 424579450, 368092258, 292954026, 756138717, 993667444, 701907719, 904564739, 614003761, 864020681, 869308294, 227981502, 570035238, 491086580, 386559437, 112925895, 877784567, 565585825, 265120540, 585717697, 19279616, 111806055, 859388470, 564246350, 131708844, 993004515, 599380275, 64232783, 900746282, 969205720, 780059120, 383311928, 751950725, 886917793, 333420879, 525208054, 864274078, 920759863, 666313790, 467161837, 701971945, 116867615, 316777974, 427679227, 330265914, 314664380, 779435621, 591378049, 244772413, 905114711, 121403507, 496294515, 304829292, 958264497, 295964082, 813916582, 413108884, 297351242, 640858708, 746159701, 577151031, 89330305, 770320329, 912964735, 12641253, 212179348, 642812573, 676754719, 427273094, 29440162, 957563277, 417830568, 283443017, 820377571, 45194963, 604603131, 104704064, 277310183, 648349986, 50267902, 628786627, 590790291, 109672105, 68625330, 217507785, 963501086, 902955930, 697973686, 672864582, 438045464, 293016391, 79143659, 944536705, 161376927, 698763531, 124933867, 28508763, 715187434, 501194922, 806948934, 484825230, 946674623, 779171017, 863705488, 243523792, 990789744, 844773823, 944305284, 878020014, 727029741, 688718605, 967966295, 105937027, 186442814, 20963697, 158461313, 841243046, 339256980, 800451540, 66649361, 171250225, 635613761, 497558316, 62135445, 630640182, 553234523, 400729659, 546500294, 357251952, 797329474, 439147213, 883440148, 977957895, 909239824, 185119335, 158331881, 446882712, 146738705, 626590085, 720532902, 855342079, 184606911, 268149635, 852929652, 90466114, 578334001, 845316040, 728487415, 836278929, 613536434, 740307081, 953461791, 704877756, 119104264, 974730116, 631006787, 138634295, 206025974, 591802989, 995231874, 46583479, 85293039, 613131780, 677608091, 719096010, 741467263, 159148696, 581328965, 298421884, 161335058, 415049051, 314350238, 144941321, 435833458, 541269302, 658680689, 12942941, 611156885, 631203752, 989849731, 755566103, 166833322, 536975517, 201223973, 422987224, 965182124, 177211510, 947267070, 671903398, 158185386, 67287874, 238904179, 115263378, 656533069, 685554748, 648184592, 307919540, 636150478, 699515221, 312586183, 339051267, 989628227, 440664259, 27000245, 995618670, 681830749, 753006289, 496251963, 192218944, 422255232, 659261828, 538451436, 184319702, 153403248, 665154128, 531436869, 164747754, 493613786, 853211562, 807919139, 762613321, 253288982, 290144289, 959207628, 698540361, 290170650, 391833554, 863332348, 505037054, 207681565, 280265789, 646204215, 480990857, 173437878, 4133267, 877499028, 903654143, 168468912, 132143966, 164878037, 343953906, 627857650, 671123811, 468421683, 706243530, 81090228, 691688622, 552071464, 381826160, 223341874, 763763880, 393121846, 693663717, 660973379, 792850084, 29739209, 499097788, 767738308, 575905875, 880573401, 533564032, 385994781, 253001633, 241881877, 854804793, 99592903, 561128596, 3793418, 876501290, 483831437, 746690276, 607151719, 732424819, 834526060, 800869698, 129826897, 673510509, 749130938, 828915787, 181232128, 387805042, 306887078, 557503320, 11432293, 688320796, 639989493, 548824434, 413518421, 355953784, 334291595, 95017942, 685235126, 746680276, 462684320, 66579030, 390244133, 857303230, 268097276, 942955908, 358337529, 878364776, 567549478, 558110597, 34350581, 202415957, 939448970, 628566047, 404074597, 401750451, 667177372, 519132487, 233792430, 402154612, 813526172, 287606698, 929831230, 587396961, 667372471, 774939868, 782199570, 617926688, 30397591, 277671519, 588569425, 312911041, 954274723, 81808406, 155897438, 69335295, 188480018, 188559261, 852132854, 609851085, 422916298, 980838387, 928688495, 515701843, 264289996, 510814903, 501831891, 244192687, 665789970, 576770407, 183231769, 687199705, 43335190, 191477944, 88670275, 175056838, 396542849, 636933951, 37115479, 628116206, 348867187, 393337622, 526779067, 88066075, 52786817, 303616324, 90634726, 807820573, 336516398, 748874138, 682162939, 713409863, 371870220, 991011966, 326168442, 461123312, 272725188, 741702618, 423520048, 793898017, 48076187, 53296261, 994289971, 431756571, 972631650, 922145511, 428827434, 90673339, 378053812, 965089720, 358106043, 535091696, 640540929, 818869765, 465406593, 612380157, 980148596, 448357509, 777845781, 931824592, 760504189, 777695628, 622385795, 973440549, 411520968, 425844160, 2308976, 263131226, 345438225, 37477582, 80127711, 915494220, 672880491, 558368527, 341365166, 922516281, 494103904, 941087785, 446401262, 315792535, 423197810, 121211067, 808600376, 36400447, 796562417, 790547749, 863179304, 948830356, 306964615, 612903785, 319446501, 599213092, 5559618, 848667123, 904305978, 741122130, 168373533, 656829688, 384740606, 140705598, 881486977, 78241897, 451518588, 363889516, 946459809, 214866693, 147194736, 487267307, 969515007, 389265043, 930099033, 486905320, 777156614, 587667016, 602989752, 714487522, 657815616, 951194162, 234151389, 408164758, 216856250, 833870627, 830763206, 812820194, 981900036, 821089420, 961008726, 642463633, 420258103, 9607129, 92574865, 708941547, 682317980, 187864095, 272214852, 629276777, 589906609, 993359119, 974072519, 269665342, 965426433, 410085088, 852647136, 152318221, 549354889, 270119654, 52293813, 808349799, 873819139, 758056944, 606597632, 852721045, 380988095, 109301435, 290735689, 38339651, 149245121, 931650963, 361863204, 647405341, 473794909, 153485143, 663469861, 597070604, 47946943, 258426829, 491546822, 500270183, 941119505, 131772229, 8535683, 668970014, 173243275, 983319890, 703369069, 282684238, 784908490, 580627357, 453398057, 757407559, 154320054, 857347756, 122771130, 274189124, 765426827, 798104933, 623302164, 399575841, 585331135, 7633714, 657262536, 557089941, 365824625, 503196220, 155948854, 55267802, 493665358, 486338398, 7002675, 9361687, 853714585, 978809620, 869000395, 331819430, 113884386, 829596119, 281616493, 534092351, 652910443, 164523123, 414284079, 162744302, 631097122, 598304247, 860111520, 944145615, 992768323, 297806878, 739804089, 703811844, 195752746, 40738492, 730032013, 882232229, 73360819, 957877582, 236587538, 558257581, 298082057, 449058231, 864236040, 671446697, 62101273, 871481098, 880902894, 146292490, 796820209, 21269340, 823614629, 337205704, 974120118, 514624063, 764450517, 475388457, 836716410, 240065753, 433805571, 574949866, 778536527, 264139462, 860881301, 510602636, 671793327, 631759217, 384872563, 272756826, 22614209, 560229531, 650453131, 688872240, 762163853, 653451338, 672517745, 794110168, 516329896, 510602764, 645801638, 754597242, 639424745, 419060302, 741493693, 254099501, 533368208, 744563744, 52305141, 266043798, 285301247, 944159409, 660889310, 54897384, 457616214, 221757963, 134731181, 557905126, 263189506, 950638005, 524049169, 861788234, 335373935, 820458248, 541449747, 203388529, 988734720, 600382550, 766970017, 482486163, 108002717, 242251301, 508643965, 30168412, 760223886, 702057615, 619471967, 160879213, 323394390, 457241076, 39471965, 138393924, 720522573, 791113189, 975915450, 361373880, 193884331, 239570123, 762029162, 551479769, 680428715, 381398287, 533049481, 766063475, 189565, 101120392, 211375086, 735657699, 27382887, 571430497, 696313221, 492436238, 206971646, 45074930, 60380878, 815365300, 275802676, 744456861, 598704308, 747763354, 18862222, 575618843, 881474969, 303594614, 263257543, 512966554, 302516989, 767388024, 356281688, 163980725, 868498089, 349554781, 684549183, 565326615, 146905698, 682887855, 732354805, 470057824, 466316545, 792889865, 733185768, 121703952, 621223662, 860066789, 635336993, 356325759, 584118690, 540906570, 651621050, 316623202, 196707973, 940279071, 699314209, 91483633, 775572796, 357933444, 706366183, 317036797, 715555695, 716698625, 64872433, 977717333, 814118395, 558631240, 397904732, 795518088, 719467953, 174254994, 257017267, 513850330, 951242, 66562384, 109510266, 908280088, 857287324, 578693545, 668523045, 920945053, 142251290, 973939538, 143716328, 424776494, 655098100, 189373058, 83338174, 318232550, 959118902, 202982793, 749806298, 247443266, 826073748, 894856575, 461141530, 977952946, 397463823, 212939722, 952397205, 44919732, 761073618, 765341980, 570426563, 501845343, 71225867, 775186908, 846486757, 28859928, 908958646, 609812095, 270008009, 692510560, 848063991, 150044616, 420026657, 341019581, 360223401, 397605094, 470384589, 832610982, 568267689, 8463995, 13479886, 129855231, 896364339, 844452822, 497461590, 7683608, 14297627, 370335036, 957098813, 774020849, 997666418, 778743822, 358389441, 860668405, 437251506, 263301446, 774340999, 110375477, 986103967, 574495450, 457642435, 823033885, 86964384, 420921575, 124491150, 134939379, 682972872, 136409067, 98059250, 258249833, 859303320, 811422452, 377569614, 343259905, 285732365, 289457387, 516183345, 901333764, 206344330, 588999766, 447045962, 107866037, 777264668, 971545458, 942917129, 65612185, 397877539, 500005910, 601231484, 584866924, 810107792, 236807618, 849906509, 219468453, 201672445, 496311596, 158587420, 377931892, 310266556, 880197548, 659573754, 334610713, 127086496, 13187515, 684507258, 248709292, 131948838, 936047079, 720930638, 143964984, 392159828, 958840267, 299426757, 902990624, 745983898, 349777857, 277148258, 160426023, 293298536, 566234313, 365774446, 545888426, 555597629, 563543207, 962441189, 85610547, 667549578, 509813821, 980817911, 189531190, 997366636, 112267383, 735116577, 389501456, 820774109, 773092196, 208232467, 842205993, 522378727, 255195857, 382744340, 48690615, 733705136, 99753627, 963031566, 826806741, 857926542, 615857736, 913362156, 535866441, 372665638, 625152741, 668814353, 254262887, 274528504, 254896641, 417144313, 773173053, 986248592, 607084492, 223037182, 8657281, 444632067, 701942563, 98747562, 133452126, 111802156, 168220044, 875083634, 80652495, 191298011, 704568958, 682786406, 106254890, 135051686, 656892670, 678239385, 113737142, 369004430, 986108623, 38051113, 343281324, 289003289, 459546960, 409168561, 678081050, 619360426, 489761656, 809555189, 337755147, 823356521, 662918259, 880731524, 679891480, 74308720, 751374405, 273278292, 125039358, 125462843, 233239230, 488440023, 38574359, 766096821, 591746525, 543846736, 515009006, 331844527, 399980769, 680370204, 225058249, 60427591, 256208355, 499051236, 637568052, 644693788, 628380009, 716606277, 38936640, 314348400, 722691726, 537176057, 772421605, 611676549, 994061986, 800582178, 532982308, 519257327, 588402868, 889093559, 123020046, 257221162, 890316372, 971156685, 161986471, 84025251, 208510470, 292491764, 356274076, 467200713, 422884779, 721005973, 306923806, 71403984, 889330467, 886005622, 539204090, 712365581, 5746694, 729476968, 409578938, 753778707, 45017239, 434958151, 364125033, 400361451, 440240001, 947824036, 194820592, 757295590, 558621791, 485465046, 77360325, 899620370, 452261402, 883551081, 338069482, 933988410, 491497380, 427018506, 545430794, 451251160, 786910570, 846391510, 12946995, 729130174, 930350736, 256844702, 790942182, 599732083, 693063061, 654501420, 48613653, 348721724, 44387399, 185459462, 418237123, 556799678, 478819446, 16790919, 121680798, 811334228, 990725278, 275349497, 316747748, 708619453, 981705924, 313720673, 194780282, 681631747, 994990281, 904324442, 505337666, 41905271, 20736456, 636381956, 53217061, 278472380, 775461785, 230802630, 435366422, 636925874, 497077266, 168096531, 945079510, 674167268, 374794393, 739197192, 235098740, 144484762, 705432650, 111654064, 872170786, 368949717, 854288895, 797413668, 712457590, 131778527, 267080596, 18482040, 370640656, 444555198, 879767581, 733600735, 499960367, 508264535, 883272531, 29901534, 28276978, 892127334, 308528862, 594552735, 14703182, 399944342, 470097397, 794111169, 344548938, 830006228, 667495670, 394435250, 427268117, 702462972, 445871304, 371296562, 550121952, 857933170, 690322820, 500092437, 243154256, 799559143, 386208996, 786089936, 543845204, 726380496, 16579011, 792836190, 837761144, 385262983, 848885863, 351526998, 48355548, 852889803, 400630227, 527883, 194266617, 61850569, 267197123, 718854175, 433706626, 227026490, 79286891, 900564941, 357461594, 811134515, 838515500, 610320407, 824004238, 282414904, 332959801, 892058376, 666977620, 597113880, 681365944, 624152638, 99365959, 213733997, 439967965, 708269304, 626067516, 754327928, 149027747, 783459859, 78556245, 104215025, 177553322, 244437985, 270860107, 669724239, 621179553, 51130954, 369930914, 123888134, 371855697, 686528060, 962432831, 461836821, 8434760, 515561816, 634552928, 998628500, 509682800, 144368701, 589073321, 397322320, 791425102, 258557762, 499241934, 802004059, 258628476, 634190072, 528534108, 977038837, 264055945, 407267927, 91250704, 797417794, 699548689, 161492882, 594569517, 575766019, 309782941, 996699681, 100311587, 581401902, 245351868, 811705570, 506236972, 47345294, 166607292, 767296710, 111712498, 771297281, 192143776, 233381586, 948857049, 179568849, 664784547, 113577378, 259169068, 326672036, 881726804, 834228289, 226708901, 625898140, 701707518, 275817165, 84995619, 291685938, 804241947, 326555597, 558277701, 695222769, 328749793, 352384839, 6379177, 813371483, 40885829, 865600004, 975642402, 942417976, 90426819, 868832853, 67694679, 213406376, 51936320, 515245201, 627246035, 90812693, 213118761, 380602940, 844927114, 790529589, 663437904, 997626048, 22866967, 973065364, 344483035, 372284541, 591857641, 607359304, 388481549, 20009794, 529649628, 574914543, 415148379, 410091619, 755528352, 847528210, 867707961, 595763659, 556808399, 201815016, 579064470, 615044085, 239868114, 464156397, 718128325, 10130726, 192480368, 736655160, 515052230, 966518620, 118457092, 901003382, 852669659, 655963897, 991785442, 569577649, 318546591, 65780804, 984590241, 99536372, 918660682, 563404242, 321792499, 200246349, 829710026, 109880160, 364933903, 797068541, 958174495, 101305114, 962588940, 791715490, 714797680, 42464851, 291702751, 159328334, 163578438, 135995336, 635171651, 330364756, 75395356, 417573565, 928928188, 867562478, 931715414, 462908990, 117823921, 502760293, 54766721, 626884844, 52760715, 135502623, 329515299, 236575135, 54669419, 393370485, 742994025, 612896070, 969906064, 744575734, 375476278, 708387027, 162073790, 433296239, 296806586, 134135163, 705589388, 787550203, 620008721, 816729488, 65205457, 412267277, 926368814, 996381961, 266273453, 78297156, 973351763, 489376840, 595514169, 931880495, 932746749, 136058413, 555843195, 230655291, 420253602, 828718340, 867459390, 907492197, 869571401, 781400921, 969802638, 216001598, 697851562, 465991123, 31617789, 857757723, 334500063, 16605778, 365810172, 580127622, 714585498, 225351720, 451141314, 20713292, 742542149, 569955635, 391367633, 634648906, 850346738, 338510100, 842635913, 60094503, 857098370, 282944470, 975492884, 118073330, 284597120, 605041287, 551293071, 205390428, 292326507, 487651066, 63255978, 593791125, 835961062, 368132549, 123623210, 44009127, 966998658, 996387344, 638019352, 855543090, 946533314, 656647970, 581398385, 594506099, 158874824, 167263850, 130751837, 344287795, 622815643, 312981049, 139556248, 405345002, 508285648, 714029900, 288582674, 913051308, 140496675, 597914383, 471694735, 626033198, 163119029, 541522457, 553993733, 95134529, 325524863, 379235376, 157179076, 984150500, 28707506, 429593366, 983562641, 540546047, 449166623, 705791123, 598238456, 942172317, 845739633, 190822179, 787587756, 811376642, 964601497, 371837002, 181257930, 888552022, 564282644, 631323464, 595162705, 428056724, 817177755, 167356554, 120733716, 654969299, 442960663, 239114640, 215334770, 664206241, 852528008, 905130682, 377179487, 395250533, 333158642, 528936636, 617730109, 249051943, 893822302, 639908422, 888520442, 370438288, 558368279, 638689701, 818641426, 639491930, 912350796, 415698866, 823406448, 786055346, 132746556, 857178937, 377961361, 45201021, 51482291, 330358675, 873834732, 604952816, 126749743, 443226778, 532163397, 190265359, 756933818, 829378089, 115082067, 392027694, 826583691, 365101597, 927935694, 578828954, 42507967, 369929159, 941520983, 105033910, 531614696, 977880632, 868925378, 617670505, 514768005, 197100907, 877010240, 520010903, 552071571, 374203961, 304476124, 201131227, 860234386, 698967019, 838963729, 760745867, 510120832, 4118583, 86882415, 431863697, 533967838, 375151870, 493804541, 510490995, 663142128, 24567010, 729625518, 635398278, 57444789, 130217231, 548026763, 6103580, 985685233, 562669861, 436069037, 865621127, 206951863, 728060701, 828592391, 885619086, 573007230, 294255222, 334418335, 695662093, 465884063, 991794096, 282518991, 560446157, 390072245, 785090926, 22378277, 440646985, 340998062, 49089970, 429819785, 232998363, 96065148, 279459900, 385092677, 866994852, 863798772, 530897695, 205913248, 25135402, 90015724, 411074567, 269316140, 380131457, 325742051, 925807185, 290810311, 229482764, 137142909, 787980627, 391722663, 561304854, 751848830, 637151275, 974935982, 501488681, 636638552, 690595246, 897025917, 563356791, 250940369, 56890834, 986946873, 104537729, 53152191, 518719585, 261221993, 499424158, 259557835, 989768536, 900384426, 787155345, 756155367, 767468641, 181761609, 141934490, 968340124, 320006524, 140828203, 972351710, 159575895, 884847720, 818866032, 965732033, 335861521, 119264017, 220482273, 116244693, 146305887, 460347187, 661233697, 184479766, 406581192, 733741534, 742650271, 304095558, 195650808, 117653029, 587648923, 325061344, 674985417, 352776258, 15112235, 382332755, 560964830, 890304758, 691517517, 589519181, 644854864, 372550438, 128273037, 652897499, 312625053, 415020962, 658413576, 718119278, 578532184, 425226334, 937064026, 269457175, 780869638, 966765327, 361818342, 267176183, 231128245, 773169512, 425920594, 210605726, 559218655, 889183819, 158860945, 552997704, 541769621, 711747694, 699638039, 93693001, 67404367, 200199552, 531263934, 282655665, 3978583, 447617790, 728694867, 471161075, 868021231, 595764087, 442668860, 954476583, 107328192, 283711017, 582552405, 540774476, 617412413, 783914378, 280321307, 182546341, 152483369, 318618212, 423512488, 946908417, 419497417, 703130351, 425354287, 345933080, 242653638, 145408295, 623897849, 700781204, 332826625, 259553187, 714598342, 483481347, 177938400, 529214126, 611196362, 809768779, 109040785, 297104054, 668182681, 103440704, 396034815, 330472982, 879164094, 723754370, 448681928, 792338524, 379695686, 513252975, 372073981, 605490492, 496136936, 296891500, 542263927, 493442740, 645087890, 907999627, 622165741, 178424517, 276571480, 391296809, 976754921, 824578320, 841898481, 573601191, 869523423, 205216317, 539569214, 380679777, 525371321, 191599629, 148959745, 359950980, 295577419, 749743431, 961620323, 101796392, 325018232, 56578418, 980852318, 877011376, 756227107, 374877413, 988824232, 561416621, 687293894, 473890706, 689391123, 333086588, 424038509, 107662378, 63915548, 187623237, 782816897, 12807847, 753622518, 125553493, 836467071, 712155463, 351164180, 129269701, 628888079, 313211891, 542828385, 718282002, 464665731, 347789710, 811357774, 348950359, 8893495, 933272123, 916326722, 215081385, 860933515, 750410072, 401127595, 703085033, 119672352, 7540763, 308861885, 841440004, 647448403, 174779130, 141108640, 959400372, 452283296, 773331256, 976085509, 477129306, 338160606, 655306628, 120851368, 529677508, 468758804, 612621141, 578021312, 212423122, 486626213, 807602376, 693585176, 133610120, 885935480, 499943638, 949691093, 445726037, 820548363, 653481506, 891828747, 214425244, 823329175, 861664407, 451702996, 15561468, 662842871, 871226380, 677965261, 964695954, 495104508, 764183029, 517393049, 629359128, 322159489, 400086304, 388612692, 679859780, 716407516, 94428528, 757270083, 446103218, 848011552, 748007006, 472605010, 772505867, 411449216, 973038743, 341262176, 377171878, 523548824, 191388222, 700886056, 955040313, 477731091, 946516138, 253233088, 55939593, 192054127, 142046920, 863871387, 908712376, 82855742, 185497439, 245925490, 777293339, 336899677, 120459645, 420741123, 26995587, 642163373, 690930764, 415916794, 906033115, 946442969, 797541982, 537779170, 302616715, 240308021, 926090576, 406177979, 105332077, 979642855, 485177059, 828185906, 832258509, 132004015, 267201158, 907202205, 827427842, 377685388, 127294971, 90818868, 173869471, 559710524, 933738157, 525840897, 970904073, 337434261, 266516329, 380017924, 56978322, 845508786, 954058292, 241187809, 147384693, 264437655, 654190579, 987771738, 693421850, 501687916, 108258223, 678623538, 536482064, 495233417, 993508758, 86117036, 940828017, 900892304, 510022295, 379054454, 452175421, 958809462, 343397021, 56058269, 163733662, 378220199, 899734499, 625663357, 695372832, 938739425, 824654137, 314962730, 619431795, 498227614, 532871474, 899584795, 311644151, 89208489, 911298468, 940718343, 705630717, 582446341, 448908397, 982576542, 225611685, 852855759, 901050841, 792503127, 277597683, 536778365, 896440646, 946310053, 650832442, 770693544, 934897333, 75544017, 79935734, 595348608, 96988500, 415112307, 225397908, 419757454, 250607053, 129697470, 175408398, 912490673, 202373163, 233356425, 18018934, 27294395, 946826435, 563162044, 779184020, 660520497, 95645828, 245795560, 661479089, 876558876, 426791997, 789529173, 359755748, 187313877, 482689664, 309772101, 681668940, 551016407, 200961507, 969559152, 985204573, 906920612, 520275289, 424185128, 151174294, 935404028, 975854344, 869817651, 932171098, 450412510, 549306452, 330141635, 428934544, 388134532, 574922118, 766607221, 136536635, 6060636, 955302653, 431668806, 260437199, 671731777, 144333905, 743777346, 475958237, 732178556, 92187375, 50737199, 701913066, 205304480, 940036741, 119382800, 42531724, 571093484, 874733479, 362579079, 396045378, 404717332, 174494767, 425000339, 309208109, 903943434, 940119386, 628890835, 453746181, 992799348, 16124088, 137442887, 236979159, 333414719, 593016293, 530460690, 237836159, 284806492, 497194365, 954104077, 200521693, 874593366, 290589739, 977368845, 263628694, 146016581, 951074662, 951630722, 346987492, 348903702, 31339909, 656530507, 181336030, 662395554, 989504734, 637675896, 342637649, 546713301, 690594019, 806080985, 686717104, 28708407, 433924969, 360742865, 391125219, 155283977, 796881090, 188627210, 173837310, 299715833, 635903438, 570223284, 22350649, 313041676, 437905433, 41032391, 111337219, 999744231, 360918738, 539212463, 837239634, 615573380, 828659591, 230331542, 163773150, 826271108, 751154235, 760515263, 939476399, 130312322, 289096809, 190879058, 924627225, 383865237, 460518680, 735057231, 860922604, 506414049, 685960775, 648746659, 223193610, 668774711, 280183732, 537781155, 795363545, 975252362, 315631293, 57044410, 12443389, 455236573, 959327403, 240158301, 267628645, 545569358, 240380078, 804011090, 157297234, 853109699, 695083052, 123765537, 60460896, 691205180, 788248841, 524841222, 154192602, 348472246, 114833740, 896050218, 591640837, 340090223, 264839770, 92989770, 491485034, 50898028, 952842162, 540889156, 649195531, 602801197, 663240483, 814932670, 168451508, 271268252, 45875265, 868374510, 91791620, 526430768, 607689029, 212446281, 617247921, 659908271, 231705447, 743480364, 663477127, 320889749, 854923353, 31813471, 645095842, 167698409, 277158867, 279911223, 158013388, 714134365, 727446566, 97825187, 708739513, 605874376, 93541882, 655627828, 218025063, 628833145, 380577698, 755752651, 362256506, 404346949, 235575156, 166026438, 924162518, 500369920, 380934533, 239024564, 191124369, 984795181, 403900970, 565570479, 21563227, 568308017, 78110163, 411709397, 547647737, 572208524, 372261271, 914053051, 226095286, 23677400, 930232910, 525059450, 364804020, 369379173, 681046827, 134283465, 839065493, 531454480, 3850304, 779448441, 178648204, 828264735, 91840705, 225919903, 837409494, 366933901, 58870327, 488383144, 873873121, 877713615, 977958352, 219826604, 573900488, 74655226, 934172520, 870613597, 158664291, 214112626, 649683406, 395811805, 568251226, 536284751, 70534607, 109646717, 660815679, 783345104, 974395597, 13417785, 266351401, 719000942, 827045237, 159350427, 321815912, 309133253, 904302247, 25106949, 736806691, 582508633, 434551974, 460736573, 210936693, 540426461, 291762162, 592294360, 103056465, 867364486, 417343735, 842156519, 639655284, 545949906, 660209053, 999440151, 457774089, 978616578, 899681782, 32960445, 586032938, 338034529, 198123733, 311715759, 194221706, 199622509, 604980537, 367144898, 26923165, 778697068, 640678384, 472952928, 499455812, 209583614, 208898960, 452937533, 982995858, 294369261, 681737133, 197733396, 791014800, 433976688, 17971646, 927538873, 700087236, 572994409, 69442935, 78882159, 607814051, 680659332, 85076503, 380770714, 342918657, 859741157, 983302751, 940086094, 529500495, 445752845, 956390593, 900547928, 885773189, 200291928, 429747305, 692410143, 294249388, 51838929, 588740705, 860901092, 904891617, 560450872, 387577620, 922449688, 995322285, 463203436, 298714080, 714976869, 921361729, 609074693, 399673711, 207547401, 443930005, 146318703, 643594021, 460502657, 510415274, 689751000, 748425898, 425568391, 475415009, 410993631, 923733776, 217029130, 159251776, 106542253, 90762267, 497824443, 546204206, 319110529, 770064546, 40270800, 906746875, 207616496, 354440783, 375592084, 485206765, 255304998, 337766398, 850359859, 826623279, 389081436, 332770494, 414768219, 222897215, 241648984, 867408079, 784001488, 684686419, 507567587, 413225567, 698600323, 305970417, 587016872, 679108925, 34932780, 273250958, 443441805, 556927257, 163932503, 361880183, 414012845, 626279268, 320409460, 171727040, 826550099, 100492078, 838846145, 534632147, 967265130, 525831928, 133245503, 404837674, 237298450, 332727753, 333085732, 962370086, 635662658, 268435114, 860034973, 981223678, 958936227, 370861937, 170303596, 654825722, 207989436, 80610580, 522717153, 665928808, 561413748, 533295179, 520150402, 807683816, 168078444, 668094435, 368688659, 433849778, 630400878, 974702200, 41521770, 680766215, 221335848, 383099521, 11635119, 836282650, 922261883, 986477933, 872483483, 528526413, 445790821, 755394551, 505713454, 956542653, 146836407, 567766311, 887944782, 304567293, 849389504, 284561086, 469735001, 200244075, 284625618, 377678844, 201025555, 681422760, 25999770, 438070630, 331779984, 788814524, 652408202, 18516841, 930370508, 62984996, 387278548, 377761845, 271869656, 611449109, 627227021, 570185371, 958020632, 658589393, 787833449, 266166205, 122173588, 401393652, 522254008, 810863943, 148384480, 506998339, 549965931, 488669235, 77120284, 958510008, 219687291, 107135849, 688362120, 161623827, 405229898, 256472357, 326391875, 7905311, 291980707, 793151949, 618591911, 317447271, 89123532, 113855671, 245408966, 46540607, 283673626, 695653104, 535197498, 876518769, 798685527, 543984285, 831173515, 798923880, 928809006, 364652738, 273118391, 386393238, 499821738, 481525547, 329180084, 355950594, 609587782, 433979842, 103617479, 852122733, 910562458, 659760435, 980398559, 720299024, 96998803, 583085189, 135171270, 152676050, 219368763, 687756824, 776619078, 251762726, 354354090, 534879879, 789609982, 829893578, 665447591, 604628001, 667665066, 196802622, 179270329, 418425788, 807736884, 802601424, 670826935, 807138725, 767294604, 432152018, 352855113, 28232137, 149689732, 753517883, 837414293, 129800441, 889404237, 147428223, 994956705, 529805075, 957342861, 679446557, 309022174, 623147757, 664805329, 81029629, 168795652, 320691175, 122269463, 845070530, 143022358, 874423599, 951196586, 553511414, 251106055, 994027502, 171497205, 616883283, 399191453, 974517467, 573831287, 917128002, 55100844, 92725962, 377559776, 509765725, 891367731, 461334293, 785550587, 856905606, 662404532, 192726163, 197077150, 226565458, 401691405, 350795840, 544660375, 568137617, 165439444, 183359583, 296794855, 735892466, 145857465, 413442113, 114334943, 601546250, 467881437, 849459702, 195640249, 436802550, 277688359, 261906584, 253902064, 74075623, 824136926, 254593472, 496108814, 329408480, 932943845, 743403470, 459397923, 598110540, 414509835, 311890136, 713316768, 918475688, 317340773, 722644867, 68822255, 863761149, 123317602, 864337861, 684889119, 374182341, 354788906, 582111842, 253831173, 616321845, 599957854, 602079918, 763983392, 340894419, 627959778, 607441231, 838575543, 209557212, 412554558, 778078613, 317459570, 891480684, 119823569, 686272517, 468521533, 617252843, 846017640, 837387188, 36361915, 214996031, 832888488, 660213018, 893351735, 345079313, 479528773, 197140866, 790562593, 226829114, 537312691, 646931645, 26407976, 340260701, 700526222, 939875232, 388312985, 739267624, 690235820, 107784097, 199365935, 763255315, 742788269, 258470229, 111865807, 530054884, 989049581, 651407844, 605424866, 29538537, 933890400, 455864022, 812941307, 263914644, 268957870, 389094048, 727911718, 380065403, 647422003, 162957601, 445711717, 691361428, 665678098, 246072502, 523254742, 661593591, 499607549, 426796650, 724268200, 934301321, 728929030, 212761142, 765523886, 532674805, 903625958, 222735991, 903271652, 355630984, 986723209, 94118122, 368473897, 553220235, 688915641, 566034531, 130416612, 659440155, 865815154, 544788221, 97592934, 90169716, 934238334, 22527588, 770263620, 644820825, 91801217, 79242190, 837659394, 598358672, 451689699, 844246617, 885116383, 950126622, 906922574, 395879091, 278341643, 899907528, 661709158, 135084325, 953671975, 438209391, 571228531, 155938256, 866379767, 603999847, 966015978, 332403317, 370102020, 605916868, 592159844, 113606737, 606794715, 388700917, 320651320, 541499640, 481215980, 499749909, 336977065, 607967961, 6981946, 10253643, 928352771, 162023545, 347149449, 105255273, 6533712, 397501843, 720150631, 485704685, 783502508, 323934876, 909086645, 955607329, 602119585, 604118285, 37515366, 537169845, 769877027, 705119381, 991737530, 291998767, 14341036, 685027067, 865441835, 854781678, 431147065, 37841526, 541146717, 340865566, 288368758, 119162522, 657437700, 31106738, 395647826, 747499950, 930604114, 102845535, 602973073, 345938828, 240599601, 289362633, 484326244, 274990431, 764525372, 512578564, 129405660, 668947173, 549921347, 626436465, 278794845, 7407931, 239970888, 528441639, 597453155, 564760117, 229166160, 185494632, 55229509, 619672773, 182538008, 469102933, 752470326, 778403983, 903805283, 679403702, 244503821, 956893514, 359748166, 199931293, 149721430, 455052479, 890640423, 224919786, 454033631, 911664887, 970786667, 760344955, 726782894, 334278102, 386958532, 955985312, 895445920, 353465503, 128219378, 633480068, 557320658, 586599664, 141266906, 435760298, 905474283, 224015936, 886798890, 414081746, 37314415, 162243090, 258905480, 613792802, 454946018, 122722165, 555356386, 178420600, 210069899, 225351798, 696861523, 308502161, 659940490, 421487233, 75826774, 110834724, 215629656, 323171451, 527217583, 425449616, 440326632, 400715884, 874880063, 620653703, 142798507, 552273317, 37838, 379315111, 841294001, 775360739, 476556334, 368696522, 22984742, 935277229, 85481472, 3584998, 308457685, 74027457, 23745841, 563625580, 578376873, 813211404, 705704987, 99288820, 5708422, 599696355, 115766971, 296266214, 888887957, 780090290, 503597338, 594663181, 734228967, 667345947, 92066597, 456587560, 829467363, 627553539, 896974503, 910345882, 22857801, 217660928, 646884608, 913948893, 505279184, 748008871, 86723654, 58277481, 158863274, 613290580, 31350008, 458624556, 140183546, 593030405, 68144790, 271695134, 316801465, 15893746, 252152036, 135727066, 930694900, 989399259, 253062839, 914355648, 500704813, 844999598, 705820684, 776871968, 873968371, 482597735, 91014542, 268053110, 506963718, 986843419, 32920965, 660406151, 768453918, 167348964, 947244711, 786931056, 506499200, 925508285, 695102141, 571889903, 947240192, 982037709, 980515269, 164876752, 452132044, 564618006, 633950179, 108651762, 167277542, 698665234, 451844477, 700944089, 235532773, 653054865, 810481585, 535498333, 734095536, 233412799, 214376964, 68651866, 645557216, 371966113, 309689337, 149275139, 546086218, 377091488, 184649901, 170255175, 30458113, 627453211, 321068711, 189504529, 339867975, 746804431, 719369679, 625361765, 521142230, 815287584, 765888798, 476369197, 493084273, 246234067, 744386279, 4108969, 194048019, 825254640, 212075204, 780325731, 692334328, 161762868, 612358782, 248446127, 158575739, 299529809, 570037451, 936637824, 311292243, 280324064, 359411368, 156958117, 364405727, 386228989, 615335659, 771632068, 611316414, 741825858, 957106556, 70972365, 565390927, 662107183, 146553531, 256156659, 771788775, 467298991, 917481570, 341324066, 401466647, 332664420, 111000343, 196208383, 505160992, 43159817, 399862336, 417705153, 932253478, 907103964, 128377521, 422792711, 337422573, 220486888, 96819810, 16589273, 901326307, 193475000, 29802939, 553417582, 334300463, 977517373, 79068423, 493632445, 651266651, 344575027, 980539982, 376162638, 762519005, 600730795, 352705476, 384944523, 703277382, 798994038, 42498160, 122941372, 912392084, 179385624, 644168024, 355439684, 852236833, 250177804, 650661888, 831014368, 483627983, 715178416, 265681744, 523544044, 287360865, 925713047, 200166849, 895702336, 884508807, 586549403, 357125363, 417489857, 392328298, 710374246, 380640997, 201677386, 487643616, 734816776, 965374539, 156608465, 556413801, 350402060, 134035883, 278132794, 576552648, 135201726, 998531429, 116846932, 84241834, 576270417, 744628013, 338943025, 198807110, 19552192, 260132363, 156149080, 252014185, 549603548, 464564408, 998390398, 181283412, 430706770, 10809424, 403855195, 44787967, 943572265, 51186951, 727786338, 939407614, 330065673, 631869508, 845674715, 646097073, 233917807, 738662361, 715236458, 344070084, 433219212, 5530696, 554177050, 511059668, 611739956, 281912470, 619074512, 343172368, 762082064, 806670976, 62356026, 753288263, 426722624, 666038446, 811410893, 247310694, 876251136, 582503735, 684164837, 770015710, 344042227, 881651796, 657692277, 102385051, 327501488, 369980880, 491094221, 205259470, 441851278, 623961568, 457685870, 152292176, 34889750, 591106316, 828487693, 933370428, 539897060, 635744174, 619898013, 895241199, 735407929, 431451107, 838565729, 138568093, 289291997, 349975932, 783185202, 44439979, 299435528, 964681665, 664884413, 588914119, 519262342, 291963820, 608434877, 146584372, 30856936, 909472186, 997373733, 298219935, 745075902, 866111394, 578482155, 391739744, 964706240, 74821298, 577612755, 115910223, 744711947, 228501898, 910095729, 604418262, 1065972, 771235803, 345225048, 658991734, 419601637, 435579076, 155908967, 555479621, 535369305, 255826207, 419607315, 981722884, 480760857, 225993967, 989065926, 764638975, 180045798, 127427655, 128825448, 416290642, 709472299, 895320572, 433017329, 854583700, 967237420, 876910928, 809672988, 894063810, 257570096, 133278008, 58781054, 271177373, 509287017, 559084918, 39246169, 165654957, 478591639, 599750396, 155996081, 831024912, 670435427, 493004098, 421715504, 97702803, 60459758, 275829604, 134782303, 822148353, 360860640, 290277840, 331639591, 849698502, 93129541, 119541073, 520502073, 783140448, 390515877, 452669017, 26471710, 648090419, 120118414, 60279264, 620607606, 370964556, 281389680, 721369663, 271984063, 112558515, 130139254, 563389279, 779354995, 207637412, 802537352, 206051085, 685299863, 33540522, 77281900, 993539890, 407213085, 363926653, 603686746, 217766190, 188831234, 228691001, 194856030, 455084385, 393472448, 795131421, 67722932, 688609113, 413899927, 852403486, 175393747, 320287768, 800431013, 761360589, 686641747, 276432535, 191223988, 469296200, 792126405, 964100350, 785919040, 423572531, 214181139, 947473784, 173109896, 911128366, 232880653, 906214433, 39206987, 792213313, 992518676, 50623082, 962062573, 298564515, 560588876, 432526576, 258934673, 30146263, 322201893, 138812201, 968130385, 751582065, 834355178, 44977802, 443574702, 726593662, 697856353, 842517338, 307994876, 487954945, 361680259, 489698034, 563877341, 451664625, 634782791, 294516161, 254875403, 364815646, 477015356, 134123401, 559385995, 149650591, 983860991, 88481264, 685962419, 984502279, 186134666, 291894804, 504487819, 329037951, 440628243, 898767110, 723958417, 222531296, 525005478, 430548359, 464271283, 796158993, 246940098, 541401799, 584756144, 246692680, 985812414, 488174840, 975378809, 364098424, 661973127, 734406693, 219476110, 635534963, 388502542, 274980961, 564107537, 261789594, 301050944, 203896191, 650439019, 531671090, 950163211, 250830296, 561280289, 582128271, 50491902, 525270302, 118452680, 638764714, 444602141, 173715592, 524061288, 844228559, 38083475, 2093496, 352769447, 58075510, 403519719, 199990599, 286297691, 803114710, 879218528, 547035096, 84371556, 260119009, 709095507, 6735373, 564034582, 12846773, 594038836, 551043612, 439019692, 191692392, 242849442, 616619579, 109334453, 494145819, 913480758, 604511921, 559897936, 108927071, 548852848, 919446305, 241627241, 856968424, 403226008, 671226288, 309078743, 63052537, 195242696, 190807542, 60091391, 876606734, 869050316, 857802995, 568354291, 432969863, 896418646, 841669957, 439957401, 461702194, 188342964, 369386443, 668226692, 969155790, 674225252, 10973752, 7879381, 10938837, 217566338, 344107106, 10720080, 341950495, 179868652, 587018253, 511793214, 456023368, 746542099, 577895980, 678057027, 652208743, 17477318, 14057240, 970100872, 428414266, 432025886, 769718448, 952255535, 649153238, 343222667, 224524331, 216759820, 164104636, 373894413, 664849205, 320699036, 134068590, 543826240, 198101994, 24815465, 955007961, 419066721, 241294301, 512036824, 592154656, 639713066, 970589707, 747078816, 214387186, 526361226, 366896491, 55942311, 871672979, 729081754, 497385593, 290591815, 919108462, 556392426, 3927952, 898458193, 401554828, 628507914, 140154638, 107748507, 28155516, 296421797, 228167892, 786346524, 623480296, 675939094, 808374143, 213198809, 460600496, 335252898, 314560457, 739390450, 434070042, 295776579, 82053466, 760932910, 961875529, 882278178, 586939783, 942454527, 260524548, 429231454, 530303540, 333569660, 224815246, 99619398, 217662006, 719859646, 458545974, 574924352, 559037595, 21934910, 803500671, 801738801, 920222122, 73658513, 463769832, 263332611, 7490133, 469375762, 842928262, 491986016, 119817287, 614408628, 318887474, 917964575, 134953579, 9253630, 81286279, 754883064, 900356131, 748990403, 220055936, 813788863, 432388872, 989644551, 476512854, 689530226, 490598100, 516167640, 409741346, 332250539, 202879134, 286459136, 427846347, 707954013, 458973660, 13937340, 254270329, 329120686, 428703632, 263303579, 951325473, 411330595, 822526996, 705167091, 682961179, 271906476, 819291964, 287545698, 773424246, 560967498, 869132268, 519031530, 973110348, 464625608, 984100705, 538142880, 864234858, 119724449, 935064463, 818905672, 61924206, 163636955, 351109927, 490862516, 863917164, 88281485, 607678137, 418625273, 616167575, 560153992, 637818482, 628461937, 72780547, 458742692, 911471310, 226358816, 292891191, 778204936, 27670945, 555051718, 830521600, 560179803, 544220635, 754984028, 66216349, 485529735, 595425494, 546107512, 109508633, 907256256, 513878831, 462798549, 919236799, 269370643, 485537822, 255166911, 963103193, 419336771, 139312626, 964672752, 390769189, 539667795, 656964685, 888234397, 267200704, 358975985, 100301384, 747756658, 423415643, 748730147, 402339418, 732650425, 422026606, 575898005, 928546788, 922513327, 120241292, 1137378, 799163898, 777716833, 707210146, 71502332, 304741210, 72298679, 127287672, 422177607, 477090112, 958436360, 352824200, 849224346, 46787681, 11267774, 105071775, 514800235, 984314825, 214793185, 124959781, 646511893, 358645891, 887298642, 169349210, 9567210, 505489554, 541928164, 571211104, 954400840, 680807698, 488040481, 756169206, 403036046, 95737766, 857032938, 687328632, 192558036, 40510588, 442913931, 154091014, 842460357, 470179615, 34304130, 23809076, 349482282, 415192337, 356461490, 686574571, 4311435, 220762690, 721964615, 238847679, 418916845, 909132557, 254861038, 853080299, 171856898, 452593628, 993147434, 375412012, 287360727, 709413347, 782276528, 814926199, 413505428, 686659621, 490518331, 947919922, 109536081, 752765946, 114134666, 336972376, 323546023, 668966234, 118624144, 146842182, 314466772, 663041372, 245936877, 360461769, 201314160, 193477164, 60016872, 537685012, 281505147, 213263496, 567594054, 533104247, 251555752, 332881441, 148991502, 903802662, 488599938, 569399087, 168439486, 371440501, 212647014, 718744894, 41405806, 267124005, 399251318, 168976920, 124722257, 83897971, 740191997, 291723674, 960326060, 708063723, 583140055, 53151246, 627147089, 420261288, 237183006, 318322949, 268016815, 261080771, 972289507, 633487164, 187930383, 559252986, 806251052, 925680238, 488241226, 120954094, 324468593, 140126, 622116686, 312337869, 552362306, 598580179, 576449976, 555710835, 705035840, 899594866, 909897876, 461054199, 819706953, 136764439, 194658846, 495267232, 828014316, 195576351, 662881205, 562977374, 768157237, 356126326, 52222709, 311859775, 796205798, 686634586, 803461937, 911411591, 320374068, 6383790, 566358952, 473321164, 414762764, 690077457, 812374364, 196198972, 198785492, 970255918, 717023451, 758441639, 509665990, 28563545, 568092618, 404819985, 339590807, 615559202, 987143506, 88424356, 72148397, 257068421, 832689001, 21453020, 736932038, 368070057, 357328651, 511593115, 84696385, 747082139, 93517356, 683193304, 835901458, 140803195, 633122860, 737847187, 538847656, 256922909, 750487066, 171885744, 736480533, 804902832, 214020699, 250052804, 808464010, 129429804, 790200416, 933340138, 773507712, 1094491, 466396511, 313353892, 688350844, 579181278, 265608697, 276710292, 571438440, 191376912, 405080760, 979234018, 207275677, 669680083, 1834942, 361115724, 842321840, 4389723, 321816267, 686355542, 977576272, 76898476, 225442231, 167432809, 303845040, 411971772, 306065688, 505582617, 272003790, 838003286, 415428136, 729201718, 71642703, 663703207, 670079693, 193167114, 599311322, 25809216, 757115613, 490833305, 384810217, 33545902, 246883483, 604201683, 838882187, 204987615, 925001434, 158437855, 763777216, 505495789, 226574115, 577002405, 52260341, 410503301, 62388429, 516213203, 915967709, 804160207, 112280519, 57865892, 39732169, 423763432, 244576804, 151855796, 690233632, 170440504, 142741273, 223376636, 98124200, 597413768, 451677512, 879115466, 249462907, 745761599, 37195527, 289746283, 432536192, 850791812, 22269782, 377693577, 37936578, 623793609, 214786049, 962213130, 392202275, 354434055, 764069891, 2522881, 241381183, 121733576, 162916135, 577931850, 55847466, 621116879, 759301088, 406555142, 432214076, 660890549, 746790345, 725609875, 274301594, 485226534, 542855182, 342803137, 982190070, 6350696, 97429364, 192957938, 74458322, 395217455, 347057333, 472628439, 178061589, 901453265, 492321642, 942688934, 316598407, 710035508, 447214150, 374579615, 641944080, 530403995, 103505854, 925379114, 409090018, 96353937, 953080783, 311896600, 992493307, 228960079, 999865209, 610397196, 463629431, 366261870, 676630032, 478756193, 488813129, 483382627, 881131379, 394390107, 805241754, 321421466, 988589389, 691578600, 613597188, 310666108, 587536570, 569935158, 976669057, 709794074, 941820071, 670061196, 783424399, 292456083, 440578107, 960055983, 598337847, 776173045, 372049344, 240271523, 353623581, 918945558, 539400820, 964802059, 338196982, 734441673, 749902479, 238764909, 373387348, 208206904, 476887245, 48099838, 673761166, 14590321, 506820266, 964871374, 54169597, 543560857, 413473622, 857508023, 254380891, 103297820, 440712633, 95076981, 152001382, 797000899, 633283829, 776663400, 102632121, 316657108, 267187837, 44436487, 888999982, 583208534, 170865903, 750485554, 79850093, 887235765, 159093540, 299631390, 33804404, 683963300, 252903158, 478897292, 136153731, 419659054, 40889466, 371647254, 15219801, 27505868, 840048595, 995041952, 299013485, 273549125, 413744387, 237820674, 295643796, 12176040, 95074378, 380164749, 577502670, 998963605, 581605387, 604714880, 698459897, 865404214, 408256558, 739578230, 536295029, 583036301, 70706713, 131525370, 443594028, 204241780, 390624083, 234095883, 5732960, 532639487, 330500742, 591240043, 338784306, 452847045, 533324229, 547157972, 70413322, 912914556, 723840487, 70537533, 740752135, 184096662, 817242784, 159602648, 98966770, 726262074, 536110817, 890953166, 138430914, 281065542, 431002239, 325735434, 951869871, 533192575, 629717031, 791951714, 463682655, 290081489, 236770573, 146440999, 776818304, 167982313, 65254803, 388737402, 311844344, 331358262, 486356316, 389686340, 563562252, 639726672, 33639570, 748687298, 734284928, 154166928, 252325607, 365826726, 428850443, 954241918, 179442538, 352055097, 739261570, 779493392, 411215302, 770548955, 936464292, 969804526, 757117867, 368967506, 317933646, 363085989, 285471754, 635640273, 142740976, 421723306, 807338822, 398682603, 926416041, 147808237, 51347494, 842487385, 723570735, 880323609, 285443454, 126088742, 449418429, 598878372, 787717448, 546526689, 917558122, 917147946, 172350270, 256405811, 994907692, 853234828, 571184408, 768430235, 57139221, 656998133, 711924378, 503182833, 211701499, 776989621, 202361803, 154136618, 964681343, 827147627, 480369258, 830425964, 43000793, 558484359, 512598342, 616333013, 963562281, 355044533, 919751525, 101817054, 118955576, 766175000, 312841609, 44904555, 339963089, 461692491, 647769816, 724808795, 389326835, 533256404, 611666741, 703382959, 471108696, 644062783, 845898947, 107710942, 885868967, 100102890, 373080672, 621138883, 994559799, 217972690, 200930721, 76227348, 404483529, 597707146, 483943685, 248530302, 318266125, 849496214, 605080522, 641118314, 641497964, 964176205, 339935135, 227385306, 968177480, 739140039, 730947413, 591460021, 856726020, 851270358, 816437192, 946970035, 571732267, 397716089, 752664934, 794506370, 282877622, 200699815, 282862254, 713406043, 302337617, 409608204, 475061645, 358481539, 975720350, 164433817, 364859909, 373717503, 786485793, 584634478, 577922375, 780078595, 752790039, 634604602, 214265669, 67148944, 84529590, 834191857, 78640560, 817817, 143346504, 658004721, 70868251, 753934713, 589674457, 925403931, 310837508, 221532757, 967543240, 598677047, 542448331, 159416314, 270367723, 750610235, 663235910, 318581683, 84413653, 873056596, 988662036, 174095071, 55169910, 944610396, 916469104, 906633027, 609915310, 585261280, 800569483, 363710843, 49638083, 571183375, 460330734, 637420241, 103595180, 828013448, 287403816, 358529321, 770882875, 682961570, 89881751, 140346955, 66434200, 138791278, 622389819, 584506080, 937752722, 483572599, 324253409, 615494595, 432882971, 398425525, 399083314, 169828633, 933099179, 481298474, 86584609, 84971468, 775705895, 425650800, 38511404, 908329512, 550737558, 822560757, 215609481, 423815471, 670590065, 639284883, 277697045, 321244339, 441265020, 957769457, 617920074, 20340373, 30269279, 337275051, 51334278, 762305402, 98590595, 874868962, 740066356, 476702413, 281169757, 733911444, 629933276, 637027124, 106318164, 18238768, 246289455, 998802069, 782789086, 363004746, 465965535, 786461408, 9256094, 242780302, 833645550, 15424135, 401001119, 625867811, 947605008, 133225530, 397080520, 223429584, 99634600, 727887940, 213255366, 436231962, 133016227, 309148503, 32409100, 497937234, 176924940, 624164290, 838641398, 29623887, 454339595, 729710362, 660774714, 21068888, 289047618, 138193133, 550319368, 261763315, 90841813, 254812705, 683557473, 423627765, 221560713, 524919080, 915430317, 93453777, 348547527, 933416146, 531828054, 908187307, 200006275, 267301612, 346597908, 212809828, 203134719, 963769014, 11710876, 114213556, 607531044, 546081337, 454948917, 407807442, 214668462, 567310547, 964971312, 649040665, 873267167, 409325853, 66728649, 814813274, 700415094, 505722713, 180483198, 993114110, 26371436, 148244661, 256136744, 6291993, 731789390, 410596031, 537860576, 444103916, 140940410, 124317340, 269314729, 442113941, 843918584, 997627784, 232487096, 350290156, 366848459, 375575612, 258502600, 675802353, 344035109, 684218544, 111425137, 628558510, 217900861, 373307914, 20105748, 351423417, 269659172, 182881681, 933002709, 468357221, 945144972, 769031749, 36718009, 804202051, 601012500, 487358994, 57683883, 978738915, 466287752, 229323661, 989848802, 522793453, 275185750, 257152160, 560371742, 279783016, 921075542, 793043783, 304834506, 678758356, 338016588, 343569408, 525316117, 387089875, 993276189, 639469748, 383079140, 744523902, 388979452, 236397944, 942988390, 837164686, 202071228, 378323988, 251432058, 433636192, 307665822, 352524027, 583793164, 900419496, 830517142, 357226301, 726887328, 479226306, 28241278, 47824365, 503603236, 526115332, 948663290, 401112592, 646065318, 428170005, 802701724, 786637845, 71165353, 54081880, 505617765, 465361972, 911634367, 483475006, 360760501, 883577583, 145753299, 820650455, 142677226, 743774119, 9568879, 434125682, 683308061, 67664926, 971337345, 32853921, 603504649, 261529724, 425083201, 951721664, 338987, 988965249, 861688759, 610844727, 317620942, 683539630, 3000971, 147413479, 926982053, 753699582, 298919057, 716342527, 195763735, 790179733, 730275290, 835891886, 578284514, 110729879, 602812729, 889886371, 702781690, 602573063, 291701299, 643161821, 327392224, 825782834, 641899731, 471912768, 281356426, 538280563, 667509496, 479578892, 654789807, 486993059, 424358215, 289625796, 639599021, 204179157, 672039412, 831825910, 948974375, 479210784, 939459834, 856736980, 551775199, 363226881, 924024482, 583670852, 672702911, 173248592, 478117057, 976572289, 479694833, 779248855, 73616522, 574426305, 604646823, 461625232, 973882342, 900983142, 580660983, 989021130, 62325882, 927251656, 55042576, 663517165, 312702889, 298181356, 61932455, 502951375, 550862460, 568887170, 472783697, 914575909, 90089862, 472723195, 282189590, 420337343, 740123369, 546350479, 369755771, 821863438, 500398057, 39510940, 920270904, 214514056, 726911606, 411612846, 879371699, 921135188, 947455366, 759830517, 612799244, 239074262, 297687466, 980367075, 464836078, 312052629, 306163090, 416098737, 425978875, 992506292, 355211390, 825195513, 539616783, 674276144, 88748777, 533429998, 336170760, 574311347, 843683537, 306125454, 726075784, 822491994, 512828410, 307470892, 297360419, 378130936, 947643630, 229780926, 611656988, 80368631, 528072882, 338687049, 843105680, 68987570, 175138325, 528358569, 386358436, 323528359, 99579628, 781659089, 906051639, 842454251, 894212954, 410275099, 808936342, 402019706, 160888979, 340572884, 968448721, 689036158, 16518031, 127888289, 129811566, 890343877, 720308035, 251858643, 154761184, 496102186, 214931033, 911033925, 844549375, 290420849, 430498793, 678019983, 971746286, 178099177, 898233088, 300808713, 866793594, 56824653, 42346312, 275848946, 14843304, 49515553, 774113427, 160340070, 617899663, 334718138, 398188494, 666712994, 812038133, 995635935, 763237127, 835573830, 163863347, 682375878, 967492562, 26483364, 677036257, 828907722, 237038745, 253491620, 51508247, 117277288, 634756436, 732812540, 805157771, 481450279, 421750559, 114594377, 764320748, 442105280, 528760249, 149917421, 226371657, 544348856, 16472657, 909845680, 445529164, 491348940, 371417395, 382794825, 460347730, 836775575, 232851411, 902702571, 172464079, 47116405, 640965213, 59105194, 683424664, 464862692, 411385423, 377344656, 145617558, 727873165, 142044091, 414419964, 645361527, 66909307, 49429805, 87598423, 698627417, 131902224, 325992889, 225659255, 34447861, 869486921, 750761654, 122962907, 439836581, 658233470, 723028137, 272085785, 130995287, 183840817, 217829276, 612215661, 594285409, 325999535, 434872867, 755976469, 697383140, 866905826, 272251820, 677428113, 14852420, 872154335, 364768801, 789301701, 345350687, 294218004, 524874541, 562470913, 172801653, 600302403, 229638369, 138482293, 40490720, 208372773, 60078635, 419568011, 906708012, 340735279, 663481306, 822198967, 532433541, 7807778, 539623951, 883625952, 10796247, 341865661, 548753100, 943147103, 844832979, 937921446, 280731904, 255819269, 798186978, 35298866, 21400651, 780870313, 8046997, 67732950, 526808042, 927859411, 328869054, 889989935, 913053696, 501969711, 626402207, 869980008, 93621134, 603179618, 477301206, 694764047, 401717431, 959457122, 205015080, 191731342, 426810452, 512074371, 36712000, 806429014, 862310299, 264363354, 315507962, 198971075, 801241898, 929505057, 705022978, 269955233, 492985369, 673174468, 569695903, 359003236, 264375844, 372755056, 287646589, 347453618, 224685170, 792807626, 403798469, 361802368, 79814150, 425471084, 737072153, 566503861, 477892362, 185725267, 415380754, 616159114, 185494462, 652032319, 953105006, 281858684, 167407757, 952096128, 837844817, 861061438, 908785730, 867979050, 434146080, 197898882, 465583353, 495973277, 298988514, 362194511, 604654036, 860988869, 392332158, 309012753, 804131754, 317855083, 774396738, 46360944, 445760487, 226869128, 281827258, 651714106, 604994134, 735659194, 188960213, 321240872, 430649561, 705431158, 638164139, 305955235, 905429973, 988032045, 471415906, 892691481, 317318763, 555704243, 117700662, 992047833, 915080391, 8505663, 658027794, 989485917, 864351643, 12307388, 672946643, 878726795, 500061503, 167105820, 815939083, 585397961, 288494406, 328075012, 972289007, 645096253, 474447263, 282184053, 464830579, 576442978, 51377825, 808340851, 400036809, 578636416, 77905733, 410189818, 887076619, 784342973, 18817767, 194014577, 909687822, 375510658, 480817034, 198060433, 798444995, 660246712, 658373391, 242633389, 697654106, 454537009, 144598001, 868916951, 414286906, 484383789, 998903782, 309911309, 295379377, 915896845, 20857247, 945982093, 83497482, 722451837, 140568488, 307146733, 259249870, 728108115, 610070627, 423949405, 579003552, 989728738, 744748140, 159006874, 464962477, 391094578, 695395868, 449495011, 95404856, 278626869, 501023876, 547214044, 380413615, 683899466, 462151699, 650855506, 541312127, 302179026, 545299956, 98528633, 944748691, 688257808, 524102278, 427919634, 680952228, 104254168, 518725687, 421973337, 854225188, 708863759, 273747213, 967513053, 847198096, 984174568, 677102566, 504061610, 488924891, 631017295, 690384947, 199939999, 797368912, 599718788, 234676152, 776960876, 644358816, 393351054, 4217820, 492069997, 553844067, 651251971, 184122751, 15353111, 450883471, 356920963, 329907720, 843968148, 712279790, 688916194, 423069243, 201314395, 392596054, 51196566, 47444449, 758684274, 131578594, 182123526, 515498183, 980744525, 994486011, 827448899, 267692251, 933957178, 958859404, 176919367, 143670409, 636918670, 168295201, 673441122, 470076296, 657337956, 541086713, 976649957, 587644804, 837176734, 581609362, 455265915, 121510145, 654741590, 267617865, 170617026, 107433199, 189483463, 511231432, 682224890, 897171472, 40540151, 496346616, 30290408, 225253676, 790595429, 428531263, 118173081, 424955085, 112382379, 573401060, 900487811, 171998858, 107761207, 130826330, 738260526, 799393065, 57267552, 353156560, 738175930, 936768100, 22822794, 2941560, 420765412, 124715606, 472681096, 542542317, 310158009, 246030833, 648104506, 130159332, 131879694, 879001753, 319763904, 326523615, 756364654, 335658720, 108696112, 235522280, 539451964, 890398215, 737874629, 648558345, 736893876, 65855452, 158961161, 430647050, 124394387, 703629256, 876183051, 770096300, 193263292, 952119040, 341431610, 442027362, 579743594, 664320480, 343307352, 827448076, 729957854, 889756814, 589262304, 33203260, 206538270, 931146278, 267859357, 793030637, 653868577, 334754690, 621512104, 174044574, 131641574, 408798400, 203992182, 522270427, 620402800, 640993904, 348709108, 373501720, 696667080, 477103152, 143465014, 608198810, 43866036, 247032657, 592132615, 337156982, 682552188, 50215007, 209335239, 894194984, 867278597, 782322450, 633080575, 851874921, 924273257, 526566217, 486547793, 342157662, 286540377, 75869128, 887685144, 448794869, 368358926, 199260455, 845916384, 566275055, 798156256, 498597805, 421734606, 550717487, 781106999, 474609207, 770842262, 244563061, 991677257, 570859913, 55783133, 679543123, 402554961, 881240132, 899746116, 807713869, 936838012, 437779915, 298128417, 531655801, 179836457, 401294854, 346592090, 512115481, 334649271, 868637099, 606647720, 269873353, 874255327, 44076118, 188026300, 847046056, 507417837, 868981793, 55673954, 641653733, 302302280, 733435560, 703290413, 457044096, 899585715, 861343254, 757321177, 672153982, 854480768, 605589617, 992625507, 780735627, 185250312, 291242785, 794221023, 307766289, 344320432, 320403583, 446114552, 299689023, 684531363, 375835347, 237009638, 424365869, 253098680, 115880784, 855798307, 911410491, 498858486, 70064328, 103038257, 962751436, 234278650, 963764322, 938590947, 689767500, 954271103, 304887710, 687883722, 763765278, 390627441, 543679068, 321459964, 5958355, 751450633, 668532369, 977207324, 610190703, 868498754, 294089357, 580518669, 237241250, 863369062, 162460073, 139661322, 327476186, 235314726, 314268560, 94278543, 8723261, 413496582, 347946865, 431805406, 145371526, 562957614, 425048550, 958170532, 532538961, 15217024, 497005253, 551033564, 431853111, 357455869, 809270900, 779345770, 551712704, 418998439, 691570683, 64529962, 720332401, 378794671, 601144769, 594293769, 539379301, 868381414, 50121061, 402769106, 486031034, 728365376, 626054866, 134841634, 181700849, 629853506, 444535523, 782247659, 111685705, 868809068, 802330510, 905901816, 263282217, 384889864, 769828654, 218303322, 501349954, 135742703, 829366823, 648803406, 496383936, 457876421, 629633308, 626726266, 608852598, 537533222, 470377440, 795807723, 856458344, 431627987, 522294080, 366611643, 470100615, 454641096, 558905667, 380393048, 990134871, 502012346, 909256125, 488480275, 226988640, 491914390, 395818180, 540909433, 472813822, 747867584, 934851568, 82441240, 352988925, 570955802, 66424618, 102289888, 750283994, 560159533, 749720086, 129955660, 580316081, 837648035, 879551836, 851544326, 474419677, 730853884, 418639057, 845127987, 15521335, 621659357, 894564760, 448939586, 690139645, 216874296, 394951019, 820605578, 737152070, 154708569, 296412468, 110621748, 409224693, 18992124, 933556003, 694065560, 844639980, 925067327, 900811999, 243689089, 653733689, 112041202, 463044046, 717253426, 618422326, 690458238, 70960200, 221262375, 987162139, 637333877, 123153887, 421623482, 653346362, 190306701, 514884327, 468412385, 869975031, 672713271, 618663263, 700507056, 914215696, 689123938, 646392675, 154216358, 155861255, 888434924, 667149574, 957964081, 126741715, 628322353, 93221399, 993008136, 476201728, 980232630, 849224399, 557981089, 642695875, 279124237, 378206964, 493530533, 492429960, 583070120, 818710544, 148792933, 260999841, 516696671, 190557755, 228102859, 570938827, 562396662, 735763283, 452412294, 763253269, 456063081, 884600675, 797738552, 241201676, 391776749, 628185159, 949837826, 255951309, 911786560, 411991614, 999038513, 931459983, 661565740, 218314895, 197590427, 877734185, 680188603, 773927042, 12837477, 298402367, 631839893, 435305165, 750368025, 749289695, 614514083, 467939596, 634852039, 335415000, 12370931, 672728046, 441285574, 935965421, 728514230, 454122185, 738112144, 723264826, 610373023, 827369867, 658824491, 313485214, 407533470, 159325371, 988467033, 179723970, 973357612, 249360747, 965634488, 233391912, 925228014, 849916146, 64058147, 788662181, 695469509, 823119912, 838539990, 775017177, 63001730, 548512517, 995551338, 29335419, 78603399, 997260310, 573837798, 385406054, 107845424, 545826513, 515422786, 317579267, 489352674, 723517081, 25722382, 550357875, 78480268, 726652592, 764349404, 562094417, 338330810, 912763067, 683798364, 523141509, 171575981, 180471994, 863529473, 864869496, 858686112, 253161995, 151320938, 766443017, 870227165, 497553339, 945956277, 780929663, 812399617, 467448568, 616907877, 364981846, 81181026, 147929791, 199334275, 873619232, 734989711, 515862483, 520589478, 1429964, 446807486, 256471655, 468783506, 858792957, 48973129, 705063885, 558457464, 821879149, 895649135, 597123625, 940037867, 467574215, 260359562, 958903924, 302376357, 488850054, 989843638, 381799005, 355314643, 551371228, 898656946, 848574594, 167148527, 214944062, 525075263, 314662020, 624297414, 915826616, 970816875, 62117013, 655640618, 658172997, 813006961, 589525491, 633727317, 315626508, 314991344, 146139544, 203494979, 883637586, 382770832, 841071350, 473426082, 708195520, 76025974, 403968623, 979906753, 688129411, 997652714, 687335624, 404452887, 523782963, 616373137, 346535269, 74427444, 485079073, 81752491, 548514962, 699458880, 143239479, 982812237, 972403384, 745732430, 839532810, 998150249, 183405570, 80723676, 342911088, 462896329, 505619272, 494127560, 86559592, 444562914, 681768776, 71104332, 842453984, 763110776, 466594251, 416869925, 932044808, 208615442, 252026300, 610571477, 383687774, 777998331, 20779506, 26515125, 496928698, 711799668, 735302468, 803905181, 370722992, 662238105, 90936212, 466920332, 861542194, 308380606, 511351898, 422700581, 334593596, 606518520, 222297826, 827018788, 934756426, 191314177, 615619982, 724585921, 992103772, 72202177, 914325773, 876853694, 184799158, 912771032, 389981419, 366205414, 57735630, 882013488, 163290521, 106373735, 204338437, 357536749, 146827647, 251404029, 878105847, 66991286, 174533925, 946742994, 430354110, 342568936, 677263333, 896300754, 645848596, 269673845, 815021831, 600291309, 622133675, 162473265, 493826836, 633095523, 810053625, 784737997, 697715829, 368363916, 245333519, 376214825, 591427509, 503004357, 52657915, 276859475, 92389882, 17040623, 625097350, 790261355, 837579052, 4611775, 247205553, 743344844, 522642220, 981731961, 326790440, 334836679, 168846402, 421582619, 188631797, 116922057, 265508324, 410390782, 509643052, 712748480, 786877735, 616031258, 424838493, 376156368, 686492522, 915160122, 561703304, 587709469, 946750296, 256035377, 726451170, 741087069, 435109576, 669377067, 849670160, 675806116, 202054476, 507017778, 486321406, 623445062, 542308865, 903946878, 260887504, 731367751, 153133948, 750710606, 850497435, 993594313, 29731572, 24365408, 208415827, 613014974, 171732379, 418494517, 610006517, 3423698, 898152822, 836908016, 721058032, 724959310, 35998286, 384639415, 31714189, 329217021, 391405260, 529394966, 869980951, 540760490, 951109367, 540173854, 689873357, 709700722, 887741347, 370770816, 303090923, 424000172, 678869901, 843317941, 575094637, 904582227, 953376354, 772826599, 346518413, 680945034, 303369935, 871685344, 684566017, 640678951, 802402884, 299390530, 655462421, 779816948, 53863989, 358610854, 62749093, 321892306, 619778992, 151450878, 577978755, 693116514, 362443282, 249734991, 79664192, 159753651, 63557069, 465673634, 609979434, 643074648, 730641825, 332517398, 858850229, 209901399, 545524703, 245440992, 655272518, 449777020, 893698600, 190734013, 143261944, 287417983, 777793900, 313055845, 622243037, 882444849, 555075825, 187242085, 874896, 969704146, 457452310, 125850668, 280784430, 113979313, 842989531, 436001393, 262507668, 705545675, 567588260, 566985493, 978349635, 697330078, 494575645, 337978818, 483893747, 850094997, 207650565, 115405196, 966371232, 191828204, 517526439, 166728434, 747804341, 86213595, 719028606, 701574655, 929289748, 512592291, 436650986, 537891842, 284918048, 273434059, 511174887, 929465460, 622967913, 755886918, 189198881, 927322872, 329886333, 723225935, 433229453, 673383381, 778820529, 45702795, 57038994, 774709303, 22771090, 406480161, 798604086, 13506508, 708424221, 761182842, 756377399, 297831835, 529253027, 650479738, 928961900, 882733878, 783937387, 849613510, 344807092, 134227605, 560658200, 503593654, 788147176, 92113272, 975663289, 33323166, 496160754, 604666859, 829954213, 359917524, 788635322, 832083317, 932320333, 34044810, 225221418, 321632865, 401785523, 449396623, 806041761, 851134724, 48533663, 591399430, 825839194, 284327832, 425275708, 74414647, 504893059, 180902115, 149571254, 732554170, 983091853, 666207547, 572193238, 177003591, 533145760, 556933695, 311430181, 867029816, 375337537, 974589439, 243219411, 671822667, 825467105, 294325261, 294448116, 230065366, 86191354, 919015675, 548932223, 386276257, 45003132, 804201622, 845185501, 989700145, 452744390, 462918130, 283649240, 536550900, 334348756, 736360735, 648246040, 450632128, 308866275, 69691399, 608036444, 191541958, 197349694, 997494010, 667609141, 537743378, 870451190, 40987567, 528833665, 560532544, 74483582, 169442697, 39744015, 394722610, 350873623, 840898045, 186156877, 350881871, 157981798, 438334675, 481965339, 820034926, 234160875, 687386964, 775574509, 667486808, 678684426, 188355355, 584396541, 779948493, 941679353, 386090640, 675987658, 32564778, 383939190, 491874961, 93512554, 949854747, 409330910, 24537451, 610073750, 569364629, 724081648, 538310388, 759042568, 298715805, 770060641, 6098283, 599431498, 618983262, 74362174, 277593302, 286572904, 709712748, 241935617, 708459600, 32829844, 852758431, 325934897, 507035730, 28511471, 387430359, 451690984, 795748116, 302591220, 368339868, 393390513, 601600768, 200410580, 641945195, 280486647, 314861604, 508479771, 430643466, 222476115, 345025441, 265684595, 689102265, 389001264, 954676044, 297364857, 316057331, 299259060, 704665162, 834340763, 269329394, 132776113, 22460377, 930578771, 964663493, 243151017, 769289501, 634847638, 689868544, 106435539, 964472699, 559866486, 981854718, 630369479, 527959211, 169888465, 699370955, 118398975, 439796917, 437321058, 527713030, 797826141, 89302475, 273157784, 701215093, 273667423, 239233638, 443162911, 203896249, 350134867, 358751729, 85947329, 105100221, 390340375, 942749489, 527616935, 194389451, 915663817, 721896510, 970127018, 485407280, 663990048, 529486307, 643380618, 562171771, 376058025, 580967139, 556524074, 495955634, 620878998, 226608451, 20085896, 155216821, 428689207, 975785781, 973757927, 767724772, 598466434, 848540502, 814035381, 147011541, 362423114, 650654924, 939118795, 444443874, 675651760, 697280700, 725317738, 492356522, 284931719, 489631655, 763882760, 998228888, 144419027, 196570680, 337941143, 772502035, 873674130, 292795059, 321735233, 791394362, 615837587, 442667163, 154925481, 795665120, 671650562, 959223846, 170575299, 516693741, 924131771, 991127335, 580052077, 981166396, 363454302, 560081162, 38217999, 680660374, 305221127, 25198732, 625764574, 268246145, 761744612, 968314381, 123187084, 882904484, 335261720, 312043189, 740865653, 393131135, 470170176, 479621541, 763015891, 375135138, 36563511, 241020851, 714848001, 473301669, 289823698, 182213953, 653454032, 930287416, 740510810, 260610211, 277375109, 532258416, 231486024, 801586852, 566233659, 420054077, 587160139, 859231393, 973907689, 657977376, 933561181, 830219494, 177381125, 882902242, 897312999, 311743796, 492726802, 785842306, 267680744, 885500292, 535067584, 474419942, 423840409, 742990371, 163555450, 34992908, 288349596, 500512150, 125276900, 219989614, 753719827, 362260284, 219275444, 82436612, 271522203, 268619811, 692865966, 379697671, 644848068, 391699770, 292028321, 353720358, 605899863, 508120091, 950648738, 651588166, 954350714, 78937947, 198373822, 889274508, 500855534, 396787301, 35420584, 612098100, 841538661, 17080676, 562985249, 792741380, 722362260, 907948720, 725242053, 97841809, 562634813, 393999736, 797419255, 483286972, 996112841, 314009539, 951119534, 657675658, 393021683, 570227227, 498056306, 681423074, 277569323, 311709254, 408832377, 931960417, 181584373, 589093032, 904736583, 297296992, 45803881, 193282557, 51905145, 655971332, 868932947, 294488828, 266267061, 963425743, 710932554, 177237686, 699037676, 691926871, 815969674, 799769435, 638595497, 477339577, 649766456, 860092744, 109781191, 780460739, 747039599, 944722766, 474701750, 656402131, 864098833, 391053859, 991094270, 950625990, 913839719, 561585704, 937662008, 278306408, 696834971, 352412340, 224990122, 77360359, 862486310, 642557967, 35209154, 858217192, 797160955, 311356672, 485142268, 348639196, 62570801, 744639198, 402888977, 870946800, 835085605, 17424345, 796880780, 609872031, 12847513, 998702807, 762199836, 807101494, 530224899, 124097605, 626181215, 584949374, 693029373, 381924269, 631728471, 353114084, 664012324, 302239469, 522474904, 838667847, 567118105, 80865466, 703121188, 241232581, 720035026, 259939407, 673626719, 767895694, 966378610, 64944453, 967449282, 114617556, 199151405, 178968207, 349453592, 832614592, 124687245, 665212193, 355686165, 602828836, 575640471, 690694849, 951950408, 594039427, 999129710, 550623934, 503417528, 817153214, 876893868, 513535028, 133336550, 967802011, 615651705, 963873777, 684786329, 23212292, 17738941, 856110851, 657420102, 999551971, 534891770, 578781914, 927419594, 385470910, 31585180, 558639904, 874495917, 544010776, 874234805, 913029496, 128008807, 468298735, 691132969, 648829675, 931581761, 694909475, 51557723, 177614648, 231008353, 798704307, 860234892, 55770570, 778666803, 697767628, 773200612, 365551479, 760407140, 756453457, 408959105, 205917574, 196759384, 22411935, 712209628, 125970041, 300606297, 581640101, 622732116, 361430742, 960997782, 376481211, 507948233, 407080924, 607210396, 179711930, 777756498, 494777866, 396075163, 176520422, 500647420, 512782036, 694755039, 461779742, 467844304, 729277708, 232253225, 822836044, 618285549, 850155018, 462109495, 262930433, 908287569, 497556154, 645573212, 753769894, 731269479, 591640643, 445192155, 523067148, 386884769, 10074760, 419598412, 520395357, 227587692, 569738406, 775214146, 260228243, 425182982, 798770807, 174818160, 262360316, 558962009, 398674654, 720333890, 930502952, 444890224, 895656752, 743993714, 250428882, 923116979, 795465786, 549075195, 508861599, 474094334, 793863895, 281167679, 949729710, 715620499, 885157578, 260454703, 685524176, 927325443, 178263890, 787055936, 64754226, 312397986, 712563821, 518628063, 695252840, 164042556, 497291863, 850975885, 603775722, 320115717, 413259902, 12044962, 920733657, 431803049, 416401547, 22821831, 454490519, 253589439, 179996491, 458246426, 147933688, 227937856, 563985577, 888264052, 78256830, 221895465, 561432376, 470791639, 180435879, 30226581, 636527051, 831881307, 611829530, 714059243, 889324980, 217910585, 977606845, 451273505, 232018943, 67884041, 860797240, 499497242, 856100606, 176300336, 247043455, 594614661, 106120296, 783456925, 814782606, 310966759, 561316771, 634294058, 595301028, 250920058, 373047970, 367810929, 259303093, 21426218, 181150476, 899821382, 674292003, 500764644, 145963513, 252512590, 30613804, 18249191, 382728493, 158328415, 802455468, 540954290, 677883259, 738220035, 688354463, 144165832, 116761615, 227619055, 938864461, 705188448, 602173834, 180064636, 72773969, 901503203, 400312700, 887898932, 615698801, 381976339, 796725157, 322354665, 555858167, 628062693, 853374092, 725977018, 40314795, 26900937, 116571882, 422068405, 631752955, 961872833, 49220886, 20839320, 130545684, 287411204, 467201975, 658335287, 31202093, 42966986, 885398450, 301542330, 380210504, 150606010, 238575093, 706480194, 234971523, 454413563, 302755442, 120911149, 736499543, 286055762, 521829343, 740013548, 526254484, 604762651, 960958366, 813592198, 222513406, 819423547, 589055281, 739878816, 148751456, 622984401, 527341531, 503018561, 36408821, 449760348, 535712593, 910035591, 352052754, 797186220, 160914865, 100109611, 243881049, 198722850, 136079409, 830093103, 96115576, 510820342, 425550374, 345121244, 780286360, 195799419, 114854882, 578308636, 15730620, 584887400, 911623538, 431148652, 64081977, 472617966, 992741957, 820431403, 336594779, 882138052, 85825962, 732901334, 9644756, 80753134, 540355184, 938279493, 439122539, 788011366, 924058458, 378494963, 787460971, 314934326, 764414294, 500895742, 867858690, 928673040, 54809155, 6634217, 796725875, 267931193, 363463516, 978752665, 597951884, 486678115, 285917972, 345058238, 856192607, 208791148, 382868687, 276472771, 384170551, 115408346, 494421588, 75306533, 697546588, 117262711, 713965904, 318892537, 60485761, 671059950, 595222826, 392169156, 43945874, 279247299, 328339991, 69746446, 831864702, 105965401, 506026269, 632412996, 795435095, 384255289, 616089728, 784526097, 648788859, 692557732, 429563564, 630871345, 500093583, 765991501, 726125396, 584957381, 52239935, 77565721, 898830734, 725630087, 737138017, 705230674, 672872935, 433403409, 990309611, 539985134, 835966405, 314144493, 469491989, 432096924, 571902091, 538152171, 691634165, 402705854, 442897920, 218220675, 681874832, 33267348, 103028116, 888467270, 287681911, 641369932, 290683120, 734533740, 372004007, 456609061, 436852023, 794938070, 359715725, 160129237, 29149680, 480936327, 811975323, 888513360, 845049197, 259686583, 480894297, 74906877, 590598135, 406071636, 340496723, 295037060, 718594896, 438944768, 715641733, 868783245, 659277340, 861492499, 8857783, 842922500, 540199002, 691818785, 555488970, 923786357, 821002543, 297891492, 50685057, 436863408, 485806934, 503852217, 458511145, 717179748, 205668832, 757753026, 375808371, 73717975, 580886494, 131764907, 924587984, 34885396, 816336080, 135768696, 726254470, 117190496, 447181012, 135834779, 791505205, 25292598, 616351096, 662759747, 42157854, 360036258, 508589515, 783773358, 338108996, 732842623, 353183049, 995116034, 395912719, 551678115, 975381021, 361575357, 640040008, 85700118, 265941744, 222871630, 69266776, 489393031, 853972219, 105739598, 990482552, 330329968, 141237393, 586193238, 96802106, 328750092, 498167937, 604529267, 846262470, 25460737, 509235566, 358378587, 12447071, 410226300, 582815079, 455350650, 213252693, 822233384, 340639742, 933753698, 882528349, 846856270, 709141183, 646473018, 526710691, 88522576, 595124049, 414940585, 374201573, 892602667, 359206607, 123423862, 752449637, 327969342, 510095146, 958683815, 863068342, 122231605, 973922235, 704731587, 235742088, 22053136, 86346119, 180747183, 710909206, 261309134, 426411975, 23127651, 811300123, 239233201, 331148913, 282797050, 410509582, 535389356, 622905891, 508389769, 774119893, 690320256, 561837124, 446969459, 20112126, 922953656, 621946644, 269726129, 664119545, 796701309, 468344204, 954607724, 730665825, 920809316, 564841794, 371510704, 50818516, 679697623, 548129798, 769655004, 101293348, 935644908, 995583538, 218499636, 234946630, 447237818, 709264684, 222982851, 394171493, 782049968, 615160362, 522829592, 327896062, 633209831, 706470958, 695179373, 366132163, 319786683, 697495798, 722112281, 479249877, 45594468, 530057693, 668822020, 144440204, 227550361, 980941304, 831516548, 269017396, 470976719, 127562002, 691850518, 350548041, 267616393, 78908189, 218547884, 179536940, 258580847, 158084136, 6124669, 219519891, 74371969, 506323379, 380411494, 157187473, 811358999, 117932510, 393926179, 986024787, 310253884, 59710607, 512191333, 636061787, 257704563, 77513804, 163548139, 748518535, 364412445, 184195654, 45300050, 995585743, 596101316, 37327856, 188831762, 954553286, 208244584, 51388118, 622464630, 448643545, 12563165, 912749979, 574957956, 467291003, 391066025, 481794106, 140006300, 789740598, 651868328, 378604317, 772446611, 890935625, 938266273, 601294180, 819427277, 567257857, 359200971, 943280057, 421747837, 322212259, 39494399, 226954420, 489992113, 91569527, 9808985, 199869746, 681756326, 856949377, 84882949, 183697706, 969644064, 590808251, 813762441, 869927054, 962919868, 466478955, 915164941, 453884884, 745889460, 36480149, 326317147, 232873601, 80196663, 174730685, 94348513, 817914938, 13593454, 901835982, 892627472, 756981721, 722493121, 283043163, 68377822, 898492312, 501032026, 377138453, 908589310, 132234520, 595370410, 823355799, 649407081, 602064829, 924216204, 355099392, 644046530, 133541443, 894247685, 358554433, 52768534, 110166990, 979156598, 55413304, 179738017, 367166743, 871900539, 466527461, 57636898, 848348364, 76445091, 619777551, 935859129, 290351825, 441374335, 600496614, 728599688, 157692886, 433793017, 728776019, 650350291, 240046377, 252442638, 948168391, 527435490, 122058947, 768927283, 845036567, 461030072, 254142357, 11337908, 403397009, 374638145, 422254486, 980264210, 272340093, 311043205, 836873291, 913618395, 418309204, 953300106, 875853617, 133617778, 466892773, 871724949, 196966027, 251295887, 870306867, 388187202, 45623277, 950250766, 532656221, 194085745, 15310193, 859657796, 763793985, 523223028, 899549738, 509914330, 720006873, 418811505, 538157385, 199013268, 450255327, 688502172, 240986710, 441368690, 164449800, 553418011, 582788748, 827299320, 561640420, 238386340, 5852100, 135473706, 298427704, 241000443, 754355037, 201605522, 878753452, 706064875, 529027792, 770285823, 70986072, 543289542, 101468136, 846858010, 930085413, 493913686, 523188786, 211159412, 458117528, 882044412, 118311644, 162962809, 352514398, 584328402, 555093676, 207228623, 461367743, 334493781, 449201242, 898817070, 753567993, 687603674, 504021148, 807922909, 695012673, 207057666, 46726870, 816071275, 1799647, 500760857, 922082957, 917128118, 535756401, 768323625, 535932745, 514608413, 49893235, 802853506, 113837960, 996064840, 141913423, 385195082, 139026288, 100279152, 92613790, 928166961, 974805101, 230656994, 103036040, 271730772, 729256348, 744053979, 380809767, 438368481, 554343973, 168102684, 613646780, 855382576, 428824434, 232661111, 39380092, 187562037, 811930625, 382554075, 204331727, 22997532, 614208659, 850556319, 479441042, 915869687, 484792133, 990769112, 909379875, 22979837, 216596016, 584497315, 617160750, 966236464, 917716209, 442673399, 1922093, 889818191, 402113445, 188778935, 773469232, 155107634, 829668171, 813079109, 652915356, 834408021, 209412210, 723335200, 258999698, 418275519, 352462142, 313624967, 274541203, 64078547, 511509221, 162354299, 810174815, 771861807, 640952167, 944125493, 885825970, 812957445, 936656337, 980170647, 176357006, 264987115, 726511200, 298016678, 94056058, 341235022, 778159476, 902906950, 303557234, 148291631, 105307649, 632488093, 540431047, 772681159, 578409590, 953084180, 63914149, 923021754, 225225930, 290748229, 281492732, 449727766, 399125560, 425716947, 541189699, 720976738, 855437201, 758729057, 362287001, 403160569, 994019260, 969017020, 739469607, 369924053, 916470187, 467166660, 519713934, 694375141, 669584100, 235383460, 658911323, 630156152, 643970207, 383287790, 763038006, 484229363, 528869193, 273918181, 542537240, 115313746, 640301998, 955093795, 343059021, 5075944, 242384454, 191728902, 49823133, 353860207, 334767362, 463825934, 616173388, 858978063, 998660688, 103380452, 779790879, 309369486, 636895607, 655879343, 19548257, 940192996, 579785241, 338951974, 807511243, 635694924, 479822166, 360625912, 420825856, 900057974, 234627371, 928535257, 866236447, 360538233, 7914483, 131117419, 195108958, 594155344, 794075247, 768817135, 180422187, 717684421, 764382480, 944551919, 871683520, 5457534, 475870680, 515501200, 826261219, 910455103, 555608943, 723568962, 680570395, 574932944, 492532140, 20908027, 881620765, 93349396, 760558845, 939875676, 588548949, 828151295, 992507721, 582785386, 95916424, 197654634, 439390077, 993265100, 222828462, 526884255, 128164898, 982229421, 175655712, 905767387, 479456218, 859520573, 748837346, 273189300, 547377105, 992528983, 743621443, 144658266, 820742348, 599331115, 200087543, 998380264, 106920545, 434661100, 803883609, 281842103, 666714278, 894759946, 688046802, 491425569, 49934238, 131221038, 260278994, 524621227, 480778588, 994729792, 625927622, 840172613, 939956938, 339912517, 155995970, 691129105, 844544413, 609346462, 257893762, 169647798, 548840713, 840769650, 377223412, 217322443, 658583656, 123035024, 528623398, 126230338, 676634339, 182166515, 949177771, 584766139, 358242759, 286111498, 401252582, 399940165, 285350515, 21822786, 402724941, 150270772, 330016021, 20639728, 492842828, 537678379, 74007541, 149003005, 192056527, 39106973, 973705186, 887441877, 128802420, 892606120, 865781067, 581091435, 53215182, 416712236, 847306953, 893511323, 176726774, 815325828, 810055680, 473932935, 508055822, 859015148, 125798220, 861827478, 582320321, 277991810, 43671532, 555045480, 571549147, 876142544, 846090951, 767320881, 369938261, 735394584, 844543625, 792624844, 255589501, 612502817, 114328642, 510908499, 239451608, 13887344, 317427921, 105881088, 875179259, 579305244, 861031029, 426525567, 841181509, 626115567, 510898955, 428101431, 797383348, 19423191, 240332686, 604106534, 150504334, 592749321, 816314160, 795492155, 436028299, 968878490, 395164231, 392010513, 784339915, 966423952, 182561429, 981769430, 161322827, 654410970, 187505723, 236115379, 231879025, 205205122, 424532635, 812478010, 601947011, 286205281, 304567207, 509942382, 271190078, 191907480, 293466554, 285043788, 957593048, 430866410, 69293214, 390276015, 540200496, 538260363, 678765516, 489740302, 548442988, 501513623, 492341873, 361219743, 499179389, 331215740, 293938619, 654321410, 294885772, 455451730, 377608149, 367514041, 788141451, 209885129, 780705141, 299844475, 682443923, 77896528, 636248807, 549636657, 381695720, 917904967, 586067331, 179235571, 434133094, 754597674, 598105344, 965987377, 901277240, 656852288, 209165029, 991018550, 91756733, 970185934, 413052948, 605655811, 220512565, 362545769, 919947030, 304469278, 67790467, 418592544, 154309809, 45933465, 254676165, 797714489, 663267110, 922380495, 221428311, 661235353, 975341378, 832740526, 646778337, 271569734, 346078680, 348800191, 920029119, 958105292, 108441773, 779770047, 87978133, 503357971, 231952469, 642232473, 164576023, 820539681, 78342222, 551084123, 39821693, 655864691, 130930675, 360188811, 741284883, 854958912, 356873346, 143156903, 431405289, 686883206, 965562104, 163356491, 310674184, 30061325, 54568697, 26034143, 269286512, 727921508, 643433711, 403702432, 888420640, 750304036, 292156948, 248141975, 62143388, 254285132, 272006089, 770883383, 889246572, 528857314, 249395239, 685037184, 286822738, 674139759, 835137489, 419055844, 476087531, 969998909, 783347487, 564598909, 581463879, 15687516, 943644673, 890874754, 633609855, 750450898, 582467557, 484093524, 509215493, 159117541, 248992040, 863729824, 318475553, 4704794, 474753805, 494459468, 865359197, 980610759, 551360223, 793105164, 456648653, 684567497, 144379041, 952670936, 11712364, 857204741, 773319951, 705218994, 802653627, 32024762, 242603445, 340485198, 434425420, 495674543, 264171388, 903949147, 696028754, 193386999, 326023740, 775410562, 288557646, 107285128, 659669556, 498368387, 326667064, 741273778, 836353611, 500123240, 115330580, 117273620, 136532065, 829688194, 979996719, 691198818, 397297796, 678144589, 326654510, 560408834, 495745452, 687646831, 205764554, 344434194, 899868214, 99130283, 843625544, 985117546, 944345064, 360093554, 912524194, 679218703, 700299561, 900340328, 55576088, 399913098, 258750398, 924183553, 278001098, 589489630, 306984842, 217270358, 887774892, 998315526, 456169984, 425121880, 230085756, 409831149, 843923940, 899783920, 212572567, 166610054, 165541065, 260385036, 601248431, 713558458, 821084220, 539706562, 750536459, 269355023, 429158348, 344255518, 34934935, 26141261, 450859715, 734469436, 155347689, 498802228, 513428943, 400470535, 833263302, 441116646, 624277924, 620130901, 241005137, 370446696, 466190593, 38915627, 387631906, 641289748, 310116959, 5423460, 161180617, 169174106, 820457290, 825784314, 15466526, 293168327, 392524372, 487917189, 678409783, 929889130, 277709796, 576686620, 758963882, 362151766, 858886310, 926027907, 753142985, 690798836, 813814775, 480738354, 977746828, 800826796, 415912892, 180631987, 166328030, 601311213, 745237346, 676257801, 129036325, 34221193, 454223, 405523739, 312211984, 917940423, 674870238, 729427107, 804860184, 43516363, 143683082, 257870017, 183468820, 662979692, 773247606, 170743896, 590415249, 641193376, 581127769, 571071884, 427245976, 350598353, 64824963, 732070187, 226150505, 512608978, 667277031, 971668844, 345811284, 173976893, 885707674, 694588465, 853248880, 391313975, 548923882, 286808818, 335715195, 541829451, 631206293, 365677802, 356936425, 512100233, 648056915, 510988833, 21965381, 519977267, 59702995, 92864739, 337147374, 823936933, 162016207, 965073062, 997818760, 974983940, 386580088, 848171672, 894912773, 484242377, 685933589, 972109470, 714950947, 505053535, 526955819, 401913425, 968749436, 676713259, 348056256, 175494653, 346623334, 944983095, 838815861, 938684374, 118038616, 687985395, 587580638, 290751073, 695856930, 884259586, 501324159, 479111421, 87175338, 34114597, 443866588, 264584011, 283053708, 673123793, 222075315, 342857652, 10440708, 472520482, 692964436, 13079855, 246792735, 273250385, 606829765, 613504066, 61549114, 120619808, 811316168, 939432288, 719002618, 290129332, 402063875, 589682332, 258310188, 515109506, 637621686, 594025166, 517757361, 645377297, 293615794, 846685369, 395849101, 900224181, 45580456, 501355016, 945046661, 39860690, 731832862, 548873012, 399979892, 620330482, 188832318, 507207920, 329248322, 638150805, 833559050, 226988661, 288870474, 268399397, 908138546, 539813313, 619536357, 283128585, 787766890, 99188757, 10490261, 186119873, 374695863, 580558233, 845361096, 931884963, 736135923, 445598903, 227973669, 630375409, 794341004, 520839311, 234150082, 471995454, 835135090, 298509989, 873185336, 707548555, 969752444, 552660672, 788134141, 26000358, 566236322, 259919866, 646635053, 505867141, 528383048, 139818739, 786183680, 845044185, 311050512, 485803388, 304294283, 990464376, 258338414, 688897509, 656640098, 942893720, 503573534, 83155581, 191996770, 762594101, 578598201, 527601114, 934009271, 312291172, 505807875, 503541922, 555176107, 59060173, 233713983, 888503884, 692254264, 699788949, 12102165, 498377082, 855216078, 481606079, 48759741, 169579192, 932565359, 612571239, 619890768, 320179148, 516290712, 922186341, 302591435, 145234056, 359558015, 501223026, 814966735, 20350944, 247835217, 438042503, 466586144, 36022943, 217372041, 600454676, 336769397, 574543760, 983759682, 397115258, 167081668, 907430836, 169742397, 137579673, 829351987, 144850060, 244895652, 996812553, 146990973, 16838411, 747419701, 438341131, 767713910, 957597799, 422355393, 550950147, 271431352, 680626574, 290529162, 805111758, 859993331, 337139931, 606961656, 425393506, 613072012, 291054839, 799102588, 545138223, 562069342, 753630161, 794442681, 968645559, 102592861, 851830426, 12528932, 722676649, 695869484, 193205098, 56818311, 554026733, 25892153, 97988840, 482311431, 633061222, 442926232, 920698130, 349946344, 150480367, 383713800, 255244614, 140290320, 882386130, 76253973, 60762854, 766355732, 674849656, 718533988, 675879227, 275109494, 510610304, 532411474, 528898093, 574260732, 294558523, 743149547, 949902864, 62574469, 284474651, 611552437, 681315102, 56086306, 289483420, 120077401, 816901455, 401852248, 671773840, 551511049, 86510311, 201501274, 697338174, 648080983, 221005547, 702716267, 197437094, 623859568, 686930296, 741405498, 97898612, 677694777, 652305904, 552081760, 501711752, 90207392, 855946082, 506052744, 787880360, 31462578, 318027905, 742859852, 708733993, 738853157, 710134050, 59276129, 482112531, 821565368, 472026067, 160916781, 94025905, 197764342, 895062038, 772429718, 174475046, 962666671, 193704816, 221402813, 279157657, 260163617, 277633265, 779555042, 670689398, 420607245, 881264644, 687861932, 861637419, 887465392, 630194025, 213235923, 481544791, 555167833, 295493458, 653391490, 921215296, 786363683, 914059580, 700920746, 121941425, 784738516, 185439181, 487432427, 685044232, 913890264, 550991659, 910086091, 953883800, 295651629, 128649353, 36197394, 475861088, 687807640, 353055396, 485745769, 554878762, 669464001, 98437152, 544450281, 481829762, 888536494, 38697683, 658035981, 62610878, 967954590, 366583773, 858629362, 468633099, 449846952, 427727108, 817144944, 537383738, 931560473, 91177649, 165651387, 679733094, 955559627, 423381718, 991968761, 341063128, 334034696, 480933738, 37994480, 848448571, 674889785, 102834892, 290931147, 324353876, 986488653, 906555415, 652953983, 886243690, 185705196, 181651837, 963860665, 475614984, 709205739, 123365827, 500111875, 676656939, 435982781, 737716994, 166517231, 262538246, 140552545, 96866735, 381613675, 498792478, 861542351, 385121570, 86549933, 609941768, 438151640, 126879140, 560030080, 545508726, 587981958, 904231052, 593590780, 922943013, 588807076, 1812529, 929777362, 648825428, 811611561, 975088689, 613762588, 142611215, 552066398, 590524979, 407011286, 724001264, 550761348, 796262332, 941742812, 73907800, 256602945, 489266841, 619828486, 738487346, 969971800, 948562569, 402936092, 631530105, 756631931, 501495032, 639446453, 5494640, 677150195, 104696082, 578477035, 207225061, 4975738, 887503672, 854959891, 36601261, 158802673, 518630784, 160290986, 347400469, 398531879, 201432807, 310521825, 596467034, 455290970, 341583798, 386963042, 388997761, 55738447, 750012164, 169045012, 157253565, 343926525, 43464873, 608962701, 422819337, 576750141, 799744461, 266862623, 646453980, 790869386, 649169676, 273072788, 906986304, 384171640, 291079481, 4423314, 852190739, 995599735, 826556590, 491109260, 966381378, 870435386, 890055414, 641225888, 505430820, 343766892, 863535994, 663622606, 678223928, 957110437, 700875951, 666423, 289394936, 136721258, 617855944, 752729092, 359471684, 566639960, 607782723, 753926621, 694042335, 792404758, 91334096, 705724001, 643506779, 780506253, 554468413, 485487899, 457324468, 900814841, 8932790, 830694525, 869577485, 756638397, 173322406, 76523826, 522530056, 41249550, 274928997, 765002976, 842396579, 184918987, 734953825, 20112114, 177588394, 541121593, 687720358, 545009410, 249656197, 4219751, 230420482, 221828248, 576752342, 914261209, 16499826, 829594357, 119578267, 409985536, 977507468, 310881061, 42009732, 269359030, 199555256, 843803976, 17194820, 814881117, 331731900, 268843009, 661980976, 722976981, 383767963, 1966975, 868746138, 124955025, 839412186, 200756277, 454259141, 298376873, 568989338, 884404026, 339794240, 116594352, 256405488, 362513416, 265009045, 527594013, 208824015, 252904929, 168316150, 809798400, 252806210, 178489810, 356252730, 766949838, 158158503, 113396367, 190504641, 645882101, 195811823, 290850764, 863052923, 59460951, 544496396, 35016513, 126930113, 262063822, 817016676, 981382243, 847162170, 329675900, 159804482, 805375649, 402252776, 925855133, 843440200, 704600314, 603004078, 770528518, 545519210, 578548739, 893801892, 179521451, 413963043, 976403789, 493977471, 679460721, 880622754, 747412406, 259961149, 548554525, 661192418, 384022704, 77363699, 733598793, 415226795, 935037005, 99566099, 925425465, 541879874, 491153046, 477571785, 42725735, 60161359, 447280267, 909381975, 244216414, 116755617, 255292295, 466910379, 179664936, 717974915, 334966250, 14398103, 559953263, 680819347, 245785042, 84056463, 138920519, 276945508, 191957613, 236476574, 989974645, 893610411, 186644023, 414878072, 145978626, 501979353, 146539913, 78139232, 440139716, 607080313, 103192907, 657234388, 273241762, 445437882, 943171095, 604733990, 811107343, 383979302, 746012833, 655152012, 843614116, 376064458, 531861659, 893031030, 791137147, 344048988, 176775761, 642311556, 91261059, 388978130, 471211941, 415426269, 791729853, 507991461, 511256988, 325697855, 254680257, 259336880, 144523210, 349688386, 804390414, 262723103, 82675726, 766388578, 691809766, 369244347, 172790561, 711615546, 85070837, 639734348, 580345922, 335229408, 737817186, 569512210, 396145737, 193668882, 375077216, 527312691, 970816275, 463742558, 381780177, 338196858, 91789593, 99899847, 10586518, 40405921, 110664294, 376311273, 422539530, 766454462, 221319177, 995161225, 561375521, 840774641, 932876494, 293563820, 881052344, 794598962, 249572366, 238622336, 3791227, 401520949, 202932, 382377498, 758274476, 638871956, 834968916, 727482997, 277225510, 332603173, 311200028, 793965679, 933075244, 278711191, 128877777, 625277280, 332247354, 610589775, 703725627, 945853671, 675079598, 47571190, 737472034, 976110125, 715656326, 225413745, 388941127, 299279403, 405924527, 417262471, 581251879, 153841054, 388771172, 570018250, 469478863, 471091360, 637828588, 489028251, 59945446, 33010928, 171144549, 759994422, 143346573, 926601005, 303084043, 365045454, 793573959, 127546570, 470595094, 750399399, 574336492, 421412597, 65608509, 267620432, 280992931, 699704105, 522496981, 299246302, 383231832, 708332179, 918573350, 883008323, 2029244, 377079547, 497768503, 805604559, 643209825, 316108784, 599457420, 698855731, 61841330, 969788225, 565568089, 921450397, 975854140, 185525267, 176682929, 851702169, 442827121, 333666010, 759022964, 258785725, 734983301, 192907119, 985496074, 622349356, 827153330, 826385695, 396756769, 43527401, 859287543, 392884168, 260967702, 723550864, 606810705, 800506434, 335561923, 780982416, 550622174, 886090087, 112807439, 740100462, 210257796, 332204390, 507072307, 172844926, 187505485, 893796997, 108009793, 984627421, 724727943, 922546869, 830092822, 317603948, 992444630, 941444304, 697704904, 352449315, 984369583, 291164658, 99763326, 931634247, 219212097, 353006947, 410664919, 727542519, 614035737, 425536726, 607884428, 275219325, 422737596, 43638888, 807173979, 463496144, 156792057, 83017564, 874736970, 872637253, 170286762, 227174840, 815265095, 793035971, 779945733, 902910781, 589310152, 745007600, 420135667, 340490781, 244423116, 602191498, 676216134, 874651137, 153478769, 865243865, 843305576, 488776634, 779893314, 917525751, 562937473, 747057760, 66254422, 59690845, 548893123, 653661720, 551974416, 394416647, 348360587, 197079288, 756860327, 949634985, 644197523, 770945871, 644559238, 548648901, 842870635, 740203116, 850127606, 91089498, 635345876, 853929191, 788799499, 971805849, 87130908, 420292413, 478021510, 410713948, 78010137, 62939463, 713292681, 371336363, 633481509, 399457293, 176799897, 835808067, 613443765, 298639967, 623168634, 56879003, 684176382, 798389073, 418221451, 883771469, 926910414, 850031670, 550880485, 400612918, 567605493, 347547130, 119531498, 828239404, 894239644, 43267930, 612869763, 246148215, 477971142, 138486370, 81139529, 250786935, 205022028, 463339722, 838358055, 269524436, 669455192, 382593139, 908393975, 671069386, 11668118, 693977749, 976943417, 564831560, 187915927, 11456132, 638229611, 268574605, 130924068, 370709231, 602559530, 456661342, 590676272, 315008704, 836630403, 546523981, 236434328, 71162711, 860458029, 380434704, 528214968, 493250275, 925833630, 766792026, 896896270, 29820755, 846897669, 974876266, 810871721, 889173644, 611572408, 578618195, 62891273, 510959735, 18602852, 160959763, 666152306, 886530358, 540377222, 822536991, 648477686, 448048453, 334369430, 170010927, 304119694, 972415336, 356551553, 36151174, 93808596, 73935891, 993094197, 725678319, 994854246, 339346363, 725535456, 27375563, 414736087, 694961824, 269810808, 516087572, 744860813, 227939263, 90784776, 369637281, 780119320, 373458108, 26980237, 290598541, 587469186, 244869514, 395950953, 524038940, 500750259, 540263325, 927776490, 770263130, 993324031, 373493623, 461357922, 238433563, 99674637, 688240034, 229616022, 928982070, 358737430, 989109512, 915996507, 4239399, 196328518, 985557797, 834579322, 121750677, 410477565, 698656857, 394344342, 829506119, 301605383, 148233752, 739946373, 816073106, 455421289, 77636712, 975941815, 532096544, 796588173, 869875432, 974045725, 853793741, 82876928, 601947453, 912414903, 853835131, 982347921, 718164293, 50684990, 197005537, 392198239, 901075515, 825618410, 112528471, 420526936, 660865761, 207515869, 849543210, 317719823, 92930433, 1303076, 840185642, 540770015, 445229585, 544089858, 621828407, 374746444, 351810735, 527101255, 340324421, 747261945, 922213217, 917440117, 969241028, 210710200, 324228279, 331443996, 282660900, 389020950, 421463411, 653382050, 92767242, 320529759, 541335164, 992786583, 270817719, 384745378, 89195447, 196951169, 592323976, 372364623, 699915369, 968454120, 755682296, 569986947, 508648552, 221803067, 619967766, 61971044, 925543273, 287684627, 236873564, 813591961, 214294544, 644910558, 755165553, 946553028, 451952122, 49485899, 218214038, 612272746, 856611640, 890442581, 256362386, 785759690, 412598432, 663846561, 271419301, 470627978, 319899634, 481918915, 31682381, 705655948, 980900710, 460607805, 854025449, 609623969, 235747872, 646527078, 593429566, 70136303, 17332119, 739305083, 84959043, 6061280, 384420488, 422362606, 628571846, 802320066, 952350878, 475465523, 930901213, 484472715, 228175282, 206979465, 395752244, 655086578, 900265749, 829565792, 331319895, 362622912, 218894752, 991528027, 823712242, 326548838, 975303249, 960287373, 659390664, 518048883, 242902403, 844901919, 853113232, 725780057, 345534559, 306917879, 382950893, 197730269, 615741416, 312710343, 633783371, 466520274, 499709731, 875308412, 272336155, 25896847, 426985175, 56644038, 385718252, 832557145, 564471350, 304129254, 427973785, 220029486, 921460338, 69467943, 106891042, 568315029, 230531352, 33580179, 739380850, 602531541, 880264646, 92329060, 400841976, 433894118, 273269961, 447082301, 744503181, 402628975, 177048251, 906071380, 206361524, 302932938, 877825209, 137101030, 205095450, 874852531, 998603571, 455762626, 140081480, 164558638, 44607562, 204217429, 199470680, 661305268, 672422889, 53919493, 274926888, 566404958, 438303363, 692352466, 146460135, 232735099, 492853448, 616643036, 53086718, 937251003, 737915129, 521937425, 483283335, 794250808, 540941957, 948036551, 534724294, 441644408, 711699333, 535021850, 64531560, 377942562, 829175739, 469545074, 178104120, 159480249, 284286837, 125535726, 38620486, 261999152, 794644485, 956113733, 491457298, 664581823, 107927702, 149780542, 944718849, 667332363, 783741706, 841471967, 606233773, 269064541, 491870975, 111717572, 159146314, 990958586, 902785146, 660910780, 575906030, 908479836, 706188952, 388600932, 461248298, 916095658, 695938738, 624519200, 214216409, 836685250, 275334944, 830971730, 300924838, 447972937, 827004652, 459483892, 454505022, 474748985, 96450593, 164417758, 201158112, 381436979, 422422510, 510872607, 585926477, 329325624, 616375195, 693475742, 985651940, 16928094, 829357598, 545799776, 82353595, 13065224, 216535520, 689139024, 639830782, 761284846, 222267369, 779484440, 253301114, 769216440, 856552956, 279211812, 246404717, 337629928, 188662622, 233945728, 75267028, 142982057, 782196505, 310102282, 583889715, 939998283, 795870181, 624107703, 5092236, 56881101, 818921069, 208715322, 666852577, 445774005, 96416399, 228286658, 502284354, 260300928, 196586296, 808759817, 999517850, 199892069, 778726179, 689565313, 752998508, 183615190, 836426914, 679636900, 81591215, 412570528, 464620329, 542387138, 637186036, 713936161, 444077999, 110440226, 960048951, 896019031, 535162543, 318426058, 264850369, 491041249, 442185225, 381604853, 698253477, 311200567, 527525242, 823551200, 152090240, 368225625, 753254561, 472833943, 127635098, 485772438, 362318583, 822099632, 855606834, 632766062, 228350737, 708261303, 289341719, 861032494, 511181634, 602639767, 532728023, 356758080, 764135778, 347737444, 609061160, 140771524, 673647250, 324179203, 749549982, 856537085, 79678979, 582332822, 804037721, 663254514, 216154214, 115560814, 868416162, 49041051, 824571735, 548362625, 629841939, 521857687, 459305477, 335124059, 351214215, 832808768, 259338465, 569266986, 620491395, 761968347, 390431155, 337457127, 334091153, 920766399, 893167178, 414542629, 664557941, 774850257, 101176372, 924378291, 418018354, 346817302, 767028593, 289414463, 403149707, 701796713, 866720515, 410174731, 179406036, 544293024, 13424131, 302445505, 866777591, 785244994, 456040252, 868912704, 660980250, 270137453, 486173219, 65607987, 459735269, 635983153, 546650921, 120025864, 429840543, 397997767, 820150986, 275290786, 11489417, 709172715, 232066790, 454873365, 965998377, 385870027, 188369321, 78510333, 148313431, 943571945, 657509801, 632080155, 165109845, 52733063, 330658374, 239596966, 487963553, 907276896, 594247457, 187135297, 174548182, 906811082, 176293691, 207891153, 867346731, 484556908, 811873378, 336032381, 104130078, 766926907, 785606759, 843596724, 538279229, 238183707, 704285527, 204991124, 709473105, 718356807, 143692598, 578718782, 988862068, 133891134, 728858309, 159118241, 957554022, 329197166, 416909998, 959647036, 602706306, 707614108, 201929384, 91237792, 308139130, 503277727, 221157243, 831142247, 373161626, 606379259, 96564552, 66704309, 821956326, 795606537, 738318130, 52813171, 643400293, 700117519, 754773515, 206219483, 249459269, 693619538, 40466966, 145164065, 410357892, 352792174, 759837751, 948208333, 173561570, 516236730, 928461483, 299045684, 283113694, 464388684, 671178928, 666819521, 829033771, 420251264, 204389942, 890620477, 996640715, 73307680, 534271411, 475808348, 908725317, 22417921, 709834005, 29040424, 587373259, 253462669, 807511577, 508348625, 584879427, 138735720, 107675056, 178653379, 884139655, 335329806, 133413934, 60079489, 713460647, 897826616, 854739291, 973305305, 303221706, 80382676, 292587336, 590768462, 244113030, 735812305, 985082308, 689312713, 305987630, 941812195, 606376786, 844165232, 676770450, 79126290, 177387372, 845056908, 721856832, 801713531, 184301435, 944833659, 937307055, 77669012, 735249577, 79756525, 452789563, 615841044, 335609742, 382999855, 921293605, 760482510, 298061936, 686133179, 385280697, 229760512, 684358221, 848132582, 378407298, 456505428, 476172417, 936543844, 74759603, 50638918, 294053750, 631129271, 635599583, 321609987, 348123919, 98393629, 524728692, 52399534, 169947695, 565331624, 78529178, 327953081, 228972134, 741275467, 336602903, 938274252, 592277558, 126518880, 396648027, 89381818, 727759805, 988272083, 964995690, 55185494, 746321708, 764901331, 360580142, 969996498, 586566607, 336123404, 904439571, 888672683, 982542735, 841357091, 426930105, 616597322, 940830380, 100429618, 210182114, 968375667, 846035619, 799761314, 483759546, 656274021, 794192250, 945336577, 453889347, 92234686, 958948922, 432063329, 682082858, 508649859, 409329661, 49519680, 494386658, 243620951, 581884048, 543649080, 913647904, 121340163, 79671844, 72523380, 780199500, 862285074, 414467818, 887374611, 872519395, 168592777, 284131918, 81901028, 290215163, 89317755, 53965710, 138406440, 338333035, 64814065, 946444478, 252905132, 851795522, 20988696, 419502502, 816975775, 280512675, 24828627, 202603956, 838547133, 709029281, 398978486, 157748376, 656642280, 858291694, 538274702, 401290184, 689000190, 484511128, 101909255, 338769946, 674579734, 558647434, 289513867, 274716969, 768469693, 261491915, 730989969, 284945124, 934102271, 133765583, 172276543, 227815136, 709566697, 473536663, 999600542, 686814613, 428493838, 305520771, 946798830, 909037753, 821453474, 147886238, 454738005, 250958815, 204535993, 256830446, 936268635, 795330165, 427640063, 910724388, 299556139, 155997939, 774282325, 395376586, 979013643, 896259145, 891389100, 172800534, 552199360, 15830494, 699432716, 697379617, 780182146, 382578137, 721303832, 871849898, 985850461, 189459478, 347011983, 919192803, 528061575, 881378278, 584398977, 799098175, 831344847, 456510983, 318236310, 459331233, 852030097, 421498118, 776563769, 574866807, 401694955, 467145136, 307261285, 899702338, 774242211, 529862377, 76603568, 19486909, 769924895, 85736890, 915522627, 306528168, 105777547, 244026672, 490670177, 330432226, 610089991, 49193372, 594958628, 232589914, 321218630, 390558720, 276611320, 362250961, 154696163, 957513128, 764347450, 67016883, 644801993, 506532455, 705818383, 527788786, 132752170, 921419184, 740663463, 678275925, 746230174, 928633549, 857077135, 868309246, 239546003, 690855114, 754154071, 218335868, 33712382, 367060300, 358835573, 254976161, 193933489, 334160730, 829312493, 492464886, 114836408, 306334042, 973751755, 452037928, 414334787, 661368334, 51574740, 247387389, 962484520, 327960442, 139917157, 891441897, 752909983, 149841964, 874040913, 844400591, 912157473, 513608263, 351269836, 559118068, 93433104, 517559374, 886339142, 935530151, 584883194, 256373312, 880571070, 800118032, 425257263, 985939619, 297690296, 330330346, 417811062, 525323298, 745743383, 887429118, 159176115, 132062997, 215694973, 526134587, 337061470, 872527665, 864670519, 780595052, 885308107, 247970976, 232290952, 77043470, 479039868, 407302446, 52558439, 11695121, 291094503, 792124865, 871570858, 737035912, 40870777, 286349911, 388791104, 168529855, 209571381, 998969126, 411977453, 724350195, 317611865, 952176757, 669986843, 870649088, 328948084, 12613416, 241183577, 736241401, 551658271, 973158109, 853802378, 339544476, 352714003, 298346590, 636079894, 418776843, 805920810, 998132040, 943056735, 376519964, 443184519, 466709750, 433710269, 761770548, 223844606, 852648080, 222204368, 406802525, 591168656, 262565305, 413662676, 423153497, 384125247, 82590388, 712836720, 414969373, 157164536, 616643841, 252119708, 651156715, 47170561, 687068493, 661900335, 524577702, 692516497, 221113187, 664303296, 16322112, 754416170, 932095022, 273430163, 808205457, 635220151, 754587887, 831141792, 396267484, 182827735, 870619849, 776723299, 741768071, 711622547, 989969726, 403132405, 430511947, 590911497, 713958009, 122547072, 539192378, 842255661, 637867207, 102399692, 646819139, 405812770, 38676737, 495490137, 995739998, 905342258, 284853474, 606179209, 297561767, 166696294, 896563348, 807552221, 227863710, 879239392, 875972422, 317138625, 318422515, 796968328, 134487361, 913586874, 969888629, 611532152, 536711267, 175156094, 505172361, 706057092, 639332712, 954997025, 821597604, 791496840, 55156916, 860470105, 462065195, 720103010, 665147741, 570622370, 689873971, 308515796, 482343374, 349864995, 444815517, 290296340, 817201692, 563376978, 859021392, 247875590, 60247835, 752224664, 628017893, 809429624, 605156570, 459449430, 348766285, 67756687, 380604139, 407836979, 749791904, 12972519, 279111245, 586715500, 467916605, 36278116, 578040423, 754561382, 214350744, 746092689, 278485558, 940115134, 137139722, 369520302, 666343663, 646522132, 480315426, 601188469, 216955489, 340828103, 974937971, 116741891, 232685286, 755973127, 306998044, 866754103, 882508321, 460884900, 34496408, 13032346, 150037958, 527906992, 657722177, 231232409, 881337711, 145697298, 611008088, 823171607, 801932886, 914515213, 214973677, 967164278, 151759137, 477999903, 182847277, 715857338, 195043444, 302810071, 186464470, 374137064, 532574484, 691708164, 996542598, 938503795, 937956864, 981500683, 989788438, 712739488, 374663173, 105970623, 930688382, 382566287, 664419847, 170735056, 480510393, 533007258, 502838513, 856384894, 905207394, 785150122, 743733425, 665991331, 744252582, 41886165, 777898909, 768224078, 105038257, 457661087, 657692162, 510002602, 738669091, 49905407, 114494318, 26728831, 355227278, 180098567, 384780910, 37375573, 544222408, 703898261, 171637291, 755780106, 753136655, 571668458, 998451409, 935325078, 133810136, 739151180, 273483673, 251041643, 697212739, 801621502, 939509563, 113570918, 176607263, 288919053, 724130632, 77662976, 999425124, 974631089, 103979733, 503834522, 656928824, 70913514, 404275112, 452161610, 256092802, 969198152, 204763224, 610010964, 124554723, 459286351, 216130783, 51236206, 68929465, 673256146, 346976683, 220896093, 356931443, 520770021, 872528914, 457152271, 466242145, 648439592, 642498163, 803069294, 43412527, 996401431, 849914908, 361881938, 902888929, 901049398, 898121646, 984435829, 935631364, 626139326, 746602585, 26044129, 884695054, 796915437, 70290877, 221385832, 140790779, 217656321, 854920207, 230613966, 782487058, 657862008, 766439909, 913523706, 492410256, 61884559, 862679249, 70558343, 519088636, 745058234, 59272282, 853867198, 608439725, 251401845, 973946069, 757455820, 125669179, 229599510, 975015862, 231006506, 214581016, 358432737, 550146689, 513944777, 311354479, 596264880, 654877551, 51659040, 575957580, 55057394, 442090284, 257007116, 265598541, 488352586, 594249218, 73392852, 863347427, 314267112, 824151873, 692804664, 10650274, 81268278, 374873515, 543079007, 783791051, 385835116, 807807902, 246515813, 964284111, 468058393, 689424831, 587708218, 661616742, 33608922, 173529585, 52210568, 299871229, 59703856, 242352132, 192356619, 531750532, 352132384, 665505034, 504557849, 947686511, 895987304, 29906760, 864425096, 736057646, 513470631, 160954312, 857871830, 994362406, 103636140, 193382909, 652260484, 348027211, 573145623, 313123860, 56578363, 726432826, 55947858, 378598315, 397540853, 275664971, 909835800, 99906283, 948082429, 850560817, 376993621, 876198904, 744036575, 802800163, 547504543, 737054499, 229140836, 858044227, 807404596, 825308225, 870081351, 658806936, 486994201, 197560019, 782263707, 733916731, 316764248, 934182770, 650102762, 784830701, 532722694, 828957629, 989483777, 162798498, 638979790, 611838414, 67568788, 406994676, 138110021, 957827841, 57429629, 110610835, 104028603, 362653624, 76012524, 495757405, 406182514, 829926282, 142850699, 446238280, 5951100, 498107777, 876541058, 258558990, 481630818, 35457170, 203848975, 375487187, 457187445, 74934145, 530712109, 823943667, 169960865, 572118491, 974406215, 539886277, 814232195, 60785384, 146519975, 859388899, 375135689, 695207265, 963432578, 494849634, 633191498, 607349361, 832023145, 232852462, 438397668, 824724667, 316122225, 285710410, 891905460, 745556241, 893039691, 538679153, 424235447, 649854460, 212076226, 664570381, 9669899, 357047638, 924628908, 931320520, 420301853, 218222456, 829858360, 668754899, 388783244, 977058122, 356365625, 281501011, 189195359, 117050239, 684957001, 781223294, 282209952, 610504650, 592769555, 725019896, 528655059, 476382367, 393448761, 95905616, 680264777, 963426, 697491727, 80032896, 94557607, 760075786, 197092778, 842771635, 97277895, 358094900, 359516776, 206273020, 238388421, 375746077, 910276541, 474555767, 570271353, 256123556, 860892193, 211273074, 504736751, 507623749, 397854732, 667142852, 500602660, 144323200, 471603544, 204429849, 698697628, 236004978, 233601767, 132702886, 930655873, 23083410, 492603450, 536572446, 510423878, 982880162, 221334799, 641258176, 397278955, 431503033, 964115413, 144966135, 827755844, 267122421, 171805471, 800084985, 973905369, 553561634, 761536960, 356527152, 714823551, 507833482, 889956822, 761409579, 27971007, 414869545, 752877675, 274733055, 25702674, 253710303, 158239421, 349376208, 159991781, 447266906, 293076982, 886511786, 289740549, 729652069, 22094378, 563286964, 147499476, 694275373, 702535261, 851431882, 637739453, 537851225, 548027352, 947897993, 785936857, 634227792, 136240895, 883931874, 490437929, 354799194, 98775336, 361533913, 155993459, 100449356, 721369606, 209553091, 322846397, 340524670, 108096289, 180735085, 773770041, 660898981, 103828519, 985333640, 687537985, 81018519, 67357261, 870729091, 356863375, 507805381, 60835597, 950689327, 632843682, 737584108, 696045196, 879556032, 760075276, 331870228, 805079217, 873163227, 488144192, 380875305, 671727512, 656367242, 226979940, 293628458, 350202045, 672441328, 517949912, 944364908, 111994582, 604744305, 995099347, 724246151, 323254586, 482594887, 378233630, 969391454, 195033807, 338256623, 90030799, 981607564, 136493031, 769299452, 501036776, 297320103, 654520763, 423318802, 927932586, 811552986, 551766608, 796967847, 141902512, 802464146, 779276035, 637674376, 950617926, 654664070, 888534106, 319356664, 232419244, 965329005, 310098669, 648322627, 26032202, 834757165, 877341769, 600627240, 847413575, 619262016, 987617116, 421276175, 287886396, 715978246, 313721816, 921581397, 154251801, 713551543, 814779504, 929437414, 719177016, 189184832, 101193533, 434696453, 301747944, 257920, 969557417, 439373498, 469910764, 316308940, 64405722, 489811263, 240595241, 461663195, 819209384, 985669711, 286693554, 479476794, 307035025, 93913014, 636598253, 421494131, 488167424, 541843931, 847630753, 787144933, 502579994, 64162114, 559846035, 782944364, 244840332, 352562271, 393892600, 209222700, 451438637, 459064514, 693695775, 173514553, 982250458, 954383467, 919606965, 183738465, 117040281, 357387797, 711667645, 529704375, 961233626, 977586728, 397650002, 673572140, 961488779, 102024424, 286982035, 576457234, 335460491, 207812776, 683191337, 967290459, 686389524, 889155181, 169074829, 894019553, 141782854, 458965586, 221613772, 956728491, 915657232, 48296961, 321018987, 964544371, 761957126, 393283190, 519559563, 769456532, 225409563, 626842806, 134099621, 815975739, 991483536, 835739673, 659536116, 181236114, 705478620, 523425340, 866205033, 173871018, 555019034, 499025427, 120068714, 200816014, 986912428, 838703761, 775952127, 144818031, 376756972, 651220603, 466588928, 984713087, 328755737, 848237773, 149031984, 529960156, 125858660, 456483418, 128386234, 230603673, 76840312, 319173966, 719558377, 311657006, 246358724, 539379047, 700492656, 90968066, 134010854, 900966785, 331234448, 648721223, 943355679, 903580554, 927900209, 646870004, 581517191, 727118271, 841258134, 477382931, 843121637, 733215557, 517748112, 277329386, 304820726, 617005704, 15420160, 221597785, 338418113, 885287265, 308831466, 393042037, 630732711, 997082770, 465219350, 582334224, 618215070, 687694476, 354916683, 734977739, 598137753, 754540360, 689439562, 696675335, 717307252, 363787203, 835224856, 876262847, 6166775, 233812647, 51529050, 27430164, 679798474, 860636208, 539086104, 701951589, 231230213, 853372107, 233287959, 76384511, 524622029, 575099339, 33629308, 57314227, 779510160, 968790210, 150081317, 858140871, 310874864, 166031575, 474195373, 534402035, 300951514, 116485431, 550034695, 306213289, 85586720, 400853445, 522410099, 473759136, 313667833, 87740350, 578291360, 224305234, 811250059, 296729541, 968514900, 548969819, 540002252, 433924984, 561137527, 84901734, 508250575, 669090901, 915759513, 772221212, 746254600, 740954474, 295556717, 777808158, 910471177, 873987287, 574053760, 79416555, 547592988, 650660316, 264933825, 986658462, 240040482, 679177652, 478761156, 722350357, 644770231, 42349041, 393933740, 168665864, 609143499, 623364659, 958336246, 905668, 290881626, 882559967, 308533610, 586952330, 494858577, 25721227, 992220593, 176015460, 4461311, 546100625, 344412411, 588214660, 687676304, 517354603, 716668649, 117598486, 818300975, 35623408, 473409545, 793913298, 905441161, 619529348, 254538193, 758836511, 127988649, 497400102, 706103062, 550254324, 572183771, 448420029, 454664369, 994867537, 152286427, 236457929, 391351312, 707176465, 601469096, 881457524, 277268146, 168708615, 155630607, 396935584, 87827395, 934515865, 855777179, 507510598, 96237008, 69584206, 164648498, 752209548, 788267307, 815038029, 870605677, 441527924, 315167423, 693360867, 411191847, 138522650, 389362338, 336664233, 59416304, 579831078, 305712741, 205902295, 583226008, 554405198, 840453165, 195718959, 302981964, 142919532, 410930336, 76905909, 923333493, 796729939, 348804791, 86400950, 444707393, 822831281, 742754979, 718895036, 717511137, 304782514, 855027847, 784054772, 661884649, 310828555, 33382512, 842073685, 71839011, 743117461, 934782455, 590102844, 982592001, 252668540, 688723192, 419740207, 854643935, 787179679, 593849309, 719835361, 630897918, 959873130, 998855982, 248216970, 232306337, 394160267, 934789422, 88286707, 404310259, 989902628, 755937273, 859533181, 953544328, 292441545, 644936790, 469635750, 455723981, 625726826, 220994968, 171438244, 30382546, 390523832, 136051339, 647800119, 597324013, 62417796, 588873808, 105051959, 594076952, 823726854, 896865960, 776423999, 640635874, 600856509, 492973027, 544470026, 912918193, 329441196, 473270815, 56931510, 488742139, 417109152, 949411049, 981352327, 472070933, 569812294, 323916468, 212166583, 37549584, 973762399, 866452403, 879007081, 553765119, 727009432, 442688921, 677946835, 285677112, 518808785, 880948127, 984013808, 374171808, 147655696, 604620546, 496367691, 44832777, 276873498, 568341544, 826268612, 719466366, 335110360, 792015961, 757872192, 833158714, 928634399, 354739177, 667079376, 713093211, 85444409, 184470374, 454514698, 739576899, 963075660, 252236232, 694333738, 569454140, 399760441, 543165075, 826292235, 912312975, 663349051, 700137073, 67269879, 681944919, 588126951, 457788128, 165042533, 192792384, 616847778, 578541113, 981850289, 887055625, 889268851, 230901715, 207510361, 147993078, 325995721, 42103558, 571775776, 265487722, 428500148, 685705086, 148212859, 322548926, 373483345, 370412408, 748064339, 471587444, 326476513, 872352410, 423183588, 140681295, 180479465, 424317095, 385564677, 142315444, 457679001, 99023607, 866915647, 121463202, 533583413, 585540435, 495646172, 919107403, 72180520, 503266090, 48325734, 955890830, 189423620, 120057608, 366303392, 576907281, 412208226, 929854080, 182699259, 520863611, 209507506, 12737975, 729278224, 768512392, 352029517, 357114656, 748644282, 894483474, 917462266, 649657268, 535688824, 928269788, 469622353, 46388909, 335584519, 211007694, 25412548, 851845124, 569109084, 528613521, 851205847, 691662417, 524550741, 457975132, 488131540, 169831579, 40244204, 181526401, 800173890, 225115944, 604767078, 756915643, 480010937, 999187357, 955195707, 355011697, 213344894, 967775280, 418182470, 448466746, 936792298, 8778225, 30997470, 692743248, 946003996, 838897553, 348645146, 620856217, 249454108, 556205669, 930238375, 702796112, 710838880, 318143244, 48841965, 81584049, 99981602, 568975786, 332822472, 829063636, 765142711, 825302104, 164862590, 937077169, 174472295, 264743536, 433789437, 353905047, 903498952, 747523131, 920823880, 983889450, 610650898, 817721123, 166364375, 590877225, 863710456, 625097726, 802842820, 493073554, 503360556, 732592638, 575609169, 292570724, 352467407, 924400980, 315888065, 201673054, 290749212, 833135277, 401673604, 694986083, 811999650, 768075601, 699057304, 26431418, 800006819, 105221143, 843208700, 731893784, 198480549, 560024515, 286273249, 601053015, 8671978, 434987664, 846466037, 244673416, 900082755, 672888013, 965068983, 257126359, 468702595, 764944459, 351334105, 653905858, 209185661, 268763357, 669352836, 96905295, 905542871, 554433918, 326785866, 454725039, 7266457, 637214524, 726643182, 682075741, 229212488, 280857510, 462590387, 214463157, 845828502, 182272131, 182003334, 597334899, 818145727, 547137790, 456381590, 866453863, 704119220, 814671028, 993973172, 650989816, 820764177, 336392043, 463916454, 664952638, 598462330, 383598864, 79696988, 29817230, 648827765, 251192989, 684089960, 652918314, 449663994, 579679450, 779266689, 639641258, 914624908, 637990972, 348440201, 671161025, 25389862, 310612270, 481595789, 413022020, 740576029, 410572455, 159775046, 764679866, 554784641, 15066689, 142099363, 791009774, 878067507, 357726155, 142104139, 583563794, 813842481, 954026998, 202282664, 326848203, 45615895, 682431341, 279671616, 208213885, 477861636, 138029526, 525220805, 946283845, 218574756, 295443802, 796539126, 126388103, 959156765, 271415778, 476184288, 696885623, 890338473, 33064907, 987430400, 450290133, 811481782, 774387257, 576197366, 336567917, 27850672, 468546617, 588127683, 951803868, 565336773, 609027440, 14971443, 6879533, 791708119, 743923801, 905420874, 35425629, 526716279, 157738011, 456413263, 49983783, 938533192, 187510150, 570796948, 514290075, 515124548, 166028419, 474581657, 529336375, 399760823, 486848094, 901137970, 929932656, 428871823, 156067225, 795992721, 504006393, 743673299, 966235601, 279160111, 108723397, 635725176, 460059727, 705069020, 328001277, 280617033, 25297864, 990589012, 167928935, 197578987, 179006414, 269755990, 277002320, 289624179, 55492310, 412882944, 8309604, 915849956, 310965097, 179099660, 812320167, 111050087, 525194582, 175846407, 245307978, 105598315, 826863084, 924445978, 785949378, 869403258, 369026619, 152670731, 756343220, 667112949, 112232253, 416647620, 339173589, 931522486, 718699267, 256634679, 396283308, 567611063, 297918489, 328150210, 228990, 742914805, 209667166, 645729415, 493952213, 471992061, 856546829, 790195418, 268455314, 645405540, 123572351, 997253146, 241844121, 667412339, 537255291, 598223860, 766724484, 696631984, 633804238, 757792108, 671402256, 301821467, 608125808, 736747037, 948632927, 4884674, 395773898, 977325329, 586003999, 881692169, 618082238, 231456571, 741156590, 979919882, 924710421, 883380906, 196680299, 752592080, 237387931, 506573342, 506452484, 530938587, 678949108, 302165435, 454492008, 35712385, 225836865, 459916727, 734178274, 973420740, 752325956, 216589547, 998752509, 642748667, 57043409, 673156316, 400524822, 22535742, 413537704, 943632647, 558312303, 788482720, 919602107, 11075459, 988543178, 708242781, 800987753, 806064976, 455591880, 649467104, 212913844, 178274140, 448509937, 260842505, 290189769, 886913598, 713375396, 530244180, 896110902, 575637318, 128542507, 255514954, 99727221, 862161367, 124783309, 413627700, 285708247, 625301893, 569585073, 820827082, 71394326, 819533740, 963867939, 898629993, 539411878, 217331938, 540543409, 439080518, 502552752, 471473187, 472377829, 425434540, 18627670, 55261780, 994408106, 4109648, 763710839, 230656989, 237433471, 572424953, 545078062, 559326689, 770709199, 810282123, 699512150, 705851026, 89531763, 402859516, 292406004, 810328011, 223491407, 54438812, 128637546, 333087963, 832417736, 830633239, 909278488, 374597281, 753625728, 879186353, 456497019, 412780429, 650248384, 331058602, 832206401, 621339133, 243410538, 990198021, 326624442, 550503987, 125927053, 80967232, 942862344, 25472765, 744694195, 35779970, 640036987, 22682078, 883077717, 322670135, 91724626, 479746326, 511763274, 640084259, 632955027, 820315586, 974733626, 193609566, 549954014, 340870604, 190882028, 221421106, 399437665, 3802957, 392415265, 959945483, 492280691, 731789600, 877117708, 441627893, 623982808, 54327408, 591764178, 554425417, 707135498, 132680778, 926563439, 262979018, 908950836, 326929176, 313443677, 433949998, 895359412, 423602181, 156016850, 49723703, 381230574, 848933980, 205200990, 201879015, 833570445, 989029949, 736991230, 727873403, 637803974, 25506537, 476180363, 767181215, 53673250, 619422420, 596043886, 121517341, 790165881, 801852924, 508080132, 353923841, 175090359, 184418739, 423009328, 890991070, 657111590, 137015664, 824893501, 769585511, 405554354, 32260350, 303392524, 82030605, 711492759, 835341829, 353817245, 949760915, 288406326, 25606118, 374729689, 195406463, 489855410, 59703934, 769998208, 990386614, 991546295, 11012545, 271431447, 908023728, 727804293, 320672313, 698090053, 894489383, 943486503, 380928372, 447385600, 852269698, 879713472, 714660959, 492546999, 741649483, 57489315, 933311621, 908631498, 57399138, 676093953, 389647728, 463777946, 98127801, 862572236, 976911958, 783772440, 231892990, 478275577, 543868585, 874542889, 768296796, 526340163, 972912941, 440821017, 865419290, 111452576, 988383273, 506535966, 839163412, 407530130, 39928245, 665376384, 123786062, 906336485, 698779052, 151532523, 341028867, 205080310, 173562327, 726524615, 548226254, 838570605, 588111313, 372284061, 229957448, 342341376, 235950770, 569885327, 682988481, 826118065, 892188272, 47197218, 573562709, 505576689, 464395067, 369612933, 973103845, 551577042, 704318031, 895602679, 419355990, 621925430, 487214286, 591739418, 374756499, 194078436, 14508428, 831217457, 172155596, 455978945, 553353626, 609263342, 889565154, 484395915, 415985746, 164790230, 263520812, 44785478, 881016516, 332702189, 325353136, 975954495, 482259475, 841353501, 818356087, 169764105, 449995630, 923201350, 702071736, 230935279, 238116314, 310582539, 443792919, 645559734, 282115412, 702100760, 432274828, 766130333, 612157103, 187472155, 164980847, 365535449, 958321269, 900754710, 348855209, 22240380, 115342090, 501503243, 332376131, 951436608, 883643034, 169346965, 35417367, 261708138, 890652939, 159067732, 568938766, 526230552, 519771275, 969399614, 637635380, 221183174, 410150018, 471010858, 790315298, 859784461, 45175643, 639703644, 240619399, 618988879, 630705686, 31736231, 323077641, 671365145, 626630258, 96411963, 165639304, 700569447, 446751749, 859475970, 24076939, 261158391, 502486228, 104839767, 965797727, 99784781, 558043350, 436224411, 392857131, 875640211, 635381828, 192020590, 602443974, 401468608, 623488705, 789568217, 117293544, 591747402, 190062963, 192060409, 474399868, 992156701, 340343270, 585302452, 298825769, 174662624, 145463887, 123853325, 669634293, 77680653, 10853640, 45139324, 884769959, 59196222, 842305689, 656113645, 420883223, 691941885, 497356915, 436612091, 584994360, 79737066, 713436461, 741449021, 551513181, 928281588, 351489643, 103502951, 524106590, 856114738, 43572112, 580740889, 683785728, 65254220, 298261248, 204180956, 393199323, 167223886, 849962548, 284589583, 74268513, 687413213, 474258797, 716160614, 219789103, 404936225, 492572490, 871787606, 236839779, 682824773, 789952133, 70036474, 777903231, 435210380, 849005455, 885860853, 342896144, 402330432, 557990996, 421344473, 672071435, 348702103, 378072127, 196421073, 10936184, 33470091, 133846413, 728136593, 455476026, 658770693, 357657725, 278013451, 806139268, 823285225, 531136578, 265182079, 839542112, 807530292, 175591032, 838215616, 458602096, 145806463, 81464313, 973533503, 116674789, 231099352, 393936071, 103000868, 161427472, 339510138, 556795976, 273832894, 942457997, 478990254, 233946058, 414302070, 18189801, 636098336, 878873984, 953941238, 751041100, 750008613, 244704772, 268022827, 351258638, 262363316, 726663635, 179993882, 337638673, 628305494, 468710258, 101796801, 838410875, 577292285, 276690395, 266744889, 523126037, 51676295, 919072151, 946780244, 411089225, 313449425, 812474046, 619534927, 537977955, 509063080, 36769227, 57020486, 60933580, 879233104, 617271009, 174848046, 360631688, 719309324, 396428412, 886096213, 555237373, 672402191, 191299196, 370584743, 485052087, 455004587, 676085525, 507247642, 654417625, 195923582, 22309933, 787785560, 527012722, 523906493, 853536557, 720596417, 225709271, 564395819, 113724381, 798252102, 900310983, 486728042, 450408854, 774972660, 240210933, 518928476, 857270779, 197851317, 615614126, 483951621, 334849852, 330597242, 284199633, 184439579, 570759013, 333919237, 146394220, 900327429, 155802224, 31210428, 985306501, 430084220, 736119949, 394176492, 245684640, 710125587, 702770306, 545739238, 905147497, 930756705, 508024587, 864019680, 158138371, 223532555, 68431229, 710797839, 105384940, 628993919, 443392756, 128541775, 142275530, 341915524, 952130345, 211137253, 937262976, 706837197, 319777548, 869541518, 559492785, 87145888, 665773099, 260269473, 141952732, 199439835, 353377580, 913801345, 686125154, 548280205, 82370198, 148927725, 877076535, 550201843, 965008174, 671083405, 886529904, 477258209, 500506393, 987008042, 502707550, 512582685, 718985560, 194860331, 186953188, 68727759, 263422761, 730932379, 195056817, 52111415, 707908839, 463639415, 304898021, 83759414, 679599434, 840062522, 92793870, 338542537, 875157034, 714487172, 706591270, 998626171, 933322844, 241524713, 348354298, 406760453, 52078136, 446693137, 258718768, 731992254, 174905002, 135994850, 607628746, 619723248, 224258318, 793133408, 271618049, 163769897, 560431294, 396654591, 160318857, 26238237, 380160002, 767030030, 940027013, 742179601, 989796906, 698374626, 574543207, 48180236, 104202421, 931558205, 696814464, 487352150, 677478916, 161585630, 416545056, 937633205, 825055925, 785140113, 42527811, 731302731, 199538349, 994762572, 123901417, 543370140, 682569039, 705449958, 256032967, 984505253, 913633056, 335654227, 583191733, 979594337, 45383677, 590220306, 996772833, 514284306, 723854817, 696358989, 989104685, 986831851, 766139930, 573514863, 116271026, 723742925, 883837833, 319162571, 913966109, 192663028, 394100575, 771954461, 198261763, 602442627, 873174990, 617038668, 529103481, 829997082, 387576375, 30258897, 560576921, 802792458, 838380727, 662189434, 313741665, 337643672, 353470417, 840532114, 784394867, 768686709, 153524351, 409534627, 131892104, 836064444, 283793633, 189399783, 15202548, 402149472, 275764570, 965895784, 776579396, 957922992, 612068573, 740562798, 715865897, 369392192, 606723388, 766552178, 501117761, 991567189, 208003124, 213093684, 300451218, 354649074, 671800712, 167181772, 188885411, 878625925, 903998692, 868548343, 486435170, 796364704, 276396718, 8661428, 767476478, 328801720, 85274123, 164310562, 451442793, 298528462, 758108141, 259256862, 257434114, 584219632, 6676958, 65846218, 535138266, 294189545, 589897559, 756881296, 976726599, 560288165, 429634634, 607927095, 264308665, 640463555, 867658436, 991570977, 73483624, 638818417, 550176234, 415646124, 846699261, 526568378, 305312175, 774078320, 629231513, 383385465, 792002193, 237400604, 705652151, 684613424, 701807631, 2405207, 565836356, 877581328, 117260922, 790980719, 140664367, 583129498, 707712081, 97701926, 466048580, 792532738, 493422100, 90153007, 348748585, 307690816, 294322291, 276980719, 501401023, 513436390, 740897191, 435499014, 513712642, 8377410, 673966075, 782637566, 181458081, 617439509, 337741339, 809029038, 528600565, 898004465, 829475207, 436948461, 646129793, 102765544, 578123684, 623338284, 564328026, 574132806, 470840197, 897736104, 795698892, 643166589, 308000295, 308382346, 997342274, 513563331, 302708089, 914673211, 706355105, 32767191, 712613157, 662610710, 132912804, 223486775, 761501594, 433045304, 929820561, 724710756, 232528687, 945897778, 752185173, 916013477, 19955326, 912472617, 957462709, 496050275, 363155549, 139451455, 916708553, 172543487, 604456212, 805750603, 831879457, 382095402, 263625881, 96999512, 668914658, 639311069, 717751837, 535365379, 383243487, 941785570, 180537566, 484875076, 733718865, 996196853, 79837061, 805937492, 893440004, 197596864, 236749418, 720596662, 182651905, 387460935, 911923503, 186500322, 34415572, 484618728, 735047428, 910688613, 490591681, 512030447, 423517989, 291464383, 739424950, 656542115, 934577754, 89965981, 482256358, 960166050, 583291117, 238206149, 56124066, 148835049, 40556419, 283575512, 855331810, 149283577, 398692775, 809843956, 614721528, 689390136, 637084665, 968245542, 475794008, 152591442, 296277557, 497404854, 35496381, 23266988, 645183902, 560729358, 969478946, 565873850, 562261210, 630908011, 166922310, 638887421, 646437798, 979052004, 116360114, 480040404, 824791817, 502209380, 751350076, 570694828, 417140031, 53730622, 246309891, 682721678, 77330792, 751395578, 189164783, 584634653, 777242079, 375682509, 202969220, 932923654, 615154941, 666158729, 438214853, 356679086, 376950609, 310725623, 938291072, 835705598, 47940100, 470030587, 545061419, 651204745, 642456190, 116650190, 350817075, 477870197, 431353110, 303437240, 754796544, 842800798, 638284045, 678394884, 382976284, 586044895, 44382379, 694363563, 407434481, 102746, 53502772, 664721428, 666211593, 475737893, 785224722, 577407803, 885339317, 21774848, 447329056, 289186593, 327713071, 169951272, 849386534, 734324208, 126408166, 692977088, 139553067, 314052816, 573581351, 684512849, 107136913, 806611023, 358863321, 634282444, 564096518, 43746784, 117680900, 457466489, 111937797, 662384916, 814620530, 538452126, 136270687, 875131300, 47904503, 66741374, 677250220, 4441301, 990030193, 567364617, 273716876, 135387598, 290321756, 651799275, 859773052, 312595428, 670310388, 860436374, 413684184, 843468751, 179868533, 954437140, 347783424, 168359437, 568800504, 37673812, 174191610, 260605305, 546544158, 201059441, 795412950, 86639814, 509877992, 838159453, 895136325, 718532683, 396431481, 508844231, 564519974, 174834802, 710657820, 888507264, 444535888, 684790794, 567232258, 539097858, 530780487, 295416531, 363746911, 871143957, 196779357, 189268027, 273507564, 501367574, 629917300, 317203574, 573707649, 551516829, 535441024, 364276202, 382861019, 43229533, 79515341, 29584042, 899630833, 852797203, 745239421, 998811269, 370220679, 780674607, 707115003, 698734497, 775466560, 55566346, 200076750, 870911764, 304895290, 279680166, 351757412, 669623825, 805757290, 317560812, 356305091, 472417993, 757441571, 227554328, 130962788, 778289040, 685952844, 19557928, 175743694, 179197416, 502722025, 188571642, 640900762, 861791988, 630538453, 483106067, 374403140, 823980452, 369848464, 816514744, 620365627, 63211158, 680671599, 836553434, 48152970, 332397232, 880300868, 529108621, 607342037, 496142339, 518407052, 372905892, 230712418, 860428377, 69871770, 516074240, 308065800, 163442017, 481467969, 936172819, 134244256, 748220509, 933693187, 323341613, 202081633, 967317498, 595788736, 79230558, 199272933, 819632898, 861714677, 560565612, 829308517, 179295282, 404629805, 961170649, 834649985, 929564266, 519571020, 796611481, 334909228, 738298254, 308549264, 738997693, 711010694, 785871167, 347166326, 895313696, 782507291, 730606988, 125648599, 369638580, 265991493, 30972756, 671580567, 896202380, 539573703, 923155918, 503511615, 411305019, 168129308, 413600356, 363831306, 640674860, 553698802, 875510506, 714562937, 695365045, 724057304, 983879537, 605570455, 479736385, 613598014, 948286657, 756537652, 106959458, 686133523, 146465582, 983863585, 569417231, 447771019, 313870434, 122567954, 144488587, 770073115, 607397269, 848615455, 631441575, 160213559, 717891006, 687299495, 426325067, 483441104, 694317916, 770328124, 775449541, 821999332, 612188418, 380340598, 918607696, 10863547, 594489180, 823545585, 223826457, 88973140, 488465021, 180906129, 969807980, 625074721, 614099257, 390502659, 55285267, 576560654, 406148170, 243663186, 267867732, 861231722, 623325523, 809968535, 449938984, 895622103, 748362240, 368977301, 29599641, 804761079, 110804596, 274250691, 559106871, 903355917, 518972924, 863279295, 909129298, 518107169, 953905293, 355725011, 255123304, 339251479, 172925187, 832515613, 438842703, 369888690, 737981847, 818163289, 251664879, 590982291, 371602470, 296545664, 913734949, 558253172, 123764420, 704746333, 93600650, 409030626, 340983928, 979736091, 164635777, 539469230, 34410663, 100973389, 63695984, 541376857, 317290084, 320046659, 199604990, 414176386, 911318744, 325967768, 704452488, 537213025, 20074872, 994518134, 848900981, 875260343, 509929572, 511628247, 129748991, 168338195, 224108911, 982664605, 421993177, 909500347, 337764859, 499277310, 45181259, 431869222, 958156302, 778799208, 100626710, 820354615, 123793936, 464159345, 484695427, 542527751, 199513436, 33095218, 305661965, 373291069, 504066553, 586217106, 449208090, 382954039, 864321741, 438451227, 262019351, 850375989, 194955584, 296540488, 222717085, 928071633, 786665976, 753733900, 43126079, 157165739, 777258626, 214926511, 330192725, 836405650, 226850237, 547907900, 115595448, 640799163, 511942152, 950656874, 46113396, 879108160, 42809770, 298497958, 102009622, 831717788, 882642767, 584714325, 75069873, 369624283, 25731550, 764506522, 897014192, 981176354, 334644533, 350517462, 105502114, 722103734, 145609634, 423797089, 620039248, 845428396, 400492216, 524944695, 403575831, 345571749, 539266439, 990074819, 265229416, 169532538, 25922475, 863014652, 40336617, 798944741, 864530459, 987977600, 303345347, 299640578, 442952239, 459090467, 196981612, 433064383, 340608146, 613771775, 804767583, 521388077, 568683711, 363355508, 963958974, 919305969, 916995757, 341574265, 227767365, 81988782, 892994365, 141937310, 86792281, 271694054, 193882152, 361785483, 12072137, 316430254, 881372287, 596585681, 293374224, 686828810, 253124006, 9810848, 963541537, 619310780, 926869345, 9682862, 560822785, 796809984, 847602812, 917152037, 694356977, 37185359, 789157130, 683502921, 67087282, 557323840, 722625411, 843837186, 820280899, 856365262, 788482202, 29084993, 146790815, 570218080, 845572352, 814293673, 48598728, 801953565, 786151819, 796606811, 706820264, 941395685, 940642068, 98776710, 77481290, 500275620, 584778996, 483970519, 19973632, 370370679, 262650680, 448988827, 98316926, 659195209, 684721430, 730782163, 247482079, 415387638, 532589252, 611306019, 221546570, 902902198, 424675586, 929900391, 124196805, 801144829, 445046102, 712921493, 612303058, 15195117, 839758291, 882380645, 335796540, 400104805, 494883039, 126998317, 187439928, 533733516, 805247118, 805124836, 85109207, 894010950, 561809948, 459163502, 640217743, 473528265, 10494287, 252598610, 621534053, 315108628, 117641941, 943440591, 9353504, 232128886, 201447337, 842073761, 38001231, 567610592, 967935631, 204720304, 799622071, 706332949, 486902239, 137257659, 555851679, 444552405, 260152339, 534528259, 525361264, 894497027, 203390724, 580834005, 934470811, 324027679, 549082144, 248703259, 532142551, 406356292, 841812256, 832779679, 575198324, 410819773, 787507769, 318669018, 67497625, 740312818, 792033866, 606097123, 182052366, 418716299, 273221144, 182306023, 355419402, 648242032, 525826443, 404668399, 114222987, 755888827, 451112429, 620003473, 849392111, 657045356, 524376299, 345754596, 144393406, 457107782, 964222132, 690377785, 33397825, 282228484, 104096789, 778832358, 670852977, 757991950, 884330505, 203840139, 926464183, 281121884, 921626842, 670607103, 374239536, 720191110, 99092859, 368667406, 459210792, 443725871, 834667670, 758335538, 37196847, 131453472, 540860030, 31939260, 330469308, 613739425, 700268689, 710697586, 322319337, 538847576, 762962806, 922051232, 418346483, 667381707, 735334369, 578170395, 127215016, 725111270, 607309701, 4418050, 366901037, 258285413, 832993291, 161184747, 647772582, 18948360, 513436879, 695406346, 442312996, 103364906, 772297236, 162929286, 471435691, 598455923, 625367343, 173860900, 878497584, 937747577, 296033112, 285349271, 247404599, 742389975, 129482552, 133222788, 179239363, 835243107, 824654030, 490714461, 723726707, 267970901, 65233687, 174057898, 106435313, 287757913, 472980668, 221541530, 347432119, 290643279, 705066381, 900861011, 579120084, 280173086, 811652573, 539410484, 181331981, 494037033, 658082884, 902559735, 669085182, 995769396, 118450161, 122622159, 389539247, 706305537, 496224731, 343149246, 660316801, 170529806, 3256787, 56208733, 903516890, 171750853, 211055229, 384965060, 970086841, 718565621, 884323960, 837127609, 588957544, 366530463, 609611380, 627012475, 741935624, 155737270, 871249954, 469517811, 936786762, 499125678, 975684537, 511949367, 904890090, 519423132, 685912395, 625104801, 945745107, 971218843, 885307942, 360686148, 867316664, 342910123, 465908540, 775737060, 792742869, 723322097, 171737005, 922116456, 680243514, 266163049, 949067755, 23755853, 725289176, 985200081, 854177990, 925247300, 396613972, 901771130, 708689973, 301155521, 807247704, 788347679, 295678616, 151535565, 513046555, 243415001, 817190764, 535640961, 880649850, 141093186, 947924397, 741281200, 904215905, 967662818, 235164411, 389225572, 612504384, 928930569, 222344003, 200545993, 281556722, 65883052, 918110516, 900568423, 732785346, 57462348, 211629110, 267978510, 149708310, 565962491, 971066875, 832075149, 913384483, 446298856, 290841228, 855910908, 384086916, 880513724, 450532063, 560515111, 856343216, 415409547, 181756872, 517973374, 920127385, 833970331, 936341848, 125356205, 592141505, 249186758, 269831905, 688499005, 68542339, 363858327, 52844092, 992673062, 340978268, 750825441, 815406025, 246750865, 460596931, 876985401, 481126069, 249834283, 618603152, 685409600, 178079501, 955223812, 401478951, 437616748, 162942823, 737011333, 559943969, 122198318, 591949916, 348318251, 270212651, 284763460, 926179080, 815471493, 761363379, 448433314, 346246585, 64725507, 403973914, 500509662, 919358929, 962222238, 188957886, 547156244, 917953579, 305628129, 450222564, 592814538, 769217361, 831719056, 404004289, 247224271, 153962491, 886980707, 661045125, 44949670, 196765088, 856516708, 985412568, 490288693, 426038400, 912111615, 51765623, 816818440, 250991983, 405546006, 73143511, 972308069, 862625707, 856536945, 79695956, 833171130, 238826868, 670056396, 453908547, 339534139, 282774218, 925747982, 203957882, 328316361, 501982884, 456271192, 363883470, 956721277, 908403639, 139221134, 688593386, 399763829, 7321529, 514472809, 434415475, 78423772, 573033470, 689989176, 493337160, 56995202, 982627666, 54422449, 569514772, 509645607, 390771582, 338657363, 771793068, 871539296, 733739011, 615959502, 352616216, 101619918, 242434560, 761749778, 115855783, 189612198, 385646946, 564299040, 209773659, 408316966, 891445324, 104131987, 752138159, 110296285, 693735492, 26311945, 455062981, 394118642, 786089500, 144374628, 304523614, 907827169, 434330646, 531364078, 510074706, 561962317, 653438909, 180026933, 389806098, 291134218, 417842703, 25608147, 320406722, 57508817, 571531295, 432640445, 853450156, 961671945, 791338566, 463816227, 587117816, 400321086, 660348901, 178195833, 939993234, 28172923, 101584356, 908579858, 700523240, 932238755, 522467248, 323537808, 724294300, 440596379, 635729987, 483787220, 491844994, 826043571, 190326399, 231896074, 241472944, 148332208, 876453782, 98608986, 657163706, 458793579, 793491459, 348660044, 592332929, 773120455, 289652955, 947636480, 995345720, 565559240, 510163500, 963616239, 847967675, 379231249, 296390249, 850066679, 853968590, 139431358, 314836829, 94391108, 737541288, 277619726, 633961339, 152630436, 1994562, 819343877, 273977979, 977773429, 99995915, 302614637, 170872203, 261558437, 255955112, 688401109, 958416664, 782452769, 663346978, 27224467, 120848706, 235115463, 706979563, 135238220, 806538279, 525709782, 767556083, 986852268, 227719090, 393540026, 227184045, 740625967, 237311001, 794716503, 845567368, 926431341, 719103330, 991817039, 793447675, 344056495, 235412363, 875258384, 574338627, 220656740, 507222580, 230027636, 791705849, 163421363, 620056614, 883855297, 975659660, 497909411, 238001938, 869995347, 316393491, 759236087, 918223880, 789991530, 698119169, 672198828, 19692972, 256581416, 486029661, 692669543, 451219708, 136177378, 981143974, 536832586, 360727416, 778370486, 783476249, 982924375, 708173682, 457831402, 152500918, 203104514, 694096166, 654251383, 488379803, 437167830, 270848416, 422215304, 739586146, 147655046, 307035731, 755243132, 157453438, 3219139, 952705655, 265454156, 243274015, 527171948, 441910706, 533693868, 282199269, 937443099, 88074088, 569743337, 787742910, 788471338, 885044752, 24110180, 625458412, 990450706, 816458634, 538452240, 778026894, 449216694, 925373078, 859860389, 55472999, 348481124, 856099206, 701215976, 373334705, 767884312, 505673764, 267431112, 81453732, 653954952, 668877143, 469247774, 511586062, 723372040, 530948139, 508183820, 873390520, 502327159, 224110522, 919626813, 609517301, 669654756, 554582767, 68200603, 257007711, 920576798, 533843096, 843394783, 640140756, 902463839, 329444564, 229705677, 456286858, 517135381, 378915557, 76367901, 162932613, 757598540, 5710557, 384358313, 253068762, 977982517, 525422961, 229854965, 389306001, 674071194, 165325171, 892414295, 426666200, 338775222, 598404869, 566913903, 689619774, 250827344, 348390951, 379760226, 719464817, 522425133, 238567288, 907594599, 387638216, 57136553, 9405182, 339994417, 4176174, 891435189, 757965408, 539061296, 657298747, 963412513, 882441251, 311991430, 562875906, 155205161, 349859780, 715558964, 569541809, 891978607, 163470729, 831678599, 179993159, 990546303, 744770571, 165135301, 449822149, 803175849, 596505271, 236924151, 604392693, 370622384, 380365208, 776453359, 120444189, 883849728, 940077431, 566187, 362268048, 247852693, 722363741, 384981065, 7189244, 445932806, 915554118, 615646741, 755217766, 214801170, 553985518, 733457179, 598600706, 440682484, 99046294, 79359751, 59327520, 561392374, 126312385, 63365514, 155251448, 182283369, 798079415, 489853593, 136797310, 418945125, 629479737, 645740358, 767379749, 551927625, 206920433, 887481251, 885959703, 208754853, 514377603, 220063721, 706852986, 741412013, 157703806, 953043210, 672828643, 707948589, 943738479, 438253872, 65573401, 31657185, 851267778, 827732493, 172475155, 122354673, 408715749, 343786402, 429426864, 778799245, 740287730, 143634245, 641234763, 446771261, 376117340, 163127414, 112067883, 338502424, 735716310, 698094050, 432186566, 452539350, 204295287, 540854481, 523492872, 165205612, 143633171, 633346041, 937156801, 820586497, 822459697, 914079715, 593383121, 140009211, 435290118, 392153160, 108634499, 312225114, 191056675, 403814283, 706557949, 700864520, 676319032, 479460980, 65850515, 365699944, 259481859, 651387224, 330460838, 985315701, 166777501, 613244474, 590642352, 966830829, 534475499, 177823958, 977750057, 115813702, 552312063, 721716640, 660991329, 215510620, 375520773, 434712463, 750701539, 19669094, 426872254, 974167064, 819446761, 906530621, 783412066, 430294693, 992096507, 391829620, 996383638, 895812502, 841142114, 667732900, 565039832, 461085918, 511335912, 255289567, 196329983, 761070314, 569560690, 787492452, 75466826, 455245691, 377728633, 747176328, 20567213, 32246757, 563751657, 535049332, 481283678, 170583898, 681116499, 208629890, 808824272, 658058861, 609301505, 659011967, 720623529, 869249459, 134951161, 333399426, 733885087, 144807292, 520223807, 515350514, 841657805, 625729974, 930526429, 200418390, 781123887, 836893689, 307926779, 528370616, 686863685, 427994429, 942330532, 449861944, 658043274, 767080012, 806360347, 445982013, 935451221, 120128818, 853898308, 114494558, 568860719, 283765382, 983229958, 312508910, 10684603, 44654333, 366583500, 996054963, 294196050, 652547804, 937458195, 4993835, 301559970, 355021633, 298503740, 734085803, 238626757, 986429996, 522486976, 729493836, 302973666, 49012563, 67860383, 690598781, 15718649, 129162268, 170641911, 844503722, 50567218, 822113234, 996133172, 75031258, 265675885, 474452031, 631671202, 386929621, 814870583, 734482629, 185060366, 532473946, 500781367, 163355476, 913770351, 714292740, 538430414, 555148706, 534728991, 560008239, 908808264, 539864508, 883977427, 281262855, 604792946, 830243427, 898298797, 931541944, 900985947, 670102255, 274051689, 57452868, 986243261, 82696978, 926326259, 631833530, 93876415, 793429885, 827110822, 517872427, 952233679, 558334576, 573896589, 319061618, 563996679, 860052781, 629833117, 2643626, 370790270, 547079223, 266527260, 959404986, 662423391, 743053874, 738636394, 696028752, 577316736, 775632887, 470430874, 444638878, 88471946, 647901693, 774286477, 844067692, 6321638, 892822757, 772866617, 112084423, 211550969, 374327644, 872542333, 445109183, 158450905, 338481526, 944713087, 867850443, 379818875, 391510213, 516740851, 441360097, 798476544, 890606648, 749260623, 69700430, 376403801, 70005654, 467411080, 10495345, 105663415, 525597444, 984853041, 119488597, 745128549, 545321897, 783805721, 210673407, 247988116, 744424479, 198453625, 888478168, 521501317, 759192305, 128718326, 530033468, 453214711, 720511129, 233561073, 86314664, 525691511, 955798871, 987547033, 650414280, 817940357, 29057853, 95566783, 862551185, 394311513, 747062367, 476278431, 795657994, 964227152, 850493460, 760043560, 143003197, 182172999, 173186035, 355709133, 371185647, 735989991, 501491211, 146806182, 750377421, 69797129, 18069503, 158832948, 318638471, 414420000, 359956487, 304324332, 322468350, 711450118, 377954423, 242896355, 118804572, 875314308, 813506593, 213743432, 410697182, 346792608, 50548081, 818720915, 916726218, 221640467, 479250540, 119877453, 165670105, 876461466, 949402575, 636064851, 271999032, 924400013, 288068562, 720566113, 756952626, 587551185, 618911981, 122114383, 691474317, 341469756, 419085190, 664360388, 561398629, 647670714, 428221736, 896210836, 202704187, 512538486, 968792870, 108931990, 751796203, 614804441, 416488396, 178419074, 213491202, 166184164, 305823392, 38527418, 368463425, 17360913, 45764478, 242087236, 516851310, 996730049, 735623209, 959425556, 712303782, 977867991, 15722878, 484802104, 217078716, 592250198, 269795749, 58300591, 164591790, 466992639, 330959585, 972865914, 595460457, 190981953, 261713890, 873395976, 719307608, 501258862, 173429769, 633836202, 829681737, 330656979, 240939335, 303985491, 211329227, 572470470, 983788723, 757277956, 745739840, 102206336, 980758850, 457359832, 714548800, 281683457, 3802468, 732487936, 889515660, 188713376, 627658477, 529058456, 648365762, 17713337, 713759296, 605823297, 317802790, 144954348, 523045486, 912953285, 159060902, 187903437, 940911875, 817749690, 162934432, 478309772, 937176173, 993241329, 669454660, 345465566, 118727985, 151482391, 448394510, 46101221, 935544962, 971515226, 140838360, 609664660, 178956016, 302891464, 980531602, 759126864, 266609714, 505623653, 784983890, 970450946, 807430403, 9154199, 963471827, 790972791, 459254881, 359626788, 500385175, 198625870, 67799767, 801398660, 709021539, 769729560, 271457971, 688512929, 181077097, 230151085, 320145683, 875872850, 67303624, 665732199, 66340548, 935640562, 697701832, 496901874, 495324928, 730037585, 992210869, 326844245, 736432624, 477544494, 560914431, 577920909, 959307201, 724545523, 568821701, 520365067, 428199654, 254675236, 13495642, 629153719, 951801392, 388819646, 725114393, 926386376, 606387404, 204282077, 756936565, 38398315, 934328472, 484878158, 770554020, 50536365, 874424839, 555109793, 395544160, 591428867, 217023857, 170426677, 476549889, 473276376, 780856354, 326851341, 961914779, 484974443, 172989918, 48811282, 423248613, 449126202, 418449235, 419584186, 326350984, 719576862, 76998373, 978218897, 449253170, 774328216, 223787726, 394276335, 941866458, 749740579, 357696606, 77483990, 599685139, 738856501, 595910230, 335597909, 963195628, 812298563, 29768857, 313798370, 287012867, 457596185, 365453755, 510250464, 295770334, 449766626, 913770306, 62658708, 79502629, 578994300, 6717748, 42182609, 223203234, 367857046, 574094747, 903209992, 546644277, 522692728, 283754349, 467101296, 973560546, 186991970, 563234820, 577343308, 786556151, 692663870, 647568508, 850340401, 723279488, 853322317, 899037, 402882551, 362605764, 724324314, 747966573, 876548467, 860392598, 477049220, 366941960, 17000795, 510246824, 201616171, 692700325, 63039910, 37452396, 295925367, 924743897, 252576026, 86282196, 335003680, 177625687, 165661540, 520831284, 910594811, 587181344, 848631600, 22356749, 247069451, 299936729, 118373185, 197610275, 545601019, 440950881, 541237423, 19666686, 793696160, 92442213, 531022868, 837497895, 373668072, 71269192, 598444416, 36088243, 802553322, 80768990, 961976491, 711067369, 323034696, 123615930, 390742802, 491992687, 240995920, 103287540, 752198158, 891537914, 914286077, 964916664, 803483938, 653314771, 638799929, 529561621, 351450108, 32633399, 545397765, 861806966, 752941892, 307550661, 738418584, 895875941, 650109631, 715102133, 597177569, 706276711, 529923676, 56328326, 329120323, 92885444, 821910315, 923092109, 817796453, 922733556, 59836031, 845718433, 762400084, 511368406, 791264165, 792272212, 477538974, 760832767, 612254058, 282487784, 264539267, 874464050, 596346387, 226574756, 197176441, 278788391, 960470091, 269993941, 400520195, 425370546, 152171659, 143546896, 185859023, 273820879, 280689387, 110477456, 151908409, 641028423, 539149119, 547100346, 110189096, 790924018, 142829791, 889821728, 841143121, 938713483, 234596169, 717165380, 868915793, 443253002, 424680517, 781827208, 661490215, 987054683, 995591285, 611643089, 142931316, 702114501, 516778091, 900806554, 882602540, 274431064, 181906240, 676447180, 649708739, 374912866, 672015198, 272017136, 794887151, 819955421, 748265638, 617536230, 598391888, 31695536, 48372356, 733370578, 688745498, 210750001, 276375383, 479751435, 424428399, 927213184, 648645759, 314928137, 189083216, 13674663, 223601404, 142038133, 649978482, 542725457, 681828832, 999460807, 272794585, 398183265, 180013505, 214117191, 686535277, 241598301, 126544064, 401692814, 224504352, 945110280, 442450668, 2778406, 951431585, 992923631, 115373114, 982509007, 482255371, 235548255, 512126972, 332019706, 4510670, 31589887, 820504486, 983611382, 242374007, 497019849, 113414523, 296823866, 419490419, 855795050, 367506198, 607809677, 710567850, 120383044, 187737214, 771318711, 541355874, 799256682, 3420884, 576312287, 499610037, 222420953, 183243458, 647228944, 289904490, 957693348, 307782036, 642707777, 229084132, 204785431, 427981778, 553874293, 962540098, 495810116, 544074177, 185444655, 494018108, 334412147, 49590381, 681430807, 435849731, 815971752, 312140075, 559134571, 79067047, 597651706, 904877011, 548644217, 184381459, 384064022, 323851519, 686593909, 416026642, 477603903, 237724142, 844754464, 616361137, 441024180, 765857441, 406819717, 395649436, 661746032, 565247436, 483302301, 685067135, 893311440, 988419688, 258997543, 504489967, 894616609, 564138678, 215857940, 625005642, 849025606, 231482845, 959447990, 129183149, 918713257, 236397271, 54914422, 368583977, 542376123, 176300135, 349982115, 550781612, 922189677, 45100729, 748053893, 127416889, 851044886, 522203887, 950311933, 984698431, 273597711, 468252662, 743750777, 83090589, 916086456, 730267431, 327717839, 487819113, 497098100, 636579071, 393467273, 314293560, 974182151, 105934175, 639760833, 227694964, 332704117, 905669173, 658672249, 243347167, 84557358, 377641022, 392629041, 882593030, 769512598, 699995192, 459406195, 901622653, 52989614, 650115102, 310366667, 805968747, 419347728, 556346785, 58203027, 961106817, 154474177, 768672383, 543484340, 194559114, 410767642, 955298077, 699902857, 763871552, 744781344, 809940355, 64286928, 718476115, 935143446, 261539381, 731948685, 816206289, 255790903, 958269877, 551051936, 196677040, 209075080, 338258842, 168659432, 444645742, 170688508, 163386044, 104362817, 93380921, 902021822, 211558569, 804465532, 999909544, 11948774, 450074487, 418611958, 427169755, 555870292, 388009780, 803647701, 522561440, 417819878, 911892054, 594429058, 765577314, 299058115, 331867422, 865630418, 988012666, 649470818, 846746516, 346660620, 321090392, 118088137, 596406959, 880145052, 371416331, 661647292, 422352712, 367681333, 450834839, 554176410, 308633864, 534469282, 877425640, 74049194, 383852921, 381535597, 651224431, 32042254, 737736878, 963909120, 201513528, 124724296, 764629632, 594815636, 674686784, 769564032, 928863533, 109894568, 662883272, 65259287, 84745221, 949508670, 296363335, 752212509, 193608128, 346405050, 372175556, 118813203, 164597114, 732301437, 999922827, 978459951, 615601006, 143629412, 948533279, 946261982, 87415865, 547722181, 529610215, 190983431, 747924160, 32067902, 737904912, 12773405, 378195625, 66711748, 565258774, 323003893, 798151722, 534962646, 543124952, 101004698, 217248881, 52624046, 949565883, 18058760, 263884460, 340963849, 885764899, 851447055, 783550110, 102235001, 740948547, 320840391, 777683843, 304266845, 37626594, 645086051, 996891440, 632003345, 712848432, 163953984, 511684696, 481201605, 660055273, 926054013, 58783555, 56705369, 901080002, 764831751, 64226361, 606442512, 479712516, 244539692, 101928496, 639252643, 749056965, 964947197, 573020863, 938111246, 171210575, 564301612, 293770838, 330346783, 888934606, 191069047, 32591654, 197151200, 915850650, 375776901, 722302118, 202674295, 747864206, 407267742, 381308407, 784481667, 534105326, 273000916, 895926754, 891108695, 695649551, 543241629, 995688821, 730172021, 958580997, 853196033, 716701682, 829981113, 275729643, 859223993, 448118616, 952517237, 755767637, 425955313, 22647337, 584496648, 108465052, 206129860, 861438216, 103565371, 772608779, 996215297, 142349668, 856797141, 521143549, 247120867, 330490667, 171031053, 484697816, 698519738, 322837392, 800817647, 467457072, 44291155, 663919678, 263733106, 273928616, 831315422, 940392444, 363345672, 470225397, 510990549, 426838269, 194043267, 422509104, 986748688, 872044352, 966126159, 297099805, 166601629, 238785585, 454361970, 163339339, 524725820, 550337806, 532228887, 239944410, 305683211, 905405510, 923114942, 783659883, 643739376, 220486450, 586992408, 220371057, 423007185, 30621877, 728897034, 856072587, 376420939, 868905501, 623156927, 422106009, 151179383, 773763551, 83380315, 987249032, 350496093, 76986976, 952854515, 625886253, 183367925, 394503956, 936756195, 903624481, 9547482, 108773822, 660321282, 110430834, 44254995, 74660444, 572737790, 555374200, 965380524, 702305899, 40587026, 536221250, 203391619, 922969382, 106747699, 747733692, 375672211, 780965182, 636640355, 144883079, 914340634, 547906538, 911260780, 227309979, 125597312, 315498003, 79998426, 552862151, 903471544, 923792394, 207088166, 114740412, 664209714, 313472012, 863007165, 363916666, 110004841, 437522395, 772134756, 667220482, 387258125, 492789299, 993560097, 373964027, 687557511, 887622961, 909896687, 949770209, 502318721, 161882337, 323974461, 327152528, 652868002, 89367006, 488425531, 863316554, 598324336, 532868957, 237476099, 385040133, 25377614, 565823229, 554047960, 251680246, 543688211, 225001352, 79191488, 884021671, 396346362, 470474756, 536632156, 569800764, 51007401, 648286606, 375473603, 457131924, 253928202, 551934601, 238959688, 153283293, 194591411, 368611992, 361034447, 651558309, 548093304, 355215672, 84144642, 75891124, 637444948, 890688616, 853314781, 879408851, 265286952, 604699630, 550661484, 679475607, 428727014, 761644212, 19845476, 76713459, 358229072, 492925385, 577477240, 939077323, 900113674, 897234075, 319951521, 560245243, 9487160, 45708014, 810137789, 448428983, 22214685, 277515134, 329883010, 243712107, 320007557, 119303298, 804287003, 855089258, 718778782, 226133066, 870442962, 648424529, 4951503, 435296858, 197346959, 255247308, 928118495, 357847654, 220541657, 997555348, 886981460, 556966459, 697113796, 933068087, 593375050, 18814291, 913157174, 334298171, 819764404, 459570547, 563033220, 464180366, 194298002, 456201721, 28142126, 620020242, 982948392, 398394041, 107227847, 808070674, 45541875, 339166704, 147108649, 747762122, 754199107, 498934594, 917655672, 584584212, 812988686] 63212)," 52873 (countComponents [619553313, 311549588, 293974034, 719177211, 636097592, 934499673, 801255312, 606234653, 293695435, 443096204, 254559470, 88637959, 205638425, 519278337, 966044078, 450440117, 510296688, 480864064, 901175583, 718718378, 948343171, 889441683, 920129735, 195548372, 561877346, 638241467, 973864051, 4908819, 68990549, 120199015, 219449025, 251732255, 611587582, 668075345, 123783754, 5532799, 536597286, 522113102, 935337690, 301801900, 457804586, 780484783, 691813774, 957548488, 979380300, 849079301, 433201131, 579704986, 799754391, 751692397, 299099982, 119475090, 808573184, 106617188, 213526319, 532776618, 60238180, 925010710, 624543914, 697331153, 392113802, 759199886, 989650345, 139763368, 796449253, 916028761, 206550547, 430071998, 763468766, 572159404, 759622820, 754256182, 190856699, 521000185, 758245454, 438495828, 173493432, 386042938, 888378403, 115431161, 569033612, 247339865, 246903616, 671577839, 539564495, 649170716, 557674538, 259412214, 739916073, 836145568, 689773337, 880817317, 85008681, 79832287, 644192628, 957343725, 608352987, 784353316, 810152762, 439746705, 399254756, 809167973, 778662394, 290858492, 177094174, 707783931, 122499546, 478392418, 930263959, 776150854, 4186698, 188164913, 579138966, 876711665, 207626902, 995791574, 947758082, 379746238, 501232394, 120083519, 44834155, 368040062, 211069461, 759034373, 748520473, 514616218, 167988953, 709356675, 830146867, 127717839, 761738919, 396554649, 286299642, 298675076, 244602402, 1790997, 407650767, 204134757, 734293613, 734739043, 507536258, 629989259, 962337723, 193681842, 38666296, 464080090, 4413762, 211292102, 151376308, 105913034, 908450661, 588536099, 7338710, 3543243, 488028477, 113262164, 833405968, 866539185, 343383164, 261945018, 882178001, 304313111, 503710909, 909243258, 399616795, 637735197, 998305001, 648150736, 790691705, 134211499, 444269169, 401903566, 767912885, 112914644, 626309100, 974304659, 720783860, 545459654, 669318312, 559430312, 240755614, 832527059, 702152848, 81992444, 920841755, 245829512, 37448087, 449250602, 24101455, 451212396, 599113364, 964743535, 422280249, 667306625, 671589288, 14015979, 288051089, 933373777, 359898618, 168510857, 884363178, 419252716, 594606785, 783905374, 794228053, 235548511, 735078976, 538565365, 682712483, 466818053, 809139113, 865593670, 609776421, 516376423, 273247315, 938732682, 939348082, 686770112, 989757488, 507052286, 918117215, 758654456, 895402836, 558739179, 110357200, 284806645, 354838805, 534024423, 986153309, 457601242, 32750345, 868241163, 111404889, 956129063, 625114367, 185618751, 320547441, 601816808, 609978143, 877891775, 809673236, 141333536, 476401960, 983949920, 380412235, 629799073, 117231993, 270165596, 32840568, 896142585, 403012937, 309779545, 596292275, 738586598, 440886126, 128452728, 665898004, 135438338, 882415788, 19076500, 871351956, 397809931, 937748986, 802675919, 548243537, 739536439, 108117401, 840895353, 946413312, 495811775, 950801516, 640243047, 575445645, 641401926, 652445943, 41200370, 713254888, 29114880, 841776, 82501674, 979032469, 470603981, 16405210, 903436153, 966070711, 495935557, 84215636, 709101557, 453786473, 208989034, 891126368, 797347712, 76736099, 954888010, 971114522, 305868488, 751271281, 161885985, 709923631, 745062670, 247107695, 66186490, 859874603, 162584190, 776580581, 93172510, 63848140, 152134989, 172667430, 79759973, 525163733, 216285869, 8927132, 266196977, 19156999, 240645777, 540470742, 950038694, 721752313, 210687105, 662261369, 318255527, 625635021, 250177038, 484161583, 991731602, 326756870, 509906969, 308845132, 38692189, 985751696, 928549539, 535763745, 196422847, 583064273, 116671681, 58871279, 598906130, 372063311, 792971648, 928573081, 696585778, 464366132, 210693588, 1650176, 574159248, 391465444, 783243487, 374982452, 715167006, 240611896, 206761968, 546132267, 102704624, 148227017, 546373946, 740370945, 657449448, 971632271, 537818547, 397908241, 368850293, 762678661, 935602216, 995025093, 493301371, 25235882, 777296544, 50987717, 813868648, 632781479, 906425765, 524904332, 666550422, 860134744, 489333224, 434017810, 400787679, 329801839, 768187851, 32704060, 557664729, 266926188, 860546030, 526747455, 424958797, 759658544, 996458028, 452075586, 941890802, 546938881, 851959626, 734844154, 694987316, 319301852, 255541305, 572654529, 747686574, 320549191, 742871799, 964452614, 572365610, 201627843, 465609423, 935921750, 867914364, 546885810, 751221150, 21034379, 34875709, 318597155, 576944490, 824885662, 668807845, 72816259, 944454790, 299341825, 174030061, 504037076, 751251398, 519413688, 782906807, 479668067, 330240736, 298766151, 379102360, 284993429, 901965471, 668148179, 47895376, 735155786, 869902842, 659655863, 903381730, 524196508, 57219697, 398333205, 429263950, 853754603, 583520973, 591729613, 382787709, 245988338, 818179750, 32869045, 650707527, 119314197, 532974385, 224204228, 243791429, 389754562, 306761867, 78066384, 14861826, 319788334, 920079303, 828765165, 839396211, 534582621, 472517165, 253952370, 898126380, 851710394, 979673150, 965060687, 716353818, 723737103, 31696877, 438685965, 795912616, 522865256, 568622590, 341597261, 546065281, 48328102, 757473527, 863124844, 579710096, 751111028, 427364400, 671047431, 851064650, 25033868, 337520147, 536499098, 915815399, 950301997, 379834843, 575135229, 924718494, 391287254, 279791859, 600584351, 426033115, 277395353, 840085476, 270501780, 715558778, 372792287, 518109537, 372058426, 879726177, 965317056, 961504436, 95580724, 159337026, 429113966, 900345070, 963709460, 214833992, 725231984, 200682973, 598654575, 134054088, 668250890, 838688941, 510418233, 384441708, 592484266, 913996405, 440933425, 29464054, 847360901, 418273364, 840452060, 221798214, 716060969, 507718779, 102524375, 725401196, 322812210, 735984091, 547459144, 273411089, 868829904, 21917598, 336177587, 223475971, 927923135, 611676754, 160526322, 105559703, 427503136, 202588804, 780801817, 101813515, 984083659, 346689697, 148468835, 285867459, 911082414, 857950173, 551288100, 869619956, 542135739, 328551680, 240790876, 48984565, 534917673, 507069092, 925981087, 596388602, 516744569, 134901175, 502707171, 403615200, 491512318, 656338182, 884016688, 803584098, 221696061, 203395345, 619480462, 330681097, 291629419, 482414308, 468808824, 883058182, 38991155, 67507916, 667133323, 545070288, 10254836, 2021161, 581201095, 932232481, 408234009, 641052081, 945346115, 112262526, 333666282, 874310387, 351716011, 822190239, 661162843, 216966080, 267401502, 986698134, 801575333, 735493228, 692893669, 480186027, 888452293, 486814501, 772766791, 969558582, 418638618, 800406108, 813315181, 916177338, 509440460, 562970395, 813157025, 256291109, 933990529, 30095941, 415829191, 2944363, 259445623, 843069346, 464202440, 411676, 643836066, 66159494, 595389988, 642864347, 350075904, 393399609, 358006940, 470756907, 463957716, 615342065, 93548341, 162024739, 192076656, 529807618, 336154801, 188989285, 358386324, 800121174, 427692083, 62318989, 294336409, 850431741, 453105669, 315313841, 302917311, 942859802, 646154125, 166314582, 735353068, 522844393, 350220666, 862133740, 82267382, 814402977, 599976140, 688271484, 490189570, 148528461, 685541230, 976177118, 396017889, 453454251, 727788097, 948874479, 238216749, 72044222, 862576362, 448434300, 840261945, 293932937, 13898420, 21747035, 158260700, 319949742, 7404278, 996112955, 85566091, 670774226, 652925358, 312546561, 517761863, 561357620, 6645003, 32692903, 841081120, 94264236, 147865682, 705608506, 531155152, 450570607, 444300729, 279143530, 355850403, 211174346, 256962976, 187733968, 536940520, 742479472, 854750392, 113407489, 547671974, 543164603, 712390730, 384958976, 991700003, 139987059, 107541024, 855175755, 184312772, 526180504, 576934495, 926902099, 251974418, 121624450, 263083563, 981939885, 688661096, 261011300, 462211488, 584277022, 173578898, 561407554, 465795144, 621294461, 33500857, 738762522, 151154537, 943541149, 442678279, 370765496, 28053244, 627710512, 398627187, 828755529, 444162151, 325238556, 627256493, 750733232, 682239572, 455339647, 76809976, 383561317, 392480722, 599919275, 378200355, 915842916, 123918718, 422796107, 228718475, 846956497, 972241502, 15689283, 657731675, 881239111, 592402488, 673369121, 634655407, 5294559, 175991703, 64149641, 315482089, 566621317, 261466043, 584041903, 78276666, 496925142, 224402163, 852644227, 112190613, 435011831, 623523803, 824407054, 551108946, 123288269, 779545757, 908627799, 131232392, 629632559, 591166429, 208839618, 120288083, 391829481, 78926656, 745340645, 331684976, 610394655, 696003165, 912328507, 637067910, 147909685, 396674325, 74326848, 818596990, 415229556, 780893499, 253820278, 826611534, 160600928, 498900227, 228321440, 474959312, 508126541, 914963493, 946531965, 598135897, 216960623, 597400923, 127895691, 77684076, 367443393, 405469018, 191400259, 845681672, 684152265, 347483278, 705722782, 943072309, 303467935, 48017983, 337662051, 798093866, 314413638, 426476858, 657404414, 143793492, 83894385, 699415722, 266324482, 443012888, 43790186, 880417046, 545109789, 420414462, 714084167, 654898309, 838075461, 999663148, 937480990, 532315542, 722682642, 231069693, 9648488, 896546005, 904791086, 711834430, 294193779, 340147117, 39654203, 394653971, 447521600, 323307430, 748012619, 248018192, 596618762, 980103597, 201612187, 524456264, 393152804, 408645626, 237104992, 659294634, 262457379, 913829649, 411546607, 137620906, 679431408, 35012685, 492944430, 49350693, 145698455, 95428865, 915764334, 515337642, 76792640, 170640527, 808243098, 844891229, 129060302, 887217930, 601171862, 967135418, 31340148, 215751239, 274372999, 686662933, 354467181, 204820889, 696170039, 210820715, 926908792, 713079125, 917631247, 568980329, 527363081, 868236966, 60054587, 978496948, 580200182, 503687516, 326760614, 62975898, 743302870, 773639586, 986827086, 510094642, 989235935, 877192488, 623191918, 837819088, 443969281, 607590801, 189258420, 227823751, 498949314, 721573952, 168797418, 962612660, 499988982, 790065753, 103805836, 364387989, 521481829, 567964400, 811367808, 936220538, 331184201, 687730482, 906750749, 336329689, 59557943, 246671042, 339993170, 987908536, 987812266, 732818660, 556849190, 803126975, 63088747, 420908124, 65719128, 756803062, 610180284, 322321329, 253013529, 198819748, 615523589, 745306849, 91730458, 917343536, 189362656, 65024809, 102737953, 755790001, 35116370, 239804239, 583820512, 439586152, 691048449, 119452757, 612211001, 18749155, 128371889, 716896426, 464134068, 553071308, 359762339, 760676686, 70231331, 643136304, 708504386, 789055973, 212693711, 45814904, 959713465, 277833, 90727752, 424389356, 485649131, 161108176, 955756761, 610002293, 751241961, 762141154, 510437862, 25728704, 273014833, 254052622, 565355551, 534495725, 346814285, 702866505, 955243191, 109535891, 970691054, 739547220, 45501725, 988409666, 387097601, 157709568, 858354660, 181865055, 59366134, 206073764, 354037108, 884497870, 697900116, 176604373, 69683632, 670262173, 961519114, 84014252, 847919754, 691067290, 302965395, 796492979, 704145266, 565537362, 830800856, 510206237, 141154643, 203035071, 134958357, 331913102, 22542867, 941871638, 72598216, 355366179, 229395358, 297299159, 89679180, 159305183, 434680275, 435512325, 108510559, 876023464, 493114642, 51119944, 58295119, 28349703, 145278619, 731029984, 781251226, 397328008, 787901525, 81908792, 727100577, 727235940, 107546785, 30792678, 255715071, 167464711, 732510895, 282566386, 770060249, 52587408, 31282072, 648980525, 254606532, 414286054, 814000469, 539031543, 122873335, 588690322, 438479128, 565871007, 43396755, 822370565, 242446739, 847250008, 443695168, 765965431, 341539486, 782046104, 599823822, 838853572, 564219063, 583543815, 771681187, 448354599, 762533598, 330391230, 373518311, 501041958, 427786569, 107649759, 461292298, 19134470, 818598357, 189584490, 571336290, 185132263, 691539987, 214858071, 424245426, 925464336, 427937426, 652297193, 230899310, 176392571, 45652054, 379322123, 767782708, 797962147, 241482588, 26617113, 437243237, 842300334, 893083053, 393389690, 422329267, 660091261, 445608982, 742512600, 473316046, 868525017, 694081924, 851756788, 717401780, 273561548, 784199740, 196884659, 442515608, 858176045, 216185154, 77654544, 495521171, 273049281, 245608886, 478895505, 783311026, 148334768, 753909787, 645331520, 891511760, 976689169, 209952124, 932194605, 381505809, 176370232, 734769748, 447132995, 937878960, 897312529, 311720522, 307921829, 469698421, 591809305, 969014287, 732593963, 12183716, 829411909, 812665671, 596178821, 543375343, 691220681, 722904862, 135158864, 238472794, 113738152, 117426128, 405067000, 386398892, 762945630, 612730667, 743644649, 936416964, 178047560, 120450868, 66734165, 734422808, 648002226, 609281800, 921619520, 198447566, 719824532, 869061383, 213238121, 892629672, 655340, 243392261, 981719256, 570210302, 517978780, 752937036, 641645994, 964747382, 691966136, 403397224, 21997794, 25650278, 588357147, 490290822, 490305994, 334528486, 15217941, 858755515, 213704276, 215564728, 271863660, 26168637, 757542944, 373710478, 76907892, 512418710, 867497265, 755091138, 774692112, 389687924, 210824481, 725960792, 877558636, 851327921, 6483604, 90309348, 216555324, 89502763, 583725597, 551484800, 579013609, 768460461, 221406350, 793471189, 31054139, 906934494, 551496815, 514771776, 522087111, 981029282, 103330556, 161667912, 634070905, 637869131, 509539353, 748123577, 452468776, 686854331, 263252381, 297948319, 584890857, 989594247, 100912360, 559865282, 167205678, 621678173, 809239897, 226412777, 570978809, 420231325, 433202346, 885067915, 142569196, 274031220, 191701380, 986914574, 734571309, 302402543, 882805327, 873051940, 905967661, 55662506, 459541825, 671127736, 251733153, 516131890, 769432089, 272890431, 230510878, 664237336, 13674397, 145011657, 744282859, 411966769, 35844695, 781208586, 353168776, 197635203, 448836548, 304073457, 998517618, 833963286, 553285790, 676985715, 388831740, 451313918, 883843919, 732790849, 567038008, 664939838, 848846898, 710735917, 55010842, 204814317, 199038295, 323519727, 841095297, 261729301, 683557930, 946792306, 476791751, 359299155, 901404523, 843435901, 680606625, 934151056, 74497091, 861630276, 525829410, 978751894, 457354411, 256290004, 564704013, 591211382, 945423798, 797673290, 858595661, 979215759, 397348748, 800214178, 747047452, 308706756, 150465498, 738977474, 516286262, 748092451, 20142946, 60714518, 347084588, 301868737, 296723587, 723177995, 357196252, 630370035, 560794376, 609197949, 804889483, 206300059, 180618200, 190275203, 927875121, 265947360, 981491839, 4183032, 598857628, 96170039, 968393530, 651270632, 913664063, 151367656, 252021764, 606364947, 937900276, 533656084, 312009270, 377106698, 692272178, 11031117, 204640768, 344632234, 763492784, 147483776, 602559416, 677469181, 104741, 286843974, 934766367, 603046596, 236243806, 3827689, 180178831, 778595144, 363287987, 364623124, 150711380, 922200711, 806857336, 784934453, 7478435, 416718511, 815795982, 346620880, 921884217, 993659673, 107441890, 312642228, 920905047, 686729404, 731563825, 135532270, 505479793, 54550261, 981116447, 560732475, 941954932, 469808068, 179001545, 521914461, 232620528, 990926494, 711204032, 14041217, 943367187, 40716978, 276832336, 250990058, 566119412, 870998817, 431898426, 306593119, 524934233, 685939606, 195864191, 521210867, 119889517, 471034038, 787256874, 6743558, 127748490, 850051296, 878882917, 367304994, 101806360, 729167830, 533997286, 431755647, 148264427, 909874527, 248321493, 133679024, 144505976, 149016943, 972982535, 759612058, 3421378, 156703458, 732924755, 197865432, 328171779, 66983066, 769133691, 577491359, 588093783, 482491344, 526583811, 711657853, 410588499, 13418939, 623205142, 256421847, 294115706, 751772138, 349156503, 820082464, 951512839, 177462309, 410384826, 207499275, 352660348, 702327795, 942316170, 5610910, 148164249, 227228577, 766811516, 554130784, 996128686, 583396280, 9786270, 497802498, 278319631, 313973318, 575838372, 705302721, 466818187, 517191086, 512073182, 461141035, 68618157, 253707790, 147444870, 883829770, 273787673, 688760195, 262608083, 134417704, 323073507, 495093696, 187233258, 807456396, 294748437, 199135525, 926888835, 261710921, 617074590, 172656054, 566846197, 590261384, 532982155, 687206145, 647943880, 881232520, 62782601, 189393001, 175484338, 742304845, 511990542, 488772879, 708282316, 900203546, 419489116, 755108376, 56048557, 439546988, 934253978, 138630668, 832925520, 828069920, 254773386, 130490590, 393256403, 898905595, 829295703, 657558984, 446068460, 17089930, 104739217, 155327068, 170429201, 558739017, 561342411, 567730840, 326346171, 648946955, 567895879, 841776757, 554290909, 201886826, 627260531, 632627563, 897501627, 57868401, 583547546, 337003241, 90681463, 155811136, 1924171, 188442421, 674845382, 722817360, 930830787, 743057950, 138254659, 780032557, 107742359, 816339823, 725127701, 573002211, 117853113, 383308212, 395911245, 390076959, 762247521, 631606903, 87767655, 919017057, 863646857, 710666414, 60615834, 495476826, 497351879, 654043160, 6628430, 989147358, 727137027, 246865044, 112833994, 36706215, 273234627, 739828280, 654127010, 89906062, 302989202, 302194090, 10158633, 41802503, 388202917, 714174928, 853323356, 737824539, 544284117, 231781242, 773174075, 108432388, 824840109, 924330880, 750898414, 444029428, 910009482, 472180628, 933074104, 510979103, 50647027, 771373193, 266164009, 179457310, 72981122, 382037702, 123953859, 274083436, 970757570, 806796085, 427897950, 276374356, 103646753, 867706607, 520165129, 755302107, 161459072, 436836467, 183321315, 545838317, 115232626, 981176284, 491286800, 363794413, 553042440, 600427129, 431120958, 218722326, 674971228, 186490161, 582840346, 825476752, 751129551, 1704867, 433396370, 772469300, 960130853, 865370776, 35847019, 355887987, 604471379, 322613172, 286719557, 294962654, 4005505, 977184745, 515487040, 944202278, 413125849, 691465271, 864872100, 667250900, 380750834, 32236664, 527446854, 923119164, 18551276, 228537975, 403473526, 19576548, 790368194, 388830751, 646574428, 997159268, 620805815, 290168835, 67698338, 740964183, 743117233, 695663886, 187662997, 304257268, 137277073, 837924327, 947587215, 833907704, 69031845, 28302556, 180417464, 336081935, 915482730, 531368929, 413260855, 227046519, 831294966, 569202104, 766081309, 38033043, 538793864, 592128271, 208388511, 178196450, 228967308, 622584158, 412707793, 182670855, 154848570, 276819951, 173404324, 167337072, 88931123, 82394227, 849460981, 662401659, 659535277, 562621617, 529629402, 947949696, 36996884, 558598001, 467931403, 128970215, 877635398, 189860812, 862446273, 590993874, 607470845, 71820898, 937584034, 408366864, 10519154, 684274893, 798518171, 907104507, 319727393, 505111627, 115565673, 142200107, 400860284, 569808456, 577425138, 266982172, 445243421, 576747307, 849583591, 137596697, 853243358, 49177451, 797544749, 768346276, 969384824, 538313256, 17891144, 216289897, 3919268, 452950822, 47843297, 13256607, 193406457, 449927907, 951579934, 574706840, 184123071, 15850354, 685820378, 461942187, 466519494, 332426366, 243922382, 492795648, 275021800, 894560067, 711806488, 970159892, 522891039, 106169795, 674682320, 895840829, 528437159, 209648146, 932420429, 758991055, 114018399, 668274092, 314325290, 660999088, 11309999, 300976387, 772528187, 895616793, 847253745, 788957123, 849939080, 323030492, 338820942, 240647990, 493545696, 535039940, 623254134, 205254658, 364804745, 385752865, 713505393, 44021087, 708315966, 400979368, 390365749, 764203858, 690357270, 903239243, 564051307, 448131806, 499224837, 500298168, 707972043, 116489365, 721840586, 283052235, 922772412, 355001759, 577952574, 925873566, 721772728, 350227809, 692444067, 617679653, 380682223, 432505262, 3705945, 42218852, 581606138, 730282666, 838222247, 764106353, 746992230, 223802263, 764359993, 590176832, 25500817, 82610676, 553976298, 772877282, 728227648, 266258002, 660336803, 144628956, 454396230, 713994035, 321621582, 578475762, 251686338, 672166138, 224455023, 476843641, 850230807, 163903541, 352403178, 989840122, 353328597, 821908097, 112341330, 944967286, 780530514, 497897131, 797367347, 106866428, 274897800, 650775621, 931069293, 489269973, 846857646, 550492863, 889364008, 824750074, 847476041, 344587006, 17090312, 417219586, 115475845, 658918142, 456945186, 196262011, 501460215, 560562431, 243929393, 69616871, 219242349, 765954463, 557205935, 975413118, 553173070, 252051003, 978284766, 56322775, 705629802, 517738636, 437991498, 90473685, 562720005, 376246965, 774491325, 457710266, 420982497, 469451740, 550315659, 793416608, 846661517, 877360925, 73644438, 988131660, 120815521, 229726560, 379916515, 135484578, 207400078, 262078712, 210700727, 48564110, 185679643, 5475685, 744272018, 79917414, 945097403, 563864518, 135311079, 328503925, 692485941, 130488168, 681140731, 705272549, 131723466, 593434343, 727695188, 775533603, 925721417, 954900136, 332835703, 476909468, 460538811, 429791164, 932616152, 154385134, 990861205, 533536016, 520770525, 276616043, 519507449, 269359571, 342354674, 112131919, 476125050, 662681930, 248671065, 556173987, 201596515, 871460262, 656634686, 333535526, 404745494, 566044601, 88839914, 6355334, 709783121, 641953885, 395029667, 104784643, 594260177, 925382171, 737819503, 938898043, 777503794, 958590645, 771062922, 493636238, 183363185, 178706388, 545811976, 359139144, 299547725, 87820624, 529986919, 338161586, 780679260, 621454174, 727113472, 440998564, 666757593, 377736432, 123620770, 356895817, 387598046, 204254870, 559740194, 218703362, 630727239, 561754564, 371194404, 842222089, 758429091, 364027397, 431902887, 968249387, 955461501, 655695405, 359931938, 330591941, 3938269, 566446995, 648535768, 901471741, 79284029, 411279825, 754143236, 60357299, 580740085, 503972262, 995770315, 543321498, 293543514, 914019026, 879493302, 540949302, 313884235, 361926923, 385144101, 940423801, 189233116, 528357160, 22469655, 781146214, 73830977, 960097761, 942412343, 6020627, 592012685, 608605120, 510191623, 680786292, 960641663, 211686182, 618817129, 771984524, 429173254, 404349063, 916981528, 664480638, 421910780, 382017402, 43182459, 327147125, 979267171, 65001715, 478699455, 424575899, 484540242, 239142060, 85594914, 672377964, 863130067, 562194407, 23977692, 617556537, 693418276, 902355317, 489952708, 16058695, 539565606, 460708669, 732765349, 153322920, 14972075, 571504169, 298563343, 574857141, 427012090, 12449616, 118878364, 483949780, 877692293, 16491775, 789412070, 741580695, 6266621, 481188298, 416624819, 52163550, 934334017, 700091407, 79247144, 23968154, 903236764, 442718664, 468641373, 406923089, 632264761, 374902878, 807419218, 431662697, 940171851, 69021456, 894419414, 601488867, 62437082, 349318684, 413724302, 745069048, 348600041, 916859128, 934869807, 457633733, 675379028, 779794825, 540140496, 853949580, 425268126, 112080353, 882295611, 278922358, 83452432, 406990505, 486340406, 805192952, 870707487, 283685086, 56595163, 437546120, 510748016, 821367251, 307344119, 740834267, 982798536, 77989955, 311260360, 948321112, 116039488, 392158288, 132652092, 533152713, 586497478, 969484785, 631325887, 717577362, 456774858, 323935135, 17498367, 701563220, 185418172, 493013173, 672881841, 361344393, 351665416, 954928029, 295358985, 163069799, 421884584, 766974329, 619625516, 312523676, 320069497, 330812980, 60660298, 288734848, 29427967, 591206280, 391076727, 774232164, 984336433, 529705811, 515002570, 316505949, 638683977, 258460977, 910436157, 641069084, 153875819, 530376885, 641148990, 705263970, 354076176, 687267609, 478333862, 848234470, 124982596, 757706973, 696286737, 482710226, 42942561, 85697887, 862885867, 475282610, 285953526, 657336329, 840811887, 390126203, 696826945, 750333948, 45480990, 130424897, 743181714, 904638699, 364958917, 632244746, 859778871, 139476096, 429452274, 169242530, 683596996, 89713011, 924338199, 685442276, 860330237, 746391611, 45482450, 459205356, 817264120, 838155467, 432453557, 208772046, 198459337, 392617898, 524340158, 177749305, 972534522, 527094485, 461665671, 298894600, 879756567, 538153165, 756902217, 548115995, 760514827, 886012456, 390296053, 323334769, 569315083, 272678520, 744343335, 282727956, 489445663, 430396546, 707772361, 338531539, 145641890, 223380359, 766186938, 229894084, 52910695, 97401807, 343212272, 982263097, 681336382, 515192600, 638687026, 765467013, 501675480, 676251425, 386092094, 371853072, 969673443, 725549722, 828468198, 867998790, 99340198, 642161523, 80882684, 207199644, 701940953, 641704656, 528694995, 491524518, 605347371, 755872489, 358442745, 720396436, 949420027, 578629157, 554259054, 212827415, 412644847, 881662786, 106525242, 684457554, 163169236, 296549828, 747327146, 405351359, 512221867, 655614988, 36163596, 129935997, 577822107, 946223906, 429501983, 896460734, 110246160, 722847183, 474716437, 537464674, 623919591, 768839599, 907502591, 718996349, 394981317, 905108327, 438112843, 783276720, 858627835, 310683395, 441697503, 798982225, 17452149, 643512334, 236116399, 892013283, 821276323, 425638018, 362623557, 876837174, 281040196, 848135263, 585971575, 400512408, 130663602, 998414685, 771192277, 549182984, 655633143, 634172361, 202546818, 84953269, 895638948, 126366211, 294999061, 514176381, 817222404, 970377709, 744176841, 96021989, 918262956, 669104748, 615394299, 220392251, 535375960, 177326961, 538906536, 551235436, 304540905, 428762551, 544238707, 917206885, 418939716, 182468454, 26413633, 864538470, 26246449, 545720863, 962618254, 56575122, 413580915, 496546184, 724850400, 971389869, 559094496, 609718409, 658665281, 487570138, 689973050, 103516450, 614015239, 912566403, 960704208, 243040568, 907979951, 1152887, 506135575, 509978180, 112070037, 430187313, 180709361, 207224652, 75218538, 642198459, 33888538, 670122878, 118487762, 663123700, 326631773, 33186651, 511809674, 119033399, 360553556, 709829999, 368036645, 407608494, 976802700, 833526790, 397473709, 491767992, 484920296, 465064499, 624347168, 396965756, 938447158, 98448025, 496071205, 54081904, 485667895, 751690440, 895724855, 67929836, 242479774, 168700491, 317629034, 9583612, 821986640, 845172180, 59223084, 370491644, 832569485, 843009966, 21152613, 951530697, 794518553, 174942798, 583603479, 610825630, 141070379, 990196326, 399771736, 379520305, 797493680, 775502833, 742735688, 469134755, 597738099, 448957071, 757584633, 35143399, 876810612, 765655984, 259447695, 989705630, 593650384, 553727648, 933791408, 860649056, 593451066, 867790881, 593630503, 405495031, 972583454, 973982873, 707583796, 121126612, 236155026, 651510291, 210229915, 146872782, 343717477, 994936426, 946427200, 231861678, 939139584, 301942083, 667104114, 337382353, 95521652, 814981632, 295864463, 124300775, 944841334, 149269959, 75693198, 206192964, 782706736, 408997908, 273529118, 479753279, 167066309, 400203204, 756252099, 915786811, 964685513, 586058001, 434819296, 240388449, 744121840, 944543252, 546799450, 489474384, 340418217, 337213767, 128418824, 360504724, 435470921, 401388618, 357020451, 607823206, 946064618, 595737037, 521746959, 79339241, 250355295, 943425574, 867511198, 945458995, 469877907, 217125788, 551571230, 886357418, 965171530, 934166359, 43087456, 48830705, 343980506, 377066804, 830196753, 391265869, 759844971, 301806541, 650189870, 773814748, 155492700, 2679293, 384998431, 200453237, 188942213, 863642271, 327706802, 466594471, 666796285, 320559457, 521213792, 191023502, 169318664, 605352796, 1111939, 433094996, 945727928, 892506551, 706889965, 918098610, 273481339, 509593783, 623739964, 847703677, 652371253, 827637326, 675525628, 935412103, 177489420, 469018155, 884216890, 233824601, 452280254, 741654529, 883076663, 404821033, 413860540, 952068261, 456585248, 532453812, 329280184, 447438722, 860549828, 676064652, 179548380, 999001669, 801262418, 972420835, 130494545, 487431675, 662329903, 632096518, 205620632, 932830560, 752758377, 842416058, 420316498, 510149387, 100060275, 518888001, 555651253, 212350497, 649362777, 924092625, 807052113, 48213931, 869921729, 252250027, 708022869, 959049096, 111510907, 412876520, 50359255, 74487520, 962789879, 718005160, 130818576, 578690438, 415718159, 696614546, 863155610, 61250377, 373028969, 97851964, 790227012, 35013368, 47996486, 885160939, 418155225, 525341155, 733653588, 356687279, 772885478, 830343632, 395428473, 219767740, 656669967, 719127581, 411498783, 900086555, 61167971, 196886391, 172157814, 776863846, 855212708, 404732215, 487301514, 216362966, 733387646, 478604553, 887892391, 264513862, 223772827, 826221580, 748642292, 159148596, 468985872, 356986562, 615698758, 854209600, 956330657, 730760329, 170274411, 597864063, 905796361, 209768253, 531256295, 548713013, 346287012, 92985129, 301103191, 63429785, 97108053, 95699237, 472865389, 535081345, 268212543, 87107549, 540669180, 434790994, 389317345, 698388686, 490878341, 393994331, 17517503, 86453285, 52519692, 658204809, 837911637, 414741752, 634980775, 437348918, 712020540, 829714913, 374985355, 704217009, 707654383, 700373435, 658314114, 102273726, 339232901, 580999425, 535727861, 497963184, 493786115, 455361397, 386241319, 515277040, 522242270, 772410439, 105719500, 278278602, 320337059, 182347438, 937108241, 309285590, 553667251, 753541121, 868763853, 56710144, 864103477, 395735927, 928144619, 955547245, 31277768, 96351044, 16450219, 984362914, 896522647, 695149819, 841016548, 181152799, 660421351, 593359111, 244067740, 572423222, 730478471, 326925173, 682738480, 281955767, 784171568, 948982309, 579300218, 812749103, 997918584, 7945926, 971941143, 189838078, 476934948, 943166555, 266886467, 624928212, 763350411, 542825593, 617614213, 395231886, 877163356, 764988077, 604058327, 97142826, 396252401, 416572417, 302015782, 204781874, 507816835, 933523428, 157339106, 53428072, 982183264, 679663788, 922988159, 422406518, 122151031, 262071358, 837741935, 420818803, 338823626, 622596185, 339087987, 225181364, 391534612, 168222104, 86647746, 462795872, 491043281, 56047597, 437654649, 100148331, 957428321, 849096725, 146071918, 775347252, 67790628, 173949037, 939337575, 523484072, 760279270, 718096596, 340662263, 844548445, 292021890, 212162932, 676529880, 840133080, 733387134, 820394909, 40878915, 399455873, 835245300, 438620688, 195892453, 372445671, 793995528, 935005950, 672935865, 964332600, 863567428, 696029825, 270000613, 698352027, 935322204, 420198114, 826729316, 596735411, 724742346, 641744743, 107711724, 695246792, 594096659, 909863766, 131843677, 789215769, 416215742, 102596729, 442802779, 172188503, 612070396, 386375813, 280350512, 762982054, 530607170, 664328561, 449749847, 185881512, 758450792, 435161528, 534377007, 640764065, 914908542, 405180912, 467301828, 653687727, 576934313, 224182368, 723887014, 303126103, 754546969, 257868042, 658053900, 234998327, 663239579, 139603424, 455155337, 832259104, 848443418, 738617561, 452572648, 450633489, 246345477, 28470513, 980281646, 817437328, 587094221, 924065041, 281507040, 747866634, 166075219, 790696921, 110246296, 297000415, 451624130, 22789291, 162882186, 409878784, 166468303, 480174105, 92384632, 273247953, 428451961, 619041692, 582423702, 156186381, 116268524, 816839659, 433009084, 985122014, 121906727, 1995819, 714095430, 951605940, 620287748, 709909897, 850310923, 382284499, 93670134, 379214117, 438521244, 864217084, 652021218, 820196065, 309718732, 145447777, 958356152, 43520025, 198742277, 835295111, 102908403, 781280228, 260585538, 563763694, 593487301, 289249057, 955319578, 104981506, 49593718, 52686675, 371717964, 934188081, 325742178, 855396720, 215261569, 919112038, 622008139, 595458775, 224718474, 532139794, 728707224, 173235636, 360719369, 605562614, 788517191, 315222212, 450410975, 760520169, 815662172, 995015839, 626264090, 137862725, 856816793, 128770860, 130455653, 114314410, 532188591, 693628922, 623267538, 692750009, 221765298, 619123094, 294539155, 203294691, 799898578, 916829366, 771523674, 173164595, 390676788, 152187398, 683868700, 713881763, 536535924, 665063225, 913512335, 975105837, 318757475, 951882141, 703011297, 221780484, 115060606, 979838425, 704889649, 820502677, 847857803, 130625894, 73798403, 453257207, 676151252, 103064657, 186528851, 626416045, 895869936, 575751359, 102665153, 756928228, 869818140, 316904875, 157042527, 843710452, 815580041, 205056727, 17787870, 259851536, 174842101, 987435692, 286913547, 981585605, 434810274, 407154457, 384890331, 169856105, 134332860, 926005108, 177829209, 706136185, 584947819, 300046186, 461261439, 995277732, 190960792, 896470406, 161999087, 101280244, 193490179, 167041804, 290858963, 825346886, 520235463, 375369648, 213039203, 515213361, 375471291, 756310425, 698343314, 722486332, 897699652, 713844721, 170152881, 852463341, 371478912, 257917016, 463184677, 500729833, 8723592, 558349747, 566847014, 431626686, 834023904, 756745998, 344714181, 88516086, 35287459, 559877711, 124811655, 727090523, 914876540, 438815514, 494620001, 979849032, 748444585, 516906865, 230007951, 901317052, 983150477, 818680557, 512981785, 156941717, 607598977, 343866689, 779679015, 650250554, 911215880, 324788636, 279882096, 585754285, 705726078, 262277397, 636621846, 344974230, 874287572, 548392622, 484854270, 444353613, 151437970, 495005351, 423405417, 510579167, 520989417, 376677037, 296044716, 525249211, 805384834, 778544289, 909120990, 695543855, 838739941, 849573059, 723463315, 922195413, 642418811, 501215474, 939640666, 545194259, 317446042, 653196500, 454888835, 322596769, 932714468, 398655822, 373104263, 692384198, 635567851, 203644234, 105338398, 758873252, 929381758, 736254414, 538587588, 389892970, 117467790, 394351796, 529164253, 55265601, 879791433, 321362405, 36666368, 405773433, 480595784, 662509727, 502085824, 267580561, 50574006, 139520860, 687557281, 885476689, 433398757, 749984473, 496757122, 518701500, 901408638, 485461845, 785980349, 324133774, 792404586, 339784267, 267528837, 962348167, 754869798, 294397459, 774408094, 790110767, 761113932, 167164060, 514870569, 582150033, 621011333, 105778665, 190442427, 240972649, 300437511, 176398521, 16542531, 239310871, 82113950, 407866672, 349662604, 677130425, 451750009, 195354906, 163798478, 553044296, 380411329, 14663896, 611034846, 387016684, 777754737, 85179293, 995178033, 752098096, 312719473, 724670003, 851476651, 673301033, 435727758, 937714, 194341371, 301023625, 365063132, 18393427, 705702430, 854408063, 66552986, 557530089, 186485543, 506784857, 751737394, 8439534, 110801598, 975925764, 535859625, 577770174, 669088226, 569520671, 542697766, 685009502, 533734284, 784521914, 578750553, 540252565, 718162505, 264472676, 891430165, 708051121, 496738585, 996098157, 664490178, 635939017, 669449864, 639601283, 843722379, 923819166, 676066477, 644260761, 634922452, 420435872, 213725653, 912555932, 857496388, 420824724, 285861182, 872035357, 543423478, 240622481, 197858650, 774928406, 843224840, 536118928, 429694043, 665160919, 945719390, 181128627, 403296906, 983445974, 842740842, 416944163, 614961227, 948469830, 20977508, 375618836, 88761106, 811450492, 144492122, 737901842, 894373371, 869873017, 639279167, 825330599, 911964195, 17654372, 422629609, 195789597, 635771348, 627466410, 779070911, 405475089, 500538477, 40005515, 862141457, 578025335, 234251874, 573717387, 624407362, 294022705, 303929763, 74043209, 456893321, 254579128, 149753515, 573302895, 613698816, 139840234, 425168821, 423651589, 716549076, 370169112, 217275132, 936788949, 686462628, 686511957, 563959070, 106423898, 673882925, 348720667, 352672556, 252534581, 380002714, 423661881, 485640555, 262492689, 881141713, 621213788, 901944958, 831080132, 440048593, 271481522, 917425560, 671893668, 65383977, 711364091, 954135232, 237372123, 854571080, 144994922, 90476956, 567031811, 770904277, 964475060, 87865424, 720133538, 844029170, 278508383, 572673894, 876449563, 203243439, 454174163, 60400419, 730336478, 686744887, 392165796, 70939660, 995563757, 197103345, 417440706, 4252941, 228126127, 37837655, 939536985, 704148091, 612487977, 802113791, 892924115, 507560844, 971925265, 94649177, 982260892, 942392971, 423236281, 771736655, 474686121, 108843077, 511924917, 786841425, 558310422, 820991138, 299525518, 332941057, 227654251, 216959266, 677417668, 288074583, 38771903, 619963334, 842357090, 444887164, 780201540, 844339200, 205658227, 632357652, 443952306, 102000235, 678887120, 401900714, 84899237, 345508243, 849519288, 727723712, 38171854, 131803893, 750575261, 171109172, 939982803, 528269235, 466868854, 950532058, 698648799, 222143639, 500497360, 955127831, 26188265, 760667465, 469490445, 346199553, 271624047, 693244695, 563988728, 800651274, 598150786, 697445050, 702357782, 946866134, 24530627, 396194159, 255366326, 863638034, 344569231, 478789311, 957419727, 228810149, 186468934, 474555747, 419695704, 994153131, 191464289, 107907989, 667725797, 743878129, 429115835, 527295383, 372125634, 185083037, 317224017, 837066207, 307959533, 726127306, 44746661, 864495180, 364549963, 474850032, 59735754, 277731218, 369979832, 737926928, 541411623, 11394831, 229289690, 386923351, 691729798, 421999627, 50108102, 542177989, 530100485, 10973103, 805943964, 77808920, 266348468, 668368967, 709208660, 648970051, 738903436, 738760879, 508465731, 469813165, 651773850, 12323636, 38316771, 100597539, 290097912, 702453113, 908209048, 521619188, 221290222, 630520274, 848906467, 321323926, 314826341, 646780082, 654078829, 895981822, 597547806, 666093067, 359935608, 738170327, 943856814, 154977015, 125684817, 299252292, 749371917, 125654826, 790833315, 867425103, 431826776, 573214977, 392085536, 19647281, 899955597, 351544811, 179743202, 778947463, 682569786, 295786806, 120424926, 432258425, 808327262, 541632387, 77006761, 234611872, 996917587, 398172216, 791498968, 472513433, 471406992, 592110577, 810740872, 999255510, 28978126, 469366029, 770153666, 526487196, 764692925, 315544851, 993453518, 182957890, 732682798, 197725320, 441836087, 936710719, 733291717, 310186000, 723406393, 767060486, 828170845, 415886770, 542767137, 854426404, 129897288, 769891751, 88328822, 11962373, 277826826, 245397794, 131625949, 848524921, 577225595, 247839883, 628164928, 336485645, 65316901, 391134399, 931314199, 521371960, 960551495, 32804015, 632377324, 240330413, 33772712, 837576194, 696327473, 206733634, 683910296, 891154820, 168331053, 786509922, 141582949, 540110374, 387351271, 373697711, 665226620, 585639259, 190377918, 956817297, 77862662, 23762947, 146096144, 492857839, 768241889, 853257324, 685038429, 746607997, 220262915, 256103565, 964320401, 474044599, 618335876, 84208335, 484043076, 641009996, 5611438, 812989284, 275548955, 713606366, 268629242, 614592398, 299883139, 414301554, 596859058, 602349076, 625297258, 498474130, 886125663, 34331395, 819676247, 658293244, 61266203, 559585079, 691867707, 659828202, 346418608, 190567580, 418014177, 396660480, 48333228, 269452595, 950260738, 216244296, 269758505, 452595213, 699731462, 87987054, 380340215, 86507604, 459427532, 309157503, 305363415, 452347479, 366056098, 962595792, 816577362, 793270609, 425637203, 85127138, 856652639, 931342252, 466963018, 998644361, 705604019, 14046992, 69973764, 249939690, 707845819, 728816603, 797659942, 67617672, 621202609, 498204710, 122167116, 133612345, 149347508, 600402149, 164292450, 209846578, 657596272, 33930451, 536648478, 519697924, 548391889, 718178149, 95147481, 796739914, 696775453, 809532215, 318384693, 746698968, 688327330, 826165508, 580311339, 326219281, 332671319, 584322904, 265425760, 331323973, 409864434, 432161741, 840113490, 64150982, 521751159, 505792352, 542051060, 370640410, 116899484, 3965498, 369306132, 949479820, 932653599, 27375833, 17201535, 111059276, 493946450, 802217766, 523603583, 841657009, 49146909, 944915866, 53705873, 430027630, 546738660, 755325887, 305231495, 279045441, 746101897, 245640201, 526687566, 579464903, 725324425, 435476384, 965942646, 195741580, 377786221, 907798027, 512867858, 330151488, 628722898, 533325506, 920601471, 854161478, 550863891, 286896378, 727975186, 14186016, 173815983, 287647707, 218252883, 527887335, 130493876, 843573673, 660993856, 356588764, 13126900, 844269641, 222429411, 963820063, 166888328, 638291995, 768569763, 611521398, 825109344, 77258492, 603236174, 516767364, 600822438, 609758628, 220208019, 682587722, 992649978, 641459439, 443555466, 5022732, 674318840, 278286254, 484139367, 320526308, 300556637, 821516228, 962506372, 477473640, 604990580, 859145182, 227591966, 753484264, 290527847, 243173416, 776700044, 597012394, 639081421, 463799270, 643382952, 427258623, 208227119, 438938776, 155389589, 411396401, 620743, 122386681, 745303537, 597547071, 302694690, 211541248, 498919071, 406195876, 977298744, 342000094, 667516297, 107827087, 226136126, 840121561, 437484382, 592086124, 865271491, 255449335, 787160709, 7563588, 324024360, 939196593, 182324162, 548367080, 23140856, 732466845, 3806670, 990382086, 360659265, 303713353, 736114117, 970975981, 327929931, 650783212, 609311887, 245674318, 506112436, 380948746, 570098250, 834893474, 286775549, 369642155, 648697912, 17877171, 661434999, 127307823, 873560346, 733532411, 507429813, 599592457, 725229888, 318912651, 894571159, 261938624, 466647680, 340702285, 291942429, 332530291, 378530425, 574609003, 688237479, 357327144, 893270043, 632299890, 448646638, 585063026, 130583152, 402101030, 488885178, 902137040, 110947430, 932540012, 526106725, 956743660, 462721746, 738541046, 25847871, 265167406, 483301568, 73496970, 942642614, 96116188, 753017821, 542762319, 8351858, 399165154, 636573052, 764895392, 703026388, 919369893, 704475418, 48333142, 648196524, 804086470, 277453312, 91396242, 359639930, 347946145, 950484168, 857624734, 971972540, 890974588, 584600519, 80956428, 405791520, 624924663, 581627315, 901745095, 118422088, 689508128, 500218532, 494870349, 763115904, 562511797, 103777375, 733250532, 726115378, 620336263, 976939759, 349728986, 75854919, 339106147, 448330689, 996940471, 141290089, 875403813, 460505375, 580541882, 395237899, 909778925, 323759104, 546262288, 725781556, 97429582, 415635000, 97855898, 55812782, 500777081, 782648116, 855645718, 684615743, 765170695, 332500145, 932483530, 850311878, 417317171, 529247051, 72365658, 200530030, 691333369, 107783799, 798635939, 239913841, 774071237, 902809367, 544344398, 382898614, 22773081, 981076315, 649022097, 806333517, 167032411, 371536230, 53921980, 878856096, 242535103, 642420011, 84214249, 60709726, 187062432, 904239623, 105852238, 522395343, 11034628, 206540395, 143805959, 831723328, 146472449, 926876321, 57721881, 321767186, 724285421, 89525524, 292784964, 743156423, 960017191, 451837955, 526670824, 112047742, 658011623, 504411301, 335586096, 584534215, 841401995, 888831379, 548305723, 157713972, 904810846, 353897721, 510473384, 172727436, 290215090, 970485704, 710625589, 881455675, 912482780, 772198287, 222056893, 63536236, 347712106, 366467053, 979773266, 405762235, 106407147, 201649980, 759076045, 585155569, 883424739, 643005512, 610867329, 553921753, 199001012, 466014558, 869638896, 693081159, 873487832, 708302927, 284316835, 118674919, 463731581, 557125655, 967922534, 13144241, 158924651, 677934614, 86227882, 246344169, 967068915, 789277973, 236843702, 885033430, 886391238, 719724116, 637123166, 937180780, 194305999, 816526175, 93765364, 24487789, 253644746, 648538190, 261960061, 332811026, 993638319, 552207707, 585121350, 193428656, 242655386, 769116062, 355567151, 864917497, 978048738, 71971967, 190445710, 628629518, 242627418, 655729094, 848156856, 532348930, 19177077, 645300430, 401049990, 876651780, 700738568, 893522244, 419739919, 980085035, 351864110, 808696824, 150135578, 556624744, 322184540, 1050495, 606935430, 921752828, 950805415, 939955806, 630408911, 203360704, 112424005, 115784310, 123265828, 78563837, 942909185, 98761543, 763363409, 1103975, 262219919, 391994246, 492868799, 940067999, 348986552, 247966563, 321016312, 634055367, 424025834, 975256771, 505035284, 886494646, 600904663, 115563080, 296486401, 502984529, 493971873, 264398970, 447326132, 354128802, 526754508, 577030406, 724367783, 916153347, 371762110, 716226484, 376939559, 117253432, 255059022, 767470610, 593807601, 814083213, 592400672, 58804411, 250277657, 911444946, 347161062, 41359540, 37857189, 407983371, 108284201, 222575705, 278676894, 474492691, 697614202, 968796489, 492180937, 951141242, 576662254, 4473929, 828049513, 530011819, 775730178, 805068532, 90744971, 648789132, 727871012, 220219158, 567094297, 806799375, 987997350, 891354335, 791209636, 309726276, 767280041, 660889180, 199030280, 719378141, 733044195, 857960980, 828828686, 572693255, 731425453, 301482852, 151648131, 590025667, 74988254, 885344244, 387657684, 95700878, 601467087, 620658621, 958519518, 226950379, 804748161, 861864201, 707089591, 342686239, 454208930, 332829279, 784167039, 954961372, 777318077, 627838902, 887865292, 411915829, 710274146, 152492861, 518572240, 696867540, 693937885, 283506387, 874340100, 382104002, 809537558, 917653266, 683423095, 861966404, 654463950, 442636349, 554095315, 694877562, 425946676, 907654040, 324542271, 186064290, 272195661, 828024924, 951709389, 166225233, 930756509, 133769809, 708467936, 305179090, 659839025, 829446847, 237912998, 774791444, 242503906, 42219852, 917710434, 490132113, 262249696, 421403177, 113794895, 332078513, 192721381, 618044510, 55014835, 721912529, 164796993, 536630501, 658448473, 200190964, 42260873, 667037386, 939177811, 27832008, 328963225, 316502013, 254417887, 755481267, 429030142, 386068956, 692164054, 604922891, 846780096, 138999278, 962290413, 891842943, 780393512, 747785877, 332406082, 857997880, 275827588, 886005847, 235635918, 257071505, 329500796, 208145765, 156967933, 866145447, 885000149, 597164854, 350142369, 219825853, 885856535, 851204224, 414811878, 756371404, 42800631, 31713569, 95397717, 409164325, 247767140, 328628022, 756960442, 471274703, 710512299, 829460257, 863876036, 389437872, 658770143, 22172126, 385030990, 795414311, 943927869, 73056133, 401722348, 122340217, 223904193, 209236439, 221272141, 413298872, 112877390, 321707749, 700901233, 206455464, 390172356, 312636830, 895077187, 612655497, 507721886, 460730459, 376803479, 343702206, 116723433, 995276065, 779445882, 845719589, 443773984, 945861996, 452663978, 189135708, 134586156, 540112574, 344338728, 737083881, 637315148, 328080948, 568501933, 651586206, 736915574, 473740, 562215498, 218714571, 378421823, 841145166, 957772064, 772994453, 608082480, 166472474, 208424384, 866707832, 556271952, 595575578, 225441764, 376688139, 893634749, 316447175, 627683280, 212498538, 561098538, 259307305, 570383257, 464461715, 482525091, 49772610, 261135864, 840457529, 61030949, 119593645, 212791808, 928083336, 174926628, 878699517, 836571245, 674607081, 39010040, 434306302, 234005150, 653411823, 463736231, 818313260, 689020235, 362687562, 899415023, 944119294, 612516391, 684514184, 307346881, 270316628, 758176550, 297291058, 628547133, 479573148, 935410273, 331632011, 722554706, 481087886, 697803462, 629864470, 946794369, 52449181, 525762369, 345335975, 659555336, 409492837, 15055462, 800424998, 576020703, 298389581, 965736510, 490641512, 780164950, 39507803, 6466752, 319833158, 247873367, 201455205, 931332257, 213221646, 63750565, 337098386, 757510442, 246100407, 802934349, 111179302, 576695987, 312477188, 934549420, 564693685, 762671603, 649925744, 269453916, 698807477, 911407500, 681409762, 145073922, 161043254, 35910947, 84625942, 291279189, 448195724, 47622020, 865943132, 687776503, 276028330, 720782685, 92380665, 839835037, 271389789, 672210892, 605511036, 282501833, 839436966, 963635776, 975349268, 524719697, 843483114, 434431214, 392151725, 639324798, 485476276, 370009010, 858868113, 951713922, 426219627, 986918872, 263625328, 479505992, 71084262, 900832784, 63199771, 459387922, 508658446, 619964666, 190759720, 410736968, 579024339, 694297353, 526405176, 135463388, 900265583, 237512927, 148699810, 242238384, 97736518, 953008562, 666879706, 660494608, 358703146, 855140195, 99505929, 852326626, 457477591, 671552633, 824148336, 4685967, 49132321, 87300674, 529668722, 677806614, 86358815, 749788705, 356915351, 505688446, 128106539, 168330657, 395149659, 861344797, 188181075, 965491019, 438878750, 41769207, 701873142, 314435564, 272830064, 189618977, 90507872, 785621473, 959139959, 921031628, 995547759, 77067497, 238518644, 414702415, 475543539, 995978543, 366310992, 636726356, 240173717, 868665019, 654120675, 386365041, 699572787, 213016141, 828582444, 817332032, 630829289, 873668017, 437453268, 337951049, 739696242, 960277922, 130869114, 908233754, 185703222, 33017525, 785927028, 294634025, 831646486, 761880742, 540353840, 455837007, 964264722, 645467578, 236778530, 495597883, 405009583, 145958568, 544910592, 638175233, 426210089, 120532704, 742614618, 569406610, 688285811, 148815018, 861500865, 587878971, 304772534, 502328654, 825530409, 46108979, 432428994, 581947460, 647392304, 164469056, 640071673, 686356950, 754239008, 898701195, 63052740, 160714364, 286232230, 102877527, 27015580, 157677953, 219716295, 935051367, 15914961, 247072265, 916029868, 882391150, 602529558, 29814421, 556448577, 754703466, 356347478, 640007994, 53979037, 698797802, 638940652, 30365844, 431142661, 28089855, 626285558, 513920241, 791054692, 779028460, 419436514, 905756106, 304499080, 790497132, 935961619, 217590163, 19580008, 952717189, 397367391, 594311431, 98131242, 112294187, 6692661, 664885262, 800289138, 237387796, 525153419, 748503678, 697116071, 799491318, 439227279, 413686850, 737619754, 497429012, 271017983, 511522618, 481106043, 437885826, 489058586, 52502244, 867584423, 864696543, 254486995, 330113112, 338973185, 525945821, 615689395, 884570166, 221126155, 849958016, 818032566, 894104479, 259823503, 484921126, 697770707, 519864467, 812285322, 910856181, 911275064, 384195104, 372036899, 176511877, 796000675, 511897162, 298805337, 359944969, 471044520, 602308545, 428641464, 805157538, 914514857, 590519747, 648787127, 478255836, 799999529, 385629049, 391766628, 117128215, 134440716, 264926607, 407935499, 560783518, 419249487, 244321871, 306517158, 405208305, 526420083, 216270789, 8474067, 956979834, 96216400, 381028744, 810801464, 373862079, 397091242, 326590318, 40353157, 839157549, 285400708, 938744898, 5499326, 46495373, 683769013, 710535712, 795152260, 756502725, 323412897, 280619010, 654148924, 420971315, 24535245, 965289923, 972456317, 461392825, 817385431, 951637831, 881714418, 803842524, 392267455, 861420026, 674825653, 192869687, 579364172, 277694848, 205494563, 44141357, 633416873, 324350534, 198256247, 108088400, 212181236, 470729431, 692835001, 730634279, 827917301, 872938420, 614946180, 788342060, 949478086, 805090530, 740009161, 14424211, 492919961, 650335505, 858622714, 991168539, 452432837, 5207303, 571263437, 325842754, 489658914, 257881471, 734827598, 613778147, 577948939, 578868987, 355529409, 864521079, 79226262, 246634667, 661942372, 62816469, 649110410, 710481416, 951522219, 895200009, 901766786, 769181756, 627299140, 209653657, 681242407, 670675888, 791164286, 68761525, 362922455, 193543204, 786589783, 196733798, 840303664, 374738447, 151364976, 664982449, 745728606, 822177065, 393891600, 328396500, 199239512, 858595925, 731286067, 454314817, 53345079, 757024464, 119228865, 395332022, 231469042, 31720632, 132443737, 662762630, 394055604, 70003445, 471108718, 306121896, 770720629, 286951106, 330837869, 932333037, 632164944, 482008177, 671753792, 931213919, 270947162, 532202632, 743754406, 349662246, 740378917, 488034727, 322012784, 902386204, 127328858, 259453306, 171610591, 775414506, 94896879, 680364659, 212425262, 868199697, 219967010, 737551921, 582313647, 135986035, 90161435, 736801758, 688458479, 717732074, 189618168, 583824821, 533583028, 741984134, 327452889, 851159126, 397813540, 154789385, 899210908, 79485603, 59818866, 970888717, 349528884, 425993536, 229585377, 781085448, 859354881, 696373849, 940883486, 774031987, 138581218, 250181149, 713436386, 202601682, 658514680, 522275398, 708297064, 848796814, 586216010, 104102780, 70149850, 498066203, 793154606, 477911934, 328131421, 666229211, 117154363, 504405502, 365250879, 515026716, 25357287, 183817455, 155395130, 13385820, 489502432, 402388438, 479675141, 317333821, 54070591, 261513009, 362643307, 465622654, 472387059, 527375502, 82577807, 241856030, 172759680, 968936335, 812833506, 689744680, 806007099, 54512692, 362145023, 364822816, 724423038, 941150486, 615944063, 419660310, 62772854, 325835688, 227963796, 296034672, 750553073, 486239741, 674493387, 700717979, 296422763, 749921151, 370544594, 593357838, 637068808, 970774042, 660145380, 35546909, 996542514, 190205783, 491520329, 434277684, 907335347, 98863003, 171848829, 554962276, 7586700, 138878565, 641178340, 163097865, 491285641, 792442580, 428629835, 122670368, 676375517, 17023528, 865018089, 239286800, 399482577, 575282880, 856414461, 958453571, 458767471, 270356808, 640461980, 362137483, 971368137, 499254615, 246559811, 574642447, 41647430, 608276264, 128652553, 509469352, 919623409, 923579159, 530149614, 212630991, 775788371, 239078961, 734707247, 459709458, 358889789, 49427458, 760660728, 340507630, 524300311, 691488141, 583305625, 959161417, 601127453, 586781433, 485997683, 414997229, 993041117, 318703327, 608324746, 142021625, 309610180, 886900585, 785523270, 64814911, 358861224, 326110799, 209831017, 274684814, 155961658, 761214484, 633640985, 524258445, 832609694, 499290424, 567438577, 834167036, 254264791, 988490749, 6021067, 353439333, 586416614, 989211773, 238462618, 992361863, 202196607, 285309967, 185312758, 409380164, 492985015, 725751526, 293081843, 882496721, 946770496, 210573105, 442543619, 953578385, 179412053, 854778059, 950152338, 590184326, 6520878, 906805639, 764936349, 130341174, 640077523, 468068691, 920964130, 495964051, 145506515, 149170093, 625564922, 780393779, 237314945, 302692348, 203409047, 162051282, 876016657, 293664565, 23559987, 407588560, 950466118, 317160723, 605845680, 149652602, 901799245, 918497203, 724580152, 295244578, 821085135, 432586745, 110158255, 848847578, 779246670, 228537370, 265695054, 237234830, 896548747, 108486180, 419843335, 125103471, 427430194, 833636969, 963289574, 208476367, 320811440, 154853704, 635302121, 559005456, 149297797, 163595911, 472582143, 669351738, 285893986, 76854190, 543717592, 476394401, 487297699, 333302360, 682387392, 800953918, 512376139, 50865918, 8186243, 983499091, 941679034, 417753763, 707666402, 1686204, 987762302, 407595046, 57436207, 934689038, 54718152, 137072548, 20011749, 44629575, 184049561, 461888891, 699977831, 714633555, 515090437, 745759569, 345697308, 578981237, 982834397, 367550750, 665622980, 113658632, 692546460, 971894358, 119744079, 790934359, 680178653, 629074336, 772950221, 833514596, 147773290, 655860794, 882428647, 973844403, 516337935, 574694611, 828297889, 239178747, 6114549, 61342943, 88895314, 809968016, 205725171, 258224363, 796223570, 761721948, 471279485, 228904245, 410085982, 754952507, 459686926, 156504911, 832060701, 483494994, 352156160, 68442393, 177428226, 794157332, 770194295, 155943759, 431778733, 240436586, 712395669, 692575165, 329832850, 907480787, 5106536, 434829130, 928398667, 594379737, 252812846, 786636245, 508017330, 954116749, 668132835, 471643992, 742356602, 921793378, 207962298, 338584388, 981989203, 95393126, 309741252, 562249921, 968515486, 283853738, 111909021, 64873069, 392066491, 786224036, 384745153, 432159302, 707605887, 796079971, 408435009, 103613884, 929803431, 13785596, 201488001, 688783833, 92377753, 101474723, 125443091, 861708627, 472709796, 540805627, 377976947, 176913302, 158333076, 506165246, 541964132, 10392117, 346849909, 594031526, 148503443, 15402806, 874535504, 100583460, 668496956, 267379183, 354184703, 784871223, 206504443, 31907006, 369991762, 554085565, 584730131, 513761946, 569238526, 55699016, 77402009, 992491593, 456520058, 421044701, 696980228, 47919808, 17167158, 718171160, 11645337, 971141018, 477225934, 911017103, 542882020, 285122533, 436596854, 942607036, 116465193, 713413115, 608556252, 524828459, 178825971, 55910716, 833351394, 792379444, 340471697, 973120825, 145563327, 63685981, 597231883, 512872970, 877184191, 544907782, 960362070, 32733943, 726963446, 33594400, 537105434, 742101526, 548503137, 531570831, 37634932, 462883670, 383165509, 913852140, 517456257, 177860176, 278263703, 318594220, 743230198, 563153302, 266629564, 747406016, 413165041, 761726421, 535137531, 882459870, 223573856, 781169760, 277512849, 512736831, 346202255, 811260702, 898844042, 278800641, 69977398, 194559613, 121494405, 596540890, 633550886, 872337438, 843481844, 835112833, 486236612, 410711873, 579537970, 46136103, 232467619, 527392087, 409613329, 465730606, 387181738, 643465201, 3206321, 235376649, 767626858, 548906120, 366579560, 114641887, 567713518, 548174255, 257594088, 831278818, 878868588, 247716576, 779433362, 305089482, 442127831, 945854834, 554849953, 816605368, 6736003, 870161955, 958703754, 697648506, 321463796, 717151218, 769523459, 215520512, 269927561, 640235880, 176746727, 1886674, 140993066, 240976877, 205151135, 823232415, 294898189, 665097099, 638278335, 934512789, 495852701, 610732876, 203041353, 205725747, 945043229, 911510103, 647580644, 3272692, 67226326, 893476968, 602879623, 134942457, 709883698, 90414599, 205927767, 271284613, 646897452, 238102555, 72153076, 339872209, 242404795, 64453526, 94004915, 815096114, 680119845, 803100913, 224686580, 323586861, 497577206, 459381439, 30041021, 259402501, 926701834, 971361755, 910775044, 726873498, 428663048, 649004225, 928908682, 530297808, 420566638, 152169955, 552053017, 59708118, 954655103, 768862759, 257575941, 773381467, 445868825, 272939704, 665424551, 337220882, 576316151, 202388202, 876806173, 246133566, 76704042, 669862975, 214287948, 242577006, 307964704, 830259160, 251587686, 79967239, 62246358, 973287214, 681041823, 251552416, 405246804, 41180119, 292955491, 469472928, 657130830, 927556467, 495373005, 257608128, 172733391, 32872548, 530693010, 866272845, 998422937, 320914268, 721830743, 495250810, 470569528, 852778764, 190174841, 105260844, 885544424, 170711356, 566644050, 734639498, 621286817, 984282986, 974156196, 193328751, 976041603, 814681929, 739757013, 272725499, 27269795, 506129893, 765035982, 539933430, 491011253, 601555142, 813947718, 879553550, 909351072, 419947085, 433746839, 125390469, 70713663, 995000517, 935105, 819992348, 78585273, 458484882, 631086092, 265053202, 827576797, 191287887, 42227274, 401687216, 685128140, 380283279, 351861034, 331702074, 451947494, 590248865, 381459779, 939503715, 355227980, 350190526, 322421187, 414258782, 424899042, 482351483, 67115039, 387010276, 269084664, 39778905, 718946053, 337260111, 460697023, 638024669, 956168538, 498077056, 360451233, 17803851, 38988814, 912055811, 950746020, 779555083, 849910879, 669272608, 270738539, 976066417, 136134048, 245378104, 801422853, 428363298, 819542338, 605820784, 838327956, 683946083, 452821207, 544917368, 69734191, 571818824, 573686259, 782384036, 514828917, 896917356, 117214850, 853559478, 569765715, 14676139, 446375733, 491352243, 613295320, 379155469, 589711062, 387973775, 827846263, 978597893, 407548407, 321775064, 892004132, 774005256, 55006817, 935176115, 874202032, 420369813, 34676962, 696842763, 439778231, 733584352, 932278615, 732934862, 922800307, 500548770, 534942400, 231093280, 913910895, 414352494, 219930450, 738617066, 835563112, 101621025, 247871277, 981038997, 854057028, 258486015, 645563347, 160628076, 799252598, 694920123, 160838808, 149036397, 581759251, 529174581, 526686572, 448967583, 159430113, 733521453, 712051757, 337961693, 387108454, 520126054, 259890612, 545238586, 332970266, 839879276, 550375257, 989728992, 937407597, 37813092, 103442885, 575684295, 781542580, 21693693, 467629246, 616321428, 522226835, 624160937, 599973782, 525222365, 560639498, 665791515, 406790220, 638278484, 643220253, 971354845, 218261187, 539866601, 757352946, 393001729, 5823919, 647899249, 980683270, 409711134, 418324797, 889794557, 459526138, 76304238, 574598972, 32845616, 475490936, 802842962, 59987540, 746710737, 720148688, 632986130, 429748756, 670796994, 647808706, 536019876, 558724897, 167379049, 462388029, 39271560, 647570283, 571584072, 729822266, 30251466, 575318159, 912427509, 146449023, 909432313, 595979632, 287226712, 386134777, 885411822, 982485906, 127118830, 987620875, 886052590, 340570007, 322238073, 303473907, 118916009, 861036335, 674902458, 968206609, 312791991, 128670871, 301500647, 7514429, 355372418, 477384918, 867367411, 398654083, 539874216, 791647323, 123737552, 615824928, 729243688, 493763125, 586746368, 914373545, 412399739, 439019141, 865603074, 434043757, 930073223, 977204973, 80712974, 941385011, 966369600, 675572081, 732198539, 299903746, 607072696, 912838211, 329010645, 359441478, 992377994, 595616720, 832493505, 54736245, 38403509, 313098117, 311600072, 157725545, 994345641, 128066431, 281633394, 426910619, 316364121, 925094388, 54521614, 13261, 819620326, 719995225, 971588225, 267773901, 609365086, 967746415, 841901899, 648846768, 214092593, 182372269, 244538522, 246961691, 213645815, 430752672, 760301329, 290676321, 669929309, 334529266, 671735764, 136965716, 45709269, 138161392, 835207426, 469651515, 84584701, 146107690, 175753689, 510564103, 15641512, 943022680, 633869251, 153797579, 848081137, 970847288, 66633236, 964702551, 799655405, 456784253, 599419712, 678560127, 240662247, 39595078, 110448432, 638294939, 903273065, 635114807, 162716292, 921151708, 171621479, 769220134, 299017133, 117723698, 780688097, 682554676, 362756803, 990411939, 739879747, 92250652, 737263150, 383968711, 392406596, 86019141, 121906088, 756338318, 620084322, 606133528, 834432888, 865895871, 520152913, 625533185, 732877069, 962983248, 622453085, 189179064, 664814636, 726674498, 384284330, 547742560, 896830670, 225840873, 450695344, 294998934, 34881951, 472817272, 407618920, 176365444, 762949389, 569412526, 837479431, 482270126, 48174034, 85328993, 438481390, 92480864, 395414628, 999205997, 675664011, 119499333, 385465360, 917922759, 160291398, 877971804, 529980353, 414964726, 182598492, 379427294, 11973472, 515253518, 402415750, 565794813, 321212845, 558986705, 292117094, 337217174, 987129901, 554104290, 348325081, 68089841, 981519786, 136538176, 114728685, 3770099, 197573660, 24353988, 698109377, 902660566, 451130778, 982433787, 782923651, 218945078, 962736037, 43656479, 995536137, 533599826, 955934454, 242161409, 713920999, 770072443, 880660909, 7629113, 772756801, 138345218, 725610328, 377298041, 324773719, 942926200, 703813698, 622734581, 28744140, 416610253, 713779030, 911041348, 595920066, 519305168, 30781194, 90961383, 607488400, 605767491, 695762823, 978420952, 82265489, 721300720, 770769124, 150569321, 680687340, 770582568, 714401748, 285568329, 597696194, 506649923, 449469490, 409634742, 73162029, 978896515, 876691307, 40552384, 600412493, 539917575, 397685658, 125102813, 814684577, 777765892, 148533029, 999502049, 170980716, 176917622, 836404437, 195857216, 785590687, 264471640, 283338040, 303691528, 727295979, 988454504, 496212878, 328212114, 64380885, 44258916, 926952503, 586215034, 627441447, 446238137, 295922900, 71179877, 789520209, 184125662, 224771143, 34354515, 619871488, 281113270, 296619234, 973957569, 701479642, 91284183, 667180980, 625519435, 797888627, 118067800, 272427543, 971342835, 933434162, 610100814, 729131809, 748454479, 636196841, 285278543, 828467848, 394842147, 365516998, 527598519, 127993289, 118617337, 115766664, 502759711, 858988076, 561473775, 698276017, 476137647, 702810438, 254007351, 795720301, 527377874, 673760516, 80412798, 542270010, 959940028, 490268989, 322632108, 788694372, 843050796, 61270236, 242950287, 159200749, 928748479, 974076530, 375559294, 816640841, 283887989, 527887529, 746720961, 964821997, 237531708, 155387048, 778440515, 26839198, 953634599, 629506229, 74071077, 894956899, 149091767, 316165111, 736481288, 399009933, 829696482, 600054701, 206537886, 659192594, 153172185, 677101334, 431034993, 933261266, 768072567, 660425242, 66790372, 481177545, 535338940, 3460090, 13596271, 832631439, 936637380, 204872955, 30933021, 588439834, 490723478, 715409474, 578599220, 673340032, 840517704, 636882958, 263911695, 867655232, 535788604, 136832701, 176711439, 466886237, 744303487, 252813300, 721131679, 19789514, 570354216, 29141179, 198142497, 156184070, 303614472, 359061377, 719667306, 292358245, 363118859, 806408343, 997011708, 65600100, 479795344, 380100572, 238994216, 385821678, 739133983, 445851376, 626061314, 712122036, 932010290, 801799956, 809990512, 787447377, 6834474, 217506970, 565009469, 353393480, 152956319, 546489877, 386292904, 804967229, 915348670, 721605025, 834070638, 388474598, 758822328, 867976124, 402669941, 71579172, 15459156, 780510394, 637133686, 982734142, 557797708, 759214831, 637585625, 714534337, 618711705, 158062791, 842353673, 924063541, 288599934, 961761360, 265894390, 893338473, 604370036, 772477302, 506681338, 164459083, 101189456, 450958680, 987488317, 219759285, 738440837, 672985314, 247437339, 425448987, 676202601, 884065659, 145076097, 566916622, 977159559, 717899015, 745733252, 539021987, 38589098, 973042273, 911143281, 750994720, 865317867, 181796726, 144417393, 642771831, 10361056, 268625838, 476599153, 605427118, 796455897, 981214394, 631552487, 36006611, 891407316, 842388233, 542013124, 153826602, 485829744, 730124086, 497094730, 482020049, 457507394, 631725761, 352825655, 683987977, 552769778, 297439300, 734971628, 46112986, 951733722, 144228295, 94332522, 91435062, 585986533, 808382846, 8373417, 868318733, 631515401, 36077878, 991107551, 967045668, 463813202, 544834025, 207230496, 434912958, 27790349, 261227114, 236685806, 399465694, 369539947, 37197023, 174890817, 513321602, 192172480, 162170118, 477686860, 123106744, 322668732, 674283019, 271348307, 279448986, 102895097, 969758396, 8042980, 857196899, 176745369, 233221605, 376516256, 774542733, 946348295, 500908038, 426123487, 752117235, 890353564, 933059448, 498402358, 430856370, 961871827, 672742199, 908363585, 354600718, 68427880, 982209591, 11917511, 132195325, 207711762, 528222589, 187130700, 534885792, 644074054, 650576256, 966455651, 387003604, 865016223, 47783468, 556303019, 877305683, 653792143, 888917797, 750698658, 258134235, 605636586, 979464959, 86727932, 471261228, 414064549, 466382694, 205966779, 470077277, 441525019, 441659697, 809435708, 187855665, 711518265, 306103307, 650061979, 1148327, 996590031, 437993866, 969704284, 366796558, 967405140, 548548201, 556441042, 826516871, 303004771, 385464156, 441808891, 368104788, 945393640, 624007146, 930078100, 684563928, 807017134, 521229565, 316230103, 295734422, 919078088, 920827253, 899349437, 766703435, 543662943, 112550611, 979757075, 724699642, 251190627, 901924127, 558414964, 816165459, 927105512, 133400019, 266183028, 414990483, 960760287, 807840304, 627974235, 349540297, 361480455, 477997714, 794169929, 188628722, 807049350, 509312641, 648452630, 120336303, 577626843, 374116859, 841295010, 662247693, 577124874, 800096686, 473075871, 33299667, 747263990, 97707214, 157017107, 865191202, 235621481, 558023113, 575892040, 965782143, 876124248, 827643569, 173385700, 138096217, 172521901, 608739780, 941481833, 668203655, 812989872, 68869612, 703094497, 6753934, 709540592, 614748389, 791014955, 397500952, 997333220, 495083438, 789217641, 244346508, 160782988, 914201654, 334566850, 297036564, 636101388, 584657620, 185455183, 881537208, 928048786, 256605774, 873907666, 156141318, 890908111, 982217238, 873449283, 655111024, 664811941, 672231597, 435728869, 479421383, 730232047, 376547070, 601127294, 933265974, 986994136, 398777000, 976731031, 190780230, 455484891, 590856076, 148929105, 365508713, 390919847, 805335947, 983320619, 622236300, 544684987, 291471367, 346566123, 115430586, 725966230, 890985609, 616614359, 763292057, 499683011, 185148783, 349196040, 644683724, 165798068, 5144867, 290916337, 280601050, 859906388, 124991363, 142515302, 742840886, 78875161, 446851265, 507747252, 226600654, 553078187, 964198955, 942374493, 802920652, 280310054, 510113955, 403059489, 591383924, 385358373, 244109175, 498277496, 977539420, 780854283, 859194959, 922077936, 417609276, 103604057, 774416509, 671811290, 535880340, 489837536, 357151578, 622308331, 520234951, 924316990, 948114759, 346870319, 643217985, 629086791, 779168850, 19322557, 323319839, 411156585, 710366072, 309392836, 105451276, 583578385, 530707114, 969201698, 664591328, 632173182, 745862912, 591819576, 722974801, 98025138, 732477615, 511554263, 786367567, 6616824, 474958158, 41565011, 224325871, 542877514, 283027548, 918337195, 911850678, 243133022, 120002549, 778355453, 829171097, 672377125, 75120252, 571369603, 69222844, 238815422, 774528013, 127565737, 739184178, 322026699, 234828744, 732920640, 785054010, 454937181, 106496544, 234817001, 255527396, 438093560, 325519341, 750107270, 987785800, 188713207, 657707303, 208198962, 958324228, 809545416, 520392008, 294870118, 968530902, 502237447, 720899520, 547772187, 850433470, 318561285, 983172707, 809442401, 337328646, 994324075, 8802333, 143963524, 113500055, 534504188, 100893364, 909509073, 789996175, 213138551, 231312120, 98964160, 137355660, 166221680, 96010164, 841596711, 953696363, 664678371, 346693787, 211801786, 999413617, 623308206, 30363865, 147656392, 363399831, 323330678, 985095303, 70681630, 852270186, 194593313, 496223875, 804721269, 283230899, 327849678, 281084834, 674579989, 123831391, 60967676, 728505448, 212447376, 948107855, 248491272, 856827380, 345553182, 832861065, 182713388, 360451392, 161817433, 550388119, 177432885, 216181494, 140632423, 953610431, 627244492, 811593383, 343229192, 359801146, 892475473, 405969334, 951443669, 107393981, 280382040, 746430803, 549659501, 782517660, 676590988, 545207638, 113853578, 712295484, 581671455, 921257004, 371209201, 167150811, 846130031, 283801675, 147388200, 754655504, 41451338, 844571149, 36998474, 798978412, 234037513, 502841110, 568914175, 355189283, 767596387, 588384154, 655675051, 676816886, 129196928, 486429709, 429918922, 428890476, 937570760, 305382061, 445500932, 453414993, 459942877, 383823707, 777330778, 259460137, 645947402, 673485731, 959642897, 401153505, 382256884, 442039807, 965090693, 456870059, 228398829, 962086674, 220386497, 878969142, 761143544, 158119870, 77948313, 339710537, 170425755, 350615178, 490330816, 37766938, 605016407, 678933967, 906900787, 270562594, 18243165, 793129849, 743549655, 352976044, 813759167, 964965012, 395421978, 375534061, 528853429, 452774068, 566921495, 344877567, 404469294, 492297941, 536365555, 585521015, 130615806, 337942227, 424079031, 264704562, 953688647, 968664916, 855134237, 186623421, 169825852, 262353426, 25659639, 727699925, 662295320, 478957917, 789894823, 361837795, 992819467, 266697013, 389562285, 272412711, 386481577, 788758185, 459794590, 158046594, 746977602, 127942648, 385689537, 643561509, 978543319, 867923368, 400089731, 294106316, 614341411, 117190105, 719252346, 524286923, 112245133, 521018975, 832911944, 668021269, 772174960, 358340924, 63069523, 154089130, 318668803, 559000131, 191694470, 227058085, 559298562, 110409746, 470714690, 710232757, 675444754, 922458543, 385264463, 772340920, 26973630, 726268318, 422496007, 998810211, 311293975, 339378757, 997603623, 420131929, 227494023, 618728956, 640520934, 323864830, 61420915, 615113013, 542959040, 542767741, 760453726, 80488421, 716551448, 513560034, 695692158, 369766654, 919181493, 316263314, 497674990, 485395069, 219009092, 704223791, 528788543, 982293020, 514454409, 13982816, 921767698, 816598650, 25384122, 888494399, 729341349, 977991746, 571493392, 361243679, 67190341, 300273893, 813599205, 614078351, 961526586, 9939737, 248516310, 328704583, 102690229, 200037667, 145804251, 74257522, 519386827, 487998246, 794943774, 113523299, 675007577, 726738043, 179138334, 117802887, 90502132, 68135084, 94222480, 963425079, 440460352, 10171279, 227214060, 486186398, 167478847, 735665905, 254459019, 428052118, 977559298, 109171534, 823990883, 922069219, 499539418, 725558056, 686706177, 169211923, 556023628, 848252859, 49462771, 42950762, 584274372, 808148019, 511525539, 591472369, 798000804, 256897988, 544824276, 993077410, 304364560, 294183753, 320364419, 463849893, 299353674, 246795600, 33651123, 175535673, 108290312, 408523968, 208034105, 251237470, 755123877, 343519950, 812873199, 834316337, 508156218, 164121298, 956726882, 298913414, 107127011, 182455102, 144480084, 766290233, 370216467, 505692940, 82800801, 317691063, 68564345, 870360068, 259669423, 870238466, 276070592, 889830789, 344769876, 635979135, 799539597, 899500390, 330625566, 221516727, 154333735, 115741625, 904701070, 343272888, 427149763, 436122730, 573539040, 202327010, 10220331, 678887931, 368459113, 51650189, 956758774, 311304080, 405974723, 442113009, 19828391, 440926832, 577625671, 577894885, 851834943, 437724202, 726486994, 566700287, 236714567, 652703299, 422828223, 576875499, 464302118, 702662112, 390041477, 364561781, 515550968, 475896191, 313899102, 55309438, 633957676, 131381735, 418089620, 367862422, 561838276, 745946541, 674748652, 887550245, 684964759, 451636661, 793760433, 410617766, 212332565, 643418529, 731389165, 921537184, 688141922, 200092985, 774479382, 280551493, 383583645, 794896896, 503105029, 933515025, 108832897, 393420401, 824342208, 969412111, 332903786, 508819114, 298336693, 677270964, 189927985, 151767119, 851942832, 280455459, 656505995, 382869665, 109901003, 974811708, 5640215, 834938356, 678763180, 970342153, 455986990, 886446021, 510229238, 187079857, 633242532, 538787283, 812268522, 110034189, 814885449, 929278520, 665254717, 551029837, 806950356, 464263630, 786229618, 581793830, 392377969, 609503856, 73195721, 736348741, 295074869, 861662564, 769362271, 282280750, 855440432, 213505078, 857005168, 321789588, 263532190, 567604687, 353651288, 72068241, 13466565, 22800590, 832815016, 378951664, 35733737, 720093466, 584440425, 99014210, 638863190, 309063492, 264133626, 354728247, 926257805, 33003925, 860251213, 789033626, 199732100, 118260848, 39857883, 112006533, 598256194, 554899256, 335468563, 254037495, 953974802, 564538906, 484313661, 532755174, 802519026, 298720333, 176883979, 598428579, 741245042, 442501123, 348755711, 102735918, 925292419, 105603175, 565951778, 774724242, 440162318, 862627009, 562194254, 482698222, 326928964, 730964258, 739051141, 22139024, 383009483, 61053695, 482638722, 565107445, 464365949, 163431646, 567933963, 265986147, 685646589, 210910426, 562199018, 332503312, 86341813, 520906501, 706583110, 470386848, 851028543, 615261000, 468471341, 791776266, 406334864, 857095053, 31136446, 24856852, 439553887, 738966837, 590377067, 583685206, 489795490, 929783996, 3996642, 656366567, 668136410, 486853286, 874138800, 811548779, 539330043, 859647307, 542929146, 45900103, 962386179, 410960891, 521846649, 696871358, 257007990, 441112527, 446934664, 655169235, 538632530, 322623637, 857731908, 931645334, 761803503, 743681097, 103449868, 636869884, 476153047, 186459293, 983702599, 151329732, 482767706, 415933471, 380215834, 764874714, 688049327, 70824747, 290418151, 811540959, 908751933, 920023697, 774120143, 394086153, 374200860, 709331174, 425592218, 316433332, 676156247, 115961186, 205787981, 644442770, 506837095, 890248786, 13042675, 378378124, 420337027, 890902373, 689519626, 196349634, 157343219, 247468483, 157740174, 14534058, 6520148, 860900665, 975280768, 239092691, 901040475, 941031010, 15865009, 443533616, 785504669, 505615498, 562771298, 53496708, 940987774, 472879654, 768307891, 241506411, 793782477, 259173484, 57168977, 519613920, 528154609, 984641141, 194875493, 987855316, 729441298, 369882966, 276332356, 439618506, 736979090, 290302328, 543267400, 7589075, 850065907, 882679130, 91293254, 77079186, 252761482, 271213840, 176894817, 592408832, 905829321, 393328714, 1676008, 304118350, 90240483, 728968039, 660066504, 506237854, 871033792, 217736195, 623465881, 471570382, 412920056, 116228975, 670843696, 705159815, 282145656, 548998636, 690930054, 922843111, 501070676, 621330479, 28496076, 356164823, 375729223, 815901454, 224326239, 444003252, 895374305, 701302456, 779392993, 970192266, 486163091, 932645759, 909873381, 728298937, 874840448, 379736069, 100276047, 689416878, 110580060, 226854786, 700879820, 2282524, 138611535, 876981794, 104075677, 940101298, 883272359, 264138585, 505002156, 840771070, 19397746, 616837299, 641394337, 550454483, 134064188, 410409130, 473248330, 558383016, 393892283, 138652008, 905680187, 898395911, 172286937, 922583943, 732854838, 88104257, 823781679, 615145038, 802732433, 922067130, 72997171, 845370964, 448235302, 579575105, 95840707, 870915621, 246843046, 264734828, 828362513, 258980062, 97724296, 445490814, 862922102, 170260100, 332948690, 198788310, 678201506, 211746003, 878442123, 535406776, 40774473, 86453957, 433410944, 200681671, 834169736, 416877497, 839676247, 411165208, 746450421, 1554898, 837575361, 341435405, 17306493, 277776906, 699509092, 431564774, 568350174, 955238973, 51974464, 327246778, 767929090, 413758043, 163446192, 257059663, 658406313, 297650458, 125608398, 975507497, 170029948, 74296162, 230602924, 158368810, 692070811, 329389941, 637119334, 458750781, 647290072, 951546923, 737133853, 746558892, 567022201, 66355813, 125677337, 984406362, 953401381, 39688338, 59382157, 501625489, 883827114, 709807339, 519779080, 227207928, 915751576, 17028762, 433502642, 49164476, 881563070, 612851287, 367267200, 718656431, 261089374, 937146900, 892094285, 743305350, 177523002, 226395404, 580750349, 299326501, 274535357, 373921199, 900905046, 592704292, 397831167, 365278322, 353028622, 268902058, 657995054, 601817185, 638084931, 311703633, 922837932, 14509338, 443098873, 117414662, 223887329, 651123652, 534738248, 161208530, 93705226, 519933051, 6249048, 978679365, 325059161, 955671429, 696992974, 244658341, 876805219, 753158546, 16546705, 708061659, 9627146, 295175786, 979445528, 33345755, 145999999, 896376729, 502470651, 184058991, 915954330, 531697076, 83598100, 510933197, 205606157, 190037533, 918237300, 736724552, 77141234, 382698903, 291109718, 119705231, 911473518, 928677125, 938041333, 335207597, 255961481, 973387575, 920397950, 985142256, 229354580, 938897615, 202156784, 189283829, 7191545, 789145693, 502890347, 735137526, 15550222, 856710901, 92810694, 698298469, 32327317, 2710911, 691148156, 246005574, 11497498, 89640407, 778259418, 312647849, 866906586, 221544915, 912810428, 520789021, 863268555, 636794253, 354809545, 47431391, 453254251, 893650772, 314821269, 916004635, 497084749, 206562314, 223808151, 939371614, 221366808, 204336850, 55220562, 982881257, 231380610, 237385218, 10893398, 956712057, 454773847, 704833733, 789976129, 731531705, 922426042, 637797376, 188645015, 33021726, 546516395, 287131408, 216528711, 534123615, 585390926, 191721120, 161740856, 386475626, 751620535, 260196434, 900133740, 734300071, 194018486, 74586842, 153804364, 315814829, 537110095, 291578217, 500183504, 721660676, 140305999, 524213031, 660809208, 715265766, 594856503, 147967828, 589676786, 903687324, 234112618, 272082489, 754963876, 494642393, 986180832, 204451613, 887524214, 321192090, 539557750, 274731657, 76881177, 76463769, 283668061, 606061754, 228497444, 681912131, 850726107, 58326352, 64323947, 248429899, 291554402, 208366017, 370685666, 213499515, 686530279, 308598040, 378097622, 983689640, 880739650, 5159398, 411931715, 85397100, 384703631, 220857542, 385980713, 22139753, 432376103, 240356663, 466965090, 585090084, 973718581, 463969725, 714876832, 943646155, 990721352, 359482370, 121525448, 641597972, 943123065, 749257433, 923216225, 228092614, 214851280, 33364939, 931688107, 452660443, 428085481, 612426077, 196166457, 237029385, 94000335, 704572802, 585161404, 177314643, 906406726, 594919605, 119306510, 403668554, 461025551, 324097508, 107140543, 119320440, 194115410, 602363112, 634173570, 623107723, 320411969, 545130028, 373028141, 145629816, 422846309, 172023683, 195953908, 744408006, 100855655, 608189779, 448515328, 989820845, 463796018, 662825100, 396220723, 467507954, 824926577, 684126403, 591698201, 26068233, 706130532, 387911091, 494715115, 196942852, 422745420, 395323699, 266400496, 26727596, 851722286, 676051501, 473069380, 558340102, 783196201, 128988989, 873559947, 441438081, 887255690, 848172126, 30337501, 735929841, 460181292, 880173827, 631994188, 803600595, 178665255, 273855678, 266160523, 623022626, 647514818, 846429536, 366201026, 905958974, 210624065, 256717334, 436243941, 670434356, 742418267, 731624485, 525952265, 215731550, 719779614, 623117021, 335878326, 720176708, 66979076, 819368662, 583423395, 781247817, 695347300, 492882544, 879302008, 788492274, 701166564, 136529717, 46213103, 650521534, 185631870, 844323083, 550195586, 579045409, 995877323, 844437084, 320578830, 918432518, 965907419, 909404594, 311145453, 711893700, 246596454, 581902867, 730161745, 765408415, 859289460, 993049306, 756985503, 290298692, 368366528, 748080205, 807473236, 102765628, 673867248, 23713659, 673127767, 345547466, 994263021, 934535730, 32374072, 644509868, 962272903, 197400920, 433594818, 64197336, 74982666, 766317035, 317340004, 551561296, 844530668, 759927510, 91209587, 203435947, 714193108, 627409241, 392269281, 253006366, 423382354, 513973228, 688770913, 30578072, 103211687, 525898956, 874616085, 230061606, 385834993, 374057120, 722561013, 430407275, 969555215, 240348293, 171092879, 750561316, 560070849, 409518228, 360830810, 673966294, 156760078, 630658857, 940287561, 404962325, 412727691, 270748576, 429393430, 430663641, 669640814, 312778421, 821432019, 621604231, 608735657, 321837592, 494082561, 867054915, 877702146, 961764447, 764146537, 398744051, 189200588, 675934023, 557186184, 327675820, 917940884, 108809641, 112574204, 920955969, 720191294, 756300774, 472930851, 158593582, 532584038, 810992724, 630637575, 463012211, 152477419, 936881000, 401973947, 922059527, 195189170, 491058904, 936026696, 633739206, 296454793, 200731916, 756806842, 559932981, 576440135, 887164811, 102736516, 922807638, 950685393, 657144215, 766627601, 294941844, 152590838, 724521805, 747166134, 571918402, 68591389, 205449823, 818762934, 264709505, 911260262, 241594797, 833540962, 813529774, 40382795, 208576403, 945841076, 33243830, 906459726, 582703212, 357589552, 478384910, 39450223, 801241357, 468485106, 841125625, 636143339, 153015664, 369289087, 248441686, 169426084, 124840573, 724089730, 450256857, 110089987, 480373651, 330564138, 913551241, 237749322, 998589826, 631111041, 406257451, 784593825, 735188960, 786576125, 569009161, 496801445, 415261564, 149727447, 613947169, 363348379, 185411177, 100532378, 45739870, 646805456, 24727790, 387143640, 380224109, 701369274, 482182355, 365327804, 12032986, 973047376, 212784929, 242861257, 799717788, 895646848, 17745836, 134564004, 229311740, 819154280, 489119927, 46028928, 107485764, 410584299, 216366565, 796219100, 508829548, 29904605, 609305734, 200271545, 95283514, 267975321, 257742433, 401135281, 412621707, 689184499, 608854968, 962250522, 400532926, 735433150, 110514525, 668719912, 849688730, 659350815, 192569994, 680829532, 911295774, 361596574, 365548766, 637481902, 270224348, 569593291, 685074998, 122727626, 789046483, 380451266, 736022111, 700683026, 599228219, 692366656, 893161539, 105039644, 787543457, 592612361, 647801392, 916971317, 554054038, 930752539, 103449035, 960168956, 608406658, 944638656, 463739948, 987656661, 141376384, 388725499, 914542874, 327909673, 126492845, 437776339, 318254320, 195906134, 752789450, 790871542, 259655510, 860558252, 789796679, 127387465, 645653024, 148372654, 651427981, 984571011, 415522088, 503661967, 202871014, 835197061, 951190396, 397170917, 941463979, 814358218, 284508724, 258551541, 17476734, 616063506, 712162120, 715287541, 196767489, 725149461, 423212715, 739880933, 269149183, 227498951, 129459584, 284318647, 807590504, 635779949, 807051648, 526724291, 108533084, 952523841, 756202899, 812065476, 162385835, 695728709, 925188251, 218050219, 578884812, 994176593, 575299053, 795101313, 54433272, 329142702, 62086113, 350330024, 327046691, 915417756, 803009008, 719936470, 235509572, 857073965, 481449719, 146728669, 84389324, 999676890, 416777312, 194966112, 775031197, 372428387, 88810686, 57301095, 695648883, 944893062, 128589916, 243423974, 453211477, 646706929, 570473282, 30288076, 719209853, 440027447, 224939463, 118496306, 368375692, 102979905, 435709180, 647523550, 479679677, 457773454, 363587412, 661577580, 123239074, 904526694, 656775778, 241217241, 251679122, 818990329, 272421175, 190748300, 822987387, 23678501, 32754957, 9686381, 297245638, 692625569, 762072250, 22865306, 232237285, 306697900, 517759559, 816741153, 882404014, 136752168, 453898798, 447414311, 400243099, 128195024, 233038529, 612278458, 243417677, 679529059, 665530323, 654640302, 26868303, 534548213, 267561148, 713681683, 102501119, 900704713, 60693906, 23148854, 320928979, 119843206, 369124964, 143238003, 279495664, 187882372, 173218715, 467301192, 313025151, 907503324, 318947089, 132146013, 616793254, 834085892, 667215305, 474207334, 968309369, 479718202, 157504353, 154691672, 214019124, 941971102, 885871026, 808913567, 784447357, 207903086, 847755613, 123970241, 385419958, 213989345, 855254779, 444126184, 826354800, 207073229, 970420521, 35080784, 986757657, 465498742, 260951735, 496270305, 938404639, 387310771, 61426724, 959499629, 505799057, 671546716, 552036844, 108157926, 605166701, 630239122, 134795961, 228642538, 113559228, 700151351, 721949693, 104836717, 769117098, 760740859, 967700057, 983644252, 427665784, 431853568, 737677560, 722718048, 546656675, 382211235, 560616793, 808601991, 570902892, 689112286, 771931746, 119328745, 907844500, 861852950, 944931412, 182343923, 827699241, 474474720, 790762150, 425095054, 434888434, 249454153, 717821751, 351431813, 99106409, 719315320, 634455403, 550611942, 918813076, 944490410, 108517355, 479201660, 353542685, 483072762, 193586759, 144778185, 295058185, 952749780, 622348479, 877106285, 700590150, 96765832, 841226968, 4445784, 613681026, 207848835, 662614467, 649513584, 986252932, 544015419, 24605076, 844938480, 709230311, 63499270, 350777348, 223859642, 946476458, 827372530, 408085202, 718593372, 332841648, 756806454, 712004738, 848366233, 344129344, 891806985, 391953384, 651413230, 469751847, 323200509, 474815607, 826518053, 596391701, 668220147, 122950103, 25773626, 603759761, 605856241, 3694409, 978172419, 548294903, 424993825, 293321384, 206294224, 235034341, 543422684, 436929976, 513027025, 913008740, 959049801, 347513728, 659120097, 735242721, 730614223, 600712808, 56976783, 278768272, 422001273, 239129431, 660697556, 405870536, 157229072, 922428399, 701017475, 596212047, 151785553, 166216221, 915016473, 456512933, 375439343, 928290919, 599239452, 178021033, 330945795, 700676134, 904960350, 705597171, 491245099, 423150009, 616934276, 47780468, 294466028, 22560657, 268877754, 478410688, 539095575, 218857758, 461600118, 225375899, 27902956, 519267339, 456152695, 859331784, 183762526, 213185771, 331790082, 582606403, 797861799, 886122621, 507458725, 701190442, 304858935, 236716855, 8052010, 841859191, 232740488, 973759675, 970624017, 793805457, 775252488, 507735224, 482110324, 985851597, 132280458, 701592295, 447595408, 437821223, 76027425, 845876149, 271201224, 516450868, 697218273, 74146802, 356028997, 94557389, 288780681, 212928825, 491208955, 621791872, 729140258, 919241276, 510729599, 555591416, 114403888, 191352428, 645575937, 876143294, 873450299, 300885375, 371349725, 543761761, 590315747, 963730762, 133491548, 112584614, 570576680, 768706446, 491454684, 719999585, 535154673, 478526906, 331729532, 345666471, 394569640, 145985717, 765553037, 945928063, 607455114, 196872628, 978894395, 542123268, 911727228, 535749933, 26030783, 8169418, 815638338, 428129327, 173411190, 351262897, 646725498, 110013453, 523670376, 999171187, 911590298, 389306419, 28570403, 500429314, 15244104, 116445123, 707650401, 516819697, 337676752, 803236895, 481421858, 997535687, 956947133, 263724600, 264174157, 215130772, 12108998, 293084757, 853866411, 107898429, 379861641, 930918518, 410285069, 138062598, 301638966, 245560409, 833238137, 451551116, 9104431, 222064993, 843005990, 486481943, 22471196, 458301956, 850827724, 549041594, 500592117, 865949490, 879094840, 402296009, 644683927, 154816794, 302147231, 337135727, 116720854, 149595100, 939504762, 290554466, 163349621, 250417747, 870407355, 593939679, 988346539, 784696141, 464481091, 784730598, 60069567, 619494929, 824123569, 401864635, 91106098, 947174630, 40598357, 50480735, 261134462, 535614931, 350536681, 116173728, 210183290, 642469554, 962360121, 474621752, 510192497, 66155796, 201870047, 94216465, 716783983, 786657741, 215162574, 858966932, 415868114, 130538647, 995438480, 70888199, 987075447, 881157796, 339690793, 518138983, 535157562, 149004595, 455337395, 419350121, 38344829, 495150560, 590965613, 330362303, 702286177, 483083348, 93761059, 242796762, 15554855, 265775143, 242237821, 958608039, 50834490, 794446147, 700123540, 653799804, 515513979, 175134861, 681244270, 380744981, 987811289, 663455234, 430548598, 660652202, 294410011, 952731091, 325527515, 332179785, 429356930, 345659564, 511219359, 307963447, 176833830, 374680749, 227491831, 186988404, 723833236, 357694533, 934299305, 276469226, 200053421, 396042074, 911149552, 395780411, 259700351, 642200617, 358595339, 175521436, 929976640, 300948148, 132548054, 852634992, 170581292, 336883143, 459087231, 543897312, 200692402, 146327685, 515682406, 159512280, 788457136, 337051718, 3114177, 14479221, 98513805, 308218358, 921134543, 346746879, 65968703, 571870918, 40218113, 825167766, 499025782, 305122406, 281055981, 714624694, 774936551, 127030097, 179355941, 689711413, 908640757, 963534824, 530117192, 77722980, 418674415, 366270155, 319366417, 755044398, 926499848, 163425561, 619220243, 114320498, 277067487, 91551002, 634362474, 13920202, 939346794, 966870253, 930886020, 467388389, 541422178, 468924898, 104256157, 287551055, 397864089, 879041293, 474040257, 542452288, 536921249, 757340596, 517652644, 725172502, 237160920, 735658615, 196538579, 455474381, 128444327, 511492814, 337962474, 825568960, 331133971, 449296101, 612363088, 575189203, 92393064, 149567963, 523637114, 1227486, 427294279, 300065679, 980186692, 549902680, 902933320, 131346278, 873004805, 793274854, 98575519, 262778736, 717288405, 470606582, 174080118, 108091055, 350885054, 690568304, 297235761, 736140867, 563848996, 305308483, 71331009, 74923404, 722910049, 75619314, 212247166, 319200271, 409942479, 850736541, 146559141, 595531922, 21744118, 11305338, 503072401, 191400730, 14035314, 625592831, 286068214, 136747013, 849505030, 328136711, 399717487, 481422667, 213166604, 630975567, 948034826, 681321157, 622004613, 269948770, 81971296, 306810307, 660364067, 816321605, 857640758, 166822153, 478451009, 192656921, 37218944, 288445809, 390239221, 38196004, 481848525, 317433629, 645472528, 99141214, 898581168, 222401711, 249138637, 472513129, 118091347, 686828921, 115453273, 83868539, 214279539, 390138925, 258133202, 331800167, 849118866, 428732560, 610739150, 61385379, 944245319, 247353545, 699863535, 533702539, 34348730, 412766941, 158885891, 986200590, 160418146, 578222116, 294422809, 670487084, 364018775, 589783620, 328995301, 919458344, 23093424, 249877209, 245992448, 261732544, 374940309, 603068785, 528164493, 266923711, 611331187, 775908016, 465991054, 811699405, 299103315, 42056634, 398160556, 66440689, 643953742, 910067810, 693816295, 616099998, 198451219, 74639099, 945073970, 211980723, 146589735, 382235416, 564228377, 382846510, 738441913, 645995365, 72602122, 314981036, 631173247, 364225152, 524438554, 383486166, 662922168, 5740447, 628235003, 70205710, 501097669, 872189965, 959155065, 894380479, 337936413, 492267413, 690005891, 244741450, 73260907, 218687991, 742978603, 674373088, 581439479, 37173106, 976901541, 215047155, 569267639, 741594079, 562542378, 667868023, 779354454, 612796698, 592699038, 833961619, 590643472, 787978210, 704161117, 712823193, 426564225, 143073363, 577979837, 327402730, 740776973, 614966220, 961631356, 127839465, 791715652, 66555531, 543345077, 255713832, 816701650, 533835907, 773932462, 845398094, 486694616, 891591569, 326203031, 960369653, 444478672, 133432880, 745535681, 411670642, 690069171, 450464112, 936626076, 10395309, 158812459, 308479754, 220567538, 973964492, 126788645, 835270637, 475296416, 50055588, 839341396, 825863198, 786078926, 316437093, 460707674, 548570155, 889856918, 273331013, 208629036, 317181468, 246533442, 732578118, 889020297, 849670301, 77996276, 809499396, 594482383, 665644022, 804273557, 839564596, 22901092, 682616981, 750046609, 795555568, 121241105, 501296408, 21160387, 600848331, 716096854, 261878839, 760864542, 75039419, 21718159, 97974304, 992704944, 152989880, 958209708, 591081206, 661306041, 272003696, 163608515, 32367776, 819081062, 238413288, 373793686, 285661383, 756152425, 261012013, 444730418, 229526516, 809939870, 646582058, 565590784, 152099481, 579266340, 683464477, 772740332, 72721580, 822813114, 808527021, 913507521, 268657975, 703842248, 318481822, 994210501, 587166848, 63739344, 483149087, 679624938, 433721193, 181931127, 972509965, 711479239, 722933325, 57916183, 893439850, 283392459, 781352776, 872675265, 375133420, 248202, 206293760, 776975298, 308015877, 875290799, 292919941, 620987833, 748510767, 977379826, 969269123, 243891186, 933817275, 211690665, 406208348, 66672434, 685367766, 190687186, 587034917, 801554814, 585964950, 876014342, 420027364, 139438656, 303466674, 122166564, 33975087, 748523968, 672212095, 357077985, 517397705, 61576681, 195564318, 861401633, 314955164, 378123480, 692638300, 44480380, 267029805, 672715265, 658014778, 95875986, 902105668, 391378423, 471732789, 231592310, 69709220, 227685668, 440538911, 201730929, 944138587, 711201, 434452532, 875405033, 133474075, 210962027, 263203654, 944995182, 647993732, 583705506, 563232610, 452070232, 347488382, 837560641, 123541110, 382754749, 265874289, 936159774, 327412467, 413892195, 168500213, 591453372, 729966644, 755215149, 307405471, 623779169, 763362245, 737724532, 779792622, 285507077, 312867744, 433668480, 832380866, 672188523, 734000081, 457624051, 568150611, 60457613, 373020027, 314366792, 781413980, 522199414, 684029948, 813414462, 860328497, 603996080, 588928357, 208637863, 207037822, 134443782, 639361575, 612326829, 353501243, 639619464, 374268875, 4218351, 378908624, 441515887, 804626265, 576809047, 302242778, 197061075, 496766054, 601532330, 761917654, 514605883, 287857401, 285655984, 306043492, 761489408, 645847529, 876725722, 416261756, 595949492, 384303035, 48790084, 409537021, 244281008, 473883116, 972113015, 173301228, 170297673, 598863447, 796586391, 107146407, 456970067, 611481696, 984262804, 596109206, 47534497, 654430352, 439874667, 361595712, 995175053, 644518671, 785603853, 468625434, 687657030, 710307420, 825268315, 529851084, 648436261, 49494269, 590532461, 462140898, 685553620, 486937989, 819577371, 517616118, 940726465, 340041497, 936736505, 822380951, 538455022, 705170385, 406946266, 924183631, 346741751, 988330715, 500021173, 455833759, 250761714, 432842298, 64939154, 945755015, 721225481, 148598404, 954379071, 882543157, 5595623, 279548381, 363344878, 775649410, 37646014, 341334393, 4559923, 287534489, 440201770, 298269957, 281568716, 649440331, 436391825, 128293629, 468130301, 347583957, 9381982, 63589626, 218499316, 309412420, 446213821, 160850263, 199344531, 469478516, 137501313, 577260995, 267888827, 444307512, 683168364, 815544437, 580842313, 615796466, 34279938, 621596517, 662228996, 635105340, 719183279, 56072599, 959298412, 451944113, 172996608, 116648453, 610220012, 236727399, 265694609, 353751012, 589566348, 81278481, 414804787, 398163154, 772186670, 419733681, 194274494, 81947210, 809031963, 888396217, 544019802, 838813176, 576516931, 782338647, 252893644, 120091599, 891622104, 33372464, 398384619, 47896024, 541905316, 559243998, 888878758, 271596677, 481034228, 575986682, 729442792, 124143050, 696955708, 830573421, 307303260, 208348158, 598348132, 231308805, 97616195, 612614373, 865489423, 520400712, 840839484, 866579682, 845406048, 696502038, 255017214, 194032670, 230961590, 311807278, 836140144, 516365543, 163909285, 787325523, 108919039, 985219555, 640548428, 892779001, 194081203, 268521771, 594164153, 451087564, 367703890, 647560201, 188676364, 900539791, 983212275, 264724251, 657819758, 451048668, 751728607, 951776716, 957120712, 206765366, 675825756, 872011410, 763544843, 690817295, 219765119, 426119343, 971398827, 469185577, 388857620, 855488563, 471746604, 185747504, 727651587, 870898338, 673220439, 387649768, 12764034, 74880132, 147538108, 169184689, 102113039, 801611866, 484930659, 459069207, 494395079, 556654292, 639901764, 813183035, 862067592, 527404849, 66184871, 124967222, 293189666, 120275116, 522770789, 31666984, 336191444, 751936927, 468253399, 935270057, 33120481, 978139185, 654781868, 908230400, 281136521, 406493146, 316247468, 19032325, 123439106, 911247450, 748529731, 495636008, 965489702, 811208640, 297016925, 585124594, 185164925, 500715210, 929598356, 673085878, 209516194, 489050157, 913148381, 157808235, 119015127, 253287678, 264574260, 80667653, 348598927, 638610780, 325057487, 59990617, 654708233, 381590905, 295228498, 884237916, 840979612, 858492699, 728806968, 256241209, 361049487, 849401445, 697964406, 669636534, 432841122, 446117023, 447462538, 350877271, 51242418, 651365463, 444239174, 803072886, 994989628, 555028334, 311204304, 391905033, 496378781, 647557602, 576735585, 87334894, 122776176, 853620031, 691311637, 961271969, 30930462, 894409951, 244908596, 14552551, 684172315, 189080835, 775303270, 915675658, 909669674, 777564921, 911232252, 177126791, 367587280, 801625354, 807028361, 259045403, 90699211, 576559978, 453376677, 887337218, 467194389, 164207021, 950119873, 589476463, 769468331, 271603848, 781434475, 445496489, 953610175, 840764311, 616045908, 259338256, 120997834, 337504175, 520478810, 30530884, 168533937, 976340152, 370892743, 968139449, 796278578, 383510492, 372248312, 526906999, 3769242, 599831599, 676140390, 545834557, 616736622, 218553148, 795003156, 349121864, 603128486, 974249406, 54959775, 90192750, 628397608, 301281335, 124150027, 183339691, 370652692, 893133260, 306576141, 941524419, 55026906, 65929196, 393836224, 824745980, 235083323, 809612050, 930589226, 280852251, 185317648, 61620488, 785237719, 277157683, 615615832, 429242396, 651976037, 632151039, 160392400, 306500844, 783156754, 70001891, 219447980, 155296372, 446111458, 823312757, 25316361, 112187401, 437610542, 65431561, 960108438, 462974495, 449668202, 553741070, 277067848, 370376477, 837684907, 767938514, 764325812, 412370925, 520394430, 487379072, 298070970, 313206692, 890104900, 350874773, 287297526, 932260658, 894255396, 888240173, 467068772, 1181749, 151097655, 838492737, 724365964, 468109124, 864028032, 406010977, 737589438, 714981488, 29588628, 335878538, 938979265, 517298765, 846393651, 510970736, 538471432, 894597621, 621884773, 738106880, 733493738, 457076778, 665827299, 318467409, 311087833, 57372989, 502357486, 165120667, 731369989, 100932420, 527250339, 617580992, 53799566, 649925803, 868688303, 867832824, 812034600, 702234163, 754445416, 477818970, 426312868, 795078813, 113990482, 749991652, 349107440, 298910550, 592289359, 677272700, 466589355, 143461324, 407591824, 550720655, 257471989, 708855167, 413908972, 315685596, 727156003, 586077665, 173358250, 950947419, 946369898, 264494591, 848768423, 833718645, 351089627, 603700591, 159908560, 739022073, 205156646, 867591945, 383109192, 895295361, 922991484, 511850977, 329457380, 337196230, 594083641, 243596871, 359519461, 816048658, 96334873, 606249330, 648882753, 660466975, 558598230, 74755944, 777924743, 178825472, 447746705, 700055957, 47114987, 88878643, 897055454, 28260738, 29726078, 447252771, 879661648, 21434875, 38882323, 773696970, 255042193, 711184386, 782938695, 609705551, 60286988, 927736005, 947432675, 923151583, 868491384, 380785896, 929371576, 298592923, 169738572, 966004281, 108613307, 542833660, 269996392, 496968961, 502997419, 380832977, 663706289, 806320562, 996430560, 473539539, 274557355, 374362989, 319645548, 960598231, 551961169, 591209124, 196659144, 117524368, 101980244, 30831854, 44000665, 950654044, 542544246, 920207940, 460568568, 362375925, 112838725, 822103396, 350796010, 820026530, 883402617, 891254085, 341772621, 684895924, 996094720, 374584773, 740377273, 103948435, 36187451, 21784822, 889451097, 403890539, 498298760, 751664871, 82354802, 494532581, 914924441, 195225151, 812393245, 253733686, 483911881, 823085697, 426322189, 439971521, 75258384, 216161159, 788818905, 677912807, 874106457, 670836799, 73258743, 747010804, 943031761, 194664254, 578323948, 904076839, 778113341, 6095726, 237757210, 397653147, 564179748, 877141161, 628370580, 115977072, 461619681, 637621290, 93128835, 256665196, 449061702, 58276287, 60466096, 608675837, 938807373, 883421612, 882157407, 111755934, 410619269, 927072677, 51087862, 425653700, 892083462, 562508029, 421686211, 418722614, 106250958, 210263856, 476051769, 58779694, 427378907, 430815475, 584426754, 489163284, 497738374, 519224123, 983812662, 447557396, 933689113, 174530969, 679672309, 217465308, 152929005, 590805104, 612002642, 738742782, 310258343, 705548774, 380321357, 285813395, 433826948, 284579794, 574192295, 766095056, 585226458, 308548197, 569040321, 920289026, 381084522, 904728736, 100742422, 576520297, 347404001, 920192598, 294368336, 364062013, 566108473, 783865545, 304068388, 258028010, 713410006, 493938403, 916850288, 598928359, 855983860, 321180360, 47301061, 757154909, 870052838, 155748164, 395381053, 777883751, 425745410, 253368758, 525677452, 836250937, 638976961, 991631458, 82655967, 921315713, 654500142, 395344254, 258750495, 59194690, 438059124, 271674936, 331405405, 497252074, 603369594, 842888393, 114694180, 202018984, 55647452, 667981702, 743821617, 94710435, 875896347, 841933342, 139950541, 705211030, 97654878, 366271133, 951347920, 738574617, 294265811, 482424807, 747789285, 741993499, 672683579, 789156834, 803111323, 611445255, 874753563, 190674058, 622467184, 342280700, 121062831, 725258632, 706937506, 142480242, 730934753, 415089210, 229339492, 265345515, 642141263, 472219068, 116770350, 881587782, 344136363, 119658702, 604819846, 830277359, 564503300, 360901732, 225852292, 535780755, 767261524, 693580657, 538727381, 434860976, 371002595, 261376934, 806609632, 228825186, 882253830, 742453375, 887699262, 666197682, 734531210, 966433717, 890463556, 511744211, 764992303, 782543325, 579924746, 186790594, 533061794, 481379269, 338047971, 333423403, 688834550, 169497528, 457485833, 604201340, 382958801, 381403398, 310557717, 286037347, 898641233, 297409599, 200509746, 56988202, 42123776, 293412357, 11677718, 24945637, 851605985, 552565227, 560917100, 213697670, 402184851, 489196748, 562845589, 148725399, 770579512, 398387274, 588591186, 714598665, 924893985, 251903647, 854120911, 723909105, 948473174, 197480368, 152584965, 738591663, 555752332, 485730657, 334914553, 233847200, 5206513, 544117519, 84766958, 438092274, 95821174, 670577926, 953410079, 839124988, 587923503, 580585765, 871378306, 863943266, 314174408, 640712522, 886180989, 41540902, 789727810, 54115225, 341798459, 531487984, 901628910, 512204899, 110529246, 866399616, 565059898, 722697572, 760993981, 738327286, 277123840, 179571707, 105370677, 838415430, 276282042, 813845781, 621533659, 877797066, 627097641, 221366497, 413787457, 916267746, 158537480, 392473724, 487451254, 100584929, 604968591, 584281866, 895995932, 526556980, 927674982, 158573013, 84899517, 897999209, 617519026, 649893307, 127390147, 850193126, 602222764, 540245064, 275761739, 666598568, 412884721, 48040397, 434918771, 361325775, 348453153, 739511847, 547875537, 897442332, 25997234, 147368265, 484470677, 766755827, 503460250, 857505613, 954674417, 599183136, 832928556, 377512, 351695379, 373880276, 643951612, 796550278, 325981237, 489180741, 469480437, 302682118, 208650062, 161965496, 20548926, 808838655, 619533326, 615602028, 372850806, 639463284, 987860106, 185814541, 570201652, 352959312, 39578330, 140121718, 403263510, 943323952, 654132435, 869220546, 407468075, 357245308, 461516658, 856451416, 812259624, 766181974, 852985829, 759068353, 628430753, 889526323, 568106578, 728681216, 883949920, 860897597, 612230003, 437282745, 991940564, 622327757, 938276059, 192014783, 735465604, 225080563, 504344814, 898326129, 727833850, 551380006, 9023720, 535976675, 350389093, 549447088, 727293728, 435930453, 764649386, 169162777, 390428942, 651768699, 148258800, 531855537, 340956205, 794959928, 940093569, 954966102, 7210715, 675415708, 576939156, 541062982, 637118496, 511390830, 864086477, 207895591, 434917930, 779751884, 166303981, 373852213, 284439285, 238095884, 300711583, 94884830, 693428303, 240103402, 97326013, 41690710, 628610091, 680119841, 132527727, 39719523, 651516407, 563296450, 984142641, 873212010, 397886476, 777774232, 812160507, 679614869, 651947397, 191239654, 149922693, 563166347, 468521144, 694619135, 80367015, 857393304, 238334977, 223795730, 187556532, 66891999, 205626053, 45265973, 12095233, 934301353, 514735923, 214653095, 450879883, 332836226, 788311272, 493755624, 468778018, 599522178, 486891512, 981257069, 195933084, 822850295, 820883930, 429523543, 977729450, 116783797, 647551266, 883700480, 574367857, 248947195, 183357865, 462994959, 610753778, 863168719, 670162245, 655961023, 57576222, 329629701, 842845161, 395925495, 702466700, 519098439, 239274844, 380520618, 748481564, 315120865, 364134146, 656353859, 233622342, 530500549, 398101605, 186737379, 383579609, 663385054, 173602050, 426648287, 723590457, 271303303, 999455808, 772694156, 386326826, 290162510, 112404024, 678964903, 177091114, 769185703, 411969603, 101760845, 474428989, 140223360, 779437059, 793856610, 514930803, 537826085, 59282566, 855786983, 510641829, 44203842, 671876711, 70542497, 407827571, 752704635, 544522959, 993171446, 286103713, 878707864, 799959502, 816810122, 364094573, 414503877, 182995597, 318968321, 206800810, 473446355, 944478732, 945504889, 139433851, 32284022, 893620165, 650933464, 133277640, 671419103, 740254860, 429057163, 103376829, 22047854, 831182494, 835901723, 864120201, 251584609, 283478080, 426472350, 430235916, 215623149, 675303096, 393247745, 338605752, 712217303, 217933915, 82112663, 572115284, 861807256, 316858435, 977242877, 405252209, 991005956, 556080441, 731941516, 801825167, 150177237, 488554708, 188184394, 568726808, 224193122, 610463494, 237534473, 388666314, 684112137, 183032206, 802132917, 441346232, 584995, 599103664, 894084681, 362641201, 208136158, 531366589, 441149714, 449149479, 801937603, 336645184, 688514431, 989117533, 162037755, 742104015, 827680519, 88532587, 693776521, 981558275, 456112458, 772753267, 830932898, 470136321, 160926318, 528662143, 594298985, 238526427, 645945583, 133487376, 132047247, 25071906, 324727118, 98234201, 427631392, 996460907, 982722577, 662910207, 861281613, 151832613, 464045163, 26545143, 832020866, 331896363, 64561118, 27478315, 941202896, 743037391, 912977442, 958016849, 175326676, 595415956, 134442044, 735573609, 57397619, 14692662, 554759681, 106924503, 577468176, 577854387, 960589987, 3286332, 238866168, 324174634, 668782952, 737331019, 58862869, 614243771, 210933039, 447528640, 459809848, 794833685, 371190000, 982541681, 929104830, 193769584, 682762730, 449511083, 326673112, 101808049, 894897690, 867300604, 393781281, 292128270, 237472222, 202363736, 150144959, 348137597, 653156653, 194840038, 513525794, 605399348, 890968247, 168687972, 574684476, 343572175, 218750351, 538947015, 281683988, 475145552, 793425699, 734418775, 36312992, 435670104, 21173069, 478250689, 82780625, 458739926, 743895178, 824929267, 195830653, 460170500, 478894161, 108533953, 504999731, 598544230, 644790745, 882653170, 988959573, 594748118, 774487896, 631020056, 685320134, 740139773, 234696064, 61757608, 398728597, 854095959, 379213375, 308963435, 229493907, 98818426, 770751301, 519118396, 931707116, 394762060, 608794539, 8711556, 679232186, 846472837, 93901650, 709915551, 882387846, 655800276, 899968788, 301750969, 217844960, 677825359, 662316996, 399778748, 494033898, 787670313, 642856365, 362995083, 396023927, 994509169, 775180509, 322918043, 340585469, 498966957, 120220269, 396199352, 877931141, 809102745, 568066246, 699290426, 874969072, 449076629, 368869549, 579208025, 234254018, 688325881, 152523389, 548513722, 523397291, 466900541, 819867176, 786839013, 983275080, 270947838, 816268767, 603337681, 473638433, 515809531, 459381140, 428073392, 591309836, 592425478, 509125237, 347378178, 534303974, 447335596, 893647672, 505534698, 42975361, 297290588, 570817798, 176457574, 786773030, 19725225, 233927255, 238780490, 560494807, 533405314, 809078978, 319960918, 763817264, 953443281, 855736319, 249824196, 311786321, 732811526, 851040371, 546091258, 642164729, 239131780, 864399497, 880712993, 143485995, 576987240, 851174007, 102121173, 685538643, 220261057, 989066618, 112744297, 281583957, 436371101, 746422840, 362184443, 174855753, 759234084, 621251586, 94469366, 706047292, 72347371, 428890652, 451615649, 507483162, 599889009, 642025640, 303376857, 997969567, 381891523, 26715195, 561539562, 877537287, 807866640, 65027807, 753473430, 701144448, 963617008, 218968088, 784838912, 27940377, 905093065, 293422076, 374285726, 624974222, 841134368, 936962177, 903160119, 12471170, 648721619, 234180756, 790604476, 183772372, 29358276, 462313263, 777708263, 470328662, 306000468, 364899126, 628939488, 388189915, 926179367, 541896604, 377416011, 796796892, 434771850, 406208653, 797189252, 716737832, 834321666, 333237366, 772627523, 335278356, 813097941, 317732340, 567641969, 340489252, 213352291, 700785015, 216284027, 196899367, 743687726, 669866549, 443477163, 187683067, 832241004, 158081043, 872361411, 443814115, 451792526, 868608118, 650765955, 783222935, 432358025, 826605831, 992691412, 763531947, 243090460, 204193805, 506922884, 558669711, 311757937, 306653493, 691649223, 896098410, 538441570, 287388290, 206854627, 5210583, 346526450, 66628627, 367289481, 680824105, 563416988, 584824649, 565685589, 927403230, 392648548, 191646561, 221318908, 534471153, 222918242, 32266351, 884208766, 394631468, 513304987, 246310879, 670787009, 47975783, 385838004, 505159493, 131703751, 795624394, 825915677, 907875311, 87402500, 433287264, 496733883, 288216734, 469854027, 915730160, 344306507, 415566760, 117309965, 931692845, 724774492, 114121866, 680883709, 609713098, 911262628, 160072216, 746672533, 726915974, 702987331, 827041367, 408413125, 570518105, 188738292, 956844647, 958517560, 249461699, 246268164, 564033503, 672389252, 494342569, 775202117, 226442367, 218559201, 450837003, 729452419, 103312380, 49845818, 543491218, 132282499, 320206541, 342953445, 137759025, 320819848, 228702834, 757032156, 711857977, 523076029, 837159859, 71457524, 440566041, 647197480, 926154545, 253493392, 6384134, 229854194, 400279506, 6425539, 781238935, 534024910, 544346852, 544787456, 609013838, 238465370, 310661429, 124412327, 839862976, 624093819, 238494400, 659323702, 86741127, 42840993, 726410185, 501873458, 867793350, 894369787, 939109206, 583813828, 740811499, 637013435, 814504169, 745474232, 673122744, 455627462, 875177913, 427485225, 164262248, 700025289, 576998928, 168787472, 758128071, 123093005, 365412794, 533669473, 419967564, 571263295, 81513965, 692775405, 74318651, 540096767, 157665128, 127792340, 758720750, 815747898, 609630894, 361122455, 417284538, 311269282, 612114015, 378020616, 672169552, 832871202, 183868925, 287744977, 688966663, 640253586, 155415683, 782447518, 730416559, 158417621, 847121697, 251841439, 981949885, 569949726, 194734492, 994150142, 178280315, 291891069, 607289255, 559460787, 549368317, 684635106, 529909438, 3007973, 396843045, 879651999, 261068485, 684456456, 797189604, 477295511, 399836091, 687715088, 506329430, 745533999, 654621574, 777617283, 69854697, 454936952, 422523838, 366079206, 7206328, 589280947, 207994383, 311313845, 845695122, 525143051, 345879534, 908076308, 251075626, 735497988, 365023853, 584448456, 887487116, 917874190, 224147945, 927041262, 150564344, 523792041, 866086376, 986796206, 118358019, 200136740, 691290270, 927466171, 552555409, 811111203, 953490122, 257241936, 900534298, 634359263, 962754290, 904937195, 759086234, 269162560, 160873845, 754623796, 977738210, 686192510, 405579885, 463370545, 56264280, 89910703, 656623458, 620620967, 664438820, 646472, 372881054, 871706577, 935523021, 136555836, 644530224, 992563854, 492935657, 237718861, 491158350, 425657597, 703284660, 150124568, 293638162, 368595158, 800754670, 150707678, 787034278, 694017085, 563967082, 392432436, 819627763, 828992017, 690656459, 39812840, 342852508, 761636484, 163534443, 641221893, 970147829, 126677791, 327240394, 748882860, 22405872, 1454474, 551989423, 430537218, 784367164, 302213283, 48649621, 807450637, 56840097, 399489319, 737501203, 532956573, 99049479, 63305044, 811397567, 821935547, 50755083, 132907789, 657752980, 612558679, 23049498, 637584753, 797344248, 74282651, 680920163, 584763915, 637116255, 182163734, 371406131, 862609074, 181102742, 501793308, 781770747, 559056711, 226744408, 469413549, 731531120, 496900417, 329889544, 905651915, 289177187, 837777665, 140753222, 181667171, 642806441, 360732285, 348314966, 603609789, 329217443, 981064292, 112410065, 252842848, 413564564, 978741693, 984063654, 932550088, 535244946, 547971654, 789066170, 3170328, 906431025, 288087109, 221805535, 514058082, 480537365, 949576463, 575814696, 920164484, 792276617, 969647318, 81211066, 540332605, 910683917, 559076057, 311789574, 755074505, 751563053, 400024775, 544772773, 835912404, 230231688, 710390021, 665758008, 333849616, 682518303, 698930525, 805730373, 964119541, 807073345, 848772982, 368820313, 59562851, 467873918, 40094777, 159777950, 863245101, 797112665, 733195561, 229919769, 940694988, 342968815, 677260141, 678607748, 19952178, 398163188, 911785885, 631950864, 810121135, 875889896, 188968587, 208133723, 872308751, 340832486, 52231645, 702307309, 495763219, 613834269, 568759699, 394021273, 273599787, 586966300, 88369225, 332345875, 700837659, 75050148, 57599073, 868905702, 916659432, 113084314, 202221208, 312696254, 401972960, 165749955, 543993927, 814292153, 332728512, 567692677, 559255250, 757879771, 154599472, 558791941, 686782244, 751791593, 610471854, 354896885, 848626309, 253560827, 792911308, 469610015, 32025894, 933252701, 368916903, 953988928, 100458585, 301021536, 707724387, 478498278, 940128436, 480733850, 99739686, 772173150, 636263600, 611805427, 943385888, 747795210, 859911625, 250155383, 818834510, 822808775, 395661296, 442002769, 903217973, 703360688, 221557652, 914467308, 78036599, 878094578, 651000228, 681571489, 602512310, 872511175, 324126196, 586367964, 55165683, 981874083, 439443762, 405104517, 378050524, 689281606, 477961687, 419005024, 542813540, 316972678, 460524264, 760143706, 322050967, 800898569, 69284611, 278467178, 347868278, 69683960, 220876964, 653171960, 605459630, 6872650, 600919155, 124122448, 21206036, 980210221, 863559370, 225289542, 474120767, 656966883, 343211853, 156150986, 624767906, 59911538, 24052488, 838725214, 134916995, 806826860, 610080316, 139715744, 755952171, 823592907, 900305328, 904170810, 433347859, 389940673, 488560571, 559984293, 92451155, 94892807, 34967543, 178628861, 163270165, 297647483, 422091488, 277481599, 540983612, 704680295, 626674414, 502903617, 415803298, 892659033, 523495958, 15628591, 592649514, 205212345, 422685954, 160575364, 259782951, 70373633, 563888086, 668267040, 57418055, 902948036, 961726473, 671027561, 12051442, 364676852, 178452607, 957058979, 188677465, 223520838, 579888202, 172630130, 900533720, 491301080, 468615502, 699848824, 315357927, 101121233, 305987627, 510837284, 822081544, 55587121, 312248218, 199869234, 569032447, 145540129, 141627081, 899359238, 993127057, 824352681, 827725644, 173863590, 52650321, 835830870, 842010087, 176454290, 926867024, 795988489, 702907125, 375661045, 495526064, 680808947, 732525916, 145728826, 468355302, 893667652, 173157200, 341765360, 32519543, 566174089, 990633671, 404127119, 360426241, 238804546, 849427427, 142896517, 74037708, 9675187, 992484492, 268431121, 600963168, 584623937, 987233823, 358702894, 309168284, 544030778, 42273377, 960187786, 616936268, 588473920, 491132927, 411614011, 229724202, 906099852, 849286461, 614887429, 950925926, 100526209, 914346740, 980311646, 972374655, 940468543, 706958307, 936214034, 704242470, 697786708, 46622075, 226512049, 600641655, 880656833, 742963063, 380885590, 208594167, 589048250, 68296771, 378720471, 975784057, 939905904, 825696181, 26426513, 103841013, 494537372, 158847948, 477433306, 656033565, 558958993, 668808284, 884815853, 447274823, 422303641, 541988633, 90005099, 83968671, 534793419, 368604905, 305508644, 882845043, 835356541, 301997968, 415851321, 750696316, 99857181, 734007305, 817469541, 204733377, 812591828, 757836752, 45430547, 557352362, 692771083, 837646297, 484521686, 443487875, 131787342, 313053841, 467646456, 408151502, 740408651, 264022771, 72414731, 655240327, 426948894, 846607109, 533942373, 849982291, 749060473, 744093184, 534342533, 478855322, 586099267, 731415552, 806037939, 415578943, 381938307, 655916881, 785376915, 679739220, 910998362, 946645163, 836136895, 9484369, 565385955, 743974638, 505289179, 859358587, 291808890, 109272533, 980417796, 41078750, 216200524, 72422330, 980498512, 781498497, 902059013, 985826027, 265489918, 416850120, 732031868, 333971139, 179735622, 682647934, 562379330, 639397300, 396610173, 833092793, 125984245, 804045997, 848876277, 715506958, 800009099, 547409146, 917841504, 819048650, 797187878, 398919062, 604509886, 927181797, 960777686, 520550388, 176231605, 290026412, 964630846, 845002049, 887868395, 509957078, 381786087, 575387112, 448934123, 43188630, 906564835, 200386803, 267127569, 969700073, 908391984, 476367527, 413139361, 567332996, 837631291, 5552896, 524781401, 468678434, 915587180, 533389439, 161857319, 14121646, 963469910, 407389205, 8951360, 232175860, 822217931, 85307468, 203300073, 600141034, 987298379, 920629428, 994442063, 55214354, 722984499, 432950608, 239755010, 471382383, 685226060, 583051365, 821731983, 624010569, 619191146, 834073440, 130238011, 904163822, 991221552, 493634885, 65138111, 296860935, 621447282, 84274834, 508668493, 636418208, 402990734, 604685377, 768513363, 948465385, 303495022, 992422226, 593499896, 555912102, 36333046, 785339830, 597442057, 425268873, 828473072, 39941793, 2344780, 785042521, 273063814, 697972729, 636683355, 812369759, 626090525, 448296673, 496989300, 152373813, 703499231, 445875359, 115208840, 812250680, 837978296, 484219302, 897991702, 110424645, 63572863, 602699462, 536653002, 519556941, 615997467, 946941880, 658078551, 938408477, 108093108, 274873135, 6287736, 539806072, 521353476, 901745379, 206209480, 440561386, 898335727, 127789426, 383406556, 798867795, 989661508, 147177192, 103903962, 894431174, 361353430, 821500556, 774145016, 962707459, 944000982, 663606986, 414503712, 629234025, 736909539, 328095109, 351624407, 940614551, 847150679, 441959904, 276922825, 491438971, 198869868, 229085240, 770713494, 525876940, 858767540, 369621488, 169725651, 784260390, 693171810, 773429823, 737650578, 67544204, 285696771, 197461831, 890332989, 149872679, 695209346, 773435535, 124563630, 536328566, 591171806, 284636058, 943589368, 356656641, 264775610, 784441504, 733865590, 720971659, 241031636, 379768921, 865865310, 913471535, 497813128, 1832844, 221733645, 504568732, 567053638, 645488468, 863845781, 215722102, 489836519, 900589911, 70752887, 647236570, 181667539, 872043123, 193197320, 887327905, 985925246, 652294531, 969480352, 725849328, 653576847, 290520548, 264334928, 216876437, 769643399, 636839415, 686949384, 614914649, 847150190, 64448042, 458386125, 66788938, 579168168, 190349558, 263541475, 872054692, 412973434, 630025986, 847505832, 304232147, 682619321, 422844387, 429951141, 15203646, 333302146, 874751545, 771259057, 386007734, 60586711, 36568187, 189457400, 53504333, 460141592, 506171135, 929485201, 245689980, 371389382, 700951980, 428535241, 224047557, 649542636, 31779937, 851128192, 487001718, 172097859, 639625385, 23492233, 962823757, 23257927, 721519912, 352884163, 668946587, 654254987, 894267732, 925543516, 14145997, 147546374, 115518097, 363783207, 525153517, 536950020, 817649638, 685935657, 658044923, 220638066, 789622492, 316741889, 362986512, 680430968, 472776553, 35362929, 543669350, 585045733, 958677587, 373350864, 566723693, 540922833, 373408507, 372359762, 824994434, 273535847, 263389068, 813311966, 900805844, 924807753, 903835378, 551538130, 465212308, 558721687, 547428785, 631899696, 160134211, 258285737, 519492325, 672688184, 972749218, 919554646, 980602596, 493345726, 583966413, 320576711, 895189048, 176850353, 219632302, 254049016, 331198157, 874455668, 536291320, 346785193, 100902768, 930138298, 436635831, 296911869, 24663999, 98187702, 98393253, 671175076, 861789126, 678156574, 122258400, 685236346, 445023525, 23903269, 704418031, 224637592, 631945466, 595233588, 739778189, 207944453, 835283970, 749160095, 479243638, 541090014, 730056720, 661313867, 177545230, 448831225, 439331184, 350586212, 108940750, 57348164, 326884956, 41265366, 987823222, 49030970, 532140116, 500062565, 483104834, 203235037, 325347127, 471504529, 936768662, 267880602, 257252566, 235076756, 763446543, 927827412, 719325553, 592011835, 159282803, 373829759, 453621371, 557493883, 373754813, 285375483, 109990618, 366455100, 399099943, 283417061, 968147781, 791594587, 794286585, 92152761, 102409393, 63858221, 488715065, 111091044, 752351435, 89487876, 767637104, 943607758, 10104791, 415720373, 568568864, 79868288, 558552606, 863782906, 442834100, 604644998, 948382099, 889976297, 133074727, 993184942, 272564340, 410795039, 656892778, 214166250, 886837246, 593361710, 744018929, 862182977, 757392448, 255289782, 600974993, 917623326, 476019768, 156773769, 290932700, 790247873, 473976762, 971537563, 170568739, 741355129, 749500986, 479943534, 31207019, 136403400, 52991999, 277475661, 348741864, 98242240, 264443407, 383365401, 791858850, 623342023, 826460207, 91503070, 596879978, 548666878, 678487302, 289953722, 698782820, 409724701, 746099025, 515771218, 608977764, 178338801, 736097546, 919208988, 447043748, 932734109, 887341012, 51017908, 471917697, 140850088, 199090133, 651317708, 793682039, 60827127, 138457400, 78827001, 555585845, 349174554, 57812443, 931701544, 55923696, 674872853, 20462192, 844865523, 779534137, 36239798, 159557045, 7258725, 509855525, 286944251, 235980126, 369896236, 346268643, 906165283, 29704853, 251022387, 479909836, 495679667, 603284709, 897336882, 144827215, 85916616, 76110534, 100437850, 636143156, 442269443, 630524626, 412290214, 291581190, 166709820, 848127293, 773130242, 332437246, 199715725, 96816015, 580862150, 563074930, 9457443, 443857674, 846369470, 927504281, 323930526, 194037772, 427064322, 531234675, 984068226, 905372304, 457748598, 827812176, 660089533, 545961525, 707368019, 777992606, 837690196, 313915950, 110720220, 67950294, 822327510, 216709700, 675106031, 725137002, 23716120, 574691026, 804742360, 610399834, 502080836, 357726985, 89308560, 427439918, 234363980, 144450651, 339390528, 565066359, 31118679, 523540425, 706970553, 34086378, 724944432, 470349074, 136359008, 862951177, 766980016, 261270006, 892158040, 964087379, 880568856, 706926204, 310883929, 482413404, 206007675, 962218912, 591961415, 994549256, 604595925, 450478841, 947599830, 310274267, 219284966, 593479182, 915228764, 451957183, 55350904, 225347020, 756408462, 999377370, 71071023, 1263546, 422039960, 566113484, 29089137, 843273435, 196478630, 29083464, 677220670, 861853078, 948995055, 141684164, 531868979, 3100668, 173702656, 906613063, 793531479, 101911997, 698714611, 151086042, 134347528, 180329108, 132145096, 564199494, 345810735, 479910819, 680800913, 392134473, 921259226, 50027039, 640857951, 887706979, 486014305, 369549407, 596400104, 271403288, 164724163, 492605474, 992763318, 952522459, 156221118, 41933402, 317738296, 209026847, 737803304, 172394319, 37259414, 419213201, 365059566, 441539390, 73521714, 402639623, 570472820, 495427905, 18837111, 320410552, 477253148, 379168893, 723780953, 276142969, 680276496, 160386000, 985065537, 562267432, 186251179, 117210230, 648992914, 892434551, 614186968, 590432655, 699791269, 65938883, 461329357, 685647268, 860418598, 413766844, 703980954, 780926907, 559645628, 639234302, 339577257, 622211846, 33838466, 472014262, 718449484, 741270693, 27857332, 572516871, 260550163, 888676862, 23969929, 507670261, 912227186, 928147009, 491390923, 370792778, 191695884, 699362996, 262288656, 13566593, 99327315, 320878076, 574993667, 955685674, 334866668, 127970744, 186344542, 92509418, 583601964, 652184333, 772812947, 271862815, 28910488, 764907399, 213712379, 582422602, 967543953, 685141215, 962845713, 892539370, 324569309, 896763054, 253993184, 120861816, 55817326, 607081625, 710076507, 445863036, 120354238, 905897608, 67281648, 751599905, 939560527, 59812124, 847118870, 660341658, 818530111, 72454966, 606851094, 216270262, 917199528, 765473957, 711616234, 819969750, 697685642, 55835802, 782949815, 713771993, 323228503, 260271443, 133444143, 842063439, 205426855, 312679813, 559062632, 472086350, 721236183, 557537815, 534859848, 442388263, 437301059, 348100399, 899064689, 82002745, 84861668, 796091817, 189486418, 905635743, 671058649, 52206898, 205630159, 16871021, 468003676, 809320665, 132980942, 360947984, 258329826, 444592387, 261554113, 288233368, 615685052, 730249539, 536061195, 419414970, 294017082, 801049602, 940055118, 31810730, 42915651, 662014059, 577370715, 797892649, 385322089, 406179453, 54995043, 335974633, 555940901, 435372883, 510993641, 54505546, 789743878, 310495206, 419963113, 640970825, 976940647, 902028384, 668464964, 42128608, 481802420, 928557761, 910344580, 729476911, 36346432, 77630771, 282231728, 581421614, 650697182, 638251496, 989507817, 137700947, 684728856, 780136695, 722474133, 745496189, 436723974, 349812436, 537414501, 103519, 118654843, 105043109, 523321642, 220276987, 169788724, 831055998, 539604419, 741347470, 205195770, 249394564, 786893658, 659978544, 438968254, 555051714, 58173192, 43514882, 906120358, 60326232, 343119579, 223053197, 79445074, 890868377, 821138758, 911298127, 1248073, 384135255, 477947032, 763452880, 199899035, 125340499, 589146989, 817990117, 559373824, 616292940, 244938134, 433731120, 227788255, 867555596, 306383260, 235108048, 707044495, 943979969, 976598079, 333484298, 357798001, 978715740, 43643620, 35766834, 691635194, 207117355, 192089411, 393599867, 498373152, 838595322, 118676, 464790685, 393215879, 656066256, 366317069, 404724086, 955695650, 68723774, 585019236, 872203721, 218420400, 697581804, 461169843, 596958348, 469277615, 321855972, 159766849, 287423685, 934250316, 592306610, 800331938, 394268676, 391691954, 825450858, 487336172, 274051620, 411770157, 278268144, 711825325, 403772244, 179949168, 491771556, 132842518, 99614480, 880011139, 886998249, 713488219, 366630641, 802645400, 301228263, 275577008, 389837171, 749301506, 8603748, 651165818, 88344277, 914232778, 680027843, 464715986, 857844323, 162801009, 689426545, 878179847, 467290352, 232842990, 547521730, 675105808, 845493404, 247034796, 734361854, 363690828, 932699131, 899517980, 858388719, 966667296, 127630477, 456694467, 285347580, 601159864, 312832706, 692243879, 293043932, 857981346, 94110909, 259720166, 99647223, 281672034, 614400730, 226004009, 661638973, 267673146, 139226805, 869942726, 951579606, 347508109, 204239682, 374839212, 887573844, 372378087, 271168543, 115227255, 158011074, 755225816, 129346458, 677264163, 235060765, 89561796, 340561907, 762071234, 294422230, 311221148, 585536711, 695267639, 748296774, 430288047, 178312223, 934882401, 802367080, 405326397, 565028766, 315455128, 545150884, 463940152, 264285287, 649823804, 712759450, 442878746, 513779397, 444262336, 791031723, 882176660, 217578171, 531211541, 115199732, 193219596, 11354145, 771867121, 159582282, 214049635, 184848597, 8203656, 777171902, 78922719, 496658096, 786873975, 399503034, 318607653, 618873386, 315878876, 90733877, 851562727, 477176614, 542639336, 31671625, 321917174, 901665934, 309097893, 82388012, 676611740, 153950878, 44966304, 726278614, 827417748, 988020891, 619994483, 207951324, 503254767, 305282666, 161285669, 254181785, 942529183, 825818114, 836460165, 139463572, 613275776, 315114188, 250840638, 304561183, 977833964, 947044331, 219987909, 895988733, 860795950, 178146569, 632684307, 771354712, 807849044, 907131112, 316841717, 568450729, 519960328, 527503551, 255346328, 207716673, 666509297, 263669932, 356651096, 269014929, 665751318, 118227654, 319803980, 979503506, 897045580, 376066296, 9767907, 734652945, 99219995, 865313499, 711807334, 635223527, 98625842, 73305603, 827404496, 645771799, 209757543, 30141715, 26417733, 206832339, 159056856, 64684792, 398294114, 60266334, 696019054, 802704924, 712938694, 92202526, 15353334, 222810230, 486471156, 624350637, 219582681, 816064964, 546003016, 948000615, 806117158, 208549259, 692813292, 704626609, 892384824, 151860837, 338149178, 331270186, 60015478, 929734900, 91465625, 827681583, 132268476, 114545663, 30950326, 969848578, 255641097, 575352180, 39197450, 626670119, 176221889, 222890270, 138602888, 585655902, 312918697, 624891826, 445815076, 103299611, 540788437, 765671127, 93322195, 241496160, 349922969, 385102917, 720797065, 819986299, 403546583, 575394145, 334348490, 820199928, 524080197, 69893178, 638726404, 716855019, 299538068, 149716047, 448640416, 58663258, 56932227, 30754313, 286929744, 550926658, 960110078, 697310616, 230378450, 749648985, 163711744, 914452814, 17344594, 466393663, 516929707, 895330298, 299740643, 126247496, 889393291, 936701995, 200845798, 198882632, 123618184, 567541998, 60902807, 413791904, 424992724, 364936678, 890275949, 522442266, 250978006, 570378148, 340705937, 678657231, 999190644, 877535998, 118091462, 912317325, 193045489, 694003791, 15914381, 550819366, 360302061, 929296768, 40216703, 441923218, 466440708, 687155220, 241318179, 500888873, 245928481, 280401495, 156657614, 873575103, 304925776, 913494804, 18458703, 755578372, 399471763, 558703132, 925200101, 770909127, 53223810, 137102952, 85298590, 108196884, 632579151, 160631187, 942586463, 906218191, 423208766, 900395467, 903861919, 719740358, 651272003, 570401320, 923300037, 925794727, 359229888, 562352163, 377126687, 39628714, 443776334, 674654992, 176968228, 799837836, 392616569, 192474159, 802365552, 834767208, 841406405, 461898500, 885044697, 578431399, 743074470, 953763303, 99028161, 78757473, 54718361, 152609855, 609259102, 693454177, 899618509, 510130103, 23299789, 325847926, 463457695, 729130461, 38545273, 616859640, 652474780, 857632457, 510883164, 387891955, 546305280, 232381950, 409801057, 325071891, 524398151, 792871712, 197709236, 736263554, 763117993, 93990380, 731404412, 507950300, 366650834, 803049355, 109390629, 243088923, 317093495, 287030037, 448389950, 505542177, 603950581, 386296731, 416280482, 993735268, 610069199, 356615434, 115724754, 52109371, 507005873, 188579445, 217650192, 490704854, 897387397, 372108756, 506499610, 365620731, 295592653, 84666614, 548357427, 205890833, 711713558, 228429887, 629874571, 83548550, 713642759, 512576649, 165937681, 135517133, 966396047, 522639098, 256520195, 735462865, 271323644, 314901886, 295745288, 333419911, 83976015, 588418434, 432960368, 669422661, 637558289, 667726066, 454271593, 635779199, 859596095, 80120723, 684724474, 122333017, 918966625, 691109644, 578523324, 733333611, 171469020, 496821069, 444171956, 622368993, 446528609, 347881085, 310338813, 471532598, 732402317, 156181259, 280949291, 532105778, 963121396, 560741083, 962961119, 715962566, 315108382, 725739094, 274458773, 489260773, 440160517, 392719209, 996992173, 132545366, 554291167, 167311284, 824162038, 232395603, 902017367, 417199825, 640586676, 218672161, 87975207, 682412863, 863835011, 511172539, 414196424, 873974003, 683715623, 747868060, 6306870, 294918164, 877249928, 339616530, 574849406, 512974169, 87562237, 837591251, 499636757, 9778999, 86552252, 325601616, 203402648, 254745453, 54517750, 543064691, 596149815, 872625170, 256519554, 63527251, 199902959, 326339703, 340003897, 190003599, 259281906, 50716353, 439095872, 455499599, 562015139, 581524977, 146727430, 316236060, 118088040, 731918977, 524411311, 606522562, 451928564, 382197268, 709612891, 204751782, 466357768, 686302020, 67327379, 76189949, 877372266, 750660999, 49016858, 917748346, 123540689, 297324834, 379187349, 637883518, 767534782, 790777720, 715676933, 35466272, 850835945, 807185198, 122341932, 420259789, 281066245, 841647184, 856833878, 758508534, 253281647, 137687670, 212829822, 745125575, 404794238, 171510686, 610367940, 679192402, 731598724, 17625659, 601473723, 745046924, 889269089, 36272815, 155775708, 190494531, 874631625, 554380906, 599173094, 632826222, 107272270, 838436736, 251942763, 507670160, 166011182, 162630270, 926084813, 823777686, 844254400, 812426241, 616857111, 297329010, 833410236, 899917690, 41168487, 417738853, 109005087, 458868179, 124997998, 517049224, 1603318, 812629999, 164539015, 426741362, 444913534, 344847814, 356970935, 738640206, 434967470, 368050326, 807480280, 726815616, 890243248, 983345425, 5342650, 142107633, 787313171, 311058705, 893035774, 144691614, 353397907, 236310455, 683996782, 247379227, 451310097, 967468242, 188949556, 927632058, 507312242, 332086376, 583604283, 863327051, 845750674, 346429884, 570460343, 801609452, 115477511, 203884153, 712186542, 395476883, 105648684, 187442181, 531090486, 273025692, 287403432, 388460290, 391750242, 455126564, 990749869, 987157317, 559817967, 353090641, 867421370, 880873759, 826922703, 814115625, 933707182, 690900375, 423462805, 791760490, 261095759, 675955453, 115713465, 938878281, 908379586, 420721737, 32941599, 418133192, 767637883, 85318429, 306301517, 92953333, 948457422, 27264505, 624148017, 762455932, 167199309, 43874043, 62184539, 623594759, 955453182, 883777640, 863085760, 52577818, 901644761, 914015, 479262825, 496651689, 819179792, 657019200, 611384134, 966822811, 455310832, 233841682, 594524319, 11788352, 80900632, 811985424, 201744221, 631767743, 413873334, 759643024, 185716295, 916291744, 533655596, 456965760, 593722743, 758997474, 758836989, 322322631, 275503376, 814654705, 908135789, 586220865, 417657211, 234120967, 381432792, 798911910, 648726163, 34637247, 483537637, 170673371, 162226376, 444705254, 304402604, 510441319, 153588889, 136035138, 133807279, 572050830, 748698431, 410285847, 671058551, 466713605, 392076100, 559157437, 440198218, 725643108, 353791857, 958206567, 434076423, 539493394, 828783756, 616063212, 996322008, 139516878, 951064722, 661662564, 783561029, 760273597, 77532379, 570978876, 9354473, 445314375, 404926396, 991798506, 643784326, 868536431, 648706455, 176153489, 489410092, 777806478, 980395063, 198325070, 100231462, 619424504, 514919374, 211379221, 173211408, 410998886, 295478289, 818068410, 221096080, 265909670, 307655183, 483502035, 508774973, 615165578, 526466963, 854580534, 614232533, 332444741, 797080309, 294470430, 759034648, 596467979, 259677284, 546210629, 345914344, 777167848, 432017538, 159693965, 27024759, 57604903, 478353800, 397595680, 832041454, 928184383, 96051538, 690775979, 332112120, 927530840, 150422215, 815991364, 88887516, 996891171, 887172994, 383578679, 431071366, 491792293, 350024226, 307723910, 662821402, 744533768, 783487182, 990550486, 104005131, 922571244, 258970910, 646830586, 118773304, 421164210, 378469991, 57037603, 787690509, 857549392, 721322456, 934381274, 701505997, 126295428, 96251100, 896963592, 580622342, 270885408, 935107284, 561255371, 519042398, 948223264, 706307429, 628714241, 611026013, 621409473, 755759505, 927706470, 5181316, 136249401, 964184005, 993957793, 694418945, 915818844, 144189955, 697778144, 271043506, 282105214, 629825602, 598709346, 506601815, 280500942, 767549080, 865789192, 484998191, 798423574, 389100702, 325774117, 532760261, 860815862, 738123107, 513385786, 375345636, 355980718, 58469180, 786909487, 375369059, 149995914, 312069610, 507838109, 332029451, 310130428, 754586916, 908295043, 819489434, 955810530, 302299579, 31923024, 6608926, 217400031, 748067942, 717301782, 591204633, 146291617, 845243737, 429199708, 285909306, 726775183, 570711038, 826224888, 459454529, 387874168, 663572688, 387456489, 97318998, 451109696, 323435493, 841750071, 958071677, 35598528, 121382538, 509959658, 307108527, 374102046, 677462153, 771511012, 6053340, 767039862, 111544862, 131033917, 726979979, 813250639, 741790946, 594381980, 387356461, 977977479, 856147099, 512928339, 958882216, 328815146, 557939108, 197655483, 31722980, 446184096, 116799945, 738382815, 205216688, 178142255, 987814825, 414663151, 68787604, 147914950, 360938245, 510670495, 686242357, 619058523, 263992340, 253413009, 939153318, 773878340, 956241373, 840409380, 566901904, 318416237, 215290101, 590353453, 434228848, 662425968, 37901860, 448173535, 18262905, 413501087, 193735190, 614082536, 347684221, 866062298, 682733472, 595409555, 927482036, 573837326, 865716765, 246253996, 661468370, 901727841, 371217004, 929463590, 243756706, 922257758, 877958035, 891099290, 667895392, 860019975, 845816241, 591919795, 522194205, 996508595, 772716901, 805574505, 447419277, 737297767, 752774052, 548044839, 712162716, 316713317, 454976601, 509146781, 809111924, 415795854, 110702143, 791777818, 69621400, 781417511, 425074055, 202415804, 659492484, 913393286, 891861500, 749436782, 642101279, 950259627, 435431250, 85964865, 802504474, 752683864, 671496422, 168078137, 598034527, 749247019, 564036920, 221821170, 890602255, 49952638, 917077497, 250795968, 173137291, 131184365, 237148093, 751179846, 716376514, 62979236, 392791242, 690103337, 891989658, 469008506, 753584062, 176067824, 874857529, 552236352, 368476285, 134934253, 364759941, 786506843, 378710579, 850573419, 628649478, 316546751, 98648997, 142328312, 457334652, 296480109, 181012107, 371467456, 670279351, 976959852, 676039830, 635533394, 623653263, 111118793, 201442311, 615249852, 174102257, 981435480, 995182567, 258848563, 151955464, 652806965, 111937913, 891607176, 184491785, 97375528, 834791146, 604396494, 264163032, 385200003, 355380019, 875250597, 972998709, 747931156, 70889695, 851292125, 70862250, 647333712, 982958627, 336999501, 145122620, 937982564, 973651719, 123003246, 559121661, 358096249, 223488143, 966209847, 345309629, 673886543, 505485284, 695538214, 240751482, 758735754, 317534589, 423457458, 322444543, 407908206, 922169748, 531171111, 593396302, 26199682, 507552653, 88817552, 590216977, 292214301, 879759760, 313230056, 46294489, 44999168, 88780076, 534594180, 407683599, 218619163, 268441819, 755547685, 169251941, 856842223, 120362737, 214067135, 713318249, 480859577, 659588275, 210956562, 18473575, 316087567, 126834035, 723896791, 661109325, 388587920, 390784061, 542510483, 414333859, 770134890, 606166898, 427398033, 895731089, 685073962, 195396996, 512282094, 514961827, 755570016, 596239970, 97528836, 642059464, 400973383, 273200927, 893623609, 561094726, 391379374, 361477120, 209527123, 760630254, 658838275, 80384403, 13087586, 820926057, 261463133, 81384358, 242348040, 357731276, 146776320, 372617820, 84002853, 526489535, 122641867, 859677439, 315294375, 268229390, 114986428, 92363949, 989450720, 915768143, 625581404, 517754156, 784283252, 383420491, 410491800, 342838504, 201336691, 228034920, 201819401, 200100636, 81755494, 788000733, 271023767, 466196822, 155689685, 293481936, 895606914, 653656676, 794410491, 583678202, 115401511, 323331487, 929031912, 939777650, 831113473, 214317793, 387983673, 20247813, 255536277, 781619559, 777937471, 453139691, 495463229, 513234428, 301774395, 587460078, 399802963, 998115085, 552787039, 716862971, 268650823, 578685566, 605100501, 172994194, 543086037, 73333042, 834617133, 640178158, 920901918, 98436274, 558662399, 693332801, 678501059, 720149701, 525947535, 104867020, 57000409, 650097330, 171815633, 740226593, 410203545, 768173245, 687697714, 670010181, 799415961, 132379009, 58969612, 165750326, 431623654, 327424617, 824771554, 475043315, 447603928, 970393361, 455507831, 361990774, 752603950, 316148225, 527685198, 883368386, 525794876, 401413478, 728491752, 274446684, 42679422, 33536139, 946488485, 874783266, 240855979, 217132302, 14844374, 251026659, 454054437, 939003587, 636994389, 481963762, 854529497, 967895666, 896318562, 737289651, 954190677, 901400256, 320791961, 701902502, 571075832, 120884392, 20435058, 380026175, 373162411, 969696427, 658887593, 64811521, 521353295, 947388498, 118474505, 805626876, 782830096, 431498425, 791999001, 950635717, 507781233, 891156551, 740958392, 453577202, 688355899, 830508145, 646695867, 324833549, 506386516, 541607659, 174623710, 994120468, 384749182, 155188852, 9009529, 871334816, 324738813, 135418188, 546978555, 434541015, 660442180, 171889494, 561260947, 374594137, 646496676, 447938910, 892554652, 211117346, 814868188, 735073639, 615812125, 613778972, 434071869, 325086860, 963884563, 535013932, 718972374, 663845896, 771314399, 828912475, 731420392, 807062672, 624810500, 595380044, 164809476, 210707783, 780594243, 672184304, 104043663, 232783626, 413471528, 393931420, 14709032, 350317680, 704324680, 68058380, 898934439, 717437640, 68736352, 335092015, 499781233, 132126896, 803669437, 494455012, 210015554, 846443212, 969412495, 886072167, 196274643, 28437505, 807832940, 98967517, 738546615, 181312450, 615543462, 409520415, 93819045, 403226389, 997633256, 902473128, 282191441, 640917647, 196511399, 307985367, 637707879, 915858289, 415261217, 599044768, 511207268, 908515971, 569726877, 863967970, 265875581, 220612807, 186168584, 908889583, 67525798, 885901877, 968418769, 509591622, 616435977, 976782604, 580413867, 32545234, 670552207, 974442297, 481736469, 863075484, 787432277, 34032911, 254717635, 14738397, 997520517, 723662904, 822793018, 178536222, 293788624, 340273795, 69072203, 378663469, 972754831, 552766366, 366029434, 178360055, 112319057, 401165015, 333025333, 260112702, 735555331, 501640241, 988339196, 557442656, 252977650, 915425373, 929668502, 15472660, 513538527, 648551324, 184771682, 670476501, 531106311, 698812620, 673825000, 660782105, 258968003, 621658420, 74440288, 519388584, 1162777, 484519919, 556077901, 282405119, 40048704, 447376844, 427579636, 253797582, 983762479, 175916909, 907825967, 640622480, 825786220, 339507219, 212196925, 744081075, 980751363, 593868084, 176708370, 472653520, 791428723, 815993332, 819112039, 5617756, 518987816, 619783144, 543488934, 219444583, 927768808, 641776731, 964230783, 55505411, 43175521, 855152172, 139616312, 284766560, 248611098, 636819426, 656744881, 165460632, 423673347, 439268655, 548116865, 748028915, 386070348, 699274798, 343724480, 71995778, 293646342, 502982866, 674745046, 420327700, 827485229, 350832106, 381807567, 961290421, 257931814, 397002796, 105615563, 131848225, 741562551, 297658326, 493429895, 808488146, 801610166, 848766311, 444161868, 774659074, 576364984, 407257877, 458258931, 559470919, 739008280, 742064534, 430739043, 117870655, 32316187, 278266697, 660921901, 101430187, 887263062, 328724054, 79025843, 250589381, 175224349, 658952426, 869409779, 357003362, 31743723, 840496188, 311048680, 652649730, 159160159, 727974466, 136568103, 95828791, 416904017, 268768131, 855820314, 932817864, 414153198, 64596071, 253804041, 755900210, 378890819, 764007811, 11049768, 815471594, 58901332, 372640090, 722761496, 236712333, 323608705, 968870956, 635812158, 73372708, 19122765, 60797283, 170430591, 2970338, 313199408, 818094133, 665749675, 331021176, 746520975, 849255162, 550778810, 671137246, 217512400, 6914191, 87303409, 333521309, 943230769, 148187764, 109863949, 447816833, 945095836, 114470269, 839286283, 64115330, 259735140, 663272597, 596446292, 394606865, 523173781, 762047499, 146073965, 985948215, 493218440, 637359655, 62510578, 629045647, 421984369, 917058946, 382541688, 61892639, 475009693, 174194675, 274959414, 456230027, 222194458, 429929479, 757070186, 134091426, 258665101, 283107941, 528539999, 938828493, 328886540, 916899815, 237668908, 381734939, 271147333, 937761935, 92547540, 192597481, 843219129, 834179175, 101898718, 605742224, 749673190, 689491344, 426549111, 51770519, 207366432, 660770862, 506306906, 9455206, 968947357, 119119640, 765981521, 964500457, 605355292, 748532950, 373610649, 839546515, 725411122, 197999142, 552420807, 790028288, 319491504, 601221874, 950112729, 322696745, 32192965, 580352822, 820728618, 209298578, 421266723, 115611901, 622880586, 701660150, 140867838, 517810825, 927238430, 377409354, 163130332, 522446590, 596400731, 481012525, 728772980, 358324140, 718936966, 876085381, 252233813, 640090272, 503039909, 991371540, 10340996, 608173561, 534171135, 729489893, 49633686, 742205047, 964213413, 785325896, 815738635, 642849277, 924803315, 502007657, 117918828, 490941601, 297288478, 495967657, 547717467, 341348302, 787960093, 845364365, 697173059, 287647548, 934876655, 540502815, 689985512, 979600266, 280440510, 560679856, 558313873, 174283355, 691624033, 636318117, 410585018, 264433144, 329091038, 734520358, 799473132, 239223430, 435142698, 315353099, 358456967, 406428785, 434084862, 725417379, 903762107, 63732489, 502245935, 154820727, 217788419, 340045861, 682681034, 232301228, 983142824, 251979452, 924023977, 699383765, 867850202, 687262428, 794773763, 864102989, 99465952, 726358261, 230744414, 171346622, 527100164, 240292164, 809045209, 369771649, 989869289, 869963725, 94743715, 120550478, 935476708, 357755241, 604855969, 637004195, 267605175, 20473114, 132117840, 216313863, 748358443, 484147307, 777111485, 632969878, 235666244, 864692904, 961515465, 5393452, 314642625, 296216664, 122180452, 662774068, 372727976, 39890813, 481522066, 195467404, 107808505, 84961808, 543198224, 855916164, 382790423, 667284694, 898602126, 817663751, 973656560, 388632311, 527633572, 173981390, 646650219, 88737774, 172245353, 892838067, 161639305, 857972419, 303345217, 945081922, 111169974, 634890610, 182707378, 335551369, 623456806, 678879650, 500532371, 695371422, 421891644, 412284235, 945078022, 959382428, 62790941, 3190059, 505229361, 438357423, 928345207, 312987128, 222272420, 70736122, 121586650, 640754876, 270895484, 445661786, 467172743, 408758236, 721973755, 915211001, 539376450, 328215902, 33172509, 504867940, 147060290, 986793125, 283838442, 286266330, 915941031, 432356385, 261132537, 969900666, 4765187, 572187514, 492508210, 398879975, 686661415, 239478323, 976598301, 283283646, 368515535, 464813966, 715817178, 558061134, 8549426, 247759026, 936031336, 634459858, 877440602, 961469423, 116032279, 137543055, 726150768, 819750735, 557676299, 944852740, 410451417, 704384331, 225975151, 81327624, 535050719, 183167489, 275044815, 648334378, 98911021, 155274948, 319042809, 699383558, 426210718, 443392894, 409430721, 991946640, 698478306, 365641757, 607864724, 647496074, 834357871, 813339960, 141484432, 369170932, 867182731, 989596836, 275493115, 510370577, 231144328, 902886815, 775065449, 712232396, 313069712, 718209014, 295420434, 135429842, 136156746, 471224617, 225208849, 129868537, 883046726, 346366790, 486605843, 746218405, 167678900, 108611820, 984439089, 865844344, 295952601, 813918557, 435386207, 558993408, 425341249, 593611519, 992759157, 745287445, 557661212, 944591531, 954634745, 527402586, 361817993, 73848251, 118965313, 332393061, 30941715, 323307896, 399030677, 330911548, 78988476, 944526351, 772257641, 532346216, 929264254, 36607830, 319330577, 457533637, 135759198, 679131655, 497066291, 865921423, 452706811, 334556672, 815871305, 476778183, 89931070, 598514522, 894408213, 350387152, 868178492, 947291891, 230934064, 790880827, 215434246, 389303983, 330066415, 52205045, 930175809, 676484816, 399842203, 450734870, 87881531, 360145888, 89227038, 381275891, 246600792, 616843546, 9592862, 800451925, 469075347, 915836911, 876235546, 802383024, 912099843, 452290359, 671818741, 75219977, 950633779, 319077330, 449576284, 148728797, 746631627, 229948567, 270806601, 548028384, 526898036, 672201815, 72747098, 959356570, 978789472, 970102367, 129087003, 94913969, 764583051, 306735608, 333645201, 698579399, 720267019, 807414747, 358698345, 894173633, 147273995, 704896978, 887854554, 820017091, 40987931, 93760365, 530267963, 817528863, 711618760, 909449875, 953578182, 668277500, 544836311, 836663111, 129756810, 459737339, 338352088, 284160165, 364912953, 537722885, 311199352, 209959964, 21031605, 684275405, 729479061, 68953210, 942917253, 858352138, 744243592, 525346214, 725469369, 535847663, 429715728, 330356417, 701741131, 715477293, 288386930, 258842569, 761908941, 577292923, 507243128, 406237239, 337438637, 99902258, 628079153, 285823010, 32888067, 186836736, 65320378, 480443418, 461856931, 291069331, 853264485, 453741567, 984984631, 232253399, 818522081, 915978998, 388838212, 542206945, 808368018, 780503654, 212610184, 524341337, 129428385, 951618576, 606982387, 29158390, 128972937, 792252565, 131183458, 474648766, 283465267, 417148168, 861162634, 298992819, 153562779, 262056659, 356696840, 908917208, 873621108, 797472580, 755227062, 517253568, 805206960, 569966568, 269205474, 154183069, 19156502, 699682237, 264800109, 63065027, 636141637, 433098127, 97050962, 433680458, 775194090, 772487052, 547223720, 59423238, 866131592, 434620582, 658482951, 240586584, 390508080, 347861431, 973290184, 825034012, 490087005, 660287252, 618816828, 645701436, 993424954, 445521615, 665800654, 213619044, 784447273, 821924065, 883293092, 174672401, 257767546, 13760237, 565431572, 649642684, 338428979, 328358645, 583984565, 696866454, 461797968, 285039068, 249620972, 384269872, 797837111, 576415942, 888042392, 744058896, 823193289, 1565653, 198509794, 15522433, 85314852, 796564938, 323510509, 194316273, 159144417, 423967472, 594264900, 150132931, 519504781, 496317823, 360133943, 577405080, 625454289, 253348060, 270514455, 215182110, 83103612, 377968361, 519536591, 262428250, 579130664, 590609074, 142532416, 541391127, 557226777, 983491040, 628768220, 262740635, 366503963, 369798108, 887325458, 61943928, 128915323, 380887502, 62247174, 827483069, 663139910, 256373700, 162539675, 402224609, 934201280, 602797021, 600242737, 663547827, 318821684, 926832814, 991814421, 789112886, 521104362, 810969680, 62375348, 48320643, 387212589, 398239062, 992733111, 819396412, 757626612, 717186431, 489506055, 254854441, 12668386, 772706091, 492905844, 254047729, 887560879, 574471371, 821347796, 517454071, 560447123, 274976361, 570101605, 868147198, 860752156, 634402849, 22018635, 473997868, 810213931, 167608355, 822058363, 802333004, 720548017, 655360712, 531877269, 999826608, 360997994, 919834032, 56124845, 747416087, 54561819, 656088466, 478278480, 39930262, 557637708, 537823620, 796419168, 218834818, 821215891, 789555574, 394828592, 735525608, 185179062, 307426829, 272526252, 433843670, 161749762, 85571127, 83666406, 848603454, 185101106, 811978419, 116491223, 713365568, 608719014, 894506746, 30193715, 311564494, 517122973, 312165756, 278642453, 263636415, 44509806, 645094860, 485852254, 771358181, 830671676, 518130532, 525012309, 230067670, 721519124, 281624940, 611419936, 468035242, 563181000, 551740749, 207870848, 332010825, 117145933, 541890543, 510440386, 794845226, 207206039, 226921337, 7655675, 360494065, 469112510, 631916835, 613452794, 636924433, 773745602, 518102981, 364363413, 634968584, 20262316, 777110218, 679149180, 794496882, 480176225, 384496049, 352274192, 204919470, 792756468, 259290303, 327491409, 31941635, 149836680, 752401274, 663682179, 947876279, 603374731, 811957538, 964878385, 78976308, 525995761, 598832837, 857920556, 172090057, 222830329, 860628780, 254777492, 678439970, 656533144, 838920671, 527756610, 445694270, 907410193, 59809340, 388325840, 851841225, 325534273, 424114562, 682328742, 812349085, 584568159, 5804985, 581597001, 925785368, 773481691, 87938949, 53772261, 769023539, 598974907, 999223324, 384075339, 613272809, 141178044, 418663549, 916728235, 687365039, 449323374, 505870634, 163107838, 845434406, 274756654, 337121932, 260346667, 214282207, 183133969, 456948941, 288907936, 309243279, 949038955, 921568822, 844086470, 371542859, 317350850, 292013902, 614194262, 386117799, 264773319, 805303155, 424920940, 331004375, 632136095, 193312334, 588745376, 188536431, 475550400, 341507433, 972762333, 947920562, 494099667, 881938014, 912964456, 288421809, 73927537, 218209349, 11439357, 532431786, 575522689, 99834731, 988259858, 762242284, 208809653, 148056853, 745478330, 605552911, 795576154, 926352421, 886566776, 738325314, 471464863, 678512796, 196888295, 450852777, 848966198, 859518248, 610234241, 425638655, 839477657, 167750665, 308230814, 243679574, 399967347, 279200788, 249336263, 911493902, 6939748, 818740783, 377907541, 758391978, 655319171, 460449798, 619459495, 179173676, 549711314, 398070773, 323640946, 702617029, 917378262, 823689168, 193695661, 619724172, 943049296, 809577667, 482096076, 718875777, 946026971, 449880693, 22938195, 530013160, 390866073, 443000233, 179985256, 983823020, 138199877, 354285542, 1957313, 306833784, 137754849, 470145491, 825711906, 390290758, 439287210, 315072306, 515065559, 866779560, 543741428, 457494466, 475091840, 72732207, 354336859, 833327900, 276087654, 309137715, 720689022, 771086172, 375774849, 708939448, 609669500, 623333637, 24244866, 997855955, 734267370, 664130298, 263555818, 31192305, 918921841, 180321590, 259338031, 634356615, 27868655, 211460282, 455481908, 79766045, 610541867, 809343669, 949532904, 727617760, 332718027, 552710978, 779471665, 750740380, 904417418, 328588081, 339690972, 385052031, 387968862, 110172576, 269872544, 824169681, 805627815, 977617845, 397229410, 960093154, 896907042, 609860015, 449560070, 428930779, 923625628, 219975035, 35908612, 825133567, 167589557, 686249742, 242874400, 67259339, 673082007, 645678312, 336159700, 301939366, 668920331, 657732683, 493002881, 280148286, 829766436, 503538209, 462538278, 630826988, 521012114, 389576164, 49630140, 413456031, 219544876, 5248173, 960144794, 369372014, 823420348, 876865965, 824216343, 748299332, 794220736, 458682138, 835235016, 27612350, 618818609, 752314703, 570132250, 648758978, 412053047, 981949742, 197599761, 76337019, 736559812, 812523547, 861749722, 80665292, 484096290, 537700853, 426983594, 208100288, 13612886, 73709251, 838421101, 671971651, 140770128, 566122520, 407852631, 513250802, 106668262, 65946537, 891517778, 604013088, 399292582, 896868164, 539126862, 435414456, 233397254, 338209086, 523813279, 244328136, 858850014, 863461123, 701119441, 202696608, 345890814, 245744795, 243631611, 40038475, 951211349, 44233994, 483030638, 995860223, 425298663, 496238392, 45415464, 46735628, 159747970, 581481915, 904884258, 140624417, 801467888, 552783241, 400486888, 115233016, 893568036, 154967509, 489134168, 763779247, 675413855, 592297042, 882170039, 862256999, 306581667, 820541934, 656683004, 500609922, 504456622, 64116087, 559386869, 28812179, 965245923, 344761283, 945113543, 250271671, 827457080, 80436891, 575092516, 159363244, 215882544, 224419658, 757143138, 388325193, 489289427, 916099400, 655179719, 817291554, 725956464, 368986881, 849468963, 737564264, 216787042, 315460925, 980574067, 166752975, 751090356, 525345871, 192488596, 153980881, 816030484, 36840733, 23200421, 100454960, 384791207, 236372850, 480167833, 417660429, 915330347, 788181076, 318360411, 601730007, 831969134, 571406701, 658076597, 760957875, 301753333, 793530971, 425418487, 599702522, 710952766, 520401106, 522345551, 983724709, 126949254, 675123197, 308190840, 185991798, 171618074, 32254484, 685937522, 303592999, 491774172, 368134273, 424032688, 783329674, 525110215, 609745226, 282045458, 776794664, 595648081, 617961915, 446779942, 204147271, 754065305, 957219963, 983475207, 733535576, 621263590, 55741310, 833234322, 386021379, 868000200, 159914780, 937171500, 63365862, 746263811, 937855047, 861553181, 436680449, 21483223, 423956335, 500527651, 877700116, 649097682, 53039300, 189303338, 233720433, 922320898, 697319928, 609193188, 246891714, 652228860, 321305136, 494385373, 530411020, 818515120, 865600802, 84972357, 894867085, 940645636, 35611656, 727074599, 101329427, 973603262, 576764078, 204408724, 528510000, 682870558, 322219830, 674523332, 321939477, 573175549, 887222198, 542794207, 567495228, 646575355, 566897972, 82825103, 184137963, 58100611, 280842334, 194635856, 564690253, 360006757, 209114717, 239063028, 479436511, 319796845, 864383889, 619417709, 491268224, 145292279, 408168771, 423923887, 198564926, 784344827, 817314859, 764904570, 701355220, 545161146, 866447725, 535302934, 242105536, 67212918, 820842981, 760549398, 106761923, 801037732, 405733250, 754124844, 350405132, 128962019, 681489817, 725267259, 612698224, 865271672, 287844311, 516002232, 733290386, 620566451, 423427880, 526099456, 204177028, 192103904, 764760530, 429259480, 774658402, 853850434, 630854932, 290836069, 19081950, 74528292, 899810627, 312381890, 356587903, 761181567, 906455697, 709299020, 27321270, 184886421, 697159243, 187622853, 550964156, 521109750, 268875422, 178237857, 713866563, 554162208, 314399129, 888047653, 78061128, 43052746, 690423976, 594772766, 784611942, 43429730, 643926430, 958927559, 900616177, 404926675, 618520061, 483354385, 11041646, 211677041, 456901234, 721088676, 237164945, 426353392, 236955869, 365623585, 480636468, 464719530, 821841187, 549432625, 563257430, 550559455, 602984394, 403446901, 850828786, 24916814, 333903117, 800723333, 368856509, 936430644, 113068591, 662377231, 43134267, 326740020, 868236548, 507289437, 880475214, 848232137, 277028546, 263560200, 726916859, 172626142, 296092499, 351146468, 256040313, 914412149, 151688008, 481249838, 280200808, 63614682, 958109069, 336966448, 494722365, 68111490, 750779224, 498538866, 344156167, 475169155, 800290866, 774650365, 157712822, 380822579, 354894646, 907213029, 140669722, 869027324, 736804419, 101057544, 384147336, 911911061, 132422614, 379832339, 576201011, 566809099, 202211272, 9707422, 392748976, 27777851, 263953, 74654045, 942591763, 357865378, 398636255, 543667346, 650894070, 372174649, 282877113, 942084131, 329492162, 581795055, 969328440, 892495968, 840247019, 790705859, 928614876, 289444353, 89518269, 229660576, 103763450, 579624033, 165374735, 738273531, 421509702, 432778758, 82502181, 321701044, 501587963, 433490856, 730784397, 254667571, 886931279, 575879458, 474965230, 147217240, 557482217, 138376867, 543862783, 566457583, 330846348, 980763470, 251474502, 211076550, 350195577, 389766729, 157790298, 902122357, 581043965, 509074869, 531550077, 588964322, 988622120, 517466662, 199536414, 51250003, 441190359, 704942874, 612265018, 669196114, 433114236, 632326661, 721302450, 128619351, 766945729, 567983447, 617579366, 822402234, 287414756, 186740403, 124822458, 721738551, 307625383, 177696643, 13188973, 695057282, 105394245, 941461264, 66823454, 253384631, 194274084, 942099397, 263926261, 619249261, 244616045, 754981566, 521065408, 114355247, 57242138, 921442969, 291474060, 353384037, 846179842, 52823400, 903362762, 100315629, 268565748, 329856930, 888257549, 451980912, 559771480, 489806054, 342137969, 200369396, 340422963, 480119312, 621595861, 554962020, 355258277, 331036117, 203673492, 441899833, 939798847, 756661013, 485638917, 462297306, 403178635, 932182070, 365944246, 132674274, 23321176, 599609395, 869413958, 981705157, 460406286, 643702399, 65460718, 369046776, 904973035, 704043849, 140747394, 695213275, 962781796, 704913921, 35790977, 251231230, 77649787, 288392921, 5139720, 492544191, 261373743, 198497683, 370800470, 374871819, 308244509, 94616160, 670666392, 816306516, 672825668, 552803905, 271983175, 792743900, 468606475, 310232609, 300752644, 582368460, 661905786, 142890995, 792916732, 368872912, 758047365, 959548357, 596496714, 749966821, 258794834, 957028768, 639807255, 884108998, 750937168, 496803905, 975550683, 537236751, 305011851, 733799532, 503359638, 626237983, 974874932, 427825814, 76929359, 28717140, 839580952, 628724118, 780155887, 272514675, 472450637, 699532884, 694017791, 161839149, 63588129, 333900178, 826852228, 26047541, 583596753, 845928863, 867225811, 489881190, 991984339, 216119272, 324283078, 467254052, 504931471, 371640325, 480678550, 201221578, 517003479, 650709776, 649621385, 275015250, 694837913, 106748615, 59644661, 681364607, 376836002, 124472301, 120849057, 617982463, 187188900, 319844210, 98921673, 861440991, 70943852, 328235221, 311813285, 810961109, 905945973, 964558224, 939733645, 755611360, 98994525, 143701635, 600294491, 647029804, 936690571, 161677516, 669175096, 380660181, 856703803, 163237169, 990898295, 622640918, 207004787, 502933456, 767253713, 496408420, 199448457, 368879737, 182597072, 922837691, 273315319, 490811384, 642965484, 178291696, 309992065, 547346078, 216925537, 951307452, 88048059, 208582883, 129357815, 699618918, 991445674, 869672747, 818519235, 599163699, 265775392, 785133807, 139252891, 661132771, 365555876, 181936479, 914760105, 610254338, 570966010, 583316656, 381482746, 510183454, 271003572, 394159732, 541370854, 726629826, 954975839, 687439945, 486433800, 509373626, 494034386, 655965448, 180373762, 220991341, 330906350, 506565218, 652310075, 379746146, 537255769, 323489623, 120693024, 837706773, 561986223, 262534469, 790667041, 407073373, 17158369, 407699102, 402276728, 808437688, 945545148, 193392617, 882617966, 356142230, 210367551, 238987215, 530351986, 433272534, 395600204, 693421005, 206189932, 898045689, 809426953, 672101167, 288123447, 780407562, 29283031, 551073853, 485161142, 2622891, 384531893, 271887584, 87880028, 945080961, 965276904, 789387188, 703685077, 742862432, 339214219, 66249297, 540594412, 526520407, 972514578, 638721874, 410747193, 283191127, 582162912, 832146515, 941681314, 345432583, 918696923, 288693998, 213169701, 418705976, 269173673, 954033850, 863629431, 966797360, 95530045, 749472450, 808758880, 756482371, 665452782, 316539499, 535208459, 84984368, 800892770, 519811052, 600090484, 613724050, 167499320, 74144418, 85776773, 523815064, 875905186, 452523010, 452833372, 668408281, 691541369, 830282625, 336900876, 260999848, 28324661, 495866420, 743202351, 256392368, 297000340, 775537536, 839305771, 102413998, 161245733, 538437834, 320905804, 679379177, 907380957, 486628953, 331350717, 116472135, 519001340, 390602276, 757563792, 439832583, 646914909, 401116420, 141225869, 620890914, 692370897, 56095397, 511037893, 500029187, 353689285, 931038674, 493365873, 990540334, 276810101, 928784132, 781126398, 101160418, 120505992, 767766913, 806286356, 545422773, 254533809, 95342045, 474829333, 426860277, 140886551, 753814438, 26756207, 700525138, 398454083, 888113155, 945007791, 611842064, 221962598, 612406072, 675871540, 590598981, 786858106, 171056459, 346799053, 670018211, 52998985, 323281069, 746872960, 53100981, 146455716, 139550017, 324755681, 495408019, 820630387, 223735928, 563835351, 689486174, 976811499, 799022677, 893919621, 610148794, 738360990, 635490416, 859169689, 100912440, 459329010, 938180266, 244020071, 997192708, 904242459, 120138332, 582233043, 744916955, 908608347, 34390047, 154767352, 340499268, 144074723, 666373101, 701290839, 721818192, 344569230, 424230766, 986955392, 228505116, 312261694, 342852096, 496529624, 240532577, 795672921, 573471962, 488946397, 960560549, 14650671, 268982351, 195417562, 94680201, 591847265, 598911079, 256147311, 255489363, 494346565, 172973283, 841299201, 968027445, 308964174, 788076149, 534343350, 244598674, 189643632, 64376460, 69474746, 396452592, 108891686, 150497309, 821857919, 554099897, 791182447, 204648122, 675122558, 46593854, 107294296, 737276275, 590403548, 246906388, 768362900, 188373050, 832608426, 469767983, 803245210, 518956862, 500367272, 856918166, 838198038, 530819735, 669742381, 463588215, 266048326, 63355721, 873338054, 760364631, 115126602, 628278600, 200787170, 61102199, 867635556, 186626910, 289074566, 346862027, 440184964, 382923968, 914735027, 848525310, 692934791, 350701363, 789172051, 936822829, 672879062, 317918758, 327261169, 858300220, 489241375, 221743009, 691664187, 695855742, 739294375, 123649116, 715500970, 964062101, 918096977, 845853086, 86262497, 679709634, 362480487, 519978829, 240976485, 379857509, 377734423, 146554768, 303794980, 919153888, 256420860, 806226238, 83748564, 188979979, 553795801, 644334500, 390053546, 32974601, 595788156, 222547343, 551474909, 512769671, 654620231, 947876961, 890360498, 936221430, 525874918, 454977852, 968088590, 187247948, 432804910, 582703476, 322824327, 930168791, 546402829, 49758069, 226614706, 708134120, 611073452, 91673148, 26967056, 209399020, 831499471, 939317073, 352397890, 594297309, 174145636, 55900426, 357576695, 955655968, 259326027, 549349817, 992783122, 40013951, 421746198, 875448669, 621081065, 440733326, 944815034, 636844487, 840758909, 451029624, 46196611, 158565035, 624801091, 302396793, 294748147, 984087477, 761719566, 524329096, 610886853, 440081245, 662110925, 518551644, 311484893, 909521160, 926696261, 445066041, 890452661, 761377591, 660179292, 343456840, 806404167, 766402425, 409116286, 463723023, 154814914, 154520651, 555104120, 571882158, 12844874, 933434623, 752631967, 243589443, 558844809, 374834167, 632666826, 529649424, 51583973, 305552369, 188005387, 307497236, 644290411, 489892277, 412931832, 565483625, 319171500, 561410762, 66310243, 309596576, 681149558, 329781674, 599974944, 667207820, 889640264, 720190930, 907230505, 519206671, 455133084, 366215881, 615769306, 505182667, 837621985, 636246551, 229623377, 931530349, 553470906, 211342862, 333228432, 511783783, 735493698, 753134040, 892792216, 38983383, 474766070, 165741623, 373869613, 270902703, 130698932, 461670206, 978620405, 455542408, 762534738, 636836310, 916103754, 839157321, 99864993, 777641405, 39903287, 470438529, 401881240, 63046922, 718654400, 116793420, 662820615, 579357266, 878276150, 255067001, 671932840, 620510330, 115486824, 18048549, 392217254, 55825518, 916886592, 513935230, 446000483, 330474886, 125586318, 599059505, 673428095, 698775591, 182114273, 51357561, 181263538, 232811963, 29783714, 943901441, 281617202, 645815265, 523272135, 680338139, 821621896, 339730933, 909645289, 515362652, 917986025, 724894494, 302374936, 131849285, 813395999, 559491623, 348648985, 304073496, 654879652, 460056527, 476937001, 391037418, 264906359, 343986954, 856536453, 260478947, 326430682, 433617819, 819535930, 791930260, 682676210, 753954449, 388561527, 594882513, 164837390, 189852608, 941304455, 741088313, 874823354, 74972918, 85610050, 612163567, 71903979, 310262680, 428617494, 384312524, 299283309, 856459496, 610402430, 800619214, 38653964, 162170911, 464119097, 884769122, 323470395, 20361036, 23195658, 934997440, 596776797, 509335616, 740021776, 733160533, 853498124, 388894515, 836641982, 482955043, 274759396, 699313803, 371351208, 871126404, 522865099, 586214748, 698425568, 521472346, 27623140, 618659744, 108344325, 230702945, 579069081, 583409578, 910541072, 814158392, 418644670, 66239702, 943252003, 85984982, 388374482, 454440289, 244752310, 262818386, 578244712, 565202807, 746279581, 969047374, 75521196, 503816072, 894786773, 276234582, 101539067, 484100656, 83631135, 634734329, 360947163, 433080993, 843381534, 405914106, 585841720, 156495364, 46417150, 957012078, 613699459, 260931795, 683523644, 436803563, 422061359, 819957202, 170814117, 223329228, 466799937, 424098825, 591720857, 379883109, 334171250, 555405165, 223783944, 792726429, 207352498, 186221326, 317570848, 724217237, 424362341, 240350305, 692035458, 596551763, 64341454, 850748399, 295020165, 514502686, 262135531, 197970263, 387272552, 743277546, 61373454, 744556399, 230784520, 30112546, 564238279, 578675838, 835208804, 800210318, 592363352, 763901608, 178305233, 14761536, 934831774, 483228887, 947141316, 161366886, 393922026, 923840249, 378757933, 350297852, 632119092, 27976305, 800744076, 942152630, 858397896, 743431942, 762672850, 258816085, 185597947, 572569067, 187691236, 224893733, 82634846, 205424740, 820478111, 275984661, 592028754, 473450522, 711906823, 51562962, 697986973, 444951547, 147505982, 163165303, 612741245, 197972066, 791136170, 999399448, 240347283, 814296373, 256445042, 40033326, 879300519, 600823468, 412112912, 135887963, 536163201, 869768624, 831144411, 238224881, 548917264, 58981599, 879676980, 300564311, 688546943, 96060246, 638861869, 468948311, 109089581, 462698676, 339619987, 688489745, 962205538, 385736044, 771143734, 768989927, 391250800, 717785772, 720272815, 191126966, 407428543, 437167004, 124873510, 32917361, 869575962, 191133279, 130081814, 73970298, 377544894, 438391306, 79547944, 788887082, 143272416, 416982873, 260266364, 125298245, 239113774, 862110857, 123221510, 126173123, 73163234, 962391993, 229176695, 422958266, 929765308, 49839086, 203274927, 357658340, 712766571, 333765231, 856210200, 52141346, 414281324, 29648949, 797713829, 724049995, 524292461, 520833327, 669687273, 675112393, 280057440, 337127937, 938211854, 185151825, 495334458, 561623356, 298713435, 776204859, 514107904, 913554530, 125970105, 471904813, 268913551, 103215810, 475253868, 960216967, 957688148, 427138973, 108224042, 920847335, 382571602, 998192868, 229018242, 970478731, 961639773, 308872082, 991580651, 162306445, 656675780, 747359800, 832360063, 863764370, 175292686, 760682596, 658355443, 488329585, 159262446, 52446631, 884959695, 585406177, 76317101, 471777968, 441480323, 278247325, 41615377, 488938048, 925507991, 276076859, 329764756, 702223218, 903244230, 734614027, 357259117, 152611099, 670839380, 333194386, 6692529, 708432675, 846164739, 609238900, 755945693, 160953979, 435159865, 814394446, 913151763, 43368752, 495594285, 15841667, 68843299, 687326635, 928584282, 842430425, 902192151, 714863156, 847652813, 234768055, 156484954, 246607666, 380446325, 544845658, 78635230, 332010372, 49379871, 868495669, 850708471, 836948470, 126890038, 536273642, 358668490, 658223254, 21946478, 998581019, 479214901, 545274950, 533962691, 840424106, 796129892, 382447797, 893487149, 186425079, 290287033, 694254923, 207985592, 438939588, 918410489, 133059713, 26530374, 836308319, 618141734, 36774407, 945691712, 864840807, 122969046, 769546135, 455215805, 300004854, 463349521, 331233138, 662125452, 983464689, 197202689, 20856400, 996723969, 263183870, 294035948, 304845877, 351891082, 934689240, 379619040, 789717885, 284555001, 313560959, 296172915, 519291810, 614091918, 196714866, 755160812, 931677755, 408851183, 48500852, 882957538, 446647243, 16634781, 768429589, 675876055, 568710958, 233196228, 552727891, 100061048, 1361525, 173820493, 868185138, 375459682, 476085605, 247745415, 619605922, 691144836, 228508678, 172760758, 151301907, 770714084, 130386166, 891807421, 115397460, 312356449, 830975824, 418505474, 251600931, 694849598, 179902590, 649627026, 656881171, 309536344, 134996777, 525029987, 263877687, 24690244, 816798199, 362869380, 654665336, 713406050, 970000540, 184437120, 657257953, 707584451, 121151619, 744826261, 448643619, 897526010, 542601521, 438331250, 833397956, 923867813, 910482322, 133987160, 592188863, 888447555, 79876585, 112159874, 63718789, 803064851, 325682074, 783522597, 378416394, 934285621, 655681807, 539547689, 430009591, 286848891, 100418540, 308539479, 122105767, 87421552, 460388325, 565429938, 814198269, 492196174, 598265980, 27745377, 180318272, 97345447, 471045108, 422778610, 495563092, 626759014, 482267902, 817198639, 964638629, 900791513, 984464326, 101262146, 790311315, 505110789, 987515624, 196859826, 575668960, 276912763, 986078184, 146615355, 644466627, 747906143, 926517275, 402175218, 6438496, 827389596, 126471772, 412020929, 855975234, 874365254, 966767371, 513099415, 616879646, 111466764, 875021779, 468330260, 252544936, 673273527, 189216939, 492804971, 439620280, 306895962, 513741087, 182207433, 223387623, 585018874, 784456621, 763864699, 318413033, 541330680, 752569357, 398397229, 993604001, 60916804, 131280042, 797241999, 535340533, 708544792, 821076387, 466593175, 576989163, 986463684, 242377237, 653064179, 349359443, 189208347, 89546594, 519759810, 888476971, 387999310, 242564256, 501423292, 749557983, 456816991, 227590667, 872851547, 211088761, 262526825, 305777357, 256863233, 698038263, 122388422, 53209452, 862744143, 797950394, 770125793, 131787066, 863656543, 130201841, 612591006, 555980236, 835729397, 716651900, 847108903, 982449040, 898481505, 600266868, 498326383, 876140757, 984534793, 609478600, 496670013, 92608802, 165213760, 987402983, 433862145, 568624009, 313198597, 729893628, 489144501, 937872404, 986182884, 663813120, 399249938, 409884124, 373441500, 635128314, 977983716, 332422467, 693647141, 32899855, 190811603, 808266991, 330942655, 619339506, 177201693, 821210613, 522780806, 322842894, 21893871, 130624300, 617180252, 738344491, 958179226, 860956158, 190222746, 940358352, 151270085, 778037217, 600932654, 606721846, 972954591, 816071042, 538576070, 95933096, 612316041, 858253914, 589835659, 296555750, 775036567, 41938054, 560352147, 816581208, 127205316, 686459313, 4817401, 900326204, 550010704, 586940926, 538275694, 518604235, 966034680, 605952045, 828424869, 20025242, 471576858, 581897593, 555214713, 154106167, 743504755, 25030674, 695445145, 667662779, 530313748, 463728477, 810785985, 840914577, 682309226, 948705202, 276967131, 725203357, 489793103, 184490344, 698018260, 236204640, 849629292, 261378879, 676229603, 891246020, 537087077, 257338668, 64906835, 534517922, 122465954, 739003755, 349722043, 692672133, 220054829, 430105710, 353550400, 204271887, 605843091, 274613192, 511688636, 724992893, 646026721, 621582043, 411636349, 218712292, 243206226, 445947276, 712596872, 365663137, 320509159, 281202998, 646210339, 244819988, 578420819, 619752686, 993936232, 813409615, 453012042, 624490213, 734795575, 423540519, 367144224, 141148180, 616755648, 979605839, 607109025, 951566916, 297057171, 518286341, 970642217, 529176875, 252779686, 327949437, 544802725, 893161943, 881402901, 982635763, 90193105, 126427421, 566112130, 780094349, 959465468, 35159507, 926837159, 748286701, 456175016, 218222016, 135037033, 392432336, 443548688, 30688294, 302361518, 518346230, 685652689, 981222026, 553933148, 145332532, 396643150, 160254248, 812222493, 8805554, 167107803, 643230125, 799005242, 680228886, 584211876, 238133079, 21892070, 245373384, 377762991, 219935327, 109334278, 700483921, 223759864, 26697019, 79235502, 743471305, 846585084, 985809575, 739014349, 964647436, 861424284, 233256599, 539727157, 990496235, 646060270, 498099445, 689847620, 171950165, 815943069, 790874633, 121787482, 917536784, 793572070, 255633328, 811474110, 932066412, 9132998, 567808064, 381509857, 855546180, 31192972, 114690530, 666688611, 201454721, 601857761, 450819428, 66871809, 96196707, 703208769, 528979671, 993806757, 377913933, 837106444, 729834978, 70608445, 857978690, 447674505, 283354577, 765805905, 250374197, 154530940, 442321733, 604176508, 447007565, 201363536, 123323951, 575744067, 260748806, 983628463, 788400345, 700270575, 329423792, 592118350, 725431266, 492720543, 733934996, 618024992, 736738941, 13259000, 640470126, 934160736, 490090245, 769108691, 688712159, 33496482, 176604482, 223183831, 682448157, 147931846, 432448017, 301375019, 829379193, 485971937, 518406931, 366454448, 3701330, 771224373, 419729178, 477695034, 421340575, 359980484, 452951240, 945861093, 80400114, 159249674, 826961650, 246464286, 524942638, 310685259, 381482436, 172070474, 470780220, 730171028, 886541428, 875008629, 67204142, 774946580, 41621333, 589896473, 917491499, 764700022, 487104898, 401643996, 867463826, 767852249, 804680778, 835035917, 292899628, 556898553, 744300665, 230056106, 328029935, 754563408, 648335967, 897779476, 392223078, 73233237, 36501184, 227251247, 950239393, 252478139, 71607364, 371366370, 708885591, 515681755, 70655342, 447851268, 43732617, 719352450, 98881023, 427877872, 102331516, 415276420, 613793316, 247846134, 243404592, 682810048, 139336058, 238880328, 72688900, 904041114, 524464039, 739689621, 77260668, 253468498, 50466927, 342011457, 98544449, 941988087, 30807307, 525344535, 47619938, 747332614, 166978303, 319311241, 361772422, 803522286, 433055815, 270205848, 254869845, 439281889, 810734475, 195880620, 2108702, 591664468, 289997893, 316071160, 40265230, 343845604, 451284012, 749761085, 8167994, 807009283, 729363795, 511064358, 225002434, 931859938, 460146962, 794008807, 260331611, 688275350, 118302741, 506187928, 777236703, 981514860, 764374679, 576850555, 841038649, 222830290, 238098747, 303080193, 786839077, 341199553, 775267181, 11037812, 283017526, 164190463, 949186362, 793756995, 700177168, 169777151, 702931296, 22133, 738499476, 71684246, 23298536, 257961826, 683411382, 555157913, 116964622, 993648319, 528270213, 915387611, 121773447, 956751658, 145391197, 26744573, 965732934, 217334991, 765890686, 834175896, 945053332, 537079047, 998977019, 646566173, 434470924, 931187861, 706821575, 749710658, 70413216, 44010284, 495419853, 556138519, 600167517, 903355548, 931369719, 669765579, 72404981, 129651726, 735878827, 121989378, 465231372, 865834003, 481688571, 853110983, 271953371, 210398452, 67094886, 402786324, 956810902, 464051206, 315091351, 982751671, 576195862, 833992266, 788847762, 49629389, 635128675, 418947502, 671520619, 871430848, 519618699, 832670988, 116159430, 554447398, 91008890, 856880262, 769742105, 571625646, 456100114, 373355022, 900829318, 225440616, 12660550, 940660338, 901688870, 684357859, 706885954, 596093275, 611824744, 875337803, 825618790, 172613260, 486994742, 912907793, 523480890, 782021432, 181309499, 490907901, 430852240, 526145470, 841900418, 898219590, 328302102, 265015114, 899366246, 288309077, 532725392, 126881180, 612879962, 602074614, 745465797, 336079512, 345195404, 562021724, 722800965, 571272387, 778485144, 414421043, 850399657, 245234994, 462762586, 761602925, 551654227, 770571584, 964547645, 741955718, 570841734, 589875389, 788356653, 729180672, 314799182, 248855594, 122508161, 491739161, 392595471, 914140186, 24288773, 783996662, 430268288, 261828567, 337923613, 931530213, 505877812, 350709609, 19175653, 735788712, 353577729, 447083244, 451052174, 418583981, 939278286, 236028643, 756286598, 4304532, 958923881, 355672517, 51400726, 438543331, 146687367, 504256536, 634112675, 234569146, 629384396, 414045145, 553019798, 817097819, 173227775, 310862585, 751433919, 64100489, 163996401, 744151516, 184725196, 309021140, 553095311, 573405370, 185419780, 243616010, 404856160, 511440389, 616119465, 742128315, 539515435, 586972862, 65048192, 629906623, 790244856, 639320457, 497384735, 347762574, 823237258, 374427407, 896327385, 463612319, 773281860, 736527893, 121131441, 122922995, 238444674, 918896486, 736019694, 99172476, 787500129, 853814917, 676158149, 595102057, 47198649, 9319127, 495742540, 493862086, 647615562, 262645882, 814494165, 903723196, 20832945, 221469477, 279493841, 66342165, 114733660, 530950765, 660078099, 155335142, 927346404, 17341832, 72014042, 387970463, 867673037, 728527199, 960453313, 38997463, 298847064, 191157998, 457654723, 267260586, 458504343, 937015417, 615948885, 603090467, 811128278, 268364535, 183574693, 692059075, 58751761, 394236580, 369419163, 639768535, 455240887, 674592468, 953081465, 730747180, 684465411, 635025988, 909701319, 306468070, 409642448, 500569113, 173020870, 747844812, 549535438, 406373111, 499815897, 259983988, 552915866, 695968798, 271264281, 575651520, 37788948, 378433715, 705310709, 472125162, 776550795, 793936374, 273996743, 299697849, 423653488, 645581776, 467692150, 806295264, 541122526, 521282788, 534560306, 754164840, 516319008, 916488292, 169302244, 425088089, 505767915, 77794499, 161798005, 792240584, 188477120, 497996651, 235669505, 417655376, 874193743, 117095951, 532098318, 407468988, 748521984, 599481208, 490593757, 362784510, 885847054, 512034221, 722909369, 680388813, 866065505, 811103546, 136388852, 665234830, 291635223, 413367827, 683315967, 126783911, 465932199, 415823481, 45722713, 605246616, 684795853, 277655072, 323369804, 470569174, 644201454, 291219642, 433979905, 97499886, 106404955, 453836663, 7838408, 869379889, 473591311, 897905521, 264607118, 215624184, 467805588, 947770128, 217310809, 226350107, 647913037, 43783737, 551541077, 949724835, 105215633, 958251941, 224583159, 493391206, 526570992, 737140819, 515335515, 872730695, 375442694, 632510629, 456544983, 545808340, 635468625, 961175918, 451769810, 583140581, 332272441, 146389373, 911286020, 57278057, 628586800, 291081396, 491503612, 892946690, 41431399, 266793453, 441007783, 488465149, 461077813, 64386673, 921285774, 595851527, 982053313, 173998642, 724234523, 17113562, 946497649, 578740821, 586464719, 808258954, 662346106, 992888160, 770998070, 266688879, 662104807, 423439455, 476463461, 897480357, 451268163, 10885440, 288014592, 278648474, 391300914, 656466467, 976210517, 159547044, 959244011, 762177488, 63373867, 949296986, 746352465, 628780438, 185423495, 922374211, 662973830, 7655104, 941727448, 506835377, 100042104, 519660875, 405953002, 367801909, 373001382, 261929672, 86955268, 599517199, 541244877, 543571222, 723526671, 950356308, 366093295, 82006883, 105932503, 86788213, 712712836, 367440175, 698964032, 652183961, 669591036, 153196044, 195600554, 129685313, 555822901, 636520207, 499036086, 465982172, 275862851, 766455922, 628526258, 549877516, 340056711, 769378853, 254361370, 133114987, 817573748, 997528314, 7205203, 372319596, 166067869, 811726328, 106288698, 535823631, 934351890, 994246562, 111497636, 338730590, 58206557, 259658654, 15936424, 499348155, 886040724, 68726868, 867810395, 500669773, 133080722, 116828288, 575796875, 269524416, 905013518, 981234631, 560799776, 883320795, 791414274, 750282164, 920347000, 192485850, 539921790, 778137355, 628387413, 751635579, 717261926, 691297124, 622206793, 89025279, 163041932, 720577906, 422023939, 889062141, 145345571, 258459718, 623745438, 810609926, 82856745, 592801577, 331292939, 460910138, 617716940, 876753522, 293005657, 506243503, 453636460, 676165975, 904320049, 764582865, 34561135, 480742779, 502764004, 175422559, 449759617, 542867895, 156041565, 47880018, 748928639, 62341657, 507124200, 253780334, 3144703, 268796, 362217212, 501425203, 525392348, 340576191, 181699226, 450238282, 991269378, 736993331, 122233589, 246605435, 527044156, 268485836, 688696590, 138136292, 157276882, 597419299, 352608221, 686495179, 784918533, 147089711, 2563286, 304764397, 805193011, 181632940, 438742376, 899576329, 609548607, 80847343, 960113456, 405155, 622224243, 788447933, 986456663, 291729362, 964796841, 689776686, 710356388, 263379843, 17743086, 599796840, 397878394, 836396021, 580903716, 553093222, 361657221, 157183508, 668062871, 920283872, 92250997, 752772252, 959290228, 425396947, 27471627, 314357173, 367296277, 373718164, 203383735, 506427895, 24708877, 503195012, 771951113, 568943689, 623818776, 5365331, 834726236, 673403681, 372011203, 642154066, 669693293, 735107950, 791296566, 158353650, 918431510, 628582207, 232621869, 915064776, 151928148, 2288533, 520286300, 432024991, 87852593, 870170390, 993176202, 746181117, 843112863, 284359925, 329800858, 932522346, 490629988, 689707250, 211621555, 908717150, 465793273, 462171897, 752580111, 547215054, 971014180, 485814514, 540779079, 430077071, 152242489, 552391051, 450199811, 263217723, 701233834, 789219327, 648755250, 707786825, 839478396, 112736093, 635707908, 579692465, 985144123, 798291066, 544674079, 750786690, 185437324, 603901318, 879251715, 724019279, 806433703, 955478291, 206282798, 797032635, 126379875, 430776548, 239135555, 912685688, 960618133, 325422994, 116617263, 19902611, 861561328, 936547313, 194973823, 427671165, 977005901, 348916947, 845342136, 583503780, 354332148, 736796324, 491089697, 70322158, 991990719, 775026693, 21289482, 810509008, 942662323, 975850728, 166776422, 209899549, 590489641, 467588184, 469156370, 179554510, 922429921, 169155972, 636231372, 808960039, 719169450, 23562650, 811291161, 614680645, 692600303, 198844944, 525846262, 541880094, 293488168, 231865247, 782851807, 724192493, 423044861, 259201133, 779007272, 596136784, 232934070, 717163135, 511777090, 235525792, 503769218, 826567599, 987238901, 889032983, 787544409, 473114143, 36315420, 162937025, 742367653, 19395446, 33170465, 139800377, 673317538, 494477665, 444368100, 632198376, 93617342, 996981250, 481323837, 99623589, 315341584, 770649985, 731084, 371864587, 36043287, 11487002, 597913864, 881584140, 334601972, 636120246, 528578098, 535499753, 946628749, 754257063, 430682856, 378722361, 22809931, 976386631, 791420502, 83727890, 585026070, 466992316, 428379962, 204639717, 46976571, 561021819, 376939881, 854907790, 970671251, 232875520, 755336588, 87746022, 65335898, 391324819, 261556813, 856267003, 912437233, 435533630, 619735509, 166070381, 552941158, 112353317, 749425147, 715183032, 918610972, 611932166, 961808848, 80540536, 360978137, 175160115, 242931500, 569737178, 259203638, 729353153, 145992650, 582499721, 96382044, 602260696, 521067242, 214340212, 665131267, 476583931, 840287016, 614920607, 202002100, 225210461, 983189892, 423573402, 111309196, 585415815, 674742950, 470059469, 681215983, 464453251, 379628502, 949165410, 326758498, 160087878, 99800875, 718990324, 182724848, 648987090, 252594377, 238896180, 165450509, 760667848, 55517182, 530073585, 184366341, 721490735, 924615847, 230672385, 472862547, 729021308, 651443741, 105674102, 35609222, 226309759, 457318648, 602791673, 365687690, 749567883, 675883909, 100704086, 670177177, 802455228, 530381555, 730997824, 396478868, 134520196, 702802260, 48696771, 626690313, 263005181, 26154378, 605422997, 868650987, 288341589, 380737637, 843683342, 414096512, 723444971, 527628825, 813394751, 889577918, 877786570, 673974290, 845525629, 140226289, 999897184, 154345661, 32613745, 1649509, 384602348, 152577050, 504330097, 764854945, 155004411, 59596154, 957287564, 57949958, 286638810, 142189392, 179599808, 604980566, 759651418, 493922848, 447676568, 416726781, 872636230, 406521230, 404069122, 246692367, 942115820, 90717867, 429966636, 934694877, 798113239, 360842848, 911150116, 884366405, 258098512, 642832696, 548932764, 468082768, 931374420, 331780898, 445055558, 224134787, 80657574, 489647145, 987148276, 448789883, 492859775, 908259567, 874037988, 624632360, 825356428, 644888255, 325799207, 47988934, 334768667, 41399247, 103289061, 100874196, 548702886, 696075057, 392441555, 515466666, 81598133, 358852122, 136910566, 824987668, 45010473, 214705204, 85612219, 842800340, 598590028, 303227574, 148126848, 837424641, 453322928, 318106408, 811511721, 833832727, 105922208, 794099349, 378913073, 150257044, 796187437, 107392777, 518063983, 423758650, 983031541, 604539831, 213188513, 690105857, 692936268, 114731472, 924343301, 722394344, 723378452, 212503051, 900724217, 625937150, 430197115, 655908897, 229480285, 934839738, 231160107, 81357851, 381461413, 573659938, 795632946, 403833280, 688742558, 876559159, 861238001, 919396467, 40591557, 983760322, 531449962, 982712406, 86144407, 534041355, 824899658, 944432854, 897840247, 812903477, 977235836, 241164848, 329542891, 848785792, 716243167, 743214283, 71694894, 861792452, 235853382, 82372357, 520845915, 683093491, 994190954, 778327247, 630342107, 246238560, 158416623, 174705919, 746154679, 789929335, 596293510, 75074579, 520856159, 679952012, 818101553, 770362457, 462960833, 532272153, 707020405, 341155427, 519343632, 696421179, 597451075, 315278237, 992607200, 828708826, 706366738, 604918476, 213718065, 285182424, 221827534, 37048196, 263692770, 233148023, 357027607, 332575940, 189154299, 660428762, 825771885, 329139862, 12700250, 749862054, 936629425, 830819418, 671035652, 599679260, 896842142, 7945137, 254528673, 911158722, 253124963, 125703050, 477789760, 141534758, 674408277, 921440530, 813237109, 555072089, 20231181, 481881001, 946794464, 995003708, 864064311, 916592670, 715014474, 324077070, 592211990, 25359630, 977932341, 457688054, 55829957, 320540523, 147135125, 555248935, 427848301, 354385282, 421492029, 643828964, 410514349, 605879074, 956565583, 294681079, 516019333, 798095133, 908966765, 360125959, 191859903, 198690594, 711003274, 956110596, 406363172, 654959036, 108505654, 567033535, 406084887, 901415043, 183432602, 105498720, 716687140, 216629551, 979068393, 141973738, 503577780, 827725798, 107868862, 17802227, 483427972, 867180124, 986923852, 360785515, 662057085, 838892422, 470966323, 762877257, 857384412, 760469454, 481603804, 712856526, 722349959, 738241660, 910924863, 315249412, 396513883, 595050126, 47479436, 317922348, 617795596, 105964993, 265573133, 36598525, 517988840, 572848559, 816117781, 958519274, 510093104, 179545434, 152316152, 429492396, 471439452, 500125749, 743173667, 489384072, 912535550, 884466971, 662662429, 666325858, 94901468, 506064019, 921494115, 793803456, 368352722, 262926198, 111588542, 697382410, 436312495, 324819936, 436297680, 117508496, 403743288, 936017982, 587601767, 309339880, 931905846, 426011339, 238491128, 756849642, 649564474, 857593518, 136557009, 629788888, 503973834, 536992925, 471427153, 653340877, 792135962, 935825149, 965811262, 777583688, 950240859, 115840775, 892672395, 652073340, 491627583, 33444899, 678482258, 701972026, 859136416, 447521649, 71261732, 456883669, 794728114, 418763677, 306943551, 554352879, 11057712, 510129191, 785427341, 912554617, 652574781, 537189751, 242870645, 678427440, 667740470, 567546876, 992705746, 661533332, 541876333, 705763577, 200719403, 164737947, 231398546, 723033478, 896555169, 872625737, 766793304, 563741111, 416950175, 242481357, 300844803, 819322004, 983538748, 847059963, 109964529, 898486576, 149114422, 554882878, 617605566, 8044872, 141326842, 829459576, 173850646, 948060101, 974776680, 253699251, 758958399, 474429234, 666404614, 29770177, 601095783, 150769227, 447732396, 718145801, 7320188, 280482394, 294617355, 216762334, 22764685, 966361213, 260540788, 608643956, 804793168, 10377801, 515132239, 508035678, 89681598, 185451613, 759104854, 271147042, 206309744, 310120207, 542666617, 205258585, 737102706, 800942739, 72310170, 654831378, 32346718, 754795000, 51049450, 587352669, 565029735, 979345202, 357861711, 79375081, 774194099, 606003861, 304580862, 64069657, 200367433, 606355244, 120109008, 680651336, 571973979, 425246271, 535763652, 858272689, 264862454, 473676735, 275341956, 669580312, 906884193, 18394118, 918504480, 737579523, 824969358, 792642181, 215527856, 45855736, 864870613, 158573047, 988079121, 95771283, 534508413, 726176210, 512327841, 62603420, 328922684, 243915721, 441193863, 698570306, 571067078, 68076835, 797089468, 220504907, 592908977, 787446671, 589994606, 832740295, 672376366, 605261729, 102183580, 721841092, 177392490, 368126991, 668048130, 586291841, 693352347, 927789694, 386359179, 471068479, 55677261, 690287167, 407050479, 124915310, 276586063, 309113534, 807877006, 553152826, 957793583, 389065851, 599730284, 636649148, 101604365, 934973202, 85912300, 401170796, 112404657, 98392269, 837375863, 271920299, 589478718, 588487219, 751572879, 936190302, 848834374, 779440410, 261401511, 812210438, 504827336, 740178943, 415180595, 572084245, 269815035, 461731989, 913107679, 127187933, 790390462, 492611775, 357064085, 98801174, 175171127, 158134567, 828764243, 865153428, 132185334, 548953813, 29901637, 758919696, 572440244, 888063421, 293399249, 314117068, 747060205, 22087331, 990274778, 216000906, 264660472, 248400801, 3997320, 720904622, 631375352, 147755300, 21419709, 365587274, 823871972, 225408422, 426182715, 517084574, 494288170, 427642240, 723440823, 73653701, 321523361, 130649330, 72231776, 426250297, 238551255, 703964779, 133874677, 518759297, 195237395, 157855863, 564446215, 720605527, 529376913, 620351904, 213320102, 705940803, 931550698, 220496551, 299811648, 440641087, 25259240, 576768380, 222167845, 694434457, 358485600, 619607373, 585734007, 121647778, 684298988, 211442003, 244838789, 479243919, 717836636, 249738937, 681743888, 650024274, 687812440, 75704723, 365395753, 209992059, 263566019, 907622440, 41603326, 734105391, 105913136, 713421161, 243234675, 285008275, 680210831, 17859759, 356950688, 728419161, 953992346, 214663967, 914255895, 192837906, 419059454, 652275477, 299863815, 301181025, 265862100, 124275572, 647722376, 790679207, 702586177, 527925762, 856539872, 513554903, 249187430, 810011345, 126612850, 46833363, 976381579, 797361869, 492123148, 21676598, 841186470, 282582206, 703878114, 482542036, 271570776, 480929720, 730260440, 325630223, 203806704, 575448669, 137861100, 464746632, 607656416, 141764290, 595736223, 734336056, 758756716, 670322164, 64780316, 363181836, 246195051, 498491325, 170168863, 39693121, 679893211, 537527894, 896961595, 319295489, 975279175, 165898898, 468398971, 496959451, 686366103, 872750221, 330050516, 254280723, 163595070, 886927516, 355995252, 122904302, 174260873, 834536939, 573168942, 937899255, 114384746, 719344995, 465131394, 669066097, 488144486, 243190047, 457133739, 589367585, 126639692, 196973184, 163063987, 707391236, 770691925, 782984950, 825118556, 956913768, 760994331, 122841319, 870811108, 543381407, 542927498, 599839226, 112964744, 117214890, 111311682, 241314538, 615482904, 207236996, 912340506, 424258239, 189272464, 740461299, 832852909, 946527402, 718006752, 435918615, 281896262, 485128519, 751222239, 224906181, 214555122, 258411492, 156218412, 493804122, 156295691, 115515938, 237290546, 82615513, 761077482, 897621031, 88561234, 493239018, 792800517, 587801948, 77035461, 854351761, 362971859, 660142360, 185346561, 92262369, 225827020, 542386087, 913627369, 80590208, 955748797, 181397600, 740462207, 5483790, 938403636, 237305027, 623759528, 766641206, 871456519, 550670987, 372495848, 818268995, 154930536, 128466424, 609929557, 856210190, 939333352, 507082595, 488575285, 854188572, 424373547, 276743269, 296726733, 618059500, 432229213, 798507296, 891553245, 826229758, 29857323, 394452048, 4044681, 795072702, 688632542, 659995219, 698031852, 845292863, 682021762, 782651890, 336985018, 364946395, 193624505, 628143873, 464292003, 264048037, 78097165, 655299682, 839504655, 82904699, 221953458, 623667232, 629176709, 158938172, 174405660, 978186250, 579350286, 443102003, 217393532, 679720367, 837102705, 949415649, 232082390, 811553527, 851410355, 361701939, 872150358, 706495675, 203667386, 373879522, 607035299, 156002002, 1823497, 158033315, 155702653, 663577594, 372083541, 563625740, 672177214, 821232629, 473635832, 750596687, 431699286, 940849896, 203410322, 828070728, 990674778, 836487158, 982419412, 151299089, 990999208, 379727204, 604282531, 311540134, 484407134, 875895323, 67638030, 993185235, 441294975, 739871697, 63596926, 491161301, 437648246, 186454410, 809366123, 499191083, 336159765, 108275310, 602808567, 76197466, 30158816, 989090054, 998989587, 210800604, 877127985, 81602566, 864294259, 478057954, 585605909, 852603932, 215821107, 377892626, 141121821, 129254561, 781328775, 192111844, 358560881, 723113026, 760946101, 554307911, 569016956, 229796915, 394841075, 741014613, 388527933, 772092324, 503816451, 284772922, 421769447, 475360411, 460542435, 466073692, 587030327, 897049980, 964082050, 650785396, 34917966, 267274296, 93555553, 732636735, 496416977, 961289292, 191370347, 997722329, 341149769, 134669263, 718644315, 560708285, 955825158, 395358113, 470944678, 166794918, 459054141, 978902110, 218034088, 971147349, 222418436, 459948442, 972583987, 334516653, 335802275, 768697683, 21929631, 383022598, 603761488, 711019485, 388397836, 329045002, 191336825, 274553073, 915941477, 122626936, 234308171, 373993410, 28761292, 445910475, 111123804, 419152625, 817234421, 967455419, 885561964, 540300667, 840067058, 512339434, 563817424, 171775624, 213754389, 550477839, 155455612, 922926140, 917356306, 49632896, 574108847, 750591825, 887699853, 432154482, 393665368, 110721242, 628480969, 250072777, 82137284, 92284718, 664988930, 12907932, 800648052, 10216271, 560584789, 727288339, 955155204, 561317836, 758523068, 250651132, 818452032, 241346128, 158089267, 257535844, 959179986, 336239599, 13968538, 444508431, 640062356, 959008090, 953789421, 997402969, 56267320, 682428844, 73596415, 952111905, 787462735, 720379797, 23562322, 925934253, 726188597, 758962472, 985447224, 758981367, 887609405, 611220825, 293072972, 321892686, 772121627, 47985672, 194329005, 478973468, 364561809, 843600358, 720193323, 11149594, 58075759, 658962231, 799168347, 146728115, 246680542, 950409572, 777325509, 875814919, 685729725, 871785619, 496279712, 254311584, 69678393, 318464676, 136091437, 780490210, 917587789, 163750198, 976593346, 813694891, 536825336, 323206673, 862629396, 597651508, 411660772, 122884430, 324665665, 52877353, 629779826, 318167464, 901740661, 41075980, 242513627, 325904472, 254525275, 146311111, 187932434, 171219010, 793034753, 84766699, 312501269, 110694165, 765698137, 288472785, 754542397, 940866189, 528846955, 747424628, 194268987, 600474514, 917003752, 894905735, 918601496, 985957949, 914445487, 129548286, 435778328, 166326397, 143772083, 266213321, 769800600, 219059843, 470199015, 594552751, 946969306, 857405252, 115043981, 754482826, 871614349, 672381141, 19098665, 343858503, 371788447, 390276142, 934006605, 314983303, 958382959, 678118644, 649909670, 844368983, 495593915, 905770319, 381996609, 894135695, 817702696, 761688315, 550892077, 651429413, 679858462, 832887717, 533640274, 123073709, 486576979, 492555393, 728008441, 834088416, 330328003, 949989778, 837410185, 402789757, 410628145, 624853635, 570060783, 249911065, 574689756, 409163048, 1058862, 792145966, 364300352, 259870380, 121875344, 395536681, 15505156, 159849507, 794120631, 309320517, 422875865, 460494860, 826133779, 535556925, 594465428, 445153707, 579243065, 941643976, 569728642, 640145969, 431459457, 929344142, 640674525, 581058669, 275930361, 459296156, 907876171, 262292574, 118203816, 732838025, 855120699, 766462964, 15791631, 126853941, 415765933, 544071911, 259769061, 962873977, 46162148, 882833546, 545107808, 25840953, 290806601, 673566936, 170968001, 575297453, 739489145, 979733309, 525480374, 778535500, 96065973, 793714365, 854887786, 178018625, 593838203, 798163143, 677259199, 746921069, 644308677, 289804484, 645863091, 616517234, 221925671, 933568374, 514831805, 220311353, 423883619, 524229279, 423466984, 156177339, 582534237, 837714329, 540243989, 784892631, 131351155, 583126432, 14123694, 665708948, 857426116, 812856082, 37566711, 876006607, 779462457, 661228558, 109948133, 776347358, 48140501, 964184062, 984943214, 501438031, 39228866, 436722486, 938855908, 285260523, 103893662, 334935331, 734127330, 12025572, 73948457, 763034013, 260685733, 946288937, 515182692, 380606638, 974481139, 610215596, 251433344, 556921008, 437797123, 270199675, 585511097, 842703502, 27499775, 848002046, 360946114, 297481589, 433903761, 866865268, 705692805, 573968910, 14945090, 514014202, 966194949, 702949701, 219176920, 650660312, 470450522, 555950570, 786096880, 523284615, 353030043, 524047696, 910195070, 609123962, 665391917, 73999254, 551405671, 375240824, 379896563, 947769362, 929223466, 131984977, 397485853, 879053886, 401558454, 345299382, 672658488, 43406985, 390981087, 566108264, 207408972, 731170874, 963759531, 763418547, 647769040, 475574809, 660713895, 333904092, 319782008, 678803527, 54176143, 638524933, 470184671, 628637687, 388242991, 569787439, 517835422, 324829864, 714519038, 62706672, 821927518, 643107307, 559855670, 909077209, 6669094, 375228670, 556482980, 75382694, 551264502, 819698218, 375867198, 64047194, 248853353, 240305502, 755665197, 901644999, 621699603, 876811850, 83433555, 370290428, 368147786, 769587351, 140078335, 322483079, 998363369, 283312423, 963946549, 107815281, 431154353, 852934745, 116477116, 79952772, 916367695, 97185710, 527054583, 171605794, 414858312, 964655981, 285264367, 158159872, 371227998, 824490870, 11157420, 195950678, 891196326, 606469235, 15433692, 953228812, 932435258, 132872237, 596792307, 566537006, 963240700, 456576923, 623279200, 467398633, 431848879, 860502001, 969289931, 887105587, 894101720, 333303060, 166965705, 279059953, 661348608, 793813164, 558835379, 414177615, 456458646, 743957455, 821028778, 832768966, 899709212, 941605429, 333708150, 967682356, 778777821, 148807380, 754904984, 112984126, 721346090, 33127459, 410713504, 384843685, 562819551, 235824790, 693994439, 317259751, 700160514, 173054337, 22652302, 791223346, 239777705, 260082899, 592761544, 208050515, 851061399, 604370767, 433394388, 864451613, 629734718, 326962123, 339425856, 744378648, 193494190, 553076940, 145153196, 990065457, 544579633, 667376639, 77315142, 971736230, 895908452, 145574270, 16304416, 37273653, 796812599, 467458158, 617188974, 477283212, 794413429, 514114875, 228744644, 151364613, 535879648, 608331869, 644317182, 814307721, 420799401, 966724092, 304565586, 616806724, 83566870, 967642852, 262848248, 291801355, 797945261, 376419918, 690831013, 709397238, 916299382, 549585241, 573164368, 202387968, 90788877, 572388825, 813382559, 565487065, 946274807, 510718683, 345896007, 121541856, 739197806, 125000168, 544119674, 241886436, 666981620, 318683774, 635248405, 337555514, 691938163, 902955138, 385732185, 257604402, 518866347, 730857367, 572585558, 245873298, 863655285, 68333805, 409271148, 465847541, 656548857, 839428810, 263500597, 221236866, 560973544, 834884522, 107338261, 704425826, 849827265, 48888928, 854270904, 333203927, 462217510, 493248654, 234670892, 793522622, 947632289, 333656890, 346792542, 432025182, 399995985, 828802253, 945976507, 671039942, 29639166, 633485376, 742524195, 729805276, 760995715, 715953718, 144896773, 460144112, 661230129, 159120855, 789135042, 891738953, 13667950, 256878826, 893567678, 786583565, 899621660, 452743096, 776586195, 606889584, 789559941, 466932465, 171280333, 700477957, 545795291, 349584889, 240115102, 484476172, 965430698, 74489821, 296549153, 904531797, 101021280, 65542318, 218138986, 696332128, 531269207, 285699745, 41348312, 275968846, 307455220, 663480987, 610472940, 352900442, 164286572, 453440758, 463342775, 923556993, 57259470, 995123858, 864821445, 239132958, 248122167, 374469370, 278293231, 622943196, 269424513, 590564595, 925469495, 655715957, 526553216, 47393955, 667819632, 271535356, 476907187, 424584169, 954637502, 103410283, 914213888, 676700812, 948692957, 958927836, 499506917, 182851209, 957036403, 74345891, 676220621, 455433808, 871769092, 498727735, 496345709, 657769155, 921255142, 980522792, 532965472, 786750451, 210184780, 527883919, 844983704, 220015076, 9650145, 269261561, 484827363, 563083792, 864052183, 877566965, 972611257, 480334981, 508539831, 101650874, 572053145, 234484393, 917048318, 891416917, 525386891, 877862210, 36663871, 747545732, 21149666, 81146308, 293680793, 338290123, 242735458, 982069328, 339309696, 575511598, 541608340, 659857263, 871303150, 782229555, 441032717, 621995869, 469567375, 44345806, 556641446, 47445101, 669175651, 73617472, 420180536, 366040749, 662325289, 91494840, 791495775, 326282609, 525213981, 833397266, 815580628, 129783863, 731701566, 133493555, 264340418, 290716253, 26571137, 609054877, 279779933, 254365918, 231129928, 112923739, 6116503, 658531688, 85972289, 841332038, 478606804, 920547021, 615891319, 221161779, 998714538, 384403694, 147640530, 984237282, 732456724, 329733178, 876571079, 382262707, 369886252, 62701062, 163173989, 640588694, 915570407, 564671763, 770510425, 770685266, 171373874, 410900046, 843436729, 198749321, 460222931, 42939167, 981727637, 291811670, 899734528, 179175803, 198510868, 285571655, 320834946, 290926984, 483202002, 181474653, 635059003, 259438081, 574678287, 827871829, 486382404, 611796952, 240043326, 229146005, 810868022, 601529478, 99959809, 848659687, 582725482, 538765075, 82311048, 456613406, 808733857, 131237508, 736918622, 195654522, 17875627, 851113201, 80445619, 302066978, 665716611, 584818257, 824902644, 498428632, 992182106, 946993511, 504840546, 214159909, 685592345, 958556766, 479685715, 847784482, 914225504, 817765552, 29309088, 192345152, 377613889, 785311913, 112178315, 785099020, 939354428, 986587375, 507058373, 563753647, 868270924, 364001272, 594353986, 788631040, 935019345, 78012102, 523510361, 399162551, 191528825, 879406057, 332469418, 428389005, 687890483, 232672346, 175009700, 814662456, 864293511, 360569365, 988870256, 488857010, 335318505, 500828748, 127929561, 368577106, 550366555, 621132357, 735801713, 551973227, 611598515, 427907111, 331203537, 130915694, 990785868, 101001187, 490285266, 143321958, 859941206, 853740806, 33757188, 824467485, 352429170, 472687442, 526283091, 322628240, 550933186, 615093259, 937369104, 417829707, 117055777, 643750297, 514707479, 707704169, 840646748, 657923706, 747500689, 904497098, 14808226, 974185824, 852619095, 670731700, 669738718, 533108904, 933986620, 337937579, 662142973, 679055317, 472547326, 834470087, 985243653, 143808192, 520613815, 911031376, 668609145, 566321900, 340554309, 824983367, 103128463, 702372833, 729506681, 683536817, 266509939, 948799893, 373871564, 894079624, 43070948, 710248993, 975957775, 387809332, 399699027, 724210395, 242905249, 834549177, 184680463, 694533130, 95013713, 358064182, 721092921, 809715793, 125087045, 285711886, 772086540, 763287176, 918006629, 574402327, 772528205, 226601168, 473102835, 629706342, 231115411, 918188866, 901901695, 370290477, 198597101, 855227541, 861858301, 31586832, 314396077, 572917280, 741568154, 221074511, 90794145, 485413585, 820818068, 435203783, 719076071, 600113963, 593349244, 545081392, 495858986, 334324203, 765630351, 600351184, 2168016, 665801240, 594286842, 919927575, 49653500, 147542542, 674856940, 36481665, 788275404, 961835611, 272140421, 975915323, 749851786, 500066700, 749087476, 499681221, 194831203, 782434284, 669871114, 717526041, 127888252, 45361351, 312085754, 888910929, 229731876, 449302979, 830175680, 346428707, 20399341, 650580253, 726452268, 432940620, 39285367, 389587991, 959047432, 653160320, 380923946, 216392558, 325670371, 523418622, 683882436, 611882054, 577063295, 325140033, 409150062, 503019141, 810428646, 529565005, 82993158, 923515665, 7693088, 596900628, 21229595, 27448470, 328256386, 441548841, 242329469, 981923810, 64751755, 525918086, 542075650, 719064116, 46910081, 226736149, 184694809, 928952743, 62901811, 758470066, 239440523, 196762760, 440119000, 166753253, 193437684, 247307509, 599766609, 605848541, 754704620, 123282347, 269482105, 275574388, 863906665, 586964174, 4368927, 236870080, 741036051, 121869501, 796854065, 709518103, 469043144, 689180255, 16639305, 706195050, 107381522, 444210763, 915659273, 539273097, 452469780, 116819028, 635805278, 271865154, 26856459, 794730453, 16588473, 186496949, 365772527, 264542922, 639835855, 817466636, 907140960, 509842715, 840879157, 425914954, 646694601, 355122593, 839348459, 752819, 632387297, 272987069, 203244062, 413984241, 747899382, 605433795, 668401282, 848147624, 686968592, 937064328, 605814370, 796505174, 706829399, 85733768, 51186334, 363090621, 646716955, 403332356, 856921601, 701299151, 12253124, 298475939, 26524956, 128123582, 467609408, 8217770, 90931308, 301704646, 645944050, 975118397, 871434900, 402912044, 34373837, 348776844, 102531768, 252685317, 581482565, 117115376, 869672503, 575244061, 120482042, 53668035, 254152205, 363739092, 600156883, 826317445, 163673219, 345141560, 976356186, 316361519, 960212260, 269081964, 91520918, 952764729, 674791365, 138727936, 531662274, 560308535, 489037027, 539758639, 229733648, 633276405, 633015595, 984363612, 207833129, 449849743, 359019403, 740033397, 865427774, 882253582, 209069653, 808321356, 811524538, 14770570, 509353219, 637100070, 366072963, 960650479, 393338249, 372085053, 636540318, 851641694, 816888812, 392572223, 408704088, 954398752, 393692490, 515259888, 380086617, 760951274, 218696438, 238514253, 913770686, 683581382, 543573210, 337393224, 603792894, 569426886, 573276786, 11313738, 186855280, 887906748, 876343702, 307555261, 329044509, 69100633, 459340551, 973035760, 978102398, 248196201, 372495217, 13859151, 397486785, 71138638, 10976756, 6737673, 743831061, 465358256, 7083858, 350728598, 352013000, 804203183, 889998628, 853728164, 982760929, 153615090, 260347166, 686526972, 512378777, 355880355, 622136739, 258222162, 373697342, 633981107, 825479173, 564334845, 573605102, 808383228, 727534497, 239192730, 69358408, 529648551, 239559448, 69107485, 696750484, 502573040, 137208671, 396944844, 435615093, 121576765, 681258609, 675676615, 141502454, 392246273, 166942051, 377930413, 592772169, 532521682, 266445947, 813732580, 523498448, 118782880, 125794352, 251056267, 15565147, 540956225, 263269905, 793788849, 99434912, 891052690, 797964115, 530397208, 651562000, 671802710, 577388137, 772484123, 845418866, 465134178, 460633905, 369487322, 443469941, 931587707, 613968220, 198779434, 930984625, 75682207, 997332594, 814508870, 897081372, 331075627, 909801358, 650254312, 100274662, 566664341, 125372871, 786710395, 200388189, 188125562, 89030265, 8950326, 288581986, 6613010, 997551829, 159035548, 367035815, 589459957, 341037236, 62820176, 640241174, 927820108, 559842092, 802532006, 277656840, 780987090, 824704745, 149388592, 567968933, 644199966, 877003696, 313982643, 914637366, 806062084, 482368286, 422341670, 19296411, 11959561, 47410066, 937285153, 344745416, 170382428, 588158754, 231678102, 390781548, 962448724, 702291576, 706725233, 264095644, 320178167, 936693136, 989161679, 717694106, 772617122, 145342771, 405422602, 285485173, 687676709, 866527476, 211509751, 70394224, 651400408, 434810544, 663152254, 864772383, 370801719, 46775853, 654305926, 368183563, 675960356, 781801685, 638672934, 538254940, 473182741, 844108824, 753198487, 627820056, 287711911, 555431750, 278436572, 600650885, 72097819, 9755496, 768494496, 336323551, 587947332, 549146164, 697972495, 679549791, 129585882, 121844231, 157837365, 848376111, 569686145, 411202116, 736616883, 478996178, 223090937, 130078707, 121083165, 355288834, 944380599, 460218740, 332570042, 808753686, 777423859, 536574218, 342129660, 891886906, 462849896, 448231956, 291541096, 523609716, 794025678, 277952344, 467996448, 481495089, 467067274, 689319850, 940737764, 873361283, 108389560, 310555604, 443838431, 913722969, 346707286, 784931603, 1172096, 775052292, 221051723, 949720928, 975362806, 281540961, 17334983, 179926842, 2156868, 960811722, 491176277, 100791628, 905263570, 957249386, 84890454, 318860962, 885202203, 71135716, 988797640, 427575078, 298678434, 503490719, 74231595, 376639748, 992413440, 494383589, 425390738, 620937172, 525391266, 387783272, 976379301, 298667287, 965024521, 485759915, 415362509, 873633836, 958775269, 140892062, 9162367, 318746451, 479860861, 172724315, 714336000, 926936092, 324955531, 989739387, 785224426, 343175980, 518758219, 196887051, 213165897, 532149903, 774574912, 726307983, 404245632, 904006292, 403400556, 830071314, 639687601, 796685533, 156831544, 522766598, 643611279, 916395192, 983425952, 355168019, 782069989, 920384698, 314044732, 878019442, 821918726, 108109447, 708782593, 179034406, 636994229, 854474907, 636496569, 393352959, 703203042, 623076575, 152483027, 996587992, 938279541, 773580875, 680130663, 728488672, 736811750, 578721297, 966046199, 931850353, 672408932, 257684475, 500682650, 213088665, 120674987, 896411525, 252278446, 639785240, 495466470, 348067964, 435123120, 426618595, 283616254, 963506268, 460174315, 28587504, 74902204, 312733599, 343476133, 367414855, 917419722, 660668950, 826742860, 389653287, 186889959, 277694510, 381732480, 40889181, 478150564, 846096665, 802735644, 186234068, 813316640, 503770962, 246051321, 655634177, 795632882, 515443288, 74406860, 781134867, 224070525, 282304562, 598444448, 87610410, 627457712, 770711521, 291573675, 818351281, 734380257, 637395019, 325660493, 428363591, 43783803, 951970613, 960817332, 164714469, 839465510, 946574171, 482550227, 505153446, 974556204, 518610751, 61404252, 731561768, 323801110, 278813545, 860672012, 613238274, 413037607, 769088719, 849805497, 869562011, 866204888, 125437466, 488237735, 747348943, 677939029, 946682618, 676648581, 305136901, 744536038, 76326976, 273641031, 677681232, 734871504, 51625303, 545615907, 686826225, 52790494, 438670231, 466384504, 774788012, 112103191, 181343316, 760002728, 60950133, 875964005, 414449464, 415734359, 670070558, 992116423, 50522905, 522750765, 9309486, 873780674, 639161190, 609344946, 255282942, 385945084, 257806780, 783128592, 289871460, 859989992, 68011240, 864629617, 963438980, 143553854, 110615762, 106463206, 290813084, 724347663, 906663541, 662698486, 10855850, 393844723, 959951928, 999743018, 313544758, 279123914, 222415940, 459731745, 600934360, 118082795, 223363372, 870196385, 69667775, 95125817, 940011362, 977057429, 278852277, 151586497, 480819981, 170402580, 665936812, 269357447, 720178538, 396863895, 884731578, 105273607, 180656911, 772786931, 506104114, 544073673, 86465617, 85370283, 58073778, 463898212, 309196188, 405239486, 505780181, 576439418, 810864022, 804246982, 997594448, 878185861, 306085617, 770116692, 520723002, 924319368, 876607266, 937329503, 973094227, 692599545, 931431925, 812080024, 507874482, 422878413, 144116964, 154787217, 250174758, 651470575, 93883786, 11125634, 891172258, 939867298, 881185337, 740665675, 214995151, 694184808, 592078551, 135836976, 259912151, 291256987, 102217225, 64274195, 450302225, 581950814, 139811696, 595488724, 11064890, 948550652, 267337458, 8056815, 345812572, 767688438, 586411269, 434425727, 290943346, 516183603, 261293038, 436200598, 604119144, 322086592, 787241064, 987386984, 124949467, 696446310, 593439226, 887506149, 943026477, 586039411, 614962091, 476218011, 500545610, 100182506, 761228016, 771841014, 558079471, 553289997, 586687812, 19593196, 735840431, 130272267, 843585154, 224763527, 306164740, 411444600, 527151970, 720761434, 568748984, 698463031, 879484678, 147090313, 478460377, 130071836, 71760290, 872313733, 4611942, 9291441, 697364756, 712398814, 403288064, 251860931, 331753565, 499335651, 860378773, 666124243, 629478540, 229158492, 88411529, 941186361, 724391049, 826733360, 439971980, 401994229, 789519708, 974443308, 296491142, 871398488, 342900801, 463970112, 710681823, 543147058, 907358165, 385578555, 45275567, 554802422, 334670245, 248581148, 953865371, 242307137, 697663024, 845696159, 721149762, 608729182, 799961738, 986510643, 352727338, 471094747, 957460, 360371515, 441720920, 910038399, 53622887, 244288109, 889633808, 41904345, 311138104, 465476327, 559257248, 586357703, 404057319, 935336170, 624226189, 743103453, 414549274, 921124734, 120232984, 140058214, 176783015, 608957988, 432154649, 359758827, 477209694, 4219900, 334887625, 978303945, 328504023, 748593223, 576101499, 437169173, 173108493, 946883215, 496905573, 949736406, 984861431, 570745769, 294373429, 831414845, 438587198, 214080081, 718457860, 173932785, 31959969, 363624059, 337474761, 516826522, 286854145, 711681662, 86957084, 927715972, 349623021, 905886379, 268517278, 536500735, 985500636, 874924925, 240187834, 906962374, 262432883, 984669155, 315384824, 875485346, 263137429, 684406473, 97118433, 496132408, 571600994, 954885828, 909061101, 916175593, 855460872, 82814637, 604825194, 341772826, 15933179, 461691469, 416513623, 476357432, 881830523, 239025806, 247083796, 412109978, 218618036, 46579515, 728667714, 222584212, 192185452, 801472402, 466028628, 67926912, 839244241, 245684336, 256502675, 576026760, 761450449, 62722096, 67960834, 402818691, 744999853, 369358778, 49965002, 96240848, 542977470, 339383042, 985278541, 505152225, 176986615, 178452457, 608484024, 191555992, 75907158, 283552191, 605602787, 512698690, 956248133, 793246406, 892149214, 964434441, 856652717, 374930396, 779307938, 91990923, 974899193, 552583425, 289817354, 991730426, 395620992, 840079287, 47910631, 576422537, 671184287, 117427893, 38060390, 363539633, 399062260, 974383325, 322050421, 659943292, 540190760, 985638361, 360570098, 796459988, 192411885, 660452601, 450534589, 923982619, 705158025, 366215282, 555580300, 900050308, 163252290, 639158947, 159474419, 481144705, 886520134, 271943846, 913797184, 528906928, 150477693, 585805577, 350871491, 324232814, 877331431, 275238203, 675806893, 383936412, 669745560, 567330246, 479512137, 219161109, 305914009, 444087748, 652757731, 51343885, 880581106, 925734929, 370687677, 610481790, 919431500, 241512979, 173036273, 166436323, 650540618, 395433860, 573614263, 582178035, 974797978, 765379232, 275369815, 851887339, 770637640, 234566094, 974000159, 358866669, 183712548, 502476229, 636129360, 847830438, 303340468, 705743822, 336135631, 597745553, 186608495, 215744263, 413707261, 115873754, 72798800, 138659280, 753892100, 517292647, 948460549, 161473180, 683967442, 99055862, 210584138, 401371242, 950110174, 795594389, 73221008, 584838777, 572766898, 591656969, 351380237, 769831120, 371504746, 78514097, 351941478, 862679989, 918968824, 497404714, 949397901, 132784569, 537645399, 9101231, 97835962, 816006267, 317211218, 978899391, 407730389, 112450731, 273013522, 46213834, 882953986, 310421144, 927664732, 40549638, 384424383, 972532932, 232980210, 927483129, 217290376, 503306055, 633717606, 53964296, 531425399, 349553971, 514671483, 743598712, 394319311, 412741298, 98708025, 623015625, 597431829, 847877676, 886425061, 949455281, 181039518, 31081154, 547679619, 542770232, 541825349, 194418368, 885130927, 116382441, 351031134, 87075468, 994195445, 106087227, 814876567, 717702564, 384056057, 435765333, 680363813, 427099951, 503378936, 450791286, 404304570, 159791820, 541036012, 721857517, 35724119, 860342781, 282979985, 444729916, 917132226, 696325897, 564334147, 672288371, 612903898, 717111160, 284526835, 426511595, 650831543, 752188850, 215582272, 346424501, 273228374, 13204293, 636281616, 800767701, 781586125, 832034491, 437055079, 325522999, 644780078, 724473387, 297979118, 502927603, 377903439, 980026974, 352963636, 521598530, 934997537, 56029913, 629910906, 71094962, 203496683, 532751995, 111446570, 993655084, 321560471, 313766510, 566544695, 330490822, 348388797, 616052632, 376678058, 739801779, 498249339, 153251435, 781553408, 604888555, 545548040, 766877960, 865623343, 937953746, 345366986, 424893590, 749861164, 763995236, 581975284, 810422001, 606087635, 58581914, 98994219, 119008779, 313866427, 874782887, 794808459, 60750968, 343902503, 244027079, 753104225, 126343750, 764120766, 89543885, 464139233, 263941545, 737367143, 289975882, 18108247, 594376885, 438064249, 734664595, 763247619, 217717647, 95325590, 508107827, 329049033, 820335679, 942461922, 180598819, 650057625, 523227406, 230485624, 380932157, 113257107, 104684090, 593297848, 567717716, 957881064, 858640368, 840669771, 240395101, 831695519, 575494988, 816535124, 569132628, 787780378, 641551021, 866748442, 908386216, 5888560, 903836232, 872616641, 45586464, 956962137, 635086737, 381911343, 97899683, 345340008, 467688833, 403418404, 441066549, 812370027, 415104537, 386105233, 632481219, 469114773, 675999692, 90162215, 911316063, 281179531, 591945881, 547640697, 377801440, 106283636, 604650372, 418853890, 213258916, 157997632, 647764563, 860381927, 819719482, 158116261, 535822700, 447542568, 552768184, 449732043, 420225606, 732528239, 165413435, 719651293, 898263757, 537926325, 621208907, 155860426, 401169890, 581280148, 425545139, 73343384, 991612810, 76779829, 313314830, 756056535, 561555997, 844459155, 556279762, 944496663, 358057845, 760662863, 618595197, 368482119, 977612404, 90679799, 440292651, 678960633, 880233891, 727386049, 512278043, 932988087, 992142631, 766927146, 279436876, 635194573, 739147253, 452974351, 409885462, 570553941, 144265610, 423027857, 309159656, 448299313, 265166326, 66748251, 113796046, 514483426, 276370823, 641672962, 581496340, 642768570, 991519231, 793515687, 155089262, 145181707, 631094977, 426164096, 504770071, 36898109, 535301648, 493435644, 3169093, 205159414, 464853899, 786768301, 932191955, 389603844, 834595694, 65346934, 319201431, 565472344, 891656567, 755791215, 769738930, 725339122, 51276197, 28717536, 577457239, 223392536, 961644454, 185464527, 506100216, 630039651, 896168734, 353259669, 709106248, 143990392, 651369500, 32104283, 100521041, 761668453, 557282113, 383173974, 784897032, 85156241, 580198086, 88743711, 620847468, 553502150, 985238875, 697971313, 555140076, 161420545, 443722564, 467370912, 890771207, 345391748, 752897910, 667617079, 327857047, 700180109, 833485528, 304300941, 751116714, 605295173, 516303504, 923339569, 666096346, 955807804, 98906423, 171960623, 856717451, 384270544, 529228337, 573758573, 224361463, 515020579, 57337569, 520612678, 448596326, 513624454, 791340730, 823849875, 687354827, 139238492, 730448623, 153139633, 446645457, 340458392, 514910188, 999846821, 947884810, 431188062, 394935633, 480012559, 119373754, 259479120, 778646724, 122034733, 831507094, 746248289, 377393744, 375524744, 290861737, 372713625, 258124587, 555561971, 761864123, 701209528, 313364399, 134759962, 337078597, 488828035, 929741404, 659311827, 217633113, 895289031, 257411025, 931628033, 804592198, 756916101, 761935109, 531257416, 338511817, 828631538, 835014571, 722381123, 277785650, 131139175, 401667690, 530515791, 646569527, 775195411, 540386481, 973313165, 702117484, 62331172, 141384210, 177260638, 418440071, 879929740, 185434195, 93607477, 746581038, 415832002, 978258174, 519699974, 366440111, 324725623, 696293772, 682263995, 374819066, 940797500, 626824268, 337917568, 51895193, 668050504, 860284871, 378000985, 26455365, 994671091, 21470009, 876683303, 411838582, 986765916, 996711736, 680808985, 1992976, 441384564, 694267866, 949442540, 207187860, 392381305, 19315077, 462468293, 39207864, 1223287, 417058646, 114190193, 771329041, 360657325, 221825334, 42479734, 160653564, 219646772, 39600368, 577068266, 212707246, 994249824, 523282043, 841988468, 310639320, 739839874, 216507364, 884928616, 596803085, 731450801, 470982790, 916256032, 63759935, 865253122, 291614845, 385889241, 787033065, 138930187, 5568905, 160384919, 619453192, 1373593, 472495251, 774092007, 997660154, 109252089, 555341421, 453666476, 165840113, 990195916, 40951905, 637611284, 534217217, 920119164, 741963437, 457897113, 663055344, 502537420, 643642484, 217202389, 485693891, 609023088, 159382105, 920902283, 192953702, 478048090, 779800679, 521059098, 110555287, 286227091, 263860289, 100083574, 697540267, 220321070, 855537879, 586017280, 988268788, 825687016, 300690817, 710978572, 486101952, 40670986, 49523568, 886115495, 598136964, 238387208, 885019689, 287891572, 804153462, 817453701, 149476972, 411780719, 696050838, 405563208, 176868969, 935034139, 610169747, 725047520, 250683337, 763984100, 262727000, 634542993, 532170826, 320560217, 953691048, 630513950, 57250452, 531255481, 345593815, 774794089, 467132478, 360024512, 19807963, 340623420, 10667795, 728098010, 176123521, 332903394, 681305392, 670351047, 677606852, 423842557, 868602908, 652630282, 149062905, 988230019, 591596426, 249013178, 307305840, 319434680, 618658377, 507731567, 376415156, 597182115, 602360185, 702872487, 731752812, 173432108, 597002763, 681203406, 413905449, 961519356, 726110833, 44335583, 66508578, 457829511, 437679644, 175908780, 528985568, 223337673, 254281668, 267221479, 924043504, 863893179, 749392632, 395027497, 818204468, 867261327, 664922465, 940778463, 719838781, 427174265, 109973243, 367412165, 916246796, 438538576, 570981272, 878925539, 835608183, 52331390, 188562365, 852169375, 702809113, 677139191, 812290249, 122723023, 890750031, 638745739, 140563721, 744215359, 604206992, 440617205, 560417728, 641189121, 720195630, 605821867, 756136040, 206431465, 256000032, 259180556, 757389738, 444032174, 223029066, 173779790, 369275547, 834545963, 269968082, 567462390, 871469547, 24487227, 926351102, 537463934, 522061659, 268400608, 169859232, 426815434, 640170591, 937543219, 203091009, 50499079, 185946464, 670748700, 772155844, 791908060, 664778572, 424273218, 654437618, 846486650, 65029432, 195073840, 743660021, 264845812, 990065157, 755474685, 931476484, 971288256, 241097503, 761494161, 630313996, 875457794, 740643102, 847628591, 490352173, 894304840, 224086577, 185588638, 318131294, 723672672, 223685962, 605473087, 515212559, 676683257, 773755282, 868485503, 879978678, 813354431, 68712, 933774528, 103626157, 59437082, 804501862, 347187664, 129830171, 643328618, 335590058, 354582189, 949453710, 212332931, 905486629, 356262905, 434068143, 265289208, 212093810, 509432069, 625368447, 612945418, 872706841, 299589006, 889373385, 399752599, 894186264, 750602667, 359311390, 347290695, 992741901, 495768068, 416775818, 744400249, 535179545, 73511250, 986969801, 568470312, 592952081, 587766751, 557205084, 143139339, 94827725, 875115018, 1032462, 324532220, 183153133, 862246443, 959056400, 104667481, 835368612, 371914679, 744284846, 314223660, 370265942, 343640509, 623385243, 674350958, 611507910, 916898996, 785828743, 337145763, 836353050, 990590761, 948033819, 391138508, 108905617, 564852851, 836077056, 494975721, 84176809, 757123563, 614531999, 10343413, 561095841, 680093841, 985773455, 784513856, 871703746, 802190559, 110129960, 872966436, 186310298, 739507065, 594842795, 136952604, 333691623, 909382975, 242471058, 297682157, 866514590, 339299471, 833025975, 393850810, 102287938, 771711060, 673097170, 796925108, 519495093, 459119373, 385447029, 920454574, 174753003, 619169869, 397505201, 210782412, 127132590, 452624917, 664032153, 569927375, 576181013, 270504796, 568200039, 253823343, 49856321, 56715367, 147972557, 289518890, 547209913, 144123941, 904348403, 481608118, 653262698, 398500078, 284449262, 652872289, 150791980, 531984032, 395713617, 813648100, 113090667, 308300923, 174678075, 25576278, 236305461, 51026154, 663276003, 844352294, 107770345, 592269651, 832945895, 635189323, 146818167, 720159403, 228662308, 271596447, 342509522, 840196184, 366624236, 260381388, 794575585, 702135832, 591217443, 605011, 55342840, 583445830, 367487543, 775337111, 800998936, 711197199, 255558140, 476610816, 56528449, 298362629, 680275832, 765666487, 404434888, 665644900, 982532839, 282158, 601124160, 473025376, 672558525, 444579964, 523424762, 109341323, 131053069, 519371490, 440453678, 92768559, 846524512, 82656137, 863055152, 356109549, 743718814, 541206751, 997309690, 479665957, 277392588, 858701153, 938717046, 659601089, 517343405, 294304041, 365665538, 324441535, 72195115, 658650687, 854487155, 763358541, 303754221, 209050812, 294831628, 129382055, 258258792, 814723111, 597578813, 952454438, 616088626, 401261434, 777494551, 148300857, 219039730, 968719857, 842136740, 317169794, 709810161, 591383182, 717882005, 665260761, 930203249, 691191083, 691112625, 820627525, 828970560, 285420318, 978916657, 860300187, 324437785, 574179301, 638118320, 371636002, 722042363, 193174857, 698435464, 62485572, 799726927, 679448743, 474197154, 233480388, 89979131, 533690196, 858372303, 307206724, 815822565, 101545749, 306239651, 702467327, 459101574, 848219393, 376283160, 390584973, 185008984, 211068745, 356805334, 617705301, 546058832, 432418825, 479113482, 499347565, 821220930, 465766385, 883215064, 59381718, 542250219, 844132733, 866803939, 239455952, 15809585, 790214877, 39048321, 157215208, 318573323, 620893916, 773677075, 4749746, 700827158, 424195691, 812720612, 479121151, 384733679, 92300987, 153964567, 91750758, 789883784, 545416986, 841943814, 765525371, 71352721, 837693126, 944481810, 307011376, 460582925, 408670900, 111107848, 668704089, 359281735, 598887255, 199491662, 698734831, 78072221, 779139427, 843608025, 20640411, 456192304, 595773491, 991663719, 290315380, 681780322, 501740116, 920987595, 844197544, 773202549, 614689326, 891712063, 869020785, 608165966, 686705527, 894075341, 6992427, 960697594, 35177662, 222613790, 746039622, 690071515, 221341575, 648920023, 528305300, 440675228, 339399449, 614803745, 751741738, 90603494, 630252467, 574902326, 827573514, 169816246, 65514125, 127663375, 703740251, 522755165, 238732092, 617218800, 923667880, 75003320, 839462802, 452832923, 538109747, 135569750, 683571523, 751337865, 735048142, 70660344, 503540789, 779879583, 305986786, 36759197, 509915016, 491611419, 674920812, 329665121, 409078005, 316595185, 822664324, 97786993, 117547493, 97080545, 211945297, 328538000, 754895975, 949632416, 125540101, 649892869, 502725636, 154517206, 861778399, 413246787, 504372709, 297237073, 734963949, 288638126, 714593414, 713424653, 45241124, 193742059, 430917132, 745201182, 191273411, 986608896, 621437497, 300532368, 244888031, 548361033, 230739495, 259141404, 769985552, 45705784, 495871904, 216479244, 879272830, 814595889, 664243384, 751777761, 889727122, 699733073, 868457872, 616783444, 694567693, 27327750, 560737142, 645467235, 810554339, 909942889, 608744688, 506210293, 19067099, 333820367, 38849835, 343989917, 345831605, 99425163, 671024755, 378464694, 886358622, 426607076, 220971988, 637854090, 939035233, 304860418, 257339018, 947262541, 826075851, 895353210, 13138035, 265134581, 768000656, 860206089, 430405563, 916003094, 362720599, 400752842, 838515533, 267714871, 106156158, 83030303, 532549435, 571587656, 750558585, 974602402, 844139018, 788365889, 159246578, 27831167, 199170229, 429389948, 200400142, 800969947, 153348234, 375033237, 831414656, 862522345, 80938336, 245878915, 652712013, 417220477, 40885557, 522020032, 643402222, 749690274, 392060261, 285707483, 514921154, 499378454, 790870020, 914966900, 979658989, 21689350, 930050464, 128124379, 25557601, 427415723, 892200047, 554106345, 736514215, 896221868, 675966940, 899436423, 753930968, 728751022, 8330588, 756776339, 460970993, 706061703, 277108859, 614749267, 458126200, 511839457, 822749206, 185709602, 696969483, 906384662, 287061067, 807773289, 130357076, 625862490, 437419698, 793075591, 772161164, 680302314, 509709407, 592805242, 957902877, 746383991, 500775288, 150082152, 64431636, 239202056, 736944420, 925411477, 702807347, 731996096, 268165407, 954595096, 730174292, 264162356, 156690300, 450174632, 927300021, 276258031, 400080922, 887669263, 927498780, 610730110, 127628909, 801750825, 442064038, 505560615, 827294940, 568497788, 845049508, 663055848, 278679299, 682952735, 16983169, 198442752, 327546359, 158500012, 135338222, 322176321, 76724776, 853223705, 751982297, 965344768, 727726872, 441598276, 488426260, 66648211, 84919442, 788228026, 570208794, 189411009, 876321216, 756813117, 276120323, 287904645, 190660294, 212747456, 919747262, 279036451, 941947603, 671376602, 788855036, 5436792, 539618110, 754928056, 944176761, 124030881, 736714314, 984911634, 437133441, 998012228, 578143121, 268107221, 413617346, 74314974, 59434487, 18402438, 148213163, 856850852, 897834029, 196581656, 201967344, 556993678, 677759193, 571333318, 739611743, 647424354, 218893656, 540188264, 116840933, 612964714, 716160938, 165807628, 498488766, 435166674, 592677192, 489276931, 730322108, 581217310, 683592009, 971317169, 256967467, 766196124, 529584757, 737744781, 343247537, 688303094, 788846285, 330228371, 625720592, 126290285, 916187191, 231758306, 774241050, 609918804, 680976394, 261799999, 601849729, 369789293, 746162940, 815039740, 551588850, 236583478, 4495067, 195481748, 525709670, 607782855, 611551663, 917490056, 340233301, 128570689, 717327254, 834380414, 745099991, 426728499, 332236313, 131277044, 837274596, 478697538, 348918814, 257690633, 930491130, 398656811, 693653332, 200020986, 685000767, 711903388, 279831039, 937476260, 471638032, 278768612, 353568814, 737933664, 823423962, 976365600, 675300923, 387714272, 106732068, 953842875, 33529716, 784190377, 888279118, 256832408, 562061025, 280601307, 536400055, 904648047, 212890818, 628812665, 659537267, 441723275, 932329138, 78183277, 290257816, 173618594, 282551827, 53592538, 345325589, 500939637, 105609979, 398165327, 521712590, 356846408, 923121739, 388576684, 985225379, 161514839, 754572729, 620220787, 823617025, 239268074, 665003488, 784869383, 715884582, 552771492, 480161803, 574279407, 463880598, 626693893, 947500469, 692241200, 116309969, 391685893, 450174494, 531480149, 955016868, 245657595, 384954399, 167474191, 34785714, 794625591, 428957955, 536633445, 502607610, 913667752, 609968835, 264598818, 508897061, 623260390, 639910344, 535311934, 33518950, 243653939, 475273488, 688013693, 72867694, 11624038, 345253356, 62272900, 711109476, 898716186, 837042503, 285820721, 724173829, 420968721, 314278311, 150184316, 303955579, 404873173, 334974826, 508764860, 693046562, 373668633, 488863514, 647034749, 773130332, 453243753, 17832560, 351760022, 911265991, 525241895, 530114025, 62538847, 414688123, 754529433, 195841987, 143917960, 648847083, 108348088, 599342714, 609842114, 342851243, 922769068, 957786687, 131901941, 976964618, 672352474, 23881159, 684938150, 31923204, 14704804, 808471305, 443427946, 654961480, 117337781, 836374353, 195921793, 62674415, 528250768, 179137687, 41253847, 545533217, 412471041, 408174725, 850968821, 14815097, 633010161, 658485306, 577710985, 319611471, 624971221, 897040606, 971736134, 435083519, 745505820, 149669098, 162945539, 747962377, 302850389, 863306090, 851049851, 145334765, 533659149, 591430224, 649908576, 706104132, 373003917, 127761089, 984561923, 351775738, 178296336, 477606830, 823630447, 377515322, 879240084, 518822823, 201851853, 157365704, 46760978, 629672740, 963252130, 258234556, 411665142, 714178913, 845897604, 644035202, 953222193, 390842572, 803361224, 826805528, 734561170, 121572174, 446511059, 48546484, 490111194, 747568558, 622496723, 678552283, 476865017, 647849945, 48637404, 10414258, 711496396, 608820916, 492491124, 558263430, 579232544, 731650675, 742686102, 932838365, 531342236, 890567541, 558550733, 374085108, 423346511, 12532262, 177118124, 486919005, 395515185, 638495821, 509677164, 288715859, 993400956, 77413759, 893783750, 818852653, 386193807, 843850448, 21341923, 885082809, 814154101, 81371672, 540010766, 433676506, 68571958, 421153379, 224421183, 576306121, 544358915, 397719403, 46905799, 242040222, 512895521, 276791972, 11506804, 702559749, 81374668, 192592290, 333951138, 479108356, 498048864, 333206694, 641119284, 602215836, 194891310, 415072834, 231219824, 192017069, 74877383, 693844104, 271748795, 255039908, 913419581, 144830820, 158292015, 909993670, 877023984, 951869396, 845713225, 41455479, 828886640, 645946496, 560197047, 978174556, 274849297, 703262770, 327792411, 730343730, 383638601, 619219751, 903376078, 172597426, 487319815, 432392031, 25529428, 167918172, 971838432, 371052021, 790879569, 199830433, 315302479, 172624758, 262523972, 391640871, 663045201, 779659725, 663559941, 995840220, 326927391, 690079474, 664649714, 23302010, 613494190, 603944644, 876459319, 921834124, 259522236, 285787193, 904349416, 685835593, 529157573, 405450599, 581870564, 481422819, 521712665, 107094674, 831624627, 496461815, 97991715, 26993455, 132532001, 351396249, 247099210, 982883664, 18529163, 960316102, 340365848, 233938040, 866981370, 156849318, 551886198, 294734297, 998883456, 894224856, 461168407, 543057751, 481484615, 388890827, 485803080, 237890849, 711025582, 7798871, 120260415, 876745099, 767985, 139593230, 355716345, 783346681, 863339059, 706503259, 476211250, 375375937, 266799981, 90461695, 836867528, 448317301, 781753016, 950962970, 34845814, 883692010, 463909708, 760352743, 228743106, 597085057, 834356568, 477018703, 20761995, 41355138, 693064899, 593082101, 830546646, 850743595, 720372275, 198526031, 456498252, 641852415, 645731430, 599897213, 176130468, 344706277, 29609200, 692299732, 342050668, 367459235, 858250438, 366228502, 431538987, 153902750, 218161079, 533030595, 300865711, 981542865, 244297708, 341325073, 351674226, 380006293, 535316719, 494111894, 799922591, 18975423, 688524171, 831725589, 123053372, 779154020, 871512970, 911303259, 532162958, 689545728, 194303481, 717115355, 848460245, 704406319, 233538127, 505742441, 152420017, 318223202, 136872939, 155174233, 409731440, 373951452, 447466355, 882887045, 687425063, 374617164, 562570487, 263917743, 953913754, 164225879, 633781359, 437971010, 678899622, 416973822, 389249019, 418056234, 538744186, 522233294, 363269025, 42366404, 862319892, 658738490, 951260869, 2074222, 770943551, 909533089, 716766650, 113067266, 936704285, 198768744, 413026995, 852142709, 522695249, 217809971, 399946030, 873641976, 474699758, 847929693, 877855794, 740121483, 117036889, 447269506, 905978718, 31886821, 341201785, 635435051, 789202008, 485588167, 981953009, 299990169, 979646933, 928892969, 224638562, 229444081, 236619011, 838780481, 796981991, 576064084, 71219667, 908670845, 16125923, 60266384, 574844883, 338047007, 298876216, 90191366, 86716336, 18841566, 855258816, 277946752, 420531567, 970412775, 921675857, 83554543, 973203572, 9269616, 551339376, 657110071, 846337112, 907154914, 667934824, 184568667, 890961242, 95608076, 649200168, 462152104, 109368929, 605098409, 160131566, 526145838, 270526892, 175025811, 870418802, 748063620, 191820087, 104309019, 229508739, 989533191, 578188847, 373924473, 418084298, 44990262, 908867160, 992778124, 834341685, 86955052, 758089024, 418859999, 326843271, 443573833, 330247761, 758716988, 56444840, 259942594, 897864514, 759399216, 474845773, 148675669, 598141471, 400728739, 209586193, 404459529, 419171942, 10934811, 517306464, 289259558, 747674369, 379826641, 58995218, 447669745, 536173850, 335611648, 828154897, 562245363, 304858875, 82146801, 684391862, 765120117, 414199302, 687379833, 560943039, 645848924, 962814136, 923759823, 597850538, 306151488, 33568566, 12581475, 919211069, 281800066, 176504487, 212373427, 171131541, 796227595, 116993898, 833618793, 923509287, 754529102, 565432340, 926876623, 127622889, 101379883, 198433136, 473697261, 214422967, 44033279, 590168617, 828773842, 570496761, 376599774, 574012324, 874605094, 617568120, 564635532, 217790377, 913546076, 916742131, 730974623, 950138688, 977331224, 935002908, 431795366, 736589168, 440605709, 87808351, 804552327, 728841904, 420470545, 871352306, 234611640, 146877941, 904429079, 153463728, 565911599, 332309459, 918162042, 836132134, 632745115, 665204260, 806916011, 451988082, 35100691, 538230500, 880448422, 435029027, 929069425, 187359420, 348790055, 863414497, 838246050, 307507092, 190925121, 64553283, 592581318, 405108560, 235150380, 841031510, 296614713, 732765781, 196635321, 144309093, 446048400, 978246086, 876915514, 957097065, 572760684, 414621828, 24122606, 762071222, 179012109, 65144543, 889329811, 73783470, 655117254, 674680654, 947359504, 791448564, 970274797, 223886853, 206755623, 82689138, 163400772, 346003434, 13296248, 847049408, 574307409, 552033516, 727470464, 280204584, 547486435, 888920096, 359878424, 762510063, 697350351, 709038246, 105669161, 706834228, 858091936, 930040417, 829313071, 792649306, 83111061, 44016821, 673846464, 434137970, 747190778, 656919241, 316133636, 855015111, 188790750, 483124262, 570460689, 951491401, 654219080, 570515356, 126269800, 68301091, 583078895, 140496262, 255309127, 987817496, 82181860, 470600388, 654264920, 548708167, 774140019, 934530250, 755718062, 630033642, 842768264, 189883277, 18371623, 869702054, 951671079, 451653556, 440035507, 723392631, 802954650, 396545016, 518026631, 687616172, 622731347, 396759784, 491705622, 728279464, 310296131, 657951068, 551324960, 522681464, 227745582, 703874360, 787797177, 14974642, 697151586, 745857720, 691577029, 70616359, 960171991, 853977886, 952861625, 878793462, 430791560, 937010952, 337327311, 768181655, 646767123, 978431333, 862711513, 957029660, 468377087, 866787156, 677740022, 903793358, 865976254, 899406935, 422531772, 207277626, 642444187, 785081087, 675754384, 978977737, 285489447, 725340716, 511827248, 219152589, 472617994, 644248506, 375483977, 197267910, 72560826, 747767236, 400384042, 830159691, 377370234, 71479127, 573692714, 895310625, 142110021, 986364186, 21066904, 671021601, 33741887, 855514369, 862654073, 783002241, 774535378, 351597300, 518598918, 53226624, 474360690, 403335506, 999944692, 491278063, 429839323, 955993786, 239582465, 293449718, 825970531, 518085770, 296723160, 502135698, 336561562, 895705885, 180905730, 390212730, 732886498, 797887546, 136759899, 199932375, 595873928, 523679647, 849819075, 340026970, 862610966, 96275366, 129612792, 651970168, 90322285, 108382286, 801804043, 419413770, 214595434, 106711886, 58876300, 627895719, 573373953, 450672341, 734946425, 918887542, 672154759, 554783904, 229727484, 249215752, 732912231, 352997882, 767260825, 718429478, 83085887, 263969756, 787843632, 466494625, 20562286, 943194304, 187462704, 866828436, 739913884, 592675592, 171082586, 680907746, 881396799, 735195900, 17408865, 65587320, 701222421, 524827628, 611585393, 195918693, 102026857, 598464155, 466012142, 315853291, 289794383, 913073837, 949245034, 63729762, 595850972, 756279634, 797674817, 572493719, 500660761, 786069914, 937165576, 738997059, 659007575, 76620843, 825235912, 379640596, 779176250, 625949011, 685518172, 309089511, 683044033, 822004170, 785795086, 262230636, 325508649, 161139707, 913059182, 705963834, 820344148, 605058038, 716809139, 112372584, 162984492, 572553379, 972134674, 968123883, 940275441, 206807251, 787800755, 106828622, 444608304, 159691714, 152316303, 994962843, 128746828, 463405524, 704197154, 291457526, 502690110, 557410656, 593882136, 499238184, 317143740, 294818755, 921933443, 985307091, 545460421, 576998031, 991095584, 127946650, 436563195, 721053941, 587787775, 461068402, 849650925, 692759697, 935624366, 603653088, 576521927, 808129034, 863271002, 212413735, 753618710, 99025521, 201082598, 204251329, 173538994, 814173630, 52555492, 401274348, 278567921, 68444884, 355148790, 669398468, 643236669, 993919975, 30575111, 29856944, 978721268, 678042545, 976705676, 410162048, 634877058, 884891648, 624043468, 979091230, 799781580, 273082725, 18516849, 882350691, 810323168, 955389040, 583209581, 924449843, 995022691, 955120581, 90220437, 160614934, 69325233, 748685031, 820988623, 207298043, 561818012, 458427608, 131749022, 147129852, 181185864, 287770224, 905945813, 587529337, 937377746, 792843811, 722537849, 395054781, 263504557, 722086050, 702934844, 743285861, 996062024, 213373806, 606870400, 387920032, 926402575, 446149668, 956813781, 735611969, 755902296, 638146534, 598794707, 553222317, 301066294, 164606345, 73799782, 356715365, 841759140, 843296862, 285580007, 618156625, 457764816, 7999090, 551463253, 953728347, 634559109, 976910699, 14182691, 150349685, 59350106, 292203960, 617633744, 35126192, 232521082, 715180471, 729762450, 60941512, 641851088, 350084260, 306089213, 17592030, 512491615, 28844065, 187156198, 225250796, 190449800, 900080616, 887134814, 389220428, 355390207, 560500920, 498644676, 873820210, 712402331, 659900450, 470218551, 905351594, 651258982, 98063428, 467635560, 477432369, 487060634, 906698379, 963149898, 297928102, 422163813, 281678713, 632851979, 809961645, 615833044, 381550780, 169784931, 541864682, 436075099, 940121057, 42927975, 713419166, 178545767, 38511897, 128859195, 403623133, 927333330, 689572215, 746718914, 592617294, 856686216, 521802007, 787662955, 780904780, 780688960, 21600988, 463090921, 291951998, 124048549, 602240639, 311175359, 182055115, 444043370, 198084588, 32051111, 2186066, 743616412, 667469987, 670007448, 471146750, 808922453, 25857930, 678317930, 121763418, 740137143, 446155326, 691765276, 722899959, 749156797, 530420615, 228805486, 454570546, 688521215, 12435306, 876096398, 596550304, 764623177, 512126590, 657757829, 68135402, 297860268, 420530132, 630819688, 817107499, 246247955, 809991224, 411886127, 518939277, 967731022, 530676406, 602621248, 854776041, 316537413, 315299670, 825385984, 873649961, 78424378, 454138745, 465442376, 473125849, 141987149, 240793459, 320509630, 25557509, 50622734, 326359594, 764037924, 658613468, 414792324, 306209033, 551709051, 471259096, 656374340, 514545120, 15847895, 27667591, 2568251, 923558434, 158298773, 284425184, 276575576, 918749072, 900568222, 626178040, 225807608, 59258737, 392084386, 335426736, 804146913, 554966838, 997506885, 498616566, 906396919, 192205654, 633723859, 193274019, 502291082, 739955416, 978043907, 529396740, 409184078, 251251844, 850754760, 532478547, 869993056, 719280586, 246526683, 626978539, 468978122, 716707216, 945504218, 650708016, 994635523, 749909907, 474518703, 307325669, 390416305, 558876691, 732209884, 355686744, 833837668, 324865649, 915575241, 502343627, 231732907, 590611734, 186621747, 606758076, 343054932, 299439203, 625114615, 104314319, 185077059, 84163275, 800459525, 248332292, 929926296, 183214398, 499312485, 997563186, 317666973, 661401252, 327322936, 543632850, 746448414, 828521808, 249145660, 284267927, 701149154, 618826659, 86339995, 580605562, 321477142, 800884299, 640661992, 750002036, 768429789, 729316423, 725047592, 227625517, 624276576, 709502420, 856084176, 249449147, 554281864, 786299665, 183730323, 233873529, 923841613, 218907663, 742176558, 239729557, 508083368, 929891699, 76273399, 435312203, 796859831, 861523620, 687601818, 546023307, 548328398, 276424502, 46989841, 142603024, 132325279, 971868426, 901768515, 135021046, 256109534, 511669139, 539095771, 28431706, 681202262, 348358344, 670237128, 79456034, 116790086, 648773818, 6571368, 537691417, 188404585, 174959816, 909367324, 955444192, 890446942, 525873194, 980942420, 355973871, 715667392, 749835997, 569847508, 80156877, 116825095, 736566846, 937578533, 201822361, 179069628, 438701050, 586101656, 514542825, 626837327, 637585034, 865213734, 924983474, 260709840, 111368207, 373144288, 80941801, 229096604, 214132772, 769497344, 588819668, 470492690, 829857179, 362069079, 699998526, 420298437, 191166498, 399382717, 441925636, 841397958, 635774397, 66388152, 740669055, 972689053, 565473083, 449099401, 84303023, 735196678, 118419462, 833236580, 971722697, 856735691, 149117333, 347527538, 399196400, 75316451, 478333214, 65117228, 578377156, 658390157, 435998420, 509896680, 494613942, 54168955, 624735119, 256536258, 889635259, 509365132, 1017782, 716397154, 74466169, 105586827, 649198459, 720995806, 360182025, 535043311, 59783848, 416999816, 826285520, 97716099, 743846540, 268175761, 612462842, 565933780, 371445232, 465598745, 992761595, 344960898, 739880291, 83611715, 108432569, 869289197, 764989527, 793692863, 939726721, 283525384, 808186991, 587983632, 656450347, 337059806, 129708358, 818389465, 491032316, 110222832, 179144248, 692263407, 621439432, 348103944, 571363338, 263413616, 373873159, 891075896, 76837531, 508938676, 192308264, 659310729, 764236614, 975067720, 597178919, 793136083, 683155750, 148257216, 270380643, 754218127, 254600842, 499031267, 393025947, 396627374, 881515236, 81020459, 981397574, 491634264, 335921874, 973975913, 810540894, 308465080, 874124922, 118604409, 748976137, 969951397, 827219393, 257597422, 905398636, 821339080, 874319265, 771506463, 431368074, 230161956, 893424337, 58729388, 573168778, 881628426, 316283679, 119622782, 226520479, 744506366, 128145165, 507156444, 318968821, 357717550, 580764069, 391247181, 516539224, 923623423, 586383510, 113493870, 104178706, 209420495, 204015034, 966527439, 852788214, 813561272, 877226613, 563436033, 305063567, 763447218, 765064465, 592701119, 305657855, 510556925, 598925401, 434303288, 726363435, 834381936, 354824074, 195556487, 245640745, 125870057, 641521232, 1488252, 272797628, 793852865, 419743817, 273005473, 610498964, 322090497, 748638841, 357056918, 915222611, 337306102, 957045887, 753828294, 96961187, 576369482, 986513249, 858270497, 819782320, 506721350, 977939591, 429482977, 709059481, 735685536, 128125943, 486177455, 367388783, 979157840, 765638850, 610726083, 761559917, 871509691, 1770220, 915768697, 176163207, 644057095, 627655, 185873462, 909498332, 325910820, 601991449, 980283437, 177509787, 471999357, 994590045, 807967769, 291033890, 769420457, 725630898, 381985222, 893666040, 114907076, 358766973, 467372447, 609768915, 337087591, 292204825, 861076813, 275891453, 475915380, 94901004, 179790090, 811575571, 91502124, 989494766, 107948573, 113732138, 104746314, 968102864, 481487871, 270517608, 215966860, 987256830, 868600572, 342909270, 159431393, 199457070, 153075542, 106434517, 144597913, 61090149, 104798778, 510536769, 615947122, 446682314, 739875748, 232382352, 697234800, 614093747, 214914912, 484439384, 775250329, 714612292, 889603162, 167042265, 439594859, 44520150, 47251637, 295596824, 367078508, 897006258, 883200325, 910627170, 135030543, 604099144, 348758898, 629842175, 88443441, 265543390, 670026063, 117214520, 699687286, 114153234, 680254023, 97289331, 866037115, 927759759, 408315364, 977035564, 428952712, 537756108, 838155553, 835617258, 564382187, 959951323, 503484409, 375885438, 320408853, 786713922, 802758851, 935178591, 245796565, 87720528, 76912345, 320618762, 199305751, 357195747, 253402262, 507143098, 203389002, 33552830, 164643877, 234643071, 582840399, 324341078, 750996640, 653505372, 159198524, 282962826, 108057725, 82813569, 984537007, 717848481, 525836452, 208947037, 408675593, 283795358, 70130411, 552869020, 985500739, 446064081, 578760101, 580395152, 908205488, 298838982, 91811369, 142984643, 346571781, 458667497, 277084416, 724172852, 79830464, 559700738, 910655980, 623397821, 91004571, 24110317, 66314396, 41121993, 958677097, 791745322, 260185776, 440795843, 879686042, 682938300, 92891768, 9388318, 624560943, 375767631, 783932111, 919457675, 501917189, 350790539, 894490199, 10775503, 480563552, 955694687, 661929123, 258443586, 750720164, 74811647, 746138038, 931172312, 945347984, 996210952, 405857107, 585537125, 427326478, 809731010, 413215097, 234584273, 33462303, 43224590, 819320466, 793758958, 573911918, 303339034, 943110132, 195814952, 627028779, 228016209, 585816738, 116420203, 869300616, 940360505, 229969859, 504674450, 573472751, 362664623, 276704689, 776871715, 793024067, 689457243, 669121182, 293169386, 656260961, 146824261, 908479365, 889515318, 700588291, 240182370, 373457952, 172798075, 10013437, 969093113, 137214406, 618352112, 479692427, 770031429, 230130694, 243351473, 190730970, 670508813, 158472492, 441690289, 527904974, 382049109, 692673439, 949869349, 397879339, 870012563, 206843581, 122587988, 812532764, 363648174, 630133990, 626299972, 100323201, 882555328, 831985930, 144299496, 827909867, 227497108, 182743273, 426748226, 594513070, 788499201, 287532848, 288957479, 313857962, 437462540, 511637766, 302574519, 28057515, 601950432, 588126606, 462221788, 767233597, 324095892, 943522566, 899729183, 332302181, 348693990, 939785330, 446909848, 952818271, 863135785, 375730006, 76050385, 409856485, 760037241, 327805914, 306637908, 648452153, 76102108, 250821889, 392646142, 104092193, 205660438, 716942862, 849326889, 944899147, 953639256, 99461427, 114186377, 270109106, 704588701, 756972897, 508803442, 334401693, 500978743, 939325781, 455207919, 770378247, 556125537, 197703318, 850967128, 713050484, 527906715, 345281629, 778446008, 682381654, 988696817, 840127163, 425563763, 126934219, 702022892, 312393689, 604980662, 534487877, 387394379, 146239636, 603537808, 64153726, 950608661, 167741551, 287908605, 8249795, 807229262, 514915686, 817371280, 433264511, 720629928, 177630927, 310917041, 169941069, 645703260, 1706007, 484156944, 222983446, 219041399, 783673342, 635445447, 363751040, 498643600, 541531007, 879072903, 97269437, 301485839, 125639926, 585847804, 298148613, 733042798, 315984669, 550440830, 373558775, 303044687, 920145537, 920067288, 214709171, 247663427, 973627446, 329677894, 339755694, 894826555, 328968991, 326445832, 676702046, 661885668, 916156910, 106819983, 636445348, 924966248, 902590145, 341800893, 698515922, 207820531, 306020110, 365129584, 779341452, 323777550, 754422981, 382607500, 192589451, 77456213, 742463890, 731713923, 671118058, 548868831, 886707460, 628426744, 165043292, 515169459, 780588263, 529806555, 163869004, 515008529, 141016514, 28456431, 675008069, 33457337, 362301280, 610062416, 679987048, 708074530, 765240778, 903701448, 323504998, 261133772, 482121684, 390934296, 374309364, 355878985, 954287045, 301620057, 634321106, 678406954, 775783790, 160443628, 971362590, 803894201, 743172599, 147648837, 475872504, 732450951, 139984237, 163529311, 516153414, 424297823, 228957555, 676144106, 883453661, 40108573, 989264280, 409749699, 864457121, 334364279, 261641803, 115039365, 434950864, 27876501, 566429597, 427736369, 685733999, 929995602, 7673012, 755143685, 361390383, 504193951, 305686444, 706884067, 810903966, 525072209, 48793910, 419617426, 741622577, 649370703, 846195932, 613963084, 75283184, 158447085, 356124978, 833140705, 575260121, 86820252, 665183256, 160004095, 270004350, 376686665, 108822132, 985221229, 192194503, 682670204, 38210613, 238385118, 651781512, 31317627, 265999060, 117021715, 446514315, 482193735, 186515873, 138662511, 156274200, 711995580, 520182754, 257965420, 868297790, 711871123, 917473000, 268355140, 714244290, 465202816, 147209252, 265619311, 480537616, 415546877, 460691273, 255869853, 371086150, 555343771, 381872201, 220877813, 749329893, 785621477, 778956984, 944849154, 259382705, 44908356, 436866839, 927944655, 262467613, 719831900, 925504844, 322095560, 980217605, 412854965, 22776894, 517813076, 160957591, 271990550, 411015767, 431893944, 387398716, 789184693, 196749779, 212229181, 672862484, 78989192, 360691007, 162609450, 857856867, 752755186, 777066790, 541852845, 162360199, 173916119, 246648745, 339601814, 30843015, 558114130, 638370510, 714283902, 107171882, 381937331, 826973251, 567214366, 465888617, 811631710, 645979967, 779312666, 653952380, 525866628, 586298812, 35114115, 287996757, 269394436, 356667218, 295612374, 175642293, 253683172, 728061696, 547595548, 718165680, 244515437, 680448320, 218905016, 45180040, 23196130, 451756504, 862639556, 512286913, 262179337, 863461573, 93099381, 888923224, 464347864, 895429356, 91590750, 375371367, 842510910, 887430686, 148507012, 847117497, 722621155, 573834045, 372403464, 871300571, 766264016, 536422387, 420146098, 891506812, 53986584, 380426875, 823405792, 694853073, 389121870, 917076205, 195581655, 334804157, 235029604, 91645011, 590976291, 364316702, 674215928, 773906933, 429720728, 522560380, 323188602, 620857837, 236664676, 85598287, 380190415, 840634545, 779906514, 410052136, 169500059, 811285449, 561012287, 461837175, 603879181, 968021107, 112281987, 92695210, 419501070, 509202129, 39858009, 813318668, 65269832, 844424151, 879783174, 990358033, 974077353, 35679292, 283845998, 648859360, 596087621, 971576312, 988199204, 269405969, 107319622, 346767221, 765831364, 569735859, 597929169, 855597259, 78692, 96548399, 200383501, 871881184, 549883504, 978420388, 954135680, 679717930, 67310676, 945525485, 876368405, 475981195, 510446354, 380076376, 548222369, 665243591, 796425441, 811063858, 214274275, 501908934, 790593003, 107135704, 412033361, 294401356, 279270990, 323414578, 572137931, 539596925, 986873563, 312259928, 29973274, 237884523, 205953319, 708790336, 478490224, 439129961, 16682486, 17002247, 362140064, 830259883, 377841582, 58742023, 346005808, 721848287, 943720566, 240232837, 516174786, 142463646, 588528715, 215598368, 522083089, 784223997, 938592696, 849239513, 670161921, 872445710, 250756545, 750660808, 355999504, 231023327, 468678405, 579751892, 150744979, 482950126, 280093495, 606907893, 560100969, 999892748, 470156734, 93407315, 280097662, 44698061, 86094600, 477976516, 54473892, 794950449, 329660109, 154462681, 280580899, 754403314, 988485774, 283858401, 850402454, 935481751, 762674849, 885955700, 948141938, 252758941, 744086937, 373939191, 211650751, 986122190, 5655363, 508337422, 441476444, 309978556, 814469154, 687214564, 404037920, 568762406, 768530613, 2196581, 898260113, 197818574, 185013097, 857609386, 677417255, 843500346, 42438090, 465054243, 705484650, 129544195, 842688608, 920026643, 728995507, 690371118, 689519948, 177477737, 853151575, 66266602, 601453261, 560611163, 344597437, 532029644, 5759296, 486653185, 838273186, 537316784, 676724026, 436995351, 682192188, 76550510, 310046680, 191333377, 59361536, 799469169, 955409488, 57610355, 226438290, 690243235, 740647974, 855703435, 664199108, 833240771, 141161828, 232597743, 350474068, 146716546, 212465275, 140465183, 843141532, 193722510, 510104969, 284488771, 233520140, 148647121, 237604705, 338137009, 519865594, 147752130, 565965335, 512651548, 244696534, 713463721, 116548329, 843703113, 817619965, 726041250, 911959021, 203925319, 906349786, 616956225, 426669816, 612747134, 2066039, 903273319, 792315551, 275024313, 774202611, 38586598, 304721497, 380735917, 858977035, 38274514, 374407990, 569775595, 364043314, 569411675, 488050657, 813555364, 294939167, 78016207, 521239082, 924174393, 734246850, 101445410, 203970201, 191465402, 574746414, 34210657, 171683683, 965751130, 176636223, 682949477, 325769664, 989282795, 357153493, 344338730, 752287365, 288775710, 731941848, 855833405, 413902936, 236360158, 131392442, 44605083, 728459811, 623269380, 862831067, 579072778, 28163734, 576030054, 155707771, 270203871, 43276228, 540326108, 765479334, 603482222, 37970991, 906264367, 375327632, 53268508, 43670481, 267707169, 443187189, 676429567, 728973455, 702581784, 436717344, 372174460, 161779363, 168549542, 868912059, 766152344, 492126269, 482366137, 463219432, 809697996, 476757081, 889214257, 702228510, 227297115, 764028215, 629789023, 204603482, 759824718, 242144932, 348196748, 542695618, 113888491, 559067438, 378610391, 578554685, 983177662, 10933537, 251026307, 826223972, 346284367, 673143046, 722083024, 406991576, 589007939, 833730435, 577508706, 556780447, 195367867, 851051617, 457203010, 96554179, 7559132, 577246381, 423119830, 25462106, 467838822, 233472496, 893920711, 429607390, 917498215, 100859521, 420410131, 608274873, 186383299, 675091162, 232613901, 761058004, 919938689, 580215430, 851039016, 115033756, 842199678, 774003145, 539613579, 28919934, 913816286, 476653185, 959352307, 639326307, 270033948, 621240767, 138630859, 505205107, 934805261, 221337149, 282201138, 803800889, 802236083, 885723826, 235156156, 257461947, 362460809, 171960939, 490042041, 600467815, 730933255, 196987181, 567578307, 304676902, 282622437, 344895265, 98614823, 752075155, 860175019, 644889580, 372491620, 664160476, 70931605, 237940932, 871448896, 824221907, 897260696, 53200015, 939924046, 182250946, 99042895, 754061638, 606354264, 392948978, 764645334, 835995504, 876798657, 827001432, 348135067, 97092779, 531627501, 604745371, 941465832, 771042565, 711751399, 244474533, 622587149, 298624185, 207956250, 562168512, 395969431, 157347815, 339040682, 516825830, 960227484, 407211549, 558332917, 404462497, 638826849, 586994450, 166319708, 804216708, 746377788, 135167362, 21061966, 23821703, 732892760, 670915507, 909497816, 29813466, 369634518, 883132619, 279967918, 431122604, 337653818, 355701971, 317454053, 608094340, 557923704, 661552636, 732254495, 512587671, 135908720, 870993574, 644909471, 512643153, 698485515, 155821703, 21394056, 397400003, 687510512, 551237138, 372773978, 663213060, 171833030, 706271068, 812209315, 845062000, 673858099, 270504288, 191144641, 375173679, 607135911, 547969325, 425171155, 952816763, 183903286, 540415541, 524916741, 130063347, 915093438, 954472764, 135040565, 157511414, 998613509, 306321964, 310129637, 596098329, 313917715, 115150316, 989012810, 647025624, 720763716, 682049107, 359725640, 635940036, 350812043, 364725892, 531232807, 892279160, 661208213, 103700917, 70155479, 563303539, 799517505, 855757859, 958952147, 239266230, 863353805, 273488911, 96601544, 696380005, 937960800, 775994595, 229920165, 377661610, 157479377, 967019072, 288840501, 208336548, 610289338, 861842923, 146229534, 190369035, 347370501, 837168061, 373870070, 441431028, 185126483, 995095528, 75743400, 63672375, 879307925, 814718054, 472178037, 197089590, 71285262, 245945568, 516004871, 631170932, 422746025, 429546217, 895493093, 353099954, 495874170, 991346209, 893732208, 716642812, 145406379, 104410038, 808501787, 765108446, 283396892, 408530318, 386597778, 669420482, 670169531, 699844876, 182633227, 706594304, 277772684, 724373565, 288957879, 769118794, 221067998, 655334919, 568997404, 874033037, 866614084, 636599456, 753041809, 300323985, 72309500, 434662229, 67036054, 79628609, 799251089, 507638952, 398856695, 932234147, 825698018, 197466521, 508504939, 847093925, 240996111, 456176643, 869642962, 712921669, 302540103, 546099537, 449167679, 925954701, 872358117, 56616862, 660445049, 798449286, 631516102, 886313030, 24165630, 259652918, 585725909, 471512395, 810043019, 999752281, 984216701, 484965633, 224313270, 102571869, 164888163, 689382134, 417324993, 631568176, 230959320, 117053459, 286092956, 569932543, 259065097, 774676466, 915355477, 126787912, 145611728, 504598379, 555613042, 646180371, 53912757, 660008532, 888680319, 775529512, 892813214, 488154304, 55280436, 254636668, 259416029, 821007557, 786967184, 77285440, 67861639, 624443391, 631996718, 812211782, 549348844, 632189219, 585062113, 456839728, 747668938, 308476033, 759738200, 622158575, 563365997, 194509667, 596890895, 822731163, 114078841, 948862261, 956375524, 380060060, 225622012, 247234895, 867311247, 38822365, 799879796, 614607151, 119419670, 836949430, 963683457, 857960699, 525493543, 64471764, 499438509, 730881859, 452477183, 786698513, 396060099, 660150400, 484069090, 544360247, 963968877, 849917212, 497513525, 962495352, 789177951, 778064460, 742036948, 639362832, 865475137, 840066341, 38793182, 397886293, 647839368, 296909357, 456124629, 883510824, 26738226, 228967230, 835043826, 267861334, 435945094, 951355972, 465899049, 190323690, 660488156, 11348417, 17647655, 942353063, 853267223, 887029362, 234888087, 821459272, 924970703, 32565077, 539650755, 98287977, 811259213, 751767039, 669530550, 281991821, 213422781, 144610354, 464900263, 792676528, 748119124, 139531036, 6962624, 793049802, 972495738, 506486145, 449820849, 877527137, 402843065, 723302982, 169945681, 59048451, 487171350, 564329222, 932190501, 975838122, 864891145, 856694152, 624268920, 452746270, 345263139, 903065134, 483131682, 932434660, 610350891, 731069143, 279295830, 748842124, 9420080, 910182642, 200138208, 452544888, 438128866, 565165788, 501783866, 657340690, 59898124, 810462597, 388854592, 704046888, 402875913, 243922621, 803481065, 248924508, 746252365, 719413094, 475194015, 666250925, 543782365, 133349740, 519969827, 701433368, 397036822, 80733448, 341467415, 315628743, 568605398, 382501977, 57358502, 579729623, 163230826, 816233671, 654845605, 824044295, 956876201, 353826534, 3619449, 751276299, 330252155, 415741980, 992362448, 926748643, 143100795, 664474151, 381257452, 571462165, 498511952, 365845977, 611460163, 19974379, 219787648, 168445084, 255985402, 968825085, 241581469, 2098122, 936826311, 529413133, 949819923, 352562585, 669840954, 925323402, 605698957, 957509576, 448327434, 604267628, 220121517, 992803285, 786921878, 27250522, 608528496, 995075513, 233539985, 512864179, 531130003, 607537465, 314198112, 730283122, 581883241, 203921271, 261897404, 884131787, 732352412, 133307519, 538978313, 955935294, 476332423, 749814584, 509792033, 578727476, 392127897, 755682954, 440974008, 383212160, 336211191, 873809499, 499113791, 62251202, 908724320, 653793162, 633402032, 160844684, 525711086, 42145109, 531555344, 535177514, 280118130, 796012268, 461527634, 100292307, 436738382, 918701110, 388762261, 199387315, 714248581, 395585394, 734734778, 974124989, 806212181, 247042484, 16767798, 836975859, 297653179, 52602191, 940409886, 360167072, 380696982, 297947111, 79618833, 299509293, 84236654, 737564722, 58905123, 207830424, 477650553, 512614203, 976977923, 973495957, 34158787, 882878781, 733801150, 317284246, 765628989, 657270468, 491772956, 652691678, 126081148, 534227812, 593791238, 954428954, 272973518, 343770725, 544849258, 952960310, 107643614, 76435980, 625281860, 574434494, 814574201, 858605604, 756747940, 807835885, 920822675, 524465796, 174007879, 764527467, 804227558, 87885876, 777038818, 316199115, 217705163, 821486054, 143383085, 142436392, 921149855, 836062081, 649756364, 854022437, 344356375, 289627553, 334937936, 968997086, 86275040, 637336336, 954698128, 479985233, 41907867, 335176492, 303865408, 544662500, 885836911, 889134594, 432292288, 410213295, 492936955, 577869565, 486099120, 249350852, 116817922, 464999869, 559808156, 3120405, 343465659, 979188928, 882134368, 377125204, 670717573, 620843765, 169614504, 174383889, 769219416, 790630591, 973350141, 507520335, 42175654, 435655138, 93390816, 775256723, 46290214, 961512867, 789540810, 415974273, 575502005, 901915204, 403598454, 728330242, 171373127, 51844024, 317936144, 766234244, 448125644, 737894077, 839507595, 818052720, 813761264, 164973537, 375101662, 400794728, 874857506, 973680436, 370727171, 996901584, 583799493, 617227951, 260724791, 206393607, 870223182, 709551750, 874166883, 445510286, 776760245, 1813575, 581698707, 997997582, 433532838, 164442665, 287800983, 652291939, 233483814, 701353148, 450342231, 79360122, 447908535, 456777328, 551158718, 470183978, 81807692, 813287066, 256595913, 759164637, 684275111, 791819778, 928753839, 110651826, 164691143, 597490763, 724013830, 926000445, 645480155, 878030379, 38042123, 474845450, 44169647, 450473111, 299094080, 842559003, 389387441, 187419502, 44193059, 49416420, 488026629, 571824228, 327095237, 845074260, 768926250, 201327022, 249185110, 640146908, 910927771, 936062776, 523789324, 887194780, 916875146, 258191988, 201513568, 66977614, 128675339, 708560249, 969543337, 349629296, 562309497, 343355267, 945179951, 405763387, 195552968, 724359753, 973881252, 560284540, 428616658, 882105838, 658364290, 527015958, 454963883, 242714766, 595714064, 245832632, 520649186, 254669290, 293029315, 995806766, 86962838, 665513961, 363403246, 452833799, 901859254, 457661686, 313411801, 410510716, 236352064, 708404396, 58581255, 101245712, 59082432, 916657707, 630443943, 407550081, 585499425, 499529045, 804331773, 144707845, 925639095, 661671781, 743582676, 860597290, 346123138, 398103618, 641142772, 349056244, 814648235, 351008210, 884011192, 10046278, 178747197, 179227756, 180986909, 772247999, 343073663, 66584083, 955758723, 150447539, 440707092, 497223214, 690689354, 894876974, 547266001, 675874616, 550087350, 753889177, 697531865, 956440532, 611340948, 126267962, 229274894, 668455552, 84209897, 897263092, 358086343, 342894070, 79136607, 182789608, 28302123, 154496903, 234438152, 767730257, 343949151, 528724519, 637129994, 821344863, 309509614, 842363229, 360863055, 710137038, 218177945, 312358285, 611029081, 436441740, 771106047, 154769232, 115562608, 520447012, 620841201, 521394539, 484740985, 819797461, 186880897, 660129524, 155492893, 948206851, 702296425, 964850447, 966283841, 631349423, 496219984, 654427365, 993552794, 658499154, 752960850, 231748268, 425992569, 827861168, 444250388, 799150010, 406556067, 193084087, 824805143, 223255103, 616674595, 144359307, 767654324, 699704939, 51516212, 364158250, 574769849, 510888378, 595936790, 545320342, 374446176, 414667909, 25269824, 314680521, 630117827, 526185532, 391311006, 225125192, 951899356, 398638852, 208171659, 237266995, 134327541, 285127068, 625406533, 241355190, 753446828, 494264148, 313290716, 226864211, 952361389, 305694244, 604283278, 310236440, 716059791, 713606071, 392650428, 663242054, 491222231, 193554057, 363346589, 606448123, 162128868, 323753366, 526353042, 960603054, 328639943, 247943446, 947750081, 649383200, 322742923, 642940254, 605257738, 590110736, 577217640, 188476578, 337518841, 179940139, 602234974, 56830837, 34208674, 421293272, 373577467, 446298805, 127216430, 213771174, 774617387, 125306486, 996329964, 241853751, 715538122, 768325474, 373870341, 447587146, 864182414, 590642938, 912144175, 657063376, 878844994, 728153302, 525825136, 576369184, 540963933, 18798472, 21608419, 687028939, 72250344, 864586652, 637174272, 895125415, 859103898, 871686134, 821748067, 375188211, 532419236, 25547613, 665574609, 962071010, 219544843, 766754837, 773929697, 957299422, 734896500, 608572277, 133070331, 663446876, 24390098, 439606957, 361806305, 859220634, 74271055, 302851653, 785266014, 912229030, 65000616, 983294366, 567777425, 788356660, 76190141, 711035076, 477976311, 976190598, 309628364, 378382279, 137697481, 141291264, 491681330, 331585797, 11950536, 931542610, 926495137, 610968657, 124584758, 819320034, 411064434, 816402475, 199565311, 679502716, 197907199, 973450024, 571862514, 328233583, 943056434, 661903134, 97167784, 492779662, 703595644, 882149607, 254371373, 106107947, 551201782, 163874484, 967400329, 426578485, 424122624, 659747845, 690000066, 186511770, 770641289, 675756582, 974661738, 499844266, 742977716, 531623405, 557545223, 516377797, 670616723, 971276279, 585135804, 370501742, 462436831, 624156924, 379348133, 68445036, 24617326, 331108173, 796346083, 205496121, 98387046, 17858145, 688445330, 834262456, 16628108, 497052950, 557261706, 851570332, 219286393, 242126875, 966160671, 57517589, 244501702, 896946279, 787928806, 926670727, 234457462, 447173778, 482999089, 287374074, 821753309, 758019666, 437532909, 73512379, 936170101, 709870094, 838791990, 644060043, 997887840, 175859414, 264584022, 327883835, 188997236, 890434960, 567414930, 302086195, 138756153, 131296122, 550816557, 167120783, 642112579, 216629120, 217226726, 967987107, 788303296, 120594119, 935484261, 672519681, 695819760, 89852568, 865307457, 628928693, 985258176, 115596705, 60658932, 766550172, 999530526, 362454745, 447138111, 632904437, 760901655, 40634776, 608264892, 935498792, 274948962, 677911350, 395998269, 588758092, 748462713, 845565866, 511933679, 659478802, 317255759, 275037545, 134683458, 181945834, 178606706, 797306482, 876691317, 731391369, 456036253, 370729775, 559941564, 458073915, 644949052, 360084290, 298747675, 911020213, 842967350, 194347443, 474396448, 787080744, 674761474, 135575828, 469163333, 256912598, 496949171, 162313616, 985007370, 332370801, 513373152, 674409473, 98044900, 372236307, 141764701, 614016531, 826258346, 879217658, 61414507, 326244488, 778026950, 491076132, 288262634, 723273173, 956773263, 963059671, 813884965, 512082439, 722099105, 489230207, 394742234, 413145287, 461250794, 6962225, 202925410, 60529872, 8975160, 979677440, 28891389, 846835135, 379370563, 239851418, 708764110, 342499082, 291322460, 196397602, 39525931, 958439413, 284019625, 734494821, 358914562, 693211392, 149228698, 292024063, 147566869, 399221603, 222994053, 579572680, 647984423, 966836908, 346805039, 139218101, 916594531, 756084523, 265414819, 778743969, 980899570, 52147528, 950620035, 813099158, 387433441, 276372722, 703477671, 189206661, 420043087, 809264752, 565382473, 36183034, 919851701, 90736788, 996190778, 40139316, 864255989, 113489881, 562395774, 377418386, 659031541, 668408372, 647049075, 733214814, 703428867, 651970690, 243794772, 361900004, 607052100, 683962452, 730426360, 141641994, 707055023, 689812223, 84472324, 525228096, 224858467, 26444789, 945940192, 482219933, 304080930, 796581986, 17105003, 558581924, 924538721, 927691253, 725056099, 756884634, 729204694, 335457332, 572894685, 535478393, 1475339, 651176110, 58574981, 271053558, 499378573, 98810527, 952220410, 36596538, 754276750, 469441559, 731241025, 447238555, 260753863, 149897326, 604137547, 810775266, 82694444, 557576502, 414942506, 66701583, 897167583, 761471082, 397509159, 520484873, 670218387, 6349208, 138314648, 845030641, 50650769, 88476967, 815017545, 210075428, 87371783, 179138551, 869311610, 707108611, 768428888, 958768989, 995814083, 516002480, 759084564, 229169946, 640556657, 801070881, 638791804, 316243136, 624433097, 99860666, 176303315, 702332039, 352720993, 530089443, 536718303, 662368288, 454404151, 623545108, 94840617, 535362274, 358742447, 236618843, 884743724, 904253068, 184058952, 554898619, 13626622, 801538288, 217787154, 93481, 527467476, 43775327, 227010423, 316934555, 636081068, 622759075, 505356392, 957641836, 542630141, 200204427, 365888064, 549178603, 21062833, 989534441, 20226089, 211984962, 55609088, 759225564, 931296186, 700201768, 626666339, 359522512, 748150271, 490318339, 315654757, 170385987, 647682300, 166112496, 559852571, 693462043, 853509197, 476644496, 372166846, 89788633, 896881023, 879154690, 748531547, 554476578, 835453096, 641587822, 758820335, 15993603, 390949701, 243539402, 205038328, 66274545, 117852847, 574321339, 208203566, 360802736, 383438787, 395962201, 266847157, 573612425, 222331143, 261297307, 49099815, 415215463, 627448021, 413277425, 489551057, 122628894, 45380132, 607147290, 808958811, 274571188, 5741445, 924771430, 639849917, 318436487, 557959074, 980422339, 149248914, 954716282, 666907023, 488486794, 145441629, 353424422, 591193192, 940998630, 459084235, 134828989, 308573261, 3565943, 622975615, 444787617, 654934300, 200015390, 740345696, 163899697, 517392939, 96121779, 757121538, 149577370, 232624719, 965816425, 522566273, 178046949, 103619488, 96259396, 979212317, 324631672, 152680644, 455353567, 351282927, 865713394, 293693996, 955599928, 976484780, 358413942, 712047468, 122705243, 174539978, 152736487, 363314566, 378968280, 36567858, 401592671, 180771906, 56424538, 702761637, 214951203, 647858852, 693526698, 351169101, 187580787, 747441998, 472948729, 184952689, 254470542, 540314575, 490536642, 345976750, 556806322, 361292408, 767982556, 669683095, 140833712, 596043446, 703741130, 718006309, 810027000, 109284283, 31075600, 51263443, 289789536, 713468040, 249951901, 102645726, 217004130, 887626221, 499909286, 763760160, 329318238, 301780904, 273680068, 583127208, 21621962, 908340796, 371873602, 842449005, 405351228, 661745648, 658271210, 472952244, 371909267, 774596565, 288225228, 926621550, 900440944, 117850855, 88748958, 160245219, 398986085, 238557064, 136205176, 329086320, 98313250, 865704553, 528259626, 236199891, 583864116, 320100714, 897830499, 19379075, 885907695, 974264243, 187049432, 144577354, 931975905, 487293515, 555715053, 337508035, 675355954, 742462334, 466599916, 959301674, 521320198, 475602252, 57317554, 831597140, 898378002, 73843212, 487259006, 413868024, 155614423, 931522446, 789112643, 706738593, 77434227, 381285723, 344617088, 835594436, 894827243, 613090962, 404201435, 346323227, 485518862, 216400424, 427659485, 674773371, 94210246, 510609916, 466222942, 488852719, 676232741, 157015424, 71661335, 405659010, 689095838, 248444114, 515757266, 631547087, 970792433, 654214166, 942350927, 883666984, 838532733, 619635226, 405834333, 556364294, 78065804, 333678678, 581505399, 608826450, 800225239, 201100836, 17856493, 312327136, 472341822, 107057485, 647674719, 924157032, 522184950, 230183408, 47192027, 458391355, 553840124, 868873858, 856903339, 497361544, 355681769, 341303768, 936890497, 716020880, 406812690, 391374342, 24435090, 356592509, 591004229, 22451240, 360029701, 445908772, 904824983, 962411355, 151580653, 894167155, 806462313, 374112253, 780667024, 345794582, 196056977, 543044909, 362037890, 475301577, 42241360, 564626677, 581592153, 662609989, 936273328, 497411878, 133431766, 447410163, 391600178, 579393603, 880827270, 795953598, 654824669, 693624514, 834925453, 600030071, 779217564, 354252091, 987955227, 163900495, 116505662, 991222424, 236210029, 145424735, 797501355, 645612547, 899911533, 264765379, 272676515, 117806135, 444810672, 853619026, 573185478, 167462674, 735651760, 573044937, 92817412, 238085179, 351293556, 922318871, 464764094, 251289272, 578371413, 388254719, 670495013, 99879938, 955807054, 51124620, 786026316, 717012624, 605063109, 756617173, 596679357, 652286505, 573536181, 866106394, 211828323, 364071849, 245366224, 290598298, 464884032, 793190500, 238214609, 457611472, 1590929, 791905018, 674632557, 732073372, 400055783, 703476301, 280097800, 762826597, 619522967, 714014379, 11742352, 221122461, 689746955, 231090507, 32876676, 505677529, 733692898, 131472010, 450186781, 338731601, 934480004, 138116337, 412847594, 577279138, 413339055, 137501791, 449771198, 821162846, 586734299, 914038240, 996082508, 718409212, 482323393, 95896153, 900089412, 749139196, 286576606, 401156941, 312650420, 473603703, 144831025, 972333323, 352273814, 954473811, 125565496, 482183394, 7272488, 994705778, 712164459, 6942589, 321894664, 127833196, 974901813, 849776800, 8343955, 746702222, 555573391, 722426689, 802114218, 348335259, 158006393, 977694653, 188118912, 674258714, 734475171, 709264381, 398654874, 408294770, 288254590, 381238761, 664469604, 830468143, 680604837, 480854265, 842333482, 518246759, 858189211, 11242462, 168316256, 415089343, 483267094, 63897546, 547678289, 163810291, 433564740, 3570402, 221098393, 517024142, 931118762, 735958694, 335298136, 766456230, 603961713, 49915833, 894242622, 269654165, 310738942, 875911100, 789563897, 616205186, 880071500, 349993324, 82617227, 741719896, 40032004, 978804745, 78694079, 459424055, 550300612, 985502207, 574253030, 303883853, 349986750, 993763146, 516418196, 137755948, 280488308, 444790615, 645800217, 673810348, 905432325, 470403585, 889274820, 164420759, 810412894, 481536337, 865886425, 516017250, 353266726, 623787331, 429510958, 873752768, 580522165, 126553774, 364615200, 533300329, 647433801, 941640592, 680043922, 639120594, 755350090, 180746880, 933181902, 759542502, 826377206, 294820546, 883018442, 105105627, 261181826, 712699019, 119130544, 913164041, 947862057, 875676894, 273159379, 225743987, 404112304, 968698951, 697957991, 684274284, 567547857, 533025212, 48091937, 978479901, 600682343, 943049771, 735611568, 104197368, 594236321, 412938055, 943155442, 536170612, 139250389, 539400385, 710416007, 538490943, 374739700, 179999195, 239353596, 347629660, 849998712, 555768366, 569207310, 363326856, 812233102, 597685071, 682766405, 958194621, 103500444, 854849260, 72084137, 672248138, 161150668, 746593147, 280526303, 401597926, 425509291, 875216472, 440429773, 718695755, 751373677, 541899050, 791683976, 389884430, 292589861, 909319565, 277309245, 509912786, 311953541, 856164802, 479904888, 443529577, 18300307, 608513003, 313474151, 275602569, 772641072, 587406824, 346108405, 135215253, 212477740, 688647684, 7111162, 763637888, 921804682, 934838920, 796201406, 403249473, 147847775, 111642077, 841167487, 225526026, 869713975, 91809097, 685211783, 523316078, 832333564, 500296175, 770574148, 647402408, 537319320, 968087679, 639190210, 921969400, 820832136, 384629019, 399938773, 758560057, 6070484, 395568992, 782541175, 502529522, 213689172, 162253735, 310740853, 292141773, 896238202, 96161322, 23894936, 425681510, 556486904, 675444664, 697816249, 283322522, 293874059, 411224547, 27601140, 551044882, 782392412, 556432658, 262075058, 259455483, 651570067, 825723753, 546260849, 2638810, 566942713, 895070942, 504283739, 210568364, 466729381, 455582988, 819921823, 999895942, 953992347, 810144012, 199099466, 855497396, 960573012, 614330505, 812735726, 826164353, 201853653, 898867571, 223868115, 703061707, 588408662, 893368905, 609856245, 478058012, 148428243, 28018592, 372369568, 423709147, 791075425, 327604594, 597792888, 961628649, 219504261, 2265515, 616548430, 10682719, 562210513, 737607262, 162499160, 84175773, 177424366, 281679470, 163573893, 951127478, 99483646, 199569996, 870646152, 463134647, 192617212, 588909703, 711611602, 180014755, 353077725, 83702126, 760960887, 210783264, 466668727, 860841334, 865127326, 854054752, 504272549, 789748997, 633726082, 673272618, 253774299, 482425362, 224961391, 133740827, 412209588, 929887896, 598506189, 654237770, 376249251, 602690334, 766918927, 846331669, 966843841, 517949335, 240174996, 162411069, 170863817, 519916356, 11818362, 124111586, 59901014, 187796708, 689079806, 146768204, 649032198, 689911811, 860605820, 55782863, 405849086, 224050832, 773095925, 185165460, 172975051, 617058678, 152656407, 856594103, 811699283, 631050196, 601645690, 807552755, 243007908, 772424962, 72703754, 132889995, 300091878, 334094412, 194348193, 990939135, 330419274, 16267933, 822724718, 927580611, 276898909, 718612821, 732330026, 734491836, 494007202, 673778345, 486219479, 755059776, 337800300, 355915830, 823956226, 696669780, 942744977, 387880923, 66423870, 68974095, 143950004, 249869582, 79297416, 636796587, 168572253, 920367163, 727447965, 696608289, 108060376, 738498381, 533282549, 4281208, 635289054, 771601887, 924413387, 994676650, 294141700, 668013093, 3521445, 451031844, 281212646, 601987358, 253190459, 227426378, 915123435, 455683505, 218758145, 544887319, 330472319, 638719451, 840206497, 241436093, 791791716, 246744125, 983905672, 14207086, 63990939, 888029489, 80849760, 964795119, 38822926, 32387724, 791575690, 861539688, 777723893, 530970160, 920648502, 162816924, 158567959, 207347760, 514497026, 739256511, 261132417, 56556538, 892299818, 939379146, 338088998, 433116509, 628131284, 191578090, 85530669, 637335770, 623652203, 429234136, 294289758, 131065389, 439071959, 752464471, 96245554, 264478439, 703159762, 973709797, 927408425, 336181173, 253627917, 826597920, 585669744, 257917333, 359940599, 212806352, 59146128, 919792220, 85224236, 712410825, 638872480, 119434570, 695978279, 181907742, 284678899, 320715804, 370530703, 708646221, 587166908, 940776449, 426607442, 68552133, 121217905, 437959819, 508499158, 285592522, 514056189, 484268337, 277252805, 487836261, 177928062, 30504959, 786835693, 701784421, 189152821, 439762145, 552676150, 890637313, 247016182, 290297663, 311509585, 859395995, 543910116, 629012243, 398900946, 681614763, 336381820, 723766928, 752827138, 13571336, 449652261, 338342941, 475976836, 791736805, 12079804, 349275223, 812888166, 889892911, 378014548, 229140373, 437501439, 316921376, 794464584, 686610271, 662380588, 780143601, 331194119, 103227549, 342512531, 705692527, 218952630, 793011760, 478030123, 437513001, 886666070, 199896326, 270400325, 787825996, 896715627, 894269116, 498126576, 444281971, 377611480, 948195766, 299104381, 633558349, 221860321, 632188192, 953663297, 482634869, 368020457, 131568563, 118435075, 264929126, 45973382, 174714218, 601998875, 606624888, 258695796, 900391311, 219717920, 782541343, 911905911, 71022375, 46503492, 635972707, 101586097, 738922696, 751146259, 777514189, 924289411, 937115894, 776822740, 369333359, 755008440, 201299919, 557358665, 544870407, 389743965, 740791129, 442762622, 109140470, 705677380, 16780094, 209986483, 462717363, 299179396, 46810628, 258837221, 5824079, 382262050, 665545319, 559538910, 572914150, 837508175, 643179373, 488388943, 232069424, 62075000, 337965013, 652672081, 605848764, 796761784, 632345492, 556057006, 220344000, 802744268, 901223246, 2227963, 340289861, 765083170, 320826793, 367827302, 541098476, 962088963, 823049507, 952680938, 703616511, 969368798, 876482613, 700849011, 39615668, 385824248, 603430831, 527952218, 224758586, 762668876, 848379354, 920210282, 807098002, 602219273, 122939479, 156678304, 588540605, 240180535, 824949674, 872893076, 931638825, 640614348, 188075251, 729058734, 637919563, 973645346, 24378367, 308896144, 128486473, 852120115, 802515213, 302982276, 769611191, 366373899, 199916945, 797778097, 525614645, 285306933, 503921381, 949238862, 724667587, 488777023, 304298748, 375495313, 803516031, 817979793, 497904387, 72726551, 741807133, 467970906, 911048330, 323335441, 960198854, 120345824, 650472116, 966885399, 803418445, 80172289, 424096894, 152672462, 863389720, 737681584, 981057107, 383256657, 987160487, 449505130, 846891408, 553409519, 839472334, 472513769, 463551555, 764284868, 583090149, 952792226, 548679756, 868125748, 691372049, 872378890, 983251044, 415067298, 168420148, 171089173, 515404849, 438331966, 541597028, 325239278, 722830421, 613876120, 195339670, 291601903, 473826241, 283776891, 568635672, 102386434, 44938672, 220190226, 970575390, 400125641, 792366562, 605176879, 834676103, 508488915, 10425148, 179407363, 710736546, 952673859, 123626871, 286295221, 973473434, 418155242, 146695035, 810635791, 744651575, 404908718, 258046397, 400727746, 950780658, 896958290, 127147856, 288688315, 532739882, 265813769, 536137709, 261653004, 557293723, 647038622, 213160037, 909910484, 321938872, 267308778, 478185778, 634981043, 360521052, 761209673, 865858901, 239269757, 132717991, 660320129, 647348410, 982294220, 437172067, 17813646, 54750922, 529531456, 379131232, 791925252, 951023844, 68013248, 219816317, 71879952, 294523156, 181560745, 786685686, 436659381, 857776809, 422270817, 670098091, 669328850, 813480367, 895788371, 934255245, 8837653, 271316967, 468192100, 896113200, 971515717, 254140873, 211138778, 588319846, 98173480, 778465863, 905638090, 104822732, 44830499, 386553685, 464914291, 824379900, 149432684, 169932223, 259588128, 655572190, 618962145, 503757919, 244336571, 351812030, 157791204, 353461338, 875258405, 563609238, 406546491, 489965836, 506367379, 466605767, 769569268, 399584366, 999142421, 72790934, 291071737, 166082911, 501980390, 54085124, 824989568, 515817479, 95411249, 248179501, 222084097, 594464865, 388330436, 135319102, 590317310, 871806824, 647211667, 989186503, 402271828, 910606538, 776332595, 367853509, 593377349, 965969825, 648411785, 393299059, 345284006, 962890223, 867566564, 610265927, 12315919, 44680207, 77774085, 18072452, 593346875, 589337129, 829095008, 776380675, 6588751, 457253991, 872436044, 289527321, 542979097, 135113451, 129668948, 325676762, 372631439, 566962970, 364847856, 487897693, 96546709, 464365847, 153224128, 218148108, 653718215, 557322695, 634310028, 987676761, 117127493, 41465668, 122718807, 744077944, 956084092, 69815988, 653222318, 441040005, 961325965, 510385226, 296479514, 680384304, 870709161, 461073371, 369066288, 765824257, 37268079, 794926759, 808696346, 166608577, 713511621, 959500605, 728691383, 929912186, 454235071, 479549781, 828194861, 122355404, 170790592, 506257388, 510835469, 307224591, 739743521, 821150762, 413593359, 303812520, 389231276, 668519027, 272176485, 640879594, 344158921, 484925397, 772396863, 548450159, 902000924, 520045559, 580610985, 427028249, 386037778, 2453892, 456812897, 209775309, 110001652, 10223652, 835877799, 592293192, 813652410, 712038111, 539966168, 19074534, 478923069, 970902436, 67214383, 155744296, 154836456, 670383947, 773568740, 858454901, 320763842, 474844262, 406864245, 253973378, 272335908, 137992043, 606414320, 749541669, 447330664, 365041390, 953252324, 487343997, 157854246, 137420788, 884964752, 27259338, 932151964, 841151608, 778263324, 692122249, 671498067, 222761185, 398220438, 320284622, 624275229, 37018158, 867433639, 983772158, 486246993, 145839501, 612056912, 758887315, 114285560, 564446086, 368978882, 388439381, 267554439, 936657727, 559156815, 761326580, 334611621, 875202372, 204701172, 384260664, 180106089, 303760502, 908853765, 8521843, 22843330, 873380423, 201777224, 105605950, 281496437, 549771674, 937714919, 909136468, 69639937, 26245965, 550447712, 996579235, 331958236, 896067039, 265671542, 539748170, 362148076, 704037820, 911947433, 591938802, 909091019, 614823041, 863470654, 719268656, 274077680, 783966409, 440296391, 507834813, 81705993, 563871415, 785256061, 195046555, 506697536, 988113743, 442020957, 92332256, 601437032, 17487380, 767760832, 794205951, 22722529, 720356165, 353594013, 611281845, 285394439, 597034084, 64443160, 421386018, 13207957, 678514289, 989186919, 297858312, 197843104, 707770601, 721891283, 212154822, 587419888, 659776150, 547203918, 537171990, 555231142, 447849467, 811510690, 577528164, 771111912, 415746315, 74148262, 568770238, 503579233, 894792232, 406413725, 463908438, 308267350, 5894294, 545904411, 883028377, 953663408, 625232784, 578407836, 713503050, 822478063, 557674943, 924923413, 249357436, 389026773, 737635100, 695299016, 623707057, 847757414, 790035962, 942408156, 197522613, 897652264, 756898455, 240231505, 737907534, 650090073, 549566646, 92721967, 33022132, 648247677, 34834141, 592639504, 434185297, 998392382, 148931383, 419997634, 400555681, 686507133, 154571032, 926058425, 59734198, 779836903, 200596490, 171017541, 764779134, 972132795, 818366025, 657283605, 369110900, 97233971, 379724778, 588503360, 110967224, 272419983, 488538402, 903026163, 166458262, 673840492, 682021595, 205346935, 602842899, 88835400, 681643921, 49287354, 541606236, 470941131, 726945839, 780503262, 145890716, 739405592, 943966229, 491386602, 877106465, 431847505, 813828225, 474504189, 477706757, 719625493, 369052718, 980409029, 26659228, 272816644, 313576573, 146464120, 777188921, 725395940, 136049398, 701990515, 567372509, 403557690, 56857415, 427523654, 275148702, 797133997, 427292700, 406601499, 467149355, 105875739, 783694474, 742180443, 124565909, 344551819, 59602272, 545404750, 81459423, 354063896, 331767068, 444529175, 194127156, 99362366, 330870046, 661493085, 73460894, 718672250, 799702744, 382382405, 397790652, 465727863, 619108648, 704874393, 996404657, 687640606, 232901490, 530894335, 955200787, 908111529, 453575335, 702402367, 901976311, 708545354, 616069915, 257829, 109886018, 743051758, 974571132, 692466368, 60036642, 34329489, 957879169, 464578867, 126932325, 682942578, 486802208, 98812320, 331237813, 8321070, 40054755, 391197306, 423379847, 231712169, 300201445, 770915948, 661455075, 917724034, 380323755, 71335721, 897799996, 761087536, 92311267, 784206425, 817181982, 638764232, 136022507, 554745812, 364361053, 777540716, 383274185, 116261161, 655233813, 963958633, 182797972, 871400407, 27300490, 788968997, 879806494, 812380024, 847595008, 381649021, 711675775, 556188208, 71180506, 201491699, 622794339, 209184320, 362269479, 940526485, 678901042, 699008335, 447578687, 916172495, 255773515, 687964595, 77300041, 709173256, 591183497, 979466224, 139875129, 628728128, 700245189, 803630554, 249317041, 54833331, 340454984, 650954865, 15886442, 198608189, 128321070, 824383180, 640383310, 679190723, 261127042, 650209868, 751223745, 696408288, 958448447, 277598938, 61081140, 820151748, 784107361, 779680187, 759676178, 422317233, 763981399, 550946836, 370675863, 566374811, 243927207, 523985352, 152207656, 169349306, 218617652, 962130635, 648047319, 910612305, 882853188, 473916498, 68820052, 939908059, 65084865, 842570076, 670513442, 549123175, 32940767, 351413561, 280487900, 597746749, 271303771, 381249673, 385817004, 732184772, 645448166, 447485848, 9547480, 595217065, 752404621, 632854030, 685654655, 196518182, 887122614, 199157863, 612422118, 980591892, 342733540, 421155117, 582616465, 881073758, 766416640, 987440167, 689129140, 482162715, 514518633, 483890653, 386420676, 82395348, 824380866, 192618874, 202397356, 704733121, 170612681, 231556629, 913806922, 666939536, 617059525, 487803401, 956241526, 682522122, 589409592, 383064833, 338571744, 623269044, 8336855, 895168162, 176606988, 241851981, 713608057, 887995717, 788018506, 296410368, 366981050, 480626879, 260136759, 313300496, 42571084, 389025635, 895305803, 209939262, 58171271, 762510477, 437724003, 202813489, 497742304, 376384612, 241478610, 71911104, 540258313, 392660622, 722403372, 491419174, 733637016, 958586747, 193497893, 228047121, 703788524, 904604776, 363067795, 460094352, 980991038, 86464206, 257220775, 882422535, 69008234, 675681526, 207144931, 528417894, 95331500, 135234278, 845111935, 183583779, 835074403, 59874918, 374707323, 865216271, 490501563, 350238068, 590581622, 296341764, 596521404, 67347725, 113322400, 953029912, 282110226, 436135433, 966368486, 397942273, 649414798, 704555935, 161067373, 363554284, 290955613, 97211278, 177683232, 137165612, 47775843, 286872141, 958098784, 986766038, 191422997, 994096872, 207510091, 743373754, 704760924, 557475539, 348715740, 405345658, 639500015, 706879662, 875019520, 674943152, 867167806, 810097211, 108839531, 740727817, 711068324, 952109471, 11192641, 438301763, 13720657, 308426683, 570785337, 790323152, 317417345, 936869986, 522730858, 508942787, 313056534, 112039419, 216169707, 625901125, 765091501, 299261966, 271182813, 775118917, 549809965, 583466196, 711286715, 377220608, 569786684, 834997409, 201203422, 166363345, 874035086, 827497597, 104465729, 67856258, 943046939, 685314001, 980369043, 159390604, 4809114, 471047483, 310897688, 130522570, 615116595, 73669240, 973942637, 34090545, 955991897, 802678881, 23701232, 234934946, 973086375, 609485401, 319177740, 114930543, 364333551, 504637482, 248650356, 626078020, 124723706, 733829531, 34371196, 437700137, 30554926, 190135457, 330392045, 62969892, 656913422, 817458893, 472293946, 192991847, 331969855, 719981393, 23713247, 614523716, 455103136, 313513119, 535265370, 333278936, 522162342, 492987299, 565741222, 351386657, 639281072, 58501819, 958884199, 90123659, 67478997, 315385342, 4159962, 875241107, 665362341, 630928827, 119877934, 326944061, 814811224, 595781489, 454018051, 917827640, 698157191, 424204009, 479269023, 373511697, 708309619, 464981946, 300556053, 705485490, 678331205, 162346929, 540871219, 523651400, 575968789, 68553977, 532785048, 980913816, 39708699, 516464409, 917711784, 808977559, 287534548, 74078436, 187671249, 716334021, 284555236, 295826040, 746137973, 257154735, 113332139, 800341216, 433304551, 722055522, 685849773, 317401948, 160044456, 383462799, 224053559, 85072865, 146746837, 992161768, 254588706, 430894824, 53377150, 632120729, 98131732, 738215090, 21944309, 635476183, 572134024, 125360272, 370549357, 170468702, 999058656, 535361162, 681932799, 493877447, 86261542, 176233117, 23849507, 783367612, 982395520, 440335895, 520422003, 744237973, 694831566, 411650098, 93746719, 194806763, 372146533, 464103004, 789808210, 778722483, 829031797, 569494781, 610030166, 464530966, 818846565, 310654091, 590531664, 139330240, 276266936, 949088487, 265108734, 430747747, 894549498, 291527898, 165027609, 759419365, 183263108, 204787241, 631281639, 223327472, 17210039, 571317038, 585929347, 104923600, 877310953, 557909540, 346521106, 419855481, 342334476, 597559889, 13376150, 336817103, 622130192, 128192037, 212601144, 73105643, 204657559, 939564833, 301917715, 284531267, 199324396, 937201186, 638666480, 511231269, 574901273, 854322673, 137478326, 643168303, 738776074, 594716388, 476330700, 270316577, 294049949, 862050356, 126545498, 786394949, 998467588, 590782213, 526217711, 605848824, 786138356, 153226421, 324290631, 579083784, 8476124, 13321697, 798479088, 380631460, 560668758, 382749691, 972906315, 784650544, 282338623, 560318863, 305405817, 445643184, 783665604, 968187613, 16270451, 392869538, 142189104, 651461289, 566278282, 992429813, 212329825, 374912364, 700592847, 940829313, 144332665, 139017091, 325265026, 740278650, 416470524, 788349515, 263079890, 416844391, 773118186, 335954800, 720978095, 672012954, 645007951, 52410374, 764097116, 538834520, 321260567, 687517498, 535691237, 470296014, 179511554, 959480050, 129304666, 659665363, 23306251, 250398261, 257073617, 289295818, 898953627, 669787397, 818256567, 879084099, 612791786, 291292286, 535428166, 172255425, 985356598, 105755893, 971461870, 844465991, 563633881, 900409067, 388498000, 728131398, 728259787, 855986411, 479183064, 313926252, 519896760, 943129718, 863546918, 927874552, 827749383, 366576427, 578356628, 909203796, 287917590, 603783371, 817390984, 477398199, 972409819, 980527899, 548732831, 412722397, 596296894, 548732616, 775656818, 744393805, 689568367, 820242924, 574106470, 15391930, 451180188, 572466571, 158185506, 955239201, 537809387, 517328969, 38523128, 284316577, 360462275, 757175723, 520361422, 493071072, 120866519, 106229743, 378696410, 120204761, 14920573, 57524975, 719539617, 341376226, 773356756, 779154706, 400531726, 899799353, 327078160, 728272433, 900679513, 641994936, 225726519, 579625511, 522519266, 868444668, 860129705, 508478386, 976259500, 890619235, 694862297, 265917893, 290383147, 580280621, 589497050, 331484836, 860592338, 433781739, 975654976, 316226894, 875720723, 711754672, 347224378, 113660267, 366164764, 299162173, 953267347, 367475734, 209184667, 303189736, 804024767, 642242894, 640341692, 593571086, 439362042, 240494514, 30423812, 800024501, 465398111, 385490645, 280911772, 773264612, 631332477, 14157729, 870607671, 900205540, 257680519, 701162099, 234626326, 454159907, 349939959, 232165132, 577972008, 807396289, 274938807, 60421668, 389340678, 33065729, 113796152, 13160620, 97332676, 459950291, 406926334, 560694708, 344192181, 200805741, 799824125, 468215744, 288593698, 97322053, 505912069, 487897893, 844638603, 311861287, 163345207, 168170039, 347739908, 357898629, 28153405, 723017938, 924297054, 762976946, 564244692, 92034345, 992860171, 595976711, 423208163, 225428751, 47437515, 198414596, 178338061, 408904599, 841756740, 740447052, 767122988, 508301238, 223004839, 935510802, 345291206, 572359955, 855417693, 269375701, 767973507, 353835771, 599852901, 307733671, 846695973, 658757248, 716014252, 269555056, 990975891, 869192733, 263178362, 369585229, 34944531, 721568401, 324333995, 142680425, 206931899, 376597978, 445041950, 113975579, 775636218, 143798146, 570299168, 549930553, 374032558, 726346612, 354444180, 559594261, 527402425, 999857068, 409261037, 603611719, 806585687, 758757333, 668445754, 952864425, 638653708, 918730710, 299319933, 790214142, 18979122, 890540105, 366326304, 346900951, 850534047, 132125165, 453889853, 747736123, 342221638, 387900008, 688509493, 861320353, 855064589, 919246136, 464156404, 904276729, 893825508, 238262076, 191693048, 82652125, 221433613, 795847187, 997054522, 899366547, 839285035, 259901518, 904545331, 967097496, 535946628, 196138668, 837634596, 290859199, 885469760, 36789195, 447345596, 323405303, 532936656, 629093515, 251994031, 35446231, 244514726, 976384790, 457224448, 939340215, 889734074, 866916327, 655607783, 87092968, 883693219, 598877205, 882676272, 97274104, 930885063, 601018364, 84617670, 752579364, 28437060, 151726249, 603661963, 735056311, 65718383, 397795937, 955800935, 454193977, 98505112, 289487942, 212626883, 662715640, 525887073, 745331142, 440264525, 170661244, 250435683, 740080189, 539889146, 706675107, 347489943, 19404730, 732148026, 476785722, 553672029, 340736790, 708174933, 933381314, 238571108, 451938159, 719755341, 341625408, 882234522, 484105300, 943055338, 17566123, 888716755, 397271848, 750310357, 416765796, 94403221, 902247411, 156509357, 52334428, 561014241, 743132849, 429106882, 51348250, 401700933, 639683604, 453544052, 898091344, 448548271, 90660413, 702234453, 830270441, 800949573, 154565406, 296298582, 357994833, 370247578, 55165630, 773075766, 140991686, 453339720, 472755996, 203383036, 671504251, 456743560, 474079051, 420600810, 594438667, 996072553, 279756819, 227916575, 745194946, 137046448, 530796349, 255032007, 277156766, 848988517, 294593459, 187923225, 800214886, 852099013, 384745690, 79877316, 390248822, 635373407, 797076152, 107835834, 491074746, 668286557, 433975039, 7229373, 462697091, 883187395, 193111372, 762006167, 536493799, 545836629, 576159970, 582032755, 902464555, 835193706, 322505418, 605297086, 830406396, 406715240, 31838114, 634410859, 985018563, 728344146, 491315476, 446608126, 231204729, 338017228, 857103297, 481904224, 823155596, 706241993, 200611634, 960990380, 932711380, 215459632, 985324281, 729645472, 474682876, 473520896, 656800440, 580768862, 151578363, 73876208, 377939358, 141494952, 718081668, 505392736, 226263940, 475500626, 280388395, 626871328, 348857107, 475298664, 973029032, 619253786, 805204698, 296760903, 662767235, 263795330, 801868931, 526744746, 390339549, 699968479, 437261705, 2972159, 607900795, 523371402, 601407860, 289907026, 870098199, 635919503, 427257764, 180004245, 206875407, 439438392, 920042571, 518002724, 399272265, 390608323, 234352436, 793812870, 125612496, 921546753, 777196344, 569011583, 934292028, 838806654, 876429338, 672025065, 902618804, 458381215, 964599574, 562789745, 83348609, 321760160, 380366525, 258994339, 615642719, 144797991, 53725451, 160404085, 887743382, 887412535, 599563283, 158846111, 304407930, 273887177, 512472504, 78332044, 458368586, 200488295, 553386508, 398887758, 649615646, 894511494, 634966241, 502956221, 199634033, 469473379, 757824856, 75366495, 494887108, 429121968, 700777190, 985559833, 301415120, 928660006, 433134559, 398273524, 26891825, 784307004, 189852533, 50750583, 900901923, 624224812, 484555893, 564768960, 771706641, 437451983, 985225331, 566360261, 307341121, 670451356, 284985312, 990015628, 828204230, 661441331, 66632799, 7755508, 982944344, 64069223, 363018232, 307422104, 427595023, 60770919, 134972891, 402385979, 319581056, 959013901, 226652642, 57314877, 950243057, 373253574, 602922217, 596575357, 476159673, 610797782, 982452176, 478061100, 839268397, 276867116, 25417229, 283684154, 610676812, 731939678, 756181340, 945805659, 189309769, 415818118, 741136666, 857245289, 914432340, 662777279, 876796325, 80042347, 598643374, 134839125, 182519018, 949342652, 566137016, 688903826, 933392835, 199825134, 237551174, 289465034, 806523840, 368923855, 707967036, 894924803, 971049697, 302265489, 24896700, 65676798, 439457610, 453453116, 431572519, 425342812, 809778667, 76615505, 873515498, 379444600, 353567645, 432585954, 465056139, 952842592, 366499998, 947427654, 990813032, 694211861, 599697645, 100933282, 82734938, 991789923, 762574905, 378372400, 77205932, 334056496, 479547192, 532143555, 615069851, 994459893, 621862802, 990203813, 697779690, 337015454, 433991623, 211434673, 768079662, 481054453, 598237166, 274218212, 720823758, 956583735, 322258295, 615681339, 521188229, 705063320, 498073547, 992936307, 624743927, 960547780, 378730542, 938652752, 40138370, 991442553, 897255640, 999356049, 188653952, 629623209, 752630626, 123751706, 930048295, 603429193, 794035067, 202748646, 309273785, 232734888, 413276958, 942449864, 967464098, 632554729, 745346734, 458873256, 68789980, 420958380, 140487510, 590197457, 322420940, 886222484, 826759555, 254662297, 515859415, 328288881, 907659165, 320267054, 511092434, 827564453, 536522956, 514634862, 752922159, 774325890, 183318731, 881474566, 221824213, 352625401, 724365083, 926903219, 252340438, 5038878, 623588493, 265511218, 393155736, 206582624, 504102998, 968918429, 236823761, 260443302, 219869748, 115105086, 986315997, 661191530, 44315925, 411768007, 275620945, 486823464, 522604244, 374322793, 419321836, 489660734, 414420571, 293725924, 611597082, 569515019, 568667371, 570575927, 49755225, 703153001, 537501921, 615594848, 817450633, 872823500, 713744893, 565711326, 854720385, 797299734, 342981166, 378737884, 70731133, 264220670, 922885526, 522864381, 542641719, 368683279, 873426952, 278618170, 635317201, 359727810, 965530862, 361736049, 152076769, 752189724, 257558641, 198399876, 443989382, 898677098, 662183951, 206353051, 551608190, 488046265, 401063296, 326422735, 911848181, 8512934, 337231013, 497564975, 402202018, 429845869, 387214288, 973760981, 871736847, 837643204, 635949359, 442136169, 223188068, 35977480, 241900443, 396777480, 943225074, 685364003, 90935623, 897658874, 421086712, 259060067, 24745977, 647599717, 195930540, 56064796, 909105334, 314616490, 236197429, 822153646, 645445454, 5737116, 380964465, 346209820, 944584204, 993200035, 810881480, 196940664, 904758327, 97487792, 208576028, 96283793, 106819763, 949288601, 188293557, 503245403, 80155781, 364220868, 848896027, 330166799, 267081564, 651942321, 280049755, 240944037, 961779556, 285574882, 122060499, 2200992, 288150183, 755360436, 381217227, 440845861, 943813013, 732477917, 454274448, 948156389, 63746735, 804414516, 842214896, 382445756, 665560422, 435064089, 872888650, 503224326, 492990485, 681698223, 952285918, 990073225, 492055867, 281261743, 952342782, 515705547, 297803613, 959204306, 145176963, 264415540, 592950728, 144280844, 919057863, 80663540, 273398667, 277815367, 974378865, 787975350, 153065714, 665338830, 427501918, 32650087, 287677307, 362340631, 359119614, 37193703, 796631170, 312741584, 270022624, 161511363, 103625293, 176323456, 173329407, 270075311, 137417903, 678831656, 818980728, 370738550, 445417382, 838668756, 477805261, 162561412, 271405785, 387792422, 934158121, 590730679, 199702694, 929089343, 373070956, 170326621, 252452698, 527483488, 484701796, 112036071, 415230515, 174257530, 678328299, 211267871, 252430389, 622078572, 12016776, 508583930, 340072840, 701980083, 777132831, 37801326, 98278174, 848968092, 985759487, 121261046, 747081420, 698894907, 503150948, 986929474, 502881902, 522200685, 563504686, 631998073, 253104702, 488131282, 284507766, 871699392, 872519654, 134235617, 249668840, 669114037, 593822402, 206400028, 896104909, 661685242, 610500278, 244108513, 789712724, 180153994, 174112743, 121525031, 307846214, 391653778, 819147733, 770647301, 454872637, 815625662, 733786159, 916776890, 937244647, 801832609, 861727093, 685283358, 822136836, 180154782, 549549099, 684694170, 582250326, 53904195, 226797096, 960132102, 89865630, 532138067, 567303333, 943787441, 272947518, 378748702, 784850190, 891708525, 90849580, 658223963, 22803091, 224504317, 403038626, 409741121, 816894526, 974475069, 726911485, 158057524, 123024625, 492944322, 981455827, 787847886, 293320905, 645903807, 297467547, 436392568, 683781247, 82306246, 701628586, 343724464, 307702157, 27887661, 731786412, 589209860, 691533249, 551658267, 898357440, 400089882, 750287758, 352396311, 180003532, 939510739, 221900799, 666272400, 213238215, 902258389, 203504750, 974271008, 534152410, 360050522, 398220633, 873143675, 328400231, 666539233, 202770755, 975089778, 971257909, 198661722, 659399331, 462685285, 747315603, 194751189, 326236476, 400739705, 847278668, 992669718, 812096028, 971907103, 793285276, 885147112, 393761002, 769688498, 743823773, 661741008, 762380437, 651548377, 293485193, 308709785, 968804857, 762774252, 873570249, 651307314, 468382717, 68150691, 666150219, 568221932, 22734347, 628005535, 711494244, 416102245, 663530035, 721813599, 525432087, 233826276, 354764948, 532184115, 14620187, 575662820, 844069685, 243282867, 99675189, 731906635, 170330228, 732090490, 245601163, 171419262, 23320293, 746146504, 46262715, 108428764, 704714401, 920244443, 200088920, 123879486, 794810919, 268723491, 797789559, 648564514, 571967570, 106844937, 334798426, 9229707, 90538, 702583297, 37359919, 779260533, 487256312, 602453577, 193115712, 981375760, 173445943, 34538780, 448802874, 816005921, 595057484, 430750035, 505879225, 521741501, 730787758, 787049311, 408139581, 966739093, 731563375, 862583073, 78869013, 301468357, 499834907, 142578214, 894902686, 336295148, 968577988, 501237669, 668268697, 482400207, 472904271, 807506831, 427694006, 769112334, 953468314, 225972776, 635619099, 920480227, 761828959, 539415976, 668315563, 651745707, 897765822, 275345269, 761841425, 860319481, 256936164, 780301057, 724320055, 895776271, 281797225, 328744278, 327495571, 922466165, 271512060, 131229126, 491433532, 563015525, 916576719, 275325809, 162316341, 960660705, 692457690, 806149590, 589451342, 198870146, 460959489, 431824705, 379606601, 762267957, 621119603, 404993395, 469067170, 990983882, 811660820, 894098326, 872895305, 799091345, 258110188, 717730299, 112598483, 316081731, 771639124, 630932112, 325715041, 309285080, 425977201, 854948513, 140317032, 411734440, 85906978, 326303459, 992403760, 839229301, 554950359, 651188816, 228375568, 116399576, 717423105, 949954687, 108934402, 606906950, 41381491, 490949136, 151428304, 415467106, 593168231, 442720686, 230200855, 961911808, 471817971, 269961732, 459760033, 225590457, 757859347, 865951663, 52282118, 648007755, 402290916, 262892239, 920867893, 225825540, 496286949, 278338402, 483914093, 250143281, 297454051, 413375030, 795355403, 88167127, 272026859, 48888500, 826564246, 914454505, 939222797, 575834165, 489923810, 966315555, 339615466, 629836255, 650198287, 83277874, 180471559, 628450452, 254912855, 267601439, 772980188, 743644222, 883799456, 293784921, 416472046, 651618222, 38569769, 721668954, 580368260, 870833050, 821390277, 390939109, 462448795, 808095948, 829441880, 356107738, 614123761, 396977200, 816318096, 894188739, 24147205, 138885402, 375455008, 656545811, 596844435, 747936246, 775013145, 698891947, 581031613, 909321607, 404398005, 643624381, 474024963, 486630703, 880425160, 660116033, 506870978, 631149979, 510850390, 510646979, 650015129, 703439552, 668338170, 807773351, 249408971, 575884731, 90707295, 637711791, 350021693, 956890569, 124491932, 467237508, 906696094, 262515644, 376092348, 383294494, 675706608, 643174196, 348291985, 32160069, 756868488, 880618377, 30989660, 484820409, 575653080, 517521063, 373959571, 219544703, 274643382, 571882865, 730017532, 152016834, 231601595, 692445985, 545353889, 591245206, 42174334, 53408420, 567515316, 763568682, 247499092, 770116901, 30969942, 955689643, 446967684, 672049802, 702551034, 437397848, 649610439, 717183487, 394812096, 166243140, 675900340, 765221582, 814951743, 531189964, 754141099, 866099864, 601263979, 272375044, 767479163, 992198539, 975642429, 971915849, 490532007, 364550574, 191255031, 772920417, 14146983, 623607607, 357723301, 13944798, 944928772, 381219909, 928262620, 352411538, 188022415, 98057660, 6079026, 640479777, 227294870, 106615858, 723674382, 72564203, 508522659, 879896254, 12679078, 316785567, 55054224, 346123748, 925270359, 182297013, 922250823, 222493852, 108270528, 954974251, 38992564, 958862928, 406874125, 756550913, 408444217, 222295950, 210378682, 720551570, 241121594, 232102460, 30750473, 290952467, 671053756, 32904423, 887731549, 728586222, 767031188, 811504732, 618731888, 364918051, 910316899, 253318464, 745434625, 793958967, 186246052, 268256609, 181749088, 852392282, 715193225, 297484294, 818862357, 487272397, 213009722, 73513547, 332852020, 914658569, 61275660, 616779954, 562996253, 55476037, 685156527, 268035988, 755882884, 231378536, 558203225, 488509943, 408900540, 696763805, 936977408, 433704516, 453609009, 205593902, 431826245, 139807145, 666935257, 370296724, 254695184, 317298490, 365924638, 206284881, 180854998, 579512, 963573556, 666121705, 915712432, 385806824, 328353416, 758066604, 500493150, 822171360, 940463207, 316110844, 726378743, 132859678, 329904441, 261045375, 211360945, 808741952, 274061648, 404035191, 223613103, 664682817, 440878245, 433367082, 750241701, 255113633, 550391527, 529170807, 301087903, 78274614, 389325727, 370503278, 417176593, 113447958, 392875825, 587264181, 775375972, 878309395, 960021598, 925936193, 14565166, 343518040, 681334833, 13023046, 862038949, 783695873, 545634814, 158723290, 208467903, 634493924, 227822989, 97419651, 509470317, 887525877, 583872861, 327478540, 184998083, 817094336, 487600260, 39282513, 891330229, 498138601, 130369662, 591505205, 369360588, 804491831, 933683579, 597427467, 778183711, 183825559, 56310114, 660043354, 544907908, 166400272, 82769446, 188178514, 432843893, 987860024, 727419929, 184851998, 933995505, 438097507, 577721033, 705563747, 884862677, 858697581, 840642271, 425647058, 819662851, 887711876, 455414381, 624173623, 300039850, 967652850, 466368688, 225894791, 295261896, 755924765, 870262394, 45583469, 158579667, 750822940, 485686602, 538423690, 254091668, 108183449, 193991359, 480442735, 742848118, 948048360, 93266924, 56296142, 768759750, 865724039, 210407463, 815783804, 748628688, 353116164, 72945504, 4285685, 453297721, 624773380, 838639159, 75039785, 140070622, 837441665, 767003964, 965066023, 506586283, 903683548, 909361264, 972036059, 356036352, 278636269, 704300103, 209642957, 167094428, 498973310, 427895124, 414741352, 912943390, 376394430, 121218616, 983283171, 790062574, 329039979, 444978404, 793982301, 954711327, 865727638, 185593211, 438208790, 977982808, 750235838, 594088502, 549764635, 805720307, 365236224, 834736207, 903007631, 321241047, 362709768, 132650759, 356135017, 983322542, 793903704, 738365866, 830085220, 510478384, 59663765, 473651501, 663545633, 210398918, 58103815, 277166470, 235226320, 210619219, 608183940, 393395407, 960968601, 507563878, 955048628, 518951887, 570637735, 32797132, 468615528, 768418446, 731058015, 662729194, 767310451, 425916112, 344463815, 203480123, 411681751, 920885868, 412005561, 276695684, 444743331, 448544378, 190227685, 276654928, 177733267, 345664621, 637989174, 214445052, 329738840, 102369112, 89418738, 714109930, 563275658, 534440542, 785778401, 781402228, 406344626, 346589225, 848115572, 300789313, 194429821, 292114674, 340653278, 870855326, 735550646, 690149573, 301311451, 663943574, 317056942, 868211833, 937776920, 282877972, 979892017, 783693798, 941221440, 644405138, 949861048, 116570084, 468979750, 911852730, 989479104, 434603036, 838580317, 38545527, 885466818, 64357640, 177041810, 682607349, 158587868, 755449688, 778003710, 523957517, 611752195, 45459410, 434073530, 8525342, 713984754, 561644721, 313697122, 851590836, 119315566, 60867577, 513843175, 114753437, 64718072, 141259203, 131276225, 189513482, 35566525, 919094645, 217253972, 837424280, 138891728, 789829048, 809676233, 826741722, 5415430, 926159616, 859206192, 304838107, 302809256, 599443365, 376722080, 752413005, 421436304, 635771317, 460155281, 998805088, 638414685, 482933566, 986598222, 921239460, 175002034, 353181073, 572410406, 761641235, 903621131, 648782396, 75422632, 813222878, 611691259, 69030449, 195345624, 545277798, 442726118, 341659867, 202833344, 612872068, 161790649, 269435019, 932957691, 622162089, 520691259, 619270703, 50186912, 176349527, 5507969, 824390992, 895333020, 868270137, 611551782, 848192108, 45693376, 775462686, 198425360, 269886094, 374459686, 453481277, 99574193, 119185107, 344592555, 905618124, 932457465, 632258615, 685419799, 437301813, 868334510, 734022898, 630071821, 486439358, 627817803, 179501867, 892190972, 782298960, 929045050, 196402336, 442174347, 409223044, 763188793, 273811337, 787432544, 384684664, 258538373, 609880682, 913150160, 330746543, 294212181, 136936762, 143980646, 495598918, 780163675, 689347860, 533104962, 550437339, 98027760, 405398629, 53892587, 595028626, 764450574, 758828197, 51582692, 11049734, 847504701, 898932168, 14931112, 946233638, 270382438, 915139361, 339086708, 525132540, 866239078, 773558962, 730326117, 36791468, 128816079, 16275579, 720724972, 207528133, 943736004, 810136993, 246516539, 541023688, 891982015, 893082576, 594685198, 742094250, 783638072, 138328338, 303467098, 522624825, 472373425, 984141478, 838445520, 943080052, 41966722, 840577488, 750394277, 362523308, 165040969, 295068273, 832520007, 993657332, 177252887, 875930559, 839047105, 92724851, 493120679, 147793052, 577930831, 201940605, 899700083, 68114558, 148501250, 831288650, 879020938, 949189198, 612789992, 34459493, 42400019, 960492569, 718855815, 206124216, 924771219, 728265172, 44405448, 173094871, 314341908, 83539021, 680347521, 998405373, 29656252, 227010409, 238911432, 499264852, 166500396, 663465505, 821608846, 732314168, 184788591, 201850623, 513073420, 899199696, 12741038, 14974318, 164006795, 969007968, 724429484, 945472085, 132794569, 669296064, 213110685, 800151606, 577479485, 675944128, 598025837, 428280698, 976996417, 489678766, 243580419, 3267793, 273851731, 736294153, 125088116, 855053248, 101044863, 291014571, 365668884, 573134369, 797468891, 254794677, 55479833, 339235441, 241982522, 429695994, 312811051, 699936312, 155177276, 135670921, 263671228, 825484133, 55869458, 677481368, 583657667, 549835291, 333562869, 610419454, 746281899, 591901092, 662872524, 732551054, 314706323, 827708943, 940671913, 418519269, 855324547, 403876839, 48789391, 640694664, 169783746, 744536667, 970898642, 207574486, 44243740, 614119955, 721421132, 28359073, 436321792, 54296331, 80641862, 75746858, 910647803, 32683771, 421139737, 108576953, 875671614, 421514569, 177664179, 153788153, 578502260, 265769902, 617511353, 272955242, 30550977, 154577280, 68762387, 879122068, 907662402, 610172880, 394743776, 723015145, 647104324, 425726131, 659022576, 402146941, 476122036, 793486176, 787355283, 143942670, 781439361, 504578416, 977158919, 505887287, 793804770, 408183416, 272398758, 367124031, 168162359, 294423742, 663106925, 888503194, 854418691, 282349786, 654729943, 126476830, 856161497, 747532583, 643282536, 771933325, 363307461, 712565377, 663706326, 415840568, 700733506, 619046346, 145014484, 413904406, 865730689, 997082292, 293995903, 171695802, 119567682, 53631704, 557381884, 287789772, 234346100, 67979867, 593955177, 643540851, 147687840, 845190504, 540920110, 99841672, 41063899, 849307825, 473310046, 965081163, 989878594, 972320298, 795481913, 9171592, 373669553, 116706552, 842158279, 675156968, 587625537, 285761746, 758453697, 448466792, 865463825, 169307807, 672539123, 473384972, 513971668, 661544508, 372862736, 622035310, 502572866, 574268698, 335989078, 459498448, 47293656, 353206825, 182783309, 211153272, 224969092, 147158214, 181580706, 831614887, 50861347, 318434926, 536888199, 402109744, 271824390, 724212806, 260913441, 435219944, 525368666, 958211269, 208478922, 389336034, 898103787, 157323884, 939613622, 326990607, 506886421, 677810533, 708343594, 591433019, 847753773, 280508053, 682297341, 193245991, 964986523, 578490249, 989307072, 894138796, 806257781, 766626422, 635535515, 175565295, 187654828, 646781964, 846305764, 374177172, 61825886, 806127160, 936824993, 297700730, 516633768, 793579603, 324710627, 289808008, 631369949, 720912, 825428304, 665310550, 378186749, 554587266, 432078876, 657628957, 286205153, 862124288, 110735660, 106583454, 395365138, 842614466, 574045854, 847052373, 503481943, 174028426, 534098697, 158745041, 831554600, 594961636, 852414826, 507995302, 629097842, 877247454, 35812143, 315200789, 491588932, 176128401, 267892426, 34047115, 795346873, 851458595, 40121937, 229267317, 656479649, 451435924, 813487800, 156959260, 167142066, 745370581, 35760314, 941025466, 229018982, 520705417, 896867127, 600503420, 941331292, 199815812, 458131382, 944596612, 835149973, 935393471, 371170832, 645569496, 302910040, 32203593, 428071323, 61459705, 834896715, 798369329, 177179222, 331800585, 490956587, 342203194, 236333240, 320025130, 879741124, 420029048, 37972341, 13864210, 892504093, 629914650, 633122878, 148335138, 513018668, 958464265, 3241433, 925342120, 616242598, 262752116, 811630024, 830644382, 393647765, 80915542, 614025686, 443642180, 502173461, 682063531, 292244866, 445279742, 701560214, 369577457, 348319691, 777094063, 115017110, 225164498, 2105715, 377662577, 523153704, 521105968, 8659253, 780923156, 6491607, 216487473, 359488843, 164177586, 944636339, 572093295, 296513896, 137622307, 61981935, 763783757, 458256034, 795211777, 858464680, 254371173, 628449105, 77519469, 679561204, 52097117, 925437316, 332378431, 436698012, 828731345, 627800899, 819275949, 951534280, 532531594, 759984209, 342472922, 83678029, 347902976, 765127371, 992299603, 556846239, 294615315, 507592023, 208134616, 978120206, 259574491, 906155125, 884836064, 716056665, 879795941, 34213048, 285704258, 369798597, 515755238, 353402360, 486324, 199268222, 812642274, 221091823, 319946201, 138395616, 441562869, 979661776, 554451769, 266690173, 566358966, 375400262, 268170695, 997290058, 681140771, 815975113, 173535397, 467838705, 783752162, 246753351, 347556061, 225194623, 217158428, 435685661, 546783274, 40626538, 982947407, 168480184, 641314933, 580832657, 972320183, 55055712, 603323357, 890903723, 147874117, 360991670, 637226269, 322447285, 40568591, 88953839, 669314140, 703541519, 580587546, 872274636, 649109826, 60864246, 666041438, 278534160, 424721456, 770549641, 77881490, 190805872, 993118748, 471849682, 735973993, 465102309, 88794146, 168797340, 738860321, 387843359, 697150590, 165613437, 241188641, 446842857, 308560560, 19423632, 567655968, 307970358, 404102906, 309359772, 645365048, 689993018, 846057608, 525646052, 765011941, 994683413, 881476229, 48293086, 394345637, 69222781, 723220118, 656635278, 575835797, 148308250, 5037646, 4788468, 118238931, 378597467, 782045221, 539036976, 10908868, 698345979, 742994961, 11781423, 215604539, 462206368, 890867361, 351853044, 716344850, 255863319, 322752821, 353208605, 306979334, 203381196, 106115645, 372170288, 673390613, 228948125, 138114215, 336576124, 511850394, 516405801, 750641904, 102655041, 559330006, 533589239, 826750957, 454070185, 635673568, 709913574, 24031330, 862242702, 688427877, 448151301, 699875319, 671609820, 11010890, 22235204, 812278813, 971521223, 422507129, 486510556, 846811265, 65880202, 908905660, 988117790, 388205759, 345595669, 960573119, 384365362, 816044698, 366230579, 757398790, 38675888, 80450119, 272712292, 273555097, 119379305, 686277541, 451603803, 42810816, 514184803, 492261461, 84405350, 125978684, 608863515, 602295859, 562758810, 328838539, 2201072, 804452055, 682096357, 99217615, 60246461, 541927806, 335144366, 113752000, 866951245, 344405697, 200033839, 414317740, 737376716, 450465464, 633032805, 490738831, 513563041, 830829064, 687557168, 268953091, 92033968, 626523849, 452387144, 666367591, 592391799, 157693657, 983202210, 174827730, 403080988, 635183666, 217314266, 923371208, 232343800, 622737908, 639691484, 445221282, 666805062, 200198705, 751253689, 987347686, 791728078, 353090673, 265416268, 392255681, 590821556, 984401349, 156875653, 954296889, 182593934, 908270346, 868001388, 883443086, 961182258, 760815433, 856897745, 391490314, 266520944, 476140721, 86916152, 453643220, 756636701, 635483967, 932968992, 53898116, 215739285, 230305421, 218601863, 929562824, 142616288, 814767807, 323538058, 263690139, 875300568, 377465264, 947004085, 66409773, 448140159, 226209725, 677175900, 3858226, 30049052, 669183355, 90795143, 412414234, 852433661, 692422582, 78449038, 977947288, 372523072, 770666522, 134338545, 920132680, 873798938, 376183803, 386070683, 48048285, 122703533, 710588630, 939900087, 790951469, 986928179, 480957313, 43097937, 870271087, 730315099, 207767157, 36004229, 811021635, 592007232, 470258639, 427496100, 846995335, 40568000, 647746620, 343023780, 608530289, 611242371, 743112231, 546230740, 958885134, 13720002, 526096669, 42745409, 984204448, 247884178, 919352803, 28119761, 655056495, 53320557, 610170322, 411924375, 861936771, 336941898, 587786841, 273830673, 477992295, 369664324, 555107368, 46178818, 323140808, 578400645, 874928877, 558326133, 645336179, 497382691, 576581147, 208886461, 737941647, 203691155, 782093417, 863549732, 720140412, 87466011, 98549673, 855037944, 920643899, 378630401, 834677248, 856844669, 487696859, 404520519, 55195617, 394378971, 324401534, 430265467, 30478525, 379284966, 803645803, 254435110, 342920422, 605975540, 598674784, 617588218, 172109997, 872798837, 986091171, 215751267, 525509090, 468321751, 460866028, 746509058, 589645455, 281920516, 200825574, 684524647, 474254393, 2454401, 711370987, 794251544, 483240024, 796666208, 160455419, 181966242, 173970934, 289616239, 88438286, 863694427, 971981913, 901994061, 2365495, 625738503, 484851301, 896843225, 918667571, 676453438, 367321989, 343916268, 420028402, 111912525, 714356351, 168623518, 9102486, 556388909, 118164720, 551158520, 989704965, 569249794, 304567014, 246622173, 37436134, 775312700, 143487528, 764355171, 775679603, 93825652, 83970893, 50238427, 447619829, 729653587, 114093114, 200356469, 984567263, 74468221, 133245576, 580380253, 614160090, 248122675, 751061263, 408312125, 88969049, 916534590, 190444640, 379945833, 489299676, 645062807, 270392398, 310558934, 700122739, 47477888, 302777451, 714026565, 119201351, 989271059, 66719807, 679613148, 673561301, 499311127, 809481398, 785464983, 937334273, 817966181, 332547965, 727425144, 463433179, 670069796, 721440090, 777038708, 885821600, 383905493, 526346041, 660617034, 924436849, 575528275, 110478950, 1327988, 646479836, 117126501, 741983352, 606355140, 253625191, 357672145, 989621719, 366787776, 763369139, 604354334, 588349146, 901557655, 319814969, 776245767, 474950303, 197981607, 718780967, 387000822, 615231193, 703509897, 928007234, 756390861, 949373419, 631581608, 524730229, 429623622, 185868476, 89667701, 186568647, 550693280, 766908981, 880482779, 686410631, 325744033, 124978476, 952245263, 985136625, 56843709, 332716873, 273550777, 30698376, 559878827, 189486096, 633907875, 671228422, 81108195, 839771407, 509204212, 662034345, 162974032, 339664421, 746813948, 219117379, 89667819, 755194435, 335987384, 138948079, 522884330, 874785111, 399505456, 965004041, 402187898, 123991034, 637566790, 711734371, 872657003, 430873561, 321624484, 387219995, 91150319, 104766231, 190715326, 541706544, 683262626, 626977081, 571687257, 140199799, 223178803, 114763048, 659063526, 784612798, 709343936, 555561235, 263319046, 724876584, 46487088, 135527117, 969466297, 558594427, 870979803, 117985280, 837988782, 108777583, 352090848, 949991063, 466112371, 705671922, 783052140, 271130866, 541316467, 303658212, 350572986, 412139584, 716806668, 302720667, 201161669, 33138217, 747257241, 701588426, 757124021, 89362956, 736668872, 384088970, 587595459, 833833656, 128171345, 780880112, 745492951, 168484402, 219389191, 685072736, 50591793, 29240025, 796118693, 596318871, 819142860, 786645027, 359331272, 92816856, 440805010, 481368363, 339858612, 758281313, 944189429, 34458862, 275186868, 22666845, 201034887, 874701844, 566417319, 991920267, 213158911, 123067175, 939470602, 899998589, 389570164, 119928206, 565339942, 307071836, 789832368, 455825495, 174076812, 650207259, 541343112, 23608288, 22015815, 305691700, 141798971, 251329838, 320745885, 604277225, 773899580, 524266111, 296039130, 501563644, 591723653, 299817648, 624558913, 834626847, 974524458, 700014963, 913959125, 316144005, 656697876, 409622320, 301838392, 395528542, 326643017, 492773220, 81098630, 773131788, 889698242, 26433885, 711195618, 962162401, 944525954, 113367713, 526956790, 325827580, 725352585, 133935135, 489265177, 381716119, 622100375, 834404957, 613529280, 822780164, 966961536, 681387195, 643006310, 5947390, 329872334, 698866640, 93061019, 671733122, 567255883, 697748453, 797677456, 685954554, 468466014, 303910280, 998173992, 212364580, 707053325, 123191653, 249316182, 450327050, 441315557, 964929561, 234535142, 148281557, 891724691, 967471238, 121498624, 366196623, 749528148, 308612357, 817951291, 912762858, 388846656, 267062020, 576679710, 879274669, 25658176, 404028250, 109351505, 767514559, 110194239, 75062453, 665699970, 5996510, 231704477, 267837144, 224573057, 507686386, 623549823, 950210993, 800563988, 712727543, 950918322, 233586651, 983431606, 489135329, 555650526, 497942501, 298804811, 909267551, 782760813, 229250212, 910376369, 151230959, 864415390, 34381698, 425511307, 267255896, 797301771, 946128025, 356511327, 670540358, 722736585, 286640193, 788257938, 517449350, 354662555, 91993026, 378028526, 332183507, 383574105, 558783060, 26240986, 449910851, 156081291, 96676249, 992594090, 231280346, 870828031, 897205419, 547002455, 674497866, 579894119, 727754814, 361106494, 728526308, 877168226, 323063304, 603614607, 99799811, 674994838, 996467015, 491812825, 753887903, 253694876, 504391947, 986314000, 682392462, 109134330, 60886837, 394092890, 889565338, 257413108, 828804096, 769289651, 49902305, 417229126, 154071375, 900914943, 734960562, 732454077, 298097944, 634355042, 906720366, 362475914, 310644648, 212052168, 307467004, 514867665, 268945480, 995563918, 88182840, 875033226, 55803072, 816155572, 874499445, 76795418, 748877649, 733692035, 805013182, 440683497, 296358115, 407049687, 471892571, 51326522, 101238929, 519786580, 606410653, 932632327, 49943022, 186815975, 809891775, 56459265, 76496094, 238721991, 98028070, 852963093, 69278337, 529330707, 362462511, 434709950, 342488506, 58656739, 871062385, 952958211, 933004255, 493366183, 544782926, 61561730, 723487874, 466782646, 971289522, 219101735, 346381023, 72728496, 186481385, 606679546, 800395249, 559076660, 698103475, 777638560, 867664055, 205811312, 600638739, 429681770, 223629736, 336013225, 386071678, 693073714, 528524737, 859448062, 856079269, 740440375, 837223867, 992724258, 984899806, 423515779, 115418069, 98939575, 692892307, 67529626, 19337767, 471516619, 704284999, 304530898, 759191055, 922851394, 827489843, 351021820, 280450193, 127053797, 818098272, 97147866, 326746394, 32799309, 803062894, 712374870, 588264156, 846907223, 586913505, 716245483, 336997085, 916634191, 3956649, 81894004, 815955034, 527824032, 100523583, 434268694, 796076826, 986884705, 668705235, 295194363, 157373874, 552596477, 503261911, 534230841, 503786387, 867421775, 381795219, 167096385, 144952453, 154915871, 947119135, 289873358, 501696702, 949508331, 572051144, 839495435, 349700508, 259176319, 764368731, 776374117, 692425408, 992396221, 951573349, 275490854, 510969340, 516862028, 708076480, 879692745, 369253145, 776809676, 130737349, 696753671, 162572772, 794744832, 967759599, 306091705, 413856626, 439831927, 621070841, 579050274, 643134747, 730102492, 188793059, 368345850, 242265422, 497855062, 279724486, 395093998, 831944210, 943542399, 76138271, 86753314, 105397254, 938452441, 163769942, 97531296, 521217615, 421347132, 549017962, 894572524, 665896688, 908611179, 481343132, 37546991, 355052915, 807192291, 780435450, 738879004, 22074543, 756931349, 800951398, 61803839, 7273332, 831342232, 81460857, 632526241, 146578982, 965767356, 108572432, 353703754, 682572981, 883359241, 692135954, 342525151, 59829847, 640259686, 850704376, 177728444, 60345519, 426413263, 882533500, 433733697, 419531586, 523680803, 673845554, 75422383, 421260624, 276524488, 751482218, 376470529, 786926438, 972766685, 319715853, 454885398, 57414055, 806979375, 330939347, 489573147, 705221793, 14510357, 618004746, 19409675, 546989266, 386388689, 171512234, 639673110, 985446329, 646948876, 826542262, 475238949, 288596651, 163264916, 88470470, 672709532, 451411927, 808798462, 23268940, 435629194, 493211393, 263368167, 408735337, 282609502, 36148119, 210502268, 55421549, 738406654, 705736050, 587173527, 8899013, 45423933, 258105065, 372711532, 198087266, 889236583, 260226446, 648684403, 805360194, 151378594, 215849335, 723204259, 161458176, 326350488, 892028834, 869677341, 786276529, 925638532, 104337362, 797713680, 327903084, 224394477, 651677761, 735699532, 534385896, 846360483, 78405398, 806469002, 638102835, 975982448, 325872701, 396580135, 875205225, 888288682, 168150653, 71869751, 463335726, 819586146, 809295286, 16338333, 13582663, 427037118, 598431826, 400259493, 817911587, 102198952, 245482940, 587286306, 279473699, 710537803, 858629111, 650622197, 814409545, 376659445, 780582727, 49217266, 152335888, 6146950, 176011807, 485394732, 177270605, 982000924, 331919108, 689558040, 180069420, 465289065, 522252735, 618336640, 324190398, 419611397, 960559108, 892600206, 352343813, 908547308, 80020252, 448749243, 820657447, 142217366, 575273717, 925367819, 200704433, 140235755, 451865750, 970205395, 593356417, 289352238, 571488166, 575039691, 544219289, 324691101, 395242478, 249884856, 447569004, 976933117, 373650005, 414339032, 604912486, 964642019, 64281210, 263238106, 618151043, 393237242, 915258886, 252740706, 536871108, 141962463, 250240888, 649379994, 131999369, 267085110, 849455986, 472457612, 71374892, 562146955, 14765012, 169402560, 509187839, 887383404, 671368546, 567459656, 934941834, 545775565, 217761811, 261473062, 305221580, 296213076, 996001769, 38944682, 790360383, 134764198, 613094737, 527117388, 592943423, 601484797, 610592923, 319329009, 350944082, 83327247, 744045936, 71983473, 392690431, 822600477, 728820317, 504633969, 46270650, 891425408, 465025096, 633427007, 161519144, 883683761, 185678867, 138428721, 331612292, 166069156, 776376909, 456605073, 375152180, 804734737, 719844460, 315940542, 416977925, 646593836, 880272863, 25668895, 474669109, 193069252, 968183365, 231770070, 350024408, 650816288, 807107024, 973399830, 778128543, 266342985, 704356923, 750359021, 438700676, 14061691, 527135908, 556911605, 74259657, 962664102, 472513689, 992548496, 61871655, 682083948, 567332005, 448842980, 528709194, 450175306, 316996975, 920155862, 87287170, 549826177, 566304559, 239644891, 724935469, 201639071, 942995811, 502457859, 803223101, 844350848, 82491887, 845356887, 861300810, 566859767, 478885222, 596772510, 750894030, 576666288, 682533449, 234495102, 710289639, 617860234, 667485377, 813108027, 538611187, 970702944, 757667250, 871670267, 141506533, 660568113, 914076655, 380358375, 203164688, 967956636, 185260835, 631414146, 331057853, 894403395, 827319889, 325762804, 579330941, 287091744, 883710753, 643453232, 314430198, 488125028, 804323045, 139032782, 235427734, 879396052, 940853768, 819416782, 347444277, 189405713, 903636739, 247410023, 935604528, 427418620, 701308334, 399566759, 249805052, 123913784, 745508774, 125576226, 552441787, 911211663, 157663382, 221507507, 17306840, 107809372, 576891363, 569462240, 574281159, 978982033, 25698500, 461688359, 583300614, 757917540, 848631771, 778103495, 639817882, 276193148, 933934275, 359165617, 718034689, 682724846, 178947921, 41601118, 931912179, 131030142, 202223801, 22021789, 117631081, 635985603, 194433979, 647567047, 685361299, 849287968, 754278437, 151909531, 690260749, 901650550, 98368760, 45462398, 765839441, 998099095, 213801555, 367440558, 227560030, 90370939, 493350564, 304593533, 966044912, 810684981, 718965679, 444709063, 924698598, 385149123, 947152624, 648503499, 450030393, 971711494, 174831385, 427687758, 301167891, 168580617, 927972243, 390196185, 550460466, 509073433, 336713512, 895781549, 915534617, 179526815, 548424188, 171397276, 409271205, 353658503, 793262078, 699062055, 110046822, 309506802, 832243990, 819509690, 797173776, 858658194, 624601446, 850066104, 749793996, 858530470, 302941844, 370806508, 170170156, 370841653, 404451130, 884077351, 869421837, 997305865, 131899462, 815321991, 239433423, 717933256, 65150297, 142911664, 452572291, 253291525, 928255604, 226896916, 991461110, 734767069, 789477422, 602740253, 790564219, 208900935, 904087155, 398566359, 895378282, 321601609, 250125453, 390596557, 561153529, 236380832, 105959030, 478118215, 250157823, 776960070, 8241845, 141988013, 256590281, 573410498, 516573427, 633154391, 446876662, 963022304, 701488085, 310425028, 24262214, 451719951, 511863450, 543699356, 33344460, 65570009, 782861777, 258096370, 458159365, 988517377, 292372573, 508002669, 73147517, 427750281, 187056021, 763084229, 703932398, 226084539, 80987493, 785749569, 106069116, 139217775, 281867579, 702326251, 40948492, 786995501, 555079373, 867929960, 356655432, 405261607, 18771956, 1266318, 332065958, 709996763, 410476156, 52698741, 650036758, 584197035, 979047506, 850552772, 123633438, 790604912, 503107093, 733780009, 445601307, 570969366, 901774438, 691626415, 572991474, 356282871, 380808697, 524566428, 767942873, 876564874, 347358340, 868334311, 141804804, 165750250, 678340929, 266158175, 361245772, 174673861, 78104727, 940833958, 271202712, 879552011, 142562794, 814510963, 903203569, 83122307, 453286141, 73486828, 21751959, 491443569, 864998953, 403135606, 907253075, 654974336, 923563012, 215453993, 180004452, 561090376, 532580877, 502656823, 785629821, 253759280, 29004968, 77727622, 819345409, 98909363, 525435029, 763697260, 918892449, 346831140, 86619898, 179755716, 573316431, 106641555, 556811476, 445879356, 458104873, 743104750, 872757823, 352425513, 98165253, 918875465, 955394401, 57920956, 948959513, 959851979, 387461207, 330492581, 747516582, 844385144, 673114062, 266034479, 974697714, 528515574, 944178796, 688958248, 432097144, 983789267, 937568598, 523565567, 636271746, 207380918, 448531364, 446790779, 431534782, 998832248, 124045714, 144043426, 164021881, 790229551, 657545202, 946717345, 860148042, 999907869, 731518338, 303572889, 163225654, 3148513, 344138351, 592608585, 546459557, 886674323, 629653779, 7319080, 240498623, 347132317, 965564130, 650686896, 514991084, 35742730, 831282726, 260191862, 807028411, 631491606, 146306969, 262094150, 888923639, 566715475, 537387070, 85720525, 957637206, 720847014, 256495112, 367865817, 14756455, 739251810, 422040953, 500476923, 280178064, 36115497, 540562899, 278665178, 240710738, 424356516, 781840525, 855958149, 680416210, 197785360, 108379592, 207378350, 611222831, 904074741, 553989071, 41278691, 655480980, 290382521, 652218108, 145946026, 434957332, 110179097, 665574639, 682030168, 580609313, 674176594, 198241420, 571046141, 361864792, 171192784, 815001796, 242576555, 613416030, 414240667, 961931428, 721521510, 843893066, 995618777, 378273581, 487484424, 580857509, 976500189, 405427680, 901526059, 287809761, 878071914, 4104899, 537929649, 147449974, 736617954, 547324984, 394958569, 416716218, 52927929, 313940211, 412201077, 961702614, 117975968, 934804600, 867512450, 413839655, 293410853, 896062251, 410069876, 122261524, 489996603, 278197517, 479343077, 586647781, 286891412, 498023362, 487000580, 842101567, 790614081, 546453809, 847520871, 432186655, 441513495, 786143434, 777834625, 404330413, 300643842, 677193064, 472956670, 606706822, 908606400, 419736913, 723273768, 466052346, 899925361, 264199661, 56374548, 580696892, 839312203, 146739708, 418129592, 484981680, 583887021, 734735907, 763506565, 170299028, 319448353, 105328570, 229085688, 463537, 711516273, 747904004, 993438605, 316296856, 99892722, 47004575, 788655969, 511170430, 332297052, 516242390, 756199560, 584693883, 106401508, 589083084, 948115755, 128593440, 255499585, 672264218, 759820076, 73655062, 211521203, 813411778, 224133645, 277034684, 950877962, 63013075, 726222989, 146747940, 766519044, 447875948, 406316911, 672828388, 20474580, 659644100, 991423180, 48997044, 407234781, 852250448, 865666002, 279265206, 870218241, 840482204, 109685647, 403002817, 974406390, 853197236, 508109850, 111214392, 311551508, 921902601, 905942826, 876924984, 800376839, 413962135, 692532007, 385993539, 898723758, 715115310, 274731462, 271178544, 490401352, 517793272, 701859759, 952505171, 571544923, 626176074, 879782470, 228592161, 576944926, 666380939, 886652092, 978169939, 823496636, 810147421, 711101665, 865927152, 846297822, 251780638, 779535021, 528249933, 328923156, 679553064, 143153997, 953111001, 209957093, 56600497, 934565782, 79705510, 901416335, 173812281, 905992530, 765854831, 272709025, 657698118, 946445002, 404773340, 951802964, 997387121, 798462677, 741820175, 165245744, 191498354, 149548337, 823263848, 819870535, 343803627, 936968241, 114523060, 94457758, 824298551, 149673264, 857110679, 299066969, 73312014, 390429862, 445092405, 788785689, 422205628, 194766210, 993021722, 221532291, 66611483, 45730410, 157067211, 939844835, 778197226, 809026134, 88612539, 749223627, 495687175, 435606559, 293237190, 404521984, 276399500, 729490876, 221164970, 456536245, 500639287, 184976930, 67436525, 239481963, 126400046, 797252193, 979534625, 722992505, 913217454, 786394997, 155216322, 527765707, 845231622, 130678211, 851862834, 851975550, 886525803, 684541394, 328948160, 766390158, 195662604, 728870039, 832996370, 447121147, 9083543, 569854981, 335830148, 177019183, 645182690, 890086940, 237428591, 540486432, 460213460, 389271582, 493507968, 150346648, 467951647, 399249554, 278095193, 91846439, 241141613, 495920543, 359975439, 943294988, 318537401, 46275074, 121632684, 243706184, 608593958, 95755434, 687020841, 357006486, 466407236, 840282142, 767342126, 589306988, 818569892, 192026828, 625726256, 35166535, 497549604, 246688709, 522099507, 291923564, 656703655, 26124438, 155696416, 722791221, 314298078, 929831681, 73553410, 749232982, 850010034, 401905256, 399443028, 641193740, 32906350, 627213239, 311950005, 214306853, 845385741, 273738910, 734657113, 397062236, 900256339, 127026843, 551390863, 475453853, 303120416, 67805162, 421660191, 678382121, 291993171, 999617966, 620184233, 349314025, 860430620, 26501853, 213632230, 517177801, 29946289, 726165149, 167598969, 358385190, 315964384, 326984593, 28049571, 728224574, 324634222, 670560343, 244105078, 147728544, 383422289, 378722309, 75055767, 890924351, 202796333, 350598517, 409238539, 832904032, 405941288, 972706367, 963139753, 718358416, 926673490, 598565161, 617302017, 633006046, 592773607, 323301537, 347647807, 104181155, 678783893, 278857061, 422790593, 394360642, 744655748, 876875466, 716753405, 86978338, 164493890, 79959613, 265806877, 638634194, 473770425, 551744187, 646146528, 247337136, 868491458, 408356141, 929240875, 586717675, 797102638, 720857309, 492101167, 348337316, 470127919, 28330627, 403521363, 33941785, 243482984, 525698851, 672888553, 553110452, 398364054, 540245812, 301174650, 888459954, 524033711, 339043406, 115169874, 785698695, 926582424, 586360708, 191301568, 355083065, 638393534, 840652138, 972464206, 709188517, 146272110, 509858230, 159278280, 591015073, 793071610, 848309199, 888907572, 805787272, 949608324, 772374986, 422092293, 526332536, 439163465, 44623826, 476717381, 422430773, 671498734, 340164062, 540773256, 565616496, 718378809, 201553161, 424304252, 568118625, 279243578, 962887443, 761171443, 514401246, 967777303, 473853500, 486412361, 924045427, 654458113, 984541295, 219768060, 644148078, 644683129, 616359085, 202462037, 961967892, 960000142, 555277131, 115072555, 990106915, 968306745, 572341280, 126861896, 350828172, 124569250, 100526202, 891722503, 189070675, 329756627, 163540806, 670945019, 964027611, 642654789, 589510289, 448658223, 771879926, 700290450, 665463700, 503403945, 675036880, 70130010, 860870690, 393170694, 418751284, 180007537, 252085910, 851695092, 358844178, 350543724, 298309012, 874346274, 470363699, 74323997, 653898605, 234444575, 173885450, 353360115, 122497976, 432852055, 728492859, 301376796, 38142860, 80340471, 124993610, 731691115, 434375653, 229111406, 387720083, 382586298, 324810098, 897270892, 379796918, 322330830, 394632701, 370969958, 531996642, 730433434, 850526805, 643181039, 204369503, 654250776, 805069511, 432341702, 740268666, 556274607, 565413978, 211988687, 223623087, 838289311, 277544989, 490050647, 602455889, 916661191, 318572078, 177651046, 799482649, 374780794, 961908674, 169751639, 176663981, 602543463, 334636808, 483178979, 292469789, 451883294, 921375923, 259518061, 708672545, 515375301, 609396199, 670875476, 947875832, 237775527, 242713192, 803267701, 346449817, 773413643, 213743777, 505572163, 936365770, 962526159, 728982983, 692311147, 168300552, 989506432, 725182570, 737632583, 642956614, 275995186, 258600807, 687762833, 99398685, 749526945, 305016501, 134804740, 12278621, 829700647, 799420275, 557078231, 221071857, 214511925, 38445134, 362773709, 110872287, 612262328, 221792982, 621857370, 787700913, 496084775, 786505058, 422581799, 753116628, 464290063, 711280030, 991288405, 482560438, 420236519, 361077581, 954565485, 381173722, 205661284, 151250788, 466037518, 438554700, 894735436, 403980436, 232978285, 81879652, 387932539, 796265487, 920676939, 48570150, 765349827, 794268471, 952166144, 289020221, 499861621, 546233685, 590336244, 666365723, 76297503, 914489631, 616161727, 366837008, 714776502, 463591357, 615331735, 908905625, 707699995, 222801906, 214820073, 315329117, 176144190, 618910283, 938547315, 272412603, 348275974, 819552934, 944029320, 481310268, 162514960, 774168272, 556005027, 946282520, 59558201, 456773199, 744271554, 483660250, 213849626, 127284501, 591179008, 446071415, 973715811, 923228806, 860405886, 707157464, 331962900, 504339912, 2244148, 295278670, 498720285, 537916802, 610997509, 989130661, 766415406, 626298752, 293722307, 577663225, 723170775, 473458340, 629388590, 281879872, 664007083, 615212969, 66508270, 71511185, 539074002, 350459701, 653739026, 262603339, 911533732, 307868704, 575328932, 692430474, 562230316, 413390630, 927696819, 820026596, 631641181, 432966876, 535323786, 826253975, 735585726, 949293244, 582503951, 112879936, 995760499, 589229521, 635504259, 97268366, 942962607, 214110442, 242790611, 29614189, 916489573, 154320735, 585932324, 664729214, 373364030, 557219729, 184344850, 208160523, 728920269, 149273675, 469430796, 807148238, 126627486, 140583761, 535891477, 38736802, 661857957, 276893284, 776306728, 986414592, 451423322, 736984499, 303134246, 532147794, 97190001, 598632185, 895605687, 721045820, 575594882, 418077829, 714677477, 791387584, 863972901, 944051804, 44479510, 634705379, 884451249, 25993590, 372005948, 146492038, 904558951, 901104132, 880831086, 372161670, 894740584, 740650866, 122429863, 514709525, 688989327, 927880137, 654009562, 742476070, 152855343, 756915483, 454675242, 34573705, 29331720, 506794706, 292264495, 887066999, 995230948, 83432624, 275692135, 140351503, 802957717, 105206751, 337262792, 459093304, 666670758, 814111694, 809820226, 849797411, 533558525, 962900851, 963130803, 337275259, 394718583, 359609631, 796133681, 946565676, 150373646, 195472344, 700442418, 465260286, 613392524, 781210461, 274390486, 625388813, 250310652, 27896152, 360803068, 806920353, 174035208, 829101723, 796706457, 858506518, 324915972, 630862414, 933046671, 266383502, 144320723, 646886272, 774596727, 178005173, 399263127, 841960197, 637649111, 847036184, 885099518, 668623184, 709532911, 439873150, 698917723, 728859836, 698225450, 733128621, 155231415, 919803133, 484493388, 795421893, 251190735, 690189237, 461736274, 594847239, 837816677, 848176093, 375723044, 288769600, 740964422, 721940432, 6981188, 940206629, 967359229, 477984904, 584555403, 842811958, 852008203, 676064472, 781166989, 396034961, 729321491, 444245487, 846292329, 856906105, 163382338, 592370071, 463260247, 7520812, 481959432, 814159285, 672900090, 899174158, 859154782, 985114707, 251509821, 685593189, 882685359, 729819713, 30565922, 108591260, 850381864, 994191562, 340840401, 686576841, 954942062, 523134283, 742452247, 837408875, 135484511, 13184907, 682816185, 18074386, 816677855, 715525086, 43502349, 942125837, 796074442, 50005077, 636753301, 332365890, 521543568, 1079253, 307353398, 255932621, 548000148, 869646847, 329691324, 923754082, 435536223, 372436282, 445466538, 778347863, 859668801, 968396504, 444680678, 480862637, 197335363, 796254330, 683052706, 491026595, 192745346, 942370300, 432024742, 998046028, 356910191, 396438381, 207521288, 201307126, 613138015, 873258605, 649907002, 614949681, 154941414, 426103306, 815967869, 845357042, 934204543, 859186394, 372983328, 12383192, 733849299, 76849607, 606910500, 136705827, 221483319, 441633569, 408549905, 452527324, 139985607, 760378371, 609916815, 441583217, 850636952, 715010590, 162054434, 502277934, 279190761, 911329071, 675254955, 995001776, 271197041, 399478374, 993428985, 304165485, 609336051, 617935979, 489067346, 401061737, 730051818, 533420231, 500149105, 29062482, 716398389, 420148471, 627884416, 727850665, 451827931, 809255982, 732882740, 395843765, 209466315, 640835723, 613578011, 675143875, 23748278, 569704289, 675935521, 804280927, 78639965, 788521463, 716710590, 898980301, 448314902, 625908116, 307313659, 172376630, 726007746, 754431826, 976667854, 831554187, 554830681, 698594283, 10890244, 979063777, 998491579, 260549574, 606090684, 989612901, 743811316, 694200023, 251497694, 987539438, 224085891, 741078439, 974298020, 282619037, 419922063, 644153398, 321861133, 973377168, 106876005, 491499803, 432262063, 182795504, 702498791, 297291282, 368780823, 295963668, 659981215, 692064129, 142779940, 91615704, 783750993, 584742838, 411090931, 530870189, 126196134, 467814927, 278447714, 484145809, 811438912, 225872240, 87120235, 122255315, 442918856, 288275404, 319038526, 112616337, 287621927, 85463993, 684216966, 803214649, 658175490, 703085356, 107573155, 954067306, 367434910, 656469370, 202864388, 296795405, 252461871, 897036957, 69820241, 135221405, 577529982, 300949902, 30829412, 388910673, 374252406, 804924205, 784571157, 425503553, 664123245, 936206222, 619543034, 474193180, 288449519, 547416764, 338231637, 305016966, 380947000, 466500368, 895470489, 802954986, 639455417, 896883157, 609987147, 763721092, 43763838, 820836722, 739912262, 895606567, 476125338, 789084690, 667038309, 522016307, 286511669, 482722382, 418316062, 463782402, 318846463, 320575411, 876606332, 251843166, 885579088, 946431979, 695920540, 667211457, 933981058, 585373885, 992326452, 567654036, 505340626, 388303530, 179257800, 912615200, 918926984, 802480074, 388347115, 803399175, 960217631, 286681722, 752102465, 783093448, 945288930, 939478392, 63720131, 785849393, 290056896, 941799431, 391625231, 42088699, 594978519, 154278612, 280366301, 451482354, 204848965, 942648197, 126787947, 276003891, 92148546, 259565554, 858428132, 917075865, 950618838, 151548276, 303237523, 613378318, 615712291, 411806278, 20828129, 843915456, 833155502, 625340506, 379139408, 16883291, 697158274, 559917791, 605658383, 29134315, 118017653, 865022530, 423580673, 617144661, 752011854, 883704010, 130961649, 997736812, 427869029, 135548412, 440270917, 810216442, 855198607, 186525194, 423536758, 67459355, 553669335, 706338484, 790871522, 954937664, 756955058, 134911059, 384820712, 358549497, 577134525, 831533140, 695605362, 325452327, 956388602, 441753345, 780156122, 919049163, 180207484, 772859959, 660953392, 714386348, 580695358, 207477997, 957554162, 24524706, 667085869, 687971662, 263888236, 465618178, 432572662, 557448416, 850127697, 345956593, 323855963, 15968681, 968958735, 968917808, 659202145, 261887758, 551222252, 246038563, 733764864, 265202539, 768935130, 117948382, 249495341, 16949372, 288610159, 718555393, 825782132, 73144702, 636731988, 808429955, 73699701, 395013885, 829700865, 232502888, 596986583, 850490742, 497877682, 357300921, 632852276, 239471768, 915995988, 43276293, 905894795, 503904929, 622265682, 159078466, 613608464, 601376720, 983313913, 893454722, 128110523, 406399160, 582401660, 983728492, 493411968, 938690364, 74850082, 568491137, 496269719, 948578465, 275639240, 890231855, 24500468, 554075686, 985133915, 337507980, 351627874, 972398129, 647316227, 287034889, 736395535, 855652265, 912602844, 743963443, 800085547, 993192507, 912391598, 85826685, 936733585, 986033367, 473951732, 454974620, 368920938, 802442926, 610455180, 359801182, 767183711, 654258962, 128926570, 962502127, 417224947, 194579391, 114806925, 27831253, 921320845, 566898079, 505290464, 472506861, 381023875, 458720706, 214426576, 673430724, 473737442, 234753880, 928485621, 709147525, 965672610, 695405812, 194654102, 142439026, 352835881, 641170429, 244470005, 174740643, 185103124, 635251831, 267994855, 868914248, 384627107, 374852557, 543014792, 152823084, 15174824, 190685921, 696860566, 454795680, 599678847, 7872287, 83651908, 597640641, 53753239, 841064750, 308139148, 566142675, 295013913, 266756316, 225835045, 933038890, 621548638, 449601649, 723910895, 604329173, 599638803, 460589898, 618462210, 104523894, 54078880, 445920445, 873876609, 927123562, 668704558, 476875971, 960690342, 689364752, 654648845, 631814673, 488518060, 903605543, 825952269, 952409718, 319522915, 798588860, 742839200, 423634451, 183285256, 145927600, 622550684, 540560161, 45523991, 766703090, 359002810, 179499291, 273024777, 414913537, 895547116, 708831649, 775861044, 209738127, 328456339, 271318186, 624501180, 422894541, 711018727, 389269315, 841665597, 459997984, 35873816, 956607801, 270131034, 982227018, 518784655, 797395422, 36277354, 210092539, 398839563, 856594559, 567878236, 538603663, 420484270, 85014884, 337212092, 267439249, 150016964, 336626538, 139904478, 506787032, 823899803, 567541126, 694897948, 801118477, 769354997, 867510212, 512975751, 494536789, 608647304, 176442548, 292542607, 810302000, 703837667, 986238911, 694369280, 708067695, 127881530, 163799599, 357260642, 570472611, 805745246, 322965324, 549201194, 746201847, 896532537, 144016198, 332352384, 499326680, 376281220, 151206772, 820839899, 289443791, 87321420, 982290652, 125689110, 908071390, 495909828, 327167804, 305485338, 476248560, 247644285, 834911495, 769109077, 354744799, 795481812, 551734845, 872243701, 271050254, 370929244, 497063770, 318360688, 248962730, 723803822, 517467288, 495038794, 75702798, 960160398, 351277736, 426636581, 207172724, 157628568, 950750274, 618890630, 865754300, 832567956, 578903005, 914025616, 881428105, 372215617, 123632077, 263724298, 191653833, 397025925, 435128028, 134137437, 676981861, 956659557, 11250189, 448004564, 500508708, 760940815, 238201965, 858643771, 455692892, 669616443, 366766899, 9574580, 997026702, 649404363, 817160146, 76743749, 390553171, 855158737, 383863810, 388395170, 691850764, 611774771, 293833100, 165089833, 793694239, 799252048, 848762317, 587586717, 864375410, 802161242, 93011576, 634201298, 901227197, 772816001, 574942038, 882169460, 225023595, 955573677, 879688455, 636969993, 882890568, 590075269, 524273663, 648162321, 256789658, 652339221, 268180037, 967807136, 565115978, 171916121, 312307346, 87116328, 554132816, 2725785, 712363769, 917318999, 120179502, 996482050, 110922380, 961502560, 950368078, 16144463, 222827700, 535706656, 172349379, 952215569, 968875437, 554868509, 399206092, 941627119, 209851437, 775928864, 391868190, 655050415, 834240460, 9555266, 739949008, 243344935, 420351285, 807979557, 637793484, 220678188, 198855071, 626566901, 783689599, 956728147, 949469661, 866472173, 572483084, 292091755, 695730171, 105860568, 786859220, 663992496, 263138918, 898761764, 34983894, 91000668, 740930961, 865471820, 993970975, 333300266, 265355301, 808022889, 891111207, 307781382, 893080468, 725829277, 575100133, 168480361, 611471426, 126361252, 97378792, 174085458, 482601290, 306799715, 101843166, 315687362, 887758866, 860883755, 489387024, 108047817, 759639785, 244418403, 308646602, 11883738, 144925129, 593948287, 293564164, 32989882, 894636191, 713439241, 607847011, 821349348, 951028727, 541380810, 4402597, 836306413, 139093863, 282665117, 915058737, 536541476, 585566830, 538145315, 518587190, 146783561, 402655249, 175725650, 514816758, 228881480, 491340395, 294809531, 752059011, 940822095, 863846039, 539525248, 924471961, 110448839, 153927974, 787847933, 326693947, 379764409, 76430075, 609818576, 483343992, 558273227, 574183975, 332387882, 502245602, 644585705, 950796448, 941274714, 911923882, 706413010, 881210799, 155910123, 970182948, 100361166, 107779860, 468697257, 650402585, 966571057, 923880096, 228294528, 116851764, 626482883, 667063315, 122255674, 620264222, 968704665, 970431388, 974882164, 243408153, 92747043, 873126786, 680224289, 337273562, 492541637, 183200086, 276605370, 640457005, 346601210, 761202305, 876357932, 815529123, 264926933, 516896826, 199773940, 48803917, 798402084, 445516812, 629097681, 835972335, 250694149, 251787313, 384373147, 42215712, 823301084, 435467687, 207679012, 988114759, 413362450, 897876607, 792443182, 802654172, 804825690, 648410692, 178499013, 519548671, 793848427, 232638531, 949759939, 900836700, 776119165, 661100705, 495953337, 292163352, 303864464, 203173595, 104393751, 604017819, 798950892, 907072778, 367213045, 664326383, 644313337, 643624661, 952217448, 541573753, 194104787, 86679316, 398624189, 503867666, 229828219, 946499340, 695387983, 495373472, 237328802, 923054204, 558498598, 182120735, 216393611, 970544540, 688499669, 830186967, 28147170, 965080813, 231634508, 127313411, 187470554, 666243632, 249870549, 70420427, 599358571, 534153861, 40531111, 734984032, 895380363, 137523238, 995088613, 891899005, 231597485, 670419434, 783375155, 742204356, 286429804, 534932430, 831778295, 267889790, 16984683, 472949279, 876285118, 557287156, 693325890, 937204942, 853103847, 404452327, 295783723, 423383778, 75575174, 828351697, 865539436, 914034984, 974603553, 249716667, 871996694, 211104226, 809897012, 799344844, 207064233, 676887040, 580554783, 677536822, 614160864, 150830357, 303181010, 261730711, 738465669, 163794545, 146925932, 787545168, 294236376, 224833960, 749555439, 655433242, 457231229, 545732934, 998498491, 601955738, 39569688, 120327610, 952334818, 706429690, 76324484, 409971413, 744713793, 596050076, 62171241, 706349142, 27395962, 809622933, 112830314, 294617533, 354019235, 5119133, 88369028, 498160762, 971922270, 722637940, 893693363, 544197982, 729582785, 460777225, 740565688, 870799707, 834953395, 913473202, 169282553, 628165439, 144676402, 294131366, 371937405, 493967, 672700519, 291905485, 407963540, 840424035, 812520122, 886043207, 48862334, 568116577, 215064663, 370908396, 586643407, 968307353, 234870230, 268672026, 899789034, 982114577, 281875869, 351704202, 428717680, 301090888, 460166512, 790050724, 601414507, 685208145, 833241794, 477590161, 105845748, 201711141, 25672055, 684223445, 400121427, 802624337, 369143444, 282954570, 193719577, 359051520, 479523355, 538278533, 871532061, 882780731, 568602639, 631511648, 88796033, 931493845, 836420106, 449840411, 898425027, 178641144, 589620560, 430133029, 45592772, 931406010, 71651892, 516839274, 191600063, 774638290, 843452212, 136803275, 660264993, 208868717, 867162110, 128570534, 707674925, 365864035, 798517598, 714181377, 924221068, 39922557, 249129880, 539285415, 237411818, 53405120, 572006851, 622276920, 752922076, 633255520, 862723189, 740935416, 561716022, 851401249, 441309669, 488422532, 299854933, 470539343, 566728685, 295977872, 447138620, 257656977, 844117781, 871789125, 296512819, 305398527, 450996917, 482701099, 477529870, 396820703, 554432810, 691526984, 458164880, 53117096, 929743718, 532772200, 257024778, 451590500, 342271855, 95133934, 961364041, 165319183, 20637045, 598514939, 199826156, 183677108, 630874104, 696768783, 760586956, 295643253, 104481882, 633174841, 346642495, 953566383, 235868664, 738466391, 605250892, 825800978, 708480393, 859162888, 496715259, 250659999, 482739182, 384347854, 34959143, 455283994, 890989350, 487537969, 31994657, 30751428, 720269385, 858498861, 807624125, 462008206, 636988703, 773286748, 497311047, 857500649, 831590249, 689308946, 663855604, 484719073, 807413352, 721094217, 69761359, 92093941, 698142168, 147164128, 352480319, 897756144, 965865014, 985588611, 641616021, 148071675, 593760830, 40892130, 868522932, 578058442, 720468211, 622911057, 533877864, 173742716, 825141101, 541221471, 643653797, 468704390, 68289573, 630382826, 212679154, 728028520, 105544721, 765668197, 943955766, 532949867, 937966566, 902846794, 66093178, 867173123, 543321367, 715055167, 189187660, 9653234, 836188132, 945378341, 369100080, 470694444, 319023462, 827118234, 94297052, 153901725, 165664566, 556540188, 230350760, 640957196, 358146406, 579883527, 970854679, 162690328, 511634796, 23655034, 139164722, 498636325, 315008570, 33440051, 327394481, 972798464, 490930625, 818495602, 950771221, 197231546, 192324080, 962842779, 145335229, 757594280, 451148234, 518358788, 514445586, 491445890, 518083602, 538916822, 91944628, 979313531, 790633552, 558897701, 650492773, 293080443, 232236993, 42406299, 953051545, 885785485, 60237267, 460214108, 532638119, 123693703, 799334829, 836272423, 832612740, 709001948, 623430019, 830505376, 478747933, 927044429, 412050330, 464548551, 315209998, 395978754, 123333228, 268443771, 797294717, 763785537, 283176369, 554955614, 552030726, 764812101, 809701884, 208690845, 742127999, 448239201, 860269590, 753539422, 520602368, 288260723, 299973380, 252297033, 790277622, 5922468, 184181556, 609065549, 859975761, 442145892, 958378793, 755377992, 352647989, 471727988, 671151477, 184428854, 374570058, 900487113, 423706249, 542811085, 852109732, 273800964, 506337842, 690520195, 789710830, 488795298, 696968000, 458698451, 235130298, 209334343, 390759144, 353599315, 821341689, 944209833, 816221500, 340614631, 571481304, 485859160, 370251784, 48221783, 239317382, 930470978, 869685515, 261331584, 151462558, 718452612, 312232006, 814327458, 325833411, 205764480, 194734925, 132979074, 152178424, 450477772, 855891840, 732453536, 572277219, 511124842, 590325883, 22117947, 790835188, 569065820, 376069778, 48232940, 617291126, 603964091, 431242952, 698674590, 596867959, 485003531, 976023481, 995384626, 831288199, 743962594, 238398032, 526311557, 818129824, 712449662, 325609648, 350247442, 431374134, 656399077, 799457571, 604578672, 863889117, 161710768, 442825156, 537504934, 808801814, 592855515, 604632731, 434896838, 429685964, 986909400, 371691662, 292458047, 539698537, 331639718, 908061346, 893212261, 982605558, 598427032, 712992619, 762244096, 543024714, 194577511, 510421719, 561072542, 710722474, 555101921, 903078920, 493664367, 601577624, 364422386, 62572713, 169299784, 796972834, 710597628, 172920631, 191639996, 466965123, 781177150, 527275120, 481755451, 714131282, 208369731, 559847400, 808403007, 672932960, 425799921, 26619619, 124547072, 613640910, 343997411, 657731143, 792248927, 610009693, 739918684, 777412492, 310277482, 859181657, 67532476, 326213989, 380735445, 467686691, 696225236, 457093995, 772790343, 963885286, 911012706, 835231183, 990031566, 119259529, 378502254, 714746301, 260109245, 678727537, 637729782, 771484937, 279028127, 294307709, 160814419, 49098459, 252542162, 539241670, 356983428, 910755442, 266851578, 85311419, 420614950, 324180255, 869403107, 977909046, 782545383, 73090073, 587073146, 147918836, 603352210, 285048730, 599284585, 628858068, 257965936, 230245945, 424099362, 742724906, 13321467, 607384049, 359525000, 630170975, 688817254, 278030963, 833546792, 186952672, 491786572, 312524295, 530253799, 29435384, 210410122, 546078578, 681828173, 5490709, 274563403, 233958144, 785873027, 225183367, 131918696, 298345997, 125036105, 988147499, 244014724, 775232082, 845820761, 723364775, 201722073, 636502475, 908721910, 90360549, 697775197, 343834096, 234231816, 353380585, 911063781, 915423087, 950857195, 853868459, 828569653, 341586747, 349454995, 829098437, 488078954, 954461178, 160730159, 100291735, 998535463, 394439182, 945054712, 351009532, 421215359, 253684954, 502325285, 427411456, 777573655, 127790516, 368364828, 654521051, 429065973, 640990714, 521504911, 677756712, 964692062, 799456372, 871384024, 733233915, 499730327, 268452212, 173886326, 677595968, 118265224, 775373749, 690972864, 696783537, 361466199, 275646591, 358246052, 604826423, 974920865, 65604052, 989004197, 357767539, 763368519, 250525977, 527761497, 912747618, 309224509, 129390653, 450041394, 31353104, 586597959, 133932564, 33166421, 812278102, 193078276, 65612668, 14296644, 853810228, 613619105, 373423069, 308990292, 720625950, 10418654, 158122067, 784760783, 791771031, 109116717, 592013563, 242451291, 743570096, 498588360, 285564546, 356452427, 121241608, 870079790, 463739461, 893252555, 468797479, 893217610, 409342243, 890030123, 109297352, 126310701, 396351820, 300446976, 670080839, 952840859, 809690805, 800770449, 470708863, 565434486, 516412960, 93837139, 393324332, 538766777, 935497159, 799720402, 273954711, 739955009, 343079840, 167048968, 909838954, 994953862, 310108519, 343110311, 201733970, 736526718, 573959511, 539874543, 672587456, 184678874, 1045398, 564856818, 984738213, 780475735, 333647432, 984072334, 765566040, 47415711, 421660518, 89682718, 279471190, 919906288, 744819993, 365008365, 615285904, 553311081, 252571859, 540994374, 94670978, 676263689, 999143379, 10567159, 119181612, 133654668, 546248906, 450633695, 463007418, 962033481, 919001160, 406949989, 353261781, 418301491, 392543747, 596065429, 682957655, 196580332, 848192795, 640864874, 537817044, 171409904, 59605145, 674167498, 947741271, 560386796, 453785638, 477586480, 458800631, 612940402, 10750465, 216276978, 854777048, 671271776, 212910602, 120349845, 803797897, 417048685, 520607230, 860050063, 358945933, 859023709, 534322561, 545599014, 111357502, 182728772, 81044008, 790770837, 648853569, 524928866, 907376631, 809457798, 417879975, 358429667, 246417409, 934786365, 314531085, 103071255, 346944477, 477622215, 802905219, 581268859, 81785551, 739285425, 302068706, 651548496, 339876719, 14806281, 426695134, 519149869, 679124890, 974068975, 490911153, 812508670, 835711314, 959780179, 71516509, 59751990, 682477424, 484026963, 784863712, 245802770, 693763779, 818233779, 415393197, 6349607, 766064129, 951028560, 869579933, 89762388, 362947231, 927278007, 636820206, 767316388, 801461491, 889860525, 796953762, 888012928, 75837253, 178967768, 437937418, 729112445, 32481196, 983264718, 357508470, 954854273, 907768184, 306576937, 950442774, 233244830, 551114644, 611114279, 964642734, 569118707, 701630617, 673043513, 741279912, 339900584, 641644735, 863351750, 902464907, 91253269, 102391448, 561710439, 615866005, 367941767, 85250601, 239093656, 739750422, 944812236, 649341759, 340596888, 504659627, 727243448, 163951220, 484700818, 791850640, 614621071, 489699495, 6571911, 459023673, 772093247, 637959629, 533461751, 789831781, 185080802, 487426135, 350090245, 836429257, 922522693, 594258111, 170533314, 639781118, 754513914, 436778005, 322289669, 33633332, 6933622, 410433667, 363494950, 457590205, 170447199, 782535132, 565267109, 720506595, 785572502, 60005682, 407179685, 58464086, 631313532, 446100724, 263939957, 221430735, 899517448, 844628327, 73126074, 716725420, 513687404, 884525179, 453681919, 18029765, 299991827, 140555045, 283771878, 34960053, 390690528, 579848832, 39912359, 948044569, 173448425, 563701627, 842355239, 542656741, 93776502, 497032115, 388726297, 310213353, 925977760, 513786146, 690117123, 445718524, 679416501, 535311222, 860597225, 620441401, 634752161, 295296225, 184503308, 79577351, 942828473, 179889379, 268567688, 252516310, 931079628, 803326786, 751110838, 350445628, 555622980, 643584398, 846810626, 637415295, 168306999, 552485783, 311153622, 964750050, 296519615, 169580043, 542012277, 266220887, 981256451, 652337246, 786339089, 821172720, 112335564, 745607780, 829645907, 168539162, 882097898, 468347646, 168868252, 473035889, 461939240, 163046234, 496321272, 438032915, 502179552, 104110779, 27400240, 66430628, 611866562, 768420128, 763064979, 881138829, 745287353, 767735480, 779574697, 971750263, 553578706, 281291448, 774393101, 353092430, 426570750, 978500239, 211789544, 839524645, 81243811, 318757968, 142296974, 900757702, 908051396, 522440853, 691276365, 284685199, 348585680, 852486840, 532166201, 793496747, 422610444, 57081948, 504443384, 707675577, 529420372, 326272815, 43161867, 257264861, 770909571, 889731532, 138584526, 32724765, 822760487, 326576836, 996053537, 425064142, 8453684, 625993073, 699848095, 46464294, 384564787, 963260845, 265072471, 831716955, 115939756, 620988773, 385044012, 149696644, 819104936, 875592941, 101239829, 572802492, 620502185, 682540225, 773757829, 829226262, 99395959, 34354195, 353426549, 994277647, 498363703, 83554153, 720173369, 731485047, 306105624, 311447002, 962287212, 363343000, 316579552, 457235742, 383619303, 178999390, 611389653, 229650063, 105677914, 913474602, 145891375, 948311871, 650037238, 864064974, 661672836, 374450732, 840057499, 799133832, 200017341, 209044380, 863414865, 325273198, 850758150, 556605065, 912665047, 940591607, 460386102, 362151145, 537217131, 815049198, 584212523, 598553743, 545417854, 651583198, 495504266, 149236939, 616926035, 789155461, 788416453, 318111568, 568996331, 706068779, 983108046, 419110412, 793940234, 35224341, 149617764, 37197075, 264342894, 780417052, 847352042, 168833865, 797490449, 475594804, 274061710, 930079066, 672485163, 653689604, 326736295, 762235305, 695875581, 781144137, 468471889, 154722594, 739997179, 447322230, 660050188, 102184976, 736509239, 510721586, 868381665, 826113641, 417457653, 596281387, 965503486, 451297843, 469389622, 377265861, 260620111, 918992602, 514855680, 166434239, 709315937, 155845034, 55505706, 261550803, 264690508, 92980405, 59143571, 457560138, 362376865, 429067672, 660938483, 799430764, 86092989, 722769907, 775207012, 139410813, 797991256, 52364961, 700641911, 791115714, 860392672, 661111831, 663278223, 297661003, 416861954, 585875566, 794050135, 641971707, 113495501, 281061110, 409388135, 473583811, 97472067, 923835518, 824352456, 767814806, 646584134, 543097159, 512466911, 304519712, 742081724, 591111241, 300221778, 441554220, 826384509, 827123132, 592970848, 423253939, 718770456, 979265509, 350093299, 405917481, 604636064, 256309494, 986073436, 345009821, 243335978, 277149614, 27439576, 483341096, 64878955, 38666916, 375499876, 945701202, 221948749, 391344909, 603222416, 25636179, 76887845, 925268645, 515278019, 73402836, 229984079, 312647372, 341820142, 838103795, 349059273, 123176781, 424858105, 879860601, 10995788, 157863536, 472776026, 6200419, 886196020, 606971393, 740832398, 431447362, 595021710, 801425689, 607673603, 977479188, 902106115, 727877061, 798965983, 354092618, 637297976, 589277093, 492720986, 829819359, 749314641, 604098456, 282989351, 21652090, 755672829, 451783009, 291375312, 624692865, 750097177, 561461854, 308177682, 399998131, 145843787, 81438135, 282033074, 80130897, 87129145, 534915008, 684705120, 451371708, 232326629, 809750717, 582934908, 854687154, 10655094, 140380440, 58953003, 938536271, 57100437, 893363070, 772387540, 839626296, 329353254, 299175058, 958882418, 133403639, 106471448, 772604973, 819572000, 440955685, 10853675, 319584578, 181101322, 715430382, 168315236, 717134078, 336603244, 404696611, 331952646, 216044098, 972130467, 134807478, 596942662, 658729929, 124087340, 274739823, 107724393, 907690871, 340317706, 292889615, 30633770, 360305509, 143512868, 422903358, 941943737, 442108273, 32675998, 960512894, 459588734, 94679482, 502805527, 751685927, 802711520, 172113175, 989491970, 848109458, 597466370, 196756086, 432749143, 646585691, 208692851, 52475903, 676973462, 222935869, 752186364, 660505206, 674073859, 72377952, 11438377, 409949226, 728553116, 525007629, 88968294, 612342013, 803091660, 256102326, 984926195, 964403642, 749513192, 313650200, 420024181, 178858382, 158043377, 786697865, 295784897, 489792226, 787049989, 948871864, 409965382, 2761712, 555484679, 523719604, 174067201, 1477290, 580660149, 588961959, 929327802, 382451324, 667199756, 254584976, 905349240, 429486181, 640285310, 441789390, 544586437, 311421288, 475840191, 498331080, 49617000, 101129527, 144001536, 640620671, 722667293, 686890123, 171871901, 416140957, 195550262, 18029150, 536874156, 141689061, 899582165, 561327768, 163715400, 252757048, 518801249, 61311682, 6235283, 648941760, 365125240, 970479451, 721587416, 944325189, 290922367, 901005826, 685516466, 242636820, 298066925, 929756457, 487615421, 280923102, 616607818, 545637081, 107576001, 21747127, 557691060, 830829372, 504923358, 711166606, 199622776, 865126523, 301317861, 501063669, 672289787, 164178855, 484227256, 631622818, 232312411, 917647227, 977676099, 747299561, 792000460, 341401168, 881940794, 360870487, 112828082, 974010447, 513086205, 60100449, 62952168, 712157199, 321168272, 161211965, 622400507, 275733189, 51907332, 88379897, 459540244, 809279640, 212701927, 225894434, 292437468, 163271492, 880888824, 867311058, 131950357, 945322402, 5887537, 412083594, 995546722, 98067721, 520824611, 842931570, 536136604, 427704588, 558928513, 66031216, 387356607, 329057858, 15833217, 203881317, 680323063, 404653445, 307010734, 193580893, 253288766, 553128174, 682564883, 755742147, 661556526, 136907413, 223803748, 56761328, 834153755, 301736359, 275615923, 270239936, 941515936, 779065715, 61603601, 468669993, 874193843, 67781123, 401838515, 442359105, 346362084, 531707769, 736927718, 80175576, 862375535, 410310265, 187499987, 173639398, 823977075, 116011163, 973964449, 409567661, 782374282, 799092961, 661797136, 506514508, 319125025, 97257644, 902121167, 325052249, 229639823, 282462816, 99511094, 466168777, 481798362, 110165010, 899807782, 267104451, 724541717, 19269282, 428604043, 900204637, 284503775, 52671884, 776090760, 584893340, 399257923, 182043505, 982590241, 730228891, 839036532, 802445926, 419677253, 171723981, 135485399, 987083187, 77270897, 199022099, 170511675, 697979419, 690177503, 197256829, 384351536, 19703977, 262511003, 45620816, 18819835, 797466508, 171049056, 413637855, 466838046, 118812582, 853053841, 260223683, 445745198, 650527603, 224008071, 160732155, 430516143, 530051985, 642496871, 698237189, 669371010, 607940706, 819494469, 455423213, 203212837, 819581227, 851598917, 7509403, 410290946, 61084766, 477777273, 252158970, 152108354, 756577559, 62548420, 845967031, 86564986, 874577748, 833280674, 55277338, 109896874, 372674196, 805627991, 492202706, 206996543, 338977474, 525242869, 866115924, 647113216, 195385266, 375452591, 833923199, 202055662, 960163120, 389637069, 652101861, 344485581, 505291320, 772378123, 832146447, 400532420, 163512364, 830650001, 46031199, 214073422, 615368183, 149429529, 708671809, 920759347, 722039257, 130094499, 271084798, 692158109, 99085760, 352399394, 43141936, 639905363, 669696228, 9421457, 483048000, 485229561, 237845552, 666222336, 122797776, 358213065, 334589037, 470798245, 939366327, 555421261, 863603404, 373790397, 243974230, 486096838, 916477538, 702333574, 215905485, 538062026, 591036861, 223987848, 63300313, 876366112, 191633942, 826194818, 247774278, 909595037, 89264334, 464923159, 323686646, 999721958, 100380369, 295214937, 364156553, 371470529, 521536210, 548615427, 532935363, 446177735, 757654618, 194065539, 571909096, 569090913, 270092407, 617063528, 363571247, 225952075, 721323090, 710493019, 188591791, 376136735, 836350940, 764315235, 5180877, 955205402, 190594038, 731802362, 827914536, 898096394, 697485687, 482138331, 593155119, 344195577, 957307588, 541455570, 414924759, 203110586, 308472232, 854712745, 344335603, 163952098, 103750888, 554781426, 809345360, 697575297, 455535055, 647720500, 953719668, 58339596, 134885217, 652177581, 929375800, 327883276, 630664549, 126856145, 1159263, 729642322, 999934067, 428051343, 688296550, 229853599, 844228793, 852113359, 963256122, 390781797, 688520127, 359168884, 231361973, 927602150, 607045112, 58975354, 471095382, 453905487, 644151323, 822706557, 605052806, 289121787, 135143084, 537975876, 624831865, 302915479, 647656087, 78437926, 684048272, 939021690, 317696021, 516874935, 123584692, 807715482, 838528857, 321259979, 961803001, 360625542, 305961883, 453115987, 323091376, 597200481, 162902271, 885584683, 400362280, 299496455, 949047378, 593406183, 254358737, 132671279, 686427331, 471217330, 689741053, 710731341, 724281240, 975296011, 131606127, 403862356, 737591850, 508016274, 976695597, 718061239, 815926145, 478465102, 677600491, 7040926, 184890981, 588462162, 176008952, 937171298, 747468051, 324834315, 657142728, 832681453, 673224645, 517284990, 430618815, 828107002, 757840610, 730379927, 3303094, 518621051, 35881972, 16356951, 344720695, 60846143, 33841386, 211408319, 111790541, 607084527, 996459782, 261109025, 568799935, 384205444, 924841030, 460307787, 567722592, 401553585, 940994749, 342007887, 327294960, 256786502, 910565191, 460560660, 824244209, 817793859, 597663286, 934655533, 638656562, 91711594, 294206553, 698536078, 428021450, 658752244, 265659604, 573006270, 231480230, 389059889, 818273092, 989899611, 224946637, 643795750, 343021169, 743740360, 706221711, 231802246, 193840712, 254603018, 911736234, 251619466, 352596746, 700797225, 738155683, 838959556, 809660325, 504183545, 610562452, 334973052, 325446599, 535862004, 904038819, 234365986, 722898261, 753040299, 636435859, 820580849, 182044628, 211942608, 677525227, 807256077, 698401280, 617961119, 859432226, 362847402, 17612690, 242178795, 852031950, 414651948, 919355216, 148449573, 680013697, 825500085, 517819957, 127425375, 504442912, 369735419, 633344242, 553446596, 496180435, 133147212, 11766622, 796260121, 623805454, 967776343, 279697618, 122955319, 563840868, 790195304, 431509234, 533166627, 44969828, 309235552, 598213138, 136022093, 119064070, 676318810, 920010834, 71479056, 48841150, 842531180, 660283077, 572562099, 390874436, 998152186, 569694712, 804884520, 798309354, 293493241, 712977405, 96385794, 842731392, 347913142, 621050181, 551653028, 119913788, 379682074, 889013826, 901086359, 34668111, 935008980, 715640686, 339258365, 559898743, 276628882, 156478896, 549436201, 568352209, 495394913, 509249143, 729843455, 781947976, 505811050, 140580601, 837647606, 442774679, 711635741, 393577589, 845786860, 345698963, 299828549, 451525081, 338385538, 480815834, 838118576, 173835127, 579856678, 41480545, 294162950, 32297212, 219553968, 75426404, 747288873, 73130687, 557159699, 567387621, 351011389, 413558742, 820892672, 342938087, 153581178, 250133581, 831550612, 473819756, 291189103, 191895048, 708408087, 317797420, 529913024, 94929695, 224329743, 686448151, 649130969, 131679891, 165073552, 497172886, 505307880, 420288192, 516123191, 117534444, 752855009, 535641529, 548791978, 917915750, 581548884, 107925838, 82107462, 872527222, 333782115, 512501730, 632648749, 2109423, 291568566, 560923156, 112239396, 475763619, 712068992, 955194046, 97931136, 349086660, 244907698, 570806803, 698456703, 881187835, 123920940, 983499825, 598678414, 699238160, 943753749, 80854912, 523888237, 515568565, 738800545, 276709197, 254168159, 902334078, 343415204, 170299277, 20918672, 501042164, 510058381, 266811066, 947543750, 559374660, 405353660, 966069074, 799301672, 216739937, 611295526, 995301746, 279809879, 605853084, 909436156, 954884474, 621750995, 514097467, 35298723, 847334852, 815483926, 649594312, 373763397, 543239272, 869719902, 692292838, 203124082, 724912863, 764553290, 674987282, 626216670, 465172863, 471334645, 953412086, 918903378, 439297395, 879656584, 446264618, 568526182, 369619208, 650699027, 293265063, 755362674, 372467919, 844764993, 791262111, 609544760, 685738885, 491839729, 676167737, 454048491, 35012907, 941136881, 60585679, 757013207, 232640056, 479142845, 683082069, 525517423, 516578203, 373957254, 862896337, 157568607, 133259866, 670822141, 280596755, 782546954, 402027813, 987410925, 263873144, 851464156, 2665011, 190110748, 484117301, 822621073, 542402723, 951160813, 424688487, 309993151, 123979855, 804073100, 395102137, 365238564, 84388436, 952938039, 465730376, 887402189, 795616246, 709574910, 701176879, 254878129, 368129069, 813239019, 92324598, 702746069, 973320610, 322002131, 357782257, 343315080, 806780470, 724607626, 894419187, 716645006, 222314604, 705977224, 771945957, 653690992, 172447895, 975675475, 588031016, 398497740, 797828717, 823308974, 611354890, 689302764, 417796916, 394980933, 463099499, 735260071, 909088750, 674402931, 171676813, 384453475, 243020065, 414038992, 623103655, 121030648, 708357297, 84086297, 696888709, 904636841, 231055568, 655614486, 583212019, 694936343, 388003362, 94347728, 58603382, 447108873, 847883031, 477303792, 122809238, 818609015, 775084754, 301154442, 719575953, 749651759, 650280499, 386705041, 865399915, 318182104, 18155731, 394848145, 3999722, 195488054, 587173561, 793075429, 52989770, 325506902, 596444863, 241491312, 749258289, 454787148, 757800892, 635422550, 435404121, 983734263, 238861532, 803385421, 906850312, 102805468, 694407189, 623140755, 110660767, 486798247, 199674868, 881740337, 294516409, 3308509, 978014172, 769318738, 667499542, 742066833, 574212103, 988244469, 973110674, 847217890, 93964911, 577727401, 589778622, 406759706, 887578366, 132426820, 639908725, 390187719, 340845787, 965362160, 714194146, 911499992, 637488157, 884076121, 381701426, 787869987, 905888185, 312750920, 578851649, 282598215, 202983203, 235618926, 466284805, 21455566, 344441460, 256376407, 125539328, 900692840, 366397944, 675039656, 84598740, 634646862, 841028453, 611235644, 761154182, 842729617, 539666841, 16146629, 484854878, 863073511, 956192885, 145505707, 956303593, 254084516, 502196752, 16285661, 856974678, 742044531, 60052563, 721252040, 476515602, 306236506, 707511156, 510047370, 56419745, 741796365, 272662302, 796094951, 941855816, 966345463, 693951697, 706345287, 555919762, 441100795, 416240581, 269522025, 322714704, 616392663, 122584980, 312785668, 522435572, 751468492, 653454439, 139773712, 285676525, 379625711, 82218535, 678833436, 319893853, 912824292, 124487969, 667560909, 628297147, 983942629, 56039628, 336951047, 172550540, 670738520, 477589574, 523478477, 860048428, 134806689, 703941614, 34031342, 252502213, 23061346, 88339370, 559428804, 54190883, 952756654, 494569184, 606068154, 785848372, 176699215, 186865437, 445170625, 59451831, 808320317, 584248428, 659353481, 654966417, 811501470, 314133067, 722406160, 590012479, 326306394, 36701360, 872603444, 687273359, 600858898, 716680923, 541688500, 707327469, 332910971, 781058543, 817952241, 956015479, 455469651, 739055188, 19923048, 901806249, 235008289, 470888974, 55358197, 853128095, 718028916, 680398976, 649196053, 408830057, 625626999, 605484762, 746128474, 678594108, 470010247, 58807723, 83453535, 851703260, 747603980, 224015394, 212639810, 655816686, 58800229, 667580333, 940043414, 667400608, 268763592, 905327433, 440789204, 359821175, 766378857, 794681162, 141652611, 568934841, 845102934, 853325854, 80769306, 94462907, 625441423, 45496012, 13308399, 285808896, 714862641, 127863098, 37442477, 669490639, 146934911, 701934365, 362707589, 304294028, 641928162, 761436017, 514804496, 83284881, 648611840, 582742763, 825126250, 881682834, 88378013, 739205703, 270022763, 512090819, 152724392, 920796408, 625409126, 52215900, 432483764, 514342112, 296177440, 885041455, 444591125, 624760549, 661916, 34018578, 460110057, 299854743, 456316673, 146879681, 573605991, 267223776, 990033670, 761099221, 469891788, 88744507, 896762167, 642279633, 599820418, 838521130, 173516768, 794506064, 281581860, 569293747, 773961571, 180002607, 614149417, 99027911, 827763707, 122701779, 607133279, 503241973, 466176901, 22500294, 479924015, 827309110, 765219213, 469488011, 903358678, 133812412, 204631034, 448621961, 629383455, 502138302, 387243135, 18927723, 179535808, 468787334, 418590377, 258579718, 988466087, 470609087, 520426382, 681346640, 356849724, 8706293, 115993904, 48860922, 600400645, 364055534, 353258638, 648583907, 785761592, 609150669, 206181372, 614934591, 703479441, 70176513, 327435227, 117430705, 504558873, 665675039, 210263912, 671483987, 349905813, 591278442, 880671257, 553359324, 238354803, 61388602, 479870198, 202318623, 7746589, 220303744, 275870417, 949178832, 849441830, 932116584, 449474036, 684862914, 229965893, 604784122, 91002400, 27228562, 817758082, 40839120, 642138073, 519907920, 131205582, 375834135, 139192204, 88368018, 772702380, 230283228, 788297241, 230860331, 150393948, 966388069, 708307316, 439198852, 931990552, 588933584, 914851887, 730966911, 183544841, 659914889, 76650519, 842647897, 916039321, 509145936, 464295277, 753442745, 812968524, 819504661, 169602373, 99855443, 562735267, 483171141, 468819342, 63404663, 129066762, 319323751, 7327205, 982065701, 258794649, 720152449, 389729, 644384840, 724793908, 791550092, 610412377, 688158251, 358214384, 464512944, 257447946, 124156751, 415064340, 400934237, 669490980, 807616953, 316397097, 400665518, 270306788, 574662219, 363535391, 341495571, 152294120, 923240832, 123537893, 501511552, 627843346, 818662127, 410466598, 624555834, 892351593, 869285502, 65683151, 106366668, 467901228, 160444827, 146597979, 932165177, 251939176, 335301327, 73321106, 696607173, 936211970, 853782353, 529967170, 297926430, 888875520, 865580665, 504438730, 104167536, 182769037, 116024642, 953877996, 611441737, 295495622, 310567275, 267654742, 167963966, 693368036, 81817546, 269159862, 877628134, 640039612, 20623605, 267977364, 886304527, 883722493, 505563794, 111144925, 976195860, 621920896, 761516034, 613121631, 482227732, 159341467, 903476433, 405315291, 394723891, 246776721, 662541836, 577818640, 938170382, 889110169, 100411029, 731620745, 639502639, 6004744, 353043851, 647607869, 608905165, 507392289, 216638667, 71604440, 16106472, 368457144, 454638638, 893499317, 82548177, 382401148, 668258837, 89327723, 795617528, 353012444, 664214373, 164871844, 958868515, 324075039, 847754131, 409384072, 171949677, 666729400, 941748244, 44307797, 599235963, 108953997, 816799010, 189904819, 52142863, 10879510, 872678237, 120259893, 656425269, 184361286, 219861032, 674746258, 696115244, 814012647, 536108279, 587669410, 431533684, 214340769, 57376041, 498004786, 739632855, 490255576, 107470530, 314913227, 432126508, 612153175, 286565046, 264854870, 796018238, 779616289, 785123512, 249869309, 763594154, 982368837, 18330113, 148516783, 799652243, 374802911, 1183, 512066023, 383598246, 823057593, 847871336, 840075588, 418042858, 381120645, 725532560, 944981689, 284123689, 984380093, 345728894, 623946316, 513101075, 491721456, 338974520, 884200580, 381990793, 775835518, 864526782, 748165537, 355630717, 123951177, 639237253, 540037542, 436801233, 841542658, 710147248, 511661397, 123808721, 564456067, 111958540, 480405841, 353161985, 685218568, 574375315, 423549478, 547034282, 260518226, 993641399, 64730621, 751303927, 271037648, 653850795, 687570951, 973130472, 538049780, 456212006, 206000846, 194154809, 243948647, 189976828, 965797983, 586804614, 153100327, 564756338, 389186473, 504268122, 499888569, 539335826, 439475448, 831704894, 4288185, 114620817, 276961862, 448246457, 452398842, 710701600, 530882355, 419324575, 968285715, 851880551, 570317647, 326413940, 28513167, 372877942, 611919747, 584716873, 184127646, 303756804, 67011481, 533167529, 101474646, 385820705, 225055445, 620016955, 156731909, 883321611, 674118554, 183557108, 554720789, 396969098, 65131510, 720324744, 595369458, 528701057, 393395543, 173118410, 171076821, 128254915, 697448248, 100280016, 202724623, 232254489, 473179149, 881023190, 755733865, 154168604, 739359313, 406332098, 647680864, 237344471, 244958346, 44156236, 445119666, 303654316, 195818181, 532559279, 5653434, 476254497, 634470904, 234533796, 327712166, 558578336, 980243350, 903282865, 212601214, 786924697, 441761508, 984733988, 326040142, 491307723, 124323988, 302153508, 781667839, 860648398, 443509685, 963587231, 501100170, 343372713, 917417426, 614219691, 736468343, 418828527, 70349733, 403555194, 954222421, 648289371, 846057730, 458421791, 500542800, 32426848, 433778986, 528039265, 855579237, 764064176, 414099462, 984417585, 614261682, 81101531, 626448736, 979976301, 501106626, 78382029, 100404481, 650821837, 700192727, 333672000, 786002038, 183208645, 205145301, 212721734, 999933088, 864516660, 55607952, 676319419, 880588000, 936319259, 472896316, 218307229, 416577388, 84990283, 244396394, 359710355, 304682298, 954199536, 566848410, 271158028, 46283130, 631532320, 747912835, 102556901, 397389392, 235159325, 864489329, 825907390, 769799356, 733417975, 241995074, 156966793, 588539075, 819185878, 195640544, 221086697, 29695327, 948592334, 791674765, 957245835, 430173196, 968574159, 981297044, 560660807, 26790765, 977526467, 581637962, 989797083, 729355194, 453886952, 15478772, 152502429, 731954518, 859831531, 880427732, 874987134, 550444833, 710738811, 175667327, 421398023, 498162812, 852197168, 588492658, 659758054, 468867506, 786270753, 434554317, 211646744, 894195349, 770237478, 763375772, 661249927, 540346292, 491547659, 253758559, 676158530, 357683707, 152975207, 530522692, 817500016, 355729976, 579497420, 707202620, 923235661, 258770689, 715994050, 204930316, 847909236, 813928003, 23439129, 432626153, 595364714, 345088548, 447570748, 554770066, 510737990, 781447211, 165440295, 65350480, 417678627, 585720160, 621108731, 533139714, 356179411, 850358675, 118909115, 436220531, 480547631, 40293152, 660802469, 572563035, 922914955, 914910478, 168740068, 901756321, 210319185, 162235317, 18260560, 465751614, 343156425, 927215509, 750858623, 669921594, 627141021, 169293146, 482820991, 72675143, 345925380, 970989863, 715711868, 563879347, 678281652, 480737618, 319656722, 872890817, 910361827, 601716608, 67946636, 310070694, 189697617, 969898049, 745910200, 326387164, 902101201, 195838287, 52069082, 864513409, 709346734, 451650505, 632208078, 227084759, 75825283, 82428393, 753666533, 346353997, 555917768, 269788444, 963300147, 806546132, 965447953, 916791349, 884446266, 825314031, 254051179, 86012514, 463563991, 843270138, 951667723, 992114437, 346938044, 69810603, 937278752, 748690736, 208824562, 88856804, 686234111, 560154085, 427500022, 888787439, 517552918, 532903533, 576280959, 183830772, 325422756, 870678276, 623880758, 69997623, 194929758, 998803955, 396069121, 969376440, 690737529, 470210818, 501170410, 175428205, 339859671, 8732675, 639817568, 131832733, 954888599, 29041747, 806334902, 603207050, 283025107, 567290308, 364756362, 12355516, 173016987, 419181901, 74941787, 217325553, 426772905, 268197283, 589213456, 247289789, 697753219, 246465492, 638968914, 986970364, 623768898, 333149385, 738261807, 43008096, 222566646, 391839354, 957059778, 686047126, 49624497, 500265001, 359120278, 903150421, 974849586, 863419183, 801564673, 266528931, 319239145, 399624397, 412806215, 932066280, 431511377, 463309675, 186925308, 941973332, 130978913, 677577183, 989558, 46563045, 993301798, 269680836, 25287135, 905222937, 860610378, 633164452, 944189073, 987115819, 341570176, 12789504, 163513645, 482478929, 622853193, 300283684, 19695773, 40913545, 25935502, 579419096, 817735539, 764674544, 63094567, 358350831, 811943787, 928797032, 142616395, 310667920, 13478941, 561522194, 782444734, 212321207, 492792870, 742855469, 454810644, 840903653, 417634482, 524951765, 675970201, 295971187, 231116244, 458262852, 13182448, 55742185, 384514501, 272165420, 581578371, 475319133, 544182772, 542801090, 831927333, 639294841, 686526668, 268575980, 556676196, 636134401, 445716308, 189822703, 816818508, 313551292, 337525046, 918879241, 992534598, 561396405, 524306540, 111865182, 624788251, 454401730, 973981600, 203887886, 625764722, 490781985, 429950000, 699335249, 667893326, 491174957, 295456839, 857783439, 772530630, 918518444, 725373218, 833710221, 483372000, 289992368, 971237537, 32351516, 930694441, 663860829, 335663362, 698932670, 294439935, 382625082, 995609803, 462180170, 617208396, 390994775, 716126628, 615142434, 658056314, 826008452, 740490344, 482001044, 807195106, 904330745, 243187610, 465508478, 400121403, 541661381, 798323324, 799854403, 251725804, 701890788, 373814356, 480787494, 962377556, 293180341, 377298286, 127547904, 787776419, 671579794, 773682946, 181551335, 322191880, 406303947, 724527662, 282834025, 425288855, 476739338, 893063330, 593086928, 201166342, 919611739, 305704228, 773175264, 197000814, 589103704, 410730110, 647151130, 890502089, 521368450, 212732420, 293405381, 265221495, 813625006, 77331749, 417880119, 562705560, 887772755, 432631163, 536484432, 643698565, 931502116, 575999506, 9551636, 98773612, 883197167, 746397092, 434259457, 35973725, 628292395, 548252853, 179786784, 730567796, 893336724, 906084454, 429887969, 422661678, 410008950, 874392884, 475505901, 965432550, 700853933, 746869388, 89901380, 702158651, 877826356, 653447034, 148126961, 836176952, 461450706, 400385604, 801669648, 877316417, 999081131, 162178307, 843596036, 531174585, 928339128, 685724075, 959795479, 513296834, 497694443, 609862063, 839495311, 448860351, 726662800, 2754432, 769830654, 453706187, 153316585, 397049964, 756841250, 76999653, 503323463, 275365722, 46579638, 354517265, 620888258, 471041179, 367611756, 608526427, 786338659, 812076022, 158499764, 586498816, 640223287, 639077020, 73030509, 465487743, 592169506, 963995694, 182078014, 360488277, 901381350, 420228750, 120553420, 214728302, 166505484, 987749367, 374483948, 654359963, 422757401, 81525967, 672036091, 972289338, 210010989, 747989912, 508418070, 761019130, 324228491, 93641384, 68415060, 811133988, 407747223, 893519899, 218612952, 24656943, 603955911, 407419851, 278274704, 675233961, 352513525, 651754661, 581197749, 168631257, 851124917, 592679324, 537219398, 567205958, 292765374, 93510343, 394691032, 448427712, 132831554, 709037363, 51193544, 386899337, 280422390, 150956099, 463682669, 306361420, 587188915, 848238201, 900851447, 791244405, 423702908, 913866340, 16305534, 976159782, 507054483, 702301593, 985980803, 87847776, 897746604, 224050898, 177649737, 267880381, 914862266, 673999369, 761521307, 866313108, 844208002, 843485710, 891731942, 149977153, 728650616, 979240561, 38246390, 921818974, 357359267, 328595504, 558335736, 885045344, 390673815, 101199077, 750718643, 847125226, 572804845, 143126454, 313270682, 75736800, 956205239, 791510989, 658273598, 849152328, 441715650, 674302212, 489759419, 995515639, 842017789, 370877074, 134598078, 176137316, 303343278, 222665718, 570233626, 277174541, 335552842, 581282787, 745749690, 844699131, 689140241, 481664121, 499521987, 604540010, 287675067, 945789314, 163661881, 363927046, 806223042, 608500385, 541726113, 323368788, 450130530, 258939093, 45487920, 615614457, 806168341, 228776159, 481866797, 635507806, 625520038, 553031710, 647210781, 48534469, 523783028, 257637301, 712254599, 919508606, 902314188, 629917478, 461837102, 882690581, 839245058, 192400334, 619627652, 497884209, 799436131, 750913965, 993469091, 758528230, 432956891, 702229721, 731965003, 285160887, 663861274, 75366686, 866524460, 34333569, 848962362, 120261776, 838896186, 689542276, 911092217, 121515505, 609962588, 919484848, 63392269, 635717165, 41217738, 3792202, 90075524, 262898358, 301790070, 228050569, 540424442, 193907761, 146443438, 695767011, 673245914, 268677729, 407386044, 389097680, 186600215, 985599361, 77934894, 898779208, 948371608, 121164715, 795478838, 258059379, 756125727, 163417116, 686974036, 446430268, 834743531, 805564818, 777330533, 439415907, 455678273, 791424713, 674111743, 166531100, 311583608, 956431433, 955402016, 40393615, 201925712, 759585500, 884645032, 162203441, 761977707, 424291241, 519367775, 270371660, 553535530, 320365086, 846732830, 211667169, 717866772, 920571846, 48997273, 588163530, 692797733, 807692141, 293177773, 428238560, 521700393, 822019265, 126390668, 223748365, 628580638, 748194425, 188534018, 781024921, 576919746, 635037188, 973893375, 280114584, 345411054, 992356061, 51173195, 592765745, 974580480, 268466369, 192240070, 94354294, 907439840, 925768764, 453097805, 759866150, 631165926, 333875331, 410421610, 715854488, 88382838, 187616819, 29924921, 971274857, 122297559, 791515812, 119014410, 681815328, 27265843, 774309546, 94702986, 707613928, 850643382, 224905591, 108919755, 453929554, 162658366, 150313673, 72755236, 853818585, 489954188, 239377837, 689505849, 732752496, 840731976, 248495508, 836767992, 198484960, 982856425, 243514655, 965439051, 596659687, 724159965, 705469989, 846087819, 509403713, 682421996, 835644254, 766496776, 233891489, 486697897, 174554715, 293605064, 338769962, 363397508, 627136057, 104255451, 241959484, 360536394, 576664112, 402967168, 711018328, 895799222, 693360169, 459404398, 775632917, 457426577, 149183543, 23958176, 387012624, 648973325, 16536577, 219414894, 187077239, 19742271, 443553713, 471426843, 341409881, 527727772, 316622067, 86745496, 683786193, 936575282, 731506907, 534870842, 277344752, 941833310, 456589413, 711330345, 921781816, 17363128, 933245486, 17396372, 646799687, 869163099, 360591385, 796223718, 270738478, 630480663, 891871256, 652536200, 466441097, 10551296, 310399017, 465995785, 411631999, 329868270, 53388629, 364345436, 568404437, 484627171, 833847558, 607340569, 155873307, 950636381, 535540451, 387237287, 179292671, 398278547, 756777774, 206950631, 172265931, 837867342, 55311072, 170886794, 872348096, 534787196, 810067946, 91047730, 30871003, 815895875, 593880376, 111485846, 561247063, 743300762, 632294258, 996249304, 274435512, 897370331, 708444681, 40681298, 869204895, 622312699, 593953506, 910994008, 512826035, 275116845, 798863146, 671540070, 15788118, 257796056, 226094994, 326929075, 108498969, 628673766, 810105132, 766386501, 556259057, 127819164, 961143461, 808727359, 1171633, 326332515, 606776250, 285250297, 455550264, 611709691, 969310780, 81564369, 420290999, 290974652, 293357191, 222475134, 300810499, 212834730, 528843729, 434331279, 304954900, 275623889, 386349603, 102945992, 587600644, 166206329, 469994547, 906461094, 847233110, 61004614, 362810844, 985345875, 293315951, 190541504, 556433223, 340915715, 279202711, 293018496, 770512808, 708032051, 452115079, 691400693, 125607915, 90948459, 828282086, 375513278, 549857195, 921328565, 574737508, 507944011, 509819372, 212106977, 941747141, 689883118, 245972088, 930069414, 161505793, 364948727, 328534875, 614843235, 616178199, 739634963, 951742467, 92535529, 640270079, 661930773, 102765277, 95396778, 708748928, 950591230, 783754152, 185057956, 831837108, 107521190, 424902291, 531978502, 71739575, 741501656, 373945569, 166168434, 29965409, 714191868, 565849806, 592070539, 478097072, 19013982, 197846444, 722684420, 590589101, 951001878, 55942169, 664427954, 679942878, 502844835, 241057866, 95943966, 658816093, 756378118, 789926014, 296282252, 86943785, 548410910, 971068120, 314593677, 119549902, 210047181, 419705822, 52901665, 789466035, 637073038, 16628493, 805269173, 249686637, 458687768, 414572529, 359774624, 395309316, 817789002, 408741324, 232039873, 400889747, 689133428, 525112893, 890513412, 187389347, 985504435, 300183911, 333652459, 13085595, 656221850, 579903510, 911759227, 669413948, 879802040, 520573693, 585555568, 87977473, 241270078, 236162694, 392694973, 753287007, 15127641, 294576400, 619778372, 591469049, 931895081, 505752079, 212306542, 688418930, 203904334, 519047152, 378521094, 842315575, 66707711, 763770501, 410472470, 792353127, 606645111, 334265504, 895917922, 901021249, 182736610, 240360411, 368188464, 747220212, 413505562, 479575718, 219041935, 379522440, 323450884, 227134791, 398943819, 288340905, 285744937, 735193748, 917969625, 67178328, 724924058, 663070078, 15757639, 885904466, 951147647, 147431535, 898494257, 227521637, 553964676, 855848866, 996119367, 765355003, 581493198, 737864797, 142736626, 70882771, 132818867, 6143409, 262298062, 265470284, 452775153, 192398420, 885393843, 707096922, 750932043, 50790913, 677978445, 757429562, 551053348, 587374941, 682534516, 766487885, 264128048, 567885390, 212020503, 79203120, 765903446, 253701406, 910022168, 354963385, 1185315, 458043601, 900339608, 354809300, 540732466, 910352027, 410917321, 226960928, 148140456, 147490863, 329155350, 103311408, 8332617, 109490414, 143957992, 478408877, 327921922, 57573835, 954254077, 40162002, 448668406, 98066657, 280789656, 892668166, 725344002, 51089472, 292109975, 414280370, 425535611, 529994243, 98141614, 691734529, 676159808, 426980577, 542753526, 129397606, 13761003, 683019965, 304731052, 479452419, 68489293, 796217174, 224249420, 392658458, 548473646, 372026142, 925757855, 976343631, 388882223, 362438742, 552860640, 139961123, 353592349, 102149484, 144635724, 470705871, 764035298, 150219078, 450723274, 790252307, 889817455, 919600132, 227841659, 106980862, 491113400, 119231740, 676922482, 915263353, 808348368, 393687434, 582641893, 333273121, 299900065, 473323665, 236272941, 519727169, 186460105, 223680599, 102452616, 927754296, 495807494, 463717199, 558350998, 859798951, 50372314, 798287668, 600658235, 790471636, 326483005, 237088860, 207725290, 987389702, 677646197, 85619948, 676578024, 877535581, 923857549, 116537797, 256219012, 991233920, 288039072, 331194776, 41511391, 473593800, 514721480, 53190279, 861149654, 120429472, 60992010, 587168044, 647907488, 326232927, 509534878, 383471111, 366305632, 49747661, 223138631, 524175431, 790820589, 777404642, 492490663, 534831286, 195524021, 907098335, 512394894, 836249690, 886489640, 216900398, 846740974, 58155855, 439757279, 194696224, 205768779, 196374985, 89425327, 533526427, 565161528, 554902743, 105265790, 363401657, 168811183, 950712976, 924905054, 278295662, 860267160, 187542782, 391879590, 334043535, 834618152, 602853722, 195014483, 331902069, 239220642, 226903906, 993684199, 808607106, 665730599, 933571832, 275231449, 75379790, 177594143, 110860342, 169340581, 578666970, 795668283, 480929318, 567008863, 621903399, 179642920, 586005104, 900007349, 765076373, 28279245, 433418081, 861331957, 537685715, 458687018, 609885773, 672064694, 509244596, 895153135, 36408492, 399405831, 794371962, 237252544, 98127542, 305350083, 371163663, 710663371, 583507298, 803849426, 790957766, 736186919, 638414868, 514957154, 700680922, 401201341, 854704258, 401870294, 334957608, 635649569, 104695792, 998400173, 492541223, 369324370, 436366636, 982878700, 56239976, 988828782, 447282596, 825103745, 929242156, 296697760, 12036881, 645504028, 966002811, 370594332, 681729171, 363876821, 577121215, 818205988, 63519615, 561242096, 393143260, 319604570, 220600919, 764631393, 483401433, 538449254, 418117195, 65670421, 491904265, 30068395, 508422635, 313156979, 160019441, 124182599, 720410083, 217462961, 167316467, 454380642, 789142004, 298376539, 870246809, 917154259, 745443315, 959454955, 418852120, 543440955, 558967526, 941995592, 333677838, 30907868, 163697680, 423145918, 307834152, 235259973, 898196428, 620876614, 815150960, 634970586, 387786910, 179476084, 567893711, 535822028, 34428277, 416895609, 422353251, 324111177, 404542042, 167049755, 455643223, 795146114, 700874300, 439993704, 801766210, 420758613, 574787688, 153314835, 179427702, 803805569, 565222674, 664548161, 466925114, 485643326, 226096734, 845654368, 72753292, 832448006, 941133737, 592337137, 128819403, 405316548, 17336717, 283854228, 813355023, 1178423, 79198260, 260083250, 155013592, 172566066, 782824523, 532362225, 520641128, 97034692, 84405280, 794298009, 681726991, 898509421, 506758689, 768816453, 883843812, 471668965, 248543011, 500354553, 441388871, 824601792, 26597271, 322885920, 131551, 936839913, 695253111, 946180022, 663981434, 883347311, 825415915, 134342180, 712140365, 90132288, 351796721, 745952408, 292174033, 312104143, 558677443, 349731095, 21516069, 369432545, 652072662, 992338056, 915614350, 123380338, 253328352, 968801573, 792102238, 605906116, 365108728, 869773274, 384629445, 520807219, 449088545, 143552038, 270281684, 989694997, 580433756, 61588458, 562325046, 221965299, 347715251, 838287985, 34354347, 825981950, 405135153, 795039695, 752331046, 175184371, 832993619, 483439517, 759500393, 741086838, 211893269, 858929012, 821477731, 206972446, 209416812, 972526007, 692507158, 679120812, 886413133, 495684722, 872902000, 775565278, 618740805, 744796029, 81596484, 590661771, 366821795, 494101147, 575093408, 511862164, 775272642, 610075872, 272719564, 303711645, 178539156, 905155521, 873193748, 524468616, 404748499, 834029764, 62689214, 802504826, 169640933, 427548634, 271264463, 878961487, 814387774, 179282483, 750657412, 993499009, 255620138, 669633446, 761510483, 452017230, 280087825, 598105112, 24494578, 187249401, 793317448, 299922920, 689526072, 169469010, 315446944, 177004784, 905129956, 456474074, 843445052, 670980301, 813124939, 617910082, 363804077, 777844347, 296218303, 210701795, 622348015, 51261425, 109454681, 927611070, 819315320, 254392133, 516655141, 829461019, 409005073, 82204596, 596410633, 855565467, 231430900, 442957180, 613537500, 866906242, 859984392, 135547283, 95260082, 764253285, 723482642, 883643010, 356847895, 476178299, 353367839, 659133101, 302721668, 735742615, 794911090, 511981913, 581990359, 974754976, 450222280, 168988104, 75156187, 10673328, 644158230, 179310691, 862498851, 980669600, 788219334, 138182366, 456748984, 6824598, 440939012, 582228252, 599753148, 601804008, 18977394, 15109478, 606462566, 815967439, 850684312, 117342368, 561221794, 996548994, 884036973, 698984971, 954540176, 445142159, 367213242, 648987495, 169044168, 844876850, 615289546, 259610992, 563463017, 902792759, 599513406, 371938424, 722892398, 61825346, 442990180, 277910328, 498357661, 875255262, 103617499, 907752607, 54156199, 465794517, 586552813, 236619152, 112657298, 663047261, 142639017, 288014687, 396709637, 728930493, 957765031, 926371187, 95398621, 161453611, 365414631, 462586106, 208080916, 345781644, 7511218, 444041281, 79840778, 692697069, 199584301, 455016426, 634099348, 506688793, 244843186, 789951549, 545865361, 679136909, 763872912, 340225135, 485242619, 839000228, 315476422, 528414121, 854760270, 379918146, 740580369, 443821571, 122870360, 448299821, 105192927, 953083952, 640071690, 655340548, 910135206, 379472538, 962371996, 522855417, 122311976, 692069727, 302246514, 65230571, 639809730, 54596846, 40949993, 460901447, 100460405, 250974929, 415768665, 560829328, 300407099, 402971884, 895228548, 344368551, 615397622, 316058659, 889257904, 701676199, 937052057, 613950908, 573691215, 728140509, 340808082, 179388436, 549606912, 267792559, 435008466, 138435118, 20777715, 991384825, 390648809, 388964178, 56366842, 935538343, 370352349, 305247657, 879573636, 391723605, 907481003, 273859616, 804264557, 310869690, 429037401, 171082084, 948646918, 540553847, 752326316, 577648768, 968817748, 930401158, 952844076, 527801766, 46196544, 663225419, 836300029, 955879691, 336373677, 273215885, 53036583, 397679743, 138773600, 874893867, 802612402, 862423961, 72429759, 803013643, 116940272, 633333143, 360594158, 527411713, 609111484, 452453260, 927061425, 813104082, 91426422, 603607165, 95056352, 64259509, 401909311, 440998377, 290352476, 704783341, 784771796, 219138898, 162999573, 516078916, 843011621, 834516118, 164232432, 848275964, 606601134, 660548613, 514399901, 248553558, 398421918, 208708432, 979868725, 978741610, 770441288, 834521664, 861910069, 610035074, 864817631, 181422317, 665812786, 332518796, 745515057, 57008302, 57214060, 342438836, 750958455, 432970391, 736007462, 949669906, 938719753, 45280827, 925194144, 590060207, 444618273, 177981707, 135535820, 342963461, 543090872, 341717799, 802879826, 663906289, 862898248, 405759778, 174232381, 568590745, 3806664, 120063290, 502235625, 950086944, 633095354, 528055635, 732266173, 225563640, 422363298, 747802870, 360535286, 786322558, 711908937, 172964083, 795401515, 65060286, 967934678, 529201948, 405284656, 80172118, 210164321, 569917390, 776267479, 172317742, 251810076, 731260933, 954367777, 868104407, 845439435, 874935226, 478304449, 397710981, 186743545, 906951060, 713476243, 51494650, 547263728, 134842154, 273411638, 990318699, 713044455, 327074285, 989234602, 362924792, 71968523, 810218206, 881174088, 311014096, 368723565, 173991069, 227198604, 893953964, 515891033, 418667503, 75150141, 749025077, 600873436, 253901141, 833782232, 416672224, 656512339, 538226918, 988004553, 120667155, 72071135, 767647616, 845882916, 371848383, 295492123, 592481539, 953016120, 671750511, 53357565, 965917790, 400883185, 186690208, 806785485, 289102142, 803078110, 321138208, 128319976, 216813285, 299565765, 193488751, 769841045, 771624107, 829256226, 229854680, 135087996, 328513372, 208055752, 208172716, 640084476, 817400228, 250853764, 17682415, 978016203, 645404156, 701135307, 840678829, 824452694, 996486113, 825577718, 770503982, 660197991, 138191539, 567496303, 642055588, 118256655, 242113082, 677231248, 135368662, 212294923, 988351679, 91372843, 565494411, 959113202, 719124321, 405050602, 427115346, 494594590, 128309991, 814696736, 174880372, 108849250, 420003498, 543437465, 229102601, 964375894, 492662831, 84170181, 453419478, 499909203, 256748900, 503968589, 829334141, 509317875, 21178403, 620606542, 737104928, 913256291, 74174679, 25086263, 144497122, 784663875, 615398998, 915747568, 851807771, 257609176, 186825763, 254988612, 458321882, 410483042, 649959978, 450327392, 238781305, 533362603, 258798495, 712061847, 640801863, 696980364, 894769779, 398301349, 532200711, 720456874, 588490531, 104742879, 520375872, 408293925, 493120375, 812605193, 713564059, 808941365, 742386286, 779212424, 961983239, 120999008, 650018076, 721332699, 855362666, 827149957, 41480236, 369849538, 151066211, 597430612, 396749942, 334065209, 150505849, 553221471, 703124163, 309945965, 936951909, 850334224, 900968399, 359895856, 82690407, 523214982, 156578629, 95239291, 213510723, 5942503, 113524398, 782131022, 637124210, 364145253, 439664634, 869533141, 389712987, 290602962, 866518109, 650411546, 917066114, 368366395, 252617773, 161337645, 38255470, 585026389, 291941039, 613789962, 139664035, 654735128, 591783057, 738698558, 847593502, 683620772, 282622128, 54810602, 783487647, 498321300, 353700684, 911455399, 339256666, 805925424, 710005918, 57422114, 544373664, 497960573, 821070017, 788440871, 306340048, 41587780, 995614405, 682743467, 625733861, 596448524, 608842554, 34473294, 618727479, 140309785, 361814131, 970294765, 702128076, 3609884, 810403316, 847157012, 82668212, 535737415, 996864337, 319169824, 328622606, 656204182, 22421427, 975525924, 557639087, 705216722, 792536996, 258407694, 312083872, 446777978, 701732890, 43495332, 40782098, 208540652, 732348643, 173888803, 479709551, 916948884, 395367103, 915462133, 221251401, 847348147, 822407218, 486775119, 960237140, 758289248, 281094157, 167609540, 239879679, 65583131, 273765774, 467374466, 523843373, 669292872, 838193755, 324209645, 953845116, 342703282, 586198084, 484245637, 529093735, 396981882, 856863887, 20653222, 503809689, 65363777, 699986956, 75799830, 108209511, 490087159, 147517448, 885847199, 220854374, 777383441, 658700683, 673872667, 943059484, 749594386, 163085153, 586228628, 723029575, 123337198, 877826264, 998620928, 995086268, 36476548, 957079972, 742886357, 545029917, 646041227, 713427668, 488662826, 944570458, 430244918, 277267621, 111444620, 249865029, 65000732, 616857212, 990790791, 893674609, 591121472, 414169108, 799415556, 624606139, 534570912, 300838498, 617511783, 255492741, 118707835, 878116054, 55094317, 291034470, 155801131, 487425725, 384061158, 711667544, 870794404, 406135588, 141105459, 230678240, 460834192, 659708304, 117798632, 738763977, 15712088, 963528836, 431795941, 377966294, 865887238, 958904987, 561980350, 414876452, 845325659, 312348938, 750279741, 448276827, 695366638, 60677360, 721777143, 915668548, 792934153, 216025496, 893114311, 961457747, 365996412, 267451076, 308176589, 134374243, 624651912, 776467895, 306630913, 2040035, 274443754, 648310201, 869610574, 913840977, 506779440, 768716144, 964637619, 749204165, 249329310, 250094090, 30198460, 842968772, 718736270, 585929524, 116420303, 45693256, 681817716, 6052886, 50276707, 383976558, 249441181, 192727430, 749385571, 938004342, 840933323, 379819809, 495168586, 879107236, 339206318, 168860299, 136089309, 79000849, 910671791, 253146117, 704091437, 5693375, 186309511, 317281861, 942456901, 660214106, 244562658, 31335059, 5621375, 107650765, 826151896, 794016230, 375245698, 707548589, 267769862, 828516980, 360333558, 937285000, 888112082, 863395708, 45399429, 911069616, 856125081, 691481880, 422326842, 380759066, 950035325, 955588962, 709362004, 583250164, 624005174, 241685742, 6040932, 84814836, 179979386, 719917952, 383389327, 126581096, 114226316, 898494431, 369783828, 96706160, 624728275, 822867800, 833457479, 969406762, 543246700, 680573176, 327050651, 460094128, 736894771, 629527549, 183827756, 386046602, 840162073, 961813726, 781451628, 280526096, 521089685, 244949700, 92006792, 438329328, 506161326, 156620403, 582179580, 496898009, 702936726, 38719508, 11196495, 628328628, 679286830, 611394390, 376005652, 54125197, 849202566, 224209632, 593303815, 479845812, 138746377, 744122466, 336841673, 282856905, 982440171, 964222891, 879566905, 973304576, 143482747, 668602617, 925571341, 40384638, 489823218, 171851342, 293863085, 280501482, 620990117, 510282968, 217221996, 304514277, 536172141, 848456771, 869420991, 23031969, 2403360, 115933752, 869327245, 642606394, 852517504, 664163415, 379289784, 381517791, 318031937, 562177528, 388126727, 311160038, 677721920, 954885203, 181044309, 149488420, 729192681, 653219526, 648268479, 705219699, 496322801, 883342833, 19867934, 862365176, 382424050, 592072399, 702439745, 150058522, 7792554, 330196478, 844548458, 929076452, 691840621, 859228725, 137481513, 96440015, 864373503, 538689326, 279498098, 26505048, 267342133, 308405171, 223646938, 78468692, 173867283, 254431212, 391277549, 260518649, 513841803, 286842385, 721252440, 145368771, 652464904, 4996741, 907820676, 827606718, 895417574, 603678792, 269078120, 910638208, 998877642, 102097464, 293791174, 525259669, 291533628, 943163234, 598170264, 819464982, 99614222, 879384673, 805082667, 745196437, 100261338, 616597808, 178135071, 302583294, 842542016, 904090561, 433913451, 313075292, 458217045, 991827093, 897761584, 446559836, 89149555, 466945915, 410729534, 294724915, 547468817, 624856478, 925309014, 752980453, 908602923, 735779725, 541367426, 321740189, 889387093, 851551625, 922799365, 563438940, 790018415, 108761872, 542373716, 126568307, 373819911, 608107380, 281237818, 885188807, 702335635, 411777949, 544846278, 262588329, 506697893, 604640215, 365674032, 81255754, 937671589, 897428095, 216842081, 540668751, 650356782, 248431055, 718252458, 69039927, 582791498, 152285342, 501189710, 189988715, 147311914, 572342649, 868333231, 637551693, 152864102, 283067174, 697481431, 612574474, 857269989, 439821041, 646532192, 61150072, 280017938, 750261685, 914651943, 469723159, 903329042, 158643237, 722637597, 989068004, 453342508, 794520732, 707487132, 77224132, 946136339, 517211104, 30400901, 223038874, 736943273, 204255053, 145475994, 173791802, 295053703, 605032254, 617444456, 689777454, 529665365, 856014741, 501213152, 261768385, 315075845, 435978260, 686797767, 791499753, 988157712, 132942753, 747075937, 522926557, 868903912, 966534170, 146990149, 880359181, 635622960, 640944254, 107253002, 705779961, 40880445, 711820669, 189352736, 141724546, 887996957, 975696402, 50716579, 58361263, 167737259, 897382505, 886890532, 732971476, 412912407, 466697832, 349063970, 108417843, 95214620, 27411062, 907403164, 319315737, 572077766, 420665712, 174342107, 187540287, 189462699, 641497117, 554047759, 492877625, 67153768, 313281764, 786103646, 161600140, 685493773, 15727141, 686330885, 918451195, 937246568, 122941297, 316540687, 855328612, 586936050, 377215988, 874512045, 315172995, 218631554, 119301384, 741119379, 339991745, 398054156, 867407748, 402109908, 905122673, 796533267, 505549203, 271269422, 776164798, 242900827, 384525687, 167588974, 729498583, 760254135, 288988518, 226207255, 113486713, 480193474, 646742136, 366425919, 890162803, 456805225, 97889396, 180149685, 323848052, 318120083, 588491604, 32168281, 423536617, 194400977, 393054968, 934319613, 487035183, 558203519, 38343287, 747372738, 914247162, 983794261, 869563636, 502775301, 917737795, 556029032, 913027581, 361131744, 633796451, 289600105, 429707315, 686816806, 712254906, 589855459, 109113671, 757929480, 136084919, 145808013, 710498865, 15174143, 385352123, 146624841, 84179391, 825401692, 142279587, 10271328, 412781536, 417137753, 676028017, 616038675, 589108090, 199999795, 901402015, 9726313, 494441068, 451243457, 426910824, 209928988, 595663415, 216067957, 548787938, 576457028, 380280631, 669710027, 52430379, 196786419, 194013913, 22699638, 964239576, 142398217, 7324874, 93030744, 698011334, 859199233, 469821805, 742984593, 109560762, 752477259, 777376214, 256464859, 804831178, 786437670, 387482627, 786716393, 382488999, 173093090, 904979836, 806652664, 372345494, 244468787, 551647305, 324540551, 631280699, 528904621, 477451578, 460428467, 437993924, 464771599, 570046065, 93668164, 843117123, 779731212, 574363487, 405093568, 890620106, 765045494, 278294330, 344660501, 605612360, 234753586, 509129454, 174263819, 559264096, 970748628, 686047207, 972250215, 971578086, 879899974, 464873924, 333267359, 571128449, 668047677, 1315412, 575248346, 360552127, 398433169, 760957081, 819620651, 422835023, 404256286, 781852028, 767121210, 37616043, 627222224, 785603108, 915113563, 914523147, 842696998, 843023999, 615809434, 105672746, 465116443, 446729677, 424899913, 633323028, 806554152, 739234414, 573639612, 8681214, 379037232, 471297848, 839680597, 961203742, 311505698, 381249240, 987733529, 787421331, 87092745, 515191816, 385083828, 836212424, 186511111, 406291124, 78223012, 641669711, 446738742, 98103213, 492442596, 556094176, 683791756, 142005826, 486569480, 847063919, 79118346, 618766756, 169021337, 775438290, 244685567, 360328672, 611086753, 175806109, 443432469, 981771862, 753211342, 145256366, 423999772, 994900226, 109933282, 175545506, 949248007, 369505788, 840264969, 516307906, 515696986, 75847231, 454655763, 53675232, 842300706, 750186951, 332221722, 856303263, 680227590, 285959334, 823956377, 484521155, 382988359, 37289298, 114220943, 388396086, 837166654, 766795666, 317458489, 863020035, 947511551, 548081507, 860092752, 787770150, 169178358, 758656518, 920848849, 21935408, 477563899, 159974083, 417606807, 249955546, 581161184, 135188060, 181102451, 345737372, 874666236, 173403177, 854047106, 845256252, 472525942, 571488862, 922795640, 55229047, 16519677, 465246657, 692600669, 524250574, 925909928, 266131769, 198568499, 496362599, 749644697, 801731321, 741346089, 166912645, 807194391, 750803843, 479947672, 545805856, 880714384, 902669325, 115650326, 502439626, 350328138, 750364580, 695344374, 10898638, 149407600, 169525729, 987272183, 284826705, 212466082, 394205213, 558572020, 450027512, 677244651, 911293563, 730879909, 668398884, 164108577, 901263651, 7224810, 103008061, 597925226, 837244357, 979824041, 997237104, 495409998, 604145855, 133056594, 405260661, 969199540, 686432691, 779456802, 439012297, 167911948, 345717177, 902092201, 820855110, 671775931, 384241136, 788306214, 142073819, 723611588, 118060636, 740466141, 545729953, 204468346, 276824202, 936999399, 170988085, 253058249, 935450875, 776225555, 435570397, 428527838, 172368642, 968762406, 277014176, 68804476, 588844969, 824432129, 943561090, 951859344, 704179808, 910835750, 635782282, 561755844, 23927519, 34961530, 57873401, 135261584, 856183502, 289543179, 310710548, 589522679, 974783884, 138441568, 684162377, 206624516, 323365164, 48735853, 295776384, 726840673, 970200787, 84893370, 987346885, 453992478, 401267192, 104514580, 122467126, 960047374, 676286238, 328406004, 879612854, 330806280, 623119198, 287796978, 115681200, 434792424, 193214927, 396955648, 645136627, 612626178, 821833431, 588629284, 865773586, 358715628, 534929311, 754542026, 31266973, 434056109, 724676238, 129445261, 260137873, 309290115, 85959716, 644327922, 775238502, 544371785, 757518392, 733337223, 814356023, 522434840, 219910292, 704315631, 549337066, 324328208, 32412538, 864508285, 371906508, 884348460, 120517335, 861331369, 540673078, 399758154, 493272787, 125690745, 651214754, 89808244, 169313933, 366996503, 802839105, 266163863, 785603349, 892391138, 612459085, 633362332, 16002821, 457720408, 408246392, 36140619, 353949156, 104354845, 151231555, 272477312, 742501898, 327133701, 939717142, 373149202, 390795780, 416300004, 783608911, 504104304, 24790872, 901678889, 339747126, 328096093, 513405218, 974950604, 340372807, 471034700, 464522636, 747844381, 126361601, 735932726, 660950437, 442218269, 5169337, 176412258, 595414654, 628916348, 262804703, 650287156, 102070008, 190920062, 572742954, 77424605, 8080988, 675555805, 984042418, 811405737, 819112519, 771084530, 677667522, 354222790, 665374768, 642018561, 326979272, 993991889, 663038809, 24525989, 203747684, 147086375, 526862454, 902320037, 634626650, 991503149, 872616195, 672012880, 535402122, 89223873, 976912394, 919780616, 301767790, 451372875, 994840759, 121064439, 881777420, 759185788, 439522462, 110591184, 153304562, 856711434, 38897324, 851195622, 753228306, 192973733, 480811236, 881292283, 167369436, 928289705, 264432453, 196340777, 414719807, 343572055, 235141308, 673986631, 62031678, 113702595, 424579450, 368092258, 292954026, 756138717, 993667444, 701907719, 904564739, 614003761, 864020681, 869308294, 227981502, 570035238, 491086580, 386559437, 112925895, 877784567, 565585825, 265120540, 585717697, 19279616, 111806055, 859388470, 564246350, 131708844, 993004515, 599380275, 64232783, 900746282, 969205720, 780059120, 383311928, 751950725, 886917793, 333420879, 525208054, 864274078, 920759863, 666313790, 467161837, 701971945, 116867615, 316777974, 427679227, 330265914, 314664380, 779435621, 591378049, 244772413, 905114711, 121403507, 496294515, 304829292, 958264497, 295964082, 813916582, 413108884, 297351242, 640858708, 746159701, 577151031, 89330305, 770320329, 912964735, 12641253, 212179348, 642812573, 676754719, 427273094, 29440162, 957563277, 417830568, 283443017, 820377571, 45194963, 604603131, 104704064, 277310183, 648349986, 50267902, 628786627, 590790291, 109672105, 68625330, 217507785, 963501086, 902955930, 697973686, 672864582, 438045464, 293016391, 79143659, 944536705, 161376927, 698763531, 124933867, 28508763, 715187434, 501194922, 806948934, 484825230, 946674623, 779171017, 863705488, 243523792, 990789744, 844773823, 944305284, 878020014, 727029741, 688718605, 967966295, 105937027, 186442814, 20963697, 158461313, 841243046, 339256980, 800451540, 66649361, 171250225, 635613761, 497558316, 62135445, 630640182, 553234523, 400729659, 546500294, 357251952, 797329474, 439147213, 883440148, 977957895, 909239824, 185119335, 158331881, 446882712, 146738705, 626590085, 720532902, 855342079, 184606911, 268149635, 852929652, 90466114, 578334001, 845316040, 728487415, 836278929, 613536434, 740307081, 953461791, 704877756, 119104264, 974730116, 631006787, 138634295, 206025974, 591802989, 995231874, 46583479, 85293039, 613131780, 677608091, 719096010, 741467263, 159148696, 581328965, 298421884, 161335058, 415049051, 314350238, 144941321, 435833458, 541269302, 658680689, 12942941, 611156885, 631203752, 989849731, 755566103, 166833322, 536975517, 201223973, 422987224, 965182124, 177211510, 947267070, 671903398, 158185386, 67287874, 238904179, 115263378, 656533069, 685554748, 648184592, 307919540, 636150478, 699515221, 312586183, 339051267, 989628227, 440664259, 27000245, 995618670, 681830749, 753006289, 496251963, 192218944, 422255232, 659261828, 538451436, 184319702, 153403248, 665154128, 531436869, 164747754, 493613786, 853211562, 807919139, 762613321, 253288982, 290144289, 959207628, 698540361, 290170650, 391833554, 863332348, 505037054, 207681565, 280265789, 646204215, 480990857, 173437878, 4133267, 877499028, 903654143, 168468912, 132143966, 164878037, 343953906, 627857650, 671123811, 468421683, 706243530, 81090228, 691688622, 552071464, 381826160, 223341874, 763763880, 393121846, 693663717, 660973379, 792850084, 29739209, 499097788, 767738308, 575905875, 880573401, 533564032, 385994781, 253001633, 241881877, 854804793, 99592903, 561128596, 3793418, 876501290, 483831437, 746690276, 607151719, 732424819, 834526060, 800869698, 129826897, 673510509, 749130938, 828915787, 181232128, 387805042, 306887078, 557503320, 11432293, 688320796, 639989493, 548824434, 413518421, 355953784, 334291595, 95017942, 685235126, 746680276, 462684320, 66579030, 390244133, 857303230, 268097276, 942955908, 358337529, 878364776, 567549478, 558110597, 34350581, 202415957, 939448970, 628566047, 404074597, 401750451, 667177372, 519132487, 233792430, 402154612, 813526172, 287606698, 929831230, 587396961, 667372471, 774939868, 782199570, 617926688, 30397591, 277671519, 588569425, 312911041, 954274723, 81808406, 155897438, 69335295, 188480018, 188559261, 852132854, 609851085, 422916298, 980838387, 928688495, 515701843, 264289996, 510814903, 501831891, 244192687, 665789970, 576770407, 183231769, 687199705, 43335190, 191477944, 88670275, 175056838, 396542849, 636933951, 37115479, 628116206, 348867187, 393337622, 526779067, 88066075, 52786817, 303616324, 90634726, 807820573, 336516398, 748874138, 682162939, 713409863, 371870220, 991011966, 326168442, 461123312, 272725188, 741702618, 423520048, 793898017, 48076187, 53296261, 994289971, 431756571, 972631650, 922145511, 428827434, 90673339, 378053812, 965089720, 358106043, 535091696, 640540929, 818869765, 465406593, 612380157, 980148596, 448357509, 777845781, 931824592, 760504189, 777695628, 622385795, 973440549, 411520968, 425844160, 2308976, 263131226, 345438225, 37477582, 80127711, 915494220, 672880491, 558368527, 341365166, 922516281, 494103904, 941087785, 446401262, 315792535, 423197810, 121211067, 808600376, 36400447, 796562417, 790547749, 863179304, 948830356, 306964615, 612903785, 319446501, 599213092, 5559618, 848667123, 904305978, 741122130, 168373533, 656829688, 384740606, 140705598, 881486977, 78241897, 451518588, 363889516, 946459809, 214866693, 147194736, 487267307, 969515007, 389265043, 930099033, 486905320, 777156614, 587667016, 602989752, 714487522, 657815616, 951194162, 234151389, 408164758, 216856250, 833870627, 830763206, 812820194, 981900036, 821089420, 961008726, 642463633, 420258103, 9607129, 92574865, 708941547, 682317980, 187864095, 272214852, 629276777, 589906609, 993359119, 974072519, 269665342, 965426433, 410085088, 852647136, 152318221, 549354889, 270119654, 52293813, 808349799, 873819139, 758056944, 606597632, 852721045, 380988095, 109301435, 290735689, 38339651, 149245121, 931650963, 361863204, 647405341, 473794909, 153485143, 663469861, 597070604, 47946943, 258426829, 491546822, 500270183, 941119505, 131772229, 8535683, 668970014, 173243275, 983319890, 703369069, 282684238, 784908490, 580627357, 453398057, 757407559, 154320054, 857347756, 122771130, 274189124, 765426827, 798104933, 623302164, 399575841, 585331135, 7633714, 657262536, 557089941, 365824625, 503196220, 155948854, 55267802, 493665358, 486338398, 7002675, 9361687, 853714585, 978809620, 869000395, 331819430, 113884386, 829596119, 281616493, 534092351, 652910443, 164523123, 414284079, 162744302, 631097122, 598304247, 860111520, 944145615, 992768323, 297806878, 739804089, 703811844, 195752746, 40738492, 730032013, 882232229, 73360819, 957877582, 236587538, 558257581, 298082057, 449058231, 864236040, 671446697, 62101273, 871481098, 880902894, 146292490, 796820209, 21269340, 823614629, 337205704, 974120118, 514624063, 764450517, 475388457, 836716410, 240065753, 433805571, 574949866, 778536527, 264139462, 860881301, 510602636, 671793327, 631759217, 384872563, 272756826, 22614209, 560229531, 650453131, 688872240, 762163853, 653451338, 672517745, 794110168, 516329896, 510602764, 645801638, 754597242, 639424745, 419060302, 741493693, 254099501, 533368208, 744563744, 52305141, 266043798, 285301247, 944159409, 660889310, 54897384, 457616214, 221757963, 134731181, 557905126, 263189506, 950638005, 524049169, 861788234, 335373935, 820458248, 541449747, 203388529, 988734720, 600382550, 766970017, 482486163, 108002717, 242251301, 508643965, 30168412, 760223886, 702057615, 619471967, 160879213, 323394390, 457241076, 39471965, 138393924, 720522573, 791113189, 975915450, 361373880, 193884331, 239570123, 762029162, 551479769, 680428715, 381398287, 533049481, 766063475, 189565, 101120392, 211375086, 735657699, 27382887, 571430497, 696313221, 492436238, 206971646, 45074930, 60380878, 815365300, 275802676, 744456861, 598704308, 747763354, 18862222, 575618843, 881474969, 303594614, 263257543, 512966554, 302516989, 767388024, 356281688, 163980725, 868498089, 349554781, 684549183, 565326615, 146905698, 682887855, 732354805, 470057824, 466316545, 792889865, 733185768, 121703952, 621223662, 860066789, 635336993, 356325759, 584118690, 540906570, 651621050, 316623202, 196707973, 940279071, 699314209, 91483633, 775572796, 357933444, 706366183, 317036797, 715555695, 716698625, 64872433, 977717333, 814118395, 558631240, 397904732, 795518088, 719467953, 174254994, 257017267, 513850330, 951242, 66562384, 109510266, 908280088, 857287324, 578693545, 668523045, 920945053, 142251290, 973939538, 143716328, 424776494, 655098100, 189373058, 83338174, 318232550, 959118902, 202982793, 749806298, 247443266, 826073748, 894856575, 461141530, 977952946, 397463823, 212939722, 952397205, 44919732, 761073618, 765341980, 570426563, 501845343, 71225867, 775186908, 846486757, 28859928, 908958646, 609812095, 270008009, 692510560, 848063991, 150044616, 420026657, 341019581, 360223401, 397605094, 470384589, 832610982, 568267689, 8463995, 13479886, 129855231, 896364339, 844452822, 497461590, 7683608, 14297627, 370335036, 957098813, 774020849, 997666418, 778743822, 358389441, 860668405, 437251506, 263301446, 774340999, 110375477, 986103967, 574495450, 457642435, 823033885, 86964384, 420921575, 124491150, 134939379, 682972872, 136409067, 98059250, 258249833, 859303320, 811422452, 377569614, 343259905, 285732365, 289457387, 516183345, 901333764, 206344330, 588999766, 447045962, 107866037, 777264668, 971545458, 942917129, 65612185, 397877539, 500005910, 601231484, 584866924, 810107792, 236807618, 849906509, 219468453, 201672445, 496311596, 158587420, 377931892, 310266556, 880197548, 659573754, 334610713, 127086496, 13187515, 684507258, 248709292, 131948838, 936047079, 720930638, 143964984, 392159828, 958840267, 299426757, 902990624, 745983898, 349777857, 277148258, 160426023, 293298536, 566234313, 365774446, 545888426, 555597629, 563543207, 962441189, 85610547, 667549578, 509813821, 980817911, 189531190, 997366636, 112267383, 735116577, 389501456, 820774109, 773092196, 208232467, 842205993, 522378727, 255195857, 382744340, 48690615, 733705136, 99753627, 963031566, 826806741, 857926542, 615857736, 913362156, 535866441, 372665638, 625152741, 668814353, 254262887, 274528504, 254896641, 417144313, 773173053, 986248592, 607084492, 223037182, 8657281, 444632067, 701942563, 98747562, 133452126, 111802156, 168220044, 875083634, 80652495, 191298011, 704568958, 682786406, 106254890, 135051686, 656892670, 678239385, 113737142, 369004430, 986108623, 38051113, 343281324, 289003289, 459546960, 409168561, 678081050, 619360426, 489761656, 809555189, 337755147, 823356521, 662918259, 880731524, 679891480, 74308720, 751374405, 273278292, 125039358, 125462843, 233239230, 488440023, 38574359, 766096821, 591746525, 543846736, 515009006, 331844527, 399980769, 680370204, 225058249, 60427591, 256208355, 499051236, 637568052, 644693788, 628380009, 716606277, 38936640, 314348400, 722691726, 537176057, 772421605, 611676549, 994061986, 800582178, 532982308, 519257327, 588402868, 889093559, 123020046, 257221162, 890316372, 971156685, 161986471, 84025251, 208510470, 292491764, 356274076, 467200713, 422884779, 721005973, 306923806, 71403984, 889330467, 886005622, 539204090, 712365581, 5746694, 729476968, 409578938, 753778707, 45017239, 434958151, 364125033, 400361451, 440240001, 947824036, 194820592, 757295590, 558621791, 485465046, 77360325, 899620370, 452261402, 883551081, 338069482, 933988410, 491497380, 427018506, 545430794, 451251160, 786910570, 846391510, 12946995, 729130174, 930350736, 256844702, 790942182, 599732083, 693063061, 654501420, 48613653, 348721724, 44387399, 185459462, 418237123, 556799678, 478819446, 16790919, 121680798, 811334228, 990725278, 275349497, 316747748, 708619453, 981705924, 313720673, 194780282, 681631747, 994990281, 904324442, 505337666, 41905271, 20736456, 636381956, 53217061, 278472380, 775461785, 230802630, 435366422, 636925874, 497077266, 168096531, 945079510, 674167268, 374794393, 739197192, 235098740, 144484762, 705432650, 111654064, 872170786, 368949717, 854288895, 797413668, 712457590, 131778527, 267080596, 18482040, 370640656, 444555198, 879767581, 733600735, 499960367, 508264535, 883272531, 29901534, 28276978, 892127334, 308528862, 594552735, 14703182, 399944342, 470097397, 794111169, 344548938, 830006228, 667495670, 394435250, 427268117, 702462972, 445871304, 371296562, 550121952, 857933170, 690322820, 500092437, 243154256, 799559143, 386208996, 786089936, 543845204, 726380496, 16579011, 792836190, 837761144, 385262983, 848885863, 351526998, 48355548, 852889803, 400630227, 527883, 194266617, 61850569, 267197123, 718854175, 433706626, 227026490, 79286891, 900564941, 357461594, 811134515, 838515500, 610320407, 824004238, 282414904, 332959801, 892058376, 666977620, 597113880, 681365944, 624152638, 99365959, 213733997, 439967965, 708269304, 626067516, 754327928, 149027747, 783459859, 78556245, 104215025, 177553322, 244437985, 270860107, 669724239, 621179553, 51130954, 369930914, 123888134, 371855697, 686528060, 962432831, 461836821, 8434760, 515561816, 634552928, 998628500, 509682800, 144368701, 589073321, 397322320, 791425102, 258557762, 499241934, 802004059, 258628476, 634190072, 528534108, 977038837, 264055945, 407267927, 91250704, 797417794, 699548689, 161492882, 594569517, 575766019, 309782941, 996699681, 100311587, 581401902, 245351868, 811705570, 506236972, 47345294, 166607292, 767296710, 111712498, 771297281, 192143776, 233381586, 948857049, 179568849, 664784547, 113577378, 259169068, 326672036, 881726804, 834228289, 226708901, 625898140, 701707518, 275817165, 84995619, 291685938, 804241947, 326555597, 558277701, 695222769, 328749793, 352384839, 6379177, 813371483, 40885829, 865600004, 975642402, 942417976, 90426819, 868832853, 67694679, 213406376, 51936320, 515245201, 627246035, 90812693, 213118761, 380602940, 844927114, 790529589, 663437904, 997626048, 22866967, 973065364, 344483035, 372284541, 591857641, 607359304, 388481549, 20009794, 529649628, 574914543, 415148379, 410091619, 755528352, 847528210, 867707961, 595763659, 556808399, 201815016, 579064470, 615044085, 239868114, 464156397, 718128325, 10130726, 192480368, 736655160, 515052230, 966518620, 118457092, 901003382, 852669659, 655963897, 991785442, 569577649, 318546591, 65780804, 984590241, 99536372, 918660682, 563404242, 321792499, 200246349, 829710026, 109880160, 364933903, 797068541, 958174495, 101305114, 962588940, 791715490, 714797680, 42464851, 291702751, 159328334, 163578438, 135995336, 635171651, 330364756, 75395356, 417573565, 928928188, 867562478, 931715414, 462908990, 117823921, 502760293, 54766721, 626884844, 52760715, 135502623, 329515299, 236575135, 54669419, 393370485, 742994025, 612896070, 969906064, 744575734, 375476278, 708387027, 162073790, 433296239, 296806586, 134135163, 705589388, 787550203, 620008721, 816729488, 65205457, 412267277, 926368814, 996381961, 266273453, 78297156, 973351763, 489376840, 595514169, 931880495, 932746749, 136058413, 555843195, 230655291, 420253602, 828718340, 867459390, 907492197, 869571401, 781400921, 969802638, 216001598, 697851562, 465991123, 31617789, 857757723, 334500063, 16605778, 365810172, 580127622, 714585498, 225351720, 451141314, 20713292, 742542149, 569955635, 391367633, 634648906, 850346738, 338510100, 842635913, 60094503, 857098370, 282944470, 975492884, 118073330, 284597120, 605041287, 551293071, 205390428, 292326507, 487651066, 63255978, 593791125, 835961062, 368132549, 123623210, 44009127, 966998658, 996387344, 638019352, 855543090, 946533314, 656647970, 581398385, 594506099, 158874824, 167263850, 130751837, 344287795, 622815643, 312981049, 139556248, 405345002, 508285648, 714029900, 288582674, 913051308, 140496675, 597914383, 471694735, 626033198, 163119029, 541522457, 553993733, 95134529, 325524863, 379235376, 157179076, 984150500, 28707506, 429593366, 983562641, 540546047, 449166623, 705791123, 598238456, 942172317, 845739633, 190822179, 787587756, 811376642, 964601497, 371837002, 181257930, 888552022, 564282644, 631323464, 595162705, 428056724, 817177755, 167356554, 120733716, 654969299, 442960663, 239114640, 215334770, 664206241, 852528008, 905130682, 377179487, 395250533, 333158642, 528936636, 617730109, 249051943, 893822302, 639908422, 888520442, 370438288, 558368279, 638689701, 818641426, 639491930, 912350796, 415698866, 823406448, 786055346, 132746556, 857178937, 377961361, 45201021, 51482291, 330358675, 873834732, 604952816, 126749743, 443226778, 532163397, 190265359, 756933818, 829378089, 115082067, 392027694, 826583691, 365101597, 927935694, 578828954, 42507967, 369929159, 941520983, 105033910, 531614696, 977880632, 868925378, 617670505, 514768005, 197100907, 877010240, 520010903, 552071571, 374203961, 304476124, 201131227, 860234386, 698967019, 838963729, 760745867, 510120832, 4118583, 86882415, 431863697, 533967838, 375151870, 493804541, 510490995, 663142128, 24567010, 729625518, 635398278, 57444789, 130217231, 548026763, 6103580, 985685233, 562669861, 436069037, 865621127, 206951863, 728060701, 828592391, 885619086, 573007230, 294255222, 334418335, 695662093, 465884063, 991794096, 282518991, 560446157, 390072245, 785090926, 22378277, 440646985, 340998062, 49089970, 429819785, 232998363, 96065148, 279459900, 385092677, 866994852, 863798772, 530897695, 205913248, 25135402, 90015724, 411074567, 269316140, 380131457, 325742051, 925807185, 290810311, 229482764, 137142909, 787980627, 391722663, 561304854, 751848830, 637151275, 974935982, 501488681, 636638552, 690595246, 897025917, 563356791, 250940369, 56890834, 986946873, 104537729, 53152191, 518719585, 261221993, 499424158, 259557835, 989768536, 900384426, 787155345, 756155367, 767468641, 181761609, 141934490, 968340124, 320006524, 140828203, 972351710, 159575895, 884847720, 818866032, 965732033, 335861521, 119264017, 220482273, 116244693, 146305887, 460347187, 661233697, 184479766, 406581192, 733741534, 742650271, 304095558, 195650808, 117653029, 587648923, 325061344, 674985417, 352776258, 15112235, 382332755, 560964830, 890304758, 691517517, 589519181, 644854864, 372550438, 128273037, 652897499, 312625053, 415020962, 658413576, 718119278, 578532184, 425226334, 937064026, 269457175, 780869638, 966765327, 361818342, 267176183, 231128245, 773169512, 425920594, 210605726, 559218655, 889183819, 158860945, 552997704, 541769621, 711747694, 699638039, 93693001, 67404367, 200199552, 531263934, 282655665, 3978583, 447617790, 728694867, 471161075, 868021231, 595764087, 442668860, 954476583, 107328192, 283711017, 582552405, 540774476, 617412413, 783914378, 280321307, 182546341, 152483369, 318618212, 423512488, 946908417, 419497417, 703130351, 425354287, 345933080, 242653638, 145408295, 623897849, 700781204, 332826625, 259553187, 714598342, 483481347, 177938400, 529214126, 611196362, 809768779, 109040785, 297104054, 668182681, 103440704, 396034815, 330472982, 879164094, 723754370, 448681928, 792338524, 379695686, 513252975, 372073981, 605490492, 496136936, 296891500, 542263927, 493442740, 645087890, 907999627, 622165741, 178424517, 276571480, 391296809, 976754921, 824578320, 841898481, 573601191, 869523423, 205216317, 539569214, 380679777, 525371321, 191599629, 148959745, 359950980, 295577419, 749743431, 961620323, 101796392, 325018232, 56578418, 980852318, 877011376, 756227107, 374877413, 988824232, 561416621, 687293894, 473890706, 689391123, 333086588, 424038509, 107662378, 63915548, 187623237, 782816897, 12807847, 753622518, 125553493, 836467071, 712155463, 351164180, 129269701, 628888079, 313211891, 542828385, 718282002, 464665731, 347789710, 811357774, 348950359, 8893495, 933272123, 916326722, 215081385, 860933515, 750410072, 401127595, 703085033, 119672352, 7540763, 308861885, 841440004, 647448403, 174779130, 141108640, 959400372, 452283296, 773331256, 976085509, 477129306, 338160606, 655306628, 120851368, 529677508, 468758804, 612621141, 578021312, 212423122, 486626213, 807602376, 693585176, 133610120, 885935480, 499943638, 949691093, 445726037, 820548363, 653481506, 891828747, 214425244, 823329175, 861664407, 451702996, 15561468, 662842871, 871226380, 677965261, 964695954, 495104508, 764183029, 517393049, 629359128, 322159489, 400086304, 388612692, 679859780, 716407516, 94428528, 757270083, 446103218, 848011552, 748007006, 472605010, 772505867, 411449216, 973038743, 341262176, 377171878, 523548824, 191388222, 700886056, 955040313, 477731091, 946516138, 253233088, 55939593, 192054127, 142046920, 863871387, 908712376, 82855742, 185497439, 245925490, 777293339, 336899677, 120459645, 420741123, 26995587, 642163373, 690930764, 415916794, 906033115, 946442969, 797541982, 537779170, 302616715, 240308021, 926090576, 406177979, 105332077, 979642855, 485177059, 828185906, 832258509, 132004015, 267201158, 907202205, 827427842, 377685388, 127294971, 90818868, 173869471, 559710524, 933738157, 525840897, 970904073, 337434261, 266516329, 380017924, 56978322, 845508786, 954058292, 241187809, 147384693, 264437655, 654190579, 987771738, 693421850, 501687916, 108258223, 678623538, 536482064, 495233417, 993508758, 86117036, 940828017, 900892304, 510022295, 379054454, 452175421, 958809462, 343397021, 56058269, 163733662, 378220199, 899734499, 625663357, 695372832, 938739425, 824654137, 314962730, 619431795, 498227614, 532871474, 899584795, 311644151, 89208489, 911298468, 940718343, 705630717, 582446341, 448908397, 982576542, 225611685, 852855759, 901050841, 792503127, 277597683, 536778365, 896440646, 946310053, 650832442, 770693544, 934897333, 75544017, 79935734, 595348608, 96988500, 415112307, 225397908, 419757454, 250607053, 129697470, 175408398, 912490673, 202373163, 233356425, 18018934, 27294395, 946826435, 563162044, 779184020, 660520497, 95645828, 245795560, 661479089, 876558876, 426791997, 789529173, 359755748, 187313877, 482689664, 309772101, 681668940, 551016407, 200961507, 969559152, 985204573, 906920612, 520275289, 424185128, 151174294, 935404028, 975854344, 869817651, 932171098, 450412510, 549306452, 330141635, 428934544, 388134532, 574922118, 766607221, 136536635, 6060636, 955302653, 431668806, 260437199, 671731777, 144333905, 743777346, 475958237, 732178556, 92187375, 50737199, 701913066, 205304480, 940036741, 119382800, 42531724, 571093484, 874733479, 362579079, 396045378, 404717332, 174494767, 425000339, 309208109, 903943434, 940119386, 628890835, 453746181, 992799348, 16124088, 137442887, 236979159, 333414719, 593016293, 530460690, 237836159, 284806492, 497194365, 954104077, 200521693, 874593366, 290589739, 977368845, 263628694, 146016581, 951074662, 951630722, 346987492, 348903702, 31339909, 656530507, 181336030, 662395554, 989504734, 637675896, 342637649, 546713301, 690594019, 806080985, 686717104, 28708407, 433924969, 360742865, 391125219, 155283977, 796881090, 188627210, 173837310, 299715833, 635903438, 570223284, 22350649, 313041676, 437905433, 41032391, 111337219, 999744231, 360918738, 539212463, 837239634, 615573380, 828659591, 230331542, 163773150, 826271108, 751154235, 760515263, 939476399, 130312322, 289096809, 190879058, 924627225, 383865237, 460518680, 735057231, 860922604, 506414049, 685960775, 648746659, 223193610, 668774711, 280183732, 537781155, 795363545, 975252362, 315631293, 57044410, 12443389, 455236573, 959327403, 240158301, 267628645, 545569358, 240380078, 804011090, 157297234, 853109699, 695083052, 123765537, 60460896, 691205180, 788248841, 524841222, 154192602, 348472246, 114833740, 896050218, 591640837, 340090223, 264839770, 92989770, 491485034, 50898028, 952842162, 540889156, 649195531, 602801197, 663240483, 814932670, 168451508, 271268252, 45875265, 868374510, 91791620, 526430768, 607689029, 212446281, 617247921, 659908271, 231705447, 743480364, 663477127, 320889749, 854923353, 31813471, 645095842, 167698409, 277158867, 279911223, 158013388, 714134365, 727446566, 97825187, 708739513, 605874376, 93541882, 655627828, 218025063, 628833145, 380577698, 755752651, 362256506, 404346949, 235575156, 166026438, 924162518, 500369920, 380934533, 239024564, 191124369, 984795181, 403900970, 565570479, 21563227, 568308017, 78110163, 411709397, 547647737, 572208524, 372261271, 914053051, 226095286, 23677400, 930232910, 525059450, 364804020, 369379173, 681046827, 134283465, 839065493, 531454480, 3850304, 779448441, 178648204, 828264735, 91840705, 225919903, 837409494, 366933901, 58870327, 488383144, 873873121, 877713615, 977958352, 219826604, 573900488, 74655226, 934172520, 870613597, 158664291, 214112626, 649683406, 395811805, 568251226, 536284751, 70534607, 109646717, 660815679, 783345104, 974395597, 13417785, 266351401, 719000942, 827045237, 159350427, 321815912, 309133253, 904302247, 25106949, 736806691, 582508633, 434551974, 460736573, 210936693, 540426461, 291762162, 592294360, 103056465, 867364486, 417343735, 842156519, 639655284, 545949906, 660209053, 999440151, 457774089, 978616578, 899681782, 32960445, 586032938, 338034529, 198123733, 311715759, 194221706, 199622509, 604980537, 367144898, 26923165, 778697068, 640678384, 472952928, 499455812, 209583614, 208898960, 452937533, 982995858, 294369261, 681737133, 197733396, 791014800, 433976688, 17971646, 927538873, 700087236, 572994409, 69442935, 78882159, 607814051, 680659332, 85076503, 380770714, 342918657, 859741157, 983302751, 940086094, 529500495, 445752845, 956390593, 900547928, 885773189, 200291928, 429747305, 692410143, 294249388, 51838929, 588740705, 860901092, 904891617, 560450872, 387577620, 922449688, 995322285, 463203436, 298714080, 714976869, 921361729, 609074693, 399673711, 207547401, 443930005, 146318703, 643594021, 460502657, 510415274, 689751000, 748425898, 425568391, 475415009, 410993631, 923733776, 217029130, 159251776, 106542253, 90762267, 497824443, 546204206, 319110529, 770064546, 40270800, 906746875, 207616496, 354440783, 375592084, 485206765, 255304998, 337766398, 850359859, 826623279, 389081436, 332770494, 414768219, 222897215, 241648984, 867408079, 784001488, 684686419, 507567587, 413225567, 698600323, 305970417, 587016872, 679108925, 34932780, 273250958, 443441805, 556927257, 163932503, 361880183, 414012845, 626279268, 320409460, 171727040, 826550099, 100492078, 838846145, 534632147, 967265130, 525831928, 133245503, 404837674, 237298450, 332727753, 333085732, 962370086, 635662658, 268435114, 860034973, 981223678, 958936227, 370861937, 170303596, 654825722, 207989436, 80610580, 522717153, 665928808, 561413748, 533295179, 520150402, 807683816, 168078444, 668094435, 368688659, 433849778, 630400878, 974702200, 41521770, 680766215, 221335848, 383099521, 11635119, 836282650, 922261883, 986477933, 872483483, 528526413, 445790821, 755394551, 505713454, 956542653, 146836407, 567766311, 887944782, 304567293, 849389504, 284561086, 469735001, 200244075, 284625618, 377678844, 201025555, 681422760, 25999770, 438070630, 331779984, 788814524, 652408202, 18516841, 930370508, 62984996, 387278548, 377761845, 271869656, 611449109, 627227021, 570185371, 958020632, 658589393, 787833449, 266166205, 122173588, 401393652, 522254008, 810863943, 148384480, 506998339, 549965931, 488669235, 77120284, 958510008, 219687291, 107135849, 688362120, 161623827, 405229898, 256472357, 326391875, 7905311, 291980707, 793151949, 618591911, 317447271, 89123532, 113855671, 245408966, 46540607, 283673626, 695653104, 535197498, 876518769, 798685527, 543984285, 831173515, 798923880, 928809006, 364652738, 273118391, 386393238, 499821738, 481525547, 329180084, 355950594, 609587782, 433979842, 103617479, 852122733, 910562458, 659760435, 980398559, 720299024, 96998803, 583085189, 135171270, 152676050, 219368763, 687756824, 776619078, 251762726, 354354090, 534879879, 789609982, 829893578, 665447591, 604628001, 667665066, 196802622, 179270329, 418425788, 807736884, 802601424, 670826935, 807138725, 767294604, 432152018, 352855113, 28232137, 149689732, 753517883, 837414293, 129800441, 889404237, 147428223, 994956705, 529805075, 957342861, 679446557, 309022174, 623147757, 664805329, 81029629, 168795652, 320691175, 122269463, 845070530, 143022358, 874423599, 951196586, 553511414, 251106055, 994027502, 171497205, 616883283, 399191453, 974517467, 573831287, 917128002, 55100844, 92725962, 377559776, 509765725, 891367731, 461334293, 785550587, 856905606, 662404532, 192726163, 197077150, 226565458, 401691405, 350795840, 544660375, 568137617, 165439444, 183359583, 296794855, 735892466, 145857465, 413442113, 114334943, 601546250, 467881437, 849459702, 195640249, 436802550, 277688359, 261906584, 253902064, 74075623, 824136926, 254593472, 496108814, 329408480, 932943845, 743403470, 459397923, 598110540, 414509835, 311890136, 713316768, 918475688, 317340773, 722644867, 68822255, 863761149, 123317602, 864337861, 684889119, 374182341, 354788906, 582111842, 253831173, 616321845, 599957854, 602079918, 763983392, 340894419, 627959778, 607441231, 838575543, 209557212, 412554558, 778078613, 317459570, 891480684, 119823569, 686272517, 468521533, 617252843, 846017640, 837387188, 36361915, 214996031, 832888488, 660213018, 893351735, 345079313, 479528773, 197140866, 790562593, 226829114, 537312691, 646931645, 26407976, 340260701, 700526222, 939875232, 388312985, 739267624, 690235820, 107784097, 199365935, 763255315, 742788269, 258470229, 111865807, 530054884, 989049581, 651407844, 605424866, 29538537, 933890400, 455864022, 812941307, 263914644, 268957870, 389094048, 727911718, 380065403, 647422003, 162957601, 445711717, 691361428, 665678098, 246072502, 523254742, 661593591, 499607549, 426796650, 724268200, 934301321, 728929030, 212761142, 765523886, 532674805, 903625958, 222735991, 903271652, 355630984, 986723209, 94118122, 368473897, 553220235, 688915641, 566034531, 130416612, 659440155, 865815154, 544788221, 97592934, 90169716, 934238334, 22527588, 770263620, 644820825, 91801217, 79242190, 837659394, 598358672, 451689699, 844246617, 885116383, 950126622, 906922574, 395879091, 278341643, 899907528, 661709158, 135084325, 953671975, 438209391, 571228531, 155938256, 866379767, 603999847, 966015978, 332403317, 370102020, 605916868, 592159844, 113606737, 606794715, 388700917, 320651320, 541499640, 481215980, 499749909, 336977065, 607967961, 6981946, 10253643, 928352771, 162023545, 347149449, 105255273, 6533712, 397501843, 720150631, 485704685, 783502508, 323934876, 909086645, 955607329, 602119585, 604118285, 37515366, 537169845, 769877027, 705119381, 991737530, 291998767, 14341036, 685027067, 865441835, 854781678, 431147065, 37841526, 541146717, 340865566, 288368758, 119162522, 657437700, 31106738, 395647826, 747499950, 930604114, 102845535, 602973073, 345938828, 240599601, 289362633, 484326244, 274990431, 764525372, 512578564, 129405660, 668947173, 549921347, 626436465, 278794845, 7407931, 239970888, 528441639, 597453155, 564760117, 229166160, 185494632, 55229509, 619672773, 182538008, 469102933, 752470326, 778403983, 903805283, 679403702, 244503821, 956893514, 359748166, 199931293, 149721430, 455052479, 890640423, 224919786, 454033631, 911664887, 970786667, 760344955, 726782894, 334278102, 386958532, 955985312, 895445920, 353465503, 128219378, 633480068, 557320658, 586599664, 141266906, 435760298, 905474283, 224015936, 886798890, 414081746, 37314415, 162243090, 258905480, 613792802, 454946018, 122722165, 555356386, 178420600, 210069899, 225351798, 696861523, 308502161, 659940490, 421487233, 75826774, 110834724, 215629656, 323171451, 527217583, 425449616, 440326632, 400715884, 874880063, 620653703, 142798507, 552273317, 37838, 379315111, 841294001, 775360739, 476556334, 368696522, 22984742, 935277229, 85481472, 3584998, 308457685, 74027457, 23745841, 563625580, 578376873, 813211404, 705704987, 99288820, 5708422, 599696355, 115766971, 296266214, 888887957, 780090290, 503597338, 594663181, 734228967, 667345947, 92066597, 456587560, 829467363, 627553539, 896974503, 910345882, 22857801, 217660928, 646884608, 913948893, 505279184, 748008871, 86723654, 58277481, 158863274, 613290580, 31350008, 458624556, 140183546, 593030405, 68144790, 271695134, 316801465, 15893746, 252152036, 135727066, 930694900, 989399259, 253062839, 914355648, 500704813, 844999598, 705820684, 776871968, 873968371, 482597735, 91014542, 268053110, 506963718, 986843419, 32920965, 660406151, 768453918, 167348964, 947244711, 786931056, 506499200, 925508285, 695102141, 571889903, 947240192, 982037709, 980515269, 164876752, 452132044, 564618006, 633950179, 108651762, 167277542, 698665234, 451844477, 700944089, 235532773, 653054865, 810481585, 535498333, 734095536, 233412799, 214376964, 68651866, 645557216, 371966113, 309689337, 149275139, 546086218, 377091488, 184649901, 170255175, 30458113, 627453211, 321068711, 189504529, 339867975, 746804431, 719369679, 625361765, 521142230, 815287584, 765888798, 476369197, 493084273, 246234067, 744386279, 4108969, 194048019, 825254640, 212075204, 780325731, 692334328, 161762868, 612358782, 248446127, 158575739, 299529809, 570037451, 936637824, 311292243, 280324064, 359411368, 156958117, 364405727, 386228989, 615335659, 771632068, 611316414, 741825858, 957106556, 70972365, 565390927, 662107183, 146553531, 256156659, 771788775, 467298991, 917481570, 341324066, 401466647, 332664420, 111000343, 196208383, 505160992, 43159817, 399862336, 417705153, 932253478, 907103964, 128377521, 422792711, 337422573, 220486888, 96819810, 16589273, 901326307, 193475000, 29802939, 553417582, 334300463, 977517373, 79068423, 493632445, 651266651, 344575027, 980539982, 376162638, 762519005, 600730795, 352705476, 384944523, 703277382, 798994038, 42498160, 122941372, 912392084, 179385624, 644168024, 355439684, 852236833, 250177804, 650661888, 831014368, 483627983, 715178416, 265681744, 523544044, 287360865, 925713047, 200166849, 895702336, 884508807, 586549403, 357125363, 417489857, 392328298, 710374246, 380640997, 201677386, 487643616, 734816776, 965374539, 156608465, 556413801, 350402060, 134035883, 278132794, 576552648, 135201726, 998531429, 116846932, 84241834, 576270417, 744628013, 338943025, 198807110, 19552192, 260132363, 156149080, 252014185, 549603548, 464564408, 998390398, 181283412, 430706770, 10809424, 403855195, 44787967, 943572265, 51186951, 727786338, 939407614, 330065673, 631869508, 845674715, 646097073, 233917807, 738662361, 715236458, 344070084, 433219212, 5530696, 554177050, 511059668, 611739956, 281912470, 619074512, 343172368, 762082064, 806670976, 62356026, 753288263, 426722624, 666038446, 811410893, 247310694, 876251136, 582503735, 684164837, 770015710, 344042227, 881651796, 657692277, 102385051, 327501488, 369980880, 491094221, 205259470, 441851278, 623961568, 457685870, 152292176, 34889750, 591106316, 828487693, 933370428, 539897060, 635744174, 619898013, 895241199, 735407929, 431451107, 838565729, 138568093, 289291997, 349975932, 783185202, 44439979, 299435528, 964681665, 664884413, 588914119, 519262342, 291963820, 608434877, 146584372, 30856936, 909472186, 997373733, 298219935, 745075902, 866111394, 578482155, 391739744, 964706240, 74821298, 577612755, 115910223, 744711947, 228501898, 910095729, 604418262, 1065972, 771235803, 345225048, 658991734, 419601637, 435579076, 155908967, 555479621, 535369305, 255826207, 419607315, 981722884, 480760857, 225993967, 989065926, 764638975, 180045798, 127427655, 128825448, 416290642, 709472299, 895320572, 433017329, 854583700, 967237420, 876910928, 809672988, 894063810, 257570096, 133278008, 58781054, 271177373, 509287017, 559084918, 39246169, 165654957, 478591639, 599750396, 155996081, 831024912, 670435427, 493004098, 421715504, 97702803, 60459758, 275829604, 134782303, 822148353, 360860640, 290277840, 331639591, 849698502, 93129541, 119541073, 520502073, 783140448, 390515877, 452669017, 26471710, 648090419, 120118414, 60279264, 620607606, 370964556, 281389680, 721369663, 271984063, 112558515, 130139254, 563389279, 779354995, 207637412, 802537352, 206051085, 685299863, 33540522, 77281900, 993539890, 407213085, 363926653, 603686746, 217766190, 188831234, 228691001, 194856030, 455084385, 393472448, 795131421, 67722932, 688609113, 413899927, 852403486, 175393747, 320287768, 800431013, 761360589, 686641747, 276432535, 191223988, 469296200, 792126405, 964100350, 785919040, 423572531, 214181139, 947473784, 173109896, 911128366, 232880653, 906214433, 39206987, 792213313, 992518676, 50623082, 962062573, 298564515, 560588876, 432526576, 258934673, 30146263, 322201893, 138812201, 968130385, 751582065, 834355178, 44977802, 443574702, 726593662, 697856353, 842517338, 307994876, 487954945, 361680259, 489698034, 563877341, 451664625, 634782791, 294516161, 254875403, 364815646, 477015356, 134123401, 559385995, 149650591, 983860991, 88481264, 685962419, 984502279, 186134666, 291894804, 504487819, 329037951, 440628243, 898767110, 723958417, 222531296, 525005478, 430548359, 464271283, 796158993, 246940098, 541401799, 584756144, 246692680, 985812414, 488174840, 975378809, 364098424, 661973127, 734406693, 219476110, 635534963, 388502542, 274980961, 564107537, 261789594, 301050944, 203896191, 650439019, 531671090, 950163211, 250830296, 561280289, 582128271, 50491902, 525270302, 118452680, 638764714, 444602141, 173715592, 524061288, 844228559, 38083475, 2093496, 352769447, 58075510, 403519719, 199990599, 286297691, 803114710, 879218528, 547035096, 84371556, 260119009, 709095507, 6735373, 564034582, 12846773, 594038836, 551043612, 439019692, 191692392, 242849442, 616619579, 109334453, 494145819, 913480758, 604511921, 559897936, 108927071, 548852848, 919446305, 241627241, 856968424, 403226008, 671226288, 309078743, 63052537, 195242696, 190807542, 60091391, 876606734, 869050316, 857802995, 568354291, 432969863, 896418646, 841669957, 439957401, 461702194, 188342964, 369386443, 668226692, 969155790, 674225252, 10973752, 7879381, 10938837, 217566338, 344107106, 10720080, 341950495, 179868652, 587018253, 511793214, 456023368, 746542099, 577895980, 678057027, 652208743, 17477318, 14057240, 970100872, 428414266, 432025886, 769718448, 952255535, 649153238, 343222667, 224524331, 216759820, 164104636, 373894413, 664849205, 320699036, 134068590, 543826240, 198101994, 24815465, 955007961, 419066721, 241294301, 512036824, 592154656, 639713066, 970589707, 747078816, 214387186, 526361226, 366896491, 55942311, 871672979, 729081754, 497385593, 290591815, 919108462, 556392426, 3927952, 898458193, 401554828, 628507914, 140154638, 107748507, 28155516, 296421797, 228167892, 786346524, 623480296, 675939094, 808374143, 213198809, 460600496, 335252898, 314560457, 739390450, 434070042, 295776579, 82053466, 760932910, 961875529, 882278178, 586939783, 942454527, 260524548, 429231454, 530303540, 333569660, 224815246, 99619398, 217662006, 719859646, 458545974, 574924352, 559037595, 21934910, 803500671, 801738801, 920222122, 73658513, 463769832, 263332611, 7490133, 469375762, 842928262, 491986016, 119817287, 614408628, 318887474, 917964575, 134953579, 9253630, 81286279, 754883064, 900356131, 748990403, 220055936, 813788863, 432388872, 989644551, 476512854, 689530226, 490598100, 516167640, 409741346, 332250539, 202879134, 286459136, 427846347, 707954013, 458973660, 13937340, 254270329, 329120686, 428703632, 263303579, 951325473, 411330595, 822526996, 705167091, 682961179, 271906476, 819291964, 287545698, 773424246, 560967498, 869132268, 519031530, 973110348, 464625608, 984100705, 538142880, 864234858, 119724449, 935064463, 818905672, 61924206, 163636955, 351109927, 490862516, 863917164, 88281485, 607678137, 418625273, 616167575, 560153992, 637818482, 628461937, 72780547, 458742692, 911471310, 226358816, 292891191, 778204936, 27670945, 555051718, 830521600, 560179803, 544220635, 754984028, 66216349, 485529735, 595425494, 546107512, 109508633, 907256256, 513878831, 462798549, 919236799, 269370643, 485537822, 255166911, 963103193, 419336771, 139312626, 964672752, 390769189, 539667795, 656964685, 888234397, 267200704, 358975985, 100301384, 747756658, 423415643, 748730147, 402339418, 732650425, 422026606, 575898005, 928546788, 922513327, 120241292, 1137378, 799163898, 777716833, 707210146, 71502332, 304741210, 72298679, 127287672, 422177607, 477090112, 958436360, 352824200, 849224346, 46787681, 11267774, 105071775, 514800235, 984314825, 214793185, 124959781, 646511893, 358645891, 887298642, 169349210, 9567210, 505489554, 541928164, 571211104, 954400840, 680807698, 488040481, 756169206, 403036046, 95737766, 857032938, 687328632, 192558036, 40510588, 442913931, 154091014, 842460357, 470179615, 34304130, 23809076, 349482282, 415192337, 356461490, 686574571, 4311435, 220762690, 721964615, 238847679, 418916845, 909132557, 254861038, 853080299, 171856898, 452593628, 993147434, 375412012, 287360727, 709413347, 782276528, 814926199, 413505428, 686659621, 490518331, 947919922, 109536081, 752765946, 114134666, 336972376, 323546023, 668966234, 118624144, 146842182, 314466772, 663041372, 245936877, 360461769, 201314160, 193477164, 60016872, 537685012, 281505147, 213263496, 567594054, 533104247, 251555752, 332881441, 148991502, 903802662, 488599938, 569399087, 168439486, 371440501, 212647014, 718744894, 41405806, 267124005, 399251318, 168976920, 124722257, 83897971, 740191997, 291723674, 960326060, 708063723, 583140055, 53151246, 627147089, 420261288, 237183006, 318322949, 268016815, 261080771, 972289507, 633487164, 187930383, 559252986, 806251052, 925680238, 488241226, 120954094, 324468593, 140126, 622116686, 312337869, 552362306, 598580179, 576449976, 555710835, 705035840, 899594866, 909897876, 461054199, 819706953, 136764439, 194658846, 495267232, 828014316, 195576351, 662881205, 562977374, 768157237, 356126326, 52222709, 311859775, 796205798, 686634586, 803461937, 911411591, 320374068, 6383790, 566358952, 473321164, 414762764, 690077457, 812374364, 196198972, 198785492, 970255918, 717023451, 758441639, 509665990, 28563545, 568092618, 404819985, 339590807, 615559202, 987143506, 88424356, 72148397, 257068421, 832689001, 21453020, 736932038, 368070057, 357328651, 511593115, 84696385, 747082139, 93517356, 683193304, 835901458, 140803195, 633122860, 737847187, 538847656, 256922909, 750487066, 171885744, 736480533, 804902832, 214020699, 250052804, 808464010, 129429804, 790200416, 933340138, 773507712, 1094491, 466396511, 313353892, 688350844, 579181278, 265608697, 276710292, 571438440, 191376912, 405080760, 979234018, 207275677, 669680083, 1834942, 361115724, 842321840, 4389723, 321816267, 686355542, 977576272, 76898476, 225442231, 167432809, 303845040, 411971772, 306065688, 505582617, 272003790, 838003286, 415428136, 729201718, 71642703, 663703207, 670079693, 193167114, 599311322, 25809216, 757115613, 490833305, 384810217, 33545902, 246883483, 604201683, 838882187, 204987615, 925001434, 158437855, 763777216, 505495789, 226574115, 577002405, 52260341, 410503301, 62388429, 516213203, 915967709, 804160207, 112280519, 57865892, 39732169, 423763432, 244576804, 151855796, 690233632, 170440504, 142741273, 223376636, 98124200, 597413768, 451677512, 879115466, 249462907, 745761599, 37195527, 289746283, 432536192, 850791812, 22269782, 377693577, 37936578, 623793609, 214786049, 962213130, 392202275, 354434055, 764069891, 2522881, 241381183, 121733576, 162916135, 577931850, 55847466, 621116879, 759301088, 406555142, 432214076, 660890549, 746790345, 725609875, 274301594, 485226534, 542855182, 342803137, 982190070, 6350696, 97429364, 192957938, 74458322, 395217455, 347057333, 472628439, 178061589, 901453265, 492321642, 942688934, 316598407, 710035508, 447214150, 374579615, 641944080, 530403995, 103505854, 925379114, 409090018, 96353937, 953080783, 311896600, 992493307, 228960079, 999865209, 610397196, 463629431, 366261870, 676630032, 478756193, 488813129, 483382627, 881131379, 394390107, 805241754, 321421466, 988589389, 691578600, 613597188, 310666108, 587536570, 569935158, 976669057, 709794074, 941820071, 670061196, 783424399, 292456083, 440578107, 960055983, 598337847, 776173045, 372049344, 240271523, 353623581, 918945558, 539400820, 964802059, 338196982, 734441673, 749902479, 238764909, 373387348, 208206904, 476887245, 48099838, 673761166, 14590321, 506820266, 964871374, 54169597, 543560857, 413473622, 857508023, 254380891, 103297820, 440712633, 95076981, 152001382, 797000899, 633283829, 776663400, 102632121, 316657108, 267187837, 44436487, 888999982, 583208534, 170865903, 750485554, 79850093, 887235765, 159093540, 299631390, 33804404, 683963300, 252903158, 478897292, 136153731, 419659054, 40889466, 371647254, 15219801, 27505868, 840048595, 995041952, 299013485, 273549125, 413744387, 237820674, 295643796, 12176040, 95074378, 380164749, 577502670, 998963605, 581605387, 604714880, 698459897, 865404214, 408256558, 739578230, 536295029, 583036301, 70706713, 131525370, 443594028, 204241780, 390624083, 234095883, 5732960, 532639487, 330500742, 591240043, 338784306, 452847045, 533324229, 547157972, 70413322, 912914556, 723840487, 70537533, 740752135, 184096662, 817242784, 159602648, 98966770, 726262074, 536110817, 890953166, 138430914, 281065542, 431002239, 325735434, 951869871, 533192575, 629717031, 791951714, 463682655, 290081489, 236770573, 146440999, 776818304, 167982313, 65254803, 388737402, 311844344, 331358262, 486356316, 389686340, 563562252, 639726672, 33639570, 748687298, 734284928, 154166928, 252325607, 365826726, 428850443, 954241918, 179442538, 352055097, 739261570, 779493392, 411215302, 770548955, 936464292, 969804526, 757117867, 368967506, 317933646, 363085989, 285471754, 635640273, 142740976, 421723306, 807338822, 398682603, 926416041, 147808237, 51347494, 842487385, 723570735, 880323609, 285443454, 126088742, 449418429, 598878372, 787717448, 546526689, 917558122, 917147946, 172350270, 256405811, 994907692, 853234828, 571184408, 768430235, 57139221, 656998133, 711924378, 503182833, 211701499, 776989621, 202361803, 154136618, 964681343, 827147627, 480369258, 830425964, 43000793, 558484359, 512598342, 616333013, 963562281, 355044533, 919751525, 101817054, 118955576, 766175000, 312841609, 44904555, 339963089, 461692491, 647769816, 724808795, 389326835, 533256404, 611666741, 703382959, 471108696, 644062783, 845898947, 107710942, 885868967, 100102890, 373080672, 621138883, 994559799, 217972690, 200930721, 76227348, 404483529, 597707146, 483943685, 248530302, 318266125, 849496214, 605080522, 641118314, 641497964, 964176205, 339935135, 227385306, 968177480, 739140039, 730947413, 591460021, 856726020, 851270358, 816437192, 946970035, 571732267, 397716089, 752664934, 794506370, 282877622, 200699815, 282862254, 713406043, 302337617, 409608204, 475061645, 358481539, 975720350, 164433817, 364859909, 373717503, 786485793, 584634478, 577922375, 780078595, 752790039, 634604602, 214265669, 67148944, 84529590, 834191857, 78640560, 817817, 143346504, 658004721, 70868251, 753934713, 589674457, 925403931, 310837508, 221532757, 967543240, 598677047, 542448331, 159416314, 270367723, 750610235, 663235910, 318581683, 84413653, 873056596, 988662036, 174095071, 55169910, 944610396, 916469104, 906633027, 609915310, 585261280, 800569483, 363710843, 49638083, 571183375, 460330734, 637420241, 103595180, 828013448, 287403816, 358529321, 770882875, 682961570, 89881751, 140346955, 66434200, 138791278, 622389819, 584506080, 937752722, 483572599, 324253409, 615494595, 432882971, 398425525, 399083314, 169828633, 933099179, 481298474, 86584609, 84971468, 775705895, 425650800, 38511404, 908329512, 550737558, 822560757, 215609481, 423815471, 670590065, 639284883, 277697045, 321244339, 441265020, 957769457, 617920074, 20340373, 30269279, 337275051, 51334278, 762305402, 98590595, 874868962, 740066356, 476702413, 281169757, 733911444, 629933276, 637027124, 106318164, 18238768, 246289455, 998802069, 782789086, 363004746, 465965535, 786461408, 9256094, 242780302, 833645550, 15424135, 401001119, 625867811, 947605008, 133225530, 397080520, 223429584, 99634600, 727887940, 213255366, 436231962, 133016227, 309148503, 32409100, 497937234, 176924940, 624164290, 838641398, 29623887, 454339595, 729710362, 660774714, 21068888, 289047618, 138193133, 550319368, 261763315, 90841813, 254812705, 683557473, 423627765, 221560713, 524919080, 915430317, 93453777, 348547527, 933416146, 531828054, 908187307, 200006275, 267301612, 346597908, 212809828, 203134719, 963769014, 11710876, 114213556, 607531044, 546081337, 454948917, 407807442, 214668462, 567310547, 964971312, 649040665, 873267167, 409325853, 66728649, 814813274, 700415094, 505722713, 180483198, 993114110, 26371436, 148244661, 256136744, 6291993, 731789390, 410596031, 537860576, 444103916, 140940410, 124317340, 269314729, 442113941, 843918584, 997627784, 232487096, 350290156, 366848459, 375575612, 258502600, 675802353, 344035109, 684218544, 111425137, 628558510, 217900861, 373307914, 20105748, 351423417, 269659172, 182881681, 933002709, 468357221, 945144972, 769031749, 36718009, 804202051, 601012500, 487358994, 57683883, 978738915, 466287752, 229323661, 989848802, 522793453, 275185750, 257152160, 560371742, 279783016, 921075542, 793043783, 304834506, 678758356, 338016588, 343569408, 525316117, 387089875, 993276189, 639469748, 383079140, 744523902, 388979452, 236397944, 942988390, 837164686, 202071228, 378323988, 251432058, 433636192, 307665822, 352524027, 583793164, 900419496, 830517142, 357226301, 726887328, 479226306, 28241278, 47824365, 503603236, 526115332, 948663290, 401112592, 646065318, 428170005, 802701724, 786637845, 71165353, 54081880, 505617765, 465361972, 911634367, 483475006, 360760501, 883577583, 145753299, 820650455, 142677226, 743774119, 9568879, 434125682, 683308061, 67664926, 971337345, 32853921, 603504649, 261529724, 425083201, 951721664, 338987, 988965249, 861688759, 610844727, 317620942, 683539630, 3000971, 147413479, 926982053, 753699582, 298919057, 716342527, 195763735, 790179733, 730275290, 835891886, 578284514, 110729879, 602812729, 889886371, 702781690, 602573063, 291701299, 643161821, 327392224, 825782834, 641899731, 471912768, 281356426, 538280563, 667509496, 479578892, 654789807, 486993059, 424358215, 289625796, 639599021, 204179157, 672039412, 831825910, 948974375, 479210784, 939459834, 856736980, 551775199, 363226881, 924024482, 583670852, 672702911, 173248592, 478117057, 976572289, 479694833, 779248855, 73616522, 574426305, 604646823, 461625232, 973882342, 900983142, 580660983, 989021130, 62325882, 927251656, 55042576, 663517165, 312702889, 298181356, 61932455, 502951375, 550862460, 568887170, 472783697, 914575909, 90089862, 472723195, 282189590, 420337343, 740123369, 546350479, 369755771, 821863438, 500398057, 39510940, 920270904, 214514056, 726911606, 411612846, 879371699, 921135188, 947455366, 759830517, 612799244, 239074262, 297687466, 980367075, 464836078, 312052629, 306163090, 416098737, 425978875, 992506292, 355211390, 825195513, 539616783, 674276144, 88748777, 533429998, 336170760, 574311347, 843683537, 306125454, 726075784, 822491994, 512828410, 307470892, 297360419, 378130936, 947643630, 229780926, 611656988, 80368631, 528072882, 338687049, 843105680, 68987570, 175138325, 528358569, 386358436, 323528359, 99579628, 781659089, 906051639, 842454251, 894212954, 410275099, 808936342, 402019706, 160888979, 340572884, 968448721, 689036158, 16518031, 127888289, 129811566, 890343877, 720308035, 251858643, 154761184, 496102186, 214931033, 911033925, 844549375, 290420849, 430498793, 678019983, 971746286, 178099177, 898233088, 300808713, 866793594, 56824653, 42346312, 275848946, 14843304, 49515553, 774113427, 160340070, 617899663, 334718138, 398188494, 666712994, 812038133, 995635935, 763237127, 835573830, 163863347, 682375878, 967492562, 26483364, 677036257, 828907722, 237038745, 253491620, 51508247, 117277288, 634756436, 732812540, 805157771, 481450279, 421750559, 114594377, 764320748, 442105280, 528760249, 149917421, 226371657, 544348856, 16472657, 909845680, 445529164, 491348940, 371417395, 382794825, 460347730, 836775575, 232851411, 902702571, 172464079, 47116405, 640965213, 59105194, 683424664, 464862692, 411385423, 377344656, 145617558, 727873165, 142044091, 414419964, 645361527, 66909307, 49429805, 87598423, 698627417, 131902224, 325992889, 225659255, 34447861, 869486921, 750761654, 122962907, 439836581, 658233470, 723028137, 272085785, 130995287, 183840817, 217829276, 612215661, 594285409, 325999535, 434872867, 755976469, 697383140, 866905826, 272251820, 677428113, 14852420, 872154335, 364768801, 789301701, 345350687, 294218004, 524874541, 562470913, 172801653, 600302403, 229638369, 138482293, 40490720, 208372773, 60078635, 419568011, 906708012, 340735279, 663481306, 822198967, 532433541, 7807778, 539623951, 883625952, 10796247, 341865661, 548753100, 943147103, 844832979, 937921446, 280731904, 255819269, 798186978, 35298866, 21400651, 780870313, 8046997, 67732950, 526808042, 927859411, 328869054, 889989935, 913053696, 501969711, 626402207, 869980008, 93621134, 603179618, 477301206, 694764047, 401717431, 959457122, 205015080, 191731342, 426810452, 512074371, 36712000, 806429014, 862310299, 264363354, 315507962, 198971075, 801241898, 929505057, 705022978, 269955233, 492985369, 673174468, 569695903, 359003236, 264375844, 372755056, 287646589, 347453618, 224685170, 792807626, 403798469, 361802368, 79814150, 425471084, 737072153, 566503861, 477892362, 185725267, 415380754, 616159114, 185494462, 652032319, 953105006, 281858684, 167407757, 952096128, 837844817, 861061438, 908785730, 867979050, 434146080, 197898882, 465583353, 495973277, 298988514, 362194511, 604654036, 860988869, 392332158, 309012753, 804131754, 317855083, 774396738, 46360944, 445760487, 226869128, 281827258, 651714106, 604994134, 735659194, 188960213, 321240872, 430649561, 705431158, 638164139, 305955235, 905429973, 988032045, 471415906, 892691481, 317318763, 555704243, 117700662, 992047833, 915080391, 8505663, 658027794, 989485917, 864351643, 12307388, 672946643, 878726795, 500061503, 167105820, 815939083, 585397961, 288494406, 328075012, 972289007, 645096253, 474447263, 282184053, 464830579, 576442978, 51377825, 808340851, 400036809, 578636416, 77905733, 410189818, 887076619, 784342973, 18817767, 194014577, 909687822, 375510658, 480817034, 198060433, 798444995, 660246712, 658373391, 242633389, 697654106, 454537009, 144598001, 868916951, 414286906, 484383789, 998903782, 309911309, 295379377, 915896845, 20857247, 945982093, 83497482, 722451837, 140568488, 307146733, 259249870, 728108115, 610070627, 423949405, 579003552, 989728738, 744748140, 159006874, 464962477, 391094578, 695395868, 449495011, 95404856, 278626869, 501023876, 547214044, 380413615, 683899466, 462151699, 650855506, 541312127, 302179026, 545299956, 98528633, 944748691, 688257808, 524102278, 427919634, 680952228, 104254168, 518725687, 421973337, 854225188, 708863759, 273747213, 967513053, 847198096, 984174568, 677102566, 504061610, 488924891, 631017295, 690384947, 199939999, 797368912, 599718788, 234676152, 776960876, 644358816, 393351054, 4217820, 492069997, 553844067, 651251971, 184122751, 15353111, 450883471, 356920963, 329907720, 843968148, 712279790, 688916194, 423069243, 201314395, 392596054, 51196566, 47444449, 758684274, 131578594, 182123526, 515498183, 980744525, 994486011, 827448899, 267692251, 933957178, 958859404, 176919367, 143670409, 636918670, 168295201, 673441122, 470076296, 657337956, 541086713, 976649957, 587644804, 837176734, 581609362, 455265915, 121510145, 654741590, 267617865, 170617026, 107433199, 189483463, 511231432, 682224890, 897171472, 40540151, 496346616, 30290408, 225253676, 790595429, 428531263, 118173081, 424955085, 112382379, 573401060, 900487811, 171998858, 107761207, 130826330, 738260526, 799393065, 57267552, 353156560, 738175930, 936768100, 22822794, 2941560, 420765412, 124715606, 472681096, 542542317, 310158009, 246030833, 648104506, 130159332, 131879694, 879001753, 319763904, 326523615, 756364654, 335658720, 108696112, 235522280, 539451964, 890398215, 737874629, 648558345, 736893876, 65855452, 158961161, 430647050, 124394387, 703629256, 876183051, 770096300, 193263292, 952119040, 341431610, 442027362, 579743594, 664320480, 343307352, 827448076, 729957854, 889756814, 589262304, 33203260, 206538270, 931146278, 267859357, 793030637, 653868577, 334754690, 621512104, 174044574, 131641574, 408798400, 203992182, 522270427, 620402800, 640993904, 348709108, 373501720, 696667080, 477103152, 143465014, 608198810, 43866036, 247032657, 592132615, 337156982, 682552188, 50215007, 209335239, 894194984, 867278597, 782322450, 633080575, 851874921, 924273257, 526566217, 486547793, 342157662, 286540377, 75869128, 887685144, 448794869, 368358926, 199260455, 845916384, 566275055, 798156256, 498597805, 421734606, 550717487, 781106999, 474609207, 770842262, 244563061, 991677257, 570859913, 55783133, 679543123, 402554961, 881240132, 899746116, 807713869, 936838012, 437779915, 298128417, 531655801, 179836457, 401294854, 346592090, 512115481, 334649271, 868637099, 606647720, 269873353, 874255327, 44076118, 188026300, 847046056, 507417837, 868981793, 55673954, 641653733, 302302280, 733435560, 703290413, 457044096, 899585715, 861343254, 757321177, 672153982, 854480768, 605589617, 992625507, 780735627, 185250312, 291242785, 794221023, 307766289, 344320432, 320403583, 446114552, 299689023, 684531363, 375835347, 237009638, 424365869, 253098680, 115880784, 855798307, 911410491, 498858486, 70064328, 103038257, 962751436, 234278650, 963764322, 938590947, 689767500, 954271103, 304887710, 687883722, 763765278, 390627441, 543679068, 321459964, 5958355, 751450633, 668532369, 977207324, 610190703, 868498754, 294089357, 580518669, 237241250, 863369062, 162460073, 139661322, 327476186, 235314726, 314268560, 94278543, 8723261, 413496582, 347946865, 431805406, 145371526, 562957614, 425048550, 958170532, 532538961, 15217024, 497005253, 551033564, 431853111, 357455869, 809270900, 779345770, 551712704, 418998439, 691570683, 64529962, 720332401, 378794671, 601144769, 594293769, 539379301, 868381414, 50121061, 402769106, 486031034, 728365376, 626054866, 134841634, 181700849, 629853506, 444535523, 782247659, 111685705, 868809068, 802330510, 905901816, 263282217, 384889864, 769828654, 218303322, 501349954, 135742703, 829366823, 648803406, 496383936, 457876421, 629633308, 626726266, 608852598, 537533222, 470377440, 795807723, 856458344, 431627987, 522294080, 366611643, 470100615, 454641096, 558905667, 380393048, 990134871, 502012346, 909256125, 488480275, 226988640, 491914390, 395818180, 540909433, 472813822, 747867584, 934851568, 82441240, 352988925, 570955802, 66424618, 102289888, 750283994, 560159533, 749720086, 129955660, 580316081, 837648035, 879551836, 851544326, 474419677, 730853884, 418639057, 845127987, 15521335, 621659357, 894564760, 448939586, 690139645, 216874296, 394951019, 820605578, 737152070, 154708569, 296412468, 110621748, 409224693, 18992124, 933556003, 694065560, 844639980, 925067327, 900811999, 243689089, 653733689, 112041202, 463044046, 717253426, 618422326, 690458238, 70960200, 221262375, 987162139, 637333877, 123153887, 421623482, 653346362, 190306701, 514884327, 468412385, 869975031, 672713271, 618663263, 700507056, 914215696, 689123938, 646392675, 154216358, 155861255, 888434924, 667149574, 957964081, 126741715, 628322353, 93221399, 993008136, 476201728, 980232630, 849224399, 557981089, 642695875, 279124237, 378206964, 493530533, 492429960, 583070120, 818710544, 148792933, 260999841, 516696671, 190557755, 228102859, 570938827, 562396662, 735763283, 452412294, 763253269, 456063081, 884600675, 797738552, 241201676, 391776749, 628185159, 949837826, 255951309, 911786560, 411991614, 999038513, 931459983, 661565740, 218314895, 197590427, 877734185, 680188603, 773927042, 12837477, 298402367, 631839893, 435305165, 750368025, 749289695, 614514083, 467939596, 634852039, 335415000, 12370931, 672728046, 441285574, 935965421, 728514230, 454122185, 738112144, 723264826, 610373023, 827369867, 658824491, 313485214, 407533470, 159325371, 988467033, 179723970, 973357612, 249360747, 965634488, 233391912, 925228014, 849916146, 64058147, 788662181, 695469509, 823119912, 838539990, 775017177, 63001730, 548512517, 995551338, 29335419, 78603399, 997260310, 573837798, 385406054, 107845424, 545826513, 515422786, 317579267, 489352674, 723517081, 25722382, 550357875, 78480268, 726652592, 764349404, 562094417, 338330810, 912763067, 683798364, 523141509, 171575981, 180471994, 863529473, 864869496, 858686112, 253161995, 151320938, 766443017, 870227165, 497553339, 945956277, 780929663, 812399617, 467448568, 616907877, 364981846, 81181026, 147929791, 199334275, 873619232, 734989711, 515862483, 520589478, 1429964, 446807486, 256471655, 468783506, 858792957, 48973129, 705063885, 558457464, 821879149, 895649135, 597123625, 940037867, 467574215, 260359562, 958903924, 302376357, 488850054, 989843638, 381799005, 355314643, 551371228, 898656946, 848574594, 167148527, 214944062, 525075263, 314662020, 624297414, 915826616, 970816875, 62117013, 655640618, 658172997, 813006961, 589525491, 633727317, 315626508, 314991344, 146139544, 203494979, 883637586, 382770832, 841071350, 473426082, 708195520, 76025974, 403968623, 979906753, 688129411, 997652714, 687335624, 404452887, 523782963, 616373137, 346535269, 74427444, 485079073, 81752491, 548514962, 699458880, 143239479, 982812237, 972403384, 745732430, 839532810, 998150249, 183405570, 80723676, 342911088, 462896329, 505619272, 494127560, 86559592, 444562914, 681768776, 71104332, 842453984, 763110776, 466594251, 416869925, 932044808, 208615442, 252026300, 610571477, 383687774, 777998331, 20779506, 26515125, 496928698, 711799668, 735302468, 803905181, 370722992, 662238105, 90936212, 466920332, 861542194, 308380606, 511351898, 422700581, 334593596, 606518520, 222297826, 827018788, 934756426, 191314177, 615619982, 724585921, 992103772, 72202177, 914325773, 876853694, 184799158, 912771032, 389981419, 366205414, 57735630, 882013488, 163290521, 106373735, 204338437, 357536749, 146827647, 251404029, 878105847, 66991286, 174533925, 946742994, 430354110, 342568936, 677263333, 896300754, 645848596, 269673845, 815021831, 600291309, 622133675, 162473265, 493826836, 633095523, 810053625, 784737997, 697715829, 368363916, 245333519, 376214825, 591427509, 503004357, 52657915, 276859475, 92389882, 17040623, 625097350, 790261355, 837579052, 4611775, 247205553, 743344844, 522642220, 981731961, 326790440, 334836679, 168846402, 421582619, 188631797, 116922057, 265508324, 410390782, 509643052, 712748480, 786877735, 616031258, 424838493, 376156368, 686492522, 915160122, 561703304, 587709469, 946750296, 256035377, 726451170, 741087069, 435109576, 669377067, 849670160, 675806116, 202054476, 507017778, 486321406, 623445062, 542308865, 903946878, 260887504, 731367751, 153133948, 750710606, 850497435, 993594313, 29731572, 24365408, 208415827, 613014974, 171732379, 418494517, 610006517, 3423698, 898152822, 836908016, 721058032, 724959310, 35998286, 384639415, 31714189, 329217021, 391405260, 529394966, 869980951, 540760490, 951109367, 540173854, 689873357, 709700722, 887741347, 370770816, 303090923, 424000172, 678869901, 843317941, 575094637, 904582227, 953376354, 772826599, 346518413, 680945034, 303369935, 871685344, 684566017, 640678951, 802402884, 299390530, 655462421, 779816948, 53863989, 358610854, 62749093, 321892306, 619778992, 151450878, 577978755, 693116514, 362443282, 249734991, 79664192, 159753651, 63557069, 465673634, 609979434, 643074648, 730641825, 332517398, 858850229, 209901399, 545524703, 245440992, 655272518, 449777020, 893698600, 190734013, 143261944, 287417983, 777793900, 313055845, 622243037, 882444849, 555075825, 187242085, 874896, 969704146, 457452310, 125850668, 280784430, 113979313, 842989531, 436001393, 262507668, 705545675, 567588260, 566985493, 978349635, 697330078, 494575645, 337978818, 483893747, 850094997, 207650565, 115405196, 966371232, 191828204, 517526439, 166728434, 747804341, 86213595, 719028606, 701574655, 929289748, 512592291, 436650986, 537891842, 284918048, 273434059, 511174887, 929465460, 622967913, 755886918, 189198881, 927322872, 329886333, 723225935, 433229453, 673383381, 778820529, 45702795, 57038994, 774709303, 22771090, 406480161, 798604086, 13506508, 708424221, 761182842, 756377399, 297831835, 529253027, 650479738, 928961900, 882733878, 783937387, 849613510, 344807092, 134227605, 560658200, 503593654, 788147176, 92113272, 975663289, 33323166, 496160754, 604666859, 829954213, 359917524, 788635322, 832083317, 932320333, 34044810, 225221418, 321632865, 401785523, 449396623, 806041761, 851134724, 48533663, 591399430, 825839194, 284327832, 425275708, 74414647, 504893059, 180902115, 149571254, 732554170, 983091853, 666207547, 572193238, 177003591, 533145760, 556933695, 311430181, 867029816, 375337537, 974589439, 243219411, 671822667, 825467105, 294325261, 294448116, 230065366, 86191354, 919015675, 548932223, 386276257, 45003132, 804201622, 845185501, 989700145, 452744390, 462918130, 283649240, 536550900, 334348756, 736360735, 648246040, 450632128, 308866275, 69691399, 608036444, 191541958, 197349694, 997494010, 667609141, 537743378, 870451190, 40987567, 528833665, 560532544, 74483582, 169442697, 39744015, 394722610, 350873623, 840898045, 186156877, 350881871, 157981798, 438334675, 481965339, 820034926, 234160875, 687386964, 775574509, 667486808, 678684426, 188355355, 584396541, 779948493, 941679353, 386090640, 675987658, 32564778, 383939190, 491874961, 93512554, 949854747, 409330910, 24537451, 610073750, 569364629, 724081648, 538310388, 759042568, 298715805, 770060641, 6098283, 599431498, 618983262, 74362174, 277593302, 286572904, 709712748, 241935617, 708459600, 32829844, 852758431, 325934897, 507035730, 28511471, 387430359, 451690984, 795748116, 302591220, 368339868, 393390513, 601600768, 200410580, 641945195, 280486647, 314861604, 508479771, 430643466, 222476115, 345025441, 265684595, 689102265, 389001264, 954676044, 297364857, 316057331, 299259060, 704665162, 834340763, 269329394, 132776113, 22460377, 930578771, 964663493, 243151017, 769289501, 634847638, 689868544, 106435539, 964472699, 559866486, 981854718, 630369479, 527959211, 169888465, 699370955, 118398975, 439796917, 437321058, 527713030, 797826141, 89302475, 273157784, 701215093, 273667423, 239233638, 443162911, 203896249, 350134867, 358751729, 85947329, 105100221, 390340375, 942749489, 527616935, 194389451, 915663817, 721896510, 970127018, 485407280, 663990048, 529486307, 643380618, 562171771, 376058025, 580967139, 556524074, 495955634, 620878998, 226608451, 20085896, 155216821, 428689207, 975785781, 973757927, 767724772, 598466434, 848540502, 814035381, 147011541, 362423114, 650654924, 939118795, 444443874, 675651760, 697280700, 725317738, 492356522, 284931719, 489631655, 763882760, 998228888, 144419027, 196570680, 337941143, 772502035, 873674130, 292795059, 321735233, 791394362, 615837587, 442667163, 154925481, 795665120, 671650562, 959223846, 170575299, 516693741, 924131771, 991127335, 580052077, 981166396, 363454302, 560081162, 38217999, 680660374, 305221127, 25198732, 625764574, 268246145, 761744612, 968314381, 123187084, 882904484, 335261720, 312043189, 740865653, 393131135, 470170176, 479621541, 763015891, 375135138, 36563511, 241020851, 714848001, 473301669, 289823698, 182213953, 653454032, 930287416, 740510810, 260610211, 277375109, 532258416, 231486024, 801586852, 566233659, 420054077, 587160139, 859231393, 973907689, 657977376, 933561181, 830219494, 177381125, 882902242, 897312999, 311743796, 492726802, 785842306, 267680744, 885500292, 535067584, 474419942, 423840409, 742990371, 163555450, 34992908, 288349596, 500512150, 125276900, 219989614, 753719827, 362260284, 219275444, 82436612, 271522203, 268619811, 692865966, 379697671, 644848068, 391699770, 292028321, 353720358, 605899863, 508120091, 950648738, 651588166, 954350714, 78937947, 198373822, 889274508, 500855534, 396787301, 35420584, 612098100, 841538661, 17080676, 562985249, 792741380, 722362260, 907948720, 725242053, 97841809, 562634813, 393999736, 797419255, 483286972, 996112841, 314009539, 951119534, 657675658, 393021683, 570227227, 498056306, 681423074, 277569323, 311709254, 408832377, 931960417, 181584373, 589093032, 904736583, 297296992, 45803881, 193282557, 51905145, 655971332, 868932947, 294488828, 266267061, 963425743, 710932554, 177237686, 699037676, 691926871, 815969674, 799769435, 638595497, 477339577, 649766456, 860092744, 109781191, 780460739, 747039599, 944722766, 474701750, 656402131, 864098833, 391053859, 991094270, 950625990, 913839719, 561585704, 937662008, 278306408, 696834971, 352412340, 224990122, 77360359, 862486310, 642557967, 35209154, 858217192, 797160955, 311356672, 485142268, 348639196, 62570801, 744639198, 402888977, 870946800, 835085605, 17424345, 796880780, 609872031, 12847513, 998702807, 762199836, 807101494, 530224899, 124097605, 626181215, 584949374, 693029373, 381924269, 631728471, 353114084, 664012324, 302239469, 522474904, 838667847, 567118105, 80865466, 703121188, 241232581, 720035026, 259939407, 673626719, 767895694, 966378610, 64944453, 967449282, 114617556, 199151405, 178968207, 349453592, 832614592, 124687245, 665212193, 355686165, 602828836, 575640471, 690694849, 951950408, 594039427, 999129710, 550623934, 503417528, 817153214, 876893868, 513535028, 133336550, 967802011, 615651705, 963873777, 684786329, 23212292, 17738941, 856110851, 657420102, 999551971, 534891770, 578781914, 927419594, 385470910, 31585180, 558639904, 874495917, 544010776, 874234805, 913029496, 128008807, 468298735, 691132969, 648829675, 931581761, 694909475, 51557723, 177614648, 231008353, 798704307, 860234892, 55770570, 778666803, 697767628, 773200612, 365551479, 760407140, 756453457, 408959105, 205917574, 196759384, 22411935, 712209628, 125970041, 300606297, 581640101, 622732116, 361430742, 960997782, 376481211, 507948233, 407080924, 607210396, 179711930, 777756498, 494777866, 396075163, 176520422, 500647420, 512782036, 694755039, 461779742, 467844304, 729277708, 232253225, 822836044, 618285549, 850155018, 462109495, 262930433, 908287569, 497556154, 645573212, 753769894, 731269479, 591640643, 445192155, 523067148, 386884769, 10074760, 419598412, 520395357, 227587692, 569738406, 775214146, 260228243, 425182982, 798770807, 174818160, 262360316, 558962009, 398674654, 720333890, 930502952, 444890224, 895656752, 743993714, 250428882, 923116979, 795465786, 549075195, 508861599, 474094334, 793863895, 281167679, 949729710, 715620499, 885157578, 260454703, 685524176, 927325443, 178263890, 787055936, 64754226, 312397986, 712563821, 518628063, 695252840, 164042556, 497291863, 850975885, 603775722, 320115717, 413259902, 12044962, 920733657, 431803049, 416401547, 22821831, 454490519, 253589439, 179996491, 458246426, 147933688, 227937856, 563985577, 888264052, 78256830, 221895465, 561432376, 470791639, 180435879, 30226581, 636527051, 831881307, 611829530, 714059243, 889324980, 217910585, 977606845, 451273505, 232018943, 67884041, 860797240, 499497242, 856100606, 176300336, 247043455, 594614661, 106120296, 783456925, 814782606, 310966759, 561316771, 634294058, 595301028, 250920058, 373047970, 367810929, 259303093, 21426218, 181150476, 899821382, 674292003, 500764644, 145963513, 252512590, 30613804, 18249191, 382728493, 158328415, 802455468, 540954290, 677883259, 738220035, 688354463, 144165832, 116761615, 227619055, 938864461, 705188448, 602173834, 180064636, 72773969, 901503203, 400312700, 887898932, 615698801, 381976339, 796725157, 322354665, 555858167, 628062693, 853374092, 725977018, 40314795, 26900937, 116571882, 422068405, 631752955, 961872833, 49220886, 20839320, 130545684, 287411204, 467201975, 658335287, 31202093, 42966986, 885398450, 301542330, 380210504, 150606010, 238575093, 706480194, 234971523, 454413563, 302755442, 120911149, 736499543, 286055762, 521829343, 740013548, 526254484, 604762651, 960958366, 813592198, 222513406, 819423547, 589055281, 739878816, 148751456, 622984401, 527341531, 503018561, 36408821, 449760348, 535712593, 910035591, 352052754, 797186220, 160914865, 100109611, 243881049, 198722850, 136079409, 830093103, 96115576, 510820342, 425550374, 345121244, 780286360, 195799419, 114854882, 578308636, 15730620, 584887400, 911623538, 431148652, 64081977, 472617966, 992741957, 820431403, 336594779, 882138052, 85825962, 732901334, 9644756, 80753134, 540355184, 938279493, 439122539, 788011366, 924058458, 378494963, 787460971, 314934326, 764414294, 500895742, 867858690, 928673040, 54809155, 6634217, 796725875, 267931193, 363463516, 978752665, 597951884, 486678115, 285917972, 345058238, 856192607, 208791148, 382868687, 276472771, 384170551, 115408346, 494421588, 75306533, 697546588, 117262711, 713965904, 318892537, 60485761, 671059950, 595222826, 392169156, 43945874, 279247299, 328339991, 69746446, 831864702, 105965401, 506026269, 632412996, 795435095, 384255289, 616089728, 784526097, 648788859, 692557732, 429563564, 630871345, 500093583, 765991501, 726125396, 584957381, 52239935, 77565721, 898830734, 725630087, 737138017, 705230674, 672872935, 433403409, 990309611, 539985134, 835966405, 314144493, 469491989, 432096924, 571902091, 538152171, 691634165, 402705854, 442897920, 218220675, 681874832, 33267348, 103028116, 888467270, 287681911, 641369932, 290683120, 734533740, 372004007, 456609061, 436852023, 794938070, 359715725, 160129237, 29149680, 480936327, 811975323, 888513360, 845049197, 259686583, 480894297, 74906877, 590598135, 406071636, 340496723, 295037060, 718594896, 438944768, 715641733, 868783245, 659277340, 861492499, 8857783, 842922500, 540199002, 691818785, 555488970, 923786357, 821002543, 297891492, 50685057, 436863408, 485806934, 503852217, 458511145, 717179748, 205668832, 757753026, 375808371, 73717975, 580886494, 131764907, 924587984, 34885396, 816336080, 135768696, 726254470, 117190496, 447181012, 135834779, 791505205, 25292598, 616351096, 662759747, 42157854, 360036258, 508589515, 783773358, 338108996, 732842623, 353183049, 995116034, 395912719, 551678115, 975381021, 361575357, 640040008, 85700118, 265941744, 222871630, 69266776, 489393031, 853972219, 105739598, 990482552, 330329968, 141237393, 586193238, 96802106, 328750092, 498167937, 604529267, 846262470, 25460737, 509235566, 358378587, 12447071, 410226300, 582815079, 455350650, 213252693, 822233384, 340639742, 933753698, 882528349, 846856270, 709141183, 646473018, 526710691, 88522576, 595124049, 414940585, 374201573, 892602667, 359206607, 123423862, 752449637, 327969342, 510095146, 958683815, 863068342, 122231605, 973922235, 704731587, 235742088, 22053136, 86346119, 180747183, 710909206, 261309134, 426411975, 23127651, 811300123, 239233201, 331148913, 282797050, 410509582, 535389356, 622905891, 508389769, 774119893, 690320256, 561837124, 446969459, 20112126, 922953656, 621946644, 269726129, 664119545, 796701309, 468344204, 954607724, 730665825, 920809316, 564841794, 371510704, 50818516, 679697623, 548129798, 769655004, 101293348, 935644908, 995583538, 218499636, 234946630, 447237818, 709264684, 222982851, 394171493, 782049968, 615160362, 522829592, 327896062, 633209831, 706470958, 695179373, 366132163, 319786683, 697495798, 722112281, 479249877, 45594468, 530057693, 668822020, 144440204, 227550361, 980941304, 831516548, 269017396, 470976719, 127562002, 691850518, 350548041, 267616393, 78908189, 218547884, 179536940, 258580847, 158084136, 6124669, 219519891, 74371969, 506323379, 380411494, 157187473, 811358999, 117932510, 393926179, 986024787, 310253884, 59710607, 512191333, 636061787, 257704563, 77513804, 163548139, 748518535, 364412445, 184195654, 45300050, 995585743, 596101316, 37327856, 188831762, 954553286, 208244584, 51388118, 622464630, 448643545, 12563165, 912749979, 574957956, 467291003, 391066025, 481794106, 140006300, 789740598, 651868328, 378604317, 772446611, 890935625, 938266273, 601294180, 819427277, 567257857, 359200971, 943280057, 421747837, 322212259, 39494399, 226954420, 489992113, 91569527, 9808985, 199869746, 681756326, 856949377, 84882949, 183697706, 969644064, 590808251, 813762441, 869927054, 962919868, 466478955, 915164941, 453884884, 745889460, 36480149, 326317147, 232873601, 80196663, 174730685, 94348513, 817914938, 13593454, 901835982, 892627472, 756981721, 722493121, 283043163, 68377822, 898492312, 501032026, 377138453, 908589310, 132234520, 595370410, 823355799, 649407081, 602064829, 924216204, 355099392, 644046530, 133541443, 894247685, 358554433, 52768534, 110166990, 979156598, 55413304, 179738017, 367166743, 871900539, 466527461, 57636898, 848348364, 76445091, 619777551, 935859129, 290351825, 441374335, 600496614, 728599688, 157692886, 433793017, 728776019, 650350291, 240046377, 252442638, 948168391, 527435490, 122058947, 768927283, 845036567, 461030072, 254142357, 11337908, 403397009, 374638145, 422254486, 980264210, 272340093, 311043205, 836873291, 913618395, 418309204, 953300106, 875853617, 133617778, 466892773, 871724949, 196966027, 251295887, 870306867, 388187202, 45623277, 950250766, 532656221, 194085745, 15310193, 859657796, 763793985, 523223028, 899549738, 509914330, 720006873, 418811505, 538157385, 199013268, 450255327, 688502172, 240986710, 441368690, 164449800, 553418011, 582788748, 827299320, 561640420, 238386340, 5852100, 135473706, 298427704, 241000443, 754355037, 201605522, 878753452, 706064875, 529027792, 770285823, 70986072, 543289542, 101468136, 846858010, 930085413, 493913686, 523188786, 211159412, 458117528, 882044412, 118311644, 162962809, 352514398, 584328402, 555093676, 207228623, 461367743, 334493781, 449201242, 898817070, 753567993, 687603674, 504021148, 807922909, 695012673, 207057666, 46726870, 816071275, 1799647, 500760857, 922082957, 917128118, 535756401, 768323625, 535932745, 514608413, 49893235, 802853506, 113837960, 996064840, 141913423, 385195082, 139026288, 100279152, 92613790, 928166961, 974805101, 230656994, 103036040, 271730772, 729256348, 744053979, 380809767, 438368481, 554343973, 168102684, 613646780, 855382576, 428824434, 232661111, 39380092, 187562037, 811930625, 382554075, 204331727, 22997532, 614208659, 850556319, 479441042, 915869687, 484792133, 990769112, 909379875, 22979837, 216596016, 584497315, 617160750, 966236464, 917716209, 442673399, 1922093, 889818191, 402113445, 188778935, 773469232, 155107634, 829668171, 813079109, 652915356, 834408021, 209412210, 723335200, 258999698, 418275519, 352462142, 313624967, 274541203, 64078547, 511509221, 162354299, 810174815, 771861807, 640952167, 944125493, 885825970, 812957445, 936656337, 980170647, 176357006, 264987115, 726511200, 298016678, 94056058, 341235022, 778159476, 902906950, 303557234, 148291631, 105307649, 632488093, 540431047, 772681159, 578409590, 953084180, 63914149, 923021754, 225225930, 290748229, 281492732, 449727766, 399125560, 425716947, 541189699, 720976738, 855437201, 758729057, 362287001, 403160569, 994019260, 969017020, 739469607, 369924053, 916470187, 467166660, 519713934, 694375141, 669584100, 235383460, 658911323, 630156152, 643970207, 383287790, 763038006, 484229363, 528869193, 273918181, 542537240, 115313746, 640301998, 955093795, 343059021, 5075944, 242384454, 191728902, 49823133, 353860207, 334767362, 463825934, 616173388, 858978063, 998660688, 103380452, 779790879, 309369486, 636895607, 655879343, 19548257, 940192996, 579785241, 338951974, 807511243, 635694924, 479822166, 360625912, 420825856, 900057974, 234627371, 928535257, 866236447, 360538233, 7914483, 131117419, 195108958, 594155344, 794075247, 768817135, 180422187, 717684421, 764382480, 944551919, 871683520, 5457534, 475870680, 515501200, 826261219, 910455103, 555608943, 723568962, 680570395, 574932944, 492532140, 20908027, 881620765, 93349396, 760558845, 939875676, 588548949, 828151295, 992507721, 582785386, 95916424, 197654634, 439390077, 993265100, 222828462, 526884255, 128164898, 982229421, 175655712, 905767387, 479456218, 859520573, 748837346, 273189300, 547377105, 992528983, 743621443, 144658266, 820742348, 599331115, 200087543, 998380264, 106920545, 434661100, 803883609, 281842103, 666714278, 894759946, 688046802, 491425569, 49934238, 131221038, 260278994, 524621227, 480778588, 994729792, 625927622, 840172613, 939956938, 339912517, 155995970, 691129105, 844544413, 609346462, 257893762, 169647798, 548840713, 840769650, 377223412, 217322443, 658583656, 123035024, 528623398, 126230338, 676634339, 182166515, 949177771, 584766139, 358242759, 286111498, 401252582, 399940165, 285350515, 21822786, 402724941, 150270772, 330016021, 20639728, 492842828, 537678379, 74007541, 149003005, 192056527, 39106973, 973705186, 887441877, 128802420, 892606120, 865781067, 581091435, 53215182, 416712236, 847306953, 893511323, 176726774, 815325828, 810055680, 473932935, 508055822, 859015148, 125798220, 861827478, 582320321, 277991810, 43671532, 555045480, 571549147, 876142544, 846090951, 767320881, 369938261, 735394584, 844543625, 792624844, 255589501, 612502817, 114328642, 510908499, 239451608, 13887344, 317427921, 105881088, 875179259, 579305244, 861031029, 426525567, 841181509, 626115567, 510898955, 428101431, 797383348, 19423191, 240332686, 604106534, 150504334, 592749321, 816314160, 795492155, 436028299, 968878490, 395164231, 392010513, 784339915, 966423952, 182561429, 981769430, 161322827, 654410970, 187505723, 236115379, 231879025, 205205122, 424532635, 812478010, 601947011, 286205281, 304567207, 509942382, 271190078, 191907480, 293466554, 285043788, 957593048, 430866410, 69293214, 390276015, 540200496, 538260363, 678765516, 489740302, 548442988, 501513623, 492341873, 361219743, 499179389, 331215740, 293938619, 654321410, 294885772, 455451730, 377608149, 367514041, 788141451, 209885129, 780705141, 299844475, 682443923, 77896528, 636248807, 549636657, 381695720, 917904967, 586067331, 179235571, 434133094, 754597674, 598105344, 965987377, 901277240, 656852288, 209165029, 991018550, 91756733, 970185934, 413052948, 605655811, 220512565, 362545769, 919947030, 304469278, 67790467, 418592544, 154309809, 45933465, 254676165, 797714489, 663267110, 922380495, 221428311, 661235353, 975341378, 832740526, 646778337, 271569734, 346078680, 348800191, 920029119, 958105292, 108441773, 779770047, 87978133, 503357971, 231952469, 642232473, 164576023, 820539681, 78342222, 551084123, 39821693, 655864691, 130930675, 360188811, 741284883, 854958912, 356873346, 143156903, 431405289, 686883206, 965562104, 163356491, 310674184, 30061325, 54568697, 26034143, 269286512, 727921508, 643433711, 403702432, 888420640, 750304036, 292156948, 248141975, 62143388, 254285132, 272006089, 770883383, 889246572, 528857314, 249395239, 685037184, 286822738, 674139759, 835137489, 419055844, 476087531, 969998909, 783347487, 564598909, 581463879, 15687516, 943644673, 890874754, 633609855, 750450898, 582467557, 484093524, 509215493, 159117541, 248992040, 863729824, 318475553, 4704794, 474753805, 494459468, 865359197, 980610759, 551360223, 793105164, 456648653, 684567497, 144379041, 952670936, 11712364, 857204741, 773319951, 705218994, 802653627, 32024762, 242603445, 340485198, 434425420, 495674543, 264171388, 903949147, 696028754, 193386999, 326023740, 775410562, 288557646, 107285128, 659669556, 498368387, 326667064, 741273778, 836353611, 500123240, 115330580, 117273620, 136532065, 829688194, 979996719, 691198818, 397297796, 678144589, 326654510, 560408834, 495745452, 687646831, 205764554, 344434194, 899868214, 99130283, 843625544, 985117546, 944345064, 360093554, 912524194, 679218703, 700299561, 900340328, 55576088, 399913098, 258750398, 924183553, 278001098, 589489630, 306984842, 217270358, 887774892, 998315526, 456169984, 425121880, 230085756, 409831149, 843923940, 899783920, 212572567, 166610054, 165541065, 260385036, 601248431, 713558458, 821084220, 539706562, 750536459, 269355023, 429158348, 344255518, 34934935, 26141261, 450859715, 734469436, 155347689, 498802228, 513428943, 400470535, 833263302, 441116646, 624277924, 620130901, 241005137, 370446696, 466190593, 38915627, 387631906, 641289748, 310116959, 5423460, 161180617, 169174106, 820457290, 825784314, 15466526, 293168327, 392524372, 487917189, 678409783, 929889130, 277709796, 576686620, 758963882, 362151766, 858886310, 926027907, 753142985, 690798836, 813814775, 480738354, 977746828, 800826796, 415912892, 180631987, 166328030, 601311213, 745237346, 676257801, 129036325, 34221193, 454223, 405523739, 312211984, 917940423, 674870238, 729427107, 804860184, 43516363, 143683082, 257870017, 183468820, 662979692, 773247606, 170743896, 590415249, 641193376, 581127769, 571071884, 427245976, 350598353, 64824963, 732070187, 226150505, 512608978, 667277031, 971668844, 345811284, 173976893, 885707674, 694588465, 853248880, 391313975, 548923882, 286808818, 335715195, 541829451, 631206293, 365677802, 356936425, 512100233, 648056915, 510988833, 21965381, 519977267, 59702995, 92864739, 337147374, 823936933, 162016207, 965073062, 997818760, 974983940, 386580088, 848171672, 894912773, 484242377, 685933589, 972109470, 714950947, 505053535, 526955819, 401913425, 968749436, 676713259, 348056256, 175494653, 346623334, 944983095, 838815861, 938684374, 118038616, 687985395, 587580638, 290751073, 695856930, 884259586, 501324159, 479111421, 87175338, 34114597, 443866588, 264584011, 283053708, 673123793, 222075315, 342857652, 10440708, 472520482, 692964436, 13079855, 246792735, 273250385, 606829765, 613504066, 61549114, 120619808, 811316168, 939432288, 719002618, 290129332, 402063875, 589682332, 258310188, 515109506, 637621686, 594025166, 517757361, 645377297, 293615794, 846685369, 395849101, 900224181, 45580456, 501355016, 945046661, 39860690, 731832862, 548873012, 399979892, 620330482, 188832318, 507207920, 329248322, 638150805, 833559050, 226988661, 288870474, 268399397, 908138546, 539813313, 619536357, 283128585, 787766890, 99188757, 10490261, 186119873, 374695863, 580558233, 845361096, 931884963, 736135923, 445598903, 227973669, 630375409, 794341004, 520839311, 234150082, 471995454, 835135090, 298509989, 873185336, 707548555, 969752444, 552660672, 788134141, 26000358, 566236322, 259919866, 646635053, 505867141, 528383048, 139818739, 786183680, 845044185, 311050512, 485803388, 304294283, 990464376, 258338414, 688897509, 656640098, 942893720, 503573534, 83155581, 191996770, 762594101, 578598201, 527601114, 934009271, 312291172, 505807875, 503541922, 555176107, 59060173, 233713983, 888503884, 692254264, 699788949, 12102165, 498377082, 855216078, 481606079, 48759741, 169579192, 932565359, 612571239, 619890768, 320179148, 516290712, 922186341, 302591435, 145234056, 359558015, 501223026, 814966735, 20350944, 247835217, 438042503, 466586144, 36022943, 217372041, 600454676, 336769397, 574543760, 983759682, 397115258, 167081668, 907430836, 169742397, 137579673, 829351987, 144850060, 244895652, 996812553, 146990973, 16838411, 747419701, 438341131, 767713910, 957597799, 422355393, 550950147, 271431352, 680626574, 290529162, 805111758, 859993331, 337139931, 606961656, 425393506, 613072012, 291054839, 799102588, 545138223, 562069342, 753630161, 794442681, 968645559, 102592861, 851830426, 12528932, 722676649, 695869484, 193205098, 56818311, 554026733, 25892153, 97988840, 482311431, 633061222, 442926232, 920698130, 349946344, 150480367, 383713800, 255244614, 140290320, 882386130, 76253973, 60762854, 766355732, 674849656, 718533988, 675879227, 275109494, 510610304, 532411474, 528898093, 574260732, 294558523, 743149547, 949902864, 62574469, 284474651, 611552437, 681315102, 56086306, 289483420, 120077401, 816901455, 401852248, 671773840, 551511049, 86510311, 201501274, 697338174, 648080983, 221005547, 702716267, 197437094, 623859568, 686930296, 741405498, 97898612, 677694777, 652305904, 552081760, 501711752, 90207392, 855946082, 506052744, 787880360, 31462578, 318027905, 742859852, 708733993, 738853157, 710134050, 59276129, 482112531, 821565368, 472026067, 160916781, 94025905, 197764342, 895062038, 772429718, 174475046, 962666671, 193704816, 221402813, 279157657, 260163617, 277633265, 779555042, 670689398, 420607245, 881264644, 687861932, 861637419, 887465392, 630194025, 213235923, 481544791, 555167833, 295493458, 653391490, 921215296, 786363683, 914059580, 700920746, 121941425, 784738516, 185439181, 487432427, 685044232, 913890264, 550991659, 910086091, 953883800, 295651629, 128649353, 36197394, 475861088, 687807640, 353055396, 485745769, 554878762, 669464001, 98437152, 544450281, 481829762, 888536494, 38697683, 658035981, 62610878, 967954590, 366583773, 858629362, 468633099, 449846952, 427727108, 817144944, 537383738, 931560473, 91177649, 165651387, 679733094, 955559627, 423381718, 991968761, 341063128, 334034696, 480933738, 37994480, 848448571, 674889785, 102834892, 290931147, 324353876, 986488653, 906555415, 652953983, 886243690, 185705196, 181651837, 963860665, 475614984, 709205739, 123365827, 500111875, 676656939, 435982781, 737716994, 166517231, 262538246, 140552545, 96866735, 381613675, 498792478, 861542351, 385121570, 86549933, 609941768, 438151640, 126879140, 560030080, 545508726, 587981958, 904231052, 593590780, 922943013, 588807076, 1812529, 929777362, 648825428, 811611561, 975088689, 613762588, 142611215, 552066398, 590524979, 407011286, 724001264, 550761348, 796262332, 941742812, 73907800, 256602945, 489266841, 619828486, 738487346, 969971800, 948562569, 402936092, 631530105, 756631931, 501495032, 639446453, 5494640, 677150195, 104696082, 578477035, 207225061, 4975738, 887503672, 854959891, 36601261, 158802673, 518630784, 160290986, 347400469, 398531879, 201432807, 310521825, 596467034, 455290970, 341583798, 386963042, 388997761, 55738447, 750012164, 169045012, 157253565, 343926525, 43464873, 608962701, 422819337, 576750141, 799744461, 266862623, 646453980, 790869386, 649169676, 273072788, 906986304, 384171640, 291079481, 4423314, 852190739, 995599735, 826556590, 491109260, 966381378, 870435386, 890055414, 641225888, 505430820, 343766892, 863535994, 663622606, 678223928, 957110437, 700875951, 666423, 289394936, 136721258, 617855944, 752729092, 359471684, 566639960, 607782723, 753926621, 694042335, 792404758, 91334096, 705724001, 643506779, 780506253, 554468413, 485487899, 457324468, 900814841, 8932790, 830694525, 869577485, 756638397, 173322406, 76523826, 522530056, 41249550, 274928997, 765002976, 842396579, 184918987, 734953825, 20112114, 177588394, 541121593, 687720358, 545009410, 249656197, 4219751, 230420482, 221828248, 576752342, 914261209, 16499826, 829594357, 119578267, 409985536, 977507468, 310881061, 42009732, 269359030, 199555256, 843803976, 17194820, 814881117, 331731900, 268843009, 661980976, 722976981, 383767963, 1966975, 868746138, 124955025, 839412186, 200756277, 454259141, 298376873, 568989338, 884404026, 339794240, 116594352, 256405488, 362513416, 265009045, 527594013, 208824015, 252904929, 168316150, 809798400, 252806210, 178489810, 356252730, 766949838, 158158503, 113396367, 190504641, 645882101, 195811823, 290850764, 863052923, 59460951, 544496396, 35016513, 126930113, 262063822, 817016676, 981382243, 847162170, 329675900, 159804482, 805375649, 402252776, 925855133, 843440200, 704600314, 603004078, 770528518, 545519210, 578548739, 893801892, 179521451, 413963043, 976403789, 493977471, 679460721, 880622754, 747412406, 259961149, 548554525, 661192418, 384022704, 77363699, 733598793, 415226795, 935037005, 99566099, 925425465, 541879874, 491153046, 477571785, 42725735, 60161359, 447280267, 909381975, 244216414, 116755617, 255292295, 466910379, 179664936, 717974915, 334966250, 14398103, 559953263, 680819347, 245785042, 84056463, 138920519, 276945508, 191957613, 236476574, 989974645, 893610411, 186644023, 414878072, 145978626, 501979353, 146539913, 78139232, 440139716, 607080313, 103192907, 657234388, 273241762, 445437882, 943171095, 604733990, 811107343, 383979302, 746012833, 655152012, 843614116, 376064458, 531861659, 893031030, 791137147, 344048988, 176775761, 642311556, 91261059, 388978130, 471211941, 415426269, 791729853, 507991461, 511256988, 325697855, 254680257, 259336880, 144523210, 349688386, 804390414, 262723103, 82675726, 766388578, 691809766, 369244347, 172790561, 711615546, 85070837, 639734348, 580345922, 335229408, 737817186, 569512210, 396145737, 193668882, 375077216, 527312691, 970816275, 463742558, 381780177, 338196858, 91789593, 99899847, 10586518, 40405921, 110664294, 376311273, 422539530, 766454462, 221319177, 995161225, 561375521, 840774641, 932876494, 293563820, 881052344, 794598962, 249572366, 238622336, 3791227, 401520949, 202932, 382377498, 758274476, 638871956, 834968916, 727482997, 277225510, 332603173, 311200028, 793965679, 933075244, 278711191, 128877777, 625277280, 332247354, 610589775, 703725627, 945853671, 675079598, 47571190, 737472034, 976110125, 715656326, 225413745, 388941127, 299279403, 405924527, 417262471, 581251879, 153841054, 388771172, 570018250, 469478863, 471091360, 637828588, 489028251, 59945446, 33010928, 171144549, 759994422, 143346573, 926601005, 303084043, 365045454, 793573959, 127546570, 470595094, 750399399, 574336492, 421412597, 65608509, 267620432, 280992931, 699704105, 522496981, 299246302, 383231832, 708332179, 918573350, 883008323, 2029244, 377079547, 497768503, 805604559, 643209825, 316108784, 599457420, 698855731, 61841330, 969788225, 565568089, 921450397, 975854140, 185525267, 176682929, 851702169, 442827121, 333666010, 759022964, 258785725, 734983301, 192907119, 985496074, 622349356, 827153330, 826385695, 396756769, 43527401, 859287543, 392884168, 260967702, 723550864, 606810705, 800506434, 335561923, 780982416, 550622174, 886090087, 112807439, 740100462, 210257796, 332204390, 507072307, 172844926, 187505485, 893796997, 108009793, 984627421, 724727943, 922546869, 830092822, 317603948, 992444630, 941444304, 697704904, 352449315, 984369583, 291164658, 99763326, 931634247, 219212097, 353006947, 410664919, 727542519, 614035737, 425536726, 607884428, 275219325, 422737596, 43638888, 807173979, 463496144, 156792057, 83017564, 874736970, 872637253, 170286762, 227174840, 815265095, 793035971, 779945733, 902910781, 589310152, 745007600, 420135667, 340490781, 244423116, 602191498, 676216134, 874651137, 153478769, 865243865, 843305576, 488776634, 779893314, 917525751, 562937473, 747057760, 66254422, 59690845, 548893123, 653661720, 551974416, 394416647, 348360587, 197079288, 756860327, 949634985, 644197523, 770945871, 644559238, 548648901, 842870635, 740203116, 850127606, 91089498, 635345876, 853929191, 788799499, 971805849, 87130908, 420292413, 478021510, 410713948, 78010137, 62939463, 713292681, 371336363, 633481509, 399457293, 176799897, 835808067, 613443765, 298639967, 623168634, 56879003, 684176382, 798389073, 418221451, 883771469, 926910414, 850031670, 550880485, 400612918, 567605493, 347547130, 119531498, 828239404, 894239644, 43267930, 612869763, 246148215, 477971142, 138486370, 81139529, 250786935, 205022028, 463339722, 838358055, 269524436, 669455192, 382593139, 908393975, 671069386, 11668118, 693977749, 976943417, 564831560, 187915927, 11456132, 638229611, 268574605, 130924068, 370709231, 602559530, 456661342, 590676272, 315008704, 836630403, 546523981, 236434328, 71162711, 860458029, 380434704, 528214968, 493250275, 925833630, 766792026, 896896270, 29820755, 846897669, 974876266, 810871721, 889173644, 611572408, 578618195, 62891273, 510959735, 18602852, 160959763, 666152306, 886530358, 540377222, 822536991, 648477686, 448048453, 334369430, 170010927, 304119694, 972415336, 356551553, 36151174, 93808596, 73935891, 993094197, 725678319, 994854246, 339346363, 725535456, 27375563, 414736087, 694961824, 269810808, 516087572, 744860813, 227939263, 90784776, 369637281, 780119320, 373458108, 26980237, 290598541, 587469186, 244869514, 395950953, 524038940, 500750259, 540263325, 927776490, 770263130, 993324031, 373493623, 461357922, 238433563, 99674637, 688240034, 229616022, 928982070, 358737430, 989109512, 915996507, 4239399, 196328518, 985557797, 834579322, 121750677, 410477565, 698656857, 394344342, 829506119, 301605383, 148233752, 739946373, 816073106, 455421289, 77636712, 975941815, 532096544, 796588173, 869875432, 974045725, 853793741, 82876928, 601947453, 912414903, 853835131, 982347921, 718164293, 50684990, 197005537, 392198239, 901075515, 825618410, 112528471, 420526936, 660865761, 207515869, 849543210, 317719823, 92930433, 1303076, 840185642, 540770015, 445229585, 544089858, 621828407, 374746444, 351810735, 527101255, 340324421, 747261945, 922213217, 917440117, 969241028, 210710200, 324228279, 331443996, 282660900, 389020950, 421463411, 653382050, 92767242, 320529759, 541335164, 992786583, 270817719, 384745378, 89195447, 196951169, 592323976, 372364623, 699915369, 968454120, 755682296, 569986947, 508648552, 221803067, 619967766, 61971044, 925543273, 287684627, 236873564, 813591961, 214294544, 644910558, 755165553, 946553028, 451952122, 49485899, 218214038, 612272746, 856611640, 890442581, 256362386, 785759690, 412598432, 663846561, 271419301, 470627978, 319899634, 481918915, 31682381, 705655948, 980900710, 460607805, 854025449, 609623969, 235747872, 646527078, 593429566, 70136303, 17332119, 739305083, 84959043, 6061280, 384420488, 422362606, 628571846, 802320066, 952350878, 475465523, 930901213, 484472715, 228175282, 206979465, 395752244, 655086578, 900265749, 829565792, 331319895, 362622912, 218894752, 991528027, 823712242, 326548838, 975303249, 960287373, 659390664, 518048883, 242902403, 844901919, 853113232, 725780057, 345534559, 306917879, 382950893, 197730269, 615741416, 312710343, 633783371, 466520274, 499709731, 875308412, 272336155, 25896847, 426985175, 56644038, 385718252, 832557145, 564471350, 304129254, 427973785, 220029486, 921460338, 69467943, 106891042, 568315029, 230531352, 33580179, 739380850, 602531541, 880264646, 92329060, 400841976, 433894118, 273269961, 447082301, 744503181, 402628975, 177048251, 906071380, 206361524, 302932938, 877825209, 137101030, 205095450, 874852531, 998603571, 455762626, 140081480, 164558638, 44607562, 204217429, 199470680, 661305268, 672422889, 53919493, 274926888, 566404958, 438303363, 692352466, 146460135, 232735099, 492853448, 616643036, 53086718, 937251003, 737915129, 521937425, 483283335, 794250808, 540941957, 948036551, 534724294, 441644408, 711699333, 535021850, 64531560, 377942562, 829175739, 469545074, 178104120, 159480249, 284286837, 125535726, 38620486, 261999152, 794644485, 956113733, 491457298, 664581823, 107927702, 149780542, 944718849, 667332363, 783741706, 841471967, 606233773, 269064541, 491870975, 111717572, 159146314, 990958586, 902785146, 660910780, 575906030, 908479836, 706188952, 388600932, 461248298, 916095658, 695938738, 624519200, 214216409, 836685250, 275334944, 830971730, 300924838, 447972937, 827004652, 459483892, 454505022, 474748985, 96450593, 164417758, 201158112, 381436979, 422422510, 510872607, 585926477, 329325624, 616375195, 693475742, 985651940, 16928094, 829357598, 545799776, 82353595, 13065224, 216535520, 689139024, 639830782, 761284846, 222267369, 779484440, 253301114, 769216440, 856552956, 279211812, 246404717, 337629928, 188662622, 233945728, 75267028, 142982057, 782196505, 310102282, 583889715, 939998283, 795870181, 624107703, 5092236, 56881101, 818921069, 208715322, 666852577, 445774005, 96416399, 228286658, 502284354, 260300928, 196586296, 808759817, 999517850, 199892069, 778726179, 689565313, 752998508, 183615190, 836426914, 679636900, 81591215, 412570528, 464620329, 542387138, 637186036, 713936161, 444077999, 110440226, 960048951, 896019031, 535162543, 318426058, 264850369, 491041249, 442185225, 381604853, 698253477, 311200567, 527525242, 823551200, 152090240, 368225625, 753254561, 472833943, 127635098, 485772438, 362318583, 822099632, 855606834, 632766062, 228350737, 708261303, 289341719, 861032494, 511181634, 602639767, 532728023, 356758080, 764135778, 347737444, 609061160, 140771524, 673647250, 324179203, 749549982, 856537085, 79678979, 582332822, 804037721, 663254514, 216154214, 115560814, 868416162, 49041051, 824571735, 548362625, 629841939, 521857687, 459305477, 335124059, 351214215, 832808768, 259338465, 569266986, 620491395, 761968347, 390431155, 337457127, 334091153, 920766399, 893167178, 414542629, 664557941, 774850257, 101176372, 924378291, 418018354, 346817302, 767028593, 289414463, 403149707, 701796713, 866720515, 410174731, 179406036, 544293024, 13424131, 302445505, 866777591, 785244994, 456040252, 868912704, 660980250, 270137453, 486173219, 65607987, 459735269, 635983153, 546650921, 120025864, 429840543, 397997767, 820150986, 275290786, 11489417, 709172715, 232066790, 454873365, 965998377, 385870027, 188369321, 78510333, 148313431, 943571945, 657509801, 632080155, 165109845, 52733063, 330658374, 239596966, 487963553, 907276896, 594247457, 187135297, 174548182, 906811082, 176293691, 207891153, 867346731, 484556908, 811873378, 336032381, 104130078, 766926907, 785606759, 843596724, 538279229, 238183707, 704285527, 204991124, 709473105, 718356807, 143692598, 578718782, 988862068, 133891134, 728858309, 159118241, 957554022, 329197166, 416909998, 959647036, 602706306, 707614108, 201929384, 91237792, 308139130, 503277727, 221157243, 831142247, 373161626, 606379259, 96564552, 66704309, 821956326, 795606537, 738318130, 52813171, 643400293, 700117519, 754773515, 206219483, 249459269, 693619538, 40466966, 145164065, 410357892, 352792174, 759837751, 948208333, 173561570, 516236730, 928461483, 299045684, 283113694, 464388684, 671178928, 666819521, 829033771, 420251264, 204389942, 890620477, 996640715, 73307680, 534271411, 475808348, 908725317, 22417921, 709834005, 29040424, 587373259, 253462669, 807511577, 508348625, 584879427, 138735720, 107675056, 178653379, 884139655, 335329806, 133413934, 60079489, 713460647, 897826616, 854739291, 973305305, 303221706, 80382676, 292587336, 590768462, 244113030, 735812305, 985082308, 689312713, 305987630, 941812195, 606376786, 844165232, 676770450, 79126290, 177387372, 845056908, 721856832, 801713531, 184301435, 944833659, 937307055, 77669012, 735249577, 79756525, 452789563, 615841044, 335609742, 382999855, 921293605, 760482510, 298061936, 686133179, 385280697, 229760512, 684358221, 848132582, 378407298, 456505428, 476172417, 936543844, 74759603, 50638918, 294053750, 631129271, 635599583, 321609987, 348123919, 98393629, 524728692, 52399534, 169947695, 565331624, 78529178, 327953081, 228972134, 741275467, 336602903, 938274252, 592277558, 126518880, 396648027, 89381818, 727759805, 988272083, 964995690, 55185494, 746321708, 764901331, 360580142, 969996498, 586566607, 336123404, 904439571, 888672683, 982542735, 841357091, 426930105, 616597322, 940830380, 100429618, 210182114, 968375667, 846035619, 799761314, 483759546, 656274021, 794192250, 945336577, 453889347, 92234686, 958948922, 432063329, 682082858, 508649859, 409329661, 49519680, 494386658, 243620951, 581884048, 543649080, 913647904, 121340163, 79671844, 72523380, 780199500, 862285074, 414467818, 887374611, 872519395, 168592777, 284131918, 81901028, 290215163, 89317755, 53965710, 138406440, 338333035, 64814065, 946444478, 252905132, 851795522, 20988696, 419502502, 816975775, 280512675, 24828627, 202603956, 838547133, 709029281, 398978486, 157748376, 656642280, 858291694, 538274702, 401290184, 689000190, 484511128, 101909255, 338769946, 674579734, 558647434, 289513867, 274716969, 768469693, 261491915, 730989969, 284945124, 934102271, 133765583, 172276543, 227815136, 709566697, 473536663, 999600542, 686814613, 428493838, 305520771, 946798830, 909037753, 821453474, 147886238, 454738005, 250958815, 204535993, 256830446, 936268635, 795330165, 427640063, 910724388, 299556139, 155997939, 774282325, 395376586, 979013643, 896259145, 891389100, 172800534, 552199360, 15830494, 699432716, 697379617, 780182146, 382578137, 721303832, 871849898, 985850461, 189459478, 347011983, 919192803, 528061575, 881378278, 584398977, 799098175, 831344847, 456510983, 318236310, 459331233, 852030097, 421498118, 776563769, 574866807, 401694955, 467145136, 307261285, 899702338, 774242211, 529862377, 76603568, 19486909, 769924895, 85736890, 915522627, 306528168, 105777547, 244026672, 490670177, 330432226, 610089991, 49193372, 594958628, 232589914, 321218630, 390558720, 276611320, 362250961, 154696163, 957513128, 764347450, 67016883, 644801993, 506532455, 705818383, 527788786, 132752170, 921419184, 740663463, 678275925, 746230174, 928633549, 857077135, 868309246, 239546003, 690855114, 754154071, 218335868, 33712382, 367060300, 358835573, 254976161, 193933489, 334160730, 829312493, 492464886, 114836408, 306334042, 973751755, 452037928, 414334787, 661368334, 51574740, 247387389, 962484520, 327960442, 139917157, 891441897, 752909983, 149841964, 874040913, 844400591, 912157473, 513608263, 351269836, 559118068, 93433104, 517559374, 886339142, 935530151, 584883194, 256373312, 880571070, 800118032, 425257263, 985939619, 297690296, 330330346, 417811062, 525323298, 745743383, 887429118, 159176115, 132062997, 215694973, 526134587, 337061470, 872527665, 864670519, 780595052, 885308107, 247970976, 232290952, 77043470, 479039868, 407302446, 52558439, 11695121, 291094503, 792124865, 871570858, 737035912, 40870777, 286349911, 388791104, 168529855, 209571381, 998969126, 411977453, 724350195, 317611865, 952176757, 669986843, 870649088, 328948084, 12613416, 241183577, 736241401, 551658271, 973158109, 853802378, 339544476, 352714003, 298346590, 636079894, 418776843, 805920810, 998132040, 943056735, 376519964, 443184519, 466709750, 433710269, 761770548, 223844606, 852648080, 222204368, 406802525, 591168656, 262565305, 413662676, 423153497, 384125247, 82590388, 712836720, 414969373, 157164536, 616643841, 252119708, 651156715, 47170561, 687068493, 661900335, 524577702, 692516497, 221113187, 664303296, 16322112, 754416170, 932095022, 273430163, 808205457, 635220151, 754587887, 831141792, 396267484, 182827735, 870619849, 776723299, 741768071, 711622547, 989969726, 403132405, 430511947, 590911497, 713958009, 122547072, 539192378, 842255661, 637867207, 102399692, 646819139, 405812770, 38676737, 495490137, 995739998, 905342258, 284853474, 606179209, 297561767, 166696294, 896563348, 807552221, 227863710, 879239392, 875972422, 317138625, 318422515, 796968328, 134487361, 913586874, 969888629, 611532152, 536711267, 175156094, 505172361, 706057092, 639332712, 954997025, 821597604, 791496840, 55156916, 860470105, 462065195, 720103010, 665147741, 570622370, 689873971, 308515796, 482343374, 349864995, 444815517, 290296340, 817201692, 563376978, 859021392, 247875590, 60247835, 752224664, 628017893, 809429624, 605156570, 459449430, 348766285, 67756687, 380604139, 407836979, 749791904, 12972519, 279111245, 586715500, 467916605, 36278116, 578040423, 754561382, 214350744, 746092689, 278485558, 940115134, 137139722, 369520302, 666343663, 646522132, 480315426, 601188469, 216955489, 340828103, 974937971, 116741891, 232685286, 755973127, 306998044, 866754103, 882508321, 460884900, 34496408, 13032346, 150037958, 527906992, 657722177, 231232409, 881337711, 145697298, 611008088, 823171607, 801932886, 914515213, 214973677, 967164278, 151759137, 477999903, 182847277, 715857338, 195043444, 302810071, 186464470, 374137064, 532574484, 691708164, 996542598, 938503795, 937956864, 981500683, 989788438, 712739488, 374663173, 105970623, 930688382, 382566287, 664419847, 170735056, 480510393, 533007258, 502838513, 856384894, 905207394, 785150122, 743733425, 665991331, 744252582, 41886165, 777898909, 768224078, 105038257, 457661087, 657692162, 510002602, 738669091, 49905407, 114494318, 26728831, 355227278, 180098567, 384780910, 37375573, 544222408, 703898261, 171637291, 755780106, 753136655, 571668458, 998451409, 935325078, 133810136, 739151180, 273483673, 251041643, 697212739, 801621502, 939509563, 113570918, 176607263, 288919053, 724130632, 77662976, 999425124, 974631089, 103979733, 503834522, 656928824, 70913514, 404275112, 452161610, 256092802, 969198152, 204763224, 610010964, 124554723, 459286351, 216130783, 51236206, 68929465, 673256146, 346976683, 220896093, 356931443, 520770021, 872528914, 457152271, 466242145, 648439592, 642498163, 803069294, 43412527, 996401431, 849914908, 361881938, 902888929, 901049398, 898121646, 984435829, 935631364, 626139326, 746602585, 26044129, 884695054, 796915437, 70290877, 221385832, 140790779, 217656321, 854920207, 230613966, 782487058, 657862008, 766439909, 913523706, 492410256, 61884559, 862679249, 70558343, 519088636, 745058234, 59272282, 853867198, 608439725, 251401845, 973946069, 757455820, 125669179, 229599510, 975015862, 231006506, 214581016, 358432737, 550146689, 513944777, 311354479, 596264880, 654877551, 51659040, 575957580, 55057394, 442090284, 257007116, 265598541, 488352586, 594249218, 73392852, 863347427, 314267112, 824151873, 692804664, 10650274, 81268278, 374873515, 543079007, 783791051, 385835116, 807807902, 246515813, 964284111, 468058393, 689424831, 587708218, 661616742, 33608922, 173529585, 52210568, 299871229, 59703856, 242352132, 192356619, 531750532, 352132384, 665505034, 504557849, 947686511, 895987304, 29906760, 864425096, 736057646, 513470631, 160954312, 857871830, 994362406, 103636140, 193382909, 652260484, 348027211, 573145623, 313123860, 56578363, 726432826, 55947858, 378598315, 397540853, 275664971, 909835800, 99906283, 948082429, 850560817, 376993621, 876198904, 744036575, 802800163, 547504543, 737054499, 229140836, 858044227, 807404596, 825308225, 870081351, 658806936, 486994201, 197560019, 782263707, 733916731, 316764248, 934182770, 650102762, 784830701, 532722694, 828957629, 989483777, 162798498, 638979790, 611838414, 67568788, 406994676, 138110021, 957827841, 57429629, 110610835, 104028603, 362653624, 76012524, 495757405, 406182514, 829926282, 142850699, 446238280, 5951100, 498107777, 876541058, 258558990, 481630818, 35457170, 203848975, 375487187, 457187445, 74934145, 530712109, 823943667, 169960865, 572118491, 974406215, 539886277, 814232195, 60785384, 146519975, 859388899, 375135689, 695207265, 963432578, 494849634, 633191498, 607349361, 832023145, 232852462, 438397668, 824724667, 316122225, 285710410, 891905460, 745556241, 893039691, 538679153, 424235447, 649854460, 212076226, 664570381, 9669899, 357047638, 924628908, 931320520, 420301853, 218222456, 829858360, 668754899, 388783244, 977058122, 356365625, 281501011, 189195359, 117050239, 684957001, 781223294, 282209952, 610504650, 592769555, 725019896, 528655059, 476382367, 393448761, 95905616, 680264777, 963426, 697491727, 80032896, 94557607, 760075786, 197092778, 842771635, 97277895, 358094900, 359516776, 206273020, 238388421, 375746077, 910276541, 474555767, 570271353, 256123556, 860892193, 211273074, 504736751, 507623749, 397854732, 667142852, 500602660, 144323200, 471603544, 204429849, 698697628, 236004978, 233601767, 132702886, 930655873, 23083410, 492603450, 536572446, 510423878, 982880162, 221334799, 641258176, 397278955, 431503033, 964115413, 144966135, 827755844, 267122421, 171805471, 800084985, 973905369, 553561634, 761536960, 356527152, 714823551, 507833482, 889956822, 761409579, 27971007, 414869545, 752877675, 274733055, 25702674, 253710303, 158239421, 349376208, 159991781, 447266906, 293076982, 886511786, 289740549, 729652069, 22094378, 563286964, 147499476, 694275373, 702535261, 851431882, 637739453, 537851225, 548027352, 947897993, 785936857, 634227792, 136240895, 883931874, 490437929, 354799194, 98775336, 361533913, 155993459, 100449356, 721369606, 209553091, 322846397, 340524670, 108096289, 180735085, 773770041, 660898981, 103828519, 985333640, 687537985, 81018519, 67357261, 870729091, 356863375, 507805381, 60835597, 950689327, 632843682, 737584108, 696045196, 879556032, 760075276, 331870228, 805079217, 873163227, 488144192, 380875305, 671727512, 656367242, 226979940, 293628458, 350202045, 672441328, 517949912, 944364908, 111994582, 604744305, 995099347, 724246151, 323254586, 482594887, 378233630, 969391454, 195033807, 338256623, 90030799, 981607564, 136493031, 769299452, 501036776, 297320103, 654520763, 423318802, 927932586, 811552986, 551766608, 796967847, 141902512, 802464146, 779276035, 637674376, 950617926, 654664070, 888534106, 319356664, 232419244, 965329005, 310098669, 648322627, 26032202, 834757165, 877341769, 600627240, 847413575, 619262016, 987617116, 421276175, 287886396, 715978246, 313721816, 921581397, 154251801, 713551543, 814779504, 929437414, 719177016, 189184832, 101193533, 434696453, 301747944, 257920, 969557417, 439373498, 469910764, 316308940, 64405722, 489811263, 240595241, 461663195, 819209384, 985669711, 286693554, 479476794, 307035025, 93913014, 636598253, 421494131, 488167424, 541843931, 847630753, 787144933, 502579994, 64162114, 559846035, 782944364, 244840332, 352562271, 393892600, 209222700, 451438637, 459064514, 693695775, 173514553, 982250458, 954383467, 919606965, 183738465, 117040281, 357387797, 711667645, 529704375, 961233626, 977586728, 397650002, 673572140, 961488779, 102024424, 286982035, 576457234, 335460491, 207812776, 683191337, 967290459, 686389524, 889155181, 169074829, 894019553, 141782854, 458965586, 221613772, 956728491, 915657232, 48296961, 321018987, 964544371, 761957126, 393283190, 519559563, 769456532, 225409563, 626842806, 134099621, 815975739, 991483536, 835739673, 659536116, 181236114, 705478620, 523425340, 866205033, 173871018, 555019034, 499025427, 120068714, 200816014, 986912428, 838703761, 775952127, 144818031, 376756972, 651220603, 466588928, 984713087, 328755737, 848237773, 149031984, 529960156, 125858660, 456483418, 128386234, 230603673, 76840312, 319173966, 719558377, 311657006, 246358724, 539379047, 700492656, 90968066, 134010854, 900966785, 331234448, 648721223, 943355679, 903580554, 927900209, 646870004, 581517191, 727118271, 841258134, 477382931, 843121637, 733215557, 517748112, 277329386, 304820726, 617005704, 15420160, 221597785, 338418113, 885287265, 308831466, 393042037, 630732711, 997082770, 465219350, 582334224, 618215070, 687694476, 354916683, 734977739, 598137753, 754540360, 689439562, 696675335, 717307252, 363787203, 835224856, 876262847, 6166775, 233812647, 51529050, 27430164, 679798474, 860636208, 539086104, 701951589, 231230213, 853372107, 233287959, 76384511, 524622029, 575099339, 33629308, 57314227, 779510160, 968790210, 150081317, 858140871, 310874864, 166031575, 474195373, 534402035, 300951514, 116485431, 550034695, 306213289, 85586720, 400853445, 522410099, 473759136, 313667833, 87740350, 578291360, 224305234, 811250059, 296729541, 968514900, 548969819, 540002252, 433924984, 561137527, 84901734, 508250575, 669090901, 915759513, 772221212, 746254600, 740954474, 295556717, 777808158, 910471177, 873987287, 574053760, 79416555, 547592988, 650660316, 264933825, 986658462, 240040482, 679177652, 478761156, 722350357, 644770231, 42349041, 393933740, 168665864, 609143499, 623364659, 958336246, 905668, 290881626, 882559967, 308533610, 586952330, 494858577, 25721227, 992220593, 176015460, 4461311, 546100625, 344412411, 588214660, 687676304, 517354603, 716668649, 117598486, 818300975, 35623408, 473409545, 793913298, 905441161, 619529348, 254538193, 758836511, 127988649, 497400102, 706103062, 550254324, 572183771, 448420029, 454664369, 994867537, 152286427, 236457929, 391351312, 707176465, 601469096, 881457524, 277268146, 168708615, 155630607, 396935584, 87827395, 934515865, 855777179, 507510598, 96237008, 69584206, 164648498, 752209548, 788267307, 815038029, 870605677, 441527924, 315167423, 693360867, 411191847, 138522650, 389362338, 336664233, 59416304, 579831078, 305712741, 205902295, 583226008, 554405198, 840453165, 195718959, 302981964, 142919532, 410930336, 76905909, 923333493, 796729939, 348804791, 86400950, 444707393, 822831281, 742754979, 718895036, 717511137, 304782514, 855027847, 784054772, 661884649, 310828555, 33382512, 842073685, 71839011, 743117461, 934782455, 590102844, 982592001, 252668540, 688723192, 419740207, 854643935, 787179679, 593849309, 719835361, 630897918, 959873130, 998855982, 248216970, 232306337, 394160267, 934789422, 88286707, 404310259, 989902628, 755937273, 859533181, 953544328, 292441545, 644936790, 469635750, 455723981, 625726826, 220994968, 171438244, 30382546, 390523832, 136051339, 647800119, 597324013, 62417796, 588873808, 105051959, 594076952, 823726854, 896865960, 776423999, 640635874, 600856509, 492973027, 544470026, 912918193, 329441196, 473270815, 56931510, 488742139, 417109152, 949411049, 981352327, 472070933, 569812294, 323916468, 212166583, 37549584, 973762399, 866452403, 879007081, 553765119, 727009432, 442688921, 677946835, 285677112, 518808785, 880948127, 984013808, 374171808, 147655696, 604620546, 496367691, 44832777, 276873498, 568341544, 826268612, 719466366, 335110360, 792015961, 757872192, 833158714, 928634399, 354739177, 667079376, 713093211, 85444409, 184470374, 454514698, 739576899, 963075660, 252236232, 694333738, 569454140, 399760441, 543165075, 826292235, 912312975, 663349051, 700137073, 67269879, 681944919, 588126951, 457788128, 165042533, 192792384, 616847778, 578541113, 981850289, 887055625, 889268851, 230901715, 207510361, 147993078, 325995721, 42103558, 571775776, 265487722, 428500148, 685705086, 148212859, 322548926, 373483345, 370412408, 748064339, 471587444, 326476513, 872352410, 423183588, 140681295, 180479465, 424317095, 385564677, 142315444, 457679001, 99023607, 866915647, 121463202, 533583413, 585540435, 495646172, 919107403, 72180520, 503266090, 48325734, 955890830, 189423620, 120057608, 366303392, 576907281, 412208226, 929854080, 182699259, 520863611, 209507506, 12737975, 729278224, 768512392, 352029517, 357114656, 748644282, 894483474, 917462266, 649657268, 535688824, 928269788, 469622353, 46388909, 335584519, 211007694, 25412548, 851845124, 569109084, 528613521, 851205847, 691662417, 524550741, 457975132, 488131540, 169831579, 40244204, 181526401, 800173890, 225115944, 604767078, 756915643, 480010937, 999187357, 955195707, 355011697, 213344894, 967775280, 418182470, 448466746, 936792298, 8778225, 30997470, 692743248, 946003996, 838897553, 348645146, 620856217, 249454108, 556205669, 930238375, 702796112, 710838880, 318143244, 48841965, 81584049, 99981602, 568975786, 332822472, 829063636, 765142711, 825302104, 164862590, 937077169, 174472295, 264743536, 433789437, 353905047, 903498952, 747523131, 920823880, 983889450, 610650898, 817721123, 166364375, 590877225, 863710456, 625097726, 802842820, 493073554, 503360556, 732592638, 575609169, 292570724, 352467407, 924400980, 315888065, 201673054, 290749212, 833135277, 401673604, 694986083, 811999650, 768075601, 699057304, 26431418, 800006819, 105221143, 843208700, 731893784, 198480549, 560024515, 286273249, 601053015, 8671978, 434987664, 846466037, 244673416, 900082755, 672888013, 965068983, 257126359, 468702595, 764944459, 351334105, 653905858, 209185661, 268763357, 669352836, 96905295, 905542871, 554433918, 326785866, 454725039, 7266457, 637214524, 726643182, 682075741, 229212488, 280857510, 462590387, 214463157, 845828502, 182272131, 182003334, 597334899, 818145727, 547137790, 456381590, 866453863, 704119220, 814671028, 993973172, 650989816, 820764177, 336392043, 463916454, 664952638, 598462330, 383598864, 79696988, 29817230, 648827765, 251192989, 684089960, 652918314, 449663994, 579679450, 779266689, 639641258, 914624908, 637990972, 348440201, 671161025, 25389862, 310612270, 481595789, 413022020, 740576029, 410572455, 159775046, 764679866, 554784641, 15066689, 142099363, 791009774, 878067507, 357726155, 142104139, 583563794, 813842481, 954026998, 202282664, 326848203, 45615895, 682431341, 279671616, 208213885, 477861636, 138029526, 525220805, 946283845, 218574756, 295443802, 796539126, 126388103, 959156765, 271415778, 476184288, 696885623, 890338473, 33064907, 987430400, 450290133, 811481782, 774387257, 576197366, 336567917, 27850672, 468546617, 588127683, 951803868, 565336773, 609027440, 14971443, 6879533, 791708119, 743923801, 905420874, 35425629, 526716279, 157738011, 456413263, 49983783, 938533192, 187510150, 570796948, 514290075, 515124548, 166028419, 474581657, 529336375, 399760823, 486848094, 901137970, 929932656, 428871823, 156067225, 795992721, 504006393, 743673299, 966235601, 279160111, 108723397, 635725176, 460059727, 705069020, 328001277, 280617033, 25297864, 990589012, 167928935, 197578987, 179006414, 269755990, 277002320, 289624179, 55492310, 412882944, 8309604, 915849956, 310965097, 179099660, 812320167, 111050087, 525194582, 175846407, 245307978, 105598315, 826863084, 924445978, 785949378, 869403258, 369026619, 152670731, 756343220, 667112949, 112232253, 416647620, 339173589, 931522486, 718699267, 256634679, 396283308, 567611063, 297918489, 328150210, 228990, 742914805, 209667166, 645729415, 493952213, 471992061, 856546829, 790195418, 268455314, 645405540, 123572351, 997253146, 241844121, 667412339, 537255291, 598223860, 766724484, 696631984, 633804238, 757792108, 671402256, 301821467, 608125808, 736747037, 948632927, 4884674, 395773898, 977325329, 586003999, 881692169, 618082238, 231456571, 741156590, 979919882, 924710421, 883380906, 196680299, 752592080, 237387931, 506573342, 506452484, 530938587, 678949108, 302165435, 454492008, 35712385, 225836865, 459916727, 734178274, 973420740, 752325956, 216589547, 998752509, 642748667, 57043409, 673156316, 400524822, 22535742, 413537704, 943632647, 558312303, 788482720, 919602107, 11075459, 988543178, 708242781, 800987753, 806064976, 455591880, 649467104, 212913844, 178274140, 448509937, 260842505, 290189769, 886913598, 713375396, 530244180, 896110902, 575637318, 128542507, 255514954, 99727221, 862161367, 124783309, 413627700, 285708247, 625301893, 569585073, 820827082, 71394326, 819533740, 963867939, 898629993, 539411878, 217331938, 540543409, 439080518, 502552752, 471473187, 472377829, 425434540, 18627670, 55261780, 994408106, 4109648, 763710839, 230656989, 237433471, 572424953, 545078062, 559326689, 770709199, 810282123, 699512150, 705851026, 89531763, 402859516, 292406004, 810328011, 223491407, 54438812, 128637546, 333087963, 832417736, 830633239, 909278488, 374597281, 753625728, 879186353, 456497019, 412780429, 650248384, 331058602, 832206401, 621339133, 243410538, 990198021, 326624442, 550503987, 125927053, 80967232, 942862344, 25472765, 744694195, 35779970, 640036987, 22682078, 883077717, 322670135, 91724626, 479746326, 511763274, 640084259, 632955027, 820315586, 974733626, 193609566, 549954014, 340870604, 190882028, 221421106, 399437665, 3802957, 392415265, 959945483, 492280691, 731789600, 877117708, 441627893, 623982808, 54327408, 591764178, 554425417, 707135498, 132680778, 926563439, 262979018, 908950836, 326929176, 313443677, 433949998, 895359412, 423602181, 156016850, 49723703, 381230574, 848933980, 205200990, 201879015, 833570445, 989029949, 736991230, 727873403, 637803974, 25506537, 476180363, 767181215, 53673250, 619422420, 596043886, 121517341, 790165881, 801852924, 508080132, 353923841, 175090359, 184418739, 423009328, 890991070, 657111590, 137015664, 824893501, 769585511, 405554354, 32260350, 303392524, 82030605, 711492759, 835341829, 353817245, 949760915, 288406326, 25606118, 374729689, 195406463, 489855410, 59703934, 769998208, 990386614, 991546295, 11012545, 271431447, 908023728, 727804293, 320672313, 698090053, 894489383, 943486503, 380928372, 447385600, 852269698, 879713472, 714660959, 492546999, 741649483, 57489315, 933311621, 908631498, 57399138, 676093953, 389647728, 463777946, 98127801, 862572236, 976911958, 783772440, 231892990, 478275577, 543868585, 874542889, 768296796, 526340163, 972912941, 440821017, 865419290, 111452576, 988383273, 506535966, 839163412, 407530130, 39928245, 665376384, 123786062, 906336485, 698779052, 151532523, 341028867, 205080310, 173562327, 726524615, 548226254, 838570605, 588111313, 372284061, 229957448, 342341376, 235950770, 569885327, 682988481, 826118065, 892188272, 47197218, 573562709, 505576689, 464395067, 369612933, 973103845, 551577042, 704318031, 895602679, 419355990, 621925430, 487214286, 591739418, 374756499, 194078436, 14508428, 831217457, 172155596, 455978945, 553353626, 609263342, 889565154, 484395915, 415985746, 164790230, 263520812, 44785478, 881016516, 332702189, 325353136, 975954495, 482259475, 841353501, 818356087, 169764105, 449995630, 923201350, 702071736, 230935279, 238116314, 310582539, 443792919, 645559734, 282115412, 702100760, 432274828, 766130333, 612157103, 187472155, 164980847, 365535449, 958321269, 900754710, 348855209, 22240380, 115342090, 501503243, 332376131, 951436608, 883643034, 169346965, 35417367, 261708138, 890652939, 159067732, 568938766, 526230552, 519771275, 969399614, 637635380, 221183174, 410150018, 471010858, 790315298, 859784461, 45175643, 639703644, 240619399, 618988879, 630705686, 31736231, 323077641, 671365145, 626630258, 96411963, 165639304, 700569447, 446751749, 859475970, 24076939, 261158391, 502486228, 104839767, 965797727, 99784781, 558043350, 436224411, 392857131, 875640211, 635381828, 192020590, 602443974, 401468608, 623488705, 789568217, 117293544, 591747402, 190062963, 192060409, 474399868, 992156701, 340343270, 585302452, 298825769, 174662624, 145463887, 123853325, 669634293, 77680653, 10853640, 45139324, 884769959, 59196222, 842305689, 656113645, 420883223, 691941885, 497356915, 436612091, 584994360, 79737066, 713436461, 741449021, 551513181, 928281588, 351489643, 103502951, 524106590, 856114738, 43572112, 580740889, 683785728, 65254220, 298261248, 204180956, 393199323, 167223886, 849962548, 284589583, 74268513, 687413213, 474258797, 716160614, 219789103, 404936225, 492572490, 871787606, 236839779, 682824773, 789952133, 70036474, 777903231, 435210380, 849005455, 885860853, 342896144, 402330432, 557990996, 421344473, 672071435, 348702103, 378072127, 196421073, 10936184, 33470091, 133846413, 728136593, 455476026, 658770693, 357657725, 278013451, 806139268, 823285225, 531136578, 265182079, 839542112, 807530292, 175591032, 838215616, 458602096, 145806463, 81464313, 973533503, 116674789, 231099352, 393936071, 103000868, 161427472, 339510138, 556795976, 273832894, 942457997, 478990254, 233946058, 414302070, 18189801, 636098336, 878873984, 953941238, 751041100, 750008613, 244704772, 268022827, 351258638, 262363316, 726663635, 179993882, 337638673, 628305494, 468710258, 101796801, 838410875, 577292285, 276690395, 266744889, 523126037, 51676295, 919072151, 946780244, 411089225, 313449425, 812474046, 619534927, 537977955, 509063080, 36769227, 57020486, 60933580, 879233104, 617271009, 174848046, 360631688, 719309324, 396428412, 886096213, 555237373, 672402191, 191299196, 370584743, 485052087, 455004587, 676085525, 507247642, 654417625, 195923582, 22309933, 787785560, 527012722, 523906493, 853536557, 720596417, 225709271, 564395819, 113724381, 798252102, 900310983, 486728042, 450408854, 774972660, 240210933, 518928476, 857270779, 197851317, 615614126, 483951621, 334849852, 330597242, 284199633, 184439579, 570759013, 333919237, 146394220, 900327429, 155802224, 31210428, 985306501, 430084220, 736119949, 394176492, 245684640, 710125587, 702770306, 545739238, 905147497, 930756705, 508024587, 864019680, 158138371, 223532555, 68431229, 710797839, 105384940, 628993919, 443392756, 128541775, 142275530, 341915524, 952130345, 211137253, 937262976, 706837197, 319777548, 869541518, 559492785, 87145888, 665773099, 260269473, 141952732, 199439835, 353377580, 913801345, 686125154, 548280205, 82370198, 148927725, 877076535, 550201843, 965008174, 671083405, 886529904, 477258209, 500506393, 987008042, 502707550, 512582685, 718985560, 194860331, 186953188, 68727759, 263422761, 730932379, 195056817, 52111415, 707908839, 463639415, 304898021, 83759414, 679599434, 840062522, 92793870, 338542537, 875157034, 714487172, 706591270, 998626171, 933322844, 241524713, 348354298, 406760453, 52078136, 446693137, 258718768, 731992254, 174905002, 135994850, 607628746, 619723248, 224258318, 793133408, 271618049, 163769897, 560431294, 396654591, 160318857, 26238237, 380160002, 767030030, 940027013, 742179601, 989796906, 698374626, 574543207, 48180236, 104202421, 931558205, 696814464, 487352150, 677478916, 161585630, 416545056, 937633205, 825055925, 785140113, 42527811, 731302731, 199538349, 994762572, 123901417, 543370140, 682569039, 705449958, 256032967, 984505253, 913633056, 335654227, 583191733, 979594337, 45383677, 590220306, 996772833, 514284306, 723854817, 696358989, 989104685, 986831851, 766139930, 573514863, 116271026, 723742925, 883837833, 319162571, 913966109, 192663028, 394100575, 771954461, 198261763, 602442627, 873174990, 617038668, 529103481, 829997082, 387576375, 30258897, 560576921, 802792458, 838380727, 662189434, 313741665, 337643672, 353470417, 840532114, 784394867, 768686709, 153524351, 409534627, 131892104, 836064444, 283793633, 189399783, 15202548, 402149472, 275764570, 965895784, 776579396, 957922992, 612068573, 740562798, 715865897, 369392192, 606723388, 766552178, 501117761, 991567189, 208003124, 213093684, 300451218, 354649074, 671800712, 167181772, 188885411, 878625925, 903998692, 868548343, 486435170, 796364704, 276396718, 8661428, 767476478, 328801720, 85274123, 164310562, 451442793, 298528462, 758108141, 259256862, 257434114, 584219632, 6676958, 65846218, 535138266, 294189545, 589897559, 756881296, 976726599, 560288165, 429634634, 607927095, 264308665, 640463555, 867658436, 991570977, 73483624, 638818417, 550176234, 415646124, 846699261, 526568378, 305312175, 774078320, 629231513, 383385465, 792002193, 237400604, 705652151, 684613424, 701807631, 2405207, 565836356, 877581328, 117260922, 790980719, 140664367, 583129498, 707712081, 97701926, 466048580, 792532738, 493422100, 90153007, 348748585, 307690816, 294322291, 276980719, 501401023, 513436390, 740897191, 435499014, 513712642, 8377410, 673966075, 782637566, 181458081, 617439509, 337741339, 809029038, 528600565, 898004465, 829475207, 436948461, 646129793, 102765544, 578123684, 623338284, 564328026, 574132806, 470840197, 897736104, 795698892, 643166589, 308000295, 308382346, 997342274, 513563331, 302708089, 914673211, 706355105, 32767191, 712613157, 662610710, 132912804, 223486775, 761501594, 433045304, 929820561, 724710756, 232528687, 945897778, 752185173, 916013477, 19955326, 912472617, 957462709, 496050275, 363155549, 139451455, 916708553, 172543487, 604456212, 805750603, 831879457, 382095402, 263625881, 96999512, 668914658, 639311069, 717751837, 535365379, 383243487, 941785570, 180537566, 484875076, 733718865, 996196853, 79837061, 805937492, 893440004, 197596864, 236749418, 720596662, 182651905, 387460935, 911923503, 186500322, 34415572, 484618728, 735047428, 910688613, 490591681, 512030447, 423517989, 291464383, 739424950, 656542115, 934577754, 89965981, 482256358, 960166050, 583291117, 238206149, 56124066, 148835049, 40556419, 283575512, 855331810, 149283577, 398692775, 809843956, 614721528, 689390136, 637084665, 968245542, 475794008, 152591442, 296277557, 497404854, 35496381, 23266988, 645183902, 560729358, 969478946, 565873850, 562261210, 630908011, 166922310, 638887421, 646437798, 979052004, 116360114, 480040404, 824791817, 502209380, 751350076, 570694828, 417140031, 53730622, 246309891, 682721678, 77330792, 751395578, 189164783, 584634653, 777242079, 375682509, 202969220, 932923654, 615154941, 666158729, 438214853, 356679086, 376950609, 310725623, 938291072, 835705598, 47940100, 470030587, 545061419, 651204745, 642456190, 116650190, 350817075, 477870197, 431353110, 303437240, 754796544, 842800798, 638284045, 678394884, 382976284, 586044895, 44382379, 694363563, 407434481, 102746, 53502772, 664721428, 666211593, 475737893, 785224722, 577407803, 885339317, 21774848, 447329056, 289186593, 327713071, 169951272, 849386534, 734324208, 126408166, 692977088, 139553067, 314052816, 573581351, 684512849, 107136913, 806611023, 358863321, 634282444, 564096518, 43746784, 117680900, 457466489, 111937797, 662384916, 814620530, 538452126, 136270687, 875131300, 47904503, 66741374, 677250220, 4441301, 990030193, 567364617, 273716876, 135387598, 290321756, 651799275, 859773052, 312595428, 670310388, 860436374, 413684184, 843468751, 179868533, 954437140, 347783424, 168359437, 568800504, 37673812, 174191610, 260605305, 546544158, 201059441, 795412950, 86639814, 509877992, 838159453, 895136325, 718532683, 396431481, 508844231, 564519974, 174834802, 710657820, 888507264, 444535888, 684790794, 567232258, 539097858, 530780487, 295416531, 363746911, 871143957, 196779357, 189268027, 273507564, 501367574, 629917300, 317203574, 573707649, 551516829, 535441024, 364276202, 382861019, 43229533, 79515341, 29584042, 899630833, 852797203, 745239421, 998811269, 370220679, 780674607, 707115003, 698734497, 775466560, 55566346, 200076750, 870911764, 304895290, 279680166, 351757412, 669623825, 805757290, 317560812, 356305091, 472417993, 757441571, 227554328, 130962788, 778289040, 685952844, 19557928, 175743694, 179197416, 502722025, 188571642, 640900762, 861791988, 630538453, 483106067, 374403140, 823980452, 369848464, 816514744, 620365627, 63211158, 680671599, 836553434, 48152970, 332397232, 880300868, 529108621, 607342037, 496142339, 518407052, 372905892, 230712418, 860428377, 69871770, 516074240, 308065800, 163442017, 481467969, 936172819, 134244256, 748220509, 933693187, 323341613, 202081633, 967317498, 595788736, 79230558, 199272933, 819632898, 861714677, 560565612, 829308517, 179295282, 404629805, 961170649, 834649985, 929564266, 519571020, 796611481, 334909228, 738298254, 308549264, 738997693, 711010694, 785871167, 347166326, 895313696, 782507291, 730606988, 125648599, 369638580, 265991493, 30972756, 671580567, 896202380, 539573703, 923155918, 503511615, 411305019, 168129308, 413600356, 363831306, 640674860, 553698802, 875510506, 714562937, 695365045, 724057304, 983879537, 605570455, 479736385, 613598014, 948286657, 756537652, 106959458, 686133523, 146465582, 983863585, 569417231, 447771019, 313870434, 122567954, 144488587, 770073115, 607397269, 848615455, 631441575, 160213559, 717891006, 687299495, 426325067, 483441104, 694317916, 770328124, 775449541, 821999332, 612188418, 380340598, 918607696, 10863547, 594489180, 823545585, 223826457, 88973140, 488465021, 180906129, 969807980, 625074721, 614099257, 390502659, 55285267, 576560654, 406148170, 243663186, 267867732, 861231722, 623325523, 809968535, 449938984, 895622103, 748362240, 368977301, 29599641, 804761079, 110804596, 274250691, 559106871, 903355917, 518972924, 863279295, 909129298, 518107169, 953905293, 355725011, 255123304, 339251479, 172925187, 832515613, 438842703, 369888690, 737981847, 818163289, 251664879, 590982291, 371602470, 296545664, 913734949, 558253172, 123764420, 704746333, 93600650, 409030626, 340983928, 979736091, 164635777, 539469230, 34410663, 100973389, 63695984, 541376857, 317290084, 320046659, 199604990, 414176386, 911318744, 325967768, 704452488, 537213025, 20074872, 994518134, 848900981, 875260343, 509929572, 511628247, 129748991, 168338195, 224108911, 982664605, 421993177, 909500347, 337764859, 499277310, 45181259, 431869222, 958156302, 778799208, 100626710, 820354615, 123793936, 464159345, 484695427, 542527751, 199513436, 33095218, 305661965, 373291069, 504066553, 586217106, 449208090, 382954039, 864321741, 438451227, 262019351, 850375989, 194955584, 296540488, 222717085, 928071633, 786665976, 753733900, 43126079, 157165739, 777258626, 214926511, 330192725, 836405650, 226850237, 547907900, 115595448, 640799163, 511942152, 950656874, 46113396, 879108160, 42809770, 298497958, 102009622, 831717788, 882642767, 584714325, 75069873, 369624283, 25731550, 764506522, 897014192, 981176354, 334644533, 350517462, 105502114, 722103734, 145609634, 423797089, 620039248, 845428396, 400492216, 524944695, 403575831, 345571749, 539266439, 990074819, 265229416, 169532538, 25922475, 863014652, 40336617, 798944741, 864530459, 987977600, 303345347, 299640578, 442952239, 459090467, 196981612, 433064383, 340608146, 613771775, 804767583, 521388077, 568683711, 363355508, 963958974, 919305969, 916995757, 341574265, 227767365, 81988782, 892994365, 141937310, 86792281, 271694054, 193882152, 361785483, 12072137, 316430254, 881372287, 596585681, 293374224, 686828810, 253124006, 9810848, 963541537, 619310780, 926869345, 9682862, 560822785, 796809984, 847602812, 917152037, 694356977, 37185359, 789157130, 683502921, 67087282, 557323840, 722625411, 843837186, 820280899, 856365262, 788482202, 29084993, 146790815, 570218080, 845572352, 814293673, 48598728, 801953565, 786151819, 796606811, 706820264, 941395685, 940642068, 98776710, 77481290, 500275620, 584778996, 483970519, 19973632, 370370679, 262650680, 448988827, 98316926, 659195209, 684721430, 730782163, 247482079, 415387638, 532589252, 611306019, 221546570, 902902198, 424675586, 929900391, 124196805, 801144829, 445046102, 712921493, 612303058, 15195117, 839758291, 882380645, 335796540, 400104805, 494883039, 126998317, 187439928, 533733516, 805247118, 805124836, 85109207, 894010950, 561809948, 459163502, 640217743, 473528265, 10494287, 252598610, 621534053, 315108628, 117641941, 943440591, 9353504, 232128886, 201447337, 842073761, 38001231, 567610592, 967935631, 204720304, 799622071, 706332949, 486902239, 137257659, 555851679, 444552405, 260152339, 534528259, 525361264, 894497027, 203390724, 580834005, 934470811, 324027679, 549082144, 248703259, 532142551, 406356292, 841812256, 832779679, 575198324, 410819773, 787507769, 318669018, 67497625, 740312818, 792033866, 606097123, 182052366, 418716299, 273221144, 182306023, 355419402, 648242032, 525826443, 404668399, 114222987, 755888827, 451112429, 620003473, 849392111, 657045356, 524376299, 345754596, 144393406, 457107782, 964222132, 690377785, 33397825, 282228484, 104096789, 778832358, 670852977, 757991950, 884330505, 203840139, 926464183, 281121884, 921626842, 670607103, 374239536, 720191110, 99092859, 368667406, 459210792, 443725871, 834667670, 758335538, 37196847, 131453472, 540860030, 31939260, 330469308, 613739425, 700268689, 710697586, 322319337, 538847576, 762962806, 922051232, 418346483, 667381707, 735334369, 578170395, 127215016, 725111270, 607309701, 4418050, 366901037, 258285413, 832993291, 161184747, 647772582, 18948360, 513436879, 695406346, 442312996, 103364906, 772297236, 162929286, 471435691, 598455923, 625367343, 173860900, 878497584, 937747577, 296033112, 285349271, 247404599, 742389975, 129482552, 133222788, 179239363, 835243107, 824654030, 490714461, 723726707, 267970901, 65233687, 174057898, 106435313, 287757913, 472980668, 221541530, 347432119, 290643279, 705066381, 900861011, 579120084, 280173086, 811652573, 539410484, 181331981, 494037033, 658082884, 902559735, 669085182, 995769396, 118450161, 122622159, 389539247, 706305537, 496224731, 343149246, 660316801, 170529806, 3256787, 56208733, 903516890, 171750853, 211055229, 384965060, 970086841, 718565621, 884323960, 837127609, 588957544, 366530463, 609611380, 627012475, 741935624, 155737270, 871249954, 469517811, 936786762, 499125678, 975684537, 511949367, 904890090, 519423132, 685912395, 625104801, 945745107, 971218843, 885307942, 360686148, 867316664, 342910123, 465908540, 775737060, 792742869, 723322097, 171737005, 922116456, 680243514, 266163049, 949067755, 23755853, 725289176, 985200081, 854177990, 925247300, 396613972, 901771130, 708689973, 301155521, 807247704, 788347679, 295678616, 151535565, 513046555, 243415001, 817190764, 535640961, 880649850, 141093186, 947924397, 741281200, 904215905, 967662818, 235164411, 389225572, 612504384, 928930569, 222344003, 200545993, 281556722, 65883052, 918110516, 900568423, 732785346, 57462348, 211629110, 267978510, 149708310, 565962491, 971066875, 832075149, 913384483, 446298856, 290841228, 855910908, 384086916, 880513724, 450532063, 560515111, 856343216, 415409547, 181756872, 517973374, 920127385, 833970331, 936341848, 125356205, 592141505, 249186758, 269831905, 688499005, 68542339, 363858327, 52844092, 992673062, 340978268, 750825441, 815406025, 246750865, 460596931, 876985401, 481126069, 249834283, 618603152, 685409600, 178079501, 955223812, 401478951, 437616748, 162942823, 737011333, 559943969, 122198318, 591949916, 348318251, 270212651, 284763460, 926179080, 815471493, 761363379, 448433314, 346246585, 64725507, 403973914, 500509662, 919358929, 962222238, 188957886, 547156244, 917953579, 305628129, 450222564, 592814538, 769217361, 831719056, 404004289, 247224271, 153962491, 886980707, 661045125, 44949670, 196765088, 856516708, 985412568, 490288693, 426038400, 912111615, 51765623, 816818440, 250991983, 405546006, 73143511, 972308069, 862625707, 856536945, 79695956, 833171130, 238826868, 670056396, 453908547, 339534139, 282774218, 925747982, 203957882, 328316361, 501982884, 456271192, 363883470, 956721277, 908403639, 139221134, 688593386, 399763829, 7321529, 514472809, 434415475, 78423772, 573033470, 689989176, 493337160, 56995202, 982627666, 54422449, 569514772, 509645607, 390771582, 338657363, 771793068, 871539296, 733739011, 615959502, 352616216, 101619918, 242434560, 761749778, 115855783, 189612198, 385646946, 564299040, 209773659, 408316966, 891445324, 104131987, 752138159, 110296285, 693735492, 26311945, 455062981, 394118642, 786089500, 144374628, 304523614, 907827169, 434330646, 531364078, 510074706, 561962317, 653438909, 180026933, 389806098, 291134218, 417842703, 25608147, 320406722, 57508817, 571531295, 432640445, 853450156, 961671945, 791338566, 463816227, 587117816, 400321086, 660348901, 178195833, 939993234, 28172923, 101584356, 908579858, 700523240, 932238755, 522467248, 323537808, 724294300, 440596379, 635729987, 483787220, 491844994, 826043571, 190326399, 231896074, 241472944, 148332208, 876453782, 98608986, 657163706, 458793579, 793491459, 348660044, 592332929, 773120455, 289652955, 947636480, 995345720, 565559240, 510163500, 963616239, 847967675, 379231249, 296390249, 850066679, 853968590, 139431358, 314836829, 94391108, 737541288, 277619726, 633961339, 152630436, 1994562, 819343877, 273977979, 977773429, 99995915, 302614637, 170872203, 261558437, 255955112, 688401109, 958416664, 782452769, 663346978, 27224467, 120848706, 235115463, 706979563, 135238220, 806538279, 525709782, 767556083, 986852268, 227719090, 393540026, 227184045, 740625967, 237311001, 794716503, 845567368, 926431341, 719103330, 991817039, 793447675, 344056495, 235412363, 875258384, 574338627, 220656740, 507222580, 230027636, 791705849, 163421363, 620056614, 883855297, 975659660, 497909411, 238001938, 869995347, 316393491, 759236087, 918223880, 789991530, 698119169, 672198828, 19692972, 256581416, 486029661, 692669543, 451219708, 136177378, 981143974, 536832586, 360727416, 778370486, 783476249, 982924375, 708173682, 457831402, 152500918, 203104514, 694096166, 654251383, 488379803, 437167830, 270848416, 422215304, 739586146, 147655046, 307035731, 755243132, 157453438, 3219139, 952705655, 265454156, 243274015, 527171948, 441910706, 533693868, 282199269, 937443099, 88074088, 569743337, 787742910, 788471338, 885044752, 24110180, 625458412, 990450706, 816458634, 538452240, 778026894, 449216694, 925373078, 859860389, 55472999, 348481124, 856099206, 701215976, 373334705, 767884312, 505673764, 267431112, 81453732, 653954952, 668877143, 469247774, 511586062, 723372040, 530948139, 508183820, 873390520, 502327159, 224110522, 919626813, 609517301, 669654756, 554582767, 68200603, 257007711, 920576798, 533843096, 843394783, 640140756, 902463839, 329444564, 229705677, 456286858, 517135381, 378915557, 76367901, 162932613, 757598540, 5710557, 384358313, 253068762, 977982517, 525422961, 229854965, 389306001, 674071194, 165325171, 892414295, 426666200, 338775222, 598404869, 566913903, 689619774, 250827344, 348390951, 379760226, 719464817, 522425133, 238567288, 907594599, 387638216, 57136553, 9405182, 339994417, 4176174, 891435189, 757965408, 539061296, 657298747, 963412513, 882441251, 311991430, 562875906, 155205161, 349859780, 715558964, 569541809, 891978607, 163470729, 831678599, 179993159, 990546303, 744770571, 165135301, 449822149, 803175849, 596505271, 236924151, 604392693, 370622384, 380365208, 776453359, 120444189, 883849728, 940077431, 566187, 362268048, 247852693, 722363741, 384981065, 7189244, 445932806, 915554118, 615646741, 755217766, 214801170, 553985518, 733457179, 598600706, 440682484, 99046294, 79359751, 59327520, 561392374, 126312385, 63365514, 155251448, 182283369, 798079415, 489853593, 136797310, 418945125, 629479737, 645740358, 767379749, 551927625, 206920433, 887481251, 885959703, 208754853, 514377603, 220063721, 706852986, 741412013, 157703806, 953043210, 672828643, 707948589, 943738479, 438253872, 65573401, 31657185, 851267778, 827732493, 172475155, 122354673, 408715749, 343786402, 429426864, 778799245, 740287730, 143634245, 641234763, 446771261, 376117340, 163127414, 112067883, 338502424, 735716310, 698094050, 432186566, 452539350, 204295287, 540854481, 523492872, 165205612, 143633171, 633346041, 937156801, 820586497, 822459697, 914079715, 593383121, 140009211, 435290118, 392153160, 108634499, 312225114, 191056675, 403814283, 706557949, 700864520, 676319032, 479460980, 65850515, 365699944, 259481859, 651387224, 330460838, 985315701, 166777501, 613244474, 590642352, 966830829, 534475499, 177823958, 977750057, 115813702, 552312063, 721716640, 660991329, 215510620, 375520773, 434712463, 750701539, 19669094, 426872254, 974167064, 819446761, 906530621, 783412066, 430294693, 992096507, 391829620, 996383638, 895812502, 841142114, 667732900, 565039832, 461085918, 511335912, 255289567, 196329983, 761070314, 569560690, 787492452, 75466826, 455245691, 377728633, 747176328, 20567213, 32246757, 563751657, 535049332, 481283678, 170583898, 681116499, 208629890, 808824272, 658058861, 609301505, 659011967, 720623529, 869249459, 134951161, 333399426, 733885087, 144807292, 520223807, 515350514, 841657805, 625729974, 930526429, 200418390, 781123887, 836893689, 307926779, 528370616, 686863685, 427994429, 942330532, 449861944, 658043274, 767080012, 806360347, 445982013, 935451221, 120128818, 853898308, 114494558, 568860719, 283765382, 983229958, 312508910, 10684603, 44654333, 366583500, 996054963, 294196050, 652547804, 937458195, 4993835, 301559970, 355021633, 298503740, 734085803, 238626757, 986429996, 522486976, 729493836, 302973666, 49012563, 67860383, 690598781, 15718649, 129162268, 170641911, 844503722, 50567218, 822113234, 996133172, 75031258, 265675885, 474452031, 631671202, 386929621, 814870583, 734482629, 185060366, 532473946, 500781367, 163355476, 913770351, 714292740, 538430414, 555148706, 534728991, 560008239, 908808264, 539864508, 883977427, 281262855, 604792946, 830243427, 898298797, 931541944, 900985947, 670102255, 274051689, 57452868, 986243261, 82696978, 926326259, 631833530, 93876415, 793429885, 827110822, 517872427, 952233679, 558334576, 573896589, 319061618, 563996679, 860052781, 629833117, 2643626, 370790270, 547079223, 266527260, 959404986, 662423391, 743053874, 738636394, 696028752, 577316736, 775632887, 470430874, 444638878, 88471946, 647901693, 774286477, 844067692, 6321638, 892822757, 772866617, 112084423, 211550969, 374327644, 872542333, 445109183, 158450905, 338481526, 944713087, 867850443, 379818875, 391510213, 516740851, 441360097, 798476544, 890606648, 749260623, 69700430, 376403801, 70005654, 467411080, 10495345, 105663415, 525597444, 984853041, 119488597, 745128549, 545321897, 783805721, 210673407, 247988116, 744424479, 198453625, 888478168, 521501317, 759192305, 128718326, 530033468, 453214711, 720511129, 233561073, 86314664, 525691511, 955798871, 987547033, 650414280, 817940357, 29057853, 95566783, 862551185, 394311513, 747062367, 476278431, 795657994, 964227152, 850493460, 760043560, 143003197, 182172999, 173186035, 355709133, 371185647, 735989991, 501491211, 146806182, 750377421, 69797129, 18069503, 158832948, 318638471, 414420000, 359956487, 304324332, 322468350, 711450118, 377954423, 242896355, 118804572, 875314308, 813506593, 213743432, 410697182, 346792608, 50548081, 818720915, 916726218, 221640467, 479250540, 119877453, 165670105, 876461466, 949402575, 636064851, 271999032, 924400013, 288068562, 720566113, 756952626, 587551185, 618911981, 122114383, 691474317, 341469756, 419085190, 664360388, 561398629, 647670714, 428221736, 896210836, 202704187, 512538486, 968792870, 108931990, 751796203, 614804441, 416488396, 178419074, 213491202, 166184164, 305823392, 38527418, 368463425, 17360913, 45764478, 242087236, 516851310, 996730049, 735623209, 959425556, 712303782, 977867991, 15722878, 484802104, 217078716, 592250198, 269795749, 58300591, 164591790, 466992639, 330959585, 972865914, 595460457, 190981953, 261713890, 873395976, 719307608, 501258862, 173429769, 633836202, 829681737, 330656979, 240939335, 303985491, 211329227, 572470470, 983788723, 757277956, 745739840, 102206336, 980758850, 457359832, 714548800, 281683457, 3802468, 732487936, 889515660, 188713376, 627658477, 529058456, 648365762, 17713337, 713759296, 605823297, 317802790, 144954348, 523045486, 912953285, 159060902, 187903437, 940911875, 817749690, 162934432, 478309772, 937176173, 993241329, 669454660, 345465566, 118727985, 151482391, 448394510, 46101221, 935544962, 971515226, 140838360, 609664660, 178956016, 302891464, 980531602, 759126864, 266609714, 505623653, 784983890, 970450946, 807430403, 9154199, 963471827, 790972791, 459254881, 359626788, 500385175, 198625870, 67799767, 801398660, 709021539, 769729560, 271457971, 688512929, 181077097, 230151085, 320145683, 875872850, 67303624, 665732199, 66340548, 935640562, 697701832, 496901874, 495324928, 730037585, 992210869, 326844245, 736432624, 477544494, 560914431, 577920909, 959307201, 724545523, 568821701, 520365067, 428199654, 254675236, 13495642, 629153719, 951801392, 388819646, 725114393, 926386376, 606387404, 204282077, 756936565, 38398315, 934328472, 484878158, 770554020, 50536365, 874424839, 555109793, 395544160, 591428867, 217023857, 170426677, 476549889, 473276376, 780856354, 326851341, 961914779, 484974443, 172989918, 48811282, 423248613, 449126202, 418449235, 419584186, 326350984, 719576862, 76998373, 978218897, 449253170, 774328216, 223787726, 394276335, 941866458, 749740579, 357696606, 77483990, 599685139, 738856501, 595910230, 335597909, 963195628, 812298563, 29768857, 313798370, 287012867, 457596185, 365453755, 510250464, 295770334, 449766626, 913770306, 62658708, 79502629, 578994300, 6717748, 42182609, 223203234, 367857046, 574094747, 903209992, 546644277, 522692728, 283754349, 467101296, 973560546, 186991970, 563234820, 577343308, 786556151, 692663870, 647568508, 850340401, 723279488, 853322317, 899037, 402882551, 362605764, 724324314, 747966573, 876548467, 860392598, 477049220, 366941960, 17000795, 510246824, 201616171, 692700325, 63039910, 37452396, 295925367, 924743897, 252576026, 86282196, 335003680, 177625687, 165661540, 520831284, 910594811, 587181344, 848631600, 22356749, 247069451, 299936729, 118373185, 197610275, 545601019, 440950881, 541237423, 19666686, 793696160, 92442213, 531022868, 837497895, 373668072, 71269192, 598444416, 36088243, 802553322, 80768990, 961976491, 711067369, 323034696, 123615930, 390742802, 491992687, 240995920, 103287540, 752198158, 891537914, 914286077, 964916664, 803483938, 653314771, 638799929, 529561621, 351450108, 32633399, 545397765, 861806966, 752941892, 307550661, 738418584, 895875941, 650109631, 715102133, 597177569, 706276711, 529923676, 56328326, 329120323, 92885444, 821910315, 923092109, 817796453, 922733556, 59836031, 845718433, 762400084, 511368406, 791264165, 792272212, 477538974, 760832767, 612254058, 282487784, 264539267, 874464050, 596346387, 226574756, 197176441, 278788391, 960470091, 269993941, 400520195, 425370546, 152171659, 143546896, 185859023, 273820879, 280689387, 110477456, 151908409, 641028423, 539149119, 547100346, 110189096, 790924018, 142829791, 889821728, 841143121, 938713483, 234596169, 717165380, 868915793, 443253002, 424680517, 781827208, 661490215, 987054683, 995591285, 611643089, 142931316, 702114501, 516778091, 900806554, 882602540, 274431064, 181906240, 676447180, 649708739, 374912866, 672015198, 272017136, 794887151, 819955421, 748265638, 617536230, 598391888, 31695536, 48372356, 733370578, 688745498, 210750001, 276375383, 479751435, 424428399, 927213184, 648645759, 314928137, 189083216, 13674663, 223601404, 142038133, 649978482, 542725457, 681828832, 999460807, 272794585, 398183265, 180013505, 214117191, 686535277, 241598301, 126544064, 401692814, 224504352, 945110280, 442450668, 2778406, 951431585, 992923631, 115373114, 982509007, 482255371, 235548255, 512126972, 332019706, 4510670, 31589887, 820504486, 983611382, 242374007, 497019849, 113414523, 296823866, 419490419, 855795050, 367506198, 607809677, 710567850, 120383044, 187737214, 771318711, 541355874, 799256682, 3420884, 576312287, 499610037, 222420953, 183243458, 647228944, 289904490, 957693348, 307782036, 642707777, 229084132, 204785431, 427981778, 553874293, 962540098, 495810116, 544074177, 185444655, 494018108, 334412147, 49590381, 681430807, 435849731, 815971752, 312140075, 559134571, 79067047, 597651706, 904877011, 548644217, 184381459, 384064022, 323851519, 686593909, 416026642, 477603903, 237724142, 844754464, 616361137, 441024180, 765857441, 406819717, 395649436, 661746032, 565247436, 483302301, 685067135, 893311440, 988419688, 258997543, 504489967, 894616609, 564138678, 215857940, 625005642, 849025606, 231482845, 959447990, 129183149, 918713257, 236397271, 54914422, 368583977, 542376123, 176300135, 349982115, 550781612, 922189677, 45100729, 748053893, 127416889, 851044886, 522203887, 950311933, 984698431, 273597711, 468252662, 743750777, 83090589, 916086456, 730267431, 327717839, 487819113, 497098100, 636579071, 393467273, 314293560, 974182151, 105934175, 639760833, 227694964, 332704117, 905669173, 658672249, 243347167, 84557358, 377641022, 392629041, 882593030, 769512598, 699995192, 459406195, 901622653, 52989614, 650115102, 310366667, 805968747, 419347728, 556346785, 58203027, 961106817, 154474177, 768672383, 543484340, 194559114, 410767642, 955298077, 699902857, 763871552, 744781344, 809940355, 64286928, 718476115, 935143446, 261539381, 731948685, 816206289, 255790903, 958269877, 551051936, 196677040, 209075080, 338258842, 168659432, 444645742, 170688508, 163386044, 104362817, 93380921, 902021822, 211558569, 804465532, 999909544, 11948774, 450074487, 418611958, 427169755, 555870292, 388009780, 803647701, 522561440, 417819878, 911892054, 594429058, 765577314, 299058115, 331867422, 865630418, 988012666, 649470818, 846746516, 346660620, 321090392, 118088137, 596406959, 880145052, 371416331, 661647292, 422352712, 367681333, 450834839, 554176410, 308633864, 534469282, 877425640, 74049194, 383852921, 381535597, 651224431, 32042254, 737736878, 963909120, 201513528, 124724296, 764629632, 594815636, 674686784, 769564032, 928863533, 109894568, 662883272, 65259287, 84745221, 949508670, 296363335, 752212509, 193608128, 346405050, 372175556, 118813203, 164597114, 732301437, 999922827, 978459951, 615601006, 143629412, 948533279, 946261982, 87415865, 547722181, 529610215, 190983431, 747924160, 32067902, 737904912, 12773405, 378195625, 66711748, 565258774, 323003893, 798151722, 534962646, 543124952, 101004698, 217248881, 52624046, 949565883, 18058760, 263884460, 340963849, 885764899, 851447055, 783550110, 102235001, 740948547, 320840391, 777683843, 304266845, 37626594, 645086051, 996891440, 632003345, 712848432, 163953984, 511684696, 481201605, 660055273, 926054013, 58783555, 56705369, 901080002, 764831751, 64226361, 606442512, 479712516, 244539692, 101928496, 639252643, 749056965, 964947197, 573020863, 938111246, 171210575, 564301612, 293770838, 330346783, 888934606, 191069047, 32591654, 197151200, 915850650, 375776901, 722302118, 202674295, 747864206, 407267742, 381308407, 784481667, 534105326, 273000916, 895926754, 891108695, 695649551, 543241629, 995688821, 730172021, 958580997, 853196033, 716701682, 829981113, 275729643, 859223993, 448118616, 952517237, 755767637, 425955313, 22647337, 584496648, 108465052, 206129860, 861438216, 103565371, 772608779, 996215297, 142349668, 856797141, 521143549, 247120867, 330490667, 171031053, 484697816, 698519738, 322837392, 800817647, 467457072, 44291155, 663919678, 263733106, 273928616, 831315422, 940392444, 363345672, 470225397, 510990549, 426838269, 194043267, 422509104, 986748688, 872044352, 966126159, 297099805, 166601629, 238785585, 454361970, 163339339, 524725820, 550337806, 532228887, 239944410, 305683211, 905405510, 923114942, 783659883, 643739376, 220486450, 586992408, 220371057, 423007185, 30621877, 728897034, 856072587, 376420939, 868905501, 623156927, 422106009, 151179383, 773763551, 83380315, 987249032, 350496093, 76986976, 952854515, 625886253, 183367925, 394503956, 936756195, 903624481, 9547482, 108773822, 660321282, 110430834, 44254995, 74660444, 572737790, 555374200, 965380524, 702305899, 40587026, 536221250, 203391619, 922969382, 106747699, 747733692, 375672211, 780965182, 636640355, 144883079, 914340634, 547906538, 911260780, 227309979, 125597312, 315498003, 79998426, 552862151, 903471544, 923792394, 207088166, 114740412, 664209714, 313472012, 863007165, 363916666, 110004841, 437522395, 772134756, 667220482, 387258125, 492789299, 993560097, 373964027, 687557511, 887622961, 909896687, 949770209, 502318721, 161882337, 323974461, 327152528, 652868002, 89367006, 488425531, 863316554, 598324336, 532868957, 237476099, 385040133, 25377614, 565823229, 554047960, 251680246, 543688211, 225001352, 79191488, 884021671, 396346362, 470474756, 536632156, 569800764, 51007401, 648286606, 375473603, 457131924, 253928202, 551934601, 238959688, 153283293, 194591411, 368611992, 361034447, 651558309, 548093304, 355215672, 84144642, 75891124, 637444948, 890688616, 853314781, 879408851, 265286952, 604699630, 550661484, 679475607, 428727014, 761644212, 19845476, 76713459, 358229072, 492925385, 577477240, 939077323, 900113674, 897234075, 319951521, 560245243, 9487160, 45708014, 810137789, 448428983, 22214685, 277515134, 329883010, 243712107, 320007557, 119303298, 804287003, 855089258, 718778782, 226133066, 870442962, 648424529, 4951503, 435296858, 197346959, 255247308, 928118495, 357847654, 220541657, 997555348, 886981460, 556966459, 697113796, 933068087, 593375050, 18814291, 913157174, 334298171, 819764404, 459570547, 563033220, 464180366, 194298002, 456201721, 28142126, 620020242, 982948392, 398394041, 107227847, 808070674, 45541875, 339166704, 147108649, 747762122, 754199107, 498934594, 917655672, 584584212, 812988686] 63212))
+
+test9 :: Test
+test9 = TestCase (assertEqual "for (countComponents [169753618, 773871081, 649247331, 639027729, 141793620, 196171651, 454444591, 498250202, 853982650, 265097348, 116637986, 488310097, 639295175, 452652394, 554842468, 608880491, 946099500, 595002691, 527223753, 405797504, 124530585, 94603669, 823804091, 653801116, 185562672, 844182417, 345653586, 459849201, 511750591, 32767287, 331113157, 482893046, 484049283, 522241074, 360854961, 222240744, 532896398, 800659302, 815644923, 121243837, 185401636, 294411738, 685749756, 800322853, 732280673, 621483720, 623188981, 574085460, 665211309, 826756809, 701748315, 636650799, 471616336, 585910243, 55994464, 28427946, 275812167, 101813415, 287165479, 29875254, 680778338, 751860509, 948139116, 943058616, 550865456, 823238657, 503322359, 867033940, 755268390, 881014892, 669243085, 990543142, 205084627, 587873373, 586233760, 436432134, 594362812, 861862487, 275090392, 694485965, 724190454, 553493052, 290971255, 421663580, 915745783, 306164444, 181865193, 289835064, 443250144, 642291269, 737649570, 2115128, 368168050, 286637833, 239559148, 920236249, 413893266, 99604433, 456154592, 533636099, 48243419, 276684009, 272826265, 243209462, 423789883, 546162677, 534422309, 671195441, 270584147, 454151569, 332301655, 222862008, 716200842, 496785043, 253243456, 547941249, 603961677, 908517286, 513457636, 595683085, 621366051, 485143400, 55876132, 619520285, 350630265, 152317192, 866448396, 713840253, 243709812, 503493635, 275891324, 219921831, 826881004, 668347300, 711647245, 572672720, 342216006, 748328414, 503078993, 403716901, 293112445, 676768702, 966289700, 766544607, 665071187, 379541005, 408605581, 197975856, 267689831, 56881445, 538122275, 5856432, 956693822, 869108484, 419397141, 312850974, 692119222, 293145146, 73071757, 962484301, 282086111, 448522152, 246309722, 647750558, 261965219, 238729172, 325858445, 370677603, 495492565, 637880232, 303128484, 888877407, 803844945, 649189369, 67648418, 127245517, 824850334, 181872237, 556002447, 928101856, 771005319, 327538145, 425223229, 140654317, 418337982, 310904443, 889435936, 529011482, 122485874, 140515712, 191328942, 699456335, 252850136, 930011339, 707020498, 322936760, 956796043, 263158625, 661311972, 886880494, 458568056, 988368583, 412471545, 960426473, 739461244, 697953573, 690835061, 26675484, 535405103, 350594349, 279234456, 254259053, 941802172, 833598590, 289813535, 355637243, 938540452, 50339369, 13831051, 191369934, 131436587, 449273197, 506251664, 568153434, 746135206, 676356996, 874871176, 377361743, 957810013, 645035169, 526462935, 31467654, 950297114, 452781776, 131313622, 995734517, 509610446, 729054514, 343263269, 271426639, 322300631, 497890529, 869389088, 480249215, 10373223, 838554973, 413137475, 362615358, 465632237, 425003746, 657447174, 960459334, 293293241, 786232650, 65548508, 407664890, 834725578, 198977869, 148626789, 428104480, 314312391, 41726767, 560115331, 987538693, 896974803, 812497329, 75767438, 392286699, 424462102, 926092045, 882978027, 211908560, 367041545, 65619447, 326940117, 316054556, 862048962, 653718986, 294612091, 947633545, 391432206, 55656727, 858618721, 485934509, 402394504, 508650390, 791523638, 16940485, 691538038, 757866380, 781405356, 874906659, 929769548, 701438095, 781253711, 661449276, 521059990, 357397725, 930705192, 218020857, 345395419, 129909902, 874553261, 92682948, 24222690, 631757336, 970082365, 779560984, 116035345, 184430808, 664072042, 445886066, 424171803, 485281730, 813937042, 926528427, 736654633, 385263949, 558195873, 111899035, 227617593, 894416375, 628445820, 229444516, 867849755, 450887642, 976866120, 874423872, 603121120, 760579069, 676343489, 396108622, 852312146, 202538913, 859438637, 483234060, 448855143, 893061211, 56721601, 315402655, 52440, 146507254, 10345453, 532962691, 499757217, 728321537, 88983386, 507181175, 468438873, 788467008, 757067766, 347713976, 417227356, 270518361, 474977315, 106266945, 549300454, 564676717, 18335972, 40631154, 212019825, 200581867, 209136545, 740834420, 489044086, 977432181, 64655185, 20322773, 790562808, 673345974, 26504435, 721623050, 702725447, 296434271, 293343470, 252521882, 512548725, 306677774, 791919872, 763867396, 486952413, 903694218, 626808355, 539616530, 16947765, 324138189, 200201944, 67430088, 629766606, 19674940, 624048507, 616936748, 106355290, 224950337, 65818909, 824616809, 201987532, 149607712, 500823100, 883550836, 877721382, 124653348, 947502941, 985805463, 890785734, 867541063, 802869412, 451654534, 671907475, 531617138, 853127965, 403194345, 464343154, 843012527, 924079484, 602793358, 821474117, 621129219, 255485912, 446920960, 486052989, 468124665, 701124643, 52680985, 932560610, 333337923, 71947098, 796373679, 50635247, 904735509, 881672351, 389802926, 122806675, 970574574, 718120112, 91596935, 447899141, 192027627, 598444775, 799604448, 775277843, 145412713, 667853203, 211378966, 309381595, 562120803, 536291633, 72136185, 858069896, 161617712, 17352383, 997006984, 588355904, 788416000, 989238892, 971622180, 182051367, 264789567, 749811252, 68520509, 87484725, 497476057, 80846072, 281221039, 491102259, 538907035, 647054811, 898103502, 269986469, 387767182, 11349952, 364592962, 591667992, 920812440, 160215263, 576868357, 569510211, 425542245, 329423030, 257148063, 617331606, 578703367, 400243759, 490678009, 196364822, 816930698, 536415194, 28867724, 834131381, 322231988, 876709573, 561585649, 242160965, 799675120, 551998585, 739705311, 993243409, 611453813, 928821589, 535011202, 107542884, 605846338, 477644509, 801416225, 244625843, 860255716, 501554977, 387767264, 634403078, 430486058, 747057006, 696667201, 3948177, 937555164, 424415464, 3005606, 347897661, 289364495, 268612188, 774311723, 704245197, 84001827, 851276394, 275940506, 207242562, 722043592, 198371107, 149744556, 511089410, 757125353, 602253910, 632559913, 599601384, 959239697, 921376195, 9054822, 41526828, 880962576, 180750453, 694820824, 21609634, 429317480, 990047860, 445276891, 818447384, 318167041, 391246185, 743415226, 587448254, 345204093, 249230579, 700252640, 921355282, 13081537, 76277920, 407170772, 407874736, 948466763, 521502803, 823348117, 617861552, 239255004, 98361097, 109477860, 636084694, 391195503, 818937127, 127822646, 535232082, 694052692, 991612468, 417678426, 643198951, 239876155, 874091372, 653641196, 665518032, 702774483, 266507061, 606367875, 13756983, 878255149, 145664074, 14581212, 573933923, 385009778, 729215219, 414330955, 881807000, 771204318, 302625093, 582193135, 856585727, 632272566, 557764258, 80051430, 149757140, 493465155, 166654698, 784057896, 492881448, 576143437, 486312148, 937251538, 764487202, 510598142, 618649908, 242583042, 570059164, 453919718, 998012075, 415675541, 588875307, 97927551, 444801659, 945944370, 855129040, 25311708, 965762356, 653476401, 324971288, 368294724, 991861746, 99583150, 76103363, 321339540, 660239511, 856381459, 895034075, 723540838, 477849304, 105141722, 889608132, 841764731, 948026775, 173198664, 10485282, 424386552, 752752598, 218718703, 59554139, 986893209, 161328463, 79746944, 25218377, 979399407, 897940713, 27847352, 279370267, 338883478, 283542763, 408083149, 91678538, 740405774, 594411827, 196195836, 919840459, 167847327, 439679420, 73161887, 587685841, 636119538, 351853238, 988313928, 345776969, 649112719, 635012547, 420450894, 507627553, 354035985, 243895482, 135183973, 377075203, 31541386, 979658629, 189965485, 827348871, 154575798, 432023772, 919353362, 78384170, 808547652, 949260449, 589351865, 914902877, 176386877, 481942335, 847111376, 110751736, 220197222, 354577283, 290408549, 552699067, 177877703, 388442256, 255502541, 854691729, 827978360, 857710156, 624026991, 509794771, 828607928, 208043615, 571290011, 707861961, 389405855, 442164295, 649806199, 117303635, 251867231, 992419960, 952535971, 551032, 998059630, 280847302, 640573513, 950660028, 613694612, 881278554, 239171465, 809260667, 754939176, 766546845, 61038774, 20777263, 161115494, 436435849, 760538555, 690564792, 139228781, 736021916, 298762126, 364844925, 66003017, 958390, 459749320, 949786062, 801870159, 444012328, 865308893, 778363445, 999522549, 394502674, 941666811, 213158037, 709136388, 484627541, 288994095, 436800488, 524225148, 785184428, 84711762, 736519359, 209888294, 839863475, 49789942, 914906656, 864618256, 260786040, 713819244, 84711038, 891562365, 913992430, 761575841, 75842742, 518427663, 692074372, 486484344, 104045960, 496913490, 160340950, 111160656, 863125273, 683746541, 978315639, 299169791, 816192422, 666237608, 303313531, 823621199, 670412843, 458069583, 692529281, 822422352, 782359126, 111825578, 99917530, 857448784, 563649518, 420391143, 818258671, 489098643, 69263655, 403241590, 72695577, 803601626, 907996838, 770797489, 68955981, 326640056, 919181499, 354670759, 231500527, 500110383, 309683209, 58057307, 504024180, 469248288, 323712984, 746951558, 27291967, 713872870, 330106076, 179090336, 239721290, 893035730, 112548582, 475448303, 273644107, 664074147, 859904547, 294153234, 52633818, 446491054, 809793663, 556602980, 672795963, 354171451, 653045185, 4336434, 767489097, 139667256, 102956507, 745470843, 538554179, 309243895, 867542958, 919066439, 576295449, 653268132, 129251337, 255787024, 234464710, 621896630, 689482872, 895430607, 906051470, 553783622, 109150647, 710155518, 275571276, 231628755, 516365475, 210233870, 40672095, 272457419, 44033366, 346158169, 671488845, 118830623, 152781209, 272551804, 91597454, 948069674, 128464109, 327995826, 735401067, 761385808, 537402017, 742267410, 315654998, 144207848, 670307267, 47559620, 339988705, 430028700, 314756431, 419947460, 615811521, 413854170, 129579609, 460836872, 46940335, 815711959, 896092422, 683999558, 671366814, 823248200, 733661815, 785040488, 648424621, 170787024, 179771456, 866907498, 863891989, 45984328, 222141802, 410293595, 331765898, 808620107, 281560604, 908847451, 323127443, 974650445, 209130647, 702861173, 12705439, 531835427, 810469628, 329472558, 39933952, 8383926, 601107499, 537089709, 530121483, 248464461, 898158062, 298028159, 697718832, 602908958, 374899954, 242821191, 294312252, 27062745, 656044486, 486027306, 550569108, 21531076, 348198355, 737633951, 753170, 985893122, 854653974, 476498458, 685782511, 218310021, 653143200, 585632043, 866680336, 695054795, 987709512, 446267448, 664188166, 103929323, 99315671, 716416479, 174497514, 387581419, 175571773, 780428174, 157657647, 698936863, 768201385, 306262993, 707287547, 520815074, 880107857, 845322576, 48121146, 792465136, 51424465, 416657306, 288243146, 292207142, 604195432, 362193498, 285055104, 838746445, 65302556, 800539188, 291650327, 614298314, 354538951, 890053334, 615857049, 653856217, 64356421, 670996682, 337983845, 278549665, 932027000, 623146993, 729007237, 832829862, 423171078, 954770641, 272513965, 100980956, 953540737, 257145627, 236812653, 211016450, 338162058, 626935239, 881085625, 534530550, 949742166, 182754020, 941481215, 518927998, 80621356, 697510027, 513587083, 153273518, 360753859, 910784073, 841308945, 788899188, 932920137, 256451536, 69058566, 579910427, 225117303, 951042692, 958351773, 531479494, 916432676, 869558409, 282622981, 340872073, 997586325, 438206103, 408440353, 270503375, 665146340, 351800481, 1603836, 591701727, 559150240, 468935815, 9928545, 333610848, 161770164, 501011057, 118760405, 680035883, 243818053, 843482279, 947568607, 829109921, 601745014, 988632143, 625800557, 67846462, 9024401, 159578350, 815467221, 835020940, 102428343, 933405197, 38613031, 665521712, 622826376, 873628216, 109795151, 61144103, 320697563, 164287031, 915418259, 726136793, 500889318, 407896176, 536368964, 22315376, 489872226, 266567477, 262100850, 267402796, 53893028, 245888405, 354464190, 647247339, 12754583, 108720865, 796524267, 26019325, 385482413, 586281106, 810537543, 447919313, 519474797, 424774403, 325201580, 209937637, 428138666, 257862622, 317718443, 488436853, 254801126, 254892751, 978016837, 647999079, 501279724, 423088196, 117072455, 915913909, 803631710, 708024864, 944778045, 632353020, 844579660, 43901974, 678905681, 293337442, 439018076, 433567607, 29142797, 624380691, 906859707, 995790452, 250174345, 280849337, 856672358, 546715842, 107303917, 175867892, 317052485, 280475932, 6949782, 311334947, 533019732, 286509730, 372884962, 36831871, 79654857, 582272122, 879497868, 700668394, 449558599, 206884201, 903172626, 60170925, 968336713, 495946017, 663479694, 213457732, 818686529, 421647994, 923002738, 600136564, 781448915, 779333248, 521300641, 195205685, 151301227, 637393111, 300754500, 101120213, 466024140, 908981776, 193543694, 481888509, 140485279, 924410726, 411286505, 167509757, 799587375, 325131805, 760933786, 44237413, 557869588, 786702726, 410395592, 861050595, 75082183, 886629957, 410413131, 813824289, 663382339, 278946298, 842160399, 762780895, 847193334, 705713643, 502393113, 289543173, 207519152, 182376307, 832669145, 652037519, 538147839, 492615061, 142311648, 955194521, 750494691, 790496278, 869589964, 685977896, 894055831, 421509604, 808556446, 519541965, 891259292, 932831095, 473696713, 538903053, 550260845, 765723378, 831265924, 297564527, 928630984, 785596148, 143787139, 212865646, 507842312, 940764771, 550579972, 670409425, 438942411, 212625130, 673149288, 938839987, 125587941, 122269343, 135944473, 196214400, 350400535, 615441958, 902385456, 282335953, 7426615, 613285752, 704721191, 456859503, 196172764, 811105715, 462181650, 301660727, 726173244, 623693061, 958751101, 762428551, 616487506, 460019318, 572166975, 409038381, 97807488, 378084008, 524822203, 397978051, 754534751, 518904816, 188195182, 896274812, 841594914, 786074790, 146429494, 830071665, 57816909, 5595196, 722823295, 709079557, 872808097, 175991833, 764483147, 555550741, 477460819, 109354482, 692869168, 638879600, 7198815, 956689341, 274691792, 183938791, 441701404, 756721599, 775133403, 512170135, 552391776, 174028862, 804258738, 409327076, 666442742, 846375443, 115292042, 794853890, 86391611, 950903134, 693992120, 736635003, 395073239, 275702752, 845685478, 453832120, 801225211, 696557801, 420484812, 992472764, 15672742, 143010902, 805298966, 424520417, 180309118, 748431146, 859570367, 816733952, 328287194, 685703503, 684639282, 365104139, 826392521, 761098311, 25486962, 585785873, 893401070, 482374416, 333003, 939955031, 665260893, 706510750, 602506720, 729070239, 55300625, 580594301, 224830935, 205900174, 842964659, 714572319, 1864281, 637169656, 687685394, 549431010, 92616530, 186615010, 355107038, 176877912, 877526697, 206322636, 406436075, 331826664, 844333861, 650663297, 803086683, 762217617, 93198446, 594950285, 665854515, 886010518, 376956056, 199522451, 241461229, 620278164, 813126667, 950403815, 796195912, 804629788, 508753863, 486579065, 279674769, 322592855, 94458265, 900473548, 121399857, 491560748, 612669492, 742905099, 716560659, 561532721, 644933548, 57703343, 624081583, 666059315, 477486600, 482126870, 780106128, 44404418, 153853759, 265629901, 303666664, 161298103, 593894220, 878990537, 697362019, 69532957, 683766669, 561359943, 518997440, 197219489, 557561275, 144222755, 286170198, 350036796, 201409118, 228120119, 11119253, 931060268, 509812544, 1923423, 230207973, 512749650, 666969627, 483283712, 316389318, 325035418, 364587159, 917485852, 814549211, 50537339, 990852790, 905982131, 148139219, 229395697, 30812057, 192544081, 825560694, 501458770, 450923439, 650498496, 33074338, 390833444, 657551935, 297556770, 386083591, 294082467, 103185036, 827413745, 745070965, 96396294, 574832490, 644018251, 419467009, 478243150, 853414547, 182100, 637731049, 220705337, 731940752, 41651159, 977212915, 589101371, 92945769, 814565101, 463588041, 189756036, 942287648, 456366482, 85672799, 667767104, 3819497, 55145587, 45398720, 724342878, 238292528, 599167428, 759896649, 792927566, 336998602, 945960732, 127377298, 999565331, 121257539, 958864256, 421236748, 134747194, 168497388, 469931924, 215462933, 690749938, 311680531, 676460709, 41148466, 49944567, 345211743, 81212758, 188888863, 840755182, 310503945, 27832626, 65238683, 242845525, 717440387, 413803570, 758464535, 647452355, 204791670, 92616595, 101927706, 160802805, 518640944, 491074916, 705728901, 732708419, 618554620, 958064049, 987936467, 292140259, 419507029, 517960587, 99901155, 316241729, 343272681, 361584503, 229825888, 389846074, 990990921, 640082763, 568784717, 71135923, 279998616, 766405349, 99220130, 316075495, 763471310, 882598007, 678190363, 681171111, 660421963, 161651298, 477481268, 344528975, 78582211, 671428907, 779503088, 253878425, 511250432, 380968063, 11454541, 247183560, 581404545, 534570266, 967515822, 727690636, 679115757, 602826189, 895177200, 657254498, 140847084, 792598099, 577122583, 114208729, 12643218, 312529310, 803890758, 330892339, 859260629, 32170359, 8588584, 632468014, 423004327, 889279454, 286390402, 586317178, 416032271, 416928456, 86129363, 489630684, 909551117, 982714834, 803028596, 668686576, 919929626, 475830268, 92938185, 816675122, 500966217, 705218988, 524607879, 650874706, 359015114, 692712954, 130293018, 152330717, 75097049, 773996805, 235413603, 106324380, 738023563, 27952946, 729934762, 184671937, 851989764, 178490914, 883800885, 706605025, 148249150, 712368730, 267830507, 968659760, 623656774, 456985907, 828249639, 383763803, 707467658, 776725714, 816697222, 677788783, 673869967, 369554891, 553668754, 745895000, 119828815, 866317324, 948355704, 313516842, 232420560, 706382129, 50230830, 488534719, 48639608, 554011701, 337470732, 839420713, 419380496, 970751151, 502317041, 792906113, 112504835, 303950177, 965071064, 970408718, 16633051, 884600628, 703248941, 383607303, 671323276, 700659584, 63766243, 650581003, 437618927, 567387932, 67493349, 732655127, 62889043, 572451577, 489100148, 890647755, 644218424, 358190589, 718561666, 539673133, 727483852, 649238950, 508273441, 590545510, 142516583, 861061813, 987053721, 495942468, 3140027, 795477616, 402932414, 200843674, 493586044, 435574022, 963477903, 396138301, 212770576, 280112710, 378233645, 934619704, 560561693, 147433655, 638121586, 9548536, 826295880, 142300456, 193301385, 95235860, 701442324, 113847495, 955116676, 487697708, 625476984, 327602746, 150227263, 80127653, 833660863, 845058860, 680148481, 241503220, 435876615, 765191162, 78486429, 619557689, 458851655, 275103650, 57585827, 433051244, 513548341, 798652824, 178014249, 324029431, 160270808, 205966151, 38769900, 709510427, 166343555, 450834336, 919362344, 402995681, 534386689, 651687782, 476011084, 248000386, 106601445, 319112243, 412021274, 457300761, 967547130, 973423258, 252544157, 653770418, 16467435, 293391611, 810913260, 487666547, 952769565, 658624419, 206657232, 790971539, 298469710, 203666680, 860256701, 268114487, 293713207, 434390880, 304956400, 20931926, 644183890, 679085980, 850610199, 646784023, 339046291, 504415678, 151716409, 146008659, 859082667, 159361163, 953485531, 797108846, 740358701, 750936143, 140059285, 392318000, 127539011, 446700703, 384079301, 239790348, 493559097, 113177891, 36317144, 206048607, 380045597, 711031378, 254062977, 866947276, 10237363, 27242162, 275492747, 268041692, 314868044, 667301047, 124443700, 813670406, 344121426, 143208425, 339195950, 926621194, 241712782, 612473344, 927856826, 537721052, 462319019, 775154856, 811324463, 793913164, 849027129, 898832118, 438579036, 178295679, 201255403, 38807000, 697100289, 227491768, 33427119, 611597785, 919534905, 618065687, 749558675, 561026888, 506479583, 827696774, 243463370, 2147342, 61771303, 182838391, 574457773, 527666057, 89043699, 68092484, 876831688, 172380658, 715136616, 504749211, 678756202, 599502463, 857887614, 627225047, 349009061, 56782601, 406880292, 940486, 781244592, 440895528, 247064477, 838166538, 435649103, 542727525, 71040171, 986751406, 534486348, 813996948, 143345112, 993590416, 562140706, 575966990, 109475817, 930693529, 29618301, 425264643, 756651230, 139757069, 50824260, 880852492, 174502505, 247795558, 111246833, 65812277, 522275160, 566408711, 519960620, 694031158, 417061856, 106032470, 821958728, 233723346, 893668774, 121524641, 7967811, 494311121, 892278240, 310550346, 891036296, 623629409, 403315010, 456051192, 349384852, 583630383, 463864894, 990083805, 208241959, 420124551, 855978555, 192189519, 60870491, 16456693, 220256211, 494127409, 172457197, 602170978, 838794745, 850166276, 352457491, 666379740, 794528893, 980557001, 550782540, 918689938, 444694863, 244472940, 23142086, 434975048, 138229021, 717923674, 615724912, 569080012, 464347824, 980083435, 472217292, 270809617, 578162146, 180129601, 779332916, 275733422, 257593191, 226483200, 253651963, 133103365, 332438028, 489247131, 901144622, 817959839, 147735808, 218353166, 512903384, 886634452, 501363969, 96537920, 491725446, 102415921, 800631004, 147062221, 229977986, 912006664, 161189956, 768143116, 2737764, 496968277, 728845733, 688498561, 489033823, 229794546, 551565430, 569893327, 967784383, 737045149, 365270660, 609716077, 925924771, 565039792, 544091367, 132497533, 967301947, 613765901, 448310601, 893660476, 885789813, 253292788, 758591091, 764609581, 154817706, 947145866, 794249051, 501797090, 262835163, 671781432, 311211283, 634469654, 246567719, 536600815, 833436096, 868898116, 946876770, 681480286, 435144144, 547541621, 143183692, 764528406, 329694214, 477863458, 205316683, 365458310, 791839380, 685114832, 152668998, 931736077, 620865464, 967360932, 789153889, 881443872, 531120587, 176463799, 69953707, 809061713, 416355468, 189048034, 75550935, 229226417, 629749758, 797892793, 460406454, 847062605, 437683800, 134220431, 206433321, 741351030, 620898328, 546560003, 405645062, 740473333, 592562864, 882194364, 684240162, 770379475, 48552527, 144513034, 578748863, 238973570, 926011421, 524776375, 280762142, 177508348, 858997122, 195154291, 267329562, 635894047, 15151732, 792529751, 290942538, 940952022, 269626627, 21223034, 724225058, 515944698, 427278378, 161356559, 239717734, 932896431, 370738620, 912951500, 954999503, 9306924, 780927605, 300903307, 497589584, 360610378, 292879240, 546696528, 776962983, 846735686, 134227826, 419036076, 669429717, 507952572, 784512306, 217286375, 4918212, 533955608, 105429179, 816344870, 314301527, 599927579, 593198583, 983835327, 818646862, 767201843, 441649509, 590091553, 958905399, 212002653, 423924975, 500943662, 90594459, 519598844, 518962061, 869652560, 213535262, 345027311, 833492994, 65782038, 347401751, 345129151, 564593311, 605355927, 954348357, 276216013, 115783584, 927659537, 330580257, 211490069, 509550356, 258886504, 274125462, 582594304, 970024065, 210318655, 428749331, 442926801, 822586449, 562825268, 684855022, 282288660, 62470776, 127800313, 589683612, 144083306, 747639666, 488028894, 98051055, 121631506, 23178304, 995014769, 693417015, 294698387, 633314398, 300711468, 980799883, 938006516, 887781325, 771919537, 470283805, 753357064, 224290512, 28792711, 699661079, 239922989, 65331698, 628506569, 295104799, 807424343, 557188117, 731800751, 625295525, 197479377, 709317010, 589392606, 126239238, 525751801, 867992816, 148982732, 38751587, 179403006, 343460512, 699274479, 931341060, 679212123, 727422380, 653024648, 222815637, 466316532, 85040052, 444854809, 689018849, 519343633, 352151227, 319555383, 263243633, 250208403, 332142936, 375134932, 586136222, 129922009, 596532370, 803547055, 674496018, 341235429, 990679557, 971459170, 118061029, 818398479, 806585928, 941269936, 263726042, 341366577, 635425364, 324670772, 360222681, 96717832, 145250447, 82304248, 202701909, 671478756, 986197606, 97462866, 487262269, 903243027, 113892859, 593307853, 768172489, 174789029, 633863452, 430683522, 253382972, 229650694, 940654608, 182540585, 463490034, 179399201, 72845261, 916750389, 855044038, 842805928, 920829227, 483781333, 749706007, 966650462, 558309385, 767271242, 763511351, 471728178, 216880906, 443439727, 917657195, 229313974, 204567829, 103696557, 794355603, 974189778, 123767484, 862313638, 521450845, 235478734, 520321153, 919561998, 533763857, 507377402, 326325592, 321874532, 696119627, 727644345, 808942330, 995863595, 300658481, 844713876, 417246332, 328474127, 706375241, 634799507, 281563692, 210446910, 306123790, 243336428, 506382925, 67620152, 10996279, 494504652, 310208384, 714519665, 769764200, 185750417, 91389911, 740932946, 199068415, 767692409, 774300085, 98515897, 464919305, 202462273, 453149228, 470252684, 583923760, 248729059, 501217049, 679011427, 797641008, 672234774, 61402282, 19668397, 427401691, 144366282, 961003858, 312697399, 472166264, 732661210, 973732002, 936071179, 139117898, 343291281, 124710417, 384246318, 948458624, 333814233, 698741612, 27666306, 20296118, 887816283, 5687020, 830397347, 234984233, 530036217, 913102956, 617523690, 355731249, 810057130, 687928131, 742486716, 221936695, 256482608, 36194972, 888748234, 819170149, 703776202, 989916037, 203866347, 218203684, 227490927, 243397200, 990325, 343178046, 257671452, 120955183, 436666563, 555098270, 692134015, 339001330, 798303928, 688916899, 915651200, 216858862, 65134692, 743977024, 478763525, 667964597, 609451459, 499051931, 222819287, 859597721, 738456035, 600144187, 338010230, 419140997, 197801410, 285350473, 452450286, 86239520, 996134185, 27963500, 904347206, 479091650, 556496014, 33273586, 160125430, 142942925, 243124057, 213025663, 529673212, 585412411, 359263824, 875295224, 470446038, 367938066, 652684380, 314269600, 414439372, 315703995, 926238139, 12868424, 578316972, 597456065, 373787100, 343300336, 423969699, 135830743, 516534749, 102015285, 466070484, 129349122, 273797500, 213862367, 989263574, 690762182, 836612030, 993353423, 148971819, 749850798, 320206843, 795450063, 610604379, 524851468, 428917474, 976922762, 610094510, 319651599, 620071014, 864300465, 312828254, 294309043, 383908816, 787415845, 943407154, 457160310, 913295699, 562361763, 647146251, 334583028, 935761110, 67318856, 888575359, 267932174, 269417911, 418008043, 843894760, 561708189, 435598884, 605700540, 451048172, 229224580, 795363586, 609643378, 389633870, 632936166, 186303600, 945926147, 139935673, 639968002, 513602099, 644069453, 625098498, 314217411, 310899350, 367390554, 784674285, 860422761, 987591915, 63181517, 710399644, 792586219, 282670973, 531508710, 17245590, 801853452, 782082819, 238163137, 199826016, 629958770, 280550931, 862421950, 169388770, 147546870, 489903191, 180337780, 985408071, 975597790, 490948548, 371074722, 790395867, 200307164, 975406788, 935433927, 422754508, 593621589, 174185255, 671453457, 367031730, 439319490, 559652921, 141115523, 525463579, 1693188, 711146446, 894712271, 246218444, 67404104, 100950037, 501439353, 885799712, 601963581, 416008763, 751001114, 204360857, 687651439, 260407961, 146671024, 115909085, 772444615, 142173129, 664315427, 904637365, 313819651, 423799641, 824737955, 981875890, 992354317, 836617446, 903694413, 55029018, 227196698, 690835074, 269576661, 227183045, 115544437, 335318353, 425500546, 992391936, 743741756, 660884457, 7381375, 620054752, 380566100, 361688931, 406679258, 843271563, 926888074, 960201062, 153288252, 173769851, 778513334, 516471312, 837922270, 570008368, 471239638, 323619517, 294124720, 187595611, 53667148, 623630535, 76719013, 748280733, 449405510, 335734148, 695715936, 900790877, 544051193, 713422467, 615335629, 586391214, 37140614, 583628462, 686237039, 212032782, 676068450, 667953856, 874055004, 71876633, 392232085, 257295757, 772076381, 705203029, 247572814, 651955481, 402621283, 841692185, 81679018, 70729787, 140901416, 94413844, 853559556, 690991374, 130583089, 186129241, 635369714, 4749822, 407816849, 180651605, 450072529, 519705659, 197131768, 350840582, 937248058, 603534317, 329011662, 12317168, 428024489, 738436793, 668187897, 764820767, 274013486, 157405492, 645719631, 799696307, 417730073, 207563782, 826000529, 663708571, 610614036, 331755082, 478529847, 859029936, 983910707, 803456302, 736610417, 658064774, 468148984, 761663462, 818676567, 86193429, 773939645, 951569754, 483260051, 879446526, 38548012, 181313862, 987338863, 515311576, 764040839, 579967432, 268818054, 627712725, 233971322, 365134700, 548112730, 24475031, 135268919, 271556521, 509738039, 449039050, 66355945, 701277374, 620894722, 512220833, 255599163, 261936606, 635310472, 570510286, 814890962, 990025835, 219610167, 549161601, 554680236, 418725368, 177019798, 10543778, 563494879, 358153479, 404969923, 113097442, 577028806, 653636381, 28315530, 707957663, 380212524, 175268990, 988435130, 348566499, 171224354, 66517853, 777483117, 184743566, 21722418, 545287339, 262827349, 210190606, 686873292, 818967941, 606355254, 463535319, 972005538, 945914685, 695610961, 207464363, 870096357, 150635761, 742408502, 311373797, 644420085, 439312603, 784205274, 501651347, 473081487, 970971146, 981809636, 599104118, 647121018, 547561624, 568183131, 872092444, 619935453, 685903715, 747128564, 368452246, 355865487, 999521187, 370519650, 59018963, 189982559, 633583200, 279257429, 799761262, 387353287, 720710838, 122465802, 766566296, 259318648, 401250607, 166182941, 895364268, 164546564, 766764135, 739344040, 492968840, 183328327, 467108827, 643626320, 241293327, 410774975, 730938881, 651623729, 632612375, 484095522, 506766380, 26385540, 768656780, 810741722, 10853725, 445088556, 44943430, 379415110, 926618059, 809787743, 88883320, 406570595, 584589931, 597777886, 557520991, 591283431, 878902539, 929657810, 636601867, 536247736, 487163992, 380363940, 504438396, 866723722, 541063280, 11578964, 804752031, 752617462, 849143681, 523371375, 432912433, 566501155, 612193620, 63536873, 941166950, 250211580, 918400078, 614903307, 453279756, 635365279, 523662884, 330935543, 72617060, 682439903, 974405330, 848492174, 700024878, 463792852, 621039252, 411198694, 837752471, 705670950, 77162708, 346177046, 499887886, 339851917, 193389237, 299690362, 22783865, 123053068, 849813433, 639196674, 7720661, 832238892, 387378429, 283381926, 89010677, 955497478, 111536625, 33167172, 273573306, 530428168, 955645548, 952516223, 199408543, 564520934, 240271386, 311643461, 529389109, 549351794, 369003102, 871517598, 631313693, 386724352, 169284282, 975449943, 397321084, 150189726, 657231195, 690863959, 594508124, 606410382, 72617871, 268983851, 554423898, 503375710, 371348509, 601974543, 424620100, 485756776, 529916981, 51751285, 368076300, 605034846, 425213601, 591766716, 311837113, 633026894, 53563802, 731212103, 23794495, 742355480, 214642511, 429151295, 914046524, 339394540, 842205840, 574933084, 478614654, 894477379, 563908607, 311924150, 772983484, 122883757, 641110600, 237596968, 347710793, 13311267, 42673012, 471666564, 662850356, 540309310, 433225948, 333518996, 218731230, 937769703, 65930001, 610537968, 825099329, 797404014, 643527896, 779675933, 338670842, 109918552, 859873096, 940267744, 986121802, 90342674, 986230121, 795368791, 148645271, 898999227, 781121488, 642711561, 761076382, 771431760, 441653749, 445196861, 893328889, 702188684, 925195617, 25361310, 511056845, 872209748, 383753525, 551756612, 186493819, 42654108, 124937807, 867797837, 60708593, 403517730, 48046759, 223840442, 89741707, 893759393, 808147582, 107051963, 748371920, 788728462, 158381588, 298305636, 803287032, 31212155, 456105682, 418822628, 670646391, 739883301, 527623996, 734895603, 363066128, 14529759, 405995619, 584546282, 653144667, 241640518, 216313292, 771275881, 621232, 358204795, 777321097, 192724275, 680878370, 939442626, 393518122, 715636031, 539685147, 337658124, 180410596, 631459653, 796153892, 749320506, 257297346, 431178498, 331481093, 789435132, 319868533, 506933385, 201056428, 350171985, 694850411, 963406543, 670163616, 757110542, 977137599, 946454030, 401145399, 388462498, 902426402, 385442739, 375893589, 944130592, 118502883, 833047612, 992391948, 500583110, 187091572, 314573794, 619074252, 730609206, 488403975, 569145303, 257079014, 450192788, 557977685, 952718920, 897793668, 235620877, 287805724, 616154973, 949978787, 744776610, 663585987, 153368553, 637715772, 327528642, 20326137, 114456488, 808743149, 797118450, 719515344, 943289572, 1180692, 465271097, 396883070, 169920648, 81828434, 711545768, 671543166, 834586703, 320695596, 916373780, 872922188, 971143331, 246073121, 735670709, 8345543, 246091398, 285260482, 742010203, 777247937, 319917398, 294654907, 409757666, 736939432, 917636261, 371447011, 159311449, 24265899, 971630570, 513248300, 662444746, 136634040, 993197426, 331236165, 221309210, 176852533, 543378183, 275399951, 873254393, 4655871, 462120950, 917673578, 877301654, 774092739, 914302978, 812964353, 626644999, 897165558, 421789331, 469038740, 358421849, 175922749, 62366458, 683341679, 820602604, 134657066, 259247884, 849921285, 347049269, 607587752, 564350578, 764098164, 539224926, 809735180, 806621173, 994568615, 244351320, 351280580, 833819429, 921411762, 380869837, 731686481, 136244890, 698145773, 808735506, 567832953, 591100140, 790329492, 123094179, 412350342, 878123507, 584647857, 286431331, 907397687, 539125160, 416817643, 512092618, 46806684, 376789481, 816091754, 261442065, 251953923, 102944549, 234679849, 46623058, 464016157, 462719102, 346272122, 108576849, 80476428, 111618519, 468824678, 738483067, 762209912, 441870692, 477374950, 254170724, 15949252, 695694286, 999693113, 756013586, 702559230, 577636756, 489732120, 917874700, 1288090, 742480487, 727761943, 571030234, 538570511, 436783388, 136041641, 127613938, 77971699, 297552331, 416497690, 272726948, 413899979, 22124327, 315694203, 885393052, 185135673, 929427561, 335295988, 602153982, 895805777, 511952740, 138598542, 961178307, 986442549, 534785830, 728061885, 567963004, 262909785, 974842197, 288970491, 887558431, 126858205, 379936618, 217589289, 808368489, 883947807, 906281702, 852907743, 247581731, 87761042, 841393894, 590865112, 689197141, 485387219, 855414539, 279916463, 202961244, 20811824, 253819072, 401391063, 233128539, 181190291, 569928066, 5540481, 766890341, 254203472, 886148045, 253849885, 228811811, 987130184, 658635315, 450575557, 2138942, 821963362, 665718308, 897312880, 864819290, 972313595, 624287933, 940633831, 547145956, 830762112, 534850686, 953109820, 250068560, 563685666, 251192018, 797823432, 35982085, 592467613, 367108262, 659729934, 35910597, 462349035, 630964849, 768865044, 662324104, 462042637, 256530002, 753597174, 62243237, 573793556, 160054638, 421465106, 139455162, 39239833, 583754388, 548867450, 143694234, 96206953, 40741162, 2094332, 939893025, 25163464, 300253183, 274158711, 595170058, 70868687, 626262508, 475123523, 480350513, 939238275, 855356443, 816986919, 914770910, 15502539, 928180690, 116735438, 152307121, 13882844, 754299942, 255052326, 736880578, 286497071, 764737310, 701905176, 326543525, 850098284, 709239882, 492518804, 615278995, 774968731, 861525931, 443026494, 38297561, 317567527, 730769062, 469893077, 718410784, 679888063, 774104306, 88947739, 153900890, 118590004, 395669417, 190919203, 260636752, 978761697, 902526363, 104919775, 687691951, 993177171, 182133972, 430228196, 505662568, 129807570, 301591518, 654073690, 398006299, 475696628, 550795317, 475448965, 129969206, 144108811, 576443767, 448352718, 487137748, 650828040, 612933368, 389210337, 176252112, 568493467, 204257615, 592800982, 563814668, 34951491, 247502094, 56107529, 256206601, 197760212, 329772612, 273064355, 77482042, 270730236, 352415489, 973363871, 217714083, 234440951, 881571470, 834718181, 635995367, 86891430, 111415646, 505303953, 322107787, 834201782, 267645237, 555006725, 773379759, 383460986, 804139080, 139732187, 922189059, 620111172, 57027697, 838902985, 658891067, 903022672, 466432270, 942865766, 47659212, 546818253, 306465851, 893469564, 236315987, 826619549, 54014536, 82793887, 984283199, 747561049, 295605407, 838109247, 5022383, 432468251, 930247543, 256116265, 760700912, 432782269, 185925816, 415106829, 750783878, 353343838, 436448471, 331769518, 241730964, 188656249, 531026183, 181199528, 160742594, 440769407, 191655305, 445626469, 975937503, 839098580, 837539538, 75884860, 923971927, 311724302, 756667106, 581624001, 176814554, 520605856, 442181861, 156339346, 125137344, 258254771, 633019268, 333419335, 16924495, 719723269, 133534234, 44345112, 536380128, 807472990, 899756811, 476585806, 530609710, 812036584, 24730993, 637864528, 960195904, 296417634, 605212021, 470065798, 145467514, 918497050, 569661320, 792179538, 629779413, 298537264, 503876326, 308633207, 209097801, 308925165, 559638754, 640840700, 794668803, 449085879, 957174828, 465101420, 855214970, 954910386, 51770754, 972519355, 164822242, 160188065, 536811117, 367385107, 761039214, 417734061, 806999891, 493007374, 695512555, 964092097, 258228302, 36291037, 379590188, 563491927, 667746225, 65130927, 421812770, 898992153, 772426100, 412729153, 370911881, 743557218, 421481881, 439370238, 207717311, 119475043, 469157528, 438039829, 750886866, 792999454, 415323397, 787898573, 288546855, 894320344, 130806716, 372176652, 116933894, 471722600, 444521760, 4488271, 725149162, 473946594, 794686290, 29296063, 676751296, 790666808, 367161754, 751406460, 164638553, 2174902, 584712149, 255567695, 969529427, 771504474, 161012287, 43751293, 835912348, 552432668, 269604350, 875482289, 214942488, 737136526, 338054228, 967440115, 461404531, 958978835, 922504463, 107322300, 497154091, 770867010, 465591503, 653018694, 339216048, 447844308, 423003942, 770465481, 391693721, 435172765, 253832363, 14252197, 75806921, 262984465, 919461196, 131390864, 583591505, 743775157, 75216976, 460448424, 137012174, 908241098, 609573499, 728634908, 121503485, 749257879, 707263527, 520184010, 954972745, 286592229, 49928284, 30300491, 920969127, 765895866, 697020386, 121422859, 958962506, 675101397, 437332007, 734319558, 992988802, 652395040, 421023238, 492561190, 185349193, 980110514, 798595409, 662955817, 820220953, 678990491, 928655539, 407973386, 718883063, 261029063, 595595762, 666148967, 672208433, 428634508, 686618491, 609209681, 127910642, 374594938, 760251686, 241617496, 153281112, 378154337, 867645326, 293113484, 596473372, 817632566, 982530374, 839564025, 597849771, 523492006, 348953160, 300726257, 244774064, 973267414, 656957795, 730510957, 528438561, 930053011, 528832029, 284802704, 237069190, 793909329, 267853023, 916356207, 655884055, 638776067, 497235315, 49508958, 892489658, 658188237, 263856829, 46089366, 854611441, 73953777, 920845031, 665985242, 550695224, 911082223, 685973319, 406829157, 471203772, 103979413, 836570805, 140502868, 11124359, 681718237, 233251038, 893942599, 34075600, 48718174, 944050639, 855987676, 99001759, 897637748, 298220285, 598085728, 151073955, 599955636, 423348397, 431739608, 976107865, 345585818, 220710680, 571113355, 240344156, 853301026, 337362841, 255687032, 219536054, 372521198, 36399469, 222564328, 134103887, 618818163, 892262164, 4370540, 342691710, 46706538, 951281131, 217279308, 667716660, 889579553, 781637858, 798292089, 682655588, 817880002, 935992753, 571432282, 822782709, 865698985, 7756063, 885178727, 968731801, 731355565, 708822247, 947986722, 184319497, 288444945, 376603970, 903980610, 65917776, 392277165, 866393464, 730117109, 523622091, 68042061, 44851120, 594939719, 669347595, 54820488, 633726970, 520194009, 116345195, 790259957, 442342993, 645573555, 271586632, 339527231, 709633800, 122606376, 803053458, 122918341, 818055663, 831296757, 660251749, 683835039, 958128979, 366005785, 721821738, 404838078, 559840640, 106568322, 850297164, 478226356, 834005043, 294020914, 621065580, 498133728, 692368021, 845789625, 188489482, 172329580, 695907594, 510847250, 376282048, 354423751, 175528343, 646184034, 946695, 141615038, 384111093, 532181294, 496150133, 257833717, 114384240, 103165036, 181462229, 769084634, 85173004, 698660959, 925869252, 631245408, 702927609, 33150050, 329534645, 653397700, 341548404, 396421868, 779569891, 502712930, 534218925, 591872244, 782409692, 486077362, 136352851, 946943807, 417766586, 682143763, 927974136, 791272674, 525848388, 528275408, 109855877, 910282084, 426110385, 577436549, 748703457, 41245909, 497846077, 943607117, 206291625, 617925264, 544329094, 789082435, 705770052, 270585656, 440760767, 385627115, 321637500, 816559543, 693191437, 977331015, 857753783, 486244455, 965827441, 776236930, 478787125, 881049389, 128065520, 719358977, 473308775, 441497367, 543140550, 787596437, 406409060, 996036122, 699648395, 376131437, 760621706, 96871920, 443262914, 898865694, 185611306, 611856834, 75099624, 319810386, 60490334, 764335554, 693728767, 568664482, 300474531, 315903263, 894612355, 6209, 287019127, 974625364, 179231335, 532834944, 334137499, 283533190, 514879681, 396316171, 837124053, 4540064, 39204961, 148939856, 420486249, 462560979, 267679118, 963233128, 377518479, 6433718, 591730496, 835875485, 546871023, 351623994, 895589106, 670815237, 98532890, 544783983, 468752746, 899260944, 603612349, 842350294, 726906541, 620003692, 220651174, 834268028, 769802912, 485639213, 410566148, 580598215, 945844833, 457880382, 549060243, 200871531, 91099328, 128586403, 408697841, 685440307, 898402134, 974296032, 867128827, 942224428, 396116484, 413987068, 417839857, 362131748, 971258100, 368428691, 710385519, 422903822, 309762534, 694412963, 331153266, 295746860, 172104341, 95681107, 395146902, 622709718, 903503339, 251828279, 849286184, 614322132, 396673104, 52827159, 629395978, 154800815, 6256794, 770019899, 754714318, 744967214, 887634632, 493057731, 782502838, 305016379, 342951992, 435683775, 238757942, 832781738, 998168574, 541417217, 21147310, 632003616, 445203421, 689389216, 588306753, 517542376, 940739742, 642295764, 651415195, 158826398, 187133844, 974987086, 866267288, 603078564, 749388431, 17076324, 996666648, 509799716, 810727031, 950418186, 508628897, 217069271, 496406083, 542183189, 609038032, 978983424, 946280835, 265977714, 240773350, 768254972, 902613041, 49686413, 701184634, 78253192, 885556879, 691651168, 664449603, 722170843, 413978811, 939605718, 502584701, 210294971, 771799936, 882090487, 264128180, 290903327, 577503335, 965718066, 542999579, 1139626, 202497830, 942808155, 970645219, 959369745, 389643692, 56286452, 605407348, 82538801, 443131048, 170230573, 462376700, 559763857, 80506987, 453294795, 624761794, 279030825, 902488818, 211034425, 746396738, 220696431, 401716965, 335309959, 531078303, 432112911, 470200067, 557468581, 127647802, 193835836, 294807226, 836335967, 228306743, 919505187, 790986485, 839585377, 262804515, 493471004, 591195562, 139545694, 215348399, 856163457, 364338199, 158350935, 427251957, 200597614, 917136508, 107027377, 60875325, 406371708, 749602120, 145080351, 82130511, 835722480, 133127912, 512548681, 663011931, 74406936, 177718059, 268361529, 717801064, 62402224, 684988320, 851439669, 200319962, 321597028, 386988278, 740224894, 443082676, 444349839, 679004863, 351377103, 57419627, 560189105, 31377518, 35310747, 995195739, 605345385, 379235439, 984408824, 84093702, 693760339, 455621253, 171047998, 441559172, 836811398, 749203456, 805839261, 280052300, 98174344, 644271955, 242883017, 130949397, 547373437, 814370225, 709429256, 792127668, 19814730, 629662024, 306821946, 270458574, 24126542, 87103055, 427245960, 37982075, 271739813, 608794480, 83150402, 866585884, 309067984, 706722510, 633793851, 432944432, 297923560, 286074060, 978320193, 398146807, 942618459, 132752155, 749175316, 324979635, 233661094, 616111311, 710907937, 92505292, 188181404, 402069449, 662496953, 419824318, 463405666, 33537394, 455827949, 674931209, 738801474, 666302608, 500077959, 8369543, 455530232, 74476553, 449745206, 508233379, 504588300, 170419016, 969209148, 434530005, 344068098, 988260782, 922259170, 539530315, 205477219, 637494968, 194817325, 435384462, 941324570, 478228027, 178912415, 449917512, 743634898, 516363679, 558818035, 356497, 567762603, 533776860, 844572334, 891006596, 357019971, 640326815, 117603404, 811107390, 647578793, 608376510, 621794083, 959890565, 128042342, 176186322, 937081839, 401247899, 882662352, 752807263, 864357314, 64973556, 944429687, 522751375, 735515244, 874388439, 902674785, 896095862, 745467845, 442374536, 544359256, 311538543, 835180313, 267014420, 324243108, 413125449, 364158181, 256478466, 159617276, 743269731, 294393724, 899220961, 767386251, 65104127, 555533087, 767659156, 580051449, 19178928, 377173823, 45490743, 962441993, 612770525, 625090917, 679541304, 72480311, 135493591, 743161665, 248588688, 12579831, 896306329, 814536785, 214988214, 366066529, 92480611, 573221505, 764106275, 247951704, 718074882, 432956349, 309805698, 940712516, 880489351, 383919686, 204087151, 938833847, 710927414, 447532778, 835302292, 795546560, 656494331, 681084989, 939877550, 810846431, 920353837, 510498831, 718955290, 584134133, 400691353, 34821769, 402675381, 743753609, 176584248, 353272610, 2113751, 631747267, 79243518, 785979881, 195434743, 761029495, 946491124, 637807939, 875025556, 993598272, 967668527, 356200512, 377638712, 374043, 160122743, 800838826, 681086822, 174047703, 885950495, 147892514, 333373262, 31055614, 802179693, 776532643, 926676635, 824377649, 684445355, 147087495, 884632612, 726032034, 537064267, 216141522, 412411088, 629034390, 411385436, 961489916, 826263915, 614063532, 976668201, 354931041, 458376054, 676420442, 712653993, 751759420, 862961446, 76426887, 771641078, 151560858, 296779609, 835779335, 311901705, 670169974, 55190117, 972784871, 59179380, 936961336, 242095392, 504809551, 944124043, 985199311, 836350955, 695827425, 354057032, 513397380, 705346644, 608109491, 717237078, 389532888, 213992867, 415280758, 521779911, 796567423, 508797404, 230611901, 13988425, 763930140, 580264568, 793918366, 221016729, 601733816, 267346964, 510497293, 415478892, 159828503, 859792867, 604011022, 534483544, 887654759, 851979828, 893659870, 501497792, 963912593, 154791774, 932657690, 662503583, 841419380, 320341445, 73288036, 403318206, 173553690, 55132874, 668865691, 119256305, 431870609, 69984433, 203880202, 543848977, 465549647, 532369545, 986273344, 933054658, 271695856, 581930051, 206048548, 160178276, 577867711, 819078096, 120659193, 941533851, 362886109, 187918963, 948516844, 85141311, 221258400, 757794185, 252821158, 186403935, 989522257, 559759073, 472452329, 339710631, 570528104, 565240164, 651162902, 632431979, 689048825, 52489243, 235473665, 66621141, 55466128, 371572882, 629355423, 135916638, 10765360, 634519732, 760376122, 311385138, 333977530, 710683779, 530925487, 555175355, 544056766, 574707896, 673743006, 545723099, 750797909, 900754173, 119456275, 790301857, 638822456, 243478716, 591808394, 516531504, 608426534, 182736746, 113522726, 356207297, 538769178, 46335033, 978317732, 665314945, 526849814, 912058624, 684960983, 419537300, 935738731, 665331039, 384946300, 515577571, 480592884, 907750250, 852374603, 793235070, 459631862, 961408335, 725495128, 478445321, 419122798, 284296494, 323891880, 131138217, 516466308, 827689248, 854648097, 664480118, 555747392, 48067870, 516751029, 930574742, 546545672, 334975352, 861864154, 823405536, 393647200, 230765892, 541885942, 934702604, 737160775, 642157617, 785218423, 818149118, 266013619, 370391332, 589881644, 309106641, 955501535, 478207355, 985315386, 2722222, 770166217, 321353785, 80558590, 629772817, 275678027, 715602006, 283517945, 949639223, 661141750, 507023846, 853701500, 868504287, 528911858, 675380194, 893798778, 232933828, 430383437, 140146769, 523853844, 435810104, 506247000, 988404165, 468351284, 594291380, 680974123, 360872316, 929302521, 658787970, 277791067, 892654245, 118299874, 393073869, 402699740, 354496193, 91313960, 422644690, 983221641, 634779391, 628511077, 703505529, 632663749, 88791773, 947009063, 636722057, 969951896, 961457770, 91004949, 394490091, 533699456, 380554462, 956218010, 823973384, 889546857, 724121996, 310352824, 482686056, 806523791, 300310730, 9555280, 45739426, 361409756, 94865804, 624804191, 928002306, 6836440, 912137571, 794104612, 52843269, 31108272, 147074187, 682901346, 104196406, 746454576, 411168746, 598801035, 545733860, 294446492, 525196062, 522080117, 329532299, 347630212, 79463046, 675443882, 811209145, 359592649, 677426399, 49738860, 134348257, 324451614, 149682274, 280591133, 377434296, 411056773, 477583726, 465297649, 907164663, 863821817, 731365420, 184912605, 819990085, 510755828, 373619228, 713496155, 652656515, 431059055, 529577969, 752171601, 441848975, 13276085, 584777471, 341549600, 347369419, 96363565, 893934774, 636733743, 833175280, 878647453, 754348249, 797005870, 475673754, 742894114, 427947784, 179716475, 128247872, 11814543, 285264731, 419004705, 800408852, 998575763, 296950249, 413155890, 709834927, 783017333, 30429631, 422253347, 763030609, 91945731, 55036798, 126232157, 600905744, 822742302, 427880571, 755439961, 141270226, 312103852, 913541345, 861310992, 55131850, 74572362, 312854957, 152111152, 635284019, 937282218, 467638728, 931515126, 740797445, 795655938, 331586375, 57344871, 247721369, 375284245, 147616684, 350473228, 776148684, 764942283, 556931146, 318772818, 11545759, 415743169, 667736622, 872029906, 899998200, 797746790, 57344546, 204547200, 330367842, 348093828, 582763135, 889202959, 113626919, 564075162, 851666877, 719124080, 428253682, 542926238, 571621899, 67659884, 22886761, 478723970, 320091770, 181221117, 348709289, 200249110, 860825199, 114862877, 975296435, 753729410, 99580085, 911735384, 658384659, 995511598, 31690776, 161873870, 358096992, 166442489, 837908679, 485203245, 116629634, 80502852, 204798135, 628124920, 829127435, 151384577, 994494551, 984038429, 782345321, 677894487, 292699080, 625815415, 987796717, 589126810, 150691257, 525017602, 783174243, 823128055, 479852404, 933331283, 899645864, 53478152, 855877352, 719559552, 722872847, 464217722, 225361805, 304197170, 274285893, 895056840, 470006583, 971992297, 990692995, 70235730, 547189816, 153838025, 547850377, 603885718, 498996968, 958690299, 491831068, 73849661, 351190239, 217551807, 240398746, 57102176, 304509672, 694890950, 872790518, 58075409, 772119248, 941462982, 816580657, 392306460, 39639244, 666398728, 477493139, 595658279, 150779815, 428334377, 612082021, 708808346, 375524771, 543051088, 309294491, 641936171, 420176825, 881737990, 803750547, 498318842, 786516314, 60409942, 987606060, 729540828, 480417339, 898964423, 676071692, 15788148, 794357120, 979340512, 447197782, 389911576, 775143980, 672716979, 379029540, 105602607, 894598678, 538975400, 528262438, 473627337, 674653176, 832558199, 531158548, 318276672, 965344006, 863173874, 629225870, 521571300, 688837219, 534808236, 984525582, 99351678, 346109032, 661605607, 612451411, 419429908, 217705713, 755644975, 344568839, 176050382, 168877858, 71316722, 271166815, 713485514, 776753836, 896199225, 425156950, 353123228, 475240699, 26802126, 144875171, 791425517, 253913229, 205090443, 894384319, 645984923, 619288479, 714052194, 522670272, 19241980, 348404083, 66329351, 237933626, 423840081, 615772295, 329610029, 140956261, 933178221, 959583592, 634316522, 276840013, 513093379, 25083502, 652280065, 762956213, 352804358, 437192039, 774406664, 234907244, 891647041, 487947523, 636396858, 457252537, 237164467, 749022428, 417479081, 911560126, 916392071, 128627963, 677122650, 235128013, 233134178, 952085028, 931928839, 123637329, 21545084, 995474669, 585639483, 115223853, 494397302, 548636900, 23200839, 841485598, 431592036, 260003308, 558527192, 15694890, 396931427, 60692925, 591074741, 956645839, 458692737, 821742390, 924649064, 622268400, 724110413, 795364163, 695068818, 924775261, 473222597, 522199361, 498614021, 143356083, 268027029, 416588559, 181866678, 45877151, 196221408, 880990124, 264958146, 239506795, 290493608, 859494600, 756146817, 314845288, 381592277, 116653818, 408462258, 324296241, 454769021, 183494940, 61760410, 698527588, 851358315, 346359812, 731101356, 464200609, 454526589, 554509101, 430657320, 561248738, 795445557, 599314489, 26309013, 282293390, 953025513, 885259682, 631061138, 199912857, 718399892, 523322046, 319269762, 486869076, 855858489, 949465191, 717860768, 182370678, 899559161, 69821485, 328400514, 62655954, 890287998, 598227277, 941348702, 897286450, 279297522, 903019748, 351039514, 952201768, 811070926, 209623456, 287704822, 849374067, 703229734, 266485196, 681130385, 686321057, 172847424, 990752675, 87955249, 498316829, 622910646, 437645161, 118199829, 932120250, 696127644, 515662822, 452134362, 820491165, 27908800, 779018171, 134000619, 109235769, 745361571, 891048452, 197224747, 607406851, 729357374, 6149760, 254314731, 5947804, 797172111, 459210574, 322764684, 494808201, 875095217, 827627582, 353453960, 633733633, 643331370, 929029736, 520910875, 582812189, 109039819, 500559612, 298213803, 541029888, 122312085, 919571952, 3006414, 48175578, 555921567, 682371155, 511745138, 742506730, 703850003, 732816720, 604939478, 107221882, 944492394, 506051449, 236130071, 469766839, 551451322, 366272362, 933264254, 756944714, 725760765, 562700659, 136473275, 589739738, 741001589, 416380033, 357441811, 464905585, 923832436, 70611148, 332611789, 547224154, 434275985, 980472246, 795289179, 392993506, 424692257, 143687717, 512318485, 505385806, 846201571, 151011400, 767301008, 834787131, 612777306, 132846493, 894473020, 502796183, 316210932, 493813932, 107565019, 815944552, 403374510, 267816783, 865152648, 780837872, 852706122, 87306919, 274089762, 78324413, 670945302, 925608011, 364871915, 300203100, 637570056, 206076683, 327698380, 50529203, 744793949, 766594264, 198052238, 775195525, 526713878, 267492882, 522147269, 841231074, 81013343, 579056319, 606017881, 444104504, 233014001, 87914036, 219473835, 579014923, 924577386, 116529439, 675261017, 63816217, 419165232, 411275949, 521443533, 717900092, 330975478, 671228162, 653673599, 794853120, 25198464, 913600731, 383022410, 759715272, 542350892, 133274066, 164849042, 609339326, 490743426, 417686092, 441911828, 762299472, 5420222, 634847654, 529247440, 869859587, 283738917, 744367321, 886557788, 256691558, 105252949, 137949391, 818989466, 128381849, 465516581, 635113222, 331710886, 597687118, 388669835, 720859329, 309273214, 439478552, 513608894, 21250965, 616958366, 213650931, 221563373, 437397334, 810544215, 763102086, 984529435, 229877922, 714777385, 905259263, 224158358, 949029892, 433864126, 194819257, 144907772, 763015109, 891181460, 795652641, 98186581, 588002881, 734868599, 199051634, 544577227, 348059311, 251211816, 31542142, 483275587, 344222692, 835959563, 882257605, 496611638, 888005292, 368165630, 407559352, 776427483, 276327285, 216497058, 359441999, 720879044, 960711692, 94018100, 477358980, 247264110, 471873656, 45715335, 279527600, 687802320, 507281713, 256814426, 973972085, 721310944, 331735016, 73095374, 160630883, 880025533, 261072136, 295258369, 44322922, 889365039, 879521780, 918591133, 203600111, 538054985, 355950728, 67845644, 70811270, 466846782, 727952063, 283177014, 744220244, 118506350, 499966346, 283362793, 156136514, 981107561, 692139269, 438905911, 38650966, 878917953, 765967680, 858357495, 659297293, 740997732, 628781893, 893432854, 776970367, 758611501, 504324700, 151522842, 464899640, 789920793, 534135195, 581660269, 220053109, 389860994, 27064114, 959859689, 656328831, 707183317, 667045579, 457474240, 676437295, 841641624, 387519845, 980794269, 689033417, 642179446, 756238070, 386455488, 518781719, 339812026, 395893028, 341068938, 234791037, 720307360, 461802933, 431091297, 626808220, 207763108, 665393828, 702494380, 484781624, 811419742, 336377357, 273082037, 761595723, 624418361, 471280598, 111477465, 502541584, 631820251, 184001323, 183314976, 179204986, 893064897, 287905432, 366547761, 136782668, 420322394, 128423295, 774595226, 933509521, 89083703, 193410221, 160140986, 132837311, 790655973, 464984273, 892187009, 571518529, 233569487, 55309109, 148658609, 891342171, 518757257, 319950889, 550131440, 607019714, 205160454, 780606381, 710889203, 58100059, 203142459, 349461809, 864952814, 589742431, 697214711, 548652385, 324000505, 953885096, 18512643, 662204016, 100742109, 205146579, 551039757, 299927299, 864999146, 729615602, 653885611, 119031151, 193692045, 864392577, 788477700, 803603502, 744453100, 778625213, 983552414, 96959969, 381214957, 67049936, 711044458, 850444653, 218418530, 515372361, 561052258, 865668241, 160692266, 344608138, 397666930, 256798067, 372924117, 692926426, 786727331, 478359287, 483746848, 138784535, 193102421, 980864106, 190265054, 391888930, 494402683, 209600498, 99513826, 376359437, 63245346, 580910779, 675819074, 728540569, 306724923, 300952486, 476280944, 6486820, 115331947, 903606692, 904740284, 328713012, 223373951, 324677142, 835746958, 651894060, 586281638, 371176467, 719943898, 756316420, 211769015, 674689533, 24866018, 728128305, 703815973, 481529178, 879867835, 89524420, 84356504, 139440305, 684412462, 660464564, 526379001, 257966298, 538725461, 150730442, 747824415, 390285019, 935632099, 752548833, 801047411, 521965180, 6717059, 338821881, 884299446, 319454511, 363423024, 392927825, 26688468, 64779406, 236591284, 95445957, 459420923, 771995600, 205557030, 235987476, 862376091, 750038970, 687225702, 333580512, 240773152, 142266866, 744798469, 820908880, 382052862, 939245899, 358956161, 781297743, 238654804, 17479095, 687319322, 365388088, 911266294, 300226428, 823271011, 667748842, 704336702, 222860946, 786886661, 536627285, 354433223, 923966183, 631586348, 897478499, 733457557, 916554254, 88933423, 222845910, 618770405, 704182099, 97850507, 617797474, 224549210, 918227044, 246163605, 55285278, 798422027, 259903512, 927112, 161447721, 740168077, 802450767, 379874935, 174631260, 730595966, 771332220, 940532183, 886894314, 167883472, 140158600, 728124716, 688372625, 371974915, 694253641, 890590553, 300737800, 43674970, 216404370, 20527463, 735986774, 552776080, 29087218, 243341192, 210321507, 367201452, 534031929, 239480357, 588072071, 664065191, 238886450, 151926244, 904214254, 89423598, 556080258, 414570610, 933322032, 966948334, 419105010, 897028141, 998441012, 872974991, 653564102, 232536662, 191986054, 703620682, 645785315, 335854242, 587148215, 731653876, 789767058, 476700358, 59317347, 483660778, 103482788, 309908578, 694609207, 554467600, 900926561, 209912988, 762908376, 601007928, 390051155, 736070077, 56096312, 980689737, 617831207, 435318872, 505645809, 982286584, 992713282, 91992776, 141155211, 700597199, 431981795, 886568818, 497283726, 388024502, 904608584, 912766880, 804606798, 188922821, 366239784, 472296917, 265121487, 707850968, 397865293, 114821145, 824384682, 954285645, 383611269, 695669322, 958235670, 146653144, 74588416, 343267647, 104712972, 699797838, 311564845, 130913583, 582989238, 581474443, 317754702, 881615694, 558175658, 311862282, 364242901, 450829400, 221701616, 384672581, 472631466, 101293788, 71397337, 644199435, 23423921, 947874811, 413505333, 686284082, 317117983, 736466447, 827333723, 45148128, 340287070, 290227100, 792101642, 92167241, 694139040, 822520153, 970422628, 857168451, 402843389, 720011242, 253499777, 771821920, 918378166, 737394434, 760975995, 831144215, 608294113, 436358685, 780938702, 250910643, 779696415, 371156680, 161734253, 718415205, 586768244, 213246895, 475951481, 350408528, 632232931, 817292535, 489895860, 917036108, 283545437, 182986235, 234125018, 851262562, 17071373, 455870169, 994869650, 447939784, 200961450, 189501371, 457975405, 14392886, 166096162, 117781283, 695314313, 199079969, 703744767, 34348441, 447263803, 367555910, 474573540, 593297242, 340786635, 532511133, 388480516, 591642310, 40240862, 958402919, 126456087, 448165295, 45031142, 443085724, 769884516, 928303449, 700231956, 426949346, 850737979, 153823596, 791606524, 980857876, 349393359, 778368009, 134900767, 524157510, 956434987, 689208641, 91935059, 231694109, 419818848, 148445998, 830127532, 435559946, 919338705, 424517218, 500424393, 933966521, 323319612, 355538850, 261045381, 471963247, 792088941, 919808361, 779263735, 746748300, 450917318, 173160285, 691651418, 309954537, 579529308, 574748636, 184029999, 804573297, 197043799, 206165992, 309611828, 558649352, 770431637, 123996599, 850290206, 174996025, 547942695, 245747096, 77526671, 834854237, 337470094, 466988694, 780091985, 810513200, 649383965, 354968468, 246789964, 842550398, 691803345, 902171611, 17842697, 42843851, 713268494, 55782960, 92308534, 783994182, 71346918, 51900993, 726171283, 420347358, 604530673, 488039137, 708199551, 969598436, 615918685, 856094248, 169814731, 808394081, 999511943, 559131769, 463416098, 60053837, 118180159, 384783981, 155238818, 881197096, 930579102, 169861363, 294788935, 267692375, 110945033, 415118683, 954219145, 721022777, 316217845, 87606329, 925033802, 144947200, 891683043, 184786143, 716122208, 98540089, 295565792, 765863776, 168232382, 691396492, 11873048, 323746877, 457323387, 547553913, 332232393, 142616591, 13388163, 289851457, 636737739, 457745547, 849608192, 489989266, 561951189, 596149820, 645952242, 983575966, 261760338, 264795150, 29288707, 424193941, 616293452, 459711522, 28550786, 284355682, 800909647, 948658686, 686322346, 365438361, 672488622, 476220287, 377996573, 784815521, 943104674, 888371055, 795394810, 267588374, 215616036, 36848449, 693620770, 412042579, 373204857, 60248341, 728287990, 940085192, 464278263, 782371945, 49251980, 182555860, 640374095, 327783589, 438507449, 842660600, 788342480, 204585029, 146342262, 196383874, 986398144, 706045774, 327231030, 886083049, 3837719, 149127921, 295755255, 968456054, 277940118, 601322666, 508209539, 146696387, 657228338, 757709814, 792851500, 502392409, 420518928, 204441317, 721094894, 463573034, 845845150, 669518892, 686780756, 640409567, 454576247, 129532976, 18828738, 215303773, 414070648, 599478775, 955873210, 702133946, 905960561, 76782795, 493757338, 523418043, 930243682, 336864450, 80616384, 669525762, 877105751, 551808772, 782572554, 351360212, 841456413, 807976561, 354444514, 354535689, 314014525, 765530010, 564515737, 703268099, 644863626, 571765630, 567823435, 734138555, 207633703, 139092316, 536654920, 800892889, 443663919, 897963864, 440444246, 280914653, 268799475, 462439988, 374541710, 978423103, 130376558, 666244733, 646355220, 772675841, 303130658, 965062986, 784260995, 838416473, 466283594, 732044972, 602288007, 334792544, 375668600, 898063585, 244925399, 855625997, 801235046, 907198367, 892902270, 948887531, 570280331, 244169732, 484808816, 856975626, 604739860, 883293515, 535877378, 715327206, 499596287, 701544884, 134157427, 579031434, 287150181, 676970529, 39104375, 440545326, 391424931, 958818460, 778463124, 260234125, 627289692, 806739247, 811243873, 160032433, 652065124, 50866909, 840839366, 767667310, 788817821, 921839141, 351791505, 31728637, 662413463, 224926441, 97190786, 25684260, 465550624, 61983719, 746614305, 325831372, 439638489, 515538500, 851019263, 270349612, 384862419, 224276576, 342042947, 766992729, 918052968, 339307635, 520674607, 543662131, 701430750, 455989250, 336490682, 153003617, 378845286, 948080104, 2878266, 476040676, 901131205, 410183640, 667888294, 450247402, 286874532, 323680120, 574578211, 359677816, 999222785, 503229334, 486403480, 166993088, 502101773, 979801211, 940494430, 833948429, 383691527, 473986276, 520798442, 42461316, 349654404, 406894898, 955457222, 249427469, 748290680, 577004391, 870018754, 355661035, 920944707, 653995026, 963387336, 201699174, 641523528, 257678573, 300787880, 949955055, 196682937, 412019339, 307708438, 948580405, 796689630, 879407695, 897068840, 658386665, 231978183, 532839665, 649197769, 868121468, 71703554, 46044201, 522540970, 952456974, 171963948, 717805731, 282982151, 683644575, 599839080, 627985785, 369951586, 662439209, 577678737, 568886476, 569714333, 610092082, 667946980, 669224184, 963293371, 622040998, 254725214, 600320325, 550395729, 414274384, 716455904, 680554429, 666372551, 877220757, 594551791, 920543204, 327089670, 6766730, 432632843, 52905015, 376618317, 539553899, 782795908, 114630301, 525964672, 413657469, 515826452, 42867974, 813403170, 505811164, 853822452, 494970945, 637636459, 331390734, 651699135, 178552370, 253077061, 707997091, 531097851, 507255810, 264716070, 107821547, 613424072, 292717467, 983583487, 979557769, 969783864, 204331667, 56911390, 443712205, 876720331, 334462679, 677772526, 167050161, 14464090, 977499489, 389805486, 597264177, 505977387, 491486780, 971357560, 487200195, 997064705, 4609508, 230103935, 465725669, 682893183, 757129545, 793870181, 729920064, 633058214, 541943313, 372245399, 558992910, 822700021, 531322961, 569581811, 218251046, 185121446, 471851029, 531874453, 814901463, 840036375, 716872407, 404419043, 228522404, 507071409, 762330663, 667622934, 56317265, 601056587, 503699568, 936249947, 307075759, 791753204, 721976896, 289975994, 370477794, 908079930, 812262107, 266495116, 193147341, 195062887, 416565849, 66214276, 488210123, 934304956, 474571288, 39280810, 17932248, 878302368, 496738250, 631890210, 634441085, 906722262, 825236215, 221996160, 635022659, 976094692, 647554324, 768811649, 287155162, 924860845, 998287687, 50852275, 369622661, 707679077, 755757920, 629573696, 473390729, 956158066, 134175278, 872953162, 649108946, 721480545, 873612206, 958900147, 87364277, 562736057, 51930683, 393984313, 436319789, 709770744, 886310582, 215116128, 977506040, 450995495, 940320346, 489716151, 375526362, 899670565, 52188298, 151339600, 174785447, 447765274, 117719079, 843678641, 880086859, 546661959, 624066631, 415264780, 862559682, 798883621, 536076438, 275680160, 144547323, 708255632, 98282948, 975186480, 76272413, 964987593, 8730274, 758260769, 443198370, 303173383, 46426320, 149542397, 587610265, 981900035, 7150903, 825253258, 611810285, 373823694, 137323502, 779928979, 404027653, 820757852, 642859638, 616464667, 602319717, 185692628, 543911774, 804835824, 814457644, 75332832, 581231560, 937426331, 933122108, 611963809, 533100441, 264888106, 455817760, 112732037, 437623306, 213025807, 772061534, 245180947, 553552970, 139063862, 81577745, 693486469, 255366147, 215453113, 528945214, 226054403, 266077807, 638416523, 566363541, 790564831, 85636330, 202031954, 52541150, 201027961, 877184261, 758554986, 737138790, 257619066, 253649862, 686417515, 414480197, 283463323, 636972643, 679219996, 962310206, 980829499, 485793110, 525604930, 866078487, 940923024, 421726500, 154353468, 747858224, 996941099, 943529661, 473230794, 21340955, 582158481, 140222762, 974089413, 703488598, 815407995, 400376073, 433808177, 174276415, 766301358, 546295601, 69702526, 660823587, 422715626, 577424937, 970831225, 298317044, 345619010, 982528503, 503205664, 770394424, 986399746, 280243972, 673980155, 621052703, 151193002, 209831439, 787915371, 25217840, 42186459, 425858127, 894157096, 126675071, 341052141, 461644979, 684747424, 52899722, 929780587, 499986482, 725162877, 259085934, 343936338, 50053694, 653775282, 330973766, 898635743, 487317987, 670758987, 219747347, 852551606, 340893459, 440916198, 757893141, 166836291, 112806420, 123248239, 686111157, 599731627, 126614362, 333157502, 349621879, 750357340, 834744543, 955706450, 414962559, 238827724, 752663086, 310547336, 834876167, 62550184, 180962146, 240366723, 945160713, 990752361, 211979967, 405587816, 748976123, 493811209, 136844775, 674540881, 698433211, 955878645, 758291719, 254111589, 525843434, 99084083, 651976066, 735201151, 789925284, 230134740, 13887643, 356548021, 266700931, 385710946, 615734980, 106123191, 818149583, 800467176, 479890153, 45386215, 92890538, 36981826, 378697850, 889014726, 578941239, 801698613, 116661616, 233945631, 928575194, 715905194, 701648714, 153865208, 442856242, 365338606, 631508890, 453546042, 899900929, 331241820, 913937302, 7204296, 14889156, 134338616, 890424703, 652142584, 759683665, 809720858, 431882655, 837178726, 100935021, 273377732, 484099863, 212874879, 435185158, 481507179, 43385733, 658190676, 785347962, 342503628, 80442650, 261227407, 936233768, 24332707, 582589121, 446994383, 80695177, 518257812, 789086715, 259330882, 224241335, 922570181, 292762596, 238576619, 627485950, 38658906, 366911059, 266364011, 404568041, 831517127, 317864974, 901158784, 96355827, 166398660, 625367844, 190285718, 528646009, 815683052, 801401234, 987299180, 486185460, 289387557, 462107331, 940191334, 340264723, 957008443, 532490874, 434147941, 180224410, 593854671, 751490729, 783087635, 508166964, 970642875, 408342231, 493071180, 619599764, 388736561, 263806190, 969154957, 535739210, 743766790, 122818627, 554206234, 868384956, 332005452, 298841062, 349215818, 104232379, 151516994, 755609429, 325594501, 495056315, 874735602, 232590957, 140547994, 558151247, 389275541, 45983844, 939664142, 362919374, 312138667, 121019910, 203520002, 912016937, 968633715, 639162987, 57438301, 838776373, 954220982, 570226153, 254159912, 42401932, 993229555, 684595254, 129792003, 730172266, 939334362, 887289879, 589466256, 353407012, 235877424, 936672147, 851167557, 890805191, 778181775, 490371685, 475196231, 743758632, 400096827, 986188955, 811481130, 928554517, 630791605, 677114019, 590629508, 584474298, 179010967, 645783833, 454962023, 563738932, 287298723, 555806393, 559549200, 779182288, 705234472, 345651467, 406645383, 630060244, 299827194, 695660021, 535374498, 350427822, 295484131, 961460961, 902978674, 926182193, 47537556, 413793721, 746897305, 272095917, 593509306, 275612878, 682107812, 661890851, 666346378, 586109512, 768654207, 345001551, 316216496, 635631497, 786540397, 847543515, 534507812, 856842999, 230656659, 743915780, 709850144, 838251235, 163173221, 103744746, 615808348, 467529309, 572197034, 716254645, 593154488, 84224021, 575010755, 535694165, 799935522, 15035979, 400133039, 323205247, 145895889, 997140984, 114356187, 15196384, 739560396, 201317107, 117618278, 762790533, 393584422, 317928278, 549532356, 791184676, 593267543, 505928575, 611770673, 386232056, 308069520, 348947328, 285688090, 757962553, 67987801, 341893261, 994327413, 506651713, 374071918, 714520038, 209205656, 604587809, 916145919, 592270362, 781762366, 592981556, 187770942, 306746948, 425325904, 897782173, 979696048, 237051818, 822730245, 971662716, 44448716, 873171961, 250671658, 215367556, 94227880, 227549451, 551145570, 311503585, 76973678, 390000445, 119808157, 790727102, 55029112, 416166577, 650626079, 604336987, 69757515, 255422931, 831942580, 106337652, 670081870, 289540378, 919107755, 334365054, 44258717, 608108964, 554228732, 968310425, 949173157, 12478603, 797881793, 859186853, 709566171, 773442898, 740143530, 87516134, 601607434, 365022291, 609852065, 356315427, 658462642, 738181340, 229689528, 129106672, 763445434, 481951809, 841072135, 340319498, 273973963, 441999869, 30139010, 806337616, 953531418, 226370006, 983206073, 44634559, 907447341, 6834737, 700992798, 727025373, 203015288, 993362300, 672771210, 589791247, 416815719, 908038559, 878100719, 498434021, 179128769, 562542042, 710044975, 883439577, 759652941, 307991761, 147389635, 373899072, 420567716, 598246332, 413979348, 107145685, 132212313, 205674858, 151879257, 36954281, 115417884, 74492766, 441911074, 284986214, 761753053, 37617022, 240270157, 466575915, 405226738, 321516375, 461201531, 233016267, 688491215, 442983880, 584967267, 101626065, 610407386, 193889926, 411742284, 157185271, 777354870, 241440224, 166106123, 729964379, 859346845, 856465235, 161435999, 352000878, 879913156, 911215156, 662913551, 699899246, 267262486, 853755524, 126647244, 63700723, 410027009, 642359092, 621334807, 945547920, 731495241, 570360307, 483959605, 714659251, 574180170, 371538969, 63685032, 880032847, 119032549, 412028128, 309066274, 852756585, 772281975, 150467215, 141880320, 153138090, 758874593, 707714746, 827668682, 187719776, 43313323, 422306348, 564779268, 707278497, 857347265, 625050640, 277154501, 115819123, 378918000, 699793698, 552477782, 35400969, 250160729, 534915989, 534586575, 24930170, 431396611, 494961327, 125961720, 981602668, 231052381, 136978911, 565983995, 810978379, 765631721, 387199610, 275699427, 43784272, 435648260, 37842495, 267556915, 221648820, 29074269, 839472423, 541796391, 468706923, 81890232, 151529568, 136683051, 21848110, 89268644, 486271512, 571736984, 154265672, 5209440, 905949136, 585839797, 818177680, 604024558, 815954825, 288794217, 619671198, 912754465, 89213777, 928731761, 273128344, 817957206, 418752591, 721079024, 481338564, 401390, 962995917, 752872028, 444801635, 450672091, 951198429, 435098746, 414063597, 746078733, 807728589, 933289539, 65781027, 411214314, 573278801, 343270028, 648491294, 434227, 750398563, 339261768, 982248009, 928655993, 472035220, 865726718, 697625093, 28852497, 216296850, 832824676, 602253433, 921934050, 896487073, 37545010, 318786042, 972211908, 283035426, 931778913, 198434383, 130664226, 119640870, 986152097, 382617692, 193195699, 49882821, 910147983, 532899784, 300448671, 763279058, 825034526, 315667770, 549101431, 142287363, 211003137, 696525457, 207061659, 471637278, 830728453, 199092672, 577044393, 399418211, 58050796, 22422256, 197504919, 396788411, 745813576, 299534320, 397861349, 940147238, 623826528, 843539183, 529550301, 328382941, 902571935, 81959093, 887737629, 439664710, 809493262, 685731496, 282882977, 206251701, 972003100, 340483107, 160171148, 285076961, 380611153, 684035200, 348249069, 182954823, 613405008, 681314038, 455023333, 115704249, 844976207, 758934777, 933756163, 237299115, 319683499, 377970446, 33949911, 504053201, 262731023, 169699135, 460498402, 251402277, 554186344, 887742625, 133200483, 165962402, 923564695, 812453044, 377487688, 587395081, 801713528, 558483218, 950365565, 803828253, 117824612, 119389583, 808563561, 374105258, 362404939, 883353091, 881653236, 916876070, 202011326, 760167155, 592758540, 385833143, 294459149, 889381276, 701512769, 733269069, 310862041, 826760699, 778059620, 930878333, 549901197, 92394151, 22937654, 348329267, 820783848, 374362533, 280936211, 308625273, 319063662, 821597427, 855652309, 342136579, 448822298, 205704111, 992146554, 813347733, 348159553, 356255279, 318537015, 105895934, 707541096, 958900409, 280344205, 336762558, 422849975, 537992613, 15449997, 519343587, 268107790, 659949923, 628659929, 597503706, 852590006, 925075123, 722630202, 783594566, 665930753, 936083039, 539148164, 305942477, 385411107, 117391858, 207767424, 702525274, 720423571, 680068988, 233723133, 147069231, 809955219, 420142326, 490337028, 754688855, 361039906, 352184293, 727822251, 468213289, 945239202, 790228748, 162701391, 238176042, 452205206, 809512150, 301412473, 45055431, 948707489, 727967364, 626861863, 800727367, 825295487, 71354976, 615313070, 868547515, 879214529, 600368290, 232799728, 568093420, 556562573, 433687480, 174472026, 509766792, 276243924, 429384236, 685621055, 226512778, 953214909, 989869134, 211090130, 127791528, 138358400, 612014107, 253521513, 911789955, 454724765, 853988633, 715205887, 479103190, 721623250, 153195375, 455843208, 260673003, 65944470, 624264199, 147672629, 870309729, 416815582, 777562819, 71387716, 474814828, 645610917, 391138441, 497858139, 916308210, 9909653, 390918332, 285665082, 261026808, 871827785, 736454329, 35458627, 24275689, 721161437, 443145766, 964684697, 903130159, 434538017, 949671664, 408458289, 647453326, 873117721, 32116028, 794982376, 83884500, 752972758, 756738377, 178359545, 300881293, 740158574, 849033113, 310138042, 583905474, 61329500, 630104592, 153429609, 561571797, 919920346, 269031051, 906422306, 556438422, 86477536, 973478220, 200737202, 100561655, 176333075, 322018064, 685436615, 198140252, 950239592, 139749265, 58084084, 161666585, 116265401, 308550870, 167952982, 554549359, 349452664, 6051349, 495097817, 221274660, 474802327, 84828457, 537544605, 152896459, 209695644, 131900407, 962850651, 298488259, 533301766, 943094661, 772953380, 15941722, 794046023, 736667477, 417101987, 580934973, 25023407, 959373953, 228908681, 364787199, 198468147, 195544794, 240541304, 991934444, 280216576, 365451303, 155093012, 862168625, 421053460, 339547538, 290378705, 423943545, 772417578, 324791453, 821647079, 187261275, 46824863, 900754864, 213055330, 807001622, 424008914, 704124241, 955909506, 201500010, 53483954, 180109757, 338401076, 480351704, 162883337, 439581229, 988988934, 72167016, 119600108, 397841413, 559234678, 784337174, 429842239, 208529131, 684119641, 530591121, 982081782, 356928708, 242033341, 389305174, 799085417, 882672527, 486782381, 117017728, 966319320, 566315986, 548462339, 594882086, 453171277, 338660266, 142606169, 783880634, 952600593, 144817138, 77175080, 908627752, 393808718, 777106713, 651384543, 572333606, 169328494, 185685470, 33045026, 517217787, 979860217, 219797823, 298846007, 301617327, 14104121, 452282727, 311240431, 660121669, 976394906, 515202123, 60349115, 670802691, 970380535, 912407099, 145893357, 839080968, 482485402, 374175550, 338475527, 853090104, 85593029, 667825252, 107873973, 761227584, 355397208, 131052060, 367674792, 497741959, 894004267, 880831213, 648877128, 756600185, 174827555, 368100934, 507468370, 757157264, 862325218, 438035272, 503737926, 706006096, 189287311, 973892480, 111545549, 784616909, 684398360, 59750833, 25592702, 709892646, 724438273, 951684867, 652038818, 891752082, 992294131, 921985944, 343910793, 675105339, 764260669, 749640474, 359306593, 941066560, 293589409, 442871943, 245391408, 114477031, 53833807, 211227460, 493202315, 427379214, 750797620, 817600586, 483768261, 653994638, 794977659, 359913896, 997887004, 435713413, 531020060, 886923950, 971931010, 105039310, 88517905, 365073078, 153919004, 738412576, 526840240, 451461829, 885895057, 417949233, 165043256, 467008415, 196475972, 683289938, 412781434, 197912250, 675531369, 391917781, 572779040, 37431411, 287232986, 240728072, 320266824, 54106115, 472975972, 362313434, 271329473, 48823357, 6148564, 157876775, 343732991, 853426340, 559013457, 678592508, 479211289, 63730335, 262748520, 402302603, 906180714, 165720031, 886273115, 447602166, 143353149, 902708664, 573272624, 797266014, 904002689, 230442066, 346367719, 481243221, 625139770, 939501369, 81918267, 400765644, 14128348, 902584040, 988995383, 381190990, 183547212, 492502805, 191174786, 848637346, 495419503, 864211975, 327117274, 710396804, 858392261, 195037512, 294768737, 476320351, 773836861, 213914578, 735780119, 57020594, 788943001, 887551865, 124239952, 821569413, 212256032, 140957334, 142161921, 457690860, 871824748, 465914967, 746606656, 617989941, 984171439, 256095990, 186588794, 699610469, 208457699, 914061780, 662465626, 590346072, 813846375, 187455044, 60216440, 814639816, 423537889, 788511175, 706179700, 704811509, 809873120, 461577122, 594671306, 23210564, 766280852, 314782452, 82785316, 691694433, 846299669, 770709720, 152649219, 608810921, 560890604, 70518122, 43191034, 943581292, 887368154, 73952569, 573881615, 490890761, 747630570, 607306765, 72207178, 481429276, 285055285, 688074467, 843297443, 200194051, 827453198, 713203365, 420917689, 518921481, 127225785, 756316134, 635829642, 552701574, 800919444, 839237357, 137399702, 94109168, 904778852, 586165821, 84989640, 877574013, 885386479, 939445429, 30557137, 209830101, 960564048, 216294274, 517328321, 411556903, 911349886, 859949328, 168143839, 901618253, 4757136, 32030354, 647799541, 857252592, 907225029, 935064457, 495798016, 30187766, 529812045, 459315760, 834677964, 880490341, 886670061, 821811233, 201300224, 364770520, 213908871, 931711231, 88122658, 462008930, 898756405, 108186096, 887868421, 286131871, 425208345, 31675963, 696956718, 3945617, 476957170, 688042070, 183611973, 711206794, 772561344, 892871675, 892835569, 667824359, 798045047, 792651972, 339639152, 862277146, 748080632, 200667634, 339602000, 619691922, 871270106, 532860820, 84857528, 766200712, 483864560, 360909335, 647397212, 953956228, 995907802, 914134300, 480197079, 724793392, 417669175, 51138591, 339474760, 533107389, 446430560, 404715703, 605450377, 490111390, 730409895, 847208342, 890936717, 792950430, 600488573, 313880927, 607282328, 123918907, 73702073, 67397472, 306780388, 60461546, 322732204, 91131794, 952736348, 117040894, 888219026, 142836049, 949077564, 214323203, 91710026, 542923991, 945883289, 711175210, 597061551, 88259511, 463437189, 771041005, 254522615, 718139151, 779101797, 551032954, 455407495, 209788817, 370145478, 87293085, 939292812, 534165287, 752486397, 639210887, 797914819, 870038537, 416201714, 443347079, 120924208, 62176265, 681169861, 132391434, 137676597, 156252572, 799380322, 749766034, 802037428, 977875025, 777663258, 818193165, 719062339, 797370531, 595784608, 685734125, 458199017, 655346953, 637457531, 510612688, 134226111, 891173578, 863464493, 24720426, 832217953, 234718013, 553441299, 944106313, 33693292, 568415800, 557962313, 881616724, 370299123, 844130359, 603685421, 954674709, 639100091, 421794363, 369415948, 117462283, 955835883, 316295985, 115235961, 78781337, 89265735, 551842003, 463684651, 184442960, 679862669, 652044477, 800482208, 309357872, 394836207, 654068097, 164109110, 931387793, 94974054, 547931291, 781607467, 58760113, 461351487, 269316972, 666051384, 593763546, 712076365, 552971792, 813728692, 326494136, 65818501, 481304331, 166906156, 663338669, 107381930, 780543666, 134496836, 537769189, 722802460, 97305052, 335440321, 20026934, 553588800, 427313282, 94768815, 916162633, 739865019, 562143093, 537244134, 87358498, 765488804, 879777811, 44606361, 408607353, 333278520, 388474835, 764227775, 508613797, 991744869, 135808860, 998775695, 717317900, 168922529, 814630463, 201387008, 382405498, 72480558, 196804850, 608513657, 497959608, 844293171, 127664424, 162488286, 282212409, 796212942, 464482871, 395022049, 769451794, 238433497, 948415160, 373695968, 686582472, 333390575, 369738939, 418830157, 63021021, 346236922, 161842988, 746228439, 156233993, 99744508, 364582417, 378073755, 852796610, 665568870, 755674467, 557347646, 160508325, 847647226, 401716195, 908066820, 868334608, 79740063, 903130397, 257547127, 286636552, 46119111, 895676499, 192410911, 732025629, 830501381, 471356237, 898622515, 71654651, 789696395, 2073492, 132420062, 751274773, 89834903, 30582777, 256551687, 166091189, 570827696, 524720099, 686615380, 987211117, 848999001, 850195667, 269611011, 39861617, 957084372, 838443112, 891663407, 441164904, 653727322, 975702425, 327942265, 55142134, 605581340, 913986234, 840652437, 774903463, 330018824, 204527461, 444928242, 723788760, 74167205, 544866665, 337188584, 11158497, 720633638, 636735293, 48573797, 235752959, 627951017, 78870122, 942970738, 678683684, 929175971, 970166527, 617096192, 721464292, 954334486, 176841801, 479149425, 195429471, 814767240, 270673483, 603507395, 468233482, 281427340, 855024194, 123312736, 471239584, 343658147, 733414482, 342599344, 807262964, 707858384, 459937652, 632069297, 29187210, 527801146, 166723147, 864445681, 303934363, 171995840, 163280094, 832196822, 28957403, 747667865, 836893141, 318160482, 130673122, 724466489, 641860218, 355862113, 181060282, 623995427, 736757225, 704964825, 510641719, 965651015, 675589833, 947481432, 159407205, 708496802, 313358223, 465187939, 61663916, 619199245, 859573453, 582141961, 741701594, 386667237, 117478515, 531443536, 855631706, 111495005, 955896394, 556442168, 682949019, 796247900, 14053505, 161483021, 33399411, 600894655, 134123016, 988369565, 511943706, 95249636, 747024769, 571298353, 139746314, 212742065, 980261318, 755747356, 633008795, 793264925, 816409509, 403691144, 773746114, 571513846, 484727514, 534553962, 31532380, 853604694, 360007206, 538387342, 96866987, 440526365, 812288023, 154067098, 342871473, 36270836, 422010800, 929884581, 802008411, 327858737, 276433859, 892866797, 381216314, 611935131, 440177605, 169675305, 323767025, 575875315, 48553993, 668091356, 2546103, 556100547, 151301418, 694967800, 408442672, 216260163, 308228060, 892428667, 902809700, 179581689, 646968228, 578653441, 705844961, 755221315, 344930002, 201555703, 96367102, 74977947, 278828630, 523042104, 715629849, 174576051, 646182193, 372796160, 20078096, 819692611, 367982683, 986230746, 380805568, 760531442, 368417091, 598683543, 923155839, 964488664, 786364618, 410097242, 608931702, 63021792, 940109342, 137246656, 973206109, 911308856, 903069975, 552933243, 908265913, 290381378, 946439245, 245031803, 883288821, 507092044, 451816534, 329202272, 823447548, 145776153, 750983182, 727698998, 144719216, 646150902, 197863012, 711200165, 346595045, 771659626, 435931987, 497692079, 798901376, 578471163, 697315023, 599389692, 494671623, 351212659, 611677205, 674486340, 615094395, 274707111, 915896076, 34399174, 262642022, 602238943, 406828365, 206478260, 701085016, 386127992, 994990516, 184065404, 84457956, 687138167, 279514723, 973496948, 716354477, 333889395, 551065463, 770538066, 662062917, 182135806, 806124816, 82531952, 388457009, 710150670, 236835914, 498751820, 562222128, 365770722, 439271504, 579268399, 245111026, 903121813, 213633618, 93820662, 935736570, 43954569, 998518430, 799466849, 25581192, 606873975, 789160418, 11536939, 249584320, 14417110, 810245838, 197108576, 552783757, 8281152, 891587747, 153276981, 368876673, 375793999, 193912062, 835765282, 830986956, 983905154, 992979385, 407126535, 284338089, 594271640, 381147582, 306398778, 183762117, 443012218, 931503216, 920245609, 243930292, 292273867, 128981141, 524214029, 714397610, 264106868, 162615341, 981644987, 398249706, 100591403, 986481343, 506128404, 223392105, 351356895, 755444244, 754898786, 847367763, 586025122, 144202872, 129074065, 78530478, 779138746, 947925985, 699560373, 152203151, 397781979, 127447451, 491735286, 556027569, 796078323, 91126376, 198331209, 173983107, 382786142, 771907227, 325772621, 122699329, 745263169, 313184211, 647814527, 16122883, 564031185, 453398805, 466978579, 681472461, 383030717, 84853760, 129546514, 411429312, 41692707, 109509166, 875978765, 919909864, 427800535, 278191313, 229007563, 711734904, 700396178, 272349189, 329208007, 974668453, 513137786, 768858271, 994012319, 269558457, 935811322, 286720490, 179920906, 324446451, 629987098, 825745038, 112021019, 416778249, 407709894, 180759296, 57682033, 326879633, 467601084, 45617350, 505776683, 196336987, 9331314, 688633966, 213526977, 465784992, 981506758, 640286154, 708672158, 694652866, 183495439, 135342818, 71864539, 785957075, 990314628, 945928272, 185530949, 540635893, 688648136, 510161908, 58061898, 915669978, 525225479, 688396946, 590180942, 627725979, 297548900, 647336672, 911430358, 681132044, 611814542, 483459948, 17382665, 629528189, 13588421, 562914524, 143177243, 210441510, 577260325, 926326562, 397415460, 221022103, 152843311, 347865767, 319793853, 355827332, 383041365, 392923605, 663502457, 724829628, 485132880, 800293604, 162431432, 471133620, 369808958, 120017413, 758643836, 866126817, 636826392, 29795244, 603232309, 812522791, 602828523, 865528839, 269961445, 722936086, 695737802, 34674673, 633074121, 335106778, 106728885, 504604544, 253539174, 135568050, 256708904, 628195018, 331456677, 264675401, 500511771, 187836836, 349880595, 721364443, 302034715, 954435930, 267013909, 39951757, 995401468, 960610091, 726335051, 88147708, 436932601, 895465201, 803743027, 725072153, 99602677, 848737554, 727283556, 442700957, 713503947, 544267985, 263342243, 263619402, 718978856, 54044922, 537252074, 883266633, 720857804, 210735657, 335454937, 543038205, 419439354, 944610070, 468350531, 729547038, 66358444, 455157503, 102306357, 198855511, 170999828, 396325645, 826161963, 908771237, 327151623, 136617269, 969325499, 787623887, 436175767, 297853734, 315637138, 31789758, 491918841, 391857944, 550198500, 822318101, 798986308, 910627560, 208160533, 758328174, 378219592, 102658779, 619253570, 547097758, 876776529, 913194130, 774004836, 677089273, 626365440, 655956091, 871796999, 32762057, 142270844, 361683137, 343921468, 1126025, 492002960, 79691445, 241512084, 749917800, 499626313, 490656903, 161939281, 652466409, 816753019, 901964956, 240187854, 365862102, 825495684, 397332916, 44941071, 330418151, 401630544, 861745243, 882286499, 230126999, 573903594, 833010243, 682670148, 913613118, 999252144, 282729639, 914234735, 790555873, 460080260, 190504846, 604348081, 988372917, 431258466, 306761187, 621721020, 32961870, 748457716, 166434153, 51196663, 144714049, 803893544, 916949593, 260256805, 522298050, 954558155, 578830584, 117084358, 236476179, 467809773, 463691319, 198256779, 132412104, 355343859, 273967540, 966256442, 917514664, 150770860, 806951810, 436418030, 841178167, 984557287, 202047960, 230419948, 875070684, 574325664, 156379422, 797159174, 254468803, 771116173, 760657081, 588781315, 138177130, 870025672, 261351859, 756039990, 733821258, 706701739, 798859171, 256754185, 372578290, 476129390, 648628762, 380081954, 949964019, 175231260, 232847576, 484819392, 963575119, 952949087, 503908103, 581068548, 622911170, 165886393, 690629264, 314933983, 866920171, 490996088, 97721073, 469820475, 599736406, 159864100, 440055895, 838758388, 113851806, 16444795, 414351146, 404819126, 243339033, 679062875, 235031169, 312397470, 329911399, 833192768, 635516175, 120885611, 601880595, 711782307, 974795957, 498860331, 134662207, 397255952, 583190711, 2638565, 418583690, 301973461, 211421441, 590031483, 42586682, 583271694, 667886604, 869629893, 314305085, 954992515, 556528619, 267914975, 376992226, 45216023, 560121966, 874963522, 974618868, 609131826, 958617575, 230473975, 835560783, 477987830, 407709683, 626182829, 878958485, 674599892, 906423094, 29552917, 768938396, 819376980, 901557441, 58503889, 50148844, 804337668, 134856880, 30872810, 25704442, 444657173, 879347716, 675973504, 567884583, 888681308, 913016321, 539525777, 426165766, 812412844, 218698608, 249334704, 26493947, 135208733, 650575331, 378824391, 769198965, 782336370, 79487479, 44055991, 671211362, 706613302, 20468713, 453234231, 704725283, 287325963, 744500761, 268151738, 204111975, 474508289, 126475073, 410842129, 24502871, 111494901, 531000974, 364349793, 886859647, 805619972, 977495943, 403997077, 842725590, 869782422, 19630614, 18407150, 846037844, 645698907, 351157984, 439486022, 290410827, 671376141, 549607294, 728939625, 213907960, 338373896, 922739229, 974891592, 125286815, 481254954, 103098728, 15934344, 997265541, 988311464, 553730568, 666495472, 542392179, 340794168, 245660711, 591015932, 623474844, 837547511, 882424111, 369202104, 991650384, 39779133, 76117006, 283029455, 228189012, 845973704, 958302475, 445821116, 464979375, 400248758, 174664003, 995272225, 552465145, 760836276, 494220271, 508867497, 454308311, 455681037, 975709645, 325243589, 705660543, 395335199, 934002572, 72478237, 164640372, 508126430, 423146889, 273260837, 945825566, 606188122, 99466890, 698676194, 893437803, 446262836, 3069554, 472193296, 634266821, 573376321, 584713206, 804659838, 666477014, 740335410, 192801428, 411809591, 821777955, 153122985, 152390774, 147714495, 885851142, 213073284, 120993613, 295334067, 641787397, 240688256, 914132197, 7293782, 905040488, 614621627, 33460767, 147527506, 806781265, 658726793, 341902612, 909615656, 386525989, 486823310, 161398936, 45235293, 693408296, 868216650, 789401505, 755452923, 195013610, 284031366, 413179944, 368552052, 414635987, 466992703, 134431968, 308040672, 670273771, 273250255, 26582109, 966259283, 704001379, 453438818, 549054315, 915317959, 42675794, 128520994, 469440711, 143041556, 685847848, 414923343, 288476084, 300604574, 424820042, 42925997, 956308285, 547863760, 619007981, 105741696, 137028662, 623458715, 18521348, 598614402, 404611137, 878101125, 129143833, 762213689, 758814785, 230619771, 313150638, 953915810, 160045874, 87424650, 409594696, 834362744, 349104338, 425279752, 981312813, 638306889, 393387619, 385780099, 266477340, 743198526, 557844779, 577219909, 862229707, 503125062, 367001283, 869695795, 223950932, 306310337, 336060096, 457062205, 185394992, 697659273, 483314768, 33531465, 45790522, 740953907, 375285256, 88510392, 122260244, 440096463, 882380639, 996501091, 429396363, 988028372, 382322619, 852150992, 722529836, 322228983, 737022500, 822627445, 488981244, 13736048, 859715133, 130517766, 683233319, 192797871, 115212031, 109747605, 739285069, 746749271, 902058512, 62066764, 462534692, 653654146, 639029457, 86653233, 78052182, 635778532, 103842332, 121758838, 149995210, 699281858, 820575211, 21278510, 928689965, 619305435, 542671560, 179733399, 890064806, 472139188, 795852142, 984166543, 403124085, 217697745, 240749165, 744989017, 246809891, 409217803, 784754195, 952493201, 141779587, 264298493, 322275517, 972117185, 708230626, 755575405, 190947032, 451218378, 411630246, 995719574, 721266214, 643628693, 320441495, 591655789, 793504506, 812550559, 441112719, 133184089, 846631168, 43021773, 440634089, 645807989, 899979445, 586774711, 657686991, 61043092, 421737602, 860004151, 907883504, 715658707, 733133528, 751939060, 107912510, 519870678, 518458364, 999667736, 574333818, 308924006, 716058725, 878655890, 175409916, 699334379, 731120676, 367083671, 452399236, 413817317, 531295148, 816976645, 634841545, 113358976, 760208780, 395609584, 834968379, 214898678, 563317434, 543142372, 577731147, 594955875, 736063100, 448593067, 657409084, 903506855, 824916453, 824942672, 937925832, 594718046, 922424154, 476183540, 989402979, 887475464, 45043367, 197232664, 725660568, 480172495, 644233914, 811046081, 549457357, 87872170, 330840558, 469050829, 27872429, 676422575, 442414037, 706210285, 922427358, 407110568, 286394945, 902109289, 114883101, 793612746, 221377270, 838181209, 37047999, 599692000, 785783244, 290113555, 837195484, 999799616, 216762300, 479736648, 581896321, 193652627, 693642962, 535196003, 733481638, 820855582, 855819093, 955086020, 988959988, 389718805, 990110120, 207034238, 779791856, 233543417, 520832708, 415911679, 55501996, 448220745, 895718681, 761890414, 392911797, 907382650, 120461701, 28448472, 659607779, 528771898, 986692795, 340973876, 934051919, 639906879, 918442613, 712633279, 228196254, 631749689, 645906665, 62715322, 555342186, 587783062, 694130130, 353621242, 390805425, 332147456, 342694815, 408422580, 835096578, 447239386, 834406922, 858148057, 788245014, 504288274, 389338450, 948971827, 670221190, 260948139, 149041628, 183859553, 329562026, 694697636, 301788056, 996413133, 593168236, 758928569, 267659005, 746939509, 618691970, 526023694, 952803933, 530584725, 629420551, 245871487, 482389292, 662370005, 560626966, 533357908, 805818385, 388388428, 70052589, 63147826, 896144841, 351874195, 971172862, 564546741, 40431323, 400591264, 327259034, 49227391, 985703983, 712371595, 745948877, 439718856, 56541705, 39463130, 149586656, 491909772, 11868623, 270547040, 864316587, 95381085, 802134015, 705769097, 839155726, 75303175, 261386189, 42672324, 618069472, 576314711, 598764014, 530428607, 705367494, 42330711, 100069341, 299458834, 990207845, 846276409, 719915598, 172778895, 932880945, 796002971, 985665184, 910819454, 351377375, 13640491, 457721693, 967664984, 561297692, 636647565, 134522936, 858726381, 134534583, 226827355, 563032290, 475036748, 364965038, 983400025, 298921411, 416969406, 185371723, 946632905, 321264308, 515141541, 979284591, 181708462, 136104383, 701389771, 346504550, 420675347, 151304714, 59250523, 719299209, 615429438, 594266787, 889685199, 864108677, 812805459, 327217652, 207595230, 820512740, 888562781, 470162414, 368894177, 570038057, 235870881, 592137692, 224640450, 933645911, 828363937, 14104018, 397537852, 894727805, 22774547, 540956840, 57557303, 886061429, 790505231, 649730107, 584035371, 34036690, 425938645, 964720301, 435408973, 644171308, 223980796, 716004985, 678201082, 982420161, 552125035, 552381036, 923316361, 677591458, 453713655, 875697120, 935938971, 980614163, 124217190, 115547308, 814516865, 508617000, 410991611, 612911595, 950181687, 703239894, 197911089, 881766966, 528317871, 564118283, 74600114, 159816760, 414332995, 968522278, 430046316, 972965258, 344708718, 239753276, 254227945, 851589856, 478609242, 981129960, 704493929, 677151604, 896682600, 643470211, 487650675, 327716016, 157585013, 475398551, 425445364, 149861347, 706720522, 697057969, 625015989, 835928219, 560265877, 483837389, 289101359, 140329779, 328585851, 797805200, 746957817, 662610393, 624641262, 368973191, 284148740, 954377202, 148014086, 14909775, 767769796, 916023910, 897523477, 917205409, 515470416, 519139947, 231249772, 684605890, 869365965, 900530785, 524385940, 542612978, 105214155, 571654449, 184063466, 653565880, 527392378, 523719425, 266368302, 71479629, 586145559, 188347328, 685884684, 265981792, 483467840, 962673743, 757140769, 12809296, 779614695, 519993601, 626622316, 983423019, 894529345, 636741173, 759067344, 971172872, 581912928, 578608203, 769700939, 524073341, 760036605, 241823217, 817934637, 925831049, 662989188, 191250267, 230704735, 960323565, 503572795, 389145600, 443430380, 574634051, 896837420, 732019467, 857438976, 126029503, 944937487, 106739405, 401178311, 538976089, 140656421, 822165323, 540581082, 229532409, 838865708, 374001012, 471359672, 485291545, 787740548, 947165510, 454985808, 797221567, 497420137, 852848965, 306632408, 676597717, 941834594, 192154443, 415429631, 337103367, 482820805, 887343937, 341668322, 580375516, 890632785, 765527055, 537015780, 942284786, 636312972, 41885576, 892691150, 317556149, 668010651, 34496307, 354087588, 837105918, 767215364, 28584523, 455998509, 705354075, 808684419, 945605791, 826617326, 629243796, 869061188, 282067493, 691725942, 423388450, 570905943, 636574387, 841035315, 890322640, 794047881, 40867423, 195498835, 107379765, 878186316, 723865099, 418713311, 495532361, 630982525, 391568080, 766753272, 204226087, 613334631, 317722987, 577380104, 706228812, 218035867, 197472201, 496711131, 911643520, 953718238, 185154870, 58746021, 329214228, 997233409, 376018184, 877356602, 424845987, 325221868, 159978533, 726784161, 625358865, 559779171, 447715549, 547961243, 408385823, 676179586, 998305853, 842443354, 817654594, 364598379, 781487830, 619133114, 949948483, 202645101, 167237026, 896368581, 461380131, 260143273, 400196198, 263787880, 117132196, 390950960, 793245719, 327046338, 481805722, 848671068, 754690766, 285241302, 546250159, 901521147, 191148978, 646302854, 576698856, 554419982, 523600971, 522968196, 586859000, 42204870, 644475569, 491958851, 149618091, 149447610, 709650179, 312927121, 99567333, 714547062, 105389351, 318678910, 425891523, 492459132, 649734784, 342703840, 51026530, 139624979, 788302993, 880020261, 758497547, 231376206, 464390392, 928051401, 911917998, 503012650, 856128255, 930772392, 693825918, 292424045, 804524793, 721485227, 109132439, 880908836, 280634700, 72323796, 703253968, 929492102, 778675314, 586054883, 703097230, 571497187, 779629290, 975765844, 248757258, 531673332, 929444993, 858014417, 876447669, 715851199, 53665421, 324250141, 763820326, 654925108, 758625783, 403325737, 660006567, 296525520, 248173530, 134213341, 100910785, 931487849, 440213055, 527434512, 718695487, 760172067, 754735025, 139902092, 527033736, 356386572, 405328903, 735857154, 984605445, 483030620, 78589722, 143384982, 362797711, 769917864, 72780820, 600369364, 812559210, 935275954, 28467241, 35909816, 161143072, 924739354, 864739808, 857625823, 807285137, 608698376, 89501400, 386463491, 65611122, 320907017, 901916261, 426444309, 319205708, 211399231, 993587361, 265852312, 776501623, 181406266, 209230702, 340157070, 789042087, 198078755, 902390238, 97644024, 901217081, 577040655, 614433014, 837476293, 185024633, 937400806, 854247779, 663085430, 184786019, 742307538, 834849631, 830933301, 18006987, 297789751, 415524378, 129154829, 838380770, 996482195, 462999712, 561550283, 306745547, 264075164, 553071856, 108160466, 881134049, 948885831, 576023601, 744345827, 851191215, 101563396, 401201286, 702973838, 255757103, 149031696, 980909168, 319914768, 226591186, 279068263, 206865164, 803373340, 569805126, 257962693, 749974175, 821107959, 458744346, 998610140, 67397046, 624233220, 675267501, 464049854, 20233569, 30717314, 362107247, 916420237, 763824906, 344692197, 814133408, 636754476, 615863858, 947125381, 277077783, 534699197, 62082626, 328078799, 917726864, 970738226, 318099406, 632410255, 772042839, 445930395, 784862687, 913962550, 606244867, 917843748, 92552683, 240276912, 847989875, 210786293, 807299163, 934028713, 504920625, 867447224, 700271615, 309282707, 911610632, 52858264, 914942558, 86494147, 353378858, 440327184, 152815741, 999544350, 787293635, 156094584, 637784679, 36504640, 485358184, 311897615, 823446185, 826174187, 131780471, 568700141, 646413620, 597114014, 256579568, 93256934, 117167211, 121466953, 767461412, 433133915, 60015930, 410217220, 302446162, 243086165, 928066596, 308096812, 1238224, 49793974, 330926745, 721994845, 625955062, 840373637, 657702028, 109863136, 456234508, 504581120, 542324374, 590295832, 444110914, 926842293, 192010889, 122146005, 267241671, 381163179, 305901242, 779339315, 945813976, 517788270, 395182657, 414257421, 411235596, 733146902, 437241163, 322401203, 955078424, 88686842, 622155307, 507049100, 415936152, 584585567, 225385197, 868899944, 361559483, 619623476, 688440638, 342735389, 795642907, 572064549, 412606439, 604467600, 15316601, 784574270, 653982563, 4647295, 490134812, 570774677, 464518988, 562524183, 419073929, 276677436, 232931824, 295865790, 222691931, 234123956, 894331800, 123997254, 880276728, 574731201, 809596124, 23463778, 561331731, 281716603, 2973780, 784751313, 63931749, 31917068, 117728251, 669790330, 438334748, 918847865, 254724725, 295742852, 360208945, 615194057, 20185327, 704039321, 142966623, 59283205, 198545484, 198609395, 592136074, 330864361, 927114241, 714109087, 754499717, 552286099, 962846982, 343197462, 392851754, 291065858, 814393253, 373733467, 517791634, 486881826, 997852128, 288532250, 263399999, 474214791, 583918716, 618362374, 582853322, 438763493, 356067278, 778322950, 911192821, 812503881, 241211749, 642368923, 539224089, 749773906, 102696034, 720802968, 260228638, 845547920, 734374856, 17883490, 427302204, 247475883, 632906972, 510894245, 978874058, 806438929, 305484943, 442717001, 186720322, 871152307, 520320490, 72619714, 189576891, 892826105, 974489025, 899480122, 736448693, 917650367, 215246160, 741000179, 500175913, 398113163, 479353077, 396252299, 212122404, 780949475, 142602650, 747417969, 106030080, 437889867, 613573919, 611194419, 122726060, 951268143, 470597543, 735524318, 679747905, 176408722, 720447320, 707415292, 956501161, 459819612, 302281143, 838882219, 320533755, 525531906, 897568474, 108799409, 936571085, 565363143, 882344137, 956408593, 264213301, 340461584, 341289742, 454889348, 684258527, 943293827, 54908454, 371167825, 696547147, 135393463, 486373410, 371001774, 971242535, 997055534, 67208148, 213786817, 699040179, 770541511, 380521918, 218350138, 906901838, 523882192, 350088311, 654852893, 565133008, 695098846, 910098955, 462071554, 341799428, 726045973, 202610436, 983665517, 585471103, 46405371, 787949097, 28094471, 660884043, 325730448, 166879777, 777750969, 249174577, 331052509, 570819492, 847755124, 775984433, 814550232, 8710892, 679825597, 91893424, 340916424, 156548986, 617565527, 193821781, 366220603, 303118120, 343795128, 673397889, 659267639, 222371094, 401164964, 928405303, 615249316, 992611805, 160977904, 914635519, 250636288, 486990638, 170092277, 639921667, 922863704, 28361304, 99671205, 246248071, 205703020, 839104391, 157592201, 882175786, 832806938, 382709719, 53227092, 833919739, 65567422, 97591255, 145057832, 923230312, 535700301, 235788012, 874685880, 277506137, 884981047, 51029839, 212873107, 115532553, 605755151, 8355150, 448656864, 971500308, 184630622, 574661211, 668158919, 776886566, 163610423, 302750664, 467943495, 708875340, 373358529, 25482285, 594779369, 779564148, 758446576, 781194321, 872506731, 796626352, 588515574, 966278341, 703340890, 950756332, 947435645, 127682481, 634788786, 617512994, 843724978, 537127556, 781030731, 560432872, 420375294, 143293808, 870329627, 391945789, 354716471, 123908569, 433624757, 737557807, 234604374, 951077716, 664244483, 879734592, 668580301, 282160443, 541472573, 389129241, 422942625, 803538783, 28482923, 110443696, 126914766, 587959385, 388551364, 609163558, 587528102, 780388884, 534089522, 599816906, 483450600, 910046620, 440126272, 627609760, 939165569, 951239413, 7937547, 790966554, 391941957, 251076782, 860320787, 673397786, 864917831, 367184893, 679967753, 494257012, 122221687, 728564868, 883420549, 543856506, 309205342, 596034565, 933092862, 647501942, 330640699, 505819251, 887425176, 939035407, 963932614, 890478391, 74832829, 799449816, 649060513, 713138649, 281279615, 359107008, 186495409, 353805883, 276873104, 834661236, 353104029, 522989692, 316700262, 550979233, 992589774, 232465106, 408889417, 165553546, 942360451, 9725246, 933047985, 689684665, 654284018, 604214548, 580792864, 790907243, 673924624, 572897215, 328870837, 799553747, 231060383, 295754068, 813281777, 683182944, 108209228, 518172803, 242666556, 541648473, 84582129, 704874588, 95908825, 711108322, 174923302, 573989577, 360000316, 914714783, 982139831, 300328828, 550124270, 525199181, 459888189, 497190581, 111587460, 10180319, 607226528, 39245512, 898733399, 427565493, 276257944, 479419101, 614834783, 255480419, 974736752, 703951651, 507745617, 669199541, 916041502, 224450653, 784059918, 571443596, 960974635, 582295299, 52667870, 216204739, 446249743, 561155373, 738569871, 975634345, 703054497, 901951023, 207012503, 709645929, 560732949, 678121877, 798194574, 975865015, 903842957, 299115387, 433320664, 745474662, 777720149, 784085129, 328460216, 362612518, 282512352, 189750089, 752767785, 95469309, 556724538, 631143736, 964174248, 758196203, 985355907, 180755205, 389641819, 744512999, 272912453, 720571445, 841670045, 636907919, 447414345, 193754150, 20094408, 171931090, 318614478, 990697200, 998034033, 163811345, 926084685, 336032822, 606744770, 978567740, 398942047, 618212197, 975054077, 185032270, 907704931, 329227724, 656297341, 208387720, 114131831, 130426664, 189314710, 572629859, 243860990, 900758740, 913470075, 517545318, 137785317, 454852762, 482747254, 334300138, 284764506, 297242697, 256985107, 55290, 161786103, 781828918, 776344854, 529331182, 384441440, 61674318, 738916774, 901317833, 740133457, 611367127, 404453451, 114813147, 641638937, 65121564, 676332230, 183477665, 341468710, 475191389, 706716705, 365471891, 262442689, 620789763, 710585800, 716840489, 129405574, 394784712, 408668810, 279984225, 988878674, 945594832, 786326061, 517629625, 406324400, 145512963, 89714731, 798029969, 198204170, 425509819, 724999620, 390601988, 542853845, 901783488, 165337119, 204332902, 300805812, 875117351, 316085874, 150248304, 301488827, 567340618, 406137832, 381466282, 520298529, 882765128, 372769694, 968145001, 274985076, 132630486, 557878808, 975240479, 823714776, 938261760, 404303161, 84908739, 370920851, 848765373, 573367242, 621483357, 478646299, 900816573, 843649231, 980823378, 361495571, 425513992, 704427410, 951697860, 258396999, 214650714, 253003, 207220271, 53589389, 456404332, 410642549, 771537372, 533995555, 206212810, 536936436, 125980550, 525253941, 502727860, 177801739, 454810311, 809141234, 954172808, 329201837, 954780364, 872296443, 783767298, 661648053, 800622735, 516115309, 248045006, 305083300, 949766608, 178157804, 801347863, 318750078, 722154733, 528670707, 651671964, 236459679, 703664841, 791588968, 847475101, 926752375, 85263607, 925746420, 125826713, 443574728, 347574715, 345064324, 437553949, 844518898, 356621132, 26811431, 659977874, 501267430, 944099874, 435074225, 77542860, 766855811, 454318433, 425734859, 677654081, 363864429, 688357105, 917939601, 31143031, 984764511, 513759854, 799705830, 683043360, 27577609, 255257507, 943909789, 1710605, 166072875, 541044750, 591212010, 873122435, 862281599, 655627301, 985845912, 575511553, 641244546, 620572843, 28260643, 959485159, 533787090, 338805534, 140155504, 642573894, 851154622, 439466629, 455924287, 898656308, 745194226, 138210869, 20016443, 569417999, 988206008, 246932161, 46254978, 686762159, 624167472, 830496455, 522531513, 208732277, 78814684, 693172415, 730202540, 984615125, 660295408, 615935668, 793717015, 505054646, 773806253, 375345992, 468894973, 733170064, 587342215, 432681288, 458099153, 688503310, 467828476, 230441713, 75352116, 421542195, 59819276, 224080126, 286516490, 904388234, 464764148, 274404229, 977810219, 284229272, 220262606, 815141289, 417754207, 468661086, 539229243, 409582833, 959623983, 676684249, 407903366, 267327033, 912349508, 21263488, 493605375, 544924551, 462378080, 89445919, 337236278, 808593304, 754269263, 840006800, 845028210, 123752563, 885363612, 752037804, 381912928, 766116226, 634472570, 450684165, 232212320, 251211665, 276033804, 831059542, 212948023, 181898131, 201209251, 377315912, 737978518, 293905852, 943171802, 682457274, 495555607, 782039024, 828062805, 996250092, 371833302, 566641290, 985167587, 435595042, 387392450, 855841386, 177576544, 786985464, 289751452, 522567097, 664835964, 334287533, 329918924, 609569692, 585488244, 180667784, 836540274, 670794447, 831471828, 839404941, 927028422, 542465710, 192512625, 664743074, 346295133, 413718290, 497950942, 806508844, 556548105, 50364809, 845366241, 16631659, 957232294, 181756843, 622180141, 292384590, 268437747, 233588047, 851519058, 45244871, 653685482, 954946357, 114553157, 696247205, 119592643, 633219398, 405441119, 431000067, 512102094, 847152029, 760580239, 881297610, 355145817, 229889024, 613697943, 7266512, 271696417, 495690975, 686534599, 353335230, 583385672, 998662033, 702267231, 108507250, 380781630, 461282957, 40398055, 850989995, 976230973, 232006816, 713857537, 609031413, 535293964, 432041841, 882343369, 243385907, 662910919, 309606140, 82437427, 959025059, 728941114, 325017819, 35200127, 213632489, 440236117, 569922897, 12416374, 466578145, 459494257, 288380091, 192007621, 79382468, 654576863, 599886573, 583550058, 785614976, 262510766, 386706128, 993368062, 948600283, 344359664, 585983281, 225113571, 230149342, 863540337, 1557576, 647093405, 677679344, 477602373, 166216784, 795581006, 570965123, 69301166, 308394612, 55057789, 359727720, 196967129, 253417403, 846311232, 830849656, 287047464, 458757073, 69777007, 328630392, 78667110, 760518276, 759207713, 145204066, 456326159, 684074304, 66424251, 88674190, 539961726, 727145282, 276843866, 991874691, 521494847, 839287993, 941658779, 26387205, 133135197, 249113484, 585503837, 403097748, 467858684, 522952884, 80490521, 428361610, 907664939, 493330290, 869865245, 256892279, 9839432, 212644714, 631935618, 84894257, 529605789, 829683379, 5905936, 90708910, 921921566, 541812449, 76591189, 404304759, 648753280, 47690264, 300085438, 763087342, 682157934, 914408553, 140377080, 287880677, 904288855, 572985916, 229939297, 340162155, 625971156, 614438823, 3692614, 122194867, 529168209, 558646876, 854760923, 263058979, 226296468, 573548446, 272825948, 658214483, 535717864, 71076426, 456328016, 863537688, 822960961, 844649381, 481432437, 465442456, 38567639, 692403790, 241569254, 456917708, 488391124, 391648992, 611488002, 931841852, 896697461, 983680961, 68203191, 673762071, 749377021, 438312700, 987768674, 31696766, 873458045, 606507888, 47569287, 855935443, 417945053, 179451552, 411226426, 263916808, 498786318, 218783312, 562720504, 860912616, 346119555, 205885856, 226592339, 687223168, 286648990, 361866646, 143154305, 753152258, 180678075, 845401779, 265663525, 416136947, 69502677, 135957776, 75843473, 973249770, 774652416, 326860618, 881835679, 267351765, 10389539, 119098168, 987772645, 424608239, 836260271, 775689108, 780118368, 258166511, 564415190, 230946531, 85639096, 608217265, 182866485, 591110945, 850642634, 278602824, 553309114, 148196576, 222166255, 675950805, 524227583, 579562838, 563510466, 786817409, 27321122, 158764653, 763819406, 537532851, 923048897, 935352224, 246264177, 501214406, 629042849, 456289430, 848843266, 490186851, 44692076, 443166203, 104973768, 873437401, 763490575, 681839280, 792469759, 809680316, 48352654, 926079304, 370101449, 344342499, 141344954, 541778292, 45608561, 380739630, 958886049, 161259222, 911905041, 487900737, 753539140, 730488367, 508574410, 89697880, 900878545, 264873119, 28870376, 210396023, 570176896, 264178384, 685969, 416762737, 885207033, 200766708, 604513346, 796937888, 45310476, 350291684, 327301354, 84003763, 715982129, 936152145, 237698561, 21147135, 803365232, 990854740, 193139758, 193415728, 680383242, 792764925, 267966435, 722314644, 454340134, 492850008, 873737112, 164148250, 449674338, 528634929, 507336075, 276115908, 355053018, 493678318, 580534518, 547302778, 346656168, 722883221, 525032897, 99200384, 380959976, 576668962, 918353584, 393556564, 773897021, 139202213, 527044757, 26980059, 400273632, 629082216, 280706902, 506267693, 912540066, 562593706, 140658456, 160686279, 373628201, 525074354, 864136948, 347348049, 392928040, 300073510, 318836045, 260490626, 215522033, 829149305, 448242221, 931335543, 404738250, 825546136, 820755220, 157774896, 72236402, 879389412, 625464696, 248571178, 762179838, 35828068, 648950225, 682623113, 41516724, 945696214, 384187772, 127281963, 143993850, 740257894, 593932002, 965077011, 240453778, 814460141, 621846013, 468844785, 311930885, 410048547, 598964832, 556036407, 367368776, 933679255, 384013187, 422452486, 787566932, 853399654, 838760556, 599585869, 175431178, 102698930, 517354037, 877167203, 386808262, 304911762, 423571604, 591034747, 477163911, 990456244, 258385857, 436333043, 806138504, 396074129, 376763015, 406059599, 411190184, 411705591, 656315428, 164548153, 289171308, 829401809, 241015504, 39079977, 691094824, 381055112, 333762116, 443832347, 702619097, 429171858, 100527284, 538920754, 954238437, 469088947, 513668278, 788918393, 733535071, 520727317, 833625819, 264396751, 237681894, 455284188, 978883125, 635319853, 966783575, 320980476, 791699758, 719235186, 372879027, 323903854, 910534072, 151793614, 834514931, 120510136, 146021596, 948619381, 583621957, 539650237, 174506528, 905826508, 606315027, 971787064, 701357664, 531416701, 425861094, 419409610, 658823380, 420580422, 157865051, 516608572, 84582917, 547260206, 229793980, 43136911, 717519278, 774120162, 381421006, 45546148, 102907202, 491978657, 889508102, 274003844, 377225768, 392950284, 255416657, 118374896, 891169418, 909849796, 83535629, 83989640, 756384871, 514895863, 528486022, 194064027, 707284973, 774891188, 763422061, 697417795, 95347329, 807455893, 915692834, 78885415, 24995642, 508679184, 588202873, 287063231, 933764688, 840758398, 168654351, 245809114, 229634481, 875026156, 905449727, 50239378, 917023851, 737916737, 619788373, 612909839, 906140375, 455827142, 736946903, 700330801, 176604097, 457458586, 151450530, 585338418, 49600127, 528978363, 935849810, 250549168, 520398750, 677689161, 90092664, 313181296, 209393280, 329909599, 786069893, 961027050, 590864303, 192620847, 71586433, 792270649, 49151217, 419068343, 296439692, 182435157, 179888776, 908785772, 914956617, 971375361, 290981714, 520252893, 64023067, 251104592, 945334661, 741091143, 169525911, 263457756, 720740382, 799171521, 553335988, 956593373, 928721645, 625201473, 234061322, 246333981, 71986827, 12385758, 401454219, 939371144, 243889978, 437491317, 952241567, 331218041, 107308526, 759526952, 305745001, 47826853, 30518095, 755242843, 975389562, 527940387, 320721225, 374715873, 460865481, 226302787, 234800912, 837536723, 268109743, 796078923, 780342285, 404518632, 457917767, 845032836, 580808618, 2244846, 787683545, 876739949, 846478438, 320462854, 430876316, 538667610, 495231602, 282075329, 657766433, 433395198, 182399066, 801813911, 131669731, 14539440, 477927071, 515338992, 454518727, 170618858, 637073032, 718470536, 389407501, 756517899, 180197215, 394175995, 129462190, 397142872, 572349350, 931422425, 490592993, 513457207, 835662380, 493613982, 769709449, 380837215, 861506816, 140145642, 997922637, 112843630, 399604350, 471458663, 50766958, 168259209, 981775605, 259566276, 779538444, 6801324, 120513543, 553370118, 297419722, 805625917, 444453507, 220613635, 904802799, 192765486, 405717031, 444110738, 641484702, 885126079, 770280492, 583989873, 267865844, 245851031, 657832078, 88616876, 702440871, 191058449, 817674869, 123845322, 653967609, 766437946, 755963504, 842268748, 194551678, 621991088, 626353479, 401496775, 452728914, 309114260, 941665941, 465068694, 122267452, 189975934, 406464537, 209679427, 802776551, 192049180, 69762608, 691121017, 899833888, 537467180, 522060259, 281077669, 169550913, 146885618, 237076494, 31459646, 329640402, 436370247, 884018088, 476885259, 326045068, 843876930, 748879075, 572761883, 399201296, 33203119, 998404853, 469208777, 833216555, 784758429, 815184043, 816809938, 554759397, 462634625, 482853522, 329320868, 851340948, 128344298, 42889214, 666940250, 909595515, 146003654, 771641629, 24225952, 436405788, 721143464, 800305663, 880290407, 336133383, 262511071, 489646766, 704349291, 959928251, 814910083, 129429817, 372681416, 293278560, 565351792, 681058664, 765462088, 654952084, 874518862, 467438906, 162471153, 887320201, 815052519, 609485431, 445006308, 382029412, 503329460, 113177608, 295301915, 207111967, 916660269, 148655747, 892502342, 729191383, 941798828, 955403260, 171423594, 433538563, 123759257, 606101305, 259420913, 456884622, 221059631, 205450071, 560825398, 772571394, 92870575, 526407195, 189953458, 6425581, 865073866, 653649252, 652813569, 849964869, 175380124, 277013586, 767426063, 269321307, 128631666, 266393790, 388354379, 496871127, 899003472, 917190210, 511567834, 151936809, 455096249, 84615864, 755553025, 281099545, 558670275, 348829517, 410126747, 833909127, 9449819, 403591043, 824867990, 831069031, 58283959, 613437871, 355020412, 587553055, 44895092, 853165379, 969371650, 356519191, 721340203, 813900163, 120874370, 81650641, 163861515, 108006607, 60885364, 984600164, 372010243, 392319845, 715334730, 493392567, 399450650, 498202562, 776020911, 971349789, 645736679, 827637056, 514055836, 740617411, 161818572, 876673624, 22490066, 478797808, 611532438, 373007197, 688380358, 864831855, 286826330, 694256532, 490874878, 17382382, 907618068, 304634701, 753386732, 320566130, 25408365, 967599985, 737504860, 372927104, 463014966, 725730517, 716002323, 884269961, 799341390, 641062352, 989439681, 369881759, 673240896, 632378549, 457413220, 895522729, 245556275, 515118722, 175839948, 431917010, 691645362, 431617896, 821212523, 713308130, 434363754, 226190543, 401863137, 649581839, 39921209, 893124396, 757911887, 276572306, 591488708, 337094789, 602623277, 463687780, 554702841, 295525530, 769429630, 475930348, 693622826, 265443007, 77808547, 958107526, 62847992, 203483690, 998741882, 940779883, 479239499, 534041049, 696720407, 654915525, 176372323, 851614993, 434534780, 84576478, 372891172, 939830811, 484350264, 222328718, 651013665, 704471784, 238171602, 262641229, 772741935, 4688404, 729896641, 811040863, 756940811, 46319893, 28018649, 676758719, 167197057, 542690644, 170054984, 476352495, 182253105, 175186684, 844861621, 541316005, 297702746, 348343947, 954105979, 878424973, 471097711, 510690326, 331613207, 432040393, 854312787, 862610756, 855869739, 121652939, 908129974, 910090345, 652117171, 73546989, 965059479, 606895390, 890960561, 288952082, 854511690, 821622854, 834801716, 138709857, 666496397, 609450380, 160876072, 596790440, 485310940, 205856210, 791449907, 794489271, 694646399, 561198355, 572961258, 29762843, 431786642, 219948545, 323139897, 659547953, 47052089, 31838083, 46930367, 984144476, 784620348, 865679722, 17837053, 153981175, 945735494, 551021041, 34535912, 250866817, 435758176, 972048706, 900078036, 971827199, 245431737, 496544700, 472388606, 247864900, 24451390, 554593155, 158620068, 361492864, 995369117, 472834101, 956258944, 9765541, 28500396, 527630215, 733587084, 337625062, 934685191, 2340250, 56211299, 655974633, 578652526, 473972177, 224916710, 423863589, 4006202, 441549952, 714937119, 824730337, 979091803, 815168685, 865758350, 645825578, 956913915, 731289029, 542861079, 718568809, 673383762, 476044093, 964278879, 91329638, 37871600, 783163522, 544992286, 125523240, 281548268, 206110460, 487669060, 499003794, 553208050, 545405454, 54847219, 152970118, 280104739, 522986988, 992936043, 910433420, 936736320, 159594875, 428627932, 355606351, 412104656, 81539723, 633304917, 199792928, 782370188, 365550988, 122835800, 269752366, 676975258, 832538378, 879354740, 749857035, 460743165, 355806773, 963976494, 314179869, 57484017, 873300300, 111175244, 983903613, 688087498, 559367186, 513366199, 378464672, 2869528, 679334133, 244842913, 209529735, 694994900, 679280674, 168215771, 583162068, 100841984, 91429990, 202528822, 868614764, 926325928, 552843778, 91204971, 115733719, 529175241, 27455434, 296050248, 478871588, 459929045, 511078689, 256993135, 137402902, 96604207, 957284208, 635330033, 53473880, 856587606, 837379640, 931459522, 461138885, 263378983, 304296426, 919318467, 784933135, 235475549, 51030745, 967580213, 38021013, 581273086, 353853941, 491406057, 121497347, 204940799, 975984750, 977682280, 454831175, 796632688, 623482281, 142385379, 914873811, 678810420, 886993667, 536022942, 658025751, 677175185, 802842332, 266776158, 515752193, 628398046, 839992909, 3213962, 380643761, 170661475, 699389416, 687305063, 100907382, 798502635, 877724660, 692060312, 118430117, 575241319, 47048327, 249702577, 521841212, 920506548, 803037861, 831074160, 768206020, 886113481, 512245115, 308707349, 314268468, 227977948, 569121674, 576166665, 205285020, 714619115, 168757024, 980763046, 291631915, 1902766, 939946126, 431336246, 714529213, 665828161, 651347065, 741073319, 8975310, 488565552, 510651657, 996520089, 902693506, 981561755, 733059603, 396164056, 321828119, 537205448, 447656632, 967526935, 927056708, 145321368, 56490275, 291478852, 746575862, 374265341, 810928260, 985867028, 851364162, 92827931, 503414795, 928132196, 882786783, 487332255, 905454314, 585761123, 586363504, 228059713, 707661982, 114549944, 442693914, 576725821, 694093160, 947239084, 47575231, 919009898, 592038443, 455023925, 744738304, 814926913, 559575281, 343683700, 528582045, 796944314, 429215152, 873713450, 576317051, 84253671, 466698366, 914100110, 164499806, 212018933, 730191437, 988964818, 569818537, 351114068, 81736706, 32883807, 287881934, 273565791, 41981439, 613431060, 467513953, 185191666, 634820914, 410351652, 473358586, 205612703, 286975576, 528441772, 223516702, 326430559, 557432815, 728823874, 303421177, 503986315, 407353212, 335501041, 857009919, 441215515, 182984154, 264457500, 277749405, 905119779, 602587455, 565210092, 108246801, 205754741, 652375720, 25676723, 26129992, 801357571, 892697921, 954726581, 911414758, 712117422, 983633020, 330485766, 833620069, 366874885, 123185215, 180924941, 703507051, 967710456, 422394535, 749566305, 841547265, 1243709, 661030261, 251814885, 996366348, 804485509, 110586826, 209650648, 317519248, 663789573, 924744115, 373874076, 80417374, 89986266, 965238757, 119977907, 117547103, 427183161, 496260297, 517204761, 35086272, 746882604, 470668375, 673896119, 826693059, 712848463, 440955720, 180339470, 697867595, 956464754, 897427018, 671535296, 309482243, 689970158, 857604415, 955275370, 63362672, 351713097, 38190169, 417957382, 513190537, 260973506, 20484969, 619479145, 530574301, 159315117, 116804505, 667555665, 366155166, 167859888, 39671298, 448050558, 605852711, 639782575, 823284854, 698408869, 948948778, 226881019, 324006100, 432134849, 203163127, 560669332, 457079542, 665866386, 264128037, 301416916, 953514988, 614047994, 330253453, 327929614, 937428575, 789750483, 167562807, 838857297, 707422727, 159960881, 864591891, 121910653, 280327015, 306544923, 805053723, 463597387, 688620139, 418229399, 409507703, 359745821, 755485316, 586963281, 519029192, 900633895, 72259001, 937287256, 314234924, 514438648, 606364629, 676275917, 219339990, 724563163, 523417122, 615396421, 480771342, 273560004, 933521219, 703038592, 203350589, 618845178, 741709459, 928411742, 966941297, 414524171, 561354494, 588954583, 375845314, 450792306, 871995097, 657642077, 141772348, 246778672, 603530592, 595927383, 699449531, 18155135, 786748511, 186691875, 225499003, 989281094, 383520512, 717087517, 861561622, 152838388, 420708732, 933250694, 755800410, 488159925, 97350855, 528203117, 308351642, 323194963, 720002063, 486602400, 767977163, 825255793, 760894093, 850697618, 195203499, 111763570, 823451156, 160815312, 646068628, 995865201, 679496505, 631041211, 957081097, 458058179, 909989325, 653286024, 177452365, 495089011, 610859357, 757046443, 424428984, 11951483, 910209371, 899343023, 196086936, 829436795, 541740053, 785265948, 643862042, 232691616, 644290289, 894775213, 937229399, 10836881, 215041553, 65198512, 181857797, 698331306, 54808851, 608561871, 991693243, 242194658, 396798453, 579936755, 567445918, 797650403, 744130595, 136199286, 500148417, 200824413, 296341138, 787295428, 622324143, 669741730, 16204879, 114026013, 824589367, 252673094, 393640900, 173506665, 307204442, 506519496, 156000232, 848167650, 772570290, 92489603, 535384027, 242690490, 478227887, 612890238, 637375191, 206840808, 382158716, 429696168, 197791508, 646939164, 873755662, 919092397, 347194545, 129839786, 55523128, 420372416, 835519486, 662849432, 894268925, 337724401, 875061883, 506250058, 723533449, 260038338, 972214946, 675045627, 527220320, 951726601, 410121345, 755666513, 752710654, 701762563, 608147459, 918904129, 329413686, 955313748, 864530567, 318178277, 556262509, 932170289, 976648011, 720467673, 782265387, 62903048, 757211680, 46846847, 656861948, 207317117, 726668575, 525363810, 710914282, 295644729, 925112765, 130158481, 282912181, 591858901, 370636122, 144273078, 840261369, 364200858, 322024766, 263068542, 764870884, 471932925, 321942846, 218068133, 529704380, 539831929, 859346330, 698978856, 309705710, 653893091, 549314126, 716258814, 572827465, 309607524, 809276209, 325164959, 669723937, 335714314, 830467037, 52784169, 398851330, 528721259, 444909169, 441439154, 458169980, 835926137, 876834851, 541223305, 541726833, 901783891, 405828203, 717039060, 916030231, 135655337, 38530942, 239264755, 393598027, 203213427, 912745364, 967962727, 727019925, 889271602, 641366140, 26057407, 724554109, 371371456, 433375333, 833709300, 318919000, 766817458, 97772534, 827686494, 817836288, 810668013, 197697273, 796706854, 624271195, 80015406, 169877495, 982722599, 664050180, 997641558, 670519659, 66515871, 929555057, 52143598, 179827443, 977220971, 436023216, 542974547, 946533089, 936539536, 580579738, 793340424, 848126935, 444505504, 225060912, 829585669, 631798939, 869004764, 812623991, 552801929, 792366770, 225662731, 481112959, 566662845, 756595372, 136076593, 74328178, 898268830, 927879584, 488814060, 283949748, 410991186, 438992713, 545072305, 367857026, 307780909, 723422128, 503001982, 911549088, 981585224, 501579121, 836031612, 570287513, 732185742, 108968859, 715933123, 699266112, 883385185, 454616626, 237482808, 758696604, 807104464, 886112809, 602539388, 267138080, 399439054, 954731684, 678120923, 210067496, 689693384, 286474791, 628518202, 461419859, 269659031, 474814604, 161829400, 182932158, 974660184, 51915930, 48744646, 1642717, 818323907, 708417258, 123152140, 912273708, 590833118, 834753639, 865759236, 993181676, 783552163, 448192883, 421676828, 650874410, 16019134, 958454993, 912128499, 48016408, 360203852, 156074800, 318561800, 334535239, 876536724, 761355826, 16647394, 378168159, 77929969, 407897969, 349635990, 780605056, 549184509, 876209696, 112795096, 688138101, 32316260, 209575532, 635475546, 644453120, 964097010, 354358154, 267977091, 587045078, 464554593, 80911981, 764745898, 844577293, 456560839, 294121283, 175006121, 355878255, 732915005, 682115219, 587456964, 925673376, 334187020, 920420896, 539941480, 488576536, 187541900, 184991840, 30187027, 291448566, 950152311, 451203536, 667694825, 928602592, 751000762, 913341867, 464621171, 440694341, 874552234, 174011986, 654607307, 661885489, 577604596, 78179091, 250700351, 127347537, 46000829, 996869041, 65659188, 713493566, 994429541, 873107083, 53639908, 445666526, 531644118, 794892139, 302437016, 361230034, 794484029, 739355111, 191607410, 217891726, 581867317, 544257252, 109303482, 692537174, 810588551, 172726786, 136671671, 834354063, 671353386, 367859346, 539920129, 685952044, 522505578, 411170765, 669466784, 656810360, 319391649, 62444327, 461303259, 515881428, 639518015, 833032092, 309769652, 630981418, 449431443, 554042262, 935725931, 431007121, 989274374, 571062631, 749332060, 177080177, 636709891, 423969654, 675169497, 883550362, 554624173, 326480452, 181157461, 126936344, 146345939, 468715505, 723332577, 284837971, 845943319, 232622874, 535803993, 6220104, 842184678, 860603762, 275235765, 735289338, 556686999, 247993389, 427866514, 290188077, 369342097, 291836297, 583159127, 317703072, 404680525, 738439038, 143045836, 872935674, 16483662, 796678131, 818152749, 690493796, 145638288, 206013814, 8059395, 44933490, 853385463, 327672064, 752506324, 67648689, 693834918, 921992300, 737588512, 148938755, 761241985, 622150808, 84608294, 325629416, 681494488, 680168232, 878628928, 500967121, 138754925, 287468580, 393241501, 8194401, 511207298, 142082867, 931616301, 37400642, 551331999, 12946536, 585480928, 382580491, 685167015, 817563544, 65842622, 26844695, 595408018, 444660006, 349394347, 1648569, 225821767, 526298662, 623758302, 930175955, 987010584, 85938655, 585926958, 733738570, 105459360, 92163796, 286733518, 754686209, 432054078, 604543609, 655603118, 620418467, 329550155, 786219198, 869930032, 100666173, 598768767, 867922272, 148696947, 857941786, 46764468, 326340998, 8778995, 633625124, 774446757, 444528251, 274739498, 680097563, 358513741, 571157831, 613020263, 645537333, 37866087, 884036777, 316089052, 679110074, 933904968, 176978441, 713236031, 201757798, 285031015, 215693396, 133910188, 194036111, 601250235, 547179152, 704046989, 703683545, 6320040, 76743593, 965043656, 945968748, 801554196, 423800708, 430655918, 591535253, 471554950, 686781779, 488351390, 491088448, 893497704, 642078615, 902211120, 723563420, 243522111, 142207270, 288592128, 652504809, 810067280, 62205833, 705695361, 36404127, 966884555, 87789348, 428026305, 637589364, 307711151, 546589593, 473346254, 752431996, 717896697, 946390249, 80605664, 873429094, 572478454, 957803240, 911148842, 989447284, 668921489, 661758585, 334079721, 46236071, 478892098, 506860143, 642023699, 119327172, 236129207, 190522822, 888211146, 512933781, 180748832, 594232907, 228897007, 228534607, 989358472, 578560618, 218724339, 992098788, 216157163, 299082993, 449949707, 939357650, 662620911, 160697502, 250051976, 366586600, 40550053, 580912385, 53592026, 624569011, 556816344, 964192292, 710757174, 972892560, 328173998, 382400377, 766218325, 618918024, 57836687, 557585691, 361258538, 674035678, 28589410, 284667340, 338234370, 852653851, 326750626, 455743791, 211062721, 80509470, 866418235, 549585745, 766649682, 661250218, 499701706, 970748485, 332037749, 479442953, 758992320, 275312847, 369447583, 143638868, 400419260, 395649781, 496918915, 812079360, 420345281, 153583208, 200560337, 312473206, 595882928, 749635293, 637000570, 12664801, 733085065, 238708817, 736625682, 44715360, 450774149, 263181366, 949848699, 908564414, 925811232, 539636925, 454743834, 981796963, 793005153, 958797330, 199978332, 993995986, 497068791, 808692387, 372273964, 334122941, 274181041, 447742256, 615749511, 936428129, 130885880, 560149464, 463185922, 937858340, 405707281, 376245890, 442915835, 17520533, 613895849, 642795651, 464275170, 562669389, 560405057, 771308189, 514617949, 950540456, 64800177, 322769833, 696153613, 709647176, 972340112, 399054045, 328982326, 761618754, 553773325, 711306659, 33780222, 900524399, 294805458, 373083270, 248476369, 802068058, 234186666, 61205181, 17968326, 926288823, 61468143, 544323725, 632399577, 319048723, 747429274, 784465553, 602673810, 968761449, 853770264, 320434175, 180688101, 558156489, 53401346, 571009414, 199554816, 397257105, 280027375, 240056904, 40608562, 905593858, 968291679, 327506275, 816002953, 105475157, 752498077, 177242683, 990394991, 878328406, 24091478, 936273035, 623614943, 780451994, 926270052, 520185103, 561926582, 727715682, 660341543, 922900056, 658185346, 645852254, 779304860, 725809658, 81290060, 185617996, 170436111, 840514546, 857288904, 71688255, 498383831, 386253630, 264624431, 776089505, 663254472, 318703720, 513142324, 675414178, 759142169, 515460434, 960947466, 668422779, 668035614, 42127592, 71619983, 132599236, 261054336, 245598460, 96893652, 637471287, 428242422, 409816754, 703492154, 405717547, 578123760, 134478740, 531018379, 632425159, 732001977, 151286055, 455231295, 796330014, 573776092, 108859882, 242560109, 375363471, 582660445, 452569462, 619166669, 81800232, 852398883, 935686335, 299586172, 394246223, 869583116, 766581253, 834728834, 639793831, 804519621, 599388551, 181791953, 64866803, 349201904, 39573501, 666827412, 321933587, 157099823, 24557946, 326869704, 879549865, 653392697, 710060199, 826715615, 325630432, 542008408, 180816835, 648425354, 561130489, 275265117, 105493023, 948161350, 929938114, 634206961, 827414447, 921580902, 747290462, 824372857, 983623057, 964530015, 682842867, 435761317, 370455903, 224204106, 77508309, 753379939, 661255964, 360447286, 784174030, 133549467, 343338547, 938410217, 575812233, 695728278, 296595816, 458445775, 667960665, 982638935, 90380598, 230573768, 543606635, 528974939, 669609956, 240594555, 609705205, 166726710, 444451371, 507360253, 8264068, 563660, 418494193, 276271540, 95081130, 625762825, 912999910, 445242049, 472233643, 86417797, 796635349, 662881620, 150157707, 953977190, 319992901, 469023032, 665460325, 737085663, 792129015, 788710519, 124119844, 577386541, 627525573, 780059094, 189922280, 431576832, 426368285, 200608885, 986490780, 881273462, 898616639, 265246232, 570793942, 851248882, 286008208, 41592669, 476357025, 676534016, 591657012, 63512974, 645124366, 425882394, 343599594, 125783872, 276628669, 295259767, 140251598, 516637592, 542611241, 966168597, 964257941, 482387937, 277061131, 812047396, 735281280, 968455020, 409943036, 776568469, 458481706, 690787941, 837730042, 568795455, 479804000, 94383424, 867686822, 138985706, 127851191, 149154321, 125015259, 544359921, 562789421, 546173291, 969759908, 784114059, 46554275, 589651030, 912105334, 114809936, 547901886, 616650990, 349791487, 204121369, 880226451, 402946516, 803311851, 483739486, 276726889, 924377094, 374295137, 457430310, 991387641, 479615409, 459662505, 302424343, 796994438, 557554407, 54570533, 669869073, 941771921, 71328074, 422336818, 389730782, 341613850, 691714868, 697114855, 163403492, 182889806, 334470071, 705035487, 447911412, 758671185, 67835196, 351278142, 871330849, 25876820, 76389814, 70483420, 416164181, 824257038, 7249275, 707426480, 460529498, 266368432, 686821520, 392295644, 660218152, 48985170, 940161987, 375542572, 870661169, 44770952, 950958188, 389384012, 786754870, 285144635, 885659601, 695323043, 89438484, 997482480, 380064751, 481955740, 421038659, 204378110, 979449465, 469739737, 697920610, 528831477, 884988794, 567752985, 171873966, 924646090, 366858435, 128813391, 465930404, 253537420, 247479310, 604096573, 311478083, 311786854, 761390768, 828727670, 197834869, 381947711, 445368582, 693344612, 464609628, 222312130, 184624141, 739649074, 661107646, 243987179, 671956284, 548494532, 681359417, 239499912, 950369518, 596294556, 924544126, 654575832, 779414169, 57233915, 708921424, 839629403, 384544752, 511182328, 355994397, 620242535, 630497138, 750304148, 203476654, 495082537, 542328475, 501054384, 610723922, 555490553, 27677100, 365284272, 337822410, 891578213, 821075783, 325403163, 448306158, 448454826, 829791389, 488118950, 957404114, 508509477, 526474213, 46292583, 760380591, 770392051, 166839762, 84440362, 37042811, 410011259, 907748248, 958566629, 218603146, 56031299, 946357526, 834240070, 88441007, 571599266, 359365469, 355365843, 953123775, 370846354, 177957661, 406748743, 502510603, 891610022, 55567129, 100928467, 884261569, 420859324, 266904182, 93692561, 905293879, 1741949, 528962534, 746008840, 762948318, 697522899, 534194737, 457198649, 390348880, 587551121, 114904197, 3639164, 787843696, 175102254, 215055265, 98641968, 319913052, 629948209, 214151012, 702492374, 11131614, 751222754, 238447218, 149423772, 194510766, 723776077, 16617525, 491421279, 392298078, 433778178, 55769282, 437520325, 983975299, 161301076, 982112398, 355494636, 782098104, 423551292, 653502853, 352147781, 842385317, 521135725, 546705759, 793583661, 206292916, 56187880, 284657189, 40086491, 407717088, 749221142, 525836995, 530863286, 929449967, 296221527, 876436231, 92887980, 275950517, 943559863, 244695183, 484095102, 466588413, 327951881, 864137020, 718813488, 322819626, 927654961, 30121705, 13190040, 52503695, 550698027, 103239217, 660472123, 563664423, 792621191, 502528038, 379452472, 148085268, 255605887, 138523581, 647849653, 195956619, 829437280, 980874646, 147492192, 876464368, 309683765, 570980614, 899864139, 486051974, 210728440, 318139177, 986647422, 993226556, 186224197, 635984430, 361431777, 165624358, 99748648, 850772310, 924078766, 539828294, 544031059, 495385814, 9616989, 425163375, 810901794, 883859162, 519235343, 350316015, 288532790, 480314770, 668882874, 380682278, 673447047, 235133019, 272038481, 225691292, 52388994, 676884028, 243403470, 55980096, 239380576, 191177697, 929877522, 822221133, 341928911, 853721744, 920138447, 851616551, 735735134, 663561453, 468149066, 1996977, 211037764, 274798251, 361752063, 736589158, 735989322, 21648896, 825977497, 402938445, 123157057, 321426818, 511590827, 956933746, 319225638, 870410260, 571610993, 383427052, 666332984, 636794073, 83687097, 715233322, 80759289, 666694259, 113357934, 257266751, 229782136, 451429129, 668127181, 125010276, 851730691, 800668406, 101396395, 142091152, 836457100, 306690383, 129847853, 457889730, 818326885, 230098107, 968712082, 874628242, 19126673, 514480738, 118578265, 982390214, 578867593, 277815273, 672607863, 327465059, 665273748, 398279032, 276813886, 599061696, 150083779, 56962990, 761989082, 263094913, 273658598, 86196179, 484759426, 880168147, 743985160, 421341233, 64066041, 285712155, 581600436, 755166363, 918287692, 14663663, 147259966, 904760738, 284443082, 800635484, 613420993, 340523805, 159953568, 940453826, 271830441, 468350040, 749020403, 196836448, 151604052, 773783953, 295520678, 936310023, 458578478, 530016312, 277811079, 157489825, 109010439, 276326065, 778934452, 890093006, 747500866, 753157460, 657750803, 657945751, 911067531, 170199466, 221650991, 104285761, 741981276, 45751177, 920479047, 192101624, 973464112, 784945187, 703128179, 467428305, 588020457, 275015678, 710452188, 546045946, 817832700, 226156724, 386821316, 812075178, 760993889, 155967398, 773948577, 184449121, 40440327, 908925288, 606270005, 578233291, 230994411, 915343357, 754359205, 728688245, 85652576, 488368193, 641280436, 730975715, 964132670, 243198461, 2845969, 222577600, 634654775, 946702246, 535162268, 161302826, 777180304, 791220312, 73302157, 509860491, 416434942, 20945331, 868678987, 796344415, 368532608, 765417152, 904947345, 985162996, 334205617, 74914184, 338470927, 920707823, 326158073, 674018782, 88743151, 187214986, 191160700, 92065317, 136175840, 677488800, 818050342, 275102289, 582833797, 65449416, 193301273, 37855260, 287762294, 308380359, 750853942, 166058156, 822074373, 905964845, 783299255, 795102776, 190920385, 193702785, 20450773, 869778808, 291165375, 981640476, 464749454, 160341247, 255255302, 793945517, 388476527, 955961749, 577486205, 293361501, 844003765, 307911074, 847849614, 419194286, 513068041, 658159091, 150358370, 91191861, 453153446, 445758900, 199862901, 204066721, 82523700, 814048514, 122203149, 538383738, 629247491, 382065124, 438115948, 220247657, 872190140, 697110308, 554896159, 13472985, 875818576, 989237992, 602497507, 469747631, 783983757, 280871324, 88360003, 309005903, 186394185, 494700094, 787087256, 645371647, 36206555, 368583408, 187952841, 948293794, 847674180, 525716045, 734778541, 59341891, 986141306, 439634277, 708457048, 134232376, 13026035, 640651470, 373333956, 975551244, 583343767, 582109537, 363897324, 308452175, 708996378, 766473155, 757361394, 801510855, 225574544, 688898174, 133549283, 724952198, 682482130, 996734660, 757868582, 44585681, 471512595, 835210009, 485697386, 840544083, 407793267, 948408782, 327581646, 24755257, 844152047, 292459043, 224369653, 75541045, 674979522, 351772729, 295979149, 136862682, 690093916, 189202966, 67025212, 922647394, 50235129, 724532171, 425240982, 877830301, 80706037, 587218979, 715609127, 102335756, 767172739, 768944434, 247062636, 438752136, 907962545, 123099898, 969216785, 109193509, 746512516, 330354632, 1319974, 653418409, 607092222, 69248719, 296233491, 968731373, 65834887, 139673133, 567463827, 918755428, 143334260, 722630543, 324132281, 717423352, 711883613, 180680792, 25043630, 391024985, 797226972, 636544441, 177432486, 609239902, 452280103, 219269218, 8233589, 200779127, 514398800, 376926043, 983261741, 269185998, 496226411, 6623213, 182963695, 575301191, 654308157, 779020738, 313369521, 55905124, 20201297, 407482691, 120881889, 995849458, 787120781, 416262481, 511115925, 43333285, 590785024, 427138637, 947843370, 979002334, 728153934, 37358934, 562021135, 670485046, 162166014, 501183910, 770473581, 455205018, 666676401, 114700418, 261483675, 133024905, 219209593, 490637239, 981864856, 385948278, 292709001, 314513619, 378850411, 753702446, 666421855, 154626941, 614927728, 525327629, 868829072, 338772158, 97981756, 525277645, 608549895, 502601079, 195159996, 246361638, 127731206, 710565202, 411712712, 255148937, 687212536, 727780123, 33459865, 91917729, 570478611, 852855081, 497881380, 111681212, 809033615, 239057610, 655132103, 900389983, 603458189, 139140982, 340021092, 346406361, 367710242, 669174570, 349987880, 709405860, 226603155, 721350738, 192957097, 219830983, 81204004, 580802596, 856626735, 592619789, 363816148, 221006322, 942470095, 282807591, 650166764, 581455647, 526139294, 670225562, 505533416, 832938266, 774200085, 742667415, 707045353, 256874415, 47530078, 363036810, 224749355, 323078459, 480867845, 72428463, 102805890, 38875200, 186309520, 388029009, 996506784, 667296309, 947451588, 924912034, 609262728, 376606466, 427874945, 154326265, 822732884, 404225975, 347174966, 400916279, 544413381, 218249580, 460245063, 570505499, 931756863, 353629651, 306155613, 381331154, 331583591, 820229097, 457015946, 617399516, 557878279, 114825782, 359289937, 126760622, 925365745, 843141322, 709109196, 444691793, 231829645, 115013083, 597400169, 408041126, 763069990, 170142206, 410254622, 828137785, 928419950, 685863972, 65817958, 89071690, 267480727, 43079165, 974546341, 840886004, 69248743, 27675155, 278994893, 216916304, 239321667, 853042242, 489064413, 325721733, 471991351, 67745783, 555368823, 112214821, 545480049, 458373481, 410037807, 421119559, 225926551, 829234506, 302421177, 71888525, 528682411, 666789747, 385329784, 716346004, 766966969, 680600992, 966177988, 431929265, 205752502, 974673238, 232010456, 741455100, 614057854, 802260184, 885368757, 116568685, 655952877, 438635561, 544662797, 914747606, 969170824, 384654385, 925080132, 512041326, 476828475, 775622395, 589556704, 422684767, 356127579, 364057297, 611497692, 541034301, 692543708, 902527171, 1128888, 502831441, 81907702, 878210612, 70626090, 344541293, 101031499, 874123025, 889270095, 561411286, 755829359, 671792470, 81688148, 808549804, 233014988, 398201036, 589267981, 993971147, 814307241, 980763097, 238983074, 736265049, 795953852, 931196199, 629758170, 78191206, 273887970, 361930511, 629776785, 188851601, 811081672, 643744710, 878846023, 921919707, 424041475, 193709247, 918890950, 621231180, 556237206, 644787511, 765779763, 827736687, 614425650, 688013893, 418484823, 576238434, 780556594, 554826790, 319255004, 224381452, 57534237, 379504779, 411410194, 188276741, 469520649, 353652591, 615707837, 36850784, 946521385, 666003607, 316836164, 819677754, 94995512, 92511984, 639590575, 900617057, 524973834, 45889112, 281498456, 394781097, 799628254, 760069488, 300278155, 756475, 265008619, 48540925, 424016327, 653849235, 154200727, 35466375, 804736429, 448646791, 150007907, 76210544, 371406389, 160135733, 499099339, 702393703, 521552112, 220668159, 929827564, 990556536, 843114293, 991895582, 425277498, 431221159, 121243418, 414972400, 606621566, 388337414, 850706700, 278304983, 266105118, 559041684, 414828532, 766775498, 409985193, 955136348, 292873306, 607890367, 942146716, 136039316, 743826095, 248853527, 904366257, 932092063, 927489325, 676163727, 635374991, 82462113, 49922903, 462727267, 236998735, 261167623, 176651757, 274682532, 794949230, 799461203, 59618274, 304461440, 438223562, 85906855, 650618157, 426640728, 752539263, 694368067, 777604642, 929274816, 384476985, 298762143, 447540201, 284548609, 892216517, 901398623, 990848534, 192158518, 56281481, 12646073, 707973774, 904696449, 374882514, 579242419, 33755867, 743579311, 770756590, 119460174, 478371203, 415255506, 941801296, 769356983, 504174410, 550881750, 811089567, 114195033, 790485469, 330616430, 226345737, 21206591, 907750798, 400400139, 391962635, 317913052, 902760298, 382937644, 42007945, 265673453, 112025455, 176739300, 488594259, 253135890, 31736556, 481684314, 375138259, 167009658, 129040592, 861658328, 723366747, 416507524, 279561411, 855975963, 810971467, 599505340, 858241837, 560890931, 165132836, 966724905, 284007194, 655560034, 37806252, 942900297, 795864603, 37913640, 824440487, 721911203, 357647353, 27156, 72683099, 700197500, 472998378, 630648222, 75244150, 513950688, 66037061, 422486439, 244988149, 453347606, 548589693, 593437543, 946139124, 648222334, 515731438, 888869759, 478308156, 114224508, 255427129, 493263357, 605774923, 458719253, 553491355, 4854369, 653860349, 438222154, 483072362, 395715398, 864347031, 82749021, 859551711, 267176217, 990266974, 234337445, 837972812, 561917593, 415842175, 199099237, 647946336, 98609970, 926267334, 550977524, 176885732, 674014134, 918405909, 492808793, 677863239, 474222308, 633368974, 544928906, 346688693, 651731194, 508316663, 265317407, 53964206, 314403239, 96452122, 604761267, 27647358, 834072460, 918111641, 735766342, 657972920, 199615338, 884851790, 628046648, 139607518, 942549869, 117361358, 918238868, 144170157, 828215547, 907603188, 880300157, 366639102, 216369629, 775324640, 162952666, 580398050, 18836719, 637047008, 102323320, 578286669, 692665073, 509095192, 330200850, 826203460, 575902721, 861051791, 361197492, 255527487, 90627328, 592955327, 568687971, 669445260, 123377376, 429983113, 798116884, 822740322, 231550917, 594845049, 900160313, 144992723, 456533443, 683730388, 646267780, 413210391, 198984978, 660934850, 754108224, 749788810, 846170293, 863323765, 185764695, 967164394, 499228088, 371000994, 468786221, 694291151, 284587252, 915361397, 375061500, 576479403, 449238003, 290894773, 278519072, 590207157, 629164082, 689866562, 155422708, 630982005, 549035998, 883878945, 918259946, 763118992, 811354967, 894665370, 818104711, 121196971, 967328861, 50612240, 225253807, 913966953, 366520919, 710735452, 56744202, 175977305, 22781176, 219791902, 969235895, 138823713, 539872885, 994612924, 335759938, 259280980, 427937211, 899423129, 774384720, 150673710, 847165463, 418586026, 495725110, 378330212, 552873320, 758832190, 959407602, 260728845, 871509036, 860198790, 835527618, 742581277, 559051514, 598744133, 844148127, 491081337, 98342012, 212938246, 764894721, 664952652, 443000119, 570001485, 971952300, 737133962, 160861423, 298057946, 229130261, 283002884, 59544244, 121060755, 138715870, 533362575, 461507133, 427835034, 624201792, 379443162, 596289813, 134595973, 764343432, 959643012, 608508095, 896159854, 418724198, 50446683, 206514905, 764688092, 586550607, 332368686, 374417998, 312094267, 404358446, 390393030, 794562786, 285671377, 465440342, 863722035, 630087048, 37832706, 948340296, 396355327, 397342615, 392184992, 441206517, 920734097, 456117414, 903651367, 241444945, 80130313, 326328242, 889258237, 400000088, 953013697, 848729759, 774277868, 902764973, 332154294, 842520825, 130085468, 619619956, 116282260, 86693107, 433988322, 285916344, 950010743, 108391516, 379178530, 442716343, 768896118, 612437825, 802289540, 586865909, 771030907, 717317671, 810434510, 898590295, 49873966, 592557290, 763693910, 204912428, 636690426, 59706609, 756566376, 402619218, 922092208, 958065654, 195253572, 723674986, 706564680, 519153493, 1046466, 489192398, 975865069, 593828558, 538273127, 178573806, 821480888, 819843011, 236422914, 777148439, 758987452, 717633577, 985120464, 524174951, 637222674, 581659962, 752322113, 808346172, 904830025, 486571329, 541699565, 2433747, 430444758, 544373749, 153735772, 899229241, 305200701, 873861740, 939420168, 681527405, 591264597, 22280745, 878605939, 321476096, 570443806, 458878100, 711935078, 823142831, 258688301, 151302113, 917964497, 159992774, 356193954, 27538993, 662598917, 216788784, 806220914, 428743910, 899740395, 651070880, 729410634, 968362559, 843384934, 830284456, 833002645, 67623633, 735182018, 892745221, 226029699, 891221514, 812022197, 300714579, 124963371, 109865709, 527673240, 842547492, 678509366, 508603087, 882064831, 191689205, 87329239, 441193767, 533166717, 2050514, 838735304, 51800053, 696927716, 628136014, 409900785, 416005007, 444090340, 92488182, 332874857, 98075072, 344572461, 615649260, 811480684, 943546217, 273855977, 164043803, 692637728, 108437720, 813509124, 731269862, 789525405, 998926973, 870206433, 557691362, 609312117, 393359321, 122189119, 296849750, 532967302, 771302882, 274981518, 132409098, 689966467, 265115949, 149858434, 941481491, 761215300, 807048756, 593548362, 580098815, 1928679, 698200443, 550995979, 101930831, 415125696, 496895459, 76176241, 621793544, 774801452, 140950975, 314957874, 610884098, 507651310, 260257373, 203158344, 835050178, 402834349, 146156925, 860020878, 717940964, 897934160, 328782783, 47029359, 337348884, 803613110, 957280712, 948888386, 630651874, 125121215, 217300665, 383604277, 193570810, 70724211, 980970757, 21294760, 337261462, 248167203, 30854212, 296563243, 36605684, 977118062, 27265431, 624041032, 916997064, 788288553, 543046555, 729952278, 951955684, 809521728, 385695820, 909125511, 134071216, 669903119, 878675366, 832180600, 487308073, 518132725, 852453501, 483565122, 338984928, 56963474, 866118178, 190360700, 564611659, 206108775, 58225616, 635926196, 786832147, 318443139, 287123033, 203541324, 498517629, 436518898, 890889980, 456371961, 546576990, 917964740, 717559083, 103613174, 909601307, 707113405, 222404178, 263476571, 310682897, 574823792, 144284444, 788108568, 208421003, 111705674, 708621497, 881487927, 135036642, 11114542, 464126045, 634701423, 624749717, 927128115, 374797537, 558802394, 530651916, 777263755, 634604399, 846809884, 42927895, 255523287, 621838192, 141191939, 370530338, 811969853, 603979809, 758505891, 189247227, 10046044, 597235572, 938729952, 704054211, 389597604, 349093469, 102250836, 957758278, 129042611, 527451254, 74213219, 693723039, 194367905, 508526239, 765293316, 545024719, 533491312, 684430303, 156200577, 56661414, 139473812, 479041274, 21690965, 199761823, 211448947, 599349182, 140733033, 95340135, 259302965, 951394226, 852714876, 899477067, 720626212, 103645563, 492073358, 938007978, 729863812, 12546652, 269689664, 66470531, 126304342, 701611081, 94005759, 601418064, 465412462, 257321149, 835356606, 794046606, 828536423, 821911276, 979018840, 933769967, 741315266, 903981856, 464742138, 671647146, 322711177, 967480976, 688304751, 793878873, 86456186, 256062715, 341230673, 362560184, 248724958, 975010795, 219291724, 272509871, 610159100, 952648074, 823217321, 95084669, 507463036, 724825052, 15913799, 887987528, 250420675, 486187911, 884990227, 771130402, 761430806, 804355308, 684143974, 928641662, 789524230, 364732870, 988569313, 632230538, 179380872, 853574812, 655372004, 672723821, 955539046, 564521718, 376181793, 273115959, 791533955, 698274839, 35223340, 185056688, 529805595, 866169533, 586167615, 518798122, 658854063, 517879066, 707689635, 299270339, 969472407, 613728866, 737116666, 316354057, 674987200, 494430145, 648961889, 580358407, 421763116, 891449604, 398609040, 791052371, 876192033, 426457608, 701524471, 273142977, 793560236, 14947139, 656460133, 76368276, 782468667, 27832877, 328401346, 131275062, 574036901, 56135483, 839464015, 832710587, 665946078, 604008859, 365822204, 555083983, 440453482, 861980989, 831287471, 169007109, 854285796, 828263055, 430617844, 445136518, 545662013, 264126735, 58595113, 443195247, 876202038, 279501545, 154059241, 984239005, 543053510, 409843387, 557467341, 874578475, 53025874, 63457568, 566248468, 908540551, 618860175, 547749566, 201851530, 437048497, 671970464, 93448222, 546179526, 425625169, 159601251, 616570114, 433133818, 757433187, 340431647, 472528318, 364390010, 992310473, 952279024, 224678156, 215565519, 259196215, 323888835, 39368920, 833622619, 74892883, 235218060, 809132535, 210403890, 788513489, 491688411, 269396487, 915791894, 901101660, 726040203, 110133535, 770414960, 971901611, 731260257, 456294506, 25732295, 463940388, 769369475, 718022335, 415294864, 929632204, 78795857, 679092126, 6085197, 890715813, 166355734, 675477926, 880870769, 441150928, 739944262, 983386252, 990725327, 658977856, 1077897, 502332829, 151065784, 615103587, 641412279, 970436568, 211032296, 550163958, 91656597, 500573593, 153370285, 463631082, 43991869, 85573964, 334380255, 617043360, 629231419, 641641540, 288207533, 199042807, 810146464, 439110776, 271103450, 166580955, 885619386, 751311293, 812933694, 327047202, 478272840, 687682831, 676291481, 680625850, 610357988, 576961305, 77973876, 522248802, 667662546, 942427955, 185242910, 128349217, 445005230, 50715945, 966113910, 933632989, 739579288, 104688536, 925517981, 215254230, 734677345, 738733952, 781194683, 885837148, 329887235, 503091185, 419489587, 451023590, 280823779, 3010429, 335604006, 533554129, 652713465, 517896336, 266125431, 701496674, 337932120, 966658468, 364384352, 112184922, 445169172, 815502839, 862718254, 420808422, 354562485, 869606933, 82916800, 751178507, 903016902, 65106876, 580737417, 375729610, 394223578, 532470058, 838407992, 310406284, 445221317, 905823194, 661848729, 493185349, 931360057, 30290483, 206024528, 276770261, 809912651, 977317811, 431115862, 234437829, 16152137, 185076676, 501912319, 789089184, 69690119, 275599968, 15840553, 295418299, 142051215, 309740076, 837191124, 939529342, 643331668, 656299527, 924091882, 354710778, 388800578, 873176841, 962544690, 403102767, 35373184, 433628819, 416152121, 455891898, 368887928, 116047700, 351348229, 847940782, 177779735, 250128340, 59723111, 729558578, 487198968, 970589167, 609923704, 835151949, 472214593, 801660934, 312445010, 414272984, 970738245, 630315645, 57055796, 557335440, 637079506, 228079282, 590000993, 868911068, 523314732, 421414616, 954684706, 185931355, 623584969, 5761987, 976373925, 269429786, 677428739, 881057809, 631310552, 830870616, 386992711, 814528971, 804796790, 248796313, 911183499, 395921914, 985822215, 254053238, 503471849, 736191832, 908400660, 192842559, 401513585, 252934147, 775642648, 113182427, 593316522, 649031108, 353265995, 237997591, 246719278, 407093188, 894431779, 610291216, 396811100, 34182395, 165215870, 663362361, 835297509, 930254530, 91665413, 1259069, 246517634, 288647829, 93049546, 831505091, 630439546, 216425622, 191946995, 263962263, 989776950, 776432843, 150048122, 831739026, 270794589, 29948870, 222820129, 271951641, 438076965, 387570150, 410303379, 857403879, 411900088, 54702500, 619874188, 251249655, 62469852, 782634712, 879300968, 305815159, 264058884, 654201256, 164561813, 862713234, 929140750, 183852943, 17484778, 101241466, 953480168, 768037631, 17388987, 473230604, 260843554, 873773741, 693490428, 939916953, 877260994, 344484759, 6242263, 728983569, 755926777, 855054164, 887534272, 45413577, 994012593, 244108128, 380696206, 167658737, 515949189, 898480257, 337061110, 5150865, 257236782, 564219728, 550685571, 231965614, 595174872, 184366767, 816794783, 228272547, 384090783, 189872540, 761996299, 304002430, 855792569, 927859967, 529891430, 941720683, 606815879, 923460029, 556314592, 754750028, 409604988, 400901372, 280524556, 640980677, 126734367, 725301992, 266680289, 893474885, 745965962, 870021420, 736991622, 629085498, 671185585, 264560691, 171529920, 646820883, 693970226, 738132324, 536449940, 541688676, 668101051, 947179750, 80201220, 923511068, 66394246, 919805900, 356321634, 13079751, 597840757, 951609138, 38901820, 447541226, 339882765, 587184004, 532928045, 348532326, 600303160, 217955794, 703918904, 209878563, 624325680, 617067330, 114158839, 658773894, 30776430, 376796745, 325843928, 764228820, 706619515, 237507136, 125513242, 8426611, 71375816, 365076995, 512814851, 557940529, 719531336, 454956845, 63259458, 691174112, 317750357, 441055430, 385437216, 375276900, 929517109, 603964774, 250487596, 917257603, 354863227, 771268570, 773299673, 265233477, 585058359, 297611388, 634321240, 686005740, 729975340, 279360312, 423164214, 916067921, 953486521, 528084457, 339635618, 431610822, 417285190, 499442968, 548917380, 148992017, 959606666, 897030796, 241803720, 277471092, 542231829, 660294357, 625993253, 142253940, 34520285, 529808628, 737890343, 869224064, 978395264, 103822169, 518638055, 360543983, 484753383, 372498537, 489933782, 453206673, 216374172, 223156110, 489606380, 588880016, 523941703, 195793762, 420719650, 310747462, 279154296, 94574935, 938716943, 233819075, 636402592, 918836665, 527037646, 665768579, 296885656, 408857843, 610122743, 414015336, 173835323, 890873265, 758623090, 838931210, 601277698, 775155452, 439546304, 547207788, 778848617, 508723667, 72139968, 555424402, 223420730, 154123340, 694848863, 387384466, 124859719, 716939086, 584175351, 794131214, 643415421, 783205265, 317727370, 941811068, 832172995, 273829515, 680397402, 625310818, 749430270, 144694569, 841510106, 294972226, 749468545, 892759624, 857620866, 944194626, 270682252, 582357041, 466662533, 296390362, 621348062, 111196783, 209268507, 733910592, 372745011, 241838744, 621765061, 908821593, 191845245, 509821750, 465500492, 73798453, 930314327, 654968785, 96396666, 932016803, 840664771, 741779793, 109173902, 325987760, 938888980, 586736172, 794941583, 872225556, 45344370, 113071099, 853928065, 713391827, 410222275, 407436910, 36181079, 464584403, 178617669, 814402934, 72823715, 206127067, 462346934, 941639262, 410696659, 134634083, 46787438, 858554314, 254854208, 574007341, 983720125, 969643673, 479760902, 539649209, 784310431, 618993274, 260809953, 42003871, 297665627, 437264180, 67289823, 939622978, 331774930, 564930002, 370465230, 374641080, 529101186, 436207389, 65640731, 548067185, 144709892, 538315406, 974360801, 727510, 515031163, 479126702, 598452495, 860515664, 325477874, 909800474, 622082689, 711874922, 509772123, 339587375, 56341417, 876917353, 616086996, 587230305, 460381880, 683650533, 679815282, 787594491, 463083300, 876960005, 389807360, 854620339, 600270775, 800073707, 155280800, 11496778, 515651205, 897210977, 341807644, 706721184, 66886431, 591078979, 995866429, 321456435, 166511501, 63503968, 606025575, 774405383, 41404508, 619926879, 710898197, 311955963, 702491452, 669817101, 762440297, 511077776, 75585557, 556012706, 812251384, 891364685, 835128751, 442380284, 580128007, 442616566, 44723819, 545018167, 190550849, 553615071, 92039406, 306536084, 325362488, 487990800, 30939189, 564896652, 76411687, 898743794, 862333718, 54105902, 977758772, 389905390, 23201110, 501439726, 558823130, 626786739, 53827250, 284215641, 336442557, 395578121, 967004875, 643648013, 713768504, 870032396, 954908102, 840632476, 987297403, 236568216, 231744, 757006887, 388201208, 419591375, 743613247, 422911593, 189324631, 666821662, 39498719, 312477275, 600537706, 270143384, 306718135, 933104895, 203897541, 934731797, 60165356, 628162149, 107752219, 224527939, 954836628, 961611702, 125696089, 561662852, 430524459, 402767788, 559955704, 79361270, 281514094, 939245432, 687875907, 865043016, 601935519, 989162091, 575448968, 270468444, 859791180, 191764984, 588578250, 523101355, 468379286, 23010576, 638567724, 805597493, 119460478, 214971211, 885462700, 836918322, 200003776, 940437041, 32139580, 927085493, 703654143, 87319015, 469859522, 700506253, 442815436, 883082070, 931504639, 502090373, 723445373, 584338194, 116972439, 957272838, 212455278, 362855704, 30711373, 739654299, 898302699, 690855941, 186669074, 808929395, 365309470, 882306776, 704487087, 328032194, 618432330, 768333151, 538214038, 947272375, 12694583, 407195239, 820310582, 429199135, 276421686, 94221340, 569459574, 447318585, 174737096, 393582496, 152003652, 277337727, 745570346, 906590889, 120310515, 626902552, 871136840, 364279767, 595534559, 288618968, 360735961, 589042626, 536460213, 505121965, 737320254, 143597960, 696803546, 296400526, 270458343, 618067035, 718745291, 504799720, 785535358, 770360893, 877491002, 391878253, 868593854, 271622163, 554661552, 411864646, 888460885, 682595216, 61749300, 349902699, 845847043, 17838813, 151162395, 645643684, 470368423, 669391709, 111930119, 360339736, 794194449, 215550102, 491241909, 118034235, 129872233, 483539871, 132958016, 466049080, 50433048, 769236024, 733500980, 608217425, 141867560, 5105300, 626428418, 407756347, 107327764, 634868363, 585250311, 174882751, 557620652, 7461373, 814763437, 857377091, 404538803, 344999432, 378331031, 145161856, 155212408, 521053792, 937375209, 295467025, 653120733, 256504795, 645457503, 88370724, 751517649, 924913220, 192347836, 323094584, 944765669, 931684710, 171521900, 845125705, 769737395, 974603305, 167848514, 738519571, 486707683, 324266289, 368717525, 159954340, 353014301, 156416820, 805050144, 731668553, 131288020, 767458910, 43039653, 505454101, 625074966, 607493907, 215093877, 130884090, 942620422, 112813944, 779947912, 108580648, 856054503, 859849648, 758054353, 400250369, 838617802, 335104634, 325123007, 886058720, 325337141, 48469766, 734115747, 185690198, 927642276, 211945537, 744789013, 123511850, 194291010, 524623399, 955424364, 183174438, 563718143, 964424042, 679478693, 704773202, 266868408, 571875065, 489166575, 178587237, 902858458, 908872619, 118781833, 542815988, 70259654, 655086956, 974456695, 881693621, 923912022, 211649771, 138494552, 562473916, 569516439, 886096733, 12434009, 326761733, 630648872, 749083560, 227361939, 780049555, 618572816, 472383243, 441156285, 236054515, 451629437, 958109190, 760829098, 299542993, 183505962, 119560782, 341212194, 532309000, 763399320, 35245654, 530413915, 311903029, 436784995, 198952017, 10387298, 858533549, 57496621, 696138992, 662926137, 100272970, 999471656, 593630137, 909669927, 171114531, 153514481, 467156457, 252269838, 919203064, 26895807, 46020172, 564286916, 143856757, 699037265, 366304131, 731503683, 79277647, 637895950, 48772967, 193910007, 832823392, 710448880, 179645314, 785693092, 677495884, 796469001, 930428563, 120719900, 324490309, 824191526, 947390801, 187157027, 181132601, 107523450, 460700463, 620062521, 467588963, 106502629, 957544451, 190536799, 225592631, 334652832, 855776654, 974734326, 434381123, 34191568, 515577502, 734809665, 149820876, 521075350, 313402000, 785127076, 961742640, 60131764, 489620801, 570061094, 666555600, 127800202, 41618881, 231930539, 213091626, 949574497, 451082467, 558213399, 705266136, 392904640, 640431095, 968106952, 285178908, 797619923, 964267904, 6391307, 281616248, 683159450, 261804659, 358744315, 431711425, 242341480, 825035222, 434195125, 539825914, 464856928, 223921145, 389668060, 522167412, 868210445, 55562960, 549622032, 802055927, 562971316, 296498515, 569467837, 981869222, 915527880, 422340313, 445649517, 329761196, 703271925, 112369747, 800487461, 893638742, 559685131, 485111566, 785396639, 107302390, 269636398, 294311684, 415214736, 418509431, 618822678, 807685767, 161069511, 105423547, 147246725, 533383767, 18006121, 507587648, 311723669, 678244668, 732808964, 890195695, 124763279, 534032147, 814536970, 695092168, 603086287, 792050441, 242168547, 101041223, 215808252, 933059362, 739598834, 183003101, 93382867, 692776282, 547083261, 962547265, 264544831, 940475098, 952911623, 251354436, 455152401, 230579274, 399898236, 20673573, 131622274, 574139055, 691021689, 520035194, 182669828, 892059488, 856050992, 995641127, 90073438, 504236342, 599876967, 929627213, 970172514, 756009149, 458023530, 231462830, 362486793, 643642086, 892872390, 322010435, 940207656, 181183022, 232398059, 441730079, 311093245, 540816385, 236842698, 262695234, 202816487, 173886447, 77954628, 493539269, 324386733, 865643638, 165341368, 204613896, 48632101, 734293588, 305152830, 98345927, 739725958, 38512907, 342740012, 547325553, 739578667, 334689230, 242449983, 645699281, 477610838, 892460760, 12622478, 798484693, 70842650, 606280005, 300557714, 489369161, 48167246, 800050021, 980673385, 713591725, 131232781, 234216278, 372888761, 480892245, 707169854, 651963632, 488604112, 585957650, 314694514, 923865621, 764004219, 262607243, 113244993, 196839076, 666681652, 456506940, 722645981, 284704262, 377004001, 483037703, 901632534, 433553706, 459482776, 726884196, 604027149, 148128328, 641723679, 719689526, 515681847, 464086910, 929534830, 836232214, 255082538, 896282210, 110921990, 527022200, 79956319, 308323082, 708113824, 523631943, 161213338, 812538944, 2004130, 874025850, 617320965, 220641260, 91560018, 891740954, 634617386, 969671108, 327617184, 912664702, 112427063, 949478590, 212485077, 242610891, 206523760, 278815954, 731497927, 333587040, 480222865, 160087712, 485568776, 198480609, 820364275, 817054692, 721844470, 351778952, 331378973, 115962505, 319984315, 763703805, 707366539, 902861911, 808458256, 839998746, 148040614, 647994308, 870487369, 778674537, 235866106, 927916178, 991525588, 300860123, 554769508, 3946327, 536510562, 391342961, 893239029, 582177351, 498238963, 670029504, 783930356, 351250939, 402561899, 62222844, 372576675, 80405362, 470970626, 371634791, 38586049, 285284873, 531431229, 579296060, 503766179, 681831426, 706652233, 191543584, 170168854, 896653257, 143811379, 54724872, 486656795, 526063619, 130315673, 276225959, 950662576, 242989079, 34016430, 475381851, 794675003, 564264143, 124983755, 995028732, 507660945, 168318954, 794295982, 470764083, 409257264, 952197734, 920175518, 355417334, 931805380, 472301035, 754759591, 381798604, 428275015, 366648278, 696621519, 941870956, 599340533, 675771756, 579425593, 427801646, 173486090, 215992904, 132671191, 837897833, 958578788, 171918463, 466137534, 28906017, 667563799, 442300719, 656276980, 413764813, 361315739, 623650826, 313810817, 316344915, 235776470, 202792824, 848780251, 687222140, 106577926, 118111336, 526141518, 263873490, 160565999, 529404593, 79344750, 248582255, 191381487, 737559177, 990360718, 323384806, 31312085, 731190500, 220045462, 590725893, 606377434, 929021577, 293603240, 96386470, 797553732, 472534195, 888579833, 352016364, 665496446, 580122450, 778463168, 839230038, 316192203, 746756900, 513758422, 608940739, 31369544, 337100006, 819204986, 374454438, 484239883, 713138830, 417661220, 320225738, 970694401, 527732711, 981142053, 145184059, 924129132, 673290817, 229974105, 142519929, 78584488, 161308231, 117642374, 708071205, 215759411, 621717551, 785884120, 796336409, 826838920, 638266246, 116087561, 4169781, 179331602, 553710097, 579567931, 740375392, 663784885, 169936104, 460856537, 174749680, 422951279, 371195955, 828254470, 225219738, 630533575, 11804342, 698938126, 208153643, 773827678, 102478768, 83510498, 155697424, 197342795, 896461194, 57314160, 489706450, 10748465, 254087518, 969950370, 362859865, 353081032, 368090014, 88375167, 492040874, 449488787, 483917244, 352974641, 606748193, 392317931, 922397858, 191606454, 99689516, 670237770, 152332266, 412414974, 419495085, 778106341, 584169936, 287823251, 619852433, 529941104, 657699445, 609934473, 600690855, 123430528, 340844532, 527827917, 441406304, 287856299, 240960357, 721950087, 739090842, 783296217, 480810439, 606990859, 281148628, 92137022, 191168019, 832244247, 982095420, 336128055, 801244843, 53856619, 453605974, 630777905, 236292214, 907775697, 121839695, 456771460, 777457990, 915889918, 781246298, 940755273, 778281701, 131279453, 102059129, 902488809, 277790026, 61673710, 797180245, 460165076, 912767693, 754511019, 938491811, 50668116, 326279526, 565998067, 199173327, 861802473, 466665215, 391537954, 696202244, 638790844, 794823714, 896339131, 540897258, 314440708, 585167364, 349455613, 893775060, 657542168, 439719398, 457010602, 616566046, 977478514, 478786891, 114090894, 480216759, 761824178, 220660416, 825345606, 137051982, 815775408, 56337361, 68463727, 806222668, 271076236, 292520665, 599920561, 494347680, 278615727, 84815644, 856621867, 307016721, 589565725, 657651432, 838042983, 816129894, 603320344, 526146689, 538892491, 148944368, 475473523, 53525317, 179726303, 462584691, 482340779, 239834570, 780935153, 380525808, 780363599, 527922070, 535993318, 388386984, 998437048, 333069077, 413122050, 323616323, 601321545, 470004658, 894986668, 576295183, 381987171, 973776062, 236224965, 99813956, 798839877, 41507097, 39689026, 53195456, 812803351, 155463147, 675048221, 592415788, 942158764, 455679015, 717089792, 959609969, 642379550, 187934365, 738838548, 140576066, 503706200, 754492176, 987941556, 705570996, 182165197, 273905188, 232040742, 452445893, 614600705, 393975672, 100671307, 317362776, 982502545, 784265649, 314361069, 194589661, 673744733, 995751190, 529941409, 194946057, 704884, 189889037, 952127489, 422255008, 189544858, 23546180, 739342290, 233271184, 679693518, 958803890, 637628904, 296008300, 930069344, 598549578, 430716714, 767711128, 134835607, 387957482, 825972336, 347227557, 848796071, 658039369, 101144295, 92690788, 540588366, 624835650, 148688571, 64482917, 955611661, 669509007, 527759651, 767908310, 440603856, 907473363, 607380714, 999394881, 628442374, 909140634, 81470311, 744019713, 707584100, 823943741, 33815199, 655088200, 449334914, 597955050, 197123682, 674557918, 842042560, 510377019, 163674733, 955836637, 709633884, 988868579, 933149594, 832546652, 154316385, 223436670, 395724720, 647079450, 980948389, 580519597, 302514143, 279378209, 450185735, 699575721, 545249468, 145602618, 888158476, 196315741, 447686349, 120540556, 849269056, 246446718, 152972266, 164949307, 873510360, 596523799, 486503327, 640448986, 210893117, 545519952, 761079087, 287160690, 21739826, 227640697, 157680321, 84258652, 465345781, 668651474, 135005674, 472493104, 115562240, 235079677, 880789808, 8146062, 472347404, 432248542, 795832061, 760178505, 815278391, 847722770, 563034161, 979093044, 358167398, 876432990, 735897870, 185159172, 458404230, 50235669, 520442781, 963600110, 476345205, 996167583, 761560931, 828940706, 98626359, 976571700, 409871768, 102033306, 773942247, 879885596, 749623640, 282856407, 82915557, 663494316, 990306483, 304983838, 182155772, 782241411, 760753372, 705736491, 239627870, 729130024, 545428298, 551542911, 314907719, 253161126, 891786721, 891642662, 522236446, 905566309, 165891719, 284692283, 634263544, 806405526, 898847737, 582136195, 189541052, 894666664, 640171606, 907539851, 400376953, 445816071, 270010681, 618075156, 864395931, 198072076, 96218342, 553600197, 152967356, 283404008, 831628635, 757470483, 861970186, 177498567, 42698763, 838548000, 800278810, 259426404, 695407244, 950465990, 144351478, 195403310, 803883142, 198393703, 45904770, 464661661, 986967242, 884716722, 123835713, 80797390, 827483325, 953843256, 162167418, 730703811, 714379630, 349260223, 526303614, 119456798, 85408026, 174161642, 816281140, 319701983, 125051007, 666247612, 759113386, 129750990, 206862068, 507584194, 205519001, 201026228, 266342199, 141456939, 724630977, 907712872, 855685545, 156488941, 373545784, 692816877, 634369244, 151162581, 521681147, 447708307, 12838910, 156894378, 498830838, 661599303, 480069199, 391616445, 957356582, 27763746, 971513275, 875329753, 830265220, 527488860, 222700482, 773314765, 793446898, 39646646, 432396812, 269911789, 678151839, 439019224, 520044967, 907308794, 926383480, 273150049, 557578449, 482155328, 315648374, 36295867, 888371900, 290688778, 346830578, 987314605, 490267250, 690708676, 763030398, 265852880, 68284796, 355030617, 804848087, 606471486, 121047307, 529080865, 24640071, 748131352, 141254845, 33392972, 170619918, 396132915, 271820112, 464498778, 252552706, 46414347, 684476359, 677720194, 100967739, 944606047, 802414780, 634938136, 60788792, 670676462, 166283797, 572977694, 14023304, 961981366, 461920116, 584276831, 689126248, 193566842, 793408026, 968517350, 225807040, 106994218, 235062049, 349841120, 508594665, 437571684, 627752654, 575119836, 791500754, 346471081, 240383829, 871687967, 461935602, 687113659, 543147908, 689993733, 246028815, 470526430, 102220251, 103387046, 70166531, 175813031, 270649422, 453875077, 837229223, 120053091, 145791246, 590442896, 791038296, 619758733, 357311281, 153018197, 628621175, 563992997, 755972974, 44184923, 387440888, 565640913, 46264780, 652214216, 434981225, 484912620, 709862842, 921503067, 511991702, 345530321, 463297424, 708225548, 940748625, 612542494, 153634915, 74119717, 448595199, 346075412, 594390435, 715041114, 854853265, 735451248, 370379254, 349905361, 269551763, 932809143, 296736121, 673274014, 828513519, 243651401, 354099574, 718127366, 466188248, 911492138, 658233289, 563267581, 961444564, 791072710, 330764393, 123177715, 319535833, 353904500, 341049049, 87642441, 90376819, 6959665, 247464446, 246605119, 813909004, 976846327, 12076305, 411820635, 847798032, 914497023, 834958291, 127448767, 375981412, 712078914, 297832611, 31257819, 698185884, 664632841, 121294040, 819695412, 163095186, 912064693, 879663977, 805636121, 138459980, 95623391, 60879769, 530370378, 511796472, 386518699, 398255033, 176500917, 395878980, 919842344, 836746386, 435664209, 565474862, 321238015, 926789895, 134228709, 663373415, 136961309, 765254464, 423080703, 772436785, 79622426, 314991753, 114548381, 402723730, 827755397, 712316832, 486350125, 546967559, 37510002, 651388191, 779177760, 756600787, 632759641, 429040453, 694388384, 538166700, 47329023, 29186679, 259449618, 61037989, 474797333, 64237148, 774101999, 830421037, 459928605, 440131640, 599677840, 933455402, 621497357, 880369329, 621752238, 473665598, 13120898, 126259027, 973468908, 63399034, 983793719, 52721269, 478817368, 495241786, 900613473, 681620588, 366265898, 531238429, 215085520, 854368141, 103880819, 851837326, 999887869, 967822189, 903767460, 174263883, 354549655, 919636861, 613822588, 820510739, 119058066, 296484231, 763256823, 897105896, 869002834, 925704554, 950816214, 251755486, 898176776, 293823576, 266841028, 16284453, 164728110, 235101139, 304485501, 347416547, 314750209, 73905643, 596814293, 663279604, 784330506, 910714850, 462744442, 760267881, 746840162, 906256976, 18939177, 233330441, 684747955, 143490505, 238597341, 800609258, 453226768, 341035661, 318743687, 308178225, 985370129, 888126285, 946962029, 494971680, 90338058, 978078497, 501682252, 770883221, 20855036, 131866886, 478321952, 288436720, 202090525, 578989911, 864142812, 942193785, 362982835, 454148790, 423668978, 63008332, 17701795, 559706148, 497527861, 248828427, 811661556, 687840520, 931089047, 434930246, 907990158, 905082647, 863391155, 192332010, 411054432, 45983697, 490260456, 32885878, 151314441, 917716540, 698282956, 793830518, 517798132, 460965753, 983932494, 498580454, 107947007, 805244756, 345752529, 640820768, 312390132, 637421190, 624997688, 348232709, 881717737, 655689389, 558888719, 108803181, 680005205, 958290122, 35430848, 154810298, 50913935, 673482416, 957576257, 251933100, 554071252, 911808168, 681613676, 475619855, 533346574, 375898915, 151280353, 910837467, 746962748, 479033356, 532555992, 378787269, 355358013, 354307829, 202677675, 120828704, 261594973, 100242646, 812072470, 173799874, 318018820, 262684682, 7428994, 829953410, 572639818, 42225077, 577591400, 600580719, 309140965, 29434495, 231278545, 800386894, 85076349, 260392746, 913638809, 281503511, 760737518, 82947074, 588302519, 704532324, 144218141, 821136332, 338948321, 574593811, 110662980, 79854448, 777571787, 601337931, 197704500, 793591853, 493528971, 118932189, 141860955, 270560588, 412476349, 751504071, 339378273, 225948334, 768012252, 537480309, 300628102, 583079528, 59602813, 964125903, 807325538, 929884429, 861655381, 581223080, 772786246, 219522270, 228306303, 804190865, 238340063, 680497881, 723520343, 329189555, 6653286, 699120163, 652259422, 778508989, 775077355, 61752366, 868518581, 575653386, 81537614, 25889354, 900896635, 568877587, 368904469, 212565930, 652805593, 306346165, 630340458, 593057355, 84922034, 539512943, 423124153, 860649672, 459071914, 683557407, 771530987, 903571065, 888962969, 139957119, 207912183, 584286337, 539249285, 8173261, 379488542, 636910679, 181677485, 351657914, 357329650, 155410767, 826844655, 17173378, 210175600, 410770621, 149683338, 732907425, 16218157, 723762631, 656801977, 714511165, 464387327, 756384914, 131905427, 676180491, 427867805, 510005358, 127986890, 185887467, 849920719, 787146518, 335575305, 770141981, 627751649, 910553596, 444022692, 787765469, 539914686, 978508140, 91233073, 585170568, 238542240, 287974514, 83074451, 50493939, 519110828, 860226156, 570069568, 662670184, 894322066, 619956238, 700685073, 545988366, 45217107, 345716173, 631687053, 509132162, 29269605, 93487723, 963816156, 32806917, 851624319, 570546417, 433495250, 819254875, 191732537, 736601340, 673561787, 750693626, 800307722, 477008176, 408173311, 551508623, 198340441, 397375350, 826046586, 339887718, 975083094, 522316569, 910501744, 585330649, 739567569, 301335311, 352486747, 874821001, 281131517, 225424850, 121843400, 598337252, 553235775, 372698384, 986141011, 40805192, 458397387, 137237050, 373651686, 706242111, 86582164, 76756560, 601666216, 152028110, 513253443, 325606670, 584130389, 392577505, 762969914, 707817963, 729289135, 605958717, 907141348, 89073496, 877502235, 244562788, 661806500, 919262204, 222322806, 202486983, 952140542, 796433890, 40687208, 846947266, 938615989, 995731442, 627877252, 548184374, 95962238, 511537875, 955859187, 854209718, 847027676, 149273552, 574809260, 544970464, 672308361, 69065477, 587948551, 919860021, 62787482, 125444187, 389852005, 223270410, 534028655, 379979485, 798343595, 679580165, 924194248, 951458345, 409657533, 640163287, 865241840, 784141136, 249242918, 532447920, 759287206, 128421670, 266543638, 936561330, 989656774, 306191184, 726730795, 682906193, 679306444, 730361002, 900371815, 782102872, 496939694, 201513191, 849261219, 906553409, 436252207, 305918212, 273475979, 450441159, 274123279, 642272998, 613061870, 388294494, 557020664, 538959298, 258498709, 998915226, 482559747, 223166142, 357147590, 350281719, 824741420, 870144580, 58445178, 134224052, 239949565, 866920276, 133831249, 323161849, 651216508, 997892692, 383579031, 642704141, 233610921, 675451402, 959222999, 312620607, 930854233, 546625937, 916254764, 404187097, 327406458, 446100069, 237148167, 473399512, 995679617, 640452434, 67018288, 62256223, 860223775, 263739533, 782052929, 902550621, 150118598, 241516013, 291161516, 337965486, 970559962, 190371502, 108642252, 74036454, 819507410, 743376428, 587381523, 910936462, 552931839, 97294953, 671417604, 329452263, 785832437, 742626328, 45752223, 261882806, 168169162, 788546888, 345417119, 267811869, 239312771, 763106672, 955243066, 365002105, 196883898, 431570124, 404478507, 843837277, 170208895, 413817479, 142447401, 920266130, 812219023, 240881509, 415302599, 150763079, 828223845, 627844347, 172915146, 567842313, 234008162, 829990751, 164430664, 120727732, 578025890, 687107019, 575336320, 560800201, 756074815, 813531301, 77505046, 306507372, 231987472, 379418951, 753861563, 642728078, 825884524, 69316310, 722645703, 170241124, 907963395, 851501861, 240586641, 337871262, 656508251, 342048793, 194910056, 615964271, 653112993, 365578991, 828039234, 233814035, 252268590, 624837556, 919634892, 477243120, 739369088, 885265560, 918171736, 661928266, 431708907, 374659550, 269930259, 608481340, 533205060, 879073447, 680216359, 394681585, 600231309, 270819585, 933125135, 43959404, 536003233, 816176769, 131825006, 789875416, 676694858, 894500991, 263157056, 181592029, 779717652, 205807335, 980800990, 384254989, 739098451, 673980228, 836195305, 392279244, 314213022, 91073455, 601863275, 787231762, 917527684, 78790182, 528138353, 832312422, 539772271, 445701168, 862269592, 996320424, 387653890, 55452807, 654053346, 600552852, 956430488, 342816999, 618165820, 527490861, 590932644, 395786506, 916307639, 631626035, 720640964, 889531613, 158860037, 882312746, 585417348, 159470960, 138263908, 386393489, 757651052, 975063392, 137995478, 901092752, 526617167, 571053378, 514989027, 515612473, 197566170, 799953352, 790999068, 802564829, 632957152, 386153231, 319163931, 240644117, 800214886, 758573626, 134939547, 742557492, 480468374, 747558641, 655138339, 437175368, 490620512, 2089424, 97149575, 476301806, 139458989, 170740180, 540349721, 103697038, 91830930, 448161974, 478364170, 361067241, 987577038, 886950366, 592545561, 45441196, 651948100, 304414825, 416827668, 948533756, 286315435, 635850958, 708209216, 788019552, 784950425, 758671900, 432880672, 512001283, 739514251, 807196488, 169627830, 267217665, 602247156, 334436557, 190440035, 403932714, 177102447, 864306911, 375910649, 269987983, 360224543, 254765644, 825209246, 607111966, 965374229, 540228659, 694255246, 745975760, 152319023, 606318515, 420945339, 789437640, 589895157, 577695081, 763557713, 764937042, 991503733, 426768106, 189645409, 786257824, 675157104, 915111798, 407342430, 656301763, 625490230, 970155290, 527411321, 319300633, 29153898, 625429262, 975253120, 879909276, 749990023, 527514999, 844671754, 418653148, 86451663, 180009160, 598830963, 131040243, 318576522, 48252208, 815070212, 899263350, 646569999, 511579547, 383903012, 620565946, 773726597, 833826401, 763215307, 553671899, 709685795, 690275167, 361753262, 707122194, 994507489, 37921652, 604399137, 66920141, 694265383, 931216336, 366095729, 340667070, 702537398, 957296593, 262271803, 836975186, 282870646, 813791555, 975217410, 974127072, 884845551, 271517711, 905402846, 441841183, 789807952, 574342343, 897922426, 34692536, 743248089, 169315777, 845738211, 212634113, 455296355, 105952982, 742140974, 971743070, 315934276, 627934469, 650398369, 186484195, 79208189, 674650312, 992144369, 194232873, 560667853, 427864000, 400865270, 57309263, 980195771, 287881131, 390367782, 928416943, 570047861, 398138728, 246122079, 844998200, 796827290, 240634467, 81788463, 324723834, 816374172, 545201489, 952740663, 101334178, 76755877, 794150490, 696618241, 769925395, 605813899, 30171152, 296545934, 584693426, 857391001, 829313952, 466883519, 876674853, 587019876, 709777531, 194731261, 238626144, 543523096, 865137225, 899245106, 337958866, 99571612, 517789322, 622235828, 528503715, 966450350, 566497511, 810970978, 255894531, 79126662, 964146257, 296061840, 506119039, 96170735, 856122119, 708936999, 367069160, 683204497, 926157156, 20131981, 970393540, 921972325, 658788214, 496563175, 73541435, 222890867, 357124135, 309766738, 637743203, 777205304, 251002949, 33155331, 884047006, 384703282, 265670518, 156901886, 478751424, 190005065, 650380317, 535400017, 124070770, 734929082, 570758179, 345679601, 47580678, 339985068, 18720894, 503394315, 909814414, 325210571, 253978995, 891415655, 383560048, 404762733, 161043801, 700286905, 88008107, 331599866, 203997931, 862073009, 552796659, 901182410, 706297897, 985722155, 978541128, 758852211, 776783938, 288734649, 725776856, 830043112, 517905834, 620259975, 596742389, 708722101, 976139845, 874182497, 907673455, 94374337, 569551034, 632796661, 728761319, 686646236, 378072633, 43550176, 427447416, 337953808, 150013489, 312116294, 608292626, 418488397, 797917921, 678098473, 828200504, 753549469, 140982102, 895228471, 279590668, 665312996, 511301729, 743152592, 768607746, 573831316, 99858566, 74534560, 73572775, 894098245, 151922242, 347563121, 742550742, 952509821, 816262670, 156535081, 560620706, 346665405, 837713685, 734553190, 351995312, 285459201, 978532401, 447258358, 86774433, 882403750, 937170514, 632858762, 476788898, 562051586, 977590833, 411022358, 668274530, 255580124, 576869062, 210883440, 575788084, 550124199, 587237858, 676061261, 175270536, 572921053, 753981907, 812647379, 950789104, 108670996, 470643041, 190743615, 541477191, 696505651, 881004743, 859356667, 388073612, 214288235, 176290183, 181885688, 100514940, 100236501, 830853456, 38478962, 936930843, 306661860, 335241553, 641793431, 468410272, 294248609, 337351441, 357773056, 38570984, 800109767, 875331156, 689023363, 93899297, 305970174, 107821816, 566136842, 323177464, 774903020, 530497031, 370788372, 136240963, 238162944, 281140914, 517183443, 553739492, 638374277, 173070397, 812892990, 366970302, 636182353, 958616724, 41529875, 221108014, 977060465, 968480733, 167249480, 777290103, 543208601, 763435051, 760021916, 948068431, 553991124, 976918170, 696254642, 293349144, 12953534, 326308362, 725508487, 341210756, 865690090, 73834437, 693265341, 648001949, 636703906, 972233092, 96025226, 250425846, 554192082, 354672093, 203085817, 254262255, 495078342, 936411471, 276669187, 855702506, 8698796, 976456527, 68527707, 120394602, 113013443, 890769616, 473083845, 359652518, 570413837, 221363315, 401808370, 527232211, 295390953, 692567264, 82189695, 852675601, 960105228, 806740793, 955904311, 769313710, 182081036, 727535324, 543748193, 961762721, 981676910, 223743100, 539629842, 199245614, 140928433, 760815673, 836847407, 256774728, 784952191, 222509738, 889914148, 138188435, 201338523, 778260444, 63964824, 73969256, 876970686, 457863242, 292460267, 662311677, 706533443, 814210182, 900735666, 552772438, 381657338, 503159913, 830645317, 377561985, 334447837, 162755539, 21808628, 97282831, 518089678, 115083865, 725040812, 129487184, 904330809, 248722195, 354623417, 591280158, 82128631, 649786932, 824504221, 633630652, 244884558, 24522758, 620379700, 67252027, 674596843, 279641969, 400783431, 713519289, 722403027, 286467359, 481135682, 742833159, 50945617, 243378478, 110409138, 51023440, 859834989, 900426712, 737535629, 579267276, 253058362, 565209141, 667727190, 722178295, 846181306, 218897956, 300101538, 324163161, 637700849, 438103725, 689078189, 842667089, 258668651, 81749485, 563015955, 191988613, 971378163, 487529313, 873763468, 208387373, 498371392, 728166169, 751188975, 140274636, 36714967, 488385078, 445964839, 949486319, 25534581, 719501365, 683308818, 406302617, 552159888, 986230260, 618803322, 154556536, 513546832, 304900541, 996823491, 327609837, 787256052, 836072943, 605328191, 689666327, 938336691, 740974797, 879342879, 406803454, 617498259, 889532755, 680980572, 735380926, 566211588, 907045701, 939534124, 430198562, 721705232, 772928575, 349720405, 223825796, 543759821, 30417158, 928647615, 395603266, 937323647, 415798261, 284904210, 200352533, 22096078, 809846920, 62115998, 281017503, 642381682, 284836468, 985045421, 813536452, 852244810, 485363216, 287365105, 19569683, 456056487, 734760868, 299783374, 542219320, 201280700, 719101667, 546583669, 319031360, 157942842, 930249576, 765985842, 271866817, 564073752, 179793569, 934886532, 40709316, 449090360, 61207331, 643433959, 155226115, 460957405, 837521790, 26945072, 470797984, 208996428, 372424537, 370256278, 831671662, 547922908, 272751400, 880033620, 573528003, 621025180, 510311076, 949654800, 919974512, 588005307, 27323744, 887962293, 613322064, 376569377, 806507202, 475434507, 327387704, 443297930, 622823088, 347226170, 867515179, 818419879, 153916161, 550855152, 375002380, 386343328, 585989858, 105340035, 913791526, 950522634, 425938159, 615724245, 537236515, 391457661, 457446570, 770814916, 266965382, 504372832, 779584603, 568139548, 189569251, 180878497, 219450796, 526079097, 413954073, 565647797, 576358131, 517140216, 480765212, 733460945, 572149661, 440630951, 18124023, 557677759, 599148422, 874698316, 947884294, 66908437, 430743112, 557528983, 923203991, 246089498, 692248281, 207471347, 763632291, 239327212, 397272123, 106777525, 112676449, 114444897, 337140442, 729235482, 762226828, 513692930, 170851671, 188073795, 438652131, 677349478, 855059283, 806805780, 293544941, 626356969, 881370527, 372060024, 494335631, 826766514, 921533312, 90442026, 791339087, 185187662, 916855889, 832451608, 760077203, 784502394, 111352992, 129948403, 28486218, 9060134, 970901499, 173753588, 552480208, 66484076, 847556997, 971085970, 234075862, 556745268, 844661601, 272153481, 500046370, 791501309, 319444793, 420355904, 557711360, 160338649, 36204665, 829885547, 888767182, 38727433, 462254538, 830282102, 940802197, 27016784, 819693453, 41754096, 145047551, 731988412, 924245595, 84752343, 328322053, 363301752, 298082007, 737196437, 568089176, 380124391, 746452043, 545949171, 171030375, 476068285, 736039223, 290837685, 135748921, 42710573, 830873849, 877776830, 247358777, 874797276, 147993236, 684730919, 740250731, 874554696, 242523205, 46130289, 745820588, 133363209, 950515552, 385719591, 659465808, 827075591, 1830294, 408421573, 544797515, 966342458, 206474112, 773361996, 342254764, 554625706, 312624846, 694020851, 911676684, 168354538, 859745780, 563106574, 571520522, 428317671, 472646639, 293197157, 489291530, 221960752, 368137940, 470868755, 900393808, 917613261, 65701893, 288771303, 270579414, 714896512, 287280412, 857684858, 480083447, 620900856, 781755052, 198736129, 950784807, 661006662, 303299179, 3217611, 654749538, 346897463, 222804155, 291126340, 485852225, 177460416, 224227268, 294679977, 705283169, 188851040, 862552185, 749016563, 931857894, 309911784, 460810443, 988258908, 463126756, 774509522, 1116619, 989135944, 21969956, 223553870, 184790457, 803661518, 637619215, 131905451, 264444662, 708124425, 132556457, 689705828, 534204705, 72932537, 882857369, 227488353, 23649483, 594567312, 450315619, 9692548, 935661999, 196122157, 986969810, 125045477, 629597990, 547689823, 276564803, 478599705, 691988503, 974792450, 253642997, 551531806, 899151814, 923910694, 606223051, 226808266, 566966152, 311550877, 760309358, 543939188, 538243091, 748024735, 658419532, 185303480, 345053157, 209197099, 77338409, 152944928, 72414022, 779353872, 203667680, 938197013, 781275279, 520798522, 144332689, 770655184, 444301683, 363798821, 476621567, 603868419, 707884798, 723481194, 561093949, 955594232, 863274813, 372626602, 860945446, 933744660, 802183265, 324110707, 255327491, 264096091, 820829677, 503014967, 624107371, 668064869, 947034363, 849974003, 411105670, 618100486, 141234965, 964826779, 336022401, 533414653, 233125977, 452480115, 607530442, 801340351, 494879628, 18169597, 982923890, 101196635, 762734919, 902034430, 647272087, 314344523, 57868109, 391534413, 157684956, 637654864, 631416657, 651366348, 432390123, 802435498, 567299719, 583443943, 78227106, 180416544, 429161782, 116663696, 471436249, 293255462, 517774056, 626558044, 130905778, 564709964, 554947879, 828663256, 992776885, 652542549, 686690528, 439534896, 387577347, 416324109, 358909277, 913917936, 225355337, 814909334, 533891842, 171254195, 741301399, 491209394, 2817078, 925979979, 543085984, 745764561, 138126396, 889245917, 46294909, 387150925, 176566854, 869542326, 72323805, 497303006, 345004789, 987241839, 271977419, 52363264, 489593729, 319638572, 469385131, 888410945, 673342651, 766226549, 707607686, 153031870, 337587085, 191863183, 549541454, 678115178, 9276961, 617955069, 556871768, 300072881, 337648063, 425653264, 42247263, 52162479, 220814991, 183027603, 980532094, 757163431, 573036174, 752910895, 652539960, 454116946, 817456835, 387878420, 71576510, 969927939, 62459835, 3164730, 789793431, 124394329, 590690482, 944646828, 891868724, 53921465, 814815529, 647688451, 442037512, 485777535, 616787574, 636056156, 236223476, 95846519, 147879880, 571077053, 809131556, 40202469, 928736271, 942613853, 208321529, 81850522, 883654211, 503694017, 524694347, 755140922, 460738520, 565418022, 72971137, 117658483, 996058755, 134688994, 211708148, 947670460, 460754603, 595571217, 669579229, 292267487, 445744723, 56255689, 580165540, 908931536, 364496669, 456189304, 995374863, 490015377, 351691468, 840688675, 501548567, 994159177, 271939597, 77770735, 563851330, 654802978, 284029832, 366128404, 235738322, 416583106, 694962629, 390182767, 831157395, 691028080, 519441329, 434613837, 547227953, 563457842, 564587759, 651339455, 439664298, 737591861, 593251604, 277332622, 618126382, 131346890, 66727706, 616939101, 706227062, 921730687, 719843229, 449603027, 64375775, 499813445, 553058979, 258434181, 597638074, 322721696, 887578089, 20265243, 355238964, 94653707, 181285506, 293298662, 925827656, 544069395, 344255584, 164532391, 464995753, 581986522, 477023583, 896995216, 338124305, 17250108, 124802337, 542157078, 229085157, 534748565, 691061373, 439882026, 868345134, 883335618, 429026505, 595199028, 783039902, 282963473, 93433760, 451882375, 892009641, 796620549, 933640472, 471872068, 833019088, 778112979, 856966773, 869865559, 149321267, 80864476, 822023070, 458483166, 644205030, 379126441, 505494479, 761659568, 799000748, 676302635, 38886555, 846492327, 495698567, 56946937, 950749482, 828797235, 452131391, 776398765, 572774696, 665789156, 973897970, 967718747, 551369917, 164131645, 456531570, 43741492, 598516466, 94006140, 888874588, 941330751, 265458389, 266380933, 838050643, 851214751, 379630608, 791257378, 75201099, 922062061, 830988871, 315033551, 418487435, 581663623, 479199914, 858855810, 457455134, 985866457, 916243759, 909858348, 307405913, 401526174, 527183066, 749761455, 479825355, 959015372, 61607262, 54373802, 14268071, 133322349, 492130682, 129725562, 343958426, 969979115, 900834380, 101751186, 806288881, 738640112, 235563769, 429636700, 860792401, 247861177, 367061959, 557768915, 550632277, 353652850, 480370628, 845995577, 677736311, 302941390, 718929130, 846792053, 452690964, 225170644, 57866512, 3531561, 14080349, 845313062, 321897895, 345250438, 534253573, 429646763, 986697370, 412144285, 235202491, 989602464, 370075657, 888550226, 638574071, 540642530, 124665524, 819168026, 358326040, 315737284, 814318929, 250231034, 772263979, 801314524, 965418959, 682272895, 906404433, 137904446, 487127889, 950840676, 920567066, 622190214, 909379533, 620474047, 209118214, 143639246, 288938416, 249775437, 190356893, 786486, 264924367, 889310420, 295283373, 369045710, 19414141, 695675958, 100061894, 721066429, 964051073, 894082423, 583461042, 724239388, 1914989, 616116309, 972495780, 239174622, 813764761, 541563351, 672680389, 645819539, 597891586, 347019434, 925969540, 530087960, 219847445, 965967641, 440833031, 338102621, 357474084, 486038538, 216899491, 75403799, 506997041, 337084913, 840581194, 197282354, 298972750, 171844336, 224154854, 516736225, 140936617, 620741307, 259095019, 101485768, 896822551, 176053768, 375019331, 57801727, 600448202, 992198426, 164514693, 105645705, 892960928, 840526527, 34651465, 44290590, 807999092, 410700413, 38544811, 346538866, 36429619, 315474469, 827309555, 571654010, 464020230, 334248863, 670382581, 299865040, 313581665, 535245653, 317907433, 894450211, 516580077, 280637582, 947794962, 180462898, 49654171, 352239699, 32611939, 15072046, 152456678, 758679147, 927555043, 575836385, 480412328, 325971548, 684815437, 423989486, 170831455, 49020151, 744729779, 469282442, 606811887, 115529077, 144820770, 101946863, 461758653, 442276930, 244043890, 702152552, 323028868, 986509448, 766978249, 181357683, 596040681, 201017491, 248250114, 178481308, 23736079, 919809498, 211866151, 742133822, 610804058, 68889644, 681746352, 889700631, 605550097, 656988139, 501416219, 668229499, 382293401, 131743576, 151838079, 647403299, 123583098, 105124363, 930774341, 81075807, 968516595, 997670275, 609083954, 100673630, 563834104, 845824466, 888111259, 716080342, 537853366, 964247597, 932715426, 865550441, 858470999, 895129650, 761294071, 2218130, 816275751, 275826059, 400367775, 557901584, 45064725, 444758449, 631364248, 310711530, 537126118, 13437816, 918916567, 626272778, 627515991, 275117044, 573058821, 782554833, 71556420, 403328053, 135297303, 251045457, 812150096, 66583929, 907011928, 264548155, 574003702, 67445150, 602817773, 852390025, 554742582, 168898044, 768331578, 630469404, 153668088, 892528011, 714360694, 710063234, 919446302, 258000773, 104382433, 697177333, 906062364, 975736569, 412912789, 853891279, 747833163, 5143295, 650181948, 359203980, 449121918, 442051657, 635268802, 34878491, 89935886, 303885461, 497465213, 135387779, 885135278, 559101398, 975400717, 731871875, 283883333, 559281154, 565897915, 376904338, 231136027, 552671440, 487863410, 501793107, 284989109, 561653945, 714049301, 454744164, 796559855, 534685285, 880832475, 199500337, 121329898, 954908945, 552667885, 713954553, 36747533, 275919588, 134096496, 300359194, 590654497, 550043470, 743815260, 811549766, 67933739, 452607989, 312383400, 630053357, 547970420, 221078276, 713237386, 335385194, 968141171, 417243969, 635737279, 225331487, 211573129, 7971443, 549498588, 945150035, 715340534, 812205416, 230149848, 761774872, 854233692, 576534501, 239154962, 74563328, 618889908, 657256981, 715501929, 507034538, 692165973, 223694941, 355042121, 945565645, 418535396, 952784852, 7172475, 521636303, 885612754, 802077547, 444136532, 537342586, 910742679, 21255342, 40484980, 947802698, 884615506, 520985672, 298579797, 558456415, 512035428, 608744536, 159165632, 850054179, 370550605, 660167191, 334433165, 691409343, 118173872, 708076386, 790880876, 431236342, 1058589, 23677393, 968550944, 550735528, 909864055, 714028751, 798999548, 497127503, 573210964, 570294281, 11253009, 659398257, 779407276, 5814338, 881045218, 674751266, 681384932, 540597117, 798558825, 821150652, 918550774, 488576640, 749064386, 620009621, 930537538, 3432825, 997975646, 931984291, 291717672, 976461322, 170091134, 161127223, 284637513, 200126779, 339715574, 223924716, 342979455, 412524082, 187991289, 169099270, 145236356, 263232779, 470868401, 925223964, 574812678, 353814020, 554982439, 528619145, 12237666, 632201860, 618840869, 174394587, 42743833, 775202616, 621242125, 385027645, 822223780, 867482608, 558508523, 155145383, 524123623, 891305305, 74027353, 494282292, 613193668, 763694902, 362415004, 138475513, 646858676, 457325332, 830299611, 850112580, 205439184, 551737495, 150238787, 393534132, 297824984, 746740777, 747992185, 712167071, 564275071, 416266807, 31369864, 403799699, 647517645, 579354501, 234200010, 834873585, 599774073, 6644281, 521301808, 590795294, 192431358, 374015049, 50532552, 524602368, 141827976, 327147273, 853092728, 925591328, 599338973, 493340644, 933551629, 598435407, 775814024, 94722160, 373443172, 481976862, 611847853, 823007163, 978119294, 40913497, 828786072, 929213506, 583554122, 17285831, 661535462, 104153862, 89424512, 408738005, 239695398, 700729297, 261188955, 175600603, 467882694, 6411338, 352457824, 919562098, 344097672, 457983435, 61305730, 868540465, 773615173, 608626123, 983826725, 148279986, 576131358, 131808538, 548698376, 205204512, 652038962, 105660110, 565642192, 206847676, 289098238, 787638929, 30219158, 520325951, 449172989, 592226886, 551948089, 126012694, 953889739, 57666906, 186512276, 363190597, 810051695, 158005764, 945864737, 563487910, 425396690, 553516501, 184907512, 215639470, 72029099, 291686509, 735315736, 883861095, 548065526, 30857853, 347928338, 644141088, 715083117, 692662340, 856273690, 963158926, 412412483, 790711574, 592143367, 134003252, 678203185, 665373270, 671557492, 474994642, 165879376, 509044179, 170185327, 389334753, 401175167, 725284518, 17539383, 957306510, 215631382, 185738037, 144717661, 680880770, 642050468, 556304436, 271523316, 679590625, 759834102, 79201066, 145489434, 461076601, 606758227, 443319694, 274925926, 76444803, 399512972, 859171802, 738666723, 696851160, 442353581, 679456934, 590581230, 60003401, 93082457, 129117856, 711083289, 502254984, 153532631, 958531173, 875956867, 817903901, 596061905, 929603500, 297335715, 850114610, 478046283, 294777687, 867801105, 60596404, 752041464, 794098974, 2153599, 438527862, 621970056, 373945814, 153954414, 536463, 138217055, 932786401, 583533015, 377006297, 4429635, 142675025, 138714497, 492036613, 585110618, 488597886, 188051352, 309654676, 55170659, 396364862, 634857823, 940229726, 117275997, 108168053, 149293797, 294008169, 988730350, 643339315, 984519622, 652341504, 698416952, 760436864, 88621376, 880059746, 11231372, 130077383, 848156587, 659300004, 114266373, 714349243, 354801735, 782516473, 704400566, 768377755, 655118981, 19289406, 588996582, 263487217, 756558799, 874657830, 119692873, 707689905, 240406969, 153021588, 521073788, 237728479, 979866636, 406961333, 354481866, 92325435, 647846749, 560020582, 904081131, 860117576, 304574098, 57722837, 930995306, 823810279, 255755073, 4741381, 357533296, 771380020, 478336253, 134910143, 79586311, 233941908, 534337232, 737039801, 78875324, 729476811, 194974529, 652256233, 165380491, 504378365, 445550547, 433484124, 622696365, 419067557, 701200527, 754345539, 617840022, 311873884, 373174615, 397421880, 183833212, 251880012, 153095739, 195971156, 880026111, 470574106, 601681365, 437606321, 984316705, 129382642, 738398259, 240941047, 763206276, 619065271, 425521435, 474073313, 59096661, 705659289, 577954554, 794350114, 263632117, 63523335, 814370557, 931145767, 193117963, 925510257, 400644955, 178530097, 873965612, 300169223, 215972488, 814083539, 309545607, 20949768, 608637436, 992558725, 719879763, 331279766, 192385107, 863928857, 829430747, 393888801, 230269863, 141931084, 229359081, 105220786, 609727100, 184370597, 719550787, 730938678, 116965215, 838024334, 21917922, 214073682, 530684778, 477814302, 621275932, 184713202, 713136354, 222310427, 124800725, 761122283, 813300432, 639972860, 156133617, 418904729, 482777589, 550221985, 252677095, 987856436, 775636796, 271849851, 512193683, 383978994, 503920462, 337542488, 399692665, 732141905, 543027280, 275330547, 863791471, 643505239, 109221830, 878992961, 742214879, 534905971, 630022129, 791006570, 284414333, 866374298, 348448619, 537274515, 80858101, 852013613, 988037892, 340010650, 96506143, 325751997, 804746283, 242552636, 245109164, 485920058, 294802167, 762833510, 119040328, 57878295, 129675056, 457987329, 768860747, 65375523, 164655884, 220357855, 341036131, 260134231, 80768168, 985299246, 891741160, 627706151, 627153111, 532708517, 745204953, 155416194, 28038136, 593191357, 510923006, 371899283, 780246686, 964641745, 153396922, 318699016, 624053741, 365891547, 242884522, 325235688, 585567408, 884145760, 464165583, 3769515, 528650688, 121914660, 631987725, 659723352, 230354845, 555568406, 596862738, 582391954, 795699738, 457961049, 967090755, 916797174, 32887197, 605890482, 513193337, 345174284, 933353984, 339064431, 409680678, 529184368, 819176615, 727895664, 498577511, 784548495, 961773142, 817769660, 509766243, 585472215, 451366097, 996986149, 196331320, 510384245, 158342276, 80286227, 470903856, 57927981, 836698522, 28972989, 655717400, 385393002, 696293792, 521808265, 508943948, 680212301, 622700927, 673641118, 913351309, 440569827, 933651901, 201988721, 196765587, 999537256, 92564056, 875398172, 531661025, 774133051, 800719982, 781891162, 115628471, 825882579, 467978218, 274900312, 971218476, 510940731, 811615813, 943921879, 158823678, 368231634, 340418095, 591541320, 137627360, 233342275, 236177914, 92222615, 384942945, 223063281, 484709062, 852412385, 622995829, 274406138, 157520525, 706411035, 162945310, 414639256, 441349191, 541996132, 864057121, 18638826, 20831795, 271836211, 499288595, 79418496, 802043548, 255023703, 659643135, 945800623, 208511496, 446843162, 987715499, 123419197, 845210167, 295361923, 459290105, 277421270, 125496247, 716830889, 238537374, 831365328, 458624030, 951703030, 561131649, 295934179, 965856427, 95859430, 628653827, 758405863, 930564025, 340281456, 567045479, 402222801, 432628881, 748159270, 48685496, 302328388, 953806793, 851029103, 210383835, 420539195, 787609132, 468246410, 250243782, 515450111, 625984253, 591848161, 44049603, 972457214, 799269904, 193966873, 152611777, 101518156, 902445233, 530617086, 91909130, 66347922, 856700834, 286567140, 884302938, 103700622, 745721152, 828098081, 156595187, 410482571, 708160251, 252561283, 492801002, 492693649, 362425575, 815973444, 333566659, 821913257, 358586484, 55514223, 666754055, 391573311, 969166524, 28931183, 763556840, 138477386, 370076881, 521613054, 774540339, 465810832, 939904137, 237116706, 315780128, 784067872, 827631549, 703741966, 37814950, 689713316, 237967922, 79036421, 554545263, 233755887, 997746119, 835346628, 919774411, 726558419, 216997150, 31936052, 777156636, 758433918, 141572566, 133612958, 48820965, 694844257, 19766600, 509351813, 565595086, 919834378, 11568847, 764118058, 496764644, 685233141, 733543924, 516126262, 990176809, 291061658, 450112965, 947861679, 158495082, 763062697, 963677785, 276666714, 869624250, 195991629, 783616832, 476280812, 843301812, 321427861, 363825834, 800649540, 521764114, 133465715, 158489189, 558327627, 272878969, 94403851, 496054058, 490616362, 891584176, 644615729, 497026216, 612365181, 94959313, 162551856, 122170384, 355931276, 36756603, 945382509, 978435345, 411395319, 730725014, 935617046, 698164911, 477492366, 673370979, 796312640, 956781493, 925805671, 747464929, 794452, 920175795, 90135206, 220908813, 233328107, 759780782, 888250211, 329098928, 880145765, 505702504, 345133883, 694842476, 173864505, 454333972, 306378104, 635696454, 775478012, 515804750, 310006847, 280192174, 212979957, 806258543, 388862893, 823490088, 427504016, 817149371, 30162247, 643858548, 122199169, 18742686, 739891811, 431908696, 599114072, 152633801, 820046123, 287822054, 728124581, 994308900, 276167066, 26209201, 431513021, 212816563, 837239791, 180986028, 826605587, 333095248, 20590790, 928580414, 958435667, 631390509, 827353888, 371955799, 109944854, 867308724, 431767623, 920369285, 479395374, 191038663, 387815774, 858972961, 430110399, 176215762, 517712848, 226353450, 829171544, 291271496, 191402855, 922029276, 608279737, 369820883, 11367061, 35288944, 232284869, 706219066, 614418628, 906101718, 14443122, 371788151, 121043548, 701904571, 245303116, 935699951, 131610952, 119653638, 870216007, 391390638, 56346986, 75975859, 158490966, 720344500, 905537309, 786129951, 300985733, 973064684, 489254656, 490440006, 254817795, 968680833, 452998641, 20882734, 24829930, 715747923, 984517305, 356049004, 549639420, 741158957, 480066163, 74400815, 298280952, 338498841, 582854497, 870464317, 300996032, 403490063, 319601822, 726177251, 183195073, 561327791, 917272788, 782389267, 41601126, 16230152, 559764428, 184119888, 445061090, 691161237, 363601444, 50120651, 49773196, 742665008, 82850987, 437428046, 318748662, 172461487, 559426972, 451872757, 963969323, 937701093, 702757585, 442333176, 654767796, 241730731, 343709664, 647440692, 557664856, 643535173, 652290069, 69608579, 152109110, 294985796, 807619481, 501258975, 143305423, 592084889, 161025374, 759283469, 539679328, 125618921, 791796093, 467208078, 487127133, 178259496, 864413222, 275960803, 572250996, 414073841, 566050809, 180956315, 100093977, 11572400, 478260880, 494392454, 782965137, 78483505, 408666331, 270135652, 529287128, 705589506, 394733162, 758544711, 840660052, 844742468, 909509468, 268211643, 296672748, 475972563, 802210783, 587796474, 458380141, 652319375, 892994036, 194792484, 263590836, 716420611, 44884937, 459851782, 146850583, 621545909, 464266980, 713539591, 45381618, 810981434, 255321060, 268163886, 81308837, 763052632, 340954630, 644825085, 757306019, 697969723, 244297455, 968988983, 665679553, 695126345, 16530013, 671396198, 213872387, 983897203, 986320957, 232074730, 335363528, 652074150, 460803790, 36084807, 416033625, 529757802, 565563947, 607633676, 846387518, 596225376, 494707799, 406128534, 895188244, 549737602, 933807101, 505280528, 701190716, 27437796, 380920860, 248872242, 999295538, 233619602, 843216865, 723663717, 668674269, 300669816, 41251695, 34153622, 114522169, 490546774, 617433563, 896416828, 276889312, 468964308, 21662404, 873286372, 734725227, 338746203, 137905231, 678883298, 527654000, 421887948, 14504039, 865659408, 805535985, 888217605, 179677267, 521418068, 134582002, 502778963, 9100286, 686058390, 900745715, 737603488, 556503913, 778796373, 353756795, 864228656, 212892440, 757160323, 643433304, 71561130, 365649711, 227808324, 452385343, 549400087, 36218802, 984853542, 700188178, 972971078, 380968548, 155848179, 251548804, 189992778, 33234887, 589064241, 510649476, 143288742, 39201626, 420456775, 244230617, 663881615, 127189080, 595933687, 59992778, 852072976, 136913044, 683439043, 839530747, 968013490, 288861843, 211234482, 428790291, 19093016, 956479035, 124731750, 410677488, 602114922, 419316056, 441989859, 590122383, 219628632, 954186584, 682880801, 327246153, 489613005, 602089772, 690393626, 245361600, 797927024, 705293869, 116336275, 139108085, 911914142, 453474257, 770994866, 69002458, 353869608, 996055937, 59601918, 815825317, 991380052, 114638395, 308811168, 437092455, 835839405, 906535847, 494388749, 294268607, 216786108, 579412877, 126396668, 877581643, 126103695, 200593980, 819899928, 364559730, 538791823, 686337448, 355026119, 877226188, 466405623, 242006897, 452374498, 226888994, 95708062, 886727353, 931669624, 187331175, 214841982, 549997598, 520635597, 459244428, 184618530, 994147003, 587168776, 250433614, 325777894, 142022480, 863459841, 889207746, 833888825, 835274766, 533971241, 170944976, 902684642, 798382713, 24172780, 258329728, 991015470, 522608304, 333845115, 64191463, 842651330, 370879139, 434261971, 553252955, 13360570, 233045246, 612690590, 911496531, 26080179, 759006721, 436288100, 502119082, 794458309, 902599682, 728951204, 374471450, 874153795, 576791507, 310270064, 516491187, 847268892, 464767033, 9215489, 318438889, 131781390, 769785465, 224852664, 232435464, 222582801, 214026857, 229166114, 252997124, 744314781, 257570382, 796566035, 986190704, 94628998, 117141557, 973843323, 542403550, 982586731, 597532410, 261374348, 35971259, 520107511, 560448777, 14251106, 692719422, 208201172, 180100648, 44316308, 739709634, 227617245, 23758294, 923475731, 785767974, 555071390, 620592136, 410613511, 794794368, 411953489, 488208052, 594026131, 661520164, 815957111, 793727937, 255421470, 399300064, 368985312, 763527290, 928057205, 311739506, 530504635, 784633401, 318498352, 241399755, 142772989, 930702682, 582239629, 858525114, 577484332, 496597943, 819362774, 844039129, 316059127, 115143304, 308056662, 539522410, 717476372, 68691619, 274891983, 931481679, 512529963, 38637644, 232506458, 249386111, 774515210, 418541112, 842156591, 604153802, 42254798, 671276265, 35076045, 228551823, 240525753, 918340576, 363149548, 209705414, 216455526, 756614764, 518335688, 819697354, 154390698, 599860480, 494655227, 95646731, 325040211, 196251959, 485053756, 719268837, 294613934, 249094782, 40491242, 716026397, 512380211, 103495343, 370520064, 629105990, 81267864, 678304325, 139305336, 653366863, 367726512, 709527745, 981405530, 3541811, 199676930, 923890385, 912422341, 892578020, 580238508, 523080643, 745028668, 248510486, 516243238, 264199661, 519310857, 217413558, 8362366, 282116569, 895326421, 92845028, 464144229, 409202600, 635739373, 233518361, 906477239, 573171759, 624341347, 603378595, 169124928, 234163319, 739712758, 306075022, 567147555, 760131906, 291694773, 66051721, 700550407, 556822526, 85190593, 205587598, 755964224, 316944277, 855906613, 114575392, 741140102, 41554685, 684883827, 418526566, 628662569, 615178354, 499880346, 406665804, 707006934, 704433882, 881046308, 885045227, 68155169, 403634710, 905098778, 878265460, 569298727, 402188938, 812072745, 904080202, 526862365, 52964287, 917762678, 155119979, 638308518, 84804294, 988277978, 304255892, 426670079, 979539126, 377966259, 115988059, 850811668, 439075870, 205147655, 217653538, 309722954, 911967412, 341138495, 634494624, 762935194, 129110736, 945757839, 899669053, 134398806, 99361082, 553124132, 553324851, 844332639, 832259597, 620846581, 990346480, 5977070, 244509292, 836314625, 527550740, 309379419, 99338836, 397469651, 11572951, 558482501, 229462651, 241701117, 354665803, 415637051, 873039328, 386037257, 862612384, 271460901, 593212298, 557736465, 639618402, 728079915, 673379092, 71769585, 710306920, 382725672, 695175421, 651689056, 172425750, 974019613, 843340407, 495648694, 555542713, 995065220, 236200917, 874643262, 430201662, 126565659, 185472443, 813145275, 236266796, 103488168, 571551141, 320521433, 739317367, 144958312, 19526796, 423493170, 41405784, 810585189, 181688483, 612595862, 615514705, 131918885, 937046790, 819843518, 379116491, 883152670, 815918563, 23839256, 752497753, 831985227, 46040439, 491569036, 143767621, 507726966, 102393547, 720976750, 696891818, 834878194, 2152190, 473609765, 895799678, 3319163, 283817086, 625417067, 365175446, 681747499, 453438308, 30011456, 263964697, 876505987, 11211526, 705328072, 638177717, 697648142, 17409667, 686108671, 441496366, 767259605, 522780450, 219991699, 214421143, 159257488, 394249592, 399254188, 737008371, 154994159, 428882613, 412651224, 689772876, 856506824, 256639840, 133117149, 889352642, 187471549, 757839079, 764425200, 160217610, 178545923, 17343617, 80542669, 184368078, 45378398, 325663614, 885187000, 211447683, 969330901, 267994102, 963364972, 75522947, 946333296, 329184151, 994351425, 68314547, 390631063, 570647063, 912274562, 237804609, 963867493, 29873969, 820685611, 292327818, 544788420, 742263052, 17157389, 18135957, 857904857, 351854830, 119892252, 525898188, 367116187, 369539915, 528883356, 77906497, 821403469, 334025509, 117158393, 790217038, 105025830, 280569637, 681616379, 690180885, 23052552, 266157592, 196534935, 674193307, 585333626, 724359109, 437246621, 390496661, 775769723, 526921062, 10500666, 734551286, 550464303, 197898056, 453590481, 223093881, 291130693, 973132050, 836226685, 383136885, 7181814, 148727288, 375692114, 714727927, 364153778, 595204731, 701616688, 925999369, 861436837, 735657726, 932274621, 629862618, 888065883, 369649953, 139779326, 696627941, 768008403, 942229990, 908651950, 901654700, 648919153, 369790409, 364735801, 615086698, 519633920, 231350591, 849484942, 446859557, 64225921, 696289371, 179368037, 269139095, 954505848, 862116872, 191600094, 616652777, 522541468, 322750218, 249193301, 660691339, 862832220, 920309312, 650332562, 408957238, 382857843, 107979925, 156363192, 163562757, 77994345, 583462803, 166123998, 184735896, 65477283, 719605741, 58892761, 106862412, 892692542, 997548195, 882949407, 435534635, 188308422, 940359491, 628698250, 427528490, 946936083, 674790559, 627296065, 131961776, 850943292, 737666236, 147596583, 253847425, 421643413, 15422040, 964695210, 432227430, 373754092, 432393882, 362412599, 166889586, 536384861, 412175334, 720964338, 500658035, 528397738, 700156880, 637681153, 460452272, 891938183, 302817104, 737581457, 701343036, 958526316, 997415861, 527227377, 944491136, 424830536, 625518888, 611944934, 15171450, 55592169, 630242797, 724503360, 867434006, 122406471, 730172176, 716015220, 925097045, 75961844, 281524045, 592573520, 179240837, 655136820, 484569439, 691382858, 9845930, 617743948, 598395662, 757800764, 940562993, 259396674, 291504314, 772916725, 17778963, 811225979, 63542759, 114846721, 87697009, 519250164, 747408974, 929532571, 415793328, 150955703, 152313815, 52898696, 457747796, 653482795, 750006582, 151337342, 300691404, 645818355, 580803551, 386365070, 975452915, 195014943, 814774481, 335986760, 540709531, 315263951, 940764327, 593520305, 537918392, 22838171, 312471660, 326244952, 25319845, 213832568, 739071686, 681328681, 793295205, 974073132, 359462364, 669822944, 375057976, 594125718, 246577037, 996058158, 145018362, 55020506, 436678158, 590424839, 377157681, 27903139, 132777948, 571729904, 416183559, 629435004, 640882630, 711292081, 162132177, 505274924, 710905219, 330491297, 584992304, 541280971, 908019177, 120799828, 134570939, 200958406, 867374428, 869766413, 566596479, 52550806, 585266250, 135102040, 12194332, 445294592, 417129568, 31771301, 747022032, 252028170, 951589479, 63019342, 378521554, 192007893, 974987583, 138648855, 419490715, 586734955, 336118898, 299707490, 914868936, 925582141, 114507166, 238954630, 86080216, 825146953, 248694156, 336102159, 257074856, 965305283, 848068937, 601652813, 772372976, 427616941, 607853500, 886579847, 443577194, 743948512, 702170985, 599014862, 279476518, 796943162, 647249306, 835934583, 149198026, 602231587, 942787301, 318848764, 198700218, 859085658, 197492471, 691452220, 783447461, 925050117, 892286640, 914681180, 26042704, 446575042, 421523687, 788325816, 706974602, 53173196, 179594970, 832683503, 407305963, 286956568, 354878883, 751001150, 557167292, 510906602, 297393876, 232537904, 530043156, 626984015, 446758869, 952419177, 731740254, 15812589, 411474041, 839813166, 969358295, 599162268, 308080022, 932165814, 809228800, 37732034, 68623802, 255959826, 874366098, 112888397, 9766933, 495423522, 92101955, 285331491, 481497754, 841186826, 359662234, 743954931, 596521684, 177954285, 146881852, 11677982, 219419518, 420511713, 67428004, 627769780, 716907755, 770292545, 579739605, 502247489, 437527841, 834075498, 374211460, 447080761, 658039498, 407724038, 923302526, 581974001, 878586728, 14114607, 845861206, 195135982, 607583622, 932526293, 793123338, 780857018, 369075667, 167913893, 259325140, 523279024, 997860554, 158952679, 468209454, 3023248, 993446409, 664829278, 250788741, 265195070, 352737207, 530369812, 117735150, 752406672, 834869470, 672274975, 894947078, 987016690, 129440013, 888229190, 416404262, 316164147, 640552534, 43395972, 986424747, 33103560, 248752423, 490387749, 367109747, 152067662, 298919073, 957446339, 337324069, 785121013, 619919612, 495683501, 990889330, 604315151, 915675726, 35226098, 466172734, 563745424, 625638951, 434038452, 998839041, 964293881, 998770292, 168383190, 763936413, 81032113, 402429879, 292659275, 698325924, 404616028, 880351338, 728680192, 269243067, 722800090, 395042031, 951577994, 913460223, 16327555, 241639050, 369044089, 337032024, 841809080, 506706876, 419255846, 915382657, 265022210, 929245006, 227886884, 155916718, 215412190, 85984439, 905013969, 685403530, 204593221, 132894934, 68275631, 746643367, 408963234, 355994699, 454177888, 686268322, 998398079, 439732989, 34417590, 677494433, 588174518, 203077267, 206701748, 359741598, 40065003, 671729734, 689100093, 598784876, 370639199, 390299919, 571177464, 134634760, 214208349, 269592619, 435206256, 535895468, 559923855, 17417985, 533836268, 693832384, 420661259, 256328868, 532208743, 174439576, 161521148, 288661678, 958748654, 220615837, 695118238, 866037609, 47900223, 873905721, 197206396, 209332885, 146128738, 827742661, 864216331, 268360391, 558701448, 958923307, 210712552, 330388158, 558394605, 577673282, 113067492, 562487918, 392353958, 752570380, 521665325, 614720911, 126025432, 948879955, 533516643, 73562532, 547241510, 593878563, 520358701, 210918674, 172086583, 94382972, 352275147, 885335331, 715819954, 327545163, 524515744, 687743934, 585202808, 671382818, 368607550, 862032770, 787431455, 214746922, 633848309, 390383828, 558412921, 897094185, 228048226, 254664188, 324624478, 432751363, 789864834, 914629488, 403508951, 563322274, 472221136, 717308658, 355263621, 794439372, 733537559, 226079081, 219047195, 800319070, 582503014, 496455052, 713686957, 577014129, 441698464, 964036190, 747337761, 785609653, 600572765, 913835388, 292997704, 762643266, 425452988, 353004653, 982883944, 338822888, 656078404, 477779853, 493833796, 11742010, 401903953, 719333439, 178507187, 162926995, 23987249, 553664507, 133797812, 239399747, 126006866, 287104561, 198973097, 237445142, 818762858, 634681743, 827193183, 848557552, 844030886, 271392599, 239326383, 540869818, 859044931, 662194819, 997568746, 961215315, 82331805, 451438477, 289645114, 292378081, 645097938, 180419323, 208163615, 988194291, 120799397, 365048767, 267371626, 136123684, 976656463, 205953631, 100642656, 75779758, 21791801, 86718246, 67005202, 831653307, 574006847, 133159332, 418279589, 709283325, 455814867, 930799122, 308944012, 251375318, 232010442, 997126507, 891450451, 86992659, 477543346, 776104886, 975683493, 580054019, 263567021, 155383561, 335337910, 488600473, 48554386, 727656815, 972965469, 578559714, 540981569, 580296339, 416051410, 482746541, 215312417, 660829354, 919207337, 924392720, 418852844, 798961430, 244375426, 396342624, 874837977, 93296655, 760394595, 203309801, 572217849, 537160975, 757167074, 119492224, 403897227, 616396266, 143581252, 428576978, 677561992, 97661621, 310450781, 805236403, 760106793, 212334383, 668099364, 443455743, 711672043, 635968460, 279305582, 589966928, 953003882, 633684265, 536539822, 348325495, 908248951, 138065809, 20975129, 563955767, 424372959, 406491454, 134720593, 762029436, 162152491, 97783502, 113514820, 780092462, 34280626, 591008108, 915061516, 510797640, 209728415, 829360852, 921386966, 309265959, 680447888, 619786607, 342747969, 744773325, 92691102, 604413468, 1295502, 982157992, 233057285, 747539998, 613514817, 175971477, 935358371, 64395996, 839418003, 517249199, 175999816, 783274223, 323178782, 875772068, 335162013, 720239642, 255436828, 245851599, 350699042, 777809988, 787183669, 257605246, 652684278, 390518558, 848512457, 911595445, 177629889, 652217526, 402205140, 385390782, 386771395, 686574916, 186164687, 194074859, 591091423, 27692445, 522110212, 468091684, 6746365, 955444959, 863629756, 55810721, 762298430, 675004011, 729942594, 763249170, 890763497, 389325682, 91035729, 112077872, 986892480, 476780094, 423272438, 154092220, 964811364, 277864448, 840354422, 992609265, 428685394, 263077398, 689791638, 498554917, 139845946, 687795821, 987275180, 688529471, 308605770, 735470419, 570573593, 845163894, 533400470, 21223568, 540792446, 715078445, 535352414, 168430668, 764114744, 123458098, 719754742, 891524880, 624828129, 808770274, 79074584, 857047485, 624366687, 67825946, 18937177, 770755087, 8011097, 744356521, 165429722, 459148877, 936127693, 459033117, 159900545, 577118709, 74311691, 573178503, 548714296, 236752563, 629912730, 658227726, 508428182, 306415175, 530759290, 778524971, 780146885, 251412151, 507867747, 325133741, 913918051, 922606081, 332413135, 63471907, 244003854, 679629137, 199012067, 13379857, 477576190, 27088753, 446849193, 368003578, 15919748, 824787801, 280484281, 66582169, 863297098, 475515581, 73293435, 141170677, 845706355, 522250350, 616561564, 791014892, 269199865, 506428049, 715803907, 293480702, 165646604, 343439861, 177378182, 877832942, 441796626, 391983244, 887833669, 791097718, 31619606, 92017760, 936685207, 620851548, 381719790, 469465423, 254443253, 417109116, 133691284, 302365324, 695885021, 14017378, 622621460, 611585855, 143372075, 82305640, 864413490, 921071623, 300869117, 625816268, 778900316, 751885021, 698272201, 730806592, 416898639, 430397684, 269851469, 231359452, 665085634, 714755584, 924511667, 46507477, 981447148, 950824249, 112616509, 788069825, 525858964, 888689984, 130079685, 669508474, 619476685, 386757622, 748962368, 521847999, 238200829, 602172167, 818962491, 122844285, 181821748, 336175606, 320573688, 486618345, 49445279, 379874953, 920678658, 428768504, 674347108, 215410804, 440798202, 422528739, 252297066, 453597790, 858235180, 956425309, 211359521, 363573962, 133478242, 800768039, 744974922, 134462403, 818907548, 915427961, 75226234, 967997679, 251650284, 543084235, 194233131, 205322861, 907894001, 677715493, 403244707, 461097450, 814760338, 392121572, 796041535, 220891624, 855425788, 459835902, 92863913, 28326087, 277751005, 451548848, 95848151, 823550659, 522861457, 7193274, 347173983, 869978060, 136048108, 568934799, 468876017, 436139904, 234240073, 791974584, 95281353, 883492083, 709604247, 357975151, 364120158, 861938072, 15018913, 533443826, 56306738, 983088720, 658131457, 413698484, 697257313, 954588111, 327678726, 407205040, 386442484, 683079995, 899705636, 556202414, 70463102, 361946124, 300383900, 57338678, 716297082, 219086432, 633406016, 879146257, 197881389, 574234071, 654392, 562647030, 854680055, 382862755, 624715747, 7692827, 110521009, 404708424, 864100911, 403698720, 209867075, 926563438, 142150795, 695658386, 685186205, 500539476, 698409898, 165615657, 196498193, 159382934, 608764768, 107462, 116015883, 52413891, 177717906, 721807854, 634712018, 189554546, 179021768, 686805208, 467597624, 212401765, 572260007, 486986470, 916172895, 395999737, 545041294, 462427582, 138393183, 855039187, 937808747, 992519499, 452495589, 592178462, 957143291, 428048633, 477513195, 297830314, 219836107, 948477847, 613356012, 681896030, 328545297, 421520203, 11990520, 473670096, 403540815, 880848267, 624723894, 730779739, 466940000, 849020912, 670458273, 286629595, 45091916, 954369972, 737368047, 202900574, 406091298, 922783088, 375276151, 315586554, 823640250, 949382252, 689917876, 944043222, 29106249, 946462581, 396367629, 718749526, 811982022, 792695388, 443496455, 260033980, 695057508, 586676457, 817164685, 332897834, 799479558, 636451790, 734199125, 289302828, 153051862, 185204088, 109827435, 884970905, 301245836, 592261854, 67224028, 135465015, 345688787, 755675446, 222669481, 41233680, 320113511, 531681277, 928959970, 375095012, 917266578, 634855014, 361460090, 334431130, 758391883, 511639107, 2323747, 776219147, 295873328, 715517036, 95185837, 268383229, 919931474, 939579146, 68372971, 848585193, 653397615, 290639193, 548529736, 112575341, 43679483, 954087751, 77507798, 30973272, 274713502, 810827381, 697042928, 48911943, 537471488, 361777972, 568987958, 370726412, 657254911, 665302203, 327087415, 342692967, 192865957, 103341706, 467776927, 81746030, 611575698, 643458263, 445550321, 634947844, 974677100, 598842821, 339796300, 425987443, 425078600, 464484732, 404073627, 350495201, 170758771, 774137337, 481092504, 271822809, 375712262, 686313634, 809393544, 687318675, 495015798, 275921503, 412054906, 5137037, 933659927, 547877143, 616198270, 525373482, 825058280, 697011729, 87132317, 835030546, 412343518, 911251774, 946696889, 26668839, 144978954, 957873326, 325771946, 596542002, 427619218, 172104867, 466402437, 918696601, 75258529, 615142100, 96700239, 307820834, 236934696, 430271287, 132613256, 764857400, 6352073, 467585791, 252879765, 928960386, 776376970, 606742638, 354182151, 192018393, 730349631, 758968638, 269223474, 221905810, 369556340, 270707704, 303779258, 254941225, 248622752, 254074140, 381469271, 597096023, 679427439, 969387453, 94164776, 823916565, 172660267, 865982645, 128536572, 768054316, 878405902, 853541453, 112601454, 29115201, 441962631, 124553132, 484681841, 12560692, 42894011, 464177619, 911990554, 374291339, 415122876, 109720851, 630923390, 416403523, 413072314, 467326433, 180398315, 983415176, 719461178, 670692118, 811328890, 190406729, 333099970, 15987104, 557738602, 536972419, 848907831, 183924413, 413810569, 108179358, 45354998, 615734850, 628560061, 885381797, 520900455, 418904321, 71935894, 788867767, 286799013, 634427749, 285837776, 728468737, 760462914, 504222229, 239195076, 236776768, 4887089, 701511767, 138712035, 273070301, 627681297, 66499297, 480642447, 993887545, 696037261, 802996622, 470071124, 329940718, 510288296, 637452433, 372924444, 919032137, 532819328, 692507642, 36316716, 617970103, 788767811, 303100032, 107050790, 85963611, 376724189, 99305665, 791898185, 533249435, 894255675, 258163775, 281466021, 72789756, 779938867, 488234490, 514469810, 69475482, 868615611, 484963470, 622979690, 558155878, 929180179, 137629071, 109081580, 355772175, 109326154, 951639474, 464626756, 975827054, 436997846, 487556585, 271618212, 476171927, 147587997, 423538650, 853244949, 528797883, 521922114, 273296850, 949615656, 920169361, 297601848, 733937694, 418408128, 387334127, 625332480, 73035342, 602350843, 378906325, 268733356, 422316958, 108445096, 69369561, 445125881, 357457095, 153336387, 154277923, 265937247, 135212608, 533926087, 437101159, 874981139, 376480076, 179284685, 468243412, 218975691, 108574368, 736226715, 292240386, 24119466, 801551758, 348735299, 981961003, 234430192, 627669899, 586060148, 110255154, 869571364, 449949288, 639953756, 282704697, 560580249, 594358612, 882553051, 968153459, 760838202, 617368777, 113595553, 727879110, 399119127, 332768436, 600686146, 405306592, 663744844, 185954282, 781266678, 48225121, 224581368, 996780087, 474852361, 972217620, 612513834, 843725482, 271893654, 232096883, 280373950, 901154783, 707306272, 289211126, 384456547, 246149508, 697996145, 538885496, 469891575, 202030602, 311197069, 873295938, 58862645, 445682018, 593144029, 990763441, 942996125, 16216540, 294577770, 379668997, 380773024, 472230159, 172161636, 75288789, 145007522, 811869861, 744167855, 38207161, 550125706, 860360402, 600995546, 158506847, 777220949, 486515070, 732334144, 836945344, 10717922, 661552709, 744791072, 43344462, 723588638, 108581963, 919707851, 106098997, 853816759, 491546486, 292312290, 334498271, 917724926, 382441542, 306311233, 277475107, 119679612, 435429966, 168125047, 421034088, 580166425, 465194001, 633053146, 646742145, 492683891, 835085672, 796698788, 84211526, 391984654, 937177270, 369259611, 113304625, 652788925, 807479277, 65421222, 935596525, 484745811, 705528854, 127880047, 154895594, 541155890, 455231172, 116289247, 654037434, 14889026, 415393715, 9031855, 683689622, 475543424, 821060279, 708803095, 532086423, 87420640, 677669438, 238921740, 276301146, 376225331, 80241787, 114006359, 911477370, 583529827, 943590978, 877472331, 982733964, 987137821, 198419422, 990355745, 904191198, 859071920, 664048513, 832974573, 762453127, 756830294, 30775798, 573941962, 349441171, 845663472, 33737979, 996517837, 12651724, 306880987, 328550337, 112465908, 211031705, 671633983, 507689225, 511816248, 868644377, 789086169, 235724735, 536465903, 50825074, 584804252, 517515583, 352121932, 475476835, 309247960, 633696852, 967665913, 931529146, 495648649, 349841328, 508051731, 307159120, 218827568, 193960676, 514518349, 766564289, 862087883, 596773468, 464105309, 92483349, 81776767, 702809413, 692778581, 168947426, 120881714, 328341923, 459593358, 260165928, 527725206, 435245506, 454293904, 305048913, 229190486, 144728466, 48340503, 710929205, 279201252, 288169784, 954056835, 725226715, 834360848, 800062820, 111080179, 662611237, 902347566, 357921213, 921201308, 835134071, 603700217, 684902751, 541386840, 295107142, 802914885, 658309236, 434545316, 138520838, 335062152, 874092604, 162968203, 642439114, 656013193, 47101315, 391094682, 902321173, 796723135, 396386176, 210301942, 854636613, 44963753, 148590329, 439338055, 248053506, 814549271, 569545183, 160652600, 891995748, 199035641, 411906535, 880727583, 26327659, 257848979, 141557545, 320991968, 888591071, 935257270, 943538597, 492884931, 8755659, 545565866, 177768138, 883219317, 347445929, 843583144, 27086419, 325318565, 630242713, 766670487, 709954763, 12080409, 504091481, 266972333, 580104996, 363249095, 302410259, 437800670, 130986815, 749779933, 645785145, 347844161, 702910606, 854542081, 96442027, 761276177, 852902139, 432726944, 664766563, 446015198, 592019468, 340160136, 823360843, 580246948, 182041920, 193876766, 191619147, 716100030, 491746555, 934675508, 498935250, 202656432, 218715895, 190968384, 192574687, 937302426, 705417734, 189902245, 783676623, 908590605, 356677951, 905429413, 714458197, 770439685, 96770742, 224694168, 102059001, 586811903, 399392184, 694483641, 443306883, 245769723, 697407374, 120930233, 73461744, 38938021, 274663438, 496642645, 480836463, 717031575, 491902759, 282461083, 374083676, 572209617, 71234615, 156349718, 565248514, 924843766, 921961696, 162555017, 848227547, 932255277, 961341018, 324025144, 706050148, 614042727, 912215782, 565960210, 638584424, 163968260, 600692537, 498977693, 19834892, 849748773, 259419742, 873062735, 287215949, 317805562, 715201699, 190604445, 906310978, 627866651, 290052742, 188045295, 222310378, 452673769, 434419135, 990651849, 741140257, 917923335, 258402912, 604850696, 954819095, 268801271, 840108724, 577640506, 570237992, 161635529, 685660583, 684150063, 32615786, 982638607, 915325707, 197703355, 716732301, 263383401, 901226328, 137502818, 137240601, 123665010, 693735385, 557374337, 718696265, 578566671, 583810161, 290572054, 800325055, 767000643, 822059093, 372619769, 496056622, 5668779, 192803924, 18057278, 160511574, 916391914, 642315649, 454093251, 913626307, 243792234, 145846553, 717992323, 664897845, 683039583, 497299748, 547064119, 416994037, 336115882, 689307767, 328128142, 392009096, 801351277, 323521474, 862500215, 227814432, 944847054, 139636701, 103257418, 821563840, 787854508, 703842652, 370138660, 659902211, 925388127, 71399461, 184290257, 244215995, 109303598, 717167913, 196775774, 802666899, 546652115, 940036048, 523854251, 142739308, 756323190, 43207777, 674318570, 476534900, 970869835, 643151099, 902619550, 533371998, 659689940, 773710074, 753327502, 407582158, 772609496, 801251725, 212354481, 335407995, 898616217, 796907631, 231713425, 112298244, 449023182, 463411204, 279745093, 432187501, 667414851, 103760987, 12328873, 696240149, 154358885, 104626182, 703684341, 312567061, 88408054, 318719937, 998475072, 49174570, 791838691, 563789044, 888779751, 317930055, 340867104, 258324955, 972725758, 6302358, 620658978, 462753300, 572103490, 741052816, 495383937, 842235194, 690433215, 525906131, 19579077, 770398831, 212202055, 96045876, 163480326, 681254310, 125754747, 795045720, 772733337, 767063689, 383402050, 234515462, 461251934, 67532573, 526986258, 762147602, 913176595, 386182647, 810776255, 509084674, 745439368, 514783019, 63798716, 125577156, 958887089, 734107027, 621361788, 152435799, 123652864, 801968258, 146491730, 676556132, 72563186, 805536995, 221652162, 359727625, 942809752, 456183233, 711278647, 851762103, 199802787, 863013140, 234940724, 39853994, 740264064, 809980216, 538860614, 720702835, 957697028, 881964359, 32236617, 539016018, 351926533, 358550033, 989192249, 372039051, 728544090, 175941895, 682383325, 971147305, 703085598, 167493247, 896912047, 883224290, 301042464, 838070673, 638586829, 591285869, 303997139, 75816443, 885623763, 623513107, 96304956, 141918987, 710801429, 722014566, 13178423, 950296313, 174179990, 978768072, 194824084, 471470815, 33085709, 122185915, 365935455, 72710374, 679227290, 793702701, 900618194, 613919563, 56569130, 77008966, 984917243, 810770560, 627665694, 268503732, 140087079, 355452025, 154007797, 506775857, 214147951, 260130011, 829760335, 219222384, 581259945, 540071366, 947597062, 715870166, 847076781, 720647645, 285222229, 673690971, 181123291, 448138079, 669889422, 910406873, 142368388, 948073064, 407181219, 655118103, 761249430, 595963816, 445764692, 655299756, 944814024, 464524665, 744760866, 941304263, 710905579, 655054070, 809305817, 259209884, 640850522, 425906321, 414370284, 597793599, 920139456, 957124537, 799589180, 493826066, 223817955, 447475315, 284807878, 490661065, 555364469, 181466563, 253661946, 368486137, 656778647, 511951161, 98033131, 340260065, 714871405, 936953940, 422967532, 641979432, 960459837, 507823796, 19154226, 75890088, 311658422, 100633476, 203465044, 829559854, 231299695, 824953420, 963232589, 458775259, 999748774, 144075778, 131954255, 909390120, 285749579, 822304604, 521614766, 248289303, 126786804, 55356451, 228246588, 713831717, 349146894, 435894989, 740342967, 572474206, 557322531, 66206517, 286375645, 791187724, 626150163, 236496157, 852714182, 649225279, 939133316, 870921164, 906266656, 328322478, 714931506, 32587332, 931947114, 277634573, 454147781, 561978319, 50378091, 670929522, 91902362, 22999359, 655252747, 10523727, 483580149, 786443700, 489936715, 865373760, 757600890, 89389926, 270415651, 151892524, 943476079, 60261780, 940965981, 180563278, 911734811, 525069043, 624171858, 847480239, 128017850, 999278657, 369049812, 211388571, 586180546, 436362310, 487570354, 448041371, 245408934, 220762860, 458466191, 794920090, 716771577, 872073080, 109311562, 119010605, 521357575, 559298167, 321286039, 441655620, 607895125, 712871837, 921770239, 637121278, 884101095, 758713564, 820581963, 856218087, 812989455, 170034142, 617325972, 55084362, 729589589, 510783523, 116552893, 79769801, 458081864, 212280947, 844984932, 273274290, 278476069, 933945821, 793614228, 409060084, 644712329, 935406687, 572552280, 999137045, 120690350, 371764186, 323225545, 301051457, 218109305, 626204101, 895470979, 299643238, 824416835, 223921841, 483236708, 92171377, 147805456, 378326732, 115145342, 253310094, 856642084, 855695706, 489216013, 617999742, 750727975, 289711087, 122079011, 684560439, 788887045, 228074620, 544588786, 79476528, 295120963, 33948690, 347122845, 929979343, 273066997, 796512397, 185872974, 75896532, 237701869, 153785257, 392926985, 692421892, 481370838, 939411219, 266528872, 562514898, 352988744, 19550987, 62077414, 143309130, 627210101, 239581723, 747432878, 693245677, 399220446, 686395953, 450262136, 818573583, 740703444, 418413473, 804326184, 189978852, 987242600, 447535184, 283075520, 366791789, 762909641, 593131458, 185187568, 147268979, 16929888, 848238561, 49112473, 503114144, 693973734, 166290657, 975983628, 149503178, 617727660, 313557624, 718182344, 154268960, 124395306, 52122604, 972939352, 22084740, 133099676, 528708970, 166128045, 411661658, 961291572, 254589480, 212704205, 196688095, 170941633, 713269120, 114408036, 56616180, 588460393, 812625116, 373859110, 928888838, 109611751, 297926634, 895803655, 802372052, 462678603, 18611109, 623423633, 277872809, 834748765, 345982163, 891520189, 825984248, 863918146, 726690563, 316806888, 74373529, 980094730, 51420080, 170861071, 512325320, 786298664, 997313094, 226178500, 148372776, 600854634, 409139067, 325411587, 352515751, 793071623, 11662735, 49457386, 37441182, 403902726, 448409369, 9145250, 522915776, 724979552, 326865166, 782695362, 750000680, 613110928, 853290001, 708177211, 253051732, 886777719, 665410872, 221495230, 557755909, 233551420, 820943417, 218681905, 621783514, 527904448, 874609990, 517753582, 218484727, 816632274, 458176909, 985404985, 792874705, 99956585, 943155871, 214126222, 689292562, 670328458, 795618829, 754278011, 639449580, 440073982, 700335039, 761685476, 446523664, 366794771, 208809835, 352677410, 430423364, 651684119, 91868869, 983872468, 352845960, 788229498, 462174788, 123499950, 782919648, 260306117, 728733218, 261837267, 689531085, 282604564, 468677617, 546965677, 199931188, 775584070, 108182717, 990956299, 702589911, 805759981, 339878327, 22205882, 849799463, 845033691, 373458131, 667257447, 137821630, 977073806, 919048103, 363465272, 295890908, 270661111, 705762152, 734514884, 55120029, 286027282, 905582155, 290531710, 767451644, 713298076, 915349079, 787585545, 762778966, 975074249, 730903820, 953129379, 908415834, 11939910, 340914935, 857450133, 671684454, 429665407, 30960859, 999365915, 818453036, 998168338, 608661480, 680117157, 152259674, 910056679, 630760867, 72706142, 192165233, 917730472, 142821957, 359959536, 707883898, 336269590, 158237571, 807788801, 848987111, 476153112, 148247448, 359583858, 117125594, 425361145, 359726578, 751302174, 441575315, 453725458, 95852962, 975917936, 355212897, 178918503, 870395885, 625816912, 224868243, 650387945, 913635180, 83092103, 691658274, 564290008, 934292952, 722134990, 947263266, 479707589, 142793347, 477433342, 446802735, 707009407, 534975541, 85725034, 411755820, 883510055, 469930645, 741708583, 132668664, 942323999, 435703281, 258195174, 782851428, 822657625, 85152800, 490771416, 524755848, 191305985, 862371032, 526793434, 389039474, 935060848, 816785898, 713269098, 224314647, 439033267, 24947644, 993817900, 321308438, 297509857, 59813964, 446978347, 455464210, 21847675, 853232218, 353659339, 256107606, 982566580, 760858433, 613030588, 143359512, 120313696, 966383083, 554149214, 454990582, 142821754, 890420520, 529359946, 908654594, 820835915, 265711733, 749643021, 294253377, 219395608, 751044197, 403250498, 861119331, 742926590, 89010334, 31870554, 433308462, 766706956, 153219480, 702456964, 420755381, 48025024, 984963062, 818668075, 712390965, 479549584, 630549676, 306362212, 696309365, 658842056, 409172004, 392277390, 659422816, 835722243, 702084393, 184838859, 819662677, 221379268, 176166523, 356514653, 153939036, 398617833, 452009497, 521428104, 919856534, 851991042, 547333786, 998215312, 196221270, 167052683, 747567802, 160784892, 633962284, 754632920, 41085330, 472341842, 269700070, 307538083, 139852489, 240971134, 619999625, 149340729, 850249961, 156519242, 210095335, 985601534, 296599459, 770941066, 603242856, 648220661, 664465246, 502760823, 522935961, 246231874, 972082991, 31040758, 469146388, 466532524, 477272793, 582473998, 61442119, 569637553, 427458344, 544171876, 512830641, 612497072, 843068071, 548006514, 647050448, 639425919, 327798048, 595155273, 277932603, 261833377, 109436763, 979356491, 167399575, 913026157, 208096748, 384994144, 991677325, 825281363, 226359241, 730344375, 706180478, 45382163, 378132017, 854270267, 261178216, 85959446, 112494393, 274237504, 462506593, 54608166, 911759575, 540795152, 856883336, 122268442, 146108099, 733884507, 510432694, 902005713, 493979629, 262375950, 122052535, 32855378, 133383160, 617934560, 196868850, 112844269, 138890035, 72201633, 92984188, 296706737, 213571415, 584727021, 896069707, 432498619, 202884790, 391546070, 568631647, 900705587, 86189468, 168209383, 843818892, 790838335, 875547024, 31988664, 589742553, 419646371, 950750656, 896989360, 918240069, 127848725, 407726805, 866743744, 480393308, 280031782, 138211786, 643380669, 889314276, 772433187, 174396006, 15215987, 433979032, 846923767, 466579233, 883300423, 824495832, 88089359, 807638572, 553065661, 239054273, 514521252, 124911694, 663496360, 363559455, 492173955, 86359783, 116726495, 913404583, 325974453, 301011284, 971690190, 290206474, 934810358, 97662082, 194603550, 633896000, 597971048, 415018563, 28499622, 183270579, 468993829, 315727178, 161288301, 69034331, 256141291, 346483937, 107789598, 540852923, 707207115, 246559390, 411068005, 776050902, 923310487, 374751590, 341654054, 903973894, 826559955, 619427116, 961730514, 428389550, 618056484, 880498074, 920878925, 174920901, 521259765, 179584110, 981933756, 350471706, 146750130, 910526937, 312758076, 348090109, 287965816, 986279132, 872555266, 801733830, 854629203, 535134840, 286373643, 439970653, 573194398, 416733203, 588314455, 209307519, 711476256, 651508771, 9121823, 944577967, 697307539, 695955883, 743169368, 892760237, 366907414, 22413334, 693240348, 591492943, 636233882, 567743204, 631698600, 869110621, 222903420, 198376679, 108577524, 625736202, 854772006, 150844878, 108458437, 134487384, 338732557, 318180147, 529389283, 633631791, 462420187, 841780265, 263678816, 513621867, 63100521, 248415942, 674547105, 236262987, 368352923, 678455338, 652910746, 613798425, 844957068, 623786088, 813770614, 474117033, 196666449, 693545691, 491003084, 395338011, 34820447, 64271550, 153970786, 262468620, 534993928, 853604381, 498588591, 488214117, 132405566, 83524187, 927998359, 121866545, 556555714, 14962504, 249729669, 950007723, 862274589, 892772319, 514699468, 88431207, 100179964, 569308945, 370831820, 243084883, 675160657, 135957126, 227932546, 669850046, 328552363, 245381513, 428159308, 746412143, 302635107, 685226985, 417474693, 209701757, 355134471, 924371097, 544827951, 599820766, 389163795, 300829531, 230603194, 245789593, 944927114, 413635378, 857995873, 993882592, 728165348, 865771233, 356096228, 818767316, 484382687, 398085141, 867371674, 490934598, 61764141, 164781188, 311664098, 45609653, 222634165, 415241563, 440836525, 936359250, 407390089, 226022052, 285374215, 721043086, 355490372, 390716111, 50603095, 958325241, 392773961, 987676377, 764812379, 200562119, 236002874, 736078163, 969704402, 155262605, 968723236, 578215072, 71366917, 996540936, 797899577, 688023187, 63468877, 315360911, 118970246, 972698285, 475725086, 156900265, 277557666, 999099985, 546102271, 403299370, 90745889, 445680655, 735831081, 224408999, 648372691, 344473854, 356256365, 985631248, 126444366, 593055540, 702997971, 251076250, 837107248, 498865088, 882279944, 650961940, 509784376, 216731599, 727308753, 579006129, 735495766, 928886460, 726529359, 843217769, 641346980, 950291427, 134841849, 53785870, 469363325, 909545809, 362605155, 150946395, 423290711, 512319259, 229644613, 140416856, 650208124, 353452897, 225115488, 227019471, 899167052, 830174540, 784193590, 70658305, 838298126, 94920723, 597191040, 888295397, 677423814, 525881788, 982205569, 30186894, 679875854, 27031515, 102698280, 12543506, 811408445, 475970574, 369316262, 179303503, 601619161, 968458525, 908094379, 347063344, 871871218, 756484322, 270951046, 759967687, 675741661, 548770756, 486379597, 517512567, 237212627, 397740675, 502609641, 775382014, 749748271, 315505490, 925319460, 971836290, 321565935, 956697699, 845902971, 21157160, 899511813, 40225806, 560476563, 784649244, 926907565, 509865208, 635113329, 587734559, 895303174, 693251225, 549581205, 396341864, 527749322, 744396055, 879008518, 665974580, 973863386, 222790741, 734198376, 373475494, 284591228, 56808642, 8736780, 951985285, 116382216, 429450952, 861491165, 88085288, 308587527, 339305776, 808898288, 758704399, 744218744, 811899661, 277400923, 592930047, 453211479, 336725568, 431751069, 353773132, 522714324, 443170631, 249113811, 134304329, 660321587, 666310216, 365981133, 365391805, 97423866, 203987853, 533571058, 795563048, 786741589, 722079258, 423674861, 380143483, 950905775, 85636803, 576935807, 11265847, 103109879, 970070287, 798707374, 308646017, 895325184, 231791384, 920451543, 691918853, 965627557, 184098267, 414864388, 550234035, 297656951, 443428901, 486023217, 520377277, 183142569, 213603777, 643729281, 43801969, 213597696, 312332131, 311513872, 799157369, 204508852, 552593328, 254396681, 831233808, 946158297, 474938931, 70968473, 466485862, 530692816, 962986768, 426481509, 432748363, 265207495, 95881813, 271955815, 598299789, 801406334, 10032220, 41409853, 199671198, 965142077, 234496409, 389886561, 697697678, 854769816, 392510398, 574633905, 71905885, 651370958, 302227195, 420532523, 655688219, 421384164, 653638722, 577421287, 214033575, 748267601, 574377738, 94906609, 327240232, 432647999, 736419990, 85518562, 147344474, 766915030, 414321783, 533709442, 34183577, 543973973, 59461339, 351164003, 853183163, 865275448, 772847324, 989861532, 169421668, 412751259, 291819656, 916671299, 984798682, 659691567, 807367259, 886857678, 396342224, 576862863, 417667107, 3612534, 870913650, 148395146, 215380814, 105685339, 196923647, 128418429, 878512666, 783861755, 99068958, 777670820, 578909555, 528339892, 763736093, 63034181, 891998337, 960408007, 509662187, 311194676, 71112549, 25222976, 438922765, 787738919, 42932373, 432687908, 787668553, 859722338, 238726218, 156289647, 826128362, 765985628, 395684483, 696654824, 855035540, 813353443, 135518329, 591113474, 885392564, 881020109, 148461242, 286418239, 419430272, 793667038, 704390195, 790940073, 283378333, 744783771, 867702492, 918376010, 198484688, 235643955, 426100441, 876178458, 910757697, 144463164, 266561266, 474633340, 913397269, 107416301, 790025493, 606224152, 935773888, 232689306, 400520154, 18009623, 353466462, 507894911, 848584908, 894031617, 674254071, 112349695, 486313770, 668871031, 838786717, 595030644, 921383040, 821243196, 123537377, 311876147, 917212611, 962029178, 852273701, 322595994, 999200080, 227913701, 575414842, 213168541, 327241507, 140500915, 898963755, 202850328, 162043756, 579416939, 754442026, 52045282, 49281274, 88868249, 227179462, 797070352, 832662430, 81835040, 70148274, 680930835, 604717258, 157998550, 749817497, 383451156, 488642970, 268146154, 305325699, 707152431, 975093635, 257426634, 314239221, 106741510, 277003708, 746346012, 313546167, 253975286, 99416136, 679512522, 569615196, 888689128, 358758018, 545583217, 99233087, 877277225, 117475800, 553669351, 289958085, 166679712, 488507806, 820204497, 125961696, 509078681, 361173054, 964075894, 442601886, 520794356, 969330730, 238185677, 690402238, 413946567, 383487353, 835068374, 956055001, 395828767, 318341542, 96958179, 107792056, 784376353, 987865966, 639082807, 331730541, 232884064, 488539880, 105403891, 916011889, 666919226, 46019002, 215219573, 331173355, 811341439, 919966296, 894140741, 155230376, 325939707, 669752168, 112926973, 284344491, 853664400, 427554741, 434663381, 396967453, 580574126, 414142848, 538541719, 62156915, 656521998, 14582008, 593067187, 747497836, 945653371, 445065177, 76841071, 151735385, 475566103, 27851311, 303928658, 281114946, 163876496, 568302809, 534154482, 681378734, 753694278, 280791897, 783029004, 928063595, 318570651, 317154233, 728453411, 462263775, 108723474, 335455886, 695713472, 260874990, 340805998, 585099734, 146494404, 336881166, 908950234, 395163039, 925447556, 61563502, 369287487, 510761131, 447155484, 483834227, 435102943, 973400595, 573682449, 863885057, 639976647, 841068471, 896889242, 106531376, 281763326, 50201984, 868409933, 234936718, 719672627, 445397193, 241836339, 562039829, 850914279, 976876748, 661628975, 206211529, 241563340, 528084355, 304230267, 620179024, 434410511, 253913996, 223232798, 108481066, 187141494, 855606390, 663786002, 204603460, 942354350, 78281861, 491780884, 211796765, 73953598, 872553550, 773224019, 644568985, 423356270, 269868229, 397679527, 101718431, 238456561, 454320144, 889083819, 710990425, 297600971, 622045203, 394032702, 750482093, 752471053, 185564302, 405751121, 870658641, 472693824, 51241648, 279938799, 188097858, 257007121, 462371017, 17568312, 208818402, 430948298, 953571188, 108391940, 996745867, 683759328, 169084817, 849717475, 244259766, 444018595, 602065386, 972089047, 968007881, 691608748, 168111728, 216385124, 753372322, 971490450, 339419174, 237165388, 446024066, 618272761, 869943997, 609942400, 8540579, 999125575, 964480300, 830201810, 129112186, 339426361, 579873373, 227822666, 117765514, 467869060, 479349567, 693513854, 825829609, 477610596, 645834775, 917131064, 111864375, 228762601, 273507251, 544453454, 988938402, 639101718, 501242156, 215442339, 58083696, 751949648, 368228970, 623882959, 267786726, 471182739, 598594717, 299867704, 846682612, 549069948, 270163807, 768308158, 751347498, 383163696, 126039099, 875711253, 143656853, 970899851, 866805740, 719836737, 794126036, 655529778, 13674546, 817026456, 992879420, 918067824, 272849948, 553188409, 889577897, 734595229, 207750698, 69958548, 39640427, 435792854, 537677517, 535063276, 413288248, 759357955, 933240611, 319895560, 453456494, 531954711, 271677373, 769443242, 559735983, 511299276, 90074044, 35405787, 847278538, 297306988, 191410484, 830157536, 343446452, 201874637, 299472879, 742823745, 358917668, 625201084, 751353309, 41739518, 196142461, 981216367, 739586973, 76490982, 520007019, 711302865, 405603638, 376489653, 242953714, 251402674, 762663780, 848065590, 327942431, 295783359, 850979005, 582403815, 269134564, 247637325, 230267313, 473543092, 879690107, 856337316, 863554226, 714761332, 450608979, 872565810, 910704026, 309688036, 901431477, 692655223, 115637900, 603938560, 420119556, 608244111, 519844712, 107280461, 893976050, 617063862, 973813032, 789521965, 227684371, 26650754, 791506329, 140956475, 407505749, 623792679, 313127299, 64342744, 362247177, 823851740, 844933307, 129933998, 280951132, 619356470, 806892171, 911079367, 610075537, 363063506, 413647176, 418743331, 937763699, 410050307, 268745019, 852364583, 120144999, 621585189, 92905794, 124484279, 941769727, 39603451, 915759291, 187119947, 918067495, 884887161, 863209834, 232083551, 915901567, 422982581, 77334226, 605526492, 168984943, 889127766, 963684083, 719786075, 644912700, 341385582, 33887583, 877312532, 460983843, 231665346, 607152590, 562474936, 984604484, 695204752, 318646545, 650292069, 899568404, 335599098, 830859275, 410482329, 811963084, 136346883, 187736101, 490080037, 526728262, 526031343, 819991202, 557680061, 235567253, 169727581, 273589283, 580930246, 43446231, 561587461, 609350677, 941055892, 593256530, 62954000, 305736237, 228175332, 190531926, 202846968, 296421219, 691881698, 448610741, 584700648, 914985824, 582376466, 363216161, 780077282, 188392220, 716847081, 146461717, 446210333, 863380214, 627417310, 885373590, 279898584, 978734478, 783939555, 667023495, 701068551, 500496860, 749171885, 669464166, 149008644, 735592707, 835891512, 934504740, 936972436, 946759543, 54637030, 480998557, 462640164, 413562995, 78700459, 112928929, 252746553, 633483764, 561598430, 480028676, 647468380, 149907873, 223754849, 916479175, 468252783, 651734850, 187192465, 546342066, 487199176, 859182959, 379427163, 156951500, 583422160, 263861617, 25318649, 31884176, 643436276, 963859504, 628105980, 112036035, 43701563, 738046076, 562109357, 624630682, 648833820, 378597644, 909565786, 695589713, 357337197, 778307078, 103262517, 578558512, 713756192, 647616383, 537925945, 68203340, 134042068, 28079564, 343271928, 331899678, 672525928, 321702781, 876110880, 776155269, 990584062, 86052030, 565892414, 185333858, 852452644, 335248607, 982294835, 762925763, 50072624, 544756497, 143598159, 620048692, 562793952, 211244883, 799245319, 488660239, 327001921, 230395738, 190768430, 633170450, 834123508, 639131333, 156899181, 922192695, 289890612, 318434416, 933369503, 677185599, 533146903, 675775654, 573530103, 397570518, 460127058, 90778906, 188378511, 882488067, 902066939, 222213493, 556850146, 640693219, 770892338, 979674849, 477739055, 486532172, 171007762, 614731260, 755302003, 330573107, 312525340, 957384061, 467566469, 504102276, 709686409, 235682806, 901693028, 276176431, 778964396, 458014661, 221734984, 704841453, 456861001, 347621859, 998475107, 329137019, 114915823, 598611152, 747942296, 150986934, 706870611, 48930624, 775433238, 355611172, 912198151, 713252346, 167471650, 670526979, 978898820, 700837023, 243751599, 210247719, 852500489, 498356120, 693434645, 762513499, 589677925, 937957460, 579103617, 746147463, 652052860, 100711334, 810257860, 394994533, 700770729, 908288525, 796733513, 378258841, 943733516, 106775590, 71334030, 681660146, 261884367, 990759958, 545943084, 44492246, 277799070, 162182210, 820740398, 892144650, 752540798, 574604061, 938506832, 189438988, 158259180, 56034456, 679065637, 175759015, 763552426, 232079873, 421082065, 897560158, 971502699, 477297691, 188306428, 135078715, 581383430, 374037593, 898172967, 549964623, 683283395, 123754407, 872636978, 451719696, 430578866, 101127980, 74071266, 332466348, 285362159, 631552553, 485390334, 28290305, 98901360, 281834742, 834662361, 591277556, 52171891, 981766392, 946037213, 678791553, 904155355, 325149862, 441815393, 951449699, 818924509, 369344322, 66544141, 347826577, 653397899, 12126720, 64901944, 79840284, 924812115, 999471956, 990894709, 241905796, 906363801, 474514108, 504356793, 118317134, 981975049, 502330468, 733176367, 814429572, 673815229, 921358177, 754768669, 145914564, 893699158, 326284907, 689082616, 199567925, 964446476, 630358229, 666925613, 195446504, 602246641, 369538209, 209555372, 434925128, 926404997, 401775857, 130334794, 611000040, 32379656, 223355023, 853771291, 291486010, 130539466, 230597212, 240590994, 965452471, 408947225, 814376206, 677432633, 497556942, 224458288, 592122020, 656203884, 256262884, 593955878, 464439415, 809103608, 490282453, 636987222, 828077656, 697168717, 896146775, 242189254, 988743549, 256458716, 722026054, 213532183, 658783895, 519430965, 161044220, 535964484, 279990432, 722420559, 837471692, 942410694, 308798667, 457924036, 48087701, 7249594, 618841946, 696369133, 594890102, 240794584, 662344542, 721162238, 810767140, 573530642, 644453284, 405384809, 572375396, 351806948, 503358073, 554108588, 576352012, 61224407, 172607364, 784974733, 519027371, 896387596, 436951095, 959734570, 302819729, 111183355, 151163647, 620400192, 970859245, 653623317, 585556979, 722474633, 84909377, 784949590, 137811591, 270100742, 786640047, 909317236, 209096602, 893774807, 282883890, 96919537, 941027410, 877198232, 568114914, 174432543, 837629112, 472596144, 382022010, 313567573, 409672953, 57332717, 507936865, 332733200, 768005174, 578184166, 153874934, 835046460, 808323826, 562332980, 422426243, 185627435, 320461025, 520410722, 455484318, 620522339, 178171997, 58561123, 162351275, 475679580, 221775980, 146936918, 601972044, 764171281, 953291959, 60808159, 534249145, 1080541, 594818295, 31494179, 457422106, 292271427, 224967338, 867287072, 486342224, 97043454, 793557090, 373665235, 176717047, 61169459, 391381967, 276686901, 70348045, 533163041, 47236753, 691741360, 958881878, 170781135, 938228867, 316028291, 422072477, 295225855, 719043370, 251088651, 851026293, 47232876, 432733671, 648470705, 950702209, 57825849, 832456928, 951724536, 804337450, 346257959, 970380891, 525349284, 484857081, 429087352, 262904639, 686753407, 849895715, 679588282, 982290252, 483388761, 542455990, 599099279, 869186053, 63604578, 534869036, 45208756, 551249456, 821644263, 605015591, 765128836, 195078780, 940832022, 655915372, 591049176, 864492373, 311239049, 213404373, 465442135, 963211110, 462387966, 249800400, 599177664, 55238485, 405742933, 941094965, 282384401, 330867134, 821692567, 298632294, 459898714, 523062770, 828970974, 210461951, 973167168, 919614265, 644739483, 844014250, 418920151, 841304766, 885493404, 935054611, 850419963, 275973725, 668322383, 33112230, 6300501, 776412816, 413518099, 267062495, 551152104, 24889301, 932948355, 246859412, 404995203, 192412755, 462045875, 962132421, 345447969, 791168388, 910896019, 820252351, 943541097, 520319209, 825032020, 714826582, 992141526, 759418458, 421200412, 398509422, 930465525, 685928110, 862931451, 754123335, 297907890, 337648527, 459348089, 992695240, 37218579, 116688325, 374673112, 951525928, 172676385, 152964034, 928393160, 908929462, 324682931, 607799452, 375968505, 614377785, 932709158, 482668487, 204511376, 229687068, 783156056, 981830647, 53767814, 297307799, 752140934, 149097310, 627234814, 150682209, 506627572, 10479461, 894253228, 242091095, 784224373, 971905576, 864875938, 81664426, 961699107, 746243303, 192523711, 247885501, 599548430, 913682471, 783133230, 759941916, 399763970, 319237422, 556134259, 811712112, 923214968, 739401670, 783517044, 732067126, 989928857, 991024648, 675236456, 31179052, 98086575, 552112663, 164308646, 829379015, 870305727, 448222107, 827616289, 637137131, 667766281, 681314024, 18331347, 142539894, 883418118, 157945072, 272063152, 908855788, 64165393, 695557908, 216071606, 297543283, 879922547, 522703430, 81500603, 937209700, 312524475, 469999248, 416981636, 50694697, 708274078, 283593183, 981090597, 445039612, 879875873, 790594617, 944480087, 189125734, 689635136, 393610975, 742998458, 464279056, 386146017, 569076655, 236344032, 851107765, 618817731, 504758739, 57589342, 965221241, 974946394, 780285183, 609862565, 673141441, 352779011, 659011251, 296184276, 183869309, 14355079, 12035234, 108443501, 543100054, 999967052, 418212308, 215447884, 796877142, 94820335, 800543499, 134429162, 678993833, 685182070, 196350361, 902171447, 181121340, 328182313, 889520033, 340937714, 433078218, 844906697, 581085558, 643740455, 240460204, 472060399, 693487194, 894767385, 878238549, 346558418, 844908329, 913857968, 397253585, 944354103, 25800803, 614247607, 608396834, 153031940, 752381551, 557295144, 269175641, 747070573, 521457431, 492172723, 360039791, 567696308, 216549942, 687469678, 347666935, 64263714, 362265987, 810132672, 177023389, 160190925, 899651089, 9016222, 375406593, 154200516, 829072335, 861830533, 600975955, 393094105, 853018915, 91387020, 795843647, 414186431, 380666556, 914436380, 654286814, 969979769, 61444626, 767719150, 758586425, 265745463, 618505160, 482188080, 410268187, 438059223, 598961191, 885039524, 556707195, 751049502, 678989136, 377999351, 530125672, 150353417, 984935079, 437513736, 98836537, 918938686, 346795415, 871008823, 764239283, 649510967, 868079554, 80625688, 540085930, 377855080, 567148797, 930707371, 909205523, 669805375, 4636707, 280639992, 84006152, 516961022, 574468513, 946882704, 132476977, 33656471, 396435515, 617817274, 927159432, 742738675, 728576368, 445476858, 347631848, 733299623, 654808267, 989037347, 224714846, 448471829, 87499852, 757160811, 205619198, 680584461, 606277343, 515894007, 57992198, 892312790, 768117135, 139836851, 245858038, 981135524, 248837267, 30253199, 747972914, 982286094, 592693171, 39471540, 500669044, 205811682, 654623014, 7369138, 61480191, 580616953, 679530537, 234539610, 315960325, 181905985, 833491461, 521261086, 690181810, 410370986, 432338472, 931602432, 886613932, 558697564, 88325810, 413029959, 323208641, 743770921, 94537681, 780684098, 858418326, 541707204, 606260165, 618575215, 68113493, 370643500, 343556901, 718005161, 460875091, 25581481, 693169126, 961921918, 893565255, 768910733, 893997772, 912270127, 330540332, 798081800, 173674054, 108449413, 130408408, 815439704, 498293869, 72740564, 162249769, 656180268, 645006146, 78275018, 741925031, 377018637, 948048413, 555451183, 116470977, 589047996, 41696044, 686835080, 779404052, 743352654, 572293446, 713252987, 56295882, 249942528, 870534455, 849350186, 606349565, 825094856, 50550948, 170743430, 997981977, 368687283, 161578348, 202159997, 987891270, 384224369, 920609865, 906977397, 292594450, 458552843, 855917191, 19498215, 646399492, 668162885, 171487813, 970151386, 947760775, 144058678, 620414770, 127486608, 771149701, 51675213, 162107300, 437652845, 385401488, 281220990, 604084236, 422572869, 224929731, 655605403, 535014908, 24009543, 501705025, 917399795, 399494929, 5725062, 393386301, 657962070, 560383830, 761467383, 804093051, 536075721, 885627040, 35649806, 183970876, 616039045, 668597380, 948153867, 792873516, 222466903, 280195302, 706149018, 457262532, 77047268, 714023209, 786191956, 486920327, 127962239, 161330968, 312650802, 967098475, 82150260, 358390874, 628514252, 869376259, 184663368, 944978518, 128771223, 119226193, 936686718, 772726025, 769391595, 898564264, 320903649, 170356327, 253861013, 321899455, 995163859, 794709303, 667951649, 441652106, 779334649, 67311841, 452910082, 267424258, 231142624, 348266258, 565016233, 614622034, 512321395, 214495396, 523893932, 599264058, 976566893, 337718652, 798464612, 841701681, 824319996, 25947796, 52827983, 114202702, 864048770, 387083210, 501319237, 946331896, 314579891, 217533219, 830283626, 964853449, 242245105, 114905780, 925890923, 86421196, 668901235, 247157849, 964951664, 292410729, 865794236, 764552610, 934444400, 834243668, 799906478, 738478491, 510408989, 479575045, 473306637, 489734060, 312905317, 759812469, 630871645, 679935865, 982475190, 683139327, 569571241, 507910435, 978944613, 674641401, 798821358, 775762257, 752866081, 995975048, 268029764, 349210436, 571324359, 112943944, 660917836, 357976570, 566745780, 478340547, 759324547, 105042706, 36671192, 815350800, 689309864, 445329495, 520836187, 189025179, 466472619, 322852807, 554441935, 119696505, 719432218, 651531717, 534642426, 760208095, 174143407, 278925585, 565173872, 481405954, 222800705, 573071305, 562009590, 845277948, 323309396, 950195679, 848254192, 344906446, 359957419, 449127085, 408286566, 384530522, 256604957, 963515333, 513911454, 498209846, 932454228, 528934179, 276503, 378460423, 640255305, 277460999, 416009539, 526778367, 254216197, 460863270, 688201559, 708335727, 995414194, 527633631, 556447957, 347184750, 726926946, 361846287, 601432511, 362911026, 714045910, 800687128, 824847915, 143606894, 824611197, 87049247, 679781103, 912520590, 436674450, 491623740, 880827083, 818751664, 950905581, 598650751, 327744881, 535748381, 686254138, 439793570, 566054625, 399170679, 528151144, 216412141, 306218915, 336268012, 329947606, 294073947, 152457180, 15665994, 9332369, 964528460, 590211595, 69454969, 274151593, 593738957, 613113141, 416515440, 715477147, 62236218, 743058992, 268314531, 258655653, 251251383, 717035584, 688079608, 273650945, 958536088, 243559823, 322209767, 949853547, 638805862, 589581987, 258473282, 576285877, 52731890, 147298501, 950057914, 718197784, 742177277, 203381420, 400822738, 386897738, 474719753, 502414743, 325751725, 886204762, 805419714, 229941569, 240013207, 513124814, 68927704, 453654237, 612010364, 672125721, 522664576, 957806933, 793516386, 131230572, 281300953, 646935381, 372336195, 870074454, 606045637, 765474438, 581525263, 678382460, 481996789, 436872521, 610729194, 823113071, 550161439, 787639798, 846948767, 371368593, 999308846, 19415940, 669060375, 334843809, 50294624, 653502021, 912698132, 779781298, 84922873, 736305135, 654597906, 512790847, 417514800, 846927071, 609578593, 325864086, 75223907, 399911836, 749112678, 124131158, 430590981, 271153148, 7120775, 555765789, 744358325, 536466725, 356273844, 270310721, 882395856, 145129192, 32087069, 219050526, 53856004, 177603441, 31285088, 238193261, 373830920, 885416858, 439380917, 34432612, 487968230, 11864563, 744710715, 447350156, 559327953, 288277076, 215117061, 96236922, 987767176, 669565114, 574688134, 812397754, 908152932, 745970058, 948468942, 300360093, 475020662, 615194529, 957429115, 399956782, 723467342, 101577767, 159438174, 335843376, 432407033, 451604613, 739825000, 572247588, 498733520, 183847186, 996370956, 341782857, 256059340, 747209526, 548675750, 5096648, 473069865, 82274378, 628360581, 979281512, 862861308, 415171987, 263167946, 978866259, 809965666, 612959825, 776983253, 141434972, 807356066, 857586874, 661534934, 829524220, 727689129, 462266042, 389137601, 850279319, 843064075, 76392116, 253126848, 635757714, 474155798, 66263238, 550286458, 97281934, 894291849, 804565811, 844273274, 972053866, 87415370, 12570653, 750648292, 481488331, 261294367, 968869302, 720575055, 195362414, 197906897, 885695285, 42393625, 956294508, 233012367, 638818444, 628138137, 946007259, 317083164, 578224895, 17558134, 376036623, 246733915, 68584100, 889558281, 369422233, 343292052, 13401713, 584299399, 890155582, 10878757, 937357789, 296602967, 172414519, 309096302, 853159617, 925910060, 442684723, 612569292, 974590943, 631362240, 486454224, 543008007, 16567417, 106191910, 622987953, 93863952, 625447619, 186220308, 293374746, 890045530, 884006149, 651843984, 695320587, 962149604, 111554964, 461677892, 411774186, 924682049, 312853185, 355718995, 205437107, 520658630, 559518766, 470115455, 679509699, 895894503, 304351317, 701813379, 207055688, 374038900, 94660339, 580446454, 595462536, 282505943, 611423843, 501164867, 60826706, 2055529, 713768793, 457658560, 834226307, 466579548, 173192292, 804236139, 1629589, 864163434, 337725526, 85410794, 488886648, 863139229, 571795343, 176197598, 861042854, 862563787, 363710845, 559762860, 741530979, 498134120, 581704027, 256813988, 872124252, 164120360, 797412609, 222039546, 868910198, 57014740, 141984254, 842290139, 827172119, 318906618, 468136164, 746700543, 515765597, 947491593, 841820654, 73621963, 341611536, 551286627, 566575832, 457347207, 130328534, 337313600, 938924764, 301562399, 645926293, 889640775, 327846991, 32769236, 792318262, 906145575, 96089917, 542870709, 69424404, 797195274, 358242795, 922388119, 685821355, 370473916, 807069356, 394733837, 497432628, 459106468, 601347884, 790535348, 982251707, 549457946, 624069474, 290535952, 834186608, 421978571, 890529635, 755293857, 453800882, 456810435, 396860584, 762927831, 545310756, 529024437, 903551323, 742983791, 677153318, 115992747, 938495592, 804506259, 444409295, 245481763, 342722317, 7469373, 418595000, 701157401, 930056297, 446487593, 881236206, 486405436, 92578969, 938147165, 310783203, 189495902, 22107334, 492726323, 489415941, 18457809, 424685410, 610489701, 941866520, 647815170, 317171073, 170568766, 53326084, 985835563, 318013034, 545364316, 808666854, 861331602, 509244127, 136594198, 553569522, 746495568, 994755056, 856779691, 515230423, 964616497, 14407067, 311408122, 325622956, 169142461, 635742038, 553069744, 322870127, 336707932, 608810322, 253626643, 184019642, 226184379, 899515420, 783141407, 729215000, 284636249, 93912007, 160136164, 987500875, 783731268, 644889127, 409847104, 534971949, 459945328, 258104299, 658034897, 316126108, 667043174, 634563151, 82173060, 645791971, 310783785, 358321210, 666806616, 486474196, 703962386, 116478353, 179385079, 670503466, 300190919, 888247495, 190365989, 611918589, 122211479, 389975566, 237351925, 213797176, 102721111, 709888884, 539425968, 345953197, 290074152, 514351643, 889073574, 270874570, 658658698, 663639961, 567379488, 906691115, 286389220, 770162679, 805030858, 13597252, 438175135, 521686878, 188103568, 394389336, 768249862, 503598930, 768584221, 555958690, 43814892, 119299222, 510165452, 999555177, 920934971, 40944369, 104764229, 257431492, 893793990, 488710303, 500145191, 406622029, 487578304, 167437080, 408967969, 789912298, 532111795, 969405148, 46172333, 377691767, 982679520, 155850618, 86188194, 563333227, 800376384, 658638445, 961897803, 170605459, 744449737, 58378526, 480468586, 654924740, 464423866, 163517277, 141297148, 3723679, 453981756, 419019239, 214057901, 48849621, 435730296, 227262955, 446210966, 271175217, 731251151, 25967950, 329177935, 296374645, 305570761, 386521672, 110528551, 497788988, 162111821, 434443458, 794922649, 449130997, 225247867, 567281101, 685799658, 269511760, 887132979, 636830934, 162064986, 699516297, 131874161, 497365404, 903493139, 780956177, 154355735, 832640809, 74872127, 285294252, 618449100, 953074099, 310126736, 329854948, 874524255, 869038451, 519905910, 55034477, 141136647, 693822201, 765755971, 295416206, 290545119, 745789312, 21298549, 98404031, 85123880, 107828663, 542987742, 344145646, 280919547, 554345809, 696490384, 596101840, 364549940, 755332960, 533584058, 281709952, 953430515, 947010402, 860861880, 491825020, 966367866, 533681229, 639981873, 616689919, 677285413, 593927501, 815565164, 404657120, 821354973, 875354810, 510981699, 505569358, 612470934, 40334239, 425403994, 458130072, 736665472, 349366442, 489913150, 441349513, 362888717, 793548168, 404327512, 452091109, 980520185, 442845116, 874721470, 527151499, 373877410, 588101062, 673589097, 841494516, 898846674, 61152986, 426630903, 866418141, 502805260, 349395037, 547327548, 426195683, 857555511, 499060215, 359998317, 983604229, 316289221, 422736083, 422692349, 707056873, 310903001, 171450639, 310499629, 919345016, 421693453, 716086985, 456108960, 662466263, 534406742, 966537430, 427790013, 674775969, 494399571, 893236353, 569239159, 869722474, 307393526, 380050539, 474248270, 140576156, 616014493, 933450903, 719976991, 865167122, 54903286, 245895532, 772581937, 553324449, 954447482, 840413791, 238330802, 653045829, 634975009, 252820763, 559452052, 324027564, 610013375, 959208893, 575358223, 669055146, 917452457, 455547997, 78104536, 254813411, 78590006, 623666023, 726964908, 237753032, 485262066, 293719134, 111793132, 279787345, 999173536, 781191667, 332981998, 393312044, 75645723, 197645136, 855474289, 789674769, 21710457, 29925934, 152543445, 856907158, 722992736, 349525196, 733531080, 718098062, 27251523, 246152050, 326025206, 315860234, 995932751, 696809090, 847613082, 756613995, 343137459, 994508269, 163913141, 503242242, 989007504, 936393174, 224967784, 305448886, 127654573, 255467956, 906958257, 924552327, 251685796, 318216823, 360881815, 683346693, 737436335, 934069925, 399360832, 494408865, 67961529, 217486624, 264986265, 259405119, 850164923, 304770189, 825738610, 930714614, 719452291, 385166772, 104172927, 911921473, 420300877, 994415057, 311286218, 709289874, 431311649, 203982007, 382698955, 672821296, 960565816, 611155146, 934652066, 554986096, 540278710, 317418409, 237130697, 420284118, 690978728, 251181679, 273112221, 315356567, 248583232, 506916870, 451996353, 788886004, 475964565, 652229386, 76189033, 272910969, 713654360, 553312468, 17854553, 17089114, 315536873, 319495438, 362608301, 796810420, 831061047, 298403725, 775774520, 28696211, 56625007, 543864151, 253103436, 176053745, 950855534, 524227435, 407234160, 897271479, 300617103, 394179044, 701877850, 606998518, 494310110, 168825345, 211468509, 104636145, 413266076, 773496311, 316811805, 118452417, 280753149, 863224063, 147411202, 925719914, 265999168, 590675588, 426287436, 836871466, 900205056, 139495687, 973251130, 182410530, 359912430, 91177692, 978292462, 316573578, 187657711, 430001673, 333545755, 112073780, 513065234, 750897759, 756917200, 30882278, 152780270, 848384404, 316715720, 990112410, 232272329, 697059418, 964348159, 441626193, 626167639, 431906565, 710035615, 556710631, 175186499, 93514595, 706517679, 144178583, 615798227, 915219981, 465013155, 602877063, 841555474, 137656217, 704543143, 76331322, 898940558, 52686017, 568397865, 150509890, 106254893, 290055347, 41091685, 889705340, 64314432, 25475895, 865625709, 132651981, 143615866, 164237820, 127099629, 674761541, 522367770, 538841151, 475949151, 371941325, 425085803, 900023646, 708172220, 303439760, 120853611, 667416503, 872568092, 797836794, 555963381, 890696628, 698256641, 34916947, 513869074, 645708899, 569116560, 593631688, 134430347, 677942638, 336947926, 889929586, 84166246, 642341496, 992762886, 340075667, 662525451, 693348580, 815067672, 868084112, 62391523, 257443727, 515548956, 550063363, 969180895, 52573732, 832014469, 629836040, 21858078, 999105465, 566633930, 319987653, 556002782, 636888118, 880371807, 104458318, 679419166, 57720480, 138352053, 786332169, 718403563, 656976857, 344421827, 867366571, 547982860, 630891910, 470049195, 948014166, 120880258, 2655714, 18993700, 515236403, 291320558, 419799192, 921530790, 382677607, 493241522, 166052610, 723783722, 857069006, 177573431, 251011060, 787163222, 120242644, 120276922, 458292100, 654526707, 160541599, 130897430, 315784947, 996883014, 497699040, 402798093, 858020440, 664249484, 732484273, 719261064, 259266782, 173003486, 392974841, 983416046, 31562911, 61957720, 242226083, 542193227, 676472381, 473227711, 996726239, 71210140, 232910076, 923691565, 544204263, 670212462, 33483944, 874132997, 259750045, 107250755, 389164979, 322974305, 499054953, 832269164, 634496442, 948110807, 849666010, 82577441, 644462348, 277798516, 371591071, 101631099, 474650563, 792604226, 875905031, 870333478, 361166728, 60451375, 305271284, 834916473, 259450458, 562293132, 370761028, 53990844, 177728321, 978195054, 996761855, 283937627, 851453762, 519001672, 254635454, 634167477, 82232616, 894835653, 366082485, 632137568, 479855470, 626102427, 615012421, 985423649, 752002468, 405932900, 894920268, 968806113, 885022363, 522266757, 16244993, 191526790, 500201777, 358330154, 860472755, 779116036, 555284853, 958448194, 721934412, 252108689, 167352808, 449746017, 136514333, 885625715, 765633974, 497295891, 907982824, 519226773, 717262668, 526387462, 949895109, 267945712, 555715970, 885336260, 874654056, 189560847, 911598445, 540424853, 147577721, 998220965, 646122476, 821801417, 160318469, 394341952, 409431392, 704118973, 869655594, 808711021, 635426568, 139402627, 211089134, 69434309, 280997497, 425083866, 537648461, 114433083, 695708308, 39139345, 532889827, 583606551, 31984312, 714475811, 571518635, 138585021, 891077488, 133337372, 346888334, 163659737, 452883003, 195046719, 612397915, 221296929, 360726495, 843788828, 50435937, 938530829, 4503308, 209625911, 791145258, 318182609, 560520168, 507257957, 557420303, 784527616, 349731493, 898970228, 730404223, 907251414, 118660369, 59956733, 317337872, 33041741, 255175299, 140572733, 828180572, 868305455, 839349596, 285300312, 521199935, 819135113, 243324632, 730810286, 286066830, 645890339, 811824820, 777493957, 714085643, 811511294, 145720154, 318877680, 283899978, 832935033, 824243487, 812541055, 371520441, 191999313, 339427399, 785196197, 969135788, 19270388, 148952188, 819273514, 798861229, 717636914, 918738219, 782333413, 736994664, 899632686, 424576665, 982685585, 367016273, 934467328, 106816319, 37108321, 164622838, 336417537, 695101576, 520833318, 599996841, 766991362, 857942245, 339147346, 360149246, 191146320, 22518351, 978772432, 18003873, 454546544, 584565376, 893279229, 612087510, 354532887, 322267067, 578354503, 71089916, 843150689, 960102470, 400581697, 424639821, 155303447, 907872874, 207440258, 604386502, 379847540, 971354841, 32558419, 944263268, 993122523, 450043314, 451593289, 438129342, 65085630, 386678518, 661619816, 959291503, 399027499, 100548763, 720313357, 118600140, 891093397, 909747735, 47908230, 703586998, 827823915, 660000565, 444330382, 643010014, 318288503, 269241221, 842296027, 95380238, 419252626, 559492748, 455253084, 195767496, 637300810, 897831957, 921736913, 757550107, 811118605, 87623209, 738951574, 108798627, 540728598, 305465770, 623190703, 338848576, 446406397, 749813848, 174877459, 616047221, 557344750, 156602279, 808094933, 226041681, 96203867, 68989940, 862703485, 314138141, 536447972, 36233991, 16927646, 694096392, 253117140, 604532726, 297611756, 412768461, 839171971, 404657332, 764671134, 281979083, 14722943, 581497983, 675148491, 287677134, 162485787, 999669512, 689070344, 744820534, 698737259, 246301877, 118622102, 504183771, 337176924, 448889335, 732589220, 716485210, 492357981, 267791572, 124149770, 756681772, 497525399, 344523282, 401106862, 390038408, 203699598, 642740741, 442121994, 742344979, 438286324, 121250046, 755129428, 330593174, 833130945, 612408243, 906064748, 200072834, 531326610, 763672948, 122867322, 855384303, 243056612, 191002089, 738042280, 857761747, 543219496, 85703099, 349730961, 331869814, 114318453, 758861430, 548670857, 965366156, 815333735, 869419732, 168639402, 229310096, 594312776, 758248809, 444575682, 138511911, 241813360, 995793643, 326539950, 919882454, 899248472, 868859935, 89478817, 930393138, 244419221, 726002883, 943317437, 539964079, 451988030, 549524384, 650941423, 225369974, 705772442, 195108513, 640177984, 412268189, 793065124, 748254124, 417877801, 120107150, 376008135, 637847221, 632201193, 416465375, 724740862, 278299995, 679425943, 356886501, 876077658, 986555614, 383767299, 811491372, 812646945, 864964349, 162979115, 984337923, 341271248, 29782413, 164462924, 320123716, 239431662, 879511437, 418803734, 318322268, 548539545, 715046634, 970361887, 262577478, 330591282, 3610054, 210602122, 599724550, 599500966, 565704373, 869932246, 825255113, 217547596, 626142345, 95168358, 137918681, 140631207, 126170736, 208927103, 837989094, 943997603, 747040954, 482919924, 761097100, 575017554, 294653933, 616761154, 488280982, 477472777, 131588867, 318204499, 204592880, 18108797, 949843288, 807597956, 283642046, 257601738, 682480136, 934606036, 122801764, 677650373, 566860520, 284252844, 613713460, 763799903, 274554813, 451627049, 800438704, 893139151, 696506326, 910580968, 175655646, 263946177, 780420868, 279839036, 336358624, 147778120, 754073391, 80016270, 64165178, 7921040, 127931779, 212657175, 203405483, 553462967, 633099544, 398024247, 462430834, 927913745, 641319966, 116761310, 743634457, 911984183, 13889988, 314204566, 298089826, 681961909, 250415066, 160674220, 476312517, 547226292, 668229549, 305383478, 457377871, 599601514, 760286034, 842901445, 157649461, 197334154, 47054978, 735682179, 640786181, 327543142, 889521345, 785401533, 330880496, 883046328, 595974575, 902299074, 464867177, 280273838, 465727541, 555983264, 457897802, 498743637, 207295580, 366300160, 278469406, 51996351, 352766955, 769783126, 675221275, 336592060, 626316276, 31505699, 406416154, 143495147, 212825577, 556497671, 617126638, 531730748, 201953360, 658936978, 193876136, 671337757, 687858800, 394500927, 616232764, 279050591, 291134071, 932712863, 477879707, 29351470, 20382846, 677140679, 625123306, 247768437, 686407747, 923913894, 768312187, 32002882, 226111401, 596193326, 713237651, 324335038, 572039578, 926247837, 521512942, 892900616, 443820184, 938912124, 57189769, 87191710, 353351013, 608403295, 693219919, 163691927, 376850087, 864554633, 5407463, 777342341, 141984302, 207263009, 348009849, 322659917, 2405288, 123896020, 392506461, 415406687, 27404940, 833700540, 254249638, 474921405, 240724501, 571175335, 696653898, 52495841, 950087564, 977312525, 423612536, 855337906, 737104283, 64342819, 284059794, 708379569, 853787951, 847448672, 456726942, 56197671, 895627120, 49469018, 621860894, 846137763, 21484518, 968202984, 714763236, 855684686, 947161366, 323760957, 984544704, 666733597, 231436836, 956226393, 885287990, 392194687, 102951927, 56623442, 416390616, 556550774, 55759656, 854611252, 585134795, 88867504, 220148576, 186510050, 168204606, 329807540, 332919119, 763072286, 198171783, 175853850, 816409875, 15335351, 6818770, 38476361, 773639858, 908880369, 786501751, 747982746, 61689576, 577279145, 871754763, 343866079, 256976161, 52813924, 439983702, 53606864, 551373475, 152690234, 554041094, 375732826, 387328256, 74234274, 964330795, 733909126, 841057805, 470662709, 884183303, 720312231, 357573238, 922976615, 26032981, 411311472, 568365034, 734403537, 924947872, 67457319, 960288197, 878101440, 256482306, 680436427, 362550605, 720897585, 995147739, 308915302, 554570550, 235175665, 915469391, 943826646, 439673521, 77528388, 541604687, 344612475, 240364508, 509303597, 635457740, 222624663, 945319937, 838784742, 49970283, 48697042, 515858109, 248362017, 724528734, 372214767, 402330447, 662081865, 264913929, 423634954, 793388059, 78253014, 526940278, 225281082, 51104141, 233061363, 568731590, 882389936, 316035823, 86518515, 863362249, 726388033, 635778480, 97580183, 194452056, 663472938, 984464909, 378182075, 385200499, 260427830, 920945290, 579586903, 533143882, 279448541, 626770209, 359783028, 222439255, 605212681, 429591594, 785804076, 591704437, 975590935, 629895502, 259937041, 240540982, 518866379, 279296430, 219422869, 57011141, 198782513, 190019281, 430432780, 75078404, 992942750, 936550659, 882182949, 574730576, 757671772, 874059070, 395945675, 984952127, 331181005, 61361136, 334990324, 494757060, 663032736, 262139896, 799670967, 683484131, 954440307, 8192096, 976669024, 367899054, 81294308, 948991185, 188528242, 354547373, 675359503, 607903514, 592174761, 782947917, 503590739, 89066450, 630648764, 57108907, 667315, 24082055, 202813159, 461117618, 170863025, 933774333, 58006395, 365538071, 205639661, 613741358, 640218803, 930830230, 51684366, 207665374, 868723337, 258983174, 684796649, 226735747, 265997274, 778549344, 274955638, 848921482, 354470851, 171518411, 241116521, 446815835, 369608554, 661805974, 807687980, 620647852, 642644003, 273729894, 307587354, 97933545, 564042353, 743675649, 642438365, 642767109, 330984764, 869952142, 502350878, 602444395, 39826612, 592191800, 968440039, 504079818, 427760376, 983555600, 309553683, 998224912, 443551273, 103192975, 502564707, 8623959, 247195616, 383551120, 215347772, 423377667, 39497797, 176602408, 761580229, 415994241, 752628522, 458784769, 139036897, 792244225, 805394881, 207610196, 656633489, 258617872, 457099969, 136507485, 767361528, 814678364, 844409844, 398563243, 685712190, 674758757, 437349231, 646686257, 947146096, 274763156, 51918652, 979479522, 904951562, 289618398, 474250240, 121985010, 787212750, 262958840, 531239583, 355934149, 470211263, 66800447, 484617272, 222518954, 898103317, 399830261, 916872368, 616103371, 13918523, 370644683, 295312931, 909674075, 558353443, 559618130, 641455051, 228462251, 554477574, 277841691, 375930018, 212726631, 20251026, 700877394, 687960128, 550027158, 877434308, 472084921, 671704736, 906346124, 5941821, 149814742, 753219800, 614648261, 348656414, 904281520, 670472839, 519123050, 736095183, 716688178, 378732368, 291098056, 496095949, 506222922, 203260467, 444962675, 866601919, 472177811, 60436050, 886793556, 88431683, 170333487, 711568453, 820895504, 619693135, 205454146, 623548189, 805665424, 33442242, 248349429, 739310973, 464569194, 388534042, 755569160, 60493543, 980679609, 449236213, 526302962, 760788876, 87082794, 43140910, 99165336, 950655723, 760754612, 733256142, 942885963, 680530084, 886183563, 362504574, 315656828, 514541687, 982352667, 10575220, 32153778, 771616546, 202197119, 872042653, 389406627, 410033346, 729091932, 526069736, 802752989, 782308875, 201003478, 981136754, 556691735, 725058895, 166380532, 415514479, 322779138, 886524657, 697902551, 22758244, 928899849, 502286435, 662067002, 837508069, 847483982, 104996233, 389226660, 302540001, 931044947, 277078333, 647761517, 122823001, 516481777, 58436518, 128631950, 549874453, 389795674, 834544417, 810776615, 539832037, 162395673, 462344465, 934627382, 671632614, 540451620, 971582012, 240044756, 768224068, 130932227, 554470778, 613963055, 455425986, 378713450, 654713483, 52839975, 505596763, 446859742, 307921466, 651564060, 796302919, 484261797, 473836767, 860954769, 955456559, 764946522, 586567417, 150552752, 233325764, 193842838, 802233808, 125044964, 364655050, 960985125, 832464685, 956926102, 6731277, 227145470, 98154826, 448873148, 593401780, 78122500, 733843970, 234082995, 130418068, 675934992, 986163410, 234182919, 444207774, 438342065, 116218537, 917185297, 10953577, 568819662, 831855799, 113179263, 862377525, 812377179, 509519018, 418995953, 154076008, 542976631, 579292824, 710874381, 634497443, 914593734, 784968376, 929671954, 462769950, 80613657, 133450134, 390211052, 877185625, 246700245, 357538696, 138167684, 135930669, 447027995, 988235365, 583717673, 633974900, 107632246, 104232937, 331533379, 461922905, 328137211, 172678238, 935794616, 28053674, 909233758, 639948157, 268319838, 110480462, 379565697, 403095820, 127789680, 406717812, 937891526, 731401635, 764827478, 19861603, 996666021, 59074454, 354324121, 592248240, 83811096, 518689440, 367006428, 734627440, 335984845, 565227611, 261097916, 624758484, 615742789, 228433309, 623905552, 255703694, 729845643, 481306913, 574162404, 549767877, 619122508, 845323706, 708625696, 125481185, 981074635, 698213029, 68636463, 977414950, 173427703, 853205391, 532912125, 220492696, 334265931, 51424889, 559205202, 957872649, 936291267, 448801928, 936420702, 916313099, 255346503, 993317485, 829161014, 442275599, 257984853, 477059485, 80789817, 590271367, 966207491, 291346928, 740344452, 70662722, 730624751, 874453278, 171748781, 651508918, 251831762, 43982282, 26235077, 154981328, 643126906, 445148187, 510826170, 990714356, 367891235, 41191151, 449487073, 828920107, 939760833, 450935136, 564096510, 846791987, 715185396, 198544529, 369242259, 385948860, 861093936, 80532220, 794653817, 773256216, 165382284, 703829973, 838564920, 759160004, 202221339, 303817662, 37213611, 80504045, 727423123, 758422379, 187144529, 643941117, 245059263, 522453974, 547891273, 249063159, 970363953, 841284194, 52394528, 148880672, 569343935, 558144277, 894637297, 643863993, 97155505, 611979591, 994576195, 388431153, 417014447, 152713337, 299837700, 956926172, 98679690, 949814770, 707614765, 87918698, 504021747, 248563809, 858339205, 506879458, 439914935, 495854893, 23783333, 595509326, 59723773, 963066379, 690153640, 297876702, 359796876, 11445107, 343898859, 231718362, 588449254, 375144658, 269636805, 254776890, 219581491, 186708799, 995089910, 967411910, 286262327, 154753654, 812941180, 738467751, 339886540, 69163745, 80640120, 460801617, 753051383, 811649811, 616195487, 167975848, 562223769, 959708196, 798272328, 940773443, 136949895, 553264497, 844121234, 897855605, 159068814, 505188166, 568169808, 712986184, 95210704, 901622862, 903374552, 158405058, 302578995, 948198006, 451361042, 170916211, 892053617, 693955983, 998507195, 54365308, 136526452, 350630502, 687877736, 107439983, 377170773, 732142718, 301072297, 812998196, 330025561, 487765140, 379419946, 281136728, 216187028, 867486445, 609724334, 276227258, 759012923, 420635621, 468141598, 447648026, 550846347, 498293832, 64644597, 811700478, 744400503, 53160756, 985916728, 281895378, 334024966, 752492816, 294947808, 613781604, 691295789, 703535272, 749581916, 926897905, 646703230, 712824485, 745964042, 787403248, 898740524, 225892520, 501673605, 448325651, 555892151, 75775006, 311123201, 38203093, 217109112, 222657804, 816013726, 630026826, 484916559, 715319225, 350279450, 849921399, 419484766, 803523202, 277049286, 621043522, 819194723, 863043258, 522730608, 579324947, 297589823, 372901256, 873909631, 774996664, 893838652, 473955617, 228560740, 624310821, 931578065, 535015729, 140788538, 652625154, 9806843, 875897806, 406786805, 675476563, 220661442, 772355521, 33551481, 904211289, 436328168, 124928186, 650001181, 793728063, 542866703, 125015246, 60543688, 778344977, 429238683, 124423950, 284128530, 81792574, 279605643, 621569538, 484981520, 401813924, 150126452, 442288439, 873351213, 13657408, 806253353, 957692210, 359132575, 756794811, 679121283, 942082135, 139587835, 889846721, 833440674, 646712347, 199402476, 518605926, 923603806, 337690681, 32021606, 966141261, 401314039, 314120482, 227423044, 186783492, 769141809, 776694331, 32481954, 103884320, 805266412, 525732869, 27558202, 750715246, 199737846, 322392399, 27280455, 842532269, 256845714, 513203464, 112198102, 465094225, 751681512, 396764105, 460004106, 824561551, 682081450, 222919551, 866753275, 985893901, 19910462, 458379740, 850760939, 657882394, 539431248, 838244342, 96105632, 814167720, 26630719, 363169024, 267104620, 551631458, 268443075, 575169625, 284266912, 435651506, 70018287, 961152972, 329015283, 428168368, 803487984, 786974205, 279359259, 430590899, 454988220, 256381978, 795615983, 716533420, 733963234, 941495477, 367252177, 201196517, 771254992, 819139479, 801838501, 460550272, 967526051, 922734208, 846032435, 494138433, 958068354, 195855907, 568208073, 524780869, 561031442, 87451, 134227278, 212414926, 362440457, 400057671, 719210678, 683509667, 641567689, 192433230, 947760566, 862182058, 434118867, 756532674, 77860094, 256416606, 733922541, 606915786, 148612204, 748189990, 968423272, 103837511, 970000381, 27552015, 125242268, 586045653, 433439916, 742987315, 654320483, 381281462, 518049545, 34123888, 810968298, 698956867, 965885714, 618479371, 384654308, 824216482, 904763591, 461059749, 810003490, 33351542, 486560053, 17094868, 382287472, 541817222, 80329721, 676503101, 275558153, 823103, 820127571, 803942378, 263382209, 789926595, 45201694, 920895515, 608346067, 899665730, 229890136, 900626414, 884613310, 656573968, 297643283, 308403837, 683060465, 504886238, 981939360, 988846877, 474078648, 587797737, 892945014, 793111724, 702450977, 93147762, 484201915, 811581541, 815651872, 916922831, 876339576, 329344250, 193406611, 657285505, 2379038, 486415349, 931714711, 743798976, 722893850, 588960313, 385710970, 785708604, 424192211, 352943589, 187742153, 111687811, 679809090, 611570069, 504403570, 610268966, 692165363, 943375177, 183264224, 892599723, 53742139, 79418633, 806247879, 808135140, 395274306, 832054660, 433142553, 411332821, 939415152, 421450231, 831176129, 31495715, 670092369, 3392694, 35502108, 982989500, 866542811, 552673229, 315486861, 986069565, 899181518, 14912494, 697161352, 22043468, 753426313, 915793525, 188087943, 368469751, 524579784, 660380834, 45910857, 116790973, 98976271, 123283733, 405104275, 650063905, 429921760, 239922479, 474114382, 737821952, 434275211, 887430912, 203980392, 108454540, 323432645, 158008713, 925386998, 297942521, 673707080, 546063136, 661199830, 551543345, 722921994, 881438921, 163741829, 803912708, 478223364, 297100932, 811622633, 842369788, 667388703, 470190892, 255048055, 619318677, 417893422, 734497420, 824204576, 956969435, 746828132, 135029952, 228661906, 312351166, 833340605, 112932564, 179187149, 911100028, 793696358, 387567200, 702447511, 184355571, 477856353, 677653968, 247019786, 483558519, 478924288, 640048565, 952311093, 310358439, 36208950, 82526513, 888227315, 864231611, 57469412, 815198605, 845628902, 270619748, 158707422, 230248617, 518011234, 645796038, 698572199, 664855930, 73390334, 574980839, 663968208, 350867982, 119215244, 337026518, 863172262, 763412554, 750712523, 471072326, 264665298, 940157962, 135293271, 789018385, 731903327, 31833647, 760543685, 950667829, 806151933, 432569743, 940844271, 993972859, 65952998, 302291464, 229593744, 35158798, 765868083, 707138044, 269262668, 675143792, 978963757, 115151084, 420280862, 956738043, 407417339, 972511247, 727053314, 610692090, 702714781, 912463549, 308815888, 245262767, 80690546, 952586628, 588283408, 392073788, 209483322, 605196279, 12109172, 579622988, 460385627, 9347216, 684694827, 162915727, 732890872, 334049236, 587963984, 637444296, 931485008, 207451444, 373122751, 638204423, 857628190, 829856633, 278049431, 540256987, 768407275, 891383056, 537759286, 872798825, 760573101, 899599890, 999024254, 428775959, 244342253, 139882719, 326598493, 9640563, 143823037, 231344443, 157701068, 744044194, 911773631, 346577039, 304763010, 626679121, 488233244, 742384258, 655542232, 596741244, 447998173, 250196870, 593733661, 439817481, 199395071, 615741209, 25661403, 463958954, 270950152, 91543304, 869659734, 878617527, 535516653, 766255662, 159065921, 263573380, 941323849, 483199287, 421423240, 990963415, 161775920, 592381912, 933964816, 420028042, 397290600, 867792648, 606817790, 690225319, 252927194, 953336583, 233277911, 148026382, 325078585, 816410684, 30400642, 601538803, 408893820, 667713954, 309069713, 346716804, 860852788, 650776117, 620077197, 781417810, 157295733, 529300443, 253930231, 948067866, 675235211, 936749300, 253187820, 392658258, 462497913, 874821691, 246257222, 466279975, 386337098, 71350893, 705507294, 883477093, 77658234, 298758559, 273700092, 802035927, 74546812, 964495223, 489550652, 836791556, 566575664, 907147681, 456766581, 67783742, 875624774, 273014459, 234733301, 667780, 379798371, 741225913, 688595663, 342828322, 521329660, 518358381, 64697153, 940713916, 441386530, 576890672, 876169231, 385433675, 107563575, 803992853, 353305874, 143035480, 483736354, 986237422, 141125539, 339222261, 236588687, 12221993, 404965653, 315364372, 793319712, 396279540, 937953478, 294952983, 457274105, 801561786, 990040320, 164358653, 800820123, 430804396, 960237783, 651337350, 932458869, 319656763, 969741202, 257385209, 547221800, 30492066, 270810147, 838982273, 600199315, 316598113, 526287729, 347202522, 481381888, 917952818, 31603306, 497602163, 999366734, 125601988, 189518659, 191230700, 941267944, 560599710, 284337651, 103959246, 295046256, 450971894, 220558480, 227279347, 576635335, 717651042, 956025606, 405141207, 912900141, 764843319, 642887265, 287622329, 993141260, 372039321, 603286904, 290678431, 917139225, 67066592, 804202383, 279781940, 910233567, 12299259, 125979377, 530266156, 378482400, 331390804, 828024161, 594263654, 599116825, 124147976, 313637455, 66290934, 67576448, 99170111, 164003828, 654219306, 473425839, 932784262, 374551791, 989586870, 694164680, 53030335, 85671398, 495525282, 208670932, 840871507, 794431699, 12521971, 172122113, 312847612, 954594064, 276824895, 756992055, 315069504, 852711678, 309198960, 402506433, 835807778, 971473928, 813468365, 303502219, 105905679, 72917837, 751932289, 418182238, 785605021, 896271632, 470235457, 594912722, 144272401, 645987911, 679360335, 230357496, 701022419, 311908701, 959350277, 272790588, 630808021, 790056441, 829996170, 164936730, 220302776, 958428268, 965406566, 358750228, 963539125, 484186866, 48835677, 468836507, 49936779, 740340405, 289236377, 106311575, 861461729, 111582020, 570044882, 348970469, 714744079, 808307087, 26641417, 382791502, 763410781, 655888846, 673186477, 7128689, 952811753, 129334006, 70731003, 603423104, 337975305, 460202635, 53483908, 293882223, 825297239, 644998956, 449891368, 859282902, 266231867, 247482441, 9947019, 725725135, 65153912, 666860899, 641213834, 728821079, 162480878, 425046473, 233211263, 652672988, 323619014, 826022198, 380789343, 252185196, 405564910, 458537430, 107111709, 737320555, 484849687, 438593813, 820756257, 167377365, 656011182, 935127768, 390134219, 299794836, 932955241, 917488505, 224866114, 749978020, 528575557, 213210243, 764358709, 504762593, 524291288, 916219161, 640781234, 155918168, 11263677, 291551865, 921646184, 96608170, 799864762, 648182737, 234090116, 911286363, 615048207, 998243561, 80401768, 965918196, 792671645, 831024602, 637393204, 303606988, 892797150, 925902644, 563605925, 653352983, 334535337, 862206318, 847156434, 209066388, 782820009, 424945498, 314311544, 600846393, 492097788, 570153658, 54398571, 27267469, 118409258, 89852404, 984154152, 885022035, 351673186, 623947694, 453519499, 959727276, 653716399, 320118244, 596257680, 326592531, 509691569, 429911511, 475343345, 369836851, 91195102, 565141691, 323325651, 358549288, 271887357, 583391344, 858590610, 28740557, 159141633, 980911236, 657705685, 718807249, 552057367, 731964238, 305545175, 659642875, 249382106, 61406817, 7347282, 551255481, 404235184, 871910785, 992863742, 623839329, 52509102, 682051481, 404919281, 898079708, 900781707, 245194404, 288357490, 837467625, 740760798, 551208976, 959220166, 605157352, 15272657, 763522224, 351063608, 453192627, 946300450, 118150211, 610358217, 554165724, 870513603, 714115429, 389763385, 788486880, 792286644, 513072517, 692713293, 891635743, 815907121, 999751255, 428266249, 600270362, 804873396, 124759733, 313951163, 824428110, 916990016, 441734304, 831119131, 416208470, 943362120, 857676265, 692314689, 569541712, 85083419, 704487727, 3316098, 747846748, 795058017, 948975532, 85285330, 460066279, 191843994, 209974007, 420223829, 310206624, 358402149, 143484725, 412436662, 859693434, 667658711, 988029042, 647007891, 123511967, 685377931, 138246796, 404921186, 27523196, 415740234, 447714681, 38023127, 342649404, 871466184, 873483756, 440642864, 257070644, 428753805, 184149020, 934249272, 92680415, 912617820, 845927355, 257889548, 787664026, 298093661, 941709760, 785530238, 91538972, 345532192, 348877136, 899438102, 876160375, 779771424, 368409540, 379334746, 224195706, 173872843, 182120735, 726944525, 198218932, 270250033, 73991526, 108625804, 342138902, 778821826, 634224374, 282936324, 915943112, 69893601, 76633412, 640006858, 275091823, 83873103, 275945913, 301152610, 56960500, 528035479, 920169620, 393981207, 405329659, 740325241, 99486725, 242542670, 97518454, 416392492, 85237711, 413827455, 322870487, 107957678, 828366467, 409901501, 629430007, 421810080, 729053496, 370295008, 810266815, 712261124, 755631, 629076133, 676927157, 712526821, 144995711, 147998197, 984248566, 31058590, 765248858, 517856432, 341502579, 414839098, 155296823, 920105251, 100433543, 453734003, 106279398, 102339260, 959181742, 953617917, 925038985, 835447638, 541005619, 54363016, 380734961, 717447026, 998641068, 877435800, 475211775, 858893673, 236269306, 951626615, 968964657, 611578726, 353694529, 178403316, 308490354, 24140224, 26789823, 929942885, 659966762, 441515906, 531376566, 563351260, 16508832, 634376515, 252128919, 339193579, 193594270, 755298601, 900179160, 513826510, 668429679, 364657601, 593844357, 543056760, 573981927, 588158695, 30165060, 332132612, 769143769, 61320127, 125515493, 883415159, 239905080, 928537265, 322756421, 330140074, 267446541, 880578219, 447381411, 894443871, 50366859, 202680539, 546498722, 860533372, 321368565, 624626230, 809791027, 432233785, 801929795, 356309046, 814209465, 890479776, 789685277, 511316124, 974657854, 284413208, 560011479, 856042364, 844627615, 506658269, 641385208, 211126593, 873868112, 750893998, 6246637, 404128871, 322299878, 359936966, 411065318, 919269369, 264422881, 49411795, 387239477, 579057721, 139850013, 671821660, 927956380, 924583709, 695387711, 874319582, 845320722, 975813958, 405852467, 613307198, 320772021, 524277711, 684396393, 215656448, 371831939, 75889331, 554890454, 505736943, 895601705, 713945726, 819857077, 280799409, 27676483, 436379321, 910759425, 591336349, 203992292, 862594252, 931108033, 614405154, 816643781, 655419741, 996456703, 924558437, 807709877, 713064871, 415625972, 242663668, 71440248, 954441960, 460516774, 804772457, 498684897, 312223121, 788937613, 453907030, 411147258, 10063021, 607515934, 63125095, 778089758, 982205546, 488642701, 540664747, 33534993, 95237833, 439868851, 97136382, 488166613, 579656542, 905403470, 354391540, 479590456, 710622292, 772178792, 118403215, 471573380, 387735138, 194857271, 691645184, 449661919, 940582497, 61927858, 327013823, 179701296, 365639332, 434123794, 601966230, 366830417, 25718911, 663355577, 288344541, 499470109, 571447555, 50964777, 978665731, 915834870, 157569665, 152155630, 252159057, 183411586, 136761346, 399636922, 26222373, 265384651, 663862238, 461377491, 256624342, 880288331, 178029284, 667741196, 858723316, 906422770, 426074705, 881754895, 319858523, 189883279, 950312770, 955280704, 249724114, 863208403, 183760211, 892310, 27354082, 865553353, 199786657, 791818122, 823106188, 860843569, 485520172, 172428863, 435525442, 615812626, 542795547, 724698123, 360261149, 520083419, 755459383, 734536855, 553199004, 222314162, 225110567, 582239596, 575278521, 793495665, 991285828, 547548174, 49804332, 3665531, 707432090, 569753063, 631413551, 400068569, 420934697, 853522832, 442180799, 18759691, 782709248, 288269017, 53869013, 855717497, 376668273, 69110027, 364584182, 106262350, 601500521, 135813534, 730395045, 721422709, 974399520, 79790642, 274538764, 892240817, 244918056, 997526842, 830692053, 338304920, 569380030, 786063093, 735319341, 137294980, 605125599, 294278419, 884572751, 482410167, 818203775, 192057745, 899788981, 214422415, 156155359, 818833515, 289087297, 271031370, 757065705, 919023779, 390433140, 115714870, 671894401, 385211539, 904545825, 888959313, 641948431, 658132572, 294767090, 74832447, 265613588, 326031573, 164660330, 82908961, 95763504, 856019052, 603063771, 524074693, 157172561, 685374562, 504719486, 413650723, 707877136, 283741867, 300200325, 133170086, 368862422, 803264864, 782951773, 591909029, 937726904, 902068316, 706132236, 911816161, 88448258, 208043048, 710405642, 304290015, 661008416, 893171850, 106268755, 825386989, 778115994, 528235217, 31955451, 985549251, 503631458, 232516332, 658690812, 860550984, 172887070, 797263982, 653259750, 107564387, 437022170, 297503213, 319947280, 256289718, 656322524, 910486056, 229041398, 800511988, 204303767, 53162486, 901066105, 330907455, 995053322, 625616171, 27183740, 704303878, 214356689, 583955031, 378328943, 266866192, 555983558, 332478837, 250061003, 367983366, 134114485, 976264760, 13414931, 383647223, 808601611, 446848725, 38360640, 412511155, 620818708, 483933372, 185860677, 835295166, 435732820, 469629734, 698097946, 650613475, 593475503, 383625004, 511990023, 159471534, 311520049, 882388717, 344825120, 150880088, 568400607, 127833872, 407099593, 372465144, 656819923, 398164427, 70282632, 420581362, 14344444, 288968054, 100450356, 952705590, 96309286, 693397770, 905824532, 11711635, 367171003, 723312051, 973595034, 337724176, 219372647, 559730852, 125465471, 744378781, 883285742, 274755653, 835182011, 819749732, 431176168, 956022143, 72689645, 837783377, 70546198, 592745204, 974879457, 838570982, 201722696, 565627617, 43121410, 677089599, 901184554, 228779433, 47422359, 405159685, 861928579, 185643896, 654034342, 613889861, 468156073, 63054355, 651198309, 216788067, 998291193, 122738748, 876184110, 398340198, 836882481, 50953707, 681290623, 406057756, 338185424, 42565277, 811407400, 221284337, 438984603, 69548980, 25192220, 619918402, 380948846, 504291068, 620216139, 667609077, 779295219, 881805589, 301168220, 273356119, 299779598, 856599546, 488434568, 315413366, 547863310, 269966034, 306501523, 804596269, 615477276, 666619332, 273560527, 190681574, 83676085, 641111241, 50878840, 557763459, 865006814, 757673203, 871355626, 472317309, 113768782, 415925912, 412001899, 693609869, 33181067, 742445527, 706835833, 689467384, 204661495, 674881154, 920899610, 662150716, 337520864, 235693042, 135792871, 271240621, 758844416, 940361853, 941158115, 800936921, 541299120, 931776239, 234399820, 444687, 301019347, 996911450, 236400875, 593363472, 818448698, 97818692, 558305487, 984777751, 900658173, 10451982, 759177152, 264252711, 23150665, 533987745, 185104480, 716287466, 441042390, 683247803, 888125485, 570489369, 175408489, 987823846, 453997744, 626908259, 212271729, 701546626, 231434351, 475305318, 764761681, 793403611, 541807461, 437357358, 763066917, 841588622, 295485753, 795200819, 627708712, 125033683, 520742012, 828649644, 717379252, 701735016, 178707129, 394889728, 986998679, 978503753, 497596976, 406370726, 355872680, 850796261, 127942682, 538935976, 333738987, 769171241, 248926528, 385250003, 425395296, 741124661, 755264422, 635003525, 182877967, 450768228, 284418374, 219911476, 392991924, 278413745, 697542863, 962125082, 948741843, 600599273, 79922368, 244216082, 894758826, 335662045, 36624623, 935550122, 715176642, 628061115, 28998048, 797897510, 391500967, 460514226, 415796187, 834612860, 604778468, 443388149, 246842275, 399113237, 981798529, 201657162, 844408611, 260706583, 869176941, 303145702, 437271506, 995132409, 912307938, 411935949, 593330196, 326940832, 296831387, 249027248, 668105184, 278268533, 206550603, 426769203, 471553558, 823512927, 467791065, 842963691, 8462534, 637558715, 973979231, 734272340, 421563249, 578113996, 369332000, 352005954, 34561049, 372589710, 538374397, 216491836, 996943071, 366861223, 33852285, 554650011, 47169433, 765346875, 403635454, 252215208, 908072602, 695728234, 733235261, 513122668, 800596855, 440399346, 221283786, 835862784, 762393071, 627190010, 212691138, 287908543, 93868446, 815774165, 292420093, 566247217, 792123484, 121789664, 45371248, 688753998, 244682120, 135230546, 984634127, 99552463, 160428758, 451840922, 489437554, 154746301, 286664662, 965982744, 275772415, 20187018, 34077660, 663139698, 325230263, 854573474, 500682086, 382170298, 260910072, 913895776, 638351594, 579548507, 810893371, 161153471, 508672118, 359217015, 475403564, 717945536, 885058120, 348341679, 266571924, 434315211, 613999622, 555930895, 704057869, 845633468, 87741295, 73030424, 901466718, 763523843, 313985288, 389046254, 537224340, 696329242, 803899765, 228719726, 273314345, 829522563, 76205235, 280769628, 172679001, 348771410, 702992001, 534347201, 688231312, 697594986, 107199799, 652129799, 891999812, 308408855, 498648240, 871082955, 331987146, 670108737, 457879189, 169615066, 121766712, 353444772, 804243990, 505069135, 272356208, 822297844, 182415831, 63402481, 639178344, 221400071, 704518770, 189918812, 302064019, 70887930, 722795700, 662880483, 782587843, 865247743, 883678371, 397908585, 236986467, 775377679, 337906311, 862919759, 837080076, 979303300, 275932371, 2837707, 14751396, 893784765, 108419323, 459189615, 382069291, 777856746, 491052543, 999626218, 236384119, 914313408, 24797334, 616242268, 569359557, 96501370, 46116266, 60912844, 497819431, 216020748, 249572044, 131404957, 988698051, 693050724, 778584245, 486052492, 368028862, 491734361, 487047892, 802684840, 437243052, 935990625, 95340992, 246082827, 666953783, 289029101, 993870895, 520028799, 238457299, 972752776, 289251347, 211722080, 943365070, 837785636, 100652442, 903038108, 197856127, 868279189, 93041529, 533759143, 998361587, 870107758, 707495049, 24072075, 704452106, 53459106, 317310881, 456573539, 143403659, 699164963, 362983295, 305093232, 143192775, 681583196, 127540804, 163921056, 47654177, 673278583, 379751882, 11229166, 92673660, 287715549, 25800545, 132319713, 529344008, 110963966, 348951048, 561602852, 627980264, 771985090, 322478656, 867936174, 548808682, 567084736, 852758124, 633839838, 920607672, 775730373, 8721794, 579635223, 5363676, 630987284, 663259476, 153330840, 545177282, 518839293, 725995942, 297757793, 626021196, 17765862, 99466553, 928566612, 612524099, 590051209, 524672542, 335272174, 819481434, 368984591, 717415733, 777144219, 923067132, 541521862, 892062192, 147918243, 41445592, 335889487, 797478177, 879763198, 341759123, 688737923, 634404927, 869017433, 805542603, 924469848, 877658982, 493725226, 704153845, 569600421, 591366982, 872086443, 701398105, 836357888, 832819374, 948890555, 777503150, 680985598, 671830023, 501474034, 734756467, 497138604, 974268243, 404554356, 96226849, 824710685, 740185403, 223723521, 670813281, 423405393, 940716320, 88599245, 165662796, 281986330, 652525100, 32443987, 374292668, 609524565, 47432884, 802466062, 625968730, 210340040, 754531321, 300559698, 295857516, 953739735, 122839938, 458732938, 552476594, 773209278, 841794491, 377337187, 500930464, 256833889, 298584949, 836106563, 129483665, 894684028, 877709618, 905041712, 597423634, 607868387, 767140318, 140837075, 930807502, 282428766, 616482623, 994686048, 306919592, 379312720, 193265237, 101767199, 517662500, 926219296, 26326210, 305554977, 507841209, 958901082, 822216986, 794725887, 185329734, 215505664, 959790279, 989720755, 299460432, 64122968, 140681714, 169026236, 65160147, 816253178, 969274144, 226459137, 25362257, 179951975, 980175290, 987556065, 588805111, 270350492, 310437419, 833344144, 364429467, 657682666, 16247967, 778519064, 450994390, 210575932, 169048473, 822739121, 678496384, 733372300, 681543435, 519964433, 279000209, 287343194, 917301519, 548915660, 686795575, 581527426, 357666599, 366254362, 291003284, 14564469, 880042180, 373523315, 322419192, 186366445, 113215999, 429635896, 741128312, 221921234, 575154612, 930357708, 651635685, 622329735, 217035311, 226670808, 197071229, 48039494, 836601194, 929570569, 812865024, 550085800, 907024235, 782143654, 393160848, 301365708, 888348982, 744135849, 34649609, 189695493, 782594545, 116558536, 280584429, 282551179, 856975668, 129181818, 863758270, 288717378, 415613813, 470391365, 335300098, 218661921, 196661648, 2835606, 70643074, 518136778, 406629926, 854782298, 473892481, 276974282, 347228454, 578867113, 189035410, 242354639, 348026924, 64844438, 384831156, 820150445, 66182755, 150728580, 108371748, 481180465, 98751161, 137488601, 175132030, 66344463, 910402752, 912075538, 722144912, 275135852, 823903551, 665513728, 872480776, 34847670, 807148678, 104942611, 13052308, 929364797, 801311086, 93906454, 385176232, 225226203, 183979046, 222179782, 220706745, 427776471, 362249895, 629227621, 492605327, 784914153, 562807475, 27073795, 381748165, 272213552, 576689677, 707978292, 220756228, 972146450, 279354740, 425968095, 265237572, 351079582, 56877619, 693346453, 160070768, 693741548, 133484963, 252920390, 364993241, 333297481, 483578211, 521881444, 609465417, 410310330, 946937461, 208422303, 372481090, 451417545, 193785525, 795348608, 620838902, 979124082, 193233182, 245007536, 18069314, 676504193, 733630230, 595568482, 917376476, 974750563, 443846979, 632012052, 305054567, 332350362, 235964077, 233609111, 946737344, 397197244, 823596078, 70167479, 471118356, 123759170, 513810092, 558437354, 483962900, 555677644, 448434669, 322726310, 765450952, 223255141, 295273643, 431255670, 39879867, 458663001, 658795442, 420835219, 450981549, 692164707, 856844747, 989000194, 859584242, 571730447, 198545379, 877006030, 491683571, 330526156, 445701099, 94094368, 893946102, 654174557, 458016617, 359290730, 234253650, 610000599, 150971913, 708771235, 192203659, 596852189, 182184788, 903349774, 60648730, 144194935, 639819528, 934075630, 307720778, 557128262, 333989660, 971468505, 269314611, 433700125, 951287933, 851639917, 171319068, 73875423, 389440152, 917599020, 316352768, 769404864, 574670278, 195270271, 506846638, 903134624, 393600362, 212026396, 420854432, 493729010, 637823352, 430218434, 861551435, 195974930, 768837691, 31950219, 111989436, 505321602, 744620596, 392539289, 803266425, 830341447, 247278310, 913645873, 315673310, 905428237, 602238613, 489684607, 698988952, 703398837, 271019093, 841353110, 944206039, 579684362, 938144208, 271699062, 689807136, 444292568, 109836942, 819028701, 829429843, 397303725, 515567263, 533608234, 59884297, 246580789, 715546539, 623490223, 766145377, 579009191, 989256503, 962013849, 344703214, 825997970, 238825570, 787484836, 863661235, 490314850, 644958272, 853661401, 306908087, 553205946, 370697258, 318947308, 487335715, 857140734, 830887813, 928731073, 175511771, 567320543, 859926835, 475471405, 692324555, 590998807, 212746318, 270844059, 413097263, 658120842, 352597252, 611611381, 498764753, 288279502, 451080118, 955469960, 599724277, 783952743, 7830670, 291942251, 563522223, 512033632, 110617169, 646826421, 450186328, 527584675, 762347259, 28848454, 401427381, 550435170, 495292807, 286112490, 278359973, 994785838, 498228866, 968968355, 852466902, 446496882, 286913136, 788644492, 71680826, 177022868, 27900994, 715689744, 881051992, 166798901, 71977980, 248703292, 868721903, 442927431, 430509837, 570250433, 435796964, 347262099, 810394119, 962050673, 193729453, 31026463, 217862717, 137201010, 749148434, 34152547, 170701174, 635064075, 526561140, 98512959, 120714229, 35232622, 709008382, 886072235, 555203645, 444523966, 109178509, 217303672, 498100768, 232185264, 514720786, 912459010, 978926219, 182311083, 347990164, 870218202, 475154532, 128136504, 184960428, 902474563, 232495590, 714275767, 498350579, 191441315, 320972159, 330070981, 489316720, 718563287, 945415425, 768170798, 180770072, 766515303, 406229163, 837289358, 678165132, 360977744, 516240, 779508759, 858095692, 396962936, 426606736, 479266407, 897500728, 86801244, 242784762, 325768850, 298123616, 42812997, 306492346, 157824151, 458353143, 992100425, 574517874, 567947339, 380435083, 987620755, 635865587, 873843382, 145337582, 471522847, 833280940, 614159848, 484813083, 10327812, 13408674, 849356248, 619106763, 810923729, 419664936, 272023416, 109692081, 362357873, 534336722, 23746579, 45332519, 471705706, 947896996, 142860247, 396735200, 533710793, 238205592, 209158078, 275707295, 954798851, 968226265, 137308023, 924486944, 657324459, 641356211, 610749469, 7287394, 329538874, 377760538, 677820031, 687582531, 560430894, 813361172, 177957017, 6229203, 109644490, 704168059, 63175436, 897953665, 322483085, 801502293, 804131832, 403216294, 380877856, 773644268, 556493797, 772717712, 958835592, 534750236, 13655774, 40989054, 562325846, 142152803, 103152370, 265906735, 256730176, 577442949, 13968098, 228023599, 43791701, 596380294, 284373239, 894802836, 698288501, 497380555, 513614921, 592214583, 638261726, 732974356, 553700683, 271323657, 400620943, 723164801, 293902865, 953264032, 186025159, 732430837, 640449641, 804167892, 705484248, 546596807, 317767685, 273995467, 702785661, 800374222, 768432058, 139228378, 864712899, 738937490, 376608099, 20521241, 614057496, 340397227, 759051712, 113553394, 30876083, 606126746, 510060129, 684389912, 912742083, 145009260, 973972647, 936030735, 426774895, 510908889, 10833547, 25573083, 801569851, 916303473, 489431265, 330201108, 176890399, 791272237, 864535458, 36430827, 152270107, 41994748, 761130058, 755051811, 573803633, 251489084, 8223358, 813084033, 160681700, 411397849, 270683552, 172058924, 145580975, 2648668, 690446489, 136158665, 926725391, 942612294, 453405682, 902036671, 15943938, 280153898, 695557458, 989874973, 595144853, 38050195, 624752436, 667725523, 265675049, 482311452, 877826692, 16098709, 493535830, 37753507, 838307694, 69153562, 677093545, 800645927, 866775426, 665157287, 795833858, 181082683, 418584797, 701923213, 768594056, 432401689, 746359686, 319915331, 487989739, 428956630, 782501754, 138882272, 769214300, 200237136, 793441656, 257529142, 565769339, 808907776, 15339761, 765601501, 968676134, 238331982, 906768467, 324980361, 82676597, 480275296, 342641778, 516719188, 491508039, 104755918, 812294250, 7910383, 309480222, 121082969, 862439062, 469500189, 493870013, 932850012, 682694932, 304213341, 887073645, 861224534, 654482446, 701413636, 699535785, 656053933, 56556748, 21839356, 14729928, 112606308, 452904585, 896065676, 412638199, 696909865, 114385612, 727629138, 479133208, 197845528, 22799414, 575086525, 884039446, 975844296, 508688584, 329552631, 179263930, 609603142, 779414450, 182020150, 956940972, 368125011, 535527741, 634942441, 180958861, 193321890, 903900866, 917568435, 198824703, 734428280, 627120360, 850167613, 952417989, 290112325, 866970504, 593069663, 996117481, 37232752, 662571550, 398116885, 65619452, 153506210, 406455449, 552553397, 268109497, 90184410, 366568007, 945146483, 657625934, 209083389, 938330129, 493336955, 826983038, 215474744, 522468926, 901811068, 595158544, 507938194, 536822936, 92374517, 612118876, 469888850, 119134299, 415230028, 717281336, 889827571, 633759511, 940831282, 332000604, 291039799, 502903431, 157234675, 899017037, 811085622, 925369054, 41156144, 564865163, 187856200, 682670040, 804630787, 37317315, 410852491, 260433732, 601800948, 965755092, 24967211, 976069321, 994897782, 831918366, 473061910, 205543015, 243665672, 205478015, 912573470, 608540400, 255255328, 979234710, 826883742, 702851027, 22573938, 173923068, 274550213, 138297459, 911509076, 172151686, 534217844, 822112293, 159598139, 537829314, 64599498, 697462815, 36160767, 545205777, 140793891, 676529694, 867025312, 341689277, 691243108, 213561095, 61180381, 429368155, 383048294, 79882921, 269075863, 6853604, 595518763, 301494435, 183676593, 399081498, 130740327, 768481716, 16245144, 844220600, 827018091, 760766743, 17241948, 790564859, 960750048, 251608061, 826156655, 685680244, 874017318, 232772314, 231397846, 33652749, 78142641, 496406728, 393736749, 367318675, 953162252, 677835494, 844734491, 6700614, 799562309, 357400564, 379930258, 248226895, 585418303, 208883742, 66138892, 373711736, 464167804, 231068454, 443244048, 526786757, 388667422, 92254768, 462663722, 556460781, 301328888, 133938604, 142184015, 974832294, 579457901, 785557346, 172647017, 656227759, 558946610, 128483066, 645218911, 78885399, 84348754, 259325932, 206301284, 249955759, 922022218, 952105017, 168293602, 811901733, 573964184, 331103657, 954851445, 432051548, 248757281, 447359917, 750204069, 509389205, 173635483, 654240906, 963894467, 176743368, 766111095, 808183300, 382303576, 198851671, 299001708, 378146254, 541836417, 347108518, 987526374, 8098317, 152253964, 755656013, 651665031, 571370063, 811317736, 7614150, 549675539, 493917204, 173822484, 448143176, 319129671, 155768858, 46405920, 256380786, 358579804, 542483923, 133092987, 202853395, 914085891, 608653999, 790492701, 118655752, 775409613, 356071835, 815710739, 287362717, 371955994, 127786743, 478711272, 181604508, 587165543, 544039928, 844228306, 969211029, 698893632, 754310216, 177354200, 617318562, 20371086, 126033965, 188105062, 475703302, 712662703, 650222842, 612236304, 142427842, 224341184, 385079681, 160451442, 524728040, 876892201, 976290420, 505306245, 899644551, 308008252, 984551012, 29164344, 179430005, 171878221, 474791553, 406638678, 103084940, 963572205, 412132741, 960675129, 468502134, 446116727, 916668583, 322737000, 175980067, 158998033, 408942548, 303354498, 157245361, 175373187, 837569834, 983350228, 350399982, 586816405, 194380015, 425755099, 548239840, 372625616, 285352582, 455414429, 707835070, 444608945, 939731582, 639967979, 45500033, 190144048, 818240653, 874801240, 202494490, 403164116, 65163056, 815874549, 847558698, 990295945, 338645410, 874149375, 86865031, 420322857, 504856502, 791557479, 591094689, 177156768, 383538978, 41646507, 906287496, 445497420, 176034272, 325480994, 921328577, 21026245, 815059417, 798736336, 121981921, 661646660, 374585835, 517758463, 206552229, 432142818, 701038497, 390729214, 157351995, 897017002, 897106951, 307858206, 23793282, 288139199, 684544850, 884577371, 453432929, 111344091, 724498324, 990292339, 602407606, 861471568, 55785479, 610183660, 931058356, 853775842, 145547189, 468057121, 285133075, 505727482, 16435503, 537477193, 659403103, 167257647, 384074744, 962731703, 115209996, 712023355, 719913403, 529885658, 311611164, 372949153, 625297040, 640309020, 950900301, 975829411, 918770212, 846588083, 676770085, 294118172, 297494402, 871522659, 47748546, 700653413, 95938693, 27266543, 209693603, 4226788, 343601018, 644272130, 641936379, 215328751, 219604625, 63451984, 620848765, 269703449, 208384175, 363342283, 172501225, 49241310, 808152205, 639662972, 800772166, 947683044, 651962113, 358159992, 5435308, 801141057, 65008711, 781848562, 309480725, 764429441, 118984594, 563611353, 875003079, 666145584, 697913533, 25684217, 240459197, 332755595, 371063221, 728438264, 709299360, 583699025, 652471995, 616521154, 477017388, 892883486, 16640490, 968578129, 537611216, 317108370, 752422284, 140156247, 404769758, 44286434, 101638096, 484780172, 895280889, 1231843, 664337417, 254111051, 164500998, 774384047, 341292714, 536433068, 287118791, 407191168, 870491390, 334938384, 114091787, 417245752, 159564010, 275047853, 428724715, 365736738, 682207144, 760290585, 870050207, 742894739, 409211523, 199524775, 201285496, 834543602, 651330480, 26082219, 549955000, 857316087, 565374681, 727169989, 332160096, 23728687, 41201227, 330288799, 444860876, 853032607, 398532977, 503642045, 605596653, 497746922, 647521091, 797372891, 944148826, 960249695, 579509663, 278847633, 968914368, 842594345, 491095246, 418580487, 723982853, 873670506, 657061080, 427840513, 461304029, 529731505, 248042244, 468832066, 614001824, 519815071, 632150779, 47343500, 95877537, 360780280, 391784087, 92428339, 260382256, 170304090, 46327143, 88692558, 209760225, 29491748, 208474195, 127479811, 620245043, 251753115, 162471791, 344156460, 844797988, 929440583, 429778590, 393403191, 715234427, 247850687, 68147358, 10813709, 371847959, 660235132, 593818639, 258668147, 315222186, 319131741, 98992763, 608202552, 770810448, 251934048, 609213876, 984870106, 106273308, 68840231, 945643490, 167824438, 560047808, 716461390, 712268490, 446434488, 526135935, 619903307, 408295157, 155258761, 351217332, 282718100, 341536339, 53266799, 397098719, 584932024, 552027918, 357130059, 75079811, 405172194, 90276591, 998136293, 632590122, 821813126, 991975834, 683617206, 436517590, 978816685, 146488182, 189907160, 611671708, 595387670, 799192199, 229223389, 568787823, 16531464, 408547968, 458973043, 303946740, 671900587, 599722976, 37834696, 380901228, 858824531, 867473246, 125662096, 202613568, 139124758, 186723320, 433894196, 765472002, 483702353, 821105570, 545102688, 318079038, 686467734, 442339463, 617481920, 581028885, 865696655, 863097991, 442882896, 69229021, 152700296, 593017903, 323034646, 142061418, 107699382, 540328635, 947274914, 40211174, 332146697, 422784763, 136175894, 842551995, 425235531, 160281021, 453483395, 917401069, 189433383, 614170697, 76759879, 890254144, 71189354, 761448596, 737492073, 999475283, 779667470, 334159960, 67903962, 91448080, 512513172, 661342970, 187853043, 804331148, 685260566, 37605701, 358037876, 711953772, 832260909, 641777281, 606150777, 994577649, 876397396, 192695249, 121637894, 232915413, 824578231, 108504900, 135927154, 398360977, 253758534, 970266207, 553769191, 221180515, 143087949, 777511453, 95889767, 441488175, 592451244, 310372192, 557752402, 276869997, 811210237, 259436406, 14005088, 981730027, 387232401, 699499446, 144943847, 650274325, 726174329, 697031029, 740078082, 204476777, 66037187, 341005502, 609261483, 974516462, 891529915, 160600496, 510924648, 785280610, 551058801, 737302636, 308119470, 112450840, 612740855, 523024638, 984619790, 192674542, 940829147, 717640036, 899348918, 211894312, 744241250, 930202869, 990156543, 909044636, 777679863, 51702582, 777548198, 851111964, 357489937, 896925546, 571708257, 873488484, 728017877, 7278553, 704613886, 333016211, 750164723, 762844729, 975797205, 634526481, 254255240, 274388218, 569552572, 466672246, 410468859, 977909584, 82092014, 711015138, 269444256, 128745442, 653158915, 254255894, 597262624, 919446164, 259084979, 97885263, 302662511, 989769563, 68812104, 511465178, 904001740, 149306073, 650868768, 993172474, 118729395, 7647049, 699758185, 727911206, 414967759, 505886573, 180646118, 660486719, 272434638, 649352699, 716620897, 606788638, 280454403, 3980508, 618180614, 970708022, 549768639, 346386658, 360225483, 685151954, 56689748, 778983715, 198252814, 649910266, 926309727, 994626736, 772559839, 718691625, 940247902, 535705324, 848504333, 104670747, 148708155, 491262198, 65597276, 142945198, 768813753, 299253040, 611889513, 486881812, 616167887, 421877833, 468396420, 168753473, 626252600, 947862428, 488512579, 993847015, 793976809, 335387650, 865700412, 511142019, 77507034, 114380011, 616832342, 621723821, 895968178, 992238885, 70844538, 717915057, 636092651, 537513959, 19242500, 11707768, 967900458, 93460908, 309458713, 541549918, 359801453, 724617353, 867701416, 268064960, 580657713, 300659812, 912633072, 239984920, 896431267, 895477416, 856688813, 868442463, 883848950, 226049826, 830639281, 941808731, 133606715, 324860825, 262278941, 203654686, 389675977, 618226161, 506999999, 827875037, 433725403, 471107028, 20117383, 519248761, 565467294, 958502985, 777514567, 189944296, 351651954, 885093341, 801499833, 453822248, 463466541, 754710760, 66508401, 286673447, 956194574, 894555575, 875707512, 387999515, 551280865, 491922582, 1186448, 50738097, 66536834, 82133782, 567991099, 905302551, 200460102, 284698803, 251969115, 968972569, 177614377, 539199368, 485137795, 762384897, 845302598, 389547590, 528734329, 811702144, 508022790, 531848917, 56928750, 351353334, 237118534, 477539381, 99942432, 627651170, 174102502, 133099049, 764987731, 92449707, 430782035, 966343991, 169866943, 119536814, 590776412, 664642298, 797626337, 585541779, 419636326, 700914395, 218219413, 767856050, 516554787, 402433655, 582459220, 792245331, 32500471, 880389096, 878744746, 596868874, 864180409, 477057376, 346240506, 173109874, 251339860, 294547244, 396130771, 520778587, 719767852, 600186280, 454654253, 834043761, 95567079, 490979545, 528414670, 366316555, 317302568, 531653694, 260456254, 306718930, 330406419, 407828997, 57439103, 7845014, 15476352, 817148365, 937262115, 422373039, 775305946, 841913269, 187709693, 228154995, 126324190, 312071193, 513128297, 568767630, 815151163, 244140520, 463980682, 260175948, 455337535, 582312552, 967283359, 117875461, 693091131, 488790393, 46893254, 625082699, 10858148, 599295451, 160906668, 573144849, 368396675, 405927901, 260251858, 965734585, 198057006, 785635809, 126090147, 873974913, 249220229, 709700840, 696075966, 466598250, 833337585, 401646361, 767539278, 698056932, 94077982, 891233253, 972752849, 896170767, 304707526, 171615299, 807144929, 619417829, 500067519, 886939033, 107290809, 170453052, 522722759, 538033289, 440961689, 27022857, 363640681, 815250928, 607305340, 333340813, 552952515, 334665631, 68274138, 852150541, 275464749, 470409938, 463902418, 158651092, 862804106, 461693298, 424999694, 751024470, 349789802, 202470272, 530750550, 922584836, 926185228, 52895743, 683584376, 156437872, 845930472, 943176265, 646130480, 248927639, 7822557, 472525583, 184017178, 898050807, 940891396, 506798963, 983485392, 389616167, 526696462, 382881811, 274749033, 631517230, 332642463, 254212409, 747839557, 176583821, 151747215, 121177322, 130579956, 717345905, 841386126, 946313045, 465098806, 878525369, 875421947, 665129644, 348161379, 963979005, 170793997, 119375541, 629723683, 617319798, 951620008, 23693949, 609793464, 23571107, 427467528, 866538846, 815505647, 177769112, 118440493, 281294787, 1348396, 285193461, 94314503, 635135755, 250419229, 113375698, 434480779, 408308386, 421979635, 9728448, 46561193, 499887382, 968622630, 823046057, 680147838, 317613132, 938946298, 867439187, 543187667, 963578415, 206300491, 967206120, 346828580, 132625087, 541881624, 966367442, 323630006, 35026052, 823765918, 113902103, 904301724, 514696979, 48752768, 973153322, 199375636, 629745693, 611420942, 838401737, 203978181, 812681289, 267875439, 766154182, 931577700, 444261650, 780646840, 284534309, 515717590, 92984829, 882787154, 482655618, 897155376, 996565975, 368066157, 82848650, 46752107, 603429995, 402560951, 203888030, 77916373, 241500392, 347450119, 446810134, 706433899, 398156298, 388037390, 282141084, 685915760, 541047372, 835989398, 623101130, 400773677, 346181625, 162066528, 236875418, 274310822, 24010012, 690295803, 639847588, 621809473, 664180898, 681397333, 72363347, 197443731, 131740592, 477890657, 675526259, 593244637, 486651821, 939290326, 830314392, 508364662, 267726290, 492285999, 742500832, 191724740, 833129335, 531541608, 735331292, 567056283, 956063265, 525795531, 22535246, 470187875, 223353699, 278592508, 115743912, 560770759, 566709590, 647371206, 316565003, 823123138, 989194652, 347819150, 736416625, 822353014, 5127077, 3627178, 134578564, 422897767, 573469301, 858784358, 734357636, 35567819, 978742839, 229296552, 134683950, 698314208, 825905903, 371782430, 528092127, 998089822, 785818170, 252155392, 116743315, 859342503, 558256469, 347486569, 838418022, 544975041, 387269994, 177931330, 250661981, 409480699, 675480549, 983607107, 685422544, 255863441, 353192467, 391047803, 740409671, 286334032, 142044257, 537948945, 626172995, 72361643, 767174844, 561507299, 568319139, 41457388, 446975501, 575568817, 207375457, 355623123, 465891870, 437008656, 310904845, 324349172, 574178286, 134072689, 384574540, 776499419, 992334073, 92219312, 42044616, 547950021, 543711314, 801557469, 69680066, 341305280, 604035146, 712653238, 125174160, 128573401, 540402890, 517086696, 159644408, 211868917, 396866092, 273142850, 765506323, 810426338, 948288238, 813659082, 246074380, 99527721, 73848558, 228744123, 188562875, 895663105, 543735373, 846851758, 580732716, 354000632, 523194414, 233183546, 817758040, 478819965, 143307015, 781808860, 700220693, 224683876, 745550809, 184579775, 921124491, 415283297, 307713057, 728544829, 926766329, 115100048, 176539326, 27786501, 680644487, 647172810, 366740392, 93144497, 877857298, 410344175, 958183549, 619753631, 28196838, 295494546, 591244382, 60671378, 810849864, 137611523, 351486184, 231693969, 724510815, 134535032, 532701416, 262955091, 643777694, 200430006, 619965855, 778050805, 116839448, 720042818, 832813635, 80784325, 96578650, 817745304, 960836244, 975159973, 343240817, 796110688, 382334, 917025174, 362997017, 400870001, 901715841, 626312192, 852329248, 309558138, 467901044, 322171485, 400126466, 4614885, 236615742, 117462238, 121421717, 576025101, 980668715, 9357562, 235718684, 297318825, 3403239, 843662527, 290454564, 123050595, 290315680, 389450473, 250936473, 227318629, 473602577, 259006047, 398183069, 20995210, 444972621, 957876363, 575466284, 835440675, 920368589, 227010924, 245606774, 770117555, 53663892, 651865378, 819956450, 323093035, 631438199, 551943414, 367585319, 810414859, 824861534, 301516015, 232569995, 829232436, 778713113, 464713652, 151093632, 793202605, 404394555, 470838956, 574547224, 748531795, 63882010, 24672926, 52547210, 370390808, 323459389, 936761718, 273780812, 521531525, 23441339, 674961731, 176341635, 723795627, 162826003, 948093619, 285365129, 810120710, 981910661, 481932223, 297939316, 990998109, 774082821, 743715914, 562643004, 784427664, 371665343, 592085205, 971471264, 760128126, 449986722, 26813936, 325491806, 363984727, 870662001, 688564878, 561848945, 271248498, 31187462, 110994227, 167268594, 569287562, 223821541, 711560606, 34282045, 255995345, 288999317, 202537558, 242632530, 418789064, 235614849, 803303715, 722017255, 445816811, 73566071, 298938699, 137878607, 26658733, 24546095, 55043943, 590534315, 745745788, 803189730, 824619021, 15203815, 239565505, 832843863, 80804645, 675154005, 993793022, 474329949, 248898847, 249272537, 172972417, 977392898, 194955183, 428654551, 288872759, 410573114, 101372645, 951078099, 952577678, 467012577, 965713296, 728683830, 10146310, 631468744, 99291261, 354597967, 204871252, 764442411, 280044075, 729797782, 713682374, 895671030, 312502080, 80891084, 151779467, 5452747, 358585041, 982258393, 597865497, 489093122, 73466832, 487535392, 908707120, 198945765, 973935357, 890004560, 476544569, 743144552, 917002626, 4582388, 578200574, 606347705, 522522967, 69827631, 292728884, 452146990, 255363737, 663880329, 982237830, 292036843, 912042815, 373664982, 888391640, 424334908, 293496033, 812165819, 91576855, 862199475, 338289009, 841923789, 227192801, 867180486, 469128717, 805939718, 595215695, 669615678, 697580220, 621569851, 855588790, 963836359, 957225804, 549762301, 350658676, 506390859, 802197924, 171647778, 616589629, 55237971, 764042650, 9970725, 946869245, 371182655, 744095365, 395866913, 536900914, 467075579, 511096385, 753490624, 776377413, 235843614, 277611767, 811620933, 505473330, 115911787, 967326481, 80026852, 233627221, 949555785, 658827729, 548019899, 389227830, 663905000, 60986696, 805276670, 546260065, 432939783, 261050259, 965537674, 162609474, 264308292, 785388783, 329811910, 280492348, 591805566, 395708077, 981449961, 174280828, 990180672, 269964053, 574756483, 978522638, 795469267, 946062715, 69751489, 594453670, 955223325, 597020326, 655012401, 758294888, 459419402, 712830344, 68981295, 640493171, 535375000, 646885992, 759129573, 831040590, 859424524, 183345144, 695225271, 743062759, 438435562, 713620577, 702071598, 825525015, 57760668, 824419795, 933061936, 435092197, 625830245, 91693722, 418065731, 366080408, 536219021, 860674528, 95044599, 264407232, 638770683, 376141490, 348315943, 891958929, 226836933, 298168389, 238415115, 312859372, 801857561, 581797126, 650099540, 926213742, 501183402, 598403523, 381416765, 259485152, 698047923, 507089577, 49821362, 322267967, 459431670, 612225895, 885110640, 66575401, 653204522, 780380664, 511916459, 770722278, 118845488, 857221072, 581032115, 756611310, 306412302, 238148062, 203307736, 338160817, 606311817, 122654256, 413502299, 868382003, 697629851, 890670703, 470784516, 844518863, 906303809, 596070898, 81162708, 450403070, 895136795, 643030150, 511172354, 739384386, 779439665, 68012264, 211151820, 751285008, 49022824, 98299120, 567745706, 213187797, 359583889, 729450023, 607815267, 77984807, 731100319, 402454903, 6143936, 720370208, 537352494, 795617149, 895698405, 856496233, 302658903, 708661009, 307359265, 632019706, 452707836, 339651790, 386312322, 128608022, 462010199, 59005567, 660366612, 837477493, 526557077, 768304852, 900874404, 104631033, 989504785, 870264808, 86229217, 527025064, 432777255, 543399605, 12193890, 400677239, 199323827, 259818968, 780699136, 333342770, 916646857, 745055676, 548430480, 866001898, 145974110, 551343656, 845433515, 849677363, 301890718, 534471424, 795285477, 791344777, 355761, 284274480, 589191400, 276729320, 383040543, 218181322, 510173155, 154253773, 168964181, 486660406, 905988632, 113941947, 630357598, 835925123, 811631543, 959643826, 685322162, 883696890, 662735594, 661649589, 640794635, 482696232, 534063553, 107991078, 672667707, 867504862, 774705606, 321734444, 774724203, 915393798, 311846666, 238950560, 398068917, 478818307, 632011028, 109723905, 839176182, 123144485, 256266528, 604161958, 733417816, 951452430, 549504610, 947203842, 827668787, 918052497, 229580409, 606693443, 496704665, 895241836, 473973240, 912911157, 977552689, 567650114, 281574376, 908974315, 601142451, 253032742, 611405911, 173993180, 232304674, 396492302, 154651089, 108822328, 101740759, 549059052, 502031451, 495571538, 826763765, 71112125, 657930307, 138617156, 135162092, 761530811, 724475574, 104213117, 612715272, 774708985, 215686830, 569327820, 239510987, 72884403, 842956436, 583292426, 629315120, 809824564, 751336404, 72639387, 325819376, 842149437, 672961969, 780406453, 953102913, 669986321, 894957088, 858798915, 414861095, 728656669, 76856221, 352260932, 760523499, 218309151, 214343520, 28271031, 651904938, 519013182, 637332568, 212141127, 652353298, 710305390, 707651168, 408519747, 910320320, 688898070, 239908437, 190166107, 106694505, 644331701, 230125868, 372598755, 769331371, 330834624, 720763600, 524568267, 307761446, 600311783, 140854650, 166443468, 354171301, 846058588, 533692644, 918479790, 707432539, 119816589, 744403634, 986455274, 181608355, 355735583, 368723220, 520362740, 137330904, 692411972, 344024838, 197236897, 173492434, 296655930, 806858848, 840930960, 67463584, 337352271, 979326497, 974130380, 930467086, 917813039, 875716403, 684432689, 387614467, 170045918, 475284012, 466150417, 349073857, 101537770, 739358555, 908368633, 319313400, 777257218, 892114811, 716533186, 168934644, 699922699, 959381024, 530622887, 717242611, 671436670, 18233144, 399591257, 303793127, 748242211, 805459494, 519743598, 582880539, 471755536, 305723030, 243835305, 12244209, 382614085, 654508057, 216465733, 412576585, 503534337, 594284258, 426673711, 606285798, 520319530, 835989954, 897968811, 952162594, 604075973, 730152534, 660176244, 903486451, 55530505, 427746261, 951414308, 632212770, 453209779, 733566862, 239307038, 325688634, 608396119, 318041135, 927762634, 104826508, 918285894, 817496398, 242823089, 455628363, 280569736, 308873261, 240306268, 587155507, 162031055, 211829409, 854458677, 639587718, 643676541, 413878824, 352279745, 967378404, 187422743, 670879771, 959696633, 998117691, 901918850, 774584536, 750698788, 729633031, 621233788, 528585527, 967079585, 625404113, 189786542, 67853907, 510802892, 339726705, 15623425, 882703159, 227423562, 986634713, 870727396, 183837404, 397269390, 349083806, 678458131, 144234022, 722235737, 368067102, 273033950, 468170959, 67405235, 905368411, 943521618, 235392668, 288344558, 641789200, 950471633, 114008427, 989999246, 970019629, 834372693, 414122018, 800264171, 898967573, 607586241, 31852640, 117151552, 958904527, 85571063, 363320600, 192704683, 38184724, 411780943, 153554770, 705922634, 14089890, 886507554, 195621666, 65838499, 750259123, 721692704, 402071857, 332810809, 768554410, 30670800, 700714126, 342756373, 796175814, 524821224, 201341757, 456874753, 552852432, 456242614, 821776465, 554349960, 675820833, 648450372, 488820860, 622604684, 710352721, 522351526, 876257760, 576436936, 31565230, 923728849, 391191250, 548986949, 402959260, 526063471, 834212948, 844969318, 365705961, 981664132, 258465757, 19677821, 58028603, 121185, 755804954, 908260246, 791277460, 929104531, 668344886, 107464196, 905186267, 182140283, 293800452, 789093840, 401002653, 217361768, 330338585, 88660472, 203168180, 211138894, 9025565, 147897761, 445149728, 484762521, 293813152, 265357786, 328508822, 820288545, 227000079, 99389735, 511839442, 436888341, 999148223, 833796375, 883074523, 646377533, 282850852, 83961558, 617916806, 899863639, 155646485, 55453018, 213884111, 978288639, 516595973, 282504962, 475536087, 95926394, 597102276, 131155603, 992053913, 165510446, 521365372, 128930603, 510864916, 472606754, 303200217, 684830497, 71868582, 422074272, 107474832, 58369275, 220125913, 235802631, 512775160, 58918840, 871456060, 906147090, 939864536, 397260548, 545443814, 105979331, 553400084, 443708153, 796180525, 445580364, 819263058, 705213082, 587909869, 847639457, 883612643, 98908950, 260517290, 988258594, 133038176, 719151937, 542261538, 246390942, 856908891, 483895683, 866411205, 248332224, 61130131, 119411402, 550712152, 562743695, 625287673, 262333631, 90376975, 793941576, 990206502, 487081471, 646814564, 388442214, 664148633, 599949991, 361881273, 927419517, 375816894, 847455369, 939200101, 812434450, 302152359, 49360735, 270632174, 452145037, 121754616, 171124627, 412206230, 504744503, 757389086, 187904757, 413009054, 109634609, 548473719, 391359497, 57337253, 387381347, 697866583, 980892550, 478974755, 90278008, 543918292, 9440987, 813948863, 907127964, 950972032, 37201379, 404938077, 419993221, 57537484, 379378306, 865476390, 929933593, 874572211, 311876892, 373252276, 754391068, 382976710, 609692082, 679288968, 221757873, 497839298, 284128548, 633151977, 413458336, 60270197, 775109421, 859636246, 728863633, 187805183, 787287421, 837853139, 532009092, 512073693, 670595550, 244995677, 89074743, 66816307, 434572133, 181923240, 81579091, 536857260, 717163478, 570588597, 727423812, 99463821, 625087588, 231120832, 288602686, 558369370, 51068726, 339846649, 504721723, 154469024, 979732182, 52632091, 299478478, 252479516, 55783750, 413114318, 629055567, 844858962, 753649755, 268547190, 856701243, 709772081, 239927320, 246592625, 614391961, 623873014, 546453657, 388721223, 544327429, 826086464, 486591073, 571145923, 318908506, 995187880, 31076258, 608287710, 321294617, 370428359, 72548232, 439154394, 930889403, 62206346, 921393405, 169054152, 130182381, 473759092, 125982368, 967900046, 399638021, 441990493, 107352464, 94699958, 209844510, 267734019, 690335587, 55714976, 648843294, 477940158, 767235537, 691147114, 47312969, 212508051, 867521862, 279679071, 213344058, 581085250, 696954096, 133861977, 237280819, 145302448, 457246211, 486052053, 176916344, 141159312, 457561610, 280686883, 909915347, 296309731, 574614208, 102391827, 631420267, 299314722, 74174337, 600634689, 170400291, 826623552, 5128208, 806196939, 346730022, 400963729, 956289027, 868176269, 475889116, 703570827, 838192480, 621948674, 3768045, 698786888, 683865561, 432189779, 592670952, 552451106, 98367668, 63525926, 146088947, 379043694, 955365390, 133082577, 48773457, 5271844, 153123928, 925026862, 491898356, 423950786, 90595664, 562240058, 711315527, 636609294, 865083654, 938988358, 384148834, 156805107, 118541795, 677629702, 510628308, 654642600, 899909117, 124323660, 694558920, 170495468, 314718648, 453502625, 676468346, 357121172, 64632451, 719422349, 438765260, 816417426, 563354045, 899020002, 946197905, 24169255, 413239144, 342869047, 189077719, 855195654, 566401226, 734612527, 369362833, 105789802, 948150867, 719379787, 568904861, 381800516, 394171705, 216556030, 756366693, 375565390, 417390652, 792585427, 133143946, 500362936, 272344871, 328984039, 752461478, 612412957, 157277299, 335948594, 165028351, 556175878, 908214425, 730586819, 336836904, 908012395, 284976574, 494995293, 262810585, 338180815, 861232826, 635289573, 943743858, 398341231, 765517976, 982177223, 216331086, 862414871, 865111136, 556065445, 391931611, 485665381, 374748469, 99041384, 580969842, 766526886, 308755556, 911783065, 763904272, 642282469, 241632101, 786204728, 866926325, 530071329, 748232063, 177827934, 222190119, 994399919, 871873102, 668102812, 545030215, 605387780, 255793725, 910824650, 811407263, 349158534, 648337434, 344719294, 627290013, 461069495, 60397891, 592350464, 995219909, 420132368, 225579575, 563624826, 180361569, 313073644, 751471242, 85269711, 848225324, 624096655, 790424448, 396539986, 439735980, 127782513, 806552874, 553705955, 933907069, 258868241, 753785022, 68942043, 302527240, 504009411, 792538817, 925470703, 823347564, 287929208, 308656082, 257950475, 278743699, 726663685, 192995501, 452216574, 326359439, 599081489, 411715416, 438363587, 590326177, 490520911, 661309822, 203056752, 714837087, 873382098, 863763212, 731784572, 65855341, 176165775, 913036384, 152339468, 323795325, 704236485, 128365583, 597483034, 139691421, 569430622, 231351807, 87449934, 893655338, 675460338, 697229270, 444490378, 59440331, 131777076, 920248752, 335318811, 742666496, 189798404, 151491295, 147611379, 582077875, 591304019, 750070487, 51208997, 497186451, 347764821, 879167434, 59971185, 176374416, 696653985, 329223209, 972653545, 517936301, 617696621, 476391111, 694271139, 340917543, 530079765, 463529036, 510680790, 548123513, 923444771, 441222995, 536607514, 670669564, 516944922, 767372558, 703404812, 638153519, 420167328, 921001679, 807031699, 319393759, 678824309, 986101887, 903523872, 524396490, 471127451, 629527858, 405852625, 381594699, 986395212, 701078448, 366936332, 161742554, 973618461, 995335153, 568546180, 970261939, 681565973, 209735516, 288682992, 242060454, 763237644, 950960028, 619609704, 990799584, 364037007, 341935050, 842223470, 503835493, 732189506, 547023459, 957806916, 363507672, 314777812, 206275669, 943415649, 865307679, 184243147, 34387389, 921789071, 236570588, 170328904, 327869807, 228647910, 869940296, 881808356, 643979176, 552746718, 464336330, 462969202, 278589495, 887146784, 378627834, 404422350, 20215989, 765895854, 412756762, 290439964, 432742974, 413706113, 301862258, 754223518, 107561973, 336933617, 835289071, 371413113, 112374751, 686383053, 630849567, 630530059, 287769089, 955628684, 733159272, 67986077, 525778973, 279522950, 613395018, 464395589, 292095649, 984752663, 213421112, 976456347, 566413403, 810223252, 247542856, 135106736, 731214617, 338869408, 434516972, 260440984, 274124228, 350186496, 850845665, 83380256, 767430038, 146248845, 896904764, 925047633, 705822138, 978168123, 622650730, 95652056, 158019922, 290827737, 600212670, 688780240, 63923193, 563973777, 685168452, 749163398, 924199800, 423061480, 148462240, 991830100, 710471813, 880461948, 345922410, 821814319, 477651314, 968442008, 171221756, 164385280, 132034958, 298379911, 978730604, 780727873, 369881407, 384958627, 966086501, 104443026, 807078906, 160579074, 941497514, 993481930, 771202499, 462882153, 614662502, 390502193, 945837208, 770468315, 109533456, 129163078, 372664049, 810544978, 674380251, 736512155, 432073122, 996437839, 602029455, 630503216, 359110404, 998862911, 368950924, 347892487, 526161061, 738603356, 399684158, 56732704, 485624640, 12197644, 684856658, 545671157, 682876697, 672688387, 212091200, 731875338, 565312092, 117881191, 518528181, 266930092, 229337389, 612332140, 853275853, 370891849, 840420935, 226555780, 225495173, 276772495, 562765584, 286425048, 10052117, 212736063, 172852982, 910804428, 43096322, 278519719, 322910016, 599484958, 755754943, 436227864, 124748173, 328180469, 424462553, 217499609, 289578855, 840800523, 877906075, 453029530, 738910501, 302085168, 362882677, 479536941, 63365264, 712767194, 308460899, 509190025, 176021449, 765073078, 628297334, 538371493, 437471377, 745338132, 703089874, 571470952, 180399186, 413192723, 773316507, 210870166, 25245078, 872603201, 431002263, 223787061, 818292580, 50900380, 268122144, 125564669, 122251028, 517979693, 763841643, 723611479, 26346205, 793343374, 83638928, 227530489, 748258248, 498991455, 87335592, 338395484, 168738678, 946011991, 67556528, 670057538, 763523265, 374691494, 881846824, 443073680, 363568040, 575255848, 570386, 926312101, 181653189, 66824913, 529597754, 551363935, 802780175, 996664335, 394635185, 496727802, 185587635, 482535544, 137207078, 376514571, 370209238, 370552928, 98287741, 230503864, 305022263, 261383204, 609633878, 413148055, 129652737, 118037195, 152799126, 11017028, 812110269, 885089542, 447042352, 614180724, 206417500, 1594629, 340821085, 885352855, 250105525, 477619973, 241062761, 745766238, 515682535, 962363230, 218993997, 862062592, 833433661, 665001037, 36180199, 638786164, 4516222, 686468241, 864360467, 935881226, 115456719, 187414864, 776020107, 666809433, 478395488, 842967377, 755453994, 783243605, 766182571, 394501580, 636244791, 968735302, 811209492, 80357886, 479316294, 61760257, 30901478, 256465622, 159868113, 217448415, 907843981, 18470491, 471543969, 867864635, 40816095, 813998497, 902883109, 949974450, 258382381, 604799300, 121756075, 760451146, 177589250, 529022283, 107020932, 550138699, 4679340, 485661607, 702123402, 666181013, 245208206, 851724712, 900134460, 658025471, 840845479, 736619019, 179529003, 465576951, 658923479, 546941129, 22087700, 899151578, 382834897, 825966996, 724808702, 139070247, 511268862, 875757258, 563269628, 481398859, 426958895, 35701545, 365541837, 881222903, 391690185, 489601740, 422431817, 294285223, 707183549, 51639277, 340535500, 387360903, 173691404, 229950013, 866672908, 620675985, 194408565, 13594707, 249167074, 279527208, 957482160, 491870234, 337630286, 356201066, 308445565, 502926059, 994548465, 24016934, 658560910, 212716912, 37193884, 285163796, 125404832, 398263862, 360725587, 208354540, 696798891, 827028520, 945225801, 570715965, 845983572, 477049762, 990561097, 613389343, 811733825, 50354965, 947484640, 769644575, 918579968, 639229171, 794306004, 436351286, 85508480, 390702612, 917521242, 506092958, 186045706, 554133234, 615493772, 918745379, 482184036, 129821178, 533817420, 789689312, 466448567, 700853405, 466977926, 820049779, 891741219, 430114345, 400886332, 487635313, 859070907, 197462796, 396575410, 762534831, 537191602, 285090039, 634956325, 643053313, 825337357, 836571738, 830117954, 340769833, 888023459, 238006513, 130996611, 955932627, 637269672, 911359543, 881944659, 825802630, 421831764, 894490463, 713356003, 54209375, 696517533, 771214550, 759283972, 362680776, 347935344, 160647202, 53491421, 841553877, 838297492, 290377938, 996793251, 758158555, 241072912, 521327458, 691437758, 80775950, 787153892, 977150483, 583338205, 437907176, 550534137, 622408311, 678335086, 803733749, 469269410, 220041674, 352936841, 539940562, 748146673, 245790537, 827316881, 562270083, 678855029, 303613546, 363331761, 782542149, 80364752, 782768458, 906700510, 677221459, 87771422, 957148406, 907893758, 786520090, 963291842, 438404141, 441563520, 271522956, 585154778, 742784332, 566638542, 461484758, 754239173, 947002855, 346162511, 12734756, 185707996, 310172977, 139381812, 362852236, 771590193, 488025410, 459657982, 870972267, 541495162, 937961521, 208857365, 153469198, 458442448, 751267167, 648566202, 44103410, 66619922, 151254080, 662940379, 490381516, 337041567, 693731443, 606255258, 960356014, 963096680, 787933807, 939428359, 268295151, 42608003, 240828121, 100097811, 439997447, 795364097, 455956317, 496188261, 218691965, 494396007, 776328568, 827652368, 979104477, 623589499, 498802508, 958805376, 690443430, 327227125, 16568816, 282146665, 597668543, 918867118, 733720514, 559107070, 938551754, 280604660, 397150285, 757338703, 28935059, 915948016, 561869645, 881587101, 444439468, 451204493, 862675231, 241644965, 799603020, 399836593, 256268981, 570238982, 881476262, 315876166, 885469843, 797774835, 87739227, 482044047, 88677085, 659451807, 72407057, 199070767, 723201434, 104654247, 306247446, 59992576, 589652106, 641005903, 448570669, 987115312, 9109258, 418454615, 821763444, 643837504, 139879453, 212117977, 685048311, 342593509, 517631756, 423493173, 845303608, 722679929, 138784898, 469280231, 592467984, 21338943, 612794088, 582517691, 701569842, 203745399, 597429294, 880863805, 144691950, 682192277, 821130297, 683830984, 151575635, 445772107, 891794556, 329161036, 702750723, 537986775, 538045402, 897789233, 911615077, 308026688, 778711347, 777615397, 709618494, 790737383, 170588942, 481918809, 466040209, 459779774, 859091373, 213034858, 36051018, 844845922, 875929075, 854339807, 31498270, 321566058, 606381375, 705545261, 330042649, 849242764, 786998401, 470937285, 716379702, 321183107, 912233827, 779727271, 357970020, 822375888, 169125346, 332790601, 434077714, 677965090, 872859918, 824844438, 665815427, 839270023, 847798660, 526926520, 279549028, 572046928, 718263240, 112253799, 831716208, 970723174, 823874345, 392972817, 963628324, 810278171, 530531064, 949859185, 205887368, 598003089, 34722142, 462139645, 767596798, 589744133, 44924686, 359696247, 850488886, 299612466, 43946071, 293145672, 564059922, 746223650, 392723824, 282536783, 360972423, 679925279, 204064391, 634609644, 48098695, 441878663, 301913424, 588770681, 712037726, 708248140, 790608851, 339186958, 114511513, 706575283, 819878466, 852316846, 777370301, 305259190, 665198544, 902082498, 97631793, 868865675, 584711718, 450355529, 77102767, 780398066, 514655422, 656691995, 880965407, 134874015, 732911143, 702542413, 370389676, 425582487, 111477790, 92954307, 20657743, 414074666, 870713918, 34611913, 297237425, 935525759, 224729, 405635599, 625645999, 98893931, 861506894, 451942280, 164225003, 924358461, 674998763, 514651332, 207843112, 343838393, 527710057, 536277233, 811962862, 849681065, 702807753, 920040871, 378244019, 400618570, 408407895, 389018626, 631685712, 357790061, 368743970, 456909937, 894584016, 345385558, 16721584, 792878984, 294895377, 7345123, 647424961, 444048014, 944120955, 907220119, 941364557, 854610256, 699167409, 776427847, 456672332, 790441742, 735972783, 358773055, 591718748, 253919033, 788842302, 359222183, 527102277, 225288104, 380073151, 206071614, 743380667, 532713706, 880161342, 205620646, 269094317, 863574210, 461157367, 542557906, 923424232, 34264676, 329185972, 459858811, 936080553, 229858626, 755931708, 523789830, 449936586, 395595198, 31650503, 354215740, 458525275, 10950635, 659752388, 939500620, 508614700, 423038684, 60752676, 29384846, 479476981, 855908616, 895095096, 819261159, 195459635, 137845891, 262679177, 259563121, 971870122, 872186422, 27452359, 9013215, 415449061, 394659864, 429528082, 323473268, 337267323, 571149077, 903687103, 165008795, 638346233, 568378069, 336030745, 386387879, 735022566, 988410817, 80834198, 430228743, 710424639, 972362240, 835264440, 430377799, 213724136, 375217653, 541063948, 158525902, 362805187, 841527586, 47380995, 100257180, 267570828, 55592042, 946273176, 788935392, 902993698, 247065701, 273470796, 326416432, 224413764, 409051404, 584631995, 618207244, 34787735, 440666408, 228022587, 800493731, 31560599, 37287788, 262905843, 199787085, 616665420, 22845849, 465384918, 970923940, 151560882, 246398142, 83293650, 752200707, 753773722, 274872107, 300967581, 710549499, 911798224, 36041137, 154314370, 267724934, 731072121, 339962586, 813044125, 957551891, 659645491, 216242766, 172281605, 45473163, 39826051, 439304017, 50783247, 171252508, 850907276, 234291651, 11040752, 886172364, 381179914, 434233950, 854697725, 844460265, 104920602, 687376247, 195875511, 477797069, 457416065, 916244566, 72125837, 721766405, 514548620, 183584898, 537299254, 540341207, 737180186, 13841582, 661837885, 715274093, 441172351, 874627498, 716642599, 865261623, 377219898, 870163311, 387604160, 412143742, 692528560, 809718850, 429522953, 256253124, 326064677, 492616068, 217374695, 421643522, 700113506, 632010089, 710759060, 574880464, 764290351, 117100795, 360826603, 590308864, 187450069, 50811304, 470851062, 861150629, 956939892, 969344514, 379509897, 155980427, 374570119, 798989556, 902780127, 665720246, 992839311, 220856643, 78171676, 811226220, 144786408, 713375891, 211863196, 304585564, 82615202, 31753420, 416886196, 82254335, 728039675, 115598287, 514733364, 819590510, 374751872, 344229452, 981249307, 48400407, 89107139, 629452835, 577719205, 230209903, 956188227, 559613853, 891083909, 988916197, 299822190, 471960051, 336734628, 142980156, 468699966, 431492369, 501333570, 711749130, 570159049, 217535235, 230614921, 923742490, 186302132, 137565564, 408456759, 299023333, 139071349, 138318106, 29800569, 391529581, 448104695, 286266002, 177134273, 185517881, 466169614, 638957138, 635673355, 417418437, 94114399, 277384691, 715425704, 1025371, 607738406, 448273468, 147011921, 661511922, 795865832, 578445751, 763711585, 618084140, 661256559, 254519859, 327399142, 164660699, 673969761, 144328688, 222007253, 768282143, 441709867, 461873182, 225632600, 604094675, 797223427, 632733745, 871897196, 879508943, 614862767, 708779739, 849616172, 455261598, 280390167, 937712010, 954809885, 184052639, 574959797, 27076579, 698457258, 329607359, 995983792, 794709152, 527763041, 736666597, 640858353, 964981395, 803944205, 528998844, 53514493, 365722514, 258267716, 89535677, 985363437, 848247316, 816978880, 711927705, 119963703, 990520426, 121418450, 444039396, 958853044, 846245037, 180339772, 444515520, 788791409, 15200736, 583875241, 764151991, 896628486, 538493011, 809338128, 457961278, 607586956, 169254206, 740574336, 660431588, 378070799, 60411946, 244547793, 56550316, 186245263, 81553087, 966398243, 426067817, 96200879, 798421516, 781464156, 857060685, 203947118, 639152207, 316698734, 924503114, 855199483, 921527392, 193186487, 187731671, 730368991, 144839224, 217985390, 398877484, 973092964, 345495406, 667404343, 257965993, 978550197, 996099460, 346291764, 159168160, 720204669, 94501843, 773458695, 125690010, 476122681, 2183296, 883049264, 636027349, 502402892, 748719556, 371436542, 579354774, 346203691, 826860227, 519517425, 371741059, 209086319, 248333142, 405340030, 37889982, 651385671, 231776696, 957781391, 101819153, 928843639, 340522901, 627634578, 976112995, 331506371, 493442508, 939946382, 460366643, 773778851, 262524902, 165606974, 963221756, 949195205, 448078593, 58634744, 695544066, 772073772, 974120850, 749964903, 594394998, 497964634, 861866156, 798717949, 207906039, 333044598, 107562803, 369281545, 314288955, 41553585, 19774241, 190844709, 298377889, 450677497, 480141546, 512455368, 400720173, 491596796, 601879775, 789441110, 137970348, 704903347, 575921536, 43204026, 327845461, 920568406, 106718128, 400606503, 810434028, 81812324, 744611203, 379545359, 700185224, 352599070, 230283697, 160058162, 274479074, 741868029, 113075633, 640792931, 512384273, 498498201, 379404317, 957538667, 648523227, 304497157, 949362667, 778971743, 780455146, 257771955, 111413951, 423305233, 86164564, 600469450, 904670286, 36062337, 775377558, 862284940, 334052889, 157839619, 848323810, 402646236, 604909903, 848196460, 59223127, 262527024, 146257787, 323184602, 91861944, 494166151, 678715833, 806205912, 986810378, 207598876, 554716438, 593759960, 294489906, 436424319, 625248292, 411095844, 27266755, 355664045, 291946230, 89928713, 661717002, 304101108, 187128225, 558393512, 961555747, 924648093, 688310057, 362873695, 60939732, 244614637, 280603605, 968792237, 981871654, 422939596, 68637018, 377871296, 68963249, 179208914, 507377143, 380276935, 389541331, 626342531, 163911355, 368627919, 664720533, 192422618, 794922487, 187371924, 998970553, 765095747, 338391554, 236330711, 914075221, 104182397, 206702383, 549468934, 950195954, 511034668, 398397308, 887368916, 21869410, 175923575, 804550294, 578322601, 898711867, 408370829, 215363769, 898964465, 764196211, 135026435, 974124702, 519438229, 589018106, 87607745, 604374781, 473169091, 960827003, 487201001, 216505546, 837654505, 880827085, 703992561, 891663796, 72187291, 604976839, 842029669, 69648927, 896371766, 562727660, 687964729, 181279735, 4226071, 934646456, 402129049, 574765356, 223292491, 94428337, 739269748, 135610010, 790034543, 25116193, 292625224, 305751928, 614637285, 664409036, 767854106, 30169951, 560153882, 11044963, 158517067, 767157876, 894901285, 883402002, 473665730, 879609906, 363305497, 827882124, 181900055, 793238224, 953545675, 713373549, 124601454, 437204524, 765714426, 452771114, 981286081, 270702451, 976379323, 808403898, 703716745, 765114372, 90671343, 314651624, 969420476, 298023643, 217071308, 329298815, 243552666, 182520948, 808097795, 664562207, 226209169, 912394923, 396727440, 574307800, 766921768, 15683078, 644569089, 725551576, 166811946, 376131280, 79307485, 453465459, 285141250, 563068220, 713743326, 376283262, 887593138, 259236860, 41568448, 431310108, 621728938, 258870901, 9649231, 311255751, 641225663, 214230341, 305000253, 223564912, 631141688, 632737204, 763244925, 17439562, 8435582, 473415751, 823434274, 81711783, 711708652, 669291746, 418476717, 4860790, 241961965, 751770885, 876429147, 674071882, 504341626, 727736293, 155730933, 507441646, 348374088, 317016136, 583809471, 678142243, 20400047, 252261930, 975836286, 746505680, 548118529, 532138982, 603461448, 363828726, 768505721, 640389524, 366575077, 124537177, 805464482, 802686988, 778146462, 262851190, 914469796, 255182903, 638265555, 470385219, 273184468, 339375909, 942337039, 449038086, 773493616, 671404933, 912846823, 644169928, 584249707, 876371974, 80570551, 617435505, 49324058, 57032523, 644334218, 949684181, 789580360, 49989698, 362762702, 45439070, 179853499, 981975597, 458369010, 233762576, 532374906, 459266750, 102422557, 79314119, 482123682, 510765251, 570631946, 287403996, 469564508, 298530542, 998508503, 201262824, 782156586, 247638682, 855614293, 218981758, 415513031, 274422774, 487152188, 635104105, 342612317, 241264816, 117264443, 221379603, 325547269, 438128741, 817983166, 916543179, 497075442, 715683885, 272640729, 338482264, 491004179, 687022492, 721544133, 640717263, 391531933, 370817482, 440178095, 328358917, 709166323, 832651922, 603945966, 643640792, 600308961, 364691088, 462384916, 125793073, 777263069, 799153447, 323197271, 962583430, 800093601, 433895660, 551872990, 461244520, 184477688, 373732812, 611649381, 37085953, 287921128, 24311914, 57971430, 94281002, 16106490, 877562801, 268121180, 222377230, 959357664, 849402101, 979201733, 74535901, 927146116, 589925827, 649852879, 712383934, 991365306, 701827011, 979815909, 55215712, 141471349, 738443413, 808865446, 231773524, 897589669, 975042118, 397992102, 642505619, 226097348, 288393934, 634894382, 483965568, 814977544, 667476722, 985046902, 993631513, 704096372, 935539567, 400226388, 886913532, 942485881, 258244654, 143012697, 552712213, 195328894, 958214111, 249064285, 172474247, 24942606, 635450510, 995387281, 157769083, 724820637, 859355198, 425339480, 297540933, 192961318, 704471534, 755498362, 383479075, 590656407, 545247413, 456378674, 108753254, 190897949, 182616910, 885973666, 854138613, 754895759, 559401563, 979460436, 267955872, 618333361, 386893340, 258419563, 965155746, 996961875, 352412133, 330660395, 532285749, 45176768, 539587841, 935828626, 47044278, 393386754, 219709701, 396055308, 343480056, 965307632, 972716107, 511527349, 334980135, 968074456, 545777115, 976272548, 936749995, 938079677, 693153583, 750280024, 892020207, 277984464, 301150549, 378642579, 94335242, 2878534, 498007762, 693591719, 515952913, 898587, 101809905, 66951690, 345597892, 32744730, 28048094, 61798316, 23603451, 900584105, 69870437, 244074093, 910675618, 993978153, 645237835, 240760881, 578782296, 403184441, 442576968, 953976887, 212490438, 413785511, 946399136, 763709472, 423469489, 332126925, 41397423, 22032435, 241519611, 443978586, 159716978, 376831185, 563402371, 399112727, 900246797, 60028572, 476739218, 890620288, 512753972, 722825486, 105708786, 150715489, 604680376, 745855933, 894927586, 262598547, 708394949, 304194550, 688155731, 196134501, 657775049, 572678213, 782308001, 510213808, 821645479, 863778171, 791603936, 16836614, 809162814, 462834042, 808779412, 916918289, 527704481, 28946066, 637411924, 409840111, 658598112, 282118876, 838121246, 206761863, 463186103, 60893923, 315814579, 843697920, 682339087, 928476938, 7172107, 505899252, 753397480, 518159172, 74014657, 571519300, 286433276, 261103280, 271071318, 44961025, 917578060, 671714476, 711033710, 494918841, 226252639, 386160144, 757065395, 604369655, 5929101, 641271820, 670134339, 556053000, 514042648, 280626711, 266671557, 505447441, 847553919, 809041827, 56548375, 944387069, 775786832, 843265058, 685866003, 178589948, 850892646, 606570805, 557859123, 202036077, 543641389, 317389611, 447764403, 301853322, 690205409, 942902360, 739441701, 770450571, 286420369, 88501516, 16029229, 941054478, 226673198, 761705434, 218255351, 892127566, 499637753, 910033722, 355038893, 51561395, 624623279, 751462278, 298363753, 675212176, 995764227, 336141562, 879189146, 125841762, 915051867, 902688834, 583099147, 246560594, 298712521, 439532159, 106577238, 94562742, 309273888, 568566758, 614077769, 228001264, 839065771, 190800472, 873780304, 112387817, 124152955, 288954772, 648356879, 439920104, 7343946, 648562164, 72828820, 824366705, 247408347, 696749333, 160131511, 886012090, 806123100, 698442297, 561541178, 937775184, 628539080, 428758522, 141997250, 629268849, 374854433, 986777655, 958174577, 411884083, 805097974, 33550605, 183433729, 610408298, 69528987, 230086994, 563300500, 259588197, 366804525, 909870307, 806895857, 741491624, 718024813, 658865093, 938203503, 907155710, 115151530, 384250460, 713737975, 43687674, 866849385, 735842358, 216871969, 383237151, 230374678, 2562589, 140051908, 569483274, 447201015, 538039078, 8504100, 888738580, 170725343, 284453315, 651759207, 826562147, 784070561, 971449235, 821389028, 551201747, 525354434, 438078811, 87739793, 482468623, 786481857, 941400047, 746168637, 173640394, 465350997, 283008038, 963586414, 916479773, 369263564, 454582221, 191728847, 456651183, 198088796, 686744800, 170367179, 772044175, 155653588, 689697102, 675941551, 260968895, 82625844, 226717362, 357925104, 970222480, 626047675, 329481037, 848138178, 721281006, 450427470, 190975057, 846262848, 523542348, 136195747, 952747797, 200431588, 546413662, 489936456, 527524853, 393055874, 975796833, 905003888, 738331036, 850368082, 936380593, 841592962, 658183698, 728796838, 311782164, 662441485, 970634502, 623473536, 541392539, 347694488, 59734735, 252052947, 994931785, 167458846, 439656039, 866703378, 834839679, 518683955, 495124295, 186192134, 351698464, 65331060, 710064201, 981826866, 280818832, 831549940, 766738068, 124266915, 996005352, 406504113, 676121593, 520408885, 843172113, 435849485, 294116952, 480741190, 357738533, 647657266, 719671510, 709171276, 768206811, 388947276, 564088170, 17847144, 308927001, 570485788, 682946490, 657546135, 499054125, 283735143, 10286886, 908781814, 481326630, 614745781, 108173281, 886931924, 427528613, 831909752, 772482938, 447959584, 795897514, 752039977, 67661780, 676977250, 397833602, 785297988, 356357727, 506061230, 849414445, 600315729, 401975144, 265148029, 209487830, 330250335, 406921429, 578708882, 442601258, 880723537, 988802515, 241759086, 536859176, 828644786, 256019690, 580406, 636595031, 653271459, 22413512, 699951622, 500640102, 38119698, 85402228, 531855404, 251475672, 835707371, 194140946, 479164727, 505487019, 329594122, 308010654, 798699952, 548806661, 146777294, 672156607, 806678342, 823796861, 44694807, 264548019, 369482962, 19160423, 524580250, 529948374, 933854419, 536405607, 507101822, 284826216, 932536282, 619806535, 78723925, 263746556, 460282421, 182704422, 717439754, 803750478, 837250423, 304541867, 519799137, 580915022, 28314257, 997285240, 877313288, 322012153, 110525772, 198534939, 557890747, 184623406, 602843480, 896315512, 852590901, 68377228, 30732779, 81751319, 2872176, 119715681, 978144310, 272853722, 842017648, 70208380, 598946547, 39352447, 708310223, 41882336, 667225188, 472743133, 140490894, 22224730, 686761520, 98601653, 820918624, 803922193, 348901407, 832985737, 346776662, 404831133, 124079412, 845644491, 802147393, 693178698, 313935949, 620790906, 213859521, 472342777, 729597510, 638768835, 113700437, 339019112, 650985356, 157603336, 569312419, 771016023, 233713772, 605746208, 112242236, 786072608, 521745707, 339304304, 887331644, 310348622, 63041573, 325313338, 477741487, 869226924, 50870678, 860231927, 946238046, 555377899, 91668535, 888079682, 842086413, 732651341, 690234201, 423688862, 150711007, 923897220, 627019759, 953153488, 670454883, 738621277, 453880878, 527887814, 952729672, 521165926, 973022255, 342890405, 89975550, 492140581, 915584345, 832715336, 146804138, 207294458, 925360823, 247116431, 975669781, 878174379, 105852270, 156712932, 111925319, 284592955, 985668146, 601003944, 341242475, 214290654, 10164904, 926926786, 273351624, 338736720, 305014792, 987441030, 642878906, 506957979, 937190572, 591634296, 417424504, 482994839, 963295600, 138859382, 717439765, 785885689, 362942953, 7093688, 764861960, 493748552, 848599709, 814531820, 947920675, 120547714, 327578379, 904629777, 29560285, 828332053, 923640561, 734756979, 137178080, 389086364, 193393703, 622615401, 284294463, 136559182, 139999053, 304533104, 20196157, 68839123, 405462527, 14837875, 494847296, 593843374, 87517081, 753010911, 57927692, 642483142, 845761733, 902201315, 568965720, 56843439, 997926246, 880761312, 767415588, 927405858, 965781797, 410094269, 962740747, 672515187, 905190710, 332679149, 241135773, 529640095, 385244844, 627249926, 654154118, 773965678, 230265543, 767517673, 373526317, 155615685, 561529323, 306263609, 680530729, 241280795, 916542903, 849520246, 645530479, 285225489, 59835202, 128006816, 621207899, 2176513, 93841830, 835292060, 883257713, 123271277, 502538802, 573157899, 246324146, 596464857, 884867600, 835282271, 135274912, 838101763, 767208902, 101669123, 566417861, 615811511, 665443067, 494080351, 325045775, 746932548, 378887763, 511333140, 195676279, 664490105, 700715475, 867012984, 578354708, 770200051, 566291384, 535409799, 825689458, 919066282, 874698469, 25547386, 847614734, 603027550, 903123371, 475568787, 23274306, 850326346, 597323503, 620799587, 232043207, 37834346, 125933996, 12425073, 555632810, 285147393, 573638484, 180490956, 412653219, 231696140, 174496082, 627756148, 723788390, 162466520, 7511465, 994480530, 558957945, 24153511, 865218616, 480721297, 753569661, 118377439, 944977099, 963609537, 849824499, 134775231, 268502558, 575796429, 89629771, 965894092, 657004214, 28979512, 189122877, 864951346, 969336341, 911087584, 278586314, 50696169, 989349095, 696249852, 784880705, 662104116, 290726449, 163268248, 619489920, 473173679, 474261024, 735158794, 42215430, 508041639, 110878718, 95262425, 565173737, 217577635, 744868643, 334700488, 111013506, 842031439, 854336344, 863684840, 370848130, 123143909, 86924113, 445614146, 459568996, 429132970, 663960565, 216775803, 81792971, 330585233, 86759986, 337078475, 199955282, 193808840, 782834235, 922656016, 716101633, 469697456, 863419200, 18173793, 13747314, 579336497, 719042665, 902007243, 243580769, 198134291, 237585137, 799252373, 448073528, 632057060, 91941764, 878314251, 182016566, 155386864, 602989764, 452282383, 497301551, 523058565, 536953483, 305678611, 591470380, 489354931, 914691394, 443198722, 672756156, 944702750, 872454911, 852000790, 842738708, 194712194, 430766629, 318098215, 195168886, 389644947, 250590555, 586993934, 809086032, 41048047, 457911664, 795045906, 951857630, 216510987, 762002851, 307077677, 93330629, 232616309, 350784856, 119618423, 643151635, 454018403, 477698196, 951252390, 728997960, 301533939, 826554351, 536055499, 905525386, 490102711, 615732229, 579669327, 241701421, 236225566, 776464341, 465701741, 591680139, 61109959, 361963450, 777186847, 972365725, 614801979, 136368711, 964903479, 715838379, 893731920, 255963188, 410346987, 60895903, 565660463, 886113524, 118025054, 963303475, 310388452, 407404024, 70821557, 727969313, 748422580, 874435555, 959935153, 411558132, 313994970, 441610662, 132302700, 524264763, 920129501, 668111399, 566329631, 832239055, 232269250, 172563039, 440555611, 501407005, 458518699, 128540812, 477735756, 803439442, 928449310, 504677468, 76132474, 218866657, 231460570, 637057799, 333013026, 51663177, 488901250, 755743919, 210170002, 36071747, 327807391, 438002668, 598370164, 131349554, 942920015, 637619767, 645313142, 789461876, 721639858, 625825072, 814350669, 780575149, 114505924, 61005624, 189666510, 982392481, 521932358, 617158874, 145100268, 563028372, 861512192, 227061353, 374936434, 970316680, 808373933, 550880987, 709012689, 254010490, 640921360, 706820747, 256508452, 507329827, 24570992, 409581836, 592265922, 536867812, 51837934, 551144661, 975828296, 371362955, 534055479, 187190679, 508425644, 772542523, 355244662, 869505359, 574471556, 492493259, 472852469, 975201461, 958110259, 91002544, 174962606, 569214584, 968203865, 878697940, 160876225, 64973510, 557658025, 812129007, 922550911, 278564620, 39773000, 990640842, 950851927, 680325617, 450267076, 668133097, 250102750, 327452106, 849626691, 559567258, 294212725, 725021178, 20944026, 561815649, 903654606, 787194008, 454424810, 362814073, 197651664, 861639047, 956473406, 763135986, 56117090, 910872, 552042158, 121929633, 241784369, 717229403, 861208587, 623658196, 467451134, 618103074, 661893946, 524979409, 158866096, 931143902, 176102250, 745301395, 900053796, 661675382, 585990570, 287495944, 982004426, 104521692, 802465707, 504872869, 267225068, 704424764, 821605157, 309439571, 467350985, 52908244, 451960607, 310970323, 378496923, 750490491, 767880485, 376954528, 10451636, 544732538, 851420403, 359642737, 296261030, 745019493, 453427965, 942249527, 646853010, 644609201, 278551946, 551265512, 489542751, 718706292, 841031443, 641343439, 619637867, 131870768, 720545536, 72870088, 657581889, 581245961, 770147755, 577413733, 6919875, 383144426, 566560347, 214674910, 88720285, 559440108, 817570492, 753647792, 575772519, 344050077, 514747599, 618768953, 352268714, 415941783, 508912349, 245889036, 828210132, 49801576, 835547457, 923336145, 507463647, 592235685, 828093141, 559036411, 180730350, 302703937, 695252420, 875475135, 635292636, 586885484, 50739783, 400818864, 636187250, 407341643, 929024867, 198907234, 999505724, 508418832, 909286877, 940599328, 624157729, 206689972, 212745034, 788240638, 755246032, 896444896, 50604911, 546121477, 669547742, 821867315, 815815949, 468722361, 77946665, 6251311, 147707709, 547245720, 698094528, 613578216, 814866802, 121984063, 128341989, 587764617, 546525460, 710512676, 826085861, 824404408, 583288854, 372431296, 575544557, 400076343, 463019495, 109393337, 232595142, 308329824, 242042580, 61867789, 507172392, 574781405, 383557190, 194991497, 941021199, 580758256, 204733113, 309565608, 622116959, 956293271, 603245476, 310814650, 309629401, 574726238, 459812003, 335881784, 115988152, 783440789, 992920565, 269608410, 264429385, 916735914, 466890155, 994901712, 950719891, 836021641, 42705076, 737754607, 950767413, 249381518, 397730227, 199498533, 724948344, 341038772, 143360214, 497047137, 518285895, 956301127, 336212655, 166453518, 23306249, 470176213, 752413871, 341547977, 471662912, 125778604, 961803124, 720421700, 819478634, 761553936, 191124921, 977831930, 305664125, 907614474, 52274476, 182421561, 618661155, 444949180, 945798036, 453583344, 759586126, 695399749, 120706109, 463015844, 794658009, 19399716, 849338446, 946262479, 40452348, 981173452, 324034105, 905972813, 759056454, 411099430, 127814618, 355672246, 614748444, 187618849, 985184636, 916446040, 692136832, 870108569, 85191853, 955698197, 324118058, 523421579, 409730883, 990586446, 242574998, 537925836, 720176611, 968209087, 41323224, 321286032, 383009598, 153762808, 457087999, 296067037, 756484386, 832007865, 135998553, 517028819, 454581098, 564355025, 817651522, 147786114, 640611162, 87522162, 272002371, 175163084, 459081329, 992123535, 100038817, 305716298, 610599783, 483530313, 840713243, 179456652, 439434742, 80662825, 304814068, 809768478, 783660512, 919577296, 45709054, 533311915, 452255803, 383073259, 827916830, 6062015, 376896797, 254533844, 695686141, 887047358, 469836947, 994399848, 41652402, 685998587, 474232203, 789143089, 588694440, 954210399, 30933550, 595734293, 632775302, 115589743, 432412497, 857135386, 68004716, 914474129, 914813591, 451757198, 888507018, 750832479, 721927426, 312303251, 317415001, 390688930, 181182147, 567812930, 922472447, 31294131, 584821735, 745442778, 532482237, 790788787, 473523141, 616084041, 594356927, 320102251, 803410124, 407373508, 606881497, 994688709, 580967203, 735165280, 390489356, 992247506, 773764766, 768384880, 517749430, 838284240, 831169162, 571103993, 171066392, 452720622, 300130696, 219232895, 528497021, 676137630, 173605627, 190619980, 522012083, 110162073, 882343305, 770782758, 846477137, 965650403, 468004705, 892559878, 334088749, 852444726, 329765621, 165369259, 554884055, 466845309, 43404945, 6082445, 443192529, 936220648, 483361514, 713281861, 833955648, 420490956, 291022092, 169210760, 973237765, 330354728, 988273149, 997450612, 279190573, 498599895, 501644942, 446872464, 291360356, 26938568, 820563673, 750076811, 573924678, 88753280, 514653863, 381870005, 29621907, 352651532, 76212862, 173840744, 880236521, 153766765, 846629235, 578762747, 699899104, 963141545, 79051618, 668010757, 509007228, 626840584, 481029526, 555361245, 768437882, 354769585, 343858891, 580626656, 933846718, 175551776, 557118026, 972968784, 644988926, 787622828, 200628255, 280977727, 419759749, 909069210, 691465448, 586190944, 663499529, 544656595, 172365723, 654469090, 754819141, 903196232, 468651491, 608547382, 562785462, 941622371, 559841223, 443412909, 459008289, 164608226, 140286960, 756260363, 251100055, 895735792, 288893714, 1043422, 836021896, 701568904, 400538992, 506632681, 851530217, 133183099, 172014052, 393343170, 127375753, 899613975, 642567279, 525404423, 317026237, 680587667, 936415746, 63347471, 343422450, 664848447, 668042810, 740594350, 472966335, 984543622, 26719768, 712167067, 868636172, 824852214, 269534410, 46757735, 702544871, 94749714, 331679493, 417201444, 587866792, 477739004, 786795398, 179166965, 31528557, 352232372, 257123466, 254471371, 414438514, 478679366, 528645558, 70655479, 331219635, 168658487, 937875349, 973166213, 159127338, 33217479, 508324672, 888725985, 361914058, 399818920, 345275694, 45479657, 844453852, 753323172, 323330981, 878840704, 707085039, 734305631, 704444756, 745577355, 189958965, 613606444, 236722023, 708544729, 964355627, 648211160, 193676245, 51607059, 602019333, 194078267, 10603123, 837783110, 922236917, 272044799, 467292650, 557878500, 734923784, 203693365, 994559070, 912850881, 359625569, 378423317, 235530752, 351138904, 307089572, 917755657, 867232076, 256200851, 764164035, 249100543, 181824625, 194914105, 727200832, 116018182, 794263972, 104239944, 62705869, 122602489, 486319792, 995567299, 71072592, 763042194, 647566182, 861906707, 328025253, 306891919, 907595185, 402238471, 597653522, 72936112, 996054782, 152680138, 136667142, 759667923, 212318188, 19938877, 638497199, 890948088, 195784929, 242658727, 402252239, 716193869, 169310369, 800135770, 267551174, 234157424, 147971082, 747379921, 118061030, 277987313, 157418006, 122133095, 715297464, 793390816, 883070228, 778953302, 397117269, 995610153, 43881216, 392852052, 280333404, 410757776, 789280482, 107488155, 343813826, 547072245, 354567629, 788076148, 647290439, 596547371, 202972575, 775823888, 68652257, 21740619, 42126715, 872067983, 723335927, 357452908, 986107773, 870878211, 475971654, 21624120, 745814025, 740018183, 463046518, 704293869, 284761016, 155498117, 423112705, 74527040, 138640773, 632060056, 899642916, 359715827, 81057865, 579286893, 446423193, 941285867, 549001021, 277744076, 438564308, 263600080, 595032213, 940743364, 850890724, 649634793, 53288578, 252253888, 570739451, 899735015, 835070755, 75023664, 785319988, 229609595, 807676300, 339077543, 943582891, 318053635, 889151786, 862859, 638013652, 638858685, 969472430, 938456719, 157876568, 285219607, 651187558, 366781078, 805538127, 785377169, 564015965, 377363370, 955739112, 644327379, 650390445, 872239118, 591563148, 950706438, 883680033, 611187708, 254761469, 96224328, 55755760, 911818333, 830398208, 74935224, 84740176, 617693894, 81227692, 522214878, 569559570, 42533503, 448533876, 476042747, 153919454, 898841992, 377692688, 56895681, 661130240, 106025812, 336855388, 607620625, 268277696, 50442528, 260655608, 249396684, 419197327, 302259666, 537785054, 94145451, 480261054, 318768533, 488317402, 129716939, 80970581, 144871139, 244193148, 473633186, 9252745, 362334931, 4507112, 828106888, 477933861, 903179189, 482230503, 293929800, 40746871, 691002007, 961280582, 223749832, 865462068, 230821279, 536146391, 244327529, 859204108, 243330321, 151938531, 30950672, 913677624, 561612316, 847594533, 772099667, 706765131, 767869497, 24147996, 781399191, 299548576, 812307456, 635190983, 95122477, 455794455, 509133987, 318510883, 324748760, 469884747, 935309908, 740313354, 557656923, 20857574, 310675814, 32703282, 629238083, 760941619, 561674236, 497028603, 702814628, 307361493, 724892739, 125847443, 74077393, 143425114, 200091069, 477396408, 397747036, 724937159, 972646566, 383269194, 994462943, 69862738, 97659232, 727609308, 384370500, 315830017, 553739817, 958666541, 166792735, 835213880, 408968954, 102024698, 556968318, 622271083, 558503604, 190665418, 190620989, 200232346, 588004150, 916642726, 404413184, 725907153, 665664466, 112252138, 842601428, 200462807, 858017652, 409596832, 760031032, 403069124, 381109978, 284527500, 970483134, 498202728, 786194995, 468999508, 173510266, 865567935, 412279803, 225333481, 258701581, 362580648, 461349604, 920733351, 574830030, 679093369, 816922308, 809698208, 250017226, 439665842, 610956603, 854893448, 434938344, 156852255, 784806300, 783798071, 511188131, 806677012, 132298831, 292214305, 94003592, 909940968, 802636027, 541876227, 995358787, 146788504, 638874864, 422401173, 344798963, 479850445, 973033718, 272742636, 484000249, 332460994, 31624313, 505289187, 777529871, 372781070, 419832772, 253602682, 905441008, 294322494, 608480581, 54996275, 297772080, 164831539, 64106263, 254487882, 53861332, 166603758, 815603805, 730335025, 675872005, 21656131, 163062923, 416195351, 813399477, 494353842, 905643093, 672553704, 431904711, 466850694, 102134657, 659300079, 835552765, 856481362, 253596817, 261262430, 963477693, 593331435, 127589443, 562555212, 895706923, 716242554, 624457138, 539595542, 800270201, 639377400, 55899160, 686969550, 258828684, 208555717, 251366608, 752858753, 672513473, 273762055, 236782153, 273451372, 290960769, 440542089, 219910404, 808490530, 606542884, 422672796, 967428430, 909601326, 593681285, 675121079, 491300499, 689973492, 37566753, 236812908, 822629885, 855992566, 389177333, 729456621, 870521671, 726386072, 470816163, 246393973, 259913360, 346816124, 674776302, 456277815, 147439533, 705644581, 185587442, 436723137, 263227627, 589719038, 23635414, 441127399, 299126398, 533311119, 170079487, 255490765, 3960861, 697849486, 31987452, 422794431, 156278808, 797770459, 439911683, 596119879, 198440949, 560472294, 614616941, 91028309, 961399819, 238962729, 993089713, 816618895, 62516593, 348773184, 820750725, 721776349, 617280657, 772868381, 778176687, 331982746, 673149921, 956931978, 500627469, 727384173, 284675880, 978902248, 676452584, 415365090, 564238556, 827406963, 852609431, 970546554, 574049006, 700780513, 24408006, 450776255, 237691577, 409792333, 155091381, 308465470, 735246442, 32832035, 208073637, 467328540, 259447746, 95064341, 523928859, 840872036, 258770027, 806158901, 289895343, 422423727, 457590267, 696491439, 838130363, 783438761, 45505532, 11181280, 452469313, 786090086, 497029159, 140983528, 858434042, 44979692, 637885282, 283765243, 405723183, 839863942, 21278299, 221756976, 59496712, 873336415, 757966061, 951540041, 922794018, 897867678, 585581078, 263487152, 604895130, 986426292, 476979997, 835007157, 419542829, 965822367, 843453457, 684623642, 545783559, 852233170, 582352490, 43364715, 833515518, 375825833, 805163355, 189740731, 157061975, 534660731, 991742723, 791691507, 832469347, 48148644, 545263947, 93135345, 846763612, 425153982, 343135935, 326831869, 956652335, 973328328, 320643556, 447943280, 447613143, 129566725, 301286523, 759653557, 52411328, 779160211, 760354877, 477711917, 850247411, 225426280, 512564691, 290870288, 766965915, 124322467, 134749701, 938272648, 938890297, 144039643, 36052059, 325199275, 929764561, 724802658, 107730018, 595787515, 21908780, 197471321, 494286050, 461906669, 386377123, 881932025, 924842208, 937928766, 834227403, 708987023, 492963803, 843795073, 15959012, 537965062, 551515766, 595235510, 369273260, 426531451, 424959725, 615597071, 109731907, 262942168, 681233470, 518690956, 568198469, 532678395, 886806940, 672743559, 124831946, 682050855, 620441983, 654446613, 979495124, 808132419, 90893943, 632723799, 666212477, 991637218, 149014737, 341470738, 700854840, 466485015, 819497131, 42162686, 33466274, 851922170, 677047217, 220172820, 571289704, 978862661, 320038408, 70144698, 767181877, 416254992, 457584812, 869638773, 939616336, 12217354, 814936359, 67979519, 636465589, 565697124, 903898250, 992358356, 63725663, 763814548, 503214808, 966146244, 307720949, 242954206, 346015825, 310307372, 773868930, 434909516, 600986554, 272837659, 173469171, 76328182, 201769157, 871262701, 491654652, 801544542, 901782101, 701041878, 999196369, 742694194, 810889301, 556594829, 647945948, 553727864, 999089513, 134157129, 195889643, 490173803, 164762651, 510400101, 167423163, 846787552, 813168935, 58890657, 343406481, 746685897, 178620904, 44845134, 454005462, 177658915, 699793798, 25193354, 177312181, 495473943, 912703687, 843808480, 825845499, 142623059, 507772317, 595048155, 17301699, 237733934, 734245305, 569953322, 858268398, 870047464, 252242090, 154831903, 721850453, 155768327, 938175957, 231859558, 737511540, 575939508, 216275259, 841955396, 190095704, 925595870, 212834246, 920142832, 456789651, 299839428, 657290116, 836439656, 609503457, 372198350, 577828686, 528271053, 921132173, 637466068, 12614002, 224382856, 961925319, 489745141, 655504839, 352157448, 182862333, 231119592, 582040536, 491588956, 733915703, 883178448, 687442159, 611908055, 831924794, 966771989, 766271003, 222936218, 991712542, 299372807, 231447933, 331869751, 192826050, 297222685, 77835947, 811426176, 888833017, 341289950, 208419077, 577092911, 222310039, 46956024, 370027840, 203930479, 503531766, 448819592, 748864086, 483239440, 31231464, 110186473, 962333680, 341514463, 792560112, 496037672, 998478787, 607093277, 999363283, 720459473, 429501545, 614868415, 250446242, 258888258, 371037677, 82400105, 843010135, 554877807, 710851756, 58732542, 479903391, 750637887, 596327268, 58479457, 825916735, 778782844, 56678346, 958864826, 58905254, 417022940, 999857971, 949567395, 24250707, 502458689, 752660240, 132451643, 409492211, 256142989, 412201956, 358293234, 994471909, 284701847, 162475892, 728894939, 802240926, 989045562, 80302905, 237259294, 593177435, 95719483, 426761914, 342493059, 932274659, 448742307, 881987866, 836319897, 732936980, 939704808, 516238406, 159439298, 888077619, 733674629, 659156246, 605800879, 719695341, 784970661, 469686207, 46392372, 237348988, 843912736, 75977544, 821752685, 256294407, 74749232, 508799439, 624099387, 767255584, 233268084, 471638694, 67516169, 706217780, 472760206, 715970422, 161455034, 984935792, 372601153, 399677298, 837125473, 527423996, 82563286, 96957026, 216755758, 436295605, 696778261, 12900110, 177842516, 466917493, 910546353, 300095285, 367459943, 321030305, 272041141, 984200308, 676070582, 143391506, 625519207, 265619180, 207335860, 340380568, 907067730, 980544234, 440962119, 499887910, 102966434, 523225056, 13065420, 681705213, 939369583, 619924677, 548252633, 143136769, 765245299, 499726460, 653986869, 12859619, 213789127, 129237349, 812823103, 564337967, 730821281, 577129204, 331524411, 332876242, 267872913, 118732624, 554550520, 366365846, 776719394, 886181574, 491493096, 487980082, 807241709, 952467805, 742990358, 383754280, 760719376, 388808891, 637355031, 957611221, 488235263, 558523868, 716433736, 89356639, 429921203, 578026290, 121555361, 314204330, 94438226, 699888165, 228125127, 603068647, 409197918, 31054926, 958169367, 676260805, 80293787, 159189284, 607759042, 454613682, 912269650, 482060232, 135044682, 869636329, 534784173, 452145703, 237539399, 413202085, 958316601, 276637331, 741410985, 931536623, 148528459, 811513135, 891353943, 999823735, 698478828, 306595704, 680454423, 125463957, 840012098, 788708051, 173867375, 637507911, 774164913, 840255830, 599282099, 558485700, 26470337, 868499519, 855628241, 134817572, 464324372, 378226845, 796619828, 549969271, 558398722, 420583018, 134199031, 959398899, 580798085, 370268098, 681825644, 78337400, 963576318, 578474439, 979780372, 392500439, 543317582, 882757195, 406715272, 137061759, 428445496, 438175880, 520362051, 978996064, 295020968, 20754840, 136567807, 160645541, 991705619, 8916063, 315293299, 223509462, 136736017, 300008623, 255737168, 68054783, 271556589, 68416481, 562209110, 707002082, 911387242, 548076738, 481655601, 720527318, 646652507, 141067368, 514646879, 419480122, 204795036, 616315786, 641468338, 637180233, 797818738, 124264813, 586218771, 844112783, 217643813, 125113605, 259012465, 245112938, 603737731, 357698873, 318927801, 321576000, 836872639, 975938066, 810387453, 850895772, 435715643, 45179059, 599948271, 83377786, 935644307, 706769492, 855928179, 561204739, 575473912, 655160646, 234093727, 142692055, 288280984, 772197205, 560035398, 984947726, 798339178, 284788142, 516734249, 452584310, 769988345, 539036332, 419721698, 752349627, 251727791, 31667517, 950050131, 528286226, 570091690, 622903645, 921411380, 449341533, 906941040, 932221711, 583449687, 583603488, 602258786, 940167930, 271364732, 695241377, 874118098, 606877012, 881475378, 786600150, 394740129, 23250026, 829732644, 909078061, 472915897, 241422223, 826521799, 123898386, 917510562, 597070855, 818499560, 592957672, 805399873, 464279742, 789750787, 93655450, 24691488, 679790443, 420146962, 737177248, 87840196, 425099139, 525906669, 98247157, 945880356, 91742744, 547056614, 996143472, 983264825, 685470342, 723231235, 368860833, 42425465, 498543880, 508607827, 553488579, 201967326, 484945673, 439113274, 604185542, 434255499, 184209131, 108184274, 511091910, 307814945, 322255597, 194066111, 570209244, 791149180, 455155027, 48969283, 220833448, 814617211, 774576183, 688464939, 668999468, 456623795, 717974182, 406224048, 734798210, 569541533, 38087504, 396670798, 195877842, 62032665, 869114246, 890239389, 278067390, 936780694, 63619211, 684114520, 773503388, 722739266, 15343537, 872790514, 616666420, 376794224, 290706069, 396196729, 175919347, 873462995, 463165082, 427731003, 981168241, 326869618, 83141016, 648920875, 274084917, 673898778, 198809453, 162225320, 573766426, 36293557, 891734233, 526297384, 942416391, 865806465, 896931203, 878409319, 392831131, 31338167, 517762344, 369087778, 989569841, 303732979, 428475726, 803069667, 374873085, 872433500, 459177210, 890709891, 164513549, 769318642, 963878502, 500009253, 310439448, 295331932, 237968814, 906992957, 256910466, 928381625, 627513135, 267993163, 20785462, 320180493, 743198964, 722878597, 294933363, 707005399, 719486502, 202486971, 836013851, 652386927, 241404969, 885503745, 418430044, 183243839, 710426442, 711999467, 874488310, 313323450, 381896200, 607456624, 704886156, 54936415, 200342483, 440166794, 704430283, 829189355, 775457281, 13528742, 612397786, 366559105, 948816730, 884819253, 125071334, 590576346, 719605553, 439399068, 570747322, 848630024, 939927571, 894854781, 514965585, 517417626, 411757280, 406797244, 965679543, 881822520, 870486932, 742460260, 354994881, 456877845, 671642159, 257559729, 752921936, 882897006, 595810492, 675939380, 77371633, 644315647, 891090524, 770866362, 73341015, 895399877, 45082803, 895638607, 757315372, 337035491, 6957775, 760435215, 251179203, 795610077, 310401234, 103962372, 299535912, 455352682, 26730309, 341764885, 452474844, 701178274, 74830265, 370733254, 277065422, 391608364, 986843539, 427669503, 836797598, 8102921, 689344600, 993650584, 653779061, 248558396, 215128987, 904969825, 522649721, 640726318, 908811201, 4130928, 816417423, 970961, 885711927, 455903581, 572151980, 608976331, 687326547, 388968157, 300350945, 136475057, 371800374, 402640256, 536755433, 793362949, 163537436, 653310917, 776281690, 111482331, 12604077, 907116561, 473637644, 208944999, 817532357, 56239896, 309974441, 3918566, 654749677, 132001397, 776959007, 784683105, 266162358, 240236982, 618686188, 279011637, 341361601, 932749563, 700399079, 541796342, 788576043, 475117629, 696900961, 342137, 658851580, 92412172, 372582717, 615444445, 778343192, 527671650, 998980607, 175034425, 921389283, 628854469, 273005079, 140779654, 858216518, 852720785, 266366451, 793152048, 141959267, 110649430, 554169574, 13055864, 994888041, 997354084, 822100169, 401571873, 732512589, 83910228, 648945664, 375420044, 382766670, 626462595, 521800639, 514695880, 643505456, 220228746, 413364536, 308509113, 3067014, 763997210, 531520776, 324718289, 281303760, 315066851, 721156314, 233691779, 979506215, 51095090, 580753320, 735963376, 129121925, 5750902, 511627039, 651502568, 159118431, 511231325, 409827903, 757683403, 760712507, 63395881, 873068399, 72364864, 579378268, 491298605, 484424399, 262122114, 981582230, 845932293, 520409005, 822677844, 803780271, 834918067, 298600594, 396399515, 458096308, 876867261, 622005870, 15221909, 760239972, 446205539, 36760900, 318846752, 552785653, 910152737, 739618694, 453219501, 213509901, 555544368, 722943125, 299090799, 921184070, 459364371, 255220791, 248483838, 748493712, 718428788, 85272338, 350243917, 898287544, 279067255, 872752337, 659609533, 520600183, 109267931, 753135428, 766872194, 823026709, 789609748, 986626457, 18051683, 522021237, 515263837, 829406043, 847037684, 547484613, 23283094, 21782078, 86777676, 87108794, 294232762, 308710973, 268733106, 646637879, 134066758, 494096849, 315718896, 73679385, 279338973, 99271799, 689124957, 336446865, 351485471, 380361177, 167118374, 117184223, 522780493, 563191636, 48576762, 722950900, 852197211, 647203460, 917028835, 500314803, 976105845, 524673880, 348713018, 497455170, 211238381, 941709362, 200870605, 971865594, 719676928, 826356385, 470565885, 555099897, 37931853, 144496118, 96512347, 463074360, 708463953, 999854365, 905553220, 778494872, 283315203, 812935664, 794597685, 247283981, 630899291, 129171643, 430347321, 141331669, 122177870, 210372743, 790970543, 672945915, 707403306, 144133624, 218747770, 284230533, 611718146, 904011753, 540432819, 769477400, 171604774, 8254488, 350204249, 432366626, 788044561, 558071024, 484550404, 433717681, 141195798, 449511236, 942536359, 111153521, 126650493, 260258170, 510323975, 377075312, 91013722, 660370956, 766322691, 117857509, 483244924, 686901630, 476577107, 321639724, 891582005, 360265435, 939206730, 178476930, 965661481, 582348432, 101705593, 85890843, 377409983, 90837156, 997780217, 934953871, 906803424, 830651346, 382329784, 585123469, 947576243, 431076598, 116434952, 22807680, 840947435, 60487916, 160171206, 578319742, 129987711, 284958267, 291661044, 530200689, 796676179, 889187841, 756160598, 428893476, 232507030, 192638060, 878308839, 323619323, 117543416, 612454117, 372278222, 355726811, 836515432, 658649846, 606636112, 850763600, 292240536, 655216479, 174881752, 383617726, 426351257, 723045906, 393000516, 386329367, 692880549, 780647319, 119335162, 853813293, 304173408, 914921524, 922622412, 416629563, 843148690, 568860185, 440253828, 855791942, 226945339, 366947986, 400192619, 196413836, 157259953, 329778813, 463964027, 803414759, 706971690, 857022612, 158455040, 921519611, 371590979, 376424658, 802907463, 205852025, 448717222, 230370979, 267773287, 751022857, 574092755, 96245399, 618569227, 639659630, 749334820, 675792775, 154971594, 284300160, 98126468, 624186516, 309594708, 806390239, 694798264, 324296498, 152900824, 847157544, 504596511, 574943704, 177370124, 908328428, 1029561, 620587903, 544832148, 405190005, 518124735, 828357159, 647076010, 538163709, 337773639, 343871129, 560944170, 26195094, 439998747, 284778323, 833944476, 667905085, 951027542, 392062113, 823681819, 656122795, 473621456, 897961092, 319674083, 705623537, 185671565, 699111068, 213152139, 679325331, 262781789, 732773555, 318302429, 722334773, 460057016, 732165484, 84171318, 315451993, 487628403, 61770164, 424207827, 685483385, 732937313, 27246151, 84561855, 762544859, 981333709, 468314486, 987145471, 500558083, 355408387, 312955708, 717103468, 807272810, 742065257, 30622509, 365772158, 142456817, 656455691, 686369232, 417296555, 289805698, 545795860, 38227345, 252358953, 946195360, 194327575, 176109313, 941380027, 789892679, 99893552, 856196566, 380212677, 843047277, 353098144, 886865413, 829453362, 577316677, 665143506, 689454837, 522691700, 779579023, 572529949, 458063911, 593538617, 355614253, 920888631, 895241216, 48344806, 496131450, 897466240, 636673386, 690696869, 994011658, 967723825, 11586367, 266384462, 247304499, 25271438, 604236239, 851830300, 350320709, 856221836, 328406508, 496192532, 738224341, 646810489, 870137920, 283545672, 601469029, 367116835, 436740277, 698307139, 600681004, 285285009, 815950488, 325465780, 817458805, 272191510, 625539416, 675857662, 319153400, 709544874, 238742411, 286090079, 54068845, 69804521, 119171030, 334974501, 787760705, 209063354, 161845602, 911069872, 59926480, 509192936, 69374591, 155408374, 695268696, 978182584, 593359429, 725474440, 523296936, 812764014, 281710847, 431828241, 497294106, 667479186, 821615802, 349915525, 255669258, 671335595, 292468221, 181760702, 183799552, 412536375, 207126795, 848444763, 494452428, 449569163, 421896066, 762120769, 99875397, 291527848, 910375140, 390756987, 558787212, 492444604, 919246789, 733518860, 733648161, 101787423, 326529111, 468288026, 663319711, 238697481, 912223847, 543508152, 319978475, 303392964, 484763715, 122809007, 101127556, 172138686, 103272190, 942192679, 469513735, 604769863, 65722802, 176778239, 577891416, 55653167, 111719760, 802709250, 2594203, 435771255, 748950639, 412734303, 363999692, 408147350, 680246750, 975325450, 619548465, 477136961, 772833379, 45535093, 926252177, 13561613, 560808604, 775635334, 702909430, 43592373, 358648571, 393272758, 62158767, 677010147, 436976680, 676598677, 478168331, 954265130, 835714422, 548780749, 120521450, 294130461, 45759037, 337590280, 217382298, 365487856, 386324046, 487029293, 56297072, 992360154, 921544042, 718290196, 718707318, 6350997, 104855524, 924262119, 619826336, 135238236, 773699576, 324745059, 188781620, 615072277, 705171689, 231872007, 902383471, 879900690, 504024800, 778586375, 445053507, 254324354, 230045080, 274381654, 164346928, 514620542, 489586597, 731105498, 721405223, 872646432, 316566836, 791864645, 801221780, 533289971, 767695599, 82688687, 495436610, 828277622, 18008411, 868961544, 327612095, 231827167, 185267211, 541784166, 558206654, 202706246, 67336242, 320292461, 299854850, 249518777, 76557921, 72245907, 124882357, 534410473, 87302786, 163054495, 399156078, 404811549, 563203332, 860168587, 979743926, 983635003, 215358656, 765948197, 275829780, 204337071, 384191509, 346391256, 278950268, 622919430, 142143380, 772592011, 112372065, 963882793, 136581803, 995313112, 25585305, 118474533, 209273026, 632157646, 302886719, 155723287, 27120181, 772344905, 536610700, 388516903, 347775503, 779051855, 185626786, 30762615, 294437553, 365272726, 165247293, 656308056, 967006286, 449057966, 714224317, 95419888, 150910784, 13215109, 557084812, 967659220, 113234572, 392313998, 330616907, 907267409, 540404761, 181246075, 357699180, 751555741, 795477138, 121876891, 809986068, 18420517, 175801189, 337058500, 965745369, 468673858, 144488746, 577525669, 497219404, 987082869, 808182355, 871173781, 384388394, 772462116, 521503676, 415898441, 389865049, 778031124, 403158418, 181785851, 193539991, 89969952, 160275415, 749452953, 193478714, 860767773, 596620292, 961821230, 751715104, 252854641, 553073062, 218094692, 886362385, 821309849, 761998550, 445538707, 357131365, 879176452, 462284959, 187802998, 229085680, 461191303, 43686410, 696679230, 196191779, 562519343, 238623962, 30962159, 716602463, 839641188, 716869563, 834174590, 206299975, 263838384, 698116374, 482259363, 978287003, 963960375, 99591142, 71646225, 558328117, 245188137, 543886361, 350533786, 250359233, 79777757, 94718371, 962133354, 821931711, 740910352, 952607799, 680748763, 375221503, 129088461, 904158944, 724638174, 440437280, 713791288, 380766955, 430736470, 534171696, 257198210, 854330293, 677254022, 576764876, 147479932, 483178849, 922617352, 740786769, 568605730, 74789878, 428658637, 296296992, 540414659, 830930893, 185867108, 818881082, 713468177, 234429764, 288841586, 127759655, 967929853, 190513890, 673583880, 73229968, 665923089, 706953154, 149135592, 451344141, 220624265, 258115912, 529556986, 12226477, 17081329, 93777435, 153695283, 399077358, 161139713, 45559292, 436237422, 174715063, 909987384, 273755519, 507294984, 769160899, 392526057, 263419490, 585911000, 807085079, 264432326, 276299512, 301011884, 440372083, 930505965, 8088086, 782937078, 91270583, 798890173, 157577456, 536025695, 196293370, 48223646, 50929803, 433656385, 617094374, 931965431, 948496551, 308351142, 722140561, 558340776, 406188566, 298352430, 205222599, 680858296, 156746880, 617663175, 808731932, 223397301, 474412791, 300943279, 518381011, 551108593, 90459684, 332686097, 634901980, 517163664, 548098647, 63146693, 147865668, 816823030, 759237671, 228535567, 566825114, 83028896, 155367198, 648024654, 329882402, 169453054, 279347071, 475593508, 712648878, 105632750, 903600034, 451728270, 683192434, 64978961, 155640423, 774512735, 886514376, 993264261, 134972930, 630611628, 392077391, 140443184, 457941001, 373220821, 246972408, 626086362, 874408012, 309319029, 232066834, 546450998, 810224193, 757209133, 121825814, 681582734, 834011013, 839266760, 174484184, 364780336, 715212458, 784797131, 806568712, 678252757, 454396031, 93383208, 551342722, 851653247, 813385398, 720164947, 308518200, 648592240, 49923268, 828324677, 787200145, 981189270, 220169754, 324793588, 131830982, 252926052, 242475606, 760657433, 810693695, 115736974, 39715789, 626281715, 202279893, 855845200, 570249103, 575705422, 777930823, 333387899, 241664036, 827172793, 866455743, 134882894, 316559598, 700393394, 809840512, 556778271, 795909436, 35635777, 938070346, 925340347, 291148547, 49625076, 977462880, 709633357, 611692368, 495514644, 550987493, 702096357, 397295893, 693383908, 114015686, 597201281, 553593285, 163258982, 69364272, 703125446, 938580591, 488072673, 339754237, 622192189, 346749785, 806386035, 602023358, 103957435, 607544567, 302253925, 996716812, 231214852, 976996126, 364161130, 396868449, 747985819, 108811747, 921395042, 642725849, 695483885, 713574493, 532370013, 940913170, 14423626, 650658112, 684947001, 709517438, 15047579, 15277330, 757272103, 374338626, 122993095, 234824566, 932697345, 876570480, 599598679, 870196286, 552991134, 908148898, 169679203, 623611345, 969888088, 879181749, 522823, 953803744, 165189111, 95561795, 55096635, 852509045, 42876822, 677208980, 289290370, 19673864, 149243591, 294094480, 22440393, 873887850, 937539343, 601136912, 420405843, 21540808, 531265996, 306966780, 566842438, 408262734, 581779568, 303991840, 977997634, 429045215, 362100797, 801784928, 511016326, 312099634, 644457995, 152576370, 406556318, 914133361, 478511368, 84460406, 281039121, 410497960, 911899131, 934243249, 936606385, 949754888, 974115594, 579080868, 539980330, 841679670, 833801906, 233495632, 869004899, 84674817, 846413688, 789175529, 242319423, 979326273, 524209707, 460376520, 927178077, 826188782, 513134147, 184034243, 598982989, 135109013, 99899567, 971096585, 992592713, 845569024, 929050421, 296755138, 748752311, 580427890, 98968393, 375670274, 580242909, 670827524, 603262556, 506234279, 392934759, 511907697, 562360822, 623472073, 42673299, 133545619, 588142803, 961133138, 129925348, 439886963, 551458147, 837916556, 575627229, 826164158, 221703701, 903587629, 347747669, 18940317, 895916832, 819661731, 465234068, 72573542, 639529060, 849579940, 355821640, 202942091, 977075728, 905632152, 756696952, 240701785, 953320047, 17615033, 751451143, 346088634, 453235559, 6581121, 565620842, 186928575, 468053182, 736824993, 500221762, 716707841, 525474480, 944051961, 747141026, 235804727, 460875739, 826144443, 840548484, 507941726, 38302807, 680923310, 102545924, 855010983, 949962039, 946876560, 710451501, 794582528, 727613267, 451114082, 842561688, 82139397, 883500422, 521508967, 567021798, 610542679, 170172929, 357777784, 278183427, 668576082, 13407701, 623216755, 103465646, 871464522, 846061284, 469248409, 398315532, 880805183, 371134184, 288521530, 434229078, 725284118, 646867409, 91942705, 53864024, 60064713, 204506785, 306596666, 513805629, 874575418, 478378687, 326123515, 780296561, 305186261, 132449805, 408813101, 777016403, 425211445, 435656702, 470458014, 582277139, 258882934, 449091144, 476356609, 588398815, 706087289, 105536001, 512080003, 55910909, 490867203, 290836567, 688237178, 568225631, 948002282, 245738065, 928328709, 349053290, 494110706, 101878697, 346186563, 933582081, 851071851, 285123224, 450747009, 486125899, 487566704, 811212867, 689413449, 446925274, 456179674, 946862668, 868663912, 979076215, 522350870, 365402974, 77581, 685696619, 872570112, 484989535, 239574826, 866976274, 916591426, 584071279, 110667170, 22691100, 321595072, 40929049, 798848330, 814834913, 882340514, 825798459, 896960924, 117786963, 84482405, 805832382, 83205393, 822712177, 987078977, 495895031, 221926201, 994785625, 680935291, 756309925, 399211662, 590988031, 502647196, 352096826, 207255155, 231293891, 586809246, 684012897, 881863689, 340484624, 907839121, 810151957, 957805774, 752501102, 655806553, 607853772, 981330411, 433945912, 520157539, 892369156, 31198283, 805692647, 93701049, 642857001, 660597122, 136734424, 907250575, 90348937, 237355226, 623071381, 652018855, 914676502, 439762270, 956960882, 923988219, 777893895, 845997978, 505084569, 298481479, 651723367, 900004749, 588932788, 794958200, 307399690, 846532492, 53943273, 556781223, 369215758, 340680240, 625179711, 656854028, 894669882, 511370619, 953244924, 57917227, 951812966, 439399287, 311827653, 982984352, 333390814, 948409496, 960834911, 242633513, 527992286, 667874110, 929517442, 294244481, 21408107, 262359388, 25458471, 693363563, 196071961, 787287128, 21905155, 481735303, 684340740, 323420811, 370396576, 985956297, 591488176, 6470286, 506932187, 246640497, 46408240, 589216964, 332491746, 467681390, 268551640, 916568726, 536090780, 126018472, 500051623, 484490292, 185358333, 614882984, 207767793, 969623643, 794601692, 494981650, 249170078, 606042099, 37192339, 552176323, 863660556, 455653901, 686727228, 389361010, 815772060, 385145863, 333969041, 611221105, 879462288, 268485762, 254406901, 287799676, 390849127, 526392025, 615379561, 140195037, 72902194, 431176405, 60786754, 28207893, 481612769, 617706039, 937284472, 755463828, 167720873, 778373741, 972324600, 701535741, 431980187, 934162296, 291681773, 13628050, 572655832, 24966289, 40625515, 590336700, 606729665, 784004460, 695582271, 987805101, 319823414, 474058418, 824032849, 332942175, 892968170, 486382228, 342134892, 974288966, 50085553, 84510431, 567269791, 452187453, 903319118, 274235114, 324976344, 428016699, 282839878, 929455183, 105364619, 20226402, 386478034, 396189753, 817926056, 7675398, 951056063, 22872018, 295321889, 766658009, 381765758, 41757836, 781804562, 242508032, 694127807, 270127633, 534961312, 843890326, 788983428, 731821337, 52684897, 952785081, 457981904, 10653152, 401353988, 742730890, 329770244, 896953963, 713969950, 460921414, 926591569, 968668291, 814759354, 135597197, 962666960, 711363076, 709073517, 13639257, 343202731, 947208247, 502122181, 749153124, 849578782, 323281586, 412372760, 657386923, 744610653, 486815591, 854372908, 231027188, 822077034, 449483083, 522785459, 119516709, 586119240, 963463223, 215178982, 942932171, 450252551, 841114101, 127879035, 429401280, 323811493, 399430697, 201464316, 79028307, 715747489, 754311928, 158819682, 489759738, 784601843, 592513808, 462369758, 453374887, 169390868, 893331940, 582393382, 924427010, 328372676, 865189507, 286906758, 488831210, 152736512, 533501519, 999282500, 637237787, 986705476, 953391146, 810535250, 272721953, 713502240, 865560594, 357313185, 384865364, 637804691, 535707359, 940615577, 805762160, 860179973, 273589515, 831806527, 807447569, 389277411, 792589663, 453427096, 742509144, 938549035, 36114506, 653871574, 190469410, 35621250, 748507212, 865316112, 778828244, 253664219, 488643350, 321329082, 186117551, 234166067, 535194011, 904837140, 365071058, 302547409, 86853684, 579070105, 741681730, 952695100, 291730577, 694797929, 729349222, 595126722, 267799533, 439285331, 482642133, 881657863, 919012118, 20331251, 421396944, 564030243, 267173111, 769519107, 588335121, 571315371, 503760419, 587245975, 917056972, 545466548, 815727259, 353788328, 337057911, 357005018, 610799818, 480316747, 382284381, 644447259, 931350998, 193225733, 196587259, 730283618, 531993300, 173363299, 780101457, 966325006, 176976420, 453051793, 662799241, 711453514, 361249357, 104272342, 21612578, 963177460, 93791608, 453335869, 213436501, 317901337, 244326039, 325195476, 79656041, 320011525, 983040505, 228234404, 478225795, 784493765, 10748676, 309458260, 296277608, 37669883, 817193593, 634404116, 799680235, 190425883, 32565425, 447322259, 334628318, 947520053, 346409810, 934042504, 742294695, 214130029, 87971463, 495092006, 116182834, 44851140, 440905864, 367106160, 523684451, 441943618, 319684068, 95350288, 272831379, 271225993, 562135867, 617207783, 781525570, 976321477, 871448640, 638328450, 800357991, 878830846, 933570398, 354046172, 792826577, 370981857, 725863008, 916554733, 776726451, 741993565, 624341276, 892481248, 640975099, 842806890, 104300416, 47732363, 330020472, 78419185, 999572243, 470092105, 141747750, 65531356, 954528987, 383262347, 163588504, 28644831, 827437596, 326824125, 805066459, 136297098, 341328832, 519449369, 928334665, 817367069, 961359055, 169885482, 846127955, 862436871, 560978962, 981828777, 988457151, 729652913, 374471520, 708955704, 381243943, 954534884, 176386475, 961694652, 422009924, 962382673, 69636156, 69618046, 805780329, 266557175, 558384587, 559409458, 714562997, 669003804, 987147968, 263180877, 497359155, 316997612, 33521280, 332669533, 224440505, 453020830, 719878952, 766664712, 295377916, 503360524, 814637354, 328862587, 603334713, 172536340, 24627942, 916680554, 301056423, 342714746, 25404291, 634374923, 808166690, 184007467, 905345968, 117386174, 139932902, 830335045, 834541008, 440870913, 905573633, 390663243, 309216922, 904170863, 450382882, 768536125, 500065604, 937608724, 326323852, 752061513, 155495881, 588440226, 158680138, 262973594, 960878598, 935296569, 533558115, 795007715, 623323293, 601894815, 270521073, 679902956, 683237858, 640882431, 470940855, 540834813, 377402935, 584568700, 947511104, 66950716, 189468592, 724384824, 623288456, 738418517, 739881110, 899430659, 395698613, 341274382, 119806516, 533208058, 573668268, 808050038, 60967635, 878264372, 840598846, 165807586, 572806751, 873380226, 200196242, 779354900, 439215703, 552793228, 610934759, 325160547, 287213024, 58772193, 255863516, 855079671, 582896336, 908437518, 218601431, 866395963, 275472904, 937703010, 912539227, 126747160, 701658406, 394831640, 634119231, 178868378, 958366758, 965457755, 372808175, 168566367, 641376347, 860184992, 245435331, 974845103, 119198321, 879555436, 420422764, 811352509, 878562588, 715178926, 91262513, 248261860, 158583635, 740137922, 795196543, 191680054, 816047946, 866300764, 640757108, 658540726, 185746489, 189940228, 994108286, 573046684, 371377808, 55164929, 758045296, 54933753, 483020691, 469428958, 975024287, 997394401, 3622332, 115550161, 594797519, 432636574, 734816868, 461008014, 496721352, 339747003, 623163127, 690446675, 219833901, 987574066, 272948373, 714521014, 271526682, 557968742, 376270760, 561800834, 986267280, 638608176, 11373188, 194253925, 752538320, 428969254, 898451442, 823366890, 318772398, 891324704, 818509654, 182718164, 579964437, 896290657, 686185060, 716675429, 496137240, 725206398, 933248424, 574733592, 7066522, 198052236, 945058356, 229534974, 201070372, 509436860, 71541496, 650247426, 831135993, 653067074, 654401671, 669642082, 134820272, 7310482, 440390368, 675276228, 543772381, 634073209, 190405792, 23885777, 390040034, 4984753, 506272840, 855860702, 487400359, 43396363, 692539659, 399326259, 715772849, 173874273, 4090939, 946537782, 471424728, 328109716, 767424981, 953145300, 734620376, 650885365, 418839969, 84911691, 98516864, 514486473, 9233601, 350322824, 750752144, 874823756, 607981600, 26046588, 772303913, 19584734, 517419428, 246855278, 106248593, 226644949, 352539063, 249020960, 832819602, 474020754, 373443908, 728566536, 259418200, 83444104, 744544817, 349819928, 601548776, 102282504, 470443236, 126985302, 399865571, 87517594, 867598314, 478560428, 11112623, 238632980, 799901338, 72280379, 234223110, 822657479, 482021926, 621057366, 456707290, 330881413, 221348995, 140774323, 377378077, 75142267, 189901925, 434178561, 241412529, 444046195, 470658831, 464751460, 9266541, 346866411, 777061378, 856919541, 796207113, 807732917, 86588053, 195516506, 634307790, 500474796, 807072324, 888835265, 288066957, 303234342, 101385450, 578453188, 27097218, 340673779, 471201842, 452559023, 468151765, 975086955, 898893957, 635101835, 557123067, 434756675, 317080707, 962341666, 787034704, 924420276, 790298962, 432482576, 294189356, 346486686, 512520226, 940797486, 535717023, 442432705, 864496107, 354379857, 765854869, 523598842, 827119467, 599253271, 43229942, 806203852, 902616023, 704432262, 807658438, 851170795, 943076506, 835078646, 444410234, 577334521, 422070857, 11435079, 788580988, 554203583, 711785488, 583879908, 702597179, 191325045, 649449901, 297408588, 454466919, 293749910, 524234668, 757576267, 955510364, 458561556, 261766296, 796808917, 531826853, 731842879, 65823012, 14580167, 542957897, 825627974, 952923596, 250446805, 271914551, 35149707, 348218472, 993329942, 381135614, 675721312, 761678401, 134880971, 856804316, 461378517, 531969046, 378630113, 663896224, 937398688, 708415242, 862714470, 507282623, 135333257, 344685724, 897397134, 877901854, 406560286, 598103107, 657684437, 662244588, 872161011, 406484691, 527649113, 833861303, 682942134, 695742754, 636918875, 332689985, 69963371, 49816673, 204574842, 530342840, 121163870, 695717742, 901919279, 318800808, 248602188, 745789826, 951065180, 611777425, 333634223, 432332876, 955994075, 466615107, 911684183, 276331030, 114124748, 174946361, 309718274, 871104074, 475679433, 35923916, 986701664, 157053247, 471440097, 45849147, 135036371, 504845630, 943486349, 210687902, 994418273, 461198474, 245534389, 632068613, 675960053, 146699989, 339134312, 254613968, 344265460, 40202186, 812190140, 656078754, 936781414, 566319864, 518337038, 542975858, 700008605, 427472038, 291519375, 395864355, 834094638, 187908623, 129631739, 61379212, 322915121, 126609466, 957673489, 225397657, 527029592, 703471961, 985870829, 472489905, 821532332, 944717809, 757497470, 809432031, 328070143, 920975649, 834870936, 315194593, 589153082, 35891261, 265050525, 97650385, 39646985, 128598936, 562198538, 348132298, 533427210, 782706303, 504238688, 760074470, 403111124, 756995617, 938786601, 49733963, 373975868, 12478546, 513262397, 565500663, 526523382, 215977419, 345791947, 998882136, 400414541, 569734297, 860398279, 638226476, 271370289, 692118596, 725836599, 275170922, 626237514, 33412802, 507945463, 588957877, 122652578, 427433491, 204103722, 61792660, 343875771, 356644388, 625863462, 234988449, 205310104, 538442753, 616030644, 541793140, 11065667, 273783736, 723807376, 354480322, 918496493, 965037705, 84292611, 183405993, 582293454, 879817908, 595615783, 829254639, 482095057, 624311316, 361460991, 567344555, 150097684, 659880585, 921206367, 600817691, 265742816, 297997091, 422305856, 713664126, 181580031, 460774603, 263240426, 703054347, 917171300, 176801885, 988221254, 929001528, 724829602, 77700823, 533648736, 614134993, 992685332, 302155738, 107263390, 491832975, 947938085, 928136438, 34419787, 906048123, 485866031, 578541415, 962185095, 587842176, 217329730, 353998079, 391262568, 684197293, 926092838, 540612110, 98346761, 125882272, 29200153, 121218490, 366593886, 322192540, 781190935, 623829972, 361742120, 465182530, 592854493, 968440843, 633418079, 827387852, 379243746, 40607080, 833553647, 361844277, 155086886, 368943484, 703074257, 419319067, 445861432, 296932712, 664378516, 98931869, 16085405, 368784958, 539412467, 779900096, 890549996, 621401506, 975937976, 595008864, 129668979, 681413853, 348476843, 421200300, 806552414, 521073595, 702571230, 99122111, 794079391, 957306066, 765530773, 485583836, 965819062, 418816098, 897447158, 149123043, 634654666, 4627294, 619745303, 939637936, 690176828, 602775901, 685214092, 815696799, 810467336, 926952556, 722074916, 429749817, 100263314, 708257925, 590362892, 677488117, 892874161, 375660729, 485948522, 861082506, 685082508, 324280375, 772190188, 122542302, 52924653, 476257647, 503185568, 332043366, 89766658, 634230552, 156231582, 34189242, 784970941, 253710518, 957224011, 933789471, 265545223, 9855793, 550948576, 542367318, 703270117, 566760912, 90689611, 655091814, 163109018, 766483330, 350159250, 195471496, 878994616, 816801033, 720994485, 411342347, 572167671, 340575980, 955583226, 831086582, 988336677, 621156368, 525567832, 590025697, 600523472, 760899791, 340417500, 994536034, 772256228, 386804015, 255737991, 931603695, 509918616, 899882067, 915186077, 526930058, 367690197, 808400772, 313281340, 975412258, 664174355, 786670350, 422122891, 152306254, 38871813, 55475887, 193888547, 156876268, 981305677, 432001377, 857902671, 85623703, 941888730, 738227900, 821472378, 492326567, 571794631, 814520547, 226792201, 682804216, 980943719, 707864268, 365284437, 194069978, 513906918, 195258893, 441825973, 880979125, 251877883, 467657184, 776767936, 133822464, 412302855, 752736991, 405147932, 884429993, 947040450, 130669657, 853796783, 807502895, 48101751, 109269598, 322449467, 761615144, 737766280, 49374686, 473772510, 135125452, 790356434, 318446648, 476527652, 912574276, 829616561, 586936010, 99715337, 652680174, 341114957, 774391211, 296648239, 201708683, 299826198, 941431356, 863806757, 183859078, 445595514, 814625927, 638148361, 908965860, 960010547, 707069064, 828908254, 45437829, 647454602, 118480172, 429019650, 417000501, 507481681, 955918511, 112132035, 507619487, 695269331, 197036905, 618098706, 906526022, 959312933, 112704589, 914882190, 365380914, 798580763, 214290595, 117869579, 479965559, 518367413, 828135417, 189102325, 348809832, 623338488, 781368632, 230238901, 481620173, 366226350, 956964404, 452915609, 534133502, 677278032, 245004565, 376266815, 747435309, 936611399, 767030270, 595348919, 77269270, 956455291, 483234677, 67110531, 303271092, 475349474, 718688606, 502105420, 675183218, 287271209, 106551915, 400296144, 422062892, 28329168, 765608071, 663332579, 988120406, 70829177, 245722513, 845317635, 716606624, 700220979, 276339779, 674070251, 791179892, 675467312, 450302840, 679151253, 634159051, 225216467, 584144975, 320144157, 266880272, 106619379, 639111095, 785814157, 885936904, 395601629, 993544810, 424600894, 47539328, 229689103, 577812254, 304860134, 350242821, 445383378, 821567980, 888167755, 449711965, 974548045, 366839026, 839004790, 409517153, 308835235, 754668523, 835324275, 252362110, 823445224, 850497102, 609004048, 437094488, 965600506, 352408952, 140997171, 730385993, 163184119, 835815394, 469926466, 334491878, 594913515, 594460838, 986508081, 679754596, 494652582, 333590882, 39875775, 775562761, 198776068, 581368168, 916819798, 81332566, 816889096, 919498555, 196610142, 563834650, 436946407, 382227704, 250055590, 460377201, 737784986, 192209006, 286629258, 496966889, 804847679, 319598775, 805785017, 994444225, 517705030, 378082610, 188749443, 257400429, 921173241, 195981577, 318837727, 830649955, 661979967, 4565063, 403457313, 32892957, 704861676, 867628063, 917365715, 89479548, 493447788, 647202128, 839478662, 21333637, 360215593, 918376046, 592720445, 878894528, 988947499, 903779359, 608571587, 319485193, 860852538, 748099775, 680695348, 182253872, 200835007, 238622018, 586953246, 663536917, 366313934, 56579371, 208622877, 319527527, 955232688, 737102840, 907925189, 505111751, 158019452, 880862187, 939332889, 704150893, 591711950, 782326059, 716530713, 656558252, 152810284, 599390833, 545363175, 933157908, 245383225, 363371840, 777522175, 166207138, 354159088, 442526680, 287796391, 580372189, 564337550, 289223640, 520561914, 173764978, 316495854, 655013531, 809205703, 393923894, 809882118, 830558708, 291907991, 809369077, 898355308, 951902137, 824657095, 388709523, 180311818, 402916361, 276370672, 431696384, 215835723, 554567688, 254184307, 473277575, 76370262, 359727772, 494336777, 564152440, 716953729, 273050891, 392284083, 649806492, 203717755, 104345361, 682718870, 276734738, 687776797, 700434992, 942791729, 366877043, 792076748, 723489080, 526715219, 334224562, 30851293, 587845590, 413265798, 720750746, 279168533, 911763410, 325126817, 565680386, 456368852, 500733732, 987980993, 750659350, 520047913, 24111341, 620086046, 432858193, 873194167, 54712380, 401326314, 195272837, 621530907, 410084001, 778136795, 603470692, 517025979, 413664258, 599061209, 911214991, 31641923, 707301301, 201308310, 442281896, 32605210, 944366339, 315316540, 813543976, 113985492, 330497951, 584828660, 582251093, 43731933, 209827344, 22841803, 452637371, 858350501, 408758148, 604362392, 205705444, 602875417, 936888006, 661785260, 180770713, 857443727, 574216752, 756865987, 93591821, 641724140, 350607718, 779211403, 676751499, 317084483, 604923561, 363195773, 276153122, 62867478, 440175068, 296297824, 866456613, 496467524, 262806942, 107196194, 36875310, 1798232, 577612462, 514495614, 861211956, 146933259, 792109259, 451431674, 696021573, 116318348, 701669593, 378738158, 840965353, 207158929, 170501646, 183760240, 846174193, 602671554, 364838864, 311354106, 918792928, 779734525, 814848384, 365300981, 287544277, 925495538, 299933533, 96968028, 118412081, 894374756, 475156057, 689953774, 389097891, 720809283, 104878354, 535283277, 501286036, 852902421, 185234093, 133937433, 970493462, 331344869, 497542427, 958273146, 442591040, 914318020, 117978150, 686336348, 643796491, 5109121, 58167195, 405662012, 897721340, 842143110, 845620974, 669070568, 46067847, 704771796, 886667121, 935095684, 420403125, 826866790, 531992825, 69218405, 834477815, 688638565, 654516922, 611019369, 332148078, 780501761, 265374541, 713714609, 270894178, 604993583, 827735227, 283862644, 535895271, 388927921, 981653758, 248468490, 216620107, 685321713, 319671006, 508873265, 355786104, 212566777, 266524282, 396283674, 434787927, 287415531, 352755186, 3667184, 588569563, 947128779, 178975176, 688703977, 563238886, 488418592, 259810982, 41012571, 721371420, 687917740, 506479977, 134029692, 302172636, 872742965, 950948411, 72810647, 233798337, 637898137, 973843859, 677405647, 906449494, 560025488, 548876671, 973351560, 773283153, 324294975, 28635643, 245506025, 551766379, 17165860, 119032947, 813879781, 821266618, 313341809, 185721824, 905545776, 725002375, 689616758, 756347188, 414094640, 265514266, 821731760, 787427011, 615366684, 285442871, 904871355, 786001588, 922759019, 58035676, 591438169, 40569424, 648342189, 914525748, 427719275, 859293265, 844665289, 945665281, 408870661, 965996420, 844298407, 9950169, 133188139, 586753986, 965022175, 221346378, 992224548, 33598309, 40618726, 802007374, 432106830, 783840559, 320755560, 715373693, 522304506, 816511512, 299371068, 9008256, 161374707, 26709412, 718774433, 779574386, 835646197, 632768682, 77995634, 597518536, 655407688, 480319851, 616289914, 209080568, 458426201, 958905817, 166787631, 726943827, 81946979, 947256081, 370728562, 328565984, 891467373, 301197586, 701790458, 175179771, 984937822, 854222621, 411758634, 366030546, 838702095, 373911770, 192347903, 674719411, 927659695, 230991878, 859526629, 897676611, 153668598, 905054382, 556528682, 764308204, 761660072, 197756077, 69703866, 47063056, 6021408, 176825692, 610217649, 368524388, 965073257, 880099705, 897998151, 826363639, 853341564, 745968545, 893076872, 73495991, 23196114, 142321561, 154117172, 843185630, 865674603, 506522948, 297258850, 139280050, 133467861, 760553135, 74072290, 926449766, 294815184, 575749838, 395057031, 640929015, 199638382, 756015576, 277074314, 88299822, 862497643, 295780147, 518204114, 78930376, 729542718, 184407179, 522693807, 593466474, 723215358, 381761128, 869055731, 797112237, 688081523, 559940374, 594429281, 413183957, 450283735, 18251548, 647374499, 567819122, 70543523, 827574740, 900737808, 475587611, 912823928, 474469189, 228754795, 921575046, 65039185, 957967200, 922763170, 572438022, 767603370, 498394374, 311594099, 30949901, 205503305, 535275768, 752939905, 611784501, 355056772, 400911479, 813576763, 764094300, 524978973, 952131929, 898921413, 85537944, 957884042, 349467698, 507811704, 390575227, 858622138, 358694506, 989818862, 76682532, 517174182, 527292013, 61219027, 374149442, 411404856, 549786456, 377464790, 704340561, 524470170, 319213746, 982110404, 637314862, 908899027, 889876703, 824271060, 982000575, 203369248, 1346495, 873556513, 836824767, 876565277, 269737484, 29689522, 677367900, 447237974, 638749019, 147595807, 231045619, 113692600, 129290455, 131923524, 712807612, 817174548, 165068386, 25303129, 608678055, 877829368, 184151818, 57259018, 202294176, 934840932, 792327902, 1198844, 458837944, 449708999, 532906891, 479986372, 511223189, 970499461, 930723424, 78114053, 855016148, 750952259, 158811907, 300743253, 562445189, 757254223, 684185165, 33964048, 482030566, 219773058, 84698112, 5822045, 871116938, 418641628, 840640043, 720367646, 868425085, 956599554, 86751144, 921755541, 505466238, 659506384, 968385823, 784543268, 759561149, 824283148, 598718111, 954630534, 247965985, 296694054, 519737715, 468717129, 349514524, 125550605, 764674759, 883142130, 934149381, 699830618, 868515452, 428769677, 974263332, 339137096, 214024627, 944088741, 578551440, 590299719, 951733473, 359513842, 558185221, 711546675, 634899058, 449235864, 139839663, 949779337, 343445228, 481984207, 381389081, 985455328, 998093081, 163051288, 368702924, 330305577, 757193384, 187409661, 921345755, 345215184, 754418115, 537096905, 152238594, 373806458, 173348651, 28505003, 760400522, 982522473, 534560856, 503014496, 382841846, 485867943, 594496089, 818641864, 618857342, 683439228, 670496675, 687133599, 995116924, 238823210, 136381817, 940063325, 195105489, 393827960, 750131213, 571221679, 838381621, 795337027, 927802877, 244574468, 97298701, 209176521, 149980755, 926144631, 268060742, 71064733, 205672471, 879775704, 261065947, 690443163, 420931482, 72207667, 674628614, 987733598, 770705281, 835836037, 439322599, 909313122, 779806301, 626254488, 452678842, 141358070, 818433971, 377815363, 554370417, 691470841, 850714338, 939520515, 263234920, 779602832, 801607203, 303015739, 486339335, 605071199, 764886621, 365800223, 24438277, 466349049, 780938199, 87224839, 93040096, 618925174, 918490433, 58055057, 29516518, 459706294, 475057201, 235465819, 321411622, 572114759, 416225939, 124347341, 948084743, 606768908, 472959694, 764195041, 840681363, 561508859, 242674687, 813185084, 849381853, 844425141, 971265075, 644952897, 978399330, 891240881, 475679028, 474680034, 490312293, 485871598, 594201230, 856001784, 8656439, 456013765, 817345096, 813306728, 930011043, 846804274, 797121954, 558177129, 426572541, 711686410, 158516210, 579989503, 28091026, 465793875, 469892804, 835972946, 831987037, 609752056, 381960276, 345893717, 612536801, 956155612, 879716040, 775111142, 168824761, 350189464, 731736785, 588167348, 958280802, 461944693, 15717156, 375958116, 318135218, 599753182, 423707744, 98197952, 700636983, 651359597, 75320156, 455286393, 339661857, 86390502, 740522607, 592157268, 800510968, 662503184, 826494308, 683993320, 321306916, 249246990, 960364428, 680109862, 460012067, 986858465, 450369697, 490314001, 735155660, 168875804, 609616262, 39696328, 556997955, 474681479, 405126617, 790059236, 726122115, 134806962, 699519631, 153321689, 99936695, 900162907, 72130970, 544884718, 366609973, 891031835, 179074699, 794512282, 937369327, 561703787, 221010046, 570189995, 200663630, 268659362, 866250786, 609609574, 454336531, 57771649, 141570240, 500399263, 563478419, 533774183, 793442932, 278096290, 365373581, 715083053, 55662737, 612153595, 975428698, 196095191, 525953828, 817715504, 479751844, 440015450, 568335552, 664105166, 208646174, 19933435, 254458109, 604072311, 137221995, 765531096, 161646540, 579869622, 421243111, 990524159, 864485853, 245102532, 295427824, 917481831, 204899932, 824843236, 868997368, 76545001, 578363495, 456048193, 462817655, 426266464, 982726238, 144231117, 436589928, 250229941, 444123954, 111768115, 546747685, 793364975, 722100176, 661628080, 231127883, 801553463, 167284712, 586155375, 25155937, 860510989, 621061548, 190207084, 653280122, 589273014, 693796904, 830951499, 665558374, 53875631, 858498431, 23548573, 69070175, 425867358, 801886630, 746028348, 991241246, 364831491, 867032936, 923416575, 218129212, 264584574, 521720555, 387156228, 804733503, 103323083, 415645002, 770644702, 783064607, 421488734, 926272049, 285669533, 212139273, 537386452, 310548513, 416526549, 740189588, 289033436, 673384772, 34627324, 745763234, 307805143, 47167346, 229840897, 317541824, 329404407, 843138528, 510366483, 68503682, 472358562, 614731868, 782141433, 232096045, 249094854, 937184363, 834051878, 604374099, 534062387, 15412469, 432028476, 675939066, 431329714, 438875837, 937479399, 509415355, 944465412, 954342495, 198961548, 518435513, 729673519, 634106617, 793963406, 476785618, 48689960, 407038597, 452520998, 562076771, 680062710, 330395851, 681419212, 603825724, 472714847, 937299156, 959774289, 32120862, 589694902, 138853799, 987934624, 500613005, 285451674, 144760227, 270050122, 471643844, 661924952, 944401415, 788292456, 726669219, 788087257, 366072657, 53736461, 664642142, 705823523, 592134732, 922400119, 139225077, 640402976, 530461533, 736201967, 600456852, 618760659, 65796018, 632469761, 583858813, 803610647, 847246401, 381198325, 428133698, 818804836, 582364283, 258316883, 539144944, 154671072, 585336693, 67906573, 201327595, 139123398, 348842795, 637309715, 34927057, 806605130, 127545850, 44912691, 249116837, 994400863, 946139452, 153166567, 919263131, 449572833, 450116463, 599235915, 130874449, 841858315, 917734034, 428249135, 545609408, 226232458, 255281002, 439172168, 238995409, 883366883, 401568855, 827935078, 233161644, 418186702, 903255396, 144947253, 292385630, 212328909, 172316418, 511775098, 803184796, 172158550, 669734082, 349895621, 943214974, 437106718, 822616604, 361327451, 68391612, 457082241, 953121795, 9855364, 630352865, 168960136, 788049712, 635466933, 917529527, 271753507, 580516164, 819324505, 880019008, 887499745, 734123019, 13475698, 713443316, 46247571, 407295783, 699752609, 836747820, 728625499, 509982437, 148563188, 197217464, 684104488, 333859909, 45696434, 370683105, 704410533, 101985302, 52045434, 23179878, 206406071, 371282750, 500666799, 945036609, 713164712, 877428227, 112342040, 81824344, 896168035, 671278941, 324133830, 211941309, 292419572, 353710958, 598646468, 951806019, 819183632, 369899116, 875575653, 483855078, 176302143, 236447423, 288604472, 436798490, 711342968, 159264014, 161258262, 632175897, 638685634, 945616643, 996994941, 535756284, 136436332, 450796543, 843040939, 343608163, 130368583, 115614366, 216529705, 57283587, 677572022, 211648067, 713678743, 222040355, 462295583, 122950128, 102922539, 183010030, 806059329, 101960450, 594712208, 941549948, 921063563, 329140101, 224765711, 426517577, 84896635, 630923062, 761001196, 971922898, 257732710, 167088264, 385507112, 529330474, 128595671, 576120540, 859125934, 244610204, 746861240, 341600067, 710017573, 303880386, 292738729, 853471804, 206303808, 354172596, 499089811, 229798613, 413832384, 989594661, 678489250, 733102437, 974949604, 19885486, 260439074, 66914563, 637622478, 416011992, 916592306, 765750871, 226009880, 649766779, 312381692, 444920291, 626250415, 678930879, 817765244, 141836553, 645385373, 533661534, 105348463, 659286110, 192873513, 636115315, 923045866, 91095495, 604321136, 546311307, 906112480, 860529975, 455593372, 908832003, 496233755, 550175036, 132378405, 858081734, 54991403, 55987075, 67458331, 543355617, 482301679, 416503362, 662048264, 669573607, 285306771, 842835892, 268363180, 559252422, 334058530, 509843932, 609182254, 808751040, 12237060, 30068302, 774442466, 888824603, 825265510, 647585604, 81086358, 807053705, 920049606, 711774290, 897258186, 227475377, 868828594, 874011230, 587588629, 221991216, 76687206, 986085263, 255675856, 798516875, 391191843, 926850346, 173642693, 933576596, 135928861, 430155083, 913035985, 629668603, 46667433, 691152535, 206258359, 711341099, 146871222, 424553400, 860166013, 407158994, 100401569, 820440177, 959124610, 758759883, 594445647, 399373526, 128835414, 836005924, 743218700, 36071399, 406211569, 124196965, 740502174, 185880607, 416641394, 371349247, 325412571, 800506, 965118718, 646240833, 393066020, 289278956, 211613571, 849799212, 84639042, 433041995, 863461411, 371943460, 162798078, 144664740, 21602389, 68907371, 905075848, 10134893, 471034758, 233495305, 657249661, 115877326, 452132960, 415222550, 945703319, 213926916, 565623012, 329228389, 331608351, 681201800, 372010843, 930688220, 425624654, 74970792, 657009303, 321576897, 105327383, 767528662, 883492275, 485751272, 613879748, 609437967, 755952394, 752993447, 533110482, 836464797, 515243305, 27730106, 589510313, 408690605, 133701596, 315288438, 320741871, 462944190, 74851001, 32128699, 760045545, 966876308, 65047532, 417782925, 673680559, 493917248, 683953337, 505563250, 268453585, 575058153, 833149702, 840742719, 117115275, 607507652, 959592953, 524131136, 117686583, 637416348, 992149807, 14447773, 267537375, 423875596, 865367963, 215811056, 443211560, 898397375, 390663460, 129766952, 105512127, 453689766, 117554740, 923612254, 150550382, 304412208, 618961601, 744524025, 401468531, 294943454, 473144048, 177435787, 199213274, 994006341, 627696900, 846250468, 715675130, 500586935, 276422201, 628352289, 660737359, 138849087, 98175534, 353069525, 482940054, 722042954, 141014819, 931858233, 426590255, 110875005, 792791081, 997192786, 673836490, 819051755, 960945428, 766372677, 936218781, 425063355, 428320970, 4436141, 807032999, 308389899, 300750198, 823353190, 923796188, 318108719, 963109228, 454051227, 104769830, 573159104, 899067091, 641186199, 153155279, 31838290, 106741903, 36410992, 593805114, 625310375, 63118551, 866490717, 947197869, 928930865, 617036756, 304119226, 179257023, 161467174, 102258179, 657297966, 362405358, 553516678, 174795342, 429965480, 249062462, 386690166, 871930505, 744508146, 478437193, 563710959, 724987043, 365685233, 36389225, 888007656, 282230189, 529676152, 269583540, 975509586, 316960565, 833926809, 515215292, 853237226, 530488736, 937853009, 516118014, 282354612, 372184699, 805507268, 443046166, 650721856, 477991906, 889767129, 258267180, 591622357, 950029077, 750679652, 575852809, 328964081, 105068366, 222227773, 351852808, 668320531, 861452535, 598036872, 70011598, 545404551, 3943250, 463103625, 502412712, 103216345, 542721264, 979464174, 360092049, 843154810, 265124409, 502316290, 349989955, 41378259, 849386005, 343139159, 768625324, 827791272, 689463864, 916092472, 332888326, 645916551, 434574425, 577561028, 281567132, 517697117, 5301920, 264198221, 201472403, 491528339, 814717786, 195475301, 621710244, 644151094, 704888245, 715031175, 402019720, 723889727, 974330793, 182127755, 283248178, 870566908, 95753167, 770796718, 33428473, 567460135, 546374326, 69187965, 486693215, 21604194, 517126477, 559576758, 944570255, 968901982, 193892788, 244595405, 429221390, 769058004, 47538157, 123449222, 839185703, 52673750, 468287108, 177801716, 775438036, 599711158, 345629329, 371888689, 109999220, 755668423, 54276185, 103914844, 992551975, 224817455, 610275027, 59761660, 325919704, 398733076, 119093801, 299220465, 604014521, 123156975, 842286749, 429579109, 552063035, 339181234, 794874657, 379494390, 217481823, 808234166, 251907722, 86569252, 343558878, 617166524, 814717492, 179159740, 524594913, 495816256, 555059621, 375788289, 726000438, 587023470, 656065899, 124341069, 309109007, 137137947, 599289259, 88837192, 170514309, 925631718, 483676343, 664233231, 712441898, 967819184, 136265112, 467805667, 869036977, 894593767, 854032493, 664975206, 236373061, 215828464, 304782704, 524659556, 537728669, 314370262, 917034916, 275999202, 846336291, 484704340, 994051026, 758537117, 195364647, 996420113, 53999053, 383174153, 937650327, 81648675, 660403718, 293514940, 429337109, 736943207, 439594508, 311498785, 237438836, 74256305, 935939407, 894165329, 341992036, 407867445, 124915364, 930474235, 611236668, 854934591, 489538253, 799464700, 738892653, 624563092, 993937703, 45275381, 972056613, 258144033, 647128398, 659579361, 754218240, 470831639, 572840580, 694017326, 174422268, 427764917, 501712486, 316780243, 712334880, 341448926, 938143729, 688018345, 778103988, 333845154, 639620383, 434375213, 86392131, 435823035, 555851451, 486520406, 987214313, 119856703, 898786800, 551693887, 399351161, 319838249, 471401122, 7509838, 356886396, 582913715, 771131336, 974645253, 135821536, 299154358, 557115147, 301985739, 60329632, 320481997, 130690380, 190587999, 943503022, 795390921, 36198711, 684539591, 982216264, 617034095, 669647370, 967141166, 972225654, 188125101, 475615999, 857969105, 829184283, 603613137, 994509720, 588380943, 974314895, 948080907, 894827096, 884047712, 626320274, 854382310, 699885693, 978914681, 939269401, 684397383, 384374299, 412561240, 541550421, 612770498, 608958246, 45025348, 969248716, 431863175, 502536671, 284848537, 836890029, 944574283, 964999785, 141565867, 177502315, 672131827, 372880435, 545164483, 649186114, 76850043, 253043526, 46953708, 487310783, 332269588, 551840973, 564525954, 242177952, 281655609, 973980026, 443554322, 920042522, 307819851, 47142070, 993433150, 100925651, 174083720, 222190787, 259855553, 972940968, 887152550, 69325740, 322940453, 331447697, 946989539, 521917167, 832527999, 548483710, 729265631, 467259236, 297702779, 173162302, 985612939, 978327780, 353894785, 951169853, 494845350, 121319104, 718343843, 936744839, 545285805, 253855829, 751856854, 342980378, 413134668, 862590175, 974883897, 115579272, 564344675, 796551590, 712790381, 819962573, 607825705, 658261816, 357840035, 456381020, 488844611, 678198724, 812583495, 507352402, 589072620, 619532176, 67205607, 146287807, 544820470, 876312188, 463859099, 53495786, 498760074, 750239246, 185998635, 716322540, 202783385, 484203663, 362593997, 782464554, 562600061, 113370155, 165979226, 915427632, 44663731, 274417426, 846454819, 328468876, 567161997, 464728712, 339493108, 281107210, 464150668, 769253575, 610178948, 181406989, 347040633, 286708470, 335362305, 812467413, 262069669, 340026076, 380350430, 642589905, 145161162, 42815742, 199721536, 547779751, 879225521, 781288811, 963188646, 914183912, 656868361, 534680605, 137037024, 126482699, 184341280, 247079461, 200438708, 796249994, 29214191, 755953437, 660096608, 746343970, 427048419, 292949386, 103002716, 106392942, 840795307, 223457631, 693943006, 437462288, 581227388, 756181470, 223320021, 102977147, 910305545, 568368974, 934796324, 810030519, 45416256, 611028054, 599520742, 308071539, 991944189, 247607086, 195582544, 57781765, 957616210, 731223631, 254467011, 415112879, 310650458, 938843589, 439037661, 355325452, 900534898, 627808871, 642484242, 270735935, 586324846, 59281858, 781741342, 582668554, 541187071, 475387664, 784795609, 838639518, 882598429, 940136021, 106392024, 15133871, 483881572, 260635859, 782931378, 519126509, 413922146, 834792917, 307379354, 961693115, 227392875, 145976043, 266907619, 508804488, 292497062, 309110254, 320243036, 749858483, 538317166, 73152603, 859347152, 150202715, 3446420, 948107995, 603363691, 740514369, 664621143, 861935408, 49172426, 357382578, 719304709, 977631054, 54852636, 796280967, 292591448, 669144082, 207604809, 163894579, 614858030, 556374372, 55743769, 616807976, 515023992, 660507488, 524135343, 721710423, 464796671, 13363316, 526982814, 191574132, 714296948, 483790763, 352180482, 297457189, 92532916, 429201508, 544801022, 430972162, 669847089, 597437892, 387303182, 160731686, 546790972, 446949252, 402525857, 379259522, 49623575, 365058938, 743124436, 700543312, 700602026, 717399623, 587770413, 727522608, 2601134, 592785626, 114986091, 203340280, 7147919, 670586237, 451886762, 964631249, 605596849, 80970878, 898747109, 919513908, 78496914, 816268999, 682560203, 169785193, 566148084, 423631132, 932537845, 655197682, 441255737, 103986423, 143399647, 10333029, 977408490, 675512659, 179093735, 204132529, 767068058, 224504729, 570524078, 987745257, 197491411, 103070975, 36366928, 304924523, 101286181, 335634030, 792117261, 708308783, 999659804, 783664613, 519645291, 728233902, 683240352, 37662095, 127118494, 605662773, 753347173, 207791751, 14240747, 107074988, 766397632, 650359946, 147660509, 63117658, 31514289, 906660420, 376670040, 588439810, 95241317, 72963888, 141016778, 422317642, 268043096, 581281302, 620715702, 723140478, 273093988, 236876380, 817963432, 36555551, 629227453, 843123165, 551962439, 490164860, 179895521, 307976621, 464972402, 118575695, 801768255, 368594345, 673769247, 310619169, 444720826, 188536452, 365052682, 655861739, 524147813, 392596392, 456365735, 256691005, 685805530, 410270351, 974939289, 38132500, 583827368, 131750480, 543842278, 398879517, 15181185, 565325588, 109972495, 299698223, 953269229, 263281298, 665435431, 656125743, 347969912, 522247021, 723938517, 183880700, 208926413, 628908138, 850434597, 252993433, 134793101, 343666142, 745091771, 359475551, 276215204, 542208021, 597735577, 842001827, 965636898, 248602532, 954440285, 45752361, 311460945, 805450186, 477877438, 999316662, 783480501, 121852346, 799439506, 504115338, 497021776, 834078993, 419380742, 309880821, 498624774, 233106449, 698640233, 386960863, 673104674, 399469900, 685106903, 254787490, 144933893, 487131791, 737068239, 929304475, 691871159, 718928852, 396516673, 747544358, 946180322, 386439145, 958776078, 417225132, 1574523, 949341523, 750458508, 401151979, 658898499, 914179874, 694524881, 231751402, 435227302, 75555835, 929794469, 777203961, 688955920, 980124828, 157841823, 864701540, 571596893, 706150198, 969387864, 441835425, 648340661, 418648506, 694421089, 949697488, 931903152, 329780020, 222649526, 263589003, 40438200, 929052613, 478282318, 460828552, 491057096, 234474574, 340811301, 615849294, 423866972, 202030886, 652679503, 41865331, 649190154, 231369037, 133420709, 135286129, 807534060, 536486478, 281964231, 789904467, 556945094, 307187691, 591969800, 132442029, 352357537, 282050416, 941445988, 916206030, 483576121, 491203481, 346321457, 603085198, 662767875, 600462395, 367266284, 226364441, 89441821, 582838808, 848921006, 375140414, 823483882, 880609587, 791038487, 959751713, 447637343, 321169120, 153026314, 913532945, 143458102, 754394011, 648087409, 630547873, 579877587, 370264923, 217696345, 810098784, 36594761, 896238118, 783754369, 392382194, 282937721, 777127092, 392242312, 867291595, 959538172, 178738438, 213922786, 102695111, 398014511, 659266656, 889525224, 610573599, 638703779, 410285792, 304805707, 147043731, 626132996, 958269559, 154621560, 654560611, 191008422, 12135319, 625070568, 831801200, 755602165, 481556555, 592579327, 944349094, 250736730, 859266013, 817276276, 383757661, 443707379, 152997386, 433422202, 705512909, 227373995, 400465161, 31353583, 595038068, 194779874, 281767668, 251458848, 373495636, 964714892, 407646921, 124176107, 101268020, 478307380, 242188553, 180973706, 854511277, 347630716, 8872045, 224317075, 217842827, 125096963, 941788359, 22764957, 270806183, 388175166, 237927779, 166303434, 829340295, 647582023, 933990200, 973715532, 585289263, 392474354, 41292887, 986477268, 210248297, 954260390, 689062244, 217314215, 400172854, 848968932, 404684933, 314993397, 905076349, 458864145, 537850376, 978085409, 735431762, 603839914, 344752562, 662516023, 679708156, 891026901, 581213064, 962588950, 122886878, 759790913, 477342338, 52425632, 29608828, 745967521, 973990040, 543296410, 665144038, 626121765, 56877101, 740695902, 465973675, 456082941, 790433216, 224509054, 41905387, 552242714, 936386471, 8301294, 127873410, 551956717, 414922839, 584144527, 105534748, 42379746, 151930307, 204102629, 860960052, 966390833, 972543669, 399936564, 502382249, 69495412, 178682917, 65470881, 975266176, 979400659, 480179588, 36529431, 278461075, 245403073, 365531478, 35457445, 120174469, 955999507, 494330459, 131815792, 737393238, 396688355, 802132307, 264453351, 508805116, 684224370, 822193060, 659488216, 506584532, 127421164, 67089420, 656207448, 276240160, 284375756, 313458090, 612268799, 5883842, 373259249, 209301319, 383513506, 496823251, 294328666, 329140864, 584946509, 763038404, 720122021, 432455460, 556842798, 909874312, 569375092, 270371889, 767189526, 415994349, 751499957, 7648759, 285317999, 481633237, 403744193, 826113835, 321635178, 491909262, 857727658, 340564081, 198485859, 961733140, 80627580, 68093504, 36462542, 894442690, 383769422, 113844727, 129486731, 346372217, 724421088, 451573062, 418945238, 362476142, 289836329, 358467887, 609871697, 139747374, 879174546, 800998741, 863960590, 971011667, 691423332, 47821926, 147261183, 77781413, 32304717, 930278560, 925191271, 251869554, 701693292, 646397403, 605931245, 305508221, 905373841, 348984748, 45660349, 319372682, 438064148, 45992020, 882866301, 415718798, 313670777, 319053492, 474501975, 24512483, 633520458, 984839678, 45850646, 753584066, 499005406, 239077399, 111187421, 49740145, 107240619, 243550237, 359355550, 446769123, 878643977, 938330536, 710796081, 958271586, 88994923, 383250400, 617611884, 364382138, 360703647, 80800423, 175114721, 84547802, 282614562, 249738119, 633772852, 542664167, 315862472, 399297026, 769931400, 673183735, 712697369, 474259166, 308323016, 948955320, 255286038, 268754280, 793417541, 42234598, 174763169, 610727913, 908941674, 778860212, 76750194, 73504067, 113063108, 496546731, 203343750, 934341438, 401455409, 392137419, 732425989, 325913308, 321745089, 647061332, 332725193, 586887945, 990367930, 385528961, 464486788, 457611783, 720621703, 662470237, 145682469, 647308032, 264230420, 174269084, 968926112, 24203671, 992081757, 863911351, 877833958, 213354794, 251807630, 759777298, 899245387, 137852844, 543866760, 953380574, 487599445, 885144845, 78333042, 370127215, 877549489, 647403339, 16156282, 907865899, 646469354, 336843585, 611667022, 215045288, 475876180, 401361150, 208685276, 570931328, 616862726, 29920464, 363825599, 786307550, 697894242, 481122856, 868975432, 865827118, 505633296, 821509075, 810713016, 74668946, 18257451, 359215956, 26980453, 617532256, 570510189, 130193936, 840713209, 347262705, 494966424, 675536799, 205606415, 381417735, 115749365, 240552717, 741099384, 456645451, 289784608, 928155789, 810899006, 951937898, 536991200, 237646669, 41583088, 906870286, 968332840, 518878148, 427717171, 317149328, 712978136, 314448853, 906446659, 909266334, 734278676, 947786136, 906930737, 838904808, 391622067, 160899968, 621271641, 139770170, 417030375, 816611390, 575126811, 349080275, 401016906, 143485319, 879991925, 318228238, 879975725, 104028296, 218858600, 774817679, 194329070, 506852297, 332465786, 803177324, 972619509, 719895148, 371244187, 852586750, 52588939, 610858822, 97457154, 504673069, 735510697, 93746589, 889741229, 110159466, 726356376, 900831226, 181049726, 328960035, 743268594, 251455384, 418269377, 295837455, 388563080, 764871285, 909412144, 148930083, 592028857, 378335714, 274021523, 591989796, 633841097, 286588438, 504416611, 100168124, 948825230, 936433085, 956409898, 41092371, 184400847, 916932384, 995831384, 87330493, 411253348, 244869002, 551893612, 964358726, 150593705, 642873551, 433535093, 524368952, 899202930, 948367327, 310328952, 79769759, 631111507, 876774143, 237780640, 509121506, 935084594, 97639600, 837267895, 258823352, 329398798, 936789037, 949924461, 203531595, 655772989, 119614879, 51773536, 804111882, 401424667, 245332286, 426638018, 253212679, 667195722, 281138601, 540915554, 951597783, 443230342, 7634191, 952801961, 838236125, 792822332, 781840636, 981192672, 920534230, 171720946, 56346094, 867906086, 180571662, 435420304, 709796755, 824577526, 666212092, 295670969, 396139754, 693923697, 941072588, 913658594, 940816699, 532765672, 558736067, 942449076, 766829023, 147818974, 434796905, 254215935, 120126670, 7102153, 143264775, 105069362, 22939706, 8168311, 184900959, 632356265, 135501760, 61095547, 809593929, 473511356, 723346513, 976949622, 661671967, 67698279, 921653381, 919591992, 88271089, 957382094, 112831820, 23229268, 983942709, 997014705, 785431088, 139825652, 815689894, 366249980, 541788993, 844351768, 88135026, 184649519, 300186761, 659722391, 495708123, 285761393, 569125960, 397880036, 341639686, 579683406, 534231399, 909628960, 739639979, 615985151, 446238690, 355168316, 461927490, 225033714, 879714161, 114310948, 21707243, 884449859, 601066015, 307454049, 92366271, 728264899, 777825581, 908678354, 858607873, 712660449, 45352181, 51838932, 714295727, 130040992, 971071574, 530818322, 539911438, 545396381, 925232743, 612174292, 612114598, 519006681, 416430514, 552410493, 232521456, 354437410, 588695825, 922109473, 370792916, 299612561, 29820179, 376709273, 149897788, 3973554, 52267095, 16346381, 587142500, 873552110, 773579985, 694648861, 604026857, 741661583, 224430382, 236690894, 195466674, 731056785, 732983209, 403121673, 276532690, 520481390, 309919382, 391625153, 669346451, 426821096, 127089620, 586875967, 149904380, 803707471, 830034580, 580440111, 796664338, 68819229, 423861579, 939330087, 602717636, 530944787, 168352171, 882279667, 493230130, 215419013, 182498971, 151692427, 892524151, 825729181, 754847527, 132337155, 933910563, 926935484, 414911033, 242108567, 282514213, 622527118, 571902426, 693943085, 185537016, 684351693, 109888535, 571548876, 609534823, 569265509, 472853047, 212209532, 421192772, 148234648, 881300001, 76669074, 917005913, 308844686, 638118617, 907798403, 695513190, 475778369, 464860436, 650049713, 654696088, 620931277, 268203909, 83000737, 687974719, 357224614, 376527132, 488356101, 260637827, 542992482, 353412419, 484194393, 109928115, 110326397, 191503517, 590438809, 600872275, 4936403, 241928231, 711922934, 966405028, 353595, 827230148, 188357309, 481039417, 250139690, 522640850, 14038137, 582439104, 630524838, 82327978, 908949100, 254016496, 874795079, 67250610, 996465287, 323974766, 223643252, 111848437, 556658164, 318441010, 234911045, 809892764, 592795219, 76699950, 332432261, 547870073, 984996638, 607860378, 943617178, 823250895, 724079217, 502985248, 639442784, 372899652, 794591250, 985503366, 817025345, 69604748, 394623196, 213088809, 284363844, 505650619, 754172189, 888135300, 326489922, 681537710, 297434011, 712489270, 825840726, 431578722, 677766071, 969069113, 631914343, 197392665, 68686688, 710250558, 639511814, 600282864, 144288153, 18405625, 322261439, 63384898, 429106317, 859756902, 592280569, 864271511, 811391066, 87264802, 236876780, 659477240, 284183021, 20429057, 824241004, 562208123, 16351194, 462266674, 201195985, 75477138, 826708225, 18303939, 277947565, 241333535, 273355803, 280225168, 633089514, 730085596, 171690515, 303158903, 530012536, 446952833, 980543683, 706119694, 574664273, 444283270, 405430470, 865505876, 373323400, 890146365, 666566053, 8121741, 973503694, 146949629, 982946848, 744375655, 873990812, 137482973, 643576440, 274589806, 692841026, 450380363, 121545755, 744942128, 920482249, 742707261, 294536815, 717821969, 620716402, 232994599, 825282480, 261303447, 144027264, 690212532, 208356403, 41006144, 571613047, 960532566, 122959506, 678448550, 902802246, 545855072, 311737659, 624778592, 631167439, 452464384, 865479363, 59495707, 266163575, 913668049, 371961444, 262969034, 715163894, 428454614, 582146943, 726164265, 955607856, 661209213, 502675814, 131067371, 149963356, 828162701, 449763993, 899468511, 793794246, 108175676, 730191105, 760489398, 39495212, 719271025, 133420813, 483356685, 634556580, 42884818, 50105055, 344643573, 945237074, 277796594, 233916315, 135480840, 450205391, 389916142, 80667429, 374626768, 589825111, 772388196, 333834316, 421486852, 639986550, 353643292, 703689699, 36803275, 875843061, 935072514, 282384622, 207397485, 160811579, 955363351, 965073563, 839230866, 995601104, 961710638, 489106261, 332143233, 768749727, 541111825, 265228996, 71111939, 257384266, 451312547, 906486116, 639647136, 62822660, 790329835, 707430067, 626354575, 436056043, 305782601, 427267475, 387549104, 889256616, 618210154, 581536654, 512769689, 157768146, 111378545, 555785644, 958533298, 198321467, 348083453, 132239436, 283971206, 15469265, 411386073, 996631247, 642410061, 713986711, 366423542, 608261271, 489351892, 967378034, 426160436, 330271663, 429608840, 65613948, 238805694, 754853666, 978615248, 492337681, 407137236, 824189431, 488579130, 263707796, 110849974, 396388302, 154440674, 33996423, 463595343, 228903051, 801495783, 841636681, 239360809, 798670523, 663791289, 39188854, 805751947, 195757047, 437484813, 849122385, 498466723, 417760460, 231785550, 41145662, 652739385, 806722339, 776983516, 624311611, 387279676, 966435497, 428584952, 272992329, 708143334, 120715452, 942623504, 125220928, 198473678, 232653284, 167908601, 643480708, 211304063, 277744539, 616721363, 446543618, 661774284, 252155257, 90624176, 89418728, 402347844, 705817778, 239523522, 424725887, 597805164, 143093422, 676955663, 9847010, 775474775, 752747327, 923893256, 176812854, 40209172, 841960330, 671713872, 975805395, 984121525, 998300131, 258803100, 816282849, 758929078, 438341050, 847427310, 660630345, 250475773, 715543867, 101796356, 260584170, 542629291, 361935662, 956362866, 594647588, 82333065, 172874959, 710875489, 311075635, 158241879, 957454404, 635419070, 839917735, 466197087, 643866879, 160396662, 955225127, 337629712, 350997813, 664973288, 174608276, 285430961, 761657576, 202659869, 244773889, 918853131, 134873498, 974136941, 564148246, 298477682, 731329023, 94773366, 629656556, 237788381, 627722770, 477272633, 288537777, 608871059, 319233262, 807201308, 465848269, 567597313, 941203314, 736968438, 255669799, 379103294, 746941575, 330928950, 432309681, 466275019, 835640104, 249120511, 580531871, 874734126, 900325246, 521726739, 445603643, 944665808, 51880351, 416935111, 709964978, 4767014, 739224465, 716756716, 759450782, 574234002, 570371780, 396073494, 114179996, 896061964, 279227309, 365799480, 285564916, 337639150, 118029285, 270606048, 884568507, 919217838, 140675094, 868879159, 894490953, 57752344, 57766922, 976078000, 253779657, 617163390, 263986658, 351016821, 871733040, 745471112, 356993091, 616476325, 313849998, 528892335, 9177023, 695580785, 248407072, 966321846, 851055779, 910442636, 172595703, 825750559, 230668232, 779092461, 232685178, 108498141, 783969539, 792458007, 939627904, 241555581, 673308506, 894844341, 483277678, 505486257, 61837110, 924665300, 848579253, 68146953, 859616077, 882711326, 317321908, 72038634, 262702825, 562908175, 593900478, 677552491, 162379335, 336942972, 691707059, 144169149, 337217051, 237650628, 546773525, 175297877, 414539696, 901434051, 88979844, 681366258, 49639322, 289017626, 178646304, 583240788, 653050763, 180011063, 427527856, 207853435, 605601336, 270703273, 805577987, 474539338, 606531431, 572267908, 285123824, 134141738, 799235150, 871723841, 959175723, 282894985, 944969174, 456266262, 205145468, 566635358, 534853015, 384388006, 228982932, 670417832, 554467497, 757096571, 752420337, 721204897, 918420116, 312340593, 321836910, 293475182, 114901625, 822204571, 38922750, 680236928, 708181446, 832274758, 263652976, 89951079, 896559070, 402599569, 701979637, 870445586, 253949194, 229767465, 689812146, 516044793, 215215494, 979868143, 277876832, 59250593, 953947321, 968266751, 180215407, 432951257, 731032821, 339348172, 722277449, 26865049, 611171469, 98926188, 206252182, 507960324, 407932315, 999527562, 928750252, 722488966, 13035804, 693688558, 371618541, 689880233, 26343605, 729319470, 288218862, 291977257, 972667924, 760127570, 687865201, 439876193, 981032533, 124274877, 40057182, 902614258, 97653571, 653254151, 540276344, 848757115, 981996798, 810059832, 85377670, 296860664, 882069241, 381538870, 147511634, 569073531, 417519834, 689493415, 449570470, 595255466, 145306414, 260598603, 965426067, 257609013, 428661475, 121150225, 911320678, 22469091, 207378556, 69574526, 501379294, 809800997, 251236871, 527142199, 225224732, 466358163, 749696080, 311289720, 209284173, 830367424, 330312763, 398400491, 841177025, 978370169, 649971108, 84366584, 278406927, 323720297, 918445540, 89875485, 349012910, 957765592, 350858290, 797405191, 961642696, 734858545, 716432681, 799614508, 647234112, 165746153, 988689553, 635885748, 595345369, 255652103, 462227594, 122645131, 154835960, 545845313, 432054872, 166259972, 718201801, 267746216, 585142054, 545664287, 989516548, 811286883, 786800723, 416220786, 515130343, 744346624, 635716746, 61297422, 560965435, 558677180, 255115968, 944689163, 2373766, 599745673, 754080047, 366168053, 490381600, 680445564, 729483603, 685205588, 865925463, 920365943, 505605533, 810456601, 594579973, 640546767, 225602518, 67960465, 302810109, 337302306, 343886211, 609719481, 950708791, 706419645, 999676169, 360194637, 449263183, 309510213, 205845593, 935576090, 117250517, 885188577, 634846047, 406433508, 990592998, 530508536, 584570594, 810978932, 964234592, 262772626, 57670687, 907036971, 785589958, 535211440, 325833732, 493920584, 458156309, 266020296, 964244332, 166080055, 916555900, 414693794, 78219567, 80481315, 90728728, 494023895, 758991605, 31791466, 249717857, 616974266, 446048878, 378267009, 111223873, 339917676, 451989004, 103017890, 80889047, 964251097, 38246604, 537313898, 993377225, 198539306, 203743874, 354640552, 932128656, 267411440, 677928786, 163295380, 523931048, 828330352, 705985462, 575119909, 51509945, 850302623, 643666810, 928931840, 998717494, 67847119, 790288439, 322229065, 836215797, 967941070, 790883168, 400618512, 539737106, 436775211, 241104838, 820137694, 416646821, 790981988, 280583891, 306339958, 612992174, 454629871, 324533188, 74521907, 851097603, 186178048, 539402571, 533126728, 326514244, 87546913, 600396181, 189682778, 313049827, 394764140, 434229269, 317790678, 767571368, 581919962, 219134035, 353820261, 492773141, 550370896, 729445389, 419832422, 964141817, 236571422, 725869991, 714823335, 335779086, 828879892, 836089989, 210719974, 425232981, 200433353, 609121961, 770136802, 773277747, 110409740, 877450627, 222309606, 996935333, 139012224, 850435281, 32999327, 477651236, 272691483, 263382375, 558137898, 345387145, 509972037, 389028775, 848890907, 288326346, 939553960, 472026942, 862576650, 725133916, 629087427, 428027347, 443557972, 910414046, 703754526, 752231500, 855340322, 179549121, 988254494, 969847551, 130375452, 353266653, 629269500, 87108248, 933458831, 606927864, 218835631, 569080391, 120381076, 40669608, 290713380, 608778660, 824652106, 192514363, 635170222, 27056328, 509324482, 151342211, 806604386, 379535505, 38578784, 173704702, 674821055, 208174878, 334539295, 660407538, 120889449, 951341922, 575732754, 471006297, 867937592, 188460459, 499811070, 906151905, 861416525, 608634648, 68142261, 649964112, 386134524, 526478146, 492530367, 406563309, 257632784, 712079279, 202066051, 840143172, 171713393, 691537073, 829416335, 580333719, 266393203, 843648959, 365998259, 547775825, 818934033, 557328285, 702818504, 789396618, 924170027, 88071615, 377374325, 958592718, 132100976, 226639446, 130818017, 174546084, 733958735, 871817216, 51574546, 510199425, 348465573, 899068839, 205070583, 149324960, 790642676, 137048516, 865447423, 799390644, 417222490, 517834589, 11236309, 579818568, 800786245, 245098188, 218852645, 888298588, 985837778, 456501119, 801375024, 717053500, 438277988, 897042268, 821467137, 930081788, 673130233, 909791391, 966957827, 453789140, 652094844, 675972631, 104360965, 385554803, 606665467, 25759322, 668600910, 308823538, 643493129, 621177869, 655426109, 196449037, 543593621, 879843419, 729062463, 380333975, 240081910, 859934829, 913284470, 759882572, 824663597, 776628134, 901455239, 195397296, 407728999, 720649730, 851483272, 789234755, 981888348, 836839974, 221057593, 831567233, 394818807, 811610124, 112779394, 706424374, 94575814, 572320616, 622153598, 689639806, 956041116, 162514583, 357237756, 466108693, 130152934, 38682175, 274678288, 452318024, 750230503, 834870132, 358231941, 568484534, 889751660, 130386092, 70828715, 601698735, 961763385, 601573590, 996957254, 291957352, 925979305, 453108409, 191303053, 535923886, 97637648, 502281235, 599276835, 278849969, 643929419, 463191598, 639313911, 608669234, 214822092, 237899061, 918316486, 452344511, 964523599, 276886894, 553269662, 682392623, 106967356, 672519196, 602294325, 103047610, 295693091, 222541902, 738674880, 92221706, 690217075, 574358087, 389489329, 775861453, 822637253, 562438760, 926017751, 930715847, 609219065, 219001886, 986556224, 773003580, 816038282, 333168701, 777474421, 253703896, 471531065, 161646980, 424671433, 255623334, 602398756, 790092918, 811547219, 690199627, 657099797, 285287725, 535165765, 441363477, 173204488, 221360425, 633960146, 974175679, 193434162, 110297659, 933039989, 542445742, 342573258, 806916576, 258171779, 733046026, 769454720, 85370116, 524071429, 562744726, 615231731, 229875011, 787296075, 265420896, 527732484, 458275368, 599129011, 837708759, 133312549, 29822222, 10066023, 493889524, 429924437, 100519443, 988392998, 563013938, 425444054, 624327721, 941626448, 931141481, 773804385, 775330854, 103479136, 924777039, 162669198, 353605352, 281162755, 841244127, 837680444, 852821645, 645790998, 209944416, 813738913, 230365906, 665955146, 400699176, 123443176, 868146103, 832017777, 801796271, 933546299, 599967348, 316952414, 718400035, 572705257, 684574290, 924829574, 516469798, 11919923, 44256526, 663304424, 689264535, 796691386, 857502200, 943183769, 990448549, 956353801, 345463798, 886676030, 340548313, 447375083, 500743465, 397700768, 956880004, 494893774, 792845785, 456247663, 133869411, 986708865, 522796447, 331621990, 299006753, 969530020, 471606527, 995948548, 267660039, 316049820, 867917668, 383493539, 753782396, 274002498, 557388610, 350861020, 139193971, 932345499, 31137528, 844965272, 865497419, 977427672, 114819081, 823115090, 995089349, 398492948, 673069555, 858808586, 486143794, 638554324, 812350146, 960903125, 787174980, 715385932, 811807353, 800550120, 961884550, 150283649, 638263530, 912050747, 753808583, 202412200, 247718398, 728671612, 887751468, 691623198, 540289267, 114811338, 197054305, 586693843, 978715074, 127921193, 989106923, 956160622, 142062414, 431009770, 29394395, 247503824, 572815657, 642991635, 875729151, 558426961, 2190738, 630684060, 781441600, 544986658, 730908532, 626848628, 305087933, 954249950, 443116790, 938094273, 148122617, 351898995, 217260288, 927177644, 898190380, 453300935, 923390363, 793978542, 345282517, 569359411, 753185362, 560391135, 657969013, 907715299, 11957960, 826926899, 422903179, 917597034, 178110861, 945628423, 931360621, 465405324, 901948719, 456528334, 477631910, 971029278, 504003736, 557284096, 164192750, 956443604, 63337963, 198447867, 590936884, 41387308, 480666422, 8527216, 422675370, 238926813, 153158808, 665050877, 391254970, 718028296, 748705947, 558213724, 838886163, 871410529, 789178084, 435968904, 249313388, 298721384, 792825211, 839941488, 685651893, 751057482, 482027756, 730123569, 367361717, 493911063, 703815106, 294778791, 561884449, 861403911, 49700150, 904033615, 192121508, 315615828, 925261162, 366861663, 965125511, 752954419, 572308652, 832817700, 97023334, 794771772, 526284784, 60583093, 516108499, 671415964, 423499754, 321061791, 311158644, 128944279, 835268224, 243021633, 578534504, 913342910, 24839776, 271756229, 902609263, 263426852, 210361614, 508273635, 14046849, 657896968, 200967797, 963357415, 794065919, 45717974, 875704021, 96796632, 103420225, 659052516, 397893235, 776770853, 164313494, 562079828, 28351621, 762026249, 440881701, 479053176, 696290891, 641934653, 929458786, 392739636, 671328211, 609183177, 884775207, 728404615, 553706045, 270097898, 106584760, 653353425, 652169502, 283661350, 222142797, 592822808, 766139351, 666366268, 52354719, 940439882, 695228741, 968774508, 749028955, 314855968, 29587804, 861729429, 932517152, 466872257, 126856696, 154128725, 480998936, 636901876, 823864669, 595255962, 921937843, 944097263, 426418232, 750143664, 709012509, 728753454, 158930699, 993211112, 707893594, 987500066, 964538828, 9960182, 668907275, 69095484, 998348482, 522800034, 174270771, 464962897, 453496235, 518896980, 846447281, 551595849, 125096247, 245378515, 534376535, 658517844, 141645346, 807290667, 494220739, 280178825, 330736373, 326994424, 940248930, 900272254, 821111796, 695109267, 902837388, 972096211, 673229957, 689363727, 180803590, 575002924, 69912361, 904302913, 78227177, 764307923, 302502792, 969921361, 881398589, 282993589, 232883774, 601537738, 264145517, 740658947, 334177280, 324002729, 282315053, 199947299, 887604133, 620250119, 587856956, 129773435, 323288663, 765155304, 224436481, 477289498, 506158067, 691379536, 636200710, 160561915, 511024401, 571728611, 575492807, 859856690, 343797594, 548787401, 691939923, 780427842, 571298197, 886414068, 167221219, 390076235, 34597641, 930122027, 136489422, 860823556, 749146925, 185004457, 623904659, 78370328, 937238773, 752588319, 611080335, 661699134, 808865198, 562986001, 972601533, 925789915, 491811817, 49877085, 741375468, 671664534, 721311249, 286539246, 509915781, 818846951, 587344244, 191268053, 915443365, 49231107, 65723830, 21416673, 264954026, 717240265, 729300932, 586496504, 843934581, 436473446, 544269434, 579832770, 25317338, 831544834, 645212142, 882981312, 256346943, 844064301, 741357352, 668443134, 924543969, 665771814, 300137953, 212701885, 87599703, 426046954, 927452538, 962604188, 115483456, 693660643, 647401377, 346034163, 24552874, 588599230, 123636175, 103618277, 403197103, 609845559, 491093951, 967134044, 459354046, 900308841, 521008269, 285209271, 818528275, 695441914, 230595367, 178842249, 295238236, 799137585, 644319738, 633256729, 699698408, 523957061, 772869647, 286998908, 507917571, 514767758, 343785772, 261133257, 390590032, 274881216, 924529335, 932426518, 42729159, 804832640, 207957566, 281912534, 821259092, 227156618, 982886620, 125596496, 167834265, 152761887, 991341633, 793903963, 606640547, 298957615, 689278595, 827777862, 19434117, 233094075, 628192247, 792451859, 730230754, 330822650, 251959830, 738059111, 580348126, 24699947, 758975833, 109002875, 421701057, 318958827, 43910369, 92798395, 885646039, 581281173, 38807194, 979771357, 883457580, 362616769, 503993845, 959867909, 441079545, 173666594, 254604301, 163199786, 784530930, 661613267, 325341801, 256179809, 402199064, 307089960, 912402686, 654688495, 940842844, 363794083, 40399086, 25415132, 6847324, 130546725, 965336256, 881925159, 768545594, 361123161, 384254081, 311902449, 750316876, 899004801, 400035137, 121635773, 611412440, 685402137, 550696461, 915466372, 265850098, 817571122, 915737737, 442800271, 336466436, 559383009, 164093889, 399115166, 442276046, 550873901, 890536023, 948695883, 135092605, 639393643, 630048248, 635135918, 963770844, 720283625, 856883146, 361093816, 894891281, 387917665, 339803949, 427417763, 622322240, 852018447, 403319160, 889088334, 357007791, 697350703, 759906777, 240810189, 405176939, 311222573, 751552572, 834706719, 604380540, 916590682, 32804078, 45491292, 116358014, 663348588, 7528995, 420555420, 721152820, 25938972, 898075474, 291441430, 687397088, 334402883, 143113714, 989441748, 919360193, 960998831, 447425322, 790802906, 988806690, 481744039, 161597921, 135787705, 934327838, 769913452, 322355923, 510380594, 26507777, 528077138, 195105331, 828444844, 958664331, 291527126, 124918589, 358617021, 736952457, 431030684, 712346290, 305112866, 902462701, 617960814, 290428829, 524828509, 839894498, 687348608, 36691246, 907599295, 397739950, 929313788, 248849661, 739213184, 369080039, 795230006, 833779197, 323352966, 818585265, 35637577, 111786240, 76120045, 964816061, 190732070, 300325439, 791705355, 585349984, 669542817, 788829614, 728365298, 182140669, 170746778, 928793046, 60217847, 900115160, 764314756, 25493263, 169376305, 903118883, 918792619, 351777788, 452917508, 587905593, 205599813, 438772400, 83972037, 591350404, 274614706, 608674858, 116704753, 818405118, 418966316, 238837801, 493996684, 300738680, 765190069, 491056338, 64097071, 469906436, 636179325, 320957044, 209312819, 378834890, 291230213, 509067148, 672184773, 567483005, 983824379, 89047317, 606377992, 182596883, 437078267, 950792842, 942264270, 977328995, 585032816, 189639358, 462515937, 228487932, 288533403, 451576627, 52137273, 541490230, 435414376, 312093347, 228583453, 786445181, 217896377, 244557709, 929730721, 855161843, 45693739, 431830595, 171260066, 577627149, 463208916, 383452442, 713067181, 32832918, 417910287, 749268087, 980138244, 519571628, 729946196, 120158413, 637525208, 939283844, 137413339, 19659750, 897856598, 683411298, 169269116, 704105294, 923150200, 252842049, 128634989, 552659747, 936142958, 530311181, 755553964, 88571423, 734024678, 396087030, 544103451, 684903861, 959844586, 606616068, 862239949, 439457611, 493888048, 289355037, 424934454, 877050165, 376513277, 752981265, 430886854, 932931508, 931369467, 479542406, 401398549, 625403771, 920595950, 393372703, 166020290, 597763034, 211088817, 219259000, 969879192, 866585334, 150033600, 775040031, 867506520, 443966632, 912108728, 731526414, 368637419, 132606279, 872591310, 436445947, 483180109, 598092468, 12125403, 520008831, 60199533, 831822058, 201175652, 47184, 418775224, 292156879, 860528572, 559064239, 939765693, 400933383, 147362099, 367520615, 555926139, 478321743, 571741430, 756987178, 221606048, 26915129, 458067616, 70499785, 104900618, 39775070, 297625198, 723571462, 51065534, 326143662, 719385170, 407873316, 398416682, 508601913, 305271569, 599474512, 87146904, 612120322, 716233509, 341902073, 826979873, 935313816, 208902817, 858852026, 975991006, 275635379, 550326951, 763827188, 639527482, 417096372, 835536376, 330249759, 888805256, 85922429, 421864018, 578317629, 594319184, 770874082, 932098640, 439293482, 226264317, 533416074, 324621091, 125105615, 151723708, 241407165, 786551471, 947632330, 252985063, 635822181, 775605625, 350839951, 400862949, 275384047, 126377594, 831467958, 52616754, 803664396, 801798909, 870609357, 343579431, 751460182, 411905334, 220894704, 850373962, 733576428, 795932502, 867036261, 309390003, 192148042, 792548533, 59816136, 227282154, 607218248, 51318822, 509357083, 864290257, 197451979, 867811214, 31611307, 319110021, 946485230, 321064130, 739246678, 879370178, 205761849, 816540537, 225360241, 227566618, 14689550, 540983053, 915201552, 454478714, 394871407, 600099704, 60586643, 862551297, 129028251, 690605255, 412953953, 510499316, 614398291, 412624119, 974534918, 957154845, 249105084, 330013808, 672069919, 581370797, 548776830, 428499848, 806739852, 118247349, 13396404, 594481872, 427003242, 408609959, 849594961, 692952180, 9744394, 30662290, 591187895, 149232810, 182844676, 523099550, 240188589, 365484429, 260841096, 776402436, 984308048, 862143814, 99399422, 346809274, 961950214, 431549579, 308397136, 2696366, 550424587, 268133529, 148449543, 152687567, 598991103, 250807103, 998762318, 39287662, 640955746, 638620020, 450690812, 444640291, 477411672, 985754454, 271266021, 71454811, 57292983, 47228914, 314222350, 361851835, 885182346, 397529563, 873475025, 282166140, 920446279, 985948738, 287709534, 358203282, 879653049, 344646648, 707770683, 864076170, 704627252, 659481626, 852051993, 116003384, 413617143, 576336949, 648088877, 705869208, 130252447, 655511424, 217678186, 438792233, 861684347, 424949355, 790191616, 414902689, 590174701, 922943372, 206587960, 473535615, 400330837, 956264565, 859590287, 34026431, 70080541, 888634319, 342854074, 526747899, 539444749, 27612225, 553905319, 846915151, 343935783, 982130955, 925401994, 657190929, 852210955, 839680622, 727487674, 300028422, 70858071, 825987994, 33046120, 872686697, 819398137, 835905888, 560702273, 242060669, 655863146, 294127707, 314401487, 963265175, 618669326, 56831394, 652102360, 390060152, 245768784, 763769265, 137124462, 931826830, 525894987, 891406009, 368922635, 307532551, 816950545, 163667666, 967765991, 283133424, 866181531, 626033149, 200938076, 843382810, 631782034, 439602230, 106193832, 147842895, 203232977, 129395145, 267262612, 624411212, 545693655, 942587081, 394767535, 530432851, 723829296, 374491410, 570292165, 633450285, 140398749, 421013300, 465828497, 981367336, 96437565, 769905570, 951444795, 209027720, 119326467, 946709456, 603932172, 526270293, 82451071, 145452987, 952662337, 805382936, 997601378, 668047188, 399869103, 984334468, 930770586, 423997878, 617791072, 714278562, 128592818, 65057884, 160154817, 314864752, 575296717, 655895372, 873563313, 747671746, 701972241, 204620583, 941536110, 363459830, 131892801, 20541328, 437699429, 491455977, 422068006, 620078149, 10152227, 218234463, 823895969, 288030725, 970889045, 633693340, 48382440, 246820247, 484740308, 514864817, 394562748, 435357635, 484733622, 909810343, 868420476, 279105148, 834477797, 640243073, 403061989, 688891806, 742345732, 814875377, 881601097, 797475514, 454059795, 493424021, 861766573, 57137563, 231718411, 54711619, 56253697, 925287165, 48909946, 208189187, 487530639, 992284083, 909318203, 745017509, 231394923, 808203691, 827320594, 54715211, 613302252, 555058714, 149010296, 752834371, 826589081, 422103549, 387737714, 97069706, 113360328, 716305190, 612778496, 644542347, 635068826, 916956721, 671458255, 403149153, 645628713, 40094068, 862089421, 771354260, 482313094, 483759154, 800058780, 122014629, 805079274, 840178467, 907646328, 996603934, 949001447, 138253496, 221039421, 287570745, 744956844, 468522308, 276296393, 662052050, 141278997, 847047222, 730223606, 312797773, 51712681, 255820501, 446396248, 179679775, 515798978, 961481098, 157931868, 260956638, 90988510, 918102029, 400102019, 896071169, 379553680, 777701330, 556943759, 137352539, 344182570, 535706034, 497726008, 632164478, 835033594, 419782810, 249415033, 539727392, 762969932, 393062876, 683366341, 583942600, 241433546, 941909524, 870567699, 28959871, 855132643, 271117791, 74345756, 458845373, 187151856, 339736825, 643760605, 261301125, 837961454, 161156953, 658140798, 882254774, 680184362, 62826876, 967058525, 276253449, 329090621, 632708112, 466379362, 732325817, 370604261, 43139218, 907015062, 425092370, 148990726, 246834268, 191962199, 741683080, 166954317, 557316515, 767842463, 896922800, 539395912, 507154319, 842235871, 714586785, 371430612, 476959552, 583748459, 547067832, 991181208, 211041568, 119377320, 356630505, 311465184, 431853083, 377331767, 723340482, 589915001, 81800201, 566189375, 77914796, 188402721, 567204278, 848351926, 690719081, 261241029, 950252555, 316413090, 481603787, 900198503, 311583357, 598847291, 872943380, 285561719, 437206634, 970528992, 642451223, 615250710, 628892684, 561555188, 504686323, 838141229, 138873493, 920343107, 780156839, 810131105, 153620687, 437436936, 343487368, 635343809, 743215053, 656900355, 231349850, 881288933, 698916132, 340211613, 660714212, 768402382, 323626028, 906989412, 252949147, 527080956, 538546270, 134709411, 995885360, 935311303, 895053040, 705960708, 937787766, 510588796, 461708641, 141482980, 482207987, 783096309, 517335206, 218373434, 686352485, 128121351, 240630284, 354098919, 902910247, 624726461, 506154225, 78740721, 421046091, 304613887, 511154337, 991239452, 505289693, 622763650, 740838493, 170509834, 763494927, 972463065, 698429435, 926975255, 554986459, 118296930, 379150596, 533532994, 394760470, 380506668, 140813345, 781998222, 2923767, 493442030, 291968836, 459162927, 28754041, 84824956, 218744832, 982189370, 878203, 87802549, 11557385, 354358323, 552460166, 632124910, 972003763, 956820066, 345864660, 103896885, 374808998, 766070385, 659137162, 445778382, 850333802, 232615708, 180279600, 896419074, 787564454, 820425920, 528395128, 799461651, 506821622, 231944514, 432593322, 674640375, 708033063, 917801450, 665819874, 950746153, 446587345, 498840190, 116941440, 759064293, 129486338, 916838488, 368568998, 542304637, 400417454, 840821704, 797268809, 939459860, 665093745, 219396629, 832411400, 444199358, 533101914, 920685131, 391482343, 795608064, 427556079, 81228142, 2994035, 593580473, 891695451, 796747253, 365766033, 183903997, 397892416, 997800298, 50035825, 528830738, 866384252, 753022757, 111323855, 135822032, 589992394, 443541357, 396774353, 893914673, 763716490, 349055039, 558916723, 794783932, 511532967, 820084016, 290674092, 221641462, 378451257, 588452615, 569399439, 331842515, 950241100, 809745508, 869112753, 254926828, 687317859, 965875668, 799737664, 452800850, 313644699, 486328474, 745290855, 153650620, 648053061, 27973572, 917269831, 152733659, 998754729, 506587076, 574422944, 931716279, 954820186, 698806278, 770247707, 8200899, 588347326, 443836853, 262342159, 777734999, 145689028, 485466983, 940590370, 179094891, 86872606, 998010086, 242969507, 551625792, 454701285, 708691253, 21827964, 391924501, 350790449, 236290730, 432206480, 140786085, 406296622, 313301148, 197389496, 605099276, 600112169, 664335372, 540420774, 63578096, 876447612, 624085193, 662578522, 240619417, 881408228, 780082584, 546832769, 880508026, 612150119, 664542062, 525902385, 144453417, 178208312, 152213577, 669540430, 630586192, 545605819, 88442489, 406737684, 485173265, 353259036, 857287992, 966284069, 25289587, 225617636, 96122108, 129427494, 798298344, 711885634, 295560605, 348256580, 977810689, 761929640, 748554073, 251865880, 195894553, 268802204, 245665045, 503456068, 861542997, 556660114, 290101689, 827998436, 125219095, 802906821, 387223282, 424389470, 888832906, 587461573, 149170855, 895954667, 658992408, 171231606, 587698570, 25153279, 266681554, 325392343, 387301296, 923596909, 10980774, 853436694, 37981473, 743918571, 105330599, 99264152, 450031959, 192814255, 530761037, 756992345, 107268391, 402171353, 127831638, 362427372, 92044968, 403592938, 2929260, 379456244, 259163421, 639216970, 791603866, 969869036, 153088457, 53435282, 507211780, 333906317, 130184885, 457213080, 331780005, 762638455, 870204598, 814705702, 315790201, 157256666, 512498139, 949240285, 871100950, 491292229, 598516989, 242149639, 283546059, 927104407, 330353739, 702183841, 224750879, 792694842, 939755338, 137452751, 77824519, 297238820, 929348900, 59364375, 407856066, 577247291, 925931592, 78155326, 624177924, 832204256, 292523662, 306113125, 777625149, 274976167, 161954284, 651756036, 771834383, 575480732, 139546030, 544219369, 204635119, 851257502, 954018945, 731185262, 830752636, 172599267, 400547011, 114989340, 104068420, 574304589, 640402869, 854856268, 152041479, 595249145, 606199282, 501745838, 598380526, 637692410, 699606507, 870247540, 568109741, 565362979, 630288342, 803343100, 712901835, 273207196, 852767899, 985217664, 628271648, 230812977, 358382522, 735488327, 126425149, 754668108, 669473098, 911005731, 300831130, 944316954, 906021927, 418493763, 280207051, 413129433, 881782875, 278852271, 425633071, 291417283, 66501802, 666812295, 539317845, 838753941, 383351593, 63463219, 475696080, 681360596, 483153377, 536743853, 344568008, 505525461, 112069485, 186791942, 156996849, 46316414, 522556201, 609111331, 720263413, 404093427, 167652496, 292053873, 79815783, 356860747, 429821602, 759771620, 176159171, 337094507, 816358492, 240518772, 97927822, 850947767, 75442213, 323964999, 573143830, 696568286, 508819599, 50390517, 411911984, 775266762, 84766872, 871385138, 887986984, 363352615, 69628470, 706780712, 703943876, 583425771, 434892999, 13333013, 989399739, 917520193, 665008072, 422371410, 895535492, 760901820, 344083332, 515702353, 277199847, 908073338, 992874031, 139372714, 363866228, 311993188, 2685564, 530481433, 189529871, 322463355, 838101814, 852208899, 735592481, 147324876, 593606068, 483147356, 291690435, 675524766, 94512866, 268019374, 738374269, 140948707, 51573781, 894511568, 484125395, 707098456, 962994281, 745075298, 141070067, 486894820, 662612323, 869581063, 531160076, 240723727, 24230981, 38964502, 896781983, 70039917, 295205303, 229942456, 316335596, 465040766, 187719701, 404648150, 525364178, 662293008, 446371272, 387294931, 4969913, 245360495, 150816883, 155070527, 779143872, 572078500, 803163239, 38089251, 32948554, 349016244, 800150625, 773262640, 343663113, 535919701, 626586242, 608422541, 974052714, 447847436, 21760946, 519358893, 548779203, 976802237, 21801010, 751469900, 289820762, 469635589, 56582323, 660476690, 732509911, 494145887, 24286879, 28783603, 132186379, 527933600, 919582463, 29906815, 216225343, 814936668, 778051352, 434319252, 940614441, 937088370, 686325620, 878847384, 625515023, 467025363, 841094110, 235506611, 512644132, 841779096, 324880616, 895424244, 655981025, 782338115, 454095015, 165425758, 13468688, 476043189, 898499866, 860033046, 399653758, 218263541, 127843472, 542859568, 20472230, 333748207, 610075690, 859585545, 890783226, 442020649, 920077092, 500476050, 864078398, 826089680, 261588626, 524014686, 73343468, 545488809, 584864699, 411986305, 996778352, 488837887, 923813348, 359659583, 257884996, 347733000, 733595880, 412011557, 395262747, 568372847, 571970423, 546114579, 726383652, 849568003, 789062417, 261617822, 563308941, 294699604, 601366339, 916585514, 80908512, 664376314, 652540151, 572437488, 291621732, 420232023, 378543606, 972355749, 189948274, 250256326, 825370822, 58166132, 564327497, 533520057, 584623279, 181845592, 324583592, 36924092, 347806992, 103174159, 745331241, 355870018, 583512823, 726049680, 863453879, 797392499, 846184391, 864266094, 567166357, 120984989, 593419544, 498705152, 742178001, 630302664, 932909498, 862814997, 659705580, 342055428, 367290378, 837444346, 75048168, 296919714, 221896772, 428623587, 491746614, 616225547, 888329990, 637078386, 738489329, 682104517, 491610014, 519722653, 415576040, 206872676, 742136120, 959029740, 168350599, 936242261, 848642035, 622305937, 358477001, 517167942, 35981714, 663850252, 424560086, 863730835, 279877018, 602189642, 197063755, 351152817, 678971480, 685019959, 938594348, 548634353, 439899423, 863377460, 482596775, 722217393, 404397028, 76096520, 265448638, 871478549, 852493522, 448352787, 875721881, 4070564, 995981104, 834698689, 997014875, 77558377, 655215061, 390559546, 632922000, 113140890, 667303033, 666719005, 245831922, 173482200, 784609826, 678036269, 335061930, 438991738, 497553977, 669872793, 971681696, 915171869, 409232791, 134772555, 150347864, 184484581, 389491237, 676018271, 99596259, 953510206, 971870760, 720114902, 779725344, 546806359, 971832251, 126103610, 383108396, 800757498, 23754472, 529114713, 210889867, 465524305, 272961361, 813837210, 854204940, 521501404, 871482493, 407227009, 729407394, 691538849, 933419875, 349615797, 839584091, 863787073, 198563276, 40742473, 329666425, 992477575, 593277337, 210937257, 7233229, 499683503, 38167862, 591712138, 385938174, 245367202, 91609692, 862528352, 79751486, 597368661, 772608731, 494554976, 23638747, 377760620, 691291824, 656857212, 122100864, 414760339, 498798257, 335162294, 532490469, 284127724, 260441640, 911288394, 376992411, 699134253, 856282437, 978162979, 9462204, 871792433, 443899588, 420424997, 296217570, 493176832, 1494517, 725264113, 980941724, 279052152, 35621910, 158623906, 216944909, 940686293, 825822496, 650024411, 50423041, 681713377, 377211198, 811962249, 222965339, 439276674, 289230597, 233862688, 915597809, 906294832, 524193238, 781272727, 999962476, 167699621, 465502166, 729431392, 544899955, 683301925, 103403194, 519757980, 547166294, 880417385, 646452013, 558029213, 718560080, 682286713, 430897685, 26915259, 296642336, 75885720, 310350765, 508905271, 654827712, 316906414, 279921438, 421474741, 314662177, 117747783, 872504123, 673091828, 44585761, 901968761, 10978022, 670073754, 895146923, 402452880, 227351993, 648474893, 914620, 527689529, 515335246, 825873199, 736449625, 226989252, 541133831, 673781365, 754636780, 860023707, 573911260, 346128051, 308157782, 459458103, 133958783, 214431846, 370361835, 144444002, 530789640, 128564337, 919324453, 47916544, 796890840, 131164680, 591208116, 508798624, 483148657, 151574584, 956268260, 82101919, 461120757, 617946217, 573128, 718321703, 160988601, 405689889, 74729020, 316579608, 71273271, 777270220, 666735643, 583679784, 148303684, 731689914, 488043478, 245441788, 314813569, 580190591, 949210162, 507965443, 318571187, 709411749, 870705511, 355247130, 748102941, 759276533, 712210403, 166401517, 930858585, 489271569, 567636605, 682904042, 28924806, 782168118, 157076363, 630763487, 108360004, 976940752, 937132980, 495245249, 581755282, 8487610, 456442947, 272496217, 642915412, 630126844, 249352504, 603385021, 968242586, 195547813, 893588110, 683939048, 21628266, 442733722, 585850996, 872131740, 796664233, 829973005, 261441163, 2392159, 834992604, 47158693, 521774329, 206632005, 156328721, 885877329, 457888121, 874391629, 862112218, 106268979, 285438126, 306309491, 152668748, 998677597, 704032249, 488683610, 877963209, 130563853, 905475523, 150229947, 72953923, 859930113, 577079728, 177243250, 538407088, 602213440, 70421670, 69963656, 27339638, 906689036, 673447125, 515752632, 156080408, 862569751, 628039114, 956841725, 237971590, 194951203, 555358460, 630561936, 743785018, 317694487, 618264628, 402968112, 186004790, 544475110, 934193248, 718694246, 491472844, 146394878, 483172265, 221525115, 611798982, 826474990, 897085659, 719981439, 102973715, 351993290, 799451917, 509858087, 333384911, 471450969, 60010666, 921758978, 314151874, 749422004, 691790472, 115763962, 773072679, 801255477, 764354233, 682799854, 588963356, 451241418, 410069664, 263347627, 972912113, 595028143, 835847908, 451790586, 975556155, 179241304, 982317388, 375421690, 641468766, 594482489, 696516147, 130127288, 589326952, 108641435, 333348515, 28851645, 145561654, 594555, 27484397, 941611513, 937077355, 215603339, 673745456, 638847208, 803959626, 912751882, 147456150, 787563091, 652194534, 690634879, 595445481, 504325803, 537274956, 58064337, 304166830, 190528605, 566655820, 435544510, 517186907, 556715816, 925814457, 47940930, 919527567, 674567542, 316522662, 385214597, 482707783, 18589562, 290864301, 243316062, 458911825, 112555620, 945472968, 400854345, 624242357, 478993706, 721860257, 944856837, 615753981, 428811965, 343477689, 22557178, 574376932, 318671526, 560907761, 918744548, 970772006, 728333721, 678106403, 351184419, 573750605, 223719412, 203066406, 488766641, 18806731, 60422015, 807061642, 256124895, 430105028, 352315930, 649892709, 2845675, 985557257, 642254947, 661112326, 24141584, 912945127, 759637485, 943690162, 164803684, 582771151, 979450246, 441802304, 92544626, 922316466, 358662081, 505497977, 113730467, 147725892, 817937843, 57128380, 893370134, 653509973, 721306083, 544523499, 805146975, 278663601, 865869798, 349632563, 90528869, 605656635, 793245797, 555335196, 613728127, 613922035, 838097514, 619491679, 190233833, 870819229, 567940667, 369042931, 280668421, 957147936, 981876953, 732283070, 229138997, 518865844, 149616590, 517467642, 217994257, 963561092, 74888022, 648610206, 945667394, 859080619, 317340956, 641023539, 173066863, 549563569, 337287364, 496151056, 339680246, 704205932, 340484459, 430155895, 228253215, 142333053, 345885783, 616826365, 980650978, 827039467, 318966763, 695361893, 202788946, 40621591, 257818317, 186838702, 343134538, 508301058, 451761429, 994651149, 759667763, 175429198, 728045807, 166083947, 264462077, 733784761, 668219651, 886197687, 318837970, 199996461, 842274734, 483920889, 897194173, 855453600, 123796147, 699012290, 735842274, 498737516, 25428830, 103661890, 585157004, 860131078, 790238453, 650373695, 587416475, 932122216, 341428054, 810700753, 302344031, 791260448, 509266912, 459255083, 410544121, 391447325, 568395087, 581949780, 543125504, 640400452, 641326770, 438165176, 755012731, 287959796, 354704391, 527113135, 22344394, 272216076, 252333997, 310448769, 458170975, 459627222, 232596004, 517272079, 817447602, 741177022, 14298900, 451178410, 873629610, 696130616, 784227926, 316557022, 403612539, 179187811, 220768102, 124691563, 860572061, 689101834, 103290224, 116542496, 209467240, 416773680, 910800043, 326189641, 968805076, 55563217, 517824852, 566900496, 464480329, 465754472, 481981260, 725474683, 470038446, 411012247, 898606171, 613779334, 276496339, 617537289, 31052589, 155798141, 359333846, 562117049, 716574152, 634719156, 731989954, 928130814, 96103146, 105004096, 273673553, 28199430, 876554678, 43442383, 235545594, 399583279, 763962416, 562957408, 735400183, 685335710, 332332424, 967748352, 562687547, 907591755, 250717531, 473134592, 666452655, 865175071, 412005668, 728326930, 299859647, 714691936, 774879401, 894404978, 247526133, 972674746, 40072836, 310556317, 967231729, 739718978, 307104583, 858664716, 135052453, 7668361, 660409219, 660531245, 641723636, 205279921, 75919681, 728442781, 627613625, 504863262, 925191939, 370481188, 261500582, 919795117, 330167377, 637808876, 910893665, 451825748, 759175915, 325267031, 873269925, 285256182, 165686939, 676057543, 803150902, 293808675, 41132261, 143027964, 389678244, 981367882, 789705013, 106269903, 784774240, 414018349, 255861916, 990541376, 284275354, 575012091, 416376343, 615636427, 944568773, 790683553, 309210112, 828374583, 697551679, 845268471, 181060031, 440405976, 845479021, 31470838, 567355214, 479164049, 69889667, 794389386, 101377813, 303793965, 138753013, 692475748, 672452730, 435106428, 130341615, 876378701, 654895829, 402479095, 43262789, 566308906, 255158794, 382827698, 573287840, 603128068, 548801286, 942645385, 29137964, 666590607, 712307687, 39117192, 660034459, 609024136, 336541322, 686662772, 825552305, 519911981, 148378868, 671469559, 511101826, 18657474, 466983460, 511372578, 563175565, 546767520, 381251192, 33804875, 573957083, 27749136, 142296649, 44196038, 51074147, 205350587, 14191456, 381329626, 618099932, 497799807, 820999941, 941228365, 72595637, 772577938, 571468704, 498321815, 493907130, 807989432, 991031185, 765030056, 608585021, 141387953, 197000841, 940075260, 14256810, 972721572, 606968790, 971353587, 294535156, 31944593, 158559535, 615473670, 127433794, 271146721, 989379162, 15154805, 232192646, 641649817, 101290172, 770558023, 683824534, 371317718, 778104055, 925363275, 526878192, 332177766, 368929455, 294767748, 289243122, 348325184, 108338354, 39752838, 719583918, 71753960, 260674653, 796811169, 489167608, 186630693, 281834448, 586191892, 532130288, 185599600, 144490944, 9767028, 805798001, 292928044, 75457180, 460593690, 111736739, 538930263, 237170132, 995384655, 249401206, 267343294, 206357057, 366897356, 343361841, 79126161, 970271138, 742479818, 189931173, 136898701, 646253628, 445615237, 937519449, 586806959, 612866995, 27337712, 756958967, 126467617, 981344798, 313026383, 277440706, 264094349, 121050975, 413718794, 508199739, 364337140, 195125286, 826116757, 848777774, 803447696, 39988385, 448745542, 118078856, 917235735, 733985388, 583881313, 766431205, 7702012, 147471879, 191864209, 237159603, 461766535, 36850552, 317365706, 781437978, 869977841, 666981705, 278548123, 732808576, 436319693, 864627840, 590102720, 63975945, 923307276, 659115651, 176559456, 534347111, 254644378, 91443182, 307240998, 577287024, 964000075, 645210547, 806850893, 959669180, 14760253, 810685166, 273054717, 137280896, 150618637, 506937344, 722704753, 672571605, 199374370, 633062729, 530994164, 786560277, 384248499, 716878567, 986441214, 247726443, 646775899, 726430740, 516859806, 386516080, 994912290, 523664149, 89485965, 393115555, 169040449, 158283457, 940561508, 173373772, 792607934, 490250390, 974421518, 403351660, 532067948, 478241514, 817059410, 909569691, 595934391, 466890814, 799698544, 785691906, 250882674, 877778799, 717012728, 69411120, 400819173, 548998668, 589250022, 71123726, 54280339, 701784623, 7089159, 986255950, 449960777, 418776774, 204526622, 662863939, 726445725, 74996776, 505729211, 122600537, 670803149, 239057817, 217286467, 348877454, 400717108, 123523353, 616102345, 302512442, 591205194, 591358258, 991764808, 606623833, 188053964, 881610712, 980322427, 524457514, 210726832, 55838094, 847712189, 431058932, 4726963, 598174396, 926331700, 391827814, 519291126, 618303727, 423735121, 290014923, 826308110, 52445538, 586229223, 593830871, 796362675, 139648283, 240233074, 735496651, 651992755, 334118561, 725538227, 53390463, 16316469, 111842897, 346737673, 92139618, 467509110, 488607769, 317401972, 795869007, 416172667, 691882250, 822268180, 564012370, 113787039, 981478575, 887589072, 156664693, 735194126, 821132814, 417556721, 888652469, 132665810, 252607648, 169130173, 613136100, 619419114, 4755728, 305745579, 42977156, 828858725, 957363332, 61227643, 144384734, 952417579, 542410050, 553751687, 577934801, 100772016, 375232645, 397292598, 182777721, 900760316, 428217487, 237303836, 933041072, 699253467, 834775872, 113975605, 135096250, 810462498, 841066606, 544398728, 525996725, 474591447, 886214589, 607329563, 45580245, 966423262, 231565882, 3596021, 489089793, 2468908, 302730013, 270765956, 389334903, 967230882, 800469225, 230811360, 249290043, 697944596, 288890194, 16639016, 994759022, 494918721, 36918707, 592603106, 65966004, 401676392, 139585493, 792570890, 30329882, 759786838, 800319489, 616539101, 332506456, 692516632] 118038)," 45136 (countComponents [169753618, 773871081, 649247331, 639027729, 141793620, 196171651, 454444591, 498250202, 853982650, 265097348, 116637986, 488310097, 639295175, 452652394, 554842468, 608880491, 946099500, 595002691, 527223753, 405797504, 124530585, 94603669, 823804091, 653801116, 185562672, 844182417, 345653586, 459849201, 511750591, 32767287, 331113157, 482893046, 484049283, 522241074, 360854961, 222240744, 532896398, 800659302, 815644923, 121243837, 185401636, 294411738, 685749756, 800322853, 732280673, 621483720, 623188981, 574085460, 665211309, 826756809, 701748315, 636650799, 471616336, 585910243, 55994464, 28427946, 275812167, 101813415, 287165479, 29875254, 680778338, 751860509, 948139116, 943058616, 550865456, 823238657, 503322359, 867033940, 755268390, 881014892, 669243085, 990543142, 205084627, 587873373, 586233760, 436432134, 594362812, 861862487, 275090392, 694485965, 724190454, 553493052, 290971255, 421663580, 915745783, 306164444, 181865193, 289835064, 443250144, 642291269, 737649570, 2115128, 368168050, 286637833, 239559148, 920236249, 413893266, 99604433, 456154592, 533636099, 48243419, 276684009, 272826265, 243209462, 423789883, 546162677, 534422309, 671195441, 270584147, 454151569, 332301655, 222862008, 716200842, 496785043, 253243456, 547941249, 603961677, 908517286, 513457636, 595683085, 621366051, 485143400, 55876132, 619520285, 350630265, 152317192, 866448396, 713840253, 243709812, 503493635, 275891324, 219921831, 826881004, 668347300, 711647245, 572672720, 342216006, 748328414, 503078993, 403716901, 293112445, 676768702, 966289700, 766544607, 665071187, 379541005, 408605581, 197975856, 267689831, 56881445, 538122275, 5856432, 956693822, 869108484, 419397141, 312850974, 692119222, 293145146, 73071757, 962484301, 282086111, 448522152, 246309722, 647750558, 261965219, 238729172, 325858445, 370677603, 495492565, 637880232, 303128484, 888877407, 803844945, 649189369, 67648418, 127245517, 824850334, 181872237, 556002447, 928101856, 771005319, 327538145, 425223229, 140654317, 418337982, 310904443, 889435936, 529011482, 122485874, 140515712, 191328942, 699456335, 252850136, 930011339, 707020498, 322936760, 956796043, 263158625, 661311972, 886880494, 458568056, 988368583, 412471545, 960426473, 739461244, 697953573, 690835061, 26675484, 535405103, 350594349, 279234456, 254259053, 941802172, 833598590, 289813535, 355637243, 938540452, 50339369, 13831051, 191369934, 131436587, 449273197, 506251664, 568153434, 746135206, 676356996, 874871176, 377361743, 957810013, 645035169, 526462935, 31467654, 950297114, 452781776, 131313622, 995734517, 509610446, 729054514, 343263269, 271426639, 322300631, 497890529, 869389088, 480249215, 10373223, 838554973, 413137475, 362615358, 465632237, 425003746, 657447174, 960459334, 293293241, 786232650, 65548508, 407664890, 834725578, 198977869, 148626789, 428104480, 314312391, 41726767, 560115331, 987538693, 896974803, 812497329, 75767438, 392286699, 424462102, 926092045, 882978027, 211908560, 367041545, 65619447, 326940117, 316054556, 862048962, 653718986, 294612091, 947633545, 391432206, 55656727, 858618721, 485934509, 402394504, 508650390, 791523638, 16940485, 691538038, 757866380, 781405356, 874906659, 929769548, 701438095, 781253711, 661449276, 521059990, 357397725, 930705192, 218020857, 345395419, 129909902, 874553261, 92682948, 24222690, 631757336, 970082365, 779560984, 116035345, 184430808, 664072042, 445886066, 424171803, 485281730, 813937042, 926528427, 736654633, 385263949, 558195873, 111899035, 227617593, 894416375, 628445820, 229444516, 867849755, 450887642, 976866120, 874423872, 603121120, 760579069, 676343489, 396108622, 852312146, 202538913, 859438637, 483234060, 448855143, 893061211, 56721601, 315402655, 52440, 146507254, 10345453, 532962691, 499757217, 728321537, 88983386, 507181175, 468438873, 788467008, 757067766, 347713976, 417227356, 270518361, 474977315, 106266945, 549300454, 564676717, 18335972, 40631154, 212019825, 200581867, 209136545, 740834420, 489044086, 977432181, 64655185, 20322773, 790562808, 673345974, 26504435, 721623050, 702725447, 296434271, 293343470, 252521882, 512548725, 306677774, 791919872, 763867396, 486952413, 903694218, 626808355, 539616530, 16947765, 324138189, 200201944, 67430088, 629766606, 19674940, 624048507, 616936748, 106355290, 224950337, 65818909, 824616809, 201987532, 149607712, 500823100, 883550836, 877721382, 124653348, 947502941, 985805463, 890785734, 867541063, 802869412, 451654534, 671907475, 531617138, 853127965, 403194345, 464343154, 843012527, 924079484, 602793358, 821474117, 621129219, 255485912, 446920960, 486052989, 468124665, 701124643, 52680985, 932560610, 333337923, 71947098, 796373679, 50635247, 904735509, 881672351, 389802926, 122806675, 970574574, 718120112, 91596935, 447899141, 192027627, 598444775, 799604448, 775277843, 145412713, 667853203, 211378966, 309381595, 562120803, 536291633, 72136185, 858069896, 161617712, 17352383, 997006984, 588355904, 788416000, 989238892, 971622180, 182051367, 264789567, 749811252, 68520509, 87484725, 497476057, 80846072, 281221039, 491102259, 538907035, 647054811, 898103502, 269986469, 387767182, 11349952, 364592962, 591667992, 920812440, 160215263, 576868357, 569510211, 425542245, 329423030, 257148063, 617331606, 578703367, 400243759, 490678009, 196364822, 816930698, 536415194, 28867724, 834131381, 322231988, 876709573, 561585649, 242160965, 799675120, 551998585, 739705311, 993243409, 611453813, 928821589, 535011202, 107542884, 605846338, 477644509, 801416225, 244625843, 860255716, 501554977, 387767264, 634403078, 430486058, 747057006, 696667201, 3948177, 937555164, 424415464, 3005606, 347897661, 289364495, 268612188, 774311723, 704245197, 84001827, 851276394, 275940506, 207242562, 722043592, 198371107, 149744556, 511089410, 757125353, 602253910, 632559913, 599601384, 959239697, 921376195, 9054822, 41526828, 880962576, 180750453, 694820824, 21609634, 429317480, 990047860, 445276891, 818447384, 318167041, 391246185, 743415226, 587448254, 345204093, 249230579, 700252640, 921355282, 13081537, 76277920, 407170772, 407874736, 948466763, 521502803, 823348117, 617861552, 239255004, 98361097, 109477860, 636084694, 391195503, 818937127, 127822646, 535232082, 694052692, 991612468, 417678426, 643198951, 239876155, 874091372, 653641196, 665518032, 702774483, 266507061, 606367875, 13756983, 878255149, 145664074, 14581212, 573933923, 385009778, 729215219, 414330955, 881807000, 771204318, 302625093, 582193135, 856585727, 632272566, 557764258, 80051430, 149757140, 493465155, 166654698, 784057896, 492881448, 576143437, 486312148, 937251538, 764487202, 510598142, 618649908, 242583042, 570059164, 453919718, 998012075, 415675541, 588875307, 97927551, 444801659, 945944370, 855129040, 25311708, 965762356, 653476401, 324971288, 368294724, 991861746, 99583150, 76103363, 321339540, 660239511, 856381459, 895034075, 723540838, 477849304, 105141722, 889608132, 841764731, 948026775, 173198664, 10485282, 424386552, 752752598, 218718703, 59554139, 986893209, 161328463, 79746944, 25218377, 979399407, 897940713, 27847352, 279370267, 338883478, 283542763, 408083149, 91678538, 740405774, 594411827, 196195836, 919840459, 167847327, 439679420, 73161887, 587685841, 636119538, 351853238, 988313928, 345776969, 649112719, 635012547, 420450894, 507627553, 354035985, 243895482, 135183973, 377075203, 31541386, 979658629, 189965485, 827348871, 154575798, 432023772, 919353362, 78384170, 808547652, 949260449, 589351865, 914902877, 176386877, 481942335, 847111376, 110751736, 220197222, 354577283, 290408549, 552699067, 177877703, 388442256, 255502541, 854691729, 827978360, 857710156, 624026991, 509794771, 828607928, 208043615, 571290011, 707861961, 389405855, 442164295, 649806199, 117303635, 251867231, 992419960, 952535971, 551032, 998059630, 280847302, 640573513, 950660028, 613694612, 881278554, 239171465, 809260667, 754939176, 766546845, 61038774, 20777263, 161115494, 436435849, 760538555, 690564792, 139228781, 736021916, 298762126, 364844925, 66003017, 958390, 459749320, 949786062, 801870159, 444012328, 865308893, 778363445, 999522549, 394502674, 941666811, 213158037, 709136388, 484627541, 288994095, 436800488, 524225148, 785184428, 84711762, 736519359, 209888294, 839863475, 49789942, 914906656, 864618256, 260786040, 713819244, 84711038, 891562365, 913992430, 761575841, 75842742, 518427663, 692074372, 486484344, 104045960, 496913490, 160340950, 111160656, 863125273, 683746541, 978315639, 299169791, 816192422, 666237608, 303313531, 823621199, 670412843, 458069583, 692529281, 822422352, 782359126, 111825578, 99917530, 857448784, 563649518, 420391143, 818258671, 489098643, 69263655, 403241590, 72695577, 803601626, 907996838, 770797489, 68955981, 326640056, 919181499, 354670759, 231500527, 500110383, 309683209, 58057307, 504024180, 469248288, 323712984, 746951558, 27291967, 713872870, 330106076, 179090336, 239721290, 893035730, 112548582, 475448303, 273644107, 664074147, 859904547, 294153234, 52633818, 446491054, 809793663, 556602980, 672795963, 354171451, 653045185, 4336434, 767489097, 139667256, 102956507, 745470843, 538554179, 309243895, 867542958, 919066439, 576295449, 653268132, 129251337, 255787024, 234464710, 621896630, 689482872, 895430607, 906051470, 553783622, 109150647, 710155518, 275571276, 231628755, 516365475, 210233870, 40672095, 272457419, 44033366, 346158169, 671488845, 118830623, 152781209, 272551804, 91597454, 948069674, 128464109, 327995826, 735401067, 761385808, 537402017, 742267410, 315654998, 144207848, 670307267, 47559620, 339988705, 430028700, 314756431, 419947460, 615811521, 413854170, 129579609, 460836872, 46940335, 815711959, 896092422, 683999558, 671366814, 823248200, 733661815, 785040488, 648424621, 170787024, 179771456, 866907498, 863891989, 45984328, 222141802, 410293595, 331765898, 808620107, 281560604, 908847451, 323127443, 974650445, 209130647, 702861173, 12705439, 531835427, 810469628, 329472558, 39933952, 8383926, 601107499, 537089709, 530121483, 248464461, 898158062, 298028159, 697718832, 602908958, 374899954, 242821191, 294312252, 27062745, 656044486, 486027306, 550569108, 21531076, 348198355, 737633951, 753170, 985893122, 854653974, 476498458, 685782511, 218310021, 653143200, 585632043, 866680336, 695054795, 987709512, 446267448, 664188166, 103929323, 99315671, 716416479, 174497514, 387581419, 175571773, 780428174, 157657647, 698936863, 768201385, 306262993, 707287547, 520815074, 880107857, 845322576, 48121146, 792465136, 51424465, 416657306, 288243146, 292207142, 604195432, 362193498, 285055104, 838746445, 65302556, 800539188, 291650327, 614298314, 354538951, 890053334, 615857049, 653856217, 64356421, 670996682, 337983845, 278549665, 932027000, 623146993, 729007237, 832829862, 423171078, 954770641, 272513965, 100980956, 953540737, 257145627, 236812653, 211016450, 338162058, 626935239, 881085625, 534530550, 949742166, 182754020, 941481215, 518927998, 80621356, 697510027, 513587083, 153273518, 360753859, 910784073, 841308945, 788899188, 932920137, 256451536, 69058566, 579910427, 225117303, 951042692, 958351773, 531479494, 916432676, 869558409, 282622981, 340872073, 997586325, 438206103, 408440353, 270503375, 665146340, 351800481, 1603836, 591701727, 559150240, 468935815, 9928545, 333610848, 161770164, 501011057, 118760405, 680035883, 243818053, 843482279, 947568607, 829109921, 601745014, 988632143, 625800557, 67846462, 9024401, 159578350, 815467221, 835020940, 102428343, 933405197, 38613031, 665521712, 622826376, 873628216, 109795151, 61144103, 320697563, 164287031, 915418259, 726136793, 500889318, 407896176, 536368964, 22315376, 489872226, 266567477, 262100850, 267402796, 53893028, 245888405, 354464190, 647247339, 12754583, 108720865, 796524267, 26019325, 385482413, 586281106, 810537543, 447919313, 519474797, 424774403, 325201580, 209937637, 428138666, 257862622, 317718443, 488436853, 254801126, 254892751, 978016837, 647999079, 501279724, 423088196, 117072455, 915913909, 803631710, 708024864, 944778045, 632353020, 844579660, 43901974, 678905681, 293337442, 439018076, 433567607, 29142797, 624380691, 906859707, 995790452, 250174345, 280849337, 856672358, 546715842, 107303917, 175867892, 317052485, 280475932, 6949782, 311334947, 533019732, 286509730, 372884962, 36831871, 79654857, 582272122, 879497868, 700668394, 449558599, 206884201, 903172626, 60170925, 968336713, 495946017, 663479694, 213457732, 818686529, 421647994, 923002738, 600136564, 781448915, 779333248, 521300641, 195205685, 151301227, 637393111, 300754500, 101120213, 466024140, 908981776, 193543694, 481888509, 140485279, 924410726, 411286505, 167509757, 799587375, 325131805, 760933786, 44237413, 557869588, 786702726, 410395592, 861050595, 75082183, 886629957, 410413131, 813824289, 663382339, 278946298, 842160399, 762780895, 847193334, 705713643, 502393113, 289543173, 207519152, 182376307, 832669145, 652037519, 538147839, 492615061, 142311648, 955194521, 750494691, 790496278, 869589964, 685977896, 894055831, 421509604, 808556446, 519541965, 891259292, 932831095, 473696713, 538903053, 550260845, 765723378, 831265924, 297564527, 928630984, 785596148, 143787139, 212865646, 507842312, 940764771, 550579972, 670409425, 438942411, 212625130, 673149288, 938839987, 125587941, 122269343, 135944473, 196214400, 350400535, 615441958, 902385456, 282335953, 7426615, 613285752, 704721191, 456859503, 196172764, 811105715, 462181650, 301660727, 726173244, 623693061, 958751101, 762428551, 616487506, 460019318, 572166975, 409038381, 97807488, 378084008, 524822203, 397978051, 754534751, 518904816, 188195182, 896274812, 841594914, 786074790, 146429494, 830071665, 57816909, 5595196, 722823295, 709079557, 872808097, 175991833, 764483147, 555550741, 477460819, 109354482, 692869168, 638879600, 7198815, 956689341, 274691792, 183938791, 441701404, 756721599, 775133403, 512170135, 552391776, 174028862, 804258738, 409327076, 666442742, 846375443, 115292042, 794853890, 86391611, 950903134, 693992120, 736635003, 395073239, 275702752, 845685478, 453832120, 801225211, 696557801, 420484812, 992472764, 15672742, 143010902, 805298966, 424520417, 180309118, 748431146, 859570367, 816733952, 328287194, 685703503, 684639282, 365104139, 826392521, 761098311, 25486962, 585785873, 893401070, 482374416, 333003, 939955031, 665260893, 706510750, 602506720, 729070239, 55300625, 580594301, 224830935, 205900174, 842964659, 714572319, 1864281, 637169656, 687685394, 549431010, 92616530, 186615010, 355107038, 176877912, 877526697, 206322636, 406436075, 331826664, 844333861, 650663297, 803086683, 762217617, 93198446, 594950285, 665854515, 886010518, 376956056, 199522451, 241461229, 620278164, 813126667, 950403815, 796195912, 804629788, 508753863, 486579065, 279674769, 322592855, 94458265, 900473548, 121399857, 491560748, 612669492, 742905099, 716560659, 561532721, 644933548, 57703343, 624081583, 666059315, 477486600, 482126870, 780106128, 44404418, 153853759, 265629901, 303666664, 161298103, 593894220, 878990537, 697362019, 69532957, 683766669, 561359943, 518997440, 197219489, 557561275, 144222755, 286170198, 350036796, 201409118, 228120119, 11119253, 931060268, 509812544, 1923423, 230207973, 512749650, 666969627, 483283712, 316389318, 325035418, 364587159, 917485852, 814549211, 50537339, 990852790, 905982131, 148139219, 229395697, 30812057, 192544081, 825560694, 501458770, 450923439, 650498496, 33074338, 390833444, 657551935, 297556770, 386083591, 294082467, 103185036, 827413745, 745070965, 96396294, 574832490, 644018251, 419467009, 478243150, 853414547, 182100, 637731049, 220705337, 731940752, 41651159, 977212915, 589101371, 92945769, 814565101, 463588041, 189756036, 942287648, 456366482, 85672799, 667767104, 3819497, 55145587, 45398720, 724342878, 238292528, 599167428, 759896649, 792927566, 336998602, 945960732, 127377298, 999565331, 121257539, 958864256, 421236748, 134747194, 168497388, 469931924, 215462933, 690749938, 311680531, 676460709, 41148466, 49944567, 345211743, 81212758, 188888863, 840755182, 310503945, 27832626, 65238683, 242845525, 717440387, 413803570, 758464535, 647452355, 204791670, 92616595, 101927706, 160802805, 518640944, 491074916, 705728901, 732708419, 618554620, 958064049, 987936467, 292140259, 419507029, 517960587, 99901155, 316241729, 343272681, 361584503, 229825888, 389846074, 990990921, 640082763, 568784717, 71135923, 279998616, 766405349, 99220130, 316075495, 763471310, 882598007, 678190363, 681171111, 660421963, 161651298, 477481268, 344528975, 78582211, 671428907, 779503088, 253878425, 511250432, 380968063, 11454541, 247183560, 581404545, 534570266, 967515822, 727690636, 679115757, 602826189, 895177200, 657254498, 140847084, 792598099, 577122583, 114208729, 12643218, 312529310, 803890758, 330892339, 859260629, 32170359, 8588584, 632468014, 423004327, 889279454, 286390402, 586317178, 416032271, 416928456, 86129363, 489630684, 909551117, 982714834, 803028596, 668686576, 919929626, 475830268, 92938185, 816675122, 500966217, 705218988, 524607879, 650874706, 359015114, 692712954, 130293018, 152330717, 75097049, 773996805, 235413603, 106324380, 738023563, 27952946, 729934762, 184671937, 851989764, 178490914, 883800885, 706605025, 148249150, 712368730, 267830507, 968659760, 623656774, 456985907, 828249639, 383763803, 707467658, 776725714, 816697222, 677788783, 673869967, 369554891, 553668754, 745895000, 119828815, 866317324, 948355704, 313516842, 232420560, 706382129, 50230830, 488534719, 48639608, 554011701, 337470732, 839420713, 419380496, 970751151, 502317041, 792906113, 112504835, 303950177, 965071064, 970408718, 16633051, 884600628, 703248941, 383607303, 671323276, 700659584, 63766243, 650581003, 437618927, 567387932, 67493349, 732655127, 62889043, 572451577, 489100148, 890647755, 644218424, 358190589, 718561666, 539673133, 727483852, 649238950, 508273441, 590545510, 142516583, 861061813, 987053721, 495942468, 3140027, 795477616, 402932414, 200843674, 493586044, 435574022, 963477903, 396138301, 212770576, 280112710, 378233645, 934619704, 560561693, 147433655, 638121586, 9548536, 826295880, 142300456, 193301385, 95235860, 701442324, 113847495, 955116676, 487697708, 625476984, 327602746, 150227263, 80127653, 833660863, 845058860, 680148481, 241503220, 435876615, 765191162, 78486429, 619557689, 458851655, 275103650, 57585827, 433051244, 513548341, 798652824, 178014249, 324029431, 160270808, 205966151, 38769900, 709510427, 166343555, 450834336, 919362344, 402995681, 534386689, 651687782, 476011084, 248000386, 106601445, 319112243, 412021274, 457300761, 967547130, 973423258, 252544157, 653770418, 16467435, 293391611, 810913260, 487666547, 952769565, 658624419, 206657232, 790971539, 298469710, 203666680, 860256701, 268114487, 293713207, 434390880, 304956400, 20931926, 644183890, 679085980, 850610199, 646784023, 339046291, 504415678, 151716409, 146008659, 859082667, 159361163, 953485531, 797108846, 740358701, 750936143, 140059285, 392318000, 127539011, 446700703, 384079301, 239790348, 493559097, 113177891, 36317144, 206048607, 380045597, 711031378, 254062977, 866947276, 10237363, 27242162, 275492747, 268041692, 314868044, 667301047, 124443700, 813670406, 344121426, 143208425, 339195950, 926621194, 241712782, 612473344, 927856826, 537721052, 462319019, 775154856, 811324463, 793913164, 849027129, 898832118, 438579036, 178295679, 201255403, 38807000, 697100289, 227491768, 33427119, 611597785, 919534905, 618065687, 749558675, 561026888, 506479583, 827696774, 243463370, 2147342, 61771303, 182838391, 574457773, 527666057, 89043699, 68092484, 876831688, 172380658, 715136616, 504749211, 678756202, 599502463, 857887614, 627225047, 349009061, 56782601, 406880292, 940486, 781244592, 440895528, 247064477, 838166538, 435649103, 542727525, 71040171, 986751406, 534486348, 813996948, 143345112, 993590416, 562140706, 575966990, 109475817, 930693529, 29618301, 425264643, 756651230, 139757069, 50824260, 880852492, 174502505, 247795558, 111246833, 65812277, 522275160, 566408711, 519960620, 694031158, 417061856, 106032470, 821958728, 233723346, 893668774, 121524641, 7967811, 494311121, 892278240, 310550346, 891036296, 623629409, 403315010, 456051192, 349384852, 583630383, 463864894, 990083805, 208241959, 420124551, 855978555, 192189519, 60870491, 16456693, 220256211, 494127409, 172457197, 602170978, 838794745, 850166276, 352457491, 666379740, 794528893, 980557001, 550782540, 918689938, 444694863, 244472940, 23142086, 434975048, 138229021, 717923674, 615724912, 569080012, 464347824, 980083435, 472217292, 270809617, 578162146, 180129601, 779332916, 275733422, 257593191, 226483200, 253651963, 133103365, 332438028, 489247131, 901144622, 817959839, 147735808, 218353166, 512903384, 886634452, 501363969, 96537920, 491725446, 102415921, 800631004, 147062221, 229977986, 912006664, 161189956, 768143116, 2737764, 496968277, 728845733, 688498561, 489033823, 229794546, 551565430, 569893327, 967784383, 737045149, 365270660, 609716077, 925924771, 565039792, 544091367, 132497533, 967301947, 613765901, 448310601, 893660476, 885789813, 253292788, 758591091, 764609581, 154817706, 947145866, 794249051, 501797090, 262835163, 671781432, 311211283, 634469654, 246567719, 536600815, 833436096, 868898116, 946876770, 681480286, 435144144, 547541621, 143183692, 764528406, 329694214, 477863458, 205316683, 365458310, 791839380, 685114832, 152668998, 931736077, 620865464, 967360932, 789153889, 881443872, 531120587, 176463799, 69953707, 809061713, 416355468, 189048034, 75550935, 229226417, 629749758, 797892793, 460406454, 847062605, 437683800, 134220431, 206433321, 741351030, 620898328, 546560003, 405645062, 740473333, 592562864, 882194364, 684240162, 770379475, 48552527, 144513034, 578748863, 238973570, 926011421, 524776375, 280762142, 177508348, 858997122, 195154291, 267329562, 635894047, 15151732, 792529751, 290942538, 940952022, 269626627, 21223034, 724225058, 515944698, 427278378, 161356559, 239717734, 932896431, 370738620, 912951500, 954999503, 9306924, 780927605, 300903307, 497589584, 360610378, 292879240, 546696528, 776962983, 846735686, 134227826, 419036076, 669429717, 507952572, 784512306, 217286375, 4918212, 533955608, 105429179, 816344870, 314301527, 599927579, 593198583, 983835327, 818646862, 767201843, 441649509, 590091553, 958905399, 212002653, 423924975, 500943662, 90594459, 519598844, 518962061, 869652560, 213535262, 345027311, 833492994, 65782038, 347401751, 345129151, 564593311, 605355927, 954348357, 276216013, 115783584, 927659537, 330580257, 211490069, 509550356, 258886504, 274125462, 582594304, 970024065, 210318655, 428749331, 442926801, 822586449, 562825268, 684855022, 282288660, 62470776, 127800313, 589683612, 144083306, 747639666, 488028894, 98051055, 121631506, 23178304, 995014769, 693417015, 294698387, 633314398, 300711468, 980799883, 938006516, 887781325, 771919537, 470283805, 753357064, 224290512, 28792711, 699661079, 239922989, 65331698, 628506569, 295104799, 807424343, 557188117, 731800751, 625295525, 197479377, 709317010, 589392606, 126239238, 525751801, 867992816, 148982732, 38751587, 179403006, 343460512, 699274479, 931341060, 679212123, 727422380, 653024648, 222815637, 466316532, 85040052, 444854809, 689018849, 519343633, 352151227, 319555383, 263243633, 250208403, 332142936, 375134932, 586136222, 129922009, 596532370, 803547055, 674496018, 341235429, 990679557, 971459170, 118061029, 818398479, 806585928, 941269936, 263726042, 341366577, 635425364, 324670772, 360222681, 96717832, 145250447, 82304248, 202701909, 671478756, 986197606, 97462866, 487262269, 903243027, 113892859, 593307853, 768172489, 174789029, 633863452, 430683522, 253382972, 229650694, 940654608, 182540585, 463490034, 179399201, 72845261, 916750389, 855044038, 842805928, 920829227, 483781333, 749706007, 966650462, 558309385, 767271242, 763511351, 471728178, 216880906, 443439727, 917657195, 229313974, 204567829, 103696557, 794355603, 974189778, 123767484, 862313638, 521450845, 235478734, 520321153, 919561998, 533763857, 507377402, 326325592, 321874532, 696119627, 727644345, 808942330, 995863595, 300658481, 844713876, 417246332, 328474127, 706375241, 634799507, 281563692, 210446910, 306123790, 243336428, 506382925, 67620152, 10996279, 494504652, 310208384, 714519665, 769764200, 185750417, 91389911, 740932946, 199068415, 767692409, 774300085, 98515897, 464919305, 202462273, 453149228, 470252684, 583923760, 248729059, 501217049, 679011427, 797641008, 672234774, 61402282, 19668397, 427401691, 144366282, 961003858, 312697399, 472166264, 732661210, 973732002, 936071179, 139117898, 343291281, 124710417, 384246318, 948458624, 333814233, 698741612, 27666306, 20296118, 887816283, 5687020, 830397347, 234984233, 530036217, 913102956, 617523690, 355731249, 810057130, 687928131, 742486716, 221936695, 256482608, 36194972, 888748234, 819170149, 703776202, 989916037, 203866347, 218203684, 227490927, 243397200, 990325, 343178046, 257671452, 120955183, 436666563, 555098270, 692134015, 339001330, 798303928, 688916899, 915651200, 216858862, 65134692, 743977024, 478763525, 667964597, 609451459, 499051931, 222819287, 859597721, 738456035, 600144187, 338010230, 419140997, 197801410, 285350473, 452450286, 86239520, 996134185, 27963500, 904347206, 479091650, 556496014, 33273586, 160125430, 142942925, 243124057, 213025663, 529673212, 585412411, 359263824, 875295224, 470446038, 367938066, 652684380, 314269600, 414439372, 315703995, 926238139, 12868424, 578316972, 597456065, 373787100, 343300336, 423969699, 135830743, 516534749, 102015285, 466070484, 129349122, 273797500, 213862367, 989263574, 690762182, 836612030, 993353423, 148971819, 749850798, 320206843, 795450063, 610604379, 524851468, 428917474, 976922762, 610094510, 319651599, 620071014, 864300465, 312828254, 294309043, 383908816, 787415845, 943407154, 457160310, 913295699, 562361763, 647146251, 334583028, 935761110, 67318856, 888575359, 267932174, 269417911, 418008043, 843894760, 561708189, 435598884, 605700540, 451048172, 229224580, 795363586, 609643378, 389633870, 632936166, 186303600, 945926147, 139935673, 639968002, 513602099, 644069453, 625098498, 314217411, 310899350, 367390554, 784674285, 860422761, 987591915, 63181517, 710399644, 792586219, 282670973, 531508710, 17245590, 801853452, 782082819, 238163137, 199826016, 629958770, 280550931, 862421950, 169388770, 147546870, 489903191, 180337780, 985408071, 975597790, 490948548, 371074722, 790395867, 200307164, 975406788, 935433927, 422754508, 593621589, 174185255, 671453457, 367031730, 439319490, 559652921, 141115523, 525463579, 1693188, 711146446, 894712271, 246218444, 67404104, 100950037, 501439353, 885799712, 601963581, 416008763, 751001114, 204360857, 687651439, 260407961, 146671024, 115909085, 772444615, 142173129, 664315427, 904637365, 313819651, 423799641, 824737955, 981875890, 992354317, 836617446, 903694413, 55029018, 227196698, 690835074, 269576661, 227183045, 115544437, 335318353, 425500546, 992391936, 743741756, 660884457, 7381375, 620054752, 380566100, 361688931, 406679258, 843271563, 926888074, 960201062, 153288252, 173769851, 778513334, 516471312, 837922270, 570008368, 471239638, 323619517, 294124720, 187595611, 53667148, 623630535, 76719013, 748280733, 449405510, 335734148, 695715936, 900790877, 544051193, 713422467, 615335629, 586391214, 37140614, 583628462, 686237039, 212032782, 676068450, 667953856, 874055004, 71876633, 392232085, 257295757, 772076381, 705203029, 247572814, 651955481, 402621283, 841692185, 81679018, 70729787, 140901416, 94413844, 853559556, 690991374, 130583089, 186129241, 635369714, 4749822, 407816849, 180651605, 450072529, 519705659, 197131768, 350840582, 937248058, 603534317, 329011662, 12317168, 428024489, 738436793, 668187897, 764820767, 274013486, 157405492, 645719631, 799696307, 417730073, 207563782, 826000529, 663708571, 610614036, 331755082, 478529847, 859029936, 983910707, 803456302, 736610417, 658064774, 468148984, 761663462, 818676567, 86193429, 773939645, 951569754, 483260051, 879446526, 38548012, 181313862, 987338863, 515311576, 764040839, 579967432, 268818054, 627712725, 233971322, 365134700, 548112730, 24475031, 135268919, 271556521, 509738039, 449039050, 66355945, 701277374, 620894722, 512220833, 255599163, 261936606, 635310472, 570510286, 814890962, 990025835, 219610167, 549161601, 554680236, 418725368, 177019798, 10543778, 563494879, 358153479, 404969923, 113097442, 577028806, 653636381, 28315530, 707957663, 380212524, 175268990, 988435130, 348566499, 171224354, 66517853, 777483117, 184743566, 21722418, 545287339, 262827349, 210190606, 686873292, 818967941, 606355254, 463535319, 972005538, 945914685, 695610961, 207464363, 870096357, 150635761, 742408502, 311373797, 644420085, 439312603, 784205274, 501651347, 473081487, 970971146, 981809636, 599104118, 647121018, 547561624, 568183131, 872092444, 619935453, 685903715, 747128564, 368452246, 355865487, 999521187, 370519650, 59018963, 189982559, 633583200, 279257429, 799761262, 387353287, 720710838, 122465802, 766566296, 259318648, 401250607, 166182941, 895364268, 164546564, 766764135, 739344040, 492968840, 183328327, 467108827, 643626320, 241293327, 410774975, 730938881, 651623729, 632612375, 484095522, 506766380, 26385540, 768656780, 810741722, 10853725, 445088556, 44943430, 379415110, 926618059, 809787743, 88883320, 406570595, 584589931, 597777886, 557520991, 591283431, 878902539, 929657810, 636601867, 536247736, 487163992, 380363940, 504438396, 866723722, 541063280, 11578964, 804752031, 752617462, 849143681, 523371375, 432912433, 566501155, 612193620, 63536873, 941166950, 250211580, 918400078, 614903307, 453279756, 635365279, 523662884, 330935543, 72617060, 682439903, 974405330, 848492174, 700024878, 463792852, 621039252, 411198694, 837752471, 705670950, 77162708, 346177046, 499887886, 339851917, 193389237, 299690362, 22783865, 123053068, 849813433, 639196674, 7720661, 832238892, 387378429, 283381926, 89010677, 955497478, 111536625, 33167172, 273573306, 530428168, 955645548, 952516223, 199408543, 564520934, 240271386, 311643461, 529389109, 549351794, 369003102, 871517598, 631313693, 386724352, 169284282, 975449943, 397321084, 150189726, 657231195, 690863959, 594508124, 606410382, 72617871, 268983851, 554423898, 503375710, 371348509, 601974543, 424620100, 485756776, 529916981, 51751285, 368076300, 605034846, 425213601, 591766716, 311837113, 633026894, 53563802, 731212103, 23794495, 742355480, 214642511, 429151295, 914046524, 339394540, 842205840, 574933084, 478614654, 894477379, 563908607, 311924150, 772983484, 122883757, 641110600, 237596968, 347710793, 13311267, 42673012, 471666564, 662850356, 540309310, 433225948, 333518996, 218731230, 937769703, 65930001, 610537968, 825099329, 797404014, 643527896, 779675933, 338670842, 109918552, 859873096, 940267744, 986121802, 90342674, 986230121, 795368791, 148645271, 898999227, 781121488, 642711561, 761076382, 771431760, 441653749, 445196861, 893328889, 702188684, 925195617, 25361310, 511056845, 872209748, 383753525, 551756612, 186493819, 42654108, 124937807, 867797837, 60708593, 403517730, 48046759, 223840442, 89741707, 893759393, 808147582, 107051963, 748371920, 788728462, 158381588, 298305636, 803287032, 31212155, 456105682, 418822628, 670646391, 739883301, 527623996, 734895603, 363066128, 14529759, 405995619, 584546282, 653144667, 241640518, 216313292, 771275881, 621232, 358204795, 777321097, 192724275, 680878370, 939442626, 393518122, 715636031, 539685147, 337658124, 180410596, 631459653, 796153892, 749320506, 257297346, 431178498, 331481093, 789435132, 319868533, 506933385, 201056428, 350171985, 694850411, 963406543, 670163616, 757110542, 977137599, 946454030, 401145399, 388462498, 902426402, 385442739, 375893589, 944130592, 118502883, 833047612, 992391948, 500583110, 187091572, 314573794, 619074252, 730609206, 488403975, 569145303, 257079014, 450192788, 557977685, 952718920, 897793668, 235620877, 287805724, 616154973, 949978787, 744776610, 663585987, 153368553, 637715772, 327528642, 20326137, 114456488, 808743149, 797118450, 719515344, 943289572, 1180692, 465271097, 396883070, 169920648, 81828434, 711545768, 671543166, 834586703, 320695596, 916373780, 872922188, 971143331, 246073121, 735670709, 8345543, 246091398, 285260482, 742010203, 777247937, 319917398, 294654907, 409757666, 736939432, 917636261, 371447011, 159311449, 24265899, 971630570, 513248300, 662444746, 136634040, 993197426, 331236165, 221309210, 176852533, 543378183, 275399951, 873254393, 4655871, 462120950, 917673578, 877301654, 774092739, 914302978, 812964353, 626644999, 897165558, 421789331, 469038740, 358421849, 175922749, 62366458, 683341679, 820602604, 134657066, 259247884, 849921285, 347049269, 607587752, 564350578, 764098164, 539224926, 809735180, 806621173, 994568615, 244351320, 351280580, 833819429, 921411762, 380869837, 731686481, 136244890, 698145773, 808735506, 567832953, 591100140, 790329492, 123094179, 412350342, 878123507, 584647857, 286431331, 907397687, 539125160, 416817643, 512092618, 46806684, 376789481, 816091754, 261442065, 251953923, 102944549, 234679849, 46623058, 464016157, 462719102, 346272122, 108576849, 80476428, 111618519, 468824678, 738483067, 762209912, 441870692, 477374950, 254170724, 15949252, 695694286, 999693113, 756013586, 702559230, 577636756, 489732120, 917874700, 1288090, 742480487, 727761943, 571030234, 538570511, 436783388, 136041641, 127613938, 77971699, 297552331, 416497690, 272726948, 413899979, 22124327, 315694203, 885393052, 185135673, 929427561, 335295988, 602153982, 895805777, 511952740, 138598542, 961178307, 986442549, 534785830, 728061885, 567963004, 262909785, 974842197, 288970491, 887558431, 126858205, 379936618, 217589289, 808368489, 883947807, 906281702, 852907743, 247581731, 87761042, 841393894, 590865112, 689197141, 485387219, 855414539, 279916463, 202961244, 20811824, 253819072, 401391063, 233128539, 181190291, 569928066, 5540481, 766890341, 254203472, 886148045, 253849885, 228811811, 987130184, 658635315, 450575557, 2138942, 821963362, 665718308, 897312880, 864819290, 972313595, 624287933, 940633831, 547145956, 830762112, 534850686, 953109820, 250068560, 563685666, 251192018, 797823432, 35982085, 592467613, 367108262, 659729934, 35910597, 462349035, 630964849, 768865044, 662324104, 462042637, 256530002, 753597174, 62243237, 573793556, 160054638, 421465106, 139455162, 39239833, 583754388, 548867450, 143694234, 96206953, 40741162, 2094332, 939893025, 25163464, 300253183, 274158711, 595170058, 70868687, 626262508, 475123523, 480350513, 939238275, 855356443, 816986919, 914770910, 15502539, 928180690, 116735438, 152307121, 13882844, 754299942, 255052326, 736880578, 286497071, 764737310, 701905176, 326543525, 850098284, 709239882, 492518804, 615278995, 774968731, 861525931, 443026494, 38297561, 317567527, 730769062, 469893077, 718410784, 679888063, 774104306, 88947739, 153900890, 118590004, 395669417, 190919203, 260636752, 978761697, 902526363, 104919775, 687691951, 993177171, 182133972, 430228196, 505662568, 129807570, 301591518, 654073690, 398006299, 475696628, 550795317, 475448965, 129969206, 144108811, 576443767, 448352718, 487137748, 650828040, 612933368, 389210337, 176252112, 568493467, 204257615, 592800982, 563814668, 34951491, 247502094, 56107529, 256206601, 197760212, 329772612, 273064355, 77482042, 270730236, 352415489, 973363871, 217714083, 234440951, 881571470, 834718181, 635995367, 86891430, 111415646, 505303953, 322107787, 834201782, 267645237, 555006725, 773379759, 383460986, 804139080, 139732187, 922189059, 620111172, 57027697, 838902985, 658891067, 903022672, 466432270, 942865766, 47659212, 546818253, 306465851, 893469564, 236315987, 826619549, 54014536, 82793887, 984283199, 747561049, 295605407, 838109247, 5022383, 432468251, 930247543, 256116265, 760700912, 432782269, 185925816, 415106829, 750783878, 353343838, 436448471, 331769518, 241730964, 188656249, 531026183, 181199528, 160742594, 440769407, 191655305, 445626469, 975937503, 839098580, 837539538, 75884860, 923971927, 311724302, 756667106, 581624001, 176814554, 520605856, 442181861, 156339346, 125137344, 258254771, 633019268, 333419335, 16924495, 719723269, 133534234, 44345112, 536380128, 807472990, 899756811, 476585806, 530609710, 812036584, 24730993, 637864528, 960195904, 296417634, 605212021, 470065798, 145467514, 918497050, 569661320, 792179538, 629779413, 298537264, 503876326, 308633207, 209097801, 308925165, 559638754, 640840700, 794668803, 449085879, 957174828, 465101420, 855214970, 954910386, 51770754, 972519355, 164822242, 160188065, 536811117, 367385107, 761039214, 417734061, 806999891, 493007374, 695512555, 964092097, 258228302, 36291037, 379590188, 563491927, 667746225, 65130927, 421812770, 898992153, 772426100, 412729153, 370911881, 743557218, 421481881, 439370238, 207717311, 119475043, 469157528, 438039829, 750886866, 792999454, 415323397, 787898573, 288546855, 894320344, 130806716, 372176652, 116933894, 471722600, 444521760, 4488271, 725149162, 473946594, 794686290, 29296063, 676751296, 790666808, 367161754, 751406460, 164638553, 2174902, 584712149, 255567695, 969529427, 771504474, 161012287, 43751293, 835912348, 552432668, 269604350, 875482289, 214942488, 737136526, 338054228, 967440115, 461404531, 958978835, 922504463, 107322300, 497154091, 770867010, 465591503, 653018694, 339216048, 447844308, 423003942, 770465481, 391693721, 435172765, 253832363, 14252197, 75806921, 262984465, 919461196, 131390864, 583591505, 743775157, 75216976, 460448424, 137012174, 908241098, 609573499, 728634908, 121503485, 749257879, 707263527, 520184010, 954972745, 286592229, 49928284, 30300491, 920969127, 765895866, 697020386, 121422859, 958962506, 675101397, 437332007, 734319558, 992988802, 652395040, 421023238, 492561190, 185349193, 980110514, 798595409, 662955817, 820220953, 678990491, 928655539, 407973386, 718883063, 261029063, 595595762, 666148967, 672208433, 428634508, 686618491, 609209681, 127910642, 374594938, 760251686, 241617496, 153281112, 378154337, 867645326, 293113484, 596473372, 817632566, 982530374, 839564025, 597849771, 523492006, 348953160, 300726257, 244774064, 973267414, 656957795, 730510957, 528438561, 930053011, 528832029, 284802704, 237069190, 793909329, 267853023, 916356207, 655884055, 638776067, 497235315, 49508958, 892489658, 658188237, 263856829, 46089366, 854611441, 73953777, 920845031, 665985242, 550695224, 911082223, 685973319, 406829157, 471203772, 103979413, 836570805, 140502868, 11124359, 681718237, 233251038, 893942599, 34075600, 48718174, 944050639, 855987676, 99001759, 897637748, 298220285, 598085728, 151073955, 599955636, 423348397, 431739608, 976107865, 345585818, 220710680, 571113355, 240344156, 853301026, 337362841, 255687032, 219536054, 372521198, 36399469, 222564328, 134103887, 618818163, 892262164, 4370540, 342691710, 46706538, 951281131, 217279308, 667716660, 889579553, 781637858, 798292089, 682655588, 817880002, 935992753, 571432282, 822782709, 865698985, 7756063, 885178727, 968731801, 731355565, 708822247, 947986722, 184319497, 288444945, 376603970, 903980610, 65917776, 392277165, 866393464, 730117109, 523622091, 68042061, 44851120, 594939719, 669347595, 54820488, 633726970, 520194009, 116345195, 790259957, 442342993, 645573555, 271586632, 339527231, 709633800, 122606376, 803053458, 122918341, 818055663, 831296757, 660251749, 683835039, 958128979, 366005785, 721821738, 404838078, 559840640, 106568322, 850297164, 478226356, 834005043, 294020914, 621065580, 498133728, 692368021, 845789625, 188489482, 172329580, 695907594, 510847250, 376282048, 354423751, 175528343, 646184034, 946695, 141615038, 384111093, 532181294, 496150133, 257833717, 114384240, 103165036, 181462229, 769084634, 85173004, 698660959, 925869252, 631245408, 702927609, 33150050, 329534645, 653397700, 341548404, 396421868, 779569891, 502712930, 534218925, 591872244, 782409692, 486077362, 136352851, 946943807, 417766586, 682143763, 927974136, 791272674, 525848388, 528275408, 109855877, 910282084, 426110385, 577436549, 748703457, 41245909, 497846077, 943607117, 206291625, 617925264, 544329094, 789082435, 705770052, 270585656, 440760767, 385627115, 321637500, 816559543, 693191437, 977331015, 857753783, 486244455, 965827441, 776236930, 478787125, 881049389, 128065520, 719358977, 473308775, 441497367, 543140550, 787596437, 406409060, 996036122, 699648395, 376131437, 760621706, 96871920, 443262914, 898865694, 185611306, 611856834, 75099624, 319810386, 60490334, 764335554, 693728767, 568664482, 300474531, 315903263, 894612355, 6209, 287019127, 974625364, 179231335, 532834944, 334137499, 283533190, 514879681, 396316171, 837124053, 4540064, 39204961, 148939856, 420486249, 462560979, 267679118, 963233128, 377518479, 6433718, 591730496, 835875485, 546871023, 351623994, 895589106, 670815237, 98532890, 544783983, 468752746, 899260944, 603612349, 842350294, 726906541, 620003692, 220651174, 834268028, 769802912, 485639213, 410566148, 580598215, 945844833, 457880382, 549060243, 200871531, 91099328, 128586403, 408697841, 685440307, 898402134, 974296032, 867128827, 942224428, 396116484, 413987068, 417839857, 362131748, 971258100, 368428691, 710385519, 422903822, 309762534, 694412963, 331153266, 295746860, 172104341, 95681107, 395146902, 622709718, 903503339, 251828279, 849286184, 614322132, 396673104, 52827159, 629395978, 154800815, 6256794, 770019899, 754714318, 744967214, 887634632, 493057731, 782502838, 305016379, 342951992, 435683775, 238757942, 832781738, 998168574, 541417217, 21147310, 632003616, 445203421, 689389216, 588306753, 517542376, 940739742, 642295764, 651415195, 158826398, 187133844, 974987086, 866267288, 603078564, 749388431, 17076324, 996666648, 509799716, 810727031, 950418186, 508628897, 217069271, 496406083, 542183189, 609038032, 978983424, 946280835, 265977714, 240773350, 768254972, 902613041, 49686413, 701184634, 78253192, 885556879, 691651168, 664449603, 722170843, 413978811, 939605718, 502584701, 210294971, 771799936, 882090487, 264128180, 290903327, 577503335, 965718066, 542999579, 1139626, 202497830, 942808155, 970645219, 959369745, 389643692, 56286452, 605407348, 82538801, 443131048, 170230573, 462376700, 559763857, 80506987, 453294795, 624761794, 279030825, 902488818, 211034425, 746396738, 220696431, 401716965, 335309959, 531078303, 432112911, 470200067, 557468581, 127647802, 193835836, 294807226, 836335967, 228306743, 919505187, 790986485, 839585377, 262804515, 493471004, 591195562, 139545694, 215348399, 856163457, 364338199, 158350935, 427251957, 200597614, 917136508, 107027377, 60875325, 406371708, 749602120, 145080351, 82130511, 835722480, 133127912, 512548681, 663011931, 74406936, 177718059, 268361529, 717801064, 62402224, 684988320, 851439669, 200319962, 321597028, 386988278, 740224894, 443082676, 444349839, 679004863, 351377103, 57419627, 560189105, 31377518, 35310747, 995195739, 605345385, 379235439, 984408824, 84093702, 693760339, 455621253, 171047998, 441559172, 836811398, 749203456, 805839261, 280052300, 98174344, 644271955, 242883017, 130949397, 547373437, 814370225, 709429256, 792127668, 19814730, 629662024, 306821946, 270458574, 24126542, 87103055, 427245960, 37982075, 271739813, 608794480, 83150402, 866585884, 309067984, 706722510, 633793851, 432944432, 297923560, 286074060, 978320193, 398146807, 942618459, 132752155, 749175316, 324979635, 233661094, 616111311, 710907937, 92505292, 188181404, 402069449, 662496953, 419824318, 463405666, 33537394, 455827949, 674931209, 738801474, 666302608, 500077959, 8369543, 455530232, 74476553, 449745206, 508233379, 504588300, 170419016, 969209148, 434530005, 344068098, 988260782, 922259170, 539530315, 205477219, 637494968, 194817325, 435384462, 941324570, 478228027, 178912415, 449917512, 743634898, 516363679, 558818035, 356497, 567762603, 533776860, 844572334, 891006596, 357019971, 640326815, 117603404, 811107390, 647578793, 608376510, 621794083, 959890565, 128042342, 176186322, 937081839, 401247899, 882662352, 752807263, 864357314, 64973556, 944429687, 522751375, 735515244, 874388439, 902674785, 896095862, 745467845, 442374536, 544359256, 311538543, 835180313, 267014420, 324243108, 413125449, 364158181, 256478466, 159617276, 743269731, 294393724, 899220961, 767386251, 65104127, 555533087, 767659156, 580051449, 19178928, 377173823, 45490743, 962441993, 612770525, 625090917, 679541304, 72480311, 135493591, 743161665, 248588688, 12579831, 896306329, 814536785, 214988214, 366066529, 92480611, 573221505, 764106275, 247951704, 718074882, 432956349, 309805698, 940712516, 880489351, 383919686, 204087151, 938833847, 710927414, 447532778, 835302292, 795546560, 656494331, 681084989, 939877550, 810846431, 920353837, 510498831, 718955290, 584134133, 400691353, 34821769, 402675381, 743753609, 176584248, 353272610, 2113751, 631747267, 79243518, 785979881, 195434743, 761029495, 946491124, 637807939, 875025556, 993598272, 967668527, 356200512, 377638712, 374043, 160122743, 800838826, 681086822, 174047703, 885950495, 147892514, 333373262, 31055614, 802179693, 776532643, 926676635, 824377649, 684445355, 147087495, 884632612, 726032034, 537064267, 216141522, 412411088, 629034390, 411385436, 961489916, 826263915, 614063532, 976668201, 354931041, 458376054, 676420442, 712653993, 751759420, 862961446, 76426887, 771641078, 151560858, 296779609, 835779335, 311901705, 670169974, 55190117, 972784871, 59179380, 936961336, 242095392, 504809551, 944124043, 985199311, 836350955, 695827425, 354057032, 513397380, 705346644, 608109491, 717237078, 389532888, 213992867, 415280758, 521779911, 796567423, 508797404, 230611901, 13988425, 763930140, 580264568, 793918366, 221016729, 601733816, 267346964, 510497293, 415478892, 159828503, 859792867, 604011022, 534483544, 887654759, 851979828, 893659870, 501497792, 963912593, 154791774, 932657690, 662503583, 841419380, 320341445, 73288036, 403318206, 173553690, 55132874, 668865691, 119256305, 431870609, 69984433, 203880202, 543848977, 465549647, 532369545, 986273344, 933054658, 271695856, 581930051, 206048548, 160178276, 577867711, 819078096, 120659193, 941533851, 362886109, 187918963, 948516844, 85141311, 221258400, 757794185, 252821158, 186403935, 989522257, 559759073, 472452329, 339710631, 570528104, 565240164, 651162902, 632431979, 689048825, 52489243, 235473665, 66621141, 55466128, 371572882, 629355423, 135916638, 10765360, 634519732, 760376122, 311385138, 333977530, 710683779, 530925487, 555175355, 544056766, 574707896, 673743006, 545723099, 750797909, 900754173, 119456275, 790301857, 638822456, 243478716, 591808394, 516531504, 608426534, 182736746, 113522726, 356207297, 538769178, 46335033, 978317732, 665314945, 526849814, 912058624, 684960983, 419537300, 935738731, 665331039, 384946300, 515577571, 480592884, 907750250, 852374603, 793235070, 459631862, 961408335, 725495128, 478445321, 419122798, 284296494, 323891880, 131138217, 516466308, 827689248, 854648097, 664480118, 555747392, 48067870, 516751029, 930574742, 546545672, 334975352, 861864154, 823405536, 393647200, 230765892, 541885942, 934702604, 737160775, 642157617, 785218423, 818149118, 266013619, 370391332, 589881644, 309106641, 955501535, 478207355, 985315386, 2722222, 770166217, 321353785, 80558590, 629772817, 275678027, 715602006, 283517945, 949639223, 661141750, 507023846, 853701500, 868504287, 528911858, 675380194, 893798778, 232933828, 430383437, 140146769, 523853844, 435810104, 506247000, 988404165, 468351284, 594291380, 680974123, 360872316, 929302521, 658787970, 277791067, 892654245, 118299874, 393073869, 402699740, 354496193, 91313960, 422644690, 983221641, 634779391, 628511077, 703505529, 632663749, 88791773, 947009063, 636722057, 969951896, 961457770, 91004949, 394490091, 533699456, 380554462, 956218010, 823973384, 889546857, 724121996, 310352824, 482686056, 806523791, 300310730, 9555280, 45739426, 361409756, 94865804, 624804191, 928002306, 6836440, 912137571, 794104612, 52843269, 31108272, 147074187, 682901346, 104196406, 746454576, 411168746, 598801035, 545733860, 294446492, 525196062, 522080117, 329532299, 347630212, 79463046, 675443882, 811209145, 359592649, 677426399, 49738860, 134348257, 324451614, 149682274, 280591133, 377434296, 411056773, 477583726, 465297649, 907164663, 863821817, 731365420, 184912605, 819990085, 510755828, 373619228, 713496155, 652656515, 431059055, 529577969, 752171601, 441848975, 13276085, 584777471, 341549600, 347369419, 96363565, 893934774, 636733743, 833175280, 878647453, 754348249, 797005870, 475673754, 742894114, 427947784, 179716475, 128247872, 11814543, 285264731, 419004705, 800408852, 998575763, 296950249, 413155890, 709834927, 783017333, 30429631, 422253347, 763030609, 91945731, 55036798, 126232157, 600905744, 822742302, 427880571, 755439961, 141270226, 312103852, 913541345, 861310992, 55131850, 74572362, 312854957, 152111152, 635284019, 937282218, 467638728, 931515126, 740797445, 795655938, 331586375, 57344871, 247721369, 375284245, 147616684, 350473228, 776148684, 764942283, 556931146, 318772818, 11545759, 415743169, 667736622, 872029906, 899998200, 797746790, 57344546, 204547200, 330367842, 348093828, 582763135, 889202959, 113626919, 564075162, 851666877, 719124080, 428253682, 542926238, 571621899, 67659884, 22886761, 478723970, 320091770, 181221117, 348709289, 200249110, 860825199, 114862877, 975296435, 753729410, 99580085, 911735384, 658384659, 995511598, 31690776, 161873870, 358096992, 166442489, 837908679, 485203245, 116629634, 80502852, 204798135, 628124920, 829127435, 151384577, 994494551, 984038429, 782345321, 677894487, 292699080, 625815415, 987796717, 589126810, 150691257, 525017602, 783174243, 823128055, 479852404, 933331283, 899645864, 53478152, 855877352, 719559552, 722872847, 464217722, 225361805, 304197170, 274285893, 895056840, 470006583, 971992297, 990692995, 70235730, 547189816, 153838025, 547850377, 603885718, 498996968, 958690299, 491831068, 73849661, 351190239, 217551807, 240398746, 57102176, 304509672, 694890950, 872790518, 58075409, 772119248, 941462982, 816580657, 392306460, 39639244, 666398728, 477493139, 595658279, 150779815, 428334377, 612082021, 708808346, 375524771, 543051088, 309294491, 641936171, 420176825, 881737990, 803750547, 498318842, 786516314, 60409942, 987606060, 729540828, 480417339, 898964423, 676071692, 15788148, 794357120, 979340512, 447197782, 389911576, 775143980, 672716979, 379029540, 105602607, 894598678, 538975400, 528262438, 473627337, 674653176, 832558199, 531158548, 318276672, 965344006, 863173874, 629225870, 521571300, 688837219, 534808236, 984525582, 99351678, 346109032, 661605607, 612451411, 419429908, 217705713, 755644975, 344568839, 176050382, 168877858, 71316722, 271166815, 713485514, 776753836, 896199225, 425156950, 353123228, 475240699, 26802126, 144875171, 791425517, 253913229, 205090443, 894384319, 645984923, 619288479, 714052194, 522670272, 19241980, 348404083, 66329351, 237933626, 423840081, 615772295, 329610029, 140956261, 933178221, 959583592, 634316522, 276840013, 513093379, 25083502, 652280065, 762956213, 352804358, 437192039, 774406664, 234907244, 891647041, 487947523, 636396858, 457252537, 237164467, 749022428, 417479081, 911560126, 916392071, 128627963, 677122650, 235128013, 233134178, 952085028, 931928839, 123637329, 21545084, 995474669, 585639483, 115223853, 494397302, 548636900, 23200839, 841485598, 431592036, 260003308, 558527192, 15694890, 396931427, 60692925, 591074741, 956645839, 458692737, 821742390, 924649064, 622268400, 724110413, 795364163, 695068818, 924775261, 473222597, 522199361, 498614021, 143356083, 268027029, 416588559, 181866678, 45877151, 196221408, 880990124, 264958146, 239506795, 290493608, 859494600, 756146817, 314845288, 381592277, 116653818, 408462258, 324296241, 454769021, 183494940, 61760410, 698527588, 851358315, 346359812, 731101356, 464200609, 454526589, 554509101, 430657320, 561248738, 795445557, 599314489, 26309013, 282293390, 953025513, 885259682, 631061138, 199912857, 718399892, 523322046, 319269762, 486869076, 855858489, 949465191, 717860768, 182370678, 899559161, 69821485, 328400514, 62655954, 890287998, 598227277, 941348702, 897286450, 279297522, 903019748, 351039514, 952201768, 811070926, 209623456, 287704822, 849374067, 703229734, 266485196, 681130385, 686321057, 172847424, 990752675, 87955249, 498316829, 622910646, 437645161, 118199829, 932120250, 696127644, 515662822, 452134362, 820491165, 27908800, 779018171, 134000619, 109235769, 745361571, 891048452, 197224747, 607406851, 729357374, 6149760, 254314731, 5947804, 797172111, 459210574, 322764684, 494808201, 875095217, 827627582, 353453960, 633733633, 643331370, 929029736, 520910875, 582812189, 109039819, 500559612, 298213803, 541029888, 122312085, 919571952, 3006414, 48175578, 555921567, 682371155, 511745138, 742506730, 703850003, 732816720, 604939478, 107221882, 944492394, 506051449, 236130071, 469766839, 551451322, 366272362, 933264254, 756944714, 725760765, 562700659, 136473275, 589739738, 741001589, 416380033, 357441811, 464905585, 923832436, 70611148, 332611789, 547224154, 434275985, 980472246, 795289179, 392993506, 424692257, 143687717, 512318485, 505385806, 846201571, 151011400, 767301008, 834787131, 612777306, 132846493, 894473020, 502796183, 316210932, 493813932, 107565019, 815944552, 403374510, 267816783, 865152648, 780837872, 852706122, 87306919, 274089762, 78324413, 670945302, 925608011, 364871915, 300203100, 637570056, 206076683, 327698380, 50529203, 744793949, 766594264, 198052238, 775195525, 526713878, 267492882, 522147269, 841231074, 81013343, 579056319, 606017881, 444104504, 233014001, 87914036, 219473835, 579014923, 924577386, 116529439, 675261017, 63816217, 419165232, 411275949, 521443533, 717900092, 330975478, 671228162, 653673599, 794853120, 25198464, 913600731, 383022410, 759715272, 542350892, 133274066, 164849042, 609339326, 490743426, 417686092, 441911828, 762299472, 5420222, 634847654, 529247440, 869859587, 283738917, 744367321, 886557788, 256691558, 105252949, 137949391, 818989466, 128381849, 465516581, 635113222, 331710886, 597687118, 388669835, 720859329, 309273214, 439478552, 513608894, 21250965, 616958366, 213650931, 221563373, 437397334, 810544215, 763102086, 984529435, 229877922, 714777385, 905259263, 224158358, 949029892, 433864126, 194819257, 144907772, 763015109, 891181460, 795652641, 98186581, 588002881, 734868599, 199051634, 544577227, 348059311, 251211816, 31542142, 483275587, 344222692, 835959563, 882257605, 496611638, 888005292, 368165630, 407559352, 776427483, 276327285, 216497058, 359441999, 720879044, 960711692, 94018100, 477358980, 247264110, 471873656, 45715335, 279527600, 687802320, 507281713, 256814426, 973972085, 721310944, 331735016, 73095374, 160630883, 880025533, 261072136, 295258369, 44322922, 889365039, 879521780, 918591133, 203600111, 538054985, 355950728, 67845644, 70811270, 466846782, 727952063, 283177014, 744220244, 118506350, 499966346, 283362793, 156136514, 981107561, 692139269, 438905911, 38650966, 878917953, 765967680, 858357495, 659297293, 740997732, 628781893, 893432854, 776970367, 758611501, 504324700, 151522842, 464899640, 789920793, 534135195, 581660269, 220053109, 389860994, 27064114, 959859689, 656328831, 707183317, 667045579, 457474240, 676437295, 841641624, 387519845, 980794269, 689033417, 642179446, 756238070, 386455488, 518781719, 339812026, 395893028, 341068938, 234791037, 720307360, 461802933, 431091297, 626808220, 207763108, 665393828, 702494380, 484781624, 811419742, 336377357, 273082037, 761595723, 624418361, 471280598, 111477465, 502541584, 631820251, 184001323, 183314976, 179204986, 893064897, 287905432, 366547761, 136782668, 420322394, 128423295, 774595226, 933509521, 89083703, 193410221, 160140986, 132837311, 790655973, 464984273, 892187009, 571518529, 233569487, 55309109, 148658609, 891342171, 518757257, 319950889, 550131440, 607019714, 205160454, 780606381, 710889203, 58100059, 203142459, 349461809, 864952814, 589742431, 697214711, 548652385, 324000505, 953885096, 18512643, 662204016, 100742109, 205146579, 551039757, 299927299, 864999146, 729615602, 653885611, 119031151, 193692045, 864392577, 788477700, 803603502, 744453100, 778625213, 983552414, 96959969, 381214957, 67049936, 711044458, 850444653, 218418530, 515372361, 561052258, 865668241, 160692266, 344608138, 397666930, 256798067, 372924117, 692926426, 786727331, 478359287, 483746848, 138784535, 193102421, 980864106, 190265054, 391888930, 494402683, 209600498, 99513826, 376359437, 63245346, 580910779, 675819074, 728540569, 306724923, 300952486, 476280944, 6486820, 115331947, 903606692, 904740284, 328713012, 223373951, 324677142, 835746958, 651894060, 586281638, 371176467, 719943898, 756316420, 211769015, 674689533, 24866018, 728128305, 703815973, 481529178, 879867835, 89524420, 84356504, 139440305, 684412462, 660464564, 526379001, 257966298, 538725461, 150730442, 747824415, 390285019, 935632099, 752548833, 801047411, 521965180, 6717059, 338821881, 884299446, 319454511, 363423024, 392927825, 26688468, 64779406, 236591284, 95445957, 459420923, 771995600, 205557030, 235987476, 862376091, 750038970, 687225702, 333580512, 240773152, 142266866, 744798469, 820908880, 382052862, 939245899, 358956161, 781297743, 238654804, 17479095, 687319322, 365388088, 911266294, 300226428, 823271011, 667748842, 704336702, 222860946, 786886661, 536627285, 354433223, 923966183, 631586348, 897478499, 733457557, 916554254, 88933423, 222845910, 618770405, 704182099, 97850507, 617797474, 224549210, 918227044, 246163605, 55285278, 798422027, 259903512, 927112, 161447721, 740168077, 802450767, 379874935, 174631260, 730595966, 771332220, 940532183, 886894314, 167883472, 140158600, 728124716, 688372625, 371974915, 694253641, 890590553, 300737800, 43674970, 216404370, 20527463, 735986774, 552776080, 29087218, 243341192, 210321507, 367201452, 534031929, 239480357, 588072071, 664065191, 238886450, 151926244, 904214254, 89423598, 556080258, 414570610, 933322032, 966948334, 419105010, 897028141, 998441012, 872974991, 653564102, 232536662, 191986054, 703620682, 645785315, 335854242, 587148215, 731653876, 789767058, 476700358, 59317347, 483660778, 103482788, 309908578, 694609207, 554467600, 900926561, 209912988, 762908376, 601007928, 390051155, 736070077, 56096312, 980689737, 617831207, 435318872, 505645809, 982286584, 992713282, 91992776, 141155211, 700597199, 431981795, 886568818, 497283726, 388024502, 904608584, 912766880, 804606798, 188922821, 366239784, 472296917, 265121487, 707850968, 397865293, 114821145, 824384682, 954285645, 383611269, 695669322, 958235670, 146653144, 74588416, 343267647, 104712972, 699797838, 311564845, 130913583, 582989238, 581474443, 317754702, 881615694, 558175658, 311862282, 364242901, 450829400, 221701616, 384672581, 472631466, 101293788, 71397337, 644199435, 23423921, 947874811, 413505333, 686284082, 317117983, 736466447, 827333723, 45148128, 340287070, 290227100, 792101642, 92167241, 694139040, 822520153, 970422628, 857168451, 402843389, 720011242, 253499777, 771821920, 918378166, 737394434, 760975995, 831144215, 608294113, 436358685, 780938702, 250910643, 779696415, 371156680, 161734253, 718415205, 586768244, 213246895, 475951481, 350408528, 632232931, 817292535, 489895860, 917036108, 283545437, 182986235, 234125018, 851262562, 17071373, 455870169, 994869650, 447939784, 200961450, 189501371, 457975405, 14392886, 166096162, 117781283, 695314313, 199079969, 703744767, 34348441, 447263803, 367555910, 474573540, 593297242, 340786635, 532511133, 388480516, 591642310, 40240862, 958402919, 126456087, 448165295, 45031142, 443085724, 769884516, 928303449, 700231956, 426949346, 850737979, 153823596, 791606524, 980857876, 349393359, 778368009, 134900767, 524157510, 956434987, 689208641, 91935059, 231694109, 419818848, 148445998, 830127532, 435559946, 919338705, 424517218, 500424393, 933966521, 323319612, 355538850, 261045381, 471963247, 792088941, 919808361, 779263735, 746748300, 450917318, 173160285, 691651418, 309954537, 579529308, 574748636, 184029999, 804573297, 197043799, 206165992, 309611828, 558649352, 770431637, 123996599, 850290206, 174996025, 547942695, 245747096, 77526671, 834854237, 337470094, 466988694, 780091985, 810513200, 649383965, 354968468, 246789964, 842550398, 691803345, 902171611, 17842697, 42843851, 713268494, 55782960, 92308534, 783994182, 71346918, 51900993, 726171283, 420347358, 604530673, 488039137, 708199551, 969598436, 615918685, 856094248, 169814731, 808394081, 999511943, 559131769, 463416098, 60053837, 118180159, 384783981, 155238818, 881197096, 930579102, 169861363, 294788935, 267692375, 110945033, 415118683, 954219145, 721022777, 316217845, 87606329, 925033802, 144947200, 891683043, 184786143, 716122208, 98540089, 295565792, 765863776, 168232382, 691396492, 11873048, 323746877, 457323387, 547553913, 332232393, 142616591, 13388163, 289851457, 636737739, 457745547, 849608192, 489989266, 561951189, 596149820, 645952242, 983575966, 261760338, 264795150, 29288707, 424193941, 616293452, 459711522, 28550786, 284355682, 800909647, 948658686, 686322346, 365438361, 672488622, 476220287, 377996573, 784815521, 943104674, 888371055, 795394810, 267588374, 215616036, 36848449, 693620770, 412042579, 373204857, 60248341, 728287990, 940085192, 464278263, 782371945, 49251980, 182555860, 640374095, 327783589, 438507449, 842660600, 788342480, 204585029, 146342262, 196383874, 986398144, 706045774, 327231030, 886083049, 3837719, 149127921, 295755255, 968456054, 277940118, 601322666, 508209539, 146696387, 657228338, 757709814, 792851500, 502392409, 420518928, 204441317, 721094894, 463573034, 845845150, 669518892, 686780756, 640409567, 454576247, 129532976, 18828738, 215303773, 414070648, 599478775, 955873210, 702133946, 905960561, 76782795, 493757338, 523418043, 930243682, 336864450, 80616384, 669525762, 877105751, 551808772, 782572554, 351360212, 841456413, 807976561, 354444514, 354535689, 314014525, 765530010, 564515737, 703268099, 644863626, 571765630, 567823435, 734138555, 207633703, 139092316, 536654920, 800892889, 443663919, 897963864, 440444246, 280914653, 268799475, 462439988, 374541710, 978423103, 130376558, 666244733, 646355220, 772675841, 303130658, 965062986, 784260995, 838416473, 466283594, 732044972, 602288007, 334792544, 375668600, 898063585, 244925399, 855625997, 801235046, 907198367, 892902270, 948887531, 570280331, 244169732, 484808816, 856975626, 604739860, 883293515, 535877378, 715327206, 499596287, 701544884, 134157427, 579031434, 287150181, 676970529, 39104375, 440545326, 391424931, 958818460, 778463124, 260234125, 627289692, 806739247, 811243873, 160032433, 652065124, 50866909, 840839366, 767667310, 788817821, 921839141, 351791505, 31728637, 662413463, 224926441, 97190786, 25684260, 465550624, 61983719, 746614305, 325831372, 439638489, 515538500, 851019263, 270349612, 384862419, 224276576, 342042947, 766992729, 918052968, 339307635, 520674607, 543662131, 701430750, 455989250, 336490682, 153003617, 378845286, 948080104, 2878266, 476040676, 901131205, 410183640, 667888294, 450247402, 286874532, 323680120, 574578211, 359677816, 999222785, 503229334, 486403480, 166993088, 502101773, 979801211, 940494430, 833948429, 383691527, 473986276, 520798442, 42461316, 349654404, 406894898, 955457222, 249427469, 748290680, 577004391, 870018754, 355661035, 920944707, 653995026, 963387336, 201699174, 641523528, 257678573, 300787880, 949955055, 196682937, 412019339, 307708438, 948580405, 796689630, 879407695, 897068840, 658386665, 231978183, 532839665, 649197769, 868121468, 71703554, 46044201, 522540970, 952456974, 171963948, 717805731, 282982151, 683644575, 599839080, 627985785, 369951586, 662439209, 577678737, 568886476, 569714333, 610092082, 667946980, 669224184, 963293371, 622040998, 254725214, 600320325, 550395729, 414274384, 716455904, 680554429, 666372551, 877220757, 594551791, 920543204, 327089670, 6766730, 432632843, 52905015, 376618317, 539553899, 782795908, 114630301, 525964672, 413657469, 515826452, 42867974, 813403170, 505811164, 853822452, 494970945, 637636459, 331390734, 651699135, 178552370, 253077061, 707997091, 531097851, 507255810, 264716070, 107821547, 613424072, 292717467, 983583487, 979557769, 969783864, 204331667, 56911390, 443712205, 876720331, 334462679, 677772526, 167050161, 14464090, 977499489, 389805486, 597264177, 505977387, 491486780, 971357560, 487200195, 997064705, 4609508, 230103935, 465725669, 682893183, 757129545, 793870181, 729920064, 633058214, 541943313, 372245399, 558992910, 822700021, 531322961, 569581811, 218251046, 185121446, 471851029, 531874453, 814901463, 840036375, 716872407, 404419043, 228522404, 507071409, 762330663, 667622934, 56317265, 601056587, 503699568, 936249947, 307075759, 791753204, 721976896, 289975994, 370477794, 908079930, 812262107, 266495116, 193147341, 195062887, 416565849, 66214276, 488210123, 934304956, 474571288, 39280810, 17932248, 878302368, 496738250, 631890210, 634441085, 906722262, 825236215, 221996160, 635022659, 976094692, 647554324, 768811649, 287155162, 924860845, 998287687, 50852275, 369622661, 707679077, 755757920, 629573696, 473390729, 956158066, 134175278, 872953162, 649108946, 721480545, 873612206, 958900147, 87364277, 562736057, 51930683, 393984313, 436319789, 709770744, 886310582, 215116128, 977506040, 450995495, 940320346, 489716151, 375526362, 899670565, 52188298, 151339600, 174785447, 447765274, 117719079, 843678641, 880086859, 546661959, 624066631, 415264780, 862559682, 798883621, 536076438, 275680160, 144547323, 708255632, 98282948, 975186480, 76272413, 964987593, 8730274, 758260769, 443198370, 303173383, 46426320, 149542397, 587610265, 981900035, 7150903, 825253258, 611810285, 373823694, 137323502, 779928979, 404027653, 820757852, 642859638, 616464667, 602319717, 185692628, 543911774, 804835824, 814457644, 75332832, 581231560, 937426331, 933122108, 611963809, 533100441, 264888106, 455817760, 112732037, 437623306, 213025807, 772061534, 245180947, 553552970, 139063862, 81577745, 693486469, 255366147, 215453113, 528945214, 226054403, 266077807, 638416523, 566363541, 790564831, 85636330, 202031954, 52541150, 201027961, 877184261, 758554986, 737138790, 257619066, 253649862, 686417515, 414480197, 283463323, 636972643, 679219996, 962310206, 980829499, 485793110, 525604930, 866078487, 940923024, 421726500, 154353468, 747858224, 996941099, 943529661, 473230794, 21340955, 582158481, 140222762, 974089413, 703488598, 815407995, 400376073, 433808177, 174276415, 766301358, 546295601, 69702526, 660823587, 422715626, 577424937, 970831225, 298317044, 345619010, 982528503, 503205664, 770394424, 986399746, 280243972, 673980155, 621052703, 151193002, 209831439, 787915371, 25217840, 42186459, 425858127, 894157096, 126675071, 341052141, 461644979, 684747424, 52899722, 929780587, 499986482, 725162877, 259085934, 343936338, 50053694, 653775282, 330973766, 898635743, 487317987, 670758987, 219747347, 852551606, 340893459, 440916198, 757893141, 166836291, 112806420, 123248239, 686111157, 599731627, 126614362, 333157502, 349621879, 750357340, 834744543, 955706450, 414962559, 238827724, 752663086, 310547336, 834876167, 62550184, 180962146, 240366723, 945160713, 990752361, 211979967, 405587816, 748976123, 493811209, 136844775, 674540881, 698433211, 955878645, 758291719, 254111589, 525843434, 99084083, 651976066, 735201151, 789925284, 230134740, 13887643, 356548021, 266700931, 385710946, 615734980, 106123191, 818149583, 800467176, 479890153, 45386215, 92890538, 36981826, 378697850, 889014726, 578941239, 801698613, 116661616, 233945631, 928575194, 715905194, 701648714, 153865208, 442856242, 365338606, 631508890, 453546042, 899900929, 331241820, 913937302, 7204296, 14889156, 134338616, 890424703, 652142584, 759683665, 809720858, 431882655, 837178726, 100935021, 273377732, 484099863, 212874879, 435185158, 481507179, 43385733, 658190676, 785347962, 342503628, 80442650, 261227407, 936233768, 24332707, 582589121, 446994383, 80695177, 518257812, 789086715, 259330882, 224241335, 922570181, 292762596, 238576619, 627485950, 38658906, 366911059, 266364011, 404568041, 831517127, 317864974, 901158784, 96355827, 166398660, 625367844, 190285718, 528646009, 815683052, 801401234, 987299180, 486185460, 289387557, 462107331, 940191334, 340264723, 957008443, 532490874, 434147941, 180224410, 593854671, 751490729, 783087635, 508166964, 970642875, 408342231, 493071180, 619599764, 388736561, 263806190, 969154957, 535739210, 743766790, 122818627, 554206234, 868384956, 332005452, 298841062, 349215818, 104232379, 151516994, 755609429, 325594501, 495056315, 874735602, 232590957, 140547994, 558151247, 389275541, 45983844, 939664142, 362919374, 312138667, 121019910, 203520002, 912016937, 968633715, 639162987, 57438301, 838776373, 954220982, 570226153, 254159912, 42401932, 993229555, 684595254, 129792003, 730172266, 939334362, 887289879, 589466256, 353407012, 235877424, 936672147, 851167557, 890805191, 778181775, 490371685, 475196231, 743758632, 400096827, 986188955, 811481130, 928554517, 630791605, 677114019, 590629508, 584474298, 179010967, 645783833, 454962023, 563738932, 287298723, 555806393, 559549200, 779182288, 705234472, 345651467, 406645383, 630060244, 299827194, 695660021, 535374498, 350427822, 295484131, 961460961, 902978674, 926182193, 47537556, 413793721, 746897305, 272095917, 593509306, 275612878, 682107812, 661890851, 666346378, 586109512, 768654207, 345001551, 316216496, 635631497, 786540397, 847543515, 534507812, 856842999, 230656659, 743915780, 709850144, 838251235, 163173221, 103744746, 615808348, 467529309, 572197034, 716254645, 593154488, 84224021, 575010755, 535694165, 799935522, 15035979, 400133039, 323205247, 145895889, 997140984, 114356187, 15196384, 739560396, 201317107, 117618278, 762790533, 393584422, 317928278, 549532356, 791184676, 593267543, 505928575, 611770673, 386232056, 308069520, 348947328, 285688090, 757962553, 67987801, 341893261, 994327413, 506651713, 374071918, 714520038, 209205656, 604587809, 916145919, 592270362, 781762366, 592981556, 187770942, 306746948, 425325904, 897782173, 979696048, 237051818, 822730245, 971662716, 44448716, 873171961, 250671658, 215367556, 94227880, 227549451, 551145570, 311503585, 76973678, 390000445, 119808157, 790727102, 55029112, 416166577, 650626079, 604336987, 69757515, 255422931, 831942580, 106337652, 670081870, 289540378, 919107755, 334365054, 44258717, 608108964, 554228732, 968310425, 949173157, 12478603, 797881793, 859186853, 709566171, 773442898, 740143530, 87516134, 601607434, 365022291, 609852065, 356315427, 658462642, 738181340, 229689528, 129106672, 763445434, 481951809, 841072135, 340319498, 273973963, 441999869, 30139010, 806337616, 953531418, 226370006, 983206073, 44634559, 907447341, 6834737, 700992798, 727025373, 203015288, 993362300, 672771210, 589791247, 416815719, 908038559, 878100719, 498434021, 179128769, 562542042, 710044975, 883439577, 759652941, 307991761, 147389635, 373899072, 420567716, 598246332, 413979348, 107145685, 132212313, 205674858, 151879257, 36954281, 115417884, 74492766, 441911074, 284986214, 761753053, 37617022, 240270157, 466575915, 405226738, 321516375, 461201531, 233016267, 688491215, 442983880, 584967267, 101626065, 610407386, 193889926, 411742284, 157185271, 777354870, 241440224, 166106123, 729964379, 859346845, 856465235, 161435999, 352000878, 879913156, 911215156, 662913551, 699899246, 267262486, 853755524, 126647244, 63700723, 410027009, 642359092, 621334807, 945547920, 731495241, 570360307, 483959605, 714659251, 574180170, 371538969, 63685032, 880032847, 119032549, 412028128, 309066274, 852756585, 772281975, 150467215, 141880320, 153138090, 758874593, 707714746, 827668682, 187719776, 43313323, 422306348, 564779268, 707278497, 857347265, 625050640, 277154501, 115819123, 378918000, 699793698, 552477782, 35400969, 250160729, 534915989, 534586575, 24930170, 431396611, 494961327, 125961720, 981602668, 231052381, 136978911, 565983995, 810978379, 765631721, 387199610, 275699427, 43784272, 435648260, 37842495, 267556915, 221648820, 29074269, 839472423, 541796391, 468706923, 81890232, 151529568, 136683051, 21848110, 89268644, 486271512, 571736984, 154265672, 5209440, 905949136, 585839797, 818177680, 604024558, 815954825, 288794217, 619671198, 912754465, 89213777, 928731761, 273128344, 817957206, 418752591, 721079024, 481338564, 401390, 962995917, 752872028, 444801635, 450672091, 951198429, 435098746, 414063597, 746078733, 807728589, 933289539, 65781027, 411214314, 573278801, 343270028, 648491294, 434227, 750398563, 339261768, 982248009, 928655993, 472035220, 865726718, 697625093, 28852497, 216296850, 832824676, 602253433, 921934050, 896487073, 37545010, 318786042, 972211908, 283035426, 931778913, 198434383, 130664226, 119640870, 986152097, 382617692, 193195699, 49882821, 910147983, 532899784, 300448671, 763279058, 825034526, 315667770, 549101431, 142287363, 211003137, 696525457, 207061659, 471637278, 830728453, 199092672, 577044393, 399418211, 58050796, 22422256, 197504919, 396788411, 745813576, 299534320, 397861349, 940147238, 623826528, 843539183, 529550301, 328382941, 902571935, 81959093, 887737629, 439664710, 809493262, 685731496, 282882977, 206251701, 972003100, 340483107, 160171148, 285076961, 380611153, 684035200, 348249069, 182954823, 613405008, 681314038, 455023333, 115704249, 844976207, 758934777, 933756163, 237299115, 319683499, 377970446, 33949911, 504053201, 262731023, 169699135, 460498402, 251402277, 554186344, 887742625, 133200483, 165962402, 923564695, 812453044, 377487688, 587395081, 801713528, 558483218, 950365565, 803828253, 117824612, 119389583, 808563561, 374105258, 362404939, 883353091, 881653236, 916876070, 202011326, 760167155, 592758540, 385833143, 294459149, 889381276, 701512769, 733269069, 310862041, 826760699, 778059620, 930878333, 549901197, 92394151, 22937654, 348329267, 820783848, 374362533, 280936211, 308625273, 319063662, 821597427, 855652309, 342136579, 448822298, 205704111, 992146554, 813347733, 348159553, 356255279, 318537015, 105895934, 707541096, 958900409, 280344205, 336762558, 422849975, 537992613, 15449997, 519343587, 268107790, 659949923, 628659929, 597503706, 852590006, 925075123, 722630202, 783594566, 665930753, 936083039, 539148164, 305942477, 385411107, 117391858, 207767424, 702525274, 720423571, 680068988, 233723133, 147069231, 809955219, 420142326, 490337028, 754688855, 361039906, 352184293, 727822251, 468213289, 945239202, 790228748, 162701391, 238176042, 452205206, 809512150, 301412473, 45055431, 948707489, 727967364, 626861863, 800727367, 825295487, 71354976, 615313070, 868547515, 879214529, 600368290, 232799728, 568093420, 556562573, 433687480, 174472026, 509766792, 276243924, 429384236, 685621055, 226512778, 953214909, 989869134, 211090130, 127791528, 138358400, 612014107, 253521513, 911789955, 454724765, 853988633, 715205887, 479103190, 721623250, 153195375, 455843208, 260673003, 65944470, 624264199, 147672629, 870309729, 416815582, 777562819, 71387716, 474814828, 645610917, 391138441, 497858139, 916308210, 9909653, 390918332, 285665082, 261026808, 871827785, 736454329, 35458627, 24275689, 721161437, 443145766, 964684697, 903130159, 434538017, 949671664, 408458289, 647453326, 873117721, 32116028, 794982376, 83884500, 752972758, 756738377, 178359545, 300881293, 740158574, 849033113, 310138042, 583905474, 61329500, 630104592, 153429609, 561571797, 919920346, 269031051, 906422306, 556438422, 86477536, 973478220, 200737202, 100561655, 176333075, 322018064, 685436615, 198140252, 950239592, 139749265, 58084084, 161666585, 116265401, 308550870, 167952982, 554549359, 349452664, 6051349, 495097817, 221274660, 474802327, 84828457, 537544605, 152896459, 209695644, 131900407, 962850651, 298488259, 533301766, 943094661, 772953380, 15941722, 794046023, 736667477, 417101987, 580934973, 25023407, 959373953, 228908681, 364787199, 198468147, 195544794, 240541304, 991934444, 280216576, 365451303, 155093012, 862168625, 421053460, 339547538, 290378705, 423943545, 772417578, 324791453, 821647079, 187261275, 46824863, 900754864, 213055330, 807001622, 424008914, 704124241, 955909506, 201500010, 53483954, 180109757, 338401076, 480351704, 162883337, 439581229, 988988934, 72167016, 119600108, 397841413, 559234678, 784337174, 429842239, 208529131, 684119641, 530591121, 982081782, 356928708, 242033341, 389305174, 799085417, 882672527, 486782381, 117017728, 966319320, 566315986, 548462339, 594882086, 453171277, 338660266, 142606169, 783880634, 952600593, 144817138, 77175080, 908627752, 393808718, 777106713, 651384543, 572333606, 169328494, 185685470, 33045026, 517217787, 979860217, 219797823, 298846007, 301617327, 14104121, 452282727, 311240431, 660121669, 976394906, 515202123, 60349115, 670802691, 970380535, 912407099, 145893357, 839080968, 482485402, 374175550, 338475527, 853090104, 85593029, 667825252, 107873973, 761227584, 355397208, 131052060, 367674792, 497741959, 894004267, 880831213, 648877128, 756600185, 174827555, 368100934, 507468370, 757157264, 862325218, 438035272, 503737926, 706006096, 189287311, 973892480, 111545549, 784616909, 684398360, 59750833, 25592702, 709892646, 724438273, 951684867, 652038818, 891752082, 992294131, 921985944, 343910793, 675105339, 764260669, 749640474, 359306593, 941066560, 293589409, 442871943, 245391408, 114477031, 53833807, 211227460, 493202315, 427379214, 750797620, 817600586, 483768261, 653994638, 794977659, 359913896, 997887004, 435713413, 531020060, 886923950, 971931010, 105039310, 88517905, 365073078, 153919004, 738412576, 526840240, 451461829, 885895057, 417949233, 165043256, 467008415, 196475972, 683289938, 412781434, 197912250, 675531369, 391917781, 572779040, 37431411, 287232986, 240728072, 320266824, 54106115, 472975972, 362313434, 271329473, 48823357, 6148564, 157876775, 343732991, 853426340, 559013457, 678592508, 479211289, 63730335, 262748520, 402302603, 906180714, 165720031, 886273115, 447602166, 143353149, 902708664, 573272624, 797266014, 904002689, 230442066, 346367719, 481243221, 625139770, 939501369, 81918267, 400765644, 14128348, 902584040, 988995383, 381190990, 183547212, 492502805, 191174786, 848637346, 495419503, 864211975, 327117274, 710396804, 858392261, 195037512, 294768737, 476320351, 773836861, 213914578, 735780119, 57020594, 788943001, 887551865, 124239952, 821569413, 212256032, 140957334, 142161921, 457690860, 871824748, 465914967, 746606656, 617989941, 984171439, 256095990, 186588794, 699610469, 208457699, 914061780, 662465626, 590346072, 813846375, 187455044, 60216440, 814639816, 423537889, 788511175, 706179700, 704811509, 809873120, 461577122, 594671306, 23210564, 766280852, 314782452, 82785316, 691694433, 846299669, 770709720, 152649219, 608810921, 560890604, 70518122, 43191034, 943581292, 887368154, 73952569, 573881615, 490890761, 747630570, 607306765, 72207178, 481429276, 285055285, 688074467, 843297443, 200194051, 827453198, 713203365, 420917689, 518921481, 127225785, 756316134, 635829642, 552701574, 800919444, 839237357, 137399702, 94109168, 904778852, 586165821, 84989640, 877574013, 885386479, 939445429, 30557137, 209830101, 960564048, 216294274, 517328321, 411556903, 911349886, 859949328, 168143839, 901618253, 4757136, 32030354, 647799541, 857252592, 907225029, 935064457, 495798016, 30187766, 529812045, 459315760, 834677964, 880490341, 886670061, 821811233, 201300224, 364770520, 213908871, 931711231, 88122658, 462008930, 898756405, 108186096, 887868421, 286131871, 425208345, 31675963, 696956718, 3945617, 476957170, 688042070, 183611973, 711206794, 772561344, 892871675, 892835569, 667824359, 798045047, 792651972, 339639152, 862277146, 748080632, 200667634, 339602000, 619691922, 871270106, 532860820, 84857528, 766200712, 483864560, 360909335, 647397212, 953956228, 995907802, 914134300, 480197079, 724793392, 417669175, 51138591, 339474760, 533107389, 446430560, 404715703, 605450377, 490111390, 730409895, 847208342, 890936717, 792950430, 600488573, 313880927, 607282328, 123918907, 73702073, 67397472, 306780388, 60461546, 322732204, 91131794, 952736348, 117040894, 888219026, 142836049, 949077564, 214323203, 91710026, 542923991, 945883289, 711175210, 597061551, 88259511, 463437189, 771041005, 254522615, 718139151, 779101797, 551032954, 455407495, 209788817, 370145478, 87293085, 939292812, 534165287, 752486397, 639210887, 797914819, 870038537, 416201714, 443347079, 120924208, 62176265, 681169861, 132391434, 137676597, 156252572, 799380322, 749766034, 802037428, 977875025, 777663258, 818193165, 719062339, 797370531, 595784608, 685734125, 458199017, 655346953, 637457531, 510612688, 134226111, 891173578, 863464493, 24720426, 832217953, 234718013, 553441299, 944106313, 33693292, 568415800, 557962313, 881616724, 370299123, 844130359, 603685421, 954674709, 639100091, 421794363, 369415948, 117462283, 955835883, 316295985, 115235961, 78781337, 89265735, 551842003, 463684651, 184442960, 679862669, 652044477, 800482208, 309357872, 394836207, 654068097, 164109110, 931387793, 94974054, 547931291, 781607467, 58760113, 461351487, 269316972, 666051384, 593763546, 712076365, 552971792, 813728692, 326494136, 65818501, 481304331, 166906156, 663338669, 107381930, 780543666, 134496836, 537769189, 722802460, 97305052, 335440321, 20026934, 553588800, 427313282, 94768815, 916162633, 739865019, 562143093, 537244134, 87358498, 765488804, 879777811, 44606361, 408607353, 333278520, 388474835, 764227775, 508613797, 991744869, 135808860, 998775695, 717317900, 168922529, 814630463, 201387008, 382405498, 72480558, 196804850, 608513657, 497959608, 844293171, 127664424, 162488286, 282212409, 796212942, 464482871, 395022049, 769451794, 238433497, 948415160, 373695968, 686582472, 333390575, 369738939, 418830157, 63021021, 346236922, 161842988, 746228439, 156233993, 99744508, 364582417, 378073755, 852796610, 665568870, 755674467, 557347646, 160508325, 847647226, 401716195, 908066820, 868334608, 79740063, 903130397, 257547127, 286636552, 46119111, 895676499, 192410911, 732025629, 830501381, 471356237, 898622515, 71654651, 789696395, 2073492, 132420062, 751274773, 89834903, 30582777, 256551687, 166091189, 570827696, 524720099, 686615380, 987211117, 848999001, 850195667, 269611011, 39861617, 957084372, 838443112, 891663407, 441164904, 653727322, 975702425, 327942265, 55142134, 605581340, 913986234, 840652437, 774903463, 330018824, 204527461, 444928242, 723788760, 74167205, 544866665, 337188584, 11158497, 720633638, 636735293, 48573797, 235752959, 627951017, 78870122, 942970738, 678683684, 929175971, 970166527, 617096192, 721464292, 954334486, 176841801, 479149425, 195429471, 814767240, 270673483, 603507395, 468233482, 281427340, 855024194, 123312736, 471239584, 343658147, 733414482, 342599344, 807262964, 707858384, 459937652, 632069297, 29187210, 527801146, 166723147, 864445681, 303934363, 171995840, 163280094, 832196822, 28957403, 747667865, 836893141, 318160482, 130673122, 724466489, 641860218, 355862113, 181060282, 623995427, 736757225, 704964825, 510641719, 965651015, 675589833, 947481432, 159407205, 708496802, 313358223, 465187939, 61663916, 619199245, 859573453, 582141961, 741701594, 386667237, 117478515, 531443536, 855631706, 111495005, 955896394, 556442168, 682949019, 796247900, 14053505, 161483021, 33399411, 600894655, 134123016, 988369565, 511943706, 95249636, 747024769, 571298353, 139746314, 212742065, 980261318, 755747356, 633008795, 793264925, 816409509, 403691144, 773746114, 571513846, 484727514, 534553962, 31532380, 853604694, 360007206, 538387342, 96866987, 440526365, 812288023, 154067098, 342871473, 36270836, 422010800, 929884581, 802008411, 327858737, 276433859, 892866797, 381216314, 611935131, 440177605, 169675305, 323767025, 575875315, 48553993, 668091356, 2546103, 556100547, 151301418, 694967800, 408442672, 216260163, 308228060, 892428667, 902809700, 179581689, 646968228, 578653441, 705844961, 755221315, 344930002, 201555703, 96367102, 74977947, 278828630, 523042104, 715629849, 174576051, 646182193, 372796160, 20078096, 819692611, 367982683, 986230746, 380805568, 760531442, 368417091, 598683543, 923155839, 964488664, 786364618, 410097242, 608931702, 63021792, 940109342, 137246656, 973206109, 911308856, 903069975, 552933243, 908265913, 290381378, 946439245, 245031803, 883288821, 507092044, 451816534, 329202272, 823447548, 145776153, 750983182, 727698998, 144719216, 646150902, 197863012, 711200165, 346595045, 771659626, 435931987, 497692079, 798901376, 578471163, 697315023, 599389692, 494671623, 351212659, 611677205, 674486340, 615094395, 274707111, 915896076, 34399174, 262642022, 602238943, 406828365, 206478260, 701085016, 386127992, 994990516, 184065404, 84457956, 687138167, 279514723, 973496948, 716354477, 333889395, 551065463, 770538066, 662062917, 182135806, 806124816, 82531952, 388457009, 710150670, 236835914, 498751820, 562222128, 365770722, 439271504, 579268399, 245111026, 903121813, 213633618, 93820662, 935736570, 43954569, 998518430, 799466849, 25581192, 606873975, 789160418, 11536939, 249584320, 14417110, 810245838, 197108576, 552783757, 8281152, 891587747, 153276981, 368876673, 375793999, 193912062, 835765282, 830986956, 983905154, 992979385, 407126535, 284338089, 594271640, 381147582, 306398778, 183762117, 443012218, 931503216, 920245609, 243930292, 292273867, 128981141, 524214029, 714397610, 264106868, 162615341, 981644987, 398249706, 100591403, 986481343, 506128404, 223392105, 351356895, 755444244, 754898786, 847367763, 586025122, 144202872, 129074065, 78530478, 779138746, 947925985, 699560373, 152203151, 397781979, 127447451, 491735286, 556027569, 796078323, 91126376, 198331209, 173983107, 382786142, 771907227, 325772621, 122699329, 745263169, 313184211, 647814527, 16122883, 564031185, 453398805, 466978579, 681472461, 383030717, 84853760, 129546514, 411429312, 41692707, 109509166, 875978765, 919909864, 427800535, 278191313, 229007563, 711734904, 700396178, 272349189, 329208007, 974668453, 513137786, 768858271, 994012319, 269558457, 935811322, 286720490, 179920906, 324446451, 629987098, 825745038, 112021019, 416778249, 407709894, 180759296, 57682033, 326879633, 467601084, 45617350, 505776683, 196336987, 9331314, 688633966, 213526977, 465784992, 981506758, 640286154, 708672158, 694652866, 183495439, 135342818, 71864539, 785957075, 990314628, 945928272, 185530949, 540635893, 688648136, 510161908, 58061898, 915669978, 525225479, 688396946, 590180942, 627725979, 297548900, 647336672, 911430358, 681132044, 611814542, 483459948, 17382665, 629528189, 13588421, 562914524, 143177243, 210441510, 577260325, 926326562, 397415460, 221022103, 152843311, 347865767, 319793853, 355827332, 383041365, 392923605, 663502457, 724829628, 485132880, 800293604, 162431432, 471133620, 369808958, 120017413, 758643836, 866126817, 636826392, 29795244, 603232309, 812522791, 602828523, 865528839, 269961445, 722936086, 695737802, 34674673, 633074121, 335106778, 106728885, 504604544, 253539174, 135568050, 256708904, 628195018, 331456677, 264675401, 500511771, 187836836, 349880595, 721364443, 302034715, 954435930, 267013909, 39951757, 995401468, 960610091, 726335051, 88147708, 436932601, 895465201, 803743027, 725072153, 99602677, 848737554, 727283556, 442700957, 713503947, 544267985, 263342243, 263619402, 718978856, 54044922, 537252074, 883266633, 720857804, 210735657, 335454937, 543038205, 419439354, 944610070, 468350531, 729547038, 66358444, 455157503, 102306357, 198855511, 170999828, 396325645, 826161963, 908771237, 327151623, 136617269, 969325499, 787623887, 436175767, 297853734, 315637138, 31789758, 491918841, 391857944, 550198500, 822318101, 798986308, 910627560, 208160533, 758328174, 378219592, 102658779, 619253570, 547097758, 876776529, 913194130, 774004836, 677089273, 626365440, 655956091, 871796999, 32762057, 142270844, 361683137, 343921468, 1126025, 492002960, 79691445, 241512084, 749917800, 499626313, 490656903, 161939281, 652466409, 816753019, 901964956, 240187854, 365862102, 825495684, 397332916, 44941071, 330418151, 401630544, 861745243, 882286499, 230126999, 573903594, 833010243, 682670148, 913613118, 999252144, 282729639, 914234735, 790555873, 460080260, 190504846, 604348081, 988372917, 431258466, 306761187, 621721020, 32961870, 748457716, 166434153, 51196663, 144714049, 803893544, 916949593, 260256805, 522298050, 954558155, 578830584, 117084358, 236476179, 467809773, 463691319, 198256779, 132412104, 355343859, 273967540, 966256442, 917514664, 150770860, 806951810, 436418030, 841178167, 984557287, 202047960, 230419948, 875070684, 574325664, 156379422, 797159174, 254468803, 771116173, 760657081, 588781315, 138177130, 870025672, 261351859, 756039990, 733821258, 706701739, 798859171, 256754185, 372578290, 476129390, 648628762, 380081954, 949964019, 175231260, 232847576, 484819392, 963575119, 952949087, 503908103, 581068548, 622911170, 165886393, 690629264, 314933983, 866920171, 490996088, 97721073, 469820475, 599736406, 159864100, 440055895, 838758388, 113851806, 16444795, 414351146, 404819126, 243339033, 679062875, 235031169, 312397470, 329911399, 833192768, 635516175, 120885611, 601880595, 711782307, 974795957, 498860331, 134662207, 397255952, 583190711, 2638565, 418583690, 301973461, 211421441, 590031483, 42586682, 583271694, 667886604, 869629893, 314305085, 954992515, 556528619, 267914975, 376992226, 45216023, 560121966, 874963522, 974618868, 609131826, 958617575, 230473975, 835560783, 477987830, 407709683, 626182829, 878958485, 674599892, 906423094, 29552917, 768938396, 819376980, 901557441, 58503889, 50148844, 804337668, 134856880, 30872810, 25704442, 444657173, 879347716, 675973504, 567884583, 888681308, 913016321, 539525777, 426165766, 812412844, 218698608, 249334704, 26493947, 135208733, 650575331, 378824391, 769198965, 782336370, 79487479, 44055991, 671211362, 706613302, 20468713, 453234231, 704725283, 287325963, 744500761, 268151738, 204111975, 474508289, 126475073, 410842129, 24502871, 111494901, 531000974, 364349793, 886859647, 805619972, 977495943, 403997077, 842725590, 869782422, 19630614, 18407150, 846037844, 645698907, 351157984, 439486022, 290410827, 671376141, 549607294, 728939625, 213907960, 338373896, 922739229, 974891592, 125286815, 481254954, 103098728, 15934344, 997265541, 988311464, 553730568, 666495472, 542392179, 340794168, 245660711, 591015932, 623474844, 837547511, 882424111, 369202104, 991650384, 39779133, 76117006, 283029455, 228189012, 845973704, 958302475, 445821116, 464979375, 400248758, 174664003, 995272225, 552465145, 760836276, 494220271, 508867497, 454308311, 455681037, 975709645, 325243589, 705660543, 395335199, 934002572, 72478237, 164640372, 508126430, 423146889, 273260837, 945825566, 606188122, 99466890, 698676194, 893437803, 446262836, 3069554, 472193296, 634266821, 573376321, 584713206, 804659838, 666477014, 740335410, 192801428, 411809591, 821777955, 153122985, 152390774, 147714495, 885851142, 213073284, 120993613, 295334067, 641787397, 240688256, 914132197, 7293782, 905040488, 614621627, 33460767, 147527506, 806781265, 658726793, 341902612, 909615656, 386525989, 486823310, 161398936, 45235293, 693408296, 868216650, 789401505, 755452923, 195013610, 284031366, 413179944, 368552052, 414635987, 466992703, 134431968, 308040672, 670273771, 273250255, 26582109, 966259283, 704001379, 453438818, 549054315, 915317959, 42675794, 128520994, 469440711, 143041556, 685847848, 414923343, 288476084, 300604574, 424820042, 42925997, 956308285, 547863760, 619007981, 105741696, 137028662, 623458715, 18521348, 598614402, 404611137, 878101125, 129143833, 762213689, 758814785, 230619771, 313150638, 953915810, 160045874, 87424650, 409594696, 834362744, 349104338, 425279752, 981312813, 638306889, 393387619, 385780099, 266477340, 743198526, 557844779, 577219909, 862229707, 503125062, 367001283, 869695795, 223950932, 306310337, 336060096, 457062205, 185394992, 697659273, 483314768, 33531465, 45790522, 740953907, 375285256, 88510392, 122260244, 440096463, 882380639, 996501091, 429396363, 988028372, 382322619, 852150992, 722529836, 322228983, 737022500, 822627445, 488981244, 13736048, 859715133, 130517766, 683233319, 192797871, 115212031, 109747605, 739285069, 746749271, 902058512, 62066764, 462534692, 653654146, 639029457, 86653233, 78052182, 635778532, 103842332, 121758838, 149995210, 699281858, 820575211, 21278510, 928689965, 619305435, 542671560, 179733399, 890064806, 472139188, 795852142, 984166543, 403124085, 217697745, 240749165, 744989017, 246809891, 409217803, 784754195, 952493201, 141779587, 264298493, 322275517, 972117185, 708230626, 755575405, 190947032, 451218378, 411630246, 995719574, 721266214, 643628693, 320441495, 591655789, 793504506, 812550559, 441112719, 133184089, 846631168, 43021773, 440634089, 645807989, 899979445, 586774711, 657686991, 61043092, 421737602, 860004151, 907883504, 715658707, 733133528, 751939060, 107912510, 519870678, 518458364, 999667736, 574333818, 308924006, 716058725, 878655890, 175409916, 699334379, 731120676, 367083671, 452399236, 413817317, 531295148, 816976645, 634841545, 113358976, 760208780, 395609584, 834968379, 214898678, 563317434, 543142372, 577731147, 594955875, 736063100, 448593067, 657409084, 903506855, 824916453, 824942672, 937925832, 594718046, 922424154, 476183540, 989402979, 887475464, 45043367, 197232664, 725660568, 480172495, 644233914, 811046081, 549457357, 87872170, 330840558, 469050829, 27872429, 676422575, 442414037, 706210285, 922427358, 407110568, 286394945, 902109289, 114883101, 793612746, 221377270, 838181209, 37047999, 599692000, 785783244, 290113555, 837195484, 999799616, 216762300, 479736648, 581896321, 193652627, 693642962, 535196003, 733481638, 820855582, 855819093, 955086020, 988959988, 389718805, 990110120, 207034238, 779791856, 233543417, 520832708, 415911679, 55501996, 448220745, 895718681, 761890414, 392911797, 907382650, 120461701, 28448472, 659607779, 528771898, 986692795, 340973876, 934051919, 639906879, 918442613, 712633279, 228196254, 631749689, 645906665, 62715322, 555342186, 587783062, 694130130, 353621242, 390805425, 332147456, 342694815, 408422580, 835096578, 447239386, 834406922, 858148057, 788245014, 504288274, 389338450, 948971827, 670221190, 260948139, 149041628, 183859553, 329562026, 694697636, 301788056, 996413133, 593168236, 758928569, 267659005, 746939509, 618691970, 526023694, 952803933, 530584725, 629420551, 245871487, 482389292, 662370005, 560626966, 533357908, 805818385, 388388428, 70052589, 63147826, 896144841, 351874195, 971172862, 564546741, 40431323, 400591264, 327259034, 49227391, 985703983, 712371595, 745948877, 439718856, 56541705, 39463130, 149586656, 491909772, 11868623, 270547040, 864316587, 95381085, 802134015, 705769097, 839155726, 75303175, 261386189, 42672324, 618069472, 576314711, 598764014, 530428607, 705367494, 42330711, 100069341, 299458834, 990207845, 846276409, 719915598, 172778895, 932880945, 796002971, 985665184, 910819454, 351377375, 13640491, 457721693, 967664984, 561297692, 636647565, 134522936, 858726381, 134534583, 226827355, 563032290, 475036748, 364965038, 983400025, 298921411, 416969406, 185371723, 946632905, 321264308, 515141541, 979284591, 181708462, 136104383, 701389771, 346504550, 420675347, 151304714, 59250523, 719299209, 615429438, 594266787, 889685199, 864108677, 812805459, 327217652, 207595230, 820512740, 888562781, 470162414, 368894177, 570038057, 235870881, 592137692, 224640450, 933645911, 828363937, 14104018, 397537852, 894727805, 22774547, 540956840, 57557303, 886061429, 790505231, 649730107, 584035371, 34036690, 425938645, 964720301, 435408973, 644171308, 223980796, 716004985, 678201082, 982420161, 552125035, 552381036, 923316361, 677591458, 453713655, 875697120, 935938971, 980614163, 124217190, 115547308, 814516865, 508617000, 410991611, 612911595, 950181687, 703239894, 197911089, 881766966, 528317871, 564118283, 74600114, 159816760, 414332995, 968522278, 430046316, 972965258, 344708718, 239753276, 254227945, 851589856, 478609242, 981129960, 704493929, 677151604, 896682600, 643470211, 487650675, 327716016, 157585013, 475398551, 425445364, 149861347, 706720522, 697057969, 625015989, 835928219, 560265877, 483837389, 289101359, 140329779, 328585851, 797805200, 746957817, 662610393, 624641262, 368973191, 284148740, 954377202, 148014086, 14909775, 767769796, 916023910, 897523477, 917205409, 515470416, 519139947, 231249772, 684605890, 869365965, 900530785, 524385940, 542612978, 105214155, 571654449, 184063466, 653565880, 527392378, 523719425, 266368302, 71479629, 586145559, 188347328, 685884684, 265981792, 483467840, 962673743, 757140769, 12809296, 779614695, 519993601, 626622316, 983423019, 894529345, 636741173, 759067344, 971172872, 581912928, 578608203, 769700939, 524073341, 760036605, 241823217, 817934637, 925831049, 662989188, 191250267, 230704735, 960323565, 503572795, 389145600, 443430380, 574634051, 896837420, 732019467, 857438976, 126029503, 944937487, 106739405, 401178311, 538976089, 140656421, 822165323, 540581082, 229532409, 838865708, 374001012, 471359672, 485291545, 787740548, 947165510, 454985808, 797221567, 497420137, 852848965, 306632408, 676597717, 941834594, 192154443, 415429631, 337103367, 482820805, 887343937, 341668322, 580375516, 890632785, 765527055, 537015780, 942284786, 636312972, 41885576, 892691150, 317556149, 668010651, 34496307, 354087588, 837105918, 767215364, 28584523, 455998509, 705354075, 808684419, 945605791, 826617326, 629243796, 869061188, 282067493, 691725942, 423388450, 570905943, 636574387, 841035315, 890322640, 794047881, 40867423, 195498835, 107379765, 878186316, 723865099, 418713311, 495532361, 630982525, 391568080, 766753272, 204226087, 613334631, 317722987, 577380104, 706228812, 218035867, 197472201, 496711131, 911643520, 953718238, 185154870, 58746021, 329214228, 997233409, 376018184, 877356602, 424845987, 325221868, 159978533, 726784161, 625358865, 559779171, 447715549, 547961243, 408385823, 676179586, 998305853, 842443354, 817654594, 364598379, 781487830, 619133114, 949948483, 202645101, 167237026, 896368581, 461380131, 260143273, 400196198, 263787880, 117132196, 390950960, 793245719, 327046338, 481805722, 848671068, 754690766, 285241302, 546250159, 901521147, 191148978, 646302854, 576698856, 554419982, 523600971, 522968196, 586859000, 42204870, 644475569, 491958851, 149618091, 149447610, 709650179, 312927121, 99567333, 714547062, 105389351, 318678910, 425891523, 492459132, 649734784, 342703840, 51026530, 139624979, 788302993, 880020261, 758497547, 231376206, 464390392, 928051401, 911917998, 503012650, 856128255, 930772392, 693825918, 292424045, 804524793, 721485227, 109132439, 880908836, 280634700, 72323796, 703253968, 929492102, 778675314, 586054883, 703097230, 571497187, 779629290, 975765844, 248757258, 531673332, 929444993, 858014417, 876447669, 715851199, 53665421, 324250141, 763820326, 654925108, 758625783, 403325737, 660006567, 296525520, 248173530, 134213341, 100910785, 931487849, 440213055, 527434512, 718695487, 760172067, 754735025, 139902092, 527033736, 356386572, 405328903, 735857154, 984605445, 483030620, 78589722, 143384982, 362797711, 769917864, 72780820, 600369364, 812559210, 935275954, 28467241, 35909816, 161143072, 924739354, 864739808, 857625823, 807285137, 608698376, 89501400, 386463491, 65611122, 320907017, 901916261, 426444309, 319205708, 211399231, 993587361, 265852312, 776501623, 181406266, 209230702, 340157070, 789042087, 198078755, 902390238, 97644024, 901217081, 577040655, 614433014, 837476293, 185024633, 937400806, 854247779, 663085430, 184786019, 742307538, 834849631, 830933301, 18006987, 297789751, 415524378, 129154829, 838380770, 996482195, 462999712, 561550283, 306745547, 264075164, 553071856, 108160466, 881134049, 948885831, 576023601, 744345827, 851191215, 101563396, 401201286, 702973838, 255757103, 149031696, 980909168, 319914768, 226591186, 279068263, 206865164, 803373340, 569805126, 257962693, 749974175, 821107959, 458744346, 998610140, 67397046, 624233220, 675267501, 464049854, 20233569, 30717314, 362107247, 916420237, 763824906, 344692197, 814133408, 636754476, 615863858, 947125381, 277077783, 534699197, 62082626, 328078799, 917726864, 970738226, 318099406, 632410255, 772042839, 445930395, 784862687, 913962550, 606244867, 917843748, 92552683, 240276912, 847989875, 210786293, 807299163, 934028713, 504920625, 867447224, 700271615, 309282707, 911610632, 52858264, 914942558, 86494147, 353378858, 440327184, 152815741, 999544350, 787293635, 156094584, 637784679, 36504640, 485358184, 311897615, 823446185, 826174187, 131780471, 568700141, 646413620, 597114014, 256579568, 93256934, 117167211, 121466953, 767461412, 433133915, 60015930, 410217220, 302446162, 243086165, 928066596, 308096812, 1238224, 49793974, 330926745, 721994845, 625955062, 840373637, 657702028, 109863136, 456234508, 504581120, 542324374, 590295832, 444110914, 926842293, 192010889, 122146005, 267241671, 381163179, 305901242, 779339315, 945813976, 517788270, 395182657, 414257421, 411235596, 733146902, 437241163, 322401203, 955078424, 88686842, 622155307, 507049100, 415936152, 584585567, 225385197, 868899944, 361559483, 619623476, 688440638, 342735389, 795642907, 572064549, 412606439, 604467600, 15316601, 784574270, 653982563, 4647295, 490134812, 570774677, 464518988, 562524183, 419073929, 276677436, 232931824, 295865790, 222691931, 234123956, 894331800, 123997254, 880276728, 574731201, 809596124, 23463778, 561331731, 281716603, 2973780, 784751313, 63931749, 31917068, 117728251, 669790330, 438334748, 918847865, 254724725, 295742852, 360208945, 615194057, 20185327, 704039321, 142966623, 59283205, 198545484, 198609395, 592136074, 330864361, 927114241, 714109087, 754499717, 552286099, 962846982, 343197462, 392851754, 291065858, 814393253, 373733467, 517791634, 486881826, 997852128, 288532250, 263399999, 474214791, 583918716, 618362374, 582853322, 438763493, 356067278, 778322950, 911192821, 812503881, 241211749, 642368923, 539224089, 749773906, 102696034, 720802968, 260228638, 845547920, 734374856, 17883490, 427302204, 247475883, 632906972, 510894245, 978874058, 806438929, 305484943, 442717001, 186720322, 871152307, 520320490, 72619714, 189576891, 892826105, 974489025, 899480122, 736448693, 917650367, 215246160, 741000179, 500175913, 398113163, 479353077, 396252299, 212122404, 780949475, 142602650, 747417969, 106030080, 437889867, 613573919, 611194419, 122726060, 951268143, 470597543, 735524318, 679747905, 176408722, 720447320, 707415292, 956501161, 459819612, 302281143, 838882219, 320533755, 525531906, 897568474, 108799409, 936571085, 565363143, 882344137, 956408593, 264213301, 340461584, 341289742, 454889348, 684258527, 943293827, 54908454, 371167825, 696547147, 135393463, 486373410, 371001774, 971242535, 997055534, 67208148, 213786817, 699040179, 770541511, 380521918, 218350138, 906901838, 523882192, 350088311, 654852893, 565133008, 695098846, 910098955, 462071554, 341799428, 726045973, 202610436, 983665517, 585471103, 46405371, 787949097, 28094471, 660884043, 325730448, 166879777, 777750969, 249174577, 331052509, 570819492, 847755124, 775984433, 814550232, 8710892, 679825597, 91893424, 340916424, 156548986, 617565527, 193821781, 366220603, 303118120, 343795128, 673397889, 659267639, 222371094, 401164964, 928405303, 615249316, 992611805, 160977904, 914635519, 250636288, 486990638, 170092277, 639921667, 922863704, 28361304, 99671205, 246248071, 205703020, 839104391, 157592201, 882175786, 832806938, 382709719, 53227092, 833919739, 65567422, 97591255, 145057832, 923230312, 535700301, 235788012, 874685880, 277506137, 884981047, 51029839, 212873107, 115532553, 605755151, 8355150, 448656864, 971500308, 184630622, 574661211, 668158919, 776886566, 163610423, 302750664, 467943495, 708875340, 373358529, 25482285, 594779369, 779564148, 758446576, 781194321, 872506731, 796626352, 588515574, 966278341, 703340890, 950756332, 947435645, 127682481, 634788786, 617512994, 843724978, 537127556, 781030731, 560432872, 420375294, 143293808, 870329627, 391945789, 354716471, 123908569, 433624757, 737557807, 234604374, 951077716, 664244483, 879734592, 668580301, 282160443, 541472573, 389129241, 422942625, 803538783, 28482923, 110443696, 126914766, 587959385, 388551364, 609163558, 587528102, 780388884, 534089522, 599816906, 483450600, 910046620, 440126272, 627609760, 939165569, 951239413, 7937547, 790966554, 391941957, 251076782, 860320787, 673397786, 864917831, 367184893, 679967753, 494257012, 122221687, 728564868, 883420549, 543856506, 309205342, 596034565, 933092862, 647501942, 330640699, 505819251, 887425176, 939035407, 963932614, 890478391, 74832829, 799449816, 649060513, 713138649, 281279615, 359107008, 186495409, 353805883, 276873104, 834661236, 353104029, 522989692, 316700262, 550979233, 992589774, 232465106, 408889417, 165553546, 942360451, 9725246, 933047985, 689684665, 654284018, 604214548, 580792864, 790907243, 673924624, 572897215, 328870837, 799553747, 231060383, 295754068, 813281777, 683182944, 108209228, 518172803, 242666556, 541648473, 84582129, 704874588, 95908825, 711108322, 174923302, 573989577, 360000316, 914714783, 982139831, 300328828, 550124270, 525199181, 459888189, 497190581, 111587460, 10180319, 607226528, 39245512, 898733399, 427565493, 276257944, 479419101, 614834783, 255480419, 974736752, 703951651, 507745617, 669199541, 916041502, 224450653, 784059918, 571443596, 960974635, 582295299, 52667870, 216204739, 446249743, 561155373, 738569871, 975634345, 703054497, 901951023, 207012503, 709645929, 560732949, 678121877, 798194574, 975865015, 903842957, 299115387, 433320664, 745474662, 777720149, 784085129, 328460216, 362612518, 282512352, 189750089, 752767785, 95469309, 556724538, 631143736, 964174248, 758196203, 985355907, 180755205, 389641819, 744512999, 272912453, 720571445, 841670045, 636907919, 447414345, 193754150, 20094408, 171931090, 318614478, 990697200, 998034033, 163811345, 926084685, 336032822, 606744770, 978567740, 398942047, 618212197, 975054077, 185032270, 907704931, 329227724, 656297341, 208387720, 114131831, 130426664, 189314710, 572629859, 243860990, 900758740, 913470075, 517545318, 137785317, 454852762, 482747254, 334300138, 284764506, 297242697, 256985107, 55290, 161786103, 781828918, 776344854, 529331182, 384441440, 61674318, 738916774, 901317833, 740133457, 611367127, 404453451, 114813147, 641638937, 65121564, 676332230, 183477665, 341468710, 475191389, 706716705, 365471891, 262442689, 620789763, 710585800, 716840489, 129405574, 394784712, 408668810, 279984225, 988878674, 945594832, 786326061, 517629625, 406324400, 145512963, 89714731, 798029969, 198204170, 425509819, 724999620, 390601988, 542853845, 901783488, 165337119, 204332902, 300805812, 875117351, 316085874, 150248304, 301488827, 567340618, 406137832, 381466282, 520298529, 882765128, 372769694, 968145001, 274985076, 132630486, 557878808, 975240479, 823714776, 938261760, 404303161, 84908739, 370920851, 848765373, 573367242, 621483357, 478646299, 900816573, 843649231, 980823378, 361495571, 425513992, 704427410, 951697860, 258396999, 214650714, 253003, 207220271, 53589389, 456404332, 410642549, 771537372, 533995555, 206212810, 536936436, 125980550, 525253941, 502727860, 177801739, 454810311, 809141234, 954172808, 329201837, 954780364, 872296443, 783767298, 661648053, 800622735, 516115309, 248045006, 305083300, 949766608, 178157804, 801347863, 318750078, 722154733, 528670707, 651671964, 236459679, 703664841, 791588968, 847475101, 926752375, 85263607, 925746420, 125826713, 443574728, 347574715, 345064324, 437553949, 844518898, 356621132, 26811431, 659977874, 501267430, 944099874, 435074225, 77542860, 766855811, 454318433, 425734859, 677654081, 363864429, 688357105, 917939601, 31143031, 984764511, 513759854, 799705830, 683043360, 27577609, 255257507, 943909789, 1710605, 166072875, 541044750, 591212010, 873122435, 862281599, 655627301, 985845912, 575511553, 641244546, 620572843, 28260643, 959485159, 533787090, 338805534, 140155504, 642573894, 851154622, 439466629, 455924287, 898656308, 745194226, 138210869, 20016443, 569417999, 988206008, 246932161, 46254978, 686762159, 624167472, 830496455, 522531513, 208732277, 78814684, 693172415, 730202540, 984615125, 660295408, 615935668, 793717015, 505054646, 773806253, 375345992, 468894973, 733170064, 587342215, 432681288, 458099153, 688503310, 467828476, 230441713, 75352116, 421542195, 59819276, 224080126, 286516490, 904388234, 464764148, 274404229, 977810219, 284229272, 220262606, 815141289, 417754207, 468661086, 539229243, 409582833, 959623983, 676684249, 407903366, 267327033, 912349508, 21263488, 493605375, 544924551, 462378080, 89445919, 337236278, 808593304, 754269263, 840006800, 845028210, 123752563, 885363612, 752037804, 381912928, 766116226, 634472570, 450684165, 232212320, 251211665, 276033804, 831059542, 212948023, 181898131, 201209251, 377315912, 737978518, 293905852, 943171802, 682457274, 495555607, 782039024, 828062805, 996250092, 371833302, 566641290, 985167587, 435595042, 387392450, 855841386, 177576544, 786985464, 289751452, 522567097, 664835964, 334287533, 329918924, 609569692, 585488244, 180667784, 836540274, 670794447, 831471828, 839404941, 927028422, 542465710, 192512625, 664743074, 346295133, 413718290, 497950942, 806508844, 556548105, 50364809, 845366241, 16631659, 957232294, 181756843, 622180141, 292384590, 268437747, 233588047, 851519058, 45244871, 653685482, 954946357, 114553157, 696247205, 119592643, 633219398, 405441119, 431000067, 512102094, 847152029, 760580239, 881297610, 355145817, 229889024, 613697943, 7266512, 271696417, 495690975, 686534599, 353335230, 583385672, 998662033, 702267231, 108507250, 380781630, 461282957, 40398055, 850989995, 976230973, 232006816, 713857537, 609031413, 535293964, 432041841, 882343369, 243385907, 662910919, 309606140, 82437427, 959025059, 728941114, 325017819, 35200127, 213632489, 440236117, 569922897, 12416374, 466578145, 459494257, 288380091, 192007621, 79382468, 654576863, 599886573, 583550058, 785614976, 262510766, 386706128, 993368062, 948600283, 344359664, 585983281, 225113571, 230149342, 863540337, 1557576, 647093405, 677679344, 477602373, 166216784, 795581006, 570965123, 69301166, 308394612, 55057789, 359727720, 196967129, 253417403, 846311232, 830849656, 287047464, 458757073, 69777007, 328630392, 78667110, 760518276, 759207713, 145204066, 456326159, 684074304, 66424251, 88674190, 539961726, 727145282, 276843866, 991874691, 521494847, 839287993, 941658779, 26387205, 133135197, 249113484, 585503837, 403097748, 467858684, 522952884, 80490521, 428361610, 907664939, 493330290, 869865245, 256892279, 9839432, 212644714, 631935618, 84894257, 529605789, 829683379, 5905936, 90708910, 921921566, 541812449, 76591189, 404304759, 648753280, 47690264, 300085438, 763087342, 682157934, 914408553, 140377080, 287880677, 904288855, 572985916, 229939297, 340162155, 625971156, 614438823, 3692614, 122194867, 529168209, 558646876, 854760923, 263058979, 226296468, 573548446, 272825948, 658214483, 535717864, 71076426, 456328016, 863537688, 822960961, 844649381, 481432437, 465442456, 38567639, 692403790, 241569254, 456917708, 488391124, 391648992, 611488002, 931841852, 896697461, 983680961, 68203191, 673762071, 749377021, 438312700, 987768674, 31696766, 873458045, 606507888, 47569287, 855935443, 417945053, 179451552, 411226426, 263916808, 498786318, 218783312, 562720504, 860912616, 346119555, 205885856, 226592339, 687223168, 286648990, 361866646, 143154305, 753152258, 180678075, 845401779, 265663525, 416136947, 69502677, 135957776, 75843473, 973249770, 774652416, 326860618, 881835679, 267351765, 10389539, 119098168, 987772645, 424608239, 836260271, 775689108, 780118368, 258166511, 564415190, 230946531, 85639096, 608217265, 182866485, 591110945, 850642634, 278602824, 553309114, 148196576, 222166255, 675950805, 524227583, 579562838, 563510466, 786817409, 27321122, 158764653, 763819406, 537532851, 923048897, 935352224, 246264177, 501214406, 629042849, 456289430, 848843266, 490186851, 44692076, 443166203, 104973768, 873437401, 763490575, 681839280, 792469759, 809680316, 48352654, 926079304, 370101449, 344342499, 141344954, 541778292, 45608561, 380739630, 958886049, 161259222, 911905041, 487900737, 753539140, 730488367, 508574410, 89697880, 900878545, 264873119, 28870376, 210396023, 570176896, 264178384, 685969, 416762737, 885207033, 200766708, 604513346, 796937888, 45310476, 350291684, 327301354, 84003763, 715982129, 936152145, 237698561, 21147135, 803365232, 990854740, 193139758, 193415728, 680383242, 792764925, 267966435, 722314644, 454340134, 492850008, 873737112, 164148250, 449674338, 528634929, 507336075, 276115908, 355053018, 493678318, 580534518, 547302778, 346656168, 722883221, 525032897, 99200384, 380959976, 576668962, 918353584, 393556564, 773897021, 139202213, 527044757, 26980059, 400273632, 629082216, 280706902, 506267693, 912540066, 562593706, 140658456, 160686279, 373628201, 525074354, 864136948, 347348049, 392928040, 300073510, 318836045, 260490626, 215522033, 829149305, 448242221, 931335543, 404738250, 825546136, 820755220, 157774896, 72236402, 879389412, 625464696, 248571178, 762179838, 35828068, 648950225, 682623113, 41516724, 945696214, 384187772, 127281963, 143993850, 740257894, 593932002, 965077011, 240453778, 814460141, 621846013, 468844785, 311930885, 410048547, 598964832, 556036407, 367368776, 933679255, 384013187, 422452486, 787566932, 853399654, 838760556, 599585869, 175431178, 102698930, 517354037, 877167203, 386808262, 304911762, 423571604, 591034747, 477163911, 990456244, 258385857, 436333043, 806138504, 396074129, 376763015, 406059599, 411190184, 411705591, 656315428, 164548153, 289171308, 829401809, 241015504, 39079977, 691094824, 381055112, 333762116, 443832347, 702619097, 429171858, 100527284, 538920754, 954238437, 469088947, 513668278, 788918393, 733535071, 520727317, 833625819, 264396751, 237681894, 455284188, 978883125, 635319853, 966783575, 320980476, 791699758, 719235186, 372879027, 323903854, 910534072, 151793614, 834514931, 120510136, 146021596, 948619381, 583621957, 539650237, 174506528, 905826508, 606315027, 971787064, 701357664, 531416701, 425861094, 419409610, 658823380, 420580422, 157865051, 516608572, 84582917, 547260206, 229793980, 43136911, 717519278, 774120162, 381421006, 45546148, 102907202, 491978657, 889508102, 274003844, 377225768, 392950284, 255416657, 118374896, 891169418, 909849796, 83535629, 83989640, 756384871, 514895863, 528486022, 194064027, 707284973, 774891188, 763422061, 697417795, 95347329, 807455893, 915692834, 78885415, 24995642, 508679184, 588202873, 287063231, 933764688, 840758398, 168654351, 245809114, 229634481, 875026156, 905449727, 50239378, 917023851, 737916737, 619788373, 612909839, 906140375, 455827142, 736946903, 700330801, 176604097, 457458586, 151450530, 585338418, 49600127, 528978363, 935849810, 250549168, 520398750, 677689161, 90092664, 313181296, 209393280, 329909599, 786069893, 961027050, 590864303, 192620847, 71586433, 792270649, 49151217, 419068343, 296439692, 182435157, 179888776, 908785772, 914956617, 971375361, 290981714, 520252893, 64023067, 251104592, 945334661, 741091143, 169525911, 263457756, 720740382, 799171521, 553335988, 956593373, 928721645, 625201473, 234061322, 246333981, 71986827, 12385758, 401454219, 939371144, 243889978, 437491317, 952241567, 331218041, 107308526, 759526952, 305745001, 47826853, 30518095, 755242843, 975389562, 527940387, 320721225, 374715873, 460865481, 226302787, 234800912, 837536723, 268109743, 796078923, 780342285, 404518632, 457917767, 845032836, 580808618, 2244846, 787683545, 876739949, 846478438, 320462854, 430876316, 538667610, 495231602, 282075329, 657766433, 433395198, 182399066, 801813911, 131669731, 14539440, 477927071, 515338992, 454518727, 170618858, 637073032, 718470536, 389407501, 756517899, 180197215, 394175995, 129462190, 397142872, 572349350, 931422425, 490592993, 513457207, 835662380, 493613982, 769709449, 380837215, 861506816, 140145642, 997922637, 112843630, 399604350, 471458663, 50766958, 168259209, 981775605, 259566276, 779538444, 6801324, 120513543, 553370118, 297419722, 805625917, 444453507, 220613635, 904802799, 192765486, 405717031, 444110738, 641484702, 885126079, 770280492, 583989873, 267865844, 245851031, 657832078, 88616876, 702440871, 191058449, 817674869, 123845322, 653967609, 766437946, 755963504, 842268748, 194551678, 621991088, 626353479, 401496775, 452728914, 309114260, 941665941, 465068694, 122267452, 189975934, 406464537, 209679427, 802776551, 192049180, 69762608, 691121017, 899833888, 537467180, 522060259, 281077669, 169550913, 146885618, 237076494, 31459646, 329640402, 436370247, 884018088, 476885259, 326045068, 843876930, 748879075, 572761883, 399201296, 33203119, 998404853, 469208777, 833216555, 784758429, 815184043, 816809938, 554759397, 462634625, 482853522, 329320868, 851340948, 128344298, 42889214, 666940250, 909595515, 146003654, 771641629, 24225952, 436405788, 721143464, 800305663, 880290407, 336133383, 262511071, 489646766, 704349291, 959928251, 814910083, 129429817, 372681416, 293278560, 565351792, 681058664, 765462088, 654952084, 874518862, 467438906, 162471153, 887320201, 815052519, 609485431, 445006308, 382029412, 503329460, 113177608, 295301915, 207111967, 916660269, 148655747, 892502342, 729191383, 941798828, 955403260, 171423594, 433538563, 123759257, 606101305, 259420913, 456884622, 221059631, 205450071, 560825398, 772571394, 92870575, 526407195, 189953458, 6425581, 865073866, 653649252, 652813569, 849964869, 175380124, 277013586, 767426063, 269321307, 128631666, 266393790, 388354379, 496871127, 899003472, 917190210, 511567834, 151936809, 455096249, 84615864, 755553025, 281099545, 558670275, 348829517, 410126747, 833909127, 9449819, 403591043, 824867990, 831069031, 58283959, 613437871, 355020412, 587553055, 44895092, 853165379, 969371650, 356519191, 721340203, 813900163, 120874370, 81650641, 163861515, 108006607, 60885364, 984600164, 372010243, 392319845, 715334730, 493392567, 399450650, 498202562, 776020911, 971349789, 645736679, 827637056, 514055836, 740617411, 161818572, 876673624, 22490066, 478797808, 611532438, 373007197, 688380358, 864831855, 286826330, 694256532, 490874878, 17382382, 907618068, 304634701, 753386732, 320566130, 25408365, 967599985, 737504860, 372927104, 463014966, 725730517, 716002323, 884269961, 799341390, 641062352, 989439681, 369881759, 673240896, 632378549, 457413220, 895522729, 245556275, 515118722, 175839948, 431917010, 691645362, 431617896, 821212523, 713308130, 434363754, 226190543, 401863137, 649581839, 39921209, 893124396, 757911887, 276572306, 591488708, 337094789, 602623277, 463687780, 554702841, 295525530, 769429630, 475930348, 693622826, 265443007, 77808547, 958107526, 62847992, 203483690, 998741882, 940779883, 479239499, 534041049, 696720407, 654915525, 176372323, 851614993, 434534780, 84576478, 372891172, 939830811, 484350264, 222328718, 651013665, 704471784, 238171602, 262641229, 772741935, 4688404, 729896641, 811040863, 756940811, 46319893, 28018649, 676758719, 167197057, 542690644, 170054984, 476352495, 182253105, 175186684, 844861621, 541316005, 297702746, 348343947, 954105979, 878424973, 471097711, 510690326, 331613207, 432040393, 854312787, 862610756, 855869739, 121652939, 908129974, 910090345, 652117171, 73546989, 965059479, 606895390, 890960561, 288952082, 854511690, 821622854, 834801716, 138709857, 666496397, 609450380, 160876072, 596790440, 485310940, 205856210, 791449907, 794489271, 694646399, 561198355, 572961258, 29762843, 431786642, 219948545, 323139897, 659547953, 47052089, 31838083, 46930367, 984144476, 784620348, 865679722, 17837053, 153981175, 945735494, 551021041, 34535912, 250866817, 435758176, 972048706, 900078036, 971827199, 245431737, 496544700, 472388606, 247864900, 24451390, 554593155, 158620068, 361492864, 995369117, 472834101, 956258944, 9765541, 28500396, 527630215, 733587084, 337625062, 934685191, 2340250, 56211299, 655974633, 578652526, 473972177, 224916710, 423863589, 4006202, 441549952, 714937119, 824730337, 979091803, 815168685, 865758350, 645825578, 956913915, 731289029, 542861079, 718568809, 673383762, 476044093, 964278879, 91329638, 37871600, 783163522, 544992286, 125523240, 281548268, 206110460, 487669060, 499003794, 553208050, 545405454, 54847219, 152970118, 280104739, 522986988, 992936043, 910433420, 936736320, 159594875, 428627932, 355606351, 412104656, 81539723, 633304917, 199792928, 782370188, 365550988, 122835800, 269752366, 676975258, 832538378, 879354740, 749857035, 460743165, 355806773, 963976494, 314179869, 57484017, 873300300, 111175244, 983903613, 688087498, 559367186, 513366199, 378464672, 2869528, 679334133, 244842913, 209529735, 694994900, 679280674, 168215771, 583162068, 100841984, 91429990, 202528822, 868614764, 926325928, 552843778, 91204971, 115733719, 529175241, 27455434, 296050248, 478871588, 459929045, 511078689, 256993135, 137402902, 96604207, 957284208, 635330033, 53473880, 856587606, 837379640, 931459522, 461138885, 263378983, 304296426, 919318467, 784933135, 235475549, 51030745, 967580213, 38021013, 581273086, 353853941, 491406057, 121497347, 204940799, 975984750, 977682280, 454831175, 796632688, 623482281, 142385379, 914873811, 678810420, 886993667, 536022942, 658025751, 677175185, 802842332, 266776158, 515752193, 628398046, 839992909, 3213962, 380643761, 170661475, 699389416, 687305063, 100907382, 798502635, 877724660, 692060312, 118430117, 575241319, 47048327, 249702577, 521841212, 920506548, 803037861, 831074160, 768206020, 886113481, 512245115, 308707349, 314268468, 227977948, 569121674, 576166665, 205285020, 714619115, 168757024, 980763046, 291631915, 1902766, 939946126, 431336246, 714529213, 665828161, 651347065, 741073319, 8975310, 488565552, 510651657, 996520089, 902693506, 981561755, 733059603, 396164056, 321828119, 537205448, 447656632, 967526935, 927056708, 145321368, 56490275, 291478852, 746575862, 374265341, 810928260, 985867028, 851364162, 92827931, 503414795, 928132196, 882786783, 487332255, 905454314, 585761123, 586363504, 228059713, 707661982, 114549944, 442693914, 576725821, 694093160, 947239084, 47575231, 919009898, 592038443, 455023925, 744738304, 814926913, 559575281, 343683700, 528582045, 796944314, 429215152, 873713450, 576317051, 84253671, 466698366, 914100110, 164499806, 212018933, 730191437, 988964818, 569818537, 351114068, 81736706, 32883807, 287881934, 273565791, 41981439, 613431060, 467513953, 185191666, 634820914, 410351652, 473358586, 205612703, 286975576, 528441772, 223516702, 326430559, 557432815, 728823874, 303421177, 503986315, 407353212, 335501041, 857009919, 441215515, 182984154, 264457500, 277749405, 905119779, 602587455, 565210092, 108246801, 205754741, 652375720, 25676723, 26129992, 801357571, 892697921, 954726581, 911414758, 712117422, 983633020, 330485766, 833620069, 366874885, 123185215, 180924941, 703507051, 967710456, 422394535, 749566305, 841547265, 1243709, 661030261, 251814885, 996366348, 804485509, 110586826, 209650648, 317519248, 663789573, 924744115, 373874076, 80417374, 89986266, 965238757, 119977907, 117547103, 427183161, 496260297, 517204761, 35086272, 746882604, 470668375, 673896119, 826693059, 712848463, 440955720, 180339470, 697867595, 956464754, 897427018, 671535296, 309482243, 689970158, 857604415, 955275370, 63362672, 351713097, 38190169, 417957382, 513190537, 260973506, 20484969, 619479145, 530574301, 159315117, 116804505, 667555665, 366155166, 167859888, 39671298, 448050558, 605852711, 639782575, 823284854, 698408869, 948948778, 226881019, 324006100, 432134849, 203163127, 560669332, 457079542, 665866386, 264128037, 301416916, 953514988, 614047994, 330253453, 327929614, 937428575, 789750483, 167562807, 838857297, 707422727, 159960881, 864591891, 121910653, 280327015, 306544923, 805053723, 463597387, 688620139, 418229399, 409507703, 359745821, 755485316, 586963281, 519029192, 900633895, 72259001, 937287256, 314234924, 514438648, 606364629, 676275917, 219339990, 724563163, 523417122, 615396421, 480771342, 273560004, 933521219, 703038592, 203350589, 618845178, 741709459, 928411742, 966941297, 414524171, 561354494, 588954583, 375845314, 450792306, 871995097, 657642077, 141772348, 246778672, 603530592, 595927383, 699449531, 18155135, 786748511, 186691875, 225499003, 989281094, 383520512, 717087517, 861561622, 152838388, 420708732, 933250694, 755800410, 488159925, 97350855, 528203117, 308351642, 323194963, 720002063, 486602400, 767977163, 825255793, 760894093, 850697618, 195203499, 111763570, 823451156, 160815312, 646068628, 995865201, 679496505, 631041211, 957081097, 458058179, 909989325, 653286024, 177452365, 495089011, 610859357, 757046443, 424428984, 11951483, 910209371, 899343023, 196086936, 829436795, 541740053, 785265948, 643862042, 232691616, 644290289, 894775213, 937229399, 10836881, 215041553, 65198512, 181857797, 698331306, 54808851, 608561871, 991693243, 242194658, 396798453, 579936755, 567445918, 797650403, 744130595, 136199286, 500148417, 200824413, 296341138, 787295428, 622324143, 669741730, 16204879, 114026013, 824589367, 252673094, 393640900, 173506665, 307204442, 506519496, 156000232, 848167650, 772570290, 92489603, 535384027, 242690490, 478227887, 612890238, 637375191, 206840808, 382158716, 429696168, 197791508, 646939164, 873755662, 919092397, 347194545, 129839786, 55523128, 420372416, 835519486, 662849432, 894268925, 337724401, 875061883, 506250058, 723533449, 260038338, 972214946, 675045627, 527220320, 951726601, 410121345, 755666513, 752710654, 701762563, 608147459, 918904129, 329413686, 955313748, 864530567, 318178277, 556262509, 932170289, 976648011, 720467673, 782265387, 62903048, 757211680, 46846847, 656861948, 207317117, 726668575, 525363810, 710914282, 295644729, 925112765, 130158481, 282912181, 591858901, 370636122, 144273078, 840261369, 364200858, 322024766, 263068542, 764870884, 471932925, 321942846, 218068133, 529704380, 539831929, 859346330, 698978856, 309705710, 653893091, 549314126, 716258814, 572827465, 309607524, 809276209, 325164959, 669723937, 335714314, 830467037, 52784169, 398851330, 528721259, 444909169, 441439154, 458169980, 835926137, 876834851, 541223305, 541726833, 901783891, 405828203, 717039060, 916030231, 135655337, 38530942, 239264755, 393598027, 203213427, 912745364, 967962727, 727019925, 889271602, 641366140, 26057407, 724554109, 371371456, 433375333, 833709300, 318919000, 766817458, 97772534, 827686494, 817836288, 810668013, 197697273, 796706854, 624271195, 80015406, 169877495, 982722599, 664050180, 997641558, 670519659, 66515871, 929555057, 52143598, 179827443, 977220971, 436023216, 542974547, 946533089, 936539536, 580579738, 793340424, 848126935, 444505504, 225060912, 829585669, 631798939, 869004764, 812623991, 552801929, 792366770, 225662731, 481112959, 566662845, 756595372, 136076593, 74328178, 898268830, 927879584, 488814060, 283949748, 410991186, 438992713, 545072305, 367857026, 307780909, 723422128, 503001982, 911549088, 981585224, 501579121, 836031612, 570287513, 732185742, 108968859, 715933123, 699266112, 883385185, 454616626, 237482808, 758696604, 807104464, 886112809, 602539388, 267138080, 399439054, 954731684, 678120923, 210067496, 689693384, 286474791, 628518202, 461419859, 269659031, 474814604, 161829400, 182932158, 974660184, 51915930, 48744646, 1642717, 818323907, 708417258, 123152140, 912273708, 590833118, 834753639, 865759236, 993181676, 783552163, 448192883, 421676828, 650874410, 16019134, 958454993, 912128499, 48016408, 360203852, 156074800, 318561800, 334535239, 876536724, 761355826, 16647394, 378168159, 77929969, 407897969, 349635990, 780605056, 549184509, 876209696, 112795096, 688138101, 32316260, 209575532, 635475546, 644453120, 964097010, 354358154, 267977091, 587045078, 464554593, 80911981, 764745898, 844577293, 456560839, 294121283, 175006121, 355878255, 732915005, 682115219, 587456964, 925673376, 334187020, 920420896, 539941480, 488576536, 187541900, 184991840, 30187027, 291448566, 950152311, 451203536, 667694825, 928602592, 751000762, 913341867, 464621171, 440694341, 874552234, 174011986, 654607307, 661885489, 577604596, 78179091, 250700351, 127347537, 46000829, 996869041, 65659188, 713493566, 994429541, 873107083, 53639908, 445666526, 531644118, 794892139, 302437016, 361230034, 794484029, 739355111, 191607410, 217891726, 581867317, 544257252, 109303482, 692537174, 810588551, 172726786, 136671671, 834354063, 671353386, 367859346, 539920129, 685952044, 522505578, 411170765, 669466784, 656810360, 319391649, 62444327, 461303259, 515881428, 639518015, 833032092, 309769652, 630981418, 449431443, 554042262, 935725931, 431007121, 989274374, 571062631, 749332060, 177080177, 636709891, 423969654, 675169497, 883550362, 554624173, 326480452, 181157461, 126936344, 146345939, 468715505, 723332577, 284837971, 845943319, 232622874, 535803993, 6220104, 842184678, 860603762, 275235765, 735289338, 556686999, 247993389, 427866514, 290188077, 369342097, 291836297, 583159127, 317703072, 404680525, 738439038, 143045836, 872935674, 16483662, 796678131, 818152749, 690493796, 145638288, 206013814, 8059395, 44933490, 853385463, 327672064, 752506324, 67648689, 693834918, 921992300, 737588512, 148938755, 761241985, 622150808, 84608294, 325629416, 681494488, 680168232, 878628928, 500967121, 138754925, 287468580, 393241501, 8194401, 511207298, 142082867, 931616301, 37400642, 551331999, 12946536, 585480928, 382580491, 685167015, 817563544, 65842622, 26844695, 595408018, 444660006, 349394347, 1648569, 225821767, 526298662, 623758302, 930175955, 987010584, 85938655, 585926958, 733738570, 105459360, 92163796, 286733518, 754686209, 432054078, 604543609, 655603118, 620418467, 329550155, 786219198, 869930032, 100666173, 598768767, 867922272, 148696947, 857941786, 46764468, 326340998, 8778995, 633625124, 774446757, 444528251, 274739498, 680097563, 358513741, 571157831, 613020263, 645537333, 37866087, 884036777, 316089052, 679110074, 933904968, 176978441, 713236031, 201757798, 285031015, 215693396, 133910188, 194036111, 601250235, 547179152, 704046989, 703683545, 6320040, 76743593, 965043656, 945968748, 801554196, 423800708, 430655918, 591535253, 471554950, 686781779, 488351390, 491088448, 893497704, 642078615, 902211120, 723563420, 243522111, 142207270, 288592128, 652504809, 810067280, 62205833, 705695361, 36404127, 966884555, 87789348, 428026305, 637589364, 307711151, 546589593, 473346254, 752431996, 717896697, 946390249, 80605664, 873429094, 572478454, 957803240, 911148842, 989447284, 668921489, 661758585, 334079721, 46236071, 478892098, 506860143, 642023699, 119327172, 236129207, 190522822, 888211146, 512933781, 180748832, 594232907, 228897007, 228534607, 989358472, 578560618, 218724339, 992098788, 216157163, 299082993, 449949707, 939357650, 662620911, 160697502, 250051976, 366586600, 40550053, 580912385, 53592026, 624569011, 556816344, 964192292, 710757174, 972892560, 328173998, 382400377, 766218325, 618918024, 57836687, 557585691, 361258538, 674035678, 28589410, 284667340, 338234370, 852653851, 326750626, 455743791, 211062721, 80509470, 866418235, 549585745, 766649682, 661250218, 499701706, 970748485, 332037749, 479442953, 758992320, 275312847, 369447583, 143638868, 400419260, 395649781, 496918915, 812079360, 420345281, 153583208, 200560337, 312473206, 595882928, 749635293, 637000570, 12664801, 733085065, 238708817, 736625682, 44715360, 450774149, 263181366, 949848699, 908564414, 925811232, 539636925, 454743834, 981796963, 793005153, 958797330, 199978332, 993995986, 497068791, 808692387, 372273964, 334122941, 274181041, 447742256, 615749511, 936428129, 130885880, 560149464, 463185922, 937858340, 405707281, 376245890, 442915835, 17520533, 613895849, 642795651, 464275170, 562669389, 560405057, 771308189, 514617949, 950540456, 64800177, 322769833, 696153613, 709647176, 972340112, 399054045, 328982326, 761618754, 553773325, 711306659, 33780222, 900524399, 294805458, 373083270, 248476369, 802068058, 234186666, 61205181, 17968326, 926288823, 61468143, 544323725, 632399577, 319048723, 747429274, 784465553, 602673810, 968761449, 853770264, 320434175, 180688101, 558156489, 53401346, 571009414, 199554816, 397257105, 280027375, 240056904, 40608562, 905593858, 968291679, 327506275, 816002953, 105475157, 752498077, 177242683, 990394991, 878328406, 24091478, 936273035, 623614943, 780451994, 926270052, 520185103, 561926582, 727715682, 660341543, 922900056, 658185346, 645852254, 779304860, 725809658, 81290060, 185617996, 170436111, 840514546, 857288904, 71688255, 498383831, 386253630, 264624431, 776089505, 663254472, 318703720, 513142324, 675414178, 759142169, 515460434, 960947466, 668422779, 668035614, 42127592, 71619983, 132599236, 261054336, 245598460, 96893652, 637471287, 428242422, 409816754, 703492154, 405717547, 578123760, 134478740, 531018379, 632425159, 732001977, 151286055, 455231295, 796330014, 573776092, 108859882, 242560109, 375363471, 582660445, 452569462, 619166669, 81800232, 852398883, 935686335, 299586172, 394246223, 869583116, 766581253, 834728834, 639793831, 804519621, 599388551, 181791953, 64866803, 349201904, 39573501, 666827412, 321933587, 157099823, 24557946, 326869704, 879549865, 653392697, 710060199, 826715615, 325630432, 542008408, 180816835, 648425354, 561130489, 275265117, 105493023, 948161350, 929938114, 634206961, 827414447, 921580902, 747290462, 824372857, 983623057, 964530015, 682842867, 435761317, 370455903, 224204106, 77508309, 753379939, 661255964, 360447286, 784174030, 133549467, 343338547, 938410217, 575812233, 695728278, 296595816, 458445775, 667960665, 982638935, 90380598, 230573768, 543606635, 528974939, 669609956, 240594555, 609705205, 166726710, 444451371, 507360253, 8264068, 563660, 418494193, 276271540, 95081130, 625762825, 912999910, 445242049, 472233643, 86417797, 796635349, 662881620, 150157707, 953977190, 319992901, 469023032, 665460325, 737085663, 792129015, 788710519, 124119844, 577386541, 627525573, 780059094, 189922280, 431576832, 426368285, 200608885, 986490780, 881273462, 898616639, 265246232, 570793942, 851248882, 286008208, 41592669, 476357025, 676534016, 591657012, 63512974, 645124366, 425882394, 343599594, 125783872, 276628669, 295259767, 140251598, 516637592, 542611241, 966168597, 964257941, 482387937, 277061131, 812047396, 735281280, 968455020, 409943036, 776568469, 458481706, 690787941, 837730042, 568795455, 479804000, 94383424, 867686822, 138985706, 127851191, 149154321, 125015259, 544359921, 562789421, 546173291, 969759908, 784114059, 46554275, 589651030, 912105334, 114809936, 547901886, 616650990, 349791487, 204121369, 880226451, 402946516, 803311851, 483739486, 276726889, 924377094, 374295137, 457430310, 991387641, 479615409, 459662505, 302424343, 796994438, 557554407, 54570533, 669869073, 941771921, 71328074, 422336818, 389730782, 341613850, 691714868, 697114855, 163403492, 182889806, 334470071, 705035487, 447911412, 758671185, 67835196, 351278142, 871330849, 25876820, 76389814, 70483420, 416164181, 824257038, 7249275, 707426480, 460529498, 266368432, 686821520, 392295644, 660218152, 48985170, 940161987, 375542572, 870661169, 44770952, 950958188, 389384012, 786754870, 285144635, 885659601, 695323043, 89438484, 997482480, 380064751, 481955740, 421038659, 204378110, 979449465, 469739737, 697920610, 528831477, 884988794, 567752985, 171873966, 924646090, 366858435, 128813391, 465930404, 253537420, 247479310, 604096573, 311478083, 311786854, 761390768, 828727670, 197834869, 381947711, 445368582, 693344612, 464609628, 222312130, 184624141, 739649074, 661107646, 243987179, 671956284, 548494532, 681359417, 239499912, 950369518, 596294556, 924544126, 654575832, 779414169, 57233915, 708921424, 839629403, 384544752, 511182328, 355994397, 620242535, 630497138, 750304148, 203476654, 495082537, 542328475, 501054384, 610723922, 555490553, 27677100, 365284272, 337822410, 891578213, 821075783, 325403163, 448306158, 448454826, 829791389, 488118950, 957404114, 508509477, 526474213, 46292583, 760380591, 770392051, 166839762, 84440362, 37042811, 410011259, 907748248, 958566629, 218603146, 56031299, 946357526, 834240070, 88441007, 571599266, 359365469, 355365843, 953123775, 370846354, 177957661, 406748743, 502510603, 891610022, 55567129, 100928467, 884261569, 420859324, 266904182, 93692561, 905293879, 1741949, 528962534, 746008840, 762948318, 697522899, 534194737, 457198649, 390348880, 587551121, 114904197, 3639164, 787843696, 175102254, 215055265, 98641968, 319913052, 629948209, 214151012, 702492374, 11131614, 751222754, 238447218, 149423772, 194510766, 723776077, 16617525, 491421279, 392298078, 433778178, 55769282, 437520325, 983975299, 161301076, 982112398, 355494636, 782098104, 423551292, 653502853, 352147781, 842385317, 521135725, 546705759, 793583661, 206292916, 56187880, 284657189, 40086491, 407717088, 749221142, 525836995, 530863286, 929449967, 296221527, 876436231, 92887980, 275950517, 943559863, 244695183, 484095102, 466588413, 327951881, 864137020, 718813488, 322819626, 927654961, 30121705, 13190040, 52503695, 550698027, 103239217, 660472123, 563664423, 792621191, 502528038, 379452472, 148085268, 255605887, 138523581, 647849653, 195956619, 829437280, 980874646, 147492192, 876464368, 309683765, 570980614, 899864139, 486051974, 210728440, 318139177, 986647422, 993226556, 186224197, 635984430, 361431777, 165624358, 99748648, 850772310, 924078766, 539828294, 544031059, 495385814, 9616989, 425163375, 810901794, 883859162, 519235343, 350316015, 288532790, 480314770, 668882874, 380682278, 673447047, 235133019, 272038481, 225691292, 52388994, 676884028, 243403470, 55980096, 239380576, 191177697, 929877522, 822221133, 341928911, 853721744, 920138447, 851616551, 735735134, 663561453, 468149066, 1996977, 211037764, 274798251, 361752063, 736589158, 735989322, 21648896, 825977497, 402938445, 123157057, 321426818, 511590827, 956933746, 319225638, 870410260, 571610993, 383427052, 666332984, 636794073, 83687097, 715233322, 80759289, 666694259, 113357934, 257266751, 229782136, 451429129, 668127181, 125010276, 851730691, 800668406, 101396395, 142091152, 836457100, 306690383, 129847853, 457889730, 818326885, 230098107, 968712082, 874628242, 19126673, 514480738, 118578265, 982390214, 578867593, 277815273, 672607863, 327465059, 665273748, 398279032, 276813886, 599061696, 150083779, 56962990, 761989082, 263094913, 273658598, 86196179, 484759426, 880168147, 743985160, 421341233, 64066041, 285712155, 581600436, 755166363, 918287692, 14663663, 147259966, 904760738, 284443082, 800635484, 613420993, 340523805, 159953568, 940453826, 271830441, 468350040, 749020403, 196836448, 151604052, 773783953, 295520678, 936310023, 458578478, 530016312, 277811079, 157489825, 109010439, 276326065, 778934452, 890093006, 747500866, 753157460, 657750803, 657945751, 911067531, 170199466, 221650991, 104285761, 741981276, 45751177, 920479047, 192101624, 973464112, 784945187, 703128179, 467428305, 588020457, 275015678, 710452188, 546045946, 817832700, 226156724, 386821316, 812075178, 760993889, 155967398, 773948577, 184449121, 40440327, 908925288, 606270005, 578233291, 230994411, 915343357, 754359205, 728688245, 85652576, 488368193, 641280436, 730975715, 964132670, 243198461, 2845969, 222577600, 634654775, 946702246, 535162268, 161302826, 777180304, 791220312, 73302157, 509860491, 416434942, 20945331, 868678987, 796344415, 368532608, 765417152, 904947345, 985162996, 334205617, 74914184, 338470927, 920707823, 326158073, 674018782, 88743151, 187214986, 191160700, 92065317, 136175840, 677488800, 818050342, 275102289, 582833797, 65449416, 193301273, 37855260, 287762294, 308380359, 750853942, 166058156, 822074373, 905964845, 783299255, 795102776, 190920385, 193702785, 20450773, 869778808, 291165375, 981640476, 464749454, 160341247, 255255302, 793945517, 388476527, 955961749, 577486205, 293361501, 844003765, 307911074, 847849614, 419194286, 513068041, 658159091, 150358370, 91191861, 453153446, 445758900, 199862901, 204066721, 82523700, 814048514, 122203149, 538383738, 629247491, 382065124, 438115948, 220247657, 872190140, 697110308, 554896159, 13472985, 875818576, 989237992, 602497507, 469747631, 783983757, 280871324, 88360003, 309005903, 186394185, 494700094, 787087256, 645371647, 36206555, 368583408, 187952841, 948293794, 847674180, 525716045, 734778541, 59341891, 986141306, 439634277, 708457048, 134232376, 13026035, 640651470, 373333956, 975551244, 583343767, 582109537, 363897324, 308452175, 708996378, 766473155, 757361394, 801510855, 225574544, 688898174, 133549283, 724952198, 682482130, 996734660, 757868582, 44585681, 471512595, 835210009, 485697386, 840544083, 407793267, 948408782, 327581646, 24755257, 844152047, 292459043, 224369653, 75541045, 674979522, 351772729, 295979149, 136862682, 690093916, 189202966, 67025212, 922647394, 50235129, 724532171, 425240982, 877830301, 80706037, 587218979, 715609127, 102335756, 767172739, 768944434, 247062636, 438752136, 907962545, 123099898, 969216785, 109193509, 746512516, 330354632, 1319974, 653418409, 607092222, 69248719, 296233491, 968731373, 65834887, 139673133, 567463827, 918755428, 143334260, 722630543, 324132281, 717423352, 711883613, 180680792, 25043630, 391024985, 797226972, 636544441, 177432486, 609239902, 452280103, 219269218, 8233589, 200779127, 514398800, 376926043, 983261741, 269185998, 496226411, 6623213, 182963695, 575301191, 654308157, 779020738, 313369521, 55905124, 20201297, 407482691, 120881889, 995849458, 787120781, 416262481, 511115925, 43333285, 590785024, 427138637, 947843370, 979002334, 728153934, 37358934, 562021135, 670485046, 162166014, 501183910, 770473581, 455205018, 666676401, 114700418, 261483675, 133024905, 219209593, 490637239, 981864856, 385948278, 292709001, 314513619, 378850411, 753702446, 666421855, 154626941, 614927728, 525327629, 868829072, 338772158, 97981756, 525277645, 608549895, 502601079, 195159996, 246361638, 127731206, 710565202, 411712712, 255148937, 687212536, 727780123, 33459865, 91917729, 570478611, 852855081, 497881380, 111681212, 809033615, 239057610, 655132103, 900389983, 603458189, 139140982, 340021092, 346406361, 367710242, 669174570, 349987880, 709405860, 226603155, 721350738, 192957097, 219830983, 81204004, 580802596, 856626735, 592619789, 363816148, 221006322, 942470095, 282807591, 650166764, 581455647, 526139294, 670225562, 505533416, 832938266, 774200085, 742667415, 707045353, 256874415, 47530078, 363036810, 224749355, 323078459, 480867845, 72428463, 102805890, 38875200, 186309520, 388029009, 996506784, 667296309, 947451588, 924912034, 609262728, 376606466, 427874945, 154326265, 822732884, 404225975, 347174966, 400916279, 544413381, 218249580, 460245063, 570505499, 931756863, 353629651, 306155613, 381331154, 331583591, 820229097, 457015946, 617399516, 557878279, 114825782, 359289937, 126760622, 925365745, 843141322, 709109196, 444691793, 231829645, 115013083, 597400169, 408041126, 763069990, 170142206, 410254622, 828137785, 928419950, 685863972, 65817958, 89071690, 267480727, 43079165, 974546341, 840886004, 69248743, 27675155, 278994893, 216916304, 239321667, 853042242, 489064413, 325721733, 471991351, 67745783, 555368823, 112214821, 545480049, 458373481, 410037807, 421119559, 225926551, 829234506, 302421177, 71888525, 528682411, 666789747, 385329784, 716346004, 766966969, 680600992, 966177988, 431929265, 205752502, 974673238, 232010456, 741455100, 614057854, 802260184, 885368757, 116568685, 655952877, 438635561, 544662797, 914747606, 969170824, 384654385, 925080132, 512041326, 476828475, 775622395, 589556704, 422684767, 356127579, 364057297, 611497692, 541034301, 692543708, 902527171, 1128888, 502831441, 81907702, 878210612, 70626090, 344541293, 101031499, 874123025, 889270095, 561411286, 755829359, 671792470, 81688148, 808549804, 233014988, 398201036, 589267981, 993971147, 814307241, 980763097, 238983074, 736265049, 795953852, 931196199, 629758170, 78191206, 273887970, 361930511, 629776785, 188851601, 811081672, 643744710, 878846023, 921919707, 424041475, 193709247, 918890950, 621231180, 556237206, 644787511, 765779763, 827736687, 614425650, 688013893, 418484823, 576238434, 780556594, 554826790, 319255004, 224381452, 57534237, 379504779, 411410194, 188276741, 469520649, 353652591, 615707837, 36850784, 946521385, 666003607, 316836164, 819677754, 94995512, 92511984, 639590575, 900617057, 524973834, 45889112, 281498456, 394781097, 799628254, 760069488, 300278155, 756475, 265008619, 48540925, 424016327, 653849235, 154200727, 35466375, 804736429, 448646791, 150007907, 76210544, 371406389, 160135733, 499099339, 702393703, 521552112, 220668159, 929827564, 990556536, 843114293, 991895582, 425277498, 431221159, 121243418, 414972400, 606621566, 388337414, 850706700, 278304983, 266105118, 559041684, 414828532, 766775498, 409985193, 955136348, 292873306, 607890367, 942146716, 136039316, 743826095, 248853527, 904366257, 932092063, 927489325, 676163727, 635374991, 82462113, 49922903, 462727267, 236998735, 261167623, 176651757, 274682532, 794949230, 799461203, 59618274, 304461440, 438223562, 85906855, 650618157, 426640728, 752539263, 694368067, 777604642, 929274816, 384476985, 298762143, 447540201, 284548609, 892216517, 901398623, 990848534, 192158518, 56281481, 12646073, 707973774, 904696449, 374882514, 579242419, 33755867, 743579311, 770756590, 119460174, 478371203, 415255506, 941801296, 769356983, 504174410, 550881750, 811089567, 114195033, 790485469, 330616430, 226345737, 21206591, 907750798, 400400139, 391962635, 317913052, 902760298, 382937644, 42007945, 265673453, 112025455, 176739300, 488594259, 253135890, 31736556, 481684314, 375138259, 167009658, 129040592, 861658328, 723366747, 416507524, 279561411, 855975963, 810971467, 599505340, 858241837, 560890931, 165132836, 966724905, 284007194, 655560034, 37806252, 942900297, 795864603, 37913640, 824440487, 721911203, 357647353, 27156, 72683099, 700197500, 472998378, 630648222, 75244150, 513950688, 66037061, 422486439, 244988149, 453347606, 548589693, 593437543, 946139124, 648222334, 515731438, 888869759, 478308156, 114224508, 255427129, 493263357, 605774923, 458719253, 553491355, 4854369, 653860349, 438222154, 483072362, 395715398, 864347031, 82749021, 859551711, 267176217, 990266974, 234337445, 837972812, 561917593, 415842175, 199099237, 647946336, 98609970, 926267334, 550977524, 176885732, 674014134, 918405909, 492808793, 677863239, 474222308, 633368974, 544928906, 346688693, 651731194, 508316663, 265317407, 53964206, 314403239, 96452122, 604761267, 27647358, 834072460, 918111641, 735766342, 657972920, 199615338, 884851790, 628046648, 139607518, 942549869, 117361358, 918238868, 144170157, 828215547, 907603188, 880300157, 366639102, 216369629, 775324640, 162952666, 580398050, 18836719, 637047008, 102323320, 578286669, 692665073, 509095192, 330200850, 826203460, 575902721, 861051791, 361197492, 255527487, 90627328, 592955327, 568687971, 669445260, 123377376, 429983113, 798116884, 822740322, 231550917, 594845049, 900160313, 144992723, 456533443, 683730388, 646267780, 413210391, 198984978, 660934850, 754108224, 749788810, 846170293, 863323765, 185764695, 967164394, 499228088, 371000994, 468786221, 694291151, 284587252, 915361397, 375061500, 576479403, 449238003, 290894773, 278519072, 590207157, 629164082, 689866562, 155422708, 630982005, 549035998, 883878945, 918259946, 763118992, 811354967, 894665370, 818104711, 121196971, 967328861, 50612240, 225253807, 913966953, 366520919, 710735452, 56744202, 175977305, 22781176, 219791902, 969235895, 138823713, 539872885, 994612924, 335759938, 259280980, 427937211, 899423129, 774384720, 150673710, 847165463, 418586026, 495725110, 378330212, 552873320, 758832190, 959407602, 260728845, 871509036, 860198790, 835527618, 742581277, 559051514, 598744133, 844148127, 491081337, 98342012, 212938246, 764894721, 664952652, 443000119, 570001485, 971952300, 737133962, 160861423, 298057946, 229130261, 283002884, 59544244, 121060755, 138715870, 533362575, 461507133, 427835034, 624201792, 379443162, 596289813, 134595973, 764343432, 959643012, 608508095, 896159854, 418724198, 50446683, 206514905, 764688092, 586550607, 332368686, 374417998, 312094267, 404358446, 390393030, 794562786, 285671377, 465440342, 863722035, 630087048, 37832706, 948340296, 396355327, 397342615, 392184992, 441206517, 920734097, 456117414, 903651367, 241444945, 80130313, 326328242, 889258237, 400000088, 953013697, 848729759, 774277868, 902764973, 332154294, 842520825, 130085468, 619619956, 116282260, 86693107, 433988322, 285916344, 950010743, 108391516, 379178530, 442716343, 768896118, 612437825, 802289540, 586865909, 771030907, 717317671, 810434510, 898590295, 49873966, 592557290, 763693910, 204912428, 636690426, 59706609, 756566376, 402619218, 922092208, 958065654, 195253572, 723674986, 706564680, 519153493, 1046466, 489192398, 975865069, 593828558, 538273127, 178573806, 821480888, 819843011, 236422914, 777148439, 758987452, 717633577, 985120464, 524174951, 637222674, 581659962, 752322113, 808346172, 904830025, 486571329, 541699565, 2433747, 430444758, 544373749, 153735772, 899229241, 305200701, 873861740, 939420168, 681527405, 591264597, 22280745, 878605939, 321476096, 570443806, 458878100, 711935078, 823142831, 258688301, 151302113, 917964497, 159992774, 356193954, 27538993, 662598917, 216788784, 806220914, 428743910, 899740395, 651070880, 729410634, 968362559, 843384934, 830284456, 833002645, 67623633, 735182018, 892745221, 226029699, 891221514, 812022197, 300714579, 124963371, 109865709, 527673240, 842547492, 678509366, 508603087, 882064831, 191689205, 87329239, 441193767, 533166717, 2050514, 838735304, 51800053, 696927716, 628136014, 409900785, 416005007, 444090340, 92488182, 332874857, 98075072, 344572461, 615649260, 811480684, 943546217, 273855977, 164043803, 692637728, 108437720, 813509124, 731269862, 789525405, 998926973, 870206433, 557691362, 609312117, 393359321, 122189119, 296849750, 532967302, 771302882, 274981518, 132409098, 689966467, 265115949, 149858434, 941481491, 761215300, 807048756, 593548362, 580098815, 1928679, 698200443, 550995979, 101930831, 415125696, 496895459, 76176241, 621793544, 774801452, 140950975, 314957874, 610884098, 507651310, 260257373, 203158344, 835050178, 402834349, 146156925, 860020878, 717940964, 897934160, 328782783, 47029359, 337348884, 803613110, 957280712, 948888386, 630651874, 125121215, 217300665, 383604277, 193570810, 70724211, 980970757, 21294760, 337261462, 248167203, 30854212, 296563243, 36605684, 977118062, 27265431, 624041032, 916997064, 788288553, 543046555, 729952278, 951955684, 809521728, 385695820, 909125511, 134071216, 669903119, 878675366, 832180600, 487308073, 518132725, 852453501, 483565122, 338984928, 56963474, 866118178, 190360700, 564611659, 206108775, 58225616, 635926196, 786832147, 318443139, 287123033, 203541324, 498517629, 436518898, 890889980, 456371961, 546576990, 917964740, 717559083, 103613174, 909601307, 707113405, 222404178, 263476571, 310682897, 574823792, 144284444, 788108568, 208421003, 111705674, 708621497, 881487927, 135036642, 11114542, 464126045, 634701423, 624749717, 927128115, 374797537, 558802394, 530651916, 777263755, 634604399, 846809884, 42927895, 255523287, 621838192, 141191939, 370530338, 811969853, 603979809, 758505891, 189247227, 10046044, 597235572, 938729952, 704054211, 389597604, 349093469, 102250836, 957758278, 129042611, 527451254, 74213219, 693723039, 194367905, 508526239, 765293316, 545024719, 533491312, 684430303, 156200577, 56661414, 139473812, 479041274, 21690965, 199761823, 211448947, 599349182, 140733033, 95340135, 259302965, 951394226, 852714876, 899477067, 720626212, 103645563, 492073358, 938007978, 729863812, 12546652, 269689664, 66470531, 126304342, 701611081, 94005759, 601418064, 465412462, 257321149, 835356606, 794046606, 828536423, 821911276, 979018840, 933769967, 741315266, 903981856, 464742138, 671647146, 322711177, 967480976, 688304751, 793878873, 86456186, 256062715, 341230673, 362560184, 248724958, 975010795, 219291724, 272509871, 610159100, 952648074, 823217321, 95084669, 507463036, 724825052, 15913799, 887987528, 250420675, 486187911, 884990227, 771130402, 761430806, 804355308, 684143974, 928641662, 789524230, 364732870, 988569313, 632230538, 179380872, 853574812, 655372004, 672723821, 955539046, 564521718, 376181793, 273115959, 791533955, 698274839, 35223340, 185056688, 529805595, 866169533, 586167615, 518798122, 658854063, 517879066, 707689635, 299270339, 969472407, 613728866, 737116666, 316354057, 674987200, 494430145, 648961889, 580358407, 421763116, 891449604, 398609040, 791052371, 876192033, 426457608, 701524471, 273142977, 793560236, 14947139, 656460133, 76368276, 782468667, 27832877, 328401346, 131275062, 574036901, 56135483, 839464015, 832710587, 665946078, 604008859, 365822204, 555083983, 440453482, 861980989, 831287471, 169007109, 854285796, 828263055, 430617844, 445136518, 545662013, 264126735, 58595113, 443195247, 876202038, 279501545, 154059241, 984239005, 543053510, 409843387, 557467341, 874578475, 53025874, 63457568, 566248468, 908540551, 618860175, 547749566, 201851530, 437048497, 671970464, 93448222, 546179526, 425625169, 159601251, 616570114, 433133818, 757433187, 340431647, 472528318, 364390010, 992310473, 952279024, 224678156, 215565519, 259196215, 323888835, 39368920, 833622619, 74892883, 235218060, 809132535, 210403890, 788513489, 491688411, 269396487, 915791894, 901101660, 726040203, 110133535, 770414960, 971901611, 731260257, 456294506, 25732295, 463940388, 769369475, 718022335, 415294864, 929632204, 78795857, 679092126, 6085197, 890715813, 166355734, 675477926, 880870769, 441150928, 739944262, 983386252, 990725327, 658977856, 1077897, 502332829, 151065784, 615103587, 641412279, 970436568, 211032296, 550163958, 91656597, 500573593, 153370285, 463631082, 43991869, 85573964, 334380255, 617043360, 629231419, 641641540, 288207533, 199042807, 810146464, 439110776, 271103450, 166580955, 885619386, 751311293, 812933694, 327047202, 478272840, 687682831, 676291481, 680625850, 610357988, 576961305, 77973876, 522248802, 667662546, 942427955, 185242910, 128349217, 445005230, 50715945, 966113910, 933632989, 739579288, 104688536, 925517981, 215254230, 734677345, 738733952, 781194683, 885837148, 329887235, 503091185, 419489587, 451023590, 280823779, 3010429, 335604006, 533554129, 652713465, 517896336, 266125431, 701496674, 337932120, 966658468, 364384352, 112184922, 445169172, 815502839, 862718254, 420808422, 354562485, 869606933, 82916800, 751178507, 903016902, 65106876, 580737417, 375729610, 394223578, 532470058, 838407992, 310406284, 445221317, 905823194, 661848729, 493185349, 931360057, 30290483, 206024528, 276770261, 809912651, 977317811, 431115862, 234437829, 16152137, 185076676, 501912319, 789089184, 69690119, 275599968, 15840553, 295418299, 142051215, 309740076, 837191124, 939529342, 643331668, 656299527, 924091882, 354710778, 388800578, 873176841, 962544690, 403102767, 35373184, 433628819, 416152121, 455891898, 368887928, 116047700, 351348229, 847940782, 177779735, 250128340, 59723111, 729558578, 487198968, 970589167, 609923704, 835151949, 472214593, 801660934, 312445010, 414272984, 970738245, 630315645, 57055796, 557335440, 637079506, 228079282, 590000993, 868911068, 523314732, 421414616, 954684706, 185931355, 623584969, 5761987, 976373925, 269429786, 677428739, 881057809, 631310552, 830870616, 386992711, 814528971, 804796790, 248796313, 911183499, 395921914, 985822215, 254053238, 503471849, 736191832, 908400660, 192842559, 401513585, 252934147, 775642648, 113182427, 593316522, 649031108, 353265995, 237997591, 246719278, 407093188, 894431779, 610291216, 396811100, 34182395, 165215870, 663362361, 835297509, 930254530, 91665413, 1259069, 246517634, 288647829, 93049546, 831505091, 630439546, 216425622, 191946995, 263962263, 989776950, 776432843, 150048122, 831739026, 270794589, 29948870, 222820129, 271951641, 438076965, 387570150, 410303379, 857403879, 411900088, 54702500, 619874188, 251249655, 62469852, 782634712, 879300968, 305815159, 264058884, 654201256, 164561813, 862713234, 929140750, 183852943, 17484778, 101241466, 953480168, 768037631, 17388987, 473230604, 260843554, 873773741, 693490428, 939916953, 877260994, 344484759, 6242263, 728983569, 755926777, 855054164, 887534272, 45413577, 994012593, 244108128, 380696206, 167658737, 515949189, 898480257, 337061110, 5150865, 257236782, 564219728, 550685571, 231965614, 595174872, 184366767, 816794783, 228272547, 384090783, 189872540, 761996299, 304002430, 855792569, 927859967, 529891430, 941720683, 606815879, 923460029, 556314592, 754750028, 409604988, 400901372, 280524556, 640980677, 126734367, 725301992, 266680289, 893474885, 745965962, 870021420, 736991622, 629085498, 671185585, 264560691, 171529920, 646820883, 693970226, 738132324, 536449940, 541688676, 668101051, 947179750, 80201220, 923511068, 66394246, 919805900, 356321634, 13079751, 597840757, 951609138, 38901820, 447541226, 339882765, 587184004, 532928045, 348532326, 600303160, 217955794, 703918904, 209878563, 624325680, 617067330, 114158839, 658773894, 30776430, 376796745, 325843928, 764228820, 706619515, 237507136, 125513242, 8426611, 71375816, 365076995, 512814851, 557940529, 719531336, 454956845, 63259458, 691174112, 317750357, 441055430, 385437216, 375276900, 929517109, 603964774, 250487596, 917257603, 354863227, 771268570, 773299673, 265233477, 585058359, 297611388, 634321240, 686005740, 729975340, 279360312, 423164214, 916067921, 953486521, 528084457, 339635618, 431610822, 417285190, 499442968, 548917380, 148992017, 959606666, 897030796, 241803720, 277471092, 542231829, 660294357, 625993253, 142253940, 34520285, 529808628, 737890343, 869224064, 978395264, 103822169, 518638055, 360543983, 484753383, 372498537, 489933782, 453206673, 216374172, 223156110, 489606380, 588880016, 523941703, 195793762, 420719650, 310747462, 279154296, 94574935, 938716943, 233819075, 636402592, 918836665, 527037646, 665768579, 296885656, 408857843, 610122743, 414015336, 173835323, 890873265, 758623090, 838931210, 601277698, 775155452, 439546304, 547207788, 778848617, 508723667, 72139968, 555424402, 223420730, 154123340, 694848863, 387384466, 124859719, 716939086, 584175351, 794131214, 643415421, 783205265, 317727370, 941811068, 832172995, 273829515, 680397402, 625310818, 749430270, 144694569, 841510106, 294972226, 749468545, 892759624, 857620866, 944194626, 270682252, 582357041, 466662533, 296390362, 621348062, 111196783, 209268507, 733910592, 372745011, 241838744, 621765061, 908821593, 191845245, 509821750, 465500492, 73798453, 930314327, 654968785, 96396666, 932016803, 840664771, 741779793, 109173902, 325987760, 938888980, 586736172, 794941583, 872225556, 45344370, 113071099, 853928065, 713391827, 410222275, 407436910, 36181079, 464584403, 178617669, 814402934, 72823715, 206127067, 462346934, 941639262, 410696659, 134634083, 46787438, 858554314, 254854208, 574007341, 983720125, 969643673, 479760902, 539649209, 784310431, 618993274, 260809953, 42003871, 297665627, 437264180, 67289823, 939622978, 331774930, 564930002, 370465230, 374641080, 529101186, 436207389, 65640731, 548067185, 144709892, 538315406, 974360801, 727510, 515031163, 479126702, 598452495, 860515664, 325477874, 909800474, 622082689, 711874922, 509772123, 339587375, 56341417, 876917353, 616086996, 587230305, 460381880, 683650533, 679815282, 787594491, 463083300, 876960005, 389807360, 854620339, 600270775, 800073707, 155280800, 11496778, 515651205, 897210977, 341807644, 706721184, 66886431, 591078979, 995866429, 321456435, 166511501, 63503968, 606025575, 774405383, 41404508, 619926879, 710898197, 311955963, 702491452, 669817101, 762440297, 511077776, 75585557, 556012706, 812251384, 891364685, 835128751, 442380284, 580128007, 442616566, 44723819, 545018167, 190550849, 553615071, 92039406, 306536084, 325362488, 487990800, 30939189, 564896652, 76411687, 898743794, 862333718, 54105902, 977758772, 389905390, 23201110, 501439726, 558823130, 626786739, 53827250, 284215641, 336442557, 395578121, 967004875, 643648013, 713768504, 870032396, 954908102, 840632476, 987297403, 236568216, 231744, 757006887, 388201208, 419591375, 743613247, 422911593, 189324631, 666821662, 39498719, 312477275, 600537706, 270143384, 306718135, 933104895, 203897541, 934731797, 60165356, 628162149, 107752219, 224527939, 954836628, 961611702, 125696089, 561662852, 430524459, 402767788, 559955704, 79361270, 281514094, 939245432, 687875907, 865043016, 601935519, 989162091, 575448968, 270468444, 859791180, 191764984, 588578250, 523101355, 468379286, 23010576, 638567724, 805597493, 119460478, 214971211, 885462700, 836918322, 200003776, 940437041, 32139580, 927085493, 703654143, 87319015, 469859522, 700506253, 442815436, 883082070, 931504639, 502090373, 723445373, 584338194, 116972439, 957272838, 212455278, 362855704, 30711373, 739654299, 898302699, 690855941, 186669074, 808929395, 365309470, 882306776, 704487087, 328032194, 618432330, 768333151, 538214038, 947272375, 12694583, 407195239, 820310582, 429199135, 276421686, 94221340, 569459574, 447318585, 174737096, 393582496, 152003652, 277337727, 745570346, 906590889, 120310515, 626902552, 871136840, 364279767, 595534559, 288618968, 360735961, 589042626, 536460213, 505121965, 737320254, 143597960, 696803546, 296400526, 270458343, 618067035, 718745291, 504799720, 785535358, 770360893, 877491002, 391878253, 868593854, 271622163, 554661552, 411864646, 888460885, 682595216, 61749300, 349902699, 845847043, 17838813, 151162395, 645643684, 470368423, 669391709, 111930119, 360339736, 794194449, 215550102, 491241909, 118034235, 129872233, 483539871, 132958016, 466049080, 50433048, 769236024, 733500980, 608217425, 141867560, 5105300, 626428418, 407756347, 107327764, 634868363, 585250311, 174882751, 557620652, 7461373, 814763437, 857377091, 404538803, 344999432, 378331031, 145161856, 155212408, 521053792, 937375209, 295467025, 653120733, 256504795, 645457503, 88370724, 751517649, 924913220, 192347836, 323094584, 944765669, 931684710, 171521900, 845125705, 769737395, 974603305, 167848514, 738519571, 486707683, 324266289, 368717525, 159954340, 353014301, 156416820, 805050144, 731668553, 131288020, 767458910, 43039653, 505454101, 625074966, 607493907, 215093877, 130884090, 942620422, 112813944, 779947912, 108580648, 856054503, 859849648, 758054353, 400250369, 838617802, 335104634, 325123007, 886058720, 325337141, 48469766, 734115747, 185690198, 927642276, 211945537, 744789013, 123511850, 194291010, 524623399, 955424364, 183174438, 563718143, 964424042, 679478693, 704773202, 266868408, 571875065, 489166575, 178587237, 902858458, 908872619, 118781833, 542815988, 70259654, 655086956, 974456695, 881693621, 923912022, 211649771, 138494552, 562473916, 569516439, 886096733, 12434009, 326761733, 630648872, 749083560, 227361939, 780049555, 618572816, 472383243, 441156285, 236054515, 451629437, 958109190, 760829098, 299542993, 183505962, 119560782, 341212194, 532309000, 763399320, 35245654, 530413915, 311903029, 436784995, 198952017, 10387298, 858533549, 57496621, 696138992, 662926137, 100272970, 999471656, 593630137, 909669927, 171114531, 153514481, 467156457, 252269838, 919203064, 26895807, 46020172, 564286916, 143856757, 699037265, 366304131, 731503683, 79277647, 637895950, 48772967, 193910007, 832823392, 710448880, 179645314, 785693092, 677495884, 796469001, 930428563, 120719900, 324490309, 824191526, 947390801, 187157027, 181132601, 107523450, 460700463, 620062521, 467588963, 106502629, 957544451, 190536799, 225592631, 334652832, 855776654, 974734326, 434381123, 34191568, 515577502, 734809665, 149820876, 521075350, 313402000, 785127076, 961742640, 60131764, 489620801, 570061094, 666555600, 127800202, 41618881, 231930539, 213091626, 949574497, 451082467, 558213399, 705266136, 392904640, 640431095, 968106952, 285178908, 797619923, 964267904, 6391307, 281616248, 683159450, 261804659, 358744315, 431711425, 242341480, 825035222, 434195125, 539825914, 464856928, 223921145, 389668060, 522167412, 868210445, 55562960, 549622032, 802055927, 562971316, 296498515, 569467837, 981869222, 915527880, 422340313, 445649517, 329761196, 703271925, 112369747, 800487461, 893638742, 559685131, 485111566, 785396639, 107302390, 269636398, 294311684, 415214736, 418509431, 618822678, 807685767, 161069511, 105423547, 147246725, 533383767, 18006121, 507587648, 311723669, 678244668, 732808964, 890195695, 124763279, 534032147, 814536970, 695092168, 603086287, 792050441, 242168547, 101041223, 215808252, 933059362, 739598834, 183003101, 93382867, 692776282, 547083261, 962547265, 264544831, 940475098, 952911623, 251354436, 455152401, 230579274, 399898236, 20673573, 131622274, 574139055, 691021689, 520035194, 182669828, 892059488, 856050992, 995641127, 90073438, 504236342, 599876967, 929627213, 970172514, 756009149, 458023530, 231462830, 362486793, 643642086, 892872390, 322010435, 940207656, 181183022, 232398059, 441730079, 311093245, 540816385, 236842698, 262695234, 202816487, 173886447, 77954628, 493539269, 324386733, 865643638, 165341368, 204613896, 48632101, 734293588, 305152830, 98345927, 739725958, 38512907, 342740012, 547325553, 739578667, 334689230, 242449983, 645699281, 477610838, 892460760, 12622478, 798484693, 70842650, 606280005, 300557714, 489369161, 48167246, 800050021, 980673385, 713591725, 131232781, 234216278, 372888761, 480892245, 707169854, 651963632, 488604112, 585957650, 314694514, 923865621, 764004219, 262607243, 113244993, 196839076, 666681652, 456506940, 722645981, 284704262, 377004001, 483037703, 901632534, 433553706, 459482776, 726884196, 604027149, 148128328, 641723679, 719689526, 515681847, 464086910, 929534830, 836232214, 255082538, 896282210, 110921990, 527022200, 79956319, 308323082, 708113824, 523631943, 161213338, 812538944, 2004130, 874025850, 617320965, 220641260, 91560018, 891740954, 634617386, 969671108, 327617184, 912664702, 112427063, 949478590, 212485077, 242610891, 206523760, 278815954, 731497927, 333587040, 480222865, 160087712, 485568776, 198480609, 820364275, 817054692, 721844470, 351778952, 331378973, 115962505, 319984315, 763703805, 707366539, 902861911, 808458256, 839998746, 148040614, 647994308, 870487369, 778674537, 235866106, 927916178, 991525588, 300860123, 554769508, 3946327, 536510562, 391342961, 893239029, 582177351, 498238963, 670029504, 783930356, 351250939, 402561899, 62222844, 372576675, 80405362, 470970626, 371634791, 38586049, 285284873, 531431229, 579296060, 503766179, 681831426, 706652233, 191543584, 170168854, 896653257, 143811379, 54724872, 486656795, 526063619, 130315673, 276225959, 950662576, 242989079, 34016430, 475381851, 794675003, 564264143, 124983755, 995028732, 507660945, 168318954, 794295982, 470764083, 409257264, 952197734, 920175518, 355417334, 931805380, 472301035, 754759591, 381798604, 428275015, 366648278, 696621519, 941870956, 599340533, 675771756, 579425593, 427801646, 173486090, 215992904, 132671191, 837897833, 958578788, 171918463, 466137534, 28906017, 667563799, 442300719, 656276980, 413764813, 361315739, 623650826, 313810817, 316344915, 235776470, 202792824, 848780251, 687222140, 106577926, 118111336, 526141518, 263873490, 160565999, 529404593, 79344750, 248582255, 191381487, 737559177, 990360718, 323384806, 31312085, 731190500, 220045462, 590725893, 606377434, 929021577, 293603240, 96386470, 797553732, 472534195, 888579833, 352016364, 665496446, 580122450, 778463168, 839230038, 316192203, 746756900, 513758422, 608940739, 31369544, 337100006, 819204986, 374454438, 484239883, 713138830, 417661220, 320225738, 970694401, 527732711, 981142053, 145184059, 924129132, 673290817, 229974105, 142519929, 78584488, 161308231, 117642374, 708071205, 215759411, 621717551, 785884120, 796336409, 826838920, 638266246, 116087561, 4169781, 179331602, 553710097, 579567931, 740375392, 663784885, 169936104, 460856537, 174749680, 422951279, 371195955, 828254470, 225219738, 630533575, 11804342, 698938126, 208153643, 773827678, 102478768, 83510498, 155697424, 197342795, 896461194, 57314160, 489706450, 10748465, 254087518, 969950370, 362859865, 353081032, 368090014, 88375167, 492040874, 449488787, 483917244, 352974641, 606748193, 392317931, 922397858, 191606454, 99689516, 670237770, 152332266, 412414974, 419495085, 778106341, 584169936, 287823251, 619852433, 529941104, 657699445, 609934473, 600690855, 123430528, 340844532, 527827917, 441406304, 287856299, 240960357, 721950087, 739090842, 783296217, 480810439, 606990859, 281148628, 92137022, 191168019, 832244247, 982095420, 336128055, 801244843, 53856619, 453605974, 630777905, 236292214, 907775697, 121839695, 456771460, 777457990, 915889918, 781246298, 940755273, 778281701, 131279453, 102059129, 902488809, 277790026, 61673710, 797180245, 460165076, 912767693, 754511019, 938491811, 50668116, 326279526, 565998067, 199173327, 861802473, 466665215, 391537954, 696202244, 638790844, 794823714, 896339131, 540897258, 314440708, 585167364, 349455613, 893775060, 657542168, 439719398, 457010602, 616566046, 977478514, 478786891, 114090894, 480216759, 761824178, 220660416, 825345606, 137051982, 815775408, 56337361, 68463727, 806222668, 271076236, 292520665, 599920561, 494347680, 278615727, 84815644, 856621867, 307016721, 589565725, 657651432, 838042983, 816129894, 603320344, 526146689, 538892491, 148944368, 475473523, 53525317, 179726303, 462584691, 482340779, 239834570, 780935153, 380525808, 780363599, 527922070, 535993318, 388386984, 998437048, 333069077, 413122050, 323616323, 601321545, 470004658, 894986668, 576295183, 381987171, 973776062, 236224965, 99813956, 798839877, 41507097, 39689026, 53195456, 812803351, 155463147, 675048221, 592415788, 942158764, 455679015, 717089792, 959609969, 642379550, 187934365, 738838548, 140576066, 503706200, 754492176, 987941556, 705570996, 182165197, 273905188, 232040742, 452445893, 614600705, 393975672, 100671307, 317362776, 982502545, 784265649, 314361069, 194589661, 673744733, 995751190, 529941409, 194946057, 704884, 189889037, 952127489, 422255008, 189544858, 23546180, 739342290, 233271184, 679693518, 958803890, 637628904, 296008300, 930069344, 598549578, 430716714, 767711128, 134835607, 387957482, 825972336, 347227557, 848796071, 658039369, 101144295, 92690788, 540588366, 624835650, 148688571, 64482917, 955611661, 669509007, 527759651, 767908310, 440603856, 907473363, 607380714, 999394881, 628442374, 909140634, 81470311, 744019713, 707584100, 823943741, 33815199, 655088200, 449334914, 597955050, 197123682, 674557918, 842042560, 510377019, 163674733, 955836637, 709633884, 988868579, 933149594, 832546652, 154316385, 223436670, 395724720, 647079450, 980948389, 580519597, 302514143, 279378209, 450185735, 699575721, 545249468, 145602618, 888158476, 196315741, 447686349, 120540556, 849269056, 246446718, 152972266, 164949307, 873510360, 596523799, 486503327, 640448986, 210893117, 545519952, 761079087, 287160690, 21739826, 227640697, 157680321, 84258652, 465345781, 668651474, 135005674, 472493104, 115562240, 235079677, 880789808, 8146062, 472347404, 432248542, 795832061, 760178505, 815278391, 847722770, 563034161, 979093044, 358167398, 876432990, 735897870, 185159172, 458404230, 50235669, 520442781, 963600110, 476345205, 996167583, 761560931, 828940706, 98626359, 976571700, 409871768, 102033306, 773942247, 879885596, 749623640, 282856407, 82915557, 663494316, 990306483, 304983838, 182155772, 782241411, 760753372, 705736491, 239627870, 729130024, 545428298, 551542911, 314907719, 253161126, 891786721, 891642662, 522236446, 905566309, 165891719, 284692283, 634263544, 806405526, 898847737, 582136195, 189541052, 894666664, 640171606, 907539851, 400376953, 445816071, 270010681, 618075156, 864395931, 198072076, 96218342, 553600197, 152967356, 283404008, 831628635, 757470483, 861970186, 177498567, 42698763, 838548000, 800278810, 259426404, 695407244, 950465990, 144351478, 195403310, 803883142, 198393703, 45904770, 464661661, 986967242, 884716722, 123835713, 80797390, 827483325, 953843256, 162167418, 730703811, 714379630, 349260223, 526303614, 119456798, 85408026, 174161642, 816281140, 319701983, 125051007, 666247612, 759113386, 129750990, 206862068, 507584194, 205519001, 201026228, 266342199, 141456939, 724630977, 907712872, 855685545, 156488941, 373545784, 692816877, 634369244, 151162581, 521681147, 447708307, 12838910, 156894378, 498830838, 661599303, 480069199, 391616445, 957356582, 27763746, 971513275, 875329753, 830265220, 527488860, 222700482, 773314765, 793446898, 39646646, 432396812, 269911789, 678151839, 439019224, 520044967, 907308794, 926383480, 273150049, 557578449, 482155328, 315648374, 36295867, 888371900, 290688778, 346830578, 987314605, 490267250, 690708676, 763030398, 265852880, 68284796, 355030617, 804848087, 606471486, 121047307, 529080865, 24640071, 748131352, 141254845, 33392972, 170619918, 396132915, 271820112, 464498778, 252552706, 46414347, 684476359, 677720194, 100967739, 944606047, 802414780, 634938136, 60788792, 670676462, 166283797, 572977694, 14023304, 961981366, 461920116, 584276831, 689126248, 193566842, 793408026, 968517350, 225807040, 106994218, 235062049, 349841120, 508594665, 437571684, 627752654, 575119836, 791500754, 346471081, 240383829, 871687967, 461935602, 687113659, 543147908, 689993733, 246028815, 470526430, 102220251, 103387046, 70166531, 175813031, 270649422, 453875077, 837229223, 120053091, 145791246, 590442896, 791038296, 619758733, 357311281, 153018197, 628621175, 563992997, 755972974, 44184923, 387440888, 565640913, 46264780, 652214216, 434981225, 484912620, 709862842, 921503067, 511991702, 345530321, 463297424, 708225548, 940748625, 612542494, 153634915, 74119717, 448595199, 346075412, 594390435, 715041114, 854853265, 735451248, 370379254, 349905361, 269551763, 932809143, 296736121, 673274014, 828513519, 243651401, 354099574, 718127366, 466188248, 911492138, 658233289, 563267581, 961444564, 791072710, 330764393, 123177715, 319535833, 353904500, 341049049, 87642441, 90376819, 6959665, 247464446, 246605119, 813909004, 976846327, 12076305, 411820635, 847798032, 914497023, 834958291, 127448767, 375981412, 712078914, 297832611, 31257819, 698185884, 664632841, 121294040, 819695412, 163095186, 912064693, 879663977, 805636121, 138459980, 95623391, 60879769, 530370378, 511796472, 386518699, 398255033, 176500917, 395878980, 919842344, 836746386, 435664209, 565474862, 321238015, 926789895, 134228709, 663373415, 136961309, 765254464, 423080703, 772436785, 79622426, 314991753, 114548381, 402723730, 827755397, 712316832, 486350125, 546967559, 37510002, 651388191, 779177760, 756600787, 632759641, 429040453, 694388384, 538166700, 47329023, 29186679, 259449618, 61037989, 474797333, 64237148, 774101999, 830421037, 459928605, 440131640, 599677840, 933455402, 621497357, 880369329, 621752238, 473665598, 13120898, 126259027, 973468908, 63399034, 983793719, 52721269, 478817368, 495241786, 900613473, 681620588, 366265898, 531238429, 215085520, 854368141, 103880819, 851837326, 999887869, 967822189, 903767460, 174263883, 354549655, 919636861, 613822588, 820510739, 119058066, 296484231, 763256823, 897105896, 869002834, 925704554, 950816214, 251755486, 898176776, 293823576, 266841028, 16284453, 164728110, 235101139, 304485501, 347416547, 314750209, 73905643, 596814293, 663279604, 784330506, 910714850, 462744442, 760267881, 746840162, 906256976, 18939177, 233330441, 684747955, 143490505, 238597341, 800609258, 453226768, 341035661, 318743687, 308178225, 985370129, 888126285, 946962029, 494971680, 90338058, 978078497, 501682252, 770883221, 20855036, 131866886, 478321952, 288436720, 202090525, 578989911, 864142812, 942193785, 362982835, 454148790, 423668978, 63008332, 17701795, 559706148, 497527861, 248828427, 811661556, 687840520, 931089047, 434930246, 907990158, 905082647, 863391155, 192332010, 411054432, 45983697, 490260456, 32885878, 151314441, 917716540, 698282956, 793830518, 517798132, 460965753, 983932494, 498580454, 107947007, 805244756, 345752529, 640820768, 312390132, 637421190, 624997688, 348232709, 881717737, 655689389, 558888719, 108803181, 680005205, 958290122, 35430848, 154810298, 50913935, 673482416, 957576257, 251933100, 554071252, 911808168, 681613676, 475619855, 533346574, 375898915, 151280353, 910837467, 746962748, 479033356, 532555992, 378787269, 355358013, 354307829, 202677675, 120828704, 261594973, 100242646, 812072470, 173799874, 318018820, 262684682, 7428994, 829953410, 572639818, 42225077, 577591400, 600580719, 309140965, 29434495, 231278545, 800386894, 85076349, 260392746, 913638809, 281503511, 760737518, 82947074, 588302519, 704532324, 144218141, 821136332, 338948321, 574593811, 110662980, 79854448, 777571787, 601337931, 197704500, 793591853, 493528971, 118932189, 141860955, 270560588, 412476349, 751504071, 339378273, 225948334, 768012252, 537480309, 300628102, 583079528, 59602813, 964125903, 807325538, 929884429, 861655381, 581223080, 772786246, 219522270, 228306303, 804190865, 238340063, 680497881, 723520343, 329189555, 6653286, 699120163, 652259422, 778508989, 775077355, 61752366, 868518581, 575653386, 81537614, 25889354, 900896635, 568877587, 368904469, 212565930, 652805593, 306346165, 630340458, 593057355, 84922034, 539512943, 423124153, 860649672, 459071914, 683557407, 771530987, 903571065, 888962969, 139957119, 207912183, 584286337, 539249285, 8173261, 379488542, 636910679, 181677485, 351657914, 357329650, 155410767, 826844655, 17173378, 210175600, 410770621, 149683338, 732907425, 16218157, 723762631, 656801977, 714511165, 464387327, 756384914, 131905427, 676180491, 427867805, 510005358, 127986890, 185887467, 849920719, 787146518, 335575305, 770141981, 627751649, 910553596, 444022692, 787765469, 539914686, 978508140, 91233073, 585170568, 238542240, 287974514, 83074451, 50493939, 519110828, 860226156, 570069568, 662670184, 894322066, 619956238, 700685073, 545988366, 45217107, 345716173, 631687053, 509132162, 29269605, 93487723, 963816156, 32806917, 851624319, 570546417, 433495250, 819254875, 191732537, 736601340, 673561787, 750693626, 800307722, 477008176, 408173311, 551508623, 198340441, 397375350, 826046586, 339887718, 975083094, 522316569, 910501744, 585330649, 739567569, 301335311, 352486747, 874821001, 281131517, 225424850, 121843400, 598337252, 553235775, 372698384, 986141011, 40805192, 458397387, 137237050, 373651686, 706242111, 86582164, 76756560, 601666216, 152028110, 513253443, 325606670, 584130389, 392577505, 762969914, 707817963, 729289135, 605958717, 907141348, 89073496, 877502235, 244562788, 661806500, 919262204, 222322806, 202486983, 952140542, 796433890, 40687208, 846947266, 938615989, 995731442, 627877252, 548184374, 95962238, 511537875, 955859187, 854209718, 847027676, 149273552, 574809260, 544970464, 672308361, 69065477, 587948551, 919860021, 62787482, 125444187, 389852005, 223270410, 534028655, 379979485, 798343595, 679580165, 924194248, 951458345, 409657533, 640163287, 865241840, 784141136, 249242918, 532447920, 759287206, 128421670, 266543638, 936561330, 989656774, 306191184, 726730795, 682906193, 679306444, 730361002, 900371815, 782102872, 496939694, 201513191, 849261219, 906553409, 436252207, 305918212, 273475979, 450441159, 274123279, 642272998, 613061870, 388294494, 557020664, 538959298, 258498709, 998915226, 482559747, 223166142, 357147590, 350281719, 824741420, 870144580, 58445178, 134224052, 239949565, 866920276, 133831249, 323161849, 651216508, 997892692, 383579031, 642704141, 233610921, 675451402, 959222999, 312620607, 930854233, 546625937, 916254764, 404187097, 327406458, 446100069, 237148167, 473399512, 995679617, 640452434, 67018288, 62256223, 860223775, 263739533, 782052929, 902550621, 150118598, 241516013, 291161516, 337965486, 970559962, 190371502, 108642252, 74036454, 819507410, 743376428, 587381523, 910936462, 552931839, 97294953, 671417604, 329452263, 785832437, 742626328, 45752223, 261882806, 168169162, 788546888, 345417119, 267811869, 239312771, 763106672, 955243066, 365002105, 196883898, 431570124, 404478507, 843837277, 170208895, 413817479, 142447401, 920266130, 812219023, 240881509, 415302599, 150763079, 828223845, 627844347, 172915146, 567842313, 234008162, 829990751, 164430664, 120727732, 578025890, 687107019, 575336320, 560800201, 756074815, 813531301, 77505046, 306507372, 231987472, 379418951, 753861563, 642728078, 825884524, 69316310, 722645703, 170241124, 907963395, 851501861, 240586641, 337871262, 656508251, 342048793, 194910056, 615964271, 653112993, 365578991, 828039234, 233814035, 252268590, 624837556, 919634892, 477243120, 739369088, 885265560, 918171736, 661928266, 431708907, 374659550, 269930259, 608481340, 533205060, 879073447, 680216359, 394681585, 600231309, 270819585, 933125135, 43959404, 536003233, 816176769, 131825006, 789875416, 676694858, 894500991, 263157056, 181592029, 779717652, 205807335, 980800990, 384254989, 739098451, 673980228, 836195305, 392279244, 314213022, 91073455, 601863275, 787231762, 917527684, 78790182, 528138353, 832312422, 539772271, 445701168, 862269592, 996320424, 387653890, 55452807, 654053346, 600552852, 956430488, 342816999, 618165820, 527490861, 590932644, 395786506, 916307639, 631626035, 720640964, 889531613, 158860037, 882312746, 585417348, 159470960, 138263908, 386393489, 757651052, 975063392, 137995478, 901092752, 526617167, 571053378, 514989027, 515612473, 197566170, 799953352, 790999068, 802564829, 632957152, 386153231, 319163931, 240644117, 800214886, 758573626, 134939547, 742557492, 480468374, 747558641, 655138339, 437175368, 490620512, 2089424, 97149575, 476301806, 139458989, 170740180, 540349721, 103697038, 91830930, 448161974, 478364170, 361067241, 987577038, 886950366, 592545561, 45441196, 651948100, 304414825, 416827668, 948533756, 286315435, 635850958, 708209216, 788019552, 784950425, 758671900, 432880672, 512001283, 739514251, 807196488, 169627830, 267217665, 602247156, 334436557, 190440035, 403932714, 177102447, 864306911, 375910649, 269987983, 360224543, 254765644, 825209246, 607111966, 965374229, 540228659, 694255246, 745975760, 152319023, 606318515, 420945339, 789437640, 589895157, 577695081, 763557713, 764937042, 991503733, 426768106, 189645409, 786257824, 675157104, 915111798, 407342430, 656301763, 625490230, 970155290, 527411321, 319300633, 29153898, 625429262, 975253120, 879909276, 749990023, 527514999, 844671754, 418653148, 86451663, 180009160, 598830963, 131040243, 318576522, 48252208, 815070212, 899263350, 646569999, 511579547, 383903012, 620565946, 773726597, 833826401, 763215307, 553671899, 709685795, 690275167, 361753262, 707122194, 994507489, 37921652, 604399137, 66920141, 694265383, 931216336, 366095729, 340667070, 702537398, 957296593, 262271803, 836975186, 282870646, 813791555, 975217410, 974127072, 884845551, 271517711, 905402846, 441841183, 789807952, 574342343, 897922426, 34692536, 743248089, 169315777, 845738211, 212634113, 455296355, 105952982, 742140974, 971743070, 315934276, 627934469, 650398369, 186484195, 79208189, 674650312, 992144369, 194232873, 560667853, 427864000, 400865270, 57309263, 980195771, 287881131, 390367782, 928416943, 570047861, 398138728, 246122079, 844998200, 796827290, 240634467, 81788463, 324723834, 816374172, 545201489, 952740663, 101334178, 76755877, 794150490, 696618241, 769925395, 605813899, 30171152, 296545934, 584693426, 857391001, 829313952, 466883519, 876674853, 587019876, 709777531, 194731261, 238626144, 543523096, 865137225, 899245106, 337958866, 99571612, 517789322, 622235828, 528503715, 966450350, 566497511, 810970978, 255894531, 79126662, 964146257, 296061840, 506119039, 96170735, 856122119, 708936999, 367069160, 683204497, 926157156, 20131981, 970393540, 921972325, 658788214, 496563175, 73541435, 222890867, 357124135, 309766738, 637743203, 777205304, 251002949, 33155331, 884047006, 384703282, 265670518, 156901886, 478751424, 190005065, 650380317, 535400017, 124070770, 734929082, 570758179, 345679601, 47580678, 339985068, 18720894, 503394315, 909814414, 325210571, 253978995, 891415655, 383560048, 404762733, 161043801, 700286905, 88008107, 331599866, 203997931, 862073009, 552796659, 901182410, 706297897, 985722155, 978541128, 758852211, 776783938, 288734649, 725776856, 830043112, 517905834, 620259975, 596742389, 708722101, 976139845, 874182497, 907673455, 94374337, 569551034, 632796661, 728761319, 686646236, 378072633, 43550176, 427447416, 337953808, 150013489, 312116294, 608292626, 418488397, 797917921, 678098473, 828200504, 753549469, 140982102, 895228471, 279590668, 665312996, 511301729, 743152592, 768607746, 573831316, 99858566, 74534560, 73572775, 894098245, 151922242, 347563121, 742550742, 952509821, 816262670, 156535081, 560620706, 346665405, 837713685, 734553190, 351995312, 285459201, 978532401, 447258358, 86774433, 882403750, 937170514, 632858762, 476788898, 562051586, 977590833, 411022358, 668274530, 255580124, 576869062, 210883440, 575788084, 550124199, 587237858, 676061261, 175270536, 572921053, 753981907, 812647379, 950789104, 108670996, 470643041, 190743615, 541477191, 696505651, 881004743, 859356667, 388073612, 214288235, 176290183, 181885688, 100514940, 100236501, 830853456, 38478962, 936930843, 306661860, 335241553, 641793431, 468410272, 294248609, 337351441, 357773056, 38570984, 800109767, 875331156, 689023363, 93899297, 305970174, 107821816, 566136842, 323177464, 774903020, 530497031, 370788372, 136240963, 238162944, 281140914, 517183443, 553739492, 638374277, 173070397, 812892990, 366970302, 636182353, 958616724, 41529875, 221108014, 977060465, 968480733, 167249480, 777290103, 543208601, 763435051, 760021916, 948068431, 553991124, 976918170, 696254642, 293349144, 12953534, 326308362, 725508487, 341210756, 865690090, 73834437, 693265341, 648001949, 636703906, 972233092, 96025226, 250425846, 554192082, 354672093, 203085817, 254262255, 495078342, 936411471, 276669187, 855702506, 8698796, 976456527, 68527707, 120394602, 113013443, 890769616, 473083845, 359652518, 570413837, 221363315, 401808370, 527232211, 295390953, 692567264, 82189695, 852675601, 960105228, 806740793, 955904311, 769313710, 182081036, 727535324, 543748193, 961762721, 981676910, 223743100, 539629842, 199245614, 140928433, 760815673, 836847407, 256774728, 784952191, 222509738, 889914148, 138188435, 201338523, 778260444, 63964824, 73969256, 876970686, 457863242, 292460267, 662311677, 706533443, 814210182, 900735666, 552772438, 381657338, 503159913, 830645317, 377561985, 334447837, 162755539, 21808628, 97282831, 518089678, 115083865, 725040812, 129487184, 904330809, 248722195, 354623417, 591280158, 82128631, 649786932, 824504221, 633630652, 244884558, 24522758, 620379700, 67252027, 674596843, 279641969, 400783431, 713519289, 722403027, 286467359, 481135682, 742833159, 50945617, 243378478, 110409138, 51023440, 859834989, 900426712, 737535629, 579267276, 253058362, 565209141, 667727190, 722178295, 846181306, 218897956, 300101538, 324163161, 637700849, 438103725, 689078189, 842667089, 258668651, 81749485, 563015955, 191988613, 971378163, 487529313, 873763468, 208387373, 498371392, 728166169, 751188975, 140274636, 36714967, 488385078, 445964839, 949486319, 25534581, 719501365, 683308818, 406302617, 552159888, 986230260, 618803322, 154556536, 513546832, 304900541, 996823491, 327609837, 787256052, 836072943, 605328191, 689666327, 938336691, 740974797, 879342879, 406803454, 617498259, 889532755, 680980572, 735380926, 566211588, 907045701, 939534124, 430198562, 721705232, 772928575, 349720405, 223825796, 543759821, 30417158, 928647615, 395603266, 937323647, 415798261, 284904210, 200352533, 22096078, 809846920, 62115998, 281017503, 642381682, 284836468, 985045421, 813536452, 852244810, 485363216, 287365105, 19569683, 456056487, 734760868, 299783374, 542219320, 201280700, 719101667, 546583669, 319031360, 157942842, 930249576, 765985842, 271866817, 564073752, 179793569, 934886532, 40709316, 449090360, 61207331, 643433959, 155226115, 460957405, 837521790, 26945072, 470797984, 208996428, 372424537, 370256278, 831671662, 547922908, 272751400, 880033620, 573528003, 621025180, 510311076, 949654800, 919974512, 588005307, 27323744, 887962293, 613322064, 376569377, 806507202, 475434507, 327387704, 443297930, 622823088, 347226170, 867515179, 818419879, 153916161, 550855152, 375002380, 386343328, 585989858, 105340035, 913791526, 950522634, 425938159, 615724245, 537236515, 391457661, 457446570, 770814916, 266965382, 504372832, 779584603, 568139548, 189569251, 180878497, 219450796, 526079097, 413954073, 565647797, 576358131, 517140216, 480765212, 733460945, 572149661, 440630951, 18124023, 557677759, 599148422, 874698316, 947884294, 66908437, 430743112, 557528983, 923203991, 246089498, 692248281, 207471347, 763632291, 239327212, 397272123, 106777525, 112676449, 114444897, 337140442, 729235482, 762226828, 513692930, 170851671, 188073795, 438652131, 677349478, 855059283, 806805780, 293544941, 626356969, 881370527, 372060024, 494335631, 826766514, 921533312, 90442026, 791339087, 185187662, 916855889, 832451608, 760077203, 784502394, 111352992, 129948403, 28486218, 9060134, 970901499, 173753588, 552480208, 66484076, 847556997, 971085970, 234075862, 556745268, 844661601, 272153481, 500046370, 791501309, 319444793, 420355904, 557711360, 160338649, 36204665, 829885547, 888767182, 38727433, 462254538, 830282102, 940802197, 27016784, 819693453, 41754096, 145047551, 731988412, 924245595, 84752343, 328322053, 363301752, 298082007, 737196437, 568089176, 380124391, 746452043, 545949171, 171030375, 476068285, 736039223, 290837685, 135748921, 42710573, 830873849, 877776830, 247358777, 874797276, 147993236, 684730919, 740250731, 874554696, 242523205, 46130289, 745820588, 133363209, 950515552, 385719591, 659465808, 827075591, 1830294, 408421573, 544797515, 966342458, 206474112, 773361996, 342254764, 554625706, 312624846, 694020851, 911676684, 168354538, 859745780, 563106574, 571520522, 428317671, 472646639, 293197157, 489291530, 221960752, 368137940, 470868755, 900393808, 917613261, 65701893, 288771303, 270579414, 714896512, 287280412, 857684858, 480083447, 620900856, 781755052, 198736129, 950784807, 661006662, 303299179, 3217611, 654749538, 346897463, 222804155, 291126340, 485852225, 177460416, 224227268, 294679977, 705283169, 188851040, 862552185, 749016563, 931857894, 309911784, 460810443, 988258908, 463126756, 774509522, 1116619, 989135944, 21969956, 223553870, 184790457, 803661518, 637619215, 131905451, 264444662, 708124425, 132556457, 689705828, 534204705, 72932537, 882857369, 227488353, 23649483, 594567312, 450315619, 9692548, 935661999, 196122157, 986969810, 125045477, 629597990, 547689823, 276564803, 478599705, 691988503, 974792450, 253642997, 551531806, 899151814, 923910694, 606223051, 226808266, 566966152, 311550877, 760309358, 543939188, 538243091, 748024735, 658419532, 185303480, 345053157, 209197099, 77338409, 152944928, 72414022, 779353872, 203667680, 938197013, 781275279, 520798522, 144332689, 770655184, 444301683, 363798821, 476621567, 603868419, 707884798, 723481194, 561093949, 955594232, 863274813, 372626602, 860945446, 933744660, 802183265, 324110707, 255327491, 264096091, 820829677, 503014967, 624107371, 668064869, 947034363, 849974003, 411105670, 618100486, 141234965, 964826779, 336022401, 533414653, 233125977, 452480115, 607530442, 801340351, 494879628, 18169597, 982923890, 101196635, 762734919, 902034430, 647272087, 314344523, 57868109, 391534413, 157684956, 637654864, 631416657, 651366348, 432390123, 802435498, 567299719, 583443943, 78227106, 180416544, 429161782, 116663696, 471436249, 293255462, 517774056, 626558044, 130905778, 564709964, 554947879, 828663256, 992776885, 652542549, 686690528, 439534896, 387577347, 416324109, 358909277, 913917936, 225355337, 814909334, 533891842, 171254195, 741301399, 491209394, 2817078, 925979979, 543085984, 745764561, 138126396, 889245917, 46294909, 387150925, 176566854, 869542326, 72323805, 497303006, 345004789, 987241839, 271977419, 52363264, 489593729, 319638572, 469385131, 888410945, 673342651, 766226549, 707607686, 153031870, 337587085, 191863183, 549541454, 678115178, 9276961, 617955069, 556871768, 300072881, 337648063, 425653264, 42247263, 52162479, 220814991, 183027603, 980532094, 757163431, 573036174, 752910895, 652539960, 454116946, 817456835, 387878420, 71576510, 969927939, 62459835, 3164730, 789793431, 124394329, 590690482, 944646828, 891868724, 53921465, 814815529, 647688451, 442037512, 485777535, 616787574, 636056156, 236223476, 95846519, 147879880, 571077053, 809131556, 40202469, 928736271, 942613853, 208321529, 81850522, 883654211, 503694017, 524694347, 755140922, 460738520, 565418022, 72971137, 117658483, 996058755, 134688994, 211708148, 947670460, 460754603, 595571217, 669579229, 292267487, 445744723, 56255689, 580165540, 908931536, 364496669, 456189304, 995374863, 490015377, 351691468, 840688675, 501548567, 994159177, 271939597, 77770735, 563851330, 654802978, 284029832, 366128404, 235738322, 416583106, 694962629, 390182767, 831157395, 691028080, 519441329, 434613837, 547227953, 563457842, 564587759, 651339455, 439664298, 737591861, 593251604, 277332622, 618126382, 131346890, 66727706, 616939101, 706227062, 921730687, 719843229, 449603027, 64375775, 499813445, 553058979, 258434181, 597638074, 322721696, 887578089, 20265243, 355238964, 94653707, 181285506, 293298662, 925827656, 544069395, 344255584, 164532391, 464995753, 581986522, 477023583, 896995216, 338124305, 17250108, 124802337, 542157078, 229085157, 534748565, 691061373, 439882026, 868345134, 883335618, 429026505, 595199028, 783039902, 282963473, 93433760, 451882375, 892009641, 796620549, 933640472, 471872068, 833019088, 778112979, 856966773, 869865559, 149321267, 80864476, 822023070, 458483166, 644205030, 379126441, 505494479, 761659568, 799000748, 676302635, 38886555, 846492327, 495698567, 56946937, 950749482, 828797235, 452131391, 776398765, 572774696, 665789156, 973897970, 967718747, 551369917, 164131645, 456531570, 43741492, 598516466, 94006140, 888874588, 941330751, 265458389, 266380933, 838050643, 851214751, 379630608, 791257378, 75201099, 922062061, 830988871, 315033551, 418487435, 581663623, 479199914, 858855810, 457455134, 985866457, 916243759, 909858348, 307405913, 401526174, 527183066, 749761455, 479825355, 959015372, 61607262, 54373802, 14268071, 133322349, 492130682, 129725562, 343958426, 969979115, 900834380, 101751186, 806288881, 738640112, 235563769, 429636700, 860792401, 247861177, 367061959, 557768915, 550632277, 353652850, 480370628, 845995577, 677736311, 302941390, 718929130, 846792053, 452690964, 225170644, 57866512, 3531561, 14080349, 845313062, 321897895, 345250438, 534253573, 429646763, 986697370, 412144285, 235202491, 989602464, 370075657, 888550226, 638574071, 540642530, 124665524, 819168026, 358326040, 315737284, 814318929, 250231034, 772263979, 801314524, 965418959, 682272895, 906404433, 137904446, 487127889, 950840676, 920567066, 622190214, 909379533, 620474047, 209118214, 143639246, 288938416, 249775437, 190356893, 786486, 264924367, 889310420, 295283373, 369045710, 19414141, 695675958, 100061894, 721066429, 964051073, 894082423, 583461042, 724239388, 1914989, 616116309, 972495780, 239174622, 813764761, 541563351, 672680389, 645819539, 597891586, 347019434, 925969540, 530087960, 219847445, 965967641, 440833031, 338102621, 357474084, 486038538, 216899491, 75403799, 506997041, 337084913, 840581194, 197282354, 298972750, 171844336, 224154854, 516736225, 140936617, 620741307, 259095019, 101485768, 896822551, 176053768, 375019331, 57801727, 600448202, 992198426, 164514693, 105645705, 892960928, 840526527, 34651465, 44290590, 807999092, 410700413, 38544811, 346538866, 36429619, 315474469, 827309555, 571654010, 464020230, 334248863, 670382581, 299865040, 313581665, 535245653, 317907433, 894450211, 516580077, 280637582, 947794962, 180462898, 49654171, 352239699, 32611939, 15072046, 152456678, 758679147, 927555043, 575836385, 480412328, 325971548, 684815437, 423989486, 170831455, 49020151, 744729779, 469282442, 606811887, 115529077, 144820770, 101946863, 461758653, 442276930, 244043890, 702152552, 323028868, 986509448, 766978249, 181357683, 596040681, 201017491, 248250114, 178481308, 23736079, 919809498, 211866151, 742133822, 610804058, 68889644, 681746352, 889700631, 605550097, 656988139, 501416219, 668229499, 382293401, 131743576, 151838079, 647403299, 123583098, 105124363, 930774341, 81075807, 968516595, 997670275, 609083954, 100673630, 563834104, 845824466, 888111259, 716080342, 537853366, 964247597, 932715426, 865550441, 858470999, 895129650, 761294071, 2218130, 816275751, 275826059, 400367775, 557901584, 45064725, 444758449, 631364248, 310711530, 537126118, 13437816, 918916567, 626272778, 627515991, 275117044, 573058821, 782554833, 71556420, 403328053, 135297303, 251045457, 812150096, 66583929, 907011928, 264548155, 574003702, 67445150, 602817773, 852390025, 554742582, 168898044, 768331578, 630469404, 153668088, 892528011, 714360694, 710063234, 919446302, 258000773, 104382433, 697177333, 906062364, 975736569, 412912789, 853891279, 747833163, 5143295, 650181948, 359203980, 449121918, 442051657, 635268802, 34878491, 89935886, 303885461, 497465213, 135387779, 885135278, 559101398, 975400717, 731871875, 283883333, 559281154, 565897915, 376904338, 231136027, 552671440, 487863410, 501793107, 284989109, 561653945, 714049301, 454744164, 796559855, 534685285, 880832475, 199500337, 121329898, 954908945, 552667885, 713954553, 36747533, 275919588, 134096496, 300359194, 590654497, 550043470, 743815260, 811549766, 67933739, 452607989, 312383400, 630053357, 547970420, 221078276, 713237386, 335385194, 968141171, 417243969, 635737279, 225331487, 211573129, 7971443, 549498588, 945150035, 715340534, 812205416, 230149848, 761774872, 854233692, 576534501, 239154962, 74563328, 618889908, 657256981, 715501929, 507034538, 692165973, 223694941, 355042121, 945565645, 418535396, 952784852, 7172475, 521636303, 885612754, 802077547, 444136532, 537342586, 910742679, 21255342, 40484980, 947802698, 884615506, 520985672, 298579797, 558456415, 512035428, 608744536, 159165632, 850054179, 370550605, 660167191, 334433165, 691409343, 118173872, 708076386, 790880876, 431236342, 1058589, 23677393, 968550944, 550735528, 909864055, 714028751, 798999548, 497127503, 573210964, 570294281, 11253009, 659398257, 779407276, 5814338, 881045218, 674751266, 681384932, 540597117, 798558825, 821150652, 918550774, 488576640, 749064386, 620009621, 930537538, 3432825, 997975646, 931984291, 291717672, 976461322, 170091134, 161127223, 284637513, 200126779, 339715574, 223924716, 342979455, 412524082, 187991289, 169099270, 145236356, 263232779, 470868401, 925223964, 574812678, 353814020, 554982439, 528619145, 12237666, 632201860, 618840869, 174394587, 42743833, 775202616, 621242125, 385027645, 822223780, 867482608, 558508523, 155145383, 524123623, 891305305, 74027353, 494282292, 613193668, 763694902, 362415004, 138475513, 646858676, 457325332, 830299611, 850112580, 205439184, 551737495, 150238787, 393534132, 297824984, 746740777, 747992185, 712167071, 564275071, 416266807, 31369864, 403799699, 647517645, 579354501, 234200010, 834873585, 599774073, 6644281, 521301808, 590795294, 192431358, 374015049, 50532552, 524602368, 141827976, 327147273, 853092728, 925591328, 599338973, 493340644, 933551629, 598435407, 775814024, 94722160, 373443172, 481976862, 611847853, 823007163, 978119294, 40913497, 828786072, 929213506, 583554122, 17285831, 661535462, 104153862, 89424512, 408738005, 239695398, 700729297, 261188955, 175600603, 467882694, 6411338, 352457824, 919562098, 344097672, 457983435, 61305730, 868540465, 773615173, 608626123, 983826725, 148279986, 576131358, 131808538, 548698376, 205204512, 652038962, 105660110, 565642192, 206847676, 289098238, 787638929, 30219158, 520325951, 449172989, 592226886, 551948089, 126012694, 953889739, 57666906, 186512276, 363190597, 810051695, 158005764, 945864737, 563487910, 425396690, 553516501, 184907512, 215639470, 72029099, 291686509, 735315736, 883861095, 548065526, 30857853, 347928338, 644141088, 715083117, 692662340, 856273690, 963158926, 412412483, 790711574, 592143367, 134003252, 678203185, 665373270, 671557492, 474994642, 165879376, 509044179, 170185327, 389334753, 401175167, 725284518, 17539383, 957306510, 215631382, 185738037, 144717661, 680880770, 642050468, 556304436, 271523316, 679590625, 759834102, 79201066, 145489434, 461076601, 606758227, 443319694, 274925926, 76444803, 399512972, 859171802, 738666723, 696851160, 442353581, 679456934, 590581230, 60003401, 93082457, 129117856, 711083289, 502254984, 153532631, 958531173, 875956867, 817903901, 596061905, 929603500, 297335715, 850114610, 478046283, 294777687, 867801105, 60596404, 752041464, 794098974, 2153599, 438527862, 621970056, 373945814, 153954414, 536463, 138217055, 932786401, 583533015, 377006297, 4429635, 142675025, 138714497, 492036613, 585110618, 488597886, 188051352, 309654676, 55170659, 396364862, 634857823, 940229726, 117275997, 108168053, 149293797, 294008169, 988730350, 643339315, 984519622, 652341504, 698416952, 760436864, 88621376, 880059746, 11231372, 130077383, 848156587, 659300004, 114266373, 714349243, 354801735, 782516473, 704400566, 768377755, 655118981, 19289406, 588996582, 263487217, 756558799, 874657830, 119692873, 707689905, 240406969, 153021588, 521073788, 237728479, 979866636, 406961333, 354481866, 92325435, 647846749, 560020582, 904081131, 860117576, 304574098, 57722837, 930995306, 823810279, 255755073, 4741381, 357533296, 771380020, 478336253, 134910143, 79586311, 233941908, 534337232, 737039801, 78875324, 729476811, 194974529, 652256233, 165380491, 504378365, 445550547, 433484124, 622696365, 419067557, 701200527, 754345539, 617840022, 311873884, 373174615, 397421880, 183833212, 251880012, 153095739, 195971156, 880026111, 470574106, 601681365, 437606321, 984316705, 129382642, 738398259, 240941047, 763206276, 619065271, 425521435, 474073313, 59096661, 705659289, 577954554, 794350114, 263632117, 63523335, 814370557, 931145767, 193117963, 925510257, 400644955, 178530097, 873965612, 300169223, 215972488, 814083539, 309545607, 20949768, 608637436, 992558725, 719879763, 331279766, 192385107, 863928857, 829430747, 393888801, 230269863, 141931084, 229359081, 105220786, 609727100, 184370597, 719550787, 730938678, 116965215, 838024334, 21917922, 214073682, 530684778, 477814302, 621275932, 184713202, 713136354, 222310427, 124800725, 761122283, 813300432, 639972860, 156133617, 418904729, 482777589, 550221985, 252677095, 987856436, 775636796, 271849851, 512193683, 383978994, 503920462, 337542488, 399692665, 732141905, 543027280, 275330547, 863791471, 643505239, 109221830, 878992961, 742214879, 534905971, 630022129, 791006570, 284414333, 866374298, 348448619, 537274515, 80858101, 852013613, 988037892, 340010650, 96506143, 325751997, 804746283, 242552636, 245109164, 485920058, 294802167, 762833510, 119040328, 57878295, 129675056, 457987329, 768860747, 65375523, 164655884, 220357855, 341036131, 260134231, 80768168, 985299246, 891741160, 627706151, 627153111, 532708517, 745204953, 155416194, 28038136, 593191357, 510923006, 371899283, 780246686, 964641745, 153396922, 318699016, 624053741, 365891547, 242884522, 325235688, 585567408, 884145760, 464165583, 3769515, 528650688, 121914660, 631987725, 659723352, 230354845, 555568406, 596862738, 582391954, 795699738, 457961049, 967090755, 916797174, 32887197, 605890482, 513193337, 345174284, 933353984, 339064431, 409680678, 529184368, 819176615, 727895664, 498577511, 784548495, 961773142, 817769660, 509766243, 585472215, 451366097, 996986149, 196331320, 510384245, 158342276, 80286227, 470903856, 57927981, 836698522, 28972989, 655717400, 385393002, 696293792, 521808265, 508943948, 680212301, 622700927, 673641118, 913351309, 440569827, 933651901, 201988721, 196765587, 999537256, 92564056, 875398172, 531661025, 774133051, 800719982, 781891162, 115628471, 825882579, 467978218, 274900312, 971218476, 510940731, 811615813, 943921879, 158823678, 368231634, 340418095, 591541320, 137627360, 233342275, 236177914, 92222615, 384942945, 223063281, 484709062, 852412385, 622995829, 274406138, 157520525, 706411035, 162945310, 414639256, 441349191, 541996132, 864057121, 18638826, 20831795, 271836211, 499288595, 79418496, 802043548, 255023703, 659643135, 945800623, 208511496, 446843162, 987715499, 123419197, 845210167, 295361923, 459290105, 277421270, 125496247, 716830889, 238537374, 831365328, 458624030, 951703030, 561131649, 295934179, 965856427, 95859430, 628653827, 758405863, 930564025, 340281456, 567045479, 402222801, 432628881, 748159270, 48685496, 302328388, 953806793, 851029103, 210383835, 420539195, 787609132, 468246410, 250243782, 515450111, 625984253, 591848161, 44049603, 972457214, 799269904, 193966873, 152611777, 101518156, 902445233, 530617086, 91909130, 66347922, 856700834, 286567140, 884302938, 103700622, 745721152, 828098081, 156595187, 410482571, 708160251, 252561283, 492801002, 492693649, 362425575, 815973444, 333566659, 821913257, 358586484, 55514223, 666754055, 391573311, 969166524, 28931183, 763556840, 138477386, 370076881, 521613054, 774540339, 465810832, 939904137, 237116706, 315780128, 784067872, 827631549, 703741966, 37814950, 689713316, 237967922, 79036421, 554545263, 233755887, 997746119, 835346628, 919774411, 726558419, 216997150, 31936052, 777156636, 758433918, 141572566, 133612958, 48820965, 694844257, 19766600, 509351813, 565595086, 919834378, 11568847, 764118058, 496764644, 685233141, 733543924, 516126262, 990176809, 291061658, 450112965, 947861679, 158495082, 763062697, 963677785, 276666714, 869624250, 195991629, 783616832, 476280812, 843301812, 321427861, 363825834, 800649540, 521764114, 133465715, 158489189, 558327627, 272878969, 94403851, 496054058, 490616362, 891584176, 644615729, 497026216, 612365181, 94959313, 162551856, 122170384, 355931276, 36756603, 945382509, 978435345, 411395319, 730725014, 935617046, 698164911, 477492366, 673370979, 796312640, 956781493, 925805671, 747464929, 794452, 920175795, 90135206, 220908813, 233328107, 759780782, 888250211, 329098928, 880145765, 505702504, 345133883, 694842476, 173864505, 454333972, 306378104, 635696454, 775478012, 515804750, 310006847, 280192174, 212979957, 806258543, 388862893, 823490088, 427504016, 817149371, 30162247, 643858548, 122199169, 18742686, 739891811, 431908696, 599114072, 152633801, 820046123, 287822054, 728124581, 994308900, 276167066, 26209201, 431513021, 212816563, 837239791, 180986028, 826605587, 333095248, 20590790, 928580414, 958435667, 631390509, 827353888, 371955799, 109944854, 867308724, 431767623, 920369285, 479395374, 191038663, 387815774, 858972961, 430110399, 176215762, 517712848, 226353450, 829171544, 291271496, 191402855, 922029276, 608279737, 369820883, 11367061, 35288944, 232284869, 706219066, 614418628, 906101718, 14443122, 371788151, 121043548, 701904571, 245303116, 935699951, 131610952, 119653638, 870216007, 391390638, 56346986, 75975859, 158490966, 720344500, 905537309, 786129951, 300985733, 973064684, 489254656, 490440006, 254817795, 968680833, 452998641, 20882734, 24829930, 715747923, 984517305, 356049004, 549639420, 741158957, 480066163, 74400815, 298280952, 338498841, 582854497, 870464317, 300996032, 403490063, 319601822, 726177251, 183195073, 561327791, 917272788, 782389267, 41601126, 16230152, 559764428, 184119888, 445061090, 691161237, 363601444, 50120651, 49773196, 742665008, 82850987, 437428046, 318748662, 172461487, 559426972, 451872757, 963969323, 937701093, 702757585, 442333176, 654767796, 241730731, 343709664, 647440692, 557664856, 643535173, 652290069, 69608579, 152109110, 294985796, 807619481, 501258975, 143305423, 592084889, 161025374, 759283469, 539679328, 125618921, 791796093, 467208078, 487127133, 178259496, 864413222, 275960803, 572250996, 414073841, 566050809, 180956315, 100093977, 11572400, 478260880, 494392454, 782965137, 78483505, 408666331, 270135652, 529287128, 705589506, 394733162, 758544711, 840660052, 844742468, 909509468, 268211643, 296672748, 475972563, 802210783, 587796474, 458380141, 652319375, 892994036, 194792484, 263590836, 716420611, 44884937, 459851782, 146850583, 621545909, 464266980, 713539591, 45381618, 810981434, 255321060, 268163886, 81308837, 763052632, 340954630, 644825085, 757306019, 697969723, 244297455, 968988983, 665679553, 695126345, 16530013, 671396198, 213872387, 983897203, 986320957, 232074730, 335363528, 652074150, 460803790, 36084807, 416033625, 529757802, 565563947, 607633676, 846387518, 596225376, 494707799, 406128534, 895188244, 549737602, 933807101, 505280528, 701190716, 27437796, 380920860, 248872242, 999295538, 233619602, 843216865, 723663717, 668674269, 300669816, 41251695, 34153622, 114522169, 490546774, 617433563, 896416828, 276889312, 468964308, 21662404, 873286372, 734725227, 338746203, 137905231, 678883298, 527654000, 421887948, 14504039, 865659408, 805535985, 888217605, 179677267, 521418068, 134582002, 502778963, 9100286, 686058390, 900745715, 737603488, 556503913, 778796373, 353756795, 864228656, 212892440, 757160323, 643433304, 71561130, 365649711, 227808324, 452385343, 549400087, 36218802, 984853542, 700188178, 972971078, 380968548, 155848179, 251548804, 189992778, 33234887, 589064241, 510649476, 143288742, 39201626, 420456775, 244230617, 663881615, 127189080, 595933687, 59992778, 852072976, 136913044, 683439043, 839530747, 968013490, 288861843, 211234482, 428790291, 19093016, 956479035, 124731750, 410677488, 602114922, 419316056, 441989859, 590122383, 219628632, 954186584, 682880801, 327246153, 489613005, 602089772, 690393626, 245361600, 797927024, 705293869, 116336275, 139108085, 911914142, 453474257, 770994866, 69002458, 353869608, 996055937, 59601918, 815825317, 991380052, 114638395, 308811168, 437092455, 835839405, 906535847, 494388749, 294268607, 216786108, 579412877, 126396668, 877581643, 126103695, 200593980, 819899928, 364559730, 538791823, 686337448, 355026119, 877226188, 466405623, 242006897, 452374498, 226888994, 95708062, 886727353, 931669624, 187331175, 214841982, 549997598, 520635597, 459244428, 184618530, 994147003, 587168776, 250433614, 325777894, 142022480, 863459841, 889207746, 833888825, 835274766, 533971241, 170944976, 902684642, 798382713, 24172780, 258329728, 991015470, 522608304, 333845115, 64191463, 842651330, 370879139, 434261971, 553252955, 13360570, 233045246, 612690590, 911496531, 26080179, 759006721, 436288100, 502119082, 794458309, 902599682, 728951204, 374471450, 874153795, 576791507, 310270064, 516491187, 847268892, 464767033, 9215489, 318438889, 131781390, 769785465, 224852664, 232435464, 222582801, 214026857, 229166114, 252997124, 744314781, 257570382, 796566035, 986190704, 94628998, 117141557, 973843323, 542403550, 982586731, 597532410, 261374348, 35971259, 520107511, 560448777, 14251106, 692719422, 208201172, 180100648, 44316308, 739709634, 227617245, 23758294, 923475731, 785767974, 555071390, 620592136, 410613511, 794794368, 411953489, 488208052, 594026131, 661520164, 815957111, 793727937, 255421470, 399300064, 368985312, 763527290, 928057205, 311739506, 530504635, 784633401, 318498352, 241399755, 142772989, 930702682, 582239629, 858525114, 577484332, 496597943, 819362774, 844039129, 316059127, 115143304, 308056662, 539522410, 717476372, 68691619, 274891983, 931481679, 512529963, 38637644, 232506458, 249386111, 774515210, 418541112, 842156591, 604153802, 42254798, 671276265, 35076045, 228551823, 240525753, 918340576, 363149548, 209705414, 216455526, 756614764, 518335688, 819697354, 154390698, 599860480, 494655227, 95646731, 325040211, 196251959, 485053756, 719268837, 294613934, 249094782, 40491242, 716026397, 512380211, 103495343, 370520064, 629105990, 81267864, 678304325, 139305336, 653366863, 367726512, 709527745, 981405530, 3541811, 199676930, 923890385, 912422341, 892578020, 580238508, 523080643, 745028668, 248510486, 516243238, 264199661, 519310857, 217413558, 8362366, 282116569, 895326421, 92845028, 464144229, 409202600, 635739373, 233518361, 906477239, 573171759, 624341347, 603378595, 169124928, 234163319, 739712758, 306075022, 567147555, 760131906, 291694773, 66051721, 700550407, 556822526, 85190593, 205587598, 755964224, 316944277, 855906613, 114575392, 741140102, 41554685, 684883827, 418526566, 628662569, 615178354, 499880346, 406665804, 707006934, 704433882, 881046308, 885045227, 68155169, 403634710, 905098778, 878265460, 569298727, 402188938, 812072745, 904080202, 526862365, 52964287, 917762678, 155119979, 638308518, 84804294, 988277978, 304255892, 426670079, 979539126, 377966259, 115988059, 850811668, 439075870, 205147655, 217653538, 309722954, 911967412, 341138495, 634494624, 762935194, 129110736, 945757839, 899669053, 134398806, 99361082, 553124132, 553324851, 844332639, 832259597, 620846581, 990346480, 5977070, 244509292, 836314625, 527550740, 309379419, 99338836, 397469651, 11572951, 558482501, 229462651, 241701117, 354665803, 415637051, 873039328, 386037257, 862612384, 271460901, 593212298, 557736465, 639618402, 728079915, 673379092, 71769585, 710306920, 382725672, 695175421, 651689056, 172425750, 974019613, 843340407, 495648694, 555542713, 995065220, 236200917, 874643262, 430201662, 126565659, 185472443, 813145275, 236266796, 103488168, 571551141, 320521433, 739317367, 144958312, 19526796, 423493170, 41405784, 810585189, 181688483, 612595862, 615514705, 131918885, 937046790, 819843518, 379116491, 883152670, 815918563, 23839256, 752497753, 831985227, 46040439, 491569036, 143767621, 507726966, 102393547, 720976750, 696891818, 834878194, 2152190, 473609765, 895799678, 3319163, 283817086, 625417067, 365175446, 681747499, 453438308, 30011456, 263964697, 876505987, 11211526, 705328072, 638177717, 697648142, 17409667, 686108671, 441496366, 767259605, 522780450, 219991699, 214421143, 159257488, 394249592, 399254188, 737008371, 154994159, 428882613, 412651224, 689772876, 856506824, 256639840, 133117149, 889352642, 187471549, 757839079, 764425200, 160217610, 178545923, 17343617, 80542669, 184368078, 45378398, 325663614, 885187000, 211447683, 969330901, 267994102, 963364972, 75522947, 946333296, 329184151, 994351425, 68314547, 390631063, 570647063, 912274562, 237804609, 963867493, 29873969, 820685611, 292327818, 544788420, 742263052, 17157389, 18135957, 857904857, 351854830, 119892252, 525898188, 367116187, 369539915, 528883356, 77906497, 821403469, 334025509, 117158393, 790217038, 105025830, 280569637, 681616379, 690180885, 23052552, 266157592, 196534935, 674193307, 585333626, 724359109, 437246621, 390496661, 775769723, 526921062, 10500666, 734551286, 550464303, 197898056, 453590481, 223093881, 291130693, 973132050, 836226685, 383136885, 7181814, 148727288, 375692114, 714727927, 364153778, 595204731, 701616688, 925999369, 861436837, 735657726, 932274621, 629862618, 888065883, 369649953, 139779326, 696627941, 768008403, 942229990, 908651950, 901654700, 648919153, 369790409, 364735801, 615086698, 519633920, 231350591, 849484942, 446859557, 64225921, 696289371, 179368037, 269139095, 954505848, 862116872, 191600094, 616652777, 522541468, 322750218, 249193301, 660691339, 862832220, 920309312, 650332562, 408957238, 382857843, 107979925, 156363192, 163562757, 77994345, 583462803, 166123998, 184735896, 65477283, 719605741, 58892761, 106862412, 892692542, 997548195, 882949407, 435534635, 188308422, 940359491, 628698250, 427528490, 946936083, 674790559, 627296065, 131961776, 850943292, 737666236, 147596583, 253847425, 421643413, 15422040, 964695210, 432227430, 373754092, 432393882, 362412599, 166889586, 536384861, 412175334, 720964338, 500658035, 528397738, 700156880, 637681153, 460452272, 891938183, 302817104, 737581457, 701343036, 958526316, 997415861, 527227377, 944491136, 424830536, 625518888, 611944934, 15171450, 55592169, 630242797, 724503360, 867434006, 122406471, 730172176, 716015220, 925097045, 75961844, 281524045, 592573520, 179240837, 655136820, 484569439, 691382858, 9845930, 617743948, 598395662, 757800764, 940562993, 259396674, 291504314, 772916725, 17778963, 811225979, 63542759, 114846721, 87697009, 519250164, 747408974, 929532571, 415793328, 150955703, 152313815, 52898696, 457747796, 653482795, 750006582, 151337342, 300691404, 645818355, 580803551, 386365070, 975452915, 195014943, 814774481, 335986760, 540709531, 315263951, 940764327, 593520305, 537918392, 22838171, 312471660, 326244952, 25319845, 213832568, 739071686, 681328681, 793295205, 974073132, 359462364, 669822944, 375057976, 594125718, 246577037, 996058158, 145018362, 55020506, 436678158, 590424839, 377157681, 27903139, 132777948, 571729904, 416183559, 629435004, 640882630, 711292081, 162132177, 505274924, 710905219, 330491297, 584992304, 541280971, 908019177, 120799828, 134570939, 200958406, 867374428, 869766413, 566596479, 52550806, 585266250, 135102040, 12194332, 445294592, 417129568, 31771301, 747022032, 252028170, 951589479, 63019342, 378521554, 192007893, 974987583, 138648855, 419490715, 586734955, 336118898, 299707490, 914868936, 925582141, 114507166, 238954630, 86080216, 825146953, 248694156, 336102159, 257074856, 965305283, 848068937, 601652813, 772372976, 427616941, 607853500, 886579847, 443577194, 743948512, 702170985, 599014862, 279476518, 796943162, 647249306, 835934583, 149198026, 602231587, 942787301, 318848764, 198700218, 859085658, 197492471, 691452220, 783447461, 925050117, 892286640, 914681180, 26042704, 446575042, 421523687, 788325816, 706974602, 53173196, 179594970, 832683503, 407305963, 286956568, 354878883, 751001150, 557167292, 510906602, 297393876, 232537904, 530043156, 626984015, 446758869, 952419177, 731740254, 15812589, 411474041, 839813166, 969358295, 599162268, 308080022, 932165814, 809228800, 37732034, 68623802, 255959826, 874366098, 112888397, 9766933, 495423522, 92101955, 285331491, 481497754, 841186826, 359662234, 743954931, 596521684, 177954285, 146881852, 11677982, 219419518, 420511713, 67428004, 627769780, 716907755, 770292545, 579739605, 502247489, 437527841, 834075498, 374211460, 447080761, 658039498, 407724038, 923302526, 581974001, 878586728, 14114607, 845861206, 195135982, 607583622, 932526293, 793123338, 780857018, 369075667, 167913893, 259325140, 523279024, 997860554, 158952679, 468209454, 3023248, 993446409, 664829278, 250788741, 265195070, 352737207, 530369812, 117735150, 752406672, 834869470, 672274975, 894947078, 987016690, 129440013, 888229190, 416404262, 316164147, 640552534, 43395972, 986424747, 33103560, 248752423, 490387749, 367109747, 152067662, 298919073, 957446339, 337324069, 785121013, 619919612, 495683501, 990889330, 604315151, 915675726, 35226098, 466172734, 563745424, 625638951, 434038452, 998839041, 964293881, 998770292, 168383190, 763936413, 81032113, 402429879, 292659275, 698325924, 404616028, 880351338, 728680192, 269243067, 722800090, 395042031, 951577994, 913460223, 16327555, 241639050, 369044089, 337032024, 841809080, 506706876, 419255846, 915382657, 265022210, 929245006, 227886884, 155916718, 215412190, 85984439, 905013969, 685403530, 204593221, 132894934, 68275631, 746643367, 408963234, 355994699, 454177888, 686268322, 998398079, 439732989, 34417590, 677494433, 588174518, 203077267, 206701748, 359741598, 40065003, 671729734, 689100093, 598784876, 370639199, 390299919, 571177464, 134634760, 214208349, 269592619, 435206256, 535895468, 559923855, 17417985, 533836268, 693832384, 420661259, 256328868, 532208743, 174439576, 161521148, 288661678, 958748654, 220615837, 695118238, 866037609, 47900223, 873905721, 197206396, 209332885, 146128738, 827742661, 864216331, 268360391, 558701448, 958923307, 210712552, 330388158, 558394605, 577673282, 113067492, 562487918, 392353958, 752570380, 521665325, 614720911, 126025432, 948879955, 533516643, 73562532, 547241510, 593878563, 520358701, 210918674, 172086583, 94382972, 352275147, 885335331, 715819954, 327545163, 524515744, 687743934, 585202808, 671382818, 368607550, 862032770, 787431455, 214746922, 633848309, 390383828, 558412921, 897094185, 228048226, 254664188, 324624478, 432751363, 789864834, 914629488, 403508951, 563322274, 472221136, 717308658, 355263621, 794439372, 733537559, 226079081, 219047195, 800319070, 582503014, 496455052, 713686957, 577014129, 441698464, 964036190, 747337761, 785609653, 600572765, 913835388, 292997704, 762643266, 425452988, 353004653, 982883944, 338822888, 656078404, 477779853, 493833796, 11742010, 401903953, 719333439, 178507187, 162926995, 23987249, 553664507, 133797812, 239399747, 126006866, 287104561, 198973097, 237445142, 818762858, 634681743, 827193183, 848557552, 844030886, 271392599, 239326383, 540869818, 859044931, 662194819, 997568746, 961215315, 82331805, 451438477, 289645114, 292378081, 645097938, 180419323, 208163615, 988194291, 120799397, 365048767, 267371626, 136123684, 976656463, 205953631, 100642656, 75779758, 21791801, 86718246, 67005202, 831653307, 574006847, 133159332, 418279589, 709283325, 455814867, 930799122, 308944012, 251375318, 232010442, 997126507, 891450451, 86992659, 477543346, 776104886, 975683493, 580054019, 263567021, 155383561, 335337910, 488600473, 48554386, 727656815, 972965469, 578559714, 540981569, 580296339, 416051410, 482746541, 215312417, 660829354, 919207337, 924392720, 418852844, 798961430, 244375426, 396342624, 874837977, 93296655, 760394595, 203309801, 572217849, 537160975, 757167074, 119492224, 403897227, 616396266, 143581252, 428576978, 677561992, 97661621, 310450781, 805236403, 760106793, 212334383, 668099364, 443455743, 711672043, 635968460, 279305582, 589966928, 953003882, 633684265, 536539822, 348325495, 908248951, 138065809, 20975129, 563955767, 424372959, 406491454, 134720593, 762029436, 162152491, 97783502, 113514820, 780092462, 34280626, 591008108, 915061516, 510797640, 209728415, 829360852, 921386966, 309265959, 680447888, 619786607, 342747969, 744773325, 92691102, 604413468, 1295502, 982157992, 233057285, 747539998, 613514817, 175971477, 935358371, 64395996, 839418003, 517249199, 175999816, 783274223, 323178782, 875772068, 335162013, 720239642, 255436828, 245851599, 350699042, 777809988, 787183669, 257605246, 652684278, 390518558, 848512457, 911595445, 177629889, 652217526, 402205140, 385390782, 386771395, 686574916, 186164687, 194074859, 591091423, 27692445, 522110212, 468091684, 6746365, 955444959, 863629756, 55810721, 762298430, 675004011, 729942594, 763249170, 890763497, 389325682, 91035729, 112077872, 986892480, 476780094, 423272438, 154092220, 964811364, 277864448, 840354422, 992609265, 428685394, 263077398, 689791638, 498554917, 139845946, 687795821, 987275180, 688529471, 308605770, 735470419, 570573593, 845163894, 533400470, 21223568, 540792446, 715078445, 535352414, 168430668, 764114744, 123458098, 719754742, 891524880, 624828129, 808770274, 79074584, 857047485, 624366687, 67825946, 18937177, 770755087, 8011097, 744356521, 165429722, 459148877, 936127693, 459033117, 159900545, 577118709, 74311691, 573178503, 548714296, 236752563, 629912730, 658227726, 508428182, 306415175, 530759290, 778524971, 780146885, 251412151, 507867747, 325133741, 913918051, 922606081, 332413135, 63471907, 244003854, 679629137, 199012067, 13379857, 477576190, 27088753, 446849193, 368003578, 15919748, 824787801, 280484281, 66582169, 863297098, 475515581, 73293435, 141170677, 845706355, 522250350, 616561564, 791014892, 269199865, 506428049, 715803907, 293480702, 165646604, 343439861, 177378182, 877832942, 441796626, 391983244, 887833669, 791097718, 31619606, 92017760, 936685207, 620851548, 381719790, 469465423, 254443253, 417109116, 133691284, 302365324, 695885021, 14017378, 622621460, 611585855, 143372075, 82305640, 864413490, 921071623, 300869117, 625816268, 778900316, 751885021, 698272201, 730806592, 416898639, 430397684, 269851469, 231359452, 665085634, 714755584, 924511667, 46507477, 981447148, 950824249, 112616509, 788069825, 525858964, 888689984, 130079685, 669508474, 619476685, 386757622, 748962368, 521847999, 238200829, 602172167, 818962491, 122844285, 181821748, 336175606, 320573688, 486618345, 49445279, 379874953, 920678658, 428768504, 674347108, 215410804, 440798202, 422528739, 252297066, 453597790, 858235180, 956425309, 211359521, 363573962, 133478242, 800768039, 744974922, 134462403, 818907548, 915427961, 75226234, 967997679, 251650284, 543084235, 194233131, 205322861, 907894001, 677715493, 403244707, 461097450, 814760338, 392121572, 796041535, 220891624, 855425788, 459835902, 92863913, 28326087, 277751005, 451548848, 95848151, 823550659, 522861457, 7193274, 347173983, 869978060, 136048108, 568934799, 468876017, 436139904, 234240073, 791974584, 95281353, 883492083, 709604247, 357975151, 364120158, 861938072, 15018913, 533443826, 56306738, 983088720, 658131457, 413698484, 697257313, 954588111, 327678726, 407205040, 386442484, 683079995, 899705636, 556202414, 70463102, 361946124, 300383900, 57338678, 716297082, 219086432, 633406016, 879146257, 197881389, 574234071, 654392, 562647030, 854680055, 382862755, 624715747, 7692827, 110521009, 404708424, 864100911, 403698720, 209867075, 926563438, 142150795, 695658386, 685186205, 500539476, 698409898, 165615657, 196498193, 159382934, 608764768, 107462, 116015883, 52413891, 177717906, 721807854, 634712018, 189554546, 179021768, 686805208, 467597624, 212401765, 572260007, 486986470, 916172895, 395999737, 545041294, 462427582, 138393183, 855039187, 937808747, 992519499, 452495589, 592178462, 957143291, 428048633, 477513195, 297830314, 219836107, 948477847, 613356012, 681896030, 328545297, 421520203, 11990520, 473670096, 403540815, 880848267, 624723894, 730779739, 466940000, 849020912, 670458273, 286629595, 45091916, 954369972, 737368047, 202900574, 406091298, 922783088, 375276151, 315586554, 823640250, 949382252, 689917876, 944043222, 29106249, 946462581, 396367629, 718749526, 811982022, 792695388, 443496455, 260033980, 695057508, 586676457, 817164685, 332897834, 799479558, 636451790, 734199125, 289302828, 153051862, 185204088, 109827435, 884970905, 301245836, 592261854, 67224028, 135465015, 345688787, 755675446, 222669481, 41233680, 320113511, 531681277, 928959970, 375095012, 917266578, 634855014, 361460090, 334431130, 758391883, 511639107, 2323747, 776219147, 295873328, 715517036, 95185837, 268383229, 919931474, 939579146, 68372971, 848585193, 653397615, 290639193, 548529736, 112575341, 43679483, 954087751, 77507798, 30973272, 274713502, 810827381, 697042928, 48911943, 537471488, 361777972, 568987958, 370726412, 657254911, 665302203, 327087415, 342692967, 192865957, 103341706, 467776927, 81746030, 611575698, 643458263, 445550321, 634947844, 974677100, 598842821, 339796300, 425987443, 425078600, 464484732, 404073627, 350495201, 170758771, 774137337, 481092504, 271822809, 375712262, 686313634, 809393544, 687318675, 495015798, 275921503, 412054906, 5137037, 933659927, 547877143, 616198270, 525373482, 825058280, 697011729, 87132317, 835030546, 412343518, 911251774, 946696889, 26668839, 144978954, 957873326, 325771946, 596542002, 427619218, 172104867, 466402437, 918696601, 75258529, 615142100, 96700239, 307820834, 236934696, 430271287, 132613256, 764857400, 6352073, 467585791, 252879765, 928960386, 776376970, 606742638, 354182151, 192018393, 730349631, 758968638, 269223474, 221905810, 369556340, 270707704, 303779258, 254941225, 248622752, 254074140, 381469271, 597096023, 679427439, 969387453, 94164776, 823916565, 172660267, 865982645, 128536572, 768054316, 878405902, 853541453, 112601454, 29115201, 441962631, 124553132, 484681841, 12560692, 42894011, 464177619, 911990554, 374291339, 415122876, 109720851, 630923390, 416403523, 413072314, 467326433, 180398315, 983415176, 719461178, 670692118, 811328890, 190406729, 333099970, 15987104, 557738602, 536972419, 848907831, 183924413, 413810569, 108179358, 45354998, 615734850, 628560061, 885381797, 520900455, 418904321, 71935894, 788867767, 286799013, 634427749, 285837776, 728468737, 760462914, 504222229, 239195076, 236776768, 4887089, 701511767, 138712035, 273070301, 627681297, 66499297, 480642447, 993887545, 696037261, 802996622, 470071124, 329940718, 510288296, 637452433, 372924444, 919032137, 532819328, 692507642, 36316716, 617970103, 788767811, 303100032, 107050790, 85963611, 376724189, 99305665, 791898185, 533249435, 894255675, 258163775, 281466021, 72789756, 779938867, 488234490, 514469810, 69475482, 868615611, 484963470, 622979690, 558155878, 929180179, 137629071, 109081580, 355772175, 109326154, 951639474, 464626756, 975827054, 436997846, 487556585, 271618212, 476171927, 147587997, 423538650, 853244949, 528797883, 521922114, 273296850, 949615656, 920169361, 297601848, 733937694, 418408128, 387334127, 625332480, 73035342, 602350843, 378906325, 268733356, 422316958, 108445096, 69369561, 445125881, 357457095, 153336387, 154277923, 265937247, 135212608, 533926087, 437101159, 874981139, 376480076, 179284685, 468243412, 218975691, 108574368, 736226715, 292240386, 24119466, 801551758, 348735299, 981961003, 234430192, 627669899, 586060148, 110255154, 869571364, 449949288, 639953756, 282704697, 560580249, 594358612, 882553051, 968153459, 760838202, 617368777, 113595553, 727879110, 399119127, 332768436, 600686146, 405306592, 663744844, 185954282, 781266678, 48225121, 224581368, 996780087, 474852361, 972217620, 612513834, 843725482, 271893654, 232096883, 280373950, 901154783, 707306272, 289211126, 384456547, 246149508, 697996145, 538885496, 469891575, 202030602, 311197069, 873295938, 58862645, 445682018, 593144029, 990763441, 942996125, 16216540, 294577770, 379668997, 380773024, 472230159, 172161636, 75288789, 145007522, 811869861, 744167855, 38207161, 550125706, 860360402, 600995546, 158506847, 777220949, 486515070, 732334144, 836945344, 10717922, 661552709, 744791072, 43344462, 723588638, 108581963, 919707851, 106098997, 853816759, 491546486, 292312290, 334498271, 917724926, 382441542, 306311233, 277475107, 119679612, 435429966, 168125047, 421034088, 580166425, 465194001, 633053146, 646742145, 492683891, 835085672, 796698788, 84211526, 391984654, 937177270, 369259611, 113304625, 652788925, 807479277, 65421222, 935596525, 484745811, 705528854, 127880047, 154895594, 541155890, 455231172, 116289247, 654037434, 14889026, 415393715, 9031855, 683689622, 475543424, 821060279, 708803095, 532086423, 87420640, 677669438, 238921740, 276301146, 376225331, 80241787, 114006359, 911477370, 583529827, 943590978, 877472331, 982733964, 987137821, 198419422, 990355745, 904191198, 859071920, 664048513, 832974573, 762453127, 756830294, 30775798, 573941962, 349441171, 845663472, 33737979, 996517837, 12651724, 306880987, 328550337, 112465908, 211031705, 671633983, 507689225, 511816248, 868644377, 789086169, 235724735, 536465903, 50825074, 584804252, 517515583, 352121932, 475476835, 309247960, 633696852, 967665913, 931529146, 495648649, 349841328, 508051731, 307159120, 218827568, 193960676, 514518349, 766564289, 862087883, 596773468, 464105309, 92483349, 81776767, 702809413, 692778581, 168947426, 120881714, 328341923, 459593358, 260165928, 527725206, 435245506, 454293904, 305048913, 229190486, 144728466, 48340503, 710929205, 279201252, 288169784, 954056835, 725226715, 834360848, 800062820, 111080179, 662611237, 902347566, 357921213, 921201308, 835134071, 603700217, 684902751, 541386840, 295107142, 802914885, 658309236, 434545316, 138520838, 335062152, 874092604, 162968203, 642439114, 656013193, 47101315, 391094682, 902321173, 796723135, 396386176, 210301942, 854636613, 44963753, 148590329, 439338055, 248053506, 814549271, 569545183, 160652600, 891995748, 199035641, 411906535, 880727583, 26327659, 257848979, 141557545, 320991968, 888591071, 935257270, 943538597, 492884931, 8755659, 545565866, 177768138, 883219317, 347445929, 843583144, 27086419, 325318565, 630242713, 766670487, 709954763, 12080409, 504091481, 266972333, 580104996, 363249095, 302410259, 437800670, 130986815, 749779933, 645785145, 347844161, 702910606, 854542081, 96442027, 761276177, 852902139, 432726944, 664766563, 446015198, 592019468, 340160136, 823360843, 580246948, 182041920, 193876766, 191619147, 716100030, 491746555, 934675508, 498935250, 202656432, 218715895, 190968384, 192574687, 937302426, 705417734, 189902245, 783676623, 908590605, 356677951, 905429413, 714458197, 770439685, 96770742, 224694168, 102059001, 586811903, 399392184, 694483641, 443306883, 245769723, 697407374, 120930233, 73461744, 38938021, 274663438, 496642645, 480836463, 717031575, 491902759, 282461083, 374083676, 572209617, 71234615, 156349718, 565248514, 924843766, 921961696, 162555017, 848227547, 932255277, 961341018, 324025144, 706050148, 614042727, 912215782, 565960210, 638584424, 163968260, 600692537, 498977693, 19834892, 849748773, 259419742, 873062735, 287215949, 317805562, 715201699, 190604445, 906310978, 627866651, 290052742, 188045295, 222310378, 452673769, 434419135, 990651849, 741140257, 917923335, 258402912, 604850696, 954819095, 268801271, 840108724, 577640506, 570237992, 161635529, 685660583, 684150063, 32615786, 982638607, 915325707, 197703355, 716732301, 263383401, 901226328, 137502818, 137240601, 123665010, 693735385, 557374337, 718696265, 578566671, 583810161, 290572054, 800325055, 767000643, 822059093, 372619769, 496056622, 5668779, 192803924, 18057278, 160511574, 916391914, 642315649, 454093251, 913626307, 243792234, 145846553, 717992323, 664897845, 683039583, 497299748, 547064119, 416994037, 336115882, 689307767, 328128142, 392009096, 801351277, 323521474, 862500215, 227814432, 944847054, 139636701, 103257418, 821563840, 787854508, 703842652, 370138660, 659902211, 925388127, 71399461, 184290257, 244215995, 109303598, 717167913, 196775774, 802666899, 546652115, 940036048, 523854251, 142739308, 756323190, 43207777, 674318570, 476534900, 970869835, 643151099, 902619550, 533371998, 659689940, 773710074, 753327502, 407582158, 772609496, 801251725, 212354481, 335407995, 898616217, 796907631, 231713425, 112298244, 449023182, 463411204, 279745093, 432187501, 667414851, 103760987, 12328873, 696240149, 154358885, 104626182, 703684341, 312567061, 88408054, 318719937, 998475072, 49174570, 791838691, 563789044, 888779751, 317930055, 340867104, 258324955, 972725758, 6302358, 620658978, 462753300, 572103490, 741052816, 495383937, 842235194, 690433215, 525906131, 19579077, 770398831, 212202055, 96045876, 163480326, 681254310, 125754747, 795045720, 772733337, 767063689, 383402050, 234515462, 461251934, 67532573, 526986258, 762147602, 913176595, 386182647, 810776255, 509084674, 745439368, 514783019, 63798716, 125577156, 958887089, 734107027, 621361788, 152435799, 123652864, 801968258, 146491730, 676556132, 72563186, 805536995, 221652162, 359727625, 942809752, 456183233, 711278647, 851762103, 199802787, 863013140, 234940724, 39853994, 740264064, 809980216, 538860614, 720702835, 957697028, 881964359, 32236617, 539016018, 351926533, 358550033, 989192249, 372039051, 728544090, 175941895, 682383325, 971147305, 703085598, 167493247, 896912047, 883224290, 301042464, 838070673, 638586829, 591285869, 303997139, 75816443, 885623763, 623513107, 96304956, 141918987, 710801429, 722014566, 13178423, 950296313, 174179990, 978768072, 194824084, 471470815, 33085709, 122185915, 365935455, 72710374, 679227290, 793702701, 900618194, 613919563, 56569130, 77008966, 984917243, 810770560, 627665694, 268503732, 140087079, 355452025, 154007797, 506775857, 214147951, 260130011, 829760335, 219222384, 581259945, 540071366, 947597062, 715870166, 847076781, 720647645, 285222229, 673690971, 181123291, 448138079, 669889422, 910406873, 142368388, 948073064, 407181219, 655118103, 761249430, 595963816, 445764692, 655299756, 944814024, 464524665, 744760866, 941304263, 710905579, 655054070, 809305817, 259209884, 640850522, 425906321, 414370284, 597793599, 920139456, 957124537, 799589180, 493826066, 223817955, 447475315, 284807878, 490661065, 555364469, 181466563, 253661946, 368486137, 656778647, 511951161, 98033131, 340260065, 714871405, 936953940, 422967532, 641979432, 960459837, 507823796, 19154226, 75890088, 311658422, 100633476, 203465044, 829559854, 231299695, 824953420, 963232589, 458775259, 999748774, 144075778, 131954255, 909390120, 285749579, 822304604, 521614766, 248289303, 126786804, 55356451, 228246588, 713831717, 349146894, 435894989, 740342967, 572474206, 557322531, 66206517, 286375645, 791187724, 626150163, 236496157, 852714182, 649225279, 939133316, 870921164, 906266656, 328322478, 714931506, 32587332, 931947114, 277634573, 454147781, 561978319, 50378091, 670929522, 91902362, 22999359, 655252747, 10523727, 483580149, 786443700, 489936715, 865373760, 757600890, 89389926, 270415651, 151892524, 943476079, 60261780, 940965981, 180563278, 911734811, 525069043, 624171858, 847480239, 128017850, 999278657, 369049812, 211388571, 586180546, 436362310, 487570354, 448041371, 245408934, 220762860, 458466191, 794920090, 716771577, 872073080, 109311562, 119010605, 521357575, 559298167, 321286039, 441655620, 607895125, 712871837, 921770239, 637121278, 884101095, 758713564, 820581963, 856218087, 812989455, 170034142, 617325972, 55084362, 729589589, 510783523, 116552893, 79769801, 458081864, 212280947, 844984932, 273274290, 278476069, 933945821, 793614228, 409060084, 644712329, 935406687, 572552280, 999137045, 120690350, 371764186, 323225545, 301051457, 218109305, 626204101, 895470979, 299643238, 824416835, 223921841, 483236708, 92171377, 147805456, 378326732, 115145342, 253310094, 856642084, 855695706, 489216013, 617999742, 750727975, 289711087, 122079011, 684560439, 788887045, 228074620, 544588786, 79476528, 295120963, 33948690, 347122845, 929979343, 273066997, 796512397, 185872974, 75896532, 237701869, 153785257, 392926985, 692421892, 481370838, 939411219, 266528872, 562514898, 352988744, 19550987, 62077414, 143309130, 627210101, 239581723, 747432878, 693245677, 399220446, 686395953, 450262136, 818573583, 740703444, 418413473, 804326184, 189978852, 987242600, 447535184, 283075520, 366791789, 762909641, 593131458, 185187568, 147268979, 16929888, 848238561, 49112473, 503114144, 693973734, 166290657, 975983628, 149503178, 617727660, 313557624, 718182344, 154268960, 124395306, 52122604, 972939352, 22084740, 133099676, 528708970, 166128045, 411661658, 961291572, 254589480, 212704205, 196688095, 170941633, 713269120, 114408036, 56616180, 588460393, 812625116, 373859110, 928888838, 109611751, 297926634, 895803655, 802372052, 462678603, 18611109, 623423633, 277872809, 834748765, 345982163, 891520189, 825984248, 863918146, 726690563, 316806888, 74373529, 980094730, 51420080, 170861071, 512325320, 786298664, 997313094, 226178500, 148372776, 600854634, 409139067, 325411587, 352515751, 793071623, 11662735, 49457386, 37441182, 403902726, 448409369, 9145250, 522915776, 724979552, 326865166, 782695362, 750000680, 613110928, 853290001, 708177211, 253051732, 886777719, 665410872, 221495230, 557755909, 233551420, 820943417, 218681905, 621783514, 527904448, 874609990, 517753582, 218484727, 816632274, 458176909, 985404985, 792874705, 99956585, 943155871, 214126222, 689292562, 670328458, 795618829, 754278011, 639449580, 440073982, 700335039, 761685476, 446523664, 366794771, 208809835, 352677410, 430423364, 651684119, 91868869, 983872468, 352845960, 788229498, 462174788, 123499950, 782919648, 260306117, 728733218, 261837267, 689531085, 282604564, 468677617, 546965677, 199931188, 775584070, 108182717, 990956299, 702589911, 805759981, 339878327, 22205882, 849799463, 845033691, 373458131, 667257447, 137821630, 977073806, 919048103, 363465272, 295890908, 270661111, 705762152, 734514884, 55120029, 286027282, 905582155, 290531710, 767451644, 713298076, 915349079, 787585545, 762778966, 975074249, 730903820, 953129379, 908415834, 11939910, 340914935, 857450133, 671684454, 429665407, 30960859, 999365915, 818453036, 998168338, 608661480, 680117157, 152259674, 910056679, 630760867, 72706142, 192165233, 917730472, 142821957, 359959536, 707883898, 336269590, 158237571, 807788801, 848987111, 476153112, 148247448, 359583858, 117125594, 425361145, 359726578, 751302174, 441575315, 453725458, 95852962, 975917936, 355212897, 178918503, 870395885, 625816912, 224868243, 650387945, 913635180, 83092103, 691658274, 564290008, 934292952, 722134990, 947263266, 479707589, 142793347, 477433342, 446802735, 707009407, 534975541, 85725034, 411755820, 883510055, 469930645, 741708583, 132668664, 942323999, 435703281, 258195174, 782851428, 822657625, 85152800, 490771416, 524755848, 191305985, 862371032, 526793434, 389039474, 935060848, 816785898, 713269098, 224314647, 439033267, 24947644, 993817900, 321308438, 297509857, 59813964, 446978347, 455464210, 21847675, 853232218, 353659339, 256107606, 982566580, 760858433, 613030588, 143359512, 120313696, 966383083, 554149214, 454990582, 142821754, 890420520, 529359946, 908654594, 820835915, 265711733, 749643021, 294253377, 219395608, 751044197, 403250498, 861119331, 742926590, 89010334, 31870554, 433308462, 766706956, 153219480, 702456964, 420755381, 48025024, 984963062, 818668075, 712390965, 479549584, 630549676, 306362212, 696309365, 658842056, 409172004, 392277390, 659422816, 835722243, 702084393, 184838859, 819662677, 221379268, 176166523, 356514653, 153939036, 398617833, 452009497, 521428104, 919856534, 851991042, 547333786, 998215312, 196221270, 167052683, 747567802, 160784892, 633962284, 754632920, 41085330, 472341842, 269700070, 307538083, 139852489, 240971134, 619999625, 149340729, 850249961, 156519242, 210095335, 985601534, 296599459, 770941066, 603242856, 648220661, 664465246, 502760823, 522935961, 246231874, 972082991, 31040758, 469146388, 466532524, 477272793, 582473998, 61442119, 569637553, 427458344, 544171876, 512830641, 612497072, 843068071, 548006514, 647050448, 639425919, 327798048, 595155273, 277932603, 261833377, 109436763, 979356491, 167399575, 913026157, 208096748, 384994144, 991677325, 825281363, 226359241, 730344375, 706180478, 45382163, 378132017, 854270267, 261178216, 85959446, 112494393, 274237504, 462506593, 54608166, 911759575, 540795152, 856883336, 122268442, 146108099, 733884507, 510432694, 902005713, 493979629, 262375950, 122052535, 32855378, 133383160, 617934560, 196868850, 112844269, 138890035, 72201633, 92984188, 296706737, 213571415, 584727021, 896069707, 432498619, 202884790, 391546070, 568631647, 900705587, 86189468, 168209383, 843818892, 790838335, 875547024, 31988664, 589742553, 419646371, 950750656, 896989360, 918240069, 127848725, 407726805, 866743744, 480393308, 280031782, 138211786, 643380669, 889314276, 772433187, 174396006, 15215987, 433979032, 846923767, 466579233, 883300423, 824495832, 88089359, 807638572, 553065661, 239054273, 514521252, 124911694, 663496360, 363559455, 492173955, 86359783, 116726495, 913404583, 325974453, 301011284, 971690190, 290206474, 934810358, 97662082, 194603550, 633896000, 597971048, 415018563, 28499622, 183270579, 468993829, 315727178, 161288301, 69034331, 256141291, 346483937, 107789598, 540852923, 707207115, 246559390, 411068005, 776050902, 923310487, 374751590, 341654054, 903973894, 826559955, 619427116, 961730514, 428389550, 618056484, 880498074, 920878925, 174920901, 521259765, 179584110, 981933756, 350471706, 146750130, 910526937, 312758076, 348090109, 287965816, 986279132, 872555266, 801733830, 854629203, 535134840, 286373643, 439970653, 573194398, 416733203, 588314455, 209307519, 711476256, 651508771, 9121823, 944577967, 697307539, 695955883, 743169368, 892760237, 366907414, 22413334, 693240348, 591492943, 636233882, 567743204, 631698600, 869110621, 222903420, 198376679, 108577524, 625736202, 854772006, 150844878, 108458437, 134487384, 338732557, 318180147, 529389283, 633631791, 462420187, 841780265, 263678816, 513621867, 63100521, 248415942, 674547105, 236262987, 368352923, 678455338, 652910746, 613798425, 844957068, 623786088, 813770614, 474117033, 196666449, 693545691, 491003084, 395338011, 34820447, 64271550, 153970786, 262468620, 534993928, 853604381, 498588591, 488214117, 132405566, 83524187, 927998359, 121866545, 556555714, 14962504, 249729669, 950007723, 862274589, 892772319, 514699468, 88431207, 100179964, 569308945, 370831820, 243084883, 675160657, 135957126, 227932546, 669850046, 328552363, 245381513, 428159308, 746412143, 302635107, 685226985, 417474693, 209701757, 355134471, 924371097, 544827951, 599820766, 389163795, 300829531, 230603194, 245789593, 944927114, 413635378, 857995873, 993882592, 728165348, 865771233, 356096228, 818767316, 484382687, 398085141, 867371674, 490934598, 61764141, 164781188, 311664098, 45609653, 222634165, 415241563, 440836525, 936359250, 407390089, 226022052, 285374215, 721043086, 355490372, 390716111, 50603095, 958325241, 392773961, 987676377, 764812379, 200562119, 236002874, 736078163, 969704402, 155262605, 968723236, 578215072, 71366917, 996540936, 797899577, 688023187, 63468877, 315360911, 118970246, 972698285, 475725086, 156900265, 277557666, 999099985, 546102271, 403299370, 90745889, 445680655, 735831081, 224408999, 648372691, 344473854, 356256365, 985631248, 126444366, 593055540, 702997971, 251076250, 837107248, 498865088, 882279944, 650961940, 509784376, 216731599, 727308753, 579006129, 735495766, 928886460, 726529359, 843217769, 641346980, 950291427, 134841849, 53785870, 469363325, 909545809, 362605155, 150946395, 423290711, 512319259, 229644613, 140416856, 650208124, 353452897, 225115488, 227019471, 899167052, 830174540, 784193590, 70658305, 838298126, 94920723, 597191040, 888295397, 677423814, 525881788, 982205569, 30186894, 679875854, 27031515, 102698280, 12543506, 811408445, 475970574, 369316262, 179303503, 601619161, 968458525, 908094379, 347063344, 871871218, 756484322, 270951046, 759967687, 675741661, 548770756, 486379597, 517512567, 237212627, 397740675, 502609641, 775382014, 749748271, 315505490, 925319460, 971836290, 321565935, 956697699, 845902971, 21157160, 899511813, 40225806, 560476563, 784649244, 926907565, 509865208, 635113329, 587734559, 895303174, 693251225, 549581205, 396341864, 527749322, 744396055, 879008518, 665974580, 973863386, 222790741, 734198376, 373475494, 284591228, 56808642, 8736780, 951985285, 116382216, 429450952, 861491165, 88085288, 308587527, 339305776, 808898288, 758704399, 744218744, 811899661, 277400923, 592930047, 453211479, 336725568, 431751069, 353773132, 522714324, 443170631, 249113811, 134304329, 660321587, 666310216, 365981133, 365391805, 97423866, 203987853, 533571058, 795563048, 786741589, 722079258, 423674861, 380143483, 950905775, 85636803, 576935807, 11265847, 103109879, 970070287, 798707374, 308646017, 895325184, 231791384, 920451543, 691918853, 965627557, 184098267, 414864388, 550234035, 297656951, 443428901, 486023217, 520377277, 183142569, 213603777, 643729281, 43801969, 213597696, 312332131, 311513872, 799157369, 204508852, 552593328, 254396681, 831233808, 946158297, 474938931, 70968473, 466485862, 530692816, 962986768, 426481509, 432748363, 265207495, 95881813, 271955815, 598299789, 801406334, 10032220, 41409853, 199671198, 965142077, 234496409, 389886561, 697697678, 854769816, 392510398, 574633905, 71905885, 651370958, 302227195, 420532523, 655688219, 421384164, 653638722, 577421287, 214033575, 748267601, 574377738, 94906609, 327240232, 432647999, 736419990, 85518562, 147344474, 766915030, 414321783, 533709442, 34183577, 543973973, 59461339, 351164003, 853183163, 865275448, 772847324, 989861532, 169421668, 412751259, 291819656, 916671299, 984798682, 659691567, 807367259, 886857678, 396342224, 576862863, 417667107, 3612534, 870913650, 148395146, 215380814, 105685339, 196923647, 128418429, 878512666, 783861755, 99068958, 777670820, 578909555, 528339892, 763736093, 63034181, 891998337, 960408007, 509662187, 311194676, 71112549, 25222976, 438922765, 787738919, 42932373, 432687908, 787668553, 859722338, 238726218, 156289647, 826128362, 765985628, 395684483, 696654824, 855035540, 813353443, 135518329, 591113474, 885392564, 881020109, 148461242, 286418239, 419430272, 793667038, 704390195, 790940073, 283378333, 744783771, 867702492, 918376010, 198484688, 235643955, 426100441, 876178458, 910757697, 144463164, 266561266, 474633340, 913397269, 107416301, 790025493, 606224152, 935773888, 232689306, 400520154, 18009623, 353466462, 507894911, 848584908, 894031617, 674254071, 112349695, 486313770, 668871031, 838786717, 595030644, 921383040, 821243196, 123537377, 311876147, 917212611, 962029178, 852273701, 322595994, 999200080, 227913701, 575414842, 213168541, 327241507, 140500915, 898963755, 202850328, 162043756, 579416939, 754442026, 52045282, 49281274, 88868249, 227179462, 797070352, 832662430, 81835040, 70148274, 680930835, 604717258, 157998550, 749817497, 383451156, 488642970, 268146154, 305325699, 707152431, 975093635, 257426634, 314239221, 106741510, 277003708, 746346012, 313546167, 253975286, 99416136, 679512522, 569615196, 888689128, 358758018, 545583217, 99233087, 877277225, 117475800, 553669351, 289958085, 166679712, 488507806, 820204497, 125961696, 509078681, 361173054, 964075894, 442601886, 520794356, 969330730, 238185677, 690402238, 413946567, 383487353, 835068374, 956055001, 395828767, 318341542, 96958179, 107792056, 784376353, 987865966, 639082807, 331730541, 232884064, 488539880, 105403891, 916011889, 666919226, 46019002, 215219573, 331173355, 811341439, 919966296, 894140741, 155230376, 325939707, 669752168, 112926973, 284344491, 853664400, 427554741, 434663381, 396967453, 580574126, 414142848, 538541719, 62156915, 656521998, 14582008, 593067187, 747497836, 945653371, 445065177, 76841071, 151735385, 475566103, 27851311, 303928658, 281114946, 163876496, 568302809, 534154482, 681378734, 753694278, 280791897, 783029004, 928063595, 318570651, 317154233, 728453411, 462263775, 108723474, 335455886, 695713472, 260874990, 340805998, 585099734, 146494404, 336881166, 908950234, 395163039, 925447556, 61563502, 369287487, 510761131, 447155484, 483834227, 435102943, 973400595, 573682449, 863885057, 639976647, 841068471, 896889242, 106531376, 281763326, 50201984, 868409933, 234936718, 719672627, 445397193, 241836339, 562039829, 850914279, 976876748, 661628975, 206211529, 241563340, 528084355, 304230267, 620179024, 434410511, 253913996, 223232798, 108481066, 187141494, 855606390, 663786002, 204603460, 942354350, 78281861, 491780884, 211796765, 73953598, 872553550, 773224019, 644568985, 423356270, 269868229, 397679527, 101718431, 238456561, 454320144, 889083819, 710990425, 297600971, 622045203, 394032702, 750482093, 752471053, 185564302, 405751121, 870658641, 472693824, 51241648, 279938799, 188097858, 257007121, 462371017, 17568312, 208818402, 430948298, 953571188, 108391940, 996745867, 683759328, 169084817, 849717475, 244259766, 444018595, 602065386, 972089047, 968007881, 691608748, 168111728, 216385124, 753372322, 971490450, 339419174, 237165388, 446024066, 618272761, 869943997, 609942400, 8540579, 999125575, 964480300, 830201810, 129112186, 339426361, 579873373, 227822666, 117765514, 467869060, 479349567, 693513854, 825829609, 477610596, 645834775, 917131064, 111864375, 228762601, 273507251, 544453454, 988938402, 639101718, 501242156, 215442339, 58083696, 751949648, 368228970, 623882959, 267786726, 471182739, 598594717, 299867704, 846682612, 549069948, 270163807, 768308158, 751347498, 383163696, 126039099, 875711253, 143656853, 970899851, 866805740, 719836737, 794126036, 655529778, 13674546, 817026456, 992879420, 918067824, 272849948, 553188409, 889577897, 734595229, 207750698, 69958548, 39640427, 435792854, 537677517, 535063276, 413288248, 759357955, 933240611, 319895560, 453456494, 531954711, 271677373, 769443242, 559735983, 511299276, 90074044, 35405787, 847278538, 297306988, 191410484, 830157536, 343446452, 201874637, 299472879, 742823745, 358917668, 625201084, 751353309, 41739518, 196142461, 981216367, 739586973, 76490982, 520007019, 711302865, 405603638, 376489653, 242953714, 251402674, 762663780, 848065590, 327942431, 295783359, 850979005, 582403815, 269134564, 247637325, 230267313, 473543092, 879690107, 856337316, 863554226, 714761332, 450608979, 872565810, 910704026, 309688036, 901431477, 692655223, 115637900, 603938560, 420119556, 608244111, 519844712, 107280461, 893976050, 617063862, 973813032, 789521965, 227684371, 26650754, 791506329, 140956475, 407505749, 623792679, 313127299, 64342744, 362247177, 823851740, 844933307, 129933998, 280951132, 619356470, 806892171, 911079367, 610075537, 363063506, 413647176, 418743331, 937763699, 410050307, 268745019, 852364583, 120144999, 621585189, 92905794, 124484279, 941769727, 39603451, 915759291, 187119947, 918067495, 884887161, 863209834, 232083551, 915901567, 422982581, 77334226, 605526492, 168984943, 889127766, 963684083, 719786075, 644912700, 341385582, 33887583, 877312532, 460983843, 231665346, 607152590, 562474936, 984604484, 695204752, 318646545, 650292069, 899568404, 335599098, 830859275, 410482329, 811963084, 136346883, 187736101, 490080037, 526728262, 526031343, 819991202, 557680061, 235567253, 169727581, 273589283, 580930246, 43446231, 561587461, 609350677, 941055892, 593256530, 62954000, 305736237, 228175332, 190531926, 202846968, 296421219, 691881698, 448610741, 584700648, 914985824, 582376466, 363216161, 780077282, 188392220, 716847081, 146461717, 446210333, 863380214, 627417310, 885373590, 279898584, 978734478, 783939555, 667023495, 701068551, 500496860, 749171885, 669464166, 149008644, 735592707, 835891512, 934504740, 936972436, 946759543, 54637030, 480998557, 462640164, 413562995, 78700459, 112928929, 252746553, 633483764, 561598430, 480028676, 647468380, 149907873, 223754849, 916479175, 468252783, 651734850, 187192465, 546342066, 487199176, 859182959, 379427163, 156951500, 583422160, 263861617, 25318649, 31884176, 643436276, 963859504, 628105980, 112036035, 43701563, 738046076, 562109357, 624630682, 648833820, 378597644, 909565786, 695589713, 357337197, 778307078, 103262517, 578558512, 713756192, 647616383, 537925945, 68203340, 134042068, 28079564, 343271928, 331899678, 672525928, 321702781, 876110880, 776155269, 990584062, 86052030, 565892414, 185333858, 852452644, 335248607, 982294835, 762925763, 50072624, 544756497, 143598159, 620048692, 562793952, 211244883, 799245319, 488660239, 327001921, 230395738, 190768430, 633170450, 834123508, 639131333, 156899181, 922192695, 289890612, 318434416, 933369503, 677185599, 533146903, 675775654, 573530103, 397570518, 460127058, 90778906, 188378511, 882488067, 902066939, 222213493, 556850146, 640693219, 770892338, 979674849, 477739055, 486532172, 171007762, 614731260, 755302003, 330573107, 312525340, 957384061, 467566469, 504102276, 709686409, 235682806, 901693028, 276176431, 778964396, 458014661, 221734984, 704841453, 456861001, 347621859, 998475107, 329137019, 114915823, 598611152, 747942296, 150986934, 706870611, 48930624, 775433238, 355611172, 912198151, 713252346, 167471650, 670526979, 978898820, 700837023, 243751599, 210247719, 852500489, 498356120, 693434645, 762513499, 589677925, 937957460, 579103617, 746147463, 652052860, 100711334, 810257860, 394994533, 700770729, 908288525, 796733513, 378258841, 943733516, 106775590, 71334030, 681660146, 261884367, 990759958, 545943084, 44492246, 277799070, 162182210, 820740398, 892144650, 752540798, 574604061, 938506832, 189438988, 158259180, 56034456, 679065637, 175759015, 763552426, 232079873, 421082065, 897560158, 971502699, 477297691, 188306428, 135078715, 581383430, 374037593, 898172967, 549964623, 683283395, 123754407, 872636978, 451719696, 430578866, 101127980, 74071266, 332466348, 285362159, 631552553, 485390334, 28290305, 98901360, 281834742, 834662361, 591277556, 52171891, 981766392, 946037213, 678791553, 904155355, 325149862, 441815393, 951449699, 818924509, 369344322, 66544141, 347826577, 653397899, 12126720, 64901944, 79840284, 924812115, 999471956, 990894709, 241905796, 906363801, 474514108, 504356793, 118317134, 981975049, 502330468, 733176367, 814429572, 673815229, 921358177, 754768669, 145914564, 893699158, 326284907, 689082616, 199567925, 964446476, 630358229, 666925613, 195446504, 602246641, 369538209, 209555372, 434925128, 926404997, 401775857, 130334794, 611000040, 32379656, 223355023, 853771291, 291486010, 130539466, 230597212, 240590994, 965452471, 408947225, 814376206, 677432633, 497556942, 224458288, 592122020, 656203884, 256262884, 593955878, 464439415, 809103608, 490282453, 636987222, 828077656, 697168717, 896146775, 242189254, 988743549, 256458716, 722026054, 213532183, 658783895, 519430965, 161044220, 535964484, 279990432, 722420559, 837471692, 942410694, 308798667, 457924036, 48087701, 7249594, 618841946, 696369133, 594890102, 240794584, 662344542, 721162238, 810767140, 573530642, 644453284, 405384809, 572375396, 351806948, 503358073, 554108588, 576352012, 61224407, 172607364, 784974733, 519027371, 896387596, 436951095, 959734570, 302819729, 111183355, 151163647, 620400192, 970859245, 653623317, 585556979, 722474633, 84909377, 784949590, 137811591, 270100742, 786640047, 909317236, 209096602, 893774807, 282883890, 96919537, 941027410, 877198232, 568114914, 174432543, 837629112, 472596144, 382022010, 313567573, 409672953, 57332717, 507936865, 332733200, 768005174, 578184166, 153874934, 835046460, 808323826, 562332980, 422426243, 185627435, 320461025, 520410722, 455484318, 620522339, 178171997, 58561123, 162351275, 475679580, 221775980, 146936918, 601972044, 764171281, 953291959, 60808159, 534249145, 1080541, 594818295, 31494179, 457422106, 292271427, 224967338, 867287072, 486342224, 97043454, 793557090, 373665235, 176717047, 61169459, 391381967, 276686901, 70348045, 533163041, 47236753, 691741360, 958881878, 170781135, 938228867, 316028291, 422072477, 295225855, 719043370, 251088651, 851026293, 47232876, 432733671, 648470705, 950702209, 57825849, 832456928, 951724536, 804337450, 346257959, 970380891, 525349284, 484857081, 429087352, 262904639, 686753407, 849895715, 679588282, 982290252, 483388761, 542455990, 599099279, 869186053, 63604578, 534869036, 45208756, 551249456, 821644263, 605015591, 765128836, 195078780, 940832022, 655915372, 591049176, 864492373, 311239049, 213404373, 465442135, 963211110, 462387966, 249800400, 599177664, 55238485, 405742933, 941094965, 282384401, 330867134, 821692567, 298632294, 459898714, 523062770, 828970974, 210461951, 973167168, 919614265, 644739483, 844014250, 418920151, 841304766, 885493404, 935054611, 850419963, 275973725, 668322383, 33112230, 6300501, 776412816, 413518099, 267062495, 551152104, 24889301, 932948355, 246859412, 404995203, 192412755, 462045875, 962132421, 345447969, 791168388, 910896019, 820252351, 943541097, 520319209, 825032020, 714826582, 992141526, 759418458, 421200412, 398509422, 930465525, 685928110, 862931451, 754123335, 297907890, 337648527, 459348089, 992695240, 37218579, 116688325, 374673112, 951525928, 172676385, 152964034, 928393160, 908929462, 324682931, 607799452, 375968505, 614377785, 932709158, 482668487, 204511376, 229687068, 783156056, 981830647, 53767814, 297307799, 752140934, 149097310, 627234814, 150682209, 506627572, 10479461, 894253228, 242091095, 784224373, 971905576, 864875938, 81664426, 961699107, 746243303, 192523711, 247885501, 599548430, 913682471, 783133230, 759941916, 399763970, 319237422, 556134259, 811712112, 923214968, 739401670, 783517044, 732067126, 989928857, 991024648, 675236456, 31179052, 98086575, 552112663, 164308646, 829379015, 870305727, 448222107, 827616289, 637137131, 667766281, 681314024, 18331347, 142539894, 883418118, 157945072, 272063152, 908855788, 64165393, 695557908, 216071606, 297543283, 879922547, 522703430, 81500603, 937209700, 312524475, 469999248, 416981636, 50694697, 708274078, 283593183, 981090597, 445039612, 879875873, 790594617, 944480087, 189125734, 689635136, 393610975, 742998458, 464279056, 386146017, 569076655, 236344032, 851107765, 618817731, 504758739, 57589342, 965221241, 974946394, 780285183, 609862565, 673141441, 352779011, 659011251, 296184276, 183869309, 14355079, 12035234, 108443501, 543100054, 999967052, 418212308, 215447884, 796877142, 94820335, 800543499, 134429162, 678993833, 685182070, 196350361, 902171447, 181121340, 328182313, 889520033, 340937714, 433078218, 844906697, 581085558, 643740455, 240460204, 472060399, 693487194, 894767385, 878238549, 346558418, 844908329, 913857968, 397253585, 944354103, 25800803, 614247607, 608396834, 153031940, 752381551, 557295144, 269175641, 747070573, 521457431, 492172723, 360039791, 567696308, 216549942, 687469678, 347666935, 64263714, 362265987, 810132672, 177023389, 160190925, 899651089, 9016222, 375406593, 154200516, 829072335, 861830533, 600975955, 393094105, 853018915, 91387020, 795843647, 414186431, 380666556, 914436380, 654286814, 969979769, 61444626, 767719150, 758586425, 265745463, 618505160, 482188080, 410268187, 438059223, 598961191, 885039524, 556707195, 751049502, 678989136, 377999351, 530125672, 150353417, 984935079, 437513736, 98836537, 918938686, 346795415, 871008823, 764239283, 649510967, 868079554, 80625688, 540085930, 377855080, 567148797, 930707371, 909205523, 669805375, 4636707, 280639992, 84006152, 516961022, 574468513, 946882704, 132476977, 33656471, 396435515, 617817274, 927159432, 742738675, 728576368, 445476858, 347631848, 733299623, 654808267, 989037347, 224714846, 448471829, 87499852, 757160811, 205619198, 680584461, 606277343, 515894007, 57992198, 892312790, 768117135, 139836851, 245858038, 981135524, 248837267, 30253199, 747972914, 982286094, 592693171, 39471540, 500669044, 205811682, 654623014, 7369138, 61480191, 580616953, 679530537, 234539610, 315960325, 181905985, 833491461, 521261086, 690181810, 410370986, 432338472, 931602432, 886613932, 558697564, 88325810, 413029959, 323208641, 743770921, 94537681, 780684098, 858418326, 541707204, 606260165, 618575215, 68113493, 370643500, 343556901, 718005161, 460875091, 25581481, 693169126, 961921918, 893565255, 768910733, 893997772, 912270127, 330540332, 798081800, 173674054, 108449413, 130408408, 815439704, 498293869, 72740564, 162249769, 656180268, 645006146, 78275018, 741925031, 377018637, 948048413, 555451183, 116470977, 589047996, 41696044, 686835080, 779404052, 743352654, 572293446, 713252987, 56295882, 249942528, 870534455, 849350186, 606349565, 825094856, 50550948, 170743430, 997981977, 368687283, 161578348, 202159997, 987891270, 384224369, 920609865, 906977397, 292594450, 458552843, 855917191, 19498215, 646399492, 668162885, 171487813, 970151386, 947760775, 144058678, 620414770, 127486608, 771149701, 51675213, 162107300, 437652845, 385401488, 281220990, 604084236, 422572869, 224929731, 655605403, 535014908, 24009543, 501705025, 917399795, 399494929, 5725062, 393386301, 657962070, 560383830, 761467383, 804093051, 536075721, 885627040, 35649806, 183970876, 616039045, 668597380, 948153867, 792873516, 222466903, 280195302, 706149018, 457262532, 77047268, 714023209, 786191956, 486920327, 127962239, 161330968, 312650802, 967098475, 82150260, 358390874, 628514252, 869376259, 184663368, 944978518, 128771223, 119226193, 936686718, 772726025, 769391595, 898564264, 320903649, 170356327, 253861013, 321899455, 995163859, 794709303, 667951649, 441652106, 779334649, 67311841, 452910082, 267424258, 231142624, 348266258, 565016233, 614622034, 512321395, 214495396, 523893932, 599264058, 976566893, 337718652, 798464612, 841701681, 824319996, 25947796, 52827983, 114202702, 864048770, 387083210, 501319237, 946331896, 314579891, 217533219, 830283626, 964853449, 242245105, 114905780, 925890923, 86421196, 668901235, 247157849, 964951664, 292410729, 865794236, 764552610, 934444400, 834243668, 799906478, 738478491, 510408989, 479575045, 473306637, 489734060, 312905317, 759812469, 630871645, 679935865, 982475190, 683139327, 569571241, 507910435, 978944613, 674641401, 798821358, 775762257, 752866081, 995975048, 268029764, 349210436, 571324359, 112943944, 660917836, 357976570, 566745780, 478340547, 759324547, 105042706, 36671192, 815350800, 689309864, 445329495, 520836187, 189025179, 466472619, 322852807, 554441935, 119696505, 719432218, 651531717, 534642426, 760208095, 174143407, 278925585, 565173872, 481405954, 222800705, 573071305, 562009590, 845277948, 323309396, 950195679, 848254192, 344906446, 359957419, 449127085, 408286566, 384530522, 256604957, 963515333, 513911454, 498209846, 932454228, 528934179, 276503, 378460423, 640255305, 277460999, 416009539, 526778367, 254216197, 460863270, 688201559, 708335727, 995414194, 527633631, 556447957, 347184750, 726926946, 361846287, 601432511, 362911026, 714045910, 800687128, 824847915, 143606894, 824611197, 87049247, 679781103, 912520590, 436674450, 491623740, 880827083, 818751664, 950905581, 598650751, 327744881, 535748381, 686254138, 439793570, 566054625, 399170679, 528151144, 216412141, 306218915, 336268012, 329947606, 294073947, 152457180, 15665994, 9332369, 964528460, 590211595, 69454969, 274151593, 593738957, 613113141, 416515440, 715477147, 62236218, 743058992, 268314531, 258655653, 251251383, 717035584, 688079608, 273650945, 958536088, 243559823, 322209767, 949853547, 638805862, 589581987, 258473282, 576285877, 52731890, 147298501, 950057914, 718197784, 742177277, 203381420, 400822738, 386897738, 474719753, 502414743, 325751725, 886204762, 805419714, 229941569, 240013207, 513124814, 68927704, 453654237, 612010364, 672125721, 522664576, 957806933, 793516386, 131230572, 281300953, 646935381, 372336195, 870074454, 606045637, 765474438, 581525263, 678382460, 481996789, 436872521, 610729194, 823113071, 550161439, 787639798, 846948767, 371368593, 999308846, 19415940, 669060375, 334843809, 50294624, 653502021, 912698132, 779781298, 84922873, 736305135, 654597906, 512790847, 417514800, 846927071, 609578593, 325864086, 75223907, 399911836, 749112678, 124131158, 430590981, 271153148, 7120775, 555765789, 744358325, 536466725, 356273844, 270310721, 882395856, 145129192, 32087069, 219050526, 53856004, 177603441, 31285088, 238193261, 373830920, 885416858, 439380917, 34432612, 487968230, 11864563, 744710715, 447350156, 559327953, 288277076, 215117061, 96236922, 987767176, 669565114, 574688134, 812397754, 908152932, 745970058, 948468942, 300360093, 475020662, 615194529, 957429115, 399956782, 723467342, 101577767, 159438174, 335843376, 432407033, 451604613, 739825000, 572247588, 498733520, 183847186, 996370956, 341782857, 256059340, 747209526, 548675750, 5096648, 473069865, 82274378, 628360581, 979281512, 862861308, 415171987, 263167946, 978866259, 809965666, 612959825, 776983253, 141434972, 807356066, 857586874, 661534934, 829524220, 727689129, 462266042, 389137601, 850279319, 843064075, 76392116, 253126848, 635757714, 474155798, 66263238, 550286458, 97281934, 894291849, 804565811, 844273274, 972053866, 87415370, 12570653, 750648292, 481488331, 261294367, 968869302, 720575055, 195362414, 197906897, 885695285, 42393625, 956294508, 233012367, 638818444, 628138137, 946007259, 317083164, 578224895, 17558134, 376036623, 246733915, 68584100, 889558281, 369422233, 343292052, 13401713, 584299399, 890155582, 10878757, 937357789, 296602967, 172414519, 309096302, 853159617, 925910060, 442684723, 612569292, 974590943, 631362240, 486454224, 543008007, 16567417, 106191910, 622987953, 93863952, 625447619, 186220308, 293374746, 890045530, 884006149, 651843984, 695320587, 962149604, 111554964, 461677892, 411774186, 924682049, 312853185, 355718995, 205437107, 520658630, 559518766, 470115455, 679509699, 895894503, 304351317, 701813379, 207055688, 374038900, 94660339, 580446454, 595462536, 282505943, 611423843, 501164867, 60826706, 2055529, 713768793, 457658560, 834226307, 466579548, 173192292, 804236139, 1629589, 864163434, 337725526, 85410794, 488886648, 863139229, 571795343, 176197598, 861042854, 862563787, 363710845, 559762860, 741530979, 498134120, 581704027, 256813988, 872124252, 164120360, 797412609, 222039546, 868910198, 57014740, 141984254, 842290139, 827172119, 318906618, 468136164, 746700543, 515765597, 947491593, 841820654, 73621963, 341611536, 551286627, 566575832, 457347207, 130328534, 337313600, 938924764, 301562399, 645926293, 889640775, 327846991, 32769236, 792318262, 906145575, 96089917, 542870709, 69424404, 797195274, 358242795, 922388119, 685821355, 370473916, 807069356, 394733837, 497432628, 459106468, 601347884, 790535348, 982251707, 549457946, 624069474, 290535952, 834186608, 421978571, 890529635, 755293857, 453800882, 456810435, 396860584, 762927831, 545310756, 529024437, 903551323, 742983791, 677153318, 115992747, 938495592, 804506259, 444409295, 245481763, 342722317, 7469373, 418595000, 701157401, 930056297, 446487593, 881236206, 486405436, 92578969, 938147165, 310783203, 189495902, 22107334, 492726323, 489415941, 18457809, 424685410, 610489701, 941866520, 647815170, 317171073, 170568766, 53326084, 985835563, 318013034, 545364316, 808666854, 861331602, 509244127, 136594198, 553569522, 746495568, 994755056, 856779691, 515230423, 964616497, 14407067, 311408122, 325622956, 169142461, 635742038, 553069744, 322870127, 336707932, 608810322, 253626643, 184019642, 226184379, 899515420, 783141407, 729215000, 284636249, 93912007, 160136164, 987500875, 783731268, 644889127, 409847104, 534971949, 459945328, 258104299, 658034897, 316126108, 667043174, 634563151, 82173060, 645791971, 310783785, 358321210, 666806616, 486474196, 703962386, 116478353, 179385079, 670503466, 300190919, 888247495, 190365989, 611918589, 122211479, 389975566, 237351925, 213797176, 102721111, 709888884, 539425968, 345953197, 290074152, 514351643, 889073574, 270874570, 658658698, 663639961, 567379488, 906691115, 286389220, 770162679, 805030858, 13597252, 438175135, 521686878, 188103568, 394389336, 768249862, 503598930, 768584221, 555958690, 43814892, 119299222, 510165452, 999555177, 920934971, 40944369, 104764229, 257431492, 893793990, 488710303, 500145191, 406622029, 487578304, 167437080, 408967969, 789912298, 532111795, 969405148, 46172333, 377691767, 982679520, 155850618, 86188194, 563333227, 800376384, 658638445, 961897803, 170605459, 744449737, 58378526, 480468586, 654924740, 464423866, 163517277, 141297148, 3723679, 453981756, 419019239, 214057901, 48849621, 435730296, 227262955, 446210966, 271175217, 731251151, 25967950, 329177935, 296374645, 305570761, 386521672, 110528551, 497788988, 162111821, 434443458, 794922649, 449130997, 225247867, 567281101, 685799658, 269511760, 887132979, 636830934, 162064986, 699516297, 131874161, 497365404, 903493139, 780956177, 154355735, 832640809, 74872127, 285294252, 618449100, 953074099, 310126736, 329854948, 874524255, 869038451, 519905910, 55034477, 141136647, 693822201, 765755971, 295416206, 290545119, 745789312, 21298549, 98404031, 85123880, 107828663, 542987742, 344145646, 280919547, 554345809, 696490384, 596101840, 364549940, 755332960, 533584058, 281709952, 953430515, 947010402, 860861880, 491825020, 966367866, 533681229, 639981873, 616689919, 677285413, 593927501, 815565164, 404657120, 821354973, 875354810, 510981699, 505569358, 612470934, 40334239, 425403994, 458130072, 736665472, 349366442, 489913150, 441349513, 362888717, 793548168, 404327512, 452091109, 980520185, 442845116, 874721470, 527151499, 373877410, 588101062, 673589097, 841494516, 898846674, 61152986, 426630903, 866418141, 502805260, 349395037, 547327548, 426195683, 857555511, 499060215, 359998317, 983604229, 316289221, 422736083, 422692349, 707056873, 310903001, 171450639, 310499629, 919345016, 421693453, 716086985, 456108960, 662466263, 534406742, 966537430, 427790013, 674775969, 494399571, 893236353, 569239159, 869722474, 307393526, 380050539, 474248270, 140576156, 616014493, 933450903, 719976991, 865167122, 54903286, 245895532, 772581937, 553324449, 954447482, 840413791, 238330802, 653045829, 634975009, 252820763, 559452052, 324027564, 610013375, 959208893, 575358223, 669055146, 917452457, 455547997, 78104536, 254813411, 78590006, 623666023, 726964908, 237753032, 485262066, 293719134, 111793132, 279787345, 999173536, 781191667, 332981998, 393312044, 75645723, 197645136, 855474289, 789674769, 21710457, 29925934, 152543445, 856907158, 722992736, 349525196, 733531080, 718098062, 27251523, 246152050, 326025206, 315860234, 995932751, 696809090, 847613082, 756613995, 343137459, 994508269, 163913141, 503242242, 989007504, 936393174, 224967784, 305448886, 127654573, 255467956, 906958257, 924552327, 251685796, 318216823, 360881815, 683346693, 737436335, 934069925, 399360832, 494408865, 67961529, 217486624, 264986265, 259405119, 850164923, 304770189, 825738610, 930714614, 719452291, 385166772, 104172927, 911921473, 420300877, 994415057, 311286218, 709289874, 431311649, 203982007, 382698955, 672821296, 960565816, 611155146, 934652066, 554986096, 540278710, 317418409, 237130697, 420284118, 690978728, 251181679, 273112221, 315356567, 248583232, 506916870, 451996353, 788886004, 475964565, 652229386, 76189033, 272910969, 713654360, 553312468, 17854553, 17089114, 315536873, 319495438, 362608301, 796810420, 831061047, 298403725, 775774520, 28696211, 56625007, 543864151, 253103436, 176053745, 950855534, 524227435, 407234160, 897271479, 300617103, 394179044, 701877850, 606998518, 494310110, 168825345, 211468509, 104636145, 413266076, 773496311, 316811805, 118452417, 280753149, 863224063, 147411202, 925719914, 265999168, 590675588, 426287436, 836871466, 900205056, 139495687, 973251130, 182410530, 359912430, 91177692, 978292462, 316573578, 187657711, 430001673, 333545755, 112073780, 513065234, 750897759, 756917200, 30882278, 152780270, 848384404, 316715720, 990112410, 232272329, 697059418, 964348159, 441626193, 626167639, 431906565, 710035615, 556710631, 175186499, 93514595, 706517679, 144178583, 615798227, 915219981, 465013155, 602877063, 841555474, 137656217, 704543143, 76331322, 898940558, 52686017, 568397865, 150509890, 106254893, 290055347, 41091685, 889705340, 64314432, 25475895, 865625709, 132651981, 143615866, 164237820, 127099629, 674761541, 522367770, 538841151, 475949151, 371941325, 425085803, 900023646, 708172220, 303439760, 120853611, 667416503, 872568092, 797836794, 555963381, 890696628, 698256641, 34916947, 513869074, 645708899, 569116560, 593631688, 134430347, 677942638, 336947926, 889929586, 84166246, 642341496, 992762886, 340075667, 662525451, 693348580, 815067672, 868084112, 62391523, 257443727, 515548956, 550063363, 969180895, 52573732, 832014469, 629836040, 21858078, 999105465, 566633930, 319987653, 556002782, 636888118, 880371807, 104458318, 679419166, 57720480, 138352053, 786332169, 718403563, 656976857, 344421827, 867366571, 547982860, 630891910, 470049195, 948014166, 120880258, 2655714, 18993700, 515236403, 291320558, 419799192, 921530790, 382677607, 493241522, 166052610, 723783722, 857069006, 177573431, 251011060, 787163222, 120242644, 120276922, 458292100, 654526707, 160541599, 130897430, 315784947, 996883014, 497699040, 402798093, 858020440, 664249484, 732484273, 719261064, 259266782, 173003486, 392974841, 983416046, 31562911, 61957720, 242226083, 542193227, 676472381, 473227711, 996726239, 71210140, 232910076, 923691565, 544204263, 670212462, 33483944, 874132997, 259750045, 107250755, 389164979, 322974305, 499054953, 832269164, 634496442, 948110807, 849666010, 82577441, 644462348, 277798516, 371591071, 101631099, 474650563, 792604226, 875905031, 870333478, 361166728, 60451375, 305271284, 834916473, 259450458, 562293132, 370761028, 53990844, 177728321, 978195054, 996761855, 283937627, 851453762, 519001672, 254635454, 634167477, 82232616, 894835653, 366082485, 632137568, 479855470, 626102427, 615012421, 985423649, 752002468, 405932900, 894920268, 968806113, 885022363, 522266757, 16244993, 191526790, 500201777, 358330154, 860472755, 779116036, 555284853, 958448194, 721934412, 252108689, 167352808, 449746017, 136514333, 885625715, 765633974, 497295891, 907982824, 519226773, 717262668, 526387462, 949895109, 267945712, 555715970, 885336260, 874654056, 189560847, 911598445, 540424853, 147577721, 998220965, 646122476, 821801417, 160318469, 394341952, 409431392, 704118973, 869655594, 808711021, 635426568, 139402627, 211089134, 69434309, 280997497, 425083866, 537648461, 114433083, 695708308, 39139345, 532889827, 583606551, 31984312, 714475811, 571518635, 138585021, 891077488, 133337372, 346888334, 163659737, 452883003, 195046719, 612397915, 221296929, 360726495, 843788828, 50435937, 938530829, 4503308, 209625911, 791145258, 318182609, 560520168, 507257957, 557420303, 784527616, 349731493, 898970228, 730404223, 907251414, 118660369, 59956733, 317337872, 33041741, 255175299, 140572733, 828180572, 868305455, 839349596, 285300312, 521199935, 819135113, 243324632, 730810286, 286066830, 645890339, 811824820, 777493957, 714085643, 811511294, 145720154, 318877680, 283899978, 832935033, 824243487, 812541055, 371520441, 191999313, 339427399, 785196197, 969135788, 19270388, 148952188, 819273514, 798861229, 717636914, 918738219, 782333413, 736994664, 899632686, 424576665, 982685585, 367016273, 934467328, 106816319, 37108321, 164622838, 336417537, 695101576, 520833318, 599996841, 766991362, 857942245, 339147346, 360149246, 191146320, 22518351, 978772432, 18003873, 454546544, 584565376, 893279229, 612087510, 354532887, 322267067, 578354503, 71089916, 843150689, 960102470, 400581697, 424639821, 155303447, 907872874, 207440258, 604386502, 379847540, 971354841, 32558419, 944263268, 993122523, 450043314, 451593289, 438129342, 65085630, 386678518, 661619816, 959291503, 399027499, 100548763, 720313357, 118600140, 891093397, 909747735, 47908230, 703586998, 827823915, 660000565, 444330382, 643010014, 318288503, 269241221, 842296027, 95380238, 419252626, 559492748, 455253084, 195767496, 637300810, 897831957, 921736913, 757550107, 811118605, 87623209, 738951574, 108798627, 540728598, 305465770, 623190703, 338848576, 446406397, 749813848, 174877459, 616047221, 557344750, 156602279, 808094933, 226041681, 96203867, 68989940, 862703485, 314138141, 536447972, 36233991, 16927646, 694096392, 253117140, 604532726, 297611756, 412768461, 839171971, 404657332, 764671134, 281979083, 14722943, 581497983, 675148491, 287677134, 162485787, 999669512, 689070344, 744820534, 698737259, 246301877, 118622102, 504183771, 337176924, 448889335, 732589220, 716485210, 492357981, 267791572, 124149770, 756681772, 497525399, 344523282, 401106862, 390038408, 203699598, 642740741, 442121994, 742344979, 438286324, 121250046, 755129428, 330593174, 833130945, 612408243, 906064748, 200072834, 531326610, 763672948, 122867322, 855384303, 243056612, 191002089, 738042280, 857761747, 543219496, 85703099, 349730961, 331869814, 114318453, 758861430, 548670857, 965366156, 815333735, 869419732, 168639402, 229310096, 594312776, 758248809, 444575682, 138511911, 241813360, 995793643, 326539950, 919882454, 899248472, 868859935, 89478817, 930393138, 244419221, 726002883, 943317437, 539964079, 451988030, 549524384, 650941423, 225369974, 705772442, 195108513, 640177984, 412268189, 793065124, 748254124, 417877801, 120107150, 376008135, 637847221, 632201193, 416465375, 724740862, 278299995, 679425943, 356886501, 876077658, 986555614, 383767299, 811491372, 812646945, 864964349, 162979115, 984337923, 341271248, 29782413, 164462924, 320123716, 239431662, 879511437, 418803734, 318322268, 548539545, 715046634, 970361887, 262577478, 330591282, 3610054, 210602122, 599724550, 599500966, 565704373, 869932246, 825255113, 217547596, 626142345, 95168358, 137918681, 140631207, 126170736, 208927103, 837989094, 943997603, 747040954, 482919924, 761097100, 575017554, 294653933, 616761154, 488280982, 477472777, 131588867, 318204499, 204592880, 18108797, 949843288, 807597956, 283642046, 257601738, 682480136, 934606036, 122801764, 677650373, 566860520, 284252844, 613713460, 763799903, 274554813, 451627049, 800438704, 893139151, 696506326, 910580968, 175655646, 263946177, 780420868, 279839036, 336358624, 147778120, 754073391, 80016270, 64165178, 7921040, 127931779, 212657175, 203405483, 553462967, 633099544, 398024247, 462430834, 927913745, 641319966, 116761310, 743634457, 911984183, 13889988, 314204566, 298089826, 681961909, 250415066, 160674220, 476312517, 547226292, 668229549, 305383478, 457377871, 599601514, 760286034, 842901445, 157649461, 197334154, 47054978, 735682179, 640786181, 327543142, 889521345, 785401533, 330880496, 883046328, 595974575, 902299074, 464867177, 280273838, 465727541, 555983264, 457897802, 498743637, 207295580, 366300160, 278469406, 51996351, 352766955, 769783126, 675221275, 336592060, 626316276, 31505699, 406416154, 143495147, 212825577, 556497671, 617126638, 531730748, 201953360, 658936978, 193876136, 671337757, 687858800, 394500927, 616232764, 279050591, 291134071, 932712863, 477879707, 29351470, 20382846, 677140679, 625123306, 247768437, 686407747, 923913894, 768312187, 32002882, 226111401, 596193326, 713237651, 324335038, 572039578, 926247837, 521512942, 892900616, 443820184, 938912124, 57189769, 87191710, 353351013, 608403295, 693219919, 163691927, 376850087, 864554633, 5407463, 777342341, 141984302, 207263009, 348009849, 322659917, 2405288, 123896020, 392506461, 415406687, 27404940, 833700540, 254249638, 474921405, 240724501, 571175335, 696653898, 52495841, 950087564, 977312525, 423612536, 855337906, 737104283, 64342819, 284059794, 708379569, 853787951, 847448672, 456726942, 56197671, 895627120, 49469018, 621860894, 846137763, 21484518, 968202984, 714763236, 855684686, 947161366, 323760957, 984544704, 666733597, 231436836, 956226393, 885287990, 392194687, 102951927, 56623442, 416390616, 556550774, 55759656, 854611252, 585134795, 88867504, 220148576, 186510050, 168204606, 329807540, 332919119, 763072286, 198171783, 175853850, 816409875, 15335351, 6818770, 38476361, 773639858, 908880369, 786501751, 747982746, 61689576, 577279145, 871754763, 343866079, 256976161, 52813924, 439983702, 53606864, 551373475, 152690234, 554041094, 375732826, 387328256, 74234274, 964330795, 733909126, 841057805, 470662709, 884183303, 720312231, 357573238, 922976615, 26032981, 411311472, 568365034, 734403537, 924947872, 67457319, 960288197, 878101440, 256482306, 680436427, 362550605, 720897585, 995147739, 308915302, 554570550, 235175665, 915469391, 943826646, 439673521, 77528388, 541604687, 344612475, 240364508, 509303597, 635457740, 222624663, 945319937, 838784742, 49970283, 48697042, 515858109, 248362017, 724528734, 372214767, 402330447, 662081865, 264913929, 423634954, 793388059, 78253014, 526940278, 225281082, 51104141, 233061363, 568731590, 882389936, 316035823, 86518515, 863362249, 726388033, 635778480, 97580183, 194452056, 663472938, 984464909, 378182075, 385200499, 260427830, 920945290, 579586903, 533143882, 279448541, 626770209, 359783028, 222439255, 605212681, 429591594, 785804076, 591704437, 975590935, 629895502, 259937041, 240540982, 518866379, 279296430, 219422869, 57011141, 198782513, 190019281, 430432780, 75078404, 992942750, 936550659, 882182949, 574730576, 757671772, 874059070, 395945675, 984952127, 331181005, 61361136, 334990324, 494757060, 663032736, 262139896, 799670967, 683484131, 954440307, 8192096, 976669024, 367899054, 81294308, 948991185, 188528242, 354547373, 675359503, 607903514, 592174761, 782947917, 503590739, 89066450, 630648764, 57108907, 667315, 24082055, 202813159, 461117618, 170863025, 933774333, 58006395, 365538071, 205639661, 613741358, 640218803, 930830230, 51684366, 207665374, 868723337, 258983174, 684796649, 226735747, 265997274, 778549344, 274955638, 848921482, 354470851, 171518411, 241116521, 446815835, 369608554, 661805974, 807687980, 620647852, 642644003, 273729894, 307587354, 97933545, 564042353, 743675649, 642438365, 642767109, 330984764, 869952142, 502350878, 602444395, 39826612, 592191800, 968440039, 504079818, 427760376, 983555600, 309553683, 998224912, 443551273, 103192975, 502564707, 8623959, 247195616, 383551120, 215347772, 423377667, 39497797, 176602408, 761580229, 415994241, 752628522, 458784769, 139036897, 792244225, 805394881, 207610196, 656633489, 258617872, 457099969, 136507485, 767361528, 814678364, 844409844, 398563243, 685712190, 674758757, 437349231, 646686257, 947146096, 274763156, 51918652, 979479522, 904951562, 289618398, 474250240, 121985010, 787212750, 262958840, 531239583, 355934149, 470211263, 66800447, 484617272, 222518954, 898103317, 399830261, 916872368, 616103371, 13918523, 370644683, 295312931, 909674075, 558353443, 559618130, 641455051, 228462251, 554477574, 277841691, 375930018, 212726631, 20251026, 700877394, 687960128, 550027158, 877434308, 472084921, 671704736, 906346124, 5941821, 149814742, 753219800, 614648261, 348656414, 904281520, 670472839, 519123050, 736095183, 716688178, 378732368, 291098056, 496095949, 506222922, 203260467, 444962675, 866601919, 472177811, 60436050, 886793556, 88431683, 170333487, 711568453, 820895504, 619693135, 205454146, 623548189, 805665424, 33442242, 248349429, 739310973, 464569194, 388534042, 755569160, 60493543, 980679609, 449236213, 526302962, 760788876, 87082794, 43140910, 99165336, 950655723, 760754612, 733256142, 942885963, 680530084, 886183563, 362504574, 315656828, 514541687, 982352667, 10575220, 32153778, 771616546, 202197119, 872042653, 389406627, 410033346, 729091932, 526069736, 802752989, 782308875, 201003478, 981136754, 556691735, 725058895, 166380532, 415514479, 322779138, 886524657, 697902551, 22758244, 928899849, 502286435, 662067002, 837508069, 847483982, 104996233, 389226660, 302540001, 931044947, 277078333, 647761517, 122823001, 516481777, 58436518, 128631950, 549874453, 389795674, 834544417, 810776615, 539832037, 162395673, 462344465, 934627382, 671632614, 540451620, 971582012, 240044756, 768224068, 130932227, 554470778, 613963055, 455425986, 378713450, 654713483, 52839975, 505596763, 446859742, 307921466, 651564060, 796302919, 484261797, 473836767, 860954769, 955456559, 764946522, 586567417, 150552752, 233325764, 193842838, 802233808, 125044964, 364655050, 960985125, 832464685, 956926102, 6731277, 227145470, 98154826, 448873148, 593401780, 78122500, 733843970, 234082995, 130418068, 675934992, 986163410, 234182919, 444207774, 438342065, 116218537, 917185297, 10953577, 568819662, 831855799, 113179263, 862377525, 812377179, 509519018, 418995953, 154076008, 542976631, 579292824, 710874381, 634497443, 914593734, 784968376, 929671954, 462769950, 80613657, 133450134, 390211052, 877185625, 246700245, 357538696, 138167684, 135930669, 447027995, 988235365, 583717673, 633974900, 107632246, 104232937, 331533379, 461922905, 328137211, 172678238, 935794616, 28053674, 909233758, 639948157, 268319838, 110480462, 379565697, 403095820, 127789680, 406717812, 937891526, 731401635, 764827478, 19861603, 996666021, 59074454, 354324121, 592248240, 83811096, 518689440, 367006428, 734627440, 335984845, 565227611, 261097916, 624758484, 615742789, 228433309, 623905552, 255703694, 729845643, 481306913, 574162404, 549767877, 619122508, 845323706, 708625696, 125481185, 981074635, 698213029, 68636463, 977414950, 173427703, 853205391, 532912125, 220492696, 334265931, 51424889, 559205202, 957872649, 936291267, 448801928, 936420702, 916313099, 255346503, 993317485, 829161014, 442275599, 257984853, 477059485, 80789817, 590271367, 966207491, 291346928, 740344452, 70662722, 730624751, 874453278, 171748781, 651508918, 251831762, 43982282, 26235077, 154981328, 643126906, 445148187, 510826170, 990714356, 367891235, 41191151, 449487073, 828920107, 939760833, 450935136, 564096510, 846791987, 715185396, 198544529, 369242259, 385948860, 861093936, 80532220, 794653817, 773256216, 165382284, 703829973, 838564920, 759160004, 202221339, 303817662, 37213611, 80504045, 727423123, 758422379, 187144529, 643941117, 245059263, 522453974, 547891273, 249063159, 970363953, 841284194, 52394528, 148880672, 569343935, 558144277, 894637297, 643863993, 97155505, 611979591, 994576195, 388431153, 417014447, 152713337, 299837700, 956926172, 98679690, 949814770, 707614765, 87918698, 504021747, 248563809, 858339205, 506879458, 439914935, 495854893, 23783333, 595509326, 59723773, 963066379, 690153640, 297876702, 359796876, 11445107, 343898859, 231718362, 588449254, 375144658, 269636805, 254776890, 219581491, 186708799, 995089910, 967411910, 286262327, 154753654, 812941180, 738467751, 339886540, 69163745, 80640120, 460801617, 753051383, 811649811, 616195487, 167975848, 562223769, 959708196, 798272328, 940773443, 136949895, 553264497, 844121234, 897855605, 159068814, 505188166, 568169808, 712986184, 95210704, 901622862, 903374552, 158405058, 302578995, 948198006, 451361042, 170916211, 892053617, 693955983, 998507195, 54365308, 136526452, 350630502, 687877736, 107439983, 377170773, 732142718, 301072297, 812998196, 330025561, 487765140, 379419946, 281136728, 216187028, 867486445, 609724334, 276227258, 759012923, 420635621, 468141598, 447648026, 550846347, 498293832, 64644597, 811700478, 744400503, 53160756, 985916728, 281895378, 334024966, 752492816, 294947808, 613781604, 691295789, 703535272, 749581916, 926897905, 646703230, 712824485, 745964042, 787403248, 898740524, 225892520, 501673605, 448325651, 555892151, 75775006, 311123201, 38203093, 217109112, 222657804, 816013726, 630026826, 484916559, 715319225, 350279450, 849921399, 419484766, 803523202, 277049286, 621043522, 819194723, 863043258, 522730608, 579324947, 297589823, 372901256, 873909631, 774996664, 893838652, 473955617, 228560740, 624310821, 931578065, 535015729, 140788538, 652625154, 9806843, 875897806, 406786805, 675476563, 220661442, 772355521, 33551481, 904211289, 436328168, 124928186, 650001181, 793728063, 542866703, 125015246, 60543688, 778344977, 429238683, 124423950, 284128530, 81792574, 279605643, 621569538, 484981520, 401813924, 150126452, 442288439, 873351213, 13657408, 806253353, 957692210, 359132575, 756794811, 679121283, 942082135, 139587835, 889846721, 833440674, 646712347, 199402476, 518605926, 923603806, 337690681, 32021606, 966141261, 401314039, 314120482, 227423044, 186783492, 769141809, 776694331, 32481954, 103884320, 805266412, 525732869, 27558202, 750715246, 199737846, 322392399, 27280455, 842532269, 256845714, 513203464, 112198102, 465094225, 751681512, 396764105, 460004106, 824561551, 682081450, 222919551, 866753275, 985893901, 19910462, 458379740, 850760939, 657882394, 539431248, 838244342, 96105632, 814167720, 26630719, 363169024, 267104620, 551631458, 268443075, 575169625, 284266912, 435651506, 70018287, 961152972, 329015283, 428168368, 803487984, 786974205, 279359259, 430590899, 454988220, 256381978, 795615983, 716533420, 733963234, 941495477, 367252177, 201196517, 771254992, 819139479, 801838501, 460550272, 967526051, 922734208, 846032435, 494138433, 958068354, 195855907, 568208073, 524780869, 561031442, 87451, 134227278, 212414926, 362440457, 400057671, 719210678, 683509667, 641567689, 192433230, 947760566, 862182058, 434118867, 756532674, 77860094, 256416606, 733922541, 606915786, 148612204, 748189990, 968423272, 103837511, 970000381, 27552015, 125242268, 586045653, 433439916, 742987315, 654320483, 381281462, 518049545, 34123888, 810968298, 698956867, 965885714, 618479371, 384654308, 824216482, 904763591, 461059749, 810003490, 33351542, 486560053, 17094868, 382287472, 541817222, 80329721, 676503101, 275558153, 823103, 820127571, 803942378, 263382209, 789926595, 45201694, 920895515, 608346067, 899665730, 229890136, 900626414, 884613310, 656573968, 297643283, 308403837, 683060465, 504886238, 981939360, 988846877, 474078648, 587797737, 892945014, 793111724, 702450977, 93147762, 484201915, 811581541, 815651872, 916922831, 876339576, 329344250, 193406611, 657285505, 2379038, 486415349, 931714711, 743798976, 722893850, 588960313, 385710970, 785708604, 424192211, 352943589, 187742153, 111687811, 679809090, 611570069, 504403570, 610268966, 692165363, 943375177, 183264224, 892599723, 53742139, 79418633, 806247879, 808135140, 395274306, 832054660, 433142553, 411332821, 939415152, 421450231, 831176129, 31495715, 670092369, 3392694, 35502108, 982989500, 866542811, 552673229, 315486861, 986069565, 899181518, 14912494, 697161352, 22043468, 753426313, 915793525, 188087943, 368469751, 524579784, 660380834, 45910857, 116790973, 98976271, 123283733, 405104275, 650063905, 429921760, 239922479, 474114382, 737821952, 434275211, 887430912, 203980392, 108454540, 323432645, 158008713, 925386998, 297942521, 673707080, 546063136, 661199830, 551543345, 722921994, 881438921, 163741829, 803912708, 478223364, 297100932, 811622633, 842369788, 667388703, 470190892, 255048055, 619318677, 417893422, 734497420, 824204576, 956969435, 746828132, 135029952, 228661906, 312351166, 833340605, 112932564, 179187149, 911100028, 793696358, 387567200, 702447511, 184355571, 477856353, 677653968, 247019786, 483558519, 478924288, 640048565, 952311093, 310358439, 36208950, 82526513, 888227315, 864231611, 57469412, 815198605, 845628902, 270619748, 158707422, 230248617, 518011234, 645796038, 698572199, 664855930, 73390334, 574980839, 663968208, 350867982, 119215244, 337026518, 863172262, 763412554, 750712523, 471072326, 264665298, 940157962, 135293271, 789018385, 731903327, 31833647, 760543685, 950667829, 806151933, 432569743, 940844271, 993972859, 65952998, 302291464, 229593744, 35158798, 765868083, 707138044, 269262668, 675143792, 978963757, 115151084, 420280862, 956738043, 407417339, 972511247, 727053314, 610692090, 702714781, 912463549, 308815888, 245262767, 80690546, 952586628, 588283408, 392073788, 209483322, 605196279, 12109172, 579622988, 460385627, 9347216, 684694827, 162915727, 732890872, 334049236, 587963984, 637444296, 931485008, 207451444, 373122751, 638204423, 857628190, 829856633, 278049431, 540256987, 768407275, 891383056, 537759286, 872798825, 760573101, 899599890, 999024254, 428775959, 244342253, 139882719, 326598493, 9640563, 143823037, 231344443, 157701068, 744044194, 911773631, 346577039, 304763010, 626679121, 488233244, 742384258, 655542232, 596741244, 447998173, 250196870, 593733661, 439817481, 199395071, 615741209, 25661403, 463958954, 270950152, 91543304, 869659734, 878617527, 535516653, 766255662, 159065921, 263573380, 941323849, 483199287, 421423240, 990963415, 161775920, 592381912, 933964816, 420028042, 397290600, 867792648, 606817790, 690225319, 252927194, 953336583, 233277911, 148026382, 325078585, 816410684, 30400642, 601538803, 408893820, 667713954, 309069713, 346716804, 860852788, 650776117, 620077197, 781417810, 157295733, 529300443, 253930231, 948067866, 675235211, 936749300, 253187820, 392658258, 462497913, 874821691, 246257222, 466279975, 386337098, 71350893, 705507294, 883477093, 77658234, 298758559, 273700092, 802035927, 74546812, 964495223, 489550652, 836791556, 566575664, 907147681, 456766581, 67783742, 875624774, 273014459, 234733301, 667780, 379798371, 741225913, 688595663, 342828322, 521329660, 518358381, 64697153, 940713916, 441386530, 576890672, 876169231, 385433675, 107563575, 803992853, 353305874, 143035480, 483736354, 986237422, 141125539, 339222261, 236588687, 12221993, 404965653, 315364372, 793319712, 396279540, 937953478, 294952983, 457274105, 801561786, 990040320, 164358653, 800820123, 430804396, 960237783, 651337350, 932458869, 319656763, 969741202, 257385209, 547221800, 30492066, 270810147, 838982273, 600199315, 316598113, 526287729, 347202522, 481381888, 917952818, 31603306, 497602163, 999366734, 125601988, 189518659, 191230700, 941267944, 560599710, 284337651, 103959246, 295046256, 450971894, 220558480, 227279347, 576635335, 717651042, 956025606, 405141207, 912900141, 764843319, 642887265, 287622329, 993141260, 372039321, 603286904, 290678431, 917139225, 67066592, 804202383, 279781940, 910233567, 12299259, 125979377, 530266156, 378482400, 331390804, 828024161, 594263654, 599116825, 124147976, 313637455, 66290934, 67576448, 99170111, 164003828, 654219306, 473425839, 932784262, 374551791, 989586870, 694164680, 53030335, 85671398, 495525282, 208670932, 840871507, 794431699, 12521971, 172122113, 312847612, 954594064, 276824895, 756992055, 315069504, 852711678, 309198960, 402506433, 835807778, 971473928, 813468365, 303502219, 105905679, 72917837, 751932289, 418182238, 785605021, 896271632, 470235457, 594912722, 144272401, 645987911, 679360335, 230357496, 701022419, 311908701, 959350277, 272790588, 630808021, 790056441, 829996170, 164936730, 220302776, 958428268, 965406566, 358750228, 963539125, 484186866, 48835677, 468836507, 49936779, 740340405, 289236377, 106311575, 861461729, 111582020, 570044882, 348970469, 714744079, 808307087, 26641417, 382791502, 763410781, 655888846, 673186477, 7128689, 952811753, 129334006, 70731003, 603423104, 337975305, 460202635, 53483908, 293882223, 825297239, 644998956, 449891368, 859282902, 266231867, 247482441, 9947019, 725725135, 65153912, 666860899, 641213834, 728821079, 162480878, 425046473, 233211263, 652672988, 323619014, 826022198, 380789343, 252185196, 405564910, 458537430, 107111709, 737320555, 484849687, 438593813, 820756257, 167377365, 656011182, 935127768, 390134219, 299794836, 932955241, 917488505, 224866114, 749978020, 528575557, 213210243, 764358709, 504762593, 524291288, 916219161, 640781234, 155918168, 11263677, 291551865, 921646184, 96608170, 799864762, 648182737, 234090116, 911286363, 615048207, 998243561, 80401768, 965918196, 792671645, 831024602, 637393204, 303606988, 892797150, 925902644, 563605925, 653352983, 334535337, 862206318, 847156434, 209066388, 782820009, 424945498, 314311544, 600846393, 492097788, 570153658, 54398571, 27267469, 118409258, 89852404, 984154152, 885022035, 351673186, 623947694, 453519499, 959727276, 653716399, 320118244, 596257680, 326592531, 509691569, 429911511, 475343345, 369836851, 91195102, 565141691, 323325651, 358549288, 271887357, 583391344, 858590610, 28740557, 159141633, 980911236, 657705685, 718807249, 552057367, 731964238, 305545175, 659642875, 249382106, 61406817, 7347282, 551255481, 404235184, 871910785, 992863742, 623839329, 52509102, 682051481, 404919281, 898079708, 900781707, 245194404, 288357490, 837467625, 740760798, 551208976, 959220166, 605157352, 15272657, 763522224, 351063608, 453192627, 946300450, 118150211, 610358217, 554165724, 870513603, 714115429, 389763385, 788486880, 792286644, 513072517, 692713293, 891635743, 815907121, 999751255, 428266249, 600270362, 804873396, 124759733, 313951163, 824428110, 916990016, 441734304, 831119131, 416208470, 943362120, 857676265, 692314689, 569541712, 85083419, 704487727, 3316098, 747846748, 795058017, 948975532, 85285330, 460066279, 191843994, 209974007, 420223829, 310206624, 358402149, 143484725, 412436662, 859693434, 667658711, 988029042, 647007891, 123511967, 685377931, 138246796, 404921186, 27523196, 415740234, 447714681, 38023127, 342649404, 871466184, 873483756, 440642864, 257070644, 428753805, 184149020, 934249272, 92680415, 912617820, 845927355, 257889548, 787664026, 298093661, 941709760, 785530238, 91538972, 345532192, 348877136, 899438102, 876160375, 779771424, 368409540, 379334746, 224195706, 173872843, 182120735, 726944525, 198218932, 270250033, 73991526, 108625804, 342138902, 778821826, 634224374, 282936324, 915943112, 69893601, 76633412, 640006858, 275091823, 83873103, 275945913, 301152610, 56960500, 528035479, 920169620, 393981207, 405329659, 740325241, 99486725, 242542670, 97518454, 416392492, 85237711, 413827455, 322870487, 107957678, 828366467, 409901501, 629430007, 421810080, 729053496, 370295008, 810266815, 712261124, 755631, 629076133, 676927157, 712526821, 144995711, 147998197, 984248566, 31058590, 765248858, 517856432, 341502579, 414839098, 155296823, 920105251, 100433543, 453734003, 106279398, 102339260, 959181742, 953617917, 925038985, 835447638, 541005619, 54363016, 380734961, 717447026, 998641068, 877435800, 475211775, 858893673, 236269306, 951626615, 968964657, 611578726, 353694529, 178403316, 308490354, 24140224, 26789823, 929942885, 659966762, 441515906, 531376566, 563351260, 16508832, 634376515, 252128919, 339193579, 193594270, 755298601, 900179160, 513826510, 668429679, 364657601, 593844357, 543056760, 573981927, 588158695, 30165060, 332132612, 769143769, 61320127, 125515493, 883415159, 239905080, 928537265, 322756421, 330140074, 267446541, 880578219, 447381411, 894443871, 50366859, 202680539, 546498722, 860533372, 321368565, 624626230, 809791027, 432233785, 801929795, 356309046, 814209465, 890479776, 789685277, 511316124, 974657854, 284413208, 560011479, 856042364, 844627615, 506658269, 641385208, 211126593, 873868112, 750893998, 6246637, 404128871, 322299878, 359936966, 411065318, 919269369, 264422881, 49411795, 387239477, 579057721, 139850013, 671821660, 927956380, 924583709, 695387711, 874319582, 845320722, 975813958, 405852467, 613307198, 320772021, 524277711, 684396393, 215656448, 371831939, 75889331, 554890454, 505736943, 895601705, 713945726, 819857077, 280799409, 27676483, 436379321, 910759425, 591336349, 203992292, 862594252, 931108033, 614405154, 816643781, 655419741, 996456703, 924558437, 807709877, 713064871, 415625972, 242663668, 71440248, 954441960, 460516774, 804772457, 498684897, 312223121, 788937613, 453907030, 411147258, 10063021, 607515934, 63125095, 778089758, 982205546, 488642701, 540664747, 33534993, 95237833, 439868851, 97136382, 488166613, 579656542, 905403470, 354391540, 479590456, 710622292, 772178792, 118403215, 471573380, 387735138, 194857271, 691645184, 449661919, 940582497, 61927858, 327013823, 179701296, 365639332, 434123794, 601966230, 366830417, 25718911, 663355577, 288344541, 499470109, 571447555, 50964777, 978665731, 915834870, 157569665, 152155630, 252159057, 183411586, 136761346, 399636922, 26222373, 265384651, 663862238, 461377491, 256624342, 880288331, 178029284, 667741196, 858723316, 906422770, 426074705, 881754895, 319858523, 189883279, 950312770, 955280704, 249724114, 863208403, 183760211, 892310, 27354082, 865553353, 199786657, 791818122, 823106188, 860843569, 485520172, 172428863, 435525442, 615812626, 542795547, 724698123, 360261149, 520083419, 755459383, 734536855, 553199004, 222314162, 225110567, 582239596, 575278521, 793495665, 991285828, 547548174, 49804332, 3665531, 707432090, 569753063, 631413551, 400068569, 420934697, 853522832, 442180799, 18759691, 782709248, 288269017, 53869013, 855717497, 376668273, 69110027, 364584182, 106262350, 601500521, 135813534, 730395045, 721422709, 974399520, 79790642, 274538764, 892240817, 244918056, 997526842, 830692053, 338304920, 569380030, 786063093, 735319341, 137294980, 605125599, 294278419, 884572751, 482410167, 818203775, 192057745, 899788981, 214422415, 156155359, 818833515, 289087297, 271031370, 757065705, 919023779, 390433140, 115714870, 671894401, 385211539, 904545825, 888959313, 641948431, 658132572, 294767090, 74832447, 265613588, 326031573, 164660330, 82908961, 95763504, 856019052, 603063771, 524074693, 157172561, 685374562, 504719486, 413650723, 707877136, 283741867, 300200325, 133170086, 368862422, 803264864, 782951773, 591909029, 937726904, 902068316, 706132236, 911816161, 88448258, 208043048, 710405642, 304290015, 661008416, 893171850, 106268755, 825386989, 778115994, 528235217, 31955451, 985549251, 503631458, 232516332, 658690812, 860550984, 172887070, 797263982, 653259750, 107564387, 437022170, 297503213, 319947280, 256289718, 656322524, 910486056, 229041398, 800511988, 204303767, 53162486, 901066105, 330907455, 995053322, 625616171, 27183740, 704303878, 214356689, 583955031, 378328943, 266866192, 555983558, 332478837, 250061003, 367983366, 134114485, 976264760, 13414931, 383647223, 808601611, 446848725, 38360640, 412511155, 620818708, 483933372, 185860677, 835295166, 435732820, 469629734, 698097946, 650613475, 593475503, 383625004, 511990023, 159471534, 311520049, 882388717, 344825120, 150880088, 568400607, 127833872, 407099593, 372465144, 656819923, 398164427, 70282632, 420581362, 14344444, 288968054, 100450356, 952705590, 96309286, 693397770, 905824532, 11711635, 367171003, 723312051, 973595034, 337724176, 219372647, 559730852, 125465471, 744378781, 883285742, 274755653, 835182011, 819749732, 431176168, 956022143, 72689645, 837783377, 70546198, 592745204, 974879457, 838570982, 201722696, 565627617, 43121410, 677089599, 901184554, 228779433, 47422359, 405159685, 861928579, 185643896, 654034342, 613889861, 468156073, 63054355, 651198309, 216788067, 998291193, 122738748, 876184110, 398340198, 836882481, 50953707, 681290623, 406057756, 338185424, 42565277, 811407400, 221284337, 438984603, 69548980, 25192220, 619918402, 380948846, 504291068, 620216139, 667609077, 779295219, 881805589, 301168220, 273356119, 299779598, 856599546, 488434568, 315413366, 547863310, 269966034, 306501523, 804596269, 615477276, 666619332, 273560527, 190681574, 83676085, 641111241, 50878840, 557763459, 865006814, 757673203, 871355626, 472317309, 113768782, 415925912, 412001899, 693609869, 33181067, 742445527, 706835833, 689467384, 204661495, 674881154, 920899610, 662150716, 337520864, 235693042, 135792871, 271240621, 758844416, 940361853, 941158115, 800936921, 541299120, 931776239, 234399820, 444687, 301019347, 996911450, 236400875, 593363472, 818448698, 97818692, 558305487, 984777751, 900658173, 10451982, 759177152, 264252711, 23150665, 533987745, 185104480, 716287466, 441042390, 683247803, 888125485, 570489369, 175408489, 987823846, 453997744, 626908259, 212271729, 701546626, 231434351, 475305318, 764761681, 793403611, 541807461, 437357358, 763066917, 841588622, 295485753, 795200819, 627708712, 125033683, 520742012, 828649644, 717379252, 701735016, 178707129, 394889728, 986998679, 978503753, 497596976, 406370726, 355872680, 850796261, 127942682, 538935976, 333738987, 769171241, 248926528, 385250003, 425395296, 741124661, 755264422, 635003525, 182877967, 450768228, 284418374, 219911476, 392991924, 278413745, 697542863, 962125082, 948741843, 600599273, 79922368, 244216082, 894758826, 335662045, 36624623, 935550122, 715176642, 628061115, 28998048, 797897510, 391500967, 460514226, 415796187, 834612860, 604778468, 443388149, 246842275, 399113237, 981798529, 201657162, 844408611, 260706583, 869176941, 303145702, 437271506, 995132409, 912307938, 411935949, 593330196, 326940832, 296831387, 249027248, 668105184, 278268533, 206550603, 426769203, 471553558, 823512927, 467791065, 842963691, 8462534, 637558715, 973979231, 734272340, 421563249, 578113996, 369332000, 352005954, 34561049, 372589710, 538374397, 216491836, 996943071, 366861223, 33852285, 554650011, 47169433, 765346875, 403635454, 252215208, 908072602, 695728234, 733235261, 513122668, 800596855, 440399346, 221283786, 835862784, 762393071, 627190010, 212691138, 287908543, 93868446, 815774165, 292420093, 566247217, 792123484, 121789664, 45371248, 688753998, 244682120, 135230546, 984634127, 99552463, 160428758, 451840922, 489437554, 154746301, 286664662, 965982744, 275772415, 20187018, 34077660, 663139698, 325230263, 854573474, 500682086, 382170298, 260910072, 913895776, 638351594, 579548507, 810893371, 161153471, 508672118, 359217015, 475403564, 717945536, 885058120, 348341679, 266571924, 434315211, 613999622, 555930895, 704057869, 845633468, 87741295, 73030424, 901466718, 763523843, 313985288, 389046254, 537224340, 696329242, 803899765, 228719726, 273314345, 829522563, 76205235, 280769628, 172679001, 348771410, 702992001, 534347201, 688231312, 697594986, 107199799, 652129799, 891999812, 308408855, 498648240, 871082955, 331987146, 670108737, 457879189, 169615066, 121766712, 353444772, 804243990, 505069135, 272356208, 822297844, 182415831, 63402481, 639178344, 221400071, 704518770, 189918812, 302064019, 70887930, 722795700, 662880483, 782587843, 865247743, 883678371, 397908585, 236986467, 775377679, 337906311, 862919759, 837080076, 979303300, 275932371, 2837707, 14751396, 893784765, 108419323, 459189615, 382069291, 777856746, 491052543, 999626218, 236384119, 914313408, 24797334, 616242268, 569359557, 96501370, 46116266, 60912844, 497819431, 216020748, 249572044, 131404957, 988698051, 693050724, 778584245, 486052492, 368028862, 491734361, 487047892, 802684840, 437243052, 935990625, 95340992, 246082827, 666953783, 289029101, 993870895, 520028799, 238457299, 972752776, 289251347, 211722080, 943365070, 837785636, 100652442, 903038108, 197856127, 868279189, 93041529, 533759143, 998361587, 870107758, 707495049, 24072075, 704452106, 53459106, 317310881, 456573539, 143403659, 699164963, 362983295, 305093232, 143192775, 681583196, 127540804, 163921056, 47654177, 673278583, 379751882, 11229166, 92673660, 287715549, 25800545, 132319713, 529344008, 110963966, 348951048, 561602852, 627980264, 771985090, 322478656, 867936174, 548808682, 567084736, 852758124, 633839838, 920607672, 775730373, 8721794, 579635223, 5363676, 630987284, 663259476, 153330840, 545177282, 518839293, 725995942, 297757793, 626021196, 17765862, 99466553, 928566612, 612524099, 590051209, 524672542, 335272174, 819481434, 368984591, 717415733, 777144219, 923067132, 541521862, 892062192, 147918243, 41445592, 335889487, 797478177, 879763198, 341759123, 688737923, 634404927, 869017433, 805542603, 924469848, 877658982, 493725226, 704153845, 569600421, 591366982, 872086443, 701398105, 836357888, 832819374, 948890555, 777503150, 680985598, 671830023, 501474034, 734756467, 497138604, 974268243, 404554356, 96226849, 824710685, 740185403, 223723521, 670813281, 423405393, 940716320, 88599245, 165662796, 281986330, 652525100, 32443987, 374292668, 609524565, 47432884, 802466062, 625968730, 210340040, 754531321, 300559698, 295857516, 953739735, 122839938, 458732938, 552476594, 773209278, 841794491, 377337187, 500930464, 256833889, 298584949, 836106563, 129483665, 894684028, 877709618, 905041712, 597423634, 607868387, 767140318, 140837075, 930807502, 282428766, 616482623, 994686048, 306919592, 379312720, 193265237, 101767199, 517662500, 926219296, 26326210, 305554977, 507841209, 958901082, 822216986, 794725887, 185329734, 215505664, 959790279, 989720755, 299460432, 64122968, 140681714, 169026236, 65160147, 816253178, 969274144, 226459137, 25362257, 179951975, 980175290, 987556065, 588805111, 270350492, 310437419, 833344144, 364429467, 657682666, 16247967, 778519064, 450994390, 210575932, 169048473, 822739121, 678496384, 733372300, 681543435, 519964433, 279000209, 287343194, 917301519, 548915660, 686795575, 581527426, 357666599, 366254362, 291003284, 14564469, 880042180, 373523315, 322419192, 186366445, 113215999, 429635896, 741128312, 221921234, 575154612, 930357708, 651635685, 622329735, 217035311, 226670808, 197071229, 48039494, 836601194, 929570569, 812865024, 550085800, 907024235, 782143654, 393160848, 301365708, 888348982, 744135849, 34649609, 189695493, 782594545, 116558536, 280584429, 282551179, 856975668, 129181818, 863758270, 288717378, 415613813, 470391365, 335300098, 218661921, 196661648, 2835606, 70643074, 518136778, 406629926, 854782298, 473892481, 276974282, 347228454, 578867113, 189035410, 242354639, 348026924, 64844438, 384831156, 820150445, 66182755, 150728580, 108371748, 481180465, 98751161, 137488601, 175132030, 66344463, 910402752, 912075538, 722144912, 275135852, 823903551, 665513728, 872480776, 34847670, 807148678, 104942611, 13052308, 929364797, 801311086, 93906454, 385176232, 225226203, 183979046, 222179782, 220706745, 427776471, 362249895, 629227621, 492605327, 784914153, 562807475, 27073795, 381748165, 272213552, 576689677, 707978292, 220756228, 972146450, 279354740, 425968095, 265237572, 351079582, 56877619, 693346453, 160070768, 693741548, 133484963, 252920390, 364993241, 333297481, 483578211, 521881444, 609465417, 410310330, 946937461, 208422303, 372481090, 451417545, 193785525, 795348608, 620838902, 979124082, 193233182, 245007536, 18069314, 676504193, 733630230, 595568482, 917376476, 974750563, 443846979, 632012052, 305054567, 332350362, 235964077, 233609111, 946737344, 397197244, 823596078, 70167479, 471118356, 123759170, 513810092, 558437354, 483962900, 555677644, 448434669, 322726310, 765450952, 223255141, 295273643, 431255670, 39879867, 458663001, 658795442, 420835219, 450981549, 692164707, 856844747, 989000194, 859584242, 571730447, 198545379, 877006030, 491683571, 330526156, 445701099, 94094368, 893946102, 654174557, 458016617, 359290730, 234253650, 610000599, 150971913, 708771235, 192203659, 596852189, 182184788, 903349774, 60648730, 144194935, 639819528, 934075630, 307720778, 557128262, 333989660, 971468505, 269314611, 433700125, 951287933, 851639917, 171319068, 73875423, 389440152, 917599020, 316352768, 769404864, 574670278, 195270271, 506846638, 903134624, 393600362, 212026396, 420854432, 493729010, 637823352, 430218434, 861551435, 195974930, 768837691, 31950219, 111989436, 505321602, 744620596, 392539289, 803266425, 830341447, 247278310, 913645873, 315673310, 905428237, 602238613, 489684607, 698988952, 703398837, 271019093, 841353110, 944206039, 579684362, 938144208, 271699062, 689807136, 444292568, 109836942, 819028701, 829429843, 397303725, 515567263, 533608234, 59884297, 246580789, 715546539, 623490223, 766145377, 579009191, 989256503, 962013849, 344703214, 825997970, 238825570, 787484836, 863661235, 490314850, 644958272, 853661401, 306908087, 553205946, 370697258, 318947308, 487335715, 857140734, 830887813, 928731073, 175511771, 567320543, 859926835, 475471405, 692324555, 590998807, 212746318, 270844059, 413097263, 658120842, 352597252, 611611381, 498764753, 288279502, 451080118, 955469960, 599724277, 783952743, 7830670, 291942251, 563522223, 512033632, 110617169, 646826421, 450186328, 527584675, 762347259, 28848454, 401427381, 550435170, 495292807, 286112490, 278359973, 994785838, 498228866, 968968355, 852466902, 446496882, 286913136, 788644492, 71680826, 177022868, 27900994, 715689744, 881051992, 166798901, 71977980, 248703292, 868721903, 442927431, 430509837, 570250433, 435796964, 347262099, 810394119, 962050673, 193729453, 31026463, 217862717, 137201010, 749148434, 34152547, 170701174, 635064075, 526561140, 98512959, 120714229, 35232622, 709008382, 886072235, 555203645, 444523966, 109178509, 217303672, 498100768, 232185264, 514720786, 912459010, 978926219, 182311083, 347990164, 870218202, 475154532, 128136504, 184960428, 902474563, 232495590, 714275767, 498350579, 191441315, 320972159, 330070981, 489316720, 718563287, 945415425, 768170798, 180770072, 766515303, 406229163, 837289358, 678165132, 360977744, 516240, 779508759, 858095692, 396962936, 426606736, 479266407, 897500728, 86801244, 242784762, 325768850, 298123616, 42812997, 306492346, 157824151, 458353143, 992100425, 574517874, 567947339, 380435083, 987620755, 635865587, 873843382, 145337582, 471522847, 833280940, 614159848, 484813083, 10327812, 13408674, 849356248, 619106763, 810923729, 419664936, 272023416, 109692081, 362357873, 534336722, 23746579, 45332519, 471705706, 947896996, 142860247, 396735200, 533710793, 238205592, 209158078, 275707295, 954798851, 968226265, 137308023, 924486944, 657324459, 641356211, 610749469, 7287394, 329538874, 377760538, 677820031, 687582531, 560430894, 813361172, 177957017, 6229203, 109644490, 704168059, 63175436, 897953665, 322483085, 801502293, 804131832, 403216294, 380877856, 773644268, 556493797, 772717712, 958835592, 534750236, 13655774, 40989054, 562325846, 142152803, 103152370, 265906735, 256730176, 577442949, 13968098, 228023599, 43791701, 596380294, 284373239, 894802836, 698288501, 497380555, 513614921, 592214583, 638261726, 732974356, 553700683, 271323657, 400620943, 723164801, 293902865, 953264032, 186025159, 732430837, 640449641, 804167892, 705484248, 546596807, 317767685, 273995467, 702785661, 800374222, 768432058, 139228378, 864712899, 738937490, 376608099, 20521241, 614057496, 340397227, 759051712, 113553394, 30876083, 606126746, 510060129, 684389912, 912742083, 145009260, 973972647, 936030735, 426774895, 510908889, 10833547, 25573083, 801569851, 916303473, 489431265, 330201108, 176890399, 791272237, 864535458, 36430827, 152270107, 41994748, 761130058, 755051811, 573803633, 251489084, 8223358, 813084033, 160681700, 411397849, 270683552, 172058924, 145580975, 2648668, 690446489, 136158665, 926725391, 942612294, 453405682, 902036671, 15943938, 280153898, 695557458, 989874973, 595144853, 38050195, 624752436, 667725523, 265675049, 482311452, 877826692, 16098709, 493535830, 37753507, 838307694, 69153562, 677093545, 800645927, 866775426, 665157287, 795833858, 181082683, 418584797, 701923213, 768594056, 432401689, 746359686, 319915331, 487989739, 428956630, 782501754, 138882272, 769214300, 200237136, 793441656, 257529142, 565769339, 808907776, 15339761, 765601501, 968676134, 238331982, 906768467, 324980361, 82676597, 480275296, 342641778, 516719188, 491508039, 104755918, 812294250, 7910383, 309480222, 121082969, 862439062, 469500189, 493870013, 932850012, 682694932, 304213341, 887073645, 861224534, 654482446, 701413636, 699535785, 656053933, 56556748, 21839356, 14729928, 112606308, 452904585, 896065676, 412638199, 696909865, 114385612, 727629138, 479133208, 197845528, 22799414, 575086525, 884039446, 975844296, 508688584, 329552631, 179263930, 609603142, 779414450, 182020150, 956940972, 368125011, 535527741, 634942441, 180958861, 193321890, 903900866, 917568435, 198824703, 734428280, 627120360, 850167613, 952417989, 290112325, 866970504, 593069663, 996117481, 37232752, 662571550, 398116885, 65619452, 153506210, 406455449, 552553397, 268109497, 90184410, 366568007, 945146483, 657625934, 209083389, 938330129, 493336955, 826983038, 215474744, 522468926, 901811068, 595158544, 507938194, 536822936, 92374517, 612118876, 469888850, 119134299, 415230028, 717281336, 889827571, 633759511, 940831282, 332000604, 291039799, 502903431, 157234675, 899017037, 811085622, 925369054, 41156144, 564865163, 187856200, 682670040, 804630787, 37317315, 410852491, 260433732, 601800948, 965755092, 24967211, 976069321, 994897782, 831918366, 473061910, 205543015, 243665672, 205478015, 912573470, 608540400, 255255328, 979234710, 826883742, 702851027, 22573938, 173923068, 274550213, 138297459, 911509076, 172151686, 534217844, 822112293, 159598139, 537829314, 64599498, 697462815, 36160767, 545205777, 140793891, 676529694, 867025312, 341689277, 691243108, 213561095, 61180381, 429368155, 383048294, 79882921, 269075863, 6853604, 595518763, 301494435, 183676593, 399081498, 130740327, 768481716, 16245144, 844220600, 827018091, 760766743, 17241948, 790564859, 960750048, 251608061, 826156655, 685680244, 874017318, 232772314, 231397846, 33652749, 78142641, 496406728, 393736749, 367318675, 953162252, 677835494, 844734491, 6700614, 799562309, 357400564, 379930258, 248226895, 585418303, 208883742, 66138892, 373711736, 464167804, 231068454, 443244048, 526786757, 388667422, 92254768, 462663722, 556460781, 301328888, 133938604, 142184015, 974832294, 579457901, 785557346, 172647017, 656227759, 558946610, 128483066, 645218911, 78885399, 84348754, 259325932, 206301284, 249955759, 922022218, 952105017, 168293602, 811901733, 573964184, 331103657, 954851445, 432051548, 248757281, 447359917, 750204069, 509389205, 173635483, 654240906, 963894467, 176743368, 766111095, 808183300, 382303576, 198851671, 299001708, 378146254, 541836417, 347108518, 987526374, 8098317, 152253964, 755656013, 651665031, 571370063, 811317736, 7614150, 549675539, 493917204, 173822484, 448143176, 319129671, 155768858, 46405920, 256380786, 358579804, 542483923, 133092987, 202853395, 914085891, 608653999, 790492701, 118655752, 775409613, 356071835, 815710739, 287362717, 371955994, 127786743, 478711272, 181604508, 587165543, 544039928, 844228306, 969211029, 698893632, 754310216, 177354200, 617318562, 20371086, 126033965, 188105062, 475703302, 712662703, 650222842, 612236304, 142427842, 224341184, 385079681, 160451442, 524728040, 876892201, 976290420, 505306245, 899644551, 308008252, 984551012, 29164344, 179430005, 171878221, 474791553, 406638678, 103084940, 963572205, 412132741, 960675129, 468502134, 446116727, 916668583, 322737000, 175980067, 158998033, 408942548, 303354498, 157245361, 175373187, 837569834, 983350228, 350399982, 586816405, 194380015, 425755099, 548239840, 372625616, 285352582, 455414429, 707835070, 444608945, 939731582, 639967979, 45500033, 190144048, 818240653, 874801240, 202494490, 403164116, 65163056, 815874549, 847558698, 990295945, 338645410, 874149375, 86865031, 420322857, 504856502, 791557479, 591094689, 177156768, 383538978, 41646507, 906287496, 445497420, 176034272, 325480994, 921328577, 21026245, 815059417, 798736336, 121981921, 661646660, 374585835, 517758463, 206552229, 432142818, 701038497, 390729214, 157351995, 897017002, 897106951, 307858206, 23793282, 288139199, 684544850, 884577371, 453432929, 111344091, 724498324, 990292339, 602407606, 861471568, 55785479, 610183660, 931058356, 853775842, 145547189, 468057121, 285133075, 505727482, 16435503, 537477193, 659403103, 167257647, 384074744, 962731703, 115209996, 712023355, 719913403, 529885658, 311611164, 372949153, 625297040, 640309020, 950900301, 975829411, 918770212, 846588083, 676770085, 294118172, 297494402, 871522659, 47748546, 700653413, 95938693, 27266543, 209693603, 4226788, 343601018, 644272130, 641936379, 215328751, 219604625, 63451984, 620848765, 269703449, 208384175, 363342283, 172501225, 49241310, 808152205, 639662972, 800772166, 947683044, 651962113, 358159992, 5435308, 801141057, 65008711, 781848562, 309480725, 764429441, 118984594, 563611353, 875003079, 666145584, 697913533, 25684217, 240459197, 332755595, 371063221, 728438264, 709299360, 583699025, 652471995, 616521154, 477017388, 892883486, 16640490, 968578129, 537611216, 317108370, 752422284, 140156247, 404769758, 44286434, 101638096, 484780172, 895280889, 1231843, 664337417, 254111051, 164500998, 774384047, 341292714, 536433068, 287118791, 407191168, 870491390, 334938384, 114091787, 417245752, 159564010, 275047853, 428724715, 365736738, 682207144, 760290585, 870050207, 742894739, 409211523, 199524775, 201285496, 834543602, 651330480, 26082219, 549955000, 857316087, 565374681, 727169989, 332160096, 23728687, 41201227, 330288799, 444860876, 853032607, 398532977, 503642045, 605596653, 497746922, 647521091, 797372891, 944148826, 960249695, 579509663, 278847633, 968914368, 842594345, 491095246, 418580487, 723982853, 873670506, 657061080, 427840513, 461304029, 529731505, 248042244, 468832066, 614001824, 519815071, 632150779, 47343500, 95877537, 360780280, 391784087, 92428339, 260382256, 170304090, 46327143, 88692558, 209760225, 29491748, 208474195, 127479811, 620245043, 251753115, 162471791, 344156460, 844797988, 929440583, 429778590, 393403191, 715234427, 247850687, 68147358, 10813709, 371847959, 660235132, 593818639, 258668147, 315222186, 319131741, 98992763, 608202552, 770810448, 251934048, 609213876, 984870106, 106273308, 68840231, 945643490, 167824438, 560047808, 716461390, 712268490, 446434488, 526135935, 619903307, 408295157, 155258761, 351217332, 282718100, 341536339, 53266799, 397098719, 584932024, 552027918, 357130059, 75079811, 405172194, 90276591, 998136293, 632590122, 821813126, 991975834, 683617206, 436517590, 978816685, 146488182, 189907160, 611671708, 595387670, 799192199, 229223389, 568787823, 16531464, 408547968, 458973043, 303946740, 671900587, 599722976, 37834696, 380901228, 858824531, 867473246, 125662096, 202613568, 139124758, 186723320, 433894196, 765472002, 483702353, 821105570, 545102688, 318079038, 686467734, 442339463, 617481920, 581028885, 865696655, 863097991, 442882896, 69229021, 152700296, 593017903, 323034646, 142061418, 107699382, 540328635, 947274914, 40211174, 332146697, 422784763, 136175894, 842551995, 425235531, 160281021, 453483395, 917401069, 189433383, 614170697, 76759879, 890254144, 71189354, 761448596, 737492073, 999475283, 779667470, 334159960, 67903962, 91448080, 512513172, 661342970, 187853043, 804331148, 685260566, 37605701, 358037876, 711953772, 832260909, 641777281, 606150777, 994577649, 876397396, 192695249, 121637894, 232915413, 824578231, 108504900, 135927154, 398360977, 253758534, 970266207, 553769191, 221180515, 143087949, 777511453, 95889767, 441488175, 592451244, 310372192, 557752402, 276869997, 811210237, 259436406, 14005088, 981730027, 387232401, 699499446, 144943847, 650274325, 726174329, 697031029, 740078082, 204476777, 66037187, 341005502, 609261483, 974516462, 891529915, 160600496, 510924648, 785280610, 551058801, 737302636, 308119470, 112450840, 612740855, 523024638, 984619790, 192674542, 940829147, 717640036, 899348918, 211894312, 744241250, 930202869, 990156543, 909044636, 777679863, 51702582, 777548198, 851111964, 357489937, 896925546, 571708257, 873488484, 728017877, 7278553, 704613886, 333016211, 750164723, 762844729, 975797205, 634526481, 254255240, 274388218, 569552572, 466672246, 410468859, 977909584, 82092014, 711015138, 269444256, 128745442, 653158915, 254255894, 597262624, 919446164, 259084979, 97885263, 302662511, 989769563, 68812104, 511465178, 904001740, 149306073, 650868768, 993172474, 118729395, 7647049, 699758185, 727911206, 414967759, 505886573, 180646118, 660486719, 272434638, 649352699, 716620897, 606788638, 280454403, 3980508, 618180614, 970708022, 549768639, 346386658, 360225483, 685151954, 56689748, 778983715, 198252814, 649910266, 926309727, 994626736, 772559839, 718691625, 940247902, 535705324, 848504333, 104670747, 148708155, 491262198, 65597276, 142945198, 768813753, 299253040, 611889513, 486881812, 616167887, 421877833, 468396420, 168753473, 626252600, 947862428, 488512579, 993847015, 793976809, 335387650, 865700412, 511142019, 77507034, 114380011, 616832342, 621723821, 895968178, 992238885, 70844538, 717915057, 636092651, 537513959, 19242500, 11707768, 967900458, 93460908, 309458713, 541549918, 359801453, 724617353, 867701416, 268064960, 580657713, 300659812, 912633072, 239984920, 896431267, 895477416, 856688813, 868442463, 883848950, 226049826, 830639281, 941808731, 133606715, 324860825, 262278941, 203654686, 389675977, 618226161, 506999999, 827875037, 433725403, 471107028, 20117383, 519248761, 565467294, 958502985, 777514567, 189944296, 351651954, 885093341, 801499833, 453822248, 463466541, 754710760, 66508401, 286673447, 956194574, 894555575, 875707512, 387999515, 551280865, 491922582, 1186448, 50738097, 66536834, 82133782, 567991099, 905302551, 200460102, 284698803, 251969115, 968972569, 177614377, 539199368, 485137795, 762384897, 845302598, 389547590, 528734329, 811702144, 508022790, 531848917, 56928750, 351353334, 237118534, 477539381, 99942432, 627651170, 174102502, 133099049, 764987731, 92449707, 430782035, 966343991, 169866943, 119536814, 590776412, 664642298, 797626337, 585541779, 419636326, 700914395, 218219413, 767856050, 516554787, 402433655, 582459220, 792245331, 32500471, 880389096, 878744746, 596868874, 864180409, 477057376, 346240506, 173109874, 251339860, 294547244, 396130771, 520778587, 719767852, 600186280, 454654253, 834043761, 95567079, 490979545, 528414670, 366316555, 317302568, 531653694, 260456254, 306718930, 330406419, 407828997, 57439103, 7845014, 15476352, 817148365, 937262115, 422373039, 775305946, 841913269, 187709693, 228154995, 126324190, 312071193, 513128297, 568767630, 815151163, 244140520, 463980682, 260175948, 455337535, 582312552, 967283359, 117875461, 693091131, 488790393, 46893254, 625082699, 10858148, 599295451, 160906668, 573144849, 368396675, 405927901, 260251858, 965734585, 198057006, 785635809, 126090147, 873974913, 249220229, 709700840, 696075966, 466598250, 833337585, 401646361, 767539278, 698056932, 94077982, 891233253, 972752849, 896170767, 304707526, 171615299, 807144929, 619417829, 500067519, 886939033, 107290809, 170453052, 522722759, 538033289, 440961689, 27022857, 363640681, 815250928, 607305340, 333340813, 552952515, 334665631, 68274138, 852150541, 275464749, 470409938, 463902418, 158651092, 862804106, 461693298, 424999694, 751024470, 349789802, 202470272, 530750550, 922584836, 926185228, 52895743, 683584376, 156437872, 845930472, 943176265, 646130480, 248927639, 7822557, 472525583, 184017178, 898050807, 940891396, 506798963, 983485392, 389616167, 526696462, 382881811, 274749033, 631517230, 332642463, 254212409, 747839557, 176583821, 151747215, 121177322, 130579956, 717345905, 841386126, 946313045, 465098806, 878525369, 875421947, 665129644, 348161379, 963979005, 170793997, 119375541, 629723683, 617319798, 951620008, 23693949, 609793464, 23571107, 427467528, 866538846, 815505647, 177769112, 118440493, 281294787, 1348396, 285193461, 94314503, 635135755, 250419229, 113375698, 434480779, 408308386, 421979635, 9728448, 46561193, 499887382, 968622630, 823046057, 680147838, 317613132, 938946298, 867439187, 543187667, 963578415, 206300491, 967206120, 346828580, 132625087, 541881624, 966367442, 323630006, 35026052, 823765918, 113902103, 904301724, 514696979, 48752768, 973153322, 199375636, 629745693, 611420942, 838401737, 203978181, 812681289, 267875439, 766154182, 931577700, 444261650, 780646840, 284534309, 515717590, 92984829, 882787154, 482655618, 897155376, 996565975, 368066157, 82848650, 46752107, 603429995, 402560951, 203888030, 77916373, 241500392, 347450119, 446810134, 706433899, 398156298, 388037390, 282141084, 685915760, 541047372, 835989398, 623101130, 400773677, 346181625, 162066528, 236875418, 274310822, 24010012, 690295803, 639847588, 621809473, 664180898, 681397333, 72363347, 197443731, 131740592, 477890657, 675526259, 593244637, 486651821, 939290326, 830314392, 508364662, 267726290, 492285999, 742500832, 191724740, 833129335, 531541608, 735331292, 567056283, 956063265, 525795531, 22535246, 470187875, 223353699, 278592508, 115743912, 560770759, 566709590, 647371206, 316565003, 823123138, 989194652, 347819150, 736416625, 822353014, 5127077, 3627178, 134578564, 422897767, 573469301, 858784358, 734357636, 35567819, 978742839, 229296552, 134683950, 698314208, 825905903, 371782430, 528092127, 998089822, 785818170, 252155392, 116743315, 859342503, 558256469, 347486569, 838418022, 544975041, 387269994, 177931330, 250661981, 409480699, 675480549, 983607107, 685422544, 255863441, 353192467, 391047803, 740409671, 286334032, 142044257, 537948945, 626172995, 72361643, 767174844, 561507299, 568319139, 41457388, 446975501, 575568817, 207375457, 355623123, 465891870, 437008656, 310904845, 324349172, 574178286, 134072689, 384574540, 776499419, 992334073, 92219312, 42044616, 547950021, 543711314, 801557469, 69680066, 341305280, 604035146, 712653238, 125174160, 128573401, 540402890, 517086696, 159644408, 211868917, 396866092, 273142850, 765506323, 810426338, 948288238, 813659082, 246074380, 99527721, 73848558, 228744123, 188562875, 895663105, 543735373, 846851758, 580732716, 354000632, 523194414, 233183546, 817758040, 478819965, 143307015, 781808860, 700220693, 224683876, 745550809, 184579775, 921124491, 415283297, 307713057, 728544829, 926766329, 115100048, 176539326, 27786501, 680644487, 647172810, 366740392, 93144497, 877857298, 410344175, 958183549, 619753631, 28196838, 295494546, 591244382, 60671378, 810849864, 137611523, 351486184, 231693969, 724510815, 134535032, 532701416, 262955091, 643777694, 200430006, 619965855, 778050805, 116839448, 720042818, 832813635, 80784325, 96578650, 817745304, 960836244, 975159973, 343240817, 796110688, 382334, 917025174, 362997017, 400870001, 901715841, 626312192, 852329248, 309558138, 467901044, 322171485, 400126466, 4614885, 236615742, 117462238, 121421717, 576025101, 980668715, 9357562, 235718684, 297318825, 3403239, 843662527, 290454564, 123050595, 290315680, 389450473, 250936473, 227318629, 473602577, 259006047, 398183069, 20995210, 444972621, 957876363, 575466284, 835440675, 920368589, 227010924, 245606774, 770117555, 53663892, 651865378, 819956450, 323093035, 631438199, 551943414, 367585319, 810414859, 824861534, 301516015, 232569995, 829232436, 778713113, 464713652, 151093632, 793202605, 404394555, 470838956, 574547224, 748531795, 63882010, 24672926, 52547210, 370390808, 323459389, 936761718, 273780812, 521531525, 23441339, 674961731, 176341635, 723795627, 162826003, 948093619, 285365129, 810120710, 981910661, 481932223, 297939316, 990998109, 774082821, 743715914, 562643004, 784427664, 371665343, 592085205, 971471264, 760128126, 449986722, 26813936, 325491806, 363984727, 870662001, 688564878, 561848945, 271248498, 31187462, 110994227, 167268594, 569287562, 223821541, 711560606, 34282045, 255995345, 288999317, 202537558, 242632530, 418789064, 235614849, 803303715, 722017255, 445816811, 73566071, 298938699, 137878607, 26658733, 24546095, 55043943, 590534315, 745745788, 803189730, 824619021, 15203815, 239565505, 832843863, 80804645, 675154005, 993793022, 474329949, 248898847, 249272537, 172972417, 977392898, 194955183, 428654551, 288872759, 410573114, 101372645, 951078099, 952577678, 467012577, 965713296, 728683830, 10146310, 631468744, 99291261, 354597967, 204871252, 764442411, 280044075, 729797782, 713682374, 895671030, 312502080, 80891084, 151779467, 5452747, 358585041, 982258393, 597865497, 489093122, 73466832, 487535392, 908707120, 198945765, 973935357, 890004560, 476544569, 743144552, 917002626, 4582388, 578200574, 606347705, 522522967, 69827631, 292728884, 452146990, 255363737, 663880329, 982237830, 292036843, 912042815, 373664982, 888391640, 424334908, 293496033, 812165819, 91576855, 862199475, 338289009, 841923789, 227192801, 867180486, 469128717, 805939718, 595215695, 669615678, 697580220, 621569851, 855588790, 963836359, 957225804, 549762301, 350658676, 506390859, 802197924, 171647778, 616589629, 55237971, 764042650, 9970725, 946869245, 371182655, 744095365, 395866913, 536900914, 467075579, 511096385, 753490624, 776377413, 235843614, 277611767, 811620933, 505473330, 115911787, 967326481, 80026852, 233627221, 949555785, 658827729, 548019899, 389227830, 663905000, 60986696, 805276670, 546260065, 432939783, 261050259, 965537674, 162609474, 264308292, 785388783, 329811910, 280492348, 591805566, 395708077, 981449961, 174280828, 990180672, 269964053, 574756483, 978522638, 795469267, 946062715, 69751489, 594453670, 955223325, 597020326, 655012401, 758294888, 459419402, 712830344, 68981295, 640493171, 535375000, 646885992, 759129573, 831040590, 859424524, 183345144, 695225271, 743062759, 438435562, 713620577, 702071598, 825525015, 57760668, 824419795, 933061936, 435092197, 625830245, 91693722, 418065731, 366080408, 536219021, 860674528, 95044599, 264407232, 638770683, 376141490, 348315943, 891958929, 226836933, 298168389, 238415115, 312859372, 801857561, 581797126, 650099540, 926213742, 501183402, 598403523, 381416765, 259485152, 698047923, 507089577, 49821362, 322267967, 459431670, 612225895, 885110640, 66575401, 653204522, 780380664, 511916459, 770722278, 118845488, 857221072, 581032115, 756611310, 306412302, 238148062, 203307736, 338160817, 606311817, 122654256, 413502299, 868382003, 697629851, 890670703, 470784516, 844518863, 906303809, 596070898, 81162708, 450403070, 895136795, 643030150, 511172354, 739384386, 779439665, 68012264, 211151820, 751285008, 49022824, 98299120, 567745706, 213187797, 359583889, 729450023, 607815267, 77984807, 731100319, 402454903, 6143936, 720370208, 537352494, 795617149, 895698405, 856496233, 302658903, 708661009, 307359265, 632019706, 452707836, 339651790, 386312322, 128608022, 462010199, 59005567, 660366612, 837477493, 526557077, 768304852, 900874404, 104631033, 989504785, 870264808, 86229217, 527025064, 432777255, 543399605, 12193890, 400677239, 199323827, 259818968, 780699136, 333342770, 916646857, 745055676, 548430480, 866001898, 145974110, 551343656, 845433515, 849677363, 301890718, 534471424, 795285477, 791344777, 355761, 284274480, 589191400, 276729320, 383040543, 218181322, 510173155, 154253773, 168964181, 486660406, 905988632, 113941947, 630357598, 835925123, 811631543, 959643826, 685322162, 883696890, 662735594, 661649589, 640794635, 482696232, 534063553, 107991078, 672667707, 867504862, 774705606, 321734444, 774724203, 915393798, 311846666, 238950560, 398068917, 478818307, 632011028, 109723905, 839176182, 123144485, 256266528, 604161958, 733417816, 951452430, 549504610, 947203842, 827668787, 918052497, 229580409, 606693443, 496704665, 895241836, 473973240, 912911157, 977552689, 567650114, 281574376, 908974315, 601142451, 253032742, 611405911, 173993180, 232304674, 396492302, 154651089, 108822328, 101740759, 549059052, 502031451, 495571538, 826763765, 71112125, 657930307, 138617156, 135162092, 761530811, 724475574, 104213117, 612715272, 774708985, 215686830, 569327820, 239510987, 72884403, 842956436, 583292426, 629315120, 809824564, 751336404, 72639387, 325819376, 842149437, 672961969, 780406453, 953102913, 669986321, 894957088, 858798915, 414861095, 728656669, 76856221, 352260932, 760523499, 218309151, 214343520, 28271031, 651904938, 519013182, 637332568, 212141127, 652353298, 710305390, 707651168, 408519747, 910320320, 688898070, 239908437, 190166107, 106694505, 644331701, 230125868, 372598755, 769331371, 330834624, 720763600, 524568267, 307761446, 600311783, 140854650, 166443468, 354171301, 846058588, 533692644, 918479790, 707432539, 119816589, 744403634, 986455274, 181608355, 355735583, 368723220, 520362740, 137330904, 692411972, 344024838, 197236897, 173492434, 296655930, 806858848, 840930960, 67463584, 337352271, 979326497, 974130380, 930467086, 917813039, 875716403, 684432689, 387614467, 170045918, 475284012, 466150417, 349073857, 101537770, 739358555, 908368633, 319313400, 777257218, 892114811, 716533186, 168934644, 699922699, 959381024, 530622887, 717242611, 671436670, 18233144, 399591257, 303793127, 748242211, 805459494, 519743598, 582880539, 471755536, 305723030, 243835305, 12244209, 382614085, 654508057, 216465733, 412576585, 503534337, 594284258, 426673711, 606285798, 520319530, 835989954, 897968811, 952162594, 604075973, 730152534, 660176244, 903486451, 55530505, 427746261, 951414308, 632212770, 453209779, 733566862, 239307038, 325688634, 608396119, 318041135, 927762634, 104826508, 918285894, 817496398, 242823089, 455628363, 280569736, 308873261, 240306268, 587155507, 162031055, 211829409, 854458677, 639587718, 643676541, 413878824, 352279745, 967378404, 187422743, 670879771, 959696633, 998117691, 901918850, 774584536, 750698788, 729633031, 621233788, 528585527, 967079585, 625404113, 189786542, 67853907, 510802892, 339726705, 15623425, 882703159, 227423562, 986634713, 870727396, 183837404, 397269390, 349083806, 678458131, 144234022, 722235737, 368067102, 273033950, 468170959, 67405235, 905368411, 943521618, 235392668, 288344558, 641789200, 950471633, 114008427, 989999246, 970019629, 834372693, 414122018, 800264171, 898967573, 607586241, 31852640, 117151552, 958904527, 85571063, 363320600, 192704683, 38184724, 411780943, 153554770, 705922634, 14089890, 886507554, 195621666, 65838499, 750259123, 721692704, 402071857, 332810809, 768554410, 30670800, 700714126, 342756373, 796175814, 524821224, 201341757, 456874753, 552852432, 456242614, 821776465, 554349960, 675820833, 648450372, 488820860, 622604684, 710352721, 522351526, 876257760, 576436936, 31565230, 923728849, 391191250, 548986949, 402959260, 526063471, 834212948, 844969318, 365705961, 981664132, 258465757, 19677821, 58028603, 121185, 755804954, 908260246, 791277460, 929104531, 668344886, 107464196, 905186267, 182140283, 293800452, 789093840, 401002653, 217361768, 330338585, 88660472, 203168180, 211138894, 9025565, 147897761, 445149728, 484762521, 293813152, 265357786, 328508822, 820288545, 227000079, 99389735, 511839442, 436888341, 999148223, 833796375, 883074523, 646377533, 282850852, 83961558, 617916806, 899863639, 155646485, 55453018, 213884111, 978288639, 516595973, 282504962, 475536087, 95926394, 597102276, 131155603, 992053913, 165510446, 521365372, 128930603, 510864916, 472606754, 303200217, 684830497, 71868582, 422074272, 107474832, 58369275, 220125913, 235802631, 512775160, 58918840, 871456060, 906147090, 939864536, 397260548, 545443814, 105979331, 553400084, 443708153, 796180525, 445580364, 819263058, 705213082, 587909869, 847639457, 883612643, 98908950, 260517290, 988258594, 133038176, 719151937, 542261538, 246390942, 856908891, 483895683, 866411205, 248332224, 61130131, 119411402, 550712152, 562743695, 625287673, 262333631, 90376975, 793941576, 990206502, 487081471, 646814564, 388442214, 664148633, 599949991, 361881273, 927419517, 375816894, 847455369, 939200101, 812434450, 302152359, 49360735, 270632174, 452145037, 121754616, 171124627, 412206230, 504744503, 757389086, 187904757, 413009054, 109634609, 548473719, 391359497, 57337253, 387381347, 697866583, 980892550, 478974755, 90278008, 543918292, 9440987, 813948863, 907127964, 950972032, 37201379, 404938077, 419993221, 57537484, 379378306, 865476390, 929933593, 874572211, 311876892, 373252276, 754391068, 382976710, 609692082, 679288968, 221757873, 497839298, 284128548, 633151977, 413458336, 60270197, 775109421, 859636246, 728863633, 187805183, 787287421, 837853139, 532009092, 512073693, 670595550, 244995677, 89074743, 66816307, 434572133, 181923240, 81579091, 536857260, 717163478, 570588597, 727423812, 99463821, 625087588, 231120832, 288602686, 558369370, 51068726, 339846649, 504721723, 154469024, 979732182, 52632091, 299478478, 252479516, 55783750, 413114318, 629055567, 844858962, 753649755, 268547190, 856701243, 709772081, 239927320, 246592625, 614391961, 623873014, 546453657, 388721223, 544327429, 826086464, 486591073, 571145923, 318908506, 995187880, 31076258, 608287710, 321294617, 370428359, 72548232, 439154394, 930889403, 62206346, 921393405, 169054152, 130182381, 473759092, 125982368, 967900046, 399638021, 441990493, 107352464, 94699958, 209844510, 267734019, 690335587, 55714976, 648843294, 477940158, 767235537, 691147114, 47312969, 212508051, 867521862, 279679071, 213344058, 581085250, 696954096, 133861977, 237280819, 145302448, 457246211, 486052053, 176916344, 141159312, 457561610, 280686883, 909915347, 296309731, 574614208, 102391827, 631420267, 299314722, 74174337, 600634689, 170400291, 826623552, 5128208, 806196939, 346730022, 400963729, 956289027, 868176269, 475889116, 703570827, 838192480, 621948674, 3768045, 698786888, 683865561, 432189779, 592670952, 552451106, 98367668, 63525926, 146088947, 379043694, 955365390, 133082577, 48773457, 5271844, 153123928, 925026862, 491898356, 423950786, 90595664, 562240058, 711315527, 636609294, 865083654, 938988358, 384148834, 156805107, 118541795, 677629702, 510628308, 654642600, 899909117, 124323660, 694558920, 170495468, 314718648, 453502625, 676468346, 357121172, 64632451, 719422349, 438765260, 816417426, 563354045, 899020002, 946197905, 24169255, 413239144, 342869047, 189077719, 855195654, 566401226, 734612527, 369362833, 105789802, 948150867, 719379787, 568904861, 381800516, 394171705, 216556030, 756366693, 375565390, 417390652, 792585427, 133143946, 500362936, 272344871, 328984039, 752461478, 612412957, 157277299, 335948594, 165028351, 556175878, 908214425, 730586819, 336836904, 908012395, 284976574, 494995293, 262810585, 338180815, 861232826, 635289573, 943743858, 398341231, 765517976, 982177223, 216331086, 862414871, 865111136, 556065445, 391931611, 485665381, 374748469, 99041384, 580969842, 766526886, 308755556, 911783065, 763904272, 642282469, 241632101, 786204728, 866926325, 530071329, 748232063, 177827934, 222190119, 994399919, 871873102, 668102812, 545030215, 605387780, 255793725, 910824650, 811407263, 349158534, 648337434, 344719294, 627290013, 461069495, 60397891, 592350464, 995219909, 420132368, 225579575, 563624826, 180361569, 313073644, 751471242, 85269711, 848225324, 624096655, 790424448, 396539986, 439735980, 127782513, 806552874, 553705955, 933907069, 258868241, 753785022, 68942043, 302527240, 504009411, 792538817, 925470703, 823347564, 287929208, 308656082, 257950475, 278743699, 726663685, 192995501, 452216574, 326359439, 599081489, 411715416, 438363587, 590326177, 490520911, 661309822, 203056752, 714837087, 873382098, 863763212, 731784572, 65855341, 176165775, 913036384, 152339468, 323795325, 704236485, 128365583, 597483034, 139691421, 569430622, 231351807, 87449934, 893655338, 675460338, 697229270, 444490378, 59440331, 131777076, 920248752, 335318811, 742666496, 189798404, 151491295, 147611379, 582077875, 591304019, 750070487, 51208997, 497186451, 347764821, 879167434, 59971185, 176374416, 696653985, 329223209, 972653545, 517936301, 617696621, 476391111, 694271139, 340917543, 530079765, 463529036, 510680790, 548123513, 923444771, 441222995, 536607514, 670669564, 516944922, 767372558, 703404812, 638153519, 420167328, 921001679, 807031699, 319393759, 678824309, 986101887, 903523872, 524396490, 471127451, 629527858, 405852625, 381594699, 986395212, 701078448, 366936332, 161742554, 973618461, 995335153, 568546180, 970261939, 681565973, 209735516, 288682992, 242060454, 763237644, 950960028, 619609704, 990799584, 364037007, 341935050, 842223470, 503835493, 732189506, 547023459, 957806916, 363507672, 314777812, 206275669, 943415649, 865307679, 184243147, 34387389, 921789071, 236570588, 170328904, 327869807, 228647910, 869940296, 881808356, 643979176, 552746718, 464336330, 462969202, 278589495, 887146784, 378627834, 404422350, 20215989, 765895854, 412756762, 290439964, 432742974, 413706113, 301862258, 754223518, 107561973, 336933617, 835289071, 371413113, 112374751, 686383053, 630849567, 630530059, 287769089, 955628684, 733159272, 67986077, 525778973, 279522950, 613395018, 464395589, 292095649, 984752663, 213421112, 976456347, 566413403, 810223252, 247542856, 135106736, 731214617, 338869408, 434516972, 260440984, 274124228, 350186496, 850845665, 83380256, 767430038, 146248845, 896904764, 925047633, 705822138, 978168123, 622650730, 95652056, 158019922, 290827737, 600212670, 688780240, 63923193, 563973777, 685168452, 749163398, 924199800, 423061480, 148462240, 991830100, 710471813, 880461948, 345922410, 821814319, 477651314, 968442008, 171221756, 164385280, 132034958, 298379911, 978730604, 780727873, 369881407, 384958627, 966086501, 104443026, 807078906, 160579074, 941497514, 993481930, 771202499, 462882153, 614662502, 390502193, 945837208, 770468315, 109533456, 129163078, 372664049, 810544978, 674380251, 736512155, 432073122, 996437839, 602029455, 630503216, 359110404, 998862911, 368950924, 347892487, 526161061, 738603356, 399684158, 56732704, 485624640, 12197644, 684856658, 545671157, 682876697, 672688387, 212091200, 731875338, 565312092, 117881191, 518528181, 266930092, 229337389, 612332140, 853275853, 370891849, 840420935, 226555780, 225495173, 276772495, 562765584, 286425048, 10052117, 212736063, 172852982, 910804428, 43096322, 278519719, 322910016, 599484958, 755754943, 436227864, 124748173, 328180469, 424462553, 217499609, 289578855, 840800523, 877906075, 453029530, 738910501, 302085168, 362882677, 479536941, 63365264, 712767194, 308460899, 509190025, 176021449, 765073078, 628297334, 538371493, 437471377, 745338132, 703089874, 571470952, 180399186, 413192723, 773316507, 210870166, 25245078, 872603201, 431002263, 223787061, 818292580, 50900380, 268122144, 125564669, 122251028, 517979693, 763841643, 723611479, 26346205, 793343374, 83638928, 227530489, 748258248, 498991455, 87335592, 338395484, 168738678, 946011991, 67556528, 670057538, 763523265, 374691494, 881846824, 443073680, 363568040, 575255848, 570386, 926312101, 181653189, 66824913, 529597754, 551363935, 802780175, 996664335, 394635185, 496727802, 185587635, 482535544, 137207078, 376514571, 370209238, 370552928, 98287741, 230503864, 305022263, 261383204, 609633878, 413148055, 129652737, 118037195, 152799126, 11017028, 812110269, 885089542, 447042352, 614180724, 206417500, 1594629, 340821085, 885352855, 250105525, 477619973, 241062761, 745766238, 515682535, 962363230, 218993997, 862062592, 833433661, 665001037, 36180199, 638786164, 4516222, 686468241, 864360467, 935881226, 115456719, 187414864, 776020107, 666809433, 478395488, 842967377, 755453994, 783243605, 766182571, 394501580, 636244791, 968735302, 811209492, 80357886, 479316294, 61760257, 30901478, 256465622, 159868113, 217448415, 907843981, 18470491, 471543969, 867864635, 40816095, 813998497, 902883109, 949974450, 258382381, 604799300, 121756075, 760451146, 177589250, 529022283, 107020932, 550138699, 4679340, 485661607, 702123402, 666181013, 245208206, 851724712, 900134460, 658025471, 840845479, 736619019, 179529003, 465576951, 658923479, 546941129, 22087700, 899151578, 382834897, 825966996, 724808702, 139070247, 511268862, 875757258, 563269628, 481398859, 426958895, 35701545, 365541837, 881222903, 391690185, 489601740, 422431817, 294285223, 707183549, 51639277, 340535500, 387360903, 173691404, 229950013, 866672908, 620675985, 194408565, 13594707, 249167074, 279527208, 957482160, 491870234, 337630286, 356201066, 308445565, 502926059, 994548465, 24016934, 658560910, 212716912, 37193884, 285163796, 125404832, 398263862, 360725587, 208354540, 696798891, 827028520, 945225801, 570715965, 845983572, 477049762, 990561097, 613389343, 811733825, 50354965, 947484640, 769644575, 918579968, 639229171, 794306004, 436351286, 85508480, 390702612, 917521242, 506092958, 186045706, 554133234, 615493772, 918745379, 482184036, 129821178, 533817420, 789689312, 466448567, 700853405, 466977926, 820049779, 891741219, 430114345, 400886332, 487635313, 859070907, 197462796, 396575410, 762534831, 537191602, 285090039, 634956325, 643053313, 825337357, 836571738, 830117954, 340769833, 888023459, 238006513, 130996611, 955932627, 637269672, 911359543, 881944659, 825802630, 421831764, 894490463, 713356003, 54209375, 696517533, 771214550, 759283972, 362680776, 347935344, 160647202, 53491421, 841553877, 838297492, 290377938, 996793251, 758158555, 241072912, 521327458, 691437758, 80775950, 787153892, 977150483, 583338205, 437907176, 550534137, 622408311, 678335086, 803733749, 469269410, 220041674, 352936841, 539940562, 748146673, 245790537, 827316881, 562270083, 678855029, 303613546, 363331761, 782542149, 80364752, 782768458, 906700510, 677221459, 87771422, 957148406, 907893758, 786520090, 963291842, 438404141, 441563520, 271522956, 585154778, 742784332, 566638542, 461484758, 754239173, 947002855, 346162511, 12734756, 185707996, 310172977, 139381812, 362852236, 771590193, 488025410, 459657982, 870972267, 541495162, 937961521, 208857365, 153469198, 458442448, 751267167, 648566202, 44103410, 66619922, 151254080, 662940379, 490381516, 337041567, 693731443, 606255258, 960356014, 963096680, 787933807, 939428359, 268295151, 42608003, 240828121, 100097811, 439997447, 795364097, 455956317, 496188261, 218691965, 494396007, 776328568, 827652368, 979104477, 623589499, 498802508, 958805376, 690443430, 327227125, 16568816, 282146665, 597668543, 918867118, 733720514, 559107070, 938551754, 280604660, 397150285, 757338703, 28935059, 915948016, 561869645, 881587101, 444439468, 451204493, 862675231, 241644965, 799603020, 399836593, 256268981, 570238982, 881476262, 315876166, 885469843, 797774835, 87739227, 482044047, 88677085, 659451807, 72407057, 199070767, 723201434, 104654247, 306247446, 59992576, 589652106, 641005903, 448570669, 987115312, 9109258, 418454615, 821763444, 643837504, 139879453, 212117977, 685048311, 342593509, 517631756, 423493173, 845303608, 722679929, 138784898, 469280231, 592467984, 21338943, 612794088, 582517691, 701569842, 203745399, 597429294, 880863805, 144691950, 682192277, 821130297, 683830984, 151575635, 445772107, 891794556, 329161036, 702750723, 537986775, 538045402, 897789233, 911615077, 308026688, 778711347, 777615397, 709618494, 790737383, 170588942, 481918809, 466040209, 459779774, 859091373, 213034858, 36051018, 844845922, 875929075, 854339807, 31498270, 321566058, 606381375, 705545261, 330042649, 849242764, 786998401, 470937285, 716379702, 321183107, 912233827, 779727271, 357970020, 822375888, 169125346, 332790601, 434077714, 677965090, 872859918, 824844438, 665815427, 839270023, 847798660, 526926520, 279549028, 572046928, 718263240, 112253799, 831716208, 970723174, 823874345, 392972817, 963628324, 810278171, 530531064, 949859185, 205887368, 598003089, 34722142, 462139645, 767596798, 589744133, 44924686, 359696247, 850488886, 299612466, 43946071, 293145672, 564059922, 746223650, 392723824, 282536783, 360972423, 679925279, 204064391, 634609644, 48098695, 441878663, 301913424, 588770681, 712037726, 708248140, 790608851, 339186958, 114511513, 706575283, 819878466, 852316846, 777370301, 305259190, 665198544, 902082498, 97631793, 868865675, 584711718, 450355529, 77102767, 780398066, 514655422, 656691995, 880965407, 134874015, 732911143, 702542413, 370389676, 425582487, 111477790, 92954307, 20657743, 414074666, 870713918, 34611913, 297237425, 935525759, 224729, 405635599, 625645999, 98893931, 861506894, 451942280, 164225003, 924358461, 674998763, 514651332, 207843112, 343838393, 527710057, 536277233, 811962862, 849681065, 702807753, 920040871, 378244019, 400618570, 408407895, 389018626, 631685712, 357790061, 368743970, 456909937, 894584016, 345385558, 16721584, 792878984, 294895377, 7345123, 647424961, 444048014, 944120955, 907220119, 941364557, 854610256, 699167409, 776427847, 456672332, 790441742, 735972783, 358773055, 591718748, 253919033, 788842302, 359222183, 527102277, 225288104, 380073151, 206071614, 743380667, 532713706, 880161342, 205620646, 269094317, 863574210, 461157367, 542557906, 923424232, 34264676, 329185972, 459858811, 936080553, 229858626, 755931708, 523789830, 449936586, 395595198, 31650503, 354215740, 458525275, 10950635, 659752388, 939500620, 508614700, 423038684, 60752676, 29384846, 479476981, 855908616, 895095096, 819261159, 195459635, 137845891, 262679177, 259563121, 971870122, 872186422, 27452359, 9013215, 415449061, 394659864, 429528082, 323473268, 337267323, 571149077, 903687103, 165008795, 638346233, 568378069, 336030745, 386387879, 735022566, 988410817, 80834198, 430228743, 710424639, 972362240, 835264440, 430377799, 213724136, 375217653, 541063948, 158525902, 362805187, 841527586, 47380995, 100257180, 267570828, 55592042, 946273176, 788935392, 902993698, 247065701, 273470796, 326416432, 224413764, 409051404, 584631995, 618207244, 34787735, 440666408, 228022587, 800493731, 31560599, 37287788, 262905843, 199787085, 616665420, 22845849, 465384918, 970923940, 151560882, 246398142, 83293650, 752200707, 753773722, 274872107, 300967581, 710549499, 911798224, 36041137, 154314370, 267724934, 731072121, 339962586, 813044125, 957551891, 659645491, 216242766, 172281605, 45473163, 39826051, 439304017, 50783247, 171252508, 850907276, 234291651, 11040752, 886172364, 381179914, 434233950, 854697725, 844460265, 104920602, 687376247, 195875511, 477797069, 457416065, 916244566, 72125837, 721766405, 514548620, 183584898, 537299254, 540341207, 737180186, 13841582, 661837885, 715274093, 441172351, 874627498, 716642599, 865261623, 377219898, 870163311, 387604160, 412143742, 692528560, 809718850, 429522953, 256253124, 326064677, 492616068, 217374695, 421643522, 700113506, 632010089, 710759060, 574880464, 764290351, 117100795, 360826603, 590308864, 187450069, 50811304, 470851062, 861150629, 956939892, 969344514, 379509897, 155980427, 374570119, 798989556, 902780127, 665720246, 992839311, 220856643, 78171676, 811226220, 144786408, 713375891, 211863196, 304585564, 82615202, 31753420, 416886196, 82254335, 728039675, 115598287, 514733364, 819590510, 374751872, 344229452, 981249307, 48400407, 89107139, 629452835, 577719205, 230209903, 956188227, 559613853, 891083909, 988916197, 299822190, 471960051, 336734628, 142980156, 468699966, 431492369, 501333570, 711749130, 570159049, 217535235, 230614921, 923742490, 186302132, 137565564, 408456759, 299023333, 139071349, 138318106, 29800569, 391529581, 448104695, 286266002, 177134273, 185517881, 466169614, 638957138, 635673355, 417418437, 94114399, 277384691, 715425704, 1025371, 607738406, 448273468, 147011921, 661511922, 795865832, 578445751, 763711585, 618084140, 661256559, 254519859, 327399142, 164660699, 673969761, 144328688, 222007253, 768282143, 441709867, 461873182, 225632600, 604094675, 797223427, 632733745, 871897196, 879508943, 614862767, 708779739, 849616172, 455261598, 280390167, 937712010, 954809885, 184052639, 574959797, 27076579, 698457258, 329607359, 995983792, 794709152, 527763041, 736666597, 640858353, 964981395, 803944205, 528998844, 53514493, 365722514, 258267716, 89535677, 985363437, 848247316, 816978880, 711927705, 119963703, 990520426, 121418450, 444039396, 958853044, 846245037, 180339772, 444515520, 788791409, 15200736, 583875241, 764151991, 896628486, 538493011, 809338128, 457961278, 607586956, 169254206, 740574336, 660431588, 378070799, 60411946, 244547793, 56550316, 186245263, 81553087, 966398243, 426067817, 96200879, 798421516, 781464156, 857060685, 203947118, 639152207, 316698734, 924503114, 855199483, 921527392, 193186487, 187731671, 730368991, 144839224, 217985390, 398877484, 973092964, 345495406, 667404343, 257965993, 978550197, 996099460, 346291764, 159168160, 720204669, 94501843, 773458695, 125690010, 476122681, 2183296, 883049264, 636027349, 502402892, 748719556, 371436542, 579354774, 346203691, 826860227, 519517425, 371741059, 209086319, 248333142, 405340030, 37889982, 651385671, 231776696, 957781391, 101819153, 928843639, 340522901, 627634578, 976112995, 331506371, 493442508, 939946382, 460366643, 773778851, 262524902, 165606974, 963221756, 949195205, 448078593, 58634744, 695544066, 772073772, 974120850, 749964903, 594394998, 497964634, 861866156, 798717949, 207906039, 333044598, 107562803, 369281545, 314288955, 41553585, 19774241, 190844709, 298377889, 450677497, 480141546, 512455368, 400720173, 491596796, 601879775, 789441110, 137970348, 704903347, 575921536, 43204026, 327845461, 920568406, 106718128, 400606503, 810434028, 81812324, 744611203, 379545359, 700185224, 352599070, 230283697, 160058162, 274479074, 741868029, 113075633, 640792931, 512384273, 498498201, 379404317, 957538667, 648523227, 304497157, 949362667, 778971743, 780455146, 257771955, 111413951, 423305233, 86164564, 600469450, 904670286, 36062337, 775377558, 862284940, 334052889, 157839619, 848323810, 402646236, 604909903, 848196460, 59223127, 262527024, 146257787, 323184602, 91861944, 494166151, 678715833, 806205912, 986810378, 207598876, 554716438, 593759960, 294489906, 436424319, 625248292, 411095844, 27266755, 355664045, 291946230, 89928713, 661717002, 304101108, 187128225, 558393512, 961555747, 924648093, 688310057, 362873695, 60939732, 244614637, 280603605, 968792237, 981871654, 422939596, 68637018, 377871296, 68963249, 179208914, 507377143, 380276935, 389541331, 626342531, 163911355, 368627919, 664720533, 192422618, 794922487, 187371924, 998970553, 765095747, 338391554, 236330711, 914075221, 104182397, 206702383, 549468934, 950195954, 511034668, 398397308, 887368916, 21869410, 175923575, 804550294, 578322601, 898711867, 408370829, 215363769, 898964465, 764196211, 135026435, 974124702, 519438229, 589018106, 87607745, 604374781, 473169091, 960827003, 487201001, 216505546, 837654505, 880827085, 703992561, 891663796, 72187291, 604976839, 842029669, 69648927, 896371766, 562727660, 687964729, 181279735, 4226071, 934646456, 402129049, 574765356, 223292491, 94428337, 739269748, 135610010, 790034543, 25116193, 292625224, 305751928, 614637285, 664409036, 767854106, 30169951, 560153882, 11044963, 158517067, 767157876, 894901285, 883402002, 473665730, 879609906, 363305497, 827882124, 181900055, 793238224, 953545675, 713373549, 124601454, 437204524, 765714426, 452771114, 981286081, 270702451, 976379323, 808403898, 703716745, 765114372, 90671343, 314651624, 969420476, 298023643, 217071308, 329298815, 243552666, 182520948, 808097795, 664562207, 226209169, 912394923, 396727440, 574307800, 766921768, 15683078, 644569089, 725551576, 166811946, 376131280, 79307485, 453465459, 285141250, 563068220, 713743326, 376283262, 887593138, 259236860, 41568448, 431310108, 621728938, 258870901, 9649231, 311255751, 641225663, 214230341, 305000253, 223564912, 631141688, 632737204, 763244925, 17439562, 8435582, 473415751, 823434274, 81711783, 711708652, 669291746, 418476717, 4860790, 241961965, 751770885, 876429147, 674071882, 504341626, 727736293, 155730933, 507441646, 348374088, 317016136, 583809471, 678142243, 20400047, 252261930, 975836286, 746505680, 548118529, 532138982, 603461448, 363828726, 768505721, 640389524, 366575077, 124537177, 805464482, 802686988, 778146462, 262851190, 914469796, 255182903, 638265555, 470385219, 273184468, 339375909, 942337039, 449038086, 773493616, 671404933, 912846823, 644169928, 584249707, 876371974, 80570551, 617435505, 49324058, 57032523, 644334218, 949684181, 789580360, 49989698, 362762702, 45439070, 179853499, 981975597, 458369010, 233762576, 532374906, 459266750, 102422557, 79314119, 482123682, 510765251, 570631946, 287403996, 469564508, 298530542, 998508503, 201262824, 782156586, 247638682, 855614293, 218981758, 415513031, 274422774, 487152188, 635104105, 342612317, 241264816, 117264443, 221379603, 325547269, 438128741, 817983166, 916543179, 497075442, 715683885, 272640729, 338482264, 491004179, 687022492, 721544133, 640717263, 391531933, 370817482, 440178095, 328358917, 709166323, 832651922, 603945966, 643640792, 600308961, 364691088, 462384916, 125793073, 777263069, 799153447, 323197271, 962583430, 800093601, 433895660, 551872990, 461244520, 184477688, 373732812, 611649381, 37085953, 287921128, 24311914, 57971430, 94281002, 16106490, 877562801, 268121180, 222377230, 959357664, 849402101, 979201733, 74535901, 927146116, 589925827, 649852879, 712383934, 991365306, 701827011, 979815909, 55215712, 141471349, 738443413, 808865446, 231773524, 897589669, 975042118, 397992102, 642505619, 226097348, 288393934, 634894382, 483965568, 814977544, 667476722, 985046902, 993631513, 704096372, 935539567, 400226388, 886913532, 942485881, 258244654, 143012697, 552712213, 195328894, 958214111, 249064285, 172474247, 24942606, 635450510, 995387281, 157769083, 724820637, 859355198, 425339480, 297540933, 192961318, 704471534, 755498362, 383479075, 590656407, 545247413, 456378674, 108753254, 190897949, 182616910, 885973666, 854138613, 754895759, 559401563, 979460436, 267955872, 618333361, 386893340, 258419563, 965155746, 996961875, 352412133, 330660395, 532285749, 45176768, 539587841, 935828626, 47044278, 393386754, 219709701, 396055308, 343480056, 965307632, 972716107, 511527349, 334980135, 968074456, 545777115, 976272548, 936749995, 938079677, 693153583, 750280024, 892020207, 277984464, 301150549, 378642579, 94335242, 2878534, 498007762, 693591719, 515952913, 898587, 101809905, 66951690, 345597892, 32744730, 28048094, 61798316, 23603451, 900584105, 69870437, 244074093, 910675618, 993978153, 645237835, 240760881, 578782296, 403184441, 442576968, 953976887, 212490438, 413785511, 946399136, 763709472, 423469489, 332126925, 41397423, 22032435, 241519611, 443978586, 159716978, 376831185, 563402371, 399112727, 900246797, 60028572, 476739218, 890620288, 512753972, 722825486, 105708786, 150715489, 604680376, 745855933, 894927586, 262598547, 708394949, 304194550, 688155731, 196134501, 657775049, 572678213, 782308001, 510213808, 821645479, 863778171, 791603936, 16836614, 809162814, 462834042, 808779412, 916918289, 527704481, 28946066, 637411924, 409840111, 658598112, 282118876, 838121246, 206761863, 463186103, 60893923, 315814579, 843697920, 682339087, 928476938, 7172107, 505899252, 753397480, 518159172, 74014657, 571519300, 286433276, 261103280, 271071318, 44961025, 917578060, 671714476, 711033710, 494918841, 226252639, 386160144, 757065395, 604369655, 5929101, 641271820, 670134339, 556053000, 514042648, 280626711, 266671557, 505447441, 847553919, 809041827, 56548375, 944387069, 775786832, 843265058, 685866003, 178589948, 850892646, 606570805, 557859123, 202036077, 543641389, 317389611, 447764403, 301853322, 690205409, 942902360, 739441701, 770450571, 286420369, 88501516, 16029229, 941054478, 226673198, 761705434, 218255351, 892127566, 499637753, 910033722, 355038893, 51561395, 624623279, 751462278, 298363753, 675212176, 995764227, 336141562, 879189146, 125841762, 915051867, 902688834, 583099147, 246560594, 298712521, 439532159, 106577238, 94562742, 309273888, 568566758, 614077769, 228001264, 839065771, 190800472, 873780304, 112387817, 124152955, 288954772, 648356879, 439920104, 7343946, 648562164, 72828820, 824366705, 247408347, 696749333, 160131511, 886012090, 806123100, 698442297, 561541178, 937775184, 628539080, 428758522, 141997250, 629268849, 374854433, 986777655, 958174577, 411884083, 805097974, 33550605, 183433729, 610408298, 69528987, 230086994, 563300500, 259588197, 366804525, 909870307, 806895857, 741491624, 718024813, 658865093, 938203503, 907155710, 115151530, 384250460, 713737975, 43687674, 866849385, 735842358, 216871969, 383237151, 230374678, 2562589, 140051908, 569483274, 447201015, 538039078, 8504100, 888738580, 170725343, 284453315, 651759207, 826562147, 784070561, 971449235, 821389028, 551201747, 525354434, 438078811, 87739793, 482468623, 786481857, 941400047, 746168637, 173640394, 465350997, 283008038, 963586414, 916479773, 369263564, 454582221, 191728847, 456651183, 198088796, 686744800, 170367179, 772044175, 155653588, 689697102, 675941551, 260968895, 82625844, 226717362, 357925104, 970222480, 626047675, 329481037, 848138178, 721281006, 450427470, 190975057, 846262848, 523542348, 136195747, 952747797, 200431588, 546413662, 489936456, 527524853, 393055874, 975796833, 905003888, 738331036, 850368082, 936380593, 841592962, 658183698, 728796838, 311782164, 662441485, 970634502, 623473536, 541392539, 347694488, 59734735, 252052947, 994931785, 167458846, 439656039, 866703378, 834839679, 518683955, 495124295, 186192134, 351698464, 65331060, 710064201, 981826866, 280818832, 831549940, 766738068, 124266915, 996005352, 406504113, 676121593, 520408885, 843172113, 435849485, 294116952, 480741190, 357738533, 647657266, 719671510, 709171276, 768206811, 388947276, 564088170, 17847144, 308927001, 570485788, 682946490, 657546135, 499054125, 283735143, 10286886, 908781814, 481326630, 614745781, 108173281, 886931924, 427528613, 831909752, 772482938, 447959584, 795897514, 752039977, 67661780, 676977250, 397833602, 785297988, 356357727, 506061230, 849414445, 600315729, 401975144, 265148029, 209487830, 330250335, 406921429, 578708882, 442601258, 880723537, 988802515, 241759086, 536859176, 828644786, 256019690, 580406, 636595031, 653271459, 22413512, 699951622, 500640102, 38119698, 85402228, 531855404, 251475672, 835707371, 194140946, 479164727, 505487019, 329594122, 308010654, 798699952, 548806661, 146777294, 672156607, 806678342, 823796861, 44694807, 264548019, 369482962, 19160423, 524580250, 529948374, 933854419, 536405607, 507101822, 284826216, 932536282, 619806535, 78723925, 263746556, 460282421, 182704422, 717439754, 803750478, 837250423, 304541867, 519799137, 580915022, 28314257, 997285240, 877313288, 322012153, 110525772, 198534939, 557890747, 184623406, 602843480, 896315512, 852590901, 68377228, 30732779, 81751319, 2872176, 119715681, 978144310, 272853722, 842017648, 70208380, 598946547, 39352447, 708310223, 41882336, 667225188, 472743133, 140490894, 22224730, 686761520, 98601653, 820918624, 803922193, 348901407, 832985737, 346776662, 404831133, 124079412, 845644491, 802147393, 693178698, 313935949, 620790906, 213859521, 472342777, 729597510, 638768835, 113700437, 339019112, 650985356, 157603336, 569312419, 771016023, 233713772, 605746208, 112242236, 786072608, 521745707, 339304304, 887331644, 310348622, 63041573, 325313338, 477741487, 869226924, 50870678, 860231927, 946238046, 555377899, 91668535, 888079682, 842086413, 732651341, 690234201, 423688862, 150711007, 923897220, 627019759, 953153488, 670454883, 738621277, 453880878, 527887814, 952729672, 521165926, 973022255, 342890405, 89975550, 492140581, 915584345, 832715336, 146804138, 207294458, 925360823, 247116431, 975669781, 878174379, 105852270, 156712932, 111925319, 284592955, 985668146, 601003944, 341242475, 214290654, 10164904, 926926786, 273351624, 338736720, 305014792, 987441030, 642878906, 506957979, 937190572, 591634296, 417424504, 482994839, 963295600, 138859382, 717439765, 785885689, 362942953, 7093688, 764861960, 493748552, 848599709, 814531820, 947920675, 120547714, 327578379, 904629777, 29560285, 828332053, 923640561, 734756979, 137178080, 389086364, 193393703, 622615401, 284294463, 136559182, 139999053, 304533104, 20196157, 68839123, 405462527, 14837875, 494847296, 593843374, 87517081, 753010911, 57927692, 642483142, 845761733, 902201315, 568965720, 56843439, 997926246, 880761312, 767415588, 927405858, 965781797, 410094269, 962740747, 672515187, 905190710, 332679149, 241135773, 529640095, 385244844, 627249926, 654154118, 773965678, 230265543, 767517673, 373526317, 155615685, 561529323, 306263609, 680530729, 241280795, 916542903, 849520246, 645530479, 285225489, 59835202, 128006816, 621207899, 2176513, 93841830, 835292060, 883257713, 123271277, 502538802, 573157899, 246324146, 596464857, 884867600, 835282271, 135274912, 838101763, 767208902, 101669123, 566417861, 615811511, 665443067, 494080351, 325045775, 746932548, 378887763, 511333140, 195676279, 664490105, 700715475, 867012984, 578354708, 770200051, 566291384, 535409799, 825689458, 919066282, 874698469, 25547386, 847614734, 603027550, 903123371, 475568787, 23274306, 850326346, 597323503, 620799587, 232043207, 37834346, 125933996, 12425073, 555632810, 285147393, 573638484, 180490956, 412653219, 231696140, 174496082, 627756148, 723788390, 162466520, 7511465, 994480530, 558957945, 24153511, 865218616, 480721297, 753569661, 118377439, 944977099, 963609537, 849824499, 134775231, 268502558, 575796429, 89629771, 965894092, 657004214, 28979512, 189122877, 864951346, 969336341, 911087584, 278586314, 50696169, 989349095, 696249852, 784880705, 662104116, 290726449, 163268248, 619489920, 473173679, 474261024, 735158794, 42215430, 508041639, 110878718, 95262425, 565173737, 217577635, 744868643, 334700488, 111013506, 842031439, 854336344, 863684840, 370848130, 123143909, 86924113, 445614146, 459568996, 429132970, 663960565, 216775803, 81792971, 330585233, 86759986, 337078475, 199955282, 193808840, 782834235, 922656016, 716101633, 469697456, 863419200, 18173793, 13747314, 579336497, 719042665, 902007243, 243580769, 198134291, 237585137, 799252373, 448073528, 632057060, 91941764, 878314251, 182016566, 155386864, 602989764, 452282383, 497301551, 523058565, 536953483, 305678611, 591470380, 489354931, 914691394, 443198722, 672756156, 944702750, 872454911, 852000790, 842738708, 194712194, 430766629, 318098215, 195168886, 389644947, 250590555, 586993934, 809086032, 41048047, 457911664, 795045906, 951857630, 216510987, 762002851, 307077677, 93330629, 232616309, 350784856, 119618423, 643151635, 454018403, 477698196, 951252390, 728997960, 301533939, 826554351, 536055499, 905525386, 490102711, 615732229, 579669327, 241701421, 236225566, 776464341, 465701741, 591680139, 61109959, 361963450, 777186847, 972365725, 614801979, 136368711, 964903479, 715838379, 893731920, 255963188, 410346987, 60895903, 565660463, 886113524, 118025054, 963303475, 310388452, 407404024, 70821557, 727969313, 748422580, 874435555, 959935153, 411558132, 313994970, 441610662, 132302700, 524264763, 920129501, 668111399, 566329631, 832239055, 232269250, 172563039, 440555611, 501407005, 458518699, 128540812, 477735756, 803439442, 928449310, 504677468, 76132474, 218866657, 231460570, 637057799, 333013026, 51663177, 488901250, 755743919, 210170002, 36071747, 327807391, 438002668, 598370164, 131349554, 942920015, 637619767, 645313142, 789461876, 721639858, 625825072, 814350669, 780575149, 114505924, 61005624, 189666510, 982392481, 521932358, 617158874, 145100268, 563028372, 861512192, 227061353, 374936434, 970316680, 808373933, 550880987, 709012689, 254010490, 640921360, 706820747, 256508452, 507329827, 24570992, 409581836, 592265922, 536867812, 51837934, 551144661, 975828296, 371362955, 534055479, 187190679, 508425644, 772542523, 355244662, 869505359, 574471556, 492493259, 472852469, 975201461, 958110259, 91002544, 174962606, 569214584, 968203865, 878697940, 160876225, 64973510, 557658025, 812129007, 922550911, 278564620, 39773000, 990640842, 950851927, 680325617, 450267076, 668133097, 250102750, 327452106, 849626691, 559567258, 294212725, 725021178, 20944026, 561815649, 903654606, 787194008, 454424810, 362814073, 197651664, 861639047, 956473406, 763135986, 56117090, 910872, 552042158, 121929633, 241784369, 717229403, 861208587, 623658196, 467451134, 618103074, 661893946, 524979409, 158866096, 931143902, 176102250, 745301395, 900053796, 661675382, 585990570, 287495944, 982004426, 104521692, 802465707, 504872869, 267225068, 704424764, 821605157, 309439571, 467350985, 52908244, 451960607, 310970323, 378496923, 750490491, 767880485, 376954528, 10451636, 544732538, 851420403, 359642737, 296261030, 745019493, 453427965, 942249527, 646853010, 644609201, 278551946, 551265512, 489542751, 718706292, 841031443, 641343439, 619637867, 131870768, 720545536, 72870088, 657581889, 581245961, 770147755, 577413733, 6919875, 383144426, 566560347, 214674910, 88720285, 559440108, 817570492, 753647792, 575772519, 344050077, 514747599, 618768953, 352268714, 415941783, 508912349, 245889036, 828210132, 49801576, 835547457, 923336145, 507463647, 592235685, 828093141, 559036411, 180730350, 302703937, 695252420, 875475135, 635292636, 586885484, 50739783, 400818864, 636187250, 407341643, 929024867, 198907234, 999505724, 508418832, 909286877, 940599328, 624157729, 206689972, 212745034, 788240638, 755246032, 896444896, 50604911, 546121477, 669547742, 821867315, 815815949, 468722361, 77946665, 6251311, 147707709, 547245720, 698094528, 613578216, 814866802, 121984063, 128341989, 587764617, 546525460, 710512676, 826085861, 824404408, 583288854, 372431296, 575544557, 400076343, 463019495, 109393337, 232595142, 308329824, 242042580, 61867789, 507172392, 574781405, 383557190, 194991497, 941021199, 580758256, 204733113, 309565608, 622116959, 956293271, 603245476, 310814650, 309629401, 574726238, 459812003, 335881784, 115988152, 783440789, 992920565, 269608410, 264429385, 916735914, 466890155, 994901712, 950719891, 836021641, 42705076, 737754607, 950767413, 249381518, 397730227, 199498533, 724948344, 341038772, 143360214, 497047137, 518285895, 956301127, 336212655, 166453518, 23306249, 470176213, 752413871, 341547977, 471662912, 125778604, 961803124, 720421700, 819478634, 761553936, 191124921, 977831930, 305664125, 907614474, 52274476, 182421561, 618661155, 444949180, 945798036, 453583344, 759586126, 695399749, 120706109, 463015844, 794658009, 19399716, 849338446, 946262479, 40452348, 981173452, 324034105, 905972813, 759056454, 411099430, 127814618, 355672246, 614748444, 187618849, 985184636, 916446040, 692136832, 870108569, 85191853, 955698197, 324118058, 523421579, 409730883, 990586446, 242574998, 537925836, 720176611, 968209087, 41323224, 321286032, 383009598, 153762808, 457087999, 296067037, 756484386, 832007865, 135998553, 517028819, 454581098, 564355025, 817651522, 147786114, 640611162, 87522162, 272002371, 175163084, 459081329, 992123535, 100038817, 305716298, 610599783, 483530313, 840713243, 179456652, 439434742, 80662825, 304814068, 809768478, 783660512, 919577296, 45709054, 533311915, 452255803, 383073259, 827916830, 6062015, 376896797, 254533844, 695686141, 887047358, 469836947, 994399848, 41652402, 685998587, 474232203, 789143089, 588694440, 954210399, 30933550, 595734293, 632775302, 115589743, 432412497, 857135386, 68004716, 914474129, 914813591, 451757198, 888507018, 750832479, 721927426, 312303251, 317415001, 390688930, 181182147, 567812930, 922472447, 31294131, 584821735, 745442778, 532482237, 790788787, 473523141, 616084041, 594356927, 320102251, 803410124, 407373508, 606881497, 994688709, 580967203, 735165280, 390489356, 992247506, 773764766, 768384880, 517749430, 838284240, 831169162, 571103993, 171066392, 452720622, 300130696, 219232895, 528497021, 676137630, 173605627, 190619980, 522012083, 110162073, 882343305, 770782758, 846477137, 965650403, 468004705, 892559878, 334088749, 852444726, 329765621, 165369259, 554884055, 466845309, 43404945, 6082445, 443192529, 936220648, 483361514, 713281861, 833955648, 420490956, 291022092, 169210760, 973237765, 330354728, 988273149, 997450612, 279190573, 498599895, 501644942, 446872464, 291360356, 26938568, 820563673, 750076811, 573924678, 88753280, 514653863, 381870005, 29621907, 352651532, 76212862, 173840744, 880236521, 153766765, 846629235, 578762747, 699899104, 963141545, 79051618, 668010757, 509007228, 626840584, 481029526, 555361245, 768437882, 354769585, 343858891, 580626656, 933846718, 175551776, 557118026, 972968784, 644988926, 787622828, 200628255, 280977727, 419759749, 909069210, 691465448, 586190944, 663499529, 544656595, 172365723, 654469090, 754819141, 903196232, 468651491, 608547382, 562785462, 941622371, 559841223, 443412909, 459008289, 164608226, 140286960, 756260363, 251100055, 895735792, 288893714, 1043422, 836021896, 701568904, 400538992, 506632681, 851530217, 133183099, 172014052, 393343170, 127375753, 899613975, 642567279, 525404423, 317026237, 680587667, 936415746, 63347471, 343422450, 664848447, 668042810, 740594350, 472966335, 984543622, 26719768, 712167067, 868636172, 824852214, 269534410, 46757735, 702544871, 94749714, 331679493, 417201444, 587866792, 477739004, 786795398, 179166965, 31528557, 352232372, 257123466, 254471371, 414438514, 478679366, 528645558, 70655479, 331219635, 168658487, 937875349, 973166213, 159127338, 33217479, 508324672, 888725985, 361914058, 399818920, 345275694, 45479657, 844453852, 753323172, 323330981, 878840704, 707085039, 734305631, 704444756, 745577355, 189958965, 613606444, 236722023, 708544729, 964355627, 648211160, 193676245, 51607059, 602019333, 194078267, 10603123, 837783110, 922236917, 272044799, 467292650, 557878500, 734923784, 203693365, 994559070, 912850881, 359625569, 378423317, 235530752, 351138904, 307089572, 917755657, 867232076, 256200851, 764164035, 249100543, 181824625, 194914105, 727200832, 116018182, 794263972, 104239944, 62705869, 122602489, 486319792, 995567299, 71072592, 763042194, 647566182, 861906707, 328025253, 306891919, 907595185, 402238471, 597653522, 72936112, 996054782, 152680138, 136667142, 759667923, 212318188, 19938877, 638497199, 890948088, 195784929, 242658727, 402252239, 716193869, 169310369, 800135770, 267551174, 234157424, 147971082, 747379921, 118061030, 277987313, 157418006, 122133095, 715297464, 793390816, 883070228, 778953302, 397117269, 995610153, 43881216, 392852052, 280333404, 410757776, 789280482, 107488155, 343813826, 547072245, 354567629, 788076148, 647290439, 596547371, 202972575, 775823888, 68652257, 21740619, 42126715, 872067983, 723335927, 357452908, 986107773, 870878211, 475971654, 21624120, 745814025, 740018183, 463046518, 704293869, 284761016, 155498117, 423112705, 74527040, 138640773, 632060056, 899642916, 359715827, 81057865, 579286893, 446423193, 941285867, 549001021, 277744076, 438564308, 263600080, 595032213, 940743364, 850890724, 649634793, 53288578, 252253888, 570739451, 899735015, 835070755, 75023664, 785319988, 229609595, 807676300, 339077543, 943582891, 318053635, 889151786, 862859, 638013652, 638858685, 969472430, 938456719, 157876568, 285219607, 651187558, 366781078, 805538127, 785377169, 564015965, 377363370, 955739112, 644327379, 650390445, 872239118, 591563148, 950706438, 883680033, 611187708, 254761469, 96224328, 55755760, 911818333, 830398208, 74935224, 84740176, 617693894, 81227692, 522214878, 569559570, 42533503, 448533876, 476042747, 153919454, 898841992, 377692688, 56895681, 661130240, 106025812, 336855388, 607620625, 268277696, 50442528, 260655608, 249396684, 419197327, 302259666, 537785054, 94145451, 480261054, 318768533, 488317402, 129716939, 80970581, 144871139, 244193148, 473633186, 9252745, 362334931, 4507112, 828106888, 477933861, 903179189, 482230503, 293929800, 40746871, 691002007, 961280582, 223749832, 865462068, 230821279, 536146391, 244327529, 859204108, 243330321, 151938531, 30950672, 913677624, 561612316, 847594533, 772099667, 706765131, 767869497, 24147996, 781399191, 299548576, 812307456, 635190983, 95122477, 455794455, 509133987, 318510883, 324748760, 469884747, 935309908, 740313354, 557656923, 20857574, 310675814, 32703282, 629238083, 760941619, 561674236, 497028603, 702814628, 307361493, 724892739, 125847443, 74077393, 143425114, 200091069, 477396408, 397747036, 724937159, 972646566, 383269194, 994462943, 69862738, 97659232, 727609308, 384370500, 315830017, 553739817, 958666541, 166792735, 835213880, 408968954, 102024698, 556968318, 622271083, 558503604, 190665418, 190620989, 200232346, 588004150, 916642726, 404413184, 725907153, 665664466, 112252138, 842601428, 200462807, 858017652, 409596832, 760031032, 403069124, 381109978, 284527500, 970483134, 498202728, 786194995, 468999508, 173510266, 865567935, 412279803, 225333481, 258701581, 362580648, 461349604, 920733351, 574830030, 679093369, 816922308, 809698208, 250017226, 439665842, 610956603, 854893448, 434938344, 156852255, 784806300, 783798071, 511188131, 806677012, 132298831, 292214305, 94003592, 909940968, 802636027, 541876227, 995358787, 146788504, 638874864, 422401173, 344798963, 479850445, 973033718, 272742636, 484000249, 332460994, 31624313, 505289187, 777529871, 372781070, 419832772, 253602682, 905441008, 294322494, 608480581, 54996275, 297772080, 164831539, 64106263, 254487882, 53861332, 166603758, 815603805, 730335025, 675872005, 21656131, 163062923, 416195351, 813399477, 494353842, 905643093, 672553704, 431904711, 466850694, 102134657, 659300079, 835552765, 856481362, 253596817, 261262430, 963477693, 593331435, 127589443, 562555212, 895706923, 716242554, 624457138, 539595542, 800270201, 639377400, 55899160, 686969550, 258828684, 208555717, 251366608, 752858753, 672513473, 273762055, 236782153, 273451372, 290960769, 440542089, 219910404, 808490530, 606542884, 422672796, 967428430, 909601326, 593681285, 675121079, 491300499, 689973492, 37566753, 236812908, 822629885, 855992566, 389177333, 729456621, 870521671, 726386072, 470816163, 246393973, 259913360, 346816124, 674776302, 456277815, 147439533, 705644581, 185587442, 436723137, 263227627, 589719038, 23635414, 441127399, 299126398, 533311119, 170079487, 255490765, 3960861, 697849486, 31987452, 422794431, 156278808, 797770459, 439911683, 596119879, 198440949, 560472294, 614616941, 91028309, 961399819, 238962729, 993089713, 816618895, 62516593, 348773184, 820750725, 721776349, 617280657, 772868381, 778176687, 331982746, 673149921, 956931978, 500627469, 727384173, 284675880, 978902248, 676452584, 415365090, 564238556, 827406963, 852609431, 970546554, 574049006, 700780513, 24408006, 450776255, 237691577, 409792333, 155091381, 308465470, 735246442, 32832035, 208073637, 467328540, 259447746, 95064341, 523928859, 840872036, 258770027, 806158901, 289895343, 422423727, 457590267, 696491439, 838130363, 783438761, 45505532, 11181280, 452469313, 786090086, 497029159, 140983528, 858434042, 44979692, 637885282, 283765243, 405723183, 839863942, 21278299, 221756976, 59496712, 873336415, 757966061, 951540041, 922794018, 897867678, 585581078, 263487152, 604895130, 986426292, 476979997, 835007157, 419542829, 965822367, 843453457, 684623642, 545783559, 852233170, 582352490, 43364715, 833515518, 375825833, 805163355, 189740731, 157061975, 534660731, 991742723, 791691507, 832469347, 48148644, 545263947, 93135345, 846763612, 425153982, 343135935, 326831869, 956652335, 973328328, 320643556, 447943280, 447613143, 129566725, 301286523, 759653557, 52411328, 779160211, 760354877, 477711917, 850247411, 225426280, 512564691, 290870288, 766965915, 124322467, 134749701, 938272648, 938890297, 144039643, 36052059, 325199275, 929764561, 724802658, 107730018, 595787515, 21908780, 197471321, 494286050, 461906669, 386377123, 881932025, 924842208, 937928766, 834227403, 708987023, 492963803, 843795073, 15959012, 537965062, 551515766, 595235510, 369273260, 426531451, 424959725, 615597071, 109731907, 262942168, 681233470, 518690956, 568198469, 532678395, 886806940, 672743559, 124831946, 682050855, 620441983, 654446613, 979495124, 808132419, 90893943, 632723799, 666212477, 991637218, 149014737, 341470738, 700854840, 466485015, 819497131, 42162686, 33466274, 851922170, 677047217, 220172820, 571289704, 978862661, 320038408, 70144698, 767181877, 416254992, 457584812, 869638773, 939616336, 12217354, 814936359, 67979519, 636465589, 565697124, 903898250, 992358356, 63725663, 763814548, 503214808, 966146244, 307720949, 242954206, 346015825, 310307372, 773868930, 434909516, 600986554, 272837659, 173469171, 76328182, 201769157, 871262701, 491654652, 801544542, 901782101, 701041878, 999196369, 742694194, 810889301, 556594829, 647945948, 553727864, 999089513, 134157129, 195889643, 490173803, 164762651, 510400101, 167423163, 846787552, 813168935, 58890657, 343406481, 746685897, 178620904, 44845134, 454005462, 177658915, 699793798, 25193354, 177312181, 495473943, 912703687, 843808480, 825845499, 142623059, 507772317, 595048155, 17301699, 237733934, 734245305, 569953322, 858268398, 870047464, 252242090, 154831903, 721850453, 155768327, 938175957, 231859558, 737511540, 575939508, 216275259, 841955396, 190095704, 925595870, 212834246, 920142832, 456789651, 299839428, 657290116, 836439656, 609503457, 372198350, 577828686, 528271053, 921132173, 637466068, 12614002, 224382856, 961925319, 489745141, 655504839, 352157448, 182862333, 231119592, 582040536, 491588956, 733915703, 883178448, 687442159, 611908055, 831924794, 966771989, 766271003, 222936218, 991712542, 299372807, 231447933, 331869751, 192826050, 297222685, 77835947, 811426176, 888833017, 341289950, 208419077, 577092911, 222310039, 46956024, 370027840, 203930479, 503531766, 448819592, 748864086, 483239440, 31231464, 110186473, 962333680, 341514463, 792560112, 496037672, 998478787, 607093277, 999363283, 720459473, 429501545, 614868415, 250446242, 258888258, 371037677, 82400105, 843010135, 554877807, 710851756, 58732542, 479903391, 750637887, 596327268, 58479457, 825916735, 778782844, 56678346, 958864826, 58905254, 417022940, 999857971, 949567395, 24250707, 502458689, 752660240, 132451643, 409492211, 256142989, 412201956, 358293234, 994471909, 284701847, 162475892, 728894939, 802240926, 989045562, 80302905, 237259294, 593177435, 95719483, 426761914, 342493059, 932274659, 448742307, 881987866, 836319897, 732936980, 939704808, 516238406, 159439298, 888077619, 733674629, 659156246, 605800879, 719695341, 784970661, 469686207, 46392372, 237348988, 843912736, 75977544, 821752685, 256294407, 74749232, 508799439, 624099387, 767255584, 233268084, 471638694, 67516169, 706217780, 472760206, 715970422, 161455034, 984935792, 372601153, 399677298, 837125473, 527423996, 82563286, 96957026, 216755758, 436295605, 696778261, 12900110, 177842516, 466917493, 910546353, 300095285, 367459943, 321030305, 272041141, 984200308, 676070582, 143391506, 625519207, 265619180, 207335860, 340380568, 907067730, 980544234, 440962119, 499887910, 102966434, 523225056, 13065420, 681705213, 939369583, 619924677, 548252633, 143136769, 765245299, 499726460, 653986869, 12859619, 213789127, 129237349, 812823103, 564337967, 730821281, 577129204, 331524411, 332876242, 267872913, 118732624, 554550520, 366365846, 776719394, 886181574, 491493096, 487980082, 807241709, 952467805, 742990358, 383754280, 760719376, 388808891, 637355031, 957611221, 488235263, 558523868, 716433736, 89356639, 429921203, 578026290, 121555361, 314204330, 94438226, 699888165, 228125127, 603068647, 409197918, 31054926, 958169367, 676260805, 80293787, 159189284, 607759042, 454613682, 912269650, 482060232, 135044682, 869636329, 534784173, 452145703, 237539399, 413202085, 958316601, 276637331, 741410985, 931536623, 148528459, 811513135, 891353943, 999823735, 698478828, 306595704, 680454423, 125463957, 840012098, 788708051, 173867375, 637507911, 774164913, 840255830, 599282099, 558485700, 26470337, 868499519, 855628241, 134817572, 464324372, 378226845, 796619828, 549969271, 558398722, 420583018, 134199031, 959398899, 580798085, 370268098, 681825644, 78337400, 963576318, 578474439, 979780372, 392500439, 543317582, 882757195, 406715272, 137061759, 428445496, 438175880, 520362051, 978996064, 295020968, 20754840, 136567807, 160645541, 991705619, 8916063, 315293299, 223509462, 136736017, 300008623, 255737168, 68054783, 271556589, 68416481, 562209110, 707002082, 911387242, 548076738, 481655601, 720527318, 646652507, 141067368, 514646879, 419480122, 204795036, 616315786, 641468338, 637180233, 797818738, 124264813, 586218771, 844112783, 217643813, 125113605, 259012465, 245112938, 603737731, 357698873, 318927801, 321576000, 836872639, 975938066, 810387453, 850895772, 435715643, 45179059, 599948271, 83377786, 935644307, 706769492, 855928179, 561204739, 575473912, 655160646, 234093727, 142692055, 288280984, 772197205, 560035398, 984947726, 798339178, 284788142, 516734249, 452584310, 769988345, 539036332, 419721698, 752349627, 251727791, 31667517, 950050131, 528286226, 570091690, 622903645, 921411380, 449341533, 906941040, 932221711, 583449687, 583603488, 602258786, 940167930, 271364732, 695241377, 874118098, 606877012, 881475378, 786600150, 394740129, 23250026, 829732644, 909078061, 472915897, 241422223, 826521799, 123898386, 917510562, 597070855, 818499560, 592957672, 805399873, 464279742, 789750787, 93655450, 24691488, 679790443, 420146962, 737177248, 87840196, 425099139, 525906669, 98247157, 945880356, 91742744, 547056614, 996143472, 983264825, 685470342, 723231235, 368860833, 42425465, 498543880, 508607827, 553488579, 201967326, 484945673, 439113274, 604185542, 434255499, 184209131, 108184274, 511091910, 307814945, 322255597, 194066111, 570209244, 791149180, 455155027, 48969283, 220833448, 814617211, 774576183, 688464939, 668999468, 456623795, 717974182, 406224048, 734798210, 569541533, 38087504, 396670798, 195877842, 62032665, 869114246, 890239389, 278067390, 936780694, 63619211, 684114520, 773503388, 722739266, 15343537, 872790514, 616666420, 376794224, 290706069, 396196729, 175919347, 873462995, 463165082, 427731003, 981168241, 326869618, 83141016, 648920875, 274084917, 673898778, 198809453, 162225320, 573766426, 36293557, 891734233, 526297384, 942416391, 865806465, 896931203, 878409319, 392831131, 31338167, 517762344, 369087778, 989569841, 303732979, 428475726, 803069667, 374873085, 872433500, 459177210, 890709891, 164513549, 769318642, 963878502, 500009253, 310439448, 295331932, 237968814, 906992957, 256910466, 928381625, 627513135, 267993163, 20785462, 320180493, 743198964, 722878597, 294933363, 707005399, 719486502, 202486971, 836013851, 652386927, 241404969, 885503745, 418430044, 183243839, 710426442, 711999467, 874488310, 313323450, 381896200, 607456624, 704886156, 54936415, 200342483, 440166794, 704430283, 829189355, 775457281, 13528742, 612397786, 366559105, 948816730, 884819253, 125071334, 590576346, 719605553, 439399068, 570747322, 848630024, 939927571, 894854781, 514965585, 517417626, 411757280, 406797244, 965679543, 881822520, 870486932, 742460260, 354994881, 456877845, 671642159, 257559729, 752921936, 882897006, 595810492, 675939380, 77371633, 644315647, 891090524, 770866362, 73341015, 895399877, 45082803, 895638607, 757315372, 337035491, 6957775, 760435215, 251179203, 795610077, 310401234, 103962372, 299535912, 455352682, 26730309, 341764885, 452474844, 701178274, 74830265, 370733254, 277065422, 391608364, 986843539, 427669503, 836797598, 8102921, 689344600, 993650584, 653779061, 248558396, 215128987, 904969825, 522649721, 640726318, 908811201, 4130928, 816417423, 970961, 885711927, 455903581, 572151980, 608976331, 687326547, 388968157, 300350945, 136475057, 371800374, 402640256, 536755433, 793362949, 163537436, 653310917, 776281690, 111482331, 12604077, 907116561, 473637644, 208944999, 817532357, 56239896, 309974441, 3918566, 654749677, 132001397, 776959007, 784683105, 266162358, 240236982, 618686188, 279011637, 341361601, 932749563, 700399079, 541796342, 788576043, 475117629, 696900961, 342137, 658851580, 92412172, 372582717, 615444445, 778343192, 527671650, 998980607, 175034425, 921389283, 628854469, 273005079, 140779654, 858216518, 852720785, 266366451, 793152048, 141959267, 110649430, 554169574, 13055864, 994888041, 997354084, 822100169, 401571873, 732512589, 83910228, 648945664, 375420044, 382766670, 626462595, 521800639, 514695880, 643505456, 220228746, 413364536, 308509113, 3067014, 763997210, 531520776, 324718289, 281303760, 315066851, 721156314, 233691779, 979506215, 51095090, 580753320, 735963376, 129121925, 5750902, 511627039, 651502568, 159118431, 511231325, 409827903, 757683403, 760712507, 63395881, 873068399, 72364864, 579378268, 491298605, 484424399, 262122114, 981582230, 845932293, 520409005, 822677844, 803780271, 834918067, 298600594, 396399515, 458096308, 876867261, 622005870, 15221909, 760239972, 446205539, 36760900, 318846752, 552785653, 910152737, 739618694, 453219501, 213509901, 555544368, 722943125, 299090799, 921184070, 459364371, 255220791, 248483838, 748493712, 718428788, 85272338, 350243917, 898287544, 279067255, 872752337, 659609533, 520600183, 109267931, 753135428, 766872194, 823026709, 789609748, 986626457, 18051683, 522021237, 515263837, 829406043, 847037684, 547484613, 23283094, 21782078, 86777676, 87108794, 294232762, 308710973, 268733106, 646637879, 134066758, 494096849, 315718896, 73679385, 279338973, 99271799, 689124957, 336446865, 351485471, 380361177, 167118374, 117184223, 522780493, 563191636, 48576762, 722950900, 852197211, 647203460, 917028835, 500314803, 976105845, 524673880, 348713018, 497455170, 211238381, 941709362, 200870605, 971865594, 719676928, 826356385, 470565885, 555099897, 37931853, 144496118, 96512347, 463074360, 708463953, 999854365, 905553220, 778494872, 283315203, 812935664, 794597685, 247283981, 630899291, 129171643, 430347321, 141331669, 122177870, 210372743, 790970543, 672945915, 707403306, 144133624, 218747770, 284230533, 611718146, 904011753, 540432819, 769477400, 171604774, 8254488, 350204249, 432366626, 788044561, 558071024, 484550404, 433717681, 141195798, 449511236, 942536359, 111153521, 126650493, 260258170, 510323975, 377075312, 91013722, 660370956, 766322691, 117857509, 483244924, 686901630, 476577107, 321639724, 891582005, 360265435, 939206730, 178476930, 965661481, 582348432, 101705593, 85890843, 377409983, 90837156, 997780217, 934953871, 906803424, 830651346, 382329784, 585123469, 947576243, 431076598, 116434952, 22807680, 840947435, 60487916, 160171206, 578319742, 129987711, 284958267, 291661044, 530200689, 796676179, 889187841, 756160598, 428893476, 232507030, 192638060, 878308839, 323619323, 117543416, 612454117, 372278222, 355726811, 836515432, 658649846, 606636112, 850763600, 292240536, 655216479, 174881752, 383617726, 426351257, 723045906, 393000516, 386329367, 692880549, 780647319, 119335162, 853813293, 304173408, 914921524, 922622412, 416629563, 843148690, 568860185, 440253828, 855791942, 226945339, 366947986, 400192619, 196413836, 157259953, 329778813, 463964027, 803414759, 706971690, 857022612, 158455040, 921519611, 371590979, 376424658, 802907463, 205852025, 448717222, 230370979, 267773287, 751022857, 574092755, 96245399, 618569227, 639659630, 749334820, 675792775, 154971594, 284300160, 98126468, 624186516, 309594708, 806390239, 694798264, 324296498, 152900824, 847157544, 504596511, 574943704, 177370124, 908328428, 1029561, 620587903, 544832148, 405190005, 518124735, 828357159, 647076010, 538163709, 337773639, 343871129, 560944170, 26195094, 439998747, 284778323, 833944476, 667905085, 951027542, 392062113, 823681819, 656122795, 473621456, 897961092, 319674083, 705623537, 185671565, 699111068, 213152139, 679325331, 262781789, 732773555, 318302429, 722334773, 460057016, 732165484, 84171318, 315451993, 487628403, 61770164, 424207827, 685483385, 732937313, 27246151, 84561855, 762544859, 981333709, 468314486, 987145471, 500558083, 355408387, 312955708, 717103468, 807272810, 742065257, 30622509, 365772158, 142456817, 656455691, 686369232, 417296555, 289805698, 545795860, 38227345, 252358953, 946195360, 194327575, 176109313, 941380027, 789892679, 99893552, 856196566, 380212677, 843047277, 353098144, 886865413, 829453362, 577316677, 665143506, 689454837, 522691700, 779579023, 572529949, 458063911, 593538617, 355614253, 920888631, 895241216, 48344806, 496131450, 897466240, 636673386, 690696869, 994011658, 967723825, 11586367, 266384462, 247304499, 25271438, 604236239, 851830300, 350320709, 856221836, 328406508, 496192532, 738224341, 646810489, 870137920, 283545672, 601469029, 367116835, 436740277, 698307139, 600681004, 285285009, 815950488, 325465780, 817458805, 272191510, 625539416, 675857662, 319153400, 709544874, 238742411, 286090079, 54068845, 69804521, 119171030, 334974501, 787760705, 209063354, 161845602, 911069872, 59926480, 509192936, 69374591, 155408374, 695268696, 978182584, 593359429, 725474440, 523296936, 812764014, 281710847, 431828241, 497294106, 667479186, 821615802, 349915525, 255669258, 671335595, 292468221, 181760702, 183799552, 412536375, 207126795, 848444763, 494452428, 449569163, 421896066, 762120769, 99875397, 291527848, 910375140, 390756987, 558787212, 492444604, 919246789, 733518860, 733648161, 101787423, 326529111, 468288026, 663319711, 238697481, 912223847, 543508152, 319978475, 303392964, 484763715, 122809007, 101127556, 172138686, 103272190, 942192679, 469513735, 604769863, 65722802, 176778239, 577891416, 55653167, 111719760, 802709250, 2594203, 435771255, 748950639, 412734303, 363999692, 408147350, 680246750, 975325450, 619548465, 477136961, 772833379, 45535093, 926252177, 13561613, 560808604, 775635334, 702909430, 43592373, 358648571, 393272758, 62158767, 677010147, 436976680, 676598677, 478168331, 954265130, 835714422, 548780749, 120521450, 294130461, 45759037, 337590280, 217382298, 365487856, 386324046, 487029293, 56297072, 992360154, 921544042, 718290196, 718707318, 6350997, 104855524, 924262119, 619826336, 135238236, 773699576, 324745059, 188781620, 615072277, 705171689, 231872007, 902383471, 879900690, 504024800, 778586375, 445053507, 254324354, 230045080, 274381654, 164346928, 514620542, 489586597, 731105498, 721405223, 872646432, 316566836, 791864645, 801221780, 533289971, 767695599, 82688687, 495436610, 828277622, 18008411, 868961544, 327612095, 231827167, 185267211, 541784166, 558206654, 202706246, 67336242, 320292461, 299854850, 249518777, 76557921, 72245907, 124882357, 534410473, 87302786, 163054495, 399156078, 404811549, 563203332, 860168587, 979743926, 983635003, 215358656, 765948197, 275829780, 204337071, 384191509, 346391256, 278950268, 622919430, 142143380, 772592011, 112372065, 963882793, 136581803, 995313112, 25585305, 118474533, 209273026, 632157646, 302886719, 155723287, 27120181, 772344905, 536610700, 388516903, 347775503, 779051855, 185626786, 30762615, 294437553, 365272726, 165247293, 656308056, 967006286, 449057966, 714224317, 95419888, 150910784, 13215109, 557084812, 967659220, 113234572, 392313998, 330616907, 907267409, 540404761, 181246075, 357699180, 751555741, 795477138, 121876891, 809986068, 18420517, 175801189, 337058500, 965745369, 468673858, 144488746, 577525669, 497219404, 987082869, 808182355, 871173781, 384388394, 772462116, 521503676, 415898441, 389865049, 778031124, 403158418, 181785851, 193539991, 89969952, 160275415, 749452953, 193478714, 860767773, 596620292, 961821230, 751715104, 252854641, 553073062, 218094692, 886362385, 821309849, 761998550, 445538707, 357131365, 879176452, 462284959, 187802998, 229085680, 461191303, 43686410, 696679230, 196191779, 562519343, 238623962, 30962159, 716602463, 839641188, 716869563, 834174590, 206299975, 263838384, 698116374, 482259363, 978287003, 963960375, 99591142, 71646225, 558328117, 245188137, 543886361, 350533786, 250359233, 79777757, 94718371, 962133354, 821931711, 740910352, 952607799, 680748763, 375221503, 129088461, 904158944, 724638174, 440437280, 713791288, 380766955, 430736470, 534171696, 257198210, 854330293, 677254022, 576764876, 147479932, 483178849, 922617352, 740786769, 568605730, 74789878, 428658637, 296296992, 540414659, 830930893, 185867108, 818881082, 713468177, 234429764, 288841586, 127759655, 967929853, 190513890, 673583880, 73229968, 665923089, 706953154, 149135592, 451344141, 220624265, 258115912, 529556986, 12226477, 17081329, 93777435, 153695283, 399077358, 161139713, 45559292, 436237422, 174715063, 909987384, 273755519, 507294984, 769160899, 392526057, 263419490, 585911000, 807085079, 264432326, 276299512, 301011884, 440372083, 930505965, 8088086, 782937078, 91270583, 798890173, 157577456, 536025695, 196293370, 48223646, 50929803, 433656385, 617094374, 931965431, 948496551, 308351142, 722140561, 558340776, 406188566, 298352430, 205222599, 680858296, 156746880, 617663175, 808731932, 223397301, 474412791, 300943279, 518381011, 551108593, 90459684, 332686097, 634901980, 517163664, 548098647, 63146693, 147865668, 816823030, 759237671, 228535567, 566825114, 83028896, 155367198, 648024654, 329882402, 169453054, 279347071, 475593508, 712648878, 105632750, 903600034, 451728270, 683192434, 64978961, 155640423, 774512735, 886514376, 993264261, 134972930, 630611628, 392077391, 140443184, 457941001, 373220821, 246972408, 626086362, 874408012, 309319029, 232066834, 546450998, 810224193, 757209133, 121825814, 681582734, 834011013, 839266760, 174484184, 364780336, 715212458, 784797131, 806568712, 678252757, 454396031, 93383208, 551342722, 851653247, 813385398, 720164947, 308518200, 648592240, 49923268, 828324677, 787200145, 981189270, 220169754, 324793588, 131830982, 252926052, 242475606, 760657433, 810693695, 115736974, 39715789, 626281715, 202279893, 855845200, 570249103, 575705422, 777930823, 333387899, 241664036, 827172793, 866455743, 134882894, 316559598, 700393394, 809840512, 556778271, 795909436, 35635777, 938070346, 925340347, 291148547, 49625076, 977462880, 709633357, 611692368, 495514644, 550987493, 702096357, 397295893, 693383908, 114015686, 597201281, 553593285, 163258982, 69364272, 703125446, 938580591, 488072673, 339754237, 622192189, 346749785, 806386035, 602023358, 103957435, 607544567, 302253925, 996716812, 231214852, 976996126, 364161130, 396868449, 747985819, 108811747, 921395042, 642725849, 695483885, 713574493, 532370013, 940913170, 14423626, 650658112, 684947001, 709517438, 15047579, 15277330, 757272103, 374338626, 122993095, 234824566, 932697345, 876570480, 599598679, 870196286, 552991134, 908148898, 169679203, 623611345, 969888088, 879181749, 522823, 953803744, 165189111, 95561795, 55096635, 852509045, 42876822, 677208980, 289290370, 19673864, 149243591, 294094480, 22440393, 873887850, 937539343, 601136912, 420405843, 21540808, 531265996, 306966780, 566842438, 408262734, 581779568, 303991840, 977997634, 429045215, 362100797, 801784928, 511016326, 312099634, 644457995, 152576370, 406556318, 914133361, 478511368, 84460406, 281039121, 410497960, 911899131, 934243249, 936606385, 949754888, 974115594, 579080868, 539980330, 841679670, 833801906, 233495632, 869004899, 84674817, 846413688, 789175529, 242319423, 979326273, 524209707, 460376520, 927178077, 826188782, 513134147, 184034243, 598982989, 135109013, 99899567, 971096585, 992592713, 845569024, 929050421, 296755138, 748752311, 580427890, 98968393, 375670274, 580242909, 670827524, 603262556, 506234279, 392934759, 511907697, 562360822, 623472073, 42673299, 133545619, 588142803, 961133138, 129925348, 439886963, 551458147, 837916556, 575627229, 826164158, 221703701, 903587629, 347747669, 18940317, 895916832, 819661731, 465234068, 72573542, 639529060, 849579940, 355821640, 202942091, 977075728, 905632152, 756696952, 240701785, 953320047, 17615033, 751451143, 346088634, 453235559, 6581121, 565620842, 186928575, 468053182, 736824993, 500221762, 716707841, 525474480, 944051961, 747141026, 235804727, 460875739, 826144443, 840548484, 507941726, 38302807, 680923310, 102545924, 855010983, 949962039, 946876560, 710451501, 794582528, 727613267, 451114082, 842561688, 82139397, 883500422, 521508967, 567021798, 610542679, 170172929, 357777784, 278183427, 668576082, 13407701, 623216755, 103465646, 871464522, 846061284, 469248409, 398315532, 880805183, 371134184, 288521530, 434229078, 725284118, 646867409, 91942705, 53864024, 60064713, 204506785, 306596666, 513805629, 874575418, 478378687, 326123515, 780296561, 305186261, 132449805, 408813101, 777016403, 425211445, 435656702, 470458014, 582277139, 258882934, 449091144, 476356609, 588398815, 706087289, 105536001, 512080003, 55910909, 490867203, 290836567, 688237178, 568225631, 948002282, 245738065, 928328709, 349053290, 494110706, 101878697, 346186563, 933582081, 851071851, 285123224, 450747009, 486125899, 487566704, 811212867, 689413449, 446925274, 456179674, 946862668, 868663912, 979076215, 522350870, 365402974, 77581, 685696619, 872570112, 484989535, 239574826, 866976274, 916591426, 584071279, 110667170, 22691100, 321595072, 40929049, 798848330, 814834913, 882340514, 825798459, 896960924, 117786963, 84482405, 805832382, 83205393, 822712177, 987078977, 495895031, 221926201, 994785625, 680935291, 756309925, 399211662, 590988031, 502647196, 352096826, 207255155, 231293891, 586809246, 684012897, 881863689, 340484624, 907839121, 810151957, 957805774, 752501102, 655806553, 607853772, 981330411, 433945912, 520157539, 892369156, 31198283, 805692647, 93701049, 642857001, 660597122, 136734424, 907250575, 90348937, 237355226, 623071381, 652018855, 914676502, 439762270, 956960882, 923988219, 777893895, 845997978, 505084569, 298481479, 651723367, 900004749, 588932788, 794958200, 307399690, 846532492, 53943273, 556781223, 369215758, 340680240, 625179711, 656854028, 894669882, 511370619, 953244924, 57917227, 951812966, 439399287, 311827653, 982984352, 333390814, 948409496, 960834911, 242633513, 527992286, 667874110, 929517442, 294244481, 21408107, 262359388, 25458471, 693363563, 196071961, 787287128, 21905155, 481735303, 684340740, 323420811, 370396576, 985956297, 591488176, 6470286, 506932187, 246640497, 46408240, 589216964, 332491746, 467681390, 268551640, 916568726, 536090780, 126018472, 500051623, 484490292, 185358333, 614882984, 207767793, 969623643, 794601692, 494981650, 249170078, 606042099, 37192339, 552176323, 863660556, 455653901, 686727228, 389361010, 815772060, 385145863, 333969041, 611221105, 879462288, 268485762, 254406901, 287799676, 390849127, 526392025, 615379561, 140195037, 72902194, 431176405, 60786754, 28207893, 481612769, 617706039, 937284472, 755463828, 167720873, 778373741, 972324600, 701535741, 431980187, 934162296, 291681773, 13628050, 572655832, 24966289, 40625515, 590336700, 606729665, 784004460, 695582271, 987805101, 319823414, 474058418, 824032849, 332942175, 892968170, 486382228, 342134892, 974288966, 50085553, 84510431, 567269791, 452187453, 903319118, 274235114, 324976344, 428016699, 282839878, 929455183, 105364619, 20226402, 386478034, 396189753, 817926056, 7675398, 951056063, 22872018, 295321889, 766658009, 381765758, 41757836, 781804562, 242508032, 694127807, 270127633, 534961312, 843890326, 788983428, 731821337, 52684897, 952785081, 457981904, 10653152, 401353988, 742730890, 329770244, 896953963, 713969950, 460921414, 926591569, 968668291, 814759354, 135597197, 962666960, 711363076, 709073517, 13639257, 343202731, 947208247, 502122181, 749153124, 849578782, 323281586, 412372760, 657386923, 744610653, 486815591, 854372908, 231027188, 822077034, 449483083, 522785459, 119516709, 586119240, 963463223, 215178982, 942932171, 450252551, 841114101, 127879035, 429401280, 323811493, 399430697, 201464316, 79028307, 715747489, 754311928, 158819682, 489759738, 784601843, 592513808, 462369758, 453374887, 169390868, 893331940, 582393382, 924427010, 328372676, 865189507, 286906758, 488831210, 152736512, 533501519, 999282500, 637237787, 986705476, 953391146, 810535250, 272721953, 713502240, 865560594, 357313185, 384865364, 637804691, 535707359, 940615577, 805762160, 860179973, 273589515, 831806527, 807447569, 389277411, 792589663, 453427096, 742509144, 938549035, 36114506, 653871574, 190469410, 35621250, 748507212, 865316112, 778828244, 253664219, 488643350, 321329082, 186117551, 234166067, 535194011, 904837140, 365071058, 302547409, 86853684, 579070105, 741681730, 952695100, 291730577, 694797929, 729349222, 595126722, 267799533, 439285331, 482642133, 881657863, 919012118, 20331251, 421396944, 564030243, 267173111, 769519107, 588335121, 571315371, 503760419, 587245975, 917056972, 545466548, 815727259, 353788328, 337057911, 357005018, 610799818, 480316747, 382284381, 644447259, 931350998, 193225733, 196587259, 730283618, 531993300, 173363299, 780101457, 966325006, 176976420, 453051793, 662799241, 711453514, 361249357, 104272342, 21612578, 963177460, 93791608, 453335869, 213436501, 317901337, 244326039, 325195476, 79656041, 320011525, 983040505, 228234404, 478225795, 784493765, 10748676, 309458260, 296277608, 37669883, 817193593, 634404116, 799680235, 190425883, 32565425, 447322259, 334628318, 947520053, 346409810, 934042504, 742294695, 214130029, 87971463, 495092006, 116182834, 44851140, 440905864, 367106160, 523684451, 441943618, 319684068, 95350288, 272831379, 271225993, 562135867, 617207783, 781525570, 976321477, 871448640, 638328450, 800357991, 878830846, 933570398, 354046172, 792826577, 370981857, 725863008, 916554733, 776726451, 741993565, 624341276, 892481248, 640975099, 842806890, 104300416, 47732363, 330020472, 78419185, 999572243, 470092105, 141747750, 65531356, 954528987, 383262347, 163588504, 28644831, 827437596, 326824125, 805066459, 136297098, 341328832, 519449369, 928334665, 817367069, 961359055, 169885482, 846127955, 862436871, 560978962, 981828777, 988457151, 729652913, 374471520, 708955704, 381243943, 954534884, 176386475, 961694652, 422009924, 962382673, 69636156, 69618046, 805780329, 266557175, 558384587, 559409458, 714562997, 669003804, 987147968, 263180877, 497359155, 316997612, 33521280, 332669533, 224440505, 453020830, 719878952, 766664712, 295377916, 503360524, 814637354, 328862587, 603334713, 172536340, 24627942, 916680554, 301056423, 342714746, 25404291, 634374923, 808166690, 184007467, 905345968, 117386174, 139932902, 830335045, 834541008, 440870913, 905573633, 390663243, 309216922, 904170863, 450382882, 768536125, 500065604, 937608724, 326323852, 752061513, 155495881, 588440226, 158680138, 262973594, 960878598, 935296569, 533558115, 795007715, 623323293, 601894815, 270521073, 679902956, 683237858, 640882431, 470940855, 540834813, 377402935, 584568700, 947511104, 66950716, 189468592, 724384824, 623288456, 738418517, 739881110, 899430659, 395698613, 341274382, 119806516, 533208058, 573668268, 808050038, 60967635, 878264372, 840598846, 165807586, 572806751, 873380226, 200196242, 779354900, 439215703, 552793228, 610934759, 325160547, 287213024, 58772193, 255863516, 855079671, 582896336, 908437518, 218601431, 866395963, 275472904, 937703010, 912539227, 126747160, 701658406, 394831640, 634119231, 178868378, 958366758, 965457755, 372808175, 168566367, 641376347, 860184992, 245435331, 974845103, 119198321, 879555436, 420422764, 811352509, 878562588, 715178926, 91262513, 248261860, 158583635, 740137922, 795196543, 191680054, 816047946, 866300764, 640757108, 658540726, 185746489, 189940228, 994108286, 573046684, 371377808, 55164929, 758045296, 54933753, 483020691, 469428958, 975024287, 997394401, 3622332, 115550161, 594797519, 432636574, 734816868, 461008014, 496721352, 339747003, 623163127, 690446675, 219833901, 987574066, 272948373, 714521014, 271526682, 557968742, 376270760, 561800834, 986267280, 638608176, 11373188, 194253925, 752538320, 428969254, 898451442, 823366890, 318772398, 891324704, 818509654, 182718164, 579964437, 896290657, 686185060, 716675429, 496137240, 725206398, 933248424, 574733592, 7066522, 198052236, 945058356, 229534974, 201070372, 509436860, 71541496, 650247426, 831135993, 653067074, 654401671, 669642082, 134820272, 7310482, 440390368, 675276228, 543772381, 634073209, 190405792, 23885777, 390040034, 4984753, 506272840, 855860702, 487400359, 43396363, 692539659, 399326259, 715772849, 173874273, 4090939, 946537782, 471424728, 328109716, 767424981, 953145300, 734620376, 650885365, 418839969, 84911691, 98516864, 514486473, 9233601, 350322824, 750752144, 874823756, 607981600, 26046588, 772303913, 19584734, 517419428, 246855278, 106248593, 226644949, 352539063, 249020960, 832819602, 474020754, 373443908, 728566536, 259418200, 83444104, 744544817, 349819928, 601548776, 102282504, 470443236, 126985302, 399865571, 87517594, 867598314, 478560428, 11112623, 238632980, 799901338, 72280379, 234223110, 822657479, 482021926, 621057366, 456707290, 330881413, 221348995, 140774323, 377378077, 75142267, 189901925, 434178561, 241412529, 444046195, 470658831, 464751460, 9266541, 346866411, 777061378, 856919541, 796207113, 807732917, 86588053, 195516506, 634307790, 500474796, 807072324, 888835265, 288066957, 303234342, 101385450, 578453188, 27097218, 340673779, 471201842, 452559023, 468151765, 975086955, 898893957, 635101835, 557123067, 434756675, 317080707, 962341666, 787034704, 924420276, 790298962, 432482576, 294189356, 346486686, 512520226, 940797486, 535717023, 442432705, 864496107, 354379857, 765854869, 523598842, 827119467, 599253271, 43229942, 806203852, 902616023, 704432262, 807658438, 851170795, 943076506, 835078646, 444410234, 577334521, 422070857, 11435079, 788580988, 554203583, 711785488, 583879908, 702597179, 191325045, 649449901, 297408588, 454466919, 293749910, 524234668, 757576267, 955510364, 458561556, 261766296, 796808917, 531826853, 731842879, 65823012, 14580167, 542957897, 825627974, 952923596, 250446805, 271914551, 35149707, 348218472, 993329942, 381135614, 675721312, 761678401, 134880971, 856804316, 461378517, 531969046, 378630113, 663896224, 937398688, 708415242, 862714470, 507282623, 135333257, 344685724, 897397134, 877901854, 406560286, 598103107, 657684437, 662244588, 872161011, 406484691, 527649113, 833861303, 682942134, 695742754, 636918875, 332689985, 69963371, 49816673, 204574842, 530342840, 121163870, 695717742, 901919279, 318800808, 248602188, 745789826, 951065180, 611777425, 333634223, 432332876, 955994075, 466615107, 911684183, 276331030, 114124748, 174946361, 309718274, 871104074, 475679433, 35923916, 986701664, 157053247, 471440097, 45849147, 135036371, 504845630, 943486349, 210687902, 994418273, 461198474, 245534389, 632068613, 675960053, 146699989, 339134312, 254613968, 344265460, 40202186, 812190140, 656078754, 936781414, 566319864, 518337038, 542975858, 700008605, 427472038, 291519375, 395864355, 834094638, 187908623, 129631739, 61379212, 322915121, 126609466, 957673489, 225397657, 527029592, 703471961, 985870829, 472489905, 821532332, 944717809, 757497470, 809432031, 328070143, 920975649, 834870936, 315194593, 589153082, 35891261, 265050525, 97650385, 39646985, 128598936, 562198538, 348132298, 533427210, 782706303, 504238688, 760074470, 403111124, 756995617, 938786601, 49733963, 373975868, 12478546, 513262397, 565500663, 526523382, 215977419, 345791947, 998882136, 400414541, 569734297, 860398279, 638226476, 271370289, 692118596, 725836599, 275170922, 626237514, 33412802, 507945463, 588957877, 122652578, 427433491, 204103722, 61792660, 343875771, 356644388, 625863462, 234988449, 205310104, 538442753, 616030644, 541793140, 11065667, 273783736, 723807376, 354480322, 918496493, 965037705, 84292611, 183405993, 582293454, 879817908, 595615783, 829254639, 482095057, 624311316, 361460991, 567344555, 150097684, 659880585, 921206367, 600817691, 265742816, 297997091, 422305856, 713664126, 181580031, 460774603, 263240426, 703054347, 917171300, 176801885, 988221254, 929001528, 724829602, 77700823, 533648736, 614134993, 992685332, 302155738, 107263390, 491832975, 947938085, 928136438, 34419787, 906048123, 485866031, 578541415, 962185095, 587842176, 217329730, 353998079, 391262568, 684197293, 926092838, 540612110, 98346761, 125882272, 29200153, 121218490, 366593886, 322192540, 781190935, 623829972, 361742120, 465182530, 592854493, 968440843, 633418079, 827387852, 379243746, 40607080, 833553647, 361844277, 155086886, 368943484, 703074257, 419319067, 445861432, 296932712, 664378516, 98931869, 16085405, 368784958, 539412467, 779900096, 890549996, 621401506, 975937976, 595008864, 129668979, 681413853, 348476843, 421200300, 806552414, 521073595, 702571230, 99122111, 794079391, 957306066, 765530773, 485583836, 965819062, 418816098, 897447158, 149123043, 634654666, 4627294, 619745303, 939637936, 690176828, 602775901, 685214092, 815696799, 810467336, 926952556, 722074916, 429749817, 100263314, 708257925, 590362892, 677488117, 892874161, 375660729, 485948522, 861082506, 685082508, 324280375, 772190188, 122542302, 52924653, 476257647, 503185568, 332043366, 89766658, 634230552, 156231582, 34189242, 784970941, 253710518, 957224011, 933789471, 265545223, 9855793, 550948576, 542367318, 703270117, 566760912, 90689611, 655091814, 163109018, 766483330, 350159250, 195471496, 878994616, 816801033, 720994485, 411342347, 572167671, 340575980, 955583226, 831086582, 988336677, 621156368, 525567832, 590025697, 600523472, 760899791, 340417500, 994536034, 772256228, 386804015, 255737991, 931603695, 509918616, 899882067, 915186077, 526930058, 367690197, 808400772, 313281340, 975412258, 664174355, 786670350, 422122891, 152306254, 38871813, 55475887, 193888547, 156876268, 981305677, 432001377, 857902671, 85623703, 941888730, 738227900, 821472378, 492326567, 571794631, 814520547, 226792201, 682804216, 980943719, 707864268, 365284437, 194069978, 513906918, 195258893, 441825973, 880979125, 251877883, 467657184, 776767936, 133822464, 412302855, 752736991, 405147932, 884429993, 947040450, 130669657, 853796783, 807502895, 48101751, 109269598, 322449467, 761615144, 737766280, 49374686, 473772510, 135125452, 790356434, 318446648, 476527652, 912574276, 829616561, 586936010, 99715337, 652680174, 341114957, 774391211, 296648239, 201708683, 299826198, 941431356, 863806757, 183859078, 445595514, 814625927, 638148361, 908965860, 960010547, 707069064, 828908254, 45437829, 647454602, 118480172, 429019650, 417000501, 507481681, 955918511, 112132035, 507619487, 695269331, 197036905, 618098706, 906526022, 959312933, 112704589, 914882190, 365380914, 798580763, 214290595, 117869579, 479965559, 518367413, 828135417, 189102325, 348809832, 623338488, 781368632, 230238901, 481620173, 366226350, 956964404, 452915609, 534133502, 677278032, 245004565, 376266815, 747435309, 936611399, 767030270, 595348919, 77269270, 956455291, 483234677, 67110531, 303271092, 475349474, 718688606, 502105420, 675183218, 287271209, 106551915, 400296144, 422062892, 28329168, 765608071, 663332579, 988120406, 70829177, 245722513, 845317635, 716606624, 700220979, 276339779, 674070251, 791179892, 675467312, 450302840, 679151253, 634159051, 225216467, 584144975, 320144157, 266880272, 106619379, 639111095, 785814157, 885936904, 395601629, 993544810, 424600894, 47539328, 229689103, 577812254, 304860134, 350242821, 445383378, 821567980, 888167755, 449711965, 974548045, 366839026, 839004790, 409517153, 308835235, 754668523, 835324275, 252362110, 823445224, 850497102, 609004048, 437094488, 965600506, 352408952, 140997171, 730385993, 163184119, 835815394, 469926466, 334491878, 594913515, 594460838, 986508081, 679754596, 494652582, 333590882, 39875775, 775562761, 198776068, 581368168, 916819798, 81332566, 816889096, 919498555, 196610142, 563834650, 436946407, 382227704, 250055590, 460377201, 737784986, 192209006, 286629258, 496966889, 804847679, 319598775, 805785017, 994444225, 517705030, 378082610, 188749443, 257400429, 921173241, 195981577, 318837727, 830649955, 661979967, 4565063, 403457313, 32892957, 704861676, 867628063, 917365715, 89479548, 493447788, 647202128, 839478662, 21333637, 360215593, 918376046, 592720445, 878894528, 988947499, 903779359, 608571587, 319485193, 860852538, 748099775, 680695348, 182253872, 200835007, 238622018, 586953246, 663536917, 366313934, 56579371, 208622877, 319527527, 955232688, 737102840, 907925189, 505111751, 158019452, 880862187, 939332889, 704150893, 591711950, 782326059, 716530713, 656558252, 152810284, 599390833, 545363175, 933157908, 245383225, 363371840, 777522175, 166207138, 354159088, 442526680, 287796391, 580372189, 564337550, 289223640, 520561914, 173764978, 316495854, 655013531, 809205703, 393923894, 809882118, 830558708, 291907991, 809369077, 898355308, 951902137, 824657095, 388709523, 180311818, 402916361, 276370672, 431696384, 215835723, 554567688, 254184307, 473277575, 76370262, 359727772, 494336777, 564152440, 716953729, 273050891, 392284083, 649806492, 203717755, 104345361, 682718870, 276734738, 687776797, 700434992, 942791729, 366877043, 792076748, 723489080, 526715219, 334224562, 30851293, 587845590, 413265798, 720750746, 279168533, 911763410, 325126817, 565680386, 456368852, 500733732, 987980993, 750659350, 520047913, 24111341, 620086046, 432858193, 873194167, 54712380, 401326314, 195272837, 621530907, 410084001, 778136795, 603470692, 517025979, 413664258, 599061209, 911214991, 31641923, 707301301, 201308310, 442281896, 32605210, 944366339, 315316540, 813543976, 113985492, 330497951, 584828660, 582251093, 43731933, 209827344, 22841803, 452637371, 858350501, 408758148, 604362392, 205705444, 602875417, 936888006, 661785260, 180770713, 857443727, 574216752, 756865987, 93591821, 641724140, 350607718, 779211403, 676751499, 317084483, 604923561, 363195773, 276153122, 62867478, 440175068, 296297824, 866456613, 496467524, 262806942, 107196194, 36875310, 1798232, 577612462, 514495614, 861211956, 146933259, 792109259, 451431674, 696021573, 116318348, 701669593, 378738158, 840965353, 207158929, 170501646, 183760240, 846174193, 602671554, 364838864, 311354106, 918792928, 779734525, 814848384, 365300981, 287544277, 925495538, 299933533, 96968028, 118412081, 894374756, 475156057, 689953774, 389097891, 720809283, 104878354, 535283277, 501286036, 852902421, 185234093, 133937433, 970493462, 331344869, 497542427, 958273146, 442591040, 914318020, 117978150, 686336348, 643796491, 5109121, 58167195, 405662012, 897721340, 842143110, 845620974, 669070568, 46067847, 704771796, 886667121, 935095684, 420403125, 826866790, 531992825, 69218405, 834477815, 688638565, 654516922, 611019369, 332148078, 780501761, 265374541, 713714609, 270894178, 604993583, 827735227, 283862644, 535895271, 388927921, 981653758, 248468490, 216620107, 685321713, 319671006, 508873265, 355786104, 212566777, 266524282, 396283674, 434787927, 287415531, 352755186, 3667184, 588569563, 947128779, 178975176, 688703977, 563238886, 488418592, 259810982, 41012571, 721371420, 687917740, 506479977, 134029692, 302172636, 872742965, 950948411, 72810647, 233798337, 637898137, 973843859, 677405647, 906449494, 560025488, 548876671, 973351560, 773283153, 324294975, 28635643, 245506025, 551766379, 17165860, 119032947, 813879781, 821266618, 313341809, 185721824, 905545776, 725002375, 689616758, 756347188, 414094640, 265514266, 821731760, 787427011, 615366684, 285442871, 904871355, 786001588, 922759019, 58035676, 591438169, 40569424, 648342189, 914525748, 427719275, 859293265, 844665289, 945665281, 408870661, 965996420, 844298407, 9950169, 133188139, 586753986, 965022175, 221346378, 992224548, 33598309, 40618726, 802007374, 432106830, 783840559, 320755560, 715373693, 522304506, 816511512, 299371068, 9008256, 161374707, 26709412, 718774433, 779574386, 835646197, 632768682, 77995634, 597518536, 655407688, 480319851, 616289914, 209080568, 458426201, 958905817, 166787631, 726943827, 81946979, 947256081, 370728562, 328565984, 891467373, 301197586, 701790458, 175179771, 984937822, 854222621, 411758634, 366030546, 838702095, 373911770, 192347903, 674719411, 927659695, 230991878, 859526629, 897676611, 153668598, 905054382, 556528682, 764308204, 761660072, 197756077, 69703866, 47063056, 6021408, 176825692, 610217649, 368524388, 965073257, 880099705, 897998151, 826363639, 853341564, 745968545, 893076872, 73495991, 23196114, 142321561, 154117172, 843185630, 865674603, 506522948, 297258850, 139280050, 133467861, 760553135, 74072290, 926449766, 294815184, 575749838, 395057031, 640929015, 199638382, 756015576, 277074314, 88299822, 862497643, 295780147, 518204114, 78930376, 729542718, 184407179, 522693807, 593466474, 723215358, 381761128, 869055731, 797112237, 688081523, 559940374, 594429281, 413183957, 450283735, 18251548, 647374499, 567819122, 70543523, 827574740, 900737808, 475587611, 912823928, 474469189, 228754795, 921575046, 65039185, 957967200, 922763170, 572438022, 767603370, 498394374, 311594099, 30949901, 205503305, 535275768, 752939905, 611784501, 355056772, 400911479, 813576763, 764094300, 524978973, 952131929, 898921413, 85537944, 957884042, 349467698, 507811704, 390575227, 858622138, 358694506, 989818862, 76682532, 517174182, 527292013, 61219027, 374149442, 411404856, 549786456, 377464790, 704340561, 524470170, 319213746, 982110404, 637314862, 908899027, 889876703, 824271060, 982000575, 203369248, 1346495, 873556513, 836824767, 876565277, 269737484, 29689522, 677367900, 447237974, 638749019, 147595807, 231045619, 113692600, 129290455, 131923524, 712807612, 817174548, 165068386, 25303129, 608678055, 877829368, 184151818, 57259018, 202294176, 934840932, 792327902, 1198844, 458837944, 449708999, 532906891, 479986372, 511223189, 970499461, 930723424, 78114053, 855016148, 750952259, 158811907, 300743253, 562445189, 757254223, 684185165, 33964048, 482030566, 219773058, 84698112, 5822045, 871116938, 418641628, 840640043, 720367646, 868425085, 956599554, 86751144, 921755541, 505466238, 659506384, 968385823, 784543268, 759561149, 824283148, 598718111, 954630534, 247965985, 296694054, 519737715, 468717129, 349514524, 125550605, 764674759, 883142130, 934149381, 699830618, 868515452, 428769677, 974263332, 339137096, 214024627, 944088741, 578551440, 590299719, 951733473, 359513842, 558185221, 711546675, 634899058, 449235864, 139839663, 949779337, 343445228, 481984207, 381389081, 985455328, 998093081, 163051288, 368702924, 330305577, 757193384, 187409661, 921345755, 345215184, 754418115, 537096905, 152238594, 373806458, 173348651, 28505003, 760400522, 982522473, 534560856, 503014496, 382841846, 485867943, 594496089, 818641864, 618857342, 683439228, 670496675, 687133599, 995116924, 238823210, 136381817, 940063325, 195105489, 393827960, 750131213, 571221679, 838381621, 795337027, 927802877, 244574468, 97298701, 209176521, 149980755, 926144631, 268060742, 71064733, 205672471, 879775704, 261065947, 690443163, 420931482, 72207667, 674628614, 987733598, 770705281, 835836037, 439322599, 909313122, 779806301, 626254488, 452678842, 141358070, 818433971, 377815363, 554370417, 691470841, 850714338, 939520515, 263234920, 779602832, 801607203, 303015739, 486339335, 605071199, 764886621, 365800223, 24438277, 466349049, 780938199, 87224839, 93040096, 618925174, 918490433, 58055057, 29516518, 459706294, 475057201, 235465819, 321411622, 572114759, 416225939, 124347341, 948084743, 606768908, 472959694, 764195041, 840681363, 561508859, 242674687, 813185084, 849381853, 844425141, 971265075, 644952897, 978399330, 891240881, 475679028, 474680034, 490312293, 485871598, 594201230, 856001784, 8656439, 456013765, 817345096, 813306728, 930011043, 846804274, 797121954, 558177129, 426572541, 711686410, 158516210, 579989503, 28091026, 465793875, 469892804, 835972946, 831987037, 609752056, 381960276, 345893717, 612536801, 956155612, 879716040, 775111142, 168824761, 350189464, 731736785, 588167348, 958280802, 461944693, 15717156, 375958116, 318135218, 599753182, 423707744, 98197952, 700636983, 651359597, 75320156, 455286393, 339661857, 86390502, 740522607, 592157268, 800510968, 662503184, 826494308, 683993320, 321306916, 249246990, 960364428, 680109862, 460012067, 986858465, 450369697, 490314001, 735155660, 168875804, 609616262, 39696328, 556997955, 474681479, 405126617, 790059236, 726122115, 134806962, 699519631, 153321689, 99936695, 900162907, 72130970, 544884718, 366609973, 891031835, 179074699, 794512282, 937369327, 561703787, 221010046, 570189995, 200663630, 268659362, 866250786, 609609574, 454336531, 57771649, 141570240, 500399263, 563478419, 533774183, 793442932, 278096290, 365373581, 715083053, 55662737, 612153595, 975428698, 196095191, 525953828, 817715504, 479751844, 440015450, 568335552, 664105166, 208646174, 19933435, 254458109, 604072311, 137221995, 765531096, 161646540, 579869622, 421243111, 990524159, 864485853, 245102532, 295427824, 917481831, 204899932, 824843236, 868997368, 76545001, 578363495, 456048193, 462817655, 426266464, 982726238, 144231117, 436589928, 250229941, 444123954, 111768115, 546747685, 793364975, 722100176, 661628080, 231127883, 801553463, 167284712, 586155375, 25155937, 860510989, 621061548, 190207084, 653280122, 589273014, 693796904, 830951499, 665558374, 53875631, 858498431, 23548573, 69070175, 425867358, 801886630, 746028348, 991241246, 364831491, 867032936, 923416575, 218129212, 264584574, 521720555, 387156228, 804733503, 103323083, 415645002, 770644702, 783064607, 421488734, 926272049, 285669533, 212139273, 537386452, 310548513, 416526549, 740189588, 289033436, 673384772, 34627324, 745763234, 307805143, 47167346, 229840897, 317541824, 329404407, 843138528, 510366483, 68503682, 472358562, 614731868, 782141433, 232096045, 249094854, 937184363, 834051878, 604374099, 534062387, 15412469, 432028476, 675939066, 431329714, 438875837, 937479399, 509415355, 944465412, 954342495, 198961548, 518435513, 729673519, 634106617, 793963406, 476785618, 48689960, 407038597, 452520998, 562076771, 680062710, 330395851, 681419212, 603825724, 472714847, 937299156, 959774289, 32120862, 589694902, 138853799, 987934624, 500613005, 285451674, 144760227, 270050122, 471643844, 661924952, 944401415, 788292456, 726669219, 788087257, 366072657, 53736461, 664642142, 705823523, 592134732, 922400119, 139225077, 640402976, 530461533, 736201967, 600456852, 618760659, 65796018, 632469761, 583858813, 803610647, 847246401, 381198325, 428133698, 818804836, 582364283, 258316883, 539144944, 154671072, 585336693, 67906573, 201327595, 139123398, 348842795, 637309715, 34927057, 806605130, 127545850, 44912691, 249116837, 994400863, 946139452, 153166567, 919263131, 449572833, 450116463, 599235915, 130874449, 841858315, 917734034, 428249135, 545609408, 226232458, 255281002, 439172168, 238995409, 883366883, 401568855, 827935078, 233161644, 418186702, 903255396, 144947253, 292385630, 212328909, 172316418, 511775098, 803184796, 172158550, 669734082, 349895621, 943214974, 437106718, 822616604, 361327451, 68391612, 457082241, 953121795, 9855364, 630352865, 168960136, 788049712, 635466933, 917529527, 271753507, 580516164, 819324505, 880019008, 887499745, 734123019, 13475698, 713443316, 46247571, 407295783, 699752609, 836747820, 728625499, 509982437, 148563188, 197217464, 684104488, 333859909, 45696434, 370683105, 704410533, 101985302, 52045434, 23179878, 206406071, 371282750, 500666799, 945036609, 713164712, 877428227, 112342040, 81824344, 896168035, 671278941, 324133830, 211941309, 292419572, 353710958, 598646468, 951806019, 819183632, 369899116, 875575653, 483855078, 176302143, 236447423, 288604472, 436798490, 711342968, 159264014, 161258262, 632175897, 638685634, 945616643, 996994941, 535756284, 136436332, 450796543, 843040939, 343608163, 130368583, 115614366, 216529705, 57283587, 677572022, 211648067, 713678743, 222040355, 462295583, 122950128, 102922539, 183010030, 806059329, 101960450, 594712208, 941549948, 921063563, 329140101, 224765711, 426517577, 84896635, 630923062, 761001196, 971922898, 257732710, 167088264, 385507112, 529330474, 128595671, 576120540, 859125934, 244610204, 746861240, 341600067, 710017573, 303880386, 292738729, 853471804, 206303808, 354172596, 499089811, 229798613, 413832384, 989594661, 678489250, 733102437, 974949604, 19885486, 260439074, 66914563, 637622478, 416011992, 916592306, 765750871, 226009880, 649766779, 312381692, 444920291, 626250415, 678930879, 817765244, 141836553, 645385373, 533661534, 105348463, 659286110, 192873513, 636115315, 923045866, 91095495, 604321136, 546311307, 906112480, 860529975, 455593372, 908832003, 496233755, 550175036, 132378405, 858081734, 54991403, 55987075, 67458331, 543355617, 482301679, 416503362, 662048264, 669573607, 285306771, 842835892, 268363180, 559252422, 334058530, 509843932, 609182254, 808751040, 12237060, 30068302, 774442466, 888824603, 825265510, 647585604, 81086358, 807053705, 920049606, 711774290, 897258186, 227475377, 868828594, 874011230, 587588629, 221991216, 76687206, 986085263, 255675856, 798516875, 391191843, 926850346, 173642693, 933576596, 135928861, 430155083, 913035985, 629668603, 46667433, 691152535, 206258359, 711341099, 146871222, 424553400, 860166013, 407158994, 100401569, 820440177, 959124610, 758759883, 594445647, 399373526, 128835414, 836005924, 743218700, 36071399, 406211569, 124196965, 740502174, 185880607, 416641394, 371349247, 325412571, 800506, 965118718, 646240833, 393066020, 289278956, 211613571, 849799212, 84639042, 433041995, 863461411, 371943460, 162798078, 144664740, 21602389, 68907371, 905075848, 10134893, 471034758, 233495305, 657249661, 115877326, 452132960, 415222550, 945703319, 213926916, 565623012, 329228389, 331608351, 681201800, 372010843, 930688220, 425624654, 74970792, 657009303, 321576897, 105327383, 767528662, 883492275, 485751272, 613879748, 609437967, 755952394, 752993447, 533110482, 836464797, 515243305, 27730106, 589510313, 408690605, 133701596, 315288438, 320741871, 462944190, 74851001, 32128699, 760045545, 966876308, 65047532, 417782925, 673680559, 493917248, 683953337, 505563250, 268453585, 575058153, 833149702, 840742719, 117115275, 607507652, 959592953, 524131136, 117686583, 637416348, 992149807, 14447773, 267537375, 423875596, 865367963, 215811056, 443211560, 898397375, 390663460, 129766952, 105512127, 453689766, 117554740, 923612254, 150550382, 304412208, 618961601, 744524025, 401468531, 294943454, 473144048, 177435787, 199213274, 994006341, 627696900, 846250468, 715675130, 500586935, 276422201, 628352289, 660737359, 138849087, 98175534, 353069525, 482940054, 722042954, 141014819, 931858233, 426590255, 110875005, 792791081, 997192786, 673836490, 819051755, 960945428, 766372677, 936218781, 425063355, 428320970, 4436141, 807032999, 308389899, 300750198, 823353190, 923796188, 318108719, 963109228, 454051227, 104769830, 573159104, 899067091, 641186199, 153155279, 31838290, 106741903, 36410992, 593805114, 625310375, 63118551, 866490717, 947197869, 928930865, 617036756, 304119226, 179257023, 161467174, 102258179, 657297966, 362405358, 553516678, 174795342, 429965480, 249062462, 386690166, 871930505, 744508146, 478437193, 563710959, 724987043, 365685233, 36389225, 888007656, 282230189, 529676152, 269583540, 975509586, 316960565, 833926809, 515215292, 853237226, 530488736, 937853009, 516118014, 282354612, 372184699, 805507268, 443046166, 650721856, 477991906, 889767129, 258267180, 591622357, 950029077, 750679652, 575852809, 328964081, 105068366, 222227773, 351852808, 668320531, 861452535, 598036872, 70011598, 545404551, 3943250, 463103625, 502412712, 103216345, 542721264, 979464174, 360092049, 843154810, 265124409, 502316290, 349989955, 41378259, 849386005, 343139159, 768625324, 827791272, 689463864, 916092472, 332888326, 645916551, 434574425, 577561028, 281567132, 517697117, 5301920, 264198221, 201472403, 491528339, 814717786, 195475301, 621710244, 644151094, 704888245, 715031175, 402019720, 723889727, 974330793, 182127755, 283248178, 870566908, 95753167, 770796718, 33428473, 567460135, 546374326, 69187965, 486693215, 21604194, 517126477, 559576758, 944570255, 968901982, 193892788, 244595405, 429221390, 769058004, 47538157, 123449222, 839185703, 52673750, 468287108, 177801716, 775438036, 599711158, 345629329, 371888689, 109999220, 755668423, 54276185, 103914844, 992551975, 224817455, 610275027, 59761660, 325919704, 398733076, 119093801, 299220465, 604014521, 123156975, 842286749, 429579109, 552063035, 339181234, 794874657, 379494390, 217481823, 808234166, 251907722, 86569252, 343558878, 617166524, 814717492, 179159740, 524594913, 495816256, 555059621, 375788289, 726000438, 587023470, 656065899, 124341069, 309109007, 137137947, 599289259, 88837192, 170514309, 925631718, 483676343, 664233231, 712441898, 967819184, 136265112, 467805667, 869036977, 894593767, 854032493, 664975206, 236373061, 215828464, 304782704, 524659556, 537728669, 314370262, 917034916, 275999202, 846336291, 484704340, 994051026, 758537117, 195364647, 996420113, 53999053, 383174153, 937650327, 81648675, 660403718, 293514940, 429337109, 736943207, 439594508, 311498785, 237438836, 74256305, 935939407, 894165329, 341992036, 407867445, 124915364, 930474235, 611236668, 854934591, 489538253, 799464700, 738892653, 624563092, 993937703, 45275381, 972056613, 258144033, 647128398, 659579361, 754218240, 470831639, 572840580, 694017326, 174422268, 427764917, 501712486, 316780243, 712334880, 341448926, 938143729, 688018345, 778103988, 333845154, 639620383, 434375213, 86392131, 435823035, 555851451, 486520406, 987214313, 119856703, 898786800, 551693887, 399351161, 319838249, 471401122, 7509838, 356886396, 582913715, 771131336, 974645253, 135821536, 299154358, 557115147, 301985739, 60329632, 320481997, 130690380, 190587999, 943503022, 795390921, 36198711, 684539591, 982216264, 617034095, 669647370, 967141166, 972225654, 188125101, 475615999, 857969105, 829184283, 603613137, 994509720, 588380943, 974314895, 948080907, 894827096, 884047712, 626320274, 854382310, 699885693, 978914681, 939269401, 684397383, 384374299, 412561240, 541550421, 612770498, 608958246, 45025348, 969248716, 431863175, 502536671, 284848537, 836890029, 944574283, 964999785, 141565867, 177502315, 672131827, 372880435, 545164483, 649186114, 76850043, 253043526, 46953708, 487310783, 332269588, 551840973, 564525954, 242177952, 281655609, 973980026, 443554322, 920042522, 307819851, 47142070, 993433150, 100925651, 174083720, 222190787, 259855553, 972940968, 887152550, 69325740, 322940453, 331447697, 946989539, 521917167, 832527999, 548483710, 729265631, 467259236, 297702779, 173162302, 985612939, 978327780, 353894785, 951169853, 494845350, 121319104, 718343843, 936744839, 545285805, 253855829, 751856854, 342980378, 413134668, 862590175, 974883897, 115579272, 564344675, 796551590, 712790381, 819962573, 607825705, 658261816, 357840035, 456381020, 488844611, 678198724, 812583495, 507352402, 589072620, 619532176, 67205607, 146287807, 544820470, 876312188, 463859099, 53495786, 498760074, 750239246, 185998635, 716322540, 202783385, 484203663, 362593997, 782464554, 562600061, 113370155, 165979226, 915427632, 44663731, 274417426, 846454819, 328468876, 567161997, 464728712, 339493108, 281107210, 464150668, 769253575, 610178948, 181406989, 347040633, 286708470, 335362305, 812467413, 262069669, 340026076, 380350430, 642589905, 145161162, 42815742, 199721536, 547779751, 879225521, 781288811, 963188646, 914183912, 656868361, 534680605, 137037024, 126482699, 184341280, 247079461, 200438708, 796249994, 29214191, 755953437, 660096608, 746343970, 427048419, 292949386, 103002716, 106392942, 840795307, 223457631, 693943006, 437462288, 581227388, 756181470, 223320021, 102977147, 910305545, 568368974, 934796324, 810030519, 45416256, 611028054, 599520742, 308071539, 991944189, 247607086, 195582544, 57781765, 957616210, 731223631, 254467011, 415112879, 310650458, 938843589, 439037661, 355325452, 900534898, 627808871, 642484242, 270735935, 586324846, 59281858, 781741342, 582668554, 541187071, 475387664, 784795609, 838639518, 882598429, 940136021, 106392024, 15133871, 483881572, 260635859, 782931378, 519126509, 413922146, 834792917, 307379354, 961693115, 227392875, 145976043, 266907619, 508804488, 292497062, 309110254, 320243036, 749858483, 538317166, 73152603, 859347152, 150202715, 3446420, 948107995, 603363691, 740514369, 664621143, 861935408, 49172426, 357382578, 719304709, 977631054, 54852636, 796280967, 292591448, 669144082, 207604809, 163894579, 614858030, 556374372, 55743769, 616807976, 515023992, 660507488, 524135343, 721710423, 464796671, 13363316, 526982814, 191574132, 714296948, 483790763, 352180482, 297457189, 92532916, 429201508, 544801022, 430972162, 669847089, 597437892, 387303182, 160731686, 546790972, 446949252, 402525857, 379259522, 49623575, 365058938, 743124436, 700543312, 700602026, 717399623, 587770413, 727522608, 2601134, 592785626, 114986091, 203340280, 7147919, 670586237, 451886762, 964631249, 605596849, 80970878, 898747109, 919513908, 78496914, 816268999, 682560203, 169785193, 566148084, 423631132, 932537845, 655197682, 441255737, 103986423, 143399647, 10333029, 977408490, 675512659, 179093735, 204132529, 767068058, 224504729, 570524078, 987745257, 197491411, 103070975, 36366928, 304924523, 101286181, 335634030, 792117261, 708308783, 999659804, 783664613, 519645291, 728233902, 683240352, 37662095, 127118494, 605662773, 753347173, 207791751, 14240747, 107074988, 766397632, 650359946, 147660509, 63117658, 31514289, 906660420, 376670040, 588439810, 95241317, 72963888, 141016778, 422317642, 268043096, 581281302, 620715702, 723140478, 273093988, 236876380, 817963432, 36555551, 629227453, 843123165, 551962439, 490164860, 179895521, 307976621, 464972402, 118575695, 801768255, 368594345, 673769247, 310619169, 444720826, 188536452, 365052682, 655861739, 524147813, 392596392, 456365735, 256691005, 685805530, 410270351, 974939289, 38132500, 583827368, 131750480, 543842278, 398879517, 15181185, 565325588, 109972495, 299698223, 953269229, 263281298, 665435431, 656125743, 347969912, 522247021, 723938517, 183880700, 208926413, 628908138, 850434597, 252993433, 134793101, 343666142, 745091771, 359475551, 276215204, 542208021, 597735577, 842001827, 965636898, 248602532, 954440285, 45752361, 311460945, 805450186, 477877438, 999316662, 783480501, 121852346, 799439506, 504115338, 497021776, 834078993, 419380742, 309880821, 498624774, 233106449, 698640233, 386960863, 673104674, 399469900, 685106903, 254787490, 144933893, 487131791, 737068239, 929304475, 691871159, 718928852, 396516673, 747544358, 946180322, 386439145, 958776078, 417225132, 1574523, 949341523, 750458508, 401151979, 658898499, 914179874, 694524881, 231751402, 435227302, 75555835, 929794469, 777203961, 688955920, 980124828, 157841823, 864701540, 571596893, 706150198, 969387864, 441835425, 648340661, 418648506, 694421089, 949697488, 931903152, 329780020, 222649526, 263589003, 40438200, 929052613, 478282318, 460828552, 491057096, 234474574, 340811301, 615849294, 423866972, 202030886, 652679503, 41865331, 649190154, 231369037, 133420709, 135286129, 807534060, 536486478, 281964231, 789904467, 556945094, 307187691, 591969800, 132442029, 352357537, 282050416, 941445988, 916206030, 483576121, 491203481, 346321457, 603085198, 662767875, 600462395, 367266284, 226364441, 89441821, 582838808, 848921006, 375140414, 823483882, 880609587, 791038487, 959751713, 447637343, 321169120, 153026314, 913532945, 143458102, 754394011, 648087409, 630547873, 579877587, 370264923, 217696345, 810098784, 36594761, 896238118, 783754369, 392382194, 282937721, 777127092, 392242312, 867291595, 959538172, 178738438, 213922786, 102695111, 398014511, 659266656, 889525224, 610573599, 638703779, 410285792, 304805707, 147043731, 626132996, 958269559, 154621560, 654560611, 191008422, 12135319, 625070568, 831801200, 755602165, 481556555, 592579327, 944349094, 250736730, 859266013, 817276276, 383757661, 443707379, 152997386, 433422202, 705512909, 227373995, 400465161, 31353583, 595038068, 194779874, 281767668, 251458848, 373495636, 964714892, 407646921, 124176107, 101268020, 478307380, 242188553, 180973706, 854511277, 347630716, 8872045, 224317075, 217842827, 125096963, 941788359, 22764957, 270806183, 388175166, 237927779, 166303434, 829340295, 647582023, 933990200, 973715532, 585289263, 392474354, 41292887, 986477268, 210248297, 954260390, 689062244, 217314215, 400172854, 848968932, 404684933, 314993397, 905076349, 458864145, 537850376, 978085409, 735431762, 603839914, 344752562, 662516023, 679708156, 891026901, 581213064, 962588950, 122886878, 759790913, 477342338, 52425632, 29608828, 745967521, 973990040, 543296410, 665144038, 626121765, 56877101, 740695902, 465973675, 456082941, 790433216, 224509054, 41905387, 552242714, 936386471, 8301294, 127873410, 551956717, 414922839, 584144527, 105534748, 42379746, 151930307, 204102629, 860960052, 966390833, 972543669, 399936564, 502382249, 69495412, 178682917, 65470881, 975266176, 979400659, 480179588, 36529431, 278461075, 245403073, 365531478, 35457445, 120174469, 955999507, 494330459, 131815792, 737393238, 396688355, 802132307, 264453351, 508805116, 684224370, 822193060, 659488216, 506584532, 127421164, 67089420, 656207448, 276240160, 284375756, 313458090, 612268799, 5883842, 373259249, 209301319, 383513506, 496823251, 294328666, 329140864, 584946509, 763038404, 720122021, 432455460, 556842798, 909874312, 569375092, 270371889, 767189526, 415994349, 751499957, 7648759, 285317999, 481633237, 403744193, 826113835, 321635178, 491909262, 857727658, 340564081, 198485859, 961733140, 80627580, 68093504, 36462542, 894442690, 383769422, 113844727, 129486731, 346372217, 724421088, 451573062, 418945238, 362476142, 289836329, 358467887, 609871697, 139747374, 879174546, 800998741, 863960590, 971011667, 691423332, 47821926, 147261183, 77781413, 32304717, 930278560, 925191271, 251869554, 701693292, 646397403, 605931245, 305508221, 905373841, 348984748, 45660349, 319372682, 438064148, 45992020, 882866301, 415718798, 313670777, 319053492, 474501975, 24512483, 633520458, 984839678, 45850646, 753584066, 499005406, 239077399, 111187421, 49740145, 107240619, 243550237, 359355550, 446769123, 878643977, 938330536, 710796081, 958271586, 88994923, 383250400, 617611884, 364382138, 360703647, 80800423, 175114721, 84547802, 282614562, 249738119, 633772852, 542664167, 315862472, 399297026, 769931400, 673183735, 712697369, 474259166, 308323016, 948955320, 255286038, 268754280, 793417541, 42234598, 174763169, 610727913, 908941674, 778860212, 76750194, 73504067, 113063108, 496546731, 203343750, 934341438, 401455409, 392137419, 732425989, 325913308, 321745089, 647061332, 332725193, 586887945, 990367930, 385528961, 464486788, 457611783, 720621703, 662470237, 145682469, 647308032, 264230420, 174269084, 968926112, 24203671, 992081757, 863911351, 877833958, 213354794, 251807630, 759777298, 899245387, 137852844, 543866760, 953380574, 487599445, 885144845, 78333042, 370127215, 877549489, 647403339, 16156282, 907865899, 646469354, 336843585, 611667022, 215045288, 475876180, 401361150, 208685276, 570931328, 616862726, 29920464, 363825599, 786307550, 697894242, 481122856, 868975432, 865827118, 505633296, 821509075, 810713016, 74668946, 18257451, 359215956, 26980453, 617532256, 570510189, 130193936, 840713209, 347262705, 494966424, 675536799, 205606415, 381417735, 115749365, 240552717, 741099384, 456645451, 289784608, 928155789, 810899006, 951937898, 536991200, 237646669, 41583088, 906870286, 968332840, 518878148, 427717171, 317149328, 712978136, 314448853, 906446659, 909266334, 734278676, 947786136, 906930737, 838904808, 391622067, 160899968, 621271641, 139770170, 417030375, 816611390, 575126811, 349080275, 401016906, 143485319, 879991925, 318228238, 879975725, 104028296, 218858600, 774817679, 194329070, 506852297, 332465786, 803177324, 972619509, 719895148, 371244187, 852586750, 52588939, 610858822, 97457154, 504673069, 735510697, 93746589, 889741229, 110159466, 726356376, 900831226, 181049726, 328960035, 743268594, 251455384, 418269377, 295837455, 388563080, 764871285, 909412144, 148930083, 592028857, 378335714, 274021523, 591989796, 633841097, 286588438, 504416611, 100168124, 948825230, 936433085, 956409898, 41092371, 184400847, 916932384, 995831384, 87330493, 411253348, 244869002, 551893612, 964358726, 150593705, 642873551, 433535093, 524368952, 899202930, 948367327, 310328952, 79769759, 631111507, 876774143, 237780640, 509121506, 935084594, 97639600, 837267895, 258823352, 329398798, 936789037, 949924461, 203531595, 655772989, 119614879, 51773536, 804111882, 401424667, 245332286, 426638018, 253212679, 667195722, 281138601, 540915554, 951597783, 443230342, 7634191, 952801961, 838236125, 792822332, 781840636, 981192672, 920534230, 171720946, 56346094, 867906086, 180571662, 435420304, 709796755, 824577526, 666212092, 295670969, 396139754, 693923697, 941072588, 913658594, 940816699, 532765672, 558736067, 942449076, 766829023, 147818974, 434796905, 254215935, 120126670, 7102153, 143264775, 105069362, 22939706, 8168311, 184900959, 632356265, 135501760, 61095547, 809593929, 473511356, 723346513, 976949622, 661671967, 67698279, 921653381, 919591992, 88271089, 957382094, 112831820, 23229268, 983942709, 997014705, 785431088, 139825652, 815689894, 366249980, 541788993, 844351768, 88135026, 184649519, 300186761, 659722391, 495708123, 285761393, 569125960, 397880036, 341639686, 579683406, 534231399, 909628960, 739639979, 615985151, 446238690, 355168316, 461927490, 225033714, 879714161, 114310948, 21707243, 884449859, 601066015, 307454049, 92366271, 728264899, 777825581, 908678354, 858607873, 712660449, 45352181, 51838932, 714295727, 130040992, 971071574, 530818322, 539911438, 545396381, 925232743, 612174292, 612114598, 519006681, 416430514, 552410493, 232521456, 354437410, 588695825, 922109473, 370792916, 299612561, 29820179, 376709273, 149897788, 3973554, 52267095, 16346381, 587142500, 873552110, 773579985, 694648861, 604026857, 741661583, 224430382, 236690894, 195466674, 731056785, 732983209, 403121673, 276532690, 520481390, 309919382, 391625153, 669346451, 426821096, 127089620, 586875967, 149904380, 803707471, 830034580, 580440111, 796664338, 68819229, 423861579, 939330087, 602717636, 530944787, 168352171, 882279667, 493230130, 215419013, 182498971, 151692427, 892524151, 825729181, 754847527, 132337155, 933910563, 926935484, 414911033, 242108567, 282514213, 622527118, 571902426, 693943085, 185537016, 684351693, 109888535, 571548876, 609534823, 569265509, 472853047, 212209532, 421192772, 148234648, 881300001, 76669074, 917005913, 308844686, 638118617, 907798403, 695513190, 475778369, 464860436, 650049713, 654696088, 620931277, 268203909, 83000737, 687974719, 357224614, 376527132, 488356101, 260637827, 542992482, 353412419, 484194393, 109928115, 110326397, 191503517, 590438809, 600872275, 4936403, 241928231, 711922934, 966405028, 353595, 827230148, 188357309, 481039417, 250139690, 522640850, 14038137, 582439104, 630524838, 82327978, 908949100, 254016496, 874795079, 67250610, 996465287, 323974766, 223643252, 111848437, 556658164, 318441010, 234911045, 809892764, 592795219, 76699950, 332432261, 547870073, 984996638, 607860378, 943617178, 823250895, 724079217, 502985248, 639442784, 372899652, 794591250, 985503366, 817025345, 69604748, 394623196, 213088809, 284363844, 505650619, 754172189, 888135300, 326489922, 681537710, 297434011, 712489270, 825840726, 431578722, 677766071, 969069113, 631914343, 197392665, 68686688, 710250558, 639511814, 600282864, 144288153, 18405625, 322261439, 63384898, 429106317, 859756902, 592280569, 864271511, 811391066, 87264802, 236876780, 659477240, 284183021, 20429057, 824241004, 562208123, 16351194, 462266674, 201195985, 75477138, 826708225, 18303939, 277947565, 241333535, 273355803, 280225168, 633089514, 730085596, 171690515, 303158903, 530012536, 446952833, 980543683, 706119694, 574664273, 444283270, 405430470, 865505876, 373323400, 890146365, 666566053, 8121741, 973503694, 146949629, 982946848, 744375655, 873990812, 137482973, 643576440, 274589806, 692841026, 450380363, 121545755, 744942128, 920482249, 742707261, 294536815, 717821969, 620716402, 232994599, 825282480, 261303447, 144027264, 690212532, 208356403, 41006144, 571613047, 960532566, 122959506, 678448550, 902802246, 545855072, 311737659, 624778592, 631167439, 452464384, 865479363, 59495707, 266163575, 913668049, 371961444, 262969034, 715163894, 428454614, 582146943, 726164265, 955607856, 661209213, 502675814, 131067371, 149963356, 828162701, 449763993, 899468511, 793794246, 108175676, 730191105, 760489398, 39495212, 719271025, 133420813, 483356685, 634556580, 42884818, 50105055, 344643573, 945237074, 277796594, 233916315, 135480840, 450205391, 389916142, 80667429, 374626768, 589825111, 772388196, 333834316, 421486852, 639986550, 353643292, 703689699, 36803275, 875843061, 935072514, 282384622, 207397485, 160811579, 955363351, 965073563, 839230866, 995601104, 961710638, 489106261, 332143233, 768749727, 541111825, 265228996, 71111939, 257384266, 451312547, 906486116, 639647136, 62822660, 790329835, 707430067, 626354575, 436056043, 305782601, 427267475, 387549104, 889256616, 618210154, 581536654, 512769689, 157768146, 111378545, 555785644, 958533298, 198321467, 348083453, 132239436, 283971206, 15469265, 411386073, 996631247, 642410061, 713986711, 366423542, 608261271, 489351892, 967378034, 426160436, 330271663, 429608840, 65613948, 238805694, 754853666, 978615248, 492337681, 407137236, 824189431, 488579130, 263707796, 110849974, 396388302, 154440674, 33996423, 463595343, 228903051, 801495783, 841636681, 239360809, 798670523, 663791289, 39188854, 805751947, 195757047, 437484813, 849122385, 498466723, 417760460, 231785550, 41145662, 652739385, 806722339, 776983516, 624311611, 387279676, 966435497, 428584952, 272992329, 708143334, 120715452, 942623504, 125220928, 198473678, 232653284, 167908601, 643480708, 211304063, 277744539, 616721363, 446543618, 661774284, 252155257, 90624176, 89418728, 402347844, 705817778, 239523522, 424725887, 597805164, 143093422, 676955663, 9847010, 775474775, 752747327, 923893256, 176812854, 40209172, 841960330, 671713872, 975805395, 984121525, 998300131, 258803100, 816282849, 758929078, 438341050, 847427310, 660630345, 250475773, 715543867, 101796356, 260584170, 542629291, 361935662, 956362866, 594647588, 82333065, 172874959, 710875489, 311075635, 158241879, 957454404, 635419070, 839917735, 466197087, 643866879, 160396662, 955225127, 337629712, 350997813, 664973288, 174608276, 285430961, 761657576, 202659869, 244773889, 918853131, 134873498, 974136941, 564148246, 298477682, 731329023, 94773366, 629656556, 237788381, 627722770, 477272633, 288537777, 608871059, 319233262, 807201308, 465848269, 567597313, 941203314, 736968438, 255669799, 379103294, 746941575, 330928950, 432309681, 466275019, 835640104, 249120511, 580531871, 874734126, 900325246, 521726739, 445603643, 944665808, 51880351, 416935111, 709964978, 4767014, 739224465, 716756716, 759450782, 574234002, 570371780, 396073494, 114179996, 896061964, 279227309, 365799480, 285564916, 337639150, 118029285, 270606048, 884568507, 919217838, 140675094, 868879159, 894490953, 57752344, 57766922, 976078000, 253779657, 617163390, 263986658, 351016821, 871733040, 745471112, 356993091, 616476325, 313849998, 528892335, 9177023, 695580785, 248407072, 966321846, 851055779, 910442636, 172595703, 825750559, 230668232, 779092461, 232685178, 108498141, 783969539, 792458007, 939627904, 241555581, 673308506, 894844341, 483277678, 505486257, 61837110, 924665300, 848579253, 68146953, 859616077, 882711326, 317321908, 72038634, 262702825, 562908175, 593900478, 677552491, 162379335, 336942972, 691707059, 144169149, 337217051, 237650628, 546773525, 175297877, 414539696, 901434051, 88979844, 681366258, 49639322, 289017626, 178646304, 583240788, 653050763, 180011063, 427527856, 207853435, 605601336, 270703273, 805577987, 474539338, 606531431, 572267908, 285123824, 134141738, 799235150, 871723841, 959175723, 282894985, 944969174, 456266262, 205145468, 566635358, 534853015, 384388006, 228982932, 670417832, 554467497, 757096571, 752420337, 721204897, 918420116, 312340593, 321836910, 293475182, 114901625, 822204571, 38922750, 680236928, 708181446, 832274758, 263652976, 89951079, 896559070, 402599569, 701979637, 870445586, 253949194, 229767465, 689812146, 516044793, 215215494, 979868143, 277876832, 59250593, 953947321, 968266751, 180215407, 432951257, 731032821, 339348172, 722277449, 26865049, 611171469, 98926188, 206252182, 507960324, 407932315, 999527562, 928750252, 722488966, 13035804, 693688558, 371618541, 689880233, 26343605, 729319470, 288218862, 291977257, 972667924, 760127570, 687865201, 439876193, 981032533, 124274877, 40057182, 902614258, 97653571, 653254151, 540276344, 848757115, 981996798, 810059832, 85377670, 296860664, 882069241, 381538870, 147511634, 569073531, 417519834, 689493415, 449570470, 595255466, 145306414, 260598603, 965426067, 257609013, 428661475, 121150225, 911320678, 22469091, 207378556, 69574526, 501379294, 809800997, 251236871, 527142199, 225224732, 466358163, 749696080, 311289720, 209284173, 830367424, 330312763, 398400491, 841177025, 978370169, 649971108, 84366584, 278406927, 323720297, 918445540, 89875485, 349012910, 957765592, 350858290, 797405191, 961642696, 734858545, 716432681, 799614508, 647234112, 165746153, 988689553, 635885748, 595345369, 255652103, 462227594, 122645131, 154835960, 545845313, 432054872, 166259972, 718201801, 267746216, 585142054, 545664287, 989516548, 811286883, 786800723, 416220786, 515130343, 744346624, 635716746, 61297422, 560965435, 558677180, 255115968, 944689163, 2373766, 599745673, 754080047, 366168053, 490381600, 680445564, 729483603, 685205588, 865925463, 920365943, 505605533, 810456601, 594579973, 640546767, 225602518, 67960465, 302810109, 337302306, 343886211, 609719481, 950708791, 706419645, 999676169, 360194637, 449263183, 309510213, 205845593, 935576090, 117250517, 885188577, 634846047, 406433508, 990592998, 530508536, 584570594, 810978932, 964234592, 262772626, 57670687, 907036971, 785589958, 535211440, 325833732, 493920584, 458156309, 266020296, 964244332, 166080055, 916555900, 414693794, 78219567, 80481315, 90728728, 494023895, 758991605, 31791466, 249717857, 616974266, 446048878, 378267009, 111223873, 339917676, 451989004, 103017890, 80889047, 964251097, 38246604, 537313898, 993377225, 198539306, 203743874, 354640552, 932128656, 267411440, 677928786, 163295380, 523931048, 828330352, 705985462, 575119909, 51509945, 850302623, 643666810, 928931840, 998717494, 67847119, 790288439, 322229065, 836215797, 967941070, 790883168, 400618512, 539737106, 436775211, 241104838, 820137694, 416646821, 790981988, 280583891, 306339958, 612992174, 454629871, 324533188, 74521907, 851097603, 186178048, 539402571, 533126728, 326514244, 87546913, 600396181, 189682778, 313049827, 394764140, 434229269, 317790678, 767571368, 581919962, 219134035, 353820261, 492773141, 550370896, 729445389, 419832422, 964141817, 236571422, 725869991, 714823335, 335779086, 828879892, 836089989, 210719974, 425232981, 200433353, 609121961, 770136802, 773277747, 110409740, 877450627, 222309606, 996935333, 139012224, 850435281, 32999327, 477651236, 272691483, 263382375, 558137898, 345387145, 509972037, 389028775, 848890907, 288326346, 939553960, 472026942, 862576650, 725133916, 629087427, 428027347, 443557972, 910414046, 703754526, 752231500, 855340322, 179549121, 988254494, 969847551, 130375452, 353266653, 629269500, 87108248, 933458831, 606927864, 218835631, 569080391, 120381076, 40669608, 290713380, 608778660, 824652106, 192514363, 635170222, 27056328, 509324482, 151342211, 806604386, 379535505, 38578784, 173704702, 674821055, 208174878, 334539295, 660407538, 120889449, 951341922, 575732754, 471006297, 867937592, 188460459, 499811070, 906151905, 861416525, 608634648, 68142261, 649964112, 386134524, 526478146, 492530367, 406563309, 257632784, 712079279, 202066051, 840143172, 171713393, 691537073, 829416335, 580333719, 266393203, 843648959, 365998259, 547775825, 818934033, 557328285, 702818504, 789396618, 924170027, 88071615, 377374325, 958592718, 132100976, 226639446, 130818017, 174546084, 733958735, 871817216, 51574546, 510199425, 348465573, 899068839, 205070583, 149324960, 790642676, 137048516, 865447423, 799390644, 417222490, 517834589, 11236309, 579818568, 800786245, 245098188, 218852645, 888298588, 985837778, 456501119, 801375024, 717053500, 438277988, 897042268, 821467137, 930081788, 673130233, 909791391, 966957827, 453789140, 652094844, 675972631, 104360965, 385554803, 606665467, 25759322, 668600910, 308823538, 643493129, 621177869, 655426109, 196449037, 543593621, 879843419, 729062463, 380333975, 240081910, 859934829, 913284470, 759882572, 824663597, 776628134, 901455239, 195397296, 407728999, 720649730, 851483272, 789234755, 981888348, 836839974, 221057593, 831567233, 394818807, 811610124, 112779394, 706424374, 94575814, 572320616, 622153598, 689639806, 956041116, 162514583, 357237756, 466108693, 130152934, 38682175, 274678288, 452318024, 750230503, 834870132, 358231941, 568484534, 889751660, 130386092, 70828715, 601698735, 961763385, 601573590, 996957254, 291957352, 925979305, 453108409, 191303053, 535923886, 97637648, 502281235, 599276835, 278849969, 643929419, 463191598, 639313911, 608669234, 214822092, 237899061, 918316486, 452344511, 964523599, 276886894, 553269662, 682392623, 106967356, 672519196, 602294325, 103047610, 295693091, 222541902, 738674880, 92221706, 690217075, 574358087, 389489329, 775861453, 822637253, 562438760, 926017751, 930715847, 609219065, 219001886, 986556224, 773003580, 816038282, 333168701, 777474421, 253703896, 471531065, 161646980, 424671433, 255623334, 602398756, 790092918, 811547219, 690199627, 657099797, 285287725, 535165765, 441363477, 173204488, 221360425, 633960146, 974175679, 193434162, 110297659, 933039989, 542445742, 342573258, 806916576, 258171779, 733046026, 769454720, 85370116, 524071429, 562744726, 615231731, 229875011, 787296075, 265420896, 527732484, 458275368, 599129011, 837708759, 133312549, 29822222, 10066023, 493889524, 429924437, 100519443, 988392998, 563013938, 425444054, 624327721, 941626448, 931141481, 773804385, 775330854, 103479136, 924777039, 162669198, 353605352, 281162755, 841244127, 837680444, 852821645, 645790998, 209944416, 813738913, 230365906, 665955146, 400699176, 123443176, 868146103, 832017777, 801796271, 933546299, 599967348, 316952414, 718400035, 572705257, 684574290, 924829574, 516469798, 11919923, 44256526, 663304424, 689264535, 796691386, 857502200, 943183769, 990448549, 956353801, 345463798, 886676030, 340548313, 447375083, 500743465, 397700768, 956880004, 494893774, 792845785, 456247663, 133869411, 986708865, 522796447, 331621990, 299006753, 969530020, 471606527, 995948548, 267660039, 316049820, 867917668, 383493539, 753782396, 274002498, 557388610, 350861020, 139193971, 932345499, 31137528, 844965272, 865497419, 977427672, 114819081, 823115090, 995089349, 398492948, 673069555, 858808586, 486143794, 638554324, 812350146, 960903125, 787174980, 715385932, 811807353, 800550120, 961884550, 150283649, 638263530, 912050747, 753808583, 202412200, 247718398, 728671612, 887751468, 691623198, 540289267, 114811338, 197054305, 586693843, 978715074, 127921193, 989106923, 956160622, 142062414, 431009770, 29394395, 247503824, 572815657, 642991635, 875729151, 558426961, 2190738, 630684060, 781441600, 544986658, 730908532, 626848628, 305087933, 954249950, 443116790, 938094273, 148122617, 351898995, 217260288, 927177644, 898190380, 453300935, 923390363, 793978542, 345282517, 569359411, 753185362, 560391135, 657969013, 907715299, 11957960, 826926899, 422903179, 917597034, 178110861, 945628423, 931360621, 465405324, 901948719, 456528334, 477631910, 971029278, 504003736, 557284096, 164192750, 956443604, 63337963, 198447867, 590936884, 41387308, 480666422, 8527216, 422675370, 238926813, 153158808, 665050877, 391254970, 718028296, 748705947, 558213724, 838886163, 871410529, 789178084, 435968904, 249313388, 298721384, 792825211, 839941488, 685651893, 751057482, 482027756, 730123569, 367361717, 493911063, 703815106, 294778791, 561884449, 861403911, 49700150, 904033615, 192121508, 315615828, 925261162, 366861663, 965125511, 752954419, 572308652, 832817700, 97023334, 794771772, 526284784, 60583093, 516108499, 671415964, 423499754, 321061791, 311158644, 128944279, 835268224, 243021633, 578534504, 913342910, 24839776, 271756229, 902609263, 263426852, 210361614, 508273635, 14046849, 657896968, 200967797, 963357415, 794065919, 45717974, 875704021, 96796632, 103420225, 659052516, 397893235, 776770853, 164313494, 562079828, 28351621, 762026249, 440881701, 479053176, 696290891, 641934653, 929458786, 392739636, 671328211, 609183177, 884775207, 728404615, 553706045, 270097898, 106584760, 653353425, 652169502, 283661350, 222142797, 592822808, 766139351, 666366268, 52354719, 940439882, 695228741, 968774508, 749028955, 314855968, 29587804, 861729429, 932517152, 466872257, 126856696, 154128725, 480998936, 636901876, 823864669, 595255962, 921937843, 944097263, 426418232, 750143664, 709012509, 728753454, 158930699, 993211112, 707893594, 987500066, 964538828, 9960182, 668907275, 69095484, 998348482, 522800034, 174270771, 464962897, 453496235, 518896980, 846447281, 551595849, 125096247, 245378515, 534376535, 658517844, 141645346, 807290667, 494220739, 280178825, 330736373, 326994424, 940248930, 900272254, 821111796, 695109267, 902837388, 972096211, 673229957, 689363727, 180803590, 575002924, 69912361, 904302913, 78227177, 764307923, 302502792, 969921361, 881398589, 282993589, 232883774, 601537738, 264145517, 740658947, 334177280, 324002729, 282315053, 199947299, 887604133, 620250119, 587856956, 129773435, 323288663, 765155304, 224436481, 477289498, 506158067, 691379536, 636200710, 160561915, 511024401, 571728611, 575492807, 859856690, 343797594, 548787401, 691939923, 780427842, 571298197, 886414068, 167221219, 390076235, 34597641, 930122027, 136489422, 860823556, 749146925, 185004457, 623904659, 78370328, 937238773, 752588319, 611080335, 661699134, 808865198, 562986001, 972601533, 925789915, 491811817, 49877085, 741375468, 671664534, 721311249, 286539246, 509915781, 818846951, 587344244, 191268053, 915443365, 49231107, 65723830, 21416673, 264954026, 717240265, 729300932, 586496504, 843934581, 436473446, 544269434, 579832770, 25317338, 831544834, 645212142, 882981312, 256346943, 844064301, 741357352, 668443134, 924543969, 665771814, 300137953, 212701885, 87599703, 426046954, 927452538, 962604188, 115483456, 693660643, 647401377, 346034163, 24552874, 588599230, 123636175, 103618277, 403197103, 609845559, 491093951, 967134044, 459354046, 900308841, 521008269, 285209271, 818528275, 695441914, 230595367, 178842249, 295238236, 799137585, 644319738, 633256729, 699698408, 523957061, 772869647, 286998908, 507917571, 514767758, 343785772, 261133257, 390590032, 274881216, 924529335, 932426518, 42729159, 804832640, 207957566, 281912534, 821259092, 227156618, 982886620, 125596496, 167834265, 152761887, 991341633, 793903963, 606640547, 298957615, 689278595, 827777862, 19434117, 233094075, 628192247, 792451859, 730230754, 330822650, 251959830, 738059111, 580348126, 24699947, 758975833, 109002875, 421701057, 318958827, 43910369, 92798395, 885646039, 581281173, 38807194, 979771357, 883457580, 362616769, 503993845, 959867909, 441079545, 173666594, 254604301, 163199786, 784530930, 661613267, 325341801, 256179809, 402199064, 307089960, 912402686, 654688495, 940842844, 363794083, 40399086, 25415132, 6847324, 130546725, 965336256, 881925159, 768545594, 361123161, 384254081, 311902449, 750316876, 899004801, 400035137, 121635773, 611412440, 685402137, 550696461, 915466372, 265850098, 817571122, 915737737, 442800271, 336466436, 559383009, 164093889, 399115166, 442276046, 550873901, 890536023, 948695883, 135092605, 639393643, 630048248, 635135918, 963770844, 720283625, 856883146, 361093816, 894891281, 387917665, 339803949, 427417763, 622322240, 852018447, 403319160, 889088334, 357007791, 697350703, 759906777, 240810189, 405176939, 311222573, 751552572, 834706719, 604380540, 916590682, 32804078, 45491292, 116358014, 663348588, 7528995, 420555420, 721152820, 25938972, 898075474, 291441430, 687397088, 334402883, 143113714, 989441748, 919360193, 960998831, 447425322, 790802906, 988806690, 481744039, 161597921, 135787705, 934327838, 769913452, 322355923, 510380594, 26507777, 528077138, 195105331, 828444844, 958664331, 291527126, 124918589, 358617021, 736952457, 431030684, 712346290, 305112866, 902462701, 617960814, 290428829, 524828509, 839894498, 687348608, 36691246, 907599295, 397739950, 929313788, 248849661, 739213184, 369080039, 795230006, 833779197, 323352966, 818585265, 35637577, 111786240, 76120045, 964816061, 190732070, 300325439, 791705355, 585349984, 669542817, 788829614, 728365298, 182140669, 170746778, 928793046, 60217847, 900115160, 764314756, 25493263, 169376305, 903118883, 918792619, 351777788, 452917508, 587905593, 205599813, 438772400, 83972037, 591350404, 274614706, 608674858, 116704753, 818405118, 418966316, 238837801, 493996684, 300738680, 765190069, 491056338, 64097071, 469906436, 636179325, 320957044, 209312819, 378834890, 291230213, 509067148, 672184773, 567483005, 983824379, 89047317, 606377992, 182596883, 437078267, 950792842, 942264270, 977328995, 585032816, 189639358, 462515937, 228487932, 288533403, 451576627, 52137273, 541490230, 435414376, 312093347, 228583453, 786445181, 217896377, 244557709, 929730721, 855161843, 45693739, 431830595, 171260066, 577627149, 463208916, 383452442, 713067181, 32832918, 417910287, 749268087, 980138244, 519571628, 729946196, 120158413, 637525208, 939283844, 137413339, 19659750, 897856598, 683411298, 169269116, 704105294, 923150200, 252842049, 128634989, 552659747, 936142958, 530311181, 755553964, 88571423, 734024678, 396087030, 544103451, 684903861, 959844586, 606616068, 862239949, 439457611, 493888048, 289355037, 424934454, 877050165, 376513277, 752981265, 430886854, 932931508, 931369467, 479542406, 401398549, 625403771, 920595950, 393372703, 166020290, 597763034, 211088817, 219259000, 969879192, 866585334, 150033600, 775040031, 867506520, 443966632, 912108728, 731526414, 368637419, 132606279, 872591310, 436445947, 483180109, 598092468, 12125403, 520008831, 60199533, 831822058, 201175652, 47184, 418775224, 292156879, 860528572, 559064239, 939765693, 400933383, 147362099, 367520615, 555926139, 478321743, 571741430, 756987178, 221606048, 26915129, 458067616, 70499785, 104900618, 39775070, 297625198, 723571462, 51065534, 326143662, 719385170, 407873316, 398416682, 508601913, 305271569, 599474512, 87146904, 612120322, 716233509, 341902073, 826979873, 935313816, 208902817, 858852026, 975991006, 275635379, 550326951, 763827188, 639527482, 417096372, 835536376, 330249759, 888805256, 85922429, 421864018, 578317629, 594319184, 770874082, 932098640, 439293482, 226264317, 533416074, 324621091, 125105615, 151723708, 241407165, 786551471, 947632330, 252985063, 635822181, 775605625, 350839951, 400862949, 275384047, 126377594, 831467958, 52616754, 803664396, 801798909, 870609357, 343579431, 751460182, 411905334, 220894704, 850373962, 733576428, 795932502, 867036261, 309390003, 192148042, 792548533, 59816136, 227282154, 607218248, 51318822, 509357083, 864290257, 197451979, 867811214, 31611307, 319110021, 946485230, 321064130, 739246678, 879370178, 205761849, 816540537, 225360241, 227566618, 14689550, 540983053, 915201552, 454478714, 394871407, 600099704, 60586643, 862551297, 129028251, 690605255, 412953953, 510499316, 614398291, 412624119, 974534918, 957154845, 249105084, 330013808, 672069919, 581370797, 548776830, 428499848, 806739852, 118247349, 13396404, 594481872, 427003242, 408609959, 849594961, 692952180, 9744394, 30662290, 591187895, 149232810, 182844676, 523099550, 240188589, 365484429, 260841096, 776402436, 984308048, 862143814, 99399422, 346809274, 961950214, 431549579, 308397136, 2696366, 550424587, 268133529, 148449543, 152687567, 598991103, 250807103, 998762318, 39287662, 640955746, 638620020, 450690812, 444640291, 477411672, 985754454, 271266021, 71454811, 57292983, 47228914, 314222350, 361851835, 885182346, 397529563, 873475025, 282166140, 920446279, 985948738, 287709534, 358203282, 879653049, 344646648, 707770683, 864076170, 704627252, 659481626, 852051993, 116003384, 413617143, 576336949, 648088877, 705869208, 130252447, 655511424, 217678186, 438792233, 861684347, 424949355, 790191616, 414902689, 590174701, 922943372, 206587960, 473535615, 400330837, 956264565, 859590287, 34026431, 70080541, 888634319, 342854074, 526747899, 539444749, 27612225, 553905319, 846915151, 343935783, 982130955, 925401994, 657190929, 852210955, 839680622, 727487674, 300028422, 70858071, 825987994, 33046120, 872686697, 819398137, 835905888, 560702273, 242060669, 655863146, 294127707, 314401487, 963265175, 618669326, 56831394, 652102360, 390060152, 245768784, 763769265, 137124462, 931826830, 525894987, 891406009, 368922635, 307532551, 816950545, 163667666, 967765991, 283133424, 866181531, 626033149, 200938076, 843382810, 631782034, 439602230, 106193832, 147842895, 203232977, 129395145, 267262612, 624411212, 545693655, 942587081, 394767535, 530432851, 723829296, 374491410, 570292165, 633450285, 140398749, 421013300, 465828497, 981367336, 96437565, 769905570, 951444795, 209027720, 119326467, 946709456, 603932172, 526270293, 82451071, 145452987, 952662337, 805382936, 997601378, 668047188, 399869103, 984334468, 930770586, 423997878, 617791072, 714278562, 128592818, 65057884, 160154817, 314864752, 575296717, 655895372, 873563313, 747671746, 701972241, 204620583, 941536110, 363459830, 131892801, 20541328, 437699429, 491455977, 422068006, 620078149, 10152227, 218234463, 823895969, 288030725, 970889045, 633693340, 48382440, 246820247, 484740308, 514864817, 394562748, 435357635, 484733622, 909810343, 868420476, 279105148, 834477797, 640243073, 403061989, 688891806, 742345732, 814875377, 881601097, 797475514, 454059795, 493424021, 861766573, 57137563, 231718411, 54711619, 56253697, 925287165, 48909946, 208189187, 487530639, 992284083, 909318203, 745017509, 231394923, 808203691, 827320594, 54715211, 613302252, 555058714, 149010296, 752834371, 826589081, 422103549, 387737714, 97069706, 113360328, 716305190, 612778496, 644542347, 635068826, 916956721, 671458255, 403149153, 645628713, 40094068, 862089421, 771354260, 482313094, 483759154, 800058780, 122014629, 805079274, 840178467, 907646328, 996603934, 949001447, 138253496, 221039421, 287570745, 744956844, 468522308, 276296393, 662052050, 141278997, 847047222, 730223606, 312797773, 51712681, 255820501, 446396248, 179679775, 515798978, 961481098, 157931868, 260956638, 90988510, 918102029, 400102019, 896071169, 379553680, 777701330, 556943759, 137352539, 344182570, 535706034, 497726008, 632164478, 835033594, 419782810, 249415033, 539727392, 762969932, 393062876, 683366341, 583942600, 241433546, 941909524, 870567699, 28959871, 855132643, 271117791, 74345756, 458845373, 187151856, 339736825, 643760605, 261301125, 837961454, 161156953, 658140798, 882254774, 680184362, 62826876, 967058525, 276253449, 329090621, 632708112, 466379362, 732325817, 370604261, 43139218, 907015062, 425092370, 148990726, 246834268, 191962199, 741683080, 166954317, 557316515, 767842463, 896922800, 539395912, 507154319, 842235871, 714586785, 371430612, 476959552, 583748459, 547067832, 991181208, 211041568, 119377320, 356630505, 311465184, 431853083, 377331767, 723340482, 589915001, 81800201, 566189375, 77914796, 188402721, 567204278, 848351926, 690719081, 261241029, 950252555, 316413090, 481603787, 900198503, 311583357, 598847291, 872943380, 285561719, 437206634, 970528992, 642451223, 615250710, 628892684, 561555188, 504686323, 838141229, 138873493, 920343107, 780156839, 810131105, 153620687, 437436936, 343487368, 635343809, 743215053, 656900355, 231349850, 881288933, 698916132, 340211613, 660714212, 768402382, 323626028, 906989412, 252949147, 527080956, 538546270, 134709411, 995885360, 935311303, 895053040, 705960708, 937787766, 510588796, 461708641, 141482980, 482207987, 783096309, 517335206, 218373434, 686352485, 128121351, 240630284, 354098919, 902910247, 624726461, 506154225, 78740721, 421046091, 304613887, 511154337, 991239452, 505289693, 622763650, 740838493, 170509834, 763494927, 972463065, 698429435, 926975255, 554986459, 118296930, 379150596, 533532994, 394760470, 380506668, 140813345, 781998222, 2923767, 493442030, 291968836, 459162927, 28754041, 84824956, 218744832, 982189370, 878203, 87802549, 11557385, 354358323, 552460166, 632124910, 972003763, 956820066, 345864660, 103896885, 374808998, 766070385, 659137162, 445778382, 850333802, 232615708, 180279600, 896419074, 787564454, 820425920, 528395128, 799461651, 506821622, 231944514, 432593322, 674640375, 708033063, 917801450, 665819874, 950746153, 446587345, 498840190, 116941440, 759064293, 129486338, 916838488, 368568998, 542304637, 400417454, 840821704, 797268809, 939459860, 665093745, 219396629, 832411400, 444199358, 533101914, 920685131, 391482343, 795608064, 427556079, 81228142, 2994035, 593580473, 891695451, 796747253, 365766033, 183903997, 397892416, 997800298, 50035825, 528830738, 866384252, 753022757, 111323855, 135822032, 589992394, 443541357, 396774353, 893914673, 763716490, 349055039, 558916723, 794783932, 511532967, 820084016, 290674092, 221641462, 378451257, 588452615, 569399439, 331842515, 950241100, 809745508, 869112753, 254926828, 687317859, 965875668, 799737664, 452800850, 313644699, 486328474, 745290855, 153650620, 648053061, 27973572, 917269831, 152733659, 998754729, 506587076, 574422944, 931716279, 954820186, 698806278, 770247707, 8200899, 588347326, 443836853, 262342159, 777734999, 145689028, 485466983, 940590370, 179094891, 86872606, 998010086, 242969507, 551625792, 454701285, 708691253, 21827964, 391924501, 350790449, 236290730, 432206480, 140786085, 406296622, 313301148, 197389496, 605099276, 600112169, 664335372, 540420774, 63578096, 876447612, 624085193, 662578522, 240619417, 881408228, 780082584, 546832769, 880508026, 612150119, 664542062, 525902385, 144453417, 178208312, 152213577, 669540430, 630586192, 545605819, 88442489, 406737684, 485173265, 353259036, 857287992, 966284069, 25289587, 225617636, 96122108, 129427494, 798298344, 711885634, 295560605, 348256580, 977810689, 761929640, 748554073, 251865880, 195894553, 268802204, 245665045, 503456068, 861542997, 556660114, 290101689, 827998436, 125219095, 802906821, 387223282, 424389470, 888832906, 587461573, 149170855, 895954667, 658992408, 171231606, 587698570, 25153279, 266681554, 325392343, 387301296, 923596909, 10980774, 853436694, 37981473, 743918571, 105330599, 99264152, 450031959, 192814255, 530761037, 756992345, 107268391, 402171353, 127831638, 362427372, 92044968, 403592938, 2929260, 379456244, 259163421, 639216970, 791603866, 969869036, 153088457, 53435282, 507211780, 333906317, 130184885, 457213080, 331780005, 762638455, 870204598, 814705702, 315790201, 157256666, 512498139, 949240285, 871100950, 491292229, 598516989, 242149639, 283546059, 927104407, 330353739, 702183841, 224750879, 792694842, 939755338, 137452751, 77824519, 297238820, 929348900, 59364375, 407856066, 577247291, 925931592, 78155326, 624177924, 832204256, 292523662, 306113125, 777625149, 274976167, 161954284, 651756036, 771834383, 575480732, 139546030, 544219369, 204635119, 851257502, 954018945, 731185262, 830752636, 172599267, 400547011, 114989340, 104068420, 574304589, 640402869, 854856268, 152041479, 595249145, 606199282, 501745838, 598380526, 637692410, 699606507, 870247540, 568109741, 565362979, 630288342, 803343100, 712901835, 273207196, 852767899, 985217664, 628271648, 230812977, 358382522, 735488327, 126425149, 754668108, 669473098, 911005731, 300831130, 944316954, 906021927, 418493763, 280207051, 413129433, 881782875, 278852271, 425633071, 291417283, 66501802, 666812295, 539317845, 838753941, 383351593, 63463219, 475696080, 681360596, 483153377, 536743853, 344568008, 505525461, 112069485, 186791942, 156996849, 46316414, 522556201, 609111331, 720263413, 404093427, 167652496, 292053873, 79815783, 356860747, 429821602, 759771620, 176159171, 337094507, 816358492, 240518772, 97927822, 850947767, 75442213, 323964999, 573143830, 696568286, 508819599, 50390517, 411911984, 775266762, 84766872, 871385138, 887986984, 363352615, 69628470, 706780712, 703943876, 583425771, 434892999, 13333013, 989399739, 917520193, 665008072, 422371410, 895535492, 760901820, 344083332, 515702353, 277199847, 908073338, 992874031, 139372714, 363866228, 311993188, 2685564, 530481433, 189529871, 322463355, 838101814, 852208899, 735592481, 147324876, 593606068, 483147356, 291690435, 675524766, 94512866, 268019374, 738374269, 140948707, 51573781, 894511568, 484125395, 707098456, 962994281, 745075298, 141070067, 486894820, 662612323, 869581063, 531160076, 240723727, 24230981, 38964502, 896781983, 70039917, 295205303, 229942456, 316335596, 465040766, 187719701, 404648150, 525364178, 662293008, 446371272, 387294931, 4969913, 245360495, 150816883, 155070527, 779143872, 572078500, 803163239, 38089251, 32948554, 349016244, 800150625, 773262640, 343663113, 535919701, 626586242, 608422541, 974052714, 447847436, 21760946, 519358893, 548779203, 976802237, 21801010, 751469900, 289820762, 469635589, 56582323, 660476690, 732509911, 494145887, 24286879, 28783603, 132186379, 527933600, 919582463, 29906815, 216225343, 814936668, 778051352, 434319252, 940614441, 937088370, 686325620, 878847384, 625515023, 467025363, 841094110, 235506611, 512644132, 841779096, 324880616, 895424244, 655981025, 782338115, 454095015, 165425758, 13468688, 476043189, 898499866, 860033046, 399653758, 218263541, 127843472, 542859568, 20472230, 333748207, 610075690, 859585545, 890783226, 442020649, 920077092, 500476050, 864078398, 826089680, 261588626, 524014686, 73343468, 545488809, 584864699, 411986305, 996778352, 488837887, 923813348, 359659583, 257884996, 347733000, 733595880, 412011557, 395262747, 568372847, 571970423, 546114579, 726383652, 849568003, 789062417, 261617822, 563308941, 294699604, 601366339, 916585514, 80908512, 664376314, 652540151, 572437488, 291621732, 420232023, 378543606, 972355749, 189948274, 250256326, 825370822, 58166132, 564327497, 533520057, 584623279, 181845592, 324583592, 36924092, 347806992, 103174159, 745331241, 355870018, 583512823, 726049680, 863453879, 797392499, 846184391, 864266094, 567166357, 120984989, 593419544, 498705152, 742178001, 630302664, 932909498, 862814997, 659705580, 342055428, 367290378, 837444346, 75048168, 296919714, 221896772, 428623587, 491746614, 616225547, 888329990, 637078386, 738489329, 682104517, 491610014, 519722653, 415576040, 206872676, 742136120, 959029740, 168350599, 936242261, 848642035, 622305937, 358477001, 517167942, 35981714, 663850252, 424560086, 863730835, 279877018, 602189642, 197063755, 351152817, 678971480, 685019959, 938594348, 548634353, 439899423, 863377460, 482596775, 722217393, 404397028, 76096520, 265448638, 871478549, 852493522, 448352787, 875721881, 4070564, 995981104, 834698689, 997014875, 77558377, 655215061, 390559546, 632922000, 113140890, 667303033, 666719005, 245831922, 173482200, 784609826, 678036269, 335061930, 438991738, 497553977, 669872793, 971681696, 915171869, 409232791, 134772555, 150347864, 184484581, 389491237, 676018271, 99596259, 953510206, 971870760, 720114902, 779725344, 546806359, 971832251, 126103610, 383108396, 800757498, 23754472, 529114713, 210889867, 465524305, 272961361, 813837210, 854204940, 521501404, 871482493, 407227009, 729407394, 691538849, 933419875, 349615797, 839584091, 863787073, 198563276, 40742473, 329666425, 992477575, 593277337, 210937257, 7233229, 499683503, 38167862, 591712138, 385938174, 245367202, 91609692, 862528352, 79751486, 597368661, 772608731, 494554976, 23638747, 377760620, 691291824, 656857212, 122100864, 414760339, 498798257, 335162294, 532490469, 284127724, 260441640, 911288394, 376992411, 699134253, 856282437, 978162979, 9462204, 871792433, 443899588, 420424997, 296217570, 493176832, 1494517, 725264113, 980941724, 279052152, 35621910, 158623906, 216944909, 940686293, 825822496, 650024411, 50423041, 681713377, 377211198, 811962249, 222965339, 439276674, 289230597, 233862688, 915597809, 906294832, 524193238, 781272727, 999962476, 167699621, 465502166, 729431392, 544899955, 683301925, 103403194, 519757980, 547166294, 880417385, 646452013, 558029213, 718560080, 682286713, 430897685, 26915259, 296642336, 75885720, 310350765, 508905271, 654827712, 316906414, 279921438, 421474741, 314662177, 117747783, 872504123, 673091828, 44585761, 901968761, 10978022, 670073754, 895146923, 402452880, 227351993, 648474893, 914620, 527689529, 515335246, 825873199, 736449625, 226989252, 541133831, 673781365, 754636780, 860023707, 573911260, 346128051, 308157782, 459458103, 133958783, 214431846, 370361835, 144444002, 530789640, 128564337, 919324453, 47916544, 796890840, 131164680, 591208116, 508798624, 483148657, 151574584, 956268260, 82101919, 461120757, 617946217, 573128, 718321703, 160988601, 405689889, 74729020, 316579608, 71273271, 777270220, 666735643, 583679784, 148303684, 731689914, 488043478, 245441788, 314813569, 580190591, 949210162, 507965443, 318571187, 709411749, 870705511, 355247130, 748102941, 759276533, 712210403, 166401517, 930858585, 489271569, 567636605, 682904042, 28924806, 782168118, 157076363, 630763487, 108360004, 976940752, 937132980, 495245249, 581755282, 8487610, 456442947, 272496217, 642915412, 630126844, 249352504, 603385021, 968242586, 195547813, 893588110, 683939048, 21628266, 442733722, 585850996, 872131740, 796664233, 829973005, 261441163, 2392159, 834992604, 47158693, 521774329, 206632005, 156328721, 885877329, 457888121, 874391629, 862112218, 106268979, 285438126, 306309491, 152668748, 998677597, 704032249, 488683610, 877963209, 130563853, 905475523, 150229947, 72953923, 859930113, 577079728, 177243250, 538407088, 602213440, 70421670, 69963656, 27339638, 906689036, 673447125, 515752632, 156080408, 862569751, 628039114, 956841725, 237971590, 194951203, 555358460, 630561936, 743785018, 317694487, 618264628, 402968112, 186004790, 544475110, 934193248, 718694246, 491472844, 146394878, 483172265, 221525115, 611798982, 826474990, 897085659, 719981439, 102973715, 351993290, 799451917, 509858087, 333384911, 471450969, 60010666, 921758978, 314151874, 749422004, 691790472, 115763962, 773072679, 801255477, 764354233, 682799854, 588963356, 451241418, 410069664, 263347627, 972912113, 595028143, 835847908, 451790586, 975556155, 179241304, 982317388, 375421690, 641468766, 594482489, 696516147, 130127288, 589326952, 108641435, 333348515, 28851645, 145561654, 594555, 27484397, 941611513, 937077355, 215603339, 673745456, 638847208, 803959626, 912751882, 147456150, 787563091, 652194534, 690634879, 595445481, 504325803, 537274956, 58064337, 304166830, 190528605, 566655820, 435544510, 517186907, 556715816, 925814457, 47940930, 919527567, 674567542, 316522662, 385214597, 482707783, 18589562, 290864301, 243316062, 458911825, 112555620, 945472968, 400854345, 624242357, 478993706, 721860257, 944856837, 615753981, 428811965, 343477689, 22557178, 574376932, 318671526, 560907761, 918744548, 970772006, 728333721, 678106403, 351184419, 573750605, 223719412, 203066406, 488766641, 18806731, 60422015, 807061642, 256124895, 430105028, 352315930, 649892709, 2845675, 985557257, 642254947, 661112326, 24141584, 912945127, 759637485, 943690162, 164803684, 582771151, 979450246, 441802304, 92544626, 922316466, 358662081, 505497977, 113730467, 147725892, 817937843, 57128380, 893370134, 653509973, 721306083, 544523499, 805146975, 278663601, 865869798, 349632563, 90528869, 605656635, 793245797, 555335196, 613728127, 613922035, 838097514, 619491679, 190233833, 870819229, 567940667, 369042931, 280668421, 957147936, 981876953, 732283070, 229138997, 518865844, 149616590, 517467642, 217994257, 963561092, 74888022, 648610206, 945667394, 859080619, 317340956, 641023539, 173066863, 549563569, 337287364, 496151056, 339680246, 704205932, 340484459, 430155895, 228253215, 142333053, 345885783, 616826365, 980650978, 827039467, 318966763, 695361893, 202788946, 40621591, 257818317, 186838702, 343134538, 508301058, 451761429, 994651149, 759667763, 175429198, 728045807, 166083947, 264462077, 733784761, 668219651, 886197687, 318837970, 199996461, 842274734, 483920889, 897194173, 855453600, 123796147, 699012290, 735842274, 498737516, 25428830, 103661890, 585157004, 860131078, 790238453, 650373695, 587416475, 932122216, 341428054, 810700753, 302344031, 791260448, 509266912, 459255083, 410544121, 391447325, 568395087, 581949780, 543125504, 640400452, 641326770, 438165176, 755012731, 287959796, 354704391, 527113135, 22344394, 272216076, 252333997, 310448769, 458170975, 459627222, 232596004, 517272079, 817447602, 741177022, 14298900, 451178410, 873629610, 696130616, 784227926, 316557022, 403612539, 179187811, 220768102, 124691563, 860572061, 689101834, 103290224, 116542496, 209467240, 416773680, 910800043, 326189641, 968805076, 55563217, 517824852, 566900496, 464480329, 465754472, 481981260, 725474683, 470038446, 411012247, 898606171, 613779334, 276496339, 617537289, 31052589, 155798141, 359333846, 562117049, 716574152, 634719156, 731989954, 928130814, 96103146, 105004096, 273673553, 28199430, 876554678, 43442383, 235545594, 399583279, 763962416, 562957408, 735400183, 685335710, 332332424, 967748352, 562687547, 907591755, 250717531, 473134592, 666452655, 865175071, 412005668, 728326930, 299859647, 714691936, 774879401, 894404978, 247526133, 972674746, 40072836, 310556317, 967231729, 739718978, 307104583, 858664716, 135052453, 7668361, 660409219, 660531245, 641723636, 205279921, 75919681, 728442781, 627613625, 504863262, 925191939, 370481188, 261500582, 919795117, 330167377, 637808876, 910893665, 451825748, 759175915, 325267031, 873269925, 285256182, 165686939, 676057543, 803150902, 293808675, 41132261, 143027964, 389678244, 981367882, 789705013, 106269903, 784774240, 414018349, 255861916, 990541376, 284275354, 575012091, 416376343, 615636427, 944568773, 790683553, 309210112, 828374583, 697551679, 845268471, 181060031, 440405976, 845479021, 31470838, 567355214, 479164049, 69889667, 794389386, 101377813, 303793965, 138753013, 692475748, 672452730, 435106428, 130341615, 876378701, 654895829, 402479095, 43262789, 566308906, 255158794, 382827698, 573287840, 603128068, 548801286, 942645385, 29137964, 666590607, 712307687, 39117192, 660034459, 609024136, 336541322, 686662772, 825552305, 519911981, 148378868, 671469559, 511101826, 18657474, 466983460, 511372578, 563175565, 546767520, 381251192, 33804875, 573957083, 27749136, 142296649, 44196038, 51074147, 205350587, 14191456, 381329626, 618099932, 497799807, 820999941, 941228365, 72595637, 772577938, 571468704, 498321815, 493907130, 807989432, 991031185, 765030056, 608585021, 141387953, 197000841, 940075260, 14256810, 972721572, 606968790, 971353587, 294535156, 31944593, 158559535, 615473670, 127433794, 271146721, 989379162, 15154805, 232192646, 641649817, 101290172, 770558023, 683824534, 371317718, 778104055, 925363275, 526878192, 332177766, 368929455, 294767748, 289243122, 348325184, 108338354, 39752838, 719583918, 71753960, 260674653, 796811169, 489167608, 186630693, 281834448, 586191892, 532130288, 185599600, 144490944, 9767028, 805798001, 292928044, 75457180, 460593690, 111736739, 538930263, 237170132, 995384655, 249401206, 267343294, 206357057, 366897356, 343361841, 79126161, 970271138, 742479818, 189931173, 136898701, 646253628, 445615237, 937519449, 586806959, 612866995, 27337712, 756958967, 126467617, 981344798, 313026383, 277440706, 264094349, 121050975, 413718794, 508199739, 364337140, 195125286, 826116757, 848777774, 803447696, 39988385, 448745542, 118078856, 917235735, 733985388, 583881313, 766431205, 7702012, 147471879, 191864209, 237159603, 461766535, 36850552, 317365706, 781437978, 869977841, 666981705, 278548123, 732808576, 436319693, 864627840, 590102720, 63975945, 923307276, 659115651, 176559456, 534347111, 254644378, 91443182, 307240998, 577287024, 964000075, 645210547, 806850893, 959669180, 14760253, 810685166, 273054717, 137280896, 150618637, 506937344, 722704753, 672571605, 199374370, 633062729, 530994164, 786560277, 384248499, 716878567, 986441214, 247726443, 646775899, 726430740, 516859806, 386516080, 994912290, 523664149, 89485965, 393115555, 169040449, 158283457, 940561508, 173373772, 792607934, 490250390, 974421518, 403351660, 532067948, 478241514, 817059410, 909569691, 595934391, 466890814, 799698544, 785691906, 250882674, 877778799, 717012728, 69411120, 400819173, 548998668, 589250022, 71123726, 54280339, 701784623, 7089159, 986255950, 449960777, 418776774, 204526622, 662863939, 726445725, 74996776, 505729211, 122600537, 670803149, 239057817, 217286467, 348877454, 400717108, 123523353, 616102345, 302512442, 591205194, 591358258, 991764808, 606623833, 188053964, 881610712, 980322427, 524457514, 210726832, 55838094, 847712189, 431058932, 4726963, 598174396, 926331700, 391827814, 519291126, 618303727, 423735121, 290014923, 826308110, 52445538, 586229223, 593830871, 796362675, 139648283, 240233074, 735496651, 651992755, 334118561, 725538227, 53390463, 16316469, 111842897, 346737673, 92139618, 467509110, 488607769, 317401972, 795869007, 416172667, 691882250, 822268180, 564012370, 113787039, 981478575, 887589072, 156664693, 735194126, 821132814, 417556721, 888652469, 132665810, 252607648, 169130173, 613136100, 619419114, 4755728, 305745579, 42977156, 828858725, 957363332, 61227643, 144384734, 952417579, 542410050, 553751687, 577934801, 100772016, 375232645, 397292598, 182777721, 900760316, 428217487, 237303836, 933041072, 699253467, 834775872, 113975605, 135096250, 810462498, 841066606, 544398728, 525996725, 474591447, 886214589, 607329563, 45580245, 966423262, 231565882, 3596021, 489089793, 2468908, 302730013, 270765956, 389334903, 967230882, 800469225, 230811360, 249290043, 697944596, 288890194, 16639016, 994759022, 494918721, 36918707, 592603106, 65966004, 401676392, 139585493, 792570890, 30329882, 759786838, 800319489, 616539101, 332506456, 692516632] 118038))
+
+
+-- Grouping test cases
+tests :: Test
+tests = TestList [TestLabel "Test1" test1, TestLabel "Test2" test2, TestLabel "Test3" test3, TestLabel "Test4" test4, TestLabel "Test5" test5, TestLabel "Test6" test6, TestLabel "Test7" test7, TestLabel "Test8" test8, TestLabel "Test9" test9]
+
+-- Running the tests
+main :: IO Counts
+main = runTestTT tests